LMFDB - Embedded newform 91.8.r.a.25.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(25,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("91.25");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.r (of order $6$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.11
Character	$\chi$	$=$	91.25
Dual form			91.8.r.a.51.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.1249 + 8.15502i) q^{2} +(19.6075 - 33.9612i) q^{3} +(69.0088 - 119.527i) q^{4} +(255.306 - 147.401i) q^{5} +639.600i q^{6} +(784.629 + 455.961i) q^{7} +163.389i q^{8} +(324.589 + 562.205i) q^{9} +O(q^{10})$	\(q+(-14.1249 + 8.15502i) q^{2} +(19.6075 - 33.9612i) q^{3} +(69.0088 - 119.527i) q^{4} +(255.306 - 147.401i) q^{5} +639.600i q^{6} +(784.629 + 455.961i) q^{7} +163.389i q^{8} +(324.589 + 562.205i) q^{9} +(-2404.11 + 4164.05i) q^{10} +(3077.12 + 1776.58i) q^{11} +(-2706.19 - 4687.25i) q^{12} +(-4486.89 + 6528.12i) q^{13} +(-14801.2 - 41.7479i) q^{14} -11560.7i q^{15} +(7500.69 + 12991.6i) q^{16} +(-7783.11 + 13480.7i) q^{17} +(-9169.60 - 5294.07i) q^{18} +(29381.7 - 16963.5i) q^{19} -40687.8i q^{20} +(30869.6 - 17706.7i) q^{21} -57952.1 q^{22} +(-23179.2 - 40147.6i) q^{23} +(5548.90 + 3203.66i) q^{24} +(4391.45 - 7606.21i) q^{25} +(10140.0 - 128800. i) q^{26} +111221. q^{27} +(108646. - 62318.8i) q^{28} -49206.8 q^{29} +(94277.5 + 163293. i) q^{30} +(96529.8 + 55731.5i) q^{31} +(-230005. - 132794. i) q^{32} +(120670. - 69668.6i) q^{33} -253886. i q^{34} +(267529. + 754.587i) q^{35} +89598.2 q^{36} +(-318007. + 183601. i) q^{37} +(-276676. + 479217. i) q^{38} +(133726. + 280381. i) q^{39} +(24083.7 + 41714.2i) q^{40} +656962. i q^{41} +(-291633. + 501848. i) q^{42} -111686. q^{43} +(424697. - 245199. i) q^{44} +(165739. + 95689.4i) q^{45} +(654809. + 378054. i) q^{46} +(-15658.2 + 9040.27i) q^{47} +588280. q^{48} +(407742. + 715521. i) q^{49} +143249. i q^{50} +(305215. + 528648. i) q^{51} +(470650. + 986802. i) q^{52} +(-46391.9 + 80353.1i) q^{53} +(-1.57099e6 + 907009. i) q^{54} +1.04748e6 q^{55} +(-74499.1 + 128200. i) q^{56} -1.33045e6i q^{57} +(695041. - 401282. i) q^{58} +(2.07334e6 + 1.19705e6i) q^{59} +(-1.38181e6 - 797788. i) q^{60} +(-233203. - 403919. i) q^{61} -1.81797e6 q^{62} +(-1661.67 + 589123. i) q^{63} +2.41156e6 q^{64} +(-183278. + 2.32804e6i) q^{65} +(-1.13630e6 + 1.96813e6i) q^{66} +(1.91335e6 + 1.10467e6i) q^{67} +(1.07421e6 + 1.86058e6i) q^{68} -1.81795e6 q^{69} +(-3.78498e6 + 2.17105e6i) q^{70} -2.94800e6i q^{71} +(-91858.2 + 53034.4i) q^{72} +(1.63257e6 + 942563. i) q^{73} +(2.99454e6 - 5.18670e6i) q^{74} +(-172211. - 298278. i) q^{75} -4.68253e6i q^{76} +(1.60435e6 + 2.79700e6i) q^{77} +(-4.17538e6 - 2.86981e6i) q^{78} +(-2.05888e6 - 3.56609e6i) q^{79} +(3.82994e6 + 2.21121e6i) q^{80} +(1.47089e6 - 2.54766e6i) q^{81} +(-5.35754e6 - 9.27953e6i) q^{82} -8.74533e6i q^{83} +(13853.8 - 4.91167e6i) q^{84} +4.58895e6i q^{85} +(1.57756e6 - 910804. i) q^{86} +(-964823. + 1.67112e6i) q^{87} +(-290274. + 502769. i) q^{88} +(5.71629e6 - 3.30030e6i) q^{89} -3.12140e6 q^{90} +(-6.49711e6 + 3.07630e6i) q^{91} -6.39829e6 q^{92} +(3.78542e6 - 2.18552e6i) q^{93} +(147447. - 255386. i) q^{94} +(5.00087e6 - 8.66176e6i) q^{95} +(-9.01967e6 + 5.20751e6i) q^{96} +1.58207e7i q^{97} +(-1.15944e7 - 6.78153e6i) q^{98} +2.30663e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9}+O(q^{10}) $ 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9	$ 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9} - 4514 q^{10} + 2090 q^{12} + 11132 q^{13} + 18748 q^{14} - 230074 q^{16} - 28972 q^{17} + 179920 q^{22} + 20508 q^{23} + 920040 q^{25} + 144684 q^{26} - 357584 q^{27} + 44600 q^{29} + 46580 q^{30} - 1216824 q^{35} - 4529248 q^{36} - 129032 q^{38} + 104546 q^{39} + 2082020 q^{40} + 2426496 q^{42} - 1434416 q^{43} - 3783940 q^{48} - 34428 q^{49} - 756008 q^{51} - 2348612 q^{52} + 1103824 q^{53} - 4216216 q^{55} + 8135574 q^{56} + 531568 q^{61} + 26627120 q^{62} - 27402496 q^{64} - 7495542 q^{65} + 2808402 q^{66} + 531760 q^{68} + 24238760 q^{69} - 7462590 q^{74} - 1547944 q^{75} - 1811116 q^{77} - 31233508 q^{78} + 2961020 q^{79} - 34639872 q^{81} - 10292872 q^{82} + 43455484 q^{87} + 21936790 q^{88} - 58442348 q^{90} + 16479848 q^{91} + 24834900 q^{92} + 26036992 q^{94} + 89048 q^{95}+O(q^{100}) $ 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9 - 4514 * q^10 + 2090 * q^12 + 11132 * q^13 + 18748 * q^14 - 230074 * q^16 - 28972 * q^17 + 179920 * q^22 + 20508 * q^23 + 920040 * q^25 + 144684 * q^26 - 357584 * q^27 + 44600 * q^29 + 46580 * q^30 - 1216824 * q^35 - 4529248 * q^36 - 129032 * q^38 + 104546 * q^39 + 2082020 * q^40 + 2426496 * q^42 - 1434416 * q^43 - 3783940 * q^48 - 34428 * q^49 - 756008 * q^51 - 2348612 * q^52 + 1103824 * q^53 - 4216216 * q^55 + 8135574 * q^56 + 531568 * q^61 + 26627120 * q^62 - 27402496 * q^64 - 7495542 * q^65 + 2808402 * q^66 + 531760 * q^68 + 24238760 * q^69 - 7462590 * q^74 - 1547944 * q^75 - 1811116 * q^77 - 31233508 * q^78 + 2961020 * q^79 - 34639872 * q^81 - 10292872 * q^82 + 43455484 * q^87 + 21936790 * q^88 - 58442348 * q^90 + 16479848 * q^91 + 24834900 * q^92 + 26036992 * q^94 + 89048 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−14.1249	+	8.15502i	−1.24848	+	0.720809i	−0.970806	−	0.239867i	$-0.922896\pi$
$2$	−14.1249	+	8.15502i	−1.24848	+	0.720809i	−0.277672	+	0.960676i	$0.589563\pi$
$3$	19.6075	−	33.9612i	0.419275	−	0.726205i	−0.576592	−	0.817032i	$-0.695618\pi$
$3$	19.6075	−	33.9612i	0.419275	−	0.726205i	0.995867	+	0.0908273i	$0.0289511\pi$
$4$	69.0088	−	119.527i	0.539132	−	0.933803i
$5$	255.306	−	147.401i	0.913409	−	0.527357i	0.0318825	−	0.999492i	$-0.489850\pi$
$5$	255.306	−	147.401i	0.913409	−	0.527357i	0.881526	+	0.472135i	$0.156516\pi$
$6$			639.600i			1.20887i
$7$	784.629	+	455.961i	0.864612	+	0.502441i
$7$	784.629	+	455.961i	0.864612	+	0.502441i
$8$			163.389i			0.112826i
$9$	324.589	+	562.205i	0.148418	+	0.257067i
$10$	−2404.11	+	4164.05i	−0.760247	+	1.31679i
$11$	3077.12	+	1776.58i	0.697060	+	0.402448i	0.806252	−	0.591573i	$-0.201493\pi$
$11$	3077.12	+	1776.58i	0.697060	+	0.402448i	−0.109191	+	0.994021i	$0.534826\pi$
$12$	−2706.19	−	4687.25i	−0.452088	−	0.783040i
$13$	−4486.89	+	6528.12i	−0.566427	+	0.824112i
$13$	−4486.89	+	6528.12i	−0.566427	+	0.824112i
$14$	−14801.2	−	41.7479i	−1.44161	−	0.00406618i
$15$		−	11560.7i		−	0.884429i
$16$	7500.69	+	12991.6i	0.457806	+	0.792943i
$17$	−7783.11	+	13480.7i	−0.384222	+	0.665492i	−0.991661	−	0.128875i	$-0.958864\pi$
$17$	−7783.11	+	13480.7i	−0.384222	+	0.665492i	0.607439	+	0.794366i	$0.292197\pi$
$18$	−9169.60	−	5294.07i	−0.370592	−	0.213962i
$19$	29381.7	−	16963.5i	0.982741	−	0.567386i	0.0796442	−	0.996823i	$-0.474622\pi$
$19$	29381.7	−	16963.5i	0.982741	−	0.567386i	0.903096	+	0.429438i	$0.141288\pi$
$20$		−	40687.8i		−	1.13726i
$21$	30869.6	−	17706.7i	0.727385	−	0.417225i
$22$	−57952.1			−1.16035
$23$	−23179.2	−	40147.6i	−0.397239	−	0.688038i	0.596145	−	0.802876i	$-0.296698\pi$
$23$	−23179.2	−	40147.6i	−0.397239	−	0.688038i	−0.993384	+	0.114839i	$0.963365\pi$
$24$	5548.90	+	3203.66i	0.0819346	+	0.0473050i
$25$	4391.45	−	7606.21i	0.0562105	−	0.0973595i
$26$	10140.0	−	128800.i	0.113144	−	1.43717i
$27$	111221.			1.08746
$28$	108646.	−	62318.8i	0.935320	−	0.536496i
$29$	−49206.8			−0.374655			−0.187328	−	0.982297i	$-0.559983\pi$
$29$	−49206.8			−0.374655			−0.187328	+	0.982297i	$0.559983\pi$
$30$	94277.5	+	163293.i	0.637505	+	1.10419i
$31$	96529.8	+	55731.5i	0.581963	+	0.335997i	0.761913	−	0.647679i	$-0.224260\pi$
$31$	96529.8	+	55731.5i	0.581963	+	0.335997i	−0.179950	+	0.983676i	$0.557594\pi$
$32$	−230005.	−	132794.i	−1.24083	−	0.716394i
$33$	120670.	−	69668.6i	0.584519	−	0.337472i
$34$		−	253886.i		−	1.10780i
$35$	267529.	+	754.587i	1.05471	+	0.00297489i
$36$	89598.2			0.320067
$37$	−318007.	+	183601.i	−1.03212	+	0.595895i	−0.917591	−	0.397525i	$-0.869869\pi$
$37$	−318007.	+	183601.i	−1.03212	+	0.595895i	−0.114528	+	0.993420i	$0.536536\pi$
$38$	−276676.	+	479217.i	−0.817953	+	1.41674i
$39$	133726.	+	280381.i	0.360986	+	0.756871i
$40$	24083.7	+	41714.2i	0.0594994	+	0.103056i
$41$			656962.i			1.48866i	0.667810	+	0.744332i	$0.267232\pi$
$41$			656962.i			1.48866i	−0.667810	+	0.744332i	$0.732768\pi$
$42$	−291633.	+	501848.i	−0.607384	+	1.04520i
$43$	−111686.			−0.214220			−0.107110	−	0.994247i	$-0.534160\pi$
$43$	−111686.			−0.214220			−0.107110	+	0.994247i	$0.534160\pi$
$44$	424697.	−	245199.i	0.751615	−	0.433945i
$45$	165739.	+	95689.4i	0.271132	+	0.156538i
$46$	654809.	+	378054.i	0.991887	+	0.572666i
$47$	−15658.2	+	9040.27i	−0.0219988	+	0.0127010i	−0.510959	−	0.859605i	$-0.670710\pi$
$47$	−15658.2	+	9040.27i	−0.0219988	+	0.0127010i	0.488960	+	0.872306i	$0.337376\pi$
$48$	588280.			0.767785
$49$	407742.	+	715521.i	0.495107	+	0.868832i
$50$			143249.i			0.162068i
$51$	305215.	+	528648.i	0.322189	+	0.558048i
$52$	470650.	+	986802.i	0.464180	+	0.973236i
$53$	−46391.9	+	80353.1i	−0.0428032	+	0.0741374i	−0.886633	−	0.462473i	$-0.846962\pi$
$53$	−46391.9	+	80353.1i	−0.0428032	+	0.0741374i	0.843830	+	0.536610i	$0.180296\pi$
$54$	−1.57099e6	+	907009.i	−1.35767	+	0.783851i
$55$	1.04748e6			0.848935
$56$	−74499.1	+	128200.i	−0.0566883	+	0.0975505i
$57$		−	1.33045e6i		−	0.951561i
$58$	695041.	−	401282.i	0.467749	−	0.270055i
$59$	2.07334e6	+	1.19705e6i	1.31428	+	0.758803i	0.982803	−	0.184659i	$-0.0591181\pi$
$59$	2.07334e6	+	1.19705e6i	1.31428	+	0.758803i	0.331482	+	0.943462i	$0.392451\pi$
$60$	−1.38181e6	−	797788.i	−0.825883	−	0.476824i
