LMFDB - Embedded newform 460.2.x.a.217.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [460,2,Mod(17,460)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("460.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(460, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([0, 11, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.4
Character	$\chi$	$=$	460.217
Dual form			460.2.x.a.53.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37822 + 0.299812i) q^{3} +(-1.16859 + 1.90641i) q^{5} +(1.39155 - 0.759843i) q^{7} +(-0.919306 + 0.419833i) q^{9} +(-0.541054 - 0.468826i) q^{11} +(-0.279660 + 0.512159i) q^{13} +(1.03901 - 2.97780i) q^{15} +(-5.53888 - 4.14635i) q^{17} +(-0.319647 + 2.22319i) q^{19} +(-1.69004 + 1.46443i) q^{21} +(-4.77560 - 0.440082i) q^{23} +(-2.26879 - 4.45563i) q^{25} +(4.52850 - 3.38999i) q^{27} +(-7.55638 + 1.08644i) q^{29} +(-1.90049 + 1.22137i) q^{31} +(0.886248 + 0.483928i) q^{33} +(-0.177581 + 3.54081i) q^{35} +(-4.22318 - 1.57517i) q^{37} +(0.231880 - 0.789711i) q^{39} +(1.16344 - 2.54758i) q^{41} +(0.909791 + 4.18224i) q^{43} +(0.273920 - 2.24319i) q^{45} +(-1.57635 - 1.57635i) q^{47} +(-2.42544 + 3.77406i) q^{49} +(8.87690 + 4.05394i) q^{51} +(-4.45752 - 8.16333i) q^{53} +(1.52604 - 0.483604i) q^{55} +(-0.225998 - 3.15987i) q^{57} +(2.38334 + 8.11691i) q^{59} +(7.46237 + 11.6117i) q^{61} +(-0.960253 + 1.28275i) q^{63} +(-0.649576 - 1.13165i) q^{65} +(6.27462 + 0.448770i) q^{67} +(6.71374 - 0.825255i) q^{69} +(4.98358 + 5.75136i) q^{71} +(-2.86187 - 3.82302i) q^{73} +(4.46273 + 5.46060i) q^{75} +(-1.10914 - 0.241278i) q^{77} +(3.15855 - 0.927433i) q^{79} +(-3.23941 + 3.73847i) q^{81} +(4.38759 - 11.7636i) q^{83} +(14.3773 - 5.71397i) q^{85} +(10.0886 - 3.76285i) q^{87} +(-11.5671 - 7.43371i) q^{89} +0.925193i q^{91} +(2.25310 - 2.25310i) q^{93} +(-3.86478 - 3.20738i) q^{95} +(0.127995 + 0.343167i) q^{97} +(0.694223 + 0.203842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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
$3$	−1.37822	+	0.299812i	−0.795713	+	0.173097i	−0.592004	−	0.805935i	$-0.701663\pi$
$3$	−1.37822	+	0.299812i	−0.795713	+	0.173097i	−0.203709	+	0.979032i	$0.565300\pi$
$4$		0			0
$5$	−1.16859	+	1.90641i	−0.522610	+	0.852572i
$5$	−1.16859	+	1.90641i	−0.522610	+	0.852572i
$6$		0			0
$7$	1.39155	−	0.759843i	0.525956	−	0.287194i	−0.194252	−	0.980952i	$-0.562228\pi$
$7$	1.39155	−	0.759843i	0.525956	−	0.287194i	0.720208	+	0.693758i	$0.244046\pi$
$8$		0			0
$9$	−0.919306	+	0.419833i	−0.306435	+	0.139944i
$10$		0			0
$11$	−0.541054	−	0.468826i	−0.163134	−	0.141356i	0.569469	−	0.822013i	$-0.307149\pi$
$11$	−0.541054	−	0.468826i	−0.163134	−	0.141356i	−0.732602	+	0.680657i	$0.761694\pi$
$12$		0			0
$13$	−0.279660	+	0.512159i	−0.0775637	+	0.142047i	−0.913582	−	0.406654i	$-0.866696\pi$
$13$	−0.279660	+	0.512159i	−0.0775637	+	0.142047i	0.836019	+	0.548701i	$0.184877\pi$
$14$		0			0
$15$	1.03901	−	2.97780i	0.268270	−	0.768865i
$16$		0			0
$17$	−5.53888	−	4.14635i	−1.34338	−	1.00564i	−0.997735	−	0.0672719i	$-0.978571\pi$
$17$	−5.53888	−	4.14635i	−1.34338	−	1.00564i	−0.345641	−	0.938367i	$-0.612339\pi$
$18$		0			0
$19$	−0.319647	+	2.22319i	−0.0733320	+	0.510035i	0.919740	+	0.392528i	$0.128399\pi$
$19$	−0.319647	+	2.22319i	−0.0733320	+	0.510035i	−0.993072	+	0.117507i	$0.962510\pi$
$20$		0			0
$21$	−1.69004	+	1.46443i	−0.368798	+	0.319565i
$22$		0			0
$23$	−4.77560	−	0.440082i	−0.995781	−	0.0917635i
$23$	−4.77560	−	0.440082i	−0.995781	−	0.0917635i
$24$		0			0
$25$	−2.26879	−	4.45563i	−0.453757	−	0.891125i
$26$		0			0
$27$	4.52850	−	3.38999i	0.871510	−	0.652404i
$28$		0			0
$29$	−7.55638	+	1.08644i	−1.40319	+	0.201748i	−0.801982	−	0.597348i	$-0.796221\pi$
$29$	−7.55638	+	1.08644i	−1.40319	+	0.201748i	−0.601203	+	0.799096i	$0.705312\pi$
$30$		0			0
$31$	−1.90049	+	1.22137i	−0.341338	+	0.219364i	−0.700067	−	0.714077i	$-0.746847\pi$
$31$	−1.90049	+	1.22137i	−0.341338	+	0.219364i	0.358729	+	0.933442i	$0.383210\pi$
$32$		0			0
$33$	0.886248	+	0.483928i	0.154276	+	0.0842411i
$34$		0			0
$35$	−0.177581	+	3.54081i	−0.0300167	+	0.598506i
$36$		0			0
$37$	−4.22318	−	1.57517i	−0.694287	−	0.258956i	−0.0225503	−	0.999746i	$-0.507179\pi$
$37$	−4.22318	−	1.57517i	−0.694287	−	0.258956i	−0.671737	+	0.740790i	$0.734451\pi$
$38$		0			0
$39$	0.231880	−	0.789711i	0.0371305	−	0.126455i
$40$		0			0
$41$	1.16344	−	2.54758i	0.181699	−	0.397865i	−0.796763	−	0.604292i	$-0.793456\pi$
$41$	1.16344	−	2.54758i	0.181699	−	0.397865i	0.978462	+	0.206427i	$0.0661834\pi$
$42$		0			0
$43$	0.909791	+	4.18224i	0.138742	+	0.637786i	0.993018	+	0.117966i	$0.0376374\pi$
$43$	0.909791	+	4.18224i	0.138742	+	0.637786i	−0.854276	+	0.519820i	$0.825999\pi$
$44$		0			0
$45$	0.273920	−	2.24319i	0.0408336	−	0.334395i
$46$		0			0
$47$	−1.57635	−	1.57635i	−0.229934	−	0.229934i	0.582731	−	0.812665i	$-0.301984\pi$
$47$	−1.57635	−	1.57635i	−0.229934	−	0.229934i	−0.812665	+	0.582731i	$0.801984\pi$
$48$		0			0
$49$	−2.42544	+	3.77406i	−0.346491	+	0.539151i
$50$		0			0
$51$	8.87690	+	4.05394i	1.24301	+	0.567666i
$52$		0			0
$53$	−4.45752	−	8.16333i	−0.612287	−	1.12132i	−0.981407	−	0.191938i	$-0.938523\pi$
$53$	−4.45752	−	8.16333i	−0.612287	−	1.12132i	0.369120	−	0.929382i	$-0.379659\pi$
$54$		0			0
$55$	1.52604	−	0.483604i	0.205772	−	0.0652091i
$56$		0			0
$57$	−0.225998	−	3.15987i	−0.0299342	−	0.418535i
$58$		0			0
$59$	2.38334	+	8.11691i	0.310284	+	1.05673i	0.956052	+	0.293198i	$0.0947194\pi$
$59$	2.38334	+	8.11691i	0.310284	+	1.05673i	−0.645767	+	0.763534i	$0.723462\pi$
$60$		0			0
$61$	7.46237	+	11.6117i	0.955459	+	1.48672i	0.871583	+	0.490247i	$0.163094\pi$
$61$	7.46237	+	11.6117i	0.955459	+	1.48672i	0.0838757	+	0.996476i	$0.473270\pi$
$62$		0			0
$63$	−0.960253	+	1.28275i	−0.120980	+	0.161611i
$64$		0			0
$65$	−0.649576	−	1.13165i	−0.0805700	−	0.140364i
$66$		0			0
$67$	6.27462	+	0.448770i	0.766567	+	0.0548259i	0.449145	−	0.893459i	$-0.351728\pi$
$67$	6.27462	+	0.448770i	0.766567	+	0.0548259i	0.317421	+	0.948285i	$0.397183\pi$
$68$		0			0
$69$	6.71374	−	0.825255i	0.808240	−	0.0993490i
$70$		0			0
$71$	4.98358	+	5.75136i	0.591443	+	0.682561i	0.970025	−	0.243007i	$-0.0781336\pi$
$71$	4.98358	+	5.75136i	0.591443	+	0.682561i	−0.378582	+	0.925568i	$0.623588\pi$
$72$		0			0
$73$	−2.86187	−	3.82302i	−0.334957	−	0.447450i	0.601165	−	0.799125i	$-0.294703\pi$
$73$	−2.86187	−	3.82302i	−0.334957	−	0.447450i	−0.936122	+	0.351674i	$0.885612\pi$
$74$		0			0
$75$	4.46273	+	5.46060i	0.515311	+	0.630536i
$76$		0			0
$77$	−1.10914	−	0.241278i	−0.126398	−	0.0274962i
$78$		0			0
$79$	3.15855	−	0.927433i	0.355364	−	0.104344i	−0.0991776	−	0.995070i	$-0.531621\pi$
$79$	3.15855	−	0.927433i	0.355364	−	0.104344i	0.454542	+	0.890725i	$0.349803\pi$
$80$		0			0
$81$	−3.23941	+	3.73847i	−0.359934	+	0.415386i
