LMFDB - Embedded newform 930.2.br.b.761.18

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			761.18
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(1.04856 - 1.37859i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.42325 - 0.987098i) q^{6} +(0.426617 - 4.05899i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.801042 - 2.89108i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(1.04856 - 1.37859i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.42325 - 0.987098i) q^{6} +(0.426617 - 4.05899i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.801042 - 2.89108i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.30515 - 1.47155i) q^{11} +(1.65862 - 0.498978i) q^{12} +(-0.315521 + 1.48441i) q^{13} +(1.66003 - 3.72850i) q^{14} +(1.59738 - 0.669617i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.831557 - 0.370233i) q^{17} +(0.131556 - 2.99711i) q^{18} +(-5.99902 + 1.27513i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-5.14837 - 4.84423i) q^{21} +(3.59812 - 0.378178i) q^{22} +(-5.09792 + 3.70386i) q^{23} +(1.73163 + 0.0379860i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.758786 + 1.31426i) q^{26} +(-4.82556 - 1.92716i) 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} +(1.43698 - 6.09947i) q^{33} +(-0.676450 - 0.609078i) q^{34} +(2.39896 - 3.30188i) q^{35} +(1.05128 - 2.80977i) q^{36} +(6.51379 - 3.76074i) q^{37} +(-6.09945 - 0.641078i) q^{38} +(1.71555 + 1.99147i) q^{39} +(0.104528 + 0.994522i) q^{40} +(4.77654 - 4.30082i) q^{41} +(-3.39944 - 6.19807i) q^{42} +(2.06985 + 9.73786i) q^{43} +(3.53888 + 0.752212i) q^{44} +(0.751816 - 2.90427i) q^{45} +(-5.99297 + 1.94723i) q^{46} +(9.32882 - 3.03112i) q^{47} +(1.63514 + 0.571231i) q^{48} +(-9.44638 - 2.00789i) q^{49} +(0.207912 + 0.978148i) q^{50} +(-1.38234 + 0.758168i) q^{51} +(-1.12778 + 1.01545i) q^{52} +(-1.09808 - 10.4475i) q^{53} +(-3.99386 - 3.32402i) q^{54} +(3.59812 + 0.378178i) q^{55} +(3.53455 - 2.04068i) q^{56} +(-4.53245 + 9.60727i) q^{57} +(0.446552 - 0.614627i) q^{58} +(6.39219 + 5.75555i) q^{59} +(1.68590 + 0.397183i) 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} +(3.25149 - 5.35689i) q^{66} +(-3.17730 + 5.50324i) q^{67} +(-0.455126 - 0.788302i) q^{68} +(-0.239364 + 10.9117i) q^{69} +(3.30188 - 2.39896i) q^{70} +(2.69884 - 0.283660i) q^{71} +(1.86809 - 2.34739i) q^{72} +(-4.41226 - 9.91010i) q^{73} +(7.35712 - 1.56380i) q^{74} +(1.71818 + 0.218783i) q^{75} +(-5.60282 - 2.49453i) q^{76} +(-4.56297 - 14.0434i) q^{77} +(1.01619 + 2.42413i) q^{78} +(-5.32318 + 11.9561i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-7.71666 + 4.63175i) q^{81} +(5.87179 - 2.61429i) q^{82} +(4.85446 + 5.39142i) q^{83} +(-1.31775 - 6.94520i) q^{84} +(-0.535033 - 0.736410i) q^{85} +(-1.04062 + 9.90088i) q^{86} +(-0.749918 - 1.08127i) q^{87} +(3.13323 + 1.80897i) q^{88} +(5.08325 + 3.69320i) q^{89} +(1.61249 - 2.52980i) q^{90} +(5.89060 + 1.91397i) q^{91} -6.30138 q^{92} +(9.63529 + 0.401428i) q^{93} +9.80891 q^{94} +(-5.83287 - 1.89522i) q^{95} +(1.37859 + 1.04856i) q^{96} +(10.0834 + 7.32599i) q^{97} +(-8.36357 - 4.82871i) q^{98} +(-6.90193 - 8.37669i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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
