LMFDB - Embedded newform 552.2.bb.a.469.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.24
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.162597 + 1.40484i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.94712 + 0.456843i) q^{4} +(-2.88170 + 0.414326i) q^{5} +(-1.04285 - 0.955226i) q^{6} +(-2.13746 + 4.68038i) q^{7} +(-0.958385 - 2.66111i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.162597 + 1.40484i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.94712 + 0.456843i) q^{4} +(-2.88170 + 0.414326i) q^{5} +(-1.04285 - 0.955226i) q^{6} +(-2.13746 + 4.68038i) q^{7} +(-0.958385 - 2.66111i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-1.05062 - 3.98095i) q^{10} +(0.715560 - 2.43697i) q^{11} +(1.17237 - 1.62035i) q^{12} +(1.25459 - 0.572954i) q^{13} +(-6.92271 - 2.24176i) q^{14} +(1.90652 - 2.20024i) q^{15} +(3.58259 - 1.77906i) q^{16} +(5.83669 + 3.75101i) q^{17} +(1.41368 + 0.0389872i) q^{18} +(-2.30229 - 3.58243i) q^{19} +(5.42175 - 2.12323i) q^{20} +(-1.44961 - 4.93693i) q^{21} +(3.53989 + 0.609000i) q^{22} +(-4.40270 - 1.90164i) q^{23} +(2.46695 + 1.38352i) q^{24} +(3.33508 - 0.979269i) q^{25} +(1.00890 + 1.66934i) q^{26} +(0.540641 + 0.841254i) q^{27} +(2.02370 - 10.0898i) q^{28} +(1.59036 - 2.47465i) q^{29} +(3.40097 + 2.32059i) q^{30} +(-2.10247 + 2.42638i) q^{31} +(3.08180 + 4.74368i) q^{32} +(1.05509 + 2.31033i) q^{33} +(-4.32053 + 8.80948i) q^{34} +(4.22032 - 14.3731i) q^{35} +(0.175088 + 1.99232i) q^{36} +(-4.72967 - 0.680024i) q^{37} +(4.65838 - 3.81683i) q^{38} +(-0.572954 + 1.25459i) q^{39} +(3.86435 + 7.27144i) q^{40} +(-1.63493 - 11.3712i) q^{41} +(6.69988 - 2.83920i) q^{42} +(-8.98707 + 7.78734i) q^{43} +(-0.279970 + 5.07199i) q^{44} +2.91134i q^{45} +(1.95563 - 6.49427i) q^{46} +3.21794 q^{47} +(-1.54250 + 3.69062i) q^{48} +(-12.7532 - 14.7180i) q^{49} +(1.91799 + 4.52602i) q^{50} +(-6.86746 + 0.987392i) q^{51} +(-2.18110 + 1.68877i) q^{52} +(-2.87684 - 1.31381i) q^{53} +(-1.09392 + 0.896296i) q^{54} +(-1.05233 + 7.31911i) q^{55} +(14.5035 + 1.20240i) q^{56} +(4.08595 + 1.19974i) q^{57} +(3.73506 + 1.83183i) q^{58} +(-2.75622 + 1.25872i) q^{59} +(-2.70707 + 5.15513i) q^{60} +(1.30434 + 1.13022i) q^{61} +(-3.75052 - 2.55910i) q^{62} +(4.32855 + 2.78179i) q^{63} +(-6.16299 + 5.10073i) q^{64} +(-3.37798 + 2.17090i) q^{65} +(-3.07408 + 1.85789i) q^{66} +(2.56768 + 8.74472i) q^{67} +(-13.0784 - 4.63723i) q^{68} +(4.57265 - 1.44599i) q^{69} +(20.8780 + 3.59183i) q^{70} +(3.77544 - 1.10857i) q^{71} +(-2.77041 + 0.569915i) q^{72} +(-1.93535 + 1.24377i) q^{73} +(0.186293 - 6.75498i) q^{74} +(-1.87920 + 2.92410i) q^{75} +(6.11945 + 5.92366i) q^{76} +(9.87649 + 8.55802i) q^{77} +(-1.85566 - 0.600913i) q^{78} +(1.06170 + 2.32479i) q^{79} +(-9.58685 + 6.61109i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(15.7088 - 4.14573i) q^{82} +(7.37017 + 1.05967i) q^{83} +(5.07798 + 8.95058i) q^{84} +(-18.3737 - 8.39101i) q^{85} +(-12.4012 - 11.3592i) q^{86} +(0.418637 + 2.91168i) q^{87} +(-7.17083 + 0.431377i) q^{88} +(1.62551 + 1.87594i) q^{89} +(-4.08995 + 0.473374i) q^{90} +7.09665i q^{91} +(9.44136 + 1.69139i) q^{92} -3.21056i q^{93} +(0.523226 + 4.52067i) q^{94} +(8.11881 + 9.36961i) q^{95} +(-5.43552 - 1.56688i) q^{96} +(-1.91268 - 13.3030i) q^{97} +(18.6027 - 20.3093i) q^{98} +(-2.31033 - 1.05509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.162597	+	1.40484i	0.114973	+	0.993369i
$2$	0.162597	+	1.40484i	0.114973	+	0.993369i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	−1.94712	+	0.456843i	−0.973562	+	0.228422i
$5$	−2.88170	+	0.414326i	−1.28874	+	0.185292i	−0.752397	−	0.658710i	$-0.771103\pi$
$5$	−2.88170	+	0.414326i	−1.28874	+	0.185292i	−0.536340	+	0.844002i	$0.680193\pi$
$6$	−1.04285	−	0.955226i	−0.425743	−	0.389969i
$7$	−2.13746	+	4.68038i	−0.807883	+	1.76902i	−0.191634	+	0.981466i	$0.561379\pi$
$7$	−2.13746	+	4.68038i	−0.807883	+	1.76902i	−0.616249	+	0.787551i	$0.711349\pi$
$8$	−0.958385	−	2.66111i	−0.338840	−	0.940844i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−1.05062	−	3.98095i	−0.332234	−	1.25889i
$11$	0.715560	−	2.43697i	0.215749	−	0.734775i	−0.778496	−	0.627650i	$-0.784017\pi$
$11$	0.715560	−	2.43697i	0.215749	−	0.734775i	0.994245	−	0.107126i	$-0.0341647\pi$
$12$	1.17237	−	1.62035i	0.338434	−	0.467756i
$13$	1.25459	−	0.572954i	0.347962	−	0.158909i	−0.233765	−	0.972293i	$-0.575105\pi$
$13$	1.25459	−	0.572954i	0.347962	−	0.158909i	0.581727	+	0.813384i	$0.302377\pi$
$14$	−6.92271	−	2.24176i	−1.85017	−	0.599136i
$15$	1.90652	−	2.20024i	0.492261	−	0.568100i
$16$	3.58259	−	1.77906i	0.895647	−	0.444765i
$17$	5.83669	+	3.75101i	1.41560	+	0.909754i	1.00000		0.000207890i	$6.61735e-5\pi$
$17$	5.83669	+	3.75101i	1.41560	+	0.909754i	0.415604	+	0.909546i	$0.363570\pi$
$18$	1.41368	+	0.0389872i	0.333207	+	0.00918938i
$19$	−2.30229	−	3.58243i	−0.528181	−	0.821866i	0.469967	−	0.882684i	$-0.344266\pi$
$19$	−2.30229	−	3.58243i	−0.528181	−	0.821866i	−0.998149	+	0.0608174i	$0.980629\pi$
$20$	5.42175	−	2.12323i	1.21234	−	0.474769i
$21$	−1.44961	−	4.93693i	−0.316332	−	1.07733i
$22$	3.53989	+	0.609000i	0.754708	+	0.129839i
$23$	−4.40270	−	1.90164i	−0.918026	−	0.396520i
$23$	−4.40270	−	1.90164i	−0.918026	−	0.396520i
$24$	2.46695	+	1.38352i	0.503565	+	0.282410i
$25$	3.33508	−	0.979269i	0.667017	−	0.195854i
$26$	1.00890	+	1.66934i	0.197861	+	0.327384i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	2.02370	−	10.0898i	0.382443	−	1.90679i
$29$	1.59036	−	2.47465i	0.295323	−	0.459531i	−0.661607	−	0.749851i	$-0.730125\pi$
$29$	1.59036	−	2.47465i	0.295323	−	0.459531i	0.956930	+	0.290320i	$0.0937616\pi$
$30$	3.40097	+	2.32059i	0.620930	+	0.423681i
$31$	−2.10247	+	2.42638i	−0.377615	+	0.435791i	−0.912464	−	0.409157i	$-0.865823\pi$
$31$	−2.10247	+	2.42638i	−0.377615	+	0.435791i	0.534849	+	0.844948i	$0.320368\pi$
$32$	3.08180	+	4.74368i	0.544791	+	0.838572i
$33$	1.05509	+	2.31033i	0.183668	+	0.402178i
$34$	−4.32053	+	8.80948i	−0.740964	+	1.51081i
$35$	4.22032	−	14.3731i	0.713364	−	2.42949i
$36$	0.175088	+	1.99232i	0.0291814	+	0.332054i
$37$	−4.72967	−	0.680024i	−0.777554	−	0.111795i	−0.257899	−	0.966172i	$-0.583030\pi$
$37$	−4.72967	−	0.680024i	−0.777554	−	0.111795i	−0.519654	+	0.854377i	$0.673939\pi$
$38$	4.65838	−	3.81683i	0.755689	−	0.619171i
$39$	−0.572954	+	1.25459i	−0.0917461	+	0.200896i
$40$	3.86435	+	7.27144i	0.611007	+	1.14972i
$41$	−1.63493	−	11.3712i	−0.255334	−	1.77588i	−0.565051	−	0.825056i	$-0.691144\pi$
$41$	−1.63493	−	11.3712i	−0.255334	−	1.77588i	0.309718	−	0.950829i	$-0.399765\pi$
$42$	6.69988	−	2.83920i	1.03381	−	0.438098i
$43$	−8.98707	+	7.78734i	−1.37051	+	1.18756i	−0.409089	+	0.912495i	$0.634153\pi$
$43$	−8.98707	+	7.78734i	−1.37051	+	1.18756i	−0.961426	+	0.275063i	$0.911301\pi$
$44$	−0.279970	+	5.07199i	−0.0422070	+	0.764631i
$45$			2.91134i			0.433996i
$46$	1.95563	−	6.49427i	0.288342	−	0.957527i
$47$	3.21794			0.469384			0.234692	−	0.972070i	$-0.424592\pi$
$47$	3.21794			0.469384			0.234692	+	0.972070i	$0.424592\pi$
$48$	−1.54250	+	3.69062i	−0.222641	+	0.532695i
$49$	−12.7532	−	14.7180i	−1.82189	−	2.10257i
$50$	1.91799	+	4.52602i	0.271244	+	0.640076i
$51$	−6.86746	+	0.987392i	−0.961637	+	0.138263i
$52$	−2.18110	+	1.68877i	−0.302464	+	0.234190i
$53$	−2.87684	−	1.31381i	−0.395164	−	0.180465i	0.207915	−	0.978147i	$-0.433332\pi$
$53$	−2.87684	−	1.31381i	−0.395164	−	0.180465i	−0.603079	+	0.797682i	$0.706060\pi$
$54$	−1.09392	+	0.896296i	−0.148863	+	0.121970i
$55$	−1.05233	+	7.31911i	−0.141896	+	0.986909i
$56$	14.5035	+	1.20240i	1.93811	+	0.160677i
$57$	4.08595	+	1.19974i	0.541197	+	0.158910i
$58$	3.73506	+	1.83183i	0.490438	+	0.240531i
$59$	−2.75622	+	1.25872i	−0.358829	+	0.163872i	−0.586669	−	0.809827i	$-0.699561\pi$
$59$	−2.75622	+	1.25872i	−0.358829	+	0.163872i	0.227840	+	0.973699i	$0.426834\pi$
$60$	−2.70707	+	5.15513i	−0.349481	+	0.665524i
$61$	1.30434	+	1.13022i	0.167003	+	0.144709i	0.734353	−	0.678768i	$-0.237486\pi$
$61$	1.30434	+	1.13022i	0.167003	+	0.144709i	−0.567350	+	0.823477i	$0.692031\pi$
$62$	−3.75052	−	2.55910i	−0.476317	−	0.325007i
$63$	4.32855	+	2.78179i	0.545346	+	0.350473i
$64$	−6.16299	+	5.10073i	−0.770374	+	0.637592i
$65$	−3.37798	+	2.17090i	−0.418987	+	0.269267i
$66$	−3.07408	+	1.85789i	−0.378394	+	0.228690i
$67$	2.56768	+	8.74472i	0.313692	+	1.06834i	0.953897	+	0.300133i	$0.0970311\pi$
$67$	2.56768	+	8.74472i	0.313692	+	1.06834i	−0.640205	+	0.768204i	$0.721151\pi$
$68$	−13.0784	−	4.63723i	−1.58599	−	0.562347i
$69$	4.57265	−	1.44599i	0.550482	−	0.174077i
$70$	20.8780	+	3.59183i	2.49540	+	0.429306i
$71$	3.77544	−	1.10857i	0.448062	−	0.131563i	−0.0499142	−	0.998754i	$-0.515895\pi$
$71$	3.77544	−	1.10857i	0.448062	−	0.131563i	0.497976	+	0.867191i	$0.334077\pi$
$72$	−2.77041	+	0.569915i	−0.326496	+	0.0671652i
$73$	−1.93535	+	1.24377i	−0.226516	+	0.145573i	−0.648977	−	0.760808i	$-0.724803\pi$
$73$	−1.93535	+	1.24377i	−0.226516	+	0.145573i	0.422461	+	0.906381i	$0.361166\pi$
$74$	0.186293	−	6.75498i	0.0216561	−	0.785251i
$75$	−1.87920	+	2.92410i	−0.216992	+	0.337646i
$76$	6.11945	+	5.92366i	0.701950	+	0.679490i
$77$	9.87649	+	8.55802i	1.12553	+	0.975277i
$78$	−1.85566	−	0.600913i	−0.210112	−	0.0680400i
$79$	1.06170	+	2.32479i	0.119450	+	0.261559i	0.959907	−	0.280320i	$-0.0904404\pi$
