LMFDB - Embedded newform 57.2.j.b.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	57.2
Dual form			57.2.j.b.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.336464 - 1.90818i) q^{2} +(-1.20126 - 1.24779i) q^{3} +(-1.64856 - 0.600025i) q^{4} +(1.09544 + 3.00968i) q^{5} +(-2.78518 + 1.87239i) q^{6} +(-1.23083 - 2.13186i) q^{7} +(0.237981 - 0.412196i) q^{8} +(-0.113935 + 2.99784i) q^{9} +O(q^{10})$	\(q+(0.336464 - 1.90818i) q^{2} +(-1.20126 - 1.24779i) q^{3} +(-1.64856 - 0.600025i) q^{4} +(1.09544 + 3.00968i) q^{5} +(-2.78518 + 1.87239i) q^{6} +(-1.23083 - 2.13186i) q^{7} +(0.237981 - 0.412196i) q^{8} +(-0.113935 + 2.99784i) q^{9} +(6.11159 - 1.07764i) q^{10} +(2.11115 + 1.21887i) q^{11} +(1.23165 + 2.77783i) q^{12} +(1.65491 + 1.97225i) q^{13} +(-4.48210 + 1.63135i) q^{14} +(2.43953 - 4.98229i) q^{15} +(-3.39430 - 2.84816i) q^{16} +(-3.75838 - 0.662704i) q^{17} +(5.68207 + 1.22607i) q^{18} +(-2.59177 + 3.50468i) q^{19} -5.61892i q^{20} +(-1.18155 + 4.09673i) q^{21} +(3.03615 - 3.61834i) q^{22} +(-0.817753 + 2.24676i) q^{23} +(-0.800210 + 0.198206i) q^{24} +(-4.02800 + 3.37989i) q^{25} +(4.32022 - 2.49428i) q^{26} +(3.87752 - 3.45902i) q^{27} +(0.749922 + 4.25302i) q^{28} +(-0.705026 - 3.99840i) q^{29} +(-8.68629 - 6.33142i) q^{30} +(-3.82192 + 2.20658i) q^{31} +(-5.84764 + 4.90675i) q^{32} +(-1.01515 - 4.09844i) q^{33} +(-2.52912 + 6.94869i) q^{34} +(5.06793 - 6.03972i) q^{35} +(1.98661 - 4.87374i) q^{36} -9.08219i q^{37} +(5.81552 + 6.12475i) q^{38} +(0.472956 - 4.43416i) q^{39} +(1.50127 + 0.264715i) q^{40} +(4.39728 + 3.68975i) q^{41} +(7.41975 + 3.63301i) q^{42} +(3.86432 - 1.40650i) q^{43} +(-2.74899 - 3.27612i) q^{44} +(-9.14735 + 2.94103i) q^{45} +(4.01207 + 2.31637i) q^{46} +(-3.04197 + 0.536381i) q^{47} +(0.523561 + 7.65674i) q^{48} +(0.470118 - 0.814268i) q^{49} +(5.09416 + 8.82335i) q^{50} +(3.68789 + 5.48573i) q^{51} +(-1.54482 - 4.24435i) q^{52} +(-3.11998 - 1.13558i) q^{53} +(-5.29579 - 8.56284i) q^{54} +(-1.35579 + 7.68908i) q^{55} -1.17166 q^{56} +(7.48647 - 0.976071i) q^{57} -7.86688 q^{58} +(1.78173 - 10.1047i) q^{59} +(-7.01121 + 6.74980i) q^{60} +(0.932543 + 0.339418i) q^{61} +(2.92462 + 8.03534i) q^{62} +(6.53120 - 3.44693i) q^{63} +(2.96450 + 5.13466i) q^{64} +(-4.12299 + 7.14123i) q^{65} +(-8.16212 + 0.558118i) q^{66} +(-6.74077 + 1.18858i) q^{67} +(5.79826 + 3.34763i) q^{68} +(3.78581 - 1.67857i) q^{69} +(-9.81970 - 11.7027i) q^{70} +(0.208227 - 0.0757884i) q^{71} +(1.20858 + 0.760393i) q^{72} +(12.8811 + 10.8085i) q^{73} +(-17.3304 - 3.05582i) q^{74} +(9.05606 + 0.965937i) q^{75} +(6.37556 - 4.22253i) q^{76} -6.00089i q^{77} +(-8.30204 - 2.39442i) q^{78} +(2.67409 - 3.18686i) q^{79} +(4.85382 - 13.3357i) q^{80} +(-8.97404 - 0.683116i) q^{81} +(8.52023 - 7.14932i) q^{82} +(2.45843 - 1.41938i) q^{83} +(4.40600 - 6.04473i) q^{84} +(-2.12253 - 12.0375i) q^{85} +(-1.38365 - 7.84704i) q^{86} +(-4.14222 + 5.68285i) q^{87} +(1.00483 - 0.580137i) q^{88} +(-6.53953 + 5.48732i) q^{89} +(2.53426 + 18.4443i) q^{90} +(2.16764 - 5.95553i) q^{91} +(2.69622 - 3.21323i) q^{92} +(7.34447 + 2.11824i) q^{93} +5.98510i q^{94} +(-13.3871 - 3.96125i) q^{95} +(13.1471 + 1.40230i) q^{96} +(3.82196 + 0.673914i) q^{97} +(-1.39559 - 1.17104i) q^{98} +(-3.89451 + 6.19000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{1}{18}\right)$

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 $

$2$	0.336464	−	1.90818i	0.237916	−	1.34929i	−0.598470	−	0.801145i	$-0.704224\pi$
$2$	0.336464	−	1.90818i	0.237916	−	1.34929i	0.836386	−	0.548141i	$-0.184664\pi$
$3$	−1.20126	−	1.24779i	−0.693549	−	0.720409i
$3$	−1.20126	−	1.24779i	−0.693549	−	0.720409i
$4$	−1.64856	−	0.600025i	−0.824278	−	0.300013i
$5$	1.09544	+	3.00968i	0.489894	+	1.34597i	0.900776	+	0.434283i	$0.142998\pi$
$5$	1.09544	+	3.00968i	0.489894	+	1.34597i	−0.410883	+	0.911688i	$0.634779\pi$
$6$	−2.78518	+	1.87239i	−1.13704	+	0.764400i
$7$	−1.23083	−	2.13186i	−0.465210	−	0.805767i	0.534001	−	0.845484i	$-0.320688\pi$
$7$	−1.23083	−	2.13186i	−0.465210	−	0.805767i	−0.999211	+	0.0397167i	$0.987354\pi$
$8$	0.237981	−	0.412196i	0.0841391	−	0.145733i
$9$	−0.113935	+	2.99784i	−0.0379783	+	0.999279i
$10$	6.11159	−	1.07764i	1.93265	−	0.340779i
$11$	2.11115	+	1.21887i	0.636535	+	0.367503i	0.783278	−	0.621671i	$-0.213546\pi$
$11$	2.11115	+	1.21887i	0.636535	+	0.367503i	−0.146744	+	0.989175i	$0.546879\pi$
$12$	1.23165	+	2.77783i	0.355546	+	0.801891i
$13$	1.65491	+	1.97225i	0.458990	+	0.547003i	0.945051	−	0.326922i	$-0.106011\pi$
$13$	1.65491	+	1.97225i	0.458990	+	0.547003i	−0.486062	+	0.873924i	$0.661567\pi$
$14$	−4.48210	+	1.63135i	−1.19789	+	0.435997i
$15$	2.43953	−	4.98229i	0.629885	−	1.28642i
$16$	−3.39430	−	2.84816i	−0.848575	−	0.712039i
$17$	−3.75838	−	0.662704i	−0.911541	−	0.160729i	−0.301838	−	0.953359i	$-0.597600\pi$
$17$	−3.75838	−	0.662704i	−0.911541	−	0.160729i	−0.609703	+	0.792630i	$0.708711\pi$
$18$	5.68207	+	1.22607i	1.33928	+	0.288988i
$19$	−2.59177	+	3.50468i	−0.594592	+	0.804028i
$19$	−2.59177	+	3.50468i	−0.594592	+	0.804028i
$20$		−	5.61892i		−	1.25643i
$21$	−1.18155	+	4.09673i	−0.257836	+	0.893981i
$22$	3.03615	−	3.61834i	0.647309	−	0.771433i
$23$	−0.817753	+	2.24676i	−0.170513	+	0.468481i	−0.995286	−	0.0969829i	$-0.969081\pi$
$23$	−0.817753	+	2.24676i	−0.170513	+	0.468481i	0.824773	+	0.565464i	$0.191303\pi$
$24$	−0.800210	+	0.198206i	−0.163342	+	0.0404586i
$25$	−4.02800	+	3.37989i	−0.805599	+	0.675978i
$26$	4.32022	−	2.49428i	0.847264	−	0.489168i
$27$	3.87752	−	3.45902i	0.746229	−	0.665689i
$28$	0.749922	+	4.25302i	0.141722	+	0.803745i
$29$	−0.705026	−	3.99840i	−0.130920	−	0.742484i	−0.977614	−	0.210405i	$-0.932522\pi$
$29$	−0.705026	−	3.99840i	−0.130920	−	0.742484i	0.846694	−	0.532080i	$-0.178589\pi$
$30$	−8.68629	−	6.33142i	−1.58589	−	1.15595i
$31$	−3.82192	+	2.20658i	−0.686436	+	0.396314i	−0.802276	−	0.596954i	$-0.796378\pi$
$31$	−3.82192	+	2.20658i	−0.686436	+	0.396314i	0.115839	+	0.993268i	$0.463044\pi$
$32$	−5.84764	+	4.90675i	−1.03373	+	0.867399i
$33$	−1.01515	−	4.09844i	−0.176715	−	0.713447i
$34$	−2.52912	+	6.94869i	−0.433740	+	1.19169i
$35$	5.06793	−	6.03972i	0.856636	−	1.02090i
$36$	1.98661	−	4.87374i	0.331101	−	0.812289i
$37$		−	9.08219i		−	1.49310i	−0.665328	−	0.746551i	$-0.731708\pi$
$37$		−	9.08219i		−	1.49310i	0.665328	−	0.746551i	$-0.268292\pi$
$38$	5.81552	+	6.12475i	0.943401	+	0.993566i
$39$	0.472956	−	4.43416i	0.0757335	−	0.710034i
$40$	1.50127	+	0.264715i	0.237372	+	0.0418551i
$41$	4.39728	+	3.68975i	0.686739	+	0.576243i	0.917967	−	0.396657i	$-0.129830\pi$
$41$	4.39728	+	3.68975i	0.686739	+	0.576243i	−0.231228	+	0.972900i	$0.574274\pi$
$42$	7.41975	+	3.63301i	1.14489	+	0.560586i
$43$	3.86432	−	1.40650i	0.589303	−	0.214489i	−0.0301200	−	0.999546i	$-0.509589\pi$
$43$	3.86432	−	1.40650i	0.589303	−	0.214489i	0.619423	+	0.785058i	$0.287367\pi$
$44$	−2.74899	−	3.27612i	−0.414426	−	0.493893i
$45$	−9.14735	+	2.94103i	−1.36361	+	0.438422i
$46$	4.01207	+	2.31637i	0.591548	+	0.341530i
$47$	−3.04197	+	0.536381i	−0.443717	+	0.0782393i	−0.391043	−	0.920372i	$-0.627886\pi$
$47$	−3.04197	+	0.536381i	−0.443717	+	0.0782393i	−0.0526741	+	0.998612i	$0.516774\pi$
$48$	0.523561	+	7.65674i	0.0755695	+	1.10516i
$49$	0.470118	−	0.814268i	0.0671597	−	0.116324i
$50$	5.09416	+	8.82335i	0.720423	+	1.24781i
$51$	3.68789	+	5.48573i	0.516408	+	0.768156i
$52$	−1.54482	−	4.24435i	−0.214227	−	0.588585i
$53$	−3.11998	−	1.13558i	−0.428562	−	0.155984i	0.118728	−	0.992927i	$-0.462118\pi$
$53$	−3.11998	−	1.13558i	−0.428562	−	0.155984i	−0.547290	+	0.836943i	$0.684341\pi$
$54$	−5.29579	−	8.56284i	−0.720666	−	1.16525i
$55$	−1.35579	+	7.68908i	−0.182815	+	1.03679i
$56$	−1.17166			−0.156569
$57$	7.48647	−	0.976071i	0.991608	−	0.129284i
$58$	−7.86688			−1.03297
$59$	1.78173	−	10.1047i	0.231961	−	1.31552i	−0.616959	−	0.786995i	$-0.711636\pi$
$59$	1.78173	−	10.1047i	0.231961	−	1.31552i	0.848920	−	0.528521i	$-0.177253\pi$
$60$	−7.01121	+	6.74980i	−0.905143	+	0.871396i
$61$	0.932543	+	0.339418i	0.119400	+	0.0434580i	0.401029	−	0.916065i	$-0.368653\pi$
$61$	0.932543	+	0.339418i	0.119400	+	0.0434580i	−0.281629	+	0.959523i	$0.590875\pi$
$62$	2.92462	+	8.03534i	0.371427	+	1.02049i
$63$	6.53120	−	3.44693i	0.822854	−	0.434273i
$64$	2.96450	+	5.13466i	0.370562	+	0.641832i
$65$	−4.12299	+	7.14123i	−0.511394	+	0.885760i
$66$	−8.16212	+	0.558118i	−1.00469	+	0.0686996i
$67$	−6.74077	+	1.18858i	−0.823516	+	0.145208i	−0.569499	−	0.821992i	$-0.692863\pi$
$67$	−6.74077	+	1.18858i	−0.823516	+	0.145208i	−0.254017	+	0.967200i	$0.581752\pi$
$68$	5.79826	+	3.34763i	0.703142	+	0.405959i
$69$	3.78581	−	1.67857i	0.455758	−	0.202076i
$70$	−9.81970	−	11.7027i	−1.17368	−	1.39874i
$71$	0.208227	−	0.0757884i	0.0247120	−	0.00899443i	−0.329635	−	0.944109i	$-0.606926\pi$
$71$	0.208227	−	0.0757884i	0.0247120	−	0.00899443i	0.354347	+	0.935114i	$0.384703\pi$
$72$	1.20858	+	0.760393i	0.142433	+	0.0896131i
$73$	12.8811	+	10.8085i	1.50761	+	1.26504i	0.868241	+	0.496142i	$0.165251\pi$
$73$	12.8811	+	10.8085i	1.50761	+	1.26504i	0.639373	+	0.768897i	$0.279194\pi$
$74$	−17.3304	−	3.05582i	−2.01462	−	0.355232i
$75$	9.05606	+	0.965937i	1.04570	+	0.111537i
$76$	6.37556	−	4.22253i	0.731327	−	0.484357i
$77$		−	6.00089i		−	0.683865i
