LMFDB - Embedded newform 820.2.bv.c.103.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bv (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	820.103
Dual form			820.2.bv.c.207.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37867 - 0.315075i) q^{2} +1.73013 q^{3} +(1.80145 + 0.868769i) q^{4} +(-1.96065 - 1.07511i) q^{5} +(-2.38528 - 0.545122i) q^{6} +(4.32334 - 1.40474i) q^{7} +(-2.20988 - 1.76534i) q^{8} -0.00664869 q^{9} +(2.36434 + 2.09998i) q^{10} +(0.524708 - 3.31288i) q^{11} +(3.11675 + 1.50308i) q^{12} +(-5.21822 - 1.69550i) q^{13} +(-6.40306 + 0.574491i) q^{14} +(-3.39217 - 1.86008i) q^{15} +(2.49048 + 3.13010i) q^{16} +(-3.42756 - 4.71763i) q^{17} +(0.00916634 + 0.00209484i) q^{18} +(-0.330761 - 0.168531i) q^{19} +(-2.59799 - 3.64012i) q^{20} +(7.47995 - 2.43038i) q^{21} +(-1.76720 + 4.40204i) q^{22} +(1.26429 + 2.48132i) q^{23} +(-3.82338 - 3.05427i) q^{24} +(2.68827 + 4.21583i) q^{25} +(6.65999 + 3.98167i) q^{26} -5.20189 q^{27} +(9.00871 + 1.22541i) q^{28} +(-3.02368 + 0.478905i) q^{29} +(4.09062 + 3.63323i) q^{30} +(-2.23580 - 3.07732i) q^{31} +(-2.44733 - 5.10006i) q^{32} +(0.907813 - 5.73171i) q^{33} +(3.23906 + 7.58399i) q^{34} +(-9.98680 - 1.89388i) q^{35} +(-0.0119773 - 0.00577618i) q^{36} +(3.09680 - 0.490485i) q^{37} +(0.402910 + 0.336564i) q^{38} +(-9.02820 - 2.93344i) q^{39} +(2.43486 + 5.83708i) q^{40} +(2.45027 + 5.91576i) q^{41} +(-11.0781 + 0.993945i) q^{42} +(2.10232 - 1.07119i) q^{43} +(3.82336 - 5.51215i) q^{44} +(0.0130357 + 0.00714809i) q^{45} +(-0.961241 - 3.81926i) q^{46} +(1.54117 - 4.74323i) q^{47} +(4.30886 + 5.41548i) q^{48} +(11.0549 - 8.03185i) q^{49} +(-2.37792 - 6.65924i) q^{50} +(-5.93013 - 8.16212i) q^{51} +(-7.92739 - 7.58780i) q^{52} +(2.21862 - 3.05367i) q^{53} +(7.17169 + 1.63899i) q^{54} +(-4.59048 + 5.93126i) q^{55} +(-12.0339 - 4.52786i) q^{56} +(-0.572260 - 0.291581i) q^{57} +(4.31955 + 0.292438i) q^{58} +(-0.610546 + 1.87907i) q^{59} +(-4.49486 - 6.29787i) q^{60} +(-3.93490 + 1.27853i) q^{61} +(2.11284 + 4.94705i) q^{62} +(-0.0287446 + 0.00933968i) q^{63} +(1.76715 + 7.80238i) q^{64} +(8.40823 + 8.93445i) q^{65} +(-3.05749 + 7.61610i) q^{66} +(8.02513 + 5.83060i) q^{67} +(-2.07606 - 11.4764i) q^{68} +(2.18739 + 4.29300i) q^{69} +(13.1718 + 5.75763i) q^{70} +(0.960600 - 6.06499i) q^{71} +(0.0146928 + 0.0117372i) q^{72} +(1.33173 - 1.33173i) q^{73} +(-4.42400 - 0.299509i) q^{74} +(4.65105 + 7.29394i) q^{75} +(-0.449437 - 0.590957i) q^{76} +(-2.38524 - 15.0598i) q^{77} +(11.5226 + 6.88881i) q^{78} +(5.38411 + 5.38411i) q^{79} +(-1.51774 - 8.81456i) q^{80} -8.98001 q^{81} +(-1.51420 - 8.92789i) q^{82} +(6.44284 - 6.44284i) q^{83} +(15.5862 + 2.12013i) q^{84} +(1.64825 + 12.9346i) q^{85} +(-3.23591 + 0.814422i) q^{86} +(-5.23137 + 0.828567i) q^{87} +(-7.00789 + 6.39478i) q^{88} +(4.00873 + 2.04255i) q^{89} +(-0.0157198 - 0.0139621i) q^{90} -24.9419 q^{91} +(0.121877 + 5.56836i) q^{92} +(-3.86823 - 5.32416i) q^{93} +(-3.61924 + 6.05376i) q^{94} +(0.467316 + 0.686036i) q^{95} +(-4.23420 - 8.82376i) q^{96} +(8.70996 - 11.9882i) q^{97} +(-17.7717 + 7.59014i) q^{98} +(-0.00348862 + 0.0220263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.37867	−	0.315075i	−0.974866	−	0.222792i
$2$	−1.37867	−	0.315075i	−0.974866	−	0.222792i
$3$	1.73013			0.998891			0.499446	−	0.866345i	$-0.333537\pi$
$3$	1.73013			0.998891			0.499446	+	0.866345i	$0.333537\pi$
$4$	1.80145	+	0.868769i	0.900727	+	0.434385i
$5$	−1.96065	−	1.07511i	−0.876828	−	0.480805i
$5$	−1.96065	−	1.07511i	−0.876828	−	0.480805i
$6$	−2.38528	−	0.545122i	−0.973785	−	0.222545i
$7$	4.32334	−	1.40474i	1.63407	−	0.530942i	0.658869	−	0.752258i	$-0.271035\pi$
$7$	4.32334	−	1.40474i	1.63407	−	0.530942i	0.975202	+	0.221316i	$0.0710353\pi$
$8$	−2.20988	−	1.76534i	−0.781311	−	0.624142i
$9$	−0.00664869			−0.00221623
$10$	2.36434	+	2.09998i	0.747670	+	0.664070i
$11$	0.524708	−	3.31288i	0.158205	−	0.998870i	−0.773008	−	0.634396i	$-0.781249\pi$
$11$	0.524708	−	3.31288i	0.158205	−	0.998870i	0.931214	−	0.364474i	$-0.118751\pi$
$12$	3.11675	+	1.50308i	0.899729	+	0.433903i
$13$	−5.21822	−	1.69550i	−1.44727	−	0.470248i	−0.523117	−	0.852261i	$-0.675231\pi$
$13$	−5.21822	−	1.69550i	−1.44727	−	0.470248i	−0.924157	+	0.382013i	$0.875231\pi$
$14$	−6.40306	+	0.574491i	−1.71129	+	0.153539i
$15$	−3.39217	−	1.86008i	−0.875855	−	0.480272i
$16$	2.49048	+	3.13010i	0.622620	+	0.782524i
$17$	−3.42756	−	4.71763i	−0.831305	−	1.14419i	−0.987679	−	0.156496i	$-0.949980\pi$
$17$	−3.42756	−	4.71763i	−0.831305	−	1.14419i	0.156373	−	0.987698i	$-0.450020\pi$
$18$	0.00916634	+	0.00209484i	0.00216053	+	0.000493758i
$19$	−0.330761	−	0.168531i	−0.0758819	−	0.0386637i	0.415638	−	0.909530i	$-0.363558\pi$
$19$	−0.330761	−	0.168531i	−0.0758819	−	0.0386637i	−0.491520	+	0.870866i	$0.663558\pi$
$20$	−2.59799	−	3.64012i	−0.580928	−	0.813955i
$21$	7.47995	−	2.43038i	1.63226	−	0.530353i
$22$	−1.76720	+	4.40204i	−0.376769	+	0.938517i
$23$	1.26429	+	2.48132i	0.263624	+	0.517390i	0.984437	−	0.175739i	$-0.0562315\pi$
$23$	1.26429	+	2.48132i	0.263624	+	0.517390i	−0.720813	+	0.693129i	$0.756231\pi$
$24$	−3.82338	−	3.05427i	−0.780445	−	0.623450i
$25$	2.68827	+	4.21583i	0.537653	+	0.843166i
$26$	6.65999	+	3.98167i	1.30613	+	0.780870i
$27$	−5.20189			−1.00111
$28$	9.00871	+	1.22541i	1.70249	+	0.231581i
$29$	−3.02368	+	0.478905i	−0.561484	+	0.0889303i	−0.430724	−	0.902484i	$-0.641742\pi$
$29$	−3.02368	+	0.478905i	−0.561484	+	0.0889303i	−0.130760	+	0.991414i	$0.541742\pi$
$30$	4.09062	+	3.63323i	0.746841	+	0.663334i
$31$	−2.23580	−	3.07732i	−0.401562	−	0.552703i	0.559573	−	0.828781i	$-0.310965\pi$
$31$	−2.23580	−	3.07732i	−0.401562	−	0.552703i	−0.961135	+	0.276078i	$0.910965\pi$
$32$	−2.44733	−	5.10006i	−0.432631	−	0.901571i
$33$	0.907813	−	5.73171i	0.158030	−	0.997762i
$34$	3.23906	+	7.58399i	0.555494	+	1.30064i
$35$	−9.98680	−	1.89388i	−1.68808	−	0.320125i
$36$	−0.0119773	−	0.00577618i	−0.00199622	−	0.000962696i
$37$	3.09680	−	0.490485i	0.509111	−	0.0806352i	0.103406	−	0.994639i	$-0.467026\pi$
$37$	3.09680	−	0.490485i	0.509111	−	0.0806352i	0.405705	+	0.914004i	$0.367026\pi$
$38$	0.402910	+	0.336564i	0.0653607	+	0.0545978i
$39$	−9.02820	−	2.93344i	−1.44567	−	0.469726i
$40$	2.43486	+	5.83708i	0.384985	+	0.922923i
$41$	2.45027	+	5.91576i	0.382668	+	0.923886i
$41$	2.45027	+	5.91576i	0.382668	+	0.923886i
$42$	−11.0781	+	0.993945i	−1.70939	+	0.153369i
$43$	2.10232	−	1.07119i	0.320601	−	0.163355i	−0.286282	−	0.958145i	$-0.592419\pi$
$43$	2.10232	−	1.07119i	0.320601	−	0.163355i	0.606883	+	0.794791i	$0.292419\pi$
$44$	3.82336	−	5.51215i	0.576394	−	0.830987i
$45$	0.0130357	+	0.00714809i	0.00194325	+	0.00106557i
$46$	−0.961241	−	3.81926i	−0.141727	−	0.563119i
$47$	1.54117	−	4.74323i	0.224803	−	0.691871i	−0.773509	−	0.633785i	$-0.781500\pi$
$47$	1.54117	−	4.74323i	0.224803	−	0.691871i	0.998312	−	0.0580861i	$-0.0184998\pi$
$48$	4.30886	+	5.41548i	0.621930	+	0.781657i
$49$	11.0549	−	8.03185i	1.57927	−	1.14741i
$50$	−2.37792	−	6.65924i	−0.336289	−	0.941759i
$51$	−5.93013	−	8.16212i	−0.830384	−	1.14293i
$52$	−7.92739	−	7.58780i	−1.09933	−	1.05224i
$53$	2.21862	−	3.05367i	0.304751	−	0.419454i	−0.628984	−	0.777418i	$-0.716529\pi$
$53$	2.21862	−	3.05367i	0.304751	−	0.419454i	0.933735	+	0.357964i	$0.116529\pi$
$54$	7.17169	+	1.63899i	0.975943	+	0.223038i
$55$	−4.59048	+	5.93126i	−0.618980	+	0.799771i
$56$	−12.0339	−	4.52786i	−1.60810	−	0.605061i
$57$	−0.572260	−	0.291581i	−0.0757977	−	0.0386209i
$58$	4.31955	+	0.292438i	0.567185	+	0.0383990i
$59$	−0.610546	+	1.87907i	−0.0794863	+	0.244634i	−0.982901	−	0.184134i	$-0.941052\pi$
$59$	−0.610546	+	1.87907i	−0.0794863	+	0.244634i	0.903415	+	0.428767i	$0.141052\pi$
$60$	−4.49486	−	6.29787i	−0.580284	−	0.813052i
$61$	−3.93490	+	1.27853i	−0.503812	+	0.163699i	−0.549886	−	0.835239i	$-0.685329\pi$
$61$	−3.93490	+	1.27853i	−0.503812	+	0.163699i	0.0460740	+	0.998938i	$0.485329\pi$
$62$	2.11284	+	4.94705i	0.268331	+	0.628276i
$63$	−0.0287446	+	0.00933968i	−0.00362148	+	0.00117669i
$64$	1.76715	+	7.80238i	0.220894	+	0.975298i
$65$	8.40823	+	8.93445i	1.04291	+	1.10818i
$66$	−3.05749	+	7.61610i	−0.376352	+	0.937477i
$67$	8.02513	+	5.83060i	0.980425	+	0.712321i	0.957804	−	0.287423i	$-0.0927987\pi$
$67$	8.02513	+	5.83060i	0.980425	+	0.712321i	0.0226218	+	0.999744i	$0.492799\pi$
$68$	−2.07606	−	11.4764i	−0.251759	−	1.39171i
$69$	2.18739	+	4.29300i	0.263331	+	0.516817i
$70$	13.1718	+	5.75763i	1.57433	+	0.688169i
$71$	0.960600	−	6.06499i	0.114002	−	0.719782i	−0.862785	−	0.505571i	$-0.831282\pi$
$71$	0.960600	−	6.06499i	0.114002	−	0.719782i	0.976787	−	0.214211i	$-0.0687180\pi$
$72$	0.0146928	+	0.0117372i	0.00173157	+	0.00138324i
$73$	1.33173	−	1.33173i	0.155868	−	0.155868i	−0.624865	−	0.780733i	$-0.714846\pi$
$73$	1.33173	−	1.33173i	0.155868	−	0.155868i	0.780733	+	0.624865i	$0.214846\pi$
$74$	−4.42400	−	0.299509i	−0.514280	−	0.0348172i
$75$	4.65105	+	7.29394i	0.537057	+	0.842231i
$76$	−0.449437	−	0.590957i	−0.0515540	−	0.0677874i
$77$	−2.38524	−	15.0598i	−0.271823	−	1.71622i
$78$	11.5226	+	6.88881i	1.30468	+	0.780004i
$79$	5.38411	+	5.38411i	0.605760	+	0.605760i	0.941835	−	0.336075i	$-0.109100\pi$
$79$	5.38411	+	5.38411i	0.605760	+	0.605760i	−0.336075	+	0.941835i	$0.609100\pi$
$80$	−1.51774	−	8.81456i	−0.169689	−	0.985498i
