LMFDB - Embedded newform 76.8.f.a.27.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.f (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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.17
Character	$\chi$	$=$	76.27
Dual form			76.8.f.a.31.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.97334 - 8.02657i) q^{2} +(-32.1577 + 55.6988i) q^{3} +(-0.851561 + 127.997i) q^{4} +(200.122 - 346.621i) q^{5} +(703.475 - 185.990i) q^{6} -134.782i q^{7} +(1034.17 - 1013.73i) q^{8} +(-974.738 - 1688.30i) q^{9} +O(q^{10})$	\(q+(-7.97334 - 8.02657i) q^{2} +(-32.1577 + 55.6988i) q^{3} +(-0.851561 + 127.997i) q^{4} +(200.122 - 346.621i) q^{5} +(703.475 - 185.990i) q^{6} -134.782i q^{7} +(1034.17 - 1013.73i) q^{8} +(-974.738 - 1688.30i) q^{9} +(-4377.82 + 1157.44i) q^{10} +5368.91i q^{11} +(-7101.91 - 4163.53i) q^{12} +(-12038.8 + 6950.61i) q^{13} +(-1081.84 + 1074.67i) q^{14} +(12870.9 + 22293.1i) q^{15} +(-16382.5 - 217.995i) q^{16} +(18996.3 - 32902.6i) q^{17} +(-5779.30 + 21285.2i) q^{18} +(-29445.1 - 5182.59i) q^{19} +(44196.1 + 25910.2i) q^{20} +(7507.22 + 4334.30i) q^{21} +(43093.9 - 42808.2i) q^{22} +(29807.8 - 17209.5i) q^{23} +(23207.1 + 90201.2i) q^{24} +(-41034.9 - 71074.6i) q^{25} +(151779. + 41210.7i) q^{26} -15276.4 q^{27} +(17251.8 + 114.776i) q^{28} +(77786.1 - 44909.8i) q^{29} +(76312.7 - 281060. i) q^{30} +243672. q^{31} +(128874. + 133234. i) q^{32} +(-299042. - 172652. i) q^{33} +(-415560. + 109869. i) q^{34} +(-46718.4 - 26972.9i) q^{35} +(216927. - 123326. i) q^{36} +55632.9i q^{37} +(193177. + 277665. i) q^{38} -894063. i q^{39} +(-144421. - 561334. i) q^{40} +(-344994. - 199183. i) q^{41} +(-25068.1 - 94816.1i) q^{42} +(-140064. - 80865.7i) q^{43} +(-687205. - 4571.95i) q^{44} -780265. q^{45} +(-375801. - 102037. i) q^{46} +(1.11745e6 - 645161. i) q^{47} +(538968. - 905478. i) q^{48} +805377. q^{49} +(-243299. + 896072. i) q^{50} +(1.22176e6 + 2.11615e6i) q^{51} +(-879406. - 1.54685e6i) q^{52} +(601763. - 347428. i) q^{53} +(121804. + 122617. i) q^{54} +(1.86098e6 + 1.07444e6i) q^{55} +(-136633. - 139388. i) q^{56} +(1.23555e6 - 1.47340e6i) q^{57} +(-980687. - 266274. i) q^{58} +(788918. - 1.36645e6i) q^{59} +(-2.86441e6 + 1.62846e6i) q^{60} +(241159. + 417699. i) q^{61} +(-1.94288e6 - 1.95585e6i) q^{62} +(-227553. + 131378. i) q^{63} +(41853.5 - 2.09673e6i) q^{64} +5.56387e6i q^{65} +(998561. + 3.77689e6i) q^{66} +(-1.72967e6 - 2.99588e6i) q^{67} +(4.19527e6 + 2.45950e6i) q^{68} +2.21368e6i q^{69} +(156002. + 590053. i) q^{70} +(-1.25967e6 + 2.18181e6i) q^{71} +(-2.71952e6 - 757859. i) q^{72} +(1.40765e6 - 2.43812e6i) q^{73} +(446541. - 443580. i) q^{74} +5.27836e6 q^{75} +(688431. - 3.76447e6i) q^{76} +723635. q^{77} +(-7.17625e6 + 7.12867e6i) q^{78} +(365246. - 632624. i) q^{79} +(-3.35407e6 + 5.63491e6i) q^{80} +(2.62301e6 - 4.54318e6i) q^{81} +(1.15201e6 + 4.35727e6i) q^{82} -2.78043e6i q^{83} +(-561171. + 957212. i) q^{84} +(-7.60316e6 - 1.31691e7i) q^{85} +(467701. + 1.76900e6i) q^{86} +5.77679e6i q^{87} +(5.44263e6 + 5.55235e6i) q^{88} +(318289. - 183764. i) q^{89} +(6.22132e6 + 6.26285e6i) q^{90} +(936820. + 1.62262e6i) q^{91} +(2.17739e6 + 3.82997e6i) q^{92} +(-7.83593e6 + 1.35722e7i) q^{93} +(-1.40883e7 - 3.82521e6i) q^{94} +(-7.68899e6 + 9.16914e6i) q^{95} +(-1.15653e7 + 2.89363e6i) q^{96} +(1.40914e6 + 813569. i) q^{97} +(-6.42155e6 - 6.46441e6i) q^{98} +(9.06431e6 - 5.23328e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.97334	−	8.02657i	−0.704751	−	0.709455i
$2$	−7.97334	−	8.02657i	−0.704751	−	0.709455i
$3$	−32.1577	+	55.6988i	−0.687640	+	1.19103i	0.284960	+	0.958539i	$0.408020\pi$
$3$	−32.1577	+	55.6988i	−0.687640	+	1.19103i	−0.972599	+	0.232487i	$0.925314\pi$
$4$	−0.851561	+	127.997i	−0.00665282	+	0.999978i
$5$	200.122	−	346.621i	0.715977	−	1.24011i	−0.246604	−	0.969116i	$-0.579315\pi$
$5$	200.122	−	346.621i	0.715977	−	1.24011i	0.962581	−	0.270993i	$-0.0873520\pi$
$6$	703.475	−	185.990i	1.32959	−	0.351528i
$7$		−	134.782i		−	0.148522i	−0.997239	−	0.0742609i	$-0.976340\pi$
$7$		−	134.782i		−	0.148522i	0.997239	−	0.0742609i	$-0.0236598\pi$
$8$	1034.17	−	1013.73i	0.714128	−	0.700015i
$9$	−974.738	−	1688.30i	−0.445696	−	0.771969i
$10$	−4377.82	+	1157.44i	−1.38439	+	0.366014i
$11$			5368.91i			1.21622i	0.793853	+	0.608109i	$0.208072\pi$
$11$			5368.91i			1.21622i	−0.793853	+	0.608109i	$0.791928\pi$
$12$	−7101.91	−	4163.53i	−1.18643	−	0.695548i
$13$	−12038.8	+	6950.61i	−1.51978	+	0.877447i	−0.520055	+	0.854133i	$0.674088\pi$
$13$	−12038.8	+	6950.61i	−1.51978	+	0.877447i	−0.999728	+	0.0233142i	$0.992578\pi$
$14$	−1081.84	+	1074.67i	−0.105370	+	0.104671i
$15$	12870.9	+	22293.1i	0.984669	+	1.70550i
$16$	−16382.5	−	217.995i	−0.999911	−	0.0133054i
$17$	18996.3	−	32902.6i	0.937775	−	1.62427i	0.168166	−	0.985759i	$-0.446215\pi$
$17$	18996.3	−	32902.6i	0.937775	−	1.62427i	0.769609	−	0.638516i	$-0.220451\pi$
$18$	−5779.30	+	21285.2i	−0.233572	+	0.860247i
$19$	−29445.1	−	5182.59i	−0.984861	−	0.173344i
$19$	−29445.1	−	5182.59i	−0.984861	−	0.173344i
$20$	44196.1	+	25910.2i	1.23532	+	0.724212i
$21$	7507.22	+	4334.30i	0.176893	+	0.102129i
$22$	43093.9	−	42808.2i	0.862852	−	0.857131i
$23$	29807.8	−	17209.5i	0.510837	−	0.294932i	−0.222341	−	0.974969i	$-0.571370\pi$
$23$	29807.8	−	17209.5i	0.510837	−	0.294932i	0.733178	+	0.680037i	$0.238036\pi$
$24$	23207.1	+	90201.2i	0.342674	+	1.33190i
$25$	−41034.9	−	71074.6i	−0.525247	−	0.909755i
$26$	151779.	+	41210.7i	1.69358	+	0.459836i
$27$	−15276.4			−0.149365
$28$	17251.8	+	114.776i	0.148519	+	0.000988089i
$29$	77786.1	−	44909.8i	0.592256	−	0.341939i	−0.173733	−	0.984793i	$-0.555583\pi$
$29$	77786.1	−	44909.8i	0.592256	−	0.341939i	0.765989	+	0.642854i	$0.222250\pi$
$30$	76312.7	−	281060.i	0.516027	−	1.90053i
$31$	243672.			1.46906			0.734529	−	0.678577i	$-0.237403\pi$
$31$	243672.			1.46906			0.734529	+	0.678577i	$0.237403\pi$
$32$	128874.	+	133234.i	0.695249	+	0.718769i
$33$	−299042.	−	172652.i	−1.44855	−	0.836320i
$34$	−415560.	+	109869.i	−1.81325	+	0.479399i
$35$	−46718.4	−	26972.9i	−0.184183	−	0.106338i
$36$	216927.	−	123326.i	0.774917	−	0.440551i
$37$			55632.9i			0.180562i	0.995916	+	0.0902809i	$0.0287765\pi$
$37$			55632.9i			0.180562i	−0.995916	+	0.0902809i	$0.971224\pi$
$38$	193177.	+	277665.i	0.571102	+	0.820879i
$39$		−	894063.i		−	2.41347i
$40$	−144421.	−	561334.i	−0.356796	−	1.38679i
$41$	−344994.	−	199183.i	−0.781751	−	0.451344i	0.0552993	−	0.998470i	$-0.482389\pi$
$41$	−344994.	−	199183.i	−0.781751	−	0.451344i	−0.837051	+	0.547125i	$0.815722\pi$
$42$	−25068.1	−	94816.1i	−0.0522095	−	0.197474i
$43$	−140064.	−	80865.7i	−0.268649	−	0.155105i	0.359624	−	0.933097i	$-0.382905\pi$
$43$	−140064.	−	80865.7i	−0.268649	−	0.155105i	−0.628274	+	0.777992i	$0.716238\pi$
$44$	−687205.	−	4571.95i	−1.21619	−	0.00809128i
$45$	−780265.			−1.27643
$46$	−375801.	−	102037.i	−0.569254	−	0.154562i
$47$	1.11745e6	−	645161.i	1.56995	−	0.906412i	0.573778	−	0.819011i	$-0.305477\pi$
$47$	1.11745e6	−	645161.i	1.56995	−	0.906412i	0.996173	−	0.0874011i	$-0.0278562\pi$
$48$	538968.	−	905478.i	0.703426	−	1.18177i
$49$	805377.			0.977941
$50$	−243299.	+	896072.i	−0.275262	+	1.01379i
$51$	1.22176e6	+	2.11615e6i	1.28970	+	2.23383i
$52$	−879406.	−	1.54685e6i	−0.867317	−	1.52559i
$53$	601763.	−	347428.i	0.555214	−	0.320553i	−0.196009	−	0.980602i	$-0.562798\pi$
$53$	601763.	−	347428.i	0.555214	−	0.320553i	0.751222	+	0.660049i	$0.229465\pi$
$54$	121804.	+	122617.i	0.105265	+	0.105968i
$55$	1.86098e6	+	1.07444e6i	1.50824	+	0.870785i
$56$	−136633.	−	139388.i	−0.103968	−	0.106064i
$57$	1.23555e6	−	1.47340e6i	0.883687	−	1.05380i
$58$	−980687.	−	266274.i	−0.659983	−	0.179197i
$59$	788918.	−	1.36645e6i	0.500092	−	0.866184i	−0.499908	−	0.866078i	$-0.666633\pi$
$59$	788918.	−	1.36645e6i	0.500092	−	0.866184i	1.00000		0.000105766i	$-3.36663e-5\pi$
$60$	−2.86441e6	+	1.62846e6i	−1.71201	+	0.973301i
$61$	241159.	+	417699.i	0.136034	+	0.235619i	0.925992	−	0.377543i	$-0.123231\pi$
$61$	241159.	+	417699.i	0.136034	+	0.235619i	−0.789958	+	0.613161i	$0.789898\pi$
$62$	−1.94288e6	−	1.95585e6i	−1.03532	−	1.04223i
$63$	−227553.	+	131378.i	−0.114654	+	0.0661956i
$64$	41853.5	−	2.09673e6i	0.0199573	−	0.999801i
$65$			5.56387e6i			2.51293i
$66$	998561.	+	3.77689e6i	0.427534	+	1.61708i
$67$	−1.72967e6	−	2.99588e6i	−0.702590	−	1.21692i	−0.967554	−	0.252664i	$-0.918693\pi$
$67$	−1.72967e6	−	2.99588e6i	−0.702590	−	1.21692i	0.264964	−	0.964258i	$-0.414640\pi$
$68$	4.19527e6	+	2.45950e6i	1.61800	+	0.948560i
$69$			2.21368e6i			0.811227i
$70$	156002.	+	590053.i	0.0543611	+	0.205612i
$71$	−1.25967e6	+	2.18181e6i	−0.417689	+	0.723459i	−0.995707	−	0.0925657i	$-0.970493\pi$
$71$	−1.25967e6	+	2.18181e6i	−0.417689	+	0.723459i	0.578018	+	0.816024i	$0.303827\pi$
$72$	−2.71952e6	−	757859.i	−0.858674	−	0.239290i
$73$	1.40765e6	−	2.43812e6i	0.423510	−	0.733541i	−0.572770	−	0.819716i	$-0.694131\pi$
$73$	1.40765e6	−	2.43812e6i	0.423510	−	0.733541i	0.996280	+	0.0861753i	$0.0274645\pi$
$74$	446541.	−	443580.i	0.128100	−	0.127251i
$75$	5.27836e6			1.44472
$76$	688431.	−	3.76447e6i	0.179892	−	0.983686i
$77$	723635.			0.180635
$78$	−7.17625e6	+	7.12867e6i	−1.71225	+	1.70089i
$79$	365246.	−	632624.i	0.0833471	−	0.144361i	−0.821339	−	0.570441i	$-0.806772\pi$
$79$	365246.	−	632624.i	0.0833471	−	0.144361i	0.904686	+	0.426080i	$0.140106\pi$
