LMFDB - Embedded newform 62.8.d.a.35.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.10
Character	$\chi$	$=$	62.35
Dual form			62.8.d.a.39.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47214 + 7.60845i) q^{2} +(21.5637 - 66.3662i) q^{3} +(-51.7771 + 37.6183i) q^{4} +325.055 q^{5} +558.253 q^{6} +(1267.82 - 921.124i) q^{7} +(-414.217 - 300.946i) q^{8} +(-2170.16 - 1576.72i) q^{9} +(803.581 + 2473.17i) q^{10} +(-4127.16 + 2998.56i) q^{11} +(1380.08 + 4247.44i) q^{12} +(398.385 - 1226.10i) q^{13} +(10142.5 + 7368.99i) q^{14} +(7009.39 - 21572.7i) q^{15} +(1265.73 - 3895.53i) q^{16} +(10457.2 + 7597.64i) q^{17} +(6631.43 - 20409.4i) q^{18} +(-8306.12 - 25563.6i) q^{19} +(-16830.4 + 12228.0i) q^{20} +(-33792.7 - 104003. i) q^{21} +(-33017.3 - 23988.5i) q^{22} +(50226.7 + 36491.9i) q^{23} +(-28904.7 + 21000.5i) q^{24} +27535.9 q^{25} +10313.6 q^{26} +(-27971.5 + 20322.5i) q^{27} +(-30992.9 + 95386.2i) q^{28} +(-69352.7 - 213446. i) q^{29} +181463. q^{30} +(37523.2 - 161569. i) q^{31} +32768.0 q^{32} +(110006. + 338564. i) q^{33} +(-31954.5 + 98345.9i) q^{34} +(412111. - 299416. i) q^{35} +171678. q^{36} +89769.3 q^{37} +(173966. - 126393. i) q^{38} +(-72781.2 - 52878.7i) q^{39} +(-134643. - 97824.1i) q^{40} +(163181. + 502220. i) q^{41} +(707763. - 514220. i) q^{42} +(79063.0 + 243331. i) q^{43} +(100892. - 310513. i) q^{44} +(-705423. - 512520. i) q^{45} +(-153479. + 472361. i) q^{46} +(-401815. + 1.23666e6i) q^{47} +(-231238. - 168004. i) q^{48} +(504405. - 1.55240e6i) q^{49} +(68072.6 + 209506. i) q^{50} +(729723. - 530175. i) q^{51} +(25496.7 + 78470.7i) q^{52} +(-1.62034e6 - 1.17725e6i) q^{53} +(-223772. - 162580. i) q^{54} +(-1.34156e6 + 974698. i) q^{55} -802360. q^{56} -1.87567e6 q^{57} +(1.45254e6 - 1.05533e6i) q^{58} +(-736650. + 2.26718e6i) q^{59} +(448601. + 1.38065e6i) q^{60} +488888. q^{61} +(1.32205e6 - 113927. i) q^{62} -4.20372e6 q^{63} +(81007.0 + 249314. i) q^{64} +(129497. - 398552. i) q^{65} +(-2.30400e6 + 1.67395e6i) q^{66} +439065. q^{67} -827256. q^{68} +(3.50490e6 - 2.54646e6i) q^{69} +(3.29689e6 + 2.39533e6i) q^{70} +(426503. + 309872. i) q^{71} +(424411. + 1.30620e6i) q^{72} +(1.69166e6 - 1.22907e6i) q^{73} +(221922. + 683006. i) q^{74} +(593777. - 1.82746e6i) q^{75} +(1.39172e6 + 1.01115e6i) q^{76} +(-2.47045e6 + 7.60326e6i) q^{77} +(222400. - 684476. i) q^{78} +(3.81452e6 + 2.77141e6i) q^{79} +(411433. - 1.26626e6i) q^{80} +(-1.06731e6 - 3.28484e6i) q^{81} +(-3.41771e6 + 2.48311e6i) q^{82} +(549305. + 1.69059e6i) q^{83} +(5.66210e6 + 4.11376e6i) q^{84} +(3.39918e6 + 2.46965e6i) q^{85} +(-1.65592e6 + 1.20309e6i) q^{86} -1.56611e7 q^{87} +2.61194e6 q^{88} +(-5.93706e6 + 4.31353e6i) q^{89} +(2.15558e6 - 6.63420e6i) q^{90} +(-624314. - 1.92144e6i) q^{91} -3.97335e6 q^{92} +(-9.91360e6 - 5.97430e6i) q^{93} -1.04024e7 q^{94} +(-2.69995e6 - 8.30958e6i) q^{95} +(706599. - 2.17469e6i) q^{96} +(4.51482e6 - 3.28021e6i) q^{97} +1.30583e7 q^{98} +1.36845e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$3$	21.5637	−	66.3662i	0.461104	−	1.41913i	−0.402713	−	0.915326i	$-0.631933\pi$
$3$	21.5637	−	66.3662i	0.461104	−	1.41913i	0.863817	−	0.503806i	$-0.168067\pi$
$4$	−51.7771	+	37.6183i	−0.404508	+	0.293893i
$5$	325.055			1.16295			0.581477	−	0.813563i	$-0.302475\pi$
$5$	325.055			1.16295			0.581477	+	0.813563i	$0.302475\pi$
$6$	558.253			1.05512
$7$	1267.82	−	921.124i	1.39706	−	1.01502i	0.402007	−	0.915637i	$-0.368313\pi$
$7$	1267.82	−	921.124i	1.39706	−	1.01502i	0.995049	−	0.0993842i	$-0.0316873\pi$
$8$	−414.217	−	300.946i	−0.286031	−	0.207813i
$9$	−2170.16	−	1576.72i	−0.992301	−	0.720949i
$10$	803.581	+	2473.17i	0.254115	+	0.782084i
$11$	−4127.16	+	2998.56i	−0.934926	+	0.679263i	−0.947194	−	0.320661i	$-0.896095\pi$
$11$	−4127.16	+	2998.56i	−0.934926	+	0.679263i	0.0122680	+	0.999925i	$0.496095\pi$
$12$	1380.08	+	4247.44i	0.230552	+	0.709566i
$13$	398.385	−	1226.10i	0.0502923	−	0.154784i	−0.922756	−	0.385384i	$-0.874069\pi$
$13$	398.385	−	1226.10i	0.0502923	−	0.154784i	0.973049	+	0.230600i	$0.0740690\pi$
$14$	10142.5	+	7368.99i	0.987868	+	0.717728i
$15$	7009.39	−	21572.7i	0.536242	−	1.65038i
$16$	1265.73	−	3895.53i	0.0772542	−	0.237764i
$17$	10457.2	+	7597.64i	0.516234	+	0.375066i	0.815183	−	0.579203i	$-0.196636\pi$
$17$	10457.2	+	7597.64i	0.516234	+	0.375066i	−0.298950	+	0.954269i	$0.596636\pi$
$18$	6631.43	−	20409.4i	0.268011	−	0.824854i
$19$	−8306.12	−	25563.6i	−0.277818	−	0.855036i	−0.988460	−	0.151482i	$-0.951595\pi$
$19$	−8306.12	−	25563.6i	−0.277818	−	0.855036i	0.710642	−	0.703554i	$-0.248405\pi$
$20$	−16830.4	+	12228.0i	−0.470424	+	0.341783i
$21$	−33792.7	−	104003.i	−0.796260	−	2.45064i
$22$	−33017.3	−	23988.5i	−0.661092	−	0.480312i
$23$	50226.7	+	36491.9i	0.860771	+	0.625387i	0.928095	−	0.372345i	$-0.121446\pi$
$23$	50226.7	+	36491.9i	0.860771	+	0.625387i	−0.0673238	+	0.997731i	$0.521446\pi$
$24$	−28904.7	+	21000.5i	−0.426805	+	0.310092i
$25$	27535.9			0.352460
$26$	10313.6			0.115081
$27$	−27971.5	+	20322.5i	−0.273490	+	0.198702i
$28$	−30992.9	+	95386.2i	−0.266814	+	0.821169i
$29$	−69352.7	−	213446.i	−0.528044	−	1.62515i	−0.758217	−	0.652003i	$-0.773929\pi$
$29$	−69352.7	−	213446.i	−0.528044	−	1.62515i	0.230173	−	0.973150i	$-0.426071\pi$
$30$	181463.			1.22705
$31$	37523.2	−	161569.i	0.226222	−	0.974076i
$31$	37523.2	−	161569.i	0.226222	−	0.974076i
$32$	32768.0			0.176777
$33$	110006.	+	338564.i	0.532866	+	1.63999i
$34$	−31954.5	+	98345.9i	−0.139430	+	0.429121i
$35$	412111.	−	299416.i	1.62471	−	1.18042i
$36$	171678.			0.613276
$37$	89769.3			0.291355			0.145677	−	0.989332i	$-0.453464\pi$
$37$	89769.3			0.291355			0.145677	+	0.989332i	$0.453464\pi$
$38$	173966.	−	126393.i	0.514305	−	0.373664i
$39$	−72781.2	−	52878.7i	−0.196469	−	0.142743i
$40$	−134643.	−	97824.1i	−0.332640	−	0.241677i
$41$	163181.	+	502220.i	0.369765	+	1.13802i	0.946943	+	0.321402i	$0.104154\pi$
$41$	163181.	+	502220.i	0.369765	+	1.13802i	−0.577178	+	0.816619i	$0.695846\pi$
$42$	707763.	−	514220.i	1.47406	−	1.07097i
$43$	79063.0	+	243331.i	0.151647	+	0.466722i	0.997806	−	0.0662094i	$-0.0210905\pi$
$43$	79063.0	+	243331.i	0.151647	+	0.466722i	−0.846159	+	0.532931i	$0.821091\pi$
$44$	100892.	−	310513.i	0.178555	−	0.549536i
$45$	−705423.	−	512520.i	−1.15400	−	0.838430i
$46$	−153479.	+	472361.i	−0.232486	+	0.715519i
$47$	−401815.	+	1.23666e6i	−0.564526	+	1.73743i	0.104832	+	0.994490i	$0.466570\pi$
$47$	−401815.	+	1.23666e6i	−0.564526	+	1.73743i	−0.669357	+	0.742941i	$0.733430\pi$
$48$	−231238.	−	168004.i	−0.301796	−	0.219268i
$49$	504405.	−	1.55240e6i	0.612482	−	1.88503i
$50$	68072.6	+	209506.i	0.0770153	+	0.237029i
$51$	729723.	−	530175.i	0.770305	−	0.559659i
$52$	25496.7	+	78470.7i	0.0251462	+	0.0773919i
$53$	−1.62034e6	−	1.17725e6i	−1.49500	−	1.08618i	−0.972321	−	0.233647i	$-0.924934\pi$
$53$	−1.62034e6	−	1.17725e6i	−1.49500	−	1.08618i	−0.522676	−	0.852532i	$-0.675066\pi$
$54$	−223772.	−	162580.i	−0.193387	−	0.140504i
$55$	−1.34156e6	+	974698.i	−1.08727	+	0.789952i
$56$	−802360.			−0.610536
$57$	−1.87567e6			−1.34151
$58$	1.45254e6	−	1.05533e6i	0.977531	−	0.710218i
$59$	−736650.	+	2.26718e6i	−0.466959	+	1.43715i	0.389542	+	0.921009i	$0.372633\pi$
$59$	−736650.	+	2.26718e6i	−0.466959	+	1.43715i	−0.856501	+	0.516145i	$0.827367\pi$
$60$	448601.	+	1.38065e6i	0.268121	+	0.825192i
$61$	488888.			0.275775			0.137887	−	0.990448i	$-0.455969\pi$
$61$	488888.			0.275775			0.137887	+	0.990448i	$0.455969\pi$
$62$	1.32205e6	−	113927.i	0.704496	−	0.0607096i
$63$	−4.20372e6			−2.11808
$64$	81007.0	+	249314.i	0.0386271	+	0.118882i
$65$	129497.	−	398552.i	0.0584876	−	0.180006i
$66$	−2.30400e6	+	1.67395e6i	−0.986458	+	0.716704i
$67$	439065.			0.178347			0.0891737	−	0.996016i	$-0.471577\pi$
$67$	439065.			0.178347			0.0891737	+	0.996016i	$0.471577\pi$
$68$	−827256.			−0.319050
$69$	3.50490e6	−	2.54646e6i	1.28441	−	0.933179i
$70$	3.29689e6	+	2.39533e6i	1.14884	+	0.834684i
$71$	426503.	+	309872.i	0.141422	+	0.102749i	0.656247	−	0.754546i	$-0.272143\pi$
$71$	426503.	+	309872.i	0.141422	+	0.102749i	−0.514825	+	0.857295i	$0.672143\pi$
$72$	424411.	+	1.30620e6i	0.134006	+	0.412427i
$73$	1.69166e6	−	1.22907e6i	0.508960	−	0.369781i	−0.303469	−	0.952841i	$-0.598145\pi$
$73$	1.69166e6	−	1.22907e6i	0.508960	−	0.369781i	0.812429	+	0.583060i	$0.198145\pi$
$74$	221922.	+	683006.i	0.0636633	+	0.195936i
$75$	593777.	−	1.82746e6i	0.162521	−	0.500187i
$76$	1.39172e6	+	1.01115e6i	0.363669	+	0.264221i
$77$	−2.47045e6	+	7.60326e6i	−0.616678	+	1.89794i
$78$	222400.	−	684476.i	0.0530644	−	0.163315i
$79$	3.81452e6	+	2.77141e6i	0.870451	+	0.632420i	0.930708	−	0.365763i	$-0.119192\pi$
$79$	3.81452e6	+	2.77141e6i	0.870451	+	0.632420i	−0.0602566	+	0.998183i	$0.519192\pi$
$80$	411433.	−	1.26626e6i	0.0898431	−	0.276509i
$81$	−1.06731e6	−	3.28484e6i	−0.223148	−	0.686779i
$82$	−3.41771e6	+	2.48311e6i	−0.684520	+	0.497333i
$83$	549305.	+	1.69059e6i	0.105449	+	0.324537i	0.989835	−	0.142217i	$-0.0454232\pi$
$83$	549305.	+	1.69059e6i	0.105449	+	0.324537i	−0.884387	+	0.466754i	$0.845423\pi$
$84$	5.66210e6	+	4.11376e6i	1.04232	+	0.757288i
$85$	3.39918e6	+	2.46965e6i	0.600355	+	0.436184i
