LMFDB - Embedded newform 731.2.f.d.259.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.2
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38680i q^{2} +(-1.32556 + 1.32556i) q^{3} -3.69681 q^{4} +(-0.620851 + 0.620851i) q^{5} +(3.16384 + 3.16384i) q^{6} +(-1.89151 - 1.89151i) q^{7} +4.04996i q^{8} -0.514207i q^{9} +O(q^{10})$	\(q-2.38680i q^{2} +(-1.32556 + 1.32556i) q^{3} -3.69681 q^{4} +(-0.620851 + 0.620851i) q^{5} +(3.16384 + 3.16384i) q^{6} +(-1.89151 - 1.89151i) q^{7} +4.04996i q^{8} -0.514207i q^{9} +(1.48185 + 1.48185i) q^{10} +(4.06640 + 4.06640i) q^{11} +(4.90034 - 4.90034i) q^{12} -1.36341 q^{13} +(-4.51465 + 4.51465i) q^{14} -1.64595i q^{15} +2.27281 q^{16} +(2.97257 - 2.85724i) q^{17} -1.22731 q^{18} -3.44292i q^{19} +(2.29517 - 2.29517i) q^{20} +5.01460 q^{21} +(9.70568 - 9.70568i) q^{22} +(1.98310 + 1.98310i) q^{23} +(-5.36845 - 5.36845i) q^{24} +4.22909i q^{25} +3.25418i q^{26} +(-3.29506 - 3.29506i) q^{27} +(6.99254 + 6.99254i) q^{28} +(3.39744 - 3.39744i) q^{29} -3.92855 q^{30} +(6.92163 - 6.92163i) q^{31} +2.67518i q^{32} -10.7805 q^{33} +(-6.81967 - 7.09492i) q^{34} +2.34869 q^{35} +1.90093i q^{36} +(2.32800 - 2.32800i) q^{37} -8.21757 q^{38} +(1.80727 - 1.80727i) q^{39} +(-2.51442 - 2.51442i) q^{40} +(-1.53715 - 1.53715i) q^{41} -11.9688i q^{42} -1.00000i q^{43} +(-15.0327 - 15.0327i) q^{44} +(0.319246 + 0.319246i) q^{45} +(4.73327 - 4.73327i) q^{46} +6.91381 q^{47} +(-3.01273 + 3.01273i) q^{48} +0.155586i q^{49} +10.0940 q^{50} +(-0.152866 + 7.72775i) q^{51} +5.04026 q^{52} -13.5500i q^{53} +(-7.86465 + 7.86465i) q^{54} -5.04926 q^{55} +(7.66051 - 7.66051i) q^{56} +(4.56380 + 4.56380i) q^{57} +(-8.10902 - 8.10902i) q^{58} +6.76237i q^{59} +6.08476i q^{60} +(5.03945 + 5.03945i) q^{61} +(-16.5205 - 16.5205i) q^{62} +(-0.972626 + 0.972626i) q^{63} +10.9307 q^{64} +(0.846472 - 0.846472i) q^{65} +25.7309i q^{66} -8.02686 q^{67} +(-10.9890 + 10.5627i) q^{68} -5.25743 q^{69} -5.60584i q^{70} +(-0.399060 + 0.399060i) q^{71} +2.08252 q^{72} +(3.61381 - 3.61381i) q^{73} +(-5.55646 - 5.55646i) q^{74} +(-5.60590 - 5.60590i) q^{75} +12.7279i q^{76} -15.3832i q^{77} +(-4.31360 - 4.31360i) q^{78} +(11.2401 + 11.2401i) q^{79} +(-1.41107 + 1.41107i) q^{80} +10.2782 q^{81} +(-3.66887 + 3.66887i) q^{82} +13.3468i q^{83} -18.5380 q^{84} +(-0.0715978 + 3.61944i) q^{85} -2.38680 q^{86} +9.00702i q^{87} +(-16.4687 + 16.4687i) q^{88} +9.36731 q^{89} +(0.761977 - 0.761977i) q^{90} +(2.57889 + 2.57889i) q^{91} +(-7.33116 - 7.33116i) q^{92} +18.3500i q^{93} -16.5019i q^{94} +(2.13754 + 2.13754i) q^{95} +(-3.54610 - 3.54610i) q^{96} +(4.69844 - 4.69844i) q^{97} +0.371353 q^{98} +(2.09097 - 2.09097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		−	2.38680i		−	1.68772i	−0.536562	−	0.843861i	$-0.680277\pi$
$2$		−	2.38680i		−	1.68772i	0.536562	−	0.843861i	$-0.319723\pi$
$3$	−1.32556	+	1.32556i	−0.765311	+	0.765311i	−0.977277	−	0.211966i	$-0.932013\pi$
$3$	−1.32556	+	1.32556i	−0.765311	+	0.765311i	0.211966	+	0.977277i	$0.432013\pi$
$4$	−3.69681			−1.84841
$5$	−0.620851	+	0.620851i	−0.277653	+	0.277653i	−0.832171	−	0.554518i	$-0.812902\pi$
$5$	−0.620851	+	0.620851i	−0.277653	+	0.277653i	0.554518	+	0.832171i	$0.312902\pi$
$6$	3.16384	+	3.16384i	1.29163	+	1.29163i
$7$	−1.89151	−	1.89151i	−0.714922	−	0.714922i	0.252639	−	0.967561i	$-0.418702\pi$
$7$	−1.89151	−	1.89151i	−0.714922	−	0.714922i	−0.967561	+	0.252639i	$0.918702\pi$
$8$			4.04996i			1.43188i
$9$		−	0.514207i		−	0.171402i
$10$	1.48185	+	1.48185i	0.468601	+	0.468601i
$11$	4.06640	+	4.06640i	1.22607	+	1.22607i	0.965440	+	0.260625i	$0.0839287\pi$
$11$	4.06640	+	4.06640i	1.22607	+	1.22607i	0.260625	+	0.965440i	$0.416071\pi$
$12$	4.90034	−	4.90034i	1.41461	−	1.41461i
$13$	−1.36341			−0.378141			−0.189070	−	0.981964i	$-0.560547\pi$
$13$	−1.36341			−0.378141			−0.189070	+	0.981964i	$0.560547\pi$
$14$	−4.51465	+	4.51465i	−1.20659	+	1.20659i
$15$		−	1.64595i		−	0.424982i
$16$	2.27281			0.568201
$17$	2.97257	−	2.85724i	0.720953	−	0.692984i
$17$	2.97257	−	2.85724i	0.720953	−	0.692984i
$18$	−1.22731			−0.289280
$19$		−	3.44292i		−	0.789861i	−0.918711	−	0.394931i	$-0.870769\pi$
$19$		−	3.44292i		−	0.789861i	0.918711	−	0.394931i	$-0.129231\pi$
$20$	2.29517	−	2.29517i	0.513216	−	0.513216i
$21$	5.01460			1.09428
$22$	9.70568	−	9.70568i	2.06926	−	2.06926i
$23$	1.98310	+	1.98310i	0.413505	+	0.413505i	0.882958	−	0.469453i	$-0.155549\pi$
$23$	1.98310	+	1.98310i	0.413505	+	0.413505i	−0.469453	+	0.882958i	$0.655549\pi$
$24$	−5.36845	−	5.36845i	−1.09583	−	1.09583i
$25$			4.22909i			0.845818i
$26$			3.25418i			0.638197i
$27$	−3.29506	−	3.29506i	−0.634135	−	0.634135i
$28$	6.99254	+	6.99254i	1.32147	+	1.32147i
$29$	3.39744	−	3.39744i	0.630890	−	0.630890i	−0.317402	−	0.948291i	$-0.602810\pi$
$29$	3.39744	−	3.39744i	0.630890	−	0.630890i	0.948291	+	0.317402i	$0.102810\pi$
$30$	−3.92855			−0.717252
$31$	6.92163	−	6.92163i	1.24316	−	1.24316i	0.284478	−	0.958682i	$-0.408180\pi$
$31$	6.92163	−	6.92163i	1.24316	−	1.24316i	0.958682	−	0.284478i	$-0.0918204\pi$
$32$			2.67518i			0.472909i
$33$	−10.7805			−1.87664
$34$	−6.81967	−	7.09492i	−1.16956	−	1.21677i
$35$	2.34869			0.397000
$36$			1.90093i			0.316821i
$37$	2.32800	−	2.32800i	0.382720	−	0.382720i	−0.489361	−	0.872081i	$-0.662770\pi$
$37$	2.32800	−	2.32800i	0.382720	−	0.382720i	0.872081	+	0.489361i	$0.162770\pi$
$38$	−8.21757			−1.33307
$39$	1.80727	−	1.80727i	0.289395	−	0.289395i
$40$	−2.51442	−	2.51442i	−0.397565	−	0.397565i
$41$	−1.53715	−	1.53715i	−0.240062	−	0.240062i	0.576813	−	0.816876i	$-0.304296\pi$
$41$	−1.53715	−	1.53715i	−0.240062	−	0.240062i	−0.816876	+	0.576813i	$0.804296\pi$
$42$		−	11.9688i		−	1.84683i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−15.0327	−	15.0327i	−2.26627	−	2.26627i
$45$	0.319246	+	0.319246i	0.0475904	+	0.0475904i
$46$	4.73327	−	4.73327i	0.697882	−	0.697882i
$47$	6.91381			1.00848			0.504242	−	0.863563i	$-0.331772\pi$
$47$	6.91381			1.00848			0.504242	+	0.863563i	$0.331772\pi$
$48$	−3.01273	+	3.01273i	−0.434851	+	0.434851i
$49$			0.155586i			0.0222266i
$50$	10.0940			1.42751
$51$	−0.152866	+	7.72775i	−0.0214055	+	1.08210i
$52$	5.04026			0.698958
$53$		−	13.5500i		−	1.86123i	−0.365996	−	0.930617i	$-0.619271\pi$
$53$		−	13.5500i		−	1.86123i	0.365996	−	0.930617i	$-0.380729\pi$
$54$	−7.86465	+	7.86465i	−1.07024	+	1.07024i
$55$	−5.04926			−0.680841
$56$	7.66051	−	7.66051i	1.02368	−	1.02368i
$57$	4.56380	+	4.56380i	0.604490	+	0.604490i
$58$	−8.10902	−	8.10902i	−1.06477	−	1.06477i
$59$			6.76237i			0.880386i	0.897903	+	0.440193i	$0.145090\pi$
$59$			6.76237i			0.880386i	−0.897903	+	0.440193i	$0.854910\pi$
$60$			6.08476i			0.785540i
$61$	5.03945	+	5.03945i	0.645235	+	0.645235i	0.951838	−	0.306602i	$-0.0991922\pi$
$61$	5.03945	+	5.03945i	0.645235	+	0.645235i	−0.306602	+	0.951838i	$0.599192\pi$
$62$	−16.5205	−	16.5205i	−2.09811	−	2.09811i
$63$	−0.972626	+	0.972626i	−0.122539	+	0.122539i
$64$	10.9307			1.36634
$65$	0.846472	−	0.846472i	0.104992	−	0.104992i
$66$			25.7309i			3.16725i
$67$	−8.02686			−0.980637			−0.490318	−	0.871543i	$-0.663119\pi$
$67$	−8.02686			−0.980637			−0.490318	+	0.871543i	$0.663119\pi$
$68$	−10.9890	+	10.5627i	−1.33262	+	1.28092i
$69$	−5.25743			−0.632920
$70$		−	5.60584i		−	0.670027i
$71$	−0.399060	+	0.399060i	−0.0473597	+	0.0473597i	−0.730390	−	0.683030i	$-0.760662\pi$
$71$	−0.399060	+	0.399060i	−0.0473597	+	0.0473597i	0.683030	+	0.730390i	$0.260662\pi$
$72$	2.08252			0.245427
$73$	3.61381	−	3.61381i	0.422965	−	0.422965i	−0.463259	−	0.886223i	$-0.653320\pi$
$73$	3.61381	−	3.61381i	0.422965	−	0.422965i	0.886223	+	0.463259i	$0.153320\pi$
$74$	−5.55646	−	5.55646i	−0.645926	−	0.645926i
$75$	−5.60590	−	5.60590i	−0.647314	−	0.647314i
$76$			12.7279i			1.45998i
$77$		−	15.3832i		−	1.75308i
$78$	−4.31360	−	4.31360i	−0.488419	−	0.488419i