$3$	1.04856	−	1.37859i	0.605387	−	0.795932i
$3$	1.04856	−	1.37859i	0.605387	−	0.795932i
$4$	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
$6$	1.42325	−	0.987098i	0.581039	−	0.402981i
$7$	0.426617	−	4.05899i	0.161246	−	1.53415i	−0.552359	−	0.833607i	$-0.686272\pi$
$7$	0.426617	−	4.05899i	0.161246	−	1.53415i	0.713605	−	0.700548i	$-0.247061\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−0.801042	−	2.89108i	−0.267014	−	0.963693i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	3.30515	−	1.47155i	0.996542	−	0.443689i	0.157361	−	0.987541i	$-0.449701\pi$
$11$	3.30515	−	1.47155i	0.996542	−	0.443689i	0.839181	+	0.543852i	$0.183035\pi$
$12$	1.65862	−	0.498978i	0.478802	−	0.144042i
$13$	−0.315521	+	1.48441i	−0.0875098	+	0.411701i	0.912487	+	0.409106i	$0.134159\pi$
$13$	−0.315521	+	1.48441i	−0.0875098	+	0.411701i	−0.999997	+	0.00259505i	$0.999174\pi$
$14$	1.66003	−	3.72850i	0.443663	−	0.996483i
$15$	1.59738	−	0.669617i	0.412441	−	0.172894i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.831557	−	0.370233i	−0.201682	−	0.0897947i	0.303410	−	0.952860i	$-0.401875\pi$
$17$	−0.831557	−	0.370233i	−0.201682	−	0.0897947i	−0.505092	+	0.863065i	$0.668542\pi$
$18$	0.131556	−	2.99711i	0.0310080	−	0.706427i
$19$	−5.99902	+	1.27513i	−1.37627	+	0.292535i	−0.835895	−	0.548889i	$-0.815051\pi$
$19$	−5.99902	+	1.27513i	−1.37627	+	0.292535i	−0.540375	+	0.841424i	$0.681718\pi$
$20$	0.406737	+	0.913545i	0.0909491	+	0.204275i
$21$	−5.14837	−	4.84423i	−1.12347	−	1.05710i
$22$	3.59812	−	0.378178i	0.767122	−	0.0806278i
$23$	−5.09792	+	3.70386i	−1.06299	+	0.772308i	−0.974639	−	0.223781i	$-0.928160\pi$
$23$	−5.09792	+	3.70386i	−1.06299	+	0.772308i	−0.0883513	+	0.996089i	$0.528160\pi$
$24$	1.73163	+	0.0379860i	0.353468	+	0.00775385i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.758786	+	1.31426i	−0.148810	+	0.257747i
$27$	−4.82556	−	1.92716i	−0.928680	−	0.370882i
$28$	2.73096	−	3.03303i	0.516102	−	0.573190i
$29$	0.234766	−	0.722537i	0.0435950	−	0.134172i	−0.926890	−	0.375333i	$-0.877528\pi$
$29$	0.234766	−	0.722537i	0.0435950	−	0.134172i	0.970485	+	0.241161i	$0.0775283\pi$
$30$	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
$33$	1.43698	−	6.09947i	0.250147	−	1.06178i
$34$	−0.676450	−	0.609078i	−0.116010	−	0.104456i
$35$	2.39896	−	3.30188i	0.405498	−	0.558120i
$36$	1.05128	−	2.80977i	0.175213	−	0.468295i
$37$	6.51379	−	3.76074i	1.07086	−	0.618262i	0.142444	−	0.989803i	$-0.454504\pi$
