LMFDB - Embedded newform 930.2.br.b.11.2

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			11.2
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.26144 - 1.18692i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.56648 + 0.739021i) q^{6} +(0.426617 + 4.05899i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.182449 + 2.99445i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.26144 - 1.18692i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.56648 + 0.739021i) q^{6} +(0.426617 + 4.05899i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.182449 + 2.99445i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.30515 - 1.47155i) q^{11} +(-1.71818 - 0.218783i) q^{12} +(-0.315521 - 1.48441i) q^{13} +(-1.66003 - 3.72850i) q^{14} +(1.68590 + 0.397183i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.831557 - 0.370233i) q^{17} +(-1.09885 - 2.79151i) q^{18} +(-5.99902 - 1.27513i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(4.27954 - 5.62652i) q^{21} +(3.59812 + 0.378178i) q^{22} +(5.09792 + 3.70386i) q^{23} +(1.70169 - 0.322871i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.758786 + 1.31426i) q^{26} +(3.32402 - 3.99386i) q^{27} +(2.73096 + 3.03303i) q^{28} +(-0.234766 - 0.722537i) q^{29} +(-1.72612 + 0.143227i) q^{30} +(3.18326 - 4.56803i) q^{31} +1.00000i q^{32} +(2.42264 + 5.77922i) q^{33} +(-0.676450 + 0.609078i) q^{34} +(-2.39896 - 3.30188i) q^{35} +(1.90770 + 2.31532i) q^{36} +(6.51379 + 3.76074i) q^{37} +(6.09945 - 0.641078i) q^{38} +(-1.36386 + 2.24699i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-4.77654 - 4.30082i) q^{41} +(-2.33139 + 6.67359i) q^{42} +(2.06985 - 9.73786i) q^{43} +(-3.53888 + 0.752212i) q^{44} +(-1.65523 - 2.50204i) q^{45} +(-5.99297 - 1.94723i) q^{46} +(-9.32882 - 3.03112i) q^{47} +(-1.51863 + 0.832920i) q^{48} +(-9.44638 + 2.00789i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-1.48839 - 0.519965i) q^{51} +(-1.12778 - 1.01545i) q^{52} +(1.09808 - 10.4475i) q^{53} +(-1.92716 + 4.82556i) q^{54} +(3.59812 - 0.378178i) q^{55} +(-3.53455 - 2.04068i) q^{56} +(6.05392 + 8.72885i) q^{57} +(0.446552 + 0.614627i) q^{58} +(-6.39219 + 5.75555i) q^{59} +(1.59738 - 0.669617i) q^{60} -10.8474i q^{61} +(-1.61586 + 5.32813i) q^{62} +(-12.0766 + 2.01804i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.01545 + 1.12778i) q^{65} +(-4.08994 - 4.74773i) q^{66} +(-3.17730 - 5.50324i) q^{67} +(0.455126 - 0.788302i) q^{68} +(-2.03453 - 10.7230i) q^{69} +(3.30188 + 2.39896i) q^{70} +(-2.69884 - 0.283660i) q^{71} +(-2.52980 - 1.61249i) q^{72} +(-4.41226 + 9.91010i) q^{73} +(-7.35712 - 1.56380i) q^{74} +(-1.65862 + 0.498978i) q^{75} +(-5.60282 + 2.49453i) q^{76} +(4.56297 - 14.0434i) q^{77} +(0.602754 - 2.55847i) q^{78} +(-5.32318 - 11.9561i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-8.93342 + 1.09267i) q^{81} +(5.87179 + 2.61429i) q^{82} +(-4.85446 + 5.39142i) q^{83} +(0.155034 - 7.06741i) q^{84} +(-0.535033 + 0.736410i) q^{85} +(1.04062 + 9.90088i) q^{86} +(-0.561449 + 1.19008i) q^{87} +(3.13323 - 1.80897i) q^{88} +(-5.08325 + 3.69320i) q^{89} +(2.34739 + 1.86809i) q^{90} +(5.89060 - 1.91397i) q^{91} +6.30138 q^{92} +(-9.43736 + 1.98401i) q^{93} +9.80891 q^{94} +(5.83287 - 1.89522i) q^{95} +(1.18692 - 1.26144i) q^{96} +(10.0834 - 7.32599i) q^{97} +(8.36357 - 4.82871i) q^{98} +(3.80346 - 10.1656i) 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} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 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 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * 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
$3$	−1.26144	−	1.18692i	−0.728291	−	0.685268i
$3$	−1.26144	−	1.18692i	−0.728291	−	0.685268i
$4$	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
$6$	1.56648	+	0.739021i	0.639511	+	0.301704i
$7$	0.426617	+	4.05899i	0.161246	+	1.53415i	0.713605	+	0.700548i	$0.247061\pi$
$7$	0.426617	+	4.05899i	0.161246	+	1.53415i	−0.552359	+	0.833607i	$0.686272\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.182449	+	2.99445i	0.0608163	+	0.998149i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−3.30515	−	1.47155i	−0.996542	−	0.443689i	−0.157361	−	0.987541i	$-0.550299\pi$
$11$	−3.30515	−	1.47155i	−0.996542	−	0.443689i	−0.839181	+	0.543852i	$0.816965\pi$
$12$	−1.71818	−	0.218783i	−0.495995	−	0.0631572i
$13$	−0.315521	−	1.48441i	−0.0875098	−	0.411701i	−0.999997	−	0.00259505i	$-0.999174\pi$
$13$	−0.315521	−	1.48441i	−0.0875098	−	0.411701i	0.912487	−	0.409106i	$-0.134159\pi$
$14$	−1.66003	−	3.72850i	−0.443663	−	0.996483i
$15$	1.68590	+	0.397183i	0.435297	+	0.102552i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.831557	−	0.370233i	0.201682	−	0.0897947i	−0.303410	−	0.952860i	$-0.598125\pi$
$17$	0.831557	−	0.370233i	0.201682	−	0.0897947i	0.505092	+	0.863065i	$0.331458\pi$
$18$	−1.09885	−	2.79151i	−0.259002	−	0.657965i
$19$	−5.99902	−	1.27513i	−1.37627	−	0.292535i	−0.540375	−	0.841424i	$-0.681718\pi$
$19$	−5.99902	−	1.27513i	−1.37627	−	0.292535i	−0.835895	+	0.548889i	$0.815051\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	4.27954	−	5.62652i	0.933873	−	1.22781i
$22$	3.59812	+	0.378178i	0.767122	+	0.0806278i
$23$	5.09792	+	3.70386i	1.06299	+	0.772308i	0.974639	−	0.223781i	$-0.0718402\pi$
$23$	5.09792	+	3.70386i	1.06299	+	0.772308i	0.0883513	+	0.996089i	$0.471840\pi$
$24$	1.70169	−	0.322871i	0.347356	−	0.0659058i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.758786	+	1.31426i	0.148810	+	0.257747i
$27$	3.32402	−	3.99386i	0.639707	−	0.768619i
$28$	2.73096	+	3.03303i	0.516102	+	0.573190i
$29$	−0.234766	−	0.722537i	−0.0435950	−	0.134172i	0.926890	−	0.375333i	$-0.122472\pi$
$29$	−0.234766	−	0.722537i	−0.0435950	−	0.134172i	−0.970485	+	0.241161i	$0.922472\pi$
$30$	−1.72612	+	0.143227i	−0.315145	+	0.0261496i
$31$	3.18326	−	4.56803i	0.571730	−	0.820442i
$31$	3.18326	−	4.56803i	0.571730	−	0.820442i
$32$			1.00000i			0.176777i
$33$	2.42264	+	5.77922i	0.421727	+	1.00603i
$34$	−0.676450	+	0.609078i	−0.116010	+	0.104456i
$35$	−2.39896	−	3.30188i	−0.405498	−	0.558120i
$36$	1.90770	+	2.31532i	0.317949	+	0.385886i
$37$	6.51379	+	3.76074i	1.07086	+	0.618262i	0.928416	−	0.371541i	$-0.121171\pi$
$37$	6.51379	+	3.76074i	1.07086	+	0.618262i	0.142444	+	0.989803i	$0.454504\pi$
$38$	6.09945	−	0.641078i	0.989461	−	0.103997i
$39$	−1.36386	+	2.24699i	−0.218393	+	0.359806i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	−4.77654	−	4.30082i	−0.745971	−	0.671675i	0.205762	−	0.978602i	$-0.434033\pi$
$41$	−4.77654	−	4.30082i	−0.745971	−	0.671675i	−0.951733	+	0.306927i	$0.900699\pi$
$42$	−2.33139	+	6.67359i	−0.359742	+	1.02976i
$43$	2.06985	−	9.73786i	0.315649	−	1.48501i	−0.478932	−	0.877852i	$-0.658976\pi$
$43$	2.06985	−	9.73786i	0.315649	−	1.48501i	0.794581	−	0.607158i	$-0.207691\pi$
$44$	−3.53888	+	0.752212i	−0.533506	+	0.113400i
$45$	−1.65523	−	2.50204i	−0.246747	−	0.372983i
$46$	−5.99297	−	1.94723i	−0.883615	−	0.287104i
$47$	−9.32882	−	3.03112i	−1.36075	−	0.442134i	−0.464456	−	0.885596i	$-0.653750\pi$
$47$	−9.32882	−	3.03112i	−1.36075	−	0.442134i	−0.896293	+	0.443462i	$0.853750\pi$
$48$	−1.51863	+	0.832920i	−0.219196	+	0.120222i
$49$	−9.44638	+	2.00789i	−1.34948	+	0.286842i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	−1.48839	−	0.519965i	−0.208417	−	0.0728096i
$52$	−1.12778	−	1.01545i	−0.156394	−	0.140818i
$53$	1.09808	−	10.4475i	0.150833	−	1.43508i	−0.613213	−	0.789918i	$-0.710123\pi$
$53$	1.09808	−	10.4475i	0.150833	−	1.43508i	0.764046	−	0.645162i	$-0.223210\pi$
$54$	−1.92716	+	4.82556i	−0.262253	+	0.656676i
$55$	3.59812	−	0.378178i	0.485171	−	0.0509935i
$56$	−3.53455	−	2.04068i	−0.472325	−	0.272697i
$57$	6.05392	+	8.72885i	0.801861	+	1.15616i
$58$	0.446552	+	0.614627i	0.0586352	+	0.0807044i
$59$	−6.39219	+	5.75555i	−0.832192	+	0.749309i	−0.970505	−	0.241080i	$-0.922499\pi$
$59$	−6.39219	+	5.75555i	−0.832192	+	0.749309i	0.138313	+	0.990389i	$0.455832\pi$
$60$	1.59738	−	0.669617i	0.206220	−	0.0864472i
$61$		−	10.8474i		−	1.38887i	−0.719556	−	0.694435i	$-0.755654\pi$
$61$		−	10.8474i		−	1.38887i	0.719556	−	0.694435i	$-0.244346\pi$
$62$	−1.61586	+	5.32813i	−0.205215	+	0.676673i
$63$	−12.0766	+	2.01804i	−1.52151	+	0.254249i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	1.01545	+	1.12778i	0.125952	+	0.139883i
$66$	−4.08994	−	4.74773i	−0.503437	−	0.584405i
$67$	−3.17730	−	5.50324i	−0.388169	−	0.672328i	0.604035	−	0.796958i	$-0.293559\pi$
$67$	−3.17730	−	5.50324i	−0.388169	−	0.672328i	−0.992203	+	0.124630i	$0.960226\pi$
$68$	0.455126	−	0.788302i	0.0551922	−	0.0955957i
$69$	−2.03453	−	10.7230i	−0.244929	−	1.29090i
$70$	3.30188	+	2.39896i	0.394650	+	0.286730i
$71$	−2.69884	−	0.283660i	−0.320293	−	0.0336642i	−0.0569824	−	0.998375i	$-0.518148\pi$
$71$	−2.69884	−	0.283660i	−0.320293	−	0.0336642i	−0.263311	+	0.964711i	$0.584815\pi$
$72$	−2.52980	−	1.61249i	−0.298140	−	0.190033i
$73$	−4.41226	+	9.91010i	−0.516416	+	1.15989i	0.447646	+	0.894211i	$0.352262\pi$
$73$	−4.41226	+	9.91010i	−0.516416	+	1.15989i	−0.964062	+	0.265678i	$0.914404\pi$
$74$	−7.35712	−	1.56380i	−0.855247	−	0.181788i
$75$	−1.65862	+	0.498978i	−0.191521	+	0.0576170i
$76$	−5.60282	+	2.49453i	−0.642687	+	0.286143i
$77$	4.56297	−	14.0434i	0.519999	−	1.60039i
$78$	0.602754	−	2.55847i	0.0682484	−	0.289689i
