LMFDB - Embedded newform 43.8.g.a.24.19

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			24.19
Character	$\chi$	$=$	43.24
Dual form			43.8.g.a.9.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.72335 - 9.68478i) q^{2} +(15.1267 - 2.27999i) q^{3} +(-5.66207 - 24.8071i) q^{4} +(-308.593 + 210.395i) q^{5} +(94.7479 - 164.108i) q^{6} +(75.0831 + 130.048i) q^{7} +(1144.57 + 551.196i) q^{8} +(-1866.22 + 575.652i) q^{9} +O(q^{10})$	\(q+(7.72335 - 9.68478i) q^{2} +(15.1267 - 2.27999i) q^{3} +(-5.66207 - 24.8071i) q^{4} +(-308.593 + 210.395i) q^{5} +(94.7479 - 164.108i) q^{6} +(75.0831 + 130.048i) q^{7} +(1144.57 + 551.196i) q^{8} +(-1866.22 + 575.652i) q^{9} +(-345.743 + 4613.62i) q^{10} +(-1588.89 + 6961.36i) q^{11} +(-142.208 - 362.341i) q^{12} +(-139.334 - 1859.28i) q^{13} +(1839.38 + 277.241i) q^{14} +(-4188.31 + 3886.18i) q^{15} +(17112.6 - 8240.98i) q^{16} +(1590.17 + 1084.16i) q^{17} +(-8838.40 + 22519.9i) q^{18} +(-11653.2 - 3594.55i) q^{19} +(6966.58 + 6464.04i) q^{20} +(1432.27 + 1796.01i) q^{21} +(55147.7 + 69153.1i) q^{22} +(21431.5 + 19885.5i) q^{23} +(18570.3 + 5728.19i) q^{24} +(22421.4 - 57128.7i) q^{25} +(-19082.9 - 13010.5i) q^{26} +(-57059.9 + 27478.6i) q^{27} +(2800.98 - 2598.93i) q^{28} +(125041. + 18846.9i) q^{29} +(5289.03 + 70577.2i) q^{30} +(-14057.4 - 35817.8i) q^{31} +(16170.6 - 70848.0i) q^{32} +(-8162.82 + 108925. i) q^{33} +(22781.3 - 7027.11i) q^{34} +(-50531.6 - 24334.7i) q^{35} +(24846.9 + 43036.1i) q^{36} +(48175.6 - 83442.6i) q^{37} +(-124814. + 85097.0i) q^{38} +(-6346.80 - 27807.2i) q^{39} +(-469176. + 70716.9i) q^{40} +(-428051. + 536759. i) q^{41} +28455.8 q^{42} +(-468866. - 227997. i) q^{43} +181688. q^{44} +(454788. - 570286. i) q^{45} +(358110. - 53976.4i) q^{46} +(-50089.4 - 219456. i) q^{47} +(240068. - 163675. i) q^{48} +(400497. - 693680. i) q^{49} +(-380111. - 658371. i) q^{50} +(26526.0 + 12774.2i) q^{51} +(-45334.5 + 13983.9i) q^{52} +(17607.0 - 234949. i) q^{53} +(-174570. + 764840. i) q^{54} +(-974319. - 2.48252e6i) q^{55} +(14256.1 + 190234. i) q^{56} +(-184471. - 27804.5i) q^{57} +(1.14826e6 - 1.06543e6i) q^{58} +(844519. - 406699. i) q^{59} +(120119. + 81896.1i) q^{60} +(-1.09805e6 + 2.79778e6i) q^{61} +(-455458. - 140490. i) q^{62} +(-214984. - 199476. i) q^{63} +(954554. + 1.19697e6i) q^{64} +(434182. + 544447. i) q^{65} +(991872. + 920323. i) q^{66} +(-1.62807e6 - 502193. i) q^{67} +(17891.3 - 45586.2i) q^{68} +(369527. + 251939. i) q^{69} +(-625949. + 301441. i) q^{70} +(2.91794e6 - 2.70745e6i) q^{71} +(-2.45332e6 - 369778. i) q^{72} +(382137. + 5.09926e6i) q^{73} +(-436046. - 1.11103e6i) q^{74} +(208909. - 915291. i) q^{75} +(-23189.0 + 309436. i) q^{76} +(-1.02461e6 + 316050. i) q^{77} +(-318325. - 153297. i) q^{78} +(3.11520e6 + 5.39568e6i) q^{79} +(-3.54696e6 + 6.14352e6i) q^{80} +(2.72853e6 - 1.86028e6i) q^{81} +(1.89240e6 + 8.29115e6i) q^{82} +(3.09434e6 - 466397. i) q^{83} +(36444.2 - 45699.6i) q^{84} -718819. q^{85} +(-5.82933e6 + 2.77996e6i) q^{86} +1.93443e6 q^{87} +(-5.65567e6 + 7.09199e6i) q^{88} +(7.90923e6 - 1.19212e6i) q^{89} +(-2.01061e6 - 8.80904e6i) q^{90} +(231334. - 157721. i) q^{91} +(371957. - 644248. i) q^{92} +(-294307. - 509755. i) q^{93} +(-2.51224e6 - 1.20983e6i) q^{94} +(4.35239e6 - 1.34253e6i) q^{95} +(83075.6 - 1.10857e6i) q^{96} +(714825. - 3.13185e6i) q^{97} +(-3.62496e6 - 9.23626e6i) q^{98} +(-1.04212e6 - 1.39061e7i) 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 $

$2$	7.72335	−	9.68478i	0.682654	−	0.856022i	−0.312941	−	0.949772i	$-0.601314\pi$
$2$	7.72335	−	9.68478i	0.682654	−	0.856022i	0.995596	+	0.0937510i	$0.0298857\pi$
$3$	15.1267	−	2.27999i	0.323460	−	0.0487537i	0.0146947	−	0.999892i	$-0.495322\pi$
$3$	15.1267	−	2.27999i	0.323460	−	0.0487537i	0.308765	+	0.951138i	$0.400084\pi$
$4$	−5.66207	−	24.8071i	−0.0442349	−	0.193806i
$5$	−308.593	+	210.395i	−1.10406	+	0.752733i	−0.971168	−	0.238397i	$-0.923378\pi$
$5$	−308.593	+	210.395i	−1.10406	+	0.752733i	−0.132889	+	0.991131i	$0.542426\pi$
$6$	94.7479	−	164.108i	0.179077	−	0.310171i
$7$	75.0831	+	130.048i	0.0827368	+	0.143304i	0.904425	−	0.426634i	$-0.140301\pi$
$7$	75.0831	+	130.048i	0.0827368	+	0.143304i	−0.821688	+	0.569938i	$0.806967\pi$
$8$	1144.57	+	551.196i	0.790365	+	0.380620i
$9$	−1866.22	+	575.652i	−0.853323	+	0.263215i
$10$	−345.743	+	4613.62i	−0.109333	+	1.45895i
$11$	−1588.89	+	6961.36i	−0.359930	+	1.57696i	0.393434	+	0.919353i	$0.371287\pi$
$11$	−1588.89	+	6961.36i	−0.359930	+	1.57696i	−0.753364	+	0.657604i	$0.771570\pi$
$12$	−142.208	−	362.341i	−0.0237570	−	0.0605318i
$13$	−139.334	−	1859.28i	−0.0175896	−	0.234716i	−0.999069	−	0.0431475i	$-0.986261\pi$
$13$	−139.334	−	1859.28i	−0.0175896	−	0.234716i	0.981479	−	0.191569i	$-0.0613576\pi$
$14$	1839.38	+	277.241i	0.179152	+	0.0270029i
$15$	−4188.31	+	3886.18i	−0.320420	+	0.297306i
$16$	17112.6	−	8240.98i	1.04447	−	0.502989i
$17$	1590.17	+	1084.16i	0.0785006	+	0.0535208i	0.601934	−	0.798546i	$-0.294397\pi$
$17$	1590.17	+	1084.16i	0.0785006	+	0.0535208i	−0.523434	+	0.852066i	$0.675349\pi$
$18$	−8838.40	+	22519.9i	−0.357207	+	0.910148i
$19$	−11653.2	−	3594.55i	−0.389770	−	0.120228i	0.0936749	−	0.995603i	$-0.470139\pi$
$19$	−11653.2	−	3594.55i	−0.389770	−	0.120228i	−0.483445	+	0.875375i	$0.660615\pi$
$20$	6966.58	+	6464.04i	0.194722	+	0.180676i
$21$	1432.27	+	1796.01i	0.0337487	+	0.0423195i
$22$	55147.7	+	69153.1i	1.10420	+	1.38462i
$23$	21431.5	+	19885.5i	0.367287	+	0.340792i	0.842127	−	0.539280i	$-0.181303\pi$
$23$	21431.5	+	19885.5i	0.367287	+	0.340792i	−0.474840	+	0.880072i	$0.657494\pi$
$24$	18570.3	+	5728.19i	0.274208	+	0.0845820i
$25$	22421.4	−	57128.7i	0.286994	−	0.731248i
$26$	−19082.9	−	13010.5i	−0.212930	−	0.145173i
$27$	−57059.9	+	27478.6i	−0.557902	+	0.268672i
$28$	2800.98	−	2598.93i	0.0241134	−	0.0223739i
$29$	125041.	+	18846.9i	0.952049	+	0.143498i	0.606660	−	0.794961i	$-0.292509\pi$
$29$	125041.	+	18846.9i	0.952049	+	0.143498i	0.345389	+	0.938460i	$0.387747\pi$
$30$	5289.03	+	70577.2i	0.0357644	+	0.477243i
$31$	−14057.4	−	35817.8i	−0.0847501	−	0.215940i	0.882216	−	0.470845i	$-0.156051\pi$
$31$	−14057.4	−	35817.8i	−0.0847501	−	0.215940i	−0.966966	+	0.254905i	$0.917956\pi$
$32$	16170.6	−	70848.0i	0.0872370	−	0.382210i
$33$	−8162.82	+	108925.i	−0.0395404	+	0.527630i
$34$	22781.3	−	7027.11i	0.0994037	−	0.0306620i
$35$	−50531.6	−	24334.7i	−0.199216	−	0.0959374i
$36$	24846.9	+	43036.1i	0.0887593	+	0.153736i
$37$	48175.6	−	83442.6i	0.156358	−	0.270821i	−0.777194	−	0.629261i	$-0.783358\pi$
$37$	48175.6	−	83442.6i	0.156358	−	0.270821i	0.933553	+	0.358440i	$0.116691\pi$
$38$	−124814.	+	85097.0i	−0.368996	+	0.251577i
$39$	−6346.80	−	27807.2i	−0.0171328	−	0.0750638i
$40$	−469176.	+	70716.9i	−1.15911	+	0.174708i
$41$	−428051.	+	536759.i	−0.969955	+	1.21629i	0.00637032	+	0.999980i	$0.497972\pi$
$41$	−428051.	+	536759.i	−0.969955	+	1.21629i	−0.976326	+	0.216306i	$0.930599\pi$
$42$	28455.8			0.0592651
$43$	−468866.	−	227997.i	−0.899310	−	0.437311i
$43$	−468866.	−	227997.i	−0.899310	−	0.437311i
$44$	181688.			0.321545
$45$	454788.	−	570286.i	0.743987	−	0.932930i
$46$	358110.	−	53976.4i	0.542456	−	0.0817620i
$47$	−50089.4	−	219456.i	−0.0703725	−	0.308322i	0.927476	−	0.373882i	$-0.121974\pi$
$47$	−50089.4	−	219456.i	−0.0703725	−	0.308322i	−0.997849	+	0.0655604i	$0.979117\pi$
$48$	240068.	−	163675.i	0.313321	−	0.213619i
$49$	400497.	−	693680.i	0.486309	−	0.842312i
$50$	−380111.	−	658371.i	−0.430046	−	0.744862i
$51$	26526.0	+	12774.2i	0.0280011	+	0.0134846i
$52$	−45334.5	+	13983.9i	−0.0447113	+	0.0137916i
$53$	17607.0	−	234949.i	0.0162450	−	0.216775i	−0.983173	−	0.182675i	$-0.941524\pi$
$53$	17607.0	−	234949.i	0.0162450	−	0.216775i	0.999418	−	0.0341000i	$-0.0108565\pi$
$54$	−174570.	+	764840.i	−0.150866	+	0.660986i
$55$	−974319.	−	2.48252e6i	−0.789645	−	2.01198i
$56$	14256.1	+	190234.i	0.0108478	+	0.144754i
$57$	−184471.	−	27804.5i	−0.131937	−	0.0198862i
$58$	1.14826e6	−	1.06543e6i	0.772758	−	0.717015i
$59$	844519.	−	406699.i	0.535337	−	0.257805i	−0.146625	−	0.989192i	$-0.546841\pi$
$59$	844519.	−	406699.i	0.535337	−	0.257805i	0.681962	+	0.731387i	$0.261127\pi$
$60$	120119.	+	81896.1i	0.0717933	+	0.0489479i
$61$	−1.09805e6	+	2.79778e6i	−0.619394	+	1.57819i	0.184120	+	0.982904i	$0.441057\pi$
$61$	−1.09805e6	+	2.79778e6i	−0.619394	+	1.57819i	−0.803514	+	0.595286i	$0.797039\pi$
$62$	−455458.	−	140490.i	−0.242704	−	0.0748643i
$63$	−214984.	−	199476.i	−0.108321	−	0.100507i
$64$	954554.	+	1.19697e6i	0.455167	+	0.570761i
$65$	434182.	+	544447.i	0.196099	+	0.245900i
$66$	991872.	+	920323.i	0.424670	+	0.394037i
$67$	−1.62807e6	−	502193.i	−0.661320	−	0.203990i	−0.0541139	−	0.998535i	$-0.517233\pi$
$67$	−1.62807e6	−	502193.i	−0.661320	−	0.203990i	−0.607206	+	0.794545i	$0.707710\pi$
$68$	17891.3	−	45586.2i	0.00690017	−	0.0175814i
$69$	369527.	+	251939.i	0.135417	+	0.0923261i
$70$	−625949.	+	301441.i	−0.218120	+	0.105041i
$71$	2.91794e6	−	2.70745e6i	0.967546	−	0.897751i	−0.0272514	−	0.999629i	$-0.508675\pi$
$71$	2.91794e6	−	2.70745e6i	0.967546	−	0.897751i	0.994797	+	0.101878i	$0.0324850\pi$
$72$	−2.45332e6	−	369778.i	−0.774622	−	0.116755i
$73$	382137.	+	5.09926e6i	0.114971	+	1.53418i	0.694656	+	0.719342i	$0.255557\pi$
$73$	382137.	+	5.09926e6i	0.114971	+	1.53418i	−0.579685	+	0.814841i	$0.696824\pi$
$74$	−436046.	−	1.11103e6i	−0.125090	−	0.318723i
$75$	208909.	−	915291.i	0.0571798	−	0.250521i
$76$	−23189.0	+	309436.i	−0.00605947	+	0.0808580i
$77$	−1.02461e6	+	316050.i	−0.255764	+	0.0788928i
$78$	−318325.	−	153297.i	−0.0759520	−	0.0365766i
$79$	3.11520e6	+	5.39568e6i	0.710871	+	1.23126i	0.964531	+	0.263971i	$0.0850323\pi$
$79$	3.11520e6	+	5.39568e6i	0.710871	+	1.23126i	−0.253660	+	0.967293i	$0.581634\pi$
$80$	−3.54696e6	+	6.14352e6i	−0.774536	+	1.34154i
$81$	2.72853e6	−	1.86028e6i	0.570468	−	0.388939i
