LMFDB - Embedded newform 770.2.bv.a.313.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			313.5
Character	$\chi$	$=$	770.313
Dual form			770.2.bv.a.647.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.838671 + 0.544639i) q^{2} +(-1.32101 - 1.63131i) q^{3} +(0.406737 - 0.913545i) q^{4} +(2.11605 - 0.722740i) q^{5} +(1.99636 + 0.648658i) q^{6} +(-2.64556 + 0.0316995i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.292371 + 1.37550i) q^{9} +O(q^{10})$	\(q+(-0.838671 + 0.544639i) q^{2} +(-1.32101 - 1.63131i) q^{3} +(0.406737 - 0.913545i) q^{4} +(2.11605 - 0.722740i) q^{5} +(1.99636 + 0.648658i) q^{6} +(-2.64556 + 0.0316995i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.292371 + 1.37550i) q^{9} +(-1.38103 + 1.75862i) q^{10} +(2.63845 + 2.00962i) q^{11} +(-2.02758 + 0.543288i) q^{12} +(3.67653 + 1.87329i) q^{13} +(2.20149 - 1.46746i) q^{14} +(-3.97432 - 2.49718i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(3.53395 + 2.29497i) q^{17} +(-0.503947 - 1.31283i) q^{18} +(3.86071 - 1.71890i) q^{19} +(0.200418 - 2.22707i) q^{20} +(3.54652 + 4.27385i) q^{21} +(-3.30731 - 0.248400i) q^{22} +(-0.328383 + 0.0879899i) q^{23} +(1.40457 - 1.55994i) q^{24} +(3.95529 - 3.05870i) q^{25} +(-4.10366 + 0.431313i) q^{26} +(-2.98085 + 1.51882i) q^{27} +(-1.04709 + 2.42973i) q^{28} +(1.61696 + 2.22556i) q^{29} +(4.69321 - 0.0702619i) q^{30} +(0.398792 + 0.359074i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.207116 - 6.95885i) q^{33} -4.21375 q^{34} +(-5.57522 + 1.97913i) q^{35} +(1.13766 + 0.826561i) q^{36} +(-8.49772 - 6.88132i) q^{37} +(-2.30168 + 3.54428i) q^{38} +(-1.80082 - 8.47218i) q^{39} +(1.04486 + 1.97693i) q^{40} +(6.66075 - 9.16774i) q^{41} +(-5.30207 - 1.65278i) q^{42} +(-1.34185 - 1.34185i) q^{43} +(2.90903 - 1.59296i) q^{44} +(0.375457 + 3.12193i) q^{45} +(0.227482 - 0.252645i) q^{46} +(-9.59546 - 3.68335i) q^{47} +(-0.328372 + 2.07326i) q^{48} +(6.99799 - 0.167726i) q^{49} +(-1.65130 + 4.71945i) q^{50} +(-0.924564 - 8.79664i) q^{51} +(3.20671 - 2.59674i) q^{52} +(8.41064 - 0.440783i) q^{53} +(1.67274 - 2.89728i) q^{54} +(7.03552 + 2.34552i) q^{55} +(-0.445166 - 2.60803i) q^{56} +(-7.90408 - 4.02733i) q^{57} +(-2.56823 - 0.985850i) q^{58} +(6.22393 + 2.77107i) q^{59} +(-3.89779 + 2.61503i) q^{60} +(-6.08203 + 5.47629i) q^{61} +(-0.530020 - 0.0839470i) q^{62} +(0.729884 - 3.64824i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(9.13361 + 1.30678i) q^{65} +(3.96376 + 5.72338i) q^{66} +(5.78837 + 1.55099i) q^{67} +(3.53395 - 2.29497i) q^{68} +(0.577335 + 0.419458i) q^{69} +(3.59786 - 4.69632i) q^{70} +(1.64543 - 5.06410i) q^{71} +(-1.40430 - 0.0735963i) q^{72} +(6.78790 - 2.60563i) q^{73} +(10.8746 + 1.14297i) q^{74} +(-10.2147 - 2.41174i) q^{75} -4.22607i q^{76} +(-7.04390 - 5.23292i) q^{77} +(6.12458 + 6.12458i) q^{78} +(2.63980 - 12.4193i) q^{79} +(-1.95301 - 1.08892i) q^{80} +(10.2694 + 4.57221i) q^{81} +(-0.593069 + 11.3164i) q^{82} +(-0.105502 - 0.207060i) q^{83} +(5.34686 - 1.50157i) q^{84} +(9.13667 + 2.30214i) q^{85} +(1.85619 + 0.394545i) q^{86} +(1.49455 - 5.57775i) q^{87} +(-1.57213 + 2.92034i) q^{88} +(-5.17427 + 8.96210i) q^{89} +(-2.01521 - 2.41378i) q^{90} +(-9.78587 - 4.83935i) q^{91} +(-0.0531825 + 0.335781i) q^{92} +(0.0589531 - 1.12489i) q^{93} +(10.0535 - 2.13694i) q^{94} +(6.92712 - 6.42756i) q^{95} +(-0.853782 - 1.91763i) q^{96} +(-4.60392 + 9.03571i) q^{97} +(-5.77766 + 3.95205i) q^{98} +(-3.53563 + 3.04164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.838671	+	0.544639i	−0.593030	+	0.385118i
$2$	−0.838671	+	0.544639i	−0.593030	+	0.385118i
$3$	−1.32101	−	1.63131i	−0.762684	−	0.941836i	0.236875	−	0.971540i	$-0.423877\pi$
$3$	−1.32101	−	1.63131i	−0.762684	−	0.941836i	−0.999559	+	0.0297038i	$0.990544\pi$
$4$	0.406737	−	0.913545i	0.203368	−	0.456773i
$5$	2.11605	−	0.722740i	0.946324	−	0.323219i
$5$	2.11605	−	0.722740i	0.946324	−	0.323219i
$6$	1.99636	+	0.648658i	0.815012	+	0.264814i
$7$	−2.64556	+	0.0316995i	−0.999928	+	0.0119813i
$7$	−2.64556	+	0.0316995i	−0.999928	+	0.0119813i
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−0.292371	+	1.37550i	−0.0974572	+	0.458500i
$10$	−1.38103	+	1.75862i	−0.436721	+	0.556125i
$11$	2.63845	+	2.00962i	0.795524	+	0.605922i
$11$	2.63845	+	2.00962i	0.795524	+	0.605922i
$12$	−2.02758	+	0.543288i	−0.585311	+	0.156834i
$13$	3.67653	+	1.87329i	1.01969	+	0.519556i	0.882164	−	0.470942i	$-0.156086\pi$
$13$	3.67653	+	1.87329i	1.01969	+	0.519556i	0.137523	+	0.990499i	$0.456086\pi$
$14$	2.20149	−	1.46746i	0.588373	−	0.392196i
$15$	−3.97432	−	2.49718i	−1.02617	−	0.644769i
$16$	−0.669131	−	0.743145i	−0.167283	−	0.185786i
$17$	3.53395	+	2.29497i	0.857109	+	0.556613i	0.896718	−	0.442602i	$-0.145945\pi$
$17$	3.53395	+	2.29497i	0.857109	+	0.556613i	−0.0396093	+	0.999215i	$0.512611\pi$
$18$	−0.503947	−	1.31283i	−0.118782	−	0.309437i
$19$	3.86071	−	1.71890i	0.885708	−	0.394342i	0.0871036	−	0.996199i	$-0.472239\pi$
$19$	3.86071	−	1.71890i	0.885708	−	0.394342i	0.798604	+	0.601857i	$0.205572\pi$
$20$	0.200418	−	2.22707i	0.0448147	−	0.497988i
$21$	3.54652	+	4.27385i	0.773914	+	0.932631i
$22$	−3.30731	−	0.248400i	−0.705121	−	0.0529591i
$23$	−0.328383	+	0.0879899i	−0.0684725	+	0.0183472i	−0.292893	−	0.956145i	$-0.594618\pi$
$23$	−0.328383	+	0.0879899i	−0.0684725	+	0.0183472i	0.224420	+	0.974492i	$0.427951\pi$
$24$	1.40457	−	1.55994i	0.286707	−	0.318421i
$25$	3.95529	−	3.05870i	0.791059	−	0.611740i
$26$	−4.10366	+	0.431313i	−0.804795	+	0.0845873i
$27$	−2.98085	+	1.51882i	−0.573665	+	0.292297i
$28$	−1.04709	+	2.42973i	−0.197881	+	0.459177i
$29$	1.61696	+	2.22556i	0.300263	+	0.413276i	0.932314	−	0.361651i	$-0.117787\pi$
$29$	1.61696	+	2.22556i	0.300263	+	0.413276i	−0.632051	+	0.774927i	$0.717787\pi$
$30$	4.69321	−	0.0702619i	0.856859	−	0.0128280i
$31$	0.398792	+	0.359074i	0.0716251	+	0.0644915i	0.704166	−	0.710036i	$-0.251321\pi$
$31$	0.398792	+	0.359074i	0.0716251	+	0.0644915i	−0.632541	+	0.774527i	$0.717988\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−0.207116	−	6.95885i	−0.0360542	−	1.21138i
$34$	−4.21375			−0.722653
$35$	−5.57522	+	1.97913i	−0.942384	+	0.334534i
$36$	1.13766	+	0.826561i	0.189611	+	0.137760i
$37$	−8.49772	−	6.88132i	−1.39702	−	1.13128i	−0.974361	−	0.224992i	$-0.927764\pi$
$37$	−8.49772	−	6.88132i	−1.39702	−	1.13128i	−0.422656	−	0.906290i	$-0.638902\pi$
$38$	−2.30168	+	3.54428i	−0.373383	+	0.574959i
$39$	−1.80082	−	8.47218i	−0.288362	−	1.35664i
$40$	1.04486	+	1.97693i	0.165208	+	0.312580i
$41$	6.66075	−	9.16774i	1.04024	−	1.43176i	0.143257	−	0.989686i	$-0.454242\pi$
$41$	6.66075	−	9.16774i	1.04024	−	1.43176i	0.896978	−	0.442075i	$-0.145758\pi$
$42$	−5.30207	−	1.65278i	−0.818127	−	0.255030i
$43$	−1.34185	−	1.34185i	−0.204629	−	0.204629i	0.597351	−	0.801980i	$-0.296220\pi$
$43$	−1.34185	−	1.34185i	−0.204629	−	0.204629i	−0.801980	+	0.597351i	$0.796220\pi$
$44$	2.90903	−	1.59296i	0.438553	−	0.240148i
$45$	0.375457	+	3.12193i	0.0559698	+	0.465390i
$46$	0.227482	−	0.252645i	0.0335404	−	0.0372504i
$47$	−9.59546	−	3.68335i	−1.39964	−	0.537272i	−0.462625	−	0.886554i	$-0.653092\pi$
$47$	−9.59546	−	3.68335i	−1.39964	−	0.537272i	−0.937018	+	0.349282i	$0.886426\pi$
$48$	−0.328372	+	2.07326i	−0.0473964	+	0.299249i
$49$	6.99799	−	0.167726i	0.999713	−	0.0239608i
$50$	−1.65130	+	4.71945i	−0.233529	+	0.667431i
$51$	−0.924564	−	8.79664i	−0.129465	−	1.23178i
$52$	3.20671	−	2.59674i	0.444691	−	0.360104i
$53$	8.41064	−	0.440783i	1.15529	−	0.0605462i	0.534953	−	0.844882i	$-0.320329\pi$
$53$	8.41064	−	0.440783i	1.15529	−	0.0605462i	0.620337	+	0.784335i	$0.286996\pi$
$54$	1.67274	−	2.89728i	0.227632	−	0.394270i
$55$	7.03552	+	2.34552i	0.948669	+	0.316270i
$56$	−0.445166	−	2.60803i	−0.0594878	−	0.348513i
$57$	−7.90408	−	4.02733i	−1.04692	−	0.533433i
$58$	−2.56823	−	0.985850i	−0.337225	−	0.129448i
$59$	6.22393	+	2.77107i	0.810287	+	0.360763i	0.769694	−	0.638413i	$-0.220409\pi$
$59$	6.22393	+	2.77107i	0.810287	+	0.360763i	0.0405929	+	0.999176i	$0.487075\pi$
$60$	−3.89779	+	2.61503i	−0.503202	+	0.337599i
$61$	−6.08203	+	5.47629i	−0.778724	+	0.701167i	−0.959298	−	0.282395i	$-0.908871\pi$
$61$	−6.08203	+	5.47629i	−0.778724	+	0.701167i	0.180574	+	0.983561i	$0.442205\pi$
$62$	−0.530020	−	0.0839470i	−0.0673127	−	0.0106613i
$63$	0.729884	−	3.64824i	0.0919567	−	0.459635i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	9.13361	+	1.30678i	1.13288	+	0.162087i
$66$	3.96376	+	5.72338i	0.487906	+	0.704500i
$67$	5.78837	+	1.55099i	0.707162	+	0.189483i	0.594436	−	0.804143i	$-0.297375\pi$
$67$	5.78837	+	1.55099i	0.707162	+	0.189483i	0.112726	+	0.993626i	$0.464042\pi$
$68$	3.53395	−	2.29497i	0.428554	−	0.278306i
$69$	0.577335	+	0.419458i	0.0695029	+	0.0504968i
$70$	3.59786	−	4.69632i	0.430026	−	0.561317i
$71$	1.64543	−	5.06410i	0.195276	−	0.600998i	−0.804697	−	0.593686i	$-0.797672\pi$
$71$	1.64543	−	5.06410i	0.195276	−	0.600998i	0.999973	−	0.00731266i	$-0.00232771\pi$
$72$	−1.40430	−	0.0735963i	−0.165499	−	0.00867341i
$73$	6.78790	−	2.60563i	0.794464	−	0.304966i	0.0729226	−	0.997338i	$-0.476767\pi$
$73$	6.78790	−	2.60563i	0.794464	−	0.304966i	0.721541	+	0.692372i	$0.243434\pi$
$74$	10.8746	+	1.14297i	1.26415	+	0.132867i
$75$	−10.2147	−	2.41174i	−1.17949	−	0.278484i
$76$		−	4.22607i		−	0.484764i
$77$	−7.04390	−	5.23292i	−0.802727	−	0.596347i
$78$	6.12458	+	6.12458i	0.693472	+	0.693472i
$79$	2.63980	−	12.4193i	0.297001	−	1.39728i	−0.536098	−	0.844156i	$-0.680102\pi$
