LMFDB - Embedded newform 630.2.cd.a.263.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.17
Character	$\chi$	$=$	630.263
Dual form			630.2.cd.a.527.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(1.03831 - 1.38633i) q^{3} +1.00000i q^{4} +(1.93621 - 1.11852i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(-2.64167 - 0.146855i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.843805 - 2.87889i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.03831 - 1.38633i) q^{3} +1.00000i q^{4} +(1.93621 - 1.11852i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(-2.64167 - 0.146855i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.843805 - 2.87889i) q^{9} +(-2.16002 - 0.578198i) q^{10} +(-4.86543 + 2.80906i) q^{11} +(1.38633 + 1.03831i) q^{12} +(1.40209 - 5.23268i) q^{13} +(1.76410 + 1.97179i) q^{14} +(0.459767 - 3.84560i) q^{15} -1.00000 q^{16} +(-3.42422 + 0.917516i) q^{17} +(-1.43902 + 2.63234i) q^{18} +(-2.96649 + 1.71270i) q^{19} +(1.11852 + 1.93621i) q^{20} +(-2.94648 + 3.50974i) q^{21} +(5.42668 + 1.45407i) q^{22} +(-1.77443 - 6.62225i) q^{23} +(-0.246082 - 1.71448i) q^{24} +(2.49784 - 4.33137i) q^{25} +(-4.69149 + 2.70864i) q^{26} +(-4.86721 - 1.81940i) q^{27} +(0.146855 - 2.64167i) q^{28} +(3.11239 - 5.39082i) q^{29} +(-3.04435 + 2.39414i) q^{30} +5.84161 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.15758 + 9.66176i) q^{33} +(3.07007 + 1.77250i) q^{34} +(-5.27910 + 2.67041i) q^{35} +(2.87889 - 0.843805i) q^{36} +(6.67262 + 1.78792i) q^{37} +(3.30869 + 0.886560i) q^{38} +(-5.79839 - 7.37693i) q^{39} +(0.578198 - 2.16002i) q^{40} +(-0.460590 + 0.265922i) q^{41} +(4.56523 - 0.398287i) q^{42} +(3.92322 - 1.05122i) q^{43} +(-2.80906 - 4.86543i) q^{44} +(-4.85387 - 4.63033i) q^{45} +(-3.42793 + 5.93734i) q^{46} +(0.0822560 + 0.0822560i) q^{47} +(-1.03831 + 1.38633i) q^{48} +(6.95687 + 0.775887i) q^{49} +(-4.82898 + 1.29651i) q^{50} +(-2.28344 + 5.69975i) q^{51} +(5.23268 + 1.40209i) q^{52} +(0.378116 + 1.41115i) q^{53} +(2.15513 + 4.72815i) q^{54} +(-6.27853 + 10.8810i) q^{55} +(-1.97179 + 1.76410i) q^{56} +(-0.705782 + 5.89085i) q^{57} +(-6.01268 + 1.61109i) q^{58} -2.80567 q^{59} +(3.84560 + 0.459767i) q^{60} -9.07471 q^{61} +(-4.13064 - 4.13064i) q^{62} +(1.80628 + 7.72899i) q^{63} -1.00000i q^{64} +(-3.13810 - 11.6998i) q^{65} +(7.65043 - 6.01337i) q^{66} +(1.81349 - 1.81349i) q^{67} +(-0.917516 - 3.42422i) q^{68} +(-11.0230 - 4.41604i) q^{69} +(5.62115 + 1.84462i) q^{70} -9.18544i q^{71} +(-2.63234 - 1.43902i) q^{72} +(5.01109 - 1.34272i) q^{73} +(-3.45400 - 5.98251i) q^{74} +(-3.41116 - 7.96015i) q^{75} +(-1.71270 - 2.96649i) q^{76} +(13.2654 - 6.70609i) q^{77} +(-1.11619 + 9.31636i) q^{78} +15.4087i q^{79} +(-1.93621 + 1.11852i) q^{80} +(-7.57599 + 4.85844i) q^{81} +(0.513722 + 0.137651i) q^{82} +(3.76758 + 14.0608i) q^{83} +(-3.50974 - 2.94648i) q^{84} +(-5.60375 + 5.60655i) q^{85} +(-3.51746 - 2.03081i) q^{86} +(-4.24180 - 9.91217i) q^{87} +(-1.45407 + 5.42668i) q^{88} +(-2.54650 - 4.41067i) q^{89} +(0.158070 + 6.70634i) q^{90} +(-4.47232 + 13.6171i) q^{91} +(6.62225 - 1.77443i) q^{92} +(6.06543 - 8.09838i) q^{93} -0.116328i q^{94} +(-3.82806 + 6.63423i) q^{95} +(1.71448 - 0.246082i) q^{96} +(0.527648 + 1.96921i) q^{97} +(-4.37061 - 5.46788i) q^{98} +(12.1924 + 11.6367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.03831	−	1.38633i	0.599471	−	0.800396i
$3$	1.03831	−	1.38633i	0.599471	−	0.800396i
$4$			1.00000i			0.500000i
$5$	1.93621	−	1.11852i	0.865901	−	0.500216i
$5$	1.93621	−	1.11852i	0.865901	−	0.500216i
$6$	−1.71448	+	0.246082i	−0.699934	+	0.100463i
$7$	−2.64167	−	0.146855i	−0.998458	−	0.0555061i
$7$	−2.64167	−	0.146855i	−0.998458	−	0.0555061i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.843805	−	2.87889i	−0.281268	−	0.959629i
$10$	−2.16002	−	0.578198i	−0.683058	−	0.182842i
$11$	−4.86543	+	2.80906i	−1.46698	+	0.846962i	−0.999317	−	0.0369434i	$-0.988238\pi$
$11$	−4.86543	+	2.80906i	−1.46698	+	0.846962i	−0.467665	+	0.883906i	$0.654905\pi$
$12$	1.38633	+	1.03831i	0.400198	+	0.299736i
$13$	1.40209	−	5.23268i	0.388871	−	1.45128i	−0.443104	−	0.896470i	$-0.646123\pi$
$13$	1.40209	−	5.23268i	0.388871	−	1.45128i	0.831974	−	0.554814i	$-0.187211\pi$
$14$	1.76410	+	1.97179i	0.471476	+	0.526982i
$15$	0.459767	−	3.84560i	0.118711	−	0.992929i
$16$	−1.00000			−0.250000
$17$	−3.42422	+	0.917516i	−0.830494	+	0.222530i	−0.648929	−	0.760849i	$-0.724783\pi$
$17$	−3.42422	+	0.917516i	−0.830494	+	0.222530i	−0.181565	+	0.983379i	$0.558116\pi$
$18$	−1.43902	+	2.63234i	−0.339180	+	0.620449i
$19$	−2.96649	+	1.71270i	−0.680559	+	0.392921i	−0.800066	−	0.599912i	$-0.795202\pi$
$19$	−2.96649	+	1.71270i	−0.680559	+	0.392921i	0.119506	+	0.992833i	$0.461869\pi$
$20$	1.11852	+	1.93621i	0.250108	+	0.432950i
$21$	−2.94648	+	3.50974i	−0.642974	+	0.765888i
$22$	5.42668	+	1.45407i	1.15697	+	0.310010i
$23$	−1.77443	−	6.62225i	−0.369993	−	1.38083i	−0.860524	−	0.509410i	$-0.829864\pi$
$23$	−1.77443	−	6.62225i	−0.369993	−	1.38083i	0.490531	−	0.871424i	$-0.336803\pi$
$24$	−0.246082	−	1.71448i	−0.0502313	−	0.349967i
$25$	2.49784	−	4.33137i	0.499568	−	0.866275i
$26$	−4.69149	+	2.70864i	−0.920078	+	0.531207i
$27$	−4.86721	−	1.81940i	−0.936696	−	0.350144i
$28$	0.146855	−	2.64167i	0.0277530	−	0.499229i
$29$	3.11239	−	5.39082i	0.577957	−	1.00105i	−0.417756	−	0.908559i	$-0.637183\pi$
$29$	3.11239	−	5.39082i	0.577957	−	1.00105i	0.995713	−	0.0924919i	$-0.0294832\pi$
$30$	−3.04435	+	2.39414i	−0.555820	+	0.437109i
$31$	5.84161			1.04918			0.524592	−	0.851354i	$-0.324218\pi$
$31$	5.84161			1.04918			0.524592	+	0.851354i	$0.324218\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.15758	+	9.66176i	−0.201508	+	1.68190i
$34$	3.07007	+	1.77250i	0.526512	+	0.303982i
$35$	−5.27910	+	2.67041i	−0.892331	+	0.451382i
$36$	2.87889	−	0.843805i	0.479815	−	0.140634i
$37$	6.67262	+	1.78792i	1.09697	+	0.293933i	0.761531	−	0.648128i	$-0.224448\pi$
$37$	6.67262	+	1.78792i	1.09697	+	0.293933i	0.335441	+	0.942061i	$0.391115\pi$
$38$	3.30869	+	0.886560i	0.536740	+	0.143819i
$39$	−5.79839	−	7.37693i	−0.928486	−	1.18125i
$40$	0.578198	−	2.16002i	0.0914211	−	0.341529i
$41$	−0.460590	+	0.265922i	−0.0719321	+	0.0415300i	−0.535535	−	0.844513i	$-0.679890\pi$
$41$	−0.460590	+	0.265922i	−0.0719321	+	0.0415300i	0.463603	+	0.886043i	$0.346557\pi$
$42$	4.56523	−	0.398287i	0.704431	−	0.0614571i
$43$	3.92322	−	1.05122i	0.598285	−	0.160310i	0.0530480	−	0.998592i	$-0.483106\pi$
$43$	3.92322	−	1.05122i	0.598285	−	0.160310i	0.545237	+	0.838282i	$0.316440\pi$
$44$	−2.80906	−	4.86543i	−0.423481	−	0.733491i
$45$	−4.85387	−	4.63033i	−0.723572	−	0.690248i
$46$	−3.42793	+	5.93734i	−0.505420	+	0.875414i
$47$	0.0822560	+	0.0822560i	0.0119983	+	0.0119983i	0.713080	−	0.701082i	$-0.247299\pi$
$47$	0.0822560	+	0.0822560i	0.0119983	+	0.0119983i	−0.701082	+	0.713080i	$0.747299\pi$
$48$	−1.03831	+	1.38633i	−0.149868	+	0.200099i
$49$	6.95687	+	0.775887i	0.993838	+	0.110841i
$50$	−4.82898	+	1.29651i	−0.682921	+	0.183354i
$51$	−2.28344	+	5.69975i	−0.319745	+	0.798125i
$52$	5.23268	+	1.40209i	0.725642	+	0.194435i
$53$	0.378116	+	1.41115i	0.0519382	+	0.193836i	0.987020	−	0.160595i	$-0.0513413\pi$
$53$	0.378116	+	1.41115i	0.0519382	+	0.193836i	−0.935082	+	0.354431i	$0.884675\pi$
$54$	2.15513	+	4.72815i	0.293276	+	0.643420i
$55$	−6.27853	+	10.8810i	−0.846596	+	1.46719i
$56$	−1.97179	+	1.76410i	−0.263491	+	0.235738i
$57$	−0.705782	+	5.89085i	−0.0934832	+	0.780262i
$58$	−6.01268	+	1.61109i	−0.789504	+	0.211547i
$59$	−2.80567			−0.365267			−0.182634	−	0.983181i	$-0.558462\pi$
$59$	−2.80567			−0.365267			−0.182634	+	0.983181i	$0.558462\pi$
$60$	3.84560	+	0.459767i	0.496464	+	0.0593557i
$61$	−9.07471			−1.16190			−0.580949	−	0.813940i	$-0.697318\pi$
$61$	−9.07471			−1.16190			−0.580949	+	0.813940i	$0.697318\pi$
$62$	−4.13064	−	4.13064i	−0.524592	−	0.524592i
$63$	1.80628	+	7.72899i	0.227570	+	0.973762i
$64$		−	1.00000i		−	0.125000i
$65$	−3.13810	−	11.6998i	−0.389233	−	1.45119i
$66$	7.65043	−	6.01337i	0.941702	−	0.740194i
$67$	1.81349	−	1.81349i	0.221553	−	0.221553i	−0.587599	−	0.809152i	$-0.699927\pi$
$67$	1.81349	−	1.81349i	0.221553	−	0.221553i	0.809152	+	0.587599i	$0.199927\pi$
$68$	−0.917516	−	3.42422i	−0.111265	−	0.415247i
$69$	−11.0230	−	4.41604i	−1.32701	−	0.531629i
$70$	5.62115	+	1.84462i	0.671856	+	0.220474i
$71$		−	9.18544i		−	1.09011i	−0.838400	−	0.545056i	$-0.816508\pi$
$71$		−	9.18544i		−	1.09011i	0.838400	−	0.545056i	$-0.183492\pi$
$72$	−2.63234	−	1.43902i	−0.310224	−	0.169590i
$73$	5.01109	−	1.34272i	0.586504	−	0.157153i	0.0466491	−	0.998911i	$-0.485146\pi$
$73$	5.01109	−	1.34272i	0.586504	−	0.157153i	0.539855	+	0.841758i	$0.318479\pi$
$74$	−3.45400	−	5.98251i	−0.401520	−	0.695453i
$75$	−3.41116	−	7.96015i	−0.393887	−	0.919159i
$76$	−1.71270	−	2.96649i	−0.196461	−	0.340280i
$77$	13.2654	−	6.70609i	1.51173	−	0.764230i
$78$	−1.11619	+	9.31636i	−0.126384	+	1.05487i
$79$			15.4087i			1.73361i	0.498646	+	0.866806i	$0.333831\pi$
$79$			15.4087i			1.73361i	−0.498646	+	0.866806i	$0.666169\pi$
$80$	−1.93621	+	1.11852i	−0.216475	+	0.125054i
$81$	−7.57599	+	4.85844i	−0.841776	+	0.539827i
$82$	0.513722	+	0.137651i	0.0567311	+	0.0152010i