$82$	1.89240e6	+	8.29115e6i	0.379022	+	1.66061i
$83$	3.09434e6	−	466397.i	0.594011	−	0.0895328i	0.154845	−	0.987939i	$-0.450512\pi$
$83$	3.09434e6	−	466397.i	0.594011	−	0.0895328i	0.439166	+	0.898406i	$0.355274\pi$
$84$	36444.2	−	45699.6i	0.00670889	−	0.00841268i
$85$	−718819.			−0.126956
$86$	−5.82933e6	+	2.77996e6i	−0.988266	+	0.471297i
$87$	1.93443e6			0.314946
$88$	−5.65567e6	+	7.09199e6i	−0.884697	+	1.10938i
$89$	7.90923e6	−	1.19212e6i	1.18924	−	0.179249i	0.475535	−	0.879697i	$-0.342254\pi$
$89$	7.90923e6	−	1.19212e6i	1.18924	−	0.179249i	0.713704	+	0.700448i	$0.247016\pi$
$90$	−2.01061e6	−	8.80904e6i	−0.290722	−	1.27374i
$91$	231334.	−	157721.i	0.0321806	−	0.0219404i
$92$	371957.	−	644248.i	0.0498006	−	0.0862572i
$93$	−294307.	−	509755.i	−0.0379411	−	0.0657160i
$94$	−2.51224e6	−	1.20983e6i	−0.311970	−	0.150237i
$95$	4.35239e6	−	1.34253e6i	0.520828	−	0.160654i
$96$	83075.6	−	1.10857e6i	0.00958350	−	0.127883i
$97$	714825.	−	3.13185e6i	0.0795241	−	0.348418i	−0.919475	−	0.393149i	$-0.871386\pi$
$97$	714825.	−	3.13185e6i	0.0795241	−	0.348418i	0.998999	+	0.0447307i	$0.0142430\pi$
$98$	−3.62496e6	−	9.23626e6i	−0.389056	−	0.991299i
$99$	−1.04212e6	−	1.39061e7i	−0.107943	−	1.44039i
$100$	−1.54415e6	−	232743.i	−0.154415	−	0.0232743i
$101$	1.28314e7	−	1.19058e7i	1.23922	−	1.14983i	0.256144	−	0.966639i	$-0.417548\pi$
$101$	1.28314e7	−	1.19058e7i	1.23922	−	1.14983i	0.983077	−	0.183191i	$-0.0586425\pi$
$102$	328585.	−	158238.i	0.0306582	−	0.0147642i
$103$	−779741.	−	531618.i	−0.0703105	−	0.0479369i	0.527655	−	0.849459i	$-0.323072\pi$
$103$	−779741.	−	531618.i	−0.0703105	−	0.0479369i	−0.597965	+	0.801522i	$0.704024\pi$
$104$	865352.	−	2.20488e6i	0.0754356	−	0.192207i
$105$	−819860.	−	252893.i	−0.0691158	−	0.0213194i
$106$	−2.13945e6	−	1.98512e6i	−0.174474	−	0.161888i
$107$	4.31420e6	+	5.40983e6i	0.340453	+	0.426914i	0.922354	−	0.386345i	$-0.126263\pi$
$107$	4.31420e6	+	5.40983e6i	0.340453	+	0.426914i	−0.581902	+	0.813259i	$0.697691\pi$
$108$	1.00474e6	+	1.25991e6i	0.0767488	+	0.0962400i
$109$	1.11308e7	+	1.03279e7i	0.823255	+	0.763869i	0.974443	−	0.224636i	$-0.0721194\pi$
$109$	1.11308e7	+	1.03279e7i	0.823255	+	0.763869i	−0.151188	+	0.988505i	$0.548310\pi$
$110$	−3.15677e7	−	9.73735e6i	−2.26135	−	0.697535i
$111$	538491.	−	1.37205e6i	0.0373722	−	0.0952227i
$112$	2.35658e6	+	1.60669e6i	0.158497	+	0.108061i
$113$	2.88052e6	−	1.38719e6i	0.187800	−	0.0904399i	−0.337621	−	0.941282i	$-0.609622\pi$
$113$	2.88052e6	−	1.38719e6i	0.187800	−	0.0904399i	0.525421	+	0.850842i	$0.323908\pi$
$114$	−1.69401e6	+	1.57181e6i	−0.107090	+	0.0993652i
$115$	−1.07974e7	−	1.62745e6i	−0.662032	−	0.0997852i
$116$	−240453.	−	3.20862e6i	−0.0143030	−	0.190860i
$117$	1.33033e6	+	3.38962e6i	0.0767906	+	0.195659i
$118$	2.58373e6	−	1.13201e7i	0.144764	−	0.634251i
$119$	−21597.6	+	288200.i	−0.00117488	+	0.0156776i
$120$	−6.93586e6	+	2.13943e6i	−0.366409	+	0.113022i
$121$	−2.83787e7	−	1.36664e7i	−1.45627	−	0.701305i
$122$	1.86153e7	+	3.22426e7i	0.928133	+	1.60757i
$123$	−5.25120e6	+	9.09535e6i	−0.254443	+	0.440709i
$124$	−808942.	+	551527.i	−0.0381014	+	0.0259771i
$125$	−1.39241e6	−	6.10057e6i	−0.0637652	−	0.279373i
$126$	−3.59227e6	+	541448.i	−0.159982	+	0.0241135i
$127$	−6.20030e6	+	7.77494e6i	−0.268596	+	0.336809i	−0.897777	−	0.440450i	$-0.854819\pi$
$127$	−6.20030e6	+	7.77494e6i	−0.268596	+	0.336809i	0.629181	+	0.777259i	$0.283390\pi$
$128$	2.82665e7			1.19135
$129$	−7.61224e6	−	2.37985e6i	−0.312211	−	0.0976078i
$130$	8.62619e6			0.344364
$131$	−8.18758e6	+	1.02669e7i	−0.318204	+	0.399016i	−0.915050	−	0.403340i	$-0.867849\pi$
$131$	−8.18758e6	+	1.02669e7i	−0.318204	+	0.399016i	0.596846	+	0.802356i	$0.296420\pi$
$132$	2.74834e6	−	414246.i	0.104007	−	0.0156765i
$133$	−407498.	−	1.78537e6i	−0.0150191	−	0.0658031i
$134$	−1.74378e7	+	1.18889e7i	−0.626073	+	0.426849i
$135$	1.18269e7	−	2.04849e7i	0.413718	−	0.716580i
$136$	1.22248e6	+	2.11740e6i	0.0416731	+	0.0721799i
$137$	1.60915e7	+	7.74924e6i	0.534655	+	0.257476i	0.681672	−	0.731658i	$-0.261253\pi$
$137$	1.60915e7	+	7.74924e6i	0.534655	+	0.257476i	−0.147017	+	0.989134i	$0.546967\pi$
$138$	5.29397e6	−	1.63297e6i	0.171476	−	0.0528935i
$139$	1.26613e6	−	1.68953e7i	0.0399876	−	0.533597i	−0.940857	−	0.338804i	$-0.889977\pi$
$139$	1.26613e6	−	1.68953e7i	0.0399876	−	0.533597i	0.980844	−	0.194793i	$-0.0624035\pi$
$140$	−317562.	+	1.39133e6i	−0.00978092	+	0.0428530i
$141$	−1.25804e6	−	3.20544e6i	−0.0377945	−	0.0962989i
$142$	−3.68479e6	−	4.91701e7i	−0.107995	−	1.44109i
$143$	1.31645e7	+	1.98423e6i	0.376469	+	0.0567435i
$144$	−2.71919e7	+	2.52304e7i	−0.758875	+	0.704133i
$145$	−4.25521e7	+	2.04920e7i	−1.15913	+	0.558209i
$146$	5.23366e7	+	3.56825e7i	1.39178	+	0.948899i
$147$	4.47662e6	−	1.14062e7i	0.116236	−	0.296164i
$148$	−2.34275e6	−	722641.i	−0.0594031	−	0.0183234i
$149$	1.29743e7	+	1.20384e7i	0.321315	+	0.298137i	0.824294	−	0.566162i	$-0.191572\pi$
$149$	1.29743e7	+	1.20384e7i	0.321315	+	0.298137i	−0.502979	+	0.864299i	$0.667763\pi$
$150$	−7.25091e6	−	9.09235e6i	−0.175418	−	0.219967i
$151$	4.44183e7	+	5.56988e7i	1.04989	+	1.31652i	0.946792	+	0.321846i	$0.104303\pi$
$151$	4.44183e7	+	5.56988e7i	1.04989	+	1.31652i	0.103095	+	0.994671i	$0.467125\pi$
$152$	−1.13566e7	−	1.05374e7i	−0.262300	−	0.243378i
$153$	−3.59171e6	−	1.10790e6i	−0.0810739	−	0.0250080i
$154$	−4.85253e6	+	1.23641e7i	−0.107065	+	0.272796i
$155$	1.18739e7	+	8.09550e6i	0.256114	+	0.174616i
$156$	−653880.	+	314892.i	−0.0137899	+	0.00664088i
$157$	2.92677e7	−	2.71565e7i	0.603587	−	0.560047i	−0.318063	−	0.948070i	$-0.603032\pi$
$157$	2.92677e7	−	2.71565e7i	0.603587	−	0.560047i	0.921650	+	0.388022i	$0.126842\pi$
$158$	7.63157e7	+	1.15027e7i	1.53927	+	0.232007i
$159$	−269345.	−	3.59416e6i	−0.00531396	−	0.0709099i
$160$	9.91595e6	+	2.52654e7i	0.191388	+	0.487648i
$161$	−976924.	+	4.28019e6i	−0.0184489	+	0.0808299i
$162$	3.05700e6	−	4.07928e7i	0.0564928	−	0.753844i
$163$	−8.47976e7	+	2.61566e7i	−1.53365	+	0.473069i	−0.942701	−	0.333639i	$-0.891724\pi$
$163$	−8.47976e7	+	2.61566e7i	−1.53365	+	0.473069i	−0.590951	+	0.806708i	$0.701247\pi$
$164$	1.57391e7	+	7.57955e6i	0.278629	+	0.134181i
$165$	−2.03984e7	−	3.53310e7i	−0.353510	−	0.612297i
$166$	1.93817e7	−	3.35701e7i	0.328862	−	0.569606i
$167$	−5.45684e7	+	3.72041e7i	−0.906638	+	0.618135i	−0.924282	−	0.381709i	$-0.875336\pi$
$167$	−5.45684e7	+	3.72041e7i	−0.906638	+	0.618135i	0.0176448	+	0.999844i	$0.494383\pi$
$168$	649380.	+	2.84512e6i	0.0105661	+	0.0462933i
$169$	5.86102e7	−	8.83406e6i	0.934048	−	0.140785i
$170$	−5.55169e6	+	6.96160e6i	−0.0866671	+	0.108677i
$171$	2.38167e7			0.364246
$172$	−3.00121e6	+	1.29222e7i	−0.0449725	+	0.193636i
$173$	−1.25067e8			−1.83646			−0.918232	−	0.396043i	$-0.870383\pi$
$173$	−1.25067e8			−1.83646			−0.918232	+	0.396043i	$0.870383\pi$
$174$	1.49403e7	−	1.87345e7i	0.214999	−	0.269600i
$175$	9.11292e6	−	1.37355e6i	0.128536	−	0.0193737i
$176$	3.01785e7	+	1.32221e8i	0.417257	+	1.82812i
$177$	1.18475e7	−	8.07751e6i	0.160591	−	0.109489i
$178$	4.95403e7	−	8.58063e7i	0.658398	−	1.14038i
$179$	−3.39545e7	−	5.88109e7i	−0.442498	−	0.766429i	0.555376	−	0.831599i	$-0.312574\pi$
$179$	−3.39545e7	−	5.88109e7i	−0.442498	−	0.766429i	−0.997874	+	0.0651700i	$0.979241\pi$
$180$	−1.67222e7	−	8.05299e6i	−0.213717	−	0.102921i
$181$	−9.58967e7	+	2.95802e7i	−1.20207	+	0.370789i	−0.830183	−	0.557491i	$-0.811764\pi$
$181$	−9.58967e7	+	2.95802e7i	−1.20207	+	0.370789i	−0.371884	+	0.928279i	$0.621288\pi$
$182$	259182.	−	3.45855e6i	0.00318681	−	0.0425250i
$183$	−1.02310e7	+	4.48248e7i	−0.123406	+	0.540679i
$184$	1.35691e7	+	3.45734e7i	0.160578	+	0.409147i
$185$	2.68927e6	+	3.58858e7i	0.0312272	+	0.416698i
$186$	−7.20990e6	−	1.08672e6i	−0.0821550	−	0.0123829i
$187$	−1.00738e7	+	9.34716e6i	−0.112655	+	0.104528i
$188$	−5.16046e6	+	2.48515e6i	−0.0566417	+	0.0272772i
$189$	−7.85777e6	−	5.35733e6i	−0.0846609	−	0.0577208i
$190$	2.06129e7	−	5.25207e7i	0.218022	−	0.555512i
$191$	9.91757e7	+	3.05916e7i	1.02988	+	0.317677i	0.763238	−	0.646117i	$-0.223608\pi$
$191$	9.91757e7	+	3.05916e7i	1.02988	+	0.317677i	0.266646	+	0.963795i	$0.414085\pi$
$192$	1.71684e7	+	1.59299e7i	0.175055	+	0.162427i
$193$	−3.94680e7	−	4.94913e7i	−0.395180	−	0.495539i	0.543943	−	0.839122i	$-0.316931\pi$
$193$	−3.94680e7	−	4.94913e7i	−0.395180	−	0.495539i	−0.939122	+	0.343583i	$0.888359\pi$
$194$	−2.48105e7	−	3.11113e7i	−0.243966	−	0.305923i
$195$	7.80908e6	+	7.24577e6i	0.0754187	+	0.0699783i
$196$	−1.94759e7	−	6.00751e6i	−0.184757	−	0.0569899i
$197$	−4.93971e7	+	1.25862e8i	−0.460331	+	1.17290i	0.492746	+	0.870173i	$0.335993\pi$
$197$	−4.93971e7	+	1.25862e8i	−0.460331	+	1.17290i	−0.953076	+	0.302730i	$0.902102\pi$
$198$	−1.42726e8	−	9.73088e7i	−1.30670	−	0.890890i
$199$	−3.94656e6	+	1.90056e6i	−0.0355003	+	0.0170961i	−0.451550	−	0.892246i	$-0.649129\pi$
$199$	−3.94656e6	+	1.90056e6i	−0.0355003	+	0.0170961i	0.416049	+	0.909342i	$0.363414\pi$
$200$	5.71520e7	−	5.30293e7i	0.505157	−	0.468717i
$201$	−2.57724e7	−	3.88456e6i	−0.223856	−	0.0337408i
$202$	−1.62036e7	−	2.16222e8i	−0.138319	−	1.84574i
$203$	6.93746e6	+	1.76764e7i	0.0582056	+	0.148305i
$204$	166700.	−	730362.i	0.00137477	−	0.00602327i
$205$	1.91621e7	−	2.55700e8i	0.155347	−	2.07297i
$206$	−1.11708e7	+	3.44574e6i	−0.0890327	+	0.0274630i
$207$	−5.14430e7	−	2.47737e7i	−0.403116	−	0.194131i
$208$	−1.77067e7	−	3.06688e7i	−0.136432	−	0.236307i
$209$	4.35386e7	−	7.54110e7i	0.329885	−	0.571377i
$210$	−8.78128e6	+	5.98698e6i	−0.0654320	+	0.0446108i
$211$	2.80775e7	+	1.23016e8i	0.205764	+	0.901513i	0.967349	+	0.253448i	$0.0815645\pi$
$211$	2.80775e7	+	1.23016e8i	0.205764	+	0.901513i	−0.761585	+	0.648065i	$0.775578\pi$
$212$	−5.92811e6	+	893519.i	−0.0427308	+	0.00644063i
$213$	3.79659e7	−	4.76077e7i	0.269193	−	0.337558i
$214$	8.57131e7			0.597859
$215$	1.92659e8	−	2.82888e7i	1.32207	−	0.194125i
