LMFDB - Embedded newform 43.8.g.a.10.19

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			10.19
Character	$\chi$	$=$	43.10
Dual form			43.8.g.a.13.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.55655 + 11.2010i) q^{2} +(-51.6901 - 47.9614i) q^{3} +(-3.60209 + 1.73467i) q^{4} +(81.6402 - 12.3053i) q^{5} +(405.067 - 701.596i) q^{6} +(118.589 + 205.402i) q^{7} +(888.263 + 1113.85i) q^{8} +(208.136 + 2777.38i) q^{9} +O(q^{10})$	\(q+(2.55655 + 11.2010i) q^{2} +(-51.6901 - 47.9614i) q^{3} +(-3.60209 + 1.73467i) q^{4} +(81.6402 - 12.3053i) q^{5} +(405.067 - 701.596i) q^{6} +(118.589 + 205.402i) q^{7} +(888.263 + 1113.85i) q^{8} +(208.136 + 2777.38i) q^{9} +(346.549 + 882.992i) q^{10} +(-7767.94 - 3740.84i) q^{11} +(269.390 + 83.0957i) q^{12} +(-712.607 + 1815.69i) q^{13} +(-1997.53 + 1853.43i) q^{14} +(-4810.17 - 3279.52i) q^{15} +(-10524.4 + 13197.1i) q^{16} +(-20556.0 - 3098.32i) q^{17} +(-30577.3 + 9431.85i) q^{18} +(-2908.89 + 38816.4i) q^{19} +(-272.729 + 185.944i) q^{20} +(3721.50 - 16305.0i) q^{21} +(22042.0 - 96572.3i) q^{22} +(21624.4 - 14743.2i) q^{23} +(7507.25 - 100177. i) q^{24} +(-68140.4 + 21018.5i) q^{25} +(-22159.4 - 3339.99i) q^{26} +(26298.2 - 32976.9i) q^{27} +(-783.473 - 534.163i) q^{28} +(-18691.1 + 17342.8i) q^{29} +(24436.4 - 62262.9i) q^{30} +(-219147. - 67597.8i) q^{31} +(-10429.0 - 5022.33i) q^{32} +(222110. + 565926. i) q^{33} +(-17848.3 - 238169. i) q^{34} +(12209.2 + 15309.8i) q^{35} +(-5567.57 - 9643.32i) q^{36} +(-180614. + 312833. i) q^{37} +(-442219. + 66653.7i) q^{38} +(123918. - 59675.8i) q^{39} +(86224.2 + 80004.4i) q^{40} +(105844. + 463733. i) q^{41} +192146. q^{42} +(-129103. - 505125. i) q^{43} +34469.9 q^{44} +(51168.7 + 224185. i) q^{45} +(220423. + 204522. i) q^{46} +(555918. - 267716. i) q^{47} +(1.17696e6 - 177398. i) q^{48} +(383645. - 664492. i) q^{49} +(-409633. - 709505. i) q^{50} +(913944. + 1.14605e6i) q^{51} +(-582.763 - 7776.43i) q^{52} +(14691.7 + 37433.8i) q^{53} +(436607. + 210259. i) q^{54} +(-680209. - 209817. i) q^{55} +(-123448. + 314541. i) q^{56} +(2.01205e6 - 1.86691e6i) q^{57} +(-242041. - 165021. i) q^{58} +(502817. - 630512. i) q^{59} +(23015.5 + 3469.04i) q^{60} +(-527624. + 162751. i) q^{61} +(196902. - 2.62748e6i) q^{62} +(-545797. + 372118. i) q^{63} +(-451188. + 1.97678e6i) q^{64} +(-35834.8 + 157002. i) q^{65} +(-5.77110e6 + 3.93467e6i) q^{66} +(131806. - 1.75883e6i) q^{67} +(79419.1 - 24497.6i) q^{68} +(-1.82487e6 - 275055. i) q^{69} +(-140271. + 175895. i) q^{70} +(2.82904e6 + 1.92881e6i) q^{71} +(-2.90870e6 + 2.69888e6i) q^{72} +(-423811. + 1.07985e6i) q^{73} +(-3.96579e6 - 1.22328e6i) q^{74} +(4.53027e6 + 2.18166e6i) q^{75} +(-56855.7 - 144866. i) q^{76} +(-152815. - 2.03917e6i) q^{77} +(985231. + 1.23544e6i) q^{78} +(-2.70131e6 - 4.67880e6i) q^{79} +(-696817. + 1.20692e6i) q^{80} +(3.08215e6 - 464560. i) q^{81} +(-4.92367e6 + 2.37111e6i) q^{82} +(-2.84191e6 - 2.63691e6i) q^{83} +(14878.6 + 65187.4i) q^{84} -1.71632e6 q^{85} +(5.32784e6 - 2.73746e6i) q^{86} +1.79793e6 q^{87} +(-2.73325e6 - 1.19752e7i) q^{88} +(-1.63318e6 - 1.51537e6i) q^{89} +(-2.38028e6 + 1.14628e6i) q^{90} +(-457455. + 68950.2i) q^{91} +(-52318.1 + 90617.6i) q^{92} +(8.08564e6 + 1.40047e7i) q^{93} +(4.41992e6 + 5.54240e6i) q^{94} +(240165. + 3.20477e6i) q^{95} +(298197. + 759794. i) q^{96} +(-1.20118e7 - 5.78460e6i) q^{97} +(8.42378e6 + 2.59839e6i) q^{98} +(8.77296e6 - 2.23531e7i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{21}\right)$

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 $

$2$	2.55655	+	11.2010i	0.225969	+	0.990037i	0.952890	+	0.303315i	$0.0980935\pi$
$2$	2.55655	+	11.2010i	0.225969	+	0.990037i	−0.726921	+	0.686721i	$0.759049\pi$
$3$	−51.6901	−	47.9614i	−1.10531	−	1.02558i	−0.999514	−	0.0311878i	$-0.990071\pi$
$3$	−51.6901	−	47.9614i	−1.10531	−	1.02558i	−0.105794	−	0.994388i	$-0.533739\pi$
$4$	−3.60209	+	1.73467i	−0.0281413	+	0.0135521i
$5$	81.6402	−	12.3053i	0.292085	−	0.0440247i	−0.00136533	−	0.999999i	$-0.500435\pi$
$5$	81.6402	−	12.3053i	0.292085	−	0.0440247i	0.293450	+	0.955974i	$0.405197\pi$
$6$	405.067	−	701.596i	0.765592	−	1.32604i
$7$	118.589	+	205.402i	0.130678	+	0.226340i	0.923938	−	0.382542i	$-0.124951\pi$
$7$	118.589	+	205.402i	0.130678	+	0.226340i	−0.793260	+	0.608883i	$0.791618\pi$
$8$	888.263	+	1113.85i	0.613376	+	0.769149i
$9$	208.136	+	2777.38i	0.0951696	+	1.26995i
$10$	346.549	+	882.992i	0.109588	+	0.279226i
$11$	−7767.94	−	3740.84i	−1.75967	−	0.847413i	−0.973259	−	0.229712i	$-0.926222\pi$
$11$	−7767.94	−	3740.84i	−1.75967	−	0.847413i	−0.786413	−	0.617701i	$-0.788064\pi$
$12$	269.390	+	83.0957i	0.0450035	+	0.0138818i
$13$	−712.607	+	1815.69i	−0.0899598	+	0.229214i	−0.968772	−	0.247955i	$-0.920242\pi$
$13$	−712.607	+	1815.69i	−0.0899598	+	0.229214i	0.878812	+	0.477168i	$0.158337\pi$
$14$	−1997.53	+	1853.43i	−0.194556	+	0.180521i
$15$	−4810.17	−	3279.52i	−0.367994	−	0.250894i
$16$	−10524.4	+	13197.1i	−0.642356	+	0.805489i
$17$	−20556.0	−	3098.32i	−1.01477	−	0.152952i	−0.379460	−	0.925208i	$-0.623890\pi$
$17$	−20556.0	−	3098.32i	−1.01477	−	0.152952i	−0.635311	+	0.772256i	$0.719128\pi$
$18$	−30577.3	+	9431.85i	−1.23579	+	0.381191i
$19$	−2908.89	+	38816.4i	−0.0972947	+	1.29831i	0.708330	+	0.705881i	$0.249449\pi$
$19$	−2908.89	+	38816.4i	−0.0972947	+	1.29831i	−0.805625	+	0.592426i	$0.798170\pi$
$20$	−272.729	+	185.944i	−0.00762302	+	0.00519729i
$21$	3721.50	−	16305.0i	0.0876901	−	0.384195i
$22$	22042.0	−	96572.3i	0.441338	−	1.93363i
$23$	21624.4	−	14743.2i	0.370592	−	0.252665i	−0.363675	−	0.931526i	$-0.618478\pi$
$23$	21624.4	−	14743.2i	0.370592	−	0.252665i	0.734267	+	0.678861i	$0.237526\pi$
$24$	7507.25	−	100177.i	0.110851	−	1.47921i
$25$	−68140.4	+	21018.5i	−0.872197	+	0.269037i
$26$	−22159.4	−	3339.99i	−0.247258	−	0.0372682i
$27$	26298.2	−	32976.9i	0.257130	−	0.322431i
$28$	−783.473	−	534.163i	−0.00674483	−	0.00459855i
$29$	−18691.1	+	17342.8i	−0.142312	+	0.132046i	−0.748117	−	0.663567i	$-0.769042\pi$
$29$	−18691.1	+	17342.8i	−0.142312	+	0.132046i	0.605805	+	0.795613i	$0.292851\pi$
$30$	24436.4	−	62262.9i	0.165239	−	0.421022i
$31$	−219147.	−	67597.8i	−1.32120	−	0.407537i	−0.447624	−	0.894222i	$-0.647730\pi$
$31$	−219147.	−	67597.8i	−1.32120	−	0.407537i	−0.873578	+	0.486685i	$0.838206\pi$
$32$	−10429.0	−	5022.33i	−0.0562622	−	0.0270945i
$33$	222110.	+	565926.i	1.07589	+	2.74133i
$34$	−17848.3	−	238169.i	−0.0778790	−	1.03922i
$35$	12209.2	+	15309.8i	0.0481335	+	0.0603575i
$36$	−5567.57	−	9643.32i	−0.0198887	−	0.0344483i
$37$	−180614.	+	312833.i	−0.586200	+	1.01533i	0.408524	+	0.912747i	$0.366043\pi$
$37$	−180614.	+	312833.i	−0.586200	+	1.01533i	−0.994725	+	0.102581i	$0.967290\pi$
$38$	−442219.	+	66653.7i	−1.30736	+	0.197052i
$39$	123918.	−	59675.8i	0.334510	−	0.161091i
$40$	86224.2	+	80004.4i	0.213019	+	0.197653i
$41$	105844.	+	463733.i	0.239840	+	1.05081i	0.941160	+	0.337962i	$0.109738\pi$
$41$	105844.	+	463733.i	0.239840	+	1.05081i	−0.701319	+	0.712847i	$0.747405\pi$
$42$	192146.			0.400183
$43$	−129103.	−	505125.i	−0.247626	−	0.968856i
$43$	−129103.	−	505125.i	−0.247626	−	0.968856i
$44$	34469.9			0.0610037
$45$	51168.7	+	224185.i	0.0837068	+	0.366743i
$46$	220423.	+	204522.i	0.333890	+	0.309805i
$47$	555918.	−	267716.i	0.781031	−	0.376125i	−0.000492857	−	1.00000i	$-0.500157\pi$
$47$	555918.	−	267716.i	0.781031	−	0.376125i	0.781524	+	0.623875i	$0.214443\pi$
$48$	1.17696e6	−	177398.i	1.53609	−	0.231528i
$49$	383645.	−	664492.i	0.465847	−	0.806870i
$50$	−409633.	−	709505.i	−0.463447	−	0.802713i
$51$	913944.	+	1.14605e6i	0.964770	+	1.20978i
$52$	−582.763	−	7776.43i	−0.000574751	−	0.00766952i
$53$	14691.7	+	37433.8i	0.0135552	+	0.0345381i	0.937491	−	0.348009i	$-0.113142\pi$
$53$	14691.7	+	37433.8i	0.0135552	+	0.0345381i	−0.923936	+	0.382547i	$0.875047\pi$
$54$	436607.	+	210259.i	0.377322	+	0.181709i
$55$	−680209.	−	209817.i	−0.551281	−	0.170048i
$56$	−123448.	+	314541.i	−0.0939349	+	0.239342i
$57$	2.01205e6	−	1.86691e6i	1.43905	−	1.33525i
$58$	−242041.	−	165021.i	−0.162889	−	0.111056i
$59$	502817.	−	630512.i	0.318734	−	0.399679i	−0.596493	−	0.802618i	$-0.703440\pi$
$59$	502817.	−	630512.i	0.318734	−	0.399679i	0.915227	+	0.402939i	$0.132011\pi$
$60$	23015.5	+	3469.04i	0.0137560	+	0.00207338i
$61$	−527624.	+	162751.i	−0.297626	+	0.0918054i	−0.439972	−	0.898012i	$-0.645012\pi$
$61$	−527624.	+	162751.i	−0.297626	+	0.0918054i	0.142346	+	0.989817i	$0.454535\pi$
$62$	196902.	−	2.62748e6i	0.104925	−	1.40013i
$63$	−545797.	+	372118.i	−0.275004	+	0.187495i
$64$	−451188.	+	1.97678e6i	−0.215143	+	0.942604i
$65$	−35834.8	+	157002.i	−0.0161848	+	0.0709104i
$66$	−5.77110e6	+	3.93467e6i	−2.47090	+	1.68463i
$67$	131806.	−	1.75883e6i	0.0535394	−	0.714434i	−0.904257	−	0.426988i	$-0.859575\pi$
$67$	131806.	−	1.75883e6i	0.0535394	−	0.714434i	0.957797	−	0.287446i	$-0.0928062\pi$
$68$	79419.1	−	24497.6i	0.0306298	−	0.00944804i
$69$	−1.82487e6	−	275055.i	−0.668745	−	0.100797i
$70$	−140271.	+	175895.i	−0.0488794	+	0.0612929i
$71$	2.82904e6	+	1.92881e6i	0.938070	+	0.639565i	0.932790	−	0.360421i	$-0.117367\pi$
$71$	2.82904e6	+	1.92881e6i	0.938070	+	0.639565i	0.00527997	+	0.999986i	$0.498319\pi$
$72$	−2.90870e6	+	2.69888e6i	−0.918406	+	0.852157i
$73$	−423811.	+	1.07985e6i	−0.127509	+	0.324889i	−0.980345	−	0.197291i	$-0.936786\pi$
$73$	−423811.	+	1.07985e6i	−0.127509	+	0.324889i	0.852836	+	0.522180i	$0.174881\pi$
$74$	−3.96579e6	−	1.22328e6i	−1.13768	−	0.350926i
$75$	4.53027e6	+	2.18166e6i	1.23996	+	0.597136i
$76$	−56855.7	−	144866.i	−0.0148568	−	0.0378546i
$77$	−152815.	−	2.03917e6i	−0.0381459	−	0.509022i
$78$	985231.	+	1.23544e6i	0.235075	+	0.294775i
$79$	−2.70131e6	−	4.67880e6i	−0.616423	−	1.06768i	−0.990133	−	0.140131i	$-0.955248\pi$
$79$	−2.70131e6	−	4.67880e6i	−0.616423	−	1.06768i	0.373710	−	0.927546i	$-0.378086\pi$
$80$	−696817.	+	1.20692e6i	−0.152161	+	0.263551i
