LMFDB - Embedded newform 930.2.br.a.11.6

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			11.6
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.164188 + 1.72425i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.688975 - 1.58912i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.94608 + 0.566203i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.164188 + 1.72425i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.688975 - 1.58912i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.94608 + 0.566203i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(0.793581 + 0.353325i) q^{11} +(1.14632 + 1.29844i) q^{12} +(0.254594 + 1.19777i) q^{13} +(1.89644 + 4.25947i) q^{14} +(1.00432 + 1.41115i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.33896 - 1.04137i) q^{17} +(2.62693 - 1.44888i) q^{18} +(-6.87933 - 1.46225i) q^{19} +(0.406737 - 0.913545i) q^{20} +(7.91539 - 1.60170i) q^{21} +(-0.863924 - 0.0908021i) q^{22} +(-3.09069 - 2.24552i) q^{23} +(-1.49146 - 0.880658i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.612264 - 1.06047i) q^{26} +(-1.45999 - 4.98683i) q^{27} +(-3.11987 - 3.46497i) q^{28} +(-1.73394 - 5.33652i) q^{29} +(-1.39123 - 1.03173i) q^{30} +(-4.35158 - 3.47329i) q^{31} +1.00000i q^{32} +(-0.478925 + 1.42635i) q^{33} +(-1.90268 + 1.71318i) q^{34} +(-2.74059 - 3.77210i) q^{35} +(-2.05063 + 2.18973i) q^{36} +(-6.74761 - 3.89573i) q^{37} +(6.99449 - 0.735150i) q^{38} +(-2.02345 + 0.635643i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(3.65338 + 3.28952i) q^{41} +(-7.03303 + 3.96930i) q^{42} +(2.00531 - 9.43422i) q^{43} +(0.849700 - 0.180609i) q^{44} +(-2.26828 + 1.96339i) q^{45} +(3.63333 + 1.18054i) q^{46} +(8.17122 + 2.65499i) q^{47} +(1.69060 + 0.376671i) q^{48} +(-14.4175 + 3.06454i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(2.17962 + 3.86198i) q^{51} +(0.910001 + 0.819369i) q^{52} +(0.0119241 - 0.113450i) q^{53} +(2.92955 + 4.29159i) q^{54} +(0.863924 - 0.0908021i) q^{55} +(4.03791 + 2.33129i) q^{56} +(1.39178 - 12.1018i) q^{57} +(3.29815 + 4.53951i) q^{58} +(7.95569 - 7.16334i) q^{59} +(1.64196 + 0.551323i) q^{60} +9.88995i q^{61} +(5.21190 + 1.95859i) q^{62} +(4.06134 + 13.3851i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.819369 + 0.910001i) q^{65} +(0.0147194 - 1.50453i) q^{66} +(-0.378654 - 0.655849i) q^{67} +(1.28016 - 2.21730i) q^{68} +(3.36438 - 5.69782i) q^{69} +(3.77210 + 2.74059i) q^{70} +(-2.04879 - 0.215337i) q^{71} +(1.27360 - 2.71624i) q^{72} +(5.12221 - 11.5047i) q^{73} +(7.62120 + 1.61994i) q^{74} +(1.57534 + 0.719934i) q^{75} +(-6.42498 + 2.86059i) q^{76} +(1.25161 - 3.85206i) q^{77} +(1.72799 - 1.22981i) q^{78} +(4.61682 + 10.3696i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(8.35883 - 3.33617i) q^{81} +(-4.49109 - 1.99956i) q^{82} +(-2.31676 + 2.57302i) q^{83} +(5.46223 - 5.94835i) q^{84} +(1.50491 - 2.07134i) q^{85} +(1.00818 + 9.59215i) q^{86} +(8.91681 - 3.86594i) q^{87} +(-0.752301 + 0.434341i) q^{88} +(-5.10306 + 3.70759i) q^{89} +(1.55054 - 2.56823i) q^{90} +(5.43001 - 1.76432i) q^{91} -3.82031 q^{92} +(5.27435 - 8.07349i) q^{93} -8.59173 q^{94} +(-6.68880 + 2.17332i) q^{95} +(-1.72425 + 0.164188i) q^{96} +(9.19646 - 6.68162i) q^{97} +(12.7649 - 7.36980i) q^{98} +(-2.53801 - 0.591597i) 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
$3$	0.164188	+	1.72425i	0.0947941	+	0.995497i
$3$	0.164188	+	1.72425i	0.0947941	+	0.995497i
$4$	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
$6$	−0.688975	−	1.58912i	−0.281273	−	0.648757i
$7$	−0.487372	−	4.63703i	−0.184209	−	1.75263i	−0.562362	−	0.826891i	$-0.690107\pi$
$7$	−0.487372	−	4.63703i	−0.184209	−	1.75263i	0.378153	−	0.925743i	$-0.376559\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−2.94608	+	0.566203i	−0.982028	+	0.188734i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	0.793581	+	0.353325i	0.239274	+	0.106532i	0.522871	−	0.852412i	$-0.324861\pi$
$11$	0.793581	+	0.353325i	0.239274	+	0.106532i	−0.283597	+	0.958944i	$0.591528\pi$
$12$	1.14632	+	1.29844i	0.330914	+	0.374828i
$13$	0.254594	+	1.19777i	0.0706115	+	0.332201i	0.999247	−	0.0387915i	$-0.0123508\pi$
$13$	0.254594	+	1.19777i	0.0706115	+	0.332201i	−0.928636	+	0.370993i	$0.879017\pi$
$14$	1.89644	+	4.25947i	0.506845	+	1.13839i
$15$	1.00432	+	1.41115i	0.259313	+	0.364358i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.33896	−	1.04137i	0.567282	−	0.252570i	−0.102994	−	0.994682i	$-0.532842\pi$
$17$	2.33896	−	1.04137i	0.567282	−	0.252570i	0.670276	+	0.742112i	$0.266176\pi$
$18$	2.62693	−	1.44888i	0.619172	−	0.341505i
$19$	−6.87933	−	1.46225i	−1.57823	−	0.335462i	−0.666257	−	0.745722i	$-0.732105\pi$
$19$	−6.87933	−	1.46225i	−1.57823	−	0.335462i	−0.911969	+	0.410260i	$0.865438\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	7.91539	−	1.60170i	1.72728	−	0.349519i
$22$	−0.863924	−	0.0908021i	−0.184189	−	0.0193591i
$23$	−3.09069	−	2.24552i	−0.644454	−	0.468223i	0.216924	−	0.976189i	$-0.430398\pi$
$23$	−3.09069	−	2.24552i	−0.644454	−	0.468223i	−0.861377	+	0.507965i	$0.830398\pi$
$24$	−1.49146	−	0.880658i	−0.304442	−	0.179764i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.612264	−	1.06047i	−0.120075	−	0.207976i
$27$	−1.45999	−	4.98683i	−0.280975	−	0.959715i
$28$	−3.11987	−	3.46497i	−0.589600	−	0.654818i
$29$	−1.73394	−	5.33652i	−0.321985	−	0.990967i	−0.972783	−	0.231716i	$-0.925566\pi$
$29$	−1.73394	−	5.33652i	−0.321985	−	0.990967i	0.650799	−	0.759250i	$-0.274434\pi$
$30$	−1.39123	−	1.03173i	−0.254003	−	0.188368i
$31$	−4.35158	−	3.47329i	−0.781566	−	0.623822i
$31$	−4.35158	−	3.47329i	−0.781566	−	0.623822i
$32$			1.00000i			0.176777i
$33$	−0.478925	+	1.42635i	−0.0833701	+	0.248295i
$34$	−1.90268	+	1.71318i	−0.326308	+	0.293809i
$35$	−2.74059	−	3.77210i	−0.463245	−	0.637602i
$36$	−2.05063	+	2.18973i	−0.341771	+	0.364956i
$37$	−6.74761	−	3.89573i	−1.10930	−	0.640454i	−0.170652	−	0.985331i	$-0.554587\pi$
$37$	−6.74761	−	3.89573i	−1.10930	−	0.640454i	−0.938648	+	0.344877i	$0.887921\pi$
$38$	6.99449	−	0.735150i	1.13466	−	0.119257i
$39$	−2.02345	+	0.635643i	−0.324012	+	0.101784i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	3.65338	+	3.28952i	0.570563	+	0.513737i	0.903144	−	0.429338i	$-0.141253\pi$
$41$	3.65338	+	3.28952i	0.570563	+	0.513737i	−0.332581	+	0.943075i	$0.607920\pi$
$42$	−7.03303	+	3.96930i	−1.08522	+	0.612476i
$43$	2.00531	−	9.43422i	0.305806	−	1.43871i	−0.509897	−	0.860235i	$-0.670317\pi$
$43$	2.00531	−	9.43422i	0.305806	−	1.43871i	0.815704	−	0.578470i	$-0.196350\pi$
$44$	0.849700	−	0.180609i	0.128097	−	0.0272279i
$45$	−2.26828	+	1.96339i	−0.338136	+	0.292685i
$46$	3.63333	+	1.18054i	0.535705	+	0.174061i
$47$	8.17122	+	2.65499i	1.19189	+	0.387270i	0.836773	−	0.547550i	$-0.184439\pi$
$47$	8.17122	+	2.65499i	1.19189	+	0.387270i	0.355122	+	0.934820i	$0.384439\pi$
$48$	1.69060	+	0.376671i	0.244017	+	0.0543677i
$49$	−14.4175	+	3.06454i	−2.05964	+	0.437791i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	2.17962	+	3.86198i	0.305208	+	0.540785i
$52$	0.910001	+	0.819369i	0.126194	+	0.113626i
$53$	0.0119241	−	0.113450i	0.00163789	−	0.0155835i	−0.993672	−	0.112317i	$-0.964173\pi$
$53$	0.0119241	−	0.113450i	0.00163789	−	0.0155835i	0.995310	+	0.0967335i	$0.0308395\pi$
$54$	2.92955	+	4.29159i	0.398661	+	0.584012i
$55$	0.863924	−	0.0908021i	0.116491	−	0.0122437i
$56$	4.03791	+	2.33129i	0.539588	+	0.311531i
$57$	1.39178	−	12.1018i	0.184345	−	1.60292i
$58$	3.29815	+	4.53951i	0.433068	+	0.596067i
$59$	7.95569	−	7.16334i	1.03574	−	0.932587i	0.0379690	−	0.999279i	$-0.487911\pi$
$59$	7.95569	−	7.16334i	1.03574	−	0.932587i	0.997774	+	0.0666921i	$0.0212445\pi$
$60$	1.64196	+	0.551323i	0.211977	+	0.0711755i
$61$			9.88995i			1.26628i	0.774038	+	0.633139i	$0.218234\pi$
$61$			9.88995i			1.26628i	−0.774038	+	0.633139i	$0.781766\pi$
$62$	5.21190	+	1.95859i	0.661912	+	0.248741i
$63$	4.06134	+	13.3851i	0.511681	+	1.68637i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.819369	+	0.910001i	0.101630	+	0.112872i
$66$	0.0147194	−	1.50453i	0.00181184	−	0.185195i
$67$	−0.378654	−	0.655849i	−0.0462600	−	0.0801247i	0.841968	−	0.539527i	$-0.181397\pi$
$67$	−0.378654	−	0.655849i	−0.0462600	−	0.0801247i	−0.888228	+	0.459402i	$0.848064\pi$
$68$	1.28016	−	2.21730i	0.155242	−	0.268887i
$69$	3.36438	−	5.69782i	0.405024	−	0.685937i
$70$	3.77210	+	2.74059i	0.450853	+	0.327564i
$71$	−2.04879	−	0.215337i	−0.243147	−	0.0255558i	−0.0178290	−	0.999841i	$-0.505675\pi$
$71$	−2.04879	−	0.215337i	−0.243147	−	0.0255558i	−0.225318	+	0.974285i	$0.572342\pi$
$72$	1.27360	−	2.71624i	0.150095	−	0.320112i
$73$	5.12221	−	11.5047i	0.599510	−	1.34652i	−0.317728	−	0.948182i	$-0.602920\pi$
$73$	5.12221	−	11.5047i	0.599510	−	1.34652i	0.917238	−	0.398339i	$-0.130413\pi$
$74$	7.62120	+	1.61994i	0.885947	+	0.188314i
$75$	1.57534	+	0.719934i	0.181905	+	0.0831309i
$76$	−6.42498	+	2.86059i	−0.736996	+	0.328132i
$77$	1.25161	−	3.85206i	0.142634	−	0.438983i
$78$	1.72799	−	1.22981i	0.195657	−	0.139249i
$79$	4.61682	+	10.3696i	0.519433	+	1.16667i	0.962773	+	0.270312i	$0.0871269\pi$
$79$	4.61682	+	10.3696i	0.519433	+	1.16667i	−0.443340	+	0.896354i	$0.646206\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	8.35883	−	3.33617i	0.928759	−	0.370685i
$82$	−4.49109	−	1.99956i	−0.495958	−	0.220815i
