LMFDB - Embedded newform 1170.2.v.d.467.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(233,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1170.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.v (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			467.3
Character	$\chi$	$=$	1170.467
Dual form			1170.2.v.d.233.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.02676 + 0.944579i) q^{5} +(-0.571888 + 0.571888i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.02676 + 0.944579i) q^{5} +(-0.571888 + 0.571888i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.765220 - 2.10106i) q^{10} -4.75079 q^{11} +(-2.30390 + 2.77346i) q^{13} +0.808772 q^{14} -1.00000 q^{16} +(4.97166 - 4.97166i) q^{17} +3.21554 q^{19} +(-0.944579 + 2.02676i) q^{20} +(3.35932 + 3.35932i) q^{22} +(5.25852 + 5.25852i) q^{23} +(3.21554 + 3.82888i) q^{25} +(3.59023 - 0.332029i) q^{26} +(-0.571888 - 0.571888i) q^{28} +4.80941 q^{29} +2.73810i q^{31} +(0.707107 + 0.707107i) q^{32} -7.03099 q^{34} +(-1.69927 + 0.618888i) q^{35} +(-8.29289 + 8.29289i) q^{37} +(-2.27373 - 2.27373i) q^{38} +(2.10106 - 0.765220i) q^{40} +0.189114 q^{41} +(-5.01005 + 5.01005i) q^{43} -4.75079i q^{44} -7.43667i q^{46} +(-7.06895 - 7.06895i) q^{47} +6.34589i q^{49} +(0.433694 - 4.98116i) q^{50} +(-2.77346 - 2.30390i) q^{52} +(7.11592 + 7.11592i) q^{53} +(-9.62873 - 4.48750i) q^{55} +0.808772i q^{56} +(-3.40076 - 3.40076i) q^{58} +4.52847i q^{59} +5.52790 q^{61} +(1.93613 - 1.93613i) q^{62} -1.00000i q^{64} +(-7.28920 + 3.44493i) q^{65} +(-6.59437 + 6.59437i) q^{67} +(4.97166 + 4.97166i) q^{68} +(1.63919 + 0.763949i) q^{70} +12.8669 q^{71} +(1.25953 + 1.25953i) q^{73} +11.7279 q^{74} +3.21554i q^{76} +(2.71692 - 2.71692i) q^{77} +7.18819i q^{79} +(-2.02676 - 0.944579i) q^{80} +(-0.133723 - 0.133723i) q^{82} +(-9.66991 + 9.66991i) q^{83} +(14.7725 - 5.38025i) q^{85} +7.08528 q^{86} +(-3.35932 + 3.35932i) q^{88} +1.07072i q^{89} +(-0.268536 - 2.90368i) q^{91} +(-5.25852 + 5.25852i) q^{92} +9.99701i q^{94} +(6.51714 + 3.03733i) q^{95} +(10.6308 - 10.6308i) q^{97} +(4.48722 - 4.48722i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{10} + 8 q^{13} - 24 q^{16} + 16 q^{19} - 8 q^{22} + 16 q^{25} - 32 q^{37} - 32 q^{43} - 24 q^{52} - 24 q^{55} + 80 q^{61} + 8 q^{67} + 8 q^{70} + 8 q^{73} - 64 q^{82} + 120 q^{85} + 8 q^{88} + 16 q^{91} + 8 q^{97}+O(q^{100}) $ 24 * q - 8 * q^10 + 8 * q^13 - 24 * q^16 + 16 * q^19 - 8 * q^22 + 16 * q^25 - 32 * q^37 - 32 * q^43 - 24 * q^52 - 24 * q^55 + 80 * q^61 + 8 * q^67 + 8 * q^70 + 8 * q^73 - 64 * q^82 + 120 * q^85 + 8 * q^88 + 16 * q^91 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	2.02676	+	0.944579i	0.906396	+	0.422429i
$5$	2.02676	+	0.944579i	0.906396	+	0.422429i
$6$		0			0
$7$	−0.571888	+	0.571888i	−0.216153	+	0.216153i	−0.806875	−	0.590722i	$-0.798843\pi$
$7$	−0.571888	+	0.571888i	−0.216153	+	0.216153i	0.590722	+	0.806875i	$0.298843\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.765220	−	2.10106i	−0.241984	−	0.664412i
$11$	−4.75079			−1.43242			−0.716209	−	0.697886i	$-0.754124\pi$
$11$	−4.75079			−1.43242			−0.716209	+	0.697886i	$0.754124\pi$
$12$		0			0
$13$	−2.30390	+	2.77346i	−0.638986	+	0.769218i
$13$	−2.30390	+	2.77346i	−0.638986	+	0.769218i
$14$	0.808772			0.216153
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.97166	−	4.97166i	1.20580	−	1.20580i	0.233432	−	0.972373i	$-0.425005\pi$
$17$	4.97166	−	4.97166i	1.20580	−	1.20580i	0.972373	−	0.233432i	$-0.0749955\pi$
$18$		0			0
$19$	3.21554			0.737696			0.368848	−	0.929490i	$-0.379752\pi$
$19$	3.21554			0.737696			0.368848	+	0.929490i	$0.379752\pi$
$20$	−0.944579	+	2.02676i	−0.211214	+	0.453198i
$21$		0			0
$22$	3.35932	+	3.35932i	0.716209	+	0.716209i
$23$	5.25852	+	5.25852i	1.09648	+	1.09648i	0.994819	+	0.101658i	$0.0324146\pi$
$23$	5.25852	+	5.25852i	1.09648	+	1.09648i	0.101658	+	0.994819i	$0.467585\pi$
$24$		0			0
$25$	3.21554	+	3.82888i	0.643108	+	0.765775i
$26$	3.59023	−	0.332029i	0.704102	−	0.0651162i
$27$		0			0
$28$	−0.571888	−	0.571888i	−0.108077	−	0.108077i
$29$	4.80941			0.893084			0.446542	−	0.894763i	$-0.352655\pi$
$29$	4.80941			0.893084			0.446542	+	0.894763i	$0.352655\pi$
$30$		0			0
$31$			2.73810i			0.491776i	0.969298	+	0.245888i	$0.0790796\pi$
$31$			2.73810i			0.491776i	−0.969298	+	0.245888i	$0.920920\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−7.03099			−1.20580
$35$	−1.69927	+	0.618888i	−0.287230	+	0.104611i
$36$		0			0
$37$	−8.29289	+	8.29289i	−1.36334	+	1.36334i	−0.493726	+	0.869618i	$0.664365\pi$
$37$	−8.29289	+	8.29289i	−1.36334	+	1.36334i	−0.869618	+	0.493726i	$0.835635\pi$
$38$	−2.27373	−	2.27373i	−0.368848	−	0.368848i
$39$		0			0
$40$	2.10106	−	0.765220i	0.332206	−	0.120992i
$41$	0.189114			0.0295346			0.0147673	−	0.999891i	$-0.495299\pi$
$41$	0.189114			0.0295346			0.0147673	+	0.999891i	$0.495299\pi$
$42$		0			0
$43$	−5.01005	+	5.01005i	−0.764026	+	0.764026i	−0.977047	−	0.213022i	$-0.931670\pi$
$43$	−5.01005	+	5.01005i	−0.764026	+	0.764026i	0.213022	+	0.977047i	$0.431670\pi$
$44$		−	4.75079i		−	0.716209i
$45$		0			0
$46$		−	7.43667i		−	1.09648i
$47$	−7.06895	−	7.06895i	−1.03111	−	1.03111i	−0.999500	−	0.0316127i	$-0.989936\pi$
$47$	−7.06895	−	7.06895i	−1.03111	−	1.03111i	−0.0316127	−	0.999500i	$-0.510064\pi$
$48$		0			0
$49$			6.34589i			0.906556i
$50$	0.433694	−	4.98116i	0.0613336	−	0.704442i
$51$		0			0
$52$	−2.77346	−	2.30390i	−0.384609	−	0.319493i
$53$	7.11592	+	7.11592i	0.977447	+	0.977447i	0.999751	−	0.0223042i	$-0.00710023\pi$
$53$	7.11592	+	7.11592i	0.977447	+	0.977447i	−0.0223042	+	0.999751i	$0.507100\pi$
$54$		0			0
$55$	−9.62873	−	4.48750i	−1.29834	−	0.605094i
$56$			0.808772i			0.108077i
$57$		0			0
$58$	−3.40076	−	3.40076i	−0.446542	−	0.446542i
$59$			4.52847i			0.589557i	0.955566	+	0.294778i	$0.0952458\pi$
$59$			4.52847i			0.589557i	−0.955566	+	0.294778i	$0.904754\pi$
$60$		0			0
$61$	5.52790			0.707775			0.353887	−	0.935288i	$-0.384860\pi$
$61$	5.52790			0.707775			0.353887	+	0.935288i	$0.384860\pi$
$62$	1.93613	−	1.93613i	0.245888	−	0.245888i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−7.28920	+	3.44493i	−0.904114	+	0.427291i
$66$		0			0
$67$	−6.59437	+	6.59437i	−0.805630	+	0.805630i	−0.983969	−	0.178339i	$-0.942928\pi$
$67$	−6.59437	+	6.59437i	−0.805630	+	0.805630i	0.178339	+	0.983969i	$0.442928\pi$
$68$	4.97166	+	4.97166i	0.602902	+	0.602902i
$69$		0			0
$70$	1.63919	+	0.763949i	0.195921	+	0.0913093i
$71$	12.8669			1.52702			0.763512	−	0.645794i	$-0.223474\pi$
$71$	12.8669			1.52702			0.763512	+	0.645794i	$0.223474\pi$
$72$		0			0
$73$	1.25953	+	1.25953i	0.147417	+	0.147417i	0.776963	−	0.629546i	$-0.216759\pi$
$73$	1.25953	+	1.25953i	0.147417	+	0.147417i	−0.629546	+	0.776963i	$0.716759\pi$
$74$	11.7279			1.36334
$75$		0			0
$76$			3.21554i			0.368848i
$77$	2.71692	−	2.71692i	0.309622	−	0.309622i
$78$		0			0
$79$			7.18819i			0.808735i	0.914597	+	0.404367i	$0.132508\pi$
