LMFDB - Embedded newform 990.2.bg.a.31.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	990.31
Dual form			990.2.bg.a.511.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.978148 + 0.207912i) q^{2} +(0.157407 - 1.72488i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(0.204657 + 1.71992i) q^{6} +(0.125602 - 1.19502i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.95045 - 0.543016i) q^{9} +1.00000 q^{10} +(-3.13299 - 1.08829i) q^{11} +(-0.557775 - 1.63978i) q^{12} +(-1.11470 - 1.23801i) q^{13} +(0.125602 + 1.19502i) q^{14} +(-0.512590 + 1.65446i) q^{15} +(0.669131 - 0.743145i) q^{16} +(1.29221 + 3.97701i) q^{17} +(2.99887 - 0.0822823i) q^{18} +(-0.426579 + 0.309928i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(-2.04150 - 0.404753i) q^{21} +(3.29080 + 0.413119i) q^{22} +(-3.19810 + 5.53927i) q^{23} +(0.886516 + 1.48798i) q^{24} +(0.913545 + 0.406737i) q^{25} +(1.34774 + 0.979192i) q^{26} +(-1.40106 + 5.00370i) q^{27} +(-0.371316 - 1.14279i) q^{28} +(-0.102140 + 0.971801i) q^{29} +(0.157407 - 1.72488i) q^{30} +(-2.16382 - 2.40316i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.37032 + 5.23274i) q^{33} +(-2.09084 - 3.62144i) q^{34} +(-0.371316 + 1.14279i) q^{35} +(-2.91623 + 0.703985i) q^{36} +(0.713302 + 0.518244i) q^{37} +(0.352820 - 0.391846i) q^{38} +(-2.31088 + 1.72787i) q^{39} +(0.913545 - 0.406737i) q^{40} +(-0.673640 - 6.40925i) q^{41} +(2.08104 - 0.0285442i) q^{42} +(-1.06710 - 1.84827i) q^{43} +(-3.30478 + 0.280103i) q^{44} +(2.77307 + 1.14458i) q^{45} +(1.97653 - 6.08315i) q^{46} +(3.28129 + 1.46092i) q^{47} +(-1.17651 - 1.27115i) q^{48} +(5.43473 + 1.15519i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(7.06328 - 1.60290i) q^{51} +(-1.52188 - 0.677583i) q^{52} +(-1.63934 + 5.04538i) q^{53} +(0.330115 - 5.18566i) q^{54} +(2.83826 + 1.71589i) q^{55} +(0.600802 + 1.04062i) q^{56} +(0.467443 + 0.784584i) q^{57} +(-0.102140 - 0.971801i) q^{58} +(-10.7240 + 4.77464i) q^{59} +(0.204657 + 1.71992i) q^{60} +(-1.33988 + 1.48808i) q^{61} +(2.61618 + 1.90076i) q^{62} +(-1.01950 + 3.45764i) q^{63} +(0.309017 - 0.951057i) q^{64} +(0.832950 + 1.44271i) q^{65} +(1.23058 - 5.61121i) q^{66} +(-5.68606 + 9.84855i) q^{67} +(2.79809 + 3.10759i) q^{68} +(9.05120 + 6.38827i) q^{69} +(0.125602 - 1.19502i) q^{70} +(-0.867887 - 2.67108i) q^{71} +(2.70614 - 1.29492i) q^{72} +(-1.88274 - 1.36789i) q^{73} +(-0.805464 - 0.358616i) q^{74} +(0.845371 - 1.51174i) q^{75} +(-0.263641 + 0.456639i) q^{76} +(-1.69403 + 3.60730i) q^{77} +(1.90113 - 2.17057i) q^{78} +(8.84011 - 1.87902i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(8.41027 + 3.20428i) q^{81} +(1.99148 + 6.12914i) q^{82} +(-8.77568 + 9.74638i) q^{83} +(-2.02963 + 0.460594i) q^{84} +(-0.437104 - 4.15877i) q^{85} +(1.42806 + 1.58602i) q^{86} +(1.66017 + 0.329148i) q^{87} +(3.17432 - 0.961084i) q^{88} -1.62027 q^{89} +(-2.95045 - 0.543016i) q^{90} +(-1.61945 + 1.17660i) q^{91} +(-0.668585 + 6.36116i) q^{92} +(-4.48577 + 3.35406i) q^{93} +(-3.51333 - 0.746781i) q^{94} +(0.481695 - 0.214465i) q^{95} +(1.41509 + 0.998760i) q^{96} +(12.5206 - 2.66133i) q^{97} -5.55615 q^{98} +(8.65277 + 4.91219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$3$	0.157407	−	1.72488i	0.0908788	−	0.995862i
$3$	0.157407	−	1.72488i	0.0908788	−	0.995862i
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	−0.978148	−	0.207912i	−0.437441	−	0.0929809i
$5$	−0.978148	−	0.207912i	−0.437441	−	0.0929809i
$6$	0.204657	+	1.71992i	0.0835507	+	0.702153i
$7$	0.125602	−	1.19502i	0.0474730	−	0.451676i	−0.944804	−	0.327636i	$-0.893748\pi$
$7$	0.125602	−	1.19502i	0.0474730	−	0.451676i	0.992277	−	0.124040i	$-0.0395851\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−2.95045	−	0.543016i	−0.983482	−	0.181005i
$10$	1.00000			0.316228
$11$	−3.13299	−	1.08829i	−0.944632	−	0.328131i
$11$	−3.13299	−	1.08829i	−0.944632	−	0.328131i
$12$	−0.557775	−	1.63978i	−0.161016	−	0.473364i
$13$	−1.11470	−	1.23801i	−0.309164	−	0.343361i	0.568460	−	0.822711i	$-0.307539\pi$
$13$	−1.11470	−	1.23801i	−0.309164	−	0.343361i	−0.877624	+	0.479350i	$0.840873\pi$
$14$	0.125602	+	1.19502i	0.0335685	+	0.319383i
$15$	−0.512590	+	1.65446i	−0.132350	+	0.427181i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	1.29221	+	3.97701i	0.313407	+	0.964567i	0.976405	+	0.215946i	$0.0692835\pi$
$17$	1.29221	+	3.97701i	0.313407	+	0.964567i	−0.662999	+	0.748621i	$0.730716\pi$
$18$	2.99887	−	0.0822823i	0.706841	−	0.0193941i
$19$	−0.426579	+	0.309928i	−0.0978640	+	0.0711024i	−0.635641	−	0.771985i	$-0.719264\pi$
$19$	−0.426579	+	0.309928i	−0.0978640	+	0.0711024i	0.537777	+	0.843087i	$0.319264\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	−2.04150	−	0.404753i	−0.445492	−	0.0883243i
$22$	3.29080	+	0.413119i	0.701600	+	0.0880773i
$23$	−3.19810	+	5.53927i	−0.666850	+	1.15502i	0.311930	+	0.950105i	$0.399024\pi$
$23$	−3.19810	+	5.53927i	−0.666850	+	1.15502i	−0.978780	+	0.204913i	$0.934309\pi$
$24$	0.886516	+	1.48798i	0.180959	+	0.303733i
$25$	0.913545	+	0.406737i	0.182709	+	0.0813473i
$26$	1.34774	+	0.979192i	0.264314	+	0.192035i
$27$	−1.40106	+	5.00370i	−0.269634	+	0.962963i
$28$	−0.371316	−	1.14279i	−0.0701721	−	0.215968i
$29$	−0.102140	+	0.971801i	−0.0189670	+	0.180459i	−0.999904	−	0.0138679i	$-0.995586\pi$
$29$	−0.102140	+	0.971801i	−0.0189670	+	0.180459i	0.980937	+	0.194327i	$0.0622522\pi$
$30$	0.157407	−	1.72488i	0.0287384	−	0.314919i
$31$	−2.16382	−	2.40316i	−0.388633	−	0.431621i	0.516803	−	0.856105i	$-0.327122\pi$
$31$	−2.16382	−	2.40316i	−0.388633	−	0.431621i	−0.905435	+	0.424484i	$0.860455\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.37032	+	5.23274i	−0.412620	+	0.910903i
$34$	−2.09084	−	3.62144i	−0.358576	−	0.621072i
$35$	−0.371316	+	1.14279i	−0.0627639	+	0.193167i
$36$	−2.91623	+	0.703985i	−0.486039	+	0.117331i
$37$	0.713302	+	0.518244i	0.117266	+	0.0851988i	0.644873	−	0.764290i	$-0.276910\pi$
$37$	0.713302	+	0.518244i	0.117266	+	0.0851988i	−0.527606	+	0.849489i	$0.676910\pi$
$38$	0.352820	−	0.391846i	0.0572349	−	0.0635659i
$39$	−2.31088	+	1.72787i	−0.370036	+	0.276680i
$40$	0.913545	−	0.406737i	0.144444	−	0.0643107i
$41$	−0.673640	−	6.40925i	−0.105205	−	1.00096i	−0.912018	−	0.410150i	$-0.865476\pi$
$41$	−0.673640	−	6.40925i	−0.105205	−	1.00096i	0.806813	−	0.590807i	$-0.201190\pi$
$42$	2.08104	−	0.0285442i	0.321112	−	0.00440447i
$43$	−1.06710	−	1.84827i	−0.162731	−	0.281859i	0.773116	−	0.634265i	$-0.218697\pi$
$43$	−1.06710	−	1.84827i	−0.162731	−	0.281859i	−0.935847	+	0.352406i	$0.885364\pi$
$44$	−3.30478	+	0.280103i	−0.498214	+	0.0422272i
$45$	2.77307	+	1.14458i	0.413385	+	0.170624i
$46$	1.97653	−	6.08315i	0.291424	−	0.896911i
$47$	3.28129	+	1.46092i	0.478625	+	0.213098i	0.631846	−	0.775094i	$-0.282298\pi$
$47$	3.28129	+	1.46092i	0.478625	+	0.213098i	−0.153220	+	0.988192i	$0.548964\pi$
$48$	−1.17651	−	1.27115i	−0.169815	−	0.183474i
$49$	5.43473	+	1.15519i	0.776390	+	0.165027i
$50$	−0.978148	−	0.207912i	−0.138331	−	0.0294032i
$51$	7.06328	−	1.60290i	0.989057	−	0.224451i
$52$	−1.52188	−	0.677583i	−0.211046	−	0.0939638i
$53$	−1.63934	+	5.04538i	−0.225181	+	0.693036i	0.773092	+	0.634294i	$0.218709\pi$
$53$	−1.63934	+	5.04538i	−0.225181	+	0.693036i	−0.998273	+	0.0587422i	$0.981291\pi$
$54$	0.330115	−	5.18566i	0.0449229	−	0.705678i
$55$	2.83826	+	1.71589i	0.382711	+	0.231371i
$56$	0.600802	+	1.04062i	0.0802855	+	0.139059i
$57$	0.467443	+	0.784584i	0.0619144	+	0.103921i
$58$	−0.102140	−	0.971801i	−0.0134117	−	0.127604i
$59$	−10.7240	+	4.77464i	−1.39615	+	0.621605i	−0.960441	−	0.278483i	$-0.910168\pi$
$59$	−10.7240	+	4.77464i	−1.39615	+	0.621605i	−0.435707	+	0.900089i	$0.643502\pi$
$60$	0.204657	+	1.71992i	0.0264210	+	0.222040i
$61$	−1.33988	+	1.48808i	−0.171553	+	0.190529i	−0.822790	−	0.568345i	$-0.807584\pi$
$61$	−1.33988	+	1.48808i	−0.171553	+	0.190529i	0.651237	+	0.758875i	$0.274250\pi$
$62$	2.61618	+	1.90076i	0.332255	+	0.241397i
$63$	−1.01950	+	3.45764i	−0.128445	+	0.435622i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.832950	+	1.44271i	0.103315	+	0.178946i
$66$	1.23058	−	5.61121i	0.151473	−	0.690692i
$67$	−5.68606	+	9.84855i	−0.694663	+	1.20319i	0.275631	+	0.961264i	$0.411113\pi$
$67$	−5.68606	+	9.84855i	−0.694663	+	1.20319i	−0.970294	+	0.241929i	$0.922220\pi$
$68$	2.79809	+	3.10759i	0.339318	+	0.376851i
$69$	9.05120	+	6.38827i	1.08964	+	0.769057i
$70$	0.125602	−	1.19502i	0.0150123	−	0.142832i
$71$	−0.867887	−	2.67108i	−0.102999	−	0.316999i	0.886256	−	0.463195i	$-0.153297\pi$
$71$	−0.867887	−	2.67108i	−0.102999	−	0.316999i	−0.989256	+	0.146196i	$0.953297\pi$
$72$	2.70614	−	1.29492i	0.318921	−	0.152608i
$73$	−1.88274	−	1.36789i	−0.220359	−	0.160100i	0.472130	−	0.881529i	$-0.343485\pi$
$73$	−1.88274	−	1.36789i	−0.220359	−	0.160100i	−0.692488	+	0.721429i	$0.743485\pi$
$74$	−0.805464	−	0.358616i	−0.0936333	−	0.0416882i
$75$	0.845371	−	1.51174i	0.0976151	−	0.174560i
$76$	−0.263641	+	0.456639i	−0.0302416	+	0.0523801i
$77$	−1.69403	+	3.60730i	−0.193053	+	0.411090i
$78$	1.90113	−	2.17057i	0.215261	−	0.245768i
$79$	8.84011	−	1.87902i	0.994590	−	0.211407i	0.318259	−	0.948004i	$-0.396902\pi$
$79$	8.84011	−	1.87902i	0.994590	−	0.211407i	0.676332	+	0.736597i	$0.263569\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	8.41027	+	3.20428i	0.934474	+	0.356031i
