LMFDB - Embedded newform 460.2.s.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	460.9
Dual form			460.2.s.a.409.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.391893 + 0.339577i) q^{3} +(-0.773120 - 2.09816i) q^{5} +(-1.88813 - 0.862281i) q^{7} +(-0.388677 + 2.70331i) q^{9} +O(q^{10})$	\(q+(-0.391893 + 0.339577i) q^{3} +(-0.773120 - 2.09816i) q^{5} +(-1.88813 - 0.862281i) q^{7} +(-0.388677 + 2.70331i) q^{9} +(-1.10245 - 0.323708i) q^{11} +(-5.66091 + 2.58525i) q^{13} +(1.01547 + 0.559721i) q^{15} +(-1.52654 + 2.37534i) q^{17} +(1.46731 - 0.942980i) q^{19} +(1.03276 - 0.303244i) q^{21} +(1.78750 + 4.45026i) q^{23} +(-3.80457 + 3.24426i) q^{25} +(-1.60671 - 2.50008i) q^{27} +(-4.96168 - 3.18867i) q^{29} +(0.641991 - 0.740897i) q^{31} +(0.541964 - 0.247507i) q^{33} +(-0.349453 + 4.62825i) q^{35} +(-9.82240 - 1.41225i) q^{37} +(1.34058 - 2.93546i) q^{39} +(0.155716 + 1.08303i) q^{41} +(3.30485 - 2.86367i) q^{43} +(5.97248 - 1.27447i) q^{45} -9.71084i q^{47} +(-1.76251 - 2.03405i) q^{49} +(-0.208371 - 1.44925i) q^{51} +(0.689112 + 0.314707i) q^{53} +(0.173132 + 2.56338i) q^{55} +(-0.254812 + 0.867810i) q^{57} +(4.94331 + 10.8243i) q^{59} +(1.61202 - 1.86037i) q^{61} +(3.06488 - 4.76905i) q^{63} +(9.80084 + 9.87880i) q^{65} +(-2.84243 - 9.68043i) q^{67} +(-2.21171 - 1.13703i) q^{69} +(-11.1753 + 3.28136i) q^{71} +(2.33540 + 3.63396i) q^{73} +(0.389307 - 2.56335i) q^{75} +(1.80244 + 1.56182i) q^{77} +(0.268099 + 0.587055i) q^{79} +(-6.38281 - 1.87416i) q^{81} +(11.9953 + 1.72466i) q^{83} +(6.16405 + 1.36650i) q^{85} +(3.02724 - 0.435252i) q^{87} +(7.89200 + 9.10785i) q^{89} +12.9178 q^{91} +0.508357i q^{93} +(-3.11293 - 2.34961i) q^{95} +(7.65107 - 1.10006i) q^{97} +(1.30358 - 2.85444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{11}\right)$

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
$3$	−0.391893	+	0.339577i	−0.226259	+	0.196055i	−0.760612	−	0.649207i	$-0.775101\pi$
$3$	−0.391893	+	0.339577i	−0.226259	+	0.196055i	0.534353	+	0.845262i	$0.320555\pi$
$4$		0			0
$5$	−0.773120	−	2.09816i	−0.345750	−	0.938327i
$5$	−0.773120	−	2.09816i	−0.345750	−	0.938327i
$6$		0			0
$7$	−1.88813	−	0.862281i	−0.713647	−	0.325911i	0.0252959	−	0.999680i	$-0.491947\pi$
$7$	−1.88813	−	0.862281i	−0.713647	−	0.325911i	−0.738942	+	0.673769i	$0.764674\pi$
$8$		0			0
$9$	−0.388677	+	2.70331i	−0.129559	+	0.901103i
$10$		0			0
$11$	−1.10245	−	0.323708i	−0.332400	−	0.0976015i	0.111274	−	0.993790i	$-0.464507\pi$
$11$	−1.10245	−	0.323708i	−0.332400	−	0.0976015i	−0.443674	+	0.896188i	$0.646325\pi$
$12$		0			0
$13$	−5.66091	+	2.58525i	−1.57005	+	0.717020i	−0.994885	−	0.101015i	$-0.967791\pi$
$13$	−5.66091	+	2.58525i	−1.57005	+	0.717020i	−0.575169	+	0.818034i	$0.695064\pi$
$14$		0			0
$15$	1.01547	+	0.559721i	0.262192	+	0.144519i
$16$		0			0
$17$	−1.52654	+	2.37534i	−0.370240	+	0.576105i	−0.975521	−	0.219907i	$-0.929424\pi$
$17$	−1.52654	+	2.37534i	−0.370240	+	0.576105i	0.605281	+	0.796012i	$0.293061\pi$
$18$		0			0
$19$	1.46731	−	0.942980i	0.336623	−	0.216334i	−0.361398	−	0.932412i	$-0.617700\pi$
$19$	1.46731	−	0.942980i	0.336623	−	0.216334i	0.698021	+	0.716077i	$0.254064\pi$
$20$		0			0
$21$	1.03276	−	0.303244i	0.225366	−	0.0661733i
$22$		0			0
$23$	1.78750	+	4.45026i	0.372719	+	0.927944i
$23$	1.78750	+	4.45026i	0.372719	+	0.927944i
$24$		0			0
$25$	−3.80457	+	3.24426i	−0.760914	+	0.648852i
$26$		0			0
$27$	−1.60671	−	2.50008i	−0.309211	−	0.481141i
$28$		0			0
$29$	−4.96168	−	3.18867i	−0.921360	−	0.592122i	−0.00830804	−	0.999965i	$-0.502645\pi$
$29$	−4.96168	−	3.18867i	−0.921360	−	0.592122i	−0.913052	+	0.407843i	$0.866281\pi$
$30$		0			0
$31$	0.641991	−	0.740897i	0.115305	−	0.133069i	−0.695163	−	0.718852i	$-0.744668\pi$
$31$	0.641991	−	0.740897i	0.115305	−	0.133069i	0.810468	+	0.585784i	$0.199213\pi$
$32$		0			0
$33$	0.541964	−	0.247507i	0.0943439	−	0.0430854i
$34$		0			0
$35$	−0.349453	+	4.62825i	−0.0590684	+	0.782317i
$36$		0			0
$37$	−9.82240	−	1.41225i	−1.61479	−	0.232172i	−0.725070	−	0.688675i	$-0.758193\pi$
$37$	−9.82240	−	1.41225i	−1.61479	−	0.232172i	−0.889722	+	0.456503i	$0.849102\pi$
$38$		0			0
$39$	1.34058	−	2.93546i	0.214664	−	0.470049i
$40$		0			0
$41$	0.155716	+	1.08303i	0.0243187	+	0.169140i	0.998361	−	0.0572242i	$-0.0182250\pi$
$41$	0.155716	+	1.08303i	0.0243187	+	0.169140i	−0.974043	+	0.226365i	$0.927316\pi$
$42$		0			0
$43$	3.30485	−	2.86367i	0.503985	−	0.436705i	−0.365393	−	0.930853i	$-0.619065\pi$
$43$	3.30485	−	2.86367i	0.503985	−	0.436705i	0.869378	+	0.494148i	$0.164520\pi$
$44$		0			0
$45$	5.97248	−	1.27447i	0.890324	−	0.189987i
$46$		0			0
$47$		−	9.71084i		−	1.41647i	−0.705976	−	0.708236i	$-0.749491\pi$
$47$		−	9.71084i		−	1.41647i	0.705976	−	0.708236i	$-0.250509\pi$
$48$		0			0
$49$	−1.76251	−	2.03405i	−0.251788	−	0.290578i
$50$		0			0
$51$	−0.208371	−	1.44925i	−0.0291778	−	0.202936i
$52$		0			0
$53$	0.689112	+	0.314707i	0.0946568	+	0.0432283i	0.462181	−	0.886786i	$-0.347067\pi$
$53$	0.689112	+	0.314707i	0.0946568	+	0.0432283i	−0.367524	+	0.930014i	$0.619794\pi$
$54$		0			0
$55$	0.173132	+	2.56338i	0.0233452	+	0.345646i
$56$		0			0
$57$	−0.254812	+	0.867810i	−0.0337507	+	0.114944i
$58$		0			0
$59$	4.94331	+	10.8243i	0.643564	+	1.40921i	0.897076	+	0.441876i	$0.145687\pi$
$59$	4.94331	+	10.8243i	0.643564	+	1.40921i	−0.253512	+	0.967332i	$0.581586\pi$
$60$		0			0
$61$	1.61202	−	1.86037i	0.206398	−	0.238196i	−0.643107	−	0.765776i	$-0.722355\pi$
$61$	1.61202	−	1.86037i	0.206398	−	0.238196i	0.849505	+	0.527580i	$0.176901\pi$
$62$		0			0
$63$	3.06488	−	4.76905i	0.386139	−	0.600844i
$64$		0			0
$65$	9.80084	+	9.87880i	1.21564	+	1.22531i
$66$		0			0
$67$	−2.84243	−	9.68043i	−0.347258	−	1.18265i	−0.929248	−	0.369456i	$-0.879544\pi$
$67$	−2.84243	−	9.68043i	−0.347258	−	1.18265i	0.581990	−	0.813196i	$-0.302274\pi$
$68$		0			0
$69$	−2.21171	−	1.13703i	−0.266259	−	0.136883i
$70$		0			0
$71$	−11.1753	+	3.28136i	−1.32626	+	0.389426i	−0.866749	−	0.498745i	$-0.833794\pi$
$71$	−11.1753	+	3.28136i	−1.32626	+	0.389426i	−0.459513	+	0.888171i	$0.651976\pi$
$72$		0			0
$73$	2.33540	+	3.63396i	0.273338	+	0.425323i	0.950600	−	0.310420i	$-0.100470\pi$
$73$	2.33540	+	3.63396i	0.273338	+	0.425323i	−0.677261	+	0.735743i	$0.736833\pi$
$74$		0			0
$75$	0.389307	−	2.56335i	0.0449533	−	0.295990i
$76$		0			0
$77$	1.80244	+	1.56182i	0.205407	+	0.177986i
$78$		0			0
$79$	0.268099	+	0.587055i	0.0301635	+	0.0660488i	0.924114	−	0.382117i	$-0.124805\pi$
$79$	0.268099	+	0.587055i	0.0301635	+	0.0660488i	−0.893951	+	0.448166i	$0.852078\pi$
$80$		0			0
$81$	−6.38281	−	1.87416i	−0.709201	−	0.208240i
$82$		0			0
$83$	11.9953	+	1.72466i	1.31665	+	0.189306i	0.764601	−	0.644504i	$-0.222936\pi$