$78$	−8.30204	−	2.39442i	−0.940021	−	0.271114i
$79$	2.67409	−	3.18686i	0.300859	−	0.358550i	−0.594342	−	0.804212i	$-0.702587\pi$
$79$	2.67409	−	3.18686i	0.300859	−	0.358550i	0.895201	+	0.445663i	$0.147032\pi$
$80$	4.85382	−	13.3357i	0.542673	−	1.49098i
$81$	−8.97404	−	0.683116i	−0.997115	−	0.0759017i
$82$	8.52023	−	7.14932i	0.940902	−	0.789511i
$83$	2.45843	−	1.41938i	0.269848	−	0.155797i	−0.358970	−	0.933349i	$-0.616872\pi$
$83$	2.45843	−	1.41938i	0.269848	−	0.155797i	0.628819	+	0.777552i	$0.283539\pi$
$84$	4.40600	−	6.04473i	0.480734	−	0.659534i
$85$	−2.12253	−	12.0375i	−0.230221	−	1.30565i
$86$	−1.38365	−	7.84704i	−0.149202	−	0.846168i
$87$	−4.14222	+	5.68285i	−0.444093	+	0.609266i
$88$	1.00483	−	0.580137i	0.107115	−	0.0618428i
$89$	−6.53953	+	5.48732i	−0.693189	+	0.581654i	−0.919827	−	0.392325i	$-0.871671\pi$
$89$	−6.53953	+	5.48732i	−0.693189	+	0.581654i	0.226638	+	0.973979i	$0.427226\pi$
$90$	2.53426	+	18.4443i	0.267134	+	1.94420i
$91$	2.16764	−	5.95553i	0.227230	−	0.624310i
$92$	2.69622	−	3.21323i	0.281101	−	0.335003i
$93$	7.34447	+	2.11824i	0.761586	+	0.219651i
$94$			5.98510i			0.617316i
$95$	−13.3871	−	3.96125i	−1.37349	−	0.406416i
$96$	13.1471	+	1.40230i	1.34182	+	0.143121i
$97$	3.82196	+	0.673914i	0.388061	+	0.0684256i	0.364275	−	0.931291i	$-0.381317\pi$
$97$	3.82196	+	0.673914i	0.388061	+	0.0684256i	0.0237859	+	0.999717i	$0.492428\pi$
$98$	−1.39559	−	1.17104i	−0.140976	−	0.118293i
$99$	−3.89451	+	6.19000i	−0.391413	+	0.622118i
$100$	8.66840	−	3.15504i	0.866840	−	0.315504i
$101$	1.71188	+	2.04014i	0.170338	+	0.203001i	0.844459	−	0.535620i	$-0.179922\pi$
$101$	1.71188	+	2.04014i	0.170338	+	0.203001i	−0.674121	+	0.738621i	$0.735477\pi$
$102$	11.7086	−	5.19141i	1.15932	−	0.514026i
$103$	−12.6300	−	7.29193i	−1.24447	−	0.718495i	−0.274469	−	0.961596i	$-0.588502\pi$
$103$	−12.6300	−	7.29193i	−1.24447	−	0.718495i	−0.970001	+	0.243101i	$0.921835\pi$
$104$	1.20679	−	0.212790i	0.118335	−	0.0208657i
$105$	−13.6242	+	0.931609i	−1.32958	+	0.0909157i
$106$	−3.21665	+	5.57140i	−0.312428	+	0.541142i
$107$	2.82927	+	4.90044i	0.273516	+	0.473744i	0.969760	−	0.244062i	$-0.0784800\pi$
$107$	2.82927	+	4.90044i	0.273516	+	0.473744i	−0.696244	+	0.717806i	$0.745147\pi$
$108$	−8.46781	+	3.37578i	−0.814815	+	0.324835i
$109$	2.04837	+	5.62784i	0.196198	+	0.539049i	0.998309	−	0.0581251i	$-0.0185122\pi$
$109$	2.04837	+	5.62784i	0.196198	+	0.539049i	−0.802111	+	0.597174i	$0.796290\pi$
$110$	14.2160	+	5.17419i	1.35544	+	0.493339i
$111$	−11.3326	+	10.9101i	−1.07564	+	1.03554i
$112$	−1.89406	+	10.7418i	−0.178972	+	1.01500i
$113$	3.46411			0.325876			0.162938	−	0.986636i	$-0.447903\pi$
$113$	3.46411			0.325876			0.162938	+	0.986636i	$0.447903\pi$
$114$	0.656407	−	14.6139i	0.0614782	−	1.36872i
$115$	−7.65783			−0.714096
$116$	−1.23687	+	7.01462i	−0.114840	+	0.651291i
$117$	−6.10102	+	4.73644i	−0.564040	+	0.437884i
$118$	−18.6820	−	6.79971i	−1.71982	−	0.625964i
$119$	3.21313	+	8.82801i	0.294547	+	0.809262i
$120$	−1.47312	−	2.19126i	−0.134476	−	0.200034i
$121$	−2.52871	−	4.37985i	−0.229883	−	0.398168i
$122$	0.961437	−	1.66526i	0.0870444	−	0.150765i
$123$	−0.678267	−	9.91922i	−0.0611572	−	0.894386i
$124$	7.62465	−	1.34443i	0.684714	−	0.120733i
$125$	−0.716113	−	0.413448i	−0.0640510	−	0.0369799i
$126$	−4.37985	−	13.6225i	−0.390188	−	1.21359i
$127$	3.39146	+	4.04178i	0.300943	+	0.358650i	0.895231	−	0.445602i	$-0.147010\pi$
$127$	3.39146	+	4.04178i	0.300943	+	0.358650i	−0.594288	+	0.804252i	$0.702566\pi$
$128$	−3.55108	+	1.29249i	−0.313874	+	0.114241i
$129$	−6.39706	−	3.13226i	−0.563230	−	0.275780i
$130$	12.2395	+	10.2702i	1.07348	+	0.900753i
$131$	15.2563	+	2.69009i	1.33295	+	0.235034i	0.794314	−	0.607507i	$-0.207831\pi$
$131$	15.2563	+	2.69009i	1.33295	+	0.235034i	0.538631	+	0.842542i	$0.318942\pi$
$132$	−0.785632	+	7.36563i	−0.0683805	+	0.641095i
$133$	10.6615	+	1.21162i	0.924469	+	0.105061i
$134$			13.2625i			1.14571i
$135$	14.6581	+	7.88097i	1.26157	+	0.678286i
$136$	−1.16759	+	1.39148i	−0.100120	+	0.119318i
$137$	−3.42271	+	9.40381i	−0.292422	+	0.803422i	0.703289	+	0.710904i	$0.251714\pi$
$137$	−3.42271	+	9.40381i	−0.292422	+	0.803422i	−0.995711	+	0.0925182i	$0.970508\pi$
$138$	−1.92922	−	7.78878i	−0.164226	−	0.663025i
$139$	6.94034	−	5.82364i	0.588672	−	0.493954i	−0.299110	−	0.954219i	$-0.596690\pi$
$139$	6.94034	−	5.82364i	0.588672	−	0.493954i	0.887782	+	0.460264i	$0.152245\pi$
$140$	−11.9787	+	6.91593i	−1.01239	+	0.584503i
$141$	4.32349	+	3.15139i	0.364104	+	0.265395i
$142$	−0.0745571	−	0.422834i	−0.00625669	−	0.0354835i
$143$	1.08985	+	6.18082i	0.0911375	+	0.516866i
$144$	8.92504	−	9.85105i	0.743753	−	0.820921i
$145$	11.2616	−	6.50189i	0.935226	−	0.539953i
$146$	24.9586	−	20.9427i	2.06558	−	1.73323i
$147$	−1.58077	+	0.391544i	−0.130379	+	0.0322940i
$148$	−5.44954	+	14.9725i	−0.447950	+	1.23073i
$149$	8.09355	−	9.64552i	0.663049	−	0.790191i	−0.324771	−	0.945793i	$-0.605287\pi$
$149$	8.09355	−	9.64552i	0.663049	−	0.790191i	0.987820	+	0.155601i	$0.0497315\pi$
$150$	4.89021	−	16.9556i	0.399284	−	1.38442i
$151$			14.4103i			1.17269i	0.810061	+	0.586345i	$0.199434\pi$
$151$			14.4103i			1.17269i	−0.810061	+	0.586345i	$0.800566\pi$
$152$	0.827821	+	1.90236i	0.0671451	+	0.154302i
$153$	2.41489	−	11.1915i	0.195232	−	0.904779i
$154$	−11.4508	−	2.01908i	−0.922729	−	0.162702i
$155$	−10.8278	−	9.08559i	−0.869708	−	0.729772i
$156$	−3.44030	+	7.02617i	−0.275445	+	0.562544i
$157$	−16.4270	+	5.97895i	−1.31102	+	0.477172i	−0.900570	−	0.434711i	$-0.856851\pi$
$157$	−16.4270	+	5.97895i	−1.31102	+	0.477172i	−0.410450	+	0.911883i	$0.634628\pi$
$158$	−5.18136	−	6.17491i	−0.412207	−	0.491249i
$159$	2.33096	+	5.25719i	0.184857	+	0.416922i
$160$	−21.1735	−	12.2245i	−1.67391	−	0.966432i
$161$	5.79629	−	1.02204i	0.456811	−	0.0805482i
$162$	−4.32294	+	16.8942i	−0.339643	+	1.32734i
$163$	1.15756	−	2.00495i	0.0906671	−	0.157040i	−0.817125	−	0.576461i	$-0.804433\pi$
$163$	1.15756	−	2.00495i	0.0906671	−	0.157040i	0.907792	+	0.419421i	$0.137767\pi$
$164$	−5.03521	−	8.72124i	−0.393184	−	0.681014i
$165$	11.2230	−	7.54487i	0.873708	−	0.587367i
$166$	−1.88125	−	5.16870i	−0.146014	−	0.401169i
$167$	−21.7247	−	7.90714i	−1.68111	−	0.611873i	−0.687646	−	0.726046i	$-0.741356\pi$
$167$	−21.7247	−	7.90714i	−1.68111	−	0.611873i	−0.993461	+	0.114173i	$0.963578\pi$
$168$	1.40747	+	1.46198i	0.108589	+	0.112794i
$169$	1.10640	−	6.27472i	0.0851079	−	0.482671i
$170$	−23.6838			−1.81647
$171$	−10.2111	−	8.16899i	−0.780866	−	0.624698i
$172$	−7.21447			−0.550098
$173$	−0.749063	+	4.24815i	−0.0569502	+	0.322981i	−0.999952	−	0.00980732i	$-0.996878\pi$
$173$	−0.749063	+	4.24815i	−0.0569502	+	0.322981i	0.943002	+	0.332788i	$0.107989\pi$
$174$	9.45019	+	9.81618i	0.716417	+	0.744162i
$175$	12.1632	+	4.42705i	0.919453	+	0.334654i
$176$	−3.69433	−	10.1501i	−0.278471	−	0.765092i
$177$	−14.7488	+	9.91515i	−1.10859	+	0.745269i
$178$	8.27047	+	14.3249i	0.619898	+	1.07369i
$179$	−0.273237	+	0.473261i	−0.0204227	+	0.0353732i	−0.876056	−	0.482209i	$-0.839835\pi$
$179$	−0.273237	+	0.473261i	−0.0204227	+	0.0353732i	0.855633	+	0.517582i	$0.173168\pi$
$180$	16.8446	+	0.640191i	1.25552	+	0.0477170i
$181$	−1.89534	+	0.334200i	−0.140880	+	0.0248409i	−0.243643	−	0.969865i	$-0.578343\pi$
$181$	−1.89534	+	0.334200i	−0.140880	+	0.0248409i	0.102764	+	0.994706i	$0.467231\pi$
$182$	−10.6349	−	6.14006i	−0.788311	−	0.455132i
$183$	−0.696709	−	1.57134i	−0.0515022	−	0.116157i
$184$	0.731494	+	0.871761i	0.0539265	+	0.0642671i
$185$	27.3345	−	9.94895i	2.00967	−	0.731461i
$186$	6.51313	−	13.3019i	0.477566	−	0.975339i
$187$	−7.12674	−	5.98004i	−0.521159	−	0.437304i
$188$	5.33670	+	0.941004i	0.389219	+	0.0686298i
$189$	−12.1467	−	4.00886i	−0.883543	−	0.291602i
$190$	−12.0630	+	24.2121i	−0.875145	+	1.75653i
$191$			13.6405i			0.986988i	0.869749	+	0.493494i	$0.164281\pi$
$191$			13.6405i			0.986988i	−0.869749	+	0.493494i	$0.835719\pi$
$192$	2.84581	−	9.86713i	0.205379	−	0.712099i
$193$	16.4792	−	19.6392i	1.18620	−	1.41366i	0.297778	−	0.954635i	$-0.403754\pi$
$193$	16.4792	−	19.6392i	1.18620	−	1.41366i	0.888423	−	0.459025i	$-0.151801\pi$
$194$	2.57190	−	7.06623i	0.184651	−	0.507326i
$195$	13.8635	−	3.43389i	0.992786	−	0.245906i
$196$	−1.26360	+	1.06028i	−0.0902570	+	0.0757346i
$197$	3.20655	−	1.85131i	0.228458	−	0.131900i	−0.381403	−	0.924409i	$-0.624559\pi$
$197$	3.20655	−	1.85131i	0.228458	−	0.131900i	0.609860	+	0.792509i	$0.291226\pi$
$198$	10.5013	+	9.51413i	0.746293	+	0.676140i
$199$	1.47970	+	8.39179i	0.104893	+	0.594878i	0.991263	+	0.131900i	$0.0421079\pi$
$199$	1.47970	+	8.39179i	0.104893	+	0.594878i	−0.886370	+	0.462978i	$0.846781\pi$
$200$	0.434589	+	2.46467i	0.0307301	+	0.174279i
$201$	9.58053	+	6.98323i	0.675758	+	0.492559i
$202$	4.46893	−	2.58014i	0.314433	−	0.181538i
$203$	−7.65626	+	6.42436i	−0.537364	+	0.450902i
$204$	−2.78812	−	11.2564i	−0.195207	−	0.788103i
$205$	−6.28806	+	17.2763i	−0.439177	+	1.20663i
$206$	−18.1638	+	21.6468i	−1.26553	+	1.50821i
$207$	−6.64224	−	2.70747i	−0.461668	−	0.188182i
$208$		−	11.4078i		−	0.790992i
$209$	−9.74334	+	4.23986i	−0.673961	+	0.293277i
$210$	−2.80637	+	26.3108i	−0.193658	+	1.81562i
$211$	3.89977	+	0.687634i	0.268471	+	0.0473387i	0.306263	−	0.951947i	$-0.400921\pi$