$83$	3.76758	+	14.0608i	0.413546	+	1.54337i	0.787730	+	0.616020i	$0.211256\pi$
$83$	3.76758	+	14.0608i	0.413546	+	1.54337i	−0.374184	+	0.927354i	$0.622077\pi$
$84$	−3.50974	−	2.94648i	−0.382944	−	0.321487i
$85$	−5.60375	+	5.60655i	−0.607812	+	0.608116i
$86$	−3.51746	−	2.03081i	−0.379297	−	0.218987i
$87$	−4.24180	−	9.91217i	−0.454769	−	1.06270i
$88$	−1.45407	+	5.42668i	−0.155005	+	0.578486i
$89$	−2.54650	−	4.41067i	−0.269929	−	0.467530i	0.698915	−	0.715205i	$-0.253667\pi$
$89$	−2.54650	−	4.41067i	−0.269929	−	0.467530i	−0.968843	+	0.247675i	$0.920333\pi$
$90$	0.158070	+	6.70634i	0.0166620	+	0.706910i
$91$	−4.47232	+	13.6171i	−0.468826	+	1.42746i
$92$	6.62225	−	1.77443i	0.690417	−	0.184997i
$93$	6.06543	−	8.09838i	0.628955	−	0.839763i
$94$		−	0.116328i		−	0.0119983i
$95$	−3.82806	+	6.63423i	−0.392751	+	0.680657i
$96$	1.71448	−	0.246082i	0.174983	−	0.0251156i
$97$	0.527648	+	1.96921i	0.0535745	+	0.199943i	0.987526	−	0.157458i	$-0.0503298\pi$
$97$	0.527648	+	1.96921i	0.0535745	+	0.199943i	−0.933951	+	0.357401i	$0.883663\pi$
$98$	−4.37061	−	5.46788i	−0.441499	−	0.552340i
$99$	12.1924	+	11.6367i	1.22539	+	1.16953i
$100$	4.33137	+	2.49784i	0.433137	+	0.249784i
$101$	−2.18344	+	1.26061i	−0.217260	+	0.125435i	−0.604681	−	0.796468i	$-0.706699\pi$
$101$	−2.18344	+	1.26061i	−0.217260	+	0.125435i	0.387421	+	0.921903i	$0.373366\pi$
$102$	5.64497	−	2.41570i	0.558935	−	0.239190i
$103$	14.4287	−	3.86616i	1.42170	−	0.380944i	0.535615	−	0.844463i	$-0.320080\pi$
$103$	14.4287	−	3.86616i	1.42170	−	0.380944i	0.886087	+	0.463519i	$0.153413\pi$
$104$	−2.70864	−	4.69149i	−0.265604	−	0.460039i
$105$	−1.77930	+	10.0913i	−0.173642	+	0.984809i
$106$	0.730463	−	1.26520i	0.0709489	−	0.122887i
$107$	0.268125	−	1.00066i	0.0259206	−	0.0967371i	−0.951754	−	0.306863i	$-0.900721\pi$
$107$	0.268125	−	1.00066i	0.0259206	−	0.0967371i	0.977674	+	0.210126i	$0.0673874\pi$
$108$	1.81940	−	4.86721i	0.175072	−	0.468348i
$109$	1.13812	+	0.657095i	0.109012	+	0.0629382i	0.553515	−	0.832839i	$-0.313286\pi$
$109$	1.13812	+	0.657095i	0.109012	+	0.0629382i	−0.444503	+	0.895778i	$0.646620\pi$
$110$	12.1336	−	3.25444i	1.15689	−	0.310299i
$111$	9.40693	−	7.39401i	0.892866	−	0.701808i
$112$	2.64167	+	0.146855i	0.249615	+	0.0138765i
$113$	−0.467015	−	0.125136i	−0.0439331	−	0.0117718i	0.236786	−	0.971562i	$-0.423906\pi$
$113$	−0.467015	−	0.125136i	−0.0439331	−	0.0117718i	−0.280719	+	0.959790i	$0.590573\pi$
$114$	4.66452	−	3.66640i	0.436873	−	0.343389i
$115$	−10.8428	−	10.8374i	−1.01109	−	1.01059i
$116$	5.39082	+	3.11239i	0.500525	+	0.288979i
$117$	−16.2474	+	0.378896i	−1.50207	+	0.0350290i
$118$	1.98391	+	1.98391i	0.182634	+	0.182634i
$119$	9.18040	−	1.92091i	0.841566	−	0.176090i
$120$	−2.39414	−	3.04435i	−0.218554	−	0.277910i
$121$	10.2816	−	17.8083i	0.934691	−	1.61893i
$122$	6.41679	+	6.41679i	0.580949	+	0.580949i
$123$	−0.109583	+	0.914640i	−0.00988076	+	0.0824703i
$124$			5.84161i			0.524592i
$125$	−0.00837164	−	11.1803i	−0.000748782	−	1.00000i
$126$	4.18799	−	6.74246i	0.373096	−	0.600666i
$127$	11.5953	−	11.5953i	1.02892	−	1.02892i	0.0293496	−	0.999569i	$-0.490656\pi$
$127$	11.5953	−	11.5953i	1.02892	−	1.02892i	0.999569	−	0.0293496i	$-0.00934362\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	2.61620	−	6.53036i	0.230343	−	0.574966i
$130$	−6.05407	+	10.4920i	−0.530977	+	0.920210i
$131$	−9.69820	−	5.59926i	−0.847336	−	0.489210i	0.0124151	−	0.999923i	$-0.496048\pi$
$131$	−9.69820	−	5.59926i	−0.847336	−	0.489210i	−0.859751	+	0.510713i	$0.829381\pi$
$132$	−9.66176	−	1.15758i	−0.840948	−	0.100754i
$133$	8.08801	−	4.08876i	0.701320	−	0.354540i
$134$	−2.56467			−0.221553
$135$	−11.4590	+	1.92132i	−0.986233	+	0.165361i
$136$	−1.77250	+	3.07007i	−0.151991	+	0.263256i
$137$	−0.303273	+	1.13183i	−0.0259104	+	0.0966988i	−0.977670	−	0.210145i	$-0.932606\pi$
$137$	−0.303273	+	1.13183i	−0.0259104	+	0.0966988i	0.951760	+	0.306844i	$0.0992730\pi$
$138$	4.67183	+	10.9171i	0.397693	+	0.929322i
$139$	16.4430	−	9.49334i	1.39467	−	0.805215i	0.400845	−	0.916146i	$-0.368717\pi$
$139$	16.4430	−	9.49334i	1.39467	−	0.805215i	0.993828	+	0.110931i	$0.0353833\pi$
$140$	−2.67041	−	5.27910i	−0.225691	−	0.446165i
$141$	0.199441	−	0.0286261i	0.0167960	−	0.00241075i
$142$	−6.49509	+	6.49509i	−0.545056	+	0.545056i
$143$	7.87712	+	29.3978i	0.658718	+	2.45837i
$144$	0.843805	+	2.87889i	0.0703171	+	0.239907i
$145$	−0.00347411	−	13.9190i	−0.000288509	−	1.15591i
$146$	−4.49282	−	2.59393i	−0.371829	−	0.214675i
$147$	8.29905	−	8.83888i	0.684494	−	0.729018i
$148$	−1.78792	+	6.67262i	−0.146966	+	0.548486i
$149$	−0.731437	+	1.26689i	−0.0599216	+	0.103787i	−0.894430	−	0.447208i	$-0.852418\pi$
$149$	−0.731437	+	1.26689i	−0.0599216	+	0.103787i	0.834508	+	0.550995i	$0.185752\pi$
$150$	−3.21662	+	8.04073i	−0.262636	+	0.656523i
$151$	2.80546	+	4.85919i	0.228305	+	0.395435i	0.957306	−	0.289077i	$-0.0933484\pi$
$151$	2.80546	+	4.85919i	0.228305	+	0.395435i	−0.729001	+	0.684513i	$0.760015\pi$
$152$	−0.886560	+	3.30869i	−0.0719095	+	0.268370i
$153$	5.53080	+	9.08373i	0.447138	+	0.734376i
$154$	−14.1220	−	4.63813i	−1.13798	−	0.373751i
$155$	11.3106	−	6.53394i	0.908489	−	0.524819i
$156$	7.37693	−	5.79839i	0.590627	−	0.464243i
$157$	−1.13591	+	1.13591i	−0.0906551	+	0.0906551i	−0.750980	−	0.660325i	$-0.770419\pi$
$157$	−1.13591	+	1.13591i	−0.0906551	+	0.0906551i	0.660325	+	0.750980i	$0.270419\pi$
$158$	10.8956	−	10.8956i	0.866806	−	0.866806i
$159$	2.34891	+	0.941022i	0.186281	+	0.0746279i
$160$	2.16002	+	0.578198i	0.170765	+	0.0457106i
$161$	3.71494	+	17.7544i	0.292778	+	1.39924i
$162$	8.79247	+	1.92159i	0.690801	+	0.150975i
$163$	5.18921	−	19.3664i	0.406450	−	1.51689i	−0.394916	−	0.918717i	$-0.629226\pi$
$163$	5.18921	−	19.3664i	0.406450	−	1.51689i	0.801366	−	0.598175i	$-0.204107\pi$
$164$	−0.265922	−	0.460590i	−0.0207650	−	0.0359661i
$165$	8.56553	+	20.0020i	0.666826	+	1.55715i
$166$	7.27841	−	12.6066i	0.564914	−	0.978460i
$167$	−5.72901	+	21.3810i	−0.443324	+	1.65451i	0.276999	+	0.960870i	$0.410660\pi$
$167$	−5.72901	+	21.3810i	−0.443324	+	1.65451i	−0.720323	+	0.693639i	$0.756006\pi$
$168$	0.398287	+	4.56523i	0.0307285	+	0.352215i
$169$	−14.1568	−	8.17341i	−1.08898	−	0.628724i
$170$	7.92688	−	0.00197850i	0.607964	−	0.000151744i
$171$	7.43382	+	7.09500i	0.568478	+	0.542568i
$172$	1.05122	+	3.92322i	0.0801550	+	0.299142i
$173$	6.78876	−	6.78876i	0.516140	−	0.516140i	−0.400261	−	0.916401i	$-0.631081\pi$
$173$	6.78876	−	6.78876i	0.516140	−	0.516140i	0.916401	+	0.400261i	$0.131081\pi$
$174$	−4.00955	+	10.0084i	−0.303964	+	0.758732i
$175$	−7.23456	+	11.0753i	−0.546881	+	0.837210i
$176$	4.86543	−	2.80906i	0.366746	−	0.211741i
$177$	−2.91317	+	3.88958i	−0.218967	+	0.292359i
$178$	−1.31817	+	4.91946i	−0.0988007	+	0.368729i
$179$	4.15894	−	7.20350i	0.310854	−	0.538415i	−0.667693	−	0.744436i	$-0.732718\pi$
$179$	4.15894	−	7.20350i	0.310854	−	0.538415i	0.978548	+	0.206021i	$0.0660516\pi$
$180$	4.63033	−	4.85387i	0.345124	−	0.361786i
$181$	12.9851			0.965173			0.482587	−	0.875848i	$-0.339697\pi$
$181$	12.9851			0.965173			0.482587	+	0.875848i	$0.339697\pi$
$182$	12.7912	−	6.46636i	0.948145	−	0.479318i
$183$	−9.42241	+	12.5805i	−0.696524	+	0.929979i
$184$	−5.93734	−	3.42793i	−0.437707	−	0.252710i
$185$	14.9194	−	4.00164i	1.09690	−	0.294207i
$186$	−10.0153	+	1.43751i	−0.734359	+	0.105404i
$187$	14.0829	−	14.0829i	1.02985	−	1.02985i
$188$	−0.0822560	+	0.0822560i	−0.00599914	+	0.00599914i
$189$	12.5904	+	5.52104i	0.915817	+	0.401596i
$190$	7.39796	−	1.98426i	0.536704	−	0.143953i
$191$			12.1652i			0.880242i	0.897938	+	0.440121i	$0.145065\pi$
$191$			12.1652i			0.880242i	−0.897938	+	0.440121i	$0.854935\pi$
$192$	−1.38633	−	1.03831i	−0.100050	−	0.0749339i
$193$	10.8381	+	10.8381i	0.780142	+	0.780142i	0.979855	−	0.199712i	$-0.0640007\pi$
$193$	10.8381	+	10.8381i	0.780142	+	0.780142i	−0.199712	+	0.979855i	$0.564001\pi$
$194$	1.01934	−	1.76554i	0.0731842	−	0.126759i
$195$	−19.4781	−	7.79770i	−1.39486	−	0.558405i
$196$	−0.775887	+	6.95687i	−0.0554205	+	0.496919i
$197$	−5.54709	−	5.54709i	−0.395214	−	0.395214i	0.481327	−	0.876541i	$-0.340155\pi$
$197$	−5.54709	−	5.54709i	−0.395214	−	0.395214i	−0.876541	+	0.481327i	$0.840155\pi$
$198$	−0.392944	−	16.8498i	−0.0279253	−	1.19746i
$199$	−4.63242	−	2.67453i	−0.328384	−	0.189592i	0.326740	−	0.945114i	$-0.394050\pi$
$199$	−4.63242	−	2.67453i	−0.328384	−	0.189592i	−0.655123	+	0.755522i	$0.727383\pi$
$200$	−1.29651	−	4.82898i	−0.0916768	−	0.341461i
$201$	−0.631118	−	4.39707i	−0.0445156	−	0.310145i
$202$	2.43531	+	0.652539i	0.171348	+	0.0459125i
$203$	−9.01360	+	13.7837i	−0.632630	+	0.967428i
$204$	−5.69975	−	2.28344i	−0.399063	−	0.159873i
$205$	−0.594363	+	1.03006i	−0.0415121	+	0.0719425i
$206$	−12.9364	−	7.46884i	−0.901323	−	0.520379i
$207$	−17.5674	+	10.6963i	−1.22102	+	0.743441i
$208$	−1.40209	+	5.23268i	−0.0972177	+	0.362821i
$209$	9.62216	−	16.6661i	0.665579	−	1.15282i
$210$	8.39377	−	5.87746i	0.579225	−	0.405583i
$211$	1.97854	+	3.42694i	0.136209	+	0.235920i	0.926059	−	0.377380i	$-0.123175\pi$
$211$	1.97854	+	3.42694i	0.136209	+	0.235920i	−0.789850	+	0.613300i	$0.789842\pi$
$212$	−1.41115	+	0.378116i	−0.0969179	+	0.0259691i