$82$		0			0
$83$	4.38759	−	11.7636i	0.481600	−	1.29122i	−0.438216	−	0.898870i	$-0.644389\pi$
$83$	4.38759	−	11.7636i	0.481600	−	1.29122i	0.919816	−	0.392350i	$-0.128338\pi$
$84$		0			0
$85$	14.3773	−	5.71397i	1.55944	−	0.619767i
$86$		0			0
$87$	10.0886	−	3.76285i	1.08161	−	0.403420i
$88$		0			0
$89$	−11.5671	−	7.43371i	−1.22611	−	0.787972i	−0.242828	−	0.970069i	$-0.578075\pi$
$89$	−11.5671	−	7.43371i	−1.22611	−	0.787972i	−0.983280	+	0.182098i	$0.941711\pi$
$90$		0			0
$91$			0.925193i			0.0969865i
$92$		0			0
$93$	2.25310	−	2.25310i	0.233636	−	0.233636i
$94$		0			0
$95$	−3.86478	−	3.20738i	−0.396518	−	0.329070i
$96$		0			0
$97$	0.127995	+	0.343167i	0.0129959	+	0.0348433i	0.943286	−	0.331982i	$-0.107717\pi$
$97$	0.127995	+	0.343167i	0.0129959	+	0.0348433i	−0.930290	+	0.366825i	$0.880445\pi$
$98$		0			0
$99$	0.694223	+	0.203842i	0.0697720	+	0.0204869i
$100$		0			0
$101$	5.36204	+	11.7412i	0.533543	+	1.16830i	0.964053	+	0.265710i	$0.0856065\pi$
$101$	5.36204	+	11.7412i	0.533543	+	1.16830i	−0.430510	+	0.902586i	$0.641666\pi$
$102$		0			0
$103$	−1.22332	+	0.0874933i	−0.120537	+	0.00862097i	−0.131477	−	0.991319i	$-0.541972\pi$
$103$	−1.22332	+	0.0874933i	−0.120537	+	0.00862097i	0.0109404	+	0.999940i	$0.496517\pi$
$104$		0			0
$105$	−0.816833	−	4.93324i	−0.0797147	−	0.481435i
$106$		0			0
$107$	−2.89056	+	13.2877i	−0.279441	+	1.28457i	0.596679	+	0.802480i	$0.296486\pi$
$107$	−2.89056	+	13.2877i	−0.279441	+	1.28457i	−0.876121	+	0.482092i	$0.839877\pi$
$108$		0			0
$109$	0.790983	+	5.50141i	0.0757625	+	0.526940i	0.991993	+	0.126289i	$0.0403067\pi$
$109$	0.790983	+	5.50141i	0.0757625	+	0.526940i	−0.916231	+	0.400650i	$0.868784\pi$
$110$		0			0
$111$	6.29271	+	0.904755i	0.597277	+	0.0858755i
$112$		0			0
$113$	−0.837699	+	11.7126i	−0.0788041	+	1.10183i	0.792106	+	0.610383i	$0.208985\pi$
$113$	−0.837699	+	11.7126i	−0.0788041	+	1.10183i	−0.870910	+	0.491442i	$0.836470\pi$
$114$		0			0
$115$	6.41970	−	8.58996i	0.598640	−	0.801018i
$116$		0			0
$117$	0.0420719	−	0.588242i	0.00388955	−	0.0543830i
$118$		0			0
$119$	−10.8582	−	1.56117i	−0.995370	−	0.143113i
$120$		0			0
$121$	−1.49252	−	10.3807i	−0.135684	−	0.943701i
$122$		0			0
$123$	−0.839676	+	3.85993i	−0.0757110	+	0.348038i
$124$		0			0
$125$	11.1455	+	0.881574i	0.996886	+	0.0788504i
$126$		0			0
$127$	2.67031	−	0.190984i	0.236952	−	0.0169471i	0.0476418	−	0.998864i	$-0.484829\pi$
$127$	2.67031	−	0.190984i	0.236952	−	0.0169471i	0.189310	+	0.981917i	$0.439375\pi$
$128$		0			0
$129$	−2.50778	−	5.49126i	−0.220797	−	0.483479i
$130$		0			0
$131$	11.5292	+	3.38528i	1.00731	+	0.295774i	0.743454	−	0.668788i	$-0.233186\pi$
$131$	11.5292	+	3.38528i	1.00731	+	0.295774i	0.263859	+	0.964561i	$0.415005\pi$
$132$		0			0
$133$	1.24447	+	3.33656i	0.107910	+	0.289317i
$134$		0			0
$135$	1.17074	+	12.5947i	0.100761	+	1.08398i
$136$		0			0
$137$	−8.25423	+	8.25423i	−0.705207	+	0.705207i	−0.965523	−	0.260317i	$-0.916173\pi$
$137$	−8.25423	+	8.25423i	−0.705207	+	0.705207i	0.260317	+	0.965523i	$0.416173\pi$
$138$		0			0
$139$		−	10.2908i		−	0.872851i	−0.899740	−	0.436426i	$-0.856244\pi$
$139$		−	10.2908i		−	0.872851i	0.899740	−	0.436426i	$-0.143756\pi$
$140$		0			0
$141$	2.64515	+	1.69994i	0.222762	+	0.143161i
$142$		0			0
$143$	0.391425	−	0.145994i	0.0327326	−	0.0122086i
$144$		0			0
$145$	6.75912	−	15.6752i	0.561315	−	1.30175i
$146$		0			0
$147$	2.21127	−	5.92864i	0.182382	−	0.488986i
$148$		0			0
$149$	−5.43492	+	6.27223i	−0.445246	+	0.513841i	−0.933361	−	0.358938i	$-0.883139\pi$
$149$	−5.43492	+	6.27223i	−0.445246	+	0.513841i	0.488116	+	0.872779i	$0.337684\pi$
$150$		0			0
$151$	−12.0285	+	3.53188i	−0.978864	+	0.287420i	−0.731755	−	0.681567i	$-0.761299\pi$
$151$	−12.0285	+	3.53188i	−0.978864	+	0.287420i	−0.247109	+	0.968988i	$0.579480\pi$
$152$		0			0
$153$	6.83270	+	1.48636i	0.552391	+	0.120165i
$154$		0			0
$155$	−0.107535	−	5.05039i	−0.00863738	−	0.405657i
$156$		0			0
$157$	1.87850	+	2.50938i	0.149920	+	0.200270i	0.869214	−	0.494436i	$-0.164625\pi$
$157$	1.87850	+	2.50938i	0.149920	+	0.200270i	−0.719294	+	0.694706i	$0.755534\pi$
$158$		0			0
$159$	8.59089	+	9.91441i	0.681302	+	0.786264i
$160$		0			0
$161$	−6.97987	+	3.01631i	−0.550091	+	0.237718i
$162$		0			0
$163$	−22.4935	−	1.60877i	−1.76183	−	0.126008i	−0.847452	−	0.530872i	$-0.821864\pi$
$163$	−22.4935	−	1.60877i	−1.76183	−	0.126008i	−0.914377	+	0.404864i	$0.867319\pi$
$164$		0			0
$165$	−1.95823	+	1.12404i	−0.152448	+	0.0875062i
$166$		0			0
$167$	1.26001	−	1.68318i	0.0975028	−	0.130248i	−0.749137	−	0.662416i	$-0.769531\pi$
$167$	1.26001	−	1.68318i	0.0975028	−	0.130248i	0.846639	+	0.532167i	$0.178622\pi$
$168$		0			0
$169$	6.84423	+	10.6498i	0.526479	+	0.819218i
$170$		0			0
$171$	−0.639516	−	2.17799i	−0.0489050	−	0.166555i
$172$		0			0
$173$	0.656520	+	9.17935i	0.0499143	+	0.697893i	0.959381	+	0.282115i	$0.0910360\pi$
$173$	0.656520	+	9.17935i	0.0499143	+	0.697893i	−0.909466	+	0.415778i	$0.863509\pi$
$174$		0			0
$175$	−6.54271	−	4.47630i	−0.494582	−	0.338377i
$176$		0			0
$177$	−5.71831	−	10.4723i	−0.429814	−	0.787146i
$178$		0			0
$179$	−18.5786	−	8.48456i	−1.38863	−	0.634166i	−0.425934	−	0.904754i	$-0.640054\pi$
$179$	−18.5786	−	8.48456i	−1.38863	−	0.634166i	−0.962695	+	0.270589i	$0.912782\pi$
$180$		0			0
$181$	−5.27006	+	8.20037i	−0.391721	+	0.609529i	−0.979969	−	0.199151i	$-0.936181\pi$
$181$	−5.27006	+	8.20037i	−0.391721	+	0.609529i	0.588248	+	0.808680i	$0.299818\pi$
$182$		0			0
$183$	−13.7661	−	13.7661i	−1.01762	−	1.01762i
$184$		0			0
$185$	7.93808	−	6.21039i	0.583620	−	0.456597i
$186$		0			0
$187$	1.05291	+	4.84017i	0.0769968	+	0.353948i
$188$		0			0
$189$	3.72576	−	8.15829i	0.271010	−	0.593428i
$190$		0			0
$191$	3.27929	−	11.1682i	0.237281	−	0.808106i	−0.751628	−	0.659587i	$-0.770731\pi$
$191$	3.27929	−	11.1682i	0.237281	−	0.808106i	0.988910	−	0.148519i	$-0.0474506\pi$
$192$		0			0
$193$	−4.27006	−	1.59265i	−0.307365	−	0.114641i	0.191048	−	0.981581i	$-0.438811\pi$
$193$	−4.27006	−	1.59265i	−0.307365	−	0.114641i	−0.498414	+	0.866939i	$0.666084\pi$
$194$		0			0
$195$	1.23454	+	1.36491i	0.0884072	+	0.0977431i
$196$		0			0
$197$	−2.60703	−	1.42354i	−0.185743	−	0.101423i	0.383687	−	0.923463i	$-0.374654\pi$
$197$	−2.60703	−	1.42354i	−0.185743	−	0.101423i	−0.569430	+	0.822040i	$0.692836\pi$
$198$		0			0
$199$	15.5257	−	9.97775i	1.10059	−	0.707304i	0.141365	−	0.989958i	$-0.454851\pi$
$199$	15.5257	−	9.97775i	1.10059	−	0.707304i	0.959222	+	0.282653i	$0.0912146\pi$
$200$		0			0
$201$	−8.78232	+	1.26271i	−0.619457	+	0.0890645i
$202$		0			0
$203$	−9.68955	+	7.25351i	−0.680073	+	0.509097i
$204$		0			0
$205$	3.49714	+	5.19507i	0.244251	+	0.362840i
$206$		0			0
$207$	4.57500	−	1.60038i	0.317984	−	0.111234i
$208$		0			0
$209$	1.21524	−	1.05301i	0.0840596	−	0.0728381i
