LMFDB - Embedded newform 637.2.i.a.489.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			489.13
Character	$\chi$	$=$	637.489
Dual form			637.2.i.a.538.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34850 + 1.34850i) q^{2} -2.64781i q^{3} +1.63690i q^{4} +(2.41949 - 2.41949i) q^{5} +(3.57057 - 3.57057i) q^{6} +(0.489646 - 0.489646i) q^{8} -4.01091 q^{9} +O(q^{10})$	\(q+(1.34850 + 1.34850i) q^{2} -2.64781i q^{3} +1.63690i q^{4} +(2.41949 - 2.41949i) q^{5} +(3.57057 - 3.57057i) q^{6} +(0.489646 - 0.489646i) q^{8} -4.01091 q^{9} +6.52537 q^{10} +(-1.21802 + 1.21802i) q^{11} +4.33419 q^{12} +(-3.57057 + 0.501030i) q^{13} +(-6.40637 - 6.40637i) q^{15} +4.59436 q^{16} +2.45192 q^{17} +(-5.40870 - 5.40870i) q^{18} +(-3.68263 + 3.68263i) q^{19} +(3.96046 + 3.96046i) q^{20} -3.28498 q^{22} +4.58614i q^{23} +(-1.29649 - 1.29649i) q^{24} -6.70790i q^{25} +(-5.49055 - 4.13927i) q^{26} +2.67669i q^{27} +0.184063 q^{29} -17.2779i q^{30} +(1.80129 - 1.80129i) q^{31} +(5.21620 + 5.21620i) q^{32} +(3.22508 + 3.22508i) q^{33} +(3.30641 + 3.30641i) q^{34} -6.56544i q^{36} +(0.153870 - 0.153870i) q^{37} -9.93205 q^{38} +(1.32663 + 9.45420i) q^{39} -2.36939i q^{40} +(4.63239 - 4.63239i) q^{41} +0.562412i q^{43} +(-1.99376 - 1.99376i) q^{44} +(-9.70437 + 9.70437i) q^{45} +(-6.18441 + 6.18441i) q^{46} +(2.72683 + 2.72683i) q^{47} -12.1650i q^{48} +(9.04560 - 9.04560i) q^{50} -6.49223i q^{51} +(-0.820134 - 5.84465i) q^{52} +5.35509 q^{53} +(-3.60952 + 3.60952i) q^{54} +5.89396i q^{55} +(9.75092 + 9.75092i) q^{57} +(0.248208 + 0.248208i) q^{58} +(10.2056 + 10.2056i) q^{59} +(10.4866 - 10.4866i) q^{60} -1.50977i q^{61} +4.85807 q^{62} +4.87935i q^{64} +(-7.42673 + 9.85121i) q^{65} +8.69802i q^{66} +(4.88364 + 4.88364i) q^{67} +4.01354i q^{68} +12.1432 q^{69} +(1.70926 + 1.70926i) q^{71} +(-1.96392 + 1.96392i) q^{72} +(-8.62699 - 8.62699i) q^{73} +0.414986 q^{74} -17.7613 q^{75} +(-6.02809 - 6.02809i) q^{76} +(-10.9600 + 14.5379i) q^{78} +2.96797 q^{79} +(11.1160 - 11.1160i) q^{80} -4.94534 q^{81} +12.4935 q^{82} +(0.504742 - 0.504742i) q^{83} +(5.93241 - 5.93241i) q^{85} +(-0.758412 + 0.758412i) q^{86} -0.487363i q^{87} +1.19279i q^{88} +(-5.27206 - 5.27206i) q^{89} -26.1726 q^{90} -7.50704 q^{92} +(-4.76947 - 4.76947i) q^{93} +7.35426i q^{94} +17.8202i q^{95} +(13.8115 - 13.8115i) q^{96} +(-12.0949 + 12.0949i) q^{97} +(4.88535 - 4.88535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.34850	+	1.34850i	0.953532	+	0.953532i	0.998967	−	0.0454350i	$-0.0144674\pi$
$2$	1.34850	+	1.34850i	0.953532	+	0.953532i	−0.0454350	+	0.998967i	$0.514467\pi$
$3$		−	2.64781i		−	1.52871i	−0.644793	−	0.764357i	$-0.723056\pi$
$3$		−	2.64781i		−	1.52871i	0.644793	−	0.764357i	$-0.276944\pi$
$4$			1.63690i			0.818448i
$5$	2.41949	−	2.41949i	1.08203	−	1.08203i	0.0857106	−	0.996320i	$-0.472684\pi$
$5$	2.41949	−	2.41949i	1.08203	−	1.08203i	0.996320	−	0.0857106i	$-0.0273161\pi$
$6$	3.57057	−	3.57057i	1.45768	−	1.45768i
$7$		0			0
$7$		0			0
$8$	0.489646	−	0.489646i	0.173116	−	0.173116i
$9$	−4.01091			−1.33697
$10$	6.52537			2.06350
$11$	−1.21802	+	1.21802i	−0.367245	+	0.367245i	−0.866472	−	0.499226i	$-0.833618\pi$
$11$	−1.21802	+	1.21802i	−0.367245	+	0.367245i	0.499226	+	0.866472i	$0.333618\pi$
$12$	4.33419			1.25117
$13$	−3.57057	+	0.501030i	−0.990298	+	0.138961i
$13$	−3.57057	+	0.501030i	−0.990298	+	0.138961i
$14$		0			0
$15$	−6.40637	−	6.40637i	−1.65412	−	1.65412i
$16$	4.59436			1.14859
$17$	2.45192			0.594678			0.297339	−	0.954772i	$-0.403901\pi$
$17$	2.45192			0.594678			0.297339	+	0.954772i	$0.403901\pi$
$18$	−5.40870	−	5.40870i	−1.27484	−	1.27484i
$19$	−3.68263	+	3.68263i	−0.844854	+	0.844854i	−0.989486	−	0.144631i	$-0.953800\pi$
$19$	−3.68263	+	3.68263i	−0.844854	+	0.844854i	0.144631	+	0.989486i	$0.453800\pi$
$20$	3.96046	+	3.96046i	0.885586	+	0.885586i
$21$		0			0
$22$	−3.28498			−0.700361
$23$			4.58614i			0.956277i	0.878284	+	0.478139i	$0.158688\pi$
$23$			4.58614i			0.956277i	−0.878284	+	0.478139i	$0.841312\pi$
$24$	−1.29649	−	1.29649i	−0.264645	−	0.264645i
$25$		−	6.70790i		−	1.34158i
$26$	−5.49055	−	4.13927i	−1.07678	−	0.811778i
$27$			2.67669i			0.515130i
$28$		0			0
$29$	0.184063			0.0341796			0.0170898	−	0.999854i	$-0.494560\pi$
$29$	0.184063			0.0341796			0.0170898	+	0.999854i	$0.494560\pi$
$30$		−	17.2779i		−	3.15451i
$31$	1.80129	−	1.80129i	0.323521	−	0.323521i	−0.526595	−	0.850116i	$-0.676532\pi$
$31$	1.80129	−	1.80129i	0.323521	−	0.323521i	0.850116	+	0.526595i	$0.176532\pi$
$32$	5.21620	+	5.21620i	0.922103	+	0.922103i
$33$	3.22508	+	3.22508i	0.561414	+	0.561414i
$34$	3.30641	+	3.30641i	0.567045	+	0.567045i
$35$		0			0
$36$		−	6.56544i		−	1.09424i
$37$	0.153870	−	0.153870i	0.0252960	−	0.0252960i	−0.694346	−	0.719642i	$-0.744306\pi$
$37$	0.153870	−	0.153870i	0.0252960	−	0.0252960i	0.719642	+	0.694346i	$0.244306\pi$
$38$	−9.93205			−1.61119
$39$	1.32663	+	9.45420i	0.212431	+	1.51388i
$40$		−	2.36939i		−	0.374634i
$41$	4.63239	−	4.63239i	0.723458	−	0.723458i	−0.245850	−	0.969308i	$-0.579067\pi$
$41$	4.63239	−	4.63239i	0.723458	−	0.723458i	0.969308	+	0.245850i	$0.0790671\pi$
$42$		0			0
$43$			0.562412i			0.0857671i	0.999080	+	0.0428835i	$0.0136544\pi$
$43$			0.562412i			0.0857671i	−0.999080	+	0.0428835i	$0.986346\pi$
$44$	−1.99376	−	1.99376i	−0.300571	−	0.300571i
$45$	−9.70437	+	9.70437i	−1.44664	+	1.44664i
$46$	−6.18441	+	6.18441i	−0.911841	+	0.911841i
$47$	2.72683	+	2.72683i	0.397750	+	0.397750i	0.877439	−	0.479689i	$-0.159251\pi$
$47$	2.72683	+	2.72683i	0.397750	+	0.397750i	−0.479689	+	0.877439i	$0.659251\pi$
$48$		−	12.1650i		−	1.75587i
$49$		0			0
$50$	9.04560	−	9.04560i	1.27924	−	1.27924i
$51$		−	6.49223i		−	0.909093i
$52$	−0.820134	−	5.84465i	−0.113732	−	0.810507i
$53$	5.35509			0.735578			0.367789	−	0.929909i	$-0.380115\pi$
$53$	5.35509			0.735578			0.367789	+	0.929909i	$0.380115\pi$
$54$	−3.60952	+	3.60952i	−0.491193	+	0.491193i
$55$			5.89396i			0.794742i
$56$		0			0
$57$	9.75092	+	9.75092i	1.29154	+	1.29154i
$58$	0.248208	+	0.248208i	0.0325913	+	0.0325913i
$59$	10.2056	+	10.2056i	1.32865	+	1.32865i	0.906547	+	0.422104i	$0.138708\pi$
$59$	10.2056	+	10.2056i	1.32865	+	1.32865i	0.422104	+	0.906547i	$0.361292\pi$
$60$	10.4866	−	10.4866i	1.35381	−	1.35381i
$61$		−	1.50977i		−	0.193306i	−0.995318	−	0.0966531i	$-0.969186\pi$
$61$		−	1.50977i		−	0.193306i	0.995318	−	0.0966531i	$-0.0308137\pi$
$62$	4.85807			0.616975
$63$		0			0
$64$			4.87935i			0.609918i
$65$	−7.42673	+	9.85121i	−0.921173	+	1.22189i
$66$			8.69802i			1.07065i
$67$	4.88364	+	4.88364i	0.596631	+	0.596631i	0.939415	−	0.342783i	$-0.111370\pi$
$67$	4.88364	+	4.88364i	0.596631	+	0.596631i	−0.342783	+	0.939415i	$0.611370\pi$
$68$			4.01354i			0.486713i
$69$	12.1432			1.46188
$70$		0			0
$71$	1.70926	+	1.70926i	0.202852	+	0.202852i	0.801221	−	0.598369i	$-0.204184\pi$
$71$	1.70926	+	1.70926i	0.202852	+	0.202852i	−0.598369	+	0.801221i	$0.704184\pi$
$72$	−1.96392	+	1.96392i	−0.231451	+	0.231451i
$73$	−8.62699	−	8.62699i	−1.00971	−	1.00971i	−0.999952	−	0.00976038i	$-0.996893\pi$
$73$	−8.62699	−	8.62699i	−1.00971	−	1.00971i	−0.00976038	−	0.999952i	$-0.503107\pi$
$74$	0.414986			0.0482412
$75$	−17.7613			−2.05089
$76$	−6.02809	−	6.02809i	−0.691469	−	0.691469i
$77$		0			0
$78$	−10.9600	+	14.5379i	−1.24098	+	1.64610i
$79$	2.96797			0.333923			0.166961	−	0.985963i	$-0.446605\pi$
$79$	2.96797			0.333923			0.166961	+	0.985963i	$0.446605\pi$
$80$	11.1160	−	11.1160i	1.24281	−	1.24281i
