LMFDB - Embedded newform 62.6.g.b.45.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,56] 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:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			45.2
Character	$\chi$	$=$	62.45
Dual form			62.6.g.b.51.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23607 + 3.80423i) q^{2} +(-13.6729 + 15.1853i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-44.8065 + 77.6071i) q^{5} +(-40.8678 - 70.7851i) q^{6} +(-13.8993 + 132.243i) q^{7} +(51.7771 - 37.6183i) q^{8} +(-18.2448 - 173.588i) q^{9} +(-239.851 - 266.381i) q^{10} +(-94.8210 + 42.2170i) q^{11} +(319.798 - 67.9751i) q^{12} +(234.028 + 49.7441i) q^{13} +(-485.901 - 216.337i) q^{14} +(-565.854 - 1741.52i) q^{15} +(79.1084 + 243.470i) q^{16} +(647.019 + 288.072i) q^{17} +(682.919 + 145.159i) q^{18} +(1094.65 - 232.675i) q^{19} +(1309.85 - 583.182i) q^{20} +(-1818.11 - 2019.21i) q^{21} +(-43.3979 - 412.904i) q^{22} +(1599.39 - 1162.02i) q^{23} +(-136.699 + 1300.61i) q^{24} +(-2452.74 - 4248.26i) q^{25} +(-478.512 + 828.807i) q^{26} +(-1131.67 - 822.208i) q^{27} +(1423.60 - 1581.07i) q^{28} +(-2473.85 + 7613.73i) q^{29} +7324.56 q^{30} +(1736.29 + 5061.07i) q^{31} -1024.00 q^{32} +(655.402 - 2017.12i) q^{33} +(-1895.65 + 2105.33i) q^{34} +(-9640.19 - 7004.01i) q^{35} +(-1396.35 + 2418.55i) q^{36} +(-6657.66 - 11531.4i) q^{37} +(-467.914 + 4451.90i) q^{38} +(-3955.23 + 2873.64i) q^{39} +(599.494 + 5703.81i) q^{40} +(11066.0 + 12290.1i) q^{41} +(9928.85 - 4420.61i) q^{42} +(-10595.4 + 2252.11i) q^{43} +(1624.42 + 345.281i) q^{44} +(14289.1 + 6361.93i) q^{45} +(2443.65 + 7520.78i) q^{46} +(386.529 + 1189.61i) q^{47} +(-4778.83 - 2127.67i) q^{48} +(-855.234 - 181.786i) q^{49} +(19193.1 - 4079.62i) q^{50} +(-13221.1 + 5886.42i) q^{51} +(-2561.50 - 2844.83i) q^{52} +(2595.60 + 24695.5i) q^{53} +(4526.69 - 3288.83i) q^{54} +(972.253 - 9250.37i) q^{55} +(4255.08 + 7370.01i) q^{56} +(-11433.9 + 19804.0i) q^{57} +(-25906.5 - 18822.2i) q^{58} +(2319.07 - 2575.59i) q^{59} +(-9053.66 + 27864.3i) q^{60} -30830.5 q^{61} +(-21399.6 + 349.426i) q^{62} +23209.3 q^{63} +(1265.73 - 3895.53i) q^{64} +(-14346.4 + 15933.3i) q^{65} +(6863.46 + 4986.59i) q^{66} +(32486.6 - 56268.5i) q^{67} +(-5666.01 - 9813.81i) q^{68} +(-4222.62 + 40175.6i) q^{69} +(38560.8 - 28016.0i) q^{70} +(-6286.16 - 59808.8i) q^{71} +(-7474.73 - 8301.53i) q^{72} +(45592.4 - 20299.0i) q^{73} +(52097.4 - 11073.6i) q^{74} +(98047.5 + 20840.6i) q^{75} +(-16357.7 - 7282.91i) q^{76} +(-4264.95 - 13126.2i) q^{77} +(-6043.05 - 18598.6i) q^{78} +(-35815.3 - 15946.0i) q^{79} +(-22439.6 - 4769.68i) q^{80} +(69446.1 - 14761.2i) q^{81} +(-60432.5 + 26906.3i) q^{82} +(-43617.1 - 48441.7i) q^{83} +(4544.26 + 43235.8i) q^{84} +(-51347.0 + 37305.8i) q^{85} +(4529.04 - 43090.9i) q^{86} +(-81792.2 - 141668. i) q^{87} +(-3321.42 + 5752.87i) q^{88} +(22848.2 + 16600.2i) q^{89} +(-41864.5 + 46495.3i) q^{90} +(-9831.12 + 30257.1i) q^{91} -31631.3 q^{92} +(-100594. - 42833.5i) q^{93} -5003.34 q^{94} +(-30990.2 + 95378.0i) q^{95} +(14001.1 - 15549.8i) q^{96} +(53517.4 + 38882.7i) q^{97} +(1748.68 - 3028.80i) q^{98} +(9058.35 + 15689.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) $ 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$	−13.6729	+	15.1853i	−0.877120	+	0.974140i	−0.999833	−	0.0183021i	$-0.994174\pi$
$3$	−13.6729	+	15.1853i	−0.877120	+	0.974140i	0.122713	+	0.992442i	$0.460841\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−44.8065	+	77.6071i	−0.801522	+	1.38828i	0.117092	+	0.993121i	$0.462643\pi$
$5$	−44.8065	+	77.6071i	−0.801522	+	1.38828i	−0.918614	+	0.395156i	$0.870691\pi$
$6$	−40.8678	−	70.7851i	−0.463450	−	0.802719i
$7$	−13.8993	+	132.243i	−0.107213	+	1.02006i	0.800174	+	0.599767i	$0.204740\pi$
$7$	−13.8993	+	132.243i	−0.107213	+	1.02006i	−0.907387	+	0.420295i	$0.861926\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	−18.2448	−	173.588i	−0.0750815	−	0.714353i
$10$	−239.851	−	266.381i	−0.758475	−	0.842372i
$11$	−94.8210	+	42.2170i	−0.236278	+	0.105198i	−0.521460	−	0.853276i	$-0.674612\pi$
$11$	−94.8210	+	42.2170i	−0.236278	+	0.105198i	0.285182	+	0.958473i	$0.407946\pi$
$12$	319.798	−	67.9751i	0.641095	−	0.136269i
$13$	234.028	+	49.7441i	0.384069	+	0.0816363i	0.395900	−	0.918294i	$-0.370433\pi$
$13$	234.028	+	49.7441i	0.384069	+	0.0816363i	−0.0118312	+	0.999930i	$0.503766\pi$
$14$	−485.901	−	216.337i	−0.662564	−	0.294992i
$15$	−565.854	−	1741.52i	−0.649346	−	1.99848i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	647.019	+	288.072i	0.542994	+	0.241757i	0.659857	−	0.751392i	$-0.270617\pi$
$17$	647.019	+	288.072i	0.542994	+	0.241757i	−0.116863	+	0.993148i	$0.537284\pi$
$18$	682.919	+	145.159i	0.496807	+	0.105600i
$19$	1094.65	−	232.675i	0.695652	−	0.147865i	0.153503	−	0.988148i	$-0.450944\pi$
$19$	1094.65	−	232.675i	0.695652	−	0.147865i	0.542148	+	0.840283i	$0.317611\pi$
$20$	1309.85	−	583.182i	0.732227	−	0.326008i
$21$	−1818.11	−	2019.21i	−0.899645	−	0.999157i
$22$	−43.3979	−	412.904i	−0.0191167	−	0.181883i
$23$	1599.39	−	1162.02i	0.630427	−	0.458032i	−0.226121	−	0.974099i	$-0.572605\pi$
$23$	1599.39	−	1162.02i	0.630427	−	0.458032i	0.856548	+	0.516067i	$0.172605\pi$
$24$	−136.699	+	1300.61i	−0.0484437	+	0.460911i
$25$	−2452.74	−	4248.26i	−0.784876	−	1.35944i
$26$	−478.512	+	828.807i	−0.138822	+	0.240447i
$27$	−1131.67	−	822.208i	−0.298752	−	0.217056i
$28$	1423.60	−	1581.07i	0.343157	−	0.381115i
$29$	−2473.85	+	7613.73i	−0.546234	+	1.68113i	0.171805	+	0.985131i	$0.445040\pi$
$29$	−2473.85	+	7613.73i	−0.546234	+	1.68113i	−0.718039	+	0.696003i	$0.754960\pi$
$30$	7324.56			1.48586
$31$	1736.29	+	5061.07i	0.324503	+	0.945885i
$31$	1736.29	+	5061.07i	0.324503	+	0.945885i
$32$	−1024.00			−0.176777
$33$	655.402	−	2017.12i	0.104767	−	0.322438i
$34$	−1895.65	+	2105.33i	−0.281229	+	0.312337i
$35$	−9640.19	−	7004.01i	−1.33020	−	0.966444i
$36$	−1396.35	+	2418.55i	−0.179572	+	0.311028i
$37$	−6657.66	−	11531.4i	−0.799498	−	1.38477i	−0.919943	−	0.392052i	$-0.871765\pi$
$37$	−6657.66	−	11531.4i	−0.799498	−	1.38477i	0.120445	−	0.992720i	$-0.461568\pi$
$38$	−467.914	+	4451.90i	−0.0525663	+	0.500135i
$39$	−3955.23	+	2873.64i	−0.416399	+	0.302532i
$40$	599.494	+	5703.81i	0.0592427	+	0.563657i
$41$	11066.0	+	12290.1i	1.02809	+	1.14181i	0.989788	+	0.142546i	$0.0455288\pi$
$41$	11066.0	+	12290.1i	1.02809	+	1.14181i	0.0383037	+	0.999266i	$0.487805\pi$
$42$	9928.85	−	4420.61i	0.868512	−	0.386686i
$43$	−10595.4	+	2252.11i	−0.873865	+	0.185746i	−0.622948	−	0.782263i	$-0.714065\pi$
$43$	−10595.4	+	2252.11i	−0.873865	+	0.185746i	−0.250917	+	0.968009i	$0.580732\pi$
$44$	1624.42	+	345.281i	0.126493	+	0.0268869i
$45$	14289.1	+	6361.93i	1.05190	+	0.468336i
$46$	2443.65	+	7520.78i	0.170272	+	0.524045i
$47$	386.529	+	1189.61i	0.0255233	+	0.0785528i	0.963007	−	0.269477i	$-0.0868508\pi$
$47$	386.529	+	1189.61i	0.0255233	+	0.0785528i	−0.937483	+	0.348030i	$0.886851\pi$
$48$	−4778.83	−	2127.67i	−0.299377	−	0.133291i
$49$	−855.234	−	181.786i	−0.0508856	−	0.0108161i
$50$	19193.1	−	4079.62i	1.08573	−	0.230778i
$51$	−13221.1	+	5886.42i	−0.711775	+	0.316903i
$52$	−2561.50	−	2844.83i	−0.131367	−	0.145898i
$53$	2595.60	+	24695.5i	0.126925	+	1.20761i	0.853710	+	0.520749i	$0.174347\pi$
$53$	2595.60	+	24695.5i	0.126925	+	1.20761i	−0.726784	+	0.686866i	$0.758986\pi$
$54$	4526.69	−	3288.83i	0.211250	−	0.153482i
$55$	972.253	−	9250.37i	0.0433384	−	0.412337i
$56$	4255.08	+	7370.01i	0.181317	+	0.314050i
$57$	−11433.9	+	19804.0i	−0.466128	+	0.807358i
$58$	−25906.5	−	18822.2i	−1.01120	−	0.734683i
$59$	2319.07	−	2575.59i	0.0867330	−	0.0963267i	−0.698216	−	0.715887i	$-0.746022\pi$
$59$	2319.07	−	2575.59i	0.0867330	−	0.0963267i	0.784949	+	0.619560i	$0.212689\pi$
$60$	−9053.66	+	27864.3i	−0.324673	+	0.999240i
$61$	−30830.5			−1.06086			−0.530428	−	0.847730i	$-0.677969\pi$
$61$	−30830.5			−1.06086			−0.530428	+	0.847730i	$0.677969\pi$
$62$	−21399.6	+	349.426i	−0.707013	+	0.0115445i
$63$	23209.3			0.736735
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−14346.4	+	15933.3i	−0.421173	+	0.467760i
$66$	6863.46	+	4986.59i	0.193947	+	0.140911i
$67$	32486.6	−	56268.5i	0.884133	−	1.53136i	0.0374299	−	0.999299i	$-0.488083\pi$
$67$	32486.6	−	56268.5i	0.884133	−	1.53136i	0.846704	−	0.532065i	$-0.178584\pi$
$68$	−5666.01	−	9813.81i	−0.148595	−	0.257374i
$69$	−4222.62	+	40175.6i	−0.106773	+	1.01587i
$70$	38560.8	−	28016.0i	0.940591	−	0.683379i
$71$	−6286.16	−	59808.8i	−0.147992	−	1.40805i	−0.776435	−	0.630198i	$-0.782974\pi$
$71$	−6286.16	−	59808.8i	−0.147992	−	1.40805i	0.628442	−	0.777856i	$-0.283693\pi$
$72$	−7474.73	−	8301.53i	−0.169928	−	0.188724i
$73$	45592.4	−	20299.0i	1.00135	−	0.445829i	0.160463	−	0.987042i	$-0.448701\pi$
$73$	45592.4	−	20299.0i	1.00135	−	0.445829i	0.840886	+	0.541213i	$0.182035\pi$
$74$	52097.4	−	11073.6i	1.10595	−	0.235078i
$75$	98047.5	+	20840.6i	2.01272	+	0.427817i
$76$	−16357.7	−	7282.91i	−0.324854	−	0.144634i
$77$	−4264.95	−	13126.2i	−0.0819761	−	0.252297i
$78$	−6043.05	−	18598.6i	−0.112466	−	0.346134i
$79$	−35815.3	−	15946.0i	−0.645656	−	0.287465i	0.0576658	−	0.998336i	$-0.481634\pi$
$79$	−35815.3	−	15946.0i	−0.645656	−	0.287465i	−0.703322	+	0.710871i	$0.748301\pi$
$80$	−22439.6	−	4769.68i	−0.392004	−	0.0833229i
$81$	69446.1	−	14761.2i	1.17608	−	0.249983i
$82$	−60432.5	+	26906.3i	−0.992513	+	0.441895i
$83$	−43617.1	−	48441.7i	−0.694963	−	0.771834i	0.287603	−	0.957750i	$-0.407142\pi$