$83$	11.9953	+	1.72466i	1.31665	+	0.189306i	0.552051	+	0.833810i	$0.313845\pi$
$84$		0			0
$85$	6.16405	+	1.36650i	0.668585	+	0.148218i
$86$		0			0
$87$	3.02724	−	0.435252i	0.324555	−	0.0466639i
$88$		0			0
$89$	7.89200	+	9.10785i	0.836550	+	0.965430i	0.999776	−	0.0211587i	$-0.00673552\pi$
$89$	7.89200	+	9.10785i	0.836550	+	0.965430i	−0.163226	+	0.986589i	$0.552190\pi$
$90$		0			0
$91$	12.9178			1.35415
$92$		0			0
$93$			0.508357i			0.0527142i
$94$		0			0
$95$	−3.11293	−	2.34961i	−0.319380	−	0.241065i
$96$		0			0
$97$	7.65107	−	1.10006i	0.776848	−	0.111694i	0.257525	−	0.966272i	$-0.417093\pi$
$97$	7.65107	−	1.10006i	0.776848	−	0.111694i	0.519323	+	0.854578i	$0.326184\pi$
$98$		0			0
$99$	1.30358	−	2.85444i	0.131014	−	0.286882i
$100$		0			0
$101$	−0.569477	+	3.96080i	−0.0566651	+	0.394114i	0.941675	+	0.336523i	$0.109251\pi$
$101$	−0.569477	+	3.96080i	−0.0566651	+	0.394114i	−0.998340	+	0.0575911i	$0.981658\pi$
$102$		0			0
$103$	0.911402	−	3.10395i	0.0898031	−	0.305841i	−0.902327	−	0.431052i	$-0.858143\pi$
$103$	0.911402	−	3.10395i	0.0898031	−	0.305841i	0.992130	+	0.125211i	$0.0399607\pi$
$104$		0			0
$105$	−1.43470	−	1.93244i	−0.140012	−	0.188587i
$106$		0			0
$107$	−6.44544	−	5.58500i	−0.623104	−	0.539923i	0.285075	−	0.958505i	$-0.407982\pi$
$107$	−6.44544	−	5.58500i	−0.623104	−	0.539923i	−0.908179	+	0.418583i	$0.862527\pi$
$108$		0			0
$109$	1.76709	+	1.13564i	0.169256	+	0.108774i	0.622526	−	0.782599i	$-0.286106\pi$
$109$	1.76709	+	1.13564i	0.169256	+	0.108774i	−0.453270	+	0.891373i	$0.649743\pi$
$110$		0			0
$111$	4.32889	−	2.78201i	0.410880	−	0.264057i
$112$		0			0
$113$	2.86986	+	9.77383i	0.269973	+	0.919445i	0.977176	+	0.212433i	$0.0681389\pi$
$113$	2.86986	+	9.77383i	0.269973	+	0.919445i	−0.707202	+	0.707011i	$0.750043\pi$
$114$		0			0
$115$	7.95543	−	7.19105i	0.741847	−	0.670569i
$116$		0			0
$117$	−4.78847	−	16.3080i	−0.442694	−	1.50768i
$118$		0			0
$119$	4.93051	−	3.16865i	0.451980	−	0.290470i
$120$		0			0
$121$	−8.14319	−	5.23331i	−0.740290	−	0.475755i
$122$		0			0
$123$	−0.428795	−	0.371553i	−0.0386631	−	0.0335018i
$124$		0			0
$125$	9.74838	+	5.47441i	0.871921	+	0.489646i
$126$		0			0
$127$	5.80633	−	19.7746i	0.515229	−	1.75471i	−0.130814	−	0.991407i	$-0.541759\pi$
$127$	5.80633	−	19.7746i	0.515229	−	1.75471i	0.646043	−	0.763301i	$-0.276423\pi$
$128$		0			0
$129$	−0.322710	+	2.24450i	−0.0284131	+	0.197617i
$130$		0			0
$131$	1.58137	−	3.46272i	0.138165	−	0.302539i	−0.827883	−	0.560900i	$-0.810455\pi$
$131$	1.58137	−	3.46272i	0.138165	−	0.302539i	0.966048	+	0.258361i	$0.0831824\pi$
$132$		0			0
$133$	−3.58358	+	0.515241i	−0.310736	+	0.0446771i
$134$		0			0
$135$	−4.00341	+	5.30399i	−0.344558	+	0.456495i
$136$		0			0
$137$			11.2593i			0.961950i	0.876734	+	0.480975i	$0.159717\pi$
$137$			11.2593i			0.961950i	−0.876734	+	0.480975i	$0.840283\pi$
$138$		0			0
$139$	−16.9025			−1.43365			−0.716827	−	0.697251i	$-0.754406\pi$
$139$	−16.9025			−1.43365			−0.716827	+	0.697251i	$0.754406\pi$
$140$		0			0
$141$	3.29758	+	3.80561i	0.277706	+	0.320490i
$142$		0			0
$143$	7.07772	−	1.01762i	0.591869	−	0.0850979i
$144$		0			0
$145$	−2.85439	+	12.8756i	−0.237044	+	1.06926i
$146$		0			0
$147$	1.38143	+	0.198620i	0.113939	+	0.0163819i
$148$		0			0
$149$	−15.2096	−	4.46595i	−1.24602	−	0.365865i	−0.408747	−	0.912648i	$-0.634034\pi$
$149$	−15.2096	−	4.46595i	−1.24602	−	0.365865i	−0.837275	+	0.546782i	$0.815852\pi$
$150$		0			0
$151$	7.50140	+	16.4258i	0.610455	+	1.33671i	0.922262	+	0.386565i	$0.126338\pi$
$151$	7.50140	+	16.4258i	0.610455	+	1.33671i	−0.311807	+	0.950145i	$0.600934\pi$
$152$		0			0
$153$	−5.82795	−	5.04995i	−0.471162	−	0.408264i
$154$		0			0
$155$	−2.05086	−	0.774199i	−0.164729	−	0.0621852i
$156$		0			0
$157$	−7.46119	−	11.6098i	−0.595468	−	0.926566i	−0.999928	−	0.0120107i	$-0.996177\pi$
$157$	−7.46119	−	11.6098i	−0.595468	−	0.926566i	0.404460	−	0.914556i	$-0.367460\pi$
$158$		0			0
$159$	−0.376925	+	0.110675i	−0.0298921	+	0.00877711i
$160$		0			0
$161$	0.462345	−	9.94401i	0.0364379	−	0.783698i
$162$		0			0
$163$	2.65540	+	9.04346i	0.207987	+	0.708338i	0.995728	+	0.0923322i	$0.0294322\pi$
$163$	2.65540	+	9.04346i	0.207987	+	0.708338i	−0.787741	+	0.616006i	$0.788750\pi$
$164$		0			0
$165$	−0.938313	−	0.945777i	−0.0730476	−	0.0736286i
$166$		0			0
$167$	−9.46304	+	14.7248i	−0.732272	+	1.13944i	0.252838	+	0.967509i	$0.418636\pi$
$167$	−9.46304	+	14.7248i	−0.732272	+	1.13944i	−0.985109	+	0.171928i	$0.945000\pi$
$168$		0			0
$169$	16.8492	−	19.4450i	1.29609	−	1.49577i
$170$		0			0
$171$	1.97886	+	4.33310i	0.151327	+	0.331360i
$172$		0			0
$173$	−0.481663	+	1.64039i	−0.0366202	+	0.124717i	−0.975775	−	0.218779i	$-0.929793\pi$
$173$	−0.481663	+	1.64039i	−0.0366202	+	0.124717i	0.939154	+	0.343495i	$0.111611\pi$
$174$		0			0
$175$	9.98099	−	2.84498i	0.754492	−	0.215061i
$176$		0			0
$177$	−5.61294	−	2.56334i	−0.421894	−	0.192673i
$178$		0			0
$179$	−2.69587	−	18.7502i	−0.201499	−	1.40146i	−0.799839	−	0.600215i	$-0.795082\pi$
$179$	−2.69587	−	18.7502i	−0.201499	−	1.40146i	0.598340	−	0.801242i	$-0.295827\pi$
$180$		0			0
$181$	5.23566	+	6.04227i	0.389163	+	0.449119i	0.916198	−	0.400725i	$-0.131242\pi$
$181$	5.23566	+	6.04227i	0.389163	+	0.449119i	−0.527035	+	0.849844i	$0.676696\pi$
$182$		0			0
$183$			1.27647i			0.0943592i
$184$		0			0
$185$	4.63077	+	21.7008i	0.340461	+	1.59548i
$186$		0			0
$187$	2.45184	−	2.12453i	0.179297	−	0.155361i
$188$		0			0
$189$	0.877898	+	6.10592i	0.0638577	+	0.444140i
$190$		0			0
$191$	−3.73510	+	8.17872i	−0.270262	+	0.591792i	−0.995292	−	0.0969263i	$-0.969099\pi$
$191$	−3.73510	+	8.17872i	−0.270262	+	0.591792i	0.725029	+	0.688718i	$0.241826\pi$
$192$		0			0
$193$	−26.0883	−	3.75093i	−1.87788	−	0.269998i	−0.893896	−	0.448273i	$-0.852039\pi$
$193$	−26.0883	−	3.75093i	−1.87788	−	0.269998i	−0.983981	+	0.178276i	$0.942948\pi$
$194$		0			0
$195$	−7.19549	−	0.543291i	−0.515280	−	0.0389059i
$196$		0			0
$197$	4.04714	−	1.84827i	0.288347	−	0.131684i	−0.265991	−	0.963976i	$-0.585699\pi$
$197$	4.04714	−	1.84827i	0.288347	−	0.131684i	0.554337	+	0.832292i	$0.312972\pi$
$198$		0			0
$199$	0.783458	−	0.904159i	0.0555379	−	0.0640941i	−0.727301	−	0.686319i	$-0.759225\pi$
$199$	0.783458	−	0.904159i	0.0555379	−	0.0640941i	0.782839	+	0.622225i	$0.213771\pi$
$200$		0			0
$201$	4.40118	+	2.82846i	0.310435	+	0.199504i
$202$		0			0
$203$	6.61876	+	10.2990i	0.464546	+	0.722848i
$204$		0			0
$205$	2.15198	−	1.16403i	0.150301	−	0.0812992i
$206$		0			0
$207$	−12.7252	+	3.10245i	−0.884462	+	0.215635i
$208$		0			0
$209$	−1.92288	+	0.564608i	−0.133008	+	0.0390547i
$210$		0			0
$211$	−13.5515	+	8.70904i	−0.932926	+	0.599555i	−0.916381	−	0.400308i	$-0.868903\pi$
$211$	−13.5515	+	8.70904i	−0.932926	+	0.599555i	−0.0165451	+	0.999863i	$0.505267\pi$
