LMFDB - Embedded newform 507.2.m.b.40.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(40,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [204] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.13
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37667 + 0.339319i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.00917504 + 0.00481543i) q^{4} +(-2.23921 + 3.24406i) q^{5} +(0.502784 - 1.32573i) q^{6} +(-3.33005 - 2.95017i) q^{7} +(-2.11159 - 1.87070i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-4.18343 + 3.70620i) q^{10} +(-0.132322 + 0.0326146i) q^{11} +(0.00588625 - 0.00852771i) q^{12} +(1.42902 + 3.31027i) q^{13} +(-3.58334 - 5.19136i) q^{14} +(2.95050 + 2.61392i) q^{15} +(-2.28397 - 3.30890i) q^{16} +(-1.97221 - 1.74723i) q^{17} +(-1.25546 - 0.658918i) q^{18} -8.48104 q^{19} +(-0.0361665 + 0.0189816i) q^{20} +(-3.33005 + 2.95017i) q^{21} -0.193231 q^{22} +5.75579 q^{23} +(-2.11159 + 1.87070i) q^{24} +(-3.73683 - 9.85321i) q^{25} +(0.844058 + 5.04205i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-0.0163470 - 0.0431035i) q^{28} +(0.664771 + 0.163851i) q^{29} +(3.17492 + 4.59966i) q^{30} +(-1.49063 + 3.93047i) q^{31} +(-0.0207853 - 0.0548064i) q^{32} +(0.0164271 + 0.135289i) q^{33} +(-2.12222 - 3.07456i) q^{34} +(17.0272 - 4.19683i) q^{35} +(-0.00775603 - 0.00687124i) q^{36} +(1.94356 - 5.12475i) q^{37} +(-11.6756 - 2.87778i) q^{38} +(3.45838 - 1.01960i) q^{39} +(10.7970 - 2.66122i) q^{40} +(-0.409865 + 3.37555i) q^{41} +(-5.58543 + 2.93146i) q^{42} +(0.413881 + 1.09132i) q^{43} +(-0.00137112 - 0.000337950i) q^{44} +(2.95050 - 2.61392i) q^{45} +(7.92383 + 1.95305i) q^{46} +(2.16792 - 1.13781i) q^{47} +(-3.56008 + 1.86847i) q^{48} +(1.54199 + 12.6994i) q^{49} +(-1.80101 - 14.8326i) q^{50} +(-1.97221 + 1.74723i) q^{51} +(-0.00282904 + 0.0372533i) q^{52} +(-7.24941 - 6.42242i) q^{53} +(-0.805443 + 1.16689i) q^{54} +(0.190495 - 0.502293i) q^{55} +(1.51281 + 12.4591i) q^{56} +(-1.02228 + 8.41920i) q^{57} +(0.859574 + 0.451139i) q^{58} +(5.52071 - 7.99812i) q^{59} +(0.0144838 + 0.0381907i) q^{60} +(-4.06143 + 3.59811i) q^{61} +(-3.38580 + 4.90517i) q^{62} +(2.52726 + 3.66137i) q^{63} +(0.959246 + 7.90010i) q^{64} +(-13.9386 - 2.77656i) q^{65} +(-0.0232915 + 0.191822i) q^{66} +(5.79985 - 3.04400i) q^{67} +(-0.00968147 - 0.0255279i) q^{68} +(0.693783 - 5.71382i) q^{69} +24.8649 q^{70} +(-0.583075 + 4.80206i) q^{71} +(1.60254 + 2.32168i) q^{72} +(-13.1138 + 3.23225i) q^{73} +(4.41457 - 6.39561i) q^{74} +(-10.2318 + 2.52191i) q^{75} +(-0.0778139 - 0.0408399i) q^{76} +(0.536859 + 0.281765i) q^{77} +(5.10703 - 0.230152i) q^{78} +(2.49010 - 1.30690i) q^{79} +15.8486 q^{80} +(0.885456 + 0.464723i) q^{81} +(-1.70964 + 4.50794i) q^{82} +(1.19032 + 9.80319i) q^{83} +(-0.0447597 + 0.0110323i) q^{84} +(10.0843 - 2.48556i) q^{85} +(0.199475 + 1.64282i) q^{86} +(0.242786 - 0.640174i) q^{87} +(0.340423 + 0.178668i) q^{88} -14.9888 q^{89} +(4.94882 - 2.59734i) q^{90} +(5.00713 - 15.2392i) q^{91} +(0.0528096 + 0.0277166i) q^{92} +(3.72214 + 1.95353i) q^{93} +(3.37059 - 0.830776i) q^{94} +(18.9909 - 27.5130i) q^{95} +(-0.0569122 + 0.0140276i) q^{96} +(-7.63754 - 11.0649i) q^{97} +(-2.18634 + 18.0062i) q^{98} +0.136283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

Coefficient data

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

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

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

$2$	1.37667	+	0.339319i	0.973454	+	0.239935i	0.693801	−	0.720166i	$-0.255935\pi$
$2$	1.37667	+	0.339319i	0.973454	+	0.239935i	0.279652	+	0.960101i	$0.409781\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	0.00917504	+	0.00481543i	0.00458752	+	0.00240772i
$5$	−2.23921	+	3.24406i	−1.00141	+	1.45079i	−0.111980	+	0.993710i	$0.535719\pi$
$5$	−2.23921	+	3.24406i	−1.00141	+	1.45079i	−0.889427	+	0.457078i	$0.848896\pi$
$6$	0.502784	−	1.32573i	0.205261	−	0.541228i
$7$	−3.33005	−	2.95017i	−1.25864	−	1.11506i	−0.988337	−	0.152283i	$-0.951338\pi$
$7$	−3.33005	−	2.95017i	−1.25864	−	1.11506i	−0.270303	−	0.962775i	$-0.587124\pi$
$8$	−2.11159	−	1.87070i	−0.746559	−	0.661394i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−4.18343	+	3.70620i	−1.32292	+	1.17200i
$11$	−0.132322	+	0.0326146i	−0.0398967	+	0.00983366i	−0.259214	−	0.965820i	$-0.583463\pi$
$11$	−0.132322	+	0.0326146i	−0.0398967	+	0.00983366i	0.219317	+	0.975654i	$0.429617\pi$
$12$	0.00588625	−	0.00852771i	0.00169922	−	0.00246174i
$13$	1.42902	+	3.31027i	0.396340	+	0.918104i
$13$	1.42902	+	3.31027i	0.396340	+	0.918104i
$14$	−3.58334	−	5.19136i	−0.957687	−	1.38745i
$15$	2.95050	+	2.61392i	0.761816	+	0.674910i
$16$	−2.28397	−	3.30890i	−0.570993	−	0.827226i
$17$	−1.97221	−	1.74723i	−0.478331	−	0.423765i	0.389195	−	0.921155i	$-0.372753\pi$
$17$	−1.97221	−	1.74723i	−0.478331	−	0.423765i	−0.867527	+	0.497391i	$0.834292\pi$
$18$	−1.25546	−	0.658918i	−0.295916	−	0.155308i
$19$	−8.48104			−1.94568			−0.972842	−	0.231472i	$-0.925646\pi$
$19$	−8.48104			−1.94568			−0.972842	+	0.231472i	$0.925646\pi$
$20$	−0.0361665	+	0.0189816i	−0.00808707	+	0.00424442i
$21$	−3.33005	+	2.95017i	−0.726676	+	0.643779i
$22$	−0.193231			−0.0411971
$23$	5.75579			1.20016			0.600082	−	0.799938i	$-0.295135\pi$
$23$	5.75579			1.20016			0.600082	+	0.799938i	$0.295135\pi$
$24$	−2.11159	+	1.87070i	−0.431026	+	0.381856i
$25$	−3.73683	−	9.85321i	−0.747366	−	1.97064i
$26$	0.844058	+	5.04205i	0.165533	+	0.988827i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	−0.0163470	−	0.0431035i	−0.00308930	−	0.00814580i
$29$	0.664771	+	0.163851i	0.123445	+	0.0304264i	0.300554	−	0.953765i	$-0.402828\pi$
$29$	0.664771	+	0.163851i	0.123445	+	0.0304264i	−0.177109	+	0.984191i	$0.556675\pi$
$30$	3.17492	+	4.59966i	0.579658	+	0.839780i
$31$	−1.49063	+	3.93047i	−0.267725	+	0.705934i	0.731972	+	0.681335i	$0.238600\pi$
$31$	−1.49063	+	3.93047i	−0.267725	+	0.705934i	−0.999697	+	0.0245992i	$0.992169\pi$
$32$	−0.0207853	−	0.0548064i	−0.00367436	−	0.00968849i
$33$	0.0164271	+	0.135289i	0.00285958	+	0.0235508i
$34$	−2.12222	−	3.07456i	−0.363958	−	0.527284i
$35$	17.0272	−	4.19683i	2.87812	−	0.709394i
$36$	−0.00775603	−	0.00687124i	−0.00129267	−	0.00114521i
$37$	1.94356	−	5.12475i	0.319520	−	0.842504i	−0.674987	−	0.737830i	$-0.735851\pi$
$37$	1.94356	−	5.12475i	0.319520	−	0.842504i	0.994507	−	0.104674i	$-0.0333800\pi$
$38$	−11.6756	−	2.87778i	−1.89403	−	0.466837i
$39$	3.45838	−	1.01960i	0.553785	−	0.163266i
$40$	10.7970	−	2.66122i	1.70715	−	0.420775i
$41$	−0.409865	+	3.37555i	−0.0640102	+	0.527172i	0.925070	+	0.379796i	$0.124006\pi$
$41$	−0.409865	+	3.37555i	−0.0640102	+	0.527172i	−0.989081	+	0.147376i	$0.952917\pi$
$42$	−5.58543	+	2.93146i	−0.861851	+	0.452334i
$43$	0.413881	+	1.09132i	0.0631163	+	0.166424i	0.962864	−	0.269986i	$-0.0870190\pi$
$43$	0.413881	+	1.09132i	0.0631163	+	0.166424i	−0.899748	+	0.436410i	$0.856250\pi$
$44$	−0.00137112		0.000337950i	−0.000206704		5.09479e-5i
$45$	2.95050	−	2.61392i	0.439835	−	0.389660i
$46$	7.92383	+	1.95305i	1.16830	+	0.287961i
$47$	2.16792	−	1.13781i	0.316223	−	0.165967i	−0.299143	−	0.954208i	$-0.596701\pi$
$47$	2.16792	−	1.13781i	0.316223	−	0.165967i	0.615366	+	0.788242i	$0.289008\pi$
$48$	−3.56008	+	1.86847i	−0.513853	+	0.269691i
$49$	1.54199	+	12.6994i	0.220284	+	1.81420i
$50$	−1.80101	−	14.8326i	−0.254701	−	2.09765i
$51$	−1.97221	+	1.74723i	−0.276165	+	0.244661i
$52$	−0.00282904	+	0.0372533i	−0.000392317	+	0.00516610i
$53$	−7.24941	−	6.42242i	−0.995783	−	0.882187i	−0.00274722	−	0.999996i	$-0.500874\pi$
$53$	−7.24941	−	6.42242i	−0.995783	−	0.882187i	−0.993036	+	0.117809i	$0.962413\pi$
$54$	−0.805443	+	1.16689i	−0.109607	+	0.158793i
$55$	0.190495	−	0.502293i	0.0256863	−	0.0677292i
$56$	1.51281	+	12.4591i	0.202157	+	1.66491i
$57$	−1.02228	+	8.41920i	−0.135404	+	1.11515i
$58$	0.859574	+	0.451139i	0.112868	+	0.0592375i
$59$	5.52071	−	7.99812i	0.718735	−	1.04127i	−0.278005	−	0.960580i	$-0.589673\pi$
$59$	5.52071	−	7.99812i	0.718735	−	1.04127i	0.996739	−	0.0806873i	$-0.0257115\pi$
$60$	0.0144838	+	0.0381907i	0.00186986	+	0.00493040i
$61$	−4.06143	+	3.59811i	−0.520013	+	0.460691i	−0.881836	−	0.471556i	$-0.843693\pi$
$61$	−4.06143	+	3.59811i	−0.520013	+	0.460691i	0.361824	+	0.932246i	$0.382154\pi$
$62$	−3.38580	+	4.90517i	−0.429997	+	0.622957i
$63$	2.52726	+	3.66137i	0.318405	+	0.461290i
$64$	0.959246	+	7.90010i	0.119906	+	0.987513i
$65$	−13.9386	−	2.77656i	−1.72887	−	0.344390i
$66$	−0.0232915	+	0.191822i	−0.00286698	+	0.0236117i
$67$	5.79985	−	3.04400i	0.708564	−	0.371883i	−0.0716207	−	0.997432i	$-0.522817\pi$
$67$	5.79985	−	3.04400i	0.708564	−	0.371883i	0.780185	+	0.625549i	$0.215125\pi$
$68$	−0.00968147	−	0.0255279i	−0.00117405	−	0.00309572i
$69$	0.693783	−	5.71382i	0.0835217	−	0.687863i
$70$	24.8649			2.97193
$71$	−0.583075	+	4.80206i	−0.0691983	+	0.569899i	0.916334	+	0.400414i	$0.131134\pi$
$71$	−0.583075	+	4.80206i	−0.0691983	+	0.569899i	−0.985533	+	0.169485i	$0.945789\pi$
$72$	1.60254	+	2.32168i	0.188861	+	0.273613i
$73$	−13.1138	+	3.23225i	−1.53485	+	0.378306i	−0.914030	−	0.405647i	$-0.867046\pi$
$73$	−13.1138	+	3.23225i	−1.53485	+	0.378306i	−0.620820	+	0.783953i	$0.713200\pi$
$74$	4.41457	−	6.39561i	0.513184	−	0.743475i
$75$	−10.2318	+	2.52191i	−1.18147	+	0.291205i
$76$	−0.0778139	−	0.0408399i	−0.00892586	−	0.00468466i