$86$	−1.65592e6	+	1.20309e6i	−0.280733	+	0.203965i
$87$	−1.56611e7			−2.54979
$88$	2.61194e6			0.408578
$89$	−5.93706e6	+	4.31353e6i	−0.892702	+	0.648586i	−0.936581	−	0.350451i	$-0.886028\pi$
$89$	−5.93706e6	+	4.31353e6i	−0.892702	+	0.648586i	0.0438794	+	0.999037i	$0.486028\pi$
$90$	2.15558e6	−	6.63420e6i	0.311685	−	0.959267i
$91$	−624314.	−	1.92144e6i	−0.0868476	−	0.267289i
$92$	−3.97335e6			−0.531986
$93$	−9.91360e6	−	5.97430e6i	−1.27803	−	0.770189i
$94$	−1.04024e7			−1.29177
$95$	−2.69995e6	−	8.30958e6i	−0.323089	−	0.994367i
$96$	706599.	−	2.17469e6i	0.0815124	−	0.250869i
$97$	4.51482e6	−	3.28021e6i	0.502272	−	0.364922i	−0.307612	−	0.951512i	$-0.599530\pi$
$97$	4.51482e6	−	3.28021e6i	0.502272	−	0.364922i	0.809884	+	0.586590i	$0.199530\pi$
$98$	1.30583e7			1.40151
$99$	1.36845e7			1.41744
$100$	−1.42573e6	+	1.03585e6i	−0.142573	+	0.103585i
$101$	3.40431e6	+	2.47338e6i	0.328779	+	0.238872i	0.739912	−	0.672703i	$-0.234867\pi$
$101$	3.40431e6	+	2.47338e6i	0.328779	+	0.238872i	−0.411133	+	0.911575i	$0.634867\pi$
$102$	5.83779e6	+	4.24140e6i	0.544688	+	0.395739i
$103$	2.71476e6	+	8.35517e6i	0.244794	+	0.753399i	0.995670	+	0.0929556i	$0.0296315\pi$
$103$	2.71476e6	+	8.35517e6i	0.244794	+	0.753399i	−0.750876	+	0.660443i	$0.770369\pi$
$104$	−534009.	+	387980.i	−0.0465513	+	0.0338215i
$105$	−1.09845e7	−	3.38068e7i	−0.926013	−	2.84998i
$106$	4.95132e6	−	1.52386e7i	0.403785	−	1.24272i
$107$	1.26153e7	+	9.16557e6i	0.995532	+	0.723297i	0.961126	−	0.276111i	$-0.0890458\pi$
$107$	1.26153e7	+	9.16557e6i	0.995532	+	0.723297i	0.0344067	+	0.999408i	$0.489046\pi$
$108$	683786.	−	2.10448e6i	0.0522320	−	0.160754i
$109$	−5.51725e6	+	1.69804e7i	−0.408066	+	1.25590i	0.510242	+	0.860031i	$0.329556\pi$
$109$	−5.51725e6	+	1.69804e7i	−0.408066	+	1.25590i	−0.918308	+	0.395867i	$0.870444\pi$
$110$	−1.07324e7	−	7.79758e6i	−0.768820	−	0.558580i
$111$	1.93576e6	−	5.95765e6i	0.134345	−	0.413471i
$112$	−1.98354e6	−	6.10472e6i	−0.133407	−	0.410585i
$113$	1.61933e7	−	1.17651e7i	1.05575	−	0.767048i	0.0824534	−	0.996595i	$-0.473724\pi$
$113$	1.61933e7	−	1.17651e7i	1.05575	−	0.767048i	0.973298	+	0.229547i	$0.0737244\pi$
$114$	−4.63691e6	−	1.42709e7i	−0.293131	−	0.902165i
$115$	1.63265e7	+	1.18619e7i	1.00104	+	0.727295i
$116$	1.16203e7	+	8.44266e6i	0.691219	+	0.502200i
$117$	−2.79778e6	+	2.03271e6i	−0.161496	+	0.117334i
$118$	−1.90708e7			−1.06852
$119$	2.02563e7			1.10191
$120$	−9.39562e6	+	6.82632e6i	−0.496354	+	0.360622i
$121$	2.02025e6	−	6.21768e6i	0.103671	−	0.319065i
$122$	1.20860e6	+	3.71968e6i	0.0602590	+	0.185458i
$123$	3.68492e7			1.78550
$124$	4.13511e6	+	9.77714e6i	0.194765	+	0.460507i
$125$	−1.64442e7			−0.753059
$126$	−1.03922e7	−	3.19838e7i	−0.462817	−	1.42441i
$127$	−4.97658e6	+	1.53163e7i	−0.215585	+	0.663501i	0.783527	+	0.621358i	$0.213419\pi$
$127$	−4.97658e6	+	1.53163e7i	−0.215585	+	0.663501i	−0.999112	+	0.0421435i	$0.986581\pi$
$128$	−1.69663e6	+	1.23268e6i	−0.0715077	+	0.0519534i
$129$	1.78539e7			0.732265
$130$	3.35250e6			0.133834
$131$	8.86320e6	−	6.43949e6i	0.344462	−	0.250266i	−0.402080	−	0.915604i	$-0.631713\pi$
$131$	8.86320e6	−	6.43949e6i	0.344462	−	0.250266i	0.746542	+	0.665338i	$0.231713\pi$
$132$	−1.84320e7	−	1.33916e7i	−0.697531	−	0.506786i
$133$	−3.40779e7	−	2.47590e7i	−1.25601	−	0.912542i
$134$	1.08543e6	+	3.34060e6i	0.0389703	+	0.119938i
$135$	−9.09227e6	+	6.60592e6i	−0.318057	+	0.231082i
$136$	−2.04509e6	−	6.29414e6i	−0.0697150	−	0.214561i
$137$	−1.80530e7	+	5.55614e7i	−0.599828	+	1.84608i	−0.0707756	+	0.997492i	$0.522547\pi$
$137$	−1.80530e7	+	5.55614e7i	−0.599828	+	1.84608i	−0.529053	+	0.848589i	$0.677453\pi$
$138$	2.80392e7	+	2.03717e7i	0.908216	+	0.659857i
$139$	−2.08787e6	+	6.42579e6i	−0.0659403	+	0.202943i	−0.978598	−	0.205781i	$-0.934026\pi$
$139$	−2.08787e6	+	6.42579e6i	−0.0659403	+	0.202943i	0.912658	+	0.408725i	$0.134026\pi$
$140$	−1.00744e7	+	3.10058e7i	−0.310292	+	0.954981i
$141$	7.34078e7	+	5.33339e7i	2.20534	+	1.60227i
$142$	−1.30328e6	+	4.01107e6i	−0.0381968	+	0.117558i
$143$	2.03234e6	+	6.25491e6i	0.0581194	+	0.178873i
$144$	−8.88899e6	+	6.45823e6i	−0.248075	+	0.180237i
$145$	−2.25434e7	−	6.93816e7i	−0.614090	−	1.88998i
$146$	1.35333e7	+	9.83252e6i	0.359889	+	0.261475i
$147$	−9.21501e7	−	6.69509e7i	−2.39268	−	1.73839i
$148$	−4.64799e6	+	3.37697e6i	−0.117855	+	0.0856270i
$149$	3.33763e7			0.826584			0.413292	−	0.910599i	$-0.364379\pi$
$149$	3.33763e7			0.826584			0.413292	+	0.910599i	$0.364379\pi$
$150$	1.53720e7			0.371887
$151$	−1.21239e7	+	8.80851e6i	−0.286564	+	0.208201i	−0.721776	−	0.692127i	$-0.756674\pi$
$151$	−1.21239e7	+	8.80851e6i	−0.286564	+	0.208201i	0.435211	+	0.900328i	$0.356674\pi$
$152$	−4.25273e6	+	1.30886e7i	−0.0982235	+	0.302301i
$153$	−1.07146e7	−	3.29762e7i	−0.241856	−	0.744356i
$154$	−6.39563e7			−1.41111
$155$	1.21971e7	−	5.25189e7i	0.263085	−	1.13280i
$156$	5.75760e6			0.121424
$157$	658957.	+	2.02806e6i	0.0135897	+	0.0418247i	0.957621	−	0.288030i	$-0.0930003\pi$
$157$	658957.	+	2.02806e6i	0.0135897	+	0.0418247i	−0.944032	+	0.329855i	$0.893000\pi$
$158$	−1.16561e7	+	3.58739e7i	−0.235101	+	0.723566i
$159$	−1.13070e8	+	8.21500e7i	−2.23078	+	1.62076i
$160$	1.06514e7			0.205583
$161$	9.72919e7			1.83733
$162$	2.23540e7	−	1.62412e7i	0.413098	−	0.300133i
$163$	−2.38008e7	−	1.72923e7i	−0.430462	−	0.312749i	0.351372	−	0.936236i	$-0.385715\pi$
$163$	−2.38008e7	−	1.72923e7i	−0.430462	−	0.312749i	−0.781834	+	0.623487i	$0.785715\pi$
$164$	−2.73417e7	−	1.98649e7i	−0.484029	−	0.351668i
$165$	3.57581e7	+	1.10052e8i	0.619699	+	1.90724i
$166$	−1.15048e7	+	8.35873e6i	−0.195209	+	0.141828i
$167$	1.29212e7	+	3.97672e7i	0.214681	+	0.660721i	0.999176	+	0.0405854i	$0.0129223\pi$
$167$	1.29212e7	+	3.97672e7i	0.214681	+	0.660721i	−0.784495	+	0.620135i	$0.787078\pi$
$168$	−1.73018e7	+	5.32496e7i	−0.281521	+	0.866431i
$169$	4.94200e7	+	3.59057e7i	0.787588	+	0.572216i
$170$	−1.03870e7	+	3.19678e7i	−0.162150	+	0.499048i
$171$	−2.22809e7	+	6.85736e7i	−0.340758	+	1.04875i
$172$	−1.32473e7	−	9.62476e6i	−0.198509	−	0.144225i
$173$	3.02908e7	−	9.32254e7i	0.444784	−	1.36890i	−0.437937	−	0.899006i	$-0.644291\pi$
$173$	3.02908e7	−	9.32254e7i	0.444784	−	1.36890i	0.882721	−	0.469898i	$-0.155709\pi$
$174$	−3.87163e7	−	1.19157e8i	−0.557149	−	1.71473i
$175$	3.49106e7	−	2.53640e7i	0.492406	−	0.357754i
$176$	6.45708e6	+	1.98729e7i	0.0892775	+	0.274768i
$177$	1.34579e8	+	9.77774e7i	1.82419	+	1.32535i
$178$	−4.74965e7	−	3.45082e7i	−0.631235	−	0.458619i
$179$	−6.35045e7	+	4.61387e7i	−0.827597	+	0.601284i	−0.918878	−	0.394541i	$-0.870904\pi$
$179$	−6.35045e7	+	4.61387e7i	−0.827597	+	0.601284i	0.0912815	+	0.995825i	$0.470904\pi$
$180$	5.58049e7			0.713211
$181$	−1.21716e8			−1.52572			−0.762859	−	0.646565i	$-0.776205\pi$
$181$	−1.21716e8			−1.52572			−0.762859	+	0.646565i	$0.776205\pi$
$182$	1.30758e7	−	9.50012e6i	0.160775	−	0.116810i
$183$	1.05422e7	−	3.24456e7i	0.127161	−	0.391361i
$184$	−9.82267e6	−	3.02311e7i	−0.116243	−	0.357760i
$185$	2.91800e7			0.338832
$186$	2.09474e7	−	9.01965e7i	0.238691	−	1.02777i
$187$	−6.59407e7			−0.737408
$188$	−2.57162e7	−	7.91462e7i	−0.282263	−	0.868715i
$189$	−1.67432e7	+	5.15304e7i	−0.180394	+	0.555197i
$190$	5.65484e7	−	4.10848e7i	0.598113	−	0.434554i
$191$	−8.29420e7			−0.861307			−0.430653	−	0.902517i	$-0.641717\pi$
$191$	−8.29420e7			−0.861307			−0.430653	+	0.902517i	$0.641717\pi$
$192$	1.82928e7			0.186520
$193$	1.31037e7	−	9.52041e6i	0.131203	−	0.0953246i	−0.520248	−	0.854015i	$-0.674161\pi$
$193$	1.31037e7	−	9.52041e6i	0.131203	−	0.0953246i	0.651451	+	0.758691i	$0.274161\pi$
$194$	3.61185e7	+	2.62416e7i	0.355160	+	0.258039i
$195$	−2.36579e7	−	1.71885e7i	−0.228484	−	0.166003i
$196$	3.22819e7	+	9.93536e7i	0.306241	+	0.942513i
$197$	1.91767e7	−	1.39327e7i	0.178707	−	0.129838i	−0.494836	−	0.868987i	$-0.664772\pi$
$197$	1.91767e7	−	1.39327e7i	0.178707	−	0.129838i	0.673543	+	0.739148i	$0.264772\pi$
$198$	3.38299e7	+	1.04118e8i	0.309723	+	0.953228i
$199$	4.23206e7	−	1.30249e8i	0.380685	−	1.17163i	−0.558878	−	0.829250i	$-0.688768\pi$
$199$	4.23206e7	−	1.30249e8i	0.380685	−	1.17163i	0.939563	−	0.342377i	$-0.111232\pi$
$200$	−1.14058e7	−	8.28683e6i	−0.100814	−	0.0732459i
$201$	9.46786e6	−	2.91391e7i	0.0822367	−	0.253099i
$202$	−1.04026e7	+	3.20160e7i	−0.0888002	+	0.273299i
$203$	−2.84536e8	−	2.06728e8i	−2.38727	−	1.73445i
$204$	−1.78387e7	+	5.49018e7i	−0.147115	+	0.452774i
$205$	5.30429e7	+	1.63249e8i	0.430020	+	1.32346i
$206$	−5.68586e7	+	4.13102e7i	−0.453170	+	0.329247i
$207$	−5.14629e7	−	1.58387e8i	−0.403272	−	1.24114i
$208$	−4.27207e6	−	3.10384e6i	−0.0329167	−	0.0239154i
$209$	1.10935e8	+	8.05988e7i	0.840534	+	0.610684i
$210$	2.30062e8	−	1.67150e8i	1.71426	−	1.24549i
$211$	1.78682e8			1.30946			0.654730	−	0.755863i	$-0.272782\pi$
$211$	1.78682e8			1.30946			0.654730	+	0.755863i	$0.272782\pi$
$212$	1.28182e8			0.923959
$213$	2.97620e7	−	2.16234e7i	0.211025	−	0.153319i
$214$	−3.85490e7	+	1.18642e8i	−0.268884	+	0.827540i
$215$	2.56999e7	+	7.90960e7i	0.176358	+	0.542775i
$216$	1.77022e7			0.119520
$217$	−1.01253e8	−	2.39404e8i	−0.672663	−	1.59046i
$218$	−1.42834e8			−0.933755
$219$	−4.50899e7	−	1.38772e8i	−0.290085	−	0.892789i