$210$		0			0
$211$	0.985488	−	6.85422i	0.0678438	−	0.471864i	−0.927370	−	0.374145i	$-0.877936\pi$
$211$	0.985488	−	6.85422i	0.0678438	−	0.471864i	0.995214	−	0.0977190i	$-0.0311546\pi$
$212$		0			0
$213$	−8.59278	−	6.43248i	−0.588768	−	0.440746i
$214$		0			0
$215$	−9.03624	−	3.15290i	−0.616266	−	0.215026i
$216$		0			0
$217$	−1.71657	+	3.14367i	−0.116529	+	0.213406i
$218$		0			0
$219$	5.09047	+	4.41092i	0.343982	+	0.298062i
$220$		0			0
$221$	3.67260	−	1.67722i	0.247046	−	0.112822i
$222$		0			0
$223$	9.61072	−	5.24785i	0.643581	−	0.351422i	−0.124085	−	0.992272i	$-0.539600\pi$
$223$	9.61072	−	5.24785i	0.643581	−	0.351422i	0.767666	+	0.640850i	$0.221418\pi$
$224$		0			0
$225$	3.95633	+	3.14357i	0.263755	+	0.209572i
$226$		0			0
$227$	10.1726	−	2.21291i	0.675178	−	0.146876i	0.138113	−	0.990417i	$-0.455896\pi$
$227$	10.1726	−	2.21291i	0.675178	−	0.146876i	0.537066	+	0.843540i	$0.319533\pi$
$228$		0			0
$229$	−6.21889			−0.410956			−0.205478	−	0.978662i	$-0.565875\pi$
$229$	−6.21889			−0.410956			−0.205478	+	0.978662i	$0.565875\pi$
$230$		0			0
$231$	1.60097			0.105336
$232$		0			0
$233$	−22.8397	+	4.96847i	−1.49628	+	0.325495i	−0.884877	−	0.465826i	$-0.845757\pi$
$233$	−22.8397	+	4.96847i	−1.49628	+	0.325495i	−0.611401	+	0.791321i	$0.709394\pi$
$234$		0			0
$235$	4.84727	−	1.16306i	0.316201	−	0.0758694i
$236$		0			0
$237$	−4.07510	+	2.22517i	−0.264706	+	0.144541i
$238$		0			0
$239$	−16.2089	+	7.40234i	−1.04846	+	0.478818i	−0.863722	−	0.503969i	$-0.831873\pi$
$239$	−16.2089	+	7.40234i	−1.04846	+	0.478818i	−0.184743	+	0.982787i	$0.559145\pi$
$240$		0			0
$241$	−10.1033	−	8.75457i	−0.650812	−	0.563931i	0.265642	−	0.964072i	$-0.414416\pi$
$241$	−10.1033	−	8.75457i	−0.650812	−	0.563931i	−0.916454	+	0.400140i	$0.868961\pi$
$242$		0			0
$243$	−4.78928	+	8.77091i	−0.307232	+	0.562654i
$244$		0			0
$245$	−4.36054	−	9.03421i	−0.278585	−	0.577174i
$246$		0			0
$247$	−1.04924	−	0.785448i	−0.0667613	−	0.0499769i
$248$		0			0
$249$	−2.52017	+	17.5282i	−0.159709	+	1.11080i
$250$		0			0
$251$	−8.56631	+	7.42275i	−0.540701	+	0.468520i	−0.881877	−	0.471479i	$-0.843720\pi$
$251$	−8.56631	+	7.42275i	−0.540701	+	0.468520i	0.341176	+	0.939999i	$0.389175\pi$
$252$		0			0
$253$	2.37753	+	2.47703i	0.149474	+	0.155730i
$254$		0			0
$255$	−18.1019	+	12.1856i	−1.13359	+	0.763091i
$256$		0			0
$257$	2.66250	−	1.99313i	0.166082	−	0.124328i	−0.513004	−	0.858386i	$-0.671467\pi$
$257$	2.66250	−	1.99313i	0.166082	−	0.124328i	0.679086	+	0.734059i	$0.262376\pi$
$258$		0			0
$259$	−7.07365	+	1.01704i	−0.439535	+	0.0631956i
$260$		0			0
$261$	6.49051	−	4.17119i	0.401752	−	0.258190i
$262$		0			0
$263$	24.3920	+	13.3190i	1.50407	+	0.821286i	0.999123	−	0.0418619i	$-0.0133289\pi$
$263$	24.3920	+	13.3190i	1.50407	+	0.821286i	0.504950	+	0.863148i	$0.331511\pi$
$264$		0			0
$265$	20.7717	+	1.04176i	1.27599	+	0.0639945i
$266$		0			0
$267$	18.1706	+	6.77730i	1.11203	+	0.414764i
$268$		0			0
$269$	3.56635	−	12.1459i	0.217444	−	0.740547i	−0.776447	−	0.630182i	$-0.782980\pi$
$269$	3.56635	−	12.1459i	0.217444	−	0.740547i	0.993891	−	0.110364i	$-0.0352017\pi$
$270$		0			0
$271$	2.57041	−	5.62842i	0.156141	−	0.341902i	−0.815353	−	0.578964i	$-0.803457\pi$
$271$	2.57041	−	5.62842i	0.156141	−	0.341902i	0.971495	+	0.237062i	$0.0761845\pi$
$272$		0			0
$273$	−0.277384	−	1.27511i	−0.0167881	−	0.0771734i
$274$		0			0
$275$	−0.861377	+	3.47440i	−0.0519430	+	0.209514i
$276$		0			0
$277$	−1.59542	−	1.59542i	−0.0958597	−	0.0958597i	0.657551	−	0.753410i	$-0.271593\pi$
$277$	−1.59542	−	1.59542i	−0.0958597	−	0.0958597i	−0.753410	+	0.657551i	$0.771593\pi$
$278$		0			0
$279$	1.23436	−	1.92070i	0.0738991	−	0.114989i
$280$		0			0
$281$	−19.1579	−	8.74912i	−1.14286	−	0.521929i	−0.248218	−	0.968704i	$-0.579845\pi$
$281$	−19.1579	−	8.74912i	−1.14286	−	0.521929i	−0.894646	+	0.446776i	$0.852572\pi$
$282$		0			0
$283$	6.10470	+	11.1799i	0.362887	+	0.664577i	0.993788	−	0.111285i	$-0.0354968\pi$
$283$	6.10470	+	11.1799i	0.362887	+	0.664577i	−0.630902	+	0.775863i	$0.717315\pi$
$284$		0			0
$285$	6.28810	+	3.26175i	0.372475	+	0.193210i
$286$		0			0
$287$	−0.316777	−	4.42912i	−0.0186987	−	0.261442i
$288$		0			0
$289$	8.69749	+	29.6209i	0.511617	+	1.74241i
$290$		0			0
$291$	−0.279290	−	0.434583i	−0.0163723	−	0.0254757i
$292$		0			0
$293$	7.43156	−	9.92740i	0.434156	−	0.579965i	−0.529097	−	0.848562i	$-0.677469\pi$
$293$	7.43156	−	9.92740i	0.434156	−	0.579965i	0.963253	+	0.268597i	$0.0865600\pi$
$294$		0			0
$295$	−18.2593	−	4.94173i	−1.06310	−	0.287719i
$296$		0			0
$297$	−4.03948	−	0.288909i	−0.234394	−	0.0167642i
$298$		0			0
$299$	1.56094	−	2.32279i	0.0902713	−	0.134331i
$300$		0			0
$301$	4.44387	+	5.12850i	0.256140	+	0.295602i
$302$		0			0
$303$	−10.9102	−	14.5743i	−0.626775	−	0.837274i
$304$		0			0
$305$	−30.8571	+	0.657019i	−1.76687	+	0.0376208i
$306$		0			0
$307$	−33.7201	−	7.33536i	−1.92451	−	0.418651i	−0.999224	−	0.0393784i	$-0.987462\pi$
$307$	−33.7201	−	7.33536i	−1.92451	−	0.418651i	−0.925285	−	0.379273i	$-0.876174\pi$
$308$		0			0
$309$	1.65976	−	0.487350i	0.0944205	−	0.0277244i
$310$		0			0
$311$	−10.7749	+	12.4348i	−0.610986	+	0.705115i	−0.973969	−	0.226680i	$-0.927213\pi$
$311$	−10.7749	+	12.4348i	−0.610986	+	0.705115i	0.362983	+	0.931796i	$0.381758\pi$
$312$		0			0
$313$	9.24427	−	24.7849i	0.522517	−	1.40092i	−0.361018	−	0.932559i	$-0.617571\pi$
$313$	9.24427	−	24.7849i	0.522517	−	1.40092i	0.883535	−	0.468364i	$-0.155157\pi$
$314$		0			0
$315$	−1.32330	−	3.32964i	−0.0745593	−	0.187604i
$316$		0			0
$317$	−6.36818	+	2.37521i	−0.357673	+	0.133405i	−0.521876	−	0.853022i	$-0.674768\pi$
$317$	−6.36818	+	2.37521i	−0.357673	+	0.133405i	0.164203	+	0.986427i	$0.447495\pi$
$318$		0			0
$319$	4.59776	+	2.95480i	0.257425	+	0.165437i
$320$		0			0
$321$		−	19.1800i		−	1.07052i
$322$		0			0
$323$	10.9886	−	10.9886i	0.611424	−	0.611424i
$324$		0			0
$325$	2.91648	+	0.0840809i	0.161777	+	0.00466397i
$326$		0			0
$327$	−2.73954	−	7.34498i	−0.151497	−	0.406178i
$328$		0			0
$329$	−3.39134	−	0.995788i	−0.186971	−	0.0548996i
$330$		0			0
$331$	−5.32475	−	11.6596i	−0.292675	−	0.640869i	0.704986	−	0.709221i	$-0.250953\pi$
$331$	−5.32475	−	11.6596i	−0.292675	−	0.640869i	−0.997661	+	0.0683521i	$0.978226\pi$
$332$		0			0
$333$	4.54370	−	0.324972i	0.248993	−	0.0178084i
$334$		0			0
$335$	−8.18801	+	11.4376i	−0.447359	+	0.624901i
$336$		0			0
$337$	3.07588	−	14.1396i	0.167554	−	0.770232i	−0.814277	−	0.580476i	$-0.802867\pi$
$337$	3.07588	−	14.1396i	0.167554	−	0.770232i	0.981831	−	0.189756i	$-0.0607698\pi$
$338$		0			0
$339$	−2.35704	−	16.3936i	−0.128017	−	0.890377i
$340$		0			0
$341$	1.60088	+	0.230171i	0.0866923	+	0.0124645i
$342$		0			0
$343$	−1.29918	+	18.1649i	−0.0701490	+	0.980811i
$344$		0			0
$345$	−6.27235	+	13.7635i	−0.337692	+	0.741003i