$216$	−8.04553e7			−0.543208
$217$	3.60254e6	−	4.51744e6i	0.0239332	−	0.0300112i
$218$	1.85991e8	−	2.80336e7i	1.21589	−	0.183265i
$219$	1.74067e7	+	7.62638e7i	0.111986	+	0.490641i
$220$	−5.60677e7	+	3.82263e7i	−0.355004	+	0.242037i
$221$	1.79420e6	−	3.10764e6i	0.0111814	−	0.0193668i
$222$	−9.12907e6	−	1.58120e7i	−0.0560004	−	0.0969955i
$223$	−2.88134e8	−	1.38758e8i	−1.73991	−	0.837898i	−0.982815	−	0.184596i	$-0.940902\pi$
$223$	−2.88134e8	−	1.38758e8i	−1.73991	−	0.837898i	−0.757098	−	0.653302i	$-0.773383\pi$
$224$	1.04278e7	−	3.21654e6i	0.0619901	−	0.0191214i
$225$	−8.95690e6	+	1.19522e8i	−0.0524227	+	0.699532i
$226$	8.81269e6	−	3.86109e7i	0.0507843	−	0.222500i
$227$	8.98577e7	+	2.28954e8i	0.509876	+	1.29914i	0.921708	+	0.387884i	$0.126794\pi$
$227$	8.98577e7	+	2.28954e8i	0.509876	+	1.29914i	−0.411832	+	0.911260i	$0.635111\pi$
$228$	354736.	+	4.73362e6i	0.00198213	+	0.0264497i
$229$	−3.19524e7	−	4.81605e6i	−0.175824	−	0.0265013i	0.0605399	−	0.998166i	$-0.480718\pi$
$229$	−3.19524e7	−	4.81605e6i	−0.175824	−	0.0265013i	−0.236364	+	0.971665i	$0.575956\pi$
$230$	−9.91540e7	+	9.20015e7i	−0.537357	+	0.498594i
$231$	−1.47784e7	+	7.11688e6i	−0.0788832	+	0.0379881i
$232$	1.32730e8	+	9.04937e7i	0.697848	+	0.475785i
$233$	4.48537e7	−	1.14285e8i	0.232302	−	0.591896i	−0.766425	−	0.642333i	$-0.777966\pi$
$233$	4.48537e7	−	1.14285e8i	0.232302	−	0.591896i	0.998727	+	0.0504379i	$0.0160617\pi$
$234$	4.31023e7	+	1.32953e7i	0.219910	+	0.0678332i
$235$	6.16297e7	+	5.71840e7i	0.309780	+	0.287433i
$236$	−1.48707e7	−	1.86473e7i	−0.0736446	−	0.0923474i
$237$	5.94248e7	+	7.45163e7i	0.289967	+	0.363607i
$238$	2.62435e6	+	2.43504e6i	0.0126183	+	0.0117081i
$239$	1.69418e8	+	5.22584e7i	0.802723	+	0.247607i	0.668856	−	0.743392i	$-0.266784\pi$
$239$	1.69418e8	+	5.22584e7i	0.802723	+	0.247607i	0.133867	+	0.990999i	$0.457260\pi$
$240$	−3.96468e7	+	1.01018e8i	−0.185126	+	0.471694i
$241$	−1.09797e8	−	7.48580e7i	−0.505276	−	0.344492i	0.283702	−	0.958912i	$-0.408437\pi$
$241$	−1.09797e8	−	7.48580e7i	−0.505276	−	0.344492i	−0.788978	+	0.614421i	$0.789390\pi$
$242$	−3.51535e8	+	1.69290e8i	−1.59446	+	0.767854i
$243$	1.38565e8	−	1.28569e8i	0.619485	−	0.574798i
$244$	7.56222e7	+	1.13982e7i	0.333261	+	0.0502310i
$245$	2.23566e7	+	2.98328e8i	0.0971234	+	1.29602i
$246$	4.75295e7	+	1.21103e8i	0.203559	+	0.518660i
$247$	−5.05958e6	+	2.21675e7i	−0.0213637	+	0.0936003i
$248$	3.65289e6	−	4.87444e7i	0.0152074	−	0.202929i
$249$	4.57438e7	−	1.41101e7i	0.187774	−	0.0579205i
$250$	−6.98367e7	−	3.36316e7i	−0.282679	−	0.136131i
$251$	−4.63105e6	−	8.02121e6i	−0.0184851	−	0.0320171i	0.856635	−	0.515923i	$-0.172551\pi$
$251$	−4.63105e6	−	8.02121e6i	−0.0184851	−	0.0320171i	−0.875120	+	0.483906i	$0.839218\pi$
$252$	−3.73117e6	+	6.46257e6i	−0.0146873	+	0.0254392i
$253$	−1.72483e8	+	1.17597e8i	−0.669613	+	0.456534i
$254$	2.74114e7	+	1.20097e8i	0.104957	+	0.459848i
$255$	−1.08734e7	+	1.63890e6i	−0.0410652	+	0.00618958i
$256$	9.61295e7	−	1.20543e8i	0.358110	−	0.449056i
$257$	2.85104e8			1.04770			0.523851	−	0.851810i	$-0.324495\pi$
$257$	2.85104e8			1.04770			0.523851	+	0.851810i	$0.324495\pi$
$258$	−8.18403e7	+	5.53425e7i	−0.296687	+	0.200627i
$259$	1.44687e7			0.0517464
$260$	1.10478e7	−	1.38535e7i	0.0389824	−	0.0488824i
$261$	−2.44203e8	+	3.68077e7i	−0.850176	+	0.128143i
$262$	3.61971e7	+	1.58590e8i	0.124342	+	0.544780i
$263$	−1.68841e8	+	1.15114e8i	−0.572312	+	0.390196i	−0.814613	−	0.580005i	$-0.803050\pi$
$263$	−1.68841e8	+	1.15114e8i	−0.572312	+	0.390196i	0.242300	+	0.970201i	$0.422098\pi$
$264$	−6.93821e7	+	1.20173e8i	−0.232078	+	0.401971i
$265$	4.39988e7	+	7.62082e7i	0.145238	+	0.251560i
$266$	−2.04381e7	−	9.84248e6i	−0.0665817	−	0.0320641i
$267$	1.16923e8	−	3.60659e7i	0.375932	−	0.115960i
$268$	−3.23973e6	+	4.32312e7i	−0.0102810	+	0.137191i
$269$	−3.78194e7	+	1.65698e8i	−0.118463	+	0.519020i	0.880523	+	0.474003i	$0.157191\pi$
$269$	−3.78194e7	+	1.65698e8i	−0.118463	+	0.519020i	−0.998986	+	0.0450169i	$0.985666\pi$
$270$	−1.07048e8	−	2.72753e8i	−0.330982	−	0.843328i
$271$	−1.95772e7	−	2.61239e8i	−0.0597527	−	0.797344i	−0.943920	−	0.330174i	$-0.892893\pi$
$271$	−1.95772e7	−	2.61239e8i	−0.0597527	−	0.797344i	0.884167	−	0.467170i	$-0.154726\pi$
$272$	3.61465e7	+	5.44821e6i	0.108912	+	0.0164158i
$273$	3.13972e6	−	2.91323e6i	0.00933946	−	0.00866575i
$274$	1.99330e8	−	9.59921e7i	0.585390	−	0.281909i
$275$	3.62069e8	+	2.46854e8i	1.04985	+	0.715774i
$276$	4.15761e6	−	1.05934e7i	0.0119031	−	0.0303287i
$277$	−2.50120e8	−	7.71519e7i	−0.707082	−	0.218106i	−0.0797015	−	0.996819i	$-0.525397\pi$
$277$	−2.50120e8	−	7.71519e7i	−0.707082	−	0.218106i	−0.627380	+	0.778713i	$0.715873\pi$
$278$	−1.53848e8	−	1.42750e8i	−0.429473	−	0.398493i
$279$	4.68528e7	+	5.87516e7i	0.129158	+	0.161959i
$280$	−4.44238e7	−	5.57056e7i	−0.120938	−	0.151651i
$281$	3.57098e8	+	3.31338e8i	0.960097	+	0.890840i	0.994087	−	0.108582i	$-0.0346310\pi$
$281$	3.57098e8	+	3.31338e8i	0.960097	+	0.890840i	−0.0339903	+	0.999422i	$0.510822\pi$
$282$	−4.07603e7	−	1.25729e7i	−0.108235	−	0.0333859i
$283$	2.46728e8	−	6.28653e8i	0.647092	−	1.64876i	−0.108798	−	0.994064i	$-0.534700\pi$
$283$	2.46728e8	−	6.28653e8i	0.647092	−	1.64876i	0.755890	−	0.654699i	$-0.227205\pi$
$284$	−8.36856e7	−	5.70559e7i	−0.216789	−	0.147804i
$285$	6.27764e7	−	3.02315e7i	0.160635	−	0.0773576i
$286$	1.20891e8	−	1.12171e8i	0.305572	−	0.283529i
$287$	−1.01944e8	−	1.53655e7i	−0.254550	−	0.0383672i
$288$	1.06059e7	+	1.41526e8i	0.0261623	+	0.349111i
$289$	−1.48560e8	−	3.78525e8i	−0.362043	−	0.922471i
$290$	−1.30184e8	+	5.70375e8i	−0.313448	+	1.37331i
$291$	3.67238e6	−	4.90045e7i	0.00873619	−	0.116576i
$292$	1.24334e8	−	3.83521e7i	0.292248	−	0.0901465i
$293$	−7.46091e8	−	3.59299e8i	−1.73283	−	0.834485i	−0.985424	−	0.170114i	$-0.945586\pi$
$293$	−7.46091e8	−	3.59299e8i	−1.73283	−	0.834485i	−0.747402	−	0.664372i	$-0.768699\pi$
$294$	−7.58924e7	−	1.31449e8i	−0.174174	−	0.301678i
$295$	−1.75045e8	+	3.03187e8i	−0.396984	+	0.687597i
$296$	1.01134e8	−	6.89518e7i	0.226660	−	0.154534i
$297$	−1.00627e8	−	4.40875e8i	−0.222878	−	0.976491i
$298$	2.16794e8	−	3.26764e7i	0.474559	−	0.0715283i
$299$	3.39867e7	−	4.26180e7i	0.0735292	−	0.0922027i
$300$	−2.38886e7			−0.0510818
$301$	−5.55339e6	−	7.80937e7i	−0.0117375	−	0.165057i
$302$	8.82489e8			1.84368
$303$	1.66952e8	−	2.09351e8i	0.344780	−	0.432340i
$304$	−2.29039e8	+	3.45221e7i	−0.467576	+	0.0704758i
$305$	−2.49790e8	−	1.09440e9i	−0.504110	−	2.20865i
$306$	−3.84698e7	+	2.62282e7i	−0.0767528	+	0.0523292i
$307$	1.86944e8	−	3.23796e8i	0.368745	−	0.638685i	−0.620624	−	0.784108i	$-0.713121\pi$
$307$	1.86944e8	−	3.23796e8i	0.368745	−	0.638685i	0.989370	+	0.145423i	$0.0464542\pi$
$308$	1.36417e7	+	2.36281e7i	0.0266036	+	0.0460788i
$309$	−1.30070e7	−	6.26384e6i	−0.0250797	−	0.0120778i
$310$	1.70110e8	−	5.24719e7i	0.324312	−	0.100037i
$311$	2.49154e7	−	3.32473e8i	0.0469686	−	0.626752i	−0.923200	−	0.384320i	$-0.874436\pi$
$311$	2.49154e7	−	3.32473e8i	0.0469686	−	0.626752i	0.970168	−	0.242432i	$-0.0779450\pi$
$312$	8.06284e6	−	3.53256e7i	0.0150296	−	0.0658489i
$313$	−4.93743e7	−	1.25804e8i	−0.0910113	−	0.231893i	0.878119	−	0.478442i	$-0.158798\pi$
$313$	−4.93743e7	−	1.25804e8i	−0.0910113	−	0.231893i	−0.969130	+	0.246549i	$0.920703\pi$
$314$	−3.69595e7	−	4.93190e8i	−0.0673709	−	0.899002i
$315$	1.08311e8	+	1.63253e7i	0.195248	+	0.0294289i
$316$	1.16213e8	−	1.07830e8i	0.207181	−	0.192236i
$317$	−4.27007e8	+	2.05636e8i	−0.752883	+	0.362569i	−0.770638	−	0.637273i	$-0.780062\pi$
$317$	−4.27007e8	+	2.05636e8i	−0.752883	+	0.362569i	0.0177552	+	0.999842i	$0.494348\pi$
$318$	−3.68889e7	−	2.51504e7i	−0.0643280	−	0.0438581i
$319$	−3.29876e8	+	8.40510e8i	−0.568962	+	1.44969i
$320$	−5.46407e8	−	1.68544e8i	−0.932161	−	0.287534i
$321$	7.75940e7	+	7.19967e7i	0.130936	+	0.121491i
$322$	3.39075e7	+	4.25187e7i	0.0565979	+	0.0709715i
$323$	−1.46336e7	−	1.83499e7i	−0.0241625	−	0.0302988i
$324$	−6.15974e7	−	5.71540e7i	−0.100613	−	0.0933554i
$325$	−1.09342e8	−	3.37277e7i	−0.176684	−	0.0544998i
$326$	−4.01601e8	+	1.02326e9i	−0.641997	+	1.63578i
$327$	1.91920e8	+	1.30849e8i	0.303531	+	0.206944i
$328$	−7.85794e8	+	3.78418e8i	−1.22956	+	0.592125i
$329$	2.47789e7	−	2.29914e7i	0.0383615	−	0.0355943i
$330$	−4.99717e8	−	7.53202e7i	−0.765465	−	0.115375i
$331$	8.35668e7	+	1.11512e9i	0.126659	+	1.69015i	0.592732	+	0.805400i	$0.298049\pi$
$331$	8.35668e7	+	1.11512e9i	0.126659	+	1.69015i	−0.466073	+	0.884746i	$0.654332\pi$
$332$	−2.90903e7	−	7.41209e7i	−0.0436280	−	0.111162i
$333$	−4.18723e7	+	1.83455e8i	−0.0621401	+	0.272254i
$334$	−6.11375e7	+	8.15824e8i	−0.0897832	+	1.19807i
$335$	6.08071e8	−	1.87565e8i	0.883685	−	0.272581i
$336$	3.93106e7	+	1.89310e7i	0.0565357	+	0.0272261i
$337$	1.60612e8	+	2.78189e8i	0.228599	+	0.395945i	0.957393	−	0.288788i	$-0.0932522\pi$
$337$	1.60612e8	+	2.78189e8i	0.228599	+	0.395945i	−0.728794	+	0.684733i	$0.759919\pi$
$338$	3.67111e8	−	6.35855e8i	0.517117	−	0.895673i
$339$	4.04101e7	−	2.75511e7i	0.0563366	−	0.0384097i
$340$	4.07000e6	+	1.78318e7i	0.00561589	+	0.0246048i
$341$	2.71676e8	−	4.09486e7i	0.371032	−	0.0559240i
$342$	1.83945e8	−	2.30659e8i	0.248654	−	0.311802i
$343$	2.43950e8			0.326416
$344$	−4.10980e8	−	5.19397e8i	−0.544334	−	0.687931i
$345$	−1.67041e8			−0.219006
$346$	−9.65939e8	+	1.21125e9i	−1.25367	+	1.57205i
$347$	1.08102e9	−	1.62937e8i	1.38892	−	0.209347i	0.588363	−	0.808597i	$-0.299773\pi$
$347$	1.08102e9	−	1.62937e8i	1.38892	−	0.209347i	0.800562	+	0.599250i	$0.204535\pi$
$348$	−1.09529e7	−	4.79877e7i	−0.0139316	−	0.0610383i
$349$	6.29357e8	−	4.29088e8i	0.792516	−	0.540328i	−0.0980504	−	0.995181i	$-0.531261\pi$
$349$	6.29357e8	−	4.29088e8i	0.792516	−	0.540328i	0.890566	+	0.454853i	$0.150308\pi$
$350$	5.70798e7	−	9.88650e7i	0.0711613	−	0.123255i
$351$	5.90409e7	+	1.02262e8i	0.0728749	+	0.126223i
$352$	4.67505e8	+	2.25139e8i	0.571330	+	0.275138i