$83$	−2.31676	+	2.57302i	−0.254297	+	0.282426i	−0.856754	−	0.515726i	$-0.827522\pi$
$83$	−2.31676	+	2.57302i	−0.254297	+	0.282426i	0.602456	+	0.798152i	$0.294189\pi$
$84$	5.46223	−	5.94835i	0.595978	−	0.649018i
$85$	1.50491	−	2.07134i	0.163231	−	0.224668i
$86$	1.00818	+	9.59215i	0.108714	+	1.03435i
$87$	8.91681	−	3.86594i	0.955982	−	0.414472i
$88$	−0.752301	+	0.434341i	−0.0801956	+	0.0463009i
$89$	−5.10306	+	3.70759i	−0.540923	+	0.393004i	−0.824428	−	0.565967i	$-0.808503\pi$
$89$	−5.10306	+	3.70759i	−0.540923	+	0.393004i	0.283505	+	0.958971i	$0.408503\pi$
$90$	1.55054	−	2.56823i	0.163442	−	0.270715i
$91$	5.43001	−	1.76432i	0.569220	−	0.184951i
$92$	−3.82031			−0.398294
$93$	5.27435	−	8.07349i	0.546925	−	0.837182i
$94$	−8.59173			−0.886169
$95$	−6.68880	+	2.17332i	−0.686256	+	0.222978i
$96$	−1.72425	+	0.164188i	−0.175981	+	0.0167574i
$97$	9.19646	−	6.68162i	0.933759	−	0.678415i	−0.0131515	−	0.999914i	$-0.504186\pi$
$97$	9.19646	−	6.68162i	0.933759	−	0.678415i	0.946910	+	0.321498i	$0.104186\pi$
$98$	12.7649	−	7.36980i	1.28945	−	0.744463i
$99$	−2.53801	−	0.591597i	−0.255080	−	0.0594578i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−10.6891	+	14.7123i	−1.06361	+	1.46393i	−0.187219	+	0.982318i	$0.559947\pi$
$101$	−10.6891	+	14.7123i	−1.06361	+	1.46393i	−0.876386	+	0.481609i	$0.840053\pi$
$102$	−3.26636	−	2.99942i	−0.323418	−	0.296987i
$103$	5.94748	−	6.60535i	0.586023	−	0.650844i	−0.375094	−	0.926987i	$-0.622390\pi$
$103$	5.94748	−	6.60535i	0.586023	−	0.650844i	0.961117	+	0.276143i	$0.0890562\pi$
$104$	−1.11866	−	0.498060i	−0.109694	−	0.0488388i
$105$	6.05408	−	5.34481i	0.590818	−	0.521600i
$106$	0.0237175	+	0.111582i	0.00230364	+	0.0108378i
$107$	−1.81808	−	4.08348i	−0.175761	−	0.394765i	0.804087	−	0.594512i	$-0.202655\pi$
$107$	−1.81808	−	4.08348i	−0.175761	−	0.394765i	−0.979848	+	0.199747i	$0.935988\pi$
$108$	−4.11234	−	3.17627i	−0.395710	−	0.305636i
$109$	−3.08864	+	9.50587i	−0.295838	+	0.910497i	0.687100	+	0.726563i	$0.258883\pi$
$109$	−3.08864	+	9.50587i	−0.295838	+	0.910497i	−0.982939	+	0.183934i	$0.941117\pi$
$110$	−0.793581	+	0.353325i	−0.0756650	+	0.0336882i
$111$	5.60934	−	12.2742i	0.532415	−	1.16502i
$112$	−4.56069	−	0.969404i	−0.430944	−	0.0916001i
$113$	5.40555	−	12.1411i	0.508512	−	1.14214i	−0.458798	−	0.888540i	$-0.651720\pi$
$113$	5.40555	−	12.1411i	0.508512	−	1.14214i	0.967310	−	0.253596i	$-0.0816133\pi$
$114$	2.41600	+	11.9396i	0.226279	+	1.11824i
$115$	−3.79938	−	0.399331i	−0.354294	−	0.0372378i
$116$	−4.53951	−	3.29815i	−0.421483	−	0.306226i
$117$	−1.42823	−	3.38458i	−0.132040	−	0.312904i
$118$	−5.35272	+	9.27118i	−0.492758	+	0.853481i
$119$	−5.96883	−	10.3383i	−0.547162	−	0.947712i
$120$	−1.73197	−	0.0169445i	−0.158106	−	0.00154682i
$121$	−6.85550	−	7.61381i	−0.623228	−	0.692164i
$122$	−3.05616	−	9.40590i	−0.276692	−	0.851571i
$123$	−5.07212	+	6.83945i	−0.457337	+	0.616693i
$124$	−5.56205	−	0.252161i	−0.499487	−	0.0226447i
$125$		−	1.00000i		−	0.0894427i
$126$	−7.99880	−	11.4750i	−0.712590	−	1.02227i
$127$	10.7113	−	9.64453i	0.950477	−	0.855814i	−0.0391848	−	0.999232i	$-0.512476\pi$
$127$	10.7113	−	9.64453i	0.950477	−	0.855814i	0.989662	+	0.143418i	$0.0458094\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	16.5962	+	1.90866i	1.46122	+	0.168048i
$130$	−1.06047	−	0.612264i	−0.0930095	−	0.0536991i
$131$	−3.50667	+	0.368566i	−0.306379	+	0.0322017i	−0.256470	−	0.966552i	$-0.582560\pi$
$131$	−3.50667	+	0.368566i	−0.306379	+	0.0322017i	−0.0499085	+	0.998754i	$0.515893\pi$
$132$	0.450927	+	1.43544i	0.0392481	+	0.124939i
$133$	−3.42769	+	32.6123i	−0.297219	+	2.82785i
$134$	0.562790	+	0.506739i	0.0486177	+	0.0437755i
$135$	−3.75780	−	3.58872i	−0.323420	−	0.308868i
$136$	−0.532319	+	2.50436i	−0.0456460	+	0.214748i
$137$	−11.0103	+	2.34032i	−0.940677	+	0.199947i	−0.652636	−	0.757671i	$-0.726337\pi$
$137$	−11.0103	+	2.34032i	−0.940677	+	0.199947i	−0.288040	+	0.957618i	$0.593004\pi$
$138$	−1.43900	+	6.45860i	−0.122496	+	0.549792i
$139$	−1.17562	−	0.381982i	−0.0997147	−	0.0323993i	0.258735	−	0.965948i	$-0.416694\pi$
$139$	−1.17562	−	0.381982i	−0.0997147	−	0.0323993i	−0.358449	+	0.933549i	$0.616694\pi$
$140$	−4.43437	−	1.44082i	−0.374773	−	0.121771i
$141$	−3.23625	+	14.5252i	−0.272542	+	1.22324i
$142$	2.01506	−	0.428314i	0.169100	−	0.0359434i
$143$	−0.221161	+	1.04048i	−0.0184944	+	0.0870094i
$144$	−0.371899	+	2.97686i	−0.0309916	+	0.248072i
$145$	−4.16990	−	3.75459i	−0.346291	−	0.311802i
$146$	−1.31637	+	12.5245i	−0.108944	+	1.03653i
$147$	−7.65122	−	24.3563i	−0.631062	−	2.00887i
$148$	−7.74878	+	0.814430i	−0.636946	+	0.0669457i
$149$	19.6833	+	11.3641i	1.61252	+	0.930987i	0.988785	+	0.149348i	$0.0477174\pi$
$149$	19.6833	+	11.3641i	1.61252	+	0.930987i	0.623731	+	0.781639i	$0.285616\pi$
$150$	−1.72071	−	0.197892i	−0.140495	−	0.0161578i
$151$	−8.07277	−	11.1112i	−0.656952	−	0.904217i	0.342423	−	0.939546i	$-0.388752\pi$
$151$	−8.07277	−	11.1112i	−0.656952	−	0.904217i	−0.999376	+	0.0353283i	$0.988752\pi$
$152$	5.22655	−	4.70601i	0.423929	−	0.381707i
$153$	−6.30115	+	4.39230i	−0.509418	+	0.355097i
$154$			4.05030i			0.326382i
$155$	−5.50522	−	0.832172i	−0.442190	−	0.0668417i
$156$	−1.26339	+	1.70360i	−0.101152	+	0.136397i
$157$	2.73678	+	8.42296i	0.218419	+	0.672225i	0.998893	+	0.0470368i	$0.0149778\pi$
$157$	2.73678	+	8.42296i	0.218419	+	0.672225i	−0.780474	+	0.625188i	$0.785022\pi$
$158$	−7.59523	−	8.43535i	−0.604244	−	0.671081i
$159$	0.197574	+	0.00193294i	0.0156686	+	0.000153292i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−8.90623	+	15.4260i	−0.701909	+	1.21574i
$162$	−6.91878	+	5.75590i	−0.543591	+	0.452226i
$163$	4.80008	+	3.48746i	0.375971	+	0.273159i	0.759683	−	0.650294i	$-0.225354\pi$
$163$	4.80008	+	3.48746i	0.375971	+	0.273159i	−0.383711	+	0.923453i	$0.625354\pi$
$164$	4.88918	+	0.513874i	0.381781	+	0.0401268i
$165$	0.298412	+	1.47471i	0.0232313	+	0.114806i
$166$	1.40826	−	3.16301i	0.109302	−	0.245497i
$167$	4.33774	+	0.922016i	0.335665	+	0.0713477i	0.372661	−	0.927968i	$-0.378446\pi$
$167$	4.33774	+	0.922016i	0.335665	+	0.0713477i	−0.0369960	+	0.999315i	$0.511779\pi$
$168$	−3.35675	+	7.34514i	−0.258979	+	0.566690i
$169$	10.5063	−	4.67769i	0.808174	−	0.359822i
$170$	−0.791180	+	2.43500i	−0.0606808	+	0.186756i
$171$	21.0950	+	0.412802i	1.61318	+	0.0315677i
$172$	−3.92297	−	8.81114i	−0.299124	−	0.671843i
$173$	3.16559	+	14.8929i	0.240675	+	1.13229i	0.917993	+	0.396597i	$0.129809\pi$
$173$	3.16559	+	14.8929i	0.240675	+	1.13229i	−0.677317	+	0.735691i	$0.736858\pi$
$174$	−7.28574	+	6.43217i	−0.552331	+	0.487622i
$175$	−4.25947	−	1.89644i	−0.321986	−	0.143357i
$176$	0.581262	−	0.645557i	0.0438143	−	0.0486607i
$177$	13.6576	+	12.5415i	1.02657	+	0.942675i
$178$	3.70759	−	5.10306i	0.277896	−	0.382491i
$179$	−0.392979	−	3.73894i	−0.0293726	−	0.279462i	−0.999343	−	0.0362392i	$-0.988462\pi$
$179$	−0.392979	−	3.73894i	−0.0293726	−	0.279462i	0.969971	−	0.243222i	$-0.0782045\pi$
$180$	−0.681028	+	2.92168i	−0.0507608	+	0.217769i
$181$	−11.8062	+	6.81633i	−0.877550	+	0.506653i	−0.869850	−	0.493317i	$-0.835784\pi$
$181$	−11.8062	+	6.81633i	−0.877550	+	0.506653i	−0.00769990	+	0.999970i	$0.502451\pi$
$182$	−4.61904	+	3.35593i	−0.342386	+	0.248758i
$183$	−17.0528	+	1.62381i	−1.26058	+	0.120036i
$184$	3.63333	−	1.18054i	0.267852	−	0.0870305i
$185$	−7.79146			−0.572840
$186$	−2.52136	+	9.30821i	−0.184875	+	0.682511i
$187$	2.22410			0.162642
$188$	8.17122	−	2.65499i	0.595947	−	0.193635i
$189$	−22.4125	+	9.20046i	−1.63027	+	0.669235i
$190$	5.68983	−	4.13390i	0.412784	−	0.299905i
$191$	−2.83469	+	1.63661i	−0.205111	+	0.118421i	−0.599037	−	0.800721i	$-0.704450\pi$
$191$	−2.83469	+	1.63661i	−0.205111	+	0.118421i	0.393926	+	0.919142i	$0.371117\pi$
$192$	1.58912	−	0.688975i	0.114685	−	0.0497225i
$193$	−0.610091	−	5.80463i	−0.0439153	−	0.417826i	−0.994289	−	0.106717i	$-0.965966\pi$
$193$	−0.610091	−	5.80463i	−0.0439153	−	0.417826i	0.950374	−	0.311109i	$-0.100701\pi$
$194$	−6.68162	+	9.19646i	−0.479712	+	0.660267i
$195$	−1.43454	+	1.56221i	−0.102730	+	0.111872i
$196$	−9.86272	+	10.9537i	−0.704480	+	0.782405i
$197$	−1.70722	−	0.760102i	−0.121634	−	0.0541550i	0.345017	−	0.938596i	$-0.387873\pi$
$197$	−1.70722	−	0.760102i	−0.121634	−	0.0541550i	−0.466651	+	0.884441i	$0.654540\pi$
$198$	2.59661	−	0.221646i	0.184533	−	0.0157517i
$199$	−3.43227	−	16.1476i	−0.243307	−	1.14467i	−0.914878	−	0.403731i	$-0.867713\pi$
$199$	−3.43227	−	16.1476i	−0.243307	−	1.14467i	0.671570	−	0.740941i	$-0.265620\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	1.06868	−	0.760578i	0.0753787	−	0.0536470i
$202$	5.61959	−	17.2953i	0.395393	−	1.21690i
$203$	−23.9005	+	10.6412i	−1.67749	+	0.746866i
$204$	4.03336	+	1.84326i	0.282392	+	0.129054i
$205$	4.80868	+	1.02212i	0.335853	+	0.0713878i
$206$	−3.61523	+	8.11993i	−0.251885	+	0.565742i
$207$	10.3769	+	4.86553i	0.721242	+	0.338178i
$208$	1.21782	+	0.127998i	0.0844406	+	0.00887506i
$209$	−4.94266	−	3.59105i	−0.341891	−	0.248398i
$210$	−4.10614	+	6.95403i	−0.283350	+	0.479873i
$211$	3.58995	−	6.21798i	0.247143	−	0.428064i	−0.715589	−	0.698521i	$-0.753842\pi$
$211$	3.58995	−	6.21798i	0.247143	−	0.428064i	0.962732	+	0.270458i	$0.0871750\pi$
$212$	−0.0570374	−	0.0987916i	−0.00391734	−	0.00678503i
$213$	0.0349071	−	3.56799i	0.00239180	−	0.244475i