$212$		0			0
$213$	3.26524	−	5.08081i	0.223730	−	0.348131i
$214$		0			0
$215$	−8.56348	−	4.72015i	−0.584025	−	0.321912i
$216$		0			0
$217$	−1.85102	+	0.845334i	−0.125656	+	0.0573850i
$218$		0			0
$219$	−2.14924	−	0.631073i	−0.145232	−	0.0426439i
$220$		0			0
$221$	2.50075	−	17.3931i	0.168218	−	1.16998i
$222$		0			0
$223$	11.7683	+	5.37440i	0.788064	+	0.359897i	0.768449	−	0.639911i	$-0.221029\pi$
$223$	11.7683	+	5.37440i	0.788064	+	0.359897i	0.0196147	+	0.999808i	$0.493756\pi$
$224$		0			0
$225$	−7.29149	−	11.5459i	−0.486100	−	0.769727i
$226$		0			0
$227$	−14.3227	+	12.4107i	−0.950632	+	0.823728i	−0.984444	−	0.175701i	$-0.943781\pi$
$227$	−14.3227	+	12.4107i	−0.950632	+	0.823728i	0.0338112	+	0.999428i	$0.489236\pi$
$228$		0			0
$229$	8.03616			0.531044			0.265522	−	0.964105i	$-0.414456\pi$
$229$	8.03616			0.531044			0.265522	+	0.964105i	$0.414456\pi$
$230$		0			0
$231$	−1.23672			−0.0813702
$232$		0			0
$233$	−7.32895	+	6.35057i	−0.480136	+	0.416040i	−0.861011	−	0.508587i	$-0.830168\pi$
$233$	−7.32895	+	6.35057i	−0.480136	+	0.416040i	0.380875	+	0.924626i	$0.375623\pi$
$234$		0			0
$235$	−20.3749	+	7.50764i	−1.32911	+	0.489745i
$236$		0			0
$237$	−0.304416	−	0.139022i	−0.0197739	−	0.00903046i
$238$		0			0
$239$	−2.38039	+	16.5560i	−0.153975	+	1.07092i	0.755497	+	0.655152i	$0.227395\pi$
$239$	−2.38039	+	16.5560i	−0.153975	+	1.07092i	−0.909472	+	0.415765i	$0.863514\pi$
$240$		0			0
$241$	−22.3124	−	6.55150i	−1.43727	−	0.422019i	−0.531956	−	0.846772i	$-0.678543\pi$
$241$	−22.3124	−	6.55150i	−1.43727	−	0.422019i	−0.905309	+	0.424753i	$0.860361\pi$
$242$		0			0
$243$	11.2477	−	5.13664i	0.721539	−	0.329516i
$244$		0			0
$245$	−2.90513	+	5.27060i	−0.185602	+	0.336726i
$246$		0			0
$247$	−5.86845	+	9.13148i	−0.373400	+	0.581022i
$248$		0			0
$249$	−5.28651	+	3.39744i	−0.335019	+	0.215304i
$250$		0			0
$251$	20.9957	−	6.16489i	1.32524	−	0.389124i	0.458856	−	0.888511i	$-0.348259\pi$
$251$	20.9957	−	6.16489i	1.32524	−	0.389124i	0.866379	+	0.499387i	$0.166441\pi$
$252$		0			0
$253$	−0.530038	−	5.48481i	−0.0333232	−	0.344827i
$254$		0			0
$255$	−2.87968	+	1.55764i	−0.180332	+	0.0975435i
$256$		0			0
$257$	3.60374	+	5.60753i	0.224795	+	0.349788i	0.935270	−	0.353934i	$-0.115156\pi$
$257$	3.60374	+	5.60753i	0.224795	+	0.349788i	−0.710475	+	0.703722i	$0.751520\pi$
$258$		0			0
$259$	17.3282	+	11.1362i	1.07672	+	0.691968i
$260$		0			0
$261$	10.5485	−	12.1736i	0.652934	−	0.753525i
$262$		0			0
$263$	−14.4630	+	6.60504i	−0.891829	+	0.407284i	−0.807991	−	0.589195i	$-0.799445\pi$
$263$	−14.4630	+	6.60504i	−0.891829	+	0.407284i	−0.0838377	+	0.996479i	$0.526718\pi$
$264$		0			0
$265$	0.127540	−	1.68918i	0.00783473	−	0.103765i
$266$		0			0
$267$	−6.18563	−	0.889359i	−0.378554	−	0.0544279i
$268$		0			0
$269$	−1.69606	+	3.71385i	−0.103411	+	0.226437i	−0.954264	−	0.298966i	$-0.903358\pi$
$269$	−1.69606	+	3.71385i	−0.103411	+	0.226437i	0.850853	+	0.525403i	$0.176086\pi$
$270$		0			0
$271$	−2.55674	−	17.7825i	−0.155311	−	1.08021i	−0.907133	−	0.420845i	$-0.861734\pi$
$271$	−2.55674	−	17.7825i	−0.155311	−	1.08021i	0.751822	−	0.659367i	$-0.229175\pi$
$272$		0			0
$273$	−5.06237	+	4.38657i	−0.306389	+	0.265487i
$274$		0			0
$275$	5.24453	−	2.34506i	0.316257	−	0.141412i
$276$		0			0
$277$		−	5.65123i		−	0.339549i	−0.985483	−	0.169775i	$-0.945696\pi$
$277$		−	5.65123i		−	0.339549i	0.985483	−	0.169775i	$-0.0543040\pi$
$278$		0			0
$279$	1.75335	+	2.02347i	0.104970	+	0.121142i
$280$		0			0
$281$	3.20113	+	22.2643i	0.190963	+	1.32818i	0.829465	+	0.558558i	$0.188645\pi$
$281$	3.20113	+	22.2643i	0.190963	+	1.32818i	−0.638502	+	0.769620i	$0.720446\pi$
$282$		0			0
$283$	−16.8241	−	7.68331i	−1.00009	−	0.456726i	−0.153029	−	0.988222i	$-0.548903\pi$
$283$	−16.8241	−	7.68331i	−1.00009	−	0.456726i	−0.847061	+	0.531496i	$0.821630\pi$
$284$		0			0
$285$	2.01781	−	0.136284i	0.119525	−	0.00807277i
$286$		0			0
$287$	0.639862	−	2.17917i	0.0377698	−	0.128632i
$288$		0			0
$289$	3.75013	+	8.21165i	0.220596	+	0.483038i
$290$		0			0
$291$	−2.62484	+	3.02923i	−0.153871	+	0.177577i
$292$		0			0
$293$	8.62733	−	13.4244i	0.504014	−	0.784261i	−0.492265	−	0.870445i	$-0.663831\pi$
$293$	8.62733	−	13.4244i	0.504014	−	0.784261i	0.996279	+	0.0861839i	$0.0274673\pi$
$294$		0			0
$295$	18.8894	−	18.7404i	1.09979	−	1.09111i
$296$		0			0
$297$	0.962012	+	3.27631i	0.0558216	+	0.190111i
$298$		0			0
$299$	−21.6239	−	20.5714i	−1.25054	−	1.18968i
$300$		0			0
$301$	−8.70927	+	2.55727i	−0.501994	+	0.147399i
$302$		0			0
$303$	−1.12182	−	1.74559i	−0.0644470	−	0.100281i
$304$		0			0
$305$	−5.14964	−	1.94399i	−0.294867	−	0.111312i
$306$		0			0
$307$	13.5365	+	11.7295i	0.772570	+	0.669435i	0.949141	−	0.314853i	$-0.101955\pi$
$307$	13.5365	+	11.7295i	0.772570	+	0.669435i	−0.176571	+	0.984288i	$0.556501\pi$
$308$		0			0
$309$	0.696858	+	1.52591i	0.0396429	+	0.0868058i
$310$		0			0
$311$	−28.6426	−	8.41022i	−1.62417	−	0.476900i	−0.662036	−	0.749472i	$-0.730307\pi$
$311$	−28.6426	−	8.41022i	−1.62417	−	0.476900i	−0.962135	+	0.272573i	$0.912126\pi$
$312$		0			0
$313$	−20.6344	−	2.96678i	−1.16632	−	0.167692i	−0.468169	−	0.883639i	$-0.655086\pi$
$313$	−20.6344	−	2.96678i	−1.16632	−	0.167692i	−0.698155	+	0.715947i	$0.745995\pi$
$314$		0			0
$315$	−12.3758	−	2.74358i	−0.697296	−	0.154583i
$316$		0			0
$317$	7.81496	−	1.12362i	0.438932	−	0.0631089i	0.0806933	−	0.996739i	$-0.474287\pi$
$317$	7.81496	−	1.12362i	0.438932	−	0.0631089i	0.358238	+	0.933630i	$0.383377\pi$
$318$		0			0
$319$	4.43778	+	5.12148i	0.248468	+	0.286748i
$320$		0			0
$321$	4.42246			0.246837
$322$		0			0
$323$			4.92485i			0.274026i
$324$		0			0
$325$	13.1501	−	28.2013i	0.729437	−	1.56432i
$326$		0			0
$327$	−1.07814	+	0.155014i	−0.0596215	+	0.00857228i
$328$		0			0
$329$	−8.37347	+	18.3353i	−0.461644	+	1.01086i
$330$		0			0
$331$	3.90128	−	27.1340i	0.214434	−	1.49142i	−0.543679	−	0.839294i	$-0.682969\pi$
$331$	3.90128	−	27.1340i	0.214434	−	1.49142i	0.758112	−	0.652124i	$-0.226122\pi$
$332$		0			0
$333$	7.63548	−	26.0041i	0.418422	−	1.42501i
$334$		0			0
$335$	−18.1136	+	13.4480i	−0.989650	+	0.734743i
$336$		0			0
$337$	18.6278	+	16.1411i	1.01472	+	0.879263i	0.992714	−	0.120495i	$-0.0384481\pi$
$337$	18.6278	+	16.1411i	1.01472	+	0.879263i	0.0220096	+	0.999758i	$0.492994\pi$
$338$		0			0
$339$	−4.44364	−	2.85576i	−0.241345	−	0.155103i
$340$		0			0
$341$	−0.947595	+	0.608982i	−0.0513151	+	0.0329782i
$342$		0			0
$343$	5.66750	+	19.3017i	0.306016	+	1.04220i
$344$		0			0
$345$	−0.675758	+	5.51960i	−0.0363816	+	0.297165i
$346$		0			0
$347$	0.0811813	+	0.276478i	0.00435804	+	0.0148421i	0.961643	−	0.274303i	$-0.0884471\pi$
$347$	0.0811813	+	0.276478i	0.00435804	+	0.0148421i	−0.957285	+	0.289145i	$0.906629\pi$