$79$	1.06170	+	2.32479i	0.119450	+	0.261559i	−0.840457	+	0.541879i	$0.817713\pi$
$80$	−9.58685	+	6.61109i	−1.07184	+	0.739142i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	15.7088	−	4.14573i	1.73475	−	0.457820i
$83$	7.37017	+	1.05967i	0.808981	+	0.116314i	0.534380	−	0.845244i	$-0.320545\pi$
$83$	7.37017	+	1.05967i	0.808981	+	0.116314i	0.274601	+	0.961558i	$0.411454\pi$
$84$	5.07798	+	8.95058i	0.554054	+	0.976588i
$85$	−18.3737	−	8.39101i	−1.99291	−	0.910132i
$86$	−12.4012	−	11.3592i	−1.33726	−	1.22489i
$87$	0.418637	+	2.91168i	0.0448826	+	0.312165i
$88$	−7.17083	+	0.431377i	−0.764413	+	0.0459850i
$89$	1.62551	+	1.87594i	0.172304	+	0.198849i	0.835333	−	0.549744i	$-0.185275\pi$
$89$	1.62551	+	1.87594i	0.172304	+	0.198849i	−0.663029	+	0.748594i	$0.730729\pi$
$90$	−4.08995	+	0.473374i	−0.431118	+	0.0498980i
$91$			7.09665i			0.743931i
$92$	9.44136	+	1.69139i	0.984329	+	0.176340i
$93$		−	3.21056i		−	0.332920i
$94$	0.523226	+	4.52067i	0.0539666	+	0.466271i
$95$	8.11881	+	9.36961i	0.832973	+	0.961302i
$96$	−5.43552	−	1.56688i	−0.554761	−	0.159919i
$97$	−1.91268	−	13.3030i	−0.194203	−	1.35071i	−0.820732	−	0.571314i	$-0.806434\pi$
$97$	−1.91268	−	13.3030i	−0.194203	−	1.35071i	0.626529	−	0.779398i	$-0.284475\pi$
$98$	18.6027	−	20.3093i	1.87916	−	2.05155i
$99$	−2.31033	−	1.05509i	−0.232197	−	0.106041i
$100$	−6.04645	+	3.43037i	−0.604645	+	0.343037i
$101$	−9.62641	−	1.38407i	−0.957863	−	0.137720i	−0.354385	−	0.935100i	$-0.615310\pi$
$101$	−9.62641	−	1.38407i	−0.957863	−	0.137720i	−0.603478	+	0.797380i	$0.706219\pi$
$102$	−2.50375	−	9.48711i	−0.247908	−	0.939363i
$103$	−4.13129	−	1.21306i	−0.407068	−	0.119526i	0.0717868	−	0.997420i	$-0.477130\pi$
$103$	−4.13129	−	1.21306i	−0.407068	−	0.119526i	−0.478855	+	0.877894i	$0.658948\pi$
$104$	−2.72708	−	2.78950i	−0.267412	−	0.273533i
$105$	6.22286	+	13.6262i	0.607289	+	1.32978i
$106$	1.37792	−	4.25510i	0.133835	−	0.413292i
$107$	−11.0595	−	9.58309i	−1.06916	−	0.926433i	−0.0716837	−	0.997427i	$-0.522837\pi$
$107$	−11.0595	−	9.58309i	−1.06916	−	0.926433i	−0.997477	+	0.0709947i	$0.977383\pi$
$108$	−1.43702	−	1.39104i	−0.138277	−	0.133853i
$109$	−0.101876	+	0.158522i	−0.00975793	+	0.0151836i	−0.846098	−	0.533027i	$-0.821054\pi$
$109$	−0.101876	+	0.158522i	−0.00975793	+	0.0151836i	0.836340	+	0.548211i	$0.184691\pi$
$110$	−10.4533	−	0.288286i	−0.996678	−	0.0274870i
$111$	4.01977	−	2.58335i	0.381540	−	0.245201i
$112$	0.669049	+	20.5705i	0.0632192	+	1.94373i
$113$	−10.1075	+	2.96782i	−0.950830	+	0.279189i	−0.720133	−	0.693837i	$-0.755919\pi$
$113$	−10.1075	+	2.96782i	−0.950830	+	0.279189i	−0.230698	+	0.973025i	$0.574101\pi$
$114$	−1.02108	+	5.93516i	−0.0956328	+	0.555879i
$115$	13.4752	+	3.65582i	1.25657	+	0.340907i
$116$	−1.96610	+	5.54500i	−0.182548	+	0.514840i
$117$	−0.388575	−	1.32336i	−0.0359238	−	0.122345i
$118$	−2.21645	−	3.66737i	−0.204041	−	0.337609i
$119$	−30.0318	+	19.3003i	−2.75301	+	1.76925i
$120$	−7.68226	−	2.96478i	−0.701291	−	0.270646i
$121$	3.82697	+	2.45945i	0.347907	+	0.223586i
$122$	−1.37569	+	2.01615i	−0.124549	+	0.182534i
$123$	8.68216	+	7.52313i	0.782844	+	0.678338i
$124$	2.98530	−	5.68497i	0.268088	−	0.510525i
$125$	4.03624	−	1.84329i	0.361012	−	0.164869i
$126$	−3.20415	+	6.53321i	−0.285448	+	0.582025i
$127$	−17.1333	−	5.03078i	−1.52033	−	0.446409i	−0.588256	−	0.808675i	$-0.700185\pi$
$127$	−17.1333	−	5.03078i	−1.52033	−	0.446409i	−0.932075	+	0.362266i	$0.882003\pi$
$128$	−8.16777	−	7.82863i	−0.721936	−	0.691960i
$129$	1.69235	−	11.7706i	0.149003	−	1.03634i
$130$	−3.59900	−	4.39253i	−0.315653	−	0.385250i
$131$	−13.7058	−	6.25921i	−1.19748	−	0.546870i	−0.286004	−	0.958228i	$-0.592327\pi$
$131$	−13.7058	−	6.25921i	−1.19748	−	0.546870i	−0.911474	+	0.411359i	$0.865054\pi$
$132$	−3.10986	−	4.01650i	−0.270679	−	0.349591i
$133$	21.6882	−	3.11829i	1.88061	−	0.270390i
$134$	−11.8674	+	5.02903i	−1.02519	+	0.434442i
$135$	−1.90652	−	2.20024i	−0.164087	−	0.189367i
$136$	4.38805	−	19.1270i	0.376272	−	1.64012i
$137$	14.8577			1.26938			0.634691	−	0.772766i	$-0.281128\pi$
$137$	14.8577			1.26938			0.634691	+	0.772766i	$0.281128\pi$
$138$	2.77487	+	6.18871i	0.236213	+	0.526818i
$139$		−	4.29106i		−	0.363963i	−0.983302	−	0.181981i	$-0.941749\pi$
$139$		−	4.29106i		−	0.363963i	0.983302	−	0.181981i	$-0.0582510\pi$
$140$	−1.65124	+	29.9142i	−0.139555	+	2.52821i
$141$	−2.43195	+	2.10730i	−0.204807	+	0.177467i
$142$	2.17123	+	5.12362i	0.182206	+	0.429965i
$143$	−0.498536	−	3.46740i	−0.0416897	−	0.289958i
$144$	−1.25110	−	3.79931i	−0.104258	−	0.316609i
$145$	−3.55764	+	7.79014i	−0.295446	+	0.646936i
$146$	−2.06198	−	2.51662i	−0.170651	−	0.208277i
$147$	19.2765	+	2.77154i	1.58990	+	0.228593i
$148$	9.51993	−	0.836627i	0.782533	−	0.0687703i
$149$	3.37208	−	11.4843i	0.276252	−	0.940826i	−0.698139	−	0.715963i	$-0.745988\pi$
$149$	3.37208	−	11.4843i	0.276252	−	0.940826i	0.974390	−	0.224864i	$-0.0721937\pi$
$150$	−4.41343	−	2.16452i	−0.360355	−	0.176733i
$151$	1.01002	+	2.21163i	0.0821940	+	0.179980i	0.946267	−	0.323387i	$-0.104822\pi$
$151$	1.01002	+	2.21163i	0.0821940	+	0.179980i	−0.864073	+	0.503367i	$0.832094\pi$
$152$	−7.32676	+	9.55999i	−0.594279	+	0.775418i
$153$	4.54348	−	5.24345i	0.367318	−	0.423908i
$154$	−10.4167	+	15.2663i	−0.839404	+	1.23020i
$155$	5.05339	−	7.86322i	0.405898	−	0.631589i
$156$	0.542460	−	2.70460i	0.0434316	−	0.216541i
$157$	2.65498	+	4.13124i	0.211891	+	0.329709i	0.930888	−	0.365304i	$-0.119035\pi$
$157$	2.65498	+	4.13124i	0.211891	+	0.329709i	−0.718997	+	0.695013i	$0.755399\pi$
$158$	−3.09332	+	1.86951i	−0.246091	+	0.148730i
$159$	3.03453	−	0.891018i	0.240654	−	0.0706623i
$160$	−10.8463	−	12.3930i	−0.857474	−	0.979753i
$161$	18.3110	−	16.5416i	1.44311	−	1.30366i
$162$	0.239777	−	1.39374i	0.0188387	−	0.109502i
$163$	−0.269801	−	0.918858i	−0.0211324	−	0.0719705i	0.948252	−	0.317520i	$-0.102850\pi$
$163$	−0.269801	−	0.918858i	−0.0211324	−	0.0719705i	−0.969384	+	0.245549i	$0.921032\pi$
$164$	8.37828	+	21.3942i	0.654233	+	1.67061i
$165$	−3.99770	−	6.22054i	−0.311221	−	0.484269i
$166$	−0.290297	+	10.5262i	−0.0225314	+	0.816989i
$167$	−4.33192	−	2.78396i	−0.335214	−	0.215429i	0.362195	−	0.932102i	$-0.382027\pi$
$167$	−4.33192	−	2.78396i	−0.335214	−	0.215429i	−0.697409	+	0.716673i	$0.745664\pi$
$168$	−11.7484	+	8.58907i	−0.906411	+	0.662661i
$169$	−7.26746	+	8.38709i	−0.559035	+	0.645161i
$170$	8.80047	−	27.1764i	0.674965	−	2.08434i
$171$	−3.87362	+	1.76902i	−0.296223	+	0.135281i
$172$	13.9413	−	19.2686i	1.06302	−	1.46922i
$173$	−1.42175	+	4.84203i	−0.108093	+	0.368133i	−0.995719	−	0.0924336i	$-0.970535\pi$
$173$	−1.42175	+	4.84203i	−0.108093	+	0.368133i	0.887625	+	0.460566i	$0.152354\pi$
$174$	−4.02236	+	1.06155i	−0.304935	+	0.0804755i
$175$	−2.54525	+	17.7026i	−0.192403	+	1.33819i
$176$	−1.77197	−	10.0037i	−0.133567	−	0.754057i
$177$	1.25872	−	2.75622i	0.0946114	−	0.207170i
$178$	−2.37109	+	2.58860i	−0.177720	+	0.194024i
$179$	2.70878	−	0.389464i	0.202464	−	0.0291099i	−0.0403366	−	0.999186i	$-0.512843\pi$
$179$	2.70878	−	0.389464i	0.202464	−	0.0291099i	0.242801	+	0.970076i	$0.421934\pi$
$180$	−1.33002	−	5.66874i	−0.0991342	−	0.422523i
$181$	−9.26925	+	8.03185i	−0.688978	+	0.597003i	−0.927361	−	0.374168i	$-0.877928\pi$
$181$	−9.26925	+	8.03185i	−0.688978	+	0.597003i	0.238383	+	0.971171i	$0.423383\pi$
$182$	−9.96962	+	1.15389i	−0.738997	+	0.0855321i
$183$	−1.72589			−0.127581
$184$	−0.840996	+	13.5386i	−0.0619991	+	0.998076i
$185$	13.9113			1.02278
$186$	4.51031	−	0.522027i	0.330712	−	0.0382769i
$187$	13.3176	−	11.5398i	0.973880	−	0.843872i
$188$	−6.26572	+	1.47009i	−0.456975	+	0.107217i
$189$	−5.09298	+	0.732261i	−0.370460	+	0.0532641i
$190$	−11.8427	+	12.9291i	−0.859157	+	0.937973i
$191$	−6.85801	+	15.0169i	−0.496228	+	1.08659i	0.481449	+	0.876474i	$0.340111\pi$
$191$	−6.85801	+	15.0169i	−0.496228	+	1.08659i	−0.977677	+	0.210114i	$0.932616\pi$
$192$	1.31741	−	7.89078i	0.0950759	−	0.569468i
$193$	−1.62645	+	11.3122i	−0.117075	+	0.814272i	0.843675	+	0.536855i	$0.180388\pi$
$193$	−1.62645	+	11.3122i	−0.117075	+	0.814272i	−0.960749	+	0.277418i	$0.910521\pi$
$194$	18.3775	−	4.85002i	1.31943	−	0.348211i
$195$	1.13127	−	3.85276i	0.0810121	−	0.275902i
$196$	31.5559	+	22.8315i	2.25399	+	1.63082i
$197$	−20.9427	+	9.56420i	−1.49210	+	0.681421i	−0.983720	−	0.179710i	$-0.942484\pi$
$197$	−20.9427	+	9.56420i	−1.49210	+	0.681421i	−0.508384	+	0.861131i	$0.669757\pi$
$198$	1.10658	−	3.41719i	0.0786413	−	0.242849i
$199$	−3.41985	+	3.94672i	−0.242427	+	0.279775i	−0.863904	−	0.503657i	$-0.831987\pi$
$199$	−3.41985	+	3.94672i	−0.242427	+	0.279775i	0.621477	+	0.783432i	$0.286533\pi$
$200$	−5.80224	−	7.93650i	−0.410280	−	0.561196i
$201$	−7.66709	−	4.92734i	−0.540795	−	0.347548i
$202$	0.379166	−	13.7486i	0.0266780	−	0.967346i
$203$	8.18298	+	12.7330i	0.574332	+	0.893679i
$204$	12.9207	−	5.05993i	0.904631	−	0.354266i
$205$	9.42278	+	32.0911i	0.658116	+	2.24134i
$206$	1.03241	−	6.00102i	0.0719314	−	0.418111i
$207$	−2.50886	+	4.08725i	−0.174378	+	0.284084i
$208$	3.47538	−	4.28466i	0.240974	−	0.297088i
$209$	−10.3777	+	3.04717i	−0.717842	+	0.210777i
$210$	−18.1307	+	10.9577i	−1.25114	+	0.756151i
$211$	11.8696	+	18.4694i	0.817134	+	1.27148i	0.959511	+	0.281672i	$0.0908891\pi$