$61$	−233203.	−	403919.i	−0.131547	−	0.227845i	0.792726	−	0.609578i	$-0.208661\pi$
$61$	−233203.	−	403919.i	−0.131547	−	0.227845i	−0.924273	+	0.381732i	$0.875328\pi$
$62$	−1.81797e6			−0.968758
$63$	−1661.67	+	589123.i	−0.000837244	+	0.296834i
$64$	2.41156e6			1.14992
$65$	−183278.	+	2.32804e6i	−0.0827780	+	1.05146i
$66$	−1.13630e6	+	1.96813e6i	−0.486507	+	0.842654i
$67$	1.91335e6	+	1.10467e6i	0.777201	+	0.448717i	0.835437	−	0.549586i	$-0.185214\pi$
$67$	1.91335e6	+	1.10467e6i	0.777201	+	0.448717i	−0.0582365	+	0.998303i	$0.518548\pi$
$68$	1.07421e6	+	1.86058e6i	0.414292	+	0.717575i
$69$	−1.81795e6			−0.666208
$70$	−3.78498e6	+	2.17105e6i	−1.31893	+	0.756530i
$71$		−	2.94800e6i		−	0.977514i	−0.872420	−	0.488757i	$-0.837451\pi$
$71$		−	2.94800e6i		−	0.977514i	0.872420	−	0.488757i	$-0.162549\pi$
$72$	−91858.2	+	53034.4i	−0.0290038	+	0.0167453i
$73$	1.63257e6	+	942563.i	0.491181	+	0.283583i	0.725064	−	0.688681i	$-0.241810\pi$
$73$	1.63257e6	+	942563.i	0.491181	+	0.283583i	−0.233884	+	0.972265i	$0.575143\pi$
$74$	2.99454e6	−	5.18670e6i	0.859052	−	1.48792i
$75$	−172211.	−	298278.i	−0.0471353	−	0.0816407i
$76$		−	4.68253e6i		−	1.22358i
$77$	1.60435e6	+	2.79700e6i	0.400480	+	0.698193i
$78$	−4.17538e6	−	2.86981e6i	−0.996243	−	0.684735i
$79$	−2.05888e6	−	3.56609e6i	−0.469826	−	0.813763i	0.529579	−	0.848261i	$-0.322350\pi$
$79$	−2.05888e6	−	3.56609e6i	−0.469826	−	0.813763i	−0.999405	+	0.0344980i	$0.989017\pi$
$80$	3.82994e6	+	2.21121e6i	0.836328	+	0.482854i
$81$	1.47089e6	−	2.54766e6i	0.307527	−	0.532652i
$82$	−5.35754e6	−	9.27953e6i	−1.07304	−	1.85856i
$83$		−	8.74533e6i		−	1.67881i	−0.543503	−	0.839407i	$-0.682902\pi$
$83$		−	8.74533e6i		−	1.67881i	0.543503	−	0.839407i	$-0.317098\pi$
$84$	13853.8	−	4.91167e6i	0.00255029	−	0.904173i
$85$			4.58895e6i			0.810488i
$86$	1.57756e6	−	910804.i	0.267449	−	0.154412i
$87$	−964823.	+	1.67112e6i	−0.157083	+	0.272076i
$88$	−290274.	+	502769.i	−0.0454065	+	0.0786464i
$89$	5.71629e6	−	3.30030e6i	0.859507	−	0.496236i	−0.00434048	−	0.999991i	$-0.501382\pi$
$89$	5.71629e6	−	3.30030e6i	0.859507	−	0.496236i	0.863847	+	0.503754i	$0.168048\pi$
$90$	−3.12140e6			−0.451336
$91$	−6.49711e6	+	3.07630e6i	−0.903807	+	0.427941i
$92$	−6.39829e6			−0.856656
$93$	3.78542e6	−	2.18552e6i	0.488005	−	0.281750i
$94$	147447.	−	255386.i	0.0183100	−	0.0317139i
$95$	5.00087e6	−	8.66176e6i	0.598429	−	1.03651i
$96$	−9.01967e6	+	5.20751e6i	−1.04050	+	0.600732i
$97$			1.58207e7i			1.76005i	0.474930	+	0.880023i	$0.342473\pi$
$97$			1.58207e7i			1.76005i	−0.474930	+	0.880023i	$0.657527\pi$
$98$	−1.15944e7	−	6.78153e6i	−1.24439	−	0.727840i
$99$			2.30663e6i			0.238922i
$100$	−606098.	−	1.04979e6i	−0.0606098	−	0.104979i
$101$	7.24253e6	−	1.25444e7i	0.699464	−	1.21151i	−0.269188	−	0.963088i	$-0.586755\pi$
$101$	7.24253e6	−	1.25444e7i	0.699464	−	1.21151i	0.968652	−	0.248420i	$-0.0799113\pi$
$102$	−8.62228e6	−	4.97808e6i	−0.804492	−	0.464473i
$103$	−2.10327e6	−	3.64296e6i	−0.189655	−	0.328492i	0.755480	−	0.655171i	$-0.227404\pi$
$103$	−2.10327e6	−	3.64296e6i	−0.189655	−	0.328492i	−0.945135	+	0.326679i	$0.894070\pi$
$104$	−1.06662e6	−	733109.i	−0.0929811	−	0.0639075i
$105$	5.27121e6	−	9.07083e6i	0.444373	−	0.764688i
$106$		−	1.51331e6i		−	0.123412i
$107$	9.80891e6	+	1.69895e7i	0.774065	+	1.34072i	0.935318	+	0.353807i	$0.115113\pi$
$107$	9.80891e6	+	1.69895e7i	0.774065	+	1.34072i	−0.161253	+	0.986913i	$0.551554\pi$
$108$	7.67523e6	−	1.32939e7i	0.586284	−	1.01547i
$109$	1.93257e6	+	1.11577e6i	0.142936	+	0.0825242i	0.569763	−	0.821809i	$-0.307035\pi$
$109$	1.93257e6	+	1.11577e6i	0.142936	+	0.0825242i	−0.426826	+	0.904334i	$0.640368\pi$
$110$	−1.47955e7	+	8.54219e6i	−1.05988	+	0.611920i
$111$			1.43999e7i			0.999374i
$112$	−38398.2	+	1.36136e7i	−0.00258255	+	0.915608i
$113$	1.68319e7			1.09738			0.548692	−	0.836025i	$-0.315126\pi$
$113$	1.68319e7			1.09738			0.548692	+	0.836025i	$0.315126\pi$
$114$	1.08499e7	+	1.87925e7i	0.685894	+	1.18800i
$115$	−1.18356e7	−	6.83327e6i	−0.725683	−	0.418973i
$116$	−3.39570e6	+	5.88153e6i	−0.201988	+	0.349854i
$117$	−5.12654e6	−	403595.i	−0.295920	−	0.0232968i
$118$	−3.90478e7			−2.18781
$119$	−1.22536e7	+	7.02858e6i	−0.666573	+	0.382343i
$120$	1.88889e6			0.0997864
$121$	−3.43113e6	−	5.94289e6i	−0.176071	−	0.304964i
$122$	6.58795e6	+	3.80355e6i	0.328466	+	0.189640i
$123$	2.23112e7	+	1.28814e7i	1.08107	+	0.624159i
$124$	1.33228e7	−	7.69194e6i	0.627510	−	0.362293i
$125$			2.04422e7i			0.936142i
$126$	−4.78084e6	−	8.33486e6i	−0.212915	−	0.371194i
$127$	1.81610e6			0.0786732			0.0393366	−	0.999226i	$-0.487476\pi$
$127$	1.81610e6			0.0786732			0.0393366	+	0.999226i	$0.487476\pi$
$128$	−4.62244e6	+	2.66877e6i	−0.194821	+	0.112480i
$129$	−2.18989e6	+	3.79300e6i	−0.0898170	+	0.155568i
$130$	−1.63964e7	−	3.43780e7i	−0.654556	−	1.37239i
$131$	5.45777e6	+	9.45313e6i	0.212112	+	0.367389i	0.952375	−	0.304928i	$-0.0986325\pi$
$131$	5.45777e6	+	9.45313e6i	0.212112	+	0.367389i	−0.740263	+	0.672317i	$0.765299\pi$
$132$		−	1.92310e7i		−	0.727768i
$133$	3.07884e7	+	86841.2i	1.13477	+	0.00320070i
$134$	−3.60346e7			−1.29376
$135$	2.83953e7	−	1.63940e7i	0.993296	−	0.573480i
$136$	−2.20261e6	−	1.27168e6i	−0.0750846	−	0.0433501i
$137$	7.51510e6	+	4.33885e6i	0.249697	+	0.144163i	0.619625	−	0.784898i	$-0.287285\pi$
$137$	7.51510e6	+	4.33885e6i	0.249697	+	0.144163i	−0.369929	+	0.929060i	$0.620618\pi$
$138$	2.56784e7	−	1.48254e7i	0.831746	−	0.480209i
$139$	−7.11119e6			−0.224590			−0.112295	−	0.993675i	$-0.535820\pi$
$139$	−7.11119e6			−0.224590			−0.112295	+	0.993675i	$0.535820\pi$
$140$	1.85521e7	−	3.19248e7i	0.571405	−	0.983287i
$141$			709030.i			0.0213009i
$142$	2.40410e7	+	4.16402e7i	0.704601	+	1.22040i
$143$	−2.54044e7	+	1.21165e7i	−0.726496	+	0.346499i
$144$	−4.86929e6	+	8.43385e6i	−0.135893	+	0.235373i
$145$	−1.25628e7	+	7.25311e6i	−0.342213	+	0.197577i
$146$	−3.07465e7			−0.817637
$147$	3.22948e7	+	182181.i	0.838536	+	0.00473035i
$148$			5.06804e7i			1.28506i
$149$	3.58740e7	−	2.07119e7i	0.888440	−	0.512941i	0.0150079	−	0.999887i	$-0.495223\pi$
$149$	3.58740e7	−	2.07119e7i	0.888440	−	0.512941i	0.873432	+	0.486946i	$0.161889\pi$
$150$	4.86493e6	+	2.80877e6i	0.117695	+	0.0679511i
$151$	−6.35493e7	−	3.66902e7i	−1.50207	−	0.867223i	−0.999997	−	0.00240095i	$-0.999236\pi$
$151$	−6.35493e7	−	3.66902e7i	−1.50207	−	0.867223i	−0.502078	−	0.864822i	$-0.667431\pi$
$152$	2.77165e6	+	4.80065e6i	0.0640157	+	0.110878i
$153$	−1.01053e7			−0.228101
$154$	−4.54709e7	−	2.64239e7i	−1.00325	−	0.583009i
$155$	3.28595e7			0.708761
$156$	4.27413e7	+	3.36488e6i	0.901388	+	0.0709633i
$157$	−8.86687e6	+	1.53579e7i	−0.182861	+	0.316725i	−0.942854	−	0.333207i	$-0.891869\pi$
$157$	−8.86687e6	+	1.53579e7i	−0.182861	+	0.316725i	0.759993	+	0.649932i	$0.225203\pi$
$158$	5.81632e7	+	3.35805e7i	1.17314	+	0.677310i
$159$	1.81926e6	+	3.15105e6i	0.0358926	+	0.0621678i
$160$	−7.82955e7			−1.51118
$161$	118661.	−	4.20698e7i	0.00224088	−	0.794474i
$162$			4.79806e7i			0.886672i
$163$	2.97808e7	−	1.71940e7i	0.538617	−	0.310971i	−0.205901	−	0.978573i	$-0.566013\pi$
$163$	2.97808e7	−	1.71940e7i	0.538617	−	0.310971i	0.744518	+	0.667602i	$0.232679\pi$
$164$	7.85245e7	+	4.53362e7i	1.39012	+	0.802585i
$165$	2.05384e7	−	3.55736e7i	0.355937	−	0.616501i
$166$	7.13184e7	+	1.23527e8i	1.21011	+	2.09596i
$167$		−	8.26809e7i		−	1.37372i	−0.726791	−	0.686859i	$-0.758989\pi$
$167$		−	8.26809e7i		−	1.37372i	0.726791	−	0.686859i	$-0.241011\pi$
$168$	2.89308e6	+	5.04377e6i	0.0470737	+	0.0820677i
$169$	−2.24842e7	−	5.85819e7i	−0.358322	−	0.933598i
$170$	−3.74230e7	−	6.48185e7i	−0.584207	−	1.01188i
$171$	1.90740e7	+	1.10124e7i	0.291712	+	0.168420i
$172$	−7.70734e6	+	1.33495e7i	−0.115493	+	0.200039i
$173$	−3.36212e7	−	5.82336e7i	−0.493687	−	0.855090i	0.506287	−	0.862365i	$-0.331018\pi$
$173$	−3.36212e7	−	5.82336e7i	−0.493687	−	0.855090i	−0.999974	+	0.00727475i	$0.997684\pi$
$174$		−	3.14726e7i		−	0.452909i
$175$	6.91380e6	−	3.96572e6i	0.0975177	−	0.0559357i
$176$			5.33022e7i			0.736972i
$177$	8.13063e7	−	4.69422e7i	1.10209	−	0.636293i
$178$	−5.38281e7	+	9.32330e7i	−0.715383	+	1.23908i
$179$	1.85692e7	−	3.21628e7i	0.241996	−	0.419149i	−0.719287	−	0.694713i	$-0.755531\pi$
$179$	1.85692e7	−	3.21628e7i	0.241996	−	0.419149i	0.961283	+	0.275564i	$0.0888647\pi$
$180$	2.28749e7	−	1.32068e7i	0.292352	−	0.168789i
$181$	−1.25650e8			−1.57503			−0.787513	−	0.616298i	$-0.788632\pi$
$181$	−1.25650e8			−1.57503			−0.787513	+	0.616298i	$0.788632\pi$
$182$	6.66839e7	−	9.64366e7i	0.819919	−	1.18575i
$183$	−1.82901e7			−0.220617
$184$	6.55968e6	−	3.78723e6i	0.0776284	−	0.0448188i
$185$	−5.41259e7	+	9.37488e7i	−0.628498	+	1.08859i
$186$	−3.56459e7	+	6.17404e7i	−0.406176	+	0.703517i
$187$	−4.78992e7	+	2.76546e7i	−0.535652	+	0.309259i
$188$			2.49543e6i			0.0273901i
$189$	8.72671e7	+	5.07124e7i	0.940231	+	0.546384i
$190$			1.63129e8i			1.72541i
$191$	7.37072e7	+	1.27665e8i	0.765408	+	1.32573i	0.940030	+	0.341091i	$0.110796\pi$
$191$	7.37072e7	+	1.27665e8i	0.765408	+	1.32573i	−0.174622	+	0.984636i	$0.555870\pi$
$192$	4.72848e7	−	8.18996e7i	0.482133	−	0.835079i
$193$	−1.50888e8	−	8.71150e7i	−1.51079	−	0.872253i	−0.999921	−	0.0125929i	$-0.995991\pi$
$193$	−1.50888e8	−	8.71150e7i	−1.51079	−	0.872253i	−0.510866	−	0.859660i	$-0.670675\pi$
$194$	−1.29018e8	−	2.23466e8i	−1.26866	−	2.19738i
$195$	7.54693e7	+	5.18714e7i	0.728869	+	0.500964i
$196$	1.13662e8	+	641189.i	1.07825	+	0.00608261i
$197$			7.82827e7i			0.729515i	0.931103	+	0.364757i	$0.118848\pi$
$197$			7.82827e7i			0.729515i	−0.931103	+	0.364757i	$0.881152\pi$