$79$	2.63980	−	12.4193i	0.297001	−	1.39728i	0.833099	−	0.553124i	$-0.186564\pi$
$80$	−1.95301	−	1.08892i	−0.218353	−	0.121745i
$81$	10.2694	+	4.57221i	1.14104	+	0.508023i
$82$	−0.593069	+	11.3164i	−0.0654935	+	1.24969i
$83$	−0.105502	−	0.207060i	−0.0115804	−	0.0227278i	0.885144	−	0.465317i	$-0.154060\pi$
$83$	−0.105502	−	0.207060i	−0.0115804	−	0.0227278i	−0.896724	+	0.442590i	$0.854060\pi$
$84$	5.34686	−	1.50157i	0.583390	−	0.163835i
$85$	9.13667	+	2.30214i	0.991011	+	0.249702i
$86$	1.85619	+	0.394545i	0.200158	+	0.0425449i
$87$	1.49455	−	5.57775i	0.160233	−	0.597997i
$88$	−1.57213	+	2.92034i	−0.167589	+	0.311310i
$89$	−5.17427	+	8.96210i	−0.548472	+	0.949981i	0.449908	+	0.893075i	$0.351457\pi$
$89$	−5.17427	+	8.96210i	−0.548472	+	0.949981i	−0.998380	+	0.0569059i	$0.981876\pi$
$90$	−2.01521	−	2.41378i	−0.212422	−	0.254435i
$91$	−9.78587	−	4.83935i	−1.02584	−	0.507302i
$92$	−0.0531825	+	0.335781i	−0.00554466	+	0.0350076i
$93$	0.0589531	−	1.12489i	0.00611315	−	0.116646i
$94$	10.0535	−	2.13694i	1.03694	−	0.220409i
$95$	6.92712	−	6.42756i	0.710708	−	0.659453i
$96$	−0.853782	−	1.91763i	−0.0871387	−	0.195717i
$97$	−4.60392	+	9.03571i	−0.467458	+	0.917437i	0.530123	+	0.847921i	$0.322146\pi$
$97$	−4.60392	+	9.03571i	−0.467458	+	0.917437i	−0.997581	+	0.0695165i	$0.977854\pi$
$98$	−5.77766	+	3.95205i	−0.583632	+	0.399217i
$99$	−3.53563	+	3.04164i	−0.355345	+	0.305696i
$100$	−1.18550	−	4.85743i	−0.118550	−	0.485743i
$101$	−5.79684	−	5.21950i	−0.576808	−	0.519360i	0.328283	−	0.944580i	$-0.393530\pi$
$101$	−5.79684	−	5.21950i	−0.576808	−	0.519360i	−0.905090	+	0.425220i	$0.860197\pi$
$102$	5.56640	+	6.87393i	0.551156	+	0.680620i
$103$	6.15853	+	4.98708i	0.606818	+	0.491391i	0.882786	−	0.469776i	$-0.155665\pi$
$103$	6.15853	+	4.98708i	0.606818	+	0.491391i	−0.275968	+	0.961167i	$0.588999\pi$
$104$	−1.27509	+	3.92431i	−0.125033	+	0.384811i
$105$	10.5935	+	6.48045i	1.03382	+	0.632428i
$106$	−6.81369	+	4.95043i	−0.661804	+	0.480829i
$107$	3.86676	−	10.0733i	0.373814	−	0.973818i	−0.609643	−	0.792676i	$-0.708687\pi$
$107$	3.86676	−	10.0733i	0.373814	−	0.973818i	0.983457	−	0.181142i	$-0.0579795\pi$
$108$	0.175089	+	3.34090i	0.0168480	+	0.321479i
$109$	1.89080	−	1.09166i	0.181106	−	0.104562i	−0.406706	−	0.913559i	$-0.633323\pi$
$109$	1.89080	−	1.09166i	0.181106	−	0.104562i	0.587812	+	0.808997i	$0.299989\pi$
$110$	−7.17795	+	1.86470i	−0.684390	+	0.177792i
$111$			22.9527i			2.17857i
$112$	1.79378	+	1.94482i	0.169497	+	0.183769i
$113$	−2.87667	−	18.1626i	−0.270614	−	1.70859i	−0.630995	−	0.775787i	$-0.717353\pi$
$113$	−2.87667	−	18.1626i	−0.270614	−	1.70859i	0.360381	−	0.932805i	$-0.382647\pi$
$114$	8.82236	−	0.927268i	0.826290	−	0.0868466i
$115$	−0.631279	+	0.423526i	−0.0588671	+	0.0394940i
$116$	2.69083	−	0.571953i	0.249837	−	0.0531045i
$117$	−3.65162	+	4.50937i	−0.337592	+	0.416892i
$118$	−6.72907	+	1.06578i	−0.619461	+	0.0981129i
$119$	−9.42203	−	5.95947i	−0.863716	−	0.546304i
$120$	1.84471	−	4.31604i	0.168398	−	0.393999i
$121$	2.92289	+	10.6046i	0.265717	+	0.964051i
$122$	2.11822	−	7.90531i	0.191775	−	0.715713i
$123$	−23.7543	+	1.24491i	−2.14186	+	0.112250i
$124$	0.490233	−	0.218266i	0.0440243	−	0.0196009i
$125$	6.15894	−	9.33100i	0.550872	−	0.834590i
$126$	1.37484	+	3.45719i	0.122480	+	0.307991i
$127$	3.24473	+	6.36815i	0.287924	+	0.565082i	0.988984	−	0.148020i	$-0.0472899\pi$
$127$	3.24473	+	6.36815i	0.287924	+	0.565082i	−0.701061	+	0.713101i	$0.747290\pi$
$128$	0.629320	−	0.777146i	0.0556246	−	0.0686906i
$129$	−0.416376	+	3.96155i	−0.0366598	+	0.348795i
$130$	−8.37181	+	3.87856i	−0.734257	+	0.340172i
$131$	−0.720018	−	0.415702i	−0.0629082	−	0.0363201i	0.468216	−	0.883614i	$-0.344897\pi$
$131$	−0.720018	−	0.415702i	−0.0629082	−	0.0363201i	−0.531124	+	0.847294i	$0.678230\pi$
$132$	−6.44147	−	2.64121i	−0.560658	−	0.229888i
$133$	−10.1593	+	4.66983i	−0.880919	+	0.404926i
$134$	−5.69927	+	1.85180i	−0.492342	+	0.159971i
$135$	−5.20991	+	5.36827i	−0.448397	+	0.462027i
$136$	−1.71389	+	3.84945i	−0.146965	+	0.330088i
$137$	1.07731	−	1.65892i	0.0920412	−	0.141731i	−0.789651	−	0.613557i	$-0.789738\pi$
$137$	1.07731	−	1.65892i	0.0920412	−	0.141731i	0.881692	+	0.471826i	$0.156405\pi$
$138$	−0.712647	−	0.0373482i	−0.0606645	−	0.00317929i
$139$	−4.80445	+	3.49064i	−0.407508	+	0.296072i	−0.772592	−	0.634903i	$-0.781040\pi$
$139$	−4.80445	+	3.49064i	−0.407508	+	0.296072i	0.365084	+	0.930974i	$0.381040\pi$
$140$	−0.459620	+	5.89820i	−0.0388450	+	0.498489i
$141$	6.66700	+	20.5189i	0.561462	+	1.72800i
$142$	1.37814	+	5.14328i	0.115651	+	0.431614i
$143$	5.93578	+	12.3310i	0.496375	+	1.03117i
$144$	1.21783	−	0.703115i	0.101486	−	0.0585929i
$145$	5.03007	+	3.54074i	0.417725	+	0.294043i
$146$	−4.27368	+	5.88222i	−0.353693	+	0.486816i
$147$	−9.51801	−	11.1943i	−0.785032	−	0.923292i
$148$	−9.74273	+	4.96417i	−0.800848	+	0.408052i
$149$	−9.21043	+	8.29311i	−0.754548	+	0.679398i	−0.953764	−	0.300558i	$-0.902827\pi$
$149$	−9.21043	+	8.29311i	−0.754548	+	0.679398i	0.199216	+	0.979956i	$0.436161\pi$
$150$	9.88026	−	3.54065i	0.806720	−	0.289093i
$151$	−1.74126	+	16.5670i	−0.141702	+	1.34820i	0.660353	+	0.750955i	$0.270407\pi$
$151$	−1.74126	+	16.5670i	−0.141702	+	1.34820i	−0.802055	+	0.597250i	$0.796260\pi$
$152$	2.30168	+	3.54428i	0.186691	+	0.287479i
$153$	−4.18996	+	4.18996i	−0.338738	+	0.338738i
$154$	8.75757	+	0.552318i	0.705705	+	0.0445070i
$155$	1.10338	+	0.471594i	0.0886255	+	0.0378793i
$156$	−8.47218	−	1.80082i	−0.678318	−	0.144181i
$157$	−5.50717	+	4.45962i	−0.439520	+	0.355916i	−0.823395	−	0.567469i	$-0.807923\pi$
$157$	−5.50717	+	4.45962i	−0.439520	+	0.355916i	0.383875	+	0.923385i	$0.374589\pi$
$158$	4.55011	+	11.8534i	0.361987	+	0.943009i
$159$	−11.8296	−	13.1381i	−0.938146	−	1.04192i
$160$	2.23100	−	0.150440i	0.176376	−	0.0118933i
$161$	0.865967	−	0.243192i	0.0682478	−	0.0191662i
$162$	−11.1028	+	1.75851i	−0.872319	+	0.138162i
$163$	4.22651	+	6.50826i	0.331046	+	0.509766i	0.964524	−	0.263994i	$-0.0850400\pi$
$163$	4.22651	+	6.50826i	0.331046	+	0.509766i	−0.633478	+	0.773761i	$0.718373\pi$
$164$	−5.66598	−	9.81376i	−0.442438	−	0.766326i
$165$	−5.46770	−	14.5756i	−0.425660	−	1.13471i
$166$	0.201255	+	0.116194i	0.0156204	+	0.00901843i
$167$	−3.38135	+	6.63627i	−0.261656	+	0.513530i	−0.984037	−	0.177966i	$-0.943048\pi$
$167$	−3.38135	+	6.63627i	−0.261656	+	0.513530i	0.722380	+	0.691496i	$0.243048\pi$
$168$	−3.66644	+	4.17143i	−0.282872	+	0.321833i
$169$	2.36648	+	3.25718i	0.182037	+	0.250552i
$170$	−8.91649	+	3.04545i	−0.683864	+	0.233575i
$171$	1.23558	+	5.81296i	0.0944874	+	0.444528i
$172$	−1.77161	+	0.680059i	−0.135084	+	0.0518540i
$173$	−0.179821	+	0.468449i	−0.0136715	+	0.0356155i	−0.940246	−	0.340495i	$-0.889405\pi$
$173$	−0.179821	+	0.468449i	−0.0136715	+	0.0356155i	0.926575	+	0.376111i	$0.122739\pi$
$174$	1.78442	+	5.49189i	0.135277	+	0.416339i
$175$	−10.3670	+	8.21736i	−0.783673	+	0.621174i
$176$	−0.272035	−	3.30545i	−0.0205054	−	0.249158i
$177$	−3.70139	−	13.8138i	−0.278213	−	1.03831i
$178$	−0.541601	−	10.3344i	−0.0405947	−	0.774593i
$179$	−24.3795	−	2.56239i	−1.82221	−	0.191522i	−0.869200	−	0.494460i	$-0.835366\pi$
$179$	−24.3795	−	2.56239i	−1.82221	−	0.191522i	−0.953010	+	0.302938i	$0.902033\pi$
$180$	3.00473	+	0.926805i	0.223960	+	0.0690800i
$181$	14.6100	+	4.74707i	1.08595	+	0.352847i	0.796681	−	0.604400i	$-0.206587\pi$
$181$	14.6100	+	4.74707i	1.08595	+	0.352847i	0.289271	+	0.957247i	$0.406587\pi$
$182$	10.8428	−	1.27115i	0.803724	−	0.0942237i
$183$	16.9679	+	2.68746i	1.25431	+	0.198662i
$184$	−0.138277	−	0.310575i	−0.0101939	−	0.0228959i
$185$	−22.9550	−	8.41954i	−1.68768	−	0.619017i
$186$	0.563218	+	0.975522i	0.0412971	+	0.0715287i
$187$	4.71215	+	13.1571i	0.344587	+	0.962140i
$188$	−7.26774	+	7.26774i	−0.530054	+	0.530054i
$189$	7.83788	−	4.11262i	0.570122	−	0.299149i
$190$	−2.30887	+	9.16338i	−0.167503	+	0.664782i
$191$	−2.61110	−	24.8430i	−0.188933	−	1.79758i	−0.520206	−	0.854041i	$-0.674145\pi$
$191$	−2.61110	−	24.8430i	−0.188933	−	1.79758i	0.331273	−	0.943535i	$-0.392522\pi$
$192$	1.76046	+	1.14325i	0.127050	+	0.0825072i
$193$	18.2869	+	11.8756i	1.31632	+	0.854827i	0.995723	−	0.0923897i	$-0.0294505\pi$
$193$	18.2869	+	11.8756i	1.31632	+	0.854827i	0.320595	+	0.947216i	$0.396117\pi$
$194$	−1.06002	−	10.0855i	−0.0761053	−	0.724094i
$195$	−9.93380	−	16.6260i	−0.711374	−	1.19061i
$196$	2.69311	−	6.46120i	0.192365	−	0.461514i
$197$	13.5807	−	13.5807i	0.967585	−	0.967585i	−0.0319055	−	0.999491i	$-0.510158\pi$
$197$	13.5807	−	13.5807i	0.967585	−	0.967585i	0.999491	+	0.0319055i	$0.0101575\pi$
$198$	1.30864	−	4.47658i	0.0930008	−	0.318137i
$199$	4.07584	+	7.05957i	0.288929	+	0.500440i	0.973554	−	0.228456i	$-0.0733675\pi$
$199$	4.07584	+	7.05957i	0.288929	+	0.500440i	−0.684625	+	0.728895i	$0.740034\pi$
$200$	3.63979	+	3.42811i	0.257372	+	0.242404i
$201$	−5.11634	−	11.4915i	−0.360879	−	0.810547i
$202$	7.70439	+	1.22026i	0.542079	+	0.0858569i
$203$	−4.34833	−	5.83660i	−0.305193	−	0.409649i
$204$	−8.41219	−	2.73328i	−0.588971	−	0.191368i
$205$	7.46857	−	24.2133i	0.521627	−	1.69113i
$206$	−7.88113	−	0.828340i	−0.549104	−	0.0577132i
$207$	−0.0250203	−	0.477416i	−0.00173903	−	0.0331827i
$208$	−1.06796	−	3.98567i	−0.0740495	−	0.276356i
$209$	13.6406	+	3.22331i	0.943542	+	0.222961i
$210$	−12.4139	+	0.334654i	−0.856644	+	0.0230933i
$211$	3.17431	+	9.76953i	0.218529	+	0.672562i	0.998884	+	0.0472259i	$0.0150381\pi$
$211$	3.17431	+	9.76953i	0.218529	+	0.672562i	−0.780356	+	0.625336i	$0.784962\pi$