$211$	3.89977	+	0.687634i	0.268471	+	0.0473387i	−0.0377920	+	0.999286i	$0.512032\pi$
$212$	4.46208	+	3.74413i	0.306457	+	0.257148i
$213$	−0.344703	−	0.168781i	−0.0236187	−	0.0115647i
$214$	10.3029	−	3.74994i	0.704290	−	0.256341i
$215$	8.46622	+	10.0896i	0.577391	+	0.688108i
$216$	−0.503017	−	2.42148i	−0.0342260	−	0.164761i
$217$	9.40825	+	5.43186i	0.638674	+	0.368738i
$218$	11.4281	−	2.01509i	0.774011	−	0.136479i
$219$	−1.98687	−	29.0566i	−0.134260	−	1.96347i
$220$	6.84874	−	11.8624i	0.461742	−	0.799760i
$221$	−4.91277	−	8.50916i	−0.330469	−	0.572388i
$222$	17.0054	+	25.2955i	1.14133	+	1.69772i
$223$	−4.89903	−	13.4600i	−0.328063	−	0.901347i	−0.988602	−	0.150555i	$-0.951894\pi$
$223$	−4.89903	−	13.4600i	−0.328063	−	0.901347i	0.660538	−	0.750792i	$-0.270328\pi$
$224$	17.6579	+	6.42697i	1.17982	+	0.429420i
$225$	−9.67343	−	12.4604i	−0.644895	−	0.830691i
$226$	1.16555	−	6.61015i	0.0775311	−	0.439701i
$227$	14.0873			0.935008			0.467504	−	0.883991i	$-0.345153\pi$
$227$	14.0873			0.935008			0.467504	+	0.883991i	$0.345153\pi$
$228$	−12.9275	−	2.88297i	−0.856147	−	0.190929i
$229$	−2.07159			−0.136894			−0.0684471	−	0.997655i	$-0.521804\pi$
$229$	−2.07159			−0.136894			−0.0684471	+	0.997655i	$0.521804\pi$
$230$	−2.57658	+	14.6125i	−0.169895	+	0.963520i
$231$	−7.48782	+	7.20864i	−0.492662	+	0.474294i
$232$	−1.81591	−	0.660936i	−0.119220	−	0.0433926i
$233$	−9.11566	−	25.0451i	−0.597187	−	1.64076i	−0.756852	−	0.653586i	$-0.773264\pi$
$233$	−9.11566	−	25.0451i	−0.597187	−	1.64076i	0.159665	−	0.987171i	$-0.448959\pi$
$234$	6.98521	+	13.2355i	0.456638	+	0.865231i
$235$	−4.94662	−	8.56780i	−0.322682	−	0.558901i
$236$	−9.00033	+	15.5890i	−0.585872	+	1.01476i
$237$	−7.18880	+	0.491563i	−0.466963	+	0.0319305i
$238$	17.9265	−	3.16093i	1.16200	−	0.204893i
$239$	15.2895	+	8.82739i	0.988995	+	0.570996i	0.904974	−	0.425468i	$-0.139890\pi$
$239$	15.2895	+	8.82739i	0.988995	+	0.570996i	0.0840210	+	0.996464i	$0.473224\pi$
$240$	−22.4709	+	9.96322i	−1.45049	+	0.643123i
$241$	−4.98745	−	5.94381i	−0.321270	−	0.382874i	0.581104	−	0.813830i	$-0.302621\pi$
$241$	−4.98745	−	5.94381i	−0.321270	−	0.382874i	−0.902373	+	0.430955i	$0.858177\pi$
$242$	−9.20836	+	3.35157i	−0.591936	+	0.215447i
$243$	9.92780	+	12.0183i	0.636868	+	0.770972i
$244$	−1.33369	−	1.11910i	−0.0853808	−	0.0716430i
$245$	2.96567	+	0.522928i	0.189470	+	0.0334087i
$246$	−19.1559	−	2.04320i	−1.22133	−	0.130270i
$247$	−11.2012	+	0.688327i	−0.712717	+	0.0437972i
$248$			2.10050i			0.133382i
$249$	−4.72431	−	1.36255i	−0.299391	−	0.0863482i
$250$	−1.02988	+	1.22736i	−0.0651352	+	0.0776251i
$251$	2.47858	−	6.80985i	0.156447	−	0.429834i	−0.836562	−	0.547872i	$-0.815438\pi$
$251$	2.47858	−	6.80985i	0.156447	−	0.429834i	0.993009	+	0.118038i	$0.0376604\pi$
$252$	−12.8353	+	1.76358i	−0.808547	+	0.111095i
$253$	−4.46490	+	3.74650i	−0.280706	+	0.235540i
$254$	8.85355	−	5.11160i	0.555521	−	0.320730i
$255$	−12.4705	+	17.1086i	−0.780931	+	1.07139i
$256$	3.33061	+	18.8888i	0.208163	+	1.18055i
$257$	−1.96119	−	11.1224i	−0.122336	−	0.693799i	−0.982855	−	0.184381i	$-0.940972\pi$
$257$	−1.96119	−	11.1224i	−0.122336	−	0.693799i	0.860519	−	0.509418i	$-0.170139\pi$
$258$	−8.12930	+	11.1529i	−0.506108	+	0.694346i
$259$	−19.3619	+	11.1786i	−1.20309	+	0.694606i
$260$	11.0819	−	9.29881i	0.687270	−	0.576688i
$261$	12.0669	−	1.65799i	0.746921	−	0.102627i
$262$	10.2663	−	28.2066i	0.634257	−	1.74261i
$263$	−14.1677	+	16.8844i	−0.873618	+	1.04114i	0.125180	+	0.992134i	$0.460049\pi$
$263$	−14.1677	+	16.8844i	−0.873618	+	1.04114i	−0.998799	+	0.0490039i	$0.984395\pi$
$264$	−1.93095	−	0.556911i	−0.118842	−	0.0342755i
$265$		−	10.6341i		−	0.653248i
$266$	5.89919	−	19.9364i	0.361703	−	1.22238i
$267$	14.7027	+	1.56822i	0.899789	+	0.0959733i
$268$	11.8257	+	2.08519i	0.722370	+	0.127373i
$269$	8.97080	+	7.52740i	0.546960	+	0.458954i	0.873910	−	0.486088i	$-0.161577\pi$
$269$	8.97080	+	7.52740i	0.546960	+	0.458954i	−0.326950	+	0.945042i	$0.606021\pi$
$270$	19.9702	−	25.3187i	1.21535	−	1.54085i
$271$	−7.86382	+	2.86220i	−0.477693	+	0.173866i	−0.569634	−	0.821898i	$-0.692915\pi$
$271$	−7.86382	+	2.86220i	−0.477693	+	0.173866i	0.0919411	+	0.995764i	$0.470693\pi$
$272$	10.8696	+	12.9539i	0.659066	+	0.785444i
$273$	−10.0351	+	4.44942i	−0.607354	+	0.269291i
$274$	16.7925	+	9.69518i	1.01447	+	0.585707i
$275$	−12.6233	+	2.22584i	−0.761216	+	0.134223i
$276$	−7.24830	+	0.495632i	−0.436296	+	0.0298335i
$277$	7.41703	−	12.8467i	0.445646	−	0.771881i	−0.552451	−	0.833545i	$-0.686307\pi$
$277$	7.41703	−	12.8467i	0.445646	−	0.771881i	0.998097	+	0.0616640i	$0.0196407\pi$
$278$	−8.77737	−	15.2029i	−0.526432	−	0.911806i
$279$	−6.17953	−	11.7089i	−0.369959	−	0.700992i
$280$	−1.28348	−	3.52632i	−0.0767023	−	0.210738i
$281$	−5.55341	−	2.02128i	−0.331289	−	0.120579i	0.171020	−	0.985268i	$-0.445294\pi$
$281$	−5.55341	−	2.02128i	−0.331289	−	0.120579i	−0.502309	+	0.864688i	$0.667516\pi$
$282$	7.46811	−	7.18968i	0.444720	−	0.428139i
$283$	−3.79608	+	21.5286i	−0.225653	+	1.27974i	0.635779	+	0.771871i	$0.280679\pi$
$283$	−3.79608	+	21.5286i	−0.225653	+	1.27974i	−0.861432	+	0.507873i	$0.830432\pi$
$284$	−0.388749			−0.0230680
$285$	11.1386	+	21.4627i	0.659794	+	1.27134i
$286$	12.1608			0.719084
$287$	2.45374	−	13.9158i	0.144839	−	0.821425i
$288$	−14.0434	−	18.0893i	−0.827514	−	1.06592i
$289$	−2.28853	−	0.832957i	−0.134620	−	0.0489975i
$290$	−8.61766	−	23.6768i	−0.506046	−	1.39035i
$291$	−3.75027	−	5.57853i	−0.219845	−	0.327019i
$292$	−14.7498	−	25.5474i	−0.863166	−	1.49505i
$293$	10.2048	−	17.6752i	0.596169	−	1.03260i	−0.397211	−	0.917727i	$-0.630022\pi$
$293$	10.2048	−	17.6752i	0.596169	−	1.03260i	0.993381	−	0.114869i	$-0.0366447\pi$
$294$	0.215266	+	3.14813i	0.0125546	+	0.183603i
$295$	32.3636	−	5.70658i	1.88428	−	0.332250i
$296$	−3.74364	−	2.16139i	−0.217595	−	0.125628i
$297$	12.4021	−	2.57631i	0.719644	−	0.149492i
$298$	−15.6822	−	18.6893i	−0.908445	−	1.08264i
$299$	−5.78447	+	2.10537i	−0.334524	+	0.121757i
$300$	−14.3498	−	7.02626i	−0.828488	−	0.405662i
$301$	−7.75476	−	6.50702i	−0.446977	−	0.375058i
$302$	27.4974	+	4.84853i	1.58230	+	0.279001i
$303$	0.489236	−	4.58680i	0.0281059	−	0.263505i
$304$	18.7791	−	4.51417i	1.07706	−	0.258905i
$305$			3.17847i			0.181999i
$306$	−20.5429	−	8.37357i	−1.17436	−	0.478685i
$307$	0.936090	−	1.11559i	0.0534255	−	0.0636700i	−0.738670	−	0.674067i	$-0.764546\pi$
$307$	0.936090	−	1.11559i	0.0534255	−	0.0636700i	0.792095	+	0.610397i	$0.208990\pi$
$308$	−3.60068	+	9.89280i	−0.205168	+	0.563695i
$309$	6.07318	+	24.5190i	0.345491	+	1.39484i
$310$	−20.9801	+	17.6044i	−1.19159	+	0.999862i
$311$	−22.8208	+	13.1756i	−1.29405	+	0.747118i	−0.979369	−	0.202081i	$-0.935230\pi$
$311$	−22.8208	+	13.1756i	−1.29405	+	0.747118i	−0.314677	+	0.949199i	$0.601896\pi$
$312$	−1.71519	−	1.25020i	−0.0971033	−	0.0707785i
$313$	3.97326	+	22.5335i	0.224582	+	1.27367i	0.863483	+	0.504379i	$0.168278\pi$
$313$	3.97326	+	22.5335i	0.224582	+	1.27367i	−0.638901	+	0.769289i	$0.720610\pi$
$314$	5.88181	+	33.3574i	0.331930	+	1.88247i
$315$	17.5287	+	15.8809i	0.987629	+	0.894790i
$316$	−6.32058	+	3.64919i	−0.355561	+	0.205283i
$317$	−4.05314	+	3.40099i	−0.227647	+	0.191019i	−0.749476	−	0.662032i	$-0.769694\pi$
$317$	−4.05314	+	3.40099i	−0.227647	+	0.191019i	0.521829	+	0.853050i	$0.325250\pi$
$318$	10.8159	−	2.67903i	0.606528	−	0.150232i
$319$	3.38512	−	9.30054i	0.189530	−	0.520730i
$320$	−12.2063	+	14.5469i	−0.682352	+	0.813196i
$321$	2.71600	−	9.41705i	0.151592	−	0.525608i
$322$		−	11.4042i		−	0.635533i
$323$	12.0634	−	11.4543i	0.671226	−	0.637336i
$324$	14.3843	+	6.51080i	0.799129	+	0.361711i
$325$	−13.3319	−	2.35078i	−0.739523	−	0.130398i
$326$	−3.43633	−	2.88343i	−0.190321	−	0.159698i
$327$	4.56171	−	9.31644i	0.252263	−	0.515200i
$328$	2.56737	−	0.934447i	0.141759	−	0.0515962i
$329$	4.88764	+	5.82486i	0.269464	+	0.321135i
$330$	−10.6208	−	23.9540i	−0.584658	−	1.31863i
$331$	22.9821	+	13.2687i	1.26321	+	0.729313i	0.973694	−	0.227860i	$-0.0731729\pi$
$331$	22.9821	+	13.2687i	1.26321	+	0.729313i	0.289514	+	0.957174i	$0.406506\pi$
$332$	−4.90453	+	0.864801i	−0.269171	+	0.0474621i
$333$	27.2269	+	1.03478i	1.49203	+	0.0567055i
$334$	−22.3978	+	38.7941i	−1.22555	+	2.12272i
$335$	−10.9613	−	18.9856i	−0.598881	−	1.03729i
$336$	15.6787	−	10.5403i	0.855342	−	0.575021i
$337$	5.20079	+	14.2890i	0.283305	+	0.778374i	0.996963	+	0.0778793i	$0.0248149\pi$
$337$	5.20079	+	14.2890i	0.283305	+	0.778374i	−0.713658	+	0.700494i	$0.752963\pi$
$338$	−11.6010	−	4.22243i	−0.631013	−	0.229670i
$339$	−4.16131	−	4.32247i	−0.226011	−	0.234764i
$340$	−3.72368	+	21.1180i	−0.201945	+	1.14529i
$341$	−10.7582			−0.582587
$342$	−19.0236	+	16.7361i	−1.02868	+	0.904987i
$343$	−19.5462			−1.05539
$344$	0.339883	−	1.92758i	0.0183253	−	0.103928i
$345$	9.19906	+	9.55532i	0.495261	+	0.514441i
$346$	7.85419	+	2.85869i	0.422244	+	0.153684i
$347$	4.51031	+	12.3920i	0.242126	+	0.665236i	0.999919	+	0.0127407i	$0.00405560\pi$
$347$	4.51031	+	12.3920i	0.242126	+	0.665236i	−0.757793	+	0.652495i	$0.773722\pi$
$348$	10.2385	−	6.88306i	0.548843	−	0.368971i
$349$	6.48287	+	11.2287i	0.347020	+	0.601056i	0.985719	−	0.168401i	$-0.0538603\pi$
$349$	6.48287	+	11.2287i	0.347020	+	0.601056i	−0.638699	+	0.769457i	$0.720527\pi$