$79$			7.18819i			0.808735i	−0.914597	+	0.404367i	$0.867492\pi$
$80$	−2.02676	−	0.944579i	−0.226599	−	0.105607i
$81$		0			0
$82$	−0.133723	−	0.133723i	−0.0147673	−	0.0147673i
$83$	−9.66991	+	9.66991i	−1.06141	+	1.06141i	−0.0634236	+	0.997987i	$0.520202\pi$
$83$	−9.66991	+	9.66991i	−1.06141	+	1.06141i	−0.997987	+	0.0634236i	$0.979798\pi$
$84$		0			0
$85$	14.7725	−	5.38025i	1.60230	−	0.583570i
$86$	7.08528			0.764026
$87$		0			0
$88$	−3.35932	+	3.35932i	−0.358104	+	0.358104i
$89$			1.07072i			0.113496i	0.998389	+	0.0567479i	$0.0180731\pi$
$89$			1.07072i			0.113496i	−0.998389	+	0.0567479i	$0.981927\pi$
$90$		0			0
$91$	−0.268536	−	2.90368i	−0.0281502	−	0.304388i
$92$	−5.25852	+	5.25852i	−0.548239	+	0.548239i
$93$		0			0
$94$			9.99701i			1.03111i
$95$	6.51714	+	3.03733i	0.668645	+	0.311624i
$96$		0			0
$97$	10.6308	−	10.6308i	1.07940	−	1.07940i	0.0828330	−	0.996563i	$-0.473603\pi$
$97$	10.6308	−	10.6308i	1.07940	−	1.07940i	0.996563	−	0.0828330i	$-0.0263968\pi$
$98$	4.48722	−	4.48722i	0.453278	−	0.453278i
$99$		0			0
$100$	−3.82888	+	3.21554i	−0.382888	+	0.321554i
$101$		−	9.99410i		−	0.994450i	−0.867622	−	0.497225i	$-0.834352\pi$
$101$		−	9.99410i		−	0.994450i	0.867622	−	0.497225i	$-0.165648\pi$
$102$		0			0
$103$	3.76158	−	3.76158i	0.370639	−	0.370639i	−0.497071	−	0.867710i	$-0.665591\pi$
$103$	3.76158	−	3.76158i	0.370639	−	0.370639i	0.867710	+	0.497071i	$0.165591\pi$
$104$	0.332029	+	3.59023i	0.0325581	+	0.352051i
$105$		0			0
$106$		−	10.0634i		−	0.977447i
$107$	−12.0491	+	12.0491i	−1.16483	+	1.16483i	−0.181423	+	0.983405i	$0.558070\pi$
$107$	−12.0491	+	12.0491i	−1.16483	+	1.16483i	−0.983405	+	0.181423i	$0.941930\pi$
$108$		0			0
$109$	12.1912			1.16771			0.583854	−	0.811858i	$-0.301544\pi$
$109$	12.1912			1.16771			0.583854	+	0.811858i	$0.301544\pi$
$110$	3.63540	+	9.98168i	0.346622	+	0.951716i
$111$		0			0
$112$	0.571888	−	0.571888i	0.0540383	−	0.0540383i
$113$	−9.51912	−	9.51912i	−0.895484	−	0.895484i	0.0995490	−	0.995033i	$-0.468260\pi$
$113$	−9.51912	−	9.51912i	−0.895484	−	0.895484i	−0.995033	+	0.0995490i	$0.968260\pi$
$114$		0			0
$115$	5.69069	+	15.6249i	0.530659	+	1.45703i
$116$			4.80941i			0.446542i
$117$		0			0
$118$	3.20211	−	3.20211i	0.294778	−	0.294778i
$119$			5.68646i			0.521277i
$120$		0			0
$121$	11.5700			1.05182
$122$	−3.90881	−	3.90881i	−0.353887	−	0.353887i
$123$		0			0
$124$	−2.73810			−0.245888
$125$	2.90046	+	10.7976i	0.259425	+	0.965763i
$126$		0			0
$127$	3.25294	+	3.25294i	0.288652	+	0.288652i	0.836547	−	0.547895i	$-0.184571\pi$
$127$	3.25294	+	3.25294i	0.288652	+	0.288652i	−0.547895	+	0.836547i	$0.684571\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	7.59018	+	2.71831i	0.665703	+	0.238412i
$131$		−	21.0694i		−	1.84084i	−0.390929	−	0.920421i	$-0.627846\pi$
$131$		−	21.0694i		−	1.84084i	0.390929	−	0.920421i	$-0.372154\pi$
$132$		0			0
$133$	−1.83893	+	1.83893i	−0.159455	+	0.159455i
$134$	9.32584			0.805630
$135$		0			0
$136$		−	7.03099i		−	0.602902i
$137$	4.78251	+	4.78251i	0.408598	+	0.408598i	0.881249	−	0.472652i	$-0.156703\pi$
$137$	4.78251	+	4.78251i	0.408598	+	0.408598i	−0.472652	+	0.881249i	$0.656703\pi$
$138$		0			0
$139$		−	12.6776i		−	1.07530i	−0.843168	−	0.537651i	$-0.819312\pi$
$139$		−	12.6776i		−	1.07530i	0.843168	−	0.537651i	$-0.180688\pi$
$140$	−0.618888	−	1.69927i	−0.0523056	−	0.143615i
$141$		0			0
$142$	−9.09829	−	9.09829i	−0.763512	−	0.763512i
$143$	10.9453	−	13.1761i	0.915295	−	1.10184i
$144$		0			0
$145$	9.74753	+	4.54287i	0.809488	+	0.377264i
$146$		−	1.78125i		−	0.147417i
$147$		0			0
$148$	−8.29289	−	8.29289i	−0.681672	−	0.681672i
$149$			6.06045i			0.496491i	0.968697	+	0.248246i	$0.0798540\pi$
$149$			6.06045i			0.496491i	−0.968697	+	0.248246i	$0.920146\pi$
$150$		0			0
$151$		−	15.4816i		−	1.25987i	−0.776647	−	0.629937i	$-0.783081\pi$
$151$		−	15.4816i		−	1.25987i	0.776647	−	0.629937i	$-0.216919\pi$
$152$	2.27373	−	2.27373i	0.184424	−	0.184424i
$153$		0			0
$154$	−3.84230			−0.309622
$155$	−2.58635	+	5.54947i	−0.207740	+	0.445744i
$156$		0			0
$157$	−3.34672	−	3.34672i	−0.267097	−	0.267097i	0.560832	−	0.827930i	$-0.310481\pi$
$157$	−3.34672	−	3.34672i	−0.267097	−	0.267097i	−0.827930	+	0.560832i	$0.810481\pi$
$158$	5.08282	−	5.08282i	0.404367	−	0.404367i
$159$		0			0
$160$	0.765220	+	2.10106i	0.0604960	+	0.166103i
$161$	−6.01457			−0.474014
$162$		0			0
$163$	4.37383	+	4.37383i	0.342585	+	0.342585i	0.857338	−	0.514753i	$-0.172116\pi$
$163$	4.37383	+	4.37383i	0.342585	+	0.342585i	−0.514753	+	0.857338i	$0.672116\pi$
$164$			0.189114i			0.0147673i
$165$		0			0
$166$	13.6753			1.06141
$167$	−10.2771	−	10.2771i	−0.795270	−	0.795270i	0.187076	−	0.982345i	$-0.440099\pi$
$167$	−10.2771	−	10.2771i	−0.795270	−	0.795270i	−0.982345	+	0.187076i	$0.940099\pi$
$168$		0			0
$169$	−2.38412	−	12.7795i	−0.183394	−	0.983039i
$170$	−14.2502	−	6.64133i	−1.09294	−	0.509366i
$171$		0			0
$172$	−5.01005	−	5.01005i	−0.382013	−	0.382013i
$173$	8.32108	+	8.32108i	0.632640	+	0.632640i	0.948729	−	0.316089i	$-0.102370\pi$
$173$	8.32108	+	8.32108i	0.632640	+	0.632640i	−0.316089	+	0.948729i	$0.602370\pi$
$174$		0			0
$175$	−4.02862	−	0.350759i	−0.304535	−	0.0265149i
$176$	4.75079			0.358104
$177$		0			0
$178$	0.757111	−	0.757111i	0.0567479	−	0.0567479i
$179$	10.2128			0.763341			0.381671	−	0.924298i	$-0.375349\pi$
$179$	10.2128			0.763341			0.381671	+	0.924298i	$0.375349\pi$
$180$		0			0
$181$	−13.6868			−1.01733			−0.508665	−	0.860964i	$-0.669861\pi$
$181$	−13.6868			−1.01733			−0.508665	+	0.860964i	$0.669861\pi$
$182$	−1.86333	+	2.24309i	−0.138119	+	0.166269i
$183$		0			0
$184$	7.43667			0.548239
$185$	−24.6410	+	8.97444i	−1.81164	+	0.659814i
$186$		0			0
$187$	−23.6193	+	23.6193i	−1.72722	+	1.72722i
$188$	7.06895	−	7.06895i	0.515556	−	0.515556i
$189$		0			0
$190$	−2.46060	−	6.75603i	−0.178510	−	0.490134i
$191$		−	3.40284i		−	0.246221i	−0.992393	−	0.123110i	$-0.960713\pi$
$191$		−	3.40284i		−	0.246221i	0.992393	−	0.123110i	$-0.0392869\pi$
$192$		0			0
$193$	−5.57977	−	5.57977i	−0.401641	−	0.401641i	0.477170	−	0.878811i	$-0.341663\pi$
$193$	−5.57977	−	5.57977i	−0.401641	−	0.401641i	−0.878811	+	0.477170i	$0.841663\pi$
$194$	−15.0343			−1.07940
$195$		0			0
$196$	−6.34589			−0.453278
$197$	4.69790	+	4.69790i	0.334711	+	0.334711i	0.854373	−	0.519661i	$-0.173942\pi$
$197$	4.69790	+	4.69790i	0.334711	+	0.334711i	−0.519661	+	0.854373i	$0.673942\pi$
$198$		0			0
$199$			16.7499i			1.18737i	0.804699	+	0.593683i	$0.202327\pi$
$199$			16.7499i			1.18737i	−0.804699	+	0.593683i	$0.797673\pi$
$200$	4.98116	+	0.433694i	0.352221	+	0.0306668i
$201$		0			0
$202$	−7.06689	+	7.06689i	−0.497225	+	0.497225i
$203$	−2.75044	+	2.75044i	−0.193043	+	0.193043i
$204$		0			0
$205$	0.383289	+	0.178633i	0.0267700	+	0.0124763i
$206$	−5.31967			−0.370639
$207$		0			0
$208$	2.30390	−	2.77346i	0.159746	−	0.192305i
$209$	−15.2764			−1.05669
$210$		0			0
$211$	9.92730			0.683423			0.341712	−	0.939805i	$-0.388993\pi$