$213$	−12.7340	−	9.53738i	−0.872521	−	0.653491i
$214$	−0.897164	+	0.517978i	−0.0613288	+	0.0354082i
$215$	6.42037	−	6.42358i	0.437866	−	0.438084i
$216$	−4.72815	+	2.15513i	−0.321710	+	0.146638i
$217$	−15.4316	−	0.857871i	−1.04757	−	0.0582360i
$218$	−0.340137	−	1.26941i	−0.0230370	−	0.0859752i
$219$	3.34165	−	8.34118i	0.225807	−	0.563645i
$220$	−10.8810	−	6.27853i	−0.733597	−	0.423298i
$221$			19.2043i			1.29182i
$222$	−11.8801	−	1.42335i	−0.797337	−	0.0955290i
$223$	−12.2407	+	3.27990i	−0.819701	+	0.219638i	−0.644216	−	0.764844i	$-0.722816\pi$
$223$	−12.2407	+	3.27990i	−0.819701	+	0.219638i	−0.175485	+	0.984482i	$0.556149\pi$
$224$	−1.76410	−	1.97179i	−0.117869	−	0.131746i
$225$	−14.5772	−	3.53616i	−0.971815	−	0.235744i
$226$	0.241745	+	0.418714i	0.0160806	+	0.0278525i
$227$	6.50931	−	24.2931i	0.432038	−	1.61239i	−0.316018	−	0.948753i	$-0.602346\pi$
$227$	6.50931	−	24.2931i	0.432038	−	1.61239i	0.748056	−	0.663635i	$-0.230987\pi$
$228$	−5.89085	−	0.705782i	−0.390131	−	0.0467416i
$229$	−12.8834	−	7.43824i	−0.851359	−	0.491532i	0.00975006	−	0.999952i	$-0.496896\pi$
$229$	−12.8834	−	7.43824i	−0.851359	−	0.491532i	−0.861109	+	0.508420i	$0.830230\pi$
$230$	0.00382632	+	15.3302i	0.000252300	+	1.01084i
$231$	4.47681	−	25.3532i	0.294553	−	1.66812i
$232$	−1.61109	−	6.01268i	−0.105773	−	0.394752i
$233$	−9.72889	−	2.60685i	−0.637361	−	0.170780i	−0.0743532	−	0.997232i	$-0.523689\pi$
$233$	−9.72889	−	2.60685i	−0.637361	−	0.170780i	−0.563008	+	0.826452i	$0.690356\pi$
$234$	11.7566	+	11.2207i	0.768551	+	0.733522i
$235$	0.251270	+	0.0672604i	0.0163910	+	0.00438758i
$236$		−	2.80567i		−	0.182634i
$237$	21.3615	+	15.9991i	1.38758	+	1.03925i
$238$	−7.84981	−	5.13323i	−0.508828	−	0.332738i
$239$	6.41530	+	11.1116i	0.414971	+	0.718752i	0.995425	−	0.0955414i	$-0.0304582\pi$
$239$	6.41530	+	11.1116i	0.414971	+	0.718752i	−0.580454	+	0.814293i	$0.697125\pi$
$240$	−0.459767	+	3.84560i	−0.0296778	+	0.248232i
$241$	−0.838705	−	1.45268i	−0.0540257	−	0.0935753i	0.837748	−	0.546057i	$-0.183872\pi$
$241$	−0.838705	−	1.45268i	−0.0540257	−	0.0935753i	−0.891773	+	0.452482i	$0.850539\pi$
$242$	−19.8625	+	5.32215i	−1.27681	+	0.342121i
$243$	−1.13087	+	15.5474i	−0.0725454	+	0.997365i
$244$		−	9.07471i		−	0.580949i
$245$	14.3378	−	6.27909i	0.916009	−	0.401157i
$246$	0.724235	−	0.569261i	0.0461755	−	0.0362948i
$247$	4.80274	+	17.9241i	0.305591	+	1.14048i
$248$	4.13064	−	4.13064i	0.262296	−	0.262296i
$249$	23.4048	+	9.37644i	1.48322	+	0.594208i
$250$	−7.89977	+	7.91161i	−0.499625	+	0.500374i
$251$			0.581820i			0.0367242i	0.999831	+	0.0183621i	$0.00584516\pi$
$251$			0.581820i			0.0367242i	−0.999831	+	0.0183621i	$0.994155\pi$
$252$	−7.72899	+	1.80628i	−0.486881	+	0.113785i
$253$	27.2356	+	27.2356i	1.71229	+	1.71229i
$254$	−16.3983			−1.02892
$255$	1.95405	+	13.5900i	0.122368	+	0.851039i
$256$	1.00000			0.0625000
$257$	−2.05250	+	0.549964i	−0.128031	+	0.0343058i	−0.322266	−	0.946649i	$-0.604444\pi$
$257$	−2.05250	+	0.549964i	−0.128031	+	0.0343058i	0.194234	+	0.980955i	$0.437778\pi$
$258$	−6.46759	+	2.76773i	−0.402655	+	0.172312i
$259$	−17.3643	−	5.70302i	−1.07897	−	0.354368i
$260$	11.6998	−	3.13810i	0.725594	−	0.194616i
$261$	−18.1458	−	4.41143i	−1.12320	−	0.273060i
$262$	2.89839	+	10.8169i	0.179063	+	0.668273i
$263$	−27.4710	−	7.36083i	−1.69393	−	0.453889i	−0.722534	−	0.691335i	$-0.757023\pi$
$263$	−27.4710	−	7.36083i	−1.69393	−	0.453889i	−0.971401	+	0.237447i	$0.923690\pi$
$264$	6.01337	+	7.65043i	0.370097	+	0.470851i
$265$	2.31050	+	2.30935i	0.141933	+	0.141862i
$266$	−8.61028	−	2.82790i	−0.527930	−	0.173390i
$267$	−8.75870	−	1.04938i	−0.536024	−	0.0642210i
$268$	1.81349	+	1.81349i	0.110777	+	0.110777i
$269$	6.07208	−	10.5171i	0.370221	−	0.641242i	−0.619378	−	0.785093i	$-0.712615\pi$
$269$	6.07208	−	10.5171i	0.370221	−	0.641242i	0.989599	+	0.143851i	$0.0459486\pi$
$270$	9.46131	+	6.74416i	0.575797	+	0.410436i
$271$	−8.51049	−	14.7406i	−0.516975	−	0.895427i	−0.999806	−	0.0197135i	$-0.993725\pi$
$271$	−8.51049	−	14.7406i	−0.516975	−	0.895427i	0.482830	−	0.875714i	$-0.339609\pi$
$272$	3.42422	−	0.917516i	0.207624	−	0.0556326i
$273$	14.2341	+	20.3390i	0.861488	+	1.23097i
$274$	1.01477	−	0.585878i	0.0613046	−	0.0353942i
$275$	0.0140225	+	28.0906i	0.000845587	+	1.69392i
$276$	4.41604	−	11.0230i	0.265814	−	0.663507i
$277$	17.2375	+	4.61878i	1.03570	+	0.277516i	0.736331	−	0.676621i	$-0.236556\pi$
$277$	17.2375	+	4.61878i	1.03570	+	0.277516i	0.299371	+	0.954137i	$0.403223\pi$
$278$	−18.3397	−	4.91412i	−1.09994	−	0.294729i
$279$	−4.92918	−	16.8173i	−0.295102	−	1.00683i
$280$	−1.84462	+	5.62115i	−0.110237	+	0.335928i
$281$	7.96344	+	4.59770i	0.475059	+	0.274276i	0.718355	−	0.695677i	$-0.244895\pi$
$281$	7.96344	+	4.59770i	0.475059	+	0.274276i	−0.243296	+	0.969952i	$0.578229\pi$
$282$	−0.161268	−	0.120785i	−0.00960337	−	0.00719262i
$283$	−17.9475	−	17.9475i	−1.06687	−	1.06687i	−0.997598	−	0.0692717i	$-0.977932\pi$
$283$	−17.9475	−	17.9475i	−1.06687	−	1.06687i	−0.0692717	−	0.997598i	$-0.522068\pi$
$284$	9.18544			0.545056
$285$	5.22247	+	12.1954i	0.309352	+	0.722391i
$286$	15.2174	−	26.3573i	0.899825	−	1.55854i
$287$	1.25578	−	0.634839i	0.0741264	−	0.0374733i
$288$	1.43902	−	2.63234i	0.0847951	−	0.155112i
$289$	−3.83901	+	2.21645i	−0.225824	+	0.130380i
$290$	−9.83980	+	9.84471i	−0.577813	+	0.578101i
$291$	3.27783	+	1.31317i	0.192150	+	0.0769792i
$292$	1.34272	+	5.01109i	0.0785767	+	0.293252i
$293$	7.43825	+	1.99307i	0.434547	+	0.116437i	0.469460	−	0.882954i	$-0.344449\pi$
$293$	7.43825	+	1.99307i	0.434547	+	0.116437i	−0.0349126	+	0.999390i	$0.511115\pi$
$294$	−12.1183	+	0.381716i	−0.706756	+	0.0222621i
$295$	−5.43238	+	3.13819i	−0.316285	+	0.182713i
$296$	5.98251	−	3.45400i	0.347726	−	0.200760i
$297$	28.7919	−	4.82011i	1.67067	−	0.279691i
$298$	1.41303	−	0.378619i	0.0818545	−	0.0219328i
$299$	−37.1400			−2.14786
$300$	7.96015	−	3.41116i	0.459579	−	0.196943i
$301$	−10.5182	+	2.20084i	−0.606261	+	0.126854i
$302$	1.45221	−	5.41972i	0.0835653	−	0.311870i
$303$	−0.519480	+	4.33587i	−0.0298434	+	0.249089i
$304$	2.96649	−	1.71270i	0.170140	−	0.0982303i
$305$	−17.5706	+	10.1502i	−1.00609	+	0.581200i
$306$	2.51230	−	10.3340i	0.143619	−	0.590757i
$307$	−7.93485	+	7.93485i	−0.452866	+	0.452866i	−0.896305	−	0.443439i	$-0.853758\pi$
$307$	−7.93485	+	7.93485i	−0.452866	+	0.452866i	0.443439	+	0.896305i	$0.353758\pi$
$308$	6.70609	+	13.2654i	0.382115	+	0.755866i
$309$	9.62177	−	24.0172i	0.547363	−	1.36629i
$310$	−12.6180	−	3.37760i	−0.716654	−	0.191835i
$311$		−	6.37175i		−	0.361309i	−0.983547	−	0.180654i	$-0.942178\pi$
$311$		−	6.37175i		−	0.361309i	0.983547	−	0.180654i	$-0.0578215\pi$
$312$	−9.31636	−	1.11619i	−0.527435	−	0.0631920i
$313$	−20.4995	−	20.4995i	−1.15870	−	1.15870i	−0.984756	−	0.173944i	$-0.944349\pi$
$313$	−20.4995	−	20.4995i	−1.15870	−	1.15870i	−0.173944	−	0.984756i	$-0.555651\pi$
$314$	1.60641			0.0906551
$315$	12.1424	+	12.9446i	0.684144	+	0.729347i
$316$	−15.4087			−0.866806
$317$	20.0120	+	20.0120i	1.12398	+	1.12398i	0.991137	+	0.132847i	$0.0424118\pi$
$317$	20.0120	+	20.0120i	1.12398	+	1.12398i	0.132847	+	0.991137i	$0.457588\pi$
$318$	−0.995529	−	2.32634i	−0.0558265	−	0.130454i
$319$			34.9716i			1.95803i
$320$	−1.11852	−	1.93621i	−0.0625270	−	0.108238i
$321$	−1.10884	−	1.41070i	−0.0618893	−	0.0787379i
$322$	9.92739	−	15.1811i	0.553232	−	0.846010i
$323$	8.58647	−	8.58647i	0.477764	−	0.477764i
$324$	−4.85844	−	7.57599i	−0.269913	−	0.420888i
$325$	−19.1625	−	19.1434i	−1.06294	−	1.06188i
$326$	−17.3634	+	10.0248i	−0.961671	+	0.555221i
$327$	2.09268	−	0.895537i	0.115725	−	0.0495233i
$328$	−0.137651	+	0.513722i	−0.00760052	+	0.0283655i
$329$	−0.205214	−	0.229373i	−0.0113138	−	0.0126458i
$330$	8.08680	−	20.2003i	0.445163	−	1.11199i
$331$	4.03334			0.221692			0.110846	−	0.993838i	$-0.464644\pi$
$331$	4.03334			0.221692			0.110846	+	0.993838i	$0.464644\pi$
$332$	−14.0608	+	3.76758i	−0.771687	+	0.206773i
$333$	−0.483162	−	20.7184i	−0.0264771	−	1.13536i
$334$	19.1697	−	11.0676i	1.04892	−	0.605592i
$335$	1.48288	−	5.53973i	0.0810186	−	0.302668i
$336$	2.94648	−	3.50974i	0.160743	−	0.191472i
$337$	−13.3424	−	3.57510i	−0.726809	−	0.194748i	−0.123601	−	0.992332i	$-0.539444\pi$
$337$	−13.3424	−	3.57510i	−0.726809	−	0.194748i	−0.603208	+	0.797584i	$0.706111\pi$
$338$	4.23087	+	15.7898i	0.230129	+	0.858853i
$339$	−0.658389	+	0.517505i	−0.0357588	+	0.0281070i
$340$	−5.60655	−	5.60375i	−0.304058	−	0.303906i
$341$	−28.4219	+	16.4094i	−1.53913	+	0.888619i
$342$	−0.239581	−	10.2734i	−0.0129550	−	0.555523i
$343$	−18.2638	−	3.07129i	−0.986154	−	0.165834i
$344$	2.03081	−	3.51746i	0.109494	−	0.189649i
$345$	−26.2823	+	3.77903i	−1.41499	+	0.203456i
$346$	−9.60076			−0.516140
$347$	−11.7459	−	11.7459i	−0.630554	−	0.630554i	0.317653	−	0.948207i	$-0.397105\pi$
$347$	−11.7459	−	11.7459i	−0.630554	−	0.630554i	−0.948207	+	0.317653i	$0.897105\pi$
$348$	9.91217	−	4.24180i	0.531348	−	0.227384i
$349$	−4.32988	−	2.49986i	−0.231773	−	0.133814i	0.379616	−	0.925144i	$-0.376056\pi$
$349$	−4.32988	−	2.49986i	−0.231773	−	0.133814i	−0.611390	+	0.791329i	$0.709389\pi$
$350$	12.9470	−	2.71578i	0.692046	−	0.145165i
$351$	−16.3446	+	22.9176i	−0.872412	+	1.22325i