$220$	3.27954e7	−	1.00934e8i	0.207651	−	0.639084i
$221$	1.34815e7	−	9.79489e6i	0.0840167	−	0.0610417i
$222$	5.01140e7			0.307414
$223$	−1.92793e8			−1.16419			−0.582096	−	0.813120i	$-0.697767\pi$
$223$	−1.92793e8			−1.16419			−0.582096	+	0.813120i	$0.697767\pi$
$224$	4.15439e7	−	3.01834e7i	0.246967	−	0.179432i
$225$	−5.97575e7	−	4.34163e7i	−0.349747	−	0.254106i
$226$	1.29547e8	+	9.41211e7i	0.746529	+	0.542385i
$227$	3.14869e7	+	9.69068e7i	0.178665	+	0.549875i	0.999782	−	0.0208854i	$-0.00664852\pi$
$227$	3.14869e7	+	9.69068e7i	0.178665	+	0.549875i	−0.821117	+	0.570760i	$0.806649\pi$
$228$	9.71167e7	−	7.05594e7i	0.542653	−	0.394260i
$229$	−3.72061e7	−	1.14509e8i	−0.204734	−	0.630107i	−0.999724	−	0.0234846i	$-0.992524\pi$
$229$	−3.72061e7	−	1.14509e8i	−0.204734	−	0.630107i	0.794990	−	0.606623i	$-0.207476\pi$
$230$	−4.98892e7	+	1.53543e8i	−0.270371	+	0.832115i
$231$	4.51327e8	+	3.27909e8i	2.40907	+	1.75029i
$232$	−3.55086e7	+	1.09284e8i	−0.186692	+	0.574578i
$233$	−4.10374e7	+	1.26300e8i	−0.212537	+	0.654121i	0.786782	+	0.617231i	$0.211745\pi$
$233$	−4.10374e7	+	1.26300e8i	−0.212537	+	0.654121i	−0.999319	+	0.0368909i	$0.988255\pi$
$234$	−2.23822e7	−	1.62616e7i	−0.114195	−	0.0829677i
$235$	−1.30612e8	+	4.01983e8i	−0.656517	+	2.02055i
$236$	−4.71456e7	−	1.45099e8i	−0.233480	−	0.718577i
$237$	2.66183e8	−	1.93393e8i	1.29886	−	0.943674i
$238$	5.00762e7	+	1.54119e8i	0.240775	+	0.741031i
$239$	−2.00773e8	−	1.45870e8i	−0.951289	−	0.691152i	−0.000177497	−	1.00000i	$-0.500056\pi$
$239$	−2.00773e8	−	1.45870e8i	−0.951289	−	0.691152i	−0.951111	+	0.308848i	$0.900056\pi$
$240$	−7.51650e7	−	5.46106e7i	−0.350975	−	0.254998i
$241$	1.74177e8	−	1.26547e8i	0.801552	−	0.582362i	−0.109817	−	0.993952i	$-0.535026\pi$
$241$	1.74177e8	−	1.26547e8i	0.801552	−	0.582362i	0.911369	+	0.411590i	$0.135026\pi$
$242$	5.23013e7			0.237224
$243$	−3.16632e8			−1.41558
$244$	−2.53132e7	+	1.83911e7i	−0.111553	+	0.0810482i
$245$	1.63960e8	−	5.04616e8i	0.712288	−	2.19220i
$246$	9.10962e7	+	2.80365e8i	0.390146	+	1.20075i
$247$	−3.46527e7			−0.146318
$248$	−6.41664e7	+	5.56322e7i	−0.267132	+	0.231604i
$249$	1.24043e8			0.509184
$250$	−4.06524e7	−	1.25115e8i	−0.164549	−	0.506431i
$251$	1.28686e8	−	3.96056e8i	0.513658	−	1.58088i	−0.272052	−	0.962282i	$-0.587702\pi$
$251$	1.28686e8	−	3.96056e8i	0.513658	−	1.58088i	0.785710	−	0.618594i	$-0.212298\pi$
$252$	2.17657e8	−	1.58137e8i	0.856781	−	0.622488i
$253$	−3.16717e8			−1.22956
$254$	−1.28836e8			−0.493311
$255$	2.37200e8	−	1.72336e8i	0.895828	−	0.650857i
$256$	−1.35731e7	−	9.86140e6i	−0.0505636	−	0.0367366i
$257$	3.09752e8	+	2.25048e8i	1.13828	+	0.827007i	0.986878	−	0.161466i	$-0.0516222\pi$
$257$	3.09752e8	+	2.25048e8i	1.13828	+	0.827007i	0.151399	+	0.988473i	$0.451622\pi$
$258$	4.41372e7	+	1.35840e8i	0.160006	+	0.492447i
$259$	1.13811e8	−	8.26887e7i	0.407039	−	0.295731i
$260$	8.28783e6	+	2.55073e7i	0.0292438	+	0.0900032i
$261$	−1.86036e8	+	5.72561e8i	−0.647673	+	1.99333i
$262$	7.09056e7	+	5.15159e7i	0.243571	+	0.176965i
$263$	3.74958e6	−	1.15400e7i	0.0127098	−	0.0391167i	−0.944501	−	0.328510i	$-0.893454\pi$
$263$	3.74958e6	−	1.15400e7i	0.0127098	−	0.0391167i	0.957210	+	0.289393i	$0.0934535\pi$
$264$	5.63232e7	−	1.73345e8i	0.188397	−	0.579825i
$265$	−5.26700e8	−	3.82670e8i	−1.73861	−	1.26318i
$266$	1.04133e8	−	3.20488e8i	0.339236	−	1.04406i
$267$	1.58248e8	+	4.87036e8i	0.508800	+	1.56593i
$268$	−2.27335e7	+	1.65169e7i	−0.0721431	+	0.0524150i
$269$	8.72897e7	+	2.68650e8i	0.273420	+	0.841499i	0.989633	+	0.143618i	$0.0458737\pi$
$269$	8.72897e7	+	2.68650e8i	0.273420	+	0.841499i	−0.716214	+	0.697881i	$0.754126\pi$
$270$	−7.27382e7	−	5.28474e7i	−0.224900	−	0.163399i
$271$	−3.35538e8	−	2.43782e8i	−1.02412	−	0.744063i	−0.0569928	−	0.998375i	$-0.518151\pi$
$271$	−3.35538e8	−	2.43782e8i	−1.02412	−	0.744063i	−0.967122	+	0.254311i	$0.918151\pi$
$272$	4.28329e7	−	3.11199e7i	0.129058	−	0.0937664i
$273$	−1.40981e8			−0.419365
$274$	−4.67365e8			−1.37255
$275$	−1.13645e8	+	8.25681e7i	−0.329524	+	0.239413i
$276$	−8.56802e7	+	2.63697e8i	−0.245301	+	0.754958i
$277$	−8.49676e7	−	2.61503e8i	−0.240201	−	0.739262i	−0.996389	−	0.0849075i	$-0.972941\pi$
$277$	−8.49676e7	−	2.61503e8i	−0.240201	−	0.739262i	0.756188	−	0.654354i	$-0.227059\pi$
$278$	−5.40518e7			−0.150888
$279$	−3.36180e8	+	2.91468e8i	−0.926739	+	0.803483i
$280$	−2.60811e8			−0.710025
$281$	−3.32526e6	−	1.02341e7i	−0.00894033	−	0.0275155i	0.946487	−	0.322742i	$-0.104605\pi$
$281$	−3.32526e6	−	1.02341e7i	−0.00894033	−	0.0275155i	−0.955427	+	0.295227i	$0.904605\pi$
$282$	−2.24314e8	+	6.90368e8i	−0.595642	+	1.83320i
$283$	−5.39572e8	+	3.92022e8i	−1.41513	+	1.02815i	−0.422580	+	0.906326i	$0.638876\pi$
$283$	−5.39572e8	+	3.92022e8i	−1.41513	+	1.02815i	−0.992551	+	0.121828i	$0.961124\pi$
$284$	−3.37399e7			−0.0874037
$285$	−6.09697e8			−1.56012
$286$	−4.25660e7	+	3.09260e7i	−0.107592	+	0.0781704i
$287$	6.69490e8	+	4.86413e8i	1.67170	+	1.21456i
$288$	−7.11119e7	−	5.16658e7i	−0.175416	−	0.127447i
$289$	−7.51716e7	−	2.31355e8i	−0.183194	−	0.563814i
$290$	4.72156e8	−	3.43041e8i	1.13682	−	0.825950i
$291$	−1.20339e8	−	3.70365e8i	−0.286273	−	0.881057i
$292$	−4.13541e7	+	1.27275e8i	−0.0972027	+	0.299159i
$293$	5.46926e7	+	3.97365e7i	0.127026	+	0.0922897i	0.649484	−	0.760375i	$-0.274985\pi$
$293$	5.46926e7	+	3.97365e7i	0.127026	+	0.0922897i	−0.522458	+	0.852665i	$0.674985\pi$
$294$	2.81586e8	−	8.66631e8i	0.646241	−	1.98893i
$295$	−2.39452e8	+	7.36957e8i	−0.543052	+	1.67134i
$296$	−3.71840e7	−	2.70157e7i	−0.0833364	−	0.0605474i
$297$	5.45047e7	−	1.67748e8i	0.120722	−	0.371544i
$298$	8.25109e7	+	2.53942e8i	0.180615	+	0.555876i
$299$	6.47524e7	−	4.70454e7i	0.140090	−	0.101781i
$300$	3.80017e7	+	1.16957e8i	0.0812603	+	0.250094i
$301$	3.24376e8	+	2.35673e8i	0.685592	+	0.498111i
$302$	−9.69910e7	−	7.04681e7i	−0.202632	−	0.147220i
$303$	2.37558e8	−	1.72596e8i	0.490592	−	0.356436i
$304$	−1.10097e8			−0.224760
$305$	1.58915e8			0.320713
$306$	2.24410e8	−	1.63043e8i	0.447731	−	0.325296i
$307$	−2.47986e8	+	7.63222e8i	−0.489151	+	1.50545i	0.336727	+	0.941602i	$0.390680\pi$
$307$	−2.47986e8	+	7.63222e8i	−0.489151	+	1.50545i	−0.825878	+	0.563849i	$0.809320\pi$
$308$	−1.58109e8	−	4.86608e8i	−0.308339	−	0.948969i
$309$	6.13041e8			1.18205
$310$	4.29741e8	−	3.70327e7i	0.819296	−	0.0706025i
$311$	6.55786e8			1.23623			0.618117	−	0.786086i	$-0.287896\pi$
$311$	6.55786e8			1.23623			0.618117	+	0.786086i	$0.287896\pi$
$312$	1.42336e7	+	4.38065e7i	0.0265322	+	0.0816577i
$313$	−6.66694e7	+	2.05187e8i	−0.122891	+	0.378221i	−0.993511	−	0.113736i	$-0.963718\pi$
$313$	−6.66694e7	+	2.05187e8i	−0.122891	+	0.378221i	0.870620	+	0.491957i	$0.163718\pi$
$314$	−1.38014e7	+	1.00273e7i	−0.0251576	+	0.0182781i
$315$	−1.36644e9			−2.46323
$316$	−3.01760e8			−0.537969
$317$	7.16038e8	−	5.20232e8i	1.26249	−	0.917254i	0.263614	−	0.964628i	$-0.415085\pi$
$317$	7.16038e8	−	5.20232e8i	1.26249	−	0.917254i	0.998877	+	0.0473745i	$0.0150854\pi$
$318$	−9.04559e8	−	6.57200e8i	−1.57740	−	1.14605i
$319$	9.26259e8	+	6.72966e8i	1.59759	+	1.16072i
$320$	2.63317e7	+	8.10408e7i	0.0449215	+	0.138254i
$321$	8.80318e8	−	6.39588e8i	1.48550	−	1.07928i
$322$	2.40519e8	+	7.40241e8i	0.401470	+	1.23560i
$323$	1.07364e8	−	3.30432e8i	0.177276	−	0.545598i
$324$	1.78832e8	+	1.29929e8i	0.292105	+	0.212226i
$325$	1.09699e7	−	3.37619e7i	0.0177260	−	0.0545551i
$326$	7.27287e7	−	2.23836e8i	0.116264	−	0.357823i
$327$	1.00795e9	+	7.32319e8i	1.59412	+	1.15820i
$328$	8.35487e7	−	2.57136e8i	0.130732	−	0.402351i
$329$	6.29688e8	+	1.93798e9i	0.974855	+	3.00029i
$330$	−7.48927e8	+	5.44127e8i	−1.14720	+	0.833493i
$331$	−8.72387e7	−	2.68493e8i	−0.132224	−	0.406945i	0.862924	−	0.505334i	$-0.168631\pi$
$331$	−8.72387e7	−	2.68493e8i	−0.132224	−	0.406945i	−0.995148	+	0.0983897i	$0.968631\pi$
$332$	−9.20384e7	−	6.68698e7i	−0.138034	−	0.100288i
$333$	−1.94814e8	−	1.41541e8i	−0.289112	−	0.210052i
$334$	−2.70624e8	+	1.96620e8i	−0.397424	+	0.288745i
$335$	1.42720e8			0.207410
$336$	−4.47920e8			−0.644188
$337$	−5.60365e8	+	4.07129e8i	−0.797565	+	0.579465i	−0.910199	−	0.414172i	$-0.864071\pi$
$337$	−5.60365e8	+	4.07129e8i	−0.797565	+	0.579465i	0.112634	+	0.993637i	$0.464071\pi$
$338$	−1.51014e8	+	4.64774e8i	−0.212720	+	0.654686i
$339$	−4.31620e8	−	1.32839e9i	−0.601731	−	1.85194i
$340$	−2.68904e8			−0.371040
$341$	3.29611e8	+	7.79338e8i	0.450154	+	1.06435i
$342$	−5.76820e8			−0.779739
$343$	−3.91646e8	−	1.20536e9i	−0.524040	−	1.61283i
$344$	4.04803e7	−	1.24585e8i	0.0536153	−	0.165011i
$345$	1.13929e9	−	8.27740e8i	1.49371	−	1.08524i
$346$	7.84184e8			1.01777
$347$	−1.11038e9			−1.42665			−0.713326	−	0.700832i	$-0.752812\pi$
$347$	−1.11038e9			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$348$	8.10885e8	−	5.89142e8i	1.03141	−	0.749364i
$349$	−1.05655e9	−	7.67629e8i	−1.33046	−	0.966634i	−0.999738	−	0.0229053i	$-0.992708\pi$
$349$	−1.05655e9	−	7.67629e8i	−1.33046	−	0.966634i	−0.330720	−	0.943729i	$-0.607292\pi$
$350$	2.79285e8	+	2.02912e8i	0.348184	+	0.252970i
$351$	1.37740e7	+	4.23921e7i	0.0170015	+	0.0523251i
$352$	−1.35239e8	+	9.82568e7i	−0.165273	+	0.120078i
