LMFDB - Embedded newform 1148.2.n.b.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$-0.437016 - 1.34500i$ of defining polynomial
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.b.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{3} +(0.335106 - 0.243469i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.82843 q^{9} +O(q^{10})$	\(q-0.414214 q^{3} +(0.335106 - 0.243469i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.82843 q^{9} +(-1.50000 - 1.08981i) q^{11} +(-0.286215 - 0.880878i) q^{13} +(-0.138805 + 0.100848i) q^{15} +(-1.49535 - 1.08644i) q^{17} +(-1.82389 + 5.61334i) q^{19} +(-0.127999 + 0.393941i) q^{21} +(1.27625 + 3.92789i) q^{23} +(-1.49207 + 4.59211i) q^{25} +2.41421 q^{27} +(-3.39344 + 2.46548i) q^{29} +(-4.11870 - 2.99241i) q^{31} +(0.621320 + 0.451416i) q^{33} +(-0.127999 - 0.393941i) q^{35} +(-2.56365 + 1.86260i) q^{37} +(0.118554 + 0.364872i) q^{39} +(-1.74197 + 6.16162i) q^{41} +(-1.97517 - 6.07894i) q^{43} +(-0.947822 + 0.688633i) q^{45} +(-1.67924 - 5.16818i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.619395 + 0.450017i) q^{51} +(5.26832 - 3.82766i) q^{53} -0.767994 q^{55} +(0.755478 - 2.32512i) q^{57} +(-0.747288 - 2.29992i) q^{59} +(-3.64951 + 11.2320i) q^{61} +(-0.874032 + 2.68999i) q^{63} +(-0.310378 - 0.225503i) q^{65} +(-9.68253 + 7.03477i) q^{67} +(-0.528640 - 1.62699i) q^{69} +(-5.93853 - 4.31459i) q^{71} -0.191503 q^{73} +(0.618034 - 1.90211i) q^{75} +(-1.50000 + 1.08981i) q^{77} +7.16885 q^{79} +7.48528 q^{81} -0.886350 q^{83} -0.765615 q^{85} +(1.40561 - 1.02124i) q^{87} +(-5.55782 + 17.1052i) q^{89} -0.926210 q^{91} +(1.70602 + 1.23950i) q^{93} +(0.755478 + 2.32512i) q^{95} +(-15.7458 + 11.4400i) q^{97} +(4.24264 + 3.08246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7	$ 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7} - 12 q^{11} + 10 q^{13} - 6 q^{15} + 12 q^{17} - 2 q^{19} - 2 q^{21} - 12 q^{23} + 4 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{31} - 12 q^{33} - 2 q^{35} + 14 q^{37} + 30 q^{39} - 18 q^{41} - 14 q^{43} - 8 q^{45} + 28 q^{47} - 2 q^{49} + 28 q^{51} + 4 q^{53} - 12 q^{55} - 30 q^{57} + 4 q^{59} - 4 q^{61} - 30 q^{65} - 28 q^{67} - 36 q^{69} - 44 q^{73} - 4 q^{75} - 12 q^{77} + 16 q^{79} - 8 q^{81} + 40 q^{83} - 12 q^{85} + 22 q^{87} + 14 q^{89} + 42 q^{93} - 30 q^{95} - 38 q^{97}+O(q^{100}) $ 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7 - 12 * q^11 + 10 * q^13 - 6 * q^15 + 12 * q^17 - 2 * q^19 - 2 * q^21 - 12 * q^23 + 4 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^31 - 12 * q^33 - 2 * q^35 + 14 * q^37 + 30 * q^39 - 18 * q^41 - 14 * q^43 - 8 * q^45 + 28 * q^47 - 2 * q^49 + 28 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 4 * q^59 - 4 * q^61 - 30 * q^65 - 28 * q^67 - 36 * q^69 - 44 * q^73 - 4 * q^75 - 12 * q^77 + 16 * q^79 - 8 * q^81 + 40 * q^83 - 12 * q^85 + 22 * q^87 + 14 * q^89 + 42 * q^93 - 30 * q^95 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.414214			−0.239146			−0.119573	−	0.992825i	$-0.538153\pi$
$3$	−0.414214			−0.239146			−0.119573	+	0.992825i	$0.538153\pi$
$4$		0			0
$5$	0.335106	−	0.243469i	0.149864	−	0.108882i	−0.510327	−	0.859981i	$-0.670476\pi$
$5$	0.335106	−	0.243469i	0.149864	−	0.108882i	0.660191	+	0.751098i	$0.270476\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	−2.82843			−0.942809
$10$		0			0
$11$	−1.50000	−	1.08981i	−0.452267	−	0.328591i	0.338223	−	0.941066i	$-0.390174\pi$
$11$	−1.50000	−	1.08981i	−0.452267	−	0.328591i	−0.790490	+	0.612475i	$0.790174\pi$
$12$		0			0
$13$	−0.286215	−	0.880878i	−0.0793816	−	0.244312i	0.903488	−	0.428613i	$-0.140998\pi$
$13$	−0.286215	−	0.880878i	−0.0793816	−	0.244312i	−0.982870	+	0.184302i	$0.940998\pi$
$14$		0			0
$15$	−0.138805	+	0.100848i	−0.0358394	+	0.0260388i
$16$		0			0
$17$	−1.49535	−	1.08644i	−0.362676	−	0.263500i	0.391491	−	0.920182i	$-0.371959\pi$
$17$	−1.49535	−	1.08644i	−0.362676	−	0.263500i	−0.754167	+	0.656682i	$0.771959\pi$
$18$		0			0
$19$	−1.82389	+	5.61334i	−0.418428	+	1.28779i	0.490721	+	0.871317i	$0.336734\pi$
$19$	−1.82389	+	5.61334i	−0.418428	+	1.28779i	−0.909149	+	0.416472i	$0.863266\pi$
$20$		0			0
$21$	−0.127999	+	0.393941i	−0.0279317	+	0.0859649i
$22$		0			0
$23$	1.27625	+	3.92789i	0.266116	+	0.819022i	0.991434	+	0.130608i	$0.0416929\pi$
$23$	1.27625	+	3.92789i	0.266116	+	0.819022i	−0.725318	+	0.688414i	$0.758307\pi$
$24$		0			0
$25$	−1.49207	+	4.59211i	−0.298413	+	0.918421i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	−3.39344	+	2.46548i	−0.630146	+	0.457828i	−0.856451	−	0.516228i	$-0.827336\pi$
$29$	−3.39344	+	2.46548i	−0.630146	+	0.457828i	0.226305	+	0.974057i	$0.427336\pi$
$30$		0			0
$31$	−4.11870	−	2.99241i	−0.739741	−	0.537453i	0.152889	−	0.988243i	$-0.451142\pi$
$31$	−4.11870	−	2.99241i	−0.739741	−	0.537453i	−0.892630	+	0.450790i	$0.851142\pi$
$32$		0			0
$33$	0.621320	+	0.451416i	0.108158	+	0.0785814i
$34$		0			0
$35$	−0.127999	−	0.393941i	−0.0216358	−	0.0665881i
$36$		0			0
$37$	−2.56365	+	1.86260i	−0.421462	+	0.306210i	−0.778226	−	0.627985i	$-0.783880\pi$
$37$	−2.56365	+	1.86260i	−0.421462	+	0.306210i	0.356764	+	0.934195i	$0.383880\pi$
$38$		0			0
$39$	0.118554	+	0.364872i	0.0189838	+	0.0584262i
$40$		0			0
$41$	−1.74197	+	6.16162i	−0.272050	+	0.962283i
$41$	−1.74197	+	6.16162i	−0.272050	+	0.962283i
$42$		0			0
$43$	−1.97517	−	6.07894i	−0.301210	−	0.927029i	−0.981064	−	0.193682i	$-0.937957\pi$
$43$	−1.97517	−	6.07894i	−0.301210	−	0.927029i	0.679854	−	0.733347i	$-0.262043\pi$
$44$		0			0
$45$	−0.947822	+	0.688633i	−0.141293	+	0.102655i
$46$		0			0
$47$	−1.67924	−	5.16818i	−0.244943	−	0.753856i	−0.995646	−	0.0932165i	$-0.970285\pi$
$47$	−1.67924	−	5.16818i	−0.244943	−	0.753856i	0.750703	−	0.660640i	$-0.229715\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	0.619395	+	0.450017i	0.0867327	+	0.0630150i
$52$		0			0
$53$	5.26832	−	3.82766i	0.723659	−	0.525769i	−0.163892	−	0.986478i	$-0.552405\pi$
$53$	5.26832	−	3.82766i	0.723659	−	0.525769i	0.887551	+	0.460709i	$0.152405\pi$
$54$		0			0
$55$	−0.767994			−0.103556
$56$		0			0
$57$	0.755478	−	2.32512i	0.100066	−	0.307970i
$58$		0			0
$59$	−0.747288	−	2.29992i	−0.0972886	−	0.299424i	0.890555	−	0.454876i	$-0.150316\pi$
$59$	−0.747288	−	2.29992i	−0.0972886	−	0.299424i	−0.987843	+	0.155452i	$0.950316\pi$
$60$		0			0
$61$	−3.64951	+	11.2320i	−0.467271	+	1.43811i	0.388832	+	0.921309i	$0.372879\pi$
$61$	−3.64951	+	11.2320i	−0.467271	+	1.43811i	−0.856103	+	0.516805i	$0.827121\pi$
$62$		0			0
$63$	−0.874032	+	2.68999i	−0.110118	+	0.338907i
$64$		0			0
$65$	−0.310378	−	0.225503i	−0.0384977	−	0.0279702i
$66$		0			0
$67$	−9.68253	+	7.03477i	−1.18291	+	0.859434i	−0.992497	−	0.122270i	$-0.960983\pi$
$67$	−9.68253	+	7.03477i	−1.18291	+	0.859434i	−0.190412	+	0.981704i	$0.560983\pi$
