LMFDB - Embedded newform 930.2.br.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.35745 - 1.07579i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62345 + 0.603659i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.685360 + 2.92066i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.35745 - 1.07579i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62345 + 0.603659i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.685360 + 2.92066i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.26789 - 1.45496i) q^{11} +(-1.73054 - 0.0724398i) q^{12} +(-0.192024 - 0.903403i) q^{13} +(-0.217038 - 0.487475i) q^{14} +(-1.71348 - 0.252933i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.44802 - 1.98039i) q^{17} +(-1.55435 - 2.56593i) q^{18} +(6.98823 + 1.48540i) q^{19} +(0.406737 - 0.913545i) q^{20} +(0.495189 - 0.780384i) q^{21} +(3.55756 + 0.373915i) q^{22} +(-2.96422 - 2.15363i) q^{23} +(1.66822 - 0.465870i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.461793 + 0.799848i) q^{26} +(2.21167 - 4.70197i) q^{27} +(0.357053 + 0.396548i) q^{28} +(-1.61663 - 4.97546i) q^{29} +(1.70778 - 0.288942i) q^{30} +(-2.08585 + 5.16229i) q^{31} +1.00000i q^{32} +(2.87079 + 5.49060i) q^{33} +(-3.61835 + 3.25797i) q^{34} +(0.313647 + 0.431698i) q^{35} +(2.27119 + 1.96002i) q^{36} +(-6.62694 - 3.82607i) q^{37} +(-7.10522 + 0.746789i) q^{38} +(-0.711206 + 1.43290i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(7.30633 + 6.57865i) q^{41} +(-0.229801 + 0.895211i) q^{42} +(0.884595 - 4.16169i) q^{43} +(-3.49899 + 0.743733i) q^{44} +(2.05387 + 2.18669i) q^{45} +(3.48465 + 1.13223i) q^{46} +(-10.3560 - 3.36487i) q^{47} +(-1.44261 + 0.958578i) q^{48} +(6.56852 - 1.39618i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-8.16846 - 2.09685i) q^{51} +(-0.686358 - 0.617999i) q^{52} +(0.214537 - 2.04118i) q^{53} +(-0.650438 + 5.15528i) q^{54} +(-3.55756 + 0.373915i) q^{55} +(-0.462118 - 0.266804i) q^{56} +(-7.88823 - 9.53422i) q^{57} +(3.07501 + 4.23238i) q^{58} +(5.93713 - 5.34582i) q^{59} +(-1.53491 + 0.802533i) q^{60} -2.90278i q^{61} +(0.388526 - 5.55419i) q^{62} +(-1.51172 + 0.526616i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.617999 - 0.686358i) q^{65} +(-4.42697 - 4.33475i) q^{66} +(-7.79547 - 13.5021i) q^{67} +(2.43448 - 4.21665i) q^{68} +(1.70694 + 6.11232i) q^{69} +(-0.431698 - 0.313647i) q^{70} +(-10.3864 - 1.09165i) q^{71} +(-2.76571 - 1.16226i) q^{72} +(6.67127 - 14.9839i) q^{73} +(7.48492 + 1.59097i) q^{74} +(-1.61039 + 0.637695i) q^{75} +(6.52669 - 2.90587i) q^{76} +(0.589851 - 1.81538i) q^{77} +(0.233605 - 1.58255i) q^{78} +(-3.95429 - 8.88148i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.06056 + 4.00341i) q^{81} +(-8.98165 - 3.99889i) q^{82} +(-2.52325 + 2.80236i) q^{83} +(-0.0580817 - 0.922409i) q^{84} +(2.86191 - 3.93907i) q^{85} +(0.444734 + 4.23136i) q^{86} +(-3.15805 + 8.49311i) q^{87} +(3.09791 - 1.78858i) q^{88} +(1.09614 - 0.796391i) q^{89} +(-2.62907 - 1.44498i) q^{90} +(0.468711 - 0.152294i) q^{91} -3.66397 q^{92} +(8.38497 - 4.76364i) q^{93} +10.8890 q^{94} +(6.79469 - 2.20773i) q^{95} +(1.07579 - 1.35745i) q^{96} +(6.70459 - 4.87117i) q^{97} +(-5.81559 + 3.35763i) q^{98} +(2.00977 - 10.5416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	−1.35745	−	1.07579i	−0.783726	−	0.621107i
$3$	−1.35745	−	1.07579i	−0.783726	−	0.621107i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.62345	+	0.603659i	0.662771	+	0.246443i
$7$	0.0557772	+	0.530685i	0.0210818	+	0.200580i	0.999993	−	0.00370565i	$-0.00117955\pi$
$7$	0.0557772	+	0.530685i	0.0210818	+	0.200580i	−0.978911	+	0.204286i	$0.934513\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.685360	+	2.92066i	0.228453	+	0.973555i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−3.26789	−	1.45496i	−0.985307	−	0.438687i	−0.150129	−	0.988666i	$-0.547969\pi$
$11$	−3.26789	−	1.45496i	−0.985307	−	0.438687i	−0.835178	+	0.549979i	$0.814636\pi$
$12$	−1.73054	−	0.0724398i	−0.499563	−	0.0209116i
$13$	−0.192024	−	0.903403i	−0.0532579	−	0.250559i	0.943463	−	0.331479i	$-0.107548\pi$
$13$	−0.192024	−	0.903403i	−0.0532579	−	0.250559i	−0.996721	+	0.0809199i	$0.974214\pi$
$14$	−0.217038	−	0.487475i	−0.0580058	−	0.130283i
$15$	−1.71348	−	0.252933i	−0.442419	−	0.0653071i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.44802	−	1.98039i	1.07880	−	0.480314i	0.211135	−	0.977457i	$-0.432284\pi$
$17$	4.44802	−	1.98039i	1.07880	−	0.480314i	0.867669	+	0.497143i	$0.165617\pi$
$18$	−1.55435	−	2.56593i	−0.366364	−	0.604795i
$19$	6.98823	+	1.48540i	1.60321	+	0.340773i	0.920751	−	0.390150i	$-0.127577\pi$
$19$	6.98823	+	1.48540i	1.60321	+	0.340773i	0.682460	+	0.730923i	$0.260910\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	0.495189	−	0.780384i	0.108059	−	0.170294i
$22$	3.55756	+	0.373915i	0.758474	+	0.0797189i
$23$	−2.96422	−	2.15363i	−0.618082	−	0.449063i	0.234169	−	0.972196i	$-0.424763\pi$
$23$	−2.96422	−	2.15363i	−0.618082	−	0.449063i	−0.852251	+	0.523133i	$0.824763\pi$
$24$	1.66822	−	0.465870i	0.340524	−	0.0950954i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.461793	+	0.799848i	0.0905650	+	0.156863i
$27$	2.21167	−	4.70197i	0.425637	−	0.904894i
$28$	0.357053	+	0.396548i	0.0674767	+	0.0749405i
$29$	−1.61663	−	4.97546i	−0.300200	−	0.923921i	−0.981425	−	0.191846i	$-0.938552\pi$
$29$	−1.61663	−	4.97546i	−0.300200	−	0.923921i	0.681225	−	0.732074i	$-0.261448\pi$
$30$	1.70778	−	0.288942i	0.311797	−	0.0527533i
$31$	−2.08585	+	5.16229i	−0.374630	+	0.927175i
$31$	−2.08585	+	5.16229i	−0.374630	+	0.927175i
$32$			1.00000i			0.176777i
$33$	2.87079	+	5.49060i	0.499740	+	0.955791i
$34$	−3.61835	+	3.25797i	−0.620541	+	0.558738i
$35$	0.313647	+	0.431698i	0.0530160	+	0.0729702i
$36$	2.27119	+	1.96002i	0.378532	+	0.326671i
$37$	−6.62694	−	3.82607i	−1.08946	−	0.629002i	−0.156029	−	0.987752i	$-0.549869\pi$
$37$	−6.62694	−	3.82607i	−1.08946	−	0.629002i	−0.933433	+	0.358751i	$0.883203\pi$
$38$	−7.10522	+	0.746789i	−1.15262	+	0.121145i
$39$	−0.711206	+	1.43290i	−0.113884	+	0.229448i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	7.30633	+	6.57865i	1.14106	+	1.02741i	0.999296	+	0.0375114i	$0.0119431\pi$
$41$	7.30633	+	6.57865i	1.14106	+	1.02741i	0.141761	+	0.989901i	$0.454724\pi$
$42$	−0.229801	+	0.895211i	−0.0354591	+	0.138134i
$43$	0.884595	−	4.16169i	0.134899	−	0.634652i	−0.857795	−	0.513993i	$-0.828166\pi$
$43$	0.884595	−	4.16169i	0.134899	−	0.634652i	0.992694	−	0.120659i	$-0.0385008\pi$
$44$	−3.49899	+	0.743733i	−0.527492	+	0.112122i
$45$	2.05387	+	2.18669i	0.306173	+	0.325972i
$46$	3.48465	+	1.13223i	0.513783	+	0.166938i
$47$	−10.3560	−	3.36487i	−1.51058	−	0.490817i	−0.567497	−	0.823375i	$-0.692088\pi$
$47$	−10.3560	−	3.36487i	−1.51058	−	0.490817i	−0.943083	+	0.332558i	$0.892088\pi$
$48$	−1.44261	+	0.958578i	−0.208223	+	0.138359i
$49$	6.56852	−	1.39618i	0.938360	−	0.199455i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	−8.16846	−	2.09685i	−1.14381	−	0.293617i
$52$	−0.686358	−	0.617999i	−0.0951807	−	0.0857011i
$53$	0.214537	−	2.04118i	0.0294689	−	0.280378i	−0.969857	−	0.243674i	$-0.921647\pi$
$53$	0.214537	−	2.04118i	0.0294689	−	0.280378i	0.999326	−	0.0367043i	$-0.0116860\pi$
$54$	−0.650438	+	5.15528i	−0.0885133	+	0.701545i
$55$	−3.55756	+	0.373915i	−0.479701	+	0.0504186i
$56$	−0.462118	−	0.266804i	−0.0617531	−	0.0356532i
$57$	−7.88823	−	9.53422i	−1.04482	−	1.26284i
$58$	3.07501	+	4.23238i	0.403768	+	0.555739i
$59$	5.93713	−	5.34582i	0.772949	−	0.695966i	−0.185053	−	0.982729i	$-0.559246\pi$
$59$	5.93713	−	5.34582i	0.772949	−	0.695966i	0.958002	+	0.286763i	$0.0925791\pi$
$60$	−1.53491	+	0.802533i	−0.198156	+	0.103607i
$61$		−	2.90278i		−	0.371663i	−0.982582	−	0.185831i	$-0.940502\pi$
$61$		−	2.90278i		−	0.371663i	0.982582	−	0.185831i	$-0.0594978\pi$
$62$	0.388526	−	5.55419i	0.0493428	−	0.705383i
$63$	−1.51172	+	0.526616i	−0.190459	+	0.0663474i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−0.617999	−	0.686358i	−0.0766534	−	0.0851322i
$66$	−4.42697	−	4.33475i	−0.544922	−	0.533571i
$67$	−7.79547	−	13.5021i	−0.952368	−	1.64955i	−0.740280	−	0.672299i	$-0.765307\pi$
$67$	−7.79547	−	13.5021i	−0.952368	−	1.64955i	−0.212088	−	0.977251i	$-0.568026\pi$
$68$	2.43448	−	4.21665i	0.295224	−	0.511344i
$69$	1.70694	+	6.11232i	0.205491	+	0.735837i
$70$	−0.431698	−	0.313647i	−0.0515978	−	0.0374880i
$71$	−10.3864	−	1.09165i	−1.23264	−	0.129555i	−0.534282	−	0.845306i	$-0.679418\pi$
$71$	−10.3864	−	1.09165i	−1.23264	−	0.129555i	−0.698356	+	0.715751i	$0.746085\pi$
$72$	−2.76571	−	1.16226i	−0.325942	−	0.136973i
$73$	6.67127	−	14.9839i	0.780813	−	1.75373i	0.134147	−	0.990961i	$-0.457171\pi$
$73$	6.67127	−	14.9839i	0.780813	−	1.75373i	0.646666	−	0.762773i	$-0.276163\pi$
$74$	7.48492	+	1.59097i	0.870104	+	0.184946i
$75$	−1.61039	+	0.637695i	−0.185951	+	0.0736347i
$76$	6.52669	−	2.90587i	0.748663	−	0.333326i
$77$	0.589851	−	1.81538i	0.0672198	−	0.206881i
$78$	0.233605	−	1.58255i	0.0264506	−	0.179188i
$79$	−3.95429	−	8.88148i	−0.444892	−	0.999245i	−0.987262	−	0.159105i	$-0.949139\pi$
$79$	−3.95429	−	8.88148i	−0.444892	−	0.999245i	0.542369	−	0.840140i	$-0.317527\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	−8.06056	+	4.00341i	−0.895618	+	0.444824i
$82$	−8.98165	−	3.99889i	−0.991857	−	0.441603i