$81$	−8.98001			−0.997779
$82$	−1.51420	−	8.92789i	−0.167215	−	0.985920i
$83$	6.44284	−	6.44284i	0.707193	−	0.707193i	−0.258751	−	0.965944i	$-0.583311\pi$
$83$	6.44284	−	6.44284i	0.707193	−	0.707193i	0.965944	+	0.258751i	$0.0833109\pi$
$84$	15.5862	+	2.12013i	1.70060	+	0.231325i
$85$	1.64825	+	12.9346i	0.178778	+	1.40296i
$86$	−3.23591	+	0.814422i	−0.348937	+	0.0878214i
$87$	−5.23137	+	0.828567i	−0.560862	+	0.0888317i
$88$	−7.00789	+	6.39478i	−0.747044	+	0.681686i
$89$	4.00873	+	2.04255i	0.424925	+	0.216510i	0.653357	−	0.757050i	$-0.273360\pi$
$89$	4.00873	+	2.04255i	0.424925	+	0.216510i	−0.228432	+	0.973560i	$0.573360\pi$
$90$	−0.0157198	−	0.0139621i	−0.00165701	−	0.00147173i
$91$	−24.9419			−2.61462
$92$	0.121877	+	5.56836i	0.0127066	+	0.580542i
$93$	−3.86823	−	5.32416i	−0.401117	−	0.552090i
$94$	−3.61924	+	6.05376i	−0.373296	+	0.624398i
$95$	0.467316	+	0.686036i	0.0479456	+	0.0703858i
$96$	−4.23420	−	8.82376i	−0.432151	−	0.900572i
$97$	8.70996	−	11.9882i	0.884362	−	1.21722i	−0.0908314	−	0.995866i	$-0.528952\pi$
$97$	8.70996	−	11.9882i	0.884362	−	1.21722i	0.975194	−	0.221354i	$-0.0710476\pi$
$98$	−17.7717	+	7.59014i	−1.79521	+	0.766720i
$99$	−0.00348862	+	0.0220263i	−0.000350620	+	0.00221373i
$100$	1.18021	+	9.93011i	0.118021	+	0.993011i
$101$	−14.1767	−	7.22338i	−1.41063	−	0.718753i	−0.427907	−	0.903823i	$-0.640749\pi$
$101$	−14.1767	−	7.22338i	−1.41063	−	0.718753i	−0.982725	+	0.185069i	$0.940749\pi$
$102$	5.60400	+	13.1213i	0.554878	+	1.29920i
$103$	−1.66292	+	3.26366i	−0.163852	+	0.321578i	−0.958305	−	0.285748i	$-0.907758\pi$
$103$	−1.66292	+	3.26366i	−0.163852	+	0.321578i	0.794452	+	0.607326i	$0.207758\pi$
$104$	8.53851	+	12.9588i	0.837270	+	1.27071i
$105$	−17.2785	−	3.27667i	−1.68621	−	0.319770i
$106$	−4.02088	+	3.51096i	−0.390542	+	0.341015i
$107$	6.78585	−	13.3180i	0.656012	−	1.28750i	−0.288014	−	0.957626i	$-0.592995\pi$
$107$	6.78585	−	13.3180i	0.656012	−	1.28750i	0.944026	−	0.329871i	$-0.107005\pi$
$108$	−9.37098	−	4.51925i	−0.901723	−	0.434865i
$109$	−12.0752	−	12.0752i	−1.15659	−	1.15659i	−0.985204	−	0.171386i	$-0.945176\pi$
$109$	−12.0752	−	12.0752i	−1.15659	−	1.15659i	−0.171386	−	0.985204i	$-0.554824\pi$
$110$	8.19755	−	6.73089i	0.781605	−	0.641765i
$111$	5.35787	−	0.848603i	0.508546	−	0.0805458i
$112$	15.1642	+	10.0340i	1.43288	+	0.948125i
$113$	18.6003	+	2.94600i	1.74977	+	0.277136i	0.947483	−	0.319806i	$-0.103618\pi$
$113$	18.6003	+	2.94600i	1.74977	+	0.277136i	0.802285	+	0.596942i	$0.203618\pi$
$114$	0.697087	+	0.582299i	0.0652882	+	0.0545373i
$115$	0.188861	−	6.22424i	0.0176114	−	0.580414i
$116$	−5.86309	−	1.76416i	−0.544374	−	0.163798i
$117$	0.0346943	+	0.0112729i	0.00320749	+	0.00104218i
$118$	1.43379	−	2.39824i	0.131991	−	0.220776i
$119$	−21.4456	−	15.5811i	−1.96591	−	1.42832i
$120$	4.21262	+	10.0989i	0.384558	+	0.921900i
$121$	−0.238209	−	0.0773987i	−0.0216553	−	0.00703625i
$122$	5.82776	−	0.522874i	0.527620	−	0.0473388i
$123$	4.23928	+	10.2350i	0.382243	+	0.922862i
$124$	−1.35422	−	7.48605i	−0.121612	−	0.672267i
$125$	−0.738249	−	11.1559i	−0.0660310	−	0.997818i
$126$	0.0425720	−	0.00381961i	0.00379261	−	0.000340278i
$127$	−3.30155	−	20.8452i	−0.292965	−	1.84971i	−0.493141	−	0.869950i	$-0.664151\pi$
$127$	−3.30155	−	20.8452i	−0.292965	−	1.84971i	0.200176	−	0.979760i	$-0.435849\pi$
$128$	0.0220176	−	11.3137i	0.00194610	−	0.999998i
$129$	3.63729	−	1.85329i	0.320246	−	0.163173i
$130$	−8.77713	−	14.9669i	−0.769806	−	1.31268i
$131$	−14.3433	+	10.4210i	−1.25318	+	0.910490i	−0.998402	−	0.0565095i	$-0.982003\pi$
$131$	−14.3433	+	10.4210i	−1.25318	+	0.910490i	−0.254779	+	0.966999i	$0.582003\pi$
$132$	6.61492	−	9.53673i	0.575755	−	0.830066i
$133$	−1.66674	−	0.263985i	−0.144525	−	0.0228904i
$134$	−9.22692	−	10.5670i	−0.797084	−	0.912848i
$135$	10.1991	+	5.59262i	0.877797	+	0.481336i
$136$	−0.753718	+	16.4762i	−0.0646308	+	1.41282i
$137$			6.17111i			0.527233i	0.964628	+	0.263617i	$0.0849154\pi$
$137$			6.17111i			0.527233i	−0.964628	+	0.263617i	$0.915085\pi$
$138$	−1.66307	−	6.60782i	−0.141570	−	0.562495i
$139$	4.17600	+	12.8524i	0.354204	+	1.09013i	0.956470	+	0.291832i	$0.0942648\pi$
$139$	4.17600	+	12.8524i	0.354204	+	1.09013i	−0.602266	+	0.798296i	$0.705735\pi$
$140$	−16.3454	−	12.0880i	−1.38144	−	1.02162i
$141$	2.66642	−	8.20641i	0.224553	−	0.691104i
$142$	−3.23528	+	8.05895i	−0.271499	+	0.676292i
$143$	−8.35503	+	16.3977i	−0.698683	+	1.37124i
$144$	−0.0165584	−	0.0208110i	−0.00137987	−	0.00173425i
$145$	6.44325	+	2.31184i	0.535083	+	0.191988i
$146$	−2.25562	+	1.41642i	−0.186676	+	0.117224i
$147$	19.1264	−	13.8962i	1.57752	−	1.14614i
$148$	6.00486	+	1.80682i	0.493597	+	0.148519i
$149$	2.39884	+	15.1457i	0.196521	+	1.24078i	0.866793	+	0.498667i	$0.166177\pi$
$149$	2.39884	+	15.1457i	0.196521	+	1.24078i	−0.670273	+	0.742115i	$0.733823\pi$
$150$	−4.11412	−	11.5214i	−0.335917	−	0.940715i
$151$	3.17225	+	6.22588i	0.258154	+	0.506655i	0.983312	−	0.181927i	$-0.0582334\pi$
$151$	3.17225	+	6.22588i	0.258154	+	0.506655i	−0.725158	+	0.688582i	$0.758233\pi$
$152$	0.433429	+	0.956341i	0.0351557	+	0.0775695i
$153$	0.0227888	+	0.0313661i	0.00184236	+	0.00253580i
$154$	−1.45652	+	21.5140i	−0.117370	+	1.73365i
$155$	1.07515	+	8.43727i	0.0863585	+	0.677698i
$156$	−13.7154	−	13.1279i	−1.09811	−	1.05107i
$157$	1.70579	+	5.24987i	0.136137	+	0.418985i	0.995765	−	0.0919342i	$-0.0293050\pi$
$157$	1.70579	+	5.24987i	0.136137	+	0.418985i	−0.859628	+	0.510920i	$0.829305\pi$
$158$	−5.72651	−	9.11931i	−0.455576	−	0.725493i
$159$	3.83850	−	5.28325i	0.304413	−	0.418989i
$160$	−0.684786	+	12.6306i	−0.0541371	+	0.998534i
$161$	8.95158	+	8.95158i	0.705484	+	0.705484i
$162$	12.3805	+	2.82938i	0.972701	+	0.222297i
$163$	10.5950	−	10.5950i	0.829861	−	0.829861i	−0.157636	−	0.987497i	$-0.550387\pi$
$163$	10.5950	−	10.5950i	0.829861	−	0.829861i	0.987497	+	0.157636i	$0.0503874\pi$
$164$	−0.725382	+	12.7857i	−0.0566428	+	0.998395i
$165$	−7.94213	+	10.2618i	−0.618294	+	0.798884i
$166$	−10.9125	+	6.85256i	−0.846975	+	0.531862i
$167$			16.4442i			1.27249i	0.771488	+	0.636244i	$0.219513\pi$
$167$			16.4442i			1.27249i	−0.771488	+	0.636244i	$0.780487\pi$
$168$	−20.8203	−	7.83379i	−1.60632	−	0.604390i
$169$	13.8379	+	10.0538i	1.06445	+	0.773369i
$170$	1.80299	−	18.3519i	0.138283	−	1.40752i
$171$	0.00219913	+	0.00112051i	0.000168172	+	8.56878e-5i
$172$	4.71786	−	0.103262i	0.359733	−	0.00787363i
$173$	−6.52709	+	6.52709i	−0.496245	+	0.496245i	−0.910267	−	0.414022i	$-0.864124\pi$
$173$	−6.52709	+	6.52709i	−0.496245	+	0.496245i	0.414022	+	0.910267i	$0.364124\pi$
$174$	7.47338	+	0.505956i	0.566556	+	0.0383564i
$175$	17.5444	+	14.4502i	1.32624	+	1.09233i
$176$	11.6764	−	6.60826i	0.880142	−	0.498117i
$177$	−1.05632	+	3.25103i	−0.0793982	+	0.244362i
$178$	−4.88316	−	4.07906i	−0.366008	−	0.305738i
$179$	17.6535	−	2.79605i	1.31949	−	0.208986i	0.543327	−	0.839521i	$-0.317165\pi$
$179$	17.6535	−	2.79605i	1.31949	−	0.208986i	0.776161	+	0.630535i	$0.217165\pi$
$180$	0.0172732	+	0.0242020i	0.00128747	+	0.00180391i
$181$	3.82099	−	24.1248i	0.284012	−	1.79318i	−0.272305	−	0.962211i	$-0.587786\pi$
$181$	3.82099	−	24.1248i	0.284012	−	1.79318i	0.556317	−	0.830970i	$-0.312214\pi$
$182$	34.3866	+	7.85858i	2.54891	+	0.582517i
$183$	−6.80789	+	2.21202i	−0.503254	+	0.163517i
$184$	1.58643	−	7.71532i	0.116953	−	0.568781i
$185$	−6.59905	−	2.36774i	−0.485172	−	0.174080i
$186$	3.65550	+	8.55904i	0.268034	+	0.627579i
$187$	−17.4274	+	8.87970i	−1.27442	+	0.649348i
$188$	6.89712	−	7.20580i	0.503024	−	0.525537i
$189$	−22.4896	+	7.30731i	−1.63588	+	0.531528i
$190$	−0.428121	−	1.09306i	−0.0310591	−	0.0792986i
$191$	12.4200	+	12.4200i	0.898676	+	0.898676i	0.995319	−	0.0966428i	$-0.0308104\pi$
$191$	12.4200	+	12.4200i	0.898676	+	0.898676i	−0.0966428	+	0.995319i	$0.530810\pi$
$192$	3.05741	+	13.4991i	0.220649	+	0.974216i
$193$	−3.84396	+	5.29076i	−0.276695	+	0.380837i	−0.924636	−	0.380853i	$-0.875630\pi$
$193$	−3.84396	+	5.29076i	−0.276695	+	0.380837i	0.647941	+	0.761691i	$0.275630\pi$
$194$	−15.7853	+	13.7835i	−1.13332	+	0.989598i
$195$	14.5473	+	15.4578i	1.04176	+	1.10695i
$196$	26.8927	−	4.86487i	1.92091	−	0.347490i
$197$	7.87304	+	1.24697i	0.560931	+	0.0888428i	0.430460	−	0.902609i	$-0.358351\pi$
$197$	7.87304	+	1.24697i	0.560931	+	0.0888428i	0.130471	+	0.991452i	$0.458351\pi$
$198$	0.0117496	−	0.0292678i	0.000835007	−	0.00207997i
$199$	6.42371	+	12.6072i	0.455365	+	0.893704i	0.998536	+	0.0540823i	$0.0172233\pi$
$199$	6.42371	+	12.6072i	0.455365	+	0.893704i	−0.543172	+	0.839622i	$0.682777\pi$
$200$	1.50162	−	14.0622i	0.106180	−	0.994347i
$201$	13.8845	+	10.0877i	0.979338	+	0.711531i
$202$	17.2690	+	14.4254i	1.21505	+	1.01497i
$203$	−12.3997	+	6.31796i	−0.870288	+	0.443434i
$204$	−3.59186	−	19.8556i	−0.251480	−	1.39017i
$205$	1.55600	−	14.2330i	0.108676	−	0.994077i
$206$	3.32091	−	3.97556i	0.231379	−	0.276991i
$207$	−0.00840590	−	0.0164975i	−0.000584250	−	0.00114666i
$208$	−7.68878	−	20.5562i	−0.533121	−	1.42531i
$209$	−0.731877	+	1.00734i	−0.0506250	+	0.0696793i
$210$	22.7889	+	9.96146i	1.57258	+	0.687406i
$211$	−10.0218	+	5.10637i	−0.689930	+	0.351537i	−0.763549	−	0.645750i	$-0.776545\pi$
$211$	−10.0218	+	5.10637i	−0.689930	+	0.351537i	0.0736196	+	0.997286i	$0.476545\pi$
$212$	6.64968	−	3.57358i	0.456702	−	0.245434i