$211$	11.8696	+	18.4694i	0.817134	+	1.27148i	−0.142377	+	0.989812i	$0.545475\pi$
$212$	6.20176	+	1.24388i	0.425939	+	0.0854303i
$213$	−2.12733	+	3.31019i	−0.145762	+	0.226810i
$214$	11.6644	−	17.0949i	0.797364	−	1.16859i
$215$	22.6716	−	26.1644i	1.54619	−	1.78440i
$216$	1.72052	−	2.24495i	0.117067	−	0.152749i
$217$	−6.86244	−	15.0267i	−0.465853	−	1.02008i
$218$	−0.239262	−	0.117344i	−0.0162049	−	0.00794751i
$219$	0.648142	−	2.20737i	0.0437973	−	0.149160i
$220$	−1.29467	−	14.7320i	−0.0872866	−	0.993229i
$221$	9.47183	+	1.36184i	0.637144	+	0.0916075i
$222$	4.28278	+	5.22707i	0.287442	+	0.350818i
$223$	9.97705	−	21.8467i	0.668112	−	1.46296i	−0.206652	−	0.978414i	$-0.566257\pi$
$223$	9.97705	−	21.8467i	0.668112	−	1.46296i	0.874765	−	0.484548i	$-0.161016\pi$
$224$	−28.7894	+	4.28461i	−1.92358	+	0.286277i
$225$	−0.494670	−	3.44050i	−0.0329780	−	0.229367i
$226$	−5.81274	−	13.7168i	−0.386658	−	0.912426i
$227$	−15.5515	+	13.4755i	−1.03219	+	0.894399i	−0.994484	−	0.104890i	$-0.966551\pi$
$227$	−15.5515	+	13.4755i	−1.03219	+	0.894399i	−0.0377072	+	0.999289i	$0.512005\pi$
$228$	−8.50395	−	0.469411i	−0.563188	−	0.0310875i
$229$		−	22.5665i		−	1.49123i	−0.666375	−	0.745617i	$-0.732155\pi$
$229$		−	22.5665i		−	1.49123i	0.666375	−	0.745617i	$-0.267845\pi$
$230$	−2.94480	+	19.5248i	−0.194175	+	1.28743i
$231$	−13.0685			−0.859842
$232$	−8.10949	−	1.86046i	−0.532414	−	0.122145i
$233$	−11.5404	−	13.3183i	−0.756035	−	0.872511i	0.239104	−	0.970994i	$-0.423146\pi$
$233$	−11.5404	−	13.3183i	−0.756035	−	0.872511i	−0.995139	+	0.0984834i	$0.968601\pi$
$234$	1.79593	−	0.761058i	0.117404	−	0.0497519i
$235$	−9.27314	+	1.33328i	−0.604913	+	0.0869733i
$236$	4.79166	−	3.71005i	0.311911	−	0.241504i
$237$	−2.32479	−	1.06170i	−0.151011	−	0.0689646i
$238$	−31.9968	−	39.0516i	−2.07404	−	2.53134i
$239$	2.14486	−	14.9178i	0.138739	−	0.964954i	−0.794900	−	0.606740i	$-0.792477\pi$
$239$	2.14486	−	14.9178i	0.138739	−	0.964954i	0.933640	−	0.358213i	$-0.116614\pi$
$240$	2.91591	−	11.2744i	0.188221	−	0.727758i
$241$	15.7174	+	4.61506i	1.01245	+	0.297282i	0.745555	−	0.666444i	$-0.232184\pi$
$241$	15.7174	+	4.61506i	1.01245	+	0.297282i	0.266894	+	0.963726i	$0.414003\pi$
$242$	−2.83286	+	5.77617i	−0.182103	+	0.371306i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	−3.05604	−	1.60479i	−0.195643	−	0.102736i
$245$	42.8490	+	37.1289i	2.73752	+	2.37208i
$246$	−9.15707	+	13.4202i	−0.583834	+	0.855643i
$247$	−4.94101	−	3.17539i	−0.314389	−	0.202045i
$248$	8.47184	+	3.26950i	0.537962	+	0.207613i
$249$	−6.26394	+	4.02559i	−0.396961	+	0.255111i
$250$	3.24579	+	5.37054i	0.205282	+	0.339663i
$251$	1.62696	+	5.54090i	0.102692	+	0.349739i	0.994770	−	0.102145i	$-0.0325705\pi$
$251$	1.62696	+	5.54090i	0.102692	+	0.349739i	−0.892077	+	0.451883i	$0.850752\pi$
$252$	−9.69907	−	3.43902i	−0.610984	−	0.216638i
$253$	−7.78465	+	9.36852i	−0.489417	+	0.588994i
$254$	4.28160	−	24.8874i	0.268652	−	1.56157i
$255$	19.3809	−	5.69074i	1.21368	−	0.356368i
$256$	9.66988	−	12.7473i	0.604368	−	0.796706i
$257$	7.21011	−	4.63366i	0.449754	−	0.289040i	−0.296090	−	0.955160i	$-0.595683\pi$
$257$	7.21011	−	4.63366i	0.449754	−	0.289040i	0.745844	+	0.666121i	$0.232046\pi$
$258$	16.8109	+	0.463620i	1.04660	+	0.0288637i
$259$	13.2923	−	20.6832i	0.825941	−	1.28519i
$260$	5.58559	−	5.77021i	0.346404	−	0.357853i
$261$	−2.22313	−	1.92635i	−0.137608	−	0.119238i
$262$	6.56465	−	20.2721i	0.405565	−	1.25241i
$263$	4.52533	+	9.90909i	0.279044	+	0.611021i	0.996315	−	0.0857737i	$-0.0273362\pi$
$263$	4.52533	+	9.90909i	0.279044	+	0.611021i	−0.717271	+	0.696795i	$0.754609\pi$
$264$	5.13686	−	5.02191i	0.316152	−	0.309077i
$265$	8.83454	+	2.59405i	0.542701	+	0.159351i
$266$	7.90712	+	29.9613i	0.484816	+	1.83705i
$267$	−2.45696	−	0.353258i	−0.150364	−	0.0216190i
$268$	−8.99456	−	15.8540i	−0.549430	−	0.968439i
$269$	10.4702	+	4.78156i	0.638377	+	0.291537i	0.708189	−	0.706023i	$-0.249513\pi$
$269$	10.4702	+	4.78156i	0.638377	+	0.291537i	−0.0698120	+	0.997560i	$0.522240\pi$
$270$	2.78098	−	3.03610i	0.169245	−	0.184771i
$271$	−0.584465	−	4.06504i	−0.0355037	−	0.246934i	0.964339	−	0.264670i	$-0.0852631\pi$
$271$	−0.584465	−	4.06504i	−0.0355037	−	0.246934i	−0.999843	+	0.0177364i	$0.994354\pi$
$272$	27.5837	+	3.05451i	1.67251	+	0.185207i
$273$	−4.64732	−	5.36329i	−0.281268	−	0.324601i
$274$	2.41582	+	20.8727i	0.145945	+	1.26096i
$275$		−	8.82824i		−	0.532363i
$276$	−8.24293	+	4.90450i	−0.496166	+	0.295216i
$277$			12.2540i			0.736269i	0.929773	+	0.368135i	$0.120003\pi$
$277$			12.2540i			0.736269i	−0.929773	+	0.368135i	$0.879997\pi$
$278$	6.02823	−	0.697712i	0.361549	−	0.0418460i
$279$	2.10247	+	2.42638i	0.125872	+	0.145264i
$280$	−42.2930	+	2.54423i	−2.52749	+	0.152047i
$281$	0.766558	+	5.33153i	0.0457290	+	0.318052i	0.999828	+	0.0185600i	$0.00590818\pi$
$281$	0.766558	+	5.33153i	0.0457290	+	0.318052i	−0.954099	+	0.299492i	$0.903183\pi$
$282$	−3.35584	−	3.07385i	−0.199837	−	0.183045i
$283$	6.76217	+	3.08818i	0.401969	+	0.183573i	0.606133	−	0.795364i	$-0.292720\pi$
$283$	6.76217	+	3.08818i	0.401969	+	0.183573i	−0.204163	+	0.978937i	$0.565447\pi$
$284$	−6.84481	+	3.88330i	−0.406165	+	0.230432i
$285$	−12.2716	−	1.76439i	−0.726906	−	0.104513i
$286$	4.79006	−	1.26415i	0.283242	−	0.0747507i
$287$	56.7162	+	16.6534i	3.34785	+	0.983018i
$288$	5.13398	−	2.37534i	0.302523	−	0.139968i
$289$	12.9348	+	28.3232i	0.760868	+	1.66607i
$290$	−11.5223	−	3.73124i	−0.676614	−	0.219106i
$291$	10.1571	+	8.80118i	0.595420	+	0.515934i
$292$	3.20016	−	3.30594i	0.187275	−	0.193465i
$293$	−10.5923	+	16.4819i	−0.618807	+	0.962882i	0.380468	+	0.924794i	$0.375763\pi$
$293$	−10.5923	+	16.4819i	−0.618807	+	0.962882i	−0.999274	+	0.0380879i	$0.987873\pi$
$294$	−0.759264	+	27.5309i	−0.0442812	+	1.60564i
$295$	7.42108	−	4.76924i	0.432072	−	0.277676i
$296$	2.72323	+	13.2379i	0.158285	+	0.769437i
$297$	2.43697	−	0.715560i	0.141408	−	0.0415210i
$298$	16.6818	+	2.86992i	0.966349	+	0.166250i
$299$	−6.61316	+	0.136753i	−0.382449	+	0.00790864i
$300$	2.32319	−	6.55209i	0.134129	−	0.378285i
$301$	−17.2382	−	58.7080i	−0.993595	−	3.38387i
$302$	−2.94275	+	1.77851i	−0.169336	+	0.102342i
$303$	8.18153	−	5.25795i	0.470016	−	0.302061i
$304$	−14.6215	−	8.73847i	−0.838602	−	0.501186i
$305$	−4.22699	−	2.71652i	−0.242037	−	0.155548i
$306$	8.10494	+	5.53027i	0.463329	+	0.316144i
$307$	11.3650	+	9.84782i	0.648634	+	0.562045i	0.915814	−	0.401602i	$-0.131546\pi$
$307$	11.3650	+	9.84782i	0.648634	+	0.562045i	−0.267180	+	0.963647i	$0.586092\pi$
$308$	−23.1404	−	12.1515i	−1.31855	−	0.692398i
$309$	3.91660	−	1.78865i	0.222808	−	0.101753i
$310$	11.8682	+	5.82064i	0.674068	+	0.330590i
$311$	−18.6304	−	5.47038i	−1.05643	−	0.310197i	−0.293020	−	0.956106i	$-0.594660\pi$
$311$	−18.6304	−	5.47038i	−1.05643	−	0.310197i	−0.763414	+	0.645910i	$0.776478\pi$
$312$	3.88772	+	0.322308i	0.220099	+	0.0182471i
$313$	2.42059	−	16.8356i	0.136820	−	0.951602i	−0.799553	−	0.600595i	$-0.794930\pi$
$313$	2.42059	−	16.8356i	0.136820	−	0.951602i	0.936373	−	0.351007i	$-0.114161\pi$
$314$	−5.37201	+	4.40154i	−0.303160	+	0.248393i
$315$	−13.6262	−	6.22286i	−0.767747	−	0.350619i
$316$	−3.12932	−	4.04163i	−0.176038	−	0.227359i
$317$	−7.00911	+	1.00776i	−0.393671	+	0.0566013i	−0.336308	−	0.941752i	$-0.609178\pi$
$317$	−7.00911	+	1.00776i	−0.393671	+	0.0566013i	−0.0573629	+	0.998353i	$0.518269\pi$
$318$	1.74514	+	4.11814i	0.0978625	+	0.230934i
$319$	−4.89266	−	5.64643i	−0.273936	−	0.316139i
$320$	15.6466	−	17.2523i	0.874669	−	0.964433i
$321$	14.6338			0.816779
$322$	26.2156	+	23.0343i	1.46094	+	1.28365i
$323$		−	29.5454i		−	1.64395i
$324$	1.99696	+	0.110231i	0.110942	+	0.00612392i
$325$	3.62310	−	3.13944i	0.200974	−	0.174145i
$326$	1.24698	−	0.528429i	0.0690636	−	0.0292670i
$327$	−0.0268171	−	0.186517i	−0.00148299	−	0.0103144i
$328$	−28.6931	+	15.2487i	−1.58431	+	0.841970i
$329$	−6.87820	+	15.0612i	−0.379208	+	0.830349i
$330$	8.08883	−	6.62755i	0.445275	−	0.364835i
$331$	−24.0842	−	3.46279i	−1.32379	−	0.190332i	−0.556079	−	0.831130i	$-0.687695\pi$
$331$	−24.0842	−	3.46279i	−1.32379	−	0.190332i	−0.767710	+	0.640798i	$0.778604\pi$
$332$	−14.8347	+	1.30370i	−0.814162	+	0.0715499i
$333$	−1.34621	+	4.58476i	−0.0737716	+	0.251243i
$334$	3.20664	−	6.53830i	0.175460	−	0.357760i
$335$	−11.0225	−	24.1358i	−0.602221	−	1.31868i
$336$	−13.9765	−	15.1080i	−0.762479	−	0.824212i
$337$	−15.9988	+	18.4636i	−0.871510	+	1.00578i	0.128391	+	0.991724i	$0.459019\pi$
$337$	−15.9988	+	18.4636i	−0.871510	+	1.00578i	−0.999901	+	0.0140527i	$0.995527\pi$
$338$	−12.9642	−	8.84587i	−0.705157	−	0.481152i
$339$	5.69520	−	8.86191i	0.309321	−	0.481313i
$340$	39.6093	+	7.94442i	2.14812	+	0.430847i
$341$	4.40858	+	6.85989i	0.238738	+	0.371484i
$342$	−3.11502	−	5.15416i	−0.168441	−	0.278705i
$343$	61.5867	−	18.0835i	3.32537	−	0.976417i
$344$	29.3360	+	16.4523i	1.58169	+	0.887048i
$345$	−12.5779	+	6.06148i	−0.677172	+	0.326339i
$346$	−7.03342	−	1.21002i	−0.378119	−	0.0650513i
$347$	2.26794	+	7.72389i	0.121749	+	0.414640i	0.997702	−	0.0677573i	$-0.0215844\pi$
$347$	2.26794	+	7.72389i	0.121749	+	0.414640i	−0.875953	+	0.482397i	$0.839766\pi$
$348$	−2.14532	−	5.47816i	−0.115001	−	0.293660i
$349$	−2.40400	−	3.74069i	−0.128683	−	0.200235i	0.770933	−	0.636916i	$-0.219790\pi$