$68$		0			0
$69$	−0.528640	−	1.62699i	−0.0636408	−	0.195866i
$70$		0			0
$71$	−5.93853	−	4.31459i	−0.704774	−	0.512048i	0.176710	−	0.984263i	$-0.443455\pi$
$71$	−5.93853	−	4.31459i	−0.704774	−	0.512048i	−0.881483	+	0.472215i	$0.843455\pi$
$72$		0			0
$73$	−0.191503			−0.0224137			−0.0112069	−	0.999937i	$-0.503567\pi$
$73$	−0.191503			−0.0224137			−0.0112069	+	0.999937i	$0.503567\pi$
$74$		0			0
$75$	0.618034	−	1.90211i	0.0713644	−	0.219637i
$76$		0			0
$77$	−1.50000	+	1.08981i	−0.170941	+	0.124196i
$78$		0			0
$79$	7.16885			0.806559			0.403279	−	0.915077i	$-0.367870\pi$
$79$	7.16885			0.806559			0.403279	+	0.915077i	$0.367870\pi$
$80$		0			0
$81$	7.48528			0.831698
$82$		0			0
$83$	−0.886350			−0.0972895			−0.0486447	−	0.998816i	$-0.515490\pi$
$83$	−0.886350			−0.0972895			−0.0486447	+	0.998816i	$0.515490\pi$
$84$		0			0
$85$	−0.765615			−0.0830426
$86$		0			0
$87$	1.40561	−	1.02124i	0.150697	−	0.109488i
$88$		0			0
$89$	−5.55782	+	17.1052i	−0.589127	+	1.81315i	−0.00710506	+	0.999975i	$0.502262\pi$
$89$	−5.55782	+	17.1052i	−0.589127	+	1.81315i	−0.582022	+	0.813173i	$0.697738\pi$
$90$		0			0
$91$	−0.926210			−0.0970932
$92$		0			0
$93$	1.70602	+	1.23950i	0.176906	+	0.128530i
$94$		0			0
$95$	0.755478	+	2.32512i	0.0775104	+	0.238553i
$96$		0			0
$97$	−15.7458	+	11.4400i	−1.59874	+	1.16155i	−0.708871	+	0.705338i	$0.750795\pi$
$97$	−15.7458	+	11.4400i	−1.59874	+	1.16155i	−0.889870	+	0.456215i	$0.849205\pi$
$98$		0			0
$99$	4.24264	+	3.08246i	0.426401	+	0.309799i
$100$		0			0
$101$	3.96978	−	12.2177i	0.395008	−	1.21571i	−0.533947	−	0.845518i	$-0.679292\pi$
$101$	3.96978	−	12.2177i	0.395008	−	1.21571i	0.928955	−	0.370192i	$-0.120708\pi$
$102$		0			0
$103$	4.70043	−	14.4664i	0.463147	−	1.42542i	−0.398151	−	0.917320i	$-0.630348\pi$
$103$	4.70043	−	14.4664i	0.463147	−	1.42542i	0.861298	−	0.508100i	$-0.169652\pi$
$104$		0			0
$105$	0.0530189	+	0.163176i	0.00517412	+	0.0159243i
$106$		0			0
$107$	0.133061	−	0.409518i	0.0128635	−	0.0395896i	−0.944419	−	0.328745i	$-0.893374\pi$
$107$	0.133061	−	0.409518i	0.0128635	−	0.0395896i	0.957282	+	0.289155i	$0.0933744\pi$
$108$		0			0
$109$	−19.6076			−1.87806			−0.939032	−	0.343829i	$-0.888276\pi$
$109$	−19.6076			−1.87806			−0.939032	+	0.343829i	$0.888276\pi$
$110$		0			0
$111$	1.06190	−	0.771516i	0.100791	−	0.0732290i
$112$		0			0
$113$	−12.2940	−	8.93211i	−1.15652	−	0.840262i	−0.167187	−	0.985925i	$-0.553468\pi$
$113$	−12.2940	−	8.93211i	−1.15652	−	0.840262i	−0.989334	+	0.145663i	$0.953468\pi$
$114$		0			0
$115$	1.38400	+	1.00553i	0.129058	+	0.0937664i
$116$		0			0
$117$	0.809537	+	2.49150i	0.0748417	+	0.230339i
$118$		0			0
$119$	−1.49535	+	1.08644i	−0.137079	+	0.0995935i
$120$		0			0
$121$	−2.33688	−	7.19218i	−0.212444	−	0.653835i
$122$		0			0
$123$	0.721548	−	2.55223i	0.0650598	−	0.230126i
$124$		0			0
$125$	1.25803	+	3.87182i	0.112522	+	0.346306i
$126$		0			0
$127$	2.61583	−	1.90051i	0.232118	−	0.168643i	−0.465647	−	0.884971i	$-0.654178\pi$
$127$	2.61583	−	1.90051i	0.232118	−	0.168643i	0.697764	+	0.716327i	$0.254178\pi$
$128$		0			0
$129$	0.818141	+	2.51798i	0.0720333	+	0.221696i
$130$		0			0
$131$	12.7295	+	9.24850i	1.11218	+	0.808046i	0.983005	−	0.183576i	$-0.0587675\pi$
$131$	12.7295	+	9.24850i	1.11218	+	0.808046i	0.129174	+	0.991622i	$0.458767\pi$
$132$		0			0
$133$	4.77499	+	3.46924i	0.414045	+	0.300821i
$134$		0			0
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$		0			0
$137$	6.71905			0.574047			0.287024	−	0.957924i	$-0.407334\pi$
$137$	6.71905			0.574047			0.287024	+	0.957924i	$0.407334\pi$
$138$		0			0
$139$	0.111355	−	0.342716i	0.00944503	−	0.0290688i	−0.946223	−	0.323515i	$-0.895135\pi$
$139$	0.111355	−	0.342716i	0.00944503	−	0.0290688i	0.955668	+	0.294446i	$0.0951353\pi$
$140$		0			0
$141$	0.695565	+	2.14073i	0.0585771	+	0.180282i
$142$		0			0
$143$	−0.530671	+	1.63324i	−0.0443769	+	0.136578i
$144$		0			0
$145$	−0.536895	+	1.65239i	−0.0445867	+	0.137224i
$146$		0			0
$147$	0.335106	+	0.243469i	0.0276391	+	0.0200810i
$148$		0			0
$149$	−10.4284	+	7.57667i	−0.854327	+	0.620705i	−0.926336	−	0.376699i	$-0.877059\pi$
$149$	−10.4284	+	7.57667i	−0.854327	+	0.620705i	0.0720086	+	0.997404i	$0.477059\pi$
$150$		0			0
$151$	−5.67324	−	17.4604i	−0.461682	−	1.42091i	−0.863108	−	0.505019i	$-0.831485\pi$
$151$	−5.67324	−	17.4604i	−0.461682	−	1.42091i	0.401426	−	0.915891i	$-0.368515\pi$
$152$		0			0
$153$	4.22950	+	3.07291i	0.341934	+	0.248430i
$154$		0			0
$155$	−2.10876			−0.169380
$156$		0			0
$157$	−1.56711	+	4.82307i	−0.125069	+	0.384923i	−0.993914	−	0.110162i	$-0.964863\pi$
$157$	−1.56711	+	4.82307i	−0.125069	+	0.384923i	0.868845	+	0.495085i	$0.164863\pi$
$158$		0			0
$159$	−2.18221	+	1.58547i	−0.173060	+	0.125736i
$160$		0			0
$161$	4.13003			0.325492
$162$		0			0
$163$	−1.69065			−0.132422			−0.0662111	−	0.997806i	$-0.521091\pi$
$163$	−1.69065			−0.132422			−0.0662111	+	0.997806i	$0.521091\pi$
$164$		0			0
$165$	0.318114			0.0247651
$166$		0			0
$167$	17.8902			1.38439			0.692193	−	0.721713i	$-0.256645\pi$
$167$	17.8902			1.38439			0.692193	+	0.721713i	$0.256645\pi$
$168$		0			0
$169$	9.82319	−	7.13697i	0.755630	−	0.548998i
$170$		0			0
$171$	5.15873	−	15.8769i	0.394498	−	1.21414i
$172$		0			0
$173$	6.27000			0.476699			0.238350	−	0.971179i	$-0.423394\pi$
$173$	6.27000			0.476699			0.238350	+	0.971179i	$0.423394\pi$
$174$		0			0
$175$	3.90628	+	2.83808i	0.295287	+	0.214539i
$176$		0			0
$177$	0.309537	+	0.952657i	0.0232662	+	0.0716061i
$178$		0			0
$179$	20.5689	−	14.9442i	1.53739	−	1.11698i	0.585444	−	0.810713i	$-0.300920\pi$
$179$	20.5689	−	14.9442i	1.53739	−	1.11698i	0.951946	−	0.306267i	$-0.0990800\pi$
$180$		0			0
$181$	1.66818	+	1.21200i	0.123995	+	0.0900876i	0.648054	−	0.761594i	$-0.275583\pi$
$181$	1.66818	+	1.21200i	0.123995	+	0.0900876i	−0.524059	+	0.851682i	$0.675583\pi$
$182$		0			0
$183$	1.51167	−	4.65246i	0.111746	−	0.343919i
$184$		0			0
$185$	−0.405610	+	1.24834i	−0.0298210	+	0.0917797i
$186$		0			0
$187$	1.05901	+	3.25931i	0.0774428	+	0.238344i
$188$		0			0
$189$	0.746033	−	2.29605i	0.0542659	−	0.167013i
$190$		0			0
$191$	−1.13003			−0.0817661			−0.0408831	−	0.999164i	$-0.513017\pi$
$191$	−1.13003			−0.0817661			−0.0408831	+	0.999164i	$0.513017\pi$
$192$		0			0
$193$	6.80192	−	4.94189i	0.489613	−	0.355725i	−0.315422	−	0.948951i	$-0.602146\pi$
$193$	6.80192	−	4.94189i	0.489613	−	0.355725i	0.805036	+	0.593227i	$0.202146\pi$
$194$		0			0
$195$	0.128563	+	0.0934064i	0.00920658	+	0.00668897i
$196$		0			0
$197$	4.68253	+	3.40206i	0.333616	+	0.242386i	0.741964	−	0.670440i	$-0.233895\pi$
$197$	4.68253	+	3.40206i	0.333616	+	0.242386i	−0.408347	+	0.912827i	$0.633895\pi$
$198$		0			0
$199$	0.717848	+	2.20931i	0.0508869	+	0.156614i	0.973271	−	0.229661i	$-0.0737617\pi$