$211$	9.92730			0.683423			0.341712	+	0.939805i	$0.388993\pi$
$212$	−7.11592	+	7.11592i	−0.488724	+	0.488724i
$213$		0			0
$214$	17.0400			1.16483
$215$	−14.8866	+	5.42180i	−1.01526	+	0.369764i
$216$		0			0
$217$	−1.56588	−	1.56588i	−0.106299	−	0.106299i
$218$	−8.62051	−	8.62051i	−0.583854	−	0.583854i
$219$		0			0
$220$	4.48750	−	9.62873i	0.302547	−	0.649169i
$221$	2.33449	+	25.2429i	0.157035	+	1.69802i
$222$		0			0
$223$	4.34930	+	4.34930i	0.291251	+	0.291251i	0.837574	−	0.546323i	$-0.183973\pi$
$223$	4.34930	+	4.34930i	0.291251	+	0.291251i	−0.546323	+	0.837574i	$0.683973\pi$
$224$	−0.808772			−0.0540383
$225$		0			0
$226$			13.4621i			0.895484i
$227$	−9.23974	−	9.23974i	−0.613263	−	0.613263i	0.330532	−	0.943795i	$-0.392772\pi$
$227$	−9.23974	−	9.23974i	−0.613263	−	0.613263i	−0.943795	+	0.330532i	$0.892772\pi$
$228$		0			0
$229$	23.3269			1.54149			0.770743	−	0.637146i	$-0.219885\pi$
$229$	23.3269			1.54149			0.770743	+	0.637146i	$0.219885\pi$
$230$	7.02452	−	15.0724i	0.463183	−	0.993843i
$231$		0			0
$232$	3.40076	−	3.40076i	0.223271	−	0.223271i
$233$	−5.72541	−	5.72541i	−0.375084	−	0.375084i	0.494241	−	0.869325i	$-0.335446\pi$
$233$	−5.72541	−	5.72541i	−0.375084	−	0.375084i	−0.869325	+	0.494241i	$0.835446\pi$
$234$		0			0
$235$	−7.64991	−	21.0043i	−0.499025	−	1.37017i
$236$	−4.52847			−0.294778
$237$		0			0
$238$	4.02094	−	4.02094i	0.260639	−	0.260639i
$239$		−	13.2799i		−	0.859005i	−0.903066	−	0.429503i	$-0.858689\pi$
$239$		−	13.2799i		−	0.859005i	0.903066	−	0.429503i	$-0.141311\pi$
$240$		0			0
$241$		−	4.48712i		−	0.289041i	−0.989502	−	0.144520i	$-0.953836\pi$
$241$		−	4.48712i		−	0.289041i	0.989502	−	0.144520i	$-0.0461639\pi$
$242$	−8.18124	−	8.18124i	−0.525910	−	0.525910i
$243$		0			0
$244$			5.52790i			0.353887i
$245$	−5.99419	+	12.8616i	−0.382955	+	0.821698i
$246$		0			0
$247$	−7.40827	+	8.91816i	−0.471377	+	0.567449i
$248$	1.93613	+	1.93613i	0.122944	+	0.122944i
$249$		0			0
$250$	5.58409	−	9.68597i	0.353169	−	0.612594i
$251$		−	19.6946i		−	1.24311i	−0.783370	−	0.621555i	$-0.786501\pi$
$251$		−	19.6946i		−	1.24311i	0.783370	−	0.621555i	$-0.213499\pi$
$252$		0			0
$253$	−24.9821	−	24.9821i	−1.57061	−	1.57061i
$254$		−	4.60035i		−	0.288652i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.0002	−	15.0002i	0.935689	−	0.935689i	−0.0623645	−	0.998053i	$-0.519864\pi$
$257$	15.0002	−	15.0002i	0.935689	−	0.935689i	0.998053	+	0.0623645i	$0.0198641\pi$
$258$		0			0
$259$		−	9.48521i		−	0.589382i
$260$	−3.44493	−	7.28920i	−0.213645	−	0.452057i
$261$		0			0
$262$	−14.8983	+	14.8983i	−0.920421	+	0.920421i
$263$	4.53797	+	4.53797i	0.279823	+	0.279823i	0.833038	−	0.553215i	$-0.186599\pi$
$263$	4.53797	+	4.53797i	0.279823	+	0.279823i	−0.553215	+	0.833038i	$0.686599\pi$
$264$		0			0
$265$	7.70074	+	21.1438i	0.473053	+	1.29886i
$266$	2.60064			0.159455
$267$		0			0
$268$	−6.59437	−	6.59437i	−0.402815	−	0.402815i
$269$	−24.3432			−1.48423			−0.742115	−	0.670273i	$-0.766177\pi$
$269$	−24.3432			−1.48423			−0.742115	+	0.670273i	$0.766177\pi$
$270$		0			0
$271$		−	2.94959i		−	0.179175i	−0.995979	−	0.0895875i	$-0.971445\pi$
$271$		−	2.94959i		−	0.179175i	0.995979	−	0.0895875i	$-0.0285549\pi$
$272$	−4.97166	+	4.97166i	−0.301451	+	0.301451i
$273$		0			0
$274$		−	6.76350i		−	0.408598i
$275$	−15.2764	−	18.1902i	−0.921199	−	1.09691i
$276$		0			0
$277$	4.29785	+	4.29785i	0.258233	+	0.258233i	0.824335	−	0.566102i	$-0.191549\pi$
$277$	4.29785	+	4.29785i	0.258233	+	0.258233i	−0.566102	+	0.824335i	$0.691549\pi$
$278$	−8.96443	+	8.96443i	−0.537651	+	0.537651i
$279$		0			0
$280$	−0.763949	+	1.63919i	−0.0456547	+	0.0979603i
$281$	33.1768			1.97916			0.989582	−	0.143968i	$-0.0459861\pi$
$281$	33.1768			1.97916			0.989582	+	0.143968i	$0.0459861\pi$
$282$		0			0
$283$	7.40227	−	7.40227i	0.440019	−	0.440019i	−0.451999	−	0.892018i	$-0.649289\pi$
$283$	7.40227	−	7.40227i	0.440019	−	0.440019i	0.892018	+	0.451999i	$0.149289\pi$
$284$			12.8669i			0.763512i
$285$		0			0
$286$	−17.0564	+	1.57740i	−1.00857	+	0.0932736i
$287$	−0.108152	+	0.108152i	−0.00638400	+	0.00638400i
$288$		0			0
$289$		−	32.4348i		−	1.90793i
$290$	−3.68025	−	10.1048i	−0.216112	−	0.593376i
$291$		0			0
$292$	−1.25953	+	1.25953i	−0.0737085	+	0.0737085i
$293$	14.4845	−	14.4845i	0.846192	−	0.846192i	−0.143464	−	0.989656i	$-0.545824\pi$
$293$	14.4845	−	14.4845i	0.846192	−	0.846192i	0.989656	+	0.143464i	$0.0458241\pi$
$294$		0			0
$295$	−4.27750	+	9.17814i	−0.249046	+	0.534372i
$296$			11.7279i			0.681672i
$297$		0			0
$298$	4.28538	−	4.28538i	0.248246	−	0.248246i
$299$	−26.6994	+	2.46919i	−1.54406	+	0.142797i
$300$		0			0
$301$		−	5.73038i		−	0.330293i
$302$	−10.9471	+	10.9471i	−0.629937	+	0.629937i
$303$		0			0
$304$	−3.21554			−0.184424
$305$	11.2037	+	5.22154i	0.641524	+	0.298984i
$306$		0			0
$307$	1.30231	−	1.30231i	0.0743270	−	0.0743270i	−0.668966	−	0.743293i	$-0.733263\pi$
$307$	1.30231	−	1.30231i	0.0743270	−	0.0743270i	0.743293	+	0.668966i	$0.233263\pi$
$308$	2.71692	+	2.71692i	0.154811	+	0.154811i
$309$		0			0
$310$	5.75289	−	2.09525i	0.326742	−	0.119002i
$311$			16.5896i			0.940709i	0.882478	+	0.470354i	$0.155874\pi$
$311$			16.5896i			0.940709i	−0.882478	+	0.470354i	$0.844126\pi$
$312$		0			0
$313$	−8.87608	+	8.87608i	−0.501706	+	0.501706i	−0.911968	−	0.410262i	$-0.865437\pi$
$313$	−8.87608	+	8.87608i	−0.501706	+	0.501706i	0.410262	+	0.911968i	$0.365437\pi$
$314$			4.73298i			0.267097i
$315$		0			0
$316$	−7.18819			−0.404367
$317$	−22.5347	−	22.5347i	−1.26568	−	1.26568i	−0.948300	−	0.317375i	$-0.897199\pi$
$317$	−22.5347	−	22.5347i	−1.26568	−	1.26568i	−0.317375	−	0.948300i	$-0.602801\pi$
$318$		0			0
$319$	−22.8485			−1.27927
$320$	0.944579	−	2.02676i	0.0528036	−	0.113300i
$321$		0			0
$322$	4.25294	+	4.25294i	0.237007	+	0.237007i
$323$	15.9866	−	15.9866i	0.889517	−	0.889517i
$324$		0			0
$325$	−18.0275	+	0.0968275i	−0.999986	+	0.00537102i
$326$		−	6.18553i		−	0.342585i
$327$		0			0
$328$	0.133723	−	0.133723i	0.00738364	−	0.00738364i
$329$	8.08530			0.445757
$330$		0			0
$331$			3.65771i			0.201046i	0.994935	+	0.100523i	$0.0320516\pi$
$331$			3.65771i			0.201046i	−0.994935	+	0.100523i	$0.967948\pi$
$332$	−9.66991	−	9.66991i	−0.530705	−	0.530705i
$333$		0			0
$334$			14.5341i			0.795270i
$335$	−19.5941	+	7.13632i	−1.07054	+	0.389899i
$336$		0			0
$337$	11.4418	+	11.4418i	0.623273	+	0.623273i	0.946367	−	0.323094i	$-0.104723\pi$
$337$	11.4418	+	11.4418i	0.623273	+	0.623273i	−0.323094	+	0.946367i	$0.604723\pi$
$338$	−7.35065	+	10.7223i	−0.399823	+	0.583217i
$339$		0			0
$340$	5.38025	+	14.7725i	0.291785	+	0.801152i
$341$		−	13.0081i		−	0.704429i
$342$		0			0
$343$	−7.63235	−	7.63235i	−0.412108	−	0.412108i
$344$			7.08528i			0.382013i
$345$		0			0
$346$		−	11.7678i		−	0.632640i
$347$	−1.62232	+	1.62232i	−0.0870906	+	0.0870906i	−0.749310	−	0.662219i	$-0.769615\pi$
$347$	−1.62232	+	1.62232i	−0.0870906	+	0.0870906i	0.662219	+	0.749310i	$0.269615\pi$
$348$		0			0
$349$	4.35270			0.232994			0.116497	−	0.993191i	$-0.462833\pi$