$81$	−4.94534			−0.549483
$82$	12.4935			1.37968
$83$	0.504742	−	0.504742i	0.0554026	−	0.0554026i	−0.678863	−	0.734265i	$-0.737527\pi$
$83$	0.504742	−	0.504742i	0.0554026	−	0.0554026i	0.734265	+	0.678863i	$0.237527\pi$
$84$		0			0
$85$	5.93241	−	5.93241i	0.643460	−	0.643460i
$86$	−0.758412	+	0.758412i	−0.0817817	+	0.0817817i
$87$		−	0.487363i		−	0.0522508i
$88$			1.19279i			0.127152i
$89$	−5.27206	−	5.27206i	−0.558837	−	0.558837i	0.370139	−	0.928976i	$-0.379310\pi$
$89$	−5.27206	−	5.27206i	−0.558837	−	0.558837i	−0.928976	+	0.370139i	$0.879310\pi$
$90$	−26.1726			−2.75884
$91$		0			0
$92$	−7.50704			−0.782663
$93$	−4.76947	−	4.76947i	−0.494571	−	0.494571i
$94$			7.35426i			0.758534i
$95$			17.8202i			1.82832i
$96$	13.8115	−	13.8115i	1.40963	−	1.40963i
$97$	−12.0949	+	12.0949i	−1.22805	+	1.22805i	−0.263356	+	0.964699i	$0.584829\pi$
$97$	−12.0949	+	12.0949i	−1.22805	+	1.22805i	−0.964699	+	0.263356i	$0.915171\pi$
$98$		0			0
$99$	4.88535	−	4.88535i	0.490996	−	0.490996i
$100$	10.9801			1.09801
$101$	−8.22714			−0.818631			−0.409316	−	0.912393i	$-0.634232\pi$
$101$	−8.22714			−0.818631			−0.409316	+	0.912393i	$0.634232\pi$
$102$	8.75476	−	8.75476i	0.866850	−	0.866850i
$103$	−7.49766			−0.738766			−0.369383	−	0.929277i	$-0.620431\pi$
$103$	−7.49766			−0.738766			−0.369383	+	0.929277i	$0.620431\pi$
$104$	−1.50299	+	1.99364i	−0.147380	+	0.195493i
$105$		0			0
$106$	7.22133	+	7.22133i	0.701398	+	0.701398i
$107$	−3.98914			−0.385645			−0.192823	−	0.981234i	$-0.561764\pi$
$107$	−3.98914			−0.385645			−0.192823	+	0.981234i	$0.561764\pi$
$108$	−4.38147			−0.421607
$109$	−8.25592	−	8.25592i	−0.790774	−	0.790774i	0.190846	−	0.981620i	$-0.438877\pi$
$109$	−8.25592	−	8.25592i	−0.790774	−	0.790774i	−0.981620	+	0.190846i	$0.938877\pi$
$110$	−7.94800	+	7.94800i	−0.757812	+	0.757812i
$111$	−0.407418	−	0.407418i	−0.0386704	−	0.0386704i
$112$		0			0
$113$	−8.36429			−0.786846			−0.393423	−	0.919358i	$-0.628709\pi$
$113$	−8.36429			−0.786846			−0.393423	+	0.919358i	$0.628709\pi$
$114$			26.2982i			2.46305i
$115$	11.0962	+	11.0962i	1.03472	+	1.03472i
$116$			0.301291i			0.0279742i
$117$	14.3212	−	2.00958i	1.32400	−	0.185786i
$118$			27.5244i			2.53382i
$119$		0			0
$120$	−6.27370			−0.572708
$121$			8.03288i			0.730262i
$122$	2.03592	−	2.03592i	0.184324	−	0.184324i
$123$	−12.2657	−	12.2657i	−1.10596	−	1.10596i
$124$	2.94852	+	2.94852i	0.264785	+	0.264785i
$125$	−4.13226	−	4.13226i	−0.369601	−	0.369601i
$126$		0			0
$127$			12.0998i			1.07368i	0.843684	+	0.536840i	$0.180382\pi$
$127$			12.0998i			1.07368i	−0.843684	+	0.536840i	$0.819618\pi$
$128$	3.85261	−	3.85261i	0.340526	−	0.340526i
$129$	1.48916			0.131113
$130$	−23.2993	+	3.26940i	−2.04348	+	0.286746i
$131$			1.78452i			0.155915i	0.996957	+	0.0779573i	$0.0248398\pi$
$131$			1.78452i			0.155915i	−0.996957	+	0.0779573i	$0.975160\pi$
$132$	−5.27911	+	5.27911i	−0.459488	+	0.459488i
$133$		0			0
$134$			13.1712i			1.13781i
$135$	6.47624	+	6.47624i	0.557386	+	0.557386i
$136$	1.20057	−	1.20057i	0.102948	−	0.102948i
$137$	13.7305	−	13.7305i	1.17307	−	1.17307i	0.191599	−	0.981473i	$-0.438633\pi$
$137$	13.7305	−	13.7305i	1.17307	−	1.17307i	0.981473	−	0.191599i	$-0.0613672\pi$
$138$	16.3751	+	16.3751i	1.39395	+	1.39395i
$139$		−	13.5866i		−	1.15240i	−0.817310	−	0.576198i	$-0.804536\pi$
$139$		−	13.5866i		−	1.15240i	0.817310	−	0.576198i	$-0.195464\pi$
$140$		0			0
$141$	7.22014	−	7.22014i	0.608046	−	0.608046i
$142$			4.60987i			0.386852i
$143$	3.73875	−	4.95927i	0.312650	−	0.414715i
$144$	−18.4276			−1.53563
$145$	0.445339	−	0.445339i	0.0369834	−	0.0369834i
$146$		−	23.2670i		−	1.92559i
$147$		0			0
$148$	0.251869	+	0.251869i	0.0207035	+	0.0207035i
$149$	2.59852	+	2.59852i	0.212879	+	0.212879i	0.805489	−	0.592610i	$-0.201903\pi$
$149$	2.59852	+	2.59852i	0.212879	+	0.212879i	−0.592610	+	0.805489i	$0.701903\pi$
$150$	−23.9510	−	23.9510i	−1.95559	−	1.95559i
$151$	12.7307	−	12.7307i	1.03601	−	1.03601i	0.0366869	−	0.999327i	$-0.488320\pi$
$151$	12.7307	−	12.7307i	1.03601	−	1.03601i	0.999327	−	0.0366869i	$-0.0116804\pi$
$152$			3.60637i			0.292515i
$153$	−9.83443			−0.795066
$154$		0			0
$155$		−	8.71641i		−	0.700119i
$156$	−15.4755	+	2.17156i	−1.23903	+	0.173864i
$157$			18.3298i			1.46287i	0.681909	+	0.731437i	$0.261150\pi$
$157$			18.3298i			1.46287i	−0.681909	+	0.731437i	$0.738850\pi$
$158$	4.00230	+	4.00230i	0.318406	+	0.318406i
$159$		−	14.1793i		−	1.12449i
$160$	25.2411			1.99549
$161$		0			0
$162$	−6.66879	−	6.66879i	−0.523949	−	0.523949i
$163$	−9.13745	+	9.13745i	−0.715700	+	0.715700i	−0.967722	−	0.252021i	$-0.918905\pi$
$163$	−9.13745	+	9.13745i	−0.715700	+	0.715700i	0.252021	+	0.967722i	$0.418905\pi$
$164$	7.58274	+	7.58274i	0.592112	+	0.592112i
$165$	15.6061			1.21493
$166$	1.36129			0.105656
$167$	−10.6807	−	10.6807i	−0.826494	−	0.826494i	0.160536	−	0.987030i	$-0.448678\pi$
$167$	−10.6807	−	10.6807i	−0.826494	−	0.826494i	−0.987030	+	0.160536i	$0.948678\pi$
$168$		0			0
$169$	12.4979	−	3.57793i	0.961380	−	0.275225i
$170$	15.9997			1.22712
$171$	14.7707	−	14.7707i	1.12954	−	1.12954i
$172$	−0.920610			−0.0701959
$173$	−2.62017			−0.199208			−0.0996041	−	0.995027i	$-0.531758\pi$
$173$	−2.62017			−0.199208			−0.0996041	+	0.995027i	$0.531758\pi$
$174$	0.657209	−	0.657209i	0.0498229	−	0.0498229i
$175$		0			0
$176$	−5.59601	+	5.59601i	−0.421815	+	0.421815i
$177$	27.0224	−	27.0224i	2.03113	−	2.03113i
$178$		−	14.2187i		−	1.06574i
$179$			25.3584i			1.89537i	0.319202	+	0.947687i	$0.396585\pi$
$179$			25.3584i			1.89537i	−0.319202	+	0.947687i	$0.603415\pi$
$180$	−15.8850	−	15.8850i	−1.18400	−	1.18400i
$181$	−1.00365			−0.0746008			−0.0373004	−	0.999304i	$-0.511876\pi$
$181$	−1.00365			−0.0746008			−0.0373004	+	0.999304i	$0.511876\pi$
$182$		0			0
$183$	−3.99758			−0.295510
$184$	2.24559	+	2.24559i	0.165547	+	0.165547i
$185$		−	0.744574i		−	0.0547422i
$186$		−	12.8632i		−	0.943179i
$187$	−2.98648	+	2.98648i	−0.218393	+	0.218393i
$188$	−4.46354	+	4.46354i	−0.325537	+	0.325537i
$189$		0			0
$190$	−24.0305	+	24.0305i	−1.74336	+	1.74336i
$191$	−1.05038			−0.0760031			−0.0380016	−	0.999278i	$-0.512099\pi$
$191$	−1.05038			−0.0760031			−0.0380016	+	0.999278i	$0.512099\pi$
$192$	12.9196			0.932391
$193$	1.39803	−	1.39803i	0.100633	−	0.100633i	−0.654998	−	0.755631i	$-0.727331\pi$
$193$	1.39803	−	1.39803i	0.100633	−	0.100633i	0.755631	+	0.654998i	$0.227331\pi$
$194$	−32.6200			−2.34198
$195$	26.0842	+	19.6646i	1.86793	+	1.40821i
$196$		0			0
$197$	−3.36094	−	3.36094i	−0.239457	−	0.239457i	0.577168	−	0.816625i	$-0.304158\pi$
$197$	−3.36094	−	3.36094i	−0.239457	−	0.239457i	−0.816625	+	0.577168i	$0.804158\pi$
$198$	13.1758			0.936361
$199$	−10.2062			−0.723500			−0.361750	−	0.932275i	$-0.617821\pi$
$199$	−10.2062			−0.723500			−0.361750	+	0.932275i	$0.617821\pi$
$200$	−3.28450	−	3.28450i	−0.232249	−	0.232249i
$201$	12.9310	−	12.9310i	0.912079	−	0.912079i
$202$	−11.0943	−	11.0943i	−0.780591	−	0.780591i
$203$		0			0
$204$	10.6271			0.744045
$205$		−	22.4161i		−	1.56561i
$206$	−10.1106	−	10.1106i	−0.704438	−	0.704438i
$207$		−	18.3946i		−	1.27851i
$208$	−16.4045	+	2.30191i	−1.13745	+	0.159609i
$209$		−	8.97101i		−	0.620538i
$210$		0			0
$211$	16.1396			1.11109			0.555547	−	0.831485i	$-0.312509\pi$
$211$	16.1396			1.11109			0.555547	+	0.831485i	$0.312509\pi$
$212$			8.76572i			0.602032i
$213$	4.52580	−	4.52580i	0.310103	−	0.310103i
$214$	−5.37935	−	5.37935i	−0.367725	−	0.367725i
$215$	1.36075	+	1.36075i	0.0928026	+	0.0928026i