$353$	1.48578e9	−	4.58302e8i	1.79780	−	0.554549i	0.798905	−	0.601457i	$-0.205413\pi$
$353$	1.48578e9	−	4.58302e8i	1.79780	−	0.554549i	0.998899	+	0.0469083i	$0.0149369\pi$
$354$	1.32738e7	−	1.77126e8i	0.0159031	−	0.212213i
$355$	−3.30821e8	+	1.44942e9i	−0.392458	+	1.71947i
$356$	−7.43558e7	−	1.89455e8i	−0.0873453	−	0.222552i
$357$	330392.	+	4.40877e6i	0.000384318	+	0.00512836i
$358$	−8.31813e8	−	1.25376e8i	−0.958153	−	0.144418i
$359$	−6.81127e8	+	6.31993e8i	−0.776958	+	0.720912i	−0.965286	−	0.261195i	$-0.915884\pi$
$359$	−6.81127e8	+	6.31993e8i	−0.776958	+	0.720912i	0.188328	+	0.982106i	$0.439693\pi$
$360$	8.34877e8	−	4.02055e8i	0.943113	−	0.454179i
$361$	−6.15674e8	−	4.19760e8i	−0.688773	−	0.469597i
$362$	−4.54166e8	+	1.15720e9i	−0.503193	+	1.28212i
$363$	−4.60436e8	−	1.42026e8i	−0.505238	−	0.155845i
$364$	−5.22242e6	−	4.84570e6i	−0.00567567	−	0.00526625i
$365$	−1.19079e9	−	1.49320e9i	−1.28177	−	1.60728i
$366$	3.55101e8	+	4.45282e8i	0.378589	+	0.474735i
$367$	1.10219e9	+	1.02268e9i	1.16392	+	1.07996i	0.995549	+	0.0942416i	$0.0300426\pi$
$367$	1.10219e9	+	1.02268e9i	1.16392	+	1.07996i	0.168376	+	0.985723i	$0.446148\pi$
$368$	5.30625e8	+	1.63676e8i	0.555035	+	0.171205i
$369$	4.89850e8	−	1.24812e9i	0.507541	−	1.29319i
$370$	3.68316e8	+	2.51113e8i	0.378020	+	0.257729i
$371$	3.18766e7	−	1.53510e7i	0.0324088	−	0.0156073i
$372$	−1.09792e7	+	1.01872e7i	−0.0110578	+	0.0102601i
$373$	−1.04584e9	−	1.57635e8i	−1.04348	−	0.157279i	−0.395131	−	0.918625i	$-0.629301\pi$
$373$	−1.04584e9	−	1.57635e8i	−1.04348	−	0.157279i	−0.648346	+	0.761346i	$0.724539\pi$
$374$	1.27213e7	+	1.69754e8i	0.0125742	+	0.167792i
$375$	−3.49719e7	−	8.91069e7i	−0.0342460	−	0.0872573i
$376$	6.36324e7	−	2.78792e8i	0.0617335	−	0.270472i
$377$	1.76192e7	−	2.35112e8i	0.0169353	−	0.225986i
$378$	−1.12573e8	+	3.47241e7i	−0.107204	+	0.0330682i
$379$	1.66796e9	+	8.03246e8i	1.57379	+	0.757899i	0.998208	−	0.0598416i	$-0.0190596\pi$
$379$	1.66796e9	+	8.03246e8i	1.57379	+	0.757899i	0.575586	+	0.817741i	$0.304774\pi$
$380$	−5.79479e7	−	1.00369e8i	−0.0541745	−	0.0938330i
$381$	−7.60635e7	+	1.31746e8i	−0.0704594	+	0.122039i
$382$	1.06224e9	−	7.24224e8i	0.974993	−	0.664739i
$383$	9.02367e7	+	3.95353e8i	0.0820706	+	0.359575i	0.999242	−	0.0389171i	$-0.0123908\pi$
$383$	9.02367e7	+	3.95353e8i	0.0820706	+	0.359575i	−0.917172	+	0.398492i	$0.869534\pi$
$384$	4.27580e8	−	6.44473e7i	0.385352	−	0.0580825i
$385$	2.49692e8	−	3.13103e8i	0.222993	−	0.279625i
$386$	−7.84137e8			−0.693963
$387$	1.00625e9	+	1.55589e8i	0.882510	+	0.136455i
$388$	−8.17397e7			−0.0710431
$389$	−7.40513e8	+	9.28573e8i	−0.637836	+	0.799821i	−0.990730	−	0.135842i	$-0.956626\pi$
$389$	−7.40513e8	+	9.28573e8i	−0.637836	+	0.799821i	0.352895	+	0.935663i	$0.385197\pi$
$390$	1.30486e8	−	1.96676e7i	0.111388	−	0.0167890i
$391$	1.25207e7	+	5.48567e7i	0.0105928	+	0.0464099i
$392$	8.40751e8	−	5.73214e8i	0.704963	−	0.480635i
$393$	−1.00443e8	+	1.73972e8i	−0.0834729	+	0.144579i
$394$	8.37433e8	+	1.45048e9i	0.689784	+	1.19474i
$395$	−2.09656e9	−	1.00965e9i	−1.71166	−	0.824290i
$396$	−3.39069e8	+	1.04589e8i	−0.274382	+	0.0846355i
$397$	2.52182e7	−	3.36514e8i	0.0202278	−	0.269921i	−0.977915	−	0.209003i	$-0.932978\pi$
$397$	2.52182e7	−	3.36514e8i	0.0202278	−	0.269921i	0.998143	−	0.0609178i	$-0.0194028\pi$
$398$	−1.20741e7	+	5.29002e7i	−0.00959986	+	0.0420597i
$399$	−1.02347e7	−	2.60776e7i	−0.00806623	−	0.0205524i
$400$	−8.71093e7	−	1.16239e9i	−0.0680542	−	0.908120i
$401$	−8.11850e8	−	1.22367e8i	−0.628739	−	0.0947672i	−0.173060	−	0.984911i	$-0.555365\pi$
$401$	−8.11850e8	−	1.22367e8i	−0.628739	−	0.0947672i	−0.455679	+	0.890144i	$0.650604\pi$
$402$	−2.36670e8	+	2.19598e8i	−0.181699	+	0.168592i
$403$	−6.46367e7	+	3.11274e7i	−0.0491939	+	0.0236905i
$404$	−3.68001e8	−	2.50899e8i	−0.277660	−	0.189306i
$405$	−4.50612e8	+	1.14814e9i	−0.337062	+	0.858821i
$406$	2.24772e8	+	6.93330e7i	0.166687	+	0.0514161i
$407$	5.04329e8	+	4.67949e8i	0.370794	+	0.344047i
$408$	2.33197e7	+	2.92420e7i	0.0169986	+	0.0213156i
$409$	6.07888e8	+	7.62268e8i	0.439331	+	0.550904i	0.951367	−	0.308060i	$-0.0996799\pi$
$409$	6.07888e8	+	7.62268e8i	0.439331	+	0.550904i	−0.512036	+	0.858964i	$0.671108\pi$
$410$	−2.32840e9	−	2.16044e9i	−1.66846	−	1.54810i
$411$	2.61079e8	+	8.05323e7i	0.185492	+	0.0572168i
$412$	−8.77298e6	+	2.23532e7i	−0.00618026	+	0.0157471i
$413$	1.16299e8	+	7.92915e7i	0.0812366	+	0.0553862i
$414$	−6.37240e8	+	3.06879e8i	−0.441369	+	0.212552i
$415$	−8.56765e8	+	7.94962e8i	−0.588428	+	0.545981i
$416$	−1.33979e8	−	2.01942e7i	−0.0912455	−	0.0137531i
$417$	−1.93687e7	−	2.58457e8i	−0.0130805	−	0.174547i
$418$	−3.94075e8	−	1.00409e9i	−0.263914	−	0.672442i
$419$	3.79122e8	−	1.66104e9i	0.251785	−	1.10314i	−0.678007	−	0.735055i	$-0.737156\pi$
$419$	3.79122e8	−	1.66104e9i	0.251785	−	1.10314i	0.929792	−	0.368086i	$-0.119987\pi$
$420$	−1.63146e6	+	2.17703e7i	−0.00107449	+	0.0143381i
$421$	6.49256e8	−	2.00269e8i	0.424062	−	0.130806i	−0.0753768	−	0.997155i	$-0.524016\pi$
$421$	6.49256e8	−	2.00269e8i	0.424062	−	0.130806i	0.499438	+	0.866349i	$0.333540\pi$
$422$	1.40823e9	+	6.78169e8i	0.912180	+	0.439283i
$423$	2.19808e8	+	3.80718e8i	0.141206	+	0.244575i
$424$	1.49656e8	−	2.59211e8i	0.0953482	−	0.165148i
$425$	9.75906e7	−	6.65361e7i	0.0616661	−	0.0420433i
$426$	−1.67846e8	−	7.35382e8i	−0.105191	−	0.460871i
$427$	−4.46290e8	+	6.72674e7i	−0.277408	+	0.0418126i
$428$	1.09775e8	−	1.37654e8i	0.0676785	−	0.0848662i
$429$	2.03660e8			0.124539
$430$	1.21400e9	−	2.08434e9i	0.736341	−	1.26424i
$431$	1.02752e9			0.618185			0.309092	−	0.951032i	$-0.399975\pi$
$431$	1.02752e9			0.618185			0.309092	+	0.951032i	$0.399975\pi$
$432$	−7.49991e8	+	9.40460e8i	−0.447572	+	0.561238i
$433$	−1.61064e9	+	2.42765e8i	−0.953433	+	0.143707i	−0.607295	−	0.794477i	$-0.707745\pi$
$433$	−1.61064e9	+	2.42765e8i	−0.953433	+	0.143707i	−0.346138	+	0.938183i	$0.612507\pi$
$434$	−1.59267e7	−	6.97796e7i	−0.00935218	−	0.0409746i
$435$	−5.96952e8	+	4.06995e8i	−0.347718	+	0.237070i
$436$	1.93182e8	−	3.34601e8i	0.111626	−	0.193341i
$437$	−1.78267e8	−	3.08767e8i	−0.102185	−	0.176989i
$438$	8.73037e8	+	4.20432e8i	0.496447	+	0.239076i
$439$	5.66525e8	−	1.74750e8i	0.319590	−	0.0985804i	−0.130810	−	0.991407i	$-0.541758\pi$
$439$	5.66525e8	−	1.74750e8i	0.319590	−	0.0985804i	0.450400	+	0.892827i	$0.351282\pi$
$440$	2.53181e8	−	3.37847e9i	0.141692	−	1.89075i
$441$	−3.48095e8	+	1.52511e9i	−0.193269	+	0.846769i
$442$	−1.62396e7	−	4.13778e7i	−0.00894534	−	0.0227924i
$443$	2.15455e8	+	2.87505e9i	0.117745	+	1.57120i	0.673077	+	0.739572i	$0.264972\pi$
$443$	2.15455e8	+	2.87505e9i	0.117745	+	1.57120i	−0.555332	+	0.831629i	$0.687409\pi$
$444$	−3.70857e7	−	5.58977e6i	−0.0201079	−	0.00303077i
$445$	−2.18992e9	+	2.03195e9i	−1.17806	+	1.09308i
$446$	−3.56920e9	+	1.71884e9i	−1.90502	+	0.917408i
$447$	2.23706e8	+	1.52520e8i	0.118468	+	0.0807701i
$448$	−8.39927e7	+	2.14010e8i	−0.0441335	+	0.112450i
$449$	−1.81706e9	−	5.60489e8i	−0.947343	−	0.292217i	−0.217678	−	0.976021i	$-0.569848\pi$
$449$	−1.81706e9	−	5.60489e8i	−0.947343	−	0.292217i	−0.729666	+	0.683804i	$0.760324\pi$
$450$	1.08836e9	+	1.00985e9i	0.563028	+	0.522413i
$451$	−3.05645e9	−	3.83266e9i	−1.56891	−	1.96736i
$452$	−5.07218e7	−	6.36031e7i	−0.0258351	−	0.0323962i
$453$	7.98896e8	+	7.41267e8i	0.403782	+	0.374655i
$454$	2.91137e9	+	8.98038e8i	1.46016	+	0.450401i
$455$	−3.82043e7	+	9.73431e7i	−0.0190140	+	0.0484468i
$456$	−1.95814e8	−	1.33504e8i	−0.0967090	−	0.0659351i
$457$	2.53858e7	−	1.22251e7i	0.0124418	−	0.00599166i	−0.427652	−	0.903943i	$-0.640659\pi$
$457$	2.53858e7	−	1.22251e7i	0.0124418	−	0.00599166i	0.440094	+	0.897952i	$0.354945\pi$
$458$	−2.93422e8	+	2.72256e8i	−0.142713	+	0.132418i
$459$	−1.20526e8	−	1.81664e7i	−0.0581752	−	0.00876850i
$460$	2.07634e7	+	2.77068e8i	0.00994595	+	0.132719i
$461$	−4.43972e8	−	1.13122e9i	−0.211058	−	0.537768i	0.785665	−	0.618652i	$-0.212321\pi$
$461$	−4.43972e8	−	1.13122e9i	−0.211058	−	0.537768i	−0.996724	+	0.0808841i	$0.974226\pi$
$462$	−4.52131e7	+	1.98091e8i	−0.0213313	+	0.0934585i
$463$	2.31905e8	−	3.09455e9i	0.108587	−	1.44899i	−0.630925	−	0.775844i	$-0.717325\pi$
$463$	2.31905e8	−	3.09455e9i	0.108587	−	1.44899i	0.739512	−	0.673144i	$-0.235056\pi$
$464$	2.29509e9	−	7.07941e8i	1.06656	−	0.328991i
$465$	1.98071e8	+	9.53861e7i	0.0913558	+	0.0439946i
$466$	−7.60408e8	−	1.31706e9i	−0.348093	−	0.602915i
$467$	1.72416e9	−	2.98633e9i	0.783373	−	1.35684i	−0.146593	−	0.989197i	$-0.546831\pi$
$467$	1.72416e9	−	2.98633e9i	0.783373	−	1.35684i	0.929966	−	0.367645i	$-0.119836\pi$
$468$	7.65543e7	−	5.21939e7i	0.0345231	−	0.0235374i
$469$	−5.69314e7	−	2.49433e8i	−0.0254828	−	0.111647i
$470$	1.02980e9	−	1.55218e8i	0.457522	−	0.0689603i
$471$	3.80808e8	−	4.77519e8i	0.167932	−	0.210580i
$472$	1.19078e9			0.521237
$473$	2.33215e9	−	2.90169e9i	1.01331	−	1.26077i
$474$	1.18063e9			0.509203
$475$	−4.66633e8	+	5.85139e8i	−0.199778	+	0.250514i
$476$	7.27171e6	−	1.09603e6i	0.00309038	−	0.000465800i
$477$	1.02391e8	+	4.48602e8i	0.0431962	+	0.189255i
$478$	1.81458e9	−	1.23716e9i	0.759940	−	0.518118i
$479$	1.85135e7	−	3.20662e7i	0.00769685	−	0.0133313i	−0.862151	−	0.506651i	$-0.830883\pi$
$479$	1.85135e7	−	3.20662e7i	0.00769685	−	0.0133313i	0.869848	+	0.493320i	$0.164217\pi$
$480$	2.07601e8	+	3.59575e8i	0.0856810	+	0.148404i
$481$	−1.61856e8	−	7.79457e7i	−0.0663164	−	0.0319363i
$482$	−1.57298e9	+	4.85200e8i	−0.639821	+	0.197359i
$483$	−5.01890e6	+	6.69726e7i	−0.00202672	+	0.0270447i
$484$	−1.78343e8	+	7.81374e8i	−0.0714988	+	0.313257i
$485$	4.38337e8	+	1.11687e9i	0.174467	+	0.444534i
$486$	−1.74981e8	−	2.33496e9i	−0.0691454	−	0.922681i
$487$	−4.91429e8	−	7.40709e7i	−0.192801	−	0.0290601i	0.0519319	−	0.998651i	$-0.483462\pi$
$487$	−4.91429e8	−	7.40709e7i	−0.192801	−	0.0290601i	−0.244733	+	0.969591i	$0.578700\pi$