$212$	3.01824	−	7.86279i	0.207294	−	0.540018i
$213$	−10.4347	+	4.00552i	−0.714976	+	0.274454i
$214$	2.24335	+	10.5541i	0.153352	+	0.721466i
$215$	−3.80921	−	1.86960i	−0.259786	−	0.127506i
$216$	−1.96643	−	2.70656i	−0.133799	−	0.184158i
$217$	−1.06641	−	0.937310i	−0.0723927	−	0.0636287i
$218$	−0.991203	+	1.94535i	−0.0671328	+	0.131755i
$219$	−13.2175	−	7.63110i	−0.893153	−	0.515662i
$220$	5.00434	−	5.47326i	0.337393	−	0.369007i
$221$	8.69354	+	15.0576i	0.584791	+	1.01289i
$222$	−12.5009	−	19.2497i	−0.839007	−	1.29196i
$223$	−22.7582	+	3.60455i	−1.52400	+	0.241378i	−0.861529	−	0.507708i	$-0.830493\pi$
$223$	−22.7582	+	3.60455i	−1.52400	+	0.241378i	−0.662473	+	0.749086i	$0.730493\pi$
$224$	−2.56362	−	0.654102i	−0.171289	−	0.0437041i
$225$	3.05082	+	6.33478i	0.203388	+	0.422319i
$226$	12.3046	+	13.6657i	0.818492	+	0.909027i
$227$	2.91251	+	7.58734i	0.193310	+	0.503590i	0.995639	−	0.0932928i	$-0.0297393\pi$
$227$	2.91251	+	7.58734i	0.193310	+	0.503590i	−0.802329	+	0.596882i	$0.796406\pi$
$228$	−6.89403	+	5.58267i	−0.456568	+	0.369722i
$229$	−8.18287	−	1.73932i	−0.540739	−	0.114938i	−0.0705583	−	0.997508i	$-0.522478\pi$
$229$	−8.18287	−	1.73932i	−0.540739	−	0.114938i	−0.470181	+	0.882570i	$0.655811\pi$
$230$	0.298766	−	0.699018i	0.0197001	−	0.0460919i
$231$	0.768529	+	18.4035i	0.0505655	+	1.21086i
$232$	−1.94521	+	1.94521i	−0.127709	+	0.127709i
$233$	1.50784	+	2.32187i	0.0987819	+	0.152111i	0.884606	−	0.466339i	$-0.154427\pi$
$233$	1.50784	+	2.32187i	0.0987819	+	0.152111i	−0.785824	+	0.618450i	$0.787761\pi$
$234$	0.606524	−	5.77069i	0.0396497	−	0.377242i
$235$	−22.9665	−	0.859120i	−1.49817	−	0.0560428i
$236$	5.06300	−	4.55875i	0.329573	−	0.296749i
$237$	−23.7469	+	12.0997i	−1.54253	+	0.785957i
$238$	11.1477	−	0.133574i	0.722601	−	0.00865830i
$239$	9.41058	−	12.9526i	0.608720	−	0.837831i	−0.387751	−	0.921764i	$-0.626748\pi$
$239$	9.41058	−	12.9526i	0.608720	−	0.837831i	0.996471	+	0.0839328i	$0.0267481\pi$
$240$	0.803576	+	4.62444i	0.0518706	+	0.298506i
$241$	10.4295	−	6.02145i	0.671821	−	0.387876i	−0.124945	−	0.992164i	$-0.539876\pi$
$241$	10.4295	−	6.02145i	0.671821	−	0.387876i	0.796766	+	0.604288i	$0.206542\pi$
$242$	−8.22700	−	7.30181i	−0.528852	−	0.469378i
$243$	−3.50958	−	13.0979i	−0.225140	−	0.840233i
$244$	2.52905	+	7.78362i	0.161906	+	0.498295i
$245$	14.6868	−	5.41264i	0.938308	−	0.345801i
$246$	19.2440	−	13.9816i	1.22695	−	0.891434i
$247$	17.4140	+	0.912630i	1.10803	+	0.0580692i
$248$	−0.292268	+	0.450053i	−0.0185590	+	0.0285784i
$249$	−0.198409	+	0.445635i	−0.0125737	+	0.0282409i
$250$	−0.0832961	+	11.1800i	−0.00526811	+	0.707087i
$251$	13.9202	−	4.52296i	0.878638	−	0.285487i	0.165246	−	0.986252i	$-0.447158\pi$
$251$	13.9202	−	4.52296i	0.878638	−	0.285487i	0.713392	+	0.700766i	$0.247158\pi$
$252$	−3.03596	−	2.15065i	−0.191247	−	0.135478i
$253$	−1.04325	−	0.427766i	−0.0655885	−	0.0268934i
$254$	−6.18960	−	3.57357i	−0.388370	−	0.224226i
$255$	−8.31410	−	17.9459i	−0.520649	−	1.12381i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−10.5932	+	13.0815i	−0.660786	+	0.816002i	−0.991824	−	0.127615i	$-0.959268\pi$
$257$	−10.5932	+	13.0815i	−0.660786	+	0.816002i	0.331038	+	0.943617i	$0.392601\pi$
$258$	−1.80841	−	3.54921i	−0.112587	−	0.220964i
$259$	22.6994	+	17.9356i	1.41047	+	1.11446i
$260$	4.90878	−	7.81245i	0.304430	−	0.484507i
$261$	−3.53401	+	1.57344i	−0.218750	+	0.0973937i
$262$	0.830265	−	0.0435124i	0.0512940	−	0.00268820i
$263$	3.03619	−	11.3312i	0.187219	−	0.698712i	−0.806925	−	0.590653i	$-0.798870\pi$
$263$	3.03619	−	11.3312i	0.187219	−	0.698712i	0.994145	−	0.108058i	$-0.0344633\pi$
$264$	6.84078	−	1.29317i	0.421021	−	0.0795891i
$265$	17.4787	−	7.01142i	1.07371	−	0.430708i
$266$	5.97690	−	9.44958i	0.366467	−	0.579391i
$267$	21.4552	−	3.39817i	1.31304	−	0.207965i
$268$	3.77124	−	4.65710i	0.230365	−	0.284477i
$269$	−27.3606	+	5.81568i	−1.66821	+	0.354588i	−0.942704	−	0.333630i	$-0.891726\pi$
$269$	−27.3606	+	5.81568i	−1.66821	+	0.354588i	−0.725503	+	0.688219i	$0.758393\pi$
$270$	1.44562	−	7.33973i	0.0879779	−	0.446682i
$271$	−14.7345	+	1.54866i	−0.895060	+	0.0940746i	−0.540877	−	0.841102i	$-0.681908\pi$
$271$	−14.7345	+	1.54866i	−0.895060	+	0.0940746i	−0.354183	+	0.935176i	$0.615241\pi$
$272$	−0.659176	−	4.16187i	−0.0399684	−	0.252351i
$273$	5.03274	+	22.3566i	0.304595	+	1.35308i
$274$			1.97803i			0.119497i
$275$	16.5827	−	0.121619i	0.999973	−	0.00733390i
$276$	0.618017	−	0.356812i	0.0372003	−	0.0214776i
$277$	−0.331406	−	6.32361i	−0.0199123	−	0.379949i	−0.990349	−	0.138594i	$-0.955742\pi$
$277$	−0.331406	−	6.32361i	−0.0199123	−	0.379949i	0.970437	−	0.241355i	$-0.0775917\pi$
$278$	2.12821	−	5.54418i	0.127642	−	0.332518i
$279$	−0.610501	+	0.443555i	−0.0365497	+	0.0265549i
$280$	−2.82692	−	5.19697i	−0.168941	−	0.310579i
$281$	−9.60412	+	29.5584i	−0.572934	+	1.76331i	0.0701768	+	0.997535i	$0.477644\pi$
$281$	−9.60412	+	29.5584i	−0.572934	+	1.76331i	−0.643110	+	0.765774i	$0.722356\pi$
$282$	−16.7668	−	13.5775i	−0.998449	−	0.808528i
$283$	4.44629	+	5.49071i	0.264305	+	0.326389i	0.891970	−	0.452094i	$-0.149323\pi$
$283$	4.44629	+	5.49071i	0.264305	+	0.326389i	−0.627666	+	0.778483i	$0.715989\pi$
$284$	−3.95703	−	3.56293i	−0.234807	−	0.211421i
$285$	−19.6361	−	2.80942i	−1.16314	−	0.166416i
$286$	−11.6941	−	7.10879i	−0.691487	−	0.420352i
$287$	−17.3308	+	24.4650i	−1.02301	+	1.44412i
$288$	−0.638415	+	1.25296i	−0.0376189	+	0.0738313i
$289$	0.307374	+	0.690372i	0.0180808	+	0.0406101i
$290$	−6.14700	−	0.229943i	−0.360964	−	0.0135027i
$291$	20.8218	−	4.42582i	1.22060	−	0.259446i
$292$	0.380526	−	7.26086i	0.0222686	−	0.424910i
$293$	−1.29565	+	8.18044i	−0.0756929	+	0.477906i	0.920501	+	0.390740i	$0.127781\pi$
$293$	−1.29565	+	8.18044i	−0.0756929	+	0.477906i	−0.996194	+	0.0871657i	$0.972219\pi$
$294$	14.0793	+	4.20446i	0.821124	+	0.245209i
$295$	15.1729	+	1.36543i	0.883400	+	0.0794986i
$296$	5.46726	−	9.46958i	0.317778	−	0.550408i
$297$	−10.9171	−	1.98303i	−0.633474	−	0.115067i
$298$	3.20777	−	11.9715i	0.185821	−	0.693493i
$299$	−1.37214	−	0.291657i	−0.0793529	−	0.0168670i
$300$	−6.35791	+	8.35061i	−0.367074	+	0.482123i
$301$	3.59247	+	3.50740i	0.207066	+	0.202163i
$302$	−7.56270	−	14.8426i	−0.435184	−	0.854098i
$303$	−0.856943	+	16.3514i	−0.0492301	+	0.939366i
$304$	−3.86071	−	1.71890i	−0.221427	−	0.0985856i
$305$	−8.91193	+	15.9838i	−0.510295	+	0.915230i
$306$	1.23198	−	5.79601i	0.0704277	−	0.331336i
$307$	14.4650	+	14.4650i	0.825558	+	0.825558i	0.986899	−	0.161340i	$-0.0515817\pi$
$307$	14.4650	+	14.4650i	0.825558	+	0.825558i	−0.161340	+	0.986899i	$0.551582\pi$
$308$	−7.64553	+	4.30650i	−0.435644	+	0.245386i
$309$		−	16.6344i		−	0.946299i
$310$	−1.18222	+	0.205431i	−0.0671455	+	0.0116677i
$311$	20.4305	+	2.14733i	1.15851	+	0.121764i	0.664221	−	0.747536i	$-0.268763\pi$
$311$	20.4305	+	2.14733i	1.15851	+	0.121764i	0.494285	+	0.869300i	$0.335430\pi$
$312$	8.08617	−	3.10399i	0.457789	−	0.175729i
$313$	−14.0280	−	0.735179i	−0.792912	−	0.0415548i	−0.348421	−	0.937338i	$-0.613282\pi$
$313$	−14.0280	−	0.735179i	−0.792912	−	0.0415548i	−0.444491	+	0.895783i	$0.646615\pi$
$314$	2.18982	−	6.73957i	0.123579	−	0.380336i
$315$	−1.09226	−	8.24735i	−0.0615418	−	0.464686i
$316$	−10.2719	−	7.46296i	−0.577839	−	0.419824i
$317$	25.4937	−	16.5558i	1.43187	−	0.929867i	0.432264	−	0.901747i	$-0.357715\pi$
$317$	25.4937	−	16.5558i	1.43187	−	0.929867i	0.999605	−	0.0281196i	$-0.00895192\pi$
$318$	17.0766	+	4.57567i	0.957609	+	0.256591i
$319$	−0.206234	+	9.12152i	−0.0115469	+	0.510707i
$320$	−1.78914	+	1.34126i	−0.100016	+	0.0749787i
$321$	−21.5406	+	6.99897i	−1.20228	+	0.390644i
$322$	−0.593809	+	0.675598i	−0.0330917	+	0.0376496i
$323$	17.5884	+	2.78573i	0.978644	+	0.155002i
$324$	8.35384	−	7.52184i	0.464102	−	0.417880i
$325$	20.2716	−	3.83601i	1.12447	−	0.212783i
$326$	−7.08931	−	3.15636i	−0.392640	−	0.174815i
$327$	−4.27860	−	1.64240i	−0.236607	−	0.0908249i
$328$	10.0968	+	5.14460i	0.557505	+	0.284063i
$329$	25.5022	+	9.44037i	1.40598	+	0.520464i
$330$	12.5240	+	9.24616i	0.689425	+	0.508985i
$331$	−1.39876	+	2.42273i	−0.0768830	+	0.133165i	−0.901904	−	0.431937i	$-0.857830\pi$
$331$	−1.39876	+	2.42273i	−0.0768830	+	0.133165i	0.825021	+	0.565103i	$0.191163\pi$
$332$	−0.232070	+	0.0121623i	−0.0127365	+	0.000667492i
$333$	11.9497	−	9.67671i	0.654842	−	0.530281i
$334$	−0.778534	−	7.40725i	−0.0425995	−	0.405307i
$335$	13.3694	−	0.901522i	0.730449	−	0.0492554i
$336$	0.803007	−	5.49534i	0.0438076	−	0.299795i
$337$	−4.18549	+	26.4261i	−0.227998	+	1.43952i	0.562367	+	0.826888i	$0.309891\pi$
$337$	−4.18549	+	26.4261i	−0.227998	+	1.43952i	−0.790365	+	0.612636i	$0.790109\pi$
$338$	−3.75868	−	1.44282i	−0.204445	−	0.0784792i
$339$	−25.8287	+	28.6857i	−1.40282	+	1.55799i
$340$	5.81933	−	7.41039i	0.315597	−	0.401885i
$341$	0.330594	+	1.74882i	0.0179027	+	0.0947038i
$342$	−4.20221	−	4.20221i	−0.227230	−	0.227230i
$343$	−18.5083	+	0.665561i	−0.999354	+	0.0359369i
$344$	1.11541	−	1.53524i	0.0601391	−	0.0827744i
$345$	1.52483	+	0.470330i	0.0820938	+	0.0253217i
$346$	−0.104325	−	0.490812i	−0.00560856	−	0.0263862i
$347$	5.63006	−	8.66953i	0.302237	−	0.465405i	−0.654622	−	0.755956i	$-0.727172\pi$
$347$	5.63006	−	8.66953i	0.302237	−	0.465405i	0.956859	+	0.290552i	$0.0938389\pi$
$348$	−4.48764	−	3.63402i	−0.240563	−	0.194804i
$349$	−4.88261	−	3.54742i	−0.261360	−	0.189889i	0.449386	−	0.893338i	$-0.351643\pi$