$77$	0.536859	+	0.281765i	0.0611807	+	0.0321101i
$78$	5.10703	−	0.230152i	0.578257	−	0.0260596i
$79$	2.49010	−	1.30690i	0.280158	−	0.147038i	−0.318792	−	0.947825i	$-0.603277\pi$
$79$	2.49010	−	1.30690i	0.280158	−	0.147038i	0.598950	+	0.800787i	$0.295585\pi$
$80$	15.8486			1.77193
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−1.70964	+	4.50794i	−0.188798	+	0.497819i
$83$	1.19032	+	9.80319i	0.130655	+	1.07604i	0.899597	+	0.436721i	$0.143860\pi$
$83$	1.19032	+	9.80319i	0.130655	+	1.07604i	−0.768942	+	0.639318i	$0.779217\pi$
$84$	−0.0447597	+	0.0110323i	−0.00488368	+	0.00120372i
$85$	10.0843	−	2.48556i	1.09380	−	0.269597i
$86$	0.199475	+	1.64282i	0.0215099	+	0.177150i
$87$	0.242786	−	0.640174i	0.0260294	−	0.0686339i
$88$	0.340423	+	0.178668i	0.0362892	+	0.0190460i
$89$	−14.9888			−1.58881			−0.794404	−	0.607390i	$-0.792217\pi$
$89$	−14.9888			−1.58881			−0.794404	+	0.607390i	$0.792217\pi$
$90$	4.94882	−	2.59734i	0.521652	−	0.273784i
$91$	5.00713	−	15.2392i	0.524890	−	1.59750i
$92$	0.0528096	+	0.0277166i	0.00550578	+	0.00288966i
$93$	3.72214	+	1.95353i	0.385968	+	0.202572i
$94$	3.37059	−	0.830776i	0.347650	−	0.0856880i
$95$	18.9909	−	27.5130i	1.94842	−	2.82277i
$96$	−0.0569122	+	0.0140276i	−0.00580857	+	0.00143168i
$97$	−7.63754	−	11.0649i	−0.775474	−	1.12347i	−0.989200	−	0.146575i	$-0.953175\pi$
$97$	−7.63754	−	11.0649i	−0.775474	−	1.12347i	0.213725	−	0.976894i	$-0.431440\pi$
$98$	−2.18634	+	18.0062i	−0.220854	+	1.81890i
$99$	0.136283			0.0136969
$100$	0.0131619	−	0.108398i	0.00131619	−	0.0108398i
$101$	−3.23677	−	8.53466i	−0.322071	−	0.849230i	−0.994076	−	0.108684i	$-0.965336\pi$
$101$	−3.23677	−	8.53466i	−0.322071	−	0.849230i	0.672006	−	0.740546i	$-0.265433\pi$
$102$	−3.30795	+	1.73615i	−0.327536	+	0.171904i
$103$	0.125032	−	1.02973i	0.0123197	−	0.101462i	−0.985252	−	0.171110i	$-0.945265\pi$
$103$	0.125032	−	1.02973i	0.0123197	−	0.101462i	0.997572	+	0.0696481i	$0.0221877\pi$
$104$	3.17503	−	9.66321i	0.311337	−	0.947556i
$105$	−2.11383	−	17.4089i	−0.206288	−	1.69894i
$106$	−7.80081	−	11.3014i	−0.757682	−	1.09769i
$107$	9.37760	−	13.5858i	0.906567	−	1.31339i	−0.0427554	−	0.999086i	$-0.513614\pi$
$107$	9.37760	−	13.5858i	0.906567	−	1.31339i	0.949322	−	0.314304i	$-0.101771\pi$
$108$	−0.00775603	+	0.00687124i	−0.000746324	+	0.000661185i
$109$	−2.96159	−	7.80908i	−0.283669	−	0.747975i	−0.998800	−	0.0489834i	$-0.984402\pi$
$109$	−2.96159	−	7.80908i	−0.283669	−	0.747975i	0.715130	−	0.698991i	$-0.246367\pi$
$110$	0.432686	−	0.626854i	0.0412550	−	0.0597682i
$111$	−4.85312	−	2.54711i	−0.460637	−	0.241761i
$112$	−2.15608	+	17.7569i	−0.203730	+	1.67787i
$113$	0.641139	+	5.28026i	0.0603133	+	0.496725i	0.991295	+	0.131659i	$0.0420304\pi$
$113$	0.641139	+	5.28026i	0.0603133	+	0.496725i	−0.930982	+	0.365066i	$0.881047\pi$
$114$	−4.26413	+	11.2436i	−0.399373	+	1.05306i
$115$	−12.8884	+	18.6721i	−1.20185	+	1.74118i
$116$	0.00531029	+	0.00470451i	0.000493048	+	0.000436802i
$117$	−0.595299	−	3.55607i	−0.0550354	−	0.328759i
$118$	10.3141	−	9.13751i	0.949491	−	0.841176i
$119$	1.41295	+	11.6367i	0.129525	+	1.06673i
$120$	−1.34038	−	11.0390i	−0.122359	−	1.00772i
$121$	−9.72357	+	5.10332i	−0.883961	+	0.463939i
$122$	−6.81216	+	3.57530i	−0.616744	+	0.323692i
$123$	3.30153	+	0.813754i	0.297689	+	0.0733737i
$124$	−0.0326036	+	0.0288842i	−0.00292789	+	0.00259388i
$125$	21.1956	+	5.22424i	1.89579	+	0.467270i
$126$	2.23684	+	5.89806i	0.199273	+	0.525441i
$127$	−7.20046	+	3.77909i	−0.638937	+	0.335340i	−0.752890	−	0.658146i	$-0.771341\pi$
$127$	−7.20046	+	3.77909i	−0.638937	+	0.335340i	0.113953	+	0.993486i	$0.463649\pi$
$128$	−1.37422	+	11.3177i	−0.121465	+	1.00035i
$129$	1.13325	−	0.279320i	0.0997768	−	0.0245928i
$130$	−18.2467	−	8.55205i	−1.60035	−	0.750065i
$131$	−4.57158	−	1.12679i	−0.399421	−	0.0984484i	0.0344880	−	0.999405i	$-0.489020\pi$
$131$	−4.57158	−	1.12679i	−0.399421	−	0.0984484i	−0.433909	+	0.900957i	$0.642866\pi$
$132$	−0.000500756		0.00132039i	−4.35852e−5		0.000114925i
$133$	28.2423	+	25.0205i	2.44891	+	2.16955i
$134$	9.01737	−	2.22258i	0.778983	−	0.192002i
$135$	−2.23921	−	3.24406i	−0.192721	−	0.279204i
$136$	0.895954	+	7.37884i	0.0768274	+	0.632731i
$137$	1.62577	+	4.28681i	0.138899	+	0.366247i	0.986358	−	0.164614i	$-0.0526379\pi$
$137$	1.62577	+	4.28681i	0.138899	+	0.366247i	−0.847459	+	0.530861i	$0.821869\pi$
$138$	2.89392	−	7.63064i	0.246347	−	0.649563i
$139$	−1.09739	−	1.58985i	−0.0930798	−	0.134849i	0.773677	−	0.633580i	$-0.218415\pi$
$139$	−1.09739	−	1.58985i	−0.0930798	−	0.134849i	−0.866757	+	0.498730i	$0.833800\pi$
$140$	0.176435	+	0.0434873i	0.0149115	+	0.00367535i
$141$	−0.868201	−	2.28926i	−0.0731158	−	0.192790i
$142$	−2.43213	+	6.41301i	−0.204100	+	0.538168i
$143$	−0.297055	−	0.391416i	−0.0248410	−	0.0327319i
$144$	1.42573	+	3.75934i	0.118811	+	0.313278i
$145$	−2.02011	+	1.78966i	−0.167761	+	0.148623i
$146$	−19.1501			−1.58487
$147$	12.7927			1.05512
$148$	0.0425102	−	0.0376607i	0.00349432	−	0.00309569i
$149$	1.16522	−	0.611553i	0.0954583	−	0.0501004i	−0.416318	−	0.909219i	$-0.636680\pi$
$149$	1.16522	−	0.611553i	0.0954583	−	0.0501004i	0.511777	+	0.859119i	$0.328988\pi$
$150$	−14.9416			−1.21997
$151$	4.46697	+	2.34445i	0.363517	+	0.190788i	0.636585	−	0.771206i	$-0.280346\pi$
$151$	4.46697	+	2.34445i	0.363517	+	0.190788i	−0.273069	+	0.961995i	$0.588039\pi$
$152$	17.9085	+	15.8655i	1.45257	+	1.28686i
$153$	1.49676	+	2.16844i	0.121006	+	0.175308i
$154$	0.643470	+	0.570064i	0.0518523	+	0.0459371i
$155$	−9.41286	−	13.6369i	−0.756059	−	1.09534i
$156$	0.0366406	+	0.00729879i	0.00293360	+	0.000584371i
$157$	−5.48789	+	7.95059i	−0.437982	+	0.634526i	−0.978363	−	0.206894i	$-0.933664\pi$
$157$	−5.48789	+	7.95059i	−0.437982	+	0.634526i	0.540382	+	0.841420i	$0.318280\pi$
$158$	3.87150	−	0.954240i	0.308000	−	0.0759152i
$159$	−7.24941	+	6.42242i	−0.574916	+	0.509331i
$160$	0.224338	+	0.0552943i	0.0177355	+	0.00437140i
$161$	−19.1670	−	16.9805i	−1.51058	−	1.33825i
$162$	1.06129	+	0.940223i	0.0833830	+	0.0738709i
$163$	−5.47506	+	14.4366i	−0.428840	+	1.13076i	0.530296	+	0.847813i	$0.322081\pi$
$163$	−5.47506	+	14.4366i	−0.428840	+	1.13076i	−0.959136	+	0.282946i	$0.908688\pi$
$164$	−0.0200153	+	0.0289971i	−0.00156293	+	0.00226429i
$165$	−0.475669	−	0.249650i	−0.0370308	−	0.0194353i
$166$	−1.68773	+	13.8997i	−0.130993	+	1.07882i
$167$	−6.30270	−	1.55348i	−0.487718	−	0.120212i	−0.0122142	−	0.999925i	$-0.503888\pi$
$167$	−6.30270	−	1.55348i	−0.487718	−	0.120212i	−0.475504	+	0.879714i	$0.657734\pi$
$168$	12.5506			0.968298
$169$	−8.91578	+	9.46091i	−0.685829	+	0.727762i
$170$	14.7262			1.12945
$171$	8.23459	+	2.02964i	0.629715	+	0.155211i
$172$	−0.00145778	+	0.0120059i	−0.000111155	+	0.000915440i
$173$	8.99916	+	4.72313i	0.684194	+	0.359093i	0.770735	−	0.637156i	$-0.219889\pi$
$173$	8.99916	+	4.72313i	0.684194	+	0.359093i	−0.0865414	+	0.996248i	$0.527581\pi$
$174$	0.551460	−	0.798928i	0.0418061	−	0.0605665i
$175$	−16.6248	+	43.8360i	−1.25672	+	3.31369i
$176$	0.410139	+	0.363351i	0.0309154	+	0.0273886i
$177$	−7.27436	−	6.44452i	−0.546774	−	0.484400i
$178$	−20.6346	−	5.08598i	−1.54663	−	0.381210i
$179$	14.6263	−	12.9577i	1.09322	−	0.968507i	0.0935857	−	0.995611i	$-0.470167\pi$
$179$	14.6263	−	12.9577i	1.09322	−	0.968507i	0.999633	+	0.0271043i	$0.00862863\pi$
$180$	0.0396581	−	0.00977485i	0.00295594	−	0.000728574i
$181$	11.5373	−	16.7146i	0.857558	−	1.24239i	−0.111055	−	0.993814i	$-0.535423\pi$
$181$	11.5373	−	16.7146i	0.857558	−	1.24239i	0.968613	−	0.248573i	$-0.0799616\pi$
$182$	12.0641	−	19.2804i	0.894253	−	1.42916i
$183$	3.08233	+	4.46552i	0.227852	+	0.330101i
$184$	−12.1539	−	10.7674i	−0.895994	−	0.793781i
$185$	12.2730	+	17.7805i	0.902326	+	1.30724i
$186$	4.46130	+	3.95236i	0.327118	+	0.289801i
$187$	0.317953	+	0.166874i	0.0232510	+	0.0122031i
$188$	0.0253698			0.00185028
$189$	3.93930	−	2.06751i	0.286542	−	0.150389i
$190$	35.4799	−	31.4324i	2.57398	−	2.28035i
$191$	−22.6784			−1.64095			−0.820476	−	0.571682i	$-0.806291\pi$
$191$	−22.6784			−1.64095			−0.820476	+	0.571682i	$0.806291\pi$
$192$	7.95812			0.574328
$193$	−17.6292	+	15.6181i	−1.26898	+	1.12422i	−0.282688	+	0.959212i	$0.591226\pi$
$193$	−17.6292	+	15.6181i	−1.26898	+	1.12422i	−0.986292	+	0.165007i	$0.947235\pi$
$194$	−6.75985	−	17.8243i	−0.485329	−	1.27971i
$195$	−4.43643	+	13.5023i	−0.317700	+	0.966920i
$196$	−0.0470055	+	0.123943i	−0.00335753	+	0.00885308i
$197$	−3.55392	−	9.37091i	−0.253206	−	0.667650i	−0.999997	−	0.00259042i	$-0.999175\pi$
$197$	−3.55392	−	9.37091i	−0.253206	−	0.667650i	0.746790	−	0.665059i	$-0.231594\pi$
$198$	0.187616	+	0.0462433i	0.0133333	+	0.00328637i
$199$	−0.445685	−	0.645687i	−0.0315938	−	0.0457715i	0.806869	−	0.590731i	$-0.201160\pi$
$199$	−0.445685	−	0.645687i	−0.0315938	−	0.0457715i	−0.838462	+	0.544959i	$0.816545\pi$
$200$	−10.5418	+	27.7964i	−0.745418	+	1.96550i
$201$	−2.32271	−	6.12448i	−0.163831	−	0.431987i
$202$	−1.56000	−	12.8477i	−0.109761	−	0.903962i
$203$	−1.73033	−	2.50682i	−0.121445	−	0.175944i
$204$	−0.0265088	+	0.00653383i	−0.00185599	+	0.000457459i
$205$	−10.0327	−	8.88820i	−0.700714	−	0.620779i
$206$	0.521534	−	1.37517i	0.0363370	−	0.0958127i
$207$	−5.58853	−	1.37745i	−0.388430	−	0.0957394i
$208$	7.68952	−	12.2891i	0.533172	−	0.852093i
$209$	1.12223	−	0.276605i	0.0776264	−	0.0191332i