$83$	−43617.1	−	48441.7i	−0.694963	−	0.771834i	−0.982566	+	0.185915i	$0.940475\pi$
$84$	4544.26	+	43235.8i	0.0702692	+	0.668567i
$85$	−51347.0	+	37305.8i	−0.770847	+	0.560053i
$86$	4529.04	−	43090.9i	0.0660328	−	0.628260i
$87$	−81792.2	−	141668.i	−1.15855	−	2.00666i
$88$	−3321.42	+	5752.87i	−0.0457212	+	0.0791914i
$89$	22848.2	+	16600.2i	0.305757	+	0.222145i	0.730074	−	0.683368i	$-0.239486\pi$
$89$	22848.2	+	16600.2i	0.305757	+	0.222145i	−0.424317	+	0.905514i	$0.639486\pi$
$90$	−41864.5	+	46495.3i	−0.544804	+	0.605066i
$91$	−9831.12	+	30257.1i	−0.124451	+	0.383022i
$92$	−31631.3			−0.389625
$93$	−100594.	−	42833.5i	−1.20605	−	0.513542i
$94$	−5003.34			−0.0584037
$95$	−30990.2	+	95378.0i	−0.352302	+	1.08427i
$96$	14001.1	−	15549.8i	0.155054	−	0.172205i
$97$	53517.4	+	38882.7i	0.577518	+	0.419591i	0.837828	−	0.545934i	$-0.183825\pi$
$97$	53517.4	+	38882.7i	0.577518	+	0.419591i	−0.260310	+	0.965525i	$0.583825\pi$
$98$	1748.68	−	3028.80i	0.0183927	−	0.0318571i
$99$	9058.35	+	15689.5i	0.0928883	+	0.160887i
$100$	−8204.18	+	78057.6i	−0.0820418	+	0.780576i
$101$	−30729.8	+	22326.5i	−0.299748	+	0.217779i	−0.727485	−	0.686124i	$-0.759311\pi$
$101$	−30729.8	+	22326.5i	−0.299748	+	0.217779i	0.427737	+	0.903903i	$0.359311\pi$
$102$	−6051.08	−	57572.2i	−0.0575881	−	0.547914i
$103$	−88002.3	−	97736.5i	−0.817337	−	0.907744i	0.179774	−	0.983708i	$-0.442463\pi$
$103$	−88002.3	−	97736.5i	−0.817337	−	0.907744i	−0.997111	+	0.0759635i	$0.975797\pi$
$104$	13988.6	−	6228.11i	0.126821	−	0.0564642i
$105$	238168.	−	50624.2i	2.10819	−	0.448110i
$106$	−97155.7	−	20651.1i	−0.839853	−	0.178516i
$107$	129288.	+	57562.7i	1.09169	+	0.486051i	0.871994	−	0.489517i	$-0.162827\pi$
$107$	129288.	+	57562.7i	1.09169	+	0.486051i	0.219695	+	0.975569i	$0.429494\pi$
$108$	6916.16	+	21285.8i	0.0570566	+	0.175602i
$109$	42336.8	+	130299.i	0.341312	+	1.05045i	0.963529	+	0.267605i	$0.0862324\pi$
$109$	42336.8	+	130299.i	0.341312	+	1.05045i	−0.622216	+	0.782845i	$0.713768\pi$
$110$	33988.7	+	15132.8i	0.267826	+	0.119244i
$111$	266138.	+	56569.4i	2.05022	+	0.435787i
$112$	−33296.8	+	7077.44i	−0.250817	+	0.0533128i
$113$	62000.9	−	27604.6i	0.456774	−	0.203369i	−0.165434	−	0.986221i	$-0.552902\pi$
$113$	62000.9	−	27604.6i	0.456774	−	0.203369i	0.622208	+	0.782852i	$0.286236\pi$
$114$	−61205.9	−	67976.1i	−0.441094	−	0.489885i
$115$	18518.3	+	176190.i	0.130574	+	1.24233i
$116$	103626.	−	75288.7i	0.715029	−	0.519499i
$117$	4365.18	−	41531.9i	0.0294807	−	0.280490i
$118$	6931.60	+	12005.9i	0.0458277	+	0.0793759i
$119$	−47088.5	+	81559.7i	−0.304823	+	0.527968i
$120$	−94811.1	−	68884.3i	−0.601044	−	0.436684i
$121$	−100555.	+	111678.i	−0.624370	+	0.693433i
$122$	38108.6	−	117286.i	0.231805	−	0.713424i
$123$	−337934.			−2.01404
$124$	25122.1	−	81841.0i	0.146724	−	0.477987i
$125$	159553.			0.913337
$126$	−28688.3	+	88293.5i	−0.160982	+	0.495453i
$127$	−190975.	+	212100.i	−1.05067	+	1.16689i	−0.0650600	+	0.997881i	$0.520724\pi$
$127$	−190975.	+	212100.i	−1.05067	+	1.16689i	−0.985614	+	0.169011i	$0.945943\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	110671.	−	191687.i	0.585542	−	1.01419i
$130$	−42880.9	−	74271.8i	−0.222538	−	0.385448i
$131$	−17766.4	+	169036.i	−0.0904524	+	0.860597i	0.851388	+	0.524537i	$0.175761\pi$
$131$	−17766.4	+	169036.i	−0.0904524	+	0.860597i	−0.941840	+	0.336061i	$0.890905\pi$
$132$	−27453.8	+	19946.4i	−0.137141	+	0.0996390i
$133$	15554.8	+	147994.i	0.0762491	+	0.725461i
$134$	173902.	+	193138.i	0.836650	+	0.929194i
$135$	114515.	−	50985.5i	0.540791	−	0.240776i
$136$	44337.5	−	9424.23i	0.205553	−	0.0436917i
$137$	100052.	+	21266.7i	0.455432	+	0.0968050i	0.429915	−	0.902869i	$-0.358544\pi$
$137$	100052.	+	21266.7i	0.455432	+	0.0968050i	0.0255169	+	0.999674i	$0.491877\pi$
$138$	−147618.	−	65723.6i	−0.659842	−	0.293781i
$139$	−81274.3	−	250137.i	−0.356793	−	1.09810i	−0.954963	−	0.296726i	$-0.904105\pi$
$139$	−81274.3	−	250137.i	−0.356793	−	1.09810i	0.598169	−	0.801370i	$-0.295895\pi$
$140$	58915.6	+	181324.i	0.254045	+	0.781870i
$141$	−23349.7	−	10396.0i	−0.0989084	−	0.0440369i
$142$	235296.	+	50013.8i	0.979252	+	0.208146i
$143$	−24290.8	+	5163.17i	−0.0993348	+	0.0211143i
$144$	40820.2	−	18174.3i	0.164047	−	0.0730385i
$145$	−480035.	−	533132.i	−1.89606	−	2.10579i
$146$	20866.8	+	198535.i	0.0810167	+	0.770823i
$147$	14454.0	−	10501.5i	0.0551691	−	0.0400827i
$148$	−22269.3	+	211878.i	−0.0835703	+	0.795119i
$149$	254744.	+	441229.i	0.940022	+	1.62817i	0.765425	+	0.643526i	$0.222529\pi$
$149$	254744.	+	441229.i	0.940022	+	1.62817i	0.174597	+	0.984640i	$0.444138\pi$
$150$	−200476.	+	347234.i	−0.727501	+	1.26007i
$151$	−201428.	−	146346.i	−0.718917	−	0.522323i	0.167121	−	0.985936i	$-0.446553\pi$
$151$	−201428.	−	146346.i	−0.718917	−	0.522323i	−0.886038	+	0.463613i	$0.846553\pi$
$152$	47925.0	−	53226.1i	0.168249	−	0.186860i
$153$	38201.0	−	117570.i	0.131931	−	0.406041i
$154$	55206.7			0.187582
$155$	−470572.	−	92020.0i	−1.57325	−	0.307647i
$156$	78222.9			0.257349
$157$	122013.	−	375517.i	0.395054	−	1.21585i	−0.533865	−	0.845570i	$-0.679261\pi$
$157$	122013.	−	375517.i	0.395054	−	1.21585i	0.928919	−	0.370283i	$-0.120739\pi$
$158$	104932.	−	116539.i	0.334401	−	0.371390i
$159$	−410499.	−	298245.i	−1.28771	−	0.935580i
$160$	45881.8	−	79469.6i	0.141690	−	0.245415i
$161$	131439.	+	227659.i	0.399631	+	0.692182i
$162$	−29685.1	+	282435.i	−0.0888691	+	0.845533i
$163$	−362487.	+	263362.i	−1.06862	+	0.776398i	−0.975664	−	0.219272i	$-0.929632\pi$
$163$	−362487.	+	263362.i	−1.06862	+	0.776398i	−0.0929569	+	0.995670i	$0.529632\pi$
$164$	−27658.9	−	263157.i	−0.0803019	−	0.764021i
$165$	127176.	+	141244.i	0.363661	+	0.403887i
$166$	238197.	−	106052.i	0.670912	−	0.298709i
$167$	396741.	−	84329.8i	1.10082	−	0.233986i	0.378537	−	0.925586i	$-0.376427\pi$
$167$	396741.	−	84329.8i	1.10082	−	0.233986i	0.722281	+	0.691600i	$0.243094\pi$
$168$	−170096.	−	36154.9i	−0.464965	−	0.0988313i
$169$	−286899.	−	127735.i	−0.772701	−	0.344029i
$170$	−78451.3	−	241448.i	−0.208199	−	0.640769i
$171$	−60361.3	−	185773.i	−0.157859	−	0.485839i
$172$	158329.	+	70492.7i	0.408075	+	0.181687i
$173$	−494554.	−	105121.i	−1.25632	−	0.267038i	−0.468784	−	0.883313i	$-0.655308\pi$
$173$	−494554.	−	105121.i	−1.25632	−	0.267038i	−0.787531	+	0.616275i	$0.788641\pi$
$174$	640039.	−	136045.i	1.60263	−	0.340650i
$175$	595893.	−	265309.i	1.47087	−	0.654872i
$176$	−17779.7	−	19746.4i	−0.0432657	−	0.0480514i
$177$	7402.68	+	70431.8i	0.0177605	+	0.168980i
$178$	−91392.6	+	66400.6i	−0.216203	+	0.157080i
$179$	34377.1	−	327077.i	0.0801931	−	0.762987i	−0.878346	−	0.478026i	$-0.841353\pi$
$179$	34377.1	−	327077.i	0.0801931	−	0.762987i	0.958539	−	0.284961i	$-0.0919807\pi$
$180$	−125131.	−	216733.i	−0.287862	−	0.498591i
$181$	−285187.	+	493958.i	−0.647042	+	1.12071i	0.336783	+	0.941582i	$0.390661\pi$
$181$	−285187.	+	493958.i	−0.647042	+	1.12071i	−0.983826	+	0.179128i	$0.942672\pi$
$182$	−102953.	−	74799.6i	−0.230388	−	0.167387i
$183$	421544.	−	468172.i	0.930497	−	1.03342i
$184$	39098.4	−	120333.i	0.0851362	−	0.262022i
$185$	1.19323e6			2.56326
$186$	287290.	−	329738.i	0.608889	−	0.698855i
$187$	−73512.5			−0.153730
$188$	6184.47	−	19033.8i	0.0127617	−	0.0392764i
$189$	124460.	−	138227.i	0.253441	−	0.281475i
$190$	−324534.	−	235787.i	−0.652192	−	0.473845i
$191$	226198.	−	391786.i	0.448647	−	0.777079i	−0.549651	−	0.835394i	$-0.685239\pi$
$191$	226198.	−	391786.i	0.448647	−	0.777079i	0.998298	+	0.0583148i	$0.0185727\pi$
$192$	41848.6	+	72483.9i	0.0819272	+	0.141902i
$193$	−44399.8	+	422435.i	−0.0858000	+	0.816333i	0.864004	+	0.503486i	$0.167949\pi$
$193$	−44399.8	+	422435.i	−0.0858000	+	0.816333i	−0.949804	+	0.312847i	$0.898717\pi$
$194$	−214070.	+	155531.i	−0.408367	+	0.296696i
$195$	−45795.1	−	435711.i	−0.0862447	−	0.820564i
$196$	9360.77	+	10396.2i	0.0174049	+	0.0193301i
$197$	−368670.	+	164143.i	−0.676819	+	0.301339i	−0.716210	−	0.697885i	$-0.754125\pi$
$197$	−368670.	+	164143.i	−0.676819	+	0.301339i	0.0393911	+	0.999224i	$0.487458\pi$
$198$	−70883.2	+	15066.7i	−0.128493	+	0.0273121i
$199$	545088.	+	115862.i	0.975739	+	0.207400i	0.668074	−	0.744095i	$-0.267119\pi$
$199$	545088.	+	115862.i	0.975739	+	0.207400i	0.307665	+	0.951495i	$0.400452\pi$
$200$	−286808.	−	127695.i	−0.507009	−	0.225735i
$201$	410269.	+	1.26268e6i	0.716272	+	2.20446i
$202$	−46950.9	−	144500.i	−0.0809591	−	0.249166i
$203$	−972476.	−	432974.i	−1.65630	−	0.737432i
$204$	226497.	+	48143.4i	0.381055	+	0.0809957i
$205$	−1.44962e6	+	308127.i	−2.40919	+	0.512089i
$206$	480589.	−	213972.i	0.789051	−	0.351308i
$207$	−230894.	−	256434.i	−0.374530	−	0.415958i
$208$	6402.32	+	60914.0i	0.0102607	+	0.0976245i
$209$	−93973.1	+	68275.4i	−0.148812	+	0.108118i
$210$	−101806.	+	968620.i	−0.159304	+	1.51567i
$211$	181534.	+	314426.i	0.280706	+	0.486198i	0.971559	−	0.236798i	$-0.0760980\pi$
$211$	181534.	+	314426.i	0.280706	+	0.486198i	−0.690853	+	0.722996i	$0.742765\pi$
$212$	198652.	−	344076.i	0.303567	−	0.525793i
$213$	994167.	+	722305.i	1.50145	+	1.09087i
$214$	−378790.	+	420689.i	−0.565411	+	0.627953i
$215$	299960.	−	923183.i	0.442556	−	1.36205i
$216$	−89524.7			−0.130560
$217$	−693423.	+	159267.i	−0.999652	+	0.229603i
$218$	−548019.			−0.781006
$219$	−315134.	+	969884.i	−0.444003	+	1.36650i
$220$	−99580.8	+	110596.i	−0.138714	+	0.154057i
$221$	137091.	+	99602.2i	0.188811	+	0.137179i