$82$	1.99148	+	6.12914i	0.219922	+	0.676850i
$83$	−8.77568	+	9.74638i	−0.963256	+	1.06980i	0.0342640	+	0.999413i	$0.489091\pi$
$83$	−8.77568	+	9.74638i	−0.963256	+	1.06980i	−0.997519	+	0.0703908i	$0.977575\pi$
$84$	−2.02963	+	0.460594i	−0.221451	+	0.0502549i
$85$	−0.437104	−	4.15877i	−0.0474106	−	0.451082i
$86$	1.42806	+	1.58602i	0.153991	+	0.171025i
$87$	1.66017	+	0.329148i	0.177989	+	0.0352884i
$88$	3.17432	−	0.961084i	0.338384	−	0.102452i
$89$	−1.62027			−0.171748			−0.0858740	−	0.996306i	$-0.527368\pi$
$89$	−1.62027			−0.171748			−0.0858740	+	0.996306i	$0.527368\pi$
$90$	−2.95045	−	0.543016i	−0.311004	−	0.0572389i
$91$	−1.61945	+	1.17660i	−0.169765	+	0.123341i
$92$	−0.668585	+	6.36116i	−0.0697048	+	0.663197i
$93$	−4.48577	+	3.35406i	−0.465153	+	0.347800i
$94$	−3.51333	−	0.746781i	−0.362372	−	0.0770246i
$95$	0.481695	−	0.214465i	0.0494209	−	0.0220036i
$96$	1.41509	+	0.998760i	0.144427	+	0.101936i
$97$	12.5206	−	2.66133i	1.27127	−	0.270217i	0.477606	−	0.878574i	$-0.341505\pi$
$97$	12.5206	−	2.66133i	1.27127	−	0.270217i	0.793663	+	0.608357i	$0.208171\pi$
$98$	−5.55615			−0.561256
$99$	8.65277	+	4.91219i	0.869636	+	0.493694i
$100$	1.00000			0.100000
$101$	3.90234	−	0.829469i	0.388298	−	0.0825352i	−0.00962618	−	0.999954i	$-0.503064\pi$
$101$	3.90234	−	0.829469i	0.388298	−	0.0825352i	0.397924	+	0.917418i	$0.369731\pi$
$102$	−6.57567	+	3.03641i	−0.651088	+	0.300650i
$103$	−16.0868	+	7.16230i	−1.58508	+	0.705722i	−0.994835	−	0.101504i	$-0.967635\pi$
$103$	−16.0868	+	7.16230i	−1.58508	+	0.705722i	−0.590243	+	0.807226i	$0.700968\pi$
$104$	1.62950	+	0.346360i	0.159785	+	0.0339634i
$105$	1.91274	+	0.820360i	0.186664	+	0.0800590i
$106$	0.554526	−	5.27596i	0.0538603	−	0.512447i
$107$	−5.59482	+	4.06488i	−0.540872	+	0.392967i	−0.824409	−	0.565995i	$-0.808492\pi$
$107$	−5.59482	+	4.06488i	−0.540872	+	0.392967i	0.283537	+	0.958961i	$0.408492\pi$
$108$	0.755257	+	5.14097i	0.0726747	+	0.494690i
$109$	−15.0171			−1.43838			−0.719190	−	0.694813i	$-0.755487\pi$
$109$	−15.0171			−1.43838			−0.719190	+	0.694813i	$0.755487\pi$
$110$	−3.13299	−	1.08829i	−0.298719	−	0.103764i
$111$	1.00619	−	1.14879i	0.0955033	−	0.109038i
$112$	−0.804030	−	0.892966i	−0.0759737	−	0.0843773i
$113$	−0.0922779	−	0.877965i	−0.00868077	−	0.0825920i	0.989324	−	0.145734i	$-0.0465545\pi$
$113$	−0.0922779	−	0.877965i	−0.00868077	−	0.0825920i	−0.998005	+	0.0631423i	$0.979888\pi$
$114$	−0.620353	−	0.670252i	−0.0581014	−	0.0627749i
$115$	4.27989	−	4.75330i	0.399102	−	0.443248i
$116$	0.301957	+	0.929329i	0.0280360	+	0.0862860i
$117$	2.61662	+	4.25797i	0.241907	+	0.393650i
$118$	9.49697	−	6.89995i	0.874267	−	0.635192i
$119$	4.91492	−	1.04470i	0.450550	−	0.0957673i
$120$	−0.557775	−	1.63978i	−0.0509177	−	0.149691i
$121$	8.63127	+	6.81918i	0.784661	+	0.619926i
$122$	1.00121	−	1.73414i	0.0906449	−	0.157002i
$123$	−11.1612	+	0.153091i	−1.00638	+	0.0138038i
$124$	−2.95420	−	1.31529i	−0.265295	−	0.118117i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	0.278335	−	3.59405i	0.0247960	−	0.320183i
$127$	−3.88906	−	11.9693i	−0.345099	−	1.06210i	−0.961531	−	0.274696i	$-0.911423\pi$
$127$	−3.88906	−	11.9693i	−0.345099	−	1.06210i	0.616432	−	0.787408i	$-0.288577\pi$
$128$	−0.104528	+	0.994522i	−0.00923910	+	0.0879041i
$129$	−3.35602	+	1.54969i	−0.295481	+	0.136443i
$130$	−1.11470	−	1.23801i	−0.0977661	−	0.108580i
$131$	8.39482	−	14.5403i	0.733459	−	1.27039i	−0.221937	−	0.975061i	$-0.571238\pi$
$131$	8.39482	−	14.5403i	0.733459	−	1.27039i	0.955396	−	0.295328i	$-0.0954288\pi$
$132$	−0.0370478	+	5.74444i	−0.00322459	+	0.499990i
$133$	0.316792	+	0.548699i	0.0274693	+	0.0475782i
$134$	3.51418	−	10.8155i	0.303579	−	0.934320i
$135$	2.41077	−	4.60306i	0.207486	−	0.396169i
$136$	−3.38305	−	2.45793i	−0.290094	−	0.210766i
$137$	−8.91340	+	9.89933i	−0.761523	+	0.845757i	−0.991857	−	0.127355i	$-0.959351\pi$
$137$	−8.91340	+	9.89933i	−0.761523	+	0.845757i	0.230334	+	0.973112i	$0.426018\pi$
$138$	−10.1816	−	4.36682i	−0.866716	−	0.371728i
$139$	−11.1043	+	4.94396i	−0.941855	+	0.419341i	−0.819457	−	0.573140i	$-0.805725\pi$
$139$	−11.1043	+	4.94396i	−0.941855	+	0.419341i	−0.122398	+	0.992481i	$0.539058\pi$
$140$	0.125602	+	1.19502i	0.0106153	+	0.100998i
$141$	3.03642	−	5.42988i	0.255713	−	0.457279i
$142$	1.40427	+	2.43227i	0.117844	+	0.204111i
$143$	2.14506	+	5.09178i	0.179379	+	0.425796i
$144$	−2.37777	+	1.82926i	−0.198148	+	0.152438i
$145$	0.301957	−	0.929329i	0.0250762	−	0.0771766i
$146$	2.12600	+	0.946557i	0.175949	+	0.0783377i
$147$	2.84803	−	9.19245i	0.234901	−	0.758180i
$148$	0.862423	+	0.183314i	0.0708907	+	0.0150683i
$149$	−13.0308	−	2.76979i	−1.06753	−	0.226910i	−0.359536	−	0.933131i	$-0.617065\pi$
$149$	−13.0308	−	2.76979i	−1.06753	−	0.226910i	−0.707991	+	0.706221i	$0.750398\pi$
$150$	−0.512590	+	1.65446i	−0.0418528	+	0.135086i
$151$	−4.02539	−	1.79222i	−0.327582	−	0.145849i	0.236355	−	0.971667i	$-0.424047\pi$
$151$	−4.02539	−	1.79222i	−0.327582	−	0.145849i	−0.563937	+	0.825818i	$0.690714\pi$
$152$	0.162939	−	0.501474i	0.0132161	−	0.0406749i
$153$	−1.65301	−	12.4356i	−0.133638	−	1.00536i
$154$	0.907016	−	3.88068i	0.0730894	−	0.312714i
$155$	1.61689	+	2.80053i	0.129871	+	0.224944i
$156$	−1.40830	+	2.51840i	−0.112755	+	0.201634i
$157$	0.677797	+	6.44881i	0.0540941	+	0.514671i	0.987699	+	0.156367i	$0.0499782\pi$
$157$	0.677797	+	6.44881i	0.0540941	+	0.514671i	−0.933605	+	0.358304i	$0.883355\pi$
$158$	−8.25626	+	3.67592i	−0.656833	+	0.292441i
$159$	8.44464	+	3.62185i	0.669704	+	0.287231i
$160$	0.669131	−	0.743145i	0.0528994	−	0.0587508i
$161$	6.21786	+	4.51754i	0.490036	+	0.356032i
$162$	−8.89269	−	1.38567i	−0.698676	−	0.108868i
$163$	1.71802	−	5.28751i	0.134565	−	0.414150i	−0.860957	−	0.508678i	$-0.830134\pi$
$163$	1.71802	−	5.28751i	0.134565	−	0.414150i	0.995522	+	0.0945285i	$0.0301344\pi$
$164$	−3.22228	−	5.58115i	−0.251618	−	0.435815i
$165$	3.40647	−	4.62558i	0.265193	−	0.360101i
$166$	6.55752	−	11.3580i	0.508962	−	0.881549i
$167$	−10.0209	−	11.1293i	−0.775439	−	0.861212i	0.217956	−	0.975959i	$-0.430061\pi$
$167$	−10.0209	−	11.1293i	−0.775439	−	0.861212i	−0.993395	+	0.114746i	$0.963394\pi$
$168$	1.88952	−	0.872513i	0.145779	−	0.0673158i
$169$	1.06878	−	10.1688i	0.0822139	−	0.782213i
$170$	1.29221	+	3.97701i	0.0991079	+	0.305023i
$171$	1.42690	−	0.682787i	0.109117	−	0.0522140i
$172$	−1.72660	−	1.25445i	−0.131652	−	0.0956510i
$173$	0.944834	+	0.420667i	0.0718344	+	0.0319827i	0.442339	−	0.896848i	$-0.354149\pi$
$173$	0.944834	+	0.420667i	0.0718344	+	0.0319827i	−0.370505	+	0.928830i	$0.620815\pi$
$174$	−1.69232	+	0.0232124i	−0.128295	+	0.00175973i
$175$	0.600802	−	1.04062i	0.0454164	−	0.0786634i
$176$	−2.90513	+	1.60006i	−0.218983	+	0.120609i
$177$	6.54767	+	19.2492i	0.492153	+	1.44686i
$178$	1.58486	−	0.336872i	0.118790	−	0.0252497i
$179$	−13.7463	+	9.98726i	−1.02745	+	0.746483i	−0.967796	−	0.251736i	$-0.918998\pi$
$179$	−13.7463	+	9.98726i	−1.02745	+	0.746483i	−0.0596498	+	0.998219i	$0.518998\pi$
$180$	2.99887	−	0.0822823i	0.223523	−	0.00613296i
$181$	0.971505	+	2.98998i	0.0722114	+	0.222244i	0.980648	−	0.195779i	$-0.0627234\pi$
$181$	0.971505	+	2.98998i	0.0722114	+	0.222244i	−0.908437	+	0.418022i	$0.862723\pi$
$182$	1.33943	−	1.48759i	0.0992854	−	0.110268i
$183$	2.35586	+	2.54536i	0.174150	+	0.188159i
$184$	−0.668585	−	6.36116i	−0.0492887	−	0.468951i
$185$	−0.589966	−	0.655223i	−0.0433751	−	0.0481730i
$186$	3.69040	−	4.21341i	0.270593	−	0.308942i
$187$	0.279646	−	13.8662i	0.0204497	−	1.01400i
$188$	3.59182			0.261960
$189$	5.80356	+	2.30277i	0.422147	+	0.167502i
$190$	−0.426579	+	0.309928i	−0.0309473	+	0.0224845i
$191$	0.334916	−	3.18651i	0.0242337	−	0.230568i	−0.975701	−	0.219108i	$-0.929685\pi$
$191$	0.334916	−	3.18651i	0.0242337	−	0.230568i	0.999934	−	0.0114601i	$-0.00364795\pi$
$192$	−1.59182	−	0.682721i	−0.114880	−	0.0492711i
$193$	−1.84638	−	0.392460i	−0.132905	−	0.0282499i	0.140979	−	0.990013i	$-0.454975\pi$
$193$	−1.84638	−	0.392460i	−0.132905	−	0.0282499i	−0.273884	+	0.961763i	$0.588308\pi$
$194$	−11.6936	+	5.20634i	−0.839554	+	0.373793i
$195$	2.61962	−	1.20965i	0.187595	−	0.0866248i
$196$	5.43473	−	1.15519i	0.388195	−	0.0825134i
$197$	6.84125			0.487419			0.243709	−	0.969848i	$-0.421636\pi$
$197$	6.84125			0.487419			0.243709	+	0.969848i	$0.421636\pi$
$198$	−9.48498	−	3.00584i	−0.674068	−	0.213616i
$199$	2.97397			0.210819			0.105410	−	0.994429i	$-0.466385\pi$
$199$	2.97397			0.210819			0.105410	+	0.994429i	$0.466385\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	16.0926	+	11.3580i	1.13508	+	0.801133i
$202$	−3.64461	+	1.62269i	−0.256434	+	0.114172i
$203$	1.14849	+	0.244120i	0.0806085	+	0.0171339i
$204$	5.80067	−	4.33722i	0.406128	−	0.303666i
$205$	−0.673640	+	6.40925i	−0.0470490	+	0.447642i
$206$	14.2461	−	10.3504i	0.992574	−	0.721148i
$207$	12.4437	−	14.6067i	0.864899	−	1.01524i
$208$	−1.66590			−0.115509
$209$	1.67376	−	0.506761i	0.115776	−	0.0350534i
$210$	−2.04150	−	0.404753i	−0.140877	−	0.0279306i
$211$	−8.82654	−	9.80286i	−0.607644	−	0.674857i	0.358301	−	0.933606i	$-0.383356\pi$
$211$	−8.82654	−	9.80286i	−0.607644	−	0.674857i	−0.965945	+	0.258749i	$0.916690\pi$
$212$	0.554526	+	5.27596i	0.0380850	+	0.362355i
$213$	−4.74392	+	1.07656i	−0.325048	+	0.0737646i
$214$	4.62743	−	5.13928i	0.316324	−	0.351314i