$349$	4.35270			0.232994			0.116497	+	0.993191i	$0.462833\pi$
$350$	2.60064	+	3.09669i	0.139010	+	0.165525i
$351$		0			0
$352$	−3.35932	−	3.35932i	−0.179052	−	0.179052i
$353$	−15.9340	+	15.9340i	−0.848081	+	0.848081i	−0.989894	−	0.141812i	$-0.954707\pi$
$353$	−15.9340	+	15.9340i	−0.848081	+	0.848081i	0.141812	+	0.989894i	$0.454707\pi$
$354$		0			0
$355$	26.0782	+	12.1538i	1.38409	+	0.645058i
$356$	−1.07072			−0.0567479
$357$		0			0
$358$	−7.22155	−	7.22155i	−0.381671	−	0.381671i
$359$			19.0860i			1.00732i	0.863901	+	0.503662i	$0.168014\pi$
$359$			19.0860i			1.00732i	−0.863901	+	0.503662i	$0.831986\pi$
$360$		0			0
$361$	−8.66030			−0.455805
$362$	9.67802	+	9.67802i	0.508665	+	0.508665i
$363$		0			0
$364$	2.90368	−	0.268536i	0.152194	−	0.0140751i
$365$	1.36305	+	3.74250i	0.0713451	+	0.195891i
$366$		0			0
$367$	−24.7437	−	24.7437i	−1.29161	−	1.29161i	−0.933790	−	0.357820i	$-0.883520\pi$
$367$	−24.7437	−	24.7437i	−1.29161	−	1.29161i	−0.357820	−	0.933790i	$-0.616480\pi$
$368$	−5.25852	−	5.25852i	−0.274119	−	0.274119i
$369$		0			0
$370$	23.7697	+	11.0780i	1.23573	+	0.575915i
$371$	−8.13902			−0.422557
$372$		0			0
$373$	10.5770	−	10.5770i	0.547658	−	0.547658i	−0.378105	−	0.925763i	$-0.623424\pi$
$373$	10.5770	−	10.5770i	0.547658	−	0.547658i	0.925763	+	0.378105i	$0.123424\pi$
$374$	33.4028			1.72722
$375$		0			0
$376$	−9.99701			−0.515556
$377$	−11.0804	+	13.3387i	−0.570668	+	0.686977i
$378$		0			0
$379$	−0.531027			−0.0272770			−0.0136385	−	0.999907i	$-0.504341\pi$
$379$	−0.531027			−0.0272770			−0.0136385	+	0.999907i	$0.504341\pi$
$380$	−3.03733	+	6.51714i	−0.155812	+	0.334322i
$381$		0			0
$382$	−2.40617	+	2.40617i	−0.123110	+	0.123110i
$383$	7.64213	−	7.64213i	0.390494	−	0.390494i	−0.484369	−	0.874864i	$-0.660951\pi$
$383$	7.64213	−	7.64213i	0.390494	−	0.390494i	0.874864	+	0.484369i	$0.160951\pi$
$384$		0			0
$385$	8.07290	−	2.94021i	0.411433	−	0.149847i
$386$			7.89099i			0.401641i
$387$		0			0
$388$	10.6308	+	10.6308i	0.539698	+	0.539698i
$389$	−21.7927			−1.10494			−0.552468	−	0.833534i	$-0.686314\pi$
$389$	−21.7927			−1.10494			−0.552468	+	0.833534i	$0.686314\pi$
$390$		0			0
$391$	52.2871			2.64427
$392$	4.48722	+	4.48722i	0.226639	+	0.226639i
$393$		0			0
$394$		−	6.64383i		−	0.334711i
$395$	−6.78982	+	14.5688i	−0.341633	+	0.733034i
$396$		0			0
$397$	6.53961	−	6.53961i	0.328214	−	0.328214i	−0.523693	−	0.851907i	$-0.675446\pi$
$397$	6.53961	−	6.53961i	0.328214	−	0.328214i	0.851907	+	0.523693i	$0.175446\pi$
$398$	11.8439	−	11.8439i	0.593683	−	0.593683i
$399$		0			0
$400$	−3.21554	−	3.82888i	−0.160777	−	0.191444i
$401$	9.75711			0.487247			0.243623	−	0.969870i	$-0.421664\pi$
$401$	9.75711			0.487247			0.243623	+	0.969870i	$0.421664\pi$
$402$		0			0
$403$	−7.59399	−	6.30829i	−0.378284	−	0.314238i
$404$	9.99410			0.497225
$405$		0			0
$406$	3.88971			0.193043
$407$	39.3978	−	39.3978i	1.95288	−	1.95288i
$408$		0			0
$409$	−1.94105			−0.0959789			−0.0479894	−	0.998848i	$-0.515281\pi$
$409$	−1.94105			−0.0959789			−0.0479894	+	0.998848i	$0.515281\pi$
$410$	−0.144713	−	0.397338i	−0.00714689	−	0.0196231i
$411$		0			0
$412$	3.76158	+	3.76158i	0.185320	+	0.185320i
$413$	−2.58978	−	2.58978i	−0.127435	−	0.127435i
$414$		0			0
$415$	−28.7326	+	10.4646i	−1.41043	+	0.513688i
$416$	−3.59023	+	0.332029i	−0.176026	+	0.0162791i
$417$		0			0
$418$	10.8020	+	10.8020i	0.528344	+	0.528344i
$419$	−15.4250			−0.753562			−0.376781	−	0.926302i	$-0.622969\pi$
$419$	−15.4250			−0.753562			−0.376781	+	0.926302i	$0.622969\pi$
$420$		0			0
$421$		−	2.77309i		−	0.135152i	−0.997714	−	0.0675761i	$-0.978473\pi$
$421$		−	2.77309i		−	0.135152i	0.997714	−	0.0675761i	$-0.0215266\pi$
$422$	−7.01966	−	7.01966i	−0.341712	−	0.341712i
$423$		0			0
$424$	10.0634			0.488724
$425$	35.0225	+	3.04930i	1.69884	+	0.147913i
$426$		0			0
$427$	−3.16134	+	3.16134i	−0.152988	+	0.152988i
$428$	−12.0491	−	12.0491i	−0.582414	−	0.582414i
$429$		0			0
$430$	14.3602	+	6.69261i	0.692510	+	0.322746i
$431$	−0.868581			−0.0418381			−0.0209190	−	0.999781i	$-0.506659\pi$
$431$	−0.868581			−0.0418381			−0.0209190	+	0.999781i	$0.506659\pi$
$432$		0			0
$433$	−11.0970	+	11.0970i	−0.533286	+	0.533286i	−0.921549	−	0.388263i	$-0.873075\pi$
$433$	−11.0970	+	11.0970i	−0.533286	+	0.533286i	0.388263	+	0.921549i	$0.373075\pi$
$434$			2.21449i			0.106299i
$435$		0			0
$436$			12.1912i			0.583854i
$437$	16.9090	+	16.9090i	0.808866	+	0.808866i
$438$		0			0
$439$			0.778414i			0.0371517i	0.999827	+	0.0185758i	$0.00591322\pi$
$439$			0.778414i			0.0371517i	−0.999827	+	0.0185758i	$0.994087\pi$
$440$	−9.98168	+	3.63540i	−0.475858	+	0.173311i
$441$		0			0
$442$	16.1987	−	19.5001i	0.770492	−	0.927527i
$443$	−0.671614	−	0.671614i	−0.0319093	−	0.0319093i	0.690972	−	0.722881i	$-0.257183\pi$
$443$	−0.671614	−	0.671614i	−0.0319093	−	0.0319093i	−0.722881	+	0.690972i	$0.757183\pi$
$444$		0			0
$445$	−1.01138	+	2.17009i	−0.0479439	+	0.102872i
$446$		−	6.15085i		−	0.291251i
$447$		0			0
$448$	0.571888	+	0.571888i	0.0270192	+	0.0270192i
$449$			4.06711i			0.191939i	0.995384	+	0.0959694i	$0.0305951\pi$
$449$			4.06711i			0.191939i	−0.995384	+	0.0959694i	$0.969405\pi$
$450$		0			0
$451$	−0.898439			−0.0423058
$452$	9.51912	−	9.51912i	0.447742	−	0.447742i
$453$		0			0
$454$			13.0670i			0.613263i
$455$	2.19849	−	6.13872i	0.103067	−	0.287788i
$456$		0			0
$457$	0.218756	−	0.218756i	0.0102330	−	0.0102330i	−0.701972	−	0.712205i	$-0.747697\pi$
$457$	0.218756	−	0.218756i	0.0102330	−	0.0102330i	0.712205	+	0.701972i	$0.247697\pi$
$458$	−16.4946	−	16.4946i	−0.770743	−	0.770743i
$459$		0			0
$460$	−15.6249	+	5.69069i	−0.728513	+	0.265330i
$461$	−8.23267			−0.383434			−0.191717	−	0.981450i	$-0.561406\pi$
$461$	−8.23267			−0.383434			−0.191717	+	0.981450i	$0.561406\pi$
$462$		0			0
$463$	−10.9647	−	10.9647i	−0.509575	−	0.509575i	0.404821	−	0.914396i	$-0.367334\pi$
$463$	−10.9647	−	10.9647i	−0.509575	−	0.509575i	−0.914396	+	0.404821i	$0.867334\pi$
$464$	−4.80941			−0.223271
$465$		0			0
$466$			8.09696i			0.375084i
$467$	−5.47264	+	5.47264i	−0.253243	+	0.253243i	−0.822299	−	0.569056i	$-0.807309\pi$
$467$	−5.47264	+	5.47264i	−0.253243	+	0.253243i	0.569056	+	0.822299i	$0.307309\pi$
$468$		0			0
$469$		−	7.54247i		−	0.348279i
$470$	−9.44297	+	20.2616i	−0.435572	+	0.934597i
$471$		0			0
$472$	3.20211	+	3.20211i	0.147389	+	0.147389i
$473$	23.8017	−	23.8017i	1.09440	−	1.09440i
$474$		0			0
$475$	10.3397	+	12.3119i	0.474418	+	0.564909i
$476$	−5.68646			−0.260639
$477$		0			0
$478$	−9.39031	+	9.39031i	−0.429503	+	0.429503i
$479$		−	15.2093i		−	0.694929i	−0.937693	−	0.347464i	$-0.887043\pi$
$479$		−	15.2093i		−	0.694929i	0.937693	−	0.347464i	$-0.112957\pi$
$480$		0			0
$481$	−3.89401	−	42.1060i	−0.177552	−	1.91987i
$482$	−3.17287	+	3.17287i	−0.144520	+	0.144520i
$483$		0			0
$484$			11.5700i			0.525910i
$485$	31.5878	−	11.5045i	1.43433	−	0.522393i
$486$		0			0
$487$	−25.6897	+	25.6897i	−1.16411	+	1.16411i	−0.180542	+	0.983567i	$0.557785\pi$
