LMFDB - Embedded newform 43.8.g.a.24.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(9,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$300$
Relative dimension:	$25$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.7
Character	$\chi$	$=$	43.24
Dual form			43.8.g.a.9.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.81088 + 8.54058i) q^{2} +(54.1377 - 8.15994i) q^{3} +(1.92934 + 8.45297i) q^{4} +(-122.186 + 83.3051i) q^{5} +(-299.035 + 517.944i) q^{6} +(-199.852 - 346.154i) q^{7} +(-1345.11 - 647.772i) q^{8} +(774.466 - 238.891i) q^{9} +O(q^{10})$	\(q+(-6.81088 + 8.54058i) q^{2} +(54.1377 - 8.15994i) q^{3} +(1.92934 + 8.45297i) q^{4} +(-122.186 + 83.3051i) q^{5} +(-299.035 + 517.944i) q^{6} +(-199.852 - 346.154i) q^{7} +(-1345.11 - 647.772i) q^{8} +(774.466 - 238.891i) q^{9} +(120.722 - 1610.92i) q^{10} +(-973.957 + 4267.18i) q^{11} +(173.426 + 441.881i) q^{12} +(749.764 + 10004.9i) q^{13} +(4317.52 + 650.762i) q^{14} +(-5935.11 + 5506.98i) q^{15} +(13693.8 - 6594.61i) q^{16} +(-20882.3 - 14237.3i) q^{17} +(-3234.53 + 8241.45i) q^{18} +(-9963.36 - 3073.29i) q^{19} +(-939.914 - 872.113i) q^{20} +(-13644.1 - 17109.2i) q^{21} +(-29810.7 - 37381.4i) q^{22} +(-30985.0 - 28749.9i) q^{23} +(-78107.0 - 24092.8i) q^{24} +(-20552.5 + 52367.0i) q^{25} +(-90554.2 - 61738.8i) q^{26} +(-67900.4 + 32699.1i) q^{27} +(2540.45 - 2357.19i) q^{28} +(25786.0 + 3886.61i) q^{29} +(-6609.43 - 88196.7i) q^{30} +(-18580.2 - 47341.7i) q^{31} +(5578.11 - 24439.3i) q^{32} +(-17907.8 + 238963. i) q^{33} +(263822. - 81378.4i) q^{34} +(53255.5 + 25646.5i) q^{35} +(3513.55 + 6085.64i) q^{36} +(-32927.8 + 57032.7i) q^{37} +(94107.0 - 64161.1i) q^{38} +(122230. + 535524. i) q^{39} +(218317. - 32906.0i) q^{40} +(97080.7 - 121735. i) q^{41} +239051. q^{42} +(57096.8 + 518226. i) q^{43} -37949.5 q^{44} +(-74728.2 + 93706.2i) q^{45} +(456576. - 68817.8i) q^{46} +(136996. + 600217. i) q^{47} +(687541. - 468758. i) q^{48} +(331890. - 574850. i) q^{49} +(-307264. - 532197. i) q^{50} +(-1.24670e6 - 600377. i) q^{51} +(-83124.7 + 25640.6i) q^{52} +(-43392.8 + 579037. i) q^{53} +(183192. - 802618. i) q^{54} +(-236474. - 602526. i) q^{55} +(44594.6 + 595074. i) q^{56} +(-564471. - 85080.4i) q^{57} +(-208819. + 193756. i) q^{58} +(1.97561e6 - 951404. i) q^{59} +(-58001.2 - 39544.5i) q^{60} +(-704448. + 1.79491e6i) q^{61} +(530873. + 163753. i) q^{62} +(-237472. - 220342. i) q^{63} +(1.38372e6 + 1.73513e6i) q^{64} +(-925071. - 1.16000e6i) q^{65} +(-1.91891e6 - 1.78049e6i) q^{66} +(4.47530e6 + 1.38045e6i) q^{67} +(80058.7 - 203986. i) q^{68} +(-1.91205e6 - 1.30362e6i) q^{69} +(-581753. + 280158. i) q^{70} +(-893206. + 828774. i) q^{71} +(-1.19649e6 - 180342. i) q^{72} +(37530.8 + 500813. i) q^{73} +(-262824. - 669666. i) q^{74} +(-685355. + 3.00274e6i) q^{75} +(6755.77 - 90149.5i) q^{76} +(1.67175e6 - 515666. i) q^{77} +(-5.40618e6 - 2.60348e6i) q^{78} +(31974.1 + 55380.7i) q^{79} +(-1.12383e6 + 1.94654e6i) q^{80} +(-4.87366e6 + 3.32280e6i) q^{81} +(378485. + 1.65825e6i) q^{82} +(-471504. + 71067.7i) q^{83} +(118299. - 148343. i) q^{84} +3.73757e6 q^{85} +(-4.81483e6 - 3.04194e6i) q^{86} +1.42771e6 q^{87} +(4.07424e6 - 5.10894e6i) q^{88} +(-1.04685e7 + 1.57787e6i) q^{89} +(-291340. - 1.27644e6i) q^{90} +(3.31339e6 - 2.25903e6i) q^{91} +(183242. - 317384. i) q^{92} +(-1.39220e6 - 2.41135e6i) q^{93} +(-6.05926e6 - 2.91799e6i) q^{94} +(1.47341e6 - 454486. i) q^{95} +(102563. - 1.36860e6i) q^{96} +(-809596. + 3.54707e6i) q^{97} +(2.64909e6 + 6.74977e6i) q^{98} +(265096. + 3.53746e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) $ 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.81088	+	8.54058i	−0.602003	+	0.754888i	−0.985689	−	0.168576i	$-0.946083\pi$
$2$	−6.81088	+	8.54058i	−0.602003	+	0.754888i	0.383686	+	0.923464i	$0.374655\pi$
$3$	54.1377	−	8.15994i	1.15764	−	0.174487i	0.457983	−	0.888961i	$-0.348572\pi$
$3$	54.1377	−	8.15994i	1.15764	−	0.174487i	0.699662	+	0.714474i	$0.253334\pi$
$4$	1.92934	+	8.45297i	0.0150729	+	0.0660389i
$5$	−122.186	+	83.3051i	−0.437147	+	0.298041i	−0.761825	−	0.647783i	$-0.775696\pi$
$5$	−122.186	+	83.3051i	−0.437147	+	0.298041i	0.324678	+	0.945825i	$0.394744\pi$
$6$	−299.035	+	517.944i	−0.565187	+	0.978933i
$7$	−199.852	−	346.154i	−0.220224	−	0.381440i	0.734652	−	0.678444i	$-0.237346\pi$
$7$	−199.852	−	346.154i	−0.220224	−	0.381440i	−0.954876	+	0.297005i	$0.904012\pi$
$8$	−1345.11	−	647.772i	−0.928845	−	0.447308i
$9$	774.466	−	238.891i	0.354123	−	0.109232i
$10$	120.722	−	1610.92i	0.0381756	−	0.509418i
$11$	−973.957	+	4267.18i	−0.220630	+	0.966645i	0.736375	+	0.676574i	$0.236536\pi$
$11$	−973.957	+	4267.18i	−0.220630	+	0.966645i	−0.957005	+	0.290071i	$0.906321\pi$
$12$	173.426	+	441.881i	0.0289720	+	0.0738195i
$13$	749.764	+	10004.9i	0.0946505	+	1.26302i	0.819082	+	0.573676i	$0.194483\pi$
$13$	749.764	+	10004.9i	0.0946505	+	1.26302i	−0.724432	+	0.689347i	$0.757898\pi$
$14$	4317.52	+	650.762i	0.420520	+	0.0633832i
$15$	−5935.11	+	5506.98i	−0.454056	+	0.421302i
$16$	13693.8	−	6594.61i	0.835806	−	0.402503i
$17$	−20882.3	−	14237.3i	−1.03088	−	0.702841i	−0.0751748	−	0.997170i	$-0.523951\pi$
$17$	−20882.3	−	14237.3i	−1.03088	−	0.702841i	−0.955704	+	0.294329i	$0.904904\pi$
$18$	−3234.53	+	8241.45i	−0.130725	+	0.333081i
$19$	−9963.36	−	3073.29i	−0.333249	−	0.102794i	0.123615	−	0.992330i	$-0.460551\pi$
$19$	−9963.36	−	3073.29i	−0.333249	−	0.102794i	−0.456864	+	0.889537i	$0.651027\pi$
$20$	−939.914	−	872.113i	−0.0262714	−	0.0243763i
$21$	−13644.1	−	17109.2i	−0.321498	−	0.403145i
$22$	−29810.7	−	37381.4i	−0.596888	−	0.748474i
$23$	−30985.0	−	28749.9i	−0.531012	−	0.492707i	0.368485	−	0.929634i	$-0.379876\pi$
$23$	−30985.0	−	28749.9i	−0.531012	−	0.492707i	−0.899497	+	0.436927i	$0.856067\pi$
$24$	−78107.0	−	24092.8i	−1.15332	−	0.355753i
$25$	−20552.5	+	52367.0i	−0.263073	+	0.670298i
$26$	−90554.2	−	61738.8i	−1.01042	−	0.688893i
$27$	−67900.4	+	32699.1i	−0.663894	+	0.319715i
$28$	2540.45	−	2357.19i	0.0218704	−	0.0202928i
$29$	25786.0	+	3886.61i	0.196332	+	0.0295923i	0.246472	−	0.969150i	$-0.420729\pi$
$29$	25786.0	+	3886.61i	0.196332	+	0.0295923i	−0.0501400	+	0.998742i	$0.515967\pi$
$30$	−6609.43	−	88196.7i	−0.0446930	−	0.596387i
$31$	−18580.2	−	47341.7i	−0.112017	−	0.285416i	0.863861	−	0.503730i	$-0.168039\pi$
$31$	−18580.2	−	47341.7i	−0.112017	−	0.285416i	−0.975878	+	0.218314i	$0.929944\pi$
$32$	5578.11	−	24439.3i	0.0300928	−	0.131845i
$33$	−17907.8	+	238963.i	−0.0867447	+	1.15753i
$34$	263822.	−	81378.4i	1.15116	−	0.355085i
$35$	53255.5	+	25646.5i	0.209955	+	0.101109i
$36$	3513.55	+	6085.64i	0.0125513	+	0.0217394i
$37$	−32927.8	+	57032.7i	−0.106870	+	0.185105i	−0.914501	−	0.404584i	$-0.867416\pi$
$37$	−32927.8	+	57032.7i	−0.106870	+	0.185105i	0.807631	+	0.589689i	$0.200750\pi$
$38$	94107.0	−	64161.1i	0.278214	−	0.189683i
$39$	122230.	+	535524.i	0.329953	+	1.44562i
$40$	218317.	−	32906.0i	0.539358	−	0.0812951i
$41$	97080.7	−	121735.i	0.219983	−	0.275850i	−0.659578	−	0.751636i	$-0.729265\pi$
$41$	97080.7	−	121735.i	0.219983	−	0.275850i	0.879561	+	0.475786i	$0.157836\pi$
$42$	239051.			0.497872
$43$	57096.8	+	518226.i	0.109515	+	0.993985i
$43$	57096.8	+	518226.i	0.109515	+	0.993985i
$44$	−37949.5			−0.0671617
$45$	−74728.2	+	93706.2i	−0.122248	+	0.153294i
$46$	456576.	−	68817.8i	0.691609	−	0.104243i
$47$	136996.	+	600217.i	0.192470	+	0.843268i	0.975274	+	0.220999i	$0.0709319\pi$
$47$	136996.	+	600217.i	0.192470	+	0.843268i	−0.782803	+	0.622269i	$0.786211\pi$
$48$	687541.	−	468758.i	0.897335	−	0.611792i
$49$	331890.	−	574850.i	0.403003	−	0.698021i
$50$	−307264.	−	532197.i	−0.347629	−	0.602112i
$51$	−1.24670e6	−	600377.i	−1.31603	−	0.633766i
$52$	−83124.7	+	25640.6i	−0.0819819	+	0.0252881i
$53$	−43392.8	+	579037.i	−0.0400361	+	0.534245i	0.940743	+	0.339122i	$0.110130\pi$
$53$	−43392.8	+	579037.i	−0.0400361	+	0.534245i	−0.980779	+	0.195123i	$0.937489\pi$
$54$	183192.	−	802618.i	0.158318	−	0.693635i
$55$	−236474.	−	602526.i	−0.191652	−	0.488322i
$56$	44594.6	+	595074.i	0.0339332	+	0.452807i
$57$	−564471.	−	85080.4i	−0.403720	−	0.0608510i
$58$	−208819.	+	193756.i	−0.140531	+	0.130394i
$59$	1.97561e6	−	951404.i	1.25233	−	0.603091i	0.314195	−	0.949358i	$-0.398265\pi$
$59$	1.97561e6	−	951404.i	1.25233	−	0.603091i	0.938136	+	0.346267i	$0.112551\pi$
$60$	−58001.2	−	39544.5i	−0.0346663	−	0.0236351i
$61$	−704448.	+	1.79491e6i	−0.397370	+	1.01248i	0.582498	+	0.812832i	$0.302075\pi$
$61$	−704448.	+	1.79491e6i	−0.397370	+	1.01248i	−0.979867	+	0.199649i	$0.936020\pi$
$62$	530873.	+	163753.i	0.282891	+	0.0872605i
$63$	−237472.	−	220342.i	−0.119652	−	0.111021i
$64$	1.38372e6	+	1.73513e6i	0.659808	+	0.827373i
$65$	−925071.	−	1.16000e6i	−0.417809	−	0.523916i
$66$	−1.91891e6	−	1.78049e6i	−0.821583	−	0.762318i
$67$	4.47530e6	+	1.38045e6i	1.81786	+	0.560735i	0.999894	−	0.0145357i	$-0.00462701\pi$
$67$	4.47530e6	+	1.38045e6i	1.81786	+	0.560735i	0.817963	+	0.575270i	$0.195103\pi$
$68$	80058.7	−	203986.i	0.0308765	−	0.0786720i
$69$	−1.91205e6	−	1.30362e6i	−0.700694	−	0.477725i
$70$	−581753.	+	280158.i	−0.202720	+	0.0976246i
$71$	−893206.	+	828774.i	−0.296174	+	0.274809i	−0.814236	−	0.580533i	$-0.802844\pi$
$71$	−893206.	+	828774.i	−0.296174	+	0.274809i	0.518062	+	0.855343i	$0.326654\pi$
$72$	−1.19649e6	−	180342.i	−0.377786	−	0.0569420i
$73$	37530.8	+	500813.i	0.0112917	+	0.150677i	1.00000		0.000821802i	$0.000261588\pi$
$73$	37530.8	+	500813.i	0.0112917	+	0.150677i	−0.988708	+	0.149855i	$0.952119\pi$
$74$	−262824.	−	669666.i	−0.0753971	−	0.192109i
$75$	−685355.	+	3.00274e6i	−0.187586	+	0.821870i
$76$	6755.77	−	90149.5i	0.00176534	−	0.0235568i
$77$	1.67175e6	−	515666.i	0.417305	−	0.128721i
$78$	−5.40618e6	−	2.60348e6i	−1.28991	−	0.621188i
$79$	31974.1	+	55380.7i	0.00729631	+	0.0126376i	0.869651	−	0.493668i	$-0.164344\pi$