$79$	−5.32318	−	11.9561i	−0.598904	−	1.34516i	−0.917676	−	0.397329i	$-0.869937\pi$
$79$	−5.32318	−	11.9561i	−0.598904	−	1.34516i	0.318772	−	0.947831i	$-0.396730\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−8.93342	+	1.09267i	−0.992603	+	0.121407i
$82$	5.87179	+	2.61429i	0.648431	+	0.288700i
$83$	−4.85446	+	5.39142i	−0.532846	+	0.591785i	−0.948121	−	0.317911i	$-0.897019\pi$
$83$	−4.85446	+	5.39142i	−0.532846	+	0.591785i	0.415275	+	0.909696i	$0.363685\pi$
$84$	0.155034	−	7.06741i	0.0169156	−	0.771117i
$85$	−0.535033	+	0.736410i	−0.0580325	+	0.0798749i
$86$	1.04062	+	9.90088i	0.112213	+	1.06764i
$87$	−0.561449	+	1.19008i	−0.0601937	+	0.127590i
$88$	3.13323	−	1.80897i	0.334003	−	0.192837i
$89$	−5.08325	+	3.69320i	−0.538823	+	0.391478i	−0.823648	−	0.567102i	$-0.808065\pi$
$89$	−5.08325	+	3.69320i	−0.538823	+	0.391478i	0.284825	+	0.958580i	$0.408065\pi$
$90$	2.34739	+	1.86809i	0.247437	+	0.196914i
$91$	5.89060	−	1.91397i	0.617503	−	0.200639i
$92$	6.30138			0.656964
$93$	−9.43736	+	1.98401i	−0.978608	+	0.205732i
$94$	9.80891			1.01171
$95$	5.83287	−	1.89522i	0.598440	−	0.194445i
$96$	1.18692	−	1.26144i	0.121139	−	0.128745i
$97$	10.0834	−	7.32599i	1.02381	−	0.743841i	0.0567493	−	0.998388i	$-0.481926\pi$
$97$	10.0834	−	7.32599i	1.02381	−	0.743841i	0.967060	+	0.254547i	$0.0819264\pi$
$98$	8.36357	−	4.82871i	0.844848	−	0.487773i
$99$	3.80346	−	10.1656i	0.382262	−	1.02168i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	4.70947	−	6.48203i	0.468610	−	0.644986i	−0.507656	−	0.861560i	$-0.669488\pi$
$101$	4.70947	−	6.48203i	0.468610	−	0.644986i	0.976266	+	0.216573i	$0.0694880\pi$
$102$	1.57623	+	0.0345768i	0.156070	+	0.00342362i
$103$	−11.2903	+	12.5392i	−1.11247	+	1.23552i	−0.143153	+	0.989701i	$0.545724\pi$
$103$	−11.2903	+	12.5392i	−1.11247	+	1.23552i	−0.969315	+	0.245820i	$0.920943\pi$
$104$	1.38637	+	0.617252i	0.135945	+	0.0605265i
$105$	−0.892930	+	7.01248i	−0.0871410	+	0.684348i
$106$	2.18413	+	10.2755i	0.212142	+	0.998047i
$107$	6.39157	+	14.3557i	0.617897	+	1.38782i	0.903133	+	0.429362i	$0.141261\pi$
$107$	6.39157	+	14.3557i	0.617897	+	1.38782i	−0.285236	+	0.958457i	$0.592072\pi$
$108$	0.341654	−	5.18491i	0.0328757	−	0.498918i
$109$	2.59598	−	7.98961i	0.248650	−	0.765265i	−0.746365	−	0.665537i	$-0.768203\pi$
$109$	2.59598	−	7.98961i	0.248650	−	0.765265i	0.995015	−	0.0997284i	$-0.0317974\pi$
$110$	−3.30515	+	1.47155i	−0.315134	+	0.140307i
$111$	−3.75305	−	12.4753i	−0.356224	−	1.18410i
$112$	3.99216	+	0.848560i	0.377224	+	0.0801814i
$113$	7.80569	−	17.5319i	0.734298	−	1.64926i	−0.0259801	−	0.999662i	$-0.508271\pi$
$113$	7.80569	−	17.5319i	0.734298	−	1.64926i	0.760278	−	0.649598i	$-0.225063\pi$
$114$	−8.45498	−	6.43087i	−0.791881	−	0.602306i
$115$	−6.26686	−	0.658674i	−0.584388	−	0.0614216i
$116$	−0.614627	−	0.446552i	−0.0570667	−	0.0414613i
$117$	4.38742	−	1.21564i	0.405617	−	0.112386i
$118$	4.30077	−	7.44915i	0.395918	−	0.685750i
$119$	1.85753	+	3.21734i	0.170280	+	0.294933i
$120$	−1.31227	+	1.13046i	−0.119794	+	0.103196i
$121$	1.39815	+	1.55281i	0.127105	+	0.141164i
$122$	3.35204	+	10.3165i	0.303479	+	0.934013i
$123$	0.920589	+	11.0946i	0.0830067	+	1.00036i
$124$	−0.109707	−	5.56668i	−0.00985196	−	0.499903i
$125$			1.00000i			0.0894427i
$126$	10.8619	−	5.65115i	0.967657	−	0.503444i
$127$	3.15317	−	2.83912i	0.279798	−	0.251931i	−0.517268	−	0.855824i	$-0.673051\pi$
$127$	3.15317	−	2.83912i	0.279798	−	0.251931i	0.797066	+	0.603892i	$0.206384\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−14.1690	+	9.82697i	−1.24751	+	0.865216i
$130$	−1.31426	−	0.758786i	−0.115268	−	0.0665499i
$131$	1.79029	−	0.188168i	0.156419	−	0.0164403i	−0.0259954	−	0.999662i	$-0.508276\pi$
$131$	1.79029	−	0.188168i	0.156419	−	0.0164403i	0.182414	+	0.983222i	$0.441609\pi$
$132$	5.35689	+	3.25149i	0.466258	+	0.283006i
$133$	2.61646	−	24.8940i	0.226876	−	2.15858i
$134$	4.72238	+	4.25205i	0.407952	+	0.367322i
$135$	−0.881753	+	5.12079i	−0.0758892	+	0.440728i
$136$	−0.189252	+	0.890362i	−0.0162282	+	0.0763479i
$137$	−4.46170	+	0.948363i	−0.381188	+	0.0810241i	−0.394521	−	0.918887i	$-0.629089\pi$
$137$	−4.46170	+	0.948363i	−0.381188	+	0.0810241i	0.0133323	+	0.999911i	$0.495756\pi$
$138$	5.24855	+	9.56948i	0.446786	+	0.814608i
$139$	−1.00223	−	0.325643i	−0.0850077	−	0.0276207i	0.266204	−	0.963917i	$-0.414230\pi$
$139$	−1.00223	−	0.325643i	−0.0850077	−	0.0276207i	−0.351212	+	0.936296i	$0.614230\pi$
$140$	−3.88159	−	1.26121i	−0.328055	−	0.106591i
$141$	8.17004	+	14.8961i	0.688041	+	1.25448i
$142$	2.65441	−	0.564211i	0.222753	−	0.0473476i
$143$	−1.14154	+	5.37051i	−0.0954601	+	0.449104i
$144$	2.90427	+	0.751816i	0.242022	+	0.0626513i
$145$	0.564582	+	0.508352i	0.0468860	+	0.0422163i
$146$	1.13392	−	10.7885i	0.0938439	−	0.892865i
$147$	14.2992	+	8.67926i	1.17938	+	0.715853i
$148$	7.48027	−	0.786208i	0.614875	−	0.0646259i
$149$	20.3089	+	11.7253i	1.66377	+	0.960577i	0.970891	+	0.239521i	$0.0769904\pi$
$149$	20.3089	+	11.7253i	1.66377	+	0.960577i	0.692877	+	0.721056i	$0.256343\pi$
$150$	1.42325	−	0.987098i	0.116208	−	0.0805962i
$151$	0.758279	+	1.04368i	0.0617078	+	0.0849336i	0.838756	−	0.544508i	$-0.183284\pi$
$151$	0.758279	+	1.04368i	0.0617078	+	0.0849336i	−0.777048	+	0.629442i	$0.783284\pi$
$152$	4.55774	−	4.10381i	0.369682	−	0.332863i
$153$	1.26036	+	2.42251i	0.101894	+	0.195848i
$154$			14.7661i			1.18989i
$155$	−0.472771	+	5.54766i	−0.0379739	+	0.445598i
$156$	0.217358	+	2.61951i	0.0174025	+	0.209729i
$157$	3.84289	+	11.8272i	0.306696	+	0.943913i	0.979039	+	0.203673i	$0.0652880\pi$
$157$	3.84289	+	11.8272i	0.306696	+	0.943913i	−0.672343	+	0.740240i	$0.734712\pi$
$158$	8.75727	+	9.72593i	0.696691	+	0.773753i
$159$	−13.7855	+	11.8756i	−1.09326	+	0.941795i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−12.8591	+	22.2726i	−1.01344	+	1.75532i
$162$	8.15854	−	3.79977i	0.640995	−	0.298538i
$163$	−18.1316	−	13.1734i	−1.42018	−	1.03182i	−0.991742	−	0.128249i	$-0.959064\pi$
$163$	−18.1316	−	13.1734i	−1.42018	−	1.03182i	−0.428437	−	0.903572i	$-0.640936\pi$
$164$	−6.39226	−	0.671854i	−0.499152	−	0.0524630i
$165$	−4.98767	−	3.79363i	−0.388290	−	0.295334i
$166$	2.95082	−	6.62766i	0.229028	−	0.514406i
$167$	−5.16142	−	1.09709i	−0.399402	−	0.0848956i	0.00383121	−	0.999993i	$-0.498780\pi$
$167$	−5.16142	−	1.09709i	−0.399402	−	0.0848956i	−0.403234	+	0.915097i	$0.632114\pi$
$168$	2.03650	+	6.76941i	0.157120	+	0.522271i
$169$	9.77217	−	4.35085i	0.751706	−	0.334681i
$170$	0.281284	−	0.865702i	0.0215735	−	0.0663963i
$171$	2.72380	−	18.1964i	0.208294	−	1.39151i
$172$	−4.04923	−	9.09472i	−0.308751	−	0.693466i
$173$	−1.25640	−	5.91088i	−0.0955221	−	0.449396i	−0.999750	−	0.0223465i	$-0.992886\pi$
$173$	−1.25640	−	5.91088i	−0.0955221	−	0.449396i	0.904228	−	0.427050i	$-0.140447\pi$
$174$	0.166214	−	1.30533i	0.0126006	−	0.0989571i
$175$	3.72850	+	1.66003i	0.281848	+	0.125487i
$176$	−2.42088	+	2.68865i	−0.182480	+	0.202665i
$177$	14.8947	+	0.326738i	1.11956	+	0.0245591i
$178$	3.69320	−	5.08325i	0.276817	−	0.381005i
$179$	−1.37631	−	13.0947i	−0.102870	−	0.978747i	−0.917222	−	0.398375i	$-0.869574\pi$
$179$	−1.37631	−	13.0947i	−0.102870	−	0.978747i	0.814352	−	0.580371i	$-0.197093\pi$
$180$	−2.80977	−	1.05128i	−0.209428	−	0.0783575i
$181$	−17.2702	+	9.97095i	−1.28368	+	0.741135i	−0.977520	−	0.210845i	$-0.932379\pi$
$181$	−17.2702	+	9.97095i	−1.28368	+	0.741135i	−0.306163	+	0.951979i	$0.599045\pi$
$182$	−5.01084	+	3.64059i	−0.371428	+	0.269859i
$183$	−12.8750	+	13.6833i	−0.951748	+	1.01150i
$184$	−5.99297	+	1.94723i	−0.441808	+	0.143552i
$185$	−7.52148			−0.552990
$186$	8.36237	−	4.80321i	0.613159	−	0.352188i
$187$	−3.29324			−0.240826
$188$	−9.32882	+	3.03112i	−0.680374	+	0.221067i
$189$	17.6291	+	11.7883i	1.28233	+	0.857473i
$190$	−4.96174	+	3.60491i	−0.359962	+	0.261528i
$191$	3.61957	−	2.08976i	0.261903	−	0.151210i	−0.363299	−	0.931673i	$-0.618350\pi$
$191$	3.61957	−	2.08976i	0.261903	−	0.151210i	0.625202	+	0.780463i	$0.285016\pi$
$192$	−0.739021	+	1.56648i	−0.0533342	+	0.113051i
$193$	−0.312514	−	2.97337i	−0.0224952	−	0.214028i	−0.999995	−	0.00309239i	$-0.999016\pi$
$193$	−0.312514	−	2.97337i	−0.0224952	−	0.214028i	0.977500	−	0.210936i	$-0.0676510\pi$
$194$	−7.32599	+	10.0834i	−0.525975	+	0.723943i
$195$	0.0576464	−	2.62788i	0.00412815	−	0.188186i
$196$	−6.46208	+	7.17686i	−0.461577	+	0.512633i
$197$	−1.85500	−	0.825899i	−0.132163	−	0.0588429i	0.339590	−	0.940574i	$-0.389712\pi$
$197$	−1.85500	−	0.825899i	−0.132163	−	0.0588429i	−0.471753	+	0.881731i	$0.656379\pi$
$198$	−0.475961	+	10.8434i	−0.0338250	+	0.770606i
$199$	−2.85520	−	13.4327i	−0.202400	−	0.952216i	−0.955655	−	0.294488i	$-0.904851\pi$
$199$	−2.85520	−	13.4327i	−0.202400	−	0.952216i	0.753255	−	0.657728i	$-0.228482\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−2.52394	+	10.7132i	−0.178025	+	0.755650i
$202$	−2.47592	+	7.62009i	−0.174205	+	0.536147i
$203$	2.83262	−	1.26116i	0.198811	−	0.0885162i
$204$	−1.50976	+	0.454196i	−0.105705	+	0.0318001i
$205$	6.28702	+	1.33635i	0.439104	+	0.0933345i
$206$	6.86291	−	15.4144i	0.478162	−	1.07397i
$207$	−10.1609	+	15.9412i	−0.706231	+	1.10799i
$208$	−1.50926	−	0.158629i	−0.104648	−	0.0109990i
$209$	17.9513	+	13.0424i	1.24172	+	0.902160i
$210$	−1.31775	−	6.94520i	−0.0909334	−	0.479264i
$211$	1.52165	−	2.63558i	0.104755	−	0.181440i	−0.808883	−	0.587969i	$-0.799928\pi$