$487$	−25.6897	+	25.6897i	−1.16411	+	1.16411i	−0.983567	+	0.180542i	$0.942215\pi$
$488$	3.90881	−	3.90881i	0.176944	−	0.176944i
$489$		0			0
$490$	13.3331	−	4.85600i	0.602327	−	0.219372i
$491$		−	25.6001i		−	1.15531i	−0.816279	−	0.577657i	$-0.803967\pi$
$491$		−	25.6001i		−	1.15531i	0.816279	−	0.577657i	$-0.196033\pi$
$492$		0			0
$493$	23.9107	−	23.9107i	1.07689	−	1.07689i
$494$	11.5445	−	1.06765i	0.519413	−	0.0480360i
$495$		0			0
$496$		−	2.73810i		−	0.122944i
$497$	−7.35844	+	7.35844i	−0.330071	+	0.330071i
$498$		0			0
$499$	16.6136			0.743726			0.371863	−	0.928288i	$-0.378719\pi$
$499$	16.6136			0.743726			0.371863	+	0.928288i	$0.378719\pi$
$500$	−10.7976	+	2.90046i	−0.482882	+	0.129713i
$501$		0			0
$502$	−13.9262	+	13.9262i	−0.621555	+	0.621555i
$503$	18.7741	+	18.7741i	0.837096	+	0.837096i	0.988476	−	0.151380i	$-0.0483716\pi$
$503$	18.7741	+	18.7741i	0.837096	+	0.837096i	−0.151380	+	0.988476i	$0.548372\pi$
$504$		0			0
$505$	9.44022	−	20.2557i	0.420084	−	0.901366i
$506$			35.3301i			1.57061i
$507$		0			0
$508$	−3.25294	+	3.25294i	−0.144326	+	0.144326i
$509$		−	16.7306i		−	0.741570i	−0.928719	−	0.370785i	$-0.879089\pi$
$509$		−	16.7306i		−	0.741570i	0.928719	−	0.370785i	$-0.120911\pi$
$510$		0			0
$511$	−1.44062			−0.0637293
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−21.2135			−0.935689
$515$	11.1769	−	4.07072i	0.492514	−	0.179377i
$516$		0			0
$517$	33.5831	+	33.5831i	1.47698	+	1.47698i
$518$	−6.70706	+	6.70706i	−0.294691	+	0.294691i
$519$		0			0
$520$	−2.71831	+	7.59018i	−0.119206	+	0.332851i
$521$			27.2152i			1.19232i	0.802866	+	0.596159i	$0.203307\pi$
$521$			27.2152i			1.19232i	−0.802866	+	0.596159i	$0.796693\pi$
$522$		0			0
$523$	−22.6140	+	22.6140i	−0.988841	+	0.988841i	−0.999938	−	0.0110978i	$-0.996467\pi$
$523$	−22.6140	+	22.6140i	−0.988841	+	0.988841i	0.0110978	+	0.999938i	$0.496467\pi$
$524$	21.0694			0.920421
$525$		0			0
$526$		−	6.41766i		−	0.279823i
$527$	13.6129	+	13.6129i	0.592986	+	0.592986i
$528$		0			0
$529$			32.3041i			1.40452i
$530$	9.50571	−	20.3962i	0.412902	−	0.885954i
$531$		0			0
$532$	−1.83893	−	1.83893i	−0.0797277	−	0.0797277i
$533$	−0.435698	+	0.524498i	−0.0188722	+	0.0227185i
$534$		0			0
$535$	−35.8019	+	13.0393i	−1.54785	+	0.563739i
$536$			9.32584i			0.402815i
$537$		0			0
$538$	17.2132	+	17.2132i	0.742115	+	0.742115i
$539$		−	30.1480i		−	1.29857i
$540$		0			0
$541$		−	21.6875i		−	0.932420i	−0.884674	−	0.466210i	$-0.845619\pi$
$541$		−	21.6875i		−	0.932420i	0.884674	−	0.466210i	$-0.154381\pi$
$542$	−2.08568	+	2.08568i	−0.0895875	+	0.0895875i
$543$		0			0
$544$	7.03099			0.301451
$545$	24.7088	+	11.5156i	1.05841	+	0.493274i
$546$		0			0
$547$	−1.40313	−	1.40313i	−0.0599934	−	0.0599934i	0.676474	−	0.736467i	$-0.263507\pi$
$547$	−1.40313	−	1.40313i	−0.0599934	−	0.0599934i	−0.736467	+	0.676474i	$0.763507\pi$
$548$	−4.78251	+	4.78251i	−0.204299	+	0.204299i
$549$		0			0
$550$	−2.06039	+	23.6644i	−0.0878553	+	1.00905i
$551$	15.4648			0.658825
$552$		0			0
$553$	−4.11084	−	4.11084i	−0.174811	−	0.174811i
$554$		−	6.07808i		−	0.258233i
$555$		0			0
$556$	12.6776			0.537651
$557$	−7.05024	−	7.05024i	−0.298728	−	0.298728i	0.541787	−	0.840516i	$-0.317748\pi$
$557$	−7.05024	−	7.05024i	−0.298728	−	0.298728i	−0.840516	+	0.541787i	$0.817748\pi$
$558$		0			0
$559$	−2.35252	−	25.4378i	−0.0995010	−	1.07590i
$560$	1.69927	−	0.618888i	0.0718075	−	0.0261528i
$561$		0			0
$562$	−23.4596	−	23.4596i	−0.989582	−	0.989582i
$563$	8.11542	+	8.11542i	0.342024	+	0.342024i	0.857128	−	0.515104i	$-0.172247\pi$
$563$	8.11542	+	8.11542i	0.342024	+	0.342024i	−0.515104	+	0.857128i	$0.672247\pi$
$564$		0			0
$565$	−10.3014	−	28.2846i	−0.433385	−	1.18994i
$566$	−10.4684			−0.440019
$567$		0			0
$568$	9.09829	−	9.09829i	0.381756	−	0.381756i
$569$	22.2869			0.934317			0.467158	−	0.884174i	$-0.345278\pi$
$569$	22.2869			0.934317			0.467158	+	0.884174i	$0.345278\pi$
$570$		0			0
$571$	−25.3024			−1.05887			−0.529437	−	0.848350i	$-0.677597\pi$
$571$	−25.3024			−1.05887			−0.529437	+	0.848350i	$0.677597\pi$
$572$	13.1761	+	10.9453i	0.550921	+	0.457647i
$573$		0			0
$574$	0.152950			0.00638400
$575$	−3.22524	+	37.0432i	−0.134502	+	1.54481i
$576$		0			0
$577$	14.1747	−	14.1747i	0.590102	−	0.590102i	−0.347557	−	0.937659i	$-0.612989\pi$
$577$	14.1747	−	14.1747i	0.590102	−	0.590102i	0.937659	+	0.347557i	$0.112989\pi$
$578$	−22.9349	+	22.9349i	−0.953965	+	0.953965i
$579$		0			0
$580$	−4.54287	+	9.74753i	−0.188632	+	0.404744i
$581$		−	11.0602i		−	0.458855i
$582$		0			0
$583$	−33.8063	−	33.8063i	−1.40011	−	1.40011i
$584$	1.78125			0.0737085
$585$		0			0
$586$	−20.4841			−0.846192
$587$	−30.5743	−	30.5743i	−1.26194	−	1.26194i	−0.950153	−	0.311785i	$-0.899073\pi$
$587$	−30.5743	−	30.5743i	−1.26194	−	1.26194i	−0.311785	−	0.950153i	$-0.600927\pi$
$588$		0			0
$589$			8.80446i			0.362781i
$590$	9.51457	−	3.46528i	0.391709	−	0.142663i
$591$		0			0
$592$	8.29289	−	8.29289i	0.340836	−	0.340836i
$593$	−7.14933	+	7.14933i	−0.293588	+	0.293588i	−0.838496	−	0.544908i	$-0.816565\pi$
$593$	−7.14933	+	7.14933i	−0.293588	+	0.293588i	0.544908	+	0.838496i	$0.316565\pi$
$594$		0			0
$595$	−5.37131	+	11.5251i	−0.220202	+	0.472484i
$596$	−6.06045			−0.248246
$597$		0			0
$598$	20.6253	+	17.1333i	0.843430	+	0.700633i
$599$	5.81155			0.237453			0.118727	−	0.992927i	$-0.462119\pi$
$599$	5.81155			0.237453			0.118727	+	0.992927i	$0.462119\pi$
$600$		0			0
$601$	−17.2460			−0.703479			−0.351739	−	0.936098i	$-0.614410\pi$
$601$	−17.2460			−0.703479			−0.351739	+	0.936098i	$0.614410\pi$
$602$	−4.05199	+	4.05199i	−0.165147	+	0.165147i
$603$		0			0
$604$	15.4816			0.629937
$605$	23.4497	+	10.9288i	0.953365	+	0.444319i
$606$		0			0
$607$	11.4384	+	11.4384i	0.464270	+	0.464270i	0.900052	−	0.435782i	$-0.143528\pi$
$607$	11.4384	+	11.4384i	0.464270	+	0.464270i	−0.435782	+	0.900052i	$0.643528\pi$
$608$	2.27373	+	2.27373i	0.0922120	+	0.0922120i
$609$		0			0
$610$	−4.23006	−	11.6144i	−0.171270	−	0.470254i
$611$	35.8916	−	3.31930i	1.45202	−	0.134284i
$612$		0			0
$613$	21.0295	+	21.0295i	0.849372	+	0.849372i	0.990055	−	0.140683i	$-0.0449298\pi$
$613$	21.0295	+	21.0295i	0.849372	+	0.849372i	−0.140683	+	0.990055i	$0.544930\pi$
$614$	−1.84175			−0.0743270
$615$		0			0
$616$		−	3.84230i		−	0.154811i
$617$	12.7832	+	12.7832i	0.514634	+	0.514634i	0.915943	−	0.401309i	$-0.131445\pi$
$617$	12.7832	+	12.7832i	0.514634	+	0.514634i	−0.401309	+	0.915943i	$0.631445\pi$
$618$		0			0
$619$	28.2508			1.13549			0.567747	−	0.823203i	$-0.307815\pi$
$619$	28.2508			1.13549			0.567747	+	0.823203i	$0.307815\pi$
$620$	−5.54947	−	2.58635i	−0.222872	−	0.103870i
$621$		0			0
$622$	11.7306	−	11.7306i	0.470354	−	0.470354i
$623$	−0.612330	−	0.612330i	−0.0245325	−	0.0245325i
$624$		0			0
$625$	−4.32059	+	24.6238i	−0.172824	+	0.984953i
$626$	12.5527			0.501706
$627$		0			0
$628$	3.34672	−	3.34672i	0.133549	−	0.133549i
$629$			82.4589i			3.28785i