$79$	31974.1	+	55380.7i	0.00729631	+	0.0126376i	−0.862354	+	0.506305i	$0.831011\pi$
$80$	−1.12383e6	+	1.94654e6i	−0.245407	+	0.425058i
$81$	−4.87366e6	+	3.32280e6i	−1.01896	+	0.694716i
$82$	378485.	+	1.65825e6i	0.0758054	+	0.332125i
$83$	−471504.	+	71067.7i	−0.0905131	+	0.0136427i	−0.194143	−	0.980973i	$-0.562192\pi$
$83$	−471504.	+	71067.7i	−0.0905131	+	0.0136427i	0.103630	+	0.994616i	$0.466954\pi$
$84$	118299.	−	148343.i	0.0217773	−	0.0273079i
$85$	3.73757e6			0.660121
$86$	−4.81483e6	−	3.04194e6i	−0.816275	−	0.515711i
$87$	1.42771e6			0.232446
$88$	4.07424e6	−	5.10894e6i	0.637320	−	0.799174i
$89$	−1.04685e7	+	1.57787e6i	−1.57405	+	0.237249i	−0.877255	−	0.480024i	$-0.840628\pi$
$89$	−1.04685e7	+	1.57787e6i	−1.57405	+	0.237249i	−0.696791	+	0.717274i	$0.745390\pi$
$90$	−291340.	−	1.27644e6i	−0.0421261	−	0.184567i
$91$	3.31339e6	−	2.25903e6i	0.460923	−	0.314252i
$92$	183242.	−	317384.i	0.0245339	−	0.0424940i
$93$	−1.39220e6	−	2.41135e6i	−0.179478	−	0.310864i
$94$	−6.05926e6	−	2.91799e6i	−0.752441	−	0.362356i
$95$	1.47341e6	−	454486.i	0.176315	−	0.0543861i
$96$	102563.	−	1.36860e6i	0.0118315	−	0.157881i
$97$	−809596.	+	3.54707e6i	−0.0900673	+	0.394611i	−0.999788	−	0.0206110i	$-0.993439\pi$
$97$	−809596.	+	3.54707e6i	−0.0900673	+	0.394611i	0.909720	+	0.415222i	$0.136296\pi$
$98$	2.64909e6	+	6.74977e6i	0.284319	+	0.724432i
$99$	265096.	+	3.53746e6i	0.0274587	+	0.366411i
$100$	−482310.	−	72696.5i	−0.0482310	−	0.00726965i
$101$	4.90114e6	−	4.54759e6i	0.473339	−	0.439194i	−0.407079	−	0.913393i	$-0.633453\pi$
$101$	4.90114e6	−	4.54759e6i	0.473339	−	0.439194i	0.880418	+	0.474199i	$0.157262\pi$
$102$	1.36187e7	−	6.55841e6i	1.27067	−	0.611925i
$103$	1.19275e7	+	8.13204e6i	1.07552	+	0.733279i	0.965435	−	0.260643i	$-0.0839345\pi$
$103$	1.19275e7	+	8.13204e6i	1.07552	+	0.733279i	0.110088	+	0.993922i	$0.464887\pi$
$104$	5.47238e6	−	1.39434e7i	0.477045	−	1.21549i
$105$	3.09240e6	+	953881.i	0.260696	+	0.0804140i
$106$	−4.64976e6	−	4.31435e6i	−0.379193	−	0.351840i
$107$	2.11414e6	+	2.65104e6i	0.166836	+	0.209206i	0.858220	−	0.513281i	$-0.171570\pi$
$107$	2.11414e6	+	2.65104e6i	0.166836	+	0.209206i	−0.691384	+	0.722487i	$0.742999\pi$
$108$	−407407.	−	510872.i	−0.0311204	−	0.0390238i
$109$	1.03074e7	+	9.56385e6i	0.762352	+	0.707359i	0.962163	−	0.272475i	$-0.0878422\pi$
$109$	1.03074e7	+	9.56385e6i	0.762352	+	0.707359i	−0.199811	+	0.979835i	$0.564033\pi$
$110$	6.75652e6	+	2.08411e6i	0.484004	+	0.149295i
$111$	−1.31725e6	+	3.35631e6i	−0.0914195	+	0.232933i
$112$	−5.01949e6	−	3.42223e6i	−0.337595	−	0.230169i
$113$	−1.63226e7	+	7.86054e6i	−1.06418	+	0.512481i	−0.882226	−	0.470826i	$-0.843956\pi$
$113$	−1.63226e7	+	7.86054e6i	−1.06418	+	0.512481i	−0.181952	+	0.983307i	$0.558242\pi$
$114$	4.57119e6	−	4.24144e6i	0.288976	−	0.268131i
$115$	6.18095e6	+	931629.i	0.378977	+	0.0571216i
$116$	16896.4	+	225467.i	0.00100506	+	0.0134116i
$117$	2.97075e6	+	7.56935e6i	0.171481	+	0.436926i
$118$	−5.33011e6	+	2.33528e7i	−0.298641	+	1.30843i
$119$	−754931.	+	1.00739e7i	−0.0410670	+	0.548001i
$120$	1.15507e7	−	3.56290e6i	0.610200	−	0.188222i
$121$	297075.	+	143064.i	0.0152446	+	0.00734142i
$122$	−1.05316e7	−	1.82413e7i	−0.525092	−	0.909486i
$123$	4.26237e6	−	7.38265e6i	0.206530	−	0.357721i
$124$	364330.	−	248396.i	0.0171601	−	0.0116996i
$125$	−4.42206e6	−	1.93743e7i	−0.202507	−	0.887240i
$126$	3.49924e6	−	527425.i	0.155839	−	0.0234890i
$127$	1.33317e7	−	1.67174e7i	0.577528	−	0.724197i	−0.404161	−	0.914688i	$-0.632437\pi$
$127$	1.33317e7	−	1.67174e7i	0.577528	−	0.724197i	0.981689	+	0.190491i	$0.0610079\pi$
$128$	−2.10346e7			−0.886544
$129$	7.31979e6	+	2.75897e7i	0.300216	+	1.13157i
$130$	1.62076e7			0.647021
$131$	9.78297e6	−	1.22675e7i	0.380208	−	0.476766i	−0.554499	−	0.832184i	$-0.687090\pi$
$131$	9.78297e6	−	1.22675e7i	0.380208	−	0.476766i	0.934707	+	0.355418i	$0.115662\pi$
$132$	−2.05450e6	+	309666.i	−0.0777493	+	0.0117188i
$133$	927367.	+	4.06306e6i	0.0341799	+	0.149752i
$134$	−4.22705e7	+	2.88196e7i	−1.51765	+	1.03471i
$135$	5.57248e6	−	9.65182e6i	0.194931	−	0.337630i
$136$	1.88665e7	+	3.26778e7i	0.643140	+	1.11395i
$137$	−6.14192e6	−	2.95779e6i	−0.204071	−	0.0982755i	0.329057	−	0.944310i	$-0.393269\pi$
$137$	−6.14192e6	−	2.95779e6i	−0.204071	−	0.0982755i	−0.533128	+	0.846035i	$0.678984\pi$
$138$	2.41564e7	−	7.45127e6i	0.782448	−	0.241353i
$139$	−1.65235e6	+	2.20490e7i	−0.0521854	+	0.696366i	0.908350	+	0.418210i	$0.137342\pi$
$139$	−1.65235e6	+	2.20490e7i	−0.0521854	+	0.696366i	−0.960536	+	0.278156i	$0.910277\pi$
$140$	−114041.	+	499648.i	−0.00351249	+	0.0153892i
$141$	1.23144e7	+	3.13765e7i	0.369952	+	0.942621i
$142$	−994687.	−	1.32732e7i	−0.0291526	−	0.389014i
$143$	−4.34230e7	−	6.54496e6i	−1.24178	−	0.187168i
$144$	9.03003e6	−	8.37864e6i	0.252011	−	0.233832i
$145$	−3.47447e6	+	1.67322e6i	−0.0946456	+	0.0455789i
$146$	−4.53285e6	−	3.09045e6i	−0.120542	−	0.0821838i
$147$	1.32770e7	−	3.38293e7i	0.344738	−	0.878379i
$148$	−545625.	−	168303.i	−0.0138350	−	0.00426752i
$149$	−5.00766e7	−	4.64643e7i	−1.24018	−	1.15071i	−0.982853	−	0.184389i	$-0.940969\pi$
$149$	−5.00766e7	−	4.64643e7i	−1.24018	−	1.15071i	−0.257322	−	0.966326i	$-0.582840\pi$
$150$	−2.09772e7	−	2.63046e7i	−0.507492	−	0.636375i
$151$	−4.54260e7	−	5.69624e7i	−1.07371	−	1.34638i	−0.934437	−	0.356129i	$-0.884096\pi$
$151$	−4.54260e7	−	5.69624e7i	−1.07371	−	1.34638i	−0.139268	−	0.990255i	$-0.544475\pi$
$152$	1.14110e7	+	1.05879e7i	0.263556	+	0.244544i
$153$	−1.95738e7	−	6.03773e6i	−0.441831	−	0.136287i
$154$	−6.98200e6	+	1.77898e7i	−0.154048	+	0.392509i
$155$	6.21405e6	+	4.23667e6i	0.134034	+	0.0913826i
$156$	−4.29095e6	+	2.06641e6i	−0.0904935	+	0.0435794i
$157$	2.11881e7	−	1.96597e7i	0.436962	−	0.405441i	−0.430780	−	0.902457i	$-0.641761\pi$
$157$	2.11881e7	−	1.96597e7i	0.436962	−	0.405441i	0.867741	+	0.497016i	$0.165571\pi$
$158$	−690755.	−	104115.i	−0.0139323	−	0.00209996i
$159$	2.37572e6	+	3.17018e7i	0.0468711	+	0.625452i
$160$	1.35435e6	+	3.45083e6i	0.0261404	+	0.0666045i
$161$	−3.75947e6	+	1.64713e7i	−0.0709963	+	0.311055i
$162$	4.81525e6	−	6.42551e7i	0.0889850	−	1.18742i
$163$	−3.18143e7	+	9.81340e6i	−0.575394	+	0.177486i	−0.568776	−	0.822493i	$-0.692583\pi$
$163$	−3.18143e7	+	9.81340e6i	−0.575394	+	0.177486i	−0.00661815	+	0.999978i	$0.502107\pi$
$164$	1.21633e6	+	585752.i	0.0215326	+	0.0103696i
$165$	−1.77187e7	−	3.06898e7i	−0.307071	−	0.531863i
$166$	2.60440e6	−	4.51095e6i	0.0441905	−	0.0765402i
$167$	−5.51271e7	+	3.75850e7i	−0.915919	+	0.624463i	−0.926832	−	0.375477i	$-0.877479\pi$
$167$	−5.51271e7	+	3.75850e7i	−0.915919	+	0.624463i	0.0109124	+	0.999940i	$0.496526\pi$
$168$	7.27002e6	+	3.18520e7i	0.118291	+	0.518268i
$169$	−3.74883e7	+	5.65046e6i	−0.597438	+	0.0900492i
$170$	−2.54562e7	+	3.19210e7i	−0.397395	+	0.498317i
$171$	−8.45047e6			−0.129239
$172$	−4.27040e6	+	1.48247e6i	−0.0639909	+	0.0222145i
$173$	−6.40244e7			−0.940122			−0.470061	−	0.882634i	$-0.655768\pi$
$173$	−6.40244e7			−0.940122			−0.470061	+	0.882634i	$0.655768\pi$
$174$	−9.72396e6	+	1.21935e7i	−0.139933	+	0.175471i
$175$	2.22345e7	−	3.35131e6i	0.313613	−	0.0472696i
$176$	1.48032e7	+	6.48570e7i	0.204673	+	0.896732i
$177$	9.91916e7	−	6.76277e7i	1.34452	−	0.916680i
$178$	5.78236e7	−	1.00153e8i	0.768484	−	1.33105i
$179$	5.09367e7	+	8.82249e7i	0.663812	+	1.14976i	0.979606	+	0.200928i	$0.0643957\pi$
$179$	5.09367e7	+	8.82249e7i	0.663812	+	1.14976i	−0.315794	+	0.948828i	$0.602271\pi$
$180$	−936272.	−	450885.i	−0.0119660	−	0.00576251i
$181$	6.38445e7	−	1.96934e7i	0.800293	−	0.246858i	0.132479	−	0.991186i	$-0.457706\pi$
$181$	6.38445e7	−	1.96934e7i	0.800293	−	0.246858i	0.667814	+	0.744328i	$0.267230\pi$
$182$	−3.27369e6	+	4.36843e7i	−0.0402520	+	0.537125i
$183$	−2.34909e7	+	1.02920e8i	−0.283348	+	1.24143i
$184$	2.30549e7	+	5.87430e7i	0.272836	+	0.695174i
$185$	−727788.	−	9.71166e6i	−0.00845092	−	0.112770i
$186$	3.00765e7	+	4.53330e6i	0.342714	+	0.0516558i
$187$	8.10918e7	−	7.52422e7i	0.906841	−	0.841426i
$188$	−4.80931e6	+	2.31604e6i	−0.0527874	+	0.0254211i
$189$	2.48889e7	+	1.69690e7i	0.268157	+	0.182827i
$190$	−6.15363e6	+	1.56792e7i	−0.0650869	+	0.165839i
$191$	4.42104e7	+	1.36371e7i	0.459100	+	0.141614i	0.515674	−	0.856785i	$-0.327542\pi$
$191$	4.42104e7	+	1.36371e7i	0.459100	+	0.141614i	−0.0565741	+	0.998398i	$0.518018\pi$
$192$	8.90698e7	+	8.26447e7i	0.908189	+	0.842676i
$193$	−1.54459e7	−	1.93686e7i	−0.154655	−	0.193931i	0.698468	−	0.715642i	$-0.253866\pi$
$193$	−1.54459e7	−	1.93686e7i	−0.154655	−	0.193931i	−0.853123	+	0.521711i	$0.825294\pi$
$194$	−2.47800e7	−	3.10731e7i	−0.243666	−	0.305548i
$195$	−5.95467e7	−	5.52513e7i	−0.575091	−	0.533607i
$196$	5.49952e6	+	1.69638e6i	0.0521709	+	0.0160926i
$197$	2.98213e7	−	7.59834e7i	0.277904	−	0.708087i	−0.721966	−	0.691929i	$-0.756761\pi$
$197$	2.98213e7	−	7.59834e7i	0.277904	−	0.708087i	0.999869	−	0.0161584i	$-0.00514360\pi$
$198$	−3.20175e7	−	2.18292e7i	−0.293129	−	0.199852i
$199$	9.47132e6	−	4.56115e6i	0.0851971	−	0.0410288i	−0.390800	−	0.920476i	$-0.627802\pi$
$199$	9.47132e6	−	4.56115e6i	0.0851971	−	0.0410288i	0.475997	+	0.879447i	$0.342087\pi$
$200$	6.15674e7	−	5.71262e7i	0.544184	−	0.504929i
$201$	2.53546e8	+	3.82160e7i	2.20227	+	0.331939i
$202$	5.45798e6	+	7.28317e7i	0.0465910	+	0.621714i
$203$	−3.80802e6	−	9.70267e6i	−0.0319494	−	0.0814057i
$204$	2.66968e6	−	1.16966e7i	0.0220168	−	0.0964617i
$205$	−1.72074e6	+	2.29617e7i	−0.0139501	+	0.186151i
$206$	−1.50689e8	+	4.64815e7i	−1.20101	+	0.370463i
$207$	−3.08649e7	−	1.48638e7i	−0.241863	−	0.116475i
$208$	7.62456e7	+	1.32061e8i	0.587480	+	1.01754i
$209$	2.28182e7	−	3.95223e7i	0.172890	−	0.299454i
$210$	−2.92087e7	+	1.99142e7i	−0.217643	+	0.148387i
$211$	−2.20137e7	−	9.64483e7i	−0.161326	−	0.706816i	−0.989281	−	0.146022i	$-0.953353\pi$
$211$	−2.20137e7	−	9.64483e7i	−0.161326	−	0.706816i	0.827955	−	0.560794i	$-0.189504\pi$
$212$	−4.97830e6	+	750358.i	−0.0358844	+	0.00540870i