$353$	−2.73771e8	−	8.42581e8i	−0.331265	−	1.01953i	−0.968532	−	0.248887i	$-0.919935\pi$
$353$	−2.73771e8	−	8.42581e8i	−0.331265	−	1.01953i	0.637267	−	0.770643i	$-0.280065\pi$
$354$	−4.11237e8	+	1.26566e9i	−0.492698	+	1.51637i
$355$	1.38637e8	+	1.00726e8i	0.164467	+	0.119493i
$356$	1.45136e8	−	4.46684e8i	0.170491	−	0.524717i
$357$	4.36800e8	−	1.34433e9i	0.508093	−	1.56375i
$358$	−5.08036e8	−	3.69110e8i	−0.585199	−	0.425172i
$359$	4.49743e8	−	1.38417e9i	0.513020	−	1.57891i	−0.273837	−	0.961776i	$-0.588293\pi$
$359$	4.49743e8	−	1.38417e9i	0.513020	−	1.57891i	0.786856	−	0.617136i	$-0.211707\pi$
$360$	1.37957e8	+	4.24589e8i	0.155842	+	0.479634i
$361$	1.38651e8	−	1.00736e8i	0.155113	−	0.112696i
$362$	−3.00899e8	−	9.26073e8i	−0.333381	−	1.02604i
$363$	−3.69080e8	−	2.68152e8i	−0.404993	−	0.294245i
$364$	1.04606e8	+	7.60010e7i	0.113685	+	0.0825970i
$365$	5.49884e8	−	3.99514e8i	0.591897	−	0.430038i
$366$	2.72923e8			0.290975
$367$	1.14104e9			1.20495			0.602476	−	0.798137i	$-0.294181\pi$
$367$	1.14104e9			1.20495			0.602476	+	0.798137i	$0.294181\pi$
$368$	2.05729e8	−	1.49471e8i	0.215193	−	0.156347i
$369$	4.37728e8	−	1.34719e9i	0.453536	−	1.39584i
$370$	7.21369e7	+	2.22015e8i	0.0740375	+	0.227864i
$371$	−3.13868e9			−3.19109
$372$	7.38040e8	−	6.36003e7i	0.743327	−	0.0640559i
$373$	1.71490e9			1.71103			0.855517	−	0.517775i	$-0.173240\pi$
$373$	1.71490e9			1.71103			0.855517	+	0.517775i	$0.173240\pi$
$374$	−1.63014e8	−	5.01707e8i	−0.161130	−	0.495906i
$375$	−3.54599e8	+	1.09134e9i	−0.347238	+	1.06869i
$376$	5.38606e8	−	3.91320e8i	0.522533	−	0.379643i
$377$	−2.89336e8			−0.278104
$378$	−4.33458e8			−0.412787
$379$	−1.52716e6	+	1.10955e6i	−0.00144095	+	0.00104691i	−0.588505	−	0.808493i	$-0.700283\pi$
$379$	−1.52716e6	+	1.10955e6i	−0.00144095	+	0.00104691i	0.587065	+	0.809540i	$0.300283\pi$
$380$	4.52387e8	+	3.28679e8i	0.422929	+	0.307276i
$381$	9.09174e8	+	6.60554e8i	0.842189	+	0.611886i
$382$	−2.05044e8	−	6.31060e8i	−0.188202	−	0.579227i
$383$	4.16360e8	−	3.02503e8i	0.378681	−	0.275128i	−0.382121	−	0.924112i	$-0.624806\pi$
$383$	4.16360e8	−	3.02503e8i	0.378681	−	0.275128i	0.760801	+	0.648985i	$0.224806\pi$
$384$	4.52223e7	+	1.39180e8i	0.0407562	+	0.125435i
$385$	−8.03032e8	+	2.47148e9i	−0.717167	+	2.20721i
$386$	1.04830e8	+	7.61632e7i	0.0927745	+	0.0674047i
$387$	2.12084e8	−	6.52728e8i	0.186003	−	0.572458i
$388$	−1.10368e8	+	3.39679e8i	−0.0959254	+	0.295228i
$389$	−9.56860e8	−	6.95200e8i	−0.824185	−	0.598806i	0.0937229	−	0.995598i	$-0.470123\pi$
$389$	−9.56860e8	−	6.95200e8i	−0.824185	−	0.598806i	−0.917908	+	0.396793i	$0.870123\pi$
$390$	7.22922e7	−	2.22492e8i	0.0617114	−	0.189928i
$391$	2.47982e8	+	7.63209e8i	0.209798	+	0.645691i
$392$	−6.76122e8	+	4.91231e8i	−0.566922	+	0.411893i
$393$	−2.36242e8	−	7.27077e8i	−0.196328	−	0.604236i
$394$	1.53413e8	+	1.11461e8i	0.126365	+	0.0918094i
$395$	1.23993e9	+	9.00861e8i	1.01229	+	0.735475i
$396$	−7.08543e8	+	5.14787e8i	−0.573368	+	0.416576i
$397$	−1.54385e9			−1.23833			−0.619167	−	0.785259i	$-0.712530\pi$
$397$	−1.54385e9			−1.23833			−0.619167	+	0.785259i	$0.712530\pi$
$398$	1.09562e9			0.871100
$399$	−2.37801e9	+	1.72772e9i	−1.87417	+	1.36166i
$400$	3.48532e7	−	1.07267e8i	0.0272290	−	0.0838023i
$401$	9.99937e7	+	3.07749e8i	0.0774403	+	0.238337i	0.982281	−	0.187413i	$-0.0600103\pi$
$401$	9.99937e7	+	3.07749e8i	0.0774403	+	0.238337i	−0.904841	+	0.425750i	$0.860010\pi$
$402$	2.45109e8			0.188178
$403$	−1.83152e8	−	1.10374e8i	−0.139394	−	0.0840040i
$404$	−2.69309e8			−0.203197
$405$	−3.46935e8	−	1.06776e9i	−0.259511	−	0.798692i
$406$	8.69466e8	−	2.67594e9i	0.644780	−	1.98443i
$407$	−3.70493e8	+	2.69179e8i	−0.272395	+	0.197907i
$408$	−4.61818e8			−0.336636
$409$	−9.32601e8			−0.674007			−0.337003	−	0.941503i	$-0.609413\pi$
$409$	−9.32601e8			−0.674007			−0.337003	+	0.941503i	$0.609413\pi$
$410$	−1.11094e9	+	8.07148e8i	−0.796065	+	0.578375i
$411$	3.29811e9	+	2.39622e9i	2.34325	+	1.70247i
$412$	−4.54869e8	−	3.30482e8i	−0.320440	−	0.232813i
$413$	1.15441e9	+	3.55291e9i	0.806372	+	2.48176i
$414$	1.07785e9	−	7.83106e8i	0.746549	−	0.542400i
$415$	1.78555e8	+	5.49535e8i	0.122632	+	0.377422i
$416$	1.30543e7	−	4.01770e7i	0.00889051	−	0.0273622i
$417$	3.81433e8	+	2.77128e8i	0.257598	+	0.187156i
$418$	−3.38986e8	+	1.04329e9i	−0.227020	+	0.698697i
$419$	6.28500e8	−	1.93432e9i	0.417404	−	1.28464i	−0.492680	−	0.870211i	$-0.663983\pi$
$419$	6.28500e8	−	1.93432e9i	0.417404	−	1.28464i	0.910083	−	0.414425i	$-0.136017\pi$
$420$	1.84050e9	+	1.33720e9i	1.21217	+	0.880691i
$421$	−6.57984e6	+	2.02507e7i	−0.00429762	+	0.0132267i	−0.953182	−	0.302396i	$-0.902213\pi$
$421$	−6.57984e6	+	2.02507e7i	−0.00429762	+	0.0132267i	0.948885	+	0.315623i	$0.102213\pi$
$422$	4.41726e8	+	1.35949e9i	0.286127	+	0.880609i
$423$	2.82186e9	−	2.05020e9i	1.81278	−	1.31706i
$424$	3.16884e8	+	9.75269e8i	0.201892	+	0.621361i
$425$	2.87950e8	+	2.09208e8i	0.181952	+	0.132196i
$426$	2.38096e8	+	1.72987e8i	0.149217	+	0.108413i
$427$	6.19821e8	−	4.50326e8i	0.385273	−	0.279917i
$428$	−9.97978e8			−0.615273
$429$	4.58940e8			0.280644
$430$	−5.38265e8	+	3.91072e8i	−0.326480	+	0.237202i
$431$	−1.63277e8	+	5.02514e8i	−0.0982322	+	0.302328i	−0.988083	−	0.153925i	$-0.950809\pi$
$431$	−1.63277e8	+	5.02514e8i	−0.0982322	+	0.302328i	0.889850	+	0.456252i	$0.150809\pi$
$432$	4.37623e7	+	1.34686e8i	0.0261160	+	0.0803768i
$433$	−4.31185e8			−0.255244			−0.127622	−	0.991823i	$-0.540734\pi$
$433$	−4.31185e8			−0.255244			−0.127622	+	0.991823i	$0.540734\pi$
$434$	1.57118e9	−	1.36222e9i	0.922599	−	0.799893i
$435$	−5.09071e9			−2.96528
$436$	−3.53104e8	−	1.08674e9i	−0.204033	−	0.627949i
$437$	5.15674e8	−	1.58708e9i	0.295590	−	0.909734i
$438$	9.44375e8	−	6.86129e8i	0.537014	−	0.390163i
$439$	−9.41280e8			−0.530998			−0.265499	−	0.964111i	$-0.585537\pi$
$439$	−9.41280e8			−0.530998			−0.265499	+	0.964111i	$0.585537\pi$
$440$	8.49026e8			0.475157
$441$	−3.54234e9	+	2.57366e9i	−1.96677	+	1.42895i
$442$	1.07852e8	+	7.83591e7i	0.0594088	+	0.0431630i
$443$	7.16358e8	+	5.20465e8i	0.391487	+	0.284432i	0.766064	−	0.642764i	$-0.222212\pi$
$443$	7.16358e8	+	5.20465e8i	0.391487	+	0.284432i	−0.374578	+	0.927196i	$0.622212\pi$
$444$	1.23889e8	+	3.81290e8i	0.0671724	+	0.206735i
$445$	−1.92987e9	+	1.40213e9i	−1.03817	+	0.754275i
$446$	−4.76611e8	−	1.46686e9i	−0.254385	−	0.782918i
$447$	7.19717e8	−	2.21506e9i	0.381141	−	1.17303i
$448$	3.32351e8	+	2.41467e8i	0.174632	+	0.126878i
$449$	−5.51140e8	+	1.69623e9i	−0.287342	+	0.884349i	0.698344	+	0.715762i	$0.253920\pi$
$449$	−5.51140e8	+	1.69623e9i	−0.287342	+	0.884349i	−0.985687	+	0.168587i	$0.946080\pi$
$450$	1.82603e8	−	5.61993e8i	0.0944633	−	0.290728i
$451$	−2.17941e9	−	1.58343e9i	−1.11872	−	0.812797i
$452$	−3.95859e8	+	1.21833e9i	−0.201630	+	0.620555i
$453$	3.23152e8	+	9.94560e8i	0.163329	+	0.502675i
$454$	−6.59471e8	+	4.79134e8i	−0.330750	+	0.240304i
$455$	−2.02936e8	−	6.24574e8i	−0.101000	−	0.310845i
$456$	7.76934e8	+	5.64476e8i	0.383714	+	0.278784i
$457$	−1.18444e9	−	8.60546e8i	−0.580506	−	0.421762i	0.258401	−	0.966038i	$-0.416805\pi$
$457$	−1.18444e9	−	8.60546e8i	−0.580506	−	0.421762i	−0.838906	+	0.544276i	$0.816805\pi$
$458$	7.79255e8	−	5.66162e8i	0.379010	−	0.275367i
$459$	−4.46907e8			−0.215711
$460$	−1.29156e9			−0.618674
$461$	−1.97105e9	+	1.43205e9i	−0.937009	+	0.680777i	−0.947699	−	0.319166i	$-0.896597\pi$
$461$	−1.97105e9	+	1.43205e9i	−0.937009	+	0.680777i	0.0106898	+	0.999943i	$0.496597\pi$
$462$	−1.37913e9	+	4.24454e9i	−0.650668	+	2.00255i
$463$	−4.59982e8	−	1.41568e9i	−0.215381	−	0.662875i	−0.999126	−	0.0417922i	$-0.986693\pi$
$463$	−4.59982e8	−	1.41568e9i	−0.215381	−	0.662875i	0.783745	−	0.621082i	$-0.213307\pi$
$464$	−9.19265e8			−0.427197
$465$	−3.22247e9	−	1.94198e9i	−1.48629	−	0.895693i
$466$	−1.06240e9			−0.486337
$467$	3.39365e8	+	1.04446e9i	0.154191	+	0.474550i	0.998078	−	0.0619703i	$-0.0197384\pi$
$467$	3.39365e8	+	1.04446e9i	0.154191	+	0.474550i	−0.843887	+	0.536521i	$0.819738\pi$
$468$	6.83940e7	−	2.10495e8i	0.0308431	−	0.0949252i
$469$	5.56654e8	−	4.04433e8i	0.249161	−	0.181026i
$470$	−3.38136e9			−1.50227
$471$	1.48804e8			0.0656210
$472$	9.87430e8	−	7.17410e8i	0.432225	−	0.314030i
$473$	−1.05595e9	−	7.67192e8i	−0.458806	−	0.333342i
$474$	2.12946e9	+	1.54715e9i	0.918430	+	0.667278i
$475$	−2.28717e8	−	7.03918e8i	−0.0979197	−	0.301366i
$476$	−1.04881e9	+	7.62005e8i	−0.445731	+	0.323842i
$477$	1.66022e9	+	5.10963e9i	0.700408	+	2.15563i
$478$	6.13507e8	−	1.88818e9i	0.256934	−	0.790763i
$479$	−1.60103e9	−	1.16322e9i	−0.665618	−	0.483600i	0.202937	−	0.979192i	$-0.434951\pi$
$479$	−1.60103e9	−	1.16322e9i	−0.665618	−	0.483600i	−0.868556	+	0.495592i	$0.834951\pi$
$480$	2.29684e8	−	7.06894e8i	0.0947951	−	0.291749i
$481$	3.57628e7	−	1.10067e8i	0.0146529	−	0.0450970i
$482$	1.39342e9	+	1.01238e9i	0.566783	+	0.411792i
$483$	2.09797e9	−	6.45690e9i	0.847198	−	2.60741i
$484$	1.29296e8	+	3.97932e8i	0.0518353	+	0.159533i
$485$	1.46756e9	−	1.06625e9i	0.584119	−	0.424387i
$486$	−7.82759e8	−	2.40908e9i	−0.309315	−	0.951973i
$487$	2.67816e9	+	1.94580e9i	1.05072	+	0.763390i	0.972349	−	0.233534i	$-0.0750291\pi$
$487$	2.67816e9	+	1.94580e9i	1.05072	+	0.763390i	0.0783679	+	0.996925i	$0.475029\pi$
