LMFDB - Embedded newform 1000.2.bd.a.109.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(29,1000)] 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("1000.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 25, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.bd (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$2960$
Relative dimension:	$148$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.15
Character	$\chi$	$=$	1000.109
Dual form			1000.2.bd.a.789.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34141 + 0.447898i) q^{2} +(0.466928 + 0.564419i) q^{3} +(1.59877 - 1.20163i) q^{4} +(0.134176 - 2.23204i) q^{5} +(-0.879145 - 0.547982i) q^{6} +(0.385630 - 0.125299i) q^{7} +(-1.60641 + 2.32797i) q^{8} +(0.461597 - 2.41978i) q^{9} +(0.819741 + 3.05418i) q^{10} +(0.382501 - 3.02781i) q^{11} +(1.42474 + 0.341302i) q^{12} +(-0.145677 + 0.763668i) q^{13} +(-0.461168 + 0.340800i) q^{14} +(1.32245 - 0.966469i) q^{15} +(1.11216 - 3.84228i) q^{16} +(1.04763 + 4.08026i) q^{17} +(0.464622 + 3.45267i) q^{18} +(-3.60386 - 2.98137i) q^{19} +(-2.46757 - 3.72976i) q^{20} +(0.250782 + 0.159151i) q^{21} +(0.843058 + 4.23286i) q^{22} +(1.76873 - 1.88351i) q^{23} +(-2.06403 + 0.180310i) q^{24} +(-4.96399 - 0.598971i) q^{25} +(-0.146632 - 1.08964i) q^{26} +(3.50704 - 1.92801i) q^{27} +(0.465972 - 0.663710i) q^{28} +(3.76540 - 0.236899i) q^{29} +(-1.34108 + 1.88876i) q^{30} +(-6.56923 + 1.68669i) q^{31} +(0.229088 + 5.65221i) q^{32} +(1.88755 - 1.19788i) q^{33} +(-3.23285 - 5.00407i) q^{34} +(-0.227929 - 0.877553i) q^{35} +(-2.16969 - 4.42335i) q^{36} +(-10.0618 - 5.53150i) q^{37} +(6.16962 + 2.38509i) q^{38} +(-0.499049 + 0.274355i) q^{39} +(4.98059 + 3.89792i) q^{40} +(2.61344 - 2.45419i) q^{41} +(-0.407686 - 0.101162i) q^{42} +(7.99972 - 5.81214i) q^{43} +(-3.02678 - 5.30040i) q^{44} +(-5.33910 - 1.35498i) q^{45} +(-1.52898 + 3.31878i) q^{46} +(-1.41864 - 3.58306i) q^{47} +(2.68795 - 1.16634i) q^{48} +(-5.53011 + 4.01786i) q^{49} +(6.92704 - 1.41990i) q^{50} +(-1.81380 + 2.49649i) q^{51} +(0.684743 + 1.39598i) q^{52} +(-5.77559 + 9.10087i) q^{53} +(-3.84084 + 4.15706i) q^{54} +(-6.70686 - 1.26002i) q^{55} +(-0.327786 + 1.09902i) q^{56} -3.42617i q^{57} +(-4.94484 + 2.00429i) q^{58} +(0.214156 - 0.100774i) q^{59} +(0.952965 - 3.13427i) q^{60} +(-9.12524 + 9.71739i) q^{61} +(8.05658 - 5.20490i) q^{62} +(-0.125189 - 0.990976i) q^{63} +(-2.83892 - 7.47934i) q^{64} +(1.68499 + 0.427624i) q^{65} +(-1.99546 + 2.45228i) q^{66} +(0.975634 - 15.5073i) q^{67} +(6.57790 + 5.26454i) q^{68} +(1.88896 + 0.118843i) q^{69} +(0.698802 + 1.07507i) q^{70} +(12.7348 - 5.04205i) q^{71} +(4.89166 + 4.96173i) q^{72} +(4.65188 + 2.18901i) q^{73} +(15.9745 + 2.91338i) q^{74} +(-1.97976 - 3.08145i) q^{75} +(-9.34428 - 0.436025i) q^{76} +(-0.231877 - 1.21554i) q^{77} +(0.546548 - 0.591546i) q^{78} +(-4.55106 - 5.50129i) q^{79} +(-8.42689 - 2.99792i) q^{80} +(-4.14552 - 1.64133i) q^{81} +(-2.40648 + 4.46263i) q^{82} +(-5.94989 + 7.19218i) q^{83} +(0.592185 - 0.0469012i) q^{84} +(9.24786 - 1.79088i) q^{85} +(-8.12767 + 11.3795i) q^{86} +(1.89188 + 2.01465i) q^{87} +(6.43420 + 5.75434i) q^{88} +(4.62955 - 9.83830i) q^{89} +(7.76883 - 0.573789i) q^{90} +(0.0395091 + 0.312746i) q^{91} +(0.564519 - 5.13668i) q^{92} +(-4.01936 - 2.92023i) q^{93} +(3.50782 + 4.17096i) q^{94} +(-7.13809 + 7.64393i) q^{95} +(-3.08325 + 2.76848i) q^{96} +(14.1048 - 0.887402i) q^{97} +(5.61856 - 7.86653i) q^{98} +(-7.15005 - 2.32319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100}) $ 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{27}{50}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34141	+	0.447898i	−0.948522	+	0.316712i
$2$	−1.34141	+	0.447898i	−0.948522	+	0.316712i
$3$	0.466928	+	0.564419i	0.269581	+	0.325867i	0.887880	−	0.460076i	$-0.152178\pi$
$3$	0.466928	+	0.564419i	0.269581	+	0.325867i	−0.618299	+	0.785943i	$0.712178\pi$
$4$	1.59877	−	1.20163i	0.799387	−	0.600816i
$5$	0.134176	−	2.23204i	0.0600053	−	0.998198i
$5$	0.134176	−	2.23204i	0.0600053	−	0.998198i
$6$	−0.879145	−	0.547982i	−0.358909	−	0.223713i
$7$	0.385630	−	0.125299i	0.145754	−	0.0473585i	−0.235231	−	0.971939i	$-0.575585\pi$
$7$	0.385630	−	0.125299i	0.145754	−	0.0473585i	0.380986	+	0.924581i	$0.375585\pi$
$8$	−1.60641	+	2.32797i	−0.567950	+	0.823063i
$9$	0.461597	−	2.41978i	0.153866	−	0.806592i
$10$	0.819741	+	3.05418i	0.259225	+	0.965817i
$11$	0.382501	−	3.02781i	0.115328	−	0.912918i	−0.823209	−	0.567739i	$-0.807818\pi$
$11$	0.382501	−	3.02781i	0.115328	−	0.912918i	0.938537	−	0.345179i	$-0.112182\pi$
$12$	1.42474	+	0.341302i	0.411286	+	0.0985255i
$13$	−0.145677	+	0.763668i	−0.0404037	+	0.211803i	−0.996764	−	0.0803874i	$-0.974384\pi$
$13$	−0.145677	+	0.763668i	−0.0404037	+	0.211803i	0.956360	+	0.292191i	$0.0943843\pi$
$14$	−0.461168	+	0.340800i	−0.123252	+	0.0910827i
$15$	1.32245	−	0.966469i	0.341456	−	0.249541i
$16$	1.11216	−	3.84228i	0.278039	−	0.960570i
$17$	1.04763	+	4.08026i	0.254088	+	0.989607i	0.959704	+	0.281013i	$0.0906704\pi$
$17$	1.04763	+	4.08026i	0.254088	+	0.989607i	−0.705616	+	0.708594i	$0.749330\pi$
$18$	0.464622	+	3.45267i	0.109512	+	0.813801i
$19$	−3.60386	−	2.98137i	−0.826782	−	0.683974i	0.124525	−	0.992216i	$-0.460259\pi$
$19$	−3.60386	−	2.98137i	−0.826782	−	0.683974i	−0.951308	+	0.308243i	$0.900259\pi$
$20$	−2.46757	−	3.72976i	−0.551766	−	0.833999i
$21$	0.250782	+	0.159151i	0.0547252	+	0.0347296i
$22$	0.843058	+	4.23286i	0.179741	+	0.902448i
$23$	1.76873	−	1.88351i	0.368807	−	0.392739i	−0.517618	−	0.855612i	$-0.673181\pi$
$23$	1.76873	−	1.88351i	0.368807	−	0.392739i	0.886425	+	0.462873i	$0.153181\pi$
$24$	−2.06403	+	0.180310i	−0.421318	+	0.0368055i
$25$	−4.96399	−	0.598971i	−0.992799	−	0.119794i
$26$	−0.146632	−	1.08964i	−0.0287569	−	0.213696i
$27$	3.50704	−	1.92801i	0.674931	−	0.371046i
$28$	0.465972	−	0.663710i	0.0880604	−	0.125429i
$29$	3.76540	−	0.236899i	0.699217	−	0.0439910i	0.290796	−	0.956785i	$-0.406080\pi$
$29$	3.76540	−	0.236899i	0.699217	−	0.0439910i	0.408420	+	0.912794i	$0.366080\pi$
$30$	−1.34108	+	1.88876i	−0.244846	+	0.344839i
$31$	−6.56923	+	1.68669i	−1.17987	+	0.302939i	−0.787175	−	0.616730i	$-0.788457\pi$
$31$	−6.56923	+	1.68669i	−1.17987	+	0.302939i	−0.392694	+	0.919669i	$0.628457\pi$
$32$	0.229088	+	5.65221i	0.0404974	+	0.999180i
$33$	1.88755	−	1.19788i	0.328580	−	0.208523i
$34$	−3.23285	−	5.00407i	−0.554428	−	0.858191i
$35$	−0.227929	−	0.877553i	−0.0385271	−	0.148334i
$36$	−2.16969	−	4.42335i	−0.361616	−	0.737224i
$37$	−10.0618	−	5.53150i	−1.65414	−	0.909373i	−0.986278	−	0.165092i	$-0.947208\pi$
$37$	−10.0618	−	5.53150i	−1.65414	−	0.909373i	−0.667866	−	0.744282i	$-0.732792\pi$
$38$	6.16962	+	2.38509i	1.00084	+	0.386912i
$39$	−0.499049	+	0.274355i	−0.0799118	+	0.0439319i
$40$	4.98059	+	3.89792i	0.787500	+	0.616315i
$41$	2.61344	−	2.45419i	0.408151	−	0.383279i	−0.453099	−	0.891460i	$-0.649682\pi$
$41$	2.61344	−	2.45419i	0.408151	−	0.383279i	0.861251	+	0.508181i	$0.169682\pi$
$42$	−0.407686	−	0.101162i	−0.0629073	−	0.0156097i
$43$	7.99972	−	5.81214i	1.21995	−	0.886342i	0.223850	−	0.974624i	$-0.428137\pi$
$43$	7.99972	−	5.81214i	1.21995	−	0.886342i	0.996096	+	0.0882813i	$0.0281374\pi$
$44$	−3.02678	−	5.30040i	−0.456304	−	0.799066i
$45$	−5.33910	−	1.35498i	−0.795906	−	0.201988i
$46$	−1.52898	+	3.31878i	−0.225436	+	0.489327i
$47$	−1.41864	−	3.58306i	−0.206929	−	0.522644i	0.788833	−	0.614608i	$-0.210686\pi$
$47$	−1.41864	−	3.58306i	−0.206929	−	0.522644i	−0.995762	+	0.0919638i	$0.970686\pi$
$48$	2.68795	−	1.16634i	0.387972	−	0.168347i
$49$	−5.53011	+	4.01786i	−0.790015	+	0.573980i
$50$	6.92704	−	1.41990i	0.979631	−	0.200804i
$51$	−1.81380	+	2.49649i	−0.253983	+	0.349578i
$52$	0.684743	+	1.39598i	0.0949568	+	0.193588i
$53$	−5.77559	+	9.10087i	−0.793338	+	1.25010i	0.170959	+	0.985278i	$0.445313\pi$
$53$	−5.77559	+	9.10087i	−0.793338	+	1.25010i	−0.964297	+	0.264822i	$0.914687\pi$
$54$	−3.84084	+	4.15706i	−0.522672	+	0.565704i
$55$	−6.70686	−	1.26002i	−0.904353	−	0.169900i
$56$	−0.327786	+	1.09902i	−0.0438023	+	0.146862i
$57$		−	3.42617i		−	0.453807i
$58$	−4.94484	+	2.00429i	−0.649290	+	0.263177i
$59$	0.214156	−	0.100774i	0.0278807	−	0.0131197i	−0.411788	−	0.911279i	$-0.635096\pi$
$59$	0.214156	−	0.100774i	0.0278807	−	0.0131197i	0.439669	+	0.898160i	$0.355096\pi$
$60$	0.952965	−	3.13427i	0.123027	−	0.404633i
$61$	−9.12524	+	9.71739i	−1.16837	+	1.24418i	−0.204188	+	0.978932i	$0.565455\pi$
$61$	−9.12524	+	9.71739i	−1.16837	+	1.24418i	−0.964179	+	0.265253i	$0.914545\pi$
$62$	8.05658	−	5.20490i	1.02319	−	0.661023i
$63$	−0.125189	−	0.990976i	−0.0157724	−	0.124851i
$64$	−2.83892	−	7.47934i	−0.354865	−	0.934918i
$65$	1.68499	+	0.427624i	0.208997	+	0.0530402i
$66$	−1.99546	+	2.45228i	−0.245624	+	0.301854i
$67$	0.975634	−	15.5073i	0.119193	−	1.89451i	−0.254668	−	0.967029i	$-0.581966\pi$
$67$	0.975634	−	15.5073i	0.119193	−	1.89451i	0.373861	−	0.927485i	$-0.378034\pi$
$68$	6.57790	+	5.26454i	0.797687	+	0.638419i
$69$	1.88896	+	0.118843i	0.227404	+	0.0143070i
$70$	0.698802	+	1.07507i	0.0835228	+	0.128496i
$71$	12.7348	−	5.04205i	1.51134	−	0.598381i	0.541191	−	0.840900i	$-0.317974\pi$
$71$	12.7348	−	5.04205i	1.51134	−	0.598381i	0.970147	+	0.242519i	$0.0779735\pi$
$72$	4.89166	+	4.96173i	0.576488	+	0.584745i
$73$	4.65188	+	2.18901i	0.544461	+	0.256204i	0.678282	−	0.734801i	$-0.262725\pi$
$73$	4.65188	+	2.18901i	0.544461	+	0.256204i	−0.133821	+	0.991006i	$0.542725\pi$