$213$	−4.15933e7	+	5.21564e7i	−0.294914	+	0.369810i
$214$	−3.70406e7			−0.258363
$215$	−5.01474e7	−	5.85636e7i	−0.344123	−	0.401877i
$216$	1.12515e8			0.759666
$217$	−1.26742e7	+	1.58929e7i	−0.0841999	+	0.105583i
$218$	−1.51883e8	+	2.28927e7i	−0.992915	+	0.149658i
$219$	6.11844e6	+	2.68066e7i	0.0393628	+	0.172460i
$220$	4.63690e6	−	3.16139e6i	0.0293595	−	0.0200170i
$221$	1.26786e8	−	2.19600e8i	0.790132	−	1.36855i
$222$	−1.96931e7	−	3.41095e7i	−0.120803	−	0.209238i
$223$	−1.83414e8	−	8.83274e7i	−1.10755	−	0.533370i	−0.211528	−	0.977372i	$-0.567844\pi$
$223$	−1.83414e8	−	8.83274e7i	−1.10755	−	0.533370i	−0.896026	+	0.444002i	$0.853558\pi$
$224$	−9.57456e6	+	2.95336e6i	−0.0569181	+	0.0175569i
$225$	−3.40723e6	+	4.54663e7i	−0.0199417	+	0.266104i
$226$	4.40377e7	−	1.92942e8i	0.253773	−	1.11185i
$227$	1.28902e7	+	3.28436e7i	0.0731423	+	0.186364i	0.962769	−	0.270324i	$-0.0871309\pi$
$227$	1.28902e7	+	3.28436e7i	0.0731423	+	0.186364i	−0.889627	+	0.456688i	$0.849036\pi$
$228$	−369873.	−	4.93561e6i	−0.00206671	−	0.0275784i
$229$	−2.07814e8	−	3.13229e7i	−1.14354	−	0.172360i	−0.450168	−	0.892944i	$-0.648636\pi$
$229$	−2.07814e8	−	3.13229e7i	−1.14354	−	0.172360i	−0.693368	+	0.720583i	$0.743874\pi$
$230$	−5.00544e7	+	4.64437e7i	−0.271266	+	0.251698i
$231$	8.62968e7	−	4.15583e7i	0.460630	−	0.221828i
$232$	−3.21674e7	−	2.19314e7i	−0.169125	−	0.115308i
$233$	−2.45091e7	+	6.24481e7i	−0.126935	+	0.323425i	−0.980187	−	0.198073i	$-0.936532\pi$
$233$	−2.45091e7	+	6.24481e7i	−0.126935	+	0.323425i	0.853252	+	0.521499i	$0.174627\pi$
$234$	−8.48801e7	−	2.61820e7i	−0.433062	−	0.133582i
$235$	−6.67401e7	−	6.19258e7i	−0.335467	−	0.311268i
$236$	1.18538e7	+	1.48642e7i	0.0587037	+	0.0736122i
$237$	2.18291e6	+	2.73728e6i	0.0106516	+	0.0133567i
$238$	−8.08948e7	−	7.50594e7i	−0.388957	−	0.360899i
$239$	−2.49237e8	−	7.68795e7i	−1.18092	−	0.364266i	−0.358710	−	0.933449i	$-0.616783\pi$
$239$	−2.49237e8	−	7.68795e7i	−1.18092	−	0.364266i	−0.822210	+	0.569184i	$0.807259\pi$
$240$	−4.49581e7	+	1.14551e8i	−0.209927	+	0.534886i
$241$	1.57093e8	+	1.07104e8i	0.722933	+	0.492888i	0.868019	−	0.496532i	$-0.165393\pi$
$241$	1.57093e8	+	1.07104e8i	0.722933	+	0.492888i	−0.145085	+	0.989419i	$0.546346\pi$
$242$	−3.24519e6	+	1.56280e6i	−0.0147193	+	0.00708842i
$243$	−1.15913e8	+	1.07551e8i	−0.518214	+	0.480832i
$244$	−1.65314e7	−	2.49171e6i	−0.0728526	−	0.0109808i
$245$	7.33561e6	+	9.78869e7i	0.0318680	+	0.425249i
$246$	3.40215e7	+	8.66855e7i	0.145707	+	0.371256i
$247$	2.32778e7	−	1.01987e8i	0.0982885	−	0.430630i
$248$	−5.67410e6	+	7.57156e7i	−0.0236220	+	0.315213i
$249$	−2.49462e7	+	7.69488e6i	−0.102402	+	0.0315867i
$250$	1.95586e8	+	9.41892e7i	0.791676	+	0.381251i
$251$	1.71599e8	+	2.97218e8i	0.684947	+	1.18636i	0.973454	+	0.228885i	$0.0735079\pi$
$251$	1.71599e8	+	2.97218e8i	0.684947	+	1.18636i	−0.288507	+	0.957478i	$0.593159\pi$
$252$	1.40438e6	−	2.43245e6i	0.00552818	−	0.00957509i
$253$	1.52859e8	−	1.04218e8i	0.593430	−	0.404594i
$254$	5.19759e7	+	2.27721e8i	0.199014	+	0.871937i
$255$	2.02344e8	−	3.04984e7i	0.764186	−	0.115182i
$256$	−3.38513e7	+	4.24482e7i	−0.126106	+	0.158132i
$257$	3.59215e8			1.32004			0.660022	−	0.751246i	$-0.270547\pi$
$257$	3.59215e8			1.32004			0.660022	+	0.751246i	$0.270547\pi$
$258$	−2.85486e8	−	1.25395e8i	−1.03494	−	0.454580i
$259$	2.63228e7			0.0941417
$260$	8.02069e6	−	1.00576e7i	0.0283012	−	0.0354886i
$261$	2.08989e7	−	3.15000e6i	0.0727580	−	0.0109665i
$262$	3.81405e7	+	1.67104e8i	0.131018	+	0.574029i
$263$	−3.69449e8	+	2.51886e8i	−1.25230	+	0.853806i	−0.993688	−	0.112175i	$-0.964218\pi$
$263$	−3.69449e8	+	2.51886e8i	−1.25230	+	0.853806i	−0.258614	+	0.965981i	$0.583266\pi$
$264$	1.78881e8	−	3.09832e8i	0.598344	−	1.03636i
$265$	−4.29347e7	−	7.43651e7i	−0.141726	−	0.245476i
$266$	−4.10171e7	−	1.97528e7i	−0.133622	−	0.0643491i
$267$	−5.53863e8	+	1.70844e8i	−1.78079	+	0.549301i
$268$	−3.03452e6	+	4.04929e7i	−0.00962983	+	0.128501i
$269$	−9.33819e6	+	4.09133e7i	−0.0292503	+	0.128154i	−0.987445	−	0.157963i	$-0.949507\pi$
$269$	−9.33819e6	+	4.09133e7i	−0.0292503	+	0.128154i	0.958195	+	0.286117i	$0.0923645\pi$
$270$	4.44786e7	+	1.13330e8i	0.137524	+	0.350405i
$271$	−4.69126e7	−	6.26004e8i	−0.143185	−	1.91067i	−0.357518	−	0.933906i	$-0.616377\pi$
$271$	−4.69126e7	−	6.26004e8i	−0.143185	−	1.91067i	0.214334	−	0.976761i	$-0.431242\pi$
$272$	−3.79849e8	−	5.72530e7i	−1.14451	−	0.172507i
$273$	1.60946e8	−	1.49336e8i	0.478752	−	0.444217i
$274$	6.70931e7	−	3.23103e7i	0.197038	−	0.0948887i
$275$	−2.03442e8	−	1.38705e8i	−0.589898	−	0.402186i
$276$	7.33044e6	−	1.86777e7i	0.0209869	−	0.0534737i
$277$	5.77876e8	+	1.78251e8i	1.63364	+	0.503910i	0.969786	−	0.243955i	$-0.0784450\pi$
$277$	5.77876e8	+	1.78251e8i	1.63364	+	0.503910i	0.663850	+	0.747866i	$0.268921\pi$
$278$	−1.77057e8	−	1.64285e8i	−0.494262	−	0.458608i
$279$	−2.56993e7	−	3.22259e7i	−0.0708445	−	0.0888362i
$280$	−5.50215e7	−	6.89948e7i	−0.149789	−	0.187829i
$281$	−2.33512e8	−	2.16667e8i	−0.627822	−	0.582534i	0.300742	−	0.953705i	$-0.402766\pi$
$281$	−2.33512e8	−	2.16667e8i	−0.627822	−	0.582534i	−0.928564	+	0.371172i	$0.878956\pi$
$282$	−3.51845e8	−	1.08530e8i	−0.934285	−	0.288189i
$283$	−1.60749e8	+	4.09583e8i	−0.421596	+	1.07421i	0.549494	+	0.835498i	$0.314820\pi$
$283$	−1.60749e8	+	4.09583e8i	−0.421596	+	1.07421i	−0.971090	+	0.238712i	$0.923275\pi$
$284$	−8.72890e6	−	5.95126e6i	−0.0226123	−	0.0154168i
$285$	7.60582e7	−	3.66277e7i	0.194621	−	0.0937244i
$286$	3.51647e8	−	3.26281e8i	0.888844	−	0.824727i
$287$	−6.15409e7	−	9.27580e6i	−0.153666	−	0.0231614i
$288$	−1.51828e6	−	2.02600e7i	−0.00374522	−	0.0499765i
$289$	8.34565e7	+	2.12644e8i	0.203384	+	0.518215i
$290$	9.37397e6	−	4.10700e7i	0.0225699	−	0.0988854i
$291$	−1.48857e7	+	1.98637e8i	−0.0354116	+	0.472535i
$292$	−4.16095e6	+	1.28348e6i	−0.00978032	+	0.00301683i
$293$	−2.82012e8	−	1.35810e8i	−0.654985	−	0.315424i	0.0767127	−	0.997053i	$-0.475558\pi$
$293$	−2.82012e8	−	1.35810e8i	−0.654985	−	0.315424i	−0.731698	+	0.681629i	$0.761272\pi$
$294$	1.98493e8	+	3.43801e8i	0.455544	+	0.789025i
$295$	−1.62135e8	+	2.80827e8i	−0.367706	+	0.636886i
$296$	8.12357e7	−	5.53856e7i	0.182065	−	0.124130i
$297$	−7.34010e7	−	3.21591e8i	−0.162575	−	0.712289i
$298$	7.37898e8	−	1.11220e8i	1.61525	−	0.243460i
$299$	2.64408e8	−	3.31558e8i	0.572040	−	0.717315i
$300$	−2.67043e7			−0.0571028
$301$	1.67975e8	−	1.23333e8i	0.355028	−	0.260673i
$302$	7.95883e8			1.66274
$303$	2.28228e8	−	2.86189e8i	0.471325	−	0.591022i
$304$	−1.56704e8	+	2.36193e7i	−0.319906	+	0.0482181i
$305$	−6.34509e7	−	2.77997e8i	−0.128053	−	0.561035i
$306$	1.84881e8	−	1.26050e8i	0.368864	−	0.251488i
$307$	−4.63395e8	+	8.02623e8i	−0.914043	+	1.58317i	−0.105747	+	0.994393i	$0.533723\pi$
$307$	−4.63395e8	+	8.02623e8i	−0.914043	+	1.58317i	−0.808296	+	0.588776i	$0.799610\pi$
$308$	7.58428e6	+	1.31364e7i	0.0147906	+	0.0256181i
$309$	7.12085e8	+	3.42922e8i	1.37302	+	0.661212i
$310$	−7.85068e7	+	2.42161e7i	−0.149672	+	0.0461678i
$311$	−6.31093e7	+	8.42135e8i	−0.118968	+	1.58752i	0.544136	+	0.838997i	$0.316857\pi$
$311$	−6.31093e7	+	8.42135e8i	−0.118968	+	1.58752i	−0.663105	+	0.748527i	$0.730762\pi$
$312$	1.82485e8	−	7.99517e8i	0.340161	−	1.49034i
$313$	2.52894e8	+	6.44364e8i	0.466159	+	1.18775i	0.949903	+	0.312544i	$0.101181\pi$
$313$	2.52894e8	+	6.44364e8i	0.466159	+	1.18775i	−0.483744	+	0.875209i	$0.660723\pi$
$314$	2.35954e7	+	3.14859e8i	0.0430104	+	0.573934i
$315$	4.73713e7	+	7.14008e6i	0.0853943	+	0.0128711i
$316$	−406443.	+	377124.i	−0.000724594	+	0.000672325i
$317$	4.61632e8	−	2.22310e8i	0.813933	−	0.391969i	0.0198680	−	0.999803i	$-0.493675\pi$
$317$	4.61632e8	−	2.22310e8i	0.813933	−	0.391969i	0.794065	+	0.607833i	$0.207961\pi$
$318$	−2.86932e8	−	1.95627e8i	−0.500362	−	0.341141i
$319$	−4.16993e7	+	1.06248e8i	−0.0719220	+	0.183254i
$320$	−3.13616e8	−	9.67378e7i	−0.535024	−	0.165033i
$321$	1.36087e8	+	1.26270e8i	0.229640	+	0.213075i
$322$	−1.15069e8	−	1.44292e8i	−0.192072	−	0.240850i
$323$	1.64303e8	+	2.06029e8i	0.271291	+	0.340189i
$324$	−3.74905e7	−	3.47861e7i	−0.0612370	−	0.0568196i
$325$	−5.39337e8	−	1.66363e8i	−0.871502	−	0.268823i
$326$	1.32871e8	−	3.38550e8i	0.212407	−	0.541205i
$327$	6.36058e8	+	4.33657e8i	1.00596	+	0.685850i
$328$	−2.09441e8	+	1.00862e8i	−0.327720	+	0.157822i
$329$	1.80388e8	−	1.67376e8i	0.279269	−	0.259124i
$330$	3.82789e8	+	5.76961e7i	0.586355	+	0.0883787i
$331$	3.25197e7	+	4.33945e8i	0.0492889	+	0.657714i	0.966063	+	0.258308i	$0.0831648\pi$
$331$	3.25197e7	+	4.33945e8i	0.0492889	+	0.657714i	−0.916774	+	0.399407i	$0.869216\pi$
$332$	−1.51042e6	−	3.84849e6i	−0.00226524	−	0.00577175i
$333$	−1.18769e7	+	5.20360e7i	−0.0176258	+	0.0772235i
$334$	5.44664e7	−	7.26804e8i	0.0799864	−	1.06734i
$335$	−6.61817e8	+	2.04144e8i	−0.961792	+	0.296674i
$336$	−2.99669e8	−	1.44313e8i	−0.430977	−	0.207547i
$337$	4.86008e8	+	8.41791e8i	0.691734	+	1.19812i	0.971269	+	0.237983i	$0.0764861\pi$
$337$	4.86008e8	+	8.41791e8i	0.691734	+	1.19812i	−0.279536	+	0.960135i	$0.590181\pi$
$338$	2.07071e8	−	3.58657e8i	0.291682	−	0.505208i
$339$	−8.19525e8	+	5.58743e8i	−1.14252	+	0.778956i
$340$	7.21104e6	+	3.15936e7i	0.00994996	+	0.0435936i
$341$	2.20112e8	−	3.31765e7i	0.300610	−	0.0453097i
$342$	5.75552e7	−	7.21719e7i	0.0778024	−	0.0975612i
$343$	−5.94489e8			−0.795452
$344$	2.58891e8	−	7.34058e8i	0.342896	−	0.972245i
$345$	3.42224e8			0.448688
$346$	4.36063e8	−	5.46806e8i	0.565956	−	0.709687i
$347$	−1.01726e8	+	1.53328e7i	−0.130702	+	0.0197001i	−0.214067	−	0.976819i	$-0.568671\pi$
$347$	−1.01726e8	+	1.53328e7i	−0.130702	+	0.0197001i	0.0833656	+	0.996519i	$0.473433\pi$
$348$	2.75453e6	+	1.20684e7i	0.00350365	+	0.0153505i
$349$	−4.51903e8	+	3.08102e8i	−0.569058	+	0.387977i	−0.813394	−	0.581714i	$-0.802382\pi$
$349$	−4.51903e8	+	3.08102e8i	−0.569058	+	0.387977i	0.244336	+	0.969691i	$0.421430\pi$