$213$	1.66196	−	10.4932i	0.113876	−	0.718984i
$214$	−13.5516	+	16.2230i	−0.926368	+	1.10898i
$215$	−5.27356	−	0.160015i	−0.359654	−	0.0109129i
$216$	11.4956	+	9.18311i	0.782175	+	0.624831i
$217$	−13.9890	−	10.1636i	−0.949634	−	0.689949i
$218$	12.8430	+	20.4522i	0.869841	+	1.38520i
$219$	2.30407	−	2.30407i	0.155695	−	0.155695i
$220$	−13.4224	+	6.69683i	−0.904941	+	0.451500i
$221$	9.88701	+	30.4291i	0.665072	+	2.04688i
$222$	−7.65410	−	0.518190i	−0.513709	−	0.0347786i
$223$	0.274262	+	0.538270i	0.0183660	+	0.0360452i	0.900007	−	0.435875i	$-0.143561\pi$
$223$	0.274262	+	0.538270i	0.0183660	+	0.0360452i	−0.881641	+	0.471920i	$0.843561\pi$
$224$	−17.7449	−	18.6114i	−1.18563	−	1.24353i
$225$	−0.0178735	−	0.0280297i	−0.00119156	−	0.00186865i
$226$	−24.7154	−	9.92204i	−1.64405	−	0.660005i
$227$	1.35004	+	4.15500i	0.0896054	+	0.275777i	0.985810	−	0.167863i	$-0.0536868\pi$
$227$	1.35004	+	4.15500i	0.0896054	+	0.275777i	−0.896205	+	0.443640i	$0.853687\pi$
$228$	−0.777585	−	1.02243i	−0.0514968	−	0.0677123i
$229$	15.8132	+	2.50456i	1.04496	+	0.165506i	0.655236	−	0.755424i	$-0.272569\pi$
$229$	15.8132	+	2.50456i	1.04496	+	0.165506i	0.389727	+	0.920930i	$0.372569\pi$
$230$	−2.22148	+	8.52166i	−0.146480	+	0.561902i
$231$	−4.12677	−	26.0554i	−0.271521	−	1.71432i
$232$	7.52741	+	4.27951i	0.494199	+	0.280963i
$233$	25.5725	+	8.30902i	1.67531	+	0.544342i	0.983993	−	0.178208i	$-0.0570299\pi$
$233$	25.5725	+	8.30902i	1.67531	+	0.544342i	0.691319	+	0.722550i	$0.257030\pi$
$234$	−0.0442802	−	0.0264729i	−0.00289469	−	0.00173059i
$235$	−8.12120	+	7.64287i	−0.529768	+	0.498566i
$236$	−2.73235	+	2.85463i	−0.177861	+	0.185821i
$237$	9.31522	+	9.31522i	0.605088	+	0.605088i
$238$	24.6571	+	28.2382i	1.59828	+	1.83041i
$239$	10.7221	−	21.0433i	0.693556	−	1.36118i	−0.228278	−	0.973596i	$-0.573310\pi$
$239$	10.7221	−	21.0433i	0.693556	−	1.36118i	0.921834	−	0.387585i	$-0.126690\pi$
$240$	−2.62589	−	15.2503i	−0.169501	−	0.984405i
$241$	5.83821	−	8.03560i	0.376072	−	0.517619i	−0.578467	−	0.815706i	$-0.696349\pi$
$241$	5.83821	−	8.03560i	0.376072	−	0.517619i	0.954539	+	0.298087i	$0.0963487\pi$
$242$	0.304025	+	0.181761i	0.0195434	+	0.0116840i
$243$	0.0690951			0.00443245
$244$	−8.19929	−	1.11531i	−0.524906	−	0.0714006i
$245$	−30.3099	+	3.86236i	−1.93643	+	0.246757i
$246$	−2.61976	−	15.4464i	−0.167030	−	0.984827i
$247$	1.44024	+	1.44024i	0.0916403	+	0.0916403i
$248$	−0.491651	+	10.7475i	−0.0312199	+	0.682464i
$249$	11.1469	−	11.1469i	0.706409	−	0.706409i
$250$	−2.49716	+	15.6129i	−0.157934	+	0.987450i
$251$	2.22455	+	1.61623i	0.140412	+	0.102016i	0.655774	−	0.754957i	$-0.272342\pi$
$251$	2.22455	+	1.61623i	0.140412	+	0.102016i	−0.515362	+	0.856973i	$0.672342\pi$
$252$	−0.0598961	−	0.00814739i	−0.00377310	−	0.000513238i
$253$	8.88368	−	2.88648i	0.558512	−	0.181472i
$254$	−2.01606	+	29.7788i	−0.126499	+	1.86849i
$255$	2.85168	+	22.3786i	0.178579	+	1.40140i
$256$	−3.59502	+	15.5909i	−0.224689	+	0.974431i
$257$	−8.83581	+	6.41959i	−0.551163	+	0.400443i	−0.828214	−	0.560412i	$-0.810643\pi$
$257$	−8.83581	+	6.41959i	−0.551163	+	0.400443i	0.277051	+	0.960855i	$0.410643\pi$
$258$	−5.59855	+	1.40906i	−0.348551	+	0.0877240i
$259$	12.6995	−	6.47073i	0.789110	−	0.402072i
$260$	7.38506	+	23.3998i	0.458002	+	1.45120i
$261$	0.0201035	−	0.00318409i	0.00124438	−	0.000197090i
$262$	23.0581	−	9.84792i	1.42453	−	0.608407i
$263$	−1.46151	−	2.01160i	−0.0901205	−	0.124040i	0.761576	−	0.648076i	$-0.224426\pi$
$263$	−1.46151	−	2.01160i	−0.0901205	−	0.124040i	−0.851696	+	0.524035i	$0.824426\pi$
$264$	−12.1246	+	11.0638i	−0.746216	+	0.680930i
$265$	−7.63297	+	3.60190i	−0.468889	+	0.221263i
$266$	2.21470	+	0.889097i	0.135792	+	0.0545140i
$267$	6.93563	+	3.53388i	0.424454	+	0.216270i
$268$	9.39146	+	17.4755i	0.573675	+	1.06749i
$269$	−4.96767	−	1.61409i	−0.302884	−	0.0984130i	0.153632	−	0.988128i	$-0.450903\pi$
$269$	−4.96767	−	1.61409i	−0.302884	−	0.0984130i	−0.456516	+	0.889715i	$0.650903\pi$
$270$	−12.2990	−	10.9238i	−0.748496	−	0.664804i
$271$	−23.1925	+	7.53571i	−1.40885	+	0.457762i	−0.912041	−	0.410100i	$-0.865494\pi$
$271$	−23.1925	+	7.53571i	−1.40885	+	0.457762i	−0.496806	+	0.867862i	$0.665494\pi$
$272$	6.23038	−	22.4778i	0.377772	−	1.36291i
$273$	−43.1527			−2.61172
$274$	1.94436	−	8.50791i	0.117463	−	0.513982i
$275$	15.3771	−	6.69382i	0.927273	−	0.403652i
$276$	0.210863	+	9.63399i	0.0126925	+	0.579898i
$277$	0.470196	−	2.96870i	0.0282514	−	0.178372i	−0.969528	−	0.244981i	$-0.921218\pi$
$277$	0.470196	−	2.96870i	0.0282514	−	0.178372i	0.997779	+	0.0666094i	$0.0212181\pi$
$278$	−1.70784	−	19.0350i	−0.102430	−	1.14164i
$279$	0.0148652	+	0.0204601i	0.000889954	+	0.00122492i
$280$	18.7263	+	21.8154i	1.11911	+	1.30372i
$281$	4.24760	+	8.33639i	0.253391	+	0.497308i	0.982303	−	0.187300i	$-0.0599736\pi$
$281$	4.24760	+	8.33639i	0.253391	+	0.497308i	−0.728912	+	0.684608i	$0.759974\pi$
$282$	−6.26175	+	10.4738i	−0.372882	+	0.623705i
$283$	9.01667	−	1.42810i	0.535985	−	0.0848917i	0.117427	−	0.993082i	$-0.462535\pi$
$283$	9.01667	−	1.42810i	0.535985	−	0.0848917i	0.418559	+	0.908190i	$0.362535\pi$
$284$	6.99955	−	10.0913i	0.415347	−	0.598806i
$285$	0.808518	+	1.18693i	0.0478924	+	0.0703078i
$286$	16.6853	−	19.9745i	0.986624	−	1.18112i
$287$	18.9035	+	22.1339i	1.11584	+	1.30652i
$288$	0.0162715	+	0.0339087i	0.000958810	+	0.00199809i
$289$	−5.25459	+	16.1720i	−0.309094	+	0.951292i
$290$	−8.15471	−	5.21737i	−0.478861	−	0.306374i
$291$	15.0694	−	20.7412i	0.883382	−	1.21587i
$292$	3.55603	−	1.24209i	0.208101	−	0.0726878i
$293$	−5.21729	+	16.0572i	−0.304797	+	0.938069i	0.674956	+	0.737858i	$0.264163\pi$
$293$	−5.21729	+	16.0572i	−0.304797	+	0.938069i	−0.979753	+	0.200211i	$0.935837\pi$
$294$	−30.7473	+	13.1319i	−1.79322	+	0.765870i
$295$	3.21727	−	3.02778i	0.187317	−	0.176284i
$296$	−7.70943	−	4.38299i	−0.448102	−	0.254756i
$297$	−2.72948	+	17.2332i	−0.158380	+	0.999974i
$298$	1.46483	−	21.6367i	0.0848551	−	1.25338i
$299$	−2.39029	−	15.0917i	−0.138234	−	0.872774i
$300$	2.04191	+	17.1804i	0.117890	+	0.991910i
$301$	7.58433	−	7.58433i	0.437154	−	0.437154i
$302$	−2.41185	−	9.58293i	−0.138787	−	0.551435i
$303$	−24.5275	−	12.4974i	−1.40907	−	0.717956i
$304$	−0.296235	−	1.45504i	−0.0169902	−	0.0834522i
$305$	9.08951	+	1.72372i	0.520464	+	0.0987000i
$306$	−0.0215355	−	0.0504236i	−0.00123110	−	0.00288253i
$307$	7.20162	+	3.66941i	0.411018	+	0.209424i	0.647259	−	0.762270i	$-0.275915\pi$
$307$	7.20162	+	3.66941i	0.411018	+	0.209424i	−0.236241	+	0.971695i	$0.575915\pi$
$308$	8.78658	−	29.2017i	0.500662	−	1.66392i
$309$	−2.87707	+	5.64656i	−0.163671	+	0.321222i
$310$	1.17609	−	11.9710i	0.0667977	−	0.679905i
$311$	−19.1762	−	3.03721i	−1.08738	−	0.172225i	−0.413091	−	0.910690i	$-0.635551\pi$
$311$	−19.1762	−	3.03721i	−1.08738	−	0.172225i	−0.674292	+	0.738465i	$0.735551\pi$
$312$	14.7727	+	22.4204i	0.836342	+	1.26930i
$313$	−9.81741	−	7.13276i	−0.554913	−	0.403168i	0.274681	−	0.961535i	$-0.411428\pi$
$313$	−9.81741	−	7.13276i	−0.554913	−	0.403168i	−0.829593	+	0.558368i	$0.811428\pi$
$314$	−0.697609	−	7.77529i	−0.0393684	−	0.438785i
$315$	0.0663992	+	0.0125918i	0.00374117	+	0.000709470i
$316$	5.02168	+	14.3768i	0.282492	+	0.808757i
$317$	−17.9031	+	13.0073i	−1.00554	+	0.730566i	−0.963268	−	0.268541i	$-0.913459\pi$
$317$	−17.9031	+	13.0073i	−1.00554	+	0.730566i	−0.0422689	+	0.999106i	$0.513459\pi$
$318$	−6.95664	+	6.07443i	−0.390109	+	0.340637i
$319$			10.2684i			0.574919i
$320$	4.92367	−	17.1976i	0.275242	−	0.961375i
$321$	11.7404	−	23.0418i	0.655285	−	1.28607i
$322$	−9.52084	−	15.1617i	−0.530576	−	0.844928i
$323$	0.338636	+	2.13806i	0.0188422	+	0.118965i
$324$	−16.1771	−	7.80156i	−0.898727	−	0.433420i
$325$	−6.88002	−	26.5571i	−0.381635	−	1.47312i
$326$	−17.9451	+	11.2687i	−0.993889	+	0.624117i
$327$	−20.8916	−	20.8916i	−1.15531	−	1.15531i
$328$	5.02852	−	17.3987i	0.277653	−	0.960681i
$329$		−	22.6716i		−	1.24992i
$330$	14.1828	−	11.6453i	0.780739	−	0.641054i
$331$	−22.7143	+	22.7143i	−1.24849	+	1.24849i	−0.292108	+	0.956385i	$0.594357\pi$
$331$	−22.7143	+	22.7143i	−1.24849	+	1.24849i	−0.956385	+	0.292108i	$0.905643\pi$
$332$	17.2038	−	6.00914i	0.944182	−	0.329794i
$333$	−0.0205897	+	0.00326108i	−0.00112831	+	0.000178706i
$334$	5.18115	−	22.6711i	0.283500	−	1.24050i
$335$	−9.46589	−	20.0597i	−0.517177	−	1.09598i
$336$	26.2360	+	17.3602i	1.43129	+	0.947074i
$337$	−6.24735	−	6.24735i	−0.340315	−	0.340315i	0.516171	−	0.856486i	$-0.327357\pi$
$337$	−6.24735	−	6.24735i	−0.340315	−	0.340315i	−0.856486	+	0.516171i	$0.827357\pi$
$338$	−15.9101	−	18.2208i	−0.865397	−	0.991083i
$339$	32.1809	+	5.09696i	1.74783	+	0.276829i
$340$	−8.26795	+	24.7331i	−0.448393	+	1.34134i
$341$	−11.3679	+	5.79224i	−0.615607	+	0.313668i
$342$	−0.00267883	−	0.00223771i	−0.000144854	−	0.000121001i
$343$	17.8076	−	24.5101i	0.961523	−	1.32342i
$344$	−6.53690	−	1.34412i	−0.352446	−	0.0724699i
$345$	0.326754	−	10.7688i	0.0175919	−	0.579770i
$346$	11.0552	−	6.94217i	0.594332	−	0.373213i
$347$	−3.20117	−	9.85220i	−0.171848	−	0.528894i	0.827627	−	0.561278i	$-0.189690\pi$
$347$	−3.20117	−	9.85220i	−0.171848	−	0.528894i	−0.999476	+	0.0323839i	$0.989690\pi$
$348$	−10.1439	−	3.05223i	−0.543771	−	0.163616i
$349$	9.16956	+	28.2210i	0.490835	+	1.51064i	0.823348	+	0.567537i	$0.192104\pi$