$211$	1.52165	−	2.63558i	0.104755	−	0.181440i	0.913638	+	0.406529i	$0.133261\pi$
$212$	−5.25254	−	9.09767i	−0.360746	−	0.624831i
$213$	3.06774	+	3.56112i	0.210198	+	0.244004i
$214$	−10.5149	−	11.6780i	−0.718784	−	0.798291i
$215$	3.07639	+	9.46816i	0.209808	+	0.645723i
$216$	1.27729	+	5.03672i	0.0869087	+	0.342705i
$217$	19.8996	+	10.9720i	1.35087	+	0.744830i
$218$			8.40077i			0.568972i
$219$	17.3283	−	7.26397i	1.17094	−	0.490854i
$220$	2.68865	−	2.42088i	0.181269	−	0.163215i
$221$	−0.811951	−	1.11756i	−0.0546178	−	0.0751749i
$222$	7.42443	+	10.7049i	0.498295	+	0.718468i
$223$	9.66341	+	5.57917i	0.647110	+	0.373609i	0.787348	−	0.616509i	$-0.211453\pi$
$223$	9.66341	+	5.57917i	0.647110	+	0.373609i	−0.140238	+	0.990118i	$0.544787\pi$
$224$	−4.05899	+	0.426617i	−0.271203	+	0.0285046i
$225$	2.68449	+	1.33922i	0.178966	+	0.0892812i
$226$	−2.00601	+	19.0859i	−0.133438	+	1.26958i
$227$	−13.3073	−	11.9820i	−0.883237	−	0.795270i	0.0965472	−	0.995328i	$-0.469220\pi$
$227$	−13.3073	−	11.9820i	−0.883237	−	0.795270i	−0.979784	+	0.200058i	$0.935887\pi$
$228$	10.0284	+	3.50339i	0.664148	+	0.232017i
$229$	1.48170	−	6.97085i	0.0979134	−	0.460647i	−0.901687	−	0.432389i	$-0.857671\pi$
$229$	1.48170	−	6.97085i	0.0979134	−	0.460647i	0.999601	−	0.0282577i	$-0.00899589\pi$
$230$	6.16368	−	1.31013i	0.406421	−	0.0863875i
$231$	−22.4243	+	12.2990i	−1.47541	+	0.809213i
$232$	0.722537	+	0.234766i	0.0474369	+	0.0154132i
$233$	−1.68590	−	0.547783i	−0.110447	−	0.0358865i	0.253272	−	0.967395i	$-0.418493\pi$
$233$	−1.68590	−	0.547783i	−0.110447	−	0.0358865i	−0.363719	+	0.931509i	$0.618493\pi$
$234$	−3.79703	+	2.51193i	−0.248220	+	0.164210i
$235$	9.59456	−	2.03939i	0.625880	−	0.133035i
$236$	−1.78836	+	8.41357i	−0.116412	+	0.547677i
$237$	−7.47600	+	21.4000i	−0.485619	+	1.39008i
$238$	−2.76083	−	2.48586i	−0.178958	−	0.161134i
$239$	0.545577	−	5.19082i	0.0352904	−	0.335766i	−0.962604	−	0.270911i	$-0.912675\pi$
$239$	0.545577	−	5.19082i	0.0352904	−	0.335766i	0.997895	−	0.0648547i	$-0.0206584\pi$
$240$	0.898714	−	1.48065i	0.0580117	−	0.0955753i
$241$	1.83884	−	0.193270i	0.118450	−	0.0124496i	−0.0451178	−	0.998982i	$-0.514366\pi$
$241$	1.83884	−	0.193270i	0.118450	−	0.0124496i	0.163568	+	0.986532i	$0.447700\pi$
$242$	−1.80956	−	1.04475i	−0.116323	−	0.0671592i
$243$	12.5659	+	9.22492i	0.806100	+	0.591779i
$244$	−6.37595	−	8.77575i	−0.408179	−	0.561810i
$245$	7.17686	−	6.46208i	0.458513	−	0.412847i
$246$	−4.30395	−	10.2671i	−0.274410	−	0.654606i
$247$			9.30734i			0.592212i
$248$	1.82454	+	5.26033i	0.115858	+	0.334031i
$249$	12.5228	−	1.03910i	0.793599	−	0.0658500i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	5.66127	+	6.28748i	0.357336	+	0.396862i	0.894831	−	0.446405i	$-0.147296\pi$
$251$	5.66127	+	6.28748i	0.357336	+	0.396862i	−0.537495	+	0.843267i	$0.680629\pi$
$252$	−8.58400	+	8.73108i	−0.540741	+	0.550006i
$253$	−11.3990	−	19.7437i	−0.716650	−	1.24127i
$254$	−2.12150	+	3.67455i	−0.133115	+	0.230562i
$255$	1.54897	−	0.293894i	0.0970002	−	0.0184044i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	28.2834	+	2.97271i	1.76427	+	0.185432i	0.930405	−	0.366534i	$-0.119456\pi$
$257$	28.2834	+	2.97271i	1.76427	+	0.185432i	0.833866	+	0.551967i	$0.186122\pi$
$258$	10.4389	−	13.7245i	0.649895	−	0.854448i
$259$	−12.4859	+	28.0438i	−0.775837	+	1.74256i
$260$	1.48441	+	0.315521i	0.0920591	+	0.0195678i
$261$	2.12077	−	0.834822i	0.131272	−	0.0516742i
$262$	−1.64452	+	0.732189i	−0.101599	+	0.0452348i
$263$	−2.42838	+	7.47379i	−0.149740	+	0.460854i	−0.997590	−	0.0693831i	$-0.977897\pi$
$263$	−2.42838	+	7.47379i	−0.149740	+	0.460854i	0.847850	+	0.530237i	$0.177897\pi$
$264$	−6.09947	−	1.43698i	−0.375397	−	0.0884403i
$265$	4.27280	+	9.59687i	0.262476	+	0.589531i
$266$	5.20426	+	24.4841i	0.319094	+	1.50122i
$267$	10.7957	+	1.37467i	0.660687	+	0.0841282i
$268$	−5.80521	−	2.58465i	−0.354610	−	0.157882i
$269$	16.8556	−	18.7200i	1.02770	−	1.14138i	0.0378492	−	0.999283i	$-0.487949\pi$
$269$	16.8556	−	18.7200i	1.02770	−	1.14138i	0.989853	−	0.142095i	$-0.0453840\pi$
$270$	−0.743814	−	5.14264i	−0.0452671	−	0.312971i
$271$	−6.39274	+	8.79886i	−0.388332	+	0.534493i	−0.957768	−	0.287543i	$-0.907162\pi$
$271$	−6.39274	+	8.79886i	−0.388332	+	0.534493i	0.569436	+	0.822036i	$0.307162\pi$
$272$	−0.0951473	−	0.905266i	−0.00576915	−	0.0548898i
$273$	−9.70235	−	4.57731i	−0.587213	−	0.277031i
$274$	3.95027	−	2.28069i	0.238644	−	0.137781i
$275$	−2.92698	+	2.12657i	−0.176503	+	0.128237i
$276$	−7.94880	−	7.47923i	−0.478461	−	0.450196i
$277$	−10.7453	+	3.49136i	−0.645622	+	0.209775i	−0.613483	−	0.789708i	$-0.710232\pi$
$277$	−10.7453	+	3.49136i	−0.645622	+	0.209775i	−0.0321394	+	0.999483i	$0.510232\pi$
$278$	1.05380			0.0632029
$279$	14.2595	+	8.69867i	0.853693	+	0.520776i
$280$	4.08135			0.243907
$281$	−6.38416	+	2.07434i	−0.380847	+	0.123745i	−0.493183	−	0.869926i	$-0.664167\pi$
$281$	−6.38416	+	2.07434i	−0.380847	+	0.123745i	0.112336	+	0.993670i	$0.464167\pi$
$282$	−12.3733	−	11.6424i	−0.736821	−	0.693293i
$283$	−12.0044	+	8.72171i	−0.713588	+	0.518452i	−0.884329	−	0.466864i	$-0.845384\pi$
$283$	−12.0044	+	8.72171i	−0.713588	+	0.518452i	0.170742	+	0.985316i	$0.445384\pi$
$284$	−2.35014	+	1.35685i	−0.139455	+	0.0805144i
$285$	−9.60727	−	4.53245i	−0.569086	−	0.268479i
$286$	−0.573912	−	5.46041i	−0.0339361	−	0.322881i
$287$	15.4192	−	21.2228i	0.910169	−	1.25274i
$288$	−2.99445	+	0.182449i	−0.176449	+	0.0107509i
$289$	−10.8208	+	12.0177i	−0.636518	+	0.706925i
$290$	−0.694039	−	0.309006i	−0.0407554	−	0.0181455i
$291$	−21.4149	−	2.72685i	−1.25536	−	0.159851i
$292$	2.25542	+	10.6109i	0.131988	+	0.620956i
$293$	−2.17429	−	4.88353i	−0.127023	−	0.285299i	0.838828	−	0.544397i	$-0.183241\pi$
$293$	−2.17429	−	4.88353i	−0.127023	−	0.285299i	−0.965851	+	0.259098i	$0.916575\pi$
$294$	−16.2814	−	3.83576i	−0.949551	−	0.223706i
$295$	2.65802	−	8.18055i	0.154756	−	0.476290i
$296$	−6.87121	+	3.05926i	−0.399381	+	0.177816i
$297$	−16.8636	+	8.30887i	−0.978523	+	0.482129i
$298$	−22.9382	−	4.87567i	−1.32878	−	0.282440i
$299$	3.88954	−	8.73605i	0.224938	−	0.505219i
$300$	−1.04856	+	1.37859i	−0.0605387	+	0.0795932i
$301$	40.4089	+	4.24715i	2.32913	+	0.244802i
$302$	−1.04368	−	0.758279i	−0.0600571	−	0.0436340i
$303$	−13.6344	+	2.58692i	−0.783273	+	0.148615i
$304$	−3.06652	+	5.31137i	−0.175877	+	0.304628i
$305$	5.42371	+	9.39414i	0.310561	+	0.537907i
$306$	−1.94727	−	1.91447i	−0.111318	−	0.109443i
$307$	0.251142	+	0.278921i	0.0143334	+	0.0159189i	0.750269	−	0.661133i	$-0.229924\pi$
$307$	0.251142	+	0.278921i	0.0143334	+	0.0159189i	−0.735935	+	0.677052i	$0.763257\pi$
$308$	−4.56297	−	14.0434i	−0.260000	−	0.800196i
$309$	29.1250	−	2.41669i	1.65686	−	0.137481i
$310$	−1.26469	−	5.42223i	−0.0718294	−	0.307962i
$311$		−	0.311811i		−	0.0176812i	−0.999961	−	0.00884058i	$-0.997186\pi$
$311$		−	0.311811i		−	0.0176812i	0.999961	−	0.00884058i	$-0.00281408\pi$
$312$	−1.01619	−	2.42413i	−0.0575305	−	0.137240i
$313$	17.5610	−	15.8120i	0.992607	−	0.893747i	−0.00173241	−	0.999998i	$-0.500551\pi$
$313$	17.5610	−	15.8120i	0.992607	−	0.893747i	0.994339	+	0.106251i	$0.0338848\pi$
$314$	−7.30961	−	10.0608i	−0.412505	−	0.567765i
$315$	9.44962	−	7.78598i	0.532426	−	0.438690i
$316$	−11.3341	−	6.54376i	−0.637595	−	0.368115i
$317$	−4.06266	+	0.427003i	−0.228182	+	0.0239829i	−0.217929	−	0.975965i	$-0.569930\pi$
$317$	−4.06266	+	0.427003i	−0.228182	+	0.0239829i	−0.0102524	+	0.999947i	$0.503264\pi$
$318$	9.44107	−	15.5543i	0.529429	−	0.872243i
$319$	−0.287309	+	2.73357i	−0.0160862	+	0.153050i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	8.97649	−	25.6951i	0.501019	−	1.43416i
$322$	5.34710	−	25.1561i	0.297982	−	1.40190i
$323$	−5.46063	+	1.16069i	−0.303837	+	0.0645827i
$324$	−6.58504	+	6.13492i	−0.365836	+	0.340829i
$325$	−1.44330	−	0.468955i	−0.0800597	−	0.0260130i
$326$	21.3150	+	6.92567i	1.18053	+	0.383577i
$327$	−12.7577	+	6.99717i	−0.705501	+	0.386944i
$328$	6.28702	−	1.33635i	0.347142	−	0.0737874i
$329$	8.32345	−	39.1588i	0.458887	−	2.15889i
$330$	5.91586	+	2.06668i	0.325657	+	0.113767i
$331$	−9.95997	−	8.96800i	−0.547449	−	0.492926i	0.348362	−	0.937360i	$-0.386738\pi$
$331$	−9.95997	−	8.96800i	−0.547449	−	0.492926i	−0.895811	+	0.444434i	$0.853405\pi$
$332$	−0.758341	+	7.21513i	−0.0416194	+	0.395982i
$333$	−10.0729	+	20.1913i	−0.551991	+	1.10648i
$334$	5.24782	−	0.551568i	0.287148	−	0.0301805i
$335$	5.50324	+	3.17730i	0.300674	+	0.173594i
$336$	−4.02869	−	5.80878i	−0.219783	−	0.316895i
$337$	15.8462	+	21.8104i	0.863197	+	1.18809i	0.980798	+	0.195027i	$0.0624795\pi$
$337$	15.8462	+	21.8104i	0.863197	+	1.18809i	−0.117601	+	0.993061i	$0.537520\pi$
$338$	−7.94940	+	7.15767i	−0.432390	+	0.389326i
$339$	−30.6553	+	12.8506i	−1.66497	+	0.697951i
$340$			0.910253i			0.0493654i
$341$	−17.2432	+	10.4137i	−0.933774	+	0.563934i
$342$	3.03251	+	18.1475i	0.163979	+	0.981305i
$343$	−3.35156	−	10.3150i	−0.180967	−	0.556960i
$344$	6.66147	+	7.39831i	0.359162	+	0.398890i
$345$	7.12346	+	8.26913i	0.383514	+	0.445195i
$346$	3.02147	+	5.23334i	0.162435	+	0.281346i
$347$	−13.8284	+	23.9514i	−0.742346	+	1.28578i	0.209079	+	0.977899i	$0.432953\pi$
$347$	−13.8284	+	23.9514i	−0.742346	+	1.28578i	−0.951425	+	0.307882i	$0.900380\pi$
$348$	0.245292	+	1.29281i	0.0131490	+	0.0693019i