$210$	2.99714	−	24.6836i	0.206822	−	1.70333i
$211$	9.33069	−	4.89712i	0.642351	−	0.337132i	−0.111898	−	0.993720i	$-0.535693\pi$
$211$	9.33069	−	4.89712i	0.642351	−	0.337132i	0.754250	+	0.656588i	$0.228001\pi$
$212$	−0.0355869	−	0.0938351i	−0.00244412	−	0.00644462i
$213$	4.69676	+	1.15765i	0.321817	+	0.0793207i
$214$	17.5198	−	15.5212i	1.19763	−	1.06101i
$215$	−4.46706	−	1.10103i	−0.304651	−	0.0750898i
$216$	2.49792	−	1.31101i	0.169962	−	0.0892028i
$217$	16.5594	−	8.69106i	1.12413	−	0.589988i
$218$	−1.42737	−	11.7555i	−0.0966739	−	0.796181i
$219$	1.62800	+	13.4078i	0.110010	+	0.906012i
$220$	0.00416656	−	0.00369125i	0.000280909	−	0.000248864i
$221$	2.96546	−	9.02538i	0.199478	−	0.607113i
$222$	−5.81686	−	5.15329i	−0.390402	−	0.345866i
$223$	8.68371	−	12.5805i	0.581504	−	0.842454i	−0.416263	−	0.909244i	$-0.636660\pi$
$223$	8.68371	−	12.5805i	0.581504	−	0.842454i	0.997767	+	0.0667900i	$0.0212758\pi$
$224$	−0.0924718	+	0.243828i	−0.00617853	+	0.0162914i
$225$	1.27022	+	10.4612i	0.0846811	+	0.697412i
$226$	−0.909053	+	7.48673i	−0.0604693	+	0.498010i
$227$	−8.15281	−	4.27893i	−0.541121	−	0.284002i	0.171936	−	0.985108i	$-0.444998\pi$
$227$	−8.15281	−	4.27893i	−0.541121	−	0.284002i	−0.713057	+	0.701106i	$0.752690\pi$
$228$	−0.0499215	+	0.0723238i	−0.00330613	+	0.00478976i
$229$	0.907120	+	2.39188i	0.0599442	+	0.158060i	0.961642	−	0.274306i	$-0.0884481\pi$
$229$	0.907120	+	2.39188i	0.0599442	+	0.158060i	−0.901698	+	0.432366i	$0.857679\pi$
$230$	−24.0790	+	21.3321i	−1.58772	+	1.40660i
$231$	0.344422	−	0.498981i	0.0226613	−	0.0328306i
$232$	−1.09721	−	1.58958i	−0.0720351	−	0.104361i
$233$	0.616657	+	5.07863i	0.0403986	+	0.332712i	0.998870	+	0.0475239i	$0.0151330\pi$
$233$	0.616657	+	5.07863i	0.0403986	+	0.332712i	−0.958472	+	0.285188i	$0.907944\pi$
$234$	0.387110	−	5.09753i	0.0253062	−	0.333236i
$235$	−1.16330	+	9.58066i	−0.0758855	+	0.624973i
$236$	0.0891672	−	0.0467985i	0.00580429	−	0.00304633i
$237$	−0.997227	−	2.62947i	−0.0647768	−	0.170802i
$238$	−2.00338	+	16.4993i	−0.129860	+	1.06949i
$239$	−7.93946			−0.513561			−0.256780	−	0.966470i	$-0.582662\pi$
$239$	−7.93946			−0.513561			−0.256780	+	0.966470i	$0.582662\pi$
$240$	1.91034	−	15.7330i	0.123312	−	1.01556i
$241$	−9.96735	−	14.4402i	−0.642054	−	0.930175i	0.357940	−	0.933745i	$-0.383479\pi$
$241$	−9.96735	−	14.4402i	−0.642054	−	0.930175i	−0.999994	+	0.00356931i	$0.998864\pi$
$242$	−15.1178	+	3.72621i	−0.971810	+	0.239530i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−0.0545902	+	0.0134553i	−0.00349478	+	0.000861387i
$245$	−44.6506	−	23.4344i	−2.85262	−	1.49717i
$246$	4.26900	+	2.24054i	0.272182	+	0.142852i
$247$	−12.1196	−	28.0745i	−0.771152	−	1.78634i
$248$	10.5004	−	5.51101i	0.666773	−	0.349950i
$249$	9.87519			0.625815
$250$	27.4066	+	14.3841i	1.73335	+	0.909731i
$251$	−6.73618	+	17.7618i	−0.425184	+	1.12112i	0.535759	+	0.844371i	$0.320026\pi$
$251$	−6.73618	+	17.7618i	−0.425184	+	1.12112i	−0.960943	+	0.276747i	$0.910744\pi$
$252$	0.00555665	+	0.0457631i	0.000350036	+	0.00288281i
$253$	−0.761620	+	0.187722i	−0.0478826	+	0.0118020i
$254$	−11.1950	+	2.75931i	−0.702436	+	0.173135i
$255$	−1.25191	−	10.3104i	−0.0783975	−	0.645661i
$256$	−0.0881831	+	0.232520i	−0.00551145	+	0.0145325i
$257$	3.99360	+	2.09600i	0.249114	+	0.130745i	0.584659	−	0.811279i	$-0.301228\pi$
$257$	3.99360	+	2.09600i	0.249114	+	0.130745i	−0.335545	+	0.942024i	$0.608921\pi$
$258$	1.65489			0.103029
$259$	−21.5910	+	11.3318i	−1.34160	+	0.704127i
$260$	−0.114517	−	0.0925956i	−0.00710204	−	0.00574253i
$261$	−0.606242	−	0.318180i	−0.0375254	−	0.0196949i
$262$	−5.91122	−	3.10245i	−0.365197	−	0.191670i
$263$	28.1064	−	6.92760i	1.73311	−	0.427174i	0.758609	−	0.651546i	$-0.225879\pi$
$263$	28.1064	−	6.92760i	1.73311	−	0.427174i	0.974504	+	0.224372i	$0.0720331\pi$
$264$	0.218398	−	0.316405i	0.0134415	−	0.0194734i
$265$	37.0677	−	9.13637i	2.27705	−	0.561243i
$266$	30.3904	+	44.0281i	1.86336	+	2.69954i
$267$	−1.80670	+	14.8795i	−0.110568	+	0.910611i
$268$	0.0678720			0.00414595
$269$	−1.05423	+	8.68240i	−0.0642778	+	0.529375i	0.924632	+	0.380861i	$0.124372\pi$
$269$	−1.05423	+	8.68240i	−0.0642778	+	0.529375i	−0.988910	+	0.148515i	$0.952551\pi$
$270$	−1.98189	−	5.22581i	−0.120614	−	0.318033i
$271$	13.8347	−	7.26103i	0.840401	−	0.441076i	0.0111398	−	0.999938i	$-0.496454\pi$
$271$	13.8347	−	7.26103i	0.840401	−	0.441076i	0.829261	+	0.558862i	$0.188762\pi$
$272$	−1.27693	+	10.5165i	−0.0774253	+	0.637654i
$273$	−14.5246	−	6.80751i	−0.879067	−	0.412009i
$274$	0.783558	+	6.45318i	0.0473365	+	0.389851i
$275$	0.815825	+	1.18193i	0.0491961	+	0.0712728i
$276$	0.0338800	−	0.0490837i	0.00203934	−	0.00295449i
$277$	−14.8317	+	13.1398i	−0.891153	+	0.789493i	−0.978406	−	0.206693i	$-0.933730\pi$
$277$	−14.8317	+	13.1398i	−0.891153	+	0.789493i	0.0872525	+	0.996186i	$0.472191\pi$
$278$	−0.971286	−	2.56107i	−0.0582538	−	0.153603i
$279$	2.38794	−	3.45953i	0.142962	−	0.207117i
$280$	−43.8055	−	22.9909i	−2.61788	−	1.37397i
$281$	−2.60639	+	21.4656i	−0.155484	+	1.28053i	0.680897	+	0.732379i	$0.261590\pi$
$281$	−2.60639	+	21.4656i	−0.155484	+	1.28053i	−0.836381	+	0.548148i	$0.815333\pi$
$282$	−0.418439	−	3.44616i	−0.0249177	−	0.205216i
$283$	5.69984	−	15.0293i	0.338821	−	0.893396i	−0.652001	−	0.758218i	$-0.726070\pi$
$283$	5.69984	−	15.0293i	0.338821	−	0.893396i	0.990821	−	0.135178i	$-0.0431606\pi$
$284$	−0.0284737	+	0.0412513i	−0.00168961	+	0.00244782i
$285$	−25.0233	−	22.1687i	−1.48225	−	1.31316i
$286$	−0.276132	−	0.639648i	−0.0163280	−	0.0378232i
$287$	11.3233	−	10.0316i	0.668393	−	0.592144i
$288$	0.00706531	+	0.0581880i	0.000416327	+	0.00342876i
$289$	−1.21231	−	9.98426i	−0.0713122	−	0.587309i
$290$	−3.38829	+	1.77831i	−0.198967	+	0.104426i
$291$	−11.9048	+	6.24813i	−0.697872	+	0.366272i
$292$	−0.135884	−	0.0334924i	−0.00795201	−	0.00196000i
$293$	9.27631	−	8.21809i	0.541928	−	0.480106i	−0.347184	−	0.937797i	$-0.612862\pi$
$293$	9.27631	−	8.21809i	0.541928	−	0.480106i	0.889111	+	0.457691i	$0.151323\pi$
$294$	17.6114	+	4.34081i	1.02711	+	0.253161i
$295$	13.5844	+	35.8190i	0.790912	+	2.08546i
$296$	−13.6909	+	7.18554i	−0.795767	+	0.417651i
$297$	0.0164271	−	0.135289i	0.000953194	−	0.00785026i
$298$	1.81163	−	0.446528i	0.104945	−	0.0258666i
$299$	8.22515	+	19.0532i	0.475673	+	1.10188i
$300$	−0.106021	−	0.0261319i	−0.00612114	−	0.00150873i
$301$	1.84132	−	4.85515i	0.106132	−	0.279846i
$302$	5.35403	+	4.74326i	0.308090	+	0.272944i
$303$	−8.86258	+	2.18443i	−0.509142	+	0.125492i
$304$	19.3704	+	28.0629i	1.11097	+	1.60952i
$305$	−2.57809	−	21.2325i	−0.147621	−	1.21577i
$306$	1.32476	+	3.49310i	0.0757315	+	0.199687i
$307$	−9.33448	+	24.6130i	−0.532747	+	1.40474i	0.350825	+	0.936441i	$0.385901\pi$
$307$	−9.33448	+	24.6130i	−0.532747	+	1.40474i	−0.883571	+	0.468296i	$0.844868\pi$
$308$	0.00356888	+	0.00517042i	0.000203356	+	0.000294612i
$309$	−1.00715	−	0.248240i	−0.0572947	−	0.0141219i
$310$	−8.33116	−	21.9675i	−0.473178	−	1.24767i
$311$	2.96555	−	7.81952i	0.168161	−	0.443404i	−0.824272	−	0.566195i	$-0.808415\pi$
$311$	2.96555	−	7.81952i	0.168161	−	0.443404i	0.992433	+	0.122790i	$0.0391843\pi$
$312$	−9.21005	−	4.31665i	−0.521416	−	0.244382i
$313$	5.62850	+	14.8411i	0.318141	+	0.838870i	0.994732	+	0.102511i	$0.0326875\pi$
$313$	5.62850	+	14.8411i	0.318141	+	0.838870i	−0.676590	+	0.736360i	$0.736543\pi$
$314$	−10.2528	+	9.08320i	−0.578600	+	0.512595i
$315$	−17.5368			−0.988087
$316$	0.0291401			0.00163926
$317$	12.5427	−	11.1119i	0.704470	−	0.624106i	−0.232876	−	0.972507i	$-0.574814\pi$
$317$	12.5427	−	11.1119i	0.704470	−	0.624106i	0.937346	+	0.348400i	$0.113275\pi$
$318$	−12.1593	+	6.38170i	−0.681860	+	0.357868i
$319$	−0.0933081			−0.00522425
$320$	−27.7764	−	14.5782i	−1.55275	−	0.814944i
$321$	−12.3564	−	10.9468i	−0.689667	−	0.610992i
$322$	−20.6249	−	29.8803i	−1.14938	−	1.66517i
$323$	16.7264	+	14.8183i	0.930681	+	0.824512i
$324$	0.00588625	+	0.00852771i	0.000327014	+	0.000473762i
$325$	27.2768	−	26.4504i	1.51304	−	1.46720i
$326$	−12.4360	+	18.0166i	−0.688764	+	0.997847i
$327$	−8.10913	+	1.99872i	−0.448436	+	0.110529i
$328$	7.18011	−	6.36103i	0.396455	−	0.351229i
$329$	−10.5760	−	2.60675i	−0.583074	−	0.143715i
$330$	−0.570129	−	0.505090i	−0.0313846	−	0.0278043i
$331$	−7.46449	−	6.61296i	−0.410286	−	0.363481i	0.432589	−	0.901591i	$-0.357600\pi$
$331$	−7.46449	−	6.61296i	−0.410286	−	0.363481i	−0.842875	+	0.538110i	$0.819139\pi$
$332$	−0.0362853	+	0.0956766i	−0.00199142	+	0.00525094i
$333$	−3.11352	+	4.51071i	−0.170620	+	0.247185i
$334$	−8.14963	−	4.27726i	−0.445928	−	0.234041i
$335$	−3.11219	+	25.6312i	−0.170037	+	1.40038i
$336$	17.3675	+	4.28072i	0.947477	+	0.233532i
$337$	−2.14601			−0.116901			−0.0584503	−	0.998290i	$-0.518616\pi$
$337$	−2.14601			−0.116901			−0.0584503	+	0.998290i	$0.518616\pi$
$338$	−15.4844	+	9.99927i	−0.842239	+	0.543889i
$339$	5.31904			0.288890
$340$	0.104493	+	0.0257552i	0.00566693	+	0.00139677i
$341$	0.0690535	−	0.568706i	0.00373945	−	0.0307972i
$342$	10.6476	+	5.58831i	0.575758	+	0.302181i
$343$	14.6397	−	21.2092i	0.790469	−	1.14519i
$344$	1.16758	−	3.07866i	0.0629517	−	0.165990i
$345$	16.9825	+	15.0451i	0.914305	+	0.810003i
$346$	10.7862	+	9.55578i	0.579872	+	0.513722i
$347$	2.51581	+	0.620092i	0.135056	+	0.0332883i	0.306264	−	0.951947i	$-0.400921\pi$