$80$	−3.35407e6	+	5.63491e6i	−0.732414	+	1.23047i
$81$	2.62301e6	−	4.54318e6i	0.548406	−	0.949867i
$82$	1.15201e6	+	4.35727e6i	0.230731	+	0.872703i
$83$		−	2.78043e6i		−	0.533751i	−0.963731	−	0.266876i	$-0.914009\pi$
$83$		−	2.78043e6i		−	0.533751i	0.963731	−	0.266876i	$-0.0859913\pi$
$84$	−561171.	+	957212.i	−0.103304	+	0.176210i
$85$	−7.60316e6	−	1.31691e7i	−1.34285	−	2.32589i
$86$	467701.	+	1.76900e6i	0.0792909	+	0.299905i
$87$			5.77679e6i			0.940523i
$88$	5.44263e6	+	5.55235e6i	0.851371	+	0.868535i
$89$	318289.	−	183764.i	0.0478582	−	0.0276310i	−0.475880	−	0.879510i	$-0.657870\pi$
$89$	318289.	−	183764.i	0.0478582	−	0.0276310i	0.523738	+	0.851879i	$0.324537\pi$
$90$	6.22132e6	+	6.26285e6i	0.899568	+	0.905573i
$91$	936820.	+	1.62262e6i	0.130320	+	0.225721i
$92$	2.17739e6	+	3.82997e6i	0.291527	+	0.512788i
$93$	−7.83593e6	+	1.35722e7i	−1.01018	+	1.74969i
$94$	−1.40883e7	−	3.82521e6i	−1.74948	−	0.475015i
$95$	−7.68899e6	+	9.16914e6i	−0.920104	+	1.09723i
$96$	−1.15653e7	+	2.89363e6i	−1.33415	+	0.333806i
$97$	1.40914e6	+	813569.i	0.156767	+	0.0905093i	0.576331	−	0.817216i	$-0.304484\pi$
$97$	1.40914e6	+	813569.i	0.156767	+	0.0905093i	−0.419564	+	0.907726i	$0.637817\pi$
$98$	−6.42155e6	−	6.46441e6i	−0.689205	−	0.693805i
$99$	9.06431e6	−	5.23328e6i	0.938883	−	0.542064i
$100$	9.13229e6	−	5.19183e6i	0.913229	−	0.519183i
$101$	−8.19703e6	−	1.41977e7i	−0.791647	−	1.37117i	−0.924947	−	0.380097i	$-0.875891\pi$
$101$	−8.19703e6	−	1.41977e7i	−0.791647	−	1.37117i	0.133299	−	0.991076i	$-0.457443\pi$
$102$	7.24390e6	−	2.66793e7i	0.675883	−	2.48928i
$103$	6.02583e6			0.543359			0.271679	−	0.962388i	$-0.412421\pi$
$103$	6.02583e6			0.543359			0.271679	+	0.962388i	$0.412421\pi$
$104$	−5.40410e6	+	1.93922e7i	−0.471093	+	1.69048i
$105$	3.00472e6	−	1.73477e6i	0.253303	−	0.146245i
$106$	−7.58672e6	−	2.05993e6i	−0.618705	−	0.167989i
$107$	1.08173e7			0.853645			0.426822	−	0.904335i	$-0.359633\pi$
$107$	1.08173e7			0.853645			0.426822	+	0.904335i	$0.359633\pi$
$108$	13008.8	−	1.95534e6i	0.000993699	−	0.149362i
$109$	4.63244e6	+	2.67454e6i	0.342623	+	0.197814i	0.661431	−	0.750006i	$-0.269949\pi$
$109$	4.63244e6	+	2.67454e6i	0.342623	+	0.197814i	−0.318808	+	0.947819i	$0.603283\pi$
$110$	−6.21418e6	−	2.35041e7i	−0.445153	−	1.68372i
$111$	−3.09869e6	−	1.78903e6i	−0.215054	−	0.124161i
$112$	−29381.9	+	2.20808e6i	−0.00197613	+	0.148509i
$113$		−	7.40240e6i		−	0.482612i	−0.970449	−	0.241306i	$-0.922424\pi$
$113$		−	7.40240e6i		−	0.482612i	0.970449	−	0.241306i	$-0.0775757\pi$
$114$	−2.16778e7	+	1.83066e6i	−1.37040	+	0.115729i
$115$		−	1.37760e7i		−	0.844658i
$116$	5.68209e6	+	9.99465e6i	0.337991	+	0.594517i
$117$	2.34694e7	+	1.35500e7i	1.35472	+	0.782150i
$118$	−1.72582e7	+	4.56284e6i	−0.966959	+	0.255651i
$119$	−4.43470e6	−	2.56037e6i	−0.241240	−	0.139280i
$120$	3.59099e7	+	1.00071e7i	1.89705	+	0.528659i
$121$	−9.33800e6			−0.479187
$122$	1.42985e6	−	5.26614e6i	0.0712904	−	0.262563i
$123$	2.21885e7	−	1.28105e7i	1.07513	−	0.620724i
$124$	−207501.	+	3.11893e7i	−0.00977339	+	1.46903i
$125$	−1.57892e6			−0.0723062
$126$	2.86887e6	+	778948.i	0.127765	+	0.0346906i
$127$	1.30264e7	+	2.25624e7i	0.564302	+	0.977400i	0.997114	+	0.0759158i	$0.0241880\pi$
$127$	1.30264e7	+	2.25624e7i	0.564302	+	0.977400i	−0.432812	+	0.901484i	$0.642479\pi$
$128$	−1.71633e7	+	1.63820e7i	−0.723379	+	0.690452i
$129$	9.00825e6	−	5.20092e6i	0.369468	−	0.213312i
$130$	4.46588e7	−	4.43627e7i	1.78281	−	1.77099i
$131$	2.53484e6	+	1.46349e6i	0.0985149	+	0.0568776i	0.548448	−	0.836185i	$-0.315219\pi$
$131$	2.53484e6	+	1.46349e6i	0.0985149	+	0.0568776i	−0.449933	+	0.893062i	$0.648552\pi$
$132$	2.23536e7	−	3.81295e7i	0.845938	−	1.44295i
$133$	−698522.	+	3.96868e6i	−0.0257454	+	0.146273i
$134$	−1.02554e7	+	3.77705e7i	−0.368200	+	1.35608i
$135$	−3.05715e6	+	5.29514e6i	−0.106942	+	0.185229i
$136$	−1.37090e7	−	5.32840e7i	−0.467325	−	1.81640i
$137$	1.51316e7	+	2.62086e7i	0.502761	+	0.870808i	0.999995	+	0.00319102i	$0.00101573\pi$
$137$	1.51316e7	+	2.62086e7i	0.502761	+	0.870808i	−0.497234	+	0.867617i	$0.665651\pi$
$138$	1.77682e7	−	1.76504e7i	0.575529	−	0.571713i
$139$	−1.40383e7	+	8.10503e6i	−0.443367	+	0.255978i	−0.705025	−	0.709183i	$-0.749064\pi$
$139$	−1.40383e7	+	8.10503e6i	−0.443367	+	0.255978i	0.261658	+	0.965161i	$0.415731\pi$
$140$	3.49224e6	−	5.95686e6i	0.107561	−	0.183472i
$141$			8.29876e7i			2.49314i
$142$	2.75563e7	−	7.28552e6i	0.807628	−	0.213526i
$143$	−3.73172e7	−	6.46352e7i	−1.06717	−	1.84839i
$144$	1.56007e7	+	2.78711e7i	0.435386	+	0.777831i
$145$		−	3.59497e7i		−	0.979282i
$146$	−3.07934e7	+	8.14136e6i	−0.818883	+	0.216502i
$147$	−2.58991e7	+	4.48585e7i	−0.672471	+	1.16475i
$148$	−7.12086e6	−	47374.8i	−0.180558	−	0.00120125i
$149$	2.62834e7	−	4.55242e7i	0.650923	−	1.12743i	−0.331976	−	0.943288i	$-0.607715\pi$
$149$	2.62834e7	−	4.55242e7i	0.650923	−	1.12743i	0.982899	−	0.184144i	$-0.0589512\pi$
$150$	−4.20862e7	−	4.23671e7i	−1.01817	−	1.02497i
$151$	−5.73750e7			−1.35614			−0.678068	−	0.734999i	$-0.737183\pi$
$151$	−5.73750e7			−1.35614			−0.678068	+	0.734999i	$0.737183\pi$
$152$	−3.57049e7	+	2.44897e7i	−0.824660	+	0.565628i
$153$	−7.40658e7			−1.67185
$154$	−5.76979e6	−	5.80830e6i	−0.127303	−	0.128152i
$155$	4.87640e7	−	8.44617e7i	1.05181	−	1.82179i
$156$	1.14437e8	+	761349.i	2.41342	+	0.0160564i
$157$	2.21264e7	−	3.83240e7i	0.456311	−	0.790354i	−0.542451	−	0.840087i	$-0.682504\pi$
$157$	2.21264e7	−	3.83240e7i	0.456311	−	0.790354i	0.998763	+	0.0497330i	$0.0158371\pi$
$158$	−7.99003e6	+	2.11246e6i	−0.161157	+	0.0426078i
$159$			4.46900e7i			0.881699i
$160$	7.19721e7	−	1.80074e7i	1.38913	−	0.347562i
$161$	−2.31954e6	−	4.01757e6i	−0.0438038	−	0.0758704i
$162$	−5.73803e7	+	1.51706e7i	−1.06038	+	0.280350i
$163$			3.99745e7i			0.722981i	0.932376	+	0.361491i	$0.117732\pi$
$163$			3.99745e7i			0.722981i	−0.932376	+	0.361491i	$0.882268\pi$
$164$	2.57886e7	−	4.39887e7i	0.456535	−	0.778731i
$165$	−1.19690e8	+	6.91028e7i	−2.07426	+	1.19757i
$166$	−2.23173e7	+	2.21693e7i	−0.378672	+	0.376161i
$167$	−3.06336e7	−	5.30589e7i	−0.508967	−	0.881558i	−0.999946	−	0.0103859i	$-0.996694\pi$
$167$	−3.06336e7	−	5.30589e7i	−0.508967	−	0.881558i	0.490979	−	0.871172i	$-0.336639\pi$
$168$	1.21575e7	−	3.12791e6i	0.197817	−	0.0508946i
$169$	6.52476e7	−	1.13012e8i	1.03983	−	1.80103i
$170$	−4.50797e7	+	1.66029e8i	−0.703737	+	2.59186i
$171$	1.99515e7	+	5.47637e7i	0.305133	+	0.837541i
$172$	1.04699e7	−	1.78589e7i	0.156889	−	0.267611i
$173$	−4.76135e7	−	2.74897e7i	−0.699148	−	0.403653i	0.107882	−	0.994164i	$-0.465593\pi$
$173$	−4.76135e7	−	2.74897e7i	−0.699148	−	0.403653i	−0.807030	+	0.590511i	$0.798926\pi$
$174$	4.63678e7	−	4.60604e7i	0.667259	−	0.662834i
$175$	−9.57961e6	+	5.53079e6i	−0.135118	+	0.0780107i
$176$	1.17039e6	−	8.79564e7i	0.0161822	−	1.21611i
$177$	5.07396e7	+	8.78835e7i	0.687766	+	1.19124i
$178$	−4.01282e6	−	1.08955e6i	−0.0533310	−	0.0144803i
$179$	−1.10554e8			−1.44074			−0.720372	−	0.693588i	$-0.756029\pi$
$179$	−1.10554e8			−1.44074			−0.720372	+	0.693588i	$0.756029\pi$
$180$	664444.	−	9.98718e7i	0.00849189	−	1.27641i
$181$	1.45386e7	−	8.39387e6i	0.182242	−	0.105217i	−0.406104	−	0.913827i	$-0.633113\pi$
$181$	1.45386e7	−	8.39387e6i	0.182242	−	0.105217i	0.588346	+	0.808610i	$0.299780\pi$
$182$	5.55448e6	−	2.04571e7i	0.0682957	−	0.251533i
$183$	−3.10205e7			−0.374171
$184$	1.33804e7	−	4.80146e7i	0.158346	−	0.568213i
$185$	1.92835e7	+	1.11334e7i	0.223916	+	0.129278i
$186$	1.71417e8	−	4.53204e7i	1.95325	−	0.516415i
$187$	1.76651e8	+	1.01990e8i	1.97547	+	1.14054i
$188$	8.16272e7	+	1.43580e8i	0.895947	+	1.57595i
$189$			2.05900e6i			0.0221840i
$190$	1.34904e8	−	1.13924e7i	1.42688	−	0.120498i
$191$			7.93862e7i			0.824382i	0.911097	+	0.412191i	$0.135236\pi$
$191$			7.93862e7i			0.824382i	−0.911097	+	0.412191i	$0.864764\pi$
$192$	1.15440e8	+	6.97574e7i	1.17707	+	0.711272i
$193$	8.41989e7	+	4.86123e7i	0.843055	+	0.486738i	0.858301	−	0.513146i	$-0.171520\pi$
$193$	8.41989e7	+	4.86123e7i	0.843055	+	0.486738i	−0.0152465	+	0.999884i	$0.504853\pi$
$194$	−4.70541e6	−	1.77974e7i	−0.0462692	−	0.175005i
$195$	−3.09901e8	−	1.78921e8i	−2.99297	−	1.72799i
$196$	−685828.	+	1.03086e8i	−0.00650607	+	0.977920i
$197$	−1.18197e8			−1.10147			−0.550735	−	0.834680i	$-0.685653\pi$
$197$	−1.18197e8			−1.10147			−0.550735	+	0.834680i	$0.685653\pi$
$198$	−1.14278e8	−	3.10285e7i	−1.04625	−	0.284075i
$199$	−7.58772e7	+	4.38077e7i	−0.682536	+	0.394062i	−0.800810	−	0.598919i	$-0.795597\pi$
$199$	−7.58772e7	+	4.38077e7i	−0.682536	+	0.394062i	0.118274	+	0.992981i	$0.462264\pi$
$200$	−1.14488e8	−	3.19047e7i	−1.01194	−	0.282000i
$201$	2.22489e8			1.93252
$202$	−4.86008e7	+	1.78997e8i	−0.414872	+	1.52797i
$203$	−6.05306e6	−	1.04842e7i	−0.0507854	−	0.0879629i
$204$	−2.71901e8	+	1.54580e8i	−2.24236	+	1.27481i
$205$	−1.38082e8	+	7.97216e7i	−1.11943	+	0.646305i
$206$	−4.80460e7	−	4.83667e7i	−0.382932	−	0.385489i
$207$	−5.81096e7	−	3.35496e7i	−0.455356	−	0.262900i
$208$	1.98741e8	−	1.11244e8i	1.53132	−	0.857148i
$209$	2.78248e7	−	1.58088e8i	0.210824	−	1.19781i
$210$	−3.78819e7	−	1.02856e7i	−0.282270	−	0.0766413i
$211$	−6.62179e7	+	1.14693e8i	−0.485274	+	0.840519i	−0.999857	−	0.0169219i	$-0.994613\pi$
$211$	−6.62179e7	+	1.14693e8i	−0.485274	+	0.840519i	0.514583	+	0.857440i	$0.327947\pi$
$212$	4.39574e7	+	7.73198e7i	0.316852	+	0.557334i
$213$	−8.10163e7	−	1.40324e8i	−0.574439	−	0.994958i