$346$		0			0
$347$	−1.71503	+	23.9793i	−0.0920678	+	1.28728i	0.715964	+	0.698137i	$0.245987\pi$
$347$	−1.71503	+	23.9793i	−0.0920678	+	1.28728i	−0.808032	+	0.589139i	$0.799467\pi$
$348$		0			0
$349$	23.1306	+	3.32567i	1.23815	+	0.178019i	0.730120	−	0.683319i	$-0.239464\pi$
$349$	23.1306	+	3.32567i	1.23815	+	0.178019i	0.508032	+	0.861338i	$0.330373\pi$
$350$		0			0
$351$	0.469775	+	3.26736i	0.0250747	+	0.174399i
$352$		0			0
$353$	−0.217653	+	1.00054i	−0.0115845	+	0.0532531i	−0.982576	−	0.185860i	$-0.940493\pi$
$353$	−0.217653	+	1.00054i	−0.0115845	+	0.0532531i	0.970992	+	0.239113i	$0.0768566\pi$
$354$		0			0
$355$	−16.7882	+	2.77975i	−0.891026	+	0.147534i
$356$		0			0
$357$	15.4330	−	1.10379i	0.816801	−	0.0584188i
$358$		0			0
$359$	−11.1531	−	24.4219i	−0.588639	−	1.28894i	−0.936261	−	0.351304i	$-0.885738\pi$
$359$	−11.1531	−	24.4219i	−0.588639	−	1.28894i	0.347623	−	0.937634i	$-0.386989\pi$
$360$		0			0
$361$	13.3900	+	3.93165i	0.704735	+	0.206929i
$362$		0			0
$363$	5.16928	+	13.8594i	0.271317	+	0.727429i
$364$		0			0
$365$	10.6326	−	0.988356i	0.556535	−	0.0517329i
$366$		0			0
$367$	6.08840	−	6.08840i	0.317812	−	0.317812i	−0.530114	−	0.847926i	$-0.677851\pi$
$367$	6.08840	−	6.08840i	0.317812	−	0.317812i	0.847926	+	0.530114i	$0.177851\pi$
$368$		0			0
$369$			2.83046i			0.147348i
$370$		0			0
$371$	−12.4057	−	7.97267i	−0.644072	−	0.413920i
$372$		0			0
$373$	19.0987	−	7.12344i	0.988892	−	0.368837i	0.197604	−	0.980282i	$-0.436684\pi$
$373$	19.0987	−	7.12344i	0.988892	−	0.368837i	0.791287	+	0.611444i	$0.209411\pi$
$374$		0			0
$375$	−15.6252	+	2.12657i	−0.806884	+	0.109816i
$376$		0			0
$377$	1.55679	−	4.17391i	0.0801786	−	0.214967i
$378$		0			0
$379$	22.7528	−	26.2581i	1.16873	−	1.34879i	0.243266	−	0.969960i	$-0.421781\pi$
$379$	22.7528	−	26.2581i	1.16873	−	1.34879i	0.925467	−	0.378829i	$-0.123673\pi$
$380$		0			0
$381$	−3.62300	+	1.06381i	−0.185612	+	0.0545006i
$382$		0			0
$383$	28.9004	+	6.28689i	1.47674	+	0.321245i	0.877598	−	0.479397i	$-0.159145\pi$
$383$	28.9004	+	6.28689i	1.47674	+	0.321245i	0.599143	+	0.800642i	$0.295508\pi$
$384$		0			0
$385$	1.75610	−	1.83251i	0.0894993	−	0.0933935i
$386$		0			0
$387$	−2.59222	−	3.46280i	−0.131770	−	0.176024i
$388$		0			0
$389$	8.09856	+	9.34624i	0.410613	+	0.473873i	0.922955	−	0.384909i	$-0.125767\pi$
$389$	8.09856	+	9.34624i	0.410613	+	0.473873i	−0.512341	+	0.858782i	$0.671222\pi$
$390$		0			0
$391$	24.6267	+	22.2389i	1.24543	+	1.12467i
$392$		0			0
$393$	−16.9047	−	1.20905i	−0.852729	−	0.0609884i
$394$		0			0
$395$	−1.92299	+	7.10527i	−0.0967559	+	0.357505i
$396$		0			0
$397$	−9.61342	+	12.8420i	−0.482484	+	0.644523i	−0.974054	−	0.226315i	$-0.927332\pi$
$397$	−9.61342	+	12.8420i	−0.482484	+	0.644523i	0.491570	+	0.870838i	$0.336423\pi$
$398$		0			0
$399$	−2.71550	−	4.22539i	−0.135945	−	0.211534i
$400$		0			0
$401$	−2.21376	−	7.53937i	−0.110550	−	0.376498i	0.885570	−	0.464506i	$-0.153768\pi$
$401$	−2.21376	−	7.53937i	−0.110550	−	0.376498i	−0.996120	+	0.0880078i	$0.971950\pi$
$402$		0			0
$403$	−0.0940450	−	1.31492i	−0.00468471	−	0.0655008i
$404$		0			0
$405$	−3.34152	−	10.5444i	−0.166041	−	0.523955i
$406$		0			0
$407$	1.54649	+	2.83219i	0.0766567	+	0.140386i
$408$		0			0
$409$	4.05337	+	1.85111i	0.200426	+	0.0915317i	0.513100	−	0.858329i	$-0.328497\pi$
$409$	4.05337	+	1.85111i	0.200426	+	0.0915317i	−0.312673	+	0.949861i	$0.601224\pi$
$410$		0			0
$411$	8.90139	−	13.8508i	0.439073	−	0.683211i
$412$		0			0
$413$	9.48412	+	9.48412i	0.466683	+	0.466683i
$414$		0			0
$415$	17.2989	+	22.1113i	0.849169	+	1.08540i
$416$		0			0
$417$	3.08530	+	14.1829i	0.151088	+	0.694539i
$418$		0			0
$419$	14.6025	−	31.9750i	0.713379	−	1.56208i	−0.109579	−	0.993978i	$-0.534950\pi$
$419$	14.6025	−	31.9750i	0.713379	−	1.56208i	0.822957	−	0.568103i	$-0.192323\pi$
$420$		0			0
$421$	−4.30844	+	14.6732i	−0.209981	+	0.715128i	0.785389	+	0.619003i	$0.212463\pi$
$421$	−4.30844	+	14.6732i	−0.209981	+	0.715128i	−0.995369	+	0.0961253i	$0.969355\pi$
$422$		0			0
$423$	2.11095	+	0.787343i	0.102638	+	0.0382819i
$424$		0			0
$425$	−5.90807	+	34.0864i	−0.286583	+	1.65343i
$426$		0			0
$427$	19.2073	+	10.4880i	0.929507	+	0.507549i
$428$		0			0
$429$	−0.495697	+	0.318565i	−0.0239325	+	0.0153805i
$430$		0			0
$431$	36.1886	−	5.20313i	1.74314	−	0.250626i	0.804116	−	0.594473i	$-0.202639\pi$
$431$	36.1886	−	5.20313i	1.74314	−	0.250626i	0.939026	+	0.343847i	$0.111730\pi$
$432$		0			0
$433$	9.77554	−	7.31788i	0.469783	−	0.351675i	−0.338009	−	0.941143i	$-0.609753\pi$
$433$	9.77554	−	7.31788i	0.469783	−	0.351675i	0.807792	+	0.589468i	$0.200663\pi$
$434$		0			0
$435$	−4.61592	+	23.6302i	−0.221316	+	1.13298i
$436$		0			0
$437$	2.50489	−	10.4764i	0.119825	−	0.501154i
$438$		0			0
$439$	−26.6688	+	23.1087i	−1.27283	+	1.10292i	−0.283237	+	0.959050i	$0.591408\pi$
$439$	−26.6688	+	23.1087i	−1.27283	+	1.10292i	−0.989597	+	0.143867i	$0.954046\pi$
$440$		0			0
$441$	0.645247	−	4.48779i	0.0307261	−	0.213704i
$442$		0			0
$443$	−4.92817	−	3.68918i	−0.234145	−	0.175278i	0.475763	−	0.879574i	$-0.342172\pi$
$443$	−4.92817	−	3.68918i	−0.234145	−	0.175278i	−0.709907	+	0.704295i	$0.751263\pi$
$444$		0			0
$445$	27.6889	−	13.3646i	1.31258	−	0.633543i
$446$		0			0
$447$	5.60999	−	10.2739i	0.265344	−	0.485940i
$448$		0			0
$449$	24.3811	+	21.1263i	1.15061	+	0.997013i	0.999964	+	0.00842621i	$0.00268218\pi$
$449$	24.3811	+	21.1263i	1.15061	+	0.997013i	0.150650	+	0.988587i	$0.451863\pi$
$450$		0			0
$451$	−1.82386	+	0.832927i	−0.0858820	+	0.0392210i
$452$		0			0
$453$	15.5189	−	8.47398i	0.729143	−	0.398142i
$454$		0			0
$455$	−1.76379	−	1.08117i	−0.0826880	−	0.0506861i
$456$		0			0
$457$	−19.1633	+	4.16872i	−0.896421	+	0.195005i	−0.637095	−	0.770785i	$-0.719864\pi$
$457$	−19.1633	+	4.16872i	−0.896421	+	0.195005i	−0.259326	+	0.965790i	$0.583501\pi$
$458$		0			0
$459$	−39.1389			−1.82685
$460$		0			0
$461$	9.17938			0.427526			0.213763	−	0.976886i	$-0.431428\pi$
$461$	9.17938			0.427526			0.213763	+	0.976886i	$0.431428\pi$
$462$		0			0
$463$	19.0371	−	4.14127i	0.884729	−	0.192461i	0.252829	−	0.967511i	$-0.418639\pi$
$463$	19.0371	−	4.14127i	0.884729	−	0.192461i	0.631900	+	0.775050i	$0.282275\pi$
$464$		0			0
$465$	1.66237	+	6.92828i	0.0770908	+	0.321291i
$466$		0			0
$467$	−14.2679	+	7.79087i	−0.660240	+	0.360518i	−0.774177	−	0.632970i	$-0.781836\pi$
$467$	−14.2679	+	7.79087i	−0.660240	+	0.360518i	0.113936	+	0.993488i	$0.463654\pi$
$468$		0			0
$469$	9.07244	−	4.14324i	0.418926	−	0.191317i
$470$		0			0
$471$	−3.34132	−	2.89527i	−0.153960	−	0.133407i
$472$		0			0
$473$	1.46850	−	2.68935i	0.0675216	−	0.123657i
$474$		0			0
$475$	10.6309	−	3.61972i	0.487780	−	0.166084i
$476$		0			0
$477$	7.52506	+	5.63319i	0.344549	+	0.257926i
$478$		0			0
$479$	−1.65519	+	11.5121i	−0.0756278	+	0.526003i	0.916428	+	0.400201i	$0.131060\pi$