$349$	9.16956	+	28.2210i	0.490835	+	1.51064i	−0.332512	+	0.943099i	$0.607896\pi$
$350$	−19.6351	−	25.4498i	−1.04954	−	1.36035i
$351$	27.1446	+	8.81982i	1.44887	+	0.470767i
$352$	−18.1800	+	5.43166i	−0.968997	+	0.289508i
$353$	1.60866	−	3.15716i	0.0856201	−	0.168039i	−0.844226	−	0.535987i	$-0.819940\pi$
$353$	1.60866	−	3.15716i	0.0856201	−	0.168039i	0.929846	+	0.367948i	$0.119940\pi$
$354$	2.48064	−	4.14927i	0.131845	−	0.220531i
$355$	−8.40394	+	10.8585i	−0.446035	+	0.576312i
$356$	5.44705	+	7.16223i	0.288693	+	0.379597i
$357$	−37.1036	−	26.9574i	−1.96373	−	1.42673i
$358$	−25.2193	−	1.70737i	−1.33288	−	0.0902376i
$359$	1.28820	−	0.935930i	0.0679884	−	0.0493965i	−0.553272	−	0.833001i	$-0.686621\pi$
$359$	1.28820	−	0.935930i	0.0679884	−	0.0493965i	0.621260	+	0.783604i	$0.286621\pi$
$360$	−0.0161886	−	0.0388089i	−0.000853215	−	0.00204541i
$361$	−11.0869	−	15.2598i	−0.583522	−	0.803149i
$362$	−12.8690	+	32.0562i	−0.676380	+	1.68484i
$363$	−0.412132	−	0.133910i	−0.0216313	−	0.00702845i
$364$	−44.9317	−	21.6688i	−2.35506	−	1.13575i
$365$	−4.04282	+	1.17930i	−0.211611	+	0.0617272i
$366$	10.0828	−	0.904641i	0.527035	−	0.0472863i
$367$	−10.9496	−	21.4899i	−0.571566	−	1.12176i	−0.978102	−	0.208126i	$-0.933263\pi$
$367$	−10.9496	−	21.4899i	−0.571566	−	1.12176i	0.406536	−	0.913635i	$-0.366737\pi$
$368$	−4.61806	+	10.1370i	−0.240733	+	0.528429i
$369$	−0.0162911	−	0.0393320i	−0.000848079	−	0.00204754i
$370$	8.35189	+	5.34353i	0.434194	+	0.277797i
$371$	5.30225	−	16.3186i	0.275279	−	0.847222i
$372$	−2.34297	−	12.9518i	−0.121478	−	0.671521i
$373$	−2.48085	−	15.6635i	−0.128453	−	0.811023i	−0.964831	−	0.262870i	$-0.915331\pi$
$373$	−2.48085	−	15.6635i	−0.128453	−	0.811023i	0.836378	−	0.548153i	$-0.184669\pi$
$374$	26.8244	−	6.75122i	1.38706	−	0.349097i
$375$	−1.27727	−	19.3012i	−0.0659578	−	0.996711i
$376$	−11.7792	+	7.76129i	−0.607467	+	0.400258i
$377$	16.5902	+	2.62763i	0.854440	+	0.135330i
$378$	33.3080	−	2.98844i	1.71318	−	0.153709i
$379$	−4.04407	+	2.93819i	−0.207730	+	0.150924i	−0.686786	−	0.726860i	$-0.740979\pi$
$379$	−4.04407	+	2.93819i	−0.207730	+	0.150924i	0.479056	+	0.877784i	$0.340979\pi$
$380$	0.245842	+	1.64185i	0.0126114	+	0.0842253i
$381$	−5.71211	−	36.0649i	−0.292640	−	1.84766i
$382$	−13.2098	−	21.0362i	−0.675871	−	1.07631i
$383$		−	22.8153i		−	1.16581i	−0.812542	−	0.582903i	$-0.801917\pi$
$383$		−	22.8153i		−	1.16581i	0.812542	−	0.582903i	$-0.198083\pi$
$384$	0.0380933	−	19.5742i	0.00194394	−	0.998889i
$385$	−11.5144	+	32.0913i	−0.586826	+	1.63552i
$386$	6.96654	−	6.08307i	0.354588	−	0.309620i
$387$	−0.0139777	+	0.00712199i	−0.000710526	+	0.000362031i
$388$	26.1056	−	14.0293i	1.32531	−	0.712230i
$389$	−3.92738	−	12.0872i	−0.199126	−	0.612847i	−0.999904	−	0.0138854i	$-0.995580\pi$
$389$	−3.92738	−	12.0872i	−0.199126	−	0.612847i	0.800777	−	0.598962i	$-0.204420\pi$
$390$	−15.1856	−	25.8946i	−0.768952	−	1.31123i
$391$	7.37249	−	14.4693i	0.372843	−	0.731746i
$392$	−38.6090	−	1.76620i	−1.95005	−	0.0892065i
$393$	−24.8158	+	18.0297i	−1.25179	+	0.909480i
$394$	−10.4614	−	4.19976i	−0.527039	−	0.211581i
$395$	−4.76781	−	16.3449i	−0.239895	−	0.822399i
$396$	−0.0254204	+	0.0366486i	−0.00127742	+	0.00184166i
$397$	2.83829	−	8.73535i	0.142450	−	0.438415i	−0.854225	−	0.519904i	$-0.825968\pi$
$397$	2.83829	−	8.73535i	0.142450	−	0.438415i	0.996674	+	0.0814895i	$0.0259677\pi$
$398$	−4.88394	−	19.4052i	−0.244810	−	0.972693i
$399$	−2.88367	−	0.456729i	−0.144364	−	0.0228651i
$400$	−6.50088	+	18.9140i	−0.325044	+	0.945699i
$401$			31.0429i			1.55021i	0.631833	+	0.775105i	$0.282303\pi$
$401$			31.0429i			1.55021i	−0.631833	+	0.775105i	$0.717697\pi$
$402$	−15.9638	−	18.2823i	−0.796200	−	0.911836i
$403$	6.44931	+	19.8489i	0.321263	+	0.988746i
$404$	−19.2632	−	25.3289i	−0.958380	−	1.26016i
$405$	17.6066	+	9.65452i	0.874880	+	0.479737i
$406$	19.0857	−	4.80353i	0.947208	−	0.238395i
$407$		−	10.5167i		−	0.521292i
$408$	−1.30403	+	28.5060i	−0.0645591	+	1.41126i
$409$			10.9610i			0.541985i	0.962582	+	0.270992i	$0.0873518\pi$
$409$			10.9610i			0.541985i	−0.962582	+	0.270992i	$0.912648\pi$
$410$	−6.62968	+	19.1324i	−0.327416	+	0.944880i
$411$			10.6768i			0.526649i
$412$	−5.83104	+	4.43465i	−0.287275	+	0.218479i
$413$			8.98151i			0.441951i
$414$	0.00639099	+	0.0253931i	0.000314100	+	0.00124800i
$415$	−19.5589	+	5.70535i	−0.960108	+	0.280065i
$416$	4.12355	+	30.7627i	0.202174	+	1.50826i
$417$	7.22503	+	22.2364i	0.353811	+	1.08892i
$418$	1.32640	−	1.15819i	0.0648766	−	0.0566491i
$419$		−	7.32461i		−	0.357831i	−0.983864	−	0.178915i	$-0.942741\pi$
$419$		−	7.32461i		−	0.357831i	0.983864	−	0.178915i	$-0.0572588\pi$
$420$	−28.2797	−	20.9138i	−1.37991	−	1.02049i
$421$	22.4897	+	3.56201i	1.09608	+	0.173602i	0.678183	−	0.734893i	$-0.262768\pi$
$421$	22.4897	+	3.56201i	1.09608	+	0.173602i	0.417896	+	0.908495i	$0.362768\pi$
$422$	15.4256	−	3.88236i	0.750908	−	0.188990i
$423$	−0.0102468	+	0.0315363i	−0.000498214	+	0.00153335i
$424$	−10.2936	+	2.83163i	−0.499904	+	0.137516i
$425$	10.6745	−	27.1323i	0.517791	−	1.31611i
$426$	−5.59745	+	13.9430i	−0.271198	+	0.675542i
$427$	−15.2159	+	11.0550i	−0.736351	+	0.534990i
$428$	23.7946	−	18.0964i	1.15016	−	0.874722i
$429$	−14.4553	+	28.3701i	−0.697908	+	1.36972i
$430$	7.22007	+	1.88218i	0.348183	+	0.0907666i
$431$	0.738065	+	2.27153i	0.0355513	+	0.109416i	0.967257	−	0.253797i	$-0.0816797\pi$
$431$	0.738065	+	2.27153i	0.0355513	+	0.109416i	−0.931706	+	0.363213i	$0.881680\pi$
$432$	−12.9552	−	16.2824i	−0.623308	−	0.783389i
$433$	−11.3807	+	5.79877i	−0.546923	+	0.278671i	−0.705541	−	0.708669i	$-0.749296\pi$
$433$	−11.3807	+	5.79877i	−0.546923	+	0.278671i	0.158618	+	0.987340i	$0.449296\pi$
$434$	16.0839	+	18.4198i	0.772050	+	0.884179i
$435$	11.1477	+	3.99978i	0.534490	+	0.191775i
$436$	−11.2623	−	32.2434i	−0.539367	−	1.54418i
$437$		−	1.03380i		−	0.0494532i
$438$	−3.90251	+	2.45060i	−0.186469	+	0.117094i
$439$	−4.05470	−	25.6004i	−0.193520	−	1.22184i	−0.872844	−	0.488000i	$-0.837727\pi$
$439$	−4.05470	−	25.6004i	−0.193520	−	1.22184i	0.679324	−	0.733839i	$-0.262273\pi$
$440$	20.6151	−	5.00362i	0.982786	−	0.238538i
$441$	−0.0735006	+	0.0534013i	−0.00350003	+	0.00254292i
$442$	−4.04345	−	45.0668i	−0.192327	−	2.14361i
$443$	1.50715	+	0.238709i	0.0716069	+	0.0113414i	0.192135	−	0.981368i	$-0.438459\pi$
$443$	1.50715	+	0.238709i	0.0716069	+	0.0113414i	−0.120528	+	0.992710i	$0.538459\pi$
$444$	10.3892	+	3.12603i	0.493049	+	0.148355i
$445$	−5.66374	−	8.31456i	−0.268487	−	0.394148i
$446$	−0.208521	−	0.828509i	−0.00987376	−	0.0392310i
$447$	4.15030	+	26.2040i	0.196303	+	1.23941i
$448$	18.6003	+	31.2500i	0.878783	+	1.47642i
$449$	−11.9737	+	36.8514i	−0.565075	+	1.73912i	0.102652	+	0.994717i	$0.467267\pi$
$449$	−11.9737	+	36.8514i	−0.565075	+	1.73912i	−0.667728	+	0.744406i	$0.732733\pi$
$450$	0.0158101	+	0.0442752i	0.000745295	+	0.00208715i
$451$	20.8838	−	5.01339i	0.983382	−	0.236071i
$452$	30.9482	+	21.4664i	1.45568	+	1.00970i
$453$	5.48840	+	10.7716i	0.257867	+	0.506093i
$454$	−0.552121	−	6.15373i	−0.0259123	−	0.288809i
$455$	48.9022	+	26.8153i	2.29257	+	1.25712i
$456$	0.749888	+	1.65459i	0.0351167	+	0.0774835i
$457$	29.9247	+	9.72311i	1.39982	+	0.454828i	0.909131	−	0.416509i	$-0.136747\pi$
$457$	29.9247	+	9.72311i	1.39982	+	0.454828i	0.490685	+	0.871337i	$0.336747\pi$
$458$	−21.0120	−	8.43530i	−0.981826	−	0.394156i
$459$	17.8298	+	24.5406i	0.832224	+	1.14546i
$460$	5.74766	−	11.0486i	0.267986	−	0.515144i
$461$	17.1200	−	12.4384i	0.797356	−	0.579313i	−0.112781	−	0.993620i	$-0.535976\pi$
$461$	17.1200	−	12.4384i	0.797356	−	0.579313i	0.910137	+	0.414307i	$0.135976\pi$
$462$	−2.51997	+	37.2220i	−0.117239	+	1.73172i
$463$	−24.7162	−	17.9574i	−1.14866	−	0.834550i	−0.160357	−	0.987059i	$-0.551265\pi$
$463$	−24.7162	−	17.9574i	−1.14866	−	0.834550i	−0.988302	+	0.152509i	$0.951265\pi$
$464$	−9.02944	−	8.27172i	−0.419181	−	0.384005i
$465$	1.86016	+	14.5976i	0.0862628	+	0.676947i
$466$	−32.6381	−	19.5127i	−1.51193	−	0.903906i
$467$	−6.55847	+	12.8717i	−0.303490	+	0.595632i	−0.991506	−	0.130063i	$-0.958482\pi$
$467$	−6.55847	+	12.8717i	−0.303490	+	0.595632i	0.688016	+	0.725696i	$0.258482\pi$
$468$	0.0527067	+	0.0504489i	0.00243637	+	0.00233200i
$469$	42.8859	+	13.9345i	1.98029	+	0.643434i
$470$	13.6045	−	7.97820i	0.627530	−	0.368007i
$471$	2.95123	+	9.08296i	0.135986	+	0.418521i
$472$	4.66643	−	3.07470i	0.214790	−	0.141524i
$473$	−2.44561	−	7.52680i	−0.112449	−	0.346083i
$474$	−9.90760	−	15.7776i	−0.455071	−	0.724689i
$475$	−0.178675	−	1.84749i	−0.00819819	−	0.0847687i
$476$	−25.0968	−	46.6999i	−1.15031	−	2.14049i
$477$	−0.0147509	+	0.0203029i	−0.000675398	+	0.000929606i
$478$	−21.4125	+	25.6335i	−0.979384	+	1.17245i
$479$	−8.81985	+	4.49394i	−0.402989	+	0.205333i	−0.643724	−	0.765258i	$-0.722612\pi$
$479$	−8.81985	+	4.49394i	−0.402989	+	0.205333i	0.240735	+	0.970591i	$0.422612\pi$
$480$	−1.18477	+	21.8525i	−0.0540770	+	0.997426i
$481$	−16.9914	−	2.69117i	−0.774741	−	0.122707i
$482$	−10.5808	+	9.23896i	−0.481941	+	0.420823i
$483$	15.4874	+	15.4874i	0.704701	+	0.704701i
$484$	−0.361881	−	0.346379i	−0.0164491	−	0.0157445i
$485$	−29.9658	+	14.1405i	−1.36068	+	0.642087i
$486$	−0.0952592	−	0.0217702i	−0.00432105	−	0.000987515i
$487$	−18.8943	+	2.99256i	−0.856181	+	0.135606i	−0.569068	−	0.822291i	$-0.692696\pi$