$214$	−8.62504e7	−	8.68261e7i	−0.601607	−	0.605623i
$215$	−5.60595e7	+	3.23660e7i	−0.384694	+	0.222103i
$216$	−1.57984e7	+	1.54862e7i	−0.106666	+	0.104558i
$217$		−	3.28427e7i		−	0.218187i
$218$	−1.54687e7	−	5.85076e7i	−0.101124	−	0.382485i
$219$	9.05334e7	+	1.56808e8i	0.582445	+	1.00882i
$220$	−1.39109e8	+	2.37285e8i	−0.880800	+	1.50242i
$221$			5.28144e8i			3.29139i
$222$	1.03471e7	+	3.91364e7i	0.0634725	+	0.240074i
$223$	5.27296e7	−	9.13304e7i	0.318411	−	0.551503i	−0.661746	−	0.749728i	$-0.730184\pi$
$223$	5.27296e7	−	9.13304e7i	0.318411	−	0.551503i	0.980157	+	0.198225i	$0.0635176\pi$
$224$	1.79576e7	−	1.73699e7i	0.106753	−	0.103260i
$225$	−7.99967e7	+	1.38558e8i	−0.468202	+	0.810949i
$226$	−5.94158e7	+	5.90219e7i	−0.342391	+	0.340121i
$227$	8.34803e7			0.473689			0.236845	−	0.971548i	$-0.423887\pi$
$227$	8.34803e7			0.473689			0.236845	+	0.971548i	$0.423887\pi$
$228$	1.87538e8	+	1.59402e8i	1.04790	+	0.890678i
$229$	−1.81986e7			−0.100142			−0.0500708	−	0.998746i	$-0.515945\pi$
$229$	−1.81986e7			−0.100142			−0.0500708	+	0.998746i	$0.515945\pi$
$230$	−1.10574e8	+	1.09841e8i	−0.599247	+	0.595273i
$231$	−2.32704e7	+	4.03056e7i	−0.124212	+	0.215141i
$232$	3.49174e7	−	1.25298e8i	0.183584	−	0.658776i
$233$	4.87579e7	−	8.44512e7i	0.252522	−	0.437381i	−0.711697	−	0.702486i	$-0.752073\pi$
$233$	4.87579e7	−	8.44512e7i	0.252522	−	0.437381i	0.964220	+	0.265105i	$0.0854066\pi$
$234$	−7.83690e7	−	2.96418e8i	−0.399842	−	1.51234i
$235$		−	5.16443e8i		−	2.59588i
$236$	1.74229e8	+	1.02143e8i	0.862838	+	0.505843i
$237$	2.34909e7	+	4.06875e7i	0.114626	+	0.198537i
$238$	1.48084e7	+	5.60101e7i	0.0712012	+	0.269307i
$239$		−	3.60846e7i		−	0.170974i	−0.996339	−	0.0854869i	$-0.972755\pi$
$239$		−	3.60846e7i		−	0.170974i	0.996339	−	0.0854869i	$-0.0272446\pi$
$240$	−2.05999e8	−	3.68023e8i	−0.961889	−	1.71845i
$241$	2.10157e8	−	1.21334e8i	0.967128	−	0.558372i	0.0687685	−	0.997633i	$-0.478093\pi$
$241$	2.10157e8	−	1.21334e8i	0.967128	−	0.558372i	0.898359	+	0.439261i	$0.144760\pi$
$242$	7.44551e7	+	7.49521e7i	0.337708	+	0.339962i
$243$	1.51995e8	+	2.63263e8i	0.679529	+	1.17698i
$244$	−5.36697e7	+	3.05120e7i	−0.236518	+	0.134464i
$245$	1.61173e8	−	2.79161e8i	0.700184	−	1.21275i
$246$	−2.79741e8	−	7.59546e7i	−1.19807	−	0.325298i
$247$	3.90506e8	−	1.42269e8i	1.64888	−	0.600718i
$248$	2.51997e8	−	2.47017e8i	1.04910	−	1.02836i
$249$	1.54867e8	+	8.94123e7i	0.635712	+	0.367028i
$250$	1.25893e7	+	1.26733e7i	0.0509578	+	0.0512980i
$251$	−3.50008e8	+	2.02077e8i	−1.39707	+	0.806601i	−0.994085	−	0.108603i	$-0.965362\pi$
$251$	−3.50008e8	+	2.02077e8i	−1.39707	+	0.806601i	−0.402989	+	0.915205i	$0.632029\pi$
$252$	−1.66222e7	−	2.92380e7i	−0.0654314	−	0.115092i
$253$	9.23964e7	+	1.60035e8i	0.358702	+	0.621289i
$254$	7.72346e7	−	2.84455e8i	0.295729	−	1.08917i
$255$	9.78002e8			3.69359
$256$	2.68340e8	+	7.14262e6i	0.999646	+	0.0266083i
$257$	−2.81570e7	+	1.62564e7i	−0.103471	+	0.0597392i	−0.550843	−	0.834609i	$-0.685694\pi$
$257$	−2.81570e7	+	1.62564e7i	−0.103471	+	0.0597392i	0.447371	+	0.894348i	$0.352360\pi$
$258$	−1.13571e8	−	3.08366e7i	−0.411718	−	0.111789i
$259$	7.49834e6			0.0268174
$260$	−7.12160e8	−	4.73798e6i	−2.51287	−	0.0167181i
$261$	−1.51642e8	−	8.75507e7i	−0.527932	−	0.304802i
$262$	−8.46436e6	−	3.20150e7i	−0.0290763	−	0.109976i
$263$	1.18042e8	+	6.81517e7i	0.400122	+	0.231010i	0.686536	−	0.727095i	$-0.259130\pi$
$263$	1.18042e8	+	6.81517e7i	0.400122	+	0.231010i	−0.286415	+	0.958106i	$0.592464\pi$
$264$	−4.84282e8	+	1.24597e8i	−1.61989	+	0.416767i
$265$		−	2.78112e8i		−	0.918034i
$266$	3.74244e7	−	2.60369e7i	0.121918	−	0.0848211i
$267$			2.36378e7i			0.0760006i
$268$	3.84937e8	−	2.18842e8i	1.22157	−	0.694479i
$269$	3.13779e7	+	1.81160e7i	0.0982858	+	0.0567453i	0.548337	−	0.836257i	$-0.315261\pi$
$269$	3.13779e7	+	1.81160e7i	0.0982858	+	0.0567453i	−0.450051	+	0.893003i	$0.648594\pi$
$270$	6.68774e7	−	1.76815e7i	0.206779	−	0.0546697i
$271$	2.48895e7	+	1.43699e7i	0.0759667	+	0.0438594i	0.537502	−	0.843262i	$-0.319368\pi$
$271$	2.48895e7	+	1.43699e7i	0.0759667	+	0.0438594i	−0.461536	+	0.887122i	$0.652701\pi$
$272$	−3.18381e8	+	5.34888e8i	−0.959304	+	1.61165i
$273$	−1.20504e8			−0.358453
$274$	8.97162e7	−	3.30425e8i	0.263478	−	0.970389i
$275$	3.81593e8	−	2.20313e8i	1.10646	−	0.638815i
$276$	−2.83344e8	−	1.88508e6i	−0.811209	−	0.00539695i
$277$	−3.43600e8			−0.971346			−0.485673	−	0.874141i	$-0.661425\pi$
$277$	−3.43600e8			−0.971346			−0.485673	+	0.874141i	$0.661425\pi$
$278$	1.76988e8	+	4.80554e7i	0.494068	+	0.134148i
$279$	−2.37516e8	−	4.11390e8i	−0.654754	−	1.13407i
$280$	−7.56580e7	+	1.94654e7i	−0.205969	+	0.0529920i
$281$	−3.17279e8	+	1.83181e8i	−0.853039	+	0.492502i	−0.861675	−	0.507461i	$-0.830584\pi$
$281$	−3.17279e8	+	1.83181e8i	−0.853039	+	0.492502i	0.00863632	+	0.999963i	$0.497251\pi$
$282$	6.66106e8	−	6.61689e8i	1.76877	−	1.75704i
$283$	1.97843e8	+	1.14225e8i	0.518883	+	0.299577i	0.736477	−	0.676462i	$-0.236488\pi$
$283$	1.97843e8	+	1.14225e8i	0.518883	+	0.299577i	−0.217595	+	0.976039i	$0.569821\pi$
$284$	−2.78193e8	−	1.63092e8i	−0.720664	−	0.422493i
$285$	−2.63449e8	−	7.23126e8i	−0.674125	−	1.85036i
$286$	−2.21256e8	+	8.14888e8i	−0.559261	+	2.05976i
$287$	−2.68463e7	+	4.64992e7i	−0.0670345	+	0.116107i
$288$	9.93197e7	−	3.47445e8i	0.244998	−	0.857063i
$289$	−5.16553e8	−	8.94695e8i	−1.25884	−	2.18038i
$290$	−2.88553e8	+	2.86640e8i	−0.694757	+	0.690150i
$291$	−9.06296e7	+	5.23250e7i	−0.215598	+	0.124476i
$292$	3.10873e8	+	1.82251e8i	0.730707	+	0.428381i
$293$			8.93322e7i			0.207478i	0.994605	+	0.103739i	$0.0330806\pi$
$293$			8.93322e7i			0.207478i	−0.994605	+	0.103739i	$0.966919\pi$
$294$	5.66562e8	−	1.49792e8i	1.30027	−	0.343773i
$295$	−3.15759e8	−	5.46911e8i	−0.716109	−	1.24034i
$296$	5.63968e7	+	5.75338e7i	0.126396	+	0.128944i
$297$		−	8.20178e7i		−	0.181660i
$298$	−5.74969e8	+	1.52014e8i	−1.25860	+	0.332758i
$299$	−2.39233e8	+	4.14364e8i	−0.517574	+	0.896465i
$300$	−4.49485e6	+	6.75615e8i	−0.00961149	+	1.44469i
$301$	−1.08993e7	+	1.88781e7i	−0.0230364	+	0.0399003i
$302$	4.57471e8	+	4.60524e8i	0.955738	+	0.962118i
$303$	1.05439e9			2.17747
$304$	4.81256e8	+	9.13229e7i	0.982468	+	0.186433i
$305$	1.93045e8			0.389590
$306$	5.90552e8	+	5.94494e8i	1.17824	+	1.18610i
$307$	1.10845e8	−	1.91989e8i	0.218641	−	0.378698i	−0.735751	−	0.677252i	$-0.763171\pi$
$307$	1.10845e8	−	1.91989e8i	0.218641	−	0.378698i	0.954393	+	0.298554i	$0.0965042\pi$
$308$	−616219.	+	9.26232e7i	−0.00120173	+	0.180631i
$309$	−1.93777e8	+	3.35632e8i	−0.373635	+	0.647155i
$310$	−1.06675e9	+	2.82035e8i	−2.03375	+	0.537696i
$311$		−	5.42884e8i		−	1.02340i	−0.859164	−	0.511700i	$-0.829016\pi$
$311$		−	5.42884e8i		−	1.02340i	0.859164	−	0.511700i	$-0.170984\pi$
$312$	−9.06338e8	−	9.24611e8i	−1.68947	−	1.72353i
$313$	5.71222e7	+	9.89386e7i	0.105293	+	0.182373i	0.913858	−	0.406034i	$-0.133089\pi$
$313$	5.71222e7	+	9.89386e7i	0.105293	+	0.182373i	−0.808565	+	0.588407i	$0.799755\pi$
$314$	−4.84031e8	+	1.27972e8i	−0.882306	+	0.233270i
$315$			1.05166e8i			0.189578i
$316$	8.06631e7	+	4.72891e7i	0.143804	+	0.0843056i
$317$	7.36758e8	−	4.25368e8i	1.29903	−	0.749992i	0.318789	−	0.947826i	$-0.396724\pi$
$317$	7.36758e8	−	4.25368e8i	1.29903	−	0.749992i	0.980236	+	0.197833i	$0.0633904\pi$
$318$	3.58707e8	−	3.56329e8i	0.625526	−	0.621378i
$319$	2.41117e8	+	4.17627e8i	0.415872	+	0.720312i
$320$	−7.18397e8	−	4.34109e8i	−1.22557	−	0.740584i
$321$	−3.47861e8	+	6.02513e8i	−0.587000	+	1.01671i
$322$	−1.37528e7	+	5.06514e7i	−0.0229559	+	0.0845466i
$323$	−7.29869e8	+	8.70370e8i	−1.20514	+	1.43713i
$324$	5.79281e8	+	3.39606e8i	0.946197	+	0.554713i
$325$	9.88023e8	+	5.70436e8i	1.59652	+	0.921754i
$326$	3.20858e8	−	3.18731e8i	0.512923	−	0.509521i
$327$	−2.97937e8	+	1.72014e8i	−0.471203	+	0.272049i
$328$	−5.58700e8	+	1.43743e8i	−0.874218	+	0.224920i
$329$	−8.69564e7	−	1.50613e8i	−0.134622	−	0.233172i
$330$	1.50898e9	+	4.09716e8i	2.31146	+	0.627601i
$331$	−3.66392e8			−0.555325			−0.277663	−	0.960679i	$-0.589560\pi$
$331$	−3.66392e8			−0.555325			−0.277663	+	0.960679i	$0.589560\pi$
$332$	3.55887e8	+	2.36771e6i	0.533739	+	0.00355095i
$333$	9.39249e7	−	5.42275e7i	0.139388	−	0.0804758i
$334$	−1.81629e8	+	6.68939e8i	−0.266730	+	0.982368i
$335$	−1.38458e9			−2.01215
$336$	−1.22043e8	−	7.26434e7i	−0.175519	−	0.104474i
$337$	−3.00217e8	−	1.73330e8i	−0.427298	−	0.246700i	0.270897	−	0.962608i	$-0.412680\pi$
$337$	−3.00217e8	−	1.73330e8i	−0.427298	−	0.246700i	−0.698195	+	0.715908i	$0.746013\pi$
$338$	−1.42734e9	+	3.77371e8i	−2.01057	+	0.531569i
$339$	4.12305e8	+	2.38044e8i	0.574803	+	0.331863i
$340$	1.69208e9	−	9.61969e8i	2.33477	−	1.32735i
$341$			1.30825e9i			1.78670i
$342$	2.80484e8	−	5.96792e8i	0.379155	−	0.806736i
$343$		−	2.19550e8i		−	0.293767i
$344$	−2.26825e8	+	5.83580e7i	−0.300426	+	0.0772940i
$345$	7.67307e8	+	4.43005e8i	1.00601	+	0.580820i
$346$	1.58991e8	+	6.01358e8i	0.206351	+	0.780489i
$347$	3.10668e8	+	1.79364e8i	0.399157	+	0.230453i	0.686120	−	0.727488i	$-0.259312\pi$
$347$	3.10668e8	+	1.79364e8i	0.399157	+	0.230453i	−0.286963	+	0.957942i	$0.592646\pi$
$348$	−7.39413e8	−	4.91929e6i	−0.940502	−	0.00625713i
$349$	−3.99979e8			−0.503673			−0.251836	−	0.967770i	$-0.581034\pi$
$349$	−3.99979e8			−0.503673			−0.251836	+	0.967770i	$0.581034\pi$
$350$	1.20775e8	+	3.27925e7i	0.150570	+	0.0408824i
$351$	1.83910e8	−	1.06180e8i	0.227002	−	0.131060i
