LMFDB - Embedded newform 1690.2.l.n.1161.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(361,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,4,12,0,0,0,0,-32,12,0,8,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1161.3
Character	$\chi$	$=$	1690.1161
Dual form			1690.2.l.n.361.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.494225 + 0.856023i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(0.856023 - 0.494225i) q^{6} +(3.00783 - 1.73657i) q^{7} -1.00000i q^{8} +(1.01148 + 1.75194i) q^{9} +(0.500000 - 0.866025i) q^{10} +(5.23297 + 3.02125i) q^{11} -0.988450 q^{12} -3.47315 q^{14} +(-0.856023 - 0.494225i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.02766 + 1.77997i) q^{17} -2.02297i q^{18} +(2.69985 - 1.55876i) q^{19} +(-0.866025 + 0.500000i) q^{20} +3.43303i q^{21} +(-3.02125 - 5.23297i) q^{22} +(3.98724 - 6.90610i) q^{23} +(0.856023 + 0.494225i) q^{24} -1.00000 q^{25} -4.96495 q^{27} +(3.00783 + 1.73657i) q^{28} +(3.36517 - 5.82865i) q^{29} +(0.494225 + 0.856023i) q^{30} +8.96482i q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.17253 + 2.98636i) q^{33} -2.05533i q^{34} +(1.73657 + 3.00783i) q^{35} +(-1.01148 + 1.75194i) q^{36} +(2.33417 + 1.34763i) q^{37} -3.11752 q^{38} +1.00000 q^{40} +(-2.80196 - 1.61772i) q^{41} +(1.71652 - 2.97309i) q^{42} +(-1.01752 - 1.76240i) q^{43} +6.04251i q^{44} +(-1.75194 + 1.01148i) q^{45} +(-6.90610 + 3.98724i) q^{46} -9.03057i q^{47} +(-0.494225 - 0.856023i) q^{48} +(2.53138 - 4.38447i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.03159 q^{51} -11.1847 q^{53} +(4.29978 + 2.48248i) q^{54} +(-3.02125 + 5.23297i) q^{55} +(-1.73657 - 3.00783i) q^{56} +3.08152i q^{57} +(-5.82865 + 3.36517i) q^{58} +(5.54418 - 3.20093i) q^{59} -0.988450i q^{60} +(-6.52411 - 11.3001i) q^{61} +(4.48241 - 7.76376i) q^{62} +(6.08475 + 3.51303i) q^{63} -1.00000 q^{64} +5.97272 q^{66} +(7.35812 + 4.24821i) q^{67} +(-1.02766 + 1.77997i) q^{68} +(3.94119 + 6.82634i) q^{69} -3.47315i q^{70} +(0.105653 - 0.0609989i) q^{71} +(1.75194 - 1.01148i) q^{72} +0.138022i q^{73} +(-1.34763 - 2.33417i) q^{74} +(0.494225 - 0.856023i) q^{75} +(2.69985 + 1.55876i) q^{76} +20.9865 q^{77} -6.71618 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-0.580644 + 1.00570i) q^{81} +(1.61772 + 2.80196i) q^{82} -3.03849i q^{83} +(-2.97309 + 1.71652i) q^{84} +(-1.77997 + 1.02766i) q^{85} +2.03505i q^{86} +(3.32631 + 5.76133i) q^{87} +(3.02125 - 5.23297i) q^{88} +(2.93073 + 1.69206i) q^{89} +2.02297 q^{90} +7.97448 q^{92} +(-7.67409 - 4.43064i) q^{93} +(-4.51529 + 7.82070i) q^{94} +(1.55876 + 2.69985i) q^{95} +0.988450i q^{96} +(-5.04478 + 2.91261i) q^{97} +(-4.38447 + 2.53138i) q^{98} +12.2238i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} + 12 q^{4} - 32 q^{9} + 12 q^{10} + 8 q^{12} + 12 q^{14} - 12 q^{16} - 6 q^{17} - 30 q^{22} - 6 q^{23} - 24 q^{25} - 80 q^{27} - 14 q^{29} - 4 q^{30} - 6 q^{35} + 32 q^{36} - 4 q^{38} + 24 q^{40}+ \cdots + 2 q^{95}+O(q^{100}) $ 24 * q + 4 * q^3 + 12 * q^4 - 32 * q^9 + 12 * q^10 + 8 * q^12 + 12 * q^14 - 12 * q^16 - 6 * q^17 - 30 * q^22 - 6 * q^23 - 24 * q^25 - 80 * q^27 - 14 * q^29 - 4 * q^30 - 6 * q^35 + 32 * q^36 - 4 * q^38 + 24 * q^40 + 4 * q^42 - 44 * q^43 + 4 * q^48 + 62 * q^49 + 88 * q^51 - 64 * q^53 - 30 * q^55 + 6 * q^56 - 66 * q^61 - 24 * q^64 + 16 * q^66 + 6 * q^68 - 12 * q^69 - 12 * q^74 - 4 * q^75 + 136 * q^77 + 80 * q^79 + 4 * q^81 + 4 * q^82 + 78 * q^87 + 30 * q^88 - 64 * q^90 - 12 * q^92 - 14 * q^94 + 2 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.494225	+	0.856023i	−0.285341	+	0.494225i	−0.972692	−	0.232100i	$-0.925440\pi$
$3$	−0.494225	+	0.856023i	−0.285341	+	0.494225i	0.687351	+	0.726326i	$0.258774\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.856023	−	0.494225i	0.349470	−	0.201767i
$7$	3.00783	−	1.73657i	1.13685	−	0.656363i	0.191205	−	0.981550i	$-0.438761\pi$
$7$	3.00783	−	1.73657i	1.13685	−	0.656363i	0.945650	+	0.325187i	$0.105427\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.01148	+	1.75194i	0.337161	+	0.583980i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	5.23297	+	3.02125i	1.57780	+	0.910942i	0.995166	+	0.0982065i	$0.0313106\pi$
$11$	5.23297	+	3.02125i	1.57780	+	0.910942i	0.582632	+	0.812736i	$0.302023\pi$
$12$	−0.988450			−0.285341
$13$		0			0
$13$		0			0
$14$	−3.47315			−0.928238
$15$	−0.856023	−	0.494225i	−0.221024	−	0.127608i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.02766	+	1.77997i	0.249245	+	0.431705i	0.963317	−	0.268368i	$-0.0864842\pi$
$17$	1.02766	+	1.77997i	0.249245	+	0.431705i	−0.714072	+	0.700073i	$0.753151\pi$
$18$		−	2.02297i		−	0.476818i
$19$	2.69985	−	1.55876i	0.619389	−	0.357604i	−0.157242	−	0.987560i	$-0.550260\pi$
$19$	2.69985	−	1.55876i	0.619389	−	0.357604i	0.776631	+	0.629956i	$0.216927\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$			3.43303i			0.749150i
$22$	−3.02125	−	5.23297i	−0.644133	−	1.11567i
$23$	3.98724	−	6.90610i	0.831396	−	1.44002i	−0.0655344	−	0.997850i	$-0.520875\pi$
$23$	3.98724	−	6.90610i	0.831396	−	1.44002i	0.896931	−	0.442171i	$-0.145791\pi$
$24$	0.856023	+	0.494225i	0.174735	+	0.100883i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−4.96495			−0.955506
$28$	3.00783	+	1.73657i	0.568427	+	0.328182i
$29$	3.36517	−	5.82865i	0.624897	−	1.08235i	−0.363664	−	0.931530i	$-0.618474\pi$
$29$	3.36517	−	5.82865i	0.624897	−	1.08235i	0.988561	−	0.150823i	$-0.0481924\pi$
$30$	0.494225	+	0.856023i	0.0902328	+	0.156288i
$31$			8.96482i			1.61013i	0.593187	+	0.805065i	$0.297869\pi$
$31$			8.96482i			1.61013i	−0.593187	+	0.805065i	$0.702131\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.17253	+	2.98636i	−0.900421	+	0.519859i
$34$		−	2.05533i		−	0.352486i
$35$	1.73657	+	3.00783i	0.293535	+	0.508417i
$36$	−1.01148	+	1.75194i	−0.168580	+	0.291990i
$37$	2.33417	+	1.34763i	0.383735	+	0.221550i	0.679442	−	0.733729i	$-0.262222\pi$
$37$	2.33417	+	1.34763i	0.383735	+	0.221550i	−0.295707	+	0.955279i	$0.595555\pi$
$38$	−3.11752			−0.505729
$39$		0			0
$40$	1.00000			0.158114
$41$	−2.80196	−	1.61772i	−0.437593	−	0.252645i	0.264983	−	0.964253i	$-0.414634\pi$
$41$	−2.80196	−	1.61772i	−0.437593	−	0.252645i	−0.702576	+	0.711608i	$0.747967\pi$
$42$	1.71652	−	2.97309i	0.264864	−	0.458759i
$43$	−1.01752	−	1.76240i	−0.155171	−	0.268764i	0.777950	−	0.628326i	$-0.216259\pi$
$43$	−1.01752	−	1.76240i	−0.155171	−	0.268764i	−0.933121	+	0.359562i	$0.882926\pi$
$44$			6.04251i			0.910942i
$45$	−1.75194	+	1.01148i	−0.261164	+	0.150783i
$46$	−6.90610	+	3.98724i	−1.01825	+	0.587886i
$47$		−	9.03057i		−	1.31724i	−0.752474	−	0.658622i	$-0.771140\pi$
$47$		−	9.03057i		−	1.31724i	0.752474	−	0.658622i	$-0.228860\pi$
$48$	−0.494225	−	0.856023i	−0.0713353	−	0.123556i
$49$	2.53138	−	4.38447i	0.361625	−	0.626353i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−2.03159			−0.284479
$52$		0			0
$53$	−11.1847			−1.53633			−0.768165	−	0.640252i	$-0.778830\pi$
$53$	−11.1847			−1.53633			−0.768165	+	0.640252i	$0.778830\pi$
$54$	4.29978	+	2.48248i	0.585125	+	0.337822i
$55$	−3.02125	+	5.23297i	−0.407386	+	0.705613i
$56$	−1.73657	−	3.00783i	−0.232059	−	0.401939i
$57$			3.08152i			0.408157i
$58$	−5.82865	+	3.36517i	−0.765340	+	0.441869i
$59$	5.54418	−	3.20093i	0.721791	−	0.416726i	−0.0936206	−	0.995608i	$-0.529844\pi$
$59$	5.54418	−	3.20093i	0.721791	−	0.416726i	0.815411	+	0.578882i	$0.196511\pi$
$60$		−	0.988450i		−	0.127608i
$61$	−6.52411	−	11.3001i	−0.835327	−	1.44683i	−0.893764	−	0.448537i	$-0.851945\pi$
$61$	−6.52411	−	11.3001i	−0.835327	−	1.44683i	0.0584376	−	0.998291i	$-0.481388\pi$
$62$	4.48241	−	7.76376i	0.569267	−	0.985999i
$63$	6.08475	+	3.51303i	0.766606	+	0.442600i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.97272			0.735191
$67$	7.35812	+	4.24821i	0.898937	+	0.519002i	0.876855	−	0.480754i	$-0.159637\pi$
$67$	7.35812	+	4.24821i	0.898937	+	0.519002i	0.0220821	+	0.999756i	$0.492970\pi$
$68$	−1.02766	+	1.77997i	−0.124622	+	0.215852i
$69$	3.94119	+	6.82634i	0.474463	+	0.821794i
$70$		−	3.47315i		−	0.415121i
$71$	0.105653	−	0.0609989i	0.0125387	−	0.00723924i	−0.493718	−	0.869622i	$-0.664362\pi$
$71$	0.105653	−	0.0609989i	0.0125387	−	0.00723924i	0.506256	+	0.862383i	$0.331029\pi$
$72$	1.75194	−	1.01148i	0.206468	−	0.119204i