$348$		0			0
$349$	15.4926	−	9.95650i	0.829301	−	0.532959i	−0.0557549	−	0.998444i	$-0.517757\pi$
$349$	15.4926	−	9.95650i	0.829301	−	0.532959i	0.885056	+	0.465485i	$0.154120\pi$
$350$		0			0
$351$	15.5588	+	9.99901i	0.830466	+	0.533708i
$352$		0			0
$353$	15.2541	+	13.2178i	0.811896	+	0.703512i	0.958316	−	0.285711i	$-0.0922297\pi$
$353$	15.2541	+	13.2178i	0.811896	+	0.703512i	−0.146420	+	0.989222i	$0.546775\pi$
$354$		0			0
$355$	15.5247	+	20.9107i	0.823963	+	1.10982i
$356$		0			0
$357$	−0.856232	+	2.91606i	−0.0453166	+	0.154334i
$358$		0			0
$359$	1.37670	−	9.57514i	0.0726593	−	0.505357i	−0.920697	−	0.390278i	$-0.872379\pi$
$359$	1.37670	−	9.57514i	0.0726593	−	0.505357i	0.993356	−	0.115079i	$-0.0367120\pi$
$360$		0			0
$361$	−6.62911	+	14.5157i	−0.348901	+	0.763986i
$362$		0			0
$363$	4.96836	−	0.714343i	0.260771	−	0.0374933i
$364$		0			0
$365$	5.81909	−	7.70954i	0.304585	−	0.403536i
$366$		0			0
$367$			2.84709i			0.148617i	0.997235	+	0.0743085i	$0.0236749\pi$
$367$			2.84709i			0.148617i	−0.997235	+	0.0743085i	$0.976325\pi$
$368$		0			0
$369$	−2.98828			−0.155564
$370$		0			0
$371$	−1.02977	−	1.18842i	−0.0534629	−	0.0616995i
$372$		0			0
$373$	−15.4218	+	2.21733i	−0.798512	+	0.114809i	−0.529480	−	0.848322i	$-0.677613\pi$
$373$	−15.4218	+	2.21733i	−0.798512	+	0.114809i	−0.269032	+	0.963131i	$0.586704\pi$
$374$		0			0
$375$	−5.67930	+	1.16494i	−0.293278	+	0.0601575i
$376$		0			0
$377$	36.3311	+	5.22363i	1.87115	+	0.269031i
$378$		0			0
$379$	−9.39304	−	2.75805i	−0.482488	−	0.141671i	0.0314380	−	0.999506i	$-0.489991\pi$
$379$	−9.39304	−	2.75805i	−0.482488	−	0.141671i	−0.513926	+	0.857834i	$0.671810\pi$
$380$		0			0
$381$	4.43952	+	9.72120i	0.227444	+	0.498032i
$382$		0			0
$383$	4.54243	+	3.93604i	0.232107	+	0.201122i	0.763147	−	0.646225i	$-0.223653\pi$
$383$	4.54243	+	3.93604i	0.232107	+	0.201122i	−0.531040	+	0.847347i	$0.678199\pi$
$384$		0			0
$385$	1.88345	−	4.98928i	0.0959897	−	0.254277i
$386$		0			0
$387$	6.45686	+	10.0471i	0.328221	+	0.510721i
$388$		0			0
$389$	19.3148	−	5.67134i	0.979299	−	0.287548i	0.247364	−	0.968923i	$-0.420436\pi$
$389$	19.3148	−	5.67134i	0.979299	−	0.287548i	0.731935	+	0.681375i	$0.238617\pi$
$390$		0			0
$391$	−13.2996	−	2.54758i	−0.672588	−	0.128837i
$392$		0			0
$393$	0.556132	+	1.89401i	0.0280531	+	0.0955402i
$394$		0			0
$395$	1.02446	−	1.01638i	0.0515464	−	0.0511396i
$396$		0			0
$397$	4.13430	−	6.43310i	0.207495	−	0.322868i	−0.721871	−	0.692027i	$-0.756718\pi$
$397$	4.13430	−	6.43310i	0.207495	−	0.322868i	0.929366	+	0.369159i	$0.120354\pi$
$398$		0			0
$399$	1.22941	−	1.41882i	0.0615477	−	0.0710298i
$400$		0			0
$401$	0.0907559	+	0.198728i	0.00453214	+	0.00992399i	0.911885	−	0.410447i	$-0.134627\pi$
$401$	0.0907559	+	0.198728i	0.00453214	+	0.00992399i	−0.907352	+	0.420371i	$0.861900\pi$
$402$		0			0
$403$	−1.71885	+	5.85386i	−0.0856219	+	0.291601i
$404$		0			0
$405$	1.00238	+	14.8411i	0.0498087	+	0.737461i
$406$		0			0
$407$	10.3715	+	4.73651i	0.514097	+	0.234780i
$408$		0			0
$409$	−4.18062	−	29.0768i	−0.206718	−	1.43776i	−0.783771	−	0.621050i	$-0.786706\pi$
$409$	−4.18062	−	29.0768i	−0.206718	−	1.43776i	0.577052	−	0.816707i	$-0.304203\pi$
$410$		0			0
$411$	−3.82341	−	4.41245i	−0.188595	−	0.217650i
$412$		0			0
$413$		−	24.7003i		−	1.21542i
$414$		0			0
$415$	−5.65517	−	26.5014i	−0.277601	−	1.30090i
$416$		0			0
$417$	6.62398	−	5.73971i	0.324378	−	0.281075i
$418$		0			0
$419$	4.57153	+	31.7957i	0.223334	+	1.55332i	0.725299	+	0.688433i	$0.241701\pi$
$419$	4.57153	+	31.7957i	0.223334	+	1.55332i	−0.501966	+	0.864888i	$0.667390\pi$
$420$		0			0
$421$	−14.6659	+	32.1138i	−0.714772	+	1.56513i	0.106317	+	0.994332i	$0.466094\pi$
$421$	−14.6659	+	32.1138i	−0.714772	+	1.56513i	−0.821089	+	0.570800i	$0.806633\pi$
$422$		0			0
$423$	26.2514	+	3.77438i	1.27639	+	0.183517i
$424$		0			0
$425$	−1.89840	−	13.9896i	−0.0920860	−	0.678597i
$426$		0			0
$427$	−4.64786	+	2.12261i	−0.224926	+	0.102720i
$428$		0			0
$429$	−2.42814	+	2.80223i	−0.117232	+	0.135293i
$430$		0			0
$431$	17.1089	+	10.9952i	0.824106	+	0.529621i	0.883400	−	0.468620i	$-0.155249\pi$
$431$	17.1089	+	10.9952i	0.824106	+	0.529621i	−0.0592938	+	0.998241i	$0.518885\pi$
$432$		0			0
$433$	−18.1740	−	28.2794i	−0.873389	−	1.35902i	−0.932652	−	0.360777i	$-0.882511\pi$
$433$	−18.1740	−	28.2794i	−0.873389	−	1.35902i	0.0592630	−	0.998242i	$-0.481125\pi$
$434$		0			0
$435$	−3.25365	−	6.01515i	−0.156001	−	0.288404i
$436$		0			0
$437$	6.81932	+	4.84432i	0.326212	+	0.231735i
$438$		0			0
$439$	−17.7483	+	5.21137i	−0.847080	+	0.248725i	−0.676339	−	0.736591i	$-0.736435\pi$
$439$	−17.7483	+	5.21137i	−0.847080	+	0.248725i	−0.170742	+	0.985316i	$0.554616\pi$
$440$		0			0
$441$	6.18371	−	3.97403i	0.294462	−	0.189240i
$442$		0			0
$443$	15.0600	−	23.4339i	0.715524	−	1.11338i	−0.272956	−	0.962027i	$-0.588001\pi$
$443$	15.0600	−	23.4339i	0.715524	−	1.11338i	0.988480	−	0.151351i	$-0.0483624\pi$
$444$		0			0
$445$	13.0083	−	23.6001i	0.616652	−	1.11875i
$446$		0			0
$447$	7.47708	−	3.41467i	0.353654	−	0.161508i
$448$		0			0
$449$	−4.85078	−	1.42432i	−0.228922	−	0.0672177i	0.165260	−	0.986250i	$-0.447154\pi$
$449$	−4.85078	−	1.42432i	−0.228922	−	0.0672177i	−0.394182	+	0.919032i	$0.628972\pi$
$450$		0			0
$451$	0.178916	−	1.24439i	0.00842481	−	0.0585959i
$452$		0			0
$453$	−8.51755	−	3.88984i	−0.400190	−	0.182760i
$454$		0			0
$455$	−9.98697	−	27.1036i	−0.468197	−	1.27063i
$456$		0			0
$457$	11.2985	−	9.79018i	0.528520	−	0.457965i	−0.349262	−	0.937025i	$-0.613568\pi$
$457$	11.2985	−	9.79018i	0.528520	−	0.457965i	0.877782	+	0.479060i	$0.159022\pi$
$458$		0			0
$459$	8.39125			0.391670
$460$		0			0
$461$	15.8546			0.738421			0.369210	−	0.929346i	$-0.379628\pi$
$461$	15.8546			0.738421			0.369210	+	0.929346i	$0.379628\pi$
$462$		0			0
$463$	−10.0248	+	8.68656i	−0.465893	+	0.403698i	−0.855923	−	0.517104i	$-0.827010\pi$
$463$	−10.0248	+	8.68656i	−0.465893	+	0.403698i	0.390030	+	0.920802i	$0.372465\pi$
$464$		0			0
$465$	1.06662	−	0.393021i	0.0494631	−	0.0182259i
$466$		0			0
$467$	−7.70556	−	3.51901i	−0.356571	−	0.162840i	0.229072	−	0.973409i	$-0.426431\pi$
$467$	−7.70556	−	3.51901i	−0.356571	−	0.162840i	−0.585643	+	0.810569i	$0.699158\pi$
$468$		0			0
$469$	−2.98036	+	20.7289i	−0.137620	+	0.957171i
$470$		0			0
$471$	6.86642	+	2.01616i	0.316388	+	0.0928999i
$472$		0			0
$473$	−4.57041	+	2.08724i	−0.210148	+	0.0959712i
$474$		0			0
$475$	−2.52320	+	8.34796i	−0.115772	+	0.383031i
$476$		0			0
$477$	−1.11859	+	1.74056i	−0.0512168	+	0.0796949i
$478$		0			0
$479$	26.6713	−	17.1406i	1.21864	−	0.783173i	0.236557	−	0.971618i	$-0.423981\pi$
$479$	26.6713	−	17.1406i	1.21864	−	0.783173i	0.982084	+	0.188444i	$0.0603445\pi$