$349$	−4.88261	−	3.54742i	−0.261360	−	0.189889i	−0.710746	+	0.703448i	$0.751643\pi$
$350$	4.21902	−	12.5379i	0.225516	−	0.670181i
$351$	−13.8044			−0.736823
$352$	2.02842	+	2.62402i	0.108115	+	0.139861i
$353$	−30.2132	−	8.09560i	−1.60809	−	0.430885i	−0.660614	−	0.750726i	$-0.729704\pi$
$353$	−30.2132	−	8.09560i	−1.60809	−	0.430885i	−0.947471	+	0.319840i	$0.896371\pi$
$354$	10.6278	+	9.56928i	0.564859	+	0.508601i
$355$	−0.178231	−	11.9051i	−0.00945950	−	0.631856i
$356$	6.08272	+	8.37215i	0.322384	+	0.443723i
$357$	2.72484	+	23.2427i	0.144214	+	1.23014i
$358$	21.8420	−	11.1290i	1.15438	−	0.588188i
$359$	18.1110	−	1.90354i	0.955861	−	0.100465i	0.386263	−	0.922388i	$-0.373766\pi$
$359$	18.1110	−	1.90354i	0.955861	−	0.100465i	0.569598	+	0.821923i	$0.307099\pi$
$360$	−3.02476	+	0.859212i	−0.159419	+	0.0452844i
$361$	−0.763014	+	0.847412i	−0.0401586	+	0.0446007i
$362$	−14.8384	+	3.97594i	−0.779890	+	0.208971i
$363$	13.4382	−	18.7768i	0.705320	−	0.985529i
$364$	−8.40124	+	6.97150i	−0.440345	+	0.365406i
$365$	12.4803	−	10.4195i	0.653249	−	0.545383i
$366$	−15.6942	+	6.98750i	−0.820349	+	0.365243i
$367$	0.636898	+	1.65917i	0.0332458	+	0.0866082i	0.949198	−	0.314678i	$-0.101897\pi$
$367$	0.636898	+	1.65917i	0.0332458	+	0.0866082i	−0.915953	+	0.401286i	$0.868563\pi$
$368$	0.285120	+	0.185159i	0.0148629	+	0.00965209i
$369$	10.6628	+	11.8423i	0.555084	+	0.616483i
$370$	23.8373	−	5.44095i	1.23924	−	0.282861i
$371$	−22.2369	+	1.43273i	−1.15448	+	0.0743837i
$372$	−1.00366	−	0.511391i	−0.0520374	−	0.0265144i
$373$	3.64252	−	0.976011i	0.188603	−	0.0505360i	−0.163281	−	0.986580i	$-0.552208\pi$
$373$	3.64252	−	0.976011i	0.188603	−	0.0505360i	0.351884	+	0.936044i	$0.385541\pi$
$374$	−11.1178	−	8.46802i	−0.574887	−	0.437871i
$375$	−23.3577	+	2.27919i	−1.20619	+	0.117697i
$376$	2.13694	−	10.0535i	0.110204	−	0.518471i
$377$	1.77571	+	11.2114i	0.0914536	+	0.577415i
$378$	−4.33350	+	7.71795i	−0.222891	+	0.396969i
$379$	−22.9956	−	7.47173i	−1.18121	−	0.383797i	−0.348391	−	0.937349i	$-0.613272\pi$
$379$	−22.9956	−	7.47173i	−1.18121	−	0.383797i	−0.832815	+	0.553552i	$0.813272\pi$
$380$	−3.05435	−	8.94256i	−0.156685	−	0.458744i
$381$	6.10210	−	13.7055i	0.312620	−	0.702156i
$382$	15.7203	+	19.4130i	0.804321	+	0.993254i
$383$	17.8463	−	11.5895i	0.911902	−	0.592196i	−0.00116781	−	0.999999i	$-0.500372\pi$
$383$	17.8463	−	11.5895i	0.911902	−	0.592196i	0.913070	+	0.407803i	$0.133705\pi$
$384$	−2.09910			−0.107119
$385$	−18.6872	−	5.98220i	−0.952390	−	0.304881i
$386$	−21.8046			−1.10982
$387$	2.23802	−	1.45339i	0.113765	−	0.0738800i
$388$	6.38195	+	7.88105i	0.323994	+	0.400100i
$389$	−4.99828	+	11.2263i	−0.253423	+	0.569197i	−0.994795	−	0.101897i	$-0.967509\pi$
$389$	−4.99828	+	11.2263i	−0.253423	+	0.569197i	0.741372	+	0.671094i	$0.234175\pi$
$390$	17.3864	+	8.53341i	0.880392	+	0.432106i
$391$	−1.36242	−	0.442678i	−0.0689007	−	0.0223872i
$392$	1.26039	+	6.88560i	0.0636592	+	0.347775i
$393$	0.273010	+	1.72372i	0.0137715	+	0.0869500i
$394$	−3.99316	+	18.7863i	−0.201172	+	0.946441i
$395$	−3.38998	−	28.1877i	−0.170568	−	1.41828i
$396$	1.34060	+	4.46711i	0.0673679	+	0.224481i
$397$	34.8431	−	9.33618i	1.74872	−	0.468569i	0.764371	−	0.644777i	$-0.223050\pi$
$397$	34.8431	−	9.33618i	1.74872	−	0.468569i	0.984353	+	0.176207i	$0.0563829\pi$
$398$	−7.26321	−	3.70079i	−0.364072	−	0.185504i
$399$	21.0384	+	10.4040i	1.05324	+	0.520851i
$400$	−4.91967	−	0.892687i	−0.245983	−	0.0446344i
$401$	2.14977	+	2.38756i	0.107354	+	0.119229i	0.794427	−	0.607360i	$-0.207771\pi$
$401$	2.14977	+	2.38756i	0.107354	+	0.119229i	−0.687073	+	0.726589i	$0.741105\pi$
$402$	10.5496	+	6.85101i	0.526168	+	0.341698i
$403$	0.793523	+	2.06720i	0.0395282	+	0.102974i
$404$	−7.12604	+	3.17272i	−0.354534	+	0.157849i
$405$	25.0349	+	2.25294i	1.24400	+	0.111949i
$406$	6.82565	+	2.52672i	0.338751	+	0.125399i
$407$	−8.59205	−	35.2332i	−0.425892	−	1.74645i
$408$	8.54371	−	2.28928i	0.422976	−	0.113336i
$409$	9.85217	−	10.9419i	0.487159	−	0.541044i	−0.448578	−	0.893744i	$-0.648069\pi$
$409$	9.85217	−	10.9419i	0.487159	−	0.541044i	0.935737	+	0.352699i	$0.114736\pi$
$410$	6.92387	+	24.3747i	0.341945	+	1.20378i
$411$	−4.12935	+	0.434012i	−0.203686	+	0.0214082i
$412$	7.06082	−	3.59767i	0.347862	−	0.177244i
$413$	−16.5536	−	7.13375i	−0.814551	−	0.351029i
$414$	0.281003	+	0.386768i	0.0138106	+	0.0190086i
$415$	−0.372898	−	0.361897i	−0.0183048	−	0.0177648i
$416$	3.06642	+	2.76101i	0.150343	+	0.135370i
$417$	12.0410	+	3.22638i	0.589651	+	0.157997i
$418$	−13.1955	+	4.72593i	−0.645415	+	0.231153i
$419$	31.6365			1.54554			0.772771	−	0.634685i	$-0.218870\pi$
$419$	31.6365			1.54554			0.772771	+	0.634685i	$0.218870\pi$
$420$	10.2289	−	7.04178i	0.499121	−	0.343604i
$421$	0.211831	+	0.153905i	0.0103240	+	0.00750085i	0.592935	−	0.805250i	$-0.297969\pi$
$421$	0.211831	+	0.153905i	0.0103240	+	0.00750085i	−0.582611	+	0.812751i	$0.697969\pi$
$422$	−7.98307	−	6.46456i	−0.388610	−	0.314690i
$423$	7.87189	−	12.1217i	0.382744	−	0.589375i
$424$	1.75107	+	8.23814i	0.0850395	+	0.400079i
$425$	20.9974	−	1.73199i	1.01853	−	0.0840140i
$426$	6.56974	−	9.04247i	0.318305	−	0.438109i
$427$	15.9168	−	14.6807i	0.770268	−	0.710446i
$428$	−7.62962	−	7.62962i	−0.368792	−	0.368792i
$429$	12.2745	−	25.9724i	0.592616	−	1.25396i
$430$	4.21293	−	0.506666i	0.203165	−	0.0244336i
$431$	−4.10960	+	4.56417i	−0.197952	+	0.219848i	−0.833946	−	0.551846i	$-0.813924\pi$
$431$	−4.10960	+	4.56417i	−0.197952	+	0.219848i	0.635994	+	0.771694i	$0.280590\pi$
$432$	3.12328	+	1.19892i	0.150269	+	0.0576829i
$433$	0.246620	−	1.55709i	0.0118518	−	0.0748292i	−0.981054	−	0.193737i	$-0.937939\pi$
$433$	0.246620	−	1.55709i	0.0118518	−	0.0748292i	0.992905	+	0.118908i	$0.0379392\pi$
$434$	1.40486	+	0.205286i	0.0674356	+	0.00985402i
$435$	−0.868718	−	12.8829i	−0.0416519	−	0.617690i
$436$	−0.228218	−	2.17135i	−0.0109297	−	0.103989i
$437$	−1.11654	+	0.904160i	−0.0534116	+	0.0432518i
$438$	15.2413	−	0.798762i	0.728257	−	0.0381663i
$439$	−14.9168	+	25.8367i	−0.711942	+	1.23312i	0.252186	+	0.967679i	$0.418851\pi$
$439$	−14.9168	+	25.8367i	−0.711942	+	1.23312i	−0.964127	+	0.265440i	$0.914483\pi$
$440$	−1.21605	+	7.31582i	−0.0579728	+	0.348768i
$441$	−1.81531	+	9.67477i	−0.0864431	+	0.460703i
$442$	−15.4920	−	7.89357i	−0.736879	−	0.375459i
$443$	14.4574	+	5.54967i	0.686891	+	0.263673i	0.676682	−	0.736275i	$-0.263417\pi$
$443$	14.4574	+	5.54967i	0.686891	+	0.263673i	0.0102089	+	0.999948i	$0.496750\pi$
$444$	20.9683	+	9.33570i	0.995113	+	0.443053i
$445$	−4.47173	+	22.7039i	−0.211980	+	1.07627i
$446$	17.1235	−	15.4180i	0.810819	−	0.730065i
$447$	25.6957	+	4.06980i	1.21536	+	0.192495i
$448$	2.50628	−	0.847671i	0.118411	−	0.0400487i
$449$	−25.6794	+	8.34374i	−1.21189	+	0.393766i	−0.844121	−	0.536153i	$-0.819877\pi$
$449$	−25.6794	+	8.34374i	−1.21189	+	0.393766i	−0.367765	+	0.929919i	$0.619877\pi$
$450$	−6.00881	−	3.65120i	−0.283258	−	0.172119i
$451$	35.9977	−	10.8031i	1.69507	−	0.508699i
$452$	−17.7624	−	4.75942i	−0.835473	−	0.223864i
$453$	29.3261	−	19.0446i	1.37786	−	0.894794i
$454$	−6.57500	−	4.77701i	−0.308580	−	0.224196i
$455$	−24.2049	−	3.16765i	−1.13475	−	0.148502i
$456$	2.74128	−	8.43678i	0.128372	−	0.395089i
$457$	−19.8128	−	1.03834i	−0.926803	−	0.0485717i	−0.417042	−	0.908887i	$-0.636933\pi$
$457$	−19.8128	−	1.03834i	−0.926803	−	0.0485717i	−0.509762	+	0.860316i	$0.670266\pi$
$458$	7.81004	−	2.99799i	0.364939	−	0.140087i
$459$	−14.0198	−	1.47354i	−0.654390	−	0.0687791i
$460$	0.130146	+	0.748965i	0.00606808	+	0.0349207i
$461$		−	34.5849i		−	1.61078i	−0.592745	−	0.805390i	$-0.701956\pi$
$461$		−	34.5849i		−	1.61078i	0.592745	−	0.805390i	$-0.298044\pi$
$462$	−10.6678	−	15.0159i	−0.496311	−	0.698603i
$463$	−1.59816	−	1.59816i	−0.0742728	−	0.0742728i	0.668995	−	0.743267i	$-0.266725\pi$
$463$	−1.59816	−	1.59816i	−0.0742728	−	0.0742728i	−0.743267	+	0.668995i	$0.766725\pi$
$464$	0.571953	−	2.69083i	0.0265523	−	0.124919i
$465$	−0.688256	−	2.42293i	−0.0319171	−	0.112361i
$466$	−2.52916	−	1.12606i	−0.117161	−	0.0521635i
$467$	−0.510026	+	9.73188i	−0.0236012	+	0.450338i	0.961113	+	0.276157i	$0.0890610\pi$
$467$	−0.510026	+	9.73188i	−0.0236012	+	0.450338i	−0.984714	+	0.174181i	$0.944272\pi$
$468$	2.63427	+	5.17005i	0.121769	+	0.238985i
$469$	−15.3627	−	3.91975i	−0.709382	−	0.180997i
$470$	19.7293	−	11.7880i	0.910044	−	0.543738i
$471$	14.5500	+	3.09270i	0.670430	+	0.142504i
$472$	−1.76332	+	6.58080i	−0.0811634	+	0.302906i
$473$	−0.843805	−	6.23699i	−0.0387982	−	0.286777i
$474$	13.3259	−	23.0811i	0.612078	−	1.06015i
$475$	10.0126	−	18.6075i	0.459412	−	0.853771i
$476$	−9.27653	+	6.18352i	−0.425189	+	0.283421i
$477$	−1.85273	+	11.6977i	−0.0848309	+	0.535601i
$478$	−0.837911	+	15.9883i	−0.0383252	+	0.731288i
$479$	−41.0981	+	8.73567i	−1.87782	+	0.399143i	−0.997207	−	0.0746920i	$-0.976203\pi$
$479$	−41.0981	+	8.73567i	−1.87782	+	0.399143i	−0.880614	+	0.473835i	$0.842869\pi$
$480$	−3.19258	−	3.44072i	−0.145721	−	0.157047i
$481$	−18.3515	−	41.2181i	−0.836755	−	1.87938i
$482$	−5.46736	+	10.7303i	−0.249032	+	0.488752i
$483$	−1.54067	−	1.09140i	−0.0701030	−	0.0496605i
$484$	10.8766	+	1.64307i	0.494391	+	0.0746851i
$485$	−3.21164	+	22.4474i	−0.145833	+	1.01928i
$486$	10.0770	+	9.07340i	0.457103	+	0.411578i
$487$	−19.9601	−	24.6486i	−0.904478	−	1.11694i	−0.992673	−	0.120834i	$-0.961443\pi$
$487$	−19.9601	−	24.6486i	−0.904478	−	1.11694i	0.0881951	−	0.996103i	$-0.471890\pi$
$488$	−6.36030	−	5.15047i	−0.287917	−	0.233151i