$214$	2.99097	+	3.32180i	0.204458	+	0.227074i
$215$	−2.98047	−	9.17293i	−0.203266	−	0.625589i
$216$	4.89259	+	1.75003i	0.332898	+	0.119074i
$217$	−13.9849	+	21.8712i	−0.949360	+	1.48471i
$218$		−	9.99506i		−	0.676951i
$219$	20.6780	+	6.94305i	1.39729	+	0.469168i
$220$	0.645557	−	0.581262i	0.0435235	−	0.0391887i
$221$	1.84281	+	2.53641i	0.123961	+	0.170617i
$222$	−1.54187	+	13.4068i	−0.103483	+	0.899808i
$223$	5.94134	+	3.43023i	0.397861	+	0.229705i	0.685561	−	0.728015i	$-0.259557\pi$
$223$	5.94134	+	3.43023i	0.397861	+	0.229705i	−0.287699	+	0.957721i	$0.592890\pi$
$224$	4.63703	−	0.487372i	0.309825	−	0.0325639i
$225$	−0.982696	+	2.83449i	−0.0655130	+	0.188966i
$226$	−1.38919	+	13.2173i	−0.0924075	+	0.879199i
$227$	−19.7967	−	17.8250i	−1.31395	−	1.18309i	−0.969724	−	0.244204i	$-0.921473\pi$
$227$	−19.7967	−	17.8250i	−1.31395	−	1.18309i	−0.344230	−	0.938885i	$-0.611860\pi$
$228$	−5.98727	−	10.6086i	−0.396517	−	0.702572i
$229$	3.02261	−	14.2203i	0.199740	−	0.939702i	−0.758042	−	0.652206i	$-0.773844\pi$
$229$	3.02261	−	14.2203i	0.199740	−	0.939702i	0.957782	−	0.287496i	$-0.0928228\pi$
$230$	3.73682	−	0.794286i	0.246399	−	0.0523737i
$231$	6.84742	+	1.52563i	0.450527	+	0.100379i
$232$	5.33652	+	1.73394i	0.350360	+	0.113839i
$233$	21.1716	+	6.87905i	1.38699	+	0.450662i	0.904962	−	0.425492i	$-0.139899\pi$
$233$	21.1716	+	6.87905i	1.38699	+	0.450662i	0.482032	+	0.876154i	$0.339899\pi$
$234$	2.40422	+	2.77757i	0.157169	+	0.181576i
$235$	8.40398	−	1.78632i	0.548215	−	0.116527i
$236$	2.22579	−	10.4715i	0.144886	−	0.681636i
$237$	−17.1217	+	9.66312i	−1.11217	+	0.627687i
$238$	8.87141	+	7.98785i	0.575048	+	0.517776i
$239$	−2.73910	+	26.0608i	−0.177178	+	1.68573i	0.439284	+	0.898348i	$0.355232\pi$
$239$	−2.73910	+	26.0608i	−0.177178	+	1.68573i	−0.616461	+	0.787385i	$0.711434\pi$
$240$	1.65244	−	0.519092i	0.106664	−	0.0335073i
$241$	26.1249	−	2.74583i	1.68285	−	0.176875i	0.785703	−	0.618604i	$-0.212302\pi$
$241$	26.1249	−	2.74583i	1.68285	−	0.176875i	0.897148	+	0.441730i	$0.145635\pi$
$242$	8.87277	+	5.12270i	0.570363	+	0.329299i
$243$	7.12481	+	13.8650i	0.457057	+	0.889438i
$244$	5.81317	+	8.00114i	0.372150	+	0.512221i
$245$	−10.9537	+	9.86272i	−0.699804	+	0.630106i
$246$	2.71036	−	8.07208i	0.172807	−	0.514657i
$247$		−	8.61212i		−	0.547976i
$248$	5.36775	−	1.47895i	0.340852	−	0.0939134i
$249$	−4.81692	−	3.57222i	−0.305260	−	0.226380i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−15.7438	−	17.4853i	−0.993742	−	1.10366i	−0.994613	−	0.103662i	$-0.966944\pi$
$251$	−15.7438	−	17.4853i	−0.993742	−	1.10366i	0.000870709	−	1.00000i	$-0.499723\pi$
$252$	11.1533	+	8.44161i	0.702591	+	0.531771i
$253$	−1.65932	−	2.87402i	−0.104320	−	0.180688i
$254$	−7.20676	+	12.4825i	−0.452192	+	0.783220i
$255$	3.81860	+	2.25476i	0.239130	+	0.141199i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−13.2187	−	1.38935i	−0.824563	−	0.0866650i	−0.317158	−	0.948373i	$-0.602729\pi$
$257$	−13.2187	−	1.38935i	−0.824563	−	0.0866650i	−0.507405	+	0.861708i	$0.669395\pi$
$258$	−16.3737	+	3.31327i	−1.01939	+	0.206275i
$259$	−14.7760	+	33.1875i	−0.918139	+	2.06217i
$260$	1.19777	+	0.254594i	0.0742824	+	0.0157892i
$261$	8.12989	+	14.7401i	0.503227	+	0.912388i
$262$	3.22115	−	1.43415i	0.199003	−	0.0886018i
$263$	−4.69372	+	14.4458i	−0.289427	+	0.890766i	0.695609	+	0.718420i	$0.255135\pi$
$263$	−4.69372	+	14.4458i	−0.289427	+	0.890766i	−0.985037	+	0.172345i	$0.944865\pi$
$264$	−0.872433	−	1.22584i	−0.0536945	−	0.0754454i
$265$	−0.0463984	−	0.104212i	−0.00285023	−	0.00640172i
$266$	−6.81783	−	32.0754i	−0.418028	−	1.96667i
$267$	−7.23068	−	8.19022i	−0.442510	−	0.501233i
$268$	−0.691836	−	0.308025i	−0.0422606	−	0.0188156i
$269$	0.600537	−	0.666964i	0.0366154	−	0.0406655i	−0.724559	−	0.689213i	$-0.757956\pi$
$269$	0.600537	−	0.666964i	0.0366154	−	0.0406655i	0.761174	+	0.648547i	$0.224623\pi$
$270$	4.68286	+	2.25185i	0.284990	+	0.137043i
$271$	−7.36133	+	10.1320i	−0.447169	+	0.615475i	−0.971786	−	0.235863i	$-0.924208\pi$
$271$	−7.36133	+	10.1320i	−0.447169	+	0.615475i	0.524618	+	0.851338i	$0.324208\pi$
$272$	−0.267626	−	2.54629i	−0.0162272	−	0.154391i
$273$	3.93367	+	9.07302i	0.238077	+	0.549124i
$274$	9.74826	−	5.62816i	0.588914	−	0.340010i
$275$	0.702779	−	0.510599i	0.0423792	−	0.0307903i
$276$	−0.627249	−	6.58717i	−0.0377560	−	0.396501i
$277$	−13.1497	+	4.27259i	−0.790088	+	0.256715i	−0.676142	−	0.736772i	$-0.736349\pi$
$277$	−13.1497	+	4.27259i	−0.790088	+	0.256715i	−0.113946	+	0.993487i	$0.536349\pi$
$278$	1.23612			0.0741375
$279$	14.7867	+	7.76874i	0.885257	+	0.465102i
$280$	4.66258			0.278642
$281$	4.54544	−	1.47690i	0.271158	−	0.0881047i	−0.170282	−	0.985395i	$-0.554468\pi$
$281$	4.54544	−	1.47690i	0.271158	−	0.0881047i	0.441440	+	0.897291i	$0.354468\pi$
$282$	−1.41066	−	14.8143i	−0.0840036	−	0.882179i
$283$	0.129955	−	0.0944175i	0.00772500	−	0.00561254i	−0.583916	−	0.811814i	$-0.698480\pi$
$283$	0.129955	−	0.0944175i	0.00772500	−	0.00561254i	0.591641	+	0.806202i	$0.298480\pi$
$284$	−1.78408	+	1.03004i	−0.105866	+	0.0611216i
$285$	−4.84557	−	11.1763i	−0.287027	−	0.662029i
$286$	−0.111190	−	1.05790i	−0.00657478	−	0.0625548i
$287$	13.4731	−	18.5441i	0.795290	−	1.09462i
$288$	−0.566203	−	2.94608i	−0.0333639	−	0.173600i
$289$	−6.98893	+	7.76199i	−0.411114	+	0.456588i
$290$	5.12604	+	2.28226i	0.301011	+	0.134019i
$291$	13.0307	+	14.7600i	0.763875	+	0.865244i
$292$	−2.61832	−	12.3182i	−0.153226	−	0.720871i
$293$	9.18876	+	20.6383i	0.536813	+	1.20570i	0.954800	+	0.297249i	$0.0960690\pi$
$293$	9.18876	+	20.6383i	0.536813	+	1.20570i	−0.417987	+	0.908453i	$0.637264\pi$
$294$	14.8032	+	20.7998i	0.863342	+	1.21307i
$295$	3.30816	−	10.1815i	0.192609	−	0.592788i
$296$	7.11786	−	3.16907i	0.413717	−	0.184199i
$297$	0.603351	−	4.47330i	0.0350100	−	0.259567i
$298$	−22.2316	−	4.72547i	−1.28784	−	0.273739i
$299$	1.90274	−	4.27363i	0.110038	−	0.247150i
$300$	1.69764	−	0.343522i	0.0980135	−	0.0198333i
$301$	−44.7241	−	4.70070i	−2.57786	−	0.270944i
$302$	11.1112	+	8.07277i	0.639378	+	0.464536i
$303$	−27.1227	−	16.0151i	−1.55816	−	0.920044i
$304$	−3.51651	+	6.09077i	−0.201686	+	0.349330i
$305$	4.94498	+	8.56495i	0.283149	+	0.490428i
$306$	4.63546	−	6.12449i	0.264991	−	0.350114i
$307$	−7.95513	−	8.83507i	−0.454023	−	0.504244i	0.472058	−	0.881567i	$-0.343511\pi$
$307$	−7.95513	−	8.83507i	−0.454023	−	0.504244i	−0.926082	+	0.377323i	$0.876845\pi$
$308$	−1.25161	−	3.85206i	−0.0713172	−	0.219492i
$309$	12.3658	+	9.17043i	0.703465	+	0.521688i
$310$	5.49293	−	0.909765i	0.311978	−	0.0516712i
$311$		−	2.78248i		−	0.157780i	−0.996883	−	0.0788900i	$-0.974862\pi$
$311$		−	2.78248i		−	0.157780i	0.996883	−	0.0788900i	$-0.0251376\pi$
$312$	0.675110	−	2.01063i	0.0382206	−	0.113829i
$313$	−19.7760	+	17.8064i	−1.11781	+	1.00648i	−0.117897	+	0.993026i	$0.537615\pi$
$313$	−19.7760	+	17.8064i	−1.11781	+	1.00648i	−0.999910	+	0.0134518i	$0.995718\pi$
$314$	−5.20567	−	7.16499i	−0.293773	−	0.404344i
$315$	10.2098	+	9.56120i	0.575257	+	0.538713i
$316$	9.83016	+	5.67544i	0.552990	+	0.319269i
$317$	−12.3644	+	1.29955i	−0.694453	+	0.0729900i	−0.445177	−	0.895443i	$-0.646859\pi$
$317$	−12.3644	+	1.29955i	−0.694453	+	0.0729900i	−0.249276	+	0.968432i	$0.580193\pi$
$318$	−0.188501	+	0.0592153i	−0.0105706	+	0.00332063i
$319$	0.509504	−	4.84761i	0.0285267	−	0.271414i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	6.74244	−	3.80529i	0.376326	−	0.212391i
$322$	3.70342	−	17.4232i	0.206384	−	0.970958i
$323$	−17.6132	+	3.74381i	−0.980027	+	0.208311i
$324$	4.80148	−	7.61221i	0.266749	−	0.422901i
$325$	1.16459	+	0.378400i	0.0646001	+	0.0209898i
$326$	−5.64283	−	1.83347i	−0.312528	−	0.101546i
$327$	−16.8976	−	3.76485i	−0.934441	−	0.208196i
$328$	−4.80868	+	1.02212i	−0.265515	+	0.0564370i
$329$	8.32886	−	39.1842i	0.459185	−	2.16029i
$330$	−0.739518	−	1.31032i	−0.0407091	−	0.0721308i
$331$	1.77779	+	1.60073i	0.0977162	+	0.0879841i	0.716541	−	0.697545i	$-0.245724\pi$
$331$	1.77779	+	1.60073i	0.0977162	+	0.0879841i	−0.618825	+	0.785529i	$0.712391\pi$
$332$	−0.361913	+	3.44338i	−0.0198626	+	0.188980i
$333$	22.0848	+	7.65664i	1.21024	+	0.419581i
$334$	−4.41036	+	0.463547i	−0.241324	+	0.0253642i
$335$	−0.655849	−	0.378654i	−0.0358328	−	0.0206881i
$336$	0.922685	−	8.02293i	0.0503366	−	0.437687i
$337$	−7.86275	−	10.8222i	−0.428311	−	0.589520i	0.539253	−	0.842144i	$-0.318707\pi$
$337$	−7.86275	−	10.8222i	−0.428311	−	0.589520i	−0.967565	+	0.252624i	$0.918707\pi$
$338$	−8.54656	+	7.69536i	−0.464872	+	0.418572i
$339$	21.8218	+	7.32711i	1.18520	+	0.397954i
$340$		−	2.56031i		−	0.138853i
$341$	−2.22613	−	4.29386i	−0.120552	−	0.232526i
$342$	−20.1901	+	6.12612i	−1.09176	+	0.331263i
$343$	11.1513	+	34.3203i	0.602116	+	1.85312i
$344$	6.45376	+	7.16762i	0.347963	+	0.386452i
$345$	0.0647334	−	6.61665i	0.00348513	−	0.356228i
$346$	−7.61282	−	13.1858i	−0.409268	−	0.708873i
$347$	−6.93837	+	12.0176i	−0.372471	+	0.645139i	−0.989945	−	0.141452i	$-0.954823\pi$
$347$	−6.93837	+	12.0176i	−0.372471	+	0.645139i	0.617474	+	0.786592i	$0.288156\pi$
$348$	4.94150	−	8.36878i	0.264892	−	0.448614i
$349$	4.88477	+	3.54899i	0.261476	+	0.189973i	0.710797	−	0.703397i	$-0.248334\pi$
$349$	4.88477	+	3.54899i	0.261476	+	0.189973i	−0.449322	+	0.893370i	$0.648334\pi$