$199$	0.717848	+	2.20931i	0.0508869	+	0.156614i	−0.922384	+	0.386275i	$0.873762\pi$
$200$		0			0
$201$	4.01063	−	2.91390i	0.282888	−	0.205530i
$202$		0			0
$203$	1.29618	+	3.98923i	0.0909740	+	0.279989i
$204$		0			0
$205$	0.916416	+	2.48891i	0.0640053	+	0.173833i
$206$		0			0
$207$	−3.60978	−	11.1098i	−0.250897	−	0.772181i
$208$		0			0
$209$	8.85333	−	6.43232i	0.612397	−	0.444933i
$210$		0			0
$211$	−3.13744	−	9.65606i	−0.215991	−	0.664751i	−0.999082	−	0.0428437i	$-0.986358\pi$
$211$	−3.13744	−	9.65606i	−0.215991	−	0.664751i	0.783091	−	0.621907i	$-0.213642\pi$
$212$		0			0
$213$	2.45982	+	1.78716i	0.168544	+	0.122454i
$214$		0			0
$215$	−2.14192	−	1.55620i	−0.146078	−	0.106132i
$216$		0			0
$217$	−4.11870	+	2.99241i	−0.279596	+	0.203138i
$218$		0			0
$219$	0.0793231			0.00536016
$220$		0			0
$221$	−0.529027	+	1.62818i	−0.0355862	+	0.109523i
$222$		0			0
$223$	7.45878	+	22.9558i	0.499477	+	1.53723i	0.809862	+	0.586621i	$0.199542\pi$
$223$	7.45878	+	22.9558i	0.499477	+	1.53723i	−0.310385	+	0.950611i	$0.600458\pi$
$224$		0			0
$225$	4.22020	−	12.9884i	0.281347	−	0.865896i
$226$		0			0
$227$	2.36861	−	7.28983i	0.157210	−	0.483843i	−0.841168	−	0.540774i	$-0.818131\pi$
$227$	2.36861	−	7.28983i	0.157210	−	0.483843i	0.998378	+	0.0569310i	$0.0181315\pi$
$228$		0			0
$229$	12.0347	+	8.74373i	0.795276	+	0.577802i	0.909524	−	0.415651i	$-0.136446\pi$
$229$	12.0347	+	8.74373i	0.795276	+	0.577802i	−0.114249	+	0.993452i	$0.536446\pi$
$230$		0			0
$231$	0.621320	−	0.451416i	0.0408799	−	0.0297010i
$232$		0			0
$233$	2.22761	+	6.85589i	0.145936	+	0.449144i	0.997130	−	0.0757063i	$-0.0241212\pi$
$233$	2.22761	+	6.85589i	0.145936	+	0.449144i	−0.851194	+	0.524851i	$0.824121\pi$
$234$		0			0
$235$	−1.82101	−	1.32304i	−0.118790	−	0.0863058i
$236$		0			0
$237$	−2.96944			−0.192886
$238$		0			0
$239$	7.11751	−	21.9055i	0.460394	−	1.41695i	−0.404291	−	0.914631i	$-0.632482\pi$
$239$	7.11751	−	21.9055i	0.460394	−	1.41695i	0.864684	−	0.502316i	$-0.167518\pi$
$240$		0			0
$241$	−11.1628	+	8.11028i	−0.719062	+	0.522429i	−0.886084	−	0.463524i	$-0.846585\pi$
$241$	−11.1628	+	8.11028i	−0.719062	+	0.522429i	0.167022	+	0.985953i	$0.446585\pi$
$242$		0			0
$243$	−10.3431			−0.663513
$244$		0			0
$245$	−0.414214			−0.0264631
$246$		0			0
$247$	5.46669			0.347837
$248$		0			0
$249$	0.367138			0.0232664
$250$		0			0
$251$	−8.52362	+	6.19277i	−0.538006	+	0.390884i	−0.823344	−	0.567543i	$-0.807894\pi$
$251$	−8.52362	+	6.19277i	−0.538006	+	0.390884i	0.285338	+	0.958427i	$0.407894\pi$
$252$		0			0
$253$	2.36630	−	7.28271i	0.148768	−	0.457860i
$254$		0			0
$255$	0.317128			0.0198593
$256$		0			0
$257$	2.68742	+	1.95252i	0.167637	+	0.121795i	0.668440	−	0.743766i	$-0.266962\pi$
$257$	2.68742	+	1.95252i	0.167637	+	0.121795i	−0.500804	+	0.865561i	$0.666962\pi$
$258$		0			0
$259$	0.979229	+	3.01376i	0.0608463	+	0.187266i
$260$		0			0
$261$	9.59810	−	6.97343i	0.594108	−	0.431645i
$262$		0			0
$263$	−23.0339	−	16.7351i	−1.42033	−	1.03193i	−0.991717	−	0.128444i	$-0.959002\pi$
$263$	−23.0339	−	16.7351i	−1.42033	−	1.03193i	−0.428615	−	0.903487i	$-0.640998\pi$
$264$		0			0
$265$	0.833529	−	2.56534i	0.0512033	−	0.157588i
$266$		0			0
$267$	2.30212	−	7.08521i	0.140888	−	0.433608i
$268$		0			0
$269$	0.554530	+	1.70667i	0.0338103	+	0.104057i	0.966537	−	0.256526i	$-0.0825778\pi$
$269$	0.554530	+	1.70667i	0.0338103	+	0.104057i	−0.932727	+	0.360583i	$0.882578\pi$
$270$		0			0
$271$	−5.67099	+	17.4535i	−0.344488	+	1.06022i	0.617369	+	0.786673i	$0.288198\pi$
$271$	−5.67099	+	17.4535i	−0.344488	+	1.06022i	−0.961857	+	0.273552i	$0.911802\pi$
$272$		0			0
$273$	0.383649			0.0232195
$274$		0			0
$275$	7.24264	−	5.26209i	0.436748	−	0.317316i
$276$		0			0
$277$	20.1839	+	14.6644i	1.21273	+	0.881101i	0.995476	−	0.0950141i	$-0.0302896\pi$
$277$	20.1839	+	14.6644i	1.21273	+	0.881101i	0.217255	+	0.976115i	$0.430290\pi$
$278$		0			0
$279$	11.6495	+	8.46382i	0.697435	+	0.506716i
$280$		0			0
$281$	−6.07159	−	18.6864i	−0.362201	−	1.11474i	−0.951716	−	0.306981i	$-0.900681\pi$
$281$	−6.07159	−	18.6864i	−0.362201	−	1.11474i	0.589515	−	0.807757i	$-0.299319\pi$
$282$		0			0
$283$	7.64700	−	5.55587i	0.454567	−	0.330262i	−0.336829	−	0.941566i	$-0.609355\pi$
$283$	7.64700	−	5.55587i	0.454567	−	0.330262i	0.791396	+	0.611304i	$0.209355\pi$
$284$		0			0
$285$	−0.312929	−	0.963097i	−0.0185363	−	0.0570490i
$286$		0			0
$287$	5.32175	+	3.56076i	0.314133	+	0.210185i
$288$		0			0
$289$	−4.19756	−	12.9187i	−0.246915	−	0.759926i
$290$		0			0
$291$	6.52211	−	4.73859i	0.382333	−	0.277781i
$292$		0			0
$293$	−1.97588	−	6.08112i	−0.115432	−	0.355263i	0.876605	−	0.481211i	$-0.159803\pi$
$293$	−1.97588	−	6.08112i	−0.115432	−	0.355263i	−0.992037	+	0.125948i	$0.959803\pi$
$294$		0			0
$295$	−0.810378	−	0.588774i	−0.0471820	−	0.0342798i
$296$		0			0
$297$	−3.62132	−	2.63104i	−0.210130	−	0.152669i
$298$		0			0
$299$	3.09471	−	2.24844i	0.178972	−	0.130031i
$300$		0			0
$301$	−6.39177			−0.368416
$302$		0			0
$303$	−1.64434	+	5.06075i	−0.0944648	+	0.290733i
$304$		0			0
$305$	1.51167	+	4.65246i	0.0865582	+	0.266399i
$306$		0			0
$307$	−1.66666	+	5.12946i	−0.0951214	+	0.292753i	−0.987285	−	0.158958i	$-0.949186\pi$
$307$	−1.66666	+	5.12946i	−0.0951214	+	0.292753i	0.892164	+	0.451712i	$0.149186\pi$
$308$		0			0
$309$	−1.94698	+	5.99219i	−0.110760	+	0.340884i
$310$		0			0
$311$	−10.6983	−	7.77280i	−0.606647	−	0.440755i	0.241585	−	0.970380i	$-0.422333\pi$
$311$	−10.6983	−	7.77280i	−0.606647	−	0.440755i	−0.848232	+	0.529625i	$0.822333\pi$
$312$		0			0
$313$	−6.87131	+	4.99230i	−0.388389	+	0.282181i	−0.764795	−	0.644273i	$-0.777160\pi$
$313$	−6.87131	+	4.99230i	−0.388389	+	0.282181i	0.376406	+	0.926455i	$0.377160\pi$
$314$		0			0
$315$	0.362036	+	1.11423i	0.0203984	+	0.0627799i
$316$		0			0
$317$	21.7546	+	15.8057i	1.22186	+	0.887734i	0.996253	−	0.0864836i	$-0.0275630\pi$
$317$	21.7546	+	15.8057i	1.22186	+	0.887734i	0.225608	+	0.974218i	$0.427563\pi$
$318$		0			0
$319$	7.77708			0.435433
$320$		0			0
$321$	−0.0551155	+	0.169628i	−0.00307625	+	0.00946772i
$322$		0			0
$323$	8.82589	−	6.41239i	0.491086	−	0.356795i
$324$		0			0
$325$	4.47214			0.248069
$326$		0			0
$327$	8.12172			0.449132
$328$		0			0
$329$	−5.43414			−0.299594
$330$		0			0
$331$	−8.51974			−0.468287			−0.234144	−	0.972202i	$-0.575229\pi$
$331$	−8.51974			−0.468287			−0.234144	+	0.972202i	$0.575229\pi$
$332$		0			0
$333$	7.25111	−	5.26824i	0.397358	−	0.288698i
$334$		0			0
$335$	−1.53193	+	4.71478i	−0.0836981	+	0.257596i
$336$		0			0
$337$	−6.56564			−0.357653			−0.178827	−	0.983881i	$-0.557230\pi$
$337$	−6.56564			−0.357653			−0.178827	+	0.983881i	$0.557230\pi$
$338$		0			0
$339$	5.09234	+	3.69980i	0.276578	+	0.200946i
$340$		0			0