$83$	−2.52325	+	2.80236i	−0.276963	+	0.307599i	−0.865537	−	0.500844i	$-0.833023\pi$
$83$	−2.52325	+	2.80236i	−0.276963	+	0.307599i	0.588574	+	0.808443i	$0.299690\pi$
$84$	−0.0580817	−	0.922409i	−0.00633724	−	0.100643i
$85$	2.86191	−	3.93907i	0.310417	−	0.427253i
$86$	0.444734	+	4.23136i	0.0479569	+	0.456279i
$87$	−3.15805	+	8.49311i	−0.338579	+	0.910557i
$88$	3.09791	−	1.78858i	0.330238	−	0.190663i
$89$	1.09614	−	0.796391i	0.116190	−	0.0844173i	−0.528173	−	0.849137i	$-0.677123\pi$
$89$	1.09614	−	0.796391i	0.116190	−	0.0844173i	0.644363	+	0.764720i	$0.277123\pi$
$90$	−2.62907	−	1.44498i	−0.277129	−	0.152315i
$91$	0.468711	−	0.152294i	0.0491343	−	0.0159647i
$92$	−3.66397			−0.381996
$93$	8.38497	−	4.76364i	0.869481	−	0.493966i
$94$	10.8890			1.12311
$95$	6.79469	−	2.20773i	0.697120	−	0.226508i
$96$	1.07579	−	1.35745i	0.109797	−	0.138545i
$97$	6.70459	−	4.87117i	0.680748	−	0.494592i	−0.192858	−	0.981227i	$-0.561776\pi$
$97$	6.70459	−	4.87117i	0.680748	−	0.494592i	0.873606	+	0.486634i	$0.161776\pi$
$98$	−5.81559	+	3.35763i	−0.587463	+	0.339172i
$99$	2.00977	−	10.5416i	0.201989	−	1.05947i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	8.20256	−	11.2899i	0.816185	−	1.12338i	−0.174155	−	0.984718i	$-0.555719\pi$
$101$	8.20256	−	11.2899i	0.816185	−	1.12338i	0.990340	−	0.138664i	$-0.0442807\pi$
$102$	8.41662	−	0.529973i	0.833370	−	0.0524752i
$103$	−0.782332	+	0.868867i	−0.0770854	+	0.0856120i	−0.780454	−	0.625214i	$-0.785012\pi$
$103$	−0.782332	+	0.868867i	−0.0770854	+	0.0856120i	0.703368	+	0.710826i	$0.251679\pi$
$104$	0.843737	+	0.375656i	0.0827352	+	0.0368361i
$105$	0.0386544	−	0.923427i	0.00377229	−	0.0901173i
$106$	0.426724	+	2.00758i	0.0414471	+	0.194993i
$107$	2.11595	+	4.75251i	0.204557	+	0.459442i	0.986469	−	0.163946i	$-0.0524223\pi$
$107$	2.11595	+	4.75251i	0.204557	+	0.459442i	−0.781912	+	0.623388i	$0.785756\pi$
$108$	−0.974467	−	5.10396i	−0.0937681	−	0.491129i
$109$	−4.04029	+	12.4347i	−0.386989	+	1.19103i	0.548038	+	0.836454i	$0.315375\pi$
$109$	−4.04029	+	12.4347i	−0.386989	+	1.19103i	−0.935027	+	0.354577i	$0.884625\pi$
$110$	3.26789	−	1.45496i	0.311582	−	0.138725i
$111$	4.87973	+	12.3229i	0.463163	+	1.16964i
$112$	0.521947	+	0.110943i	0.0493194	+	0.0104832i
$113$	−4.91174	+	11.0319i	−0.462058	+	1.03780i	0.520842	+	0.853653i	$0.325618\pi$
$113$	−4.91174	+	11.0319i	−0.462058	+	1.03780i	−0.982899	+	0.184145i	$0.941048\pi$
$114$	10.4484	+	6.62998i	0.978581	+	0.620954i
$115$	−3.64390	−	0.382990i	−0.339796	−	0.0357140i
$116$	−4.23238	−	3.07501i	−0.392967	−	0.285507i
$117$	2.50693	−	1.17999i	0.231766	−	0.109091i
$118$	−3.99460	+	6.91885i	−0.367733	+	0.636932i
$119$	1.29906	+	2.25004i	0.119085	+	0.206260i
$120$	1.21179	−	1.23757i	0.110621	−	0.112974i
$121$	1.20179	+	1.33472i	0.109254	+	0.121338i
$122$	0.897008	+	2.76071i	0.0812112	+	0.249943i
$123$	−2.84077	−	16.7903i	−0.256144	−	1.51393i
$124$	1.34683	+	5.40241i	0.120949	+	0.485151i
$125$		−	1.00000i		−	0.0894427i
$126$	1.27500	−	0.967990i	0.113586	−	0.0862354i
$127$	2.07482	−	1.86818i	0.184111	−	0.165774i	−0.571922	−	0.820308i	$-0.693802\pi$
$127$	2.07482	−	1.86818i	0.184111	−	0.165774i	0.756032	+	0.654534i	$0.227135\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−5.67789	+	4.69766i	−0.499911	+	0.413606i
$130$	0.799848	+	0.461793i	0.0701513	+	0.0405019i
$131$	−2.06866	+	0.217425i	−0.180740	+	0.0189965i	−0.194466	−	0.980909i	$-0.562297\pi$
$131$	−2.06866	+	0.217425i	−0.180740	+	0.0189965i	0.0137261	+	0.999906i	$0.495631\pi$
$132$	5.54981	+	2.75459i	0.483049	+	0.239756i
$133$	−0.398492	+	3.79140i	−0.0345537	+	0.328756i
$134$	11.5863	+	10.4324i	1.00091	+	0.901219i
$135$	−0.435619	−	5.17786i	−0.0374922	−	0.445639i
$136$	−1.01231	+	4.76257i	−0.0868053	+	0.408387i
$137$	−11.3232	+	2.40681i	−0.967402	+	0.205628i	−0.664413	−	0.747366i	$-0.731318\pi$
$137$	−11.3232	+	2.40681i	−0.967402	+	0.205628i	−0.302990	+	0.952994i	$0.597985\pi$
$138$	−3.51220	−	5.28569i	−0.298979	−	0.449948i
$139$	4.29889	+	1.39679i	0.364627	+	0.118475i	0.485600	−	0.874181i	$-0.338601\pi$
$139$	4.29889	+	1.39679i	0.364627	+	0.118475i	−0.120973	+	0.992656i	$0.538601\pi$
$140$	0.507491	+	0.164894i	0.0428908	+	0.0139361i
$141$	10.4379	+	15.7085i	0.879031	+	1.32290i
$142$	10.2154	−	2.17135i	0.857256	−	0.182215i
$143$	−0.686901	+	3.23161i	−0.0574415	+	0.270241i
$144$	2.98950	+	0.250719i	0.249125	+	0.0208933i
$145$	−3.88777	−	3.50057i	−0.322862	−	0.290706i
$146$	−1.71447	+	16.3121i	−0.141891	+	1.35000i
$147$	−10.4185	−	5.17108i	−0.859300	−	0.426504i
$148$	−7.61022	+	0.799866i	−0.625556	+	0.0657486i
$149$	−15.5131	−	8.95649i	−1.27088	−	0.733745i	−0.295729	−	0.955272i	$-0.595562\pi$
$149$	−15.5131	−	8.95649i	−1.27088	−	0.733745i	−0.975154	+	0.221527i	$0.928896\pi$
$150$	1.33451	−	1.10412i	0.108962	−	0.0901511i
$151$	−10.5527	−	14.5246i	−0.858770	−	1.18200i	−0.981861	−	0.189600i	$-0.939281\pi$
$151$	−10.5527	−	14.5246i	−0.858770	−	1.18200i	0.123091	−	0.992395i	$-0.460719\pi$
$152$	−5.30929	+	4.78051i	−0.430640	+	0.387750i
$153$	8.83254	+	11.6339i	0.714068	+	0.940545i
$154$			1.90880i			0.153815i
$155$	0.774746	+	5.51360i	0.0622291	+	0.442863i
$156$	0.266862	+	1.57728i	0.0213661	+	0.126284i
$157$	−4.78962	−	14.7409i	−0.382253	−	1.17645i	−0.938453	−	0.345406i	$-0.887741\pi$
$157$	−4.78962	−	14.7409i	−0.382253	−	1.17645i	0.556200	−	0.831048i	$-0.312259\pi$
$158$	6.50528	+	7.22485i	0.517532	+	0.574778i
$159$	−2.48711	+	2.54002i	−0.197240	+	0.201436i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.977562	−	1.69319i	0.0770427	−	0.133442i
$162$	6.42893	−	6.29832i	0.505104	−	0.494843i
$163$	6.54365	+	4.75424i	0.512538	+	0.372381i	0.813786	−	0.581165i	$-0.197403\pi$
$163$	6.54365	+	4.75424i	0.512538	+	0.372381i	−0.301247	+	0.953546i	$0.597403\pi$
$164$	9.77778	+	1.02769i	0.763516	+	0.0802488i
$165$	5.23148	+	3.31961i	0.407270	+	0.258431i
$166$	1.53378	−	3.44493i	0.119045	−	0.267378i
$167$	7.88557	+	1.67613i	0.610204	+	0.129703i	0.502641	−	0.864496i	$-0.332362\pi$
$167$	7.88557	+	1.67613i	0.610204	+	0.129703i	0.107563	+	0.994198i	$0.465695\pi$
$168$	0.340279	+	0.859315i	0.0262531	+	0.0662976i
$169$	11.0968	−	4.94063i	0.853602	−	0.380048i
$170$	−1.50459	+	4.63066i	−0.115397	+	0.355155i
$171$	0.451113	+	21.4283i	0.0344975	+	1.63866i
$172$	−1.73053	−	3.88683i	−0.131952	−	0.296368i
$173$	−0.334418	−	1.57332i	−0.0254254	−	0.119617i	0.963605	−	0.267331i	$-0.0861418\pi$
$173$	−0.334418	−	1.57332i	−0.0254254	−	0.119617i	−0.989030	+	0.147714i	$0.952808\pi$
$174$	0.378970	−	9.05332i	0.0287296	−	0.686330i
$175$	0.487475	+	0.217038i	0.0368496	+	0.0164065i
$176$	−2.39358	+	2.65835i	−0.180423	+	0.200380i
$177$	−13.8103	+	0.869602i	−1.03805	+	0.0653633i
$178$	−0.796391	+	1.09614i	−0.0596920	+	0.0821590i
$179$	1.99466	+	18.9780i	0.149088	+	1.41848i	0.771719	+	0.635964i	$0.219397\pi$
$179$	1.99466	+	18.9780i	0.149088	+	1.41848i	−0.622631	+	0.782516i	$0.713936\pi$
$180$	2.94692	+	0.561834i	0.219651	+	0.0418766i
$181$	7.82137	−	4.51567i	0.581358	−	0.335647i	−0.180315	−	0.983609i	$-0.557712\pi$
$181$	7.82137	−	4.51567i	0.581358	−	0.335647i	0.761673	+	0.647962i	$0.224378\pi$
$182$	−0.398710	+	0.289680i	−0.0295543	+	0.0214725i
$183$	−3.12277	+	3.94039i	−0.230842	+	0.291282i
$184$	3.48465	−	1.13223i	0.256892	−	0.0834691i
$185$	−7.65214			−0.562596
$186$	−6.50254	+	7.12159i	−0.476789	+	0.522180i
$187$	−17.4170			−1.27366
$188$	−10.3560	+	3.36487i	−0.755290	+	0.245409i
$189$	2.61862	+	0.911438i	0.190477	+	0.0662974i
$190$	−5.77991	+	4.19935i	−0.419318	+	0.304653i
$191$	11.0534	−	6.38167i	0.799795	−	0.461762i	−0.0436045	−	0.999049i	$-0.513884\pi$
$191$	11.0534	−	6.38167i	0.799795	−	0.461762i	0.843399	+	0.537287i	$0.180551\pi$
$192$	−0.603659	+	1.62345i	−0.0435653	+	0.117163i
$193$	2.86137	+	27.2241i	0.205966	+	1.95963i	0.273377	+	0.961907i	$0.411859\pi$
$193$	2.86137	+	27.2241i	0.205966	+	1.95963i	−0.0674118	+	0.997725i	$0.521474\pi$
$194$	−4.87117	+	6.70459i	−0.349730	+	0.481362i
$195$	0.100530	+	1.59653i	0.00719908	+	0.114330i
$196$	4.49339	−	4.99041i	0.320956	−	0.356458i
$197$	23.2027	+	10.3305i	1.65312	+	0.736017i	0.999779	−	0.0210451i	$-0.00669934\pi$
$197$	23.2027	+	10.3305i	1.65312	+	0.736017i	0.653343	+	0.757062i	$0.273366\pi$
$198$	1.34613	+	10.6467i	0.0956652	+	0.756629i
$199$	1.28362	+	6.03897i	0.0909936	+	0.428091i	0.999938	+	0.0111730i	$0.00355654\pi$
$199$	1.28362	+	6.03897i	0.0909936	+	0.428091i	−0.908944	+	0.416918i	$0.863110\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−3.94346	+	26.7148i	−0.278150	+	1.88432i
$202$	−4.31234	+	13.2720i	−0.303415	+	0.933816i
$203$	2.55023	−	1.13544i	0.178991	−	0.0796920i
$204$	−7.84091	+	3.10491i	−0.548974	+	0.217388i
$205$	9.61679	+	2.04411i	0.671666	+	0.142767i
$206$	0.475547	−	1.06810i	0.0331329	−	0.0744178i
$207$	4.25848	−	10.1335i	0.295984	−	0.704327i
$208$	−0.918526	−	0.0965410i	−0.0636883	−	0.00669391i
$209$	−20.6756	−	15.0217i	−1.43016	−	1.03907i
$210$	0.248592	+	0.890176i	0.0171545	+	0.0614280i
$211$	12.3160	−	21.3319i	0.847866	−	1.46855i	−0.0352432	−	0.999379i	$-0.511221\pi$
$211$	12.3160	−	21.3319i	0.847866	−	1.46855i	0.883109	−	0.469168i	$-0.155446\pi$
$212$	−1.02621	−	1.77745i	−0.0704806	−	0.122076i
$213$	12.9247	+	12.6554i	0.885582	+	0.867135i
$214$	−3.48100	−	3.86604i	−0.237956	−	0.264277i