$81$	3.08215e6	−	464560.i	0.644402	−	0.0971279i
$82$	−4.92367e6	+	2.37111e6i	−0.986143	+	0.474902i
$83$	−2.84191e6	−	2.63691e6i	−0.545554	−	0.506200i	0.358551	−	0.933510i	$-0.383271\pi$
$83$	−2.84191e6	−	2.63691e6i	−0.545554	−	0.506200i	−0.904105	+	0.427310i	$0.859461\pi$
$84$	14878.6	+	65187.4i	0.00273895	+	0.0120001i
$85$	−1.71632e6			−0.303133
$86$	5.32784e6	−	2.73746e6i	0.903247	−	0.464091i
$87$	1.79793e6			0.292722
$88$	−2.73325e6	−	1.19752e7i	−0.427553	−	1.87323i
$89$	−1.63318e6	−	1.51537e6i	−0.245567	−	0.227853i	0.547780	−	0.836622i	$-0.315473\pi$
$89$	−1.63318e6	−	1.51537e6i	−0.245567	−	0.227853i	−0.793347	+	0.608769i	$0.791663\pi$
$90$	−2.38028e6	+	1.14628e6i	−0.344174	+	0.165746i
$91$	−457455.	+	68950.2i	−0.0636360	+	0.00959159i
$92$	−52318.1	+	90617.6i	−0.00700478	+	0.0121326i
$93$	8.08564e6	+	1.40047e7i	1.04237	+	1.80545i
$94$	4.41992e6	+	5.54240e6i	0.548866	+	0.688257i
$95$	240165.	+	3.20477e6i	0.0287393	+	0.383499i
$96$	298197.	+	759794.i	0.0343996	+	0.0876489i
$97$	−1.20118e7	−	5.78460e6i	−1.33631	−	0.643535i	−0.377089	−	0.926177i	$-0.623075\pi$
$97$	−1.20118e7	−	5.78460e6i	−1.33631	−	0.643535i	−0.959225	+	0.282642i	$0.908789\pi$
$98$	8.42378e6	+	2.59839e6i	0.904098	+	0.278877i
$99$	8.77296e6	−	2.23531e7i	0.908705	−	2.31534i
$100$	208987.	−	193912.i	0.0208987	−	0.0193912i
$101$	1.00875e7	+	6.87757e6i	0.974228	+	0.664217i	0.942123	−	0.335267i	$-0.108827\pi$
$101$	1.00875e7	+	6.87757e6i	0.974228	+	0.664217i	0.0321049	+	0.999485i	$0.489779\pi$
$102$	−1.05003e7	+	1.31670e7i	−0.979721	+	1.22853i
$103$	−1.40256e7	−	2.11402e6i	−1.26471	−	0.190624i	−0.517772	−	0.855519i	$-0.673238\pi$
$103$	−1.40256e7	−	2.11402e6i	−1.26471	−	0.190624i	−0.746937	+	0.664895i	$0.768476\pi$
$104$	−2.65539e6	+	819079.i	−0.231479	+	0.0714018i
$105$	103187.	−	1.37693e6i	0.00869886	−	0.116078i
$106$	−381735.	+	260263.i	−0.0311309	+	0.0212247i
$107$	1.44632e6	−	6.33676e6i	0.114136	−	0.500062i	−0.885253	−	0.465110i	$-0.846015\pi$
$107$	1.44632e6	−	6.33676e6i	0.114136	−	0.500062i	0.999389	−	0.0349526i	$-0.0111280\pi$
$108$	−37524.2	+	164404.i	−0.00286635	+	0.0125583i
$109$	−7.26694e6	+	4.95451e6i	−0.537475	+	0.366445i	−0.801428	−	0.598091i	$-0.795926\pi$
$109$	−7.26694e6	+	4.95451e6i	−0.537475	+	0.366445i	0.263953	+	0.964536i	$0.414974\pi$
$110$	611164.	−	8.15541e6i	0.0437807	−	0.584213i
$111$	2.43399e7	−	7.50786e6i	1.68923	−	0.521058i
$112$	−3.95879e6	−	596692.i	−0.266256	−	0.0401316i
$113$	4.29224e6	−	5.38230e6i	0.279840	−	0.350908i	−0.621970	−	0.783041i	$-0.713668\pi$
$113$	4.29224e6	−	5.38230e6i	0.279840	−	0.350908i	0.901810	+	0.432133i	$0.142239\pi$
$114$	2.60551e7	+	1.77641e7i	1.64712	+	1.12299i
$115$	1.58400e6	−	1.46973e6i	0.0971208	−	0.0901149i
$116$	37242.9	−	94893.3i	0.00221534	−	0.00564459i
$117$	−5.19119e6	−	1.60127e6i	−0.299652	−	0.0924303i
$118$	8.34784e6	+	4.02011e6i	0.467721	+	0.225243i
$119$	−1.80132e6	−	4.58968e6i	−0.0979885	−	0.249671i
$120$	−619816.	−	8.27087e6i	−0.0327438	−	0.436935i
$121$	3.41970e7	+	4.28816e7i	1.75484	+	2.20051i
$122$	−3.17187e6	−	5.49383e6i	−0.158145	−	0.273915i
$123$	1.67702e7	−	2.90468e7i	0.812587	−	1.40744i
$124$	906646.	−	136655.i	0.0427033	−	0.00643649i
$125$	−1.11158e7	+	5.35308e6i	−0.509043	+	0.245142i
$126$	−5.56345e6	−	5.16213e6i	−0.247769	−	0.229896i
$127$	7.25984e6	+	3.18074e7i	0.314495	+	1.37789i	0.847057	+	0.531502i	$0.178372\pi$
$127$	7.25984e6	+	3.18074e7i	0.314495	+	1.37789i	−0.532562	+	0.846391i	$0.678771\pi$
$128$	−2.47770e7			−1.04427
$129$	−1.75532e7	+	3.23019e7i	−0.719932	+	1.32484i
$130$	−1.85020e6			−0.0738611
$131$	−3.27964e6	−	1.43690e7i	−0.127461	−	0.558442i	−0.997818	−	0.0660217i	$-0.978969\pi$
$131$	−3.27964e6	−	1.43690e7i	−0.127461	−	0.558442i	0.870357	−	0.492421i	$-0.163888\pi$
$132$	−1.78176e6	−	1.65323e6i	−0.0674279	−	0.0625639i
$133$	−8.31793e6	+	4.00570e6i	−0.306573	+	0.147638i
$134$	2.00376e7	−	3.02018e6i	0.719414	−	0.108434i
$135$	1.74120e6	−	3.01585e6i	0.0609089	−	0.105497i
$136$	−1.48081e7	−	2.56484e7i	−0.504793	−	0.874327i
$137$	2.54746e7	+	3.19442e7i	0.846420	+	1.06138i	0.997344	+	0.0728322i	$0.0232038\pi$
$137$	2.54746e7	+	3.19442e7i	0.846420	+	1.06138i	−0.150924	+	0.988545i	$0.548225\pi$
$138$	−1.58449e6	−	2.11436e7i	−0.0513231	−	0.684859i
$139$	−1.18617e7	−	3.02232e7i	−0.374624	−	0.954527i	−0.986528	−	0.163594i	$-0.947691\pi$
$139$	−1.18617e7	−	3.02232e7i	−0.374624	−	0.954527i	0.611903	−	0.790932i	$-0.290404\pi$
$140$	−70535.9	−	33968.3i	−0.00217251	−	0.00104623i
$141$	−4.15755e7	−	1.28244e7i	−1.24902	−	0.385273i
$142$	−1.43720e7	+	3.66191e7i	−0.421218	+	1.07325i
$143$	1.23277e7	−	1.14385e7i	0.352539	−	0.327108i
$144$	−3.88440e7	−	2.64834e7i	−1.08406	−	0.739102i
$145$	−1.31254e6	+	1.64587e6i	−0.0357539	+	0.0448340i
$146$	−1.31789e7	−	1.98640e6i	−0.350465	−	0.0528241i
$147$	−5.17007e7	+	1.59475e7i	−1.34241	+	0.414079i
$148$	107925.	−	1.44016e6i	0.00273656	−	0.0365169i
$149$	5.98526e7	−	4.08068e7i	1.48228	−	1.01060i	0.492144	−	0.870514i	$-0.336213\pi$
$149$	5.98526e7	−	4.08068e7i	1.48228	−	1.01060i	0.990139	−	0.140090i	$-0.0447392\pi$
$150$	−1.28549e7	+	5.63210e7i	−0.310992	+	1.36254i
$151$	−5.41988e6	+	2.37461e7i	−0.128106	+	0.561270i	0.869611	+	0.493738i	$0.164370\pi$
$151$	−5.41988e6	+	2.37461e7i	−0.128106	+	0.561270i	−0.997717	+	0.0675325i	$0.978487\pi$
$152$	−4.58194e7	+	3.12391e7i	−1.05827	+	0.721516i
$153$	4.32677e6	−	5.77368e7i	0.0976662	−	1.30326i
$154$	2.24501e7	−	6.92493e6i	0.495331	−	0.152789i
$155$	−1.87230e7	−	2.82204e6i	−0.403845	−	0.0608698i
$156$	−342845.	+	429915.i	−0.00723040	+	0.00906663i
$157$	−3.68512e7	−	2.51247e7i	−0.759982	−	0.518147i	0.120220	−	0.992747i	$-0.461640\pi$
$157$	−3.68512e7	−	2.51247e7i	−0.759982	−	0.518147i	−0.880201	+	0.474601i	$0.842593\pi$
$158$	4.55011e7	−	4.22189e7i	0.917746	−	0.851544i
$159$	1.03596e6	−	2.63959e6i	0.0204388	−	0.0520771i
$160$	−913225.	−	281693.i	−0.0176262	−	0.00543695i
$161$	5.59270e6	+	2.69330e6i	0.105616	+	0.0508621i
$162$	1.30832e7	+	3.33355e7i	0.241775	+	0.616033i
$163$	−2.49762e6	−	3.33284e7i	−0.0451720	−	0.602778i	−0.973154	−	0.230154i	$-0.926077\pi$
$163$	−2.49762e6	−	3.33284e7i	−0.0451720	−	0.602778i	0.927982	−	0.372624i	$-0.121542\pi$
$164$	−1.18568e6	−	1.48680e6i	−0.0209901	−	0.0263208i
$165$	2.50970e7	+	4.34692e7i	0.434938	+	0.753335i
$166$	2.22705e7	−	3.85736e7i	0.377878	−	0.654504i
$167$	2.82740e7	−	4.26162e6i	0.469764	−	0.0708056i	0.0901057	−	0.995932i	$-0.471280\pi$
$167$	2.82740e7	−	4.26162e6i	0.469764	−	0.0708056i	0.379659	+	0.925127i	$0.376041\pi$
$168$	2.14669e7	−	1.03379e7i	0.349290	−	0.168209i
$169$	4.32090e7	+	4.00921e7i	0.688606	+	0.638933i
$170$	−4.38787e6	−	1.92245e7i	−0.0684987	−	0.300113i
$171$	−1.08413e8			−1.65805
$172$	1.34127e6	+	1.59555e6i	0.0200986	+	0.0239090i
$173$	−7.67577e7			−1.12709			−0.563547	−	0.826084i	$-0.690564\pi$
$173$	−7.67577e7			−1.12709			−0.563547	+	0.826084i	$0.690564\pi$
$174$	4.59651e6	+	2.01386e7i	0.0661463	+	0.289806i
$175$	−1.23979e7	−	1.15036e7i	−0.174871	−	0.162256i
$176$	1.31121e8	−	6.31446e7i	1.81292	−	0.873055i
$177$	−5.62310e7	+	8.47545e6i	−0.762200	+	0.114883i
$178$	1.27984e7	−	2.21674e7i	0.170092	−	0.294608i
$179$	−2.09341e7	−	3.62590e7i	−0.272815	−	0.472530i	0.696766	−	0.717298i	$-0.254622\pi$
$179$	−2.09341e7	−	3.62590e7i	−0.272815	−	0.472530i	−0.969582	+	0.244768i	$0.921288\pi$
$180$	−573201.	−	718772.i	−0.00732577	−	0.00918623i
$181$	2.26379e6	+	3.02082e7i	0.0283767	+	0.378661i	0.993254	+	0.115960i	$0.0369943\pi$
$181$	2.26379e6	+	3.02082e7i	0.0283767	+	0.378661i	−0.964877	+	0.262701i	$0.915387\pi$
$182$	−1.94182e6	−	4.94767e6i	−0.0238758	−	0.0608346i
$183$	3.50787e7	+	1.68930e7i	0.423121	+	0.203765i
$184$	3.56298e7	+	1.09903e7i	0.421649	+	0.130062i
$185$	−1.08959e7	+	2.77623e7i	−0.126521	+	0.322369i
$186$	−1.36195e8	+	1.26371e8i	−1.55191	+	1.43996i
$187$	1.48088e8	+	1.00964e8i	1.65605	+	1.12908i
$188$	−1.53807e6	+	1.92867e6i	−0.0168819	+	0.0211693i
$189$	9.89220e6	+	1.49101e6i	0.106580	+	0.0160644i
$190$	−3.52826e7	+	1.08832e7i	−0.373184	+	0.115112i
$191$	−7.95101e6	+	1.06099e8i	−0.0825668	+	1.10178i	0.789943	+	0.613180i	$0.210110\pi$
$191$	−7.95101e6	+	1.06099e8i	−0.0825668	+	1.10178i	−0.872510	+	0.488597i	$0.837509\pi$
$192$	1.18131e8	−	8.05406e7i	1.20451	−	0.821222i
$193$	−3.40483e7	+	1.49175e8i	−0.340914	+	1.49364i	0.456234	+	0.889860i	$0.349198\pi$
$193$	−3.40483e7	+	1.49175e8i	−0.340914	+	1.49364i	−0.797149	+	0.603783i	$0.793659\pi$
$194$	3.40843e7	−	1.49333e8i	0.335157	−	1.46842i
$195$	9.38237e6	−	6.39679e6i	0.0906132	−	0.0617790i
$196$	−229245.	+	3.05906e6i	−0.00217472	+	0.0290196i
$197$	−1.58062e8	+	4.87557e7i	−1.47298	+	0.454353i	−0.924295	−	0.381678i	$-0.875346\pi$
$197$	−1.58062e8	+	4.87557e7i	−1.47298	+	0.454353i	−0.548681	+	0.836032i	$0.684870\pi$
$198$	2.72806e8	+	4.11188e7i	2.49761	+	0.376455i
$199$	−4.06713e6	+	5.10002e6i	−0.0365849	+	0.0458761i	−0.799787	−	0.600283i	$-0.795054\pi$
$199$	−4.06713e6	+	5.10002e6i	−0.0365849	+	0.0458761i	0.763202	+	0.646159i	$0.223626\pi$
$200$	−8.39381e7	−	5.72280e7i	−0.741915	−	0.505829i
$201$	−9.11691e7	+	8.45926e7i	−0.791884	+	0.734761i
$202$	−5.12462e7	+	1.30573e8i	−0.437454	+	1.11461i
$203$	−5.77881e6	−	1.78253e6i	−0.0484844	−	0.0149555i
$204$	−5.28012e6	−	2.54277e6i	−0.0435450	−	0.0209702i
$205$	1.43475e7	+	3.65568e7i	0.116315	+	0.296367i
$206$	−1.21781e7	−	1.62505e8i	−0.0970606	−	1.29518i
$207$	4.54484e7	+	5.69905e7i	0.356141	+	0.446587i
$208$	−1.64622e7	−	2.85134e7i	−0.126843	−	0.219699i
$209$	1.67802e8	−	2.90642e8i	1.27141	−	2.20215i
$210$	1.56868e7	−	2.36441e6i	0.116887	−	0.0176179i
$211$	1.63428e8	−	7.87030e7i	1.19767	−	0.576770i	0.274663	−	0.961541i	$-0.411434\pi$
$211$	1.63428e8	−	7.87030e7i	1.19767	−	0.576770i	0.923012	+	0.384771i	$0.125719\pi$
$212$	−117856.	−	109354.i	−0.000849526	−	0.000788245i
$213$	−5.37251e7	−	2.35385e8i	−0.380933	−	1.66898i