$341$	2.91688	+	8.97724i	0.157958	+	0.486145i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	−0.573270	−	0.416505i	−0.0308638	−	0.0224239i
$346$		0			0
$347$	−1.46181	+	4.49899i	−0.0784740	+	0.241518i	−0.982596	−	0.185757i	$-0.940526\pi$
$347$	−1.46181	+	4.49899i	−0.0784740	+	0.241518i	0.904122	+	0.427275i	$0.140526\pi$
$348$		0			0
$349$	−0.770156	+	2.37030i	−0.0412255	+	0.126879i	−0.969551	−	0.244889i	$-0.921248\pi$
$349$	−0.770156	+	2.37030i	−0.0412255	+	0.126879i	0.928326	+	0.371768i	$0.121248\pi$
$350$		0			0
$351$	−0.690983	−	2.12663i	−0.0368819	−	0.113511i
$352$		0			0
$353$	10.0186	−	30.8342i	0.533238	−	1.64114i	−0.214189	−	0.976792i	$-0.568711\pi$
$353$	10.0186	−	30.8342i	0.533238	−	1.64114i	0.747427	−	0.664345i	$-0.231289\pi$
$354$		0			0
$355$	−3.04050			−0.161373
$356$		0			0
$357$	0.619395	−	0.450017i	0.0327819	−	0.0238174i
$358$		0			0
$359$	16.3891	+	11.9073i	0.864981	+	0.628445i	0.929235	−	0.369488i	$-0.120467\pi$
$359$	16.3891	+	11.9073i	0.864981	+	0.628445i	−0.0642545	+	0.997934i	$0.520467\pi$
$360$		0			0
$361$	−12.8117	−	9.30827i	−0.674302	−	0.489909i
$362$		0			0
$363$	0.967968	+	2.97910i	0.0508051	+	0.156362i
$364$		0			0
$365$	−0.0641738	+	0.0466250i	−0.00335901	+	0.00244046i
$366$		0			0
$367$	−7.44222	−	22.9048i	−0.388481	−	1.19562i	−0.933924	−	0.357472i	$-0.883639\pi$
$367$	−7.44222	−	22.9048i	−0.388481	−	1.19562i	0.545443	−	0.838148i	$-0.316361\pi$
$368$		0			0
$369$	4.92704	−	17.4277i	0.256491	−	0.907249i
$370$		0			0
$371$	−2.01232	−	6.19328i	−0.104474	−	0.321539i
$372$		0			0
$373$	−29.5114	+	21.4413i	−1.52804	+	1.11019i	−0.570732	+	0.821137i	$0.693340\pi$
$373$	−29.5114	+	21.4413i	−1.52804	+	1.11019i	−0.957313	+	0.289053i	$0.906660\pi$
$374$		0			0
$375$	−0.521093	−	1.60376i	−0.0269091	−	0.0828177i
$376$		0			0
$377$	3.14304	+	2.28355i	0.161875	+	0.117609i
$378$		0			0
$379$	−10.5907	−	7.69457i	−0.544006	−	0.395244i	0.281565	−	0.959542i	$-0.409147\pi$
$379$	−10.5907	−	7.69457i	−0.544006	−	0.395244i	−0.825571	+	0.564299i	$0.809147\pi$
$380$		0			0
$381$	−1.08351	+	0.787218i	−0.0555100	+	0.0403304i
$382$		0			0
$383$	15.1891			0.776127			0.388064	−	0.921633i	$-0.373144\pi$
$383$	15.1891			0.776127			0.388064	+	0.921633i	$0.373144\pi$
$384$		0			0
$385$	−0.237323	+	0.730406i	−0.0120951	+	0.0372249i
$386$		0			0
$387$	5.58661	+	17.1938i	0.283984	+	0.874012i
$388$		0			0
$389$	−7.53070	+	23.1771i	−0.381821	+	1.17513i	0.556939	+	0.830554i	$0.311976\pi$
$389$	−7.53070	+	23.1771i	−0.381821	+	1.17513i	−0.938760	+	0.344572i	$0.888024\pi$
$390$		0			0
$391$	2.35896	−	7.26015i	0.119298	−	0.367161i
$392$		0			0
$393$	−5.27272	−	3.83086i	−0.265974	−	0.193241i
$394$		0			0
$395$	2.40232	−	1.74539i	0.120874	−	0.0878201i
$396$		0			0
$397$	6.81736	+	20.9817i	0.342154	+	1.05304i	0.963090	+	0.269180i	$0.0867526\pi$
$397$	6.81736	+	20.9817i	0.342154	+	1.05304i	−0.620936	+	0.783861i	$0.713247\pi$
$398$		0			0
$399$	−1.97787	−	1.43700i	−0.0990172	−	0.0719402i
$400$		0			0
$401$	24.7203			1.23447			0.617237	−	0.786778i	$-0.288252\pi$
$401$	24.7203			1.23447			0.617237	+	0.786778i	$0.288252\pi$
$402$		0			0
$403$	−1.45712	+	4.48455i	−0.0725842	+	0.223391i
$404$		0			0
$405$	2.50836	−	1.82243i	0.124641	−	0.0905573i
$406$		0			0
$407$	5.87537			0.291231
$408$		0			0
$409$	−16.5025			−0.815996			−0.407998	−	0.912983i	$-0.633773\pi$
$409$	−16.5025			−0.815996			−0.407998	+	0.912983i	$0.633773\pi$
$410$		0			0
$411$	−2.78312			−0.137281
$412$		0			0
$413$	−2.41828			−0.118996
$414$		0			0
$415$	−0.297021	+	0.215798i	−0.0145802	+	0.0105931i
$416$		0			0
$417$	−0.0461249	+	0.141958i	−0.00225874	+	0.00695170i
$418$		0			0
$419$	6.81528			0.332948			0.166474	−	0.986046i	$-0.446762\pi$
$419$	6.81528			0.332948			0.166474	+	0.986046i	$0.446762\pi$
$420$		0			0
$421$	−24.8825	−	18.0782i	−1.21270	−	0.881076i	−0.217224	−	0.976122i	$-0.569700\pi$
$421$	−24.8825	−	18.0782i	−1.21270	−	0.881076i	−0.995473	+	0.0950461i	$0.969700\pi$
$422$		0			0
$423$	4.74962	+	14.6178i	0.230934	+	0.710742i
$424$		0			0
$425$	7.22020	−	5.24578i	0.350231	−	0.254458i
$426$		0			0
$427$	9.55453	+	6.94177i	0.462376	+	0.335936i
$428$		0			0
$429$	0.219811	−	0.676509i	0.0106126	−	0.0326622i
$430$		0			0
$431$	2.12022	−	6.52538i	0.102128	−	0.314316i	−0.886918	−	0.461927i	$-0.847158\pi$
$431$	2.12022	−	6.52538i	0.102128	−	0.314316i	0.989046	+	0.147611i	$0.0471582\pi$
$432$		0			0
$433$	7.40038	+	22.7760i	0.355639	+	1.09455i	0.955638	+	0.294544i	$0.0951679\pi$
$433$	7.40038	+	22.7760i	0.355639	+	1.09455i	−0.599998	+	0.800001i	$0.704832\pi$
$434$		0			0
$435$	0.222389	−	0.684444i	0.0106627	−	0.0328166i
$436$		0			0
$437$	−24.3763			−1.16608
$438$		0			0
$439$	−22.9965	+	16.7080i	−1.09756	+	0.797427i	−0.980661	−	0.195716i	$-0.937297\pi$
$439$	−22.9965	+	16.7080i	−1.09756	+	0.797427i	−0.116904	+	0.993143i	$0.537297\pi$
$440$		0			0
$441$	2.28825	+	1.66251i	0.108964	+	0.0791670i
$442$		0			0
$443$	−18.2355	−	13.2489i	−0.866397	−	0.629474i	0.0632207	−	0.998000i	$-0.479863\pi$
$443$	−18.2355	−	13.2489i	−0.866397	−	0.629474i	−0.929618	+	0.368525i	$0.879863\pi$
$444$		0			0
$445$	2.30212	+	7.08521i	0.109131	+	0.335871i
$446$		0			0
$447$	4.31958	−	3.13836i	0.204309	−	0.148439i
$448$		0			0
$449$	−9.61261	−	29.5846i	−0.453647	−	1.39618i	−0.872716	−	0.488228i	$-0.837643\pi$
$449$	−9.61261	−	29.5846i	−0.453647	−	1.39618i	0.419069	−	0.907954i	$-0.362357\pi$
$450$		0			0
$451$	9.32797	−	7.34400i	0.439237	−	0.345816i
$452$		0			0
$453$	2.34993	+	7.23235i	0.110410	+	0.339806i
$454$		0			0
$455$	−0.310378	+	0.225503i	−0.0145508	+	0.0105717i
$456$		0			0
$457$	−3.11564	−	9.58896i	−0.145744	−	0.448553i	0.851362	−	0.524578i	$-0.175777\pi$
$457$	−3.11564	−	9.58896i	−0.145744	−	0.448553i	−0.997106	+	0.0760256i	$0.975777\pi$
$458$		0			0
$459$	−3.61010	−	2.62289i	−0.168505	−	0.122426i
$460$		0			0
$461$	6.03714	+	4.38624i	0.281178	+	0.204287i	0.719431	−	0.694564i	$-0.244403\pi$
$461$	6.03714	+	4.38624i	0.281178	+	0.204287i	−0.438253	+	0.898852i	$0.644403\pi$
$462$		0			0
$463$	−0.388539	+	0.282290i	−0.0180569	+	0.0131191i	−0.596777	−	0.802407i	$-0.703552\pi$
$463$	−0.388539	+	0.282290i	−0.0180569	+	0.0131191i	0.578720	+	0.815526i	$0.303552\pi$
$464$		0			0
$465$	0.873477			0.0405065
$466$		0			0
$467$	−5.74526	+	17.6821i	−0.265859	+	0.818229i	0.725636	+	0.688079i	$0.241546\pi$
$467$	−5.74526	+	17.6821i	−0.265859	+	0.818229i	−0.991494	+	0.130150i	$0.958454\pi$
$468$		0			0
$469$	3.69840	+	11.3825i	0.170776	+	0.525595i
$470$		0			0
$471$	0.649119	−	1.99778i	0.0299098	−	0.0920530i
$472$		0			0
$473$	−3.66216	+	11.2710i	−0.168386	+	0.518240i
$474$		0			0
$475$	−23.0557	−	16.7510i	−1.05787	−	0.768587i
$476$		0			0
$477$	−14.9010	+	10.8262i	−0.682272	+	0.495700i
$478$		0			0