$487$	−18.8943	+	2.99256i	−0.856181	+	0.135606i	−0.287114	+	0.957897i	$0.592696\pi$
$488$	10.9527	+	4.12104i	0.495805	+	0.186551i
$489$	18.3307	−	18.3307i	0.828941	−	0.828941i
$490$	43.0042	+	4.22498i	1.94273	+	0.190865i
$491$		−	21.2787i		−	0.960295i	−0.877188	−	0.480147i	$-0.840583\pi$
$491$		−	21.2787i		−	0.960295i	0.877188	−	0.480147i	$-0.159417\pi$
$492$	−1.25500	+	22.1209i	−0.0565800	+	0.997288i
$493$	12.6232	+	12.6232i	0.568518	+	0.568518i
$494$	−1.53183	−	2.43940i	−0.0689203	−	0.109754i
$495$	0.0305207	−	0.0394351i	0.00137180	−	0.00177248i
$496$	4.06408	−	14.6623i	0.182483	−	0.658356i
$497$	−4.36673	−	27.5704i	−0.195875	−	1.23670i
$498$	−18.8801	+	11.8558i	−0.846036	+	0.531272i
$499$	−2.89370	+	5.67921i	−0.129540	+	0.254236i	−0.946662	−	0.322228i	$-0.895568\pi$
$499$	−2.89370	+	5.67921i	−0.129540	+	0.254236i	0.817122	+	0.576465i	$0.195568\pi$
$500$	8.36202	−	20.7383i	0.373961	−	0.927445i
$501$			28.4505i			1.27108i
$502$	−2.55768	−	2.92915i	−0.114155	−	0.130734i
$503$	−20.3485	+	14.7841i	−0.907295	+	0.659189i	−0.940329	−	0.340266i	$-0.889483\pi$
$503$	−20.3485	+	14.7841i	−0.907295	+	0.659189i	0.0330341	+	0.999454i	$0.489483\pi$
$504$	0.0800098	+	0.0301043i	0.00356392	+	0.00134095i
$505$	20.0295	+	29.4040i	0.891302	+	1.30846i
$506$	−13.1571	+	1.18047i	−0.584905	+	0.0524785i
$507$	23.9413	+	17.3944i	1.06327	+	0.772512i
$508$	12.1620	−	40.4199i	0.539604	−	1.79334i
$509$	1.77379	+	0.280940i	0.0786217	+	0.0124525i	0.195621	−	0.980679i	$-0.437328\pi$
$509$	1.77379	+	0.280940i	0.0786217	+	0.0124525i	−0.117000	+	0.993132i	$0.537328\pi$
$510$	3.11941	−	31.7511i	0.138130	−	1.40596i
$511$	3.88681	−	7.62829i	0.171942	−	0.337456i
$512$	9.86865	−	20.3620i	0.436137	−	0.899880i
$513$	1.72059	+	0.876682i	0.0759657	+	0.0387065i
$514$	14.2043	−	6.06655i	0.626525	−	0.267584i
$515$	6.76920	−	4.61106i	0.298287	−	0.203188i
$516$	8.16251	−	0.178656i	0.359334	−	0.00786490i
$517$	−14.9051	−	7.59452i	−0.655525	−	0.334006i
$518$	−19.5472	+	4.91969i	−0.858855	+	0.216159i
$519$	−11.2927	+	11.2927i	−0.495695	+	0.495695i
$520$	−2.80885	−	34.5875i	−0.123176	−	1.51676i
$521$	−2.24203	−	14.1556i	−0.0982253	−	0.620170i	−0.986863	−	0.161560i	$-0.948347\pi$
$521$	−2.24203	−	14.1556i	−0.0982253	−	0.620170i	0.888638	−	0.458610i	$-0.151653\pi$
$522$	−0.0287193	−	0.00194433i	−0.00125701	−	8.51010e-5i
$523$	−4.33593	+	27.3760i	−0.189597	+	1.19707i	0.690876	+	0.722973i	$0.257225\pi$
$523$	−4.33593	+	27.3760i	−0.189597	+	1.19707i	−0.880473	+	0.474095i	$0.842775\pi$
$524$	−34.8923	+	6.31198i	−1.52428	+	0.275740i
$525$	30.3542	+	25.0007i	1.32477	+	1.09112i
$526$	1.38113	+	3.23381i	0.0602203	+	0.141001i
$527$	−6.85431	+	21.0954i	−0.298578	+	0.918929i
$528$	20.2017	−	11.4332i	0.879166	−	0.497564i
$529$	8.96057	−	12.3332i	0.389590	−	0.536224i
$530$	11.6582	−	2.56086i	0.506400	−	0.111237i
$531$	0.00405933	−	0.0124933i	0.000176160	−	0.000542165i
$532$	−2.77321	−	1.92357i	−0.120234	−	0.0833973i
$533$	−2.75585	−	35.0242i	−0.119369	−	1.51706i
$534$	−8.44850	−	7.05730i	−0.365602	−	0.305399i
$535$	−27.6230	+	18.8163i	−1.19424	+	0.813499i
$536$	−7.44160	−	27.0520i	−0.321428	−	1.16847i
$537$	30.5429	−	4.83752i	1.31802	−	0.208755i
$538$	6.34021	+	3.79049i	0.273346	+	0.163420i
$539$	−20.8079	−	40.8379i	−0.896261	−	1.75901i
$540$	13.5145	+	18.9355i	0.581570	+	0.814854i
$541$	−22.8867	−	31.5009i	−0.983977	−	1.35433i	−0.934659	−	0.355545i	$-0.884295\pi$
$541$	−22.8867	−	31.5009i	−0.983977	−	1.35433i	−0.0493179	−	0.998783i	$-0.515705\pi$
$542$	34.3491	−	3.08185i	1.47542	−	0.132377i
$543$	6.61081	−	41.7390i	0.283697	−	1.79119i
$544$	−15.6718	+	29.0263i	−0.671924	+	1.24449i
$545$	10.6930	+	36.6572i	0.458036	+	1.57022i
$546$	59.4933	+	13.5964i	2.54608	+	0.581871i
$547$	−28.3024			−1.21012			−0.605061	−	0.796179i	$-0.706851\pi$
$547$	−28.3024			−1.21012			−0.605061	+	0.796179i	$0.706851\pi$
$548$	−5.36127	+	11.1170i	−0.229022	+	0.474893i
$549$	0.0261619	−	0.00850053i	0.00111656	−	0.000362794i
$550$	−23.3090	+	4.38361i	−0.993897	+	0.186918i
$551$	1.08083	+	0.351182i	0.0460448	+	0.0149609i
$552$	2.74472	−	13.3485i	0.116823	−	0.568151i
$553$	30.8407	+	15.7141i	1.31148	+	0.668231i
$554$	−1.58361	+	3.94471i	−0.0672812	+	0.167595i
$555$	−11.4172	−	4.09650i	−0.484634	−	0.173887i
$556$	−3.64290	+	26.7810i	−0.154493	+	1.13577i
$557$	−20.7164	−	28.5137i	−0.877783	−	1.20816i	−0.977030	−	0.213102i	$-0.931643\pi$
$557$	−20.7164	−	28.5137i	−0.877783	−	1.20816i	0.0992469	−	0.995063i	$-0.468357\pi$
$558$	−0.0140476	−	0.0328914i	−0.000594684	−	0.00139240i
$559$	−12.7866	+	2.02520i	−0.540815	+	0.0856567i
$560$	−18.9439	−	35.9763i	−0.800525	−	1.52028i
$561$	−30.1517	+	15.3630i	−1.27300	+	0.648628i
$562$	−3.22945	−	12.8314i	−0.136226	−	0.541262i
$563$	0.126411	−	0.0918430i	0.00532759	−	0.00387072i	−0.585118	−	0.810948i	$-0.698952\pi$
$563$	0.126411	−	0.0918430i	0.00532759	−	0.00387072i	0.590446	+	0.807077i	$0.298952\pi$
$564$	11.9329	−	12.4670i	0.502467	−	0.524954i
$565$	−33.3013	−	25.7735i	−1.40100	−	1.08430i
$566$	−12.8810	−	0.872054i	−0.541427	−	0.0366552i
$567$	−38.8237	+	12.6146i	−1.63044	+	0.529762i
$568$	−12.8296	+	11.7071i	−0.538317	+	0.491220i
$569$	14.2950	+	10.3859i	0.599276	+	0.435399i	0.845622	−	0.533783i	$-0.179230\pi$
$569$	14.2950	+	10.3859i	0.599276	+	0.435399i	−0.246346	+	0.969182i	$0.579230\pi$
$570$	−0.740705	−	1.89113i	−0.0310247	−	0.0792107i
$571$	32.4481	−	32.4481i	1.35791	−	1.35791i	0.481419	−	0.876490i	$-0.340121\pi$
$571$	32.4481	−	32.4481i	1.35791	−	1.35791i	0.876490	−	0.481419i	$-0.159879\pi$
$572$	−29.2970	+	22.2811i	−1.22497	+	0.931619i
$573$	21.4881	+	21.4881i	0.897680	+	0.897680i
$574$	−19.0878	−	36.4713i	−0.796708	−	1.52228i
$575$	−7.06205	+	12.0005i	−0.294508	+	0.500455i
$576$	−0.0117493	−	0.0518756i	−0.000489553	−	0.00216148i
$577$	28.6405			1.19232			0.596160	−	0.802865i	$-0.296692\pi$
$577$	28.6405			1.19232			0.596160	+	0.802865i	$0.296692\pi$
$578$	12.3397	−	20.6402i	0.513265	−	0.858519i
$579$	−6.65056	+	9.15371i	−0.276388	+	0.380415i
$580$	9.59877	+	9.76237i	0.398567	+	0.405360i
$581$	18.8041	−	36.9051i	0.780125	−	1.53108i
$582$	−27.3107	+	23.8473i	−1.13206	+	0.988501i
$583$	−8.95230	−	8.95230i	−0.370766	−	0.370766i
$584$	−5.29394	+	0.592013i	−0.219065	+	0.0244977i
$585$	−0.0559037	−	0.0594024i	−0.00231133	−	0.00245599i
$586$	12.2521	−	20.4937i	0.506131	−	0.846585i
$587$	7.90947	+	2.56994i	0.326459	+	0.106073i	0.467661	−	0.883908i	$-0.345097\pi$
$587$	7.90947	+	2.56994i	0.326459	+	0.106073i	−0.141202	+	0.989981i	$0.545097\pi$
$588$	46.5279	−	8.41685i	1.91878	−	0.347105i
$589$	0.220893	+	1.39466i	0.00910172	+	0.0574660i
$590$	−5.38953	+	3.16062i	−0.221884	+	0.130121i
$591$	13.6214	+	2.15742i	0.560309	+	0.0887442i
$592$	9.24778	+	8.47174i	0.380081	+	0.348186i
$593$	−4.48128	−	13.7920i	−0.184024	−	0.566368i	0.815906	−	0.578185i	$-0.196239\pi$
$593$	−4.48128	−	13.7920i	−0.184024	−	0.566368i	−0.999930	+	0.0118162i	$0.996239\pi$
$594$	9.19281	−	22.8989i	0.377186	−	0.939554i
$595$	25.2957	+	53.6055i	1.03702	+	2.19761i
$596$	−8.83670	+	29.3683i	−0.361965	+	1.20297i
$597$	11.1139	+	21.8122i	0.454860	+	0.892713i
$598$	−1.45960	+	21.5595i	−0.0596876	+	0.881635i
$599$	11.5083	+	35.4190i	0.470218	+	1.44718i	0.852300	+	0.523053i	$0.175207\pi$
$599$	11.5083	+	35.4190i	0.470218	+	1.44718i	−0.382083	+	0.924128i	$0.624793\pi$
$600$	2.59800	−	24.3294i	0.106063	−	0.993244i
$601$	9.49204	−	9.49204i	0.387189	−	0.387189i	−0.486495	−	0.873683i	$-0.661725\pi$
$601$	9.49204	−	9.49204i	0.387189	−	0.387189i	0.873683	+	0.486495i	$0.161725\pi$
$602$	−12.8459	+	8.06664i	−0.523560	+	0.328772i
$603$	−0.0533566	−	0.0387658i	−0.00217285	−	0.00157867i
$604$	0.305802	+	13.9716i	0.0124429	+	0.568496i
$605$	0.383831	+	0.407853i	0.0156049	+	0.0165816i
$606$	29.8777	+	24.9578i	1.21370	+	1.01384i
$607$	2.95857	−	18.6797i	0.120085	−	0.758185i	−0.851998	−	0.523545i	$-0.824609\pi$
$607$	2.95857	−	18.6797i	0.120085	−	0.758185i	0.972082	−	0.234639i	$-0.0753909\pi$
$608$	−0.0500371	+	2.09935i	−0.00202927	+	0.0851400i
$609$	−21.4531	+	10.9309i	−0.869323	+	0.442942i
$610$	−11.9883	−	5.24032i	−0.485393	−	0.212174i
$611$	−16.0843	+	22.1382i	−0.650702	+	0.895615i
$612$	0.0138031	+	0.0763028i	0.000557957	+	0.00308436i
$613$	5.95277	+	11.6830i	0.240430	+	0.471871i	0.979417	−	0.201850i	$-0.0646952\pi$
$613$	5.95277	+	11.6830i	0.240430	+	0.471871i	−0.738986	+	0.673720i	$0.764695\pi$
$614$	−8.77251	−	7.32795i	−0.354030	−	0.295732i
$615$	2.69208	−	24.6250i	0.108555	−	0.992975i
$616$	−21.3145	+	37.4911i	−0.858787	+	1.51056i
$617$	42.1625	−	21.4828i	1.69740	−	0.864867i	0.710464	−	0.703733i	$-0.248485\pi$
$617$	42.1625	−	21.4828i	1.69740	−	0.864867i	0.986933	−	0.161133i	$-0.0515149\pi$
$618$	5.74561	−	6.87824i	0.231123	−	0.276684i
$619$	0.445971	+	0.324017i	0.0179251	+	0.0130233i	0.596712	−	0.802456i	$-0.296474\pi$
$619$	0.445971	+	0.324017i	0.0179251	+	0.0130233i	−0.578787	+	0.815479i	$0.696474\pi$
$620$	−5.39320	+	16.1334i	−0.216596	+	0.647934i
$621$	−6.57672	−	12.9075i	−0.263915	−	0.517962i
$622$	25.4807	+	10.2293i	1.02168	+	0.410156i
$623$	20.2004	+	3.19943i	0.809312	+	0.128182i
$624$	−13.3026	−	35.5648i	−0.532530	−	1.42373i
$625$	−10.5464	+	22.6666i	−0.421858	+	0.906662i
$626$	11.2876	+	12.9269i	0.451143	+	0.516664i
$627$	−1.26624	+	1.74283i	−0.0505688	+	0.0696020i