$479$	−1.65519	+	11.5121i	−0.0756278	+	0.526003i	−0.992055	+	0.125802i	$0.959850\pi$
$480$		0			0
$481$	1.98779	−	1.72243i	0.0906355	−	0.0785361i
$482$		0			0
$483$	8.71544	−	6.24978i	0.396566	−	0.284375i
$484$		0			0
$485$	−0.803789	−	0.157012i	−0.0364982	−	0.00712954i
$486$		0			0
$487$	−23.9362	+	17.9184i	−1.08465	+	0.811959i	−0.983136	−	0.182875i	$-0.941460\pi$
$487$	−23.9362	+	17.9184i	−1.08465	+	0.811959i	−0.101515	+	0.994834i	$0.532369\pi$
$488$		0			0
$489$	31.4832	−	4.52661i	1.42372	−	0.204700i
$490$		0			0
$491$	17.1710	−	11.0351i	0.774915	−	0.498008i	−0.0924273	−	0.995719i	$-0.529463\pi$
$491$	17.1710	−	11.0351i	0.774915	−	0.498008i	0.867343	+	0.497712i	$0.165826\pi$
$492$		0			0
$493$	46.3587	+	25.3138i	2.08789	+	1.14007i
$494$		0			0
$495$	−1.19987	+	1.08526i	−0.0539301	+	0.0487790i
$496$		0			0
$497$	11.3050	+	4.21656i	0.507100	+	0.189139i
$498$		0			0
$499$	3.39258	−	11.5541i	0.151873	−	0.517231i	−0.848047	−	0.529921i	$-0.822221\pi$
$499$	3.39258	−	11.5541i	0.151873	−	0.517231i	0.999919	+	0.0126904i	$0.00403958\pi$
$500$		0			0
$501$	−1.23193	+	2.69755i	−0.0550386	+	0.120518i
$502$		0			0
$503$	−2.64546	−	12.1610i	−0.117955	−	0.542231i	−0.997760	−	0.0668960i	$-0.978690\pi$
$503$	−2.64546	−	12.1610i	−0.117955	−	0.542231i	0.879805	−	0.475335i	$-0.157673\pi$
$504$		0			0
$505$	−28.6496	−	3.49847i	−1.27489	−	0.155680i
$506$		0			0
$507$	−12.6258	−	12.6258i	−0.560731	−	0.560731i
$508$		0			0
$509$	−14.9492	+	23.2613i	−0.662610	+	1.03104i	0.333486	+	0.942755i	$0.391775\pi$
$509$	−14.9492	+	23.2613i	−0.662610	+	1.03104i	−0.996095	+	0.0882855i	$0.971861\pi$
$510$		0			0
$511$	−6.88733	−	3.14534i	−0.304678	−	0.139142i
$512$		0			0
$513$	6.08908	+	11.1513i	0.268839	+	0.492343i
$514$		0			0
$515$	1.26276	−	2.43438i	0.0556438	−	0.107272i
$516$		0			0
$517$	0.113856	+	1.59192i	0.00500740	+	0.0700126i
$518$		0			0
$519$	−3.65691	−	12.4543i	−0.160520	−	0.546682i
$520$		0			0
$521$	−20.4134	−	31.7639i	−0.894328	−	1.39160i	−0.919994	−	0.391931i	$-0.871807\pi$
$521$	−20.4134	−	31.7639i	−0.894328	−	1.39160i	0.0256662	−	0.999671i	$-0.491829\pi$
$522$		0			0
$523$	−11.7380	+	15.6801i	−0.513265	+	0.685642i	−0.980055	−	0.198726i	$-0.936320\pi$
$523$	−11.7380	+	15.6801i	−0.513265	+	0.685642i	0.466790	+	0.884368i	$0.345410\pi$
$524$		0			0
$525$	10.3593	+	4.20772i	0.452117	+	0.183640i
$526$		0			0
$527$	15.5908	+	1.11508i	0.679146	+	0.0485735i
$528$		0			0
$529$	22.6127	+	4.20331i	0.983159	+	0.182753i
$530$		0			0
$531$	−5.59877	−	6.46132i	−0.242966	−	0.280397i
$532$		0			0
$533$	0.979398	+	1.30832i	0.0424225	+	0.0566698i
$534$		0			0
$535$	−21.9539	−	21.0385i	−0.949151	−	0.909574i
$536$		0			0
$537$	28.1491	+	6.12345i	1.21472	+	0.264247i
$538$		0			0
$539$	3.08167	−	0.904859i	0.132737	−	0.0389750i
$540$		0			0
$541$	−19.2494	+	22.2150i	−0.827596	+	0.955096i	−0.999550	−	0.0300087i	$-0.990446\pi$
$541$	−19.2494	+	22.2150i	−0.827596	+	0.955096i	0.171954	+	0.985105i	$0.444992\pi$
$542$		0			0
$543$	4.80470	−	12.8819i	0.206190	−	0.552816i
$544$		0			0
$545$	−11.4123	−	4.92097i	−0.488848	−	0.210791i
$546$		0			0
$547$	−42.3781	+	15.8062i	−1.81196	+	0.675824i	−0.816868	+	0.576825i	$0.804291\pi$
$547$	−42.3781	+	15.8062i	−1.81196	+	0.675824i	−0.995088	+	0.0989993i	$0.968436\pi$
$548$		0			0
$549$	−11.7352	−	7.54174i	−0.500845	−	0.321874i
$550$		0			0
$551$		−	17.1466i		−	0.730468i
$552$		0			0
$553$	3.69057	−	3.69057i	0.156939	−	0.156939i
$554$		0			0
$555$	−9.07844	+	10.9392i	−0.385358	+	0.464342i
$556$		0			0
$557$	−5.92871	−	15.8955i	−0.251208	−	0.673514i	−0.999943	−	0.0106451i	$-0.996611\pi$
$557$	−5.92871	−	15.8955i	−0.251208	−	0.673514i	0.748736	−	0.662869i	$-0.230661\pi$
$558$		0			0
$559$	−2.39641	−	0.703648i	−0.101357	−	0.0297612i
$560$		0			0
$561$	−2.90229	−	6.35512i	−0.122535	−	0.268313i
$562$		0			0
$563$	15.2396	−	1.08996i	0.642274	−	0.0459363i	0.253596	−	0.967310i	$-0.418387\pi$
$563$	15.2396	−	1.08996i	0.642274	−	0.0459363i	0.388678	+	0.921374i	$0.372932\pi$
$564$		0			0
$565$	−21.3500	−	15.2842i	−0.898201	−	0.643011i
$566$		0			0
$567$	−1.66714	+	7.66371i	−0.0700132	+	0.321846i
$568$		0			0
$569$	−3.81203	−	26.5133i	−0.159809	−	1.11149i	−0.898984	−	0.437981i	$-0.855694\pi$
$569$	−3.81203	−	26.5133i	−0.159809	−	1.11149i	0.739176	−	0.673513i	$-0.235215\pi$
$570$		0			0
$571$	−37.6164	−	5.40842i	−1.57420	−	0.226335i	−0.700804	−	0.713353i	$-0.747175\pi$
$571$	−37.6164	−	5.40842i	−1.57420	−	0.226335i	−0.873392	+	0.487018i	$0.838085\pi$
$572$		0			0
$573$	−1.17119	+	16.3754i	−0.0489273	+	0.684093i
$574$		0			0
$575$	8.87397	+	22.2767i	0.370070	+	0.929004i
$576$		0			0
$577$	1.30519	−	18.2490i	0.0543359	−	0.759715i	−0.895122	−	0.445821i	$-0.852912\pi$
$577$	1.30519	−	18.2490i	0.0543359	−	0.759715i	0.949458	−	0.313894i	$-0.101634\pi$
$578$		0			0
$579$	6.36255	+	0.914797i	0.264419	+	0.0380177i
$580$		0			0
$581$	−2.83293	−	19.7035i	−0.117530	−	0.817438i
$582$		0			0
$583$	−1.41542	+	6.50660i	−0.0586209	+	0.269476i
$584$		0			0
$585$	1.07226	+	0.767620i	0.0443327	+	0.0317372i
$586$		0			0
$587$	15.9358	−	1.13975i	0.657740	−	0.0470425i	0.261520	−	0.965198i	$-0.415776\pi$
$587$	15.9358	−	1.13975i	0.657740	−	0.0470425i	0.396220	+	0.918156i	$0.370322\pi$
$588$		0			0
$589$	−2.10785	−	4.61556i	−0.0868526	−	0.190181i
$590$		0			0
$591$	4.01984	+	1.18033i	0.165354	+	0.0485524i
$592$		0			0
$593$	8.32386	+	22.3171i	0.341820	+	0.916455i	0.988163	+	0.153408i	$0.0490248\pi$
$593$	8.32386	+	22.3171i	0.341820	+	0.916455i	−0.646343	+	0.763047i	$0.723703\pi$
$594$		0			0
$595$	15.6650	−	18.8758i	0.642204	−	0.773832i
$596$		0			0
$597$	−18.4063	+	18.4063i	−0.753319	+	0.753319i
$598$		0			0
$599$		−	42.5107i		−	1.73694i	−0.495742	−	0.868470i	$-0.665104\pi$
$599$		−	42.5107i		−	1.73694i	0.495742	−	0.868470i	$-0.334896\pi$
$600$		0			0
$601$	−18.7457	−	12.0471i	−0.764654	−	0.491413i	0.0992544	−	0.995062i	$-0.468354\pi$
$601$	−18.7457	−	12.0471i	−0.764654	−	0.491413i	−0.863909	+	0.503649i	$0.831991\pi$
$602$		0			0
$603$	−5.95671	+	2.22174i	−0.242576	+	0.0904761i
$604$		0			0
$605$	21.5340	+	9.28546i	0.875483	+	0.377508i
$606$		0			0
$607$	−0.223088	+	0.598122i	−0.00905486	+	0.0242770i	−0.941399	−	0.337296i	$-0.890488\pi$
$607$	−0.223088	+	0.598122i	−0.00905486	+	0.0242770i	0.932344	+	0.361573i	$0.117760\pi$
$608$		0			0
$609$	11.1796	−	12.9019i	0.453020	−	0.522813i
$610$		0			0
$611$	1.24818	−	0.366499i	0.0504960	−	0.0148270i
$612$		0			0
$613$	−21.0215	−	4.57295i	−0.849051	−	0.184700i	−0.233069	−	0.972460i	$-0.574877\pi$
$613$	−21.0215	−	4.57295i	−0.849051	−	0.184700i	−0.615982	+	0.787761i	$0.711240\pi$
$614$		0			0
$615$	−6.37736	−	6.11144i	−0.257160	−	0.246437i
$616$		0			0
$617$	−4.64534	−	6.20545i	−0.187014	−	0.249822i	0.697229	−	0.716849i	$-0.254416\pi$