$215$	−1.31476	−	4.04643i	−0.0896661	−	0.275964i
$216$	2.50398	+	4.55303i	0.170375	+	0.309794i
$217$	−2.85589	−	0.818990i	−0.193870	−	0.0555967i
$218$		−	13.0746i		−	0.885527i
$219$	−25.1755	+	13.1631i	−1.70120	+	0.889480i
$220$	−2.65835	+	2.39358i	−0.179226	+	0.161375i
$221$	−2.64321	−	3.63807i	−0.177802	−	0.244723i
$222$	−8.44888	−	10.2119i	−0.567052	−	0.685375i
$223$	11.6159	+	6.70641i	0.777855	+	0.449095i	0.835670	−	0.549233i	$-0.185080\pi$
$223$	11.6159	+	6.70641i	0.777855	+	0.449095i	−0.0578146	+	0.998327i	$0.518413\pi$
$224$	−0.530685	+	0.0557772i	−0.0354579	+	0.00372677i
$225$	2.87205	+	0.866793i	0.191470	+	0.0577862i
$226$	1.26228	−	12.0098i	0.0839658	−	0.798881i
$227$	−2.73661	−	2.46405i	−0.181635	−	0.163545i	0.573298	−	0.819347i	$-0.305664\pi$
$227$	−2.73661	−	2.46405i	−0.181635	−	0.163545i	−0.754933	+	0.655802i	$0.772330\pi$
$228$	−11.9858	−	3.07676i	−0.793778	−	0.203763i
$229$	−2.26195	+	10.6416i	−0.149474	+	0.703219i	0.838030	+	0.545624i	$0.183707\pi$
$229$	−2.26195	+	10.6416i	−0.149474	+	0.703219i	−0.987504	+	0.157595i	$0.949626\pi$
$230$	3.58391	−	0.761783i	0.236316	−	0.0502305i
$231$	−2.75365	+	1.82973i	−0.181177	+	0.120388i
$232$	4.97546	+	1.61663i	0.326655	+	0.106137i
$233$	23.4239	+	7.61088i	1.53455	+	0.498606i	0.949867	−	0.312656i	$-0.101219\pi$
$233$	23.4239	+	7.61088i	1.53455	+	0.498606i	0.584684	+	0.811261i	$0.301219\pi$
$234$	−2.01959	+	1.89693i	−0.132025	+	0.124006i
$235$	−10.6510	+	2.26394i	−0.694795	+	0.147683i
$236$	1.66105	−	7.81461i	0.108125	−	0.508688i
$237$	−4.18683	+	16.3102i	−0.271964	+	1.05946i
$238$	−1.93078	−	1.73848i	−0.125154	−	0.112689i
$239$	−0.491079	+	4.67230i	−0.0317652	+	0.302226i	0.967092	+	0.254428i	$0.0818871\pi$
$239$	−0.491079	+	4.67230i	−0.0317652	+	0.302226i	−0.998857	+	0.0477982i	$0.984780\pi$
$240$	−0.770049	+	1.55146i	−0.0497065	+	0.100146i
$241$	−15.1891	+	1.59644i	−0.978419	+	0.102836i	−0.580217	−	0.814462i	$-0.697032\pi$
$241$	−15.1891	+	1.59644i	−0.978419	+	0.102836i	−0.398202	+	0.917298i	$0.630366\pi$
$242$	−1.55542	−	0.898024i	−0.0999864	−	0.0577272i
$243$	15.2487	+	3.23701i	0.978202	+	0.207655i
$244$	−1.70621	−	2.34840i	−0.109229	−	0.150341i
$245$	4.99041	−	4.49339i	0.318826	−	0.287072i
$246$	7.89021	+	15.0907i	0.503062	+	0.962145i
$247$		−	6.59842i		−	0.419848i
$248$	−2.95035	−	4.72181i	−0.187347	−	0.299835i
$249$	6.43995	−	1.08958i	0.408115	−	0.0690495i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	7.59356	+	8.43350i	0.479301	+	0.532318i	0.933498	−	0.358584i	$-0.116740\pi$
$251$	7.59356	+	8.43350i	0.479301	+	0.532318i	−0.454196	+	0.890902i	$0.650074\pi$
$252$	−0.913473	+	1.31461i	−0.0575434	+	0.0828127i
$253$	6.55330	+	11.3507i	0.412003	+	0.713610i
$254$	−1.39597	+	2.41790i	−0.0875912	+	0.151712i
$255$	−8.12251	+	2.26831i	−0.508652	+	0.142047i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	19.0451	+	2.00172i	1.18800	+	0.124864i	0.677836	−	0.735213i	$-0.262918\pi$
$257$	19.0451	+	2.00172i	1.18800	+	0.124864i	0.510165	+	0.860077i	$0.329585\pi$
$258$	3.94834	−	6.22231i	0.245813	−	0.387384i
$259$	1.66080	−	3.73022i	0.103197	−	0.231785i
$260$	−0.903403	−	0.192024i	−0.0560267	−	0.0119088i
$261$	13.4237	−	8.13161i	0.830906	−	0.503334i
$262$	1.90023	−	0.846036i	0.117396	−	0.0522682i
$263$	2.13997	−	6.58614i	0.131956	−	0.406119i	−0.863148	−	0.504951i	$-0.831511\pi$
$263$	2.13997	−	6.58614i	0.131956	−	0.406119i	0.995104	+	0.0988319i	$0.0315106\pi$
$264$	−6.12940	−	0.904781i	−0.377238	−	0.0556854i
$265$	−0.834797	−	1.87499i	−0.0512812	−	0.115179i
$266$	−0.792618	−	3.72898i	−0.0485986	−	0.228638i
$267$	−2.34470	−	0.0981488i	−0.143494	−	0.00600661i
$268$	−14.2430	−	6.34140i	−0.870031	−	0.387363i
$269$	4.02839	−	4.47398i	0.245615	−	0.272784i	−0.607714	−	0.794156i	$-0.707913\pi$
$269$	4.02839	−	4.47398i	0.245615	−	0.272784i	0.853329	+	0.521373i	$0.174580\pi$
$270$	2.01435	+	4.78982i	0.122589	+	0.291499i
$271$	−11.6934	+	16.0947i	−0.710326	+	0.977681i	0.289464	+	0.957189i	$0.406523\pi$
$271$	−11.6934	+	16.0947i	−0.710326	+	0.977681i	−0.999790	+	0.0204915i	$0.993477\pi$
$272$	−0.508945	−	4.84229i	−0.0308593	−	0.293607i
$273$	−0.800090	−	0.297503i	−0.0484236	−	0.0180057i
$274$	10.0252	−	5.78806i	0.605645	−	0.349670i
$275$	−2.89398	+	2.10260i	−0.174514	+	0.126792i
$276$	4.97367	+	3.94166i	0.299380	+	0.237260i
$277$	13.1585	−	4.27544i	0.790615	−	0.256886i	0.114249	−	0.993452i	$-0.463554\pi$
$277$	13.1585	−	4.27544i	0.790615	−	0.256886i	0.676366	+	0.736566i	$0.263554\pi$
$278$	−4.52012			−0.271099
$279$	−16.5069	−	2.55404i	−0.988241	−	0.152906i
$280$	−0.533608			−0.0318892
$281$	4.24780	−	1.38019i	0.253403	−	0.0823355i	−0.179561	−	0.983747i	$-0.557468\pi$
$281$	4.24780	−	1.38019i	0.253403	−	0.0823355i	0.432964	+	0.901411i	$0.357468\pi$
$282$	−14.7813	−	11.7142i	−0.880211	−	0.697571i
$283$	−10.4808	+	7.61475i	−0.623019	+	0.452650i	−0.853975	−	0.520314i	$-0.825815\pi$
$283$	−10.4808	+	7.61475i	−0.623019	+	0.452650i	0.230956	+	0.972964i	$0.425815\pi$
$284$	−9.04442	+	5.22180i	−0.536688	+	0.309857i
$285$	−11.5985	−	4.31276i	−0.687037	−	0.255466i
$286$	−0.345342	−	3.28571i	−0.0204205	−	0.194288i
$287$	−3.08366	+	4.24430i	−0.182023	+	0.250533i
$288$	−2.92066	+	0.685360i	−0.172102	+	0.0403852i
$289$	4.48773	−	4.98413i	0.263984	−	0.293184i
$290$	4.77923	+	2.12785i	0.280646	+	0.124952i
$291$	−14.3415	−	0.600332i	−0.840715	−	0.0351921i
$292$	−3.41015	−	16.0435i	−0.199564	−	0.938876i
$293$	1.18132	+	2.65329i	0.0690136	+	0.155007i	0.944759	−	0.327767i	$-0.106296\pi$
$293$	1.18132	+	2.65329i	0.0690136	+	0.155007i	−0.875745	+	0.482774i	$0.839629\pi$
$294$	11.5065	+	1.69851i	0.671072	+	0.0990593i
$295$	2.46880	−	7.59818i	0.143739	−	0.442383i
$296$	6.99057	−	3.11240i	0.406319	−	0.180905i
$297$	−14.0687	+	12.1476i	−0.816348	+	0.704878i
$298$	17.5215	+	3.72432i	1.01500	+	0.215744i
$299$	−1.37639	+	3.09143i	−0.0795989	+	0.178782i
$300$	−0.928002	+	1.46247i	−0.0535782	+	0.0844356i
$301$	2.25789	+	0.237313i	0.130142	+	0.0136785i
$302$	14.5246	+	10.5527i	0.835797	+	0.607242i
$303$	−23.2801	+	6.50123i	−1.33741	+	0.373486i
$304$	3.57218	−	6.18719i	0.204878	−	0.354860i
$305$	−1.45139	−	2.51388i	−0.0831063	−	0.143944i
$306$	−11.9953	−	8.33509i	−0.685727	−	0.476485i
$307$	−11.4054	−	12.6670i	−0.650941	−	0.722943i	0.323839	−	0.946112i	$-0.395026\pi$
$307$	−11.4054	−	12.6670i	−0.650941	−	0.722943i	−0.974780	+	0.223169i	$0.928360\pi$
$308$	−0.589851	−	1.81538i	−0.0336099	−	0.103441i
$309$	1.99670	−	0.337824i	0.113588	−	0.0192181i
$310$	−2.44062	−	5.00433i	−0.138618	−	0.284227i
$311$		−	8.73371i		−	0.495243i	−0.968857	−	0.247622i	$-0.920351\pi$
$311$		−	8.73371i		−	0.495243i	0.968857	−	0.247622i	$-0.0796490\pi$
$312$	−0.741208	−	1.41762i	−0.0419626	−	0.0802568i
$313$	−21.8884	+	19.7084i	−1.23721	+	1.11399i	−0.247801	+	0.968811i	$0.579708\pi$
$313$	−21.8884	+	19.7084i	−1.23721	+	1.11399i	−0.989406	+	0.145175i	$0.953625\pi$
$314$	9.11040	+	12.5394i	0.514129	+	0.707638i
$315$	−1.04588	+	1.21193i	−0.0589289	+	0.0682843i
$316$	−8.41949	−	4.86100i	−0.473633	−	0.273452i
$317$	−20.1882	+	2.12187i	−1.13388	+	0.119176i	−0.652822	−	0.757511i	$-0.726415\pi$
$317$	−20.1882	+	2.12187i	−1.13388	+	0.119176i	−0.481061	+	0.876687i	$0.659748\pi$
$318$	1.58047	−	3.18426i	0.0886284	−	0.178564i
$319$	−1.95614	+	18.6114i	−0.109523	+	1.04204i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	2.24038	−	8.72762i	0.125046	−	0.487128i
$322$	−0.406493	+	1.91240i	−0.0226530	+	0.106574i
$323$	34.0255	−	7.23234i	1.89323	−	0.402418i
$324$	−4.16799	+	7.97671i	−0.231555	+	0.443150i
$325$	−0.878382	−	0.285404i	−0.0487239	−	0.0158313i
$326$	−7.69252	−	2.49945i	−0.426049	−	0.138432i
$327$	18.8616	−	12.5331i	1.04305	−	0.693080i
$328$	−9.61679	+	2.04411i	−0.530999	+	0.112867i
$329$	1.20806	−	5.68346i	0.0666023	−	0.313339i
$330$	−6.00124	−	1.54052i	−0.330358	−	0.0848029i
$331$	6.53075	+	5.88032i	0.358963	+	0.323211i	0.828804	−	0.559540i	$-0.189022\pi$
$331$	6.53075	+	5.88032i	0.358963	+	0.323211i	−0.469841	+	0.882751i	$0.655689\pi$
$332$	−0.394171	+	3.75029i	−0.0216330	+	0.205824i
$333$	6.63282	−	21.9773i	0.363476	−	1.20435i
$334$	−8.01757	+	0.842681i	−0.438702	+	0.0461094i
$335$	−13.5021	−	7.79547i	−0.737701	−	0.425912i
$336$	−0.589168	−	0.712105i	−0.0321417	−	0.0388485i
$337$	1.37733	+	1.89573i	0.0750280	+	0.103267i	0.844882	−	0.534953i	$-0.179671\pi$
$337$	1.37733	+	1.89573i	0.0750280	+	0.103267i	−0.769854	+	0.638221i	$0.779671\pi$
$338$	−9.02697	+	8.12792i	−0.491003	+	0.442101i
$339$	18.5355	−	9.69136i	1.00671	−	0.526363i
$340$		−	4.86896i		−	0.264057i
$341$	14.3273	−	13.8350i	0.775865	−	0.749207i
$342$	−7.05075	−	20.2401i	−0.381261	−	1.09446i
$343$	2.26156	+	6.96037i	0.122113	+	0.375825i
$344$	2.84693	+	3.16183i	0.153496	+	0.170475i
$345$	4.53441	+	4.43996i	0.244125	+	0.239039i
$346$	0.804232	+	1.39297i	0.0432358	+	0.0748866i
$347$	9.55161	−	16.5439i	0.512757	−	0.888122i	−0.487133	−	0.873328i	$-0.661957\pi$
$347$	9.55161	−	16.5439i	0.512757	−	0.888122i	0.999891	−	0.0147942i	$-0.00470931\pi$
$348$	2.43721	+	8.72733i	0.130648	+	0.467834i
$349$	18.6175	+	13.5264i	0.996572	+	0.724052i	0.961350	−	0.275328i	$-0.0887864\pi$
$349$	18.6175	+	13.5264i	0.996572	+	0.724052i	0.0352212	+	0.999380i	$0.488786\pi$
$350$	−0.530685	−	0.0557772i	−0.0283663	−	0.00298142i