$349$	−16.3863	−	11.9053i	−0.877139	−	0.637278i	0.0553543	−	0.998467i	$-0.482371\pi$
$349$	−16.3863	−	11.9053i	−0.877139	−	0.637278i	−0.932493	+	0.361188i	$0.882371\pi$
$350$	−4.05899	−	0.426617i	−0.216962	−	0.0228037i
$351$	−6.97732	−	3.67405i	−0.372422	−	0.196107i
$352$	1.47155	−	3.30515i	0.0784339	−	0.176165i
$353$	−16.3938	−	3.48461i	−0.872554	−	0.185467i	−0.250192	−	0.968196i	$-0.580494\pi$
$353$	−16.3938	−	3.48461i	−0.872554	−	0.185467i	−0.622362	+	0.782729i	$0.713827\pi$
$354$	−14.2667	+	4.29197i	−0.758266	+	0.228116i
$355$	2.47909	−	1.10376i	0.131577	−	0.0585817i
$356$	−1.94163	+	5.97572i	−0.102906	+	0.316712i
$357$	1.47556	−	6.26321i	0.0780948	−	0.331484i
$358$	5.35545	+	12.0285i	0.283044	+	0.635728i
$359$	−1.47596	−	6.94385i	−0.0778982	−	0.366482i	0.921882	−	0.387472i	$-0.126652\pi$
$359$	−1.47596	−	6.94385i	−0.0778982	−	0.366482i	−0.999780	+	0.0209898i	$0.993318\pi$
$360$	2.99711	+	0.131556i	0.157962	+	0.00693359i
$361$	17.0050	+	7.57110i	0.894998	+	0.398479i
$362$	13.3437	−	14.8197i	0.701331	−	0.778907i
$363$	0.0793719	−	3.61826i	0.00416594	−	0.189909i
$364$	3.64059	−	5.01084i	0.190819	−	0.262640i
$365$	−1.13392	−	10.7885i	−0.0593521	−	0.564697i
$366$	8.01647	−	16.9922i	0.419028	−	0.888198i
$367$	−15.3589	+	8.86747i	−0.801729	+	0.462878i	−0.844075	−	0.536225i	$-0.819850\pi$
$367$	−15.3589	+	8.86747i	−0.801729	+	0.462878i	0.0423466	+	0.999103i	$0.486517\pi$
$368$	5.09792	−	3.70386i	0.265748	−	0.193077i
$369$	12.0071	−	15.0878i	0.625065	−	0.785439i
$370$	7.15335	−	2.32426i	0.371885	−	0.120833i
$371$	42.8749			2.22596
$372$	−6.46881	+	7.15224i	−0.335392	+	0.370826i
$373$	19.7139			1.02075			0.510373	−	0.859953i	$-0.329507\pi$
$373$	19.7139			1.02075			0.510373	+	0.859953i	$0.329507\pi$
$374$	3.13206	−	1.01767i	0.161955	−	0.0526224i
$375$	1.18692	−	1.26144i	0.0612922	−	0.0651403i
$376$	7.93557	−	5.76553i	0.409246	−	0.297335i
$377$	−0.998467	+	0.576465i	−0.0514237	+	0.0296895i
$378$	−20.4091	−	5.76365i	−1.04973	−	0.296450i
$379$	−1.53231	−	14.5790i	−0.0787096	−	0.748872i	−0.960697	−	0.277599i	$-0.910461\pi$
$379$	−1.53231	−	14.5790i	−0.0787096	−	0.748872i	0.881988	−	0.471273i	$-0.156205\pi$
$380$	3.60491	−	4.96174i	0.184928	−	0.254532i
$381$	−7.34733	−	0.161175i	−0.376415	−	0.00825722i
$382$	−2.79665	+	3.10599i	−0.143089	+	0.158916i
$383$	−18.5617	−	8.26419i	−0.948458	−	0.422281i	−0.126588	−	0.991955i	$-0.540402\pi$
$383$	−18.5617	−	8.26419i	−0.948458	−	0.422281i	−0.821870	+	0.569675i	$0.807069\pi$
$384$	0.218783	−	1.71818i	0.0111647	−	0.0876804i
$385$	3.07004	+	14.4434i	0.156464	+	0.736105i
$386$	1.21604	+	2.73127i	0.0618948	+	0.139018i
$387$	29.5372	+	4.42138i	1.50146	+	0.224752i
$388$	3.85150	−	11.8537i	0.195530	−	0.601780i
$389$	−19.6680	+	8.75676i	−0.997207	+	0.443985i	−0.839417	−	0.543488i	$-0.817103\pi$
$389$	−19.6680	+	8.75676i	−0.997207	+	0.443985i	−0.157790	+	0.987473i	$0.550437\pi$
$390$	0.757234	+	2.51708i	0.0383440	+	0.127457i
$391$	5.61051	+	1.19255i	0.283736	+	0.0603099i
$392$	3.92803	−	8.82249i	0.198395	−	0.445603i
$393$	−2.48168	−	1.88757i	−0.125184	−	0.0952154i
$394$	2.01943	+	0.212250i	0.101737	+	0.0106930i
$395$	10.5880	+	7.69266i	0.532742	+	0.387060i
$396$	−2.89812	−	10.4598i	−0.145636	−	0.525622i
$397$	−15.9955	+	27.7050i	−0.802790	+	1.39047i	0.114984	+	0.993367i	$0.463318\pi$
$397$	−15.9955	+	27.7050i	−0.802790	+	1.39047i	−0.917773	+	0.397105i	$0.870015\pi$
$398$	6.86638	+	11.8929i	0.344180	+	0.596138i
$399$	−32.8476	+	28.2967i	−1.64444	+	1.41661i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	3.66934	+	11.2931i	0.183238	+	0.563949i	0.999914	−	0.0131485i	$-0.00418543\pi$
$401$	3.66934	+	11.2931i	0.183238	+	0.563949i	−0.816676	+	0.577097i	$0.804185\pi$
$402$	−0.910151	−	10.9688i	−0.0453942	−	0.547073i
$403$	−7.78520	−	3.28395i	−0.387809	−	0.163585i
$404$		−	8.01223i		−	0.398624i
$405$	7.19024	−	5.41299i	0.357286	−	0.268974i
$406$	−2.30426	+	2.07476i	−0.114358	+	0.102969i
$407$	−15.9950	−	22.0152i	−0.792841	−	1.09125i
$408$	1.29552	−	0.898509i	0.0641376	−	0.0444828i
$409$	−17.2967	−	9.98626i	−0.855267	−	0.493789i	0.00715718	−	0.999974i	$-0.497722\pi$
$409$	−17.2967	−	9.98626i	−0.855267	−	0.493789i	−0.862425	+	0.506185i	$0.831055\pi$
$410$	−6.39226	+	0.671854i	−0.315691	+	0.0331805i
$411$	6.75378	+	4.09937i	0.333139	+	0.202207i
$412$	−1.76372	+	16.7807i	−0.0868923	+	0.826725i
$413$	−26.0888	−	23.4904i	−1.28374	−	1.15589i
$414$	4.73748	−	18.3009i	0.232834	−	0.899440i
$415$	1.50837	−	7.09634i	0.0740431	−	0.348345i
$416$	1.48441	−	0.315521i	0.0727791	−	0.0154697i
$417$	0.877734	+	1.60034i	0.0429828	+	0.0783689i
$418$	−21.1030	−	6.85678i	−1.03218	−	0.335376i
$419$	1.39230	+	0.452387i	0.0680185	+	0.0221006i	0.342829	−	0.939398i	$-0.388615\pi$
$419$	1.39230	+	0.452387i	0.0680185	+	0.0221006i	−0.274810	+	0.961499i	$0.588615\pi$
$420$	3.39944	+	6.19807i	0.165876	+	0.302435i
$421$	3.89011	−	0.826869i	0.189593	−	0.0402991i	−0.112137	−	0.993693i	$-0.535769\pi$
$421$	3.89011	−	0.826869i	0.189593	−	0.0402991i	0.301729	+	0.953394i	$0.402436\pi$
$422$	−0.632738	+	2.97680i	−0.0308012	+	0.144908i
$423$	7.37449	−	28.4877i	0.358560	−	1.38512i
$424$	7.80680	+	7.02928i	0.379132	+	0.341372i
$425$	0.0951473	−	0.905266i	0.00461532	−	0.0439119i
$426$	−4.01804	−	2.43885i	−0.194675	−	0.118162i
$427$	44.0296	−	4.62770i	2.13074	−	0.223950i
$428$	13.6090	+	7.85714i	0.657814	+	0.379789i
$429$	7.81433	−	5.41965i	0.377279	−	0.261663i
$430$	−5.85164	−	8.05410i	−0.282191	−	0.388403i
$431$	21.8945	−	19.7139i	1.05462	−	0.949584i	0.0558144	−	0.998441i	$-0.482225\pi$
$431$	21.8945	−	19.7139i	1.05462	−	0.949584i	0.998806	+	0.0488569i	$0.0155578\pi$
$432$	−2.77121	−	4.39550i	−0.133330	−	0.211479i
$433$			24.6658i			1.18536i	0.805438	+	0.592680i	$0.201930\pi$
$433$			24.6658i			1.18536i	−0.805438	+	0.592680i	$0.798070\pi$
$434$	−22.3162	−	4.28570i	−1.07121	−	0.205720i
$435$	−0.108813	−	1.31137i	−0.00521716	−	0.0628753i
$436$	−2.59598	−	7.98961i	−0.124325	−	0.382633i
$437$	−25.8597	−	28.7201i	−1.23704	−	1.37387i
$438$	−14.2355	+	12.2632i	−0.680197	+	0.585957i
$439$	3.75883	+	6.51048i	0.179399	+	0.310728i	0.941675	−	0.336524i	$-0.109251\pi$
$439$	3.75883	+	6.51048i	0.179399	+	0.310728i	−0.762276	+	0.647252i	$0.775918\pi$
$440$	−1.80897	+	3.13323i	−0.0862393	+	0.149371i
$441$	−7.73600	−	27.9204i	−0.368381	−	1.32954i
$442$	1.11756	+	0.811951i	0.0531567	+	0.0386206i
$443$	−21.9356	−	2.30552i	−1.04219	−	0.109539i	−0.432064	−	0.901843i	$-0.642215\pi$
$443$	−21.9356	−	2.30552i	−1.04219	−	0.109539i	−0.610126	+	0.792304i	$0.708881\pi$
$444$	−10.3691	−	7.88672i	−0.492094	−	0.374287i
$445$	2.55562	−	5.74002i	0.121148	−	0.272103i
$446$	−10.9145	−	2.31995i	−0.516817	−	0.109853i
$447$	−11.7014	−	38.8958i	−0.553455	−	1.83971i
$448$	3.72850	−	1.66003i	0.176155	−	0.0784293i
$449$	3.36491	−	10.3561i	0.158800	−	0.488737i	−0.839726	−	0.543010i	$-0.817284\pi$
$449$	3.36491	−	10.3561i	0.158800	−	0.488737i	0.998526	+	0.0542738i	$0.0172844\pi$
$450$	−2.96694	−	0.444119i	−0.139863	−	0.0209360i
$451$	9.45835	+	21.2438i	0.445376	+	1.00033i
$452$	−3.99004	−	18.7717i	−0.187676	−	0.882945i
$453$	0.282243	−	2.21655i	0.0132609	−	0.104143i
$454$	16.3586	+	7.28333i	0.767748	+	0.341824i
$455$	−4.14442	+	4.60285i	−0.194294	+	0.215785i
$456$	−10.6202	−	0.232970i	−0.497336	−	0.0109098i
$457$	13.5484	−	18.6478i	0.633768	−	0.872307i	−0.364496	−	0.931205i	$-0.618759\pi$
$457$	13.5484	−	18.6478i	0.633768	−	0.872307i	0.998264	+	0.0588978i	$0.0187586\pi$
$458$	0.744930	+	7.08754i	0.0348083	+	0.331179i
$459$	1.28545	−	4.55178i	0.0599997	−	0.212459i
$460$	−5.45716	+	3.15069i	−0.254441	+	0.146902i
$461$	−19.7483	+	14.3480i	−0.919769	+	0.668251i	−0.943466	−	0.331468i	$-0.892456\pi$
$461$	−19.7483	+	14.3480i	−0.919769	+	0.668251i	0.0236977	+	0.999719i	$0.492456\pi$
$462$	17.5261	−	18.6265i	0.815390	−	0.866583i
$463$	−9.07616	+	2.94902i	−0.421805	+	0.137053i	−0.512226	−	0.858851i	$-0.671179\pi$
$463$	−9.07616	+	2.94902i	−0.421805	+	0.137053i	0.0904208	+	0.995904i	$0.471179\pi$
$464$	−0.759720			−0.0352691
$465$	7.18099	−	6.43688i	0.333010	−	0.298503i
$466$	1.77266			0.0821171
$467$	8.35410	−	2.71441i	0.386582	−	0.125608i	−0.109277	−	0.994011i	$-0.534853\pi$
$467$	8.35410	−	2.71441i	0.386582	−	0.125608i	0.495858	+	0.868403i	$0.334853\pi$
$468$	2.83496	−	3.56233i	0.131046	−	0.164669i
$469$	20.9821	−	15.2444i	0.968864	−	0.703921i
$470$	−8.49476	+	4.90445i	−0.391834	+	0.226226i
$471$	9.19035	−	19.4805i	0.423469	−	0.897612i
$472$	−0.899105	−	8.55442i	−0.0413847	−	0.393749i
$473$	−21.1709	+	29.1393i	−0.973440	+	1.33982i
$474$	0.497142	−	22.6628i	0.0228345	−	1.04094i
$475$	−4.10381	+	4.55774i	−0.188296	+	0.209123i
$476$	3.39388	+	1.51105i	0.155558	+	0.0692589i
$477$	31.4849	+	1.38200i	1.44160	+	0.0632776i
$478$	1.08518	+	5.10535i	0.0496348	+	0.233513i
$479$	−7.12197	−	15.9962i	−0.325411	−	0.730885i	0.674562	−	0.738218i	$-0.264332\pi$
$479$	−7.12197	−	15.9962i	−0.325411	−	0.730885i	−0.999973	+	0.00733307i	$0.997666\pi$
$480$	−0.397183	+	1.68590i	−0.0181288	+	0.0769503i
$481$	3.52724	−	10.8557i	0.160828	−	0.494978i
$482$	−1.68912	+	0.752045i	−0.0769373	+	0.0342547i
$483$	42.6566	−	12.8328i	1.94094	−	0.583912i
$484$	2.04384	+	0.434433i	0.0929020	+	0.0197469i
$485$	−5.06945	+	11.3862i	−0.230192	+	0.517019i
$486$	−14.8015	−	4.89035i	−0.671410	−	0.221831i