$198$	−1.88106e7	−	3.25810e7i	−0.172217	−	0.298288i
$199$	−9.05391e7	+	1.56818e8i	−0.814424	+	1.41062i	0.0953167	+	0.995447i	$0.469614\pi$
$199$	−9.05391e7	+	1.56818e8i	−0.814424	+	1.41062i	−0.909741	+	0.415177i	$0.863720\pi$
$200$	1.24277e6	+	717515.i	0.0109847	+	0.00634200i
$201$	7.50323e7	−	4.33199e7i	0.651721	−	0.376271i
$202$			2.36252e8i			2.01672i
$203$	−3.86090e7	−	2.24364e7i	−0.323931	−	0.188242i
$204$	8.42502e7			0.694809
$205$	9.68366e7	+	1.67726e8i	0.785057	+	1.35976i
$206$	5.94169e7	+	3.43044e7i	0.473560	+	0.273410i
$207$	1.50475e7	−	2.60630e7i	0.117914	−	0.204234i
$208$	−1.18465e8	−	9.32638e6i	−0.912787	−	0.0718607i
$209$	1.20548e8			0.913373
$210$	−482634.	+	1.71112e8i	−0.00359625	+	1.27500i
$211$	1.96995e8			1.44367			0.721833	−	0.692067i	$-0.243300\pi$
$211$	1.96995e8			1.44367			0.721833	+	0.692067i	$0.243300\pi$
$212$	6.40290e6	+	1.10902e7i	0.0461531	+	0.0799396i
$213$	−1.00118e8	−	5.78029e7i	−0.709875	−	0.409847i
$214$	−2.77100e8	−	1.59984e8i	−1.93281	−	1.11591i
$215$	−2.85141e7	+	1.64626e7i	−0.195671	+	0.112970i
$216$			1.81723e7i			0.122694i
$217$	5.03287e7	+	8.77424e7i	0.334354	+	0.582909i
$218$	−3.63965e7			−0.237937
$219$	6.40212e7	−	3.69627e7i	0.411879	−	0.237798i
$220$	7.22851e7	−	1.25201e8i	0.457688	−	0.792738i
$221$	−5.30819e7	−	1.11296e8i	−0.330806	−	0.693594i
$222$	−1.17431e8	−	2.03397e8i	−0.720358	−	1.24770i
$223$			1.35076e7i			0.0815661i	0.999168	+	0.0407831i	$0.0129853\pi$
$223$			1.35076e7i			0.0815661i	−0.999168	+	0.0407831i	$0.987015\pi$
$224$	−1.19920e8	−	2.09067e8i	−0.712891	−	1.24285i
$225$	5.70167e6			0.0333705
$226$	−2.37749e8	+	1.37264e8i	−1.37006	+	0.791004i
$227$	−9.60630e7	−	5.54620e7i	−0.545087	−	0.314706i	0.202051	−	0.979375i	$-0.435239\pi$
$227$	−9.60630e7	−	5.54620e7i	−0.545087	−	0.314706i	−0.747138	+	0.664669i	$0.768573\pi$
$228$	−1.59025e8	−	9.18129e7i	−0.888571	−	0.513017i
$229$	−1.03425e7	+	5.97126e6i	−0.0569118	+	0.0328581i	−0.528186	−	0.849129i	$-0.677128\pi$
$229$	−1.03425e7	+	5.97126e6i	−0.0569118	+	0.0328581i	0.471274	+	0.881987i	$0.343794\pi$
$230$	2.22902e8			1.20800
$231$	1.26447e8	+	356654.i	0.674942	+	0.00190373i
$232$		−	8.03985e6i		−	0.0422708i
$233$	−1.20535e8	−	2.08772e8i	−0.624261	−	1.08125i	−0.988683	−	0.150018i	$-0.952067\pi$
$233$	−1.20535e8	−	2.08772e8i	−0.624261	−	1.08125i	0.364422	−	0.931234i	$-0.381266\pi$
$234$	7.57033e7	−	3.61063e7i	0.386242	−	0.184216i
$235$	−2.66508e6	+	4.61606e6i	−0.0133959	+	0.0232025i
$236$	2.86158e8	−	1.65214e8i	1.41714	−	0.818189i
$237$	−1.61479e8			−0.787945
$238$	1.15762e8	−	1.99206e8i	0.556605	−	0.957819i
$239$		−	2.58582e8i		−	1.22520i	−0.790394	−	0.612599i	$-0.790124\pi$
$239$		−	2.58582e8i		−	1.22520i	0.790394	−	0.612599i	$-0.209876\pi$
$240$	1.50191e8	−	8.67129e7i	0.701302	−	0.404897i
$241$	1.83502e8	+	1.05945e8i	0.844464	+	0.487552i	0.858779	−	0.512346i	$-0.171223\pi$
$241$	1.83502e8	+	1.05945e8i	0.844464	+	0.487552i	−0.0143149	+	0.999898i	$0.504557\pi$
$242$	9.69288e7	+	5.59619e7i	0.439642	+	0.253827i
$243$	6.39390e7	+	1.10746e8i	0.285854	+	0.495113i
$244$	−6.43723e7			−0.283684
$245$	2.09567e8	+	1.22575e8i	0.910419	+	0.532501i
$246$	−4.20192e8			−1.79960
$247$	−2.10925e7	+	2.67920e8i	−0.0890612	+	1.13127i
$248$	−9.10593e6	+	1.57719e7i	−0.0379091	+	0.0656605i
$249$	−2.97002e8	−	1.71474e8i	−1.21916	−	0.703884i
$250$	−1.66706e8	−	2.88744e8i	−0.674779	−	1.16875i
$251$	−2.84141e8			−1.13416			−0.567082	−	0.823661i	$-0.691928\pi$
$251$	−2.84141e8			−1.13416			−0.567082	+	0.823661i	$0.691928\pi$
$252$	7.03013e7	+	4.08533e7i	0.276733	+	0.160814i
$253$		−	1.64719e8i		−	0.639472i
$254$	−2.56523e7	+	1.48103e7i	−0.0982218	+	0.0567084i
$255$	1.55846e8	+	8.99779e7i	0.588580	+	0.339817i
$256$	−1.10812e8	+	1.91932e8i	−0.412807	+	0.715004i
$257$	−7.68091e7	−	1.33037e8i	−0.282258	−	0.488886i	0.689682	−	0.724112i	$-0.257750\pi$
$257$	−7.68091e7	−	1.33037e8i	−0.282258	−	0.488886i	−0.971941	+	0.235226i	$0.924417\pi$
$258$		−	7.14345e7i		−	0.258964i
$259$	−3.33232e8	−	939908.i	−1.19178	−	0.00336152i
$260$	2.65615e8	+	1.82562e8i	0.937229	+	0.644174i
$261$	−1.59720e7	−	2.76643e7i	−0.0556054	−	0.0963114i
$262$	−1.54181e8	−	8.90164e7i	−0.529634	−	0.305785i
$263$	1.41515e8	−	2.45112e8i	0.479687	−	0.830843i	−0.520041	−	0.854141i	$-0.674083\pi$
$263$	1.41515e8	−	2.45112e8i	0.479687	−	0.830843i	0.999729	+	0.0232985i	$0.00741682\pi$
$264$	1.13831e7	+	1.97161e7i	0.0380756	+	0.0659489i
$265$			2.73528e7i			0.0902903i
$266$	−4.35592e8	+	2.49854e8i	−1.41904	+	0.813954i
$267$		−	2.58843e8i		−	0.832237i
$268$	2.64077e8	−	1.52465e8i	0.838027	−	0.483835i
$269$	2.07106e8	−	3.58718e8i	0.648724	−	1.12362i	−0.334704	−	0.942323i	$-0.608636\pi$
$269$	2.07106e8	−	3.58718e8i	0.648724	−	1.12362i	0.983428	−	0.181299i	$-0.0580302\pi$
$270$	−2.67388e8	+	4.63129e8i	−0.826739	+	1.43195i
$271$	2.59306e8	−	1.49710e8i	0.791443	−	0.456940i	−0.0490271	−	0.998797i	$-0.515612\pi$
$271$	2.59306e8	−	1.49710e8i	0.791443	−	0.456940i	0.840470	+	0.541857i	$0.182279\pi$
$272$	−2.33515e8			−0.703596
$273$	−2.29173e7	+	2.80969e8i	−0.0681702	+	0.835774i
$274$	−1.41534e8			−0.415655
$275$	2.70261e7	−	1.56035e7i	0.0783643	−	0.0452436i
$276$	−1.25455e8	+	2.17294e8i	−0.359174	+	0.622108i
$277$	−6.66639e7	+	1.15465e8i	−0.188457	+	0.326416i	−0.944736	−	0.327833i	$-0.893682\pi$
$277$	−6.66639e7	+	1.15465e8i	−0.188457	+	0.326416i	0.756279	+	0.654249i	$0.227015\pi$
$278$	1.00445e8	−	5.79919e7i	0.280396	−	0.161886i
$279$			7.23594e7i			0.199471i
$280$	−123291.	+	4.37114e7i	−0.000335645	+	0.118998i
$281$			3.80897e8i			1.02408i	0.858961	+	0.512041i	$0.171110\pi$
$281$			3.80897e8i			1.02408i	−0.858961	+	0.512041i	$0.828890\pi$
$282$	−5.78215e6	−	1.00150e7i	−0.0153539	−	0.0265937i
$283$	1.63114e8	−	2.82521e8i	0.427797	−	0.740967i	−0.568880	−	0.822421i	$-0.692623\pi$
$283$	1.63114e8	−	2.82521e8i	0.427797	−	0.740967i	0.996677	+	0.0814540i	$0.0259564\pi$
$284$	−3.52365e8	−	2.03438e8i	−0.912806	−	0.527009i
$285$	−1.96109e8	−	3.39671e8i	−0.501812	−	0.869165i
$286$	2.60025e8	−	3.78318e8i	0.657255	−	0.956261i
$287$	−2.99549e8	+	5.15471e8i	−0.747965	+	1.28712i
$288$		−	1.72413e8i		−	0.425302i
$289$	8.40157e7	+	1.45519e8i	0.204747	+	0.354633i
$290$	1.18299e8	−	2.04899e8i	0.284831	−	0.493341i
$291$	5.37290e8	+	3.10205e8i	1.27815	+	0.737943i
$292$	2.25323e8	−	1.30090e8i	0.529622	−	0.305777i
$293$		−	1.14706e8i		−	0.266410i	−0.991088	−	0.133205i	$-0.957473\pi$
$293$		−	1.14706e8i		−	0.266410i	0.991088	−	0.133205i	$-0.0425269\pi$
$294$	−4.57647e8	+	2.60791e8i	−1.05030	+	0.598519i
$295$	7.05782e8			1.60064
$296$	−2.99984e7	−	5.19588e7i	−0.0672323	−	0.116450i
$297$	3.42240e8	+	1.97593e8i	0.758025	+	0.437646i
$298$	−3.37812e8	+	5.85107e8i	−0.739465	+	1.28079i
$299$	3.66091e8	+	2.88211e7i	0.792027	+	0.0623536i
$300$	−4.75363e7			−0.101649
$301$	−8.76323e7	−	5.09246e7i	−0.185217	−	0.107633i
$302$	1.19684e9			2.50041
$303$	−2.84016e8	−	4.91931e8i	−0.586535	−	1.01591i
$304$	4.40766e8	+	2.54476e8i	0.899809	+	0.519505i
$305$	−1.19076e8	−	6.87486e7i	−0.240312	−	0.138744i
$306$	1.42736e8	−	8.24086e7i	0.284779	−	0.164417i
$307$		−	1.37128e8i		−	0.270485i	−0.990813	−	0.135242i	$-0.956819\pi$
$307$		−	1.37128e8i		−	0.270485i	0.990813	−	0.135242i	$-0.0431813\pi$
$308$	4.45031e8	+	1.25525e6i	0.867886	+	0.00244794i
$309$	−1.64959e8			−0.318070
$310$	−4.64137e8	+	2.67970e8i	−0.884872	+	0.510881i
$311$	2.29363e8	−	3.97269e8i	0.432377	−	0.748899i	−0.564700	−	0.825296i	$-0.691008\pi$
$311$	2.29363e8	−	3.97269e8i	0.432377	−	0.748899i	0.997077	+	0.0763970i	$0.0243416\pi$
$312$	−4.58112e7	+	2.18494e7i	−0.0853946	+	0.0407285i
$313$	1.22478e8	+	2.12138e8i	0.225763	+	0.391033i	0.956548	−	0.291575i	$-0.0941793\pi$
$313$	1.22478e8	+	2.12138e8i	0.225763	+	0.391033i	−0.730785	+	0.682607i	$0.760846\pi$
$314$		−	2.89238e8i		−	0.527232i
$315$	8.64129e7	+	1.50651e8i	0.155773	+	0.271572i
$316$	−5.68325e8			−1.01319
$317$	−6.55445e8	+	3.78421e8i	−1.15566	+	0.667218i	−0.950259	−	0.311460i	$-0.899182\pi$
$317$	−6.55445e8	+	3.78421e8i	−1.15566	+	0.667218i	−0.205397	+	0.978679i	$0.565849\pi$
$318$	−5.13938e7	−	2.96722e7i	−0.0896223	−	0.0517434i
$319$	−1.51415e8	−	8.74196e7i	−0.261157	−	0.150779i
$320$	6.15685e8	−	3.55466e8i	1.05035	−	0.606419i
$321$	7.69314e8			1.29818
$322$	3.41404e8	+	5.95200e8i	0.569867	+	0.993499i
$323$			5.28116e8i			0.872008i
$324$	−2.03009e8	−	3.51622e8i	−0.331595	−	0.574339i
$325$	2.99503e7	+	6.27961e7i	0.0483960	+	0.101471i
$326$	−2.80434e8	+	4.85726e8i	−0.448301	+	0.776480i
$327$	7.57858e7	−	4.37549e7i	0.119859	−	0.0692006i
$328$	−1.07340e8			−0.167960
$329$	−1.64079e7	−	46279.8i	−0.0254020	−	7.16482e-5i
$330$			6.69965e8i			1.02625i
$331$	3.11628e8	−	1.79919e8i	0.472323	−	0.272696i	−0.244889	−	0.969551i	$-0.578751\pi$
$331$	3.11628e8	−	1.79919e8i	0.472323	−	0.272696i	0.717212	+	0.696855i	$0.245418\pi$
$332$	−1.04530e9	−	6.03505e8i	−1.56768	−	0.905102i
$333$	−2.06443e8	−	1.19190e8i	−0.306369	−	0.176883i
$334$	6.74265e8	+	1.16786e9i	0.990188	+	1.71506i
$335$	6.51319e8			0.946536
$336$	4.61581e8	+	2.68233e8i	0.663836	+	0.385767i
$337$	−1.38881e9			−1.97668			−0.988341	−	0.152255i	$-0.951347\pi$
$337$	−1.38881e9			−1.97668			−0.988341	+	0.152255i	$0.951347\pi$
$338$	7.95324e8	+	6.44106e8i	1.12030	+	0.907295i
$339$	3.30032e8	−	5.71632e8i	0.460105	−	0.796925i
$340$	5.48502e8	+	3.16678e8i	0.756837	+	0.436960i
$341$	1.98023e8	+	3.42986e8i	0.270442	+	0.468420i
$342$	−3.59224e8			−0.485595
$343$	−6.32387e6	+	7.47333e8i	−0.00846162	+	0.999964i
$344$		−	1.82483e7i		−	0.0241695i
$345$	−4.64133e8	+	2.67967e8i	−0.608521	+	0.351330i