$73$			0.138022i			0.0161543i	0.999967	+	0.00807713i	$0.00257106\pi$
$73$			0.138022i			0.0161543i	−0.999967	+	0.00807713i	$0.997429\pi$
$74$	−1.34763	−	2.33417i	−0.156659	−	0.271342i
$75$	0.494225	−	0.856023i	0.0570682	−	0.0988450i
$76$	2.69985	+	1.55876i	0.309694	+	0.178802i
$77$	20.9865			2.39164
$78$		0			0
$79$	−6.71618			−0.755630			−0.377815	−	0.925881i	$-0.623324\pi$
$79$	−6.71618			−0.755630			−0.377815	+	0.925881i	$0.623324\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−0.580644	+	1.00570i	−0.0645160	+	0.111745i
$82$	1.61772	+	2.80196i	0.178647	+	0.309425i
$83$		−	3.03849i		−	0.333518i	−0.985998	−	0.166759i	$-0.946670\pi$
$83$		−	3.03849i		−	0.333518i	0.985998	−	0.166759i	$-0.0533302\pi$
$84$	−2.97309	+	1.71652i	−0.324391	+	0.187287i
$85$	−1.77997	+	1.02766i	−0.193064	+	0.111466i
$86$			2.03505i			0.219445i
$87$	3.32631	+	5.76133i	0.356618	+	0.617680i
$88$	3.02125	−	5.23297i	0.322067	−	0.557836i
$89$	2.93073	+	1.69206i	0.310657	+	0.179358i	0.647220	−	0.762303i	$-0.275931\pi$
$89$	2.93073	+	1.69206i	0.310657	+	0.179358i	−0.336564	+	0.941661i	$0.609265\pi$
$90$	2.02297			0.213239
$91$		0			0
$92$	7.97448			0.831396
$93$	−7.67409	−	4.43064i	−0.795766	−	0.459436i
$94$	−4.51529	+	7.82070i	−0.465716	+	0.806644i
$95$	1.55876	+	2.69985i	0.159925	+	0.276999i
$96$			0.988450i			0.100883i
$97$	−5.04478	+	2.91261i	−0.512220	+	0.295730i	−0.733746	−	0.679424i	$-0.762230\pi$
$97$	−5.04478	+	2.91261i	−0.512220	+	0.295730i	0.221526	+	0.975155i	$0.428896\pi$
$98$	−4.38447	+	2.53138i	−0.442899	+	0.255708i
$99$			12.2238i			1.22854i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−4.23936	+	7.34278i	−0.421832	+	0.730634i	−0.996119	−	0.0880200i	$-0.971946\pi$
$101$	−4.23936	+	7.34278i	−0.421832	+	0.730634i	0.574287	+	0.818654i	$0.305279\pi$
$102$	1.75941	+	1.01579i	0.174207	+	0.100579i
$103$	4.96891			0.489601			0.244801	−	0.969573i	$-0.421278\pi$
$103$	4.96891			0.489601			0.244801	+	0.969573i	$0.421278\pi$
$104$		0			0
$105$	−3.43303			−0.335030
$106$	9.68619	+	5.59233i	0.940806	+	0.543175i
$107$	2.58471	−	4.47685i	0.249874	−	0.432794i	−0.713617	−	0.700536i	$-0.752944\pi$
$107$	2.58471	−	4.47685i	0.249874	−	0.432794i	0.963491	+	0.267742i	$0.0862776\pi$
$108$	−2.48248	−	4.29978i	−0.238876	−	0.413746i
$109$			8.09832i			0.775678i	0.921727	+	0.387839i	$0.126778\pi$
$109$			8.09832i			0.775678i	−0.921727	+	0.387839i	$0.873222\pi$
$110$	5.23297	−	3.02125i	0.498944	−	0.288065i
$111$	−2.30721	+	1.33207i	−0.218991	+	0.126434i
$112$			3.47315i			0.328182i
$113$	9.12839	+	15.8108i	0.858726	+	1.48736i	0.873144	+	0.487462i	$0.162077\pi$
$113$	9.12839	+	15.8108i	0.858726	+	1.48736i	−0.0144182	+	0.999896i	$0.504590\pi$
$114$	1.54076	−	2.66867i	0.144305	−	0.249944i
$115$	6.90610	+	3.98724i	0.643997	+	0.371812i
$116$	6.73035			0.624897
$117$		0			0
$118$	−6.40187			−0.589340
$119$	6.18208	+	3.56923i	0.566711	+	0.327190i
$120$	−0.494225	+	0.856023i	−0.0451164	+	0.0781439i
$121$	12.7560	+	22.0940i	1.15963	+	2.00854i
$122$			13.0482i			1.18133i
$123$	2.76960	−	1.59903i	0.249727	−	0.144180i
$124$	−7.76376	+	4.48241i	−0.697206	+	0.402532i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.51303	−	6.08475i	−0.312966	−	0.542072i
$127$	0.144813	−	0.250823i	0.0128501	−	0.0222570i	−0.859529	−	0.511087i	$-0.829243\pi$
$127$	0.144813	−	0.250823i	0.0128501	−	0.0222570i	0.872379	+	0.488830i	$0.162576\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.01154			0.177107
$130$		0			0
$131$	−19.4914			−1.70297			−0.851486	−	0.524378i	$-0.824298\pi$
$131$	−19.4914			−1.70297			−0.851486	+	0.524378i	$0.824298\pi$
$132$	−5.17253	−	2.98636i	−0.450211	−	0.259929i
$133$	5.41381	−	9.37699i	0.469436	−	0.813088i
$134$	−4.24821	−	7.35812i	−0.366990	−	0.635645i
$135$		−	4.96495i		−	0.427315i
$136$	1.77997	−	1.02766i	0.152631	−	0.0881214i
$137$	3.20947	−	1.85299i	0.274204	−	0.158312i	−0.356593	−	0.934260i	$-0.616062\pi$
$137$	3.20947	−	1.85299i	0.274204	−	0.158312i	0.630796	+	0.775948i	$0.282728\pi$
$138$		−	7.88237i		−	0.670992i
$139$	5.19164	+	8.99218i	0.440349	+	0.762707i	0.997715	−	0.0675600i	$-0.0215214\pi$
$139$	5.19164	+	8.99218i	0.440349	+	0.762707i	−0.557366	+	0.830267i	$0.688188\pi$
$140$	−1.73657	+	3.00783i	−0.146767	+	0.254208i
$141$	7.73038	+	4.46314i	0.651015	+	0.375864i
$142$	−0.121998			−0.0102378
$143$		0			0
$144$	−2.02297			−0.168580
$145$	5.82865	+	3.36517i	0.484043	+	0.279462i
$146$	0.0690110	−	0.119531i	0.00571139	−	0.00989242i
$147$	2.50214	+	4.33384i	0.206373	+	0.357449i
$148$			2.69527i			0.221550i
$149$	17.9543	−	10.3659i	1.47087	−	0.849209i	0.471407	−	0.881916i	$-0.343746\pi$
$149$	17.9543	−	10.3659i	1.47087	−	0.849209i	0.999465	+	0.0327070i	$0.0104128\pi$
$150$	−0.856023	+	0.494225i	−0.0698940	+	0.0403533i
$151$			20.5005i			1.66831i	0.551531	+	0.834154i	$0.314044\pi$
$151$			20.5005i			1.66831i	−0.551531	+	0.834154i	$0.685956\pi$
$152$	−1.55876	−	2.69985i	−0.126432	−	0.218987i
$153$	−2.07893	+	3.60081i	−0.168071	+	0.291108i
$154$	−18.1749	−	10.4933i	−1.46457	−	0.845571i
$155$	−8.96482			−0.720072
$156$		0			0
$157$	11.6082			0.926434			0.463217	−	0.886245i	$-0.346695\pi$
$157$	11.6082			0.926434			0.463217	+	0.886245i	$0.346695\pi$
$158$	5.81638	+	3.35809i	0.462727	+	0.267155i
$159$	5.52774	−	9.57432i	0.438378	−	0.759293i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$		−	27.6965i		−	2.18279i
$162$	1.00570	−	0.580644i	0.0790156	−	0.0456197i
$163$	7.59971	−	4.38770i	0.595256	−	0.343671i	−0.171917	−	0.985111i	$-0.554996\pi$
$163$	7.59971	−	4.38770i	0.595256	−	0.343671i	0.767173	+	0.641440i	$0.221663\pi$
$164$		−	3.23543i		−	0.252645i
$165$	−2.98636	−	5.17253i	−0.232488	−	0.402681i
$166$	−1.51925	+	2.63141i	−0.117916	+	0.204237i
$167$	−8.37270	−	4.83398i	−0.647899	−	0.374065i	0.139752	−	0.990187i	$-0.455370\pi$
$167$	−8.37270	−	4.83398i	−0.647899	−	0.374065i	−0.787651	+	0.616122i	$0.788703\pi$
$168$	3.43303			0.264864
$169$		0			0
$170$	2.05533			0.157636
$171$	5.46171	+	3.15332i	0.417667	+	0.241140i
$172$	1.01752	−	1.76240i	0.0775855	−	0.134382i
$173$	−4.50037	−	7.79487i	−0.342157	−	0.592633i	0.642676	−	0.766138i	$-0.277824\pi$
$173$	−4.50037	−	7.79487i	−0.342157	−	0.592633i	−0.984833	+	0.173505i	$0.944491\pi$
$174$		−	6.65262i		−	0.504333i
$175$	−3.00783	+	1.73657i	−0.227371	+	0.131273i
$176$	−5.23297	+	3.02125i	−0.394450	+	0.227736i
$177$			6.32793i			0.475636i
$178$	−1.69206	−	2.93073i	−0.126825	−	0.219668i
$179$	−5.56726	+	9.64278i	−0.416117	+	0.720735i	−0.995545	−	0.0942881i	$-0.969943\pi$
$179$	−5.56726	+	9.64278i	−0.416117	+	0.720735i	0.579428	+	0.815023i	$0.303276\pi$
$180$	−1.75194	−	1.01148i	−0.130582	−	0.0753915i
$181$	−1.63511			−0.121536			−0.0607682	−	0.998152i	$-0.519355\pi$
$181$	−1.63511			−0.121536			−0.0607682	+	0.998152i	$0.519355\pi$
$182$		0			0
$183$	12.8975			0.953412
$184$	−6.90610	−	3.98724i	−0.509124	−	0.293943i
$185$	−1.34763	+	2.33417i	−0.0990800	+	0.171612i
$186$	4.43064	+	7.67409i	0.324870	+	0.562692i
$187$			12.4193i			0.908191i
$188$	7.82070	−	4.51529i	0.570383	−	0.329311i
$189$	−14.9338	+	8.62201i	−1.08627	+	0.627159i
$190$		−	3.11752i		−	0.226169i
$191$	−4.61924	−	8.00075i	−0.334236	−	0.578914i	0.649102	−	0.760702i	$-0.275145\pi$
$191$	−4.61924	−	8.00075i	−0.334236	−	0.578914i	−0.983338	+	0.181788i	$0.941812\pi$
$192$	0.494225	−	0.856023i	0.0356676	−	0.0617782i
$193$	6.30719	+	3.64146i	0.454001	+	0.262118i	0.709519	−	0.704687i	$-0.248912\pi$
$193$	6.30719	+	3.64146i	0.454001	+	0.262118i	−0.255517	+	0.966804i	$0.582246\pi$
$194$	5.82521			0.418226
$195$		0			0
$196$	5.06275			0.361625
$197$	−17.8180	−	10.2872i	−1.26948	−	0.732933i	−0.294588	−	0.955624i	$-0.595182\pi$
$197$	−17.8180	−	10.2872i	−1.26948	−	0.732933i	−0.974889	+	0.222692i	$0.928516\pi$
$198$	6.11189	−	10.5861i	0.434353	−	0.752322i
$199$	−1.38553	−	2.39981i	−0.0982179	−	0.170118i	0.812729	−	0.582642i	$-0.197981\pi$
$199$	−1.38553	−	2.39981i	−0.0982179	−	0.170118i	−0.910947	+	0.412523i	$0.864648\pi$
$200$			1.00000i			0.0707107i
$201$	−7.27314	+	4.19915i	−0.513007	+	0.296185i
$202$	7.34278	−	4.23936i	0.516636	−	0.298280i
$203$		−	23.3755i		−	1.64064i
$204$	−1.01579	−	1.75941i	−0.0711198	−	0.123183i
$205$	1.61772	−	2.80196i	0.112986	−	0.195698i
$206$	−4.30320	−	2.48445i	−0.299818	−	0.173100i
$207$	16.1321			1.12126
$208$		0			0