$628$	−1.48803	+	10.9393i	−0.0593788	+	0.436527i
$629$	−12.9284	−	12.9284i	−0.515489	−	0.515489i
$630$	−0.0875751	−	0.0382807i	−0.00348907	−	0.00152514i
$631$	15.8804	−	5.15984i	0.632187	−	0.205410i	0.0246435	−	0.999696i	$-0.492155\pi$
$631$	15.8804	−	5.15984i	0.632187	−	0.205410i	0.607544	+	0.794286i	$0.292155\pi$
$632$	−2.39347	−	21.4030i	−0.0952070	−	0.851367i
$633$	−17.3390	+	8.83468i	−0.689165	+	0.351147i
$634$	28.7807	−	12.2920i	1.14303	−	0.488178i
$635$	−15.9377	+	44.4195i	−0.632469	+	1.76274i
$636$	11.5048	−	6.18276i	0.456195	−	0.245162i
$637$	−71.3049	+	23.1684i	−2.82520	+	0.917964i
$638$	3.23531	−	14.1567i	0.128087	−	0.560469i
$639$	−0.00638673	+	0.0403242i	−0.000252655	+	0.00159520i
$640$	−12.2067	+	22.1585i	−0.482510	+	0.875890i
$641$	−11.4602	+	1.81512i	−0.452651	+	0.0716929i	−0.378598	−	0.925561i	$-0.623594\pi$
$641$	−11.4602	+	1.81512i	−0.452651	+	0.0716929i	−0.0740536	+	0.997254i	$0.523594\pi$
$642$	−23.4460	+	28.0679i	−0.925341	+	1.10775i
$643$	3.62274	−	11.1496i	0.142867	−	0.439699i	−0.853864	−	0.520497i	$-0.825747\pi$
$643$	3.62274	−	11.1496i	0.142867	−	0.439699i	0.996730	+	0.0807980i	$0.0257469\pi$
$644$	8.34901	+	23.9027i	0.328997	+	0.941900i
$645$	−9.12395	−	0.276846i	−0.359255	−	0.0109008i
$646$	0.206784	−	3.05437i	0.00813582	−	0.120173i
$647$	8.26066	−	8.26066i	0.324760	−	0.324760i	−0.525830	−	0.850590i	$-0.676245\pi$
$647$	8.26066	−	8.26066i	0.324760	−	0.324760i	0.850590	+	0.525830i	$0.176245\pi$
$648$	19.8448	+	15.8528i	0.779576	+	0.622755i
$649$	5.90476	+	3.00862i	0.231782	+	0.118099i
$650$	1.11778	+	38.7812i	0.0438429	+	1.52112i
$651$	−24.2028	−	17.5843i	−0.948581	−	0.689184i
$652$	28.2909	−	9.88176i	1.10796	−	0.387000i
$653$		−	45.1969i		−	1.76869i	−0.466831	−	0.884347i	$-0.654604\pi$
$653$		−	45.1969i		−	1.76869i	0.466831	−	0.884347i	$-0.345396\pi$
$654$	22.2202	+	35.3850i	0.868877	+	1.38366i
$655$	39.3260	−	5.01127i	1.53659	−	0.195807i
$656$	−12.4146	+	22.4027i	−0.484707	+	0.874677i
$657$	−0.00885429	+	0.00885429i	−0.000345439	+	0.000345439i
$658$	−7.14325	+	31.2566i	−0.278473	+	1.21851i
$659$	−34.4536	−	34.4536i	−1.34212	−	1.34212i	−0.893947	−	0.448173i	$-0.852075\pi$
$659$	−34.4536	−	34.4536i	−1.34212	−	1.34212i	−0.448173	−	0.893947i	$-0.647925\pi$
$660$	−23.2226	+	11.5864i	−0.903937	+	0.450999i
$661$	−15.6989	+	21.6077i	−0.610616	+	0.840441i	−0.996628	−	0.0820528i	$-0.973852\pi$
$661$	−15.6989	+	21.6077i	−0.610616	+	0.840441i	0.386012	+	0.922494i	$0.373852\pi$
$662$	38.4723	−	24.1588i	1.49527	−	0.938959i
$663$	17.1058	+	52.6463i	0.664335	+	2.04461i
$664$	−25.6117	+	2.86411i	−0.993927	+	0.111149i
$665$	2.98407	+	2.30951i	0.115717	+	0.0895591i
$666$	0.0294138	+	0.00199134i	0.00113976	+	7.71630e-5i
$667$	−5.01114	−	6.89724i	−0.194032	−	0.267062i
$668$	−14.2862	+	29.6234i	−0.552749	+	1.14616i
$669$	0.474509	+	0.931277i	0.0183456	+	0.0360053i
$670$	6.73002	+	30.6381i	0.260003	+	1.18365i
$671$	2.17093	+	13.7067i	0.0838077	+	0.529141i
$672$	−30.7010	−	32.2002i	−1.18432	−	1.24215i
$673$	−17.1487	+	12.4593i	−0.661035	+	0.480270i	−0.867012	−	0.498287i	$-0.833963\pi$
$673$	−17.1487	+	12.4593i	−0.661035	+	0.480270i	0.205977	+	0.978557i	$0.433963\pi$
$674$	6.64464	+	10.5814i	0.255942	+	0.407581i
$675$	−13.9841	−	21.9303i	−0.538247	−	0.844098i
$676$	16.1939	+	30.1334i	0.622841	+	1.15898i
$677$	−0.618779	+	1.21442i	−0.0237816	+	0.0466740i	−0.902592	−	0.430498i	$-0.858338\pi$
$677$	−0.618779	+	1.21442i	−0.0237816	+	0.0466740i	0.878810	+	0.477172i	$0.158338\pi$
$678$	−42.7609	−	17.1664i	−1.64222	−	0.659273i
$679$	20.8158	−	64.0645i	0.798837	−	2.45857i
$680$	19.1916	−	31.4937i	0.735962	−	1.20773i
$681$	2.33575	+	7.18869i	0.0895060	+	0.275471i
$682$	17.4976	−	4.40383i	0.670017	−	0.168631i
$683$			7.94393i			0.303966i	0.988383	+	0.151983i	$0.0485659\pi$
$683$			7.94393i			0.303966i	−0.988383	+	0.151983i	$0.951434\pi$
$684$	0.00298817	+	0.00392909i	0.000114255	+	0.000150233i
$685$	6.63463	−	12.0994i	0.253496	−	0.462293i
$686$	−32.2734	+	28.1806i	−1.23220	+	1.07594i
$687$	27.3588	+	4.33321i	1.04380	+	0.165322i
$688$	8.58872	+	3.91271i	0.327442	+	0.149171i
$689$	−16.7548	+	12.1730i	−0.638305	+	0.463756i
$690$	−3.84345	+	14.7436i	−0.146318	+	0.561279i
$691$	−23.4913	+	11.9694i	−0.893650	+	0.455337i	−0.839603	−	0.543201i	$-0.817212\pi$
$691$	−23.4913	+	11.9694i	−0.893650	+	0.455337i	−0.0540472	+	0.998538i	$0.517212\pi$
$692$	−17.4288	+	6.08772i	−0.662543	+	0.231420i
$693$	0.0158587	+	0.100128i	0.000602422	+	0.00380354i
$694$	1.30917	+	14.5915i	0.0496955	+	0.553887i
$695$	5.63013	−	29.6887i	0.213563	−	1.12616i
$696$	13.0234	+	7.40410i	0.493651	+	0.280652i
$697$	19.5099	−	31.8361i	0.738991	−	1.20588i
$698$	−3.75004	−	41.7965i	−0.141941	−	1.58202i
$699$	44.2438	+	14.3757i	1.67345	+	0.543738i
$700$	19.0517	+	41.2734i	0.720085	+	1.55999i
$701$	−11.6754	−	8.48264i	−0.440972	−	0.320385i	0.345049	−	0.938585i	$-0.387862\pi$
$701$	−11.6754	−	8.48264i	−0.440972	−	0.320385i	−0.786021	+	0.618200i	$0.787862\pi$
$702$	−34.6445	−	20.7122i	−1.30757	−	0.781732i
$703$	−1.10696	−	0.359674i	−0.0417499	−	0.0135654i
$704$	26.7756	−	1.76039i	1.00914	−	0.0663473i
$705$	−14.0507	+	13.2232i	−0.529181	+	0.498013i
$706$	−3.21255	+	3.84584i	−0.120906	+	0.144740i
$707$	−71.4377	−	11.3146i	−2.68669	−	0.425530i
$708$	−4.72732	+	4.93888i	−0.177663	+	0.185615i
$709$	41.9172	−	6.63903i	1.57423	−	0.249334i	0.692619	−	0.721304i	$-0.256457\pi$
$709$	41.9172	−	6.63903i	1.57423	−	0.249334i	0.881615	+	0.471970i	$0.156457\pi$
$710$	15.0075	−	12.3225i	0.563222	−	0.462454i
$711$	−0.0357973	−	0.0357973i	−0.00134250	−	0.00134250i
$712$	−5.25303	−	11.5906i	−0.196866	−	0.434375i
$713$	4.80909	−	9.43837i	0.180102	−	0.353470i
$714$	42.6600	+	48.8557i	1.59651	+	1.82838i
$715$	34.0106	−	23.1674i	1.27192	−	0.866413i
$716$	34.2312	+	10.2999i	1.27928	+	0.384925i
$717$	18.5507	−	36.4077i	0.692787	−	1.35967i
$718$	−2.07088	+	0.884458i	−0.0772847	+	0.0330077i
$719$	6.47131	+	3.29730i	0.241339	+	0.122968i	0.570477	−	0.821313i	$-0.306758\pi$
$719$	6.47131	+	3.29730i	0.241339	+	0.122968i	−0.329138	+	0.944282i	$0.606758\pi$
$720$	0.0100910	+	0.0586053i	0.000376070	+	0.00218409i
$721$	−2.60478	+	16.4459i	−0.0970069	+	0.612477i
$722$	10.4772	+	24.5315i	0.389921	+	0.912967i
$723$	10.1009	−	13.9026i	0.375655	−	0.517045i
$724$	27.8422	−	40.1402i	1.03475	−	1.49180i
$725$	−10.1475	−	11.4599i	−0.376867	−	0.425611i
$726$	0.526002	+	0.314470i	0.0195218	+	0.0116711i
$727$	24.6560	+	33.9361i	0.914441	+	1.25862i	0.965627	+	0.259931i	$0.0837000\pi$
$727$	24.6560	+	33.9361i	0.914441	+	1.25862i	−0.0511857	+	0.998689i	$0.516300\pi$
$728$	55.1187	+	44.0309i	2.04283	+	1.63189i
$729$	27.0596			1.00221
$730$	5.94528	−	0.352064i	0.220045	−	0.0130305i
$731$	−12.2593	−	6.24643i	−0.453427	−	0.231033i
$732$	−14.1858	−	1.92964i	−0.524324	−	0.0713214i
$733$	−12.2061	+	1.93326i	−0.450843	+	0.0714066i	−0.377727	−	0.925917i	$-0.623294\pi$
$733$	−12.2061	+	1.93326i	−0.450843	+	0.0714066i	−0.0731160	+	0.997323i	$0.523294\pi$
$734$	8.32498	+	33.0773i	0.307281	+	1.22091i
$735$	−52.4401	+	6.68239i	−1.93428	+	0.246484i
$736$	9.56071	−	12.5206i	0.352412	−	0.461514i
$737$	23.5269	−	23.5269i	0.866624	−	0.866624i
$738$	0.0100674	+	0.0593588i	0.000370587	+	0.00218503i
$739$	11.2656			0.414413			0.207206	−	0.978297i	$-0.433563\pi$
$739$	11.2656			0.414413			0.207206	+	0.978297i	$0.433563\pi$
$740$	−9.83088	−	9.99843i	−0.361390	−	0.367550i
$741$	2.49180	+	2.49180i	0.0915387	+	0.0915387i
$742$	−12.4517	+	20.8274i	−0.457114	+	0.764598i
$743$	4.67394	+	29.5101i	0.171470	+	1.08262i	0.911878	+	0.410462i	$0.134633\pi$
$743$	4.67394	+	29.5101i	0.171470	+	1.08262i	−0.740407	+	0.672158i	$0.765367\pi$
$744$	−0.850621	+	18.5945i	−0.0311853	+	0.681708i
$745$	11.5800	−	32.2743i	0.424259	−	1.18244i
$746$	−1.51490	+	22.3764i	−0.0554646	+	0.819258i
$747$	−0.0428364	+	0.0428364i	−0.00156730	+	0.00156730i
$748$	−39.1091	+	0.855997i	−1.42997	+	0.0312983i
$749$	10.6293	−	67.1105i	0.388385	−	2.45217i
$750$	−4.32042	+	27.0124i	−0.157759	+	0.986355i
$751$	24.2120	+	47.5187i	0.883508	+	1.73398i	0.647228	+	0.762297i	$0.275928\pi$
$751$	24.2120	+	47.5187i	0.883508	+	1.73398i	0.236280	+	0.971685i	$0.424072\pi$
$752$	18.6850	−	6.98891i	0.681373	−	0.254859i
$753$	3.84876	+	2.79629i	0.140257	+	0.101902i
$754$	−22.0445	−	8.84981i	−0.802815	−	0.322291i
$755$	0.473872	−	15.6173i	0.0172460	−	0.568371i
$756$	−46.8623	−	6.37447i	−1.70437	−	0.231837i
$757$	−15.5173	+	5.04189i	−0.563988	+	0.183251i	−0.577115	−	0.816663i	$-0.695821\pi$
$757$	−15.5173	+	5.04189i	−0.563988	+	0.183251i	0.0131270	+	0.999914i	$0.495821\pi$
$758$	6.50118	−	2.77660i	0.236133	−	0.100851i
$759$	15.3699	−	4.99399i	0.557893	−	0.181270i
$760$	0.178373	−	2.34103i	0.00647028	−	0.0849181i
$761$	7.77260	−	23.9216i	0.281756	−	0.867157i	−0.705596	−	0.708615i	$-0.749320\pi$
$761$	7.77260	−	23.9216i	0.281756	−	0.867157i	0.987352	−	0.158543i	$-0.0506795\pi$
$762$	−3.48804	+	51.5212i	−0.126358	+	1.86642i
$763$	−69.1675	−	35.2426i	−2.50403	−	1.27587i
$764$	11.5839	+	33.1641i	0.419091	+	1.19983i
$765$	−0.0109587	−	0.0859983i	−0.000396212	−	0.00310927i
$766$	−7.18853	+	31.4547i	−0.259732	+	1.13650i
$767$	6.37193	−	8.77020i	0.230077	−	0.316674i
$768$	−6.21985	+	26.9743i	−0.224440	+	0.973350i
$769$	−16.4639	−	22.6606i	−0.593703	−	0.817161i	0.401411	−	0.915898i	$-0.368520\pi$