$216$	1.31063	+	1.31063i	0.0891772	+	0.0891772i
$217$		0			0
$218$		−	22.2662i		−	1.50806i
$219$	−22.8426	+	22.8426i	−1.54356	+	1.54356i
$220$	−9.64780			−0.650454
$221$	−8.75476	+	1.22849i	−0.588909	+	0.0826369i
$222$		−	1.09881i		−	0.0737470i
$223$	−0.0939482	+	0.0939482i	−0.00629124	+	0.00629124i	−0.710245	−	0.703954i	$-0.751416\pi$
$223$	−0.0939482	+	0.0939482i	−0.00629124	+	0.00629124i	0.703954	+	0.710245i	$0.251416\pi$
$224$		0			0
$225$			26.9048i			1.79365i
$226$	−11.2792	−	11.2792i	−0.750283	−	0.750283i
$227$	−18.7468	+	18.7468i	−1.24427	+	1.24427i	−0.286057	+	0.958213i	$0.592345\pi$
$227$	−18.7468	+	18.7468i	−1.24427	+	1.24427i	−0.958213	+	0.286057i	$0.907655\pi$
$228$	−15.9612	+	15.9612i	−1.05706	+	1.05706i
$229$	12.4557	+	12.4557i	0.823094	+	0.823094i	0.986551	−	0.163457i	$-0.0522643\pi$
$229$	12.4557	+	12.4557i	0.823094	+	0.823094i	−0.163457	+	0.986551i	$0.552264\pi$
$230$			29.9263i			1.97328i
$231$		0			0
$232$	0.0901255	−	0.0901255i	0.00591703	−	0.00591703i
$233$		−	5.08687i		−	0.333252i	−0.986020	−	0.166626i	$-0.946713\pi$
$233$		−	5.08687i		−	0.333252i	0.986020	−	0.166626i	$-0.0532873\pi$
$234$	22.0221	+	16.6022i	1.43963	+	1.08532i
$235$	13.1951			0.860754
$236$	−16.7054	+	16.7054i	−1.08743	+	1.08743i
$237$		−	7.85862i		−	0.510472i
$238$		0			0
$239$	−13.0182	−	13.0182i	−0.842079	−	0.842079i	0.147050	−	0.989129i	$-0.453022\pi$
$239$	−13.0182	−	13.0182i	−0.842079	−	0.842079i	−0.989129	+	0.147050i	$0.953022\pi$
$240$	−29.4332	−	29.4332i	−1.89990	−	1.89990i
$241$	1.92809	+	1.92809i	0.124199	+	0.124199i	0.766474	−	0.642275i	$-0.222009\pi$
$241$	1.92809	+	1.92809i	0.124199	+	0.124199i	−0.642275	+	0.766474i	$0.722009\pi$
$242$	−10.8323	+	10.8323i	−0.696328	+	0.696328i
$243$			21.1244i			1.35513i
$244$	2.47133			0.158211
$245$		0			0
$246$		−	33.0805i		−	2.10914i
$247$	11.3040	−	14.9942i	0.719256	−	0.954059i
$248$		−	1.76399i		−	0.112013i
$249$	−1.33646	−	1.33646i	−0.0846948	−	0.0846948i
$250$		−	11.1447i		−	0.704853i
$251$	−21.4230			−1.35221			−0.676105	−	0.736805i	$-0.736334\pi$
$251$	−21.4230			−1.35221			−0.676105	+	0.736805i	$0.736334\pi$
$252$		0			0
$253$	−5.58599	−	5.58599i	−0.351188	−	0.351188i
$254$	−16.3165	+	16.3165i	−1.02379	+	1.02379i
$255$	−15.7079	−	15.7079i	−0.983667	−	0.983667i
$256$	20.1492			1.25932
$257$	−9.60921			−0.599406			−0.299703	−	0.954033i	$-0.596888\pi$
$257$	−9.60921			−0.599406			−0.299703	+	0.954033i	$0.596888\pi$
$258$	2.00813	+	2.00813i	0.125021	+	0.125021i
$259$		0			0
$260$	−16.1254	−	12.1568i	−1.00006	−	0.753932i
$261$	−0.738258			−0.0456970
$262$	−2.40643	+	2.40643i	−0.148670	+	0.148670i
$263$	−7.86998			−0.485284			−0.242642	−	0.970116i	$-0.578014\pi$
$263$	−7.86998			−0.485284			−0.242642	+	0.970116i	$0.578014\pi$
$264$	3.15829			0.194379
$265$	12.9566	−	12.9566i	0.795918	−	0.795918i
$266$		0			0
$267$	−13.9594	+	13.9594i	−0.854303	+	0.854303i
$268$	−7.99401	+	7.99401i	−0.488312	+	0.488312i
$269$			3.97368i			0.242279i	0.992635	+	0.121140i	$0.0386549\pi$
$269$			3.97368i			0.242279i	−0.992635	+	0.121140i	$0.961345\pi$
$270$			17.4664i			1.06297i
$271$	12.0885	+	12.0885i	0.734327	+	0.734327i	0.971474	−	0.237147i	$-0.0762123\pi$
$271$	12.0885	+	12.0885i	0.734327	+	0.734327i	−0.237147	+	0.971474i	$0.576212\pi$
$272$	11.2650			0.683042
$273$		0			0
$274$	37.0310			2.23712
$275$	8.17033	+	8.17033i	0.492689	+	0.492689i
$276$			19.8772i			1.19647i
$277$		−	25.0918i		−	1.50762i	−0.657092	−	0.753811i	$-0.728214\pi$
$277$		−	25.0918i		−	1.50762i	0.657092	−	0.753811i	$-0.271786\pi$
$278$	18.3214	−	18.3214i	1.09885	−	1.09885i
$279$	−7.22480	+	7.22480i	−0.432537	+	0.432537i
$280$		0			0
$281$	−2.15639	+	2.15639i	−0.128639	+	0.128639i	−0.768495	−	0.639856i	$-0.778994\pi$
$281$	−2.15639	+	2.15639i	−0.128639	+	0.128639i	0.639856	+	0.768495i	$0.278994\pi$
$282$	19.4727			1.15958
$283$	11.3590			0.675225			0.337613	−	0.941285i	$-0.390381\pi$
$283$	11.3590			0.675225			0.337613	+	0.941285i	$0.390381\pi$
$284$	−2.79788	+	2.79788i	−0.166024	+	0.166024i
$285$	47.1846			2.79497
$286$	11.7293	−	1.64588i	0.693566	−	0.0973226i
$287$		0			0
$288$	−20.9217	−	20.9217i	−1.23282	−	1.23282i
$289$	−10.9881			−0.646358
$290$	1.20108			0.0705296
$291$	32.0251	+	32.0251i	1.87735	+	1.87735i
$292$	14.1215	−	14.1215i	0.826397	−	0.826397i
$293$	10.2833	+	10.2833i	0.600758	+	0.600758i	0.940514	−	0.339756i	$-0.110344\pi$
$293$	10.2833	+	10.2833i	0.600758	+	0.600758i	−0.339756	+	0.940514i	$0.610344\pi$
$294$		0			0
$295$	49.3846			2.87528
$296$		−	0.150683i		−	0.00875829i
$297$	−3.26025	−	3.26025i	−0.189179	−	0.189179i
$298$			7.00819i			0.405974i
$299$	−2.29780	−	16.3751i	−0.132885	−	0.946999i
$300$		−	29.0733i		−	1.67855i
$301$		0			0
$302$	34.3348			1.97575
$303$			21.7839i			1.25145i
$304$	−16.9194	+	16.9194i	−0.970392	+	0.970392i
$305$	−3.65288	−	3.65288i	−0.209163	−	0.209163i
$306$	−13.2617	−	13.2617i	−0.758122	−	0.758122i
$307$	−7.01794	−	7.01794i	−0.400535	−	0.400535i	0.477886	−	0.878422i	$-0.341403\pi$
$307$	−7.01794	−	7.01794i	−0.400535	−	0.400535i	−0.878422	+	0.477886i	$0.841403\pi$
$308$		0			0
$309$			19.8524i			1.12936i
$310$	11.7541	−	11.7541i	0.667586	−	0.667586i
$311$	2.52712			0.143300			0.0716498	−	0.997430i	$-0.477174\pi$
$311$	2.52712			0.143300			0.0716498	+	0.997430i	$0.477174\pi$
$312$	5.27879	+	3.97963i	0.298853	+	0.225302i
$313$		−	3.44804i		−	0.194895i	−0.995241	−	0.0974473i	$-0.968932\pi$
$313$		−	3.44804i		−	0.194895i	0.995241	−	0.0974473i	$-0.0310677\pi$
$314$	−24.7177	+	24.7177i	−1.39490	+	1.39490i
$315$		0			0
$316$			4.85825i			0.273298i
$317$	−22.3865	−	22.3865i	−1.25735	−	1.25735i	−0.952353	−	0.304997i	$-0.901345\pi$
$317$	−22.3865	−	22.3865i	−1.25735	−	1.25735i	−0.304997	−	0.952353i	$-0.598655\pi$
$318$	19.1207	−	19.1207i	1.07224	−	1.07224i
$319$	−0.224191	+	0.224191i	−0.0125523	+	0.0125523i
$320$	11.8056	+	11.8056i	0.659950	+	0.659950i
$321$			10.5625i			0.589541i
$322$		0			0
$323$	−9.02953	+	9.02953i	−0.502416	+	0.502416i
$324$		−	8.09501i		−	0.449723i
$325$	3.36086	+	23.9510i	0.186427	+	1.32856i
$326$	−24.6437			−1.36489
$327$	−21.8601	+	21.8601i	−1.20887	+	1.20887i
$328$		−	4.53646i		−	0.250484i
$329$		0			0
$330$	21.0448	+	21.0448i	1.15848	+	1.15848i
$331$	23.0593	+	23.0593i	1.26745	+	1.26745i	0.947399	+	0.320054i	$0.103701\pi$
$331$	23.0593	+	23.0593i	1.26745	+	1.26745i	0.320054	+	0.947399i	$0.396299\pi$
$332$	0.826209	+	0.826209i	0.0453441	+	0.0453441i
$333$	−0.617157	+	0.617157i	−0.0338200	+	0.0338200i
$334$		−	28.8057i		−	1.57618i
$335$	23.6319			1.29115
$336$		0			0
$337$		−	8.54695i		−	0.465582i	−0.972527	−	0.232791i	$-0.925214\pi$
$337$		−	8.54695i		−	0.465582i	0.972527	−	0.232791i	$-0.0747858\pi$
$338$	21.6783	+	12.0286i	1.17914	+	0.654271i
$339$			22.1471i			1.20286i
$340$	9.71073	+	9.71073i	0.526638	+	0.526638i
$341$			4.38799i			0.237623i
$342$	39.8365			2.15411
$343$		0			0
$344$	0.275383	+	0.275383i	0.0148476	+	0.0148476i
$345$	29.3805	−	29.3805i	1.58179	−	1.58179i
$346$	−3.53330	−	3.53330i	−0.189951	−	0.189951i
$347$	2.73578			0.146864			0.0734321	−	0.997300i	$-0.476605\pi$
$347$	2.73578			0.146864			0.0734321	+	0.997300i	$0.476605\pi$
$348$	0.797763			0.0427646
$349$	−8.57575	−	8.57575i	−0.459049	−	0.459049i	0.439294	−	0.898343i	$-0.355229\pi$
$349$	−8.57575	−	8.57575i	−0.459049	−	0.459049i	−0.898343	+	0.439294i	$0.855229\pi$
$350$		0			0
$351$	−1.34110	−	9.55732i	−0.0715828	−	0.510132i
$352$	−12.7068			−0.677276