$349$	−2.40400	−	3.74069i	−0.128683	−	0.200235i	−0.899616	+	0.436681i	$0.856154\pi$
$350$	−25.2831	−	0.697273i	−1.35144	−	0.0372708i
$351$	1.16028	+	0.745670i	0.0619314	+	0.0398009i
$352$	13.7654	−	4.11589i	0.733700	−	0.219378i
$353$	1.86960	−	2.15764i	0.0995089	−	0.114839i	−0.703811	−	0.710388i	$-0.748520\pi$
$353$	1.86960	−	2.15764i	0.0995089	−	0.114839i	0.803320	+	0.595548i	$0.203065\pi$
$354$	4.07670	+	1.32015i	0.216674	+	0.0701650i
$355$	−10.4204	+	4.75883i	−0.553057	+	0.252573i
$356$	−4.02209	−	2.91009i	−0.213170	−	0.154234i
$357$	10.0575	−	34.2528i	0.532302	−	1.81285i
$358$	0.987573	+	3.74207i	0.0521948	+	0.197775i
$359$	−4.11318	+	28.6078i	−0.217085	+	1.50986i	0.531635	+	0.846974i	$0.321578\pi$
$359$	−4.11318	+	28.6078i	−0.217085	+	1.50986i	−0.748720	+	0.662886i	$0.769331\pi$
$360$	7.74738	−	2.79018i	0.408323	−	0.147056i
$361$	0.359601	−	0.787416i	0.0189264	−	0.0414429i
$362$	−12.7906	−	11.7158i	−0.672258	−	0.615770i
$363$	−4.50283	+	0.647409i	−0.236337	+	0.0339802i
$364$	−3.24205	−	13.8181i	−0.169930	−	0.724263i
$365$	5.06178	−	4.38606i	0.264946	−	0.229577i
$366$	−0.280623	−	2.42459i	−0.0146684	−	0.126735i
$367$	−35.0592			−1.83008			−0.915039	−	0.403366i	$-0.867840\pi$
$367$	−35.0592			−1.83008			−0.915039	+	0.403366i	$0.867840\pi$
$368$	−19.1562	+	1.01986i	−0.998586	+	0.0531641i
$369$	−11.4881			−0.598049
$370$	2.26193	+	19.5430i	0.117592	+	1.01599i
$371$	12.2982	−	10.6565i	0.638493	−	0.553257i
$372$	1.46672	+	6.25137i	0.0760461	+	0.324118i
$373$	35.8483	−	5.15421i	1.85616	−	0.266875i	0.878601	−	0.477556i	$-0.158477\pi$
$373$	35.8483	−	5.15421i	1.85616	−	0.266875i	0.977555	+	0.210681i	$0.0675683\pi$
$374$	18.3769	+	16.8327i	0.950246	+	0.870399i
$375$	−1.84329	+	4.03624i	−0.0951870	+	0.208430i
$376$	−3.08402	−	8.56327i	−0.159046	−	0.441617i
$377$	0.577398	−	4.01589i	0.0297375	−	0.206829i
$378$	−1.85681	−	7.03574i	−0.0955039	−	0.361879i
$379$	−10.4363	+	35.5429i	−0.536079	+	1.82572i	0.0274537	+	0.999623i	$0.491260\pi$
$379$	−10.4363	+	35.5429i	−0.536079	+	1.82572i	−0.563533	+	0.826094i	$0.690558\pi$
$380$	−20.0888	−	14.5348i	−1.03053	−	0.745618i
$381$	16.2429	−	7.41789i	0.832149	−	0.380030i
$382$	−22.2114	−	7.19267i	−1.13644	−	0.368009i
$383$	15.1779	−	17.5163i	0.775555	−	0.895039i	−0.221225	−	0.975223i	$-0.571005\pi$
$383$	15.1779	−	17.5163i	0.775555	−	0.895039i	0.996780	+	0.0801842i	$0.0255509\pi$
$384$	11.2995	+	0.567729i	0.576623	+	0.0289718i
$385$	−32.0069	−	20.5696i	−1.63122	−	1.04832i
$386$	−16.1563	−	0.445568i	−0.822333	−	0.0226788i
$387$	6.42908	+	10.0038i	0.326809	+	0.508524i
$388$	9.80160	+	25.0288i	0.497601	+	1.27064i
$389$	0.488808	+	1.66473i	0.0247835	+	0.0844050i	0.970956	−	0.239257i	$-0.0769040\pi$
$389$	0.488808	+	1.66473i	0.0247835	+	0.0844050i	−0.946173	+	0.323662i	$0.895086\pi$
$390$	5.59643	+	0.962805i	0.283386	+	0.0487536i
$391$	−18.5641	−	27.6139i	−0.938826	−	1.39649i
$392$	−26.9437	+	48.0432i	−1.36086	+	2.42655i
$393$	14.4570	−	4.24497i	0.729261	−	0.214130i
$394$	−16.8413	−	27.8659i	−0.848454	−	1.40386i
$395$	−4.02271	−	6.25947i	−0.202405	−	0.314948i
$396$	4.98052	+	0.998940i	0.250281	+	0.0501986i
$397$	−1.56478	+	2.43485i	−0.0785342	+	0.122202i	−0.878299	−	0.478112i	$-0.841321\pi$
$397$	−1.56478	+	2.43485i	−0.0785342	+	0.122202i	0.799765	+	0.600314i	$0.204958\pi$
$398$	−6.10054	−	4.16260i	−0.305793	−	0.208652i
$399$	−14.3488	+	16.5594i	−0.718338	+	0.829007i
$400$	10.2061	−	9.44164i	0.510303	−	0.472082i
$401$	−1.52979	−	3.34978i	−0.0763943	−	0.167280i	0.867581	−	0.497295i	$-0.165673\pi$
$401$	−1.52979	−	3.34978i	−0.0763943	−	0.167280i	−0.943976	+	0.330015i	$0.892946\pi$
$402$	5.67546	−	11.5722i	0.283066	−	0.577168i
$403$	−1.24754	+	4.24874i	−0.0621446	+	0.211645i
$404$	19.3761	−	1.70280i	0.963998	−	0.0847177i
$405$	2.88170	+	0.414326i	0.143193	+	0.0205880i
$406$	−16.5572	+	13.5661i	−0.821720	+	0.673273i
$407$	−5.04157	+	11.0395i	−0.249901	+	0.547207i
$408$	9.20923	+	17.3288i	0.455925	+	0.857901i
$409$	1.30324	+	9.06425i	0.0644412	+	0.448198i	0.996340	+	0.0854796i	$0.0272423\pi$
$409$	1.30324	+	9.06425i	0.0644412	+	0.448198i	−0.931899	+	0.362718i	$0.881849\pi$
$410$	−43.5505	+	18.4554i	−2.15081	+	0.911445i
$411$	−11.2287	+	9.72974i	−0.553872	+	0.479933i
$412$	8.59832	+	0.474620i	0.423609	+	0.0233829i
$413$		−	15.5906i		−	0.767164i
$414$	−6.14985	−	2.85996i	−0.302249	−	0.140559i
$415$	−21.6777			−1.06412
$416$	6.58433	+	4.18566i	0.322823	+	0.205219i
$417$	2.81004	+	3.24296i	0.137608	+	0.158809i
$418$	−5.96816	−	14.0835i	−0.291912	−	0.688848i
$419$	−15.6690	+	2.25286i	−0.765480	+	0.110059i	−0.513985	−	0.857799i	$-0.671831\pi$
$419$	−15.6690	+	2.25286i	−0.765480	+	0.110059i	−0.251495	+	0.967859i	$0.580922\pi$
$420$	−18.3417	−	23.6890i	−0.894984	−	1.15590i
$421$	4.81909	+	2.20081i	0.234868	+	0.107261i	0.529373	−	0.848389i	$-0.322427\pi$
$421$	4.81909	+	2.20081i	0.234868	+	0.107261i	−0.294505	+	0.955650i	$0.595155\pi$
$422$	−24.0165	+	19.6778i	−1.16910	+	0.957902i
$423$	0.457960	−	3.18518i	0.0222668	−	0.154869i
$424$	−0.739065	+	8.91471i	−0.0358922	+	0.432937i
$425$	23.1391	+	6.79425i	1.12241	+	0.329569i
$426$	−4.99616	−	2.45032i	−0.242065	−	0.118718i
$427$	−8.07781	+	3.68901i	−0.390913	+	0.178524i
$428$	25.9122	+	13.6070i	1.25251	+	0.657721i
$429$	2.64743	+	2.29401i	0.127819	+	0.110756i
$430$	40.4430	+	27.5956i	1.95033	+	1.33078i
$431$	−12.2635	−	7.88127i	−0.590712	−	0.379627i	0.210869	−	0.977514i	$-0.432371\pi$
$431$	−12.2635	−	7.88127i	−0.590712	−	0.379627i	−0.801580	+	0.597887i	$0.796007\pi$
$432$	3.43354	+	2.05203i	0.165196	+	0.0987285i
$433$	−21.1049	+	13.5633i	−1.01424	+	0.651810i	−0.938486	−	0.345317i	$-0.887771\pi$
$433$	−21.1049	+	13.5633i	−1.01424	+	0.651810i	−0.0757499	+	0.997127i	$0.524135\pi$
$434$	19.9942	−	12.0839i	0.959751	−	0.580045i
$435$	−2.41277	−	8.21715i	−0.115684	−	0.393982i
$436$	0.125945	−	0.355203i	0.00603168	−	0.0170111i
$437$	3.32378	+	20.1505i	0.158998	+	0.963929i
$438$	3.20637	+	0.551622i	0.153206	+	0.0263575i
$439$	6.43616	−	1.88983i	0.307181	−	0.0901965i	−0.124509	−	0.992218i	$-0.539736\pi$
$439$	6.43616	−	1.88983i	0.307181	−	0.0901965i	0.431690	+	0.902022i	$0.357917\pi$
$440$	20.4855	−	4.21417i	0.976607	−	0.200903i
$441$	−16.3832	+	10.5288i	−0.780150	+	0.501372i
$442$	−0.373078	+	13.5278i	−0.0177455	+	0.643452i
$443$	6.08182	−	9.46350i	0.288956	−	0.449624i	−0.666180	−	0.745791i	$-0.732072\pi$
$443$	6.08182	−	9.46350i	0.288956	−	0.449624i	0.955136	+	0.296166i	$0.0957083\pi$
$444$	−6.64681	+	6.86651i	−0.315444	+	0.325870i
$445$	−5.46150	−	4.73242i	−0.258900	−	0.224338i
$446$	32.3132	+	10.4639i	1.53008	+	0.495480i
$447$	4.97214	+	10.8875i	0.235174	+	0.514959i
$448$	−10.7002	−	39.7478i	−0.505539	−	1.87791i
$449$	−10.0307	−	2.94528i	−0.473378	−	0.138996i	0.0363371	−	0.999340i	$-0.488431\pi$
$449$	−10.0307	−	2.94528i	−0.473378	−	0.138996i	−0.509715	+	0.860343i	$0.670249\pi$
$450$	4.75291	−	1.25434i	0.224054	−	0.0591303i
$451$	−28.8812	−	4.15249i	−1.35996	−	0.195533i
$452$	18.3247	−	10.3962i	0.861920	−	0.488998i
$453$	−2.21163	−	1.01002i	−0.103911	−	0.0474547i
$454$	−21.4594	−	19.6563i	−1.00714	−	0.922514i
$455$	−2.94033	−	20.4504i	−0.137845	−	0.958731i
$456$	−0.723268	−	12.0230i	−0.0338701	−	0.563027i
$457$	−8.01044	−	9.24454i	−0.374712	−	0.432441i	0.536803	−	0.843708i	$-0.319632\pi$
$457$	−8.01044	−	9.24454i	−0.374712	−	0.432441i	−0.911515	+	0.411267i	$0.865087\pi$
$458$	31.7022	−	3.66923i	1.48134	−	0.171452i
$459$			6.93808i			0.323842i
$460$	−27.9080	−	0.962292i	−1.30122	−	0.0448671i
$461$		−	8.28230i		−	0.385745i	−0.981224	−	0.192873i	$-0.938220\pi$
$461$		−	8.28230i		−	0.385745i	0.981224	−	0.192873i	$-0.0617804\pi$
$462$	−2.12489	−	18.3590i	−0.0988588	−	0.854140i
$463$	−5.05565	−	5.83453i	−0.234956	−	0.271153i	0.626011	−	0.779814i	$-0.284686\pi$
$463$	−5.05565	−	5.83453i	−0.234956	−	0.271153i	−0.860967	+	0.508660i	$0.830141\pi$
$464$	1.29506	−	11.6950i	0.0601215	−	0.542927i
$465$	1.33022	+	9.25189i	0.0616875	+	0.429046i
$466$	16.8336	−	18.3778i	0.779801	−	0.851336i
$467$	28.9123	+	13.2038i	1.33790	+	0.611000i	0.950447	−	0.310888i	$-0.100626\pi$
$467$	28.9123	+	13.2038i	1.33790	+	0.611000i	0.387457	+	0.921888i	$0.373354\pi$
$468$	1.36117	+	2.39924i	0.0629203	+	0.110905i
$469$	−46.4169	−	6.67374i	−2.14333	−	0.308165i
$470$	−3.38081	−	12.8104i	−0.155945	−	0.590902i
$471$	−4.71189	−	1.38354i	−0.217112	−	0.0637499i
$472$	5.99112	+	6.12826i	0.275764	+	0.282076i
$473$	12.5467	+	27.4736i	0.576900	+	1.26324i
$474$	1.11350	−	3.43858i	0.0511450	−	0.157939i
$475$	−11.1865	−	9.69315i	−0.513272	−	0.444752i
$476$	49.6585	−	51.2999i	2.27609	−	2.35133i
$477$	−1.70985	+	2.66058i	−0.0782887	+	0.121820i
$478$	21.3058	+	0.587585i	0.974506	+	0.0268755i
$479$	−0.171049	+	0.109926i	−0.00781542	+	0.00502267i	−0.544543	−	0.838733i	$-0.683297\pi$
$479$	−0.171049	+	0.109926i	−0.00781542	+	0.00502267i	0.536727	+	0.843756i	$0.319660\pi$
$480$	16.3128	+	2.26320i	0.744572	+	0.103301i
$481$	−6.32345	+	1.85673i	−0.288324	+	0.0846597i
$482$	−3.92779	+	22.8308i	−0.178906	+	1.03992i
$483$	−3.00607	+	24.4925i	−0.136781	+	1.11445i
$484$	−8.57518	−	3.04052i	−0.389781	−	0.138206i
$485$	11.0235	+	37.5428i	0.500553	+	1.70473i
$486$	0.731493	+	1.21034i	0.0331812	+	0.0549020i