$222$	−544168.	+	942526.i	−0.741055	+	1.28355i
$223$	47715.9	+	82646.4i	0.0642542	+	0.111291i	0.896363	−	0.443321i	$-0.146200\pi$
$223$	47715.9	+	82646.4i	0.0642542	+	0.111291i	−0.832109	+	0.554613i	$0.812866\pi$
$224$	14232.9	−	135417.i	0.0189527	−	0.180323i
$225$	−692697.	+	503274.i	−0.912194	+	0.662747i
$226$	28376.7	+	269986.i	0.0369565	+	0.351618i
$227$	51004.4	+	56646.2i	0.0656967	+	0.0729635i	0.775097	−	0.631842i	$-0.217701\pi$
$227$	51004.4	+	56646.2i	0.0656967	+	0.0729635i	−0.709400	+	0.704806i	$0.751034\pi$
$228$	334251.	−	148818.i	0.425829	−	0.189591i
$229$	891655.	−	189527.i	1.12359	−	0.238827i	0.391596	−	0.920137i	$-0.371923\pi$
$229$	891655.	−	189527.i	1.12359	−	0.238827i	0.731994	+	0.681311i	$0.238590\pi$
$230$	−693157.	−	147335.i	−0.863997	−	0.183648i
$231$	257640.	+	114709.i	0.317675	+	0.141438i
$232$	158326.	+	487279.i	0.193123	+	0.594371i
$233$	39031.8	+	120128.i	0.0471009	+	0.144962i	0.971841	−	0.235637i	$-0.0757178\pi$
$233$	39031.8	+	120128.i	0.0471009	+	0.144962i	−0.924740	+	0.380599i	$0.875718\pi$
$234$	152601.	+	67942.4i	0.182187	+	0.0811150i
$235$	−109641.	−	23305.0i	−0.129511	−	0.0275283i
$236$	−54241.0	+	11529.3i	−0.0633939	+	0.0134748i
$237$	731847.	−	325839.i	0.846349	−	0.376819i
$238$	−252067.	−	279949.i	−0.288452	−	0.320358i
$239$	−28002.0	−	266422.i	−0.0317099	−	0.301700i	−0.998870	−	0.0475308i	$-0.984865\pi$
$239$	−28002.0	−	266422.i	−0.0317099	−	0.301700i	0.967160	−	0.254169i	$-0.0818019\pi$
$240$	379244.	−	275537.i	0.425002	−	0.308782i
$241$	22521.0	−	214273.i	0.0249773	−	0.237643i	−0.974910	−	0.222601i	$-0.928545\pi$
$241$	22521.0	−	214273.i	0.0249773	−	0.237643i	0.999887	−	0.0150418i	$-0.00478812\pi$
$242$	−300555.	−	520577.i	−0.329903	−	0.571409i
$243$	−555421.	+	962018.i	−0.603402	+	1.04512i
$244$	399079.	+	289948.i	0.429125	+	0.311778i
$245$	52427.9	−	58227.0i	0.0558016	−	0.0619740i
$246$	417709.	−	1.28558e6i	0.440085	−	1.35444i
$247$	267753.			0.279249
$248$	280289.	+	196731.i	0.289385	+	0.203116i
$249$	1.33198e6			1.36144
$250$	−197219.	+	606977.i	−0.199571	+	0.614218i
$251$	−651897.	+	724005.i	−0.653123	+	0.725366i	−0.975195	−	0.221349i	$-0.928954\pi$
$251$	−651897.	+	724005.i	−0.653123	+	0.725366i	0.322072	+	0.946715i	$0.395621\pi$
$252$	−300428.	−	218274.i	−0.298015	−	0.216521i
$253$	−102598.	+	177706.i	−0.100772	+	0.174542i
$254$	−570816.	−	988683.i	−0.555152	−	0.961552i
$255$	135564.	−	1.28980e6i	0.130555	−	1.24215i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−140568.	−	1.33741e6i	−0.132756	−	1.26308i	−0.834641	−	0.550795i	$-0.814325\pi$
$257$	−140568.	−	1.33741e6i	−0.132756	−	1.26308i	0.701885	−	0.712290i	$-0.252342\pi$
$258$	592425.	+	657954.i	0.554095	+	0.615384i
$259$	1.61748e6	−	720150.i	1.49827	−	0.667073i
$260$	335550.	−	71323.4i	0.307840	−	0.0654333i
$261$	1.36679e6	+	290519.i	1.24194	+	0.263982i
$262$	−621089.	−	276527.i	−0.558986	−	0.248877i
$263$	427204.	+	1.31480e6i	0.380843	+	1.17211i	0.939451	+	0.342683i	$0.111336\pi$
$263$	427204.	+	1.31480e6i	0.380843	+	1.17211i	−0.558608	+	0.829432i	$0.688664\pi$
$264$	−41945.7	−	129096.i	−0.0370406	−	0.113999i
$265$	−2.03285e6	−	905081.i	−1.77824	−	0.791722i
$266$	−582229.	−	123756.i	−0.504533	−	0.107242i
$267$	−564481.	+	119984.i	−0.484586	+	0.103002i
$268$	−949697.	+	422832.i	−0.807696	+	0.359609i
$269$	1.40618e6	+	1.56172e6i	1.18484	+	1.31590i	0.937916	+	0.346863i	$0.112753\pi$
$269$	1.40618e6	+	1.56172e6i	1.18484	+	1.31590i	0.246924	+	0.969035i	$0.420580\pi$
$270$	52411.7	+	498664.i	0.0437541	+	0.416292i
$271$	−368075.	+	267422.i	−0.304448	+	0.221195i	−0.729511	−	0.683969i	$-0.760252\pi$
$271$	−368075.	+	267422.i	−0.304448	+	0.221195i	0.425062	+	0.905164i	$0.360252\pi$
$272$	−18952.3	+	180319.i	−0.0155324	+	0.147781i
$273$	−325044.	−	562992.i	−0.263958	−	0.457189i
$274$	−204574.	+	354333.i	−0.164617	+	0.285125i
$275$	411920.	+	299277.i	0.328459	+	0.238639i
$276$	432493.	−	480332.i	0.341748	−	0.379550i
$277$	324535.	−	998816.i	0.254134	−	0.782143i	−0.739865	−	0.672755i	$-0.765111\pi$
$277$	324535.	−	998816.i	0.254134	−	0.782143i	0.993999	−	0.109388i	$-0.0348892\pi$
$278$	1.05204e6			0.816430
$279$	846862.	−	393738.i	0.651331	−	0.302828i
$280$	−762620.			−0.581317
$281$	−355411.	+	1.09384e6i	−0.268513	+	0.826398i	0.722350	+	0.691528i	$0.243062\pi$
$281$	−355411.	+	1.09384e6i	−0.268513	+	0.826398i	−0.990863	+	0.134871i	$0.956938\pi$
$282$	68410.4	−	75977.4i	0.0512270	−	0.0568934i
$283$	1.48097e6	+	1.07599e6i	1.09921	+	0.798622i	0.980931	−	0.194358i	$-0.0622624\pi$
$283$	1.48097e6	+	1.07599e6i	1.09921	+	0.798622i	0.118279	+	0.992980i	$0.462262\pi$
$284$	−481106.	+	833300.i	−0.353952	+	0.613064i
$285$	−1.02462e6	−	1.77470e6i	−0.747224	−	1.29423i
$286$	10383.2	−	98789.7i	0.00750614	−	0.0714161i
$287$	−1.77908e6	+	1.29258e6i	−1.27494	+	0.926301i
$288$	18682.7	+	177754.i	0.0132727	+	0.126281i
$289$	−614421.	−	682384.i	−0.432734	−	0.480600i
$290$	2.62151e6	−	1.16717e6i	1.83045	−	0.814967i
$291$	−1.32219e6	+	281039.i	−0.915293	+	0.194552i
$292$	−781064.	−	166020.i	−0.536080	−	0.113947i
$293$	−2.04455e6	−	910292.i	−1.39132	−	0.619458i	−0.432029	−	0.901860i	$-0.642202\pi$
$293$	−2.04455e6	−	910292.i	−1.39132	−	0.619458i	−0.959296	+	0.282402i	$0.908869\pi$
$294$	22083.8	+	67967.0i	0.0149007	+	0.0458595i
$295$	95974.6	+	295379.i	0.0642098	+	0.197617i
$296$	−778506.	−	346613.i	−0.516455	−	0.229941i
$297$	142017.	+	30186.7i	0.0934223	+	0.0198575i
$298$	−1.99342e6	+	423714.i	−1.30034	+	0.276396i
$299$	432105.	−	192386.i	0.279519	−	0.124450i
$300$	−1.07316e6	−	1.19186e6i	−0.688430	−	0.764579i
$301$	−150558.	−	1.43246e6i	−0.0957827	−	0.911311i
$302$	805714.	−	585385.i	0.508351	−	0.369338i
$303$	81131.1	−	771911.i	0.0507669	−	0.483015i
$304$	143246.	+	248109.i	0.0888991	+	0.153978i
$305$	1.38141e6	−	2.39267e6i	0.850299	−	1.47276i
$306$	400046.	+	290650.i	0.244234	+	0.177446i
$307$	812809.	−	902716.i	0.492201	−	0.546645i	−0.444956	−	0.895552i	$-0.646781\pi$
$307$	812809.	−	902716.i	0.492201	−	0.546645i	0.937157	+	0.348908i	$0.113447\pi$
$308$	−68239.2	+	210019.i	−0.0409881	+	0.126148i
$309$	2.68741e6			1.60117
$310$	931724.	−	1.67642e6i	0.550659	−	0.990783i
$311$	−701026.			−0.410992			−0.205496	−	0.978658i	$-0.565881\pi$
$311$	−701026.			−0.410992			−0.205496	+	0.978658i	$0.565881\pi$
$312$	−96688.8	+	297578.i	−0.0562328	+	0.173067i
$313$	1.95313e6	−	2.16918e6i	1.12686	−	1.25151i	0.162563	−	0.986698i	$-0.448024\pi$
$313$	1.95313e6	−	2.16918e6i	1.12686	−	1.25151i	0.964301	−	0.264810i	$-0.0853093\pi$
$314$	1.27774e6	+	928330.i	0.731336	+	0.531347i
$315$	−1.03993e6	+	1.80121e6i	−0.590509	+	1.02279i
$316$	313638.	+	543237.i	0.176690	+	0.306036i
$317$	−166344.	+	1.58266e6i	−0.0929735	+	0.884583i	0.844272	+	0.535914i	$0.180033\pi$
$317$	−166344.	+	1.58266e6i	−0.0929735	+	0.884583i	−0.937246	+	0.348669i	$0.886634\pi$
$318$	1.64200e6	−	1.19298e6i	0.910552	−	0.661555i
$319$	−86856.0	−	826380.i	−0.0477885	−	0.454677i
$320$	245607.	+	272775.i	0.134081	+	0.148912i
$321$	−2.64186e6	+	1.17623e6i	−1.43102	+	0.637133i
$322$	−1.02853e6	+	218622.i	−0.552814	+	0.117504i
$323$	775288.	+	164793.i	0.413482	+	0.0878883i
$324$	−1.03775e6	−	462037.i	−0.549201	−	0.244520i
$325$	−362682.	−	1.11622e6i	−0.190466	−	0.586194i
$326$	−553831.	−	1.70452e6i	−0.288625	−	0.888295i
$327$	−2.55751e6	−	1.13868e6i	−1.32266	−	0.588885i
$328$	1.03530e6	+	220059.i	0.531350	+	0.112942i
$329$	−162690.	+	34580.9i	−0.0828652	+	0.0176135i
$330$	−694522.	+	309221.i	−0.351076	+	0.156309i
$331$	−499933.	−	555232.i	−0.250808	−	0.278551i	0.604573	−	0.796550i	$-0.293344\pi$
$331$	−499933.	−	555232.i	−0.250808	−	0.278551i	−0.855381	+	0.517999i	$0.826677\pi$
$332$	109019.	+	1.03724e6i	0.0542819	+	0.516458i
$333$	−1.88024e6	+	1.36608e6i	−0.929188	+	0.675095i
$334$	−169589.	+	1.61353e6i	−0.0831823	+	0.791426i
$335$	2.91122e6	+	5.04239e6i	1.41731	+	2.45484i
$336$	347791.	−	602392.i	0.168062	−	0.291093i
$337$	792496.	+	575782.i	0.380121	+	0.276174i	0.761395	−	0.648288i	$-0.224515\pi$
$337$	792496.	+	575782.i	0.380121	+	0.276174i	−0.381274	+	0.924462i	$0.624515\pi$
$338$	840561.	−	933537.i	0.400200	−	0.444467i
$339$	−428550.	+	1.31894e6i	−0.202536	+	0.623341i
$340$	1.01549e6			0.476410
$341$	−378300.	−	406595.i	−0.176178	−	0.189354i
$342$	781333.			0.361219
$343$	−654679.	+	2.01489e6i	−0.300464	+	0.924734i
$344$	−463876.	+	515187.i	−0.211352	+	0.234730i
$345$	−2.92871e6	−	2.12783e6i	−1.32473	−	0.962475i
$346$	1.01121e6	−	1.75146e6i	0.454098	−	0.786520i
$347$	−1.60957e6	−	2.78786e6i	−0.717608	−	1.24293i	−0.961945	−	0.273243i	$-0.911904\pi$
$347$	−1.60957e6	−	2.78786e6i	−0.717608	−	1.24293i	0.244338	−	0.969690i	$-0.421430\pi$
$348$	−273588.	+	2.60301e6i	−0.121101	+	1.15220i
$349$	−857603.	+	623085.i	−0.376897	+	0.273832i	−0.760065	−	0.649847i	$-0.774833\pi$
$349$	−857603.	+	623085.i	−0.376897	+	0.273832i	0.383168	+	0.923679i	$0.374833\pi$
$350$	272730.	+	2.59485e6i	0.119004	+	1.13225i
$351$	−223943.	−	248713.i	−0.0970217	−	0.107754i
$352$	97096.7	−	43230.2i	0.0417684	−	0.0185965i
$353$	−1.99019e6	+	423028.i	−0.850077	+	0.180689i	−0.612295	−	0.790629i	$-0.709754\pi$
$353$	−1.99019e6	+	423028.i	−0.850077	+	0.180689i	−0.237782	+	0.971319i	$0.576420\pi$
$354$	−277089.	−	58897.0i	−0.117520	−	0.0249796i
$355$	4.92325e6	+	2.19197e6i	2.07339	+	0.923132i
$356$	−139635.	−	429754.i	−0.0583943	−	0.179719i
$357$	−594673.	−	1.83022e6i	−0.246949	−	0.760032i