$617$	−4.64534	−	6.20545i	−0.187014	−	0.249822i	−0.884243	+	0.467027i	$0.845325\pi$
$618$		0			0
$619$	14.6330	+	16.8874i	0.588149	+	0.678760i	0.969336	−	0.245738i	$-0.0790302\pi$
$619$	14.6330	+	16.8874i	0.588149	+	0.678760i	−0.381187	+	0.924498i	$0.624485\pi$
$620$		0			0
$621$	−23.1182	+	14.1963i	−0.927700	+	0.569679i
$622$		0			0
$623$	−21.7446	−	1.55521i	−0.871180	−	0.0623080i
$624$		0			0
$625$	−14.7052	+	20.2177i	−0.588209	+	0.808709i
$626$		0			0
$627$	−1.35915	+	1.81561i	−0.0542793	+	0.0725087i
$628$		0			0
$629$	16.8605	+	26.2355i	0.672272	+	1.04608i
$630$		0			0
$631$	−11.9918	−	40.8404i	−0.477386	−	1.62583i	−0.748396	−	0.663252i	$-0.769176\pi$
$631$	−11.9918	−	40.8404i	−0.477386	−	1.62583i	0.271010	−	0.962577i	$-0.412642\pi$
$632$		0			0
$633$	0.696765	+	9.74205i	0.0276939	+	0.387212i
$634$		0			0
$635$	−2.75641	+	5.31389i	−0.109385	+	0.210875i
$636$		0			0
$637$	−1.25462	−	2.29766i	−0.0497098	−	0.0910367i
$638$		0			0
$639$	−6.99605	−	3.19499i	−0.276760	−	0.126392i
$640$		0			0
$641$	−17.7482	+	27.6168i	−0.701014	+	1.09080i	0.289998	+	0.957027i	$0.406345\pi$
$641$	−17.7482	+	27.6168i	−0.701014	+	1.09080i	−0.991012	+	0.133772i	$0.957291\pi$
$642$		0			0
$643$	−16.1813	−	16.1813i	−0.638129	−	0.638129i	0.311964	−	0.950094i	$-0.399013\pi$
$643$	−16.1813	−	16.1813i	−0.638129	−	0.638129i	−0.950094	+	0.311964i	$0.899013\pi$
$644$		0			0
$645$	13.3992	+	1.63620i	0.527591	+	0.0644253i
$646$		0			0
$647$	1.15565	+	5.31242i	0.0454331	+	0.208853i	0.994267	−	0.106922i	$-0.0340994\pi$
$647$	1.15565	+	5.31242i	0.0454331	+	0.208853i	−0.948834	+	0.315774i	$0.897736\pi$
$648$		0			0
$649$	2.51590	−	5.50906i	0.0987578	−	0.216249i
$650$		0			0
$651$	1.42330	−	4.84730i	0.0557834	−	0.189981i
$652$		0			0
$653$	−39.0566	−	14.5673i	−1.52840	−	0.570064i	−0.562008	−	0.827132i	$-0.689971\pi$
$653$	−39.0566	−	14.5673i	−1.52840	−	0.570064i	−0.966394	+	0.257067i	$0.917244\pi$
$654$		0			0
$655$	−19.9267	+	18.0234i	−0.778600	+	0.704232i
$656$		0			0
$657$	4.23597	+	2.31301i	0.165261	+	0.0902393i
$658$		0			0
$659$	−13.8603	+	8.90745i	−0.539919	+	0.346985i	−0.782007	−	0.623269i	$-0.785804\pi$
$659$	−13.8603	+	8.90745i	−0.539919	+	0.346985i	0.242088	+	0.970254i	$0.422168\pi$
$660$		0			0
$661$	28.4707	−	4.09347i	1.10738	−	0.159217i	0.435725	−	0.900080i	$-0.356492\pi$
$661$	28.4707	−	4.09347i	1.10738	−	0.159217i	0.671657	+	0.740863i	$0.265583\pi$
$662$		0			0
$663$	−4.55878	+	3.41266i	−0.177048	+	0.132537i
$664$		0			0
$665$	−7.81513	−	1.52660i	−0.303058	−	0.0591992i
$666$		0			0
$667$	36.5644	−	1.86299i	1.41578	−	0.0721351i
$668$		0			0
$669$	−11.6723	+	10.1141i	−0.451276	+	0.391033i
$670$		0			0
$671$	1.40631	−	9.78110i	0.0542900	−	0.377595i
$672$		0			0
$673$	−23.9806	−	17.9517i	−0.924386	−	0.691986i	0.0271152	−	0.999632i	$-0.491368\pi$
$673$	−23.9806	−	17.9517i	−0.924386	−	0.691986i	−0.951501	+	0.307646i	$0.900459\pi$
$674$		0			0
$675$	−25.3787	−	12.4861i	−0.976828	−	0.480591i
$676$		0			0
$677$	−3.44758	+	6.31378i	−0.132501	+	0.242658i	−0.935503	−	0.353319i	$-0.885053\pi$
$677$	−3.44758	+	6.31378i	−0.132501	+	0.242658i	0.803002	+	0.595977i	$0.203235\pi$
$678$		0			0
$679$	0.438864	+	0.380278i	0.0168420	+	0.0145937i
$680$		0			0
$681$	−13.3566	+	6.09974i	−0.511824	+	0.233742i
$682$		0			0
$683$	−39.5615	+	21.6022i	−1.51378	+	0.826587i	−0.999518	−	0.0310463i	$-0.990116\pi$
$683$	−39.5615	+	21.6022i	−1.51378	+	0.826587i	−0.514262	+	0.857633i	$0.671934\pi$
$684$		0			0
$685$	−6.09011	−	25.3818i	−0.232691	−	0.969787i
$686$		0			0
$687$	8.57097	−	1.86450i	0.327003	−	0.0711352i
$688$		0			0
$689$	5.42752			0.206772
$690$		0			0
$691$	−41.9500			−1.59585			−0.797927	−	0.602754i	$-0.794070\pi$
$691$	−41.9500			−1.59585			−0.797927	+	0.602754i	$0.794070\pi$
$692$		0			0
$693$	1.12093	−	0.243844i	0.0425807	−	0.00926287i
$694$		0			0
$695$	19.6184	+	12.0257i	0.744169	+	0.456161i
$696$		0			0
$697$	−17.0073	+	9.28670i	−0.644198	+	0.351759i
$698$		0			0
$699$	29.9884	−	13.6952i	1.13427	−	0.518002i
$700$		0			0
$701$	7.49851	+	6.49750i	0.283215	+	0.245407i	0.784870	−	0.619661i	$-0.212730\pi$
$701$	7.49851	+	6.49750i	0.283215	+	0.245407i	−0.501655	+	0.865068i	$0.667275\pi$
$702$		0			0
$703$	4.85182	−	8.88545i	0.182990	−	0.335121i
$704$		0			0
$705$	−6.33188	+	3.05621i	−0.238472	+	0.115104i
$706$		0			0
$707$	16.3830	+	12.2642i	0.616148	+	0.461242i
$708$		0			0
$709$	−5.28011	+	36.7240i	−0.198299	+	1.37920i	0.610921	+	0.791692i	$0.290799\pi$
$709$	−5.28011	+	36.7240i	−0.198299	+	1.37920i	−0.809220	+	0.587506i	$0.800110\pi$
$710$		0			0
$711$	−2.51430	+	2.17866i	−0.0942938	+	0.0817060i
$712$		0			0
$713$	9.61347	−	4.99640i	0.360027	−	0.187117i
$714$		0			0
$715$	−0.179092	+	0.916822i	−0.00669765	+	0.0342872i
$716$		0			0
$717$	20.1200	−	15.0616i	0.751395	−	0.562487i
$718$		0			0
$719$	3.73257	−	0.536662i	0.139201	−	0.0200141i	−0.0723620	−	0.997378i	$-0.523054\pi$
$719$	3.73257	−	0.536662i	0.139201	−	0.0200141i	0.211563	+	0.977364i	$0.432145\pi$
$720$		0			0
$721$	−1.63582	+	1.05128i	−0.0609212	+	0.0391517i
$722$		0			0
$723$	16.5493	+	9.03658i	0.615474	+	0.336074i
$724$		0			0
$725$	21.9846	+	31.2035i	0.816488	+	1.15887i
$726$		0			0
$727$	−7.78414	−	2.90333i	−0.288698	−	0.107679i	0.200943	−	0.979603i	$-0.435599\pi$
$727$	−7.78414	−	2.90333i	−0.288698	−	0.107679i	−0.489641	+	0.871924i	$0.662872\pi$
$728$		0			0
$729$	8.15198	−	27.7631i	0.301925	−	1.02826i
$730$		0			0
$731$	12.3018	−	26.9373i	0.455000	−	0.996311i
$732$		0			0
$733$	−10.5120	−	48.3230i	−0.388271	−	1.78485i	−0.592121	−	0.805849i	$-0.701709\pi$
$733$	−10.5120	−	48.3230i	−0.388271	−	1.78485i	0.203851	−	0.979002i	$-0.434654\pi$
$734$		0			0
$735$	8.71834	+	11.1437i	0.321581	+	0.411043i
$736$		0			0
$737$	−3.18451	−	3.18451i	−0.117303	−	0.117303i
$738$		0			0
$739$	−15.4539	+	24.0467i	−0.568479	+	0.884571i	−0.999845	−	0.0176063i	$-0.994395\pi$
$739$	−15.4539	+	24.0467i	−0.568479	+	0.884571i	0.431366	+	0.902177i	$0.358032\pi$
$740$		0			0
$741$	1.68156	+	0.767942i	0.0617736	+	0.0282111i
$742$		0			0
$743$	22.0384	+	40.3604i	0.808512	+	1.48068i	0.875655	+	0.482936i	$0.160430\pi$
$743$	22.0384	+	40.3604i	0.808512	+	1.48068i	−0.0671431	+	0.997743i	$0.521388\pi$
$744$		0			0
$745$	−5.60623	−	17.6908i	−0.205396	−	0.648142i
$746$		0			0
$747$	0.905202	+	12.6564i	0.0331196	+	0.463073i
$748$		0			0
$749$	6.07422	+	20.6869i	0.221947	+	0.755882i
$750$		0			0
$751$	4.47196	+	6.95850i	0.163184	+	0.253919i	0.913210	−	0.407489i	$-0.133596\pi$
$751$	4.47196	+	6.95850i	0.163184	+	0.253919i	−0.750026	+	0.661408i	$0.769959\pi$
$752$		0			0
$753$	9.58079	−	12.7984i	0.349143	−	0.466401i
$754$		0			0
$755$	7.32318	−	27.0585i	0.266518	−	0.984761i
$756$		0			0
$757$	−5.63748	−	0.403201i	−0.204898	−	0.0146546i	−0.0314870	−	0.999504i	$-0.510024\pi$