$352$	−7.15320e8	+	6.91912e8i	−0.874180	+	0.845574i
$353$	1.36492e9			1.65157			0.825784	−	0.563986i	$-0.190733\pi$
$353$	1.36492e9			1.65157			0.825784	+	0.563986i	$0.190733\pi$
$354$	3.00839e8	−	1.10799e9i	0.360431	−	1.32747i
$355$	5.04175e8	+	8.73257e8i	0.598112	+	1.03596i
$356$	2.32503e7	+	4.08966e7i	0.0273120	+	0.0480410i
$357$	2.85219e8	−	1.64672e8i	0.331773	−	0.191549i
$358$	8.81481e8	+	8.87365e8i	1.01537	+	1.02214i
$359$	−8.13661e8	−	4.69767e8i	−0.928139	−	0.535861i	−0.0419163	−	0.999121i	$-0.513346\pi$
$359$	−8.13661e8	−	4.69767e8i	−0.928139	−	0.535861i	−0.886222	+	0.463260i	$0.846680\pi$
$360$	−8.06925e8	+	7.90979e8i	−0.911537	+	0.893524i
$361$	8.40153e8	+	3.05203e8i	0.939904	+	0.341440i
$362$	−1.83295e8	−	4.97679e7i	−0.203082	−	0.0551403i
$363$	3.00289e8	−	5.20116e8i	0.329508	−	0.570725i
$364$	−2.08488e8	+	1.18529e8i	−0.226583	+	0.128815i
$365$	−5.63402e8	−	9.75840e8i	−0.606447	−	1.05040i
$366$	2.47337e8	+	2.48988e8i	0.263697	+	0.265457i
$367$	−1.06459e9	+	6.14641e8i	−1.12422	+	0.649068i	−0.942475	−	0.334277i	$-0.891508\pi$
$367$	−1.06459e9	+	6.14641e8i	−1.12422	+	0.649068i	−0.181745	+	0.983346i	$0.558174\pi$
$368$	−4.92079e8	+	2.75438e8i	−0.514716	+	0.288109i
$369$			7.76604e8i			0.804650i
$370$	−6.43917e7	−	2.43551e8i	−0.0660882	−	0.249967i
$371$	−4.68272e7	−	8.11071e7i	−0.0476091	−	0.0824613i
$372$	−1.73053e9	−	1.01453e9i	−1.74293	−	1.02180i
$373$			6.63231e8i			0.661735i	0.943677	+	0.330868i	$0.107341\pi$
$373$			6.63231e8i			0.661735i	−0.943677	+	0.330868i	$0.892659\pi$
$374$	−5.89874e8	−	2.23110e9i	−0.583054	−	2.20530i
$375$	5.07745e7	−	8.79440e7i	0.0497206	−	0.0861186i
$376$	5.01613e8	−	1.80000e9i	0.486644	−	1.74628i
$377$	−6.24301e8	+	1.08132e9i	−0.600067	+	1.03935i
$378$	1.65267e7	−	1.64171e7i	0.0157385	−	0.0156342i
$379$	8.27238e8			0.780536			0.390268	−	0.920701i	$-0.372382\pi$
$379$	8.27238e8			0.780536			0.390268	+	0.920701i	$0.372382\pi$
$380$	−1.16708e9	−	9.91978e8i	−1.09108	−	0.927383i
$381$	−1.67560e9			−1.55215
$382$	6.37199e8	−	6.32974e8i	0.584862	−	0.580984i
$383$	1.13765e8	−	1.97048e8i	0.103470	−	0.179215i	−0.809642	−	0.586924i	$-0.800339\pi$
$383$	1.13765e8	−	1.97048e8i	0.103470	−	0.179215i	0.913112	+	0.407709i	$0.133672\pi$
$384$	−3.60528e8	−	1.48278e9i	−0.324922	−	1.33635i
$385$	1.44815e8	−	2.50827e8i	0.129331	−	0.224007i
$386$	−2.81157e8	−	1.06343e9i	−0.248825	−	0.941138i
$387$			3.15292e8i			0.276518i
$388$	−1.05334e8	+	1.79673e8i	−0.0915502	+	0.156161i
$389$	−3.90948e8	−	6.77142e8i	−0.336740	−	0.583252i	0.647077	−	0.762425i	$-0.275991\pi$
$389$	−3.90948e8	−	6.77142e8i	−0.336740	−	0.583252i	−0.983818	+	0.179173i	$0.942658\pi$
$390$	1.03482e9	+	3.91404e9i	0.883364	+	3.34118i
$391$		−	1.30767e9i		−	1.10632i
$392$	8.32895e8	−	8.16435e8i	0.698375	−	0.684574i
$393$	−1.63030e8	+	9.41252e7i	−0.135485	+	0.0782226i
$394$	9.42422e8	+	9.48712e8i	0.776262	+	0.781444i
$395$	−1.46187e8	−	2.53204e8i	−0.119349	−	0.206719i
$396$	6.62126e8	+	1.16466e9i	0.535806	+	0.942468i
$397$	2.03186e8	−	3.51929e8i	0.162978	−	0.282286i	−0.772958	−	0.634458i	$-0.781223\pi$
$397$	2.03186e8	−	3.51929e8i	0.162978	−	0.282286i	0.935935	+	0.352172i	$0.114557\pi$
$398$	9.56621e8	+	2.59739e8i	0.760587	+	0.206513i
$399$	−1.98588e8	−	1.66531e8i	−0.156512	−	0.131247i
$400$	6.56763e8	+	1.17333e9i	0.513096	+	0.916663i
$401$	−4.80637e7	−	2.77496e7i	−0.0372231	−	0.0214907i	0.481273	−	0.876571i	$-0.340175\pi$
$401$	−4.80637e7	−	2.77496e7i	−0.0372231	−	0.0214907i	−0.518496	+	0.855080i	$0.673508\pi$
$402$	−1.77398e9	−	1.78583e9i	−1.36194	−	1.37103i
$403$	−2.93351e9	+	1.69367e9i	−2.23265	+	1.28902i
$404$	1.82424e9	−	1.03711e9i	1.37641	−	0.782507i
$405$	−1.04984e9	−	1.81838e9i	−0.785292	−	1.36017i
$406$	−3.58891e7	+	1.32179e8i	−0.0266147	+	0.0980218i
$407$	−2.98688e8			−0.219603
$408$	3.40871e9	+	9.49918e8i	2.48473	+	0.692429i
$409$	−9.25398e8	+	5.34279e8i	−0.668801	+	0.386133i	−0.795622	−	0.605793i	$-0.792856\pi$
$409$	−9.25398e8	+	5.34279e8i	−0.668801	+	0.386133i	0.126821	+	0.991926i	$0.459523\pi$
$410$	1.74086e9	+	4.72675e8i	1.24745	+	0.338703i
$411$	−1.94639e9			−1.38287
$412$	−5.13136e6	+	7.71289e8i	−0.00361487	+	0.543347i
$413$	−1.84173e8	−	1.06332e8i	−0.128647	−	0.0742745i
$414$	1.94040e8	+	7.33923e8i	0.134397	+	0.508334i
$415$	−9.63756e8	−	5.56425e8i	−0.661910	−	0.382154i
$416$	−2.47754e9	−	7.08223e8i	−1.68731	−	0.482329i
$417$		−	1.04256e9i		−	0.704083i
$418$	−1.49076e9	+	1.03715e9i	−0.998368	+	0.694585i
$419$		−	1.66933e9i		−	1.10864i	−0.832302	−	0.554322i	$-0.812978\pi$
$419$		−	1.66933e9i		−	1.10864i	0.832302	−	0.554322i	$-0.187022\pi$
$420$	2.19487e8	+	3.86073e8i	0.144556	+	0.254271i
$421$	2.03855e9	+	1.17696e9i	1.33148	+	0.768728i	0.985526	−	0.169525i	$-0.0542235\pi$
$421$	2.03855e9	+	1.17696e9i	1.33148	+	0.768728i	0.345950	+	0.938253i	$0.387557\pi$
$422$	1.44857e9	−	3.82982e8i	0.938307	−	0.248076i
$423$	−2.17845e9	−	1.25773e9i	−1.39944	−	0.807969i
$424$	2.70126e8	−	9.69325e8i	0.172102	−	0.617574i
$425$	−3.11806e9			−1.97026
$426$	−4.80352e8	+	1.76914e9i	−0.301041	+	1.10874i
$427$	5.62985e7	−	3.25040e7i	0.0349945	−	0.0202041i
$428$	−9.21163e6	+	1.38459e9i	−0.00567915	+	0.853626i
$429$	4.80014e9			2.93531
$430$	7.06770e8	+	1.91900e8i	0.428685	+	0.116396i
$431$	1.06983e9	+	1.85300e9i	0.643641	+	1.11482i	0.984613	+	0.174746i	$0.0559105\pi$
$431$	1.06983e9	+	1.85300e9i	0.643641	+	1.11482i	−0.340972	+	0.940073i	$0.610756\pi$
$432$	2.50267e8	+	3.33018e6i	0.149352	+	0.00198735i
$433$	−4.95747e8	+	2.86220e8i	−0.293462	+	0.169431i	−0.639502	−	0.768789i	$-0.720860\pi$
$433$	−4.95747e8	+	2.86220e8i	−0.293462	+	0.169431i	0.346040	+	0.938220i	$0.387526\pi$
$434$	−2.63614e8	+	2.61866e8i	−0.154794	+	0.153768i
$435$	2.00236e9	+	1.15606e9i	1.16635	+	0.673393i
$436$	−3.46278e8	+	5.90661e8i	−0.200089	+	0.341300i
$437$	−9.66882e8	+	3.52255e8i	−0.554228	+	0.201916i
$438$	5.36780e8	−	1.97696e9i	0.305237	−	1.12419i
$439$	7.00080e7	−	1.21257e8i	0.0394931	−	0.0684041i	−0.845603	−	0.533812i	$-0.820759\pi$
$439$	7.00080e7	−	1.21257e8i	0.0394931	−	0.0684041i	0.885096	+	0.465408i	$0.154092\pi$
$440$	3.01375e9	−	7.75382e8i	1.68664	−	0.433942i
$441$	−7.85031e8	−	1.35971e9i	−0.435865	−	0.754940i
$442$	4.23919e9	−	4.21108e9i	2.33509	−	2.31961i
$443$	2.23779e9	−	1.29199e9i	1.22294	−	0.706066i	0.257398	−	0.966305i	$-0.417135\pi$
$443$	2.23779e9	−	1.29199e9i	1.22294	−	0.706066i	0.965544	+	0.260239i	$0.0838015\pi$
$444$	2.31629e8	−	3.95100e8i	0.125589	−	0.214223i
$445$		−	1.47101e8i		−	0.0791326i
$446$	−1.15350e9	+	3.04971e8i	−0.615667	+	0.162774i
$447$	1.69043e9	+	2.92791e9i	0.895201	+	1.55053i
$448$	−2.82603e8	−	5.64111e6i	−0.148492	−	0.00296409i
$449$		−	1.31519e9i		−	0.685689i	−0.939392	−	0.342845i	$-0.888610\pi$
$449$		−	1.31519e9i		−	0.685689i	0.939392	−	0.342845i	$-0.111390\pi$
$450$	1.74999e9	−	4.62674e8i	0.905298	−	0.239349i
$451$	1.06939e9	−	1.85224e9i	0.548933	−	0.950780i
$452$	9.47486e8	+	6.30359e6i	0.482601	+	0.00321073i
$453$	1.84505e9	−	3.19572e9i	0.932533	−	1.61520i
$454$	−6.65617e8	−	6.70061e8i	−0.333833	−	0.336061i
$455$	7.49912e8			0.373225
$456$	−2.15859e8	−	2.77625e9i	−0.106609	−	1.37114i
$457$	−1.73107e9			−0.848414			−0.424207	−	0.905565i	$-0.639447\pi$
$457$	−1.73107e9			−0.848414			−0.424207	+	0.905565i	$0.639447\pi$
$458$	1.45104e8	+	1.46073e8i	0.0705749	+	0.0710460i
$459$	−2.90196e8	+	5.02635e8i	−0.140071	+	0.242610i
$460$	1.76329e9	+	1.17311e7i	0.844639	+	0.00561936i
$461$	−1.01011e9	+	1.74957e9i	−0.480195	+	0.831722i	−0.999742	−	0.0227200i	$-0.992767\pi$
$461$	−1.01011e9	+	1.74957e9i	−0.480195	+	0.831722i	0.519547	+	0.854442i	$0.326101\pi$
$462$	5.09059e8	−	1.34589e8i	0.240171	−	0.0634982i
$463$		−	3.97311e9i		−	1.86036i	−0.367105	−	0.930179i	$-0.619651\pi$
$463$		−	3.97311e9i		−	1.86036i	0.367105	−	0.930179i	$-0.380349\pi$
$464$	−1.28413e9	+	7.18781e8i	−0.596753	+	0.334028i
$465$	3.13628e9	+	5.43219e9i	1.44654	+	2.50547i
$466$	−1.06662e9	+	2.82000e8i	−0.488267	+	0.129092i
$467$		−	1.42566e9i		−	0.647751i	−0.946100	−	0.323876i	$-0.895014\pi$
$467$		−	1.42566e9i		−	0.647751i	0.946100	−	0.323876i	$-0.104986\pi$
$468$	−1.75435e9	+	2.99247e9i	−0.791146	+	1.34949i
$469$	−4.03792e8	+	2.33129e8i	−0.180739	+	0.104350i
$470$	−4.14526e9	+	4.11778e9i	−1.84166	+	1.82945i
$471$	1.42307e9	+	2.46482e9i	0.627555	+	1.08696i
$472$	−5.69334e8	−	2.21288e9i	−0.249213	−	0.968638i
$473$	4.34161e8	−	7.51988e8i	0.188641	−	0.326736i
$474$	1.39280e8	−	5.12967e8i	0.0600708	−	0.221241i
$475$	8.39927e8	+	2.30546e9i	0.359595	+	0.987031i
$476$	3.31497e8	−	5.65448e8i	0.140882	−	0.240308i
$477$	−1.17312e9	−	6.77303e8i	−0.494914	−	0.285738i
$478$	−2.89636e8	+	2.87715e8i	−0.121298	+	0.120494i
$479$	−3.86545e9	+	2.23172e9i	−1.60704	+	0.927823i	−0.617007	+	0.786958i	$0.711655\pi$
$479$	−3.86545e9	+	2.23172e9i	−1.60704	+	0.927823i	−0.990029	+	0.140865i	$0.955012\pi$
$480$	−1.31147e9	+	4.58784e9i	−0.541268	+	1.89349i
$481$	−3.86683e8	−	6.69754e8i	−0.158433	−	0.274415i
$482$	−2.64955e9	−	7.19399e8i	−1.07772	−	0.292621i
$483$	2.98365e8			0.120485
$484$	7.95188e6	−	1.19524e9i	0.00318795	−	0.479177i
$485$	5.64000e8	−	3.25626e8i	0.224483	−	0.129605i
$486$	9.01191e8	−	3.31909e9i	0.356115	−	1.31157i
$487$	−1.68390e9			−0.660642			−0.330321	−	0.943869i	$-0.607157\pi$
$487$	−1.68390e9			−0.660642			−0.330321	+	0.943869i	$0.607157\pi$
$488$	6.72833e8	+	1.87501e8i	0.262083	+	0.0730356i