$630$		0			0
$631$			14.0284i			0.558461i	0.960224	+	0.279231i	$0.0900794\pi$
$631$			14.0284i			0.558461i	−0.960224	+	0.279231i	$0.909921\pi$
$632$	5.08282	+	5.08282i	0.202184	+	0.202184i
$633$		0			0
$634$			31.8689i			1.26568i
$635$	3.52028	+	9.66560i	0.139698	+	0.383568i
$636$		0			0
$637$	−17.6000	−	14.6203i	−0.697339	−	0.579276i
$638$	16.1563	+	16.1563i	0.639635	+	0.639635i
$639$		0			0
$640$	−2.10106	+	0.765220i	−0.0830515	+	0.0302480i
$641$		−	5.67596i		−	0.224187i	−0.993698	−	0.112093i	$-0.964244\pi$
$641$		−	5.67596i		−	0.224187i	0.993698	−	0.112093i	$-0.0357556\pi$
$642$		0			0
$643$	12.6396	+	12.6396i	0.498457	+	0.498457i	0.910957	−	0.412501i	$-0.135345\pi$
$643$	12.6396	+	12.6396i	0.498457	+	0.498457i	−0.412501	+	0.910957i	$0.635345\pi$
$644$		−	6.01457i		−	0.237007i
$645$		0			0
$646$	−22.6084			−0.889517
$647$	32.2126	−	32.2126i	1.26641	−	1.26641i	0.318479	−	0.947930i	$-0.396828\pi$
$647$	32.2126	−	32.2126i	1.26641	−	1.26641i	0.947930	−	0.318479i	$-0.103172\pi$
$648$		0			0
$649$		−	21.5138i		−	0.844491i
$650$	12.8158	+	12.6789i	0.502678	+	0.497307i
$651$		0			0
$652$	−4.37383	+	4.37383i	−0.171293	+	0.171293i
$653$	−5.68536	−	5.68536i	−0.222485	−	0.222485i	0.587059	−	0.809544i	$-0.300286\pi$
$653$	−5.68536	−	5.68536i	−0.222485	−	0.222485i	−0.809544	+	0.587059i	$0.800286\pi$
$654$		0			0
$655$	19.9017	−	42.7027i	0.777624	−	1.66853i
$656$	−0.189114			−0.00738364
$657$		0			0
$658$	−5.71717	−	5.71717i	−0.222878	−	0.222878i
$659$	38.0612			1.48265			0.741327	−	0.671144i	$-0.234197\pi$
$659$	38.0612			1.48265			0.741327	+	0.671144i	$0.234197\pi$
$660$		0			0
$661$			5.42738i			0.211101i	0.994414	+	0.105550i	$0.0336604\pi$
$661$			5.42738i			0.211101i	−0.994414	+	0.105550i	$0.966340\pi$
$662$	2.58639	−	2.58639i	0.100523	−	0.100523i
$663$		0			0
$664$			13.6753i			0.530705i
$665$	−5.46409	+	1.99006i	−0.211888	+	0.0771712i
$666$		0			0
$667$	25.2904	+	25.2904i	0.979247	+	0.979247i
$668$	10.2771	−	10.2771i	0.397635	−	0.397635i
$669$		0			0
$670$	18.9013	+	8.80899i	0.730220	+	0.340321i
$671$	−26.2619			−1.01383
$672$		0			0
$673$	9.11717	−	9.11717i	0.351441	−	0.351441i	−0.509205	−	0.860646i	$-0.670060\pi$
$673$	9.11717	−	9.11717i	0.351441	−	0.351441i	0.860646	+	0.509205i	$0.170060\pi$
$674$		−	16.1811i		−	0.623273i
$675$		0			0
$676$	12.7795	−	2.38412i	0.491520	−	0.0916970i
$677$	−11.9187	+	11.9187i	−0.458071	+	0.458071i	−0.898022	−	0.439951i	$-0.854996\pi$
$677$	−11.9187	+	11.9187i	−0.458071	+	0.458071i	0.439951	+	0.898022i	$0.354996\pi$
$678$		0			0
$679$			12.1593i			0.466630i
$680$	6.64133	−	14.2502i	0.254683	−	0.546468i
$681$		0			0
$682$	−9.19813	+	9.19813i	−0.352215	+	0.352215i
$683$	−12.6077	+	12.6077i	−0.482421	+	0.482421i	−0.905904	−	0.423483i	$-0.860807\pi$
$683$	−12.6077	+	12.6077i	−0.482421	+	0.482421i	0.423483	+	0.905904i	$0.360807\pi$
$684$		0			0
$685$	5.17556	+	14.2105i	0.197748	+	0.542955i
$686$			10.7938i			0.412108i
$687$		0			0
$688$	5.01005	−	5.01005i	0.191006	−	0.191006i
$689$	−36.1300	+	3.34135i	−1.37645	+	0.127295i
$690$		0			0
$691$			35.2190i			1.33979i	0.742454	+	0.669897i	$0.233662\pi$
$691$			35.2190i			1.33979i	−0.742454	+	0.669897i	$0.766338\pi$
$692$	−8.32108	+	8.32108i	−0.316320	+	0.316320i
$693$		0			0
$694$	2.29430			0.0870906
$695$	11.9750	−	25.6945i	0.454238	−	0.974649i
$696$		0			0
$697$	0.940208	−	0.940208i	0.0356129	−	0.0356129i
$698$	−3.07782	−	3.07782i	−0.116497	−	0.116497i
$699$		0			0
$700$	0.350759	−	4.02862i	0.0132575	−	0.152267i
$701$			17.7758i			0.671383i	0.941972	+	0.335691i	$0.108970\pi$
$701$			17.7758i			0.671383i	−0.941972	+	0.335691i	$0.891030\pi$
$702$		0			0
$703$	−26.6661	+	26.6661i	−1.00573	+	1.00573i
$704$			4.75079i			0.179052i
$705$		0			0
$706$	22.5341			0.848081
$707$	5.71550	+	5.71550i	0.214954	+	0.214954i
$708$		0			0
$709$	25.9200			0.973446			0.486723	−	0.873556i	$-0.338192\pi$
$709$	25.9200			0.973446			0.486723	+	0.873556i	$0.338192\pi$
$710$	−9.84603	−	27.0341i	−0.369515	−	1.01457i
$711$		0			0
$712$	0.757111	+	0.757111i	0.0283739	+	0.0283739i
$713$	−14.3983	+	14.3983i	−0.539222	+	0.539222i
$714$		0			0
$715$	34.6295	−	16.3661i	1.29507	−	0.612059i
$716$			10.2128i			0.381671i
$717$		0			0
$718$	13.4959	−	13.4959i	0.503662	−	0.503662i
$719$	6.65415			0.248158			0.124079	−	0.992272i	$-0.460402\pi$
$719$	6.65415			0.248158			0.124079	+	0.992272i	$0.460402\pi$
$720$		0			0
$721$			4.30240i			0.160230i
$722$	6.12375	+	6.12375i	0.227903	+	0.227903i
$723$		0			0
$724$		−	13.6868i		−	0.508665i
$725$	15.4648	+	18.4146i	0.574350	+	0.683902i
$726$		0			0
$727$	0.332792	+	0.332792i	0.0123426	+	0.0123426i	0.713251	−	0.700909i	$-0.247222\pi$
$727$	0.332792	+	0.332792i	0.0123426	+	0.0123426i	−0.700909	+	0.713251i	$0.747222\pi$
$728$	−2.24309	−	1.86333i	−0.0831345	−	0.0690595i
$729$		0			0
$730$	1.68253	−	3.61017i	0.0622732	−	0.133618i
$731$			49.8166i			1.84253i
$732$		0			0
$733$	2.49486	+	2.49486i	0.0921496	+	0.0921496i	0.751679	−	0.659529i	$-0.229244\pi$
$733$	2.49486	+	2.49486i	0.0921496	+	0.0921496i	−0.659529	+	0.751679i	$0.729244\pi$
$734$			34.9929i			1.29161i
$735$		0			0
$736$			7.43667i			0.274119i
$737$	31.3285	−	31.3285i	1.15400	−	1.15400i
$738$		0			0
$739$	−40.3044			−1.48262			−0.741310	−	0.671163i	$-0.765795\pi$
$739$	−40.3044			−1.48262			−0.741310	+	0.671163i	$0.765795\pi$
$740$	−8.97444	−	24.6410i	−0.329907	−	0.905822i
$741$		0			0
$742$	5.75516	+	5.75516i	0.211278	+	0.211278i
$743$	0.200265	−	0.200265i	0.00734702	−	0.00734702i	−0.703424	−	0.710771i	$-0.748346\pi$
$743$	0.200265	−	0.200265i	0.00734702	−	0.00734702i	0.710771	+	0.703424i	$0.248346\pi$
$744$		0			0
$745$	−5.72457	+	12.2831i	−0.209732	+	0.450018i
$746$	−14.9582			−0.547658
$747$		0			0
$748$	−23.6193	−	23.6193i	−0.863608	−	0.863608i
$749$		−	13.7814i		−	0.503563i
$750$		0			0
$751$	7.82748			0.285629			0.142814	−	0.989749i	$-0.454385\pi$
$751$	7.82748			0.285629			0.142814	+	0.989749i	$0.454385\pi$
$752$	7.06895	+	7.06895i	0.257778	+	0.257778i
$753$		0			0
$754$	17.2669	−	1.59686i	0.628823	−	0.0581543i
$755$	14.6236	−	31.3775i	0.532206	−	1.14194i
$756$		0			0
$757$	22.9331	+	22.9331i	0.833519	+	0.833519i	0.987996	−	0.154477i	$-0.0493693\pi$
$757$	22.9331	+	22.9331i	0.833519	+	0.833519i	−0.154477	+	0.987996i	$0.549369\pi$
$758$	0.375493	+	0.375493i	0.0136385	+	0.0136385i
$759$		0			0
$760$	6.75603	−	2.46060i	0.245067	−	0.0892552i
$761$	−19.2950			−0.699443			−0.349721	−	0.936854i	$-0.613724\pi$
$761$	−19.2950			−0.699443			−0.349721	+	0.936854i	$0.613724\pi$
$762$		0			0
$763$	−6.97202	+	6.97202i	−0.252404	+	0.252404i
$764$	3.40284			0.123110
$765$		0			0
$766$	−10.8076			−0.390494
$767$	−12.5595	−	10.4331i	−0.453498	−	0.376718i
$768$		0			0
$769$	−14.7875			−0.533249			−0.266625	−	0.963800i	$-0.585908\pi$
$769$	−14.7875			−0.533249			−0.266625	+	0.963800i	$0.585908\pi$
$770$	−7.78744	−	3.62936i	−0.280640	−	0.130793i
$771$		0			0
$772$	5.57977	−	5.57977i	0.200820	−	0.200820i