$352$	−5.42668	−	1.45407i	−0.289243	−	0.0775024i
$353$	23.1138	+	6.19331i	1.23022	+	0.329637i	0.814666	−	0.579931i	$-0.196920\pi$
$353$	23.1138	+	6.19331i	1.23022	+	0.329637i	0.415556	+	0.909568i	$0.363587\pi$
$354$	4.81027	−	0.690425i	0.255663	−	0.0366957i
$355$	−10.2741	−	17.7850i	−0.545291	−	0.943928i
$356$	4.41067	−	2.54650i	0.233765	−	0.134964i
$357$	6.86913	−	14.7215i	0.363553	−	0.779147i
$358$	−8.03446	+	2.15283i	−0.424635	+	0.113781i
$359$	5.48263	+	9.49619i	0.289362	+	0.501190i	0.973658	−	0.228015i	$-0.0732235\pi$
$359$	5.48263	+	9.49619i	0.289362	+	0.501190i	−0.684296	+	0.729205i	$0.739890\pi$
$360$	−6.70634	+	0.158070i	−0.353455	+	0.00833100i
$361$	−3.63330	+	6.29305i	−0.191226	+	0.331213i
$362$	−9.18184	−	9.18184i	−0.482587	−	0.482587i
$363$	−14.0125	−	32.7442i	−0.735467	−	1.71863i
$364$	−13.6171	−	4.47232i	−0.713731	−	0.234413i
$365$	8.20069	−	8.20478i	0.429244	−	0.429458i
$366$	15.5584	−	2.23312i	0.813251	−	0.116727i
$367$	11.3666	+	3.04568i	0.593333	+	0.158983i	0.542976	−	0.839748i	$-0.317297\pi$
$367$	11.3666	+	3.04568i	0.593333	+	0.158983i	0.0503572	+	0.998731i	$0.483964\pi$
$368$	1.77443	+	6.62225i	0.0924983	+	0.345208i
$369$	1.15421	+	1.10160i	0.0600857	+	0.0573471i
$370$	−13.3792	−	7.72005i	−0.695553	−	0.401346i
$371$	−0.791623	−	3.78332i	−0.0410990	−	0.196420i
$372$	8.09838	+	6.06543i	0.419881	+	0.314478i
$373$	−18.2136	+	4.88033i	−0.943067	+	0.252694i	−0.697418	−	0.716665i	$-0.745668\pi$
$373$	−18.2136	+	4.88033i	−0.943067	+	0.252694i	−0.245649	+	0.969359i	$0.579001\pi$
$374$	−19.9163			−1.02985
$375$	−15.5083	−	11.5971i	−0.800845	−	0.598872i
$376$	0.116328			0.00599914
$377$	−23.8446	−	23.8446i	−1.22806	−	1.22806i
$378$	−4.99879	−	12.8067i	−0.257110	−	0.658707i
$379$			29.2781i			1.50392i	0.659211	+	0.751958i	$0.270891\pi$
$379$			29.2781i			1.50392i	−0.659211	+	0.751958i	$0.729109\pi$
$380$	−6.63423	−	3.82806i	−0.340329	−	0.196376i
$381$	−4.03532	−	28.1145i	−0.206736	−	1.44035i
$382$	8.60209	−	8.60209i	0.440121	−	0.440121i
$383$	−5.21778	−	19.4730i	−0.266616	−	0.995025i	−0.961254	−	0.275665i	$-0.911102\pi$
$383$	−5.21778	−	19.4730i	−0.266616	−	0.995025i	0.694638	−	0.719360i	$-0.255565\pi$
$384$	0.246082	+	1.71448i	0.0125578	+	0.0874917i
$385$	18.1837	−	27.8220i	0.926729	−	1.41794i
$386$		−	15.3274i		−	0.780142i
$387$	−6.33678	−	10.4075i	−0.322117	−	0.529042i
$388$	−1.96921	+	0.527648i	−0.0999715	+	0.0267873i
$389$	3.48455	+	6.03541i	0.176673	+	0.306007i	0.940739	−	0.339131i	$-0.110133\pi$
$389$	3.48455	+	6.03541i	0.176673	+	0.306007i	−0.764066	+	0.645138i	$0.776800\pi$
$390$	8.25932	+	19.2869i	0.418227	+	0.976632i
$391$	12.1520	+	21.0479i	0.614555	+	1.06444i
$392$	5.46788	−	4.37061i	0.276170	−	0.220749i
$393$	−17.8322	+	7.63109i	−0.899515	+	0.384937i
$394$			7.84477i			0.395214i
$395$	17.2349	+	29.8345i	0.867180	+	1.50113i
$396$	−11.6367	+	12.1924i	−0.584767	+	0.612693i
$397$	−12.8233	−	3.43599i	−0.643583	−	0.172448i	−0.0777571	−	0.996972i	$-0.524776\pi$
$397$	−12.8233	−	3.43599i	−0.643583	−	0.172448i	−0.565826	+	0.824525i	$0.691443\pi$
$398$	1.38444	+	5.16679i	0.0693956	+	0.258988i
$399$	2.72955	−	15.4580i	0.136648	−	0.773870i
$400$	−2.49784	+	4.33137i	−0.124892	+	0.216569i
$401$	20.3543	+	11.7516i	1.01645	+	0.586845i	0.913072	−	0.407798i	$-0.133703\pi$
$401$	20.3543	+	11.7516i	1.01645	+	0.586845i	0.103373	+	0.994643i	$0.467036\pi$
$402$	−2.66293	+	3.55546i	−0.132815	+	0.177330i
$403$	8.19048	−	30.5673i	0.407997	−	1.52266i
$404$	−1.26061	−	2.18344i	−0.0627177	−	0.108630i
$405$	−9.23447	+	17.8808i	−0.458864	+	0.888506i
$406$	16.1201	−	3.37299i	0.800029	−	0.167399i
$407$	−37.4876	+	10.0448i	−1.85819	+	0.497900i
$408$	2.41570	+	5.64497i	0.119595	+	0.279468i
$409$			16.8126i			0.831327i	0.909518	+	0.415664i	$0.136451\pi$
$409$			16.8126i			0.831327i	−0.909518	+	0.415664i	$0.863549\pi$
$410$	1.14864	−	0.308084i	0.0567273	−	0.0152152i
$411$	1.25419	+	1.59563i	0.0618648	+	0.0787067i
$412$	3.86616	+	14.4287i	0.190472	+	0.710851i
$413$	7.41167	+	0.412028i	0.364704	+	0.0202745i
$414$	19.9854	+	4.85865i	0.982231	+	0.238790i
$415$	23.0221	+	23.0106i	1.13011	+	1.12955i
$416$	4.69149	−	2.70864i	0.230019	−	0.132802i
$417$	3.91208	−	32.6524i	0.191575	−	1.59899i
$418$	−18.5886	+	4.98080i	−0.909198	+	0.243619i
$419$	17.4144	+	30.1626i	0.850748	+	1.47354i	0.880534	+	0.473983i	$0.157184\pi$
$419$	17.4144	+	30.1626i	0.850748	+	1.47354i	−0.0297862	+	0.999556i	$0.509483\pi$
$420$	−10.0913	−	1.77930i	−0.492404	−	0.0868210i
$421$	−14.0377	+	24.3140i	−0.684155	+	1.18499i	0.289546	+	0.957164i	$0.406496\pi$
$421$	−14.0377	+	24.3140i	−0.684155	+	1.18499i	−0.973701	+	0.227828i	$0.926838\pi$
$422$	1.02417	−	3.82225i	0.0498558	−	0.186064i
$423$	0.167398	−	0.306214i	0.00813916	−	0.0148886i
$424$	1.26520	+	0.730463i	0.0614435	+	0.0354744i
$425$	−4.57903	+	17.1234i	−0.222116	+	0.830605i
$426$	2.26037	+	15.7483i	0.109515	+	0.763006i
$427$	23.9724	+	1.33267i	1.16011	+	0.0644924i
$428$	1.00066	+	0.268125i	0.0483685	+	0.0129603i
$429$	48.9339	+	19.6039i	2.36255	+	0.946486i
$430$	−9.08204	+	0.00226682i	−0.437975	+	0.000109316i
$431$	−29.0585	−	16.7770i	−1.39970	−	0.808117i	−0.405339	−	0.914166i	$-0.632847\pi$
$431$	−29.0585	−	16.7770i	−1.39970	−	0.808117i	−0.994361	+	0.106049i	$0.966180\pi$
$432$	4.86721	+	1.81940i	0.234174	+	0.0875360i
$433$	−11.1429	−	11.1429i	−0.535495	−	0.535495i	0.386707	−	0.922202i	$-0.373612\pi$
$433$	−11.1429	−	11.1429i	−0.535495	−	0.535495i	−0.922202	+	0.386707i	$0.873612\pi$
$434$	10.3052	+	11.5184i	0.494665	+	0.552901i
$435$	−19.3000	−	14.4475i	−0.925362	−	0.692706i
$436$	−0.657095	+	1.13812i	−0.0314691	+	0.0545061i
$437$	16.6058	+	16.6058i	0.794361	+	0.794361i
$438$	−8.26100	+	3.53520i	−0.394726	+	0.168919i
$439$			31.5056i			1.50368i	0.659345	+	0.751841i	$0.270834\pi$
$439$			31.5056i			1.50368i	−0.659345	+	0.751841i	$0.729166\pi$
$440$	3.25444	+	12.1336i	0.155149	+	0.578447i
$441$	−3.63655	−	20.6827i	−0.173169	−	0.984892i
$442$	13.5795	−	13.5795i	0.645910	−	0.645910i
$443$	22.8593	−	22.8593i	1.08608	−	1.08608i	0.0901493	−	0.995928i	$-0.471266\pi$
$443$	22.8593	−	22.8593i	1.08608	−	1.08608i	0.995928	−	0.0901493i	$-0.0287344\pi$
$444$	7.39401	+	9.40693i	0.350904	+	0.446433i
$445$	−9.86398	−	5.69169i	−0.467597	−	0.269812i
$446$	10.9748	+	6.33628i	0.519670	+	0.300031i
$447$	0.996856	+	2.32944i	0.0471497	+	0.110179i
$448$	−0.146855	+	2.64167i	−0.00693826	+	0.124807i
$449$	34.0514			1.60699			0.803493	−	0.595315i	$-0.202973\pi$
$449$	34.0514			1.60699			0.803493	+	0.595315i	$0.202973\pi$
$450$	7.80722	+	12.8081i	0.368036	+	0.603780i
$451$	1.49398	−	2.58765i	0.0703488	−	0.121848i
$452$	0.125136	−	0.467015i	0.00588592	−	0.0219665i
$453$	9.64937	+	1.15609i	0.453367	+	0.0543179i
$454$	−21.7806	+	12.5750i	−1.02221	+	0.590175i
$455$	6.57164	+	31.3680i	0.308083	+	1.47056i
$456$	3.66640	+	4.66452i	0.171695	+	0.218436i
$457$	19.8236	−	19.8236i	0.927310	−	0.927310i	−0.0702215	−	0.997531i	$-0.522371\pi$
$457$	19.8236	−	19.8236i	0.927310	−	0.927310i	0.997531	+	0.0702215i	$0.0223706\pi$
$458$	3.85031	+	14.3696i	0.179913	+	0.671446i
$459$	18.3357	+	1.76428i	0.855838	+	0.0823494i
$460$	10.8374	−	10.8428i	0.505294	−	0.505546i
$461$	5.23792	+	3.02411i	0.243954	+	0.140847i	0.616993	−	0.786969i	$-0.288351\pi$
$461$	5.23792	+	3.02411i	0.243954	+	0.140847i	−0.373039	+	0.927816i	$0.621684\pi$
$462$	−21.0930	+	14.7618i	−0.981336	+	0.686783i
$463$	3.06112	−	11.4243i	0.142263	−	0.530931i	−0.857599	−	0.514318i	$-0.828045\pi$
$463$	3.06112	−	11.4243i	0.142263	−	0.530931i	0.999862	−	0.0166128i	$-0.00528827\pi$
$464$	−3.11239	+	5.39082i	−0.144489	+	0.250263i
$465$	2.68578	−	22.4645i	0.124550	−	1.04176i
$466$	5.03605	+	8.72269i	0.233290	+	0.404071i
$467$	−3.63120	+	13.5518i	−0.168032	+	0.627104i	0.829602	+	0.558355i	$0.188567\pi$
$467$	−3.63120	+	13.5518i	−0.168032	+	0.627104i	−0.997634	+	0.0687487i	$0.978099\pi$
$468$	−0.378896	−	16.2474i	−0.0175145	−	0.751036i
$469$	−5.05697	+	4.52433i	−0.233509	+	0.208914i
$470$	−0.130114	−	0.225235i	−0.00600173	−	0.0103893i
$471$	0.395309	+	2.75416i	0.0182149	+	0.126905i
$472$	−1.98391	+	1.98391i	−0.0913168	+	0.0913168i
$473$	−16.1352	+	16.1352i	−0.741897	+	0.741897i
$474$	−3.79180	−	26.4179i	−0.174163	−	1.21341i
$475$	0.00854961	+	17.1270i	0.000392283	+	0.785842i
$476$	1.92091	+	9.18040i	0.0880449	+	0.420783i
$477$	3.74348	−	2.27929i	0.171402	−	0.104361i
$478$	3.32081	−	12.3934i	0.151890	−	0.566862i
$479$	−20.9047	−	36.2079i	−0.955158	−	1.65438i	−0.734006	−	0.679143i	$-0.762351\pi$
$479$	−20.9047	−	36.2079i	−0.955158	−	1.65438i	−0.221152	−	0.975239i	$-0.570982\pi$
$480$	3.04435	−	2.39414i	0.138955	−	0.109277i
$481$	18.7113	−	32.4089i	0.853161	−	1.47772i
$482$	−0.434146	+	1.62025i	−0.0197748	+	0.0738005i
$483$	28.4707	+	13.2845i	1.29546	+	0.604467i
$484$	17.8083	+	10.2816i	0.809466	+	0.467345i
$485$	3.22423	+	3.22262i	0.146405	+	0.146332i
$486$	11.7933	−	10.1940i	0.534955	−	0.462410i
$487$	−0.371900	−	1.38795i	−0.0168524	−	0.0628940i	0.956988	−	0.290129i	$-0.0936982\pi$
$487$	−0.371900	−	1.38795i	−0.0168524	−	0.0628940i	−0.973840	+	0.227235i	$0.927031\pi$
$488$	−6.41679	+	6.41679i	−0.290474	+	0.290474i
$489$	−21.4601	−	27.3023i	−0.970460	−	1.23465i