$351$	−4.67247	−	1.09514i	−0.249398	−	0.0584542i
$352$	1.45496	−	3.26789i	0.0775497	−	0.174179i
$353$	−19.9966	−	4.25042i	−1.06431	−	0.226227i	−0.357707	−	0.933834i	$-0.616442\pi$
$353$	−19.9966	−	4.25042i	−1.06431	−	0.226227i	−0.706606	+	0.707607i	$0.749775\pi$
$354$	12.8657	−	5.09467i	0.683804	−	0.270779i
$355$	−9.54070	+	4.24779i	−0.506368	+	0.225450i
$356$	0.418688	−	1.28859i	0.0221904	−	0.0682950i
$357$	0.657150	−	4.45183i	0.0347801	−	0.235616i
$358$	−7.76155	−	17.4327i	−0.410211	−	0.921348i
$359$	0.567143	+	2.66820i	0.0299327	+	0.140822i	0.990576	−	0.136961i	$-0.0437336\pi$
$359$	0.567143	+	2.66820i	0.0299327	+	0.140822i	−0.960644	+	0.277783i	$0.910400\pi$
$360$	−2.97630	+	0.376313i	−0.156865	+	0.0198334i
$361$	29.2717	+	13.0326i	1.54061	+	0.685926i
$362$	−6.04314	+	6.71159i	−0.317621	+	0.352753i
$363$	−0.195495	−	3.10470i	−0.0102608	−	0.162954i
$364$	0.289680	−	0.398710i	0.0151833	−	0.0208981i
$365$	−1.71447	−	16.3121i	−0.0897394	−	0.853814i
$366$	1.75229	−	4.71252i	0.0915936	−	0.246327i
$367$	−20.5506	+	11.8649i	−1.07273	+	0.619343i	−0.928927	−	0.370263i	$-0.879268\pi$
$367$	−20.5506	+	11.8649i	−1.07273	+	0.619343i	−0.143806	+	0.989606i	$0.545934\pi$
$368$	−2.96422	+	2.15363i	−0.154520	+	0.112266i
$369$	−14.2066	+	25.8481i	−0.739564	+	1.34560i
$370$	7.27761	−	2.36464i	0.378345	−	0.122932i
$371$	1.09519			0.0568595
$372$	3.98359	−	8.78243i	0.206540	−	0.455348i
$373$	18.2194			0.943363			0.471681	−	0.881769i	$-0.343647\pi$
$373$	18.2194			0.943363			0.471681	+	0.881769i	$0.343647\pi$
$374$	16.5646	−	5.38216i	0.856535	−	0.278305i
$375$	−1.07579	+	1.35745i	−0.0555535	+	0.0700986i
$376$	8.80935	−	6.40037i	0.454308	−	0.330074i
$377$	−4.18442	+	2.41587i	−0.215508	+	0.124424i
$378$	−2.77211	−	0.0576300i	−0.142582	−	0.00296417i
$379$	−0.109845	−	1.04510i	−0.00564235	−	0.0536834i	0.991338	−	0.131332i	$-0.0419254\pi$
$379$	−0.109845	−	1.04510i	−0.00564235	−	0.0536834i	−0.996981	+	0.0776487i	$0.975259\pi$
$380$	4.19935	−	5.77991i	0.215422	−	0.296503i
$381$	−4.82623	+	0.303896i	−0.247256	+	0.0155690i
$382$	−8.54035	+	9.48502i	−0.436962	+	0.485296i
$383$	27.3267	+	12.1666i	1.39633	+	0.621685i	0.960483	−	0.278337i	$-0.0897833\pi$
$383$	27.3267	+	12.1666i	1.39633	+	0.621685i	0.435844	+	0.900022i	$0.356450\pi$
$384$	0.0724398	−	1.73054i	0.00369668	−	0.0883110i
$385$	−0.396862	−	1.86709i	−0.0202259	−	0.0951555i
$386$	−11.1340	−	25.0074i	−0.566707	−	1.27284i
$387$	12.7612	−	0.268651i	0.648687	−	0.0136563i
$388$	2.56093	−	7.88172i	0.130011	−	0.400134i
$389$	−7.39136	+	3.29084i	−0.374757	+	0.166852i	−0.585467	−	0.810696i	$-0.699089\pi$
$389$	−7.39136	+	3.29084i	−0.374757	+	0.166852i	0.210711	+	0.977548i	$0.432422\pi$
$390$	−0.588966	−	1.48733i	−0.0298234	−	0.0753139i
$391$	−17.4499	−	3.70909i	−0.882480	−	0.187577i
$392$	−2.73134	+	6.13470i	−0.137954	+	0.309849i
$393$	3.04202	+	1.93030i	0.153449	+	0.0973707i
$394$	−25.2593	−	2.65486i	−1.27255	−	0.133750i
$395$	−7.86526	−	5.71444i	−0.395744	−	0.287525i
$396$	−4.57026	−	9.70964i	−0.229664	−	0.487928i
$397$	10.1240	−	17.5354i	0.508111	−	0.880075i	−0.491845	−	0.870683i	$-0.663677\pi$
$397$	10.1240	−	17.5354i	0.508111	−	0.880075i	0.999956	−	0.00939159i	$-0.00298948\pi$
$398$	−3.08694	−	5.34674i	−0.154734	−	0.268008i
$399$	4.61968	−	4.71796i	0.231273	−	0.236193i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−1.74782	−	5.37923i	−0.0872819	−	0.268626i	0.897884	−	0.440233i	$-0.145104\pi$
$401$	−1.74782	−	5.37923i	−0.0872819	−	0.268626i	−0.985166	+	0.171607i	$0.945104\pi$
$402$	−4.50487	−	26.6259i	−0.224683	−	1.32798i
$403$	5.06416	+	0.893078i	0.252264	+	0.0444874i
$404$		−	13.9550i		−	0.694288i
$405$	−4.97895	+	7.49734i	−0.247406	+	0.372546i
$406$	−2.07455	+	1.86793i	−0.102958	+	0.0927038i
$407$	16.0894	+	22.1451i	0.797521	+	1.09769i
$408$	6.49768	−	5.37593i	0.321683	−	0.266148i
$409$	8.36292	+	4.82833i	0.413520	+	0.238746i	0.692301	−	0.721609i	$-0.256597\pi$
$409$	8.36292	+	4.82833i	0.413520	+	0.238746i	−0.278781	+	0.960355i	$0.589930\pi$
$410$	−9.77778	+	1.02769i	−0.482890	+	0.0507538i
$411$	17.9599	+	8.91418i	0.885895	+	0.439704i
$412$	−0.122212	+	1.16277i	−0.00602096	+	0.0572856i
$413$	3.16810	+	2.85257i	0.155892	+	0.140366i
$414$	−0.918629	+	10.9535i	−0.0451481	+	0.538334i
$415$	−0.784024	+	3.68854i	−0.0384862	+	0.181063i
$416$	0.903403	−	0.192024i	0.0442930	−	0.00941476i
$417$	−4.33289	−	6.52078i	−0.212182	−	0.319324i
$418$	24.3057	+	7.89739i	1.18883	+	0.386274i
$419$	−23.1426	−	7.51949i	−1.13059	−	0.367351i	−0.316790	−	0.948496i	$-0.602605\pi$
$419$	−23.1426	−	7.51949i	−1.13059	−	0.367351i	−0.813800	+	0.581145i	$0.802605\pi$
$420$	−0.511505	−	0.769789i	−0.0249589	−	0.0375618i
$421$	22.9900	−	4.88668i	1.12047	−	0.238162i	0.389801	−	0.920899i	$-0.372544\pi$
$421$	22.9900	−	4.88668i	1.12047	−	0.238162i	0.730664	+	0.682737i	$0.239210\pi$
$422$	−5.12126	+	24.0937i	−0.249299	+	1.17286i
$423$	2.73007	−	32.5526i	0.132741	−	1.58276i
$424$	1.52525	+	1.37334i	0.0740727	+	0.0666954i
$425$	0.508945	−	4.84229i	0.0246875	−	0.234886i
$426$	−16.2028	−	8.04208i	−0.785029	−	0.389640i
$427$	1.54046	−	0.161909i	0.0745481	−	0.00783532i
$428$	4.50529	+	2.60113i	0.217772	+	0.125730i
$429$	4.40897	−	3.64780i	0.212867	−	0.176118i
$430$	2.50083	+	3.44210i	0.120601	+	0.165993i
$431$	−6.09708	+	5.48983i	−0.293686	+	0.264436i	−0.802781	−	0.596275i	$-0.796647\pi$
$431$	−6.09708	+	5.48983i	−0.293686	+	0.264436i	0.509095	+	0.860711i	$0.329980\pi$
$432$	−3.78839	−	3.55641i	−0.182269	−	0.171108i
$433$			8.78818i			0.422333i	0.977450	+	0.211166i	$0.0677262\pi$
$433$			8.78818i			0.422333i	−0.977450	+	0.211166i	$0.932274\pi$
$434$	2.96920	−	0.103613i	0.142526	−	0.00497357i
$435$	1.51160	+	8.93427i	0.0724758	+	0.428366i
$436$	4.04029	+	12.4347i	0.193495	+	0.595515i
$437$	−17.5157	−	19.4531i	−0.837887	−	0.930568i
$438$	19.8757	−	20.2985i	0.949696	−	0.969900i
$439$	3.55757	+	6.16189i	0.169794	+	0.294091i	0.938347	−	0.345694i	$-0.112357\pi$
$439$	3.55757	+	6.16189i	0.169794	+	0.294091i	−0.768554	+	0.639785i	$0.779023\pi$
$440$	1.78858	−	3.09791i	0.0852671	−	0.147687i
$441$	8.57958	+	18.2276i	0.408551	+	0.867979i
$442$	3.63807	+	2.64321i	0.173045	+	0.125725i
$443$	10.6857	+	1.12311i	0.507691	+	0.0533604i	0.354912	−	0.934900i	$-0.384511\pi$
$443$	10.6857	+	1.12311i	0.507691	+	0.0533604i	0.152779	+	0.988260i	$0.451178\pi$
$444$	11.1910	+	7.10120i	0.531101	+	0.337008i
$445$	0.551088	−	1.23776i	0.0261241	−	0.0586756i
$446$	−13.1197	−	2.78868i	−0.621237	−	0.132048i
$447$	11.4230	+	28.8468i	0.540290	+	1.36441i
$448$	0.487475	−	0.217038i	0.0230310	−	0.0102541i
$449$	−3.51712	+	10.8246i	−0.165983	+	0.510843i	−0.999107	−	0.0422426i	$-0.986550\pi$
$449$	−3.51712	+	10.8246i	−0.165983	+	0.510843i	0.833124	+	0.553086i	$0.186550\pi$
$450$	−2.99934	+	0.0631426i	−0.141390	+	0.00297657i
$451$	−14.3046	−	32.1288i	−0.673579	−	1.51288i
$452$	2.51074	+	11.8121i	0.118095	+	0.555594i
$453$	−1.30054	+	31.0690i	−0.0611047	+	1.45975i
$454$	3.36410	+	1.49779i	0.157885	+	0.0702949i
$455$	0.329769	−	0.366246i	0.0154598	−	0.0171699i
$456$	12.3499	−	0.777644i	0.578338	−	0.0364165i
$457$	5.07938	−	6.99117i	0.237603	−	0.327033i	−0.673518	−	0.739171i	$-0.735218\pi$
$457$	5.07938	−	6.99117i	0.237603	−	0.327033i	0.911122	+	0.412138i	$0.135218\pi$
$458$	−1.13720	−	10.8198i	−0.0531381	−	0.505575i
$459$	0.525851	−	25.2944i	0.0245446	−	1.18064i
$460$	−3.17309	+	1.83199i	−0.147946	+	0.0854168i
$461$	25.5208	−	18.5419i	1.18862	−	0.863583i	0.195503	−	0.980703i	$-0.437366\pi$
$461$	25.5208	−	18.5419i	1.18862	−	0.863583i	0.993118	+	0.117120i	$0.0373661\pi$
$462$	2.05346	−	2.59111i	0.0955357	−	0.120549i
$463$	8.93121	−	2.90193i	0.415069	−	0.134864i	−0.0940357	−	0.995569i	$-0.529977\pi$
$463$	8.93121	−	2.90193i	0.415069	−	0.134864i	0.509104	+	0.860705i	$0.329977\pi$
$464$	−5.23151			−0.242867
$465$	4.87978	−	8.31792i	0.226294	−	0.385734i
$466$	−24.6293			−1.14093
$467$	−3.38397	+	1.09952i	−0.156591	+	0.0508796i	−0.386264	−	0.922388i	$-0.626235\pi$
$467$	−3.38397	+	1.09952i	−0.156591	+	0.0508796i	0.229672	+	0.973268i	$0.426235\pi$
$468$	1.33457	−	2.42817i	0.0616904	−	0.112242i
$469$	6.73057	−	4.89005i	0.310789	−	0.225801i
$470$	9.43011	−	5.44448i	0.434979	−	0.251135i
$471$	−9.35643	+	25.1627i	−0.431122	+	1.15944i
$472$	0.835098	+	7.94543i	0.0384385	+	0.365718i
$473$	−8.94586	+	12.3129i	−0.411331	+	0.566148i
$474$	−1.05821	−	16.8057i	−0.0486053	−	0.771911i
$475$	4.78051	−	5.30929i	0.219345	−	0.243607i
$476$	2.37350	+	1.05675i	0.108789	+	0.0484360i
$477$	6.10865	−	0.772354i	0.279696	−	0.0353637i
$478$	−0.976777	−	4.59537i	−0.0446767	−	0.210188i
$479$	−8.92492	−	20.0457i	−0.407790	−	0.915911i	−0.994364	−	0.106016i	$-0.966191\pi$
$479$	−8.92492	−	20.0457i	−0.407790	−	0.915911i	0.586575	−	0.809895i	$-0.300476\pi$
$480$	0.252933	−	1.71348i	0.0115448	−	0.0782095i
$481$	−2.18395	+	6.72150i	−0.0995794	+	0.306474i
$482$	13.9524	−	6.21201i	0.635515	−	0.282949i
$483$	−3.14851	+	1.24677i	−0.143262	+	0.0567302i
$484$	1.75680	+	0.373419i	0.0798545	+	0.0169736i
$485$	3.37076	−	7.57085i	0.153058	−	0.343775i
$486$	−15.5026	+	1.63351i	−0.703214	+	0.0740976i
$487$	−30.6427	−	3.22068i	−1.38855	−	0.145943i	−0.619435	−	0.785048i	$-0.712638\pi$
$487$	−30.6427	−	3.22068i	−1.38855	−	0.145943i	−0.769119	+	0.639105i	$0.779305\pi$