$350$	−1.22815e8	+	2.12721e8i	−0.153113	+	0.265199i
$351$	−3.78061e8	−	6.54820e8i	−0.466645	−	0.808253i
$352$	9.88542e7	+	4.76057e7i	0.120808	+	0.0581781i
$353$	−1.42169e9	+	4.38532e8i	−1.72025	+	0.530628i	−0.988537	−	0.150981i	$-0.951757\pi$
$353$	−1.42169e9	+	4.38532e8i	−1.72025	+	0.530628i	−0.731717	+	0.681609i	$0.761281\pi$
$354$	−9.80029e7	+	1.30776e9i	−0.117416	+	1.56681i
$355$	4.00963e7	−	1.75673e8i	0.0475669	−	0.208404i
$356$	−3.35348e7	−	8.54453e7i	−0.0393932	−	0.100372i
$357$	4.13319e7	+	5.51535e8i	0.0480780	+	0.641556i
$358$	−1.10042e9	−	1.65861e8i	−1.26755	−	0.191053i
$359$	6.62999e8	−	6.15173e8i	0.756279	−	0.701725i	−0.204553	−	0.978856i	$-0.565574\pi$
$359$	6.62999e8	−	6.15173e8i	0.756279	−	0.701725i	0.960832	+	0.277131i	$0.0893835\pi$
$360$	1.61218e8	−	7.76385e7i	0.182119	−	0.0877038i
$361$	−6.48728e8	−	4.42295e8i	−0.725751	−	0.494808i
$362$	−2.66644e8	+	6.79399e8i	−0.295429	+	0.752740i
$363$	1.72503e7	+	5.32102e6i	0.0189288	+	0.00583877i
$364$	2.54882e7	+	2.36496e7i	0.0277003	+	0.0257021i
$365$	−4.63061e7	−	5.80660e7i	−0.0498440	−	0.0625024i
$366$	−7.19005e8	−	9.01604e8i	−0.766563	−	0.961240i
$367$	−1.33526e9	−	1.23894e9i	−1.41005	−	1.30833i	−0.891309	−	0.453397i	$-0.850212\pi$
$367$	−1.33526e9	−	1.23894e9i	−1.41005	−	1.30833i	−0.518736	−	0.854934i	$-0.673597\pi$
$368$	−6.13898e8	−	1.89362e8i	−0.642139	−	0.198074i
$369$	4.61042e7	−	1.17472e8i	0.0477693	−	0.121714i
$370$	8.79001e7	+	5.99293e7i	0.0902159	+	0.0615082i
$371$	2.09108e8	−	1.00701e8i	0.212599	−	0.102382i
$372$	1.76971e7	−	1.64205e7i	0.0178239	−	0.0165381i
$373$	1.40575e9	+	2.11883e8i	1.40258	+	0.211405i	0.806365	−	0.591418i	$-0.201432\pi$
$373$	1.40575e9	+	2.11883e8i	1.40258	+	0.211405i	0.596217	+	0.802823i	$0.296670\pi$
$374$	9.03050e7	+	1.20504e9i	0.0892609	+	1.19110i
$375$	−3.97493e8	−	1.01280e9i	−0.389243	−	0.991774i
$376$	2.04529e8	−	8.96101e8i	0.198426	−	0.869359i
$377$	−1.95518e7	+	2.60901e8i	−0.0187928	+	0.250773i
$378$	−3.14441e8	+	9.69921e7i	−0.299445	+	0.0923666i
$379$	−2.24111e7	−	1.07926e7i	−0.0211459	−	0.0101833i	0.423281	−	0.905998i	$-0.360878\pi$
$379$	−2.24111e7	−	1.07926e7i	−0.0211459	−	0.0101833i	−0.444427	+	0.895815i	$0.646593\pi$
$380$	6.68445e6	+	1.15778e7i	0.00624918	+	0.0108239i
$381$	5.85335e8	−	1.01383e9i	0.542209	−	0.939134i
$382$	−4.17580e8	+	2.84701e8i	−0.383282	+	0.261317i
$383$	−2.64348e8	−	1.15818e9i	−0.240425	−	1.05337i	−0.940631	−	0.339430i	$-0.889766\pi$
$383$	−2.64348e8	−	1.15818e9i	−0.240425	−	1.05337i	0.700206	−	0.713941i	$-0.253091\pi$
$384$	−1.13877e9	+	1.71642e8i	−1.02630	+	0.154690i
$385$	−1.61307e8	+	2.02272e8i	−0.144059	+	0.180644i
$386$	2.70619e8			0.239499
$387$	1.68019e8	+	3.87709e8i	0.147357	+	0.340030i
$388$	−3.15453e7			−0.0274172
$389$	1.33503e9	−	1.67407e9i	1.14992	−	1.44195i	0.272544	−	0.962143i	$-0.412135\pi$
$389$	1.33503e9	−	1.67407e9i	1.14992	−	1.44195i	0.877374	−	0.479808i	$-0.159294\pi$
$390$	8.77444e8	−	1.32253e8i	0.749020	−	0.112897i
$391$	2.37717e8	+	1.04151e9i	0.201114	+	0.881138i
$392$	−8.18801e8	+	5.58249e8i	−0.686557	+	0.468087i
$393$	4.29526e8	−	7.43960e8i	0.356956	−	0.618267i
$394$	4.45833e8	+	7.72205e8i	0.367227	+	0.636057i
$395$	−8.52028e6	−	4.10315e6i	−0.00695608	−	0.00334987i
$396$	−2.93906e7	+	9.06580e6i	−0.0237835	+	0.00733623i
$397$	−8.23252e7	+	1.09855e9i	−0.0660338	+	0.881160i	0.861581	+	0.507621i	$0.169475\pi$
$397$	−8.23252e7	+	1.09855e9i	−0.0660338	+	0.881160i	−0.927614	+	0.373539i	$0.878144\pi$
$398$	−2.55532e7	+	1.11956e8i	−0.0203168	+	0.0890137i
$399$	8.33598e7	+	2.12397e8i	0.0656979	+	0.167396i
$400$	6.38967e7	+	8.52642e8i	0.0499193	+	0.666127i
$401$	2.08967e9	+	3.14967e8i	1.61835	+	0.243927i	0.894840	−	0.446387i	$-0.147289\pi$
$401$	2.08967e9	+	3.14967e8i	1.61835	+	0.243927i	0.723510	+	0.690314i	$0.242528\pi$
$402$	−2.05326e9	+	1.90515e9i	−1.57635	+	1.46264i
$403$	4.59718e8	−	2.21389e8i	0.349884	−	0.168495i
$404$	4.78966e7	+	3.26554e7i	0.0361385	+	0.0246388i
$405$	3.18687e8	−	8.12001e8i	0.238381	−	0.607385i
$406$	1.08802e8	+	3.35611e7i	0.0806858	+	0.0248883i
$407$	−2.11299e8	−	1.96056e8i	−0.155352	−	0.144145i
$408$	1.28804e9	+	1.61515e9i	0.938898	+	1.17734i
$409$	−1.14172e9	−	1.43167e9i	−0.825139	−	1.03469i	−0.998755	−	0.0498783i	$-0.984117\pi$
$409$	−1.14172e9	−	1.43167e9i	−0.825139	−	1.03469i	0.173616	−	0.984813i	$-0.444455\pi$
$410$	−1.84386e8	−	1.71086e8i	−0.132125	−	0.122594i
$411$	−3.56644e8	−	1.10010e8i	−0.253390	−	0.0781604i
$412$	−4.57278e7	+	1.16512e8i	−0.0322136	+	0.0820790i
$413$	−7.24161e8	−	4.93725e8i	−0.505837	−	0.344874i
$414$	3.37163e8	−	1.62369e8i	0.233528	−	0.112461i
$415$	5.16909e7	−	4.79622e7i	0.0355014	−	0.0329405i
$416$	2.48695e8	+	3.74848e7i	0.169372	+	0.0255287i
$417$	9.04646e7	+	1.20717e9i	0.0610945	+	0.815250i
$418$	1.82131e8	+	4.64062e8i	0.121974	+	0.310784i
$419$	1.15081e8	−	5.04202e8i	0.0764283	−	0.334854i	−0.922230	−	0.386642i	$-0.873635\pi$
$419$	1.15081e8	−	5.04202e8i	0.0764283	−	0.334854i	0.998658	+	0.0517879i	$0.0164920\pi$
$420$	−2.09684e6	+	2.79804e7i	−0.00138100	+	0.0184281i
$421$	1.12554e8	−	3.47183e7i	0.0735146	−	0.0226762i	−0.257780	−	0.966204i	$-0.582991\pi$
$421$	1.12554e8	−	3.47183e7i	0.0735146	−	0.0226762i	0.331294	+	0.943527i	$0.392515\pi$
$422$	9.73657e8	+	4.68889e8i	0.630685	+	0.303722i
$423$	2.49485e8	+	4.32121e8i	0.160270	+	0.277596i
$424$	4.33452e8	−	7.50760e8i	0.276160	−	0.478322i
$425$	1.17475e9	−	8.00932e8i	0.742309	−	0.506098i
$426$	−1.62158e8	−	7.10462e8i	−0.101626	−	0.445254i
$427$	7.62098e8	−	1.14868e8i	0.473711	−	0.0714004i
$428$	−1.83303e7	+	2.29855e7i	−0.0113010	+	0.0141710i
$429$	−2.40423e9			−1.47020
$430$	8.41715e8	−	2.94172e7i	0.510535	−	0.0178428i
$431$	2.69572e9			1.62183			0.810913	−	0.585167i	$-0.198971\pi$
$431$	2.69572e9			1.62183			0.810913	+	0.585167i	$0.198971\pi$
$432$	−7.14179e8	+	8.95552e8i	−0.426201	+	0.534439i
$433$	−2.01810e8	+	3.04180e7i	−0.119463	+	0.0180062i	−0.208502	−	0.978022i	$-0.566859\pi$
$433$	−2.01810e8	+	3.04180e7i	−0.119463	+	0.0180062i	0.0890384	+	0.996028i	$0.471621\pi$
$434$	−4.94124e7	−	2.16490e8i	−0.0290150	−	0.127123i
$435$	−1.74446e8	+	1.18935e8i	−0.101613	+	0.0692786i
$436$	−6.09566e7	+	1.05580e8i	−0.0352223	+	0.0610069i
$437$	2.20358e8	+	3.81672e8i	0.126312	+	0.218779i
$438$	−2.70616e8	−	1.30322e8i	−0.153884	−	0.0741068i
$439$	−2.95810e8	+	9.12454e7i	−0.166873	+	0.0514737i	−0.377066	−	0.926186i	$-0.623067\pi$
$439$	−2.95810e8	+	9.12454e7i	−0.166873	+	0.0514737i	0.210193	+	0.977660i	$0.432591\pi$
$440$	−7.22153e7	+	9.63646e8i	−0.0404152	+	0.539304i
$441$	1.19711e8	−	5.24488e8i	0.0664659	−	0.291206i
$442$	1.01199e9	+	2.57850e9i	0.557439	+	1.42033i
$443$	1.70933e8	+	2.28095e9i	0.0934143	+	1.24653i	0.825140	+	0.564928i	$0.191096\pi$
$443$	1.70933e8	+	2.28095e9i	0.0934143	+	1.24653i	−0.731726	+	0.681599i	$0.761285\pi$
$444$	−3.09122e7	−	4.65926e6i	−0.0167606	−	0.00252625i
$445$	1.14766e9	−	1.06487e9i	0.617379	−	0.572844i
$446$	2.00358e9	−	9.64871e8i	1.06938	−	0.514988i
$447$	−3.09018e9	−	2.10685e9i	−1.63647	−	1.11572i
$448$	3.24082e8	−	8.25747e8i	0.170287	−	0.433885i
$449$	2.21337e9	+	6.82735e8i	1.15396	+	0.355951i	0.811940	−	0.583741i	$-0.198412\pi$
$449$	2.21337e9	+	6.82735e8i	1.15396	+	0.355951i	0.342024	+	0.939691i	$0.388888\pi$
$450$	−3.65103e8	−	3.38766e8i	−0.188874	−	0.175249i
$451$	4.24915e8	+	5.32826e8i	0.218114	+	0.273507i
$452$	−9.79367e7	−	1.22809e8i	−0.0498840	−	0.0625525i
$453$	−2.92407e9	−	2.71314e9i	−1.47790	−	1.37129i
$454$	−3.68297e8	−	1.13605e8i	−0.184715	−	0.0569772i
$455$	−2.16662e8	+	5.52045e8i	−0.107831	+	0.274748i
$456$	7.04164e8	+	4.80091e8i	0.347774	+	0.237108i
$457$	−1.44761e7	+	6.97130e6i	−0.00709485	+	0.00341670i	−0.437428	−	0.899254i	$-0.644110\pi$
$457$	−1.44761e7	+	6.97130e6i	−0.00709485	+	0.00341670i	0.430333	+	0.902670i	$0.358396\pi$
$458$	1.68291e9	−	1.56151e9i	0.818525	−	0.759480i
$459$	1.88347e9	+	2.83887e8i	0.909103	+	0.137025i
$460$	4.05010e6	+	5.40449e7i	0.00194005	+	0.0258882i
$461$	6.68945e8	+	1.70444e9i	0.318007	+	0.810269i	0.997092	+	0.0762092i	$0.0242817\pi$
$461$	6.68945e8	+	1.70444e9i	0.318007	+	0.810269i	−0.679085	+	0.734060i	$0.737623\pi$
$462$	−2.32825e8	+	1.02007e9i	−0.109846	+	0.481265i
$463$	−1.76525e8	+	2.35556e9i	−0.0826556	+	1.10296i	0.789506	+	0.613743i	$0.210337\pi$
$463$	−1.76525e8	+	2.35556e9i	−0.0826556	+	1.10296i	−0.872161	+	0.489219i	$0.837282\pi$
$464$	3.78740e8	−	1.16826e8i	0.176006	−	0.0542908i
$465$	3.70985e8	+	1.78657e8i	0.171108	+	0.0824015i
$466$	−3.66415e8	−	6.34649e8i	−0.167734	−	0.290525i
$467$	−9.31198e8	+	1.61288e9i	−0.423090	+	0.732814i	−0.996240	−	0.0866368i	$-0.972388\pi$
$467$	−9.31198e8	+	1.61288e9i	−0.423090	+	0.732814i	0.573150	+	0.819451i	$0.305721\pi$
$468$	−5.82519e7	+	3.97155e7i	−0.0262694	+	0.0179102i
$469$	−4.16550e8	−	1.82502e9i	−0.186450	−	0.816890i
$470$	9.83441e8	−	1.48230e8i	0.436924	−	0.0658557i
$471$	9.86653e8	−	1.23722e9i	0.435102	−	0.545601i
$472$	−3.27371e9			−1.43299
$473$	−2.26698e9	−	2.61088e8i	−0.984993	−	0.113442i
$474$	−3.82454e7			−0.0164951
$475$	3.65712e8	−	4.58588e8i	0.156571	−	0.196334i
$476$	−8.66105e7	+	1.30544e7i	−0.0368084	+	0.00554797i
$477$	1.04721e8	+	4.58811e8i	0.0441792	+	0.193562i
$478$	2.35412e9	−	1.60501e9i	0.985897	−	0.672173i
$479$	8.18647e8	−	1.41794e9i	0.340347	−	0.589499i	−0.644150	−	0.764899i	$-0.722789\pi$
$479$	8.18647e8	−	1.41794e9i	0.340347	−	0.589499i	0.984497	+	0.175401i	$0.0561220\pi$
$480$	1.01480e8	+	1.75769e8i	0.0418829	+	0.0725432i
$481$	−5.95295e8	−	2.86679e8i	−0.243907	−	0.117459i
$482$	−1.98468e9	+	6.12192e8i	−0.807283	+	0.249014i
$483$	−6.91239e7	+	9.22395e8i	−0.0279134	+	0.372479i
$484$	−636156.	+	2.78718e6i	−0.000255038	+	0.00111739i
$485$	−1.96568e8	−	5.00847e8i	−0.0782378	−	0.199347i
$486$	−1.29082e8	−	1.72248e9i	−0.0510081	−	0.680656i
$487$	−3.02345e9	−	4.55712e8i	−1.18618	−	0.178788i	−0.473834	−	0.880614i	$-0.657130\pi$