$79$	11.2401	+	11.2401i	1.26461	+	1.26461i	0.948833	+	0.315779i	$0.102266\pi$
$79$	11.2401	+	11.2401i	1.26461	+	1.26461i	0.315779	+	0.948833i	$0.397734\pi$
$80$	−1.41107	+	1.41107i	−0.157763	+	0.157763i
$81$	10.2782			1.14202
$82$	−3.66887	+	3.66887i	−0.405159	+	0.405159i
$83$			13.3468i			1.46500i	0.680766	+	0.732501i	$0.261647\pi$
$83$			13.3468i			1.46500i	−0.680766	+	0.732501i	$0.738353\pi$
$84$	−18.5380			−2.02267
$85$	−0.0715978	+	3.61944i	−0.00776587	+	0.392584i
$86$	−2.38680			−0.257375
$87$			9.00702i			0.965654i
$88$	−16.4687	+	16.4687i	−1.75557	+	1.75557i
$89$	9.36731			0.992933			0.496467	−	0.868056i	$-0.334631\pi$
$89$	9.36731			0.992933			0.496467	+	0.868056i	$0.334631\pi$
$90$	0.761977	−	0.761977i	0.0803194	−	0.0803194i
$91$	2.57889	+	2.57889i	0.270341	+	0.270341i
$92$	−7.33116	−	7.33116i	−0.764326	−	0.764326i
$93$			18.3500i			1.90281i
$94$		−	16.5019i		−	1.70204i
$95$	2.13754	+	2.13754i	0.219307	+	0.219307i
$96$	−3.54610	−	3.54610i	−0.361923	−	0.361923i
$97$	4.69844	−	4.69844i	0.477054	−	0.477054i	−0.427134	−	0.904188i	$-0.640477\pi$
$97$	4.69844	−	4.69844i	0.477054	−	0.477054i	0.904188	+	0.427134i	$0.140477\pi$
$98$	0.371353			0.0375123
$99$	2.09097	−	2.09097i	0.210151	−	0.210151i
$100$		−	15.6342i		−	1.56342i
$101$	14.6035			1.45310			0.726551	−	0.687113i	$-0.241122\pi$
$101$	14.6035			1.45310			0.726551	+	0.687113i	$0.241122\pi$
$102$	18.4446	+	0.364861i	1.82629	+	0.0361266i
$103$	4.80146			0.473102			0.236551	−	0.971619i	$-0.423983\pi$
$103$	4.80146			0.473102			0.236551	+	0.971619i	$0.423983\pi$
$104$		−	5.52173i		−	0.541450i
$105$	−3.11332	+	3.11332i	−0.303829	+	0.303829i
$106$	−32.3411			−3.14125
$107$	−8.39380	+	8.39380i	−0.811459	+	0.811459i	−0.984853	−	0.173394i	$-0.944527\pi$
$107$	−8.39380	+	8.39380i	−0.811459	+	0.811459i	0.173394	+	0.984853i	$0.444527\pi$
$108$	12.1812	+	12.1812i	1.17214	+	1.17214i
$109$	2.79605	+	2.79605i	0.267813	+	0.267813i	0.828218	−	0.560405i	$-0.189355\pi$
$109$	2.79605	+	2.79605i	0.267813	+	0.267813i	−0.560405	+	0.828218i	$0.689355\pi$
$110$			12.0516i			1.14907i
$111$			6.17179i			0.585800i
$112$	−4.29902	−	4.29902i	−0.406220	−	0.406220i
$113$	−8.16596	−	8.16596i	−0.768189	−	0.768189i	0.209598	−	0.977788i	$-0.432784\pi$
$113$	−8.16596	−	8.16596i	−0.768189	−	0.768189i	−0.977788	+	0.209598i	$0.932784\pi$
$114$	10.8929	−	10.8929i	1.02021	−	1.02021i
$115$	−2.46242			−0.229622
$116$	−12.5597	+	12.5597i	−1.16614	+	1.16614i
$117$			0.701073i			0.0648142i
$118$	16.1404			1.48585
$119$	−11.0271	−	0.218132i	−1.01085	−	0.0199962i
$120$	6.66602			0.608521
$121$			22.0712i			2.00647i
$122$	12.0282	−	12.0282i	1.08898	−	1.08898i
$123$	4.07516			0.367445
$124$	−25.5880	+	25.5880i	−2.29787	+	2.29787i
$125$	−5.72989	−	5.72989i	−0.512497	−	0.512497i
$126$	2.32146	+	2.32146i	0.206812	+	0.206812i
$127$			5.54196i			0.491770i	0.969299	+	0.245885i	$0.0790785\pi$
$127$			5.54196i			0.491770i	−0.969299	+	0.245885i	$0.920922\pi$
$128$		−	20.7391i		−	1.83310i
$129$	1.32556	+	1.32556i	0.116709	+	0.116709i
$130$	−2.02036	−	2.02036i	−0.177197	−	0.177197i
$131$	−0.148951	+	0.148951i	−0.0130139	+	0.0130139i	−0.713584	−	0.700570i	$-0.752929\pi$
$131$	−0.148951	+	0.148951i	−0.0130139	+	0.0130139i	0.700570	+	0.713584i	$0.252929\pi$
$132$	39.8535			3.46880
$133$	−6.51231	+	6.51231i	−0.564689	+	0.564689i
$134$			19.1585i			1.65504i
$135$	4.09149			0.352139
$136$	11.5717	+	12.0388i	0.992266	+	1.03232i
$137$	4.14006			0.353709			0.176855	−	0.984237i	$-0.443408\pi$
$137$	4.14006			0.353709			0.176855	+	0.984237i	$0.443408\pi$
$138$			12.5484i			1.06819i
$139$	1.07183	−	1.07183i	0.0909110	−	0.0909110i	−0.660189	−	0.751100i	$-0.729524\pi$
$139$	1.07183	−	1.07183i	0.0909110	−	0.0909110i	0.751100	+	0.660189i	$0.229524\pi$
$140$	−8.68266			−0.733818
$141$	−9.16466	+	9.16466i	−0.771804	+	0.771804i
$142$	0.952477	+	0.952477i	0.0799301	+	0.0799301i
$143$	−5.54415	−	5.54415i	−0.463625	−	0.463625i
$144$		−	1.16869i		−	0.0973911i
$145$			4.21861i			0.350337i
$146$	−8.62545	−	8.62545i	−0.713847	−	0.713847i
$147$	−0.206239	−	0.206239i	−0.0170103	−	0.0170103i
$148$	−8.60617	+	8.60617i	−0.707423	+	0.707423i
$149$	−2.80542			−0.229829			−0.114915	−	0.993375i	$-0.536659\pi$
$149$	−2.80542			−0.229829			−0.114915	+	0.993375i	$0.536659\pi$
$150$	−13.3802	+	13.3802i	−1.09249	+	1.09249i
$151$			13.1540i			1.07046i	0.844706	+	0.535230i	$0.179775\pi$
$151$			13.1540i			1.07046i	−0.844706	+	0.535230i	$0.820225\pi$
$152$	13.9437			1.13098
$153$	−1.46922	−	1.52852i	−0.118779	−	0.123573i
$154$	−36.7167			−2.95872
$155$			8.59460i			0.690335i
$156$	−6.68115	+	6.68115i	−0.534920	+	0.534920i
$157$	6.99389			0.558174			0.279087	−	0.960266i	$-0.409968\pi$
$157$	6.99389			0.558174			0.279087	+	0.960266i	$0.409968\pi$
$158$	26.8279	−	26.8279i	2.13431	−	2.13431i
$159$	17.9613	+	17.9613i	1.42442	+	1.42442i
$160$	−1.66089	−	1.66089i	−0.131305	−	0.131305i
$161$		−	7.50209i		−	0.591248i
$162$		−	24.5320i		−	1.92742i
$163$	−10.5442	−	10.5442i	−0.825884	−	0.825884i	0.161060	−	0.986945i	$-0.448509\pi$
$163$	−10.5442	−	10.5442i	−0.825884	−	0.825884i	−0.986945	+	0.161060i	$0.948509\pi$
$164$	5.68256	+	5.68256i	0.443733	+	0.443733i
$165$	6.69308	−	6.69308i	0.521056	−	0.521056i
$166$	31.8561			2.47252
$167$	16.7681	−	16.7681i	1.29755	−	1.29755i	0.367548	−	0.930004i	$-0.380197\pi$
$167$	16.7681	−	16.7681i	1.29755	−	1.29755i	0.930004	−	0.367548i	$-0.119803\pi$
$168$			20.3089i			1.56687i
$169$	−11.1411			−0.857010
$170$	8.63889	+	0.170890i	0.662573	+	0.0131066i
$171$	−1.77038			−0.135384
$172$			3.69681i			0.281879i
$173$	15.4503	−	15.4503i	1.17467	−	1.17467i	0.193583	−	0.981084i	$-0.437989\pi$
$173$	15.4503	−	15.4503i	1.17467	−	1.17467i	0.981084	−	0.193583i	$-0.0620107\pi$
$174$	21.4980			1.62976
$175$	7.99934	−	7.99934i	0.604694	−	0.604694i
$176$	9.24213	+	9.24213i	0.696652	+	0.696652i
$177$	−8.96391	−	8.96391i	−0.673769	−	0.673769i
$178$		−	22.3579i		−	1.67580i
$179$		−	18.1711i		−	1.35817i	−0.734059	−	0.679085i	$-0.762377\pi$
$179$		−	18.1711i		−	1.35817i	0.734059	−	0.679085i	$-0.237623\pi$
$180$	−1.18019	−	1.18019i	−0.0879664	−	0.0879664i
$181$	−10.8704	−	10.8704i	−0.807993	−	0.807993i	0.176337	−	0.984330i	$-0.443575\pi$
$181$	−10.8704	−	10.8704i	−0.807993	−	0.807993i	−0.984330	+	0.176337i	$0.943575\pi$
$182$	6.15529	−	6.15529i	0.456261	−	0.456261i
$183$	−13.3602			−0.987612
$184$	−8.03147	+	8.03147i	−0.592088	+	0.592088i
$185$			2.89068i			0.212527i
$186$	43.7979			3.21141
$187$	23.7063	+	0.468945i	1.73358	+	0.0342927i
$188$	−25.5591			−1.86409
$189$			12.4653i			0.906714i
$190$	5.10189	−	5.10189i	0.370130	−	0.370130i
$191$	−10.7489			−0.777764			−0.388882	−	0.921288i	$-0.627139\pi$
$191$	−10.7489			−0.777764			−0.388882	+	0.921288i	$0.627139\pi$
$192$	−14.4893	+	14.4893i	−1.04568	+	1.04568i
$193$	8.67068	+	8.67068i	0.624129	+	0.624129i	0.946585	−	0.322455i	$-0.104508\pi$
$193$	8.67068	+	8.67068i	0.624129	+	0.624129i	−0.322455	+	0.946585i	$0.604508\pi$
$194$	−11.2142	−	11.2142i	−0.805135	−	0.805135i
$195$			2.24409i			0.160703i
$196$		−	0.575173i		−	0.0410838i
$197$	−16.5260	−	16.5260i	−1.17743	−	1.17743i	−0.980398	−	0.197029i	$-0.936871\pi$
$197$	−16.5260	−	16.5260i	−1.17743	−	1.17743i	−0.197029	−	0.980398i	$-0.563129\pi$
$198$	−4.99073	−	4.99073i	−0.354676	−	0.354676i
$199$	−3.88185	+	3.88185i	−0.275177	+	0.275177i	−0.831180	−	0.556003i	$-0.812334\pi$
$199$	−3.88185	+	3.88185i	−0.275177	+	0.275177i	0.556003	+	0.831180i	$0.312334\pi$
$200$	−17.1276			−1.21111
$201$	10.6401	−	10.6401i	0.750492	−	0.750492i
$202$		−	34.8556i		−	2.45243i
$203$	−12.8526			−0.902074
$204$	0.565117	−	28.5681i	0.0395661	−	2.00016i
$205$	1.90868			0.133308
$206$		−	11.4601i		−	0.798465i
$207$	1.01972	−	1.01972i	0.0708758	−	0.0708758i
$208$	−3.09876			−0.214860
$209$	14.0003	−	14.0003i	0.968421	−	0.968421i
$210$	7.43087	+	7.43087i	0.512779	+	0.512779i