$214$	7.46756e7			0.520871
$215$	−1.67557e7	−	3.96498e7i	−0.114981	−	0.272086i
$216$	6.00910e7			0.405715
$217$	−1.21036e7	−	5.30296e7i	−0.0804095	−	0.352297i
$218$	−7.40737e7	−	6.87304e7i	−0.484247	−	0.449315i
$219$	7.36981e7	−	3.54912e7i	0.474135	−	0.228331i
$220$	2.81413e6	−	424162.i	0.0178183	−	0.00268567i
$221$	2.02740e7	−	3.51156e7i	0.126347	−	0.218840i
$222$	1.46322e8	+	2.53437e8i	0.897580	+	1.55465i
$223$	8.33512e7	+	1.04519e8i	0.503321	+	0.631144i	0.966975	−	0.254872i	$-0.0820333\pi$
$223$	8.33512e7	+	1.04519e8i	0.503321	+	0.631144i	−0.463654	+	0.886016i	$0.653462\pi$
$224$	−205164.	−	2.73773e6i	−0.00121965	−	0.0162750i
$225$	−7.25590e7	−	1.84877e8i	−0.424671	−	1.08204i
$226$	7.12603e7	+	3.43172e7i	0.410647	+	0.197757i
$227$	−2.12146e8	−	6.54384e7i	−1.20377	−	0.371315i	−0.372950	−	0.927851i	$-0.621654\pi$
$227$	−2.12146e8	−	6.54384e7i	−1.20377	−	0.371315i	−0.830823	+	0.556537i	$0.812130\pi$
$228$	−4.00910e6	+	1.02150e7i	−0.0224014	+	0.0570778i
$229$	−1.03332e8	+	9.58780e7i	−0.568604	+	0.527588i	−0.911237	−	0.411882i	$-0.864872\pi$
$229$	−1.03332e8	+	9.58780e7i	−0.568604	+	0.527588i	0.342633	+	0.939469i	$0.388681\pi$
$230$	2.05120e7	+	1.39849e7i	0.111163	+	0.0757899i
$231$	−8.99027e7	+	1.12734e8i	−0.479878	+	0.601748i
$232$	−3.59199e7	−	5.41405e6i	−0.188854	−	0.0284652i
$233$	8.59538e7	−	2.65132e7i	0.445163	−	0.137315i	−0.0640658	−	0.997946i	$-0.520407\pi$
$233$	8.59538e7	−	2.65132e7i	0.445163	−	0.137315i	0.509229	+	0.860631i	$0.329931\pi$
$234$	4.66426e6	−	6.22402e7i	0.0237973	−	0.317552i
$235$	4.20910e7	−	2.86971e7i	0.211569	−	0.144245i
$236$	−717457.	+	3.14338e6i	−0.00355307	+	0.0155670i
$237$	−8.47711e7	+	3.71406e8i	−0.413646	+	1.81230i
$238$	4.68037e7	−	3.19102e7i	0.225041	−	0.153430i
$239$	1.36369e7	−	1.81971e8i	0.0646132	−	0.862204i	−0.866897	−	0.498488i	$-0.833889\pi$
$239$	1.36369e7	−	1.81971e8i	0.0646132	−	0.862204i	0.931510	−	0.363716i	$-0.118492\pi$
$240$	9.39042e7	−	2.89656e7i	0.438476	−	0.135252i
$241$	−1.61377e8	−	2.43236e7i	−0.742644	−	0.111936i	−0.233188	−	0.972432i	$-0.574916\pi$
$241$	−1.61377e8	−	2.43236e7i	−0.742644	−	0.111936i	−0.509457	+	0.860496i	$0.670154\pi$
$242$	−3.92890e8	+	4.92669e8i	−1.78204	+	2.23461i
$243$	−2.57815e8	−	1.75775e8i	−1.15262	−	0.785842i
$244$	1.61823e6	−	1.50150e6i	0.00713141	−	0.00661698i
$245$	2.31441e7	−	5.89702e7i	0.100545	−	0.256183i
$246$	3.68227e8	+	1.13583e8i	1.57704	+	0.486452i
$247$	−6.84058e7	−	3.29425e7i	−0.288837	−	0.139097i
$248$	−1.19366e8	−	3.04141e8i	−0.496937	−	1.26617i
$249$	2.04289e7	+	2.72604e8i	0.0838585	+	1.11901i
$250$	−8.83778e7	−	1.10822e8i	−0.357728	−	0.448577i
$251$	−9.04647e7	−	1.56689e8i	−0.361095	−	0.625434i	0.627047	−	0.778982i	$-0.284264\pi$
$251$	−9.04647e7	−	1.56689e8i	−0.361095	−	0.625434i	−0.988141	+	0.153548i	$0.950930\pi$
$252$	1.32050e6	−	2.28718e6i	0.00519802	−	0.00900324i
$253$	−2.23129e8	+	3.36313e7i	−0.866232	+	0.130563i
$254$	−3.37714e8	+	1.62635e8i	−1.29310	+	0.622723i
$255$	8.87170e7	+	8.23174e7i	0.335055	+	0.310886i
$256$	−5.59174e6	−	2.44990e7i	−0.0208308	−	0.0912659i
$257$	−1.67784e8			−0.616571			−0.308286	−	0.951294i	$-0.599755\pi$
$257$	−1.67784e8			−0.616571			−0.308286	+	0.951294i	$0.599755\pi$
$258$	−4.06689e8	−	1.14031e8i	−1.47433	−	0.413385i
$259$	−8.56754e7			−0.306413
$260$	−143268.	−	627698.i	−0.000505525	−	0.00221485i
$261$	−5.20579e7	−	4.83027e7i	−0.181236	−	0.168163i
$262$	1.52563e8	−	7.34704e7i	0.524076	−	0.252382i
$263$	1.51334e8	−	2.28099e7i	0.512968	−	0.0773175i	0.112543	−	0.993647i	$-0.464100\pi$
$263$	1.51334e8	−	2.28099e7i	0.512968	−	0.0773175i	0.400425	+	0.916329i	$0.368862\pi$
$264$	−4.33063e8	+	7.50088e8i	−1.44856	+	2.50899i
$265$	1.66007e6	+	2.87532e6i	0.00547980	+	0.00949129i
$266$	−6.61330e7	−	8.29282e7i	−0.215443	−	0.270157i
$267$	1.17400e7	+	1.56660e8i	0.0377467	+	0.503695i
$268$	2.57622e6	+	6.56410e6i	0.00817543	+	0.0208307i
$269$	4.05638e8	+	1.95345e8i	1.27059	+	0.611884i	0.942955	−	0.332921i	$-0.108034\pi$
$269$	4.05638e8	+	1.95345e8i	1.27059	+	0.611884i	0.327635	+	0.944804i	$0.393748\pi$
$270$	3.82319e7	+	1.17930e7i	0.118210	+	0.0364629i
$271$	−7.99259e7	+	2.03648e8i	−0.243947	+	0.621566i	−0.999436	−	0.0335955i	$-0.989304\pi$
$271$	−7.99259e7	+	2.03648e8i	−0.243947	+	0.621566i	0.755489	+	0.655162i	$0.227399\pi$
$272$	2.57228e8	−	2.38673e8i	0.775045	−	0.719137i
$273$	2.69528e7	+	1.83761e7i	0.0801743	+	0.0546619i
$274$	−2.92679e8	+	3.67008e8i	−0.859538	+	1.07783i
$275$	6.07938e8	+	9.16319e7i	1.76277	+	0.265694i
$276$	7.05048e6	−	2.17478e6i	0.0201854	−	0.00622636i
$277$	4.91069e7	−	6.55286e8i	0.138824	−	1.85247i	−0.300050	−	0.953924i	$-0.597003\pi$
$277$	4.91069e7	−	6.55286e8i	0.138824	−	1.85247i	0.438873	−	0.898549i	$-0.355378\pi$
$278$	3.08204e8	−	2.10130e8i	0.860363	−	0.586586i
$279$	1.42133e8	−	6.22724e8i	0.391813	−	1.71665i
$280$	−6.20783e6	+	2.71983e7i	−0.0169000	+	0.0740437i
$281$	4.32880e8	−	2.95132e8i	1.16385	−	0.793496i	0.182022	−	0.983294i	$-0.441736\pi$
$281$	4.32880e8	−	2.95132e8i	1.16385	−	0.793496i	0.981823	+	0.189798i	$0.0607834\pi$
$282$	3.73554e7	−	4.98473e8i	0.0991931	−	1.32364i
$283$	5.25158e8	−	1.61990e8i	1.37733	−	0.424849i	0.484320	−	0.874891i	$-0.339067\pi$
$283$	5.25158e8	−	1.61990e8i	1.37733	−	0.424849i	0.893007	+	0.450042i	$0.148591\pi$
$284$	−1.35363e7	−	2.04027e6i	−0.0350660	−	0.00528534i
$285$	1.41291e8	−	1.77174e8i	0.361542	−	0.453359i
$286$	1.59638e8	+	1.08840e8i	0.403512	+	0.275110i
$287$	−8.26997e7	+	7.67341e7i	−0.206499	+	0.191603i
$288$	1.17783e7	−	3.00106e7i	0.0290542	−	0.0740288i
$289$	2.08420e7	+	6.42892e6i	0.0507923	+	0.0156673i
$290$	−2.17909e7	−	1.04940e7i	−0.0524666	−	0.0252666i
$291$	3.43456e8	+	8.75112e8i	0.817045	+	2.08180i
$292$	−346588.	−	4.62490e6i	−0.000814655	−	0.0108708i
$293$	−1.62314e8	−	2.03536e8i	−0.376982	−	0.472720i	0.556757	−	0.830675i	$-0.312045\pi$
$293$	−1.62314e8	−	2.03536e8i	−0.376982	−	0.472720i	−0.933739	+	0.357955i	$0.883474\pi$
$294$	−3.10804e8	−	5.38328e8i	−0.713297	−	1.23547i
$295$	3.32914e7	−	5.76625e7i	0.0755015	−	0.130772i
$296$	−5.08881e8	+	7.67015e7i	−1.14050	+	0.171903i
$297$	−3.27644e8	+	1.57785e8i	−0.725697	+	0.349477i
$298$	6.10093e8	+	5.66083e8i	1.33549	+	1.23915i
$299$	1.13595e7	+	4.97694e7i	0.0245760	+	0.107674i
$300$	−2.01029e7			−0.0429867
$301$	8.84435e7	−	8.64202e7i	0.186932	−	0.182655i
$302$	−2.79835e8			−0.584626
$303$	−1.91568e8	−	8.39316e8i	−0.395617	−	1.73331i
$304$	−4.81651e8	−	4.46907e8i	−0.983274	−	0.912345i
$305$	−4.10727e7	+	1.97796e7i	−0.0828903	+	0.0399178i
$306$	6.57770e8	−	9.91429e7i	1.31235	−	0.197805i
$307$	−1.84695e8	+	3.19901e8i	−0.364309	+	0.631002i	−0.988665	−	0.150138i	$-0.952028\pi$
$307$	−1.84695e8	+	3.19901e8i	−0.364309	+	0.631002i	0.624356	+	0.781140i	$0.285362\pi$
$308$	4.08775e6	+	7.08019e6i	0.00797181	+	0.0138076i
$309$	6.23593e8	+	7.81961e8i	1.20239	+	1.50775i
$310$	−1.62567e7	−	2.16931e8i	−0.0309932	−	0.413576i
$311$	3.07753e8	+	7.84141e8i	0.580150	+	1.47820i	0.855989	+	0.516995i	$0.172949\pi$
$311$	3.07753e8	+	7.84141e8i	0.580150	+	1.47820i	−0.275838	+	0.961204i	$0.588955\pi$
$312$	1.76542e8	+	8.50179e7i	0.329083	+	0.158478i
$313$	2.24410e8	+	6.92215e7i	0.413655	+	0.127596i	0.494595	−	0.869123i	$-0.335316\pi$
$313$	2.24410e8	+	6.92215e7i	0.413655	+	0.127596i	−0.0809407	+	0.996719i	$0.525792\pi$
$314$	1.87210e8	−	4.77003e8i	0.341252	−	0.869495i
$315$	−3.99800e7	+	3.70960e7i	−0.0720702	+	0.0668713i
$316$	1.78465e7	+	1.21676e7i	0.0318162	+	0.0216920i
$317$	−5.94807e8	+	7.45865e8i	−1.04874	+	1.31508i	−0.101404	+	0.994845i	$0.532334\pi$
$317$	−5.94807e8	+	7.45865e8i	−1.04874	+	1.31508i	−0.947338	+	0.320236i	$0.896238\pi$
$318$	3.22145e7	+	4.85556e6i	0.0561768	+	0.00846729i
$319$	2.10068e8	−	6.47975e7i	0.362321	−	0.111761i
$320$	−1.25102e7	+	1.66937e8i	−0.0213422	+	0.284792i
$321$	−3.78681e8	+	2.58180e8i	−0.639007	+	0.435668i
$322$	−1.58696e7	+	6.95293e7i	−0.0264893	+	0.116057i
$323$	1.80061e8	−	7.88898e8i	0.297311	−	1.30260i
$324$	−1.02963e7	+	7.01991e6i	−0.0168180	+	0.0114663i
$325$	1.03941e7	−	1.38700e8i	0.0167956	−	0.224122i
$326$	3.66925e8	−	1.13181e8i	0.586565	−	0.180931i
$327$	6.13255e8	+	9.24332e7i	0.969893	+	0.146188i
$328$	−4.22510e8	+	5.29811e8i	−0.661117	+	0.829014i
$329$	1.20915e8	+	8.24386e7i	0.187195	+	0.127628i
$330$	−4.22736e8	+	3.92242e8i	−0.647546	+	0.600835i
$331$	−4.06502e8	+	1.03575e9i	−0.616119	+	1.56984i	0.192364	+	0.981324i	$0.438385\pi$
$331$	−4.06502e8	+	1.03575e9i	−0.616119	+	1.56984i	−0.808482	+	0.588521i	$0.799711\pi$
$332$	1.48110e7	+	4.56859e6i	0.0222127	+	0.00685170i
$333$	−9.06449e8	−	4.36523e8i	−1.34521	−	0.647817i
$334$	1.20018e8	+	3.05802e8i	0.176252	+	0.449084i
$335$	−1.08822e7	−	1.45213e8i	−0.0158147	−	0.211032i
$336$	1.76012e8	+	2.20712e8i	0.253137	+	0.317423i
$337$	−3.91908e8	−	6.78805e8i	−0.557801	−	0.966141i	−0.997680	−	0.0680831i	$-0.978312\pi$
$337$	−3.91908e8	−	6.78805e8i	−0.557801	−	0.966141i	0.439878	−	0.898057i	$-0.355022\pi$
$338$	−3.38605e8	+	5.86481e8i	−0.476963	+	0.826124i
$339$	−4.80009e8	+	7.23497e7i	−0.669191	+	0.100864i
$340$	6.18235e6	−	2.97726e6i	0.00853055	−	0.00410810i
$341$	1.44945e9	+	1.34489e9i	1.97953	+	1.83673i
$342$	−2.77164e8	−	1.21434e9i	−0.374667	−	1.64153i
$343$	3.77310e8			0.504858
$344$	4.47954e8	−	5.92485e8i	0.593306	−	0.784734i
$345$	−1.52368e8			−0.199768
$346$	−1.96235e8	−	8.59761e8i	−0.254689	−	1.11586i
$347$	−3.87782e8	−	3.59809e8i	−0.498236	−	0.462295i	0.390574	−	0.920572i	$-0.372277\pi$
$347$	−3.87782e8	−	3.59809e8i	−0.498236	−	0.462295i	−0.888810	+	0.458276i	$0.848467\pi$
$348$	−6.47631e6	+	3.11883e6i	−0.00823759	+	0.00396701i
$349$	−6.71018e8	+	1.01140e8i	−0.844978	+	0.127360i	−0.557242	−	0.830350i	$-0.688140\pi$
$349$	−6.71018e8	+	1.01140e8i	−0.844978	+	0.127360i	−0.287736	+	0.957710i	$0.592902\pi$
$350$	9.71558e7	−	1.68279e8i	0.121124	−	0.209793i
$351$	4.11357e7	+	7.12491e7i	0.0507743	+	0.0879436i