$74$	15.9745	+	2.91338i	1.85700	+	0.338673i
$75$	−1.97976	−	3.08145i	−0.228602	−	0.355815i
$76$	−9.34428	−	0.436025i	−1.07186	−	0.0500155i
$77$	−0.231877	−	1.21554i	−0.0264248	−	0.138524i
$78$	0.546548	−	0.591546i	0.0618844	−	0.0669794i
$79$	−4.55106	−	5.50129i	−0.512034	−	0.618943i	0.449616	−	0.893222i	$-0.351561\pi$
$79$	−4.55106	−	5.50129i	−0.512034	−	0.618943i	−0.961650	+	0.274279i	$0.911561\pi$
$80$	−8.42689	−	2.99792i	−0.942155	−	0.335178i
$81$	−4.14552	−	1.64133i	−0.460613	−	0.182370i
$82$	−2.40648	+	4.46263i	−0.265751	+	0.492815i
$83$	−5.94989	+	7.19218i	−0.653085	+	0.789444i	−0.988271	−	0.152708i	$-0.951201\pi$
$83$	−5.94989	+	7.19218i	−0.653085	+	0.789444i	0.335186	+	0.942152i	$0.391201\pi$
$84$	0.592185	−	0.0469012i	0.0646127	−	0.00511734i
$85$	9.24786	−	1.79088i	1.00307	−	0.194248i
$86$	−8.12767	+	11.3795i	−0.876430	+	1.22709i
$87$	1.89188	+	2.01465i	0.202831	+	0.215993i
$88$	6.43420	+	5.75434i	0.685888	+	0.613414i
$89$	4.62955	−	9.83830i	0.490732	−	1.04286i	−0.494109	−	0.869400i	$-0.664506\pi$
$89$	4.62955	−	9.83830i	0.490732	−	1.04286i	0.984841	−	0.173458i	$-0.0554942\pi$
$90$	7.76883	−	0.573789i	0.818906	−	0.0604827i
$91$	0.0395091	+	0.312746i	0.00414168	+	0.0327847i
$92$	0.564519	−	5.13668i	0.0588551	−	0.535536i
$93$	−4.01936	−	2.92023i	−0.416788	−	0.302814i
$94$	3.50782	+	4.17096i	0.361804	+	0.430202i
$95$	−7.13809	+	7.64393i	−0.732353	+	0.784251i
$96$	−3.08325	+	2.76848i	−0.314683	+	0.282556i
$97$	14.1048	−	0.887402i	1.43213	−	0.0901020i	0.672327	−	0.740255i	$-0.265295\pi$
$97$	14.1048	−	0.887402i	1.43213	−	0.0901020i	0.759804	+	0.650153i	$0.225295\pi$
$98$	5.61856	−	7.86653i	0.567561	−	0.794640i
$99$	−7.15005	−	2.32319i	−0.718607	−	0.233490i
$100$	−8.65605	+	5.00728i	−0.865605	+	0.500728i
$101$	3.88457	−	1.26217i	0.386529	−	0.125591i	−0.109305	−	0.994008i	$-0.534862\pi$
$101$	3.88457	−	1.26217i	0.386529	−	0.125591i	0.495834	+	0.868417i	$0.334862\pi$
$102$	1.31489	−	4.16122i	0.130193	−	0.412022i
$103$	0.188563	−	0.734406i	0.0185797	−	0.0723632i	−0.958617	−	0.284698i	$-0.908107\pi$
$103$	0.188563	−	0.734406i	0.0185797	−	0.0723632i	0.977197	+	0.212335i	$0.0681067\pi$
$104$	−1.54378	−	1.56589i	−0.151380	−	0.153549i
$105$	0.388881	−	0.538401i	0.0379509	−	0.0525426i
$106$	3.67118	−	14.7949i	0.356577	−	1.43701i
$107$	1.48528	−	4.57121i	0.143587	−	0.441915i	−0.853240	−	0.521519i	$-0.825365\pi$
$107$	1.48528	−	4.57121i	0.143587	−	0.441915i	0.996827	+	0.0796037i	$0.0253655\pi$
$108$	3.29021	−	7.29664i	0.316600	−	0.702119i
$109$	7.23380	−	13.1582i	0.692872	−	1.26033i	−0.262502	−	0.964932i	$-0.584548\pi$
$109$	7.23380	−	13.1582i	0.692872	−	1.26033i	0.955374	−	0.295399i	$-0.0954525\pi$
$110$	9.56102	−	1.31379i	0.911608	−	0.125265i
$111$	−1.57603	−	8.26186i	−0.149590	−	0.784181i
$112$	−0.0525514	−	1.62105i	−0.00496564	−	0.153175i
$113$	3.25362	−	1.53104i	0.306075	−	0.144028i	−0.266607	−	0.963805i	$-0.585903\pi$
$113$	3.25362	−	1.53104i	0.306075	−	0.144028i	0.572683	+	0.819777i	$0.305903\pi$
$114$	1.53458	+	4.59591i	0.143726	+	0.430446i
$115$	−3.96675	−	4.20060i	−0.369901	−	0.391708i
$116$	5.73536	−	4.90337i	0.532514	−	0.455267i
$117$	1.78066	+	0.705014i	0.164622	+	0.0651786i
$118$	−0.242135	+	0.231100i	−0.0222903	+	0.0212745i
$119$	0.915249	+	1.44220i	0.0839007	+	0.132206i
$120$	0.125515	+	4.63118i	0.0114579	+	0.422767i
$121$	1.63311	+	0.419312i	0.148465	+	0.0381193i
$122$	7.88830	−	17.1222i	0.714173	−	1.55017i
$123$	2.60548	+	0.329148i	0.234928	+	0.0296783i
$124$	−8.47593	+	10.5904i	−0.761161	+	0.951050i
$125$	−2.00298	+	10.9995i	−0.179152	+	0.983821i
$126$	0.611787	+	1.27323i	0.0545023	+	0.113429i
$127$	0.108676	−	0.860259i	0.00964344	−	0.0763357i	−0.986559	−	0.163408i	$-0.947751\pi$
$127$	0.108676	−	0.860259i	0.00964344	−	0.0763357i	0.996202	+	0.0870726i	$0.0277512\pi$
$128$	7.15814	+	8.76133i	0.632697	+	0.774400i
$129$	7.01577	+	1.80134i	0.617704	+	0.158599i
$130$	−2.45180	+	0.181085i	−0.215037	+	0.0158822i
$131$	6.49365	−	4.12099i	0.567353	−	0.360053i	−0.221003	−	0.975273i	$-0.570933\pi$
$131$	6.49365	−	4.12099i	0.567353	−	0.360053i	0.788355	+	0.615220i	$0.210933\pi$
$132$	1.57836	−	4.18327i	0.137379	−	0.364107i
$133$	−1.76332	−	0.698147i	−0.152899	−	0.0605370i
$134$	5.63695	+	21.2386i	0.486958	+	1.83474i
$135$	−3.83284	−	8.08655i	−0.329878	−	0.695979i
$136$	−11.1816	−	4.11569i	−0.958818	−	0.352918i
$137$	14.7944	−	6.96173i	1.26397	−	0.594781i	0.327279	−	0.944928i	$-0.393868\pi$
$137$	14.7944	−	6.96173i	1.26397	−	0.594781i	0.936695	+	0.350147i	$0.113868\pi$
$138$	−2.58710	+	0.686644i	−0.220229	+	0.0584510i
$139$	4.45286	−	0.849429i	0.377687	−	0.0720476i	0.00495747	−	0.999988i	$-0.498422\pi$
$139$	4.45286	−	0.849429i	0.377687	−	0.0720476i	0.372729	+	0.927940i	$0.378422\pi$
$140$	−1.41890	−	1.12912i	−0.119919	−	0.0954282i
$141$	1.35995	−	2.47374i	0.114528	−	0.208326i
$142$	−14.8242	+	12.4673i	−1.24402	+	1.04624i
$143$	2.25652	+	0.733187i	0.188699	+	0.0613122i
$144$	−8.78409	−	4.46476i	−0.732007	−	0.372063i
$145$	−0.0235416	−	8.43630i	−0.00195503	−	0.700597i
$146$	−7.22054	−	0.852794i	−0.597576	−	0.0705777i
$147$	−4.84991	−	1.24525i	−0.400014	−	0.102706i
$148$	−22.7333	+	3.24692i	−1.86867	+	0.266895i
$149$	−15.9736	+	5.19015i	−1.30861	+	0.425194i	−0.878569	−	0.477615i	$-0.841502\pi$
$149$	−15.9736	+	5.19015i	−1.30861	+	0.425194i	−0.430043	+	0.902809i	$0.641502\pi$
$150$	4.03584	+	3.24676i	0.329525	+	0.265097i
$151$	4.46855	−	13.7528i	0.363646	−	1.11919i	−0.587179	−	0.809457i	$-0.699762\pi$
$151$	4.46855	−	13.7528i	0.363646	−	1.11919i	0.950825	−	0.309729i	$-0.100238\pi$
$152$	12.7298	−	3.60040i	1.03252	−	0.292031i
$153$	10.3569	−	0.651600i	0.837305	−	0.0526788i
$154$	0.855480	+	1.52668i	0.0689365	+	0.123024i
$155$	2.88333	+	14.8891i	0.231595	+	1.19592i
$156$	−0.468194	+	1.03831i	−0.0374855	+	0.0831309i
$157$	−0.450063	−	0.326990i	−0.0359189	−	0.0260966i	0.569681	−	0.821866i	$-0.307067\pi$
$157$	−0.450063	−	0.326990i	−0.0359189	−	0.0260966i	−0.605600	+	0.795769i	$0.707067\pi$
$158$	8.56887	+	5.34108i	0.681702	+	0.424914i
$159$	−7.83348	+	0.989599i	−0.621235	+	0.0784803i
$160$	12.6467	+	0.247058i	0.999809	+	0.0195316i
$161$	0.446075	−	0.947958i	0.0351556	−	0.0747096i
$162$	6.29600	+	0.344926i	0.494661	+	0.0270999i
$163$	−15.8260	+	14.8616i	−1.23959	+	1.16405i	−0.259444	+	0.965758i	$0.583539\pi$
$163$	−15.8260	+	14.8616i	−1.23959	+	1.16405i	−0.980143	+	0.198291i	$0.936461\pi$
$164$	1.22927	−	7.06409i	0.0959902	−	0.551612i
$165$	−2.42044	−	4.37381i	−0.188431	−	0.340501i
$166$	4.75989	−	12.3126i	0.369439	−	0.955645i
$167$	−5.84349	−	4.83416i	−0.452183	−	0.374078i	0.383273	−	0.923635i	$-0.374797\pi$
$167$	−5.84349	−	4.83416i	−0.452183	−	0.374078i	−0.835457	+	0.549556i	$0.814797\pi$
$168$	−0.773358	+	0.328153i	−0.0596658	+	0.0253175i
$169$	11.5251	+	4.56312i	0.886548	+	0.351009i
$170$	−11.6031	+	6.54441i	−0.889914	+	0.501933i
$171$	−8.87779	+	7.34435i	−0.678901	+	0.561636i
$172$	5.80569	−	18.9050i	0.442680	−	1.44149i
$173$	3.10268	+	16.2648i	0.235893	+	1.23659i	0.881227	+	0.472693i	$0.156718\pi$
$173$	3.10268	+	16.2648i	0.235893	+	1.23659i	−0.645335	+	0.763900i	$0.723282\pi$
$174$	−3.44014	−	1.85510i	−0.260797	−	0.140635i
$175$	−1.98931	+	0.391001i	−0.150378	+	0.0295569i
$176$	−11.2083	−	4.83707i	−0.844855	−	0.364608i
$177$	0.156874	+	0.0738194i	0.0117914	+	0.00554860i
$178$	−1.80358	+	15.2708i	−0.135184	+	1.14459i
$179$	−0.394903	−	0.997411i	−0.0295164	−	0.0745500i	0.914271	−	0.405104i	$-0.132765\pi$
$179$	−0.394903	−	0.997411i	−0.0295164	−	0.0745500i	−0.943787	+	0.330554i	$0.892765\pi$
$180$	−10.1642	+	4.24933i	−0.757595	+	0.316727i
$181$	−6.29348	−	0.395952i	−0.467791	−	0.0294309i	−0.172854	−	0.984948i	$-0.555299\pi$
$181$	−6.29348	−	0.395952i	−0.467791	−	0.0294309i	−0.294937	+	0.955517i	$0.595299\pi$
$182$	−0.193077	−	0.401826i	−0.0143118	−	0.0297853i
$183$	−9.74550	−	0.613135i	−0.720408	−	0.0453242i
$184$	1.54346	+	7.14325i	0.113785	+	0.526607i
$185$	−13.6966	+	21.7161i	−1.00699	+	1.59660i
$186$	6.69958	+	2.11697i	0.491237	+	0.155224i
$187$	12.7549	−	1.61132i	0.932734	−	0.117832i
$188$	−6.57361	−	4.02383i	−0.479429	−	0.293468i
$189$	1.11084	−	1.18293i	0.0808019	−	0.0860453i
$190$	6.15142	−	13.4508i	0.446271	−	0.975824i
$191$	−0.677648	−	1.44008i	−0.0490329	−	0.104200i	0.878809	−	0.477173i	$-0.158338\pi$
$191$	−0.677648	−	1.44008i	−0.0490329	−	0.104200i	−0.927842	+	0.372973i	$0.878338\pi$
$192$	2.89591	−	5.09465i	0.208994	−	0.367675i
$193$			7.91080i			0.569432i	0.958612	+	0.284716i	$0.0918993\pi$
$193$			7.91080i			0.569432i	−0.958612	+	0.284716i	$0.908101\pi$
$194$	−18.5229	+	7.50791i	−1.32987	+	0.539036i
$195$	0.545410	+	1.15071i	0.0390576	+	0.0824040i
$196$	−4.01340	+	13.0688i	−0.286672	+	0.933486i
$197$	−0.438820	+	0.691470i	−0.0312647	+	0.0492652i	−0.859601	−	0.510966i	$-0.829288\pi$
$197$	−0.438820	+	0.691470i	−0.0312647	+	0.0492652i	0.828336	+	0.560231i	$0.189288\pi$
$198$	10.6317	−	0.0861369i	0.755564	−	0.00612148i
$199$	−20.4837	−	14.8823i	−1.45205	−	1.05498i	−0.985347	−	0.170563i	$-0.945441\pi$
$199$	−20.4837	−	14.8823i	−1.45205	−	1.05498i	−0.466704	−	0.884414i	$-0.654559\pi$
$200$	9.36858	−	10.5939i	0.662459	−	0.749099i
$201$	9.20814	−	6.69010i	0.649492	−	0.471883i
$202$	−4.64549	+	3.43299i	−0.326855	+	0.241544i
$203$	1.42237	−	0.563155i	0.0998306	−	0.0395257i
$204$	0.0999974	+	6.17084i	0.00700122	+	0.432046i
$205$	−5.12718	−	6.16260i	−0.358098	−	0.430414i
$206$	0.0759979	+	1.06960i	0.00529503	+	0.0745224i