$487$	−0.292873	+	0.188218i	−0.0132713	+	0.00852896i	−0.547260	−	0.836963i	$-0.684329\pi$
$487$	−0.292873	+	0.188218i	−0.0132713	+	0.00852896i	0.533988	+	0.845492i	$0.320693\pi$
$488$	1.75757	−	4.55417i	0.0795613	−	0.206157i
$489$	0.805626	+	0.517744i	0.0364317	+	0.0234132i
$490$	−45.1929	+	66.2329i	−2.04161	+	2.99210i
$491$	−28.4707	−	24.6700i	−1.28487	−	1.11334i	−0.987338	−	0.158630i	$-0.949292\pi$
$491$	−28.4707	−	24.6700i	−1.28487	−	1.11334i	−0.297528	−	0.954713i	$-0.596162\pi$
$492$	−20.3421	−	10.6821i	−0.917094	−	0.481586i
$493$	18.5649	−	8.47830i	0.836120	−	0.381843i
$494$	3.65751	−	7.45761i	0.164559	−	0.335534i
$495$	7.09485	+	2.08324i	0.318890	+	0.0936345i
$496$	−3.21561	+	12.4332i	−0.144385	+	0.558265i
$497$	−2.88132	+	20.0400i	−0.129245	+	0.898917i
$498$	−6.67378	−	8.14525i	−0.299059	−	0.364998i
$499$	18.7539	+	8.56462i	0.839540	+	0.383405i	0.788308	−	0.615281i	$-0.210958\pi$
$499$	18.7539	+	8.56462i	0.839540	+	0.383405i	0.0512329	+	0.998687i	$0.483685\pi$
$500$	−7.01696	+	5.43304i	−0.313808	+	0.242973i
$501$	5.09695	−	0.732831i	0.227715	−	0.0327405i
$502$	−7.51951	+	3.18654i	−0.335612	+	0.142222i
$503$	−2.54269	−	2.93442i	−0.113373	−	0.130839i	0.696226	−	0.717822i	$-0.254861\pi$
$503$	−2.54269	−	2.93442i	−0.113373	−	0.130839i	−0.809599	+	0.586983i	$0.800316\pi$
$504$	3.25423	−	14.1848i	0.144955	−	0.631840i
$505$	28.3139			1.25995
$506$	−14.4270	−	9.41286i	−0.641358	−	0.418453i
$507$		−	11.0977i		−	0.492867i
$508$	35.6589	+	1.96834i	1.58211	+	0.0873310i
$509$	6.41130	−	5.55543i	0.284176	−	0.246240i	−0.501095	−	0.865392i	$-0.667069\pi$
$509$	6.41130	−	5.55543i	0.284176	−	0.246240i	0.785271	+	0.619152i	$0.212524\pi$
$510$	11.1458	+	26.3017i	0.493545	+	1.16466i
$511$	−1.68461	−	11.7167i	−0.0745226	−	0.518316i
$512$	19.4801	+	11.5119i	0.860908	+	0.508760i
$513$	1.76902	−	3.87362i	0.0781042	−	0.171024i
$514$	7.68187	+	9.37560i	0.338833	+	0.413540i
$515$	12.4078	+	1.78397i	0.546751	+	0.0786110i
$516$	2.08208	+	23.6919i	0.0916585	+	1.04298i
$517$	2.30263	−	7.84202i	0.101269	−	0.344892i
$518$	31.2177	+	15.3104i	1.37163	+	0.672701i
$519$	−2.09637	−	4.59041i	−0.0920204	−	0.201497i
$520$	9.01440	+	6.90862i	0.395307	+	0.302963i
$521$	−17.7426	+	20.4761i	−0.777318	+	0.897073i	−0.996913	−	0.0785180i	$-0.974981\pi$
$521$	−17.7426	+	20.4761i	−0.777318	+	0.897073i	0.219594	+	0.975591i	$0.429527\pi$
$522$	2.34474	−	3.43635i	0.102626	−	0.150405i
$523$	−14.1956	+	22.0888i	−0.620732	+	0.965877i	0.378458	+	0.925619i	$0.376455\pi$
$523$	−14.1956	+	22.0888i	−0.620732	+	0.965877i	−0.999189	+	0.0402588i	$0.987182\pi$
$524$	29.5463	+	5.92608i	1.29074	+	0.258882i
$525$	−9.66917	−	15.0455i	−0.421997	−	0.656641i
$526$	−13.1848	+	7.96853i	−0.574886	+	0.347444i
$527$	−21.3728	+	6.27563i	−0.931016	+	0.273371i
$528$	7.89019	+	6.39990i	0.343377	+	0.278520i
$529$	15.7675	+	16.7447i	0.685544	+	0.728031i
$530$	−2.20775	+	12.8329i	−0.0958986	+	0.557424i
$531$	0.853660	+	2.90730i	0.0370457	+	0.126166i
$532$	−40.8051	+	15.9798i	−1.76912	+	0.692812i
$533$	−8.56636	−	13.3295i	−0.371050	−	0.577365i
$534$	0.0967752	−	3.50907i	0.00418787	−	0.151852i
$535$	35.8407	+	23.0334i	1.54953	+	0.995821i
$536$	20.8098	−	15.2137i	0.898847	−	0.657131i
$537$	−1.79212	+	2.06821i	−0.0773356	+	0.0892500i
$538$	−5.01489	+	15.4863i	−0.216207	+	0.667662i
$539$	−44.9930	+	20.5476i	−1.93799	+	0.885049i
$540$	4.71740	+	3.41316i	0.203004	+	0.146879i
$541$	−6.36432	+	21.6749i	−0.273623	+	0.931876i	0.701954	+	0.712222i	$0.252311\pi$
$541$	−6.36432	+	21.6749i	−0.273623	+	0.931876i	−0.975578	+	0.219654i	$0.929507\pi$
$542$	5.61568	−	1.48204i	0.241214	−	0.0636591i
$543$	1.74549	−	12.1401i	0.0749061	−	0.520983i
$544$	0.193943	+	39.2472i	0.00831525	+	1.68271i
$545$	0.227896	−	0.499023i	0.00976200	−	0.0213758i
$546$	6.77890	−	7.40077i	0.290110	−	0.316724i
$547$	−19.7747	+	2.84318i	−0.845507	+	0.121566i	−0.551435	−	0.834218i	$-0.685920\pi$
$547$	−19.7747	+	2.84318i	−0.845507	+	0.121566i	−0.294072	+	0.955783i	$0.595011\pi$
$548$	−28.9298	+	6.78765i	−1.23582	+	0.289954i
$549$	1.30434	−	1.13022i	0.0556678	−	0.0482364i
$550$	12.4022	−	1.43544i	0.528833	−	0.0612075i
$551$	−12.5267			−0.533657
$552$	−8.23029	−	10.7825i	−0.350304	−	0.458934i
$553$	−13.1502			−0.559205
$554$	−17.2148	+	1.99245i	−0.731387	+	0.0846512i
$555$	−10.5134	+	9.10995i	−0.446271	+	0.386696i
$556$	1.96034	+	8.35522i	0.0831369	+	0.354340i
$557$	−32.4121	+	4.66015i	−1.37334	+	0.197457i	−0.789171	−	0.614173i	$-0.789490\pi$
$557$	−32.4121	+	4.66015i	−1.37334	+	0.197457i	−0.584172	+	0.811630i	$0.698581\pi$
$558$	−3.06681	+	3.34815i	−0.129828	+	0.141738i
$559$	−6.81334	+	14.9191i	−0.288173	+	0.631012i
$560$	−10.4509	−	59.0010i	−0.441632	−	2.49325i
$561$	−2.50783	+	17.4424i	−0.105881	+	0.736417i
$562$	−7.36528	+	1.94378i	−0.310686	+	0.0819933i
$563$	6.30982	−	21.4893i	0.265927	−	0.905665i	−0.712950	−	0.701215i	$-0.752641\pi$
$563$	6.30982	−	21.4893i	0.265927	−	0.905665i	0.978877	−	0.204450i	$-0.0655406\pi$
$564$	3.77261	−	5.21420i	0.158856	−	0.219557i
$565$	27.8971	−	12.7402i	1.17364	−	0.535983i
$566$	−3.23888	+	10.0019i	−0.136140	+	0.420410i
$567$	3.36949	−	3.88860i	0.141505	−	0.163306i
$568$	−6.56835	−	8.98441i	−0.275602	−	0.376978i
$569$	−6.36323	−	4.08940i	−0.266761	−	0.171437i	0.400422	−	0.916331i	$-0.368864\pi$
$569$	−6.36323	−	4.08940i	−0.266761	−	0.171437i	−0.667183	+	0.744894i	$0.732500\pi$
$570$	0.483355	−	17.5264i	0.0202455	−	0.734101i
$571$	−15.7363	−	24.4861i	−0.658543	−	1.02471i	−0.996503	−	0.0835525i	$-0.973373\pi$
$571$	−15.7363	−	24.4861i	−0.658543	−	1.02471i	0.337960	−	0.941160i	$-0.390263\pi$
$572$	2.55477	+	6.52370i	0.106820	+	0.272770i
$573$	−4.65107	−	15.8401i	−0.194301	−	0.661729i
$574$	−14.1734	+	82.3847i	−0.591586	+	3.43867i
$575$	−16.5456	−	2.03071i	−0.689999	−	0.0846866i
$576$	4.17173	+	6.82617i	0.173822	+	0.284424i
$577$	4.96694	−	1.45842i	0.206776	−	0.0607150i	−0.176704	−	0.984264i	$-0.556544\pi$
$577$	4.96694	−	1.45842i	0.206776	−	0.0607150i	0.383480	+	0.923549i	$0.374725\pi$
$578$	−37.6863	+	22.7765i	−1.56754	+	0.947376i
$579$	−6.17875	−	9.61432i	−0.256780	−	0.399557i
$580$	3.36829	−	16.7937i	0.139861	−	0.697319i
$581$	−20.7131	+	32.2302i	−0.859324	+	1.33713i
$582$	−10.7127	+	15.7001i	−0.444055	+	0.650790i
$583$	−5.26026	+	6.07067i	−0.217858	+	0.251421i
$584$	5.16463	+	3.95816i	0.213714	+	0.163790i
$585$	1.66806	+	3.65255i	0.0689659	+	0.151014i
$586$	−24.8766	−	12.2005i	−1.02764	−	0.503998i
$587$	6.32925	−	21.5555i	0.261236	−	0.889689i	−0.719523	−	0.694468i	$-0.755640\pi$
$587$	6.32925	−	21.5555i	0.261236	−	0.889689i	0.980759	−	0.195220i	$-0.0625422\pi$
$588$	−38.7998	+	3.40979i	−1.60008	+	0.140618i
$589$	13.5328	+	1.94573i	0.557611	+	0.0801724i
$590$	7.90664	+	9.64994i	0.325511	+	0.397282i
$591$	9.56420	−	20.9427i	0.393419	−	0.861466i
$592$	−18.1543	+	5.97813i	−0.746136	+	0.245700i
$593$	−0.379025	−	2.63618i	−0.0155647	−	0.108255i	0.980558	−	0.196229i	$-0.0628697\pi$
$593$	−0.379025	−	2.63618i	−0.0155647	−	0.108255i	−0.996123	+	0.0879745i	$0.971961\pi$
$594$	1.40149	+	3.30720i	0.0575037	+	0.135696i
$595$	78.5462	−	68.0607i	3.22008	−	2.79022i
$596$	−1.31936	+	23.9018i	−0.0540431	+	0.979055i
$597$		−	5.22225i		−	0.213733i
$598$	−1.26739	−	9.26816i	−0.0518276	−	0.379003i
$599$	24.7861			1.01273			0.506366	−	0.862318i	$-0.330988\pi$
$599$	24.7861			1.01273			0.506366	+	0.862318i	$0.330988\pi$
$600$	9.58234	+	2.19835i	0.391198	+	0.0897473i
$601$	9.54701	+	11.0178i	0.389431	+	0.449427i	0.916284	−	0.400529i	$-0.131174\pi$
$601$	9.54701	+	11.0178i	0.389431	+	0.449427i	−0.526853	+	0.849956i	$0.676628\pi$
$602$	79.6722	−	33.7626i	3.24720	−	1.37606i
$603$	9.02113	−	1.29704i	0.367369	−	0.0528196i
$604$	−2.97699	−	3.84489i	−0.121132	−	0.156447i
$605$	−12.0472	−	5.50178i	−0.489789	−	0.223679i
$606$	8.71684	+	10.6388i	0.354097	+	0.432171i
$607$	1.04648	−	7.27845i	0.0424754	−	0.295423i	−0.957500	−	0.288433i	$-0.906866\pi$
$607$	1.04648	−	7.27845i	0.0424754	−	0.295423i	0.999976	−	0.00699035i	$-0.00222512\pi$
$608$	9.89870	−	21.9617i	0.401445	−	0.890664i
$609$	−14.5226	−	4.26422i	−0.588485	−	0.172795i
$610$	3.12897	−	6.37993i	0.126688	−	0.258316i
$611$	4.03720	−	1.84373i	0.163328	−	0.0745893i
$612$	−6.45128	+	12.2853i	−0.260778	+	0.496604i
$613$	12.7486	+	11.0467i	0.514911	+	0.446173i	0.873146	−	0.487458i	$-0.162076\pi$
$613$	12.7486	+	11.0467i	0.514911	+	0.446173i	−0.358235	+	0.933631i	$0.616621\pi$
$614$	−11.9867	+	17.5672i	−0.483742	+	0.708953i
$615$	−28.1364	−	18.0822i	−1.13457	−	0.729144i
$616$	13.3083	−	34.4843i	0.536209	−	1.38941i
$617$	−13.0904	+	8.41268i	−0.526999	+	0.338682i	−0.776935	−	0.629581i	$-0.783227\pi$
$617$	−13.0904	+	8.41268i	−0.526999	+	0.338682i	0.249936	+	0.968262i	$0.419590\pi$
$618$	3.14959	+	5.21136i	0.126695	+	0.209631i
$619$	9.16555	+	31.2150i	0.368395	+	1.25464i	0.910213	+	0.414141i	$0.135918\pi$
$619$	9.16555	+	31.2150i	0.368395	+	1.25464i	−0.541818	+	0.840496i	$0.682264\pi$
$620$	−6.24731	+	17.6193i	−0.250898	+	0.707607i
$621$	−0.780515	−	4.73189i	−0.0313210	−	0.189884i
$622$	4.65574	−	27.0621i	0.186678	−	1.08509i
$623$	−12.2546	+	3.59827i	−0.490970	+	0.144162i
$624$	0.179341	+	5.51402i	0.00717940	+	0.220737i
$625$	−25.4880	+	16.3801i	−1.01952	+	0.655206i
$626$	24.0448	+	0.663121i	0.961022	+	0.0265037i
$627$	5.84748	−	9.09886i	0.233526	−	0.363374i