$352$	6.22239e7	+	7.80263e7i	0.0760428	+	0.0953547i
$353$	−1.90041e7	−	2.53592e8i	−0.0229951	−	0.306848i	−0.996828	−	0.0795838i	$-0.974641\pi$
$353$	−1.90041e7	−	2.53592e8i	−0.0229951	−	0.306848i	0.973833	−	0.227264i	$-0.0729782\pi$
$354$	−2.38691e8	−	6.08174e8i	−0.285972	−	0.728646i
$355$	2.54698e8	+	1.22656e8i	0.302153	+	0.145509i
$356$	8.51155e6	+	2.62546e6i	0.00999847	+	0.00308412i
$357$	−1.27017e8	+	3.23635e8i	−0.147749	+	0.376458i
$358$	3.52617e8	−	3.27181e8i	0.406174	−	0.376875i
$359$	8.35006e8	+	5.69297e8i	0.952487	+	0.649394i	0.936571	−	0.350479i	$-0.113981\pi$
$359$	8.35006e8	+	5.69297e8i	0.952487	+	0.649394i	0.0159161	+	0.999873i	$0.494934\pi$
$360$	−2.04256e8	+	2.56129e8i	−0.230737	+	0.289335i
$361$	−6.14363e8	−	9.26003e7i	−0.687305	−	0.103595i
$362$	−3.32574e8	+	1.02586e8i	−0.368476	+	0.113660i
$363$	2.89019e8	−	3.85669e9i	0.317142	−	4.23196i
$364$	1.52818e6	−	1.04190e6i	0.00166081	−	0.00113232i
$365$	−2.13121e7	+	9.33745e7i	−0.0229404	+	0.100509i
$366$	−9.95379e7	+	4.36104e8i	−0.106122	+	0.464950i
$367$	6.57069e8	−	4.47982e8i	0.693872	−	0.473074i	−0.164317	−	0.986408i	$-0.552542\pi$
$367$	6.57069e8	−	4.47982e8i	0.693872	−	0.473074i	0.858189	+	0.513333i	$0.171590\pi$
$368$	−3.30141e7	+	4.40543e8i	−0.0345328	+	0.460809i
$369$	−1.26593e9	+	3.90488e8i	−1.31165	+	0.404591i
$370$	−3.38821e8	−	5.10690e7i	−0.347747	−	0.0524145i
$371$	−5.94671e6	+	7.45694e6i	−0.00604600	+	0.00758144i
$372$	−5.34188e7	−	3.64203e7i	−0.0538014	−	0.0366812i
$373$	−1.03206e9	+	9.57613e8i	−1.02973	+	0.955452i	−0.999028	−	0.0440762i	$-0.985966\pi$
$373$	−1.03206e9	+	9.57613e8i	−1.02973	+	0.955452i	−0.0307045	+	0.999529i	$0.509775\pi$
$374$	−7.52308e8	+	1.91685e9i	−0.743609	+	1.89469i
$375$	8.31317e8	+	2.56427e8i	0.814062	+	0.251105i
$376$	7.91996e8	+	3.81405e8i	0.768362	+	0.370024i
$377$	−1.81698e7	−	4.62960e7i	−0.0174645	−	0.0444988i
$378$	8.58915e6	+	1.14614e8i	0.00817954	+	0.109148i
$379$	−1.02465e9	−	1.28487e9i	−0.966806	−	1.21234i	−0.977185	−	0.212391i	$-0.931875\pi$
$379$	−1.02465e9	−	1.28487e9i	−0.966806	−	1.21234i	0.0103786	−	0.999946i	$-0.496696\pi$
$380$	−6.42433e6	−	1.11273e7i	−0.00600600	−	0.0104027i
$381$	1.15027e9	−	1.99232e9i	1.06552	−	1.84553i
$382$	−1.20874e9	+	1.82188e8i	−1.10946	+	0.167224i
$383$	−1.84620e9	+	8.89083e8i	−1.67913	+	0.808624i	−0.682124	+	0.731237i	$0.738944\pi$
$383$	−1.84620e9	+	8.89083e8i	−1.67913	+	0.808624i	−0.997001	+	0.0773874i	$0.975342\pi$
$384$	1.28073e9	+	1.18834e9i	1.15424	+	1.07098i
$385$	−3.75685e7	−	1.64598e8i	−0.0335514	−	0.146998i
$386$	−1.75796e9			−1.55580
$387$	1.37605e9	−	4.63703e8i	1.20683	−	0.406679i
$388$	5.33021e7			0.0463269
$389$	3.25970e8	+	1.42817e9i	0.280773	+	1.23014i	0.896806	+	0.442425i	$0.145882\pi$
$389$	3.25970e8	+	1.42817e9i	0.280773	+	1.23014i	−0.616033	+	0.787720i	$0.711261\pi$
$390$	9.56369e7	+	8.87380e7i	0.0816393	+	0.0757502i
$391$	−4.90190e8	+	2.36063e8i	−0.414711	+	0.199714i
$392$	1.08092e9	−	1.62923e8i	0.906343	−	0.136609i
$393$	−5.19635e8	+	9.00034e8i	−0.431842	+	0.747971i
$394$	−9.50206e8	−	1.64580e9i	−0.782674	−	1.35563i
$395$	−2.78109e8	−	3.48738e8i	−0.227052	−	0.284714i
$396$	7.17443e6	+	9.57361e7i	0.00580570	+	0.0774716i
$397$	−7.48329e7	−	1.90671e8i	−0.0600241	−	0.152939i	0.897715	−	0.440576i	$-0.145226\pi$
$397$	−7.48329e7	−	1.90671e8i	−0.0600241	−	0.152939i	−0.957740	+	0.287637i	$0.907130\pi$
$398$	−6.75231e7	−	3.25174e7i	−0.0536861	−	0.0258538i
$399$	6.22074e8	+	1.91884e8i	0.490272	+	0.151229i
$400$	4.39750e8	−	1.12046e9i	0.343555	−	0.875363i
$401$	−2.14592e8	+	1.99112e8i	−0.166191	+	0.154203i	−0.758884	−	0.651225i	$-0.774255\pi$
$401$	−2.14592e8	+	1.99112e8i	−0.166191	+	0.154203i	0.592693	+	0.805428i	$0.298065\pi$
$402$	−1.18060e9	−	8.04918e8i	−0.906381	−	0.617960i
$403$	2.78903e8	−	3.49733e8i	0.212268	−	0.266176i
$404$	−4.82665e7	−	7.27501e6i	−0.0364176	−	0.00548907i
$405$	2.45911e8	−	7.58535e7i	0.183944	−	0.0567392i
$406$	5.19223e6	−	6.92855e7i	0.00385046	−	0.0513808i
$407$	2.57326e9	−	1.75442e9i	1.89192	−	1.28989i
$408$	−4.64701e8	+	2.03599e9i	−0.338737	+	1.48410i
$409$	−1.81182e8	+	7.93812e8i	−0.130944	+	0.573702i	0.866301	+	0.499522i	$0.166491\pi$
$409$	−1.81182e8	+	7.93812e8i	−0.130944	+	0.573702i	−0.997245	+	0.0741796i	$0.976366\pi$
$410$	−3.72792e8	+	2.54165e8i	−0.267130	+	0.182126i
$411$	2.15302e8	−	2.87300e9i	0.152968	−	2.04122i
$412$	5.41885e7	−	1.67149e7i	0.0381739	−	0.0117751i
$413$	1.89137e8	+	2.85078e7i	0.132115	+	0.0199131i
$414$	−5.22158e8	+	6.54766e8i	−0.361660	+	0.453508i
$415$	−2.64462e8	−	1.80307e8i	−0.181633	−	0.123835i
$416$	1.65508e7	−	1.53569e7i	0.0112718	−	0.0104587i
$417$	−8.36413e8	+	2.13114e9i	−0.564865	+	1.43925i
$418$	3.68447e9	+	1.13651e9i	2.46750	+	0.761124i
$419$	−1.49926e9	−	7.22007e8i	−0.995701	−	0.479504i	−0.136224	−	0.990678i	$-0.543497\pi$
$419$	−1.49926e9	−	7.22007e8i	−0.995701	−	0.479504i	−0.859477	+	0.511174i	$0.829211\pi$
$420$	2.01684e6	+	5.13883e6i	0.00132831	+	0.00338448i
$421$	1.47095e8	+	1.96285e9i	0.0960751	+	1.28203i	0.811918	+	0.583772i	$0.198424\pi$
$421$	1.47095e8	+	1.96285e9i	0.0960751	+	1.28203i	−0.715843	+	0.698261i	$0.753957\pi$
$422$	1.29936e9	+	1.62935e9i	0.841661	+	1.05541i
$423$	8.59256e8	+	1.48828e9i	0.551990	+	0.956075i
$424$	−2.86454e7	+	4.96154e7i	−0.0182505	+	0.0316108i
$425$	1.46582e9	−	2.20937e8i	0.926230	−	0.139607i
$426$	2.49920e9	−	1.20355e9i	1.56627	−	0.754276i
$427$	−9.59997e7	−	8.90747e7i	−0.0596722	−	0.0553677i
$428$	5.78243e6	+	2.53345e7i	0.00356498	+	0.0156192i
$429$	−1.18583e9			−0.725138
$430$	4.01281e8	−	2.89047e8i	0.243393	−	0.175319i
$431$	2.07966e9			1.25119			0.625594	−	0.780149i	$-0.284857\pi$
$431$	2.07966e9			1.25119			0.625594	+	0.780149i	$0.284857\pi$
$432$	1.58429e8	+	6.94122e8i	0.0945455	+	0.414231i
$433$	−2.16776e9	−	2.01139e9i	−1.28323	−	1.19066i	−0.970576	−	0.240795i	$-0.922592\pi$
$433$	−2.16776e9	−	2.01139e9i	−1.28323	−	1.19066i	−0.312653	−	0.949867i	$-0.601218\pi$
$434$	5.63040e8	−	2.71146e8i	0.330617	−	0.159217i
$435$	1.46784e8	−	2.21241e7i	0.0854998	−	0.0128870i
$436$	1.75817e7	−	3.04523e7i	0.0101591	−	0.0175962i
$437$	5.09376e8	+	8.82266e8i	0.291980	+	0.505725i
$438$	5.85949e8	+	7.34757e8i	0.333197	+	0.417815i
$439$	6.56186e7	+	8.75619e8i	0.0370170	+	0.493957i	0.984644	+	0.174577i	$0.0558557\pi$
$439$	6.56186e7	+	8.75619e8i	0.0370170	+	0.493957i	−0.947627	+	0.319380i	$0.896525\pi$
$440$	−3.70501e8	−	9.44021e8i	−0.207350	−	0.528320i
$441$	1.92540e9	+	9.27223e8i	1.06902	+	0.514813i
$442$	4.45160e8	+	1.37314e8i	0.245210	+	0.0756373i
$443$	−8.35427e8	+	2.12863e9i	−0.456558	+	1.16329i	0.498505	+	0.866887i	$0.333882\pi$
$443$	−8.35427e8	+	2.12863e9i	−0.456558	+	1.16329i	−0.955063	+	0.296403i	$0.904213\pi$
$444$	−7.46507e7	+	6.92657e7i	−0.0404756	+	0.0375559i
$445$	−1.51981e8	−	1.03619e8i	−0.0817576	−	0.0557414i
$446$	−9.57625e8	+	1.20082e9i	−0.511121	+	0.640925i
$447$	−5.05094e9	−	7.61307e8i	−2.67483	−	0.403166i
$448$	−4.59541e8	+	1.41750e8i	−0.241464	+	0.0744816i
$449$	1.17797e7	−	1.57189e8i	0.00614147	−	0.0819523i	−0.993291	−	0.115643i	$-0.963107\pi$
$449$	1.17797e7	−	1.57189e8i	0.00614147	−	0.0819523i	0.999432	+	0.0336908i	$0.0107262\pi$
$450$	1.88531e9	−	1.28538e9i	0.975300	−	0.664948i
$451$	9.12562e8	−	3.99819e9i	0.468430	−	2.05232i
$452$	−6.12448e6	+	2.68331e7i	−0.00311950	+	0.0136674i
$453$	1.41905e9	−	9.67491e8i	0.717222	−	0.488994i
$454$	1.90612e8	−	2.54354e9i	0.0955994	−	1.27568i
$455$	−3.64982e7	+	1.12582e7i	−0.0181649	+	0.00560312i
$456$	3.86668e9	+	5.82809e8i	1.90968	+	0.287839i
$457$	−7.31364e7	+	9.17101e7i	−0.0358449	+	0.0449480i	−0.799431	−	0.600758i	$-0.794865\pi$
$457$	−7.31364e7	+	9.17101e7i	−0.0358449	+	0.0449480i	0.763586	+	0.645706i	$0.223437\pi$
$458$	−1.33810e9	−	9.12302e8i	−0.650818	−	0.443720i
$459$	−6.42760e8	+	5.96394e8i	−0.310245	+	0.287865i
$460$	−3.15619e6	+	8.04183e6i	−0.00151185	+	0.00385214i
$461$	−3.93604e9	−	1.21411e9i	−1.87114	−	0.577170i	−0.995564	−	0.0940895i	$-0.970006\pi$
$461$	−3.93604e9	−	1.21411e9i	−1.87114	−	0.577170i	−0.875576	−	0.483081i	$-0.839518\pi$
$462$	−1.49258e9	−	7.18787e8i	−0.704190	−	0.339120i
$463$	4.54104e8	+	1.15704e9i	0.212629	+	0.541769i	0.996903	−	0.0786454i	$-0.0250595\pi$
$463$	4.54104e8	+	1.15704e9i	0.212629	+	0.541769i	−0.784274	+	0.620415i	$0.786964\pi$
$464$	−3.21634e7	−	4.29191e8i	−0.0149468	−	0.199452i
$465$	8.32445e8	+	1.04385e9i	0.383946	+	0.481453i
$466$	5.16720e8	+	8.94985e8i	0.236540	+	0.409699i
$467$	1.14979e9	−	1.99149e9i	0.522406	−	0.904834i	−0.477254	−	0.878765i	$-0.658368\pi$
$467$	1.14979e9	−	1.99149e9i	0.522406	−	0.904834i	0.999660	−	0.0260688i	$-0.00829889\pi$
$468$	2.14768e7	−	3.23711e6i	0.00968521	−	0.00145981i
$469$	3.76898e8	−	1.81505e8i	0.168701	−	0.0812424i
$470$	4.29044e8	+	3.98094e8i	0.190616	+	0.176866i
$471$	6.99826e8	+	3.06614e9i	0.308615	+	1.35213i
$472$	1.14893e9			0.502916
$473$	−8.86728e8	+	4.40673e9i	−0.385280	+	1.91471i
$474$	−4.37684e9			−1.88771
$475$	−6.17651e8	−	2.70611e9i	−0.264433	−	1.15856i
$476$	1.44501e7	+	1.34077e7i	0.00614110	+	0.00569810i
$477$	−1.00910e8	+	4.85957e7i	−0.0425716	+	0.0205014i
$478$	2.07312e9	−	3.12472e8i	0.868214	−	0.130862i
$479$	−2.00497e9	+	3.47272e9i	−0.833555	+	1.44376i	0.0616460	+	0.998098i	$0.480365\pi$
$479$	−2.00497e9	+	3.47272e9i	−0.833555	+	1.44376i	−0.895201	+	0.445662i	$0.852968\pi$
$480$	3.36943e7	+	5.83603e7i	0.0139063	+	0.0240865i
$481$	−4.39302e8	−	5.50867e8i	−0.179993	−	0.225704i
$482$	−1.40119e8	−	1.86976e9i	−0.0569945	−	0.760539i
$483$	−1.59913e8	−	4.07451e8i	−0.0645756	−	0.164536i
$484$	−1.97566e8	−	9.51428e7i	−0.0792052	−	0.0381432i
$485$	−1.05183e9	−	3.24447e8i	−0.418649	−	0.129136i
$486$	1.30974e9	−	3.33716e9i	0.517556	−	1.31871i
$487$	−2.71198e9	+	2.51635e9i	−1.06399	+	0.987234i	−0.999943	−	0.0107129i	$-0.996590\pi$
$487$	−2.71198e9	+	2.51635e9i	−1.06399	+	0.987234i	−0.0640429	+	0.997947i	$0.520399\pi$