$488$	2.34840	+	1.70621i	0.106307	+	0.0772365i
$489$	−3.76814	−	13.4932i	−0.170401	−	0.610185i
$490$	−3.35763	+	5.81559i	−0.151682	+	0.262721i
$491$	−16.9919	−	29.4308i	−0.766834	−	1.32820i	−0.939272	−	0.343175i	$-0.888498\pi$
$491$	−16.9919	−	29.4308i	−0.766834	−	1.32820i	0.172438	−	0.985020i	$-0.444836\pi$
$492$	−12.1673	−	11.9139i	−0.548545	−	0.537118i
$493$	−17.0441	−	18.9294i	−0.767629	−	0.852538i
$494$	2.03902	+	6.27547i	0.0917401	+	0.282347i
$495$	−3.53029	−	10.1342i	−0.158675	−	0.455497i
$496$	4.26507	+	3.57900i	0.191507	+	0.160702i
$497$		−	5.57279i		−	0.249974i
$498$	−5.78805	+	3.02631i	−0.259369	+	0.135612i
$499$	13.0651	−	11.7639i	0.584876	−	0.526624i	−0.322706	−	0.946499i	$-0.604593\pi$
$499$	13.0651	−	11.7639i	0.584876	−	0.526624i	0.907582	+	0.419875i	$0.137926\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−8.90113	−	10.7585i	−0.397673	−	0.480653i
$502$	−9.82800	−	5.67420i	−0.438645	−	0.253252i
$503$	−7.96026	+	0.836657i	−0.354930	+	0.0373047i	−0.280316	−	0.959908i	$-0.590439\pi$
$503$	−7.96026	+	0.836657i	−0.354930	+	0.0373047i	−0.0746143	+	0.997212i	$0.523773\pi$
$504$	0.462528	−	1.53255i	0.0206026	−	0.0682651i
$505$	1.45870	−	13.8786i	0.0649112	−	0.617588i
$506$	−9.74011	−	8.77003i	−0.433001	−	0.389875i
$507$	−20.3785	−	5.23117i	−0.905041	−	0.232324i
$508$	0.580478	−	2.73094i	0.0257546	−	0.121166i
$509$	−10.8782	+	2.31224i	−0.482169	+	0.102488i	−0.442582	−	0.896728i	$-0.645937\pi$
$509$	−10.8782	+	2.31224i	−0.482169	+	0.102488i	−0.0395867	+	0.999216i	$0.512604\pi$
$510$	7.02402	−	4.66728i	0.311029	−	0.206671i
$511$	8.32384	+	2.70458i	0.368225	+	0.119644i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	22.4400	−	29.5733i	0.990749	−	1.30569i
$514$	−18.7315	+	3.98151i	−0.826213	+	0.175617i
$515$	−0.243085	+	1.14363i	−0.0107116	+	0.0503942i
$516$	−1.83229	+	7.13787i	−0.0806622	+	0.314227i
$517$	28.9466	+	26.0636i	1.27307	+	1.14628i
$518$	−0.426815	+	4.06087i	−0.0187532	+	0.178424i
$519$	−1.23860	+	2.49547i	−0.0543683	+	0.109539i
$520$	0.918526	−	0.0965410i	0.0402800	−	0.00423360i
$521$	−35.2408	−	20.3463i	−1.54393	−	0.891388i	−0.998585	−	0.0531755i	$-0.983066\pi$
$521$	−35.2408	−	20.3463i	−1.54393	−	0.891388i	−0.545344	−	0.838212i	$-0.683601\pi$
$522$	−10.2539	+	11.8818i	−0.448800	+	0.520051i
$523$	12.0602	+	16.5995i	0.527357	+	0.725845i	0.986725	−	0.162401i	$-0.0519239\pi$
$523$	12.0602	+	16.5995i	0.527357	+	0.725845i	−0.459367	+	0.888246i	$0.651924\pi$
$524$	−1.54578	+	1.39183i	−0.0675279	+	0.0608024i
$525$	−0.428238	−	0.819039i	−0.0186898	−	0.0357458i
$526$			6.92508i			0.301948i
$527$	0.945426	+	27.0928i	0.0411834	+	1.18018i
$528$	6.10900	−	1.03359i	0.265860	−	0.0449812i
$529$	−2.95893	−	9.10665i	−0.128649	−	0.395941i
$530$	1.37334	+	1.52525i	0.0596542	+	0.0662527i
$531$	19.6824	+	13.6766i	0.854144	+	0.593512i
$532$	1.90614	+	3.30154i	0.0826417	+	0.143140i
$533$	4.54018	−	7.86382i	0.196657	−	0.340620i
$534$	2.26028	−	0.631209i	0.0978117	−	0.0273151i
$535$	4.20872	+	3.05781i	0.181959	+	0.132201i
$536$	15.5055	+	1.62970i	0.669737	+	0.0703922i
$537$	17.7086	−	27.9075i	0.764183	−	1.20430i
$538$	−2.44869	+	5.49985i	−0.105571	+	0.237116i
$539$	−23.4966	−	4.99436i	−1.01207	−	0.215122i
$540$	−3.39589	−	3.93293i	−0.146136	−	0.169246i
$541$	−20.1809	+	8.98512i	−0.867646	+	0.386301i	−0.791772	−	0.610817i	$-0.790841\pi$
$541$	−20.1809	+	8.98512i	−0.867646	+	0.386301i	−0.0758735	+	0.997117i	$0.524175\pi$
$542$	6.14761	−	18.9204i	0.264062	−	0.812701i
$543$	−15.4750	−	2.28432i	−0.664098	−	0.0980297i
$544$	1.98039	+	4.44802i	0.0849084	+	0.190707i
$545$	2.71837	+	12.7889i	0.116442	+	0.547818i
$546$	0.852864	+	0.0357007i	0.0364992	+	0.00152785i
$547$	7.81794	+	3.48077i	0.334271	+	0.148827i	0.567007	−	0.823713i	$-0.308101\pi$
$547$	7.81794	+	3.48077i	0.334271	+	0.148827i	−0.232736	+	0.972540i	$0.574768\pi$
$548$	−7.74594	+	8.60273i	−0.330890	+	0.367491i
$549$	8.47804	−	1.98945i	0.361834	−	0.0849075i
$550$	2.10260	−	2.89398i	0.0896552	−	0.123400i
$551$	−3.90683	−	37.1710i	−0.166437	−	1.58354i
$552$	−5.94828	−	2.21179i	−0.253176	−	0.0941401i
$553$	4.49271	−	2.59387i	0.191049	−	0.110302i
$554$	−11.1933	+	8.13237i	−0.475556	+	0.345511i
$555$	10.3874	+	8.23208i	0.440921	+	0.349432i
$556$	4.29889	−	1.39679i	0.182314	−	0.0592373i
$557$	−27.3110			−1.15721			−0.578603	−	0.815610i	$-0.696402\pi$
$557$	−27.3110			−1.15721			−0.578603	+	0.815610i	$0.696402\pi$
$558$	16.4882	−	2.67187i	0.698002	−	0.113109i
$559$	−3.92955			−0.166202
$560$	0.507491	−	0.164894i	0.0214454	−	0.00696804i
$561$	23.6428	+	18.7371i	0.998201	+	0.791079i
$562$	−3.61339	+	2.62529i	−0.152422	+	0.110741i
$563$	16.7486	−	9.66979i	0.705868	−	0.407533i	−0.103661	−	0.994613i	$-0.533056\pi$
$563$	16.7486	−	9.66979i	0.705868	−	0.407533i	0.809529	+	0.587080i	$0.199723\pi$
$564$	17.6777	+	6.57322i	0.744365	+	0.276782i
$565$	1.26228	+	12.0098i	0.0531046	+	0.505257i
$566$	7.61475	−	10.4808i	0.320072	−	0.440541i
$567$	−2.57414	−	4.05432i	−0.108104	−	0.170265i
$568$	6.98813	−	7.76111i	0.293216	−	0.325649i
$569$	22.0126	+	9.80062i	0.922814	+	0.410863i	0.812452	−	0.583028i	$-0.198132\pi$
$569$	22.0126	+	9.80062i	0.922814	+	0.410863i	0.110362	+	0.993891i	$0.464799\pi$
$570$	12.3636	+	0.517536i	0.517853	+	0.0216772i
$571$	9.43585	+	44.3922i	0.394878	+	1.85776i	0.503966	+	0.863724i	$0.331874\pi$
$571$	9.43585	+	44.3922i	0.394878	+	1.85776i	−0.109087	+	0.994032i	$0.534793\pi$
$572$	1.34378	+	3.01818i	0.0561863	+	0.126196i
$573$	−21.8698	−	3.22827i	−0.913623	−	0.134863i
$574$	1.62118	−	4.98947i	0.0676666	−	0.208256i
$575$	−3.34721	+	1.49027i	−0.139588	+	0.0621487i
$576$	2.56593	−	1.55435i	0.106914	−	0.0647646i
$577$	−22.8442	−	4.85569i	−0.951017	−	0.202145i	−0.293817	−	0.955862i	$-0.594926\pi$
$577$	−22.8442	−	4.85569i	−0.951017	−	0.202145i	−0.657199	+	0.753717i	$0.728259\pi$
$578$	−2.72791	+	6.12698i	−0.113466	+	0.254849i
$579$	25.4032	−	40.0336i	1.05572	−	1.66374i
$580$	−5.20285	−	0.546842i	−0.216037	−	0.0227064i
$581$	−1.62791	−	1.18274i	−0.0675370	−	0.0490685i
$582$	13.8251	−	3.86082i	0.573069	−	0.160036i
$583$	−3.67093	+	6.35823i	−0.152034	+	0.263331i
$584$	8.20097	+	14.2045i	0.339359	+	0.587786i
$585$	1.58107	−	2.27537i	0.0653692	−	0.0940750i
$586$	−1.94342	−	2.15838i	−0.0802818	−	0.0891620i
$587$	5.48446	+	16.8794i	0.226368	+	0.696688i	0.998150	+	0.0608012i	$0.0193656\pi$
$587$	5.48446	+	16.8794i	0.226368	+	0.696688i	−0.771782	+	0.635887i	$0.780634\pi$
$588$	−11.4682	+	1.94032i	−0.472940	+	0.0800174i
$589$	−22.2444	+	32.9770i	−0.916566	+	1.35879i
$590$			7.98920i			0.328910i
$591$	−20.3831	−	38.9843i	−0.838449	−	1.60360i
$592$	−5.68665	+	5.12028i	−0.233720	+	0.210442i
$593$	−9.94222	−	13.6843i	−0.408278	−	0.561947i	0.554519	−	0.832171i	$-0.312902\pi$
$593$	−9.94222	−	13.6843i	−0.408278	−	0.561947i	−0.962797	+	0.270224i	$0.912902\pi$
$594$	9.62629	−	15.9006i	0.394972	−	0.652408i
$595$	2.25004	+	1.29906i	0.0922425	+	0.0532562i
$596$	−17.8149	+	1.87242i	−0.729725	+	0.0766972i
$597$	4.75419	−	9.57853i	0.194576	−	0.392023i
$598$	0.353724	−	3.36545i	0.0144648	−	0.137624i
$599$	28.1265	+	25.3252i	1.14922	+	1.03476i	0.998936	+	0.0461180i	$0.0146850\pi$
$599$	28.1265	+	25.3252i	1.14922	+	1.03476i	0.150283	+	0.988643i	$0.451982\pi$
$600$	0.430655	−	1.67766i	0.0175814	−	0.0684901i
$601$	−4.58335	+	21.5630i	−0.186959	+	0.879572i	0.780226	+	0.625498i	$0.215104\pi$
$601$	−4.58335	+	21.5630i	−0.186959	+	0.879572i	−0.967185	+	0.254074i	$0.918229\pi$
$602$	−2.22071	+	0.472027i	−0.0905094	+	0.0192384i
$603$	34.0925	−	32.0218i	1.38836	−	1.30403i
$604$	−17.0747	−	5.54791i	−0.694760	−	0.225741i
$605$	1.70814	+	0.555009i	0.0694459	+	0.0225643i
$606$	20.1317	−	13.3770i	0.817793	−	0.543403i
$607$	7.08341	−	1.50563i	0.287507	−	0.0611115i	−0.0619007	−	0.998082i	$-0.519716\pi$
$607$	7.08341	−	1.50563i	0.287507	−	0.0611115i	0.349408	+	0.936971i	$0.386383\pi$
$608$	−1.48540	+	6.98823i	−0.0602407	+	0.283410i
$609$	−4.68331	−	1.20221i	−0.189777	−	0.0487159i
$610$	2.15718	+	1.94234i	0.0873418	+	0.0786429i
$611$	−1.05123	+	10.0018i	−0.0425282	+	0.404629i
$612$	13.9839	+	4.22039i	0.565266	+	0.170599i
$613$	−9.45474	+	0.993733i	−0.381873	+	0.0401365i	−0.293521	−	0.955953i	$-0.594827\pi$
$613$	−9.45474	+	0.993733i	−0.381873	+	0.0401365i	−0.0883527	+	0.996089i	$0.528160\pi$
$614$	14.7615	+	8.52255i	0.595725	+	0.343942i
$615$	−10.8553	−	13.1204i	−0.437729	−	0.529066i
$616$	1.12196	+	1.54425i	0.0452052	+	0.0622196i
$617$	−8.53848	+	7.68808i	−0.343746	+	0.309511i	−0.822862	−	0.568241i	$-0.807624\pi$
$617$	−8.53848	+	7.68808i	−0.343746	+	0.309511i	0.479116	+	0.877752i	$0.340957\pi$
$618$	−1.79458	+	0.938303i	−0.0721885	+	0.0377441i
$619$		−	10.9887i		−	0.441672i	−0.975311	−	0.220836i	$-0.929121\pi$
$619$		−	10.9887i		−	0.441672i	0.975311	−	0.220836i	$-0.0708785\pi$
$620$	3.86759	+	4.00521i	0.155326	+	0.160853i
$621$	−16.6822	+	9.17453i	−0.669433	+	0.368161i
$622$	2.69886	+	8.30625i	0.108215	+	0.333050i
$623$	0.483772	+	0.537283i	0.0193819	+	0.0215258i
$624$	1.14300	+	1.11919i	0.0457566	+	0.0448034i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	14.7269	−	25.5077i	0.588605	−	1.01949i
$627$	11.9060	+	42.6339i	0.475480	+	1.70263i
$628$	−12.5394	−	9.11040i	−0.500376	−	0.363544i
$629$	−37.0539	−	3.89452i	−1.47743	−	0.155285i
$630$	0.620189	−	1.47581i	0.0247089	−	0.0587975i