$358$	1.20178e6	+	535067.i	0.495585	+	0.220648i
$359$	3.89573e6	+	828064.i	1.59534	+	0.339100i	0.918003	−	0.396573i	$-0.129801\pi$
$359$	3.89573e6	+	828064.i	1.59534	+	0.339100i	0.677337	+	0.735673i	$0.263134\pi$
$360$	979174.	−	208130.i	0.398202	−	0.0846405i
$361$	−1.11790e6	+	497723.i	−0.451478	+	0.201011i
$362$	−1.52662e6	−	1.69548e6i	−0.612292	−	0.680019i
$363$	−320982.	−	3.05394e6i	−0.127854	−	1.21645i
$364$	411811.	−	299198.i	0.162909	−	0.118360i
$365$	−467485.	+	4.44782e6i	−0.183669	+	1.74749i
$366$	1.25998e6	+	2.18234e6i	0.491654	+	0.851569i
$367$	1.22473e6	−	2.12130e6i	0.474652	−	0.822121i	−0.524927	−	0.851147i	$-0.675907\pi$
$367$	1.22473e6	−	2.12130e6i	0.474652	−	0.822121i	0.999579	+	0.0290261i	$0.00924059\pi$
$368$	409444.	+	297478.i	0.157607	+	0.114508i
$369$	1.93151e6	−	2.14516e6i	0.738466	−	0.820150i
$370$	−1.47491e6	+	4.53930e6i	−0.560093	+	1.72379i
$371$	−3.30188e6			−1.24545
$372$	899290.	+	1.50049e6i	0.336932	+	0.562182i
$373$	1.73150e6			0.644392			0.322196	−	0.946673i	$-0.395579\pi$
$373$	1.73150e6			0.644392			0.322196	+	0.946673i	$0.395579\pi$
$374$	90866.5	−	279658.i	0.0335911	−	0.103383i
$375$	−2.18156e6	+	2.42287e6i	−0.801106	+	0.889718i
$376$	64764.6	+	47054.2i	0.0236248	+	0.0171644i
$377$	−957688.	+	1.65876e6i	−0.347033	+	0.601078i
$378$	372006.	+	644334.i	0.133912	+	0.231943i
$379$	−126870.	+	1.20708e6i	−0.0453691	+	0.431658i	0.948136	+	0.317866i	$0.102966\pi$
$379$	−126870.	+	1.20708e6i	−0.0453691	+	0.431658i	−0.993505	+	0.113792i	$0.963700\pi$
$380$	1.29813e6	−	943150.i	0.461170	−	0.335059i
$381$	−609610.	−	5.80005e6i	−0.215149	−	2.04701i
$382$	1.21085e6	+	1.34478e6i	0.424552	+	0.471512i
$383$	−1.63874e6	+	729614.i	−0.570838	+	0.254154i	−0.671795	−	0.740737i	$-0.734476\pi$
$383$	−1.63874e6	+	729614.i	−0.570838	+	0.254154i	0.100956	+	0.994891i	$0.467810\pi$
$384$	−327473.	+	69606.5i	−0.113331	+	0.0240892i
$385$	1.20978e6	+	257147.i	0.415963	+	0.0884157i
$386$	−1.55216e6	−	691066.i	−0.530234	−	0.236076i
$387$	584249.	+	1.79813e6i	0.198299	+	0.610302i
$388$	−327069.	−	1.00662e6i	−0.110296	−	0.339457i
$389$	−144050.	−	64135.4i	−0.0482659	−	0.0214894i	0.382462	−	0.923971i	$-0.375076\pi$
$389$	−144050.	−	64135.4i	−0.0482659	−	0.0214894i	−0.430728	+	0.902482i	$0.641743\pi$
$390$	1.71415e6	+	364354.i	0.570673	+	0.121300i
$391$	1.36958e6	−	291114.i	0.453050	−	0.0962988i
$392$	−51120.0	+	22760.1i	−0.0168026	+	0.00748098i
$393$	−2.32395e6	−	2.58100e6i	−0.759005	−	0.842960i
$394$	−168734.	−	1.60540e6i	−0.0547598	−	0.521005i
$395$	2.84228e6	−	2.06504e6i	0.916589	−	0.665941i
$396$	30299.4	−	288279.i	0.00970947	−	0.0923795i
$397$	1.33462e6	+	2.31164e6i	0.424994	+	0.736110i	0.996420	−	0.0845429i	$-0.0269430\pi$
$397$	1.33462e6	+	2.31164e6i	0.424994	+	0.736110i	−0.571426	+	0.820653i	$0.693610\pi$
$398$	−1.11453e6	+	1.93042e6i	−0.352683	+	0.610865i
$399$	−2.46002e6	−	1.78731e6i	−0.773581	−	0.562039i
$400$	840295.	−	933242.i	0.262592	−	0.291638i
$401$	−961117.	+	2.95801e6i	−0.298480	+	0.918627i	0.683550	+	0.729904i	$0.260435\pi$
$401$	−961117.	+	2.95801e6i	−0.298480	+	0.918627i	−0.982030	+	0.188724i	$0.939565\pi$
$402$	−5.31063e6			−1.63901
$403$	154582.	+	1.27080e6i	0.0474130	+	0.389776i
$404$	607745.			0.185254
$405$	−1.96606e6	+	6.05091e6i	−0.595606	+	1.83309i
$406$	2.84918e6	−	3.16433e6i	0.857836	−	0.952724i
$407$	1.11811e6	+	812353.i	0.334578	+	0.243085i
$408$	−463114.	+	802138.i	−0.137733	+	0.238560i
$409$	−1.68995e6	−	2.92708e6i	−0.499535	−	0.865221i	0.500465	−	0.865757i	$-0.333163\pi$
$409$	−1.68995e6	−	2.92708e6i	−0.499535	−	0.865221i	−1.00000		0.000536497i	$0.999829\pi$
$410$	619649.	−	5.89557e6i	0.182048	−	1.73207i
$411$	−1.69094e6	+	1.22854e6i	−0.493770	+	0.358745i
$412$	219957.	+	2.09275e6i	0.0638403	+	0.607400i
$413$	308370.	+	342479.i	0.0889604	+	0.0988005i
$414$	1.26093e6	−	561403.i	0.361569	−	0.160981i
$415$	5.71374e6	−	1.21449e6i	1.62855	−	0.346159i
$416$	−239644.	−	50938.0i	−0.0678944	−	0.0144314i
$417$	4.90967e6	+	2.18593e6i	1.38265	+	0.615595i
$418$	−143578.	−	441888.i	−0.0401927	−	0.123700i
$419$	−16053.8	−	49408.4i	−0.00446727	−	0.0137488i	0.948798	−	0.315883i	$-0.102301\pi$
$419$	−16053.8	−	49408.4i	−0.00446727	−	0.0137488i	−0.953265	+	0.302135i	$0.902301\pi$
$420$	−3.55901e6	−	1.58457e6i	−0.984478	−	0.438318i
$421$	−2.15489e6	−	458036.i	−0.592543	−	0.125949i	−0.0981262	−	0.995174i	$-0.531285\pi$
$421$	−2.15489e6	−	458036.i	−0.592543	−	0.125949i	−0.494417	+	0.869225i	$0.664618\pi$
$422$	−1.42054e6	+	301945.i	−0.388304	+	0.0825365i
$423$	199450.	−	88801.0i	0.0541981	−	0.0241305i
$424$	1.06340e6	+	1.18102e6i	0.287263	+	0.319038i
$425$	−363164.	−	3.45527e6i	−0.0975282	−	0.927919i
$426$	−3.97667e6	+	2.88922e6i	−1.06168	+	0.771359i
$427$	428522.	−	4.07711e6i	0.113737	−	1.08214i
$428$	−1.13219e6	−	1.96101e6i	−0.298751	−	0.517451i
$429$	253722.	−	439460.i	0.0665603	−	0.115286i
$430$	3.14123e6	+	2.28224e6i	0.819272	+	0.595236i
$431$	−4.59971e6	+	5.10849e6i	−1.19272	+	1.32465i	−0.259323	+	0.965791i	$0.583499\pi$
$431$	−4.59971e6	+	5.10849e6i	−1.19272	+	1.32465i	−0.933393	+	0.358855i	$0.883167\pi$
$432$	110659.	−	340572.i	0.0285283	−	0.0878011i
$433$	−1.33409e6			−0.341953			−0.170977	−	0.985275i	$-0.554692\pi$
$433$	−1.33409e6			−0.341953			−0.170977	+	0.985275i	$0.554692\pi$
$434$	251230.	−	2.83480e6i	0.0640247	−	0.722435i
$435$	1.46593e7			3.71441
$436$	677389.	−	2.08479e6i	0.170656	−	0.525225i
$437$	1.48040e6	−	1.64415e6i	0.370831	−	0.411849i
$438$	−3.30013e6	−	2.39768e6i	−0.821951	−	0.597182i
$439$	2.16008e6	−	3.74138e6i	0.534945	−	0.926552i	−0.464221	−	0.885720i	$-0.653666\pi$
$439$	2.16008e6	−	3.74138e6i	0.534945	−	0.926552i	0.999166	−	0.0408329i	$-0.0130011\pi$
$440$	−297642.	−	515532.i	−0.0732931	−	0.126947i
$441$	−15952.2	+	151775.i	−0.00390592	+	0.0371624i
$442$	−548362.	+	398409.i	−0.133509	+	0.0970003i
$443$	473295.	+	4.50310e6i	0.114584	+	1.09019i	0.889124	+	0.457666i	$0.151315\pi$
$443$	473295.	+	4.50310e6i	0.114584	+	1.09019i	−0.774540	+	0.632525i	$0.782019\pi$
$444$	−2.91296e6	−	3.23516e6i	−0.701256	−	0.778823i
$445$	−2.31203e6	+	1.02938e6i	−0.553470	+	0.246421i
$446$	−373386.	+	79365.6i	−0.0888834	+	0.0188928i
$447$	−1.01833e7	−	2.16453e6i	−2.41057	−	0.512383i
$448$	497563.	+	221529.i	0.117126	+	0.0521478i
$449$	−1.99311e6	−	6.13415e6i	−0.466568	−	1.43595i	−0.857000	−	0.515316i	$-0.827674\pi$
$449$	−1.99311e6	−	6.13415e6i	−0.466568	−	1.43595i	0.390432	−	0.920632i	$-0.372326\pi$
$450$	−1.05835e6	−	3.25726e6i	−0.246375	−	0.758265i
$451$	−1.56814e6	−	698181.i	−0.363031	−	0.161632i
$452$	−1.06217e6	−	225770.i	−0.244538	−	0.0519781i
$453$	4.97644e6	−	1.05777e6i	1.13939	−	0.242185i
$454$	−278540.	+	124014.i	−0.0634231	+	0.0282378i
$455$	−1.90766e6	−	2.11868e6i	−0.431990	−	0.479773i
$456$	152981.	+	1.45552e6i	0.0344528	+	0.327797i
$457$	−2.97394e6	+	2.16069e6i	−0.666103	+	0.483952i	−0.868718	−	0.495306i	$-0.835056\pi$
$457$	−2.97394e6	+	2.16069e6i	−0.666103	+	0.483952i	0.202615	+	0.979258i	$0.435056\pi$
$458$	−381142.	+	3.62632e6i	−0.0849030	+	0.807798i
$459$	−495359.	−	857987.i	−0.109746	−	0.190085i
$460$	1.41729e6	−	2.45481e6i	0.312293	−	0.540908i
$461$	−431497.	−	313501.i	−0.0945640	−	0.0687048i	0.539499	−	0.841987i	$-0.318614\pi$
$461$	−431497.	−	313501.i	−0.0945640	−	0.0687048i	−0.634063	+	0.773282i	$0.718614\pi$
$462$	−754838.	+	838333.i	−0.164531	+	0.182731i
$463$	−2.32445e6	+	7.15392e6i	−0.503927	+	1.55093i	0.298640	+	0.954366i	$0.403467\pi$
$463$	−2.32445e6	+	7.15392e6i	−0.503927	+	1.55093i	−0.802567	+	0.596562i	$0.796533\pi$
$464$	−2.04942e6			−0.441912
$465$	7.83146e6	−	5.88761e6i	1.67962	−	1.26272i
$466$	−505239.			−0.107778
$467$	−732016.	+	2.25291e6i	−0.155320	+	0.478027i	−0.998193	−	0.0600860i	$-0.980863\pi$
$467$	−732016.	+	2.25291e6i	−0.155320	+	0.478027i	0.842873	+	0.538113i	$0.180863\pi$
$468$	−447094.	+	496548.i	−0.0943591	+	0.104796i
$469$	6.98956e6	+	5.07822e6i	1.46730	+	1.06605i
$470$	224182.	−	388294.i	0.0468118	−	0.0810805i
$471$	4.03408e6	+	6.98724e6i	0.837901	+	1.45129i
$472$	23185.6	−	220596.i	0.00479030	−	0.0455767i
$473$	909585.	−	660852.i	0.186935	−	0.135816i
$474$	334954.	+	3.18687e6i	0.0684761	+	0.651506i
$475$	−3.67336e6	−	4.07968e6i	−0.747015	−	0.829644i
$476$	1.37656e6	−	612884.i	0.278469	−	0.123983i
$477$	4.23948e6	−	901130.i	0.853134	−	0.181339i
$478$	1.04814e6	+	222789.i	0.209821	+	0.0445989i
$479$	−1.33237e6	−	593207.i	−0.265329	−	0.118132i	0.269761	−	0.962927i	$-0.413055\pi$
$479$	−1.33237e6	−	593207.i	−0.265329	−	0.118132i	−0.535089	+	0.844795i	$0.679722\pi$
$480$	579434.	+	1.78331e6i	0.114789	+	0.353285i
$481$	−984458.	−	3.02985e6i	−0.194015	−	0.597115i
$482$	787306.	+	350531.i	0.154357	+	0.0687241i
$483$	−5.25424e6	−	1.11682e6i	−1.02481	−	0.217829i
$484$	2.35190e6	−	499912.i	0.456358	−	0.0970019i
$485$	−5.41549e6	+	2.41113e6i	−1.04540	+	0.465443i
$486$	−2.97320e6	−	3.30207e6i	−0.570996	−	0.634155i
$487$	−363638.	−	3.45978e6i	−0.0694779	−	0.661038i	−0.972732	−	0.231932i	$-0.925495\pi$
$487$	−363638.	−	3.45978e6i	−0.0694779	−	0.661038i	0.903254	−	0.429106i	$-0.141171\pi$
$488$	−1.59631e6	+	1.15979e6i	−0.303437	+	0.220460i
$489$	957019.	−	9.10543e6i	0.180987	−	1.72198i
$490$	156704.	+	271420.i	0.0294843	+	0.0510683i
$491$	282475.	−	489262.i	0.0528782	−	0.0915878i	−0.838375	−	0.545094i	$-0.816494\pi$
$491$	282475.	−	489262.i	0.0528782	−	0.0915878i	0.891253	+	0.453507i	$0.149827\pi$
$492$	4.37431e6	+	3.17812e6i	0.814698	+	0.591913i