$487$	21.8795	+	2.29963i	0.991455	+	0.104206i	0.586345	−	0.810062i	$-0.300566\pi$
$487$	21.8795	+	2.29963i	0.991455	+	0.104206i	0.405111	+	0.914268i	$0.367233\pi$
$488$	8.77575	+	6.37595i	0.397259	+	0.288626i
$489$	7.23617	+	38.1382i	0.327231	+	1.72467i
$490$	−4.82871	+	8.36357i	−0.218139	+	0.377828i
$491$	−1.16691	−	2.02115i	−0.0526619	−	0.0912131i	0.838493	−	0.544913i	$-0.183437\pi$
$491$	−1.16691	−	2.02115i	−0.0526619	−	0.0912131i	−0.891155	+	0.453700i	$0.850104\pi$
$492$	7.26600	+	8.43460i	0.327577	+	0.380261i
$493$	−0.462729	−	0.513913i	−0.0208403	−	0.0231455i
$494$	−2.87613	−	8.85180i	−0.129403	−	0.398261i
$495$	1.78891	+	10.7054i	0.0804054	+	0.481171i
$496$	−3.36077	−	4.43906i	−0.150903	−	0.199320i
$497$		−	11.0756i		−	0.496808i
$498$	−11.5888	+	4.85799i	−0.519305	+	0.217692i
$499$	−2.81885	+	2.53810i	−0.126189	+	0.113621i	−0.729809	−	0.683651i	$-0.760391\pi$
$499$	−2.81885	+	2.53810i	−0.126189	+	0.113621i	0.603620	+	0.797272i	$0.293724\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	5.20864	+	7.51010i	0.232705	+	0.335526i
$502$	−7.32713	−	4.23032i	−0.327026	−	0.188808i
$503$	15.8829	−	1.66936i	0.708184	−	0.0744331i	0.256413	−	0.966567i	$-0.417459\pi$
$503$	15.8829	−	1.66936i	0.708184	−	0.0744331i	0.451771	+	0.892134i	$0.350793\pi$
$504$	5.46582	−	10.9564i	0.243467	−	0.488035i
$505$	−0.837506	+	7.96834i	−0.0372685	+	0.354587i
$506$	16.9422	+	15.2549i	0.753174	+	0.678161i
$507$	−17.4911	−	6.11045i	−0.776807	−	0.271374i
$508$	0.882170	−	4.15028i	0.0391400	−	0.184139i
$509$	24.1466	−	5.13251i	1.07028	−	0.227494i	0.361102	−	0.932526i	$-0.382401\pi$
$509$	24.1466	−	5.13251i	1.07028	−	0.227494i	0.709176	+	0.705032i	$0.249067\pi$
$510$	−1.38234	+	0.758168i	−0.0612110	+	0.0335722i
$511$	−42.1073	−	13.6815i	−1.86272	−	0.605234i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−25.0336	+	19.7207i	−1.10526	+	0.870690i
$514$	−27.8177	+	5.91284i	−1.22699	+	0.260804i
$515$	3.50812	−	16.5044i	0.154586	−	0.727271i
$516$	−5.68684	+	16.2785i	−0.250349	+	0.716622i
$517$	26.3728	+	23.7461i	1.15987	+	1.04435i
$518$	3.20879	−	30.5296i	0.140986	−	1.34139i
$519$	−5.43087	+	8.94745i	−0.238389	+	0.392749i
$520$	−1.50926	+	0.158629i	−0.0661854	+	0.00695636i
$521$	28.8955	+	16.6828i	1.26593	+	0.730887i	0.974216	−	0.225617i	$-0.0724398\pi$
$521$	28.8955	+	16.6828i	1.26593	+	0.730887i	0.291718	+	0.956504i	$0.405773\pi$
$522$	−1.75899	+	1.44932i	−0.0769891	+	0.0634348i
$523$	14.0585	+	19.3498i	0.614733	+	0.846108i	0.996956	−	0.0779624i	$-0.0248414\pi$
$523$	14.0585	+	19.3498i	0.614733	+	0.846108i	−0.382223	+	0.924070i	$0.624841\pi$
$524$	1.33778	−	1.20454i	0.0584410	−	0.0526205i
$525$	−2.73294	−	6.51945i	−0.119275	−	0.284532i
$526$		−	7.85841i		−	0.342643i
$527$	0.955828	−	4.97712i	0.0416365	−	0.216807i
$528$	6.24500	−	0.518188i	0.271779	−	0.0225512i
$529$	5.16287	+	15.8897i	0.224473	+	0.690856i
$530$	−7.02928	−	7.80680i	−0.305332	−	0.339106i
$531$	−18.4009	−	18.0910i	−0.798533	−	0.785081i
$532$	−12.5156	−	21.6776i	−0.542618	−	0.939842i
$533$	−4.87708	+	8.44734i	−0.211250	+	0.365895i
$534$	−10.6921	+	2.02868i	−0.462694	+	0.0877894i
$535$	−12.7131	−	9.23662i	−0.549636	−	0.399334i
$536$	6.31978	+	0.664236i	0.272973	+	0.0286906i
$537$	−13.8063	+	18.1518i	−0.595784	+	0.783306i
$538$	−10.2458	+	23.0124i	−0.441728	+	0.992137i
$539$	34.1765	+	7.26443i	1.47208	+	0.312901i
$540$	2.29657	+	4.66109i	0.0988287	+	0.200581i
$541$	−22.8778	+	10.1858i	−0.983592	+	0.437924i	−0.834565	−	0.550910i	$-0.814281\pi$
$541$	−22.8778	+	10.1858i	−0.983592	+	0.437924i	−0.149027	+	0.988833i	$0.547614\pi$
$542$	3.36086	−	10.3437i	0.144361	−	0.444299i
$543$	33.6200	+	7.92058i	1.44277	+	0.339905i
$544$	0.370233	+	0.831557i	0.0158736	+	0.0356527i
$545$	1.74662	+	8.21719i	0.0748169	+	0.351986i
$546$	10.6419	+	1.35509i	0.455433	+	0.0579923i
$547$	−35.4599	−	15.7878i	−1.51616	−	0.675036i	−0.531106	−	0.847305i	$-0.678223\pi$
$547$	−35.4599	−	15.7878i	−1.51616	−	0.675036i	−0.985050	+	0.172269i	$0.944890\pi$
$548$	−3.05215	+	3.38976i	−0.130382	+	0.144803i
$549$	32.4820	−	1.97910i	1.38630	−	0.0844659i
$550$	2.12657	−	2.92698i	0.0906774	−	0.124807i
$551$	0.487040	+	4.63387i	0.0207486	+	0.197410i
$552$	9.87096	+	4.65685i	0.420136	+	0.198209i
$553$	46.2586	−	26.7074i	1.96711	−	1.13571i
$554$	9.14050	−	6.64096i	0.388342	−	0.282147i
$555$	9.48787	+	8.92738i	0.402738	+	0.378946i
$556$	−1.00223	+	0.325643i	−0.0425038	+	0.0138103i
$557$	−30.8934			−1.30900			−0.654499	−	0.756063i	$-0.727120\pi$
$557$	−30.8934			−1.30900			−0.654499	+	0.756063i	$0.727120\pi$
$558$	−16.2496	−	3.86650i	−0.687901	−	0.163682i
$559$	−15.1081			−0.639003
$560$	−3.88159	+	1.26121i	−0.164027	+	0.0532957i
$561$	4.15422	+	3.90881i	0.175391	+	0.165030i
$562$	5.43069	−	3.94563i	0.229080	−	0.166436i
$563$	−16.1560	+	9.32770i	−0.680896	+	0.393116i	−0.800193	−	0.599743i	$-0.795269\pi$
$563$	−16.1560	+	9.32770i	−0.680896	+	0.393116i	0.119296	+	0.992859i	$0.461936\pi$
$564$	15.3654	+	7.24899i	0.647001	+	0.305237i
$565$	2.00601	+	19.0859i	0.0843934	+	0.802950i
$566$	8.72171	−	12.0044i	0.366601	−	0.504583i
$567$	−8.24628	−	35.7946i	−0.346311	−	1.50323i
$568$	1.81582	−	2.01668i	0.0761903	−	0.0846179i
$569$	−32.4767	−	14.4596i	−1.36149	−	0.606176i	−0.409505	−	0.912308i	$-0.634298\pi$
$569$	−32.4767	−	14.4596i	−1.36149	−	0.606176i	−0.951989	+	0.306132i	$0.900965\pi$
$570$	10.5377	+	1.34181i	0.441374	+	0.0562021i
$571$	−4.71064	−	22.1618i	−0.197134	−	0.927443i	−0.959808	−	0.280659i	$-0.909447\pi$
$571$	−4.71064	−	22.1618i	−0.197134	−	0.927443i	0.762673	−	0.646784i	$-0.223886\pi$
$572$	2.23318	+	5.01581i	0.0933740	+	0.209722i
$573$	−7.04625	−	1.66004i	−0.294361	−	0.0693490i
$574$	−8.10637	+	24.9488i	−0.338353	+	1.04134i
$575$	5.75660	−	2.56300i	0.240067	−	0.106885i
$576$	2.79151	−	1.09885i	0.116313	−	0.0457856i
$577$	−36.0102	−	7.65420i	−1.49912	−	0.318649i	−0.615984	−	0.787759i	$-0.711241\pi$
$577$	−36.0102	−	7.65420i	−1.49912	−	0.318649i	−0.883140	+	0.469110i	$0.844575\pi$
$578$	6.57752	−	14.7733i	0.273589	−	0.614490i
$579$	−3.13493	+	4.12165i	−0.130283	+	0.171290i
$580$	0.755558	+	0.0794124i	0.0313729	+	0.00329742i
$581$	−23.9547	−	17.4041i	−0.993810	−	0.722045i
$582$	21.2094	−	4.02417i	0.879158	−	0.166807i
$583$	−19.0034	+	32.9149i	−0.787040	+	1.36319i
$584$	−5.42398	−	9.39460i	−0.224446	−	0.388751i
$585$	−3.19180	+	3.24648i	−0.131965	+	0.134226i
$586$	3.57697	+	3.97262i	0.147763	+	0.164108i
$587$	−5.36028	−	16.4972i	−0.221242	−	0.680914i	−0.998651	−	0.0519183i	$-0.983466\pi$
$587$	−5.36028	−	16.4972i	−0.221242	−	0.680914i	0.777409	−	0.628995i	$-0.216534\pi$
$588$	16.6699	−	1.38321i	0.687453	−	0.0570424i
$589$	−24.9213	+	23.3446i	−1.02686	+	0.961898i
$590$			8.60154i			0.354120i
$591$	1.35969	+	3.24355i	0.0559302	+	0.133422i
$592$	5.58955	−	5.03285i	0.229729	−	0.206849i
$593$	−9.32275	−	12.8317i	−0.382839	−	0.526933i	0.573495	−	0.819209i	$-0.305587\pi$
$593$	−9.32275	−	12.8317i	−0.382839	−	0.526933i	−0.956334	+	0.292276i	$0.905587\pi$
$594$	13.4706	−	13.1133i	0.552706	−	0.538046i
$595$	−3.21734	−	1.85753i	−0.131898	−	0.0761513i
$596$	23.3222	−	2.45126i	0.955315	−	0.100408i
$597$	−12.3418	+	20.3334i	−0.505117	+	0.832189i
$598$	−0.999584	+	9.51041i	−0.0408760	+	0.388910i
$599$	25.1003	+	22.6004i	1.02557	+	0.923426i	0.997095	−	0.0761685i	$-0.0242687\pi$
$599$	25.1003	+	22.6004i	1.02557	+	0.923426i	0.0284735	+	0.999595i	$0.490935\pi$
$600$	0.571231	−	1.63514i	0.0233204	−	0.0667545i
$601$	−2.64159	+	12.4277i	−0.107753	+	0.506937i	0.890860	+	0.454278i	$0.150103\pi$
$601$	−2.64159	+	12.4277i	−0.107753	+	0.506937i	−0.998613	+	0.0526588i	$0.983230\pi$
$602$	−39.7436	+	8.44777i	−1.61983	+	0.344305i
$603$	15.8995	−	10.5183i	0.647476	−	0.428339i
$604$	1.22692	+	0.398651i	0.0499227	+	0.0162209i
$605$	−1.98724	−	0.645693i	−0.0807927	−	0.0262511i
$606$	12.1676	−	6.67355i	0.494276	−	0.271095i
$607$	−30.1846	+	6.41593i	−1.22515	+	0.260415i	−0.774668	−	0.632368i	$-0.782083\pi$
$607$	−30.1846	+	6.41593i	−1.22515	+	0.260415i	−0.450487	+	0.892783i	$0.648750\pi$
$608$	1.27513	−	5.99902i	0.0517134	−	0.243293i
$609$	−5.07007	−	1.77121i	−0.205449	−	0.0717730i
$610$	−8.06120	−	7.25834i	−0.326389	−	0.293882i
$611$	−1.55598	+	14.8042i	−0.0629483	+	0.598913i
$612$	2.44357	+	1.21903i	0.0987753	+	0.0492763i
$613$	32.8955	−	3.45746i	1.32864	−	0.139646i	0.586531	−	0.809927i	$-0.300493\pi$
$613$	32.8955	−	3.45746i	1.32864	−	0.139646i	0.742107	+	0.670281i	$0.233826\pi$
$614$	−0.325041	−	0.187663i	−0.0131176	−	0.00757345i
$615$	−6.34454	−	9.14790i	−0.255837	−	0.368879i
$616$	8.67929	+	11.9460i	0.349699	+	0.481319i
$617$	12.0771	−	10.8743i	0.486206	−	0.437782i	−0.389212	−	0.921148i	$-0.627253\pi$
$617$	12.0771	−	10.8743i	0.486206	−	0.437782i	0.875418	+	0.483366i	$0.160586\pi$
$618$	−26.9527	+	11.2985i	−1.08420	+	0.454493i
$619$		−	15.9164i		−	0.639735i	−0.947462	−	0.319868i	$-0.896362\pi$
$619$		−	15.9164i		−	0.639735i	0.947462	−	0.319868i	$-0.103638\pi$
$620$	2.87835	+	4.76604i	0.115597	+	0.191409i
$621$	31.7383	−	8.04870i	1.27361	−	0.322983i
$622$	0.0963548	+	0.296550i	0.00386348	+	0.0118906i
$623$	−17.1593	−	19.0573i	−0.687471	−	0.763514i
$624$	1.71555	+	1.99147i	0.0686772	+	0.0797225i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.8153	+	20.4648i	−0.472236	+	0.817936i
$627$	−7.16419	−	37.7588i	−0.286110	−	1.50794i
$628$	10.0608	+	7.30961i	0.401470	+	0.291685i