$631$	1.81735	−	4.08185i	0.0723477	−	0.162496i	−0.873751	−	0.486373i	$-0.838320\pi$
$631$	1.81735	−	4.08185i	0.0723477	−	0.162496i	0.946099	+	0.323877i	$0.104986\pi$
$632$	9.50954	+	2.02132i	0.378269	+	0.0804036i
$633$	−39.6669	+	15.7077i	−1.57662	+	0.624323i
$634$	18.5444	−	8.25651i	0.736494	−	0.327908i
$635$	0.862759	−	2.65530i	0.0342375	−	0.105372i
$636$	−0.519127	+	3.51680i	−0.0205847	+	0.139450i
$637$	−2.52263	−	5.66592i	−0.0999502	−	0.224492i
$638$	−3.89085	−	18.3050i	−0.154040	−	0.724702i
$639$	−3.93006	−	31.0833i	−0.155471	−	1.22964i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	−7.79429	+	8.65644i	−0.307856	+	0.341909i	−0.877142	−	0.480231i	$-0.840553\pi$
$641$	−7.79429	+	8.65644i	−0.307856	+	0.341909i	0.569286	+	0.822139i	$0.307220\pi$
$642$	0.566252	+	8.99278i	0.0223482	+	0.354917i
$643$	−14.3459	+	19.7454i	−0.565746	+	0.778683i	−0.992043	−	0.125901i	$-0.959818\pi$
$643$	−14.3459	+	19.7454i	−0.565746	+	0.778683i	0.426297	+	0.904583i	$0.359818\pi$
$644$	−0.204366	−	1.94441i	−0.00805316	−	0.0766207i
$645$	−2.56837	+	6.90724i	−0.101129	+	0.271972i
$646$	−30.1252	+	17.3928i	−1.18526	+	0.684311i
$647$	33.9661	−	24.6778i	1.33534	−	0.970184i	0.335743	−	0.941954i	$-0.391013\pi$
$647$	33.9661	−	24.6778i	1.33534	−	0.970184i	0.999601	−	0.0282304i	$-0.00898720\pi$
$648$	1.49905	−	8.87428i	0.0588883	−	0.348615i
$649$	−27.1799	+	8.83127i	−1.06690	+	0.346658i
$650$	0.923585			0.0362260
$651$	2.99568	+	4.18407i	0.117410	+	0.163987i
$652$	8.08839			0.316766
$653$	−28.8170	+	9.36320i	−1.12769	+	0.366410i	−0.812700	−	0.582683i	$-0.802003\pi$
$653$	−28.8170	+	9.36320i	−1.12769	+	0.366410i	−0.314995	+	0.949093i	$0.602003\pi$
$654$	−14.0655	+	17.7482i	−0.550006	+	0.694010i
$655$	−1.68280	+	1.22263i	−0.0657525	+	0.0477720i
$656$	8.51445	−	4.91582i	0.332433	−	0.191930i
$657$	48.3352	+	9.21517i	1.88574	+	0.359518i
$658$	0.607356	+	5.77860i	0.0236772	+	0.225273i
$659$	−9.40858	+	12.9498i	−0.366506	+	0.504453i	−0.951947	−	0.306263i	$-0.900921\pi$
$659$	−9.40858	+	12.9498i	−0.366506	+	0.504453i	0.585441	+	0.810715i	$0.300921\pi$
$660$	6.18357	−	0.389364i	0.240695	−	0.0151560i
$661$	21.8829	−	24.3034i	0.851146	−	0.945293i	−0.147899	−	0.989003i	$-0.547251\pi$
$661$	21.8829	−	24.3034i	0.851146	−	0.945293i	0.999044	+	0.0437095i	$0.0139176\pi$
$662$	−8.02823	−	3.57440i	−0.312026	−	0.138923i
$663$	−0.325755	+	7.78205i	−0.0126513	+	0.302230i
$664$	−0.784024	−	3.68854i	−0.0304260	−	0.143143i
$665$	1.55060	+	3.48269i	0.0601295	+	0.135053i
$666$	0.483176	+	22.9513i	0.0187227	+	0.889346i
$667$	−5.92328	+	18.2300i	−0.229350	+	0.705867i
$668$	7.36476	−	3.27900i	0.284951	−	0.126868i
$669$	−8.55330	−	21.5998i	−0.330689	−	0.835098i
$670$	15.2502	+	3.24154i	0.589168	+	0.125231i
$671$	−4.22343	+	9.48597i	−0.163044	+	0.366202i
$672$	0.780384	+	0.495189i	0.0301040	+	0.0191023i
$673$	−45.5304	−	4.78544i	−1.75507	−	0.184465i	−0.828348	−	0.560215i	$-0.810719\pi$
$673$	−45.5304	−	4.78544i	−1.75507	−	0.184465i	−0.926721	+	0.375749i	$0.877385\pi$
$674$	−1.89573	−	1.37733i	−0.0730210	−	0.0530528i
$675$	−2.96619	−	4.26635i	−0.114169	−	0.164212i
$676$	6.07350	−	10.5196i	0.233596	−	0.404600i
$677$	9.16902	+	15.8812i	0.352394	+	0.610364i	0.986668	−	0.162744i	$-0.0520344\pi$
$677$	9.16902	+	15.8812i	0.352394	+	0.610364i	−0.634274	+	0.773108i	$0.718701\pi$
$678$	−14.6335	+	14.9448i	−0.561996	+	0.573952i
$679$	2.95902	+	3.28632i	0.113557	+	0.126118i
$680$	1.50459	+	4.63066i	0.0576985	+	0.177578i
$681$	1.06402	+	6.28884i	0.0407733	+	0.240989i
$682$	−9.35079	+	17.5852i	−0.358060	+	0.673373i
$683$		−	3.32817i		−	0.127349i	−0.997971	−	0.0636745i	$-0.979718\pi$
$683$		−	3.32817i		−	0.127349i	0.997971	−	0.0636745i	$-0.0202819\pi$
$684$	12.9602	+	17.0707i	0.495546	+	0.652715i
$685$	−8.60273	+	7.74594i	−0.328694	+	0.295957i
$686$	−4.30175	−	5.92085i	−0.164242	−	0.226059i
$687$	14.5186	−	12.0122i	0.553921	−	0.458292i
$688$	−3.68465	−	2.12733i	−0.140476	−	0.0811038i
$689$	−1.88521	+	0.198143i	−0.0718207	+	0.00754866i
$690$	−5.68450	−	2.82144i	−0.216405	−	0.107410i
$691$	−1.35809	+	12.9214i	−0.0516643	+	0.491553i	0.937842	+	0.347063i	$0.112821\pi$
$691$	−1.35809	+	12.9214i	−0.0516643	+	0.491553i	−0.989506	+	0.144490i	$0.953846\pi$
$692$	−1.19532	−	1.07627i	−0.0454393	−	0.0409137i
$693$	5.70636	+	0.478572i	0.216767	+	0.0181795i
$694$	−3.97178	+	18.6858i	−0.150767	+	0.709302i
$695$	4.42134	−	0.939786i	0.167711	−	0.0356481i
$696$	−5.01481	−	7.54704i	−0.190086	−	0.286070i
$697$	45.5270	+	14.7926i	1.72446	+	0.560310i
$698$	−21.8862	−	7.11125i	−0.828404	−	0.269165i
$699$	−23.6091	−	35.5306i	−0.892980	−	1.34389i
$700$	0.521947	−	0.110943i	0.0197277	−	0.00419326i
$701$	−5.32543	+	25.0542i	−0.201139	+	0.946283i	0.755532	+	0.655112i	$0.227378\pi$
$701$	−5.32543	+	25.0542i	−0.201139	+	0.946283i	−0.956671	+	0.291172i	$0.905955\pi$
$702$	4.78220	−	0.402332i	0.180492	−	0.0151850i
$703$	−40.6274	−	36.5811i	−1.53229	−	1.37968i
$704$	−0.373915	+	3.55756i	−0.0140924	+	0.134081i
$705$	16.8938	+	8.38503i	0.636256	+	0.315799i
$706$	20.3314	−	2.13692i	0.765182	−	0.0804239i
$707$	6.44887	+	3.72325i	0.242535	+	0.140027i
$708$	−10.6617	+	8.82104i	−0.400690	+	0.331515i
$709$	−11.3362	−	15.6030i	−0.425741	−	0.585983i	0.541228	−	0.840876i	$-0.317960\pi$
$709$	−11.3362	−	15.6030i	−0.425741	−	0.585983i	−0.966969	+	0.254893i	$0.917960\pi$
$710$	7.76111	−	6.98813i	0.291269	−	0.262260i
$711$	23.2297	−	17.6362i	0.871182	−	0.661408i
$712$			1.35490i			0.0507771i
$713$	17.3006	−	10.8100i	0.647911	−	0.404838i
$714$	0.750705	+	4.43701i	0.0280944	+	0.166051i
$715$	1.02093	+	3.14211i	0.0381807	+	0.117508i
$716$	12.7687	+	14.1811i	0.477188	+	0.529971i
$717$	5.69302	−	5.81413i	0.212610	−	0.217133i
$718$	−1.36390	−	2.36235i	−0.0509004	−	0.0881621i
$719$	15.2004	−	26.3279i	0.566880	−	0.981864i	−0.429992	−	0.902833i	$-0.641484\pi$
$719$	15.2004	−	26.3279i	0.566880	−	0.981864i	0.996872	−	0.0790319i	$-0.0251829\pi$
$720$	2.71435	−	1.27762i	0.101158	−	0.0476142i
$721$	−0.504731	−	0.366708i	−0.0187972	−	0.0136569i
$722$	−31.8663	−	3.34928i	−1.18594	−	0.124647i
$723$	22.3360	+	14.1732i	0.830685	+	0.527107i
$724$	3.67337	−	8.25054i	0.136520	−	0.306629i
$725$	−5.11719	−	1.08769i	−0.190048	−	0.0403959i
$726$	1.14533	+	2.89233i	0.0425072	+	0.107344i
$727$	−5.87174	+	2.61427i	−0.217771	+	0.0969578i	−0.512723	−	0.858554i	$-0.671363\pi$
$727$	−5.87174	+	2.61427i	−0.217771	+	0.0969578i	0.294952	+	0.955512i	$0.404696\pi$
$728$	−0.152294	+	0.468711i	−0.00564438	+	0.0173716i
$729$	−17.2170	−	20.7984i	−0.637667	−	0.770312i
$730$	6.67127	+	14.9839i	0.246915	+	0.554580i
$731$	−4.30706	−	20.2631i	−0.159302	−	0.749459i
$732$	−0.210277	+	5.02336i	−0.00777205	+	0.185669i
$733$	−2.19460	−	0.977098i	−0.0810593	−	0.0360899i	0.365807	−	0.930691i	$-0.380793\pi$
$733$	−2.19460	−	0.977098i	−0.0810593	−	0.0360899i	−0.446866	+	0.894601i	$0.647460\pi$
$734$	15.8783	−	17.6347i	0.586080	−	0.650908i
$735$	−11.6082	+	0.730938i	−0.428174	+	0.0269610i
$736$	2.15363	−	2.96422i	0.0793838	−	0.109262i
$737$	5.82968	+	55.4657i	0.214739	+	2.04310i
$738$	5.52375	−	28.9731i	0.203332	−	1.06651i
$739$	9.71635	−	5.60974i	0.357422	−	0.206358i	−0.310527	−	0.950564i	$-0.600506\pi$
$739$	9.71635	−	5.60974i	0.357422	−	0.206358i	0.667949	+	0.744207i	$0.267172\pi$
$740$	−6.19071	+	4.49781i	−0.227575	+	0.165343i
$741$	−7.09851	+	8.95705i	−0.260770	+	0.329046i
$742$	−1.04159	+	0.338433i	−0.0382379	+	0.0124243i
$743$	−5.98609			−0.219608			−0.109804	−	0.993953i	$-0.535022\pi$
$743$	−5.98609			−0.219608			−0.109804	+	0.993953i	$0.535022\pi$
$744$	−1.07470	+	9.58358i	−0.0394005	+	0.351351i
$745$	−17.9130			−0.656281
$746$	−17.3276	+	5.63009i	−0.634410	+	0.206132i
$747$	−9.91409	−	5.44896i	−0.362737	−	0.199367i
$748$	−14.0907	+	10.2375i	−0.515207	+	0.374319i
$749$	−2.40406	+	1.38798i	−0.0878424	+	0.0507159i
$750$	0.603659	−	1.62345i	0.0220425	−	0.0592801i
$751$	−2.20658	−	20.9942i	−0.0805192	−	0.766089i	−0.958056	−	0.286580i	$-0.907481\pi$
$751$	−2.20658	−	20.9942i	−0.0805192	−	0.766089i	0.877537	−	0.479509i	$-0.159185\pi$
$752$	−6.40037	+	8.80935i	−0.233397	+	0.321244i
$753$	−1.23524	−	19.6172i	−0.0450147	−	0.714889i
$754$	3.23307	−	3.59069i	0.117742	−	0.130765i
$755$	−16.4012	−	7.30231i	−0.596902	−	0.265758i
$756$	2.65424	−	0.801819i	0.0965338	−	0.0291619i
$757$	−2.19536	−	10.3284i	−0.0797917	−	0.375390i	0.920075	−	0.391743i	$-0.128128\pi$
$757$	−2.19536	−	10.3284i	−0.0797917	−	0.375390i	−0.999866	+	0.0163528i	$0.994794\pi$
$758$	0.427424	+	0.960009i	0.0155247	+	0.0348691i
$759$	3.31510	−	22.4580i	0.120330	−	0.815172i
$760$	−2.20773	+	6.79469i	−0.0800827	+	0.246469i
$761$	0.700532	−	0.311897i	0.0253943	−	0.0113063i	−0.394000	−	0.919110i	$-0.628909\pi$
$761$	0.700532	−	0.311897i	0.0253943	−	0.0113063i	0.419394	+	0.907804i	$0.362242\pi$
$762$	4.49611	−	1.78041i	0.162877	−	0.0644975i
$763$	−6.82427	−	1.45054i	−0.247055	−	0.0525132i
$764$	5.19132	−	11.6599i	0.187815	−	0.421840i
$765$	13.4662	+	5.65898i	0.486870	+	0.204601i
$766$	−29.7489	−	3.12673i	−1.07487	−	0.112974i
$767$	−5.96950	−	4.33709i	−0.215546	−	0.156603i
$768$	0.465870	+	1.66822i	0.0168107	+	0.0601968i
$769$	−10.1381	+	17.5598i	−0.365591	+	0.633222i	−0.988871	−	0.148777i	$-0.952466\pi$
$769$	−10.1381	+	17.5598i	−0.365591	+	0.633222i	0.623280	+	0.781999i	$0.285800\pi$