$493$	−3.79393e6	+	4.21358e6i	−0.703027	+	0.780790i
$494$	−330961.	+	1.01859e6i	−0.0610182	+	0.187795i
$495$	−1.62349e6			−0.297808
$496$	−1.09487e6	+	823109.i	−0.199828	+	0.150229i
$497$	7.99665e6			1.45217
$498$	−1.64641e6	+	5.06714e6i	−0.297486	+	0.915567i
$499$	7.21233e6	−	8.01010e6i	1.29665	−	1.44008i	0.464461	−	0.885593i	$-0.346248\pi$
$499$	7.21233e6	−	8.01010e6i	1.29665	−	1.44008i	0.832193	−	0.554487i	$-0.187085\pi$
$500$	−2.06530e6	−	1.50053e6i	−0.369452	−	0.268423i
$501$	−4.14403e6	+	7.17768e6i	−0.737614	+	1.27758i
$502$	−1.94849e6	−	3.37488e6i	−0.345095	−	0.597722i
$503$	525584.	−	5.00060e6i	0.0926237	−	0.881256i	−0.845271	−	0.534337i	$-0.820561\pi$
$503$	525584.	−	5.00060e6i	0.0926237	−	0.881256i	0.937895	−	0.346919i	$-0.112772\pi$
$504$	1.20171e6	−	873094.i	0.210729	−	0.153103i
$505$	−355801.	−	3.38522e6i	−0.0620838	−	0.590688i
$506$	−549214.	−	609964.i	−0.0953599	−	0.105908i
$507$	5.86245e6	−	2.61013e6i	1.01288	−	0.450965i
$508$	4.46674e6	−	949435.i	0.767948	−	0.163232i
$509$	−6.84309e6	−	1.45454e6i	−1.17073	−	0.248847i	−0.418795	−	0.908081i	$-0.637547\pi$
$509$	−6.84309e6	−	1.45454e6i	−1.17073	−	0.248847i	−0.751938	+	0.659234i	$0.770881\pi$
$510$	4.73913e6	+	2.11000e6i	0.806814	+	0.359217i
$511$	2.05070e6	+	6.31141e6i	0.347416	+	1.06924i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−1.43009e6	−	636719.i	−0.239923	−	0.106820i
$514$	5.26157e6	+	1.11838e6i	0.878431	+	0.186716i
$515$	1.15281e7	−	2.45038e6i	1.91531	−	0.407113i
$516$	−3.23528e6	+	1.44044e6i	−0.534919	+	0.238161i
$517$	−86873.0	−	96482.3i	−0.0142942	−	0.0158753i
$518$	740294.	+	7.04342e6i	0.121221	+	1.15335i
$519$	8.35831e6	−	6.07267e6i	1.36207	−	0.989603i
$520$	−143433.	+	1.36467e6i	−0.0232616	+	0.221319i
$521$	2.74298e6	+	4.75098e6i	0.442719	+	0.766811i	0.997890	−	0.0649246i	$-0.0206807\pi$
$521$	2.74298e6	+	4.75098e6i	0.442719	+	0.766811i	−0.555171	+	0.831736i	$0.687347\pi$
$522$	−2.79464e6	+	4.84046e6i	−0.448900	+	0.777518i
$523$	−1.06310e6	−	772390.i	−0.169950	−	0.123476i	0.499559	−	0.866280i	$-0.333495\pi$
$523$	−1.06310e6	−	772390.i	−0.169950	−	0.123476i	−0.669509	+	0.742804i	$0.733495\pi$
$524$	1.81968e6	−	2.02096e6i	0.289512	−	0.321536i
$525$	−4.11881e6	+	1.26764e7i	−0.652189	+	2.00723i
$526$	−5.52985e6			−0.871463
$527$	−334535.	+	3.77479e6i	−0.0524705	+	0.592060i
$528$	542957.			0.0847580
$529$	−781193.	+	2.40426e6i	−0.121372	+	0.373545i
$530$	5.95587e6	−	6.61466e6i	0.920991	−	1.02286i
$531$	−489402.	−	355571.i	−0.0753233	−	0.0547256i
$532$	1.19047e6	−	2.06196e6i	0.182364	−	0.315864i
$533$	1.97840e6	+	3.42669e6i	0.301645	+	0.522464i
$534$	241290.	−	2.29572e6i	0.0366173	−	0.348390i
$535$	−1.02602e7	+	7.45448e6i	−1.54979	+	1.12599i
$536$	−434660.	−	4.13551e6i	−0.0653488	−	0.621752i
$537$	4.49673e6	+	4.99413e6i	0.672917	+	0.747350i
$538$	−7.67926e6	+	3.41903e6i	−1.14384	+	0.509269i
$539$	88768.6	−	18868.3i	0.0131610	−	0.00279745i
$540$	−1.96181e6	−	416996.i	−0.289517	−	0.0615386i
$541$	−715887.	−	318734.i	−0.105160	−	0.0468204i	0.353482	−	0.935441i	$-0.384997\pi$
$541$	−715887.	−	318734.i	−0.105160	−	0.0468204i	−0.458643	+	0.888621i	$0.651664\pi$
$542$	−562369.	−	1.73079e6i	−0.0822287	−	0.253074i
$543$	−3.60158e6	−	1.10845e7i	−0.524195	−	1.61331i
$544$	−662548.	−	294985.i	−0.0959887	−	0.0427369i
$545$	−1.20091e7	−	2.55261e6i	−1.73189	−	0.368124i
$546$	2.54352e6	−	540643.i	0.365136	−	0.0776120i
$547$	1.15803e6	−	515589.i	0.165483	−	0.0736776i	−0.322324	−	0.946630i	$-0.604464\pi$
$547$	1.15803e6	−	515589.i	0.165483	−	0.0736776i	0.487806	+	0.872952i	$0.337797\pi$
$548$	−1.09509e6	−	1.21623e6i	−0.155776	−	0.173007i
$549$	562497.	+	5.35180e6i	0.0796507	+	0.757826i
$550$	−1.64768e6	+	1.19711e6i	−0.232256	+	0.168744i
$551$	−936477.	+	8.90998e6i	−0.131407	+	1.25025i
$552$	1.29270e6	+	2.23902e6i	0.180572	+	0.312760i
$553$	2.60655e6	−	4.51468e6i	0.362455	−	0.627790i
$554$	3.39858e6	+	2.46921e6i	0.470460	+	0.341809i
$555$	−1.63149e7	+	1.81195e7i	−2.24829	+	2.49698i
$556$	−1.30039e6	+	4.00219e6i	−0.178397	+	0.549048i
$557$	−9.50143e6			−1.29763			−0.648815	−	0.760946i	$-0.724735\pi$
$557$	−9.50143e6			−1.29763			−0.648815	+	0.760946i	$0.724735\pi$
$558$	451088.	+	3.70834e6i	0.0613304	+	0.504190i
$559$	−2.59164e6			−0.350788
$560$	942650.	−	2.90118e6i	0.127022	−	0.390935i
$561$	1.00513e6	−	1.11631e6i	0.134839	−	0.149754i
$562$	−3.72192e6	−	2.70413e6i	−0.497079	−	0.361149i
$563$	1.11923e6	−	1.93857e6i	0.148816	−	0.257757i	−0.781974	−	0.623311i	$-0.785787\pi$
$563$	1.11923e6	−	1.93857e6i	0.148816	−	0.257757i	0.930790	+	0.365554i	$0.119120\pi$
$564$	204475.	+	354162.i	0.0270672	+	0.0468817i
$565$	−635730.	+	6.04857e6i	−0.0837822	+	0.797134i
$566$	−5.92388e6	+	4.30395e6i	−0.777258	+	0.564711i
$567$	986815.	+	9.38892e6i	0.128907	+	1.22647i
$568$	−2.57538e6	−	2.86025e6i	−0.334943	−	0.371992i
$569$	−4818.46	+	2145.32i	−0.000623918	+	0.000277786i	−0.407049	−	0.913407i	$-0.633442\pi$
$569$	−4818.46	+	2145.32i	−0.000623918	+	0.000277786i	0.406425	+	0.913684i	$0.366775\pi$
$570$	8.01784e6	−	1.70425e6i	1.03364	−	0.219708i
$571$	3.01793e6	+	641482.i	0.387364	+	0.0823368i	0.397477	−	0.917612i	$-0.369886\pi$
$571$	3.01793e6	+	641482.i	0.387364	+	0.0823368i	−0.0101130	+	0.999949i	$0.503219\pi$
$572$	362984.	+	161611.i	0.0463871	+	0.0206529i
$573$	2.85661e6	+	8.79176e6i	0.363467	+	1.11864i
$574$	−2.71820e6	−	8.36574e6i	−0.344351	−	1.05980i
$575$	−8.85947e6	−	3.94449e6i	−1.11748	−	0.497532i
$576$	−699309.	−	148643.i	−0.0878239	−	0.0186676i
$577$	8.67025e6	−	1.84292e6i	1.08416	−	0.230445i	0.369015	−	0.929424i	$-0.379695\pi$
$577$	8.67025e6	−	1.84292e6i	1.08416	−	0.230445i	0.715142	+	0.698979i	$0.246362\pi$
$578$	3.35541e6	−	1.49392e6i	0.417759	−	0.185998i
$579$	−5.80775e6	−	6.45016e6i	−0.719965	−	0.799603i
$580$	1.19982e6	+	1.14155e7i	0.148097	+	1.40905i
$581$	7.01231e6	−	5.09474e6i	0.861828	−	0.626155i
$582$	565175.	−	5.37728e6i	0.0691633	−	0.658044i
$583$	−1.28869e6	−	2.23207e6i	−0.157028	−	0.271980i
$584$	1.59703e6	−	2.76613e6i	0.193767	−	0.335615i
$585$	3.02758e6	+	2.19967e6i	0.365768	+	0.265746i
$586$	5.99016e6	−	6.65275e6i	0.720600	−	0.800307i
$587$	−827249.	+	2.54601e6i	−0.0990925	+	0.304975i	−0.988299	−	0.152531i	$-0.951257\pi$
$587$	−827249.	+	2.54601e6i	−0.0990925	+	0.304975i	0.889206	+	0.457507i	$0.151257\pi$
$588$	−285859.			−0.0340964
$589$	3.07822e6	+	5.13612e6i	0.365605	+	0.610024i
$590$	−1.24232e6			−0.146928
$591$	2.54825e6	−	7.84270e6i	0.300105	−	0.923627i
$592$	2.28088e6	−	2.53318e6i	0.267484	−	0.297072i
$593$	−3.80414e6	−	2.76387e6i	−0.444242	−	0.322761i	0.343076	−	0.939308i	$-0.388531\pi$
$593$	−3.80414e6	−	2.76387e6i	−0.444242	−	0.322761i	−0.787318	+	0.616547i	$0.788531\pi$
$594$	−290380.	+	502953.i	−0.0337677	+	0.0584873i
$595$	−4.21974e6	−	7.30880e6i	−0.488644	−	0.846357i
$596$	852095.	−	8.10714e6i	0.0982590	−	0.934872i
$597$	−9.21236e6	+	6.69317e6i	−1.05788	+	0.768592i
$598$	197767.	+	1.88163e6i	0.0226152	+	0.215170i
$599$	8.05912e6	+	8.95056e6i	0.917742	+	1.01926i	0.999744	+	0.0226234i	$0.00720187\pi$
$599$	8.05912e6	+	8.95056e6i	0.917742	+	1.01926i	−0.0820022	+	0.996632i	$0.526131\pi$
$600$	5.86060e6	−	2.60931e6i	0.664606	−	0.295901i
$601$	−2.60421e6	+	553543.i	−0.294097	+	0.0625122i	−0.352597	−	0.935775i	$-0.614701\pi$
$601$	−2.60421e6	+	553543.i	−0.294097	+	0.0625122i	0.0585004	+	0.998287i	$0.481368\pi$
$602$	5.63551e6	+	1.19786e6i	0.633785	+	0.134715i
$603$	−1.03602e7	−	4.61268e6i	−1.16032	−	0.516606i
$604$	1.23102e6	+	3.78869e6i	0.137301	+	0.422569i
$605$	−4.16148e6	−	1.28077e7i	−0.462231	−	1.42260i
$606$	2.83624e6	+	1.26277e6i	0.313734	+	0.139683i
$607$	7.99080e6	+	1.69850e6i	0.880275	+	0.187108i	0.625812	−	0.779974i	$-0.284768\pi$
$607$	7.99080e6	+	1.69850e6i	0.880275	+	0.187108i	0.254464	+	0.967082i	$0.418101\pi$
$608$	−1.12092e6	+	238260.i	−0.122975	+	0.0261391i
$609$	1.98715e7	−	8.84735e6i	2.17113	−	0.966651i
$610$	7.39473e6	+	8.21268e6i	0.804633	+	0.893635i
$611$	31282.2	+	297630.i	0.00338996	+	0.0322533i
$612$	−1.60018e6	+	1.16260e6i	−0.172699	+	0.125474i
$613$	1.44360e6	−	1.37350e7i	0.155166	−	1.47631i	−0.588903	−	0.808204i	$-0.700440\pi$
$613$	1.44360e6	−	1.37350e7i	0.155166	−	1.47631i	0.744069	−	0.668103i	$-0.232893\pi$
$614$	2.42945e6	+	4.20793e6i	0.260068	+	0.450451i
$615$	1.51416e7	−	2.62261e7i	1.61430	−	2.79605i
$616$	−714611.	−	519195.i	−0.0758783	−	0.0551288i
$617$	7.49671e6	−	8.32594e6i	0.792789	−	0.880481i	−0.202314	−	0.979321i	$-0.564846\pi$
$617$	7.49671e6	−	8.32594e6i	0.792789	−	0.880481i	0.995103	+	0.0988392i	$0.0315130\pi$
$618$	−3.32182e6	+	1.02235e7i	−0.349869	+	1.07679i
$619$	3.47991e6			0.365041			0.182521	−	0.983202i	$-0.441574\pi$
$619$	3.47991e6			0.365041			0.182521	+	0.983202i	$0.441574\pi$
$620$	5.22580e6	+	5.61666e6i	0.545976	+	0.586811i
$621$	−2.76541e6			−0.287760
$622$	866516.	−	2.66686e6i	0.0898050	−	0.276391i
$623$	−2.51282e6	+	2.79077e6i	−0.259383	+	0.288074i
$624$	−1.01254e6	−	735652.i	−0.104100	−	0.0756330i
$625$	515782.	−	893360.i	0.0528161	−	0.0914801i
$626$	5.83783e6	+	1.01114e7i	0.595409	+	1.03128i
$627$	248103.	−	2.36054e6i	0.0252036	−	0.239796i
$628$	−5.11095e6	+	3.71332e6i	−0.517133	+	0.375719i
$629$	−985765.	−	9.37893e6i	−0.0993452	−	0.945207i
$630$	−5.56678e6	−	6.18253e6i	−0.558795	−	0.620605i
$631$	2.13175e6	−	949116.i	0.213139	−	0.0948956i	−0.297390	−	0.954756i	$-0.596116\pi$
$631$	2.13175e6	−	949116.i	0.213139	−	0.0948956i	0.510529	+	0.859860i	$0.329450\pi$