$769$	−16.4639	−	22.6606i	−0.593703	−	0.817161i	−0.995114	+	0.0987366i	$0.968520\pi$
$770$	25.9857	−	40.6154i	0.936458	−	1.46368i
$771$	−15.2871	+	11.1067i	−0.550552	+	0.399999i
$772$	−11.5212	+	6.19155i	−0.414656	+	0.222839i
$773$	−11.6073	+	35.7235i	−0.417484	+	1.28488i	0.492526	+	0.870298i	$0.336074\pi$
$773$	−11.6073	+	35.7235i	−0.417484	+	1.28488i	−0.910010	+	0.414586i	$0.863926\pi$
$774$	0.0215146	−	0.00541484i	0.000773326	−	0.000194632i
$775$	6.96302	−	17.6984i	0.250119	−	0.635746i
$776$	−40.4113	+	11.1165i	−1.45068	+	0.399060i
$777$	21.9718	−	11.1952i	0.788235	−	0.401626i
$778$	1.60617	+	17.9017i	0.0575839	+	0.641808i
$779$	0.186537	−	2.36965i	0.00668337	−	0.0849016i
$780$	12.7771	+	40.4847i	0.457494	+	1.44959i
$781$	−19.5885	−	6.36470i	−0.700933	−	0.227747i
$782$	−14.7232	+	17.6255i	−0.526499	+	0.630288i
$783$	15.7289	−	2.49121i	0.562105	−	0.0890286i
$784$	52.6725	+	14.5997i	1.88116	+	0.521419i
$785$	2.29976	−	12.1271i	0.0820819	−	0.432833i
$786$	39.8935	−	17.0382i	1.42295	−	0.607732i
$787$	−1.36415	+	8.61292i	−0.0486268	+	0.307017i	−0.999999	−	0.00102477i	$-0.999674\pi$
$787$	−1.36415	+	8.61292i	−0.0486268	+	0.307017i	0.951373	+	0.308042i	$0.0996738\pi$
$788$	13.0996	+	9.08621i	0.466654	+	0.323683i
$789$	−2.52860	−	3.48032i	−0.0900206	−	0.123903i
$790$	1.42337	+	24.0364i	0.0506412	+	0.855176i
$791$	84.5538	−	13.3920i	3.00639	−	0.476165i
$792$	0.0465933	−	0.0425169i	0.00165562	−	0.00151077i
$793$	22.7009			0.806133
$794$	−6.66535	+	11.1489i	−0.236544	+	0.395659i
$795$	−13.2060	+	6.23175i	−0.468370	+	0.221018i
$796$	0.619241	+	28.2921i	0.0219484	+	1.00279i
$797$	15.3246	+	30.0763i	0.542827	+	1.06536i	0.985658	+	0.168753i	$0.0539739\pi$
$797$	15.3246	+	30.0763i	0.542827	+	1.06536i	−0.442832	+	0.896605i	$0.646026\pi$
$798$	3.83173	+	1.53825i	0.135642	+	0.0544536i
$799$	−27.6593	+	8.98704i	−0.978515	+	0.317939i
$800$	14.9219	−	24.0278i	0.527569	−	0.849512i
$801$	−0.0266528	−	0.0135803i	−0.000941732	−	0.000479836i
$802$	9.78086	−	42.7979i	0.345374	−	1.51125i
$803$	−3.71310	−	5.11064i	−0.131032	−	0.180351i
$804$	16.2485	+	30.2350i	0.573039	+	1.06631i
$805$	−7.92693	−	27.1748i	−0.279388	−	0.957788i
$806$	−2.63755	−	29.3971i	−0.0929037	−	1.03547i
$807$	−8.59472	−	2.79259i	−0.302548	−	0.0983039i
$808$	18.5771	+	40.9895i	0.653539	+	1.44200i
$809$	−5.42911	+	34.2781i	−0.190877	+	1.20515i	0.687140	+	0.726525i	$0.258866\pi$
$809$	−5.42911	+	34.2781i	−0.190877	+	1.20515i	−0.878018	+	0.478628i	$0.841134\pi$
$810$	−21.2318	−	18.8578i	−0.746009	−	0.662595i
$811$	7.89730			0.277312			0.138656	−	0.990341i	$-0.455722\pi$
$811$	7.89730			0.277312			0.138656	+	0.990341i	$0.455722\pi$
$812$	−27.8263	+	0.609047i	−0.976513	+	0.0213733i
$813$	−40.1261	+	13.0378i	−1.40728	+	0.457254i
$814$	−3.31355	+	14.4990i	−0.116140	+	0.508190i
$815$	−32.1637	+	9.38219i	−1.12665	+	0.328644i
$816$	10.7794	−	38.8895i	0.377353	−	1.36140i
$817$	−0.875896			−0.0306437
$818$	3.45353	−	15.1115i	0.120750	−	0.528362i
$819$	0.165831			0.00579460
$820$	15.1683	−	24.2883i	0.529699	−	0.848186i
$821$	42.4541			1.48166			0.740829	−	0.671693i	$-0.234433\pi$
$821$	42.4541			1.48166			0.740829	+	0.671693i	$0.234433\pi$
$822$	3.36400	−	14.7198i	0.117333	−	0.513412i
$823$	−23.9428			−0.834594			−0.417297	−	0.908770i	$-0.637022\pi$
$823$	−23.9428			−0.834594			−0.417297	+	0.908770i	$0.637022\pi$
$824$	9.43632	−	4.27669i	0.328730	−	0.148986i
$825$	26.6044	−	11.5812i	0.926245	−	0.403205i
$826$	2.82985	−	12.3825i	0.0984632	−	0.430843i
$827$	10.4175	−	3.38484i	0.362251	−	0.117702i	−0.122236	−	0.992501i	$-0.539006\pi$
$827$	10.4175	−	3.38484i	0.362251	−	0.117702i	0.484487	+	0.874799i	$0.339006\pi$
$828$	−0.000810322	−	0.0370223i	−2.81607e−5	−	0.00128661i
$829$	−4.75367			−0.165102			−0.0825509	−	0.996587i	$-0.526307\pi$
$829$	−4.75367			−0.165102			−0.0825509	+	0.996587i	$0.526307\pi$
$830$	28.7629	−	1.70326i	0.998373	−	0.0591210i
$831$	0.813501	−	5.13624i	0.0282200	−	0.178174i
$832$	4.00755	−	43.7108i	0.138937	−	1.51540i
$833$	−75.7826	−	24.6233i	−2.62571	−	0.853146i
$834$	−2.95479	−	32.9330i	−0.102316	−	1.14038i
$835$	17.6793	−	32.2412i	0.611818	−	1.11575i
$836$	−2.19359	+	1.17885i	−0.0758669	+	0.0407713i
$837$	11.6304	+	16.0079i	0.402006	+	0.553313i
$838$	−2.30780	+	10.0982i	−0.0797218	+	0.348837i
$839$	38.3002	+	19.5149i	1.32227	+	0.673730i	0.965486	−	0.260456i	$-0.0838730\pi$
$839$	38.3002	+	19.5149i	1.32227	+	0.673730i	0.356785	+	0.934187i	$0.383873\pi$
$840$	32.3990	+	37.7434i	1.11787	+	1.30227i
$841$	−18.6673	+	6.06538i	−0.643701	+	0.209151i
$842$	−29.8835	−	11.9968i	−1.02985	−	0.413436i
$843$	7.34891	+	14.4230i	0.253110	+	0.496756i
$844$	−22.4901	+	0.492250i	−0.774141	+	0.0169439i
$845$	−16.3222	−	34.5892i	−0.561501	−	1.18990i
$846$	0.0240632	−	0.0402496i	0.000827310	−	0.00138381i
$847$	−1.13858			−0.0391222
$848$	15.0837	−	0.660603i	0.517977	−	0.0226852i
$849$	15.6000	−	2.47080i	0.535391	−	0.0847976i
$850$	−23.2654	+	34.0431i	−0.797995	+	1.16767i
$851$	5.13231	+	7.06402i	0.175933	+	0.242152i
$852$	12.1101	−	17.4592i	0.414887	−	0.598143i
$853$	5.11665	−	32.3052i	0.175191	−	1.10611i	−0.730731	−	0.682665i	$-0.760821\pi$
$853$	5.11665	−	32.3052i	0.175191	−	1.10611i	0.905922	−	0.423445i	$-0.139179\pi$
$854$	24.4609	−	10.4470i	0.837035	−	0.357491i
$855$	−0.00310704	−	0.00456124i	−0.000106258	−	0.000155991i
$856$	−38.5067	+	17.4518i	−1.31613	+	0.596491i
$857$	−54.9747	+	8.70713i	−1.87790	+	0.297430i	−0.987484	−	0.157720i	$-0.949586\pi$
$857$	−54.9747	+	8.70713i	−1.87790	+	0.297430i	−0.890415	+	0.455150i	$0.849586\pi$
$858$	28.8678	−	34.5585i	0.985530	−	1.17981i
$859$	−36.1753	−	11.7541i	−1.23428	−	0.401043i	−0.382020	−	0.924154i	$-0.624771\pi$
$859$	−36.1753	−	11.7541i	−1.23428	−	0.401043i	−0.852265	+	0.523111i	$0.824771\pi$
$860$	−9.36106	−	4.86977i	−0.319210	−	0.166058i
$861$	32.7054	+	38.2945i	1.11460	+	1.30507i
$862$	−0.301844	−	3.36424i	−0.0102808	−	0.114586i
$863$	1.69022	−	0.861211i	0.0575358	−	0.0293160i	−0.424986	−	0.905200i	$-0.639721\pi$
$863$	1.69022	−	0.861211i	0.0575358	−	0.0293160i	0.482522	+	0.875884i	$0.339721\pi$
$864$	12.7308	+	26.5300i	0.433109	+	0.902567i
$865$	19.8147	−	5.77996i	0.673719	−	0.196524i
$866$	17.5173	−	4.40880i	0.595262	−	0.149817i
$867$	−9.09113	+	27.9796i	−0.308751	+	0.950237i
$868$	−16.3707	−	30.4624i	−0.555658	−	1.03396i
$869$	20.6620	−	15.0118i	0.700910	−	0.509241i
$870$	−14.1087	−	9.02673i	−0.478330	−	0.306035i
$871$	−31.9911	−	44.0320i	−1.08398	−	1.49197i
$872$	5.36792	+	48.0014i	0.181781	+	1.62553i
$873$	−0.0579098	+	0.0797060i	−0.00195995	+	0.00269764i
$874$	−0.325724	+	1.42526i	−0.0110178	+	0.0482103i
$875$	−18.8629	−	47.1939i	−0.637682	−	1.59545i
$876$	6.15239	−	2.14898i	0.207870	−	0.0726072i
$877$	−25.3186	−	12.9005i	−0.854949	−	0.435618i	−0.0291450	−	0.999575i	$-0.509278\pi$
$877$	−25.3186	−	12.9005i	−0.854949	−	0.435618i	−0.825804	+	0.563957i	$0.809278\pi$
$878$	−2.47596	+	36.5720i	−0.0835595	+	1.23424i
$879$	−9.02659	+	27.7810i	−0.304459	+	0.937029i
$880$	−29.9979	+	0.403026i	−1.01123	+	0.0135860i
$881$	45.6728	−	14.8400i	1.53876	−	0.499972i	0.587723	−	0.809062i	$-0.300024\pi$
$881$	45.6728	−	14.8400i	1.53876	−	0.499972i	0.951033	+	0.309090i	$0.100024\pi$
$882$	0.118158	−	0.0504645i	0.00397860	−	0.00169923i
$883$	44.1493	−	14.3450i	1.48574	−	0.482747i	0.549920	−	0.835217i	$-0.314658\pi$
$883$	44.1493	−	14.3450i	1.48574	−	0.482747i	0.935823	+	0.352470i	$0.114658\pi$
$884$	−8.62485	+	63.4061i	−0.290085	+	2.13258i
$885$	5.56630	−	5.23846i	0.187109	−	0.176089i
$886$	−2.00265	−	0.803967i	−0.0672804	−	0.0270098i
$887$	32.3147	+	23.4780i	1.08502	+	0.788315i	0.978552	−	0.206001i	$-0.0660450\pi$
$887$	32.3147	+	23.4780i	1.08502	+	0.788315i	0.106471	+	0.994316i	$0.466045\pi$
$888$	−13.3383	−	7.58314i	−0.447605	−	0.254474i
$889$	−43.5558	−	85.4830i	−1.46081	−	2.86701i
$890$	5.18870	+	13.2475i	0.173926	+	0.444058i
$891$	−4.71188	+	29.7497i	−0.157854	+	0.996651i
$892$	0.0264387	+	1.20794i	0.000885232	+	0.0404448i
$893$	−1.30914	+	1.30914i	−0.0438088	+	0.0438088i
$894$	2.53434	−	37.4343i	0.0847610	−	1.25199i
$895$	−37.6184	−	13.4975i	−1.25744	−	0.451171i
$896$	−15.7976	−	48.9439i	−0.527761	−	1.63510i
$897$	−4.13551	−	26.1106i	−0.138081	−	0.871806i
$898$	28.1188	−	47.0332i	0.938335	−	1.56952i
$899$	8.23410	+	8.23410i	0.274623	+	0.274623i
$900$	−0.00784684	−	0.0660222i	−0.000261561	−	0.00220074i
$901$	−22.0105			−0.733277
$902$	−30.3715	+	0.331814i	−1.01126	+	0.0110482i
$903$	13.1219	−	13.1219i	0.436669	−	0.436669i
$904$	−35.9037	−	39.3461i	−1.19414	−	1.30863i
$905$	−33.4285	+	43.1922i	−1.11120	+	1.43576i
$906$	−4.17282	−	16.5797i	−0.138633	−	0.550824i
$907$	−49.5308	+	7.84491i	−1.64464	+	0.260486i	−0.908973	−	0.416854i	$-0.863132\pi$
$907$	−49.5308	+	7.84491i	−1.64464	+	0.260486i	−0.735670	+	0.677340i	$0.763132\pi$
$908$	−1.17770	+	8.65792i	−0.0390833	+	0.287323i
$909$	0.0942564	+	0.0480260i	0.00312629	+	0.00159292i
$910$	−58.9711	−	52.3774i	−1.95487	−	1.73629i
$911$	−21.2435			−0.703827			−0.351914	−	0.936032i	$-0.614469\pi$
$911$	−21.2435			−0.703827			−0.351914	+	0.936032i	$0.614469\pi$
$912$	−0.512525	−	2.51741i	−0.0169714	−	0.0833597i
$913$	−17.9637	−	24.7249i	−0.594512	−	0.818276i
$914$	−38.1927	−	22.8335i	−1.26330	−	0.755264i
$915$	15.7260	+	2.98226i	0.519887	+	0.0985906i