$350$	12.5401	−	21.7201i	0.670296	−	1.16099i
$351$	13.2390	+	1.92305i	0.706645	+	0.102645i
$352$	−18.3259	+	3.23135i	−0.976774	+	0.172232i
$353$	−31.2379	−	18.0352i	−1.66262	−	0.959916i	−0.971455	−	0.237222i	$-0.923763\pi$
$353$	−31.2379	−	18.0352i	−1.66262	−	0.959916i	−0.691168	−	0.722694i	$-0.742904\pi$
$354$	13.9575	+	31.4794i	0.741831	+	1.67311i
$355$	0.456198	+	0.543676i	0.0242125	+	0.0288553i
$356$	14.0733	−	5.12226i	0.745884	−	0.271479i
$357$	7.15564	−	14.6141i	0.378717	−	0.773458i
$358$	0.811132	+	0.680620i	0.0428696	+	0.0359719i
$359$	9.61424	+	1.69525i	0.507420	+	0.0894719i	0.421497	−	0.906830i	$-0.361505\pi$
$359$	9.61424	+	1.69525i	0.507420	+	0.0894719i	0.0859235	+	0.996302i	$0.472616\pi$
$360$	−0.964619	+	4.47041i	−0.0508399	+	0.235611i
$361$	−5.56550	−	18.1666i	−0.292921	−	0.956137i
$362$			3.72910i			0.195997i
$363$	−2.42747	+	8.41663i	−0.127409	+	0.441759i
$364$	−7.14694	+	8.51739i	−0.374602	+	0.446433i
$365$	−18.4198	+	50.6079i	−0.964136	+	2.64894i
$366$	−3.23282	+	0.800746i	−0.168982	+	0.0418557i
$367$	10.0386	−	8.42341i	0.524012	−	0.439698i	−0.342016	−	0.939694i	$-0.611110\pi$
$367$	10.0386	−	8.42341i	0.524012	−	0.439698i	0.866028	+	0.499996i	$0.166665\pi$
$368$	9.17482	−	5.29709i	0.478271	−	0.276130i
$369$	−11.5623	+	12.7619i	−0.601908	+	0.664359i
$370$	−9.78731	−	55.5066i	−0.508818	−	2.88565i
$371$	1.41927	+	8.04906i	0.0736846	+	0.417886i
$372$	−10.8368	−	7.89891i	−0.561860	−	0.409539i
$373$	−27.0751	+	15.6318i	−1.40190	+	0.809385i	−0.994587	−	0.103905i	$-0.966866\pi$
$373$	−27.0751	+	15.6318i	−1.40190	+	0.809385i	−0.407309	+	0.913290i	$0.633533\pi$
$374$	−13.8089	+	11.5870i	−0.714040	+	0.599151i
$375$	0.344345	+	1.39021i	0.0177819	+	0.0717903i
$376$	−0.502838	+	1.38154i	−0.0259319	+	0.0712473i
$377$	6.71907	−	8.00748i	0.346050	−	0.412406i
$378$	−11.7365	+	21.8293i	−0.603663	+	1.12278i
$379$			8.43182i			0.433114i	0.976270	+	0.216557i	$0.0694827\pi$
$379$			8.43182i			0.433114i	−0.976270	+	0.216557i	$0.930517\pi$
$380$	19.6925	+	14.5629i	1.01020	+	0.747062i
$381$	0.969243	−	9.08706i	0.0496558	−	0.465544i
$382$	26.0284	+	4.58951i	1.33173	+	0.234820i
$383$	−2.71999	−	2.28234i	−0.138985	−	0.116622i	0.570645	−	0.821197i	$-0.306693\pi$
$383$	−2.71999	−	2.28234i	−0.138985	−	0.116622i	−0.709630	+	0.704575i	$0.751138\pi$
$384$	5.87853	+	2.87837i	0.299987	+	0.146886i
$385$	18.0608	−	6.57359i	0.920462	−	0.335021i
$386$	−31.9304	−	38.0532i	−1.62522	−	1.93686i
$387$	3.77616	+	11.7448i	0.191953	+	0.597023i
$388$	−5.89634	−	3.40425i	−0.299341	−	0.172825i
$389$	31.7209	−	5.59325i	1.60831	−	0.283589i	0.703917	−	0.710282i	$-0.251433\pi$
$389$	31.7209	−	5.59325i	1.60831	−	0.283589i	0.904396	+	0.426693i	$0.140322\pi$
$390$	−1.88791	−	27.6094i	−0.0955979	−	1.39806i
$391$	4.56236	−	7.90224i	0.230729	−	0.399634i
$392$	−0.223759	−	0.387561i	−0.0113015	−	0.0195748i
$393$	−14.9701	−	22.2680i	−0.755143	−	1.12327i
$394$	−2.45373	−	6.74158i	−0.123617	−	0.339636i
$395$	12.5207	+	4.55717i	0.629986	+	0.229296i
$396$	10.1345	−	7.86775i	0.509276	−	0.395370i
$397$	3.01861	−	17.1194i	0.151500	−	0.859197i	−0.810417	−	0.585854i	$-0.800759\pi$
$397$	3.01861	−	17.1194i	0.151500	−	0.859197i	0.961917	−	0.273343i	$-0.0881295\pi$
$398$	16.5109			0.827617
$399$	−11.2954	−	14.7587i	−0.565478	−	0.738861i
$400$	23.2987			1.16493
$401$	−5.63502	+	31.9578i	−0.281399	+	1.59589i	0.436471	+	0.899718i	$0.356228\pi$
$401$	−5.63502	+	31.9578i	−0.281399	+	1.59589i	−0.717871	+	0.696177i	$0.754883\pi$
$402$	16.5488	−	15.9318i	0.825377	−	0.794604i
$403$	−10.6769	−	3.88606i	−0.531852	−	0.193578i
$404$	−1.59799	−	4.39045i	−0.0795031	−	0.218433i
$405$	−7.77452	−	27.7573i	−0.386319	−	1.37927i
$406$	9.68279	+	16.7711i	0.480549	+	0.832335i
$407$	11.0700	−	19.1738i	0.548720	−	0.950411i
$408$	3.13885	−	0.214631i	0.155396	−	0.0106258i
$409$	−19.4539	+	3.43025i	−0.961933	+	0.169615i	−0.632497	−	0.774563i	$-0.717970\pi$
$409$	−19.4539	+	3.43025i	−0.961933	+	0.169615i	−0.329436	+	0.944178i	$0.606859\pi$
$410$	30.8506	+	17.8116i	1.52360	+	0.879652i
$411$	15.8455	−	7.02565i	0.781601	−	0.346550i
$412$	16.4459	+	19.5995i	0.810231	+	0.965596i
$413$	−23.7347	+	8.63874i	−1.16791	+	0.425084i
$414$	−7.40122	+	11.7636i	−0.363750	+	0.578150i
$415$	6.96494	+	5.84428i	0.341895	+	0.286884i
$416$	−19.3546	−	3.41274i	−0.948939	−	0.167324i
$417$	−15.6038	−	1.66433i	−0.764122	−	0.0815027i
$418$	4.81213	+	20.0186i	0.235369	+	0.979142i
$419$		−	26.9961i		−	1.31884i	−0.751773	−	0.659422i	$-0.770801\pi$
$419$		−	26.9961i		−	1.31884i	0.751773	−	0.659422i	$-0.229199\pi$
$420$	23.0192	+	6.63905i	1.12322	+	0.323952i
$421$	−18.8465	+	22.4604i	−0.918522	+	1.09465i	0.0767040	+	0.997054i	$0.475560\pi$
$421$	−18.8465	+	22.4604i	−0.918522	+	1.09465i	−0.995226	+	0.0975979i	$0.968884\pi$
$422$	2.62426	−	7.21009i	0.127747	−	0.350982i
$423$	−1.26140	−	9.18044i	−0.0613312	−	0.446368i
$424$	−1.21058	+	1.01580i	−0.0587909	+	0.0493314i
$425$	17.3786	−	10.0335i	0.842986	−	0.486698i
$426$	−0.438044	+	0.600966i	−0.0212233	+	0.0291169i
$427$	−0.424210	−	2.40582i	−0.0205290	−	0.116426i
$428$	−1.72382	−	9.77629i	−0.0833242	−	0.472555i
$429$	6.40315	−	8.78468i	0.309147	−	0.424129i
$430$	22.1014	−	12.7603i	1.06583	−	0.615355i
$431$	7.56785	−	6.35018i	0.364530	−	0.305877i	−0.442063	−	0.896984i	$-0.645753\pi$
$431$	7.56785	−	6.35018i	0.364530	−	0.305877i	0.806593	+	0.591107i	$0.201309\pi$
$432$	−23.0133	+	0.697179i	−1.10723	+	0.0335431i
$433$	−12.4605	+	34.2348i	−0.598811	+	1.64522i	0.154835	+	0.987940i	$0.450515\pi$
$433$	−12.4605	+	34.2348i	−0.598811	+	1.64522i	−0.753646	+	0.657280i	$0.771707\pi$
$434$	13.5305	−	16.1250i	0.649484	−	0.774025i
$435$	−21.6411	−	6.24158i	−1.03761	−	0.299261i
$436$		−	10.5069i		−	0.503188i
$437$	−5.75473	−	8.68903i	−0.275286	−	0.415653i
$438$	−56.1138	−	5.98521i	−2.68122	−	0.285984i
$439$	−36.5493	−	6.44463i	−1.74440	−	0.307586i	−0.791571	−	0.611078i	$-0.790736\pi$
$439$	−36.5493	−	6.44463i	−1.74440	−	0.307586i	−0.952834	+	0.303492i	$0.901847\pi$
$440$	2.84675	+	2.38871i	0.135714	+	0.113877i
$441$	2.38748	+	1.50211i	0.113690	+	0.0715291i
$442$	−17.8900	+	6.51142i	−0.850940	+	0.309717i
$443$	13.6540	+	16.2722i	0.648719	+	0.773113i	0.985720	−	0.168391i	$-0.0538571\pi$
$443$	13.6540	+	16.2722i	0.648719	+	0.773113i	−0.337001	+	0.941504i	$0.609413\pi$
$444$	25.2288	−	11.1860i	1.19731	−	0.530866i
$445$	−23.6787	−	13.6709i	−1.12248	−	0.648063i
$446$	−27.3324	+	4.81944i	−1.29423	+	0.228207i
$447$	−21.7580	+	1.48779i	−1.02912	+	0.0703701i
$448$	7.29758	−	12.6398i	0.344778	−	0.597173i
$449$	12.1746	+	21.0870i	0.574553	+	0.995155i	0.996090	+	0.0883439i	$0.0281575\pi$
$449$	12.1746	+	21.0870i	0.574553	+	0.995155i	−0.421537	+	0.906811i	$0.638509\pi$
$450$	−27.0314	+	14.2662i	−1.27427	+	0.672514i
$451$	4.78596	+	13.1493i	0.225362	+	0.619177i
$452$	−5.71078	−	2.07855i	−0.268613	−	0.0977670i
$453$	17.9809	−	17.3105i	0.844817	−	0.813319i
$454$	4.73987	−	26.8811i	0.222453	−	1.26159i
$455$	20.2988			0.951622
$456$	1.37931	−	3.31818i	0.0645921	−	0.155388i
$457$	22.9690			1.07444			0.537221	−	0.843441i	$-0.319474\pi$
$457$	22.9690			1.07444			0.537221	+	0.843441i	$0.319474\pi$
$458$	−0.697013	+	3.95296i	−0.0325693	+	0.184710i
$459$	−16.8655	+	10.4307i	−0.787214	+	0.486862i
$460$	12.6244	+	4.59489i	0.588614	+	0.214238i
$461$	1.89821	+	5.21530i	0.0884086	+	0.242901i	0.976015	−	0.217701i	$-0.0698559\pi$
$461$	1.89821	+	5.21530i	0.0884086	+	0.242901i	−0.887607	+	0.460602i	$0.847634\pi$
$462$	11.2360	+	16.7135i	0.522746	+	0.777585i
$463$	−1.08672	−	1.88225i	−0.0505040	−	0.0874755i	0.839668	−	0.543100i	$-0.182749\pi$
$463$	−1.08672	−	1.88225i	−0.0505040	−	0.0874755i	−0.890172	+	0.455624i	$0.849416\pi$
$464$	−8.99500	+	15.5798i	−0.417583	+	0.723274i
$465$	1.67015	+	24.4249i	0.0774515	+	1.13268i
$466$	−50.8576	+	8.96757i	−2.35593	+	0.415414i
$467$	−20.8547	−	12.0405i	−0.965040	−	0.557166i	−0.0673192	−	0.997731i	$-0.521445\pi$
$467$	−20.8547	−	12.0405i	−0.965040	−	0.557166i	−0.897720	+	0.440566i	$0.854778\pi$
$468$	12.8999	−	4.14752i	0.596296	−	0.191719i
$469$	10.8306	+	12.9074i	0.500111	+	0.596010i
$470$	−18.0133	+	6.55629i	−0.830889	+	0.302419i
$471$	27.1936	+	13.3151i	1.25302	+	0.613528i
$472$	−3.74109	−	3.13914i	−0.172197	−	0.144491i
$473$	9.87247	+	1.74078i	0.453937	+	0.0800413i
$474$	−1.48078	+	13.8829i	−0.0680144	+	0.637663i
$475$	−1.40580	−	22.8767i	−0.0645024	−	1.04966i
$476$		−	16.4814i		−	0.755425i
$477$	3.75975	−	9.22380i	0.172147	−	0.422329i
$478$	21.9886	−	26.2050i	1.00574	−	1.19859i
$479$	9.79379	−	26.9082i	0.447490	−	1.22947i	−0.486976	−	0.873415i	$-0.661900\pi$
$479$	9.79379	−	26.9082i	0.447490	−	1.22947i	0.934466	−	0.356053i	$-0.115878\pi$
$480$	10.1813	+	41.1048i	0.464713	+	1.87617i
$481$	17.9123	−	15.0302i	0.816731	−	0.685319i
$482$	−13.0199	+	7.51707i	−0.593042	+	0.342393i
$483$	−8.23815	−	6.00478i	−0.374849	−	0.273227i
$484$	1.54070	+	8.73772i	0.0700316	+	0.397169i
$485$	2.15844	+	12.2411i	0.0980096	+	0.555840i
$486$	26.2734	−	14.9003i	1.19178	−	0.675892i
$487$	23.5201	−	13.5793i	1.06580	−	0.615338i	0.138766	−	0.990325i	$-0.455686\pi$
$487$	23.5201	−	13.5793i	1.06580	−	0.615338i	0.927030	+	0.374987i	$0.122353\pi$
$488$	0.361835	−	0.303615i	0.0163795	−	0.0137440i