$488$	−6.49948e8	−	4.43127e8i	−0.253168	−	0.172607i
$489$	−1.46937e9	+	1.84254e9i	−0.568266	+	0.712582i
$490$	7.19693e8	+	1.08476e8i	0.276351	+	0.0416532i
$491$	−1.14120e9	+	3.52014e8i	−0.435088	+	0.134207i	−0.504559	−	0.863377i	$-0.668345\pi$
$491$	−1.14120e9	+	3.52014e8i	−0.435088	+	0.134207i	0.0694712	+	0.997584i	$0.477869\pi$
$492$	−1.00209e7	+	1.33720e8i	−0.00379341	+	0.0506196i
$493$	4.37949e8	−	2.98588e8i	0.164611	−	0.112230i
$494$	1.94105e8	−	8.50431e8i	0.0724425	−	0.317391i
$495$	4.41165e8	−	1.93287e9i	0.163487	−	0.716282i
$496$	3.19848e9	−	2.18068e9i	1.17695	−	0.802430i
$497$	−6.06881e7	+	8.09826e8i	−0.0221746	+	0.295900i
$498$	−3.00121e9	+	9.25751e8i	−1.08891	+	0.335886i
$499$	3.18611e9	+	4.80229e8i	1.14791	+	0.173020i	0.695322	−	0.718698i	$-0.255262\pi$
$499$	3.18611e9	+	4.80229e8i	1.14791	+	0.173020i	0.452591	+	0.891718i	$0.350500\pi$
$500$	3.07541e7	−	3.85645e7i	0.0110029	−	0.0137972i
$501$	−1.66588e9	−	1.13578e9i	−0.591851	−	0.403517i
$502$	1.52380e9	−	1.41388e9i	0.537606	−	0.498826i
$503$	9.34739e8	−	2.38168e9i	0.327493	−	0.834439i	−0.668392	−	0.743810i	$-0.733017\pi$
$503$	9.34739e8	−	2.38168e9i	0.327493	−	0.834439i	0.995885	−	0.0906293i	$-0.0288878\pi$
$504$	−8.99294e8	−	2.77396e8i	−0.312892	−	0.0965145i
$505$	9.08180e8	+	4.37356e8i	0.313799	+	0.151118i
$506$	−9.47144e8	−	2.41328e9i	−0.325004	−	0.828098i
$507$	−3.10605e8	−	4.14473e9i	−0.105847	−	1.41243i
$508$	−8.13260e7	−	1.01980e8i	−0.0275237	−	0.0345136i
$509$	1.59327e9	+	2.75963e9i	0.535523	+	0.927554i	0.999138	+	0.0415167i	$0.0132190\pi$
$509$	1.59327e9	+	2.75963e9i	0.535523	+	0.927554i	−0.463614	+	0.886037i	$0.653448\pi$
$510$	−6.95226e8	+	1.20417e9i	−0.232076	+	0.401967i
$511$	−2.72063e8	+	4.10069e7i	−0.0901980	+	0.0135952i
$512$	−2.59727e9	+	1.25078e9i	−0.855209	+	0.411847i
$513$	1.20355e9	+	1.11673e9i	0.393597	+	0.365205i
$514$	−4.28947e8	−	1.87934e9i	−0.139326	−	0.610428i
$515$	−1.17107e9			−0.377795
$516$	7.19469e6	−	1.46803e8i	0.00230536	−	0.0470394i
$517$	−5.31982e9			−1.69309
$518$	−2.19034e8	−	9.59649e8i	−0.0692399	−	0.303360i
$519$	3.96761e9	+	3.68141e9i	1.24579	+	1.15592i
$520$	−2.06707e8	+	9.95451e7i	−0.0644680	+	0.0310462i
$521$	2.90553e9	−	4.37938e8i	0.900104	−	0.135669i	0.317342	−	0.948311i	$-0.397210\pi$
$521$	2.90553e9	−	4.37938e8i	0.900104	−	0.135669i	0.582763	+	0.812642i	$0.301972\pi$
$522$	4.07949e8	−	7.06588e8i	0.125533	−	0.217430i
$523$	3.76216e8	+	6.51626e8i	0.114996	+	0.199178i	0.917778	−	0.397094i	$-0.129981\pi$
$523$	3.76216e8	+	6.51626e8i	0.114996	+	0.199178i	−0.802782	+	0.596272i	$0.796648\pi$
$524$	3.67391e7	+	4.60694e7i	0.0111550	+	0.0139879i
$525$	8.91217e7	+	1.18925e9i	0.0268798	+	0.358686i
$526$	6.42385e8	+	1.63677e9i	0.192462	+	0.490386i
$527$	4.29535e9	+	2.06853e9i	1.27838	+	0.615637i
$528$	−9.80617e9	−	3.02480e9i	−2.89922	−	0.894290i
$529$	−9.93673e8	+	2.53184e9i	−0.291842	+	0.743602i
$530$	−2.79624e7	+	2.59453e7i	−0.00815846	+	0.00756994i
$531$	1.85583e9	+	1.26528e9i	0.537907	+	0.366738i
$532$	2.30133e7	−	2.88578e7i	0.00662656	−	0.00830945i
$533$	−9.17422e8	−	1.38279e8i	−0.262436	−	0.0395559i
$534$	−1.72473e9	+	5.32008e8i	−0.490147	+	0.151190i
$535$	4.01026e7	−	5.35132e8i	0.0113223	−	0.151086i
$536$	2.07615e9	−	1.41549e9i	0.582346	−	0.397037i
$537$	−6.56944e8	+	2.87826e9i	−0.183071	+	0.802084i
$538$	−1.15102e9	+	5.04295e9i	−0.318673	+	1.39620i
$539$	−5.46589e9	+	3.72658e9i	−1.50349	+	1.02506i
$540$	−1.04044e6	+	1.38838e7i	−0.000284342	+	0.00379428i
$541$	−2.29248e9	+	7.07136e8i	−0.622465	+	0.192005i	−0.589915	−	0.807465i	$-0.700839\pi$
$541$	−2.29248e9	+	7.07136e8i	−0.622465	+	0.192005i	−0.0325497	+	0.999470i	$0.510363\pi$
$542$	−2.48539e9	−	3.74612e8i	−0.670498	−	0.101061i
$543$	1.33181e9	−	1.67004e9i	0.356980	−	0.447639i
$544$	1.98817e8	+	1.35551e8i	0.0529491	+	0.0361001i
$545$	−5.32308e8	+	4.93909e8i	−0.140856	+	0.130695i
$546$	−1.36924e8	+	3.48878e8i	−0.0360004	+	0.0917274i
$547$	−6.64213e8	−	2.04883e8i	−0.173521	−	0.0535241i	0.206777	−	0.978388i	$-0.433702\pi$
$547$	−6.64213e8	−	2.04883e8i	−0.173521	−	0.0535241i	−0.380298	+	0.924864i	$0.624179\pi$
$548$	−1.47175e8	−	7.08755e7i	−0.0382033	−	0.0183977i
$549$	−5.61838e8	−	1.43154e9i	−0.144913	−	0.369233i
$550$	5.27857e8	+	7.04377e9i	0.135284	+	1.80524i
$551$	−6.18815e8	−	7.75970e8i	−0.157591	−	0.197612i
$552$	−1.31460e9	−	2.27695e9i	−0.332664	−	0.576191i
$553$	6.40690e8	−	1.10971e9i	0.161105	−	0.279043i
$554$	7.46539e9	−	1.12523e9i	1.86539	−	0.281162i
$555$	1.89473e9	−	9.12453e8i	0.470459	−	0.226561i
$556$	9.51542e7	+	8.82902e7i	0.0234783	+	0.0217847i
$557$	−6.95370e8	−	3.04662e9i	−0.170499	−	0.747007i	−0.985794	−	0.167960i	$-0.946282\pi$
$557$	−6.95370e8	−	3.04662e9i	−0.170499	−	0.747007i	0.815294	−	0.579047i	$-0.196575\pi$
$558$	7.33849e9			1.78808
$559$	1.00915e9	+	1.25544e8i	0.244352	+	0.0303987i
$560$	−3.30539e8			−0.0795361
$561$	−2.81227e9	−	1.23214e10i	−0.672492	−	2.94638i
$562$	4.41245e9	+	4.09416e9i	1.04858	+	0.972943i
$563$	−2.27870e9	+	1.09736e9i	−0.538156	+	0.259162i	−0.683160	−	0.730269i	$-0.739395\pi$
$563$	−2.27870e9	+	1.09736e9i	−0.538156	+	0.259162i	0.145004	+	0.989431i	$0.453681\pi$
$564$	1.72005e8	−	2.59255e7i	0.0403704	−	0.00608486i
$565$	2.84188e8	−	4.92229e8i	0.0662883	−	0.114815i
$566$	3.15704e9	+	5.46815e9i	0.731850	+	1.26760i
$567$	4.60931e8	+	5.77989e8i	0.106193	+	0.133162i
$568$	3.64537e8	+	4.86441e9i	0.0834685	+	1.11381i
$569$	−1.48398e9	−	3.78111e9i	−0.337703	−	0.860452i	−0.994340	−	0.106246i	$-0.966117\pi$
$569$	−1.48398e9	−	3.78111e9i	−0.337703	−	0.860452i	0.656637	−	0.754206i	$-0.271978\pi$
$570$	2.34574e9	+	1.12965e9i	0.530540	+	0.255494i
$571$	−2.90293e9	−	8.95436e8i	−0.652545	−	0.201284i	−0.0492314	−	0.998787i	$-0.515677\pi$
$571$	−2.90293e9	−	8.95436e8i	−0.652545	−	0.201284i	−0.603314	+	0.797504i	$0.706153\pi$
$572$	−2.45635e7	+	6.25868e7i	−0.00548788	+	0.0139829i
$573$	5.49964e9	−	5.10292e9i	1.22122	−	1.13312i
$574$	−1.07092e9	−	7.30143e8i	−0.236356	−	0.161145i
$575$	−1.16361e9	+	1.45912e9i	−0.255253	+	0.320077i
$576$	−5.58419e9	−	8.41681e8i	−1.21754	−	0.183514i
$577$	3.76752e9	−	1.16213e9i	0.816471	−	0.251848i	0.141733	−	0.989905i	$-0.454733\pi$
$577$	3.76752e9	−	1.16213e9i	0.816471	−	0.251848i	0.674738	+	0.738057i	$0.264256\pi$
$578$	−1.87265e7	+	2.49887e8i	−0.00403374	+	0.0538266i
$579$	8.91463e9	−	6.07789e9i	1.90866	−	1.30130i
$580$	1.87283e6	−	8.20539e6i	0.000398566	−	0.00174623i
$581$	2.04607e8	−	8.96443e8i	0.0432817	−	0.189630i
$582$	−8.92405e9	+	6.08431e9i	−1.87643	+	1.27933i
$583$	2.59099e7	−	3.45743e8i	0.00541533	−	0.0722626i
$584$	−1.57925e9	+	4.87133e8i	−0.328099	+	0.101205i
$585$	−4.43514e8	−	6.68490e7i	−0.0915929	−	0.0138054i
$586$	1.86484e9	−	2.33843e9i	0.382824	−	0.480046i
$587$	2.40580e9	+	1.64025e9i	0.490938	+	0.334716i	0.783355	−	0.621575i	$-0.213507\pi$
$587$	2.40580e9	+	1.64025e9i	0.490938	+	0.334716i	−0.292416	+	0.956291i	$0.594459\pi$
$588$	1.58566e8	−	1.47128e8i	0.0321655	−	0.0298452i
$589$	3.26138e9	−	8.30985e9i	0.657654	−	1.67568i
$590$	7.30988e8	+	2.25480e8i	0.146531	+	0.0451987i
$591$	1.05086e10	+	5.06070e9i	2.09407	+	1.00845i
$592$	−2.22765e9	−	5.67596e9i	−0.441287	−	1.12438i
$593$	−2.12437e8	−	2.83478e9i	−0.0418349	−	0.558249i	−0.978260	−	0.207381i	$-0.933506\pi$
$593$	−2.12437e8	−	2.83478e9i	−0.0418349	−	0.558249i	0.936425	−	0.350867i	$-0.114113\pi$
$594$	−2.60499e9	−	3.26655e9i	−0.509980	−	0.639495i
$595$	−2.03537e8	−	3.52536e8i	−0.0396127	−	0.0686111i
$596$	−1.44808e8	+	2.50814e8i	−0.0280175	+	0.0485278i
$597$	4.54835e8	−	6.85553e7i	0.0874870	−	0.0131865i
$598$	−5.28425e8	+	2.54476e8i	−0.101048	+	0.0486623i
$599$	−1.34514e9	−	1.24810e9i	−0.255724	−	0.237278i	0.541884	−	0.840453i	$-0.317711\pi$
$599$	−1.34514e9	−	1.24810e9i	−0.255724	−	0.237278i	−0.797608	+	0.603176i	$0.793902\pi$
$600$	1.59403e9	+	6.98391e9i	0.301278	+	1.31999i
$601$	9.01800e9			1.69453			0.847266	−	0.531170i	$-0.178247\pi$
$601$	9.01800e9			1.69453			0.847266	+	0.531170i	$0.178247\pi$
$602$	1.19410e9	+	7.69716e8i	0.223076	+	0.143795i
$603$	4.91237e9			0.912391
$604$	−2.16688e7	−	9.49370e7i	−0.00400133	−	0.0175310i
$605$	3.31952e9	+	3.08006e9i	0.609440	+	0.565478i
$606$	8.91141e9	−	4.29151e9i	1.62664	−	0.783350i
$607$	−5.30294e9	+	7.99290e8i	−0.962402	+	0.145059i	−0.611405	−	0.791318i	$-0.709395\pi$
$607$	−5.30294e9	+	7.99290e8i	−0.962402	+	0.145059i	−0.350997	+	0.936377i	$0.614157\pi$
$608$	2.25285e8	−	3.90206e8i	0.0406509	−	0.0704095i
$609$	2.13215e8	+	3.69299e8i	0.0382523	+	0.0662549i
$610$	−3.26555e8	−	4.09487e8i	−0.0582508	−	0.0730442i
$611$	8.99391e7	+	1.20015e9i	0.0159516	+	0.212859i
$612$	8.45690e7	+	2.15478e8i	0.0149136	+	0.0379991i
$613$	5.38134e9	+	2.59152e9i	0.943581	+	0.454405i	0.841431	−	0.540364i	$-0.181714\pi$
$613$	5.38134e9	+	2.59152e9i	0.943581	+	0.454405i	0.102150	+	0.994769i	$0.467428\pi$
$614$	−4.05538e9	−	1.25092e9i	−0.707038	−	0.218092i
$615$	1.01169e9	−	2.57775e9i	0.175382	−	0.446867i
$616$	2.13559e9	−	1.98154e9i	0.368116	−	0.341562i
$617$	4.02171e9	+	2.74195e9i	0.689307	+	0.469961i	0.856624	−	0.515942i	$-0.172558\pi$
$617$	4.02171e9	+	2.74195e9i	0.689307	+	0.469961i	−0.167317	+	0.985903i	$0.553510\pi$
$618$	−7.16448e9	+	8.98398e9i	−1.22103	+	1.53112i
$619$	−1.42558e9	−	2.14872e8i	−0.241588	−	0.0364135i	0.0271320	−	0.999632i	$-0.491363\pi$
$619$	−1.42558e9	−	2.14872e8i	−0.241588	−	0.0364135i	−0.268720	+	0.963218i	$0.586601\pi$
$620$	7.23372e7	−	2.23131e7i	0.0121896	−	0.00376000i
$621$	8.24955e7	−	1.10083e9i	0.0138232	−	0.184458i
$622$	−7.99637e9	+	5.45183e9i	−1.33237	+	0.908398i
$623$	1.17583e8	−	5.15166e8i	0.0194822	−	0.0853569i
$624$	−5.16609e8	+	2.26341e9i	−0.0851169	+	0.372922i
$625$	3.76133e9	−	2.56443e9i	0.616256	−	0.420157i
$626$	−2.01632e8	+	2.69059e9i	−0.0328510	+	0.438366i
$627$	−2.26133e10	+	6.97528e9i	−3.66377	+	1.13012i
$628$	1.76324e8	+	2.65766e7i	0.0284089	+	0.00428195i