$209$	18.8376			1.30303
$210$	2.97309	+	1.71652i	0.205163	+	0.118451i
$211$	−10.6377	+	18.4251i	−0.732332	+	1.26844i	0.223552	+	0.974692i	$0.428235\pi$
$211$	−10.6377	+	18.4251i	−0.732332	+	1.26844i	−0.955884	+	0.293745i	$0.905098\pi$
$212$	−5.59233	−	9.68619i	−0.384083	−	0.665250i
$213$			0.120589i			0.00826261i
$214$	−4.47685	+	2.58471i	−0.306031	+	0.176687i
$215$	1.76240	−	1.01752i	0.120195	−	0.0693945i
$216$			4.96495i			0.337822i
$217$	15.5681	+	26.9647i	1.05683	+	1.83048i
$218$	4.04916	−	7.01335i	0.274244	−	0.475004i
$219$	−0.118150	−	0.0682140i	−0.00798384	−	0.00460947i
$220$	−6.04251			−0.407386
$221$		0			0
$222$	2.66414			0.178805
$223$	−6.37306	−	3.67949i	−0.426772	−	0.246397i	0.271199	−	0.962523i	$-0.412580\pi$
$223$	−6.37306	−	3.67949i	−0.426772	−	0.246397i	−0.697970	+	0.716127i	$0.745913\pi$
$224$	1.73657	−	3.00783i	0.116030	−	0.200969i
$225$	−1.01148	−	1.75194i	−0.0674322	−	0.116796i
$226$		−	18.2568i		−	1.21442i
$227$	−18.4665	+	10.6616i	−1.22566	+	0.707637i	−0.966120	−	0.258095i	$-0.916905\pi$
$227$	−18.4665	+	10.6616i	−1.22566	+	0.707637i	−0.259543	+	0.965732i	$0.583572\pi$
$228$	−2.66867	+	1.54076i	−0.176737	+	0.102039i
$229$		−	15.7929i		−	1.04363i	−0.853060	−	0.521813i	$-0.825256\pi$
$229$		−	15.7929i		−	1.04363i	0.853060	−	0.521813i	$-0.174744\pi$
$230$	−3.98724	−	6.90610i	−0.262911	−	0.455375i
$231$	−10.3721	+	17.9649i	−0.682432	+	1.18201i
$232$	−5.82865	−	3.36517i	−0.382670	−	0.220934i
$233$	−8.13040			−0.532640			−0.266320	−	0.963885i	$-0.585808\pi$
$233$	−8.13040			−0.532640			−0.266320	+	0.963885i	$0.585808\pi$
$234$		0			0
$235$	9.03057			0.589089
$236$	5.54418	+	3.20093i	0.360895	+	0.208363i
$237$	3.31931	−	5.74921i	0.215612	−	0.373451i
$238$	−3.56923	−	6.18208i	−0.231359	−	0.400725i
$239$			12.5247i			0.810154i	0.914283	+	0.405077i	$0.132755\pi$
$239$			12.5247i			0.810154i	−0.914283	+	0.405077i	$0.867245\pi$
$240$	0.856023	−	0.494225i	0.0552561	−	0.0319021i
$241$	3.10711	−	1.79389i	0.200146	−	0.115555i	−0.396577	−	0.918001i	$-0.629802\pi$
$241$	3.10711	−	1.79389i	0.200146	−	0.115555i	0.596724	+	0.802447i	$0.296469\pi$
$242$		−	25.5119i		−	1.63997i
$243$	−8.02137	−	13.8934i	−0.514571	−	0.891263i
$244$	6.52411	−	11.3001i	0.417663	−	0.723414i
$245$	4.38447	+	2.53138i	0.280114	+	0.161724i
$246$	−3.19806			−0.203901
$247$		0			0
$248$	8.96482			0.569267
$249$	2.60102	+	1.50170i	0.164833	+	0.0951664i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−7.53629	−	13.0532i	−0.475686	−	0.823912i	0.523926	−	0.851764i	$-0.324467\pi$
$251$	−7.53629	−	13.0532i	−0.475686	−	0.823912i	−0.999612	+	0.0278513i	$0.991134\pi$
$252$			7.02606i			0.442600i
$253$	41.7302	−	24.0929i	2.62355	−	1.51471i
$254$	−0.250823	+	0.144813i	−0.0157381	+	0.00908637i
$255$		−	2.03159i		−	0.127223i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.1902	−	19.3820i	0.698026	−	1.20902i	−0.271124	−	0.962544i	$-0.587395\pi$
$257$	11.1902	−	19.3820i	0.698026	−	1.20902i	0.969150	−	0.246472i	$-0.0792714\pi$
$258$	−1.74205	−	1.00577i	−0.108455	−	0.0626166i
$259$	9.36106			0.581668
$260$		0			0
$261$	13.6153			0.842764
$262$	16.8800	+	9.74570i	1.04285	+	0.602091i
$263$	−9.36507	+	16.2208i	−0.577475	+	1.00022i	0.418293	+	0.908312i	$0.362629\pi$
$263$	−9.36507	+	16.2208i	−0.577475	+	1.00022i	−0.995768	+	0.0919039i	$0.970705\pi$
$264$	2.98636	+	5.17253i	0.183798	+	0.318347i
$265$		−	11.1847i		−	0.687068i
$266$	−9.37699	+	5.41381i	−0.574940	+	0.331942i
$267$	−2.89688	+	1.67252i	−0.177286	+	0.102356i
$268$			8.49642i			0.519002i
$269$	−3.26966	−	5.66322i	−0.199355	−	0.345292i	0.748965	−	0.662610i	$-0.230551\pi$
$269$	−3.26966	−	5.66322i	−0.199355	−	0.345292i	−0.948319	+	0.317317i	$0.897218\pi$
$270$	−2.48248	+	4.29978i	−0.151079	+	0.261676i
$271$	2.48068	+	1.43222i	0.150691	+	0.0870013i	0.573449	−	0.819241i	$-0.305605\pi$
$271$	2.48068	+	1.43222i	0.150691	+	0.0870013i	−0.422759	+	0.906242i	$0.638938\pi$
$272$	−2.05533			−0.124622
$273$		0			0
$274$	−3.70598			−0.223886
$275$	−5.23297	−	3.02125i	−0.315560	−	0.182188i
$276$	−3.94119	+	6.82634i	−0.237232	+	0.410897i
$277$	−1.40342	−	2.43079i	−0.0843233	−	0.146052i	0.820779	−	0.571245i	$-0.193540\pi$
$277$	−1.40342	−	2.43079i	−0.0843233	−	0.146052i	−0.905103	+	0.425193i	$0.860206\pi$
$278$		−	10.3833i		−	0.622747i
$279$	−15.7058	+	9.06776i	−0.940283	+	0.542873i
$280$	3.00783	−	1.73657i	0.179752	−	0.103780i
$281$			25.8974i			1.54491i	0.635071	+	0.772453i	$0.280971\pi$
$281$			25.8974i			1.54491i	−0.635071	+	0.772453i	$0.719029\pi$
$282$	−4.46314	−	7.73038i	−0.265776	−	0.460337i
$283$	−14.4387	+	25.0086i	−0.858292	+	1.48661i	0.0152651	+	0.999883i	$0.495141\pi$
$283$	−14.4387	+	25.0086i	−0.858292	+	1.48661i	−0.873557	+	0.486722i	$0.838193\pi$
$284$	0.105653	+	0.0609989i	0.00626937	+	0.00361962i
$285$	−3.08152			−0.182533
$286$		0			0
$287$	−11.2371			−0.663307
$288$	1.75194	+	1.01148i	0.103234	+	0.0596022i
$289$	6.38782	−	11.0640i	0.375754	−	0.650825i
$290$	−3.36517	−	5.82865i	−0.197610	−	0.342270i
$291$		−	5.75794i		−	0.337536i
$292$	−0.119531	+	0.0690110i	−0.00699500	+	0.00403856i
$293$	9.59726	−	5.54098i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$293$	9.59726	−	5.54098i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$294$		−	5.00428i		−	0.291856i
$295$	3.20093	+	5.54418i	0.186366	+	0.322795i
$296$	1.34763	−	2.33417i	0.0783296	−	0.135671i
$297$	−25.9814	−	15.0004i	−1.50760	−	0.870410i
$298$	−20.7318			−1.20096
$299$		0			0
$300$	0.988450			0.0570682
$301$	−6.12108	−	3.53401i	−0.352813	−	0.203697i
$302$	10.2503	−	17.7540i	0.589836	−	1.02163i
$303$	−4.19039	−	7.25798i	−0.240732	−	0.416960i
$304$			3.11752i			0.178802i
$305$	11.3001	−	6.52411i	0.647041	−	0.373569i
$306$	3.60081	−	2.07893i	0.205845	−	0.118844i
$307$			6.38045i			0.364152i	0.983284	+	0.182076i	$0.0582816\pi$
$307$			6.38045i			0.364152i	−0.983284	+	0.182076i	$0.941718\pi$
$308$	10.4933	+	18.1749i	0.597909	+	1.03561i
$309$	−2.45576	+	4.25350i	−0.139703	+	0.241973i
$310$	7.76376	+	4.48241i	0.440952	+	0.254584i
$311$	−18.9443			−1.07423			−0.537115	−	0.843509i	$-0.680486\pi$
$311$	−18.9443			−1.07423			−0.537115	+	0.843509i	$0.680486\pi$
$312$		0			0
$313$	−17.5007			−0.989196			−0.494598	−	0.869122i	$-0.664685\pi$
$313$	−17.5007			−0.989196			−0.494598	+	0.869122i	$0.664685\pi$
$314$	−10.0530	−	5.80409i	−0.567323	−	0.327544i
$315$	−3.51303	+	6.08475i	−0.197937	+	0.342837i
$316$	−3.35809	−	5.81638i	−0.188907	−	0.327197i
$317$		−	34.2450i		−	1.92339i	−0.274121	−	0.961695i	$-0.588387\pi$
$317$		−	34.2450i		−	1.92339i	0.274121	−	0.961695i	$-0.411613\pi$
$318$	−9.57432	+	5.52774i	−0.536901	+	0.309980i
$319$	35.2197	−	20.3341i	1.97192	−	1.13849i
$320$		−	1.00000i		−	0.0559017i
$321$	2.55486	+	4.42515i	0.142598	+	0.246988i
$322$	−13.8483	+	23.9859i	−0.771734	+	1.33668i
$323$	5.54908	+	3.20376i	0.308759	+	0.178262i
$324$	−1.16129			−0.0645160
$325$		0			0
$326$	−8.77539			−0.486024
$327$	−6.93235	−	4.00239i	−0.383360	−	0.221333i
$328$	−1.61772	+	2.80196i	−0.0893234	+	0.154713i
$329$	−15.6823	−	27.1625i	−0.864591	−	1.49751i
$330$			5.97272i			0.328787i
$331$	7.14286	−	4.12393i	0.392607	−	0.226672i	−0.290682	−	0.956820i	$-0.593882\pi$
$331$	7.14286	−	4.12393i	0.392607	−	0.226672i	0.683289	+	0.730148i	$0.260549\pi$
$332$	2.63141	−	1.51925i	0.144417	−	0.0833795i
$333$			5.45243i			0.298792i
$334$	4.83398	+	8.37270i	0.264504	+	0.458134i
$335$	−4.24821	+	7.35812i	−0.232105	+	0.402017i
$336$	−2.97309	−	1.71652i	−0.162196	−	0.0936437i
$337$	−12.1509			−0.661902			−0.330951	−	0.943648i	$-0.607369\pi$
$337$	−12.1509			−0.661902			−0.330951	+	0.943648i	$0.607369\pi$
$338$		0			0
$339$	−18.0459			−0.980120
$340$	−1.77997	−	1.02766i	−0.0965322	−	0.0557329i
$341$	−27.0850	+	46.9126i	−1.46673	+	2.54046i
$342$	−3.15332	−	5.46171i	−0.170512	−	0.295335i
$343$			6.72834i			0.363296i
$344$	−1.76240	+	1.01752i	−0.0950224	+	0.0548612i
$345$	−6.82634	+	3.94119i	−0.367518	+	0.212186i
$346$			9.00074i			0.483883i
$347$	7.35376	+	12.7371i	0.394770	+	0.683762i	0.993072	−	0.117509i	$-0.0374908\pi$
$347$	7.35376	+	12.7371i	0.394770	+	0.683762i	−0.598301	+	0.801271i	$0.704157\pi$
$348$	−3.32631	+	5.76133i	−0.178309	+	0.308840i
$349$	−23.9415	−	13.8226i	−1.28156	−	0.739908i	−0.304425	−	0.952536i	$-0.598464\pi$