$350$	4.63703	+	0.487372i	0.247860	+	0.0260511i
$351$	5.60136	−	3.01834i	0.298978	−	0.161107i
$352$	−0.353325	+	0.793581i	−0.0188323	+	0.0422980i
$353$	14.8127	+	3.14853i	0.788399	+	0.167579i	0.584480	−	0.811408i	$-0.301299\pi$
$353$	14.8127	+	3.14853i	0.788399	+	0.167579i	0.203919	+	0.978988i	$0.434632\pi$
$354$	−16.8647	−	7.70721i	−0.896349	−	0.409634i
$355$	−1.88198	+	0.837910i	−0.0998849	+	0.0444716i
$356$	−1.94920	+	5.99901i	−0.103307	+	0.317947i
$357$	16.8458	−	11.9892i	0.891576	−	0.634535i
$358$	1.52914	+	3.43451i	0.0808177	+	0.181519i
$359$	0.0614367	+	0.289037i	0.00324251	+	0.0152548i	0.979739	−	0.200278i	$-0.0641845\pi$
$359$	0.0614367	+	0.289037i	0.00324251	+	0.0152548i	−0.976497	+	0.215533i	$0.930851\pi$
$360$	−0.255152	−	2.98913i	−0.0134477	−	0.157541i
$361$	27.8296	+	12.3905i	1.46472	+	0.652134i
$362$	9.12202	−	10.1310i	0.479443	−	0.532475i
$363$	12.0025	−	13.0707i	0.629969	−	0.686034i
$364$	3.35593	−	4.61904i	0.175899	−	0.242104i
$365$	−1.31637	−	12.5245i	−0.0689021	−	0.655560i
$366$	15.7164	−	6.81393i	0.821507	−	0.356170i
$367$	−4.12072	+	2.37910i	−0.215100	+	0.124188i	−0.603679	−	0.797227i	$-0.706299\pi$
$367$	−4.12072	+	2.37910i	−0.215100	+	0.124188i	0.388580	+	0.921415i	$0.372966\pi$
$368$	−3.09069	+	2.24552i	−0.161113	+	0.117056i
$369$	−12.6257	−	7.62265i	−0.657268	−	0.396819i
$370$	7.41012	−	2.40769i	0.385234	−	0.125170i
$371$	−0.531882			−0.0276139
$372$	−0.478435	−	9.63178i	−0.0248057	−	0.499384i
$373$	−2.15281			−0.111468			−0.0557341	−	0.998446i	$-0.517750\pi$
$373$	−2.15281			−0.111468			−0.0557341	+	0.998446i	$0.517750\pi$
$374$	−2.11525	+	0.687285i	−0.109377	+	0.0355387i
$375$	1.72425	−	0.164188i	0.0890399	−	0.00847864i
$376$	−6.95085	+	5.05009i	−0.358463	+	0.260439i
$377$	5.95046	−	3.43550i	0.306464	−	0.176937i
$378$	18.4725	−	15.6760i	0.950122	−	0.806287i
$379$	−1.54016	−	14.6537i	−0.0791128	−	0.752708i	−0.960117	−	0.279599i	$-0.909798\pi$
$379$	−1.54016	−	14.6537i	−0.0791128	−	0.752708i	0.881004	−	0.473109i	$-0.156868\pi$
$380$	−4.13390	+	5.68983i	−0.212065	+	0.291882i
$381$	18.3883	+	16.8855i	0.942060	+	0.865071i
$382$	2.19021	−	2.43247i	0.112061	−	0.124456i
$383$	24.3409	+	10.8373i	1.24376	+	0.553758i	0.919828	−	0.392322i	$-0.128328\pi$
$383$	24.3409	+	10.8373i	1.24376	+	0.553758i	0.323933	+	0.946080i	$0.394995\pi$
$384$	−1.29844	+	1.14632i	−0.0662608	+	0.0584979i
$385$	−0.842105	−	3.96179i	−0.0429176	−	0.201912i
$386$	2.37396	+	5.33200i	0.120831	+	0.271392i
$387$	−0.566111	+	28.9294i	−0.0287770	+	1.47057i
$388$	3.51273	−	10.8111i	0.178332	−	0.548850i
$389$	−1.52527	+	0.679094i	−0.0773343	+	0.0344314i	−0.445039	−	0.895511i	$-0.646810\pi$
$389$	−1.52527	+	0.679094i	−0.0773343	+	0.0344314i	0.367705	+	0.929942i	$0.380144\pi$
$390$	0.881579	−	1.92905i	0.0446405	−	0.0976810i
$391$	−9.56744	−	2.03362i	−0.483846	−	0.102845i
$392$	5.99514	−	13.4653i	0.302800	−	0.680101i
$393$	−1.21125	−	5.98586i	−0.0610996	−	0.301947i
$394$	1.85854	+	0.195341i	0.0936321	+	0.00984113i
$395$	9.18306	+	6.67188i	0.462050	+	0.335699i
$396$	−2.40103	+	1.01319i	−0.120656	+	0.0509149i
$397$	−12.5616	+	21.7573i	−0.630447	+	1.09197i	0.357013	+	0.934099i	$0.383795\pi$
$397$	−12.5616	+	21.7573i	−0.630447	+	1.09197i	−0.987460	+	0.157867i	$0.949538\pi$
$398$	8.25416	+	14.2966i	0.413744	+	0.716625i
$399$	−56.7946	−	0.555645i	−2.84329	−	0.0278170i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−11.1442	−	34.2984i	−0.556516	−	1.71278i	−0.691906	−	0.721987i	$-0.743229\pi$
$401$	−11.1442	−	34.2984i	−0.556516	−	1.71278i	0.135390	−	0.990792i	$-0.456771\pi$
$402$	−0.781341	+	1.05359i	−0.0389698	+	0.0525484i
$403$	3.05232	−	6.09646i	0.152047	−	0.303686i
$404$			18.1854i			0.904757i
$405$	5.57087	−	7.06862i	0.276819	−	0.351242i
$406$	19.4425	−	17.5061i	0.964913	−	0.868811i
$407$	−3.97831	−	5.47568i	−0.197198	−	0.271419i
$408$	−4.40555	−	0.506665i	−0.218107	−	0.0250836i
$409$	16.8910	+	9.75203i	0.835207	+	0.482207i	0.855632	−	0.517584i	$-0.173169\pi$
$409$	16.8910	+	9.75203i	0.835207	+	0.482207i	−0.0204250	+	0.999791i	$0.506502\pi$
$410$	−4.88918	+	0.513874i	−0.241459	+	0.0253784i
$411$	−5.84307	−	18.6003i	−0.288217	−	0.917487i
$412$	0.929088	−	8.83968i	0.0457729	−	0.435500i
$413$	−37.0940	−	33.3996i	−1.82528	−	1.64349i
$414$	−11.3725	−	1.42077i	−0.558929	−	0.0698269i
$415$	−0.719862	+	3.38668i	−0.0353366	+	0.166246i
$416$	−1.19777	+	0.254594i	−0.0587254	+	0.0124825i
$417$	0.465610	−	2.08978i	0.0228010	−	0.102337i
$418$	5.81044	+	1.88793i	0.284198	+	0.0923415i
$419$	34.1565	+	11.0981i	1.66866	+	0.542179i	0.982658	−	0.185425i	$-0.0593663\pi$
$419$	34.1565	+	11.0981i	1.66866	+	0.542179i	0.685997	+	0.727604i	$0.259366\pi$
$420$	1.75626	−	7.88254i	0.0856965	−	0.384628i
$421$	37.1038	−	7.88667i	1.80833	−	0.384373i	0.824845	−	0.565359i	$-0.191262\pi$
$421$	37.1038	−	7.88667i	1.80833	−	0.384373i	0.983486	+	0.180986i	$0.0579290\pi$
$422$	−1.49279	+	7.02301i	−0.0726677	+	0.341875i
$423$	−25.5764	−	3.19525i	−1.24357	−	0.155358i
$424$	0.0847740	+	0.0763309i	0.00411699	+	0.00370696i
$425$	0.267626	−	2.54629i	0.0129818	−	0.123513i
$426$	1.06937	+	3.40415i	0.0518112	+	0.164931i
$427$	45.8600	−	4.82008i	2.21932	−	0.233260i
$428$	−3.87107	−	2.23496i	−0.187115	−	0.108031i
$429$	−1.83036	−	0.210502i	−0.0883707	−	0.0101632i
$430$	5.66918	+	7.80296i	0.273392	+	0.376292i
$431$	12.3383	−	11.1094i	0.594314	−	0.535123i	−0.316151	−	0.948709i	$-0.602391\pi$
$431$	12.3383	−	11.1094i	0.594314	−	0.535123i	0.910465	+	0.413586i	$0.135724\pi$
$432$	−5.19391	−	0.152481i	−0.249892	−	0.00733627i
$433$		−	14.1567i		−	0.680329i	−0.940366	−	0.340165i	$-0.889517\pi$
$433$		−	14.1567i		−	0.680329i	0.940366	−	0.340165i	$-0.110483\pi$
$434$	6.54190	−	25.1223i	0.314021	−	1.20591i
$435$	5.78921	−	7.80641i	0.277571	−	0.374289i
$436$	3.08864	+	9.50587i	0.147919	+	0.455249i
$437$	17.9784	+	19.9670i	0.860023	+	0.955152i
$438$	−21.8114	−	0.213390i	−1.04219	−	0.0101962i
$439$	−4.54416	−	7.87071i	−0.216881	−	0.375649i	0.736972	−	0.675923i	$-0.236255\pi$
$439$	−4.54416	−	7.87071i	−0.216881	−	0.375649i	−0.953853	+	0.300275i	$0.902922\pi$
$440$	−0.434341	+	0.752301i	−0.0207064	+	0.0358646i
$441$	40.7401	−	17.1916i	1.94000	−	0.818649i
$442$	−2.53641	−	1.84281i	−0.120645	−	0.0876535i
$443$	−0.986515	−	0.103687i	−0.0468707	−	0.00492631i	0.0810641	−	0.996709i	$-0.474168\pi$
$443$	−0.986515	−	0.103687i	−0.0468707	−	0.00492631i	−0.127935	+	0.991783i	$0.540835\pi$
$444$	−2.67654	−	13.2271i	−0.127023	−	0.627732i
$445$	−2.56558	+	5.76240i	−0.121620	+	0.273164i
$446$	−6.71055	−	1.42637i	−0.317754	−	0.0675406i
$447$	−16.3629	+	35.8048i	−0.773937	+	1.69351i
$448$	−4.25947	+	1.89644i	−0.201241	+	0.0895984i
$449$	7.25903	−	22.3410i	0.342575	−	1.05434i	−0.620295	−	0.784369i	$-0.712987\pi$
$449$	7.25903	−	22.3410i	0.342575	−	1.05434i	0.962869	−	0.269968i	$-0.0870131\pi$
$450$	0.0586948	−	2.99943i	0.00276690	−	0.141394i
$451$	1.73699	+	3.90133i	0.0817915	+	0.183707i
$452$	−2.76316	−	12.9996i	−0.129968	−	0.611452i
$453$	17.8331	−	15.7438i	0.837870	−	0.739709i
$454$	24.3360	+	10.8351i	1.14215	+	0.508516i
$455$	3.82037	−	4.24295i	0.179102	−	0.198913i
$456$	8.97247	+	8.23921i	0.420175	+	0.385836i
$457$	0.376629	−	0.518385i	0.0176179	−	0.0242490i	−0.800117	−	0.599844i	$-0.795229\pi$
$457$	0.376629	−	0.518385i	0.0176179	−	0.0242490i	0.817735	+	0.575595i	$0.195229\pi$
$458$	1.51963	+	14.4583i	0.0710076	+	0.675593i
$459$	−8.60801	−	10.1436i	−0.401787	−	0.473463i
$460$	−3.30848	+	1.91015i	−0.154259	+	0.0890613i
$461$	−28.4844	+	20.6951i	−1.32665	+	0.963868i	−0.326827	+	0.945084i	$0.605979\pi$
$461$	−28.4844	+	20.6951i	−1.32665	+	0.963868i	−0.999824	+	0.0187836i	$0.994021\pi$
$462$	−6.98373	+	0.665011i	−0.324913	+	0.0309391i
$463$	5.95894	−	1.93618i	0.276935	−	0.0899817i	−0.167257	−	0.985913i	$-0.553491\pi$
$463$	5.95894	−	1.93618i	0.276935	−	0.0899817i	0.444192	+	0.895932i	$0.353491\pi$
$464$	−5.61115			−0.260491
$465$	0.530981	−	9.62902i	0.0246236	−	0.446535i
$466$	−22.2611			−1.03122
$467$	29.8707	−	9.70556i	1.38225	−	0.449120i	0.478841	−	0.877902i	$-0.341057\pi$
$467$	29.8707	−	9.70556i	1.38225	−	0.449120i	0.903408	+	0.428782i	$0.141057\pi$
$468$	−3.14487	−	1.89868i	−0.145372	−	0.0877667i
$469$	−2.85665	+	2.07548i	−0.131908	+	0.0958366i
$470$	−7.44065	+	4.29586i	−0.343212	+	0.198153i
$471$	−14.0739	+	6.10185i	−0.648493	+	0.281159i
$472$	1.11902	+	10.6468i	0.0515072	+	0.490058i
$473$	4.92472	−	6.77830i	0.226439	−	0.311666i
$474$	13.2976	−	14.4811i	0.610780	−	0.665137i
$475$	−4.70601	+	5.22655i	−0.215926	+	0.239811i
$476$	−10.9056	−	4.85548i	−0.499857	−	0.222551i
$477$	0.0291064	+	0.340984i	0.00133269	+	0.0156126i
$478$	−5.44819	−	25.6317i	−0.249195	−	1.17237i
$479$	1.60604	+	3.60724i	0.0733821	+	0.164819i	0.946512	−	0.322669i	$-0.104580\pi$
$479$	1.60604	+	3.60724i	0.0733821	+	0.164819i	−0.873130	+	0.487488i	$0.837913\pi$
$480$	−1.41115	+	1.00432i	−0.0644099	+	0.0458406i
$481$	2.94829	−	9.07390i	0.134430	−	0.413734i
$482$	−23.9977	+	10.6845i	−1.09307	+	0.486664i
$483$	−28.0607	−	12.8238i	−1.27681	−	0.583503i
$484$	−10.0215	−	2.13014i	−0.455523	−	0.0968244i
$485$	4.62356	−	10.3847i	0.209945	−	0.471544i
$486$	−11.0606	−	10.9847i	−0.501719	−	0.498275i
$487$	0.431094	+	0.0453098i	0.0195347	+	0.00205318i	0.114291	−	0.993447i	$-0.463540\pi$