$629$	6.80894	+	0.715649i	0.271490	+	0.0285348i
$630$	−6.58113	+	10.3250i	−0.262198	+	0.411358i
$631$	−9.57691	+	21.5101i	−0.381251	+	0.856303i	0.616376	+	0.787452i	$0.288600\pi$
$631$	−9.57691	+	21.5101i	−0.381251	+	0.856303i	−0.997627	+	0.0688515i	$0.978067\pi$
$632$	12.8015	+	2.72105i	0.509218	+	0.108238i
$633$	−5.04768	+	1.51854i	−0.200627	+	0.0603565i
$634$	3.73187	−	1.66153i	0.148211	−	0.0659879i
$635$	−1.31116	+	4.03534i	−0.0520318	+	0.160137i
$636$	−4.17244	+	17.7105i	−0.165448	+	0.702266i
$637$	5.96106	+	13.3888i	0.236186	+	0.530482i
$638$	−0.571471	−	2.68856i	−0.0226248	−	0.106441i
$639$	0.357003	−	8.13329i	0.0141228	−	0.321748i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−14.0213	+	15.5722i	−0.553806	+	0.615064i	−0.953430	−	0.301615i	$-0.902474\pi$
$641$	−14.0213	+	15.5722i	−0.553806	+	0.615064i	0.399623	+	0.916679i	$0.369141\pi$
$642$	−0.596922	+	27.2114i	−0.0235586	+	1.07395i
$643$	3.56059	−	4.90072i	0.140416	−	0.193266i	−0.733017	−	0.680210i	$-0.761889\pi$
$643$	3.56059	−	4.90072i	0.140416	−	0.193266i	0.873433	+	0.486944i	$0.161889\pi$
$644$	2.68828	+	25.5773i	0.105933	+	1.00789i
$645$	7.35726	−	15.5949i	0.289692	−	0.614049i
$646$	4.83469	−	2.79131i	0.190218	−	0.109823i
$647$	21.4776	−	15.6044i	0.844371	−	0.613471i	−0.0792172	−	0.996857i	$-0.525242\pi$
$647$	21.4776	−	15.6044i	0.844371	−	0.613471i	0.923588	+	0.383386i	$0.125242\pi$
$648$	4.36695	−	7.86955i	0.171550	−	0.309145i
$649$	29.5967	−	9.61657i	1.16177	−	0.377483i
$650$	1.51757			0.0595241
$651$	−12.0792	−	37.4597i	−0.473422	−	1.46816i
$652$	−22.4119			−0.877719
$653$	11.4812	−	3.73046i	0.449293	−	0.145984i	−0.0756261	−	0.997136i	$-0.524096\pi$
$653$	11.4812	−	3.73046i	0.449293	−	0.145984i	0.524919	+	0.851152i	$0.324096\pi$
$654$	9.97103	−	10.5970i	0.389898	−	0.414377i
$655$	−1.45636	+	1.05811i	−0.0569046	+	0.0413436i
$656$	−5.56636	+	3.21374i	−0.217330	+	0.125475i
$657$	−30.4803	−	11.4042i	−1.18915	−	0.444920i
$658$	4.18465	+	39.8143i	0.163135	+	1.55212i
$659$	−17.3549	+	23.8870i	−0.676053	+	0.930507i	−0.999878	−	0.0156102i	$-0.995031\pi$
$659$	−17.3549	+	23.8870i	−0.676053	+	0.930507i	0.323826	+	0.946117i	$0.395031\pi$
$660$	−6.26495	−	0.137431i	−0.243863	−	0.00534950i
$661$	−31.1022	+	34.5425i	−1.20974	+	1.34355i	−0.287088	+	0.957904i	$0.592687\pi$
$661$	−31.1022	+	34.5425i	−1.20974	+	1.34355i	−0.922648	+	0.385644i	$0.873979\pi$
$662$	12.2438	+	5.45127i	0.475867	+	0.211870i
$663$	−0.302221	+	2.37345i	−0.0117373	+	0.0921770i
$664$	−1.50837	−	7.09634i	−0.0585362	−	0.275391i
$665$	10.1811	+	22.8671i	0.394805	+	0.886746i
$666$	3.34043	−	22.3158i	0.129439	−	0.864720i
$667$	1.47935	−	4.55298i	0.0572808	−	0.176292i
$668$	−4.82053	+	2.14624i	−0.186512	+	0.0830404i
$669$	−5.56777	−	18.5075i	−0.215262	−	0.715540i
$670$	−6.21573	−	1.32119i	−0.240135	−	0.0510422i
$671$	−15.9625	+	35.8524i	−0.616226	+	1.38407i
$672$	5.62652	+	4.27954i	0.217048	+	0.165087i
$673$	−25.8039	−	2.71210i	−0.994669	−	0.104544i	−0.406814	−	0.913511i	$-0.633360\pi$
$673$	−25.8039	−	2.71210i	−0.994669	−	0.104544i	−0.587854	+	0.808967i	$0.700027\pi$
$674$	−21.8104	−	15.8462i	−0.840105	−	0.610372i
$675$	−1.79678	−	4.87561i	−0.0691579	−	0.187662i
$676$	5.34849	−	9.26385i	0.205711	−	0.356302i
$677$	−11.0710	−	19.1756i	−0.425494	−	0.736977i	0.570972	−	0.820969i	$-0.306566\pi$
$677$	−11.0710	−	19.1756i	−0.425494	−	0.736977i	−0.996466	+	0.0839919i	$0.973233\pi$
$678$	25.1839	−	21.6947i	0.967180	−	0.833180i
$679$	34.0379	+	37.8029i	1.30625	+	1.45074i
$680$	−0.281284	−	0.865702i	−0.0107867	−	0.0331982i
$681$	2.56473	+	30.9092i	0.0982808	+	1.18444i
$682$	13.1813	−	15.2325i	0.504738	−	0.583282i
$683$		−	2.20750i		−	0.0844677i	−0.999108	−	0.0422338i	$-0.986553\pi$
$683$		−	2.20750i		−	0.0844677i	0.999108	−	0.0422338i	$-0.0134474\pi$
$684$	−8.49198	−	16.3222i	−0.324699	−	0.624095i
$685$	3.38976	−	3.05215i	0.129516	−	0.116617i
$686$	6.37504	+	8.77449i	0.243400	+	0.335012i
$687$	−10.1429	+	7.03463i	−0.386976	+	0.268388i
$688$	−8.62164	−	4.97771i	−0.328697	−	0.189773i
$689$	−15.8549	+	1.66642i	−0.604023	+	0.0634854i
$690$	−9.33012	−	5.66314i	−0.355191	−	0.215592i
$691$	−5.20613	+	49.5330i	−0.198050	+	1.88432i	0.219417	+	0.975631i	$0.429585\pi$
$691$	−5.20613	+	49.5330i	−0.198050	+	1.88432i	−0.417467	+	0.908692i	$0.637082\pi$
$692$	−4.49078	−	4.04351i	−0.170714	−	0.153711i
$693$	42.8847	+	11.1014i	1.62905	+	0.421707i
$694$	5.75016	−	27.0524i	0.218273	−	1.02689i
$695$	1.03077	−	0.219098i	0.0390995	−	0.00831086i
$696$	−0.632786	−	1.15374i	−0.0239857	−	0.0437322i
$697$	−5.56428	−	1.80794i	−0.210762	−	0.0684807i
$698$	19.2633	+	6.25901i	0.729125	+	0.236907i
$699$	1.47649	+	2.69203i	0.0558459	+	0.101822i
$700$	3.99216	−	0.848560i	0.150890	−	0.0320726i
$701$	1.33306	−	6.27154i	0.0503489	−	0.236873i	−0.945776	−	0.324818i	$-0.894697\pi$
$701$	1.33306	−	6.27154i	0.0503489	−	0.236873i	0.996125	+	0.0879456i	$0.0280302\pi$
$702$	7.77117	+	1.33812i	0.293304	+	0.0505042i
$703$	−34.2809	−	30.8667i	−1.29293	−	1.16416i
$704$	−0.378178	+	3.59812i	−0.0142531	+	0.135609i
$705$	−14.5235	−	8.81540i	−0.546987	−	0.332007i
$706$	16.6682	−	1.75190i	0.627317	−	0.0659337i
$707$	28.3197	+	16.3504i	1.06507	+	0.614919i
$708$	12.2421	−	8.49056i	0.460087	−	0.319095i
$709$	3.87884	+	5.33877i	0.145673	+	0.200502i	0.875618	−	0.483004i	$-0.160454\pi$
$709$	3.87884	+	5.33877i	0.145673	+	0.200502i	−0.729945	+	0.683506i	$0.760454\pi$
$710$	−2.01668	+	1.81582i	−0.0756845	+	0.0681467i
$711$	34.8306	−	18.1213i	1.30625	−	0.679603i
$712$		−	6.28324i		−	0.235474i
$713$	33.1473	−	11.4971i	1.24138	−	0.430570i
$714$	0.532098	+	6.41264i	0.0199133	+	0.239987i
$715$	−1.69665	−	5.22176i	−0.0634513	−	0.195283i
$716$	−8.81035	−	9.78489i	−0.329258	−	0.365678i
$717$	−6.84929	+	5.90034i	−0.255791	+	0.220352i
$718$	3.54949	+	6.14789i	0.132466	+	0.229437i
$719$	7.51176	−	13.0108i	0.280141	−	0.485219i	−0.691278	−	0.722589i	$-0.742952\pi$
$719$	7.51176	−	13.0108i	0.280141	−	0.485219i	0.971419	+	0.237370i	$0.0762853\pi$
$720$	−2.89108	+	0.801042i	−0.107744	+	0.0298531i
$721$	−55.7130	−	40.4779i	−2.07486	−	1.50748i
$722$	−18.5123	−	1.94572i	−0.688955	−	0.0724121i
$723$	−2.54898	−	1.93876i	−0.0947977	−	0.0721032i
$724$	−8.11110	+	18.2178i	−0.301447	+	0.677060i
$725$	−0.743119	−	0.157955i	−0.0275987	−	0.00586629i
$726$	1.04262	+	3.46570i	0.0386951	+	0.128624i
$727$	−4.39587	+	1.95717i	−0.163034	+	0.0725874i	−0.486631	−	0.873608i	$-0.661774\pi$
$727$	−4.39587	+	1.95717i	−0.163034	+	0.0725874i	0.323597	+	0.946195i	$0.395108\pi$
$728$	−1.91397	+	5.89060i	−0.0709365	+	0.218320i
$729$	−4.90182	−	26.5513i	−0.181549	−	0.983382i
$730$	4.41226	+	9.91010i	0.163305	+	0.366789i
$731$	−1.88408	−	8.86392i	−0.0696854	−	0.327844i
$732$	−2.37323	+	18.6378i	−0.0877171	+	0.688873i
$733$	−1.31670	−	0.586235i	−0.0486336	−	0.0216531i	0.382276	−	0.924048i	$-0.375140\pi$
$733$	−1.31670	−	0.586235i	−0.0486336	−	0.0216531i	−0.430909	+	0.902395i	$0.641807\pi$
$734$	11.8670	−	13.1796i	0.438019	−	0.486469i
$735$	−16.7231	−	0.366847i	−0.616842	−	0.0135313i
$736$	−3.70386	+	5.09792i	−0.136526	+	0.187912i
$737$	2.40317	+	22.8646i	0.0885218	+	0.842229i
$738$	−6.75705	+	18.0597i	−0.248730	+	0.664788i
$739$	40.1286	−	23.1682i	1.47615	−	0.852258i	0.476516	−	0.879166i	$-0.341899\pi$
$739$	40.1286	−	23.1682i	1.47615	−	0.852258i	0.999638	+	0.0269081i	$0.00856615\pi$
$740$	−6.08500	+	4.42101i	−0.223689	+	0.162520i
$741$	11.0470	−	11.7406i	0.405824	−	0.431303i
$742$	−40.7765	+	13.2491i	−1.49695	+	0.486389i
$743$	−1.55250			−0.0569556			−0.0284778	−	0.999594i	$-0.509066\pi$
$743$	−1.55250			−0.0569556			−0.0284778	+	0.999594i	$0.509066\pi$
$744$	3.94204	−	8.80115i	0.144522	−	0.322666i
$745$	−23.4507			−0.859166
$746$	−18.7490	+	6.09192i	−0.686450	+	0.223041i
$747$	−17.0300	−	13.5528i	−0.623096	−	0.495869i
$748$	−2.66429	+	1.93572i	−0.0974161	+	0.0707769i
$749$	−55.5430	+	32.0677i	−2.02950	+	1.17173i
$750$	−0.739021	+	1.56648i	−0.0269852	+	0.0571996i
$751$	2.22312	+	21.1516i	0.0811229	+	0.771833i	0.957154	+	0.289579i	$0.0935152\pi$
$751$	2.22312	+	21.1516i	0.0811229	+	0.771833i	−0.876031	+	0.482254i	$0.839818\pi$
$752$	−5.76553	+	7.93557i	−0.210247	+	0.289381i
$753$	0.321385	−	14.6507i	0.0117119	−	0.533902i
$754$	0.771461	−	0.856794i	0.0280949	−	0.0312026i
$755$	−1.17853	−	0.524715i	−0.0428911	−	0.0190963i
$756$	21.1913	−	0.825198i	0.770719	−	0.0300122i
$757$	1.50186	+	7.06571i	0.0545862	+	0.256808i	0.996976	−	0.0777086i	$-0.0247604\pi$
$757$	1.50186	+	7.06571i	0.0545862	+	0.256808i	−0.942390	+	0.334516i	$0.891427\pi$
$758$	5.96247	+	13.3919i	0.216567	+	0.486416i
$759$	−9.05499	+	38.4351i	−0.328675	+	1.39511i
$760$	−1.89522	+	5.83287i	−0.0687467	+	0.211581i
$761$	−24.2538	+	10.7985i	−0.879199	+	0.391445i	−0.796149	−	0.605101i	$-0.793133\pi$
$761$	−24.2538	+	10.7985i	−0.879199	+	0.391445i	−0.0830503	+	0.996545i	$0.526466\pi$
$762$	7.03753	−	2.11716i	0.254943	−	0.0766967i
$763$	33.5372	+	7.12856i	1.21413	+	0.258071i
$764$	1.69997	−	3.81819i	0.0615026	−	0.138137i
$765$	−2.30276	−	1.46777i	−0.0832564	−	0.0530674i
$766$	20.2070	+	2.12384i	0.730108	+	0.0767375i
$767$	10.5605	+	7.67263i	0.381316	+	0.277042i
$768$	0.322871	+	1.70169i	0.0116506	+	0.0614045i
$769$	−11.1980	+	19.3954i	−0.403808	+	0.699417i	−0.994182	−	0.107713i	$-0.965647\pi$