$479$	3.38854	+	10.4288i	0.154826	+	0.476506i	0.998143	−	0.0609102i	$-0.0194003\pi$
$479$	3.38854	+	10.4288i	0.154826	+	0.476506i	−0.843317	+	0.537417i	$0.819400\pi$
$480$		0			0
$481$	2.37448	+	1.72516i	0.108267	+	0.0786606i
$482$		0			0
$483$	−1.71071			−0.0778402
$484$		0			0
$485$	−2.49122	+	7.66720i	−0.113121	+	0.348150i
$486$		0			0
$487$	−2.96640	+	2.15522i	−0.134421	+	0.0976623i	−0.652964	−	0.757389i	$-0.726475\pi$
$487$	−2.96640	+	2.15522i	−0.134421	+	0.0976623i	0.518543	+	0.855052i	$0.326475\pi$
$488$		0			0
$489$	0.700292			0.0316683
$490$		0			0
$491$	21.0142			0.948356			0.474178	−	0.880429i	$-0.342745\pi$
$491$	21.0142			0.948356			0.474178	+	0.880429i	$0.342745\pi$
$492$		0			0
$493$	7.75298			0.349177
$494$		0			0
$495$	2.17222			0.0976338
$496$		0			0
$497$	−5.93853	+	4.31459i	−0.266379	+	0.193536i
$498$		0			0
$499$	−4.32122	+	13.2993i	−0.193444	+	0.595360i	0.806547	+	0.591170i	$0.201334\pi$
$499$	−4.32122	+	13.2993i	−0.193444	+	0.595360i	−0.999991	+	0.00419014i	$0.998666\pi$
$500$		0			0
$501$	−7.41036			−0.331071
$502$		0			0
$503$	−31.8618	−	23.1489i	−1.42065	−	1.03216i	−0.991665	−	0.128845i	$-0.958873\pi$
$503$	−31.8618	−	23.1489i	−1.42065	−	1.03216i	−0.428981	−	0.903314i	$-0.641127\pi$
$504$		0			0
$505$	−1.64434	−	5.06075i	−0.0731721	−	0.225201i
$506$		0			0
$507$	−4.06890	+	2.95623i	−0.180706	+	0.131291i
$508$		0			0
$509$	−7.35028	−	5.34029i	−0.325796	−	0.236704i	0.412849	−	0.910800i	$-0.364534\pi$
$509$	−7.35028	−	5.34029i	−0.325796	−	0.236704i	−0.738644	+	0.674095i	$0.764534\pi$
$510$		0			0
$511$	−0.0591777	+	0.182130i	−0.00261787	+	0.00805696i
$512$		0			0
$513$	−4.40325	+	13.5518i	−0.194408	+	0.598327i
$514$		0			0
$515$	−1.94698	−	5.99219i	−0.0857942	−	0.264048i
$516$		0			0
$517$	−3.11349	+	9.58233i	−0.136931	+	0.421430i
$518$		0			0
$519$	−2.59712			−0.114001
$520$		0			0
$521$	20.1720	−	14.6558i	0.883749	−	0.642082i	−0.0504913	−	0.998725i	$-0.516079\pi$
$521$	20.1720	−	14.6558i	0.883749	−	0.642082i	0.934241	+	0.356643i	$0.116079\pi$
$522$		0			0
$523$	−14.5526	−	10.5731i	−0.636340	−	0.462328i	0.222251	−	0.974990i	$-0.428660\pi$
$523$	−14.5526	−	10.5731i	−0.636340	−	0.462328i	−0.858591	+	0.512661i	$0.828660\pi$
$524$		0			0
$525$	−1.61803	−	1.17557i	−0.0706168	−	0.0513061i
$526$		0			0
$527$	2.90784	+	8.94943i	0.126668	+	0.389843i
$528$		0			0
$529$	4.80787	−	3.49312i	0.209038	−	0.151875i
$530$		0			0
$531$	2.11365	+	6.50515i	0.0917246	+	0.282299i
$532$		0			0
$533$	5.92621	−	0.229081i	0.256693	−	0.00992261i
$534$		0			0
$535$	−0.0551155	−	0.169628i	−0.00238285	−	0.00733366i
$536$		0			0
$537$	−8.51991	+	6.19008i	−0.367661	+	0.267121i
$538$		0			0
$539$	0.572949	+	1.76336i	0.0246787	+	0.0759531i
$540$		0			0
$541$	21.9292	+	15.9325i	0.942811	+	0.684993i	0.949096	−	0.314988i	$-0.102000\pi$
$541$	21.9292	+	15.9325i	0.942811	+	0.684993i	−0.00628442	+	0.999980i	$0.502000\pi$
$542$		0			0
$543$	−0.690983	−	0.502029i	−0.0296529	−	0.0215441i
$544$		0			0
$545$	−6.57061	+	4.77383i	−0.281454	+	0.204488i
$546$		0			0
$547$	−26.6765			−1.14060			−0.570302	−	0.821435i	$-0.693174\pi$
$547$	−26.6765			−1.14060			−0.570302	+	0.821435i	$0.693174\pi$
$548$		0			0
$549$	10.3224	−	31.7690i	0.440548	−	1.35587i
$550$		0			0
$551$	−7.65033	−	23.5453i	−0.325915	−	1.00306i
$552$		0			0
$553$	2.21530	−	6.81798i	0.0942040	−	0.289930i
$554$		0			0
$555$	0.168009	−	0.517079i	0.00713159	−	0.0219488i
$556$		0			0
$557$	4.82235	+	3.50364i	0.204330	+	0.148454i	0.685244	−	0.728313i	$-0.259695\pi$
$557$	4.82235	+	3.50364i	0.204330	+	0.148454i	−0.480915	+	0.876767i	$0.659695\pi$
$558$		0			0
$559$	−4.78948	+	3.47976i	−0.202573	+	0.147178i
$560$		0			0
$561$	−0.438658	−	1.35005i	−0.0185202	−	0.0569992i
$562$		0			0
$563$	25.2594	+	18.3521i	1.06456	+	0.773447i	0.974926	−	0.222528i	$-0.0714308\pi$
$563$	25.2594	+	18.3521i	1.06456	+	0.773447i	0.0896324	+	0.995975i	$0.471431\pi$
$564$		0			0
$565$	−6.29448			−0.264811
$566$		0			0
$567$	2.31308	−	7.11893i	0.0971402	−	0.298967i
$568$		0			0
$569$	−17.1088	+	12.4302i	−0.717236	+	0.521103i	−0.885500	−	0.464639i	$-0.846184\pi$
$569$	−17.1088	+	12.4302i	−0.717236	+	0.521103i	0.168264	+	0.985742i	$0.446184\pi$
$570$		0			0
$571$	−38.0060			−1.59050			−0.795252	−	0.606279i	$-0.792661\pi$
$571$	−38.0060			−1.59050			−0.795252	+	0.606279i	$0.792661\pi$
$572$		0			0
$573$	0.468074			0.0195541
$574$		0			0
$575$	−19.9415			−0.831620
$576$		0			0
$577$	−30.1363			−1.25459			−0.627294	−	0.778782i	$-0.715838\pi$
$577$	−30.1363			−1.25459			−0.627294	+	0.778782i	$0.715838\pi$
$578$		0			0
$579$	−2.81745	+	2.04700i	−0.117089	+	0.0850703i
$580$		0			0
$581$	−0.273897	+	0.842968i	−0.0113632	+	0.0349722i
$582$		0			0
$583$	−12.0739			−0.500050
$584$		0			0
$585$	0.877882	+	0.637819i	0.0362960	+	0.0263706i
$586$		0			0
$587$	14.4298	+	44.4104i	0.595582	+	1.83301i	0.551806	+	0.833972i	$0.313939\pi$
$587$	14.4298	+	44.4104i	0.595582	+	1.83301i	0.0437763	+	0.999041i	$0.486061\pi$
$588$		0			0
$589$	24.3095	−	17.6619i	1.00165	−	0.727745i
$590$		0			0
$591$	−1.93957	−	1.40918i	−0.0797831	−	0.0579658i
$592$		0			0
$593$	−2.17564	+	6.69592i	−0.0893426	+	0.274968i	−0.985738	−	0.168287i	$-0.946176\pi$
$593$	−2.17564	+	6.69592i	−0.0893426	+	0.274968i	0.896395	+	0.443255i	$0.146176\pi$
$594$		0			0
$595$	−0.236588	+	0.728143i	−0.00969916	+	0.0298509i
$596$		0			0
$597$	−0.297342	−	0.915125i	−0.0121694	−	0.0374536i
$598$		0			0
$599$	−3.23064	+	9.94290i	−0.132001	+	0.406256i	−0.995111	−	0.0987585i	$-0.968513\pi$
$599$	−3.23064	+	9.94290i	−0.132001	+	0.406256i	0.863111	+	0.505014i	$0.168513\pi$
$600$		0			0
$601$	−29.5569			−1.20565			−0.602825	−	0.797873i	$-0.705958\pi$
$601$	−29.5569			−1.20565			−0.602825	+	0.797873i	$0.705958\pi$
$602$		0			0
$603$	27.3863	−	19.8973i	1.11526	−	0.810282i
$604$		0			0
$605$	−2.53417	−	1.84118i	−0.103029	−	0.0748548i
$606$		0			0
$607$	27.1613	+	19.7339i	1.10244	+	0.800972i	0.981457	−	0.191682i	$-0.0613941\pi$
$607$	27.1613	+	19.7339i	1.10244	+	0.800972i	0.120987	+	0.992654i	$0.461394\pi$
$608$		0			0
$609$	−0.536895	−	1.65239i	−0.0217561	−	0.0669584i
$610$		0			0
$611$	−4.07191	+	2.95842i	−0.164732	+	0.119685i
$612$		0			0
$613$	12.5175	+	38.5250i	0.505579	+	1.55601i	0.799796	+	0.600272i	$0.204941\pi$
$613$	12.5175	+	38.5250i	0.505579	+	1.55601i	−0.294217	+	0.955739i	$0.595059\pi$
$614$		0			0
$615$	−0.379592	−	1.03094i	−0.0153066	−	0.0415715i
$616$		0			0
$617$	−4.47162	−	13.7622i	−0.180020	−	0.554046i	0.819807	−	0.572640i	$-0.194081\pi$
$617$	−4.47162	−	13.7622i	−0.180020	−	0.554046i	−0.999827	+	0.0185944i	$0.994081\pi$
$618$		0			0
$619$	−11.5196	+	8.36945i	−0.463010	+	0.336397i	−0.794711	−	0.606988i	$-0.792378\pi$
$619$	−11.5196	+	8.36945i	−0.463010	+	0.336397i	0.331701	+	0.943385i	$0.392378\pi$