$480$		0			0
$481$	59.2547	−	17.3988i	2.70178	−	0.793315i
$482$		0			0
$483$	3.19556	+	4.05398i	0.145403	+	0.184463i
$484$		0			0
$485$	−8.22329	−	15.2027i	−0.373400	−	0.690319i
$486$		0			0
$487$	15.3658	+	23.9096i	0.696291	+	1.08345i	0.991762	+	0.128097i	$0.0408870\pi$
$487$	15.3658	+	23.9096i	0.696291	+	1.08345i	−0.295471	+	0.955352i	$0.595477\pi$
$488$		0			0
$489$	−4.11158	−	2.64235i	−0.185932	−	0.119491i
$490$		0			0
$491$	5.04330	−	5.82028i	0.227601	−	0.262666i	−0.630450	−	0.776230i	$-0.717130\pi$
$491$	5.04330	−	5.82028i	0.227601	−	0.262666i	0.858051	+	0.513564i	$0.171675\pi$
$492$		0			0
$493$	15.1484	−	6.91803i	0.682248	−	0.311572i
$494$		0			0
$495$	−6.99689	−	0.528296i	−0.314487	−	0.0237451i
$496$		0			0
$497$	23.9299	+	3.44059i	1.07340	+	0.154332i
$498$		0			0
$499$	−7.59922	+	16.6400i	−0.340188	+	0.744908i	−0.999979	−	0.00654171i	$-0.997918\pi$
$499$	−7.59922	+	16.6400i	−0.340188	+	0.744908i	0.659791	+	0.751449i	$0.270645\pi$
$500$		0			0
$501$	−1.29170	−	8.98396i	−0.0577088	−	0.401374i
$502$		0			0
$503$	22.6785	−	19.6510i	1.01118	−	0.876195i	0.0188547	−	0.999822i	$-0.493998\pi$
$503$	22.6785	−	19.6510i	1.01118	−	0.876195i	0.992329	+	0.123627i	$0.0394525\pi$
$504$		0			0
$505$	8.75068	−	1.86732i	0.389400	−	0.0830945i
$506$		0			0
$507$			13.3420i			0.592537i
$508$		0			0
$509$	7.06111	+	8.14896i	0.312978	+	0.361196i	0.890343	−	0.455290i	$-0.150464\pi$
$509$	7.06111	+	8.14896i	0.312978	+	0.361196i	−0.577365	+	0.816486i	$0.695919\pi$
$510$		0			0
$511$	−1.27606	−	8.87517i	−0.0564494	−	0.392614i
$512$		0			0
$513$	−4.71506	−	2.15330i	−0.208175	−	0.0950703i
$514$		0			0
$515$	−7.21722	+	0.487456i	−0.318029	+	0.0214799i
$516$		0			0
$517$	−3.14347	+	10.7057i	−0.138250	+	0.470836i
$518$		0			0
$519$	−0.368280	−	0.806420i	−0.0161657	−	0.0353979i
$520$		0			0
$521$	−0.521542	+	0.601892i	−0.0228492	+	0.0263693i	−0.767059	−	0.641576i	$-0.778281\pi$
$521$	−0.521542	+	0.601892i	−0.0228492	+	0.0263693i	0.744210	+	0.667946i	$0.232826\pi$
$522$		0			0
$523$	−12.9314	+	20.1217i	−0.565452	+	0.879861i	−0.999782	−	0.0208932i	$-0.993349\pi$
$523$	−12.9314	+	20.1217i	−0.565452	+	0.879861i	0.434329	+	0.900754i	$0.356985\pi$
$524$		0			0
$525$	−2.94539	+	4.50424i	−0.128547	+	0.196581i
$526$		0			0
$527$	0.779858	+	2.65595i	0.0339712	+	0.115695i
$528$		0			0
$529$	−16.6097	+	15.9097i	−0.722161	+	0.691725i
$530$		0			0
$531$	−31.1829	+	9.15612i	−1.35322	+	0.397342i
$532$		0			0
$533$	−3.68139	−	5.72836i	−0.159459	−	0.248123i
$534$		0			0
$535$	−6.73515	+	17.8415i	−0.291186	+	0.771353i
$536$		0			0
$537$	7.42363	+	6.43261i	0.320353	+	0.277588i
$538$		0			0
$539$	1.28464	+	2.81297i	0.0553334	+	0.121163i
$540$		0			0
$541$	−30.1063	−	8.84001i	−1.29437	−	0.380062i	−0.439192	−	0.898393i	$-0.644735\pi$
$541$	−30.1063	−	8.84001i	−1.29437	−	0.380062i	−0.855180	+	0.518332i	$0.826553\pi$
$542$		0			0
$543$	−4.10363	−	0.590013i	−0.176104	−	0.0253199i
$544$		0			0
$545$	1.01658	−	4.58562i	0.0435456	−	0.196426i
$546$		0			0
$547$	19.1828	−	2.75807i	0.820197	−	0.117926i	0.280573	−	0.959833i	$-0.409476\pi$
$547$	19.1828	−	2.75807i	0.820197	−	0.117926i	0.539624	+	0.841906i	$0.318566\pi$
$548$		0			0
$549$	4.40259	+	5.08087i	0.187898	+	0.216846i
$550$		0			0
$551$	−10.2872			−0.438247
$552$		0			0
$553$		−	1.33961i		−	0.0569661i
$554$		0			0
$555$	−9.18386	−	6.93189i	−0.389833	−	0.294242i
$556$		0			0
$557$	−28.7185	+	4.12910i	−1.21684	+	0.174955i	−0.720676	−	0.693272i	$-0.756168\pi$
$557$	−28.7185	+	4.12910i	−1.21684	+	0.174955i	−0.496166	+	0.868228i	$0.665259\pi$
$558$		0			0
$559$	−11.3052	+	24.7548i	−0.478157	+	1.04702i
$560$		0			0
$561$	−0.239416	+	1.66518i	−0.0101082	+	0.0703039i
$562$		0			0
$563$	−2.69210	+	9.16846i	−0.113459	+	0.386404i	−0.996570	−	0.0827598i	$-0.973627\pi$
$563$	−2.69210	+	9.16846i	−0.113459	+	0.386404i	0.883111	+	0.469164i	$0.155445\pi$
$564$		0			0
$565$	18.2883	−	13.5778i	0.769396	−	0.571221i
$566$		0			0
$567$	10.4355	+	9.04244i	0.438251	+	0.379747i
$568$		0			0
$569$	−23.0051	−	14.7845i	−0.964426	−	0.619799i	−0.0392062	−	0.999231i	$-0.512483\pi$
$569$	−23.0051	−	14.7845i	−0.964426	−	0.619799i	−0.925219	+	0.379432i	$0.876119\pi$
$570$		0			0
$571$	2.88673	−	1.85519i	0.120806	−	0.0776371i	−0.478843	−	0.877901i	$-0.658944\pi$
$571$	2.88673	−	1.85519i	0.120806	−	0.0776371i	0.599648	+	0.800264i	$0.295307\pi$
$572$		0			0
$573$	−1.31355	−	4.47353i	−0.0548743	−	0.186885i
$574$		0			0
$575$	−21.2385	−	11.1322i	−0.885706	−	0.464246i
$576$		0			0
$577$	7.02521	+	23.9257i	0.292463	+	0.996039i	0.966356	+	0.257209i	$0.0828029\pi$
$577$	7.02521	+	23.9257i	0.292463	+	0.996039i	−0.673892	+	0.738829i	$0.735379\pi$
$578$		0			0
$579$	11.4975	−	7.38902i	0.477821	−	0.307077i
$580$		0			0
$581$	−21.1615	−	13.5997i	−0.877927	−	0.564210i
$582$		0			0
$583$	−0.657836	−	0.570019i	−0.0272448	−	0.0236078i
$584$		0			0
$585$	−30.5148	+	22.6550i	−1.26163	+	0.936671i
$586$		0			0
$587$	−3.84790	+	13.1048i	−0.158820	+	0.540891i	0.841180	+	0.540755i	$0.181861\pi$
$587$	−3.84790	+	13.1048i	−0.158820	+	0.540891i	−1.00000		0.000135980i	$0.999957\pi$
$588$		0			0
$589$	0.243346	−	1.69251i	0.0100269	−	0.0697385i
$590$		0			0
$591$	−0.958416	+	2.09864i	−0.0394240	+	0.0863264i
$592$		0			0
$593$	8.25986	−	1.18759i	0.339192	−	0.0487684i	0.0293857	−	0.999568i	$-0.490645\pi$
$593$	8.25986	−	1.18759i	0.339192	−	0.0487684i	0.309806	+	0.950800i	$0.399736\pi$
$594$		0			0
$595$	−10.4602	−	7.89527i	−0.428827	−	0.323675i
$596$		0			0
$597$			0.620377i			0.0253904i
$598$		0			0
$599$	15.0540			0.615091			0.307546	−	0.951533i	$-0.400492\pi$
$599$	15.0540			0.615091			0.307546	+	0.951533i	$0.400492\pi$
$600$		0			0
$601$	5.20323	+	6.00485i	0.212244	+	0.244943i	0.851882	−	0.523733i	$-0.175461\pi$
$601$	5.20323	+	6.00485i	0.212244	+	0.244943i	−0.639638	+	0.768676i	$0.720916\pi$
$602$		0			0
$603$	27.2740	−	3.92141i	1.11068	−	0.159692i
$604$		0			0
$605$	−4.68467	+	21.1317i	−0.190459	+	0.859126i
$606$		0			0
$607$	−38.7134	−	5.56615i	−1.57133	−	0.225923i	−0.699102	−	0.715022i	$-0.746417\pi$
$607$	−38.7134	−	5.56615i	−1.57133	−	0.225923i	−0.872228	+	0.489099i	$0.837326\pi$
$608$		0			0
$609$	−6.09114	−	1.78852i	−0.246826	−	0.0724745i
$610$		0			0
$611$	25.1050	+	54.9722i	1.01564	+	2.22394i
$612$		0			0
$613$	−26.8136	−	23.2341i	−1.08299	−	0.938417i	−0.0846743	−	0.996409i	$-0.526985\pi$
$613$	−26.8136	−	23.2341i	−1.08299	−	0.938417i	−0.998317	+	0.0579913i	$0.981530\pi$
$614$		0			0
$615$	−0.448068	+	1.18694i	−0.0180679	+	0.0478619i
$616$		0			0
$617$	15.8905	+	24.7260i	0.639726	+	0.995433i	0.998085	+	0.0618494i	$0.0196999\pi$
$617$	15.8905	+	24.7260i	0.639726	+	0.995433i	−0.358359	+	0.933584i	$0.616664\pi$