$769$	−11.1980	+	19.3954i	−0.403808	+	0.699417i	0.590374	+	0.807130i	$0.298980\pi$
$770$	−7.38304	−	12.7878i	−0.266066	−	0.460841i
$771$	−32.1494	−	37.3200i	−1.15783	−	1.34405i
$772$	−2.00053	−	2.22182i	−0.0720007	−	0.0799649i
$773$	5.07522	+	15.6199i	0.182543	+	0.561809i	0.999897	−	0.0143259i	$-0.00456024\pi$
$773$	5.07522	+	15.6199i	0.182543	+	0.561809i	−0.817355	+	0.576135i	$0.804560\pi$
$774$	−29.4578	+	4.92250i	−1.05884	+	0.176935i
$775$	−2.36440	−	5.04080i	−0.0849316	−	0.181071i
$776$			12.4637i			0.447421i
$777$	49.0359	−	20.5558i	1.75915	−	0.737434i
$778$	15.9994	−	14.4059i	0.573606	−	0.516477i
$779$	23.1705	+	31.8914i	0.830169	+	1.14263i
$780$	−1.49799	−	2.15988i	−0.0536367	−	0.0773362i
$781$	8.50267	+	4.90902i	0.304249	+	0.175658i
$782$	−5.70443	+	0.599560i	−0.203990	+	0.0214402i
$783$	−3.66608	−	1.46410i	−0.131015	−	0.0523227i
$784$	−1.00948	+	9.60452i	−0.0360527	+	0.343018i
$785$	−9.24164	−	8.32121i	−0.329848	−	0.296997i
$786$	2.94351	+	1.02831i	0.104992	+	0.0366784i
$787$	5.21614	−	24.5400i	0.185935	−	0.874756i	−0.781946	−	0.623347i	$-0.785773\pi$
$787$	5.21614	−	24.5400i	0.185935	−	0.874756i	0.967881	−	0.251410i	$-0.0808941\pi$
$788$	−1.98618	+	0.422175i	−0.0707547	+	0.0150394i
$789$	11.9340	−	6.54543i	0.424863	−	0.233023i
$790$	−12.4470	−	4.04427i	−0.442844	−	0.143889i
$791$	74.4918	+	24.2039i	2.64862	+	0.860590i
$792$	5.98852	+	9.05225i	0.212793	+	0.321658i
$793$	−16.1020	+	3.42259i	−0.571799	+	0.121540i
$794$	6.65129	−	31.2919i	0.236045	−	1.11051i
$795$	6.00083	−	17.1773i	0.212828	−	0.609217i
$796$	−10.2054	−	9.18901i	−0.361722	−	0.325696i
$797$	5.01908	−	47.7534i	0.177785	−	1.69151i	−0.434340	−	0.900749i	$-0.643018\pi$
$797$	5.01908	−	47.7534i	0.177785	−	1.69151i	0.612125	−	0.790761i	$-0.290315\pi$
$798$	22.4958	−	37.0622i	0.796343	−	1.31199i
$799$	−8.87967	+	0.933291i	−0.314140	+	0.0330175i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−11.9865	−	14.5477i	−0.423522	−	0.514018i
$802$	−6.97950	−	9.60645i	−0.246455	−	0.339216i
$803$	29.1664	−	26.2615i	1.02926	−	0.926750i
$804$	4.25515	+	10.1507i	0.150067	+	0.357987i
$805$		−	25.7181i		−	0.906445i
$806$	8.41897	+	0.717464i	0.296545	+	0.0252716i
$807$	−43.4814	+	3.60793i	−1.53062	+	0.127005i
$808$	2.47592	+	7.62009i	0.0871024	+	0.268074i
$809$	−20.4160	−	22.6742i	−0.717787	−	0.797184i	0.268313	−	0.963332i	$-0.413534\pi$
$809$	−20.4160	−	22.6742i	−0.717787	−	0.797184i	−0.986101	+	0.166148i	$0.946867\pi$
$810$	−5.16562	+	7.36997i	−0.181501	+	0.258954i
$811$	5.64396	+	9.77563i	0.198186	+	0.343269i	0.947940	−	0.318448i	$-0.103162\pi$
$811$	5.64396	+	9.77563i	0.198186	+	0.343269i	−0.749754	+	0.661717i	$0.769828\pi$
$812$	1.55034	−	2.68527i	0.0544064	−	0.0942346i
$813$	18.5076	−	3.51154i	0.649089	−	0.123155i
$814$	22.0152	+	15.9950i	0.771632	+	0.560623i
$815$	22.2892	+	2.34268i	0.780755	+	0.0820607i
$816$	−0.954455	+	1.25487i	−0.0334126	+	0.0439292i
$817$	−24.8341	+	55.7783i	−0.868836	+	1.95144i
$818$	19.5361	+	4.15252i	0.683063	+	0.145190i
$819$	6.80602	+	17.2899i	0.237822	+	0.604157i
$820$	5.87179	−	2.61429i	0.205052	−	0.0912949i
$821$	−5.40345	+	16.6301i	−0.188582	+	0.580394i	−0.999992	−	0.00408290i	$-0.998700\pi$
$821$	−5.40345	+	16.6301i	−0.188582	+	0.580394i	0.811410	+	0.584477i	$0.198700\pi$
$822$	−7.69000	−	1.81170i	−0.268220	−	0.0631903i
$823$	3.95567	+	8.88459i	0.137886	+	0.309697i	0.969269	−	0.246002i	$-0.0791171\pi$
$823$	3.95567	+	8.88459i	0.137886	+	0.309697i	−0.831383	+	0.555700i	$0.812450\pi$
$824$	−3.50812	−	16.5044i	−0.122211	−	0.574958i
$825$	6.21627	+	0.791544i	0.216423	+	0.0275580i
$826$	32.0708	+	14.2789i	1.11589	+	0.496825i
$827$	−29.6184	+	32.8946i	−1.02993	+	1.14386i	−0.0404533	+	0.999181i	$0.512880\pi$
$827$	−29.6184	+	32.8946i	−1.02993	+	1.14386i	−0.989479	+	0.144675i	$0.953786\pi$
$828$	1.14968	+	18.8691i	0.0399541	+	0.655748i
$829$	−3.36160	+	4.62684i	−0.116753	+	0.160697i	−0.863394	−	0.504531i	$-0.831666\pi$
$829$	−3.36160	+	4.62684i	−0.116753	+	0.160697i	0.746641	+	0.665228i	$0.231666\pi$
$830$	0.758341	+	7.21513i	0.0263224	+	0.250441i
$831$	17.6985	+	8.34966i	0.613953	+	0.289647i
$832$	−1.31426	+	0.758786i	−0.0455636	+	0.0263062i
$833$	−7.11182	+	5.16704i	−0.246410	+	0.179027i
$834$	−1.32931	−	1.25078i	−0.0460301	−	0.0433109i
$835$	5.01847	−	1.63060i	0.173671	−	0.0564292i
$836$	22.1890			0.767423
$837$	−7.66284	−	27.8977i	−0.264867	−	0.964285i
$838$	−1.46396			−0.0505715
$839$	−19.8627	+	6.45378i	−0.685736	+	0.222809i	−0.631105	−	0.775697i	$-0.717398\pi$
$839$	−19.8627	+	6.45378i	−0.685736	+	0.222809i	−0.0546313	+	0.998507i	$0.517398\pi$
$840$	−5.14837	−	4.84423i	−0.177636	−	0.167142i
$841$	22.9945	−	16.7065i	0.792915	−	0.576087i
$842$	−3.44420	+	1.98851i	−0.118695	+	0.0685286i
$843$	10.5153	+	4.96083i	0.362166	+	0.170860i
$844$	−0.318111	−	3.02663i	−0.0109498	−	0.104181i
$845$	−6.28752	+	8.65404i	−0.216297	+	0.297708i
$846$	1.78962	+	29.3723i	0.0615285	+	1.00984i
$847$	−5.70635	+	6.33754i	−0.196072	+	0.217761i
$848$	−9.59687	−	4.27280i	−0.329558	−	0.146729i
$849$	25.4948	+	3.24636i	0.874978	+	0.111415i
$850$	0.189252	+	0.890362i	0.00649130	+	0.0305392i
$851$	19.2776	+	43.2981i	0.660826	+	1.48424i
$852$	4.57503	+	1.07784i	0.156738	+	0.0369261i
$853$	−8.55122	+	26.3179i	−0.292788	+	0.901109i	0.691167	+	0.722695i	$0.257097\pi$
$853$	−8.55122	+	26.3179i	−0.292788	+	0.901109i	−0.983955	+	0.178414i	$0.942903\pi$
$854$	−40.4446	+	18.0071i	−1.38399	+	0.616190i
$855$	6.73932	+	17.1204i	0.230480	+	0.585507i
$856$	−15.3709	−	3.26718i	−0.525366	−	0.111670i
$857$	−1.91825	+	4.30847i	−0.0655263	+	0.147174i	−0.943340	−	0.331828i	$-0.892335\pi$
$857$	−1.91825	+	4.30847i	−0.0655263	+	0.147174i	0.877814	+	0.479002i	$0.159001\pi$
$858$	−5.75711	+	7.56915i	−0.196544	+	0.258407i
$859$	35.8092	+	3.76369i	1.22179	+	0.128416i	0.693380	−	0.720572i	$-0.256121\pi$
$859$	35.8092	+	3.76369i	1.22179	+	0.128416i	0.528413	+	0.848988i	$0.322787\pi$
$860$	8.05410	+	5.85164i	0.274642	+	0.199539i
$861$	−44.6401	+	8.46980i	−1.52133	+	0.288650i
$862$	−14.7310	+	25.5148i	−0.501739	+	0.869037i
$863$	20.7560	+	35.9505i	0.706543	+	1.22377i	0.966132	+	0.258049i	$0.0830797\pi$
$863$	20.7560	+	35.9505i	0.706543	+	1.22377i	−0.259589	+	0.965719i	$0.583587\pi$
$864$	3.99386	+	3.32402i	0.135874	+	0.113085i
$865$	4.04351	+	4.49078i	0.137484	+	0.152691i
$866$	−7.62214	−	23.4585i	−0.259011	−	0.797153i
$867$	27.9138	−	2.31619i	0.948003	−	0.0786619i
$868$	22.5483	−	2.82014i	0.765340	−	0.0957219i
$869$			47.3499i			1.60624i
$870$	0.508722	+	1.21356i	0.0172473	+	0.0411435i
$871$	−7.16656	+	6.45280i	−0.242830	+	0.218645i
$872$	4.93785	+	6.79636i	0.167217	+	0.230154i
$873$	23.7770	+	28.8575i	0.804729	+	0.976677i
$874$	33.4690	+	19.3233i	1.13211	+	0.653621i
$875$	−4.05899	+	0.426617i	−0.137219	+	0.0144223i
$876$	9.74920	−	16.0620i	0.329395	−	0.542684i
$877$	4.58158	−	43.5909i	0.154709	−	1.47196i	−0.591531	−	0.806282i	$-0.701476\pi$
$877$	4.58158	−	43.5909i	0.154709	−	1.47196i	0.746240	−	0.665677i	$-0.231857\pi$
$878$	−5.58671	−	5.03029i	−0.188542	−	0.169764i
$879$	−3.05363	+	8.74098i	−0.102996	+	0.294826i
$880$	0.752212	−	3.53888i	0.0253571	−	0.119296i
$881$	−26.9008	+	5.71795i	−0.906312	+	0.192643i	−0.637410	−	0.770525i	$-0.719994\pi$
$881$	−26.9008	+	5.71795i	−0.906312	+	0.192643i	−0.268902	+	0.963167i	$0.586661\pi$
$882$	15.9852	+	24.1633i	0.538251	+	0.813620i
$883$	−7.88334	−	2.56145i	−0.265296	−	0.0861998i	0.173349	−	0.984860i	$-0.444541\pi$
$883$	−7.88334	−	2.56145i	−0.265296	−	0.0861998i	−0.438644	+	0.898661i	$0.644541\pi$
$884$	−1.31376	−	0.426868i	−0.0441867	−	0.0143571i
$885$	−13.0626	+	7.16439i	−0.439094	+	0.240828i
$886$	21.5744	−	4.58578i	0.724806	−	0.154062i
$887$	1.79158	−	8.42873i	0.0601554	−	0.283009i	−0.937780	−	0.347229i	$-0.887123\pi$
$887$	1.79158	−	8.42873i	0.0601554	−	0.283009i	0.997936	+	0.0642201i	$0.0204560\pi$
$888$	12.2987	+	4.29650i	0.412717	+	0.144181i
$889$	12.8692	+	11.5875i	0.431618	+	0.388631i
$890$	−0.656777	+	6.24882i	−0.0220152	+	0.209461i
$891$	31.1343	+	9.53455i	1.04304	+	0.319419i
$892$	11.0972	−	1.16637i	0.371562	−	0.0390528i
$893$	52.0988	+	30.0792i	1.74342	+	1.00656i
$894$	23.1481	+	33.3761i	0.774188	+	1.11627i
$895$	7.73929	+	10.6522i	0.258696	+	0.356064i
$896$	−3.03303	+	2.73096i	−0.101327	+	0.0912349i
$897$	−15.2754	+	6.40341i	−0.510030	+	0.213804i
$898$			10.8891i			0.363374i
$899$	−4.04789	−	1.22760i	−0.135005	−	0.0409429i
$900$	2.95897	−	0.494454i	0.0986324	−	0.0164818i
$901$	−2.95491	−	9.09427i	−0.0984423	−	0.302974i
$902$	−15.5601	−	17.2813i	−0.518095	−	0.575403i
$903$	−45.9323	−	53.3196i	−1.52853	−	1.77437i
$904$	9.59551	+	16.6199i	0.319142	+	0.552770i
$905$	9.97095	−	17.2702i	0.331445	−	0.574080i
$906$	0.416523	+	2.19529i	0.0138381	+	0.0729335i
$907$	31.3940	+	22.8091i	1.04242	+	0.757363i	0.970757	−	0.240065i	$-0.0771689\pi$
$907$	31.3940	+	22.8091i	1.04242	+	0.757363i	0.0716646	+	0.997429i	$0.477169\pi$
$908$	−17.8086	−	1.87176i	−0.591001	−	0.0621167i
$909$	20.2693	+	12.9196i	0.672292	+	0.428517i
$910$	2.51922	−	5.65826i	0.0835114	−	0.187570i
$911$	19.4928	+	4.14333i	0.645826	+	0.137275i	0.519168	−	0.854672i	$-0.326242\pi$
$911$	19.4928	+	4.14333i	0.645826	+	0.137275i	0.126658	+	0.991947i	$0.459575\pi$
$912$	10.1724	−	3.06025i	0.336842	−	0.101335i
$913$	23.9785	−	10.6759i	0.793572	−	0.353321i
$914$	−7.12283	+	21.9218i	−0.235602	+	0.725109i