$629$	4.68197e9	−	5.87100e9i	0.750155	−	0.940665i
$630$	−5.17723e8	−	3.52977e8i	−0.0824907	−	0.0562412i
$631$	−7.11209e9	+	6.59906e9i	−1.12692	+	1.04563i	−0.128378	+	0.991725i	$0.540977\pi$
$631$	−7.11209e9	+	6.59906e9i	−1.12692	+	1.04563i	−0.998546	+	0.0539074i	$0.982832\pi$
$632$	2.81200e9	−	7.16485e9i	0.443103	−	1.12901i
$633$	−1.22223e10	−	3.77009e9i	−1.91532	−	0.590798i
$634$	−9.87507e9	−	4.75558e9i	−1.53896	−	0.741125i
$635$	9.84094e8	+	2.50743e9i	0.152521	+	0.388616i
$636$	847200.	+	1.13051e7i	0.000130583	+	0.00174251i
$637$	9.33127e8	+	1.17010e9i	0.143038	+	0.179364i
$638$	1.26285e9	+	2.18731e9i	0.192521	+	0.333456i
$639$	−4.76821e9	+	8.25878e9i	−0.722940	+	1.25217i
$640$	−2.02280e9	+	3.04889e8i	−0.305017	+	0.0459739i
$641$	8.69071e9	−	4.18523e9i	1.30332	−	0.627648i	0.352046	−	0.935983i	$-0.385486\pi$
$641$	8.69071e9	−	4.18523e9i	1.30332	−	0.627648i	0.951278	+	0.308335i	$0.0997717\pi$
$642$	−3.85999e9	−	3.58155e9i	−0.575723	−	0.534193i
$643$	5.71161e8	+	2.50242e9i	0.0847266	+	0.371211i	0.999460	−	0.0328454i	$-0.0104569\pi$
$643$	5.71161e8	+	2.50242e9i	0.0847266	+	0.371211i	−0.914734	+	0.404057i	$0.867600\pi$
$644$	−2.48174e7			−0.00366147
$645$	−1.03556e9	+	2.85313e9i	−0.151955	+	0.418661i
$646$	9.29677e9			1.35681
$647$	−9.78908e7	−	4.28888e8i	−0.0142094	−	0.0622556i	0.967326	−	0.253535i	$-0.0815934\pi$
$647$	−9.78908e7	−	4.28888e8i	−0.0142094	−	0.0622556i	−0.981536	+	0.191280i	$0.938736\pi$
$648$	3.25521e9	+	3.02040e9i	0.469966	+	0.436065i
$649$	−6.26450e9	+	3.01682e9i	−0.899560	+	0.433205i
$650$	1.58015e9	−	2.38169e8i	0.225685	−	0.0340165i
$651$	−1.91773e9	+	3.32161e9i	−0.272430	+	0.471863i
$652$	6.68104e7	+	1.15719e8i	0.00944012	+	0.0163508i
$653$	−1.30787e8	−	1.64002e8i	−0.0183810	−	0.0230491i	0.772556	−	0.634947i	$-0.218978\pi$
$653$	−1.30787e8	−	1.64002e8i	−0.0183810	−	0.0230491i	−0.790937	+	0.611898i	$0.790406\pi$
$654$	5.32473e8	+	7.10537e9i	0.0744348	+	0.993263i
$655$	−4.44566e8	−	1.13273e9i	−0.0618146	−	0.157501i
$656$	−7.23388e9	−	3.48365e9i	−1.00048	−	0.481805i
$657$	−3.08737e9	−	9.52329e8i	−0.424727	−	0.131011i
$658$	−6.14267e8	+	1.56513e9i	−0.0840556	+	0.214170i
$659$	2.40180e9	−	2.22854e9i	0.326917	−	0.303335i	−0.499589	−	0.866263i	$-0.666516\pi$
$659$	2.40180e9	−	2.22854e9i	0.326917	−	0.303335i	0.826506	+	0.562928i	$0.190325\pi$
$660$	−1.65806e8	−	1.13045e8i	−0.0224490	−	0.0153055i
$661$	−3.71941e9	+	4.66399e9i	−0.500920	+	0.628134i	−0.966437	−	0.256905i	$-0.917297\pi$
$661$	−3.71941e9	+	4.66399e9i	−0.500920	+	0.628134i	0.465517	+	0.885039i	$0.345869\pi$
$662$	−1.26407e10	−	1.90527e9i	−1.69343	−	0.255243i
$663$	−2.73216e9	+	8.42759e8i	−0.364090	+	0.112307i
$664$	4.12747e8	−	5.50773e9i	0.0547137	−	0.730103i
$665$	−6.29786e8	+	4.29381e8i	−0.0830457	+	0.0566196i
$666$	2.57210e9	−	1.12691e10i	0.337387	−	1.47819i
$667$	−1.48494e8	+	6.50595e8i	−0.0193762	+	0.0848927i
$668$	−9.44530e7	+	6.43969e7i	−0.0122602	+	0.00835887i
$669$	7.04451e8	−	9.40025e9i	0.0909619	−	1.21380i
$670$	1.59871e9	−	4.93137e8i	0.205356	−	0.0633440i
$671$	4.70738e9	+	7.09523e8i	0.601520	+	0.0906646i
$672$	−1.20700e8	+	1.51353e8i	−0.0153432	+	0.0192398i
$673$	5.59339e9	+	3.81351e9i	0.707331	+	0.482250i	0.862771	−	0.505595i	$-0.168727\pi$
$673$	5.59339e9	+	3.81351e9i	0.707331	+	0.482250i	−0.155440	+	0.987845i	$0.549679\pi$
$674$	6.60135e9	−	6.12516e9i	0.830468	−	0.770562i
$675$	−1.09884e9	+	2.79981e9i	−0.137522	+	0.350401i
$676$	−2.25189e8	−	6.94616e7i	−0.0280372	−	0.00864832i
$677$	−1.05616e10	−	5.08621e9i	−1.30819	−	0.629991i	−0.355710	−	0.934596i	$-0.615761\pi$
$677$	−1.05616e10	−	5.08621e9i	−1.30819	−	0.629991i	−0.952479	+	0.304606i	$0.901475\pi$
$678$	−2.03756e9	−	5.19161e9i	−0.251076	−	0.639732i
$679$	−2.36303e8	−	3.15325e9i	−0.0289684	−	0.386557i
$680$	−1.52455e9	−	1.91172e9i	−0.185934	−	0.233154i
$681$	7.82734e9	+	1.35574e10i	0.949728	+	1.64498i
$682$	−1.13585e10	+	1.96735e10i	−1.37112	+	2.37485i
$683$	1.78148e9	−	2.68515e8i	0.213948	−	0.0322475i	−0.0411936	−	0.999151i	$-0.513116\pi$
$683$	1.78148e9	−	2.68515e8i	0.213948	−	0.0322475i	0.255142	+	0.966904i	$0.417878\pi$
$684$	3.90514e8	−	1.88062e8i	0.0466595	−	0.0224700i
$685$	2.47284e9	+	2.29446e9i	0.293953	+	0.272749i
$686$	9.64613e8	+	4.22625e9i	0.114082	+	0.499828i
$687$	9.93969e9			1.16956
$688$	8.02492e9	+	3.61233e9i	0.939467	+	0.422890i
$689$	−7.84377e7			−0.00913604
$690$	−3.89536e8	−	1.70667e9i	−0.0451414	−	0.197778i
$691$	−2.39854e9	−	2.22552e9i	−0.276550	−	0.256601i	0.529688	−	0.848193i	$-0.322309\pi$
$691$	−2.39854e9	−	2.22552e9i	−0.276550	−	0.256601i	−0.806237	+	0.591592i	$0.798500\pi$
$692$	2.76488e8	−	1.33149e8i	0.0317179	−	0.0152745i
$693$	5.63176e9	−	8.48851e8i	0.642802	−	0.0968869i
$694$	3.03883e9	−	5.26342e9i	0.345103	−	0.597736i
$695$	−1.34030e9	−	2.32146e9i	−0.151445	−	0.262310i
$696$	1.59704e9	+	2.00262e9i	0.179549	+	0.225147i
$697$	−7.38938e8	−	9.86044e9i	−0.0826595	−	1.10301i
$698$	−2.84836e9	−	7.25749e9i	−0.317030	−	0.807779i
$699$	−5.71458e9	−	2.75200e9i	−0.632869	−	0.304774i
$700$	6.46135e7	+	1.99306e7i	0.00712000	+	0.00219623i
$701$	6.07291e9	−	1.54735e10i	0.665861	−	1.69659i	−0.0503761	−	0.998730i	$-0.516042\pi$
$701$	6.07291e9	−	1.54735e10i	0.665861	−	1.69659i	0.716237	−	0.697857i	$-0.245863\pi$
$702$	−6.92894e8	+	6.42912e8i	−0.0755940	+	0.0701410i
$703$	−1.16177e10	−	7.92079e9i	−1.26117	−	0.859854i
$704$	1.08996e10	−	1.36677e10i	1.17736	−	1.47636i
$705$	−3.55204e9	−	5.35384e8i	−0.381783	−	0.0575445i
$706$	2.79189e9	−	8.61185e8i	0.298595	−	0.0921043i
$707$	−2.16396e8	+	2.88761e9i	−0.0230293	+	0.307305i
$708$	1.87847e8	−	1.28072e8i	0.0198924	−	0.0135624i
$709$	2.15204e9	−	9.42869e9i	0.226771	−	0.993550i	−0.725482	−	0.688241i	$-0.758383\pi$
$709$	2.15204e9	−	9.42869e9i	0.226771	−	0.993550i	0.952253	−	0.305309i	$-0.0987597\pi$
$710$	−7.22721e8	+	3.16645e9i	−0.0757820	+	0.332023i
$711$	1.24326e10	−	8.47639e9i	1.29723	−	0.884437i
$712$	2.37197e8	−	3.16517e9i	0.0246280	−	0.328637i
$713$	−5.73552e9	+	1.76917e9i	−0.592597	+	0.182792i
$714$	−3.94975e9	−	5.95329e8i	−0.406094	−	0.0612088i
$715$	8.65684e8	−	1.08553e9i	0.0885704	−	0.111064i
$716$	1.38304e8	+	9.42940e7i	0.0140812	+	0.00960038i
$717$	−9.43249e9	+	8.75207e9i	−0.955673	+	0.886735i
$718$	−4.24196e9	+	1.08083e10i	−0.427691	+	1.08974i
$719$	6.10127e8	+	1.88199e8i	0.0612166	+	0.0188828i	0.325212	−	0.945641i	$-0.394564\pi$
$719$	6.10127e8	+	1.88199e8i	0.0612166	+	0.0188828i	−0.263996	+	0.964524i	$0.585040\pi$
$720$	−3.49711e9	−	1.68412e9i	−0.349177	−	0.168155i
$721$	−1.22906e9	−	3.13158e9i	−0.122123	−	0.311165i
$722$	−5.33436e8	−	7.11820e9i	−0.0527475	−	0.703866i
$723$	7.17498e9	+	8.99714e9i	0.706052	+	0.885362i
$724$	−6.05558e7	−	1.04886e8i	−0.00593022	−	0.0102714i
$725$	9.09100e8	−	1.57461e9i	0.0885989	−	0.153458i
$726$	4.39376e10	−	6.62253e9i	4.26146	−	0.642312i
$727$	−1.42886e10	+	6.88102e9i	−1.37917	+	0.664175i	−0.968823	−	0.247754i	$-0.920308\pi$
$727$	−1.42886e10	+	6.88102e9i	−1.37917	+	0.664175i	−0.410350	+	0.911928i	$0.634593\pi$
$728$	−4.83140e8	−	4.48288e8i	−0.0464102	−	0.0430623i
$729$	3.37917e9	+	1.48051e10i	0.323045	+	1.41535i
$730$	−1.10037e9			−0.104691
$731$	1.08880e9	+	1.07834e10i	0.103095	+	1.02104i
$732$	−1.55660e8			−0.0146686
$733$	4.53787e9	+	1.98817e10i	0.425587	+	1.86462i	0.497899	+	0.867235i	$0.334105\pi$
$733$	4.53787e9	+	1.98817e10i	0.425587	+	1.86462i	−0.0723126	+	0.997382i	$0.523038\pi$
$734$	6.69767e9	+	6.21453e9i	0.625155	+	0.580059i
$735$	−4.02461e9	+	1.93815e9i	−0.373868	+	0.180045i
$736$	−2.99565e8	+	4.51522e7i	−0.0276961	+	0.00417452i
$737$	−7.60337e9	+	1.31694e10i	−0.699632	+	1.21180i
$738$	−7.61027e9	−	1.31814e10i	−0.696952	−	1.20716i
$739$	−9.69854e9	−	1.21616e10i	−0.883997	−	1.10850i	−0.993423	−	0.114502i	$-0.963473\pi$
$739$	−9.69854e9	−	1.21616e10i	−0.883997	−	1.10850i	0.109426	−	0.993995i	$-0.465099\pi$
$740$	−8.91054e6	−	1.18903e8i	−0.000808338	−	0.0107865i
$741$	1.95594e9	+	4.98364e9i	0.176600	+	0.449969i
$742$	−9.87281e7	−	4.75450e7i	−0.00887211	−	0.00427259i
$743$	8.69882e8	+	2.68323e8i	0.0778036	+	0.0239992i	0.333413	−	0.942781i	$-0.391800\pi$
$743$	8.69882e8	+	2.68323e8i	0.0778036	+	0.0239992i	−0.255609	+	0.966780i	$0.582276\pi$
$744$	−8.41696e9	+	2.14461e10i	−0.749290	+	1.90916i
$745$	4.38424e9	−	4.06798e9i	0.388461	−	0.360439i
$746$	−1.33647e10	−	9.11191e9i	−1.17862	−	0.803570i
$747$	6.73220e9	−	8.44191e9i	0.590928	−	0.741001i
$748$	−7.08565e8	−	1.06799e8i	−0.0619047	−	0.00933064i
$749$	1.47310e9	−	4.54392e8i	0.128099	−	0.0395134i
$750$	−7.46934e8	+	9.96714e9i	−0.0646499	+	0.862693i
$751$	−7.16503e9	+	4.88503e9i	−0.617274	+	0.420850i	−0.831180	−	0.556004i	$-0.812334\pi$
$751$	−7.16503e9	+	4.88503e9i	−0.617274	+	0.420850i	0.213906	+	0.976854i	$0.431382\pi$
$752$	−2.31760e9	+	1.01541e10i	−0.198736	+	0.870718i
$753$	−2.83892e9	+	1.24381e10i	−0.242309	+	1.06163i
$754$	4.72108e8	−	3.21878e8i	0.0401090	−	0.0273459i
$755$	−1.50278e8	+	2.00533e9i	−0.0127081	+	0.169578i
$756$	−3.82190e7	+	1.17890e7i	−0.00321701	+	0.000992317i
$757$	7.10075e9	+	1.07027e9i	0.594933	+	0.0896718i	0.439605	−	0.898191i	$-0.355118\pi$
$757$	7.10075e9	+	1.07027e9i	0.594933	+	0.0896718i	0.155328	+	0.987863i	$0.450356\pi$
$758$	1.17723e10	−	1.47620e10i	0.981789	−	1.23112i
$759$	1.31466e10	+	8.96318e9i	1.09136	+	0.744073i
$760$	−3.35630e9	+	3.11419e9i	−0.277340	+	0.257334i
$761$	−1.73903e9	+	4.43097e9i	−0.143041	+	0.364462i	−0.984383	−	0.176041i	$-0.943671\pi$
$761$	−1.73903e9	+	4.43097e9i	−0.143041	+	0.364462i	0.841342	+	0.540503i	$0.181766\pi$
$762$	2.52567e10	+	7.79066e9i	2.06792	+	0.637869i
$763$	−1.87945e9	−	9.05093e8i	−0.153177	−	0.0737662i
$764$	−1.55407e8	−	3.95969e8i	−0.0126079	−	0.0321244i
$765$	−3.57229e8	−	4.76689e9i	−0.0288490	−	0.384964i
$766$	−1.46785e10	−	1.84063e10i	−1.18000	−	1.47967i
$767$	7.86507e8	+	1.36227e9i	0.0629388	+	0.109013i
$768$	−8.85970e8	+	1.53454e9i	−0.0705756	+	0.122241i