$490$	−14.5784	−	5.69838i	−0.658583	−	0.257426i
$491$	2.09234	−	1.20802i	0.0944262	−	0.0545170i	−0.452043	−	0.891996i	$-0.649305\pi$
$491$	2.09234	−	1.20802i	0.0944262	−	0.0545170i	0.546470	+	0.837479i	$0.315971\pi$
$492$	−0.914640	−	0.109583i	−0.0412351	−	0.00494038i
$493$	−5.71134	+	21.3150i	−0.257226	+	0.959980i
$494$	9.27818	−	16.0703i	0.417445	−	0.723036i
$495$	36.6230	+	8.89373i	1.64608	+	0.399743i
$496$	−5.84161			−0.262296
$497$	−1.34893	+	24.2649i	−0.0605078	+	1.08843i
$498$	−9.91956	−	23.1799i	−0.444506	−	1.03871i
$499$	5.91319	+	3.41398i	0.264711	+	0.152831i	0.626482	−	0.779436i	$-0.284494\pi$
$499$	5.91319	+	3.41398i	0.264711	+	0.152831i	−0.361771	+	0.932267i	$0.617828\pi$
$500$	11.1803	−	0.00837164i	0.500000	−	0.000374391i
$501$	23.6925	+	30.1425i	1.05850	+	1.34667i
$502$	0.411409	−	0.411409i	0.0183621	−	0.0183621i
$503$	10.6908	−	10.6908i	0.476680	−	0.476680i	−0.427389	−	0.904068i	$-0.640566\pi$
$503$	10.6908	−	10.6908i	0.476680	−	0.476680i	0.904068	+	0.427389i	$0.140566\pi$
$504$	6.74246	+	4.18799i	0.300333	+	0.186548i
$505$	−2.81759	+	4.88302i	−0.125381	+	0.217292i
$506$		−	38.5170i		−	1.71229i
$507$	−26.0302	+	11.1393i	−1.15604	+	0.494715i
$508$	11.5953	+	11.5953i	0.514459	+	0.514459i
$509$	1.54586	−	2.67750i	0.0685189	−	0.118678i	−0.829731	−	0.558164i	$-0.811506\pi$
$509$	1.54586	−	2.67750i	0.0685189	−	0.118678i	0.898250	+	0.439486i	$0.144839\pi$
$510$	8.22786	−	10.9913i	0.364336	−	0.486703i
$511$	−13.4349	+	2.81112i	−0.594323	+	0.124357i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	17.5546	−	2.93886i	0.775056	−	0.129754i
$514$	1.84022	+	1.06245i	0.0811685	+	0.0468626i
$515$	23.6127	−	23.6244i	1.04050	−	1.04102i
$516$	6.53036	+	2.61620i	0.287483	+	0.115172i
$517$	−0.631273	−	0.169149i	−0.0277633	−	0.00743917i
$518$	8.24578	+	16.3111i	0.362299	+	0.716667i
$519$	−2.36257	−	16.4603i	−0.103705	−	0.722527i
$520$	−10.4920	−	6.05407i	−0.460105	−	0.265489i
$521$	11.7621	+	6.79086i	0.515307	+	0.297513i	0.735013	−	0.678053i	$-0.237176\pi$
$521$	11.7621	+	6.79086i	0.515307	+	0.297513i	−0.219705	+	0.975566i	$0.570510\pi$
$522$	9.71169	+	15.9504i	0.425069	+	0.698130i
$523$	−3.83312	+	14.3054i	−0.167611	+	0.625532i	0.830082	+	0.557641i	$0.188294\pi$
$523$	−3.83312	+	14.3054i	−0.167611	+	0.625532i	−0.997693	+	0.0678906i	$0.978373\pi$
$524$	5.59926	−	9.69820i	0.244605	−	0.423668i
$525$	7.84218	+	21.5291i	0.342261	+	0.939605i
$526$	14.2200	+	24.6298i	0.620023	+	1.07391i
$527$	−20.0029	+	5.35977i	−0.871341	+	0.233475i
$528$	1.15758	−	9.66176i	0.0503770	−	0.420474i
$529$	−20.7870	+	12.0014i	−0.903781	+	0.521798i
$530$	−0.000815357	−	3.26673i	−3.54168e−5	−	0.141898i
$531$	2.36744	+	8.07721i	0.102738	+	0.350521i
$532$	4.08876	+	8.08801i	0.177270	+	0.350660i
$533$	0.745695	+	2.78297i	0.0322996	+	0.120544i
$534$	5.45131	+	6.93536i	0.235901	+	0.300122i
$535$	−0.600104	−	2.23739i	−0.0259448	−	0.0967306i
$536$		−	2.56467i		−	0.110777i
$537$	−5.66812	−	13.2452i	−0.244597	−	0.571571i
$538$	−11.7304	+	3.14314i	−0.505731	+	0.135510i
$539$	−36.0277	+	15.7672i	−1.55182	+	0.679142i
$540$	−1.92132	−	11.4590i	−0.0826803	−	0.493117i
$541$	20.8408	+	36.0974i	0.896017	+	1.55195i	0.832540	+	0.553965i	$0.186886\pi$
$541$	20.8408	+	36.0974i	0.896017	+	1.55195i	0.0634772	+	0.997983i	$0.479781\pi$
$542$	−4.40535	+	16.4410i	−0.189226	+	0.706201i
$543$	13.4826	−	18.0016i	0.578594	−	0.772521i
$544$	−3.07007	−	1.77250i	−0.131628	−	0.0759955i
$545$	2.93862		0.000733461i	0.125876		3.14180e-5i
$546$	4.31677	−	24.4469i	0.184741	−	1.04623i
$547$	−7.15975	−	26.7205i	−0.306129	−	1.14249i	−0.931969	−	0.362537i	$-0.881911\pi$
$547$	−7.15975	−	26.7205i	−0.306129	−	1.14249i	0.625841	−	0.779951i	$-0.284756\pi$
$548$	−1.13183	−	0.303273i	−0.0483494	−	0.0129552i
$549$	7.65729	+	26.1251i	0.326805	+	1.11499i
$550$	19.8531	−	19.8729i	0.846540	−	0.847385i
$551$			21.3224i			0.908366i
$552$	−10.9171	+	4.67183i	−0.464661	+	0.198846i
$553$	2.26284	−	40.7047i	0.0962259	−	1.73094i
$554$	−8.92280	−	15.4547i	−0.379093	−	0.656609i
$555$	9.94349	−	24.8382i	0.422078	−	1.05432i
$556$	9.49334	+	16.4430i	0.402607	+	0.697337i
$557$	19.8166	−	5.30984i	0.839655	−	0.224985i	0.186734	−	0.982411i	$-0.440210\pi$
$557$	19.8166	−	5.30984i	0.839655	−	0.224985i	0.652922	+	0.757426i	$0.273543\pi$
$558$	−8.40619	+	15.3771i	−0.355863	+	0.650965i
$559$		−	22.0029i		−	0.930622i
$560$	5.27910	−	2.67041i	0.223083	−	0.112846i
$561$	−4.90103	−	34.1461i	−0.206922	−	1.44165i
$562$	−2.37994	−	8.88207i	−0.100392	−	0.374667i
$563$	−23.0459	+	23.0459i	−0.971270	+	0.971270i	−0.999599	−	0.0283287i	$-0.990981\pi$
$563$	−23.0459	+	23.0459i	−0.971270	+	0.971270i	0.0283287	+	0.999599i	$0.490981\pi$
$564$	0.0286261	+	0.199441i	0.00120538	+	0.00839800i
$565$	−1.04421	+	0.280074i	−0.0439301	+	0.0117828i
$566$			25.3816i			1.06687i
$567$	20.7268	−	11.7218i	0.870442	−	0.492271i
$568$	−6.49509	−	6.49509i	−0.272528	−	0.272528i
$569$	−16.5598			−0.694223			−0.347111	−	0.937824i	$-0.612837\pi$
$569$	−16.5598			−0.694223			−0.347111	+	0.937824i	$0.612837\pi$
$570$	4.93058	−	12.3163i	0.206519	−	0.515872i
$571$	−2.47193			−0.103447			−0.0517236	−	0.998661i	$-0.516471\pi$
$571$	−2.47193			−0.103447			−0.0517236	+	0.998661i	$0.516471\pi$
$572$	−29.3978	+	7.87712i	−1.22918	+	0.329359i
$573$	16.8649	+	12.6313i	0.704543	+	0.527680i
$574$	−1.33687	−	0.439072i	−0.0557999	−	0.0183265i
$575$	−33.1157	−	8.85560i	−1.38102	−	0.369304i
$576$	−2.87889	+	0.843805i	−0.119954	+	0.0351585i
$577$	2.09826	+	7.83081i	0.0873516	+	0.326001i	0.995749	−	0.0921069i	$-0.0293602\pi$
$577$	2.09826	+	7.83081i	0.0873516	+	0.326001i	−0.908398	+	0.418108i	$0.862693\pi$
$578$	4.28186	+	1.14732i	0.178102	+	0.0477222i
$579$	26.2785	−	3.77179i	1.09210	−	0.156750i
$580$	13.9190	−	0.00347411i	0.577957	−	0.000144255i
$581$	−7.88782	−	37.6973i	−0.327242	−	1.56395i
$582$	−1.38923	−	3.24633i	−0.0575854	−	0.134565i
$583$	−5.80369	−	5.80369i	−0.240364	−	0.240364i
$584$	2.59393	−	4.49282i	0.107338	−	0.185914i
$585$	−31.0346	+	18.9066i	−1.28312	+	0.781692i
$586$	−3.85032	−	6.66895i	−0.159055	−	0.275492i
$587$	−19.7343	+	5.28778i	−0.814521	+	0.218250i	−0.641950	−	0.766747i	$-0.721874\pi$
$587$	−19.7343	+	5.28778i	−0.814521	+	0.218250i	−0.172571	+	0.984997i	$0.555208\pi$
$588$	8.83888	+	8.29905i	0.364509	+	0.342247i
$589$	−17.3291	+	10.0049i	−0.714032	+	0.412246i
$590$	6.06031	+	1.62223i	0.249499	+	0.0667863i
$591$	−13.4497	+	1.93046i	−0.553247	+	0.0794083i
$592$	−6.67262	−	1.78792i	−0.274243	−	0.0734832i
$593$	10.5168	+	2.81796i	0.431872	+	0.115720i	0.468205	−	0.883620i	$-0.344901\pi$
$593$	10.5168	+	2.81796i	0.431872	+	0.115720i	−0.0363328	+	0.999340i	$0.511568\pi$
$594$	−23.7673	−	16.9506i	−0.975183	−	0.695492i
$595$	15.6266	−	13.9877i	0.640629	−	0.573441i
$596$	−1.26689	−	0.731437i	−0.0518937	−	0.0299608i
$597$	−8.51768	+	3.64505i	−0.348606	+	0.149182i
$598$	26.2620	+	26.2620i	1.07393	+	1.07393i
$599$	37.8278			1.54560			0.772802	−	0.634648i	$-0.218855\pi$
$599$	37.8278			1.54560			0.772802	+	0.634648i	$0.218855\pi$
$600$	−8.04073	−	3.21662i	−0.328261	−	0.131318i
$601$	−5.75054	+	9.96023i	−0.234569	+	0.406286i	−0.959147	−	0.282907i	$-0.908701\pi$
$601$	−5.75054	+	9.96023i	−0.234569	+	0.406286i	0.724578	+	0.689193i	$0.242035\pi$
$602$	8.99374	+	5.88128i	0.366558	+	0.239703i
$603$	−6.75107	−	3.69061i	−0.274925	−	0.150293i
$604$	−4.85919	+	2.80546i	−0.197718	+	0.114152i
$605$	−0.0114765	−	45.9807i	−0.000466587	−	1.86938i
$606$	3.43325	−	2.69859i	0.139466	−	0.109623i
$607$	3.12103	+	11.6479i	0.126679	+	0.472772i	0.999894	−	0.0145631i	$-0.00463575\pi$
$607$	3.12103	+	11.6479i	0.126679	+	0.472772i	−0.873215	+	0.487335i	$0.837969\pi$
$608$	−3.30869	−	0.886560i	−0.134185	−	0.0359548i
$609$	9.74980	+	26.8076i	0.395082	+	1.08630i
$610$	19.6016	+	5.24698i	0.793644	+	0.212444i
$611$	0.545750	−	0.315089i	0.0220787	−	0.0127471i
$612$	−9.08373	+	5.53080i	−0.367188	+	0.223569i
$613$	34.3116	−	9.19377i	1.38583	−	0.371333i	0.512597	−	0.858630i	$-0.328684\pi$
$613$	34.3116	−	9.19377i	1.38583	−	0.371333i	0.873236	+	0.487297i	$0.162017\pi$
$614$	11.2216			0.452866
$615$	0.810864	+	1.89351i	0.0326972	+	0.0763536i
$616$	4.63813	−	14.1220i	0.186875	−	0.568991i
$617$	−2.87544	+	10.7313i	−0.115761	+	0.432025i	−0.999343	−	0.0362515i	$-0.988458\pi$
$617$	−2.87544	+	10.7313i	−0.115761	+	0.432025i	0.883582	+	0.468277i	$0.155125\pi$
$618$	−23.7863	+	10.1791i	−0.956826	+	0.409463i
$619$	10.8710	−	6.27637i	0.436942	−	0.252269i	−0.265358	−	0.964150i	$-0.585490\pi$
$619$	10.8710	−	6.27637i	0.436942	−	0.252269i	0.702300	+	0.711882i	$0.252157\pi$
$620$	6.53394	+	11.3106i	0.262409	+	0.454244i
$621$	−3.41201	+	35.4603i	−0.136919	+	1.42297i
$622$	−4.50550	+	4.50550i	−0.180654	+	0.180654i
$623$	6.07929	+	12.0255i	0.243562	+	0.481792i
$624$	5.79839	+	7.37693i	0.232122	+	0.295314i
$625$	−12.5216	−	21.6381i	−0.500864	−	0.865526i
$626$			28.9906i			1.15870i
$627$	−13.1138	−	30.6441i	−0.523714	−	1.22381i
$628$	−1.13591	−	1.13591i	−0.0453276	−	0.0453276i
$629$	−24.4890			−0.976439
$630$	0.567293	−	17.7392i	0.0226015	−	0.706745i
$631$	26.3199			1.04778			0.523889	−	0.851786i	$-0.324480\pi$
$631$	26.3199			1.04778			0.523889	+	0.851786i	$0.324480\pi$