$487$	0.431094	+	0.0453098i	0.0195347	+	0.00205318i	−0.0947561	+	0.995501i	$0.530207\pi$
$488$	−8.00114	−	5.81317i	−0.362195	−	0.263150i
$489$	−5.22514	+	8.84914i	−0.236289	+	0.400172i
$490$	7.36980	−	12.7649i	0.332934	−	0.576658i
$491$	−20.5882	−	35.6598i	−0.929132	−	1.60930i	−0.784777	−	0.619778i	$-0.787223\pi$
$491$	−20.5882	−	35.6598i	−0.929132	−	1.60930i	−0.144355	−	0.989526i	$-0.546111\pi$
$492$	−0.0833013	+	8.51455i	−0.00375551	+	0.383865i
$493$	−9.61293	−	10.6762i	−0.432945	−	0.480834i
$494$	2.66129	+	8.19061i	0.119737	+	0.368513i
$495$	−2.49378	+	0.756667i	−0.112087	+	0.0340097i
$496$	−4.64801	+	3.06529i	−0.208702	+	0.137636i
$497$			9.60527i			0.430855i
$498$	5.68504	+	1.90887i	0.254753	+	0.0855385i
$499$	3.81835	−	3.43806i	0.170933	−	0.153909i	−0.579224	−	0.815168i	$-0.696645\pi$
$499$	3.81835	−	3.43806i	0.170933	−	0.153909i	0.750157	+	0.661260i	$0.229978\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−0.877580	+	7.63074i	−0.0392074	+	0.340916i
$502$	20.3765	+	11.7644i	0.909449	+	0.525071i
$503$	−14.5269	+	1.52684i	−0.647724	+	0.0680785i	−0.422693	−	0.906273i	$-0.638915\pi$
$503$	−14.5269	+	1.52684i	−0.647724	+	0.0680785i	−0.225031	+	0.974352i	$0.572248\pi$
$504$	−13.2160	−	4.58189i	−0.588688	−	0.204094i
$505$	−1.90089	+	18.0858i	−0.0845885	+	0.804806i
$506$	2.46623	+	2.22060i	0.109637	+	0.0987177i
$507$	9.79051	+	17.3474i	0.434812	+	0.770426i
$508$	2.99674	−	14.0986i	0.132959	−	0.625522i
$509$	−6.02541	+	1.28074i	−0.267072	+	0.0567678i	−0.339501	−	0.940606i	$-0.610258\pi$
$509$	−6.02541	+	1.28074i	−0.267072	+	0.0567678i	0.0724293	+	0.997374i	$0.476925\pi$
$510$	−4.32846	−	0.964395i	−0.191667	−	0.0427041i
$511$	−55.8440	−	18.1448i	−2.47039	−	0.802680i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	2.75178	+	36.4409i	0.121494	+	1.60890i
$514$	13.0011	−	2.76347i	0.573454	−	0.121891i
$515$	1.84800	−	8.69414i	0.0814324	−	0.383109i
$516$	14.5485	−	8.21087i	0.640462	−	0.361463i
$517$	5.54645	+	4.99405i	0.243933	+	0.219638i
$518$	3.79734	−	36.1293i	0.166846	−	1.58743i
$519$	−25.1594	+	7.90351i	−1.10437	+	0.346926i
$520$	−1.21782	+	0.127998i	−0.0534049	+	0.00561308i
$521$	16.4739	+	9.51122i	0.721735	+	0.416694i	0.815391	−	0.578911i	$-0.196522\pi$
$521$	16.4739	+	9.51122i	0.721735	+	0.416694i	−0.0936558	+	0.995605i	$0.529855\pi$
$522$	−12.2869	−	11.5064i	−0.537784	−	0.503620i
$523$	1.91090	+	2.63012i	0.0835576	+	0.115007i	0.848750	−	0.528795i	$-0.177356\pi$
$523$	1.91090	+	2.63012i	0.0835576	+	0.115007i	−0.765192	+	0.643802i	$0.777356\pi$
$524$	−2.62032	+	2.35934i	−0.114469	+	0.103068i
$525$	2.57058	−	7.65578i	0.112189	−	0.334126i
$526$		−	15.1892i		−	0.662281i
$527$	−13.7952	−	3.59229i	−0.600927	−	0.156483i
$528$	1.20854	+	0.896249i	0.0525949	+	0.0390042i
$529$	−2.59737	−	7.99388i	−0.112929	−	0.347560i
$530$	0.0763309	+	0.0847740i	0.00331560	+	0.00368235i
$531$	−19.3822	+	25.6083i	−0.841117	+	1.11131i
$532$	16.3960	+	28.3987i	0.710856	+	1.23124i
$533$	−3.00996	+	5.21340i	−0.130376	+	0.225817i
$534$	9.40770	+	5.55495i	0.407111	+	0.240386i
$535$	−3.61625	−	2.62736i	−0.156344	−	0.113591i
$536$	0.753160	+	0.0791603i	0.0325316	+	0.00341921i
$537$	6.38235	−	1.29148i	0.275419	−	0.0557317i
$538$	−0.365041	+	0.819896i	−0.0157381	+	0.0353482i
$539$	−12.5242	−	2.66211i	−0.539457	−	0.114665i
$540$	−5.14952	−	0.694558i	−0.221600	−	0.0298890i
$541$	0.493101	−	0.219543i	0.0212001	−	0.00943888i	−0.396109	−	0.918203i	$-0.629640\pi$
$541$	0.493101	−	0.219543i	0.0212001	−	0.00943888i	0.417309	+	0.908765i	$0.362973\pi$
$542$	3.87008	−	11.9109i	0.166234	−	0.511616i
$543$	−13.6915	−	19.2377i	−0.587559	−	0.825570i
$544$	1.04137	+	2.33896i	0.0446485	+	0.100282i
$545$	2.07809	+	9.77665i	0.0890156	+	0.418785i
$546$	−6.54486	−	7.41339i	−0.280094	−	0.317264i
$547$	−35.1596	−	15.6541i	−1.50332	−	0.669320i	−0.520494	−	0.853865i	$-0.674252\pi$
$547$	−35.1596	−	15.6541i	−1.50332	−	0.669320i	−0.982824	+	0.184545i	$0.940919\pi$
$548$	−7.53195	+	8.36507i	−0.321749	+	0.357338i
$549$	−5.59973	−	29.1366i	−0.238990	−	1.24352i
$550$	−0.510599	+	0.702779i	−0.0217720	+	0.0299666i
$551$	4.12504	+	39.2471i	0.175732	+	1.67198i
$552$	2.63210	+	6.07094i	0.112029	+	0.258396i
$553$	45.8339	−	26.4622i	1.94905	−	1.12529i
$554$	11.1858	−	8.12695i	0.475239	−	0.345281i
$555$	−1.27927	−	13.4344i	−0.0543018	−	0.570260i
$556$	−1.17562	+	0.381982i	−0.0498574	+	0.0161996i
$557$	28.1529			1.19288			0.596439	−	0.802659i	$-0.296582\pi$
$557$	28.1529			1.19288			0.596439	+	0.802659i	$0.296582\pi$
$558$	−16.4637	−	2.81917i	−0.696963	−	0.119345i
$559$	11.8106			0.499533
$560$	−4.43437	+	1.44082i	−0.187386	+	0.0608855i
$561$	0.365171	+	3.83491i	0.0154175	+	0.161910i
$562$	−3.86658	+	2.80924i	−0.163102	+	0.118501i
$563$	31.6236	−	18.2579i	1.33278	−	0.769478i	0.347051	−	0.937846i	$-0.387183\pi$
$563$	31.6236	−	18.2579i	1.33278	−	0.769478i	0.985724	+	0.168368i	$0.0538496\pi$
$564$	5.91949	+	13.6533i	0.249255	+	0.574908i
$565$	−1.38919	−	13.2173i	−0.0584436	−	0.556054i
$566$	−0.0944175	+	0.129955i	−0.00396866	+	0.00546240i
$567$	−19.5438	−	37.1342i	−0.820761	−	1.55949i
$568$	1.37846	−	1.53094i	0.0578390	−	0.0642367i
$569$	22.7409	+	10.1249i	0.953348	+	0.424458i	0.823652	−	0.567096i	$-0.191933\pi$
$569$	22.7409	+	10.1249i	0.953348	+	0.424458i	0.129696	+	0.991554i	$0.458600\pi$
$570$	8.06209	+	9.13196i	0.337684	+	0.382496i
$571$	4.02840	+	18.9522i	0.168583	+	0.793123i	0.978446	+	0.206503i	$0.0662084\pi$
$571$	4.02840	+	18.9522i	0.168583	+	0.793123i	−0.809862	+	0.586620i	$0.800458\pi$
$572$	0.432656	+	0.971762i	0.0180903	+	0.0406314i
$573$	−3.28735	−	4.61901i	−0.137331	−	0.192962i
$574$	−7.08321	+	21.7999i	−0.295647	+	0.909909i
$575$	−3.49002	+	1.55386i	−0.145544	+	0.0648004i
$576$	1.44888	+	2.62693i	0.0603701	+	0.109455i
$577$	5.27651	+	1.12156i	0.219664	+	0.0466911i	0.316429	−	0.948616i	$-0.397516\pi$
$577$	5.27651	+	1.12156i	0.219664	+	0.0466911i	−0.0967648	+	0.995307i	$0.530849\pi$
$578$	4.24828	−	9.54179i	0.176705	−	0.396886i
$579$	9.90847	−	2.00500i	0.411782	−	0.0833250i
$580$	−5.58041	−	0.586525i	−0.231714	−	0.0243541i
$581$	13.0603	+	9.48887i	0.541833	+	0.393665i
$582$	−16.9540	−	10.0108i	−0.702768	−	0.414963i
$583$	0.0495474	−	0.0858186i	0.00205204	−	0.00355424i
$584$	6.29672	+	10.9062i	0.260560	+	0.451303i
$585$	−2.92918	−	2.21701i	−0.121106	−	0.0916621i
$586$	−15.1166	−	16.7887i	−0.624461	−	0.693535i
$587$	1.11231	+	3.42333i	0.0459098	+	0.141296i	0.971384	−	0.237515i	$-0.0763330\pi$
$587$	1.11231	+	3.42333i	0.0459098	+	0.141296i	−0.925474	+	0.378811i	$0.876333\pi$
$588$	−20.5062	−	15.2074i	−0.845662	−	0.627141i
$589$	24.8571	+	30.2570i	1.02422	+	1.24672i
$590$			10.7054i			0.440736i
$591$	1.03030	−	3.06847i	0.0423809	−	0.126220i
$592$	−5.79019	+	5.21351i	−0.237975	+	0.214274i
$593$	−2.48623	−	3.42200i	−0.102097	−	0.140525i	0.754911	−	0.655827i	$-0.227680\pi$
$593$	−2.48623	−	3.42200i	−0.102097	−	0.140525i	−0.857009	+	0.515302i	$0.827680\pi$
$594$	0.808506	+	4.44081i	0.0331734	+	0.182209i
$595$	−10.3383	−	5.96883i	−0.423830	−	0.244698i
$596$	22.6038	−	2.37575i	0.925887	−	0.0973146i
$597$	27.2789	−	8.56934i	1.11645	−	0.350720i
$598$	−0.488991	+	4.65244i	−0.0199963	+	0.190252i
$599$	−5.23221	−	4.71111i	−0.213782	−	0.192491i	0.555281	−	0.831663i	$-0.312611\pi$
$599$	−5.23221	−	4.71111i	−0.213782	−	0.192491i	−0.769064	+	0.639172i	$0.779277\pi$
$600$	−1.50840	+	0.851310i	−0.0615802	+	0.0347546i
$601$	−3.39396	+	15.9673i	−0.138443	+	0.651321i	0.853122	+	0.521711i	$0.174706\pi$
$601$	−3.39396	+	15.9673i	−0.138443	+	0.651321i	−0.991565	+	0.129610i	$0.958627\pi$
$602$	43.9878	−	9.34989i	1.79281	−	0.381073i
$603$	1.48689	+	1.71779i	0.0605509	+	0.0699538i
$604$	−13.0620	−	4.24410i	−0.531486	−	0.172690i
$605$	−9.74395	−	3.16600i	−0.396148	−	0.128716i
$606$	30.7442	+	6.84990i	1.24890	+	0.278258i
$607$	5.01573	−	1.06613i	0.203582	−	0.0432728i	−0.104992	−	0.994473i	$-0.533482\pi$
$607$	5.01573	−	1.06613i	0.203582	−	0.0432728i	0.308574	+	0.951200i	$0.400148\pi$
$608$	1.46225	−	6.87933i	0.0593019	−	0.278994i
$609$	−22.2723	−	39.4634i	−0.902519	−	1.59914i
$610$	−7.34967	−	6.61767i	−0.297579	−	0.267942i
$611$	−1.09972	+	10.4632i	−0.0444901	+	0.423295i
$612$	−2.51601	+	7.25717i	−0.101704	+	0.293354i
$613$	43.8992	−	4.61399i	1.77307	−	0.186357i	0.839166	−	0.543875i	$-0.183043\pi$
$613$	43.8992	−	4.61399i	1.77307	−	0.186357i	0.933907	+	0.357517i	$0.116377\pi$
$614$	10.2960	+	5.94438i	0.415511	+	0.239896i
$615$	−0.972858	+	8.45920i	−0.0392294	+	0.341108i
$616$	2.38071	+	3.27676i	0.0959214	+	0.132024i
$617$	−20.2178	+	18.2042i	−0.813938	+	0.732873i	−0.966844	−	0.255368i	$-0.917804\pi$
$617$	−20.2178	+	18.2042i	−0.813938	+	0.732873i	0.152906	+	0.988241i	$0.451137\pi$
$618$	−14.5944	−	4.90036i	−0.587072	−	0.197121i
$619$		−	26.1180i		−	1.04977i	−0.851173	−	0.524885i	$-0.824108\pi$
$619$		−	26.1180i		−	1.04977i	0.851173	−	0.524885i	$-0.175892\pi$
$620$	−4.94296	+	2.56265i	−0.198514	+	0.102918i
$621$	−6.68564	+	18.6912i	−0.268285	+	0.750051i
$622$	0.859834	+	2.64630i	0.0344762	+	0.106107i
$623$	19.6793	+	21.8561i	0.788435	+	0.875646i
$624$	−0.0207491	+	2.12084i	−0.000830627	+	0.0849016i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.3056	−	23.0460i	0.531800	−	0.921104i
$627$	5.38035	−	9.11199i	0.214870	−	0.363898i
$628$	7.16499	+	5.20567i	0.285914	+	0.207729i