$770$	0.954399	+	1.65307i	0.0343942	+	0.0595724i
$771$	−23.6994	−	23.2057i	−0.853513	−	0.835734i
$772$	18.3168	+	20.3429i	0.659236	+	0.732156i
$773$	−1.35939	−	4.18378i	−0.0488940	−	0.150480i	0.923629	−	0.383289i	$-0.125209\pi$
$773$	−1.35939	−	4.18378i	−0.0488940	−	0.150480i	−0.972523	+	0.232808i	$0.925209\pi$
$774$	−12.0536	+	4.19892i	−0.433257	+	0.150927i
$775$	3.42775	+	4.38754i	0.123128	+	0.157605i
$776$			8.28733i			0.297498i
$777$	−6.26739	+	3.27693i	−0.224842	+	0.117559i
$778$	6.01267	−	5.41383i	0.215565	−	0.194095i
$779$	41.2865	+	56.8259i	1.47924	+	2.03600i
$780$	1.01975	+	1.23253i	0.0365129	+	0.0441318i
$781$	32.3533	+	18.6792i	1.15769	+	0.668394i
$782$	17.7420	−	1.86476i	0.634454	−	0.0666838i
$783$	−26.9699	−	3.40277i	−0.963826	−	0.121605i
$784$	0.701936	−	6.67848i	0.0250691	−	0.238517i
$785$	−11.5184	−	10.3712i	−0.411109	−	0.370164i
$786$	−3.48962	−	0.895788i	−0.124471	−	0.0319517i
$787$	−1.11269	+	5.23478i	−0.0396630	+	0.186600i	−0.993519	−	0.113664i	$-0.963741\pi$
$787$	−1.11269	+	5.23478i	−0.0396630	+	0.186600i	0.953856	+	0.300264i	$0.0970746\pi$
$788$	24.8435	−	5.28064i	0.885012	−	0.188115i
$789$	−9.99020	+	6.63823i	−0.355661	+	0.236327i
$790$	9.24616	+	3.00426i	0.328964	+	0.106887i
$791$	−6.12845	−	1.99125i	−0.217903	−	0.0708008i
$792$	7.34702	+	7.82213i	0.261065	+	0.277947i
$793$	−2.62238	+	0.557403i	−0.0931233	+	0.0197940i
$794$	−4.20982	+	19.8056i	−0.149401	+	0.702875i
$795$	−0.883889	+	3.44327i	−0.0313483	+	0.122120i
$796$	4.58809	+	4.13113i	0.162621	+	0.146424i
$797$	−3.87177	+	36.8374i	−0.137145	+	1.30485i	0.682038	+	0.731317i	$0.261094\pi$
$797$	−3.87177	+	36.8374i	−0.137145	+	1.30485i	−0.819183	+	0.573532i	$0.805573\pi$
$798$	−2.93565	+	5.91460i	−0.103921	+	0.209375i
$799$	−52.7275	+	5.54188i	−1.86537	+	0.196058i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	3.07724	+	2.65564i	0.108729	+	0.0938324i
$802$	3.32455	+	4.57585i	0.117394	+	0.161579i
$803$	−43.6020	+	39.2594i	−1.53868	+	1.38544i
$804$	12.5122	+	23.9306i	0.441273	+	0.843968i
$805$		−	1.95512i		−	0.0689091i
$806$	−5.09228	+	0.715544i	−0.179368	+	0.0252040i
$807$	−10.2814	+	1.73953i	−0.361923	+	0.0612343i
$808$	4.31234	+	13.2720i	0.151708	+	0.466908i
$809$	20.9667	+	23.2859i	0.737151	+	0.818689i	0.988818	−	0.149125i	$-0.0476456\pi$
$809$	20.9667	+	23.2859i	0.737151	+	0.818689i	−0.251668	+	0.967814i	$0.580979\pi$
$810$	2.41846	−	8.66897i	0.0849759	−	0.304597i
$811$	−2.68607	−	4.65241i	−0.0943207	−	0.163368i	0.815004	−	0.579455i	$-0.196735\pi$
$811$	−2.68607	−	4.65241i	−0.0943207	−	0.163368i	−0.909325	+	0.416087i	$0.863401\pi$
$812$	1.39579	−	2.41758i	0.0489826	−	0.0848403i
$813$	33.1878	−	9.26807i	1.16395	−	0.325045i
$814$	−22.1451	−	16.0894i	−0.776186	−	0.563932i
$815$	8.04408	+	0.845467i	0.281772	+	0.0296154i
$816$	−4.51841	+	7.12070i	−0.158176	+	0.249274i
$817$	12.3635	−	27.7689i	0.432544	−	0.971511i
$818$	−9.44565	−	2.00773i	−0.330259	−	0.0701988i
$819$	0.766034	+	1.26457i	0.0267674	+	0.0441878i
$820$	8.98165	−	3.99889i	0.313653	−	0.139647i
$821$	13.7853	−	42.4267i	0.481110	−	1.48070i	−0.356428	−	0.934323i	$-0.616005\pi$
$821$	13.7853	−	42.4267i	0.481110	−	1.48070i	0.837537	−	0.546380i	$-0.183995\pi$
$822$	−19.8355	−	2.92798i	−0.691842	−	0.102125i
$823$	12.6343	+	28.3772i	0.440405	+	0.989166i	0.988286	+	0.152610i	$0.0487679\pi$
$823$	12.6343	+	28.3772i	0.440405	+	0.989166i	−0.547881	+	0.836556i	$0.684565\pi$
$824$	−0.243085	−	1.14363i	−0.00846828	−	0.0398401i
$825$	6.19040	+	0.259128i	0.215522	+	0.00902169i
$826$	−3.89453	−	1.73396i	−0.135508	−	0.0603321i
$827$	−2.85621	+	3.17214i	−0.0993202	+	0.110306i	−0.790755	−	0.612132i	$-0.790312\pi$
$827$	−2.85621	+	3.17214i	−0.0993202	+	0.110306i	0.691435	+	0.722438i	$0.256979\pi$
$828$	−2.51114	−	10.7012i	−0.0872681	−	0.371894i
$829$	−12.7413	+	17.5370i	−0.442525	+	0.609084i	−0.970771	−	0.240008i	$-0.922850\pi$
$829$	−12.7413	+	17.5370i	−0.442525	+	0.609084i	0.528246	+	0.849092i	$0.322850\pi$
$830$	−0.394171	−	3.75029i	−0.0136819	−	0.130174i
$831$	−22.4615	−	8.35200i	−0.779180	−	0.289728i
$832$	−0.799848	+	0.461793i	−0.0277298	+	0.0160098i
$833$	26.4519	−	19.2184i	0.916505	−	0.665880i
$834$	6.13585	+	4.86269i	0.212467	+	0.168381i
$835$	7.66717	−	2.49121i	0.265333	−	0.0862120i
$836$	−25.5565			−0.883889
$837$	19.6597	+	21.2249i	0.679539	+	0.733640i
$838$	24.3336			0.840589
$839$	35.3767	−	11.4946i	1.22134	−	0.396837i	0.373770	−	0.927521i	$-0.378065\pi$
$839$	35.3767	−	11.4946i	1.22134	−	0.396837i	0.847570	+	0.530684i	$0.178065\pi$
$840$	0.724348	+	0.574049i	0.0249924	+	0.0198066i
$841$	1.31972	−	0.958836i	0.0455078	−	0.0330633i
$842$	−20.3547	+	11.7518i	−0.701471	+	0.404994i
$843$	−7.25099	−	2.69618i	−0.249737	−	0.0928615i
$844$	−2.57474	−	24.4970i	−0.0886261	−	0.843221i
$845$	7.13982	−	9.82712i	0.245617	−	0.338063i
$846$	7.46285	+	31.8030i	0.256578	+	1.09341i
$847$	−0.641285	+	0.712219i	−0.0220348	+	0.0244721i
$848$	−1.87499	−	0.834797i	−0.0643873	−	0.0286671i
$849$	22.4191	+	0.938457i	0.769420	+	0.0322077i
$850$	1.01231	+	4.76257i	0.0347221	+	0.163355i
$851$	11.4038	+	25.6133i	0.390916	+	0.878012i
$852$	17.8949	+	2.64153i	0.613070	+	0.0904974i
$853$	−11.9929	+	36.9102i	−0.410628	+	1.26378i	0.505476	+	0.862841i	$0.331317\pi$
$853$	−11.9929	+	36.9102i	−0.410628	+	1.26378i	−0.916104	+	0.400942i	$0.868683\pi$
$854$	−1.41503	+	0.630013i	−0.0484214	+	0.0215586i
$855$	11.1048	+	18.3319i	0.379777	+	0.626938i
$856$	−5.08858	−	1.08161i	−0.173924	−	0.0369687i
$857$	−3.04907	+	6.84833i	−0.104154	+	0.233935i	−0.958104	−	0.286422i	$-0.907534\pi$
$857$	−3.04907	+	6.84833i	−0.104154	+	0.233935i	0.853949	+	0.520356i	$0.174201\pi$
$858$	−3.06594	+	4.83171i	−0.104670	+	0.164952i
$859$	35.6297	+	3.74483i	1.21567	+	0.127772i	0.690567	−	0.723268i	$-0.257361\pi$
$859$	35.6297	+	3.74483i	1.21567	+	0.127772i	0.525101	+	0.851040i	$0.324028\pi$
$860$	−3.44210	−	2.50083i	−0.117374	−	0.0852776i
$861$	8.75189	−	2.44407i	0.298264	−	0.0832936i
$862$	4.10221	−	7.10524i	0.139722	−	0.242005i
$863$	19.2181	+	33.2867i	0.654192	+	1.13309i	0.982096	+	0.188383i	$0.0603245\pi$
$863$	19.2181	+	33.2867i	0.654192	+	1.13309i	−0.327904	+	0.944711i	$0.606342\pi$
$864$	4.70197	+	2.21167i	0.159964	+	0.0752426i
$865$	−1.07627	−	1.19532i	−0.0365944	−	0.0406422i
$866$	−2.71570	−	8.35805i	−0.0922831	−	0.284018i
$867$	−11.4538	+	1.93788i	−0.388990	+	0.0658138i
$868$	−2.79185	+	1.01607i	−0.0947617	+	0.0344878i
$869$			34.7771i			1.17973i
$870$	−4.19846	−	8.02989i	−0.142341	−	0.272239i
$871$	−10.7010	+	9.63518i	−0.362588	+	0.326476i
$872$	−7.68508	−	10.5776i	−0.260250	−	0.358203i
$873$	18.8221	+	16.2434i	0.637032	+	0.549754i
$874$	22.6697	+	13.0884i	0.766815	+	0.442721i
$875$	0.530685	−	0.0557772i	0.0179404	−	0.00188561i
$876$	−12.6303	+	25.4469i	−0.426738	+	0.859772i
$877$	−1.37193	+	13.0530i	−0.0463267	+	0.440769i	0.946633	+	0.322314i	$0.104461\pi$
$877$	−1.37193	+	13.0530i	−0.0463267	+	0.440769i	−0.992959	+	0.118455i	$0.962206\pi$
$878$	−5.28758	−	4.76096i	−0.178447	−	0.160675i
$879$	1.25079	−	4.87258i	0.0421882	−	0.164348i
$880$	−0.743733	+	3.49899i	−0.0250712	+	0.117951i
$881$	48.3176	−	10.2702i	1.62786	−	0.346013i	0.698622	−	0.715491i	$-0.253797\pi$
$881$	48.3176	−	10.2702i	1.62786	−	0.346013i	0.929239	+	0.369478i	$0.120464\pi$
$882$	−13.7923	−	14.6842i	−0.464410	−	0.494443i
$883$	−14.7448	−	4.79088i	−0.496202	−	0.161226i	0.0502159	−	0.998738i	$-0.484009\pi$
$883$	−14.7448	−	4.79088i	−0.496202	−	0.161226i	−0.546418	+	0.837513i	$0.684009\pi$
$884$	−4.27681	−	1.38962i	−0.143845	−	0.0467380i
$885$	−11.5253	+	7.65827i	−0.387419	+	0.257430i
$886$	−10.5097	+	2.23391i	−0.353081	+	0.0750497i
$887$	−11.5583	+	54.3773i	−0.388088	+	1.82581i	0.157203	+	0.987566i	$0.449752\pi$
$887$	−11.5583	+	54.3773i	−0.388088	+	1.82581i	−0.545292	+	0.838246i	$0.683581\pi$
$888$	−12.8377	−	3.29543i	−0.430804	−	0.110587i
$889$	1.10714	+	0.996874i	0.0371323	+	0.0334341i
$890$	−0.141626	+	1.34748i	−0.00474731	+	0.0451676i
$891$	32.1659	−	1.35493i	1.07760	−	0.0453917i
$892$	13.3394	−	1.40202i	0.446635	−	0.0469432i
$893$	−67.3721	−	38.8973i	−2.25452	−	1.30165i
$894$	−19.7781	−	23.9051i	−0.661479	−	0.799505i
$895$	11.2164	+	15.4381i	0.374923	+	0.516038i
$896$	−0.396548	+	0.357053i	−0.0132477	+	0.0119283i
$897$	5.19412	−	2.71577i	0.173426	−	0.0906768i
$898$		−	11.3816i		−	0.379810i
$899$	29.0568	+	2.03258i	0.969099	+	0.0677902i
$900$	2.83303	−	0.986898i	0.0944342	−	0.0328966i
$901$	−3.08807	−	9.50409i	−0.102878	−	0.316627i
$902$	23.5329	+	26.1359i	0.783558	+	0.870230i
$903$	−2.80968	−	2.75115i	−0.0935001	−	0.0915525i
$904$	−6.03798	−	10.4581i	−0.200820	−	0.347831i
$905$	4.51567	−	7.82137i	0.150106	−	0.259991i
$906$	−8.36396	−	29.9503i	−0.277874	−	0.995031i
$907$	44.8404	+	32.5785i	1.48890	+	1.08175i	0.974550	+	0.224171i	$0.0719674\pi$
$907$	44.8404	+	32.5785i	1.48890	+	1.08175i	0.514352	+	0.857579i	$0.328033\pi$
$908$	−3.66229	−	0.384922i	−0.121537	−	0.0127741i
$909$	38.5956	+	16.2193i	1.28013	+	0.537960i
$910$	−0.200453	+	0.450225i	−0.00664495	+	0.0149248i
$911$	−41.9322	−	8.91297i	−1.38928	−	0.295300i	−0.548259	−	0.836308i	$-0.684709\pi$
$911$	−41.9322	−	8.91297i	−1.38928	−	0.295300i	−0.841017	+	0.541009i	$0.818043\pi$
$912$	−11.5052	+	4.55592i	−0.380974	+	0.150862i