$211$	−8.67058	−	8.67058i	−0.596908	−	0.596908i	0.342581	−	0.939488i	$-0.388699\pi$
$211$	−8.67058	−	8.67058i	−0.596908	−	0.596908i	−0.939488	+	0.342581i	$0.888699\pi$
$212$			50.0918i			3.44032i
$213$		−	1.05796i		−	0.0724899i
$214$	20.0343	+	20.0343i	1.36952	+	1.36952i
$215$	0.620851	+	0.620851i	0.0423417	+	0.0423417i
$216$	13.3449	−	13.3449i	0.908002	−	0.908002i
$217$	−26.1846			−1.77753
$218$	6.67362	−	6.67362i	0.451994	−	0.451994i
$219$			9.58063i			0.647399i
$220$	18.6662			1.25847
$221$	−4.05281	+	3.89558i	−0.272622	+	0.262045i
$222$	14.7308			0.988669
$223$			17.6125i			1.17942i	0.807615	+	0.589710i	$0.200758\pi$
$223$			17.6125i			1.17942i	−0.807615	+	0.589710i	$0.799242\pi$
$224$	5.06012	−	5.06012i	0.338093	−	0.338093i
$225$	2.17463			0.144975
$226$	−19.4905	+	19.4905i	−1.29649	+	1.29649i
$227$	−0.714487	−	0.714487i	−0.0474222	−	0.0474222i	0.682998	−	0.730420i	$-0.260676\pi$
$227$	−0.714487	−	0.714487i	−0.0474222	−	0.0474222i	−0.730420	+	0.682998i	$0.760676\pi$
$228$	−16.8715	−	16.8715i	−1.11734	−	1.11734i
$229$			26.0549i			1.72175i	0.508814	+	0.860877i	$0.330084\pi$
$229$			26.0549i			1.72175i	−0.508814	+	0.860877i	$0.669916\pi$
$230$			5.87731i			0.387538i
$231$	20.3914	+	20.3914i	1.34165	+	1.34165i
$232$	13.7595	+	13.7595i	0.903355	+	0.903355i
$233$	10.0577	−	10.0577i	0.658904	−	0.658904i	−0.296217	−	0.955121i	$-0.595725\pi$
$233$	10.0577	−	10.0577i	0.658904	−	0.658904i	0.955121	+	0.296217i	$0.0957251\pi$
$234$	1.67332			0.109388
$235$	−4.29245	+	4.29245i	−0.280008	+	0.280008i
$236$		−	24.9992i		−	1.62731i
$237$	−29.7988			−1.93564
$238$	−0.520638	+	26.3195i	−0.0337480	+	1.70604i
$239$	17.6070			1.13890			0.569452	−	0.822024i	$-0.307155\pi$
$239$	17.6070			1.13890			0.569452	+	0.822024i	$0.307155\pi$
$240$		−	3.74092i		−	0.241475i
$241$	13.5794	−	13.5794i	0.874725	−	0.874725i	−0.118258	−	0.992983i	$-0.537731\pi$
$241$	13.5794	−	13.5794i	0.874725	−	0.874725i	0.992983	+	0.118258i	$0.0377311\pi$
$242$	52.6795			3.38637
$243$	−3.73918	+	3.73918i	−0.239868	+	0.239868i
$244$	−18.6299	−	18.6299i	−1.19266	−	1.19266i
$245$	−0.0965959	−	0.0965959i	−0.00617128	−	0.00617128i
$246$		−	9.72659i		−	0.620145i
$247$			4.69410i			0.298679i
$248$	28.0323	+	28.0323i	1.78005	+	1.78005i
$249$	−17.6919	−	17.6919i	−1.12118	−	1.12118i
$250$	−13.6761	+	13.6761i	−0.864952	+	0.864952i
$251$	−9.05460			−0.571521			−0.285761	−	0.958301i	$-0.592246\pi$
$251$	−9.05460			−0.571521			−0.285761	+	0.958301i	$0.592246\pi$
$252$	3.59562	−	3.59562i	0.226503	−	0.226503i
$253$			16.1282i			1.01397i
$254$	13.2276			0.829970
$255$	−4.70288	−	4.89269i	−0.294506	−	0.306392i
$256$	−27.6386			−1.72741
$257$		−	10.9504i		−	0.683068i	−0.939869	−	0.341534i	$-0.889054\pi$
$257$		−	10.9504i		−	0.683068i	0.939869	−	0.341534i	$-0.110946\pi$
$258$	3.16384	−	3.16384i	0.196972	−	0.196972i
$259$	−8.80684			−0.547230
$260$	−3.12925	+	3.12925i	−0.194068	+	0.194068i
$261$	−1.74699	−	1.74699i	−0.108136	−	0.108136i
$262$	0.355517	+	0.355517i	0.0219639	+	0.0219639i
$263$			27.3534i			1.68668i	0.537378	+	0.843342i	$0.319415\pi$
$263$			27.3534i			1.68668i	−0.537378	+	0.843342i	$0.680585\pi$
$264$		−	43.6605i		−	2.68712i
$265$	8.41252	+	8.41252i	0.516777	+	0.516777i
$266$	15.5436	+	15.5436i	0.953038	+	0.953038i
$267$	−12.4169	+	12.4169i	−0.759903	+	0.759903i
$268$	29.6738			1.81262
$269$	−14.4415	+	14.4415i	−0.880511	+	0.880511i	−0.993586	−	0.113075i	$-0.963930\pi$
$269$	−14.4415	+	14.4415i	−0.880511	+	0.880511i	0.113075	+	0.993586i	$0.463930\pi$
$270$		−	9.76556i		−	0.594313i
$271$	−22.9318			−1.39301			−0.696504	−	0.717553i	$-0.745262\pi$
$271$	−22.9318			−1.39301			−0.696504	+	0.717553i	$0.745262\pi$
$272$	6.75607	−	6.49396i	0.409647	−	0.393754i
$273$	−6.83693			−0.413790
$274$		−	9.88149i		−	0.596963i
$275$	−17.1972	+	17.1972i	−1.03703	+	1.03703i
$276$	19.4357			1.16989
$277$	−12.0240	+	12.0240i	−0.722453	+	0.722453i	−0.969104	−	0.246651i	$-0.920670\pi$
$277$	−12.0240	+	12.0240i	−0.722453	+	0.722453i	0.246651	+	0.969104i	$0.420670\pi$
$278$	−2.55823	−	2.55823i	−0.153433	−	0.153433i
$279$	−3.55915	−	3.55915i	−0.213081	−	0.213081i
$280$			9.51208i			0.568455i
$281$		−	13.1276i		−	0.783127i	−0.920151	−	0.391563i	$-0.871934\pi$
$281$		−	13.1276i		−	0.783127i	0.920151	−	0.391563i	$-0.128066\pi$
$282$	21.8742	+	21.8742i	1.30259	+	1.30259i
$283$	8.70718	+	8.70718i	0.517588	+	0.517588i	0.916841	−	0.399253i	$-0.130730\pi$
$283$	8.70718	+	8.70718i	0.517588	+	0.517588i	−0.399253	+	0.916841i	$0.630730\pi$
$284$	1.47525	−	1.47525i	0.0875401	−	0.0875401i
$285$	−5.66687			−0.335677
$286$	−13.2328	+	13.2328i	−0.782471	+	0.782471i
$287$			5.81505i			0.343252i
$288$	1.37560			0.0810578
$289$	0.672306	−	16.9867i	0.0395474	−	0.999218i
$290$	10.0690			0.591271
$291$			12.4561i			0.730189i
$292$	−13.3596	+	13.3596i	−0.781811	+	0.781811i
$293$	−31.2345			−1.82474			−0.912371	−	0.409365i	$-0.865750\pi$
$293$	−31.2345			−1.82474			−0.912371	+	0.409365i	$0.865750\pi$
$294$	−0.492250	+	0.492250i	−0.0287086	+	0.0287086i
$295$	−4.19843	−	4.19843i	−0.244442	−	0.244442i
$296$	9.42829	+	9.42829i	0.548008	+	0.548008i
$297$		−	26.7981i		−	1.55498i
$298$			6.69598i			0.387888i
$299$	−2.70377	−	2.70377i	−0.156363	−	0.156363i
$300$	20.7240	+	20.7240i	1.19650	+	1.19650i
$301$	−1.89151	+	1.89151i	−0.109025	+	0.109025i
$302$	31.3960			1.80664
$303$	−19.3578	+	19.3578i	−1.11207	+	1.11207i
$304$		−	7.82510i		−	0.448800i
$305$	−6.25749			−0.358303
$306$	−3.64826	+	3.50672i	−0.208557	+	0.200466i
$307$	8.48639			0.484344			0.242172	−	0.970233i	$-0.422140\pi$
$307$	8.48639			0.484344			0.242172	+	0.970233i	$0.422140\pi$
$308$			56.8689i			3.24041i
$309$	−6.36462	+	6.36462i	−0.362070	+	0.362070i
$310$	20.5136			1.16509
$311$	3.15606	−	3.15606i	0.178964	−	0.178964i	−0.611940	−	0.790904i	$-0.709611\pi$
$311$	3.15606	−	3.15606i	0.178964	−	0.178964i	0.790904	+	0.611940i	$0.209611\pi$
$312$	7.31938	+	7.31938i	0.414378	+	0.414378i
$313$	0.840465	+	0.840465i	0.0475059	+	0.0475059i	0.730461	−	0.682955i	$-0.239305\pi$
$313$	0.840465	+	0.840465i	0.0475059	+	0.0475059i	−0.682955	+	0.730461i	$0.739305\pi$
$314$		−	16.6930i		−	0.942042i
$315$		−	1.20771i		−	0.0680468i
$316$	−41.5526	−	41.5526i	−2.33752	−	2.33752i
$317$	−2.63689	−	2.63689i	−0.148102	−	0.148102i	0.629167	−	0.777270i	$-0.283396\pi$
$317$	−2.63689	−	2.63689i	−0.148102	−	0.148102i	−0.777270	+	0.629167i	$0.783396\pi$
$318$	42.8700	−	42.8700i	2.40403	−	2.40403i
$319$	27.6307			1.54702
$320$	−6.78635	+	6.78635i	−0.379369	+	0.379369i
$321$		−	22.2529i		−	1.24204i
$322$	−17.9060			−0.997862
$323$	−9.83728	−	10.2343i	−0.547361	−	0.569453i
$324$	−37.9966			−2.11092
$325$		−	5.76596i		−	0.319838i
$326$	−25.1669	+	25.1669i	−1.39386	+	1.39386i
$327$	−7.41266			−0.409921
$328$	6.22539	−	6.22539i	0.343739	−	0.343739i
$329$	−13.0775	−	13.0775i	−0.720987	−	0.720987i
$330$	−15.9750	−	15.9750i	−0.879397	−	0.879397i
$331$			19.8429i			1.09066i	0.838220	+	0.545332i	$0.183597\pi$
$331$			19.8429i			1.09066i	−0.838220	+	0.545332i	$0.816403\pi$
$332$		−	49.3406i		−	2.70792i
$333$	−1.19707	−	1.19707i	−0.0655992	−	0.0655992i
$334$	−40.0220	−	40.0220i	−2.18991	−	2.18991i
$335$	4.98348	−	4.98348i	0.272277	−	0.272277i
$336$	11.3972			0.621769
$337$	12.2569	−	12.2569i	0.667674	−	0.667674i	−0.289503	−	0.957177i	$-0.593490\pi$
$337$	12.2569	−	12.2569i	0.667674	−	0.667674i	0.957177	+	0.289503i	$0.0934900\pi$
$338$			26.5916i			1.44639i
$339$	21.6489			1.17581
$340$	0.264684	−	13.3804i	0.0143545	−	0.725655i
$341$	56.2922			3.04839
$342$			4.22553i			0.228491i
$343$	−12.9462	+	12.9462i	−0.699032	+	0.699032i
$344$	4.04996			0.218359
$345$	3.26408	−	3.26408i	0.175732	−	0.175732i
$346$	−36.8768	−	36.8768i	−1.98251	−	1.98251i
$347$	−7.85066	−	7.85066i	−0.421446	−	0.421446i	0.464256	−	0.885701i	$-0.346322\pi$
$347$	−7.85066	−	7.85066i	−0.421446	−	0.421446i	−0.885701	+	0.464256i	$0.846322\pi$