$353$	7.75839	−	7.75839i	0.412937	−	0.412937i	−0.469823	−	0.882761i	$-0.655682\pi$
$353$	7.75839	−	7.75839i	0.412937	−	0.412937i	0.882761	+	0.469823i	$0.155682\pi$
$354$	72.8794			3.87350
$355$	8.27109			0.438984
$356$	8.62981	−	8.62981i	0.457379	−	0.457379i
$357$		0			0
$358$	−34.1957	+	34.1957i	−1.80730	+	1.80730i
$359$	−0.757181	+	0.757181i	−0.0399625	+	0.0399625i	−0.726806	−	0.686843i	$-0.758996\pi$
$359$	−0.757181	+	0.757181i	−0.0399625	+	0.0399625i	0.686843	+	0.726806i	$0.258996\pi$
$360$			9.50341i			0.500874i
$361$		−	8.12359i		−	0.427557i
$362$	−1.35342	−	1.35342i	−0.0711343	−	0.0711343i
$363$	21.2695			1.11636
$364$		0			0
$365$	−41.7459			−2.18508
$366$	−5.39074	−	5.39074i	−0.281778	−	0.281778i
$367$		−	7.76773i		−	0.405472i	−0.979233	−	0.202736i	$-0.935017\pi$
$367$		−	7.76773i		−	0.405472i	0.979233	−	0.202736i	$-0.0649833\pi$
$368$			21.0704i			1.09837i
$369$	−18.5801	+	18.5801i	−0.967241	+	0.967241i
$370$	1.00406	−	1.00406i	0.0521984	−	0.0521984i
$371$		0			0
$372$	7.80712	−	7.80712i	0.404781	−	0.404781i
$373$	−17.7824			−0.920737			−0.460368	−	0.887728i	$-0.652283\pi$
$373$	−17.7824			−0.920737			−0.460368	+	0.887728i	$0.652283\pi$
$374$	−8.05452			−0.416489
$375$	−10.9415	+	10.9415i	−0.565014	+	0.565014i
$376$	2.67037			0.137714
$377$	−0.657209	+	0.0922209i	−0.0338480	+	0.00474962i
$378$		0			0
$379$	−25.3241	−	25.3241i	−1.30081	−	1.30081i	−0.927846	−	0.372964i	$-0.878341\pi$
$379$	−25.3241	−	25.3241i	−1.30081	−	1.30081i	−0.372964	−	0.927846i	$-0.621659\pi$
$380$	−29.1698			−1.49638
$381$	32.0379			1.64135
$382$	−1.41644	−	1.41644i	−0.0724714	−	0.0724714i
$383$	−14.6854	+	14.6854i	−0.750391	+	0.750391i	−0.974552	−	0.224161i	$-0.928036\pi$
$383$	−14.6854	+	14.6854i	−0.750391	+	0.750391i	0.224161	+	0.974552i	$0.428036\pi$
$384$	−10.2010	−	10.2010i	−0.520567	−	0.520567i
$385$		0			0
$386$	3.77049			0.191913
$387$		−	2.25578i		−	0.114668i
$388$	−19.7981	−	19.7981i	−1.00510	−	1.00510i
$389$			7.96839i			0.404013i	0.979384	+	0.202007i	$0.0647463\pi$
$389$			7.96839i			0.404013i	−0.979384	+	0.202007i	$0.935254\pi$
$390$	8.65677	+	61.6921i	0.438353	+	3.12390i
$391$			11.2449i			0.568677i
$392$		0			0
$393$	4.72508			0.238349
$394$		−	9.06446i		−	0.456661i
$395$	7.18098	−	7.18098i	0.361314	−	0.361314i
$396$	7.99680	+	7.99680i	0.401854	+	0.401854i
$397$	21.7266	+	21.7266i	1.09043	+	1.09043i	0.995483	+	0.0949450i	$0.0302675\pi$
$397$	21.7266	+	21.7266i	1.09043	+	1.09043i	0.0949450	+	0.995483i	$0.469732\pi$
$398$	−13.7631	−	13.7631i	−0.689880	−	0.689880i
$399$		0			0
$400$		−	30.8186i		−	1.54093i
$401$	15.9341	−	15.9341i	0.795710	−	0.795710i	−0.186706	−	0.982416i	$-0.559781\pi$
$401$	15.9341	−	15.9341i	0.795710	−	0.795710i	0.982416	+	0.186706i	$0.0597812\pi$
$402$	34.8747			1.73939
$403$	−5.52912	+	7.33412i	−0.275425	+	0.365339i
$404$		−	13.4670i		−	0.670007i
$405$	−11.9652	+	11.9652i	−0.594557	+	0.594557i
$406$		0			0
$407$			0.374831i			0.0185797i
$408$	−3.17889	−	3.17889i	−0.157379	−	0.157379i
$409$	27.9033	−	27.9033i	1.37973	−	1.37973i	0.534669	−	0.845061i	$-0.320436\pi$
$409$	27.9033	−	27.9033i	1.37973	−	1.37973i	0.845061	−	0.534669i	$-0.179564\pi$
$410$	30.2280	−	30.2280i	1.49286	−	1.49286i
$411$	−36.3557	−	36.3557i	−1.79329	−	1.79329i
$412$		−	12.2729i		−	0.604642i
$413$		0			0
$414$	24.8051	−	24.8051i	1.21910	−	1.21910i
$415$		−	2.44244i		−	0.119895i
$416$	−21.2383	−	16.0113i	−1.04129	−	0.785020i
$417$	−35.9746			−1.76169
$418$	12.0974	−	12.0974i	0.591703	−	0.591703i
$419$			6.86945i			0.335595i	0.985821	+	0.167797i	$0.0536654\pi$
$419$			6.86945i			0.335595i	−0.985821	+	0.167797i	$0.946335\pi$
$420$		0			0
$421$	−16.8752	−	16.8752i	−0.822445	−	0.822445i	0.164013	−	0.986458i	$-0.447556\pi$
$421$	−16.8752	−	16.8752i	−0.822445	−	0.822445i	−0.986458	+	0.164013i	$0.947556\pi$
$422$	21.7642	+	21.7642i	1.05946	+	1.05946i
$423$	−10.9371	−	10.9371i	−0.531779	−	0.531779i
$424$	2.62210	−	2.62210i	0.127340	−	0.127340i
$425$		−	16.4473i		−	0.797809i
$426$	12.2061			0.591386
$427$		0			0
$428$		−	6.52981i		−	0.315630i
$429$	−13.1312	−	9.89950i	−0.633981	−	0.477952i
$430$			3.66995i			0.176981i
$431$	−25.1375	−	25.1375i	−1.21083	−	1.21083i	−0.970754	−	0.240075i	$-0.922828\pi$
$431$	−25.1375	−	25.1375i	−1.21083	−	1.21083i	−0.240075	−	0.970754i	$-0.577172\pi$
$432$			12.2977i			0.591673i
$433$	6.53945			0.314266			0.157133	−	0.987577i	$-0.449775\pi$
$433$	6.53945			0.314266			0.157133	+	0.987577i	$0.449775\pi$
$434$		0			0
$435$	−1.17917	−	1.17917i	−0.0565370	−	0.0565370i
$436$	13.5141	−	13.5141i	0.647207	−	0.647207i
$437$	−16.8891	−	16.8891i	−0.807915	−	0.807915i
$438$	−61.6065			−2.94367
$439$	24.5863			1.17344			0.586719	−	0.809791i	$-0.300419\pi$
$439$	24.5863			1.17344			0.586719	+	0.809791i	$0.300419\pi$
$440$	2.88595	+	2.88595i	0.137582	+	0.137582i
$441$		0			0
$442$	−13.4624	−	10.1492i	−0.640340	−	0.482746i
$443$	−15.5990			−0.741133			−0.370566	−	0.928806i	$-0.620836\pi$
$443$	−15.5990			−0.741133			−0.370566	+	0.928806i	$0.620836\pi$
$444$	0.666901	−	0.666901i	0.0316497	−	0.0316497i
$445$	−25.5114			−1.20936
$446$	−0.253378			−0.0119978
$447$	6.88038	−	6.88038i	0.325431	−	0.325431i
$448$		0			0
$449$	28.6271	−	28.6271i	1.35100	−	1.35100i	0.466445	−	0.884550i	$-0.345535\pi$
$449$	28.6271	−	28.6271i	1.35100	−	1.35100i	0.884550	−	0.466445i	$-0.154465\pi$
$450$	−36.2811	+	36.2811i	−1.71031	+	1.71031i
$451$			11.2846i			0.531373i
$452$		−	13.6915i		−	0.643992i
$453$	−33.7086	−	33.7086i	−1.58377	−	1.58377i
$454$	−50.5601			−2.37290
$455$		0			0
$456$	9.54900			0.447173
$457$	−9.24111	−	9.24111i	−0.432281	−	0.432281i	0.457123	−	0.889404i	$-0.348880\pi$
$457$	−9.24111	−	9.24111i	−0.432281	−	0.432281i	−0.889404	+	0.457123i	$0.848880\pi$
$458$			33.5929i			1.56969i
$459$			6.56304i			0.306336i
$460$	−18.1632	+	18.1632i	−0.846865	+	0.846865i
$461$	3.55813	−	3.55813i	0.165719	−	0.165719i	−0.619376	−	0.785095i	$-0.712614\pi$
$461$	3.55813	−	3.55813i	0.165719	−	0.165719i	0.785095	+	0.619376i	$0.212614\pi$
$462$		0			0
$463$	−11.6246	+	11.6246i	−0.540241	+	0.540241i	−0.923600	−	0.383359i	$-0.874767\pi$
$463$	−11.6246	+	11.6246i	−0.540241	+	0.540241i	0.383359	+	0.923600i	$0.374767\pi$
$464$	0.845651			0.0392584
$465$	−23.0794			−1.07028
$466$	6.85964	−	6.85964i	0.317767	−	0.317767i
$467$	−5.73082			−0.265191			−0.132595	−	0.991170i	$-0.542331\pi$
$467$	−5.73082			−0.265191			−0.132595	+	0.991170i	$0.542331\pi$
$468$	3.28948	+	23.4423i	0.152056	+	1.08362i
$469$		0			0
$470$	17.7936	+	17.7936i	0.820757	+	0.820757i
$471$	48.5338			2.23632
$472$	9.99423			0.460022
$473$	−0.685027	−	0.685027i	−0.0314976	−	0.0314976i
$474$	10.5973	−	10.5973i	0.486752	−	0.486752i
$475$	24.7028	+	24.7028i	1.13344	+	1.13344i
$476$		0			0
$477$	−21.4788			−0.983445
$478$		−	35.1101i		−	1.60590i
$479$	−14.3160	−	14.3160i	−0.654114	−	0.654114i	0.299867	−	0.953981i	$-0.403058\pi$
$479$	−14.3160	−	14.3160i	−0.654114	−	0.654114i	−0.953981	+	0.299867i	$0.903058\pi$
$480$		−	66.8338i		−	3.05053i
$481$	−0.472309	+	0.626496i	−0.0215355	+	0.0285658i
$482$			5.20006i			0.236856i
$483$		0			0
$484$	−13.1490			−0.597681
$485$			58.5272i			2.65759i
$486$	−28.4862	+	28.4862i	−1.29216	+	1.29216i
$487$	−1.12008	−	1.12008i	−0.0507557	−	0.0507557i	0.681273	−	0.732029i	$-0.261426\pi$
$487$	−1.12008	−	1.12008i	−0.0507557	−	0.0507557i	−0.732029	+	0.681273i	$0.761426\pi$
$488$	−0.739252	−	0.739252i	−0.0334644	−	0.0334644i
$489$	24.1942	+	24.1942i	1.09410	+	1.09410i
$490$		0			0