$632$	−2.45428e6	+	521672.i	−0.244417	+	0.0519523i
$633$	−7.25678e6	−	1.54248e6i	−0.719838	−	0.153006i
$634$	−5.81517e6	−	2.58908e6i	−0.574566	−	0.255813i
$635$	−7.90350e6	−	2.43245e7i	−0.777831	−	2.39392i
$636$	2.50875e6	+	7.72114e6i	0.245932	+	0.756900i
$637$	−191106.	−	85085.7i	−0.0186606	−	0.00830822i
$638$	3.25110e6	+	691042.i	0.316212	+	0.0672129i
$639$	−1.02674e7	+	2.18240e6i	−0.994736	+	0.211438i
$640$	−1.34128e6	+	597178.i	−0.129441	+	0.0576307i
$641$	1.22172e6	+	1.35685e6i	0.117442	+	0.130433i	0.798999	−	0.601333i	$-0.205363\pi$
$641$	1.22172e6	+	1.35685e6i	0.117442	+	0.130433i	−0.681556	+	0.731766i	$0.738697\pi$
$642$	−1.20913e6	−	1.15041e7i	−0.115781	−	1.10158i
$643$	−1.54036e7	+	1.11914e7i	−1.46925	+	1.06747i	−0.488414	+	0.872612i	$0.662424\pi$
$643$	−1.54036e7	+	1.11914e7i	−1.46925	+	1.06747i	−0.980832	+	0.194857i	$0.937576\pi$
$644$	439652.	−	4.18301e6i	0.0417729	−	0.397442i
$645$	9.91751e6	+	1.71776e7i	0.938650	+	1.62579i
$646$	−1.58522e6	+	2.74568e6i	−0.149454	+	0.258862i
$647$	1.44965e6	+	1.05323e6i	0.136145	+	0.0989151i	0.653773	−	0.756690i	$-0.273185\pi$
$647$	1.44965e6	+	1.05323e6i	0.136145	+	0.0989151i	−0.517628	+	0.855606i	$0.673185\pi$
$648$	3.04043e6	−	3.37674e6i	0.284444	−	0.315907i
$649$	−111163.	+	342124.i	−0.0103597	+	0.0318840i
$650$	4.69466e6			0.435833
$651$	7.06261e6	−	1.27075e7i	0.653150	−	1.17519i
$652$	7.16894e6			0.660444
$653$	−3.05919e6	+	9.41521e6i	−0.280752	+	0.864067i	0.706888	+	0.707326i	$0.250099\pi$
$653$	−3.05919e6	+	9.41521e6i	−0.280752	+	0.864067i	−0.987640	+	0.156741i	$0.949901\pi$
$654$	7.49303e6	−	8.32186e6i	0.685036	−	0.760809i
$655$	−1.23223e7	−	8.95268e6i	−1.12225	−	0.815361i
$656$	−2.11685e6	+	3.66650e6i	−0.192057	+	0.332653i
$657$	−4.35549e6	−	7.54393e6i	−0.393662	−	0.681843i
$658$	69542.8	−	661655.i	0.00626163	−	0.0595754i
$659$	−1.28304e7	+	9.32184e6i	−1.15087	+	0.836158i	−0.988597	−	0.150588i	$-0.951883\pi$
$659$	−1.28304e7	+	9.32184e6i	−1.15087	+	0.836158i	−0.162276	+	0.986745i	$0.551883\pi$
$660$	−317871.	−	3.02434e6i	−0.0284047	−	0.270253i
$661$	1.01273e7	+	1.12475e7i	0.901553	+	1.00128i	0.999981	+	0.00613198i	$0.00195188\pi$
$661$	1.01273e7	+	1.12475e7i	0.901553	+	1.00128i	−0.0984281	+	0.995144i	$0.531381\pi$
$662$	2.73018e6	−	1.21555e6i	0.242129	−	0.107803i
$663$	−3.38692e6	+	719913.i	−0.299241	+	0.0636057i
$664$	−4.08066e6	−	867371.i	−0.359178	−	0.0763457i
$665$	−1.21823e7	−	5.42392e6i	−1.06826	−	0.475619i
$666$	−2.87276e6	−	8.84144e6i	−0.250965	−	0.772391i
$667$	4.89069e6	+	1.50520e7i	0.425653	+	1.31002i
$668$	−5.92860e6	−	2.63958e6i	−0.514057	−	0.228873i
$669$	−1.90743e6	−	405437.i	−0.164772	−	0.0350234i
$670$	−2.27808e7	+	4.84222e6i	−1.96057	+	0.416732i
$671$	2.92338e6	−	1.30157e6i	0.250657	−	0.111599i
$672$	1.86174e6	+	2.06767e6i	0.159036	+	0.176628i
$673$	−1.29280e6	−	1.23001e7i	−0.110025	−	1.04682i	−0.900658	−	0.434529i	$-0.856915\pi$
$673$	−1.29280e6	−	1.23001e7i	−0.110025	−	1.04682i	0.790632	−	0.612291i	$-0.209752\pi$
$674$	−3.16998e6	+	2.30313e6i	−0.268786	+	0.195285i
$675$	−717263.	+	6.82430e6i	−0.0605925	+	0.576499i
$676$	2.51240e6	+	4.35160e6i	0.211457	+	0.366254i
$677$	−24413.9	+	42286.0i	−0.00204722	+	0.00354589i	−0.867047	−	0.498226i	$-0.833985\pi$
$677$	−24413.9	+	42286.0i	−0.00204722	+	0.00354589i	0.865000	+	0.501772i	$0.167318\pi$
$678$	−4.48783e6	−	3.26060e6i	−0.374940	−	0.272410i
$679$	−5.88580e6	+	6.53685e6i	−0.489927	+	0.544119i
$680$	−1.25522e6	+	3.86317e6i	−0.104099	+	0.320385i
$681$	−1.55757e6			−0.128701
$682$	2.01438e6	−	936562.i	0.165837	−	0.0771037i
$683$	1.69244e7			1.38823			0.694114	−	0.719865i	$-0.255796\pi$
$683$	1.69244e7			1.38823			0.694114	+	0.719865i	$0.255796\pi$
$684$	−965781.	+	2.97237e6i	−0.0789293	+	0.242920i
$685$	−6.13341e6	+	6.81184e6i	−0.499431	+	0.554674i
$686$	−6.85588e6	−	4.98109e6i	−0.556228	−	0.404124i
$687$	−9.31351e6	+	1.61315e7i	−0.752873	+	1.30401i
$688$	−1.38650e6	−	2.40150e6i	−0.111673	−	0.193424i
$689$	−621014.	+	5.90855e6i	−0.0498371	+	0.474169i
$690$	1.17148e7	−	8.51132e6i	0.936727	−	0.680572i
$691$	−238225.	−	2.26656e6i	−0.0189798	−	0.180581i	0.980925	−	0.194387i	$-0.0622718\pi$
$691$	−238225.	−	2.26656e6i	−0.0189798	−	0.180581i	−0.999905	+	0.0138064i	$0.995605\pi$
$692$	5.41303e6	+	6.01178e6i	0.429710	+	0.477241i
$693$	−2.20073e6	+	979828.i	−0.174074	+	0.0775027i
$694$	1.25952e7	−	2.67719e6i	0.992674	−	0.210999i
$695$	2.30540e7	+	4.90028e6i	1.81044	+	0.384821i
$696$	−9.56428e6	−	4.25829e6i	−0.748392	−	0.333206i
$697$	3.61951e6	+	1.11397e7i	0.282207	+	0.868545i
$698$	−1.31030e6	−	4.03269e6i	−0.101796	−	0.313297i
$699$	−2.35786e6	−	1.04979e6i	−0.182526	−	0.0812659i
$700$	−1.02085e7	−	2.16989e6i	−0.787441	−	0.167376i
$701$	7.33092e6	−	1.55824e6i	0.563461	−	0.119767i	0.0826294	−	0.996580i	$-0.473668\pi$
$701$	7.33092e6	−	1.55824e6i	0.563461	−	0.119767i	0.480831	+	0.876813i	$0.340335\pi$
$702$	1.22297e6	−	544501.i	0.0936641	−	0.0417019i
$703$	−9.97090e6	−	1.10738e7i	−0.760932	−	0.845101i
$704$	44439.5	+	422813.i	0.00337938	+	0.0321527i
$705$	1.85302e6	−	1.34629e6i	0.140413	−	0.102016i
$706$	850717.	−	8.09403e6i	0.0642353	−	0.611158i
$707$	−2.52539e6	−	4.37411e6i	−0.190012	−	0.329110i
$708$	566558.	−	981307.i	0.0424777	−	0.0735736i
$709$	1.85253e7	+	1.34595e7i	1.38405	+	1.00557i	0.996489	+	0.0837232i	$0.0266812\pi$
$709$	1.85253e7	+	1.34595e7i	1.38405	+	1.00557i	0.387558	+	0.921846i	$0.373319\pi$
$710$	−1.44242e7	+	1.60197e7i	−1.07386	+	1.19264i
$711$	−2.11459e6	+	6.50804e6i	−0.156874	+	0.482810i
$712$	1.80748e6			0.133621
$713$	8.65810e6	+	6.07701e6i	0.637821	+	0.447678i
$714$	7.69761e6			0.565081
$715$	687686.	−	2.11648e6i	0.0503066	−	0.154828i
$716$	−3.52100e6	+	3.91047e6i	−0.256675	+	0.285066i
$717$	4.42857e6	+	3.21755e6i	0.321711	+	0.233737i
$718$	−7.96554e6	+	1.37967e7i	−0.576639	+	0.998768i
$719$	5.61424e6	+	9.72414e6i	0.405013	+	0.701502i	0.994323	−	0.106404i	$-0.0339338\pi$
$719$	5.61424e6	+	9.72414e6i	0.405013	+	0.701502i	−0.589310	+	0.807907i	$0.700600\pi$
$720$	−418552.	+	3.98226e6i	−0.0300898	+	0.286285i
$721$	1.41481e7	−	1.02792e7i	1.01359	−	0.736413i
$722$	−511646.	−	4.86798e6i	−0.0365280	−	0.347541i
$723$	2.94588e6	+	3.27173e6i	0.209590	+	0.232773i
$724$	8.33699e6	−	3.71187e6i	0.591103	−	0.263176i
$725$	3.84128e7	−	8.16490e6i	2.71413	−	0.576907i
$726$	1.20146e7	+	2.55379e6i	0.845996	+	0.179822i
$727$	4.58248e6	+	2.04025e6i	0.321562	+	0.143169i	0.561169	−	0.827701i	$-0.310352\pi$
$727$	4.58248e6	+	2.04025e6i	0.321562	+	0.143169i	−0.239607	+	0.970870i	$0.577019\pi$
$728$	629191.	+	1.93645e6i	0.0440002	+	0.135419i
$729$	−1.68304e6	−	5.17986e6i	−0.117294	−	0.360994i
$730$	−1.63427e7	−	7.27622e6i	−1.13505	−	0.505358i
$731$	−7.50417e6	−	1.59506e6i	−0.519409	−	0.110404i
$732$	−9.85953e6	+	2.09571e6i	−0.680109	+	0.144562i
$733$	−1.64061e7	+	7.30445e6i	−1.12783	+	0.502143i	−0.883912	−	0.467652i	$-0.845100\pi$
$733$	−1.64061e7	+	7.30445e6i	−1.12783	+	0.502143i	−0.243919	+	0.969796i	$0.578433\pi$
$734$	6.55604e6	+	7.28122e6i	0.449160	+	0.498843i
$735$	167354.	+	1.59227e6i	0.0114266	+	0.108717i
$736$	−1.63778e6	+	1.18991e6i	−0.111445	+	0.0809694i
$737$	−704926.	+	6.70693e6i	−0.0478052	+	0.454836i
$738$	5.77319e6	+	9.99945e6i	0.390189	+	0.675827i
$739$	6.43340e6	−	1.11430e7i	0.433341	−	0.750568i	−0.563818	−	0.825899i	$-0.690668\pi$
$739$	6.43340e6	−	1.11430e7i	0.433341	−	0.750568i	0.997159	+	0.0753311i	$0.0240014\pi$
$740$	−1.54454e7	−	1.12218e7i	−1.03686	−	0.753324i
$741$	−3.66097e6	+	4.06592e6i	−0.244935	+	0.272028i
$742$	4.08135e6	−	1.25611e7i	0.272141	−	0.837564i
$743$	−1.45436e7			−0.966497			−0.483249	−	0.875483i	$-0.660543\pi$
$743$	−1.45436e7			−0.966497			−0.483249	+	0.875483i	$0.660543\pi$
$744$	−6.81980e6	+	1.56639e6i	−0.451689	+	0.103745i
$745$	−4.56567e7			−3.01379
$746$	−2.14025e6	+	6.58701e6i	−0.140805	+	0.433353i
$747$	−7.61310e6	+	8.45520e6i	−0.499183	+	0.554399i
$748$	951566.	+	691353.i	0.0621849	+	0.0451800i
$749$	−9.40927e6	+	1.62973e7i	−0.612846	+	1.06148i
$750$	−6.52059e6	−	1.12940e7i	−0.423286	−	0.733153i
$751$	1.35897e6	−	1.29298e7i	0.0879246	−	0.836547i	−0.858324	−	0.513108i	$-0.828494\pi$
$751$	1.35897e6	−	1.29298e7i	0.0879246	−	0.836547i	0.946249	−	0.323439i	$-0.104839\pi$
$752$	−259058.	+	188217.i	−0.0167052	+	0.0121371i
$753$	−2.08091e6	−	1.97986e7i	−0.133742	−	1.27247i
$754$	−5.12655e6	−	5.69361e6i	−0.328395	−	0.364720i
$755$	2.03828e7	−	9.07501e6i	1.30136	−	0.579402i
$756$	−2.91102e6	+	618756.i	−0.185242	+	0.0393745i
$757$	2.15054e7	+	4.57112e6i	1.36398	+	0.289923i	0.831032	−	0.556224i	$-0.187750\pi$
$757$	2.15054e7	+	4.57112e6i	1.36398	+	0.289923i	0.532949	+	0.846147i	$0.321084\pi$
$758$	−4.43520e6	−	1.97468e6i	−0.280376	−	0.124831i
$759$	−1.29570e6	−	3.98775e6i	−0.0816394	−	0.251260i
$760$	1.98337e6	+	6.10419e6i	0.124558	+	0.383349i
$761$	4.28714e6	+	1.90876e6i	0.268353	+	0.119478i	0.536502	−	0.843899i	$-0.319745\pi$
$761$	4.28714e6	+	1.90876e6i	0.268353	+	0.119478i	−0.268149	+	0.963377i	$0.586412\pi$
$762$	2.28182e7	+	4.85016e6i	1.42362	+	0.302600i
$763$	−1.78196e7	+	3.78767e6i	−1.10812	+	0.235538i
$764$	−6.61254e6	+	2.94409e6i	−0.409859	+	0.182481i
$765$	7.41265e6	+	8.23258e6i	0.457952	+	0.508607i
$766$	−750023.	−	7.13599e6i	−0.0461852	−	0.439423i
$767$	670847.	−	487399.i	0.0411752	−	0.0299155i
$768$	139980.	−	1.33182e6i	0.00856372	−	0.0814784i