$488$	−2.79892e9	+	2.59702e9i	−1.09024	+	1.01159i
$489$	−1.22307e9	+	5.89001e8i	−0.473011	+	0.227790i
$490$	3.06191e9	+	2.08757e9i	1.17572	+	0.801595i
$491$	−9.33417e8	+	2.37831e9i	−0.355869	+	0.906740i	0.635073	+	0.772452i	$0.280970\pi$
$491$	−9.33417e8	+	2.37831e9i	−0.355869	+	0.906740i	−0.990942	+	0.134288i	$0.957125\pi$
$492$	2.55362e8	+	7.87688e7i	0.0966671	+	0.0298179i
$493$	1.78404e8	+	1.65534e8i	0.0670563	+	0.0622191i
$494$	1.75610e8	+	2.20208e8i	0.0655399	+	0.0821844i
$495$	3.24736e9	+	4.07206e9i	1.20341	+	1.50902i
$496$	−5.35732e8	−	4.97087e8i	−0.197134	−	0.182914i
$497$	5.71185e8	+	1.76187e8i	0.208703	+	0.0643764i
$498$	2.16643e8	−	5.51996e8i	0.0786033	−	0.200278i
$499$	−2.18570e9	−	1.49018e9i	−0.787478	−	0.536893i	0.101504	−	0.994835i	$-0.467634\pi$
$499$	−2.18570e9	−	1.49018e9i	−0.787478	−	0.536893i	−0.888982	+	0.457942i	$0.848587\pi$
$500$	−1.43454e8	+	6.90836e7i	−0.0513235	+	0.0247161i
$501$	−7.40617e8	+	6.87192e8i	−0.263125	+	0.244144i
$502$	−1.13451e8	−	1.71000e7i	−0.0400262	−	0.00603298i
$503$	6.52004e7	+	8.70039e8i	0.0228435	+	0.304825i	0.996909	+	0.0785604i	$0.0250323\pi$
$503$	6.52004e7	+	8.70039e8i	0.0228435	+	0.304825i	−0.974066	+	0.226265i	$0.927349\pi$
$504$	−1.36114e8	−	3.46812e8i	−0.0473582	−	0.120667i
$505$	−1.45476e9	+	6.37371e9i	−0.502656	+	2.20228i
$506$	−1.93247e8	+	2.57870e9i	−0.0663109	+	0.884858i
$507$	8.66438e8	−	2.67261e8i	0.295263	−	0.0910767i
$508$	2.27980e8	+	1.09790e8i	0.0771569	+	0.0371568i
$509$	−6.85717e8	−	1.18770e9i	−0.230480	−	0.399203i	0.727470	−	0.686140i	$-0.240696\pi$
$509$	−6.85717e8	−	1.18770e9i	−0.230480	−	0.399203i	−0.957949	+	0.286937i	$0.907363\pi$
$510$	−6.81066e7	+	1.17964e8i	−0.0227349	+	0.0393780i
$511$	−6.34455e8	+	4.32564e8i	−0.210343	+	0.143409i
$512$	3.80121e8	+	1.66542e9i	0.125163	+	0.548376i
$513$	7.63706e8	−	1.15110e8i	0.249756	−	0.0376446i
$514$	2.20196e9	−	2.76117e9i	0.715218	−	0.896855i
$515$	3.52473e8			0.113710
$516$	−1.59361e7	+	2.02313e8i	−0.00510632	+	0.0648260i
$517$	1.60730e9			0.511540
$518$	1.11747e8	−	1.40126e8i	0.0353249	−	0.0442960i
$519$	−1.89186e9	+	2.85152e8i	−0.594022	+	0.0895345i
$520$	1.96855e8	+	8.62478e8i	0.0613952	+	0.268990i
$521$	−2.63772e9	+	1.79837e9i	−0.817142	+	0.557118i	−0.898198	−	0.439592i	$-0.855123\pi$
$521$	−2.63772e9	+	1.79837e9i	−0.817142	+	0.557118i	0.0810560	+	0.996710i	$0.474171\pi$
$522$	−1.52959e9	+	2.64933e9i	−0.470683	+	0.815247i
$523$	8.72476e8	+	1.51117e9i	0.266684	+	0.461911i	0.968004	−	0.250937i	$-0.0807386\pi$
$523$	8.72476e8	+	1.51117e9i	0.266684	+	0.461911i	−0.701319	+	0.712847i	$0.747405\pi$
$524$	3.01051e8	+	1.44979e8i	0.0914073	+	0.0440194i
$525$	1.34717e8	−	4.15547e7i	0.0406317	−	0.0125332i
$526$	−1.89167e8	+	2.52425e9i	−0.0566754	+	0.756281i
$527$	1.64785e7	−	7.21969e7i	0.00490433	−	0.0214873i
$528$	7.57964e8	+	1.93126e9i	0.224094	+	0.570982i
$529$	−1.90568e8	−	2.54295e9i	−0.0559699	−	0.746867i
$530$	1.07788e9	+	1.62464e8i	0.314488	+	0.0474014i
$531$	−1.34194e9	+	1.24514e9i	−0.388957	+	0.360900i
$532$	−4.19825e7	+	2.02177e7i	−0.0120886	+	0.00582158i
$533$	1.05763e9	+	7.21078e8i	0.302543	+	0.206271i
$534$	5.53745e8	−	1.41092e9i	0.157368	−	0.400966i
$535$	−2.46954e9	−	7.61751e8i	−0.697232	−	0.215068i
$536$	−1.58663e9	−	1.47218e9i	−0.445041	−	0.412938i
$537$	−6.47708e8	−	8.12200e8i	−0.180497	−	0.226336i
$538$	1.31265e9	+	1.64602e9i	0.363423	+	0.455718i
$539$	4.19262e9	+	3.89018e9i	1.15325	+	1.07006i
$540$	−5.75136e8	−	1.77406e8i	−0.157178	−	0.0484830i
$541$	1.29139e9	−	3.29041e9i	0.350645	−	0.893429i	−0.641361	−	0.767239i	$-0.721630\pi$
$541$	1.29139e9	−	3.29041e9i	0.350645	−	0.893429i	0.992006	−	0.126190i	$-0.0402748\pi$
$542$	−2.68124e9	−	1.82804e9i	−0.723334	−	0.493161i
$543$	−1.38316e9	+	6.66095e8i	−0.370743	+	0.178541i
$544$	1.02525e8	−	9.51290e7i	0.0273044	−	0.0253348i
$545$	−5.60784e9	−	8.45245e8i	−1.48391	−	0.223663i
$546$	−3.96486e6	−	5.29074e7i	−0.00104245	−	0.0139105i
$547$	−8.03334e8	−	2.04686e9i	−0.209865	−	0.534728i	0.786719	−	0.617312i	$-0.211778\pi$
$547$	−8.03334e8	−	2.04686e9i	−0.209865	−	0.534728i	−0.996584	+	0.0825833i	$0.973683\pi$
$548$	1.01126e8	−	4.43060e8i	0.0262500	−	0.115009i
$549$	4.38649e8	−	5.85336e9i	0.113139	−	1.50974i
$550$	5.18711e9	−	1.60001e9i	1.32940	−	0.410066i
$551$	−1.38938e9	−	6.69092e8i	−0.353828	−	0.170394i
$552$	2.84082e8	+	4.92045e8i	0.0718881	+	0.124514i
$553$	−4.67797e8	+	8.10248e8i	−0.117630	+	0.203742i
$554$	−2.67897e9	+	1.82649e9i	−0.669396	+	0.456386i
$555$	1.22499e8	+	5.36702e8i	0.0304163	+	0.133263i
$556$	−4.26292e8	+	6.42532e7i	−0.105183	+	0.0158538i
$557$	4.79097e9	−	6.00769e9i	1.17471	−	1.47304i	0.325057	−	0.945695i	$-0.394617\pi$
$557$	4.79097e9	−	6.00769e9i	1.17471	−	1.47304i	0.849652	−	0.527344i	$-0.176812\pi$
$558$	9.30857e8			0.226811
$559$	−3.58583e8	+	9.03523e8i	−0.0868256	+	0.218775i
$560$	−1.06527e9			−0.256330
$561$	−1.31073e8	+	1.64360e8i	−0.0313431	+	0.0393031i
$562$	5.96693e9	−	8.99370e8i	1.41799	−	0.213728i
$563$	7.07801e8	+	3.10108e9i	0.167160	+	0.732375i	0.987124	+	0.159960i	$0.0511364\pi$
$563$	7.07801e8	+	3.10108e9i	0.167160	+	0.732375i	−0.819964	+	0.572415i	$0.806006\pi$
$564$	−7.23948e7	+	4.93579e7i	−0.0169914	+	0.0115846i
$565$	−5.97052e8	+	1.03412e9i	−0.139265	+	0.241214i
$566$	−4.18279e9	−	7.24481e9i	−0.969636	−	1.67946i
$567$	4.46792e8	+	2.15164e8i	0.102935	+	0.0495710i
$568$	4.83212e9	−	1.49051e9i	1.10642	−	0.341284i
$569$	1.66719e8	−	2.22471e9i	0.0379395	−	0.506267i	−0.945571	−	0.325416i	$-0.894496\pi$
$569$	1.66719e8	−	2.22471e9i	0.0379395	−	0.506267i	0.983510	−	0.180851i	$-0.0578853\pi$
$570$	1.92059e8	−	8.41464e8i	0.0434382	−	0.190315i
$571$	−2.47176e9	−	6.29793e9i	−0.555622	−	1.41570i	−0.882355	−	0.470584i	$-0.844043\pi$
$571$	−2.47176e9	−	6.29793e9i	−0.555622	−	1.41570i	0.326734	−	0.945116i	$-0.394052\pi$
$572$	−2.53153e7	−	3.37809e8i	−0.00565583	−	0.0754719i
$573$	1.56995e9	+	2.36632e8i	0.348614	+	0.0525451i
$574$	−9.36158e8	+	8.68627e8i	−0.206613	+	0.191709i
$575$	1.61656e9	−	7.78494e8i	0.354613	−	0.170772i
$576$	−2.47045e9	−	1.68432e9i	−0.538638	−	0.367237i
$577$	1.94312e8	−	4.95098e8i	0.0421099	−	0.107294i	−0.908272	−	0.418381i	$-0.862598\pi$
$577$	1.94312e8	−	4.95098e8i	0.0421099	−	0.107294i	0.950382	+	0.311087i	$0.100693\pi$
$578$	−4.81332e9	−	1.48471e9i	−1.03681	−	0.319812i
$579$	−7.09861e8	−	6.58655e8i	−0.151984	−	0.141021i
$580$	7.49281e8	+	9.39568e8i	0.159458	+	0.199954i
$581$	2.92986e8	+	3.67393e8i	0.0619770	+	0.0777167i
$582$	−4.46234e8	−	4.14045e8i	−0.0938280	−	0.0870597i
$583$	1.60759e9	+	4.95876e8i	0.335997	+	0.103641i
$584$	−2.37331e9	+	6.04710e9i	−0.493071	+	1.25633i
$585$	−1.12369e9	−	7.66119e8i	−0.232060	−	0.158216i
$586$	−9.24205e9	+	4.45074e9i	−1.89726	+	0.913672i
$587$	3.58789e9	−	3.32908e9i	0.732160	−	0.679345i	−0.223206	−	0.974771i	$-0.571652\pi$
$587$	3.58789e9	−	3.32908e9i	0.732160	−	0.679345i	0.955366	+	0.295426i	$0.0954617\pi$
$588$	−3.08303e8	−	4.64692e7i	−0.0625399	−	0.00942637i
$589$	3.50660e7	+	4.67923e8i	0.00707102	+	0.0943562i
$590$	1.58437e9	+	4.03690e9i	0.317595	+	0.809218i
$591$	−4.60253e8	+	2.01650e9i	−0.0917151	+	0.401830i
$592$	1.36760e8	−	1.82493e9i	0.0270914	−	0.361510i
$593$	4.20277e8	−	1.29638e8i	0.0827646	−	0.0255295i	−0.253096	−	0.967441i	$-0.581449\pi$
$593$	4.20277e8	−	1.29638e8i	0.0827646	−	0.0255295i	0.335861	+	0.941912i	$0.390973\pi$
$594$	−5.04696e9	−	2.43049e9i	−0.988046	−	0.475818i
$595$	−5.39711e7	−	9.34808e7i	−0.0105039	−	0.0181934i
$596$	2.25176e8	−	3.90017e8i	0.0435673	−	0.0754608i
$597$	−5.53652e7	+	3.77474e7i	−0.0106494	+	0.00726066i
$598$	−1.50254e8	−	6.58307e8i	−0.0287325	−	0.125885i
$599$	7.36804e9	−	1.11055e9i	1.40074	−	0.211128i	0.595157	−	0.803609i	$-0.297090\pi$
$599$	7.36804e9	−	1.11055e9i	1.40074	−	0.211128i	0.805584	+	0.592482i	$0.201852\pi$
$600$	7.43616e8	−	9.32465e8i	0.140546	−	0.176240i
$601$	−3.03003e8			−0.0569358			−0.0284679	−	0.999595i	$-0.509063\pi$
$601$	−3.03003e8			−0.0569358			−0.0284679	+	0.999595i	$0.509063\pi$
$602$	−7.99211e8	−	5.49362e8i	−0.149305	−	0.102629i
$603$	3.32742e9			0.618013
$604$	1.13023e9	−	1.41726e9i	0.208707	−	0.261710i
$605$	1.16328e10	−	1.75337e9i	2.13571	−	0.321906i
$606$	−7.38090e8	−	3.23378e9i	−0.134727	−	0.590278i
$607$	4.38810e9	−	2.99176e9i	0.796372	−	0.542957i	−0.0954017	−	0.995439i	$-0.530414\pi$
$607$	4.38810e9	−	2.99176e9i	0.796372	−	0.542957i	0.891774	+	0.452482i	$0.149461\pi$
$608$	−4.43106e8	+	7.67482e8i	−0.0799549	+	0.138486i
$609$	1.45243e8	+	2.51568e8i	0.0260576	+	0.0451331i
$610$	−1.25282e10	−	6.03328e9i	−2.23479	−	1.07622i
$611$	−4.01051e8	+	1.23708e8i	−0.0711305	+	0.0219408i
$612$	−7.14722e6	+	9.53730e7i	−0.00126040	+	0.0168188i
$613$	−1.85638e9	+	8.13335e9i	−0.325504	+	1.42613i	0.502098	+	0.864811i	$0.332562\pi$
$613$	−1.85638e9	+	8.13335e9i	−0.325504	+	1.42613i	−0.827602	+	0.561315i	$0.810296\pi$
$614$	−1.69206e9	−	4.31130e9i	−0.295003	−	0.751655i
$615$	−2.93133e8	−	3.91159e9i	−0.0508162	−	0.678095i
$616$	−1.34694e9	−	2.03019e8i	−0.232175	−	0.0349948i
$617$	1.08008e9	−	1.00217e9i	0.185122	−	0.171768i	−0.582168	−	0.813069i	$-0.697795\pi$
$617$	1.08008e9	−	1.00217e9i	0.185122	−	0.171768i	0.767290	+	0.641301i	$0.221605\pi$
$618$	−1.61122e8	+	7.75921e7i	−0.0274596	+	0.0132238i
$619$	3.09618e9	+	2.11094e9i	0.524697	+	0.357733i	0.796518	−	0.604615i	$-0.206673\pi$
$619$	3.09618e9	+	2.11094e9i	0.524697	+	0.357733i	−0.271820	+	0.962348i	$0.587626\pi$
$620$	1.33595e8	−	3.40395e8i	0.0225123	−	0.0573605i
$621$	−1.76931e9	−	5.45759e8i	−0.296471	−	0.0914493i
$622$	−3.02750e9	−	2.80911e9i	−0.504450	−	0.468061i
$623$	7.48882e8	+	9.39068e8i	0.124081	+	0.155593i
$624$	−3.37768e8	−	4.23548e8i	−0.0556510	−	0.0697842i
$625$	5.22792e9	+	4.85080e9i	0.856543	+	0.794756i
$626$	−1.59971e9	−	4.93447e8i	−0.260635	−	0.0803952i
$627$	4.86660e8	−	1.23999e9i	0.0788477	−	0.200901i
$628$	−8.39390e8	−	5.72286e8i	−0.135240	−	0.0922051i