$215$	0.659504	+	2.02974i	0.0449778	+	0.138427i
$216$	−1.80762	−	4.87160i	−0.122993	−	0.331471i
$217$	−3.14361	+	2.28397i	−0.213402	+	0.155046i
$218$	14.6890	−	3.12224i	0.994862	−	0.211465i
$219$	−2.65581	+	3.03220i	−0.179463	+	0.204897i
$220$	3.29080	+	0.413119i	0.221865	+	0.0278525i
$221$	3.48313	−	6.03295i	0.234301	−	0.405820i
$222$	−0.745355	+	1.33288i	−0.0500250	+	0.0894572i
$223$	9.14650	+	4.07229i	0.612495	+	0.272700i	0.689449	−	0.724334i	$-0.257853\pi$
$223$	9.14650	+	4.07229i	0.612495	+	0.272700i	−0.0769538	+	0.997035i	$0.524519\pi$
$224$	0.972118	+	0.706285i	0.0649524	+	0.0471907i
$225$	−2.47450	−	1.69612i	−0.164967	−	0.113075i
$226$	0.272801	+	0.839594i	0.0181464	+	0.0558490i
$227$	2.23111	−	21.2276i	0.148084	−	1.40893i	−0.627959	−	0.778246i	$-0.716109\pi$
$227$	2.23111	−	21.2276i	0.148084	−	1.40893i	0.776043	−	0.630680i	$-0.217224\pi$
$228$	0.746150	+	0.526627i	0.0494150	+	0.0348767i
$229$	−2.65047	−	2.94365i	−0.175148	−	0.194522i	0.649179	−	0.760636i	$-0.275113\pi$
$229$	−2.65047	−	2.94365i	−0.175148	−	0.194522i	−0.824327	+	0.566114i	$0.808446\pi$
$230$	−3.19810	+	5.53927i	−0.210876	+	0.365249i
$231$	5.95552	+	3.48983i	0.391845	+	0.229614i
$232$	−0.488577	−	0.846240i	−0.0320767	−	0.0555584i
$233$	1.14558	−	3.52572i	0.0750492	−	0.230978i	−0.906494	−	0.422219i	$-0.861251\pi$
$233$	1.14558	−	3.52572i	0.0750492	−	0.230978i	0.981543	+	0.191241i	$0.0612513\pi$
$234$	−3.44472	−	3.62090i	−0.225189	−	0.236706i
$235$	−2.90584	−	2.11122i	−0.189556	−	0.137721i
$236$	−7.85486	+	8.72370i	−0.511308	+	0.567865i
$237$	−1.84960	−	15.5439i	−0.120145	−	1.00969i
$238$	−4.59031	+	2.04374i	−0.297546	+	0.132476i
$239$	−1.30623	−	12.4280i	−0.0844930	−	0.803898i	−0.951923	−	0.306338i	$-0.900896\pi$
$239$	−1.30623	−	12.4280i	−0.0844930	−	0.803898i	0.867430	−	0.497560i	$-0.165770\pi$
$240$	0.886516	+	1.48798i	0.0572244	+	0.0960488i
$241$	−11.3784	−	19.7079i	−0.732946	−	1.26950i	−0.955619	−	0.294606i	$-0.904811\pi$
$241$	−11.3784	−	19.7079i	−0.732946	−	1.26950i	0.222673	−	0.974893i	$-0.428522\pi$
$242$	−9.86044	−	4.87562i	−0.633853	−	0.313417i
$243$	6.85084	−	14.0024i	0.439482	−	0.898252i
$244$	−0.618779	+	1.90441i	−0.0396133	+	0.121917i
$245$	−5.07579	−	2.25989i	−0.324281	−	0.144379i
$246$	10.8855	−	2.47030i	0.694035	−	0.157501i
$247$	0.859203	+	0.182629i	0.0546698	+	0.0116204i
$248$	3.16311	+	0.672339i	0.200857	+	0.0426936i
$249$	15.4300	+	16.6712i	0.977837	+	1.05649i
$250$	0.913545	+	0.406737i	0.0577777	+	0.0257243i
$251$	9.48786	−	29.2006i	0.598868	−	1.84313i	0.0644266	−	0.997922i	$-0.479478\pi$
$251$	9.48786	−	29.2006i	0.598868	−	1.84313i	0.534442	−	0.845205i	$-0.320522\pi$
$252$	0.474993	+	3.57338i	0.0299217	+	0.225102i
$253$	16.0479	−	13.8740i	1.00892	−	0.872254i
$254$	6.29264	+	10.8992i	0.394835	+	0.683875i
$255$	−7.24219	+	0.0993361i	−0.453524	+	0.00622067i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	−16.0316	+	7.13774i	−1.00003	+	0.445240i	−0.840417	−	0.541940i	$-0.817690\pi$
$257$	−16.0316	+	7.13774i	−1.00003	+	0.445240i	−0.159609	+	0.987180i	$0.551023\pi$
$258$	2.96048	−	2.21358i	0.184312	−	0.137812i
$259$	0.708905	−	0.787319i	0.0440492	−	0.0489216i
$260$	1.34774	+	0.979192i	0.0835834	+	0.0607269i
$261$	0.829064	−	2.81178i	0.0513177	−	0.174045i
$262$	−5.18829	+	15.9679i	−0.320533	+	0.986500i
$263$	−7.23935	−	12.5389i	−0.446397	−	0.773183i	0.551751	−	0.834009i	$-0.313960\pi$
$263$	−7.23935	−	12.5389i	−0.446397	−	0.773183i	−0.998148	+	0.0608260i	$0.980627\pi$
$264$	−1.15810	−	5.62662i	−0.0712760	−	0.346294i
$265$	2.65251	−	4.59429i	0.162943	−	0.282225i
$266$	−0.423950	−	0.470844i	−0.0259940	−	0.0288693i
$267$	−0.255041	+	2.79477i	−0.0156082	+	0.171037i
$268$	−1.18871	+	11.3098i	−0.0726121	+	0.690858i
$269$	3.07829	+	9.47400i	0.187687	+	0.577640i	0.999984	−	0.00560319i	$-0.00178356\pi$
$269$	3.07829	+	9.47400i	0.187687	+	0.577640i	−0.812298	+	0.583243i	$0.801784\pi$
$270$	−1.40106	+	5.00370i	−0.0852658	+	0.304516i
$271$	16.5010	+	11.9887i	1.00236	+	0.728261i	0.962594	−	0.270948i	$-0.0873373\pi$
$271$	16.5010	+	11.9887i	1.00236	+	0.728261i	0.0397707	+	0.999209i	$0.487337\pi$
$272$	3.82015	+	1.70084i	0.231631	+	0.103129i
$273$	1.77459	+	2.97857i	0.107403	+	0.180271i
$274$	6.66043	−	11.5362i	0.402371	−	0.696928i
$275$	−2.41948	−	2.26850i	−0.145900	−	0.136796i
$276$	10.8670	+	2.15452i	0.654118	+	0.129687i
$277$	−2.67861	+	0.569356i	−0.160942	+	0.0342093i	−0.287678	−	0.957727i	$-0.592883\pi$
$277$	−2.67861	+	0.569356i	−0.160942	+	0.0342093i	0.126736	+	0.991936i	$0.459550\pi$
$278$	9.83375	−	7.14464i	0.589789	−	0.428507i
$279$	5.07927	+	8.26539i	0.304088	+	0.494836i
$280$	−0.371316	−	1.14279i	−0.0221904	−	0.0682950i
$281$	−3.79790	+	4.21800i	−0.226564	+	0.251625i	−0.845700	−	0.533659i	$-0.820816\pi$
$281$	−3.79790	+	4.21800i	−0.226564	+	0.251625i	0.619136	+	0.785284i	$0.287483\pi$
$282$	−1.84113	+	5.94254i	−0.109638	+	0.353873i
$283$	2.98076	+	28.3601i	0.177188	+	1.68583i	0.616389	+	0.787442i	$0.288595\pi$
$283$	2.98076	+	28.3601i	0.177188	+	1.68583i	−0.439201	+	0.898389i	$0.644738\pi$
$284$	−1.87928	−	2.08715i	−0.111515	−	0.123850i
$285$	−0.294104	−	0.864626i	−0.0174212	−	0.0512160i
$286$	−3.15682	−	4.53453i	−0.186667	−	0.268132i
$287$	−7.74380			−0.457102
$288$	1.94549	−	2.28365i	0.114639	−	0.134566i
$289$	−0.393520	+	0.285909i	−0.0231483	+	0.0168182i
$290$	−0.102140	+	0.971801i	−0.00599789	+	0.0570661i
$291$	−2.61966	−	22.0154i	−0.153567	−	1.29057i
$292$	−2.27634	−	0.483852i	−0.133213	−	0.0283153i
$293$	26.6940	−	11.8850i	1.55948	−	0.694326i	0.567816	−	0.823156i	$-0.307789\pi$
$293$	26.6940	−	11.8850i	1.55948	−	0.694326i	0.991667	+	0.128829i	$0.0411220\pi$
$294$	−0.874574	+	9.58371i	−0.0510062	+	0.558933i
$295$	11.4824	−	2.44065i	0.668530	−	0.142100i
$296$	−0.881690			−0.0512472
$297$	9.83497	−	14.1518i	0.570683	−	0.821171i
$298$	13.3219			0.771720
$299$	10.4226	−	2.21539i	0.602754	−	0.128119i
$300$	0.157407	−	1.72488i	0.00908788	−	0.0995862i
$301$	−2.34275	+	1.04306i	−0.135034	+	0.0601210i
$302$	4.31005	+	0.916130i	0.248016	+	0.0527174i
$303$	−0.816482	−	6.86165i	−0.0469057	−	0.394192i
$304$	−0.0551159	+	0.524393i	−0.00316111	+	0.0300760i
$305$	1.61999	−	1.17699i	0.0927601	−	0.0673941i
$306$	4.20241	+	11.8202i	0.240236	+	0.675717i
$307$	−23.0570			−1.31593			−0.657966	−	0.753048i	$-0.728583\pi$
$307$	−23.0570			−1.31593			−0.657966	+	0.753048i	$0.728583\pi$
$308$	−0.0803562	+	3.98446i	−0.00457872	+	0.227036i
$309$	9.82196	+	28.8752i	0.558752	+	1.64265i
$310$	−2.16382	−	2.40316i	−0.122897	−	0.136490i
$311$	−3.64787	−	34.7072i	−0.206852	−	1.96806i	−0.247496	−	0.968889i	$-0.579608\pi$
$311$	−3.64787	−	34.7072i	−0.206852	−	1.96806i	0.0406443	−	0.999174i	$-0.487059\pi$
$312$	0.853924	−	2.75617i	0.0483440	−	0.156038i
$313$	−3.27172	+	3.63361i	−0.184929	+	0.205384i	−0.828480	−	0.560019i	$-0.810794\pi$
$313$	−3.27172	+	3.63361i	−0.184929	+	0.205384i	0.643551	+	0.765403i	$0.277460\pi$
$314$	−2.00377	−	6.16696i	−0.113079	−	0.348022i
$315$	1.71610	−	3.17012i	0.0966915	−	0.178616i
$316$	7.31158	−	5.31217i	0.411308	−	0.298833i
$317$	25.8244	−	5.48915i	1.45044	−	0.308302i	0.585706	−	0.810524i	$-0.300817\pi$
$317$	25.8244	−	5.48915i	1.45044	−	0.308302i	0.864739	+	0.502222i	$0.167484\pi$
$318$	−9.01313	−	1.78696i	−0.505431	−	0.100208i
$319$	1.37760	−	2.93349i	0.0771309	−	0.164244i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	6.13078	+	10.2903i	0.342187	+	0.574346i
$322$	−7.02124	−	3.12606i	−0.391278	−	0.174208i
$323$	−1.78382	−	1.29602i	−0.0992542	−	0.0721124i
$324$	8.98646	−	0.493508i	0.499248	−	0.0274171i
$325$	−0.514792	−	1.58437i	−0.0285555	−	0.0878848i
$326$	−0.581138	+	5.52916i	−0.0321863	+	0.306232i
$327$	−2.36380	+	25.9028i	−0.130718	+	1.43243i
$328$	4.31225	+	4.78924i	0.238104	+	0.264441i
$329$	2.15797	−	3.73772i	0.118973	−	0.206067i
$330$	−2.37032	+	5.23274i	−0.130482	+	0.288053i
$331$	0.385561	+	0.667811i	0.0211923	+	0.0367062i	0.876427	−	0.481535i	$-0.159920\pi$
$331$	0.385561	+	0.667811i	0.0211923	+	0.0367062i	−0.855235	+	0.518241i	$0.826587\pi$
$332$	−4.05277	+	12.4731i	−0.222425	+	0.684553i
$333$	−1.82314	−	1.91639i	−0.0999077	−	0.105017i
$334$	12.1158	+	8.80266i	0.662948	+	0.481660i
$335$	7.60944	−	8.45114i	0.415748	−	0.461735i
$336$	−1.66682	+	1.24630i	−0.0909326	+	0.0679912i
$337$	−10.5413	+	4.69329i	−0.574221	+	0.255660i	−0.673238	−	0.739426i	$-0.735097\pi$
$337$	−10.5413	+	4.69329i	−0.574221	+	0.255660i	0.0990167	+	0.995086i	$0.468430\pi$
$338$	1.06878	+	10.1688i	0.0581340	+	0.553108i
$339$	−1.52891	+	0.0209710i	−0.0830392	+	0.00113899i
$340$	−2.09084	−	3.62144i	−0.113392	−	0.196400i
$341$	4.16389	+	9.88393i	0.225487	+	0.535245i
$342$	−1.25376	+	0.964534i	−0.0677953	+	0.0521560i
$343$	4.66230	−	14.3491i	0.251740	−	0.774778i
$344$	1.94969	+	0.868057i	0.105120	+	0.0468025i
$345$	−7.52521	−	8.13052i	−0.405144	−	0.437732i
$346$	−1.01165	−	0.215033i	−0.0543866	−	0.0115602i
$347$	−30.5981	−	6.50382i	−1.64259	−	0.349144i	−0.708371	−	0.705840i	$-0.750570\pi$
$347$	−30.5981	−	6.50382i	−1.64259	−	0.349144i	−0.934220	+	0.356696i	$0.883903\pi$
$348$	1.65051	−	0.374559i	0.0884768	−	0.0200784i
$349$	−24.4094	−	10.8678i	−1.30661	−	0.581739i	−0.368998	−	0.929430i	$-0.620299\pi$
$349$	−24.4094	−	10.8678i	−1.30661	−	0.581739i	−0.937609	+	0.347691i	$0.886966\pi$