$769$	9.18125e6	+	1.59024e7i	0.559869	+	0.969721i	0.997507	+	0.0705698i	$0.0224818\pi$
$769$	9.18125e6	+	1.59024e7i	0.559869	+	0.969721i	−0.437638	+	0.899151i	$0.644185\pi$
$770$	−2.47362e6	+	4.28443e6i	−0.150351	+	0.260415i
$771$	2.22310e7	+	1.61518e7i	1.34686	+	0.978554i
$772$	4.54754e6	−	5.05056e6i	0.274621	−	0.304997i
$773$	7.74290e6	−	2.38302e7i	0.466074	−	1.43443i	−0.391553	−	0.920156i	$-0.628062\pi$
$773$	7.74290e6	−	2.38302e7i	0.466074	−	1.43443i	0.857627	−	0.514272i	$-0.171938\pi$
$774$	−7.56268e6			−0.453757
$775$	1.72421e7	−	1.97897e7i	1.03118	−	1.18355i
$776$	4.23367e6			0.252385
$777$	−1.11800e7	+	3.44086e7i	−0.664340	+	2.04463i
$778$	422042.	−	468725.i	0.0249981	−	0.0277632i
$779$	1.49730e7	+	1.08785e7i	0.884028	+	0.642284i
$780$	−3.50489e6	+	6.07065e6i	−0.206271	+	0.357272i
$781$	3.12101e6	+	5.40575e6i	0.183091	+	0.317123i
$782$	−585435.	+	5.57004e6i	−0.0342343	+	0.325718i
$783$	9.05965e6	−	6.58222e6i	0.528089	−	0.383679i
$784$	−23396.7	−	222605.i	−0.00135946	−	0.0129344i
$785$	2.36758e7	+	2.62947e7i	1.37130	+	1.52298i
$786$	1.26913e7	−	5.65052e6i	0.732738	−	0.326236i
$787$	−4.23406e6	+	899977.i	−0.243680	+	0.0517958i	−0.328132	−	0.944632i	$-0.606419\pi$
$787$	−4.23406e6	+	899977.i	−0.243680	+	0.0517958i	0.0844524	+	0.996428i	$0.473086\pi$
$788$	6.31586e6	+	1.34248e6i	0.362340	+	0.0770178i
$789$	−2.58068e7	−	1.14899e7i	−1.47585	−	0.657090i
$790$	4.34262e6	+	1.33652e7i	0.247562	+	0.761918i
$791$	2.78874e6	+	8.58285e6i	0.158477	+	0.487742i
$792$	1.05923e6	+	471598.i	0.0600035	+	0.0267153i
$793$	−7.21520e6	−	1.53364e6i	−0.407441	−	0.0866044i
$794$	−1.04437e7	+	2.21987e6i	−0.587898	+	0.124962i
$795$	4.15390e7	−	1.84943e7i	2.33098	−	1.03782i
$796$	−5.96613e6	−	6.62606e6i	−0.333742	−	0.370658i
$797$	−601948.	−	5.72716e6i	−0.0335671	−	0.319369i	−0.998402	−	0.0565124i	$-0.982002\pi$
$797$	−601948.	−	5.72716e6i	−0.0335671	−	0.319369i	0.964835	−	0.262857i	$-0.0846647\pi$
$798$	9.84006e6	−	7.14922e6i	0.547004	−	0.397422i
$799$	−92602.3	+	881052.i	−0.00513162	+	0.0488241i
$800$	2.51160e6	+	4.35022e6i	0.138748	+	0.240318i
$801$	2.46472e6	−	4.26903e6i	0.135733	−	0.235097i
$802$	−1.00649e7	−	7.31261e6i	−0.552555	−	0.401455i
$803$	−3.46615e6	+	3.84955e6i	−0.189696	+	0.210679i
$804$	6.56430e6	−	2.02028e7i	0.358136	−	1.10223i
$805$	−2.35573e7			−1.28125
$806$	−5.02549e6	−	982731.i	−0.272484	−	0.0532840i
$807$	−4.29418e7			−2.32112
$808$	−751214.	+	2.31200e6i	−0.0404795	+	0.124583i
$809$	3.93811e6	−	4.37371e6i	0.211552	−	0.234952i	−0.628025	−	0.778193i	$-0.716136\pi$
$809$	3.93811e6	−	4.37371e6i	0.211552	−	0.234952i	0.839577	+	0.543241i	$0.182803\pi$
$810$	−2.05888e7	−	1.49587e7i	−1.10260	−	0.801088i
$811$	−8.35093e6	+	1.44642e7i	−0.445844	+	0.772224i	−0.998111	−	0.0614436i	$-0.980430\pi$
$811$	−8.35093e6	+	1.44642e7i	−0.445844	+	0.772224i	0.552267	+	0.833667i	$0.313763\pi$
$812$	8.51606e6	+	1.47502e7i	0.453261	+	0.785071i
$813$	971773.	−	9.24580e6i	0.0515630	−	0.490589i
$814$	−4.47243e6	+	3.24941e6i	−0.236583	+	0.171887i
$815$	−4.19701e6	−	3.99319e7i	−0.221333	−	2.10584i
$816$	−2.47907e6	−	2.75329e6i	−0.130336	−	0.144753i
$817$	−1.10742e7	+	4.93056e6i	−0.580440	+	0.258429i
$818$	1.32242e7	−	2.81089e6i	0.691012	−	0.146879i
$819$	5.43162e6	+	1.15453e6i	0.282957	+	0.0601443i
$820$	2.16621e7	+	9.64461e6i	1.12504	+	0.500899i
$821$	9.54646e6	+	2.93810e7i	0.494293	+	1.52128i	0.818055	+	0.575140i	$0.195052\pi$
$821$	9.54646e6	+	2.93810e7i	0.494293	+	1.52128i	−0.323762	+	0.946139i	$0.604948\pi$
$822$	−2.58353e6	−	7.95130e6i	−0.133363	−	0.410448i
$823$	−2.57816e7	−	1.14787e7i	−1.32682	−	0.590737i	−0.383779	−	0.923425i	$-0.625378\pi$
$823$	−2.57816e7	−	1.14787e7i	−1.32682	−	0.590737i	−0.943037	+	0.332688i	$0.892044\pi$
$824$	−8.23318e6	−	1.75002e6i	−0.422425	−	0.0897892i
$825$	−1.01768e7	+	2.16314e6i	−0.520566	+	0.110650i
$826$	−1.68403e6	+	749781.i	−0.0858818	+	0.0382370i
$827$	−1.57286e7	−	1.74684e7i	−0.799698	−	0.888155i	0.196020	−	0.980600i	$-0.437198\pi$
$827$	−1.57286e7	−	1.74684e7i	−0.799698	−	0.888155i	−0.995718	+	0.0924452i	$0.970532\pi$
$828$	577107.	+	5.49080e6i	0.0292537	+	0.278330i
$829$	−5.27812e6	+	3.83478e6i	−0.266743	+	0.193800i	−0.713114	−	0.701048i	$-0.752716\pi$
$829$	−5.27812e6	+	3.83478e6i	−0.266743	+	0.193800i	0.446372	+	0.894848i	$0.352716\pi$
$830$	−2.44237e6	+	2.32376e7i	−0.123060	+	1.17083i
$831$	1.07300e7	+	1.85849e7i	0.539011	+	0.933595i
$832$	489996.	−	848699.i	0.0245406	−	0.0425055i
$833$	−500986.	−	363988.i	−0.0250157	−	0.0181750i
$834$	−1.43844e7	+	1.59755e7i	−0.716107	+	0.795317i
$835$	−1.12320e7	+	3.45684e7i	−0.557492	+	1.71579i
$836$	1.85851e6			0.0919708
$837$	2.19634e6	−	7.15507e6i	0.108364	−	0.353021i
$838$	207804.			0.0102222
$839$	1.08741e7	−	3.34672e7i	0.533323	−	1.64140i	−0.213923	−	0.976851i	$-0.568624\pi$
$839$	1.08741e7	−	3.34672e7i	0.533323	−	1.64140i	0.747246	−	0.664548i	$-0.231376\pi$
$840$	1.04273e7	−	1.15806e7i	0.509885	−	0.566284i
$841$	−3.52551e7	−	2.56143e7i	−1.71882	−	1.24880i
$842$	4.40606e6	−	7.63152e6i	0.214176	−	0.370963i
$843$	−1.17509e7	−	2.03531e7i	−0.569510	−	0.986420i
$844$	607215.	−	5.77727e6i	0.0293418	−	0.279169i
$845$	2.27681e7	−	1.65420e7i	1.09694	−	0.796977i
$846$	91285.0	+	868518.i	0.00438504	+	0.0417208i
$847$	−1.33710e7	−	1.48500e7i	−0.640405	−	0.711241i
$848$	−5.80729e6	+	2.58557e6i	−0.277322	+	0.123472i
$849$	−3.65885e7	+	7.77712e6i	−1.74211	+	0.370296i
$850$	1.35935e7	+	2.88940e6i	0.645335	+	0.137170i
$851$	−2.40480e7	−	1.07069e7i	−1.13829	−	0.506802i
$852$	−6.07581e6	−	1.86994e7i	−0.286751	−	0.882529i
$853$	9.59017e6	+	2.95155e7i	0.451288	+	1.38892i	0.875438	+	0.483330i	$0.160573\pi$
$853$	9.59017e6	+	2.95155e7i	0.451288	+	1.38892i	−0.424150	+	0.905592i	$0.639427\pi$
$854$	1.49806e7	+	6.66978e6i	0.702885	+	0.312944i
$855$	1.71219e7	+	3.63937e6i	0.801006	+	0.170259i
$856$	8.85957e6	−	1.88316e6i	0.413264	−	0.0878421i
$857$	1.85034e7	−	8.23824e6i	0.860596	−	0.383162i	0.0715062	−	0.997440i	$-0.477219\pi$
$857$	1.85034e7	−	8.23824e6i	0.860596	−	0.383162i	0.789089	+	0.614278i	$0.210553\pi$
$858$	1.35819e6	+	1.50842e6i	0.0629856	+	0.0699525i
$859$	−1.18090e6	−	1.12355e7i	−0.0546048	−	0.519530i	−0.987300	−	0.158865i	$-0.949216\pi$
$859$	−1.18090e6	−	1.12355e7i	−0.0546048	−	0.519530i	0.932695	−	0.360665i	$-0.117450\pi$
$860$	−1.25649e7	+	9.12894e6i	−0.579313	+	0.420895i
$861$	4.69704e6	−	4.46893e7i	0.215932	−	2.05445i
$862$	−1.37483e7	−	2.38128e7i	−0.630204	−	1.09155i
$863$	−1.24764e7	+	2.16098e7i	−0.570247	+	0.987696i	0.426294	+	0.904585i	$0.359819\pi$
$863$	−1.24764e7	+	2.16098e7i	−0.570247	+	0.987696i	−0.996540	+	0.0831114i	$0.973514\pi$
$864$	1.15883e6	+	841941.i	0.0528124	+	0.0383705i
$865$	3.03173e7	−	3.36708e7i	1.37769	−	1.53008i
$866$	1.64903e6	−	5.07520e6i	0.0747195	−	0.229963i
$867$	1.87632e7			0.847732
$868$	1.04737e7	+	4.45975e6i	0.471846	+	0.200914i
$869$	4.06924e6			0.182795
$870$	−1.81199e7	+	5.57672e7i	−0.811628	+	2.49793i
$871$	1.04018e7	−	1.15524e7i	0.464583	−	0.515972i
$872$	7.09371e6	+	5.15388e6i	0.315924	+	0.229532i
$873$	5.77314e6	−	9.99937e6i	0.256375	−	0.444055i
$874$	4.42485e6	+	7.66406e6i	0.195938	+	0.339375i
$875$	−2.21768e6	+	2.10998e7i	−0.0979215	+	0.931661i
$876$	1.32005e7	−	9.59074e6i	0.581207	−	0.422271i
$877$	506445.	+	4.81850e6i	0.0222348	+	0.211550i	0.999998	+	0.00183950i	$0.000585531\pi$
$877$	506445.	+	4.81850e6i	0.0222348	+	0.211550i	−0.977763	+	0.209711i	$0.932748\pi$
$878$	1.15630e7	+	1.28420e7i	0.506215	+	0.562209i
$879$	4.17781e7	−	1.86008e7i	1.82380	−	0.812007i
$880$	2.32911e6	−	495067.i	0.101387	−	0.0215505i
$881$	1.00911e7	+	2.14493e6i	0.438026	+	0.0931053i	0.421646	−	0.906761i	$-0.361453\pi$
$881$	1.00911e7	+	2.14493e6i	0.438026	+	0.0931053i	0.0163799	+	0.999866i	$0.494786\pi$
$882$	−557668.	−	248290.i	−0.0241382	−	0.0107470i
$883$	−8.94996e6	−	2.75451e7i	−0.386295	−	1.18889i	−0.935536	−	0.353230i	$-0.885083\pi$
$883$	−8.94996e6	−	2.75451e7i	−0.386295	−	1.18889i	0.549241	−	0.835664i	$-0.314917\pi$
$884$	−837823.	−	2.57855e6i	−0.0360597	−	0.110980i
$885$	−5.79769e6	−	2.58130e6i	−0.248827	−	0.110785i
$886$	−1.77158e7	−	3.76562e6i	−0.758189	−	0.161158i
$887$	2.50213e7	−	5.31845e6i	1.06783	−	0.226974i	0.359707	−	0.933065i	$-0.382877\pi$
$887$	2.50213e7	−	5.31845e6i	1.06783	−	0.226974i	0.708121	+	0.706091i	$0.249543\pi$
$888$	1.59079e7	−	7.08266e6i	0.676988	−	0.301414i
$889$	−2.53942e7	−	2.82031e7i	−1.07766	−	1.19686i
$890$	−1.05818e6	−	1.00679e7i	−0.0447799	−	0.426053i
$891$	−5.96177e6	+	4.33148e6i	−0.251583	+	0.182786i
$892$	159606.	−	1.51855e6i	0.00671639	−	0.0639022i
$893$	699909.	+	1.21228e6i	0.0293706	+	0.0508714i
$894$	2.08216e7	−	3.60641e7i	0.871306	−	1.50915i
$895$	2.38431e7	+	1.73231e7i	0.994960	+	0.722881i
$896$	−1.45777e6	+	1.61902e6i	−0.0606622	+	0.0673722i
$897$	−2.98671e6	+	9.19215e6i	−0.123940	+	0.381448i
$898$	2.57993e7			1.06762
$899$	−4.28289e7	+	699337.i	−1.76741	+	0.0288594i
$900$	1.36995e7			0.563767
$901$	−5.43467e6	+	1.67262e7i	−0.223029	+	0.686413i
$902$	4.59437e6	−	5.10256e6i	0.188022	−	0.208820i
$903$	2.38110e7	+	1.72997e7i	0.971758	+	0.706023i
$904$	2.17179e6	−	3.76165e6i	0.0883887	−	0.153094i
$905$	−2.55564e7	−	4.42650e7i	−1.03724	−	1.79655i
$906$	−2.12720e6	+	2.02390e7i	−0.0860971	+	0.819159i
$907$	−1.34694e7	+	9.78610e6i	−0.543663	+	0.394995i	−0.825444	−	0.564484i	$-0.809075\pi$
$907$	−1.34694e7	+	9.78610e6i	−0.543663	+	0.394995i	0.281780	+	0.959479i	$0.409075\pi$