$916$	26.3108	+	18.2498i	0.869334	+	0.602992i
$917$	−47.3723	+	65.2023i	−1.56437	+	2.15317i
$918$	−16.8492	−	39.4511i	−0.556108	−	1.30208i
$919$	0.894894	−	5.65014i	0.0295198	−	0.186381i	−0.968522	−	0.248927i	$-0.919922\pi$
$919$	0.894894	−	5.65014i	0.0295198	−	0.186381i	0.998042	+	0.0625461i	$0.0199221\pi$
$920$	−11.4053	+	13.4214i	−0.376020	+	0.442492i
$921$	12.4597	+	6.34856i	0.410562	+	0.209192i
$922$	−27.5218	+	11.7543i	−0.906381	+	0.387108i
$923$	−15.2958	+	30.0197i	−0.503468	+	0.988112i
$924$	15.2019	−	50.5228i	0.500107	−	1.66208i
$925$	10.3928	+	11.7370i	0.341714	+	0.385911i
$926$	28.4175	+	32.5447i	0.933858	+	1.06949i
$927$	0.0110562	−	0.0216991i	0.000363134	−	0.000712691i
$928$	9.84239	+	14.2489i	0.323092	+	0.467744i
$929$	16.0940	+	16.0940i	0.528026	+	0.528026i	0.919983	−	0.391957i	$-0.128202\pi$
$929$	16.0940	+	16.0940i	0.528026	+	0.528026i	−0.391957	+	0.919983i	$0.628202\pi$
$930$	2.03480	−	20.7113i	0.0667236	−	0.679151i
$931$	−5.01015	+	0.793530i	−0.164201	+	0.0260069i
$932$	38.8491	+	37.1849i	1.27255	+	1.21803i
$933$	−33.1774	−	5.25478i	−1.08618	−	0.172034i
$934$	13.0975	−	15.6794i	0.428564	−	0.513046i
$935$	43.7156	+	1.32646i	1.42965	+	0.0433797i
$936$	−0.0567699	−	0.0861590i	−0.00185558	−	0.00281619i
$937$	33.4237	+	10.8600i	1.09190	+	0.354781i	0.798982	−	0.601355i	$-0.205372\pi$
$937$	33.4237	+	10.8600i	1.09190	+	0.354781i	0.292922	+	0.956136i	$0.405372\pi$
$938$	−54.7350	−	32.7233i	−1.78716	−	1.06845i
$939$	−16.9854	−	12.3406i	−0.554297	−	0.402721i
$940$	−21.2699	+	6.71284i	−0.693746	+	0.218949i
$941$	4.04299	+	1.31365i	0.131798	+	0.0428236i	0.374173	−	0.927359i	$-0.377927\pi$
$941$	4.04299	+	1.31365i	0.131798	+	0.0428236i	−0.242375	+	0.970183i	$0.577927\pi$
$942$	−1.20696	−	13.4523i	−0.0393247	−	0.438298i
$943$	−11.5810	+	13.5591i	−0.377130	+	0.441547i
$944$	−7.40222	+	2.76871i	−0.240922	+	0.0901139i
$945$	51.9503	+	9.85178i	1.68994	+	0.320479i
$946$	1.00017	+	11.1475i	0.0325183	+	0.362437i
$947$	−4.33006	−	27.3389i	−0.140708	−	0.888395i	−0.952520	−	0.304476i	$-0.901519\pi$
$947$	−4.33006	−	27.3389i	−0.140708	−	0.888395i	0.811812	−	0.583919i	$-0.198481\pi$
$948$	8.68817	+	24.8737i	0.282179	+	0.807861i
$949$	−9.20724	+	4.69132i	−0.298880	+	0.152287i
$950$	−0.335765	+	2.60337i	−0.0108937	+	0.0844646i
$951$	−30.9747	+	22.5044i	−1.00442	+	0.729756i
$952$	19.8862	+	72.2911i	0.644516	+	2.34297i
$953$	10.8305	+	1.71538i	0.350834	+	0.0555666i	0.329364	−	0.944203i	$-0.393166\pi$
$953$	10.8305	+	1.71538i	0.350834	+	0.0555666i	0.0214694	+	0.999770i	$0.493166\pi$
$954$	0.0267336	−	0.0233433i	0.000865531	−	0.000755768i
$955$	−10.9983	−	37.7040i	−0.355896	−	1.22007i
$956$	37.5972	−	28.5936i	1.21598	−	0.924783i
$957$			17.7656i			0.574281i
$958$	13.5756	−	3.41674i	0.438607	−	0.110390i
$959$	8.66880	+	26.6798i	0.279930	+	0.861536i
$960$	8.51859	−	29.7541i	0.274936	−	0.960309i
$961$	5.10845	−	15.7222i	0.164789	−	0.507168i
$962$	22.5776	+	9.06381i	0.727931	+	0.292229i
$963$	−0.0451170	+	0.0885471i	−0.00145387	+	0.00285339i
$964$	17.4984	−	9.40372i	0.563584	−	0.302874i
$965$	13.2248	−	6.24062i	0.425722	−	0.200893i
$966$	−16.4723	−	26.2317i	−0.529988	−	0.843991i
$967$	17.8988	−	13.0042i	0.575587	−	0.418188i	−0.261544	−	0.965192i	$-0.584232\pi$
$967$	17.8988	−	13.0042i	0.575587	−	0.418188i	0.837130	+	0.547003i	$0.184232\pi$
$968$	0.389778	+	0.591561i	0.0125279	+	0.0190135i
$969$	0.585884	+	3.69913i	0.0188213	+	0.118833i
$970$	45.7683	−	10.0536i	1.46953	−	0.322800i
$971$	−11.1799	−	21.9417i	−0.358778	−	0.704142i	0.639108	−	0.769117i	$-0.279303\pi$
$971$	−11.1799	−	21.9417i	−0.358778	−	0.704142i	−0.997887	+	0.0649742i	$0.979303\pi$
$972$	0.124472	+	0.0600277i	0.00399243	+	0.00192539i
$973$	36.1086	+	49.6992i	1.15759	+	1.59328i
$974$	26.9918	+	1.82737i	0.864874	+	0.0585528i
$975$	−11.9033	−	45.9472i	−0.381212	−	1.47149i
$976$	−13.8017	−	9.13248i	−0.441782	−	0.292323i
$977$	−1.48185	−	4.56066i	−0.0474086	−	0.145909i	0.924550	−	0.381061i	$-0.124441\pi$
$977$	−1.48185	−	4.56066i	−0.0474086	−	0.145909i	−0.971959	+	0.235152i	$0.924441\pi$
$978$	−31.0474	+	19.4964i	−0.992787	+	0.623425i
$979$	8.87014	−	12.2087i	0.283491	−	0.390192i
$980$	−57.9574	−	19.3744i	−1.85138	−	0.618893i
$981$	0.0802839	+	0.0802839i	0.00256327	+	0.00256327i
$982$	−6.70440	+	29.3363i	−0.213946	+	0.936159i
$983$	−28.8420	+	28.8420i	−0.919917	+	0.919917i	−0.997023	−	0.0771060i	$-0.975432\pi$
$983$	−28.8420	+	28.8420i	−0.919917	+	0.919917i	0.0771060	+	0.997023i	$0.475432\pi$
$984$	8.69999	−	30.1020i	0.277346	−	0.959616i
$985$	−14.0956	−	10.9093i	−0.449124	−	0.347598i
$986$	−13.4259	−	21.3804i	−0.427568	−	0.680890i
$987$		−	39.2248i		−	1.24854i
$988$	1.34329	+	3.84577i	0.0427358	+	0.122350i
$989$	5.31591	+	3.86224i	0.169036	+	0.122812i
$990$	−0.0545029	+	0.0447516i	−0.00173222	+	0.00142230i
$991$	31.2153	+	15.9050i	0.991587	+	0.505239i	0.873008	−	0.487706i	$-0.162166\pi$
$991$	31.2153	+	15.9050i	0.991587	+	0.505239i	0.118579	+	0.992945i	$0.462166\pi$
$992$	−10.2227	+	18.9339i	−0.324573	+	0.601153i
$993$	−39.2988	+	39.2988i	−1.24711	+	1.24711i
$994$	−2.66650	+	39.3863i	−0.0845761	+	1.24926i
$995$	0.959579	−	31.6246i	0.0304207	−	1.00257i
$996$	29.7648	−	10.3966i	0.943135	−	0.329429i
$997$	−1.37244	+	4.22394i	−0.0434657	+	0.133774i	−0.970434	−	0.241365i	$-0.922405\pi$
$997$	−1.37244	+	4.22394i	−0.0434657	+	0.133774i	0.926969	+	0.375139i	$0.122405\pi$
$998$	5.77883	−	6.91801i	0.182926	−	0.218986i
$999$	−16.1092	+	2.55145i	−0.509673	+	0.0807243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bv.c.103.8	yes	960
4.3	odd	2	inner	820.2.bv.c.103.45	yes	960
5.2	odd	4		820.2.bk.c.267.69	yes	960
20.7	even	4		820.2.bk.c.267.17	yes	960
41.2	even	20		820.2.bk.c.43.17	✓	960
164.43	odd	20		820.2.bk.c.43.69	yes	960
205.2	odd	20	inner	820.2.bv.c.207.45	yes	960
820.207	even	20	inner	820.2.bv.c.207.8	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.17	✓	960	41.2	even	20
820.2.bk.c.43.69	yes	960	164.43	odd	20
820.2.bk.c.267.17	yes	960	20.7	even	4
820.2.bk.c.267.69	yes	960	5.2	odd	4
820.2.bv.c.103.8	yes	960	1.1	even	1	trivial
820.2.bv.c.103.45	yes	960	4.3	odd	2	inner
820.2.bv.c.207.8	yes	960	820.207	even	20	inner
820.2.bv.c.207.45	yes	960	205.2	odd	20	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37867 - 0.315075i) q^{2} +1.73013 q^{3} +(1.80145 + 0.868769i) q^{4} +(-1.96065 - 1.07511i) q^{5} +(-2.38528 - 0.545122i) q^{6} +(4.32334 - 1.40474i) q^{7} +(-2.20988 - 1.76534i) q^{8} -0.00664869 q^{9} +(2.36434 + 2.09998i) q^{10} +(0.524708 - 3.31288i) q^{11} +(3.11675 + 1.50308i) q^{12} +(-5.21822 - 1.69550i) q^{13} +(-6.40306 + 0.574491i) q^{14} +(-3.39217 - 1.86008i) q^{15} +(2.49048 + 3.13010i) q^{16} +(-3.42756 - 4.71763i) q^{17} +(0.00916634 + 0.00209484i) q^{18} +(-0.330761 - 0.168531i) q^{19} +(-2.59799 - 3.64012i) q^{20} +(7.47995 - 2.43038i) q^{21} +(-1.76720 + 4.40204i) q^{22} +(1.26429 + 2.48132i) q^{23} +(-3.82338 - 3.05427i) q^{24} +(2.68827 + 4.21583i) q^{25} +(6.65999 + 3.98167i) q^{26} -5.20189 q^{27} +(9.00871 + 1.22541i) q^{28} +(-3.02368 + 0.478905i) q^{29} +(4.09062 + 3.63323i) q^{30} +(-2.23580 - 3.07732i) q^{31} +(-2.44733 - 5.10006i) q^{32} +(0.907813 - 5.73171i) q^{33} +(3.23906 + 7.58399i) q^{34} +(-9.98680 - 1.89388i) q^{35} +(-0.0119773 - 0.00577618i) q^{36} +(3.09680 - 0.490485i) q^{37} +(0.402910 + 0.336564i) q^{38} +(-9.02820 - 2.93344i) q^{39} +(2.43486 + 5.83708i) q^{40} +(2.45027 + 5.91576i) q^{41} +(-11.0781 + 0.993945i) q^{42} +(2.10232 - 1.07119i) q^{43} +(3.82336 - 5.51215i) q^{44} +(0.0130357 + 0.00714809i) q^{45} +(-0.961241 - 3.81926i) q^{46} +(1.54117 - 4.74323i) q^{47} +(4.30886 + 5.41548i) q^{48} +(11.0549 - 8.03185i) q^{49} +(-2.37792 - 6.65924i) q^{50} +(-5.93013 - 8.16212i) q^{51} +(-7.92739 - 7.58780i) q^{52} +(2.21862 - 3.05367i) q^{53} +(7.17169 + 1.63899i) q^{54} +(-4.59048 + 5.93126i) q^{55} +(-12.0339 - 4.52786i) q^{56} +(-0.572260 - 0.291581i) q^{57} +(4.31955 + 0.292438i) q^{58} +(-0.610546 + 1.87907i) q^{59} +(-4.49486 - 6.29787i) q^{60} +(-3.93490 + 1.27853i) q^{61} +(2.11284 + 4.94705i) q^{62} +(-0.0287446 + 0.00933968i) q^{63} +(1.76715 + 7.80238i) q^{64} +(8.40823 + 8.93445i) q^{65} +(-3.05749 + 7.61610i) q^{66} +(8.02513 + 5.83060i) q^{67} +(-2.07606 - 11.4764i) q^{68} +(2.18739 + 4.29300i) q^{69} +(13.1718 + 5.75763i) q^{70} +(0.960600 - 6.06499i) q^{71} +(0.0146928 + 0.0117372i) q^{72} +(1.33173 - 1.33173i) q^{73} +(-4.42400 - 0.299509i) q^{74} +(4.65105 + 7.29394i) q^{75} +(-0.449437 - 0.590957i) q^{76} +(-2.38524 - 15.0598i) q^{77} +(11.5226 + 6.88881i) q^{78} +(5.38411 + 5.38411i) q^{79} +(-1.51774 - 8.81456i) q^{80} -8.98001 q^{81} +(-1.51420 - 8.92789i) q^{82} +(6.44284 - 6.44284i) q^{83} +(15.5862 + 2.12013i) q^{84} +(1.64825 + 12.9346i) q^{85} +(-3.23591 + 0.814422i) q^{86} +(-5.23137 + 0.828567i) q^{87} +(-7.00789 + 6.39478i) q^{88} +(4.00873 + 2.04255i) q^{89} +(-0.0157198 - 0.0139621i) q^{90} -24.9419 q^{91} +(0.121877 + 5.56836i) q^{92} +(-3.86823 - 5.32416i) q^{93} +(-3.61924 + 6.05376i) q^{94} +(0.467316 + 0.686036i) q^{95} +(-4.23420 - 8.82376i) q^{96} +(8.70996 - 11.9882i) q^{97} +(-17.7717 + 7.59014i) q^{98} +(-0.00348862 + 0.0220263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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