$487$	−3.02345e9	−	4.55712e8i	−1.18618	−	0.178788i	−0.712348	+	0.701826i	$0.752368\pi$
$488$	2.11025e9	−	1.95803e9i	0.821986	−	0.762692i
$489$	−1.64227e9	+	7.90878e8i	−0.635133	+	0.305864i
$490$	−8.85973e8	−	6.04046e8i	−0.340200	−	0.231944i
$491$	1.05701e9	−	2.69322e9i	0.402990	−	1.02680i	−0.575000	−	0.818153i	$-0.694998\pi$
$491$	1.05701e9	−	2.69322e9i	0.402990	−	1.02680i	0.977991	−	0.208649i	$-0.0669067\pi$
$492$	7.06289e7	+	2.17861e7i	0.0267365	+	0.00824711i
$493$	−4.83137e8	−	4.48285e8i	−0.181596	−	0.168496i
$494$	7.12484e8	+	8.93426e8i	0.265907	+	0.333437i
$495$	−3.27080e8	−	4.10145e8i	−0.121209	−	0.151991i
$496$	−5.66635e8	−	5.25760e8i	−0.208505	−	0.193465i
$497$	4.65392e8	+	1.43554e8i	0.170048	+	0.0524529i
$498$	1.04187e8	−	2.65464e8i	0.0378016	−	0.0963170i
$499$	−2.15605e9	−	1.46997e9i	−0.776797	−	0.529611i	0.108801	−	0.994064i	$-0.465299\pi$
$499$	−2.15605e9	−	1.46997e9i	−0.776797	−	0.529611i	−0.885598	+	0.464452i	$0.846251\pi$
$500$	1.55239e8	−	7.47591e7i	0.0555400	−	0.0267466i
$501$	−2.67776e9	+	2.48460e9i	−0.951348	+	0.882722i
$502$	−3.70716e9	−	5.58764e8i	−1.30791	−	0.197136i
$503$	−1.23608e8	−	1.64943e9i	−0.0433071	−	0.577893i	−0.976078	−	0.217422i	$-0.930235\pi$
$503$	−1.23608e8	−	1.64943e9i	−0.0433071	−	0.577893i	0.932771	−	0.360471i	$-0.117384\pi$
$504$	1.76695e8	+	4.50211e8i	0.0614776	+	0.156642i
$505$	−2.20014e8	+	9.63943e8i	−0.0760204	+	0.333067i
$506$	−1.51027e8	+	2.01532e9i	−0.0518237	+	0.691539i
$507$	−1.98342e9	+	6.11805e8i	−0.675908	+	0.208490i
$508$	1.67033e8	+	8.04391e7i	0.0565302	+	0.0272235i
$509$	2.52035e9	+	4.36538e9i	0.847128	+	1.46727i	0.883760	+	0.467940i	$0.155004\pi$
$509$	2.52035e9	+	4.36538e9i	0.847128	+	1.46727i	−0.0366323	+	0.999329i	$0.511663\pi$
$510$	−1.11767e9	+	1.93585e9i	−0.373092	+	0.646214i
$511$	1.65858e8	−	1.13080e8i	0.0549874	−	0.0374897i
$512$	−7.31098e8	−	3.20315e9i	−0.240730	−	1.05471i
$513$	7.77010e8	−	1.17115e8i	0.254106	−	0.0383004i
$514$	−2.44657e9	+	3.06790e9i	−0.794671	+	0.996485i
$515$	−2.13482e9			−0.688709
$516$	−2.19092e8	+	1.15104e8i	−0.0702026	+	0.0368821i
$517$	−2.69466e9			−0.857606
$518$	−1.79281e8	+	2.24812e8i	−0.0566736	+	0.0710664i
$519$	−3.46613e9	+	5.22436e8i	−1.08833	+	0.164039i
$520$	4.92907e8	+	2.15957e9i	0.153728	+	0.673527i
$521$	2.13885e9	−	1.45824e9i	0.662594	−	0.451749i	−0.184755	−	0.982785i	$-0.559149\pi$
$521$	2.13885e9	−	1.45824e9i	0.662594	−	0.451749i	0.847350	+	0.531035i	$0.178197\pi$
$522$	−1.15437e8	+	1.99943e8i	−0.0355221	+	0.0615260i
$523$	1.84908e9	+	3.20270e9i	0.565197	+	0.978950i	0.997031	+	0.0769967i	$0.0245331\pi$
$523$	1.84908e9	+	3.20270e9i	0.565197	+	0.978950i	−0.431835	+	0.901953i	$0.642134\pi$
$524$	1.22571e8	+	5.90272e7i	0.0372159	+	0.0179222i
$525$	1.17638e9	−	3.62865e8i	0.354805	−	0.109443i
$526$	3.65022e8	−	4.87087e9i	0.109363	−	1.45934i
$527$	−2.86020e8	+	1.25314e9i	−0.0851255	+	0.372959i
$528$	1.33064e9	+	3.39041e9i	0.393407	+	1.00238i
$529$	−1.20928e8	−	1.61367e9i	−0.0355167	−	0.473937i
$530$	9.27545e8	+	1.39805e8i	0.270626	+	0.0407903i
$531$	1.30276e9	−	1.20879e9i	0.377602	−	0.350363i
$532$	−3.25557e7	+	1.56780e7i	−0.00937425	+	0.00451440i
$533$	1.29074e9	+	8.80011e8i	0.369227	+	0.251735i
$534$	2.31319e9	−	5.89391e9i	0.657380	−	1.67498i
$535$	−4.79164e8	−	1.47802e8i	−0.135284	−	0.0417295i
$536$	−5.12556e9	−	4.75582e9i	−1.43769	−	1.33398i
$537$	3.47750e9	+	4.36065e9i	0.969075	+	1.21518i
$538$	−2.85822e8	−	3.58409e8i	−0.0791329	−	0.0992296i
$539$	2.12974e9	+	1.97611e9i	0.585824	+	0.543565i
$540$	9.23378e7	+	2.84824e7i	0.0252349	+	0.00778393i
$541$	1.12398e9	−	2.86386e9i	0.305189	−	0.777608i	−0.693194	−	0.720751i	$-0.743797\pi$
$541$	1.12398e9	−	2.86386e9i	0.305189	−	0.777608i	0.998382	−	0.0568567i	$-0.0181078\pi$
$542$	5.66596e9	+	3.86298e9i	1.52854	+	1.04214i
$543$	3.29570e9	−	1.58712e9i	0.883381	−	0.425414i
$544$	−4.64435e8	+	4.30932e8i	−0.123688	+	0.114766i
$545$	−2.05614e9	−	3.09913e8i	−0.544082	−	0.0820072i
$546$	1.79232e8	+	2.39168e9i	0.0471238	+	0.628824i
$547$	2.24175e8	+	5.71188e8i	0.0585641	+	0.149219i	0.957161	−	0.289556i	$-0.0935077\pi$
$547$	2.24175e8	+	5.71188e8i	0.0585641	+	0.149219i	−0.898597	+	0.438775i	$0.855412\pi$
$548$	1.31523e7	−	5.76240e7i	0.00341405	−	0.0149579i
$549$	−1.16784e8	+	1.55838e9i	−0.0301219	+	0.401948i
$550$	2.57024e9	−	7.92815e8i	0.658726	−	0.203190i
$551$	−2.44971e8	−	1.17972e8i	−0.0623855	−	0.0300433i
$552$	1.72748e9	+	2.99208e9i	0.437146	+	0.757159i
$553$	1.27802e7	−	2.21359e7i	0.00321365	−	0.00556620i
$554$	−5.45822e9	+	3.72135e9i	−1.36385	+	0.929857i
$555$	−1.18647e8	−	5.19828e8i	−0.0294600	−	0.129073i
$556$	−1.89568e8	+	2.85727e7i	−0.0467738	+	0.00705001i
$557$	7.85029e8	−	9.84395e8i	0.192483	−	0.241366i	−0.676220	−	0.736700i	$-0.736383\pi$
$557$	7.85029e8	−	9.84395e8i	0.192483	−	0.241366i	0.868703	+	0.495334i	$0.164954\pi$
$558$	4.50262e8			0.109710
$559$	−5.14200e9	+	9.59796e8i	−1.24506	+	0.232401i
$560$	8.98401e8			0.216178
$561$	3.77615e9	−	4.73514e9i	0.902982	−	1.13230i
$562$	3.44088e9	−	5.18630e8i	0.817698	−	0.123248i
$563$	5.00624e8	+	2.19338e9i	0.118231	+	0.518005i	0.999010	+	0.0444775i	$0.0141623\pi$
$563$	5.00624e8	+	2.19338e9i	0.118231	+	0.518005i	−0.880779	+	0.473527i	$0.842981\pi$
$564$	−2.41466e8	+	1.64629e8i	−0.0566734	+	0.0386393i
$565$	1.33957e9	−	2.32020e9i	0.312461	−	0.541199i
$566$	−2.40323e9	−	4.16251e9i	−0.557105	−	0.964935i
$567$	2.12421e9	+	1.02297e9i	0.489392	+	0.235679i
$568$	1.73832e9	−	5.36200e8i	0.398025	−	0.122774i
$569$	−3.50629e8	+	4.67882e9i	−0.0797911	+	1.06474i	0.803312	+	0.595559i	$0.203069\pi$
$569$	−3.50629e8	+	4.67882e9i	−0.0797911	+	1.06474i	−0.883103	+	0.469180i	$0.844550\pi$
$570$	−2.05202e8	+	8.99048e8i	−0.0464108	+	0.203339i
$571$	−7.06680e8	−	1.80059e9i	−0.158853	−	0.404752i	0.829182	−	0.558979i	$-0.188807\pi$
$571$	−7.06680e8	−	1.80059e9i	−0.158853	−	0.404752i	−0.988035	+	0.154227i	$0.950711\pi$
$572$	−2.84532e7	−	3.79681e8i	−0.00635688	−	0.0848267i
$573$	2.50472e9	+	3.77526e8i	0.556184	+	0.0838313i
$574$	4.98369e8	−	4.62419e8i	0.109992	−	0.102057i
$575$	2.14237e9	−	1.03171e9i	0.469955	−	0.226318i
$576$	1.48615e9	+	1.01324e9i	0.324029	+	0.220919i
$577$	1.00199e9	−	2.55304e9i	0.217145	−	0.553277i	−0.780245	−	0.625474i	$-0.784906\pi$
$577$	1.00199e9	−	2.55304e9i	0.217145	−	0.553277i	0.997390	+	0.0721970i	$0.0230010\pi$
$578$	−2.38451e9	−	7.35525e8i	−0.513632	−	0.158435i
$579$	−9.94253e8	−	9.22532e8i	−0.212874	−	0.197518i
$580$	−2.08471e7	−	2.61414e7i	−0.00443657	−	0.00556328i
$581$	1.18831e8	+	1.49010e8i	0.0251370	+	0.0315209i
$582$	−1.59509e9	−	1.48002e9i	−0.335393	−	0.311199i
$583$	−2.42859e9	−	7.49122e8i	−0.507592	−	0.156571i
$584$	2.73930e8	−	6.97961e8i	0.0569107	−	0.145006i
$585$	−9.93550e8	−	6.77391e8i	−0.205184	−	0.139892i
$586$	3.08065e9	−	1.48356e9i	0.632413	−	0.304554i
$587$	−6.41897e9	+	5.95593e9i	−1.30988	+	1.21539i	−0.349424	+	0.936965i	$0.613623\pi$
$587$	−6.41897e9	+	5.95593e9i	−1.30988	+	1.21539i	−0.960457	+	0.278427i	$0.910187\pi$
$588$	3.11574e8	+	4.69622e7i	0.0632033	+	0.00952637i
$589$	3.96269e7	+	5.28785e8i	0.00799074	+	0.106629i
$590$	−1.29414e9	−	3.29741e9i	−0.259417	−	0.660984i
$591$	9.94435e8	−	4.35690e9i	0.198162	−	0.868204i
$592$	−7.48004e7	+	9.98142e8i	−0.0148176	+	0.197727i
$593$	5.85425e9	−	1.80580e9i	1.15287	−	0.355613i	0.341348	−	0.939937i	$-0.389116\pi$
$593$	5.85425e9	−	1.80580e9i	1.15287	−	0.355613i	0.811521	+	0.584324i	$0.198640\pi$
$594$	3.24650e9	+	1.56343e9i	0.635569	+	0.306074i
$595$	−7.46961e8	−	1.29378e9i	−0.145375	−	0.251796i
$596$	2.96147e8	−	5.12942e8i	0.0572988	−	0.0992444i
$597$	4.75537e8	−	3.24215e8i	0.0914690	−	0.0623625i
$598$	1.03084e9	+	4.51640e9i	0.197123	+	0.863651i
$599$	−6.12441e9	+	9.23106e8i	−1.16431	+	0.175492i	−0.702632	−	0.711553i	$-0.747992\pi$
$599$	−6.12441e9	+	9.23106e8i	−1.16431	+	0.175492i	−0.461682	+	0.887045i	$0.652754\pi$
$600$	2.86697e9	−	3.59506e9i	0.541868	−	0.679481i
$601$	−9.41432e9			−1.76900			−0.884501	−	0.466538i	$-0.845501\pi$
$601$	−9.41432e9			−1.76900			−0.884501	+	0.466538i	$0.845501\pi$
$602$	−9.07252e7	+	2.27461e9i	−0.0169489	+	0.424932i
$603$	3.79574e9			0.704995
$604$	3.93860e8	−	4.93884e8i	0.0727297	−	0.0912002i
$605$	−4.82163e7	+	7.26744e6i	−0.00885218	+	0.00133425i
$606$	8.89785e8	+	3.89840e9i	0.162417	+	0.711594i
$607$	6.97394e9	−	4.75475e9i	1.26566	−	0.862913i	0.270650	−	0.962678i	$-0.412761\pi$
$607$	6.97394e9	−	4.75475e9i	1.26566	−	0.862913i	0.995011	+	0.0997643i	$0.0318089\pi$
$608$	−1.30686e8	+	2.26355e8i	−0.0235812	+	0.0408439i
$609$	−2.85330e8	−	4.94207e8i	−0.0511903	−	0.0886642i
$610$	2.80641e9	+	1.35150e9i	0.500607	+	0.241080i
$611$	−5.90240e9	+	1.82065e9i	−1.04685	+	0.322910i
$612$	1.32723e7	−	1.77106e8i	0.00234053	−	0.0312322i
$613$	−1.03801e9	+	4.54782e9i	−0.182008	+	0.797428i	0.798665	+	0.601775i	$0.205540\pi$
$613$	−1.03801e9	+	4.54782e9i	−0.182008	+	0.797428i	−0.980673	+	0.195653i	$0.937317\pi$
$614$	−3.69874e9	−	9.42423e9i	−0.644858	−	1.64307i
$615$	9.42092e7	+	1.25713e9i	0.0163317	+	0.217931i
$616$	−2.58272e9	−	3.89283e8i	−0.445190	−	0.0671016i
$617$	5.20769e9	−	4.83203e9i	0.892580	−	0.828193i	−0.0933014	−	0.995638i	$-0.529742\pi$
$617$	5.20769e9	−	4.83203e9i	0.892580	−	0.828193i	0.985881	+	0.167445i	$0.0535516\pi$
$618$	−7.77868e9	+	3.74602e9i	−1.32570	+	0.638425i
$619$	9.11491e9	+	6.21444e9i	1.54467	+	1.05314i	0.972472	+	0.233019i	$0.0748603\pi$
$619$	9.11491e9	+	6.21444e9i	1.54467	+	1.05314i	0.572195	+	0.820118i	$0.306092\pi$
$620$	−2.38235e7	+	6.07012e7i	−0.00401452	+	0.0102288i
$621$	3.04399e9	+	9.38946e8i	0.510061	+	0.157333i
$622$	−6.76249e9	−	6.27467e9i	−1.12678	−	1.04550i
$623$	2.63833e9	+	3.30836e9i	0.437140	+	0.548156i
$624$	5.20537e9	+	6.52733e9i	0.857641	+	1.07545i
$625$	−1.06746e9	−	9.90456e8i	−0.174892	−	0.162276i
$626$	−7.22568e9	−	2.22883e9i	−1.17725	−	0.363133i
$627$	9.12824e8	−	2.32584e9i	0.147894	−	0.376828i