$629$	−19.8393	−	2.08520i	−0.791045	−	0.0831422i
$630$	−12.6647	−	5.93824i	−0.504572	−	0.236585i
$631$	7.18246	−	16.1321i	0.285929	−	0.642207i	−0.712288	−	0.701887i	$-0.752341\pi$
$631$	7.18246	−	16.1321i	0.285929	−	0.642207i	0.998218	+	0.0596794i	$0.0190078\pi$
$632$	−11.1028	−	2.35998i	−0.441647	−	0.0938751i
$633$	11.3108	+	5.16906i	0.449564	+	0.205452i
$634$	11.3576	−	5.05675i	0.451070	−	0.200829i
$635$	4.45402	−	13.7081i	0.176753	−	0.543988i
$636$	0.160977	−	0.114567i	0.00638314	−	0.00454288i
$637$	−7.34121	−	16.4886i	−0.290869	−	0.653303i
$638$	1.01343	+	4.76779i	0.0401219	+	0.188759i
$639$	6.15784	−	0.525633i	0.243601	−	0.0207937i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	−32.0977	+	35.6481i	−1.26778	+	1.40802i	−0.395908	+	0.918290i	$0.629570\pi$
$641$	−32.0977	+	35.6481i	−1.26778	+	1.40802i	−0.871876	+	0.489727i	$0.837097\pi$
$642$	−5.23654	+	5.70258i	−0.206670	+	0.225063i
$643$	12.9807	−	17.8665i	0.511910	−	0.704584i	−0.472330	−	0.881422i	$-0.656587\pi$
$643$	12.9807	−	17.8665i	0.511910	−	0.704584i	0.984240	+	0.176838i	$0.0565868\pi$
$644$	1.86191	+	17.7149i	0.0733695	+	0.698064i
$645$	15.3271	−	6.64516i	0.603503	−	0.261653i
$646$	15.5943	−	9.00336i	0.613549	−	0.354233i
$647$	14.8380	−	10.7805i	0.583343	−	0.423824i	−0.256585	−	0.966522i	$-0.582597\pi$
$647$	14.8380	−	10.7805i	0.583343	−	0.423824i	0.839928	+	0.542698i	$0.182597\pi$
$648$	−2.21418	+	8.72338i	−0.0869812	+	0.342687i
$649$	8.84447	−	2.87374i	0.347176	−	0.112804i
$650$	−1.22453			−0.0480299
$651$	−40.0076	−	20.5226i	−1.56802	−	0.804343i
$652$	5.93322			0.232363
$653$	28.3984	−	9.22720i	1.11131	−	0.361088i	0.304868	−	0.952395i	$-0.401388\pi$
$653$	28.3984	−	9.22720i	1.11131	−	0.361088i	0.806447	+	0.591307i	$0.201388\pi$
$654$	17.2340	−	1.64107i	0.673903	−	0.0641710i
$655$	−2.85258	+	2.07252i	−0.111460	+	0.0809801i
$656$	4.25748	−	2.45806i	0.166227	−	0.0959710i
$657$	−8.57648	+	36.7940i	−0.334601	+	1.43547i
$658$	4.18737	+	39.8401i	0.163241	+	1.55313i
$659$	1.00751	−	1.38673i	0.0392472	−	0.0540191i	−0.788942	−	0.614467i	$-0.789371\pi$
$659$	1.00751	−	1.38673i	0.0392472	−	0.0540191i	0.828190	+	0.560448i	$0.189371\pi$
$660$	1.10823	+	1.01767i	0.0431380	+	0.0396126i
$661$	15.1732	−	16.8515i	0.590169	−	0.655449i	−0.371894	−	0.928275i	$-0.621292\pi$
$661$	15.1732	−	16.8515i	0.590169	−	0.655449i	0.962063	+	0.272826i	$0.0879583\pi$
$662$	−2.18543	−	0.973017i	−0.0849392	−	0.0378174i
$663$	−4.07084	+	3.59391i	−0.158098	+	0.139576i
$664$	−0.719862	−	3.38668i	−0.0279361	−	0.131429i
$665$	13.3377	+	29.9570i	0.517214	+	1.16168i
$666$	−23.3699	−	0.457319i	−0.905566	−	0.0177207i
$667$	−6.62418	+	20.3871i	−0.256489	+	0.789393i
$668$	4.05126	−	1.80373i	0.156748	−	0.0697886i
$669$	−4.93909	+	10.8076i	−0.190956	+	0.417845i
$670$	0.740760	+	0.157453i	0.0286181	+	0.00608295i
$671$	−3.49437	+	7.84848i	−0.134899	+	0.302987i
$672$	1.60170	+	7.91539i	0.0617868	+	0.305343i
$673$	−26.5778	−	2.79344i	−1.02450	−	0.107679i	−0.422652	−	0.906292i	$-0.638901\pi$
$673$	−26.5778	−	2.79344i	−1.02450	−	0.107679i	−0.601845	+	0.798613i	$0.705568\pi$
$674$	10.8222	+	7.86275i	0.416854	+	0.302862i
$675$	−5.04871	−	1.22902i	−0.194325	−	0.0473052i
$676$	5.75027	−	9.95975i	0.221164	−	0.383067i
$677$	−2.26108	−	3.91630i	−0.0869002	−	0.150516i	0.819299	−	0.573366i	$-0.194363\pi$
$677$	−2.26108	−	3.91630i	−0.0869002	−	0.150516i	−0.906199	+	0.422851i	$0.861029\pi$
$678$	−23.0180	−	0.225194i	−0.883999	−	0.00864853i
$679$	−35.4650	−	39.3878i	−1.36102	−	1.51157i
$680$	0.791180	+	2.43500i	0.0303404	+	0.0933781i
$681$	27.4845	−	37.0612i	1.05321	−	1.42019i
$682$	3.44405	+	3.39579i	0.131879	+	0.130032i
$683$			46.0641i			1.76260i	0.472562	+	0.881298i	$0.343329\pi$
$683$			46.0641i			1.76260i	−0.472562	+	0.881298i	$0.656671\pi$
$684$	17.3089	−	12.0654i	0.661821	−	0.461331i
$685$	−8.36507	+	7.53195i	−0.319613	+	0.287781i
$686$	−21.2111	−	29.1946i	−0.809844	−	1.11466i
$687$	25.0156	+	2.87694i	0.954404	+	0.109762i
$688$	−8.35280	−	4.82249i	−0.318448	−	0.183856i
$689$	0.138922	−	0.0146013i	0.00529252	−	0.000556266i
$690$	1.98309	+	6.31281i	0.0754950	+	0.240325i
$691$	−2.98625	+	28.4123i	−0.113602	+	1.08085i	0.778072	+	0.628175i	$0.216198\pi$
$691$	−2.98625	+	28.4123i	−0.113602	+	1.08085i	−0.891674	+	0.452678i	$0.850469\pi$
$692$	11.3149	+	10.1879i	0.430126	+	0.387287i
$693$	−1.50630	+	12.0572i	−0.0572196	+	0.458014i
$694$	2.88514	−	13.5735i	0.109518	−	0.515243i
$695$	−1.20911	+	0.257004i	−0.0458641	+	0.00974870i
$696$	−2.11355	+	9.48619i	−0.0801141	+	0.359573i
$697$	11.9707	+	3.88953i	0.453424	+	0.147327i
$698$	−5.74239	−	1.86581i	−0.217353	−	0.0706221i
$699$	−8.38510	+	37.6345i	−0.317154	+	1.42347i
$700$	−4.56069	+	0.969404i	−0.172378	+	0.0366400i
$701$	−6.25875	+	29.4451i	−0.236390	+	1.11213i	0.686520	+	0.727111i	$0.259137\pi$
$701$	−6.25875	+	29.4451i	−0.236390	+	1.11213i	−0.922910	+	0.385016i	$0.874196\pi$
$702$	−4.39449	+	4.60153i	−0.165859	+	0.173674i
$703$	40.7225	+	36.6667i	1.53588	+	1.38291i
$704$	0.0908021	−	0.863924i	0.00342223	−	0.0325604i
$705$	4.45990	+	14.1973i	0.167970	+	0.534700i
$706$	−15.0606	+	1.58294i	−0.566815	+	0.0595746i
$707$	73.4309	+	42.3954i	2.76165	+	1.59444i
$708$	18.4209	+	2.11852i	0.692301	+	0.0796187i
$709$	30.1045	+	41.4352i	1.13060	+	1.55613i	0.786930	+	0.617042i	$0.211669\pi$
$709$	30.1045	+	41.4352i	1.13060	+	1.55613i	0.343667	+	0.939092i	$0.388331\pi$
$710$	1.53094	−	1.37846i	0.0574550	−	0.0517327i
$711$	−19.4728	−	27.9355i	−0.730288	−	1.04766i
$712$		−	6.30773i		−	0.236392i
$713$	5.65004	+	20.5064i	0.211596	+	0.767972i
$714$	−12.3165	+	16.6080i	−0.460933	+	0.621541i
$715$	0.328709	+	1.01166i	0.0122930	+	0.0378341i
$716$	−2.51562	−	2.79388i	−0.0940132	−	0.104412i
$717$	−45.3851	−	0.444021i	−1.69494	−	0.0165823i
$718$	−0.147747	−	0.255906i	−0.00551388	−	0.00955031i
$719$	8.08232	−	13.9990i	0.301420	−	0.522075i	−0.675038	−	0.737783i	$-0.735873\pi$
$719$	8.08232	−	13.9990i	0.301420	−	0.522075i	0.976458	+	0.215709i	$0.0692061\pi$
$720$	1.16636	+	2.76399i	0.0434675	+	0.103008i
$721$	−33.5278	−	24.3594i	−1.24864	−	0.907192i
$722$	−30.2964	−	3.18428i	−1.12752	−	0.118507i
$723$	9.02391	+	44.5950i	0.335603	+	1.65851i
$724$	−5.54490	+	12.4540i	−0.206075	+	0.462851i
$725$	−5.48853	−	1.16662i	−0.203839	−	0.0433273i
$726$	−7.37601	+	16.1400i	−0.273749	+	0.599010i
$727$	30.3896	−	13.5303i	1.12709	−	0.501812i	0.243417	−	0.969922i	$-0.421732\pi$
$727$	30.3896	−	13.5303i	1.12709	−	0.501812i	0.883670	+	0.468110i	$0.155065\pi$
$728$	−1.76432	+	5.43001i	−0.0653899	+	0.201250i
$729$	−22.7369	+	14.5614i	−0.842106	+	0.539312i
$730$	5.12221	+	11.5047i	0.189582	+	0.425807i
$731$	−5.13421	−	24.1546i	−0.189896	−	0.893389i
$732$	−12.8415	+	11.3371i	−0.474636	+	0.419030i
$733$	20.5968	+	9.17027i	0.760759	+	0.338712i	0.750181	−	0.661232i	$-0.229966\pi$
$733$	20.5968	+	9.17027i	0.760759	+	0.338712i	0.0105777	+	0.999944i	$0.496633\pi$
$734$	3.18385	−	3.53603i	0.117518	−	0.130517i
$735$	−18.8043	−	17.2675i	−0.693606	−	0.636922i
$736$	2.24552	−	3.09069i	0.0827710	−	0.113924i
$737$	−0.0687652	−	0.654257i	−0.00253300	−	0.0240999i
$738$	14.3633	+	3.34801i	0.528720	+	0.123242i
$739$	−29.8678	+	17.2442i	−1.09871	+	0.634338i	−0.935881	−	0.352317i	$-0.885394\pi$
$739$	−29.8678	+	17.2442i	−1.09871	+	0.634338i	−0.162825	+	0.986655i	$0.552060\pi$
$740$	−6.30343	+	4.57971i	−0.231719	+	0.168353i
$741$	14.8495	−	1.41401i	0.545508	−	0.0519449i
$742$	0.505850	−	0.164361i	0.0185703	−	0.00603387i
$743$	−12.5487			−0.460368			−0.230184	−	0.973147i	$-0.573933\pi$
$743$	−12.5487			−0.460368			−0.230184	+	0.973147i	$0.573933\pi$
$744$	3.43140	+	9.01252i	0.125801	+	0.330415i
$745$	22.7283			0.832700
$746$	2.04744	−	0.665255i	0.0749622	−	0.0243567i
$747$	5.36852	−	8.89210i	0.196424	−	0.325345i
$748$	1.79934	−	1.30729i	0.0657902	−	0.0477994i
$749$	−18.0492	+	10.4207i	−0.659502	+	0.380764i
$750$	−1.58912	+	0.688975i	−0.0580266	+	0.0251578i
$751$	2.15160	+	20.4711i	0.0785129	+	0.747000i	0.960978	+	0.276623i	$0.0892154\pi$
$751$	2.15160	+	20.4711i	0.0785129	+	0.747000i	−0.882466	+	0.470377i	$0.844118\pi$
$752$	5.05009	−	6.95085i	0.184158	−	0.253472i
$753$	27.5641	−	30.0172i	1.00449	−	1.09389i
$754$	−4.59760	+	5.10615i	−0.167435	+	0.185955i
$755$	−12.5468	−	5.58621i	−0.456626	−	0.203303i
$756$	−12.7242	+	20.6171i	−0.462775	+	0.749836i
$757$	4.76628	+	22.4236i	0.173233	+	0.814999i	0.975839	+	0.218490i	$0.0701130\pi$
$757$	4.76628	+	22.4236i	0.173233	+	0.814999i	−0.802606	+	0.596510i	$0.796554\pi$
$758$	5.99301	+	13.4605i	0.217676	+	0.488908i
$759$	4.68309	−	3.33296i	0.169986	−	0.120979i
$760$	2.17332	−	6.68880i	0.0788346	−	0.242628i
$761$	41.4014	−	18.4331i	1.50080	−	0.668199i	0.518426	−	0.855123i	$-0.326518\pi$
$761$	41.4014	−	18.4331i	1.50080	−	0.668199i	0.982375	+	0.186923i	$0.0598515\pi$
$762$	−22.7062	−	10.3768i	−0.822559	−	0.375912i
$763$	45.5843	+	9.68925i	1.65026	+	0.350774i
$764$	−1.33134	+	2.99023i	−0.0481661	+	0.108183i
$765$	−3.26081	+	6.95442i	−0.117895	+	0.251438i
$766$	−26.4985	−	2.78510i	−0.957428	−	0.100630i
$767$	10.6055	+	7.70533i	0.382942	+	0.278224i
$768$	0.880658	−	1.49146i	0.0317780	−	0.0538183i
$769$	7.46653	−	12.9324i	0.269250	−	0.466355i	−0.699418	−	0.714713i	$-0.746558\pi$
$769$	7.46653	−	12.9324i	0.269250	−	0.466355i	0.968668	+	0.248358i	$0.0798908\pi$