$757$	−5.63748	−	0.403201i	−0.204898	−	0.0146546i	−0.173411	+	0.984850i	$0.555479\pi$
$758$		0			0
$759$	−4.01940	−	2.70107i	−0.145895	−	0.0980426i
$760$		0			0
$761$	−30.6670	−	35.3916i	−1.11168	−	1.28295i	−0.955427	−	0.295228i	$-0.904604\pi$
$761$	−30.6670	−	35.3916i	−1.11168	−	1.28295i	−0.156251	−	0.987717i	$-0.549941\pi$
$762$		0			0
$763$	5.28090	+	7.05446i	0.191182	+	0.255389i
$764$		0			0
$765$	−10.8183	+	11.2890i	−0.391135	+	0.408154i
$766$		0			0
$767$	−4.82367	−	1.04933i	−0.174173	−	0.0378890i
$768$		0			0
$769$	10.7345	−	3.15194i	0.387097	−	0.113662i	−0.0823926	−	0.996600i	$-0.526256\pi$
$769$	10.7345	−	3.15194i	0.387097	−	0.113662i	0.469490	+	0.882938i	$0.344438\pi$
$770$		0			0
$771$	−3.07194	+	3.54521i	−0.110633	+	0.127678i
$772$		0			0
$773$	10.2355	−	27.4423i	0.368144	−	0.987031i	−0.612369	−	0.790572i	$-0.709783\pi$
$773$	10.2355	−	27.4423i	0.368144	−	0.987031i	0.980512	−	0.196459i	$-0.0629441\pi$
$774$		0			0
$775$	9.75377	+	5.69684i	0.350366	+	0.204636i
$776$		0			0
$777$	9.44409	−	3.52246i	0.338805	−	0.126368i
$778$		0			0
$779$	5.29187	+	3.40088i	0.189601	+	0.121849i
$780$		0			0
$781$		−	5.44823i		−	0.194953i
$782$		0			0
$783$	−30.5360	+	30.5360i	−1.09127	+	1.09127i
$784$		0			0
$785$	−6.97910	+	0.648744i	−0.249095	+	0.0231547i
$786$		0			0
$787$	11.4216	+	30.6224i	0.407135	+	1.09157i	0.965140	+	0.261734i	$0.0842944\pi$
$787$	11.4216	+	30.6224i	0.407135	+	1.09157i	−0.558005	+	0.829838i	$0.688433\pi$
$788$		0			0
$789$	−37.6106	−	11.0435i	−1.33897	−	0.393158i
$790$		0			0
$791$	7.73402	+	16.9351i	0.274990	+	0.602144i
$792$		0			0
$793$	−8.03396	+	0.574600i	−0.285294	+	0.0204046i
$794$		0			0
$795$	−28.9402	+	4.79184i	−1.02640	+	0.169949i
$796$		0			0
$797$	1.33651	−	6.14385i	0.0473417	−	0.217626i	−0.947399	−	0.320056i	$-0.896298\pi$
$797$	1.33651	−	6.14385i	0.0473417	−	0.217626i	0.994740	+	0.102430i	$0.0326618\pi$
$798$		0			0
$799$	2.19511	+	15.2673i	0.0776572	+	0.540118i
$800$		0			0
$801$	13.7546	+	1.97761i	0.485995	+	0.0698756i
$802$		0			0
$803$	−0.243901	+	3.41018i	−0.00860707	+	0.120343i
$804$		0			0
$805$	2.40630	−	16.8313i	0.0848111	−	0.593226i
$806$		0			0
$807$	−1.27371	+	17.8089i	−0.0448369	+	0.626901i
$808$		0			0
$809$	−18.5623	−	2.66886i	−0.652617	−	0.0938322i	−0.191950	−	0.981405i	$-0.561481\pi$
$809$	−18.5623	−	2.66886i	−0.652617	−	0.0938322i	−0.460668	+	0.887573i	$0.652390\pi$
$810$		0			0
$811$	1.39897	+	9.73002i	0.0491243	+	0.341667i	0.999530	+	0.0306544i	$0.00975912\pi$
$811$	1.39897	+	9.73002i	0.0491243	+	0.341667i	−0.950406	+	0.311013i	$0.899332\pi$
$812$		0			0
$813$	−1.85511	+	8.52781i	−0.0650616	+	0.299083i
$814$		0			0
$815$	29.3527	−	41.0018i	1.02818	−	1.43623i
$816$		0			0
$817$	−9.58874	+	0.685800i	−0.335468	+	0.0239931i
$818$		0			0
$819$	−0.388426	−	0.850535i	−0.0135727	−	0.0297201i
$820$		0			0
$821$	−10.6467	−	3.12614i	−0.371571	−	0.109103i	0.0906153	−	0.995886i	$-0.471117\pi$
$821$	−10.6467	−	3.12614i	−0.371571	−	0.109103i	−0.462186	+	0.886783i	$0.652935\pi$
$822$		0			0
$823$	−0.0756791	−	0.202904i	−0.00263801	−	0.00707278i	0.935624	−	0.352998i	$-0.114838\pi$
$823$	−0.0756791	−	0.202904i	−0.00263801	−	0.00707278i	−0.938262	+	0.345925i	$0.887565\pi$
$824$		0			0
$825$	0.145495	−	5.04672i	0.00506548	−	0.175704i
$826$		0			0
$827$	30.2192	−	30.2192i	1.05083	−	1.05083i	0.0521884	−	0.998637i	$-0.483380\pi$
$827$	30.2192	−	30.2192i	1.05083	−	1.05083i	0.998637	−	0.0521884i	$-0.0166196\pi$
$828$		0			0
$829$		−	0.803491i		−	0.0279064i	−0.999903	−	0.0139532i	$-0.995558\pi$
$829$		−	0.803491i		−	0.0279064i	0.999903	−	0.0139532i	$-0.00444159\pi$
$830$		0			0
$831$	2.67717	+	1.72051i	0.0928698	+	0.0596838i
$832$		0			0
$833$	29.0828	−	10.8473i	1.00766	−	0.375837i
$834$		0			0
$835$	1.73639	+	4.36905i	0.0600902	+	0.151197i
$836$		0			0
$837$	−4.46592	+	11.9736i	−0.154365	+	0.413868i
$838$		0			0
$839$	26.7423	−	30.8622i	0.923246	−	1.06548i	−0.0744219	−	0.997227i	$-0.523711\pi$
$839$	26.7423	−	30.8622i	0.923246	−	1.06548i	0.997668	−	0.0682557i	$-0.0217434\pi$
$840$		0			0
$841$	28.0933	−	8.24893i	0.968734	−	0.284446i
$842$		0			0
$843$	29.0268	+	6.31439i	0.999736	+	0.217479i
$844$		0			0
$845$	−28.3011	+	0.602595i	−0.973586	+	0.0207299i
$846$		0			0
$847$	−9.96464	−	13.3112i	−0.342389	−	0.457378i
$848$		0			0
$849$	−11.7655	−	13.5781i	−0.403790	−	0.465998i
$850$		0			0
$851$	19.4750	+	9.38090i	0.667595	+	0.321573i
$852$		0			0
$853$	−47.9592	−	3.43011i	−1.64209	−	0.117445i	−0.780537	−	0.625109i	$-0.785054\pi$
$853$	−47.9592	−	3.43011i	−1.64209	−	0.117445i	−0.861555	+	0.507665i	$0.830509\pi$
$854$		0			0
$855$	4.89948	+	1.32600i	0.167559	+	0.0453484i
$856$		0			0
$857$	−22.8729	+	30.5546i	−0.781323	+	1.04373i	0.216401	+	0.976304i	$0.430568\pi$
$857$	−22.8729	+	30.5546i	−0.781323	+	1.04373i	−0.997725	+	0.0674211i	$0.978523\pi$
$858$		0			0
$859$	−17.1614	−	26.7036i	−0.585538	−	0.911115i	−0.999999	−	0.00104807i	$-0.999666\pi$
$859$	−17.1614	−	26.7036i	−0.585538	−	0.911115i	0.414461	−	0.910067i	$-0.363970\pi$
$860$		0			0
$861$	1.76449	+	6.00930i	0.0601337	+	0.204796i
$862$		0			0
$863$	2.79225	+	39.0408i	0.0950494	+	1.32896i	0.791416	+	0.611278i	$0.209344\pi$
$863$	2.79225	+	39.0408i	0.0950494	+	1.32896i	−0.696366	+	0.717686i	$0.745201\pi$
$864$		0			0
$865$	−18.2668	−	9.47531i	−0.621089	−	0.322170i
$866$		0			0
$867$	−20.8677	−	38.2164i	−0.708706	−	1.29790i
$868$		0			0
$869$	−2.14375	−	0.979017i	−0.0727217	−	0.0332109i
$870$		0			0
$871$	−1.98460	+	3.08810i	−0.0672457	+	0.104636i
$872$		0			0
$873$	−0.261739	−	0.261739i	−0.00885852	−	0.00885852i
$874$		0			0
$875$	16.1794	−	7.24210i	0.546964	−	0.244828i
$876$		0			0
$877$	−1.82597	−	8.39387i	−0.0616588	−	0.283441i	0.935986	−	0.352038i	$-0.114511\pi$
$877$	−1.82597	−	8.39387i	−0.0616588	−	0.283441i	−0.997644	+	0.0685973i	$0.978148\pi$
$878$		0			0
$879$	−7.26593	+	15.9102i	−0.245074	+	0.536636i
$880$		0			0
$881$	6.90179	−	23.5053i	0.232527	−	0.791915i	−0.757719	−	0.652582i	$-0.773686\pi$
$881$	6.90179	−	23.5053i	0.232527	−	0.791915i	0.990246	−	0.139333i	$-0.0444958\pi$
$882$		0			0
$883$	0.699197	+	0.260787i	0.0235299	+	0.00877618i	0.361202	−	0.932488i	$-0.382367\pi$
$883$	0.699197	+	0.260787i	0.0235299	+	0.00877618i	−0.337672	+	0.941264i	$0.609639\pi$
$884$		0			0
$885$	26.6468	+	1.33641i	0.895724	+	0.0449230i
$886$		0			0
$887$	35.0791	+	19.1547i	1.17784	+	0.643150i	0.944264	−	0.329188i	$-0.106775\pi$
$887$	35.0791	+	19.1547i	1.17784	+	0.643150i	0.233577	+	0.972338i	$0.424957\pi$
$888$		0			0
$889$	3.57075	−	2.29478i	0.119759	−	0.0769645i
$890$		0			0
$891$	3.50539	−	0.503999i	0.117435	−	0.0168846i
$892$		0			0
$893$	4.00840	−	3.00065i	0.134136	−	0.100413i
$894$		0			0
$895$	37.8858	−	25.5034i	1.26638	−	0.852484i
$896$		0			0
$897$	−1.45490	+	3.66930i	−0.0485778	+	0.122514i