$629$	1.67073e8	−	8.04580e7i	0.0267688	−	0.0128912i
$630$	9.94633e8	−	9.22884e8i	0.158479	−	0.147047i
$631$	−5.90677e9	−	8.90303e8i	−0.935939	−	0.141070i	−0.336674	−	0.941621i	$-0.609302\pi$
$631$	−5.90677e9	−	8.90303e8i	−0.935939	−	0.141070i	−0.599265	+	0.800551i	$0.704540\pi$
$632$	5.91485e8	+	7.89282e9i	0.0932039	+	1.24372i
$633$	7.05195e8	+	1.79681e9i	0.110509	+	0.281572i
$634$	−1.30639e9	+	5.72366e9i	−0.203592	+	0.891993i
$635$	2.77562e8	−	3.70381e9i	0.0430182	−	0.574038i
$636$	−8.76357e7	+	2.70320e7i	−0.0135077	+	0.00416657i
$637$	−1.34555e9	−	6.47983e8i	−0.206259	−	0.0993289i
$638$	5.59240e9	+	9.68633e9i	0.852562	+	1.47668i
$639$	−3.88696e9	+	6.73241e9i	−0.589327	+	1.02074i
$640$	−8.72286e9	+	5.94715e9i	−1.31531	+	0.896765i
$641$	2.27123e8	+	9.95090e8i	0.0340610	+	0.149231i	0.989099	−	0.147253i	$-0.0470431\pi$
$641$	2.27123e8	+	9.95090e8i	0.0340610	+	0.149231i	−0.955038	+	0.296484i	$0.904186\pi$
$642$	1.29656e9	−	1.95425e8i	0.193383	−	0.0291479i
$643$	−2.24765e9	+	2.81847e9i	−0.333419	+	0.418095i	−0.920075	−	0.391742i	$-0.871873\pi$
$643$	−2.24765e9	+	2.81847e9i	−0.333419	+	0.418095i	0.586656	+	0.809836i	$0.300444\pi$
$644$	1.11711e8			0.0164814
$645$	2.84980e9	−	8.67177e8i	0.418172	−	0.127247i
$646$	−2.90735e8			−0.0424311
$647$	−5.79004e9	+	7.26048e9i	−0.840459	+	1.05390i	0.157336	+	0.987545i	$0.449709\pi$
$647$	−5.79004e9	+	7.26048e9i	−0.840459	+	1.05390i	−0.997796	+	0.0663577i	$0.978862\pi$
$648$	4.14838e9	−	6.25268e8i	0.598916	−	0.0902721i
$649$	1.48933e9	+	6.52520e9i	0.213863	+	0.936995i
$650$	−1.17114e9	+	7.98467e8i	−0.167267	+	0.114041i
$651$	4.41949e7	−	7.65479e7i	0.00627826	−	0.0108743i
$652$	1.12900e9	+	1.95548e9i	0.159524	+	0.276304i
$653$	−5.82999e8	−	2.80758e8i	−0.0819354	−	0.0394580i	0.392467	−	0.919766i	$-0.371622\pi$
$653$	−5.82999e8	−	2.80758e8i	−0.0819354	−	0.0394580i	−0.474403	+	0.880308i	$0.657336\pi$
$654$	2.74951e9	−	8.48112e8i	0.384356	−	0.118558i
$655$	3.66524e8	−	4.89093e9i	0.0509634	−	0.680059i
$656$	−2.90163e9	+	1.27129e10i	−0.401309	+	1.75825i
$657$	−3.64855e9	−	9.29636e9i	−0.501928	−	1.27889i
$658$	−3.12909e7	−	4.17549e8i	−0.00428182	−	0.0571369i
$659$	1.11389e10	+	1.67892e9i	1.51616	+	0.228524i	0.853775	−	0.520642i	$-0.174307\pi$
$659$	1.11389e10	+	1.67892e9i	1.51616	+	0.228524i	0.662382	+	0.749166i	$0.269545\pi$
$660$	−7.60964e8	+	7.06072e8i	−0.103029	+	0.0955972i
$661$	1.26319e9	−	6.08322e8i	0.170124	−	0.0819273i	−0.346884	−	0.937908i	$-0.612760\pi$
$661$	1.26319e9	−	6.08322e8i	0.170124	−	0.0819273i	0.517008	+	0.855981i	$0.327046\pi$
$662$	1.14451e10	+	7.80315e9i	1.53327	+	1.04536i
$663$	2.00549e7	−	5.10992e7i	0.00267254	−	0.00680952i
$664$	3.79877e9	+	1.17176e9i	0.503564	+	0.155329i
$665$	5.01384e8	+	4.65216e8i	0.0661142	+	0.0613450i
$666$	1.45332e9	+	1.82241e9i	0.190635	+	0.239048i
$667$	2.30504e9	+	2.89042e9i	0.300772	+	0.377156i
$668$	1.23190e9	+	1.14303e9i	0.159903	+	0.148368i
$669$	−4.67489e9	−	1.44201e9i	−0.603642	−	0.186199i
$670$	2.87982e9	−	7.33766e9i	0.369916	−	0.942531i
$671$	−1.77317e10	−	1.20893e10i	−2.26580	−	1.54480i
$672$	1.50404e8	−	7.24308e7i	0.0191191	−	0.00920727i
$673$	6.01163e9	−	5.57797e9i	0.760220	−	0.705381i	−0.201478	−	0.979493i	$-0.564574\pi$
$673$	6.01163e9	−	5.57797e9i	0.760220	−	0.705381i	0.961698	+	0.274112i	$0.0883839\pi$
$674$	3.93466e9	+	5.93055e8i	0.494992	+	0.0746080i
$675$	2.90456e8	+	3.87587e9i	0.0363511	+	0.485072i
$676$	−5.51002e8	−	1.40393e9i	−0.0686025	−	0.174796i
$677$	−1.82299e9	+	7.98706e9i	−0.225801	+	0.989297i	0.727223	+	0.686401i	$0.240811\pi$
$677$	−1.82299e9	+	7.98706e9i	−0.225801	+	0.989297i	−0.953024	+	0.302896i	$0.902047\pi$
$678$	4.52748e7	−	6.04150e8i	0.00557895	−	0.0744459i
$679$	4.60962e8	−	1.42188e8i	0.0565094	−	0.0174308i
$680$	−8.22740e8	−	3.96210e8i	−0.100342	−	0.0483220i
$681$	1.88126e9	+	3.25845e9i	0.228263	+	0.395363i
$682$	1.70167e9	−	2.94738e9i	0.205414	−	0.355788i
$683$	6.97272e9	−	4.75392e9i	0.837394	−	0.570925i	−0.0669372	−	0.997757i	$-0.521323\pi$
$683$	6.97272e9	−	4.75392e9i	0.837394	−	0.570925i	0.904331	+	0.426832i	$0.140370\pi$
$684$	−1.34852e8	−	5.90824e8i	−0.0161124	−	0.0705930i
$685$	−6.59612e9	+	9.94206e8i	−0.784101	+	0.118184i
$686$	1.88411e9	−	2.36260e9i	0.222830	−	0.279419i
$687$	−4.94315e8			−0.0581642
$688$	−9.90243e9	−	3.77036e7i	−1.15926	−	0.00441390i
$689$	−4.39290e8			−0.0511663
$690$	−1.29011e9	+	1.61775e9i	−0.149505	+	0.187473i
$691$	−2.67849e9	+	4.03718e8i	−0.308828	+	0.0465484i	−0.301628	−	0.953426i	$-0.597530\pi$
$691$	−2.67849e9	+	4.03718e8i	−0.308828	+	0.0465484i	−0.00720043	+	0.999974i	$0.502292\pi$
$692$	7.08139e8	+	3.10256e9i	0.0812358	+	0.355917i
$693$	1.73021e9	−	1.17963e9i	0.197484	−	0.134642i
$694$	6.77105e9	−	1.17278e10i	0.768950	−	1.33186i
$695$	3.16397e9	+	5.48016e9i	0.357508	+	0.619222i
$696$	2.21409e9	+	1.06625e9i	0.248922	+	0.119875i
$697$	−1.26261e9	+	3.89463e8i	−0.141239	+	0.0435664i
$698$	7.05121e8	−	9.40918e9i	0.0784819	−	1.04727i
$699$	4.17921e8	−	1.83103e9i	0.0462832	−	0.202780i
$700$	−8.56718e7	−	2.18288e8i	−0.00944050	−	0.0240540i
$701$	−3.55211e8	−	4.73996e9i	−0.0389469	−	0.519711i	−0.982225	−	0.187707i	$-0.939894\pi$
$701$	−3.55211e8	−	4.73996e9i	−0.0389469	−	0.519711i	0.943278	−	0.332004i	$-0.107725\pi$
$702$	1.44638e9	+	2.18006e8i	0.157798	+	0.0237842i
$703$	−8.61340e8	+	7.99206e8i	−0.0935041	+	0.0867592i
$704$	−9.84924e9	+	4.74314e9i	−1.06389	+	0.512344i
$705$	1.06263e9	+	7.24492e8i	0.114215	+	0.0778703i
$706$	7.03663e9	−	1.79291e10i	0.752573	−	1.91752i
$707$	2.51174e9	+	7.74769e8i	0.267305	+	0.0824526i
$708$	−2.67461e8	−	2.48168e8i	−0.0283234	−	0.0262802i
$709$	9.90607e9	+	1.24218e10i	1.04385	+	1.30895i	0.949621	+	0.313400i	$0.101468\pi$
$709$	9.90607e9	+	1.24218e10i	1.04385	+	1.30895i	0.0942319	+	0.995550i	$0.469960\pi$
$710$	1.14823e10	+	1.43983e10i	1.20399	+	1.50976i
$711$	−8.91967e9	−	8.27625e9i	−0.930690	−	0.863555i
$712$	9.70977e9	+	2.99507e9i	1.00816	+	0.310976i
$713$	4.10983e8	−	1.04717e9i	0.0424630	−	0.108194i
$714$	4.52497e7	+	3.08507e7i	0.00465234	+	0.00317191i
$715$	−4.47996e9	+	2.15743e9i	−0.458356	+	0.220733i
$716$	−1.26668e9	+	1.17530e9i	−0.128965	+	0.119662i
$717$	2.68188e9	+	4.04229e8i	0.271721	+	0.0409553i
$718$	8.60132e8	+	1.14777e10i	0.0867221	+	1.15723i
$719$	−2.68613e9	−	6.84416e9i	−0.269511	−	0.686703i	−0.999993	−	0.00377075i	$-0.998800\pi$
$719$	−2.68613e9	−	6.84416e9i	−0.269511	−	0.686703i	0.730482	−	0.682932i	$-0.239296\pi$
$720$	3.08288e9	−	1.35070e10i	0.307817	−	1.34863i
$721$	1.05904e7	−	1.41319e8i	0.00105230	−	0.0140419i
$722$	−8.82035e9	+	2.72072e9i	−0.872179	+	0.269032i
$723$	−1.83154e9	−	8.82022e8i	−0.180232	−	0.0867951i
$724$	1.27677e9	+	2.21144e9i	0.125034	+	0.216566i
$725$	3.88029e9	−	6.72086e9i	0.378165	−	0.655000i
$726$	−4.93159e9	+	3.36230e9i	−0.478310	+	0.326106i
$727$	−1.60204e9	−	7.01901e9i	−0.154634	−	0.677494i	−0.991502	−	0.130090i	$-0.958473\pi$
$727$	−1.60204e9	−	7.01901e9i	−0.154634	−	0.677494i	0.836869	−	0.547404i	$-0.184384\pi$
$728$	3.51713e8	−	5.30122e7i	0.0337854	−	0.00509232i
$729$	−2.70010e9	+	3.38582e9i	−0.258127	+	0.323681i
$730$	−2.36582e10			−2.25087
$731$	−4.98393e8	−	8.70882e8i	−0.0471912	−	0.0824610i
$732$	1.16990e9			0.110246
$733$	−4.66576e9	+	5.85067e9i	−0.437581	+	0.548709i	−0.950904	−	0.309487i	$-0.899843\pi$
$733$	−4.66576e9	+	5.85067e9i	−0.437581	+	0.548709i	0.513323	+	0.858195i	$0.328414\pi$
$734$	1.84170e10	−	2.77592e9i	1.71903	−	0.259102i
$735$	1.01837e9	+	4.46175e9i	0.0946015	+	0.414476i
$736$	1.75541e9	−	1.19682e9i	0.162295	−	0.110651i
$737$	6.08277e9	−	1.05357e10i	0.559712	−	0.969450i
$738$	−8.30445e9	−	1.43837e10i	−0.760526	−	1.31727i
$739$	−5.64719e9	−	2.71954e9i	−0.514727	−	0.247879i	0.158442	−	0.987368i	$-0.449353\pi$
$739$	−5.64719e9	−	2.71954e9i	−0.514727	−	0.247879i	−0.673169	+	0.739489i	$0.735067\pi$
$740$	8.74996e8	−	2.69901e8i	0.0793771	−	0.0244846i
$741$	−2.59934e7	+	3.46857e8i	−0.00234692	+	0.0313175i
$742$	9.75236e7	−	4.27279e8i	0.00876387	−	0.0383970i
$743$	5.61917e9	+	1.43174e10i	0.502587	+	1.28057i	0.926986	+	0.375096i	$0.122390\pi$
$743$	5.61917e9	+	1.43174e10i	0.502587	+	1.28057i	−0.424399	+	0.905475i	$0.639515\pi$
$744$	−5.58803e7	−	7.45671e8i	−0.00497455	−	0.0663807i
$745$	−6.53660e9	−	9.85234e8i	−0.579168	−	0.0872956i
$746$	−9.60402e9	+	8.91123e9i	−0.846968	+	0.785872i
$747$	−5.50623e9	+	2.65166e9i	−0.483317	+	0.232753i
$748$	2.88915e8	+	1.96979e8i	0.0252415	+	0.0172093i
$749$	−3.79613e8	+	9.67238e8i	−0.0330107	+	0.0841099i
$750$	−1.13308e9	−	3.49509e8i	−0.0980723	−	0.0302513i
$751$	−6.05156e9	−	5.61503e9i	−0.521348	−	0.483740i	0.375041	−	0.927008i	$-0.377629\pi$
$751$	−6.05156e9	−	5.61503e9i	−0.521348	−	0.483740i	−0.896389	+	0.443268i	$0.853819\pi$
$752$	−2.66569e9	−	3.34267e9i	−0.228585	−	0.286636i
$753$	−8.83408e7	−	1.10776e8i	−0.00754013	−	0.00945503i
$754$	−2.14093e9	−	1.98649e9i	−0.181888	−	0.168767i
$755$	−2.54260e10	−	7.84287e9i	−2.15012	−	0.663225i
$756$	−8.84089e7	+	2.25262e8i	−0.00744166	+	0.0189610i
$757$	4.22133e9	+	2.87805e9i	0.353682	+	0.241137i	0.727107	−	0.686524i	$-0.240864\pi$
$757$	4.22133e9	+	2.87805e9i	0.353682	+	0.241137i	−0.373425	+	0.927660i	$0.621817\pi$
$758$	2.06615e10	−	9.95005e9i	1.72314	−	0.829818i
$759$	−2.34098e9	+	2.17211e9i	−0.194335	+	0.180317i
$760$	5.72161e9	+	8.62394e8i	0.472793	+	0.0712621i
$761$	−1.10102e9	−	1.46921e10i	−0.0905628	−	1.20848i	−0.838573	−	0.544789i	$-0.816610\pi$
$761$	−1.10102e9	−	1.46921e10i	−0.0905628	−	1.20848i	0.748010	−	0.663687i	$-0.231009\pi$
$762$	6.88464e8	+	1.75418e9i	0.0563688	+	0.143625i
$763$	−5.07382e8	+	2.22299e9i	−0.0413523	+	0.181176i
$764$	1.97352e8	−	2.63348e9i	0.0160108	−	0.213650i
$765$	1.34147e9	−	4.13790e8i	0.108335	−	0.0334168i
$766$	4.52584e9	+	2.17953e9i	0.363830	+	0.175211i
$767$	−8.73838e8	−	1.51353e9i	−0.0699273	−	0.121118i
$768$	1.17929e9	−	2.04259e9i	0.0939411	−	0.162711i