$491$			22.7308i			1.02583i	0.858440	+	0.512913i	$0.171434\pi$
$491$			22.7308i			1.02583i	−0.858440	+	0.512913i	$0.828566\pi$
$492$	20.0777	−	20.0777i	0.905171	−	0.905171i
$493$	0.451307			0.0203259
$494$	35.4631	−	4.97626i	1.59556	−	0.223892i
$495$		−	23.6401i		−	1.06255i
$496$	8.27577	−	8.27577i	0.371593	−	0.371593i
$497$		0			0
$498$		−	3.60443i		−	0.161518i
$499$	−4.16766	−	4.16766i	−0.186570	−	0.186570i	0.607641	−	0.794212i	$-0.292116\pi$
$499$	−4.16766	−	4.16766i	−0.186570	−	0.186570i	−0.794212	+	0.607641i	$0.792116\pi$
$500$	6.76408	−	6.76408i	0.302499	−	0.302499i
$501$	−28.2804	+	28.2804i	−1.26347	+	1.26347i
$502$	−28.8889	−	28.8889i	−1.28938	−	1.28938i
$503$		−	11.3499i		−	0.506069i	−0.967457	−	0.253035i	$-0.918571\pi$
$503$		−	11.3499i		−	0.506069i	0.967457	−	0.253035i	$-0.0814286\pi$
$504$		0			0
$505$	−19.9055	+	19.9055i	−0.885784	+	0.885784i
$506$		−	15.0654i		−	0.669739i
$507$	−9.47367	−	33.0922i	−0.420741	−	1.46968i
$508$	−19.8060			−0.878751
$509$	−20.9705	+	20.9705i	−0.929501	+	0.929501i	−0.997674	−	0.0681727i	$-0.978283\pi$
$509$	−20.9705	+	20.9705i	−0.929501	+	0.929501i	0.0681727	+	0.997674i	$0.478283\pi$
$510$		−	42.3642i		−	1.87592i
$511$		0			0
$512$	19.4659	+	19.4659i	0.860279	+	0.860279i
$513$	−9.85728	−	9.85728i	−0.435210	−	0.435210i
$514$	−12.9580	−	12.9580i	−0.571553	−	0.571553i
$515$	−18.1405	+	18.1405i	−0.799368	+	0.799368i
$516$			2.43760i			0.107309i
$517$	−6.64265			−0.292143
$518$		0			0
$519$			6.93773i			0.304532i
$520$	1.18714	+	8.46007i	0.0520593	+	0.370999i
$521$		−	40.4706i		−	1.77305i	−0.462682	−	0.886524i	$-0.653113\pi$
$521$		−	40.4706i		−	1.77305i	0.462682	−	0.886524i	$-0.346887\pi$
$522$	−0.995540	−	0.995540i	−0.0435736	−	0.0435736i
$523$		−	33.7833i		−	1.47724i	−0.674121	−	0.738621i	$-0.735477\pi$
$523$		−	33.7833i		−	1.47724i	0.674121	−	0.738621i	$-0.264523\pi$
$524$	−2.92108			−0.127608
$525$		0			0
$526$	−10.6127	−	10.6127i	−0.462734	−	0.462734i
$527$	4.41661	−	4.41661i	0.192391	−	0.192391i
$528$	14.8172	+	14.8172i	0.644835	+	0.644835i
$529$	1.96728			0.0855338
$530$	34.9439			1.51787
$531$	−40.9336	−	40.9336i	−1.77637	−	1.77637i
$532$		0			0
$533$	−14.2193	+	18.8612i	−0.615906	+	0.816971i
$534$	−37.6485			−1.62921
$535$	−9.65171	+	9.65171i	−0.417280	+	0.417280i
$536$	4.78251			0.206573
$537$	67.1442			2.89749
$538$	−5.35850	+	5.35850i	−0.231021	+	0.231021i
$539$		0			0
$540$	−10.6009	+	10.6009i	−0.456192	+	0.456192i
$541$	−11.3745	+	11.3745i	−0.489029	+	0.489029i	−0.908000	−	0.418971i	$-0.862391\pi$
$541$	−11.3745	+	11.3745i	−0.489029	+	0.489029i	0.418971	+	0.908000i	$0.362391\pi$
$542$			32.6028i			1.40041i
$543$			2.65748i			0.114043i
$544$	12.7897	+	12.7897i	0.548354	+	0.548354i
$545$	−39.9503			−1.71128
$546$		0			0
$547$	4.19513			0.179371			0.0896853	−	0.995970i	$-0.471414\pi$
$547$	4.19513			0.179371			0.0896853	+	0.995970i	$0.471414\pi$
$548$	22.4753	+	22.4753i	0.960098	+	0.960098i
$549$			6.05554i			0.258444i
$550$			22.0354i			0.939591i
$551$	−0.677835	+	0.677835i	−0.0288768	+	0.0288768i
$552$	5.94589	−	5.94589i	0.253074	−	0.253074i
$553$		0			0
$554$	33.8363	−	33.8363i	1.43757	−	1.43757i
$555$	−1.97149			−0.0836852
$556$	22.2398			0.943176
$557$	24.0463	−	24.0463i	1.01887	−	1.01887i	0.0190554	−	0.999818i	$-0.493934\pi$
$557$	24.0463	−	24.0463i	1.01887	−	1.01887i	0.999818	−	0.0190554i	$-0.00606588\pi$
$558$	−19.4853			−0.824877
$559$	−0.281785	−	2.00813i	−0.0119183	−	0.0849349i
$560$		0			0
$561$	7.90763	+	7.90763i	0.333860	+	0.333860i
$562$	−5.81578			−0.245324
$563$	−29.7781			−1.25500			−0.627498	−	0.778618i	$-0.715921\pi$
$563$	−29.7781			−1.25500			−0.627498	+	0.778618i	$0.715921\pi$
$564$	11.8186	+	11.8186i	0.497654	+	0.497654i
$565$	−20.2373	+	20.2373i	−0.851391	+	0.851391i
$566$	15.3177	+	15.3177i	0.643849	+	0.643849i
$567$		0			0
$568$	1.67386			0.0702338
$569$		−	12.6038i		−	0.528379i	−0.964471	−	0.264189i	$-0.914896\pi$
$569$		−	12.6038i		−	0.528379i	0.964471	−	0.264189i	$-0.0851044\pi$
$570$	63.6284	+	63.6284i	2.66510	+	2.66510i
$571$		−	4.98312i		−	0.208537i	−0.994549	−	0.104269i	$-0.966750\pi$
$571$		−	4.98312i		−	0.208537i	0.994549	−	0.104269i	$-0.0332501\pi$
$572$	8.11781	+	6.11994i	0.339423	+	0.255887i
$573$			2.78122i			0.116187i
$574$		0			0
$575$	30.7634			1.28292
$576$		−	19.5706i		−	0.815442i
$577$	0.412530	−	0.412530i	0.0171739	−	0.0171739i	−0.698468	−	0.715642i	$-0.746134\pi$
$577$	0.412530	−	0.412530i	0.0171739	−	0.0171739i	0.715642	+	0.698468i	$0.246134\pi$
$578$	−14.8174	−	14.8174i	−0.616323	−	0.616323i
$579$	−3.70173	−	3.70173i	−0.153839	−	0.153839i
$580$	0.728973	+	0.728973i	0.0302689	+	0.0302689i
$581$		0			0
$582$			86.3716i			3.58022i
$583$	−6.52258	+	6.52258i	−0.270138	+	0.270138i
$584$	−8.44834			−0.349595
$585$	29.7879	−	39.5123i	1.23158	−	1.63363i
$586$			27.7341i			1.14568i
$587$	2.10756	−	2.10756i	0.0869883	−	0.0869883i	−0.662274	−	0.749262i	$-0.730408\pi$
$587$	2.10756	−	2.10756i	0.0869883	−	0.0869883i	0.749262	+	0.662274i	$0.230408\pi$
$588$		0			0
$589$			13.2670i			0.546656i
$590$	66.5951	+	66.5951i	2.74168	+	2.74168i
$591$	−8.89915	+	8.89915i	−0.366062	+	0.366062i
$592$	0.706934	−	0.706934i	0.0290548	−	0.0290548i
$593$	0.992200	+	0.992200i	0.0407448	+	0.0407448i	0.727186	−	0.686441i	$-0.240828\pi$
$593$	0.992200	+	0.992200i	0.0407448	+	0.0407448i	−0.686441	+	0.727186i	$0.740828\pi$
$594$		−	8.79289i		−	0.360777i
$595$		0			0
$596$	−4.25350	+	4.25350i	−0.174230	+	0.174230i
$597$			27.0241i			1.10602i
$598$	18.9833	−	25.1804i	0.776284	−	1.02970i
$599$	46.3213			1.89264			0.946319	−	0.323234i	$-0.104770\pi$
$599$	46.3213			1.89264			0.946319	+	0.323234i	$0.104770\pi$
$600$	−8.69673	+	8.69673i	−0.355043	+	0.355043i
$601$			41.2270i			1.68169i	0.541279	+	0.840843i	$0.317940\pi$
$601$			41.2270i			1.68169i	−0.541279	+	0.840843i	$0.682060\pi$
$602$		0			0
$603$	−19.5878	−	19.5878i	−0.797678	−	0.797678i
$604$	20.8389	+	20.8389i	0.847923	+	0.847923i
$605$	19.4355	+	19.4355i	0.790165	+	0.790165i
$606$	−29.3756	+	29.3756i	−1.19330	+	1.19330i
$607$		−	8.28510i		−	0.336282i	−0.985763	−	0.168141i	$-0.946224\pi$
$607$		−	8.28510i		−	0.336282i	0.985763	−	0.168141i	$-0.0537764\pi$
$608$	−38.4187			−1.55808
$609$		0			0
$610$		−	9.85180i		−	0.398888i
$611$	−11.1026	−	8.37012i	−0.449162	−	0.338619i
$612$		−	16.0979i		−	0.650720i
$613$	12.5961	+	12.5961i	0.508751	+	0.508751i	0.914143	−	0.405392i	$-0.132865\pi$
$613$	12.5961	+	12.5961i	0.508751	+	0.508751i	−0.405392	+	0.914143i	$0.632865\pi$
$614$		−	18.9274i		−	0.763847i
$615$	−59.3536			−2.39337
$616$		0			0
$617$	−1.41807	−	1.41807i	−0.0570895	−	0.0570895i	0.677986	−	0.735075i	$-0.262853\pi$
$617$	−1.41807	−	1.41807i	−0.0570895	−	0.0570895i	−0.735075	+	0.677986i	$0.762853\pi$
$618$	−26.7709	+	26.7709i	−1.07688	+	1.07688i
$619$	−7.20890	−	7.20890i	−0.289750	−	0.289750i	0.547231	−	0.836981i	$-0.315682\pi$
$619$	−7.20890	−	7.20890i	−0.289750	−	0.289750i	−0.836981	+	0.547231i	$0.815682\pi$
$620$	14.2678			0.573011
$621$	−12.2757			−0.492607
$622$	3.40781	+	3.40781i	0.136641	+	0.136641i
$623$		0			0
$624$	6.09504	+	43.4360i	0.243997	+	1.73883i
$625$	13.5435			0.541742
$626$	4.64967	−	4.64967i	0.185838	−	0.185838i
$627$	−23.7535			−0.948625
$628$	−30.0039			−1.19729
$629$	0.377276	−	0.377276i	0.0150430	−	0.0150430i
$630$		0			0
$631$	−4.32633	+	4.32633i	−0.172228	+	0.172228i	−0.787958	−	0.615729i	$-0.788861\pi$
$631$	−4.32633	+	4.32633i	−0.172228	+	0.172228i	0.615729	+	0.787958i	$0.288861\pi$