$349$	−23.9415	−	13.8226i	−1.28156	−	0.739908i	−0.977133	+	0.212629i	$0.931798\pi$
$350$	3.47315			0.185648
$351$		0			0
$352$	6.04251			0.322067
$353$	−13.0685	−	7.54512i	−0.695568	−	0.401586i	0.110127	−	0.993918i	$-0.464874\pi$
$353$	−13.0685	−	7.54512i	−0.695568	−	0.401586i	−0.805694	+	0.592331i	$0.798208\pi$
$354$	3.16396	−	5.48015i	0.168163	−	0.291267i
$355$	0.0609989	+	0.105653i	0.00323749	+	0.00560749i
$356$			3.38412i			0.179358i
$357$	−6.11068	+	3.52800i	−0.323412	+	0.186722i
$358$	9.64278	−	5.56726i	0.509637	−	0.294239i
$359$		−	10.0380i		−	0.529786i	−0.964278	−	0.264893i	$-0.914663\pi$
$359$		−	10.0380i		−	0.529786i	0.964278	−	0.264893i	$-0.0853367\pi$
$360$	1.01148	+	1.75194i	0.0533098	+	0.0923353i
$361$	−4.64053	+	8.03763i	−0.244238	+	0.423033i
$362$	1.41604	+	0.817553i	0.0744256	+	0.0429696i
$363$	−25.2172			−1.32356
$364$		0			0
$365$	−0.138022			−0.00722440
$366$	−11.1696	−	6.44876i	−0.583843	−	0.337082i
$367$	12.2676	−	21.2482i	0.640365	−	1.10915i	−0.344986	−	0.938608i	$-0.612116\pi$
$367$	12.2676	−	21.2482i	0.640365	−	1.10915i	0.985351	−	0.170537i	$-0.0545503\pi$
$368$	3.98724	+	6.90610i	0.207849	+	0.360005i
$369$		−	6.54516i		−	0.340728i
$370$	2.33417	−	1.34763i	0.121348	−	0.0700601i
$371$	−33.6416	+	19.4230i	−1.74658	+	1.00839i
$372$		−	8.86128i		−	0.459436i
$373$	0.621835	+	1.07705i	0.0321974	+	0.0557675i	0.881675	−	0.471857i	$-0.156416\pi$
$373$	0.621835	+	1.07705i	0.0321974	+	0.0557675i	−0.849478	+	0.527625i	$0.823083\pi$
$374$	6.20966	−	10.7555i	0.321094	−	0.556151i
$375$	0.856023	+	0.494225i	0.0442048	+	0.0255217i
$376$	−9.03057			−0.465716
$377$		0			0
$378$	17.2440			0.886936
$379$	−15.9619	−	9.21560i	−0.819907	−	0.473373i	0.0304775	−	0.999535i	$-0.490297\pi$
$379$	−15.9619	−	9.21560i	−0.819907	−	0.473373i	−0.850384	+	0.526162i	$0.823631\pi$
$380$	−1.55876	+	2.69985i	−0.0799627	+	0.138500i
$381$	0.143140	+	0.247926i	0.00733330	+	0.0127017i
$382$			9.23847i			0.472681i
$383$	−22.3707	+	12.9157i	−1.14309	+	0.659963i	−0.947194	−	0.320662i	$-0.896095\pi$
$383$	−22.3707	+	12.9157i	−1.14309	+	0.659963i	−0.195896	+	0.980625i	$0.562761\pi$
$384$	−0.856023	+	0.494225i	−0.0436838	+	0.0252208i
$385$			20.9865i			1.06957i
$386$	−3.64146	−	6.30719i	−0.185345	−	0.321027i
$387$	2.05842	−	3.56528i	0.104635	−	0.181233i
$388$	−5.04478	−	2.91261i	−0.256110	−	0.147865i
$389$	−31.2329			−1.58357			−0.791784	−	0.610801i	$-0.790848\pi$
$389$	−31.2329			−1.58357			−0.791784	+	0.610801i	$0.790848\pi$
$390$		0			0
$391$	16.3902			0.828886
$392$	−4.38447	−	2.53138i	−0.221449	−	0.127854i
$393$	9.63314	−	16.6851i	0.485928	−	0.841651i
$394$	10.2872	+	17.8180i	0.518262	+	0.897655i
$395$		−	6.71618i		−	0.337928i
$396$	−10.5861	+	6.11189i	−0.531972	+	0.307134i
$397$	24.3492	−	14.0580i	1.22205	−	0.705553i	0.256698	−	0.966492i	$-0.417365\pi$
$397$	24.3492	−	14.0580i	1.22205	−	0.705553i	0.965355	+	0.260939i	$0.0840321\pi$
$398$			2.77107i			0.138901i
$399$	5.35128	+	9.26869i	0.267899	+	0.464015i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	5.33234	+	3.07863i	0.266284	+	0.153739i	0.627198	−	0.778860i	$-0.284202\pi$
$401$	5.33234	+	3.07863i	0.266284	+	0.153739i	−0.360914	+	0.932599i	$0.617535\pi$
$402$	8.39829			0.418869
$403$		0			0
$404$	−8.47871			−0.421832
$405$	−1.00570	−	0.580644i	−0.0499739	−	0.0288524i
$406$	−11.6877	+	20.2438i	−0.580053	+	1.00468i
$407$	8.14309	+	14.1042i	0.403638	+	0.699121i
$408$			2.03159i			0.100579i
$409$	−22.9330	+	13.2403i	−1.13396	+	0.654693i	−0.944928	−	0.327278i	$-0.893869\pi$
$409$	−22.9330	+	13.2403i	−1.13396	+	0.654693i	−0.189033	+	0.981971i	$0.560535\pi$
$410$	−2.80196	+	1.61772i	−0.138379	+	0.0798933i
$411$			3.66318i			0.180691i
$412$	2.48445	+	4.30320i	0.122400	+	0.212003i
$413$	11.1173	−	19.2558i	0.547047	−	0.947514i
$414$	−13.9708	−	8.06604i	−0.686627	−	0.396424i
$415$	3.03849			0.149154
$416$		0			0
$417$	−10.2634			−0.502599
$418$	−16.3139	−	9.41882i	−0.797938	−	0.460690i
$419$	5.92699	−	10.2659i	0.289553	−	0.501520i	−0.684150	−	0.729341i	$-0.739827\pi$
$419$	5.92699	−	10.2659i	0.289553	−	0.501520i	0.973703	+	0.227821i	$0.0731602\pi$
$420$	−1.71652	−	2.97309i	−0.0837575	−	0.145072i
$421$			9.48437i			0.462240i	0.972925	+	0.231120i	$0.0742390\pi$
$421$			9.48437i			0.462240i	−0.972925	+	0.231120i	$0.925761\pi$
$422$	18.4251	−	10.6377i	0.896920	−	0.517837i
$423$	15.8210	−	9.13427i	0.769244	−	0.444123i
$424$			11.1847i			0.543175i
$425$	−1.02766	−	1.77997i	−0.0498490	−	0.0863410i
$426$	0.0602944	−	0.104433i	0.00292127	−	0.00505979i
$427$	−39.2469	−	22.6592i	−1.89929	−	1.09656i
$428$	5.16942			0.249874
$429$		0			0
$430$	−2.03505			−0.0981387
$431$	12.2261	+	7.05875i	0.588911	+	0.340008i	0.764667	−	0.644426i	$-0.222904\pi$
$431$	12.2261	+	7.05875i	0.588911	+	0.340008i	−0.175756	+	0.984434i	$0.556237\pi$
$432$	2.48248	−	4.29978i	0.119438	−	0.206873i
$433$	13.1597	+	22.7932i	0.632414	+	1.09537i	0.987057	+	0.160371i	$0.0512691\pi$
$433$	13.1597	+	22.7932i	0.632414	+	1.09537i	−0.354643	+	0.935002i	$0.615398\pi$
$434$		−	31.1361i		−	1.49458i
$435$	−5.76133	+	3.32631i	−0.276235	+	0.159484i
$436$	−7.01335	+	4.04916i	−0.335879	+	0.193920i
$437$		−	24.8606i		−	1.18924i
$438$	0.0682140	+	0.118150i	0.00325939	+	0.00564543i
$439$	−13.2985	+	23.0336i	−0.634702	+	1.09934i	0.351877	+	0.936046i	$0.385544\pi$
$439$	−13.2985	+	23.0336i	−0.634702	+	1.09934i	−0.986578	+	0.163289i	$0.947790\pi$
$440$	5.23297	+	3.02125i	0.249472	+	0.144033i
$441$	10.2418			0.487704
$442$		0			0
$443$	15.9166			0.756222			0.378111	−	0.925760i	$-0.376574\pi$
$443$	15.9166			0.756222			0.378111	+	0.925760i	$0.376574\pi$
$444$	−2.30721	−	1.33207i	−0.109495	−	0.0632172i
$445$	−1.69206	+	2.93073i	−0.0802113	+	0.138930i
$446$	3.67949	+	6.37306i	0.174229	+	0.301773i
$447$			20.4924i			0.969256i
$448$	−3.00783	+	1.73657i	−0.142107	+	0.0820454i
$449$	33.5454	−	19.3675i	1.58311	−	0.914007i	0.588705	−	0.808348i	$-0.299638\pi$
$449$	33.5454	−	19.3675i	1.58311	−	0.914007i	0.994402	−	0.105659i	$-0.0336953\pi$
$450$			2.02297i			0.0953635i
$451$	−9.77506	−	16.9309i	−0.460289	−	0.797245i
$452$	−9.12839	+	15.8108i	−0.429363	+	0.743679i
$453$	−17.5489	−	10.1319i	−0.824520	−	0.476037i
$454$	21.3232			1.00075
$455$		0			0
$456$	3.08152			0.144305
$457$	12.1538	+	7.01701i	0.568532	+	0.328242i	0.756563	−	0.653921i	$-0.226877\pi$
$457$	12.1538	+	7.01701i	0.568532	+	0.328242i	−0.188031	+	0.982163i	$0.560210\pi$
$458$	−7.89647	+	13.6771i	−0.368978	+	0.639088i
$459$	−5.10230	−	8.83744i	−0.238155	−	0.412497i
$460$			7.97448i			0.371812i
$461$	7.79551	−	4.50074i	0.363073	−	0.209620i	−0.307355	−	0.951595i	$-0.599444\pi$
$461$	7.79551	−	4.50074i	0.363073	−	0.209620i	0.670428	+	0.741975i	$0.266111\pi$
$462$	17.9649	−	10.3721i	0.835805	−	0.482552i
$463$		−	34.7780i		−	1.61627i	−0.588997	−	0.808135i	$-0.700477\pi$
$463$		−	34.7780i		−	1.61627i	0.588997	−	0.808135i	$-0.299523\pi$
$464$	3.36517	+	5.82865i	0.156224	+	0.270588i
$465$	4.43064	−	7.67409i	0.205466	−	0.355878i
$466$	7.04113	+	4.06520i	0.326174	+	0.188317i
$467$	−18.1864			−0.841568			−0.420784	−	0.907161i	$-0.638245\pi$
$467$	−18.1864			−0.841568			−0.420784	+	0.907161i	$0.638245\pi$
$468$		0			0
$469$	29.5093			1.36261
$470$	−7.82070	−	4.51529i	−0.360742	−	0.208275i
$471$	−5.73706	+	9.93687i	−0.264350	+	0.457867i
$472$	−3.20093	−	5.54418i	−0.147335	−	0.255192i
$473$		−	12.2968i		−	0.565407i
$474$	−5.74921	+	3.31931i	−0.264070	+	0.152461i
$475$	−2.69985	+	1.55876i	−0.123878	+	0.0715208i
$476$			7.13845i			0.327190i
$477$	−11.3131	−	19.5948i	−0.517991	−	0.897186i
$478$	6.26234	−	10.8467i	0.286433	−	0.496116i
$479$	27.7954	+	16.0477i	1.27000	+	0.733238i	0.974989	−	0.222255i	$-0.0713417\pi$
$479$	27.7954	+	16.0477i	1.27000	+	0.733238i	0.295016	+	0.955492i	$0.404675\pi$
$480$	−0.988450			−0.0451164
$481$		0			0
$482$	−3.58778			−0.163419
$483$	23.7089	+	13.6883i	1.07879	+	0.622840i
$484$	−12.7560	+	22.0940i	−0.579816	+	1.00427i
$485$	−2.91261	−	5.04478i	−0.132255	−	0.229072i
$486$			16.0427i			0.727713i
$487$	−27.1309	+	15.6640i	−1.22942	+	0.709804i	−0.966908	−	0.255125i	$-0.917883\pi$
$487$	−27.1309	+	15.6640i	−1.22942	+	0.709804i	−0.262509	+	0.964929i	$0.584550\pi$
$488$	−11.3001	+	6.52411i	−0.511531	+	0.295333i
$489$			8.67404i			0.392254i
$490$	−2.53138	−	4.38447i	−0.114356	−	0.198070i