$489$	−2.22653e9	−	1.28549e9i	−0.861090	−	0.497150i
$490$	−3.52579e9	+	9.32174e8i	−1.35385	+	0.357940i
$491$	2.52896e9	+	1.46010e9i	0.964178	+	0.556668i	0.897456	−	0.441103i	$-0.145413\pi$
$491$	2.52896e9	+	1.46010e9i	0.964178	+	0.556668i	0.0667215	+	0.997772i	$0.478746\pi$
$492$	1.62082e9	+	2.85097e9i	0.613558	+	1.07923i
$493$		−	3.41249e9i		−	1.28265i
$494$	−4.25557e9	−	2.00006e9i	−1.58823	−	0.746446i
$495$		−	4.18917e9i		−	1.55242i
$496$	−3.99196e9	−	5.31192e7i	−1.46893	−	0.0195463i
$497$	2.94070e8	+	1.69782e8i	0.107449	+	0.0620359i
$498$	−5.17131e8	−	1.95596e9i	−0.187628	−	0.709672i
$499$	−2.24644e9	−	1.29698e9i	−0.809361	−	0.467285i	0.0373731	−	0.999301i	$-0.488101\pi$
$499$	−2.24644e9	−	1.29698e9i	−0.809361	−	0.467285i	−0.846734	+	0.532017i	$0.821434\pi$
$500$	1.34455e6	−	2.02097e8i	0.000481040	−	0.0723046i
$501$	3.94042e9			1.39994
$502$	4.41272e9	+	1.19813e9i	1.55684	+	0.422709i
$503$	−1.47958e9	+	8.54238e8i	−0.518384	+	0.299289i	−0.736273	−	0.676684i	$-0.763416\pi$
$503$	−1.47958e9	+	8.54238e8i	−0.518384	+	0.299289i	0.217889	+	0.975973i	$0.430083\pi$
$504$	−1.02146e8	+	3.66544e8i	−0.0355398	+	0.127532i
$505$	−6.56162e9			−2.26721
$506$	5.47825e8	−	2.01764e9i	0.187982	−	0.692337i
$507$	4.19643e9	+	7.26843e9i	1.43005	+	2.47692i
$508$	−2.89902e9	+	1.64813e9i	−0.981133	+	0.557787i
$509$	−7.39369e8	+	4.26875e8i	−0.248513	+	0.143479i	−0.619083	−	0.785325i	$-0.712496\pi$
$509$	−7.39369e8	+	4.26875e8i	−0.248513	+	0.143479i	0.370570	+	0.928804i	$0.379162\pi$
$510$	−7.79794e9	−	7.85000e9i	−2.60306	−	2.62044i
$511$	−3.28615e8	−	1.89726e8i	−0.108947	−	0.0629005i
$512$	−2.08224e9	−	2.21080e9i	−0.685624	−	0.727956i
$513$	4.49816e8	+	7.91715e7i	0.147104	+	0.0258915i
$514$	3.54989e8	+	9.63857e7i	0.115304	+	0.0313070i
$515$	1.20590e9	−	2.08868e9i	0.389033	−	0.673824i
$516$	6.58031e8	+	1.15746e9i	0.210850	+	0.370879i
$517$	3.46381e9	+	5.99949e9i	1.10239	+	1.90940i
$518$	−5.97869e7	−	6.01859e7i	−0.0188996	−	0.0190257i
$519$	3.06228e9	−	1.76801e9i	0.961523	−	0.555136i
$520$	5.64026e9	+	5.75397e9i	1.75909	+	1.79455i
$521$			6.08319e9i			1.88451i	0.334889	+	0.942257i	$0.391301\pi$
$521$			6.08319e9i			1.88451i	−0.334889	+	0.942257i	$0.608699\pi$
$522$	5.06364e8	+	1.91524e9i	0.155817	+	0.589354i
$523$	6.42176e8	+	1.11228e9i	0.196290	+	0.339984i	0.947323	−	0.320281i	$-0.103777\pi$
$523$	6.42176e8	+	1.11228e9i	0.196290	+	0.339984i	−0.751033	+	0.660265i	$0.770444\pi$
$524$	−1.89482e8	+	3.23207e8i	−0.0575317	+	0.0981343i
$525$		−	7.11431e8i		−	0.214573i
$526$	−3.94167e8	−	1.49087e9i	−0.118095	−	0.446673i
$527$	4.62887e9	−	8.01744e9i	1.37765	−	2.38615i
$528$	4.86143e9	+	2.89367e9i	1.43729	+	0.855519i
$529$	−1.11008e9	+	1.92271e9i	−0.326030	+	0.564701i
$530$	−2.23228e9	+	2.21748e9i	−0.651304	+	0.646985i
$531$	−3.07595e9			−0.891556
$532$	−5.07385e8	−	9.27884e7i	−0.146099	−	0.0267179i
$533$	5.53776e9			1.58412
$534$	1.89730e8	−	1.88472e8i	0.0539190	−	0.0535615i
$535$	2.16479e9	−	3.74952e9i	0.611191	−	1.05861i
$536$	−4.82579e9	−	1.34482e9i	−1.35360	−	0.377214i
$537$	3.55515e9	−	6.15770e9i	0.990713	−	1.71596i
$538$	−1.04777e8	−	3.96302e8i	−0.0290087	−	0.109721i
$539$			4.32399e9i			1.18939i
$540$	−6.75159e8	−	3.95815e8i	−0.184513	−	0.108172i
$541$	1.00007e9	+	1.73218e9i	0.271544	+	0.470329i	0.969257	−	0.246049i	$-0.0791323\pi$
$541$	1.00007e9	+	1.73218e9i	0.271544	+	0.470329i	−0.697713	+	0.716377i	$0.745799\pi$
$542$	−8.31110e7	−	3.14354e8i	−0.0224213	−	0.0848049i
$543$			1.07971e9i			0.289406i
$544$	6.83188e9	−	1.70934e9i	1.81947	−	0.455231i
$545$	1.85410e9	−	1.07047e9i	0.490621	−	0.283260i
$546$	9.60820e8	+	9.67233e8i	0.252620	+	0.254306i
$547$	−1.77743e9	−	3.07859e9i	−0.464340	−	0.804260i	0.534832	−	0.844959i	$-0.320375\pi$
$547$	−1.77743e9	−	3.07859e9i	−0.464340	−	0.804260i	−0.999171	+	0.0406985i	$0.987042\pi$
$548$	−3.36751e9	+	1.91448e9i	−0.874133	+	0.496957i
$549$	4.70133e8	−	8.14295e8i	0.121260	−	0.210029i
$550$	−4.81093e9	−	1.30625e9i	−1.23299	−	0.334779i
$551$	−2.52317e9	+	9.19240e8i	−0.642563	+	0.234098i
$552$	2.24407e9	+	2.28931e9i	0.567871	+	0.579320i
$553$	−8.52666e7	−	4.92287e7i	−0.0214408	−	0.0123789i
$554$	2.73964e9	+	2.75793e9i	0.684557	+	0.689126i
$555$	−1.24023e9	+	7.16047e8i	−0.307948	+	0.177794i
$556$	−1.02547e9	−	1.80377e9i	−0.253023	−	0.445060i
$557$	−1.82544e9	−	3.16175e9i	−0.447583	−	0.775236i	0.550645	−	0.834739i	$-0.314382\pi$
$557$	−1.82544e9	−	3.16175e9i	−0.447583	−	0.775236i	−0.998228	+	0.0595031i	$0.981048\pi$
$558$	−1.40825e9	+	5.18659e9i	−0.343131	+	1.26375i
$559$	2.24826e9			0.544385
$560$	7.59487e8	+	4.52069e8i	0.182752	+	0.108779i
$561$	−1.13614e10	+	6.55951e9i	−2.71683	+	1.56856i
$562$	4.00009e9	+	1.08609e9i	0.950588	+	0.258101i
$563$	3.19239e9			0.753939			0.376970	−	0.926226i	$-0.376966\pi$
$563$	3.19239e9			0.753939			0.376970	+	0.926226i	$0.376966\pi$
$564$	−1.06222e10	−	7.06690e7i	−2.49308	−	0.0165864i
$565$	−2.56583e9	−	1.48138e9i	−0.598491	−	0.345539i
$566$	−6.60640e8	−	2.49876e9i	−0.153146	−	0.579251i
$567$	−6.12341e8	−	3.53535e8i	−0.141076	−	0.0814502i
$568$	9.09061e8	+	3.53333e9i	0.208149	+	0.809031i
$569$		−	2.37445e9i		−	0.540343i	−0.962812	−	0.270172i	$-0.912920\pi$
$569$		−	2.37445e9i		−	0.540343i	0.962812	−	0.270172i	$-0.0870805\pi$
$570$	−3.70365e9	+	7.88033e9i	−0.837660	+	1.78231i
$571$			3.00554e9i			0.675610i	0.941216	+	0.337805i	$0.109684\pi$
$571$			3.00554e9i			0.675610i	−0.941216	+	0.337805i	$0.890316\pi$
$572$	8.30490e9	−	4.72145e9i	1.85545	−	1.05485i
$573$	−4.42172e9	−	2.55288e9i	−0.981861	−	0.566878i
$574$	5.87284e8	−	1.55270e8i	0.129615	−	0.0342686i
$575$	−2.44632e9	−	1.41238e9i	−0.536631	−	0.309824i
$576$	−3.58070e9	+	1.97311e9i	−0.780710	+	0.430201i
$577$	8.94066e9			1.93756			0.968778	−	0.247931i	$-0.0797507\pi$
$577$	8.94066e9			1.93756			0.968778	+	0.247931i	$0.0797507\pi$
$578$	−3.06268e9	+	1.12799e10i	−0.659712	+	2.42972i
$579$	−5.41529e9	+	3.12652e9i	−1.15944	+	0.669401i
$580$	4.60147e9	+	3.06134e7i	0.979260	+	0.00651499i
$581$	−3.74753e8			−0.0792737
$582$	1.14261e9	+	3.10239e8i	0.240253	+	0.0652328i
$583$	1.86531e9	+	3.23081e9i	0.389862	+	0.675261i
$584$	−1.01585e9	−	3.94839e9i	−0.211049	−	0.820305i
$585$	9.39346e9	−	5.42332e9i	1.93990	−	1.12000i
$586$	7.17031e8	−	7.12276e8i	0.147196	−	0.146220i
$587$	5.01257e9	+	2.89401e9i	1.02289	+	0.590563i	0.914938	−	0.403593i	$-0.132239\pi$
$587$	5.01257e9	+	2.89401e9i	1.02289	+	0.590563i	0.107947	+	0.994157i	$0.465572\pi$
$588$	−5.71971e9	−	3.35321e9i	−1.16025	−	0.680205i
$589$	−7.17493e9	−	1.26285e9i	−1.44682	−	0.254653i
$590$	−1.87216e9	+	6.89517e9i	−0.375285	+	1.38217i
$591$	3.80093e9	−	6.58341e9i	0.757415	−	1.31188i
$592$	1.21277e7	−	9.11409e8i	0.00240244	−	0.180546i
$593$	3.70060e9	+	6.40962e9i	0.728753	+	1.26224i	0.957411	+	0.288730i	$0.0932330\pi$
$593$	3.70060e9	+	6.40962e9i	0.728753	+	1.26224i	−0.228658	+	0.973507i	$0.573434\pi$
$594$	−6.58321e8	+	6.53956e8i	−0.128880	+	0.128025i
$595$	−1.77496e9	+	1.02477e9i	−0.345445	+	0.199443i
$596$	5.80458e9	+	3.40297e9i	1.12308	+	0.658409i
$597$		−	5.63503e9i		−	1.08389i
$598$	5.23341e9	−	1.38365e9i	1.00076	−	0.264589i
$599$	1.72323e9	+	2.98473e9i	0.327605	+	0.567429i	0.982036	−	0.188693i	$-0.0604251\pi$
$599$	1.72323e9	+	2.98473e9i	0.327605	+	0.567429i	−0.654431	+	0.756122i	$0.727092\pi$
$600$	5.45871e9	−	5.35084e9i	1.03172	−	1.01133i
$601$		−	1.01592e9i		−	0.190896i	−0.995434	−	0.0954482i	$-0.969572\pi$
$601$		−	1.01592e9i		−	0.190896i	0.995434	−	0.0954482i	$-0.0304284\pi$
$602$	2.38430e8	−	6.30379e7i	0.0445424	−	0.0117764i
$603$	−3.37196e9	+	5.84040e9i	−0.626284	+	1.08476i
$604$	4.88583e7	−	7.34384e9i	0.00902214	−	1.35611i
$605$	−1.86874e9	+	3.23675e9i	−0.343087	+	0.594244i
$606$	−8.40702e9	−	8.46314e9i	−1.53457	−	1.54482i
$607$	5.02816e9			0.912533			0.456266	−	0.889843i	$-0.349186\pi$
$607$	5.02816e9			0.912533			0.456266	+	0.889843i	$0.349186\pi$
$608$	−3.10421e9	−	4.59098e9i	−0.560129	−	0.828405i
$609$	7.78610e8			0.139688
$610$	−1.53921e9	−	1.54948e9i	−0.274564	−	0.276397i
$611$	−8.96852e9	+	1.55339e10i	−1.59066	+	2.75510i
$612$	6.30716e7	−	9.48022e9i	0.0111225	−	1.67182i
$613$	−8.24163e8	+	1.42749e9i	−0.144511	+	0.250301i	−0.929190	−	0.369601i	$-0.879494\pi$
$613$	−8.24163e8	+	1.42749e9i	−0.144511	+	0.250301i	0.784679	+	0.619902i	$0.212828\pi$
$614$	−2.42482e9	+	6.41092e8i	−0.422757	+	0.111771i
$615$		−	1.02547e10i		−	1.77770i
$616$	7.48359e8	−	7.33570e8i	0.128996	−	0.126447i
$617$	−3.06905e9	−	5.31574e9i	−0.526024	−	0.911100i	−0.999540	−	0.0303149i	$-0.990349\pi$
$617$	−3.06905e9	−	5.31574e9i	−0.526024	−	0.911100i	0.473517	−	0.880785i	$-0.342984\pi$
$618$	4.23902e9	−	1.12074e9i	0.722447	−	0.191006i
$619$		−	5.14880e9i		−	0.872546i	−0.899814	−	0.436273i	$-0.856298\pi$
$619$		−	5.14880e9i		−	0.872546i	0.899814	−	0.436273i	$-0.143702\pi$
$620$	1.07693e10	+	6.31358e9i	1.81476	+	1.06391i
$621$	−4.55357e8	+	2.62900e8i	−0.0763012	+	0.0440525i
$622$	−4.35750e9	+	4.32860e9i	−0.726057	+	0.721243i
$623$	−2.47682e7	−	4.28998e7i	−0.00410380	−	0.00710799i
$624$	−1.94901e8	+	1.46470e10i	−0.0321121	+	2.41326i
$625$	2.88988e9	−	5.00542e9i	0.473478	−	0.820088i
$626$	3.38682e8	−	1.24737e9i	0.0551800	−	0.203228i
$627$	7.91052e9	+	6.63356e9i	1.28165	+	1.07476i
$628$	4.88652e9	+	2.86475e9i	0.787301	+	0.461559i
$629$	1.83047e9	+	1.05682e9i	0.293282	+	0.169326i
$630$	8.44123e8	−	8.38525e8i	0.134497	−	0.133605i