$489$	−3.89228	+	0.964089i	−0.176015	+	0.0435976i
$490$	1.99568	−	5.48309i	0.0901558	−	0.247701i
$491$	−8.78555	+	10.4702i	−0.396486	+	0.472514i	−0.926945	−	0.375197i	$-0.877575\pi$
$491$	−8.78555	+	10.4702i	−0.396486	+	0.472514i	0.530459	+	0.847711i	$0.322020\pi$
$492$	−4.83362	+	16.7594i	−0.217916	+	0.755570i
$493$			15.4947i			0.697848i
$494$	−2.45535	+	21.6055i	−0.110472	+	0.972079i
$495$	−22.8961	−	4.94049i	−1.02910	−	0.222059i
$496$	19.2574	+	3.39561i	0.864684	+	0.152467i
$497$	−0.417862	−	0.350628i	−0.0187437	−	0.0157278i
$498$	−4.18955	+	8.55637i	−0.187738	+	0.383420i
$499$	27.5375	−	10.0228i	1.23275	−	0.448684i	0.358211	−	0.933640i	$-0.383387\pi$
$499$	27.5375	−	10.0228i	1.23275	−	0.448684i	0.874538	+	0.484956i	$0.161164\pi$
$500$	0.932472	+	1.11128i	0.0417014	+	0.0496978i
$501$	16.2307	+	36.6063i	0.725132	+	1.63545i
$502$	−12.1605	−	7.02084i	−0.542748	−	0.313356i
$503$	−28.9203	+	5.09943i	−1.28949	+	0.227372i	−0.776006	−	0.630726i	$-0.782757\pi$
$503$	−28.9203	+	5.09943i	−1.28949	+	0.227372i	−0.513486	+	0.858098i	$0.671646\pi$
$504$	0.133493	−	3.51244i	0.00594623	−	0.156456i
$505$	−4.26492	+	7.38705i	−0.189786	+	0.328719i
$506$	5.64672	+	9.78040i	0.251027	+	0.434792i
$507$	−9.15858	+	6.15704i	−0.406747	+	0.273444i
$508$	−3.16584	−	8.69807i	−0.140461	−	0.385914i
$509$	−26.4535	−	9.62828i	−1.17253	−	0.426766i	−0.318972	−	0.947764i	$-0.603338\pi$
$509$	−26.4535	−	9.62828i	−1.17253	−	0.426766i	−0.853558	+	0.520998i	$0.825560\pi$
$510$	28.4505	+	29.5523i	1.25981	+	1.30860i
$511$	7.18780	−	40.7640i	0.317969	−	1.80329i
$512$	29.6059			1.30841
$513$	2.07313	+	22.5544i	0.0915309	+	0.995802i
$514$	−21.8835			−0.965240
$515$	8.11106	−	46.0001i	0.357416	−	2.02701i
$516$	8.66648	+	9.00211i	0.381521	+	0.396296i
$517$	−7.07582	−	2.57539i	−0.311194	−	0.113265i
$518$	14.8162	+	40.7073i	0.650988	+	1.78857i
$519$	6.20059	−	4.16847i	0.272176	−	0.182976i
$520$	1.96239	+	3.39896i	0.0860565	+	0.149054i
$521$	0.605033	−	1.04795i	0.0265070	−	0.0459115i	−0.852468	−	0.522780i	$-0.824895\pi$
$521$	0.605033	−	1.04795i	0.0265070	−	0.0459115i	0.878975	+	0.476869i	$0.158228\pi$
$522$	0.896312	−	23.5836i	0.0392305	−	1.03223i
$523$	14.2503	−	2.51272i	0.623124	−	0.109873i	0.146833	−	0.989161i	$-0.453092\pi$
$523$	14.2503	−	2.51272i	0.623124	−	0.109873i	0.476291	+	0.879288i	$0.341981\pi$
$524$	−23.5367	−	13.5889i	−1.02820	−	0.593634i
$525$	−9.08722	−	20.4951i	−0.396599	−	0.894481i
$526$	27.4516	+	32.7155i	1.19695	+	1.42646i
$527$	15.8265	−	5.76038i	0.689414	−	0.250926i
$528$	−8.22727	+	16.8027i	−0.358046	+	0.731242i
$529$	13.2398	+	11.1095i	0.575644	+	0.483023i
$530$	−20.2918	−	3.57799i	−0.881418	−	0.155418i
$531$	30.0891	+	6.49260i	1.30576	+	0.281755i
$532$	−16.8491	−	8.39459i	−0.730500	−	0.363952i
$533$			14.7787i			0.640137i
$534$	7.93935	−	27.5277i	0.343569	−	1.19124i
$535$	−11.6495	+	13.8833i	−0.503652	+	0.600229i
$536$	−1.11425	+	3.06138i	−0.0481283	+	0.132231i
$537$	0.918757	−	0.227569i	0.0396473	−	0.00982034i
$538$	17.3820	−	14.5852i	0.749390	−	0.628813i
$539$	1.98498	−	1.14603i	0.0854990	−	0.0493629i
$540$	−19.4360	−	21.7875i	−0.836391	−	0.937584i
$541$	−7.38884	−	41.9042i	−0.317671	−	1.80160i	−0.556835	−	0.830623i	$-0.687984\pi$
$541$	−7.38884	−	41.9042i	−0.317671	−	1.80160i	0.239164	−	0.970979i	$-0.423127\pi$
$542$	2.81570	+	15.9686i	0.120944	+	0.685910i
$543$	2.69381	+	1.96352i	0.115603	+	0.0842625i
$544$	25.2294	−	14.5662i	1.08170	−	0.624520i
$545$	−14.6942	+	12.3299i	−0.629429	+	0.528154i
$546$	5.11383	+	20.6459i	0.218852	+	0.883563i
$547$	−3.75150	+	10.3072i	−0.160403	+	0.440703i	−0.993693	−	0.112132i	$-0.964232\pi$
$547$	−3.75150	+	10.3072i	−0.160403	+	0.440703i	0.833291	+	0.552835i	$0.186454\pi$
$548$	11.2851	−	13.4490i	0.482073	−	0.574513i
$549$	−1.12377	+	2.75694i	−0.0479613	+	0.117663i
$550$			24.8365i			1.05903i
$551$	15.8404	+	7.89203i	0.674822	+	0.336212i
$552$	0.209053	−	1.95996i	0.00889790	−	0.0834215i
$553$	−10.0853	−	1.77831i	−0.428870	−	0.0756213i
$554$	−22.0182	−	18.4755i	−0.935463	−	0.784947i
$555$	−45.2501	−	22.1563i	−1.92076	−	0.940482i
$556$	−14.9359	+	5.43621i	−0.633422	+	0.230547i
$557$	−0.363563	−	0.433278i	−0.0154047	−	0.0183586i	0.758287	−	0.651921i	$-0.226037\pi$
$557$	−0.363563	−	0.433278i	−0.0154047	−	0.0183586i	−0.773692	+	0.633562i	$0.781592\pi$
$558$	−24.4218	+	7.85203i	−1.03386	+	0.332403i
$559$	9.16905	+	5.29376i	0.387810	+	0.223902i
$560$	−34.4042	+	6.06638i	−1.45384	+	0.256351i
$561$	1.09928	+	16.0762i	0.0464116	+	0.678740i
$562$	−5.72548	+	9.91682i	−0.241515	+	0.418316i
$563$	15.0497	+	26.0669i	0.634271	+	1.09859i	0.986669	+	0.162739i	$0.0520330\pi$
$563$	15.0497	+	26.0669i	0.634271	+	1.09859i	−0.352398	+	0.935850i	$0.614634\pi$
$564$	−5.23661	−	7.78945i	−0.220501	−	0.327995i
$565$	3.79471	+	10.4259i	0.159645	+	0.438620i
$566$	39.8032	+	14.4872i	1.67306	+	0.608942i
$567$	9.58920	+	19.9722i	0.402709	+	0.838753i
$568$	0.0183145	−	0.103866i	0.000768458	−	0.00435814i
$569$	1.55575			0.0652205			0.0326103	−	0.999468i	$-0.489618\pi$
$569$	1.55575			0.0652205			0.0326103	+	0.999468i	$0.489618\pi$
$570$	44.7024	−	14.0331i	1.87238	−	0.587780i
$571$	11.9752			0.501147			0.250574	−	0.968098i	$-0.419381\pi$
$571$	11.9752			0.501147			0.250574	+	0.968098i	$0.419381\pi$
$572$	1.91198	−	10.8434i	0.0799438	−	0.453384i
$573$	17.0204	−	16.3858i	0.711035	−	0.684525i
$574$	−25.7283	−	9.36434i	−1.07388	−	0.390860i
$575$	−4.29989	−	11.8138i	−0.179318	−	0.492672i
$576$	−15.7306	+	8.30206i	−0.655443	+	0.345919i
$577$	1.38649	+	2.40147i	0.0577204	+	0.0999746i	0.893442	−	0.449179i	$-0.148283\pi$
$577$	1.38649	+	2.40147i	0.0577204	+	0.0999746i	−0.835721	+	0.549154i	$0.814950\pi$
$578$	−2.35944	+	4.08667i	−0.0981398	+	0.169983i
$579$	−44.3014	+	3.02929i	−1.84110	+	0.125893i
$580$	−22.4667	+	3.96148i	−0.932879	+	0.164492i
$581$	−6.05183	−	3.49402i	−0.251072	−	0.144957i
$582$	−11.9067	+	5.27922i	−0.493547	+	0.218831i
$583$	−5.20261	−	6.20022i	−0.215470	−	0.256787i
$584$	7.52067	−	2.73730i	0.311208	−	0.113270i
$585$	−20.9385	−	13.1737i	−0.865699	−	0.544664i
$586$	−30.2939	−	25.4196i	−1.25143	−	1.05007i
$587$	−12.2045	−	2.15199i	−0.503735	−	0.0888221i	−0.0839947	−	0.996466i	$-0.526768\pi$
$587$	−12.2045	−	2.15199i	−0.503735	−	0.0888221i	−0.419741	+	0.907644i	$0.637879\pi$
$588$	2.84092	+	0.303018i	0.117158	+	0.0124962i
$589$	2.17215	−	19.1135i	0.0895018	−	0.787559i
$590$		−	63.6757i		−	2.62149i
$591$	−6.16195	−	1.77719i	−0.253469	−	0.0731037i
$592$	−25.8675	+	30.8277i	−1.06315	+	1.26701i
$593$	9.59916	−	26.3735i	0.394190	−	1.08303i	−0.570879	−	0.821034i	$-0.693398\pi$
$593$	9.59916	−	26.3735i	0.394190	−	1.08303i	0.965069	−	0.261994i	$-0.0843802\pi$
$594$	−0.743196	−	24.5323i	−0.0304937	−	1.00657i
$595$	−23.0497	+	19.3410i	−0.944947	+	0.792905i
$596$	−19.1302	+	11.0448i	−0.783604	+	0.452414i
$597$	8.69364	−	11.9271i	0.355807	−	0.488143i
$598$	2.07117	+	11.7462i	0.0846964	+	0.480337i
$599$	−4.69683	−	26.6371i	−0.191907	−	1.08836i	−0.916754	−	0.399451i	$-0.869201\pi$
$599$	−4.69683	−	26.6371i	−0.191907	−	1.08836i	0.724847	−	0.688910i	$-0.241910\pi$
$600$	2.55333	−	3.50300i	0.104239	−	0.143009i
$601$	−6.54900	+	3.78107i	−0.267139	+	0.154233i	−0.627587	−	0.778547i	$-0.715957\pi$
$601$	−6.54900	+	3.78107i	−0.267139	+	0.154233i	0.360448	+	0.932779i	$0.382624\pi$
$602$	−15.0258	+	12.6081i	−0.612404	+	0.513868i
$603$	−2.79516	−	20.3431i	−0.113828	−	0.828436i
$604$	8.64652	−	23.7561i	0.351822	−	0.966623i
$605$	10.4119	−	12.4085i	0.423305	−	0.504475i
$606$	−8.58782	−	2.47684i	−0.348856	−	0.100615i
$607$			14.7418i			0.598352i	0.954198	+	0.299176i	$0.0967117\pi$
$607$			14.7418i			0.598352i	−0.954198	+	0.299176i	$0.903288\pi$
$608$	−2.04086	−	33.2112i	−0.0827679	−	1.34689i
$609$	17.2134	+	1.83601i	0.697522	+	0.0743991i
$610$	6.06509	+	1.06944i	0.245568	+	0.0433003i
$611$	−6.09206	−	5.11185i	−0.246459	−	0.206803i
$612$	−10.6963	+	17.0008i	−0.432371	+	0.687217i
$613$	3.20258	−	1.16564i	0.129351	−	0.0470799i	−0.276534	−	0.961004i	$-0.589186\pi$
$613$	3.20258	−	1.16564i	0.129351	−	0.0470799i	0.405885	+	0.913924i	$0.366963\pi$
$614$	−1.81378	−	2.16158i	−0.0731983	−	0.0872343i
$615$	29.1107	−	12.9072i	1.17386	−	0.520470i
$616$	−2.47354	−	1.42810i	−0.0996618	−	0.0575398i
$617$	31.0226	−	5.47012i	1.24892	−	0.220219i	0.490187	−	0.871617i	$-0.336929\pi$
$617$	31.0226	−	5.47012i	1.24892	−	0.220219i	0.758736	+	0.651399i	$0.225818\pi$
$618$	48.8301	−	3.33896i	1.96424	−	0.134313i
$619$	9.59361	−	16.6166i	0.385600	−	0.667878i	−0.606253	−	0.795272i	$-0.707328\pi$
$619$	9.59361	−	16.6166i	0.385600	−	0.667878i	0.991852	+	0.127394i	$0.0406612\pi$
$620$	12.3986	+	21.4750i	0.497941	+	0.862458i
$621$	4.60073	+	11.5405i	0.184621	+	0.463103i
$622$	17.4630	+	47.9792i	0.700202	+	1.92379i
$623$	19.7472	+	7.18740i	0.791156	+	0.287957i
$624$	−14.2345	+	13.7038i	−0.569837	+	0.548592i
$625$	−4.10547	+	23.2833i	−0.164219	+	0.931331i
$626$	44.3348			1.77197
$627$	16.9947	+	7.06442i	0.678705	+	0.282126i
$628$	30.6684			1.22380
$629$	−6.01880	+	34.1343i	−0.239985	+	1.36102i
$630$	36.2015	−	28.1045i	1.44230	−	1.11971i
$631$	33.0297	+	12.0218i	1.31489	+	0.478581i	0.901818	−	0.432116i	$-0.142233\pi$
$631$	33.0297	+	12.0218i	1.31489	+	0.478581i	0.413074	+	0.910698i	$0.364455\pi$