$628$	−7.05691	−	6.83112i	−0.281601	−	0.272591i
$629$	−25.0548	−	21.7101i	−0.999002	−	0.865640i
$630$	6.52653	−	20.1543i	0.260023	−	0.802968i
$631$	3.76163	+	8.23682i	0.149748	+	0.327902i	0.969609	−	0.244660i	$-0.0786765\pi$
$631$	3.76163	+	8.23682i	0.149748	+	0.327902i	−0.819861	+	0.572563i	$0.805949\pi$
$632$	5.16900	−	5.05333i	0.205612	−	0.201011i
$633$	−21.0653	−	6.18532i	−0.837270	−	0.245845i
$634$	−2.55539	−	9.68279i	−0.101488	−	0.384553i
$635$	51.4574	+	7.39845i	2.04202	+	0.293599i
$636$	−5.50155	+	3.12123i	−0.218151	+	0.123765i
$637$	−24.4328	−	11.1581i	−0.968065	−	0.442100i
$638$	7.13678	−	7.79147i	0.282548	−	0.308467i
$639$	−0.559984	−	3.89478i	−0.0221526	−	0.154075i
$640$	26.7807	+	19.1757i	1.05860	+	0.757985i
$641$	21.7830	+	25.1389i	0.860376	+	0.992927i	0.999996	+	0.00272173i	$0.000866354\pi$
$641$	21.7830	+	25.1389i	0.860376	+	0.992927i	−0.139620	+	0.990205i	$0.544588\pi$
$642$	2.37941	+	20.5581i	0.0939077	+	0.811362i
$643$		−	19.8397i		−	0.782401i	−0.920305	−	0.391201i	$-0.872060\pi$
$643$		−	19.8397i		−	0.782401i	0.920305	−	0.391201i	$-0.127940\pi$
$644$	−28.0969	+	40.5739i	−1.10717	+	1.59883i
$645$			34.6204i			1.36318i
$646$	41.5065	−	4.80399i	1.63305	−	0.189010i
$647$	4.14787	+	4.78690i	0.163070	+	0.188193i	0.831404	−	0.555669i	$-0.187538\pi$
$647$	4.14787	+	4.78690i	0.163070	+	0.188193i	−0.668334	+	0.743861i	$0.732992\pi$
$648$	0.169843	+	2.82332i	0.00667207	+	0.110911i
$649$	1.09523	+	7.61752i	0.0429917	+	0.299014i
$650$	4.99950	+	4.57940i	0.196096	+	0.179619i
$651$	15.0267	+	6.86244i	0.588941	+	0.268960i
$652$	0.945110	+	1.66587i	0.0370134	+	0.0652407i
$653$	−25.1800	−	3.62034i	−0.985370	−	0.141675i	−0.369253	−	0.929329i	$-0.620386\pi$
$653$	−25.1800	−	3.62034i	−0.985370	−	0.141675i	−0.616118	+	0.787654i	$0.711295\pi$
$654$	0.257666	−	0.0680008i	0.0100755	−	0.00265904i
$655$	42.0893	+	12.3585i	1.64456	+	0.482888i
$656$	−26.0874	−	37.8297i	−1.01854	−	1.47700i
$657$	0.955686	+	2.09266i	0.0372848	+	0.0816424i
$658$	−22.2768	−	7.21385i	−0.868441	−	0.281225i
$659$	11.0289	+	9.55656i	0.429623	+	0.372271i	0.842662	−	0.538443i	$-0.180987\pi$
$659$	11.0289	+	9.55656i	0.429623	+	0.372271i	−0.413039	+	0.910713i	$0.635533\pi$
$660$	10.6258	+	10.2859i	0.413610	+	0.400376i
$661$	19.3917	−	30.1741i	0.754251	−	1.17364i	−0.225661	−	0.974206i	$-0.572454\pi$
$661$	19.3917	−	30.1741i	0.754251	−	1.17364i	0.979912	−	0.199432i	$-0.0639096\pi$
$662$	0.948633	−	34.3974i	0.0368697	−	1.33689i
$663$	−8.05015	+	5.17352i	−0.312642	+	0.200923i
$664$	−4.24356	−	20.6284i	−0.164682	−	0.800537i
$665$	−61.2070	+	17.9720i	−2.37350	+	0.696924i
$666$	−6.65972	−	1.14573i	−0.258059	−	0.0443962i
$667$	−11.7078	+	7.87084i	−0.453327	+	0.304760i
$668$	9.70662	+	3.44170i	0.375560	+	0.133163i
$669$	6.76639	+	23.0442i	0.261604	+	0.890940i
$670$	32.1146	−	19.4091i	1.24070	−	0.749841i
$671$	3.68764	−	2.36990i	0.142360	−	0.0914890i
$672$	18.9518	−	22.0912i	0.731081	−	0.852185i
$673$	−0.204334	−	0.131317i	−0.00787648	−	0.00506191i	0.536697	−	0.843775i	$-0.319672\pi$
$673$	−0.204334	−	0.131317i	−0.00787648	−	0.00506191i	−0.544573	+	0.838713i	$0.683308\pi$
$674$	−28.5397	−	19.4736i	−1.09931	−	0.750093i
$675$	2.62690	+	2.27622i	0.101109	+	0.0876117i
$676$	10.3191	−	19.6508i	0.396887	−	0.755800i
$677$	−29.3762	+	13.4157i	−1.12902	+	0.515606i	−0.890251	−	0.455471i	$-0.849471\pi$
$677$	−29.3762	+	13.4157i	−1.12902	+	0.515606i	−0.238768	+	0.971077i	$0.576744\pi$
$678$	13.3755	+	6.55991i	0.513685	+	0.251932i
$679$	66.3513	+	19.4825i	2.54633	+	0.747669i
$680$	−4.72025	+	56.9363i	−0.181013	+	2.18341i
$681$	2.92850	−	20.3682i	0.112220	−	0.780510i
$682$	−8.92019	+	7.30873i	−0.341572	+	0.279866i
$683$	−27.3749	−	12.5017i	−1.04747	−	0.478364i	−0.184087	−	0.982910i	$-0.558933\pi$
$683$	−27.3749	−	12.5017i	−1.04747	−	0.478364i	−0.863385	+	0.504546i	$0.831660\pi$
$684$	6.73425	−	5.21414i	0.257491	−	0.199368i
$685$	−42.8156	+	6.15595i	−1.63590	+	0.235207i
$686$	35.4181	+	83.5789i	1.35227	+	3.19106i
$687$	14.7779	+	17.0546i	0.563811	+	0.650673i
$688$	−18.3428	+	43.8874i	−0.699313	+	1.67319i
$689$	−4.36202			−0.166180
$690$	−10.5605	−	16.6843i	−0.402032	−	0.635161i
$691$		−	25.5785i		−	0.973053i	−0.873666	−	0.486527i	$-0.838264\pi$
$691$		−	25.5785i		−	0.973053i	0.873666	−	0.486527i	$-0.161736\pi$
$692$	0.556273	−	10.0775i	0.0211463	−	0.383091i
$693$	9.87649	−	8.55802i	0.375177	−	0.325092i
$694$	−10.4820	+	4.44196i	−0.397892	+	0.168614i
$695$	1.77790	+	12.3656i	0.0674395	+	0.469052i
$696$	7.34709	−	3.90455i	0.278491	−	0.148002i
$697$	33.1109	−	72.5028i	1.25417	−	2.74624i
$698$	4.86418	−	3.98545i	0.184112	−	0.150851i
$699$	17.4433	+	2.50796i	0.659765	+	0.0948598i
$700$	−3.13140	−	35.6320i	−0.118356	−	1.34676i
$701$	−8.35296	+	28.4476i	−0.315487	+	1.07445i	0.637251	+	0.770656i	$0.280071\pi$
$701$	−8.35296	+	28.4476i	−0.315487	+	1.07445i	−0.952738	+	0.303794i	$0.901747\pi$
$702$	−0.858885	+	1.75125i	−0.0324165	+	0.0660968i
$703$	8.45294	+	18.5094i	0.318809	+	0.698093i
$704$	8.02036	+	18.6689i	0.302279	+	0.703612i
$705$	6.13506	−	7.08023i	0.231060	−	0.266657i
$706$	3.33512	+	2.27566i	0.125519	+	0.0856456i
$707$	27.0540	−	42.0969i	1.01747	−	1.58322i
$708$	−1.19173	+	5.94174i	−0.0447880	+	0.223304i
$709$	26.0403	+	40.5195i	0.977964	+	1.52174i	0.847846	+	0.530243i	$0.177899\pi$
$709$	26.0403	+	40.5195i	0.977964	+	1.52174i	0.130118	+	0.991499i	$0.458464\pi$
$710$	−8.37969	−	13.8652i	−0.314484	−	0.520350i
$711$	2.45222	−	0.720037i	0.0919655	−	0.0270035i
$712$	3.43422	−	6.12354i	0.128703	−	0.229489i
$713$	13.8707	−	6.68447i	0.519460	−	0.250336i
$714$	49.7549	+	8.55979i	1.86203	+	0.320342i
$715$	2.87327	+	9.78545i	0.107454	+	0.365955i
$716$	−5.09642	+	1.99582i	−0.190462	+	0.0745875i
$717$	8.14812	+	12.6787i	0.304297	+	0.473495i
$718$	−40.8580	−	1.12681i	−1.52481	−	0.0420521i
$719$	−3.32775	−	2.13861i	−0.124104	−	0.0797568i	0.477116	−	0.878840i	$-0.341682\pi$
$719$	−3.32775	−	2.13861i	−0.124104	−	0.0797568i	−0.601220	+	0.799083i	$0.705318\pi$
$720$	5.17945	+	10.4301i	0.193027	+	0.388708i
$721$	14.5080	−	16.7432i	0.540307	−	0.623548i
$722$	1.16466	+	0.377149i	0.0433441	+	0.0140360i
$723$	−14.9007	+	6.80491i	−0.554162	+	0.253077i
$724$	14.3791	−	19.8736i	0.534395	−	0.738597i
$725$	2.88064	−	9.81056i	0.106984	−	0.364355i
$726$	−1.64165	−	6.22047i	−0.0609273	−	0.230863i
$727$	4.78992	−	33.3147i	0.177648	−	1.23557i	−0.684536	−	0.728979i	$-0.739995\pi$
$727$	4.78992	−	33.3147i	0.177648	−	1.23557i	0.862185	−	0.506594i	$-0.169096\pi$
$728$	18.8849	−	6.80132i	0.699923	−	0.252074i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	6.98472	+	6.39781i	0.258516	+	0.236794i
$731$	−81.6651	+	11.7417i	−3.02049	+	0.434281i
$732$	3.36052	−	0.788460i	0.124208	−	0.0291423i
$733$	−15.9163	+	13.7916i	−0.587883	+	0.509403i	−0.897240	−	0.441542i	$-0.854431\pi$
$733$	−15.9163	+	13.7916i	−0.587883	+	0.509403i	0.309358	+	0.950946i	$0.399886\pi$
$734$	−5.70052	−	49.2524i	−0.210410	−	1.81794i
$735$	−56.6974			−2.09131
$736$	−4.54748	−	26.7455i	−0.167622	−	0.985851i
$737$	23.1480			0.852666
$738$	−1.86793	−	16.1389i	−0.0687596	−	0.594083i
$739$	33.6546	−	29.1619i	1.23800	−	1.07274i	0.243301	−	0.969951i	$-0.421770\pi$
$739$	33.6546	−	29.1619i	1.23800	−	1.07274i	0.994703	−	0.102786i	$-0.0327758\pi$
$740$	−27.0870	+	6.35527i	−0.995737	+	0.233624i
$741$	5.81361	−	0.835870i	0.213568	−	0.0307065i
$742$	16.9703	+	15.5443i	0.622998	+	0.570649i
$743$	16.7505	−	36.6786i	0.614518	−	1.34561i	−0.304923	−	0.952377i	$-0.598631\pi$
$743$	16.7505	−	36.6786i	0.614518	−	1.34561i	0.919441	−	0.393229i	$-0.128642\pi$
$744$	−8.54365	+	3.07696i	−0.313226	+	0.112807i
$745$	−4.95911	+	34.4913i	−0.181688	+	1.26367i
$746$	13.0696	+	49.5229i	0.478513	+	1.81316i
$747$	2.09777	−	7.14434i	0.0767533	−	0.261398i
$748$	−20.6592	+	28.5534i	−0.755374	+	1.04402i
$749$	68.4917	−	31.2791i	2.50263	−	1.14291i
$750$	−5.96996	−	1.93324i	−0.217992	−	0.0705918i
$751$	6.56295	−	7.57405i	0.239485	−	0.276381i	−0.623265	−	0.782010i	$-0.714194\pi$
$751$	6.56295	−	7.57405i	0.239485	−	0.276381i	0.862751	+	0.505630i	$0.168740\pi$
$752$	11.5285	−	5.72490i	0.420403	−	0.208766i
$753$	−4.85809	−	3.12210i	−0.177039	−	0.113776i
$754$	5.73554	+	0.158178i	0.208876	+	0.00576052i
$755$	−3.82690	−	5.95478i	−0.139275	−	0.216717i
$756$	9.58215	−	3.75250i	0.348499	−	0.136477i
$757$	−10.7893	−	36.7449i	−0.392143	−	1.33552i	−0.885075	−	0.465449i	$-0.845893\pi$
$757$	−10.7893	−	36.7449i	−0.392143	−	1.33552i	0.492932	−	0.870068i	$-0.335925\pi$
$758$	−51.6289	−	8.88218i	−1.87524	−	0.322615i
$759$	−0.251831	−	12.1781i	−0.00914088	−	0.442038i
$760$	17.1526	−	30.5847i	0.622190	−	1.10942i
$761$	−24.4923	+	7.19158i	−0.887844	+	0.260694i	−0.693687	−	0.720276i	$-0.744015\pi$
$761$	−24.4923	+	7.19158i	−0.887844	+	0.260694i	−0.194156	+	0.980971i	$0.562197\pi$
$762$	13.0620	+	21.6125i	0.473185	+	0.782938i
$763$	−0.524187	−	0.815651i	−0.0189769	−	0.0295286i
$764$	6.49301	−	32.3729i	0.234909	−	1.17121i
$765$	−10.9205	+	16.9926i	−0.394830	+	0.614367i
$766$	27.0753	+	18.4744i	0.978271	+	0.667507i
$767$	−2.73675	+	3.15837i	−0.0988182	+	0.114042i
$768$	1.03969	+	15.9662i	0.0375165	+	0.576130i
$769$	7.22408	+	15.8185i	0.260507	+	0.570430i	0.994014	−	0.109251i	$-0.0348453\pi$