$628$	2.07062e8	+	1.41172e8i	0.0333612	+	0.0227453i
$629$	1.49960e9	−	7.22171e8i	0.240270	−	0.115708i
$630$	−3.83621e8	+	3.55948e8i	−0.0611238	+	0.0567146i
$631$	7.33542e9	+	1.10564e9i	1.16231	+	0.175190i	0.701740	−	0.712433i	$-0.252407\pi$
$631$	7.33542e9	+	1.10564e9i	1.16231	+	0.175190i	0.460571	+	0.887623i	$0.347645\pi$
$632$	−7.13464e6	−	9.52051e7i	−0.00112425	−	0.0150020i
$633$	−1.97878e9	−	5.04186e9i	−0.310088	−	0.790092i
$634$	−1.24546e9	+	5.45673e9i	−0.194097	+	0.850394i
$635$	−2.36303e8	+	3.15324e9i	−0.0366236	+	0.488707i
$636$	−2.63391e8	+	8.12453e7i	−0.0405976	+	0.0125227i
$637$	6.00016e9	+	2.88953e9i	0.919761	+	0.442933i
$638$	−6.23412e8	−	1.07978e9i	−0.0950391	−	0.164613i
$639$	−4.93771e8	+	8.55236e8i	−0.0748639	+	0.129668i
$640$	2.57014e9	−	1.75229e9i	0.387550	−	0.264227i
$641$	2.65772e9	+	1.16442e10i	0.398571	+	1.74625i	0.633030	+	0.774127i	$0.281811\pi$
$641$	2.65772e9	+	1.16442e10i	0.398571	+	1.74625i	−0.234459	+	0.972126i	$0.575332\pi$
$642$	−2.00529e9	+	3.02249e8i	−0.299092	+	0.0450809i
$643$	−3.35663e9	+	4.20908e9i	−0.497926	+	0.624380i	−0.965760	−	0.259437i	$-0.916463\pi$
$643$	−3.35663e9	+	4.20908e9i	−0.497926	+	0.624380i	0.467834	+	0.883816i	$0.345035\pi$
$644$	−1.46485e8			−0.0216118
$645$	−3.19274e9	−	2.76130e9i	−0.468494	−	0.405186i
$646$	−2.87866e9			−0.420123
$647$	−1.17121e9	+	1.46865e9i	−0.170008	+	0.213184i	−0.859535	−	0.511076i	$-0.829247\pi$
$647$	−1.17121e9	+	1.46865e9i	−0.170008	+	0.213184i	0.689527	+	0.724260i	$0.257818\pi$
$648$	8.70803e9	−	1.31252e9i	1.25721	−	0.189494i
$649$	2.13566e9	+	9.35692e9i	0.306672	+	1.34362i
$650$	5.09420e9	−	3.47317e9i	0.727578	−	0.496054i
$651$	−5.56466e8	+	9.63828e8i	−0.0790506	+	0.136920i
$652$	−1.44333e8	−	2.49992e8i	−0.0203938	−	0.0353231i
$653$	−4.42588e9	−	2.13139e9i	−0.622019	−	0.299549i	0.0962039	−	0.995362i	$-0.469330\pi$
$653$	−4.42588e9	−	2.13139e9i	−0.622019	−	0.299549i	−0.718223	+	0.695813i	$0.755044\pi$
$654$	−8.03580e9	+	2.47872e9i	−1.12333	+	0.346501i
$655$	−1.73402e8	+	2.31389e9i	−0.0241107	+	0.321734i
$656$	5.26611e8	−	2.30723e9i	0.0728327	−	0.319101i
$657$	1.48706e8	+	3.78897e8i	0.0204574	+	0.0521246i
$658$	2.00883e8	+	2.68060e9i	0.0274886	+	0.366810i
$659$	5.04091e9	+	7.59795e8i	0.686136	+	0.103418i	0.482853	−	0.875702i	$-0.339601\pi$
$659$	5.04091e9	+	7.59795e8i	0.686136	+	0.103418i	0.203283	+	0.979120i	$0.434839\pi$
$660$	2.25234e8	−	2.08987e8i	0.0304952	−	0.0282954i
$661$	−6.57018e9	+	3.16403e9i	−0.884855	+	0.426124i	−0.820396	−	0.571796i	$-0.806247\pi$
$661$	−6.57018e9	+	3.16403e9i	−0.884855	+	0.426124i	−0.0644598	+	0.997920i	$0.520532\pi$
$662$	−3.92763e9	−	2.67782e9i	−0.526172	−	0.358738i
$663$	5.07199e9	−	1.29232e10i	0.675898	−	1.72216i
$664$	6.80260e8	+	2.09833e8i	0.0901752	+	0.0278154i
$665$	−4.51785e8	−	4.19195e8i	−0.0595739	−	0.0552765i
$666$	−3.63526e8	−	4.55847e8i	−0.0476843	−	0.0597942i
$667$	−6.87240e8	−	8.61771e8i	−0.0896743	−	0.112448i
$668$	−4.24064e8	−	3.93473e8i	−0.0550444	−	0.0510738i
$669$	−1.06503e10	−	3.28519e9i	−1.37522	−	0.424199i
$670$	2.76406e9	−	7.04270e9i	0.355046	−	0.904644i
$671$	−6.97309e9	−	4.75417e9i	−0.891038	−	0.607499i
$672$	−4.94245e8	+	2.38016e8i	−0.0628275	+	0.0302561i
$673$	7.24342e8	−	6.72091e8i	0.0915990	−	0.0849915i	−0.633044	−	0.774115i	$-0.718195\pi$
$673$	7.24342e8	−	6.72091e8i	0.0915990	−	0.0849915i	0.724643	+	0.689124i	$0.242004\pi$
$674$	−1.04995e10	−	1.58255e9i	−1.32087	−	0.199089i
$675$	−3.16829e8	−	4.22779e9i	−0.0396517	−	0.529115i
$676$	−1.20091e8	−	3.05986e8i	−0.0149519	−	0.0380968i
$677$	−1.22384e8	+	5.36201e8i	−0.0151588	+	0.0664152i	−0.981942	−	0.189184i	$-0.939416\pi$
$677$	−1.22384e8	+	5.36201e8i	−0.0151588	+	0.0664152i	0.966783	+	0.255599i	$0.0822728\pi$
$678$	8.09704e8	−	1.08048e10i	0.0997752	−	1.33141i
$679$	1.38963e9	−	4.28645e8i	0.170355	−	0.0525476i
$680$	−5.02745e9	−	2.42109e9i	−0.613150	−	0.295278i
$681$	9.65847e8	+	1.67290e9i	0.117191	+	0.202980i
$682$	−1.21581e9	+	2.10584e9i	−0.146764	+	0.254203i
$683$	−1.14372e10	+	7.79774e9i	−1.37356	+	0.936476i	−0.373597	+	0.927591i	$0.621876\pi$
$683$	−1.14372e10	+	7.79774e9i	−1.37356	+	0.936476i	−0.999961	+	0.00888477i	$0.997172\pi$
$684$	−1.63038e7	−	7.14316e7i	−0.00194802	−	0.00853482i
$685$	9.96856e8	−	1.50252e8i	0.118499	−	0.0178609i
$686$	4.04899e9	−	5.07728e9i	0.478865	−	0.600477i
$687$	−1.15061e10			−1.35388
$688$	4.19937e9	+	6.71998e9i	0.491615	+	0.786699i
$689$	−5.82574e9			−0.678553
$690$	−2.33085e9	+	2.92280e9i	−0.270111	+	0.338709i
$691$	3.77480e9	−	5.68960e8i	0.435232	−	0.0656007i	0.0722278	−	0.997388i	$-0.476989\pi$
$691$	3.77480e9	−	5.68960e8i	0.435232	−	0.0656007i	0.363004	+	0.931787i	$0.381751\pi$
$692$	−1.23525e8	−	5.41197e8i	−0.0141704	−	0.0620846i
$693$	1.17152e9	−	7.98732e8i	0.133717	−	0.0911664i
$694$	5.61896e8	−	9.73233e8i	0.0638114	−	0.110525i
$695$	−1.63490e9	−	2.83173e9i	−0.184733	−	0.319967i
$696$	−1.92043e9	−	9.24829e8i	−0.215906	−	0.103975i
$697$	−3.76046e9	+	1.15995e9i	−0.420655	+	0.129755i
$698$	4.46487e8	−	5.95796e9i	0.0496953	−	0.663138i
$699$	−8.17292e8	+	3.58079e9i	−0.0905122	+	0.396560i
$700$	7.12264e7	+	1.81482e8i	0.00784870	+	0.0199982i
$701$	2.35935e8	+	3.14834e9i	0.0258690	+	0.345198i	0.995088	+	0.0989968i	$0.0315634\pi$
$701$	2.35935e8	+	3.14834e9i	0.0258690	+	0.345198i	−0.969219	+	0.246201i	$0.920818\pi$
$702$	8.16747e9	+	1.23105e9i	0.891061	+	0.134306i
$703$	5.03350e8	−	4.67040e8i	0.0546420	−	0.0507003i
$704$	−8.75178e9	+	4.21464e9i	−0.945349	+	0.455256i
$705$	−4.11847e9	−	2.80792e9i	−0.442663	−	0.301803i
$706$	5.93763e9	−	1.51288e10i	0.635033	−	1.61804i
$707$	−2.55367e9	−	7.87702e8i	−0.271767	−	0.0838290i
$708$	7.63029e8	+	7.07987e8i	0.0808024	+	0.0749737i
$709$	8.36588e9	+	1.04905e10i	0.881556	+	1.10544i	0.993736	+	0.111749i	$0.0356452\pi$
$709$	8.36588e9	+	1.04905e10i	0.881556	+	1.10544i	−0.112180	+	0.993688i	$0.535783\pi$
$710$	1.22726e9	+	1.53894e9i	0.128686	+	0.161368i
$711$	3.79928e7	+	3.52522e7i	0.00396422	+	0.00367826i
$712$	1.51033e10	+	4.65876e9i	1.56817	+	0.483716i
$713$	−7.85359e8	+	2.00106e9i	−0.0811437	+	0.206751i
$714$	−4.99194e9	−	3.40345e9i	−0.513246	−	0.349925i
$715$	5.85092e9	−	2.81765e9i	0.598622	−	0.288281i
$716$	−6.47489e8	+	6.00782e8i	−0.0659229	+	0.0611676i
$717$	−1.41205e10	−	2.12832e9i	−1.43065	−	0.215635i
$718$	7.38325e8	+	9.85227e9i	0.0744410	+	0.993346i
$719$	6.36340e8	+	1.62137e9i	0.0638466	+	0.162679i	0.959237	−	0.282604i	$-0.0911983\pi$
$719$	6.36340e8	+	1.62137e9i	0.0638466	+	0.162679i	−0.895390	+	0.445283i	$0.853103\pi$
$720$	−4.05361e8	+	1.77600e9i	−0.0404742	+	0.177329i
$721$	4.31200e8	−	5.75396e9i	0.0428455	−	0.571733i
$722$	8.19587e9	−	2.52809e9i	0.810429	−	0.249984i
$723$	9.37864e9	+	4.51651e9i	0.922902	+	0.444446i
$724$	2.89646e8	+	5.01681e8i	0.0283650	+	0.0491295i
$725$	−7.33498e8	+	1.27046e9i	−0.0714852	+	0.123816i
$726$	−1.62934e8	+	1.11087e8i	−0.0158028	+	0.0107742i
$727$	−2.81133e9	−	1.23172e10i	−0.271357	−	1.18889i	−0.908412	−	0.418075i	$-0.862705\pi$
$727$	−2.81133e9	−	1.23172e10i	−0.271357	−	1.18889i	0.637055	−	0.770818i	$-0.280152\pi$
$728$	−5.92022e9	+	8.92330e8i	−0.568693	+	0.0857167i
$729$	2.64554e9	−	3.31741e9i	0.252911	−	0.317141i
$730$	8.11302e8			0.0771885
$731$	6.18585e9	−	1.16347e10i	0.585718	−	1.10165i
$732$	−9.15304e8			−0.0862535
$733$	2.75388e9	−	3.45325e9i	0.258274	−	0.323865i	−0.635741	−	0.771902i	$-0.719305\pi$
$733$	2.75388e9	−	3.45325e9i	0.258274	−	0.323865i	0.894015	+	0.448037i	$0.147877\pi$
$734$	1.96755e10	−	2.96560e9i	1.83649	−	0.276807i
$735$	1.19588e9	+	5.23951e9i	0.111092	+	0.486727i
$736$	−8.75465e8	+	5.96882e8i	−0.0809406	+	0.0551844i
$737$	−1.02494e10	+	1.77524e10i	−0.943106	+	1.63351i
$738$	6.89266e8	+	1.19384e9i	0.0631232	+	0.109333i
$739$	9.10210e9	+	4.38334e9i	0.829633	+	0.399530i	0.799978	−	0.600030i	$-0.204845\pi$
$739$	9.10210e9	+	4.38334e9i	0.829633	+	0.399530i	0.0296557	+	0.999560i	$0.490559\pi$
$740$	8.06883e7	−	2.48890e7i	0.00731980	−	0.00225786i
$741$	4.28001e8	−	5.71127e9i	0.0386439	−	0.515667i
$742$	−5.64164e8	+	2.47176e9i	−0.0506981	+	0.222123i
$743$	−5.04824e9	−	1.28627e10i	−0.451522	−	1.15046i	−0.957633	−	0.287991i	$-0.907013\pi$
$743$	−5.04824e9	−	1.28627e10i	−0.451522	−	1.15046i	0.506111	−	0.862468i	$-0.331083\pi$
$744$	3.10652e8	+	4.14537e9i	0.0276547	+	0.369027i
$745$	9.98939e9	+	1.50566e9i	0.885099	+	0.133407i
$746$	−1.13840e10	+	1.05628e10i	−1.00395	+	0.931525i
$747$	−3.48186e8	+	1.67678e8i	−0.0305625	+	0.0147181i
$748$	7.92473e8	+	5.40299e8i	0.0692355	+	0.0472040i
$749$	4.95154e8	−	1.26163e9i	0.0430580	−	0.109710i
$750$	1.13571e10	+	3.50322e9i	0.983003	+	0.303216i
$751$	5.05538e9	+	4.69071e9i	0.435526	+	0.404109i	0.867231	−	0.497906i	$-0.165897\pi$
$751$	5.05538e9	+	4.69071e9i	0.435526	+	0.404109i	−0.431705	+	0.902015i	$0.642088\pi$
$752$	5.83419e9	+	7.31584e9i	0.500286	+	0.627339i
$753$	1.17153e10	+	1.46905e10i	0.999930	+	1.25387i
$754$	−2.09508e9	−	1.94395e9i	−0.177992	−	0.165152i
$755$	1.02957e10	+	3.17580e9i	0.870645	+	0.268558i
$756$	−9.54193e7	+	2.43124e8i	−0.00803174	+	0.0204645i
$757$	−1.32635e10	−	9.04290e9i	−1.11128	−	0.757656i	−0.138723	−	0.990331i	$-0.544300\pi$
$757$	−1.32635e10	−	9.04290e9i	−1.11128	−	0.757656i	−0.972555	+	0.232675i	$0.925252\pi$
$758$	2.44815e8	−	1.17897e8i	0.0204172	−	0.00983240i
$759$	7.42503e9	−	6.88942e9i	0.616385	−	0.571921i
$760$	−2.27630e9	−	3.43097e8i	−0.188097	−	0.0283510i
$761$	−5.25995e8	−	7.01892e9i	−0.0432649	−	0.577330i	−0.976142	−	0.217134i	$-0.930329\pi$
$761$	−5.25995e8	−	7.01892e9i	−0.0432649	−	0.577330i	0.932877	−	0.360195i	$-0.117290\pi$
$762$	4.67204e9	+	1.19042e10i	0.382529	+	0.974668i
$763$	1.25061e9	−	5.47929e9i	0.101926	−	0.446569i
$764$	−2.99773e7	+	4.00020e8i	−0.00243201	+	0.0324530i
$765$	2.89463e9	−	8.92874e8i	0.233764	−	0.0721066i
$766$	1.16920e10	+	5.63056e9i	0.939913	+	0.452638i