$207$	−3.74123	−	5.14936i	−0.260034	−	0.357906i
$208$	2.77221	+	1.40905i	0.192218	+	0.0977002i
$209$	−10.4055	+	9.77141i	−0.719763	+	0.675903i
$210$	−0.280500	+	0.896397i	−0.0193564	+	0.0618573i
$211$	9.96454	+	18.1254i	0.685987	+	1.24781i	0.958346	+	0.285610i	$0.0921964\pi$
$211$	9.96454	+	18.1254i	0.685987	+	1.24781i	−0.272358	+	0.962196i	$0.587804\pi$
$212$	1.70204	+	21.4904i	0.116897	+	1.47596i
$213$	8.79204	+	4.83346i	0.602420	+	0.331183i
$214$	0.0550695	+	6.79713i	0.00376447	+	0.464642i
$215$	−11.8995	−	18.6355i	−0.811542	−	1.27093i
$216$	−1.14537	+	11.2615i	−0.0779327	+	0.766246i
$217$	−2.32195	+	1.47356i	−0.157624	+	0.100031i
$218$	−3.80996	+	20.8906i	−0.258043	+	1.41489i
$219$	0.936574	+	3.64772i	0.0632878	+	0.246490i
$220$	−12.2368	+	6.04470i	−0.825007	+	0.407534i
$221$	−3.26858	+	0.205641i	−0.219868	+	0.0138329i
$222$	5.81458	+	10.3767i	0.390249	+	0.696435i
$223$	9.69511	+	17.6353i	0.649232	+	1.18095i	0.972114	+	0.234510i	$0.0753485\pi$
$223$	9.69511	+	17.6353i	0.649232	+	1.18095i	−0.322881	+	0.946439i	$0.604651\pi$
$224$	0.796558	+	2.15096i	0.0532223	+	0.143717i
$225$	−3.74074	+	11.7353i	−0.249383	+	0.782351i
$226$	−3.67870	+	3.51105i	−0.244704	+	0.233551i
$227$	7.24137	+	6.80010i	0.480626	+	0.451338i	0.886593	−	0.462549i	$-0.153065\pi$
$227$	7.24137	+	6.80010i	0.480626	+	0.451338i	−0.405967	+	0.913888i	$0.633065\pi$
$228$	−4.11700	−	5.47767i	−0.272655	−	0.362768i
$229$	13.3286	+	8.45858i	0.880778	+	0.558959i	0.897556	−	0.440900i	$-0.145341\pi$
$229$	13.3286	+	8.45858i	0.880778	+	0.558959i	−0.0167777	+	0.999859i	$0.505341\pi$
$230$	7.20249	+	3.85804i	0.474918	+	0.254392i
$231$	0.577803	−	0.698444i	0.0380167	−	0.0459543i
$232$	−5.49726	+	9.14630i	−0.360913	+	0.600484i
$233$	3.46570	+	13.4980i	0.227046	+	0.884284i	0.975302	+	0.220875i	$0.0708912\pi$
$233$	3.46570	+	13.4980i	0.227046	+	0.884284i	−0.748257	+	0.663409i	$0.769109\pi$
$234$	−2.70438	−	0.148159i	−0.176791	−	0.00968545i
$235$	−8.18789	+	2.68569i	−0.534119	+	0.175195i
$236$	0.221294	−	0.418452i	0.0144050	−	0.0272389i
$237$	0.980013	−	5.13741i	0.0636587	−	0.333710i
$238$	−1.87369	−	1.52465i	−0.121453	−	0.0988283i
$239$	−2.97884	−	0.376315i	−0.192685	−	0.0243418i	0.0283984	−	0.999597i	$-0.490959\pi$
$239$	−2.97884	−	0.376315i	−0.192685	−	0.0243418i	−0.221083	+	0.975255i	$0.570959\pi$
$240$	−2.24267	−	6.15610i	−0.144763	−	0.397375i
$241$	3.74204	−	19.6165i	0.241046	−	1.26361i	−0.631616	−	0.775282i	$-0.717608\pi$
$241$	3.74204	−	19.6165i	0.241046	−	1.26361i	0.872662	−	0.488325i	$-0.162392\pi$
$242$	−2.37849	+	0.168998i	−0.152895	+	0.0108636i
$243$	−4.71939	−	14.5248i	−0.302749	−	0.931765i
$244$	−2.91246	+	26.5011i	−0.186451	+	1.69656i
$245$	8.22601	+	12.8825i	0.525540	+	0.823034i
$246$	−3.64244	+	0.725465i	−0.232234	+	0.0462540i
$247$	2.80178	−	2.31783i	0.178273	−	0.147480i
$248$	6.62628	−	18.0025i	0.420769	−	1.14316i
$249$	−6.83757			−0.433313
$250$	−2.23982	−	15.6519i	−0.141659	−	0.989916i
$251$			6.58360i			0.415553i	0.978176	+	0.207777i	$0.0666227\pi$
$251$			6.58360i			0.415553i	−0.978176	+	0.207777i	$0.933377\pi$
$252$	−1.39094	−	1.43391i	−0.0876209	−	0.0903281i
$253$	−5.02636	−	6.07583i	−0.316005	−	0.381984i
$254$	0.239529	+	1.20264i	0.0150294	+	0.0754602i
$255$	5.32889	+	4.38345i	0.333708	+	0.274502i
$256$	−13.5262	−	8.54644i	−0.845388	−	0.534153i
$257$	−13.1028	+	4.25737i	−0.817332	+	0.265567i	−0.687700	−	0.725995i	$-0.741380\pi$
$257$	−13.1028	+	4.25737i	−0.817332	+	0.265567i	−0.129632	+	0.991562i	$0.541380\pi$
$258$	−10.2179	+	0.726007i	−0.636136	+	0.0451992i
$259$	−4.57321	−	0.872386i	−0.284165	−	0.0542074i
$260$	3.20777	−	1.34107i	0.198937	−	0.0831694i
$261$	1.16485	−	9.22077i	0.0721027	−	0.570751i
$262$	−6.86487	+	8.43645i	−0.424113	+	0.521205i
$263$	28.2541	+	5.38977i	1.74223	+	0.332347i	0.957704	−	0.287755i	$-0.0929088\pi$
$263$	28.2541	+	5.38977i	1.74223	+	0.332347i	0.784521	+	0.620102i	$0.212909\pi$
$264$	−0.243550	+	6.31844i	−0.0149894	+	0.388873i
$265$	19.5385	+	14.1125i	1.20024	+	0.866921i
$266$	2.67804	+	0.146716i	0.164201	+	0.00899573i
$267$	7.71459	−	1.98077i	0.472125	−	0.121221i
$268$	−17.0742	−	25.9650i	−1.04297	−	1.58606i
$269$	19.6455	+	16.2522i	1.19781	+	0.990914i	0.999943	+	0.0106850i	$0.00340119\pi$
$269$	19.6455	+	16.2522i	1.19781	+	0.990914i	0.197866	+	0.980229i	$0.436599\pi$
$270$	8.76337	+	9.13067i	0.533322	+	0.555675i
$271$	−13.1212	+	20.6757i	−0.797055	+	1.25596i	0.165859	+	0.986149i	$0.446960\pi$
$271$	−13.1212	+	20.6757i	−0.797055	+	1.25596i	−0.962914	+	0.269808i	$0.913040\pi$
$272$	16.8426	+	0.512596i	1.02123	+	0.0310807i
$273$	−0.158072	+	0.168330i	−0.00956695	+	0.0101878i
$274$	−16.7273	+	15.9649i	−1.01053	+	0.964478i
$275$	−3.71230	+	14.8009i	−0.223860	+	0.892528i
$276$	3.16282	−	2.07983i	0.190380	−	0.125191i
$277$	−13.9346	+	7.66062i	−0.837250	+	0.460282i	−0.841853	−	0.539707i	$-0.818535\pi$
$277$	−13.9346	+	7.66062i	−0.837250	+	0.460282i	0.00460272	+	0.999989i	$0.498535\pi$
$278$	−5.59267	+	3.13386i	−0.335426	+	0.187957i
$279$	1.04908	+	16.6746i	0.0628068	+	0.998285i
$280$	2.40907	+	0.879093i	0.143969	+	0.0525358i
$281$	9.53108	−	2.44717i	0.568577	−	0.145986i	0.0465516	−	0.998916i	$-0.485177\pi$
$281$	9.53108	−	2.44717i	0.568577	−	0.145986i	0.522025	+	0.852930i	$0.325177\pi$
$282$	−0.716269	+	3.92742i	−0.0426532	+	0.233874i
$283$	−6.40432	−	10.0916i	−0.380697	−	0.599883i	0.598907	−	0.800818i	$-0.295602\pi$
$283$	−6.40432	−	10.0916i	−0.380697	−	0.599883i	−0.979604	+	0.200936i	$0.935602\pi$
$284$	14.3013	−	23.3636i	0.848627	−	1.38637i
$285$	−7.64735	−	0.459710i	−0.452990	−	0.0272308i
$286$	−3.35531	+	0.0271843i	−0.198404	+	0.00160744i
$287$	0.700315	−	1.27387i	0.0413383	−	0.0751941i
$288$	13.7828	+	2.05470i	0.812162	+	0.121075i
$289$	−0.653743	+	0.359398i	−0.0384555	+	0.0211411i
$290$	3.81018	+	11.3060i	0.223742	+	0.663912i
$291$	7.08681	+	7.54668i	0.415436	+	0.442394i
$292$	10.0677	−	2.09012i	0.589167	−	0.122315i
$293$	3.68585	−	2.67793i	0.215330	−	0.156446i	−0.474892	−	0.880044i	$-0.657513\pi$
$293$	3.68585	−	2.67793i	0.215330	−	0.156446i	0.690222	+	0.723598i	$0.257513\pi$
$294$	7.06348	−	0.501880i	0.411950	−	0.0292702i
$295$	−0.196197	−	0.491526i	−0.0114230	−	0.0286177i
$296$	29.0405	−	14.5377i	1.68794	−	0.844985i
$297$	−4.49620	−	11.3561i	−0.260896	−	0.658948i
$298$	19.1026	−	14.1167i	1.10658	−	0.817759i
$299$	1.18071	+	1.62511i	0.0682823	+	0.0939826i
$300$	−6.86795	−	2.54760i	−0.396521	−	0.147086i
$301$	2.35668	−	3.24369i	0.135837	−	0.186963i
$302$	0.165680	+	20.4496i	0.00953383	+	1.17674i
$303$	2.52621	+	1.60318i	0.145127	+	0.0921003i
$304$	−15.4633	+	10.5313i	−0.886883	+	0.604010i
$305$	20.4652	+	21.6717i	1.17183	+	1.24092i
$306$	−13.6010	+	5.51290i	−0.777518	+	0.315151i
$307$	9.45012			0.539347			0.269673	−	0.962952i	$-0.413084\pi$
$307$	9.45012			0.539347			0.269673	+	0.962952i	$0.413084\pi$
$308$	−1.83135	−	1.66474i	−0.104351	−	0.0948575i
$309$	0.502558	−	0.236486i	0.0285895	−	0.0134532i
$310$	−10.5365	−	18.6810i	−0.598435	−	1.06101i
$311$	−6.32294	−	5.93764i	−0.358541	−	0.336693i	0.484254	−	0.874928i	$-0.339091\pi$
$311$	−6.32294	−	5.93764i	−0.358541	−	0.336693i	−0.842795	+	0.538235i	$0.819091\pi$
$312$	0.162986	−	1.60250i	0.00922724	−	0.0907236i
$313$	3.05934	+	24.2171i	0.172924	+	1.36883i	0.804699	+	0.593683i	$0.202327\pi$
$313$	3.05934	+	24.2171i	0.172924	+	1.36883i	−0.631775	+	0.775152i	$0.717673\pi$
$314$	0.750178	+	0.237046i	0.0423350	+	0.0133773i
$315$	−2.22869	+	0.146462i	−0.125573	+	0.00825222i
$316$	−13.8866	−	3.32661i	−0.781185	−	0.187137i
$317$	0.830402	−	13.1989i	0.0466400	−	0.741322i	−0.903323	−	0.428961i	$-0.858880\pi$
$317$	0.830402	−	13.1989i	0.0466400	−	0.741322i	0.949963	−	0.312362i	$-0.101120\pi$
$318$	10.0647	−	4.83606i	0.564400	−	0.271193i
$319$	0.722984	−	11.4915i	0.0404794	−	0.643401i
$320$	−17.0751	+	5.33303i	−0.954527	+	0.298125i
$321$	3.27359	−	1.29611i	0.182714	−	0.0723416i
$322$	−0.173782	+	1.47140i	−0.00968449	+	0.0819979i
$323$	8.38925	−	17.8281i	0.466790	−	0.991980i
$324$	−8.60003	+	2.35728i	−0.477779	+	0.130960i
$325$	1.18056	−	3.70359i	0.0654856	−	0.205438i
$326$	14.5727	−	27.0240i	0.807107	−	1.49672i
$327$	10.8044	−	2.06105i	0.597485	−	0.113976i
$328$	1.51503	+	10.0264i	0.0836535	+	0.553618i
$329$	−0.996022	−	1.20398i	−0.0549125	−	0.0663778i
$330$	5.20583	+	4.78297i	0.286572	+	0.263294i
$331$	−1.41069	+	3.56299i	−0.0775383	+	0.195839i	−0.963375	−	0.268158i	$-0.913585\pi$
$331$	−1.41069	+	3.56299i	−0.0775383	+	0.195839i	0.885837	+	0.463997i	$0.153585\pi$
$332$	−0.870170	+	18.6483i	−0.0477568	+	1.02346i
$333$	−18.0295	+	21.7939i	−0.988009	+	1.19430i
$334$	10.0037	+	3.86731i	0.547381	+	0.211610i
$335$	−34.4819	−	4.25835i	−1.88395	−	0.232659i
$336$	0.890413	−	0.786574i	0.0485760	−	0.0429111i
$337$	−13.0579	−	13.9052i	−0.711309	−	0.757467i	0.267207	−	0.963639i	$-0.413899\pi$
$337$	−13.0579	−	13.9052i	−0.711309	−	0.757467i	−0.978516	+	0.206172i	$0.933899\pi$
$338$	−17.5038	−	0.958941i	−0.952079	−	0.0521595i
$339$	2.38335	+	1.12152i	0.129446	+	0.0609127i
$340$	12.6333	−	13.9757i	0.685134	−	0.757941i
$341$	2.59424	+	20.5355i	0.140486	+	1.11206i
$342$	8.61926	−	13.8281i	0.466076	−	0.747740i
$343$	−3.29747	+	4.53858i	−0.178047	+	0.245060i
$344$	0.679699	+	27.9598i	0.0366469	+	1.50749i
$345$	0.518715	−	4.20028i	0.0279267	−	0.226136i
$346$	−11.4470	−	20.4282i	−0.615393	−	1.09822i
$347$	−2.08002	−	33.0610i	−0.111662	−	1.77481i	−0.512525	−	0.858672i	$-0.671290\pi$