$631$	2.25652e9	−	1.30280e9i	0.357550	−	0.206432i	−0.310455	−	0.950588i	$-0.600482\pi$
$631$	2.25652e9	−	1.30280e9i	0.357550	−	0.206432i	0.668006	+	0.744156i	$0.267148\pi$
$632$	−2.63585e8	−	1.02450e9i	−0.0415347	−	0.161437i
$633$	−4.25883e9	−	7.37651e9i	−0.667387	−	1.15595i
$634$	−9.28867e9	−	2.52204e9i	−1.44757	−	0.393042i
$635$	1.04275e10			1.61611
$636$	−5.72019e9	−	3.80563e7i	−0.881680	−	0.00586579i
$637$	−9.69577e9	+	5.59786e9i	−1.48626	+	0.858092i
$638$	1.42960e9	−	5.26522e9i	0.217943	−	0.802683i
$639$	4.91140e9			0.744650
$640$	2.24361e9	+	9.22756e9i	0.338313	+	1.39142i
$641$	1.95678e8	+	1.12975e8i	0.0293453	+	0.0169425i	0.514601	−	0.857430i	$-0.327940\pi$
$641$	1.95678e8	+	1.12975e8i	0.0293453	+	0.0169425i	−0.485256	+	0.874372i	$0.661273\pi$
$642$	7.60973e9	−	2.01191e9i	1.13500	−	0.300080i
$643$	−1.13548e10	−	6.55571e9i	−1.68439	−	0.972481i	−0.958685	−	0.284471i	$-0.908182\pi$
$643$	−1.13548e10	−	6.55571e9i	−1.68439	−	0.972481i	−0.725702	−	0.688010i	$-0.758485\pi$
$644$	5.16212e8	−	2.93474e8i	0.0761602	−	0.0432981i
$645$		−	4.16327e9i		−	0.610907i
$646$	1.28056e10	−	1.08142e9i	1.86890	−	0.157826i
$647$		−	1.03015e10i		−	1.49533i	−0.664078	−	0.747664i	$-0.731176\pi$
$647$		−	1.03015e10i		−	1.49533i	0.664078	−	0.747664i	$-0.268824\pi$
$648$	−1.89293e9	−	7.35744e9i	−0.273289	−	1.06222i
$649$	7.33632e9	+	4.23563e9i	1.05347	+	0.608221i
$650$	−3.29921e9	−	1.24787e10i	−0.471209	−	1.78227i
$651$	1.82930e9	+	1.05615e9i	0.259867	+	0.150034i
$652$	−5.11663e9	−	3.40408e7i	−0.722965	−	0.00480986i
$653$	−3.51014e9			−0.493319			−0.246660	−	0.969102i	$-0.579333\pi$
$653$	−3.51014e9			−0.493319			−0.246660	+	0.969102i	$0.579333\pi$
$654$	3.75624e9	+	1.01989e9i	0.525087	+	0.142570i
$655$	1.01455e9	−	5.85754e8i	0.141069	−	0.0814461i
$656$	5.60847e9	+	3.33833e9i	0.775677	+	0.461706i
$657$	−5.48835e9			−0.755028
$658$	−5.15571e8	+	1.89885e9i	−0.0705502	+	0.259836i
$659$	−1.14232e9	−	1.97855e9i	−0.155485	−	0.269308i	0.777751	−	0.628573i	$-0.216361\pi$
$659$	−1.14232e9	−	1.97855e9i	−0.155485	−	0.269308i	−0.933236	+	0.359265i	$0.883027\pi$
$660$	−8.74304e9	−	1.53788e10i	−1.18375	−	2.08218i
$661$	−3.55534e9	+	2.05267e9i	−0.478823	+	0.276449i	−0.719926	−	0.694051i	$-0.755824\pi$
$661$	−3.55534e9	+	2.05267e9i	−0.478823	+	0.276449i	0.241103	+	0.970500i	$0.422491\pi$
$662$	2.92137e9	+	2.94087e9i	0.391366	+	0.393978i
$663$	−2.94170e10	−	1.69839e10i	−3.92014	−	2.26329i
$664$	−2.81861e9	−	2.87543e9i	−0.373634	−	0.381167i
$665$	1.23584e9	+	1.03634e9i	0.162962	+	0.136656i
$666$	−1.18416e9	−	3.21519e8i	−0.155328	−	0.0421742i
$667$	1.54575e9	−	2.67733e9i	0.201697	−	0.349350i
$668$	6.81748e9	−	3.87583e9i	0.884924	−	0.503091i
$669$	3.39133e9	+	5.87395e9i	0.437903	+	0.758471i
$670$	1.10397e10	+	1.11134e10i	1.41807	+	1.42753i
$671$	−2.24259e9	+	1.29476e9i	−0.286564	+	0.165448i
$672$	3.90011e8	+	1.55879e9i	0.0495774	+	0.198151i
$673$		−	9.46811e9i		−	1.19732i	−0.801003	−	0.598660i	$-0.795700\pi$
$673$		−	9.46811e9i		−	1.19732i	0.801003	−	0.598660i	$-0.204300\pi$
$674$	1.00249e9	+	3.79173e9i	0.126115	+	0.477011i
$675$	6.26868e8	+	1.08577e9i	0.0784536	+	0.135886i
$676$	1.44097e10	+	8.44774e9i	1.79408	+	1.05179i
$677$			1.24092e10i			1.53703i	0.639830	+	0.768517i	$0.279005\pi$
$677$			1.24092e10i			1.53703i	−0.639830	+	0.768517i	$0.720995\pi$
$678$	−1.37677e9	−	5.20740e9i	−0.169651	−	0.641678i
$679$	1.09655e8	−	1.89928e8i	0.0134426	−	0.0232833i
$680$	−2.12128e10	−	5.91146e9i	−2.58712	−	0.720964i
$681$	−2.68454e9	+	4.64976e9i	−0.325728	+	0.564177i
$682$	1.05008e10	−	1.04311e10i	1.26758	−	1.25918i
$683$	9.69527e9			1.16436			0.582180	−	0.813060i	$-0.302200\pi$
$683$	9.69527e9			1.16436			0.582180	+	0.813060i	$0.302200\pi$
$684$	−7.02658e9	+	2.50710e9i	−0.839553	+	0.299554i
$685$	1.21126e10			1.43986
$686$	−1.76223e9	+	1.75055e9i	−0.208415	+	0.207033i
$687$	5.85227e8	−	1.01364e9i	0.0688614	−	0.119271i
$688$	2.27697e9	+	1.35532e9i	0.266562	+	0.158665i
$689$	−4.82967e9	+	8.36524e9i	−0.562536	+	0.974341i
$690$	−2.56220e9	−	9.69108e9i	−0.296921	−	1.12305i
$691$		−	1.23615e10i		−	1.42527i	−0.701536	−	0.712634i	$-0.747502\pi$
$691$		−	1.23615e10i		−	1.42527i	0.701536	−	0.712634i	$-0.252498\pi$
$692$	3.55915e9	−	6.07099e9i	0.408295	−	0.696447i
$693$	−7.05354e8	−	1.22171e9i	−0.0805084	−	0.139445i
$694$	−1.03738e9	−	3.92373e9i	−0.117810	−	0.445596i
$695$			6.48797e9i			0.733099i
$696$	5.85611e9	+	5.97417e9i	0.658380	+	0.671654i
$697$	−1.31073e10	+	7.56748e9i	−1.46621	+	0.846519i
$698$	3.18917e9	+	3.21046e9i	0.354964	+	0.357333i
$699$	3.13589e9	+	5.43152e9i	0.347288	+	0.601521i
$700$	−6.99768e8	−	1.23087e9i	−0.0771100	−	0.135634i
$701$	4.70169e9	−	8.14357e9i	0.515515	−	0.892897i	−0.484323	−	0.874889i	$-0.660934\pi$
$701$	4.70169e9	−	8.14357e9i	0.515515	−	0.892897i	0.999838	−	0.0180083i	$-0.00573254\pi$
$702$	−2.31864e9	−	6.29552e8i	−0.252961	−	0.0686834i
$703$	2.88322e8	−	1.63812e9i	0.0312993	−	0.177828i
$704$	1.12572e10	+	2.24707e8i	1.21598	+	0.0242724i
$705$	2.87653e10	+	1.66076e10i	3.09176	+	1.78503i
$706$	−1.08830e10	−	1.09556e10i	−1.16394	−	1.17171i
$707$	−1.91360e9	+	1.10482e9i	−0.203649	+	0.117577i
$708$	−1.12921e10	+	6.41968e9i	−1.19579	+	0.679825i
$709$	−8.71013e8	−	1.50864e9i	−0.0917831	−	0.158973i	0.816478	−	0.577376i	$-0.195923\pi$
$709$	−8.71013e8	−	1.50864e9i	−0.0917831	−	0.158973i	−0.908261	+	0.418403i	$0.862590\pi$
$710$	2.98929e9	−	1.10096e10i	0.313447	−	1.15443i
$711$	−1.42408e9			−0.148590
$712$	1.42877e8	−	5.12702e8i	0.0148348	−	0.0532335i
$713$	7.26331e9	−	4.19348e9i	0.750449	−	0.433272i
$714$	−3.59590e9	−	9.76350e8i	−0.369712	−	0.100383i
$715$	−2.98719e10			−3.05627
$716$	9.41431e7	−	1.41505e10i	0.00958502	−	1.44071i
$717$	2.00987e9	+	1.16040e9i	0.203634	+	0.117568i
$718$	2.71698e9	+	1.02765e10i	0.273937	+	1.03612i
$719$	1.97681e9	+	1.14131e9i	0.198342	+	0.114513i	0.595882	−	0.803072i	$-0.296803\pi$
$719$	1.97681e9	+	1.14131e9i	0.198342	+	0.114513i	−0.397540	+	0.917585i	$0.630136\pi$
$720$	1.27827e10	+	1.70094e8i	1.27632	+	0.0169834i
$721$		−	8.12176e8i		−	0.0807006i
$722$	−4.24910e9	−	9.17704e9i	−0.420162	−	0.907449i
$723$			1.56073e10i			1.53583i
$724$	1.06201e9	+	1.86805e9i	0.104003	+	0.182938i
$725$	−6.38390e9	−	3.68575e9i	−0.622161	−	0.359205i
$726$	−6.56905e9	+	1.73677e9i	−0.637125	+	0.168448i
$727$	8.32354e9	+	4.80560e9i	0.803411	+	0.463849i	0.844662	−	0.535299i	$-0.179801\pi$
$727$	8.32354e9	+	4.80560e9i	0.803411	+	0.463849i	−0.0412517	+	0.999149i	$0.513135\pi$
$728$	2.61373e9	+	7.28378e8i	0.251073	+	0.0699676i
$729$	−8.07823e9			−0.772271
$730$	−3.34045e9	+	1.23029e10i	−0.317816	+	1.17052i
$731$	−5.32139e9	+	3.07231e9i	−0.503865	+	0.290907i
$732$	2.64158e7	−	3.97053e9i	0.00248929	−	0.374162i
$733$	3.51314e9			0.329482			0.164741	−	0.986337i	$-0.447321\pi$
$733$	3.51314e9			0.329482			0.164741	+	0.986337i	$0.447321\pi$
$734$	1.34218e10	+	3.64426e9i	1.25278	+	0.340152i
$735$	1.03659e10	+	1.79543e10i	0.962948	+	1.66788i
$736$	6.13434e9	+	1.75354e9i	0.567147	+	0.162123i
$737$	1.60846e10	−	9.28645e9i	1.48004	−	0.854503i
$738$	6.23346e9	−	6.19213e9i	0.570863	−	0.567078i
$739$	3.95572e9	+	2.28383e9i	0.360553	+	0.208166i	0.669323	−	0.742971i	$-0.266584\pi$
$739$	3.95572e9	+	2.28383e9i	0.360553	+	0.208166i	−0.308770	+	0.951137i	$0.599917\pi$
$740$	−1.44146e9	+	2.45876e9i	−0.130765	+	0.223051i
$741$	−4.63356e9	+	2.63257e10i	−0.418361	+	2.37693i
$742$	−2.77642e8	+	1.02256e9i	−0.0249501	+	0.0918912i
$743$	−1.00662e9	+	1.74352e9i	−0.0900339	+	0.155943i	−0.907525	−	0.419998i	$-0.862031\pi$
$743$	−1.00662e9	+	1.74352e9i	−0.0900339	+	0.155943i	0.817491	+	0.575941i	$0.195364\pi$
$744$	5.65491e9	+	2.19795e10i	0.503409	+	1.95664i
$745$	−1.05198e10	−	1.82208e10i	−0.932092	−	1.61443i
$746$	5.32347e9	−	5.28817e9i	0.469471	−	0.466358i
$747$	−4.69419e9	+	2.71019e9i	−0.412039	+	0.237891i
$748$	−1.32048e10	+	2.25240e10i	−1.15366	+	1.96784i
$749$		−	1.45799e9i		−	0.126785i
$750$	−1.11073e9	+	2.93663e8i	−0.0961379	+	0.0254176i
$751$	−1.00078e10	−	1.73341e10i	−0.862184	−	1.49335i	−0.869816	−	0.493376i	$-0.835763\pi$
$751$	−1.00078e10	−	1.73341e10i	−0.862184	−	1.49335i	0.00763221	−	0.999971i	$-0.497571\pi$
$752$	−1.84473e10	+	1.03258e10i	−1.58187	+	0.885443i
$753$		−	2.59934e10i		−	2.21860i
$754$	1.36571e10	−	3.61075e9i	1.16027	−	0.306759i
$755$	−1.14820e10	+	1.98874e10i	−0.970963	+	1.68176i
$756$	−2.63546e8	−	1.75336e6i	−0.0221835	−	0.000147586i
$757$	1.75891e9	−	3.04652e9i	0.147370	−	0.255252i	−0.782885	−	0.622167i	$-0.786253\pi$
$757$	1.75891e9	−	3.04652e9i	0.147370	−	0.255252i	0.930255	+	0.366915i	$0.119586\pi$
$758$	−6.59585e9	−	6.63988e9i	−0.550084	−	0.553755i
$759$	−1.18850e10			−0.986629
$760$	1.34332e9	+	1.72770e10i	0.111002	+	1.42765i
$761$	−7.59112e9			−0.624395			−0.312198	−	0.950017i	$-0.601065\pi$
$761$	−7.59112e9			−0.624395			−0.312198	+	0.950017i	$0.601065\pi$
$762$	1.33601e10	+	1.34493e10i	1.09388	+	1.10118i
$763$	3.60481e8	−	6.24371e8i	0.0293796	−	0.0508870i
$764$	−1.01612e10	−	6.76022e7i	−0.824364	−	0.00548447i
$765$	−1.48222e10	+	2.56728e10i	−1.19701	+	2.07328i
$766$	−2.48871e9	+	6.57982e8i	−0.200066	+	0.0528949i
$767$			2.19338e10i			1.75522i
$768$	−9.02705e9	+	1.47166e10i	−0.719087	+	1.17231i
$769$	1.24511e10	+	2.15660e10i	0.987341	+	1.71012i	0.631034	+	0.775755i	$0.282631\pi$
$769$	1.24511e10	+	2.15660e10i	0.987341	+	1.71012i	0.356307	+	0.934369i	$0.384036\pi$
$770$	−3.16794e9	+	8.37562e8i	−0.250069	+	0.0661149i