$489$	5.03372	−	15.4922i	0.227633	−	0.700582i
$490$	−9.36949	+	12.5384i	−0.423270	+	0.566429i
$491$	8.62184	−	6.26414i	0.389098	−	0.282697i	−0.375988	−	0.926625i	$-0.622696\pi$
$491$	8.62184	−	6.26414i	0.389098	−	0.282697i	0.765086	+	0.643928i	$0.222696\pi$
$492$	−8.52447	+	22.2070i	−0.384313	+	1.00117i
$493$	0.606668	+	11.5759i	0.0273229	+	0.521353i
$494$	−15.1017	+	8.71896i	−0.679456	+	0.392284i
$495$	−5.28325	+	8.99159i	−0.237464	+	0.404142i
$496$		−	0.536627i		−	0.0240953i
$497$	−4.19255	+	13.4496i	−0.188061	+	0.603295i
$498$	−0.0763099	−	0.481802i	−0.00341953	−	0.0215901i
$499$	14.3480	−	1.50804i	0.642306	−	0.0675091i	0.222224	−	0.974996i	$-0.428668\pi$
$499$	14.3480	−	1.50804i	0.642306	−	0.0675091i	0.420081	+	0.907486i	$0.362002\pi$
$500$	−6.01922	−	9.42173i	−0.269188	−	0.421352i
$501$	15.2926	−	3.25054i	0.683222	−	0.145223i
$502$	−9.21112	+	11.3748i	−0.411112	+	0.507681i
$503$	−1.12970	+	0.178927i	−0.0503707	+	0.00797794i	−0.181569	−	0.983378i	$-0.558118\pi$
$503$	−1.12970	+	0.178927i	−0.0503707	+	0.00797794i	0.131198	+	0.991356i	$0.458118\pi$
$504$	3.71750	+	0.150188i	0.165591	+	0.00668991i
$505$	−16.0387	−	6.85509i	−0.713714	−	0.305048i
$506$	1.10792	−	0.209439i	0.0492530	−	0.00931072i
$507$	2.18733	−	8.16321i	0.0971425	−	0.362541i
$508$	7.13734	−	0.374052i	0.316668	−	0.0165959i
$509$	−27.0998	+	12.0656i	−1.20118	+	0.534798i	−0.907072	−	0.420975i	$-0.861688\pi$
$509$	−27.0998	+	12.0656i	−1.20118	+	0.534798i	−0.294104	+	0.955773i	$0.595021\pi$
$510$	16.7468	+	10.5225i	0.741561	+	0.465944i
$511$	−17.8752	+	7.10853i	−0.790753	+	0.314463i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	−8.89751	+	10.9875i	−0.392834	+	0.485110i
$514$	1.75950	−	16.7405i	0.0776083	−	0.738394i
$515$	16.6361	+	6.10187i	0.733073	+	0.268880i
$516$	3.44970	+	1.99169i	0.151865	+	0.0876791i
$517$	−17.9151	−	29.0016i	−0.787904	−	1.27549i
$518$	−28.8057	−	2.67908i	−1.26565	−	0.117712i
$519$	1.00173	−	0.325482i	0.0439710	−	0.0142871i
$520$	0.138116	+	9.22558i	0.00605679	+	0.404569i
$521$	−9.01907	+	20.2572i	−0.395133	+	0.887482i	0.600969	+	0.799272i	$0.294781\pi$
$521$	−9.01907	+	20.2572i	−0.395133	+	0.887482i	−0.996102	+	0.0882101i	$0.971885\pi$
$522$	2.10691	−	3.24436i	0.0922170	−	0.142002i
$523$	−21.7026	−	1.13738i	−0.948987	−	0.0497343i	−0.428443	−	0.903569i	$-0.640938\pi$
$523$	−21.7026	−	1.13738i	−0.948987	−	0.0497343i	−0.520545	+	0.853835i	$0.674271\pi$
$524$	−0.672621	+	0.488688i	−0.0293836	+	0.0213484i
$525$	27.1000	+	6.05661i	1.18274	+	0.264332i
$526$	3.62505	+	11.1568i	0.158060	+	0.486458i
$527$	0.585245	+	2.18416i	0.0254937	+	0.0951437i
$528$	−5.03285	+	4.81030i	−0.219027	+	0.209341i
$529$	−19.8185	+	11.4422i	−0.861674	+	0.497487i
$530$	−10.8402	+	15.3999i	−0.470868	+	0.668928i
$531$	−5.63131	+	7.75084i	−0.244378	+	0.336358i
$532$	0.133964	+	11.1803i	0.00580809	+	0.484729i
$533$	41.6623	−	21.2280i	1.80459	−	0.919487i
$534$	−16.1431	+	14.5353i	−0.698579	+	0.629003i
$535$	0.901898	−	24.1101i	0.0389925	−	1.04237i
$536$	−0.626393	+	5.95973i	−0.0270561	+	0.257421i
$537$	28.0255	+	43.1555i	1.20939	+	1.86230i
$538$	19.7791	−	19.7791i	0.852738	−	0.852738i
$539$	18.8009	+	13.6207i	0.809814	+	0.586687i
$540$	2.78510	+	6.94296i	0.119852	+	0.298777i
$541$	−33.1033	−	7.03632i	−1.42322	−	0.302515i	−0.568963	−	0.822363i	$-0.692655\pi$
$541$	−33.1033	−	7.03632i	−1.42322	−	0.302515i	−0.854259	+	0.519848i	$0.825988\pi$
$542$	11.5140	−	9.32383i	0.494567	−	0.400493i
$543$	−11.5560	−	30.1043i	−0.495914	−	1.29190i
$544$	2.81955	+	3.13143i	0.120887	+	0.134259i
$545$	3.21204	−	3.67655i	0.137589	−	0.157486i
$546$	−16.3971	−	16.0088i	−0.701731	−	0.685113i
$547$	2.93359	−	0.464635i	0.125431	−	0.0198663i	−0.0934032	−	0.995628i	$-0.529775\pi$
$547$	2.93359	−	0.464635i	0.125431	−	0.0198663i	0.218834	+	0.975762i	$0.429775\pi$
$548$	−1.07731	−	1.65892i	−0.0460206	−	0.0708655i
$549$	−5.75442	−	9.96694i	−0.245593	−	0.425379i
$550$	−13.8412	+	9.13357i	−0.590189	+	0.389457i
$551$	10.0681	+	5.81284i	0.428917	+	0.247635i
$552$	−0.323979	+	0.635844i	−0.0137895	+	0.0270633i
$553$	−6.59007	+	32.9397i	−0.280238	+	1.40074i
$554$	3.72202	+	5.12293i	0.158134	+	0.217652i
$555$	16.5888	+	48.5689i	0.704156	+	2.06164i
$556$	1.23471	+	5.80885i	0.0523633	+	0.246350i
$557$	23.6116	−	9.06365i	1.00046	−	0.384039i	0.197646	−	0.980273i	$-0.436670\pi$
$557$	23.6116	−	9.06365i	1.00046	−	0.384039i	0.802811	+	0.596234i	$0.203337\pi$
$558$	0.270432	−	0.704499i	0.0114483	−	0.0298238i
$559$	−2.41968	−	7.44700i	−0.102341	−	0.314974i
$560$	5.20133	+	2.81890i	0.219796	+	0.119120i
$561$	15.2384	−	25.0676i	0.643368	−	1.05835i
$562$	−8.04399	−	30.0206i	−0.339315	−	1.26634i
$563$	1.27507	+	24.3297i	0.0537377	+	1.02538i	0.883847	+	0.467776i	$0.154945\pi$
$563$	1.27507	+	24.3297i	0.0537377	+	1.02538i	−0.830109	+	0.557601i	$0.811722\pi$
$564$	21.4567	+	2.25519i	0.903488	+	0.0949605i
$565$	−19.2140	−	36.3538i	−0.808338	−	1.52941i
$566$	−6.71943	−	2.18328i	−0.282439	−	0.0917699i
$567$	−27.3131	−	11.7705i	−1.14704	−	0.494316i
$568$	5.25916	+	0.832968i	0.220669	+	0.0349506i
$569$	1.35058	+	3.03346i	0.0566193	+	0.127169i	0.939640	−	0.342166i	$-0.111160\pi$
$569$	1.35058	+	3.03346i	0.0566193	+	0.127169i	−0.883020	+	0.469335i	$0.844494\pi$
$570$	17.9983	−	8.33841i	0.753868	−	0.349258i
$571$	−8.05969	−	13.9598i	−0.337288	−	0.584199i	0.646634	−	0.762800i	$-0.276176\pi$
$571$	−8.05969	−	13.9598i	−0.337288	−	0.584199i	−0.983922	+	0.178601i	$0.942843\pi$
$572$	13.6792	−	0.407134i	0.571957	−	0.0170231i
$573$	−37.0773	+	37.0773i	−1.54893	+	1.54893i
$574$	1.21027	−	29.9571i	0.0505159	−	1.25038i
$575$	−1.02972	+	1.35245i	−0.0429421	+	0.0564011i
$576$	−0.146991	−	1.39853i	−0.00612462	−	0.0582719i
$577$	13.6165	+	8.84266i	0.566862	+	0.368125i	0.796025	−	0.605263i	$-0.206932\pi$
$577$	13.6165	+	8.84266i	0.566862	+	0.368125i	−0.229163	+	0.973388i	$0.573599\pi$
$578$	−0.633789	−	0.411587i	−0.0263621	−	0.0171198i
$579$	−4.78427	−	45.5193i	−0.198828	−	1.89172i
$580$	5.28054	−	3.15505i	0.219263	−	0.131006i
$581$	0.285676	+	0.544445i	0.0118519	+	0.0225874i
$582$	−15.0522	+	15.0522i	−0.623934	+	0.623934i
$583$	23.0769	+	15.7392i	0.955748	+	0.651850i
$584$	3.63541	+	6.29672i	0.150434	+	0.260560i
$585$	−4.46789	+	12.1812i	−0.184724	+	0.503631i
$586$	−3.36876	−	7.56635i	−0.139162	−	0.312563i
$587$	−15.6417	−	2.47740i	−0.645601	−	0.102253i	−0.174956	−	0.984576i	$-0.555978\pi$
$587$	−15.6417	−	2.47740i	−0.645601	−	0.102253i	−0.470644	+	0.882323i	$0.655978\pi$
$588$	−14.0978	+	4.14200i	−0.581385	+	0.170813i
$589$	2.15683	+	0.700797i	0.0888707	+	0.0288758i
$590$	−13.4687	+	7.11860i	−0.554499	+	0.293068i
$591$	−40.0945	−	4.21411i	−1.64927	−	0.173345i
$592$	0.572269	+	10.9195i	0.0235201	+	0.448790i
$593$	8.13938	+	30.3766i	0.334244	+	1.24742i	0.904686	+	0.426078i	$0.140105\pi$
$593$	8.13938	+	30.3766i	0.334244	+	1.24742i	−0.570442	+	0.821338i	$0.693228\pi$
$594$	10.2359	−	4.28276i	0.419983	−	0.175724i
$595$	−24.2446	−	5.80083i	−0.993931	−	0.237811i
$596$	3.82991	+	11.7873i	0.156879	+	0.482825i
$597$	6.13211	−	15.9747i	0.250971	−	0.653801i
$598$	1.30962	−	0.502716i	0.0535544	−	0.0205576i
$599$	−1.03851	−	4.88578i	−0.0424322	−	0.199628i	0.951825	−	0.306640i	$-0.0992048\pi$
$599$	−1.03851	−	4.88578i	−0.0424322	−	0.199628i	−0.994258	+	0.107013i	$0.965872\pi$
$600$	0.784123	−	10.4662i	0.0320117	−	0.427280i
$601$	−6.70737	−	9.23190i	−0.273599	−	0.376577i	0.650001	−	0.759933i	$-0.274768\pi$
$601$	−6.70737	−	9.23190i	−0.273599	−	0.376577i	−0.923601	+	0.383356i	$0.874768\pi$
$602$	−4.92316	−	0.984952i	−0.200653	−	0.0401437i
$603$	−3.82574	+	7.50844i	−0.155796	+	0.305767i
$604$	14.4265	+	8.32914i	0.587006	+	0.338908i
$605$	13.8493	+	20.3272i	0.563054	+	0.826420i
$606$	−8.18694	−	14.1802i	−0.332572	−	0.576031i
$607$	11.4158	+	17.5788i	0.463355	+	0.713503i	0.990688	−	0.136155i	$-0.0434746\pi$
$607$	11.4158	+	17.5788i	0.463355	+	0.713503i	−0.527333	+	0.849659i	$0.676808\pi$
$608$	4.17404	−	0.661103i	0.169280	−	0.0268113i
$609$	−3.77712	+	14.8037i	−0.153057	+	0.599874i
$610$	−1.23123	−	18.2589i	−0.0498510	−	0.739282i
$611$	−28.3781	−	31.5170i	−1.14805	−	1.27504i
$612$	2.12351	+	5.53193i	0.0858378	+	0.223615i
$613$	−15.2104	+	12.3171i	−0.614340	+	0.497483i	−0.885246	−	0.465123i	$-0.846010\pi$
$613$	−15.2104	+	12.3171i	−0.614340	+	0.497483i	0.270906	+	0.962606i	$0.412677\pi$
$614$	−20.0095	−	4.25315i	−0.807518	−	0.171643i
$615$	−49.3655	+	19.8025i	−1.99061	+	0.798513i
$616$	4.06659	−	7.77579i	0.163848	−	0.313295i
$617$	−0.269198	+	0.269198i	−0.0108375	+	0.0108375i	−0.712505	−	0.701667i	$-0.752439\pi$
$617$	−0.269198	+	0.269198i	−0.0108375	+	0.0108375i	0.701667	+	0.712505i	$0.252439\pi$
$618$	9.05975	+	13.9508i	0.364437	+	0.561183i
$619$	3.33420	−	31.7228i	0.134013	−	1.27505i	−0.696300	−	0.717751i	$-0.745172\pi$
$619$	3.33420	−	31.7228i	0.134013	−	1.27505i	0.830313	−	0.557297i	$-0.188162\pi$
$620$	0.879606	−	0.816172i	0.0353258	−	0.0327782i
$621$	0.845219	−	0.761039i	0.0339175	−	0.0305394i
$622$	−18.3040	+	9.32633i	−0.733922	+	0.373952i
$623$	13.4048	−	23.8738i	0.537050	−	0.956484i
$624$	−5.09108	+	7.00727i	−0.203806	+	0.280515i
$625$	6.28871	−	24.1961i	0.251548	−	0.967845i
$626$	12.1653	−	7.02365i	0.486224	−	0.280722i
$627$	−12.7612	−	26.5101i	−0.509632	−	1.05871i
$628$	1.83410	+	6.84494i	0.0731884	+	0.273143i
$629$	−14.2381	−	43.8203i	−0.567709	−	1.74723i
$630$	5.40787	+	6.32192i	0.215455	+	0.251871i
$631$	6.36752	−	4.62627i	0.253487	−	0.184169i	−0.453784	−	0.891112i	$-0.649926\pi$