$632$	1.45325	−	1.45325i	0.0578073	−	0.0578073i
$633$		−	42.7345i		−	1.69854i
$634$		−	60.3763i		−	2.39785i
$635$	29.2753	+	29.2753i	1.16175	+	1.16175i
$636$	23.2100			0.920336
$637$		0			0
$638$	−0.604643			−0.0239380
$639$	−6.85569	−	6.85569i	−0.271207	−	0.271207i
$640$		−	18.6427i		−	0.736919i
$641$			29.2074i			1.15362i	0.816877	+	0.576812i	$0.195703\pi$
$641$			29.2074i			1.15362i	−0.816877	+	0.576812i	$0.804297\pi$
$642$	−14.2435	+	14.2435i	−0.562147	+	0.562147i
$643$	14.6743	−	14.6743i	0.578699	−	0.578699i	−0.355846	−	0.934545i	$-0.615807\pi$
$643$	14.6743	−	14.6743i	0.578699	−	0.578699i	0.934545	+	0.355846i	$0.115807\pi$
$644$		0			0
$645$	3.60302	−	3.60302i	0.141869	−	0.141869i
$646$	−24.3526			−0.958140
$647$	9.71986			0.382127			0.191064	−	0.981578i	$-0.438806\pi$
$647$	9.71986			0.382127			0.191064	+	0.981578i	$0.438806\pi$
$648$	−2.42147	+	2.42147i	−0.0951242	+	0.0951242i
$649$	−24.8611			−0.975882
$650$	−27.7658	+	36.8301i	−1.08907	+	1.44459i
$651$		0			0
$652$	−14.9570	−	14.9570i	−0.585763	−	0.585763i
$653$	14.3250			0.560579			0.280289	−	0.959916i	$-0.409570\pi$
$653$	14.3250			0.560579			0.280289	+	0.959916i	$0.409570\pi$
$654$	−58.9567			−2.30539
$655$	4.31764	+	4.31764i	0.168704	+	0.168704i
$656$	21.2829	−	21.2829i	0.830957	−	0.830957i
$657$	34.6021	+	34.6021i	1.34995	+	1.34995i
$658$		0			0
$659$	−19.4182			−0.756424			−0.378212	−	0.925719i	$-0.623461\pi$
$659$	−19.4182			−0.756424			−0.378212	+	0.925719i	$0.623461\pi$
$660$			25.5456i			0.994359i
$661$	17.8557	+	17.8557i	0.694507	+	0.694507i	0.963220	−	0.268713i	$-0.0865983\pi$
$661$	17.8557	+	17.8557i	0.694507	+	0.694507i	−0.268713	+	0.963220i	$0.586598\pi$
$662$			62.1908i			2.41712i
$663$	3.25280	+	23.1809i	0.126328	+	0.900273i
$664$		−	0.494289i		−	0.0191821i
$665$		0			0
$666$	−1.66447			−0.0644970
$667$			0.844138i			0.0326852i
$668$	17.4831	−	17.4831i	0.676442	−	0.676442i
$669$	0.248757	+	0.248757i	0.00961751	+	0.00961751i
$670$	31.8675	+	31.8675i	1.23115	+	1.23115i
$671$	1.83892	+	1.83892i	0.0709908	+	0.0709908i
$672$		0			0
$673$		−	39.3180i		−	1.51560i	−0.652488	−	0.757799i	$-0.726275\pi$
$673$		−	39.3180i		−	1.51560i	0.652488	−	0.757799i	$-0.273725\pi$
$674$	11.5255	−	11.5255i	0.443947	−	0.443947i
$675$	17.9550			0.691088
$676$	5.85669	+	20.4578i	0.225257	+	0.786839i
$677$			14.0135i			0.538584i	0.963059	+	0.269292i	$0.0867897\pi$
$677$			14.0135i			0.538584i	−0.963059	+	0.269292i	$0.913210\pi$
$678$	−29.8653	+	29.8653i	−1.14697	+	1.14697i
$679$		0			0
$680$		−	5.80956i		−	0.222786i
$681$	49.6380	+	49.6380i	1.90213	+	1.90213i
$682$	−5.91720	+	5.91720i	−0.226581	+	0.226581i
$683$	−4.22369	+	4.22369i	−0.161615	+	0.161615i	−0.783282	−	0.621667i	$-0.786456\pi$
$683$	−4.22369	+	4.22369i	−0.161615	+	0.161615i	0.621667	+	0.783282i	$0.286456\pi$
$684$	24.1781	+	24.1781i	0.924473	+	0.924473i
$685$		−	66.4415i		−	2.53860i
$686$		0			0
$687$	32.9803	−	32.9803i	1.25828	−	1.25828i
$688$			2.58393i			0.0985113i
$689$	−19.1207	+	2.68306i	−0.728442	+	0.102216i
$690$	79.2392			3.01658
$691$	17.5853	−	17.5853i	0.668977	−	0.668977i	−0.288503	−	0.957479i	$-0.593157\pi$
$691$	17.5853	−	17.5853i	0.668977	−	0.668977i	0.957479	+	0.288503i	$0.0931574\pi$
$692$		−	4.28895i		−	0.163041i
$693$		0			0
$694$	3.68919	+	3.68919i	0.140040	+	0.140040i
$695$	−32.8726	−	32.8726i	−1.24693	−	1.24693i
$696$	−0.238635	−	0.238635i	−0.00904545	−	0.00904545i
$697$	11.3583	−	11.3583i	0.430224	−	0.430224i
$698$		−	23.1288i		−	0.875436i
$699$	−13.4691			−0.509448
$700$		0			0
$701$			50.8136i			1.91920i	0.281364	+	0.959601i	$0.409213\pi$
$701$			50.8136i			1.91920i	−0.281364	+	0.959601i	$0.590787\pi$
$702$	11.0796	−	14.6965i	0.418171	−	0.554684i
$703$			1.13329i			0.0427429i
$704$	−5.94312	−	5.94312i	−0.223990	−	0.223990i
$705$		−	34.9382i		−	1.31585i
$706$	20.9243			0.787498
$707$		0			0
$708$	44.2329	+	44.2329i	1.66237	+	1.66237i
$709$	11.5687	−	11.5687i	0.434473	−	0.434473i	−0.455674	−	0.890147i	$-0.650602\pi$
$709$	11.5687	−	11.5687i	0.434473	−	0.434473i	0.890147	+	0.455674i	$0.150602\pi$
$710$	11.1536	+	11.1536i	0.418585	+	0.418585i
$711$	−11.9042			−0.446444
$712$	−5.16288			−0.193487
$713$	8.26096	+	8.26096i	0.309376	+	0.309376i
$714$		0			0
$715$	−2.95305	−	21.0448i	−0.110438	−	0.787031i
$716$	−41.5090			−1.55126
$717$	−34.4698	+	34.4698i	−1.28730	+	1.28730i
$718$	−2.04211			−0.0762110
$719$	−26.5364			−0.989642			−0.494821	−	0.868995i	$-0.664766\pi$
$719$	−26.5364			−0.989642			−0.494821	+	0.868995i	$0.664766\pi$
$720$	−44.5854	+	44.5854i	−1.66160	+	1.66160i
$721$		0			0
$722$	10.9546	−	10.9546i	0.407690	−	0.407690i
$723$	5.10522	−	5.10522i	0.189865	−	0.189865i
$724$		−	1.64287i		−	0.0610569i
$725$		−	1.23467i		−	0.0458547i
$726$	28.6820	+	28.6820i	1.06449	+	1.06449i
$727$	−30.2407			−1.12157			−0.560783	−	0.827963i	$-0.689500\pi$
$727$	−30.2407			−1.12157			−0.560783	+	0.827963i	$0.689500\pi$
$728$		0			0
$729$	41.0975			1.52213
$730$	−56.2943	−	56.2943i	−2.08354	−	2.08354i
$731$			1.37899i			0.0510038i
$732$		−	6.54363i		−	0.241859i
$733$	−9.43319	+	9.43319i	−0.348423	+	0.348423i	−0.859522	−	0.511099i	$-0.829239\pi$
$733$	−9.43319	+	9.43319i	−0.348423	+	0.348423i	0.511099	+	0.859522i	$0.329239\pi$
$734$	10.4748	−	10.4748i	0.386631	−	0.386631i
$735$		0			0
$736$	−23.9223	+	23.9223i	−0.881786	+	0.881786i
$737$	−11.8967			−0.438220
$738$	−50.1104			−1.84459
$739$	−6.21982	+	6.21982i	−0.228800	+	0.228800i	−0.812191	−	0.583391i	$-0.801725\pi$
$739$	−6.21982	+	6.21982i	−0.228800	+	0.228800i	0.583391	+	0.812191i	$0.301725\pi$
$740$	1.21879			0.0448036
$741$	−39.7019	−	29.9308i	−1.45848	−	1.09954i
$742$		0			0
$743$	−7.57023	−	7.57023i	−0.277725	−	0.277725i	0.554475	−	0.832200i	$-0.312919\pi$
$743$	−7.57023	−	7.57023i	−0.277725	−	0.277725i	−0.832200	+	0.554475i	$0.812919\pi$
$744$	−4.67070			−0.171236
$745$	12.5742			0.460683
$746$	−23.9795	−	23.9795i	−0.877952	−	0.877952i
$747$	−2.02447	+	2.02447i	−0.0740716	+	0.0740716i
$748$	−4.88855	−	4.88855i	−0.178743	−	0.178743i
$749$		0			0
$750$	−29.5091			−1.07752
$751$			36.8729i			1.34551i	0.739864	+	0.672756i	$0.234890\pi$
$751$			36.8729i			1.34551i	−0.739864	+	0.672756i	$0.765110\pi$
$752$	12.5281	+	12.5281i	0.456852	+	0.456852i
$753$			56.7242i			2.06714i
$754$	−1.01060	−	0.761885i	−0.0368040	−	0.0277462i
$755$		−	61.6040i		−	2.24200i
$756$		0			0
$757$	4.46764			0.162379			0.0811896	−	0.996699i	$-0.474128\pi$
$757$	4.46764			0.162379			0.0811896	+	0.996699i	$0.474128\pi$
$758$		−	68.2989i		−	2.48073i
$759$	−14.7907	+	14.7907i	−0.536867	+	0.536867i
$760$	8.72560	+	8.72560i	0.316511	+	0.316511i
$761$	−31.6430	−	31.6430i	−1.14706	−	1.14706i	−0.987128	−	0.159931i	$-0.948873\pi$
$761$	−31.6430	−	31.6430i	−1.14706	−	1.14706i	−0.159931	−	0.987128i	$-0.551127\pi$
$762$	43.2030	+	43.2030i	1.56508	+	1.56508i
$763$		0			0
$764$		−	1.71937i		−	0.0622046i
$765$	−23.7943	+	23.7943i	−0.860286	+	0.860286i
$766$	−39.6066			−1.43104
$767$	−41.5530	−	31.3264i	−1.50039	−	1.13113i
$768$		−	53.3512i		−	1.92515i
$769$	19.6232	−	19.6232i	0.707631	−	0.707631i	−0.258406	−	0.966036i	$-0.583197\pi$
$769$	19.6232	−	19.6232i	0.707631	−	0.707631i	0.966036	+	0.258406i	$0.0831971\pi$
$770$		0			0
$771$			25.4434i			0.916321i
$772$	2.28843	+	2.28843i	0.0823626	+	0.0823626i
$773$	−7.39513	+	7.39513i	−0.265985	+	0.265985i	−0.827480	−	0.561495i	$-0.810226\pi$
$773$	−7.39513	+	7.39513i	−0.265985	+	0.265985i	0.561495	+	0.827480i	$0.310226\pi$