$618$		0			0
$619$	7.47241	−	2.19410i	0.300342	−	0.0881883i	−0.128090	−	0.991763i	$-0.540885\pi$
$619$	7.47241	−	2.19410i	0.300342	−	0.0881883i	0.428431	+	0.903574i	$0.359066\pi$
$620$		0			0
$621$	8.25405	−	11.6192i	0.331224	−	0.466261i
$622$		0			0
$623$	−7.04760	−	24.0019i	−0.282356	−	0.961617i
$624$		0			0
$625$	3.94953	−	24.6861i	0.157981	−	0.987442i
$626$		0			0
$627$	0.561833	−	0.874230i	0.0224375	−	0.0349134i
$628$		0			0
$629$	18.3488	−	21.1757i	0.731616	−	0.844330i
$630$		0			0
$631$	−11.7331	−	25.6919i	−0.467087	−	1.02278i	−0.985815	−	0.167838i	$-0.946321\pi$
$631$	−11.7331	−	25.6919i	−0.467087	−	1.02278i	0.518727	−	0.854940i	$-0.326406\pi$
$632$		0			0
$633$	2.35336	−	8.01479i	0.0935375	−	0.318559i
$634$		0			0
$635$	−45.9792	+	3.10547i	−1.82463	+	0.123237i
$636$		0			0
$637$	15.2360	+	6.95803i	0.603671	+	0.275687i
$638$		0			0
$639$	−4.52695	−	31.4856i	−0.179083	−	1.24555i
$640$		0			0
$641$	−3.63922	−	4.19989i	−0.143741	−	0.165885i	0.679314	−	0.733848i	$-0.262277\pi$
$641$	−3.63922	−	4.19989i	−0.143741	−	0.165885i	−0.823055	+	0.567962i	$0.807732\pi$
$642$		0			0
$643$			41.7185i			1.64522i	0.568607	+	0.822609i	$0.307482\pi$
$643$			41.7185i			1.64522i	−0.568607	+	0.822609i	$0.692518\pi$
$644$		0			0
$645$	4.95882	−	1.05817i	0.195253	−	0.0416653i
$646$		0			0
$647$	−10.2322	+	8.86627i	−0.402270	+	0.348569i	−0.832378	−	0.554209i	$-0.813021\pi$
$647$	−10.2322	+	8.86627i	−0.402270	+	0.348569i	0.430108	+	0.902777i	$0.358476\pi$
$648$		0			0
$649$	−1.94581	−	13.5334i	−0.0763799	−	0.531234i
$650$		0			0
$651$	0.438346	−	0.959845i	0.0171802	−	0.0376193i
$652$		0			0
$653$	−32.6483	−	4.69412i	−1.27763	−	0.183695i	−0.530105	−	0.847932i	$-0.677848\pi$
$653$	−32.6483	−	4.69412i	−1.27763	−	0.183695i	−0.747522	+	0.664237i	$0.768757\pi$
$654$		0			0
$655$	−8.48794	−	0.640876i	−0.331651	−	0.0250411i
$656$		0			0
$657$	−10.7314	+	4.90088i	−0.418673	+	0.191202i
$658$		0			0
$659$	9.36076	−	10.8029i	0.364643	−	0.420821i	−0.543547	−	0.839379i	$-0.682919\pi$
$659$	9.36076	−	10.8029i	0.364643	−	0.420821i	0.908190	+	0.418558i	$0.137464\pi$
$660$		0			0
$661$	27.4304	+	17.6285i	1.06692	+	0.685668i	0.951500	−	0.307649i	$-0.0995423\pi$
$661$	27.4304	+	17.6285i	1.06692	+	0.685668i	0.115420	+	0.993317i	$0.463179\pi$
$662$		0			0
$663$	4.92626	+	7.66541i	0.191320	+	0.297700i
$664$		0			0
$665$	3.85160	+	7.12059i	0.149358	+	0.276125i
$666$		0			0
$667$	5.32146	−	27.7805i	0.206048	−	1.07567i
$668$		0			0
$669$	−6.43693	+	1.89005i	−0.248866	+	0.0730737i
$670$		0			0
$671$	−2.37938	+	1.52913i	−0.0918549	+	0.0590316i
$672$		0			0
$673$	−15.2919	+	23.7947i	−0.589459	+	0.917217i	0.410526	+	0.911849i	$0.365345\pi$
$673$	−15.2919	+	23.7947i	−0.589459	+	0.917217i	−0.999986	+	0.00536788i	$0.998291\pi$
$674$		0			0
$675$	14.2238	+	4.29917i	0.547473	+	0.165475i
$676$		0			0
$677$	−27.1092	+	12.3804i	−1.04189	+	0.475816i	−0.861489	−	0.507776i	$-0.830468\pi$
$677$	−27.1092	+	12.3804i	−1.04189	+	0.475816i	−0.180404	+	0.983593i	$0.557740\pi$
$678$		0			0
$679$	−15.3948	−	4.52031i	−0.590797	−	0.173474i
$680$		0			0
$681$	1.39858	−	9.72733i	0.0535937	−	0.372752i
$682$		0			0
$683$	−44.6312	−	20.3824i	−1.70777	−	0.779911i	−0.997077	−	0.0764048i	$-0.975656\pi$
$683$	−44.6312	−	20.3824i	−1.70777	−	0.779911i	−0.710689	−	0.703506i	$-0.751617\pi$
$684$		0			0
$685$	23.6239	−	8.70482i	0.902624	−	0.332594i
$686$		0			0
$687$	−3.14931	+	2.72889i	−0.120154	+	0.104114i
$688$		0			0
$689$	−4.71460			−0.179612
$690$		0			0
$691$	−14.2508			−0.542124			−0.271062	−	0.962562i	$-0.587375\pi$
$691$	−14.2508			−0.542124			−0.271062	+	0.962562i	$0.587375\pi$
$692$		0			0
$693$	−4.92265	+	4.26550i	−0.186996	+	0.162033i
$694$		0			0
$695$	13.0677	+	35.4643i	0.495686	+	1.34524i
$696$		0			0
$697$	−2.81026	−	1.28340i	−0.106446	−	0.0486124i
$698$		0			0
$699$	0.715654	−	4.97749i	0.0270685	−	0.188266i
$700$		0			0
$701$	−34.6764	−	10.1819i	−1.30971	−	0.384565i	−0.448940	−	0.893562i	$-0.648198\pi$
$701$	−34.6764	−	10.1819i	−1.30971	−	0.384565i	−0.860769	+	0.508997i	$0.830017\pi$
$702$		0			0
$703$	−15.7442	+	7.19013i	−0.593803	+	0.271181i
$704$		0			0
$705$	5.43536	−	9.86104i	0.204707	−	0.371388i
$706$		0			0
$707$	4.49057	−	6.98746i	0.168885	−	0.262791i
$708$		0			0
$709$	10.8671	−	6.98385i	0.408122	−	0.262284i	−0.320433	−	0.947271i	$-0.603829\pi$
$709$	10.8671	−	6.98385i	0.408122	−	0.262284i	0.728555	+	0.684987i	$0.240192\pi$
$710$		0			0
$711$	−1.69119	+	0.496579i	−0.0634247	+	0.0186232i
$712$		0			0
$713$	4.44474	+	1.53268i	0.166457	+	0.0573992i
$714$		0			0
$715$	−7.60706	−	14.0635i	−0.284488	−	0.525944i
$716$		0			0
$717$	−4.68917	−	7.29649i	−0.175120	−	0.272492i
$718$		0			0
$719$	−1.46253	−	0.939910i	−0.0545431	−	0.0350527i	0.513085	−	0.858338i	$-0.328503\pi$
$719$	−1.46253	−	0.939910i	−0.0545431	−	0.0350527i	−0.567628	+	0.823285i	$0.692139\pi$
$720$		0			0
$721$	−4.39732	+	5.07478i	−0.163765	+	0.188995i
$722$		0			0
$723$	10.9688	−	5.00928i	0.407934	−	0.186297i
$724$		0			0
$725$	29.2219	−	3.96543i	1.08528	−	0.147272i
$726$		0			0
$727$	49.9061	+	7.17542i	1.85092	+	0.266122i	0.975939	−	0.218043i	$-0.0699673\pi$
$727$	49.9061	+	7.17542i	1.85092	+	0.266122i	0.874977	+	0.484165i	$0.160876\pi$
$728$		0			0
$729$	5.62677	−	12.3209i	0.208399	−	0.456330i
$730$		0			0
$731$	1.75721	+	12.2216i	0.0649926	+	0.452034i
$732$		0			0
$733$	−30.8646	+	26.7443i	−1.14001	+	0.987824i	−0.999997	−	0.00232544i	$-0.999260\pi$
$733$	−30.8646	+	26.7443i	−1.14001	+	0.987824i	−0.140013	+	0.990150i	$0.544714\pi$
$734$		0			0
$735$	−0.651275	−	3.05203i	−0.0240227	−	0.112576i
$736$		0			0
$737$			11.5923i			0.427007i
$738$		0			0
$739$	−30.2791	−	34.9439i	−1.11383	−	1.28543i	−0.954501	−	0.298207i	$-0.903611\pi$
$739$	−30.2791	−	34.9439i	−1.11383	−	1.28543i	−0.159332	−	0.987225i	$-0.550934\pi$
$740$		0			0
$741$	−0.801039	−	5.57135i	−0.0294269	−	0.204669i
$742$		0			0
$743$	2.48829	+	1.13637i	0.0912866	+	0.0416892i	0.460535	−	0.887642i	$-0.347658\pi$
$743$	2.48829	+	1.13637i	0.0912866	+	0.0416892i	−0.369248	+	0.929331i	$0.620385\pi$
$744$		0			0
$745$	2.38858	+	35.3650i	0.0875107	+	1.29567i
$746$		0			0
$747$	−9.32458	+	31.7566i	−0.341168	+	1.16191i
$748$		0			0
$749$	7.35399	+	16.1030i	0.268709	+	0.588391i
$750$		0			0
$751$	13.7132	−	15.8259i	0.500403	−	0.577496i	−0.448212	−	0.893927i	$-0.647939\pi$
$751$	13.7132	−	15.8259i	0.500403	−	0.577496i	0.948616	+	0.316431i	$0.102485\pi$
$752$		0			0
$753$	−6.13459	+	9.54562i	−0.223557	+	0.347862i
$754$		0			0
$755$	28.6645	−	28.4382i	1.04321	−	1.03497i
$756$		0			0
$757$	5.33880	+	18.1823i	0.194042	+	0.660846i	0.997825	+	0.0659231i	$0.0209992\pi$
$757$	5.33880	+	18.1823i	0.194042	+	0.660846i	−0.803783	+	0.594923i	$0.797183\pi$