$346$	9.49792e8	+	5.48363e8i	1.23271	+	0.711708i
$347$	−6.34337e8	+	1.09870e9i	−0.815017	+	1.41165i	0.0942983	+	0.995544i	$0.469939\pi$
$347$	−6.34337e8	+	1.09870e9i	−0.815017	+	1.41165i	−0.909316	+	0.416107i	$0.863394\pi$
$348$	1.33163e8	+	2.30644e8i	0.169377	+	0.293370i
$349$			5.14699e8i			0.648133i	0.946034	+	0.324066i	$0.105050\pi$
$349$			5.14699e8i			0.648133i	−0.946034	+	0.324066i	$0.894950\pi$
$350$	−6.53162e7	+	1.12398e8i	−0.0814297	+	0.140126i
$351$	−4.99036e8	+	7.26063e8i	−0.615966	+	0.896189i
$352$	−4.71836e8	−	8.17244e8i	−0.576623	−	0.998740i
$353$	−6.47888e8	−	3.74058e8i	−0.783951	−	0.452614i	0.0538780	−	0.998548i	$-0.482842\pi$
$353$	−6.47888e8	−	3.74058e8i	−0.783951	−	0.452614i	−0.837829	+	0.545933i	$0.816175\pi$
$354$	−7.65630e8	+	1.32611e9i	−0.917292	+	1.58880i
$355$	−4.34537e8	−	7.52640e8i	−0.515499	−	0.892870i
$356$		−	9.11000e8i		−	1.07015i
$357$	−1.56249e6	+	5.53959e8i	−0.00181751	+	0.644375i
$358$			6.05729e8i			0.697730i
$359$	−9.39185e6	+	5.42239e6i	−0.0107132	+	0.00618529i	−0.505347	−	0.862916i	$-0.668636\pi$
$359$	−9.39185e6	+	5.42239e6i	−0.0107132	+	0.00618529i	0.494634	+	0.869101i	$0.335302\pi$
$360$	−1.56346e7	+	2.70799e7i	−0.0176615	+	0.0305907i
$361$	1.28586e8	−	2.22717e8i	0.143853	−	0.249160i
$362$	1.77480e9	−	1.02468e9i	1.96639	−	1.13529i
$363$	−2.69104e8			−0.295289
$364$	−8.06576e7	+	9.88871e8i	−0.0876578	+	1.07469i
$365$	5.55738e8			0.598198
$366$	2.58347e8	−	1.49157e8i	0.275435	−	0.159022i
$367$	−4.29799e8	+	7.44434e8i	−0.453873	+	0.786131i	−0.998623	−	0.0524678i	$-0.983291\pi$
$367$	−4.29799e8	+	7.44434e8i	−0.453873	+	0.786131i	0.544750	+	0.838599i	$0.316625\pi$
$368$	3.47720e8	−	6.02269e8i	0.363716	−	0.629975i
$369$	−3.69347e8	+	2.13243e8i	−0.382686	+	0.220944i
$370$		−	1.76559e9i		−	1.81211i
$371$	−7.30383e7	+	4.18945e7i	−0.0742578	+	0.0425939i
$372$		−	6.03280e8i		−	0.607601i
$373$	−9.53919e8	−	1.65224e9i	−0.951766	−	1.64851i	−0.741600	−	0.670842i	$-0.765933\pi$
$373$	−9.53919e8	−	1.65224e9i	−0.951766	−	1.64851i	−0.210166	−	0.977666i	$-0.567401\pi$
$374$	4.51048e8	−	7.81238e8i	0.445833	−	0.772205i
$375$	6.94241e8	+	4.00820e8i	0.679831	+	0.392500i
$376$	−1.47708e6	−	2.55838e6i	−0.00143300	−	0.00248203i
$377$	2.20785e8	−	3.21228e8i	0.212215	−	0.308758i
$378$	−1.64620e9	−	4.64325e6i	−1.56770	−	0.00442181i
$379$		−	7.96802e7i		−	0.0751818i	−0.999293	−	0.0375909i	$-0.988032\pi$
$379$		−	7.96802e7i		−	0.0751818i	0.999293	−	0.0375909i	$-0.0119684\pi$
$380$	−6.90209e8	−	1.19548e9i	−0.645264	−	1.11763i
$381$	3.56093e7	−	6.16771e7i	0.0329857	−	0.0571329i
$382$	−2.08222e9	−	1.20217e9i	−1.91119	−	1.10343i
$383$	2.29766e8	−	1.32655e8i	0.208973	−	0.120650i	−0.391861	−	0.920024i	$-0.628169\pi$
$383$	2.29766e8	−	1.32655e8i	0.208973	−	0.120650i	0.600834	+	0.799374i	$0.294835\pi$
$384$			2.09312e8i			0.188640i
$385$	8.21879e8	+	4.77608e8i	0.733999	+	0.426539i
$386$	2.84170e9			2.51491
$387$	−3.62522e7	−	6.27906e7i	−0.0317940	−	0.0550689i
$388$	1.89100e9	+	1.09177e9i	1.64354	+	0.948897i
$389$	3.38884e8	−	5.86965e8i	0.291896	−	0.505578i	−0.682362	−	0.731014i	$-0.739047\pi$
$389$	3.38884e8	−	5.86965e8i	0.291896	−	0.505578i	0.974258	+	0.225436i	$0.0723806\pi$
$390$	−1.48901e9	−	1.17225e8i	−1.27108	−	0.100068i
$391$	7.21626e8			0.610511
$392$	−1.16908e8	+	6.66206e7i	−0.0980267	+	0.0558608i
$393$	4.28053e8			0.355733
$394$	−6.38398e8	−	1.10574e9i	−0.525841	−	0.910783i
$395$	−1.05129e9	−	6.06962e8i	−0.858287	−	0.495532i
$396$	2.75705e8	+	1.59178e8i	0.223106	+	0.128810i
$397$	9.46548e8	−	5.46490e8i	0.759234	−	0.438344i	−0.0697864	−	0.997562i	$-0.522232\pi$
$397$	9.46548e8	−	5.46490e8i	0.759234	−	0.438344i	0.829021	+	0.559218i	$0.188898\pi$
$398$		−	2.95340e9i		−	2.34818i
$399$	6.06634e8	−	1.04391e9i	0.478103	−	0.822731i
$400$	1.31756e8			0.102934
$401$	9.60652e8	−	5.54633e8i	0.743979	−	0.429537i	−0.0795350	−	0.996832i	$-0.525344\pi$
$401$	9.60652e8	−	5.54633e8i	0.743979	−	0.429537i	0.823514	+	0.567295i	$0.192010\pi$
$402$	−7.06550e8	+	1.22378e9i	−0.542440	+	0.939533i
$403$	−7.96941e8	+	3.80097e8i	−0.606539	+	0.289286i
$404$	−9.99597e8	−	1.73135e9i	−0.754207	−	1.30632i
$405$		−	8.67242e8i		−	0.648705i
$406$	7.28319e8	+	2.05428e6i	0.540108	+	0.00152342i
$407$	−1.30473e9			−0.959266
$408$	−8.63754e7	+	4.98689e7i	−0.0629621	+	0.0363512i
$409$	−1.35599e9	−	7.82884e8i	−0.980001	−	0.565804i	−0.0777305	−	0.996974i	$-0.524767\pi$
$409$	−1.35599e9	−	7.82884e8i	−0.980001	−	0.565804i	−0.902270	+	0.431171i	$0.858101\pi$
$410$	−2.73562e9	−	1.57941e9i	−1.96025	−	1.13175i
$411$	2.94705e8	−	1.70148e8i	0.209383	−	0.120887i
$412$	−5.80576e8			−0.408996
$413$	1.08100e9	+	1.88460e9i	0.755093	+	1.31642i
$414$			4.90850e8i			0.339975i
$415$	−1.28907e9	−	2.23273e9i	−0.885335	−	1.53344i
$416$	1.89890e9	−	9.05671e8i	1.29323	−	0.616799i
$417$	−1.39433e8	+	2.41505e8i	−0.0941648	+	0.163098i
$418$	−1.70273e9	+	9.83072e8i	−1.14033	+	0.658368i
$419$	−7.62491e8			−0.506391			−0.253195	−	0.967415i	$-0.581482\pi$
$419$	−7.62491e8			−0.506391			−0.253195	+	0.967415i	$0.581482\pi$
$420$	−7.20447e8	−	1.25602e9i	−0.474492	−	0.827225i
$421$			8.50461e8i			0.555478i	0.960657	+	0.277739i	$0.0895850\pi$
$421$			8.50461e8i			0.555478i	−0.960657	+	0.277739i	$0.910415\pi$
$422$	−2.78254e9	+	1.60650e9i	−1.80239	+	1.04061i
$423$	−1.01650e7	−	5.86875e6i	−0.00653003	−	0.00377011i
$424$	−1.31288e7	−	7.57993e6i	−0.00836460	−	0.00482931i
$425$	6.83583e7	+	1.18400e8i	0.0431946	+	0.0748153i
$426$	1.88554e9			1.18168
$427$	1.19383e6	−	4.23258e8i	0.000742073	−	0.263092i
$428$	2.70761e9			1.66929
$429$	−8.66262e7	+	1.10034e9i	−0.0529723	+	0.672863i
$430$	2.68506e8	−	4.65067e8i	0.162860	−	0.282082i
$431$	2.25071e9	+	1.29945e9i	1.35410	+	0.781788i	0.988820	−	0.149111i	$-0.0476412\pi$
$431$	2.25071e9	+	1.29945e9i	1.35410	+	0.781788i	0.365276	+	0.930899i	$0.380975\pi$
$432$	8.34234e8	+	1.44494e9i	0.497846	+	0.862294i
$433$	−2.84767e9			−1.68571			−0.842854	−	0.538143i	$-0.819126\pi$
$433$	−2.84767e9			−1.68571			−0.842854	+	0.538143i	$0.819126\pi$
$434$	−1.42643e9	−	8.28923e8i	−0.837599	−	0.486743i
$435$			5.68862e8i			0.331356i
$436$	2.66729e8	−	1.53996e8i	0.154123	−	0.0889828i
$437$	−1.36209e9	−	7.86402e8i	−0.780765	−	0.450775i
$438$	−6.02863e8	+	1.04419e9i	−0.342815	+	0.593772i
$439$	−3.43864e8	−	5.95590e8i	−0.193982	−	0.335986i	0.752585	−	0.658496i	$-0.228807\pi$
$439$	−3.43864e8	−	5.95590e8i	−0.193982	−	0.335986i	−0.946566	+	0.322509i	$0.895474\pi$
$440$			1.71146e8i			0.0957817i
$441$	−2.69921e8	+	4.61485e8i	−0.149865	+	0.256226i
$442$	1.65740e9	+	1.13916e9i	0.912953	+	0.627489i
$443$	−2.70915e8	−	4.69238e8i	−0.148054	−	0.256437i	0.782454	−	0.622708i	$-0.213968\pi$
$443$	−2.70915e8	−	4.69238e8i	−0.148054	−	0.256437i	−0.930508	+	0.366271i	$0.880634\pi$
$444$	1.72117e9	+	9.93718e8i	0.933219	+	0.538794i
$445$	9.72934e8	−	1.68517e9i	0.523387	−	0.906533i
$446$	−1.10154e8	−	1.90793e8i	−0.0587936	−	0.101834i
$447$		−	1.62443e9i		−	0.860252i
$448$	1.89218e9	+	1.09958e9i	0.994236	+	0.577768i
$449$			9.77637e8i			0.509701i	0.966980	+	0.254851i	$0.0820263\pi$
$449$			9.77637e8i			0.509701i	−0.966980	+	0.254851i	$0.917974\pi$
$450$	−8.05356e7	+	4.64973e7i	−0.0416624	+	0.0240538i
$451$	−1.16714e9	+	2.02155e9i	−0.599110	+	1.03769i
$452$	1.16155e9	−	2.01186e9i	0.591634	−	1.02474i
$453$	−2.49209e9	+	1.43881e9i	−1.25956	+	0.727209i
$454$	1.80918e9			0.907372
$455$	−1.20530e9	+	1.74308e9i	−0.599867	+	0.867514i
$456$	2.17381e8			0.107361
$457$	2.91060e9	−	1.68044e9i	1.42652	−	0.823599i	0.429671	−	0.902985i	$-0.358629\pi$
$457$	2.91060e9	−	1.68044e9i	1.42652	−	0.823599i	0.996844	+	0.0793866i	$0.0252962\pi$
$458$	9.73916e7	−	1.68687e8i	0.0473688	−	0.0820452i
$459$	−8.65645e8	+	1.49934e9i	−0.417826	+	0.723696i
$460$	−1.63352e9	+	9.43112e8i	−0.782477	+	0.451763i
$461$			3.75756e9i			1.78629i	0.449767	+	0.893146i	$0.351507\pi$
$461$			3.75756e9i			1.78629i	−0.449767	+	0.893146i	$0.648493\pi$
$462$	−1.78896e9	+	1.02614e9i	−0.844023	+	0.484128i
$463$			1.87992e9i			0.880251i	0.897936	+	0.440126i	$0.145066\pi$
$463$			1.87992e9i			0.880251i	−0.897936	+	0.440126i	$0.854934\pi$
$464$	−3.69085e8	−	6.39273e8i	−0.171519	−	0.297080i
$465$	6.44293e8	−	1.11595e9i	0.297165	−	0.514705i
$466$	3.40508e9	+	1.96593e9i	1.55875	+	0.899946i
$467$	−3.37085e8	−	5.83848e8i	−0.153155	−	0.265271i	0.779231	−	0.626737i	$-0.215610\pi$
$467$	−3.37085e8	−	5.83848e8i	−0.153155	−	0.265271i	−0.932386	+	0.361465i	$0.882277\pi$
$468$	−4.02017e8	+	5.84907e8i	−0.181294	+	0.263771i
$469$	9.97583e8	+	1.73917e9i	0.446523	+	0.778463i
$470$		−	8.69353e7i		−	0.0386237i
$471$	3.47715e8	+	6.02260e8i	0.153338	+	0.265589i
$472$	−1.95584e8	+	3.38762e8i	−0.0856125	+	0.148285i
$473$	−3.43672e8	−	1.98419e8i	−0.149324	−	0.0862125i
$474$	2.28087e9	−	1.31686e9i	0.983732	−	0.567958i
$475$		−	2.97978e8i		−	0.127572i
$476$	−5.49918e6	+	1.94966e9i	−0.00233708	+	0.828581i
$477$	−6.02332e7			−0.0254110
$478$	2.10875e9	+	3.65246e9i	0.883134	+	1.52963i
$479$	−3.07471e9	−	1.77518e9i	−1.27829	−	0.738021i	−0.301756	−	0.953385i	$-0.597573\pi$
$479$	−3.07471e9	−	1.77518e9i	−1.27829	−	0.738021i	−0.976534	+	0.215364i	$0.930906\pi$
$480$	−1.53518e9	+	2.65901e9i	−0.633600	+	1.09743i
$481$	2.28290e8	−	2.89978e9i	0.0935362	−	1.18811i
$482$	−3.45593e9			−1.40573
$483$	−1.42642e9	−	8.28915e8i	−0.576011	−	0.334730i
$484$	−9.47113e8			−0.379702
$485$	2.33198e9	+	4.03911e9i	0.928173	+	1.60764i
$486$	−1.80627e9	−	1.04285e9i	−0.713764	−	0.412092i
$487$	−6.50434e8	−	3.75528e8i	−0.255183	−	0.147330i	0.366952	−	0.930240i	$-0.380401\pi$