$350$	−0.371316	+	1.14279i	−0.0198477	+	0.0610849i
$351$	7.75638	−	3.84313i	0.414005	−	0.205131i
$352$	2.50898	−	2.16911i	0.133729	−	0.115614i
$353$	6.14114	+	10.6368i	0.326860	+	0.566138i	0.981887	−	0.189467i	$-0.0606761\pi$
$353$	6.14114	+	10.6368i	0.326860	+	0.566138i	−0.655027	+	0.755605i	$0.727343\pi$
$354$	−10.4067	−	17.4673i	−0.553111	−	0.928374i
$355$	0.293573	+	2.79316i	0.0155812	+	0.148245i
$356$	−1.48019	+	0.659022i	−0.0784498	+	0.0349281i
$357$	−1.02834	−	8.64210i	−0.0544256	−	0.457388i
$358$	11.3694	−	12.6270i	0.600893	−	0.667359i
$359$	−11.1210	−	8.07986i	−0.586942	−	0.426438i	0.254278	−	0.967131i	$-0.418162\pi$
$359$	−11.1210	−	8.07986i	−0.586942	−	0.426438i	−0.841220	+	0.540693i	$0.818162\pi$
$360$	−2.91623	+	0.703985i	−0.153699	+	0.0371033i
$361$	−5.78541	+	17.8057i	−0.304495	+	0.937140i
$362$	−1.57193	−	2.72266i	−0.0826187	−	0.143100i
$363$	13.1209	−	13.8145i	0.688669	−	0.725076i
$364$	−1.00088	+	1.73357i	−0.0524602	+	0.0908637i
$365$	1.55720	+	1.72945i	0.0815076	+	0.0905234i
$366$	−2.83359	−	1.99993i	−0.148114	−	0.104538i
$367$	2.04957	−	19.5003i	0.106987	−	1.01791i	−0.800930	−	0.598758i	$-0.795661\pi$
$367$	2.04957	−	19.5003i	0.106987	−	1.01791i	0.907917	−	0.419151i	$-0.137672\pi$
$368$	1.97653	+	6.08315i	0.103034	+	0.317106i
$369$	−1.49279	+	19.2760i	−0.0777116	+	1.00347i
$370$	0.713302	+	0.518244i	0.0370828	+	0.0269422i
$371$	5.82343	+	2.59276i	0.302337	+	0.134609i
$372$	−2.73374	+	4.88861i	−0.141738	+	0.253463i
$373$	−2.00574	+	3.47404i	−0.103853	+	0.179879i	−0.913269	−	0.407357i	$-0.866451\pi$
$373$	−2.00574	+	3.47404i	−0.103853	+	0.179879i	0.809416	+	0.587236i	$0.199784\pi$
$374$	2.60942	+	13.6214i	0.134930	+	0.704344i
$375$	−1.14121	+	1.30294i	−0.0589316	+	0.0672835i
$376$	−3.51333	+	0.746781i	−0.181186	+	0.0385123i
$377$	1.31695	−	0.956821i	0.0678264	−	0.0492788i
$378$	−6.15551	−	1.04582i	−0.316605	−	0.0537913i
$379$	7.74487	+	23.8363i	0.397827	+	1.22439i	0.926738	+	0.375709i	$0.122601\pi$
$379$	7.74487	+	23.8363i	0.397827	+	1.22439i	−0.528911	+	0.848677i	$0.677399\pi$
$380$	0.352820	−	0.391846i	0.0180993	−	0.0201013i
$381$	−21.2578	+	4.82413i	−1.08907	+	0.247148i
$382$	0.334916	+	3.18651i	0.0171358	+	0.163036i
$383$	9.44095	+	10.4852i	0.482410	+	0.535771i	0.934387	−	0.356259i	$-0.115948\pi$
$383$	9.44095	+	10.4852i	0.482410	+	0.535771i	−0.451977	+	0.892029i	$0.649281\pi$
$384$	1.69898	+	0.336844i	0.0867008	+	0.0171895i
$385$	2.40702	−	3.17626i	0.122673	−	0.161877i
$386$	1.88763			0.0960779
$387$	2.14478	+	6.03268i	0.109025	+	0.306658i
$388$	10.3556	−	7.52381i	0.525728	−	0.381964i
$389$	−2.17694	+	20.7122i	−0.110375	+	1.05015i	0.789425	+	0.613847i	$0.210379\pi$
$389$	−2.17694	+	20.7122i	−0.110375	+	1.05015i	−0.899800	+	0.436302i	$0.856288\pi$
$390$	−2.31088	+	1.72787i	−0.117016	+	0.0874939i
$391$	−26.1624	−	5.56098i	−1.32309	−	0.281231i
$392$	−5.07579	+	2.25989i	−0.256366	+	0.114142i
$393$	−23.7589	−	16.7688i	−1.19848	−	0.845875i
$394$	−6.69175	+	1.42238i	−0.337126	+	0.0716583i
$395$	−9.03760			−0.454731
$396$	9.90266	+	0.968116i	0.497628	+	0.0486497i
$397$	−6.69748			−0.336137			−0.168069	−	0.985775i	$-0.553753\pi$
$397$	−6.69748			−0.336137			−0.168069	+	0.985775i	$0.553753\pi$
$398$	−2.90898	+	0.618323i	−0.145814	+	0.0309937i
$399$	0.996307	−	0.460060i	0.0498777	−	0.0230318i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	−5.78678	−	1.23002i	−0.288978	−	0.0614242i	0.0611417	−	0.998129i	$-0.480526\pi$
$401$	−5.78678	−	1.23002i	−0.288978	−	0.0614242i	−0.350120	+	0.936705i	$0.613859\pi$
$402$	−18.1024	−	7.76399i	−0.902865	−	0.387233i
$403$	−0.563110	+	5.35763i	−0.0280505	+	0.266883i
$404$	3.22759	−	2.34498i	0.160579	−	0.116667i
$405$	−7.56028	−	4.88285i	−0.375673	−	0.242631i
$406$	−1.17415			−0.0582722
$407$	−1.67077	−	2.39993i	−0.0828170	−	0.118960i
$408$	−4.77215	+	5.44847i	−0.236257	+	0.269739i
$409$	13.7135	+	15.2304i	0.678089	+	0.753095i	0.979729	−	0.200327i	$-0.0642006\pi$
$409$	13.7135	+	15.2304i	0.678089	+	0.753095i	−0.301640	+	0.953422i	$0.597534\pi$
$410$	−0.673640	−	6.40925i	−0.0332687	−	0.316530i
$411$	15.6722	+	16.9328i	0.773051	+	0.835233i
$412$	−11.7828	+	13.0862i	−0.580499	+	0.644709i
$413$	4.35884	+	13.4151i	0.214485	+	0.660116i
$414$	−9.13491	+	16.8747i	−0.448956	+	0.829347i
$415$	10.6103	−	7.70883i	0.520839	−	0.378411i
$416$	1.62950	−	0.346360i	0.0798926	−	0.0169817i
$417$	6.77986	+	19.9319i	0.332011	+	0.976067i
$418$	−1.53182	+	0.843682i	−0.0749239	+	0.0412658i
$419$	−6.04699	+	10.4737i	−0.295415	+	0.511673i	−0.975081	−	0.221848i	$-0.928791\pi$
$419$	−6.04699	+	10.4737i	−0.295415	+	0.511673i	0.679667	+	0.733521i	$0.262124\pi$
$420$	2.08104	−	0.0285442i	0.101545	−	0.00139282i
$421$	−28.5508	−	12.7116i	−1.39148	−	0.619527i	−0.432148	−	0.901803i	$-0.642244\pi$
$421$	−28.5508	−	12.7116i	−1.39148	−	0.619527i	−0.959333	+	0.282275i	$0.908911\pi$
$422$	10.6718	+	7.75351i	0.519495	+	0.377435i
$423$	−8.88796	−	6.09217i	−0.432148	−	0.296212i
$424$	−1.63934	−	5.04538i	−0.0796135	−	0.245025i
$425$	−0.437104	+	4.15877i	−0.0212027	+	0.201730i
$426$	4.41642	−	2.03935i	0.213976	−	0.0988068i
$427$	1.61000	+	1.78809i	0.0779133	+	0.0865315i
$428$	−3.45779	+	5.98907i	−0.167139	+	0.289493i
$429$	9.12037	−	2.89849i	0.440336	−	0.139941i
$430$	−1.06710	−	1.84827i	−0.0514601	−	0.0891315i
$431$	2.33893	−	7.19848i	0.112662	−	0.346739i	−0.878790	−	0.477209i	$-0.841649\pi$
$431$	2.33893	−	7.19848i	0.112662	−	0.346739i	0.991452	+	0.130470i	$0.0416486\pi$
$432$	2.78098	+	4.38932i	0.133800	+	0.211181i
$433$	9.68671	+	7.03781i	0.465514	+	0.338215i	0.795690	−	0.605704i	$-0.207108\pi$
$433$	9.68671	+	7.03781i	0.465514	+	0.338215i	−0.330177	+	0.943919i	$0.607108\pi$
$434$	2.60005	−	2.88765i	0.124806	−	0.138612i
$435$	−1.55545	−	0.667124i	−0.0745783	−	0.0319861i
$436$	−13.7188	+	6.10802i	−0.657013	+	0.292521i
$437$	−0.352532	−	3.35412i	−0.0168639	−	0.160449i
$438$	1.96735	−	3.51811i	0.0940035	−	0.168102i
$439$	−9.04130	−	15.6600i	−0.431518	−	0.747411i	0.565486	−	0.824758i	$-0.308688\pi$
$439$	−9.04130	−	15.6600i	−0.431518	−	0.747411i	−0.997004	+	0.0773468i	$0.975355\pi$
$440$	−3.30478	+	0.280103i	−0.157549	+	0.0133534i
$441$	−15.4076	−	6.35947i	−0.733695	−	0.302832i
$442$	−2.15269	+	6.62530i	−0.102393	+	0.315134i
$443$	−18.1624	−	8.08641i	−0.862920	−	0.384197i	−0.0729452	−	0.997336i	$-0.523240\pi$
$443$	−18.1624	−	8.08641i	−0.862920	−	0.384197i	−0.789975	+	0.613139i	$0.789906\pi$
$444$	0.451946	−	1.45872i	0.0214484	−	0.0692280i
$445$	1.58486	+	0.336872i	0.0751296	+	0.0159693i
$446$	−9.79331	−	2.08163i	−0.463727	−	0.0985681i
$447$	−6.82870	+	22.0407i	−0.322987	+	1.04249i
$448$	−1.09772	−	0.488736i	−0.0518624	−	0.0230906i
$449$	−10.1522	+	31.2452i	−0.479111	+	1.47455i	0.361221	+	0.932480i	$0.382360\pi$
$449$	−10.1522	+	31.2452i	−0.479111	+	1.47455i	−0.840332	+	0.542072i	$0.817640\pi$
$450$	2.77307	+	1.14458i	0.130724	+	0.0539561i
$451$	−4.86459	+	20.8132i	−0.229065	+	0.980057i
$452$	−0.441401	−	0.764528i	−0.0207617	−	0.0359604i
$453$	−3.72500	+	6.66123i	−0.175016	+	0.312972i
$454$	2.23111	+	21.2276i	0.104711	+	0.996261i
$455$	1.82869	−	0.814186i	0.0857304	−	0.0381696i
$456$	−0.839337	−	0.359986i	−0.0393055	−	0.0168579i
$457$	−7.47143	+	8.29786i	−0.349499	+	0.388158i	−0.892104	−	0.451830i	$-0.850771\pi$
$457$	−7.47143	+	8.29786i	−0.349499	+	0.388158i	0.542605	+	0.839988i	$0.317438\pi$
$458$	3.20457	+	2.32826i	0.149740	+	0.108792i
$459$	−21.7102	+	0.893801i	−1.01335	+	0.0417191i
$460$	1.97653	−	6.08315i	0.0921564	−	0.283628i
$461$	−10.6501	−	18.4465i	−0.496023	−	0.859138i	0.503966	−	0.863723i	$-0.331874\pi$
$461$	−10.6501	−	18.4465i	−0.496023	−	0.859138i	−0.999989	+	0.00458582i	$0.998540\pi$
$462$	−6.55095	−	2.17534i	−0.304778	−	0.101206i
$463$	−13.7600	+	23.8330i	−0.639480	+	1.10761i	0.346067	+	0.938210i	$0.387517\pi$
$463$	−13.7600	+	23.8330i	−0.639480	+	1.10761i	−0.985547	+	0.169402i	$0.945816\pi$
$464$	0.653844	+	0.726167i	0.0303539	+	0.0337115i
$465$	5.08510	−	2.34812i	0.235816	−	0.108891i
$466$	−0.387504	+	3.68686i	−0.0179508	+	0.170790i
$467$	0.401428	+	1.23547i	0.0185759	+	0.0571707i	0.959915	−	0.280292i	$-0.0904313\pi$
$467$	0.401428	+	1.23547i	0.0185759	+	0.0571707i	−0.941339	+	0.337463i	$0.890431\pi$
$468$	4.12227	+	2.82557i	0.190552	+	0.130612i
$469$	11.0551	+	8.03196i	0.510475	+	0.370882i
$470$	3.28129	+	1.46092i	0.151355	+	0.0673874i
$471$	11.2301	−	0.154036i	0.517457	−	0.00709760i
$472$	5.86945	−	10.1662i	0.270163	−	0.467937i
$473$	1.33177	+	6.95193i	0.0612347	+	0.319650i
$474$	5.04095	+	14.8197i	0.231539	+	0.680692i
$475$	−0.515759	+	0.109628i	−0.0236646	+	0.00503007i
$476$	4.06508	−	2.95346i	0.186323	−	0.135371i
$477$	7.57651	−	13.9959i	0.346905	−	0.640829i
$478$	3.86160	+	11.8848i	0.176626	+	0.543598i
$479$	23.3317	−	25.9125i	1.06605	−	1.18397i	0.0837873	−	0.996484i	$-0.473298\pi$
$479$	23.3317	−	25.9125i	1.06605	−	1.18397i	0.982267	−	0.187489i	$-0.0600350\pi$
$480$	−1.17651	−	1.27115i	−0.0537002	−	0.0580197i
$481$	−0.153532	−	1.46076i	−0.00700046	−	0.0666050i
$482$	15.2272	+	16.9116i	0.693582	+	0.770301i
$483$	8.77096	−	10.0140i	0.399093	−	0.455653i
$484$	10.6587	+	2.71898i	0.484485	+	0.123590i
$485$	−12.8003			−0.581230
$486$	−3.78988	+	15.1207i	−0.171912	+	0.685891i
$487$	−8.41952	+	6.11714i	−0.381525	+	0.277194i	−0.761974	−	0.647608i	$-0.775769\pi$