$773$	14.8963	−	14.8963i	0.535781	−	0.535781i	−0.386506	−	0.922287i	$-0.626318\pi$
$773$	14.8963	−	14.8963i	0.535781	−	0.535781i	0.922287	+	0.386506i	$0.126318\pi$
$774$		0			0
$775$	−10.4838	+	8.80446i	−0.376590	+	0.316265i
$776$		−	15.0343i		−	0.539698i
$777$		0			0
$778$	15.4098	+	15.4098i	0.552468	+	0.552468i
$779$	0.608102			0.0217875
$780$		0			0
$781$	−61.1281			−2.18733
$782$	−36.9726	−	36.9726i	−1.32214	−	1.32214i
$783$		0			0
$784$		−	6.34589i		−	0.226639i
$785$	−3.62177	−	9.94426i	−0.129267	−	0.354926i
$786$		0			0
$787$	27.8492	−	27.8492i	0.992718	−	0.992718i	−0.00725556	−	0.999974i	$-0.502310\pi$
$787$	27.8492	−	27.8492i	0.992718	−	0.992718i	0.999974	+	0.00725556i	$0.00230954\pi$
$788$	−4.69790	+	4.69790i	−0.167356	+	0.167356i
$789$		0			0
$790$	15.1028	−	5.50055i	0.537334	−	0.195701i
$791$	10.8877			0.387123
$792$		0			0
$793$	−12.7357	+	15.3314i	−0.452258	+	0.544433i
$794$	−9.24841			−0.328214
$795$		0			0
$796$	−16.7499			−0.593683
$797$	23.6370	−	23.6370i	0.837267	−	0.837267i	−0.151232	−	0.988498i	$-0.548324\pi$
$797$	23.6370	−	23.6370i	0.837267	−	0.837267i	0.988498	+	0.151232i	$0.0483240\pi$
$798$		0			0
$799$	−70.2889			−2.48664
$800$	−0.433694	+	4.98116i	−0.0153334	+	0.176110i
$801$		0			0
$802$	−6.89932	−	6.89932i	−0.243623	−	0.243623i
$803$	−5.98377	−	5.98377i	−0.211163	−	0.211163i
$804$		0			0
$805$	−12.1901	−	5.68123i	−0.429645	−	0.200237i
$806$	0.909127	+	9.83039i	0.0320226	+	0.346261i
$807$		0			0
$808$	−7.06689	−	7.06689i	−0.248612	−	0.248612i
$809$	−29.8920			−1.05095			−0.525473	−	0.850810i	$-0.676112\pi$
$809$	−29.8920			−1.05095			−0.525473	+	0.850810i	$0.676112\pi$
$810$		0			0
$811$			12.5461i			0.440554i	0.975437	+	0.220277i	$0.0706961\pi$
$811$			12.5461i			0.440554i	−0.975437	+	0.220277i	$0.929304\pi$
$812$	−2.75044	−	2.75044i	−0.0965216	−	0.0965216i
$813$		0			0
$814$	−55.7169			−1.95288
$815$	4.73329	+	12.9962i	0.165800	+	0.455236i
$816$		0			0
$817$	−16.1100	+	16.1100i	−0.563619	+	0.563619i
$818$	1.37253	+	1.37253i	0.0479894	+	0.0479894i
$819$		0			0
$820$	−0.178633	+	0.383289i	−0.00623813	+	0.0133850i
$821$	45.1649			1.57626			0.788132	−	0.615506i	$-0.211048\pi$
$821$	45.1649			1.57626			0.788132	+	0.615506i	$0.211048\pi$
$822$		0			0
$823$	6.36791	−	6.36791i	0.221972	−	0.221972i	−0.587357	−	0.809328i	$-0.699831\pi$
$823$	6.36791	−	6.36791i	0.221972	−	0.221972i	0.809328	+	0.587357i	$0.199831\pi$
$824$		−	5.31967i		−	0.185320i
$825$		0			0
$826$			3.66250i			0.127435i
$827$	16.3162	+	16.3162i	0.567371	+	0.567371i	0.931391	−	0.364020i	$-0.118596\pi$
$827$	16.3162	+	16.3162i	0.567371	+	0.567371i	−0.364020	+	0.931391i	$0.618596\pi$
$828$		0			0
$829$		−	7.46637i		−	0.259318i	−0.991559	−	0.129659i	$-0.958612\pi$
$829$		−	7.46637i		−	0.259318i	0.991559	−	0.129659i	$-0.0413882\pi$
$830$	27.7166	+	12.9174i	0.962058	+	0.448370i
$831$		0			0
$832$	2.77346	+	2.30390i	0.0961523	+	0.0798732i
$833$	31.5496	+	31.5496i	1.09313	+	1.09313i
$834$		0			0
$835$	−11.1218	−	30.5369i	−0.384885	−	1.05677i
$836$		−	15.2764i		−	0.528344i
$837$		0			0
$838$	10.9071	+	10.9071i	0.376781	+	0.376781i
$839$		−	47.9382i		−	1.65501i	−0.561457	−	0.827506i	$-0.689759\pi$
$839$		−	47.9382i		−	1.65501i	0.561457	−	0.827506i	$-0.310241\pi$
$840$		0			0
$841$	−5.86960			−0.202400
$842$	−1.96087	+	1.96087i	−0.0675761	+	0.0675761i
$843$		0			0
$844$			9.92730i			0.341712i
$845$	7.23921	−	28.1530i	0.249036	−	0.968494i
$846$		0			0
$847$	−6.61675	+	6.61675i	−0.227354	+	0.227354i
$848$	−7.11592	−	7.11592i	−0.244362	−	0.244362i
$849$		0			0
$850$	−22.6084	−	26.9208i	−0.775463	−	0.923376i
$851$	−87.2167			−2.98975
$852$		0			0
$853$	27.3007	+	27.3007i	0.934757	+	0.934757i	0.997998	−	0.0632415i	$-0.0201438\pi$
$853$	27.3007	+	27.3007i	0.934757	+	0.934757i	−0.0632415	+	0.997998i	$0.520144\pi$
$854$	4.47081			0.152988
$855$		0			0
$856$			17.0400i			0.582414i
$857$	−7.67255	+	7.67255i	−0.262089	+	0.262089i	−0.825902	−	0.563813i	$-0.809334\pi$
$857$	−7.67255	+	7.67255i	−0.262089	+	0.262089i	0.563813	+	0.825902i	$0.309334\pi$
$858$		0			0
$859$		−	35.2757i		−	1.20359i	−0.798650	−	0.601795i	$-0.794452\pi$
$859$		−	35.2757i		−	1.20359i	0.798650	−	0.601795i	$-0.205548\pi$
$860$	−5.42180	−	14.8866i	−0.184882	−	0.507628i
$861$		0			0
$862$	0.614179	+	0.614179i	0.0209190	+	0.0209190i
$863$	−3.78096	+	3.78096i	−0.128705	+	0.128705i	−0.768525	−	0.639820i	$-0.779009\pi$
$863$	−3.78096	+	3.78096i	−0.128705	+	0.128705i	0.639820	+	0.768525i	$0.279009\pi$
$864$		0			0
$865$	9.00495	+	24.7248i	0.306177	+	0.840668i
$866$	15.6935			0.533286
$867$		0			0
$868$	1.56588	−	1.56588i	0.0531496	−	0.0531496i
$869$		−	34.1496i		−	1.15845i
$870$		0			0
$871$	−3.09645	−	33.4819i	−0.104919	−	1.13449i
$872$	8.62051	−	8.62051i	0.291927	−	0.291927i
$873$		0			0
$874$		−	23.9129i		−	0.808866i
$875$	−7.83373	−	4.51625i	−0.264829	−	0.152677i
$876$		0			0
$877$	2.16812	−	2.16812i	0.0732123	−	0.0732123i	−0.669552	−	0.742765i	$-0.733514\pi$
$877$	2.16812	−	2.16812i	0.0732123	−	0.0732123i	0.742765	+	0.669552i	$0.233514\pi$
$878$	0.550422	−	0.550422i	0.0185758	−	0.0185758i
$879$		0			0
$880$	9.62873	+	4.48750i	0.324584	+	0.151274i
$881$			8.32353i			0.280427i	0.990121	+	0.140213i	$0.0447789\pi$
$881$			8.32353i			0.280427i	−0.990121	+	0.140213i	$0.955221\pi$
$882$		0			0
$883$	−11.8822	+	11.8822i	−0.399867	+	0.399867i	−0.878186	−	0.478319i	$-0.841246\pi$
$883$	−11.8822	+	11.8822i	−0.399867	+	0.399867i	0.478319	+	0.878186i	$0.341246\pi$
$884$	−25.2429	+	2.33449i	−0.849010	+	0.0785175i
$885$		0			0
$886$			0.949805i			0.0319093i
$887$	−7.44170	+	7.44170i	−0.249868	+	0.249868i	−0.820916	−	0.571049i	$-0.806537\pi$
$887$	−7.44170	+	7.44170i	−0.249868	+	0.249868i	0.571049	+	0.820916i	$0.306537\pi$
$888$		0			0
$889$	−3.72063			−0.124786
$890$	2.24964	−	0.819334i	0.0754080	−	0.0274641i
$891$		0			0
$892$	−4.34930	+	4.34930i	−0.145626	+	0.145626i
$893$	−22.7305	−	22.7305i	−0.760648	−	0.760648i
$894$		0			0
$895$	20.6989	+	9.64680i	0.691889	+	0.322457i
$896$		−	0.808772i		−	0.0270192i
$897$		0			0
$898$	2.87588	−	2.87588i	0.0959694	−	0.0959694i
$899$			13.1686i			0.439198i
$900$		0			0
$901$	70.7559			2.35722
$902$	0.635292	+	0.635292i	0.0211529	+	0.0211529i
$903$		0			0
$904$	−13.4621			−0.447742
$905$	−27.7399	−	12.9283i	−0.922105	−	0.429750i
$906$		0			0
$907$	8.39307	+	8.39307i	0.278687	+	0.278687i	0.832585	−	0.553897i	$-0.186860\pi$
$907$	8.39307	+	8.39307i	0.278687	+	0.278687i	−0.553897	+	0.832585i	$0.686860\pi$
$908$	9.23974	−	9.23974i	0.306632	−	0.306632i
$909$		0			0
$910$	−5.89530	+	2.78616i	−0.195427	+	0.0923603i
$911$		−	27.4465i		−	0.909345i	−0.890659	−	0.454672i	$-0.849756\pi$
$911$		−	27.4465i		−	0.909345i	0.890659	−	0.454672i	$-0.150244\pi$
$912$		0			0
$913$	45.9397	−	45.9397i	1.52038	−	1.52038i
$914$	−0.309367			−0.0102330
$915$		0			0
$916$			23.3269i			0.770743i
$917$	12.0493	+	12.0493i	0.397904	+	0.397904i
$918$		0			0
$919$			4.57794i			0.151012i	0.997145	+	0.0755062i	$0.0240573\pi$