$767$	1.09999e10	+	1.90525e10i	0.880252	+	1.52464i
$768$	−1.48626e9	+	2.57427e9i	−0.118394	+	0.205064i
$769$	2.84702e7	−	1.94107e7i	0.00225761	−	0.00153921i	−0.562191	−	0.827008i	$-0.690041\pi$
$769$	2.84702e7	−	1.94107e7i	0.00225761	−	0.00153921i	0.564448	+	0.825468i	$0.309089\pi$
$770$	−6.28881e8	−	2.75531e9i	−0.0496422	−	0.217497i
$771$	1.94471e10	−	2.93117e9i	1.52814	−	0.230330i
$772$	1.33922e8	−	1.67933e8i	0.0104759	−	0.0131363i
$773$	−7.63333e9			−0.594409			−0.297205	−	0.954814i	$-0.596054\pi$
$773$	−7.63333e9			−0.594409			−0.297205	+	0.954814i	$0.596054\pi$
$774$	−4.45562e9	−	1.20566e9i	−0.345394	−	0.0934611i
$775$	2.86101e9			0.220782
$776$	3.38669e9	−	4.24677e9i	0.260171	−	0.326244i
$777$	1.42505e9	−	2.14792e8i	0.108983	−	0.0164265i
$778$	5.20482e9	+	2.28038e10i	0.396257	+	1.73612i
$779$	−1.34138e9	+	9.14537e8i	−0.101665	+	0.0693139i
$780$	3.52152e8	−	6.09945e8i	0.0265705	−	0.0460214i
$781$	−2.66659e9	−	4.61866e9i	−0.200298	−	0.346927i
$782$	−1.05141e10	−	5.06335e9i	−0.786232	−	0.378629i
$783$	−1.87797e9	+	5.79276e8i	−0.139805	+	0.0431240i
$784$	7.53937e8	−	1.00606e10i	0.0558765	−	0.745620i
$785$	−9.51141e8	+	4.16722e9i	−0.0701780	+	0.307470i
$786$	3.42840e9	+	8.73543e9i	0.251833	+	0.641660i
$787$	−1.06351e9	−	1.41916e10i	−0.0777734	−	1.03781i	−0.890445	−	0.455091i	$-0.849607\pi$
$787$	−1.06351e9	−	1.41916e10i	−0.0777734	−	1.03781i	0.812671	−	0.582722i	$-0.198012\pi$
$788$	6.99821e8	+	1.05481e8i	0.0509501	+	0.00767949i
$789$	−1.79457e10	+	1.66512e10i	−1.30074	+	1.20691i
$790$	9.30740e7	−	4.48221e7i	0.00671635	−	0.00323442i
$791$	5.98306e9	+	4.07918e9i	0.429839	+	0.293059i
$792$	1.93488e9	−	4.93000e9i	0.138394	−	0.352621i
$793$	−1.84860e10	−	5.70218e9i	−1.31640	−	0.406055i
$794$	−8.82158e9	−	8.18523e9i	−0.625424	−	0.580309i
$795$	−2.93120e9	−	3.67561e9i	−0.206900	−	0.259445i
$796$	5.68286e7	+	7.12608e7i	0.00399366	+	0.00500789i
$797$	7.97153e8	+	7.39650e8i	0.0557747	+	0.0517514i	0.707568	−	0.706646i	$-0.249792\pi$
$797$	7.97153e8	+	7.39650e8i	0.0557747	+	0.0517514i	−0.651793	+	0.758397i	$0.725983\pi$
$798$	−2.38175e9	−	7.34673e8i	−0.165915	−	0.0511781i
$799$	5.68470e9	−	1.44844e10i	0.394270	−	1.00458i
$800$	1.16517e9	+	7.94400e8i	0.0804590	+	0.0548560i
$801$	−7.73053e9	+	3.72283e9i	−0.531490	+	0.255952i
$802$	−1.69225e10	+	1.57018e10i	−1.15839	+	1.07483i
$803$	−2.17362e9	−	3.27620e8i	−0.148142	−	0.0223288i
$804$	1.66138e8	+	2.21695e9i	0.0112738	+	0.150439i
$805$	−9.12789e8	−	2.32575e9i	−0.0616715	−	0.157136i
$806$	−1.24030e9	+	5.43411e9i	−0.0834362	+	0.365558i
$807$	−1.71698e8	+	2.29115e9i	−0.0115003	+	0.153460i
$808$	−9.53838e9	+	2.94220e9i	−0.636114	+	0.196215i
$809$	−2.24546e10	−	1.08136e10i	−1.49103	−	0.718041i	−0.501876	−	0.864939i	$-0.667357\pi$
$809$	−2.24546e10	−	1.08136e10i	−1.49103	−	0.718041i	−0.989152	+	0.146898i	$0.953071\pi$
$810$	4.76442e9	+	8.25222e9i	0.315001	+	0.545599i
$811$	9.93851e9	−	1.72140e10i	0.654257	−	1.13321i	−0.327823	−	0.944739i	$-0.606315\pi$
$811$	9.93851e9	−	1.72140e10i	0.654257	−	1.13321i	0.982080	−	0.188467i	$-0.0603518\pi$
$812$	7.46694e7	−	5.09088e7i	0.00489437	−	0.00333693i
$813$	−7.64790e9	−	3.35076e10i	−0.499143	−	2.18689i
$814$	3.11357e9	−	4.69294e8i	0.202336	−	0.0304972i
$815$	3.06976e9	−	3.84935e9i	0.198633	−	0.249078i
$816$	−2.10313e10			−1.35504
$817$	1.02378e9	−	5.33875e9i	0.0656797	−	0.342502i
$818$	2.00034e10			1.27781
$819$	2.02645e9	−	2.54109e9i	0.128897	−	0.161631i
$820$	−1.97415e8	+	2.97555e7i	−0.0125035	+	0.00188460i
$821$	−2.65115e9	−	1.16154e10i	−0.167199	−	0.732545i	−0.987109	−	0.160052i	$-0.948834\pi$
$821$	−2.65115e9	−	1.16154e10i	−0.167199	−	0.732545i	0.819910	−	0.572493i	$-0.194023\pi$
$822$	3.36862e9	−	2.29668e9i	0.211544	−	0.144228i
$823$	−3.35678e9	+	5.81411e9i	−0.209905	+	0.363567i	−0.951684	−	0.307078i	$-0.900649\pi$
$823$	−3.35678e9	+	5.81411e9i	−0.209905	+	0.363567i	0.741779	+	0.670644i	$0.233982\pi$
$824$	−1.07761e10	−	1.86648e10i	−0.670992	−	1.16219i
$825$	−1.21457e10	−	5.84907e9i	−0.753069	−	0.362659i
$826$	9.14888e9	−	2.82205e9i	0.564856	−	0.174235i
$827$	−8.41950e7	+	1.12350e9i	−0.00517627	+	0.0690726i	−0.999194	−	0.0401490i	$-0.987217\pi$
$827$	−8.41950e7	+	1.12350e9i	−0.00517627	+	0.0690726i	0.994017	+	0.109222i	$0.0348358\pi$
$828$	6.60942e7	−	2.89578e8i	0.00404629	−	0.0177280i
$829$	−5.14890e8	−	1.31192e9i	−0.0313887	−	0.0799771i	0.914320	−	0.404992i	$-0.132726\pi$
$829$	−5.14890e8	−	1.31192e9i	−0.0313887	−	0.0799771i	−0.945709	+	0.325015i	$0.894631\pi$
$830$	5.75638e7	+	7.68135e8i	0.00349443	+	0.0466299i
$831$	3.27394e10	+	4.93467e9i	1.97910	+	0.298301i
$832$	−1.63223e10	+	1.51449e10i	−0.982540	+	0.911664i
$833$	−1.51150e10	+	7.27898e9i	−0.906045	+	0.436328i
$834$	−1.09260e10	−	7.44925e9i	−0.652201	−	0.444663i
$835$	3.60474e9	−	9.18473e9i	0.214275	−	0.545964i
$836$	3.78104e8	+	1.16630e8i	0.0223815	+	0.00690379i
$837$	2.80963e9	+	2.60696e9i	0.165619	+	0.153672i
$838$	3.52238e9	+	4.41692e9i	0.206767	+	0.259278i
$839$	1.65130e10	+	2.07067e10i	0.965294	+	1.21044i	0.977591	+	0.210515i	$0.0675142\pi$
$839$	1.65130e10	+	2.07067e10i	0.965294	+	1.21044i	−0.0122969	+	0.999924i	$0.503914\pi$
$840$	−3.54173e9	−	3.28625e9i	−0.206176	−	0.191303i
$841$	−1.58337e10	−	4.88405e9i	−0.917902	−	0.283135i
$842$	−4.70078e8	+	1.19774e9i	−0.0271380	+	0.0691464i
$843$	−1.44098e10	−	9.82442e9i	−0.828439	−	0.564820i
$844$	7.72803e8	−	3.72162e8i	0.0442456	−	0.0213076i
$845$	4.10984e9	−	3.81338e9i	0.234329	−	0.217426i
$846$	−5.38978e9	−	8.12378e8i	−0.306037	−	0.0461277i
$847$	−9.84894e6	−	1.31425e8i	−0.000556926	−	0.00743166i
$848$	3.22430e9	+	8.21539e9i	0.181573	+	0.462640i
$849$	−5.36043e9	+	2.34856e10i	−0.300623	+	1.31712i
$850$	−1.16067e9	+	1.54881e10i	−0.0648252	+	0.865033i
$851$	2.65995e9	−	8.20486e8i	0.147952	−	0.0456371i
$852$	−5.21124e8	−	2.50960e8i	−0.0288671	−	0.0139016i
$853$	−1.17115e10	−	2.02849e10i	−0.646086	−	1.11905i	−0.984050	−	0.177894i	$-0.943071\pi$
$853$	−1.17115e10	−	2.02849e10i	−0.646086	−	1.11905i	0.337964	−	0.941159i	$-0.390262\pi$
$854$	−4.20953e9	+	7.29111e9i	−0.231276	+	0.400582i
$855$	1.03253e9	−	7.03968e8i	0.0564965	−	0.0385187i
$856$	−1.12648e9	−	4.93543e9i	−0.0613854	−	0.268947i
$857$	2.66782e10	−	4.02109e9i	1.44785	−	0.218228i	0.622397	−	0.782701i	$-0.286159\pi$
$857$	2.66782e10	−	4.02109e9i	1.44785	−	0.218228i	0.825451	+	0.564473i	$0.190921\pi$
$858$	1.63749e10	−	2.05335e10i	0.885062	−	1.10983i
$859$	1.57098e9			0.0845656			0.0422828	−	0.999106i	$-0.486537\pi$
$859$	1.57098e9			0.0845656			0.0422828	+	0.999106i	$0.486537\pi$
$860$	3.98286e8	−	5.36883e8i	0.0213526	−	0.0287829i
$861$	−3.40737e9			−0.181932
$862$	−1.83602e10	+	2.30230e10i	−0.976343	+	1.22430i
$863$	1.59024e10	−	2.39689e9i	0.842216	−	0.126944i	0.286257	−	0.958153i	$-0.407589\pi$
$863$	1.59024e10	−	2.39689e9i	0.842216	−	0.126944i	0.555960	+	0.831209i	$0.312351\pi$
$864$	4.20387e8	+	1.84184e9i	0.0221744	+	0.0971523i
$865$	7.82290e9	−	5.33356e9i	0.410971	−	0.280195i
$866$	1.11472e9	−	1.93075e9i	0.0583247	−	0.101021i
$867$	6.25330e9	+	1.08310e10i	0.325869	+	0.564421i
$868$	−1.58795e8	−	7.64718e7i	−0.00824174	−	0.00396901i
$869$	−2.67461e8	+	8.25008e7i	−0.0138258	+	0.00426470i
$870$	1.72356e8	−	2.29993e9i	0.00887378	−	0.118412i
$871$	−1.04558e10	+	4.58099e10i	−0.536160	+	2.34907i
$872$	−7.66939e9	−	1.95413e10i	−0.391699	−	0.998034i
$873$	2.20359e8	+	2.94049e9i	0.0112094	+	0.149579i
$874$	−4.76053e9	−	7.17534e8i	−0.241193	−	0.0363540i
$875$	−5.82273e9	+	5.40271e9i	−0.293832	+	0.272636i
$876$	−2.14791e8	+	1.03438e8i	−0.0107957	+	0.00519895i
$877$	1.61875e10	+	1.10365e10i	0.810366	+	0.552498i	0.896117	−	0.443818i	$-0.146376\pi$
$877$	1.61875e10	+	1.10365e10i	0.810366	+	0.552498i	−0.0857507	+	0.996317i	$0.527329\pi$
$878$	1.23544e9	−	3.14785e9i	0.0616015	−	0.156958i
$879$	−1.63757e10	−	5.05124e9i	−0.813278	−	0.250863i
$880$	−7.21167e9	−	6.69145e9i	−0.356735	−	0.331002i
$881$	1.05757e10	+	1.32615e10i	0.521066	+	0.653396i	0.970835	−	0.239749i	$-0.0770650\pi$
$881$	1.05757e10	+	1.32615e10i	0.521066	+	0.653396i	−0.449769	+	0.893145i	$0.648494\pi$
$882$	3.66409e9	+	4.59463e9i	0.179815	+	0.225481i
$883$	−6.04270e9	−	5.60681e9i	−0.295372	−	0.274065i	0.518540	−	0.855053i	$-0.326476\pi$
$883$	−6.04270e9	−	5.60681e9i	−0.295372	−	0.274065i	−0.813912	+	0.580988i	$0.802666\pi$
$884$	2.10089e9	+	6.48039e8i	0.102287	+	0.0315514i
$885$	−6.48611e9	+	1.65263e10i	−0.314545	+	0.801447i
$886$	−2.06448e10	−	1.40754e10i	−0.997224	−	0.679896i
$887$	−2.25647e10	+	1.08666e10i	−1.08567	+	0.522830i	−0.889124	−	0.457665i	$-0.848686\pi$
$887$	−2.25647e10	+	1.08666e10i	−1.08567	+	0.522830i	−0.196543	+	0.980495i	$0.562971\pi$
$888$	3.94597e9	−	3.66133e9i	0.189107	−	0.175466i
$889$	−8.45117e9	−	1.27381e9i	−0.403423	−	0.0608063i
$890$	1.27805e9	+	1.70544e10i	0.0607690	+	0.810905i
$891$	−9.43228e9	−	2.40331e10i	−0.446730	−	1.13825i
$892$	3.92762e8	−	1.72080e9i	0.0185290	−	0.0811810i
$893$	4.79704e8	−	6.40121e9i	0.0225421	−	0.300803i
$894$	3.90406e10	−	1.20424e10i	1.82740	−	0.563680i
$895$	−1.35733e10	−	6.53658e9i	−0.632858	−	0.304768i
$896$	4.20382e9	+	7.28122e9i	0.195239	+	0.338163i
$897$	1.16090e10	−	2.01073e10i	0.537057	−	0.930209i
$898$	−2.09060e10	+	1.42534e10i	−0.963392	+	0.656830i
$899$	−2.95111e8	−	1.29297e9i	−0.0135465	−	0.0593510i
$900$	−3.90899e8	+	5.89186e7i	−0.0178738	+	0.00269404i
$901$	9.15008e9	−	1.14738e10i	0.416762	−	0.522603i
$902$	−7.44469e9			−0.337772
$903$	8.08739e9	−	8.04762e9i	0.365512	−	0.363714i
$904$	2.70475e10			1.21769
$905$	−6.16036e9	+	7.72484e9i	−0.276271	+	0.346433i
$906$	4.30873e10	−	6.49436e9i	1.92486	−	0.290127i
$907$	3.49752e8	+	1.53236e9i	0.0155645	+	0.0681924i	0.982114	−	0.188289i	$-0.0602940\pi$
$907$	3.49752e8	+	1.53236e9i	0.0155645	+	0.0681924i	−0.966549	+	0.256481i	$0.917437\pi$
$908$	−2.52757e8	+	1.72327e8i	−0.0112048	+	0.00763928i
$909$	2.70939e9	−	4.69280e9i	0.119646	−	0.207233i