$348$		−	33.2973i		−	1.78492i
$349$		−	7.62592i		−	0.408206i	−0.978949	−	0.204103i	$-0.934572\pi$
$349$		−	7.62592i		−	0.408206i	0.978949	−	0.204103i	$-0.0654278\pi$
$350$	−19.0928	−	19.0928i	−1.02055	−	1.02055i
$351$	4.49251	+	4.49251i	0.239792	+	0.239792i
$352$	−10.8783	+	10.8783i	−0.579818	+	0.579818i
$353$	−15.4635			−0.823037			−0.411519	−	0.911401i	$-0.635002\pi$
$353$	−15.4635			−0.823037			−0.411519	+	0.911401i	$0.635002\pi$
$354$	−21.3951	+	21.3951i	−1.13714	+	1.13714i
$355$		−	0.495514i		−	0.0262992i
$356$	−34.6292			−1.83534
$357$	14.9062	−	14.3279i	0.788922	−	0.758315i
$358$	−43.3708			−2.29222
$359$		−	5.97272i		−	0.315228i	−0.987501	−	0.157614i	$-0.949620\pi$
$359$		−	5.97272i		−	0.315228i	0.987501	−	0.157614i	$-0.0503802\pi$
$360$	−1.29293	+	1.29293i	−0.0681435	+	0.0681435i
$361$	7.14627			0.376119
$362$	−25.9456	+	25.9456i	−1.36367	+	1.36367i
$363$	−29.2566	−	29.2566i	−1.53558	−	1.53558i
$364$	−9.53367	−	9.53367i	−0.499700	−	0.499700i
$365$			4.48728i			0.234875i
$366$			31.8880i			1.66681i
$367$	−3.67282	−	3.67282i	−0.191720	−	0.191720i	0.604719	−	0.796439i	$-0.293285\pi$
$367$	−3.67282	−	3.67282i	−0.191720	−	0.191720i	−0.796439	+	0.604719i	$0.793285\pi$
$368$	4.50720	+	4.50720i	0.234954	+	0.234954i
$369$	−0.790413	+	0.790413i	−0.0411473	+	0.0411473i
$370$	6.89947			0.358687
$371$	−25.6299	+	25.6299i	−1.33064	+	1.33064i
$372$		−	67.8367i		−	3.51717i
$373$	10.8089			0.559661			0.279831	−	0.960049i	$-0.409722\pi$
$373$	10.8089			0.559661			0.279831	+	0.960049i	$0.409722\pi$
$374$	1.11928	−	56.5823i	0.0578765	−	2.92580i
$375$	15.1906			0.784439
$376$			28.0006i			1.44402i
$377$	−4.63210	+	4.63210i	−0.238565	+	0.238565i
$378$	29.7521			1.53028
$379$	5.67677	−	5.67677i	0.291596	−	0.291596i	−0.546114	−	0.837711i	$-0.683894\pi$
$379$	5.67677	−	5.67677i	0.291596	−	0.291596i	0.837711	+	0.546114i	$0.183894\pi$
$380$	−7.90210	−	7.90210i	−0.405369	−	0.405369i
$381$	−7.34619	−	7.34619i	−0.376357	−	0.376357i
$382$			25.6555i			1.31265i
$383$			3.42448i			0.174983i	0.996165	+	0.0874914i	$0.0278850\pi$
$383$			3.42448i			0.174983i	−0.996165	+	0.0874914i	$0.972115\pi$
$384$	27.4909	+	27.4909i	1.40289	+	1.40289i
$385$	9.55069	+	9.55069i	0.486748	+	0.486748i
$386$	20.6952	−	20.6952i	1.05336	−	1.05336i
$387$	−0.514207			−0.0261386
$388$	−17.3692	+	17.3692i	−0.881790	+	0.881790i
$389$			19.0355i			0.965137i	0.875858	+	0.482569i	$0.160296\pi$
$389$			19.0355i			0.965137i	−0.875858	+	0.482569i	$0.839704\pi$
$390$	5.35621			0.271222
$391$	11.5611	+	0.228695i	0.584670	+	0.0115656i
$392$	−0.630117			−0.0318257
$393$		−	0.394887i		−	0.0199194i
$394$	−39.4442	+	39.4442i	−1.98717	+	1.98717i
$395$	−13.9569			−0.702246
$396$	−7.72993	+	7.72993i	−0.388444	+	0.388444i
$397$	12.2389	+	12.2389i	0.614255	+	0.614255i	0.944052	−	0.329797i	$-0.106980\pi$
$397$	12.2389	+	12.2389i	0.614255	+	0.614255i	−0.329797	+	0.944052i	$0.606980\pi$
$398$	9.26520	+	9.26520i	0.464422	+	0.464422i
$399$		−	17.2649i		−	0.864326i
$400$			9.61189i			0.480595i
$401$	−2.59779	−	2.59779i	−0.129727	−	0.129727i	0.639262	−	0.768989i	$-0.279240\pi$
$401$	−2.59779	−	2.59779i	−0.129727	−	0.129727i	−0.768989	+	0.639262i	$0.779240\pi$
$402$	−25.3957	−	25.3957i	−1.26662	−	1.26662i
$403$	−9.43698	+	9.43698i	−0.470090	+	0.470090i
$404$	−53.9864			−2.68592
$405$	−6.38124	+	6.38124i	−0.317086	+	0.317086i
$406$			30.6765i			1.52245i
$407$	18.9331			0.938480
$408$	−31.2971	−	0.619101i	−1.54943	−	0.0306501i
$409$	−4.91776			−0.243168			−0.121584	−	0.992581i	$-0.538797\pi$
$409$	−4.91776			−0.243168			−0.121584	+	0.992581i	$0.538797\pi$
$410$		−	4.55564i		−	0.224987i
$411$	−5.48789	+	5.48789i	−0.270698	+	0.270698i
$412$	−17.7501			−0.874485
$413$	12.7911	−	12.7911i	0.629407	−	0.629407i
$414$	−2.43388	−	2.43388i	−0.119619	−	0.119619i
$415$	−8.28637	−	8.28637i	−0.406762	−	0.406762i
$416$		−	3.64735i		−	0.178826i
$417$			2.84153i			0.139150i
$418$	−33.4159	−	33.4159i	−1.63443	−	1.63443i
$419$	14.6400	+	14.6400i	0.715210	+	0.715210i	0.967620	−	0.252410i	$-0.0812233\pi$
$419$	14.6400	+	14.6400i	0.715210	+	0.715210i	−0.252410	+	0.967620i	$0.581223\pi$
$420$	11.5094	−	11.5094i	0.561599	−	0.561599i
$421$	17.6177			0.858634			0.429317	−	0.903154i	$-0.358754\pi$
$421$	17.6177			0.858634			0.429317	+	0.903154i	$0.358754\pi$
$422$	−20.6950	+	20.6950i	−1.00741	+	1.00741i
$423$		−	3.55513i		−	0.172856i
$424$	54.8768			2.66505
$425$	12.0835	+	12.5712i	0.586138	+	0.609795i
$426$	−2.52513			−0.122343
$427$		−	19.0643i		−	0.922586i
$428$	31.0303	−	31.0303i	1.49991	−	1.49991i
$429$	14.6982			0.709635
$430$	1.48185	−	1.48185i	0.0714610	−	0.0714610i
$431$	−3.66743	−	3.66743i	−0.176654	−	0.176654i	0.613242	−	0.789895i	$-0.289865\pi$
$431$	−3.66743	−	3.66743i	−0.176654	−	0.176654i	−0.789895	+	0.613242i	$0.789865\pi$
$432$	−7.48904	−	7.48904i	−0.360316	−	0.360316i
$433$		−	37.9949i		−	1.82592i	−0.408050	−	0.912960i	$-0.633791\pi$
$433$		−	37.9949i		−	1.82592i	0.408050	−	0.912960i	$-0.366209\pi$
$434$			62.4974i			2.99997i
$435$	−5.59202	−	5.59202i	−0.268117	−	0.268117i
$436$	−10.3365	−	10.3365i	−0.495028	−	0.495028i
$437$	6.82767	−	6.82767i	0.326612	−	0.326612i
$438$	22.8671			1.09263
$439$	10.6646	−	10.6646i	0.508995	−	0.508995i	−0.405223	−	0.914218i	$-0.632806\pi$
$439$	10.6646	−	10.6646i	0.508995	−	0.508995i	0.914218	+	0.405223i	$0.132806\pi$
$440$		−	20.4493i		−	0.974880i
$441$	0.0800036			0.00380969
$442$	9.29798	+	9.67326i	0.442260	+	0.460110i
$443$	−8.47713			−0.402760			−0.201380	−	0.979513i	$-0.564543\pi$
$443$	−8.47713			−0.402760			−0.201380	+	0.979513i	$0.564543\pi$
$444$		−	22.8160i		−	1.08280i
$445$	−5.81571	+	5.81571i	−0.275691	+	0.275691i
$446$	42.0375			1.99054
$447$	3.71875	−	3.71875i	0.175891	−	0.175891i
$448$	−20.6755	−	20.6755i	−0.976827	−	0.976827i
$449$	−0.466435	−	0.466435i	−0.0220124	−	0.0220124i	0.696015	−	0.718027i	$-0.254955\pi$
$449$	−0.466435	−	0.466435i	−0.0220124	−	0.0220124i	−0.718027	+	0.696015i	$0.754955\pi$
$450$		−	5.19040i		−	0.244678i
$451$		−	12.5013i		−	0.588664i
$452$	30.1881	+	30.1881i	1.41993	+	1.41993i
$453$	−17.4364	−	17.4364i	−0.819235	−	0.819235i
$454$	−1.70534	+	1.70534i	−0.0800354	+	0.0800354i
$455$	−3.20221			−0.150122
$456$	−18.4832	+	18.4832i	−0.865554	+	0.865554i
$457$			12.3047i			0.575592i	0.957692	+	0.287796i	$0.0929225\pi$
$457$			12.3047i			0.575592i	−0.957692	+	0.287796i	$0.907078\pi$
$458$	62.1877			2.90584
$459$	−19.2096	−	0.379993i	−0.896627	−	0.0177366i
$460$	9.10311			0.424435
$461$		−	3.03785i		−	0.141487i	−0.997495	−	0.0707433i	$-0.977463\pi$
$461$		−	3.03785i		−	0.141487i	0.997495	−	0.0707433i	$-0.0225371\pi$
$462$	48.6701	−	48.6701i	2.26434	−	2.26434i
$463$	9.67335			0.449559			0.224779	−	0.974410i	$-0.427834\pi$
$463$	9.67335			0.449559			0.224779	+	0.974410i	$0.427834\pi$
$464$	7.72173	−	7.72173i	0.358472	−	0.358472i
$465$	−11.3926	−	11.3926i	−0.528321	−	0.528321i
$466$	−24.0058	−	24.0058i	−1.11205	−	1.11205i
$467$		−	31.6474i		−	1.46447i	−0.681054	−	0.732233i	$-0.738478\pi$
$467$		−	31.6474i		−	1.46447i	0.681054	−	0.732233i	$-0.261522\pi$
$468$		−	2.59174i		−	0.119803i
$469$	15.1828	+	15.1828i	0.701079	+	0.701079i
$470$	10.2452	+	10.2452i	0.472577	+	0.472577i
$471$	−9.27081	+	9.27081i	−0.427176	+	0.427176i
$472$	−27.3873			−1.26060
$473$	4.06640	−	4.06640i	0.186973	−	0.186973i
$474$			71.1239i			3.26683i
$475$	14.5604			0.668078
$476$	40.7652	+	0.806395i	1.86847	+	0.0369610i
$477$	−6.96750			−0.319020
$478$		−	42.0245i		−	1.92216i
$479$	7.50186	−	7.50186i	0.342769	−	0.342769i	−0.514638	−	0.857407i	$-0.672074\pi$
$479$	7.50186	−	7.50186i	0.342769	−	0.342769i	0.857407	+	0.514638i	$0.172074\pi$
$480$	4.40321			0.200978
$481$	−3.17401	+	3.17401i	−0.144722	+	0.144722i
$482$	−32.4113	−	32.4113i	−1.47629	−	1.47629i
$483$	9.94446	+	9.94446i	0.452489	+	0.452489i