$631$	6.36752	−	4.62627i	0.253487	−	0.184169i	0.707271	+	0.706943i	$0.249926\pi$
$632$	12.6793	+	0.664497i	0.504357	+	0.0264323i
$633$	11.7438	−	18.0839i	0.466775	−	0.718770i
$634$	−12.3639	+	27.7697i	−0.491032	+	1.10288i
$635$	11.4685	+	11.1302i	0.455114	+	0.441688i
$636$	−16.8137	+	5.46312i	−0.666708	+	0.216627i
$637$	26.0425	+	12.4926i	1.03184	+	0.494975i
$638$	−4.79497	−	7.76227i	−0.189835	−	0.307311i
$639$	6.48459	+	3.74388i	0.256527	+	0.148106i
$640$	0.769996	−	2.09931i	0.0304368	−	0.0829825i
$641$	1.32554	−	12.6117i	0.0523557	−	0.498132i	−0.936651	−	0.350263i	$-0.886092\pi$
$641$	1.32554	−	12.6117i	0.0523557	−	0.498132i	0.989007	−	0.147868i	$-0.0472412\pi$
$642$	14.2536	−	17.6017i	0.562543	−	0.694683i
$643$	−5.22931	−	10.2631i	−0.206224	−	0.404737i	0.764609	−	0.644495i	$-0.222932\pi$
$643$	−5.22931	−	10.2631i	−0.206224	−	0.404737i	−0.970833	+	0.239757i	$0.922932\pi$
$644$	0.130054	−	0.890016i	0.00512483	−	0.0350715i
$645$	1.98210	+	8.68375i	0.0780451	+	0.341922i
$646$	−16.2681	+	7.24301i	−0.640059	+	0.284973i
$647$	−13.9203	+	0.729533i	−0.547264	+	0.0286809i	−0.323965	−	0.946069i	$-0.605016\pi$
$647$	−13.9203	+	0.729533i	−0.547264	+	0.0286809i	−0.223299	+	0.974750i	$0.571683\pi$
$648$	−2.90944	+	10.8582i	−0.114294	+	0.426549i
$649$	10.8528	+	19.8191i	0.426009	+	0.777967i
$650$	−14.9119	+	14.2578i	−0.584895	+	0.559239i
$651$	−0.120305	+	2.97784i	−0.00471514	+	0.116711i
$652$	7.66467	−	1.21396i	0.300172	−	0.0475425i
$653$	−20.4149	+	25.2103i	−0.798898	+	0.986557i	0.201077	+	0.979575i	$0.435556\pi$
$653$	−20.4149	+	25.2103i	−0.798898	+	0.986557i	−0.999976	+	0.00698183i	$0.997778\pi$
$654$	4.48285	−	0.952859i	0.175293	−	0.0372597i
$655$	−1.82403	−	0.359260i	−0.0712709	−	0.0140374i
$656$	−11.2699	+	1.18451i	−0.440015	+	0.0462474i
$657$	1.59946	+	10.0986i	0.0624007	+	0.393983i
$658$	−26.5295	+	5.97211i	−1.03423	+	0.232817i
$659$			46.1565i			1.79800i	0.437946	+	0.899001i	$0.355706\pi$
$659$			46.1565i			1.79800i	−0.437946	+	0.899001i	$0.644294\pi$
$660$	−15.5393	−	0.933415i	−0.604868	−	0.0363331i
$661$	−24.4425	+	14.1119i	−0.950703	+	0.548889i	−0.893299	−	0.449462i	$-0.851616\pi$
$661$	−24.4425	+	14.1119i	−0.950703	+	0.548889i	−0.0574038	+	0.998351i	$0.518282\pi$
$662$	−0.146411	−	2.79369i	−0.00569043	−	0.108580i
$663$	13.0794	−	34.0731i	0.507963	−	1.32329i
$664$	0.188006	−	0.136595i	0.00729607	−	0.00530090i
$665$	−18.1224	+	17.2241i	−0.702755	+	0.667921i
$666$	−4.75158	+	14.6239i	−0.184120	+	0.566664i
$667$	−0.726810	−	0.588559i	−0.0281422	−	0.0227891i
$668$	4.68721	+	5.78823i	0.181354	+	0.223953i
$669$	35.9439	+	32.3640i	1.38967	+	1.25127i
$670$	−10.7215	+	8.03759i	−0.414209	+	0.310519i
$671$	−27.0524	+	2.22639i	−1.04435	+	0.0859487i
$672$	2.31952	+	5.04613i	0.0894774	+	0.194659i
$673$	−7.26447	+	14.2573i	−0.280025	+	0.549579i	−0.987587	−	0.157071i	$-0.949795\pi$
$673$	−7.26447	+	14.2573i	−0.280025	+	0.549579i	0.707563	+	0.706651i	$0.249795\pi$
$674$	−10.8825	−	24.4424i	−0.419177	−	0.941487i
$675$	−7.14453	+	15.1249i	−0.274993	+	0.582158i
$676$	3.93811	−	0.837071i	0.151466	−	0.0321951i
$677$	2.51144	−	47.9210i	0.0965223	−	1.84176i	−0.338062	−	0.941124i	$-0.609771\pi$
$677$	2.51144	−	47.9210i	0.0965223	−	1.84176i	0.434584	−	0.900631i	$-0.356895\pi$
$678$	6.03843	−	38.1251i	0.231904	−	1.46419i
$679$	11.8935	−	24.0505i	0.456432	−	0.922972i
$680$	−0.844510	+	9.38431i	−0.0323855	+	0.359872i
$681$	8.52985	−	14.7741i	0.326865	−	0.566146i
$682$	−1.22973	−	1.28663i	−0.0470889	−	0.0492675i
$683$	4.12139	−	15.3813i	0.157701	−	0.588547i	−0.841158	−	0.540789i	$-0.818126\pi$
$683$	4.12139	−	15.3813i	0.157701	−	0.588547i	0.998859	−	0.0477580i	$-0.0152076\pi$
$684$	5.81296	+	1.23558i	0.222264	+	0.0472437i
$685$	1.08068	−	4.28897i	0.0412907	−	0.163873i
$686$	15.1599	−	10.6385i	0.578807	−	0.406181i
$687$	7.97226	+	15.6464i	0.304161	+	0.596949i
$688$	−0.0993156	+	1.89505i	−0.00378637	+	0.0722483i
$689$	31.7477	+	14.1350i	1.20949	+	0.538500i
$690$	−1.53499	+	0.436028i	−0.0584359	+	0.0165993i
$691$	−3.55882	+	16.7429i	−0.135384	+	0.636931i	0.857161	+	0.515049i	$0.172226\pi$
$691$	−3.55882	+	16.7429i	−0.135384	+	0.636931i	−0.992545	+	0.121882i	$0.961107\pi$
$692$	0.354810	+	0.354810i	0.0134878	+	0.0134878i
$693$	9.25732	−	8.15892i	0.351657	−	0.309932i
$694$			10.3372i			0.392396i
$695$	−7.64361	+	10.8587i	−0.289939	+	0.411894i
$696$	5.74288	+	0.603601i	0.217683	+	0.0228794i
$697$	44.5785	−	17.1121i	1.68853	−	0.648166i
$698$	6.02697	+	0.315860i	0.228124	+	0.0119555i
$699$	1.79582	−	5.52696i	0.0679241	−	0.209049i
$700$	3.29029	+	12.8130i	0.124361	+	0.484287i
$701$	−8.31280	−	6.03961i	−0.313970	−	0.228113i	0.419628	−	0.907696i	$-0.362161\pi$
$701$	−8.31280	−	6.03961i	−0.313970	−	0.228113i	−0.733598	+	0.679583i	$0.762161\pi$
$702$	11.5773	−	7.51840i	0.436958	−	0.283764i
$703$	−44.6355	−	11.9601i	−1.68346	−	0.451082i
$704$	−3.13033	−	1.09593i	−0.117979	−	0.0413044i
$705$	28.9375	+	38.6004i	1.08985	+	1.45378i
$706$	29.7481	−	9.66574i	1.11958	−	0.363775i
$707$	15.5014	+	13.6248i	0.582989	+	0.512412i
$708$	−14.1250	−	2.23718i	−0.530850	−	0.0840783i
$709$	−24.3563	+	21.9305i	−0.914720	+	0.823617i	−0.984759	−	0.173927i	$-0.944354\pi$
$709$	−24.3563	+	21.9305i	−0.914720	+	0.823617i	0.0700387	+	0.997544i	$0.477688\pi$
$710$	6.63345	+	9.88737i	0.248949	+	0.371066i
$711$	16.3109	+	7.26209i	0.611708	+	0.272350i
$712$	−9.66120	−	3.70859i	−0.362069	−	0.138985i
$713$	−0.162551	−	0.0828239i	−0.00608759	−	0.00310178i
$714$	−14.9441	−	18.0090i	−0.559271	−	0.673968i
$715$	21.4725	+	21.8029i	0.803025	+	0.815383i
$716$	−12.2569	+	21.2296i	−0.458062	+	0.793387i
$717$	−33.5611	+	1.75886i	−1.25336	+	0.0656859i
$718$	−14.1524	+	11.4604i	−0.528163	+	0.427698i
$719$	2.00142	+	19.0422i	0.0746403	+	0.710155i	0.966295	+	0.257438i	$0.0828784\pi$
$719$	2.00142	+	19.0422i	0.0746403	+	0.710155i	−0.891655	+	0.452717i	$0.850455\pi$
$720$	2.06881	−	2.36800i	0.0771002	−	0.0882500i
$721$	−16.4508	−	12.9984i	−0.612661	−	0.484085i
$722$	0.178383	−	1.12627i	0.00663873	−	0.0419153i
$723$	−23.6002	−	9.05929i	−0.877703	−	0.336918i
$724$	10.2791	−	11.4161i	0.382019	−	0.424275i
$725$	13.2029	+	3.85694i	0.490343	+	0.143243i
$726$	−1.04358	+	23.0665i	−0.0387310	+	0.856079i
$727$	35.6687	+	35.6687i	1.32288	+	1.32288i	0.911436	+	0.411441i	$0.134974\pi$
$727$	35.6687	+	35.6687i	1.32288	+	1.32288i	0.411441	+	0.911436i	$0.365026\pi$
$728$	3.24892	−	10.4224i	0.120413	−	0.386281i
$729$	3.09166	−	4.25531i	0.114506	−	0.157604i
$730$	−4.79199	+	15.5358i	−0.177360	+	0.575006i
$731$	−1.66251	−	7.82151i	−0.0614903	−	0.289289i
$732$	9.35659	−	14.4079i	0.345830	−	0.532531i
$733$	34.0489	+	27.5722i	1.25762	+	1.01840i	0.998620	+	0.0525267i	$0.0167275\pi$
$733$	34.0489	+	27.5722i	1.25762	+	1.01840i	0.259004	+	0.965876i	$0.416606\pi$
$734$	−1.43780	−	1.04462i	−0.0530701	−	0.0385577i
$735$	−28.2311	−	16.8086i	−1.04132	−	0.619996i
$736$	−0.339967			−0.0125313
$737$	12.1555	+	15.7246i	0.447752	+	0.579224i
$738$	−15.3923	−	4.12436i	−0.566600	−	0.151820i
$739$	8.33045	+	7.50077i	0.306440	+	0.275920i	0.807974	−	0.589218i	$-0.200564\pi$
$739$	8.33045	+	7.50077i	0.306440	+	0.275920i	−0.501534	+	0.865138i	$0.667231\pi$
$740$	−17.0283	+	17.5459i	−0.625971	+	0.644999i
$741$	−21.5153	−	29.6132i	−0.790383	−	1.08787i
$742$	17.8691	−	13.3127i	0.655996	−	0.488723i
$743$	−2.05087	+	1.04497i	−0.0752392	+	0.0383363i	−0.491205	−	0.871044i	$-0.663444\pi$
$743$	−2.05087	+	1.04497i	−0.0752392	+	0.0383363i	0.415966	+	0.909380i	$0.363444\pi$
$744$	1.12026	−	0.117745i	0.0410709	−	0.00431672i
$745$	−13.4959	+	24.2053i	−0.494453	+	0.886815i
$746$	−2.52330	+	2.80241i	−0.0923847	+	0.102604i
$747$	0.315657	−	0.0845800i	0.0115493	−	0.00309462i
$748$	13.9362	+	1.04670i	0.509557	+	0.0382710i
$749$	−9.91044	+	26.7720i	−0.362119	+	0.978227i
$750$	18.3481	−	14.6330i	0.669978	−	0.534322i
$751$	−15.1328	+	6.73756i	−0.552204	+	0.245857i	−0.663817	−	0.747895i	$-0.731065\pi$
$751$	−15.1328	+	6.73756i	−0.552204	+	0.245857i	0.111614	+	0.993752i	$0.464398\pi$
$752$	3.68335	+	9.59546i	0.134318	+	0.349911i
$753$	−25.7671	−	16.7333i	−0.939005	−	0.609797i
$754$	−7.59539	−	8.43553i	−0.276608	−	0.307204i
$755$	8.28905	+	36.3150i	0.301669	+	1.32164i
$756$	−0.569114	−	8.83301i	−0.0206985	−	0.321254i
$757$	−6.52509	−	3.32470i	−0.237158	−	0.120838i	0.331373	−	0.943500i	$-0.392488\pi$
$757$	−6.52509	−	3.32470i	−0.237158	−	0.120838i	−0.568531	+	0.822662i	$0.692488\pi$
$758$	23.3552	−	6.25799i	0.848297	−	0.227301i
$759$	0.680322	+	2.26694i	0.0246941	+	0.0822848i
$760$	7.43206	+	5.83634i	0.269589	+	0.211706i
$761$	−10.7007	+	50.3429i	−0.387901	+	1.82493i	0.158443	+	0.987368i	$0.449353\pi$
$761$	−10.7007	+	50.3429i	−0.387901	+	1.82493i	−0.546344	+	0.837561i	$0.683981\pi$
$762$	2.34692	+	14.8179i	0.0850199	+	0.536795i
$763$	−4.96763	+	2.94798i	−0.179840	+	0.106724i
$764$	−23.7572	−	7.71919i	−0.859506	−	0.279271i
$765$	−5.83790	+	11.8944i	−0.211070	+	0.430043i
$766$	−8.65505	+	19.4396i	−0.312720	+	0.702380i
$767$	17.6915	+	21.8472i	0.638802	+	0.788855i
$768$	1.76046	−	1.14325i	0.0635249	−	0.0412536i
$769$	13.5287			0.487858			0.243929	−	0.969793i	$-0.421564\pi$
$769$	13.5287			0.487858			0.243929	+	0.969793i	$0.421564\pi$
$770$	18.9306	−	5.16071i	0.682211	−	0.185979i
$771$	35.3337			1.27251
$772$	18.2869	−	11.8756i	0.658159	−	0.427413i
$773$	−5.86681	−	7.24490i	−0.211014	−	0.260581i	0.660639	−	0.750704i	$-0.270285\pi$