$491$	−3.63614	+	6.29798i	−0.164097	+	0.284224i	−0.936334	−	0.351110i	$-0.885804\pi$
$491$	−3.63614	+	6.29798i	−0.164097	+	0.284224i	0.772237	+	0.635334i	$0.219138\pi$
$492$	2.76960	+	1.59903i	0.124863	+	0.0720899i
$493$	13.8331			0.623010
$494$		0			0
$495$	−12.2238			−0.549418
$496$	−7.76376	−	4.48241i	−0.348603	−	0.201266i
$497$	0.211858	−	0.366949i	0.00950314	−	0.0164599i
$498$	−1.50170	−	2.60102i	−0.0672928	−	0.116555i
$499$			9.57876i			0.428804i	0.976745	+	0.214402i	$0.0687803\pi$
$499$			9.57876i			0.428804i	−0.976745	+	0.214402i	$0.931220\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	8.27600	−	4.77815i	0.369744	−	0.213472i
$502$			15.0726i			0.672722i
$503$	−3.22712	−	5.58954i	−0.143890	−	0.249225i	0.785068	−	0.619409i	$-0.212628\pi$
$503$	−3.22712	−	5.58954i	−0.143890	−	0.249225i	−0.928958	+	0.370184i	$0.879295\pi$
$504$	3.51303	−	6.08475i	0.156483	−	0.271036i
$505$	−7.34278	−	4.23936i	−0.326750	−	0.188649i
$506$	−48.1858			−2.14212
$507$		0			0
$508$	0.289626			0.0128501
$509$	−2.69443	−	1.55563i	−0.119429	−	0.0689521i	0.439096	−	0.898440i	$-0.355299\pi$
$509$	−2.69443	−	1.55563i	−0.119429	−	0.0689521i	−0.558524	+	0.829488i	$0.688632\pi$
$510$	−1.01579	+	1.75941i	−0.0449801	+	0.0779079i
$511$	0.239685	+	0.415147i	0.0106031	+	0.0183650i
$512$			1.00000i			0.0441942i
$513$	−13.4046	+	7.73917i	−0.591829	+	0.341693i
$514$	−19.3820	+	11.1902i	−0.854904	+	0.493579i
$515$			4.96891i			0.218956i
$516$	1.00577	+	1.74205i	0.0442766	+	0.0766894i
$517$	27.2836	−	47.2567i	1.19993	−	2.07835i
$518$	−8.10692	−	4.68053i	−0.356198	−	0.205651i
$519$	8.89678			0.390525
$520$		0			0
$521$	42.6003			1.86635			0.933177	−	0.359416i	$-0.117024\pi$
$521$	42.6003			1.86635			0.933177	+	0.359416i	$0.117024\pi$
$522$	−11.7912	−	6.80763i	−0.516085	−	0.297962i
$523$	0.673013	−	1.16569i	0.0294288	−	0.0509722i	−0.850936	−	0.525270i	$-0.823964\pi$
$523$	0.673013	−	1.16569i	0.0294288	−	0.0509722i	0.880365	+	0.474297i	$0.157298\pi$
$524$	−9.74570	−	16.8800i	−0.425743	−	0.737408i
$525$		−	3.43303i		−	0.149830i
$526$	16.2208	−	9.36507i	0.707260	−	0.408337i
$527$	−15.9571	+	9.21282i	−0.695101	+	0.401317i
$528$		−	5.97272i		−	0.259929i
$529$	−20.2961	−	35.1539i	−0.882440	−	1.52843i
$530$	−5.59233	+	9.68619i	−0.242915	+	0.420741i
$531$	11.2157	+	6.47538i	0.486719	+	0.281008i
$532$	10.8276			0.469436
$533$		0			0
$534$	3.34503			0.144754
$535$	4.47685	+	2.58471i	0.193551	+	0.111747i
$536$	4.24821	−	7.35812i	0.183495	−	0.317822i
$537$	−5.50296	−	9.53141i	−0.237470	−	0.411311i
$538$			6.53932i			0.281930i
$539$	26.4932	−	15.2959i	1.14114	−	0.658840i
$540$	4.29978	−	2.48248i	0.185033	−	0.106829i
$541$			21.9468i			0.943567i	0.881714	+	0.471784i	$0.156390\pi$
$541$			21.9468i			0.943567i	−0.881714	+	0.471784i	$0.843610\pi$
$542$	−1.43222	−	2.48068i	−0.0615192	−	0.106554i
$543$	0.808110	−	1.39969i	0.0346793	−	0.0600664i
$544$	1.77997	+	1.02766i	0.0763154	+	0.0440607i
$545$	−8.09832			−0.346894
$546$		0			0
$547$	−26.7344			−1.14308			−0.571540	−	0.820574i	$-0.693654\pi$
$547$	−26.7344			−1.14308			−0.571540	+	0.820574i	$0.693654\pi$
$548$	3.20947	+	1.85299i	0.137102	+	0.0791558i
$549$	13.1980	−	22.8597i	0.563279	−	0.975628i
$550$	3.02125	+	5.23297i	0.128827	+	0.223134i
$551$		−	20.9820i		−	0.893863i
$552$	6.82634	−	3.94119i	0.290548	−	0.167748i
$553$	−20.2012	+	11.6631i	−0.859041	+	0.495967i
$554$			2.80684i			0.119251i
$555$	−1.33207	−	2.30721i	−0.0565432	−	0.0979357i
$556$	−5.19164	+	8.99218i	−0.220174	+	0.381353i
$557$	−14.9708	−	8.64340i	−0.634333	−	0.366233i	0.148095	−	0.988973i	$-0.452686\pi$
$557$	−14.9708	−	8.64340i	−0.634333	−	0.366233i	−0.782428	+	0.622741i	$0.786019\pi$
$558$	18.1355			0.767738
$559$		0			0
$560$	−3.47315			−0.146767
$561$	−10.6312	−	6.13795i	−0.448851	−	0.259144i
$562$	12.9487	−	22.4278i	0.546207	−	0.946058i
$563$	−18.1162	−	31.3782i	−0.763508	−	1.32243i	−0.941032	−	0.338318i	$-0.890142\pi$
$563$	−18.1162	−	31.3782i	−0.763508	−	1.32243i	0.177524	−	0.984117i	$-0.443191\pi$
$564$			8.92627i			0.375864i
$565$	−15.8108	+	9.12839i	−0.665167	+	0.384034i
$566$	25.0086	−	14.4387i	1.05119	−	0.606904i
$567$			4.03332i			0.169384i
$568$	−0.0609989	−	0.105653i	−0.00255946	−	0.00443311i
$569$	10.7431	−	18.6076i	0.450375	−	0.780072i	−0.548034	−	0.836456i	$-0.684624\pi$
$569$	10.7431	−	18.6076i	0.450375	−	0.780072i	0.998409	+	0.0563839i	$0.0179571\pi$
$570$	2.66867	+	1.54076i	0.111778	+	0.0645352i
$571$	−16.8212			−0.703944			−0.351972	−	0.936011i	$-0.614489\pi$
$571$	−16.8212			−0.703944			−0.351972	+	0.936011i	$0.614489\pi$
$572$		0			0
$573$	9.13177			0.381485
$574$	9.73164	+	5.61856i	0.406191	+	0.234514i
$575$	−3.98724	+	6.90610i	−0.166279	+	0.288004i
$576$	−1.01148	−	1.75194i	−0.0421451	−	0.0729975i
$577$			33.5996i			1.39877i	0.714746	+	0.699384i	$0.246542\pi$
$577$			33.5996i			1.39877i	−0.714746	+	0.699384i	$0.753458\pi$
$578$	−11.0640	+	6.38782i	−0.460203	+	0.265698i
$579$	−6.23434	+	3.59940i	−0.259090	+	0.149586i
$580$			6.73035i			0.279462i
$581$	−5.27657	−	9.13928i	−0.218909	−	0.379161i
$582$	−2.87897	+	4.98652i	−0.119337	+	0.206698i
$583$	−58.5289	−	33.7917i	−2.42402	−	1.39951i
$584$	0.138022			0.00571139
$585$		0			0
$586$	−11.0820			−0.457792
$587$	−22.9482	−	13.2491i	−0.947172	−	0.546850i	−0.0549709	−	0.998488i	$-0.517507\pi$
$587$	−22.9482	−	13.2491i	−0.947172	−	0.546850i	−0.892201	+	0.451638i	$0.850840\pi$
$588$	−2.50214	+	4.33384i	−0.103187	+	0.178724i
$589$	13.9740	+	24.2037i	0.575789	+	0.997296i
$590$		−	6.40187i		−	0.263561i
$591$	17.6122	−	10.1684i	0.724468	−	0.418272i
$592$	−2.33417	+	1.34763i	−0.0959338	+	0.0553874i
$593$			33.8602i			1.39047i	0.718783	+	0.695235i	$0.244700\pi$
$593$			33.8602i			1.39047i	−0.718783	+	0.695235i	$0.755300\pi$
$594$	15.0004	+	25.9814i	0.615473	+	1.06603i
$595$	−3.56923	+	6.18208i	−0.146324	+	0.253441i
$596$	17.9543	+	10.3659i	0.735436	+	0.424604i
$597$	2.73906			0.112102
$598$		0			0
$599$	15.5745			0.636358			0.318179	−	0.948031i	$-0.396929\pi$
$599$	15.5745			0.636358			0.318179	+	0.948031i	$0.396929\pi$
$600$	−0.856023	−	0.494225i	−0.0349470	−	0.0201767i
$601$	16.8801	−	29.2372i	0.688555	−	1.19261i	−0.283751	−	0.958898i	$-0.591579\pi$
$601$	16.8801	−	29.2372i	0.688555	−	1.19261i	0.972305	−	0.233714i	$-0.0750879\pi$
$602$	3.53401	+	6.12108i	0.144035	+	0.249477i
$603$			17.1880i			0.699948i
$604$	−17.7540	+	10.2503i	−0.722399	+	0.417077i
$605$	−22.0940	+	12.7560i	−0.898247	+	0.518603i
$606$			8.38079i			0.340446i
$607$	3.55160	+	6.15154i	0.144155	+	0.249683i	0.929057	−	0.369936i	$-0.120620\pi$
$607$	3.55160	+	6.15154i	0.144155	+	0.249683i	−0.784902	+	0.619619i	$0.787287\pi$
$608$	1.55876	−	2.69985i	0.0632161	−	0.109493i
$609$	20.0100	+	11.5528i	0.810845	+	0.468141i
$610$	−13.0482			−0.528307
$611$		0			0
$612$	−4.15786			−0.168071
$613$	14.8367	+	8.56598i	0.599249	+	0.345976i	0.768746	−	0.639554i	$-0.220881\pi$
$613$	14.8367	+	8.56598i	0.599249	+	0.345976i	−0.169497	+	0.985531i	$0.554214\pi$
$614$	3.19023	−	5.52563i	0.128747	−	0.222996i
$615$	1.59903	+	2.76960i	0.0644792	+	0.111681i
$616$		−	20.9865i		−	0.845571i
$617$	18.3916	−	10.6184i	0.740416	−	0.427479i	−0.0818045	−	0.996648i	$-0.526068\pi$
$617$	18.3916	−	10.6184i	0.740416	−	0.427479i	0.822221	+	0.569169i	$0.192735\pi$
$618$	4.25350	−	2.45576i	0.171101	−	0.0987851i
$619$		−	23.8169i		−	0.957284i	−0.878010	−	0.478642i	$-0.841129\pi$
$619$		−	23.8169i		−	0.957284i	0.878010	−	0.478642i	$-0.158871\pi$
$620$	−4.48241	−	7.76376i	−0.180018	−	0.311800i
$621$	−19.7964	+	34.2884i	−0.794404	+	1.37595i
$622$	16.4062	+	9.47213i	0.657829	+	0.379798i
$623$	11.7535			0.470896
$624$		0			0
$625$	1.00000			0.0400000
$626$	15.1560	+	8.75033i	0.605756	+	0.349734i
$627$	−9.31004	+	16.1255i	−0.371807	+	0.643989i
$628$	5.80409	+	10.0530i	0.231608	+	0.401158i
$629$			5.53966i			0.220881i
$630$	6.08475	−	3.51303i	0.242422	−	0.139962i
$631$	−9.64325	+	5.56753i	−0.383892	+	0.221640i	−0.679510	−	0.733666i	$-0.737808\pi$
$631$	−9.64325	+	5.56753i	−0.383892	+	0.221640i	0.295619	+	0.955306i	$0.404474\pi$
$632$			6.71618i			0.267155i
$633$	−10.5149	−	18.2123i	−0.417929	−	0.723874i
$634$	−17.1225	+	29.6570i	−0.680021	+	1.17783i
$635$	0.250823	+	0.144813i	0.00995362	+	0.00574672i
$636$	11.0555			0.438378
$637$		0			0