$771$		−	2.09108e9i		−	0.164316i
$772$	−6.29393e9	+	1.07358e10i	−0.492336	+	0.839798i
$773$	9.71590e9	−	5.60948e9i	0.756580	−	0.436812i	−0.0714863	−	0.997442i	$-0.522774\pi$
$773$	9.71590e9	−	5.60948e9i	0.756580	−	0.436812i	0.828067	+	0.560630i	$0.189441\pi$
$774$	2.53071e9	−	2.51393e9i	0.196177	−	0.194877i
$775$	−9.99905e9	−	1.73189e10i	−0.771619	−	1.33648i
$776$	2.28203e9	−	5.87124e8i	0.175309	−	0.0451039i
$777$	−2.41130e8	+	4.17649e8i	−0.0184407	+	0.0319402i
$778$	−2.31796e9	+	8.53705e9i	−0.176473	+	0.649949i
$779$	9.12611e9	+	7.65291e9i	0.691679	+	0.580024i
$780$	2.31653e10	−	3.95141e10i	1.74786	−	2.98140i
$781$	−1.17140e10	−	6.76306e9i	−0.879884	−	0.508001i
$782$	−1.04961e10	+	1.04265e10i	−0.784884	+	0.779679i
$783$	−1.18829e9	+	6.86062e8i	−0.0884623	+	0.0510737i
$784$	−1.31941e10	−	1.75568e8i	−0.977855	−	0.0130119i
$785$	−8.85593e9	−	1.53389e10i	−0.653417	−	1.13175i
$786$	2.05539e9	+	5.58076e8i	0.150979	+	0.0409934i
$787$	−8.07819e9			−0.590748			−0.295374	−	0.955382i	$-0.595444\pi$
$787$	−8.07819e9			−0.590748			−0.295374	+	0.955382i	$0.595444\pi$
$788$	1.00652e8	−	1.51288e10i	0.00732789	−	1.10145i
$789$	−7.59193e9	+	4.38320e9i	−0.550279	+	0.317704i
$790$	−8.66756e8	+	3.19226e9i	−0.0625463	+	0.230358i
$791$	−9.97713e8			−0.0716784
$792$	4.06888e9	−	1.46009e10i	0.291029	−	1.04434i
$793$	−5.80653e9	−	3.35240e9i	−0.413486	−	0.238726i
$794$	−4.44486e9	+	1.17516e9i	−0.315128	+	0.0833156i
$795$	1.54905e10	+	8.94344e9i	1.09340	+	0.631277i
$796$	−5.54265e9	−	9.74937e9i	−0.389513	−	0.685142i
$797$		−	2.66113e10i		−	1.86192i	−0.365115	−	0.930962i	$-0.618970\pi$
$797$		−	2.66113e10i		−	1.86192i	0.365115	−	0.930962i	$-0.381030\pi$
$798$	2.46741e8	+	2.92178e9i	0.0171882	+	0.203534i
$799$		−	4.90228e10i		−	3.40004i
$800$	4.18120e9	−	1.46269e10i	0.288726	−	1.01004i
$801$	−6.20497e8	−	3.58244e8i	−0.0426605	−	0.0246300i
$802$	1.60495e8	+	6.07044e8i	0.0109863	+	0.0415537i
$803$	1.30900e10	+	7.55753e9i	0.892146	+	0.515081i
$804$	−1.89463e8	+	2.84780e10i	−0.0128567	+	1.93247i
$805$	−1.85676e9			−0.125450
$806$	3.69842e10	+	1.00419e10i	2.48796	+	0.675526i
$807$	−2.01808e9	+	1.16514e9i	−0.135170	+	0.0780406i
$808$	−2.28697e10	−	6.37319e9i	−1.52518	−	0.425028i
$809$	1.47536e10			0.979667			0.489833	−	0.871816i	$-0.337058\pi$
$809$	1.47536e10			0.979667			0.489833	+	0.871816i	$0.337058\pi$
$810$	−6.22459e9	+	2.29252e10i	−0.411541	+	1.51571i
$811$	−1.18958e10	−	2.06042e10i	−0.783107	−	1.35638i	−0.930123	−	0.367247i	$-0.880300\pi$
$811$	−1.18958e10	−	2.06042e10i	−0.783107	−	1.35638i	0.147016	−	0.989134i	$-0.453033\pi$
$812$	1.34710e9	−	7.65846e8i	0.0882988	−	0.0501991i
$813$	−1.60078e9	+	9.24210e8i	−0.104475	+	0.0603189i
$814$	2.38154e9	+	2.39744e9i	0.154765	+	0.155798i
$815$	1.38560e10	+	7.99978e9i	0.896575	+	0.517638i
$816$	−1.95542e10	−	3.49342e10i	−1.25987	−	2.25079i
$817$	3.70509e9	+	3.10699e9i	0.237696	+	0.199325i
$818$	1.16669e10	+	3.16778e9i	0.745282	+	0.202357i
$819$	1.82631e9	−	3.16326e9i	0.116166	−	0.201206i
$820$	−1.00865e10	−	1.77420e10i	−0.638843	−	1.12371i
$821$	1.22610e10	+	2.12367e10i	0.773259	+	1.33932i	0.935768	+	0.352617i	$0.114708\pi$
$821$	1.22610e10	+	2.12367e10i	0.773259	+	1.33932i	−0.162509	+	0.986707i	$0.551959\pi$
$822$	1.55192e10	+	1.56228e10i	0.974581	+	0.981086i
$823$	−1.67644e10	+	9.67896e9i	−1.04831	+	0.605242i	−0.922176	−	0.386771i	$-0.873590\pi$
$823$	−1.67644e10	+	9.67896e9i	−1.04831	+	0.605242i	−0.126134	+	0.992013i	$0.540257\pi$
$824$	6.23172e9	−	6.10857e9i	0.388028	−	0.380359i
$825$			2.83390e10i			1.75710i
$826$	6.14991e8	+	2.32610e9i	0.0379698	+	0.143614i
$827$	1.18481e10	+	2.05216e10i	0.728419	+	1.26166i	0.957551	+	0.288263i	$0.0930778\pi$
$827$	1.18481e10	+	2.05216e10i	0.728419	+	1.26166i	−0.229132	+	0.973395i	$0.573589\pi$
$828$	4.34373e9	−	7.40929e9i	0.265924	−	0.453597i
$829$			4.74192e9i			0.289077i	0.989499	+	0.144538i	$0.0461697\pi$
$829$			4.74192e9i			0.289077i	−0.989499	+	0.144538i	$0.953830\pi$
$830$	3.21818e9	+	1.21722e10i	0.195360	+	0.738918i
$831$	1.10494e10	−	1.91381e10i	0.667936	−	1.15690i
$832$	1.40697e10	+	2.55331e10i	0.846942	+	1.53699i
$833$	1.52992e10	−	2.64990e10i	0.917089	−	1.58844i
$834$	−8.36816e9	+	8.31267e9i	−0.499515	+	0.496203i
$835$	−2.45218e10			−1.45764
$836$	2.02111e10	+	3.69612e9i	1.19638	+	0.218788i
$837$	−3.72243e9			−0.219426
$838$	−1.33990e10	+	1.33101e10i	−0.786533	+	0.781318i
$839$	1.03515e10	−	1.79294e10i	0.605115	−	1.04809i	−0.386918	−	0.922114i	$-0.626460\pi$
$839$	1.03515e10	−	1.79294e10i	0.605115	−	1.04809i	0.992033	−	0.125976i	$-0.0402062\pi$
$840$	1.34879e9	−	4.84002e9i	0.0785174	−	0.281754i
$841$	−4.59115e9	+	7.95211e9i	−0.266156	+	0.460995i
$842$	−6.80712e9	−	2.57468e10i	−0.392981	−	1.48638i
$843$		−	2.35627e10i		−	1.35466i
$844$	−1.46240e10	−	8.57337e9i	−0.837272	−	0.490855i
$845$	−2.61149e10	−	4.52324e10i	−1.48899	−	2.57900i
$846$	7.27427e9	+	2.75137e10i	0.413041	+	1.56226i
$847$			1.25860e9i			0.0711697i
$848$	−9.93415e9	+	5.56058e9i	−0.559430	+	0.313137i
$849$	−1.27244e10	+	7.34643e9i	−0.713609	+	0.412002i
$850$	2.48613e10	+	2.50273e10i	1.38854	+	1.39781i
$851$	9.57417e8	+	1.65829e9i	0.0532534	+	0.0922376i
$852$	1.80301e10	−	1.02504e10i	0.998757	−	0.567807i
$853$	5.74723e9	−	9.95450e9i	0.317057	−	0.549158i	−0.662816	−	0.748783i	$-0.730639\pi$
$853$	5.74723e9	−	9.95450e9i	0.317057	−	0.549158i	0.979873	+	0.199624i	$0.0639721\pi$
$854$	−7.09783e8	−	1.92719e8i	−0.0389963	−	0.0105882i
$855$	2.29750e10	+	4.04379e9i	1.25711	+	0.221262i
$856$	1.11869e10	−	1.09659e10i	0.609612	−	0.597564i
$857$	2.16959e10	+	1.25261e10i	1.17746	+	0.679805i	0.955425	−	0.295234i	$-0.0953976\pi$
$857$	2.16959e10	+	1.25261e10i	1.17746	+	0.679805i	0.222032	+	0.975039i	$0.428731\pi$
$858$	−3.82732e10	−	3.85286e10i	−2.06866	−	2.08247i
$859$	−1.42394e10	+	8.22112e9i	−0.766506	+	0.442542i	−0.831627	−	0.555335i	$-0.812590\pi$
$859$	−1.42394e10	+	8.22112e9i	−0.766506	+	0.442542i	0.0651210	+	0.997877i	$0.479257\pi$
$860$	−4.09502e9	−	7.20302e9i	−0.219539	−	0.386163i
$861$	−1.72663e9	−	2.99062e9i	−0.0921911	−	0.159680i
$862$	6.34310e9	−	2.33617e10i	0.337308	−	1.24230i
$863$	8.94460e9			0.473721			0.236861	−	0.971544i	$-0.423882\pi$
$863$	8.94460e9			0.473721			0.236861	+	0.971544i	$0.423882\pi$
$864$	−1.96873e9	−	2.03534e9i	−0.103846	−	0.107359i
$865$	−1.90570e10	+	1.10026e10i	−1.00115	+	0.578013i
$866$	6.25012e9	+	1.69702e9i	0.327021	+	0.0887921i
$867$	6.64446e10			3.46253
$868$	4.20377e9	+	2.79675e7i	0.218182	+	0.00145156i
$869$	3.39650e9	+	1.96097e9i	0.175575	+	0.101368i
$870$	−6.68628e9	−	2.52897e10i	−0.344245	−	1.30205i
$871$	4.16464e10	+	2.40445e10i	2.13557	+	1.23297i
$872$	7.50198e9	−	1.93012e9i	0.383149	−	0.0985773i
$873$		−	3.17207e9i		−	0.161359i
$874$	1.05367e10	+	4.95210e9i	0.533843	+	0.250899i
$875$			2.12811e8i			0.0107390i
$876$	−2.01481e10	+	1.14545e10i	−1.01268	+	0.575720i
$877$	6.08411e9	+	3.51266e9i	0.304578	+	0.175848i	0.644498	−	0.764606i	$-0.277067\pi$
$877$	6.08411e9	+	3.51266e9i	0.304578	+	0.175848i	−0.339920	+	0.940454i	$0.610400\pi$
$878$	−1.53148e9	+	4.04903e8i	−0.0763625	+	0.0201893i
$879$	−4.97570e9	−	2.87272e9i	−0.247111	−	0.142670i
$880$	−3.02533e10	−	1.80077e10i	−1.49652	−	0.890776i
$881$	2.62889e9			0.129526			0.0647630	−	0.997901i	$-0.479371\pi$
$881$	2.62889e9			0.129526			0.0647630	+	0.997901i	$0.479371\pi$
$882$	−4.65451e9	+	1.71426e10i	−0.228420	+	0.841271i
$883$	3.34429e10	−	1.93083e10i	1.63471	−	0.943803i	0.652103	−	0.758130i	$-0.273887\pi$
$883$	3.34429e10	−	1.93083e10i	1.63471	−	0.943803i	0.982612	−	0.185673i	$-0.0594464\pi$
$884$	−6.76010e10	−	4.49747e8i	−3.29132	−	0.0218970i
$885$	4.06164e10			1.96970
$886$	−2.82129e10	−	7.66029e9i	−1.36279	−	0.370022i
$887$	−1.80124e10	−	3.11984e10i	−0.866640	−	1.50106i	−0.865410	−	0.501065i	$-0.832942\pi$
$887$	−1.80124e10	−	3.11984e10i	−0.866640	−	1.50106i	−0.00122967	−	0.999999i	$-0.500391\pi$
$888$	−5.01815e9	+	1.29108e9i	−0.240491	+	0.0618739i
$889$	3.04102e9	−	1.75573e9i	0.145165	−	0.0838112i
$890$	−1.18072e9	+	1.17289e9i	−0.0561410	+	0.0557687i
$891$	2.43919e10	+	1.40827e10i	1.15525	+	0.666981i
$892$	1.16451e10	+	6.82701e9i	0.549373	+	0.322073i
$893$	−3.62470e10	+	1.32055e10i	−1.70331	+	0.620548i
$894$	1.00227e10	−	3.69136e10i	0.469140	−	1.72784i
$895$	−2.21242e10	+	3.83202e10i	−1.03154	+	1.78668i
$896$	2.20801e9	+	2.31331e9i	0.102547	+	0.107437i
$897$	−1.53864e10	−	2.66500e10i	−0.711809	−	1.23289i
$898$	−1.05565e10	+	1.04865e10i	−0.486466	+	0.483240i
$899$	1.89543e10	−	1.09433e10i	0.870058	−	0.502328i
$900$	−1.76669e10	−	1.03573e10i	−0.807816	−	0.473587i
$901$		−	2.63995e10i		−	1.20243i
$902$	−2.33938e10	+	6.18502e9i	−1.06140	+	0.280620i
$903$	−7.00992e8	−	1.21415e9i	−0.0316815	−	0.0548740i
$904$	−7.50403e9	−	7.65532e9i	−0.337836	−	0.344646i
$905$		−	6.71919e9i		−	0.301333i
$906$	−4.03619e10	+	1.06712e10i	−1.80311	+	0.476720i
$907$	−1.13504e9	+	1.96595e9i	−0.0505110	+	0.0874875i	−0.890175	−	0.455618i	$-0.849418\pi$
$907$	−1.13504e9	+	1.96595e9i	−0.0505110	+	0.0874875i	0.839664	+	0.543106i	$0.182752\pi$
$908$	−7.10886e7	+	1.06852e10i	−0.00315137	+	0.473679i
$909$	−1.59799e10	+	2.76780e10i	−0.705669	+	1.22225i
$910$	−5.97931e9	−	6.01922e9i	−0.263030	−	0.264786i
$911$	−3.67176e10			−1.60901			−0.804507	−	0.593942i	$-0.797571\pi$
$911$	−3.67176e10			−1.60901			−0.804507	+	0.593942i	$0.797571\pi$
$912$	−2.05627e10	+	2.38686e10i	−0.897630	+	1.04195i