$487$	−6.50434e8	−	3.75528e8i	−0.255183	−	0.147330i	−0.622135	+	0.782910i	$0.713735\pi$
$488$	6.59961e7	−	3.81028e7i	0.0257068	−	0.0148418i
$489$		−	1.34852e9i		−	0.521528i
$490$	−3.95972e9	−	2.23376e7i	−1.52047	−	0.00857728i
$491$	−2.05688e9			−0.784193			−0.392096	−	0.919924i	$-0.628250\pi$
$491$	−2.05688e9			−0.784193			−0.392096	+	0.919924i	$0.628250\pi$
$492$	3.07934e9	−	1.77786e9i	1.16568	−	0.673007i
$493$	3.82982e8	−	6.63344e8i	0.143951	−	0.249330i
$494$	−1.88697e9	−	3.95636e9i	−0.704239	−	1.47656i
$495$	3.39999e8	+	5.88896e8i	0.125997	+	0.218233i
$496$			1.67210e9i			0.615285i
$497$	1.34417e9	−	2.31308e9i	0.491143	−	0.845170i
$498$	5.59351e9			2.02947
$499$	−5.03347e8	+	2.90608e8i	−0.181349	+	0.104702i	−0.587926	−	0.808914i	$-0.700056\pi$
$499$	−5.03347e8	+	2.90608e8i	−0.181349	+	0.104702i	0.406577	+	0.913616i	$0.366722\pi$
$500$	2.44339e9	+	1.41069e9i	0.874172	+	0.504704i
$501$	−2.80795e9	−	1.62117e9i	−0.997600	−	0.575965i
$502$	4.01347e9	−	2.31718e9i	1.41598	−	0.817516i
$503$	1.07133e9			0.375348			0.187674	−	0.982231i	$-0.439905\pi$
$503$	1.07133e9			0.375348			0.187674	+	0.982231i	$0.439905\pi$
$504$	−9.62562e7	−	271498.i	−0.0334905	−	9.44627e-5i
$505$		−	4.27022e9i		−	1.47547i
$506$	1.34329e9	+	2.32664e9i	0.460937	+	0.798366i
$507$	−2.43037e9	−	3.85057e8i	−0.828219	−	0.131219i
$508$	1.25327e8	−	2.17073e8i	0.0424152	−	0.0734653i
$509$	−1.79179e9	+	1.03449e9i	−0.602248	+	0.347708i	−0.769925	−	0.638134i	$-0.779707\pi$
$509$	−1.79179e9	+	1.03449e9i	−0.602248	+	0.347708i	0.167677	+	0.985842i	$0.446373\pi$
$510$	−2.93509e9			−0.979773
$511$	8.51187e8	+	1.48395e9i	0.282197	+	0.491978i
$512$		−	4.29791e9i		−	1.41518i
$513$	3.26786e9	−	1.88670e9i	1.06869	−	0.617009i
$514$	2.16985e9	+	1.25276e9i	0.704787	+	0.406909i
$515$	−1.07395e9	−	6.20046e8i	−0.346465	−	0.200032i
$516$	3.02244e8	+	5.23502e8i	0.0968464	+	0.167743i
$517$	−6.42430e7			−0.0204460
$518$	4.71454e9	−	2.70424e9i	1.49034	−	0.854852i
$519$	−2.63691e9			−0.827961
$520$	−3.80376e8	−	2.99457e7i	−0.118632	−	0.00933949i
$521$	2.41066e9	−	4.17539e9i	0.746801	−	1.29350i	−0.202548	−	0.979272i	$-0.564922\pi$
$521$	2.41066e9	−	4.17539e9i	0.746801	−	1.29350i	0.949349	−	0.314225i	$-0.101744\pi$
$522$	4.51206e8	+	2.60504e8i	0.138844	+	0.0801618i
$523$	7.55965e8	+	1.30937e9i	0.231071	+	0.400227i	0.958124	−	0.286355i	$-0.0924436\pi$
$523$	7.55965e8	+	1.30937e9i	0.231071	+	0.400227i	−0.727052	+	0.686582i	$0.759110\pi$
$524$	1.50654e9			0.457425
$525$	881598.	−	3.12559e8i	0.000265897	−	0.0942702i
$526$			4.61624e9i			1.38305i
$527$	−1.50260e9	+	8.67529e8i	−0.447206	+	0.258195i
$528$	1.81021e9	+	1.04513e9i	0.535193	+	0.308994i
$529$	6.27860e8	−	1.08748e9i	0.184403	−	0.319395i
$530$	−2.23063e8	−	3.86356e8i	−0.0650821	−	0.112725i
$531$			1.55419e9i			0.450479i
$532$	2.13505e9	−	3.67405e9i	0.614777	−	1.05792i
$533$	−4.28872e9	−	2.94771e9i	−1.22683	−	0.843219i
$534$	2.11087e9	+	3.65614e9i	0.599884	+	1.03903i
$535$	5.00854e9	+	2.89168e9i	1.41408	+	0.816417i
$536$	−1.80492e8	+	3.12621e8i	−0.0506269	+	0.0876883i
$537$	−7.28192e8	−	1.26127e9i	−0.202925	−	0.351477i
$538$			6.75582e9i			1.87042i
$539$	−1.65069e7	+	2.92613e9i	−0.00454051	+	0.804883i
$540$		−	4.52534e9i		−	1.23672i
$541$	2.21026e9	−	1.27610e9i	0.600142	−	0.346492i	−0.168956	−	0.985624i	$-0.554039\pi$
$541$	2.21026e9	−	1.27610e9i	0.600142	−	0.346492i	0.769097	+	0.639132i	$0.220706\pi$
$542$	−2.44178e9	+	4.22929e9i	−0.658733	+	1.14096i
$543$	−2.46369e9	+	4.26723e9i	−0.660368	+	1.14379i
$544$	3.58031e9	−	2.06709e9i	0.953509	−	0.550508i
$545$	6.57861e8			0.174079
$546$	−1.96760e9	−	4.15555e9i	−0.517324	−	1.09258i
$547$	−7.00643e9			−1.83038			−0.915189	−	0.403024i	$-0.867959\pi$
$547$	−7.00643e9			−1.83038			−0.915189	+	0.403024i	$0.867959\pi$
$548$	1.03722e9	−	5.98838e8i	0.269239	−	0.155445i
$549$	1.51390e8	−	2.62216e8i	0.0390477	−	0.0676326i
$550$	−2.54494e8	+	4.40796e8i	−0.0652241	+	0.112971i
$551$	−1.44578e9	+	8.34720e8i	−0.368189	+	0.212574i
$552$		−	2.97033e8i		−	0.0751655i
$553$	1.05400e7	−	3.73683e9i	0.00265035	−	0.939649i
$554$		−	2.17458e9i		−	0.543365i
$555$	2.12255e9	+	3.67637e9i	0.527027	+	0.912837i
$556$	−4.90735e8	+	8.49978e8i	−0.121084	+	0.209723i
$557$	1.38571e9	+	8.00040e8i	0.339765	+	0.196164i	0.660168	−	0.751118i	$-0.270485\pi$
$557$	1.38571e9	+	8.00040e8i	0.339765	+	0.196164i	−0.320403	+	0.947281i	$0.603818\pi$
$558$	−5.90093e8	−	1.02207e9i	−0.143781	−	0.249036i
$559$	5.01124e8	−	7.29101e8i	0.121340	−	0.176541i
$560$	1.99685e9	+	3.48128e9i	0.480493	+	0.837686i
$561$			2.16895e9i			0.518657i
$562$	−3.10622e9	−	5.38013e9i	−0.738168	−	1.27854i
$563$	−2.44334e9	+	4.23200e9i	−0.577039	+	0.999461i	0.418778	+	0.908089i	$0.362459\pi$
$563$	−2.44334e9	+	4.23200e9i	−0.577039	+	0.999461i	−0.995817	+	0.0913724i	$0.970875\pi$
$564$	8.47481e7	+	4.89293e7i	0.0198908	+	0.0114840i
$565$	4.29728e9	−	2.48103e9i	1.00236	−	0.578713i
$566$			5.32079e9i			1.23344i
$567$	2.31574e9	−	1.32830e9i	0.533517	−	0.306023i
$568$	4.81671e8			0.110289
$569$	−2.80539e8	−	4.85908e8i	−0.0638411	−	0.110576i	0.832338	−	0.554268i	$-0.187002\pi$
$569$	−2.80539e8	−	4.85908e8i	−0.0638411	−	0.110576i	−0.896179	+	0.443692i	$0.853668\pi$
$570$	5.54006e9	+	3.19855e9i	1.25300	+	0.723422i
$571$	1.44527e9	−	2.50328e9i	0.324880	−	0.562708i	−0.656608	−	0.754232i	$-0.728010\pi$
$571$	1.44527e9	−	2.50328e9i	0.324880	−	0.562708i	0.981488	+	0.191524i	$0.0613429\pi$
$572$	−3.04881e8	+	3.87266e9i	−0.0681153	+	0.865213i
$573$	5.78087e9			1.28367
$574$	2.74268e7	−	9.72381e9i	0.00605318	−	2.14608i
$575$	−4.07162e8			−0.0893160
$576$	7.82767e8	+	1.35579e9i	0.170669	+	0.295607i
$577$	−5.59334e9	−	3.22931e9i	−1.21215	−	0.699834i	−0.248921	−	0.968524i	$-0.580076\pi$
$577$	−5.59334e9	−	3.22931e9i	−1.21215	−	0.699834i	−0.963227	+	0.268690i	$0.913409\pi$
$578$	−2.37343e9	−	1.37030e9i	−0.511245	−	0.295167i
$579$	−5.91707e9	+	3.41622e9i	−1.26687	+	0.731427i
$580$			2.00212e9i			0.426080i
$581$	3.98753e9	−	6.86184e9i	0.843505	−	1.45152i
$582$	−1.01189e10			−2.12766
$583$	−2.85507e8	+	1.64838e8i	−0.0596729	+	0.0344521i
$584$	−1.54005e8	+	2.66744e8i	−0.0319955	+	0.0554178i
$585$	−1.36832e9	+	6.52615e8i	−0.282581	+	0.134776i
$586$	9.35433e8	+	1.62022e9i	0.192031	+	0.332607i
$587$			6.55662e9i			1.33797i	0.743275	+	0.668986i	$0.233271\pi$
$587$			6.55662e9i			1.33797i	−0.743275	+	0.668986i	$0.766729\pi$
$588$	2.25040e9	−	3.84752e9i	0.456498	−	0.780477i
$589$	3.78161e9			0.762559
$590$	−9.96911e9	+	5.75567e9i	−1.99836	+	1.15376i
$591$	2.65858e9	+	1.53493e9i	0.529777	+	0.305867i
$592$	−4.77054e9	−	2.75427e9i	−0.945021	−	0.545608i
$593$	4.77753e9	−	2.75831e9i	0.940832	−	0.543190i	0.0506112	−	0.998718i	$-0.483883\pi$
$593$	4.77753e9	−	2.75831e9i	0.940832	−	0.543190i	0.890221	+	0.455529i	$0.150550\pi$
$594$	−6.44549e9			−1.26184
$595$	−2.09238e9	+	3.60062e9i	−0.407222	+	0.700757i
$596$		−	5.71721e9i		−	1.10617i
$597$	3.55050e9	+	6.14964e9i	0.682935	+	1.18288i
$598$	−5.40604e9	+	2.57838e9i	−1.03377	+	0.493053i
$599$	2.72850e9	−	4.72591e9i	0.518717	−	0.898445i	−0.481046	−	0.876695i	$-0.659743\pi$
$599$	2.72850e9	−	4.72591e9i	0.518717	−	0.898445i	0.999763	−	0.0217496i	$-0.00692367\pi$
$600$	4.87354e7	−	2.81374e7i	0.00921118	−	0.00531808i
$601$	−8.12584e8			−0.152689			−0.0763445	−	0.997081i	$-0.524325\pi$
$601$	−8.12584e8			−0.152689			−0.0763445	+	0.997081i	$0.524325\pi$
$602$	1.65309e9	+	4.66267e6i	0.308822	+	0.000871058i
$603$			1.43426e9i			0.266390i
$604$	−8.77093e9	+	5.06390e9i	−1.61963	+	0.935095i
$605$	−1.75197e9	−	1.01150e9i	−0.321650	−	0.185705i
$606$	8.02341e9	+	4.63232e9i	1.46455	+	0.845560i
$607$	−3.37578e9	−	5.84702e9i	−0.612652	−	1.06114i	−0.990792	−	0.135395i	$-0.956770\pi$
$607$	−3.37578e9	−	5.84702e9i	−0.612652	−	1.06114i	0.378140	−	0.925748i	$-0.376564\pi$
$608$	−9.01058e9			−1.62589
$609$	−1.51900e9	+	8.71289e8i	−0.272518	+	0.156315i
$610$	2.24259e9			0.400032
$611$	1.12407e7	−	1.42781e8i	0.00199365	−	0.0253237i
$612$	−6.97352e8	+	1.20785e9i	−0.122977	+	0.213002i
$613$	5.35835e9	+	3.09364e9i	0.939549	+	0.542449i	0.889819	−	0.456314i	$-0.150831\pi$
$613$	5.35835e9	+	3.09364e9i	0.939549	+	0.542449i	0.0497301	+	0.998763i	$0.484164\pi$
$614$	1.11828e9	+	1.93692e9i	0.194968	+	0.337694i
$615$	7.59491e9			1.31662
$616$	−4.57000e8	+	2.62133e8i	−0.0787741	+	0.0451845i
$617$			1.38127e9i			0.236745i	0.992969	+	0.118372i	$0.0377676\pi$
$617$			1.38127e9i			0.236745i	−0.992969	+	0.118372i	$0.962232\pi$
$618$	2.33004e9	−	1.34525e9i	0.397103	−	0.229268i
$619$	4.96431e9	+	2.86615e9i	0.841283	+	0.485715i	0.857700	−	0.514150i	$-0.171893\pi$
$619$	4.96431e9	+	2.86615e9i	0.841283	+	0.485715i	−0.0164173	+	0.999865i	$0.505226\pi$
$620$	2.26759e9	−	3.92759e9i	0.382115	−	0.661843i
$621$	−2.57802e9	−	4.46525e9i	−0.431981	−	0.748213i
$622$			7.48185e9i			1.24665i
$623$	5.98997e9	+	1.68952e7i	0.992469	+	0.00279934i
$624$	−2.63955e9	+	3.84036e9i	−0.434894	+	0.632741i
$625$	3.35627e9	+	5.81323e9i	0.549891	+	0.952440i
$626$	−3.45998e9	−	1.99762e9i	−0.563720	−	0.325464i
$627$	2.36365e9	−	4.09396e9i	0.382954	−	0.663296i
$628$	1.22378e9	+	2.11966e9i	0.197172	+	0.341513i
$629$		−	5.71595e9i		−	0.915823i
$630$	−2.44914e9	−	1.42324e9i	−0.390231	−	0.226770i
$631$			9.71636e9i			1.53958i	0.638300	+	0.769788i	$0.279638\pi$
$631$			9.71636e9i			1.53958i	−0.638300	+	0.769788i	$0.720362\pi$
$632$	5.82661e8	−	3.36399e8i	0.0918134	−	0.0530085i
$633$	3.86259e9	−	6.69020e9i	0.605293	−	1.04840i
$634$	6.17207e9	−	1.06903e10i	0.961874	−	1.66601i
$635$	4.63661e8	−	2.67695e8i	0.0718608	−	0.0414889i
$636$	5.02180e8			0.0774034