$620$		0			0
$621$	3.08114	+	9.48277i	0.123642	+	0.380530i
$622$		0			0
$623$	14.5506	+	10.5716i	0.582956	+	0.423542i
$624$		0			0
$625$	−18.1672	−	13.1992i	−0.726686	−	0.527969i
$626$		0			0
$627$	−3.66717	+	2.66435i	−0.146453	+	0.106404i
$628$		0			0
$629$	5.85717			0.233541
$630$		0			0
$631$	3.07753	−	9.47167i	0.122515	−	0.377061i	−0.870925	−	0.491415i	$-0.836480\pi$
$631$	3.07753	−	9.47167i	0.122515	−	0.377061i	0.993440	+	0.114354i	$0.0364798\pi$
$632$		0			0
$633$	1.29957	+	3.99967i	0.0516533	+	0.158973i
$634$		0			0
$635$	0.413865	−	1.27375i	0.0164237	−	0.0505471i
$636$		0			0
$637$	−0.286215	+	0.880878i	−0.0113402	+	0.0349016i
$638$		0			0
$639$	16.7967	+	12.2035i	0.664467	+	0.482763i
$640$		0			0
$641$	31.7194	−	23.0455i	1.25284	−	0.910241i	0.254456	−	0.967084i	$-0.418104\pi$
$641$	31.7194	−	23.0455i	1.25284	−	0.910241i	0.998383	+	0.0568435i	$0.0181036\pi$
$642$		0			0
$643$	2.73826	+	8.42749i	0.107986	+	0.332348i	0.990420	−	0.138090i	$-0.0440962\pi$
$643$	2.73826	+	8.42749i	0.107986	+	0.332348i	−0.882433	+	0.470437i	$0.844096\pi$
$644$		0			0
$645$	0.887212	+	0.644598i	0.0349340	+	0.0253810i
$646$		0			0
$647$	−38.2224			−1.50268			−0.751338	−	0.659918i	$-0.770591\pi$
$647$	−38.2224			−1.50268			−0.751338	+	0.659918i	$0.770591\pi$
$648$		0			0
$649$	−1.38555	+	4.26428i	−0.0543875	+	0.167388i
$650$		0			0
$651$	1.70602	−	1.23950i	0.0668643	−	0.0485798i
$652$		0			0
$653$	−23.1928			−0.907605			−0.453803	−	0.891102i	$-0.649933\pi$
$653$	−23.1928			−0.907605			−0.453803	+	0.891102i	$0.649933\pi$
$654$		0			0
$655$	6.51744			0.254657
$656$		0			0
$657$	0.541652			0.0211319
$658$		0			0
$659$	39.6207			1.54340			0.771702	−	0.635984i	$-0.219405\pi$
$659$	39.6207			1.54340			0.771702	+	0.635984i	$0.219405\pi$
$660$		0			0
$661$	−39.2891	+	28.5452i	−1.52817	+	1.11028i	−0.570921	+	0.821005i	$0.693414\pi$
$661$	−39.2891	+	28.5452i	−1.52817	+	1.11028i	−0.957247	+	0.289273i	$0.906586\pi$
$662$		0			0
$663$	0.219130	−	0.674413i	0.00851031	−	0.0261920i
$664$		0			0
$665$	2.44478			0.0948044
$666$		0			0
$667$	−14.0150	−	10.1825i	−0.542664	−	0.394268i
$668$		0			0
$669$	−3.08953	−	9.50859i	−0.119448	−	0.367623i
$670$		0			0
$671$	17.7151	−	12.8708i	0.683883	−	0.496870i
$672$		0			0
$673$	−11.6929	−	8.49536i	−0.450726	−	0.327472i	0.339156	−	0.940730i	$-0.389859\pi$
$673$	−11.6929	−	8.49536i	−0.450726	−	0.327472i	−0.789883	+	0.613258i	$0.789859\pi$
$674$		0			0
$675$	−3.60217	+	11.0863i	−0.138647	+	0.426713i
$676$		0			0
$677$	−5.87657	+	18.0862i	−0.225855	+	0.695111i	0.772349	+	0.635199i	$0.219082\pi$
$677$	−5.87657	+	18.0862i	−0.225855	+	0.695111i	−0.998204	+	0.0599116i	$0.980918\pi$
$678$		0			0
$679$	6.01435	+	18.5103i	0.230810	+	0.710359i
$680$		0			0
$681$	−0.981110	+	3.01955i	−0.0375962	+	0.115709i
$682$		0			0
$683$	13.8906			0.531508			0.265754	−	0.964041i	$-0.414379\pi$
$683$	13.8906			0.531508			0.265754	+	0.964041i	$0.414379\pi$
$684$		0			0
$685$	2.25159	−	1.63588i	0.0860289	−	0.0625037i
$686$		0			0
$687$	−4.98494	−	3.62177i	−0.190187	−	0.138179i
$688$		0			0
$689$	−4.87956	−	3.54521i	−0.185897	−	0.135062i
$690$		0			0
$691$	−3.59762	−	11.0723i	−0.136860	−	0.421212i	0.859015	−	0.511951i	$-0.171077\pi$
$691$	−3.59762	−	11.0723i	−0.136860	−	0.421212i	−0.995875	+	0.0907390i	$0.971077\pi$
$692$		0			0
$693$	4.24264	−	3.08246i	0.161165	−	0.117093i
$694$		0			0
$695$	−0.0461249	−	0.141958i	−0.00174962	−	0.00538477i
$696$		0			0
$697$	9.29907	−	7.32125i	0.352227	−	0.277312i
$698$		0			0
$699$	−0.922708	−	2.83980i	−0.0349000	−	0.107411i
$700$		0			0
$701$	0.386336	−	0.280690i	0.0145917	−	0.0106015i	−0.580465	−	0.814285i	$-0.697129\pi$
$701$	0.386336	−	0.280690i	0.0145917	−	0.0106015i	0.595057	+	0.803683i	$0.297129\pi$
$702$		0			0
$703$	−5.77962	−	17.7878i	−0.217983	−	0.670881i
$704$		0			0
$705$	0.754288	+	0.548023i	0.0284081	+	0.0206397i
$706$		0			0
$707$	−10.3930	−	7.55098i	−0.390870	−	0.283984i
$708$		0			0
$709$	11.3448	−	8.24248i	0.426063	−	0.309553i	−0.354010	−	0.935242i	$-0.615182\pi$
$709$	11.3448	−	8.24248i	0.426063	−	0.309553i	0.780073	+	0.625689i	$0.215182\pi$
$710$		0			0
$711$	−20.2766			−0.760431
$712$		0			0
$713$	6.49738	−	19.9969i	0.243329	−	0.748889i
$714$		0			0
$715$	0.219811	+	0.676509i	0.00822047	+	0.0253000i
$716$		0			0
$717$	−2.94817	+	9.07354i	−0.110101	+	0.338857i
$718$		0			0
$719$	−10.0698	+	30.9915i	−0.375539	+	1.15579i	0.567576	+	0.823321i	$0.307881\pi$
$719$	−10.0698	+	30.9915i	−0.375539	+	1.15579i	−0.943114	+	0.332468i	$0.892119\pi$
$720$		0			0
$721$	−12.3059	−	8.94075i	−0.458295	−	0.332971i
$722$		0			0
$723$	4.62380	−	3.35939i	0.171961	−	0.124937i
$724$		0			0
$725$	−6.25851	−	19.2617i	−0.232435	−	0.715362i
$726$		0			0
$727$	16.7214	+	12.1488i	0.620164	+	0.450575i	0.852979	−	0.521946i	$-0.174794\pi$
$727$	16.7214	+	12.1488i	0.620164	+	0.450575i	−0.232815	+	0.972521i	$0.574794\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−3.65081	+	11.2360i	−0.135030	+	0.415580i
$732$		0			0
$733$	−16.6706	+	12.1119i	−0.615744	+	0.447364i	−0.851432	−	0.524464i	$-0.824266\pi$
$733$	−16.6706	+	12.1119i	−0.615744	+	0.447364i	0.235688	+	0.971829i	$0.424266\pi$
$734$		0			0
$735$	0.171573			0.00632856
$736$		0			0
$737$	22.1904			0.817393
$738$		0			0
$739$	−24.4688			−0.900098			−0.450049	−	0.893004i	$-0.648594\pi$
$739$	−24.4688			−0.900098			−0.450049	+	0.893004i	$0.648594\pi$
$740$		0			0
$741$	−2.26438			−0.0831840
$742$		0			0
$743$	−38.0008	+	27.6092i	−1.39411	+	1.01288i	−0.398715	+	0.917075i	$0.630544\pi$
$743$	−38.0008	+	27.6092i	−1.39411	+	1.01288i	−0.995400	+	0.0958085i	$0.969456\pi$
$744$		0			0
$745$	−1.64993	+	5.07797i	−0.0604489	+	0.186042i
$746$		0			0
$747$	2.50698			0.0917254
$748$		0			0
$749$	−0.348357	−	0.253096i	−0.0127287	−	0.00924794i
$750$		0			0
$751$	−10.9069	−	33.5680i	−0.397999	−	1.22492i	−0.926601	−	0.376045i	$-0.877284\pi$
$751$	−10.9069	−	33.5680i	−0.397999	−	1.22492i	0.528602	−	0.848870i	$-0.322716\pi$
$752$		0			0
$753$	3.53060	−	2.56513i	0.128662	−	0.0934786i
$754$		0			0
$755$	−6.15221	−	4.46984i	−0.223902	−	0.162674i
$756$		0			0
$757$	−6.29043	+	19.3600i	−0.228630	+	0.703650i	0.769273	+	0.638920i	$0.220619\pi$
$757$	−6.29043	+	19.3600i	−0.228630	+	0.703650i	−0.997903	+	0.0647299i	$0.979381\pi$
$758$		0			0
$759$	−0.980152	+	3.01660i	−0.0355773	+	0.109496i
$760$		0			0
$761$	−9.64171	−	29.6741i	−0.349512	−	1.07569i	−0.959124	−	0.282987i	$-0.908675\pi$
$761$	−9.64171	−	29.6741i	−0.349512	−	1.07569i	0.609612	−	0.792700i	$-0.291325\pi$
$762$		0			0
$763$	−6.05907	+	18.6479i	−0.219353	+	0.675099i
$764$		0			0
$765$	2.16549			0.0782933
$766$		0			0
$767$	−1.81206	+	1.31654i	−0.0654297	+	0.0475375i
$768$		0			0