$913$	1.49279e10			0.649158
$914$	1.38024e10	+	1.38945e10i	0.597920	+	0.601911i
$915$	−6.20787e9	+	1.07524e10i	−0.267898	+	0.464012i
$916$	1.54973e7	−	2.32937e9i	0.000666225	−	0.100139i
$917$	1.97253e8	−	3.41652e8i	0.00844756	−	0.0146316i
$918$	6.34827e9	−	1.67840e9i	0.270836	−	0.0716055i
$919$			4.26465e10i			1.81251i	0.422736	+	0.906253i	$0.361070\pi$
$919$			4.26465e10i			1.81251i	−0.422736	+	0.906253i	$0.638930\pi$
$920$	−1.39652e10	−	1.42467e10i	−0.591274	−	0.603194i
$921$	7.12906e9	+	1.23479e10i	0.300693	+	0.520816i
$922$	2.20970e10	−	5.84217e9i	0.928487	−	0.245480i
$923$		−	3.50219e10i		−	1.46600i
$924$	−5.13918e9	−	3.01287e9i	−0.214310	−	0.125640i
$925$	3.95409e9	−	2.28289e9i	0.164267	−	0.0948396i
$926$	−3.18904e10	+	3.16789e10i	−1.31984	+	1.31109i
$927$	−5.87361e9	−	1.01734e10i	−0.242173	−	0.419456i
$928$	1.60081e10	+	4.57603e9i	0.657540	+	0.187962i
$929$	−8.40976e8	+	1.45661e9i	−0.0344135	+	0.0596059i	−0.882719	−	0.469901i	$-0.844290\pi$
$929$	−8.40976e8	+	1.45661e9i	−0.0344135	+	0.0596059i	0.848306	+	0.529507i	$0.177623\pi$
$930$	1.85952e10	−	6.84863e10i	0.758074	−	2.79199i
$931$	−2.37144e10	−	4.17393e9i	−0.963137	−	0.169520i
$932$	1.07680e10	+	6.31279e9i	0.435692	+	0.255426i
$933$	3.02380e10	+	1.74579e10i	1.21890	+	0.703731i
$934$	−1.14432e10	+	1.13673e10i	−0.459550	+	0.456503i
$935$	7.07035e10	−	4.08207e10i	2.82879	−	1.63320i
$936$	3.80073e10	−	9.77859e9i	1.51496	−	0.389772i
$937$	7.97493e9	+	1.38130e10i	0.316693	+	0.548528i	0.979796	−	0.200000i	$-0.0640942\pi$
$937$	7.97493e9	+	1.38130e10i	0.316693	+	0.548528i	−0.663103	+	0.748528i	$0.730761\pi$
$938$	5.09080e9	+	1.38224e9i	0.201408	+	0.0546858i
$939$	−7.34768e9			−0.289615
$940$	6.61032e10	+	4.39783e8i	2.59582	+	0.0172699i
$941$	1.02495e10	−	5.91753e9i	0.400993	−	0.231514i	−0.285919	−	0.958254i	$-0.592299\pi$
$941$	1.02495e10	−	5.91753e9i	0.400993	−	0.231514i	0.686913	+	0.726740i	$0.258966\pi$
$942$	8.43747e9	−	3.10752e10i	0.328878	−	1.21126i
$943$	−1.37114e10			−0.532463
$944$	−1.32224e10	+	2.22139e10i	−0.511572	+	0.859453i
$945$	7.13691e8	+	4.12050e8i	0.0275105	+	0.0158832i
$946$	−9.49760e9	+	2.51104e9i	−0.364750	+	0.0964351i
$947$	2.29735e10	+	1.32638e10i	0.879028	+	0.507507i	0.870338	−	0.492455i	$-0.163900\pi$
$947$	2.29735e10	+	1.32638e10i	0.879028	+	0.507507i	0.00869028	+	0.999962i	$0.497234\pi$
$948$	−5.22789e9	+	2.97213e9i	−0.199295	+	0.113302i
$949$			3.91360e10i			1.48643i
$950$	1.18079e10	−	2.51240e10i	0.446829	−	0.950728i
$951$			5.47154e10i			2.06290i
$952$	−7.18175e9	+	1.84773e9i	−0.269774	+	0.0694080i
$953$	−4.00238e10	−	2.31078e10i	−1.49794	−	0.864834i	−0.497940	−	0.867212i	$-0.665910\pi$
$953$	−4.00238e10	−	2.31078e10i	−1.49794	−	0.864834i	−0.999997	+	0.00237709i	$0.999243\pi$
$954$	3.91730e9	+	1.48165e10i	0.146072	+	0.552493i
$955$	2.75169e10	+	1.58869e10i	1.02232	+	0.590239i
$956$	4.61873e9	+	3.07283e7i	0.170970	+	0.00113746i
$957$	−3.10151e10			−1.14388
$958$	4.87336e10	+	1.32320e10i	1.79081	+	0.486236i
$959$	3.53246e9	−	2.03947e9i	0.129334	−	0.0746710i
$960$	4.72814e10	−	2.60539e10i	1.72481	−	0.950436i
$961$	3.18633e10			1.15813
$962$	−2.29267e9	+	8.44391e9i	−0.0830288	+	0.305795i
$963$	−1.05441e10	−	1.82629e10i	−0.380467	−	0.658987i
$964$	1.53515e10	+	2.70028e10i	0.551925	+	0.970821i
$965$	3.37001e10	−	1.94567e10i	1.20722	−	0.696987i
$966$	−2.37897e9	−	2.39485e9i	−0.0849118	−	0.0854786i
$967$	−3.46609e10	−	2.00115e10i	−1.23267	−	0.711682i	−0.265084	−	0.964225i	$-0.585400\pi$
$967$	−3.46609e10	−	2.00115e10i	−1.23267	−	0.711682i	−0.967586	+	0.252543i	$0.918733\pi$
$968$	−9.65706e9	+	9.46622e9i	−0.342201	+	0.335438i
$969$	−2.50076e10	−	6.86420e10i	−0.882957	−	2.42358i
$970$	−7.11062e9	−	1.93066e9i	−0.250153	−	0.0679211i
$971$	1.00080e10	−	1.73343e10i	0.350816	−	0.607630i	−0.635577	−	0.772037i	$-0.719238\pi$
$971$	1.00080e10	−	1.73343e10i	0.350816	−	0.607630i	0.986393	+	0.164407i	$0.0525711\pi$
$972$	−3.38264e10	+	1.92308e10i	−1.18147	+	0.671683i
$973$	1.09242e9	+	1.89212e9i	0.0380183	+	0.0658497i
$974$	1.34264e10	+	1.35160e10i	0.465588	+	0.468696i
$975$	−6.35452e10	+	3.66878e10i	−2.19567	+	1.26767i
$976$	−3.85974e9	−	6.89555e9i	−0.132887	−	0.237408i
$977$			3.76350e10i			1.29110i	0.763716	+	0.645552i	$0.223373\pi$
$977$			3.76350e10i			1.29110i	−0.763716	+	0.645552i	$0.776627\pi$
$978$	7.43485e9	+	2.81211e10i	0.254148	+	0.961272i
$979$	9.86613e8	+	1.70886e9i	0.0336053	+	0.0582061i
$980$	3.55945e10	+	2.08675e10i	1.20807	+	0.708237i
$981$		−	1.04279e10i		−	0.352659i
$982$	−8.44472e9	−	3.19407e10i	−0.284574	−	1.07635i
$983$	4.19919e9	−	7.27321e9i	0.141003	−	0.244224i	−0.786872	−	0.617117i	$-0.788301\pi$
$983$	4.19919e9	−	7.27321e9i	0.141003	−	0.244224i	0.927875	+	0.372892i	$0.121634\pi$
$984$	9.96019e9	−	3.57414e10i	0.333261	−	1.19588i
$985$	−2.36537e10	+	4.09694e10i	−0.788628	+	1.36594i
$986$	−2.73906e10	+	2.72090e10i	−0.909980	+	0.903946i
$987$	1.11853e10			0.370285
$988$	1.78775e10	+	5.01048e10i	0.589735	+	1.65284i
$989$	−5.56665e9			−0.182981
$990$	−3.36247e10	+	3.34017e10i	−1.10137	+	1.09407i
$991$	1.41616e10	−	2.45286e10i	0.462226	−	0.800599i	−0.536845	−	0.843681i	$-0.680384\pi$
$991$	1.41616e10	−	2.45286e10i	0.462226	−	0.800599i	0.999072	+	0.0430815i	$0.0137175\pi$
$992$	3.14029e10	+	3.24653e10i	1.02136	+	1.05591i
$993$	1.17823e10	−	2.04076e10i	0.381864	−	0.661407i
$994$	−9.81961e8	−	3.71410e9i	−0.0317133	−	0.119950i
$995$			3.50675e10i			1.12856i
$996$	−1.15764e10	+	1.97464e10i	−0.371250	+	0.633256i
$997$	−1.61825e10	−	2.80289e10i	−0.517145	−	0.895721i	−0.999802	−	0.0199115i	$-0.993662\pi$
$997$	−1.61825e10	−	2.80289e10i	−0.517145	−	0.895721i	0.482657	−	0.875809i	$-0.339672\pi$
$998$	7.50131e9	+	2.83724e10i	0.238880	+	0.903524i
$999$		−	8.49873e8i		−	0.0269696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.f.a.27.17	yes	136
4.3	odd	2	inner	76.8.f.a.27.6	✓	136
19.12	odd	6	inner	76.8.f.a.31.6	yes	136
76.31	even	6	inner	76.8.f.a.31.17	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.f.a.27.6	✓	136	4.3	odd	2	inner
76.8.f.a.27.17	yes	136	1.1	even	1	trivial
76.8.f.a.31.6	yes	136	19.12	odd	6	inner
76.8.f.a.31.17	yes	136	76.31	even	6	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.97334 - 8.02657i) q^{2} +(-32.1577 + 55.6988i) q^{3} +(-0.851561 + 127.997i) q^{4} +(200.122 - 346.621i) q^{5} +(703.475 - 185.990i) q^{6} -134.782i q^{7} +(1034.17 - 1013.73i) q^{8} +(-974.738 - 1688.30i) q^{9} +O(q^{10})\)	\(q+(-7.97334 - 8.02657i) q^{2} +(-32.1577 + 55.6988i) q^{3} +(-0.851561 + 127.997i) q^{4} +(200.122 - 346.621i) q^{5} +(703.475 - 185.990i) q^{6} -134.782i q^{7} +(1034.17 - 1013.73i) q^{8} +(-974.738 - 1688.30i) q^{9} +(-4377.82 + 1157.44i) q^{10} +5368.91i q^{11} +(-7101.91 - 4163.53i) q^{12} +(-12038.8 + 6950.61i) q^{13} +(-1081.84 + 1074.67i) q^{14} +(12870.9 + 22293.1i) q^{15} +(-16382.5 - 217.995i) q^{16} +(18996.3 - 32902.6i) q^{17} +(-5779.30 + 21285.2i) q^{18} +(-29445.1 - 5182.59i) q^{19} +(44196.1 + 25910.2i) q^{20} +(7507.22 + 4334.30i) q^{21} +(43093.9 - 42808.2i) q^{22} +(29807.8 - 17209.5i) q^{23} +(23207.1 + 90201.2i) q^{24} +(-41034.9 - 71074.6i) q^{25} +(151779. + 41210.7i) q^{26} -15276.4 q^{27} +(17251.8 + 114.776i) q^{28} +(77786.1 - 44909.8i) q^{29} +(76312.7 - 281060. i) q^{30} +243672. q^{31} +(128874. + 133234. i) q^{32} +(-299042. - 172652. i) q^{33} +(-415560. + 109869. i) q^{34} +(-46718.4 - 26972.9i) q^{35} +(216927. - 123326. i) q^{36} +55632.9i q^{37} +(193177. + 277665. i) q^{38} -894063. i q^{39} +(-144421. - 561334. i) q^{40} +(-344994. - 199183. i) q^{41} +(-25068.1 - 94816.1i) q^{42} +(-140064. - 80865.7i) q^{43} +(-687205. - 4571.95i) q^{44} -780265. q^{45} +(-375801. - 102037. i) q^{46} +(1.11745e6 - 645161. i) q^{47} +(538968. - 905478. i) q^{48} +805377. q^{49} +(-243299. + 896072. i) q^{50} +(1.22176e6 + 2.11615e6i) q^{51} +(-879406. - 1.54685e6i) q^{52} +(601763. - 347428. i) q^{53} +(121804. + 122617. i) q^{54} +(1.86098e6 + 1.07444e6i) q^{55} +(-136633. - 139388. i) q^{56} +(1.23555e6 - 1.47340e6i) q^{57} +(-980687. - 266274. i) q^{58} +(788918. - 1.36645e6i) q^{59} +(-2.86441e6 + 1.62846e6i) q^{60} +(241159. + 417699. i) q^{61} +(-1.94288e6 - 1.95585e6i) q^{62} +(-227553. + 131378. i) q^{63} +(41853.5 - 2.09673e6i) q^{64} +5.56387e6i q^{65} +(998561. + 3.77689e6i) q^{66} +(-1.72967e6 - 2.99588e6i) q^{67} +(4.19527e6 + 2.45950e6i) q^{68} +2.21368e6i q^{69} +(156002. + 590053. i) q^{70} +(-1.25967e6 + 2.18181e6i) q^{71} +(-2.71952e6 - 757859. i) q^{72} +(1.40765e6 - 2.43812e6i) q^{73} +(446541. - 443580. i) q^{74} +5.27836e6 q^{75} +(688431. - 3.76447e6i) q^{76} +723635. q^{77} +(-7.17625e6 + 7.12867e6i) q^{78} +(365246. - 632624. i) q^{79} +(-3.35407e6 + 5.63491e6i) q^{80} +(2.62301e6 - 4.54318e6i) q^{81} +(1.15201e6 + 4.35727e6i) q^{82} -2.78043e6i q^{83} +(-561171. + 957212. i) q^{84} +(-7.60316e6 - 1.31691e7i) q^{85} +(467701. + 1.76900e6i) q^{86} +5.77679e6i q^{87} +(5.44263e6 + 5.55235e6i) q^{88} +(318289. - 183764. i) q^{89} +(6.22132e6 + 6.26285e6i) q^{90} +(936820. + 1.62262e6i) q^{91} +(2.17739e6 + 3.82997e6i) q^{92} +(-7.83593e6 + 1.35722e7i) q^{93} +(-1.40883e7 - 3.82521e6i) q^{94} +(-7.68899e6 + 9.16914e6i) q^{95} +(-1.15653e7 + 2.89363e6i) q^{96} +(1.40914e6 + 813569. i) q^{97} +(-6.42155e6 - 6.46441e6i) q^{98} +(9.06431e6 - 5.23328e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more