$774$	3.04192	−	3.04192i	0.109340	−	0.109340i
$775$	−12.0829	−	12.0829i	−0.434029	−	0.434029i
$776$			11.8445i			0.425192i
$777$		0			0
$778$	−10.7454	+	10.7454i	−0.385240	+	0.385240i
$779$			34.1188i			1.22243i
$780$	−32.1889	+	42.6970i	−1.15255	+	1.52880i
$781$	−4.16381			−0.148993
$782$	−15.1637	+	15.1637i	−0.542252	+	0.542252i
$783$			0.492679i			0.0176069i
$784$		0			0
$785$	44.3488	+	44.3488i	1.58287	+	1.58287i
$786$	6.37177	+	6.37177i	0.227273	+	0.227273i
$787$	−4.69753	−	4.69753i	−0.167449	−	0.167449i	0.618408	−	0.785857i	$-0.287778\pi$
$787$	−4.69753	−	4.69753i	−0.167449	−	0.167449i	−0.785857	+	0.618408i	$0.787778\pi$
$788$	5.50151	−	5.50151i	0.195983	−	0.195983i
$789$			20.8382i			0.741860i
$790$	19.3671			0.689050
$791$		0			0
$792$		−	4.78418i		−	0.169998i
$793$	0.756440	+	5.39074i	0.0268620	+	0.191431i
$794$			58.5966i			2.07952i
$795$	−34.3067	−	34.3067i	−1.21673	−	1.21673i
$796$		−	16.7065i		−	0.592147i
$797$	21.9115			0.776146			0.388073	−	0.921629i	$-0.373141\pi$
$797$	21.9115			0.776146			0.388073	+	0.921629i	$0.373141\pi$
$798$		0			0
$799$	6.68598	+	6.68598i	0.236533	+	0.236533i
$800$	34.9898	−	34.9898i	1.23708	−	1.23708i
$801$	21.1457	+	21.1457i	0.747148	+	0.747148i
$802$	42.9741			1.51747
$803$	21.0156			0.741625
$804$	21.1666	+	21.1666i	0.746489	+	0.746489i
$805$		0			0
$806$	−17.3461	+	2.43404i	−0.610989	+	0.0857353i
$807$	10.5216			0.370376
$808$	−4.02839	+	4.02839i	−0.141718	+	0.141718i
$809$	−22.4972			−0.790960			−0.395480	−	0.918475i	$-0.629422\pi$
$809$	−22.4972			−0.790960			−0.395480	+	0.918475i	$0.629422\pi$
$810$	−32.2702			−1.13386
$811$	−12.3587	+	12.3587i	−0.433973	+	0.433973i	−0.889978	−	0.456004i	$-0.849280\pi$
$811$	−12.3587	+	12.3587i	−0.433973	+	0.433973i	0.456004	+	0.889978i	$0.349280\pi$
$812$		0			0
$813$	32.0082	−	32.0082i	1.12258	−	1.12258i
$814$	−0.505460	+	0.505460i	−0.0177163	+	0.0177163i
$815$			44.2160i			1.54882i
$816$		−	29.8276i		−	1.04418i
$817$	−2.07116	−	2.07116i	−0.0724607	−	0.0724607i
$818$	75.2552			2.63124
$819$		0			0
$820$	36.6928			1.28137
$821$	−17.8214	−	17.8214i	−0.621971	−	0.621971i	0.324064	−	0.946035i	$-0.394951\pi$
$821$	−17.8214	−	17.8214i	−0.621971	−	0.621971i	−0.946035	+	0.324064i	$0.894951\pi$
$822$		−	98.0511i		−	3.41993i
$823$			40.6548i			1.41714i	0.705643	+	0.708568i	$0.250658\pi$
$823$			40.6548i			1.41714i	−0.705643	+	0.708568i	$0.749342\pi$
$824$	−3.67120	+	3.67120i	−0.127892	+	0.127892i
$825$	21.6335	−	21.6335i	0.753182	−	0.753182i
$826$		0			0
$827$	−21.0284	+	21.0284i	−0.731228	+	0.731228i	−0.970863	−	0.239635i	$-0.922972\pi$
$827$	−21.0284	+	21.0284i	−0.731228	+	0.731228i	0.239635	+	0.970863i	$0.422972\pi$
$828$	30.1100			1.04640
$829$	17.8242			0.619059			0.309530	−	0.950890i	$-0.399828\pi$
$829$	17.8242			0.619059			0.309530	+	0.950890i	$0.399828\pi$
$830$	3.29363	−	3.29363i	0.114323	−	0.114323i
$831$	−66.4384			−2.30472
$832$	−2.44470	−	17.4221i	−0.0847547	−	0.604001i
$833$		0			0
$834$	−48.5117	−	48.5117i	−1.67982	−	1.67982i
$835$	−51.6836			−1.78858
$836$	14.6846			0.507878
$837$	4.82149	+	4.82149i	0.166655	+	0.166655i
$838$	−9.26345	+	9.26345i	−0.320001	+	0.320001i
$839$	−19.0512	−	19.0512i	−0.657721	−	0.657721i	0.297119	−	0.954840i	$-0.403974\pi$
$839$	−19.0512	−	19.0512i	−0.657721	−	0.657721i	−0.954840	+	0.297119i	$0.903974\pi$
$840$		0			0
$841$	−28.9661			−0.998832
$842$		−	45.5122i		−	1.56846i
$843$	5.70971	+	5.70971i	0.196653	+	0.196653i
$844$			26.4188i			0.909372i
$845$	21.5819	−	38.8955i	0.742441	−	1.33804i
$846$		−	29.4973i		−	1.01414i
$847$		0			0
$848$	24.6032			0.844879
$849$		−	30.0766i		−	1.03223i
$850$	22.1791	−	22.1791i	0.760737	−	0.760737i
$851$	0.705669	+	0.705669i	0.0241900	+	0.0241900i
$852$	7.40826	+	7.40826i	0.253803	+	0.253803i
$853$	9.31374	+	9.31374i	0.318896	+	0.318896i	0.848343	−	0.529447i	$-0.177600\pi$
$853$	9.31374	+	9.31374i	0.318896	+	0.318896i	−0.529447	+	0.848343i	$0.677600\pi$
$854$		0			0
$855$		−	71.4753i		−	2.44440i
$856$	−1.95327	+	1.95327i	−0.0667613	+	0.0667613i
$857$	35.9048			1.22648			0.613242	−	0.789895i	$-0.289865\pi$
$857$	35.9048			1.22648			0.613242	+	0.789895i	$0.289865\pi$
$858$	−4.35797	−	31.0569i	−0.148779	−	1.06026i
$859$		−	20.3532i		−	0.694444i	−0.937783	−	0.347222i	$-0.887125\pi$
$859$		−	20.3532i		−	0.694444i	0.937783	−	0.347222i	$-0.112875\pi$
$860$	−2.22741	+	2.22741i	−0.0759541	+	0.0759541i
$861$		0			0
$862$		−	67.7957i		−	2.30913i
$863$	−5.76670	−	5.76670i	−0.196301	−	0.196301i	0.602111	−	0.798412i	$-0.294326\pi$
$863$	−5.76670	−	5.76670i	−0.196301	−	0.196301i	−0.798412	+	0.602111i	$0.794326\pi$
$864$	−13.9622	+	13.9622i	−0.475003	+	0.475003i
$865$	−6.33950	+	6.33950i	−0.215549	+	0.215549i
$866$	8.81844	+	8.81844i	0.299663	+	0.299663i
$867$			29.0944i			0.988097i
$868$		0			0
$869$	−3.61503	+	3.61503i	−0.122632	+	0.122632i
$870$		−	3.18022i		−	0.107820i
$871$	−19.8842	−	14.9905i	−0.673751	−	0.507935i
$872$	−8.08496			−0.273791
$873$	48.5117	−	48.5117i	1.64187	−	1.64187i
$874$		−	45.5498i		−	1.54075i
$875$		0			0
$876$	−37.3910	−	37.3910i	−1.26333	−	1.26333i
$877$	−31.5642	−	31.5642i	−1.06585	−	1.06585i	−0.997673	−	0.0681738i	$-0.978283\pi$
$877$	−31.5642	−	31.5642i	−1.06585	−	1.06585i	−0.0681738	−	0.997673i	$-0.521717\pi$
$878$	33.1545	+	33.1545i	1.11891	+	1.11891i
$879$	27.2283	−	27.2283i	0.918387	−	0.918387i
$880$			27.0790i			0.912833i
$881$	0.616060			0.0207556			0.0103778	−	0.999946i	$-0.496697\pi$
$881$	0.616060			0.0207556			0.0103778	+	0.999946i	$0.496697\pi$
$882$		0			0
$883$			16.5050i			0.555437i	0.960662	+	0.277719i	$0.0895783\pi$
$883$			16.5050i			0.555437i	−0.960662	+	0.277719i	$0.910422\pi$
$884$	−2.01090	−	14.3306i	−0.0676340	−	0.481991i
$885$		−	130.761i		−	4.39549i
$886$	−21.0353	−	21.0353i	−0.706694	−	0.706694i
$887$			18.5087i			0.621461i	0.950498	+	0.310731i	$0.100574\pi$
$887$			18.5087i			0.621461i	−0.950498	+	0.310731i	$0.899426\pi$
$888$	−0.398981			−0.0133889
$889$		0			0
$890$	−34.4021	−	34.4021i	−1.15316	−	1.15316i
$891$	6.02350	−	6.02350i	0.201795	−	0.201795i
$892$	−0.153783	−	0.153783i	−0.00514905	−	0.00514905i
$893$	−20.0839			−0.672081
$894$	18.5564			0.620618
$895$	61.3544	+	61.3544i	2.05085	+	2.05085i
$896$		0			0
$897$	−43.3583	+	6.08413i	−1.44769	+	0.203143i
$898$	77.2071			2.57644
$899$	0.331550	−	0.331550i	0.0110578	−	0.0110578i
$900$	−44.0403			−1.46801
$901$	13.1303			0.437432
$902$	−15.2173	+	15.2173i	−0.506681	+	0.506681i
$903$		0			0
$904$	−4.09554	+	4.09554i	−0.136216	+	0.136216i
$905$	−2.42833	+	2.42833i	−0.0807204	+	0.0807204i
$906$		−	90.9121i		−	3.02035i
$907$		−	27.6753i		−	0.918944i	−0.888192	−	0.459472i	$-0.848039\pi$
$907$		−	27.6753i		−	0.918944i	0.888192	−	0.459472i	$-0.151961\pi$
$908$	−30.6866	−	30.6866i	−1.01837	−	1.01837i
$909$	32.9983			1.09448
$910$		0			0
$911$	23.1900			0.768320			0.384160	−	0.923267i	$-0.374491\pi$
$911$	23.1900			0.768320			0.384160	+	0.923267i	$0.374491\pi$
$912$	44.7993	+	44.7993i	1.48345	+	1.48345i
$913$			1.22957i			0.0406927i
$914$		−	24.9232i		−	0.824387i
$915$	−9.67213	+	9.67213i	−0.319751	+	0.319751i
$916$	−20.3886	+	20.3886i	−0.673659	+	0.673659i
$917$		0			0
$918$	−8.85025	+	8.85025i	−0.292102	+	0.292102i
$919$	22.2165			0.732856			0.366428	−	0.930446i	$-0.380581\pi$
$919$	22.2165			0.732856			0.366428	+	0.930446i	$0.380581\pi$
$920$	10.8664			0.358254
$921$	−18.5822	+	18.5822i	−0.612304	+	0.612304i
$922$	9.59628			0.316037
$923$	−6.95942	−	5.24664i	−0.229072	−	0.172695i