$347$	−2.08002	−	33.0610i	−0.111662	−	1.77481i	0.400864	−	0.916138i	$-0.368710\pi$
$348$	5.44555	+	0.947621i	0.291912	+	0.0507978i
$349$	8.02959	+	2.60897i	0.429814	+	0.139655i	0.515931	−	0.856630i	$-0.327446\pi$
$349$	8.02959	+	2.60897i	0.429814	+	0.139655i	−0.0861172	+	0.996285i	$0.527446\pi$
$350$	2.49336	−	1.41550i	0.133276	−	0.0756619i
$351$	0.961465	+	2.95909i	0.0513192	+	0.157944i
$352$	17.2014	+	1.46834i	0.916839	+	0.0782629i
$353$	−6.58789	+	25.6582i	−0.350638	+	1.36565i	0.511635	+	0.859203i	$0.329040\pi$
$353$	−6.58789	+	25.6582i	−0.350638	+	1.36565i	−0.862273	+	0.506443i	$0.830960\pi$
$354$	−0.243497	−	0.0287586i	−0.0129417	−	0.00152850i
$355$	−9.54535	−	29.1010i	−0.506615	−	1.54452i
$356$	−4.42042	−	21.2923i	−0.234282	−	1.12849i
$357$	−0.386650	+	1.18999i	−0.0204637	+	0.0629808i
$358$	0.976466	+	1.16106i	0.0516079	+	0.0613641i
$359$	16.9147	+	9.29894i	0.892724	+	0.490779i	0.860935	−	0.508715i	$-0.169879\pi$
$359$	16.9147	+	9.29894i	0.892724	+	0.490779i	0.0317895	+	0.999495i	$0.489879\pi$
$360$	11.7311	−	10.2526i	0.618284	−	0.540361i
$361$	0.538984	+	2.82545i	0.0283676	+	0.148708i
$362$	8.61950	−	2.28770i	0.453031	−	0.120239i
$363$	0.525878	+	1.11755i	0.0276014	+	0.0586560i
$364$	0.438972	+	0.452536i	0.0230084	+	0.0237193i
$365$	5.51012	−	10.0895i	0.288413	−	0.528107i
$366$	13.3474	−	3.54253i	0.697678	−	0.185171i
$367$	−11.2241	+	28.3488i	−0.585892	+	1.47979i	0.270114	+	0.962828i	$0.412939\pi$
$367$	−11.2241	+	28.3488i	−0.585892	+	1.47979i	−0.856006	+	0.516966i	$0.827061\pi$
$368$	−5.26986	−	8.89073i	−0.274710	−	0.463461i
$369$	−4.73222	−	7.45679i	−0.246350	−	0.388185i
$370$	8.64617	−	35.2649i	0.449493	−	1.83333i
$371$	−1.08691	+	4.23324i	−0.0564296	+	0.219779i
$372$	−9.93509	+	0.160996i	−0.515110	+	0.00834727i
$373$	−7.63283	−	0.964251i	−0.395213	−	0.0499270i	−0.0747846	−	0.997200i	$-0.523827\pi$
$373$	−7.63283	−	0.964251i	−0.395213	−	0.0499270i	−0.320429	+	0.947273i	$0.603827\pi$
$374$	−16.3879	+	7.87437i	−0.847400	+	0.407174i
$375$	−7.14354	+	4.00543i	−0.368891	+	0.206840i
$376$	10.6202	+	2.45331i	0.547694	+	0.126520i
$377$	−0.367622	+	2.91002i	−0.0189335	+	0.149874i
$378$	−0.960267	+	2.08434i	−0.0493908	+	0.107207i
$379$	3.12531	−	12.1723i	0.160536	−	0.625248i	−0.836476	−	0.548004i	$-0.815388\pi$
$379$	3.12531	−	12.1723i	0.160536	−	0.625248i	0.997012	−	0.0772443i	$-0.0246121\pi$
$380$	−2.22700	+	20.7983i	−0.114243	+	1.06693i
$381$	0.536290	−	0.340340i	0.0274750	−	0.0174362i
$382$	1.55401	+	1.62822i	0.0795102	+	0.0833069i
$383$	5.21677	−	13.1761i	0.266565	−	0.673266i	−0.733414	−	0.679782i	$-0.762074\pi$
$383$	5.21677	−	13.1761i	0.266565	−	0.673266i	0.999979	+	0.00651658i	$0.00207431\pi$
$384$	−1.60272	+	8.13110i	−0.0817887	+	0.414938i
$385$	−2.74424	+	0.354461i	−0.139860	+	0.0180650i
$386$	−3.54324	−	10.6116i	−0.180346	−	0.540119i
$387$	−10.3714	−	22.0404i	−0.527209	−	1.12038i
$388$	21.4841	−	18.3676i	1.09069	−	0.932474i
$389$	10.8051	−	2.06118i	0.547838	−	0.104506i	0.0939709	−	0.995575i	$-0.470044\pi$
$389$	10.8051	−	2.06118i	0.547838	−	0.104506i	0.453868	+	0.891069i	$0.350044\pi$
$390$	−1.24702	−	1.29929i	−0.0631453	−	0.0657920i
$391$	9.53819	+	5.24366i	0.482367	+	0.265183i
$392$	−0.469868	−	19.3283i	−0.0237319	−	0.976224i
$393$	5.35803	+	1.74093i	0.270277	+	0.0878183i
$394$	0.278931	−	1.12409i	0.0140523	−	0.0566310i
$395$	−12.8897	+	9.42000i	−0.648553	+	0.473972i
$396$	−14.2229	+	4.87748i	−0.714730	+	0.245102i
$397$	11.2683	+	2.89321i	0.565540	+	0.145206i	0.520626	−	0.853785i	$-0.325699\pi$
$397$	11.2683	+	2.89321i	0.565540	+	0.145206i	0.0449139	+	0.998991i	$0.485699\pi$
$398$	34.1428	+	10.7887i	1.71143	+	0.540786i
$399$	−0.429295	−	1.32123i	−0.0214916	−	0.0661444i
$400$	−7.82216	+	18.4069i	−0.391108	+	0.920345i
$401$	0.833455	−	2.56511i	0.0416208	−	0.128096i	−0.928087	−	0.372363i	$-0.878548\pi$
$401$	0.833455	−	2.56511i	0.0416208	−	0.128096i	0.969708	+	0.244268i	$0.0785476\pi$
$402$	−9.35542	+	13.0985i	−0.466606	+	0.653294i
$403$	−0.331084	−	5.26243i	−0.0164925	−	0.262140i
$404$	4.69388	−	6.68576i	0.233529	−	0.332629i
$405$	−4.21974	+	9.03274i	−0.209680	+	0.448840i
$406$	−1.65574	+	1.39250i	−0.0821732	+	0.0691085i
$407$	−20.5969	+	28.3493i	−1.02095	+	1.40522i
$408$	−2.89805	−	8.23286i	−0.143475	−	0.407587i
$409$	0.690487	−	0.0872288i	0.0341424	−	0.00431319i	−0.108243	−	0.994124i	$-0.534523\pi$
$409$	0.690487	−	0.0872288i	0.0341424	−	0.00431319i	0.142386	+	0.989811i	$0.454523\pi$
$410$	9.63788	+	5.97013i	0.475981	+	0.294844i
$411$	10.8373	+	5.09963i	0.534562	+	0.251546i
$412$	−0.581016	−	1.40073i	−0.0286246	−	0.0690092i
$413$	0.0699581	−	0.0656950i	0.00344241	−	0.00323264i
$414$	7.32493	+	5.23173i	0.360000	+	0.257125i
$415$	15.2549	+	14.2454i	0.748833	+	0.699279i
$416$	−4.34979	−	0.648453i	−0.213266	−	0.0317930i
$417$	2.55860	+	2.11666i	0.125295	+	0.103653i
$418$	9.58147	−	17.7681i	0.468645	−	0.869066i
$419$	0.0976937	−	0.246746i	0.00477265	−	0.0120543i	−0.927371	−	0.374144i	$-0.877937\pi$
$419$	0.0976937	−	0.246746i	0.00477265	−	0.0120543i	0.932143	+	0.362090i	$0.117937\pi$
$420$	−0.0252283	−	1.32807i	−0.00123102	−	0.0648034i
$421$	10.2012	−	8.43919i	0.497177	−	0.411301i	−0.354750	−	0.934961i	$-0.615434\pi$
$421$	10.2012	−	8.43919i	0.497177	−	0.411301i	0.851927	+	0.523660i	$0.175434\pi$
$422$	−21.4849	−	19.8506i	−1.04587	−	0.966311i
$423$	−9.32505	+	1.77885i	−0.453400	+	0.0864906i
$424$	−11.9086	−	28.0651i	−0.578335	−	1.36296i
$425$	−2.75648	−	20.8819i	−0.133709	−	1.01292i
$426$	−13.9586	−	2.54573i	−0.676299	−	0.123341i
$427$	−2.30139	+	4.89070i	−0.111372	+	0.236677i
$428$	−3.11829	−	9.09309i	−0.150728	−	0.439531i
$429$	0.639806	+	1.61597i	0.0308901	+	0.0780195i
$430$	24.3090	+	19.6681i	1.17228	+	0.948482i
$431$	0.527898	−	8.39070i	0.0254279	−	0.404166i	−0.964640	−	0.263573i	$-0.915099\pi$
$431$	0.527898	−	8.39070i	0.0254279	−	0.404166i	0.990067	−	0.140593i	$-0.0449009\pi$
$432$	−3.50758	−	15.6193i	−0.168758	−	0.751484i
$433$	−27.9235	−	1.75680i	−1.34192	−	0.0844264i	−0.624476	−	0.781044i	$-0.714687\pi$
$433$	−27.9235	−	1.75680i	−1.34192	−	0.0844264i	−0.717443	+	0.696618i	$0.754687\pi$
$434$	2.45469	−	3.01664i	0.117829	−	0.144804i
$435$	4.75061	−	3.95243i	0.227774	−	0.189504i
$436$	−4.24615	−	29.7294i	−0.203354	−	1.42378i
$437$	−11.9897	+	1.51465i	−0.573546	+	0.0724557i
$438$	−2.89014	−	4.47360i	−0.138096	−	0.213757i
$439$	−3.33420	−	3.13102i	−0.159133	−	0.149435i	0.600891	−	0.799331i	$-0.294813\pi$
$439$	−3.33420	−	3.13102i	−0.159133	−	0.149435i	−0.760023	+	0.649896i	$0.774813\pi$
$440$	13.7072	−	13.5893i	0.653466	−	0.647844i
$441$	7.16964	+	15.2363i	0.341411	+	0.725536i
$442$	4.29240	−	1.73984i	0.204169	−	0.0827558i
$443$	−11.0352			−0.524298			−0.262149	−	0.965027i	$-0.584431\pi$
$443$	−11.0352			−0.524298			−0.262149	+	0.965027i	$0.584431\pi$
$444$	−12.4474	−	11.3150i	−0.590729	−	0.536988i
$445$	−21.3383	−	11.6534i	−1.01153	−	0.552425i
$446$	−20.9040	−	19.3138i	−0.989832	−	0.914537i
$447$	−10.3880	−	6.59240i	−0.491333	−	0.311810i
$448$	−2.03192	−	2.52854i	−0.0959994	−	0.119462i
$449$	−7.78855	−	5.65871i	−0.367564	−	0.267051i	0.388636	−	0.921391i	$-0.372946\pi$
$449$	−7.78855	−	5.65871i	−0.367564	−	0.267051i	−0.756200	+	0.654340i	$0.772946\pi$
$450$	−0.238331	−	17.4173i	−0.0112350	−	0.821060i
$451$	−6.43115	−	8.85172i	−0.302831	−	0.416811i
$452$	3.36206	−	6.35745i	0.158138	−	0.299029i
$453$	9.84882	−	3.89942i	0.462738	−	0.183211i
$454$	−12.7594	−	5.87834i	−0.598829	−	0.275884i
$455$	0.703363	−	0.0462227i	0.0329742	−	0.00216696i
$456$	7.97604	+	5.50382i	0.373512	+	0.257740i
$457$	−0.909894	−	1.25236i	−0.0425630	−	0.0585830i	0.787205	−	0.616691i	$-0.211527\pi$
$457$	−0.909894	−	1.25236i	−0.0425630	−	0.0585830i	−0.829768	+	0.558108i	$0.811527\pi$
$458$	−21.6677	−	5.37659i	−1.01247	−	0.251232i
$459$	11.5409	+	12.2898i	0.538682	+	0.573638i
$460$	−11.3895	−	1.94925i	−0.531039	−	0.0908840i
$461$	−15.7112	−	28.5786i	−0.731744	−	1.33104i	−0.935958	−	0.352111i	$-0.885464\pi$
$461$	−15.7112	−	28.5786i	−0.731744	−	1.33104i	0.204214	−	0.978926i	$-0.434536\pi$
$462$	−0.462241	+	1.19570i	−0.0215054	+	0.0556289i
$463$	−2.25297	+	4.09813i	−0.104704	+	0.190456i	−0.923469	−	0.383673i	$-0.874659\pi$
$463$	−2.25297	+	4.09813i	−0.104704	+	0.190456i	0.818765	+	0.574129i	$0.194659\pi$
$464$	3.27749	−	14.7312i	0.152153	−	0.683878i
$465$	−7.05737	+	8.57953i	−0.327278	+	0.397866i
$466$	−10.6947	−	16.5541i	−0.495421	−	0.766855i
$467$	5.64900	+	8.90139i	0.261404	+	0.411907i	0.949526	−	0.313688i	$-0.101565\pi$
$467$	5.64900	+	8.90139i	0.261404	+	0.411907i	−0.688122	+	0.725595i	$0.741565\pi$
$468$	3.69404	−	1.01254i	0.170757	−	0.0468048i
$469$	−1.56681	−	6.10231i	−0.0723484	−	0.281778i
$470$	9.78042	−	7.26996i	0.451137	−	0.335338i
$471$	−0.0255877	−	0.406704i	−0.00117902	−	0.0187400i
$472$	−0.109422	+	0.660434i	−0.00503655	+	0.0303989i
$473$	−14.5381	−	26.4447i	−0.668463	−	1.21593i
$474$	0.986434	+	7.33033i	0.0453084	+	0.336693i
$475$	16.1038	+	16.9581i	0.738892	+	0.778092i
$476$	3.19627	+	1.20596i	0.146501	+	0.0552752i
$477$	19.3561	+	18.1766i	0.886254	+	0.832248i
$478$	4.16440	−	0.829423i	0.190475	−	0.0379369i
$479$	3.12748	−	4.92812i	0.142898	−	0.225171i	−0.765339	−	0.643627i	$-0.777429\pi$
$479$	3.12748	−	4.92812i	0.142898	−	0.225171i	0.908237	+	0.418456i	$0.137429\pi$
$480$	5.76565	+	7.25339i	0.263165	+	0.331070i
$481$	5.69000	−	6.87803i	0.259442	−	0.313611i
$482$	3.76656	+	27.9898i	0.171562	+	1.27490i
$483$	0.743330	−	0.190855i	0.0338227	−	0.00868419i