$487$	−8.41952	+	6.11714i	−0.381525	+	0.277194i	0.380449	+	0.924802i	$0.375769\pi$
$488$	0.209309	−	1.99144i	0.00947498	−	0.0901484i
$489$	−8.84991	−	3.79566i	−0.400207	−	0.171646i
$490$	5.43473	+	1.15519i	0.245516	+	0.0521861i
$491$	32.0597	−	14.2739i	1.44683	−	0.644172i	0.475032	−	0.879969i	$-0.342437\pi$
$491$	32.0597	−	14.2739i	1.44683	−	0.644172i	0.971802	+	0.235796i	$0.0757699\pi$
$492$	−10.1340	+	4.67954i	−0.456878	+	0.210970i
$493$	−3.99685	+	0.849557i	−0.180009	+	0.0382621i
$494$	−0.878398			−0.0395210
$495$	−7.44238	−	6.60386i	−0.334510	−	0.296822i
$496$	−3.23377			−0.145201
$497$	−3.30101	+	0.701651i	−0.148070	+	0.0314733i
$498$	−18.5590	−	13.0988i	−0.831647	−	0.586970i
$499$	−8.01524	+	3.56861i	−0.358811	+	0.159753i	−0.578222	−	0.815880i	$-0.696253\pi$
$499$	−8.01524	+	3.56861i	−0.358811	+	0.159753i	0.219411	+	0.975633i	$0.429587\pi$
$500$	−0.978148	−	0.207912i	−0.0437441	−	0.00929809i
$501$	−20.7741	+	15.5330i	−0.928119	+	0.693964i
$502$	−3.20938	+	30.5352i	−0.143241	+	1.36285i
$503$	−27.6701	+	20.1035i	−1.23375	+	0.896372i	−0.997166	−	0.0752383i	$-0.976028\pi$
$503$	−27.6701	+	20.1035i	−1.23375	+	0.896372i	−0.236585	+	0.971611i	$0.576028\pi$
$504$	−1.20756	−	3.39654i	−0.0537890	−	0.151294i
$505$	−3.98952			−0.177531
$506$	−12.8127	+	16.9074i	−0.569593	+	0.751626i
$507$	−17.3717	−	3.44415i	−0.771504	−	0.152960i
$508$	−8.42119	−	9.35268i	−0.373630	−	0.414958i
$509$	−3.40069	−	32.3554i	−0.150733	−	1.43413i	−0.764491	−	0.644634i	$-0.777010\pi$
$509$	−3.40069	−	32.3554i	−0.150733	−	1.43413i	0.613758	−	0.789494i	$-0.289657\pi$
$510$	7.06328	−	1.60290i	0.312767	−	0.0709777i
$511$	−1.87114	+	2.07811i	−0.0827743	+	0.0919302i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−0.953125	−	2.56870i	−0.0420815	−	0.113411i
$514$	14.1973	−	10.3149i	0.626215	−	0.454972i
$515$	17.2244	−	3.66115i	0.758997	−	0.161330i
$516$	−2.43556	+	2.78073i	−0.107220	+	0.122415i
$517$	−8.69035	−	8.14805i	−0.382201	−	0.358351i
$518$	−0.529721	+	0.917504i	−0.0232746	+	0.0403128i
$519$	0.874325	−	1.56351i	0.0383786	−	0.0686306i
$520$	−1.52188	−	0.677583i	−0.0667387	−	0.0297140i
$521$	16.9050	+	12.2822i	0.740623	+	0.538094i	0.892906	−	0.450243i	$-0.148663\pi$
$521$	16.9050	+	12.2822i	0.740623	+	0.538094i	−0.152283	+	0.988337i	$0.548663\pi$
$522$	−0.226344	+	2.92271i	−0.00990680	+	0.127924i
$523$	7.74378	+	23.8329i	0.338612	+	1.04214i	0.964915	+	0.262561i	$0.0845670\pi$
$523$	7.74378	+	23.8329i	0.338612	+	1.04214i	−0.626304	+	0.779579i	$0.715433\pi$
$524$	1.75500	−	16.6977i	0.0766674	−	0.729441i
$525$	−1.70038	−	1.20011i	−0.0742105	−	0.0523773i
$526$	9.68814	+	10.7598i	0.422423	+	0.469148i
$527$	6.76130	−	11.7109i	0.294527	−	0.510135i
$528$	2.30263	+	5.26288i	0.100209	+	0.229037i
$529$	−8.95569	−	15.5117i	−0.389378	−	0.674422i
$530$	−1.63934	+	5.04538i	−0.0712085	+	0.219157i
$531$	34.2333	−	8.26400i	1.48560	−	0.358627i
$532$	0.512579	+	0.372411i	0.0222231	+	0.0161461i
$533$	−7.18378	+	7.97839i	−0.311164	+	0.345583i
$534$	−0.331598	−	2.78672i	−0.0143497	−	0.120593i
$535$	6.31770	−	2.81282i	0.273138	−	0.121609i
$536$	−1.18871	−	11.3098i	−0.0513445	−	0.488510i
$537$	15.0631	+	25.2828i	0.650021	+	1.09103i
$538$	−4.98077	−	8.62695i	−0.214736	−	0.371934i
$539$	−15.7698	−	9.53374i	−0.679253	−	0.410647i
$540$	0.330115	−	5.18566i	0.0142059	−	0.223155i
$541$	−7.72420	+	23.7727i	−0.332089	+	1.02207i	0.636049	+	0.771649i	$0.280568\pi$
$541$	−7.72420	+	23.7727i	−0.332089	+	1.02207i	−0.968138	+	0.250417i	$0.919432\pi$
$542$	−18.6330	−	8.29595i	−0.800356	−	0.356341i
$543$	5.31030	−	1.20509i	0.227887	−	0.0517153i
$544$	−4.09030	−	0.869419i	−0.175370	−	0.0372761i
$545$	14.6890	+	3.12224i	0.629206	+	0.133742i
$546$	−2.35509	−	2.54452i	−0.100788	−	0.108896i
$547$	8.32624	+	3.70708i	0.356004	+	0.158503i	0.576943	−	0.816784i	$-0.304245\pi$
$547$	8.32624	+	3.70708i	0.356004	+	0.158503i	−0.220939	+	0.975288i	$0.570912\pi$
$548$	−4.11637	+	12.6689i	−0.175843	+	0.541188i
$549$	4.76128	−	3.66293i	0.203207	−	0.156330i
$550$	2.83826	+	1.71589i	0.121024	+	0.0731658i
$551$	−0.257617	−	0.446207i	−0.0109749	−	0.0190090i
$552$	−11.0775	+	0.151942i	−0.471490	+	0.00646710i
$553$	−1.13514	−	10.8001i	−0.0482710	−	0.459268i
$554$	2.50170	−	1.11383i	0.106287	−	0.0473220i
$555$	−1.22305	+	0.914486i	−0.0519155	+	0.0388177i
$556$	−8.13340	+	9.03306i	−0.344933	+	0.383087i
$557$	10.6841	+	7.76245i	0.452699	+	0.328905i	0.790661	−	0.612255i	$-0.209737\pi$
$557$	10.6841	+	7.76245i	0.452699	+	0.328905i	−0.337961	+	0.941160i	$0.609737\pi$
$558$	−6.68674	−	7.02873i	−0.283072	−	0.297550i
$559$	−1.09867	+	3.38135i	−0.0464687	+	0.143016i
$560$	0.600802	+	1.04062i	0.0253885	+	0.0439742i
$561$	−23.8736	−	2.66499i	−1.00794	−	0.112516i
$562$	2.83794	−	4.91545i	0.119711	−	0.207346i
$563$	27.1198	+	30.1196i	1.14296	+	1.26939i	0.958040	+	0.286636i	$0.0925370\pi$
$563$	27.1198	+	30.1196i	1.14296	+	1.26939i	0.184923	+	0.982753i	$0.440796\pi$
$564$	0.565376	−	6.19547i	0.0238066	−	0.260876i
$565$	−0.0922779	+	0.877965i	−0.00388216	+	0.0369363i
$566$	−8.81201	−	27.1206i	−0.370397	−	1.13996i
$567$	4.88553	−	9.64799i	0.205173	−	0.405177i
$568$	2.27216	+	1.65082i	0.0953376	+	0.0692668i
$569$	−14.4059	−	6.41390i	−0.603925	−	0.268885i	0.0819123	−	0.996640i	$-0.473897\pi$
$569$	−14.4059	−	6.41390i	−0.603925	−	0.268885i	−0.685838	+	0.727755i	$0.740564\pi$
$570$	0.467443	+	0.784584i	0.0195790	+	0.0328626i
$571$	−7.93660	+	13.7466i	−0.332136	+	0.575277i	−0.982930	−	0.183977i	$-0.941103\pi$
$571$	−7.93660	+	13.7466i	−0.332136	+	0.575277i	0.650794	+	0.759254i	$0.274436\pi$
$572$	4.03062	+	3.77910i	0.168529	+	0.158012i
$573$	−5.44364	−	1.07927i	−0.227411	−	0.0450871i
$574$	7.57458	−	1.61003i	0.316157	−	0.0672012i
$575$	−5.17463	+	3.75959i	−0.215797	+	0.156786i
$576$	−1.42818	+	2.63824i	−0.0595074	+	0.109927i
$577$	9.43391	+	29.0346i	0.392739	+	1.20873i	0.930709	+	0.365762i	$0.119191\pi$
$577$	9.43391	+	29.0346i	0.392739	+	1.20873i	−0.537970	+	0.842964i	$0.680809\pi$
$578$	0.325477	−	0.361479i	0.0135381	−	0.0150355i
$579$	−0.967581	+	3.12302i	−0.0402113	+	0.129788i
$580$	−0.102140	−	0.971801i	−0.00424115	−	0.0403518i
$581$	10.5449	+	11.7113i	0.437476	+	0.485866i
$582$	7.13967	+	20.9897i	0.295949	+	0.870049i
$583$	10.6269	−	14.0230i	0.440120	−	0.580775i
$584$	2.32720			0.0963002
$585$	−1.67416	−	4.70895i	−0.0692179	−	0.194691i
$586$	−23.6397	+	17.1752i	−0.976547	+	0.709503i
$587$	3.83734	−	36.5099i	0.158384	−	1.50692i	−0.569937	−	0.821689i	$-0.693032\pi$
$587$	3.83734	−	36.5099i	0.158384	−	1.50692i	0.728321	−	0.685236i	$-0.240301\pi$
$588$	−1.13710	−	9.55612i	−0.0468933	−	0.394088i
$589$	1.66785	+	0.354512i	0.0687224	+	0.0146074i
$590$	−10.7240	+	4.77464i	−0.441501	+	0.196569i
$591$	1.07686	−	11.8004i	0.0442960	−	0.485402i
$592$	0.862423	−	0.183314i	0.0354454	−	0.00753414i
$593$	9.69590			0.398163			0.199081	−	0.979983i	$-0.436204\pi$
$593$	9.69590			0.398163			0.199081	+	0.979983i	$0.436204\pi$
$594$	−6.67772	+	15.8874i	−0.273990	+	0.651866i
$595$	−5.02472			−0.205993
$596$	−13.0308	+	2.76979i	−0.533764	+	0.113455i
$597$	0.468122	−	5.12975i	0.0191590	−	0.209947i
$598$	−9.73422	+	4.33395i	−0.398062	+	0.177229i
$599$	−8.60471	−	1.82899i	−0.351579	−	0.0747304i	0.0287371	−	0.999587i	$-0.490851\pi$
$599$	−8.60471	−	1.82899i	−0.351579	−	0.0747304i	−0.380316	+	0.924857i	$0.624185\pi$
$600$	0.204657	+	1.71992i	0.00835507	+	0.0702153i
$601$	−3.41281	+	32.4707i	−0.139211	+	1.32451i	0.672348	+	0.740236i	$0.265286\pi$
$601$	−3.41281	+	32.4707i	−0.139211	+	1.32451i	−0.811559	+	0.584271i	$0.801381\pi$
$602$	2.07469	−	1.50735i	0.0845582	−	0.0614351i
$603$	22.1244	−	25.9700i	0.900973	−	1.05758i
$604$	−4.40634			−0.179292
$605$	−7.02487	−	8.46471i	−0.285601	−	0.344139i
$606$	2.22526	+	6.54195i	0.0903949	+	0.265749i
$607$	−3.98649	−	4.42744i	−0.161807	−	0.179704i	0.656790	−	0.754074i	$-0.271914\pi$
$607$	−3.98649	−	4.42744i	−0.161807	−	0.179704i	−0.818596	+	0.574369i	$0.805247\pi$
$608$	−0.0551159	−	0.524393i	−0.00223524	−	0.0212669i
$609$	0.601859	−	1.94259i	0.0243886	−	0.0787178i
$610$	−1.33988	+	1.48808i	−0.0542500	+	0.0602507i
$611$	−1.84904	−	5.69075i	−0.0748041	−	0.230223i
$612$	−6.56814	−	10.6882i	−0.265501	−	0.432044i
$613$	25.8528	−	18.7832i	1.04419	−	0.758646i	0.0730882	−	0.997325i	$-0.476715\pi$
$613$	25.8528	−	18.7832i	1.04419	−	0.758646i	0.971098	+	0.238680i	$0.0767145\pi$
$614$	22.5531	−	4.79382i	0.910170	−	0.193463i
$615$	10.9492	+	2.17081i	0.441513	+	0.0875354i
$616$	−0.749815	−	3.91410i	−0.0302109	−	0.157703i
$617$	17.5180	−	30.3420i	0.705247	−	1.22152i	−0.261355	−	0.965243i	$-0.584169\pi$
$617$	17.5180	−	30.3420i	0.705247	−	1.22152i	0.966602	−	0.256281i	$-0.0824973\pi$
$618$	−15.6108	−	26.2021i	−0.627959	−	1.05400i
$619$	−17.0360	−	7.58493i	−0.684736	−	0.304864i	0.0347251	−	0.999397i	$-0.488944\pi$
$619$	−17.0360	−	7.58493i	−0.684736	−	0.304864i	−0.719461	+	0.694533i	$0.755611\pi$
$620$	2.61618	+	1.90076i	0.105068	+	0.0763365i
$621$	−23.2361	−	23.7632i	−0.932434	−	0.953584i
$622$	10.7842	+	33.1903i	0.432406	+	1.33081i
$623$	−0.203508	+	1.93625i	−0.00815339	+	0.0775744i
$624$	−0.262224	+	2.87348i	−0.0104974	+	0.115031i
$625$	0.669131	+	0.743145i	0.0267652	+	0.0297258i
$626$	2.44476	−	4.23444i	0.0977121	−	0.169242i