$769$	7.22408	+	15.8185i	0.260507	+	0.570430i	−0.733507	+	0.679682i	$0.762118\pi$
$770$	23.6927	−	48.3090i	0.853825	−	1.74094i
$771$	−2.41464	+	8.22350i	−0.0869611	+	0.296162i
$772$	−2.00101	−	22.7694i	−0.0720179	−	0.819487i
$773$	43.8931	+	6.31088i	1.57873	+	0.226987i	0.875228	−	0.483711i	$-0.160711\pi$
$773$	43.8931	+	6.31088i	1.57873	+	0.226987i	0.703498	+	0.710697i	$0.251620\pi$
$774$	−13.0084	+	10.6584i	−0.467578	+	0.383108i
$775$	−4.63584	+	10.1511i	−0.166524	+	0.364637i
$776$	−33.5676	+	17.8392i	−1.20501	+	0.640391i
$777$	3.49897	+	24.3359i	0.125525	+	0.873044i
$778$	−2.25919	+	0.957374i	−0.0809958	+	0.0343235i
$779$	−36.9725	+	32.0368i	−1.32468	+	1.14784i
$780$	−0.442621	+	8.01862i	−0.0158484	+	0.287113i
$781$		−	9.99389i		−	0.357610i
$782$	35.7745	−	30.5694i	1.27929	−	1.09316i
$783$	2.94162			0.105125
$784$	−71.8737	−	30.0398i	−2.56692	−	1.07285i
$785$	−9.36256	−	10.8050i	−0.334164	−	0.385646i
$786$	8.31415	+	19.6195i	0.296556	+	0.699805i
$787$	−39.4912	+	5.67798i	−1.40771	+	0.202398i	−0.803916	−	0.594742i	$-0.797254\pi$
$787$	−39.4912	+	5.67798i	−1.40771	+	0.202398i	−0.603794	+	0.797141i	$0.706345\pi$
$788$	36.4087	−	28.1902i	1.29700	−	1.00423i
$789$	−9.90909	−	4.52533i	−0.352773	−	0.161106i
$790$	8.13944	−	6.66902i	0.289588	−	0.237273i
$791$	7.71376	−	53.6504i	0.274270	−	1.90759i
$792$	−0.593530	+	7.15924i	−0.0210902	+	0.254392i
$793$	2.28398	+	0.670636i	0.0811064	+	0.0238150i
$794$	−3.67499	−	1.80236i	−0.130421	−	0.0639635i
$795$	−8.37544	+	3.82494i	−0.297046	+	0.135657i
$796$	4.85584	−	9.24708i	0.172111	−	0.327754i
$797$	−4.90169	−	4.24734i	−0.173627	−	0.150449i	0.563712	−	0.825971i	$-0.309373\pi$
$797$	−4.90169	−	4.24734i	−0.173627	−	0.150449i	−0.737339	+	0.675523i	$0.763918\pi$
$798$	−25.5963	−	17.4652i	−0.906099	−	0.618261i
$799$	18.7821	+	12.0705i	0.664462	+	0.427024i
$800$	14.9234	+	12.8027i	0.527623	+	0.452642i
$801$	2.08818	−	1.34199i	0.0737823	−	0.0474170i
$802$	4.45715	−	2.69377i	0.157388	−	0.0951204i
$803$	1.64619	+	5.60639i	0.0580926	+	0.197845i
$804$	17.1798	+	6.09149i	0.605885	+	0.214830i
$805$	−45.9132	+	55.2548i	−1.61823	+	1.94748i
$806$	−6.17163	−	1.06176i	−0.217387	−	0.0373990i
$807$	−11.0441	+	3.24283i	−0.388770	+	0.114153i
$808$	5.54265	+	26.9434i	0.194990	+	0.947865i
$809$	−18.7058	+	12.0215i	−0.657659	+	0.422652i	−0.826458	−	0.562999i	$-0.809648\pi$
$809$	−18.7058	+	12.0215i	−0.657659	+	0.422652i	0.168799	+	0.985651i	$0.446011\pi$
$810$	−0.113505	+	4.11569i	−0.00398816	+	0.144611i
$811$	7.37302	−	11.4726i	0.258902	−	0.402859i	−0.687332	−	0.726344i	$-0.741218\pi$
$811$	7.37302	−	11.4726i	0.258902	−	0.402859i	0.946233	+	0.323485i	$0.104854\pi$
$812$	−21.7502	−	21.0543i	−0.763284	−	0.738862i
$813$	3.10375	+	2.68941i	0.108853	+	0.0943218i
$814$	−16.3284	−	5.28759i	−0.572311	−	0.185330i
$815$	1.15819	+	2.53609i	0.0405698	+	0.0888354i
$816$	−22.8467	+	15.7551i	−0.799793	+	0.551537i
$817$	48.5884	+	14.2669i	1.69989	+	0.499134i
$818$	−12.5219	+	3.30466i	−0.437817	+	0.115545i
$819$	7.02441	+	1.00996i	0.245453	+	0.0352908i
$820$	−33.0079	−	58.1805i	−1.15269	−	2.03175i
$821$	−10.5327	−	4.81012i	−0.367594	−	0.167874i	0.223050	−	0.974807i	$-0.428399\pi$
$821$	−10.5327	−	4.81012i	−0.367594	−	0.167874i	−0.590644	+	0.806933i	$0.701126\pi$
$822$	−15.4944	−	14.1925i	−0.540431	−	0.495020i
$823$	−1.86760	−	12.9894i	−0.0651004	−	0.452783i	−0.996134	−	0.0878492i	$-0.972001\pi$
$823$	−1.86760	−	12.9894i	−0.0651004	−	0.452783i	0.931033	−	0.364934i	$-0.118908\pi$
$824$	0.731294	+	12.1564i	0.0254758	+	0.423488i
$825$	5.78127	+	6.67194i	0.201278	+	0.232287i
$826$	21.9023	−	2.53498i	0.762077	−	0.0882034i
$827$		−	6.26926i		−	0.218004i	−0.994042	−	0.109002i	$-0.965235\pi$
$827$		−	6.26926i		−	0.218004i	0.994042	−	0.109002i	$-0.0347654\pi$
$828$	3.01782	−	9.10455i	0.104877	−	0.316405i
$829$		−	23.2097i		−	0.806108i	−0.915176	−	0.403054i	$-0.867949\pi$
$829$		−	23.2097i		−	0.806108i	0.915176	−	0.403054i	$-0.132051\pi$
$830$	−3.52472	−	30.4536i	−0.122345	−	1.05706i
$831$	−8.02464	−	9.26093i	−0.278372	−	0.321258i
$832$	−4.80957	+	9.93047i	−0.166742	+	0.344277i
$833$	−19.2292	−	133.742i	−0.666251	−	4.63388i
$834$	−4.09893	+	4.47494i	−0.141934	+	0.154955i
$835$	13.6368	+	6.22771i	0.471920	+	0.215519i
$836$	18.8146	−	10.6742i	0.650718	−	0.369175i
$837$	−3.17788	−	0.456911i	−0.109844	−	0.0157931i
$838$	−5.71262	−	21.6460i	−0.197339	−	0.747750i
$839$	−31.5297	−	9.25795i	−1.08853	−	0.319620i	−0.312241	−	0.950003i	$-0.601080\pi$
$839$	−31.5297	−	9.25795i	−1.08853	−	0.319620i	−0.776285	+	0.630383i	$0.782898\pi$
$840$	30.2968	−	29.6188i	1.04534	−	1.02195i
$841$	8.45239	+	18.5081i	0.291462	+	0.638212i
$842$	−2.30820	+	7.12787i	−0.0795459	+	0.245643i
$843$	−4.07073	−	3.52731i	−0.140204	−	0.121487i
$844$	−31.5491	−	30.5397i	−1.08597	−	1.05122i
$845$	17.4677	−	27.1802i	0.600906	−	0.935028i
$846$	4.54912	+	0.125458i	0.156402	+	0.00431335i
$847$	−19.6911	+	12.6547i	−0.676596	+	0.434822i
$848$	−12.6439	+	0.411237i	−0.434192	+	0.0141219i
$849$	−7.13283	+	2.09439i	−0.244798	+	0.0718792i
$850$	−5.78246	+	33.6113i	−0.198337	+	1.15286i
$851$	19.5302	+	11.9881i	0.669485	+	0.410947i
$852$	2.62994	−	7.41720i	0.0901001	−	0.254109i
$853$	−5.22145	−	17.7826i	−0.178779	−	0.608865i	−0.999306	−	0.0372570i	$-0.988138\pi$
$853$	−5.22145	−	17.7826i	−0.178779	−	0.608865i	0.820527	−	0.571608i	$-0.193680\pi$
$854$	−6.49588	−	10.7482i	−0.222284	−	0.367795i
$855$	10.4297	−	6.70274i	0.356687	−	0.229229i
$856$	−14.9024	+	38.6148i	−0.509354	+	1.31983i
$857$	17.0166	+	10.9359i	0.581275	+	0.373563i	0.797989	−	0.602672i	$-0.205897\pi$
$857$	17.0166	+	10.9359i	0.581275	+	0.373563i	−0.216713	+	0.976235i	$0.569534\pi$
$858$	−2.79225	+	4.09220i	−0.0953257	+	0.139706i
$859$	6.39720	+	5.54321i	0.218270	+	0.189132i	0.757132	−	0.653262i	$-0.226600\pi$
$859$	6.39720	+	5.54321i	0.218270	+	0.189132i	−0.538862	+	0.842394i	$0.681146\pi$
$860$	−32.1913	+	61.3026i	−1.09772	+	2.09040i
$861$	−53.7689	+	24.5554i	−1.83244	+	0.836847i
$862$	9.07788	−	18.5097i	0.309194	−	0.630442i
$863$	−17.7093	−	5.19991i	−0.602830	−	0.177007i	−0.0339448	−	0.999424i	$-0.510807\pi$
$863$	−17.7093	−	5.19991i	−0.602830	−	0.177007i	−0.568885	+	0.822417i	$0.692625\pi$
$864$	−2.32449	+	5.15721i	−0.0790806	+	0.175452i
$865$	2.09088	−	14.5424i	0.0710919	−	0.494455i
$866$	−22.4858	−	27.4435i	−0.764098	−	0.932570i
$867$	−28.3232	−	12.9348i	−0.961906	−	0.439288i
$868$	20.2269	+	26.1237i	0.686544	+	0.886697i
$869$	6.42516	−	0.923798i	0.217959	−	0.0313377i
$870$	11.1514	−	4.72563i	0.378069	−	0.160214i
$871$	8.23172	+	9.49991i	0.278921	+	0.321892i
$872$	0.519480	+	0.119178i	0.0175918	+	0.00403586i
$873$	−13.4398			−0.454867
$874$	−27.7677	+	7.94577i	−0.939257	+	0.268770i
$875$			22.8311i			0.771831i
$876$	−0.253592	+	4.59412i	−0.00856807	+	0.155221i
$877$	5.01047	−	4.34160i	0.169192	−	0.146605i	−0.566149	−	0.824303i	$-0.691567\pi$
$877$	5.01047	−	4.34160i	0.169192	−	0.146605i	0.735341	+	0.677697i	$0.237022\pi$
$878$	3.70139	+	8.73447i	0.124916	+	0.294774i
$879$	−2.78824	−	19.3926i	−0.0940450	−	0.654097i
$880$	9.25108	+	28.0935i	0.311854	+	0.947033i
$881$	−22.8995	+	50.1429i	−0.771504	+	1.68936i	−0.0481902	+	0.998838i	$0.515345\pi$
$881$	−22.8995	+	50.1429i	−0.771504	+	1.68936i	−0.723314	+	0.690520i	$0.757382\pi$
$882$	−17.4551	−	21.3037i	−0.587744	−	0.717332i
$883$	6.19835	+	0.891188i	0.208591	+	0.0299909i	0.245818	−	0.969316i	$-0.420943\pi$
$883$	6.19835	+	0.891188i	0.208591	+	0.0299909i	−0.0372270	+	0.999307i	$0.511852\pi$
$884$	−19.0650	+	1.67546i	−0.641225	+	0.0563519i
$885$	−2.48529	+	8.46413i	−0.0835422	+	0.284519i
$886$	14.2835	+	7.00522i	0.479865	+	0.235345i
$887$	−2.62118	−	5.73958i	−0.0880105	−	0.192716i	0.860509	−	0.509436i	$-0.170146\pi$
$887$	−2.62118	−	5.73958i	−0.0880105	−	0.192716i	−0.948519	+	0.316720i	$0.897419\pi$
$888$	−10.7271	−	8.22120i	−0.359977	−	0.275885i
$889$	60.1676	−	69.4371i	2.01796	−	2.32885i
$890$	5.76024	−	8.44198i	0.193084	−	0.282976i
$891$	−1.37315	+	2.13666i	−0.0460022	+	0.0715809i
$892$	−9.44604	+	47.0962i	−0.316277	+	1.57690i
$893$	−7.40862	−	11.5280i	−0.247920	−	0.385771i
$894$	−14.4866	+	8.75530i	−0.484506	+	0.292821i
$895$	−7.64455	+	2.24464i	−0.255529	+	0.0750301i
$896$	54.0993	−	21.4949i	1.80733	−	0.718095i
$897$	4.90834	−	4.43405i	0.163885	−	0.148049i
$898$	2.50667	−	14.5704i	0.0836488	−	0.486220i
$899$	2.66076	+	9.06171i	0.0887412	+	0.302225i
$900$	2.53495	+	6.47310i	0.0844985	+	0.215770i
$901$	−11.8631	−	18.4593i	−0.395217	−	0.614969i
$902$	1.13758	−	41.2485i	0.0378772	−	1.37343i
$903$	51.4733	+	33.0799i	1.71293	+	1.10083i
$904$	17.5845	+	24.0527i	0.584853	+	0.799982i
$905$	23.3834	−	26.9859i	0.777292	−	0.897042i
$906$	1.05930	−	3.27120i	0.0351930	−	0.108678i
$907$	8.64528	−	3.94817i	0.287062	−	0.131097i	−0.266680	−	0.963785i	$-0.585927\pi$
$907$	8.64528	−	3.94817i	0.287062	−	0.131097i	0.553742	+	0.832688i	$0.313199\pi$
$908$	24.1246	−	33.3430i	0.800602	−	1.10653i
$909$	−2.73996	+	9.33145i	−0.0908788	+	0.309505i
$910$	28.2514	−	7.45585i	0.936525	−	0.247159i
$911$	1.51017	−	10.5035i	0.0500341	−	0.347995i	−0.949391	−	0.314096i	$-0.898299\pi$
$911$	1.51017	−	10.5035i	0.0500341	−	0.347995i	0.999425	−	0.0338988i	$-0.0107924\pi$
$912$	16.7727	−	2.97097i	0.555399	−	0.0983786i