$637$	−6.50050e9	−	5.48677e8i	−0.996457	−	0.0841063i
$638$	2.85164e9			0.434732
$639$	1.65738e9	−	9.56888e8i	0.251286	−	0.145080i
$640$	−7.86757e8	+	1.36270e9i	−0.118634	+	0.205481i
$641$	4.72967e9	−	8.19203e9i	0.709297	−	1.22854i	−0.255822	−	0.966724i	$-0.582346\pi$
$641$	4.72967e9	−	8.19203e9i	0.709297	−	1.22854i	0.965118	−	0.261814i	$-0.0843207\pi$
$642$	−1.08665e10	+	6.27377e9i	−1.62075	+	0.935742i
$643$		−	1.20848e10i		−	1.79267i	−0.443378	−	0.896335i	$-0.646220\pi$
$643$		−	1.20848e10i		−	1.79267i	0.443378	−	0.896335i	$-0.353780\pi$
$644$	−5.02028e9	−	2.91737e9i	−0.740675	−	0.430419i
$645$			1.29117e9i			0.189463i
$646$	−4.30680e9	−	7.45959e9i	−0.628551	−	1.08868i
$647$	2.31722e9	−	4.01355e9i	0.336359	−	0.582590i	−0.647386	−	0.762162i	$-0.724138\pi$
$647$	2.31722e9	−	4.01355e9i	0.336359	−	0.582590i	0.983745	+	0.179572i	$0.0574712\pi$
$648$	4.16260e8	+	2.40328e8i	0.0600969	+	0.0346969i
$649$	4.25329e9	+	7.36692e9i	0.610757	+	1.05786i
$650$	−9.35150e8	−	6.42745e8i	−0.133562	−	0.0917998i
$651$	3.96666e9	+	1.11883e7i	0.563497	+	0.00158939i
$652$		−	4.74614e9i		−	0.670616i
$653$	2.48103e9	+	4.29726e9i	0.348686	+	0.603943i	0.986016	−	0.166648i	$-0.0532945\pi$
$653$	2.48103e9	+	4.29726e9i	0.348686	+	0.603943i	−0.637330	+	0.770591i	$0.719961\pi$
$654$	−7.13645e8	+	1.23607e9i	−0.0997609	+	0.172791i
$655$	2.78680e9	+	1.60896e9i	0.387490	+	0.223717i
$656$	−8.53497e9	+	4.92767e9i	−1.18042	+	0.681519i
$657$			1.22378e9i			0.168355i
$658$	2.32138e8	−	1.33153e8i	0.0317654	−	0.0182205i
$659$	−8.00563e9			−1.08967			−0.544837	−	0.838542i	$-0.683408\pi$
$659$	−8.00563e9			−1.08967			−0.544837	+	0.838542i	$0.683408\pi$
$660$	−2.83466e9	−	4.90978e9i	−0.383794	−	0.664750i
$661$	1.15583e9	+	6.67319e8i	0.155664	+	0.0898729i	0.575809	−	0.817584i	$-0.304687\pi$
$661$	1.15583e9	+	6.67319e8i	0.155664	+	0.0898729i	−0.420144	+	0.907457i	$0.638021\pi$
$662$	−2.93448e9	+	5.08267e9i	−0.393123	+	0.680909i
$663$	−4.82055e9	−	3.79506e8i	−0.642390	−	0.0505732i
$664$	1.42889e9			0.189414
$665$	7.87325e9	−	4.51606e9i	1.03819	−	0.595503i
$666$	3.88799e9			0.509994
$667$	1.14057e9	+	1.97553e9i	0.148828	+	0.257777i
$668$	−9.88258e9	−	5.70571e9i	−1.28278	−	0.740615i
$669$	4.58733e8	+	2.64850e8i	0.0592337	+	0.0341986i
$670$	−9.19983e9	+	5.31153e9i	−1.18173	+	0.682272i
$671$		−	1.65721e9i		−	0.211763i
$672$	−9.45151e9	−	2.66587e7i	−1.20146	−	0.00338881i
$673$	−5.59948e9			−0.708100			−0.354050	−	0.935226i	$-0.615196\pi$
$673$	−5.59948e9			−0.708100			−0.354050	+	0.935226i	$0.615196\pi$
$674$	1.96168e10	−	1.13257e10i	2.46784	−	1.42481i
$675$	4.88421e8	−	8.45970e8i	0.0611267	−	0.105875i
$676$	−8.55371e9	−	1.35521e9i	−1.06498	−	0.168730i
$677$	2.37964e9	+	4.12167e9i	0.294749	+	0.510520i	0.974926	−	0.222528i	$-0.0714308\pi$
$677$	2.37964e9	+	4.12167e9i	0.294749	+	0.510520i	−0.680178	+	0.733047i	$0.738097\pi$
$678$			1.07657e10i			1.32659i
$679$	−7.21362e9	+	1.24134e10i	−0.884319	+	1.52176i
$680$	−7.49784e8			−0.0914439
$681$	−3.76712e9	+	2.17495e9i	−0.457082	+	0.263897i
$682$	−5.59411e9	−	3.22976e9i	−0.675283	−	0.389875i
$683$	1.07394e10	+	6.20040e9i	1.28976	+	0.744641i	0.978611	−	0.205721i	$-0.0659538\pi$
$683$	1.07394e10	+	6.20040e9i	1.28976	+	0.744641i	0.311146	+	0.950362i	$0.399287\pi$
$684$	2.63254e9	−	1.51990e9i	0.314542	−	0.181601i
$685$	2.55820e9			0.304100
$686$	−6.00519e9	−	1.06076e10i	−0.710219	−	1.25453i
$687$			4.68327e8i			0.0551062i
$688$	−8.37724e8	−	1.45098e9i	−0.0980712	−	0.169864i
$689$	−3.16399e8	−	6.63387e8i	−0.0368526	−	0.0772680i
$690$	4.37056e9	−	7.57003e9i	0.506483	−	0.877254i
$691$	−5.72072e8	+	3.30286e8i	−0.0659595	+	0.0380817i	−0.532617	−	0.846356i	$-0.678791\pi$
$691$	−5.72072e8	+	3.30286e8i	−0.0659595	+	0.0380817i	0.466658	+	0.884438i	$0.345458\pi$
$692$	−9.28063e9			−1.06465
$693$	−1.05174e9	+	1.80985e9i	−0.120044	+	0.206574i
$694$		−	2.06921e10i		−	2.34989i
$695$	−1.81553e9	+	1.04819e9i	−0.205142	+	0.118439i
$696$	−2.73043e8	−	1.57642e8i	−0.0306972	−	0.0177231i
$697$	−8.85633e9	−	5.11321e9i	−0.990693	−	0.571977i
$698$	−4.19738e9	−	7.27007e9i	−0.467180	−	0.809180i
$699$	−9.45355e9			−1.04695
$700$	3.10279e6	−	1.10005e9i	0.000341908	−	0.121219i
$701$	8.22795e9			0.902150			0.451075	−	0.892486i	$-0.351041\pi$
$701$	8.22795e9			0.902150			0.451075	+	0.892486i	$0.351041\pi$
$702$	1.12778e9	−	1.43252e10i	0.123039	−	1.56287i
$703$	−6.22904e9	+	1.07890e10i	−0.676204	+	1.17122i
$704$	7.42067e9	+	4.28433e9i	0.801565	+	0.462784i
$705$	1.04511e8	+	1.81019e8i	0.0112332	+	0.0194564i
$706$	1.22018e10			1.30499
$707$	1.14025e10	−	6.54041e9i	1.21348	−	0.696044i
$708$		−	1.29577e10i		−	1.37218i
$709$	2.66200e9	−	1.53691e9i	0.280509	−	0.161952i	−0.353145	−	0.935569i	$-0.614888\pi$
$709$	2.66200e9	−	1.53691e9i	0.280509	−	0.161952i	0.633654	+	0.773617i	$0.281554\pi$
$710$	1.22756e10	+	7.08732e9i	1.28718	+	0.743152i
$711$	1.33658e9	−	2.31503e9i	0.139461	−	0.241554i
$712$	5.39233e8	+	9.33980e8i	0.0559882	+	0.0969745i
$713$		−	5.16725e9i		−	0.533883i
$714$	−4.49548e9	−	7.83737e9i	−0.462202	−	0.805798i
$715$	−4.69991e9	+	6.83804e9i	−0.480859	+	0.699618i
$716$	−2.56288e9	−	4.43903e9i	−0.260935	−	0.451953i
$717$	−8.78178e9	−	5.07016e9i	−0.889745	−	0.513695i
$718$	8.84394e7	−	1.53181e8i	0.00891682	−	0.0154444i
$719$	3.55394e8	+	6.15561e8i	0.0356582	+	0.0617618i	0.883304	−	0.468801i	$-0.155314\pi$
$719$	3.55394e8	+	6.15561e8i	0.0356582	+	0.0617618i	−0.847646	+	0.530563i	$0.821981\pi$
$720$			2.87095e9i			0.286656i
$721$	1.07672e7	−	3.81738e9i	0.00106987	−	0.379308i
$722$			4.19449e9i			0.414762i
$723$	7.19604e9	−	4.15464e9i	0.708125	−	0.408836i
$724$	−8.67097e9	+	1.50186e10i	−0.849146	+	1.47076i
$725$	−2.16089e8	+	3.74277e8i	−0.0210596	+	0.0364762i
$726$	3.80107e9	−	2.19455e9i	0.368661	−	0.212847i
$727$	1.18823e10			1.14691			0.573456	−	0.819236i	$-0.305602\pi$
$727$	1.18823e10			1.14691			0.573456	+	0.819236i	$0.305602\pi$
$728$	−5.02634e8	−	1.06156e9i	−0.0482828	−	0.101973i
$729$	1.14484e10			1.09446
$730$	−7.84975e9	+	4.53206e9i	−0.746837	+	0.431187i
$731$	8.69267e8	−	1.50561e9i	0.0823080	−	0.142562i
$732$	−1.26218e9	+	2.18616e9i	−0.118941	+	0.206013i
$733$	−1.30578e10	+	7.53892e9i	−1.22463	+	0.707042i	−0.965902	−	0.258908i	$-0.916637\pi$
$733$	−1.30578e10	+	7.53892e9i	−1.22463	+	0.707042i	−0.258730	+	0.965950i	$0.583304\pi$
$734$		−	1.40201e10i		−	1.30862i
$735$	8.27189e9	−	4.71376e9i	0.768421	−	0.437887i
$736$			1.23122e10i			1.13832i
$737$	3.92508e9	+	6.79844e9i	0.361171	+	0.625566i
$738$	3.47800e9	−	6.02407e9i	0.318517	−	0.551687i
$739$	7.28503e9	+	4.20601e9i	0.664012	+	0.383367i	0.793804	−	0.608174i	$-0.208098\pi$
$739$	7.28503e9	+	4.20601e9i	0.664012	+	0.383367i	−0.129792	+	0.991541i	$0.541431\pi$
$740$	7.47033e9	+	1.29390e10i	0.677686	+	1.17379i
$741$	8.68534e9	+	5.96959e9i	0.784193	+	0.538990i
$742$	6.90010e8	−	1.18738e9i	0.0620071	−	0.106703i
$743$		−	1.66547e10i		−	1.48962i	−0.667278	−	0.744809i	$-0.732541\pi$
$743$		−	1.66547e10i		−	1.48962i	0.667278	−	0.744809i	$-0.267459\pi$
$744$	3.57090e8	+	6.18497e8i	0.0317886	+	0.0550595i
$745$	6.10589e9	−	1.05757e10i	0.541006	−	0.937050i
$746$	2.69480e10	+	1.55585e10i	2.37652	+	1.37208i
$747$	4.91667e9	−	2.83864e9i	0.431568	−	0.249166i
$748$			7.63365e9i			0.666924i
$749$	−5.02147e7	+	1.78030e10i	−0.00436661	+	1.54812i
$750$	−1.30748e10			−1.13167
$751$	8.89695e8	+	1.54100e9i	0.0766481	+	0.132758i	0.901802	−	0.432150i	$-0.142245\pi$
$751$	8.89695e8	+	1.54100e9i	0.0766481	+	0.132758i	−0.825154	+	0.564908i	$0.808912\pi$
$752$	−2.34895e8	−	1.35617e8i	−0.0201424	−	0.0116292i
$753$	−5.57130e9	+	9.64978e9i	−0.475526	+	0.823635i
$754$	−4.98956e8	+	6.33782e9i	−0.0423899	+	0.538444i
$755$	−2.16327e10			−1.82934
$756$	1.20837e10	−	6.93116e9i	1.01712	−	0.583418i
$757$	8.48821e9			0.711182			0.355591	−	0.934642i	$-0.384280\pi$
$757$	8.48821e9			0.711182			0.355591	+	0.934642i	$0.384280\pi$
$758$	6.49794e8	+	1.12548e9i	0.0541918	+	0.0938629i
$759$	−5.59405e9	−	3.22973e9i	−0.464387	−	0.268114i
$760$	1.41524e9	+	8.17088e8i	0.116945	+	0.0675183i
$761$	−1.84327e9	+	1.06421e9i	−0.151615	+	0.0875352i	−0.573888	−	0.818934i	$-0.694566\pi$
$761$	−1.84327e9	+	1.06421e9i	−0.151615	+	0.0875352i	0.422273	+	0.906469i	$0.361232\pi$
$762$			1.16158e9i			0.0951055i
$763$	1.00760e9	+	1.75664e9i	0.0821207	+	0.143168i
$764$	2.03458e10			1.65062
$765$	−2.57993e9	+	1.48952e9i	−0.208350	+	0.120291i
$766$	−2.16361e9	+	3.74749e9i	−0.173932	+	0.301259i
$767$	−1.71173e10	+	8.16403e9i	−1.36978	+	0.653312i
$768$	4.34551e9	+	7.52664e9i	0.346159	+	0.599566i
$769$		−	8.93127e9i		−	0.708224i	−0.935203	−	0.354112i	$-0.884783\pi$
$769$		−	8.93127e9i		−	0.708224i	0.935203	−	0.354112i	$-0.115217\pi$
$770$	−1.55039e10	−	4.37299e7i	−1.22384	−	0.00345193i
$771$	−6.02415e9			−0.473375
$772$	−2.08252e10	+	1.20234e10i	−1.62903	+	0.940519i
$773$	−1.14761e10	−	6.62574e9i	−0.893648	−	0.515948i	−0.0185144	−	0.999829i	$-0.505894\pi$
$773$	−1.14761e10	−	6.62574e9i	−0.893648	−	0.515948i	−0.875134	+	0.483880i	$0.839227\pi$
$774$	1.02412e9	+	5.91275e8i	0.0793883	+	0.0458349i
$775$	8.47812e8	−	4.89484e8i	0.0654250	−	0.0377731i
$776$	−2.58493e9			−0.198579
$777$	−6.56578e9	+	1.12985e10i	−0.502126	+	0.864070i
$778$			1.10544e10i			0.841604i
$779$	1.11444e10	+	1.93026e10i	0.844646	+	1.46297i
$780$	1.14081e10	−	5.44103e9i	0.860759	−	0.410535i
$781$	5.23735e9	−	9.07135e9i	0.393398	−	0.681386i
$782$	−1.01929e10	+	5.88488e9i	−0.762210	+	0.440062i
$783$	−5.47282e9			−0.407423
$784$	−6.23740e9	+	1.06641e10i	−0.462272	+	0.790348i
$785$			5.22793e9i			0.385732i
$786$	−6.04622e9	+	3.49078e9i	−0.444125	+	0.256415i