$37$	6.51379	−	3.76074i	1.07086	−	0.618262i	0.928416	+	0.371541i	$0.121171\pi$
$38$	−6.09945	−	0.641078i	−0.989461	−	0.103997i
$39$	1.71555	+	1.99147i	0.274709	+	0.318890i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	4.77654	−	4.30082i	0.745971	−	0.671675i	−0.205762	−	0.978602i	$-0.565967\pi$
$41$	4.77654	−	4.30082i	0.745971	−	0.671675i	0.951733	+	0.306927i	$0.0993007\pi$
$42$	−3.39944	−	6.19807i	−0.524545	−	0.956383i
$43$	2.06985	+	9.73786i	0.315649	+	1.48501i	0.794581	+	0.607158i	$0.207691\pi$
$43$	2.06985	+	9.73786i	0.315649	+	1.48501i	−0.478932	+	0.877852i	$0.658976\pi$
$44$	3.53888	+	0.752212i	0.533506	+	0.113400i
$45$	0.751816	−	2.90427i	0.112074	−	0.432943i
$46$	−5.99297	+	1.94723i	−0.883615	+	0.287104i
$47$	9.32882	−	3.03112i	1.36075	−	0.442134i	0.464456	−	0.885596i	$-0.346250\pi$
$47$	9.32882	−	3.03112i	1.36075	−	0.442134i	0.896293	+	0.443462i	$0.146250\pi$
$48$	1.63514	+	0.571231i	0.236013	+	0.0824501i
$49$	−9.44638	−	2.00789i	−1.34948	−	0.286842i
$50$	0.207912	+	0.978148i	0.0294032	+	0.138331i
$51$	−1.38234	+	0.758168i	−0.193566	+	0.106165i
$52$	−1.12778	+	1.01545i	−0.156394	+	0.140818i
$53$	−1.09808	−	10.4475i	−0.150833	−	1.43508i	−0.764046	−	0.645162i	$-0.776790\pi$
$53$	−1.09808	−	10.4475i	−0.150833	−	1.43508i	0.613213	−	0.789918i	$-0.289877\pi$
$54$	−3.99386	−	3.32402i	−0.543495	−	0.452341i
$55$	3.59812	+	0.378178i	0.485171	+	0.0509935i
$56$	3.53455	−	2.04068i	0.472325	−	0.272697i
$57$	−4.53245	+	9.60727i	−0.600338	+	1.27251i
$58$	0.446552	−	0.614627i	0.0586352	−	0.0807044i
$59$	6.39219	+	5.75555i	0.832192	+	0.749309i	0.970505	−	0.241080i	$-0.0775015\pi$
$59$	6.39219	+	5.75555i	0.832192	+	0.749309i	−0.138313	+	0.990389i	$0.544168\pi$
$60$	1.68590	+	0.397183i	0.217648	+	0.0512761i
$61$			10.8474i			1.38887i	0.719556	+	0.694435i	$0.244346\pi$
$61$			10.8474i			1.38887i	−0.719556	+	0.694435i	$0.755654\pi$
$62$	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
$66$	3.25149	−	5.35689i	0.400231	−	0.659388i
$67$	−3.17730	+	5.50324i	−0.388169	+	0.672328i	−0.992203	−	0.124630i	$-0.960226\pi$
$67$	−3.17730	+	5.50324i	−0.388169	+	0.672328i	0.604035	+	0.796958i	$0.293559\pi$
$68$	−0.455126	−	0.788302i	−0.0551922	−	0.0955957i
$69$	−0.239364	+	10.9117i	−0.0288160	+	1.31361i
$70$	3.30188	−	2.39896i	0.394650	−	0.286730i
$71$	2.69884	−	0.283660i	0.320293	−	0.0336642i	0.0569824	−	0.998375i	$-0.481852\pi$
$71$	2.69884	−	0.283660i	0.320293	−	0.0336642i	0.263311	+	0.964711i	$0.415185\pi$
$72$	1.86809	−	2.34739i	0.220157	−	0.276643i
$73$	−4.41226	−	9.91010i	−0.516416	−	1.15989i	−0.964062	−	0.265678i	$-0.914404\pi$
$73$	−4.41226	−	9.91010i	−0.516416	−	1.15989i	0.447646	−	0.894211i	$-0.352262\pi$
$74$	7.35712	−	1.56380i	0.855247	−	0.181788i
$75$	1.71818	+	0.218783i	0.198398	+	0.0252629i
$76$	−5.60282	−	2.49453i	−0.642687	−	0.286143i
$77$	−4.56297	−	14.0434i	−0.519999	−	1.60039i