$638$	−40.6682			−1.61007
$639$	0.213733	+	0.123399i	0.00845514	+	0.00488158i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−0.521743	−	0.903685i	−0.0206076	−	0.0356934i	0.855538	−	0.517741i	$-0.173227\pi$
$641$	−0.521743	−	0.903685i	−0.0206076	−	0.0356934i	−0.876145	+	0.482047i	$0.839893\pi$
$642$		−	5.10972i		−	0.201665i
$643$	−5.87873	+	3.39409i	−0.231835	+	0.133850i	−0.611418	−	0.791308i	$-0.709401\pi$
$643$	−5.87873	+	3.39409i	−0.231835	+	0.133850i	0.379583	+	0.925157i	$0.376067\pi$
$644$	23.9859	−	13.8483i	0.945177	−	0.545698i
$645$			2.01154i			0.0792044i
$646$	−3.20376	−	5.54908i	−0.126050	−	0.218326i
$647$	−5.50186	+	9.52950i	−0.216300	+	0.374643i	−0.953674	−	0.300842i	$-0.902732\pi$
$647$	−5.50186	+	9.52950i	−0.216300	+	0.374643i	0.737374	+	0.675485i	$0.236066\pi$
$648$	1.00570	+	0.580644i	0.0395078	+	0.0228098i
$649$	38.6833			1.51845
$650$		0			0
$651$	−30.7765			−1.20623
$652$	7.59971	+	4.38770i	0.297628	+	0.171835i
$653$	1.67573	−	2.90244i	0.0655762	−	0.113581i	−0.831373	−	0.555714i	$-0.812445\pi$
$653$	1.67573	−	2.90244i	0.0655762	−	0.113581i	0.896949	+	0.442133i	$0.145778\pi$
$654$	4.00239	+	6.93235i	0.156506	+	0.271076i
$655$		−	19.4914i		−	0.761592i
$656$	2.80196	−	1.61772i	0.109398	−	0.0631612i
$657$	−0.241806	+	0.139607i	−0.00943376	+	0.00544658i
$658$			31.3645i			1.22272i
$659$	2.23147	+	3.86501i	0.0869256	+	0.150560i	0.906210	−	0.422828i	$-0.138962\pi$
$659$	2.23147	+	3.86501i	0.0869256	+	0.150560i	−0.819285	+	0.573387i	$0.805629\pi$
$660$	2.98636	−	5.17253i	0.116244	−	0.201340i
$661$	−9.26094	−	5.34681i	−0.360209	−	0.207967i	0.308963	−	0.951074i	$-0.400018\pi$
$661$	−9.26094	−	5.34681i	−0.360209	−	0.207967i	−0.669172	+	0.743107i	$0.733351\pi$
$662$	−8.24786			−0.320562
$663$		0			0
$664$	−3.03849			−0.117916
$665$	9.37699	+	5.41381i	0.363624	+	0.209938i
$666$	2.72622	−	4.72195i	0.105639	−	0.182972i
$667$	−26.8355	−	46.4804i	−1.03907	−	1.79973i
$668$		−	9.66796i		−	0.374065i
$669$	6.29945	−	3.63699i	0.243551	−	0.140614i
$670$	7.35812	−	4.24821i	0.284269	−	0.164123i
$671$		−	78.8440i		−	3.04374i
$672$	1.71652	+	2.97309i	0.0662161	+	0.114690i
$673$	4.16705	−	7.21754i	0.160628	−	0.278216i	−0.774466	−	0.632615i	$-0.781981\pi$
$673$	4.16705	−	7.21754i	0.160628	−	0.278216i	0.935094	+	0.354400i	$0.115315\pi$
$674$	10.5230	+	6.07545i	0.405330	+	0.234018i
$675$	4.96495			0.191101
$676$		0			0
$677$	−10.4945			−0.403338			−0.201669	−	0.979454i	$-0.564637\pi$
$677$	−10.4945			−0.403338			−0.201669	+	0.979454i	$0.564637\pi$
$678$	15.6282	+	9.02296i	0.600198	+	0.346525i
$679$	−10.1159	+	17.5213i	−0.388213	+	0.672405i
$680$	1.02766	+	1.77997i	0.0394091	+	0.0682586i
$681$		−	21.0770i		−	0.807671i
$682$	46.9126	−	27.0850i	1.79638	−	1.03714i
$683$	3.71581	−	2.14532i	0.142182	−	0.0820886i	−0.427222	−	0.904147i	$-0.640508\pi$
$683$	3.71581	−	2.14532i	0.142182	−	0.0820886i	0.569403	+	0.822058i	$0.307174\pi$
$684$			6.30664i			0.241140i
$685$	1.85299	+	3.20947i	0.0707991	+	0.122628i
$686$	3.36417	−	5.82691i	0.128445	−	0.222473i
$687$	13.5191	+	7.80527i	0.515787	+	0.297790i
$688$	2.03505			0.0775855
$689$		0			0
$690$	7.88237			0.300077
$691$	26.5236	+	15.3134i	1.00901	+	0.582550i	0.910901	−	0.412626i	$-0.135388\pi$
$691$	26.5236	+	15.3134i	1.00901	+	0.582550i	0.0981061	+	0.995176i	$0.468722\pi$
$692$	4.50037	−	7.79487i	0.171078	−	0.296316i
$693$	21.2275	+	36.7671i	0.806366	+	1.39667i
$694$		−	14.7075i		−	0.558290i
$695$	−8.99218	+	5.19164i	−0.341093	+	0.196930i
$696$	5.76133	−	3.32631i	0.218383	−	0.126083i
$697$		−	6.64987i		−	0.251882i
$698$	13.8226	+	23.9415i	0.523194	+	0.906198i
$699$	4.01825	−	6.95981i	0.151984	−	0.263244i
$700$	−3.00783	−	1.73657i	−0.113685	−	0.0656363i
$701$	−8.16045			−0.308216			−0.154108	−	0.988054i	$-0.549250\pi$
$701$	−8.16045			−0.308216			−0.154108	+	0.988054i	$0.549250\pi$
$702$		0			0
$703$	8.40255			0.316908
$704$	−5.23297	−	3.02125i	−0.197225	−	0.113868i
$705$	−4.46314	+	7.73038i	−0.168091	+	0.291143i
$706$	7.54512	+	13.0685i	0.283964	+	0.491841i
$707$			29.4478i			1.10750i
$708$	−5.48015	+	3.16396i	−0.205957	+	0.118909i
$709$	−27.8250	+	16.0648i	−1.04499	+	0.603325i	−0.921243	−	0.388989i	$-0.872825\pi$
$709$	−27.8250	+	16.0648i	−1.04499	+	0.603325i	−0.123747	+	0.992314i	$0.539491\pi$
$710$		−	0.121998i		−	0.00457850i
$711$	−6.79330	−	11.7663i	−0.254769	−	0.441272i
$712$	1.69206	−	2.93073i	0.0634126	−	0.109834i
$713$	61.9119	+	35.7449i	2.31862	+	1.33866i
$714$	7.05601			0.264064
$715$		0			0
$716$	−11.1345			−0.416117
$717$	−10.7214	−	6.19001i	−0.400399	−	0.231170i
$718$	−5.01901	+	8.69318i	−0.187308	+	0.324427i
$719$	0.414515	+	0.717961i	0.0154588	+	0.0267754i	0.873651	−	0.486553i	$-0.161746\pi$
$719$	0.414515	+	0.717961i	0.0154588	+	0.0267754i	−0.858193	+	0.513328i	$0.828412\pi$
$720$		−	2.02297i		−	0.0753915i
$721$	14.9457	−	8.62888i	0.556605	−	0.321356i
$722$	8.03763	−	4.64053i	0.299130	−	0.172703i
$723$			3.54634i			0.131890i
$724$	−0.817553	−	1.41604i	−0.0303841	−	0.0526268i
$725$	−3.36517	+	5.82865i	−0.124979	+	0.216471i
$726$	21.8388	+	12.6086i	0.810513	+	0.467950i
$727$	42.6451			1.58162			0.790810	−	0.612061i	$-0.209659\pi$
$727$	42.6451			1.58162			0.790810	+	0.612061i	$0.209659\pi$
$728$		0			0
$729$	12.3736			0.458281
$730$	0.119531	+	0.0690110i	0.00442403	+	0.00255421i
$731$	2.09134	−	3.62231i	0.0773511	−	0.133976i
$732$	6.44876	+	11.1696i	0.238353	+	0.412839i
$733$			30.2477i			1.11722i	0.829429	+	0.558612i	$0.188666\pi$
$733$			30.2477i			1.11722i	−0.829429	+	0.558612i	$0.811334\pi$
$734$	−21.2482	+	12.2676i	−0.784284	+	0.452807i
$735$	−4.33384	+	2.50214i	−0.159856	+	0.0922929i
$736$		−	7.97448i		−	0.293943i
$737$	25.6699	+	44.4615i	0.945561	+	1.63776i
$738$	−3.27258	+	5.66828i	−0.120465	+	0.208652i
$739$	13.7656	+	7.94757i	0.506376	+	0.292356i	0.731343	−	0.682010i	$-0.238894\pi$
$739$	13.7656	+	7.94757i	0.506376	+	0.292356i	−0.224967	+	0.974366i	$0.572227\pi$
$740$	−2.69527			−0.0990800
$741$		0			0
$742$	38.8459			1.42608
$743$	−6.62750	−	3.82639i	−0.243139	−	0.140377i	0.373479	−	0.927638i	$-0.378165\pi$
$743$	−6.62750	−	3.82639i	−0.243139	−	0.140377i	−0.616619	+	0.787262i	$0.711498\pi$
$744$	−4.43064	+	7.67409i	−0.162435	+	0.281346i
$745$	10.3659	+	17.9543i	0.379778	+	0.657794i
$746$		−	1.24367i		−	0.0455340i
$747$	5.32326	−	3.07338i	0.194768	−	0.112449i
$748$	−10.7555	+	6.20966i	−0.393258	+	0.227048i
$749$		−	17.9542i		−	0.656031i
$750$	−0.494225	−	0.856023i	−0.0180466	−	0.0312575i
$751$	15.1630	−	26.2631i	0.553305	−	0.958352i	−0.444728	−	0.895666i	$-0.646700\pi$
$751$	15.1630	−	26.2631i	0.553305	−	0.958352i	0.998033	−	0.0626868i	$-0.0199669\pi$
$752$	7.82070	+	4.51529i	0.285192	+	0.164656i
$753$	14.8985			0.542931
$754$		0			0
$755$	−20.5005			−0.746090
$756$	−14.9338	−	8.62201i	−0.543135	−	0.313579i
$757$	10.4654	−	18.1266i	0.380372	−	0.658823i	−0.610744	−	0.791828i	$-0.709129\pi$
$757$	10.4654	−	18.1266i	0.380372	−	0.658823i	0.991115	+	0.133005i	$0.0424628\pi$
$758$	9.21560	+	15.9619i	0.334726	+	0.579762i
$759$			47.6293i			1.72883i
$760$	2.69985	−	1.55876i	0.0979339	−	0.0565422i
$761$	−13.2186	+	7.63175i	−0.479173	+	0.276651i	−0.720072	−	0.693900i	$-0.755891\pi$
$761$	−13.2186	+	7.63175i	−0.479173	+	0.276651i	0.240899	+	0.970550i	$0.422558\pi$
$762$		−	0.286281i		−	0.0103709i
$763$	14.0633	+	24.3584i	0.509127	+	0.881833i
$764$	4.61924	−	8.00075i	0.167118	−	0.289457i
$765$	−3.60081	−	2.07893i	−0.130188	−	0.0751638i
$766$	25.8315			0.933329
$767$		0			0
$768$	0.988450			0.0356676
$769$	−14.1819	−	8.18791i	−0.511411	−	0.295263i	0.222002	−	0.975046i	$-0.428741\pi$
$769$	−14.1819	−	8.18791i	−0.511411	−	0.295263i	−0.733414	+	0.679783i	$0.762074\pi$
$770$	10.4933	−	18.1749i	0.378151	−	0.654977i
$771$	11.0610	+	19.1582i	0.398351	+	0.689964i
$772$			7.28291i			0.262118i
$773$	−4.66097	+	2.69101i	−0.167643	+	0.0967890i	−0.581474	−	0.813565i	$-0.697524\pi$
$773$	−4.66097	+	2.69101i	−0.167643	+	0.0967890i	0.413831	+	0.910354i	$0.364191\pi$
$774$	−3.56528	+	2.05842i	−0.128151	+	0.0739882i
$775$		−	8.96482i		−	0.322026i
$776$	2.91261	+	5.04478i	0.104557	+	0.181097i
$777$	−4.62647	+	8.01329i	−0.165974	+	0.287475i
$778$	27.0485	+	15.6164i	0.969734	+	0.559876i
$779$	−10.0865			−0.361387
$780$		0			0
$781$	0.737173			0.0263781