$632$	10.8956	+	10.8956i	0.433403	+	0.433403i
$633$	6.80521	+	0.815332i	0.270483	+	0.0324065i
$634$		−	28.3012i		−	1.12398i
$635$	9.48144	−	35.4206i	0.376260	−	1.40562i
$636$	−0.941022	+	2.34891i	−0.0373140	+	0.0931405i
$637$	13.8141	−	35.3152i	0.547336	−	1.39924i
$638$	24.7286	−	24.7286i	0.979016	−	0.979016i
$639$	−26.4439	+	7.75073i	−1.04610	+	0.306614i
$640$	−0.578198	+	2.16002i	−0.0228553	+	0.0853823i
$641$	6.11664	−	3.53145i	0.241593	−	0.139484i	−0.374316	−	0.927301i	$-0.622122\pi$
$641$	6.11664	−	3.53145i	0.241593	−	0.139484i	0.615909	+	0.787818i	$0.288789\pi$
$642$	−0.213452	+	1.78159i	−0.00842427	+	0.0703136i
$643$	4.92522	−	18.3812i	0.194232	−	0.724882i	−0.798233	−	0.602349i	$-0.794232\pi$
$643$	4.92522	−	18.3812i	0.194232	−	0.724882i	0.992464	−	0.122533i	$-0.0391018\pi$
$644$	−17.7544	+	3.71494i	−0.699621	+	0.146389i
$645$	−2.23881	−	15.5704i	−0.0881531	−	0.613085i
$646$	−12.1431			−0.477764
$647$	−8.72870	+	2.33885i	−0.343161	+	0.0919496i	−0.426283	−	0.904590i	$-0.640177\pi$
$647$	−8.72870	+	2.33885i	−0.343161	+	0.0919496i	0.0831226	+	0.996539i	$0.473511\pi$
$648$	−1.92159	+	8.79247i	−0.0754874	+	0.345401i
$649$	13.6508	−	7.88129i	0.535841	−	0.309368i
$650$	0.0135212	+	27.0864i	0.000530345	+	1.06241i
$651$	−17.2122	+	20.5025i	−0.674598	+	0.803557i
$652$	19.3664	+	5.18921i	0.758446	+	0.203225i
$653$	−0.272208	−	1.01589i	−0.0106523	−	0.0397550i	0.960395	−	0.278642i	$-0.0898842\pi$
$653$	−0.272208	−	1.01589i	−0.0106523	−	0.0397550i	−0.971047	+	0.238887i	$0.923218\pi$
$654$	−2.11299	−	0.846505i	−0.0826243	−	0.0331010i
$655$	−25.0407	+	0.00625000i	−0.978419	+	0.000244208i
$656$	0.460590	−	0.265922i	0.0179830	−	0.0103825i
$657$	−8.09392	−	13.2934i	−0.315774	−	0.518624i
$658$	−0.0170833	+	0.307299i	−0.000665977	+	0.0119798i
$659$	−21.3289	+	36.9428i	−0.830857	+	1.43909i	0.0665027	+	0.997786i	$0.478816\pi$
$659$	−21.3289	+	36.9428i	−0.830857	+	1.43909i	−0.897360	+	0.441300i	$0.854517\pi$
$660$	−20.0020	+	8.56553i	−0.778576	+	0.333413i
$661$	−17.6558			−0.686731			−0.343366	−	0.939202i	$-0.611567\pi$
$661$	−17.6558			−0.686731			−0.343366	+	0.939202i	$0.611567\pi$
$662$	−2.85200	−	2.85200i	−0.110846	−	0.110846i
$663$	26.6234	+	19.9401i	1.03397	+	0.774409i
$664$	12.6066	+	7.27841i	0.489230	+	0.282457i
$665$	11.0868	−	16.9633i	0.429926	−	0.657808i
$666$	−14.3085	+	14.9918i	−0.554442	+	0.580919i
$667$	−41.2221	−	11.0454i	−1.59613	−	0.427680i
$668$	−21.3810	−	5.72901i	−0.827254	−	0.221662i
$669$	−8.16273	+	20.3752i	−0.315590	+	0.787752i
$670$	−4.96574	+	2.86862i	−0.191843	+	0.110825i
$671$	44.1524	−	25.4914i	1.70448	−	0.984084i
$672$	−4.56523	+	0.398287i	−0.176108	+	0.0153643i
$673$	16.5132	−	4.42470i	0.636537	−	0.170560i	0.0739027	−	0.997265i	$-0.476455\pi$
$673$	16.5132	−	4.42470i	0.636537	−	0.170560i	0.562634	+	0.826706i	$0.309788\pi$
$674$	6.90656	+	11.9625i	0.266031	+	0.460779i
$675$	−20.0380	+	16.5372i	−0.771264	+	0.636516i
$676$	8.17341	−	14.1568i	0.314362	−	0.544491i
$677$	29.3496	+	29.3496i	1.12800	+	1.12800i	0.990502	+	0.137495i	$0.0439052\pi$
$677$	29.3496	+	29.3496i	1.12800	+	1.12800i	0.137495	+	0.990502i	$0.456095\pi$
$678$	0.831482	+	0.0996199i	0.0319329	+	0.00382588i
$679$	−1.10468	−	5.27949i	−0.0423939	−	0.202608i
$680$	0.00197850	+	7.92688i	7.58721e−5	+	0.303982i
$681$	−26.9194	−	34.2479i	−1.03156	−	1.31238i
$682$	31.7005	+	8.49413i	1.21388	+	0.325257i
$683$	−7.83441	−	29.2384i	−0.299775	−	1.11878i	−0.937350	−	0.348389i	$-0.886729\pi$
$683$	−7.83441	−	29.2384i	−0.299775	−	1.11878i	0.637575	−	0.770389i	$-0.279938\pi$
$684$	−7.09500	+	7.43382i	−0.271284	+	0.284239i
$685$	0.678771	+	2.53068i	0.0259345	+	0.0966923i
$686$	10.7427	+	15.0862i	0.410160	+	0.575994i
$687$	−23.6889	+	10.1374i	−0.903786	+	0.386765i
$688$	−3.92322	+	1.05122i	−0.149571	+	0.0400775i
$689$	7.91423			0.301508
$690$	21.2566	+	15.9122i	0.809224	+	0.605768i
$691$	12.9829			0.493891			0.246946	−	0.969029i	$-0.420573\pi$
$691$	12.9829			0.493891			0.246946	+	0.969029i	$0.420573\pi$
$692$	6.78876	+	6.78876i	0.258070	+	0.258070i
$693$	−30.4995	−	32.5309i	−1.15858	−	1.23575i
$694$			16.6112i			0.630554i
$695$	21.2186	−	36.7729i	0.804867	−	1.39487i
$696$	−10.0084	−	4.00955i	−0.379366	−	0.151982i
$697$	1.33317	−	1.33317i	0.0504975	−	0.0504975i
$698$	1.29402	+	4.82936i	0.0489795	+	0.182794i
$699$	−13.7156	+	10.7807i	−0.518772	+	0.407763i
$700$	−11.0753	−	7.23456i	−0.418605	−	0.273440i
$701$		−	24.9232i		−	0.941337i	−0.882310	−	0.470669i	$-0.844013\pi$
$701$		−	24.9232i		−	0.941337i	0.882310	−	0.470669i	$-0.155987\pi$
$702$	27.7626	−	4.64780i	1.04783	−	0.175420i
$703$	−22.8564	+	6.12437i	−0.862047	+	0.230985i
$704$	2.80906	+	4.86543i	0.105870	+	0.183373i
$705$	0.354142	−	0.278505i	0.0133378	−	0.0104891i
$706$	−11.9646	−	20.7232i	−0.450292	−	0.779929i
$707$	5.95306	−	3.00947i	0.223888	−	0.113183i
$708$	−3.88958	−	2.91317i	−0.146179	−	0.109484i
$709$		−	37.7319i		−	1.41705i	−0.705685	−	0.708526i	$-0.749361\pi$
$709$		−	37.7319i		−	1.41705i	0.705685	−	0.708526i	$-0.250639\pi$
$710$	−5.31100	+	19.8407i	−0.199318	+	0.744610i
$711$	44.3598	−	13.0019i	1.66362	−	0.487610i
$712$	−4.91946	−	1.31817i	−0.184365	−	0.0494004i
$713$	−10.3655	−	38.6846i	−0.388191	−	1.44875i
$714$	−15.2669	+	5.55250i	−0.571350	+	0.207797i
$715$	48.1337	+	48.1097i	1.80010	+	1.79920i
$716$	7.20350	+	4.15894i	0.269208	+	0.155427i
$717$	22.0655	+	2.64366i	0.824050	+	0.0987294i
$718$	2.83802	−	10.5916i	0.105914	−	0.395276i
$719$	−0.510343	−	0.883941i	−0.0190326	−	0.0329654i	0.856352	−	0.516392i	$-0.172725\pi$
$719$	−0.510343	−	0.883941i	−0.0190326	−	0.0329654i	−0.875385	+	0.483427i	$0.839392\pi$
$720$	4.85387	+	4.63033i	0.180893	+	0.172562i
$721$	−38.6837	+	8.09419i	−1.44065	+	0.301443i
$722$	7.01899	−	1.88073i	0.261220	−	0.0699936i
$723$	−2.88473	−	0.345619i	−0.107284	−	0.0128537i
$724$			12.9851i			0.482587i
$725$	−15.5754	−	26.9463i	−0.578457	−	1.00076i
$726$	−13.2453	+	33.0620i	−0.491580	+	1.22705i
$727$	−6.95656	−	25.9622i	−0.258005	−	0.962886i	−0.966394	−	0.257065i	$-0.917245\pi$
$727$	−6.95656	−	25.9622i	−0.258005	−	0.962886i	0.708390	−	0.705822i	$-0.249422\pi$
$728$	6.46636	+	12.7912i	0.239659	+	0.474072i
$729$	20.3796	+	17.7108i	0.754798	+	0.655957i
$730$	−11.6004	+	0.00289540i	−0.429351	+	0.000107163i
$731$	−12.4694	+	7.19923i	−0.461199	+	0.266273i
$732$	−12.5805	−	9.42241i	−0.464989	−	0.348262i
$733$	33.5678	−	8.99448i	1.23986	−	0.332219i	0.421447	−	0.906853i	$-0.361522\pi$
$733$	33.5678	−	8.99448i	1.23986	−	0.332219i	0.818410	+	0.574635i	$0.194856\pi$
$734$	−5.88380	−	10.1910i	−0.217175	−	0.376158i
$735$	6.18229	−	26.3966i	0.228037	−	0.973652i
$736$	3.42793	−	5.93734i	0.126355	−	0.218853i
$737$	−3.72921	+	13.9176i	−0.137367	+	0.512662i
$738$	−0.0371984	−	1.59510i	−0.00136929	−	0.0587164i
$739$	−31.7659	−	18.3401i	−1.16853	−	0.674650i	−0.215195	−	0.976571i	$-0.569039\pi$
$739$	−31.7659	−	18.3401i	−1.16853	−	0.674650i	−0.953333	+	0.301921i	$0.902372\pi$
$740$	4.00164	+	14.9194i	0.147103	+	0.548450i
$741$	29.8354	+	11.9527i	1.09603	+	0.439092i
$742$	−2.11545	+	3.23497i	−0.0776605	+	0.118759i
$743$	−7.96238	−	2.13351i	−0.292111	−	0.0782710i	0.109787	−	0.993955i	$-0.464983\pi$
$743$	−7.96238	−	2.13351i	−0.292111	−	0.0782710i	−0.401899	+	0.915684i	$0.631650\pi$
$744$	−1.43751	−	10.0153i	−0.0527018	−	0.367180i
$745$	0.000816443		3.27108i	2.99122e−5		0.119843i
$746$	16.3299	+	9.42808i	0.597880	+	0.345186i
$747$	37.3004	−	22.7110i	1.36475	−	0.830953i
$748$	14.0829	+	14.0829i	0.514923	+	0.514923i
$749$	−0.855250	+	2.60403i	−0.0312502	+	0.0951492i
$750$	2.76563	+	19.1664i	0.100987	+	0.699858i
$751$	−5.04124	+	8.73168i	−0.183957	+	0.318623i	−0.943225	−	0.332155i	$-0.892224\pi$
$751$	−5.04124	+	8.73168i	−0.183957	+	0.318623i	0.759267	+	0.650779i	$0.225557\pi$
$752$	−0.0822560	−	0.0822560i	−0.00299957	−	0.00299957i
$753$	0.806593	+	0.604113i	0.0293939	+	0.0220151i
$754$			33.7214i			1.22806i
$755$	10.8670	+	6.27048i	0.395492	+	0.228206i
$756$	−5.52104	+	12.5904i	−0.200798	+	0.457908i
$757$	−33.3785	+	33.3785i	−1.21316	+	1.21316i	−0.243180	+	0.969981i	$0.578190\pi$
$757$	−33.3785	+	33.3785i	−1.21316	+	1.21316i	−0.969981	+	0.243180i	$0.921810\pi$
$758$	20.7028	−	20.7028i	0.751958	−	0.751958i
$759$	66.0366	−	9.47833i	2.39698	−	0.344041i
$760$	1.98426	+	7.39796i	0.0719765	+	0.268352i
$761$	−36.2138	−	20.9081i	−1.31275	−	0.757917i	−0.330199	−	0.943911i	$-0.607116\pi$
$761$	−36.2138	−	20.9081i	−1.31275	−	0.757917i	−0.982551	+	0.185995i	$0.940449\pi$
$762$	−17.0266	+	22.7334i	−0.616807	+	0.823543i
$763$	−2.91005	−	1.90297i	−0.105351	−	0.0688921i
$764$	−12.1652			−0.440121
$765$	20.8691	+	11.4017i	0.754524	+	0.412231i
$766$	−10.0800	+	17.4590i	−0.364204	+	0.630820i
$767$	−3.93381	+	14.6812i	−0.142042	+	0.530107i
$768$	1.03831	−	1.38633i	0.0374670	−	0.0500248i
$769$	−41.6771	+	24.0623i	−1.50292	+	0.867709i	−0.502922	+	0.864332i	$0.667742\pi$
$769$	−41.6771	+	24.0623i	−1.50292	+	0.867709i	−0.999994	+	0.00337699i	$0.998925\pi$
$770$	−32.5310	+	6.81528i	−1.17233	+	0.245606i
$771$	−1.36871	+	3.41647i	−0.0492927	+	0.123041i
$772$	−10.8381	+	10.8381i	−0.390071	+	0.390071i
$773$	−4.00832	−	14.9592i	−0.144169	−	0.538046i	−0.999791	−	0.0204450i	$-0.993492\pi$