$770$	2.02515	+	3.50766i	0.0729813	+	0.126407i
$771$	0.225220	−	23.0206i	0.00811108	−	0.829065i
$772$	−3.90545	−	4.33744i	−0.140560	−	0.156108i
$773$	−11.0966	−	34.1517i	−0.399116	−	1.22835i	−0.925710	−	0.378235i	$-0.876531\pi$
$773$	−11.0966	−	34.1517i	−0.399116	−	1.22835i	0.526594	−	0.850117i	$-0.323469\pi$
$774$	−8.40128	−	27.6885i	−0.301978	−	0.995241i
$775$	−5.18375	+	2.03193i	−0.186206	+	0.0729891i
$776$			11.3674i			0.408068i
$777$	−59.6497	−	20.0286i	−2.13992	−	0.718523i
$778$	1.24077	−	1.11719i	0.0444836	−	0.0400533i
$779$	−20.3227	−	27.9718i	−0.728137	−	1.00220i
$780$	−0.242324	+	2.10705i	−0.00867658	+	0.0754447i
$781$	−1.54980	−	0.894777i	−0.0554562	−	0.0320177i
$782$	9.72760	−	1.02241i	0.347858	−	0.0365614i
$783$	−24.0808	+	16.4381i	−0.860576	+	0.587450i
$784$	−1.54071	+	14.6589i	−0.0550253	+	0.523531i
$785$	6.58160	+	5.92610i	0.234907	+	0.211512i
$786$	3.00170	+	5.31859i	0.107067	+	0.189708i
$787$	−7.34405	+	34.5510i	−0.261787	+	1.23161i	0.629078	+	0.777343i	$0.283433\pi$
$787$	−7.34405	+	34.5510i	−0.261787	+	1.23161i	−0.890865	+	0.454269i	$0.849901\pi$
$788$	−1.82794	+	0.388541i	−0.0651178	+	0.0138412i
$789$	−25.6788	−	5.72133i	−0.914190	−	0.203685i
$790$	−10.7953	−	3.50762i	−0.384081	−	0.124795i
$791$	−58.9331	−	19.1485i	−2.09542	−	0.680843i
$792$	1.97042	−	1.70556i	0.0700157	−	0.0606045i
$793$	−11.8459	+	2.51792i	−0.420659	+	0.0894139i
$794$	5.22340	−	24.5741i	0.185371	−	0.872104i
$795$	0.172070	−	0.0971129i	0.00610271	−	0.00344424i
$796$	−12.2681	−	11.0462i	−0.434830	−	0.391523i
$797$	4.70756	−	44.7894i	0.166750	−	1.58652i	−0.516466	−	0.856308i	$-0.672753\pi$
$797$	4.70756	−	44.7894i	0.166750	−	1.58652i	0.683217	−	0.730216i	$-0.260580\pi$
$798$	54.1866	−	17.0221i	1.91819	−	0.602574i
$799$	21.8770	−	2.29937i	0.773953	−	0.0813458i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	12.9348	−	13.8122i	0.457029	−	0.488032i
$802$	21.1976	+	29.1760i	0.748512	+	1.03024i
$803$	8.12979	−	7.32009i	0.286894	−	0.258320i
$804$	0.417522	−	1.24347i	0.0147249	−	0.0438539i
$805$			17.8125i			0.627807i
$806$	−1.01902	+	6.74130i	−0.0358934	+	0.237452i
$807$	1.24861	+	0.925969i	0.0439533	+	0.0325956i
$808$	−5.61959	−	17.2953i	−0.197697	−	0.608448i
$809$	−32.1695	−	35.7279i	−1.13102	−	1.25612i	−0.962753	−	0.270384i	$-0.912850\pi$
$809$	−32.1695	−	35.7279i	−1.13102	−	1.25612i	−0.168267	−	0.985741i	$-0.553817\pi$
$810$	−3.11389	+	8.44415i	−0.109411	+	0.296697i
$811$	24.0154	+	41.5959i	0.843294	+	1.46063i	0.887095	+	0.461588i	$0.152720\pi$
$811$	24.0154	+	41.5959i	0.843294	+	1.46063i	−0.0438005	+	0.999040i	$0.513947\pi$
$812$	−13.0812	+	22.6573i	−0.459060	+	0.795115i
$813$	−18.6788	−	11.0292i	−0.655092	−	0.386812i
$814$	5.47568	+	3.97831i	0.191922	+	0.139440i
$815$	5.90072	+	0.620191i	0.206693	+	0.0217243i
$816$	4.34650	−	0.879524i	0.152158	−	0.0307895i
$817$	−27.5903	+	61.9689i	−0.965263	+	2.16802i
$818$	−19.0779	−	4.05512i	−0.667042	−	0.141784i
$819$	−14.9983	+	8.27232i	−0.524083	+	0.289058i
$820$	4.49109	−	1.99956i	0.156836	−	0.0698278i
$821$	−5.74811	+	17.6908i	−0.200610	+	0.617415i	0.799255	+	0.600992i	$0.205228\pi$
$821$	−5.74811	+	17.6908i	−0.200610	+	0.617415i	−0.999865	+	0.0164227i	$0.994772\pi$
$822$	11.3049	+	15.8844i	0.394304	+	0.554031i
$823$	−11.7137	−	26.3095i	−0.408315	−	0.917091i	−0.994285	−	0.106758i	$-0.965953\pi$
$823$	−11.7137	−	26.3095i	−0.408315	−	0.917091i	0.585970	−	0.810333i	$-0.300714\pi$
$824$	1.84800	+	8.69414i	0.0643780	+	0.302875i
$825$	0.995789	+	1.12793i	0.0346689	+	0.0392696i
$826$	45.5995	+	20.3022i	1.58661	+	0.706405i
$827$	16.7835	−	18.6399i	0.583619	−	0.648174i	−0.376945	−	0.926236i	$-0.623025\pi$
$827$	16.7835	−	18.6399i	0.583619	−	0.648174i	0.960563	+	0.278062i	$0.0896919\pi$
$828$	11.2549	−	2.16307i	0.391136	−	0.0751719i
$829$	12.3367	−	16.9800i	0.428472	−	0.589741i	−0.539130	−	0.842223i	$-0.681247\pi$
$829$	12.3367	−	16.9800i	0.428472	−	0.589741i	0.967602	+	0.252482i	$0.0812468\pi$
$830$	−0.361913	−	3.44338i	−0.0125622	−	0.119521i
$831$	−9.52604	−	21.9719i	−0.330455	−	0.762195i
$832$	1.06047	−	0.612264i	0.0367652	−	0.0212264i
$833$	−30.5307	+	22.1819i	−1.05783	+	0.768556i
$834$	0.202956	+	2.13138i	0.00702780	+	0.0738037i
$835$	4.21760	−	1.37038i	0.145956	−	0.0474240i
$836$	−6.10946			−0.211300
$837$	−10.9675	+	26.7715i	−0.379091	+	0.925360i
$838$	−35.9143			−1.24064
$839$	39.7085	−	12.9021i	1.37089	−	0.445429i	0.471227	−	0.882012i	$-0.343811\pi$
$839$	39.7085	−	12.9021i	1.37089	−	0.445429i	0.899664	+	0.436583i	$0.143811\pi$
$840$	0.765540	+	8.03945i	0.0264136	+	0.277387i
$841$	−2.01039	+	1.46063i	−0.0693238	+	0.0503667i
$842$	−32.8507	+	18.9664i	−1.13211	+	0.653625i
$843$	3.29286	+	7.59499i	0.113412	+	0.261585i
$844$	−0.750505	−	7.14058i	−0.0258334	−	0.245789i
$845$	6.75984	−	9.30413i	0.232546	−	0.320072i
$846$	25.3120	−	4.86467i	0.870243	−	0.167251i
$847$	−31.9643	+	35.5000i	−1.09831	+	1.21979i
$848$	−0.104212	−	0.0463984i	−0.00357867	−	0.00159333i
$849$	0.184137	+	0.208572i	0.00631955	+	0.00715817i
$850$	0.532319	+	2.50436i	0.0182584	+	0.0858990i
$851$	12.1068	+	27.1924i	0.415017	+	0.932143i
$852$	−2.06897	−	2.90708i	−0.0708818	−	0.0995950i
$853$	7.29158	−	22.4412i	0.249659	−	0.768371i	−0.745176	−	0.666867i	$-0.767635\pi$
$853$	7.29158	−	22.4412i	0.249659	−	0.768371i	0.994835	−	0.101503i	$-0.0323653\pi$
$854$	−42.1260	+	18.7557i	−1.44152	+	0.641807i
$855$	18.4752	−	10.1900i	0.631839	−	0.348491i
$856$	4.37225	+	0.929351i	0.149440	+	0.0317645i
$857$	−12.5525	+	28.1933i	−0.428784	+	0.963064i	0.561941	+	0.827177i	$0.310055\pi$
$857$	−12.5525	+	28.1933i	−0.428784	+	0.963064i	−0.990724	+	0.135886i	$0.956612\pi$
$858$	1.80583	−	0.365413i	0.0616499	−	0.0124750i
$859$	−18.6364	−	1.95876i	−0.635865	−	0.0668321i	−0.218889	−	0.975750i	$-0.570243\pi$
$859$	−18.6364	−	1.95876i	−0.635865	−	0.0668321i	−0.416976	+	0.908918i	$0.636910\pi$
$860$	−7.80296	−	5.66918i	−0.266079	−	0.193318i
$861$	34.1868	+	20.1862i	1.16508	+	0.687945i
$862$	−8.30140	+	14.3784i	−0.282747	+	0.489732i
$863$	3.47493	+	6.01875i	0.118288	+	0.204881i	0.919089	−	0.394049i	$-0.128926\pi$
$863$	3.47493	+	6.01875i	0.118288	+	0.204881i	−0.800801	+	0.598930i	$0.795593\pi$
$864$	4.98683	−	1.45999i	0.169655	−	0.0496698i
$865$	10.1879	+	11.3149i	0.346400	+	0.384717i
$866$	4.37467	+	13.4639i	0.148657	+	0.457520i
$867$	−14.5311	−	10.7762i	−0.493503	−	0.365980i
$868$	1.54151	+	25.9143i	0.0523222	+	0.879589i
$869$			9.86032i			0.334488i
$870$	−3.09355	+	9.21330i	−0.104881	+	0.312360i
$871$	0.689152	−	0.620515i	0.0233510	−	0.0210254i
$872$	−5.87495	−	8.08617i	−0.198951	−	0.273832i
$873$	−23.3104	+	24.8917i	−0.788937	+	0.842456i
$874$	−23.2686	−	13.4341i	−0.787072	−	0.454416i
$875$	−4.63703	+	0.487372i	−0.156760	+	0.0164762i
$876$	20.8099	−	6.53716i	0.703100	−	0.220870i
$877$	5.13297	−	48.8370i	0.173328	−	1.64911i	−0.469380	−	0.882996i	$-0.655522\pi$
$877$	5.13297	−	48.8370i	0.173328	−	1.64911i	0.642708	−	0.766111i	$-0.277811\pi$
$878$	6.75393	+	6.08127i	0.227934	+	0.205233i
$879$	−34.0769	+	19.2323i	−1.14939	+	0.648689i
$880$	0.180609	−	0.849700i	0.00608834	−	0.0286434i
$881$	−34.3766	+	7.30696i	−1.15818	+	0.246178i	−0.746648	−	0.665219i	$-0.768338\pi$
$881$	−34.3766	+	7.30696i	−1.15818	+	0.246178i	−0.411528	+	0.911397i	$0.635005\pi$
$882$	−33.4336	+	28.9396i	−1.12577	+	0.974447i
$883$	−8.71119	−	2.83044i	−0.293155	−	0.0952518i	0.158747	−	0.987319i	$-0.449254\pi$
$883$	−8.71119	−	2.83044i	−0.293155	−	0.0952518i	−0.451902	+	0.892067i	$0.649254\pi$
$884$	2.98173	+	0.968822i	0.100286	+	0.0325850i
$885$	18.0986	+	4.03242i	0.608377	+	0.135548i
$886$	0.970272	−	0.206238i	0.0325969	−	0.00692869i
$887$	3.40174	−	16.0039i	0.114219	−	0.537359i	−0.883414	−	0.468594i	$-0.844761\pi$
$887$	3.40174	−	16.0039i	0.114219	−	0.537359i	0.997633	−	0.0687650i	$-0.0219059\pi$
$888$	6.63295	+	11.7526i	0.222587	+	0.394393i
$889$	−49.9424	−	44.9684i	−1.67501	−	1.50819i
$890$	0.659337	−	6.27318i	0.0221010	−	0.210277i
$891$	7.81216	+	0.305865i	0.261717	+	0.0102468i
$892$	6.82289	−	0.717114i	0.228447	−	0.0240108i
$893$	−52.3302	−	30.2129i	−1.75116	−	1.01104i
$894$	4.49774	−	39.1087i	0.150427	−	1.30799i
$895$	−2.20980	−	3.04153i	−0.0738655	−	0.101667i
$896$	3.46497	−	3.11987i	0.115756	−	0.104228i
$897$	7.68122	+	2.57913i	0.256468	+	0.0861145i
$898$			23.4907i			0.783895i
$899$	−10.9899	+	29.2448i	−0.366534	+	0.975367i
$900$	0.871051	+	2.87076i	0.0290350	+	0.0956920i
$901$	−0.0902537	−	0.277772i	−0.00300679	−	0.00925394i
$902$	−2.85755	−	3.17363i	−0.0951460	−	0.105670i
$903$	0.762005	−	77.8874i	0.0253579	−	2.59193i
$904$	6.64503	+	11.5095i	0.221010	+	0.382801i
$905$	−6.81633	+	11.8062i	−0.226582	+	0.392452i
$906$	−12.0951	+	20.4840i	−0.401834	+	0.680534i
$907$	−19.3507	−	14.0591i	−0.642530	−	0.466826i	0.218188	−	0.975907i	$-0.429985\pi$
$907$	−19.3507	−	14.0591i	−0.642530	−	0.466826i	−0.860719	+	0.509081i	$0.829985\pi$
$908$	−26.4932	−	2.78454i	−0.879207	−	0.0924084i
$909$	23.1608	−	49.3958i	0.768197	−	1.63836i
$910$	−2.32224	+	5.21584i	−0.0769816	+	0.172904i
$911$	7.14472	+	1.51866i	0.236715	+	0.0503153i	0.324742	−	0.945803i	$-0.394723\pi$
$911$	7.14472	+	1.51866i	0.236715	+	0.0503153i	−0.0880265	+	0.996118i	$0.528056\pi$
$912$	−11.0794	−	5.06331i	−0.366875	−	0.167663i