$632$	−0.677226	−	1.86066i	−0.0269386	−	0.0740132i
$633$	−3.82663	−	5.69210i	−0.152095	−	0.226241i
$634$	5.12596	+	8.87843i	0.203578	+	0.352608i
$635$	−8.44937	+	14.6347i	−0.335303	+	0.580762i
$636$	−0.688263	−	10.0654i	−0.0272914	−	0.399119i
$637$	2.38394	−	0.420353i	0.0944552	−	0.0166550i
$638$	−16.6081	−	9.58871i	−0.657522	−	0.379621i
$639$	0.203477	+	0.632865i	0.00804942	+	0.0250357i
$640$	−7.77996	−	9.27180i	−0.307530	−	0.366500i
$641$	−13.3925	+	4.87448i	−0.528972	+	0.192530i	−0.592679	−	0.805438i	$-0.701930\pi$
$641$	−13.3925	+	4.87448i	−0.528972	+	0.192530i	0.0637070	+	0.997969i	$0.479708\pi$
$642$	−17.0556	−	8.35111i	−0.673130	−	0.329592i
$643$	10.2448	+	8.59638i	0.404014	+	0.339008i	0.822043	−	0.569426i	$-0.192834\pi$
$643$	10.2448	+	8.59638i	0.404014	+	0.339008i	−0.418029	+	0.908434i	$0.637279\pi$
$644$	−10.1688	−	1.79303i	−0.400705	−	0.0706551i
$645$	2.41955	−	22.6843i	0.0952699	−	0.893195i
$646$	−17.7980	−	26.8731i	−0.700254	−	1.05731i
$647$			44.1193i			1.73451i	0.497867	+	0.867254i	$0.334117\pi$
$647$			44.1193i			1.73451i	−0.497867	+	0.867254i	$0.665883\pi$
$648$	−2.41723	+	3.53649i	−0.0949578	+	0.138927i
$649$	16.0778	−	19.1607i	0.631108	−	0.752125i
$650$	−8.97143	+	24.6488i	−0.351888	+	0.966805i
$651$	−4.52399	−	18.2646i	−0.177309	−	0.715845i
$652$	−3.11132	+	2.61071i	−0.121849	+	0.102243i
$653$	−0.0130791	+	0.00755119i	−0.000511823	+	0.000295501i	−0.500256	−	0.865878i	$-0.666761\pi$
$653$	−0.0130791	+	0.00755119i	−0.000511823	+	0.000295501i	0.499744	+	0.866173i	$0.333427\pi$
$654$	−16.2426	−	11.8392i	−0.635135	−	0.462949i
$655$	8.61592	+	48.8633i	0.336652	+	1.90925i
$656$	−4.41669	−	25.0483i	−0.172443	−	0.977971i
$657$	−33.8697	+	37.3838i	−1.32138	+	1.45848i
$658$	12.7594	−	7.36663i	0.497413	−	0.287181i
$659$	−12.3679	+	10.3779i	−0.481784	+	0.404264i	−0.851071	−	0.525051i	$-0.824046\pi$
$659$	−12.3679	+	10.3779i	−0.481784	+	0.404264i	0.369287	+	0.929315i	$0.379602\pi$
$660$	−23.0288	+	5.70406i	−0.896395	+	0.222030i
$661$	16.1067	−	44.2528i	0.626477	−	1.72123i	−0.0640698	−	0.997945i	$-0.520408\pi$
$661$	16.1067	−	44.2528i	0.626477	−	1.72123i	0.690547	−	0.723287i	$-0.257370\pi$
$662$	33.0517	−	39.3895i	1.28459	−	1.53091i
$663$	−4.71608	+	16.3518i	−0.183157	+	0.635052i
$664$		−	1.35114i		−	0.0524345i
$665$	8.03238	+	33.4150i	0.311482	+	1.29578i
$666$	11.1354	−	51.6057i	0.431488	−	1.99968i
$667$	9.55997	+	1.68568i	0.370164	+	0.0652698i
$668$	31.0699	+	26.0707i	1.20213	+	1.00871i
$669$	−10.9101	+	22.2819i	−0.421810	+	0.861469i
$670$	−39.9160	+	14.5282i	−1.54209	+	0.561274i
$671$	1.55503	+	1.85321i	0.0600312	+	0.0715424i
$672$	−13.1924	−	29.7538i	−0.508906	−	1.14778i
$673$	−24.0985	−	13.9133i	−0.928928	−	0.536317i	−0.0424553	−	0.999098i	$-0.513518\pi$
$673$	−24.0985	−	13.9133i	−0.928928	−	0.536317i	−0.886472	+	0.462782i	$0.846851\pi$
$674$	29.0159	−	5.11629i	1.11765	−	0.197072i
$675$	−3.92752	+	27.0385i	−0.151170	+	1.04071i
$676$	−5.58896	+	9.68036i	−0.214960	+	0.372321i
$677$	11.1265	+	19.2717i	0.427626	+	0.740670i	0.996662	−	0.0816430i	$-0.0260167\pi$
$677$	11.1265	+	19.2717i	0.427626	+	0.740670i	−0.569036	+	0.822313i	$0.692683\pi$
$678$	−9.64817	+	6.48617i	−0.370536	+	0.249100i
$679$	−3.26749	−	8.97734i	−0.125395	−	0.344519i
$680$	−5.46692	−	1.98980i	−0.209647	−	0.0763053i
$681$	−16.9226	−	17.5779i	−0.648474	−	0.673588i
$682$	−3.61973	+	20.5285i	−0.138607	+	0.786077i
$683$	−27.9609			−1.06989			−0.534947	−	0.844886i	$-0.679668\pi$
$683$	−27.9609			−1.06989			−0.534947	+	0.844886i	$0.679668\pi$
$684$	11.9320	+	19.5940i	0.456233	+	0.749195i
$685$	−32.0519			−1.22464
$686$	−6.57657	+	37.2976i	−0.251094	+	1.42403i
$687$	2.48852	+	2.58489i	0.0949430	+	0.0986199i
$688$	−17.1226	−	6.23211i	−0.652792	−	0.237597i
$689$	−2.92364	−	8.03264i	−0.111382	−	0.306019i
$690$	21.3284	−	14.3384i	0.811959	−	0.545855i
$691$	−21.6169	−	37.4416i	−0.822346	−	1.42435i	−0.903931	−	0.427679i	$-0.859331\pi$
$691$	−21.6169	−	37.4416i	−0.822346	−	1.42435i	0.0815844	−	0.996666i	$-0.474002\pi$
$692$	3.78387	−	6.55385i	0.143841	−	0.249140i
$693$	17.9897	+	0.683710i	0.683371	+	0.0259720i
$694$	25.1637	−	4.43703i	0.955200	−	0.168427i
$695$	25.1300	+	14.5088i	0.953235	+	0.550350i
$696$	1.35668	+	3.05982i	0.0514247	+	0.115982i
$697$	−14.0814	−	16.7816i	−0.533372	−	0.635648i
$698$	23.6075	−	8.59244i	0.893559	−	0.325229i
$699$	−20.3006	+	41.4601i	−0.767838	+	1.56817i
$700$	−17.3954	−	14.5965i	−0.657485	−	0.551695i
$701$	−43.7303	−	7.71084i	−1.65167	−	0.291234i	−0.731235	−	0.682125i	$-0.761056\pi$
$701$	−43.7303	−	7.71084i	−1.65167	−	0.291234i	−0.920437	+	0.390891i	$0.872167\pi$
$702$	8.12396	−	24.6153i	0.306619	−	0.929046i
$703$	31.8301	+	23.5389i	1.20050	+	0.887786i
$704$			14.4534i			0.544731i
$705$	−4.74858	+	16.4645i	−0.178842	+	0.620089i
$706$	−44.9248	+	53.5393i	−1.69077	+	2.01498i
$707$	2.24225	−	6.16054i	0.0843286	−	0.231691i
$708$	30.2635	−	7.49605i	1.13737	−	0.281719i
$709$	−20.8623	+	17.5055i	−0.783500	+	0.657434i	−0.944127	−	0.329581i	$-0.893093\pi$
$709$	−20.8623	+	17.5055i	−0.783500	+	0.657434i	0.160628	+	0.987015i	$0.448648\pi$
$710$	1.19093	−	0.687581i	0.0446946	−	0.0258045i
$711$	9.24901	+	8.37958i	0.346865	+	0.314259i
$712$	0.705563	+	4.00145i	0.0264421	+	0.149961i
$713$	−1.83228	−	10.3914i	−0.0686193	−	0.389160i
$714$	−25.4786	−	18.5713i	−0.953514	−	0.695015i
$715$	−17.4085	+	10.0508i	−0.651040	+	0.375878i
$716$	0.734415	−	0.616247i	0.0274464	−	0.0230302i
$717$	−7.35201	−	29.6820i	−0.274566	−	1.10849i
$718$	6.46968	−	17.7753i	0.241446	−	0.663369i
$719$	3.69216	−	4.40015i	0.137694	−	0.164098i	−0.692791	−	0.721139i	$-0.743619\pi$
$719$	3.69216	−	4.40015i	0.137694	−	0.164098i	0.830485	+	0.557041i	$0.188063\pi$
$720$	39.4254	+	16.0703i	1.46930	+	0.598906i
$721$			35.9005i			1.33700i
$722$	−36.5377	+	4.50758i	−1.35979	+	0.167755i
$723$	−1.42536	+	13.3633i	−0.0530097	+	0.496988i
$724$	3.32510	+	0.586305i	0.123576	+	0.0217899i
$725$	16.3540	+	13.7226i	0.607372	+	0.509646i
$726$	15.2437	+	7.46394i	0.565747	+	0.277013i
$727$	−22.9240	+	8.34367i	−0.850206	+	0.309450i	−0.730124	−	0.683314i	$-0.760538\pi$
$727$	−22.9240	+	8.34367i	−0.850206	+	0.309450i	−0.120081	+	0.992764i	$0.538316\pi$
$728$	−1.93899	−	2.31080i	−0.0718637	−	0.0856439i
$729$	3.07032	−	26.8249i	0.113716	−	0.993513i
$730$	90.3714	+	52.1760i	3.34480	+	1.93112i
$731$	−15.4557	+	2.72525i	−0.571648	+	0.100797i
$732$	0.205718	+	3.00849i	0.00760355	+	0.111197i
$733$	5.91692	−	10.2484i	0.218546	−	0.378533i	−0.735817	−	0.677180i	$-0.763202\pi$
$733$	5.91692	−	10.2484i	0.218546	−	0.378533i	0.954364	+	0.298647i	$0.0965352\pi$
$734$	−12.6957	−	21.9897i	−0.468609	−	0.811654i
$735$	−2.91005	−	4.32870i	−0.107339	−	0.159666i
$736$	−6.24236	−	17.1507i	−0.230096	−	0.632184i
$737$	−15.6795	−	5.70686i	−0.577561	−	0.210215i
$738$	20.4617	+	26.3568i	0.753207	+	0.970208i
$739$	6.52457	−	37.0027i	0.240010	−	1.36117i	−0.591791	−	0.806092i	$-0.701579\pi$
$739$	6.52457	−	37.0027i	0.240010	−	1.36117i	0.831801	−	0.555074i	$-0.187310\pi$
$740$	−51.0321			−1.87598
$741$	14.3145	+	13.1499i	0.525856	+	0.483072i
$742$	15.8366			0.581379
$743$	4.39621	−	24.9322i	0.161281	−	0.914672i	−0.791535	−	0.611124i	$-0.790718\pi$
$743$	4.39621	−	24.9322i	0.161281	−	0.914672i	0.952816	−	0.303548i	$-0.0981713\pi$
$744$	2.62098	−	2.52326i	0.0960897	−	0.0925071i
$745$	37.8959	+	13.7930i	1.38840	+	0.505336i
$746$	20.7185	+	56.9237i	0.758559	+	2.08413i
$747$	3.97496	+	7.53170i	0.145436	+	0.275571i
$748$	8.16065	+	14.1347i	0.298383	+	0.516814i
$749$	6.96470	−	12.0632i	0.254485	−	0.440780i
$750$	2.76864	−	0.189317i	0.101096	−	0.00691287i
$751$	−2.04271	+	0.360186i	−0.0745397	+	0.0131434i	−0.210794	−	0.977531i	$-0.567605\pi$
$751$	−2.04271	+	0.360186i	−0.0745397	+	0.0131434i	0.136254	+	0.990674i	$0.456494\pi$
$752$	11.8531	+	6.84337i	0.432237	+	0.249552i
$753$	−11.4747	+	5.08768i	−0.418160	+	0.185405i
$754$	−13.0190	−	15.5154i	−0.474123	−	0.565038i
$755$	−43.3703	+	15.7855i	−1.57841	+	0.574494i
$756$	17.6191	+	13.8972i	0.640801	+	0.505435i
$757$	−25.7099	−	21.5732i	−0.934443	−	0.784091i	0.0421666	−	0.999111i	$-0.486574\pi$
$757$	−25.7099	−	21.5732i	−0.934443	−	0.784091i	−0.976610	+	0.215020i	$0.931018\pi$
$758$	16.0894	+	2.83700i	0.584395	+	0.103045i
$759$	10.0383	+	1.07071i	0.364369	+	0.0388643i
$760$	−4.81869	+	4.57539i	−0.174792	+	0.165967i
$761$		−	46.4063i		−	1.68223i	−0.540859	−	0.841113i	$-0.681901\pi$
$761$		−	46.4063i		−	1.68223i	0.540859	−	0.841113i	$-0.318099\pi$
$762$	−17.0136	−	4.90695i	−0.616338	−	0.177760i
$763$	9.47657	−	11.2937i	0.343075	−	0.408861i
$764$	8.18462	−	22.4870i	0.296109	−	0.813553i
$765$	36.3282	−	4.99152i	1.31345	−	0.180469i
$766$	−5.27030	+	4.42231i	−0.190424	+	0.159784i
$767$	22.8775	−	13.2083i	0.826058	−	0.476925i
$768$	19.5682	−	26.8463i	0.706108	−	0.968733i
$769$	−2.30707	−	13.0840i	−0.0831950	−	0.471822i	−0.997732	−	0.0673188i	$-0.978556\pi$
$769$	−2.30707	−	13.0840i	−0.0831950	−	0.471822i	0.914537	−	0.404503i	$-0.132556\pi$
$770$	−6.46679	−	36.6750i	−0.233047	−	1.32167i
$771$	−11.5225	+	15.8081i	−0.414973	+	0.569316i
$772$	−38.9510	+	22.4883i	−1.40188	+	0.809373i
$773$	31.9821	−	26.8362i	1.15032	−	0.965230i	0.150590	−	0.988596i	$-0.451883\pi$