$627$	−0.610644	−	2.96681i	−0.0243868	−	0.118483i
$628$	3.24216	+	5.61559i	0.129376	+	0.224087i
$629$	−1.13933	+	3.50649i	−0.0454280	+	0.139813i
$630$	−1.01950	+	3.45764i	−0.0406177	+	0.137756i
$631$	17.0736	+	12.4047i	0.679691	+	0.493825i	0.873255	−	0.487263i	$-0.162005\pi$
$631$	17.0736	+	12.4047i	0.679691	+	0.493825i	−0.193564	+	0.981088i	$0.562005\pi$
$632$	−6.04734	+	6.71625i	−0.240550	+	0.267158i
$633$	−18.2982	+	13.6817i	−0.727286	+	0.543799i
$634$	−24.1188	+	10.7384i	−0.957882	+	0.426476i
$635$	1.31552	+	12.5163i	0.0522048	+	0.496695i
$636$	9.18771	−	0.126021i	0.364316	−	0.00499707i
$637$	−4.62799	−	8.01592i	−0.183368	−	0.317602i
$638$	−0.737593	+	3.15580i	−0.0292016	+	0.124939i
$639$	1.11021	+	8.35216i	0.0439194	+	0.330406i
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	12.7891	+	5.69407i	0.505138	+	0.224902i	0.643452	−	0.765486i	$-0.277502\pi$
$641$	12.7891	+	5.69407i	0.505138	+	0.224902i	−0.138314	+	0.990388i	$0.544168\pi$
$642$	−8.13627	−	8.79073i	−0.321113	−	0.346942i
$643$	41.8336	+	8.89201i	1.64976	+	0.350666i	0.936617	−	0.350356i	$-0.113939\pi$
$643$	41.8336	+	8.89201i	1.64976	+	0.350666i	0.713139	+	0.701022i	$0.247273\pi$
$644$	7.51775	+	1.59795i	0.296241	+	0.0629679i
$645$	3.60488	−	0.818072i	0.141942	−	0.0322116i
$646$	2.01429	+	0.896821i	0.0792513	+	0.0352850i
$647$	11.0604	−	34.0405i	0.434831	−	1.33827i	−0.458429	−	0.888731i	$-0.651588\pi$
$647$	11.0604	−	34.0405i	0.434831	−	1.33827i	0.893260	−	0.449541i	$-0.148412\pi$
$648$	−8.68748	+	2.35111i	−0.341276	+	0.0923605i
$649$	38.7944	−	3.28811i	1.52281	−	0.129069i
$650$	0.832950	+	1.44271i	0.0326710	+	0.0565878i
$651$	3.44475	+	5.78187i	0.135010	+	0.226609i
$652$	−0.581138	−	5.52916i	−0.0227591	−	0.216539i
$653$	−10.3014	+	4.58649i	−0.403126	+	0.179483i	−0.598276	−	0.801290i	$-0.704147\pi$
$653$	−10.3014	+	4.58649i	−0.403126	+	0.179483i	0.195150	+	0.980773i	$0.437481\pi$
$654$	−3.07335	−	25.8282i	−0.120178	−	1.00996i
$655$	−11.2345	+	12.4771i	−0.438967	+	0.487522i
$656$	−5.21376	−	3.78802i	−0.203563	−	0.147897i
$657$	4.81215	+	5.05826i	0.187740	+	0.197341i
$658$	−1.33370	+	4.10471i	−0.0519930	+	0.160018i
$659$	7.71489	+	13.3626i	0.300529	+	0.520532i	0.976256	−	0.216620i	$-0.0695033\pi$
$659$	7.71489	+	13.3626i	0.300529	+	0.520532i	−0.675727	+	0.737152i	$0.736170\pi$
$660$	1.23058	−	5.61121i	0.0479001	−	0.218416i
$661$	−13.5791	+	23.5197i	−0.528166	+	0.914810i	0.471295	+	0.881975i	$0.343787\pi$
$661$	−13.5791	+	23.5197i	−0.528166	+	0.914810i	−0.999461	+	0.0328341i	$0.989547\pi$
$662$	−0.515981	−	0.573055i	−0.0200542	−	0.0222724i
$663$	−9.85788	−	6.95762i	−0.382848	−	0.270211i
$664$	1.37090	−	13.0432i	0.0532010	−	0.506174i
$665$	−0.195788	−	0.602573i	−0.00759233	−	0.0233668i
$666$	2.18174	+	1.49546i	0.0845408	+	0.0579477i
$667$	−5.05642	−	3.67370i	−0.195785	−	0.142246i
$668$	−13.6812	−	6.09128i	−0.529343	−	0.235679i
$669$	8.46394	−	15.1357i	0.327235	−	0.585178i
$670$	−5.68606	+	9.84855i	−0.219672	+	0.380483i
$671$	5.81728	−	3.20398i	0.224573	−	0.123688i
$672$	1.37128	−	1.56562i	0.0528982	−	0.0603950i
$673$	35.3493	−	7.51373i	1.36262	−	0.289633i	0.532125	−	0.846666i	$-0.321393\pi$
$673$	35.3493	−	7.51373i	1.36262	−	0.289633i	0.830491	+	0.557033i	$0.188060\pi$
$674$	9.33515	−	6.78239i	0.359577	−	0.261248i
$675$	−3.31512	+	4.00125i	−0.127599	+	0.154008i
$676$	−3.15963	−	9.72434i	−0.121524	−	0.374013i
$677$	−22.2503	+	24.7115i	−0.855149	+	0.949739i	−0.999206	−	0.0398304i	$-0.987318\pi$
$677$	−22.2503	+	24.7115i	−0.855149	+	0.949739i	0.144058	+	0.989569i	$0.453985\pi$
$678$	1.49114	−	0.338392i	0.0572670	−	0.0129959i
$679$	−1.60774	−	15.2966i	−0.0616993	−	0.587030i
$680$	2.79809	+	3.10759i	0.107302	+	0.119171i
$681$	−36.2640	−	7.18977i	−1.38964	−	0.275513i
$682$	−6.12788	−	8.80223i	−0.234649	−	0.337055i
$683$	−42.1959			−1.61458			−0.807291	−	0.590154i	$-0.799067\pi$
$683$	−42.1959			−1.61458			−0.807291	+	0.590154i	$0.799067\pi$
$684$	1.02582	−	1.20413i	0.0392232	−	0.0460410i
$685$	10.7768	−	7.82981i	0.411760	−	0.299161i
$686$	−1.57707	+	15.0049i	−0.0602130	+	0.572888i
$687$	−5.49465	+	4.10840i	−0.209634	+	0.156745i
$688$	−2.08756	−	0.443725i	−0.0795876	−	0.0169169i
$689$	8.07359	−	3.59459i	0.307579	−	0.136943i
$690$	9.05120	+	6.38827i	0.344573	+	0.243197i
$691$	−28.2461	+	6.00390i	−1.07453	+	0.228399i	−0.711007	−	0.703185i	$-0.751761\pi$
$691$	−28.2461	+	6.00390i	−1.07453	+	0.228399i	−0.363527	+	0.931584i	$0.618427\pi$
$692$	1.03425			0.0393163
$693$	6.95698	−	9.72326i	0.264274	−	0.369356i
$694$	31.2817			1.18744
$695$	11.8896	−	2.52720i	0.450997	−	0.0958623i
$696$	−1.53657	+	0.709535i	−0.0582436	+	0.0268948i
$697$	24.6192	−	10.9612i	0.932518	−	0.415184i
$698$	26.1356	+	5.55529i	0.989246	+	0.210271i
$699$	−5.90114	−	2.53096i	−0.223202	−	0.0957297i
$700$	0.125602	−	1.19502i	0.00474730	−	0.0451676i
$701$	16.5608	−	12.0321i	0.625493	−	0.454447i	−0.229343	−	0.973346i	$-0.573658\pi$
$701$	16.5608	−	12.0321i	0.625493	−	0.454447i	0.854836	+	0.518898i	$0.173658\pi$
$702$	−6.78785	+	5.37179i	−0.256191	+	0.202745i
$703$	−0.464898			−0.0175340
$704$	−2.00317	+	2.64335i	−0.0754973	+	0.0996251i
$705$	−4.09900	+	4.67992i	−0.154377	+	0.176256i
$706$	−8.21845	−	9.12751i	−0.309305	−	0.343519i
$707$	−0.501091	−	4.76757i	−0.0188455	−	0.179303i
$708$	13.8110	+	14.9219i	0.519048	+	0.560799i
$709$	7.69703	−	8.54842i	0.289068	−	0.321043i	−0.581067	−	0.813856i	$-0.697365\pi$
$709$	7.69703	−	8.54842i	0.289068	−	0.321043i	0.870135	+	0.492813i	$0.164031\pi$
$710$	−0.867887	−	2.67108i	−0.0325712	−	0.100244i
$711$	−27.1026	+	0.743635i	−1.01643	+	0.0278885i
$712$	1.31082	−	0.952369i	0.0491252	−	0.0356915i
$713$	20.2319	−	4.30042i	0.757689	−	0.161052i
$714$	2.80266	+	8.23945i	0.104887	+	0.308354i
$715$	−1.03954	−	5.42649i	−0.0388767	−	0.202939i
$716$	−8.49567	+	14.7149i	−0.317498	+	0.549923i
$717$	−21.6424	+	0.296853i	−0.808250	+	0.0110862i
$718$	12.5578	+	5.59111i	0.468655	+	0.208658i
$719$	11.0831	+	8.05235i	0.413330	+	0.300302i	0.774949	−	0.632024i	$-0.217776\pi$
$719$	11.0831	+	8.05235i	0.413330	+	0.300302i	−0.361619	+	0.932326i	$0.617776\pi$
$720$	2.70614	−	1.29492i	0.100852	−	0.0482588i
$721$	6.53857	+	20.1236i	0.243509	+	0.749444i
$722$	1.95698	−	18.6194i	0.0728312	−	0.692943i
$723$	−35.7849	+	16.5242i	−1.33086	+	0.614543i
$724$	2.10365	+	2.33634i	0.0781815	+	0.0868294i
$725$	−0.488577	+	0.846240i	−0.0181453	+	0.0314286i
$726$	−9.96198	+	16.2407i	−0.369724	+	0.602747i
$727$	20.5124	+	35.5285i	0.760763	+	1.31768i	0.942458	+	0.334325i	$0.108508\pi$
$727$	20.5124	+	35.5285i	0.760763	+	1.31768i	−0.181695	+	0.983355i	$0.558158\pi$
$728$	0.618576	−	1.90378i	0.0229259	−	0.0705588i
$729$	−23.0741	−	14.0210i	−0.854595	−	0.519295i
$730$	−1.88274	−	1.36789i	−0.0696835	−	0.0506280i
$731$	5.97168	−	6.63222i	0.220870	−	0.245302i
$732$	3.18748	+	1.36709i	0.117813	+	0.0505290i
$733$	0.433773	−	0.193128i	0.0160218	−	0.00713335i	−0.398710	−	0.917077i	$-0.630542\pi$
$733$	0.433773	−	0.193128i	0.0160218	−	0.00713335i	0.414732	+	0.909944i	$0.363875\pi$
$734$	2.04957	+	19.5003i	0.0756509	+	0.719770i
$735$	−4.69701	+	8.39943i	−0.173252	+	0.309818i
$736$	−3.19810	−	5.53927i	−0.117884	−	0.204180i
$737$	28.5324	−	24.6674i	1.05101	−	0.908634i
$738$	−2.54753	−	19.1651i	−0.0937758	−	0.705477i
$739$	−1.94477	+	5.98539i	−0.0715395	+	0.220176i	−0.980433	−	0.196852i	$-0.936928\pi$
$739$	−1.94477	+	5.98539i	−0.0715395	+	0.220176i	0.908894	+	0.417028i	$0.136928\pi$
$740$	−0.805464	−	0.358616i	−0.0296094	−	0.0131830i
$741$	0.450258	−	1.45328i	0.0165406	−	0.0533875i
$742$	−6.23524	−	1.32534i	−0.228903	−	0.0486548i
$743$	52.5400	+	11.1677i	1.92751	+	0.409704i	0.999291	+	0.0376617i	$0.0119909\pi$
$743$	52.5400	+	11.1677i	1.92751	+	0.409704i	0.928216	+	0.372042i	$0.121342\pi$
$744$	1.65760	−	5.35016i	0.0607706	−	0.196146i
$745$	12.1702	+	5.41852i	0.445882	+	0.198519i
$746$	1.23962	−	3.81514i	0.0453855	−	0.139682i
$747$	31.1846	−	23.9908i	1.14098	−	0.877778i
$748$	−5.38444	−	12.7812i	−0.196874	−	0.467326i
$749$	4.15490	+	7.19649i	0.151817	+	0.262954i
$750$	0.845371	−	1.51174i	0.0308686	−	0.0552008i
$751$	4.07989	+	38.8176i	0.148877	+	1.41647i	0.772632	+	0.634854i	$0.218940\pi$
$751$	4.07989	+	38.8176i	0.148877	+	1.41647i	−0.623755	+	0.781620i	$0.714394\pi$
$752$	3.28129	−	1.46092i	0.119656	−	0.0532744i
$753$	−48.8742	−	20.9618i	−1.78108	−	0.763891i
$754$	−1.08924	+	1.20972i	−0.0396677	+	0.0440555i
$755$	3.56481	+	2.58998i	0.129737	+	0.0942591i
$756$	6.23843	−	0.256834i	0.226890	−	0.00934095i
$757$	11.5702	−	35.6095i	0.420527	−	1.29425i	−0.486686	−	0.873577i	$-0.661795\pi$
$757$	11.5702	−	35.6095i	0.420527	−	1.29425i	0.907213	−	0.420671i	$-0.138205\pi$
$758$	−12.5315	−	21.7051i	−0.455163	−	0.788366i
$759$	−21.4051	−	29.8647i	−0.776954	−	1.08402i
$760$	−0.263641	+	0.456639i	−0.00956325	+	0.0165640i
$761$	35.1457	+	39.0333i	1.27403	+	1.41496i	0.864479	+	0.502669i	$0.167648\pi$
$761$	35.1457	+	39.0333i	1.27403	+	1.41496i	0.409552	+	0.912287i	$0.365685\pi$
$762$	19.7903	−	9.13846i	0.716927	−	0.331052i
$763$	−1.88618	+	17.9458i	−0.0682842	+	0.649681i
$764$	−0.990110	−	3.04725i	−0.0358209	−	0.110245i
$765$	−0.968626	+	12.5076i	−0.0350208	+	0.452212i
$766$	−11.4146	−	8.29323i	−0.412428	−	0.299646i
$767$	17.8651	+	7.95407i	0.645073	+	0.287205i