$782$	−14.1943	−	8.19508i	−0.507587	−	0.293055i
$783$	−16.7079	+	28.9390i	−0.597093	+	1.03419i
$784$	2.53138	+	4.38447i	0.0904063	+	0.156588i
$785$			11.6082i			0.414314i
$786$	−16.6851	+	9.63314i	−0.595137	+	0.343603i
$787$	−22.7928	+	13.1594i	−0.812477	+	0.469084i	−0.847815	−	0.530292i	$-0.822082\pi$
$787$	−22.7928	+	13.1594i	−0.812477	+	0.469084i	0.0353385	+	0.999375i	$0.488749\pi$
$788$		−	20.5744i		−	0.732933i
$789$	−9.25691	−	16.0334i	−0.329555	−	0.570806i
$790$	−3.35809	+	5.81638i	−0.119476	+	0.206938i
$791$	54.9133	+	31.7042i	1.95249	+	1.12727i
$792$	12.2238			0.434353
$793$		0			0
$794$	−28.1161			−0.997802
$795$	9.57432	+	5.52774i	0.339566	+	0.196049i
$796$	1.38553	−	2.39981i	0.0491089	−	0.0850592i
$797$	−11.4362	−	19.8081i	−0.405091	−	0.701639i	0.589241	−	0.807957i	$-0.299427\pi$
$797$	−11.4362	−	19.8081i	−0.405091	−	0.701639i	−0.994332	+	0.106319i	$0.966094\pi$
$798$		−	10.7026i		−	0.378866i
$799$	16.0741	−	9.28039i	0.568661	−	0.328317i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$			6.84595i			0.241890i
$802$	−3.07863	−	5.33234i	−0.108710	−	0.188291i
$803$	−0.417000	+	0.722264i	−0.0147156	+	0.0254882i
$804$	−7.27314	−	4.19915i	−0.256504	−	0.148093i
$805$	27.6965			0.976174
$806$		0			0
$807$	6.46379			0.227536
$808$	7.34278	+	4.23936i	0.258318	+	0.149140i
$809$	9.56123	−	16.5605i	0.336155	−	0.582238i	−0.647551	−	0.762022i	$-0.724207\pi$
$809$	9.56123	−	16.5605i	0.336155	−	0.582238i	0.983706	+	0.179785i	$0.0575401\pi$
$810$	0.580644	+	1.00570i	0.0204017	+	0.0353369i
$811$		−	13.2144i		−	0.464019i	−0.972714	−	0.232009i	$-0.925470\pi$
$811$		−	13.2144i		−	0.464019i	0.972714	−	0.232009i	$-0.0745300\pi$
$812$	20.2438	−	11.6877i	0.710417	−	0.410159i
$813$	−2.45203	+	1.41568i	−0.0859965	+	0.0496501i
$814$		−	16.2862i		−	0.570830i
$815$	4.38770	+	7.59971i	0.153694	+	0.266206i
$816$	1.01579	−	1.75941i	0.0355599	−	0.0615916i
$817$	−5.49433	−	3.17215i	−0.192222	−	0.110980i
$818$	26.4807			0.925876
$819$		0			0
$820$	3.23543			0.112986
$821$	8.10356	+	4.67859i	0.282816	+	0.163284i	0.634698	−	0.772761i	$-0.281125\pi$
$821$	8.10356	+	4.67859i	0.282816	+	0.163284i	−0.351881	+	0.936045i	$0.614458\pi$
$822$	1.83159	−	3.17240i	0.0638840	−	0.110650i
$823$	5.27953	+	9.14441i	0.184033	+	0.318754i	0.943250	−	0.332083i	$-0.107751\pi$
$823$	5.27953	+	9.14441i	0.184033	+	0.318754i	−0.759217	+	0.650837i	$0.774418\pi$
$824$		−	4.96891i		−	0.173100i
$825$	5.17253	−	2.98636i	0.180084	−	0.103972i
$826$	−19.2558	+	11.1173i	−0.669994	+	0.386821i
$827$		−	12.6564i		−	0.440107i	−0.975488	−	0.220054i	$-0.929377\pi$
$827$		−	12.6564i		−	0.440107i	0.975488	−	0.220054i	$-0.0706232\pi$
$828$	8.06604	+	13.9708i	0.280314	+	0.485519i
$829$	27.2877	−	47.2636i	0.947740	−	1.64153i	0.197570	−	0.980289i	$-0.436695\pi$
$829$	27.2877	−	47.2636i	0.947740	−	1.64153i	0.750170	−	0.661245i	$-0.229972\pi$
$830$	−2.63141	−	1.51925i	−0.0913376	−	0.0527338i
$831$	2.77442			0.0962436
$832$		0			0
$833$	10.4056			0.360533
$834$	8.88832	+	5.13168i	0.307777	+	0.177695i
$835$	4.83398	−	8.37270i	0.167287	−	0.289749i
$836$	9.41882	+	16.3139i	0.325757	+	0.564227i
$837$		−	44.5099i		−	1.53849i
$838$	−10.2659	+	5.92699i	−0.354628	+	0.204745i
$839$	−10.4662	+	6.04265i	−0.361333	+	0.208616i	−0.669665	−	0.742663i	$-0.733562\pi$
$839$	−10.4662	+	6.04265i	−0.361333	+	0.208616i	0.308333	+	0.951279i	$0.400229\pi$
$840$			3.43303i			0.118451i
$841$	−8.14879	−	14.1141i	−0.280993	−	0.486694i
$842$	4.74218	−	8.21370i	0.163426	−	0.283063i
$843$	−22.1687	−	12.7991i	−0.763532	−	0.440825i
$844$	−21.2755			−0.732332
$845$		0			0
$846$	−18.2685			−0.628085
$847$	76.7356	+	44.3033i	2.63667	+	1.52228i
$848$	5.59233	−	9.68619i	0.192041	−	0.332625i
$849$	−14.2719	−	24.7197i	−0.489812	−	0.848379i
$850$			2.05533i			0.0704971i
$851$	18.6138	−	10.7467i	0.638072	−	0.368391i
$852$	−0.104433	+	0.0602944i	−0.00357782	+	0.00206565i
$853$			16.2371i			0.555947i	0.960589	+	0.277973i	$0.0896627\pi$
$853$			16.2371i			0.555947i	−0.960589	+	0.277973i	$0.910337\pi$
$854$	22.6592	+	39.2469i	0.775382	+	1.34300i
$855$	−3.15332	+	5.46171i	−0.107841	+	0.186787i
$856$	−4.47685	−	2.58471i	−0.153016	−	0.0883436i
$857$	−30.2096			−1.03194			−0.515970	−	0.856607i	$-0.672568\pi$
$857$	−30.2096			−1.03194			−0.515970	+	0.856607i	$0.672568\pi$
$858$		0			0
$859$	18.9280			0.645814			0.322907	−	0.946431i	$-0.395340\pi$
$859$	18.9280			0.645814			0.322907	+	0.946431i	$0.395340\pi$
$860$	1.76240	+	1.01752i	0.0600974	+	0.0346973i
$861$	5.55367	−	9.61924i	0.189269	−	0.327823i
$862$	−7.05875	−	12.2261i	−0.240422	−	0.416423i
$863$		−	9.02786i		−	0.307312i	−0.988124	−	0.153656i	$-0.950895\pi$
$863$		−	9.02786i		−	0.307312i	0.988124	−	0.153656i	$-0.0491048\pi$
$864$	−4.29978	+	2.48248i	−0.146281	+	0.0844556i
$865$	7.79487	−	4.50037i	0.265033	−	0.153017i
$866$		−	26.3194i		−	0.894368i
$867$	6.31404	+	10.9362i	0.214436	+	0.371414i
$868$	−15.5681	+	26.9647i	−0.528415	+	0.915241i
$869$	−35.1456	−	20.2913i	−1.19223	−	0.688335i
$870$	6.65262			0.225545
$871$		0			0
$872$	8.09832			0.274244
$873$	−10.2054	−	5.89210i	−0.345401	−	0.199418i
$874$	−12.4303	+	21.5299i	−0.420461	+	0.728260i
$875$	−1.73657	−	3.00783i	−0.0587069	−	0.101683i
$876$		−	0.136428i		−	0.00460947i
$877$	−36.8628	+	21.2827i	−1.24477	+	0.718667i	−0.970061	−	0.242861i	$-0.921914\pi$
$877$	−36.8628	+	21.2827i	−1.24477	+	0.718667i	−0.274707	+	0.961528i	$0.588581\pi$
$878$	23.0336	−	13.2985i	0.777348	−	0.448802i
$879$			10.9540i			0.369468i
$880$	−3.02125	−	5.23297i	−0.101846	−	0.176403i
$881$	19.9663	−	34.5826i	0.672680	−	1.16512i	−0.304461	−	0.952525i	$-0.598476\pi$
$881$	19.9663	−	34.5826i	0.672680	−	1.16512i	0.977141	−	0.212591i	$-0.0681903\pi$
$882$	−8.86964	−	5.12089i	−0.298656	−	0.172429i
$883$	26.1186			0.878962			0.439481	−	0.898252i	$-0.355162\pi$
$883$	26.1186			0.878962			0.439481	+	0.898252i	$0.355162\pi$
$884$		0			0
$885$	−6.32793			−0.212711
$886$	−13.7842	−	7.95831i	−0.463089	−	0.267365i
$887$	−11.6005	+	20.0926i	−0.389506	+	0.674644i	−0.992383	−	0.123190i	$-0.960687\pi$
$887$	−11.6005	+	20.0926i	−0.389506	+	0.674644i	0.602877	+	0.797834i	$0.294021\pi$
$888$	1.33207	+	2.30721i	0.0447013	+	0.0774250i
$889$		−	1.00591i		−	0.0337372i
$890$	2.93073	−	1.69206i	0.0982383	−	0.0567179i
$891$	−6.07698	+	3.50854i	−0.203586	+	0.117541i
$892$		−	7.35898i		−	0.246397i
$893$	−14.0765	−	24.3812i	−0.471052	−	0.815886i
$894$	10.2462	−	17.7469i	0.342684	−	0.593546i
$895$	−9.64278	−	5.56726i	−0.322323	−	0.186093i
$896$	3.47315			0.116030
$897$		0			0
$898$	−38.7349			−1.29260
$899$	52.2528	+	30.1682i	1.74273	+	1.00617i
$900$	1.01148	−	1.75194i	0.0337161	−	0.0583980i
$901$	−11.4941	−	19.9083i	−0.382923	−	0.663241i
$902$			19.5501i			0.650948i
$903$	6.05039	−	3.49319i	0.201344	−	0.116246i
$904$	15.8108	−	9.12839i	0.525860	−	0.303606i
$905$		−	1.63511i		−	0.0543527i
$906$	10.1319	+	17.5489i	0.336609	+	0.583024i
$907$	11.0787	−	19.1889i	0.367862	−	0.637156i	−0.621369	−	0.783518i	$-0.713423\pi$
$907$	11.0787	−	19.1889i	0.367862	−	0.637156i	0.989231	+	0.146362i	$0.0467566\pi$
$908$	−18.4665	−	10.6616i	−0.612831	−	0.353818i
$909$	−17.1521			−0.568901
$910$		0			0
$911$	−10.5539			−0.349666			−0.174833	−	0.984598i	$-0.555939\pi$
$911$	−10.5539			−0.349666			−0.174833	+	0.984598i	$0.555939\pi$
$912$	−2.66867	−	1.54076i	−0.0883685	−	0.0510196i
$913$	9.18006	−	15.9003i	0.303816	−	0.526224i
$914$	−7.01701	−	12.1538i	−0.232102	−	0.402013i
$915$			12.8975i			0.426379i
$916$	13.6771	−	7.89647i	0.451904	−	0.260907i
$917$	−58.6269	+	33.8483i	−1.93603	+	1.11777i
$918$			10.2046i			0.336802i
$919$	−14.9497	−	25.8937i	−0.493146	−	0.854153i	0.506823	−	0.862050i	$-0.330820\pi$
$919$	−14.9497	−	25.8937i	−0.493146	−	0.854153i	−0.999969	+	0.00789664i	$0.997486\pi$
$920$	3.98724	−	6.90610i	0.131455	−	0.227687i
$921$	−5.46182	−	3.15338i	−0.179973	−	0.103907i
$922$	−9.00148			−0.296448
$923$		0			0
$924$	−20.7441			−0.682432
$925$	−2.33417	−	1.34763i	−0.0767470	−	0.0443099i
$926$	−17.3890	+	30.1186i	−0.571438	+	0.989759i
$927$	5.02597	+	8.70523i	0.165074	+	0.285917i
$928$		−	6.73035i		−	0.220934i
$929$	49.0656	−	28.3280i	1.60979	−	0.929413i	0.620374	−	0.784306i	$-0.286981\pi$
$929$	49.0656	−	28.3280i	1.60979	−	0.929413i	0.989416	−	0.145107i	$-0.0463527\pi$
$930$	−7.67409	+	4.43064i	−0.251643	+	0.145286i