$913$	7.85619	−	17.2026i	0.260002	−	0.569325i
$914$	11.6846	−	12.7565i	0.386492	−	0.421947i
$915$	4.97349	−	0.715081i	0.164419	−	0.0236398i
$916$	10.3093	+	43.9397i	0.340630	+	1.45181i
$917$	58.5910	−	50.7694i	1.93484	−	1.67655i
$918$	−9.74686	+	1.12811i	−0.321694	+	0.0372331i
$919$	−59.5481			−1.96431			−0.982156	−	0.188070i	$-0.939777\pi$
$919$	−59.5481			−1.96431			−0.982156	+	0.188070i	$0.939777\pi$
$920$	−3.18588	−	39.3626i	−0.105035	−	1.29775i
$921$	−15.0380			−0.495520
$922$	11.6353	−	1.34667i	0.383187	−	0.0443504i
$923$	4.10149	−	3.55396i	0.135002	−	0.116980i
$924$	25.4459	−	5.97024i	0.837110	−	0.196406i
$925$	−16.4398	+	2.36369i	−0.540537	+	0.0777175i
$926$	7.37452	−	8.05103i	0.242342	−	0.264573i
$927$	−1.78865	+	3.91660i	−0.0587471	+	0.128638i
$928$	16.6401	−	0.0822286i	0.546239	−	0.00269928i
$929$	3.38480	−	23.5418i	0.111052	−	0.772382i	−0.855848	−	0.517227i	$-0.826964\pi$
$929$	3.38480	−	23.5418i	0.111052	−	0.772382i	0.966900	−	0.255155i	$-0.0821265\pi$
$930$	−12.7811	+	3.37307i	−0.419109	+	0.110607i
$931$	−23.3646	+	79.5726i	−0.765745	+	2.60789i
$932$	28.5549	+	20.6602i	0.935347	+	0.676749i
$933$	17.6623	−	8.06608i	0.578236	−	0.264072i
$934$	−13.8481	+	42.7640i	−0.453125	+	1.39928i
$935$	−33.5962	+	38.7721i	−1.09871	+	1.26798i
$936$	−3.14921	+	2.30233i	−0.102935	+	0.0752541i
$937$	−33.8599	−	21.7604i	−1.10615	−	0.710882i	−0.145702	−	0.989329i	$-0.546544\pi$
$937$	−33.8599	−	21.7604i	−1.10615	−	0.710882i	−0.960452	+	0.278447i	$0.910180\pi$
$938$	1.82828	−	66.2932i	0.0596953	−	2.16455i
$939$	9.19559	+	14.3086i	0.300087	+	0.466944i
$940$	17.4469	−	6.83242i	0.569054	−	0.222849i
$941$	−13.8499	−	47.1685i	−0.451495	−	1.53765i	−0.799799	−	0.600268i	$-0.795061\pi$
$941$	−13.8499	−	47.1685i	−0.451495	−	1.53765i	0.348304	−	0.937382i	$-0.386758\pi$
$942$	1.17750	−	6.84438i	0.0383651	−	0.223002i
$943$	−14.4259	+	53.1731i	−0.469771	+	1.73155i
$944$	−7.63505	+	9.41297i	−0.248500	+	0.306366i
$945$	14.3731	−	4.22032i	0.467556	−	0.137287i
$946$	−36.5558	+	22.0932i	−1.18853	+	0.718313i
$947$	24.6425	+	38.3445i	0.800774	+	1.24603i	0.965684	+	0.259720i	$0.0836303\pi$
$947$	24.6425	+	38.3445i	0.800774	+	1.24603i	−0.164910	+	0.986309i	$0.552733\pi$
$948$	5.01168	+	1.00519i	0.162772	+	0.0326471i
$949$	−1.71546	+	2.66930i	−0.0556860	+	0.0866492i
$950$	11.7984	−	17.2913i	0.382791	−	0.561003i
$951$	4.63719	−	5.35160i	0.150371	−	0.173538i
$952$	80.1422	+	61.4208i	2.59742	+	1.99066i
$953$	7.78552	+	17.0479i	0.252198	+	0.552236i	0.992811	−	0.119696i	$-0.0381920\pi$
$953$	7.78552	+	17.0479i	0.252198	+	0.552236i	−0.740613	+	0.671932i	$0.765465\pi$
$954$	−4.01569	−	1.96946i	−0.130013	−	0.0637636i
$955$	13.5408	−	46.1159i	0.438171	−	1.49227i
$956$	2.63880	+	30.0267i	0.0853448	+	0.971133i
$957$	7.39525	+	1.06328i	0.239055	+	0.0343709i
$958$	−0.182240	−	0.222422i	−0.00588792	−	0.00718612i
$959$	−31.7578	+	69.5398i	−1.02551	+	2.24556i
$960$	−0.527025	+	23.2847i	−0.0170097	+	0.751511i
$961$	2.94482	+	20.4817i	0.0949942	+	0.660699i
$962$	−3.63657	−	8.58150i	−0.117248	−	0.276679i
$963$	−11.0595	+	9.58309i	−0.356387	+	0.308811i
$964$	−32.7122	−	1.80569i	−1.05359	−	0.0581572i
$965$		−	33.2724i		−	1.07108i
$966$	−34.8967	−	0.240638i	−1.12278	−	0.00774239i
$967$	7.14131			0.229649			0.114825	−	0.993386i	$-0.463369\pi$
$967$	7.14131			0.229649			0.114825	+	0.993386i	$0.463369\pi$
$968$	2.87714	−	12.5411i	0.0924747	−	0.403086i
$969$	19.3481	+	22.3290i	0.621552	+	0.717309i
$970$	−50.9490	+	21.5906i	−1.63587	+	0.693232i
$971$	33.5001	−	4.81658i	1.07507	−	0.154572i	0.418034	−	0.908432i	$-0.362719\pi$
$971$	33.5001	−	4.81658i	1.07507	−	0.154572i	0.657035	+	0.753860i	$0.271810\pi$
$972$	−1.58139	+	1.22442i	−0.0507230	+	0.0392734i
$973$	20.0838	+	9.17195i	0.643856	+	0.294039i
$974$	−0.312035	−	0.380834i	−0.00999825	−	0.0122027i
$975$	−0.682265	+	4.74526i	−0.0218500	+	0.151970i
$976$	6.68363	+	1.72860i	0.213938	+	0.0553311i
$977$	−0.0613739	−	0.0180210i	−0.00196352	−	0.000576543i	0.280751	−	0.959781i	$-0.409417\pi$
$977$	−0.0613739	−	0.0180210i	−0.00196352	−	0.000576543i	−0.282714	+	0.959204i	$0.591235\pi$
$978$	−0.596353	+	1.21596i	−0.0190693	+	0.0388820i
$979$	5.73477	−	2.61898i	0.183284	−	0.0837031i
$980$	−100.394	−	52.7193i	−3.20698	−	1.68406i
$981$	0.142410	+	0.123399i	0.00454680	+	0.00393982i
$982$	30.0281	−	44.0080i	0.958235	−	1.40435i
$983$	27.1875	+	17.4723i	0.867146	+	0.557281i	0.896879	−	0.442277i	$-0.145829\pi$
$983$	27.1875	+	17.4723i	0.867146	+	0.557281i	−0.0297323	+	0.999558i	$0.509465\pi$
$984$	11.6990	−	30.3142i	0.372951	−	0.966382i
$985$	56.3879	−	36.2383i	1.79667	−	1.15465i
$986$	14.9292	+	24.7021i	0.475443	+	0.786674i
$987$	−4.66477	−	15.8867i	−0.148481	−	0.505680i
$988$	11.0714	+	3.92562i	0.352229	+	0.124891i
$989$	54.3761	−	17.1951i	1.72906	−	0.546773i
$990$	−1.77300	+	10.3058i	−0.0563498	+	0.327541i
$991$	14.5937	−	4.28509i	0.463584	−	0.136120i	−0.0415962	−	0.999135i	$-0.513244\pi$
$991$	14.5937	−	4.28509i	0.463584	−	0.136120i	0.505180	+	0.863014i	$0.331426\pi$
$992$	−17.9894	−	2.49581i	−0.571163	−	0.0792421i
$993$	20.4693	−	13.1548i	0.649573	−	0.417455i
$994$	−28.6214	−	0.789339i	−0.907816	−	0.0250363i
$995$	8.21976	−	12.7902i	0.260584	−	0.405477i
$996$	10.3576	−	10.7000i	0.328193	−	0.339041i
$997$	25.2909	+	21.9147i	0.800971	+	0.694045i	0.955839	−	0.293890i	$-0.0949499\pi$
$997$	25.2909	+	21.9147i	0.800971	+	0.694045i	−0.154868	+	0.987935i	$0.549495\pi$
$998$	−8.98256	+	27.7387i	−0.284338	+	0.878054i
$999$	−1.98498	−	4.34650i	−0.0628020	−	0.137517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.24	yes	480
8.5	even	2	inner	552.2.bb.a.469.16	yes	480
23.18	even	11	inner	552.2.bb.a.133.16	✓	480
184.133	even	22	inner	552.2.bb.a.133.24	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.16	✓	480	23.18	even	11	inner
552.2.bb.a.133.24	yes	480	184.133	even	22	inner
552.2.bb.a.469.16	yes	480	8.5	even	2	inner
552.2.bb.a.469.24	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.162597 + 1.40484i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.94712 + 0.456843i) q^{4} +(-2.88170 + 0.414326i) q^{5} +(-1.04285 - 0.955226i) q^{6} +(-2.13746 + 4.68038i) q^{7} +(-0.958385 - 2.66111i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.162597 + 1.40484i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.94712 + 0.456843i) q^{4} +(-2.88170 + 0.414326i) q^{5} +(-1.04285 - 0.955226i) q^{6} +(-2.13746 + 4.68038i) q^{7} +(-0.958385 - 2.66111i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-1.05062 - 3.98095i) q^{10} +(0.715560 - 2.43697i) q^{11} +(1.17237 - 1.62035i) q^{12} +(1.25459 - 0.572954i) q^{13} +(-6.92271 - 2.24176i) q^{14} +(1.90652 - 2.20024i) q^{15} +(3.58259 - 1.77906i) q^{16} +(5.83669 + 3.75101i) q^{17} +(1.41368 + 0.0389872i) q^{18} +(-2.30229 - 3.58243i) q^{19} +(5.42175 - 2.12323i) q^{20} +(-1.44961 - 4.93693i) q^{21} +(3.53989 + 0.609000i) q^{22} +(-4.40270 - 1.90164i) q^{23} +(2.46695 + 1.38352i) q^{24} +(3.33508 - 0.979269i) q^{25} +(1.00890 + 1.66934i) q^{26} +(0.540641 + 0.841254i) q^{27} +(2.02370 - 10.0898i) q^{28} +(1.59036 - 2.47465i) q^{29} +(3.40097 + 2.32059i) q^{30} +(-2.10247 + 2.42638i) q^{31} +(3.08180 + 4.74368i) q^{32} +(1.05509 + 2.31033i) q^{33} +(-4.32053 + 8.80948i) q^{34} +(4.22032 - 14.3731i) q^{35} +(0.175088 + 1.99232i) q^{36} +(-4.72967 - 0.680024i) q^{37} +(4.65838 - 3.81683i) q^{38} +(-0.572954 + 1.25459i) q^{39} +(3.86435 + 7.27144i) q^{40} +(-1.63493 - 11.3712i) q^{41} +(6.69988 - 2.83920i) q^{42} +(-8.98707 + 7.78734i) q^{43} +(-0.279970 + 5.07199i) q^{44} +2.91134i q^{45} +(1.95563 - 6.49427i) q^{46} +3.21794 q^{47} +(-1.54250 + 3.69062i) q^{48} +(-12.7532 - 14.7180i) q^{49} +(1.91799 + 4.52602i) q^{50} +(-6.86746 + 0.987392i) q^{51} +(-2.18110 + 1.68877i) q^{52} +(-2.87684 - 1.31381i) q^{53} +(-1.09392 + 0.896296i) q^{54} +(-1.05233 + 7.31911i) q^{55} +(14.5035 + 1.20240i) q^{56} +(4.08595 + 1.19974i) q^{57} +(3.73506 + 1.83183i) q^{58} +(-2.75622 + 1.25872i) q^{59} +(-2.70707 + 5.15513i) q^{60} +(1.30434 + 1.13022i) q^{61} +(-3.75052 - 2.55910i) q^{62} +(4.32855 + 2.78179i) q^{63} +(-6.16299 + 5.10073i) q^{64} +(-3.37798 + 2.17090i) q^{65} +(-3.07408 + 1.85789i) q^{66} +(2.56768 + 8.74472i) q^{67} +(-13.0784 - 4.63723i) q^{68} +(4.57265 - 1.44599i) q^{69} +(20.8780 + 3.59183i) q^{70} +(3.77544 - 1.10857i) q^{71} +(-2.77041 + 0.569915i) q^{72} +(-1.93535 + 1.24377i) q^{73} +(0.186293 - 6.75498i) q^{74} +(-1.87920 + 2.92410i) q^{75} +(6.11945 + 5.92366i) q^{76} +(9.87649 + 8.55802i) q^{77} +(-1.85566 - 0.600913i) q^{78} +(1.06170 + 2.32479i) q^{79} +(-9.58685 + 6.61109i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(15.7088 - 4.14573i) q^{82} +(7.37017 + 1.05967i) q^{83} +(5.07798 + 8.95058i) q^{84} +(-18.3737 - 8.39101i) q^{85} +(-12.4012 - 11.3592i) q^{86} +(0.418637 + 2.91168i) q^{87} +(-7.17083 + 0.431377i) q^{88} +(1.62551 + 1.87594i) q^{89} +(-4.08995 + 0.473374i) q^{90} +7.09665i q^{91} +(9.44136 + 1.69139i) q^{92} -3.21056i q^{93} +(0.523226 + 4.52067i) q^{94} +(8.11881 + 9.36961i) q^{95} +(-5.43552 - 1.56688i) q^{96} +(-1.91268 - 13.3030i) q^{97} +(18.6027 - 20.3093i) q^{98} +(-2.31033 - 1.05509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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