$484$	3.11484	−	1.29202i	0.141584	−	0.0587280i
$485$	−0.0881849	−	31.6016i	−0.00400427	−	1.43496i
$486$	12.8363	+	17.3699i	0.582265	+	0.787915i
$487$	27.7556	+	5.29467i	1.25773	+	0.239924i	0.772811	−	0.634636i	$-0.218850\pi$
$487$	27.7556	+	5.29467i	1.25773	+	0.239924i	0.484917	+	0.874560i	$0.338850\pi$
$488$	−7.96299	−	36.8534i	−0.360468	−	1.66827i
$489$	−15.7777	−	1.99319i	−0.713494	−	0.0901353i
$490$	−16.8045	−	13.5963i	−0.759151	−	0.614220i
$491$	43.1045	+	8.22262i	1.94528	+	0.371082i	0.998837	+	0.0482064i	$0.0153505\pi$
$491$	43.1045	+	8.22262i	1.94528	+	0.371082i	0.946441	+	0.322875i	$0.104649\pi$
$492$	4.56108	−	2.60459i	0.205630	−	0.117424i
$493$	4.91136	+	15.1156i	0.221196	+	0.680773i
$494$	−2.72019	+	4.36409i	−0.122387	+	0.196349i
$495$	−6.14482	+	15.6475i	−0.276189	+	0.703302i
$496$	−0.825282	+	27.1167i	−0.0370562	+	1.21758i
$497$	4.27914	−	3.54001i	0.191946	−	0.158791i
$498$	9.17200	−	3.06253i	0.411007	−	0.137235i
$499$		−	29.4285i		−	1.31740i	−0.752405	−	0.658700i	$-0.771106\pi$
$499$		−	29.4285i		−	1.31740i	0.752405	−	0.658700i	$-0.228894\pi$
$500$	10.0150	+	19.9925i	0.447885	+	0.894091i
$501$		−	5.55538i		−	0.248196i
$502$	−2.94878	−	8.83132i	−0.131611	−	0.394161i
$503$	29.9733	−	24.7961i	1.33644	−	1.10560i	0.350858	−	0.936429i	$-0.385890\pi$
$503$	29.9733	−	24.7961i	1.33644	−	1.10560i	0.985586	−	0.169174i	$-0.0541100\pi$
$504$	2.50807	+	1.30047i	0.111718	+	0.0579276i
$505$	−2.29601	−	8.83987i	−0.102171	−	0.393369i
$506$	9.46378	+	5.89889i	0.420716	+	0.262238i
$507$	2.80589	+	8.63564i	0.124614	+	0.383522i
$508$	−0.859967	−	1.50595i	−0.0381549	−	0.0668157i
$509$	28.0903	+	5.35851i	1.24508	+	0.237512i	0.767484	−	0.641068i	$-0.221508\pi$
$509$	28.0903	+	5.35851i	1.24508	+	0.237512i	0.477596	+	0.878579i	$0.341508\pi$
$510$	−9.11157	−	3.49321i	−0.403467	−	0.154682i
$511$	2.06818	+	0.261272i	0.0914911	+	0.0115580i
$512$	21.9722	+	5.40593i	0.971042	+	0.238911i
$513$	−18.3870	−	3.50751i	−0.811807	−	0.154860i
$514$	15.6694	−	11.5796i	0.691149	−	0.510755i
$515$	−1.61392	−	0.519420i	−0.0711179	−	0.0228884i
$516$	13.3812	−	5.55043i	0.589073	−	0.244344i
$517$	−11.3915	+	2.92483i	−0.500996	+	0.128634i
$518$	6.52530	−	0.878103i	0.286705	−	0.0385816i
$519$	−7.73145	+	9.34571i	−0.339373	+	0.410231i
$520$	−3.70228	+	3.23568i	−0.162356	+	0.141894i
$521$	9.19744	−	14.4928i	0.402947	−	0.634943i	−0.580895	−	0.813978i	$-0.697298\pi$
$521$	9.19744	−	14.4928i	0.402947	−	0.634943i	0.983843	+	0.179035i	$0.0572975\pi$
$522$	2.56742	+	12.8906i	0.112373	+	0.564206i
$523$	14.1139	+	13.2538i	0.617158	+	0.579550i	0.928769	−	0.370660i	$-0.120868\pi$
$523$	14.1139	+	13.2538i	0.617158	+	0.579550i	−0.311611	+	0.950210i	$0.600868\pi$
$524$	5.42996	−	14.3915i	0.237209	−	0.628696i
$525$	−1.14955	−	0.940237i	−0.0501707	−	0.0410353i
$526$	−40.3145	+	5.42509i	−1.75780	+	0.236545i
$527$	−13.7643	−	25.0371i	−0.599581	−	1.09063i
$528$	−2.50332	−	8.58472i	−0.108943	−	0.373602i
$529$	1.02499	+	16.2918i	0.0445648	+	0.708337i
$530$	−32.5302	−	10.1793i	−1.41302	−	0.442162i
$531$	−0.144997	−	0.564727i	−0.00629234	−	0.0245071i
$532$	−3.65807	+	1.00268i	−0.158597	+	0.0434718i
$533$	1.49346	+	2.35332i	0.0646891	+	0.101934i
$534$	−9.46126	+	6.11238i	−0.409429	+	0.264509i
$535$	−10.0038	−	3.92854i	−0.432503	−	0.169846i
$536$	34.5332	+	27.1822i	1.49161	+	1.17409i
$537$	0.378566	−	0.688609i	0.0163363	−	0.0297157i
$538$	−33.6321	−	13.0017i	−1.44998	−	0.560543i
$539$	10.0500	+	18.2809i	0.432885	+	0.787415i
$540$	−15.8449	−	8.32290i	−0.681856	−	0.358161i
$541$	20.1485	+	21.4560i	0.866252	+	0.922465i	0.997626	−	0.0688678i	$-0.0219387\pi$
$541$	20.1485	+	21.4560i	0.866252	+	0.922465i	−0.131373	+	0.991333i	$0.541939\pi$
$542$	8.34031	−	33.6115i	0.358247	−	1.44374i
$543$	−2.71512	−	3.73704i	−0.116517	−	0.160372i
$544$	−22.8225	+	6.85618i	−0.978506	+	0.293956i
$545$	−28.3991	−	17.9116i	−1.21648	−	0.767250i
$546$	0.136645	−	0.296600i	0.00584788	−	0.0126933i
$547$	13.3080	−	5.26902i	0.569010	−	0.225287i	−0.0659622	−	0.997822i	$-0.521012\pi$
$547$	13.3080	−	5.26902i	0.569010	−	0.225287i	0.634972	+	0.772535i	$0.281012\pi$
$548$	15.2875	−	28.9077i	0.653050	−	1.23488i
$549$	19.3017	+	26.5666i	0.823778	+	1.13383i
$550$	−1.64957	−	21.5168i	−0.0703380	−	0.917481i
$551$	−14.2763	−	10.3723i	−0.608189	−	0.441875i
$552$	−3.31110	+	4.20654i	−0.140930	+	0.179042i
$553$	−2.44433	−	1.55122i	−0.103943	−	0.0659645i
$554$	15.2609	−	16.5173i	0.648373	−	0.701755i
$555$	−18.6523	+	2.40923i	−0.791744	+	0.102266i
$556$	6.09842	−	6.70875i	0.258631	−	0.284514i
$557$	−12.2988			−0.521117			−0.260559	−	0.965458i	$-0.583907\pi$
$557$	−12.2988			−0.521117			−0.260559	+	0.965458i	$0.583907\pi$
$558$	−8.87579	−	21.8977i	−0.375742	−	0.927003i
$559$	3.27316	+	6.95583i	0.138440	+	0.294200i
$560$	−3.62530	−	0.100209i	−0.153197	−	0.00423460i
$561$	6.86510	+	6.44675i	0.289845	+	0.272182i
$562$	−11.6890	+	7.55161i	−0.493072	+	0.318546i
$563$	19.2856	−	2.43634i	0.812791	−	0.102679i	0.292060	−	0.956400i	$-0.405659\pi$
$563$	19.2856	−	2.43634i	0.812791	−	0.102679i	0.520731	+	0.853721i	$0.325659\pi$
$564$	−0.798272	−	5.58910i	−0.0336133	−	0.235344i
$565$	−2.98078	−	7.46765i	−0.125402	−	0.314166i
$566$	13.1108	+	10.6685i	0.551089	+	0.448430i
$567$	−1.80429	−	0.113517i	−0.0757732	−	0.00476725i
$568$	−8.71944	+	37.7458i	−0.365860	+	1.58378i
$569$	−2.53590	+	40.3069i	−0.106310	+	1.68975i	0.478108	+	0.878301i	$0.341323\pi$
$569$	−2.53590	+	40.3069i	−0.106310	+	1.68975i	−0.584419	+	0.811452i	$0.698677\pi$
$570$	10.4641	−	2.80857i	0.438295	−	0.117638i
$571$	11.9836	+	30.2670i	0.501496	+	1.26663i	0.931478	+	0.363797i	$0.118520\pi$
$571$	11.9836	+	30.2670i	0.501496	+	1.26663i	−0.429982	+	0.902837i	$0.641480\pi$
$572$	4.48868	−	1.53930i	0.187681	−	0.0643616i
$573$	0.496393	−	1.05489i	0.0207371	−	0.0440686i
$574$	−0.368848	+	2.02245i	−0.0153954	+	0.0844155i
$575$	−9.90815	+	8.29031i	−0.413199	+	0.345730i
$576$	−19.4088	+	3.41711i	−0.808699	+	0.142379i
$577$	7.59259	−	1.44836i	0.316084	−	0.0602962i	−0.0268982	−	0.999638i	$-0.508563\pi$
$577$	7.59259	−	1.44836i	0.316084	−	0.0602962i	0.342982	+	0.939342i	$0.388563\pi$
$578$	0.715965	−	0.774912i	0.0297802	−	0.0322321i
$579$	−4.46500	+	3.69377i	−0.185559	+	0.153508i
$580$	−10.1750	−	13.4594i	−0.422493	−	0.558873i
$581$	−1.39328	+	3.51903i	−0.0578031	+	0.145994i
$582$	−12.8865	−	6.94905i	−0.534162	−	0.288047i
$583$	25.3465	+	20.9684i	1.04974	+	0.868424i
$584$	−12.5688	+	7.31302i	−0.520099	+	0.302615i
$585$	1.81254	−	3.87991i	0.0749393	−	0.160415i
$586$	−3.74481	+	5.24310i	−0.154697	+	0.216590i
$587$	−7.62228	+	7.15780i	−0.314605	+	0.295434i	−0.825722	−	0.564077i	$-0.809232\pi$
$587$	−7.62228	+	7.15780i	−0.314605	+	0.295434i	0.511117	+	0.859511i	$0.329232\pi$
$588$	−9.25025	+	3.83695i	−0.381474	+	0.158233i
$589$	28.7033	+	13.5067i	1.18270	+	0.556535i
$590$	0.483335	+	0.571463i	0.0198986	+	0.0235267i
$591$	−0.595176	+	0.0751882i	−0.0244823	+	0.00309283i
$592$	−32.4438	+	32.5082i	−1.33343	+	1.33608i
$593$	4.34264	−	5.97714i	0.178331	−	0.245452i	−0.710489	−	0.703709i	$-0.751526\pi$
$593$	4.34264	−	5.97714i	0.178331	−	0.245452i	0.888820	+	0.458257i	$0.151526\pi$
$594$	11.1176	+	13.2194i	0.456163	+	0.542398i
$595$	3.34185	−	1.84936i	0.137003	−	0.0758165i
$596$	−19.3016	+	27.4923i	−0.790624	+	1.12613i
$597$	−1.16457	−	18.5103i	−0.0476627	−	0.757577i
$598$	−2.31171	−	1.65110i	−0.0945327	−	0.0675187i
$599$	3.91305	−	12.0431i	0.159883	−	0.492070i	−0.838740	−	0.544532i	$-0.816707\pi$
$599$	3.91305	−	12.0431i	0.159883	−	0.492070i	0.998623	+	0.0524629i	$0.0167071\pi$
$600$	10.3538	+	0.341238i	0.422693	+	0.0139310i
$601$	−8.87441	−	27.3126i	−0.361995	−	1.11411i	−0.951842	−	0.306590i	$-0.900812\pi$
$601$	−8.87441	−	27.3126i	−0.361995	−	1.11411i	0.589847	−	0.807515i	$-0.299188\pi$
$602$	−1.70843	+	5.40667i	−0.0696305	+	0.220360i
$603$	−37.0738	−	9.51892i	−1.50976	−	0.387641i
$604$	−9.38160	−	27.3572i	−0.381732	−	1.11315i
$605$	1.15505	−	3.58891i	0.0469593	−	0.145910i
$606$	−4.10675	−	1.01904i	−0.166825	−	0.0413957i
$607$	5.10278	+	1.65799i	0.207115	+	0.0672958i	0.410737	−	0.911754i	$-0.365271\pi$
$607$	5.10278	+	1.65799i	0.207115	+	0.0672958i	−0.203622	+	0.979050i	$0.565271\pi$
$608$	16.0258	−	21.0528i	0.649930	−	0.853803i
$609$	0.981997	+	0.539858i	0.0397925	+	0.0218761i
$610$	−37.1590	−	19.9044i	−1.50452	−	0.805905i
$611$	2.94294	−	0.561395i	0.119058	−	0.0227116i
$612$	15.7753	−	13.4869i	0.637681	−	0.545177i
$613$	−7.91745	−	16.8254i	−0.319783	−	0.679573i	0.678713	−	0.734404i	$-0.262538\pi$
$613$	−7.91745	−	16.8254i	−0.319783	−	0.679573i	−0.998496	+	0.0548309i	$0.982538\pi$
$614$	−12.6765	+	4.23269i	−0.511582	+	0.170818i
$615$	1.08426	−	5.77136i	0.0437217	−	0.232724i
$616$	3.20223	+	1.41285i	0.129022	+	0.0569252i
$617$	−11.4682	+	28.9653i	−0.461691	+	1.16610i	0.493405	+	0.869800i	$0.335752\pi$
$617$	−11.4682	+	28.9653i	−0.461691	+	1.16610i	−0.955096	+	0.296298i	$0.904248\pi$
$618$	−0.568216	+	0.542320i	−0.0228570	+	0.0218153i
$619$	11.2107	−	7.11451i	0.450595	−	0.285956i	−0.291101	−	0.956692i	$-0.594022\pi$
$619$	11.2107	−	7.11451i	0.450595	−	0.285956i	0.741696	+	0.670736i	$0.234022\pi$
$620$	22.5010	+	20.3396i	0.903662	+	0.816858i
$621$	2.57159	−	10.0157i	0.103194	−	0.401916i
$622$	11.1411	+	5.13279i	0.446719	+	0.205806i
$623$	0.552567	−	4.37402i	0.0221381	−	0.175241i
$624$	0.499126	+	2.22261i	0.0199810	+	0.0889757i
$625$	24.2825	+	5.94658i	0.971299	+	0.237863i