$769$	−1.24463e10	+	8.48574e9i	−0.986956	+	0.672895i	−0.945288	−	0.326236i	$-0.894219\pi$
$769$	−1.24463e10	+	8.48574e9i	−0.986956	+	0.672895i	−0.0416677	+	0.999132i	$0.513267\pi$
$770$	−1.10388e9	−	4.83642e9i	−0.0871374	−	0.381774i
$771$	4.31269e9	−	6.50034e8i	0.338890	−	0.0510794i
$772$	−1.00427e9	+	1.25931e9i	−0.0785577	+	0.0985082i
$773$	−1.64082e9			−0.127771			−0.0638857	−	0.997957i	$-0.520349\pi$
$773$	−1.64082e9			−0.127771			−0.0638857	+	0.997957i	$0.520349\pi$
$774$	9.27850e9	−	8.54368e9i	0.719258	−	0.662295i
$775$	−2.36141e9			−0.182228
$776$	2.54443e9	−	3.19062e9i	0.195468	−	0.245109i
$777$	2.18864e8	−	3.29884e7i	0.0167379	−	0.00252283i
$778$	3.27379e9	+	1.43434e10i	0.249242	+	1.09200i
$779$	6.91758e9	−	4.71632e9i	0.524292	−	0.357456i
$780$	1.35531e8	−	2.34747e8i	0.0102261	−	0.0177121i
$781$	1.42113e10	+	2.46146e10i	1.06747	+	1.84891i
$782$	6.27976e8	+	3.02417e8i	0.0469591	+	0.0226143i
$783$	−7.65271e9	+	2.36055e9i	−0.569704	+	0.175730i
$784$	1.13692e9	−	1.51711e10i	0.0842604	−	1.12438i
$785$	−3.31823e9	+	1.45381e10i	−0.244829	+	1.07266i
$786$	9.09126e8	+	2.31642e9i	0.0667798	+	0.170152i
$787$	−9.47480e8	−	1.26432e10i	−0.0692881	−	0.924585i	−0.918217	−	0.396078i	$-0.870371\pi$
$787$	−9.47480e8	−	1.26432e10i	−0.0692881	−	0.924585i	0.848929	−	0.528507i	$-0.177248\pi$
$788$	3.40196e9	+	5.12763e8i	0.247678	+	0.0373315i
$789$	−2.29155e9	+	2.12625e9i	−0.166097	+	0.154115i
$790$	−2.59706e10	+	1.25068e10i	−1.87408	+	0.902509i
$791$	3.96679e8	+	2.70451e8i	0.0284984	+	0.0194299i
$792$	6.47220e9	−	1.64909e10i	0.462928	−	1.17952i
$793$	5.35486e9	+	1.65176e9i	0.381322	+	0.117622i
$794$	−3.06429e9	−	2.84325e9i	−0.217249	−	0.201578i
$795$	8.39312e8	+	1.05246e9i	0.0592432	+	0.0742886i
$796$	6.94931e7	+	8.71416e7i	0.00488367	+	0.00612393i
$797$	−4.51032e9	−	4.18497e9i	−0.315575	−	0.292811i	0.506441	−	0.862274i	$-0.330961\pi$
$797$	−4.51032e9	−	4.18497e9i	−0.315575	−	0.292811i	−0.822017	+	0.569463i	$0.807151\pi$
$798$	−3.31602e8	−	1.02286e8i	−0.0230998	−	0.00712533i
$799$	1.58275e8	−	4.03278e8i	0.0109774	−	0.0279699i
$800$	−3.68489e9	−	2.51231e9i	−0.254454	−	0.173484i
$801$	−1.40741e10	+	6.77773e9i	−0.967624	+	0.465983i
$802$	−7.45530e9	+	6.91751e9i	−0.510334	+	0.473521i
$803$	−3.61050e10	−	5.44195e9i	−2.46072	−	0.370894i
$804$	4.95601e7	+	6.61333e8i	0.00336307	+	0.0448770i
$805$	−5.99059e8	−	1.52638e9i	−0.0404747	−	0.103128i
$806$	−1.97750e8	+	8.66399e8i	−0.0133028	+	0.0582835i
$807$	−1.94295e8	+	2.59269e9i	−0.0130138	+	0.173658i
$808$	2.12489e10	−	6.55441e9i	1.41708	−	0.437113i
$809$	2.43023e10	+	1.17034e10i	1.61372	+	0.777124i	0.999924	−	0.0123436i	$-0.00392920\pi$
$809$	2.43023e10	+	1.17034e10i	1.61372	+	0.777124i	0.613792	+	0.789468i	$0.289643\pi$
$810$	7.63925e9	+	1.32316e10i	0.505072	+	0.874811i
$811$	2.44453e9	−	4.23404e9i	0.160924	−	0.278729i	−0.774276	−	0.632848i	$-0.781886\pi$
$811$	2.44453e9	−	4.23404e9i	0.160924	−	0.278729i	0.935200	+	0.354119i	$0.115219\pi$
$812$	3.99220e8	−	2.72183e8i	0.0261677	−	0.0178408i
$813$	−8.91760e8	−	3.90706e9i	−0.0582011	−	0.254996i
$814$	8.42709e9	−	1.27018e9i	0.547636	−	0.0825429i
$815$	2.06647e10	−	2.59128e10i	1.33714	−	1.67673i
$816$	5.59200e8			0.0360289
$817$	4.64426e9	+	4.34227e9i	0.297947	+	0.278573i
$818$	1.20773e10			0.771497
$819$	−3.40927e8	+	4.27509e8i	−0.0216854	+	0.0271926i
$820$	−6.45168e9	+	9.72435e8i	−0.408625	+	0.0615902i
$821$	5.11968e9	+	2.24308e10i	0.322880	+	1.41463i	0.832402	+	0.554173i	$0.186965\pi$
$821$	5.11968e9	+	2.24308e10i	0.322880	+	1.41463i	−0.509521	+	0.860458i	$0.670178\pi$
$822$	2.79635e9	−	1.90652e9i	0.175606	−	0.119726i
$823$	7.89051e9	−	1.36668e10i	0.493408	−	0.854607i	−0.506564	−	0.862203i	$-0.669084\pi$
$823$	7.89051e9	−	1.36668e10i	0.493408	−	0.854607i	0.999971	+	0.00759567i	$0.00241780\pi$
$824$	−5.99443e8	−	1.03827e9i	−0.0373252	−	0.0646492i
$825$	6.03974e9	+	2.90858e9i	0.374481	+	0.180340i
$826$	1.66614e9	−	5.13936e8i	0.102868	−	0.0317307i
$827$	−2.37636e9	+	3.17104e10i	−0.146098	+	1.94954i	0.137282	+	0.990532i	$0.456163\pi$
$827$	−2.37636e9	+	3.17104e10i	−0.146098	+	1.94954i	−0.283380	+	0.959008i	$0.591456\pi$
$828$	−3.23290e8	+	1.41642e9i	−0.0197918	+	0.0867136i
$829$	9.95856e8	+	2.53740e9i	0.0607093	+	0.154685i	0.958010	−	0.286735i	$-0.0925700\pi$
$829$	9.95856e8	+	2.53740e9i	0.0607093	+	0.154685i	−0.897300	+	0.441420i	$0.854475\pi$
$830$	1.08193e9	+	1.44373e10i	0.0656789	+	0.876423i
$831$	−3.95941e9	−	5.96784e8i	−0.239346	−	0.0360756i
$832$	2.09251e9	−	1.94156e9i	0.125961	−	0.116875i
$833$	1.38892e9	−	6.68869e8i	0.0832568	−	0.0400944i
$834$	−2.65269e9	−	1.80857e9i	−0.158345	−	0.107958i
$835$	9.01188e9	−	2.29619e10i	0.535689	−	1.36491i
$836$	−2.11725e9	−	6.53085e8i	−0.125329	−	0.0386588i
$837$	1.78634e9	+	1.65748e9i	0.105299	+	0.0977033i
$838$	−1.31587e10	−	1.65005e10i	−0.772431	−	0.968597i
$839$	3.54474e9	+	4.44496e9i	0.207213	+	0.259837i	0.874568	−	0.484903i	$-0.161145\pi$
$839$	3.54474e9	+	4.44496e9i	0.207213	+	0.259837i	−0.667355	+	0.744740i	$0.732574\pi$
$840$	−7.98994e8	−	7.41358e8i	−0.0465121	−	0.0431569i
$841$	−1.20348e9	−	3.71225e8i	−0.0697676	−	0.0215205i
$842$	3.07487e9	−	7.83465e9i	0.177515	−	0.452301i
$843$	6.15717e9	+	4.19789e9i	0.353985	+	0.241343i
$844$	2.89269e9	−	1.39305e9i	0.165616	−	0.0797567i
$845$	−1.62281e10	+	1.50574e10i	−0.925269	+	0.858524i
$846$	5.38483e9	+	8.11632e8i	0.305756	+	0.0460854i
$847$	−3.53468e8	−	4.71670e9i	−0.0199875	−	0.266714i
$848$	−1.63491e9	−	4.16569e9i	−0.0920680	−	0.234585i
$849$	2.29887e9	−	1.00720e10i	0.128925	−	0.564857i
$850$	1.09339e8	−	1.45903e9i	0.00610672	−	0.0814885i
$851$	2.69178e9	−	8.30303e8i	0.149722	−	0.0461831i
$852$	−1.39598e9	−	6.72266e8i	−0.0773284	−	0.0372394i
$853$	9.62110e9	+	1.66642e10i	0.530766	+	0.919313i	0.999355	+	0.0358974i	$0.0114289\pi$
$853$	9.62110e9	+	1.66642e10i	0.530766	+	0.919313i	−0.468590	+	0.883416i	$0.655238\pi$
$854$	−2.79538e9	+	4.84175e9i	−0.153581	+	0.266011i
$855$	−7.34967e9	+	5.01092e9i	−0.402148	+	0.274180i
$856$	1.95603e9	+	8.56991e9i	0.106590	+	0.467001i
$857$	1.72927e10	−	2.60646e9i	0.938493	−	0.141455i	0.338055	−	0.941126i	$-0.390231\pi$
$857$	1.72927e10	−	2.60646e9i	0.938493	−	0.141455i	0.600438	+	0.799671i	$0.294993\pi$
$858$	1.57294e9	−	1.97240e9i	0.0850171	−	0.106608i
$859$	−1.73695e10			−0.934998			−0.467499	−	0.883994i	$-0.654845\pi$
$859$	−1.73695e10			−0.934998			−0.467499	+	0.883994i	$0.654845\pi$
$860$	−1.79261e9	−	4.61914e9i	−0.0961040	−	0.247637i
$861$	−1.57711e9			−0.0842073
$862$	7.93587e9	−	9.95127e9i	0.422006	−	0.529179i
$863$	−9.07846e9	+	1.36836e9i	−0.480811	+	0.0724706i	−0.384976	−	0.922927i	$-0.625790\pi$
$863$	−9.07846e9	+	1.36836e9i	−0.480811	+	0.0724706i	−0.0958351	+	0.995397i	$0.530552\pi$
$864$	1.02411e9	+	4.48693e9i	0.0540193	+	0.236674i
$865$	3.85949e10	−	2.63136e10i	2.02756	−	1.38237i
$866$	−1.00884e10	+	1.74736e10i	−0.527849	+	0.914261i
$867$	−3.11026e9	−	5.38713e9i	−0.162080	−	0.280731i
$868$	−1.32463e8	−	6.37907e7i	−0.00687503	−	0.00331084i
$869$	−4.25110e10	+	1.31129e10i	−2.19751	+	0.677844i
$870$	−6.68815e8	+	8.92472e9i	−0.0344341	+	0.459491i
$871$	−7.06873e8	+	3.09701e9i	−0.0362475	+	0.158811i
$872$	7.04731e9	+	1.79563e10i	0.359928	+	0.917082i
$873$	4.68838e8	+	6.25621e9i	0.0238492	+	0.318245i
$874$	−4.36716e9	−	6.58244e8i	−0.221263	−	0.0333501i
$875$	6.88818e8	−	6.39130e8i	0.0347597	−	0.0322523i
$876$	1.79333e9	−	8.63622e8i	0.0901354	−	0.0434069i
$877$	−9.02159e9	−	6.15082e9i	−0.451632	−	0.307917i	0.316057	−	0.948740i	$-0.397641\pi$
$877$	−9.02159e9	−	6.15082e9i	−0.451632	−	0.307917i	−0.767689	+	0.640823i	$0.778593\pi$
$878$	2.68306e9	−	6.83632e9i	0.133782	−	0.340872i
$879$	−1.21051e10	−	3.73393e9i	−0.601184	−	0.185441i
$880$	−3.71315e10	−	3.44530e10i	−1.83676	−	1.70427i
$881$	1.75169e10	+	2.19655e10i	0.863060	+	1.08224i	0.995842	+	0.0910975i	$0.0290375\pi$
$881$	1.75169e10	+	2.19655e10i	0.863060	+	1.08224i	−0.132782	+	0.991145i	$0.542391\pi$
$882$	1.20818e10	+	1.51502e10i	0.592916	+	0.743493i
$883$	−1.85670e10	−	1.72277e10i	−0.907568	−	0.842100i	0.0803994	−	0.996763i	$-0.474380\pi$
$883$	−1.85670e10	−	1.72277e10i	−0.907568	−	0.842100i	−0.987967	+	0.154663i	$0.950571\pi$
$884$	−8.72505e7	−	2.69132e7i	−0.00424800	−	0.00131034i
$885$	−1.95660e9	+	4.98533e9i	−0.0948856	+	0.241765i
$886$	2.95082e10	+	2.01184e10i	1.42536	+	0.971795i
$887$	1.30337e10	−	6.27670e9i	0.627097	−	0.301994i	−0.0932131	−	0.995646i	$-0.529714\pi$
$887$	1.30337e10	−	6.27670e9i	0.627097	−	0.301994i	0.720310	+	0.693652i	$0.243999\pi$
$888$	1.37261e9	−	1.27360e9i	0.0657813	−	0.0610361i
$889$	−1.47665e9	−	2.22569e8i	−0.0704890	−	0.0106245i
$890$	2.76545e9	+	3.69023e10i	0.131492	+	1.75464i
$891$	8.61477e9	+	2.19501e10i	0.408011	+	1.03959i
$892$	−1.81075e9	+	7.93343e9i	−0.0854245	+	0.374269i
$893$	−2.05141e8	+	2.73742e9i	−0.00963990	+	0.128636i
$894$	3.20488e9	−	9.88575e8i	0.150014	−	0.0462731i
$895$	2.28517e10	+	1.10048e10i	1.06546	+	0.513099i
$896$	2.12234e9	+	3.67600e9i	0.0985681	+	0.170725i
$897$	4.16939e8	−	7.22159e8i	0.0192885	−	0.0334087i
$898$	−1.94620e10	+	1.32690e10i	−0.896852	+	0.611463i
$899$	−1.08270e9	−	4.74363e9i	−0.0496993	−	0.217747i
$900$	3.01570e9	−	4.54544e8i	0.137892	−	0.0207839i
$901$	2.82721e8	−	3.54521e8i	0.0128772	−	0.0161475i
$902$	−6.07245e10			−2.75512
$903$	−2.62057e8	−	1.16864e9i	−0.0118437	−	0.0528170i
$904$	4.06157e9			0.182854
$905$	2.33695e10	−	2.93045e10i	1.04805	−	1.31421i
$906$	1.33492e10	−	2.01206e9i	0.596356	−	0.0898862i
$907$	1.67496e9	+	7.33846e9i	0.0745380	+	0.326572i	0.998426	−	0.0560916i	$-0.0178639\pi$
$907$	1.67496e9	+	7.33846e9i	0.0745380	+	0.326572i	−0.923888	+	0.382664i	$0.875007\pi$
$908$	5.17090e9	−	3.52546e9i	0.229227	−	0.156284i
$909$	−1.70926e10	+	2.96052e10i	−0.754804	+	1.30736i
$910$	6.47681e8	+	1.12182e9i	0.0284915	+	0.0493488i