$484$		−	81.5931i		−	3.70878i
$485$			5.83406i			0.264911i
$486$	8.92467	+	8.92467i	0.404831	+	0.404831i
$487$	13.2005	+	13.2005i	0.598172	+	0.598172i	0.939826	−	0.341654i	$-0.110987\pi$
$487$	13.2005	+	13.2005i	0.598172	+	0.598172i	−0.341654	+	0.939826i	$0.610987\pi$
$488$	−20.4095	+	20.4095i	−0.923897	+	0.923897i
$489$	27.9538			1.26412
$490$	−0.230555	+	0.230555i	−0.0104154	+	0.0104154i
$491$			12.6860i			0.572510i	0.958154	+	0.286255i	$0.0924104\pi$
$491$			12.6860i			0.572510i	−0.958154	+	0.286255i	$0.907590\pi$
$492$	−15.0651			−0.679188
$493$	0.391800	−	19.8065i	0.0176458	−	0.892038i
$494$	11.2039			0.504087
$495$			2.59636i			0.116698i
$496$	15.7315	−	15.7315i	0.706366	−	0.706366i
$497$	1.50965			0.0677170
$498$	−42.2271	+	42.2271i	−1.89224	+	1.89224i
$499$	−21.3439	−	21.3439i	−0.955483	−	0.955483i	0.0435670	−	0.999051i	$-0.486128\pi$
$499$	−21.3439	−	21.3439i	−0.955483	−	0.955483i	−0.999051	+	0.0435670i	$0.986128\pi$
$500$	21.1823	+	21.1823i	0.947303	+	0.947303i
$501$			44.4541i			1.98606i
$502$			21.6115i			0.964569i
$503$	11.9290	+	11.9290i	0.531888	+	0.531888i	0.921134	−	0.389246i	$-0.127264\pi$
$503$	11.9290	+	11.9290i	0.531888	+	0.531888i	−0.389246	+	0.921134i	$0.627264\pi$
$504$	−3.93909	−	3.93909i	−0.175461	−	0.175461i
$505$	−9.06659	+	9.06659i	−0.403458	+	0.403458i
$506$	38.4947			1.71130
$507$	14.7682	−	14.7682i	0.655879	−	0.655879i
$508$		−	20.4876i		−	0.908990i
$509$	−14.0304			−0.621886			−0.310943	−	0.950429i	$-0.600645\pi$
$509$	−14.0304			−0.621886			−0.310943	+	0.950429i	$0.600645\pi$
$510$	−11.6779	+	11.2248i	−0.517105	+	0.497044i
$511$	−13.6711			−0.604773
$512$			24.4897i			1.08230i
$513$	−11.3447	+	11.3447i	−0.500879	+	0.500879i
$514$	−26.1365			−1.15283
$515$	−2.98099	+	2.98099i	−0.131358	+	0.131358i
$516$	−4.90034	−	4.90034i	−0.215725	−	0.215725i
$517$	28.1143	+	28.1143i	1.23647	+	1.23647i
$518$			21.0202i			0.923573i
$519$			40.9606i			1.79797i
$520$	3.42817	+	3.42817i	0.150335	+	0.150335i
$521$	13.9854	+	13.9854i	0.612709	+	0.612709i	0.943651	−	0.330942i	$-0.107366\pi$
$521$	13.9854	+	13.9854i	0.612709	+	0.612709i	−0.330942	+	0.943651i	$0.607366\pi$
$522$	−4.16972	+	4.16972i	−0.182504	+	0.182504i
$523$	3.01748			0.131945			0.0659726	−	0.997821i	$-0.478985\pi$
$523$	3.01748			0.131945			0.0659726	+	0.997821i	$0.478985\pi$
$524$	0.550646	−	0.550646i	0.0240551	−	0.0240551i
$525$			21.2072i			0.925557i
$526$	65.2871			2.84665
$527$	0.798216	−	40.3518i	0.0347708	−	1.75775i
$528$	−24.5020			−1.06631
$529$		−	15.1346i		−	0.658027i
$530$	20.0790	−	20.0790i	0.872176	−	0.872176i
$531$	3.47726			0.150900
$532$	24.0748	−	24.0748i	1.04378	−	1.04378i
$533$	2.09576	+	2.09576i	0.0907774	+	0.0907774i
$534$	29.6367	+	29.6367i	1.28251	+	1.28251i
$535$		−	10.4226i		−	0.450608i
$536$		−	32.5084i		−	1.40415i
$537$	24.0868	+	24.0868i	1.03942	+	1.03942i
$538$	34.4689	+	34.4689i	1.48606	+	1.48606i
$539$	−0.632676	+	0.632676i	−0.0272513	+	0.0272513i
$540$	−15.1255			−0.650896
$541$	6.57917	−	6.57917i	0.282861	−	0.282861i	−0.551388	−	0.834249i	$-0.685902\pi$
$541$	6.57917	−	6.57917i	0.282861	−	0.282861i	0.834249	+	0.551388i	$0.185902\pi$
$542$			54.7336i			2.35101i
$543$	28.8188			1.23673
$544$	7.64364	+	7.95215i	0.327718	+	0.340946i
$545$	−3.47186			−0.148718
$546$			16.3184i			0.698363i
$547$	−25.8815	+	25.8815i	−1.10661	+	1.10661i	−0.113021	+	0.993593i	$0.536053\pi$
$547$	−25.8815	+	25.8815i	−1.10661	+	1.10661i	−0.993593	+	0.113021i	$0.963947\pi$
$548$	−15.3050			−0.653798
$549$	2.59132	−	2.59132i	0.110595	−	0.110595i
$550$	41.0462	+	41.0462i	1.75021	+	1.75021i
$551$	−11.6971	−	11.6971i	−0.498315	−	0.498315i
$552$		−	21.2924i		−	0.906263i
$553$		−	42.5215i		−	1.80820i
$554$	28.6989	+	28.6989i	1.21930	+	1.21930i
$555$	−3.83176	−	3.83176i	−0.162649	−	0.162649i
$556$	−3.96234	+	3.96234i	−0.168041	+	0.168041i
$557$	−40.6263			−1.72139			−0.860695	−	0.509121i	$-0.829971\pi$
$557$	−40.6263			−1.72139			−0.860695	+	0.509121i	$0.829971\pi$
$558$	−8.49498	+	8.49498i	−0.359621	+	0.359621i
$559$			1.36341i			0.0576659i
$560$	5.33811			0.225576
$561$	−32.0457	+	30.8025i	−1.35297	+	1.30048i
$562$	−31.3330			−1.32170
$563$			6.66100i			0.280728i	0.990100	+	0.140364i	$0.0448273\pi$
$563$			6.66100i			0.280728i	−0.990100	+	0.140364i	$0.955173\pi$
$564$	33.8800	−	33.8800i	1.42661	−	1.42661i
$565$	10.1397			0.426580
$566$	20.7823	−	20.7823i	0.873545	−	0.873545i
$567$	−19.4413	−	19.4413i	−0.816458	−	0.816458i
$568$	−1.61618	−	1.61618i	−0.0678133	−	0.0678133i
$569$			1.14008i			0.0477948i	0.999714	+	0.0238974i	$0.00760750\pi$
$569$			1.14008i			0.0477948i	−0.999714	+	0.0238974i	$0.992392\pi$
$570$			13.5257i			0.566529i
$571$	5.15031	+	5.15031i	0.215534	+	0.215534i	0.806613	−	0.591080i	$-0.201298\pi$
$571$	5.15031	+	5.15031i	0.215534	+	0.215534i	−0.591080	+	0.806613i	$0.701298\pi$
$572$	20.4957	+	20.4957i	0.856968	+	0.856968i
$573$	14.2483	−	14.2483i	0.595231	−	0.595231i
$574$	13.8794			0.579314
$575$	−8.38671	+	8.38671i	−0.349750	+	0.349750i
$576$		−	5.62066i		−	0.234194i
$577$	−9.25894			−0.385455			−0.192727	−	0.981252i	$-0.561733\pi$
$577$	−9.25894			−0.385455			−0.192727	+	0.981252i	$0.561733\pi$
$578$	−40.5439	−	1.60466i	−1.68640	−	0.0667450i
$579$	−22.9870			−0.955306
$580$		−	15.5954i		−	0.647565i
$581$	25.2455	−	25.2455i	1.04736	−	1.04736i
$582$	29.7302			1.23236
$583$	55.0996	−	55.0996i	2.28199	−	2.28199i
$584$	14.6358	+	14.6358i	0.605633	+	0.605633i
$585$	−0.435262	−	0.435262i	−0.0179959	−	0.0179959i
$586$			74.5506i			3.07966i
$587$			39.5740i			1.63339i	0.577067	+	0.816697i	$0.304197\pi$
$587$			39.5740i			1.63339i	−0.577067	+	0.816697i	$0.695803\pi$
$588$	0.762426	+	0.762426i	0.0314419	+	0.0314419i
$589$	−23.8306	−	23.8306i	−0.981924	−	0.981924i
$590$	−10.0208	+	10.0208i	−0.412550	+	0.412550i
$591$	43.8122			1.80219
$592$	5.29109	−	5.29109i	0.217462	−	0.217462i
$593$		−	22.7497i		−	0.934218i	−0.884200	−	0.467109i	$-0.845296\pi$
$593$		−	22.7497i		−	0.934218i	0.884200	−	0.467109i	$-0.154704\pi$
$594$	−63.9616			−2.62438
$595$	6.98163	−	6.71077i	0.286219	−	0.275115i
$596$	10.3711			0.424818
$597$		−	10.2912i		−	0.421192i
$598$	−6.45336	+	6.45336i	−0.263898	+	0.263898i
$599$	−24.5133			−1.00159			−0.500794	−	0.865567i	$-0.666958\pi$
$599$	−24.5133			−1.00159			−0.500794	+	0.865567i	$0.666958\pi$
$600$	22.7036	−	22.7036i	0.926873	−	0.926873i
$601$	−8.94188	−	8.94188i	−0.364747	−	0.364747i	0.500810	−	0.865557i	$-0.333035\pi$
$601$	−8.94188	−	8.94188i	−0.364747	−	0.364747i	−0.865557	+	0.500810i	$0.833035\pi$
$602$	4.51465	+	4.51465i	0.184003	+	0.184003i
$603$			4.12747i			0.168083i
$604$		−	48.6280i		−	1.97865i
$605$	−13.7029	−	13.7029i	−0.557103	−	0.557103i
$606$	46.2031	+	46.2031i	1.87687	+	1.87687i
$607$	9.74780	−	9.74780i	0.395651	−	0.395651i	−0.481045	−	0.876696i	$-0.659743\pi$
$607$	9.74780	−	9.74780i	0.395651	−	0.395651i	0.876696	+	0.481045i	$0.159743\pi$
$608$	9.21044			0.373533
$609$	17.0368	−	17.0368i	0.690367	−	0.690367i
$610$			14.9354i			0.604716i
$611$	−9.42633			−0.381349
$612$	5.43142	+	5.65064i	0.219552	+	0.228413i
$613$	−4.63064			−0.187030			−0.0935149	−	0.995618i	$-0.529810\pi$
$613$	−4.63064			−0.187030			−0.0935149	+	0.995618i	$0.529810\pi$
$614$		−	20.2553i		−	0.817438i
$615$	−2.53007	+	2.53007i	−0.102022	+	0.102022i
$616$	62.3014			2.51019
$617$	11.0765	−	11.0765i	0.445921	−	0.445921i	−0.448075	−	0.893996i	$-0.647890\pi$
$617$	11.0765	−	11.0765i	0.445921	−	0.445921i	0.893996	+	0.448075i	$0.147890\pi$
$618$	15.1911	+	15.1911i	0.611074	+	0.611074i
$619$	−5.06460	−	5.06460i	−0.203564	−	0.203564i	0.597961	−	0.801525i	$-0.295978\pi$
$619$	−5.06460	−	5.06460i	−0.203564	−	0.203564i	−0.801525	+	0.597961i	$0.795978\pi$
$620$		−	31.7726i		−	1.27602i
$621$		−	13.0689i		−	0.524436i
$622$	−7.53290	−	7.53290i	−0.302042	−	0.302042i
$623$	−17.7183	−	17.7183i	−0.709870	−	0.709870i