$787$	−8.89222e9	−	5.13392e9i	−0.650277	−	0.375438i	0.138285	−	0.990392i	$-0.455841\pi$
$787$	−8.89222e9	−	5.13392e9i	−0.650277	−	0.375438i	−0.788562	+	0.614955i	$0.789174\pi$
$788$	9.35689e9	+	5.40220e9i	0.681223	+	0.393305i
$789$	−5.54953e9	−	9.61207e9i	−0.402241	−	0.696702i
$790$	1.97992e10			1.42874
$791$	1.32068e10	+	7.67469e9i	0.948810	+	0.551370i
$792$	−3.76879e8			−0.0269565
$793$	3.68319e9	+	2.89965e8i	0.262282	+	0.0206486i
$794$	−8.91328e9	+	1.54382e10i	−0.631925	+	1.09453i
$795$	9.28935e8	+	5.36321e8i	0.0655693	+	0.0378564i
$796$	1.24960e10	+	2.16437e10i	0.878164	+	1.52102i
$797$	1.02198e10			0.715055			0.357528	−	0.933903i	$-0.383620\pi$
$797$	1.02198e10			0.715055			0.357528	+	0.933903i	$0.383620\pi$
$798$	−5.55436e7	+	1.96923e10i	−0.00386922	+	1.37178i
$799$		−	2.81446e8i		−	0.0195200i
$800$	−2.02011e9	+	1.16631e9i	−0.139496	+	0.0805378i
$801$	3.71089e9	+	2.14249e9i	0.255132	+	0.147300i
$802$	−9.04609e9	+	1.56683e10i	−0.619228	+	1.07253i
$803$	3.34907e9	+	5.80077e9i	0.228255	+	0.395349i
$804$		−	1.19578e10i		−	0.811439i
$805$	−6.17082e9	−	1.07581e10i	−0.416925	−	0.726861i
$806$	8.15702e9	−	1.18679e10i	0.548730	−	0.798365i
$807$	−8.12168e9	−	1.40672e10i	−0.543987	−	0.942213i
$808$	2.04962e9	+	1.18335e9i	0.136689	+	0.0789176i
$809$	5.32743e9	−	9.22739e9i	0.353752	−	0.612716i	−0.633152	−	0.774028i	$-0.718239\pi$
$809$	5.32743e9	−	9.22739e9i	0.353752	−	0.612716i	0.986903	+	0.161312i	$0.0515725\pi$
$810$	7.07238e9	+	1.22497e10i	0.467593	+	0.809895i
$811$			4.02594e9i			0.265030i	0.991181	+	0.132515i	$0.0423052\pi$
$811$			4.02594e9i			0.265030i	−0.991181	+	0.132515i	$0.957695\pi$
$812$	−5.34611e9	+	3.06651e9i	−0.350423	+	0.201001i
$813$		−	1.17418e10i		−	0.766333i
$814$	1.84292e10	−	1.06401e10i	1.19762	−	0.691448i
$815$	5.06880e9	−	8.77943e9i	0.327985	−	0.568086i
$816$	−4.57865e9	+	7.93045e9i	−0.295000	+	0.510955i
$817$	−3.28153e9	+	1.89459e9i	−0.210523	+	0.121545i
$818$	2.55378e10			1.63135
$819$	−3.83841e9	−	2.65418e9i	−0.244150	−	0.168825i
$820$	2.67303e10			1.69300
$821$	−9.42862e8	+	5.44362e8i	−0.0594631	+	0.0343310i	−0.529437	−	0.848349i	$-0.677597\pi$
$821$	−9.42862e8	+	5.44362e8i	−0.0594631	+	0.0343310i	0.469974	+	0.882680i	$0.344263\pi$
$822$	−2.77513e9	+	4.80666e9i	−0.174273	+	0.301850i
$823$	5.29194e9	−	9.16591e9i	0.330914	−	0.573161i	−0.651777	−	0.758411i	$-0.725976\pi$
$823$	5.29194e9	−	9.16591e9i	0.330914	−	0.573161i	0.982691	+	0.185250i	$0.0593095\pi$
$824$	5.95221e8	−	3.43651e8i	0.0370623	−	0.0213980i
$825$		−	1.22378e9i		−	0.0758781i
$826$	−3.06380e10	−	1.78043e10i	−1.89160	−	1.09924i
$827$			1.52140e10i			0.935348i	0.883901	+	0.467674i	$0.154908\pi$
$827$			1.52140e10i			0.935348i	−0.883901	+	0.467674i	$0.845092\pi$
$828$	−2.07682e9	−	3.59715e9i	−0.127143	−	0.220218i
$829$	−5.00318e9	+	8.66576e9i	−0.305004	+	0.528282i	−0.977262	−	0.212035i	$-0.931991\pi$
$829$	−5.00318e9	+	8.66576e9i	−0.305004	+	0.528282i	0.672258	+	0.740316i	$0.265324\pi$
$830$	3.64160e10	+	2.10248e10i	2.21064	+	1.27631i
$831$	2.61423e9	+	4.52798e9i	0.158030	+	0.273716i
$832$	−1.08204e10	+	1.57430e10i	−0.651347	+	0.947665i
$833$	−1.28193e10	−	7.23160e7i	−0.768431	−	0.00433488i
$834$		−	4.54831e9i		−	0.271500i
$835$	−1.21872e10	−	2.11089e10i	−0.724439	−	1.25477i
$836$	8.31888e9	−	1.44087e10i	0.492428	−	0.852911i
$837$	1.07361e10	+	6.19851e9i	0.632862	+	0.365383i
$838$	1.07701e10	−	6.21813e9i	0.632218	−	0.365011i
$839$		−	6.55346e9i		−	0.383093i	−0.981484	−	0.191546i	$-0.938650\pi$
$839$		−	6.55346e9i		−	0.383093i	0.981484	−	0.191546i	$-0.0613502\pi$
$840$	1.48207e9	+	8.61259e8i	0.0862765	+	0.0501368i
$841$	−1.48286e10			−0.859634
$842$	−6.93553e9	−	1.20127e10i	−0.400394	−	0.693502i
$843$	1.29357e10	+	7.46844e9i	0.743694	+	0.429372i
$844$	1.35944e10	−	2.35462e10i	0.778326	−	1.34810i
$845$	−1.43753e10	−	1.16421e10i	−0.819634	−	0.663794i
$846$	1.91439e8			0.0108701
$847$	1.75649e7	−	6.22742e9i	0.000993241	−	0.352141i
$848$	−1.39188e9			−0.0783823
$849$	−6.39652e9	−	1.10791e10i	−0.358729	−	0.621337i
$850$	−1.93111e9	−	1.11493e9i	−0.107855	−	0.0622702i
$851$	1.47423e10	+	8.51147e9i	0.819996	+	0.473425i
$852$	−1.38180e10	+	7.97783e9i	−0.765432	+	0.441923i
$853$		−	3.05814e10i		−	1.68708i	−0.537068	−	0.843539i	$-0.680468\pi$
$853$		−	3.05814e10i		−	1.68708i	0.537068	−	0.843539i	$-0.319532\pi$
$854$	3.43482e9	+	5.98822e9i	0.188713	+	0.329000i
$855$	6.49292e9			0.355270
$856$	−2.77590e9	+	1.60267e9i	−0.151268	+	0.0873345i
$857$	−3.14628e9	+	5.44951e9i	−0.170751	+	0.295750i	−0.938683	−	0.344782i	$-0.887953\pi$
$857$	−3.14628e9	+	5.44951e9i	−0.170751	+	0.295750i	0.767931	+	0.640532i	$0.221286\pi$
$858$	−7.74972e9	−	1.62487e10i	−0.418871	−	0.878238i
$859$	2.71406e9	+	4.70089e9i	0.146098	+	0.253049i	0.929782	−	0.368111i	$-0.119995\pi$
$859$	2.71406e9	+	4.70089e9i	0.146098	+	0.253049i	−0.783684	+	0.621160i	$0.786662\pi$
$860$			4.54427e9i			0.243624i
$861$	1.16326e10	+	2.02802e10i	0.621107	+	1.08283i
$862$	−4.23882e10			−2.25408
$863$	−3.02669e10	+	1.74746e10i	−1.60299	+	0.925487i	−0.612105	+	0.790776i	$0.709677\pi$
$863$	−3.02669e10	+	1.74746e10i	−1.60299	+	0.925487i	−0.990885	+	0.134710i	$0.956990\pi$
$864$	−2.55814e10	−	1.47694e10i	−1.34935	−	0.779050i
$865$	−1.71673e10	−	9.91157e9i	−0.901876	−	0.520698i
$866$	4.02231e10	−	2.32228e10i	2.10457	−	1.21507i
$867$	6.58936e9			0.343381
$868$	1.39607e10	+	3.93773e7i	0.724583	+	0.00204374i
$869$		−	1.46311e10i		−	0.756323i
$870$	−4.63909e9	−	8.03514e9i	−0.238844	−	0.413691i
$871$	−1.57965e10	+	7.53404e9i	−0.810021	+	0.386335i
$872$	−1.82305e8	+	3.15761e8i	−0.00931086	+	0.0161269i
$873$	−8.89447e9	+	5.13523e9i	−0.452450	+	0.261222i
$874$	2.56525e10			1.29969
$875$	−9.32083e9	+	1.60395e10i	−0.470356	+	0.809399i
$876$		−	1.02030e10i		−	0.512819i
$877$	−6.06671e9	+	3.50262e9i	−0.303707	+	0.175345i	−0.644107	−	0.764935i	$-0.722771\pi$
$877$	−6.06671e9	+	3.50262e9i	−0.303707	+	0.175345i	0.340400	+	0.940281i	$0.389438\pi$
$878$	9.71410e9	+	5.60844e9i	0.484364	+	0.279648i
$879$	−3.89557e9	−	2.24911e9i	−0.193468	−	0.111699i
$880$	7.85679e9	+	1.36084e10i	0.388647	+	0.673157i
$881$	−1.21984e10			−0.601017			−0.300508	−	0.953779i	$-0.597156\pi$
$881$	−1.21984e10			−0.601017			−0.300508	+	0.953779i	$0.597156\pi$
$882$	4.91893e7	−	8.71965e9i	0.00241396	−	0.427916i
$883$	−1.78219e10			−0.871148			−0.435574	−	0.900153i	$-0.643455\pi$
$883$	−1.78219e10			−0.871148			−0.435574	+	0.900153i	$0.643455\pi$
$884$	−1.69659e10	−	1.33567e9i	−0.826029	−	0.0650305i
$885$	1.38386e10	−	2.39692e10i	0.671107	−	1.16239i
$886$	7.65330e9	+	4.41864e9i	0.369684	+	0.213437i
$887$	−8.98185e9	−	1.55570e10i	−0.432149	−	0.748503i	0.564909	−	0.825153i	$-0.308911\pi$
$887$	−8.98185e9	−	1.55570e10i	−0.432149	−	0.748503i	−0.997058	+	0.0766495i	$0.975578\pi$
$888$	−2.35278e9			−0.112755
$889$	1.42497e9	+	8.28072e8i	0.0680218	+	0.0395286i
$890$			3.17372e10i			1.50905i
$891$	9.05223e9	−	5.22630e9i	0.428730	−	0.247527i
$892$	1.61452e9	+	9.32141e8i	0.0761667	+	0.0439749i
$893$	−3.06710e8	+	5.31237e8i	−0.0144128	+	0.0249636i
$894$	1.32473e10	+	2.29450e10i	0.620078	+	1.07401i
$895$		−	1.09484e10i		−	0.510472i
$896$	−4.84376e9	−	1.36622e7i	−0.224960	−	0.000634516i
$897$	8.15694e9	−	1.18678e10i	0.377358	−	0.549030i
$898$	−7.97266e9	−	1.38090e10i	−0.367397	−	0.636351i
$899$	−4.74992e9	−	2.74237e9i	−0.218036	−	0.125883i
$900$	3.93466e8	−	6.81503e8i	0.0179911	−	0.0311615i
$901$	−7.22146e8	−	1.25079e9i	−0.0328919	−	0.0569704i
$902$		−	3.80723e10i		−	1.72737i
$903$	−3.44772e9	+	1.97759e9i	−0.155820	+	0.0893779i
$904$			2.75015e9i			0.123813i
$905$	−3.20792e10	+	1.85209e10i	−1.43864	+	0.830601i
$906$	2.34670e10	−	4.06461e10i	1.04836	−	1.81581i
$907$	2.51803e8	−	4.36136e8i	0.0112056	−	0.0194087i	−0.860368	−	0.509673i	$-0.829766\pi$
$907$	2.51803e8	−	4.36136e8i	0.0112056	−	0.0194087i	0.871574	+	0.490264i	$0.163100\pi$
$908$	−1.32584e10	+	7.65474e9i	−0.587747	+	0.339336i
$909$	9.40339e9			0.415251
$910$	2.80993e9	−	3.44501e10i	0.123609	−	1.51546i
$911$	−4.26175e10			−1.86756			−0.933778	−	0.357852i	$-0.883509\pi$
$911$	−4.26175e10			−1.86756			−0.933778	+	0.357852i	$0.883509\pi$
$912$	1.72847e10	−	9.97930e9i	0.754534	−	0.435630i
$913$	1.55368e10	−	2.69105e10i	0.675636	−	1.17024i
$914$	−2.74080e10	+	4.74721e10i	−1.18732	+	2.05649i
$915$	−4.66957e9	+	2.69598e9i	−0.201513	+	0.116344i
$916$			1.64828e9i			0.0708593i
$917$	−2.79399e7	+	9.90573e9i	−0.00119655	+	0.424222i
$918$		−	2.82374e10i		−	1.20469i
$919$	1.78901e10	+	3.09866e10i	0.760342	+	1.31695i	0.942675	+	0.333713i	$0.108302\pi$
$919$	1.78901e10	+	3.09866e10i	0.760342	+	1.31695i	−0.182333	+	0.983237i	$0.558365\pi$
$920$	1.11648e9	−	1.93380e9i	0.0472710	−	0.0818757i
$921$	−4.65704e9	−	2.68875e9i	−0.196427	−	0.113407i
$922$	−3.06430e10	−	5.30752e10i	−1.28758	−	2.23015i
$923$	1.92449e10	+	1.32273e10i	0.805581	+	0.553690i
$924$	8.76859e9	−	1.50892e10i	0.365660	−	0.629237i
$925$			3.22510e9i			0.133982i
$926$	−1.53308e10	−	2.65538e10i	−0.634493	−	1.09897i
$927$	1.36540e9	−	2.36493e9i	0.0562963	−	0.0975080i
$928$	1.13178e10	+	6.53434e9i	0.464884	+	0.268401i
$929$	2.03950e10	−	1.17751e10i	0.834583	−	0.481847i	−0.0208363	−	0.999783i	$-0.506633\pi$
$929$	2.03950e10	−	1.17751e10i	0.834583	−	0.481847i	0.855419	+	0.517936i	$0.173300\pi$
$930$			2.10169e10i			0.856798i
$931$	2.41179e10	+	1.41065e10i	0.979524	+	0.572920i
$932$	−3.32718e10			−1.34624
$933$	−8.99450e9	−	1.55789e10i	−0.362569	−	0.627989i
$934$	9.52258e9	+	5.49787e9i	0.382420	+	0.220790i
$935$	−8.15262e9	+	1.41207e10i	−0.326179	+	0.564959i