$773$	31.9821	−	26.8362i	1.15032	−	0.965230i	0.999727	+	0.0233660i	$0.00743830\pi$
$774$	23.6818	−	3.25389i	0.851224	−	0.116959i
$775$	7.93665	−	21.8058i	0.285093	−	0.783286i
$776$	1.18734	−	1.41502i	0.0426230	−	0.0507961i
$777$	37.2073	+	10.7311i	1.33480	+	0.384975i
$778$		−	62.4111i		−	2.23755i
$779$	−24.3281	+	5.84805i	−0.871644	+	0.209528i
$780$	−24.9152	−	2.65750i	−0.892107	−	0.0951538i
$781$	0.531974	+	0.0938013i	0.0190355	+	0.00335647i
$782$	−13.5438	−	11.3646i	−0.484326	−	0.406398i
$783$	−16.5643	−	13.0652i	−0.591960	−	0.466911i
$784$	−3.91489	+	1.42490i	−0.139817	+	0.0508894i
$785$	−35.9895	−	42.8906i	−1.28452	−	1.53083i
$786$	−47.5283	+	21.0733i	−1.69528	+	0.751660i
$787$	19.3803	+	11.1892i	0.690834	+	0.398853i	0.803924	−	0.594731i	$-0.202742\pi$
$787$	19.3803	+	11.1892i	0.690834	+	0.398853i	−0.113090	+	0.993585i	$0.536075\pi$
$788$	−6.39701	+	1.12797i	−0.227884	+	0.0401821i
$789$	38.0873	−	2.60437i	1.35594	−	0.0927181i
$790$	12.9087	−	22.3585i	0.459270	−	0.795479i
$791$	−4.26373	−	7.38500i	−0.151601	−	0.262580i
$792$	1.62467	+	3.07840i	0.0577302	+	0.109386i
$793$	0.873860	+	2.40091i	0.0310317	+	0.0852589i
$794$	−31.6512	−	11.5201i	−1.12326	−	0.408833i
$795$	−13.2691	+	12.7744i	−0.470605	+	0.453060i
$796$	2.59592	−	14.7222i	0.0920099	−	0.521814i
$797$	−43.7593			−1.55003			−0.775016	−	0.631941i	$-0.782258\pi$
$797$	−43.7593			−1.55003			−0.775016	+	0.631941i	$0.782258\pi$
$798$	−31.9628	+	16.5879i	−1.13147	+	0.587206i
$799$	11.7883			0.417042
$800$	6.96998	−	39.5287i	0.246426	−	1.39755i
$801$	−15.7050	−	20.2296i	−0.554909	−	0.714779i
$802$	59.0852	+	21.5052i	2.08637	+	0.759377i
$803$	14.0196	+	38.5187i	0.494743	+	1.35929i
$804$	−11.6039	−	17.2608i	−0.409239	−	0.608742i
$805$	9.42548	+	16.3254i	0.332204	+	0.575395i
$806$	−11.0077	+	19.0658i	−0.387729	+	0.671565i
$807$	−1.38372	−	20.2360i	−0.0487092	−	0.712342i
$808$	1.24833	−	0.220114i	0.0439161	−	0.00774360i
$809$	27.8324	+	16.0690i	0.978534	+	0.564957i	0.901827	−	0.432097i	$-0.142226\pi$
$809$	27.8324	+	16.0690i	0.978534	+	0.564957i	0.0767067	+	0.997054i	$0.475559\pi$
$810$	−55.5818	+	5.49584i	−1.95295	+	0.193104i
$811$	18.1542	+	21.6354i	0.637481	+	0.759720i	0.983970	−	0.178334i	$-0.0570706\pi$
$811$	18.1542	+	21.6354i	0.637481	+	0.759720i	−0.346489	+	0.938054i	$0.612626\pi$
$812$	16.4766	−	5.99697i	0.578214	−	0.210453i
$813$	13.0179	+	6.37410i	0.456558	+	0.223550i
$814$	−32.8624	−	27.5749i	−1.15183	−	0.966499i
$815$	7.30231	+	1.28759i	0.255789	+	0.0451024i
$816$	3.10641	−	29.1239i	0.108746	−	1.01954i
$817$	−5.08609	+	17.1885i	−0.177940	+	0.601349i
$818$			38.2757i			1.33828i
$819$	17.6067	+	7.17676i	0.615229	+	0.250776i
$820$	20.7324	−	24.7079i	0.724008	−	0.862839i
$821$	15.2947	−	42.0220i	0.533790	−	1.46658i	−0.320736	−	0.947169i	$-0.603930\pi$
$821$	15.2947	−	42.0220i	0.533790	−	1.46658i	0.854526	−	0.519408i	$-0.173847\pi$
$822$	−8.07476	−	32.5999i	−0.281640	−	1.13705i
$823$	−12.7225	+	10.6754i	−0.443478	+	0.372122i	−0.837009	−	0.547189i	$-0.815698\pi$
$823$	−12.7225	+	10.6754i	−0.443478	+	0.372122i	0.393531	+	0.919311i	$0.371253\pi$
$824$	−6.01140	+	3.47069i	−0.209417	+	0.120907i
$825$	17.9413	+	13.0774i	0.624636	+	0.455297i
$826$	8.49839	+	48.1967i	0.295697	+	1.67698i
$827$	7.61025	+	43.1599i	0.264634	+	1.50082i	0.770075	+	0.637954i	$0.220219\pi$
$827$	7.61025	+	43.1599i	0.264634	+	1.50082i	−0.505441	+	0.862861i	$0.668670\pi$
$828$	9.32555	+	8.44893i	0.324085	+	0.293621i
$829$	−13.7220	+	7.92240i	−0.476585	+	0.275156i	−0.718992	−	0.695018i	$-0.755396\pi$
$829$	−13.7220	+	7.92240i	−0.476585	+	0.275156i	0.242407	+	0.970175i	$0.422063\pi$
$830$	13.4954	−	11.3240i	0.468431	−	0.393060i
$831$	−24.9397	+	6.17737i	−0.865148	+	0.214291i
$832$	−5.22083	+	14.3441i	−0.181000	+	0.497293i
$833$	−2.30650	+	2.74878i	−0.0799155	+	0.0952396i
$834$	−8.42596	+	29.2149i	−0.291767	+	1.01163i
$835$		−	74.0462i		−	2.56247i
$836$	18.6065	−	1.14339i	0.643518	−	0.0395448i
$837$	−7.18693	+	21.7762i	−0.248417	+	0.752694i
$838$	−51.5134	−	9.08319i	−1.77950	−	0.313774i
$839$	−35.1972	−	29.5340i	−1.21514	−	1.01963i	−0.999064	−	0.0432501i	$-0.986229\pi$
$839$	−35.1972	−	29.5340i	−1.21514	−	1.01963i	−0.216079	−	0.976376i	$-0.569327\pi$
$840$	−2.85830	+	5.83754i	−0.0986206	+	0.201414i
$841$	11.7609	−	4.28063i	0.405550	−	0.147608i
$842$	36.5173	+	43.5196i	1.25847	+	1.49978i
$843$	4.14899	+	9.35755i	0.142899	+	0.322291i
$844$	−6.01639	−	3.47356i	−0.207093	−	0.119565i
$845$	20.0969	−	3.54363i	0.691355	−	0.121905i
$846$	−17.9423	−	0.681911i	−0.616870	−	0.0234446i
$847$	−6.22482	+	10.7817i	−0.213887	+	0.370463i
$848$	7.35584	+	12.7407i	0.252601	+	0.437517i
$849$	31.4232	−	21.1249i	1.07844	−	0.725003i
$850$	−13.2985	−	36.5374i	−0.456136	−	1.25322i
$851$	20.4055	+	7.42699i	0.699491	+	0.254594i
$852$	0.466989	+	0.485075i	0.0159988	+	0.0166184i
$853$	−4.05515	+	22.9979i	−0.138846	+	0.787434i	0.833258	+	0.552884i	$0.186473\pi$
$853$	−4.05515	+	22.9979i	−0.138846	+	0.787434i	−0.972104	+	0.234550i	$0.924638\pi$
$854$	−4.73346			−0.161976
$855$	13.4004	−	39.6809i	0.458285	−	1.35706i
$856$	2.69326			0.0920536
$857$	1.22427	−	6.94316i	0.0418201	−	0.237174i	−0.956732	−	0.290972i	$-0.906022\pi$
$857$	1.22427	−	6.94316i	0.0418201	−	0.237174i	0.998552	+	0.0537977i	$0.0171326\pi$
$858$	−14.6083	−	15.1741i	−0.498720	−	0.518034i
$859$	35.1960	+	12.8103i	1.20087	+	0.437081i	0.863528	−	0.504301i	$-0.168250\pi$
$859$	35.1960	+	12.8103i	1.20087	+	0.437081i	0.337343	+	0.941382i	$0.390472\pi$
$860$	−7.90299	−	21.7133i	−0.269490	−	0.740417i
$861$	−20.3115	+	13.6548i	−0.692216	+	0.465355i
$862$	−9.57098	−	16.5774i	−0.325989	−	0.564629i
$863$	−13.0428	+	22.5907i	−0.443981	+	0.768998i	−0.997981	−	0.0635192i	$-0.979768\pi$
$863$	−13.0428	+	22.5907i	−0.443981	+	0.768998i	0.554000	+	0.832517i	$0.313101\pi$
$864$	−5.70177	+	39.2531i	−0.193978	+	1.33542i
$865$	−13.6061	+	2.39913i	−0.462622	+	0.0815728i
$866$	61.1337	+	35.2956i	2.07741	+	1.19939i
$867$	1.70978	+	3.85620i	0.0580671	+	0.130963i
$868$	−12.2508	−	14.5999i	−0.415818	−	0.495553i
$869$	9.52977	−	3.46855i	0.323275	−	0.117663i
$870$	−19.1915	+	39.1951i	−0.650653	+	1.32884i
$871$	−13.4995	−	11.3275i	−0.457414	−	0.383816i
$872$	2.80725	+	0.494993i	0.0950653	+	0.0167626i
$873$	−2.45574	+	11.3808i	−0.0831141	+	0.385182i
$874$	−18.5165	+	8.05752i	−0.626329	+	0.272550i
$875$			2.03553i			0.0688136i
$876$	−14.1593	+	49.0937i	−0.478397	+	1.65872i
$877$	−11.0745	+	13.1981i	−0.373959	+	0.445667i	−0.919898	−	0.392158i	$-0.871729\pi$
$877$	−11.0745	+	13.1981i	−0.373959	+	0.445667i	0.545939	+	0.837825i	$0.316173\pi$
$878$	−24.5950	+	67.5743i	−0.830042	+	2.28052i
$879$	−34.3135	+	8.49919i	−1.15736	+	0.286670i
$880$	26.5017	−	22.2375i	0.893371	−	0.749627i
$881$	17.2569	−	9.96325i	0.581398	−	0.335670i	−0.180291	−	0.983613i	$-0.557704\pi$
$881$	17.2569	−	9.96325i	0.581398	−	0.335670i	0.761689	+	0.647943i	$0.224370\pi$
$882$	3.66960	−	4.05034i	0.123562	−	0.136382i
$883$	−1.89794	−	10.7637i	−0.0638707	−	0.362229i	−0.999946	−	0.0104281i	$-0.996681\pi$
$883$	−1.89794	−	10.7637i	−0.0638707	−	0.362229i	0.936075	−	0.351801i	$-0.114431\pi$
$884$	2.99326	+	16.9756i	0.100674	+	0.570952i
$885$	−45.9978	−	33.5277i	−1.54620	−	1.12702i
$886$	35.6442	−	20.5792i	1.19749	−	0.691372i
$887$	4.00496	−	3.36056i	0.134473	−	0.112837i	−0.573070	−	0.819506i	$-0.694248\pi$
$887$	4.00496	−	3.36056i	0.134473	−	0.112837i	0.707544	+	0.706670i	$0.249803\pi$
$888$	1.80014	+	7.26766i	0.0604089	+	0.243887i
$889$	4.44220	−	12.2049i	0.148987	−	0.409338i
$890$	−34.0536	+	40.5835i	−1.14148	+	1.36036i
$891$	−18.1129	−	12.3804i	−0.606804	−	0.414757i
$892$			25.1291i			0.841384i
$893$	6.00423	−	12.0513i	0.200924	−	0.403281i
$894$	−4.48180	+	42.0188i	−0.149894	+	1.40532i
$895$	−1.72368	−	0.303931i	−0.0576162	−	0.0101593i
$896$	7.12618	+	5.97957i	0.238069	+	0.199764i
$897$	9.57572	+	4.68866i	0.319724	+	0.156550i
$898$	44.3340	−	16.1363i	1.47944	−	0.538474i
$899$	11.5174	+	13.7258i	0.384125	+	0.457783i
$900$	8.47065	+	26.3459i	0.282355	+	0.878197i
$901$	10.9735	+	6.33556i	0.365581	+	0.211068i
$902$	26.7016	−	4.70821i	0.889065	−	0.156766i
$903$	1.19615	+	17.4929i	0.0398053	+	0.582128i
$904$	0.824394	−	1.42789i	0.0274189	−	0.0474910i
$905$	−3.08206	−	5.33828i	−0.102451	−	0.177450i
$906$	−26.9817	−	40.1352i	−0.896405	−	1.33340i
$907$	−4.16304	−	11.4378i	−0.138231	−	0.379788i	0.851190	−	0.524858i	$-0.175881\pi$
$907$	−4.16304	−	11.4378i	−0.138231	−	0.379788i	−0.989421	+	0.145070i	$0.953659\pi$
$908$	−23.2237	−	8.45275i	−0.770706	−	0.280514i
$909$	−6.31104	+	4.89949i	−0.209324	+	0.162506i
$910$	6.82980	−	38.7337i	0.226406	−	1.28401i
$911$	−4.05874			−0.134472			−0.0672360	−	0.997737i	$-0.521418\pi$
$911$	−4.05874			−0.134472			−0.0672360	+	0.997737i	$0.521418\pi$
$912$	−28.1914	−	18.0096i	−0.933509	−	0.596357i
$913$	6.92015			0.229024
$914$	7.72822	−	43.8289i	0.255627	−	1.44973i
$915$	3.96605	−	3.81818i	0.131114	−	0.126225i
$916$	3.41513	+	1.24300i	0.112839	+	0.0410700i
$917$	−13.0430	−	35.8352i	−0.430716	−	1.18338i
$918$	14.2290	+	35.6919i	0.469626	+	1.17801i
$919$	−14.3647	−	24.8804i	−0.473848	−	0.820729i	0.525703	−	0.850668i	$-0.323802\pi$
$919$	−14.3647	−	24.8804i	−0.473848	−	0.820729i	−0.999552	+	0.0299386i	$0.990469\pi$
$920$	−1.82242	+	3.15652i	−0.0600834	+	0.104068i