$769$	−4.34526	−	3.15701i	−0.156694	−	0.113845i	0.506676	−	0.862137i	$-0.330874\pi$
$769$	−4.34526	−	3.15701i	−0.156694	−	0.113845i	−0.663369	+	0.748292i	$0.730874\pi$
$770$		0			0
$771$	−1.11317	−	0.808762i	−0.0400897	−	0.0291269i
$772$		0			0
$773$	−0.0443174	−	0.136395i	−0.00159399	−	0.00490579i	0.950256	−	0.311469i	$-0.100821\pi$
$773$	−0.0443174	−	0.136395i	−0.00159399	−	0.00490579i	−0.951850	+	0.306563i	$0.900821\pi$
$774$		0			0
$775$	19.8869	−	14.4487i	0.714357	−	0.519011i
$776$		0			0
$777$	−0.405610	−	1.24834i	−0.0145512	−	0.0447839i
$778$		0			0
$779$	−31.4101	−	21.0164i	−1.12538	−	0.752989i
$780$		0			0
$781$	4.20569	+	12.9438i	0.150491	+	0.463165i
$782$		0			0
$783$	−8.19249	+	5.95220i	−0.292776	+	0.212714i
$784$		0			0
$785$	0.649119	+	1.99778i	0.0231680	+	0.0713039i
$786$		0			0
$787$	37.6225	+	27.3343i	1.34110	+	0.974364i	0.999403	+	0.0345523i	$0.0110005\pi$
$787$	37.6225	+	27.3343i	1.34110	+	0.974364i	0.341694	+	0.939811i	$0.388999\pi$
$788$		0			0
$789$	9.54096	+	6.93191i	0.339667	+	0.246783i
$790$		0			0
$791$	−12.2940	+	8.93211i	−0.437124	+	0.317589i
$792$		0			0
$793$	10.9386			0.388440
$794$		0			0
$795$	−0.345259	+	1.06260i	−0.0122451	+	0.0376865i
$796$		0			0
$797$	0.773707	+	2.38122i	0.0274061	+	0.0843473i	0.963824	−	0.266539i	$-0.0858802\pi$
$797$	0.773707	+	2.38122i	0.0274061	+	0.0843473i	−0.936418	+	0.350887i	$0.885880\pi$
$798$		0			0
$799$	−3.10384	+	9.55264i	−0.109806	+	0.337948i
$800$		0			0
$801$	15.7199	−	48.3808i	0.555435	−	1.70945i
$802$		0			0
$803$	0.287254	+	0.208703i	0.0101370	+	0.00736495i
$804$		0			0
$805$	1.38400	−	1.00553i	0.0487795	−	0.0354404i
$806$		0			0
$807$	−0.229694	−	0.706925i	−0.00808561	−	0.0248849i
$808$		0			0
$809$	−11.3060	−	8.21426i	−0.397497	−	0.288798i	0.371024	−	0.928623i	$-0.379007\pi$
$809$	−11.3060	−	8.21426i	−0.397497	−	0.288798i	−0.768521	+	0.639825i	$0.779007\pi$
$810$		0			0
$811$	−11.2472			−0.394944			−0.197472	−	0.980309i	$-0.563273\pi$
$811$	−11.2472			−0.394944			−0.197472	+	0.980309i	$0.563273\pi$
$812$		0			0
$813$	2.34900	−	7.22948i	0.0823830	−	0.253549i
$814$		0			0
$815$	−0.566548	+	0.411621i	−0.0198453	+	0.0144185i
$816$		0			0
$817$	37.7256			1.31985
$818$		0			0
$819$	2.61972			0.0915403
$820$		0			0
$821$	24.3377			0.849391			0.424696	−	0.905336i	$-0.360381\pi$
$821$	24.3377			0.849391			0.424696	+	0.905336i	$0.360381\pi$
$822$		0			0
$823$	−14.4907			−0.505114			−0.252557	−	0.967582i	$-0.581272\pi$
$823$	−14.4907			−0.505114			−0.252557	+	0.967582i	$0.581272\pi$
$824$		0			0
$825$	−3.00000	+	2.17963i	−0.104447	+	0.0758849i
$826$		0			0
$827$	−13.2920	+	40.9085i	−0.462208	+	1.42253i	0.400253	+	0.916405i	$0.368922\pi$
$827$	−13.2920	+	40.9085i	−0.462208	+	1.42253i	−0.862460	+	0.506125i	$0.831078\pi$
$828$		0			0
$829$	10.1592			0.352843			0.176421	−	0.984315i	$-0.443548\pi$
$829$	10.1592			0.352843			0.176421	+	0.984315i	$0.443548\pi$
$830$		0			0
$831$	−8.36043	−	6.07421i	−0.290020	−	0.210712i
$832$		0			0
$833$	0.571174	+	1.75789i	0.0197900	+	0.0609074i
$834$		0			0
$835$	5.99511	−	4.35570i	0.207469	−	0.150735i
$836$		0			0
$837$	−9.94343	−	7.22433i	−0.343695	−	0.249709i
$838$		0			0
$839$	−8.18852	+	25.2017i	−0.282699	+	0.870058i	0.704380	+	0.709823i	$0.251225\pi$
$839$	−8.18852	+	25.2017i	−0.282699	+	0.870058i	−0.987079	+	0.160235i	$0.948775\pi$
$840$		0			0
$841$	−3.52463	+	10.8477i	−0.121539	+	0.374059i
$842$		0			0
$843$	2.51493	+	7.74017i	0.0866189	+	0.266586i
$844$		0			0
$845$	1.55418	−	4.78328i	0.0534655	−	0.164550i
$846$		0			0
$847$	−7.56231			−0.259844
$848$		0			0
$849$	−3.16749	+	2.30132i	−0.108708	+	0.0789809i
$850$		0			0
$851$	−10.5880	−	7.69261i	−0.362951	−	0.263699i
$852$		0			0
$853$	10.9659	+	7.96718i	0.375465	+	0.272791i	0.759473	−	0.650538i	$-0.225457\pi$
$853$	10.9659	+	7.96718i	0.375465	+	0.272791i	−0.384009	+	0.923330i	$0.625457\pi$
$854$		0			0
$855$	−2.13681	−	6.57644i	−0.0730775	−	0.224909i
$856$		0			0
$857$	34.9033	−	25.3587i	1.19227	−	0.866238i	0.198771	−	0.980046i	$-0.436305\pi$
$857$	34.9033	−	25.3587i	1.19227	−	0.866238i	0.993503	+	0.113808i	$0.0363050\pi$
$858$		0			0
$859$	−4.48229	−	13.7951i	−0.152934	−	0.470682i	0.845012	−	0.534748i	$-0.179593\pi$
$859$	−4.48229	−	13.7951i	−0.152934	−	0.470682i	−0.997946	+	0.0640657i	$0.979593\pi$
$860$		0			0
$861$	−2.20434	−	1.47491i	−0.0751237	−	0.0502649i
$862$		0			0
$863$	5.81404	+	17.8938i	0.197912	+	0.609111i	0.999930	+	0.0118112i	$0.00375972\pi$
$863$	5.81404	+	17.8938i	0.197912	+	0.609111i	−0.802018	+	0.597300i	$0.796240\pi$
$864$		0			0
$865$	2.10111	−	1.52655i	0.0714400	−	0.0519042i
$866$		0			0
$867$	1.73868	+	5.35112i	0.0590488	+	0.181734i
$868$		0			0
$869$	−10.7533	−	7.81271i	−0.364780	−	0.265028i
$870$		0			0
$871$	8.96805	+	6.51567i	0.303871	+	0.220775i
$872$		0			0
$873$	44.5358	−	32.3571i	1.50731	−	1.09512i
$874$		0			0
$875$	4.07107			0.137627
$876$		0			0
$877$	−2.19087	+	6.74279i	−0.0739803	+	0.227688i	−0.981208	−	0.192951i	$-0.938194\pi$
$877$	−2.19087	+	6.74279i	−0.0739803	+	0.227688i	0.907228	+	0.420639i	$0.138194\pi$
$878$		0			0
$879$	0.818435	+	2.51888i	0.0276051	+	0.0849598i
$880$		0			0
$881$	1.26832	−	3.90347i	0.0427306	−	0.131511i	−0.927415	−	0.374033i	$-0.877975\pi$
$881$	1.26832	−	3.90347i	0.0427306	−	0.131511i	0.970146	+	0.242522i	$0.0779746\pi$
$882$		0			0
$883$	−8.09861	+	24.9250i	−0.272540	+	0.838792i	0.717320	+	0.696744i	$0.245369\pi$
$883$	−8.09861	+	24.9250i	−0.272540	+	0.838792i	−0.989860	+	0.142048i	$0.954631\pi$
$884$		0			0
$885$	0.335670	+	0.243878i	0.0112834	+	0.00819788i
$886$		0			0
$887$	4.00615	−	2.91063i	0.134513	−	0.0977296i	−0.518494	−	0.855081i	$-0.673507\pi$
$887$	4.00615	−	2.91063i	0.134513	−	0.0977296i	0.653007	+	0.757352i	$0.273507\pi$
$888$		0			0
$889$	−0.999159	−	3.07509i	−0.0335107	−	0.103135i
$890$		0			0
$891$	−11.2279	−	8.15756i	−0.376150	−	0.273289i
$892$		0			0
$893$	32.0735			1.07330
$894$		0			0
$895$	3.25432	−	10.0158i	0.108780	−	0.334790i
$896$		0			0
$897$	−1.28187	+	0.931334i	−0.0428004	+	0.0310963i
$898$		0			0
$899$	21.3543			0.712206
$900$		0			0
$901$	−12.0365			−0.400994
$902$		0			0
$903$	2.64756			0.0881052
$904$		0			0
$905$	0.854102			0.0283913
$906$		0			0
$907$	34.2421	−	24.8784i	1.13699	−	0.826072i	0.150294	−	0.988641i	$-0.451978\pi$
$907$	34.2421	−	24.8784i	1.13699	−	0.826072i	0.986697	+	0.162569i	$0.0519781\pi$
$908$		0			0
$909$	−11.2282	+	34.5570i	−0.372417	+	1.14618i
$910$		0			0
$911$	42.3590			1.40342			0.701708	−	0.712465i	$-0.252421\pi$
$911$	42.3590			1.40342			0.701708	+	0.712465i	$0.252421\pi$
$912$		0			0
$913$	1.32952	+	0.965956i	0.0440008	+	0.0319685i
$914$		0			0
$915$	−0.626156	−	1.92711i	−0.0207001	−	0.0637083i
$916$		0			0
$917$	12.7295	−	9.24850i	0.420364	−	0.305413i
$918$		0			0