$768$	−1.73189	+	0.0237551i	−0.0624941	+	0.000857188i
$769$	−11.2722	+	19.5240i	−0.406486	+	0.704054i	−0.994493	−	0.104801i	$-0.966579\pi$
$769$	−11.2722	+	19.5240i	−0.406486	+	0.704054i	0.588007	+	0.808856i	$0.299913\pi$
$770$	−1.69403	+	3.60730i	−0.0610488	+	0.129998i
$771$	9.78829	+	28.7762i	0.352517	+	1.03635i
$772$	−1.84638	+	0.392460i	−0.0664527	+	0.0141250i
$773$	−8.36280	+	6.07593i	−0.300789	+	0.218536i	−0.727934	−	0.685647i	$-0.759519\pi$
$773$	−8.36280	+	6.07593i	−0.300789	+	0.218536i	0.427145	+	0.904183i	$0.359519\pi$
$774$	−3.35217	−	5.45492i	−0.120491	−	0.196073i
$775$	−0.999291	−	3.07550i	−0.0358956	−	0.110475i
$776$	−8.56505	+	9.51246i	−0.307467	+	0.341477i
$777$	−1.24645	−	1.34671i	−0.0447160	−	0.0483129i
$778$	−2.17694	−	20.7122i	−0.0780470	−	0.742567i
$779$	2.27377	+	2.52528i	0.0814662	+	0.0904774i
$780$	1.90113	−	2.17057i	0.0680716	−	0.0777187i
$781$	−0.187819	+	9.31299i	−0.00672068	+	0.333245i
$782$	26.7468			0.956465
$783$	−4.71950	−	1.87263i	−0.168661	−	0.0669224i
$784$	4.49502	−	3.26582i	0.160536	−	0.116636i
$785$	0.677797	−	6.44881i	0.0241916	−	0.230168i
$786$	26.7261	+	11.4626i	0.953289	+	0.408859i
$787$	−30.2950	−	6.43941i	−1.07990	−	0.229540i	−0.366587	−	0.930384i	$-0.619474\pi$
$787$	−30.2950	−	6.43941i	−1.07990	−	0.229540i	−0.713315	+	0.700844i	$0.752807\pi$
$788$	6.24979	−	2.78259i	0.222640	−	0.0991256i
$789$	−22.7677	+	10.5133i	−0.810551	+	0.374284i
$790$	8.84011	−	1.87902i	0.314517	−	0.0668527i
$791$	−1.06078			−0.0377169
$792$	−9.88755	+	1.11192i	−0.351339	+	0.0395103i
$793$	3.33582			0.118458
$794$	6.55113	−	1.39249i	0.232491	−	0.0494174i
$795$	−7.50708	−	5.29844i	−0.266249	−	0.187916i
$796$	2.71686	−	1.20962i	0.0962964	−	0.0428739i
$797$	−1.98292	−	0.421484i	−0.0702388	−	0.0149297i	0.172658	−	0.984982i	$-0.444764\pi$
$797$	−1.98292	−	0.421484i	−0.0702388	−	0.0149297i	−0.242897	+	0.970052i	$0.578098\pi$
$798$	−0.878883	+	0.657150i	−0.0311121	+	0.0232629i
$799$	−1.57000	+	14.9375i	−0.0555426	+	0.528452i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	4.78051	+	0.879831i	0.168911	+	0.0310873i
$802$	5.91607			0.208904
$803$	4.40996	+	6.33456i	0.155624	+	0.223542i
$804$	19.3210	+	3.83063i	0.681400	+	0.135096i
$805$	−5.14274	−	5.71159i	−0.181258	−	0.201307i
$806$	−0.563110	−	5.35763i	−0.0198347	−	0.188715i
$807$	16.8261	−	3.81842i	0.592306	−	0.134415i
$808$	−2.66951	+	2.96479i	−0.0939131	+	0.104301i
$809$	9.71655	+	29.9045i	0.341616	+	1.05138i	0.963371	+	0.268173i	$0.0864199\pi$
$809$	9.71655	+	29.9045i	0.341616	+	1.05138i	−0.621755	+	0.783212i	$0.713580\pi$
$810$	8.41027	+	3.20428i	0.295507	+	0.112587i
$811$	32.3726	−	23.5201i	1.13676	−	0.825902i	0.150093	−	0.988672i	$-0.452043\pi$
$811$	32.3726	−	23.5201i	1.13676	−	0.825902i	0.986664	+	0.162769i	$0.0520427\pi$
$812$	1.14849	−	0.244120i	0.0403042	−	0.00856693i
$813$	23.2764	−	26.5752i	0.816341	−	0.932033i
$814$	2.13323	+	2.00011i	0.0747698	+	0.0701040i
$815$	−2.77981	+	4.81477i	−0.0973724	+	0.168654i
$816$	3.53507	−	6.32159i	0.123752	−	0.221300i
$817$	1.02803	+	0.457710i	0.0359663	+	0.0160132i
$818$	−16.5804	−	12.0464i	−0.579721	−	0.421192i
$819$	5.41702	−	2.59211i	0.189286	−	0.0905756i
$820$	1.99148	+	6.12914i	0.0695454	+	0.214039i
$821$	3.13390	−	29.8171i	0.109374	−	1.04062i	−0.792868	−	0.609393i	$-0.791413\pi$
$821$	3.13390	−	29.8171i	0.109374	−	1.04062i	0.902242	−	0.431230i	$-0.141920\pi$
$822$	−18.8502	−	13.3043i	−0.657477	−	0.464042i
$823$	−23.7504	−	26.3774i	−0.827885	−	0.919460i	0.169935	−	0.985455i	$-0.445644\pi$
$823$	−23.7504	−	26.3774i	−0.827885	−	0.919460i	−0.997820	+	0.0659957i	$0.978978\pi$
$824$	8.80459	−	15.2500i	0.306722	−	0.531259i
$825$	−4.29374	+	3.81625i	−0.149489	+	0.132865i
$826$	−7.05275	−	12.2157i	−0.245397	−	0.425039i
$827$	0.451425	−	1.38934i	0.0156976	−	0.0483122i	−0.942901	−	0.333073i	$-0.891914\pi$
$827$	0.451425	−	1.38934i	0.0156976	−	0.0483122i	0.958598	+	0.284761i	$0.0919143\pi$
$828$	5.42684	−	18.4052i	0.188596	−	0.639625i
$829$	−9.02729	−	6.55871i	−0.313531	−	0.227793i	0.419879	−	0.907580i	$-0.362072\pi$
$829$	−9.02729	−	6.55871i	−0.313531	−	0.227793i	−0.733410	+	0.679787i	$0.762072\pi$
$830$	−8.77568	+	9.74638i	−0.304608	+	0.338302i
$831$	0.560442	+	4.70991i	0.0194415	+	0.163385i
$832$	−1.52188	+	0.677583i	−0.0527615	+	0.0234910i
$833$	2.42862	+	23.1067i	0.0841465	+	0.800601i
$834$	−10.7758	−	18.0867i	−0.373134	−	0.626291i
$835$	7.48799	+	12.9696i	0.259132	+	0.448831i
$836$	1.32294	−	1.14373i	0.0457547	−	0.0395567i
$837$	15.0563	−	7.46012i	0.520423	−	0.257859i
$838$	3.73724	−	11.5021i	0.129101	−	0.397332i
$839$	−39.2113	−	17.4580i	−1.35372	−	0.602716i	−0.403698	−	0.914892i	$-0.632276\pi$
$839$	−39.2113	−	17.4580i	−1.35372	−	0.602716i	−0.950024	+	0.312176i	$0.898942\pi$
$840$	−2.02963	+	0.460594i	−0.0700290	+	0.0158920i
$841$	27.4323	+	5.83092i	0.945942	+	0.201066i
$842$	30.5698	+	6.49781i	1.05351	+	0.223929i
$843$	6.67774	+	7.21488i	0.229994	+	0.248494i
$844$	−12.0506	−	5.36529i	−0.414800	−	0.184681i
$845$	−3.15963	+	9.72434i	−0.108695	+	0.334527i
$846$	9.96038	+	4.11113i	0.342445	+	0.141344i
$847$	9.23317	−	9.45805i	0.317256	−	0.324982i
$848$	2.65251	+	4.59429i	0.0910876	+	0.157768i
$849$	49.3870	−	0.677407i	1.69496	−	0.0232485i
$850$	−0.437104	−	4.15877i	−0.0149926	−	0.142645i
$851$	−5.15191	+	2.29378i	−0.176605	+	0.0786297i
$852$	−3.89591	+	2.91301i	−0.133472	+	0.0997981i
$853$	3.83211	−	4.25598i	0.131209	−	0.145722i	−0.673960	−	0.738768i	$-0.735408\pi$
$853$	3.83211	−	4.25598i	0.131209	−	0.145722i	0.805169	+	0.593046i	$0.202075\pi$
$854$	−1.94658	−	1.41427i	−0.0666106	−	0.0483954i
$855$	−1.53767	+	0.371198i	−0.0525873	+	0.0126947i
$856$	2.13703	−	6.57711i	0.0730423	−	0.224801i
$857$	18.3768	+	31.8296i	0.627740	+	1.08728i	0.988004	+	0.154427i	$0.0493531\pi$
$857$	18.3768	+	31.8296i	0.627740	+	1.08728i	−0.360265	+	0.932850i	$0.617314\pi$
$858$	−8.31844	+	4.73139i	−0.283987	+	0.161527i
$859$	−16.7371	+	28.9895i	−0.571063	+	0.989110i	0.425394	+	0.905008i	$0.360135\pi$
$859$	−16.7371	+	28.9895i	−0.571063	+	0.989110i	−0.996457	+	0.0841019i	$0.973198\pi$
$860$	1.42806	+	1.58602i	0.0486964	+	0.0540828i
$861$	−1.21893	+	13.3572i	−0.0415409	+	0.455211i
$862$	−0.791169	+	7.52747i	−0.0269473	+	0.256387i
$863$	−13.3245	−	41.0085i	−0.453570	−	1.39594i	−0.872806	−	0.488067i	$-0.837702\pi$
$863$	−13.3245	−	41.0085i	−0.453570	−	1.39594i	0.419236	−	0.907877i	$-0.362298\pi$
$864$	−3.63280	−	3.71520i	−0.123590	−	0.126394i
$865$	−0.836726	−	0.607917i	−0.0284495	−	0.0206698i
$866$	−10.9383	−	4.87003i	−0.371698	−	0.165490i
$867$	0.431218	+	0.723781i	0.0146449	+	0.0245809i
$868$	−1.94286	+	3.36513i	−0.0659449	+	0.114220i
$869$	−29.7409	−	3.73361i	−1.00889	−	0.126654i
$870$	1.66017	+	0.329148i	0.0562849	+	0.0111592i
$871$	18.5308	−	3.93885i	0.627894	−	0.133463i
$872$	12.1491	−	8.82685i	0.411421	−	0.298915i
$873$	−38.3864	+	1.05324i	−1.29918	+	0.0356466i
$874$	1.04219	+	3.20753i	0.0352526	+	0.108496i
$875$	−0.804030	+	0.892966i	−0.0271812	+	0.0301878i
$876$	−1.19290	+	3.85027i	−0.0403044	+	0.130089i
$877$	−3.94268	−	37.5121i	−0.133135	−	1.26669i	−0.833344	−	0.552755i	$-0.813576\pi$
$877$	−3.94268	−	37.5121i	−0.133135	−	1.26669i	0.700209	−	0.713938i	$-0.253090\pi$
$878$	12.0996	+	13.4380i	0.408343	+	0.453510i
$879$	−16.2983	−	47.9149i	−0.549729	−	1.61613i
$880$	3.17432	−	0.961084i	0.107006	−	0.0323981i
$881$	−9.38824			−0.316298			−0.158149	−	0.987415i	$-0.550553\pi$
$881$	−9.38824			−0.316298			−0.158149	+	0.987415i	$0.550553\pi$
$882$	16.3931	+	3.01708i	0.551985	+	0.101590i
$883$	23.8337	−	17.3162i	0.802068	−	0.582736i	−0.109452	−	0.993992i	$-0.534910\pi$
$883$	23.8337	−	17.3162i	0.802068	−	0.582736i	0.911520	+	0.411256i	$0.134910\pi$
$884$	0.728172	−	6.92809i	0.0244911	−	0.233017i
$885$	−2.40244	−	20.1899i	−0.0807572	−	0.678677i
$886$	19.4467	+	4.13353i	0.653326	+	0.138869i
$887$	15.7835	−	7.02727i	0.529958	−	0.235953i	−0.124272	−	0.992248i	$-0.539660\pi$
$887$	15.7835	−	7.02727i	0.529958	−	0.235953i	0.654230	+	0.756296i	$0.272993\pi$
$888$	−0.138784	+	1.52081i	−0.00465728	+	0.0510351i
$889$	−14.7921	+	3.14415i	−0.496109	+	0.105451i
$890$	−1.62027			−0.0543115
$891$	−22.8621	−	19.1918i	−0.765910	−	0.642948i
$892$	10.0121			0.335230
$893$	−1.85251	+	0.393764i	−0.0619920	+	0.0131768i
$894$	2.09696	−	22.9788i	0.0701329	−	0.768526i
$895$	15.5224	−	6.91100i	0.518855	−	0.231009i
$896$	1.17535	+	0.249828i	0.0392656	+	0.00834615i
$897$	−2.18070	−	18.3265i	−0.0728116	−	0.611903i
$898$	3.43409	−	32.6732i	0.114597	−	1.09032i
$899$	2.55641	−	1.85734i	0.0852610	−	0.0619457i
$900$	−2.95045	−	0.543016i	−0.0983482	−	0.0181005i
$901$	−22.1839			−0.739053
$902$	0.430974	−	21.3698i	0.0143499	−	0.711537i
$903$	1.43039	+	4.20516i	0.0476005	+	0.139939i
$904$	0.590709	+	0.656049i	0.0196467	+	0.0218199i
$905$	−0.328622	−	3.12663i	−0.0109238	−	0.103933i
$906$	2.25865	−	7.29013i	0.0750386	−	0.242199i
$907$	−14.8645	+	16.5087i	−0.493569	+	0.548164i	−0.937540	−	0.347877i	$-0.886903\pi$
$907$	−14.8645	+	16.5087i	−0.493569	+	0.548164i	0.443971	+	0.896041i	$0.353569\pi$
$908$	−6.59583	−	20.2999i	−0.218890	−	0.673675i
$909$	−11.9641	+	0.328267i	−0.396823	+	0.0108879i
$910$	−1.61945	+	1.17660i	−0.0536843	+	0.0390039i
$911$	17.8383	−	3.79165i	0.591009	−	0.125623i	0.0973077	−	0.995254i	$-0.468977\pi$