$626$	−14.9507	−	31.1149i	−0.597548	−	1.24360i
$627$	−10.3738	−	1.31051i	−0.414289	−	0.0523369i
$628$	−1.11247	+	0.0180274i	−0.0443924	+	0.000719371i
$629$	12.0289	−	46.8496i	0.479624	−	1.86801i
$630$	2.92400	−	1.19469i	0.116495	−	0.0475978i
$631$	21.4036	+	33.7267i	0.852065	+	1.34264i	0.938106	+	0.346349i	$0.112579\pi$
$631$	21.4036	+	33.7267i	0.852065	+	1.34264i	−0.0860404	+	0.996292i	$0.527421\pi$
$632$	20.1177	−	1.75745i	0.800239	−	0.0699074i
$633$	−5.57761	+	14.0874i	−0.221690	+	0.559925i
$634$	4.79784	+	18.0771i	0.190547	+	0.717932i
$635$	−1.90555	−	0.357995i	−0.0756195	−	0.0142066i
$636$	−11.3348	+	10.9951i	−0.449455	+	0.435985i
$637$	−2.26270	−	4.80848i	−0.0896514	−	0.190519i
$638$	4.17721	+	15.7387i	0.165377	+	0.623100i
$639$	−6.32230	−	33.1427i	−0.250106	−	1.31110i
$640$	20.5161	−	14.8017i	0.810970	−	0.585088i
$641$	3.95540	+	2.17450i	0.156229	+	0.0858875i	0.557950	−	0.829874i	$-0.311588\pi$
$641$	3.95540	+	2.17450i	0.156229	+	0.0858875i	−0.401721	+	0.915762i	$0.631588\pi$
$642$	−3.81071	+	3.20485i	−0.150397	+	0.126485i
$643$	8.10711	−	24.9511i	0.319713	−	0.983976i	−0.654058	−	0.756445i	$-0.726935\pi$
$643$	8.10711	−	24.9511i	0.319713	−	0.983976i	0.973771	−	0.227531i	$-0.0730654\pi$
$644$	−0.425924	−	2.05159i	−0.0167838	−	0.0808439i
$645$	4.96201	−	15.4178i	0.195379	−	0.607074i
$646$	−3.26828	+	27.6723i	−0.128589	+	1.08875i
$647$	7.79635	−	30.3648i	0.306506	−	1.19376i	−0.609561	−	0.792739i	$-0.708654\pi$
$647$	7.79635	−	30.3648i	0.306506	−	1.19376i	0.916067	−	0.401024i	$-0.131346\pi$
$648$	10.4804	−	7.01402i	0.411707	−	0.275537i
$649$	−0.223210	−	0.686969i	−0.00876175	−	0.0269659i
$650$	0.0752160	+	5.49681i	0.00295021	+	0.215603i
$651$	−1.91589	−	0.622509i	−0.0750895	−	0.0243980i
$652$	−7.44401	+	42.7773i	−0.291530	+	1.67529i
$653$	2.38343	+	37.8836i	0.0932710	+	1.48250i	0.714921	+	0.699205i	$0.246463\pi$
$653$	2.38343	+	37.8836i	0.0932710	+	1.48250i	−0.621650	+	0.783295i	$0.713537\pi$
$654$	−13.5700	+	7.60400i	−0.530630	+	0.297340i
$655$	−8.32693	−	15.0470i	−0.325360	−	0.587935i
$656$	−6.52311	−	12.7710i	−0.254684	−	0.498624i
$657$	7.44421	−	10.2461i	0.290426	−	0.399737i
$658$	1.87534	+	1.16892i	0.0731083	+	0.0455693i
$659$	−5.00751	−	39.6385i	−0.195065	−	1.54410i	−0.720615	−	0.693335i	$-0.756141\pi$
$659$	−5.00751	−	39.6385i	−0.195065	−	1.54410i	0.525550	−	0.850762i	$-0.323859\pi$
$660$	−9.12545	−	4.08425i	−0.355208	−	0.158979i
$661$	1.87536	+	0.882480i	0.0729432	+	0.0343245i	0.461905	−	0.886929i	$-0.347166\pi$
$661$	1.87536	+	0.882480i	0.0729432	+	0.0343245i	−0.388962	+	0.921254i	$0.627166\pi$
$662$	0.296456	−	5.41128i	0.0115221	−	0.210315i
$663$	−1.64226	−	1.74883i	−0.0637800	−	0.0679188i
$664$	−7.18526	−	25.4047i	−0.278842	−	0.985895i
$665$	−1.79489	+	3.84212i	−0.0696027	+	0.148991i
$666$	14.4235	−	37.3100i	0.558900	−	1.44573i
$667$	6.21379	−	7.51118i	0.240599	−	0.290834i
$668$	−15.1513	−	0.706995i	−0.586222	−	0.0273544i
$669$	−5.42680	+	13.7065i	−0.209812	+	0.529925i
$670$	48.1618	−	9.73218i	1.86065	−	0.375987i
$671$	25.9320	+	31.3464i	1.00109	+	1.21011i
$672$	−0.842105	+	1.45393i	−0.0324849	+	0.0560867i
$673$	43.3775	−	8.27470i	1.67208	−	0.318966i	0.737668	−	0.675163i	$-0.235927\pi$
$673$	43.3775	−	8.27470i	1.67208	−	0.318966i	0.934411	+	0.356197i	$0.115927\pi$
$674$	23.7442	+	12.8041i	0.914591	+	0.493194i
$675$	−18.5638	+	7.47003i	−0.714520	+	0.287521i
$676$	23.9093	−	6.55357i	0.919587	−	0.252060i
$677$	0.0277678	−	0.0590097i	0.00106720	−	0.00226793i	−0.904293	−	0.426913i	$-0.859601\pi$
$677$	0.0277678	−	0.0590097i	0.00106720	−	0.00226793i	0.905360	+	0.424645i	$0.139601\pi$
$678$	−3.69939	−	0.436922i	−0.142074	−	0.0167799i
$679$	5.32806	−	2.10953i	0.204472	−	0.0809563i
$680$	−10.6867	+	24.4056i	−0.409816	+	0.935914i
$681$	−0.456906	+	7.26231i	−0.0175087	+	0.278292i
$682$	−12.6778	−	26.3846i	−0.485457	−	1.01032i
$683$	−1.87167	+	29.7494i	−0.0716176	+	1.13833i	0.784014	+	0.620744i	$0.213169\pi$
$683$	−1.87167	+	29.7494i	−0.0716176	+	1.13833i	−0.855631	+	0.517586i	$0.826831\pi$
$684$	−5.36837	+	22.4098i	−0.205265	+	0.856860i
$685$	−13.5538	−	33.9558i	−0.517864	−	1.29739i
$686$	2.39044	−	7.56503i	0.0912676	−	0.288834i
$687$	1.44931	+	11.4725i	0.0552945	+	0.437701i
$688$	−13.4349	−	37.2012i	−0.512201	−	1.41828i
$689$	−6.10867	−	5.73642i	−0.232722	−	0.218540i
$690$	1.18549	+	5.86664i	0.0451308	+	0.223339i
$691$	−21.3132	+	10.0292i	−0.810791	+	0.381529i	−0.786049	−	0.618164i	$-0.787877\pi$
$691$	−21.3132	+	10.0292i	−0.810791	+	0.381529i	−0.0247425	+	0.999694i	$0.507877\pi$
$692$	24.5048	+	22.2755i	0.931535	+	0.846788i
$693$	−3.04837			−0.115798
$694$	17.5982	+	43.4169i	0.668017	+	1.64808i
$695$	−1.29849	−	10.0529i	−0.0492546	−	0.381330i
$696$	−7.72917	+	1.16790i	−0.292973	+	0.0442692i
$697$	12.7516	+	8.09243i	0.483002	+	0.306523i
$698$	−11.9395	+	0.0967327i	−0.451919	+	0.00366139i
$699$	−6.00030	+	8.25870i	−0.226952	+	0.312373i
$700$	−2.71063	+	3.01555i	−0.102452	+	0.113977i
$701$	0.732711	+	1.00849i	0.0276741	+	0.0380901i	0.822630	−	0.568577i	$-0.192506\pi$
$701$	0.732711	+	1.00849i	0.0276741	+	0.0380901i	−0.794956	+	0.606667i	$0.792506\pi$
$702$	−2.61509	−	3.53871i	−0.0987002	−	0.133560i
$703$	19.7697	+	49.9326i	0.745630	+	1.88325i
$704$	−23.7319	+	5.73484i	−0.894429	+	0.216140i
$705$	−5.33900	−	3.36737i	−0.201078	−	0.126823i
$706$	−2.65516	−	37.3689i	−0.0999283	−	1.40640i
$707$	1.33986	−	0.973464i	0.0503906	−	0.0366109i
$708$	0.339510	−	0.0704846i	0.0127596	−	0.00264897i
$709$	−10.3349	−	11.0056i	−0.388137	−	0.413324i	0.504993	−	0.863124i	$-0.331495\pi$
$709$	−10.3349	−	11.0056i	−0.388137	−	0.413324i	−0.893129	+	0.449800i	$0.851495\pi$
$710$	25.8385	+	34.7611i	0.969703	+	1.30456i
$711$	−15.4126	+	8.47317i	−0.578019	+	0.317769i
$712$	15.4664	+	26.5818i	0.579626	+	0.996195i
$713$	−8.44232	+	15.3565i	−0.316167	+	0.575106i
$714$	−0.0143358	−	1.76944i	−0.000536504	−	0.0662198i
$715$	1.93927	−	4.93826i	0.0725247	−	0.184680i
$716$	−1.82988	−	1.12011i	−0.0683859	−	0.0418604i
$717$	−1.17850	−	1.85702i	−0.0440120	−	0.0693518i
$718$	−26.8546	−	4.89764i	−1.00220	−	0.182778i
$719$	42.9750	−	11.0341i	1.60270	−	0.411503i	0.661659	−	0.749805i	$-0.269853\pi$
$719$	42.9750	−	11.0341i	1.60270	−	0.411503i	0.941037	+	0.338302i	$0.109853\pi$
$720$	−11.1441	+	19.0074i	−0.415317	+	0.708362i
$721$	−0.0193045	−	0.306836i	−0.000718936	−	0.0114272i
$722$	−1.98851	−	3.54869i	−0.0740048	−	0.132068i
$723$	12.8192	−	7.04739i	0.476749	−	0.262095i
$724$	−10.5376	+	6.92941i	−0.391628	+	0.257530i
$725$	−18.8333	−	1.07940i	−0.699451	−	0.0400880i
$726$	−1.20597	−	1.26355i	−0.0447576	−	0.0468948i
$727$	−28.8617	+	30.7346i	−1.07042	+	1.13988i	−0.0807211	+	0.996737i	$0.525722\pi$
$727$	−28.8617	+	30.7346i	−1.07042	+	1.13988i	−0.989701	+	0.143147i	$0.954278\pi$
$728$	−0.791533	−	0.410422i	−0.0293362	−	0.0152112i
$729$	−1.17270	+	1.84788i	−0.0434334	+	0.0684402i
$730$	−2.87229	+	16.0021i	−0.106308	+	0.592265i
$731$	32.0958	+	26.5519i	1.18710	+	0.982058i
$732$	−16.3176	+	10.7302i	−0.603117	+	0.396601i
$733$	−18.9352	+	4.86174i	−0.699388	+	0.179572i	−0.581610	−	0.813468i	$-0.697577\pi$
$733$	−18.9352	+	4.86174i	−0.699388	+	0.179572i	−0.117778	+	0.993040i	$0.537577\pi$
$734$	2.35874	−	43.0547i	0.0870628	−	1.58918i
$735$	−3.43018	+	10.6581i	−0.126524	+	0.393130i
$736$	11.0512	+	9.56577i	0.407353	+	0.352599i
$737$	−46.5798	−	8.88557i	−1.71579	−	0.327304i
$738$	9.68775	+	7.88308i	0.356611	+	0.290180i
$739$	−2.89211	+	22.8934i	−0.106388	+	0.842148i	0.845131	+	0.534559i	$0.179522\pi$
$739$	−2.89211	+	22.8934i	−0.106388	+	0.842148i	−0.951519	+	0.307589i	$0.900478\pi$
$740$	4.19699	+	51.1773i	0.154285	+	1.88132i
$741$	2.61646	+	0.499116i	0.0961180	+	0.0183355i
$742$	−0.438065	−	6.16535i	−0.0160819	−	0.226337i
$743$	−2.72262	+	0.884631i	−0.0998831	+	0.0324540i	−0.358532	−	0.933517i	$-0.616723\pi$
$743$	−2.72262	+	0.884631i	−0.0998831	+	0.0324540i	0.258649	+	0.965971i	$0.416723\pi$
$744$	13.2549	−	4.66587i	0.485950	−	0.171059i
$745$	9.44134	+	36.3502i	0.345904	+	1.33177i
$746$	10.6707	−	2.12528i	0.390681	−	0.0778119i
$747$	14.6570	+	17.7173i	0.536272	+	0.648242i
$748$	18.4561	−	17.9029i	0.674820	−	0.654595i
$749$		−	1.94890i		−	0.0712112i
$750$	7.78841	−	8.57252i	0.284392	−	0.313024i
$751$	−8.77949			−0.320368			−0.160184	−	0.987087i	$-0.551209\pi$
$751$	−8.77949			−0.320368			−0.160184	+	0.987087i	$0.551209\pi$
$752$	−15.3449	+	1.46586i	−0.559570	+	0.0534544i
$753$	−3.71591	+	3.07406i	−0.135415	+	0.112025i
$754$	−0.810263	−	4.06820i	−0.0295080	−	0.148155i
$755$	−30.0972	−	11.8193i	−1.09535	−	0.430148i
$756$	0.354543	−	3.22606i	0.0128946	−	0.117331i
$757$	−2.30132	−	7.08272i	−0.0836427	−	0.257426i	0.900485	−	0.434887i	$-0.143212\pi$
$757$	−2.30132	−	7.08272i	−0.0836427	−	0.257426i	−0.984128	+	0.177461i	$0.943212\pi$
$758$	1.25961	+	17.7279i	0.0457513	+	0.643905i
$759$	1.08236	−	5.67394i	0.0392873	−	0.205951i
$760$	−6.32819	−	28.8965i	−0.229547	−	1.04819i
$761$	−17.2352	−	2.17731i	−0.624774	−	0.0789273i	−0.193429	−	0.981114i	$-0.561961\pi$
$761$	−17.2352	−	2.17731i	−0.624774	−	0.0789273i	−0.431345	+	0.902187i	$0.641961\pi$
$762$	−0.566949	+	0.696740i	−0.0205384	+	0.0252402i
$763$	1.14086	−	5.98059i	0.0413019	−	0.216512i
$764$	−2.81385	−	1.48807i	−0.101801	−	0.0538365i
$765$	−0.0647523	−	23.2044i	−0.00234112	−	0.838957i
$766$	−1.09631	+	20.0111i	−0.0396112	+	0.723031i
$767$	0.0457603	+	0.178225i	0.00165231	+	0.00643532i
$768$	−1.49199	−	11.6250i	−0.0538376	−	0.419482i