$936$	6.59431e7	−	8.37621e8i	0.00262848	−	0.0333874i
$937$	−3.28535e10			−1.30465			−0.652323	−	0.757941i	$-0.726206\pi$
$937$	−3.28535e10			−1.30465			−0.652323	+	0.757941i	$0.726206\pi$
$938$	−2.82738e10	−	1.64304e10i	−1.11860	−	0.650036i
$939$	9.60595e9			0.378626
$940$	3.67829e8	+	6.37098e8i	0.0144444	+	0.0250184i
$941$	−1.89583e10	−	1.09456e10i	−0.741713	−	0.428228i	0.0809788	−	0.996716i	$-0.474195\pi$
$941$	−1.89583e10	−	1.09456e10i	−0.741713	−	0.428228i	−0.822692	+	0.568488i	$0.807529\pi$
$942$	−9.82289e9	−	5.67125e9i	−0.382878	−	0.221055i
$943$	2.63754e10	−	1.52279e10i	1.02426	−	0.591355i
$944$			3.59147e10i			1.38954i
$945$	2.97548e10	+	8.39259e7i	1.14695	+	0.00323508i
$946$	6.47246e9			0.248571
$947$	−3.11734e10	+	1.79980e10i	−1.19278	+	0.688650i	−0.958935	−	0.283625i	$-0.908463\pi$
$947$	−3.11734e10	+	1.79980e10i	−1.19278	+	0.688650i	−0.233841	+	0.972275i	$0.575129\pi$
$948$	−1.11435e10	+	1.93010e10i	−0.424806	+	0.735786i
$949$	−1.34783e10	+	6.42842e9i	−0.511922	+	0.244159i
$950$	2.43002e9	+	4.20891e9i	0.0919552	+	0.159271i
$951$			2.96796e10i			1.11899i
$952$	−1.14839e9	−	2.00210e9i	−0.0431382	−	0.0752066i
$953$	−1.74174e10			−0.651865			−0.325933	−	0.945393i	$-0.605678\pi$
$953$	−1.74174e10			−0.651865			−0.325933	+	0.945393i	$0.605678\pi$
$954$	8.50790e8	−	4.91204e8i	0.0317251	−	0.0183165i
$955$	3.76357e10	+	2.17290e10i	1.39826	+	0.807287i
$956$	−3.09075e10	−	1.78445e10i	−1.14409	−	0.660543i
$957$	−5.93776e9	+	3.42817e9i	−0.218993	+	0.126436i
$958$	5.79066e10			2.12789
$959$	3.91822e9	+	6.83098e9i	0.143458	+	0.250102i
$960$		−	2.78792e10i		−	1.01702i
$961$	−7.54430e9	−	1.30671e10i	−0.274212	−	0.474950i
$962$	2.04232e10	+	4.28209e10i	0.739625	+	1.55075i
$963$	−6.36773e9	+	1.10292e10i	−0.229770	+	0.397973i
$964$	2.53265e10	−	1.46223e10i	0.910555	−	0.525709i
$965$	−5.13633e10			−1.83995
$966$	2.69078e10	+	7.58957e7i	0.960414	+	0.00270893i
$967$		−	2.02998e10i		−	0.721936i	−0.932578	−	0.360968i	$-0.882446\pi$
$967$		−	2.02998e10i		−	0.721936i	0.932578	−	0.360968i	$-0.117554\pi$
$968$	9.71004e8	−	5.60609e8i	0.0344078	−	0.0198654i
$969$	1.79355e10	+	1.03550e10i	0.633256	+	0.365611i
$970$	−6.58781e10	−	3.80347e10i	−2.31761	−	1.33807i
$971$	−1.07072e10	−	1.85453e10i	−0.375325	−	0.650081i	0.615051	−	0.788487i	$-0.289135\pi$
$971$	−1.07072e10	−	1.85453e10i	−0.375325	−	0.650081i	−0.990376	+	0.138406i	$0.955802\pi$
$972$	1.76494e10			0.616451
$973$	−5.57964e9	−	3.24243e9i	−0.194183	−	0.112843i
$974$	1.22498e10			0.424787
$975$	2.71989e9	+	2.14128e8i	0.0939798	+	0.00739872i
$976$	3.49837e9	−	6.05935e9i	0.120446	−	0.208618i
$977$	2.47449e10	+	1.42865e10i	0.848896	+	0.490110i	0.860278	−	0.509825i	$-0.170290\pi$
$977$	2.47449e10	+	1.42865e10i	0.848896	+	0.490110i	−0.0113820	+	0.999935i	$0.503623\pi$
$978$	1.09972e10	+	1.90478e10i	0.375922	+	0.651116i
$979$	2.34530e10			0.798837
$980$	2.91130e10	−	1.65901e10i	0.988087	−	0.563065i
$981$			1.44867e9i			0.0489922i
$982$	2.90532e10	−	1.67739e10i	0.979047	−	0.565253i
$983$	−3.84410e10	−	2.21939e10i	−1.29080	−	0.745242i	−0.312001	−	0.950082i	$-0.600999\pi$
$983$	−3.84410e10	−	2.21939e10i	−1.29080	−	0.745242i	−0.978795	+	0.204840i	$0.934332\pi$
$984$	−2.10468e9	+	3.64541e9i	−0.0704212	+	0.121973i
$985$	1.15389e10	+	1.99860e10i	0.384715	+	0.666345i
$986$			1.24929e10i			0.415044i
$987$	−3.23290e8	+	5.56325e8i	−0.0107024	+	0.0184170i
$988$	3.05681e10	+	2.10100e10i	1.00837	+	0.693070i
$989$	2.58880e9	+	4.48394e9i	0.0850965	+	0.147391i
$990$	−9.60493e9	−	5.54541e9i	−0.314609	−	0.181639i
$991$	2.79101e10	−	4.83418e10i	0.910971	−	1.57785i	0.0982746	−	0.995159i	$-0.468668\pi$
$991$	2.79101e10	−	4.83418e10i	0.910971	−	1.57785i	0.812696	−	0.582688i	$-0.197999\pi$
$992$	−1.48016e10	−	2.56371e10i	−0.481412	−	0.833830i
$993$		−	1.41110e10i		−	0.457338i
$994$	−1.23073e8	+	4.36339e10i	−0.00397475	+	1.40920i
$995$			5.33821e10i			1.71797i
$996$	−4.09916e10	+	2.36665e10i	−1.31458	+	0.758973i
$997$	2.00694e10	−	3.47611e10i	0.641358	−	1.11086i	−0.343772	−	0.939053i	$-0.611705\pi$
$997$	2.00694e10	−	3.47611e10i	0.641358	−	1.11086i	0.985130	−	0.171811i	$-0.0549619\pi$
$998$	4.73983e9	−	8.20962e9i	0.150940	−	0.261437i
$999$	−3.53690e10	+	2.04203e10i	−1.12239	+	0.648012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.r.a.25.11	✓	128
7.2	even	3	inner	91.8.r.a.51.54	yes	128
13.12	even	2	inner	91.8.r.a.25.54	yes	128
91.51	even	6	inner	91.8.r.a.51.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.r.a.25.11	✓	128	1.1	even	1	trivial
91.8.r.a.25.54	yes	128	13.12	even	2	inner
91.8.r.a.51.11	yes	128	91.51	even	6	inner
91.8.r.a.51.54	yes	128	7.2	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.1249 + 8.15502i) q^{2} +(19.6075 - 33.9612i) q^{3} +(69.0088 - 119.527i) q^{4} +(255.306 - 147.401i) q^{5} +639.600i q^{6} +(784.629 + 455.961i) q^{7} +163.389i q^{8} +(324.589 + 562.205i) q^{9} +O(q^{10})\)	\(q+(-14.1249 + 8.15502i) q^{2} +(19.6075 - 33.9612i) q^{3} +(69.0088 - 119.527i) q^{4} +(255.306 - 147.401i) q^{5} +639.600i q^{6} +(784.629 + 455.961i) q^{7} +163.389i q^{8} +(324.589 + 562.205i) q^{9} +(-2404.11 + 4164.05i) q^{10} +(3077.12 + 1776.58i) q^{11} +(-2706.19 - 4687.25i) q^{12} +(-4486.89 + 6528.12i) q^{13} +(-14801.2 - 41.7479i) q^{14} -11560.7i q^{15} +(7500.69 + 12991.6i) q^{16} +(-7783.11 + 13480.7i) q^{17} +(-9169.60 - 5294.07i) q^{18} +(29381.7 - 16963.5i) q^{19} -40687.8i q^{20} +(30869.6 - 17706.7i) q^{21} -57952.1 q^{22} +(-23179.2 - 40147.6i) q^{23} +(5548.90 + 3203.66i) q^{24} +(4391.45 - 7606.21i) q^{25} +(10140.0 - 128800. i) q^{26} +111221. q^{27} +(108646. - 62318.8i) q^{28} -49206.8 q^{29} +(94277.5 + 163293. i) q^{30} +(96529.8 + 55731.5i) q^{31} +(-230005. - 132794. i) q^{32} +(120670. - 69668.6i) q^{33} -253886. i q^{34} +(267529. + 754.587i) q^{35} +89598.2 q^{36} +(-318007. + 183601. i) q^{37} +(-276676. + 479217. i) q^{38} +(133726. + 280381. i) q^{39} +(24083.7 + 41714.2i) q^{40} +656962. i q^{41} +(-291633. + 501848. i) q^{42} -111686. q^{43} +(424697. - 245199. i) q^{44} +(165739. + 95689.4i) q^{45} +(654809. + 378054. i) q^{46} +(-15658.2 + 9040.27i) q^{47} +588280. q^{48} +(407742. + 715521. i) q^{49} +143249. i q^{50} +(305215. + 528648. i) q^{51} +(470650. + 986802. i) q^{52} +(-46391.9 + 80353.1i) q^{53} +(-1.57099e6 + 907009. i) q^{54} +1.04748e6 q^{55} +(-74499.1 + 128200. i) q^{56} -1.33045e6i q^{57} +(695041. - 401282. i) q^{58} +(2.07334e6 + 1.19705e6i) q^{59} +(-1.38181e6 - 797788. i) q^{60} +(-233203. - 403919. i) q^{61} -1.81797e6 q^{62} +(-1661.67 + 589123. i) q^{63} +2.41156e6 q^{64} +(-183278. + 2.32804e6i) q^{65} +(-1.13630e6 + 1.96813e6i) q^{66} +(1.91335e6 + 1.10467e6i) q^{67} +(1.07421e6 + 1.86058e6i) q^{68} -1.81795e6 q^{69} +(-3.78498e6 + 2.17105e6i) q^{70} -2.94800e6i q^{71} +(-91858.2 + 53034.4i) q^{72} +(1.63257e6 + 942563. i) q^{73} +(2.99454e6 - 5.18670e6i) q^{74} +(-172211. - 298278. i) q^{75} -4.68253e6i q^{76} +(1.60435e6 + 2.79700e6i) q^{77} +(-4.17538e6 - 2.86981e6i) q^{78} +(-2.05888e6 - 3.56609e6i) q^{79} +(3.82994e6 + 2.21121e6i) q^{80} +(1.47089e6 - 2.54766e6i) q^{81} +(-5.35754e6 - 9.27953e6i) q^{82} -8.74533e6i q^{83} +(13853.8 - 4.91167e6i) q^{84} +4.58895e6i q^{85} +(1.57756e6 - 910804. i) q^{86} +(-964823. + 1.67112e6i) q^{87} +(-290274. + 502769. i) q^{88} +(5.71629e6 - 3.30030e6i) q^{89} -3.12140e6 q^{90} +(-6.49711e6 + 3.07630e6i) q^{91} -6.39829e6 q^{92} +(3.78542e6 - 2.18552e6i) q^{93} +(147447. - 255386. i) q^{94} +(5.00087e6 - 8.66176e6i) q^{95} +(-9.01967e6 + 5.20751e6i) q^{96} +1.58207e7i q^{97} +(-1.15944e7 - 6.78153e6i) q^{98} +2.30663e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9}+O(q^{10}) \) 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9	\( 128 q + 52 q^{3} + 4094 q^{4} - 44052 q^{9} - 4514 q^{10} + 2090 q^{12} + 11132 q^{13} + 18748 q^{14} - 230074 q^{16} - 28972 q^{17} + 179920 q^{22} + 20508 q^{23} + 920040 q^{25} + 144684 q^{26} - 357584 q^{27} + 44600 q^{29} + 46580 q^{30} - 1216824 q^{35} - 4529248 q^{36} - 129032 q^{38} + 104546 q^{39} + 2082020 q^{40} + 2426496 q^{42} - 1434416 q^{43} - 3783940 q^{48} - 34428 q^{49} - 756008 q^{51} - 2348612 q^{52} + 1103824 q^{53} - 4216216 q^{55} + 8135574 q^{56} + 531568 q^{61} + 26627120 q^{62} - 27402496 q^{64} - 7495542 q^{65} + 2808402 q^{66} + 531760 q^{68} + 24238760 q^{69} - 7462590 q^{74} - 1547944 q^{75} - 1811116 q^{77} - 31233508 q^{78} + 2961020 q^{79} - 34639872 q^{81} - 10292872 q^{82} + 43455484 q^{87} + 21936790 q^{88} - 58442348 q^{90} + 16479848 q^{91} + 24834900 q^{92} + 26036992 q^{94} + 89048 q^{95}+O(q^{100}) \) 128 * q + 52 * q^3 + 4094 * q^4 - 44052 * q^9 - 4514 * q^10 + 2090 * q^12 + 11132 * q^13 + 18748 * q^14 - 230074 * q^16 - 28972 * q^17 + 179920 * q^22 + 20508 * q^23 + 920040 * q^25 + 144684 * q^26 - 357584 * q^27 + 44600 * q^29 + 46580 * q^30 - 1216824 * q^35 - 4529248 * q^36 - 129032 * q^38 + 104546 * q^39 + 2082020 * q^40 + 2426496 * q^42 - 1434416 * q^43 - 3783940 * q^48 - 34428 * q^49 - 756008 * q^51 - 2348612 * q^52 + 1103824 * q^53 - 4216216 * q^55 + 8135574 * q^56 + 531568 * q^61 + 26627120 * q^62 - 27402496 * q^64 - 7495542 * q^65 + 2808402 * q^66 + 531760 * q^68 + 24238760 * q^69 - 7462590 * q^74 - 1547944 * q^75 - 1811116 * q^77 - 31233508 * q^78 + 2961020 * q^79 - 34639872 * q^81 - 10292872 * q^82 + 43455484 * q^87 + 21936790 * q^88 - 58442348 * q^90 + 16479848 * q^91 + 24834900 * q^92 + 26036992 * q^94 + 89048 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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