$773$	−4.00832	−	14.9592i	−0.144169	−	0.538046i	0.855622	−	0.517601i	$-0.173175\pi$
$774$	−2.87841	+	11.8400i	−0.103462	+	0.425579i
$775$	14.5914	−	25.3022i	0.524138	−	0.908881i
$776$	1.76554	+	1.01934i	0.0633794	+	0.0365921i
$777$	−25.9359	+	18.1511i	−0.930444	+	0.651167i
$778$	1.80373	−	6.73162i	0.0646670	−	0.241340i
$779$	0.910891	−	1.57771i	0.0326360	−	0.0565273i
$780$	7.79770	−	19.4781i	0.279202	−	0.697430i
$781$	25.8024	+	44.6911i	0.923284	+	1.59917i
$782$	6.29036	−	23.4759i	0.224943	−	0.839497i
$783$	−24.9568	+	20.5756i	−0.891882	+	0.735312i
$784$	−6.95687	−	0.775887i	−0.248460	−	0.0277102i
$785$	−0.928824	+	3.46988i	−0.0331512	+	0.123845i
$786$	18.0053	+	7.21327i	0.642226	+	0.257289i
$787$	−20.7940	+	20.7940i	−0.741226	+	0.741226i	−0.972814	−	0.231588i	$-0.925608\pi$
$787$	−20.7940	+	20.7940i	−0.741226	+	0.741226i	0.231588	+	0.972814i	$0.425608\pi$
$788$	5.54709	−	5.54709i	0.197607	−	0.197607i
$789$	−38.7281	+	30.4409i	−1.37876	+	1.08373i
$790$	8.90926	−	33.2830i	0.316977	−	1.18416i
$791$	1.21532	+	0.399153i	0.0432120	+	0.0141922i
$792$	16.8498	−	0.392944i	0.598730	−	0.0139627i
$793$	−12.7236	+	47.4851i	−0.451828	+	1.68624i
$794$	6.63783	+	11.4971i	0.235568	+	0.408015i
$795$	5.60055	−	0.805281i	0.198631	−	0.0285604i
$796$	2.67453	−	4.63242i	0.0947962	−	0.164192i
$797$	−5.80399	+	21.6608i	−0.205588	+	0.767265i	0.783681	+	0.621163i	$0.213339\pi$
$797$	−5.80399	+	21.6608i	−0.205588	+	0.767265i	−0.989270	+	0.146102i	$0.953327\pi$
$798$	−12.8606	+	9.00041i	−0.455259	+	0.318611i
$799$	−0.357134	−	0.206191i	−0.0126345	−	0.00729452i
$800$	4.82898	−	1.29651i	0.170730	−	0.0458384i
$801$	−10.5491	+	11.0528i	−0.372733	+	0.390533i
$802$	−6.08306	−	22.7023i	−0.214800	−	0.801645i
$803$	−20.6093	+	20.6093i	−0.727288	+	0.727288i
$804$	4.39707	−	0.631118i	0.155073	−	0.0222578i
$805$	27.0515	+	30.2210i	0.953440	+	1.06515i
$806$	−27.4059	+	15.8228i	−0.965331	+	0.557334i
$807$	−8.27548	−	19.3380i	−0.291311	−	0.680730i
$808$	−0.652539	+	2.43531i	−0.0229563	+	0.0856739i
$809$	−0.895949	+	1.55183i	−0.0314999	+	0.0545594i	−0.881346	−	0.472472i	$-0.843362\pi$
$809$	−0.895949	+	1.55183i	−0.0314999	+	0.0545594i	0.849846	+	0.527032i	$0.176695\pi$
$810$	19.1734	−	6.11391i	0.673685	−	0.214821i
$811$	44.6319			1.56724			0.783619	−	0.621242i	$-0.213371\pi$
$811$	44.6319			1.56724			0.783619	+	0.621242i	$0.213371\pi$
$812$	−13.7837	−	9.01360i	−0.483714	−	0.316315i
$813$	−29.2718	−	3.50706i	−1.02661	−	0.122998i
$814$	33.6104	+	19.4050i	1.17804	+	0.680144i
$815$	−11.6142	−	43.3017i	−0.406829	−	1.51679i
$816$	2.28344	−	5.69975i	0.0799363	−	0.199531i
$817$	−9.83775	+	9.83775i	−0.344179	+	0.344179i
$818$	11.8883	−	11.8883i	0.415664	−	0.415664i
$819$	42.9759	+	1.38509i	1.50170	+	0.0483991i
$820$	−1.03006	−	0.594363i	−0.0359712	−	0.0207560i
$821$			56.1200i			1.95860i	0.202407	+	0.979301i	$0.435124\pi$
$821$			56.1200i			1.95860i	−0.202407	+	0.979301i	$0.564876\pi$
$822$	0.241433	−	2.01513i	0.00842093	−	0.0702857i
$823$	18.5562	+	18.5562i	0.646829	+	0.646829i	0.952225	−	0.305397i	$-0.0987890\pi$
$823$	18.5562	+	18.5562i	0.646829	+	0.646829i	−0.305397	+	0.952225i	$0.598789\pi$
$824$	7.46884	−	12.9364i	0.260189	−	0.450661i
$825$	38.9573	+	29.1474i	1.35632	+	1.01478i
$826$	−4.94949	−	5.53219i	−0.172215	−	0.192489i
$827$	31.1516	+	31.1516i	1.08325	+	1.08325i	0.996205	+	0.0870414i	$0.0277412\pi$
$827$	31.1516	+	31.1516i	1.08325	+	1.08325i	0.0870414	+	0.996205i	$0.472259\pi$
$828$	−10.6963	−	17.5674i	−0.371721	−	0.610510i
$829$	−28.9067	−	16.6893i	−1.00397	−	0.579642i	−0.0945496	−	0.995520i	$-0.530141\pi$
$829$	−28.9067	−	16.6893i	−1.00397	−	0.579642i	−0.909421	+	0.415878i	$0.863474\pi$
$830$	−0.00812430	−	32.5500i	−0.000281999	−	1.12983i
$831$	24.3011	−	19.1011i	0.842996	−	0.662610i
$832$	−5.23268	−	1.40209i	−0.181411	−	0.0486088i
$833$	−24.5337	+	3.72623i	−0.850043	+	0.129106i
$834$	−25.8550	+	20.3225i	−0.895285	+	0.703709i
$835$	12.8224	+	47.8061i	0.443737	+	1.65440i
$836$	16.6661	+	9.62216i	0.576408	+	0.332789i
$837$	−28.4324	−	10.6282i	−0.982766	−	0.367365i
$838$	9.01435	−	33.6420i	0.311395	−	1.16214i
$839$	3.20025	−	5.54299i	0.110485	−	0.191365i	−0.805481	−	0.592622i	$-0.798093\pi$
$839$	3.20025	−	5.54299i	0.110485	−	0.191365i	0.915966	+	0.401256i	$0.131426\pi$
$840$	5.87746	+	8.39377i	0.202792	+	0.289613i
$841$	−4.87399	−	8.44200i	−0.168069	−	0.291103i
$842$	27.1187	−	7.26645i	0.934574	−	0.250418i
$843$	14.6425	−	6.26608i	0.504314	−	0.215815i
$844$	−3.42694	+	1.97854i	−0.117960	+	0.0681043i
$845$	−36.5526	+	0.00912332i	−1.25745	+	0.000313852i
$846$	−0.334894	+	0.0981578i	−0.0115139	+	0.00337474i
$847$	−29.7759	+	45.5337i	−1.02311	+	1.56456i
$848$	−0.378116	−	1.41115i	−0.0129845	−	0.0484590i
$849$	−43.5163	+	6.24596i	−1.49348	+	0.214361i
$850$	15.3459	−	8.87019i	0.526361	−	0.304245i
$851$		−	47.3603i		−	1.62349i
$852$	9.53738	−	12.7340i	0.326745	−	0.436261i
$853$	−2.22906	+	0.597276i	−0.0763217	+	0.0204503i	−0.296778	−	0.954947i	$-0.595912\pi$
$853$	−2.22906	+	0.597276i	−0.0763217	+	0.0204503i	0.220456	+	0.975397i	$0.429245\pi$
$854$	−16.0087	−	17.8934i	−0.547807	−	0.612299i
$855$	22.3293	+	5.42257i	0.763647	+	0.185448i
$856$	−0.517978	−	0.897164i	−0.0177041	−	0.0306644i
$857$	1.76739	−	6.59599i	0.0603729	−	0.225315i	−0.929147	−	0.369710i	$-0.879457\pi$
$857$	1.76739	−	6.59599i	0.0603729	−	0.225315i	0.989520	+	0.144395i	$0.0461237\pi$
$858$	−20.7394	−	48.4635i	−0.708032	−	1.65452i
$859$	35.6407	+	20.5772i	1.21605	+	0.702084i	0.964070	−	0.265650i	$-0.0855864\pi$
$859$	35.6407	+	20.5772i	1.21605	+	0.702084i	0.251976	+	0.967734i	$0.418920\pi$
$860$	6.42358	+	6.42037i	0.219042	+	0.218933i
$861$	0.423802	−	2.40009i	0.0144431	−	0.0817947i
$862$	8.68439	+	32.4106i	0.295791	+	1.10391i
$863$	−39.2484	−	10.5166i	−1.33603	−	0.357989i	−0.481071	−	0.876682i	$-0.659752\pi$
$863$	−39.2484	−	10.5166i	−1.33603	−	0.357989i	−0.854961	+	0.518693i	$0.826419\pi$
$864$	−2.15513	−	4.72815i	−0.0733190	−	0.160855i
$865$	5.55114	−	20.7378i	0.188744	−	0.705107i
$866$			15.7585i			0.535495i
$867$	−0.913371	+	7.62350i	−0.0310197	+	0.258908i
$868$	0.857871	−	15.4316i	0.0291180	−	0.523783i
$869$	−43.2838	−	74.9698i	−1.46830	−	2.54318i
$870$	3.43118	+	23.8631i	0.116328	+	0.809034i
$871$	−6.94674	−	12.0321i	−0.235381	−	0.407693i
$872$	1.26941	−	0.340137i	0.0429876	−	0.0115185i
$873$	5.22390	−	3.18067i	0.176802	−	0.107649i
$874$		−	23.4841i		−	0.794361i
$875$	−1.61978	+	29.5360i	−0.0547584	+	0.998500i
$876$	8.34118	+	3.34165i	0.281822	+	0.112904i
$877$	3.41455	+	12.7433i	0.115301	+	0.430310i	0.999309	−	0.0371619i	$-0.0118317\pi$
$877$	3.41455	+	12.7433i	0.115301	+	0.430310i	−0.884008	+	0.467472i	$0.845165\pi$
$878$	22.2778	−	22.2778i	0.751841	−	0.751841i
$879$	10.4863	−	8.24241i	0.353694	−	0.278010i
$880$	6.27853	−	10.8810i	0.211649	−	0.366798i
$881$		−	9.10886i		−	0.306885i	−0.988158	−	0.153443i	$-0.950964\pi$
$881$		−	9.10886i		−	0.306885i	0.988158	−	0.153443i	$-0.0490360\pi$
$882$	−12.0535	+	17.1963i	−0.405862	+	0.579031i
$883$	−12.5456	−	12.5456i	−0.422195	−	0.422195i	0.463764	−	0.885959i	$-0.346499\pi$
$883$	−12.5456	−	12.5456i	−0.422195	−	0.422195i	−0.885959	+	0.463764i	$0.846499\pi$
$884$	−19.2043			−0.645910
$885$	−1.28996	+	10.7895i	−0.0433614	+	0.362684i
$886$	−32.3279			−1.08608
$887$	12.5627	−	3.36617i	0.421815	−	0.113025i	−0.0416665	−	0.999132i	$-0.513267\pi$
$887$	12.5627	−	3.36617i	0.421815	−	0.113025i	0.463482	+	0.886107i	$0.346600\pi$
$888$	1.42335	−	11.8801i	0.0477645	−	0.398669i
$889$	−32.3339	+	28.9282i	−1.08444	+	0.970221i
$890$	2.95025	+	10.9995i	0.0988927	+	0.368705i
$891$	23.2128	−	44.9198i	0.777658	−	1.50487i
$892$	−3.27990	−	12.2407i	−0.109819	−	0.409850i
$893$	−0.384892	−	0.103131i	−0.0128799	−	0.00345116i
$894$	0.942276	−	2.35204i	0.0315144	−	0.0786641i
$895$	−0.00464229	−	18.5994i	−0.000155175	−	0.621708i
$896$	1.97179	−	1.76410i	0.0658728	−	0.0589345i
$897$	−38.5630	+	51.4882i	−1.28758	+	1.71914i
$898$	−24.0780	−	24.0780i	−0.803493	−	0.803493i
$899$	18.1814	−	31.4911i	0.606383	−	1.05029i
$900$	3.53616	−	14.5772i	0.117872	−	0.485908i
$901$	−2.58950	−	4.48514i	−0.0862687	−	0.149422i
$902$	−2.88615	+	0.773341i	−0.0960982	+	0.0257494i
$903$	−7.87015	+	16.8669i	−0.261902	+	0.561294i
$904$	−0.418714	+	0.241745i	−0.0139262	+	0.00804031i
$905$	25.1419	−	14.5240i	0.835744	−	0.482795i
$906$	−6.00566	−	7.64062i	−0.199525	−	0.253843i
$907$	27.7082	+	7.42440i	0.920036	+	0.246523i	0.687601	−	0.726089i	$-0.258664\pi$
$907$	27.7082	+	7.42440i	0.920036	+	0.246523i	0.232435	+	0.972612i	$0.425331\pi$
$908$	24.2931	+	6.50931i	0.806194	+	0.216019i
$909$	5.47155	+	5.22217i	0.181480	+	0.173208i
$910$	17.5337	−	26.8274i	0.581236	−	0.889319i
$911$	−28.5182	−	16.4650i	−0.944850	−	0.545509i	−0.0533726	−	0.998575i	$-0.516997\pi$
$911$	−28.5182	−	16.4650i	−0.944850	−	0.545509i	−0.891477	+	0.453065i	$0.850330\pi$
$912$	0.705782	−	5.89085i	0.0233708	−	0.195065i
$913$	−57.8285	−	57.8285i	−1.91384	−	1.91384i
$914$	−28.0348			−0.927310
$915$	−4.17225	+	34.8977i	−0.137930	+	1.15368i
$916$	7.43824	−	12.8834i	0.245766	−	0.425680i
$917$	24.7972	+	16.2156i	0.818876	+	0.535488i