$624$	4.10758	−	4.10758i	0.164435	−	0.164435i
$625$	−14.0306			−0.561225
$626$	2.00602	−	2.00602i	0.0801767	−	0.0801767i
$627$			37.1164i			1.48229i
$628$	−25.8551			−1.03173
$629$	0.268469	−	13.5718i	0.0107046	−	0.541143i
$630$	−2.88257			−0.114844
$631$		−	8.62814i		−	0.343481i	−0.985142	−	0.171740i	$-0.945061\pi$
$631$		−	8.62814i		−	0.343481i	0.985142	−	0.171740i	$-0.0549390\pi$
$632$	−45.5220	+	45.5220i	−1.81077	+	1.81077i
$633$	22.9867			0.913640
$634$	−6.29372	+	6.29372i	−0.249956	+	0.249956i
$635$	−3.44073	−	3.44073i	−0.136541	−	0.136541i
$636$	−66.3995	−	66.3995i	−2.63291	−	2.63291i
$637$		−	0.212127i		−	0.00840478i
$638$		−	65.9490i		−	2.61095i
$639$	0.205200	+	0.205200i	0.00811757	+	0.00811757i
$640$	12.8759	+	12.8759i	0.508964	+	0.508964i
$641$	1.47253	−	1.47253i	0.0581614	−	0.0581614i	−0.677428	−	0.735589i	$-0.736905\pi$
$641$	1.47253	−	1.47253i	0.0581614	−	0.0581614i	0.735589	+	0.677428i	$0.236905\pi$
$642$	−53.1133			−2.09621
$643$	20.8027	−	20.8027i	0.820377	−	0.820377i	−0.165785	−	0.986162i	$-0.553016\pi$
$643$	20.8027	−	20.8027i	0.820377	−	0.820377i	0.986162	+	0.165785i	$0.0530159\pi$
$644$			27.7338i			1.09287i
$645$	−1.64595			−0.0648091
$646$	−24.4273	+	23.4796i	−0.961079	+	0.923793i
$647$	34.6627			1.36273			0.681365	−	0.731943i	$-0.261386\pi$
$647$	34.6627			1.36273			0.681365	+	0.731943i	$0.261386\pi$
$648$			41.6263i			1.63524i
$649$	−27.4985	+	27.4985i	−1.07941	+	1.07941i
$650$	−13.7622			−0.539798
$651$	34.7092	−	34.7092i	1.36036	−	1.36036i
$652$	38.9799	+	38.9799i	1.52657	+	1.52657i
$653$	31.9691	+	31.9691i	1.25105	+	1.25105i	0.955252	+	0.295794i	$0.0955844\pi$
$653$	31.9691	+	31.9691i	1.25105	+	1.25105i	0.295794	+	0.955252i	$0.404416\pi$
$654$			17.6925i			0.691833i
$655$		−	0.184953i		−	0.00722672i
$656$	−3.49364	−	3.49364i	−0.136404	−	0.136404i
$657$	−1.85825	−	1.85825i	−0.0724972	−	0.0724972i
$658$	−31.2134	+	31.2134i	−1.21683	+	1.21683i
$659$	−25.0934			−0.977501			−0.488751	−	0.872424i	$-0.662547\pi$
$659$	−25.0934			−0.977501			−0.488751	+	0.872424i	$0.662547\pi$
$660$	−24.7431	+	24.7431i	−0.963123	+	0.963123i
$661$		−	35.2468i		−	1.37094i	−0.728099	−	0.685472i	$-0.759596\pi$
$661$		−	35.2468i		−	1.37094i	0.728099	−	0.685472i	$-0.240404\pi$
$662$	47.3610			1.84074
$663$	0.208418	−	10.5361i	0.00809430	−	0.409187i
$664$	−54.0539			−2.09770
$665$		−	8.08635i		−	0.313575i
$666$	−2.85717	+	2.85717i	−0.110713	+	0.110713i
$667$	13.4750			0.521752
$668$	−61.9885	+	61.9885i	−2.39841	+	2.39841i
$669$	−23.3464	−	23.3464i	−0.902624	−	0.902624i
$670$	−11.8946	−	11.8946i	−0.459528	−	0.459528i
$671$			40.9848i			1.58220i
$672$			13.4150i			0.517493i
$673$	32.8423	+	32.8423i	1.26598	+	1.26598i	0.948148	+	0.317830i	$0.102954\pi$
$673$	32.8423	+	32.8423i	1.26598	+	1.26598i	0.317830	+	0.948148i	$0.397046\pi$
$674$	−29.2547	−	29.2547i	−1.12685	−	1.12685i
$675$	13.9351	−	13.9351i	0.536363	−	0.536363i
$676$	41.1867			1.58410
$677$	8.47665	−	8.47665i	0.325784	−	0.325784i	−0.525197	−	0.850981i	$-0.676008\pi$
$677$	8.47665	−	8.47665i	0.325784	−	0.325784i	0.850981	+	0.525197i	$0.176008\pi$
$678$		−	51.6716i		−	1.98444i
$679$	−17.7742			−0.682113
$680$	−14.6586	−	0.289968i	−0.562131	−	0.0111198i
$681$	1.89419			0.0725854
$682$		−	134.358i		−	5.14484i
$683$	33.2520	−	33.2520i	1.27235	−	1.27235i	0.327502	−	0.944850i	$-0.393793\pi$
$683$	33.2520	−	33.2520i	1.27235	−	1.27235i	0.944850	−	0.327502i	$-0.106207\pi$
$684$	6.54475			0.250245
$685$	−2.57036	+	2.57036i	−0.0982084	+	0.0982084i
$686$	30.9001	+	30.9001i	1.17977	+	1.17977i
$687$	−34.5372	−	34.5372i	−1.31768	−	1.31768i
$688$		−	2.27281i		−	0.0866499i
$689$			18.4741i			0.703808i
$690$	−7.79071	−	7.79071i	−0.296587	−	0.296587i
$691$	1.65526	+	1.65526i	0.0629691	+	0.0629691i	0.737890	−	0.674921i	$-0.235822\pi$
$691$	1.65526	+	1.65526i	0.0629691	+	0.0629691i	−0.674921	+	0.737890i	$0.735822\pi$
$692$	−57.1170	+	57.1170i	−2.17126	+	2.17126i
$693$	−7.91017			−0.300482
$694$	−18.7380	+	18.7380i	−0.711283	+	0.711283i
$695$			1.33089i			0.0504834i
$696$	−36.4780			−1.38270
$697$	−8.96129	−	0.177267i	−0.339433	−	0.00671448i
$698$	−18.2015			−0.688939
$699$			26.6642i			1.00853i
$700$	−29.5721	+	29.5721i	−1.11772	+	1.11772i
$701$	−0.807921			−0.0305148			−0.0152574	−	0.999884i	$-0.504857\pi$
$701$	−0.807921			−0.0305148			−0.0152574	+	0.999884i	$0.504857\pi$
$702$	10.7227	−	10.7227i	0.404703	−	0.404703i
$703$	−8.01512	−	8.01512i	−0.302296	−	0.302296i
$704$	44.4487	+	44.4487i	1.67522	+	1.67522i
$705$		−	11.3798i		−	0.428587i
$706$			36.9082i			1.38906i
$707$	−27.6226	−	27.6226i	−1.03885	−	1.03885i
$708$	33.1379	+	33.1379i	1.24540	+	1.24540i
$709$	6.06150	−	6.06150i	0.227644	−	0.227644i	−0.584064	−	0.811708i	$-0.698538\pi$
$709$	6.06150	−	6.06150i	0.227644	−	0.227644i	0.811708	+	0.584064i	$0.198538\pi$
$710$	−1.18269			−0.0443857
$711$	5.77975	−	5.77975i	0.216757	−	0.216757i
$712$			37.9372i			1.42176i
$713$	27.4526			1.02811
$714$	−34.1979	−	35.5782i	−1.27983	−	1.33148i
$715$	6.88418			0.257454
$716$			67.1751i			2.51045i
$717$	−23.3392	+	23.3392i	−0.871617	+	0.871617i
$718$	−14.2557			−0.532017
$719$	−1.61052	+	1.61052i	−0.0600624	+	0.0600624i	−0.736500	−	0.676438i	$-0.763523\pi$
$719$	−1.61052	+	1.61052i	−0.0600624	+	0.0600624i	0.676438	+	0.736500i	$0.263523\pi$
$720$	0.725584	+	0.725584i	0.0270409	+	0.0270409i
$721$	−9.08199	−	9.08199i	−0.338231	−	0.338231i
$722$		−	17.0567i		−	0.634785i
$723$			36.0005i			1.33887i
$724$	40.1860	+	40.1860i	1.49350	+	1.49350i
$725$	14.3681	+	14.3681i	0.533618	+	0.533618i
$726$	−69.8297	+	69.8297i	−2.59162	+	2.59162i
$727$	−5.28330			−0.195947			−0.0979733	−	0.995189i	$-0.531236\pi$
$727$	−5.28330			−0.195947			−0.0979733	+	0.995189i	$0.531236\pi$
$728$	−10.4444	+	10.4444i	−0.387095	+	0.387095i
$729$			20.9216i			0.774876i
$730$	10.7102			0.396404
$731$	−2.85724	−	2.97257i	−0.105679	−	0.109944i
$732$	49.3900			1.82551
$733$		−	49.2136i		−	1.81774i	−0.417074	−	0.908872i	$-0.636944\pi$
$733$		−	49.2136i		−	1.81774i	0.417074	−	0.908872i	$-0.363056\pi$
$734$	−8.76628	+	8.76628i	−0.323569	+	0.323569i
$735$	0.256087			0.00944591
$736$	−5.30515	+	5.30515i	−0.195550	+	0.195550i
$737$	−32.6404	−	32.6404i	−1.20232	−	1.20232i
$738$	1.88656	+	1.88656i	0.0694452	+	0.0694452i
$739$			50.5841i			1.86077i	0.366590	+	0.930383i	$0.380525\pi$
$739$			50.5841i			1.86077i	−0.366590	+	0.930383i	$0.619475\pi$
$740$		−	10.6863i		−	0.392836i
$741$	−6.22230	−	6.22230i	−0.228582	−	0.228582i
$742$	61.1734	+	61.1734i	2.24574	+	2.24574i
$743$	−30.1950	+	30.1950i	−1.10775	+	1.10775i	−0.114302	+	0.993446i	$0.536463\pi$
$743$	−30.1950	+	30.1950i	−1.10775	+	1.10775i	−0.993446	+	0.114302i	$0.963537\pi$
$744$	−74.3168			−2.72459
$745$	1.74175	−	1.74175i	0.0638127	−	0.0638127i
$746$		−	25.7986i		−	0.944553i
$747$	6.86302			0.251105
$748$	−87.6379	−	1.73360i	−3.20436	−	0.0633868i
$749$	31.7538			1.16026
$750$		−	36.2569i		−	1.32392i
$751$	−6.70828	+	6.70828i	−0.244789	+	0.244789i	−0.818828	−	0.574039i	$-0.805376\pi$
$751$	−6.70828	+	6.70828i	−0.244789	+	0.244789i	0.574039	+	0.818828i	$0.305376\pi$
$752$	15.7138			0.573022
$753$	12.0024	−	12.0024i	0.437391	−	0.437391i
$754$	11.0559	+	11.0559i	0.402632	+	0.402632i
$755$	−8.16669	−	8.16669i	−0.297216	−	0.297216i
$756$		−	46.0817i		−	1.67598i
$757$			36.9555i			1.34317i	0.740927	+	0.671585i	$0.234386\pi$
$757$			36.9555i			1.34317i	−0.740927	+	0.671585i	$0.765614\pi$
$758$	−13.5493	−	13.5493i	−0.492133	−	0.492133i
$759$	−21.3788	−	21.3788i	−0.776001	−	0.776001i
$760$	−8.65696	+	8.65696i	−0.314021	+	0.314021i
$761$	−47.8209			−1.73350			−0.866752	−	0.498739i	$-0.833797\pi$
$761$	−47.8209			−1.73350			−0.866752	+	0.498739i	$0.833797\pi$
$762$	−17.5339	+	17.5339i	−0.635186	+	0.635186i
$763$		−	10.5775i		−	0.382931i
$764$	39.7367			1.43762
$765$	1.86114	+	0.0368161i	0.0672898	+	0.00133109i