$773$	−5.86681	−	7.24490i	−0.211014	−	0.260581i	−0.871654	+	0.490123i	$0.836952\pi$
$774$	−1.08539	+	2.43783i	−0.0390136	+	0.0876260i
$775$	2.67564	+	0.200458i	0.0961117	+	0.00720067i
$776$	−9.64468	−	3.13375i	−0.346224	−	0.112495i
$777$	−0.727588	−	60.7227i	−0.0261021	−	2.17842i
$778$	−1.92238	−	12.1374i	−0.0689207	−	0.435148i
$779$	9.95682	−	46.8432i	0.356740	−	1.67833i
$780$	−19.2290	+	2.31257i	−0.688510	+	0.0828033i
$781$	14.5183	−	10.0547i	0.519505	−	0.359786i
$782$	1.38372	−	0.370767i	0.0494818	−	0.0132586i
$783$	−8.20015	−	4.17819i	−0.293050	−	0.149316i
$784$	−4.80721	−	5.08829i	−0.171686	−	0.181725i
$785$	−8.43028	+	13.4170i	−0.300890	+	0.478874i
$786$	−1.16777	−	1.29694i	−0.0416529	−	0.0462603i
$787$	34.3504	+	22.3074i	1.22446	+	0.795173i	0.984461	−	0.175601i	$-0.0561869\pi$
$787$	34.3504	+	22.3074i	1.22446	+	0.795173i	0.239997	+	0.970774i	$0.422854\pi$
$788$	−6.88282	−	17.9304i	−0.245190	−	0.638743i
$789$	−22.4955	+	10.0156i	−0.800861	+	0.356566i
$790$	18.1952	+	21.7939i	0.647356	+	0.775391i
$791$	8.18615	+	47.9590i	0.291066	+	1.70523i
$792$	−3.55729	−	3.01629i	−0.126403	−	0.107179i
$793$	−32.6194	+	8.74035i	−1.15835	+	0.310379i
$794$	−24.1370	+	26.8069i	−0.856591	+	0.951341i
$795$	−34.5273	−	19.2511i	−1.22456	−	0.682765i
$796$	8.10703	−	0.852083i	0.287346	−	0.0302013i
$797$	−40.3200	+	20.5441i	−1.42821	+	0.727708i	−0.985614	−	0.169015i	$-0.945941\pi$
$797$	−40.3200	+	20.5441i	−1.42821	+	0.727708i	−0.442593	+	0.896723i	$0.645941\pi$
$798$	−23.3107	+	2.73281i	−0.825190	+	0.0967403i
$799$	−25.4567	−	35.0381i	−0.900593	−	1.23956i
$800$	4.61217	−	1.93077i	0.163065	−	0.0682631i
$801$	−10.8146	−	9.73747i	−0.382114	−	0.344057i
$802$	−3.10331	−	0.831528i	−0.109582	−	0.0293623i
$803$	23.1459	+	6.76623i	0.816801	+	0.238775i
$804$	−12.5790			−0.443627
$805$	1.65666	−	1.14047i	0.0583896	−	0.0401964i
$806$	−1.79138	−	1.30151i	−0.0630987	−	0.0458439i
$807$	45.6308	+	36.9511i	1.60628	+	1.30074i
$808$	4.24842	−	6.54199i	0.149459	−	0.230146i
$809$	−4.50688	−	21.2032i	−0.158453	−	0.745465i	−0.983574	−	0.180507i	$-0.942226\pi$
$809$	−4.50688	−	21.2032i	−0.158453	−	0.745465i	0.825120	−	0.564957i	$-0.191107\pi$
$810$	−22.2231	+	11.7455i	−0.780840	+	0.412696i
$811$	18.3057	−	25.1957i	0.642801	−	0.884740i	−0.355960	−	0.934501i	$-0.615846\pi$
$811$	18.3057	−	25.1957i	0.642801	−	0.884740i	0.998761	+	0.0497612i	$0.0158460\pi$
$812$	−7.10062	+	1.59844i	−0.249183	+	0.0560941i
$813$	21.9908	+	21.9908i	0.771251	+	0.771251i
$814$	26.3953	+	24.8695i	0.925154	+	0.871675i
$815$	13.6473	+	10.7171i	0.478043	+	0.375404i
$816$	−5.91852	+	6.57319i	−0.207190	+	0.230108i
$817$	−7.48697	−	2.87398i	−0.261936	−	0.100548i
$818$	−2.30332	+	14.5426i	−0.0805336	+	0.508469i
$819$	9.51763	−	12.0456i	0.332573	−	0.420907i
$820$	−19.0823	−	16.6713i	−0.666381	−	0.582188i
$821$	−1.51189	−	14.3847i	−0.0527655	−	0.502030i	−0.988706	−	0.149871i	$-0.952114\pi$
$821$	−1.51189	−	14.3847i	−0.0527655	−	0.502030i	0.935940	−	0.352159i	$-0.114552\pi$
$822$	3.22678	−	2.61300i	0.112547	−	0.0911388i
$823$	19.7969	−	1.03751i	0.690078	−	0.0361655i	0.295926	−	0.955211i	$-0.404372\pi$
$823$	19.7969	−	1.03751i	0.690078	−	0.0361655i	0.394152	+	0.919045i	$0.371038\pi$
$824$	−3.96227	+	6.86285i	−0.138032	+	0.239079i
$825$	−22.1042	−	26.8908i	−0.769571	−	0.936218i
$826$	17.7684	−	3.03289i	0.618241	−	0.105528i
$827$	−11.1440	−	5.67814i	−0.387514	−	0.197448i	0.249369	−	0.968408i	$-0.419777\pi$
$827$	−11.1440	−	5.67814i	−0.387514	−	0.197448i	−0.636883	+	0.770960i	$0.719777\pi$
$828$	−0.446318	−	0.171325i	−0.0155106	−	0.00595397i
$829$	−28.2072	−	12.5586i	−0.979676	−	0.436180i	−0.146514	−	0.989209i	$-0.546805\pi$
$829$	−28.2072	−	12.5586i	−0.979676	−	0.436180i	−0.833162	+	0.553029i	$0.813472\pi$
$830$	0.509842	+	0.100418i	0.0176969	+	0.00348556i
$831$	−9.87796	+	8.89416i	−0.342663	+	0.308535i
$832$	−4.07547	−	0.645491i	−0.141291	−	0.0223784i
$833$	25.1155	+	15.4675i	0.870200	+	0.535916i
$834$	−11.8557	+	3.85214i	−0.410528	+	0.133389i
$835$	−2.35879	+	16.4865i	−0.0816293	+	0.570538i
$836$	8.49278	−	11.1503i	0.293729	−	0.385641i
$837$	−1.73411	−	0.464653i	−0.0599395	−	0.0160607i
$838$	−26.5326	+	17.2305i	−0.916553	+	0.595216i
$839$	−0.217962	−	0.158358i	−0.00752487	−	0.00546714i	0.584016	−	0.811742i	$-0.301480\pi$
$839$	−0.217962	−	0.158358i	−0.00752487	−	0.00546714i	−0.591541	+	0.806275i	$0.701480\pi$
$840$	−4.74348	+	11.4768i	−0.163666	+	0.395988i
$841$	6.62295	−	20.3833i	0.228378	−	0.702874i
$842$	−0.261479	−	0.0137035i	−0.00901117	−	0.000472255i
$843$	60.9060	−	23.3796i	2.09772	−	0.805237i
$844$	10.2160	+	1.07375i	0.351650	+	0.0369599i
$845$	7.36166	+	5.18199i	0.253249	+	0.178266i
$846$			14.4534i			0.496918i
$847$	−8.06884	−	27.9624i	−0.277249	−	0.960798i
$848$	−5.95538	−	5.95538i	−0.204509	−	0.204509i
$849$	3.08346	−	14.5066i	0.105824	−	0.497864i
$850$	−16.6666	+	12.8886i	−0.571661	+	0.442075i
$851$	3.39599	+	1.51199i	0.116413	+	0.0518304i
$852$	−0.584965	+	11.1618i	−0.0200406	+	0.382397i
$853$	−10.3847	−	20.3812i	−0.355567	−	0.697839i	0.642063	−	0.766652i	$-0.278079\pi$
$853$	−10.3847	−	20.3812i	−0.355567	−	0.697839i	−0.997630	+	0.0688129i	$0.978079\pi$
$854$	−5.35329	+	20.9811i	−0.183186	+	0.717960i
$855$	6.81581	+	11.4075i	0.233096	+	0.390128i
$856$	10.5541	+	2.24335i	0.360733	+	0.0766761i
$857$	−8.84541	+	33.0115i	−0.302154	+	1.12765i	0.633214	+	0.773976i	$0.281735\pi$
$857$	−8.84541	+	33.0115i	−0.302154	+	1.12765i	−0.935368	+	0.353676i	$0.884932\pi$
$858$	3.85137	+	28.4675i	0.131484	+	0.971863i
$859$	12.4435	−	21.5528i	0.424567	−	0.735372i	−0.571813	−	0.820384i	$-0.693760\pi$
$859$	12.4435	−	21.5528i	0.424567	−	0.735372i	0.996380	+	0.0850124i	$0.0270930\pi$
$860$	−3.25731	+	2.71945i	−0.111073	+	0.0927325i
$861$	62.8041	−	4.04649i	2.14036	−	0.137904i
$862$	0.960773	−	6.06608i	0.0327241	−	0.206612i
$863$	0.581215	−	11.0903i	0.0197848	−	0.377517i	−0.970736	−	0.240151i	$-0.922803\pi$
$863$	0.581215	−	11.0903i	0.0197848	−	0.377517i	0.990520	−	0.137366i	$-0.0438636\pi$
$864$	−3.27238	+	0.695566i	−0.111329	+	0.0236636i
$865$	−0.0419421	+	1.12122i	−0.00142607	+	0.0381227i
$866$	0.641222	+	1.44021i	0.0217896	+	0.0489403i
$867$	0.720167	−	1.41341i	0.0244582	−	0.0480019i
$868$	−1.29002	+	0.592976i	−0.0437863	+	0.0201269i
$869$	31.9230	−	27.4628i	1.08291	−	0.931610i
$870$	7.74512	+	10.3314i	0.262584	+	0.350267i
$871$	18.3757	+	16.5455i	0.622636	+	0.560624i
$872$	1.37400	+	1.69675i	0.0465296	+	0.0574593i
$873$	−11.0826	−	8.97448i	−0.375088	−	0.303740i
$874$	0.443972	−	1.36641i	0.0150176	−	0.0462194i
$875$	−15.9981	+	24.8810i	−0.540833	+	0.841130i
$876$	−12.3474	+	8.97090i	−0.417179	+	0.303099i
$877$	−3.82761	+	9.97128i	−0.129249	+	0.336706i	−0.982900	−	0.184140i	$-0.941050\pi$
$877$	−3.82761	+	9.97128i	−0.129249	+	0.336706i	0.853651	+	0.520846i	$0.174383\pi$
$878$	−1.56137	−	29.7928i	−0.0526938	−	1.00546i
$879$	15.0564	−	8.69281i	0.507839	−	0.293201i
$880$	−2.96462	−	6.79787i	−0.0999373	−	0.229156i
$881$		−	26.3183i		−	0.886686i	−0.896352	−	0.443343i	$-0.853792\pi$
$881$		−	26.3183i		−	0.886686i	0.896352	−	0.443343i	$-0.146208\pi$
$882$	−3.74681	−	9.10263i	−0.126162	−	0.306502i
$883$	0.728280	+	4.59818i	0.0245086	+	0.154741i	0.996908	−	0.0785833i	$-0.0250396\pi$
$883$	0.728280	+	4.59818i	0.0245086	+	0.154741i	−0.972399	+	0.233324i	$0.925040\pi$
$884$	17.2918	−	1.81744i	0.581587	−	0.0611273i
$885$	−17.8161	−	26.5554i	−0.598880	−	0.892651i
$886$	−15.1476	+	3.21971i	−0.508892	+	0.108168i
$887$	−13.0906	+	16.1655i	−0.439538	+	0.542785i	−0.947988	−	0.318307i	$-0.896886\pi$
$887$	−13.0906	+	16.1655i	−0.439538	+	0.542785i	0.508449	+	0.861092i	$0.330219\pi$
$888$	−22.6701	+	3.59059i	−0.760759	+	0.120492i
$889$	−8.78601	−	16.7445i	−0.294673	−	0.561591i
$890$	−8.61511	−	21.4765i	−0.288779	−	0.719895i
$891$	17.9068	+	32.7010i	0.599902	+	1.09553i
$892$	−5.96368	+	22.2568i	−0.199679	+	0.745211i
$893$	−43.3766	+	2.27327i	−1.45154	+	0.0760722i
$894$	−23.7668	+	10.5817i	−0.794880	+	0.353903i
$895$	−53.4401	+	12.1979i	−1.78631	+	0.407731i
$896$	−1.64027	+	2.07594i	−0.0547976	+	0.0693522i
$897$	1.33682	+	2.62366i	0.0446353	+	0.0876016i
$898$	16.9922	−	20.9837i	0.567038	−	0.700234i
$899$	−0.154308	+	1.46814i	−0.00514647	+	0.0489653i
$900$	7.02799	−	0.210479i	0.234266	−	0.00701597i
$901$	30.7344	+	17.7445i	1.02391	+	0.591155i
$902$	−24.3064	+	28.6660i	−0.809316	+	0.954474i
$903$	0.975969	−	10.4937i	0.0324782	−	0.349209i
$904$	17.4890	−	5.68251i	0.581674	−	0.188997i
$905$	34.3463	−	0.514198i	1.14171	−	0.0170925i
$906$	−14.2225	+	31.9443i	−0.472512	+	1.06128i
$907$	−13.9362	+	21.4598i	−0.462743	+	0.712561i	−0.990603	−	0.136770i	$-0.956328\pi$
$907$	−13.9362	+	21.4598i	−0.462743	+	0.712561i	0.527860	+	0.849331i	$0.322994\pi$
$908$	8.11600	+	0.425342i	0.269339	+	0.0141155i
$909$	8.87425	−	6.44752i	0.294340	−	0.213851i
$910$	22.0252	−	10.5263i	0.730128	−	0.348945i
$911$	5.00556	+	15.4055i	0.165842	+	0.510408i	0.999097	−	0.0424797i	$-0.0135258\pi$
$911$	5.00556	+	15.4055i	0.165842	+	0.510408i	−0.833256	+	0.552888i	$0.813526\pi$
$912$	2.29597	+	8.56869i	0.0760273	+	0.283738i
$913$	0.137748	−	0.758337i	0.00455879	−	0.0250973i
$914$	17.1819	−	9.91999i	0.568328	−	0.328124i
$915$	37.8472	−	6.57662i	1.25119	−	0.217416i
$916$	−4.91722	+	6.76798i	−0.162470	+	0.223620i
$917$	1.91803	+	1.07694i	0.0633389	+	0.0355638i
$918$	12.5606	−	6.39993i	0.414561	−	0.211229i
$919$	−21.0885	+	18.9882i	−0.695645	+	0.626361i	−0.939138	−	0.343541i	$-0.888373\pi$