$347$	2.51581	+	0.620092i	0.135056	+	0.0332883i	−0.171208	+	0.985235i	$0.554767\pi$
$348$	0.00531029	−	0.00470451i	0.000284661	−	0.000252188i
$349$	−0.762068	+	0.187833i	−0.0407926	+	0.0100545i	−0.259659	−	0.965700i	$-0.583610\pi$
$349$	−0.762068	+	0.187833i	−0.0407926	+	0.0100545i	0.218867	+	0.975755i	$0.429764\pi$
$350$	−37.7612	+	54.7066i	−2.01842	+	2.92419i
$351$	−3.60190	+	0.162322i	−0.192255	+	0.00866411i
$352$	0.00453785	+	0.00657421i	0.000241868	+	0.000350407i
$353$	15.8732	+	14.0625i	0.844847	+	0.748469i	0.969854	−	0.243686i	$-0.0783568\pi$
$353$	15.8732	+	14.0625i	0.844847	+	0.748469i	−0.125007	+	0.992156i	$0.539895\pi$
$354$	−7.82766	−	11.3403i	−0.416035	−	0.602731i
$355$	−14.2725	−	12.6444i	−0.757508	−	0.671093i
$356$	−0.137523	−	0.0721775i	−0.00728869	−	0.00382540i
$357$	11.7222			0.620403
$358$	24.5324	−	12.8756i	1.29658	−	0.680496i
$359$	0.646154	−	0.572442i	0.0341027	−	0.0302123i	−0.645899	−	0.763423i	$-0.723517\pi$
$359$	0.646154	−	0.572442i	0.0341027	−	0.0302123i	0.680002	+	0.733210i	$0.261979\pi$
$360$	−11.1201			−0.586081
$361$	52.9280			2.78568
$362$	21.5546	−	19.0957i	1.13289	−	1.00365i
$363$	3.89407	+	10.2678i	0.204386	+	0.538920i
$364$	0.119324	−	0.115709i	0.00625428	−	0.00606480i
$365$	18.8789	−	49.7796i	0.988167	−	2.60558i
$366$	2.72811	+	7.19345i	0.142601	+	0.376007i
$367$	−29.5775	−	7.29021i	−1.54393	−	0.380546i	−0.626818	−	0.779166i	$-0.715643\pi$
$367$	−29.5775	−	7.29021i	−1.54393	−	0.380546i	−0.917116	+	0.398620i	$0.869489\pi$
$368$	−13.1460	−	19.0453i	−0.685285	−	0.992807i
$369$	1.20578	−	3.17937i	0.0627702	−	0.165511i
$370$	10.8626	+	28.6423i	0.564719	+	1.48904i
$371$	5.19370	+	42.7739i	0.269643	+	2.22071i
$372$	0.0247437	+	0.0358475i	0.00128290	+	0.00185860i
$373$	−25.4754	+	6.27913i	−1.31907	+	0.325121i	−0.835165	−	0.550000i	$-0.814628\pi$
$373$	−25.4754	+	6.27913i	−1.31907	+	0.325121i	−0.483904	+	0.875121i	$0.660782\pi$
$374$	0.381093	+	0.337619i	0.0197058	+	0.0174578i
$375$	7.74099	−	20.4113i	0.399743	−	1.05404i
$376$	−6.70626	−	1.65294i	−0.345849	−	0.0852441i
$377$	0.407581	+	2.43472i	0.0209915	+	0.125394i
$378$	6.12467	−	1.50960i	0.315019	−	0.0776453i
$379$	4.15483	−	34.2181i	0.213420	−	1.75767i	−0.354941	−	0.934889i	$-0.615499\pi$
$379$	4.15483	−	34.2181i	0.213420	−	1.75767i	0.568361	−	0.822779i	$-0.307578\pi$
$380$	0.306729	−	0.160984i	0.0157349	−	0.00825829i
$381$	2.88362	+	7.60348i	0.147732	+	0.389538i
$382$	−31.2207	−	7.69521i	−1.59739	−	0.393721i
$383$	−12.6770	+	11.2309i	−0.647767	+	0.573871i	−0.921712	−	0.387874i	$-0.873210\pi$
$383$	−12.6770	+	11.2309i	−0.647767	+	0.573871i	0.273946	+	0.961745i	$0.411671\pi$
$384$	11.0695	+	2.72840i	0.564890	+	0.139233i
$385$	−2.11620	+	1.11067i	−0.107852	+	0.0566050i
$386$	−29.5692	+	15.5191i	−1.50503	+	0.789902i
$387$	−0.140686	−	1.15865i	−0.00715146	−	0.0588976i
$388$	−0.0167925	−	0.138299i	−0.000852511	−	0.00702106i
$389$	18.1769	−	16.1034i	0.921607	−	0.816472i	−0.0617623	−	0.998091i	$-0.519672\pi$
$389$	18.1769	−	16.1034i	0.921607	−	0.816472i	0.983369	+	0.181619i	$0.0581336\pi$
$390$	−10.6891	+	17.0829i	−0.541264	+	0.865025i
$391$	−11.3516	−	10.0567i	−0.574076	−	0.508587i
$392$	20.5008	−	29.7006i	1.03545	−	1.50011i
$393$	−1.66962	+	4.40243i	−0.0842213	+	0.222073i
$394$	−1.71285	−	14.1066i	−0.0862921	−	0.710679i
$395$	−1.33618	+	11.0045i	−0.0672307	+	0.553695i
$396$	0.00125040		0.000656260i	6.28349e−5		3.29783e-5i
$397$	2.15121	−	3.11656i	0.107966	−	0.156416i	−0.765276	−	0.643702i	$-0.777398\pi$
$397$	2.15121	−	3.11656i	0.107966	−	0.156416i	0.873242	+	0.487286i	$0.162013\pi$
$398$	−0.394469	−	1.04013i	−0.0197729	−	0.0521369i
$399$	28.2423	−	25.0205i	1.41388	−	1.25259i
$400$	−24.0685	+	34.8693i	−1.20343	+	1.74346i
$401$	4.67330	+	6.77044i	0.233373	+	0.338100i	0.922121	−	0.386901i	$-0.126455\pi$
$401$	4.67330	+	6.77044i	0.233373	+	0.338100i	−0.688748	+	0.725001i	$0.741839\pi$
$402$	−1.11945	−	9.21953i	−0.0558333	−	0.459828i
$403$	−15.1411	+	0.682344i	−0.754231	+	0.0339900i
$404$	0.0114006	−	0.0938923i	0.000567201	−	0.00467132i
$405$	−3.49032	+	1.83186i	−0.173435	+	0.0910258i
$406$	−1.53149	−	4.03820i	−0.0760064	−	0.200413i
$407$	−0.0900354	+	0.741508i	−0.00446289	+	0.0367552i
$408$	7.43304			0.367990
$409$	−4.59944	+	37.8798i	−0.227428	+	1.87303i	0.215537	+	0.976496i	$0.430850\pi$
$409$	−4.59944	+	37.8798i	−0.227428	+	1.87303i	−0.442964	+	0.896539i	$0.646073\pi$
$410$	−10.7958	−	15.6404i	−0.533167	−	0.772425i
$411$	4.45152	−	1.09720i	0.219577	−	0.0541209i
$412$	0.00610576	−	0.00884572i	0.000300809	−	0.000435797i
$413$	−41.9800	+	10.3471i	−2.06570	+	0.509150i
$414$	−7.22618	−	3.79259i	−0.355147	−	0.186396i
$415$	−34.4675	−	18.0900i	−1.69194	−	0.888001i
$416$	0.151721	−	0.147125i	0.00743874	−	0.00721338i
$417$	−1.71054	+	0.897758i	−0.0837653	+	0.0439634i
$418$	1.63880			0.0801564
$419$	31.3971	+	16.4785i	1.53385	+	0.805027i	0.999198	−	0.0400444i	$-0.0127499\pi$
$419$	31.3971	+	16.4785i	1.53385	+	0.805027i	0.534653	+	0.845072i	$0.320442\pi$
$420$	0.0644371	−	0.169907i	0.00314421	−	0.00829060i
$421$	−2.61853	−	21.5656i	−0.127619	−	1.05104i	−0.906009	−	0.423259i	$-0.860886\pi$
$421$	−2.61853	−	21.5656i	−0.127619	−	1.05104i	0.778389	−	0.627782i	$-0.216037\pi$
$422$	14.5070	−	3.57565i	0.706189	−	0.174060i
$423$	−2.37722	+	0.585932i	−0.115584	+	0.0284890i
$424$	3.29333	+	27.1230i	0.159938	+	1.31721i
$425$	−9.84597	+	25.9617i	−0.477600	+	1.25933i
$426$	6.07309	+	3.18740i	0.294242	+	0.154430i
$427$	24.1398			1.16821
$428$	0.151461	−	0.0794931i	0.00732117	−	0.00384244i
$429$	−0.424368	+	0.247709i	−0.0204887	+	0.0119595i
$430$	−5.77608	−	3.03152i	−0.278547	−	0.146193i
$431$	−14.1439	−	7.42329i	−0.681288	−	0.357567i	0.0883129	−	0.996093i	$-0.471852\pi$
$431$	−14.1439	−	7.42329i	−0.681288	−	0.357567i	−0.769601	+	0.638525i	$0.779545\pi$
$432$	3.90378	−	0.962197i	0.187821	−	0.0462937i
$433$	−1.68890	+	2.44680i	−0.0811635	+	0.117586i	−0.861463	−	0.507821i	$-0.830451\pi$
$433$	−1.68890	+	2.44680i	−0.0811635	+	0.117586i	0.780299	+	0.625406i	$0.215067\pi$
$434$	25.7459	−	6.34580i	1.23584	−	0.304608i
$435$	1.53311	+	2.22110i	0.0735072	+	0.106494i
$436$	0.0104314	−	0.0859101i	0.000499572	−	0.00411435i
$437$	−48.8150			−2.33514
$438$	−2.30829	+	19.0105i	−0.110294	+	0.908356i
$439$	−12.2046	−	32.1810i	−0.582495	−	1.53591i	−0.824631	−	0.565671i	$-0.808617\pi$
$439$	−12.2046	−	32.1810i	−0.582495	−	1.53591i	0.242136	−	0.970242i	$-0.422152\pi$
$440$	−1.34189	+	0.704277i	−0.0639720	+	0.0335751i
$441$	1.54199	−	12.6994i	0.0734281	−	0.604735i
$442$	7.14494	−	11.4187i	0.339850	−	0.543134i
$443$	2.94216	+	24.2309i	0.139786	+	1.15124i	0.878676	+	0.477418i	$0.158427\pi$
$443$	2.94216	+	24.2309i	0.139786	+	1.15124i	−0.738890	+	0.673826i	$0.764650\pi$
$444$	−0.0322621	−	0.0467397i	−0.00153109	−	0.00221817i
$445$	33.5631	−	48.6245i	1.59104	−	2.30502i
$446$	16.2234	−	14.3727i	0.768202	−	0.680567i
$447$	−0.466643	−	1.23044i	−0.0220715	−	0.0581976i
$448$	20.1123	−	29.1377i	0.950215	−	1.37662i
$449$	−12.9128	−	6.77715i	−0.609392	−	0.319834i	0.131646	−	0.991297i	$-0.457974\pi$
$449$	−12.9128	−	6.77715i	−0.609392	−	0.319834i	−0.741038	+	0.671463i	$0.765666\pi$
$450$	−1.80101	+	14.8326i	−0.0849002	+	0.699216i
$451$	−0.0558575	−	0.460028i	−0.00263023	−	0.0216619i
$452$	−0.0195442	+	0.0515339i	−0.000919284	+	0.00242395i
$453$	2.86579	−	4.15181i	0.134646	−	0.195069i
$454$	−9.77182	−	8.65708i	−0.458614	−	0.406297i
$455$	38.2249	+	50.3673i	1.79201	+	2.36126i
$456$	17.9085	−	15.8655i	0.838640	−	0.742970i
$457$	−1.72259	−	14.1868i	−0.0805795	−	0.663632i	−0.975901	−	0.218212i	$-0.929977\pi$
$457$	−1.72259	−	14.1868i	−0.0805795	−	0.663632i	0.895322	−	0.445420i	$-0.146946\pi$
$458$	0.437196	+	3.60064i	0.0204288	+	0.168247i
$459$	2.33304	−	1.22447i	0.108897	−	0.0571535i
$460$	−0.208166	+	0.109254i	−0.00970581	+	0.00509400i
$461$	26.9226	+	6.63583i	1.25391	+	0.309061i	0.809691	−	0.586856i	$-0.199635\pi$
$461$	26.9226	+	6.63583i	1.25391	+	0.309061i	0.444220	+	0.895918i	$0.353481\pi$
$462$	0.643470	−	0.570064i	0.0299369	−	0.0265218i
$463$	19.3450	+	4.76812i	0.899040	+	0.221593i	0.661643	−	0.749819i	$-0.269860\pi$
$463$	19.3450	+	4.76812i	0.899040	+	0.221593i	0.237397	+	0.971413i	$0.423706\pi$
$464$	−0.976150	−	2.57389i	−0.0453166	−	0.119490i
$465$	−14.6720	+	7.70048i	−0.680400	+	0.357101i
$466$	−0.874341	+	7.20085i	−0.0405031	+	0.333573i
$467$	−5.99991	+	1.47884i	−0.277643	+	0.0684328i	−0.375678	−	0.926750i	$-0.622590\pi$
$467$	−5.99991	+	1.47884i	−0.277643	+	0.0684328i	0.0980356	+	0.995183i	$0.468744\pi$
$468$	0.0116621	−	0.0354937i	0.000539082	−	0.00164070i
$469$	−28.2941	−	6.97386i	−1.30650	−	0.322023i
$470$	−4.85239	+	12.7947i	−0.223824	+	0.590175i
$471$	7.23113	+	6.40622i	0.333193	+	0.295183i
$472$	−26.6196	+	6.56114i	−1.22527	+	0.302001i
$473$	−0.0903586	−	0.130907i	−0.00415469	−	0.00601911i
$474$	−0.480624	−	3.95830i	−0.0220758	−	0.181811i
$475$	31.6922	+	83.5655i	1.45414	+	3.83425i
$476$	−0.0430719	+	0.113571i	−0.00197420	+	0.00520553i
$477$	5.50177	+	7.97069i	0.251909	+	0.364953i
$478$	−10.9300	−	2.69401i	−0.499928	−	0.123221i
$479$	6.65487	+	17.5474i	0.304069	+	0.801763i	0.996753	+	0.0805221i	$0.0256588\pi$
$479$	6.65487	+	17.5474i	0.304069	+	0.801763i	−0.692684	+	0.721241i	$0.743572\pi$
$480$	0.0819321	−	0.216037i	0.00373967	−	0.00986071i