$769$	31.6424	−	38.2491i	1.14105	−	1.37930i	0.226906	−	0.973917i	$-0.427139\pi$
$769$	31.6424	−	38.2491i	1.14105	−	1.37930i	0.914148	−	0.405381i	$-0.132861\pi$
$770$	3.52240	−	1.70462i	0.126938	−	0.0614303i
$771$	−8.52101	−	5.40760i	−0.306877	−	0.194750i
$772$	9.50588	+	12.6476i	0.342124	+	0.455197i
$773$	30.5269	+	28.6666i	1.09797	+	1.03107i	0.999354	+	0.0359421i	$0.0114432\pi$
$773$	30.5269	+	28.6666i	1.09797	+	1.03107i	0.0986211	+	0.995125i	$0.468557\pi$
$774$	23.7842	+	24.9199i	0.854906	+	0.895728i
$775$	33.6199	−	4.43795i	1.20766	−	0.159416i
$776$	−20.5923	+	34.2612i	−0.739219	+	1.22991i
$777$	−1.64297	−	2.98854i	−0.0589411	−	0.107213i
$778$	−13.5708	+	7.60446i	−0.486538	+	0.272633i
$779$	−16.7353	+	1.05290i	−0.599605	+	0.0377240i
$780$	2.25472	+	1.18434i	0.0807318	+	0.0424062i
$781$	−10.3953	−	40.4870i	−0.371973	−	1.44874i
$782$	−15.1433	−	2.76178i	−0.541522	−	0.0987609i
$783$	12.7487	−	8.09055i	0.455600	−	0.289133i
$784$	9.28738	+	25.7167i	0.331692	+	0.918454i
$785$	−0.790242	+	0.960684i	−0.0282049	+	0.0342883i
$786$	−7.96709	+	0.0645483i	−0.284177	+	0.00230236i
$787$	−8.69944	−	4.78256i	−0.310101	−	0.170480i	0.319102	−	0.947720i	$-0.396619\pi$
$787$	−8.69944	−	4.78256i	−0.310101	−	0.170480i	−0.629203	+	0.777241i	$0.716619\pi$
$788$	0.129319	+	1.63281i	0.00460678	+	0.0581663i
$789$	10.1506	+	18.4638i	0.361369	+	0.657329i
$790$	13.0712	−	18.4094i	0.465054	−	0.654977i
$791$	1.06286	−	0.998090i	0.0377909	−	0.0354880i
$792$	16.8942	−	12.9131i	0.600310	−	0.458848i
$793$	−6.09152	−	8.38426i	−0.216316	−	0.297734i
$794$	−16.4113	+	1.16607i	−0.582415	+	0.0413822i
$795$	1.15776	+	17.6174i	0.0410615	+	0.624825i
$796$	−50.6318	+	0.820479i	−1.79460	+	0.0290811i
$797$	−33.3197	+	13.1922i	−1.18025	+	0.467292i	−0.874596	−	0.484852i	$-0.838873\pi$
$797$	−33.3197	+	13.1922i	−1.18025	+	0.467292i	−0.305649	+	0.952144i	$0.598873\pi$
$798$	1.16764	+	1.58004i	0.0413340	+	0.0559328i
$799$	13.1336	−	9.54213i	0.464634	−	0.337576i
$800$	2.24832	−	28.1948i	0.0794902	−	0.996836i
$801$	−21.6695	−	15.7438i	−0.765654	−	0.556281i
$802$	0.0309020	+	3.81418i	0.00109119	+	0.134683i
$803$	8.40724	−	13.2477i	0.296685	−	0.467501i
$804$	6.68268	−	21.7608i	0.235680	−	0.767443i
$805$	−2.05603	−	1.12285i	−0.0724654	−	0.0395753i
$806$	2.80115	+	6.91079i	0.0986664	+	0.243422i
$807$			18.6769i			0.657458i
$808$	−3.30189	+	11.0707i	−0.116160	+	0.389467i
$809$	−22.7813	−	48.4128i	−0.800949	−	1.70210i	−0.707758	−	0.706455i	$-0.750293\pi$
$809$	−22.7813	−	48.4128i	−0.800949	−	1.70210i	−0.0931910	−	0.995648i	$-0.529707\pi$
$810$	1.61466	−	14.0066i	0.0567333	−	0.492143i
$811$	18.8786	−	20.1036i	0.662917	−	0.705935i	−0.306358	−	0.951916i	$-0.599110\pi$
$811$	18.8786	−	20.1036i	0.662917	−	0.705935i	0.969274	+	0.245982i	$0.0791104\pi$
$812$	1.59734	−	2.60952i	0.0560556	−	0.0915762i
$813$	−17.7964	+	2.24820i	−0.624146	+	0.0788480i
$814$	14.9314	−	47.2534i	0.523346	−	1.65623i
$815$	31.0482	+	37.3183i	1.08757	+	1.30720i
$816$	7.57496	+	9.74563i	0.265177	+	0.341165i
$817$	−46.1580	−	2.90402i	−1.61486	−	0.101599i
$818$	−0.887159	+	0.426278i	−0.0310188	+	0.0149045i
$819$	0.775014	+	0.0487597i	0.0270812	+	0.00170380i
$820$	−15.6024	−	3.69162i	−0.544859	−	0.128917i
$821$	9.37506	+	23.6787i	0.327192	+	0.826392i	0.996514	+	0.0834204i	$0.0265844\pi$
$821$	9.37506	+	23.6787i	0.327192	+	0.826392i	−0.669323	+	0.742972i	$0.733416\pi$
$822$	−16.8213	−	1.98671i	−0.586712	−	0.0692945i
$823$	−13.7056	−	6.44937i	−0.477748	−	0.224811i	0.171800	−	0.985132i	$-0.445042\pi$
$823$	−13.7056	−	6.44937i	−0.477748	−	0.224811i	−0.649548	+	0.760321i	$0.725042\pi$
$824$	1.40677	+	1.61872i	0.0490071	+	0.0563909i
$825$	−10.0873	+	4.81566i	−0.351194	+	0.167660i
$826$	−0.0644179	+	0.119458i	−0.00224139	+	0.00415648i
$827$	7.95751	+	41.7147i	0.276710	+	1.45056i	0.800816	+	0.598910i	$0.204399\pi$
$827$	7.95751	+	41.7147i	0.276710	+	1.45056i	−0.524106	+	0.851653i	$0.675601\pi$
$828$	−12.1690	−	3.73708i	−0.422903	−	0.129873i
$829$	21.6477	−	17.9085i	0.751854	−	0.621988i	−0.180483	−	0.983578i	$-0.557766\pi$
$829$	21.6477	−	17.9085i	0.751854	−	0.621988i	0.932337	+	0.361590i	$0.117766\pi$
$830$	−26.8436	−	12.2763i	−0.931755	−	0.426117i
$831$	−10.8303	−	4.28800i	−0.375697	−	0.148749i
$832$	6.12530	−	1.07842i	0.212357	−	0.0373875i
$833$	−22.1874	−	18.3550i	−0.768748	−	0.635964i
$834$	−4.38018	−	1.69332i	−0.151673	−	0.0586348i
$835$	−11.5741	+	12.3943i	−0.400538	+	0.428922i
$836$	−4.89439	+	28.1259i	−0.169276	+	0.972754i
$837$	−19.7866	+	18.5809i	−0.683925	+	0.642249i
$838$	−0.0205304	+	0.374745i	−0.000709209	+	0.0129454i
$839$	−9.95025	+	21.1454i	−0.343521	+	0.730019i	−0.999698	−	0.0245882i	$-0.992173\pi$
$839$	−9.95025	+	21.1454i	−0.343521	+	0.730019i	0.656177	+	0.754607i	$0.272173\pi$
$840$	0.628684	+	1.77019i	0.0216916	+	0.0610775i
$841$	−14.6492	+	1.85063i	−0.505146	+	0.0638148i
$842$	−9.90415	+	15.8895i	−0.341320	+	0.547590i
$843$	5.83155	+	4.23687i	0.200849	+	0.145926i
$844$	37.7112	+	17.0048i	1.29807	+	0.585328i
$845$	11.7315	−	25.1123i	0.403574	−	0.863888i
$846$	11.7120	−	6.56285i	0.402667	−	0.225635i
$847$	0.682316	−	0.0429277i	0.0234447	−	0.00147501i
$848$	28.5447	+	32.3130i	0.980229	+	1.10963i
$849$	2.70553	−	8.32675i	0.0928534	−	0.285773i
$850$	13.0505	+	26.7766i	0.447629	+	0.918429i
$851$	−28.2152	+	9.16768i	−0.967206	+	0.314264i
$852$	19.8645	−	2.83718i	0.680547	−	0.0972003i
$853$	24.4390	+	6.27488i	0.836777	+	0.214848i	0.642680	−	0.766135i	$-0.277822\pi$
$853$	24.4390	+	6.27488i	0.836777	+	0.214848i	0.194097	+	0.980982i	$0.437822\pi$
$854$	0.896574	−	7.59123i	0.0306801	−	0.259767i
$855$	15.2017	+	20.8010i	0.519886	+	0.711379i
$856$	8.25570	+	10.8009i	0.282174	+	0.369167i
$857$	−34.5064	−	11.2118i	−1.17871	−	0.382988i	−0.346826	−	0.937930i	$-0.612740\pi$
$857$	−34.5064	−	11.2118i	−1.17871	−	0.382988i	−0.831889	+	0.554942i	$0.812740\pi$
$858$	−1.58203	−	1.88111i	−0.0540097	−	0.0642200i
$859$	−8.88469	+	16.1612i	−0.303142	+	0.551413i	−0.983376	−	0.181582i	$-0.941878\pi$
$859$	−8.88469	+	16.1612i	−0.303142	+	0.551413i	0.680234	+	0.732995i	$0.261878\pi$
$860$	−41.4177	−	15.4951i	−1.41233	−	0.528379i
$861$	1.04599	−	0.199534i	0.0356473	−	0.00680008i
$862$	3.05005	+	11.4918i	0.103885	+	0.391413i
$863$	1.47126	−	0.692324i	0.0500824	−	0.0235670i	−0.400575	−	0.916264i	$-0.631190\pi$
$863$	1.47126	−	0.692324i	0.0500824	−	0.0235670i	0.450657	+	0.892697i	$0.351190\pi$
$864$	11.7010	+	19.3809i	0.398075	+	0.659351i
$865$	36.7200	−	4.74296i	1.24852	−	0.161265i
$866$	38.2438	−	10.1503i	1.29958	−	0.344921i
$867$	−0.508102	−	0.201172i	−0.0172560	−	0.00683215i
$868$	−1.94160	+	5.14602i	−0.0659023	+	0.174667i
$869$	−18.3976	+	11.6755i	−0.624096	+	0.396064i
$870$	−4.60224	+	7.42963i	−0.156031	+	0.251888i
$871$	11.7003	+	3.00412i	0.396449	+	0.101791i
$872$	19.0116	+	37.9776i	0.643814	+	1.28608i
$873$	4.36344	−	34.5402i	0.147680	−	1.16901i
$874$	15.4047	−	7.40195i	0.521073	−	0.250375i
$875$	0.605811	+	4.49269i	0.0204802	+	0.151881i
$876$	5.88059	+	4.70646i	0.198687	+	0.159016i
$877$	−18.1863	−	2.29746i	−0.614106	−	0.0775796i	−0.187873	−	0.982193i	$-0.560159\pi$
$877$	−18.1863	−	2.29746i	−0.614106	−	0.0775796i	−0.426233	+	0.904614i	$0.640159\pi$
$878$	5.87491	+	2.70661i	0.198269	+	0.0913436i
$879$	3.23250	+	0.829965i	0.109030	+	0.0279940i
$880$	−12.3004	+	24.3683i	−0.414647	+	0.821455i
$881$	19.9757	+	31.4767i	0.672999	+	1.06048i	0.993566	+	0.113251i	$0.0361264\pi$
$881$	19.9757	+	31.4767i	0.672999	+	1.06048i	−0.320567	+	0.947226i	$0.603874\pi$
$882$	−16.4417	−	17.2268i	−0.553622	−	0.580058i
$883$	−45.9709	−	18.2012i	−1.54704	−	0.612518i	−0.569264	−	0.822155i	$-0.692772\pi$
$883$	−45.9709	−	18.2012i	−1.54704	−	0.612518i	−0.977779	+	0.209637i	$0.932772\pi$
$884$	−4.97861	+	4.25640i	−0.167449	+	0.143158i
$885$	0.185816	−	0.340244i	0.00624615	−	0.0114372i
$886$	14.8027	−	4.94264i	0.497308	−	0.166051i
$887$	−1.92176	+	0.904313i	−0.0645265	+	0.0303639i	−0.457772	−	0.889070i	$-0.651352\pi$
$887$	−1.92176	+	0.904313i	−0.0645265	+	0.0303639i	0.393245	+	0.919434i	$0.371352\pi$
$888$	21.7651	+	9.60293i	0.730390	+	0.322253i
$889$	−0.0658807	−	0.345359i	−0.00220957	−	0.0115830i
$890$	33.8430	+	6.07464i	1.13442	+	0.203622i
$891$	−6.55529	+	11.9240i	−0.219610	+	0.399470i
$892$	36.6915	+	16.5450i	1.22852	+	0.553966i
$893$	−5.56989	+	17.1423i	−0.186389	+	0.573647i
$894$	16.8873	+	4.19037i	0.564794	+	0.140147i
$895$	−2.27925	+	0.747610i	−0.0761868	+	0.0249899i
$896$	3.85818	+	2.48173i	0.128893	+	0.0829086i
$897$	−0.365936	+	1.42522i	−0.0122182	+	0.0475869i
$898$	12.9822	+	4.10219i	0.433221	+	0.136892i
$899$	−24.3362	+	7.90731i	−0.811658	+	0.263724i
$900$	8.12088	+	23.2570i	0.270696	+	0.775235i
$901$	−43.1846	−	14.0315i	−1.43869	−	0.467458i
$902$	12.5915	+	8.99331i	0.419251	+	0.299444i
$903$	2.93119	−	0.184415i	0.0975441	−	0.00613695i
$904$	−1.66242	+	10.0338i	−0.0552914	+	0.333720i
$905$	−1.72821	+	13.9942i	−0.0574478	+	0.465182i
$906$	−11.4648	+	9.64201i	−0.380892	+	0.320334i
$907$	3.14864	+	2.28762i	0.104549	+	0.0759592i	0.638831	−	0.769347i	$-0.279418\pi$
$907$	3.14864	+	2.28762i	0.104549	+	0.0759592i	−0.534283	+	0.845306i	$0.679418\pi$
$908$	19.7485	+	2.17036i	0.655378	+	0.0720258i
$909$	−1.26107	−	9.98241i	−0.0418271	−	0.331096i
$910$	−0.922797	+	0.377039i	−0.0305904	+	0.0124987i
$911$	9.52637	−	20.2446i	0.315623	−	0.670732i	−0.682571	−	0.730820i	$-0.739138\pi$
$911$	9.52637	−	20.2446i	0.315623	−	0.670732i	0.998193	+	0.0600876i	$0.0191380\pi$