$769$	−3.34124e9	+	5.03611e8i	−0.264951	+	0.0399349i	−0.280174	−	0.959949i	$-0.590392\pi$
$769$	−3.34124e9	+	5.03611e8i	−0.264951	+	0.0399349i	0.0152233	+	0.999884i	$0.495154\pi$
$770$	1.74762e9	−	8.41607e8i	0.137952	−	0.0664342i
$771$	8.67275e9	+	8.04714e9i	0.681501	+	0.632341i
$772$	−1.36126e8	−	5.96405e8i	−0.0106483	−	0.0466532i
$773$	1.53572e10			1.19587			0.597935	−	0.801545i	$-0.295988\pi$
$773$	1.53572e10			1.19587			0.597935	+	0.801545i	$0.295988\pi$
$774$	8.71188e9	+	1.42277e10i	0.675334	+	1.10291i
$775$	1.63536e10			1.26199
$776$	−4.22652e9	−	1.85176e10i	−0.324689	−	1.42255i
$777$	4.42857e9	+	4.10911e9i	0.338681	+	0.314250i
$778$	−1.51635e10	+	7.30238e9i	−1.15444	+	0.555950i
$779$	−1.83083e10	+	2.75953e9i	−1.38761	+	0.209148i
$780$	−2.26998e7	+	3.93171e7i	−0.00171273	+	0.00296654i
$781$	−1.47605e10	−	2.55659e10i	−1.10872	−	1.92036i
$782$	−3.89734e9	−	4.88710e9i	−0.291437	−	0.365450i
$783$	8.03698e7	+	1.07246e9i	0.00598311	+	0.0798390i
$784$	4.73178e9	+	1.20564e10i	0.350686	+	0.893532i
$785$	−3.31771e9	−	1.59772e9i	−0.244790	−	0.117885i
$786$	−1.14097e10	−	3.51944e9i	−0.838102	−	0.258520i
$787$	6.18335e9	−	1.57549e10i	0.452181	−	1.15214i	−0.505121	−	0.863048i	$-0.668552\pi$
$787$	6.18335e9	−	1.57549e10i	0.452181	−	1.15214i	0.957302	−	0.289090i	$-0.0933526\pi$
$788$	4.84778e8	−	4.49808e8i	0.0352940	−	0.0327481i
$789$	−8.91645e9	−	6.07913e9i	−0.646283	−	0.440628i
$790$	3.19521e9	−	4.00666e9i	0.230571	−	0.289127i
$791$	1.61455e9	+	2.43354e8i	0.115993	+	0.0174832i
$792$	3.26907e10	−	1.00837e10i	2.33822	−	0.721246i
$793$	8.04838e7	−	1.07398e9i	0.00573129	−	0.0764787i
$794$	1.94439e9	−	1.32566e9i	0.137852	−	0.0939856i
$795$	5.20954e7	−	2.28245e8i	0.00367717	−	0.0161108i
$796$	5.80328e6	−	2.54259e7i	0.000407829	−	0.00178682i
$797$	−2.53294e8	+	1.72693e8i	−0.0177224	+	0.0120829i	−0.572149	−	0.820150i	$-0.693890\pi$
$797$	−2.53294e8	+	1.72693e8i	−0.0177224	+	0.0120829i	0.554426	+	0.832233i	$0.312938\pi$
$798$	−5.58930e8	+	7.45840e9i	−0.0389356	+	0.519560i
$799$	−1.22569e10	+	3.78076e9i	−0.850097	+	0.262220i
$800$	8.16197e8	+	1.23022e8i	0.0563612	+	0.00849508i
$801$	3.86884e9	−	4.85138e9i	0.265991	−	0.333543i
$802$	−2.77887e9	−	1.89460e9i	−0.190221	−	0.129690i
$803$	7.33170e9	−	6.80282e9i	0.499690	−	0.463644i
$804$	1.81658e8	−	4.62858e8i	0.0123271	−	0.0314088i
$805$	4.89731e8	+	1.51062e8i	0.0330881	+	0.0102063i
$806$	4.63038e9	+	2.22987e9i	0.311490	+	0.150006i
$807$	−1.15984e10	−	2.95524e10i	−0.776859	−	1.97941i
$808$	1.29983e9	+	1.73451e10i	0.0866858	+	1.15674i
$809$	4.43644e9	+	5.56312e9i	0.294588	+	0.369401i	0.906995	−	0.421141i	$-0.138370\pi$
$809$	4.43644e9	+	5.56312e9i	0.294588	+	0.369401i	−0.612408	+	0.790542i	$0.709799\pi$
$810$	1.47832e9	+	2.56052e9i	0.0977396	+	0.169290i
$811$	−1.49415e10	+	2.58794e10i	−0.983606	+	1.70366i	−0.335633	+	0.941993i	$0.608950\pi$
$811$	−1.49415e10	+	2.58794e10i	−0.983606	+	1.70366i	−0.647973	+	0.761663i	$0.724383\pi$
$812$	2.39079e7	−	3.60353e6i	0.00156709	−	0.000236201i
$813$	1.38986e10	−	6.69322e9i	0.907099	−	0.436836i
$814$	2.62299e10	+	2.43378e10i	1.70456	+	1.58160i
$815$	−6.14021e8	−	2.69020e9i	−0.0397312	−	0.174074i
$816$	−2.47432e10			−1.59419
$817$	1.99827e10	−	3.54196e9i	1.28197	−	0.227230i
$818$	−9.35468e9			−0.597575
$819$	−2.86714e8	−	1.25617e9i	−0.0182371	−	0.0799018i
$820$	−1.15095e8	−	1.06792e8i	−0.00728967	−	0.00676382i
$821$	1.67125e10	−	8.04833e9i	1.05400	−	0.507580i	0.175084	−	0.984554i	$-0.443980\pi$
$821$	1.67125e10	−	8.04833e9i	1.05400	−	0.507580i	0.878918	+	0.476973i	$0.158266\pi$
$822$	3.27309e10	−	4.93338e9i	2.05545	−	0.309809i
$823$	9.98904e9	−	1.73015e10i	0.624632	−	1.08189i	−0.363980	−	0.931407i	$-0.618582\pi$
$823$	9.98904e9	−	1.73015e10i	0.624632	−	1.08189i	0.988612	−	0.150488i	$-0.0480844\pi$
$824$	−1.01037e10	−	1.75002e10i	−0.629124	−	1.08967i
$825$	−2.70296e10	−	3.38940e10i	−1.67591	−	2.10152i
$826$	1.64223e8	+	2.19140e9i	0.0101392	+	0.135298i
$827$	9.87087e8	+	2.51506e9i	0.0606856	+	0.154625i	0.958000	−	0.286767i	$-0.0925804\pi$
$827$	9.87087e8	+	2.51506e9i	0.0606856	+	0.154625i	−0.897315	+	0.441391i	$0.854485\pi$
$828$	−2.62569e8	−	1.26447e8i	−0.0160745	−	0.00774106i
$829$	1.92394e10	+	5.93458e9i	1.17288	+	0.361784i	0.819158	−	0.573568i	$-0.194441\pi$
$829$	1.92394e10	+	5.93458e9i	1.17288	+	0.361784i	0.353717	+	0.935352i	$0.384917\pi$
$830$	1.34351e9	−	3.42320e9i	0.0815581	−	0.207807i
$831$	−3.39668e10	+	3.15166e10i	−2.05329	+	1.90518i
$832$	−3.26771e9	−	2.22789e9i	−0.196704	−	0.134110i
$833$	−9.94502e9	+	1.24707e10i	−0.596140	+	0.747536i
$834$	−2.60093e10	−	3.92026e9i	−1.55255	−	0.234010i
$835$	2.25586e9	−	6.95840e8i	0.134094	−	0.0413625i
$836$	−1.00269e8	+	1.33800e9i	−0.00593533	+	0.0792015i
$837$	−7.99234e9	+	5.44908e9i	−0.471123	+	0.321206i
$838$	4.25425e9	−	1.86391e10i	0.249729	−	1.09413i
$839$	1.68267e9	−	7.37227e9i	0.0983633	−	0.430958i	−0.901636	−	0.432497i	$-0.857633\pi$
$839$	1.68267e9	−	7.37227e9i	0.0983633	−	0.430958i	0.999999	+	0.00153896i	$0.000489866\pi$
$840$	1.62535e9	−	1.10815e9i	0.0946171	−	0.0645088i
$841$	−1.24050e9	+	1.65533e10i	−0.0719136	+	0.959620i
$842$	−2.16098e10	+	6.66573e9i	−1.24755	+	0.384818i
$843$	−3.65306e10	−	5.50610e9i	−2.10020	−	0.316554i
$844$	−4.52159e8	+	5.66990e8i	−0.0258877	+	0.0324621i
$845$	4.02093e9	+	2.74143e9i	0.229260	+	0.156307i
$846$	−1.44734e10	+	1.34294e10i	−0.821816	+	0.762534i
$847$	−4.75259e9	+	1.21094e10i	−0.268744	+	0.684749i
$848$	−6.48639e8	−	2.00079e8i	−0.0365273	−	0.0112672i
$849$	−3.49147e10	−	1.68140e10i	−1.95809	−	0.942964i
$850$	6.22215e9	+	1.58538e10i	0.347515	+	0.885455i
$851$	7.06505e8	+	9.42765e9i	0.0392972	+	0.524385i
$852$	6.01839e8	+	7.54682e8i	0.0333382	+	0.0418047i
$853$	−1.38294e10	−	2.39531e10i	−0.762922	−	1.32142i	−0.941338	−	0.337465i	$-0.890431\pi$
$853$	−1.38294e10	−	2.39531e10i	−0.762922	−	1.32142i	0.178416	−	0.983955i	$-0.442903\pi$
$854$	7.52296e8	−	1.30302e9i	0.0413320	−	0.0715891i
$855$	−8.85089e9	+	1.33406e9i	−0.484290	+	0.0729950i
$856$	8.34290e9	−	4.01773e9i	0.454631	−	0.218939i
$857$	−8.26184e9	−	7.66587e9i	−0.448378	−	0.416034i	0.423394	−	0.905945i	$-0.360838\pi$
$857$	−8.26184e9	−	7.66587e9i	−0.448378	−	0.416034i	−0.871772	+	0.489912i	$0.837029\pi$
$858$	−3.03163e9	−	1.32824e10i	−0.163859	−	0.717913i
$859$	3.08948e10			1.66307			0.831533	−	0.555475i	$-0.187464\pi$
$859$	3.08948e10			1.66307			0.831533	+	0.555475i	$0.187464\pi$
$860$	1.29135e8	+	1.13756e8i	0.00692308	+	0.00609862i
$861$	7.95504e9			0.424748
$862$	5.31677e9	+	2.32943e10i	0.282730	+	1.23872i
$863$	−2.14283e10	−	1.98825e10i	−1.13488	−	1.05301i	−0.998050	−	0.0624193i	$-0.980118\pi$
$863$	−2.14283e10	−	1.98825e10i	−1.13488	−	1.05301i	−0.136829	−	0.990595i	$-0.543691\pi$
$864$	−4.39884e8	+	2.11837e8i	−0.0232028	+	0.0111739i
$865$	−6.26651e9	+	9.44525e8i	−0.329207	+	0.0496200i
$866$	1.69876e10	−	2.94233e10i	0.888829	−	1.53950i
$867$	−7.68988e8	−	1.33193e9i	−0.0400731	−	0.0694086i
$868$	1.35587e8	+	1.70021e8i	0.00703720	+	0.00882437i
$869$	3.48093e9	+	4.64498e10i	0.179939	+	2.40113i
$870$	6.23071e8	+	1.58756e9i	0.0320790	+	0.0817359i
$871$	3.09957e9	+	1.49267e9i	0.158942	+	0.0765423i
$872$	−1.19735e10	−	3.69334e9i	−0.611525	−	0.188630i
$873$	1.35659e10	−	3.45654e10i	0.690081	−	1.75830i
$874$	−8.58000e9	+	7.96108e9i	−0.434708	+	0.403350i
$875$	−2.41774e9	−	1.64839e9i	−0.122006	−	0.0831823i
$876$	−2.03901e8	+	2.55684e8i	−0.0102484	+	0.0128511i
$877$	1.75993e10	+	2.65266e9i	0.881041	+	0.132796i	0.573955	−	0.818886i	$-0.305408\pi$
$877$	1.75993e10	+	2.65266e9i	0.881041	+	0.132796i	0.307085	+	0.951682i	$0.400646\pi$
$878$	−9.64003e9	+	2.97356e9i	−0.480671	+	0.148267i
$879$	−1.37182e9	+	1.83056e10i	−0.0681295	+	0.909125i
$880$	9.92774e9	−	6.76862e9i	0.491090	−	0.334819i
$881$	−7.16573e9	+	3.13951e10i	−0.353057	+	1.54684i	0.417022	+	0.908896i	$0.363074\pi$
$881$	−7.16573e9	+	3.13951e10i	−0.353057	+	1.54684i	−0.770079	+	0.637948i	$0.779783\pi$
$882$	−5.46343e9	+	2.39369e10i	−0.268118	+	1.17470i
$883$	2.56112e10	−	1.74615e10i	1.25190	−	0.853528i	0.258250	−	0.966078i	$-0.416854\pi$
$883$	2.56112e10	−	1.74615e10i	1.25190	−	0.853528i	0.993646	+	0.112550i	$0.0359018\pi$
$884$	−1.21146e7	+	1.61658e8i	−0.000589829	+	0.00787072i
$885$	−4.48641e9	+	1.38388e9i	−0.217569	+	0.0671113i
$886$	−2.59786e10	−	3.91565e9i	−1.25487	−	0.189141i
$887$	−7.74151e9	+	9.70755e9i	−0.372472	+	0.467065i	−0.932375	−	0.361493i	$-0.882267\pi$
$887$	−7.74151e9	+	9.70755e9i	−0.372472	+	0.467065i	0.559903	+	0.828558i	$0.310838\pi$
$888$	2.99828e10	+	2.04420e10i	1.43690	+	0.979664i
$889$	−5.67237e9	+	5.26319e9i	−0.270775	+	0.251243i
$890$	7.72084e8	−	1.96724e9i	0.0367113	−	0.0935388i
$891$	−2.56798e10	−	7.92118e9i	−1.21624	−	0.375161i
$892$	−4.81545e8	−	2.31900e8i	−0.0227175	−	0.0109401i
$893$	8.77467e9	+	2.23575e10i	0.412335	+	1.05061i
$894$	−4.38561e9	−	5.85219e10i	−0.205281	−	2.73928i
$895$	−2.15524e9	−	2.70259e9i	−0.100488	−	0.126008i
$896$	−2.93828e9	−	5.08926e9i	−0.136463	−	0.236361i
$897$	1.79983e9	−	3.11740e9i	0.0832643	−	0.144218i
$898$	1.79079e9	−	2.69918e8i	0.0825235	−	0.0124384i
$899$	5.26844e9	−	2.53714e9i	0.241837	−	0.116463i
$900$	5.82065e8	+	5.40077e8i	0.0266148	+	0.0246949i
$901$	−1.86021e8	−	8.15010e8i	−0.00847275	−	0.0371215i
$902$	4.71167e10			2.13773
$903$	−8.71649e9	+	2.25196e8i	−0.393944	+	0.0101778i
$904$	9.80769e9			0.441547
$905$	5.56537e8	+	2.43835e9i	0.0249588	+	0.109352i
$906$	1.44647e10	+	1.34213e10i	0.646192	+	0.599579i
$907$	1.48496e10	−	7.15119e9i	0.660829	−	0.318238i	−0.0732391	−	0.997314i	$-0.523334\pi$
$907$	1.48496e10	−	7.15119e9i	0.660829	−	0.318238i	0.734068	+	0.679076i	$0.237619\pi$
$908$	8.77683e8	−	1.32289e8i	0.0389078	−	0.00586441i
$909$	−1.70021e10	+	2.94484e10i	−0.750806	+	1.30043i
$910$	−2.19413e8	−	3.80034e8i	−0.00965199	−	0.0167177i