$481$	19.7417	−	0.889675i	0.900145	−	0.0405657i
$482$	−8.82193	−	23.2615i	−0.401828	−	1.05953i
$483$	−19.1670	+	16.9805i	−0.872131	+	0.772641i
$484$	−0.113789			−0.00517222
$485$	52.9972			2.40648
$486$	1.06129	−	0.940223i	0.0481412	−	0.0426494i
$487$	0.940398	−	0.493559i	0.0426135	−	0.0223653i	−0.443282	−	0.896382i	$-0.646186\pi$
$487$	0.940398	−	0.493559i	0.0426135	−	0.0223653i	0.485895	+	0.874017i	$0.338494\pi$
$488$	15.3071			0.692918
$489$	13.6713	+	7.17528i	0.618240	+	0.324477i
$490$	−53.5174	−	47.4123i	−2.41767	−	2.14187i
$491$	−11.5924	−	16.7944i	−0.523156	−	0.757923i	0.468963	−	0.883218i	$-0.344628\pi$
$491$	−11.5924	−	16.7944i	−0.523156	−	0.757923i	−0.992120	+	0.125295i	$0.960012\pi$
$492$	0.0263731	+	0.0233645i	0.00118899	+	0.00105335i
$493$	−1.02478	−	1.48465i	−0.0461539	−	0.0668655i
$494$	−7.15849	−	42.7618i	−0.322076	−	1.92394i
$495$	−0.305166	+	0.442109i	−0.0137162	+	0.0198713i
$496$	16.4101	−	4.04473i	0.736836	−	0.181614i
$497$	16.1085	−	14.2709i	0.722566	−	0.640138i
$498$	13.5949	+	3.35084i	0.609202	+	0.150155i
$499$	−11.9249	−	10.5645i	−0.533831	−	0.472933i	0.352613	−	0.935769i	$-0.385293\pi$
$499$	−11.9249	−	10.5645i	−0.533831	−	0.472933i	−0.886444	+	0.462837i	$0.846832\pi$
$500$	0.169313	+	0.149998i	0.00757192	+	0.00670814i
$501$	−2.30186	+	6.06950i	−0.102839	+	0.271165i
$502$	−15.3004	+	22.1665i	−0.682892	+	0.989340i
$503$	21.2580	+	11.1571i	0.947848	+	0.497469i	0.866478	−	0.499215i	$-0.166378\pi$
$503$	21.2580	+	11.1571i	0.947848	+	0.497469i	0.0813696	+	0.996684i	$0.474071\pi$
$504$	1.51281	−	12.4591i	0.0673857	−	0.554971i
$505$	34.9348	+	8.61065i	1.55458	+	0.383169i
$506$	−1.11220			−0.0494432
$507$	8.31725	+	9.99116i	0.369382	+	0.443723i
$508$	−0.0842625			−0.00373854
$509$	7.50068	+	1.84875i	0.332462	+	0.0819445i	0.402013	−	0.915634i	$-0.368311\pi$
$509$	7.50068	+	1.84875i	0.332462	+	0.0819445i	−0.0695514	+	0.997578i	$0.522157\pi$
$510$	1.77504	−	14.6188i	0.0786003	−	0.647332i
$511$	53.2051	+	27.9242i	2.35366	+	1.23529i
$512$	12.7525	−	18.4752i	0.563587	−	0.816497i
$513$	3.00742	−	7.92991i	0.132781	−	0.350114i
$514$	4.78666	+	4.24061i	0.211130	+	0.187045i
$515$	3.06053	+	2.71139i	0.134863	+	0.119478i
$516$	0.0117426	+	0.00289430i	0.000516941	+	0.000127414i
$517$	−0.249755	+	0.221264i	−0.0109842	+	0.00973116i
$518$	−33.5689	+	8.27398i	−1.47493	+	0.363538i
$519$	5.77342	−	8.36424i	0.253425	−	0.367149i
$520$	24.2385	+	31.9380i	1.06293	+	1.40057i
$521$	−18.4663	−	26.7530i	−0.809021	−	1.17207i	−0.982322	−	0.187201i	$-0.940059\pi$
$521$	−18.4663	−	26.7530i	−0.809021	−	1.17207i	0.173301	−	0.984869i	$-0.444557\pi$
$522$	−0.726631	−	0.643739i	−0.0318038	−	0.0281757i
$523$	18.0310	+	26.1225i	0.788442	+	1.14226i	0.986771	+	0.162120i	$0.0518331\pi$
$523$	18.0310	+	26.1225i	0.788442	+	1.14226i	−0.198329	+	0.980135i	$0.563551\pi$
$524$	−0.0365185	−	0.0323525i	−0.00159532	−	0.00141333i
$525$	41.5124	+	21.7874i	1.81175	+	0.950881i
$526$	41.0439			1.78960
$527$	9.80727	−	5.14725i	0.427211	−	0.224218i
$528$	0.410139	−	0.363351i	0.0178490	−	0.0158128i
$529$	10.1291			0.440394
$530$	54.1302			2.35127
$531$	−7.27436	+	6.44452i	−0.315680	+	0.279668i
$532$	0.138640	+	0.365563i	0.00601079	+	0.0158492i
$533$	−11.7597	+	3.46697i	−0.509368	+	0.150171i
$534$	−7.53613	+	19.8711i	−0.326120	+	0.859908i
$535$	23.0747	+	60.8430i	0.997607	+	2.63047i
$536$	−17.9413	−	4.42214i	−0.774947	−	0.191007i
$537$	−11.1003	−	16.0815i	−0.479012	−	0.693968i
$538$	−4.39744	+	11.5951i	−0.189587	+	0.499900i
$539$	−0.618226	−	1.63013i	−0.0266289	−	0.0702146i
$540$	−0.00492332	−	0.0405472i	−0.000211866	−	0.00174487i
$541$	14.7775	+	21.4089i	0.635334	+	0.920441i	0.999943	−	0.0107203i	$-0.00341245\pi$
$541$	14.7775	+	21.4089i	0.635334	+	0.920441i	−0.364608	+	0.931161i	$0.618797\pi$
$542$	21.5097	−	5.30167i	0.923921	−	0.227726i
$543$	−15.2021	−	13.4679i	−0.652384	−	0.577962i
$544$	−0.0547661	+	0.144406i	−0.00234808	+	0.00619137i
$545$	31.9648	+	7.87861i	1.36922	+	0.337483i
$546$	−17.6856	−	14.3002i	−0.756875	−	0.611990i
$547$	3.81607	−	0.940578i	0.163164	−	0.0402162i	−0.156888	−	0.987616i	$-0.550146\pi$
$547$	3.81607	−	0.940578i	0.163164	−	0.0402162i	0.320051	+	0.947400i	$0.396300\pi$
$548$	−0.00572632	+	0.0471605i	−0.000244616	+	0.00201460i
$549$	4.80449	−	2.52159i	0.205051	−	0.107619i
$550$	0.722073	+	1.90395i	0.0307893	+	0.0811847i
$551$	−5.63795	−	1.38963i	−0.240185	−	0.0592002i
$552$	−12.1539	+	10.7674i	−0.517302	+	0.458290i
$553$	−12.1477	−	2.99415i	−0.516574	−	0.127324i
$554$	−24.8770	+	13.0565i	−1.05692	+	0.554716i
$555$	19.1302	−	10.0403i	0.812030	−	0.426186i
$556$	−0.00241282	−	0.0198714i	−0.000102327	−	0.000842735i
$557$	0.518692	+	4.27182i	0.0219777	+	0.181003i	0.999564	−	0.0295334i	$-0.00940214\pi$
$557$	0.518692	+	4.27182i	0.0219777	+	0.181003i	−0.977586	+	0.210536i	$0.932479\pi$
$558$	4.46130	−	3.95236i	0.188862	−	0.167317i
$559$	−3.02110	+	2.92957i	−0.127779	+	0.123908i
$560$	−52.7766	−	46.7559i	−2.23022	−	1.97580i
$561$	0.203983	−	0.295520i	0.00861216	−	0.0124769i
$562$	−10.8718	+	28.6666i	−0.458600	+	1.20923i
$563$	2.00309	+	16.4970i	0.0844203	+	0.695264i	0.972061	+	0.234727i	$0.0754198\pi$
$563$	2.00309	+	16.4970i	0.0844203	+	0.695264i	−0.887641	+	0.460536i	$0.847657\pi$
$564$	0.00305799	−	0.0251848i	0.000128765	−	0.00106047i
$565$	−18.5651	−	9.74373i	−0.781040	−	0.409922i
$566$	12.9465	−	18.7563i	0.544183	−	0.788385i
$567$	−1.57760	−	4.15979i	−0.0662530	−	0.174695i
$568$	10.2144	−	9.04921i	0.428588	−	0.379696i
$569$	−22.5628	+	32.6879i	−0.945883	+	1.37035i	−0.0170486	+	0.999855i	$0.505427\pi$
$569$	−22.5628	+	32.6879i	−0.945883	+	1.37035i	−0.928835	+	0.370494i	$0.879188\pi$
$570$	−26.9266	−	39.0099i	−1.12783	−	1.63395i
$571$	−2.01438	−	16.5899i	−0.0842990	−	0.694265i	−0.972187	−	0.234205i	$-0.924751\pi$
$571$	−2.01438	−	16.5899i	−0.0842990	−	0.694265i	0.887888	−	0.460059i	$-0.152172\pi$
$572$	−0.000840653	−	0.00502171i	−3.51495e−5	−	0.000209968i
$573$	−2.73358	+	22.5130i	−0.114197	+	0.940496i
$574$	18.9924	−	9.96796i	0.792726	−	0.416054i
$575$	−21.5084	−	56.7130i	−0.896962	−	2.36510i
$576$	0.959246	−	7.90010i	0.0399686	−	0.329171i
$577$	12.8385			0.534475			0.267238	−	0.963631i	$-0.413889\pi$
$577$	12.8385			0.534475			0.267238	+	0.963631i	$0.413889\pi$
$578$	1.71890	−	14.1564i	0.0714967	−	0.588829i
$579$	13.3793	+	19.3833i	0.556025	+	0.805541i
$580$	−0.0271526	+	0.00669251i	−0.00112745	+	0.000277891i
$581$	24.9572	−	36.1567i	1.03540	−	1.50003i
$582$	−18.5091	+	4.56209i	−0.767228	+	0.189105i
$583$	1.16872	+	0.613394i	0.0484036	+	0.0254042i
$584$	33.7375	+	17.7068i	1.39607	+	0.732712i
$585$	12.8691	+	6.03161i	0.532072	+	0.249376i
$586$	15.5590	−	8.16598i	0.642736	−	0.337334i
$587$	14.2852			0.589612			0.294806	−	0.955557i	$-0.404745\pi$
$587$	14.2852			0.589612			0.294806	+	0.955557i	$0.404745\pi$
$588$	0.117374	+	0.0616024i	0.00484041	+	0.00254044i
$589$	12.6421	−	33.3345i	0.520909	−	1.37352i
$590$	6.54713	+	53.9205i	0.269541	+	2.21987i
$591$	−9.73096	+	2.39847i	−0.400278	+	0.0986598i
$592$	−21.3963	+	5.27373i	−0.879384	+	0.216749i
$593$	−3.72542	−	30.6816i	−0.152985	−	1.25994i	−0.843700	−	0.536814i	$-0.819628\pi$
$593$	−3.72542	−	30.6816i	−0.152985	−	1.25994i	0.690716	−	0.723126i	$-0.257296\pi$
$594$	0.0685208	−	0.180674i	0.00281144	−	0.00741316i
$595$	−40.9141	−	21.4734i	−1.67731	−	0.880322i
$596$	0.0136358			0.000558545
$597$	−0.694700	+	0.364607i	−0.0284322	+	0.0149224i
$598$	4.85822	+	29.0210i	0.198667	+	1.18676i
$599$	−17.6215	−	9.24846i	−0.719993	−	0.377882i	0.0645843	−	0.997912i	$-0.479428\pi$
$599$	−17.6215	−	9.24846i	−0.719993	−	0.377882i	−0.784578	+	0.620031i	$0.787120\pi$
$600$	26.3231	+	13.8154i	1.07464	+	0.564012i
$601$	−45.1190	+	11.1208i	−1.84044	+	0.453628i	−0.996558	−	0.0828993i	$-0.973582\pi$
$601$	−45.1190	+	11.1208i	−1.84044	+	0.453628i	−0.843883	+	0.536527i	$0.819736\pi$
$602$	4.18233	−	6.05916i	0.170459	−	0.246953i
$603$	−6.35979	+	1.56755i	−0.258991	+	0.0638355i
$604$	0.0296951	+	0.0430208i	0.00120828	+	0.00175049i
$605$	5.21766	−	42.9713i	0.212128	−	1.74703i
$606$	−12.9421			−0.525736
$607$	2.49807	−	20.5735i	0.101394	−	0.835053i	−0.849938	−	0.526883i	$-0.823361\pi$
$607$	2.49807	−	20.5735i	0.101394	−	0.835053i	0.951331	−	0.308169i	$-0.0997164\pi$
$608$	0.176281	+	0.464815i	0.00714914	+	0.0188507i
$609$	−2.69711	+	1.41555i	−0.109292	+	0.0573611i
$610$	3.65540	−	30.1049i	0.148003	−	1.21891i
$611$	6.86447	+	5.55044i	0.277707	+	0.224547i
$612$	0.00329091	+	0.0271031i	0.000133027	+	0.00109558i
$613$	0.0646154	+	0.0936115i	0.00260979	+	0.00378093i	0.824287	−	0.566173i	$-0.191577\pi$
$613$	0.0646154	+	0.0936115i	0.00260979	+	0.00378093i	−0.821677	+	0.569954i	$0.806961\pi$
$614$	−21.2022	+	30.7166i	−0.855650	+	1.23962i
$615$	−10.0327	+	8.88820i	−0.404558	+	0.358407i
$616$	−0.606525	−	1.59928i	−0.0244376	−	0.0644366i
$617$	−19.1530	+	27.7480i	−0.771072	+	1.11709i	0.218889	+	0.975750i	$0.429757\pi$
$617$	−19.1530	+	27.7480i	−0.771072	+	1.11709i	−0.989961	+	0.141341i	$0.954859\pi$
$618$	−1.30228	−	0.683490i	−0.0523854	−	0.0274940i
$619$	2.93157	−	24.1437i	0.117830	−	0.970417i	−0.807136	−	0.590366i	$-0.798983\pi$
$619$	2.93157	−	24.1437i	0.117830	−	0.970417i	0.924966	−	0.380051i	$-0.124093\pi$
$620$	−0.0206959	−	0.170446i	−0.000831167	−	0.00684527i
$621$	−2.04103	+	5.38175i	−0.0819037	+	0.215962i