$911$	1.12524e10	+	5.41887e9i	0.493095	+	0.237462i	0.663870	−	0.747848i	$-0.268913\pi$
$911$	1.12524e10	+	5.41887e9i	0.493095	+	0.237462i	−0.170775	+	0.985310i	$0.554627\pi$
$912$	−3.38590e9	+	1.04441e9i	−0.147806	+	0.0455922i
$913$	−1.66980e9	+	2.22819e10i	−0.0726132	+	0.968956i
$914$	7.76655e7	−	3.40275e8i	0.00336447	−	0.0147407i
$915$	−6.27372e9	−	1.59852e10i	−0.270739	−	0.689833i
$916$	6.14442e7	+	8.19916e8i	0.00264148	+	0.0352481i
$917$	−1.94994e9	−	2.93906e8i	−0.0835079	−	0.0125868i
$918$	−1.10681e9	+	1.02697e9i	−0.0472196	+	0.0438134i
$919$	2.49409e10	−	1.20109e10i	1.06001	−	0.510472i	0.179134	−	0.983825i	$-0.442671\pi$
$919$	2.49409e10	−	1.20109e10i	1.06001	−	0.510472i	0.880873	+	0.473352i	$0.156956\pi$
$920$	−1.14614e10	−	7.81425e9i	−0.485266	−	0.330849i
$921$	2.08959e9	−	5.32420e9i	0.0881360	−	0.224567i
$922$	−1.43846e10	−	4.43706e9i	−0.604421	−	0.186439i
$923$	−5.44048e9	−	5.04803e9i	−0.227736	−	0.211308i
$924$	2.60226e8	+	3.26313e8i	0.0108517	+	0.0136076i
$925$	−3.68681e9	−	4.62311e9i	−0.153163	−	0.192060i
$926$	−2.81790e10	−	2.61463e10i	−1.16624	−	1.08211i
$927$	1.76119e9	+	5.43256e8i	0.0726153	+	0.0223989i
$928$	3.35725e9	−	8.55413e9i	0.137900	−	0.351365i
$929$	−2.23870e10	−	1.52632e10i	−0.916098	−	0.624585i	0.0107827	−	0.999942i	$-0.496568\pi$
$929$	−2.23870e10	−	1.52632e10i	−0.916098	−	0.624585i	−0.926880	+	0.375357i	$0.877520\pi$
$930$	2.45357e9	−	1.18158e9i	0.100025	−	0.0481694i
$931$	−7.16054e9	+	6.64401e9i	−0.290819	+	0.269840i
$932$	−3.08906e9	−	4.65601e8i	−0.124989	−	0.0188390i
$933$	−3.81146e8	−	5.08604e9i	−0.0153640	−	0.205019i
$934$	−1.56057e10	−	3.97626e10i	−0.626713	−	1.59684i
$935$	1.14212e9	−	5.00396e9i	0.0456953	−	0.200204i
$936$	−3.45691e8	+	4.61293e9i	−0.0137792	+	0.183870i
$937$	4.68563e10	−	1.44532e10i	1.86071	−	0.573954i	0.863089	−	0.505052i	$-0.168527\pi$
$937$	4.68563e10	−	1.44532e10i	1.86071	−	0.573954i	0.997623	−	0.0689012i	$-0.0219493\pi$
$938$	−2.85540e9	−	1.37509e9i	−0.112969	−	0.0544028i
$939$	−1.03370e9	−	1.79042e9i	−0.0407442	−	0.0705710i
$940$	1.06962e9	−	1.85264e9i	0.0420032	−	0.0727516i
$941$	3.17801e10	−	2.16673e10i	1.24335	−	0.847698i	0.250618	−	0.968086i	$-0.419366\pi$
$941$	3.17801e10	−	2.16673e10i	1.24335	−	0.847698i	0.992727	+	0.120388i	$0.0384137\pi$
$942$	−1.68354e9	−	7.37609e9i	−0.0656215	−	0.287507i
$943$	−1.98475e10	+	2.99153e9i	−0.770753	+	0.116172i
$944$	1.11003e10	−	1.39193e10i	0.429469	−	0.538538i
$945$	3.55201e9			0.136919
$946$	−1.00902e10	−	4.49971e10i	−0.387508	−	1.72809i
$947$	2.50328e10			0.957820			0.478910	−	0.877864i	$-0.341032\pi$
$947$	2.50328e10			0.957820			0.478910	+	0.877864i	$0.341032\pi$
$948$	1.51207e9	−	1.89608e9i	0.0576425	−	0.0722814i
$949$	9.42772e9	−	1.42100e9i	0.358076	−	0.0539712i
$950$	2.06297e9	+	9.03848e9i	0.0780658	+	0.342029i
$951$	−5.99037e9	+	4.08416e9i	−0.225851	+	0.153982i
$952$	−1.83575e8	+	3.17961e8i	−0.00689579	+	0.0119439i
$953$	−2.15805e10	−	3.73786e10i	−0.807676	−	1.39894i	−0.914470	−	0.404654i	$-0.867392\pi$
$953$	−2.15805e10	−	3.73786e10i	−0.807676	−	1.39894i	0.106794	−	0.994281i	$-0.465941\pi$
$954$	5.13541e9	+	2.47308e9i	0.191494	+	0.0922188i
$955$	−3.70413e10	+	1.14257e10i	−1.37618	+	0.424494i
$956$	3.37128e8	−	4.49866e9i	0.0124793	−	0.166525i
$957$	−3.07359e9	+	1.34663e10i	−0.113358	+	0.496656i
$958$	−1.67568e8	−	4.26958e8i	−0.00615762	−	0.0156894i
$959$	2.00426e8	+	2.67449e9i	0.00733818	+	0.0979212i
$960$	−8.64962e9	−	1.30372e9i	−0.315535	−	0.0475593i
$961$	1.90829e10	−	1.77063e10i	0.693604	−	0.643571i
$962$	−2.00496e9	+	9.65536e8i	−0.0726093	+	0.0349668i
$963$	−1.11654e10	−	7.61245e9i	−0.402887	−	0.274683i
$964$	−1.23534e9	+	3.14759e9i	−0.0444136	+	0.113164i
$965$	2.25923e10	+	6.96880e9i	0.809310	+	0.249639i
$966$	6.09852e8	+	5.65860e8i	0.0217673	+	0.0201971i
$967$	2.31570e10	+	2.90379e10i	0.823548	+	1.03270i	0.998839	+	0.0481794i	$0.0153419\pi$
$967$	2.31570e10	+	2.90379e10i	0.823548	+	1.03270i	−0.175291	+	0.984517i	$0.556087\pi$
$968$	−2.49485e10	−	3.12844e10i	−0.884058	−	1.10857i
$969$	−2.63196e8	−	2.44210e8i	−0.00929278	−	0.00862244i
$970$	1.42020e10	+	4.38074e9i	0.499631	+	0.154116i
$971$	1.84310e10	−	4.69613e10i	0.646071	−	1.64616i	−0.111778	−	0.993733i	$-0.535654\pi$
$971$	1.84310e10	−	4.69613e10i	0.646071	−	1.64616i	0.757849	−	0.652430i	$-0.226250\pi$
$972$	−3.97400e9	−	2.70943e9i	−0.138802	−	0.0946337i
$973$	2.29226e9	−	1.10389e9i	0.0797753	−	0.0384177i
$974$	−4.51284e9	+	4.18730e9i	−0.156492	+	0.145204i
$975$	−1.73089e9	−	2.60890e8i	−0.0598072	−	0.00901449i
$976$	4.26603e9	+	5.69262e10i	0.146876	+	1.95992i
$977$	−1.10394e10	−	2.81280e10i	−0.378718	−	0.964957i	−0.985437	−	0.170041i	$-0.945610\pi$
$977$	−1.10394e10	−	2.81280e10i	−0.378718	−	0.964957i	0.606719	−	0.794916i	$-0.292485\pi$
$978$	−3.74188e9	+	1.63942e10i	−0.127910	+	0.560410i
$979$	−4.26805e9	+	5.69531e10i	−0.145375	+	1.93990i
$980$	7.27407e9	−	2.24375e9i	0.246880	−	0.0761525i
$981$	−2.67178e10	−	1.28666e10i	−0.903565	−	0.435134i
$982$	1.58243e10	+	2.74084e10i	0.533253	+	0.923622i
$983$	5.47096e9	−	9.47598e9i	0.183707	−	0.318190i	−0.759433	−	0.650586i	$-0.774524\pi$
$983$	5.47096e9	−	9.47598e9i	0.183707	−	0.318190i	0.943140	+	0.332395i	$0.107857\pi$
$984$	−1.10237e10	+	7.51583e9i	−0.368845	+	0.251475i
$985$	−1.12371e10	−	4.92331e10i	−0.374652	−	1.64146i
$986$	2.98104e9	−	4.49319e8i	0.0990372	−	0.0149274i
$987$	3.22403e8	−	4.04280e8i	0.0106731	−	0.0133836i
$988$	5.78560e8			0.0190853
$989$	−5.51467e9	−	1.42100e10i	−0.181273	−	0.467097i
$990$	6.45176e10			2.11327
$991$	1.41877e10	−	1.77909e10i	0.463079	−	0.580683i	−0.494382	−	0.869245i	$-0.664606\pi$
$991$	1.41877e10	−	1.77909e10i	0.463079	−	0.580683i	0.957461	+	0.288562i	$0.0931770\pi$
$992$	−2.76493e9	+	4.16747e8i	−0.0899278	+	0.0135544i
$993$	3.80655e9	+	1.66776e10i	0.123370	+	0.540520i
$994$	6.11780e9	−	4.17104e9i	0.197580	−	0.134708i
$995$	8.18012e8	−	1.41684e9i	0.0263256	−	0.0455973i
$996$	−6.09036e8	−	1.05488e9i	−0.0195315	−	0.0338295i
$997$	−3.51416e10	−	1.69233e10i	−1.12302	−	0.540819i	−0.222198	−	0.975002i	$-0.571323\pi$
$997$	−3.51416e10	−	1.69233e10i	−1.12302	−	0.540819i	−0.900825	+	0.434182i	$0.857037\pi$
$998$	−3.13130e10	+	9.65879e9i	−0.997167	+	0.307585i
$999$	−4.56010e8	+	6.08503e9i	−0.0144709	+	0.193101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.24.19	yes	300
43.9	even	21	inner	43.8.g.a.9.19	✓	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.19	✓	300	43.9	even	21	inner
43.8.g.a.24.19	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)

\(f(q)\)	\(=\)	\(q+(7.72335 - 9.68478i) q^{2} +(15.1267 - 2.27999i) q^{3} +(-5.66207 - 24.8071i) q^{4} +(-308.593 + 210.395i) q^{5} +(94.7479 - 164.108i) q^{6} +(75.0831 + 130.048i) q^{7} +(1144.57 + 551.196i) q^{8} +(-1866.22 + 575.652i) q^{9} +O(q^{10})\)	\(q+(7.72335 - 9.68478i) q^{2} +(15.1267 - 2.27999i) q^{3} +(-5.66207 - 24.8071i) q^{4} +(-308.593 + 210.395i) q^{5} +(94.7479 - 164.108i) q^{6} +(75.0831 + 130.048i) q^{7} +(1144.57 + 551.196i) q^{8} +(-1866.22 + 575.652i) q^{9} +(-345.743 + 4613.62i) q^{10} +(-1588.89 + 6961.36i) q^{11} +(-142.208 - 362.341i) q^{12} +(-139.334 - 1859.28i) q^{13} +(1839.38 + 277.241i) q^{14} +(-4188.31 + 3886.18i) q^{15} +(17112.6 - 8240.98i) q^{16} +(1590.17 + 1084.16i) q^{17} +(-8838.40 + 22519.9i) q^{18} +(-11653.2 - 3594.55i) q^{19} +(6966.58 + 6464.04i) q^{20} +(1432.27 + 1796.01i) q^{21} +(55147.7 + 69153.1i) q^{22} +(21431.5 + 19885.5i) q^{23} +(18570.3 + 5728.19i) q^{24} +(22421.4 - 57128.7i) q^{25} +(-19082.9 - 13010.5i) q^{26} +(-57059.9 + 27478.6i) q^{27} +(2800.98 - 2598.93i) q^{28} +(125041. + 18846.9i) q^{29} +(5289.03 + 70577.2i) q^{30} +(-14057.4 - 35817.8i) q^{31} +(16170.6 - 70848.0i) q^{32} +(-8162.82 + 108925. i) q^{33} +(22781.3 - 7027.11i) q^{34} +(-50531.6 - 24334.7i) q^{35} +(24846.9 + 43036.1i) q^{36} +(48175.6 - 83442.6i) q^{37} +(-124814. + 85097.0i) q^{38} +(-6346.80 - 27807.2i) q^{39} +(-469176. + 70716.9i) q^{40} +(-428051. + 536759. i) q^{41} +28455.8 q^{42} +(-468866. - 227997. i) q^{43} +181688. q^{44} +(454788. - 570286. i) q^{45} +(358110. - 53976.4i) q^{46} +(-50089.4 - 219456. i) q^{47} +(240068. - 163675. i) q^{48} +(400497. - 693680. i) q^{49} +(-380111. - 658371. i) q^{50} +(26526.0 + 12774.2i) q^{51} +(-45334.5 + 13983.9i) q^{52} +(17607.0 - 234949. i) q^{53} +(-174570. + 764840. i) q^{54} +(-974319. - 2.48252e6i) q^{55} +(14256.1 + 190234. i) q^{56} +(-184471. - 27804.5i) q^{57} +(1.14826e6 - 1.06543e6i) q^{58} +(844519. - 406699. i) q^{59} +(120119. + 81896.1i) q^{60} +(-1.09805e6 + 2.79778e6i) q^{61} +(-455458. - 140490. i) q^{62} +(-214984. - 199476. i) q^{63} +(954554. + 1.19697e6i) q^{64} +(434182. + 544447. i) q^{65} +(991872. + 920323. i) q^{66} +(-1.62807e6 - 502193. i) q^{67} +(17891.3 - 45586.2i) q^{68} +(369527. + 251939. i) q^{69} +(-625949. + 301441. i) q^{70} +(2.91794e6 - 2.70745e6i) q^{71} +(-2.45332e6 - 369778. i) q^{72} +(382137. + 5.09926e6i) q^{73} +(-436046. - 1.11103e6i) q^{74} +(208909. - 915291. i) q^{75} +(-23189.0 + 309436. i) q^{76} +(-1.02461e6 + 316050. i) q^{77} +(-318325. - 153297. i) q^{78} +(3.11520e6 + 5.39568e6i) q^{79} +(-3.54696e6 + 6.14352e6i) q^{80} +(2.72853e6 - 1.86028e6i) q^{81} +(1.89240e6 + 8.29115e6i) q^{82} +(3.09434e6 - 466397. i) q^{83} +(36444.2 - 45699.6i) q^{84} -718819. q^{85} +(-5.82933e6 + 2.77996e6i) q^{86} +1.93443e6 q^{87} +(-5.65567e6 + 7.09199e6i) q^{88} +(7.90923e6 - 1.19212e6i) q^{89} +(-2.01061e6 - 8.80904e6i) q^{90} +(231334. - 157721. i) q^{91} +(371957. - 644248. i) q^{92} +(-294307. - 509755. i) q^{93} +(-2.51224e6 - 1.20983e6i) q^{94} +(4.35239e6 - 1.34253e6i) q^{95} +(83075.6 - 1.10857e6i) q^{96} +(714825. - 3.13185e6i) q^{97} +(-3.62496e6 - 9.23626e6i) q^{98} +(-1.04212e6 - 1.39061e7i) 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

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