$758$		0			0
$759$	2.07023	+	1.96947i	0.0751446	+	0.0714871i
$760$		0			0
$761$	−20.7735	+	6.09965i	−0.753038	+	0.221112i	−0.635653	−	0.771975i	$-0.719269\pi$
$761$	−20.7735	+	6.09965i	−0.753038	+	0.221112i	−0.117385	+	0.993087i	$0.537451\pi$
$762$		0			0
$763$	−2.35725	−	3.66796i	−0.0853383	−	0.132789i
$764$		0			0
$765$	−6.08990	+	16.1322i	−0.220181	+	0.583261i
$766$		0			0
$767$	−55.9673	−	48.4959i	−2.02086	−	1.75109i
$768$		0			0
$769$	10.5060	+	23.0049i	0.378856	+	0.829580i	0.998983	+	0.0450783i	$0.0143537\pi$
$769$	10.5060	+	23.0049i	0.378856	+	0.829580i	−0.620127	+	0.784501i	$0.712919\pi$
$770$		0			0
$771$	−3.31647	−	0.973803i	−0.119440	−	0.0350706i
$772$		0			0
$773$	32.7465	+	4.70824i	1.17781	+	0.169344i	0.703292	−	0.710901i	$-0.251713\pi$
$773$	32.7465	+	4.70824i	1.17781	+	0.169344i	0.474519	+	0.880245i	$0.342622\pi$
$774$		0			0
$775$	−0.0388364	+	4.90158i	−0.00139504	+	0.176070i
$776$		0			0
$777$	−10.5724	+	1.52008i	−0.379282	+	0.0545326i
$778$		0			0
$779$	1.24976	+	1.44230i	0.0447772	+	0.0516756i
$780$		0			0
$781$	13.3824			0.478858
$782$		0			0
$783$			17.5279i			0.626395i
$784$		0			0
$785$	−18.5909	+	24.6306i	−0.663539	+	0.879104i
$786$		0			0
$787$	7.44794	−	1.07085i	0.265490	−	0.0381717i	−0.00828407	−	0.999966i	$-0.502637\pi$
$787$	7.44794	−	1.07085i	0.265490	−	0.0381717i	0.273774	+	0.961794i	$0.411728\pi$
$788$		0			0
$789$	3.42503	−	7.49978i	0.121934	−	0.266999i
$790$		0			0
$791$	3.00912	−	20.9289i	0.106992	−	0.744146i
$792$		0			0
$793$	−4.31597	+	14.6989i	−0.153265	+	0.521971i
$794$		0			0
$795$	0.523623	+	0.705285i	0.0185710	+	0.0250139i
$796$		0			0
$797$	−15.8540	−	13.7375i	−0.561576	−	0.486608i	0.327197	−	0.944956i	$-0.393896\pi$
$797$	−15.8540	−	13.7375i	−0.561576	−	0.486608i	−0.888773	+	0.458348i	$0.848441\pi$
$798$		0			0
$799$	23.0665	+	14.8240i	0.816036	+	0.524434i
$800$		0			0
$801$	−27.6888	+	17.7945i	−0.978334	+	0.628737i
$802$		0			0
$803$	−1.39832	−	4.76224i	−0.0493456	−	0.168056i
$804$		0			0
$805$	−21.2216	+	6.71784i	−0.747963	+	0.236773i
$806$		0			0
$807$	−0.596465	−	2.03137i	−0.0209966	−	0.0715077i
$808$		0			0
$809$	−7.83228	+	5.03350i	−0.275368	+	0.176968i	−0.671035	−	0.741426i	$-0.734150\pi$
$809$	−7.83228	+	5.03350i	−0.275368	+	0.176968i	0.395667	+	0.918394i	$0.370514\pi$
$810$		0			0
$811$	8.39363	+	5.39426i	0.294740	+	0.189418i	0.679651	−	0.733536i	$-0.262131\pi$
$811$	8.39363	+	5.39426i	0.294740	+	0.189418i	−0.384910	+	0.922954i	$0.625768\pi$
$812$		0			0
$813$	7.04050	+	6.10063i	0.246921	+	0.213958i
$814$		0			0
$815$	16.9217	−	12.5631i	0.592741	−	0.440067i
$816$		0			0
$817$	2.14884	−	7.31828i	0.0751784	−	0.256034i
$818$		0			0
$819$	−5.02084	+	34.9207i	−0.175442	+	1.22023i
$820$		0			0
$821$	3.49529	−	7.65362i	0.121987	−	0.267113i	−0.838781	−	0.544470i	$-0.816731\pi$
$821$	3.49529	−	7.65362i	0.121987	−	0.267113i	0.960767	+	0.277356i	$0.0894583\pi$
$822$		0			0
$823$	10.3128	−	1.48275i	0.359480	−	0.0516855i	0.0397914	−	0.999208i	$-0.487331\pi$
$823$	10.3128	−	1.48275i	0.359480	−	0.0516855i	0.319689	+	0.947523i	$0.396422\pi$
$824$		0			0
$825$	−1.25897	+	2.69993i	−0.0438315	+	0.0939995i
$826$		0			0
$827$		−	23.8469i		−	0.829239i	−0.909995	−	0.414620i	$-0.863915\pi$
$827$		−	23.8469i		−	0.829239i	0.909995	−	0.414620i	$-0.136085\pi$
$828$		0			0
$829$	−11.1889			−0.388608			−0.194304	−	0.980941i	$-0.562245\pi$
$829$	−11.1889			−0.388608			−0.194304	+	0.980941i	$0.562245\pi$
$830$		0			0
$831$	1.91903	+	2.21467i	0.0665702	+	0.0768262i
$832$		0			0
$833$	7.52210	−	1.08151i	0.260625	−	0.0374723i
$834$		0			0
$835$	38.2110	+	8.47097i	1.32235	+	0.293150i
$836$		0			0
$837$	−2.88379	−	0.414627i	−0.0996785	−	0.0143316i
$838$		0			0
$839$	−2.40196	−	0.705279i	−0.0829249	−	0.0243489i	0.240007	−	0.970771i	$-0.422850\pi$
$839$	−2.40196	−	0.705279i	−0.0829249	−	0.0243489i	−0.322932	+	0.946422i	$0.604668\pi$
$840$		0			0
$841$	2.40354	+	5.26301i	0.0828806	+	0.181483i
$842$		0			0
$843$	−8.81495	−	7.63820i	−0.303603	−	0.263073i
$844$		0			0
$845$	−53.8253	−	20.3190i	−1.85165	−	0.698996i
$846$		0			0
$847$	10.8628	+	16.9029i	0.373251	+	0.580790i
$848$		0			0
$849$	9.20232	−	2.70204i	0.315823	−	0.0927339i
$850$		0			0
$851$	−11.2726	−	46.2367i	−0.386421	−	1.58497i
$852$		0			0
$853$	4.67478	+	15.9208i	0.160061	+	0.545119i	0.999997	+	0.00243292i	$0.000774423\pi$
$853$	4.67478	+	15.9208i	0.160061	+	0.545119i	−0.839936	+	0.542686i	$0.817407\pi$
$854$		0			0
$855$	7.56164	−	7.50197i	0.258603	−	0.256562i
$856$		0			0
$857$	23.1044	−	35.9512i	0.789231	−	1.22807i	−0.180423	−	0.983589i	$-0.557747\pi$
$857$	23.1044	−	35.9512i	0.789231	−	1.22807i	0.969655	−	0.244479i	$-0.0786169\pi$
$858$		0			0
$859$	1.65308	−	1.90775i	0.0564023	−	0.0650917i	−0.726847	−	0.686799i	$-0.759015\pi$
$859$	1.65308	−	1.90775i	0.0564023	−	0.0650917i	0.783250	+	0.621707i	$0.213561\pi$
$860$		0			0
$861$	0.489238	+	1.07128i	0.0166732	+	0.0365092i
$862$		0			0
$863$	5.85422	−	19.9376i	0.199280	−	0.678685i	−0.797842	−	0.602867i	$-0.794025\pi$
$863$	5.85422	−	19.9376i	0.199280	−	0.678685i	0.997122	−	0.0758181i	$-0.0241568\pi$
$864$		0			0
$865$	3.81420	−	0.257614i	0.129687	−	0.00875912i
$866$		0			0
$867$	−4.25814	−	1.94463i	−0.144614	−	0.0660429i
$868$		0			0
$869$	−0.105531	−	0.733982i	−0.00357988	−	0.0248986i
$870$		0			0
$871$	41.1171	+	47.4516i	1.39320	+	1.60784i
$872$		0			0
$873$			21.1108i			0.714491i
$874$		0			0
$875$	−13.6857	−	18.7422i	−0.462663	−	0.633603i
$876$		0			0
$877$	−30.2040	+	26.1720i	−1.01992	+	0.883764i	−0.993263	−	0.115880i	$-0.963031\pi$
$877$	−30.2040	+	26.1720i	−1.01992	+	0.883764i	−0.0266551	+	0.999645i	$0.508486\pi$
$878$		0			0
$879$	1.17763	+	8.19056i	0.0397203	+	0.276261i
$880$		0			0
$881$	−0.703851	+	1.54122i	−0.0237133	+	0.0519250i	−0.921118	−	0.389283i	$-0.872723\pi$
$881$	−0.703851	+	1.54122i	−0.0237133	+	0.0519250i	0.897405	+	0.441208i	$0.145450\pi$
$882$		0			0
$883$	22.2845	+	3.20403i	0.749934	+	0.107824i	0.506675	−	0.862137i	$-0.330874\pi$
$883$	22.2845	+	3.20403i	0.749934	+	0.107824i	0.243259	+	0.969961i	$0.421784\pi$
$884$		0			0
$885$	−1.03884	+	13.7586i	−0.0349201	+	0.462491i
$886$		0			0
$887$	−0.424576	+	0.193897i	−0.0142559	+	0.00651043i	−0.422530	−	0.906349i	$-0.638858\pi$
$887$	−0.424576	+	0.193897i	−0.0142559	+	0.00651043i	0.408274	+	0.912859i	$0.366131\pi$
$888$		0			0
$889$	−28.0143	+	32.3303i	−0.939571	+	1.08432i
$890$		0			0
$891$	6.43003	+	4.13233i	0.215414	+	0.138438i
$892$		0			0
$893$	−9.15713	−	14.2488i	−0.306432	−	0.476817i
$894$		0			0
$895$	−37.2568	+	20.1525i	−1.24536	+	0.673625i
$896$		0			0
$897$	15.4598	+	0.718802i	0.516189	+	0.0240001i
$898$		0			0
$899$	−5.54783	+	1.62899i	−0.185030	+	0.0543298i
$900$		0			0