$78$	1.01619	+	2.42413i	0.115061	+	0.274479i
$79$	−5.32318	+	11.9561i	−0.598904	+	1.34516i	0.318772	+	0.947831i	$0.396730\pi$
$79$	−5.32318	+	11.9561i	−0.598904	+	1.34516i	−0.917676	+	0.397329i	$0.869937\pi$
$80$	−0.207912	+	0.978148i	−0.0232452	+	0.109360i
$81$	−7.71666	+	4.63175i	−0.857407	+	0.514639i
$82$	5.87179	−	2.61429i	0.648431	−	0.288700i
$83$	4.85446	+	5.39142i	0.532846	+	0.591785i	0.948121	−	0.317911i	$-0.102981\pi$
$83$	4.85446	+	5.39142i	0.532846	+	0.591785i	−0.415275	+	0.909696i	$0.636315\pi$
$84$	−1.31775	−	6.94520i	−0.143778	−	0.757783i
$85$	−0.535033	−	0.736410i	−0.0580325	−	0.0798749i
$86$	−1.04062	+	9.90088i	−0.112213	+	1.06764i
$87$	−0.749918	−	1.08127i	−0.0803997	−	0.115924i
$88$	3.13323	+	1.80897i	0.334003	+	0.192837i
$89$	5.08325	+	3.69320i	0.538823	+	0.391478i	0.823648	−	0.567102i	$-0.191935\pi$
$89$	5.08325	+	3.69320i	0.538823	+	0.391478i	−0.284825	+	0.958580i	$0.591935\pi$
$90$	1.61249	−	2.52980i	0.169971	−	0.266664i
$91$	5.89060	+	1.91397i	0.617503	+	0.200639i
$92$	−6.30138			−0.656964
$93$	9.63529	+	0.401428i	0.999133	+	0.0416261i
$94$	9.80891			1.01171
$95$	−5.83287	−	1.89522i	−0.598440	−	0.194445i
$96$	1.37859	+	1.04856i	0.140702	+	0.107018i
$97$	10.0834	+	7.32599i	1.02381	+	0.743841i	0.967060	−	0.254547i	$-0.0819264\pi$
$97$	10.0834	+	7.32599i	1.02381	+	0.743841i	0.0567493	+	0.998388i	$0.481926\pi$
$98$	−8.36357	−	4.82871i	−0.844848	−	0.487773i
$99$	−6.90193	−	8.37669i	−0.693670	−	0.841889i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−4.70947	−	6.48203i	−0.468610	−	0.644986i	0.507656	−	0.861560i	$-0.330512\pi$
$101$	−4.70947	−	6.48203i	−0.468610	−	0.644986i	−0.976266	+	0.216573i	$0.930512\pi$
$102$	−1.54897	+	0.293894i	−0.153371	+	0.0290999i
$103$	−11.2903	−	12.5392i	−1.11247	−	1.23552i	−0.969315	−	0.245820i	$-0.920943\pi$
$103$	−11.2903	−	12.5392i	−1.11247	−	1.23552i	−0.143153	−	0.989701i	$-0.545724\pi$
$104$	−1.38637	+	0.617252i	−0.135945	+	0.0605265i
$105$	−2.03650	−	6.76941i	−0.198742	−	0.660627i
$106$	2.18413	−	10.2755i	0.212142	−	0.998047i
$107$	−6.39157	+	14.3557i	−0.617897	+	1.38782i	0.285236	+	0.958457i	$0.407928\pi$
$107$	−6.39157	+	14.3557i	−0.617897	+	1.38782i	−0.903133	+	0.429362i	$0.858739\pi$
$108$	−2.77121	−	4.39550i	−0.266660	−	0.422957i
$109$	2.59598	+	7.98961i	0.248650	+	0.765265i	0.995015	+	0.0997284i	$0.0317974\pi$
$109$	2.59598	+	7.98961i	0.248650	+	0.765265i	−0.746365	+	0.665537i	$0.768203\pi$
$110$	3.30515	+	1.47155i	0.315134	+	0.140307i
$111$	1.64557	−	12.9232i	0.156191	−	1.22662i
$112$	3.99216	−	0.848560i	0.377224	−	0.0801814i
$113$	−7.80569	−	17.5319i	−0.734298	−	1.64926i	−0.760278	−	0.649598i	$-0.774937\pi$
$113$	−7.80569	−	17.5319i	−0.734298	−	1.64926i	0.0259801	−	0.999662i	$-0.491729\pi$
$114$	−7.27943	+	7.73645i	−0.681781	+	0.724585i
$115$	−6.26686	+	0.658674i	−0.584388	+	0.0614216i