$921$	−2.51650	+	0.172076i	−0.0829216	+	0.00567010i
$922$	10.5904	−	1.86737i	0.348776	−	0.0614987i
$923$	0.494070	+	0.285252i	0.0162625	+	0.00938917i
$924$	16.6695	−	7.39097i	0.548385	−	0.243145i
$925$	30.6968	+	36.5830i	1.00930	+	1.20284i
$926$	−3.95731	+	1.44034i	−0.130045	+	0.0473326i
$927$	23.2990	−	37.0318i	0.765239	−	1.21628i
$928$	23.7419	+	19.9218i	0.779366	+	0.653965i
$929$	10.5318	+	1.85704i	0.345537	+	0.0609274i	0.343723	−	0.939071i	$-0.388312\pi$
$929$	10.5318	+	1.85704i	0.345537	+	0.0609274i	0.00181316	+	0.999998i	$0.499423\pi$
$930$	47.1691	+	5.03114i	1.54674	+	0.164978i
$931$	1.63531	+	3.75800i	0.0535951	+	0.123164i
$932$			46.7578i			1.53160i
$933$	43.8540	+	12.6481i	1.43572	+	0.414079i
$934$	−29.9922	+	35.7433i	−0.981374	+	1.16956i
$935$	10.1912	−	28.0000i	0.333287	−	0.915697i
$936$	0.500413	+	3.64200i	0.0163565	+	0.119043i
$937$	11.7918	−	9.89450i	0.385221	−	0.323239i	−0.429527	−	0.903054i	$-0.641320\pi$
$937$	11.7918	−	9.89450i	0.385221	−	0.323239i	0.814748	+	0.579815i	$0.196875\pi$
$938$	28.2738	−	16.3239i	0.923172	−	0.532994i
$939$	23.3440	−	32.0264i	0.761803	−	1.04514i
$940$	3.01388	+	17.0926i	0.0983021	+	0.557499i
$941$	−4.24400	−	24.0689i	−0.138351	−	0.784625i	−0.972468	−	0.233038i	$-0.925133\pi$
$941$	−4.24400	−	24.0689i	−0.138351	−	0.784625i	0.834117	−	0.551587i	$-0.185978\pi$
$942$	34.5573	−	47.4103i	1.12594	−	1.54471i
$943$	−11.8859	+	6.86231i	−0.387057	+	0.223468i
$944$	−34.8274	+	29.2237i	−1.13354	+	0.951149i
$945$	−1.24054	−	40.9492i	−0.0403548	−	1.33208i
$946$	6.64345	−	18.2527i	0.215997	−	0.593448i
$947$	−35.5983	+	42.4244i	−1.15679	+	1.37861i	−0.244202	+	0.969724i	$0.578526\pi$
$947$	−35.5983	+	42.4244i	−1.15679	+	1.37861i	−0.912587	+	0.408883i	$0.865918\pi$
$948$	12.1461	+	3.50309i	0.394487	+	0.113775i
$949$			43.2917i			1.40531i
$950$	−44.1259	−	5.01466i	−1.43163	−	0.162697i
$951$	9.11259	+	0.971967i	0.295496	+	0.0315182i
$952$	4.40354	+	0.776462i	0.142719	+	0.0251653i
$953$	31.1019	+	26.0976i	1.00749	+	0.845384i	0.988004	−	0.154426i	$-0.0493528\pi$
$953$	31.1019	+	26.0976i	1.00749	+	0.845384i	0.0194854	+	0.999810i	$0.493797\pi$
$954$	−16.3356	−	10.2778i	−0.528886	−	0.332755i
$955$	−41.0534	+	14.9422i	−1.32846	+	0.483519i
$956$	−19.9089	−	23.7265i	−0.643900	−	0.767371i
$957$	−15.6715	+	6.94849i	−0.506588	+	0.224613i
$958$	−48.0505	−	27.7419i	−1.55244	−	0.896301i
$959$	24.2604	−	4.27776i	0.783408	−	0.138136i
$960$	32.8143	−	2.24381i	1.05908	−	0.0724188i
$961$	−5.76197	+	9.98003i	−0.185870	+	0.321937i
$962$	−22.6535	−	39.2370i	−0.730378	−	1.26505i
$963$	−15.0131	+	7.92336i	−0.483790	+	0.255327i
$964$	4.65565	+	12.7913i	0.149948	+	0.411980i
$965$	77.1597	+	28.0838i	2.48386	+	0.904051i
$966$	−14.2300	+	13.6995i	−0.457844	+	0.440774i
$967$	−0.448828	+	2.54543i	−0.0144333	+	0.0818556i	−0.991174	−	0.132570i	$-0.957677\pi$
$967$	−0.448828	+	2.54543i	−0.0144333	+	0.0818556i	0.976740	+	0.214426i	$0.0687881\pi$
$968$	−2.40714			−0.0773685
$969$	−28.7839	−	1.29287i	−0.924671	−	0.0415330i
$970$	24.0845			0.773306
$971$	−0.137845	+	0.781759i	−0.00442366	+	0.0250878i	−0.986940	−	0.161090i	$-0.948499\pi$
$971$	−0.137845	+	0.781759i	−0.00442366	+	0.0250878i	0.982516	+	0.186178i	$0.0596101\pi$
$972$	−9.15526	−	25.7697i	−0.293655	−	0.826564i
$973$	−20.9575	−	7.62792i	−0.671868	−	0.244540i
$974$	−17.9981	−	49.4495i	−0.576698	−	1.58446i
$975$	13.0819	+	19.4593i	0.418956	+	0.623197i
$976$	−2.19862	−	3.80812i	−0.0703760	−	0.121895i
$977$	−18.5513	+	32.1317i	−0.593508	+	1.02799i	0.400248	+	0.916407i	$0.368924\pi$
$977$	−18.5513	+	32.1317i	−0.593508	+	1.02799i	−0.993756	+	0.111578i	$0.964409\pi$
$978$	0.530044	+	7.75156i	0.0169489	+	0.247867i
$979$	−20.4942	+	3.61369i	−0.654998	+	0.115494i
$980$	−4.57531	−	2.64156i	−0.146153	−	0.0843814i
$981$	−17.1047	+	5.49946i	−0.546112	+	0.175584i
$982$	17.0230	+	20.2873i	0.543227	+	0.647392i
$983$	−3.33834	+	1.21506i	−0.106476	+	0.0387542i	−0.394709	−	0.918806i	$-0.629155\pi$
$983$	−3.33834	+	1.21506i	−0.106476	+	0.0387542i	0.288233	+	0.957560i	$0.406932\pi$
$984$	−4.25008	−	2.08101i	−0.135487	−	0.0663402i
$985$	9.08442	+	7.62273i	0.289454	+	0.242880i
$986$	29.5667	+	5.21341i	0.941596	+	0.166029i
$987$	1.39683	−	13.0959i	0.0444617	−	0.416847i
$988$	18.8789	+	5.58627i	0.600616	+	0.177723i
$989$			9.83235i			0.312651i
$990$	−17.1311	+	42.0276i	−0.544461	+	1.33573i
$991$	16.2156	−	19.3250i	0.515104	−	0.613877i	−0.444312	−	0.895872i	$-0.646552\pi$
$991$	16.2156	−	19.3250i	0.515104	−	0.613877i	0.959416	+	0.281995i	$0.0909962\pi$
$992$	11.5220	−	31.6565i	0.365824	−	1.00509i
$993$	−11.0510	−	44.6159i	−0.350693	−	1.41584i
$994$	−0.809656	+	0.679382i	−0.0256807	+	0.0215487i
$995$	−23.6357	+	13.6461i	−0.749303	+	0.432610i
$996$	6.97072	+	5.08095i	0.220876	+	0.160996i
$997$	−4.50827	−	25.5677i	−0.142778	−	0.809737i	−0.969124	−	0.246574i	$-0.920695\pi$
$997$	−4.50827	−	25.5677i	−0.142778	−	0.809737i	0.826346	−	0.563163i	$-0.190416\pi$
$998$	−9.86001	−	55.9189i	−0.312113	−	1.77008i
$999$	−31.4155	−	35.2164i	−0.993942	−	1.11420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.2.3	yes	24
3.2	odd	2	inner	57.2.j.b.2.2	✓	24
4.3	odd	2		912.2.cc.e.401.3		24
12.11	even	2		912.2.cc.e.401.1		24
19.3	odd	18		1083.2.d.d.1082.7		24
19.10	odd	18	inner	57.2.j.b.29.2	yes	24
19.16	even	9		1083.2.d.d.1082.17		24
57.29	even	18	inner	57.2.j.b.29.3	yes	24
57.35	odd	18		1083.2.d.d.1082.8		24
57.41	even	18		1083.2.d.d.1082.18		24
76.67	even	18		912.2.cc.e.257.1		24
228.143	odd	18		912.2.cc.e.257.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.2.2	✓	24	3.2	odd	2	inner
57.2.j.b.2.3	yes	24	1.1	even	1	trivial
57.2.j.b.29.2	yes	24	19.10	odd	18	inner
57.2.j.b.29.3	yes	24	57.29	even	18	inner
912.2.cc.e.257.1		24	76.67	even	18
912.2.cc.e.257.3		24	228.143	odd	18
912.2.cc.e.401.1		24	12.11	even	2
912.2.cc.e.401.3		24	4.3	odd	2
1083.2.d.d.1082.7		24	19.3	odd	18
1083.2.d.d.1082.8		24	57.35	odd	18
1083.2.d.d.1082.17		24	19.16	even	9
1083.2.d.d.1082.18		24	57.41	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.336464 - 1.90818i) q^{2} +(-1.20126 - 1.24779i) q^{3} +(-1.64856 - 0.600025i) q^{4} +(1.09544 + 3.00968i) q^{5} +(-2.78518 + 1.87239i) q^{6} +(-1.23083 - 2.13186i) q^{7} +(0.237981 - 0.412196i) q^{8} +(-0.113935 + 2.99784i) q^{9} +O(q^{10})\)	\(q+(0.336464 - 1.90818i) q^{2} +(-1.20126 - 1.24779i) q^{3} +(-1.64856 - 0.600025i) q^{4} +(1.09544 + 3.00968i) q^{5} +(-2.78518 + 1.87239i) q^{6} +(-1.23083 - 2.13186i) q^{7} +(0.237981 - 0.412196i) q^{8} +(-0.113935 + 2.99784i) q^{9} +(6.11159 - 1.07764i) q^{10} +(2.11115 + 1.21887i) q^{11} +(1.23165 + 2.77783i) q^{12} +(1.65491 + 1.97225i) q^{13} +(-4.48210 + 1.63135i) q^{14} +(2.43953 - 4.98229i) q^{15} +(-3.39430 - 2.84816i) q^{16} +(-3.75838 - 0.662704i) q^{17} +(5.68207 + 1.22607i) q^{18} +(-2.59177 + 3.50468i) q^{19} -5.61892i q^{20} +(-1.18155 + 4.09673i) q^{21} +(3.03615 - 3.61834i) q^{22} +(-0.817753 + 2.24676i) q^{23} +(-0.800210 + 0.198206i) q^{24} +(-4.02800 + 3.37989i) q^{25} +(4.32022 - 2.49428i) q^{26} +(3.87752 - 3.45902i) q^{27} +(0.749922 + 4.25302i) q^{28} +(-0.705026 - 3.99840i) q^{29} +(-8.68629 - 6.33142i) q^{30} +(-3.82192 + 2.20658i) q^{31} +(-5.84764 + 4.90675i) q^{32} +(-1.01515 - 4.09844i) q^{33} +(-2.52912 + 6.94869i) q^{34} +(5.06793 - 6.03972i) q^{35} +(1.98661 - 4.87374i) q^{36} -9.08219i q^{37} +(5.81552 + 6.12475i) q^{38} +(0.472956 - 4.43416i) q^{39} +(1.50127 + 0.264715i) q^{40} +(4.39728 + 3.68975i) q^{41} +(7.41975 + 3.63301i) q^{42} +(3.86432 - 1.40650i) q^{43} +(-2.74899 - 3.27612i) q^{44} +(-9.14735 + 2.94103i) q^{45} +(4.01207 + 2.31637i) q^{46} +(-3.04197 + 0.536381i) q^{47} +(0.523561 + 7.65674i) q^{48} +(0.470118 - 0.814268i) q^{49} +(5.09416 + 8.82335i) q^{50} +(3.68789 + 5.48573i) q^{51} +(-1.54482 - 4.24435i) q^{52} +(-3.11998 - 1.13558i) q^{53} +(-5.29579 - 8.56284i) q^{54} +(-1.35579 + 7.68908i) q^{55} -1.17166 q^{56} +(7.48647 - 0.976071i) q^{57} -7.86688 q^{58} +(1.78173 - 10.1047i) q^{59} +(-7.01121 + 6.74980i) q^{60} +(0.932543 + 0.339418i) q^{61} +(2.92462 + 8.03534i) q^{62} +(6.53120 - 3.44693i) q^{63} +(2.96450 + 5.13466i) q^{64} +(-4.12299 + 7.14123i) q^{65} +(-8.16212 + 0.558118i) q^{66} +(-6.74077 + 1.18858i) q^{67} +(5.79826 + 3.34763i) q^{68} +(3.78581 - 1.67857i) q^{69} +(-9.81970 - 11.7027i) q^{70} +(0.208227 - 0.0757884i) q^{71} +(1.20858 + 0.760393i) q^{72} +(12.8811 + 10.8085i) q^{73} +(-17.3304 - 3.05582i) q^{74} +(9.05606 + 0.965937i) q^{75} +(6.37556 - 4.22253i) q^{76} -6.00089i q^{77} +(-8.30204 - 2.39442i) q^{78} +(2.67409 - 3.18686i) q^{79} +(4.85382 - 13.3357i) q^{80} +(-8.97404 - 0.683116i) q^{81} +(8.52023 - 7.14932i) q^{82} +(2.45843 - 1.41938i) q^{83} +(4.40600 - 6.04473i) q^{84} +(-2.12253 - 12.0375i) q^{85} +(-1.38365 - 7.84704i) q^{86} +(-4.14222 + 5.68285i) q^{87} +(1.00483 - 0.580137i) q^{88} +(-6.53953 + 5.48732i) q^{89} +(2.53426 + 18.4443i) q^{90} +(2.16764 - 5.95553i) q^{91} +(2.69622 - 3.21323i) q^{92} +(7.34447 + 2.11824i) q^{93} +5.98510i q^{94} +(-13.3871 - 3.96125i) q^{95} +(13.1471 + 1.40230i) q^{96} +(3.82196 + 0.673914i) q^{97} +(-1.39559 - 1.17104i) q^{98} +(-3.89451 + 6.19000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more