$919$			4.57794i			0.151012i	−0.997145	+	0.0755062i	$0.975943\pi$
$920$	15.0724	+	7.02452i	0.496921	+	0.231592i
$921$		0			0
$922$	5.82138	+	5.82138i	0.191717	+	0.191717i
$923$	−29.6441	+	35.6859i	−0.975746	+	1.17461i
$924$		0			0
$925$	−58.4186	−	5.08633i	−1.92079	−	0.167237i
$926$			15.5065i			0.509575i
$927$		0			0
$928$	3.40076	+	3.40076i	0.111636	+	0.111636i
$929$		−	39.1293i		−	1.28379i	−0.766793	−	0.641895i	$-0.778149\pi$
$929$		−	39.1293i		−	1.28379i	0.766793	−	0.641895i	$-0.221851\pi$
$930$		0			0
$931$			20.4055i			0.668762i
$932$	5.72541	−	5.72541i	0.187542	−	0.187542i
$933$		0			0
$934$	7.73948			0.253243
$935$	−70.1811	+	25.5605i	−2.29517	+	0.835917i
$936$		0			0
$937$	−21.5631	−	21.5631i	−0.704435	−	0.704435i	0.260924	−	0.965359i	$-0.415973\pi$
$937$	−21.5631	−	21.5631i	−0.704435	−	0.704435i	−0.965359	+	0.260924i	$0.915973\pi$
$938$	−5.33333	+	5.33333i	−0.174140	+	0.174140i
$939$		0			0
$940$	21.0043	−	7.64991i	0.685084	−	0.249513i
$941$	−11.5975			−0.378069			−0.189034	−	0.981970i	$-0.560536\pi$
$941$	−11.5975			−0.378069			−0.189034	+	0.981970i	$0.560536\pi$
$942$		0			0
$943$	0.994457	+	0.994457i	0.0323840	+	0.0323840i
$944$		−	4.52847i		−	0.147389i
$945$		0			0
$946$	−33.6607			−1.09440
$947$	12.5596	+	12.5596i	0.408132	+	0.408132i	0.881087	−	0.472955i	$-0.156813\pi$
$947$	12.5596	+	12.5596i	0.408132	+	0.408132i	−0.472955	+	0.881087i	$0.656813\pi$
$948$		0			0
$949$	−6.39509	+	0.591426i	−0.207593	+	0.0191985i
$950$	1.39456	−	16.0171i	0.0452455	−	0.519664i
$951$		0			0
$952$	4.02094	+	4.02094i	0.130319	+	0.130319i
$953$	−17.4513	−	17.4513i	−0.565303	−	0.565303i	0.365506	−	0.930809i	$-0.380896\pi$
$953$	−17.4513	−	17.4513i	−0.565303	−	0.565303i	−0.930809	+	0.365506i	$0.880896\pi$
$954$		0			0
$955$	3.21425	−	6.89675i	0.104011	−	0.223174i
$956$	13.2799			0.429503
$957$		0			0
$958$	−10.7546	+	10.7546i	−0.347464	+	0.347464i
$959$	−5.47012			−0.176640
$960$		0			0
$961$	23.5028			0.758156
$962$	−27.0199	+	32.5269i	−0.871157	+	1.04871i
$963$		0			0
$964$	4.48712			0.144520
$965$	−6.03834	−	16.5794i	−0.194381	−	0.533710i
$966$		0			0
$967$	7.44766	−	7.44766i	0.239501	−	0.239501i	−0.577143	−	0.816643i	$-0.695832\pi$
$967$	7.44766	−	7.44766i	0.239501	−	0.239501i	0.816643	+	0.577143i	$0.195832\pi$
$968$	8.18124	−	8.18124i	0.262955	−	0.262955i
$969$		0			0
$970$	−30.4709	−	14.2010i	−0.978361	−	0.455968i
$971$		−	19.1051i		−	0.613112i	−0.951853	−	0.306556i	$-0.900823\pi$
$971$		−	19.1051i		−	0.613112i	0.951853	−	0.306556i	$-0.0991767\pi$
$972$		0			0
$973$	7.25017	+	7.25017i	0.232430	+	0.232430i
$974$	36.3307			1.16411
$975$		0			0
$976$	−5.52790			−0.176944
$977$	6.83785	+	6.83785i	0.218762	+	0.218762i	0.807977	−	0.589215i	$-0.200563\pi$
$977$	6.83785	+	6.83785i	0.218762	+	0.218762i	−0.589215	+	0.807977i	$0.700563\pi$
$978$		0			0
$979$		−	5.08675i		−	0.162573i
$980$	−12.8616	−	5.99419i	−0.410849	−	0.191477i
$981$		0			0
$982$	−18.1020	+	18.1020i	−0.577657	+	0.577657i
$983$	1.30019	−	1.30019i	0.0414698	−	0.0414698i	−0.686068	−	0.727538i	$-0.740665\pi$
$983$	1.30019	−	1.30019i	0.0414698	−	0.0414698i	0.727538	+	0.686068i	$0.240665\pi$
$984$		0			0
$985$	5.08399	+	13.9591i	0.161990	+	0.444773i
$986$	−33.8149			−1.07689
$987$		0			0
$988$	−8.91816	−	7.40827i	−0.283725	−	0.235689i
$989$	−52.6909			−1.67547
$990$		0			0
$991$	−17.5466			−0.557385			−0.278692	−	0.960380i	$-0.589901\pi$
$991$	−17.5466			−0.557385			−0.278692	+	0.960380i	$0.589901\pi$
$992$	−1.93613	+	1.93613i	−0.0614721	+	0.0614721i
$993$		0			0
$994$	10.4064			0.330071
$995$	−15.8216	+	33.9480i	−0.501578	+	1.07622i
$996$		0			0
$997$	−2.81837	−	2.81837i	−0.0892586	−	0.0892586i	0.661068	−	0.750326i	$-0.270104\pi$
$997$	−2.81837	−	2.81837i	−0.0892586	−	0.0892586i	−0.750326	+	0.661068i	$0.770104\pi$
$998$	−11.7476	−	11.7476i	−0.371863	−	0.371863i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.v.d.467.3	yes	24
3.2	odd	2	inner	1170.2.v.d.467.7	yes	24
5.3	odd	4		1170.2.v.c.233.3	✓	24
13.12	even	2		1170.2.v.c.467.7	yes	24
15.8	even	4		1170.2.v.c.233.7	yes	24
39.38	odd	2		1170.2.v.c.467.3	yes	24
65.38	odd	4	inner	1170.2.v.d.233.7	yes	24
195.38	even	4	inner	1170.2.v.d.233.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.v.c.233.3	✓	24	5.3	odd	4
1170.2.v.c.233.7	yes	24	15.8	even	4
1170.2.v.c.467.3	yes	24	39.38	odd	2
1170.2.v.c.467.7	yes	24	13.12	even	2
1170.2.v.d.233.3	yes	24	195.38	even	4	inner
1170.2.v.d.233.7	yes	24	65.38	odd	4	inner
1170.2.v.d.467.3	yes	24	1.1	even	1	trivial
1170.2.v.d.467.7	yes	24	3.2	odd	2	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.02676 + 0.944579i) q^{5} +(-0.571888 + 0.571888i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.02676 + 0.944579i) q^{5} +(-0.571888 + 0.571888i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.765220 - 2.10106i) q^{10} -4.75079 q^{11} +(-2.30390 + 2.77346i) q^{13} +0.808772 q^{14} -1.00000 q^{16} +(4.97166 - 4.97166i) q^{17} +3.21554 q^{19} +(-0.944579 + 2.02676i) q^{20} +(3.35932 + 3.35932i) q^{22} +(5.25852 + 5.25852i) q^{23} +(3.21554 + 3.82888i) q^{25} +(3.59023 - 0.332029i) q^{26} +(-0.571888 - 0.571888i) q^{28} +4.80941 q^{29} +2.73810i q^{31} +(0.707107 + 0.707107i) q^{32} -7.03099 q^{34} +(-1.69927 + 0.618888i) q^{35} +(-8.29289 + 8.29289i) q^{37} +(-2.27373 - 2.27373i) q^{38} +(2.10106 - 0.765220i) q^{40} +0.189114 q^{41} +(-5.01005 + 5.01005i) q^{43} -4.75079i q^{44} -7.43667i q^{46} +(-7.06895 - 7.06895i) q^{47} +6.34589i q^{49} +(0.433694 - 4.98116i) q^{50} +(-2.77346 - 2.30390i) q^{52} +(7.11592 + 7.11592i) q^{53} +(-9.62873 - 4.48750i) q^{55} +0.808772i q^{56} +(-3.40076 - 3.40076i) q^{58} +4.52847i q^{59} +5.52790 q^{61} +(1.93613 - 1.93613i) q^{62} -1.00000i q^{64} +(-7.28920 + 3.44493i) q^{65} +(-6.59437 + 6.59437i) q^{67} +(4.97166 + 4.97166i) q^{68} +(1.63919 + 0.763949i) q^{70} +12.8669 q^{71} +(1.25953 + 1.25953i) q^{73} +11.7279 q^{74} +3.21554i q^{76} +(2.71692 - 2.71692i) q^{77} +7.18819i q^{79} +(-2.02676 - 0.944579i) q^{80} +(-0.133723 - 0.133723i) q^{82} +(-9.66991 + 9.66991i) q^{83} +(14.7725 - 5.38025i) q^{85} +7.08528 q^{86} +(-3.35932 + 3.35932i) q^{88} +1.07072i q^{89} +(-0.268536 - 2.90368i) q^{91} +(-5.25852 + 5.25852i) q^{92} +9.99701i q^{94} +(6.51714 + 3.03733i) q^{95} +(10.6308 - 10.6308i) q^{97} +(4.48722 - 4.48722i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{10} + 8 q^{13} - 24 q^{16} + 16 q^{19} - 8 q^{22} + 16 q^{25} - 32 q^{37} - 32 q^{43} - 24 q^{52} - 24 q^{55} + 80 q^{61} + 8 q^{67} + 8 q^{70} + 8 q^{73} - 64 q^{82} + 120 q^{85} + 8 q^{88} + 16 q^{91} + 8 q^{97}+O(q^{100}) \) 24 * q - 8 * q^10 + 8 * q^13 - 24 * q^16 + 16 * q^19 - 8 * q^22 + 16 * q^25 - 32 * q^37 - 32 * q^43 - 24 * q^52 - 24 * q^55 + 80 * q^61 + 8 * q^67 + 8 * q^70 + 8 * q^73 - 64 * q^82 + 120 * q^85 + 8 * q^88 + 16 * q^91 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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