$488$	−2.02505e8	−	1.47129e8i	−0.0788801	−	0.0573097i
$489$	−1.66086e9	+	1.20668e9i	−0.642320	+	0.466672i
$490$	4.24467e9			1.62989
$491$	1.28027e9			0.488109			0.244054	−	0.969762i	$-0.421522\pi$
$491$	1.28027e9			0.488109			0.244054	+	0.969762i	$0.421522\pi$
$492$	−1.90794e9	+	1.38620e9i	−0.722251	+	0.524746i
$493$	8.96443e8	−	2.75897e9i	0.336945	−	1.03701i
$494$	−8.56661e7	−	2.63653e8i	−0.0319716	−	0.0983985i
$495$	4.44822e9			1.64842
$496$	−5.81903e8	−	3.50676e8i	−0.214124	−	0.129039i
$497$	8.26159e8			0.301867
$498$	3.06651e8	+	9.43775e8i	0.111261	+	0.342425i
$499$	−9.54624e8	+	2.93803e9i	−0.343938	+	1.05853i	0.618212	+	0.786012i	$0.287857\pi$
$499$	−9.54624e8	+	2.93803e9i	−0.343938	+	1.05853i	−0.962150	+	0.272521i	$0.912143\pi$
$500$	8.51435e8	−	6.18604e8i	0.304619	−	0.221318i
$501$	2.91783e9			1.03664
$502$	3.33150e9			1.17538
$503$	−3.49800e9	+	2.54144e9i	−1.22555	+	0.890415i	−0.996549	−	0.0830105i	$-0.973547\pi$
$503$	−3.49800e9	+	2.54144e9i	−1.22555	+	0.890415i	−0.229003	+	0.973426i	$0.573547\pi$
$504$	1.74125e9	+	1.26509e9i	0.605836	+	0.440165i
$505$	1.10659e9	+	8.03984e8i	0.382355	+	0.277797i
$506$	−7.82967e8	−	2.40973e9i	−0.268669	−	0.826877i
$507$	3.44861e9	−	2.50556e9i	1.17521	−	0.853840i
$508$	−3.18501e8	−	9.80245e8i	−0.107792	−	0.331751i
$509$	1.22823e9	−	3.78011e9i	0.412827	−	1.27055i	−0.501352	−	0.865243i	$-0.667164\pi$
$509$	1.22823e9	−	3.78011e9i	0.412827	−	1.27055i	0.914180	−	0.405309i	$-0.132836\pi$
$510$	1.89760e9	+	1.37869e9i	0.633446	+	0.460226i
$511$	1.01260e9	−	3.11646e9i	0.335710	−	1.03321i
$512$	4.14756e7	−	1.27649e8i	0.0136568	−	0.0420312i
$513$	7.51850e8	+	5.46251e8i	0.245878	+	0.178641i
$514$	−9.46518e8	+	2.91308e9i	−0.307438	+	0.946197i
$515$	8.82446e8	+	2.71589e9i	0.284684	+	0.876167i
$516$	−9.24421e8	+	6.71631e8i	−0.296207	+	0.215207i
$517$	−2.04984e9	−	6.30876e9i	−0.652384	−	2.00783i
$518$	9.10490e8	+	6.61509e8i	0.287820	+	0.209113i
$519$	−5.53384e9	−	4.02057e9i	−1.73756	−	1.26241i
$520$	−1.73582e8	+	1.26115e8i	−0.0541370	+	0.0393328i
$521$	6.03703e8			0.187021			0.0935107	−	0.995618i	$-0.470191\pi$
$521$	6.03703e8			0.187021			0.0935107	+	0.995618i	$0.470191\pi$
$522$	−4.81621e9			−1.48204
$523$	5.27890e8	−	3.83535e8i	0.161357	−	0.117233i	−0.504177	−	0.863601i	$-0.668204\pi$
$523$	5.27890e8	−	3.83535e8i	0.161357	−	0.117233i	0.665534	+	0.746368i	$0.268204\pi$
$524$	−2.16668e8	+	6.66836e8i	−0.0657864	+	0.202470i
$525$	−9.30513e8	−	2.86382e9i	−0.280650	−	0.863751i
$526$	9.70712e7			0.0290831
$527$	1.61993e9	−	1.40448e9i	0.482126	−	0.418003i
$528$	1.45812e9			0.431098
$529$	1.38920e8	+	4.27552e8i	0.0408010	+	0.125572i
$530$	1.60945e9	−	4.95338e9i	0.469583	−	1.44523i
$531$	5.17334e9	−	3.75865e9i	1.49948	−	1.08944i
$532$	2.69585e9			0.776255
$533$	6.80782e8			0.194744
$534$	−3.31438e9	+	2.40804e9i	−0.941906	+	0.684335i
$535$	4.10068e9	+	2.97932e9i	1.15776	+	0.841160i
$536$	−1.81868e8	−	1.32135e8i	−0.0510128	−	0.0370630i
$537$	1.69266e9	+	5.20948e9i	0.471694	+	1.45172i
$538$	−1.82822e9	+	1.32828e9i	−0.506163	+	0.367749i
$539$	2.57320e9	+	7.91949e9i	0.707804	+	2.17840i
$540$	2.22268e8	−	6.84071e8i	0.0607434	−	0.186949i
$541$	−4.42557e9	−	3.21537e9i	−1.20165	−	0.873052i	−0.207207	−	0.978297i	$-0.566437\pi$
$541$	−4.42557e9	−	3.21537e9i	−1.20165	−	0.873052i	−0.994446	+	0.105245i	$0.966437\pi$
$542$	1.02531e9	−	3.15559e9i	0.276604	−	0.851300i
$543$	−2.62465e9	+	8.07786e9i	−0.703514	+	2.16519i
$544$	3.42663e8	+	2.48959e8i	0.0912581	+	0.0663029i
$545$	−1.79341e9	+	5.51956e9i	−0.474561	+	1.46055i
$546$	−3.48525e8	−	1.07265e9i	−0.0916346	−	0.282022i
$547$	−1.17956e9	+	8.56999e8i	−0.308151	+	0.223885i	−0.731103	−	0.682267i	$-0.760994\pi$
$547$	−1.17956e9	+	8.56999e8i	−0.308151	+	0.223885i	0.422952	+	0.906152i	$0.360994\pi$
$548$	−1.15539e9	−	3.55593e9i	−0.299914	−	0.923041i
$549$	−1.06097e9	−	7.70837e8i	−0.273652	−	0.198820i
$550$	−9.09162e8	−	6.60545e8i	−0.233009	−	0.169291i
$551$	−4.88038e9	+	3.54581e9i	−1.24286	+	0.902993i
$552$	−2.21814e9			−0.561308
$553$	7.38892e9			1.85799
$554$	1.77959e9	−	1.29294e9i	0.444667	−	0.323069i
$555$	6.29228e8	−	1.93657e9i	0.156237	−	0.480847i
$556$	−1.33623e8	−	4.11251e8i	−0.0329701	−	0.101472i
$557$	−3.41457e9			−0.837227			−0.418614	−	0.908164i	$-0.637484\pi$
$557$	−3.41457e9			−0.837227			−0.418614	+	0.908164i	$0.637484\pi$
$558$	−3.04871e9	−	1.83726e9i	−0.742841	−	0.447663i
$559$	3.29847e8			0.0798676
$560$	−6.44761e8	−	1.98437e9i	−0.155146	−	0.477491i
$561$	−1.42193e9	+	4.37624e9i	−0.340022	+	1.04648i
$562$	6.96452e7	−	5.06002e7i	0.0165506	−	0.0120247i
$563$	2.11447e9			0.499370			0.249685	−	0.968327i	$-0.419673\pi$
$563$	2.11447e9			0.499370			0.249685	+	0.968327i	$0.419673\pi$
$564$	−5.80717e9			−1.36297
$565$	5.26373e9	−	3.82432e9i	1.22779	−	0.892041i
$566$	−4.31658e9	−	3.13618e9i	−1.00065	−	0.727014i
$567$	−4.37890e9	−	3.18146e9i	−1.00885	−	0.732969i
$568$	−8.34097e7	−	2.56709e8i	−0.0190984	−	0.0587789i
$569$	4.99089e9	−	3.62610e9i	1.13576	−	0.825176i	0.149234	−	0.988802i	$-0.452319\pi$
$569$	4.99089e9	−	3.62610e9i	1.13576	−	0.825176i	0.986522	+	0.163626i	$0.0523191\pi$
$570$	−1.50725e9	−	4.63885e9i	−0.340898	−	1.04918i
$571$	6.41981e8	−	1.97582e9i	0.144310	−	0.444140i	−0.852612	−	0.522545i	$-0.824983\pi$
$571$	6.41981e8	−	1.97582e9i	0.144310	−	0.444140i	0.996922	+	0.0784048i	$0.0249827\pi$
$572$	−3.40528e8	−	2.47408e8i	−0.0760793	−	0.0552748i
$573$	−1.78854e9	+	5.50455e9i	−0.397152	+	1.22231i
$574$	−2.04578e9	+	6.29626e9i	−0.451510	+	1.38960i
$575$	1.38304e9	+	1.00484e9i	0.303387	+	0.220424i
$576$	2.17299e8	−	6.68777e8i	0.0473782	−	0.145815i
$577$	−1.23884e9	−	3.81275e9i	−0.268472	−	0.826272i	−0.990873	−	0.134797i	$-0.956962\pi$
$577$	−1.23884e9	−	3.81275e9i	−0.268472	−	0.826272i	0.722401	−	0.691474i	$-0.243038\pi$
$578$	1.57442e9	−	1.14388e9i	0.339134	−	0.246396i
$579$	−3.49269e8	−	1.07494e9i	−0.0747799	−	0.230149i
$580$	3.77725e9	+	2.74433e9i	0.803855	+	0.584035i
$581$	2.25366e9	+	1.63738e9i	0.476730	+	0.346364i
$582$	2.52041e9	−	1.83118e9i	0.529957	−	0.385036i
$583$	1.02174e10			2.13551
$584$	−1.07060e9			−0.222424
$585$	−9.09433e8	+	6.60742e8i	−0.187813	+	0.136454i
$586$	−1.67126e8	+	5.14360e8i	−0.0343085	+	0.105591i
$587$	2.11620e9	+	6.51299e9i	0.431840	+	1.32907i	0.896290	+	0.443468i	$0.146252\pi$
$587$	2.11620e9	+	6.51299e9i	0.431840	+	1.32907i	−0.464450	+	0.885599i	$0.653748\pi$
$588$	7.28984e9			1.47876
$589$	−4.44196e9	+	3.82784e8i	−0.895718	+	0.0771882i
$590$	−6.19906e9			−1.24264
$591$	−5.11139e8	−	1.57312e9i	−0.101855	−	0.313478i
$592$	1.13624e8	−	3.49699e8i	0.0225084	−	0.0692737i
$593$	2.13322e8	−	1.54987e8i	0.0420091	−	0.0305214i	−0.566583	−	0.824005i	$-0.691735\pi$
$593$	2.13322e8	−	1.54987e8i	0.0420091	−	0.0305214i	0.608592	+	0.793484i	$0.291735\pi$
$594$	1.41105e9			0.276242
$595$	6.58440e9			1.28147
$596$	−1.72813e9	+	1.25556e9i	−0.334360	+	0.242927i
$597$	−7.73157e9	−	5.61731e9i	−1.48716	−	1.08048i
$598$	5.18019e8	+	3.76363e8i	0.0990585	+	0.0719702i
$599$	−1.64368e9	−	5.05872e9i	−0.312480	−	0.961715i	−0.976779	−	0.214248i	$-0.931270\pi$
$599$	−1.64368e9	−	5.05872e9i	−0.312480	−	0.961715i	0.664299	−	0.747467i	$-0.268730\pi$
$600$	−7.95918e8	+	5.78268e8i	−0.150432	+	0.109295i
$601$	−1.57150e9	−	4.83657e9i	−0.295293	−	0.908817i	−0.983123	−	0.182946i	$-0.941437\pi$
$601$	−1.57150e9	−	4.83657e9i	−0.295293	−	0.908817i	0.687830	−	0.725871i	$-0.258563\pi$
$602$	−9.91204e8	+	3.05061e9i	−0.185172	+	0.569901i
$603$	−9.52842e8	−	6.92281e8i	−0.176974	−	0.128579i
$604$	2.96378e8	−	9.12158e8i	0.0547289	−	0.168438i
$605$	6.56692e8	−	2.02109e9i	0.120564	−	0.371058i
$606$	1.90046e9	+	1.38077e9i	0.346901	+	0.252038i
$607$	−1.19961e9	+	3.69201e9i	−0.217710	+	0.670043i	0.781240	+	0.624231i	$0.214588\pi$
$607$	−1.19961e9	+	3.69201e9i	−0.217710	+	0.670043i	−0.998950	+	0.0458121i	$0.985412\pi$
$608$	−2.72175e8	−	8.37668e8i	−0.0491118	−	0.151150i
$609$	−1.98554e10	+	1.44258e10i	−3.56220	+	2.58809i
$610$	3.92861e8	+	1.20910e9i	0.0700784	+	0.215679i
$611$	1.35620e9	+	9.85334e8i	0.240535	+	0.174759i
$612$	1.79528e9	+	1.30435e9i	0.316594	+	0.230019i
$613$	6.64300e9	−	4.82642e9i	1.16480	−	0.846279i	0.174426	−	0.984670i	$-0.444193\pi$
$613$	6.64300e9	−	4.82642e9i	1.16480	−	0.846279i	0.990378	+	0.138391i	$0.0441931\pi$
$614$	−6.41999e9			−1.11930
$615$	1.19780e10			2.07645
$616$	3.31147e9	−	2.40592e9i	0.570806	−	0.414715i
$617$	−1.76274e9	+	5.42516e9i	−0.302128	+	0.929854i	0.678606	+	0.734503i	$0.262585\pi$
$617$	−1.76274e9	+	5.42516e9i	−0.302128	+	0.929854i	−0.980733	+	0.195351i	$0.937415\pi$
$618$	1.51552e9	+	4.66429e9i	0.258287	+	0.794925i
$619$	−2.27716e9			−0.385901			−0.192950	−	0.981208i	$-0.561806\pi$
$619$	−2.27716e9			−0.385901			−0.192950	+	0.981208i	$0.561806\pi$
$620$	1.34414e9	+	3.17811e9i	0.226503	+	0.535548i
$621$	−2.14652e9			−0.359678
$622$	1.62119e9	+	4.98952e9i	0.270127	+	0.831366i
$623$	−3.55382e9	+	1.09375e10i	−0.588826	+	1.81222i
$624$	−2.98112e8	+	2.16591e8i	−0.0491172	+	0.0356857i
$625$	−7.49653e9			−1.22823
$626$	−1.72597e9			−0.281206
$627$	7.74120e9	−	5.62431e9i	1.25421	−	0.911240i
$628$	−1.10411e8	−	8.02183e7i	−0.0177891	−	0.0129245i