$898$		0			0
$899$	13.0339	−	11.2939i	0.434704	−	0.376673i
$900$		0			0
$901$	−9.15842	+	63.6982i	−0.305111	+	2.12209i
$902$		0			0
$903$	−7.66220	−	5.73585i	−0.254982	−	0.190877i
$904$		0			0
$905$	−9.47471	−	19.6298i	−0.314950	−	0.652516i
$906$		0			0
$907$	−24.3824	+	44.6531i	−0.809605	+	1.48268i	0.0650220	+	0.997884i	$0.479288\pi$
$907$	−24.3824	+	44.6531i	−0.809605	+	1.48268i	−0.874627	+	0.484797i	$0.838894\pi$
$908$		0			0
$909$	−9.85872	−	8.54263i	−0.326993	−	0.283341i
$910$		0			0
$911$	−28.0350	+	12.8032i	−0.928842	+	0.424188i	−0.821612	−	0.570047i	$-0.806925\pi$
$911$	−28.0350	+	12.8032i	−0.928842	+	0.424188i	−0.107229	+	0.994234i	$0.534198\pi$
$912$		0			0
$913$	−7.88899	+	4.30771i	−0.261087	+	0.142565i
$914$		0			0
$915$	42.3307	−	10.1568i	1.39941	−	0.335775i
$916$		0			0
$917$	18.6158	−	4.04961i	0.614747	−	0.133730i
$918$		0			0
$919$	24.5059			0.808375			0.404187	−	0.914676i	$-0.367554\pi$
$919$	24.5059			0.808375			0.404187	+	0.914676i	$0.367554\pi$
$920$		0			0
$921$	48.6728			1.60382
$922$		0			0
$923$	−4.33932	+	0.943962i	−0.142831	+	0.0310709i
$924$		0			0
$925$	2.56315	+	22.3906i	0.0842759	+	0.736200i
$926$		0			0
$927$	1.08787	−	0.594021i	0.0357303	−	0.0195102i
$928$		0			0
$929$	−17.6731	+	8.07106i	−0.579837	+	0.264803i	−0.683669	−	0.729792i	$-0.739617\pi$
$929$	−17.6731	+	8.07106i	−0.579837	+	0.264803i	0.103832	+	0.994595i	$0.466890\pi$
$930$		0			0
$931$	−7.61517	−	6.59858i	−0.249577	−	0.216260i
$932$		0			0
$933$	11.1219	−	20.3683i	0.364116	−	0.666829i
$934$		0			0
$935$	−10.4578	−	3.64890i	−0.342006	−	0.119332i
$936$		0			0
$937$	−35.3226	−	26.4422i	−1.15394	−	0.863827i	−0.161537	−	0.986867i	$-0.551645\pi$
$937$	−35.3226	−	26.4422i	−1.15394	−	0.863827i	−0.992402	+	0.123039i	$0.960736\pi$
$938$		0			0
$939$	−5.30979	+	36.9304i	−0.173279	+	1.20518i
$940$		0			0
$941$	−12.0757	+	10.4636i	−0.393655	+	0.341104i	−0.829089	−	0.559117i	$-0.811140\pi$
$941$	−12.0757	+	10.4636i	−0.393655	+	0.341104i	0.435434	+	0.900221i	$0.356595\pi$
$942$		0			0
$943$	−6.67727	+	11.6542i	−0.217442	+	0.379513i
$944$		0			0
$945$	11.1991	+	16.6365i	0.364308	+	0.541187i
$946$		0			0
$947$	28.5335	−	21.3599i	0.927213	−	0.694103i	−0.0249514	−	0.999689i	$-0.507943\pi$
$947$	28.5335	−	21.3599i	0.927213	−	0.694103i	0.952165	+	0.305586i	$0.0988522\pi$
$948$		0			0
$949$	2.75835	−	0.396590i	0.0895397	−	0.0128739i
$950$		0			0
$951$	8.06461	−	5.18281i	0.261513	−	0.168064i
$952$		0			0
$953$	16.2011	+	8.84649i	0.524806	+	0.286566i	0.719732	−	0.694252i	$-0.244265\pi$
$953$	16.2011	+	8.84649i	0.524806	+	0.286566i	−0.194926	+	0.980818i	$0.562447\pi$
$954$		0			0
$955$	17.4591	+	19.3028i	0.564963	+	0.624624i
$956$		0			0
$957$	−7.22259	−	2.69389i	−0.233473	−	0.0870811i
$958$		0			0
$959$	−5.21425	+	17.7581i	−0.168377	+	0.573439i
$960$		0			0
$961$	−10.7578	+	23.5562i	−0.347024	+	0.759877i
$962$		0			0
$963$	−2.92131	−	13.4290i	−0.0941378	−	0.432745i
$964$		0			0
$965$	8.02619	−	6.27932i	0.258372	−	0.202138i
$966$		0			0
$967$	−11.8568	−	11.8568i	−0.381290	−	0.381290i	0.490277	−	0.871567i	$-0.336896\pi$
$967$	−11.8568	−	11.8568i	−0.381290	−	0.381290i	−0.871567	+	0.490277i	$0.836896\pi$
$968$		0			0
$969$	−11.8502	+	18.4392i	−0.380682	+	0.592353i
$970$		0			0
$971$	23.7730	+	10.8568i	0.762913	+	0.348411i	0.758580	−	0.651580i	$-0.225893\pi$
$971$	23.7730	+	10.8568i	0.762913	+	0.348411i	0.00433317	+	0.999991i	$0.498621\pi$
$972$		0			0
$973$	−7.81937	−	14.3201i	−0.250678	−	0.459082i
$974$		0			0
$975$	−4.04474	+	0.758515i	−0.129535	+	0.0242919i
$976$		0			0
$977$	0.929466	+	12.9956i	0.0297363	+	0.415767i	0.990417	+	0.138111i	$0.0441031\pi$
$977$	0.929466	+	12.9956i	0.0297363	+	0.415767i	−0.960680	+	0.277656i	$0.910442\pi$
$978$		0			0
$979$	2.77330	+	9.44499i	0.0886350	+	0.301863i
$980$		0			0
$981$	−3.03683	−	4.72540i	−0.0969585	−	0.150870i
$982$		0			0
$983$	17.6077	−	23.5211i	0.561597	−	0.750206i	−0.426424	−	0.904523i	$-0.640227\pi$
$983$	17.6077	−	23.5211i	0.561597	−	0.750206i	0.988021	+	0.154317i	$0.0493179\pi$
$984$		0			0
$985$	5.76041	−	3.30652i	0.183542	−	0.105354i
$986$		0			0
$987$	4.97255	+	0.355644i	0.158278	+	0.0113203i
$988$		0			0
$989$	−2.50426	−	20.3731i	−0.0796310	−	0.647827i
$990$		0			0
$991$	28.3806	+	32.7530i	0.901540	+	1.04043i	0.998978	+	0.0451914i	$0.0143898\pi$
$991$	28.3806	+	32.7530i	0.901540	+	1.04043i	−0.0974380	+	0.995242i	$0.531065\pi$
$992$		0			0
$993$	10.8343	+	14.4730i	0.343818	+	0.459287i
$994$		0			0
$995$	0.878484	+	41.2582i	0.0278498	+	1.30797i
$996$		0			0
$997$	−10.3745	−	2.25684i	−0.328565	−	0.0714750i	0.0452570	−	0.998975i	$-0.485589\pi$
$997$	−10.3745	−	2.25684i	−0.328565	−	0.0714750i	−0.373822	+	0.927500i	$0.621953\pi$
$998$		0			0
$999$	−24.4645	+	7.18341i	−0.774021	+	0.227273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.217.4	yes	240
5.3	odd	4	inner	460.2.x.a.33.4	✓	240
23.7	odd	22	inner	460.2.x.a.237.4	yes	240
115.53	even	44	inner	460.2.x.a.53.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.4	✓	240	5.3	odd	4	inner
460.2.x.a.53.4	yes	240	115.53	even	44	inner
460.2.x.a.217.4	yes	240	1.1	even	1	trivial
460.2.x.a.237.4	yes	240	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37822 + 0.299812i) q^{3} +(-1.16859 + 1.90641i) q^{5} +(1.39155 - 0.759843i) q^{7} +(-0.919306 + 0.419833i) q^{9} +(-0.541054 - 0.468826i) q^{11} +(-0.279660 + 0.512159i) q^{13} +(1.03901 - 2.97780i) q^{15} +(-5.53888 - 4.14635i) q^{17} +(-0.319647 + 2.22319i) q^{19} +(-1.69004 + 1.46443i) q^{21} +(-4.77560 - 0.440082i) q^{23} +(-2.26879 - 4.45563i) q^{25} +(4.52850 - 3.38999i) q^{27} +(-7.55638 + 1.08644i) q^{29} +(-1.90049 + 1.22137i) q^{31} +(0.886248 + 0.483928i) q^{33} +(-0.177581 + 3.54081i) q^{35} +(-4.22318 - 1.57517i) q^{37} +(0.231880 - 0.789711i) q^{39} +(1.16344 - 2.54758i) q^{41} +(0.909791 + 4.18224i) q^{43} +(0.273920 - 2.24319i) q^{45} +(-1.57635 - 1.57635i) q^{47} +(-2.42544 + 3.77406i) q^{49} +(8.87690 + 4.05394i) q^{51} +(-4.45752 - 8.16333i) q^{53} +(1.52604 - 0.483604i) q^{55} +(-0.225998 - 3.15987i) q^{57} +(2.38334 + 8.11691i) q^{59} +(7.46237 + 11.6117i) q^{61} +(-0.960253 + 1.28275i) q^{63} +(-0.649576 - 1.13165i) q^{65} +(6.27462 + 0.448770i) q^{67} +(6.71374 - 0.825255i) q^{69} +(4.98358 + 5.75136i) q^{71} +(-2.86187 - 3.82302i) q^{73} +(4.46273 + 5.46060i) q^{75} +(-1.10914 - 0.241278i) q^{77} +(3.15855 - 0.927433i) q^{79} +(-3.23941 + 3.73847i) q^{81} +(4.38759 - 11.7636i) q^{83} +(14.3773 - 5.71397i) q^{85} +(10.0886 - 3.76285i) q^{87} +(-11.5671 - 7.43371i) q^{89} +0.925193i q^{91} +(2.25310 - 2.25310i) q^{93} +(-3.86478 - 3.20738i) q^{95} +(0.127995 + 0.343167i) q^{97} +(0.694223 + 0.203842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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