$924$		0			0
$925$	−1.03214	−	1.03214i	−0.0339367	−	0.0339367i
$926$	−31.3515			−1.03027
$927$	30.0724			0.987708
$928$	0.960108	+	0.960108i	0.0315171	+	0.0315171i
$929$	−14.0994	+	14.0994i	−0.462588	+	0.462588i	−0.899503	−	0.436915i	$-0.856071\pi$
$929$	−14.0994	+	14.0994i	−0.462588	+	0.462588i	0.436915	+	0.899503i	$0.356071\pi$
$930$	−31.1225	−	31.1225i	−1.02055	−	1.02055i
$931$		0			0
$932$	8.32668			0.272750
$933$		−	6.69133i		−	0.219064i
$934$	−7.72800	−	7.72800i	−0.252868	−	0.252868i
$935$			14.4515i			0.472616i
$936$	6.02834	−	7.99631i	0.197043	−	0.261368i
$937$		−	32.0817i		−	1.04806i	−0.851699	−	0.524031i	$-0.824428\pi$
$937$		−	32.0817i		−	1.04806i	0.851699	−	0.524031i	$-0.175572\pi$
$938$		0			0
$939$	−9.12975			−0.297938
$940$			21.5990i			0.704483i
$941$	−5.67492	+	5.67492i	−0.184997	+	0.184997i	−0.793529	−	0.608532i	$-0.791759\pi$
$941$	−5.67492	+	5.67492i	−0.184997	+	0.184997i	0.608532	+	0.793529i	$0.291759\pi$
$942$	65.4477	+	65.4477i	2.13240	+	2.13240i
$943$	21.2448	+	21.2448i	0.691826	+	0.691826i
$944$	46.8881	+	46.8881i	1.52608	+	1.52608i
$945$		0			0
$946$		−	1.84751i		−	0.0600679i
$947$	11.7161	−	11.7161i	0.380721	−	0.380721i	−0.490641	−	0.871362i	$-0.663237\pi$
$947$	11.7161	−	11.7161i	0.380721	−	0.380721i	0.871362	+	0.490641i	$0.163237\pi$
$948$	12.8637			0.417795
$949$	35.1256	+	26.4809i	1.14023	+	0.859606i
$950$			66.6233i			2.16154i
$951$	−59.2752	+	59.2752i	−1.92213	+	1.92213i
$952$		0			0
$953$		−	37.7682i		−	1.22343i	−0.791077	−	0.611717i	$-0.790479\pi$
$953$		−	37.7682i		−	1.22343i	0.791077	−	0.611717i	$-0.209521\pi$
$954$	−28.9641	−	28.9641i	−0.937747	−	0.937747i
$955$	−2.54140	+	2.54140i	−0.0822377	+	0.0822377i
$956$	21.3095	−	21.3095i	0.689197	−	0.689197i
$957$	0.593616	+	0.593616i	0.0191889	+	0.0191889i
$958$		−	38.6101i		−	1.24744i
$959$		0			0
$960$	31.2589	−	31.2589i	1.00888	−	1.00888i
$961$			24.5107i			0.790669i
$962$	−1.48174	+	0.207921i	−0.0477731	+	0.00670363i
$963$	16.0001			0.515596
$964$	−3.15608	+	3.15608i	−0.101651	+	0.101651i
$965$		−	6.76507i		−	0.217775i
$966$		0			0
$967$	−33.4886	−	33.4886i	−1.07692	−	1.07692i	−0.996784	−	0.0801380i	$-0.974464\pi$
$967$	−33.4886	−	33.4886i	−1.07692	−	1.07692i	−0.0801380	−	0.996784i	$-0.525536\pi$
$968$	3.93327	+	3.93327i	0.126420	+	0.126420i
$969$	23.9085	+	23.9085i	0.768051	+	0.768051i
$970$	−78.9239	+	78.9239i	−2.53409	+	2.53409i
$971$			59.9544i			1.92403i	0.272997	+	0.962015i	$0.411985\pi$
$971$			59.9544i			1.92403i	−0.272997	+	0.962015i	$0.588015\pi$
$972$	−34.5785			−1.10910
$973$		0			0
$974$		−	3.02085i		−	0.0967944i
$975$	63.4178	−	8.89893i	2.03100	−	0.284994i
$976$		−	6.93643i		−	0.222030i
$977$	21.2897	+	21.2897i	0.681118	+	0.681118i	0.960252	−	0.279134i	$-0.0900475\pi$
$977$	21.2897	+	21.2897i	0.681118	+	0.681118i	−0.279134	+	0.960252i	$0.590048\pi$
$978$			65.2518i			2.08652i
$979$	12.8429			0.410461
$980$		0			0
$981$	33.1137	+	33.1137i	1.05724	+	1.05724i
$982$	−30.6524	+	30.6524i	−0.978159	+	0.978159i
$983$	11.1585	+	11.1585i	0.355900	+	0.355900i	0.862299	−	0.506399i	$-0.169024\pi$
$983$	11.1585	+	11.1585i	0.355900	+	0.355900i	−0.506399	+	0.862299i	$0.669024\pi$
$984$	−12.0117			−0.382919
$985$	−16.2636			−0.518200
$986$	0.608587	+	0.608587i	0.0193814	+	0.0193814i
$987$		0			0
$988$	24.5440	+	18.5035i	0.780847	+	0.588673i
$989$	−2.57930			−0.0820171
$990$	31.8787	−	31.8787i	1.01317	−	1.01317i
$991$	30.2270			0.960191			0.480096	−	0.877216i	$-0.340602\pi$
$991$	30.2270			0.960191			0.480096	+	0.877216i	$0.340602\pi$
$992$	18.7918			0.596639
$993$	61.0567	−	61.0567i	1.93757	−	1.93757i
$994$		0			0
$995$	−24.6939	+	24.6939i	−0.782849	+	0.782849i
$996$	2.18765	−	2.18765i	0.0693182	−	0.0693182i
$997$			46.2391i			1.46441i	0.681087	+	0.732203i	$0.261508\pi$
$997$			46.2391i			1.46441i	−0.681087	+	0.732203i	$0.738492\pi$
$998$		−	11.2402i		−	0.355802i
$999$	0.411862	+	0.411862i	0.0130307	+	0.0130307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.489.13		32
7.2	even	3		91.2.bb.a.73.7	yes	32
7.3	odd	6		91.2.bb.a.47.2	yes	32
7.4	even	3		637.2.bc.b.411.2		32
7.5	odd	6		637.2.bc.b.619.7		32
7.6	odd	2	inner	637.2.i.a.489.14		32
13.5	odd	4	inner	637.2.i.a.538.13		32
21.2	odd	6		819.2.fn.e.73.2		32
21.17	even	6		819.2.fn.e.775.7		32
91.5	even	12		637.2.bc.b.31.2		32
91.18	odd	12		637.2.bc.b.460.7		32
91.31	even	12		91.2.bb.a.5.7	✓	32
91.44	odd	12		91.2.bb.a.31.2	yes	32
91.83	even	4	inner	637.2.i.a.538.14		32
273.44	even	12		819.2.fn.e.577.7		32
273.122	odd	12		819.2.fn.e.460.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.7	✓	32	91.31	even	12
91.2.bb.a.31.2	yes	32	91.44	odd	12
91.2.bb.a.47.2	yes	32	7.3	odd	6
91.2.bb.a.73.7	yes	32	7.2	even	3
637.2.i.a.489.13		32	1.1	even	1	trivial
637.2.i.a.489.14		32	7.6	odd	2	inner
637.2.i.a.538.13		32	13.5	odd	4	inner
637.2.i.a.538.14		32	91.83	even	4	inner
637.2.bc.b.31.2		32	91.5	even	12
637.2.bc.b.411.2		32	7.4	even	3
637.2.bc.b.460.7		32	91.18	odd	12
637.2.bc.b.619.7		32	7.5	odd	6
819.2.fn.e.73.2		32	21.2	odd	6
819.2.fn.e.460.2		32	273.122	odd	12
819.2.fn.e.577.7		32	273.44	even	12
819.2.fn.e.775.7		32	21.17	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34850 + 1.34850i) q^{2} -2.64781i q^{3} +1.63690i q^{4} +(2.41949 - 2.41949i) q^{5} +(3.57057 - 3.57057i) q^{6} +(0.489646 - 0.489646i) q^{8} -4.01091 q^{9} +O(q^{10})\)	\(q+(1.34850 + 1.34850i) q^{2} -2.64781i q^{3} +1.63690i q^{4} +(2.41949 - 2.41949i) q^{5} +(3.57057 - 3.57057i) q^{6} +(0.489646 - 0.489646i) q^{8} -4.01091 q^{9} +6.52537 q^{10} +(-1.21802 + 1.21802i) q^{11} +4.33419 q^{12} +(-3.57057 + 0.501030i) q^{13} +(-6.40637 - 6.40637i) q^{15} +4.59436 q^{16} +2.45192 q^{17} +(-5.40870 - 5.40870i) q^{18} +(-3.68263 + 3.68263i) q^{19} +(3.96046 + 3.96046i) q^{20} -3.28498 q^{22} +4.58614i q^{23} +(-1.29649 - 1.29649i) q^{24} -6.70790i q^{25} +(-5.49055 - 4.13927i) q^{26} +2.67669i q^{27} +0.184063 q^{29} -17.2779i q^{30} +(1.80129 - 1.80129i) q^{31} +(5.21620 + 5.21620i) q^{32} +(3.22508 + 3.22508i) q^{33} +(3.30641 + 3.30641i) q^{34} -6.56544i q^{36} +(0.153870 - 0.153870i) q^{37} -9.93205 q^{38} +(1.32663 + 9.45420i) q^{39} -2.36939i q^{40} +(4.63239 - 4.63239i) q^{41} +0.562412i q^{43} +(-1.99376 - 1.99376i) q^{44} +(-9.70437 + 9.70437i) q^{45} +(-6.18441 + 6.18441i) q^{46} +(2.72683 + 2.72683i) q^{47} -12.1650i q^{48} +(9.04560 - 9.04560i) q^{50} -6.49223i q^{51} +(-0.820134 - 5.84465i) q^{52} +5.35509 q^{53} +(-3.60952 + 3.60952i) q^{54} +5.89396i q^{55} +(9.75092 + 9.75092i) q^{57} +(0.248208 + 0.248208i) q^{58} +(10.2056 + 10.2056i) q^{59} +(10.4866 - 10.4866i) q^{60} -1.50977i q^{61} +4.85807 q^{62} +4.87935i q^{64} +(-7.42673 + 9.85121i) q^{65} +8.69802i q^{66} +(4.88364 + 4.88364i) q^{67} +4.01354i q^{68} +12.1432 q^{69} +(1.70926 + 1.70926i) q^{71} +(-1.96392 + 1.96392i) q^{72} +(-8.62699 - 8.62699i) q^{73} +0.414986 q^{74} -17.7613 q^{75} +(-6.02809 - 6.02809i) q^{76} +(-10.9600 + 14.5379i) q^{78} +2.96797 q^{79} +(11.1160 - 11.1160i) q^{80} -4.94534 q^{81} +12.4935 q^{82} +(0.504742 - 0.504742i) q^{83} +(5.93241 - 5.93241i) q^{85} +(-0.758412 + 0.758412i) q^{86} -0.487363i q^{87} +1.19279i q^{88} +(-5.27206 - 5.27206i) q^{89} -26.1726 q^{90} -7.50704 q^{92} +(-4.76947 - 4.76947i) q^{93} +7.35426i q^{94} +17.8202i q^{95} +(13.8115 - 13.8115i) q^{96} +(-12.0949 + 12.0949i) q^{97} +(4.88535 - 4.88535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

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