$766$	8.17355			0.295322
$767$		−	9.21986i		−	0.332910i
$768$	36.6366	−	36.6366i	1.32201	−	1.32201i
$769$	6.88804			0.248389			0.124195	−	0.992258i	$-0.460365\pi$
$769$	6.88804			0.248389			0.124195	+	0.992258i	$0.460365\pi$
$770$	22.7956	−	22.7956i	0.821496	−	0.821496i
$771$	14.5154	+	14.5154i	0.522760	+	0.522760i
$772$	−32.0539	−	32.0539i	−1.15364	−	1.15364i
$773$		−	28.0163i		−	1.00767i	−0.863799	−	0.503837i	$-0.831921\pi$
$773$		−	28.0163i		−	1.00767i	0.863799	−	0.503837i	$-0.168079\pi$
$774$			1.22731i			0.0441147i
$775$	29.2722	+	29.2722i	1.05149	+	1.05149i
$776$	19.0285	+	19.0285i	0.683082	+	0.683082i
$777$	11.6740	−	11.6740i	0.418802	−	0.418802i
$778$	45.4339			1.62888
$779$	−5.29229	+	5.29229i	−0.189616	+	0.189616i
$780$		−	8.29600i		−	0.297044i
$781$	−3.24548			−0.116132
$782$	0.545850	−	27.5940i	0.0195196	−	0.986761i
$783$	−22.3896			−0.800138
$784$			0.353617i			0.0126292i
$785$	−4.34217	+	4.34217i	−0.154979	+	0.154979i
$786$	−0.942517			−0.0336185
$787$	−21.2358	+	21.2358i	−0.756976	+	0.756976i	−0.975771	−	0.218795i	$-0.929787\pi$
$787$	−21.2358	+	21.2358i	−0.756976	+	0.756976i	0.218795	+	0.975771i	$0.429787\pi$
$788$	61.0934	+	61.0934i	2.17636	+	2.17636i
$789$	−36.2585	−	36.2585i	−1.29084	−	1.29084i
$790$			33.3123i			1.18520i
$791$			30.8919i			1.09839i
$792$	8.46834	+	8.46834i	0.300909	+	0.300909i
$793$	−6.87081	−	6.87081i	−0.243990	−	0.243990i
$794$	29.2119	−	29.2119i	1.03669	−	1.03669i
$795$	−22.3026			−0.790991
$796$	14.3505	−	14.3505i	0.508639	−	0.508639i
$797$		−	2.22633i		−	0.0788607i	−0.999222	−	0.0394303i	$-0.987446\pi$
$797$		−	2.22633i		−	0.0788607i	0.999222	−	0.0394303i	$-0.0125543\pi$
$798$	−41.2078			−1.45874
$799$	20.5518	−	19.7545i	0.727069	−	0.698862i
$800$	−11.3136			−0.399995
$801$		−	4.81674i		−	0.170191i
$802$	−6.20040	+	6.20040i	−0.218944	+	0.218944i
$803$	29.3904			1.03716
$804$	−39.3343	+	39.3343i	−1.38721	+	1.38721i
$805$	4.65768	+	4.65768i	0.164162	+	0.164162i
$806$	22.5242	+	22.5242i	0.793381	+	0.793381i
$807$		−	38.2860i		−	1.34773i
$808$			59.1435i			2.08066i
$809$	28.4864	+	28.4864i	1.00153	+	1.00153i	0.999999	+	0.00153038i	$0.000487135\pi$
$809$	28.4864	+	28.4864i	1.00153	+	1.00153i	0.00153038	+	0.999999i	$0.499513\pi$
$810$	15.2307	+	15.2307i	0.535154	+	0.535154i
$811$	−0.796588	+	0.796588i	−0.0279720	+	0.0279720i	−0.720954	−	0.692982i	$-0.756296\pi$
$811$	−0.796588	+	0.796588i	−0.0279720	+	0.0279720i	0.692982	+	0.720954i	$0.256296\pi$
$812$	47.5136			1.66740
$813$	30.3974	−	30.3974i	1.06608	−	1.06608i
$814$		−	45.1896i		−	1.58389i
$815$	13.0927			0.458618
$816$	−0.347435	+	17.5637i	−0.0121627	+	0.614852i
$817$	−3.44292			−0.120453
$818$			11.7377i			0.410400i
$819$	1.32608	−	1.32608i	0.0463371	−	0.0463371i
$820$	−7.05604			−0.246408
$821$	−33.7615	+	33.7615i	−1.17829	+	1.17829i	−0.198105	+	0.980181i	$0.563479\pi$
$821$	−33.7615	+	33.7615i	−1.17829	+	1.17829i	−0.980181	+	0.198105i	$0.936521\pi$
$822$	13.0985	+	13.0985i	0.456862	+	0.456862i
$823$	−4.74761	−	4.74761i	−0.165491	−	0.165491i	0.619503	−	0.784994i	$-0.287334\pi$
$823$	−4.74761	−	4.74761i	−0.165491	−	0.165491i	−0.784994	+	0.619503i	$0.787334\pi$
$824$			19.4457i			0.677423i
$825$		−	45.5916i		−	1.58730i
$826$	−30.5297	−	30.5297i	−1.06226	−	1.06226i
$827$	16.5472	+	16.5472i	0.575402	+	0.575402i	0.933633	−	0.358231i	$-0.116620\pi$
$827$	16.5472	+	16.5472i	0.575402	+	0.575402i	−0.358231	+	0.933633i	$0.616620\pi$
$828$	−3.76973	+	3.76973i	−0.131007	+	0.131007i
$829$	13.9659			0.485055			0.242527	−	0.970145i	$-0.422024\pi$
$829$	13.9659			0.485055			0.242527	+	0.970145i	$0.422024\pi$
$830$	−19.7779	+	19.7779i	−0.686501	+	0.686501i
$831$		−	31.8771i		−	1.10580i
$832$	−14.9030			−0.516669
$833$	0.444548	+	0.462490i	0.0154027	+	0.0160243i
$834$	6.78217			0.234847
$835$			20.8210i			0.720539i
$836$	−51.7565	+	51.7565i	−1.79004	+	1.79004i
$837$	−45.6144			−1.57666
$838$	34.9427	−	34.9427i	1.20708	−	1.20708i
$839$	35.3020	+	35.3020i	1.21876	+	1.21876i	0.968067	+	0.250692i	$0.0806581\pi$
$839$	35.3020	+	35.3020i	1.21876	+	1.21876i	0.250692	+	0.968067i	$0.419342\pi$
$840$	−12.6088	−	12.6088i	−0.435045	−	0.435045i
$841$			5.91474i			0.203957i
$842$		−	42.0499i		−	1.44914i
$843$	17.4014	+	17.4014i	0.599336	+	0.599336i
$844$	32.0535	+	32.0535i	1.10333	+	1.10333i
$845$	6.91698	−	6.91698i	0.237951	−	0.237951i
$846$	−8.48539			−0.291734
$847$	41.7478	−	41.7478i	1.43447	−	1.43447i
$848$		−	30.7965i		−	1.05756i
$849$	−23.0837			−0.792232
$850$	30.0050	−	28.8410i	1.02916	−	0.989238i
$851$	9.23331			0.316514
$852$			3.91106i			0.133991i
$853$	6.99060	−	6.99060i	0.239353	−	0.239353i	−0.577229	−	0.816582i	$-0.695866\pi$
$853$	6.99060	−	6.99060i	0.239353	−	0.239353i	0.816582	+	0.577229i	$0.195866\pi$
$854$	−45.5026			−1.55707
$855$	1.09914	−	1.09914i	0.0375898	−	0.0375898i
$856$	−33.9945	−	33.9945i	−1.16191	−	1.16191i
$857$	−8.90735	−	8.90735i	−0.304269	−	0.304269i	0.538412	−	0.842682i	$-0.319024\pi$
$857$	−8.90735	−	8.90735i	−0.304269	−	0.304269i	−0.842682	+	0.538412i	$0.819024\pi$
$858$		−	35.0816i		−	1.19767i
$859$			39.3138i			1.34137i	0.741742	+	0.670685i	$0.234000\pi$
$859$			39.3138i			1.34137i	−0.741742	+	0.670685i	$0.766000\pi$
$860$	−2.29517	−	2.29517i	−0.0782647	−	0.0782647i
$861$	−7.70819	−	7.70819i	−0.262694	−	0.262694i
$862$	−8.75342	+	8.75342i	−0.298143	+	0.298143i
$863$	−33.9757			−1.15655			−0.578273	−	0.815843i	$-0.696273\pi$
$863$	−33.9757			−1.15655			−0.578273	+	0.815843i	$0.696273\pi$
$864$	8.81488	−	8.81488i	0.299888	−	0.299888i
$865$			19.1847i			0.652299i
$866$	−90.6863			−3.08164
$867$	21.6257	+	23.4080i	0.734446	+	0.794979i
$868$	96.7996			3.28559
$869$			91.4136i			3.10099i
$870$	−13.3470	+	13.3470i	−0.452507	+	0.452507i
$871$	10.9439			0.370819
$872$	−11.3239	+	11.3239i	−0.383475	+	0.383475i
$873$	−2.41597	−	2.41597i	−0.0817682	−	0.0817682i
$874$	−16.2963	−	16.2963i	−0.551230	−	0.551230i
$875$			21.6762i			0.732790i
$876$		−	35.4178i		−	1.19666i
$877$	1.94453	+	1.94453i	0.0656621	+	0.0656621i	0.739175	−	0.673513i	$-0.235216\pi$
$877$	1.94453	+	1.94453i	0.0656621	+	0.0656621i	−0.673513	+	0.739175i	$0.735216\pi$
$878$	−25.4543	−	25.4543i	−0.859042	−	0.859042i
$879$	41.4032	−	41.4032i	1.39649	−	1.39649i
$880$	−11.4760			−0.386855
$881$	11.1064	−	11.1064i	0.374185	−	0.374185i	−0.494814	−	0.868999i	$-0.664764\pi$
$881$	11.1064	−	11.1064i	0.374185	−	0.374185i	0.868999	+	0.494814i	$0.164764\pi$
$882$		−	0.190952i		−	0.00642970i
$883$	45.9485			1.54629			0.773145	−	0.634229i	$-0.218682\pi$
$883$	45.9485			1.54629			0.773145	+	0.634229i	$0.218682\pi$
$884$	14.9825	−	14.4012i	0.503916	−	0.484366i
$885$	11.1305			0.374148
$886$			20.2332i			0.679748i
$887$	−6.54688	+	6.54688i	−0.219823	+	0.219823i	−0.808424	−	0.588601i	$-0.799679\pi$
$887$	−6.54688	+	6.54688i	−0.219823	+	0.219823i	0.588601	+	0.808424i	$0.299679\pi$
$888$	−24.9955			−0.838793
$889$	10.4826	−	10.4826i	0.351577	−	0.351577i
$890$	13.8809	+	13.8809i	0.465290	+	0.465290i
$891$	41.7953	+	41.7953i	1.40020	+	1.40020i
$892$		−	65.1102i		−	2.18005i
$893$		−	23.8037i		−	0.796562i
$894$	−8.87591	−	8.87591i	−0.296855	−	0.296855i
$895$	11.2815	+	11.2815i	0.377100	+	0.377100i
$896$	−39.2281	+	39.2281i	−1.31052	+	1.31052i
$897$	7.16801			0.239333
$898$	−1.11329	+	1.11329i	−0.0371508	+	0.0371508i
$899$		−	47.0317i		−	1.56859i
$900$	−8.03919			−0.267973
$901$	−38.7156	−	40.2782i	−1.28980	−	1.34186i
$902$	−29.8382			−0.993502
$903$		−	5.01460i		−	0.166875i
$904$	33.0718	−	33.0718i	1.09995	−	1.09995i
$905$	13.4978			0.448684
$906$	−41.6173	+	41.6173i	−1.38264	+	1.38264i
$907$	30.4965	+	30.4965i	1.01262	+	1.01262i	0.999919	+	0.0127018i	$0.00404323\pi$
$907$	30.4965	+	30.4965i	1.01262	+	1.01262i	0.0127018	+	0.999919i	$0.495957\pi$
$908$	2.64133	+	2.64133i	0.0876555	+	0.0876555i
$909$		−	7.50922i		−	0.249065i
$910$			7.64304i			0.253364i