$919$	−21.0885	+	18.9882i	−0.695645	+	0.626361i	0.243493	+	0.969903i	$0.421707\pi$
$920$	−0.517065	−	0.557253i	−0.0170471	−	0.0183721i
$921$	4.48849	−	42.7051i	0.147901	−	1.40718i
$922$	18.8363	+	29.0054i	0.620340	+	0.955241i
$923$	15.5360	−	15.5360i	0.511373	−	0.511373i
$924$	17.1250	+	6.78329i	0.563372	+	0.223154i
$925$	−54.6589	−	1.22567i	−1.79717	−	0.0402997i
$926$	2.21075	+	0.469909i	0.0726497	+	0.0154422i
$927$	−8.66030	+	7.01297i	−0.284441	+	0.230336i
$928$	0.985850	+	2.56823i	0.0323621	+	0.0843062i
$929$	−1.63996	−	1.82136i	−0.0538053	−	0.0597568i	0.715641	−	0.698468i	$-0.246135\pi$
$929$	−1.63996	−	1.82136i	−0.0538053	−	0.0597568i	−0.769447	+	0.638711i	$0.779468\pi$
$930$	1.89684	+	1.65719i	0.0621999	+	0.0543413i
$931$	26.7289	−	12.6764i	0.876005	−	0.415451i
$932$	2.73443	−	0.433091i	0.0895692	−	0.0141864i
$933$	−23.4859	−	36.1651i	−0.768893	−	1.18399i
$934$	−4.87262	−	8.43962i	−0.159437	−	0.276153i
$935$	19.4803	+	24.4353i	0.637073	+	0.799119i
$936$	−5.02509	−	2.90124i	−0.164250	−	0.0948300i
$937$	−6.79100	+	13.3281i	−0.221852	+	0.435410i	−0.974927	−	0.222525i	$-0.928570\pi$
$937$	−6.79100	+	13.3281i	−0.221852	+	0.435410i	0.753075	+	0.657935i	$0.228570\pi$
$938$	15.0191	−	5.07972i	0.490390	−	0.165859i
$939$	17.3319	+	23.8553i	0.565604	+	0.778487i
$940$	−10.1262	+	20.6315i	−0.330280	+	0.672927i
$941$	8.11230	+	38.1654i	0.264454	+	1.24416i	0.887072	+	0.461631i	$0.152735\pi$
$941$	8.11230	+	38.1654i	0.264454	+	1.24416i	−0.622619	+	0.782525i	$0.713931\pi$
$942$	−13.8871	+	5.33075i	−0.452466	+	0.173685i
$943$	−1.38061	+	3.59661i	−0.0449588	+	0.117122i
$944$	−2.10532	−	6.47949i	−0.0685222	−	0.210890i
$945$	13.6130	−	14.3672i	0.442829	−	0.467366i
$946$	4.10458	+	4.77121i	0.133452	+	0.155125i
$947$	−12.2649	−	45.7731i	−0.398554	−	1.48743i	−0.815641	−	0.578558i	$-0.803616\pi$
$947$	−12.2649	−	45.7731i	−0.398554	−	1.48743i	0.417087	−	0.908867i	$-0.363051\pi$
$948$	1.39485	+	26.6152i	0.0453025	+	0.864423i
$949$	29.8370	+	3.13600i	0.968551	+	0.101799i
$950$	1.73706	+	21.0588i	0.0563576	+	0.683239i
$951$	−60.6850	−	19.7178i	−1.96785	−	0.639392i
$952$	4.41217	−	10.2383i	0.142999	−	0.331825i
$953$	−56.1251	−	8.88935i	−1.81807	−	0.287954i	−0.847861	−	0.530218i	$-0.822110\pi$
$953$	−56.1251	−	8.88935i	−1.81807	−	0.287954i	−0.970210	+	0.242264i	$0.922110\pi$
$954$	−4.81719	−	10.8196i	−0.155962	−	0.350297i
$955$	−23.4802	−	50.6817i	−0.759802	−	1.64002i
$956$	−8.00512	−	13.8653i	−0.258904	−	0.448435i
$957$	15.1524	−	11.7132i	0.489809	−	0.378633i
$958$	29.7100	−	29.7100i	0.959886	−	0.959886i
$959$	−2.79752	+	4.42292i	−0.0903365	+	0.142824i
$960$	4.55148	+	1.14682i	0.146898	+	0.0370136i
$961$	−3.21028	−	30.5438i	−0.103557	−	0.985283i
$962$	37.8398	+	24.5735i	1.22000	+	0.792280i
$963$	12.7252	+	8.26386i	0.410065	+	0.266299i
$964$	−1.25883	−	11.9769i	−0.0405441	−	0.385751i
$965$	47.2788	+	11.9127i	1.52196	+	0.383484i
$966$	1.88653	+	0.0762165i	0.0606983	+	0.00245223i
$967$	−21.2577	+	21.2577i	−0.683602	+	0.683602i	−0.960810	−	0.277208i	$-0.910591\pi$
$967$	−21.2577	+	21.2577i	−0.683602	+	0.683602i	0.277208	+	0.960810i	$0.410591\pi$
$968$	−10.0168	+	4.54582i	−0.321951	+	0.146108i
$969$	−18.6900	−	32.3720i	−0.600410	−	1.03994i
$970$	−9.53222	−	20.5752i	−0.306061	−	0.660629i
$971$	−1.21790	−	2.73546i	−0.0390844	−	0.0877850i	0.892948	−	0.450159i	$-0.148633\pi$
$971$	−1.21790	−	2.73546i	−0.0390844	−	0.0877850i	−0.932033	+	0.362374i	$0.881966\pi$
$972$	−13.3930	−	2.12125i	−0.429582	−	0.0680390i
$973$	12.5998	−	9.38699i	0.403931	−	0.300933i
$974$	30.1645	+	9.80106i	0.966534	+	0.314046i
$975$	−33.0366	−	28.0018i	−1.05802	−	0.896776i
$976$	8.13935	+	0.855480i	0.260534	+	0.0273832i
$977$	−2.15048	−	41.0337i	−0.0688001	−	1.31278i	−0.787003	−	0.616949i	$-0.788368\pi$
$977$	−2.15048	−	41.0337i	−0.0688001	−	1.31278i	0.718203	−	0.695834i	$-0.244965\pi$
$978$	4.21603	+	15.7344i	0.134814	+	0.503131i
$979$	−31.6625	+	13.2478i	−1.01194	+	0.423402i
$980$	1.02898	−	15.6186i	0.0328697	−	0.498918i
$981$	0.948756	+	2.91997i	0.0302914	+	0.0932275i
$982$	−3.81919	+	9.94934i	−0.121875	+	0.317496i
$983$	45.2351	−	17.3641i	1.44278	−	0.553830i	0.493911	−	0.869513i	$-0.335567\pi$
$983$	45.2351	−	17.3641i	1.44278	−	0.553830i	0.948865	+	0.315683i	$0.102234\pi$
$984$	−4.94558	−	23.2671i	−0.157659	−	0.741729i
$985$	18.9221	−	38.5527i	0.602907	−	1.22839i
$986$	−6.81349	−	9.37796i	−0.216986	−	0.298655i
$987$	−18.2884	−	54.0727i	−0.582126	−	1.72115i
$988$	7.91665	−	15.5373i	0.251862	−	0.494307i
$989$	0.558707	+	0.322570i	0.0177659	+	0.0102571i
$990$	−0.466265	−	10.4184i	−0.0148189	−	0.331120i
$991$	−0.0829972	−	0.143755i	−0.00263649	−	0.00456654i	0.864704	−	0.502282i	$-0.167506\pi$
$991$	−0.0829972	−	0.143755i	−0.00263649	−	0.00456654i	−0.867341	+	0.497715i	$0.834173\pi$
$992$	0.292268	+	0.450053i	0.00927952	+	0.0142892i
$993$	5.79999	−	0.918629i	0.184057	−	0.0291518i
$994$	−3.80898	−	13.5632i	−0.120814	−	0.430198i
$995$	13.7269	+	11.9926i	0.435172	+	0.380191i
$996$	0.326407	+	0.362512i	0.0103426	+	0.0114866i
$997$	12.7741	+	33.2777i	0.404560	+	1.05391i	0.972922	+	0.231136i	$0.0742441\pi$
$997$	12.7741	+	33.2777i	0.404560	+	1.05391i	−0.568362	+	0.822779i	$0.692423\pi$
$998$	−11.2119	+	9.07924i	−0.354907	+	0.287398i
$999$	35.7819	+	7.60568i	1.13209	+	0.240633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.313.5	✓	768
5.2	odd	4	inner	770.2.bv.a.467.5	yes	768
7.3	odd	6	inner	770.2.bv.a.423.20	yes	768
11.9	even	5	inner	770.2.bv.a.383.29	yes	768
35.17	even	12	inner	770.2.bv.a.577.29	yes	768
55.42	odd	20	inner	770.2.bv.a.537.20	yes	768
77.31	odd	30	inner	770.2.bv.a.493.5	yes	768
385.262	even	60	inner	770.2.bv.a.647.5	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.5	✓	768	1.1	even	1	trivial
770.2.bv.a.383.29	yes	768	11.9	even	5	inner
770.2.bv.a.423.20	yes	768	7.3	odd	6	inner
770.2.bv.a.467.5	yes	768	5.2	odd	4	inner
770.2.bv.a.493.5	yes	768	77.31	odd	30	inner
770.2.bv.a.537.20	yes	768	55.42	odd	20	inner
770.2.bv.a.577.29	yes	768	35.17	even	12	inner
770.2.bv.a.647.5	yes	768	385.262	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.838671 + 0.544639i) q^{2} +(-1.32101 - 1.63131i) q^{3} +(0.406737 - 0.913545i) q^{4} +(2.11605 - 0.722740i) q^{5} +(1.99636 + 0.648658i) q^{6} +(-2.64556 + 0.0316995i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.292371 + 1.37550i) q^{9} +O(q^{10})\)	\(q+(-0.838671 + 0.544639i) q^{2} +(-1.32101 - 1.63131i) q^{3} +(0.406737 - 0.913545i) q^{4} +(2.11605 - 0.722740i) q^{5} +(1.99636 + 0.648658i) q^{6} +(-2.64556 + 0.0316995i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.292371 + 1.37550i) q^{9} +(-1.38103 + 1.75862i) q^{10} +(2.63845 + 2.00962i) q^{11} +(-2.02758 + 0.543288i) q^{12} +(3.67653 + 1.87329i) q^{13} +(2.20149 - 1.46746i) q^{14} +(-3.97432 - 2.49718i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(3.53395 + 2.29497i) q^{17} +(-0.503947 - 1.31283i) q^{18} +(3.86071 - 1.71890i) q^{19} +(0.200418 - 2.22707i) q^{20} +(3.54652 + 4.27385i) q^{21} +(-3.30731 - 0.248400i) q^{22} +(-0.328383 + 0.0879899i) q^{23} +(1.40457 - 1.55994i) q^{24} +(3.95529 - 3.05870i) q^{25} +(-4.10366 + 0.431313i) q^{26} +(-2.98085 + 1.51882i) q^{27} +(-1.04709 + 2.42973i) q^{28} +(1.61696 + 2.22556i) q^{29} +(4.69321 - 0.0702619i) q^{30} +(0.398792 + 0.359074i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.207116 - 6.95885i) q^{33} -4.21375 q^{34} +(-5.57522 + 1.97913i) q^{35} +(1.13766 + 0.826561i) q^{36} +(-8.49772 - 6.88132i) q^{37} +(-2.30168 + 3.54428i) q^{38} +(-1.80082 - 8.47218i) q^{39} +(1.04486 + 1.97693i) q^{40} +(6.66075 - 9.16774i) q^{41} +(-5.30207 - 1.65278i) q^{42} +(-1.34185 - 1.34185i) q^{43} +(2.90903 - 1.59296i) q^{44} +(0.375457 + 3.12193i) q^{45} +(0.227482 - 0.252645i) q^{46} +(-9.59546 - 3.68335i) q^{47} +(-0.328372 + 2.07326i) q^{48} +(6.99799 - 0.167726i) q^{49} +(-1.65130 + 4.71945i) q^{50} +(-0.924564 - 8.79664i) q^{51} +(3.20671 - 2.59674i) q^{52} +(8.41064 - 0.440783i) q^{53} +(1.67274 - 2.89728i) q^{54} +(7.03552 + 2.34552i) q^{55} +(-0.445166 - 2.60803i) q^{56} +(-7.90408 - 4.02733i) q^{57} +(-2.56823 - 0.985850i) q^{58} +(6.22393 + 2.77107i) q^{59} +(-3.89779 + 2.61503i) q^{60} +(-6.08203 + 5.47629i) q^{61} +(-0.530020 - 0.0839470i) q^{62} +(0.729884 - 3.64824i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(9.13361 + 1.30678i) q^{65} +(3.96376 + 5.72338i) q^{66} +(5.78837 + 1.55099i) q^{67} +(3.53395 - 2.29497i) q^{68} +(0.577335 + 0.419458i) q^{69} +(3.59786 - 4.69632i) q^{70} +(1.64543 - 5.06410i) q^{71} +(-1.40430 - 0.0735963i) q^{72} +(6.78790 - 2.60563i) q^{73} +(10.8746 + 1.14297i) q^{74} +(-10.2147 - 2.41174i) q^{75} -4.22607i q^{76} +(-7.04390 - 5.23292i) q^{77} +(6.12458 + 6.12458i) q^{78} +(2.63980 - 12.4193i) q^{79} +(-1.95301 - 1.08892i) q^{80} +(10.2694 + 4.57221i) q^{81} +(-0.593069 + 11.3164i) q^{82} +(-0.105502 - 0.207060i) q^{83} +(5.34686 - 1.50157i) q^{84} +(9.13667 + 2.30214i) q^{85} +(1.85619 + 0.394545i) q^{86} +(1.49455 - 5.57775i) q^{87} +(-1.57213 + 2.92034i) q^{88} +(-5.17427 + 8.96210i) q^{89} +(-2.01521 - 2.41378i) q^{90} +(-9.78587 - 4.83935i) q^{91} +(-0.0531825 + 0.335781i) q^{92} +(0.0589531 - 1.12489i) q^{93} +(10.0535 - 2.13694i) q^{94} +(6.92712 - 6.42756i) q^{95} +(-0.853782 - 1.91763i) q^{96} +(-4.60392 + 9.03571i) q^{97} +(-5.77766 + 3.95205i) q^{98} +(-3.53563 + 3.04164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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