$912$	−13.1643	−	3.81044i	−0.435914	−	0.126176i
$913$	19.5007	+	20.7661i	0.645379	+	0.687258i
$914$	1.78147	+	1.27239i	0.0589259	+	0.0420870i
$915$	−2.67615	+	21.6701i	−0.0884709	+	0.716390i
$916$	31.4735	−	2.49271i	1.03991	−	0.0823615i
$917$	1.98779	−	2.40282i	0.0656426	−	0.0793483i
$918$	−20.9856	−	11.3165i	−0.692630	−	0.373501i
$919$	6.05634	+	2.39787i	0.199780	+	0.0790986i	0.465884	−	0.884846i	$-0.345736\pi$
$919$	6.05634	+	2.39787i	0.199780	+	0.0790986i	−0.266104	+	0.963944i	$0.585736\pi$
$920$	16.1511	−	2.48660i	0.532486	−	0.0819809i
$921$	4.41252	+	5.33382i	0.145397	+	0.175755i
$922$	33.8755	+	31.2986i	1.11563	+	1.03077i
$923$	1.99528	+	10.4596i	0.0656756	+	0.344283i
$924$	0.0845036	−	1.81096i	0.00277997	−	0.0595763i
$925$	46.6333	+	33.4851i	1.53329	+	1.10098i
$926$	1.18661	−	6.50638i	0.0389945	−	0.213813i
$927$	−1.69006	−	0.795281i	−0.0555088	−	0.0261204i
$928$	2.20161	+	21.2286i	0.0722714	+	0.696862i
$929$	−13.1815	+	5.21893i	−0.432472	+	0.171228i	−0.574266	−	0.818668i	$-0.694713\pi$
$929$	−13.1815	+	5.21893i	−0.432472	+	0.171228i	0.141795	+	0.989896i	$0.454713\pi$
$930$	5.62409	−	14.6697i	0.184421	−	0.481038i
$931$	31.9085	+	2.00751i	1.04576	+	0.0657935i
$932$	21.7605	+	17.4158i	0.712790	+	0.570473i
$933$	0.398957	−	6.34123i	0.0130613	−	0.207603i
$934$	−11.5646	−	9.41026i	−0.378404	−	0.307913i
$935$	−1.88513	−	28.6857i	−0.0616504	−	0.938124i
$936$	−4.50172	+	3.01279i	−0.147143	+	0.0984763i
$937$	−4.06986	−	32.2163i	−0.132957	−	1.05246i	−0.907533	−	0.419980i	$-0.862037\pi$
$937$	−4.06986	−	32.2163i	−0.132957	−	1.05246i	0.774577	−	0.632480i	$-0.217963\pi$
$938$	4.83495	+	7.48394i	0.157867	+	0.244359i
$939$	−12.2401	+	13.0344i	−0.399441	+	0.425362i
$940$	−9.86337	+	14.1326i	−0.321708	+	0.460956i
$941$	−28.5136	+	13.4175i	−0.929517	+	0.437397i	−0.830079	−	0.557646i	$-0.811705\pi$
$941$	−28.5136	+	13.4175i	−0.929517	+	0.437397i	−0.0994381	+	0.995044i	$0.531705\pi$
$942$	0.216486	+	0.534098i	0.00705349	+	0.0174018i
$943$		−	9.26325i		−	0.301653i
$944$	−0.149027	−	0.934924i	−0.00485042	−	0.0304292i
$945$	−2.49129	−	2.63816i	−0.0810417	−	0.0858195i
$946$	31.3462	+	28.9617i	1.01915	+	0.941626i
$947$	22.9278	−	36.1284i	0.745052	−	1.17401i	−0.234361	−	0.972150i	$-0.575300\pi$
$947$	22.9278	−	36.1284i	0.745052	−	1.17401i	0.979413	−	0.201865i	$-0.0647003\pi$
$948$	−4.60646	−	9.39117i	−0.149611	−	0.305011i
$949$	−2.34935	+	3.23360i	−0.0762631	+	0.104967i
$950$	−29.1973	−	15.5350i	−0.947287	−	0.504021i
$951$	7.83742	−	5.69422i	0.254146	−	0.184648i
$952$	−4.82767	−	0.186087i	−0.156466	−	0.00603110i
$953$	−0.915393	−	2.31202i	−0.0296525	−	0.0748936i	0.914196	−	0.405273i	$-0.132823\pi$
$953$	−0.915393	−	2.31202i	−0.0296525	−	0.0748936i	−0.943848	+	0.330379i	$0.892823\pi$
$954$	−34.1057	−	15.7127i	−1.10421	−	0.508718i
$955$	−3.30523	+	1.31931i	−0.106955	+	0.0426920i
$956$	−5.21468	+	2.97783i	−0.168655	+	0.0963098i
$957$	6.82360	−	4.95764i	0.220576	−	0.160258i
$958$	−1.98794	+	8.01143i	−0.0642275	+	0.258837i
$959$	4.83288	−	4.53837i	0.156062	−	0.146552i
$960$	−10.9829	−	7.14736i	−0.354471	−	0.230680i
$961$	13.1444	−	7.22618i	0.424012	−	0.233103i
$962$	−4.55198	+	11.7748i	−0.146762	+	0.379636i
$963$	−10.3757	−	5.70409i	−0.334352	−	0.183812i
$964$	−17.5891	−	35.8588i	−0.566507	−	1.15494i
$965$	17.6572	+	1.06144i	0.568406	+	0.0341689i
$966$	−0.911628	+	0.588951i	−0.0293312	+	0.0189492i
$967$	−22.8756	+	14.5173i	−0.735630	+	0.466845i	−0.850126	−	0.526579i	$-0.823474\pi$
$967$	−22.8756	+	14.5173i	−0.735630	+	0.466845i	0.114497	+	0.993424i	$0.463474\pi$
$968$	−3.59959	+	3.12826i	−0.115695	+	0.100546i
$969$	13.9797	−	3.58937i	0.449091	−	0.115307i
$970$	14.2726	+	42.3513i	0.458266	+	1.35982i
$971$	11.9029	−	0.748870i	0.381984	−	0.0240324i	0.129362	−	0.991597i	$-0.458707\pi$
$971$	11.9029	−	0.748870i	0.381984	−	0.0240324i	0.252622	+	0.967565i	$0.418707\pi$
$972$	−24.9987	−	17.5509i	−0.801833	−	0.562945i
$973$	1.61072	−	0.885503i	0.0516375	−	0.0283879i
$974$	−39.6032	+	5.32937i	−1.26897	+	0.170764i
$975$	2.64161	−	1.06298i	0.0845992	−	0.0340426i
$976$	27.1882	+	45.8690i	0.870274	+	1.46823i
$977$	6.73174	−	7.16857i	0.215367	−	0.229343i	−0.612209	−	0.790696i	$-0.709719\pi$
$977$	6.73174	−	7.16857i	0.215367	−	0.229343i	0.827577	+	0.561353i	$0.189719\pi$
$978$	22.0572	−	4.39313i	0.705312	−	0.140477i
$979$	−28.0177	−	17.7806i	−0.895449	−	0.568269i
$980$	28.6316	+	10.7116i	0.914602	+	0.342169i
$981$	−28.5009	−	23.5780i	−0.909963	−	0.752787i
$982$	−61.5038	+	8.27651i	−1.96267	+	0.264114i
$983$	−8.44562	−	32.8935i	−0.269374	−	1.04914i	−0.948922	−	0.315510i	$-0.897824\pi$
$983$	−8.44562	−	32.8935i	−0.269374	−	1.04914i	0.679549	−	0.733630i	$-0.262176\pi$
$984$	−4.95170	+	5.53673i	−0.157854	+	0.176505i
$985$	1.48451	+	1.07224i	0.0473004	+	0.0341645i
$986$	−13.3584	−	18.0765i	−0.425418	−	0.575672i
$987$	0.214481	−	1.12435i	0.00682699	−	0.0357883i
$988$	1.69423	−	7.07241i	0.0539006	−	0.225003i
$989$	3.20216	−	25.3477i	0.101823	−	0.806009i
$990$	1.23426	−	23.7420i	0.0392274	−	0.754570i
$991$	4.74638	−	24.8814i	0.150774	−	0.790383i	−0.823897	−	0.566739i	$-0.808205\pi$
$991$	4.74638	−	24.8814i	0.150774	−	0.790383i	0.974671	−	0.223644i	$-0.0717953\pi$
$992$	−11.0385	−	36.7443i	−0.350472	−	1.16663i
$993$	−2.66970	+	0.867439i	−0.0847205	+	0.0275273i
$994$	−4.15453	+	6.66524i	−0.131774	+	0.211409i
$995$	−35.9662	+	43.7236i	−1.14021	+	1.38613i
$996$	−10.9317	+	8.21624i	−0.346385	+	0.260342i
$997$	17.5724	+	21.2414i	0.556523	+	0.672721i	0.971480	−	0.237120i	$-0.0762035\pi$
$997$	17.5724	+	21.2414i	0.556523	+	0.672721i	−0.414957	+	0.909841i	$0.636204\pi$
$998$	13.1810	+	39.4758i	0.417237	+	1.24958i
$999$	−45.9519			−1.45385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.bd.a.109.15	✓	2960
8.5	even	2	inner	1000.2.bd.a.109.123	yes	2960
125.39	even	50	inner	1000.2.bd.a.789.123	yes	2960
1000.789	even	50	inner	1000.2.bd.a.789.15	yes	2960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.bd.a.109.15	✓	2960	1.1	even	1	trivial
1000.2.bd.a.109.123	yes	2960	8.5	even	2	inner
1000.2.bd.a.789.15	yes	2960	1000.789	even	50	inner
1000.2.bd.a.789.123	yes	2960	125.39	even	50	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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.bd (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34141 + 0.447898i) q^{2} +(0.466928 + 0.564419i) q^{3} +(1.59877 - 1.20163i) q^{4} +(0.134176 - 2.23204i) q^{5} +(-0.879145 - 0.547982i) q^{6} +(0.385630 - 0.125299i) q^{7} +(-1.60641 + 2.32797i) q^{8} +(0.461597 - 2.41978i) q^{9} +(0.819741 + 3.05418i) q^{10} +(0.382501 - 3.02781i) q^{11} +(1.42474 + 0.341302i) q^{12} +(-0.145677 + 0.763668i) q^{13} +(-0.461168 + 0.340800i) q^{14} +(1.32245 - 0.966469i) q^{15} +(1.11216 - 3.84228i) q^{16} +(1.04763 + 4.08026i) q^{17} +(0.464622 + 3.45267i) q^{18} +(-3.60386 - 2.98137i) q^{19} +(-2.46757 - 3.72976i) q^{20} +(0.250782 + 0.159151i) q^{21} +(0.843058 + 4.23286i) q^{22} +(1.76873 - 1.88351i) q^{23} +(-2.06403 + 0.180310i) q^{24} +(-4.96399 - 0.598971i) q^{25} +(-0.146632 - 1.08964i) q^{26} +(3.50704 - 1.92801i) q^{27} +(0.465972 - 0.663710i) q^{28} +(3.76540 - 0.236899i) q^{29} +(-1.34108 + 1.88876i) q^{30} +(-6.56923 + 1.68669i) q^{31} +(0.229088 + 5.65221i) q^{32} +(1.88755 - 1.19788i) q^{33} +(-3.23285 - 5.00407i) q^{34} +(-0.227929 - 0.877553i) q^{35} +(-2.16969 - 4.42335i) q^{36} +(-10.0618 - 5.53150i) q^{37} +(6.16962 + 2.38509i) q^{38} +(-0.499049 + 0.274355i) q^{39} +(4.98059 + 3.89792i) q^{40} +(2.61344 - 2.45419i) q^{41} +(-0.407686 - 0.101162i) q^{42} +(7.99972 - 5.81214i) q^{43} +(-3.02678 - 5.30040i) q^{44} +(-5.33910 - 1.35498i) q^{45} +(-1.52898 + 3.31878i) q^{46} +(-1.41864 - 3.58306i) q^{47} +(2.68795 - 1.16634i) q^{48} +(-5.53011 + 4.01786i) q^{49} +(6.92704 - 1.41990i) q^{50} +(-1.81380 + 2.49649i) q^{51} +(0.684743 + 1.39598i) q^{52} +(-5.77559 + 9.10087i) q^{53} +(-3.84084 + 4.15706i) q^{54} +(-6.70686 - 1.26002i) q^{55} +(-0.327786 + 1.09902i) q^{56} -3.42617i q^{57} +(-4.94484 + 2.00429i) q^{58} +(0.214156 - 0.100774i) q^{59} +(0.952965 - 3.13427i) q^{60} +(-9.12524 + 9.71739i) q^{61} +(8.05658 - 5.20490i) q^{62} +(-0.125189 - 0.990976i) q^{63} +(-2.83892 - 7.47934i) q^{64} +(1.68499 + 0.427624i) q^{65} +(-1.99546 + 2.45228i) q^{66} +(0.975634 - 15.5073i) q^{67} +(6.57790 + 5.26454i) q^{68} +(1.88896 + 0.118843i) q^{69} +(0.698802 + 1.07507i) q^{70} +(12.7348 - 5.04205i) q^{71} +(4.89166 + 4.96173i) q^{72} +(4.65188 + 2.18901i) q^{73} +(15.9745 + 2.91338i) q^{74} +(-1.97976 - 3.08145i) q^{75} +(-9.34428 - 0.436025i) q^{76} +(-0.231877 - 1.21554i) q^{77} +(0.546548 - 0.591546i) q^{78} +(-4.55106 - 5.50129i) q^{79} +(-8.42689 - 2.99792i) q^{80} +(-4.14552 - 1.64133i) q^{81} +(-2.40648 + 4.46263i) q^{82} +(-5.94989 + 7.19218i) q^{83} +(0.592185 - 0.0469012i) q^{84} +(9.24786 - 1.79088i) q^{85} +(-8.12767 + 11.3795i) q^{86} +(1.89188 + 2.01465i) q^{87} +(6.43420 + 5.75434i) q^{88} +(4.62955 - 9.83830i) q^{89} +(7.76883 - 0.573789i) q^{90} +(0.0395091 + 0.312746i) q^{91} +(0.564519 - 5.13668i) q^{92} +(-4.01936 - 2.92023i) q^{93} +(3.50782 + 4.17096i) q^{94} +(-7.13809 + 7.64393i) q^{95} +(-3.08325 + 2.76848i) q^{96} +(14.1048 - 0.887402i) q^{97} +(5.61856 - 7.86653i) q^{98} +(-7.15005 - 2.32319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100}) \) 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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