$915$	4.30841	−	18.2876i	0.142432	−	0.604570i
$916$	−2.89864	−	6.51045i	−0.0957738	−	0.215111i
$917$	1.52754	+	7.18652i	0.0504439	+	0.237320i
$918$	0.184042	+	4.72623i	0.00607429	+	0.155989i
$919$	−53.7487	−	23.9305i	−1.77301	−	0.789393i	−0.984734	−	0.174066i	$-0.944309\pi$
$919$	−53.7487	−	23.9305i	−1.77301	−	0.789393i	−0.788272	−	0.615327i	$-0.789024\pi$
$920$	4.21645	−	4.68284i	0.139012	−	0.154389i
$921$	0.0142571	−	0.649926i	0.000469787	−	0.0214158i
$922$	14.3480	−	19.7483i	0.472525	−	0.650375i
$923$	0.430474	+	4.09568i	0.0141692	+	0.134811i
$924$	−10.9125	+	23.1307i	−0.358993	+	0.760945i
$925$	6.51379	−	3.76074i	0.214172	−	0.123652i
$926$	7.72064	−	5.60937i	0.253716	−	0.184335i
$927$	−39.6078	−	31.5205i	−1.30089	−	1.03527i
$928$	0.722537	−	0.234766i	0.0237184	−	0.00770659i
$929$	23.8745			0.783297			0.391648	−	0.920115i	$-0.371905\pi$
$929$	23.8745			0.783297			0.391648	+	0.920115i	$0.371905\pi$
$930$	−4.84042	+	8.34088i	−0.158724	+	0.273508i
$931$	59.2294			1.94117
$932$	−1.68590	+	0.547783i	−0.0552236	+	0.0179432i
$933$	−0.370094	+	0.393330i	−0.0121163	+	0.0128770i
$934$	−7.10642	+	5.16312i	−0.232529	+	0.168942i
$935$	2.85203	−	1.64662i	0.0932714	−	0.0538503i
$936$	−1.59539	+	4.26403i	−0.0521468	+	0.139374i
$937$	−2.12343	−	20.2031i	−0.0693694	−	0.660006i	−0.972859	−	0.231397i	$-0.925670\pi$
$937$	−2.12343	−	20.2031i	−0.0693694	−	0.660006i	0.903490	−	0.428609i	$-0.140996\pi$
$938$	−15.2444	+	20.9821i	−0.497747	+	0.685091i
$939$	−40.9197	−	0.897634i	−1.33536	−	0.0292932i
$940$	6.56344	−	7.28944i	0.214076	−	0.237755i
$941$	3.40473	+	1.51588i	0.110991	+	0.0494164i	0.461481	−	0.887150i	$-0.347318\pi$
$941$	3.40473	+	1.51588i	0.110991	+	0.0494164i	−0.350490	+	0.936567i	$0.613985\pi$
$942$	−2.72075	+	21.3670i	−0.0886469	+	0.696174i
$943$	−8.42083	−	39.6169i	−0.274220	−	1.29010i
$944$	3.49856	+	7.85790i	0.113868	+	0.255753i
$945$	−21.1614	−	1.39441i	−0.688381	−	0.0453602i
$946$	11.1302	−	34.2553i	0.361874	−	1.11373i
$947$	54.2192	−	24.1399i	1.76189	−	0.784443i	0.773254	−	0.634097i	$-0.218628\pi$
$947$	54.2192	−	24.1399i	1.76189	−	0.784443i	0.988633	−	0.150346i	$-0.0480388\pi$
$948$	6.53038	+	21.7072i	0.212097	+	0.705018i
$949$	16.1028	+	3.42276i	0.522719	+	0.111107i
$950$	2.49453	−	5.60282i	0.0809334	−	0.181779i
$951$	5.63161	+	4.28341i	0.182617	+	0.138899i
$952$	−3.69471	−	0.388330i	−0.119746	−	0.0125858i
$953$	20.2339	+	14.7008i	0.655439	+	0.476205i	0.865120	−	0.501565i	$-0.167242\pi$
$953$	20.2339	+	14.7008i	0.655439	+	0.476205i	−0.209680	+	0.977770i	$0.567242\pi$
$954$	−30.3710	+	8.41502i	−0.983298	+	0.272446i
$955$	−2.08976	+	3.61957i	−0.0676231	+	0.117127i
$956$	−2.60971	−	4.52014i	−0.0844039	−	0.146192i
$957$	3.60694	−	3.10721i	0.116596	−	0.100442i
$958$	11.7165	+	13.0125i	0.378543	+	0.420414i
$959$	−5.75284	−	17.7054i	−0.185769	−	0.571737i
$960$	−0.143227	−	1.72612i	−0.00462264	−	0.0557102i
$961$	−10.7337	−	29.0824i	−0.346249	−	0.938143i
$962$			11.4144i			0.368014i
$963$	−41.8213	+	21.7584i	−1.34767	+	0.701155i
$964$	1.37405	−	1.23720i	0.0442553	−	0.0398477i
$965$	1.75733	+	2.41876i	0.0565705	+	0.0778626i
$966$	−36.6033	+	25.3863i	−1.17769	+	0.816791i
$967$	8.24683	+	4.76131i	0.265200	+	0.153113i	0.626704	−	0.779257i	$-0.284403\pi$
$967$	8.24683	+	4.76131i	0.265200	+	0.153113i	−0.361504	+	0.932370i	$0.617737\pi$
$968$	−2.07806	+	0.218413i	−0.0667913	+	0.00702005i
$969$	8.26589	+	5.01718i	0.265539	+	0.161175i
$970$	1.30281	−	12.3954i	0.0418308	−	0.397993i
$971$	−34.7046	−	31.2482i	−1.11372	−	1.00280i	−0.999957	−	0.00929403i	$-0.997042\pi$
$971$	−34.7046	−	31.2482i	−1.11372	−	1.00280i	−0.113767	−	0.993507i	$-0.536292\pi$
$972$	15.5883	+	0.0770860i	0.499994	+	0.00247253i
$973$	0.894215	−	4.20695i	0.0286672	−	0.134869i
$974$	−21.5193	+	4.57406i	−0.689522	+	0.146562i
$975$	1.26402	+	2.30463i	0.0404809	+	0.0738073i
$976$	−10.3165	−	3.35204i	−0.330223	−	0.107296i
$977$	10.8165	+	3.51450i	0.346051	+	0.112439i	0.476885	−	0.878965i	$-0.341766\pi$
$977$	10.8165	+	3.51450i	0.346051	+	0.112439i	−0.130835	+	0.991404i	$0.541766\pi$
$978$	−18.6674	−	34.0355i	−0.596916	−	1.08833i
$979$	22.2356	−	4.72633i	0.710654	−	0.151054i
$980$	2.00789	−	9.44638i	0.0641397	−	0.301754i
$981$	24.3981	+	6.31583i	0.778971	+	0.201649i
$982$	1.73437	+	1.56163i	0.0553459	+	0.0498336i
$983$	1.90111	−	18.0878i	0.0606359	−	0.576912i	−0.921453	−	0.388491i	$-0.872996\pi$
$983$	1.90111	−	18.0878i	0.0606359	−	0.576912i	0.982088	−	0.188421i	$-0.0603369\pi$
$984$	−9.51681	−	5.77646i	−0.303385	−	0.184147i
$985$	2.01943	−	0.212250i	0.0643443	−	0.00676286i
$986$	0.598889	+	0.345769i	0.0190725	+	0.0110115i
$987$	−56.9778	+	39.5171i	−1.81362	+	1.25784i
$988$	5.47071	+	7.52979i	0.174047	+	0.239555i
$989$	46.6196	−	41.9765i	1.48242	−	1.33477i
$990$	−5.00950	−	9.62863i	−0.159212	−	0.306018i
$991$			5.47667i			0.173972i	0.996210	+	0.0869861i	$0.0277236\pi$
$991$			5.47667i			0.173972i	−0.996210	+	0.0869861i	$0.972276\pi$
$992$	4.56803	+	3.18326i	0.145035	+	0.101069i
$993$	1.91960	+	23.1342i	0.0609166	+	0.734143i
$994$	3.42254	+	10.5335i	0.108557	+	0.334103i
$995$	9.18901	+	10.2054i	0.291311	+	0.323534i
$996$	9.52037	−	8.20135i	0.301665	−	0.259870i
$997$	−24.0548	−	41.6642i	−0.761825	−	1.31952i	−0.941909	−	0.335868i	$-0.890970\pi$
$997$	−24.0548	−	41.6642i	−0.761825	−	1.31952i	0.180084	−	0.983651i	$-0.442363\pi$
$998$	1.89657	−	3.28495i	0.0600348	−	0.103983i
$999$	36.6718	−	13.5144i	1.16024	−	0.427577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.2	✓	176
3.2	odd	2	inner	930.2.br.b.11.18	yes	176
31.17	odd	30	inner	930.2.br.b.761.18	yes	176
93.17	even	30	inner	930.2.br.b.761.2	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.2	✓	176	1.1	even	1	trivial
930.2.br.b.11.18	yes	176	3.2	odd	2	inner
930.2.br.b.761.2	yes	176	93.17	even	30	inner
930.2.br.b.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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.26144 - 1.18692i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.56648 + 0.739021i) q^{6} +(0.426617 + 4.05899i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.182449 + 2.99445i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.26144 - 1.18692i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.56648 + 0.739021i) q^{6} +(0.426617 + 4.05899i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.182449 + 2.99445i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.30515 - 1.47155i) q^{11} +(-1.71818 - 0.218783i) q^{12} +(-0.315521 - 1.48441i) q^{13} +(-1.66003 - 3.72850i) q^{14} +(1.68590 + 0.397183i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.831557 - 0.370233i) q^{17} +(-1.09885 - 2.79151i) q^{18} +(-5.99902 - 1.27513i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(4.27954 - 5.62652i) q^{21} +(3.59812 + 0.378178i) q^{22} +(5.09792 + 3.70386i) q^{23} +(1.70169 - 0.322871i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.758786 + 1.31426i) q^{26} +(3.32402 - 3.99386i) q^{27} +(2.73096 + 3.03303i) q^{28} +(-0.234766 - 0.722537i) q^{29} +(-1.72612 + 0.143227i) q^{30} +(3.18326 - 4.56803i) q^{31} +1.00000i q^{32} +(2.42264 + 5.77922i) q^{33} +(-0.676450 + 0.609078i) q^{34} +(-2.39896 - 3.30188i) q^{35} +(1.90770 + 2.31532i) q^{36} +(6.51379 + 3.76074i) q^{37} +(6.09945 - 0.641078i) q^{38} +(-1.36386 + 2.24699i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-4.77654 - 4.30082i) q^{41} +(-2.33139 + 6.67359i) q^{42} +(2.06985 - 9.73786i) q^{43} +(-3.53888 + 0.752212i) q^{44} +(-1.65523 - 2.50204i) q^{45} +(-5.99297 - 1.94723i) q^{46} +(-9.32882 - 3.03112i) q^{47} +(-1.51863 + 0.832920i) q^{48} +(-9.44638 + 2.00789i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(-1.48839 - 0.519965i) q^{51} +(-1.12778 - 1.01545i) q^{52} +(1.09808 - 10.4475i) q^{53} +(-1.92716 + 4.82556i) q^{54} +(3.59812 - 0.378178i) q^{55} +(-3.53455 - 2.04068i) q^{56} +(6.05392 + 8.72885i) q^{57} +(0.446552 + 0.614627i) q^{58} +(-6.39219 + 5.75555i) q^{59} +(1.59738 - 0.669617i) q^{60} -10.8474i q^{61} +(-1.61586 + 5.32813i) q^{62} +(-12.0766 + 2.01804i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.01545 + 1.12778i) q^{65} +(-4.08994 - 4.74773i) q^{66} +(-3.17730 - 5.50324i) q^{67} +(0.455126 - 0.788302i) q^{68} +(-2.03453 - 10.7230i) q^{69} +(3.30188 + 2.39896i) q^{70} +(-2.69884 - 0.283660i) q^{71} +(-2.52980 - 1.61249i) q^{72} +(-4.41226 + 9.91010i) q^{73} +(-7.35712 - 1.56380i) q^{74} +(-1.65862 + 0.498978i) q^{75} +(-5.60282 + 2.49453i) q^{76} +(4.56297 - 14.0434i) q^{77} +(0.602754 - 2.55847i) q^{78} +(-5.32318 - 11.9561i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-8.93342 + 1.09267i) q^{81} +(5.87179 + 2.61429i) q^{82} +(-4.85446 + 5.39142i) q^{83} +(0.155034 - 7.06741i) q^{84} +(-0.535033 + 0.736410i) q^{85} +(1.04062 + 9.90088i) q^{86} +(-0.561449 + 1.19008i) q^{87} +(3.13323 - 1.80897i) q^{88} +(-5.08325 + 3.69320i) q^{89} +(2.34739 + 1.86809i) q^{90} +(5.89060 - 1.91397i) q^{91} +6.30138 q^{92} +(-9.43736 + 1.98401i) q^{93} +9.80891 q^{94} +(5.83287 - 1.89522i) q^{95} +(1.18692 - 1.26144i) q^{96} +(10.0834 - 7.32599i) q^{97} +(8.36357 - 4.82871i) q^{98} +(3.80346 - 10.1656i) 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	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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