$918$	−11.7178	−	14.2128i	−0.386745	−	0.469094i
$919$	20.3805	−	11.7667i	0.672292	−	0.388148i	−0.124653	−	0.992200i	$-0.539782\pi$
$919$	20.3805	−	11.7667i	0.672292	−	0.388148i	0.796944	+	0.604053i	$0.206448\pi$
$920$	−15.3302	+	0.00382632i	−0.505420	+	0.000126150i
$921$	2.76143	+	19.2392i	0.0909921	+	0.633952i
$922$	−1.56540	−	5.84214i	−0.0515536	−	0.192401i
$923$	−48.0645	−	12.8788i	−1.58206	−	0.423912i
$924$	25.3532	+	4.47681i	0.834059	+	0.147276i
$925$	24.4113	−	24.4357i	0.802639	−	0.803440i
$926$	−10.2427	+	5.91364i	−0.336597	+	0.194334i
$927$	−23.3052	−	38.2763i	−0.765445	−	1.25716i
$928$	6.01268	−	1.61109i	0.197376	−	0.0528867i
$929$	−29.6079			−0.971404			−0.485702	−	0.874124i	$-0.661436\pi$
$929$	−29.6079			−0.971404			−0.485702	+	0.874124i	$0.661436\pi$
$930$	−17.7839	+	13.9856i	−0.583157	+	0.458607i
$931$	−21.9663	+	9.61339i	−0.719917	+	0.315066i
$932$	2.60685	−	9.72889i	0.0853902	−	0.318680i
$933$	−8.83332	−	6.61588i	−0.289190	−	0.216594i
$934$	12.1502	−	7.01494i	0.397568	−	0.229536i
$935$	11.5155	−	43.0195i	0.376599	−	1.40689i
$936$	−11.2207	+	11.7566i	−0.366761	+	0.384275i
$937$	9.71004	−	9.71004i	0.317213	−	0.317213i	−0.530483	−	0.847696i	$-0.677989\pi$
$937$	9.71004	−	9.71004i	0.317213	−	0.317213i	0.847696	+	0.530483i	$0.177989\pi$
$938$	6.77501	+	0.376634i	0.221212	+	0.0122976i
$939$	−49.7039	+	7.13407i	−1.62203	+	0.232812i
$940$	−0.0672604	+	0.251270i	−0.00219379	+	0.00819552i
$941$			37.5406i			1.22379i	0.790940	+	0.611894i	$0.209592\pi$
$941$			37.5406i			1.22379i	−0.790940	+	0.611894i	$0.790408\pi$
$942$	1.66796	−	2.22701i	0.0543451	−	0.0725600i
$943$	2.57828	+	2.57828i	0.0839605	+	0.0839605i
$944$	2.80567			0.0913168
$945$	30.5531	−	3.39268i	0.993891	−	0.110364i
$946$	22.8186			0.741897
$947$	27.2675	+	27.2675i	0.886074	+	0.886074i	0.994143	−	0.108070i	$-0.0344669\pi$
$947$	27.2675	+	27.2675i	0.886074	+	0.886074i	−0.108070	+	0.994143i	$0.534467\pi$
$948$	−15.9991	+	21.3615i	−0.519625	+	0.693788i
$949$		−	28.1041i		−	0.912297i
$950$	12.1046	−	12.1167i	0.392725	−	0.393117i
$951$	48.5218	−	6.96441i	1.57343	−	0.225836i
$952$	5.13323	−	7.84981i	0.166369	−	0.254414i
$953$	26.9503	−	26.9503i	0.873007	−	0.873007i	−0.119792	−	0.992799i	$-0.538223\pi$
$953$	26.9503	−	26.9503i	0.873007	−	0.873007i	0.992799	+	0.119792i	$0.0382227\pi$
$954$	−4.25874	−	1.03534i	−0.137882	−	0.0335204i
$955$	13.6070	+	23.5544i	0.440311	+	0.762202i
$956$	−11.1116	+	6.41530i	−0.359376	+	0.207486i
$957$	48.4820	+	36.3115i	1.56720	+	1.17378i
$958$	−10.8210	+	40.3847i	−0.349612	+	1.30477i
$959$	0.967363	−	2.94539i	0.0312378	−	0.0951115i
$960$	−3.84560	−	0.459767i	−0.124116	−	0.0148389i
$961$	3.12438			0.100786
$962$	−36.1474	+	9.68567i	−1.16544	+	0.312278i
$963$	−3.10702	+	0.0724571i	−0.100122	+	0.00233490i
$964$	1.45268	−	0.838705i	0.0467876	−	0.0270129i
$965$	33.1074	+	8.86225i	1.06577	+	0.285286i
$966$	−10.7382	−	29.5254i	−0.345497	−	0.949963i
$967$	−15.4296	−	4.13435i	−0.496183	−	0.132952i	0.00204486	−	0.999998i	$-0.499349\pi$
$967$	−15.4296	−	4.13435i	−0.496183	−	0.132952i	−0.498228	+	0.867046i	$0.666016\pi$
$968$	−5.32215	−	19.8625i	−0.171060	−	0.638406i
$969$	−2.98820	−	20.8191i	−0.0959947	−	0.668806i
$970$	−0.00113780	−	4.55862i	−3.65327e−5	−	0.146368i
$971$	18.9731	−	10.9541i	0.608876	−	0.351535i	−0.163649	−	0.986519i	$-0.552327\pi$
$971$	18.9731	−	10.9541i	0.608876	−	0.351535i	0.772526	+	0.634984i	$0.218993\pi$
$972$	−15.5474	−	1.13087i	−0.498683	−	0.0362727i
$973$	−44.8310	+	22.6636i	−1.43722	+	0.726561i
$974$	−0.718455	+	1.24440i	−0.0230208	+	0.0398732i
$975$	−46.4357	+	6.68864i	−1.48713	+	0.214208i
$976$	9.07471			0.290474
$977$	−7.49874	−	7.49874i	−0.239906	−	0.239906i	0.576905	−	0.816811i	$-0.304260\pi$
$977$	−7.49874	−	7.49874i	−0.239906	−	0.239906i	−0.816811	+	0.576905i	$0.804260\pi$
$978$	−4.13108	+	34.4803i	−0.132097	+	1.10256i
$979$	24.7796	+	14.3065i	0.791961	+	0.457239i
$980$	6.27909	+	14.3378i	0.200578	+	0.458005i
$981$	0.931349	−	3.83098i	0.0297357	−	0.122314i
$982$	−2.33371	−	0.625315i	−0.0744716	−	0.0199546i
$983$	24.8955	+	6.67073i	0.794043	+	0.212763i	0.632967	−	0.774179i	$-0.281837\pi$
$983$	24.8955	+	6.67073i	0.794043	+	0.212763i	0.161076	+	0.986942i	$0.448503\pi$
$984$	0.569261	+	0.724235i	0.0181474	+	0.0230878i
$985$	−16.9449	−	4.53583i	−0.539908	−	0.144524i
$986$	19.1105	−	11.0335i	0.608603	−	0.351377i
$987$	−0.531063	+	0.0463318i	−0.0169039	+	0.00147476i
$988$	−17.9241	+	4.80274i	−0.570240	+	0.152795i
$989$	−13.9229	−	24.1152i	−0.442723	−	0.766818i
$990$	−19.6076	−	32.1852i	−0.623169	−	1.02291i
$991$	−0.122795	+	0.212687i	−0.00390070	+	0.00675621i	−0.867969	−	0.496618i	$-0.834575\pi$
$991$	−0.122795	+	0.212687i	−0.00390070	+	0.00675621i	0.864068	+	0.503374i	$0.167908\pi$
$992$	4.13064	+	4.13064i	0.131148	+	0.131148i
$993$	4.18788	−	5.59153i	0.132898	−	0.177442i
$994$	18.1117	−	16.2041i	0.574469	−	0.513962i
$995$	−11.9609	+	0.00298536i	−0.379185	+	9.46423e-5i
$996$	−9.37644	+	23.4048i	−0.297104	+	0.741610i
$997$	−51.5381	−	13.8096i	−1.63223	−	0.437354i	−0.677666	−	0.735370i	$-0.737009\pi$
$997$	−51.5381	−	13.8096i	−1.63223	−	0.437354i	−0.954561	+	0.298016i	$0.903675\pi$
$998$	−1.76721	−	6.59530i	−0.0559399	−	0.208771i
$999$	−29.2241	−	20.8424i	−0.924611	−	0.659424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.263.17	yes	192
5.2	odd	4	inner	630.2.cd.a.137.30	yes	192
7.2	even	3		630.2.bt.a.443.15	yes	192
9.5	odd	6		630.2.bt.a.473.22	yes	192
35.2	odd	12		630.2.bt.a.317.22	✓	192
45.32	even	12		630.2.bt.a.347.15	yes	192
63.23	odd	6	inner	630.2.cd.a.23.30	yes	192
315.212	even	12	inner	630.2.cd.a.527.17	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.22	✓	192	35.2	odd	12
630.2.bt.a.347.15	yes	192	45.32	even	12
630.2.bt.a.443.15	yes	192	7.2	even	3
630.2.bt.a.473.22	yes	192	9.5	odd	6
630.2.cd.a.23.30	yes	192	63.23	odd	6	inner
630.2.cd.a.137.30	yes	192	5.2	odd	4	inner
630.2.cd.a.263.17	yes	192	1.1	even	1	trivial
630.2.cd.a.527.17	yes	192	315.212	even	12	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.03831 - 1.38633i) q^{3} +1.00000i q^{4} +(1.93621 - 1.11852i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(-2.64167 - 0.146855i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.843805 - 2.87889i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.03831 - 1.38633i) q^{3} +1.00000i q^{4} +(1.93621 - 1.11852i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(-2.64167 - 0.146855i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.843805 - 2.87889i) q^{9} +(-2.16002 - 0.578198i) q^{10} +(-4.86543 + 2.80906i) q^{11} +(1.38633 + 1.03831i) q^{12} +(1.40209 - 5.23268i) q^{13} +(1.76410 + 1.97179i) q^{14} +(0.459767 - 3.84560i) q^{15} -1.00000 q^{16} +(-3.42422 + 0.917516i) q^{17} +(-1.43902 + 2.63234i) q^{18} +(-2.96649 + 1.71270i) q^{19} +(1.11852 + 1.93621i) q^{20} +(-2.94648 + 3.50974i) q^{21} +(5.42668 + 1.45407i) q^{22} +(-1.77443 - 6.62225i) q^{23} +(-0.246082 - 1.71448i) q^{24} +(2.49784 - 4.33137i) q^{25} +(-4.69149 + 2.70864i) q^{26} +(-4.86721 - 1.81940i) q^{27} +(0.146855 - 2.64167i) q^{28} +(3.11239 - 5.39082i) q^{29} +(-3.04435 + 2.39414i) q^{30} +5.84161 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.15758 + 9.66176i) q^{33} +(3.07007 + 1.77250i) q^{34} +(-5.27910 + 2.67041i) q^{35} +(2.87889 - 0.843805i) q^{36} +(6.67262 + 1.78792i) q^{37} +(3.30869 + 0.886560i) q^{38} +(-5.79839 - 7.37693i) q^{39} +(0.578198 - 2.16002i) q^{40} +(-0.460590 + 0.265922i) q^{41} +(4.56523 - 0.398287i) q^{42} +(3.92322 - 1.05122i) q^{43} +(-2.80906 - 4.86543i) q^{44} +(-4.85387 - 4.63033i) q^{45} +(-3.42793 + 5.93734i) q^{46} +(0.0822560 + 0.0822560i) q^{47} +(-1.03831 + 1.38633i) q^{48} +(6.95687 + 0.775887i) q^{49} +(-4.82898 + 1.29651i) q^{50} +(-2.28344 + 5.69975i) q^{51} +(5.23268 + 1.40209i) q^{52} +(0.378116 + 1.41115i) q^{53} +(2.15513 + 4.72815i) q^{54} +(-6.27853 + 10.8810i) q^{55} +(-1.97179 + 1.76410i) q^{56} +(-0.705782 + 5.89085i) q^{57} +(-6.01268 + 1.61109i) q^{58} -2.80567 q^{59} +(3.84560 + 0.459767i) q^{60} -9.07471 q^{61} +(-4.13064 - 4.13064i) q^{62} +(1.80628 + 7.72899i) q^{63} -1.00000i q^{64} +(-3.13810 - 11.6998i) q^{65} +(7.65043 - 6.01337i) q^{66} +(1.81349 - 1.81349i) q^{67} +(-0.917516 - 3.42422i) q^{68} +(-11.0230 - 4.41604i) q^{69} +(5.62115 + 1.84462i) q^{70} -9.18544i q^{71} +(-2.63234 - 1.43902i) q^{72} +(5.01109 - 1.34272i) q^{73} +(-3.45400 - 5.98251i) q^{74} +(-3.41116 - 7.96015i) q^{75} +(-1.71270 - 2.96649i) q^{76} +(13.2654 - 6.70609i) q^{77} +(-1.11619 + 9.31636i) q^{78} +15.4087i q^{79} +(-1.93621 + 1.11852i) q^{80} +(-7.57599 + 4.85844i) q^{81} +(0.513722 + 0.137651i) q^{82} +(3.76758 + 14.0608i) q^{83} +(-3.50974 - 2.94648i) q^{84} +(-5.60375 + 5.60655i) q^{85} +(-3.51746 - 2.03081i) q^{86} +(-4.24180 - 9.91217i) q^{87} +(-1.45407 + 5.42668i) q^{88} +(-2.54650 - 4.41067i) q^{89} +(0.158070 + 6.70634i) q^{90} +(-4.47232 + 13.6171i) q^{91} +(6.62225 - 1.77443i) q^{92} +(6.06543 - 8.09838i) q^{93} -0.116328i q^{94} +(-3.82806 + 6.63423i) q^{95} +(1.71448 - 0.246082i) q^{96} +(0.527648 + 1.96921i) q^{97} +(-4.37061 - 5.46788i) q^{98} +(12.1924 + 11.6367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more