$911$	17.8383	−	3.79165i	0.591009	−	0.125623i	0.493701	+	0.869632i	$0.335644\pi$
$912$	0.895841	+	0.177611i	0.0296642	+	0.00588130i
$913$	38.1010	−	20.9849i	1.26096	−	0.694498i
$914$	5.58294	−	9.66993i	0.184667	−	0.319853i
$915$	−1.77517	−	2.97955i	−0.0586853	−	0.0985009i
$916$	−3.61861	−	1.61111i	−0.119562	−	0.0532326i
$917$	−16.3215	−	11.8583i	−0.538984	−	0.391595i
$918$	21.0500	−	5.38808i	0.694753	−	0.177833i
$919$	−10.1179	−	31.1396i	−0.333758	−	1.02720i	−0.967331	−	0.253517i	$-0.918412\pi$
$919$	−10.1179	−	31.1396i	−0.333758	−	1.02720i	0.633573	−	0.773683i	$-0.281588\pi$
$920$	−0.668585	+	6.36116i	−0.0220426	+	0.209721i
$921$	−3.62932	+	39.7706i	−0.119590	+	1.31049i
$922$	14.2526	+	15.8291i	0.469384	+	0.521303i
$923$	−2.33938	+	4.05192i	−0.0770015	+	0.133370i
$924$	6.86008	+	0.765785i	0.225680	+	0.0251925i
$925$	0.440845	+	0.763566i	0.0144949	+	0.0251059i
$926$	8.50412	−	26.1730i	0.279463	−	0.860098i
$927$	51.3524	−	12.3966i	1.68664	−	0.407157i
$928$	−0.790534	−	0.574357i	−0.0259506	−	0.0188542i
$929$	−15.4119	+	17.1166i	−0.505648	+	0.561579i	−0.940880	−	0.338739i	$-0.890000\pi$
$929$	−15.4119	+	17.1166i	−0.505648	+	0.561579i	0.435232	+	0.900318i	$0.356666\pi$
$930$	−4.48577	+	3.35406i	−0.147094	+	0.109984i
$931$	−2.67637	+	1.19160i	−0.0877145	+	0.0390530i
$932$	−0.387504	−	3.68686i	−0.0126931	−	0.120767i
$933$	−60.4400	+	0.829013i	−1.97872	+	0.0271407i
$934$	−0.649525	−	1.12501i	−0.0212531	−	0.0368115i
$935$	−3.15649	+	13.5051i	−0.103228	+	0.441663i
$936$	−4.61966	−	1.90676i	−0.150998	−	0.0623244i
$937$	−8.06489	+	24.8212i	−0.263469	+	0.810873i	0.728574	+	0.684967i	$0.240184\pi$
$937$	−8.06489	+	24.8212i	−0.263469	+	0.810873i	−0.992042	+	0.125905i	$0.959816\pi$
$938$	−12.4834	−	5.55797i	−0.407598	−	0.181474i
$939$	5.75257	+	6.21529i	0.187728	+	0.202828i
$940$	−3.51333	−	0.746781i	−0.114592	−	0.0243573i
$941$	−45.3751	−	9.64477i	−1.47918	−	0.314410i	−0.603527	−	0.797343i	$-0.706238\pi$
$941$	−45.3751	−	9.64477i	−1.47918	−	0.314410i	−0.875658	+	0.482932i	$0.839572\pi$
$942$	−10.9527	+	2.48554i	−0.356858	+	0.0809834i
$943$	37.6570	+	16.7660i	1.22628	+	0.545975i
$944$	−3.62752	+	11.1644i	−0.118066	+	0.363369i
$945$	−5.19796	−	3.45908i	−0.169090	−	0.112524i
$946$	−2.74805	−	6.52312i	−0.0893468	−	0.212085i
$947$	23.4057	+	40.5399i	0.760584	+	1.31737i	0.942550	+	0.334065i	$0.108420\pi$
$947$	23.4057	+	40.5399i	0.760584	+	1.31737i	−0.181966	+	0.983305i	$0.558246\pi$
$948$	−8.01198	−	13.4478i	−0.260217	−	0.436764i
$949$	0.405245	+	3.85564i	0.0131548	+	0.125160i
$950$	0.481695	−	0.214465i	0.0156283	−	0.00695815i
$951$	−5.40321	−	45.4082i	−0.175211	−	1.47246i
$952$	−3.36219	+	3.73409i	−0.108969	+	0.121023i
$953$	−11.9984	−	8.71734i	−0.388666	−	0.282382i	0.376243	−	0.926521i	$-0.377216\pi$
$953$	−11.9984	−	8.71734i	−0.388666	−	0.282382i	−0.764909	+	0.644139i	$0.777216\pi$
$954$	−4.50103	+	15.2653i	−0.145726	+	0.494233i
$955$	−0.990110	+	3.04725i	−0.0320392	+	0.0986065i
$956$	−6.24821	−	10.8222i	−0.202081	−	0.350015i
$957$	−4.84308	−	2.83795i	−0.156554	−	0.0917380i
$958$	−17.4344	+	30.1972i	−0.563279	+	0.975627i
$959$	10.7104	+	11.8951i	0.345856	+	0.384112i
$960$	1.41509	+	0.998760i	0.0456718	+	0.0322348i
$961$	2.14730	−	20.4302i	0.0692677	−	0.659038i
$962$	0.453886	+	1.39692i	0.0146339	+	0.0450385i
$963$	18.7145	−	8.95512i	0.603067	−	0.288575i
$964$	−18.4106	−	13.3761i	−0.592966	−	0.430815i
$965$	1.72444	+	0.767768i	0.0555116	+	0.0247153i
$966$	−6.49727	+	11.6188i	−0.209046	+	0.373827i
$967$	16.5552	−	28.6745i	0.532380	−	0.922109i	−0.466905	−	0.884307i	$-0.654631\pi$
$967$	16.5552	−	28.6745i	0.532380	−	0.922109i	0.999285	−	0.0378020i	$-0.0120356\pi$
$968$	−10.9911	−	0.443503i	−0.353266	−	0.0142547i
$969$	−2.51627	+	2.87287i	−0.0808341	+	0.0922900i
$970$	12.5206	−	2.66133i	0.402011	−	0.0854500i
$971$	−20.8675	+	15.1611i	−0.669670	+	0.486544i	−0.869915	−	0.493202i	$-0.835826\pi$
$971$	−20.8675	+	15.1611i	−0.669670	+	0.486544i	0.200245	+	0.979746i	$0.435826\pi$
$972$	0.563284	−	15.5783i	0.0180673	−	0.499673i
$973$	4.51341	+	13.8909i	0.144693	+	0.445321i
$974$	6.96371	−	7.73398i	0.223132	−	0.247813i
$975$	−2.81388	+	0.638566i	−0.0901162	+	0.0204505i
$976$	0.209309	+	1.99144i	0.00669982	+	0.0637445i
$977$	10.2240	+	11.3549i	0.327095	+	0.363276i	0.884153	−	0.467198i	$-0.154736\pi$
$977$	10.2240	+	11.3549i	0.327095	+	0.363276i	−0.557058	+	0.830474i	$0.688070\pi$
$978$	9.44568	+	1.87272i	0.302039	+	0.0598830i
$979$	5.07628	+	1.76331i	0.162239	+	0.0563558i
$980$	−5.55615			−0.177485
$981$	44.3072	+	8.15454i	1.41462	+	0.260355i
$982$	−28.3914	+	20.6276i	−0.906006	+	0.658252i
$983$	−2.43953	+	23.2106i	−0.0778088	+	0.740302i	0.884168	+	0.467170i	$0.154726\pi$
$983$	−2.43953	+	23.2106i	−0.0778088	+	0.740302i	−0.961977	+	0.273132i	$0.911940\pi$
$984$	8.93966	−	6.68427i	0.284986	−	0.213087i
$985$	−6.69175	−	1.42238i	−0.213217	−	0.0453207i
$986$	3.73288	−	1.66198i	0.118879	−	0.0529283i
$987$	−6.10745	−	4.31059i	−0.194402	−	0.137208i
$988$	0.859203	−	0.182629i	0.0273349	−	0.00581021i
$989$	13.6508			0.434069
$990$	8.65277	+	4.91219i	0.275003	+	0.156120i
$991$	−14.6965			−0.466851			−0.233426	−	0.972375i	$-0.574994\pi$
$991$	−14.6965			−0.466851			−0.233426	+	0.972375i	$0.574994\pi$
$992$	3.16311	−	0.672339i	0.100429	−	0.0213468i
$993$	1.21259	−	0.559930i	0.0384803	−	0.0177688i
$994$	3.08299	−	1.37264i	0.0977866	−	0.0435374i
$995$	−2.90898	−	0.618323i	−0.0922209	−	0.0196022i
$996$	20.8768	+	8.95391i	0.661506	+	0.283716i
$997$	2.11726	−	20.1444i	0.0670544	−	0.637980i	−0.908449	−	0.417996i	$-0.862733\pi$
$997$	2.11726	−	20.1444i	0.0670544	−	0.637980i	0.975503	−	0.219984i	$-0.0706007\pi$
$998$	7.09813	−	5.15709i	0.224687	−	0.163245i
$999$	−3.59252	+	2.84306i	−0.113662	+	0.0899504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.31.7	✓	88
9.7	even	3	inner	990.2.bg.a.691.11	yes	88
11.5	even	5	inner	990.2.bg.a.841.11	yes	88
99.16	even	15	inner	990.2.bg.a.511.7	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.31.7	✓	88	1.1	even	1	trivial
990.2.bg.a.511.7	yes	88	99.16	even	15	inner
990.2.bg.a.691.11	yes	88	9.7	even	3	inner
990.2.bg.a.841.11	yes	88	11.5	even	5	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 + 0.207912i) q^{2} +(0.157407 - 1.72488i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(0.204657 + 1.71992i) q^{6} +(0.125602 - 1.19502i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.95045 - 0.543016i) q^{9} +1.00000 q^{10} +(-3.13299 - 1.08829i) q^{11} +(-0.557775 - 1.63978i) q^{12} +(-1.11470 - 1.23801i) q^{13} +(0.125602 + 1.19502i) q^{14} +(-0.512590 + 1.65446i) q^{15} +(0.669131 - 0.743145i) q^{16} +(1.29221 + 3.97701i) q^{17} +(2.99887 - 0.0822823i) q^{18} +(-0.426579 + 0.309928i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(-2.04150 - 0.404753i) q^{21} +(3.29080 + 0.413119i) q^{22} +(-3.19810 + 5.53927i) q^{23} +(0.886516 + 1.48798i) q^{24} +(0.913545 + 0.406737i) q^{25} +(1.34774 + 0.979192i) q^{26} +(-1.40106 + 5.00370i) q^{27} +(-0.371316 - 1.14279i) q^{28} +(-0.102140 + 0.971801i) q^{29} +(0.157407 - 1.72488i) q^{30} +(-2.16382 - 2.40316i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.37032 + 5.23274i) q^{33} +(-2.09084 - 3.62144i) q^{34} +(-0.371316 + 1.14279i) q^{35} +(-2.91623 + 0.703985i) q^{36} +(0.713302 + 0.518244i) q^{37} +(0.352820 - 0.391846i) q^{38} +(-2.31088 + 1.72787i) q^{39} +(0.913545 - 0.406737i) q^{40} +(-0.673640 - 6.40925i) q^{41} +(2.08104 - 0.0285442i) q^{42} +(-1.06710 - 1.84827i) q^{43} +(-3.30478 + 0.280103i) q^{44} +(2.77307 + 1.14458i) q^{45} +(1.97653 - 6.08315i) q^{46} +(3.28129 + 1.46092i) q^{47} +(-1.17651 - 1.27115i) q^{48} +(5.43473 + 1.15519i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(7.06328 - 1.60290i) q^{51} +(-1.52188 - 0.677583i) q^{52} +(-1.63934 + 5.04538i) q^{53} +(0.330115 - 5.18566i) q^{54} +(2.83826 + 1.71589i) q^{55} +(0.600802 + 1.04062i) q^{56} +(0.467443 + 0.784584i) q^{57} +(-0.102140 - 0.971801i) q^{58} +(-10.7240 + 4.77464i) q^{59} +(0.204657 + 1.71992i) q^{60} +(-1.33988 + 1.48808i) q^{61} +(2.61618 + 1.90076i) q^{62} +(-1.01950 + 3.45764i) q^{63} +(0.309017 - 0.951057i) q^{64} +(0.832950 + 1.44271i) q^{65} +(1.23058 - 5.61121i) q^{66} +(-5.68606 + 9.84855i) q^{67} +(2.79809 + 3.10759i) q^{68} +(9.05120 + 6.38827i) q^{69} +(0.125602 - 1.19502i) q^{70} +(-0.867887 - 2.67108i) q^{71} +(2.70614 - 1.29492i) q^{72} +(-1.88274 - 1.36789i) q^{73} +(-0.805464 - 0.358616i) q^{74} +(0.845371 - 1.51174i) q^{75} +(-0.263641 + 0.456639i) q^{76} +(-1.69403 + 3.60730i) q^{77} +(1.90113 - 2.17057i) q^{78} +(8.84011 - 1.87902i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(8.41027 + 3.20428i) q^{81} +(1.99148 + 6.12914i) q^{82} +(-8.77568 + 9.74638i) q^{83} +(-2.02963 + 0.460594i) q^{84} +(-0.437104 - 4.15877i) q^{85} +(1.42806 + 1.58602i) q^{86} +(1.66017 + 0.329148i) q^{87} +(3.17432 - 0.961084i) q^{88} -1.62027 q^{89} +(-2.95045 - 0.543016i) q^{90} +(-1.61945 + 1.17660i) q^{91} +(-0.668585 + 6.36116i) q^{92} +(-4.48577 + 3.35406i) q^{93} +(-3.51333 - 0.746781i) q^{94} +(0.481695 - 0.214465i) q^{95} +(1.41509 + 0.998760i) q^{96} +(12.5206 - 2.66133i) q^{97} -5.55615 q^{98} +(8.65277 + 4.91219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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