$622$	6.73591	−	9.75864i	0.270085	−	0.391286i
$623$	49.9134	+	44.2194i	1.99974	+	1.77161i
$624$	−11.2726	−	9.11473i	−0.451265	−	0.364881i
$625$	−24.9701	+	22.1215i	−0.998803	+	0.884862i
$626$	2.71271	+	22.3412i	0.108422	+	0.892934i
$627$	−0.139318	−	1.14739i	−0.00556384	−	0.0458224i
$628$	−0.0886372	+	0.0465204i	−0.00353701	+	0.00185637i
$629$	−12.7872	+	6.71125i	−0.509860	+	0.267595i
$630$	−24.1424	−	5.95057i	−0.961857	−	0.237076i
$631$	6.17175	−	5.46770i	0.245694	−	0.217666i	−0.531284	−	0.847194i	$-0.678290\pi$
$631$	6.17175	−	5.46770i	0.245694	−	0.217666i	0.776978	+	0.629528i	$0.216752\pi$
$632$	−7.70289	−	1.89859i	−0.306404	−	0.0755219i
$633$	−3.73673	−	9.85294i	−0.148522	−	0.391619i
$634$	21.0377	−	11.0414i	0.835514	−	0.438512i
$635$	3.86376	−	31.8209i	0.153329	−	1.26277i
$636$	−0.0974404	+	0.0240169i	−0.00386376	+	0.000952332i
$637$	−39.8350	+	23.2522i	−1.57832	+	0.921285i
$638$	−0.128455	−	0.0316612i	−0.00508557	−	0.00125348i
$639$	1.71534	−	4.52298i	0.0678578	−	0.178926i
$640$	−33.6382	−	29.8008i	−1.32967	−	1.17798i
$641$	−9.75398	+	2.40414i	−0.385259	+	0.0949578i	−0.427188	−	0.904163i	$-0.640496\pi$
$641$	−9.75398	+	2.40414i	−0.385259	+	0.0949578i	0.0419291	+	0.999121i	$0.486650\pi$
$642$	−13.2962	−	19.2629i	−0.524761	−	0.760247i
$643$	−2.01428	−	16.5891i	−0.0794354	−	0.654209i	−0.976987	−	0.213299i	$-0.931579\pi$
$643$	−2.01428	−	16.5891i	−0.0794354	−	0.654209i	0.897551	−	0.440910i	$-0.145344\pi$
$644$	−0.0940899	−	0.248095i	−0.00370766	−	0.00977630i
$645$	−1.63145	+	4.30178i	−0.0642382	+	0.169382i
$646$	17.9986	+	26.0755i	0.708146	+	1.02593i
$647$	6.17658	+	1.52239i	0.242826	+	0.0598513i	0.358850	−	0.933395i	$-0.383169\pi$
$647$	6.17658	+	1.52239i	0.242826	+	0.0598513i	−0.116024	+	0.993246i	$0.537015\pi$
$648$	−1.00036	−	2.63773i	−0.0392978	−	0.103620i
$649$	−0.469658	+	1.23839i	−0.0184357	+	0.0486109i
$650$	46.5263	−	27.1580i	1.82491	−	1.06522i
$651$	−6.63167	−	17.4863i	−0.259916	−	0.685341i
$652$	−0.119752	+	0.106091i	−0.00468986	+	0.00415485i
$653$	20.4632			0.800786			0.400393	−	0.916344i	$-0.368874\pi$
$653$	20.4632			0.800786			0.400393	+	0.916344i	$0.368874\pi$
$654$	−11.8418			−0.463051
$655$	13.8921	−	12.3074i	0.542811	−	0.480888i
$656$	12.1055	−	6.35344i	0.472639	−	0.248060i
$657$	13.5062			0.526928
$658$	−13.6752	−	7.17728i	−0.533113	−	0.279799i
$659$	−30.6056	−	27.1142i	−1.19222	−	1.05622i	−0.997151	−	0.0754286i	$-0.975968\pi$
$659$	−30.6056	−	27.1142i	−1.19222	−	1.05622i	−0.195072	−	0.980789i	$-0.562494\pi$
$660$	−0.00316211	−	0.00458111i	−0.000123085	−	0.000178319i
$661$	12.3334	+	10.9264i	0.479712	+	0.424988i	0.868010	−	0.496546i	$-0.165399\pi$
$661$	12.3334	+	10.9264i	0.479712	+	0.424988i	−0.388299	+	0.921534i	$0.626937\pi$
$662$	−8.03225	−	11.6367i	−0.312182	−	0.452274i
$663$	−8.60213	−	4.03172i	−0.334079	−	0.156579i
$664$	15.8254	−	22.9270i	0.614144	−	0.889741i
$665$	−144.408	+	35.5935i	−5.59992	+	1.38026i
$666$	−5.81686	+	5.15329i	−0.225399	+	0.199686i
$667$	3.82628	+	0.943094i	0.148154	+	0.0365167i
$668$	−0.0503469	−	0.0446035i	−0.00194798	−	0.00172576i
$669$	−11.4421	−	10.1368i	−0.442377	−	0.391912i
$670$	−12.9816	+	34.2298i	−0.501524	+	1.32241i
$671$	0.420067	−	0.608573i	0.0162165	−	0.0234937i
$672$	0.230904	+	0.121188i	0.00890731	+	0.00467492i
$673$	0.978683	−	8.06018i	0.0377255	−	0.310697i	−0.961616	−	0.274400i	$-0.911521\pi$
$673$	0.978683	−	8.06018i	0.0377255	−	0.310697i	0.999341	−	0.0362969i	$-0.0115562\pi$
$674$	−2.95435	−	0.728182i	−0.113797	−	0.0280485i
$675$	10.5380			0.405608
$676$	−0.127361	+	0.0438709i	−0.00489850	+	0.00168734i
$677$	50.9739			1.95909			0.979544	−	0.201231i	$-0.0644942\pi$
$677$	50.9739			1.95909			0.979544	+	0.201231i	$0.0644942\pi$
$678$	7.32257	+	1.80485i	0.281221	+	0.0693149i
$679$	−7.20987	+	59.3786i	−0.276689	+	2.27874i
$680$	−25.9437	−	13.6163i	−0.994894	−	0.522161i
$681$	−5.23044	+	7.57760i	−0.200431	+	0.290374i
$682$	0.288037	−	0.759491i	0.0110295	−	0.0290824i
$683$	3.98906	+	3.53400i	0.152637	+	0.135225i	0.735985	−	0.676998i	$-0.236719\pi$
$683$	3.98906	+	3.53400i	0.152637	+	0.135225i	−0.583348	+	0.812222i	$0.698258\pi$
$684$	0.0657791	+	0.0582752i	0.00251513	+	0.00222821i
$685$	−17.5471	−	4.32498i	−0.670441	−	0.165249i
$686$	27.3507	−	24.2306i	1.04426	−	0.925130i
$687$	2.48378	−	0.612197i	0.0947622	−	0.0233568i
$688$	2.66576	−	3.86202i	0.101631	−	0.147238i
$689$	10.9004	−	33.1753i	0.415271	−	1.26388i
$690$	18.2742	+	26.4747i	0.695685	+	1.00787i
$691$	−14.3680	−	12.7289i	−0.546584	−	0.484231i	0.344050	−	0.938951i	$-0.388201\pi$
$691$	−14.3680	−	12.7289i	−0.546584	−	0.484231i	−0.890635	+	0.454720i	$0.849739\pi$
$692$	0.0598238	+	0.0866698i	0.00227416	+	0.00329469i
$693$	−0.453828	−	0.402056i	−0.0172395	−	0.0152729i
$694$	3.25304	+	1.70733i	0.123484	+	0.0648092i
$695$	7.61488			0.288849
$696$	−1.71024	+	0.897603i	−0.0648265	+	0.0340236i
$697$	6.70618	−	5.94116i	0.254015	−	0.225037i
$698$	−1.11285			−0.0421221
$699$	5.11593			0.193502
$700$	−0.363622	+	0.322141i	−0.0137436	+	0.0121758i
$701$	11.5449	+	30.4415i	0.436046	+	1.14976i	0.955430	+	0.295218i	$0.0953924\pi$
$701$	11.5449	+	30.4415i	0.436046	+	1.14976i	−0.519383	+	0.854541i	$0.673838\pi$
$702$	−5.01371	−	0.998728i	−0.189230	−	0.0376945i
$703$	−16.4834	+	43.4632i	−0.621684	+	1.63925i
$704$	−0.384588	−	1.01408i	−0.0144947	−	0.0382194i
$705$	9.37059	+	2.30964i	0.352917	+	0.0869862i
$706$	17.0806	+	24.7455i	0.642836	+	0.931309i
$707$	−14.4001	+	37.9698i	−0.541570	+	1.42800i
$708$	−0.0357094	−	0.0941580i	−0.00134204	−	0.00353867i
$709$	1.32006	+	10.8717i	0.0495761	+	0.408296i	0.996279	+	0.0861875i	$0.0274684\pi$
$709$	1.32006	+	10.8717i	0.0495761	+	0.408296i	−0.946703	+	0.322108i	$0.895609\pi$
$710$	−15.3581	−	22.2501i	−0.576380	−	0.835031i
$711$	−2.73050	+	0.673008i	−0.102402	+	0.0252398i
$712$	31.6501	+	28.0396i	1.18614	+	1.05083i
$713$	−8.57976	+	22.6230i	−0.321315	+	0.847237i
$714$	16.1376	+	3.97755i	0.603933	+	0.148856i
$715$	1.93495	−	0.0871999i	0.0723629	−	0.00326109i
$716$	0.196594	−	0.0484560i	0.00734705	−	0.00181089i
$717$	−0.956996	+	7.88157i	−0.0357397	+	0.294343i
$718$	1.08378	−	0.568813i	0.0404464	−	0.0212279i
$719$	−0.0991818	−	0.261521i	−0.00369886	−	0.00975308i	0.933154	−	0.359477i	$-0.117045\pi$
$719$	−0.0991818	−	0.261521i	−0.00369886	−	0.00975308i	−0.936853	+	0.349724i	$0.886276\pi$
$720$	−15.3881	−	3.79281i	−0.573479	−	0.141350i
$721$	−3.45423	+	3.06018i	−0.128642	+	0.113967i
$722$	72.8644	+	17.9595i	2.71173	+	0.668382i
$723$	−15.5363	+	8.15411i	−0.577803	+	0.303254i
$724$	0.186343	−	0.0978004i	0.00692538	−	0.00363472i
$725$	−0.869675	−	7.16242i	−0.0322989	−	0.266006i
$726$	1.87679	+	15.4567i	0.0696541	+	0.573653i
$727$	−15.3430	+	13.5927i	−0.569039	+	0.504124i	−0.897868	−	0.440265i	$-0.854884\pi$
$727$	−15.3430	+	13.5927i	−0.569039	+	0.504124i	0.328829	+	0.944389i	$0.393346\pi$
$728$	−39.0811	+	22.8121i	−1.44844	+	0.845473i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	42.8812	−	62.1241i	1.58710	−	2.29932i
$731$	1.09051	−	2.87545i	0.0403341	−	0.106352i
$732$	0.00677706	+	0.0558141i	0.000250487	+	0.00206295i
$733$	0.655357	−	5.39735i	0.0242062	−	0.199356i	−0.975589	−	0.219605i	$-0.929523\pi$
$733$	0.655357	−	5.39735i	0.0242062	−	0.199356i	0.999795	+	0.0202497i	$0.00644611\pi$
$734$	−38.2448	−	20.0724i	−1.41164	−	0.740887i
$735$	−28.6456	+	41.5003i	−1.05661	+	1.53076i
$736$	−0.119636	−	0.315454i	−0.00440983	−	0.0116278i
$737$	−0.668172	+	0.591949i	−0.0246124	+	0.0218047i
$738$	2.73878	−	3.96781i	0.100816	−	0.146057i
$739$	−19.7360	−	28.5926i	−0.726001	−	1.05179i	−0.996037	−	0.0889442i	$-0.971651\pi$
$739$	−19.7360	−	28.5926i	−0.726001	−	1.05179i	0.270035	−	0.962850i	$-0.412965\pi$
$740$	0.0269843	+	0.222236i	0.000991964	+	0.00816956i
$741$	−29.3307	+	8.64723i	−1.07749	+	0.317664i
$742$	−7.36400	+	60.6480i	−0.270341	+	2.22646i
$743$	27.9213	−	14.6542i	1.02433	−	0.537612i	0.133074	−	0.991106i	$-0.457515\pi$
$743$	27.9213	−	14.6542i	1.02433	−	0.537612i	0.891259	+	0.453494i	$0.149823\pi$
$744$	−4.20515	−	11.0881i	−0.154168	−	0.406509i
$745$	−0.625255	+	5.14944i	−0.0229076	+	0.188661i
$746$	−37.2019			−1.36206
$747$	1.19032	−	9.80319i	0.0435516	−	0.358680i
$748$	0.00211366	+	0.00306216i	7.72830e−5	+	0.000111964i
$749$	−71.3083	+	17.5759i	−2.60555	+	0.642210i
$750$	17.5827	−	25.4730i	0.642031	−	0.930143i
$751$	−37.2165	+	9.17303i	−1.35805	+	0.334729i	−0.850083	−	0.526649i	$-0.823448\pi$
$751$	−37.2165	+	9.17303i	−1.35805	+	0.334729i	−0.507965	+	0.861378i	$0.669602\pi$
$752$	−8.71637	−	4.57470i	−0.317853	−	0.166822i
$753$	16.8204	+	8.82802i	0.612969	+	0.321711i
$754$	−0.265041	+	3.49011i	−0.00965224	+	0.127102i
$755$	−17.6080	+	9.24140i	−0.640821	+	0.336329i
$756$	0.0460992			0.00167661
$757$	−35.0089	−	18.3741i	−1.27242	−	0.667818i	−0.312988	−	0.949757i	$-0.601330\pi$
$757$	−35.0089	−	18.3741i	−1.27242	−	0.667818i	−0.959432	+	0.281939i	$0.909022\pi$
$758$	17.3307	−	45.6973i	0.629480	−	1.65980i
$759$	0.0945506	+	0.778694i	0.00343197	+	0.0282648i
$760$	−91.5695	+	22.5699i	−3.32158	+	0.818695i
$761$	1.98376	−	0.488954i	0.0719114	−	0.0177246i	−0.203196	−	0.979138i	$-0.565133\pi$
$761$	1.98376	−	0.488954i	0.0719114	−	0.0177246i	0.275107	+	0.961414i	$0.411287\pi$
$762$	1.38979	+	11.4460i	0.0503468	+	0.414643i
$763$	−13.1758	+	34.7418i	−0.476997	+	1.25774i