$931$		−	15.7832i		−	0.517275i
$932$	−4.06520	−	7.04113i	−0.133160	−	0.230640i
$933$	9.36273	−	16.2167i	0.306522	−	0.530912i
$934$	15.7499	+	9.09322i	0.515353	+	0.297539i
$935$	−12.4193			−0.406155
$936$		0			0
$937$	−37.4212			−1.22250			−0.611249	−	0.791439i	$-0.709332\pi$
$937$	−37.4212			−1.22250			−0.611249	+	0.791439i	$0.709332\pi$
$938$	−25.5558	−	14.7547i	−0.834428	−	0.481757i
$939$	8.64927	−	14.9810i	0.282258	−	0.488886i
$940$	4.51529	+	7.82070i	0.147272	+	0.255083i
$941$			0.100449i			0.00327454i	0.999999	+	0.00163727i	$0.000521159\pi$
$941$			0.100449i			0.00327454i	−0.999999	+	0.00163727i	$0.999479\pi$
$942$	9.93687	−	5.73706i	0.323761	−	0.186923i
$943$	−22.3442	+	12.9004i	−0.727627	+	0.420096i
$944$			6.40187i			0.208363i
$945$	−8.62201	−	14.9338i	−0.280474	−	0.485795i
$946$	−6.14839	+	10.6493i	−0.199902	+	0.346240i
$947$	24.1724	+	13.9559i	0.785497	+	0.453507i	0.838375	−	0.545094i	$-0.183506\pi$
$947$	24.1724	+	13.9559i	0.785497	+	0.453507i	−0.0528777	+	0.998601i	$0.516839\pi$
$948$	6.63861			0.215612
$949$		0			0
$950$	3.11752			0.101146
$951$	29.3145	+	16.9247i	0.950588	+	0.548822i
$952$	3.56923	−	6.18208i	0.115679	−	0.200362i
$953$	2.14253	+	3.71097i	0.0694033	+	0.120210i	0.898639	−	0.438689i	$-0.144557\pi$
$953$	2.14253	+	3.71097i	0.0694033	+	0.120210i	−0.829235	+	0.558899i	$0.811224\pi$
$954$			22.6262i			0.732549i
$955$	8.00075	−	4.61924i	0.258898	−	0.149475i
$956$	−10.8467	+	6.26234i	−0.350807	+	0.202539i
$957$			40.1985i			1.29943i
$958$	−16.0477	−	27.7954i	−0.518477	−	0.898029i
$959$	6.43571	−	11.1470i	0.207820	−	0.359954i
$960$	0.856023	+	0.494225i	0.0276280	+	0.0159511i
$961$	−49.3680			−1.59252
$962$		0			0
$963$	10.4576			0.336990
$964$	3.10711	+	1.79389i	0.100073	+	0.0577773i
$965$	−3.64146	+	6.30719i	−0.117223	+	0.203036i
$966$	−13.6883	−	23.7089i	−0.440415	−	0.762820i
$967$		−	28.0511i		−	0.902062i	−0.892508	−	0.451031i	$-0.851056\pi$
$967$		−	28.0511i		−	0.902062i	0.892508	−	0.451031i	$-0.148944\pi$
$968$	22.0940	−	12.7560i	0.710127	−	0.409992i
$969$	−5.48499	+	3.16676i	−0.176203	+	0.101731i
$970$			5.82521i			0.187036i
$971$	14.6521	+	25.3782i	0.470209	+	0.814426i	0.999420	−	0.0340646i	$-0.0108452\pi$
$971$	14.6521	+	25.3782i	0.470209	+	0.814426i	−0.529211	+	0.848491i	$0.677512\pi$
$972$	8.02137	−	13.8934i	0.257285	−	0.445631i
$973$	31.2312	+	18.0313i	1.00123	+	0.578058i
$974$	31.3280			1.00382
$975$		0			0
$976$	13.0482			0.417663
$977$	18.3016	+	10.5664i	0.585519	+	0.338049i	0.763324	−	0.646016i	$-0.223566\pi$
$977$	18.3016	+	10.5664i	0.585519	+	0.338049i	−0.177805	+	0.984066i	$0.556900\pi$
$978$	4.33702	−	7.51194i	0.138683	−	0.240205i
$979$	10.2243	+	17.7090i	0.326769	+	0.565981i
$980$			5.06275i			0.161724i
$981$	−14.1878	+	8.19131i	−0.452981	+	0.261528i
$982$	6.29798	−	3.63614i	0.200977	−	0.116034i
$983$			30.8904i			0.985250i	0.870242	+	0.492625i	$0.163963\pi$
$983$			30.8904i			0.985250i	−0.870242	+	0.492625i	$0.836037\pi$
$984$	−1.59903	−	2.76960i	−0.0509753	−	0.0882917i
$985$	10.2872	−	17.8180i	0.327777	−	0.567727i
$986$	−11.9798	−	6.91653i	−0.381514	−	0.220267i
$987$	31.0023			0.986813
$988$		0			0
$989$	−16.2284			−0.516034
$990$	10.5861	+	6.11189i	0.336449	+	0.194249i
$991$	−9.98310	+	17.2912i	−0.317124	+	0.549274i	−0.979887	−	0.199555i	$-0.936050\pi$
$991$	−9.98310	+	17.2912i	−0.317124	+	0.549274i	0.662763	+	0.748829i	$0.269384\pi$
$992$	4.48241	+	7.76376i	0.142317	+	0.246500i
$993$			8.15260i			0.258715i
$994$	−0.366949	+	0.211858i	−0.0116389	+	0.00671974i
$995$	2.39981	−	1.38553i	0.0760792	−	0.0439244i
$996$			3.00340i			0.0951664i
$997$	−0.779576	−	1.35027i	−0.0246894	−	0.0427633i	0.853417	−	0.521229i	$-0.174526\pi$
$997$	−0.779576	−	1.35027i	−0.0246894	−	0.0427633i	−0.878106	+	0.478466i	$0.841193\pi$
$998$	4.78938	−	8.29545i	0.151605	−	0.262588i
$999$	−11.5890	−	6.69094i	−0.366661	−	0.211692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.l.n.1161.3		24
13.2	odd	12		1690.2.e.u.991.3		12
13.3	even	3	inner	1690.2.l.n.361.8		24
13.4	even	6		1690.2.d.l.1351.4		12
13.5	odd	4		1690.2.e.u.191.3		12
13.6	odd	12		1690.2.a.w.1.4	yes	6
13.7	odd	12		1690.2.a.v.1.4	✓	6
13.8	odd	4		1690.2.e.v.191.3		12
13.9	even	3		1690.2.d.l.1351.10		12
13.10	even	6	inner	1690.2.l.n.361.3		24
13.11	odd	12		1690.2.e.v.991.3		12
13.12	even	2	inner	1690.2.l.n.1161.8		24
65.19	odd	12		8450.2.a.cp.1.3		6
65.59	odd	12		8450.2.a.cq.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.v.1.4	✓	6	13.7	odd	12
1690.2.a.w.1.4	yes	6	13.6	odd	12
1690.2.d.l.1351.4		12	13.4	even	6
1690.2.d.l.1351.10		12	13.9	even	3
1690.2.e.u.191.3		12	13.5	odd	4
1690.2.e.u.991.3		12	13.2	odd	12
1690.2.e.v.191.3		12	13.8	odd	4
1690.2.e.v.991.3		12	13.11	odd	12
1690.2.l.n.361.3		24	13.10	even	6	inner
1690.2.l.n.361.8		24	13.3	even	3	inner
1690.2.l.n.1161.3		24	1.1	even	1	trivial
1690.2.l.n.1161.8		24	13.12	even	2	inner
8450.2.a.cp.1.3		6	65.19	odd	12
8450.2.a.cq.1.3		6	65.59	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.494225 + 0.856023i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(0.856023 - 0.494225i) q^{6} +(3.00783 - 1.73657i) q^{7} -1.00000i q^{8} +(1.01148 + 1.75194i) q^{9} +(0.500000 - 0.866025i) q^{10} +(5.23297 + 3.02125i) q^{11} -0.988450 q^{12} -3.47315 q^{14} +(-0.856023 - 0.494225i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.02766 + 1.77997i) q^{17} -2.02297i q^{18} +(2.69985 - 1.55876i) q^{19} +(-0.866025 + 0.500000i) q^{20} +3.43303i q^{21} +(-3.02125 - 5.23297i) q^{22} +(3.98724 - 6.90610i) q^{23} +(0.856023 + 0.494225i) q^{24} -1.00000 q^{25} -4.96495 q^{27} +(3.00783 + 1.73657i) q^{28} +(3.36517 - 5.82865i) q^{29} +(0.494225 + 0.856023i) q^{30} +8.96482i q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.17253 + 2.98636i) q^{33} -2.05533i q^{34} +(1.73657 + 3.00783i) q^{35} +(-1.01148 + 1.75194i) q^{36} +(2.33417 + 1.34763i) q^{37} -3.11752 q^{38} +1.00000 q^{40} +(-2.80196 - 1.61772i) q^{41} +(1.71652 - 2.97309i) q^{42} +(-1.01752 - 1.76240i) q^{43} +6.04251i q^{44} +(-1.75194 + 1.01148i) q^{45} +(-6.90610 + 3.98724i) q^{46} -9.03057i q^{47} +(-0.494225 - 0.856023i) q^{48} +(2.53138 - 4.38447i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.03159 q^{51} -11.1847 q^{53} +(4.29978 + 2.48248i) q^{54} +(-3.02125 + 5.23297i) q^{55} +(-1.73657 - 3.00783i) q^{56} +3.08152i q^{57} +(-5.82865 + 3.36517i) q^{58} +(5.54418 - 3.20093i) q^{59} -0.988450i q^{60} +(-6.52411 - 11.3001i) q^{61} +(4.48241 - 7.76376i) q^{62} +(6.08475 + 3.51303i) q^{63} -1.00000 q^{64} +5.97272 q^{66} +(7.35812 + 4.24821i) q^{67} +(-1.02766 + 1.77997i) q^{68} +(3.94119 + 6.82634i) q^{69} -3.47315i q^{70} +(0.105653 - 0.0609989i) q^{71} +(1.75194 - 1.01148i) q^{72} +0.138022i q^{73} +(-1.34763 - 2.33417i) q^{74} +(0.494225 - 0.856023i) q^{75} +(2.69985 + 1.55876i) q^{76} +20.9865 q^{77} -6.71618 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-0.580644 + 1.00570i) q^{81} +(1.61772 + 2.80196i) q^{82} -3.03849i q^{83} +(-2.97309 + 1.71652i) q^{84} +(-1.77997 + 1.02766i) q^{85} +2.03505i q^{86} +(3.32631 + 5.76133i) q^{87} +(3.02125 - 5.23297i) q^{88} +(2.93073 + 1.69206i) q^{89} +2.02297 q^{90} +7.97448 q^{92} +(-7.67409 - 4.43064i) q^{93} +(-4.51529 + 7.82070i) q^{94} +(1.55876 + 2.69985i) q^{95} +0.988450i q^{96} +(-5.04478 + 2.91261i) q^{97} +(-4.38447 + 2.53138i) q^{98} +12.2238i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} + 12 q^{4} - 32 q^{9} + 12 q^{10} + 8 q^{12} + 12 q^{14} - 12 q^{16} - 6 q^{17} - 30 q^{22} - 6 q^{23} - 24 q^{25} - 80 q^{27} - 14 q^{29} - 4 q^{30} - 6 q^{35} + 32 q^{36} - 4 q^{38} + 24 q^{40}+ \cdots + 2 q^{95}+O(q^{100}) \) 24 * q + 4 * q^3 + 12 * q^4 - 32 * q^9 + 12 * q^10 + 8 * q^12 + 12 * q^14 - 12 * q^16 - 6 * q^17 - 30 * q^22 - 6 * q^23 - 24 * q^25 - 80 * q^27 - 14 * q^29 - 4 * q^30 - 6 * q^35 + 32 * q^36 - 4 * q^38 + 24 * q^40 + 4 * q^42 - 44 * q^43 + 4 * q^48 + 62 * q^49 + 88 * q^51 - 64 * q^53 - 30 * q^55 + 6 * q^56 - 66 * q^61 - 24 * q^64 + 16 * q^66 + 6 * q^68 - 12 * q^69 - 12 * q^74 - 4 * q^75 + 136 * q^77 + 80 * q^79 + 4 * q^81 + 4 * q^82 + 78 * q^87 + 30 * q^88 - 64 * q^90 - 12 * q^92 - 14 * q^94 + 2 * q^95

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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