$911$	7.60319e8	+	9.53410e8i	0.0333182	+	0.0417797i	0.798211	−	0.602377i	$-0.205780\pi$
$911$	7.60319e8	+	9.53410e8i	0.0333182	+	0.0417797i	−0.764893	+	0.644157i	$0.777208\pi$
$912$	3.46231e9	+	4.62013e10i	0.151142	+	2.01684i
$913$	1.22115e10	+	3.11145e10i	0.531035	+	1.35305i
$914$	−1.21422e9	−	5.84738e8i	−0.0526000	−	0.0253308i
$915$	3.07171e9	+	9.47496e8i	0.132558	+	0.0408887i
$916$	2.05893e8	−	5.24608e8i	0.00885132	−	0.0225528i
$917$	2.56250e9	−	2.37765e9i	0.109742	−	0.101825i
$918$	−8.32345e9	−	5.67483e9i	−0.355103	−	0.242105i
$919$	−8.10767e9	+	1.01667e10i	−0.344582	+	0.432092i	−0.923679	−	0.383167i	$-0.874834\pi$
$919$	−8.10767e9	+	1.01667e10i	−0.344582	+	0.432092i	0.579098	+	0.815258i	$0.303405\pi$
$920$	3.04407e9	+	4.58819e8i	0.128883	+	0.0194260i
$921$	2.48898e10	−	7.67749e9i	1.04981	−	0.323825i
$922$	3.53651e9	−	4.71914e10i	0.148599	−	1.98292i
$923$	−5.51812e9	+	3.76219e9i	−0.230986	+	0.157483i
$924$	1.28280e8	−	5.62031e8i	0.00534942	−	0.0234373i
$925$	5.73184e9	−	2.51128e10i	0.238121	−	1.04328i
$926$	−1.17990e10	+	8.04445e9i	−0.488324	+	0.332934i
$927$	2.95220e9	−	3.93944e10i	0.121721	−	1.62426i
$928$	2.82031e8	−	8.69949e7i	0.0115845	−	0.00357335i
$929$	1.04285e10	+	1.57185e9i	0.426744	+	0.0643213i	0.358903	−	0.933375i	$-0.383151\pi$
$929$	1.04285e10	+	1.57185e9i	0.426744	+	0.0643213i	0.0678410	+	0.997696i	$0.478389\pi$
$930$	−9.56400e9	+	1.19929e10i	−0.389896	+	0.488915i
$931$	2.46772e10	+	1.68246e10i	1.00224	+	0.683316i
$932$	−2.63621e8	+	2.44605e8i	−0.0106666	+	0.00989713i
$933$	2.17008e10	−	5.52926e10i	0.874760	−	2.22885i
$934$	2.52461e10	+	7.78740e9i	1.01387	+	0.312736i
$935$	1.33323e10	+	6.42050e9i	0.533414	+	0.256879i
$936$	−2.82758e9	−	7.20454e9i	−0.112706	−	0.287171i
$937$	−1.10013e9	−	1.46803e10i	−0.0436875	−	0.582969i	−0.975496	−	0.220018i	$-0.929388\pi$
$937$	−1.10013e9	−	1.46803e10i	−0.0436875	−	0.582969i	0.931808	−	0.362951i	$-0.118231\pi$
$938$	2.99659e9	+	3.75760e9i	0.118554	+	0.148662i
$939$	−8.27985e9	−	1.43411e10i	−0.326357	−	0.565267i
$940$	−1.01835e8	+	1.76384e8i	−0.00399899	+	0.00692645i
$941$	1.41151e10	−	2.12750e9i	0.552229	−	0.0832352i	0.133001	−	0.991116i	$-0.457539\pi$
$941$	1.41151e10	−	2.12750e9i	0.552229	−	0.0832352i	0.419228	+	0.907881i	$0.362301\pi$
$942$	−3.25546e10	+	1.56775e10i	−1.26892	+	0.611080i
$943$	9.12573e9	+	8.46744e9i	0.354386	+	0.328822i
$944$	3.02913e9	+	1.32715e10i	0.117197	+	0.513473i
$945$	8.25949e8			0.0318377
$946$	−5.16267e10	+	1.33381e9i	−1.98269	+	0.0512242i
$947$	−3.14024e10			−1.20154			−0.600769	−	0.799423i	$-0.705139\pi$
$947$	−3.14024e10			−1.20154			−0.600769	+	0.799423i	$0.705139\pi$
$948$	−3.38916e8	−	1.48489e9i	−0.0129200	−	0.0566063i
$949$	−1.65867e9	−	1.53902e9i	−0.0629983	−	0.0584539i
$950$	2.87320e10	−	1.38366e10i	1.08726	−	0.523596i
$951$	6.65184e10	−	1.00260e10i	2.50790	−	0.378005i
$952$	3.51215e9	−	6.08323e9i	0.131930	−	0.228510i
$953$	4.34148e8	+	7.51966e8i	0.0162485	+	0.0281432i	0.874035	−	0.485862i	$-0.161494\pi$
$953$	4.34148e8	+	7.51966e8i	0.0162485	+	0.0281432i	−0.857787	+	0.514006i	$0.828161\pi$
$954$	−8.02302e8	−	1.00605e9i	−0.0299170	−	0.0375148i
$955$	6.56454e8	+	8.75977e9i	0.0243889	+	0.325447i
$956$	2.66539e8	+	6.79131e8i	0.00986640	+	0.0251392i
$957$	−1.39662e10	−	6.72579e9i	−0.515095	−	0.248057i
$958$	−4.40237e10	−	1.35795e10i	−1.61773	−	0.499005i
$959$	−3.54039e9	+	9.02077e9i	−0.129624	+	0.330277i
$960$	8.65319e9	−	8.02899e9i	0.315666	−	0.292895i
$961$	2.07239e10	+	1.41293e10i	0.753249	+	0.513557i
$962$	5.04716e9	−	6.32894e9i	0.182782	−	0.229202i
$963$	1.79006e10	+	2.69809e9i	0.645917	+	0.0973563i
$964$	6.23486e8	−	1.92320e8i	0.0224159	−	0.00691440i
$965$	−9.44066e8	+	1.25977e10i	−0.0338187	+	0.451279i
$966$	4.15503e9	−	2.83285e9i	0.148304	−	0.101112i
$967$	4.11056e9	−	1.80096e10i	0.146187	−	0.640487i	−0.847737	−	0.530417i	$-0.822035\pi$
$967$	4.11056e9	−	1.80096e10i	0.146187	−	0.640487i	0.993924	−	0.110070i	$-0.0351075\pi$
$968$	−1.73877e10	+	7.61804e10i	−0.616137	+	2.69947i
$969$	−4.71440e10	+	3.21423e10i	−1.66454	+	1.13486i
$970$	9.45064e8	−	1.26110e10i	0.0332476	−	0.443658i
$971$	1.10197e10	−	3.39913e9i	0.386281	−	0.119152i	−0.0955313	−	0.995426i	$-0.530455\pi$
$971$	1.10197e10	−	3.39913e9i	0.386281	−	0.119152i	0.481812	+	0.876275i	$0.339979\pi$
$972$	1.23358e9	+	1.85933e8i	0.0430860	+	0.00649417i
$973$	4.80123e9	−	6.02055e9i	0.167093	−	0.209528i
$974$	−3.51190e10	−	2.39437e10i	−1.21783	−	0.830300i
$975$	−7.18953e9	+	6.67091e9i	−0.248419	+	0.230499i
$976$	3.40507e9	−	8.67597e9i	0.117233	−	0.298706i
$977$	4.25464e10	+	1.31238e10i	1.45959	+	0.450225i	0.920073	−	0.391747i	$-0.128129\pi$
$977$	4.25464e10	+	1.31238e10i	1.45959	+	0.450225i	0.539521	+	0.841972i	$0.318605\pi$
$978$	−2.43948e10	−	1.17479e10i	−0.833893	−	0.401582i
$979$	7.01770e9	+	1.78808e10i	0.239032	+	0.609043i
$980$	1.89270e7	+	2.52563e8i	0.000642377	+	0.00857193i
$981$	−1.52731e10	−	1.91518e10i	−0.516518	−	0.647693i
$982$	−6.86044e9	−	1.18826e10i	−0.231186	−	0.400426i
$983$	−1.23521e10	+	2.13944e10i	−0.414765	+	0.718394i	−0.995404	−	0.0957670i	$-0.969470\pi$
$983$	−1.23521e10	+	2.13944e10i	−0.414765	+	0.718394i	0.580639	+	0.814161i	$0.302803\pi$
$984$	4.72501e10	−	7.12180e9i	1.58096	−	0.238291i
$985$	−1.23043e10	+	5.92542e9i	−0.410231	+	0.197557i
$986$	4.46412e9	+	4.14210e9i	0.148309	+	0.137610i
$987$	−2.29625e9	−	1.00605e10i	−0.0760167	−	0.333051i
$988$	3.03548e8			0.0100133
$989$	−1.02389e10	−	9.01960e9i	−0.336564	−	0.296483i
$990$	2.27779e10			0.746089
$991$	2.35509e9	+	1.03183e10i	0.0768686	+	0.336783i	0.998710	−	0.0507849i	$-0.0161723\pi$
$991$	2.35509e9	+	1.03183e10i	0.0768686	+	0.336783i	−0.921841	+	0.387568i	$0.873315\pi$
$992$	1.94598e9	+	1.80560e9i	0.0632917	+	0.0587262i
$993$	7.06881e10	−	3.40416e10i	2.29099	−	1.10329i
$994$	−9.22600e9	+	1.39060e9i	−0.297962	+	0.0449106i
$995$	−2.69284e8	+	4.66414e8i	−0.00866623	+	0.0150103i
$996$	−5.46466e8	−	9.46507e8i	−0.0175249	−	0.0303540i
$997$	−1.71555e10	−	2.15123e10i	−0.548239	−	0.687470i	0.428096	−	0.903733i	$-0.359184\pi$
$997$	−1.71555e10	−	2.15123e10i	−0.548239	−	0.687470i	−0.976335	+	0.216263i	$0.930613\pi$
$998$	2.76642e9	+	3.69153e10i	0.0880970	+	1.17557i
$999$	5.56644e9	+	1.41830e10i	0.176644	+	0.450081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.10.19	✓	300
43.13	even	21	inner	43.8.g.a.13.19	yes	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.10.19	✓	300	1.1	even	1	trivial
43.8.g.a.13.19	yes	300	43.13	even	21	inner

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)

\(f(q)\)	\(=\)	\(q+(2.55655 + 11.2010i) q^{2} +(-51.6901 - 47.9614i) q^{3} +(-3.60209 + 1.73467i) q^{4} +(81.6402 - 12.3053i) q^{5} +(405.067 - 701.596i) q^{6} +(118.589 + 205.402i) q^{7} +(888.263 + 1113.85i) q^{8} +(208.136 + 2777.38i) q^{9} +O(q^{10})\)	\(q+(2.55655 + 11.2010i) q^{2} +(-51.6901 - 47.9614i) q^{3} +(-3.60209 + 1.73467i) q^{4} +(81.6402 - 12.3053i) q^{5} +(405.067 - 701.596i) q^{6} +(118.589 + 205.402i) q^{7} +(888.263 + 1113.85i) q^{8} +(208.136 + 2777.38i) q^{9} +(346.549 + 882.992i) q^{10} +(-7767.94 - 3740.84i) q^{11} +(269.390 + 83.0957i) q^{12} +(-712.607 + 1815.69i) q^{13} +(-1997.53 + 1853.43i) q^{14} +(-4810.17 - 3279.52i) q^{15} +(-10524.4 + 13197.1i) q^{16} +(-20556.0 - 3098.32i) q^{17} +(-30577.3 + 9431.85i) q^{18} +(-2908.89 + 38816.4i) q^{19} +(-272.729 + 185.944i) q^{20} +(3721.50 - 16305.0i) q^{21} +(22042.0 - 96572.3i) q^{22} +(21624.4 - 14743.2i) q^{23} +(7507.25 - 100177. i) q^{24} +(-68140.4 + 21018.5i) q^{25} +(-22159.4 - 3339.99i) q^{26} +(26298.2 - 32976.9i) q^{27} +(-783.473 - 534.163i) q^{28} +(-18691.1 + 17342.8i) q^{29} +(24436.4 - 62262.9i) q^{30} +(-219147. - 67597.8i) q^{31} +(-10429.0 - 5022.33i) q^{32} +(222110. + 565926. i) q^{33} +(-17848.3 - 238169. i) q^{34} +(12209.2 + 15309.8i) q^{35} +(-5567.57 - 9643.32i) q^{36} +(-180614. + 312833. i) q^{37} +(-442219. + 66653.7i) q^{38} +(123918. - 59675.8i) q^{39} +(86224.2 + 80004.4i) q^{40} +(105844. + 463733. i) q^{41} +192146. q^{42} +(-129103. - 505125. i) q^{43} +34469.9 q^{44} +(51168.7 + 224185. i) q^{45} +(220423. + 204522. i) q^{46} +(555918. - 267716. i) q^{47} +(1.17696e6 - 177398. i) q^{48} +(383645. - 664492. i) q^{49} +(-409633. - 709505. i) q^{50} +(913944. + 1.14605e6i) q^{51} +(-582.763 - 7776.43i) q^{52} +(14691.7 + 37433.8i) q^{53} +(436607. + 210259. i) q^{54} +(-680209. - 209817. i) q^{55} +(-123448. + 314541. i) q^{56} +(2.01205e6 - 1.86691e6i) q^{57} +(-242041. - 165021. i) q^{58} +(502817. - 630512. i) q^{59} +(23015.5 + 3469.04i) q^{60} +(-527624. + 162751. i) q^{61} +(196902. - 2.62748e6i) q^{62} +(-545797. + 372118. i) q^{63} +(-451188. + 1.97678e6i) q^{64} +(-35834.8 + 157002. i) q^{65} +(-5.77110e6 + 3.93467e6i) q^{66} +(131806. - 1.75883e6i) q^{67} +(79419.1 - 24497.6i) q^{68} +(-1.82487e6 - 275055. i) q^{69} +(-140271. + 175895. i) q^{70} +(2.82904e6 + 1.92881e6i) q^{71} +(-2.90870e6 + 2.69888e6i) q^{72} +(-423811. + 1.07985e6i) q^{73} +(-3.96579e6 - 1.22328e6i) q^{74} +(4.53027e6 + 2.18166e6i) q^{75} +(-56855.7 - 144866. i) q^{76} +(-152815. - 2.03917e6i) q^{77} +(985231. + 1.23544e6i) q^{78} +(-2.70131e6 - 4.67880e6i) q^{79} +(-696817. + 1.20692e6i) q^{80} +(3.08215e6 - 464560. i) q^{81} +(-4.92367e6 + 2.37111e6i) q^{82} +(-2.84191e6 - 2.63691e6i) q^{83} +(14878.6 + 65187.4i) q^{84} -1.71632e6 q^{85} +(5.32784e6 - 2.73746e6i) q^{86} +1.79793e6 q^{87} +(-2.73325e6 - 1.19752e7i) q^{88} +(-1.63318e6 - 1.51537e6i) q^{89} +(-2.38028e6 + 1.14628e6i) q^{90} +(-457455. + 68950.2i) q^{91} +(-52318.1 + 90617.6i) q^{92} +(8.08564e6 + 1.40047e7i) q^{93} +(4.41992e6 + 5.54240e6i) q^{94} +(240165. + 3.20477e6i) q^{95} +(298197. + 759794. i) q^{96} +(-1.20118e7 - 5.78460e6i) q^{97} +(8.42378e6 + 2.59839e6i) q^{98} +(8.77296e6 - 2.23531e7i) 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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