$629$	9.38740e8	+	6.82035e8i	0.150407	+	0.109277i
$630$	−3.37803e9	−	1.03965e10i	−0.538235	−	1.65652i
$631$	−7.31398e9	+	5.31392e9i	−1.15891	+	0.842000i	−0.989640	−	0.143569i	$-0.954142\pi$
$631$	−7.31398e9	+	5.31392e9i	−1.15891	+	0.842000i	−0.169274	+	0.985569i	$0.554142\pi$
$632$	−7.45992e8	−	2.29593e9i	−0.117550	−	0.361783i
$633$	3.85304e9	−	1.18584e10i	0.603797	−	1.85830i
$634$	5.72830e9	+	4.16185e9i	0.892716	+	0.648596i
$635$	−1.61766e9	+	4.97866e9i	−0.250715	+	0.771621i
$636$	2.76408e9	−	8.50698e9i	0.426041	−	1.31122i
$637$	−1.70246e9	−	1.23691e9i	−0.260968	−	0.189605i
$638$	−2.83039e9	+	8.71106e9i	−0.431494	+	1.32800i
$639$	−4.37000e8	−	1.34495e9i	−0.0662565	−	0.203916i
$640$	−5.51499e8	+	4.00688e8i	−0.0831601	+	0.0604193i
$641$	−6.19457e7	−	1.90649e8i	−0.00928984	−	0.0285912i	0.946304	−	0.323278i	$-0.104785\pi$
$641$	−6.19457e7	−	1.90649e8i	−0.00928984	−	0.0285912i	−0.955594	+	0.294686i	$0.904785\pi$
$642$	7.04254e9	+	5.11671e9i	1.05041	+	0.763164i
$643$	6.10054e9	+	4.43230e9i	0.904960	+	0.657492i	0.939735	−	0.341903i	$-0.111071\pi$
$643$	6.10054e9	+	4.43230e9i	0.904960	+	0.657492i	−0.0347748	+	0.999395i	$0.511071\pi$
$644$	−5.03749e9	+	3.65995e9i	−0.743214	+	0.539976i
$645$	5.80349e9			0.851589
$646$	2.77949e9			0.405650
$647$	9.40654e9	−	6.83425e9i	1.36542	−	0.992033i	0.367337	−	0.930088i	$-0.380270\pi$
$647$	9.40654e9	−	6.83425e9i	1.36542	−	0.992033i	0.998080	−	0.0619452i	$-0.0197304\pi$
$648$	−5.46463e8	+	1.68184e9i	−0.0788947	+	0.242813i
$649$	−3.75799e9	−	1.15659e10i	−0.539633	−	1.66082i
$650$	2.83995e8			0.0405615
$651$	−1.80717e10	+	1.55732e9i	−2.56724	+	0.221231i
$652$	1.88284e9			0.266040
$653$	−1.11298e9	−	3.42540e9i	−0.156420	−	0.481410i	0.841882	−	0.539661i	$-0.181448\pi$
$653$	−1.11298e9	−	3.42540e9i	−0.156420	−	0.481410i	−0.998302	+	0.0582509i	$0.981448\pi$
$654$	−3.08002e9	+	9.47933e9i	−0.430558	+	1.32512i
$655$	2.88103e9	−	2.09319e9i	0.400593	−	0.291048i
$656$	2.16295e9			0.299146
$657$	−5.60907e9			−0.771635
$658$	−1.31884e10	+	9.58190e9i	−1.80468	+	1.31118i
$659$	6.43553e9	+	4.67568e9i	0.875962	+	0.636424i	0.932180	−	0.361995i	$-0.117904\pi$
$659$	6.43553e9	+	4.67568e9i	0.875962	+	0.636424i	−0.0562182	+	0.998419i	$0.517904\pi$
$660$	−5.99142e9	−	4.35302e9i	−0.811196	−	0.589368i
$661$	3.95970e9	+	1.21867e10i	0.533282	+	1.64127i	0.747333	+	0.664450i	$0.231334\pi$
$661$	3.95970e9	+	1.21867e10i	0.533282	+	1.64127i	−0.214051	+	0.976823i	$0.568666\pi$
$662$	1.82715e9	−	1.32750e9i	0.244778	−	0.177841i
$663$	−3.59339e8	−	1.10593e9i	−0.0478858	−	0.147377i
$664$	2.81244e8	−	8.65581e8i	0.0372817	−	0.114741i
$665$	−1.10772e10	−	8.04806e9i	−1.46068	−	1.06124i
$666$	5.95299e8	−	1.83214e9i	0.0780864	−	0.240325i
$667$	4.30567e9	−	1.32515e10i	0.561824	−	1.72912i
$668$	−2.16499e9	−	1.57296e9i	−0.281021	−	0.204174i
$669$	−4.15734e9	+	1.27950e10i	−0.536814	+	1.65214i
$670$	3.52824e8	+	1.08588e9i	0.0453207	+	0.139483i
$671$	−2.01772e9	+	1.46596e9i	−0.257829	+	0.187324i
$672$	−1.10732e9	−	3.40798e9i	−0.140760	−	0.433216i
$673$	1.60972e9	+	1.16953e9i	0.203563	+	0.147897i	0.684896	−	0.728641i	$-0.259847\pi$
$673$	1.60972e9	+	1.16953e9i	0.203563	+	0.147897i	−0.481334	+	0.876537i	$0.659847\pi$
$674$	−4.48292e9	−	3.25703e9i	−0.563964	−	0.409744i
$675$	−7.70221e8	+	5.59598e8i	−0.0963944	+	0.0700347i
$676$	−3.90953e9			−0.486756
$677$	−9.29542e9			−1.15135			−0.575677	−	0.817677i	$-0.695261\pi$
$677$	−9.29542e9			−1.15135			−0.575677	+	0.817677i	$0.695261\pi$
$678$	9.03997e9	−	6.56792e9i	1.11394	−	0.809327i
$679$	2.70249e9	−	8.31741e9i	0.331299	−	1.01963i
$680$	−6.64767e8	−	2.04594e9i	−0.0810752	−	0.249524i
$681$	7.11032e9			0.862728
$682$	−5.11472e9	+	4.43446e9i	−0.617414	+	0.535297i
$683$	−2.60346e9			−0.312664			−0.156332	−	0.987705i	$-0.549967\pi$
$683$	−2.60346e9			−0.312664			−0.156332	+	0.987705i	$0.549967\pi$
$684$	−1.42598e9	−	4.38871e9i	−0.170379	−	0.524373i
$685$	−5.86822e9	+	1.80605e10i	−0.697572	+	2.14691i
$686$	8.20275e9	−	5.95965e9i	0.970119	−	0.704833i
$687$	−8.40181e9			−0.988609
$688$	1.04798e9			0.122685
$689$	−2.08894e9	+	1.51771e9i	−0.243310	+	0.176775i
$690$	9.11429e9	+	6.62192e9i	1.05621	+	0.767383i
$691$	−2.40947e9	−	1.75058e9i	−0.277810	−	0.201841i	0.440151	−	0.897924i	$-0.354925\pi$
$691$	−2.40947e9	−	1.75058e9i	−0.277810	−	0.201841i	−0.717962	+	0.696083i	$0.754925\pi$
$692$	1.93861e9	+	5.96642e9i	0.222392	+	0.684452i
$693$	1.73495e10	−	1.26051e10i	1.98025	−	1.43873i
$694$	−2.74501e9	−	8.44827e9i	−0.311735	−	0.959422i
$695$	−6.78672e8	+	2.08874e9i	−0.0766854	+	0.236014i
$696$	6.48708e9	+	4.71314e9i	0.729318	+	0.529880i
$697$	−2.10926e9	+	6.49162e9i	−0.235947	+	0.726171i
$698$	3.22853e9	−	9.93639e9i	0.359344	−	1.10595i
$699$	7.49715e9	+	5.44700e9i	0.830283	+	0.603236i
$700$	−8.53418e8	+	2.62655e9i	−0.0940413	+	0.289429i
$701$	−1.96214e9	−	6.03886e9i	−0.215138	−	0.662128i	−0.999144	−	0.0413738i	$-0.986827\pi$
$701$	−1.96214e9	−	6.03886e9i	−0.215138	−	0.662128i	0.784005	−	0.620754i	$-0.213173\pi$
$702$	−2.88487e8	+	2.09598e8i	−0.0314736	+	0.0228669i
$703$	−7.45635e8	−	2.29483e9i	−0.0809436	−	0.249119i
$704$	−1.08191e9	−	7.86054e8i	−0.116866	−	0.0849079i
$705$	2.38616e10	+	1.73365e10i	2.56471	+	1.86337i
$706$	5.73394e9	−	4.16595e9i	0.613248	−	0.445551i
$707$	6.59433e9			0.701783
$708$	−1.06463e10			−1.12741
$709$	7.88894e9	−	5.73165e9i	0.831298	−	0.603973i	−0.0886284	−	0.996065i	$-0.528248\pi$
$709$	7.88894e9	−	5.73165e9i	0.831298	−	0.603973i	0.919926	+	0.392092i	$0.128248\pi$
$710$	−4.23637e8	+	1.30382e9i	−0.0444211	+	0.136714i
$711$	−3.90840e9	−	1.20288e10i	−0.407808	−	1.25510i
$712$	3.75737e9			0.390125
$713$	7.78063e9	−	6.74580e9i	0.803899	−	0.696980i
$714$	1.13081e10			1.16264
$715$	6.60624e8	+	2.03319e9i	0.0675901	+	0.208021i
$716$	1.55242e9	−	4.77786e9i	0.158057	−	0.486449i
$717$	−1.40102e10	+	1.01790e10i	−1.41948	+	1.03131i
$718$	1.16432e10			1.17392
$719$	4.86782e9			0.488409			0.244204	−	0.969724i	$-0.421473\pi$
$719$	4.86782e9			0.488409			0.244204	+	0.969724i	$0.421473\pi$
$720$	−2.88941e9	+	2.09928e9i	−0.288500	+	0.209608i
$721$	1.11380e10	+	8.09220e9i	1.10671	+	0.804069i
$722$	1.10921e9	+	8.05889e8i	0.109682	+	0.0796884i
$723$	−4.64256e9	−	1.42883e10i	−0.456849	−	1.40604i
$724$	6.30212e9	−	4.57876e9i	0.617165	−	0.448397i
$725$	−1.90969e9	−	5.87742e9i	−0.186114	−	0.572801i
$726$	1.12781e9	−	3.47104e9i	0.109385	−	0.336652i
$727$	−1.27884e10	−	9.29132e9i	−1.23437	−	0.896823i	−0.237161	−	0.971470i	$-0.576217\pi$
$727$	−1.27884e10	−	9.29132e9i	−1.23437	−	0.896823i	−0.997210	+	0.0746471i	$0.976217\pi$
$728$	−3.19649e8	+	9.83777e8i	−0.0307053	+	0.0945011i
$729$	−4.49356e9	+	1.38298e10i	−0.429580	+	1.32211i
$730$	4.39907e9	+	3.19611e9i	0.418534	+	0.304083i
$731$	−1.02196e9	+	3.14527e9i	−0.0967659	+	0.297815i
$732$	6.74702e8	+	2.07652e9i	0.0635804	+	0.195680i
$733$	1.05995e10	−	7.70098e9i	0.994080	−	0.722241i	0.0332692	−	0.999446i	$-0.489408\pi$
$733$	1.05995e10	−	7.70098e9i	0.994080	−	0.722241i	0.960811	+	0.277205i	$0.0894081\pi$
$734$	2.82081e9	+	8.68155e9i	0.263292	+	0.810329i
$735$	−2.99539e10	−	2.17628e10i	−2.78258	−	2.02166i
$736$	1.64583e9	+	1.19577e9i	0.152164	+	0.110554i
$737$	−1.81209e9	+	1.31656e9i	−0.166742	+	0.121145i
$738$	1.13321e10			1.03780
$739$	−1.26487e10			−1.15289			−0.576447	−	0.817134i	$-0.695561\pi$
$739$	−1.26487e10			−1.15289			−0.576447	+	0.817134i	$0.695561\pi$
$740$	−1.51086e9	+	1.09770e9i	−0.137060	+	0.0995802i
$741$	−7.47240e8	+	2.29977e9i	−0.0674677	+	0.207644i
$742$	−7.75925e9	−	2.38805e10i	−0.697278	−	2.14600i
$743$	−6.09048e9			−0.544741			−0.272371	−	0.962192i	$-0.587808\pi$
$743$	−6.09048e9			−0.544741			−0.272371	+	0.962192i	$0.587808\pi$
$744$	2.30844e9	+	5.45812e9i	0.205500	+	0.485890i
$745$	1.08492e10			0.961278
$746$	4.23947e9	+	1.30478e10i	0.373875	+	1.15067i
$747$	1.47349e9	−	4.53495e9i	0.129338	−	0.398062i
$748$	3.41422e9	−	2.48058e9i	0.298288	−	0.216719i
$749$	2.44366e10			2.12498
$750$	−9.18004e9			−0.794567
$751$	1.88748e9	−	1.37133e9i	0.162608	−	0.118142i	−0.503505	−	0.863992i	$-0.667957\pi$
$751$	1.88748e9	−	1.37133e9i	0.162608	−	0.118142i	0.666114	+	0.745850i	$0.267957\pi$
$752$	4.30885e9	+	3.13056e9i	0.369487	+	0.268448i
$753$	−2.35098e10	−	1.70808e10i	−2.00662	−	1.45790i
$754$	−7.15277e8	−	2.20140e9i	−0.0607679	−	0.187024i
$755$	−3.94093e9	+	2.86325e9i	−0.333261	+	0.242128i
$756$	−1.07157e9	−	3.29794e9i	−0.0901972	−	0.277598i
$757$	−9.71004e8	+	2.98844e9i	−0.0813552	+	0.250386i	−0.983458	−	0.181135i	$-0.942023\pi$
$757$	−9.71004e8	+	2.98844e9i	−0.0813552	+	0.250386i	0.902103	+	0.431521i	$0.142023\pi$
$758$	−1.22173e7	−	8.87639e6i	−0.00101890	−	0.000740276i
$759$	−6.82959e9	+	2.10193e10i	−0.566955	+	1.74491i
$760$	−1.38237e9	+	4.25451e9i	−0.114229	+	0.351562i
$761$	−7.85711e9	−	5.70852e9i	−0.646273	−	0.469545i	0.215726	−	0.976454i	$-0.430788\pi$
$761$	−7.85711e9	−	5.70852e9i	−0.646273	−	0.469545i	−0.862000	+	0.506909i	$0.830788\pi$
$762$	−2.77819e9	+	8.55039e9i	−0.227467	+	0.700073i
$763$	8.64614e9	+	2.66101e10i	0.704671	+	2.16875i
$764$	4.29450e9	−	3.12013e9i	0.348406	−	0.253132i
$765$	−3.48285e9	−	1.07191e10i	−0.281267	−	0.865652i
$766$	3.33088e9	+	2.42002e9i	0.267768	+	0.194545i