$911$	−37.4464	−	37.4464i	−1.24066	−	1.24066i	−0.959729	−	0.280926i	$-0.909358\pi$
$911$	−37.4464	−	37.4464i	−1.24066	−	1.24066i	−0.280926	−	0.959729i	$-0.590642\pi$
$912$	10.3726	+	10.3726i	0.343472	+	0.343472i
$913$	−54.2734	+	54.2734i	−1.79619	+	1.79619i
$914$	29.3690			0.971439
$915$	8.29467	−	8.29467i	0.274213	−	0.274213i
$916$		−	96.3200i		−	3.18250i
$917$	0.563485			0.0186079
$918$	−0.906968	+	45.8495i	−0.0299344	+	1.51326i
$919$	−22.2232			−0.733076			−0.366538	−	0.930403i	$-0.619457\pi$
$919$	−22.2232			−0.733076			−0.366538	+	0.930403i	$0.619457\pi$
$920$		−	9.97269i		−	0.328790i
$921$	−11.2492	+	11.2492i	−0.370674	+	0.370674i
$922$	−7.25073			−0.238790
$923$	0.544081	−	0.544081i	0.0179086	−	0.0179086i
$924$	−75.3831	−	75.3831i	−2.47992	−	2.47992i
$925$	9.84531	+	9.84531i	0.323712	+	0.323712i
$926$		−	23.0884i		−	0.758730i
$927$		−	2.46895i		−	0.0810908i
$928$	9.08877	+	9.08877i	0.298354	+	0.298354i
$929$	−34.7130	−	34.7130i	−1.13890	−	1.13890i	−0.988648	−	0.150248i	$-0.951993\pi$
$929$	−34.7130	−	34.7130i	−1.13890	−	1.13890i	−0.150248	−	0.988648i	$-0.548007\pi$
$930$	−27.1919	+	27.1919i	−0.891659	+	0.891659i
$931$	0.535672			0.0175559
$932$	−37.1816	+	37.1816i	−1.21792	+	1.21792i
$933$			8.36709i			0.273926i
$934$	−75.5359			−2.47161
$935$	−15.0092	+	14.4270i	−0.490855	+	0.471812i
$936$	−2.83931			−0.0928059
$937$			17.2056i			0.562084i	0.959696	+	0.281042i	$0.0906800\pi$
$937$			17.2056i			0.562084i	−0.959696	+	0.281042i	$0.909320\pi$
$938$	36.2384	−	36.2384i	1.18323	−	1.18323i
$939$	−2.22817			−0.0727136
$940$	15.8684	−	15.8684i	0.517570	−	0.517570i
$941$	9.20615	+	9.20615i	0.300112	+	0.300112i	0.841057	−	0.540946i	$-0.181934\pi$
$941$	9.20615	+	9.20615i	0.300112	+	0.300112i	−0.540946	+	0.841057i	$0.681934\pi$
$942$	22.1276	+	22.1276i	0.720955	+	0.720955i
$943$		−	6.09665i		−	0.198534i
$944$			15.3696i			0.500236i
$945$	−7.73907	−	7.73907i	−0.251752	−	0.251752i
$946$	−9.70568	−	9.70568i	−0.315559	−	0.315559i
$947$	−18.1780	+	18.1780i	−0.590707	+	0.590707i	−0.937822	−	0.347116i	$-0.887161\pi$
$947$	−18.1780	+	18.1780i	−0.590707	+	0.590707i	0.347116	+	0.937822i	$0.387161\pi$
$948$	110.161			3.57786
$949$	−4.92709	+	4.92709i	−0.159940	+	0.159940i
$950$		−	34.7528i		−	1.12753i
$951$	6.99069			0.226689
$952$	0.883426	−	44.6593i	0.0286320	−	1.44742i
$953$	−18.7293			−0.606703			−0.303351	−	0.952879i	$-0.598106\pi$
$953$	−18.7293			−0.606703			−0.303351	+	0.952879i	$0.598106\pi$
$954$			16.6300i			0.538417i
$955$	6.67347	−	6.67347i	0.215949	−	0.215949i
$956$	−65.0900			−2.10516
$957$	−36.6261	+	36.6261i	−1.18395	+	1.18395i
$958$	−17.9054	−	17.9054i	−0.578499	−	0.578499i
$959$	−7.83095	−	7.83095i	−0.252874	−	0.252874i
$960$		−	17.9914i		−	0.580670i
$961$		−	64.8178i		−	2.09090i
$962$	7.57572	+	7.57572i	0.244251	+	0.244251i
$963$	4.31615	+	4.31615i	0.139086	+	0.139086i
$964$	−50.2004	+	50.2004i	−1.61685	+	1.61685i
$965$	−10.7664			−0.346583
$966$	23.7354	−	23.7354i	0.763675	−	0.763675i
$967$			3.64706i			0.117282i	0.998279	+	0.0586408i	$0.0186766\pi$
$967$			3.64706i			0.117282i	−0.998279	+	0.0586408i	$0.981323\pi$
$968$	−89.3873			−2.87302
$969$	26.6061	+	0.526306i	0.854710	+	0.0169074i
$970$	13.9247			0.447096
$971$			14.2430i			0.457079i	0.973535	+	0.228540i	$0.0733950\pi$
$971$			14.2430i			0.457079i	−0.973535	+	0.228540i	$0.926605\pi$
$972$	13.8230	−	13.8230i	0.443374	−	0.443374i
$973$	−4.05473			−0.129989
$974$	31.5069	−	31.5069i	1.00955	−	1.00955i
$975$	7.64312	+	7.64312i	0.244776	+	0.244776i
$976$	11.4537	+	11.4537i	0.366624	+	0.366624i
$977$			13.3816i			0.428115i	0.976821	+	0.214057i	$0.0686680\pi$
$977$			13.3816i			0.428115i	−0.976821	+	0.214057i	$0.931332\pi$
$978$		−	66.7202i		−	2.13348i
$979$	38.0912	+	38.0912i	1.21740	+	1.21740i
$980$	0.357097	+	0.357097i	0.0114070	+	0.0114070i
$981$	1.43775	−	1.43775i	0.0459038	−	0.0459038i
$982$	30.2789			0.966238
$983$	25.4608	−	25.4608i	0.812074	−	0.812074i	−0.172871	−	0.984945i	$-0.555304\pi$
$983$	25.4608	−	25.4608i	0.812074	−	0.812074i	0.984945	+	0.172871i	$0.0553043\pi$
$984$			16.5042i			0.526135i
$985$	20.5203			0.653832
$986$	−47.2741	−	0.935149i	−1.50551	−	0.0297812i
$987$	34.6700			1.10356
$988$		−	17.3532i		−	0.552080i
$989$	1.98310	−	1.98310i	0.0630589	−	0.0630589i
$990$	6.19700			0.196954
$991$	0.590981	−	0.590981i	0.0187731	−	0.0187731i	−0.697658	−	0.716431i	$-0.745774\pi$
$991$	0.590981	−	0.590981i	0.0187731	−	0.0187731i	0.716431	+	0.697658i	$0.245774\pi$
$992$	18.5166	+	18.5166i	0.587902	+	0.587902i
$993$	−26.3029	−	26.3029i	−0.834698	−	0.834698i
$994$		−	3.60323i		−	0.114288i
$995$		−	4.82010i		−	0.152807i
$996$	65.4038	+	65.4038i	2.07240	+	2.07240i
$997$	4.18619	+	4.18619i	0.132578	+	0.132578i	0.770282	−	0.637704i	$-0.220116\pi$
$997$	4.18619	+	4.18619i	0.132578	+	0.132578i	−0.637704	+	0.770282i	$0.720116\pi$
$998$	−50.9436	+	50.9436i	−1.61259	+	1.61259i
$999$	−15.3418			−0.485393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.2	✓	68
17.13	even	4	inner	731.2.f.d.302.33	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.2	✓	68	1.1	even	1	trivial
731.2.f.d.302.33	yes	68	17.13	even	4	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.38680i q^{2} +(-1.32556 + 1.32556i) q^{3} -3.69681 q^{4} +(-0.620851 + 0.620851i) q^{5} +(3.16384 + 3.16384i) q^{6} +(-1.89151 - 1.89151i) q^{7} +4.04996i q^{8} -0.514207i q^{9} +O(q^{10})\)	\(q-2.38680i q^{2} +(-1.32556 + 1.32556i) q^{3} -3.69681 q^{4} +(-0.620851 + 0.620851i) q^{5} +(3.16384 + 3.16384i) q^{6} +(-1.89151 - 1.89151i) q^{7} +4.04996i q^{8} -0.514207i q^{9} +(1.48185 + 1.48185i) q^{10} +(4.06640 + 4.06640i) q^{11} +(4.90034 - 4.90034i) q^{12} -1.36341 q^{13} +(-4.51465 + 4.51465i) q^{14} -1.64595i q^{15} +2.27281 q^{16} +(2.97257 - 2.85724i) q^{17} -1.22731 q^{18} -3.44292i q^{19} +(2.29517 - 2.29517i) q^{20} +5.01460 q^{21} +(9.70568 - 9.70568i) q^{22} +(1.98310 + 1.98310i) q^{23} +(-5.36845 - 5.36845i) q^{24} +4.22909i q^{25} +3.25418i q^{26} +(-3.29506 - 3.29506i) q^{27} +(6.99254 + 6.99254i) q^{28} +(3.39744 - 3.39744i) q^{29} -3.92855 q^{30} +(6.92163 - 6.92163i) q^{31} +2.67518i q^{32} -10.7805 q^{33} +(-6.81967 - 7.09492i) q^{34} +2.34869 q^{35} +1.90093i q^{36} +(2.32800 - 2.32800i) q^{37} -8.21757 q^{38} +(1.80727 - 1.80727i) q^{39} +(-2.51442 - 2.51442i) q^{40} +(-1.53715 - 1.53715i) q^{41} -11.9688i q^{42} -1.00000i q^{43} +(-15.0327 - 15.0327i) q^{44} +(0.319246 + 0.319246i) q^{45} +(4.73327 - 4.73327i) q^{46} +6.91381 q^{47} +(-3.01273 + 3.01273i) q^{48} +0.155586i q^{49} +10.0940 q^{50} +(-0.152866 + 7.72775i) q^{51} +5.04026 q^{52} -13.5500i q^{53} +(-7.86465 + 7.86465i) q^{54} -5.04926 q^{55} +(7.66051 - 7.66051i) q^{56} +(4.56380 + 4.56380i) q^{57} +(-8.10902 - 8.10902i) q^{58} +6.76237i q^{59} +6.08476i q^{60} +(5.03945 + 5.03945i) q^{61} +(-16.5205 - 16.5205i) q^{62} +(-0.972626 + 0.972626i) q^{63} +10.9307 q^{64} +(0.846472 - 0.846472i) q^{65} +25.7309i q^{66} -8.02686 q^{67} +(-10.9890 + 10.5627i) q^{68} -5.25743 q^{69} -5.60584i q^{70} +(-0.399060 + 0.399060i) q^{71} +2.08252 q^{72} +(3.61381 - 3.61381i) q^{73} +(-5.55646 - 5.55646i) q^{74} +(-5.60590 - 5.60590i) q^{75} +12.7279i q^{76} -15.3832i q^{77} +(-4.31360 - 4.31360i) q^{78} +(11.2401 + 11.2401i) q^{79} +(-1.41107 + 1.41107i) q^{80} +10.2782 q^{81} +(-3.66887 + 3.66887i) q^{82} +13.3468i q^{83} -18.5380 q^{84} +(-0.0715978 + 3.61944i) q^{85} -2.38680 q^{86} +9.00702i q^{87} +(-16.4687 + 16.4687i) q^{88} +9.36731 q^{89} +(0.761977 - 0.761977i) q^{90} +(2.57889 + 2.57889i) q^{91} +(-7.33116 - 7.33116i) q^{92} +18.3500i q^{93} -16.5019i q^{94} +(2.13754 + 2.13754i) q^{95} +(-3.54610 - 3.54610i) q^{96} +(4.69844 - 4.69844i) q^{97} +0.371353 q^{98} +(2.09097 - 2.09097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

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