$764$	−0.208075	−	0.109206i	−0.00752790	−	0.00395095i
$765$	−10.3861			−0.375511
$766$	−21.2630	+	11.1597i	−0.768263	+	0.403215i
$767$	34.3652	+	6.84552i	1.24085	+	0.247178i
$768$	0.220195	+	0.115567i	0.00794561	+	0.00417018i
$769$	2.21336	+	1.16166i	0.0798160	+	0.0418906i	0.504159	−	0.863611i	$-0.331803\pi$
$769$	2.21336	+	1.16166i	0.0798160	+	0.0418906i	−0.424343	+	0.905502i	$0.639495\pi$
$770$	−3.29019	+	0.810959i	−0.118570	+	0.0292249i
$771$	2.56209	−	3.71183i	0.0922716	−	0.133678i
$772$	−0.236957	+	0.0584047i	−0.00852828	+	0.00210203i
$773$	5.78574	+	8.38209i	0.208099	+	0.301483i	0.913110	−	0.407713i	$-0.133674\pi$
$773$	5.78574	+	8.38209i	0.208099	+	0.301483i	−0.705012	+	0.709196i	$0.749058\pi$
$774$	0.199475	−	1.64282i	0.00716996	−	0.0590500i
$775$	44.2980			1.59123
$776$	−4.57179	+	37.6520i	−0.164118	+	1.35163i
$777$	8.64671	+	22.7995i	0.310199	+	0.817928i
$778$	30.4878	−	16.0012i	1.09304	−	0.573673i
$779$	3.47608	−	28.6281i	0.124544	−	1.02571i
$780$	−0.105724	+	0.102521i	−0.00378552	+	0.00367084i
$781$	−0.0794630	−	0.654437i	−0.00284341	−	0.0234176i
$782$	−12.2150	−	17.6965i	−0.436809	−	0.632827i
$783$	−0.388935	+	0.563469i	−0.0138994	+	0.0201368i
$784$	38.4993	−	34.1074i	1.37498	−	1.21812i
$785$	−13.5036	−	35.6061i	−0.481965	−	1.27084i
$786$	−3.79235	+	5.49417i	−0.135269	+	0.195970i
$787$	5.68624	+	2.98437i	0.202693	+	0.106381i	0.563015	−	0.826446i	$-0.309641\pi$
$787$	5.68624	+	2.98437i	0.202693	+	0.106381i	−0.360323	+	0.932828i	$0.617333\pi$
$788$	0.0125177	−	0.103092i	0.000445923	−	0.00367251i
$789$	−3.48924	−	28.7365i	−0.124220	−	1.02305i
$790$	−5.57351	+	14.6961i	−0.198297	+	0.522865i
$791$	13.4426	−	19.4750i	0.477964	−	0.692450i
$792$	−0.287773	−	0.254944i	−0.0102256	−	0.00905905i
$793$	−17.7146	−	8.30264i	−0.629064	−	0.294835i
$794$	4.01902	−	3.56054i	0.142630	−	0.126359i
$795$	−4.60174	−	37.8987i	−0.163207	−	1.34413i
$796$	−0.000979921	−	0.00807037i	−3.47324e−5	−	0.000286047i
$797$	24.3296	−	12.7691i	0.861798	−	0.452306i	0.0249158	−	0.999690i	$-0.492068\pi$
$797$	24.3296	−	12.7691i	0.861798	−	0.452306i	0.836882	+	0.547383i	$0.184376\pi$
$798$	47.3702	−	24.8618i	1.67689	−	0.880099i
$799$	−6.26360	−	1.54384i	−0.221590	−	0.0546171i
$800$	−0.462348	+	0.409604i	−0.0163465	+	0.0144817i
$801$	14.5532	+	3.58705i	0.514213	+	0.126742i
$802$	4.13626	+	10.9064i	0.146056	+	0.385119i
$803$	1.62983	−	0.855399i	0.0575153	−	0.0301864i
$804$	0.00818107	−	0.0673772i	0.000288524	−	0.00237621i
$805$	98.0050	−	24.1561i	3.45422	−	0.851389i
$806$	−21.0758	−	4.19829i	−0.742364	−	0.147879i
$807$	8.49202	+	2.09309i	0.298933	+	0.0736804i
$808$	−9.13110	+	24.0767i	−0.321231	+	0.847016i
$809$	19.2531	+	17.0567i	0.676902	+	0.599683i	0.929913	−	0.367780i	$-0.119882\pi$
$809$	19.2531	+	17.0567i	0.676902	+	0.599683i	−0.253010	+	0.967464i	$0.581421\pi$
$810$	−5.42660	+	1.33754i	−0.190671	+	0.0469963i
$811$	−16.4740	−	23.8667i	−0.578480	−	0.838073i	0.419076	−	0.907951i	$-0.362354\pi$
$811$	−16.4740	−	23.8667i	−0.578480	−	0.838073i	−0.997556	+	0.0698785i	$0.977739\pi$
$812$	−0.00380445	−	0.0313325i	−0.000133510	−	0.00109955i
$813$	−5.54050	−	14.6091i	−0.194314	−	0.512363i
$814$	−0.375557	+	0.990263i	−0.0131633	+	0.0347087i
$815$	−34.5732	−	50.0880i	−1.21105	−	1.75451i
$816$	10.2859	+	2.53524i	0.360077	+	0.0887511i
$817$	−3.51014	−	9.25548i	−0.122804	−	0.323808i
$818$	−19.1853	+	50.5873i	−0.670797	+	1.76875i
$819$	−8.50861	+	13.5981i	−0.297315	+	0.475156i
$820$	−0.0492499	−	0.129861i	−0.00171988	−	0.00453496i
$821$	−17.6282	+	15.6172i	−0.615228	+	0.545045i	−0.912150	−	0.409857i	$-0.865579\pi$
$821$	−17.6282	+	15.6172i	−0.615228	+	0.545045i	0.296921	+	0.954902i	$0.404040\pi$
$822$	6.50058			0.226734
$823$	−5.47016			−0.190678			−0.0953388	−	0.995445i	$-0.530393\pi$
$823$	−5.47016			−0.190678			−0.0953388	+	0.995445i	$0.530393\pi$
$824$	−2.19033	+	1.94046i	−0.0763038	+	0.0675993i
$825$	1.27165	−	0.667411i	0.0442730	−	0.0232363i
$826$	−61.3037			−2.13303
$827$	−16.4453	−	8.63115i	−0.571858	−	0.300134i	0.153897	−	0.988087i	$-0.450817\pi$
$827$	−16.4453	−	8.63115i	−0.571858	−	0.300134i	−0.725756	+	0.687952i	$0.758510\pi$
$828$	−0.0446420	−	0.0395494i	−0.00155142	−	0.00137444i
$829$	−16.9040	−	24.4897i	−0.587101	−	0.850563i	0.411033	−	0.911620i	$-0.365168\pi$
$829$	−16.9040	−	24.4897i	−0.587101	−	0.850563i	−0.998134	+	0.0610577i	$0.980553\pi$
$830$	−41.3122	−	36.5994i	−1.43397	−	1.27038i
$831$	11.2562	+	16.3074i	0.390474	+	0.565699i
$832$	−24.7807	+	14.4648i	−0.859116	+	0.501476i
$833$	19.1476	−	27.7402i	0.663427	−	0.961139i
$834$	−2.65947	+	0.655501i	−0.0920900	+	0.0226981i
$835$	19.1527	−	16.9678i	0.662806	−	0.587195i
$836$	0.0116285	+	0.00286617i	0.000402180	+	9.91285e-5i
$837$	−3.14647	−	2.78753i	−0.108758	−	0.0963512i
$838$	37.6321	+	33.3391i	1.29998	+	1.15168i
$839$	8.36620	−	22.0599i	0.288833	−	0.761591i	−0.709545	−	0.704660i	$-0.751099\pi$
$839$	8.36620	−	22.0599i	0.288833	−	0.761591i	0.998378	−	0.0569307i	$-0.0181314\pi$
$840$	−28.1034	+	40.7148i	−0.969661	+	1.40480i
$841$	−25.2632	−	13.2591i	−0.871143	−	0.457211i
$842$	3.71274	−	30.5772i	0.127950	−	1.05376i
$843$	20.9949	+	5.17477i	0.723102	+	0.178229i
$844$	0.109191			0.00375852
$845$	−10.7274	−	50.1083i	−0.369035	−	1.72378i
$846$	−3.47147			−0.119351
$847$	47.4356	+	11.6918i	1.62991	+	0.401736i
$848$	−4.69371	+	38.6562i	−0.161183	+	1.32746i
$849$	−14.2326	−	7.46986i	−0.488463	−	0.256365i
$850$	−22.3640	+	32.3998i	−0.767078	+	1.11130i
$851$	11.1867	−	29.4970i	0.383476	−	1.01114i
$852$	0.0375184	+	0.0332384i	0.00128536	+	0.00113873i
$853$	−25.1520	−	22.2827i	−0.861189	−	0.762947i	0.111817	−	0.993729i	$-0.464333\pi$
$853$	−25.1520	−	22.2827i	−0.861189	−	0.762947i	−0.973005	+	0.230782i	$0.925871\pi$
$854$	33.2325	+	8.19109i	1.13719	+	0.280293i
$855$	−25.0233	+	22.1687i	−0.855779	+	0.758154i
$856$	−45.2167	+	11.1449i	−1.54547	+	0.380925i
$857$	1.37460	−	1.99145i	0.0469554	−	0.0680266i	−0.798803	−	0.601593i	$-0.794533\pi$
$857$	1.37460	−	1.99145i	0.0469554	−	0.0680266i	0.845758	+	0.533566i	$0.179148\pi$
$858$	−0.668268	+	0.197018i	−0.0228143	+	0.00672607i
$859$	14.6299	+	21.1951i	0.499166	+	0.723167i	0.988880	−	0.148716i	$-0.0475142\pi$
$859$	14.6299	+	21.1951i	0.499166	+	0.723167i	−0.489714	+	0.871883i	$0.662899\pi$
$860$	−0.0356835	−	0.0316129i	−0.00121680	−	0.00107799i
$861$	−8.59355	−	12.4499i	−0.292867	−	0.424292i
$862$	−16.9526	−	15.0187i	−0.577409	−	0.511540i
$863$	18.1453	+	9.52341i	0.617674	+	0.324181i	0.744376	−	0.667760i	$-0.232747\pi$
$863$	18.1453	+	9.52341i	0.617674	+	0.324181i	−0.126702	+	0.991941i	$0.540439\pi$
$864$	0.0586154			0.00199414
$865$	−35.4732	+	18.6178i	−1.20612	+	0.633023i
$866$	−3.15531	+	2.79536i	−0.107222	+	0.0949902i
$867$	−10.0576			−0.341574
$868$	0.193785			0.00657748
$869$	−0.286872	+	0.254146i	−0.00973145	+	0.00862132i
$870$	1.35693	+	3.57794i	0.0460044	+	0.121304i
$871$	18.3646	+	14.8491i	0.622260	+	0.503144i
$872$	−8.35482	+	22.0298i	−0.282930	+	0.746024i
$873$	4.76760	+	12.5711i	0.161359	+	0.425469i
$874$	−67.2023	−	16.5639i	−2.27315	−	0.560281i
$875$	−55.1699	−	79.9274i	−1.86508	−	2.70204i
$876$	−0.0496272	+	0.130856i	−0.00167675	+	0.00442122i
$877$	6.26407	+	16.5170i	0.211523	+	0.557739i	0.998223	−	0.0595963i	$-0.0189813\pi$
$877$	6.26407	+	16.5170i	0.211523	+	0.557739i	−0.786700	+	0.617336i	$0.788212\pi$
$878$	−5.88215	−	48.4439i	−0.198513	−	1.63490i
$879$	−7.04004	−	10.1993i	−0.237455	−	0.344012i
$880$	−2.09712	+	0.516894i	−0.0706940	+	0.0174245i
$881$	−0.194291	−	0.172127i	−0.00654585	−	0.00579911i	0.659843	−	0.751403i	$-0.270623\pi$
$881$	−0.194291	−	0.172127i	−0.00654585	−	0.00579911i	−0.666389	+	0.745604i	$0.732161\pi$
$882$	6.43197	−	16.9597i	0.216576	−	0.571063i
$883$	−31.4075	−	7.74126i	−1.05695	−	0.260514i	−0.327713	−	0.944777i	$-0.606278\pi$
$883$	−31.4075	−	7.74126i	−1.05695	−	0.260514i	−0.729235	+	0.684263i	$0.760124\pi$
$884$	0.0706693	−	0.0685283i	0.00237687	−	0.00230486i
$885$	37.1953	−	9.16781i	1.25031	−	0.308173i
$886$	−4.17161	+	34.3563i	−0.140148	+	1.15422i
$887$	−24.2970	+	12.7520i	−0.815812	+	0.428171i	−0.820380	−	0.571818i	$-0.806238\pi$
$887$	−24.2970	+	12.7520i	−0.815812	+	0.428171i	0.00456833	+	0.999990i	$0.498546\pi$
$888$	5.48289	+	14.4572i	0.183994	+	0.485152i
$889$	35.1268	+	8.65798i	1.17812	+	0.290379i
$890$	62.7046	−	55.5514i	2.10186	−	1.86209i
$891$	−0.132322	−	0.0326146i	−0.00443297	−	0.00109263i
$892$	0.140254	−	0.0736110i	0.00469606	−	0.00246468i
$893$	−18.3862	+	9.64982i	−0.615270	+	0.322919i
$894$	−0.224904	−	1.85225i	−0.00752190	−	0.0619484i
$895$	9.28437	+	76.4637i	0.310342	+	2.55590i
$896$	37.9653	−	33.6344i	1.26833	−	1.12364i
$897$	19.9057	−	5.86857i	0.664633	−	0.195946i
$898$	−15.4770	−	13.7115i	−0.516476	−	0.457558i
$899$	−1.63494	+	2.36862i	−0.0545284	+	0.0789980i
$900$	−0.0387208	+	0.102098i	−0.00129069	+	0.00340328i
$901$	3.07595	+	25.3327i	0.102475	+	0.843955i
$902$	0.0791988	−	0.652261i	0.00263703	−	0.0217179i
$903$	−4.59781	−	2.41311i	−0.153005	−	0.0803034i
$904$	8.52397	−	12.3491i	0.283503	−	0.410725i
$905$	28.3888	+	74.8552i	0.943677	+	2.48827i
$906$	5.35403	−	4.74326i	0.177876	−	0.157584i
$907$	21.3000	−	30.8584i	0.707255	−	1.02464i	−0.290448	−	0.956891i	$-0.593804\pi$
$907$	21.3000	−	30.8584i	0.707255	−	1.02464i	0.997703	−	0.0677451i	$-0.0215804\pi$