$919$	9.80629	+	7.12469i	0.323480	+	0.235022i	0.737659	−	0.675174i	$-0.235931\pi$
$919$	9.80629	+	7.12469i	0.323480	+	0.235022i	−0.414179	+	0.910195i	$0.635931\pi$
$920$		0			0
$921$	0.690354	−	2.12469i	0.0227479	−	0.0700109i
$922$		0			0
$923$	−2.10094	+	6.46602i	−0.0691531	+	0.212831i
$924$		0			0
$925$	−4.72813	−	14.5517i	−0.155460	−	0.478457i
$926$		0			0
$927$	−13.2948	+	40.9172i	−0.436659	+	1.34390i
$928$		0			0
$929$	−25.1707			−0.825824			−0.412912	−	0.910771i	$-0.635488\pi$
$929$	−25.1707			−0.825824			−0.412912	+	0.910771i	$0.635488\pi$
$930$		0			0
$931$	4.77499	−	3.46924i	0.156494	−	0.113700i
$932$		0			0
$933$	4.43140	+	3.21960i	0.145078	+	0.105405i
$934$		0			0
$935$	1.14842	+	0.834377i	0.0375574	+	0.0272871i
$936$		0			0
$937$	−17.0982	−	52.6230i	−0.558575	−	1.71912i	−0.686309	−	0.727310i	$-0.740770\pi$
$937$	−17.0982	−	52.6230i	−0.558575	−	1.71912i	0.127734	−	0.991808i	$-0.459230\pi$
$938$		0			0
$939$	2.84619	−	2.06788i	0.0928819	−	0.0674826i
$940$		0			0
$941$	−16.1040	−	49.5630i	−0.524975	−	1.61571i	−0.764365	−	0.644784i	$-0.776947\pi$
$941$	−16.1040	−	49.5630i	−0.524975	−	1.61571i	0.239390	−	0.970923i	$-0.423053\pi$
$942$		0			0
$943$	−26.4254	+	1.02149i	−0.860528	+	0.0332642i
$944$		0			0
$945$	−0.309017	−	0.951057i	−0.0100523	−	0.0309379i
$946$		0			0
$947$	−19.6194	+	14.2543i	−0.637543	+	0.463202i	−0.859005	−	0.511967i	$-0.828917\pi$
$947$	−19.6194	+	14.2543i	−0.637543	+	0.463202i	0.221462	+	0.975169i	$0.428917\pi$
$948$		0			0
$949$	0.0548109	+	0.168691i	0.00177924	+	0.00547593i
$950$		0			0
$951$	−9.01106	−	6.54692i	−0.292204	−	0.212298i
$952$		0			0
$953$	8.52025	+	6.19033i	0.275998	+	0.200524i	0.717170	−	0.696898i	$-0.245437\pi$
$953$	8.52025	+	6.19033i	0.275998	+	0.200524i	−0.441172	+	0.897423i	$0.645437\pi$
$954$		0			0
$955$	−0.378680	+	0.275127i	−0.0122538	+	0.00890290i
$956$		0			0
$957$	−3.22137			−0.104132
$958$		0			0
$959$	2.07630	−	6.39020i	0.0670473	−	0.206350i
$960$		0			0
$961$	−1.57034	−	4.83302i	−0.0506563	−	0.155904i
$962$		0			0
$963$	−0.376352	+	1.15829i	−0.0121278	+	0.0373255i
$964$		0			0
$965$	1.07617	−	3.31211i	0.0346431	−	0.106621i
$966$		0			0
$967$	−4.15111	−	3.01596i	−0.133491	−	0.0969867i	0.519036	−	0.854752i	$-0.326291\pi$
$967$	−4.15111	−	3.01596i	−0.133491	−	0.0969867i	−0.652527	+	0.757766i	$0.726291\pi$
$968$		0			0
$969$	−3.65581	+	2.65610i	−0.117441	+	0.0853262i
$970$		0			0
$971$	−11.5742	−	35.6217i	−0.371434	−	1.14316i	−0.945853	−	0.324594i	$-0.894772\pi$
$971$	−11.5742	−	35.6217i	−0.371434	−	1.14316i	0.574420	−	0.818561i	$-0.305228\pi$
$972$		0			0
$973$	−0.291532	−	0.211810i	−0.00934609	−	0.00679033i
$974$		0			0
$975$	−1.85242			−0.0593249
$976$		0			0
$977$	−2.75452	+	8.47754i	−0.0881249	+	0.271220i	−0.985401	−	0.170249i	$-0.945543\pi$
$977$	−2.75452	+	8.47754i	−0.0881249	+	0.271220i	0.897276	+	0.441470i	$0.145543\pi$
$978$		0			0
$979$	26.9782	−	19.6008i	0.862227	−	0.626445i
$980$		0			0
$981$	55.4586			1.77066
$982$		0			0
$983$	45.4617			1.45000			0.725002	−	0.688747i	$-0.241839\pi$
$983$	45.4617			1.45000			0.725002	+	0.688747i	$0.241839\pi$
$984$		0			0
$985$	2.39744			0.0763887
$986$		0			0
$987$	2.25090			0.0716468
$988$		0			0
$989$	21.3566	−	15.5165i	0.679101	−	0.493395i
$990$		0			0
$991$	1.65184	−	5.08385i	0.0524725	−	0.161494i	−0.921386	−	0.388648i	$-0.872942\pi$
$991$	1.65184	−	5.08385i	0.0524725	−	0.161494i	0.973859	+	0.227154i	$0.0729422\pi$
$992$		0			0
$993$	3.52899			0.111989
$994$		0			0
$995$	0.778452	+	0.565579i	0.0246786	+	0.0179300i
$996$		0			0
$997$	8.48490	+	26.1138i	0.268720	+	0.827034i	0.990813	+	0.135238i	$0.0431800\pi$
$997$	8.48490	+	26.1138i	0.268720	+	0.827034i	−0.722094	+	0.691795i	$0.756820\pi$
$998$		0			0
$999$	−6.18921	+	4.49672i	−0.195818	+	0.142270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.b.141.1	yes	8
41.16	even	5	inner	1148.2.n.b.57.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.b.57.1	✓	8	41.16	even	5	inner
1148.2.n.b.141.1	yes	8	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.414214 q^{3} +(0.335106 - 0.243469i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.82843 q^{9} +O(q^{10})\)	\(q-0.414214 q^{3} +(0.335106 - 0.243469i) q^{5} +(0.309017 - 0.951057i) q^{7} -2.82843 q^{9} +(-1.50000 - 1.08981i) q^{11} +(-0.286215 - 0.880878i) q^{13} +(-0.138805 + 0.100848i) q^{15} +(-1.49535 - 1.08644i) q^{17} +(-1.82389 + 5.61334i) q^{19} +(-0.127999 + 0.393941i) q^{21} +(1.27625 + 3.92789i) q^{23} +(-1.49207 + 4.59211i) q^{25} +2.41421 q^{27} +(-3.39344 + 2.46548i) q^{29} +(-4.11870 - 2.99241i) q^{31} +(0.621320 + 0.451416i) q^{33} +(-0.127999 - 0.393941i) q^{35} +(-2.56365 + 1.86260i) q^{37} +(0.118554 + 0.364872i) q^{39} +(-1.74197 + 6.16162i) q^{41} +(-1.97517 - 6.07894i) q^{43} +(-0.947822 + 0.688633i) q^{45} +(-1.67924 - 5.16818i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.619395 + 0.450017i) q^{51} +(5.26832 - 3.82766i) q^{53} -0.767994 q^{55} +(0.755478 - 2.32512i) q^{57} +(-0.747288 - 2.29992i) q^{59} +(-3.64951 + 11.2320i) q^{61} +(-0.874032 + 2.68999i) q^{63} +(-0.310378 - 0.225503i) q^{65} +(-9.68253 + 7.03477i) q^{67} +(-0.528640 - 1.62699i) q^{69} +(-5.93853 - 4.31459i) q^{71} -0.191503 q^{73} +(0.618034 - 1.90211i) q^{75} +(-1.50000 + 1.08981i) q^{77} +7.16885 q^{79} +7.48528 q^{81} -0.886350 q^{83} -0.765615 q^{85} +(1.40561 - 1.02124i) q^{87} +(-5.55782 + 17.1052i) q^{89} -0.926210 q^{91} +(1.70602 + 1.23950i) q^{93} +(0.755478 + 2.32512i) q^{95} +(-15.7458 + 11.4400i) q^{97} +(4.24264 + 3.08246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7	\( 8 q + 8 q^{3} - 2 q^{5} - 2 q^{7} - 12 q^{11} + 10 q^{13} - 6 q^{15} + 12 q^{17} - 2 q^{19} - 2 q^{21} - 12 q^{23} + 4 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{31} - 12 q^{33} - 2 q^{35} + 14 q^{37} + 30 q^{39} - 18 q^{41} - 14 q^{43} - 8 q^{45} + 28 q^{47} - 2 q^{49} + 28 q^{51} + 4 q^{53} - 12 q^{55} - 30 q^{57} + 4 q^{59} - 4 q^{61} - 30 q^{65} - 28 q^{67} - 36 q^{69} - 44 q^{73} - 4 q^{75} - 12 q^{77} + 16 q^{79} - 8 q^{81} + 40 q^{83} - 12 q^{85} + 22 q^{87} + 14 q^{89} + 42 q^{93} - 30 q^{95} - 38 q^{97}+O(q^{100}) \) 8 * q + 8 * q^3 - 2 * q^5 - 2 * q^7 - 12 * q^11 + 10 * q^13 - 6 * q^15 + 12 * q^17 - 2 * q^19 - 2 * q^21 - 12 * q^23 + 4 * q^25 + 8 * q^27 - 2 * q^29 + 14 * q^31 - 12 * q^33 - 2 * q^35 + 14 * q^37 + 30 * q^39 - 18 * q^41 - 14 * q^43 - 8 * q^45 + 28 * q^47 - 2 * q^49 + 28 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 4 * q^59 - 4 * q^61 - 30 * q^65 - 28 * q^67 - 36 * q^69 - 44 * q^73 - 4 * q^75 - 12 * q^77 + 16 * q^79 - 8 * q^81 + 40 * q^83 - 12 * q^85 + 22 * q^87 + 14 * q^89 + 42 * q^93 - 30 * q^95 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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