$901$	−1.79949	+	1.15646i	−0.0599498	+	0.0385274i
$902$		0			0
$903$	2.54471	−	3.95964i	0.0846826	−	0.131769i
$904$		0			0
$905$	8.62988	−	15.6567i	0.286867	−	0.520445i
$906$		0			0
$907$	16.3964	−	7.48799i	0.544434	−	0.248634i	−0.124160	−	0.992262i	$-0.539624\pi$
$907$	16.3964	−	7.48799i	0.544434	−	0.248634i	0.668594	+	0.743628i	$0.266896\pi$
$908$		0			0
$909$	−10.4859	−	3.07895i	−0.347796	−	0.102122i
$910$		0			0
$911$	6.24057	−	43.4041i	0.206759	−	1.43804i	−0.576882	−	0.816828i	$-0.695731\pi$
$911$	6.24057	−	43.4041i	0.206759	−	1.43804i	0.783641	−	0.621214i	$-0.213360\pi$
$912$		0			0
$913$	−12.6659	−	5.78431i	−0.419179	−	0.191433i
$914$		0			0
$915$	2.67824	−	0.986863i	0.0885398	−	0.0326247i
$916$		0			0
$917$	−5.97167	+	5.17449i	−0.197202	+	0.170877i
$918$		0			0
$919$	58.7758			1.93884			0.969418	−	0.245416i	$-0.0789246\pi$
$919$	58.7758			1.93884			0.969418	+	0.245416i	$0.0789246\pi$
$920$		0			0
$921$	−9.28791			−0.306047
$922$		0			0
$923$	54.7791	−	47.4664i	1.80308	−	1.56238i
$924$		0			0
$925$	41.9517	−	26.4934i	1.37936	−	0.871099i
$926$		0			0
$927$	8.03670	+	3.67024i	0.263960	+	0.120546i
$928$		0			0
$929$	−1.31393	+	9.13857i	−0.0431086	+	0.299827i	0.956849	+	0.290587i	$0.0938504\pi$
$929$	−1.31393	+	9.13857i	−0.0431086	+	0.299827i	−0.999957	+	0.00924029i	$0.997059\pi$
$930$		0			0
$931$	−4.50421	−	1.32256i	−0.147620	−	0.0433450i
$932$		0			0
$933$	14.0807	−	6.43045i	0.460982	−	0.210524i
$934$		0			0
$935$	−6.35319	−	3.50185i	−0.207771	−	0.114523i
$936$		0			0
$937$	20.2433	−	31.4992i	0.661319	−	1.02903i	−0.334908	−	0.942251i	$-0.608705\pi$
$937$	20.2433	−	31.4992i	0.661319	−	1.02903i	0.996227	−	0.0867822i	$-0.0276584\pi$
$938$		0			0
$939$	9.09390	−	5.84430i	0.296768	−	0.190721i
$940$		0			0
$941$	42.0223	−	12.3388i	1.36989	−	0.402235i	0.487649	−	0.873040i	$-0.337855\pi$
$941$	42.0223	−	12.3388i	1.36989	−	0.402235i	0.882237	+	0.470805i	$0.156036\pi$
$942$		0			0
$943$	−4.54142	+	2.62889i	−0.147889	+	0.0856083i
$944$		0			0
$945$	12.1325	−	6.56258i	0.394670	−	0.213481i
$946$		0			0
$947$	−16.5433	−	25.7419i	−0.537586	−	0.836501i	0.461121	−	0.887337i	$-0.347448\pi$
$947$	−16.5433	−	25.7419i	−0.537586	−	0.836501i	−0.998707	+	0.0508367i	$0.983811\pi$
$948$		0			0
$949$	−22.6152	−	14.5339i	−0.734121	−	0.471791i
$950$		0			0
$951$	−2.68107	+	3.09412i	−0.0869396	+	0.100334i
$952$		0			0
$953$	−12.2799	+	5.60806i	−0.397786	+	0.181663i	−0.604256	−	0.796790i	$-0.706530\pi$
$953$	−12.2799	+	5.60806i	−0.397786	+	0.181663i	0.206470	+	0.978453i	$0.433802\pi$
$954$		0			0
$955$	20.0480	+	1.51371i	0.648737	+	0.0489825i
$956$		0			0
$957$	−3.47827	−	0.500100i	−0.112436	−	0.0161659i
$958$		0			0
$959$	9.70871	−	21.2591i	0.313511	−	0.686493i
$960$		0			0
$961$	4.27498	+	29.7332i	0.137903	+	0.959134i
$962$		0			0
$963$	17.6032	−	15.2532i	0.567255	−	0.491529i
$964$		0			0
$965$	12.2993	+	57.6374i	0.395929	+	1.85541i
$966$		0			0
$967$		−	19.4522i		−	0.625539i	−0.949829	−	0.312770i	$-0.898743\pi$
$967$		−	19.4522i		−	0.625539i	0.949829	−	0.312770i	$-0.101257\pi$
$968$		0			0
$969$	−1.67236	−	1.93001i	−0.0537240	−	0.0620009i
$970$		0			0
$971$	3.71323	+	25.8261i	0.119163	+	0.828798i	0.958481	+	0.285157i	$0.0920457\pi$
$971$	3.71323	+	25.8261i	0.119163	+	0.828798i	−0.839318	+	0.543641i	$0.817045\pi$
$972$		0			0
$973$	31.9142	+	14.5747i	1.02312	+	0.467244i
$974$		0			0
$975$	4.42306	+	15.5173i	0.141651	+	0.496952i
$976$		0			0
$977$	12.8564	−	43.7850i	0.411314	−	1.40081i	−0.450134	−	0.892961i	$-0.648624\pi$
$977$	12.8564	−	43.7850i	0.411314	−	1.40081i	0.861448	−	0.507846i	$-0.169558\pi$
$978$		0			0
$979$	−5.75223	−	12.5956i	−0.183842	−	0.402558i
$980$		0			0
$981$	−3.75681	+	4.33559i	−0.119946	+	0.138425i
$982$		0			0
$983$	11.2835	−	17.5575i	0.359889	−	0.559998i	−0.613345	−	0.789815i	$-0.710176\pi$
$983$	11.2835	−	17.5575i	0.359889	−	0.559998i	0.973234	+	0.229817i	$0.0738128\pi$
$984$		0			0
$985$	−7.00689	−	7.06263i	−0.223258	−	0.225034i
$986$		0			0
$987$	−2.94476	−	10.0289i	−0.0937326	−	0.319224i
$988$		0			0
$989$	18.6515	+	9.58865i	0.593083	+	0.304901i
$990$		0			0
$991$	−9.93555	+	2.91734i	−0.315613	+	0.0926724i	−0.435703	−	0.900091i	$-0.643500\pi$
$991$	−9.93555	+	2.91734i	−0.315613	+	0.0926724i	0.120089	+	0.992763i	$0.461682\pi$
$992$		0			0
$993$	7.68519	+	11.9584i	0.243882	+	0.379488i
$994$		0			0
$995$	−2.50278	−	0.944800i	−0.0793435	−	0.0299522i
$996$		0			0
$997$	−5.55020	−	4.80927i	−0.175776	−	0.152311i	0.562529	−	0.826777i	$-0.309828\pi$
$997$	−5.55020	−	4.80927i	−0.175776	−	0.152311i	−0.738306	+	0.674466i	$0.764374\pi$
$998$		0			0
$999$	12.2510	+	26.8259i	0.387604	+	0.848733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.9.6	✓	120
5.4	even	2	inner	460.2.s.a.9.7	yes	120
23.18	even	11	inner	460.2.s.a.409.7	yes	120
115.64	even	22	inner	460.2.s.a.409.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.9.6	✓	120	1.1	even	1	trivial
460.2.s.a.9.7	yes	120	5.4	even	2	inner
460.2.s.a.409.6	yes	120	115.64	even	22	inner
460.2.s.a.409.7	yes	120	23.18	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.391893 + 0.339577i) q^{3} +(-0.773120 - 2.09816i) q^{5} +(-1.88813 - 0.862281i) q^{7} +(-0.388677 + 2.70331i) q^{9} +O(q^{10})\)	\(q+(-0.391893 + 0.339577i) q^{3} +(-0.773120 - 2.09816i) q^{5} +(-1.88813 - 0.862281i) q^{7} +(-0.388677 + 2.70331i) q^{9} +(-1.10245 - 0.323708i) q^{11} +(-5.66091 + 2.58525i) q^{13} +(1.01547 + 0.559721i) q^{15} +(-1.52654 + 2.37534i) q^{17} +(1.46731 - 0.942980i) q^{19} +(1.03276 - 0.303244i) q^{21} +(1.78750 + 4.45026i) q^{23} +(-3.80457 + 3.24426i) q^{25} +(-1.60671 - 2.50008i) q^{27} +(-4.96168 - 3.18867i) q^{29} +(0.641991 - 0.740897i) q^{31} +(0.541964 - 0.247507i) q^{33} +(-0.349453 + 4.62825i) q^{35} +(-9.82240 - 1.41225i) q^{37} +(1.34058 - 2.93546i) q^{39} +(0.155716 + 1.08303i) q^{41} +(3.30485 - 2.86367i) q^{43} +(5.97248 - 1.27447i) q^{45} -9.71084i q^{47} +(-1.76251 - 2.03405i) q^{49} +(-0.208371 - 1.44925i) q^{51} +(0.689112 + 0.314707i) q^{53} +(0.173132 + 2.56338i) q^{55} +(-0.254812 + 0.867810i) q^{57} +(4.94331 + 10.8243i) q^{59} +(1.61202 - 1.86037i) q^{61} +(3.06488 - 4.76905i) q^{63} +(9.80084 + 9.87880i) q^{65} +(-2.84243 - 9.68043i) q^{67} +(-2.21171 - 1.13703i) q^{69} +(-11.1753 + 3.28136i) q^{71} +(2.33540 + 3.63396i) q^{73} +(0.389307 - 2.56335i) q^{75} +(1.80244 + 1.56182i) q^{77} +(0.268099 + 0.587055i) q^{79} +(-6.38281 - 1.87416i) q^{81} +(11.9953 + 1.72466i) q^{83} +(6.16405 + 1.36650i) q^{85} +(3.02724 - 0.435252i) q^{87} +(7.89200 + 9.10785i) q^{89} +12.9178 q^{91} +0.508357i q^{93} +(-3.11293 - 2.34961i) q^{95} +(7.65107 - 1.10006i) q^{97} +(1.30358 - 2.85444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more