$910$	−3.23913e9	−	5.61033e9i	−0.142490	−	0.246799i
$911$	2.18823e10	+	1.05379e10i	0.958910	+	0.461787i	0.846801	−	0.531909i	$-0.178525\pi$
$911$	2.18823e10	+	1.05379e10i	0.958910	+	0.461787i	0.112109	+	0.993696i	$0.464239\pi$
$912$	−8.29085e9	+	2.55739e9i	−0.361924	+	0.111639i
$913$	1.55965e8	−	2.08121e9i	0.00678234	−	0.0905040i
$914$	3.90558e7	−	1.71115e8i	0.00169190	−	0.00741268i
$915$	−5.70352e9	−	1.45323e10i	−0.246133	−	0.627136i
$916$	−1.36171e8	−	1.81708e9i	−0.00585397	−	0.0781158i
$917$	−6.20157e9	−	9.34737e8i	−0.265588	−	0.0400310i
$918$	−1.52526e10	+	1.41524e10i	−0.650721	+	0.603781i
$919$	1.68103e10	−	8.09541e9i	0.714449	−	0.344060i	−0.0410979	−	0.999155i	$-0.513086\pi$
$919$	1.68103e10	−	8.09541e9i	0.714449	−	0.344060i	0.755547	+	0.655095i	$0.227371\pi$
$920$	−7.71059e9	−	5.25699e9i	−0.326460	−	0.222577i
$921$	−1.85378e10	+	4.72334e10i	−0.781895	+	1.99224i
$922$	−1.91130e10	−	5.89559e9i	−0.803104	−	0.247725i
$923$	−8.96150e9	−	8.31505e9i	−0.375124	−	0.348064i
$924$	5.17787e8	+	6.49284e8i	0.0215923	+	0.0270759i
$925$	−2.30988e9	−	2.89650e9i	−0.0959607	−	0.120331i
$926$	−1.89155e10	−	1.75511e10i	−0.782853	−	0.726382i
$927$	1.11801e10	+	3.44861e9i	0.460965	+	0.142189i
$928$	2.38823e8	−	6.08512e8i	0.00980977	−	0.0249949i
$929$	1.88538e10	+	1.28543e10i	0.771516	+	0.526011i	0.883912	−	0.467653i	$-0.154900\pi$
$929$	1.88538e10	+	1.28543e10i	0.771516	+	0.526011i	−0.112396	+	0.993663i	$0.535853\pi$
$930$	−4.05257e9	+	1.95162e9i	−0.165212	+	0.0795617i
$931$	−5.07342e9	+	4.70745e9i	−0.206052	+	0.191188i
$932$	−5.75159e8	−	8.66913e7i	−0.0232719	−	0.00350768i
$933$	3.45518e9	+	4.61062e10i	0.139279	+	1.85855i
$934$	−7.43267e9	−	1.89381e10i	−0.298491	−	0.760542i
$935$	−3.64024e9	+	1.59489e10i	−0.145643	+	0.638103i
$936$	9.07218e8	−	1.21060e10i	0.0361615	−	0.482542i
$937$	3.39640e10	−	1.04765e10i	1.34875	−	0.416033i	0.465544	−	0.885025i	$-0.345859\pi$
$937$	3.39640e10	−	1.04765e10i	1.34875	−	0.416033i	0.883203	+	0.468991i	$0.155382\pi$
$938$	1.84238e10	+	8.87245e9i	0.728904	+	0.351022i
$939$	1.89491e10	+	3.28208e10i	0.746894	+	1.29366i
$940$	3.94693e8	−	6.83628e8i	0.0154993	−	0.0268456i
$941$	−4.84218e9	+	3.30134e9i	−0.189442	+	0.129160i	−0.654327	−	0.756211i	$-0.727048\pi$
$941$	−4.84218e9	+	3.30134e9i	−0.189442	+	0.129160i	0.464885	+	0.885371i	$0.346096\pi$
$942$	3.84663e9	+	1.68532e10i	0.149935	+	0.656907i
$943$	−6.50793e9	+	9.80912e8i	−0.252727	+	0.0380925i
$944$	2.07796e10	−	2.60567e10i	0.803960	−	1.00813i
$945$	−4.45469e9			−0.171714
$946$	1.76700e10	−	1.75831e10i	0.678604	−	0.675267i
$947$	2.35361e10			0.900553			0.450276	−	0.892889i	$-0.351325\pi$
$947$	2.35361e10			0.900553			0.450276	+	0.892889i	$0.351325\pi$
$948$	−1.89266e7	+	2.37332e7i	−0.000721511	+	0.000904746i
$949$	−4.98245e9	+	7.50984e8i	−0.189239	+	0.0285232i
$950$	1.42579e9	+	6.24678e9i	0.0539538	+	0.236387i
$951$	2.31776e10	−	1.58023e10i	0.873851	−	0.595782i
$952$	7.54102e9	−	1.30614e10i	0.283270	−	0.490638i
$953$	1.49012e10	+	2.58097e10i	0.557695	+	0.965956i	0.997688	+	0.0679551i	$0.0216475\pi$
$953$	1.49012e10	+	2.58097e10i	0.557695	+	0.965956i	−0.439993	+	0.898001i	$0.645019\pi$
$954$	−4.63175e9	−	2.23053e9i	−0.172713	−	0.0831743i
$955$	−6.53793e9	+	2.01669e9i	−0.242901	+	0.0749249i
$956$	1.68998e8	−	2.25512e9i	0.00625575	−	0.0834772i
$957$	−1.39053e9	+	6.09229e9i	−0.0512847	+	0.224693i
$958$	6.53430e9	+	1.66491e10i	0.240115	+	0.611804i
$959$	2.03624e8	+	2.71717e9i	0.00745526	+	0.0994835i
$960$	−1.77678e10	−	2.67807e9i	−0.648164	−	0.0976950i
$961$	1.82722e10	−	1.69541e10i	0.664138	−	0.616230i
$962$	6.50289e9	−	3.13162e9i	0.235501	−	0.113411i
$963$	2.27064e9	+	1.54809e9i	0.0819325	+	0.0558606i
$964$	−6.02265e8	+	1.53455e9i	−0.0216530	+	0.0551709i
$965$	3.50078e9	+	1.07985e9i	0.125406	+	0.0386827i
$966$	−7.40699e9	−	6.87268e9i	−0.264376	−	0.245305i
$967$	−2.71246e10	−	3.40132e10i	−0.964653	−	1.20964i	−0.977761	−	0.209722i	$-0.932744\pi$
$967$	−2.71246e10	−	3.40132e10i	−0.964653	−	1.20964i	0.0131085	−	0.999914i	$-0.495827\pi$
$968$	−3.06926e8	−	3.84873e8i	−0.0108760	−	0.0136381i
$969$	1.05762e10	+	9.81324e9i	0.373418	+	0.346481i
$970$	5.61632e9	+	1.73241e9i	0.197584	+	0.0609465i
$971$	1.70515e10	−	4.34465e10i	0.597716	−	1.52296i	−0.236565	−	0.971616i	$-0.576022\pi$
$971$	1.70515e10	−	4.34465e10i	0.597716	−	1.52296i	0.834281	−	0.551340i	$-0.185883\pi$
$972$	−1.13276e9	−	7.72305e8i	−0.0395646	−	0.0269747i
$973$	7.96257e9	−	3.83457e9i	0.277114	−	0.133451i
$974$	2.44844e10	−	2.27182e10i	0.849050	−	0.787803i
$975$	−3.05560e10	−	4.60557e9i	−1.05580	−	0.159136i
$976$	2.19009e9	+	2.92247e10i	0.0754028	+	1.00618i
$977$	−1.06829e10	−	2.72196e10i	−0.366487	−	0.933795i	−0.988559	−	0.150834i	$-0.951804\pi$
$977$	−1.06829e10	−	2.72196e10i	−0.366487	−	0.933795i	0.622072	−	0.782960i	$-0.286291\pi$
$978$	4.43079e9	−	1.94125e10i	0.151459	−	0.663585i
$979$	3.46278e9	−	4.62076e10i	0.117947	−	1.57389i
$980$	−8.13282e8	+	2.50864e8i	−0.0276026	+	0.00851428i
$981$	1.02674e10	+	4.94454e9i	0.347233	+	0.167218i
$982$	1.58025e10	+	2.73707e10i	0.532519	+	0.922350i
$983$	−1.07926e10	+	1.86933e10i	−0.362399	+	0.627693i	−0.988355	−	0.152165i	$-0.951376\pi$
$983$	−1.07926e10	+	1.86933e10i	−0.362399	+	0.627693i	0.625956	+	0.779858i	$0.284709\pi$
$984$	−1.05156e10	+	7.16944e9i	−0.351846	+	0.239885i
$985$	2.68606e9	+	1.17684e10i	0.0895547	+	0.392365i
$986$	7.11920e9	−	1.07305e9i	0.236517	−	0.0356492i
$987$	8.40004e9	−	1.05333e10i	0.278081	−	0.348702i
$988$	9.07002e8			0.0299198
$989$	1.31298e10	−	1.76988e10i	0.431590	−	0.581776i
$990$	5.73057e9			0.187705
$991$	−3.22367e10	+	4.04236e10i	−1.05219	+	1.31940i	−0.106505	+	0.994312i	$0.533966\pi$
$991$	−3.22367e10	+	4.04236e10i	−1.05219	+	1.31940i	−0.945683	+	0.325090i	$0.894605\pi$
$992$	−1.26064e9	+	1.90011e8i	−0.0410016	+	0.00617999i
$993$	5.30151e9	+	2.32274e10i	0.171821	+	0.752799i
$994$	−4.39577e9	+	2.99698e9i	−0.141965	+	0.0967904i
$995$	−7.77297e8	+	1.34632e9i	−0.0250153	+	0.0433278i
$996$	−1.13174e8	−	1.96024e8i	−0.00362944	−	0.00628638i
$997$	−4.56369e10	−	2.19776e10i	−1.45842	−	0.702339i	−0.474387	−	0.880316i	$-0.657330\pi$
$997$	−4.56369e10	−	2.19776e10i	−1.45842	−	0.702339i	−0.984035	+	0.177978i	$0.943045\pi$
$998$	2.72390e10	−	8.40213e9i	0.867431	−	0.267567i
$999$	3.70895e8	−	4.94925e9i	0.0117699	−	0.157058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.24.7	yes	300
43.9	even	21	inner	43.8.g.a.9.7	✓	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.7	✓	300	43.9	even	21	inner
43.8.g.a.24.7	yes	300	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.81088 + 8.54058i) q^{2} +(54.1377 - 8.15994i) q^{3} +(1.92934 + 8.45297i) q^{4} +(-122.186 + 83.3051i) q^{5} +(-299.035 + 517.944i) q^{6} +(-199.852 - 346.154i) q^{7} +(-1345.11 - 647.772i) q^{8} +(774.466 - 238.891i) q^{9} +O(q^{10})\)	\(q+(-6.81088 + 8.54058i) q^{2} +(54.1377 - 8.15994i) q^{3} +(1.92934 + 8.45297i) q^{4} +(-122.186 + 83.3051i) q^{5} +(-299.035 + 517.944i) q^{6} +(-199.852 - 346.154i) q^{7} +(-1345.11 - 647.772i) q^{8} +(774.466 - 238.891i) q^{9} +(120.722 - 1610.92i) q^{10} +(-973.957 + 4267.18i) q^{11} +(173.426 + 441.881i) q^{12} +(749.764 + 10004.9i) q^{13} +(4317.52 + 650.762i) q^{14} +(-5935.11 + 5506.98i) q^{15} +(13693.8 - 6594.61i) q^{16} +(-20882.3 - 14237.3i) q^{17} +(-3234.53 + 8241.45i) q^{18} +(-9963.36 - 3073.29i) q^{19} +(-939.914 - 872.113i) q^{20} +(-13644.1 - 17109.2i) q^{21} +(-29810.7 - 37381.4i) q^{22} +(-30985.0 - 28749.9i) q^{23} +(-78107.0 - 24092.8i) q^{24} +(-20552.5 + 52367.0i) q^{25} +(-90554.2 - 61738.8i) q^{26} +(-67900.4 + 32699.1i) q^{27} +(2540.45 - 2357.19i) q^{28} +(25786.0 + 3886.61i) q^{29} +(-6609.43 - 88196.7i) q^{30} +(-18580.2 - 47341.7i) q^{31} +(5578.11 - 24439.3i) q^{32} +(-17907.8 + 238963. i) q^{33} +(263822. - 81378.4i) q^{34} +(53255.5 + 25646.5i) q^{35} +(3513.55 + 6085.64i) q^{36} +(-32927.8 + 57032.7i) q^{37} +(94107.0 - 64161.1i) q^{38} +(122230. + 535524. i) q^{39} +(218317. - 32906.0i) q^{40} +(97080.7 - 121735. i) q^{41} +239051. q^{42} +(57096.8 + 518226. i) q^{43} -37949.5 q^{44} +(-74728.2 + 93706.2i) q^{45} +(456576. - 68817.8i) q^{46} +(136996. + 600217. i) q^{47} +(687541. - 468758. i) q^{48} +(331890. - 574850. i) q^{49} +(-307264. - 532197. i) q^{50} +(-1.24670e6 - 600377. i) q^{51} +(-83124.7 + 25640.6i) q^{52} +(-43392.8 + 579037. i) q^{53} +(183192. - 802618. i) q^{54} +(-236474. - 602526. i) q^{55} +(44594.6 + 595074. i) q^{56} +(-564471. - 85080.4i) q^{57} +(-208819. + 193756. i) q^{58} +(1.97561e6 - 951404. i) q^{59} +(-58001.2 - 39544.5i) q^{60} +(-704448. + 1.79491e6i) q^{61} +(530873. + 163753. i) q^{62} +(-237472. - 220342. i) q^{63} +(1.38372e6 + 1.73513e6i) q^{64} +(-925071. - 1.16000e6i) q^{65} +(-1.91891e6 - 1.78049e6i) q^{66} +(4.47530e6 + 1.38045e6i) q^{67} +(80058.7 - 203986. i) q^{68} +(-1.91205e6 - 1.30362e6i) q^{69} +(-581753. + 280158. i) q^{70} +(-893206. + 828774. i) q^{71} +(-1.19649e6 - 180342. i) q^{72} +(37530.8 + 500813. i) q^{73} +(-262824. - 669666. i) q^{74} +(-685355. + 3.00274e6i) q^{75} +(6755.77 - 90149.5i) q^{76} +(1.67175e6 - 515666. i) q^{77} +(-5.40618e6 - 2.60348e6i) q^{78} +(31974.1 + 55380.7i) q^{79} +(-1.12383e6 + 1.94654e6i) q^{80} +(-4.87366e6 + 3.32280e6i) q^{81} +(378485. + 1.65825e6i) q^{82} +(-471504. + 71067.7i) q^{83} +(118299. - 148343. i) q^{84} +3.73757e6 q^{85} +(-4.81483e6 - 3.04194e6i) q^{86} +1.42771e6 q^{87} +(4.07424e6 - 5.10894e6i) q^{88} +(-1.04685e7 + 1.57787e6i) q^{89} +(-291340. - 1.27644e6i) q^{90} +(3.31339e6 - 2.25903e6i) q^{91} +(183242. - 317384. i) q^{92} +(-1.39220e6 - 2.41135e6i) q^{93} +(-6.05926e6 - 2.91799e6i) q^{94} +(1.47341e6 - 454486. i) q^{95} +(102563. - 1.36860e6i) q^{96} +(-809596. + 3.54707e6i) q^{97} +(2.64909e6 + 6.74977e6i) q^{98} +(265096. + 3.53746e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more