$913$	−2.74765	+	1.22333i	−0.0909340	+	0.0404864i
$914$	−0.198005	+	0.609398i	−0.00654944	+	0.0201571i
$915$	−13.9562	+	9.93265i	−0.461378	+	0.328363i
$916$	−5.91312	−	13.2811i	−0.195375	−	0.438819i
$917$	3.41810	+	16.0809i	0.112876	+	0.531038i
$918$	11.3213	+	6.98712i	0.373657	+	0.230609i
$919$	−12.1067	−	5.39023i	−0.399362	−	0.177807i	0.197221	−	0.980359i	$-0.436808\pi$
$919$	−12.1067	−	5.39023i	−0.399362	−	0.177807i	−0.596583	+	0.802552i	$0.703475\pi$
$920$	2.55628	−	2.83904i	0.0842782	−	0.0936004i
$921$	13.9277	−	15.1673i	0.458935	−	0.499778i
$922$	20.6951	−	28.4844i	0.681557	−	0.938083i
$923$	−0.263686	−	2.50880i	−0.00867933	−	0.0825783i
$924$	6.43642	−	2.79056i	0.211743	−	0.0918025i
$925$	−6.74761	+	3.89573i	−0.221860	+	0.128091i
$926$	−5.06897	+	3.68283i	−0.166577	+	0.121025i
$927$	−13.7818	+	22.8274i	−0.452654	+	0.749750i
$928$	5.33652	−	1.73394i	0.175180	−	0.0569194i
$929$	43.2109			1.41770			0.708852	−	0.705357i	$-0.249213\pi$
$929$	43.2109			1.41770			0.708852	+	0.705357i	$0.249213\pi$
$930$	2.47054	+	9.32183i	0.0810122	+	0.305675i
$931$	103.664			3.39745
$932$	21.1716	−	6.87905i	0.693497	−	0.225331i
$933$	4.79769	−	0.456850i	0.157069	−	0.0149566i
$934$	−25.4095	+	18.4611i	−0.831424	+	0.604065i
$935$	1.92613	−	1.11205i	0.0629911	−	0.0363679i
$936$	3.57767	+	0.833937i	0.116940	+	0.0272581i
$937$	−2.04339	−	19.4416i	−0.0667548	−	0.635129i	−0.975835	−	0.218508i	$-0.929881\pi$
$937$	−2.04339	−	19.4416i	−0.0667548	−	0.635129i	0.909080	−	0.416621i	$-0.136786\pi$
$938$	2.07548	−	2.85665i	0.0677667	−	0.0932728i
$939$	−33.9497	−	31.1752i	−1.10791	−	1.01736i
$940$	5.74899	−	6.38490i	0.187511	−	0.208252i
$941$	−15.2392	−	6.78494i	−0.496784	−	0.221183i	0.143021	−	0.989720i	$-0.454318\pi$
$941$	−15.2392	−	6.78494i	−0.496784	−	0.221183i	−0.639805	+	0.768537i	$0.720985\pi$
$942$	11.4995	−	10.1523i	0.374675	−	0.330780i
$943$	−3.90480	−	18.3706i	−0.127158	−	0.598230i
$944$	−4.35429	−	9.77990i	−0.141720	−	0.318309i
$945$	−14.8096	+	19.1741i	−0.481756	+	0.623733i
$946$	−2.58908	+	7.96837i	−0.0841782	+	0.259074i
$947$	−22.6375	+	10.0789i	−0.735620	+	0.327519i	−0.740124	−	0.672471i	$-0.765233\pi$
$947$	−22.6375	+	10.0789i	−0.735620	+	0.327519i	0.00450372	+	0.999990i	$0.498566\pi$
$948$	−8.17190	+	17.8815i	−0.265411	+	0.580764i
$949$	15.0840	+	3.20621i	0.489648	+	0.104078i
$950$	2.86059	−	6.42498i	0.0928096	−	0.208454i
$951$	−4.27084	−	21.1059i	−0.138491	−	0.684407i
$952$	11.8723	+	1.24782i	0.384782	+	0.0404422i
$953$	−5.90735	−	4.29194i	−0.191358	−	0.139030i	0.487981	−	0.872854i	$-0.337733\pi$
$953$	−5.90735	−	4.29194i	−0.191358	−	0.139030i	−0.679339	+	0.733824i	$0.737733\pi$
$954$	−0.133052	−	0.315301i	−0.00430771	−	0.0102082i
$955$	−1.63661	+	2.83469i	−0.0529594	+	0.0917284i
$956$	13.1022	+	22.6936i	0.423755	+	0.733965i
$957$	8.44214	+	0.0825929i	0.272896	+	0.00266985i
$958$	−2.64214	−	2.93439i	−0.0853635	−	0.0948058i
$959$	16.2183	+	49.9147i	0.523715	+	1.61183i
$960$	1.03173	−	1.39123i	0.0332991	−	0.0449018i
$961$	6.87246	+	30.2286i	0.221692	+	0.975117i
$962$			9.54086i			0.307610i
$963$	7.66831	+	11.0009i	0.247108	+	0.354498i
$964$	19.5215	−	17.5772i	0.628745	−	0.566125i
$965$	−3.43067	−	4.72191i	−0.110437	−	0.152004i
$966$	30.6501	+	3.52494i	0.986150	+	0.113413i
$967$	19.5399	+	11.2813i	0.628360	+	0.362784i	0.780117	−	0.625634i	$-0.215160\pi$
$967$	19.5399	+	11.2813i	0.628360	+	0.362784i	−0.151757	+	0.988418i	$0.548493\pi$
$968$	10.1893	−	1.07093i	0.327495	−	0.0344212i
$969$	−9.34715	−	29.7550i	−0.300274	−	0.955867i
$970$	−1.18822	+	11.3052i	−0.0381515	+	0.362987i
$971$	−37.4116	−	33.6855i	−1.20059	−	1.08102i	−0.994739	−	0.102437i	$-0.967336\pi$
$971$	−37.4116	−	33.6855i	−1.20059	−	1.08102i	−0.205855	−	0.978583i	$-0.565997\pi$
$972$	13.9137	+	7.02913i	0.446282	+	0.225459i
$973$	−1.19830	+	5.63755i	−0.0384157	+	0.180732i
$974$	−0.423996	+	0.0901231i	−0.0135857	+	0.00288773i
$975$	−0.461243	+	2.07018i	−0.0147716	+	0.0662989i
$976$	9.40590	+	3.05616i	0.301076	+	0.0978254i
$977$	−19.8816	−	6.45994i	−0.636070	−	0.206672i	−0.0268079	−	0.999641i	$-0.508534\pi$
$977$	−19.8816	−	6.45994i	−0.636070	−	0.206672i	−0.609262	+	0.792969i	$0.708534\pi$
$978$	2.23487	−	10.0307i	0.0714633	−	0.320746i
$979$	−5.35968	+	1.13923i	−0.171296	+	0.0364101i
$980$	−3.06454	+	14.4175i	−0.0978931	+	0.460551i
$981$	3.71715	−	29.7539i	0.118679	−	0.949969i
$982$	30.6000	+	27.5524i	0.976486	+	0.879232i
$983$	5.92454	−	56.3682i	0.188964	−	1.79787i	−0.330949	−	0.943649i	$-0.607369\pi$
$983$	5.92454	−	56.3682i	0.188964	−	1.79787i	0.519913	−	0.854219i	$-0.325964\pi$
$984$	−2.55192	−	8.12356i	−0.0813521	−	0.258970i
$985$	−1.85854	+	0.195341i	−0.0592181	+	0.00622407i
$986$	12.4416	+	7.18315i	0.396221	+	0.228758i
$987$	68.9309	+	7.92746i	2.19409	+	0.252334i
$988$	−5.06208	−	6.96735i	−0.161046	−	0.221661i
$989$	−27.3825	+	24.6553i	−0.870713	+	0.783994i
$990$	2.13790	−	1.49025i	0.0679470	−	0.0473634i
$991$		−	11.0220i		−	0.350125i	−0.984557	−	0.175063i	$-0.943987\pi$
$991$		−	11.0220i		−	0.350125i	0.984557	−	0.175063i	$-0.0560128\pi$
$992$	3.47329	−	4.35158i	0.110277	−	0.138163i
$993$	−2.46817	+	3.32818i	−0.0783249	+	0.105617i
$994$	−2.96819	−	9.13516i	−0.0941453	−	0.289750i
$995$	−11.0462	−	12.2681i	−0.350189	−	0.388924i
$996$	−5.99667	−	0.0586679i	−0.190012	−	0.00185896i
$997$	−26.4098	−	45.7431i	−0.836406	−	1.44870i	−0.892880	−	0.450294i	$-0.851319\pi$
$997$	−26.4098	−	45.7431i	−0.836406	−	1.44870i	0.0564744	−	0.998404i	$-0.482014\pi$
$998$	−2.56905	+	4.44972i	−0.0813218	+	0.140853i
$999$	−9.57590	+	39.3369i	−0.302968	+	1.24456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.6	✓	176
3.2	odd	2	inner	930.2.br.a.11.12	yes	176
31.17	odd	30	inner	930.2.br.a.761.12	yes	176
93.17	even	30	inner	930.2.br.a.761.6	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.6	✓	176	1.1	even	1	trivial
930.2.br.a.11.12	yes	176	3.2	odd	2	inner
930.2.br.a.761.6	yes	176	93.17	even	30	inner
930.2.br.a.761.12	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.164188 + 1.72425i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.688975 - 1.58912i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.94608 + 0.566203i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.164188 + 1.72425i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.688975 - 1.58912i) q^{6} +(-0.487372 - 4.63703i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-2.94608 + 0.566203i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(0.793581 + 0.353325i) q^{11} +(1.14632 + 1.29844i) q^{12} +(0.254594 + 1.19777i) q^{13} +(1.89644 + 4.25947i) q^{14} +(1.00432 + 1.41115i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.33896 - 1.04137i) q^{17} +(2.62693 - 1.44888i) q^{18} +(-6.87933 - 1.46225i) q^{19} +(0.406737 - 0.913545i) q^{20} +(7.91539 - 1.60170i) q^{21} +(-0.863924 - 0.0908021i) q^{22} +(-3.09069 - 2.24552i) q^{23} +(-1.49146 - 0.880658i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.612264 - 1.06047i) q^{26} +(-1.45999 - 4.98683i) q^{27} +(-3.11987 - 3.46497i) q^{28} +(-1.73394 - 5.33652i) q^{29} +(-1.39123 - 1.03173i) q^{30} +(-4.35158 - 3.47329i) q^{31} +1.00000i q^{32} +(-0.478925 + 1.42635i) q^{33} +(-1.90268 + 1.71318i) q^{34} +(-2.74059 - 3.77210i) q^{35} +(-2.05063 + 2.18973i) q^{36} +(-6.74761 - 3.89573i) q^{37} +(6.99449 - 0.735150i) q^{38} +(-2.02345 + 0.635643i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(3.65338 + 3.28952i) q^{41} +(-7.03303 + 3.96930i) q^{42} +(2.00531 - 9.43422i) q^{43} +(0.849700 - 0.180609i) q^{44} +(-2.26828 + 1.96339i) q^{45} +(3.63333 + 1.18054i) q^{46} +(8.17122 + 2.65499i) q^{47} +(1.69060 + 0.376671i) q^{48} +(-14.4175 + 3.06454i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(2.17962 + 3.86198i) q^{51} +(0.910001 + 0.819369i) q^{52} +(0.0119241 - 0.113450i) q^{53} +(2.92955 + 4.29159i) q^{54} +(0.863924 - 0.0908021i) q^{55} +(4.03791 + 2.33129i) q^{56} +(1.39178 - 12.1018i) q^{57} +(3.29815 + 4.53951i) q^{58} +(7.95569 - 7.16334i) q^{59} +(1.64196 + 0.551323i) q^{60} +9.88995i q^{61} +(5.21190 + 1.95859i) q^{62} +(4.06134 + 13.3851i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.819369 + 0.910001i) q^{65} +(0.0147194 - 1.50453i) q^{66} +(-0.378654 - 0.655849i) q^{67} +(1.28016 - 2.21730i) q^{68} +(3.36438 - 5.69782i) q^{69} +(3.77210 + 2.74059i) q^{70} +(-2.04879 - 0.215337i) q^{71} +(1.27360 - 2.71624i) q^{72} +(5.12221 - 11.5047i) q^{73} +(7.62120 + 1.61994i) q^{74} +(1.57534 + 0.719934i) q^{75} +(-6.42498 + 2.86059i) q^{76} +(1.25161 - 3.85206i) q^{77} +(1.72799 - 1.22981i) q^{78} +(4.61682 + 10.3696i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(8.35883 - 3.33617i) q^{81} +(-4.49109 - 1.99956i) q^{82} +(-2.31676 + 2.57302i) q^{83} +(5.46223 - 5.94835i) q^{84} +(1.50491 - 2.07134i) q^{85} +(1.00818 + 9.59215i) q^{86} +(8.91681 - 3.86594i) q^{87} +(-0.752301 + 0.434341i) q^{88} +(-5.10306 + 3.70759i) q^{89} +(1.55054 - 2.56823i) q^{90} +(5.43001 - 1.76432i) q^{91} -3.82031 q^{92} +(5.27435 - 8.07349i) q^{93} -8.59173 q^{94} +(-6.68880 + 2.17332i) q^{95} +(-1.72425 + 0.164188i) q^{96} +(9.19646 - 6.68162i) q^{97} +(12.7649 - 7.36980i) q^{98} +(-2.53801 - 0.591597i) 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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