$767$	2.48632e9	+	1.80642e9i	0.198964	+	0.144556i
$768$	−9.47149e8	+	6.88144e8i	−0.0754491	+	0.0548170i
$769$	−3.62003e9			−0.287058			−0.143529	−	0.989646i	$-0.545845\pi$
$769$	−3.62003e9			−0.287058			−0.143529	+	0.989646i	$0.545845\pi$
$770$	−2.07893e10			−1.64105
$771$	2.16150e10	−	1.57042e10i	1.69850	−	1.23403i
$772$	−3.20331e8	+	9.85878e8i	−0.0250575	+	0.0771192i
$773$	−1.50955e9	−	4.64591e9i	−0.117549	−	0.361778i	0.874921	−	0.484265i	$-0.160913\pi$
$773$	−1.50955e9	−	4.64591e9i	−0.117549	−	0.361778i	−0.992470	+	0.122487i	$0.960913\pi$
$774$	5.49055e9			0.425621
$775$	1.03324e9	−	4.44896e9i	0.0797341	−	0.343323i
$776$	−2.85728e9			−0.219501
$777$	−3.03355e9	−	9.33629e9i	−0.231994	−	0.714004i
$778$	2.92390e9	−	8.99885e9i	0.222605	−	0.685107i
$779$	1.14831e10	−	8.34299e9i	0.870321	−	0.632325i
$780$	1.87154e9			0.141211
$781$	−2.68942e9			−0.202013
$782$	−5.19379e9	+	3.77351e9i	−0.388384	+	0.282177i
$783$	6.27763e9	+	4.56097e9i	0.467337	+	0.339540i
$784$	−5.40897e9	−	3.92985e9i	−0.400875	−	0.291252i
$785$	2.14198e8	+	6.59232e8i	0.0158041	+	0.0486401i
$786$	4.94791e9	−	3.59486e9i	0.363448	−	0.264061i
$787$	1.31899e9	+	4.05944e9i	0.0964563	+	0.296862i	0.987630	−	0.156799i	$-0.0501176\pi$
$787$	1.31899e9	+	4.05944e9i	0.0964563	+	0.296862i	−0.891174	+	0.453661i	$0.850118\pi$
$788$	−4.68789e8	+	1.44279e9i	−0.0341300	+	0.105041i
$789$	−6.85013e8	−	4.97691e8i	−0.0496512	−	0.0360737i
$790$	−3.78888e9	+	1.16610e10i	−0.273411	+	0.841474i
$791$	9.69304e9	−	2.98321e10i	0.696374	−	2.14322i
$792$	−5.66835e9	−	4.11829e9i	−0.405432	−	0.294564i
$793$	1.94766e8	−	5.99427e8i	0.0138694	−	0.0426855i
$794$	−3.81660e9	−	1.17463e10i	−0.270586	−	0.832778i
$795$	−3.67539e10	+	2.67033e10i	−2.59429	+	1.88486i
$796$	2.70852e9	+	8.33595e9i	0.190342	+	0.585814i
$797$	−1.27797e10	−	9.28496e9i	−0.894159	−	0.649645i	0.0427999	−	0.999084i	$-0.486372\pi$
$797$	−1.27797e10	−	9.28496e9i	−0.894159	−	0.649645i	−0.936959	+	0.349439i	$0.886372\pi$
$798$	−1.90241e10	−	1.38218e10i	−1.32524	−	0.962841i
$799$	−1.35976e10	+	9.87921e9i	−0.943078	+	0.685186i
$800$	9.02298e8			0.0623067
$801$	1.96856e10			1.35343
$802$	−2.09429e9	+	1.52159e9i	−0.143360	+	0.104157i
$803$	−3.29634e9	+	1.01451e10i	−0.224661	+	0.691436i
$804$	6.05943e8	+	1.86490e9i	0.0411183	+	0.126549i
$805$	3.16252e10			2.13672
$806$	3.87000e8	−	1.66636e9i	0.0260339	−	0.112098i
$807$	1.97116e10			1.32027
$808$	−6.65769e8	−	2.04903e9i	−0.0444001	−	0.136649i
$809$	−4.98458e8	+	1.53410e9i	−0.0330985	+	0.101867i	−0.966241	−	0.257640i	$-0.917055\pi$
$809$	−4.98458e8	+	1.53410e9i	−0.0330985	+	0.101867i	0.933142	+	0.359507i	$0.117055\pi$
$810$	7.26630e9	−	5.27927e9i	0.480414	−	0.349041i
$811$	1.28085e10			0.843191			0.421596	−	0.906784i	$-0.361470\pi$
$811$	1.28085e10			0.843191			0.421596	+	0.906784i	$0.361470\pi$
$812$	2.25092e10			1.47541
$813$	−2.34144e10	+	1.70115e10i	−1.52815	+	1.11026i
$814$	−2.96394e9	−	2.15343e9i	−0.192612	−	0.139941i
$815$	−7.73657e9	−	5.62095e9i	−0.500607	−	0.363712i
$816$	−1.14168e9	−	3.51372e9i	−0.0735576	−	0.226387i
$817$	5.56371e9	−	4.04227e9i	0.356933	−	0.259327i
$818$	−2.30552e9	−	7.09565e9i	−0.147276	−	0.453269i
$819$	−1.67470e9	+	5.15420e9i	−0.106523	+	0.327844i
$820$	−8.88755e9	−	6.45718e9i	−0.562903	−	0.408973i
$821$	−8.49322e9	+	2.61394e10i	−0.535638	+	1.64852i	0.206629	+	0.978419i	$0.433751\pi$
$821$	−8.49322e9	+	2.61394e10i	−0.535638	+	1.64852i	−0.742267	+	0.670104i	$0.766249\pi$
$822$	−1.00781e10	+	3.10173e10i	−0.632890	+	1.94784i
$823$	−6.34350e9	−	4.60882e9i	−0.396670	−	0.288198i	0.371513	−	0.928428i	$-0.378839\pi$
$823$	−6.34350e9	−	4.60882e9i	−0.396670	−	0.288198i	−0.768183	+	0.640230i	$0.778839\pi$
$824$	1.38996e9	−	4.27785e9i	0.0865478	−	0.266367i
$825$	3.02912e9	+	9.32268e9i	0.187814	+	0.578032i
$826$	−2.41783e10	+	1.75666e10i	−1.49278	+	1.08457i
$827$	−9.08000e9	−	2.79454e10i	−0.558234	−	1.71807i	−0.687245	−	0.726426i	$-0.741180\pi$
$827$	−9.08000e9	−	2.79454e10i	−0.558234	−	1.71807i	0.129011	−	0.991643i	$-0.458820\pi$
$828$	8.62283e9	+	6.26485e9i	0.527890	+	0.383535i
$829$	−9.17606e9	−	6.66680e9i	−0.559391	−	0.406421i	0.271845	−	0.962341i	$-0.412366\pi$
$829$	−9.17606e9	−	6.66680e9i	−0.559391	−	0.406421i	−0.831236	+	0.555920i	$0.812366\pi$
$830$	−3.73970e9	+	2.71705e9i	−0.227019	+	0.164939i
$831$	−1.91872e10			−1.15987
$832$	3.37957e8			0.0203437
$833$	1.70693e10	−	1.24015e10i	1.02319	−	0.743393i
$834$	−1.16556e9	+	3.58721e9i	−0.0695748	+	0.214129i
$835$	4.20009e9	+	1.29266e10i	0.249664	+	0.768387i
$836$	−8.77586e9			−0.519479
$837$	2.23391e9	+	5.28189e9i	0.131682	+	0.311351i
$838$	1.62709e10			0.955122
$839$	5.29447e9	+	1.62947e10i	0.309496	+	0.952532i	0.977961	+	0.208788i	$0.0669518\pi$
$839$	5.29447e9	+	1.62947e10i	0.309496	+	0.952532i	−0.668465	+	0.743744i	$0.733048\pi$
$840$	−5.62406e9	+	1.73091e10i	−0.327395	+	1.00762i
$841$	−2.67938e10	+	1.94668e10i	−1.55327	+	1.12852i
$842$	−1.70342e8			−0.00983401
$843$	−7.50904e8			−0.0431706
$844$	−9.25163e9	+	6.72170e9i	−0.529687	+	0.384840i
$845$	1.60642e10	+	1.16713e10i	0.915928	+	0.665461i
$846$	2.25749e10	+	1.64016e10i	1.28183	+	0.931303i
$847$	−3.16595e9	−	9.74379e9i	−0.179024	−	0.550980i
$848$	−6.63691e9	+	4.82200e9i	−0.373749	+	0.271545i
$849$	1.43819e10	+	4.42628e10i	0.806562	+	2.48234i
$850$	−8.79897e8	+	2.70805e9i	−0.0491435	+	0.151248i
$851$	4.50882e9	+	3.27585e9i	0.250790	+	0.182209i
$852$	−7.27557e8	+	2.23919e9i	−0.0403022	+	0.124037i
$853$	3.18393e9	−	9.79913e9i	0.175648	−	0.540588i	−0.824015	−	0.566568i	$-0.808271\pi$
$853$	3.18393e9	−	9.79913e9i	0.175648	−	0.540588i	0.999662	+	0.0259805i	$0.00827079\pi$
$854$	4.95857e9	+	3.60261e9i	0.272429	+	0.197931i
$855$	−7.24253e9	+	2.22902e10i	−0.396286	+	1.21964i
$856$	−2.46714e9	−	7.59307e9i	−0.134442	−	0.413770i
$857$	1.16627e9	−	8.47343e8i	0.0632944	−	0.0459861i	−0.555688	−	0.831391i	$-0.687545\pi$
$857$	1.16627e9	−	8.47343e8i	0.0632944	−	0.0459861i	0.618983	+	0.785405i	$0.287545\pi$
$858$	1.13456e9	+	3.49182e9i	0.0613229	+	0.188732i
$859$	−1.68881e8	−	1.22699e8i	−0.00909086	−	0.00660490i	0.583231	−	0.812307i	$-0.301788\pi$
$859$	−1.68881e8	−	1.22699e8i	−0.00909086	−	0.00660490i	−0.592321	+	0.805702i	$0.701788\pi$
$860$	−4.30612e9	−	3.12858e9i	−0.230856	−	0.167727i
$861$	4.67181e10	−	3.39427e10i	2.49445	−	1.81232i
$862$	−4.22700e9			−0.224779
$863$	2.65668e10			1.40702			0.703511	−	0.710684i	$-0.251615\pi$
$863$	2.65668e10			1.40702			0.703511	+	0.710684i	$0.251615\pi$
$864$	−9.16569e8	+	6.65926e8i	−0.0483467	+	0.0351260i
$865$	9.84617e9	−	3.03034e10i	0.517262	−	1.59197i
$866$	−1.06595e9	−	3.28065e9i	−0.0557729	−	0.171651i
$867$	−1.69751e10			−0.884597
$868$	1.42485e10	+	8.58669e9i	0.739522	+	0.445663i
$869$	−2.40534e10			−1.24339
$870$	−1.25849e10	−	3.87325e10i	−0.647938	−	1.99415i
$871$	1.74917e8	−	5.38339e8i	0.00896951	−	0.0276053i
$872$	7.39551e9	−	5.37315e9i	0.377712	−	0.274424i
$873$	−1.49698e10			−0.761496
$874$	1.33501e10			0.676383
$875$	−2.08483e10	+	1.51472e10i	−1.05207	+	0.764370i
$876$	7.55500e9	+	5.48903e9i	0.379726	+	0.275887i
$877$	−2.36511e10	−	1.71835e10i	−1.18400	−	0.860229i	−0.191386	−	0.981515i	$-0.561298\pi$
$877$	−2.36511e10	−	1.71835e10i	−1.18400	−	0.860229i	−0.992618	+	0.121286i	$0.961298\pi$
$878$	−2.32697e9	−	7.16169e9i	−0.116027	−	0.357096i
$879$	3.81654e9	−	2.77288e9i	0.189543	−	0.137711i
$880$	2.09891e9	+	6.45978e9i	0.103826	+	0.319542i
$881$	1.49852e9	−	4.61198e9i	0.0738325	−	0.227233i	−0.907329	−	0.420421i	$-0.861883\pi$
$881$	1.49852e9	−	4.61198e9i	0.0738325	−	0.227233i	0.981162	+	0.193187i	$0.0618826\pi$
$882$	−2.83387e10	−	2.05893e10i	−1.39072	−	1.01042i
$883$	4.98566e9	−	1.53443e10i	0.243703	−	0.750040i	−0.752144	−	0.658999i	$-0.770980\pi$
$883$	4.98566e9	−	1.53443e10i	0.243703	−	0.750040i	0.995847	−	0.0910417i	$-0.0290197\pi$
$884$	−3.29567e8	+	1.01430e9i	−0.0160458	+	0.0493838i
$885$	4.37456e10	+	3.17830e10i	2.12145	+	1.54132i
$886$	−2.18900e9	+	6.73703e9i	−0.105737	+	0.325425i
$887$	6.82917e9	+	2.10180e10i	0.328576	+	1.01125i	0.969801	+	0.243899i	$0.0784265\pi$
$887$	6.82917e9	+	2.10180e10i	0.328576	+	1.01125i	−0.641225	+	0.767353i	$0.721573\pi$
$888$	−2.59476e9	+	1.88520e9i	−0.124351	+	0.0903466i
$889$	7.79885e9	+	2.40024e10i	0.372284	+	1.14577i
$890$	−1.54390e10	−	1.12171e10i	−0.734097	−	0.533353i
$891$	1.42548e10	+	1.03567e10i	0.675131	+	0.490511i
$892$	9.98228e9	−	7.25255e9i	0.470926	−	0.342148i
$893$	3.49510e10			1.64240
$894$	1.86324e10			0.872144
$895$	−2.06425e10	+	1.49976e10i	−0.962457	+	0.699266i
$896$	−1.01557e9	+	3.12562e9i	−0.0471665	+	0.145164i
$897$	−1.72592e9	−	5.31185e9i	−0.0798450	−	0.245738i
$898$	−1.42682e10			−0.657510
$899$	−3.70886e10	+	3.19609e9i	−1.70248	+	0.146710i
$900$	4.72732e9			0.216155
$901$	−8.00001e9	−	2.46215e10i	−0.364379	−	1.12144i
$902$	6.65968e9	−	2.04964e10i	0.302156	−	0.929939i
$903$	2.26354e10	−	1.64456e10i	1.02301	−	0.743264i
$904$	−1.02482e10			−0.461380
$905$	−3.95645e10			−1.77434
$906$	−6.76819e9	+	4.91738e9i	−0.302359	+	0.219677i
$907$	1.24561e10	+	9.04989e9i	0.554315	+	0.402733i	0.829374	−	0.558694i	$-0.188697\pi$
$907$	1.24561e10	+	9.04989e9i	0.554315	+	0.402733i	−0.275059	+	0.961427i	$0.588697\pi$