$913$	12.3231	−	5.48658i	0.407834	−	0.181579i
$914$	−2.67039	+	8.21861i	−0.0883286	+	0.271848i
$915$	−0.734209	+	4.97386i	−0.0242722	+	0.164431i
$916$	4.42504	+	9.93881i	0.146208	+	0.328387i
$917$	−0.230768	−	1.08568i	−0.00762064	−	0.0358523i
$918$	7.31629	+	24.2189i	0.241474	+	0.799343i
$919$	−17.9198	−	7.97840i	−0.591119	−	0.263183i	0.0893020	−	0.996005i	$-0.471536\pi$
$919$	−17.9198	−	7.97840i	−0.591119	−	0.263183i	−0.680421	+	0.732822i	$0.738203\pi$
$920$	2.45168	−	2.72286i	0.0808294	−	0.0897701i
$921$	1.85531	+	29.4646i	0.0611346	+	0.970893i
$922$	−18.5419	+	25.5208i	−0.610646	+	0.840482i
$923$	1.00824	+	9.59272i	0.0331865	+	0.315748i
$924$	−1.15226	+	3.09884i	−0.0379067	+	0.101944i
$925$	−6.62694	+	3.82607i	−0.217893	+	0.125800i
$926$	−7.59734	+	5.51979i	−0.249664	+	0.181392i
$927$	−3.07385	−	1.68944i	−0.100958	−	0.0554885i
$928$	4.97546	−	1.61663i	0.163328	−	0.0530684i
$929$	−12.5238			−0.410893			−0.205447	−	0.978668i	$-0.565865\pi$
$929$	−12.5238			−0.410893			−0.205447	+	0.978668i	$0.565865\pi$
$930$	−2.07057	+	9.41874i	−0.0678967	+	0.308853i
$931$	47.9762			1.57236
$932$	23.4239	−	7.61088i	0.767275	−	0.249303i
$933$	−9.39562	+	11.8556i	−0.307599	+	0.388135i
$934$	2.87857	−	2.09141i	0.0941898	−	0.0684329i
$935$	−15.0836	+	8.70852i	−0.493287	+	0.284799i
$936$	−0.518902	+	2.72173i	−0.0169608	+	0.0889626i
$937$	−3.63924	−	34.6251i	−0.118889	−	1.13115i	−0.877489	−	0.479596i	$-0.840783\pi$
$937$	−3.63924	−	34.6251i	−0.118889	−	1.13115i	0.758600	−	0.651556i	$-0.225884\pi$
$938$	−4.89005	+	6.73057i	−0.159666	+	0.219761i
$939$	50.9146	−	3.20596i	1.66154	−	0.104623i
$940$	−7.28613	+	8.09207i	−0.237648	+	0.263934i
$941$	30.4726	+	13.5673i	0.993377	+	0.442280i	0.838056	−	0.545584i	$-0.183692\pi$
$941$	30.4726	+	13.5673i	0.993377	+	0.442280i	0.155321	+	0.987864i	$0.450359\pi$
$942$	1.12278	−	26.8225i	0.0365822	−	0.873924i
$943$	−7.48957	−	35.2357i	−0.243894	−	1.14743i
$944$	−3.24950	−	7.29849i	−0.105762	−	0.237546i
$945$	2.72351	−	0.519983i	0.0885959	−	0.0169151i
$946$	4.70312	−	14.4747i	0.152911	−	0.470613i
$947$	29.3965	−	13.0882i	0.955257	−	0.425308i	0.130911	−	0.991394i	$-0.458210\pi$
$947$	29.3965	−	13.0882i	0.955257	−	0.425308i	0.824346	+	0.566086i	$0.191543\pi$
$948$	6.19967	+	15.6562i	0.201356	+	0.508489i
$949$	−14.8176	−	3.14957i	−0.480998	−	0.102239i
$950$	−2.90587	+	6.52669i	−0.0942789	+	0.211754i
$951$	29.6872	+	18.8379i	0.962674	+	0.610861i
$952$	−2.58388	−	0.271577i	−0.0837442	−	0.00880187i
$953$	25.9178	+	18.8304i	0.839561	+	0.609977i	0.922248	−	0.386599i	$-0.126350\pi$
$953$	25.9178	+	18.8304i	0.839561	+	0.609977i	−0.0826870	+	0.996576i	$0.526350\pi$
$954$	−5.57100	+	2.62223i	−0.180368	+	0.0848978i
$955$	6.38167	−	11.0534i	0.206506	−	0.357679i
$956$	2.34902	+	4.06862i	0.0759727	+	0.131589i
$957$	22.6773	−	23.1597i	0.733054	−	0.748648i
$958$	14.6826	+	16.3066i	0.474372	+	0.526843i
$959$	−1.90883	−	5.87478i	−0.0616394	−	0.189707i
$960$	0.288942	+	1.70778i	0.00932555	+	0.0551184i
$961$	−22.2985	−	21.5355i	−0.719305	−	0.694694i
$962$		−	7.06740i		−	0.227862i
$963$	−12.4303	+	9.43716i	−0.400560	+	0.304108i
$964$	−11.3499	+	10.2195i	−0.365556	+	0.329148i
$965$	16.0901	+	22.1461i	0.517957	+	0.712907i
$966$	2.60913	−	2.15869i	0.0839475	−	0.0694548i
$967$	−0.782812	−	0.451956i	−0.0251735	−	0.0145339i	0.487360	−	0.873201i	$-0.337960\pi$
$967$	−0.782812	−	0.451956i	−0.0251735	−	0.0145339i	−0.512534	+	0.858667i	$0.671293\pi$
$968$	−1.78621	+	0.187738i	−0.0574109	+	0.00603413i
$969$	−53.9684	−	26.7866i	−1.73372	−	0.860511i
$970$	−0.866262	+	8.24193i	−0.0278140	+	0.264632i
$971$	20.1800	+	18.1702i	0.647608	+	0.583108i	0.926076	−	0.377337i	$-0.123160\pi$
$971$	20.1800	+	18.1702i	0.647608	+	0.583108i	−0.278468	+	0.960445i	$0.589827\pi$
$972$	14.2391	−	6.34414i	0.456719	−	0.203488i
$973$	−0.501477	+	2.35926i	−0.0160766	+	0.0756345i
$974$	30.1382	−	6.40607i	0.965690	−	0.205264i
$975$	0.885329	+	1.33237i	0.0283532	+	0.0426701i
$976$	−2.76071	−	0.897008i	−0.0883680	−	0.0287125i
$977$	−47.2521	−	15.3532i	−1.51173	−	0.491191i	−0.568317	−	0.822810i	$-0.692405\pi$
$977$	−47.2521	−	15.3532i	−1.51173	−	0.491191i	−0.943413	+	0.331619i	$0.892405\pi$
$978$	7.75336	+	11.6684i	0.247925	+	0.373115i
$979$	−4.74078	+	1.00768i	−0.151516	+	0.0322057i
$980$	1.39618	−	6.56852i	0.0445994	−	0.209824i
$981$	−39.0867	−	3.27806i	−1.24794	−	0.104661i
$982$	25.2549	+	22.7396i	0.805916	+	0.725650i
$983$	−4.20843	+	40.0405i	−0.134228	+	1.27709i	0.695337	+	0.718684i	$0.255255\pi$
$983$	−4.20843	+	40.0405i	−0.134228	+	1.27709i	−0.829565	+	0.558410i	$0.811412\pi$
$984$	15.2534	+	7.57084i	0.486260	+	0.241350i
$985$	25.2593	−	2.65486i	0.804830	−	0.0845910i
$986$	22.0594	+	12.7360i	0.702516	+	0.405598i
$987$	−7.75408	+	6.41542i	−0.246815	+	0.204205i
$988$	−3.87846	−	5.33824i	−0.123390	−	0.169832i
$989$	−11.5849	+	10.4311i	−0.368377	+	0.331689i
$990$	6.48914	+	8.54725i	0.206238	+	0.271650i
$991$		−	52.6598i		−	1.67279i	−0.548124	−	0.836397i	$-0.684658\pi$
$991$		−	52.6598i		−	1.67279i	0.548124	−	0.836397i	$-0.315342\pi$
$992$	−5.16229	−	2.08585i	−0.163903	−	0.0662258i
$993$	−2.53922	−	15.0080i	−0.0805797	−	0.476263i
$994$	1.72209	+	5.30003i	0.0546212	+	0.168107i
$995$	4.13113	+	4.58809i	0.130966	+	0.145452i
$996$	4.56958	−	4.66680i	0.144793	−	0.147873i
$997$	−10.6734	−	18.4869i	−0.338031	−	0.585487i	0.646031	−	0.763311i	$-0.276428\pi$
$997$	−10.6734	−	18.4869i	−0.338031	−	0.585487i	−0.984062	+	0.177824i	$0.943094\pi$
$998$	−8.79043	+	15.2255i	−0.278256	+	0.481954i
$999$	−32.6467	+	22.6977i	−1.03290	+	0.718123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.3	✓	176
3.2	odd	2	inner	930.2.br.a.11.18	yes	176
31.17	odd	30	inner	930.2.br.a.761.18	yes	176
93.17	even	30	inner	930.2.br.a.761.3	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.3	✓	176	1.1	even	1	trivial
930.2.br.a.11.18	yes	176	3.2	odd	2	inner
930.2.br.a.761.3	yes	176	93.17	even	30	inner
930.2.br.a.761.18	yes	176	31.17	odd	30	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.35745 - 1.07579i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62345 + 0.603659i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.685360 + 2.92066i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.35745 - 1.07579i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.62345 + 0.603659i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.685360 + 2.92066i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.26789 - 1.45496i) q^{11} +(-1.73054 - 0.0724398i) q^{12} +(-0.192024 - 0.903403i) q^{13} +(-0.217038 - 0.487475i) q^{14} +(-1.71348 - 0.252933i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.44802 - 1.98039i) q^{17} +(-1.55435 - 2.56593i) q^{18} +(6.98823 + 1.48540i) q^{19} +(0.406737 - 0.913545i) q^{20} +(0.495189 - 0.780384i) q^{21} +(3.55756 + 0.373915i) q^{22} +(-2.96422 - 2.15363i) q^{23} +(1.66822 - 0.465870i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.461793 + 0.799848i) q^{26} +(2.21167 - 4.70197i) q^{27} +(0.357053 + 0.396548i) q^{28} +(-1.61663 - 4.97546i) q^{29} +(1.70778 - 0.288942i) q^{30} +(-2.08585 + 5.16229i) q^{31} +1.00000i q^{32} +(2.87079 + 5.49060i) q^{33} +(-3.61835 + 3.25797i) q^{34} +(0.313647 + 0.431698i) q^{35} +(2.27119 + 1.96002i) q^{36} +(-6.62694 - 3.82607i) q^{37} +(-7.10522 + 0.746789i) q^{38} +(-0.711206 + 1.43290i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(7.30633 + 6.57865i) q^{41} +(-0.229801 + 0.895211i) q^{42} +(0.884595 - 4.16169i) q^{43} +(-3.49899 + 0.743733i) q^{44} +(2.05387 + 2.18669i) q^{45} +(3.48465 + 1.13223i) q^{46} +(-10.3560 - 3.36487i) q^{47} +(-1.44261 + 0.958578i) q^{48} +(6.56852 - 1.39618i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-8.16846 - 2.09685i) q^{51} +(-0.686358 - 0.617999i) q^{52} +(0.214537 - 2.04118i) q^{53} +(-0.650438 + 5.15528i) q^{54} +(-3.55756 + 0.373915i) q^{55} +(-0.462118 - 0.266804i) q^{56} +(-7.88823 - 9.53422i) q^{57} +(3.07501 + 4.23238i) q^{58} +(5.93713 - 5.34582i) q^{59} +(-1.53491 + 0.802533i) q^{60} -2.90278i q^{61} +(0.388526 - 5.55419i) q^{62} +(-1.51172 + 0.526616i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.617999 - 0.686358i) q^{65} +(-4.42697 - 4.33475i) q^{66} +(-7.79547 - 13.5021i) q^{67} +(2.43448 - 4.21665i) q^{68} +(1.70694 + 6.11232i) q^{69} +(-0.431698 - 0.313647i) q^{70} +(-10.3864 - 1.09165i) q^{71} +(-2.76571 - 1.16226i) q^{72} +(6.67127 - 14.9839i) q^{73} +(7.48492 + 1.59097i) q^{74} +(-1.61039 + 0.637695i) q^{75} +(6.52669 - 2.90587i) q^{76} +(0.589851 - 1.81538i) q^{77} +(0.233605 - 1.58255i) q^{78} +(-3.95429 - 8.88148i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.06056 + 4.00341i) q^{81} +(-8.98165 - 3.99889i) q^{82} +(-2.52325 + 2.80236i) q^{83} +(-0.0580817 - 0.922409i) q^{84} +(2.86191 - 3.93907i) q^{85} +(0.444734 + 4.23136i) q^{86} +(-3.15805 + 8.49311i) q^{87} +(3.09791 - 1.78858i) q^{88} +(1.09614 - 0.796391i) q^{89} +(-2.62907 - 1.44498i) q^{90} +(0.468711 - 0.152294i) q^{91} -3.66397 q^{92} +(8.38497 - 4.76364i) q^{93} +10.8890 q^{94} +(6.79469 - 2.20773i) q^{95} +(1.07579 - 1.35745i) q^{96} +(6.70459 - 4.87117i) q^{97} +(-5.81559 + 3.35763i) q^{98} +(2.00977 - 10.5416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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