$908$	−0.0541975	−	0.0785187i	−0.00179861	−	0.00260573i
$909$	1.10024	+	9.06127i	0.0364926	+	0.300543i
$910$	35.5326	+	82.3097i	1.17789	+	2.72854i
$911$	5.97105	−	49.1760i	0.197830	−	1.62927i	−0.468392	−	0.883521i	$-0.655166\pi$
$911$	5.97105	−	49.1760i	0.197830	−	1.62927i	0.666222	−	0.745754i	$-0.267910\pi$
$912$	30.1932	−	15.8466i	0.999795	−	0.524733i
$913$	−0.477233	−	1.25836i	−0.0157941	−	0.0416456i
$914$	2.44242	−	20.1151i	0.0807880	−	0.665349i
$915$	−21.3884			−0.707079
$916$	−0.00319507	+	0.0263138i	−0.000105568	+	0.000869432i
$917$	11.8994	+	17.2392i	0.392952	+	0.569289i
$918$	3.62732	−	0.894053i	0.119719	−	0.0295082i
$919$	−4.36596	+	6.32519i	−0.144020	+	0.208649i	−0.888355	−	0.459158i	$-0.848151\pi$
$919$	−4.36596	+	6.32519i	−0.144020	+	0.208649i	0.744335	+	0.667807i	$0.232767\pi$
$920$	62.1451	−	15.3174i	2.04886	−	0.504999i
$921$	23.3084	+	12.2332i	0.768037	+	0.403097i
$922$	34.8119	+	18.2707i	1.14647	+	0.601714i
$923$	−16.7293	+	4.93212i	−0.550653	+	0.162343i
$924$	0.00556290	−	0.00291963i	0.000183006	−	9.60489e-5i
$925$	−57.7580			−1.89907
$926$	25.0138	+	13.1283i	0.822006	+	0.431422i
$927$	−0.367828	+	0.969884i	−0.0120811	+	0.0318552i
$928$	−0.00483738	−	0.0398394i	−0.000158795	−	0.00130779i
$929$	1.35888	−	0.334933i	0.0445833	−	0.0109888i	−0.216961	−	0.976180i	$-0.569614\pi$
$929$	1.35888	−	0.334933i	0.0445833	−	0.0109888i	0.261544	+	0.965191i	$0.415768\pi$
$930$	−22.8115	+	5.62253i	−0.748019	+	0.184370i
$931$	−13.0777	−	107.704i	−0.428603	−	3.52987i
$932$	−0.0187980	+	0.0495661i	−0.000615747	+	0.00162359i
$933$	−7.40505	−	3.88647i	−0.242430	−	0.127237i
$934$	−8.76170			−0.286692
$935$	−1.25332	+	0.657791i	−0.0409878	+	0.0215121i
$936$	−5.39532	+	8.62258i	−0.176352	+	0.281838i
$937$	−20.1381	−	10.5693i	−0.657882	−	0.345283i	0.102525	−	0.994730i	$-0.467308\pi$
$937$	−20.1381	−	10.5693i	−0.657882	−	0.345283i	−0.760406	+	0.649447i	$0.775000\pi$
$938$	−36.5853	−	19.2014i	−1.19455	−	0.626949i
$939$	15.4114	−	3.79856i	0.502931	−	0.123961i
$940$	−0.0568084	+	0.0823012i	−0.00185289	+	0.00268437i
$941$	43.4877	−	10.7187i	1.41766	−	0.349421i	0.545280	−	0.838254i	$-0.316423\pi$
$941$	43.4877	−	10.7187i	1.41766	−	0.349421i	0.872378	+	0.488833i	$0.162577\pi$
$942$	7.78113	+	11.2729i	0.253523	+	0.367292i
$943$	−2.35910	+	19.4289i	−0.0768228	+	0.632693i
$944$	−39.0741			−1.27176
$945$	−2.11383	+	17.4089i	−0.0687628	+	0.566313i
$946$	−0.0799748	−	0.210876i	−0.00260021	−	0.00685618i
$947$	18.4494	−	9.68299i	0.599525	−	0.314655i	−0.137520	−	0.990499i	$-0.543913\pi$
$947$	18.4494	−	9.68299i	0.599525	−	0.314655i	0.737045	+	0.675844i	$0.236221\pi$
$948$	0.00351245	−	0.0289276i	0.000114079	−	0.000939525i
$949$	−29.4395	−	38.7911i	−0.955647	−	1.25921i
$950$	15.2744	+	125.796i	0.495567	+	4.08136i
$951$	−9.51902	−	13.7907i	−0.308675	−	0.447193i
$952$	18.7852	−	27.2151i	0.608833	−	0.882047i
$953$	−23.9871	+	21.2507i	−0.777018	+	0.688378i	−0.955312	−	0.295599i	$-0.904481\pi$
$953$	−23.9871	+	21.2507i	−0.777018	+	0.688378i	0.178294	+	0.983977i	$0.442942\pi$
$954$	4.86953	+	12.8399i	0.157657	+	0.415707i
$955$	50.7818	−	73.5701i	1.64326	−	2.38067i
$956$	−0.0728449	−	0.0382319i	−0.00235597	−	0.00123651i
$957$	−0.0112470	+	0.0926278i	−0.000363565	+	0.00299423i
$958$	3.20738	+	26.4152i	0.103626	+	0.853436i
$959$	7.23290	−	19.0716i	0.233562	−	0.615854i
$960$	−17.8199	+	25.8166i	−0.575136	+	0.833229i
$961$	9.97719	+	8.83902i	0.321845	+	0.285130i
$962$	27.4797	+	5.47395i	0.885982	+	0.176487i
$963$	−12.3564	+	10.9468i	−0.398180	+	0.352756i
$964$	−0.0219150	−	0.180487i	−0.000705836	−	0.00581308i
$965$	−11.1906	−	92.1627i	−0.360238	−	2.96682i
$966$	−32.1485	+	16.8729i	−1.03436	+	0.542875i
$967$	−33.2138	+	17.4319i	−1.06808	+	0.560573i	−0.904726	−	0.425994i	$-0.859924\pi$
$967$	−33.2138	+	17.4319i	−1.06808	+	0.560573i	−0.163357	+	0.986567i	$0.552232\pi$
$968$	30.0790	+	7.41380i	0.966775	+	0.238289i
$969$	16.7264	−	14.8183i	0.537329	−	0.476032i
$970$	72.9598	+	17.9830i	2.34260	+	0.577398i
$971$	−3.84309	−	10.1334i	−0.123330	−	0.325196i	0.859105	−	0.511800i	$-0.171021\pi$
$971$	−3.84309	−	10.1334i	−0.123330	−	0.325196i	−0.982435	+	0.186604i	$0.940252\pi$
$972$	0.00917504	−	0.00481543i	0.000294290	−	0.000154455i
$973$	−1.03595	+	8.53178i	−0.0332109	+	0.273516i
$974$	1.46209	−	0.360374i	0.0468485	−	0.0115471i
$975$	−22.9697	−	30.2661i	−0.735619	−	0.969293i
$976$	21.1820	+	5.22089i	0.678019	+	0.167117i
$977$	−16.7951	+	44.2849i	−0.537322	+	1.41680i	0.341605	+	0.939844i	$0.389029\pi$
$977$	−16.7951	+	44.2849i	−0.537322	+	1.41680i	−0.878927	+	0.476957i	$0.841740\pi$
$978$	16.3862	+	14.5170i	0.523974	+	0.464201i
$979$	1.98335	−	0.488853i	0.0633882	−	0.0156238i
$980$	−0.296824	−	0.430024i	−0.00948170	−	0.0137366i
$981$	1.00670	+	8.29092i	0.0321415	+	0.264709i
$982$	−10.2602	−	27.0539i	−0.327416	−	0.863326i
$983$	19.0925	−	50.3427i	0.608955	−	1.60568i	−0.174793	−	0.984605i	$-0.555926\pi$
$983$	19.0925	−	50.3427i	0.608955	−	1.60568i	0.783749	−	0.621078i	$-0.213305\pi$
$984$	−5.44918	−	7.89450i	−0.173714	−	0.251667i
$985$	38.3578	+	9.45435i	1.22218	+	0.301241i
$986$	−0.907018	−	2.39161i	−0.0288853	−	0.0761644i
$987$	−3.86254	+	10.1847i	−0.122946	+	0.324182i
$988$	0.0239932	−	0.315946i	0.000763324	−	0.0100516i
$989$	2.38221	+	6.28138i	0.0757499	+	0.199736i
$990$	−0.570129	+	0.505090i	−0.0181199	+	0.0160528i
$991$	−44.4604			−1.41233			−0.706165	−	0.708047i	$-0.749576\pi$
$991$	−44.4604			−1.41233			−0.706165	+	0.708047i	$0.749576\pi$
$992$	0.246398			0.00782315
$993$	−7.46449	+	6.61296i	−0.236879	+	0.209856i
$994$	27.0186	−	14.1804i	0.856976	−	0.449776i
$995$	3.09263			0.0980430
$996$	0.0906053	+	0.0475533i	0.00287094	+	0.00150678i
$997$	1.68399	+	1.49189i	0.0533326	+	0.0472486i	0.689368	−	0.724411i	$-0.257888\pi$
$997$	1.68399	+	1.49189i	0.0533326	+	0.0472486i	−0.636035	+	0.771660i	$0.719427\pi$
$998$	−12.8319	−	18.5902i	−0.406186	−	0.588463i
$999$	4.10253	+	3.63452i	0.129798	+	0.114991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.13	✓	204
169.131	even	13	inner	507.2.m.b.469.13	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.13	✓	204	1.1	even	1	trivial
507.2.m.b.469.13	yes	204	169.131	even	13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37667 + 0.339319i) q^{2} +(0.120537 - 0.992709i) q^{3} +(0.00917504 + 0.00481543i) q^{4} +(-2.23921 + 3.24406i) q^{5} +(0.502784 - 1.32573i) q^{6} +(-3.33005 - 2.95017i) q^{7} +(-2.11159 - 1.87070i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-4.18343 + 3.70620i) q^{10} +(-0.132322 + 0.0326146i) q^{11} +(0.00588625 - 0.00852771i) q^{12} +(1.42902 + 3.31027i) q^{13} +(-3.58334 - 5.19136i) q^{14} +(2.95050 + 2.61392i) q^{15} +(-2.28397 - 3.30890i) q^{16} +(-1.97221 - 1.74723i) q^{17} +(-1.25546 - 0.658918i) q^{18} -8.48104 q^{19} +(-0.0361665 + 0.0189816i) q^{20} +(-3.33005 + 2.95017i) q^{21} -0.193231 q^{22} +5.75579 q^{23} +(-2.11159 + 1.87070i) q^{24} +(-3.73683 - 9.85321i) q^{25} +(0.844058 + 5.04205i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-0.0163470 - 0.0431035i) q^{28} +(0.664771 + 0.163851i) q^{29} +(3.17492 + 4.59966i) q^{30} +(-1.49063 + 3.93047i) q^{31} +(-0.0207853 - 0.0548064i) q^{32} +(0.0164271 + 0.135289i) q^{33} +(-2.12222 - 3.07456i) q^{34} +(17.0272 - 4.19683i) q^{35} +(-0.00775603 - 0.00687124i) q^{36} +(1.94356 - 5.12475i) q^{37} +(-11.6756 - 2.87778i) q^{38} +(3.45838 - 1.01960i) q^{39} +(10.7970 - 2.66122i) q^{40} +(-0.409865 + 3.37555i) q^{41} +(-5.58543 + 2.93146i) q^{42} +(0.413881 + 1.09132i) q^{43} +(-0.00137112 - 0.000337950i) q^{44} +(2.95050 - 2.61392i) q^{45} +(7.92383 + 1.95305i) q^{46} +(2.16792 - 1.13781i) q^{47} +(-3.56008 + 1.86847i) q^{48} +(1.54199 + 12.6994i) q^{49} +(-1.80101 - 14.8326i) q^{50} +(-1.97221 + 1.74723i) q^{51} +(-0.00282904 + 0.0372533i) q^{52} +(-7.24941 - 6.42242i) q^{53} +(-0.805443 + 1.16689i) q^{54} +(0.190495 - 0.502293i) q^{55} +(1.51281 + 12.4591i) q^{56} +(-1.02228 + 8.41920i) q^{57} +(0.859574 + 0.451139i) q^{58} +(5.52071 - 7.99812i) q^{59} +(0.0144838 + 0.0381907i) q^{60} +(-4.06143 + 3.59811i) q^{61} +(-3.38580 + 4.90517i) q^{62} +(2.52726 + 3.66137i) q^{63} +(0.959246 + 7.90010i) q^{64} +(-13.9386 - 2.77656i) q^{65} +(-0.0232915 + 0.191822i) q^{66} +(5.79985 - 3.04400i) q^{67} +(-0.00968147 - 0.0255279i) q^{68} +(0.693783 - 5.71382i) q^{69} +24.8649 q^{70} +(-0.583075 + 4.80206i) q^{71} +(1.60254 + 2.32168i) q^{72} +(-13.1138 + 3.23225i) q^{73} +(4.41457 - 6.39561i) q^{74} +(-10.2318 + 2.52191i) q^{75} +(-0.0778139 - 0.0408399i) q^{76} +(0.536859 + 0.281765i) q^{77} +(5.10703 - 0.230152i) q^{78} +(2.49010 - 1.30690i) q^{79} +15.8486 q^{80} +(0.885456 + 0.464723i) q^{81} +(-1.70964 + 4.50794i) q^{82} +(1.19032 + 9.80319i) q^{83} +(-0.0447597 + 0.0110323i) q^{84} +(10.0843 - 2.48556i) q^{85} +(0.199475 + 1.64282i) q^{86} +(0.242786 - 0.640174i) q^{87} +(0.340423 + 0.178668i) q^{88} -14.9888 q^{89} +(4.94882 - 2.59734i) q^{90} +(5.00713 - 15.2392i) q^{91} +(0.0528096 + 0.0277166i) q^{92} +(3.72214 + 1.95353i) q^{93} +(3.37059 - 0.830776i) q^{94} +(18.9909 - 27.5130i) q^{95} +(-0.0569122 + 0.0140276i) q^{96} +(-7.63754 - 11.0649i) q^{97} +(-2.18634 + 18.0062i) q^{98} +0.136283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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