$908$	−5.27577e9	−	3.83307e9i	−0.233876	−	0.169921i
$909$	−3.48810e9	−	1.07353e10i	−0.154033	−	0.474066i
$910$	4.25036e9	−	3.08806e9i	0.186974	−	0.135844i
$911$	3.89439e8	+	1.19857e9i	0.0170657	+	0.0525229i	0.959227	−	0.282638i	$-0.0912094\pi$
$911$	3.89439e8	+	1.19857e9i	0.0170657	+	0.0525229i	−0.942161	+	0.335161i	$0.891209\pi$
$912$	−2.37410e9	+	7.30673e9i	−0.103637	+	0.318963i
$913$	−7.33640e9	−	5.33021e9i	−0.319033	−	0.231791i
$914$	3.61933e9	−	1.11391e10i	0.156789	−	0.482548i
$915$	3.42681e9	−	1.05466e10i	0.147882	−	0.455134i
$916$	6.23404e9	+	4.52930e9i	0.268001	+	0.194714i
$917$	5.30536e9	−	1.63282e10i	0.227207	−	0.699272i
$918$	−1.10482e9	−	3.40027e9i	−0.0471347	−	0.145066i
$919$	−7.58920e9	+	5.51388e9i	−0.322546	+	0.234343i	−0.737261	−	0.675608i	$-0.763881\pi$
$919$	−7.58920e9	+	5.51388e9i	−0.322546	+	0.234343i	0.414715	+	0.909951i	$0.363881\pi$
$920$	−3.19291e9	−	9.82677e9i	−0.135185	−	0.416058i
$921$	4.53047e10	+	3.29158e10i	1.91088	+	1.38834i
$922$	−1.57684e10	−	1.14564e10i	−0.662565	−	0.481382i
$923$	5.49848e8	−	3.99488e8i	0.0230164	−	0.0167224i
$924$	−3.57038e10			−1.48889
$925$	2.47188e9			0.102691
$926$	9.63399e9	−	6.99950e9i	0.398720	−	0.289687i
$927$	7.28226e9	−	2.24125e10i	0.300253	−	0.924083i
$928$	−2.27255e9	−	6.99418e9i	−0.0933459	−	0.287289i
$929$	1.35382e10			0.553996			0.276998	−	0.960870i	$-0.410660\pi$
$929$	1.35382e10			0.553996			0.276998	+	0.960870i	$0.410660\pi$
$930$	6.80908e9	−	2.93188e10i	0.277586	−	1.19524i
$931$	−4.38746e10			−1.78192
$932$	−2.62640e9	−	8.08321e9i	−0.106268	−	0.327061i
$933$	1.41412e10	−	4.35220e10i	0.570032	−	1.75438i
$934$	−7.10776e9	+	5.16409e9i	−0.285442	+	0.207386i
$935$	−2.14344e10			−0.857571
$936$	1.77062e9			0.0705765
$937$	−1.02385e10	+	7.43874e9i	−0.406583	+	0.295400i	−0.772217	−	0.635359i	$-0.780852\pi$
$937$	−1.02385e10	+	7.43874e9i	−0.406583	+	0.295400i	0.365634	+	0.930759i	$0.380852\pi$
$938$	4.45324e9	+	3.23547e9i	0.176184	+	0.128005i
$939$	1.21799e10	+	8.84919e9i	0.480079	+	0.348798i
$940$	−8.35917e9	−	2.57269e10i	−0.328258	−	1.01028i
$941$	−5.17431e9	+	3.75936e9i	−0.202437	+	0.147079i	−0.684385	−	0.729121i	$-0.739929\pi$
$941$	−5.17431e9	+	3.75936e9i	−0.202437	+	0.147079i	0.481948	+	0.876200i	$0.339929\pi$
$942$	3.67865e8	+	1.13217e9i	0.0143387	+	0.0441300i
$943$	−1.01309e10	+	3.11796e10i	−0.393420	+	1.21082i
$944$	7.89944e9	+	5.73928e9i	0.305629	+	0.222052i
$945$	−5.44248e9	+	1.67502e10i	−0.209790	+	0.645668i
$946$	3.22669e9	−	9.93074e9i	0.123919	−	0.381384i
$947$	3.18935e10	+	2.31720e10i	1.22033	+	0.886621i	0.996127	−	0.0879218i	$-0.0280226\pi$
$947$	3.18935e10	+	2.31720e10i	1.22033	+	0.886621i	0.224202	+	0.974543i	$0.428023\pi$
$948$	−6.50706e9	+	2.00267e10i	−0.248059	+	0.763448i
$949$	−8.33028e8	−	2.56380e9i	−0.0316394	−	0.0973760i
$950$	4.79030e9	−	3.48036e9i	0.181272	−	0.131702i
$951$	−1.90854e10	−	5.87388e10i	−0.719564	−	2.21459i
$952$	−8.39048e9	−	6.09604e9i	−0.315179	−	0.228991i
$953$	−2.60308e10	−	1.89125e10i	−0.974233	−	0.707822i	−0.0178207	−	0.999841i	$-0.505673\pi$
$953$	−2.60308e10	−	1.89125e10i	−0.974233	−	0.707822i	−0.956412	+	0.292019i	$0.905673\pi$
$954$	−3.47721e10	+	2.52634e10i	−1.29662	+	0.942047i
$955$	−2.69607e10			−1.00166
$956$	1.58828e10			0.587929
$957$	6.46358e10	−	4.69607e10i	2.38386	−	1.73198i
$958$	4.89231e9	−	1.50570e10i	0.179777	−	0.553298i
$959$	2.82910e10	+	8.70707e10i	1.03582	+	3.18792i
$960$	5.94618e9			0.216915
$961$	−2.46966e10	−	1.21252e10i	−0.897648	−	0.440714i
$962$	9.25846e8			0.0335294
$963$	−1.29258e10	−	3.97816e10i	−0.466408	−	1.43546i
$964$	−4.25791e9	+	1.31045e10i	−0.153083	+	0.471141i
$965$	4.25943e9	−	3.09466e9i	0.152583	−	0.110858i
$966$	5.43135e10			1.93860
$967$	−1.98924e10			−0.707449			−0.353725	−	0.935350i	$-0.615085\pi$
$967$	−1.98924e10			−0.707449			−0.353725	+	0.935350i	$0.615085\pi$
$968$	−2.70801e9	+	1.96748e9i	−0.0959591	+	0.0697183i
$969$	−1.96144e10	−	1.42507e10i	−0.692533	−	0.503155i
$970$	1.17405e10	+	8.52999e9i	0.413034	+	0.300087i
$971$	7.45161e9	+	2.29337e10i	0.261206	+	0.803909i	0.992543	+	0.121893i	$0.0388965\pi$
$971$	7.45161e9	+	2.29337e10i	0.261206	+	0.803909i	−0.731337	+	0.682016i	$0.761104\pi$
$972$	1.63943e10	−	1.19112e10i	0.572613	−	0.416028i
$973$	3.27191e9	+	1.00699e10i	0.113869	+	0.350454i
$974$	−8.18374e9	+	2.51869e10i	−0.283789	+	0.873412i
$975$	−2.00410e9	−	1.45606e9i	−0.0692474	−	0.0503111i
$976$	6.18801e8	−	1.90447e9i	0.0213048	−	0.0655694i
$977$	−1.92142e9	+	5.91354e9i	−0.0659162	+	0.202869i	−0.978590	−	0.205820i	$-0.934014\pi$
$977$	−1.92142e9	+	5.91354e9i	−0.0659162	+	0.202869i	0.912674	+	0.408689i	$0.134014\pi$
$978$	−1.32869e10	−	9.65346e9i	−0.454188	−	0.329987i
$979$	1.15688e10	−	3.56052e10i	0.394049	−	1.21276i
$980$	1.04934e10	+	3.22954e10i	0.356144	+	1.09610i
$981$	3.87466e10	−	2.81510e10i	1.31036	−	0.952034i
$982$	3.16500e9	+	9.74088e9i	0.106656	+	0.328252i
$983$	−2.92341e10	−	2.12398e10i	−0.981641	−	0.713204i	−0.0235663	−	0.999722i	$-0.507502\pi$
$983$	−2.92341e10	−	2.12398e10i	−0.981641	−	0.713204i	−0.958075	+	0.286518i	$0.907502\pi$
$984$	−1.52636e10	−	1.10896e10i	−0.510708	−	0.371051i
$985$	6.23348e9	−	4.52889e9i	0.207828	−	0.150996i
$986$	2.32076e10			0.771012
$987$	1.42195e11			4.70732
$988$	1.79421e9	−	1.30357e9i	0.0591868	−	0.0430017i
$989$	−4.90852e9	+	1.51069e10i	−0.161348	+	0.496578i
$990$	1.09966e10	+	3.38440e10i	0.360193	+	1.10856i
$991$	4.58862e10			1.49770			0.748849	−	0.662741i	$-0.230607\pi$
$991$	4.58862e10			1.49770			0.748849	+	0.662741i	$0.230607\pi$
$992$	1.22956e9	−	5.29430e9i	0.0399907	−	0.172194i
$993$	−1.97001e10			−0.638477
$994$	2.04238e9	+	6.28579e9i	0.0659604	+	0.203005i
$995$	1.37565e10	−	4.23382e10i	0.442719	−	1.36255i
$996$	−6.42259e9	+	4.66628e9i	−0.205969	+	0.149645i
$997$	2.55089e10			0.815188			0.407594	−	0.913163i	$-0.366368\pi$
$997$	2.55089e10			0.815188			0.407594	+	0.913163i	$0.366368\pi$
$998$	−2.47138e10			−0.787015
$999$	−2.51098e9	+	1.82433e9i	−0.0796827	+	0.0578929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.35.10	✓	40
31.8	even	5	inner	62.8.d.a.39.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.35.10	✓	40	1.1	even	1	trivial
62.8.d.a.39.10	yes	40	31.8	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47214 + 7.60845i) q^{2} +(21.5637 - 66.3662i) q^{3} +(-51.7771 + 37.6183i) q^{4} +325.055 q^{5} +558.253 q^{6} +(1267.82 - 921.124i) q^{7} +(-414.217 - 300.946i) q^{8} +(-2170.16 - 1576.72i) q^{9} +(803.581 + 2473.17i) q^{10} +(-4127.16 + 2998.56i) q^{11} +(1380.08 + 4247.44i) q^{12} +(398.385 - 1226.10i) q^{13} +(10142.5 + 7368.99i) q^{14} +(7009.39 - 21572.7i) q^{15} +(1265.73 - 3895.53i) q^{16} +(10457.2 + 7597.64i) q^{17} +(6631.43 - 20409.4i) q^{18} +(-8306.12 - 25563.6i) q^{19} +(-16830.4 + 12228.0i) q^{20} +(-33792.7 - 104003. i) q^{21} +(-33017.3 - 23988.5i) q^{22} +(50226.7 + 36491.9i) q^{23} +(-28904.7 + 21000.5i) q^{24} +27535.9 q^{25} +10313.6 q^{26} +(-27971.5 + 20322.5i) q^{27} +(-30992.9 + 95386.2i) q^{28} +(-69352.7 - 213446. i) q^{29} +181463. q^{30} +(37523.2 - 161569. i) q^{31} +32768.0 q^{32} +(110006. + 338564. i) q^{33} +(-31954.5 + 98345.9i) q^{34} +(412111. - 299416. i) q^{35} +171678. q^{36} +89769.3 q^{37} +(173966. - 126393. i) q^{38} +(-72781.2 - 52878.7i) q^{39} +(-134643. - 97824.1i) q^{40} +(163181. + 502220. i) q^{41} +(707763. - 514220. i) q^{42} +(79063.0 + 243331. i) q^{43} +(100892. - 310513. i) q^{44} +(-705423. - 512520. i) q^{45} +(-153479. + 472361. i) q^{46} +(-401815. + 1.23666e6i) q^{47} +(-231238. - 168004. i) q^{48} +(504405. - 1.55240e6i) q^{49} +(68072.6 + 209506. i) q^{50} +(729723. - 530175. i) q^{51} +(25496.7 + 78470.7i) q^{52} +(-1.62034e6 - 1.17725e6i) q^{53} +(-223772. - 162580. i) q^{54} +(-1.34156e6 + 974698. i) q^{55} -802360. q^{56} -1.87567e6 q^{57} +(1.45254e6 - 1.05533e6i) q^{58} +(-736650. + 2.26718e6i) q^{59} +(448601. + 1.38065e6i) q^{60} +488888. q^{61} +(1.32205e6 - 113927. i) q^{62} -4.20372e6 q^{63} +(81007.0 + 249314. i) q^{64} +(129497. - 398552. i) q^{65} +(-2.30400e6 + 1.67395e6i) q^{66} +439065. q^{67} -827256. q^{68} +(3.50490e6 - 2.54646e6i) q^{69} +(3.29689e6 + 2.39533e6i) q^{70} +(426503. + 309872. i) q^{71} +(424411. + 1.30620e6i) q^{72} +(1.69166e6 - 1.22907e6i) q^{73} +(221922. + 683006. i) q^{74} +(593777. - 1.82746e6i) q^{75} +(1.39172e6 + 1.01115e6i) q^{76} +(-2.47045e6 + 7.60326e6i) q^{77} +(222400. - 684476. i) q^{78} +(3.81452e6 + 2.77141e6i) q^{79} +(411433. - 1.26626e6i) q^{80} +(-1.06731e6 - 3.28484e6i) q^{81} +(-3.41771e6 + 2.48311e6i) q^{82} +(549305. + 1.69059e6i) q^{83} +(5.66210e6 + 4.11376e6i) q^{84} +(3.39918e6 + 2.46965e6i) q^{85} +(-1.65592e6 + 1.20309e6i) q^{86} -1.56611e7 q^{87} +2.61194e6 q^{88} +(-5.93706e6 + 4.31353e6i) q^{89} +(2.15558e6 - 6.63420e6i) q^{90} +(-624314. - 1.92144e6i) q^{91} -3.97335e6 q^{92} +(-9.91360e6 - 5.97430e6i) q^{93} -1.04024e7 q^{94} +(-2.69995e6 - 8.30958e6i) q^{95} +(706599. - 2.17469e6i) q^{96} +(4.51482e6 - 3.28021e6i) q^{97} +1.30583e7 q^{98} +1.36845e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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