$908$	−127483.	−	1.21292e6i	−0.00513141	−	0.0488221i
$909$	4.43626e6	+	4.92697e6i	0.178077	+	0.197774i
$910$	1.04179e7	−	4.63836e6i	0.417040	−	0.185678i
$911$	−1.58926e7	+	3.37808e6i	−0.634453	+	0.134857i	−0.513901	−	0.857850i	$-0.671800\pi$
$911$	−1.58926e7	+	3.37808e6i	−0.634453	+	0.134857i	−0.120553	+	0.992707i	$0.538467\pi$
$912$	−5.72621e6	−	1.21714e6i	−0.227971	−	0.0484568i
$913$	6.18088e6	+	2.75190e6i	0.245399	+	0.109259i
$914$	−4.54377e6	−	1.39843e7i	−0.179908	−	0.553701i
$915$	1.74456e7	+	5.36919e7i	0.688862	+	2.12010i
$916$	−1.33242e7	−	5.93233e6i	−0.524691	−	0.233608i
$917$	−2.21068e7	−	4.69895e6i	−0.868166	−	0.184534i
$918$	3.87627e6	−	823927.i	0.151813	−	0.0322688i
$919$	−2.15437e7	+	9.59186e6i	−0.841455	+	0.374640i	−0.781762	−	0.623577i	$-0.785679\pi$
$919$	−2.15437e7	+	9.59186e6i	−0.841455	+	0.374640i	−0.0596930	+	0.998217i	$0.519012\pi$
$920$	7.58679e6	+	8.42598e6i	0.295521	+	0.328209i
$921$	2.59456e6	+	2.46856e7i	0.100789	+	0.958946i
$922$	1.72599e6	−	1.25400e6i	0.0668668	−	0.0485816i
$923$	1.50400e6	−	1.43096e7i	0.0581091	−	0.552871i
$924$	−2.25618e6	−	3.90781e6i	−0.0869347	−	0.150575i
$925$	−3.26590e7	+	5.65670e7i	−1.25501	+	2.17375i
$926$	−2.43419e7	−	1.76855e7i	−0.932884	−	0.677780i
$927$	−1.53603e7	+	1.70593e7i	−0.587083	+	0.652022i
$928$	2.53322e6	−	7.79646e6i	0.0965614	−	0.297185i
$929$	−1.26393e7			−0.480490			−0.240245	−	0.970712i	$-0.577228\pi$
$929$	−1.26393e7			−0.480490			−0.240245	+	0.970712i	$0.577228\pi$
$930$	1.27176e7	+	3.70701e7i	0.482167	+	1.40545i
$931$	−978480.			−0.0369980
$932$	624510.	−	1.92204e6i	0.0235505	−	0.0724808i
$933$	9.58509e6	−	1.06453e7i	0.360489	−	0.400364i
$934$	−7.66577e6	−	5.56951e6i	−0.287533	−	0.208905i
$935$	3.29384e6	−	5.70509e6i	0.123218	−	0.213419i
$936$	−1.33634e6	−	2.31461e6i	−0.0498572	−	0.0863552i
$937$	306674.	−	2.91780e6i	0.0114111	−	0.108569i	−0.987334	−	0.158657i	$-0.949284\pi$
$937$	306674.	−	2.91780e6i	0.0114111	−	0.108569i	0.998745	+	0.0500880i	$0.0159502\pi$
$938$	−2.79583e7	+	2.03129e7i	−1.03754	+	0.753814i
$939$	6.23458e6	+	5.93180e7i	0.230751	+	2.19545i
$940$	1.20006e6	+	1.33280e6i	0.0442977	+	0.0491976i
$941$	1.04463e7	−	4.65101e6i	0.384583	−	0.171227i	−0.205333	−	0.978692i	$-0.565828\pi$
$941$	1.04463e7	−	4.65101e6i	0.384583	−	0.171227i	0.589916	+	0.807465i	$0.299161\pi$
$942$	−3.15674e7	+	6.70986e6i	−1.15908	+	0.246369i
$943$	3.19802e7	+	6.79761e6i	1.17112	+	0.248930i
$944$	810538.	+	360875.i	0.0296035	+	0.0131803i
$945$	5.15078e6	+	1.58525e7i	0.187626	+	0.577455i
$946$	1.38972e6	+	4.27712e6i	0.0504894	+	0.155390i
$947$	−1.24163e7	−	5.52810e6i	−0.449902	−	0.200309i	0.169262	−	0.985571i	$-0.445862\pi$
$947$	−1.24163e7	−	5.52810e6i	−0.449902	−	0.200309i	−0.619164	+	0.785262i	$0.712528\pi$
$948$	−1.25376e7	−	2.66495e6i	−0.453100	−	0.0963093i
$949$	1.16796e7	−	2.48258e6i	0.420982	−	0.0894826i
$950$	2.00605e7	−	8.93153e6i	0.721163	−	0.321083i
$951$	−2.17588e7	−	2.41656e7i	−0.780159	−	0.866455i
$952$	630027.	+	5.99431e6i	0.0225303	+	0.214361i
$953$	9.03497e6	−	6.56429e6i	0.322251	−	0.234129i	−0.414884	−	0.909874i	$-0.636178\pi$
$953$	9.03497e6	−	6.56429e6i	0.322251	−	0.234129i	0.737135	+	0.675745i	$0.236178\pi$
$954$	−1.81219e6	+	1.72418e7i	−0.0644662	+	0.613355i
$955$	2.02702e7	+	3.51091e7i	0.719201	+	1.24569i
$956$	−2.14311e6	+	3.71198e6i	−0.0758404	+	0.131359i
$957$	1.37364e7	+	9.98011e6i	0.484835	+	0.352253i
$958$	3.90359e6	−	4.33537e6i	0.137420	−	0.152620i
$959$	−4.20301e6	+	1.29355e7i	−0.147575	+	0.454190i
$960$	−7.50035e6			−0.262666
$961$	−2.25997e7	+	1.75750e7i	−0.789395	+	0.613885i
$962$	1.27431e7			0.443953
$963$	7.63335e6	−	2.34930e7i	0.265246	−	0.816345i
$964$	−2.30666e6	+	2.56181e6i	−0.0799450	+	0.0887880i
$965$	−3.07946e7	−	2.23736e7i	−1.06453	−	0.773423i
$966$	1.07432e7	−	1.86078e7i	0.370418	−	0.641584i
$967$	9.51955e6	+	1.64883e7i	0.327379	+	0.567036i	0.981991	−	0.188929i	$-0.0605015\pi$
$967$	9.51955e6	+	1.64883e7i	0.327379	+	0.567036i	−0.654612	+	0.755965i	$0.727168\pi$
$968$	−1.00533e6	+	9.56509e6i	−0.0344842	+	0.328096i
$969$	−1.31029e7	+	9.51981e6i	−0.448289	+	0.325701i
$970$	−2.47858e6	−	2.35821e7i	−0.0845810	−	0.804735i
$971$	−1.06804e7	−	1.18618e7i	−0.363528	−	0.403739i	0.533437	−	0.845840i	$-0.320900\pi$
$971$	−1.06804e7	−	1.18618e7i	−0.363528	−	0.403739i	−0.896965	+	0.442101i	$0.854233\pi$
$972$	1.62369e7	−	7.22913e6i	0.551235	−	0.245426i
$973$	3.42084e7	−	7.27122e6i	1.15838	−	0.246221i
$974$	1.36113e7	+	2.89316e6i	0.459728	+	0.0977183i
$975$	2.19091e7	+	9.75457e6i	0.738097	+	0.328622i
$976$	−2.43895e6	−	7.50632e6i	−0.0819556	−	0.252233i
$977$	−8.06653e6	−	2.48262e7i	−0.270365	−	0.832098i	−0.990409	−	0.138169i	$-0.955878\pi$
$977$	−8.06653e6	−	2.48262e7i	−0.270365	−	0.832098i	0.720044	−	0.693929i	$-0.244122\pi$
$978$	3.34562e7	+	1.48956e7i	1.11848	+	0.497980i
$979$	−2.86729e6	−	609462.i	−0.0956127	−	0.0203231i
$980$	−1.22624e6	+	260645.i	−0.0407859	+	0.00866932i
$981$	2.18459e7	−	9.72644e6i	0.724766	−	0.322687i
$982$	1.51210e6	+	1.67936e6i	0.0500383	+	0.0555732i
$983$	3.47361e6	+	3.30492e7i	0.114656	+	1.09088i	0.888935	+	0.458034i	$0.151446\pi$
$983$	3.47361e6	+	3.30492e7i	0.114656	+	1.09088i	−0.774279	+	0.632845i	$0.781887\pi$
$984$	−1.74972e7	+	1.27125e7i	−0.576079	+	0.418546i
$985$	3.78019e6	−	3.59661e7i	0.124143	−	1.18114i
$986$	−1.13399e7	−	1.96412e7i	−0.371463	−	0.643393i
$987$	1.69933e6	−	2.94333e6i	0.0555246	−	0.0961715i
$988$	−3.46587e6	−	2.51810e6i	−0.112959	−	0.0820693i
$989$	−1.43291e7	+	1.59141e7i	−0.465831	+	0.517357i
$990$	2.00674e6	−	6.17612e6i	0.0650735	−	0.200276i
$991$	3.80862e7			1.23192			0.615961	−	0.787777i	$-0.288768\pi$
$991$	3.80862e7			1.23192			0.615961	+	0.787777i	$0.288768\pi$
$992$	−1.77796e6	−	5.18254e6i	−0.0573646	−	0.167210i
$993$	1.52669e7			0.491337
$994$	−9.88441e6	+	3.04211e7i	−0.317311	+	0.976582i
$995$	−3.34152e7	+	3.71113e7i	−1.07001	+	1.18836i
$996$	−1.72415e7	−	1.25267e7i	−0.550714	−	0.400117i
$997$	2.00983e7	−	3.48113e7i	0.640357	−	1.10913i	−0.344996	−	0.938604i	$-0.612120\pi$
$997$	2.00983e7	−	3.48113e7i	0.640357	−	1.10913i	0.985353	−	0.170527i	$-0.0545469\pi$
$998$	2.15573e7	+	3.73384e7i	0.685122	+	1.18667i
$999$	−1.94693e6	+	1.85238e7i	−0.0617214	+	0.587240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.b.45.2	✓	56
31.20	even	15	inner	62.6.g.b.51.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.b.45.2	✓	56	1.1	even	1	trivial
62.6.g.b.51.2	yes	56	31.20	even	15	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-13.6729 + 15.1853i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-44.8065 + 77.6071i) q^{5} +(-40.8678 - 70.7851i) q^{6} +(-13.8993 + 132.243i) q^{7} +(51.7771 - 37.6183i) q^{8} +(-18.2448 - 173.588i) q^{9} +(-239.851 - 266.381i) q^{10} +(-94.8210 + 42.2170i) q^{11} +(319.798 - 67.9751i) q^{12} +(234.028 + 49.7441i) q^{13} +(-485.901 - 216.337i) q^{14} +(-565.854 - 1741.52i) q^{15} +(79.1084 + 243.470i) q^{16} +(647.019 + 288.072i) q^{17} +(682.919 + 145.159i) q^{18} +(1094.65 - 232.675i) q^{19} +(1309.85 - 583.182i) q^{20} +(-1818.11 - 2019.21i) q^{21} +(-43.3979 - 412.904i) q^{22} +(1599.39 - 1162.02i) q^{23} +(-136.699 + 1300.61i) q^{24} +(-2452.74 - 4248.26i) q^{25} +(-478.512 + 828.807i) q^{26} +(-1131.67 - 822.208i) q^{27} +(1423.60 - 1581.07i) q^{28} +(-2473.85 + 7613.73i) q^{29} +7324.56 q^{30} +(1736.29 + 5061.07i) q^{31} -1024.00 q^{32} +(655.402 - 2017.12i) q^{33} +(-1895.65 + 2105.33i) q^{34} +(-9640.19 - 7004.01i) q^{35} +(-1396.35 + 2418.55i) q^{36} +(-6657.66 - 11531.4i) q^{37} +(-467.914 + 4451.90i) q^{38} +(-3955.23 + 2873.64i) q^{39} +(599.494 + 5703.81i) q^{40} +(11066.0 + 12290.1i) q^{41} +(9928.85 - 4420.61i) q^{42} +(-10595.4 + 2252.11i) q^{43} +(1624.42 + 345.281i) q^{44} +(14289.1 + 6361.93i) q^{45} +(2443.65 + 7520.78i) q^{46} +(386.529 + 1189.61i) q^{47} +(-4778.83 - 2127.67i) q^{48} +(-855.234 - 181.786i) q^{49} +(19193.1 - 4079.62i) q^{50} +(-13221.1 + 5886.42i) q^{51} +(-2561.50 - 2844.83i) q^{52} +(2595.60 + 24695.5i) q^{53} +(4526.69 - 3288.83i) q^{54} +(972.253 - 9250.37i) q^{55} +(4255.08 + 7370.01i) q^{56} +(-11433.9 + 19804.0i) q^{57} +(-25906.5 - 18822.2i) q^{58} +(2319.07 - 2575.59i) q^{59} +(-9053.66 + 27864.3i) q^{60} -30830.5 q^{61} +(-21399.6 + 349.426i) q^{62} +23209.3 q^{63} +(1265.73 - 3895.53i) q^{64} +(-14346.4 + 15933.3i) q^{65} +(6863.46 + 4986.59i) q^{66} +(32486.6 - 56268.5i) q^{67} +(-5666.01 - 9813.81i) q^{68} +(-4222.62 + 40175.6i) q^{69} +(38560.8 - 28016.0i) q^{70} +(-6286.16 - 59808.8i) q^{71} +(-7474.73 - 8301.53i) q^{72} +(45592.4 - 20299.0i) q^{73} +(52097.4 - 11073.6i) q^{74} +(98047.5 + 20840.6i) q^{75} +(-16357.7 - 7282.91i) q^{76} +(-4264.95 - 13126.2i) q^{77} +(-6043.05 - 18598.6i) q^{78} +(-35815.3 - 15946.0i) q^{79} +(-22439.6 - 4769.68i) q^{80} +(69446.1 - 14761.2i) q^{81} +(-60432.5 + 26906.3i) q^{82} +(-43617.1 - 48441.7i) q^{83} +(4544.26 + 43235.8i) q^{84} +(-51347.0 + 37305.8i) q^{85} +(4529.04 - 43090.9i) q^{86} +(-81792.2 - 141668. i) q^{87} +(-3321.42 + 5752.87i) q^{88} +(22848.2 + 16600.2i) q^{89} +(-41864.5 + 46495.3i) q^{90} +(-9831.12 + 30257.1i) q^{91} -31631.3 q^{92} +(-100594. - 42833.5i) q^{93} -5003.34 q^{94} +(-30990.2 + 95378.0i) q^{95} +(14001.1 - 15549.8i) q^{96} +(53517.4 + 38882.7i) q^{97} +(1748.68 - 3028.80i) q^{98} +(9058.35 + 15689.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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