$116$	0.614627	−	0.446552i	0.0570667	−	0.0414613i
$117$	4.54429	−	0.276879i	0.420120	−	0.0255975i
$118$	4.30077	+	7.44915i	0.395918	+	0.685750i
$119$	−1.85753	+	3.21734i	−0.170280	+	0.294933i
$120$	1.48065	+	0.898714i	0.135164	+	0.0820410i
$121$	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
$126$	−12.1091	−	1.81260i	−1.07877	−	0.161480i
$127$	3.15317	+	2.83912i	0.279798	+	0.251931i	0.797066	−	0.603892i	$-0.206384\pi$
$127$	3.15317	+	2.83912i	0.279798	+	0.251931i	−0.517268	+	0.855824i	$0.673051\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	15.5949	+	7.35726i	1.37306	+	0.647771i
$130$	−1.31426	+	0.758786i	−0.115268	+	0.0665499i
$131$	−1.79029	−	0.188168i	−0.156419	−	0.0164403i	0.0259954	−	0.999662i	$-0.491724\pi$
$131$	−1.79029	−	0.188168i	−0.156419	−	0.0164403i	−0.182414	+	0.983222i	$0.558391\pi$
$132$	4.74773	−	4.08994i	0.413237	−	0.355984i
$133$	2.61646	+	24.8940i	0.226876	+	2.15858i
$134$	−4.72238	+	4.25205i	−0.407952	+	0.367322i
$135$	−3.21548	−	4.08175i	−0.276745	−	0.351301i
$136$	−0.189252	−	0.890362i	−0.0162282	−	0.0763479i
$137$	4.46170	+	0.948363i	0.381188	+	0.0810241i	0.394521	−	0.918887i	$-0.370911\pi$
$137$	4.46170	+	0.948363i	0.381188	+	0.0810241i	−0.0133323	+	0.999911i	$0.504244\pi$
$138$	−3.59955	+	10.3037i	−0.306414	+	0.877106i
$139$	−1.00223	+	0.325643i	−0.0850077	+	0.0276207i	−0.351212	−	0.936296i	$-0.614230\pi$
$139$	−1.00223	+	0.325643i	−0.0850077	+	0.0276207i	0.266204	+	0.963917i	$0.414230\pi$
$140$	3.88159	−	1.26121i	0.328055	−	0.106591i
$141$	5.60315	−	16.0390i	0.471871	−	1.35073i
$142$	2.65441	+	0.564211i	0.222753	+	0.0473476i
$143$	1.14154	+	5.37051i	0.0954601	+	0.449104i
$144$	2.50204	−	1.65523i	0.208504	−	0.137936i
$145$	0.564582	−	0.508352i	0.0468860	−	0.0422163i
$146$	−1.13392	−	10.7885i	−0.0938439	−	0.892865i
$147$	−12.6732	+	10.9173i	−1.04527	+	0.900446i
$148$	7.48027	+	0.786208i	0.614875	+	0.0646259i
$149$	−20.3089	+	11.7253i	−1.66377	+	0.960577i	−0.692877	+	0.721056i	$0.743657\pi$
$149$	−20.3089	+	11.7253i	−1.66377	+	0.960577i	−0.970891	+	0.239521i	$0.923010\pi$
$150$	1.56648	+	0.739021i	0.127902	+	0.0603408i
$151$	0.758279	−	1.04368i	0.0617078	−	0.0849336i	−0.777048	−	0.629442i	$-0.783284\pi$
$151$	0.758279	−	1.04368i	0.0617078	−	0.0849336i	0.838756	+	0.544508i	$0.183284\pi$
$152$	−4.55774	−	4.10381i	−0.369682	−	0.332863i
$153$	−0.404260	+	2.70067i	−0.0326825	+	0.218336i
$154$		−	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	−0.672343	−	0.740240i	$-0.734712\pi$
$157$	3.84289	−	11.8272i	0.306696	−	0.943913i	0.979039	−	0.203673i	$-0.0652880\pi$
$158$	−8.75727	+	9.72593i	−0.696691	+	0.773753i
$159$	−15.5543	−	9.44107i	−1.23354	−	0.748725i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.8591	+	22.2726i	1.01344	+	1.75532i
$162$	−8.77027	+	2.02048i	−0.689058	+	0.158744i
$163$	−18.1316	+	13.1734i	−1.42018	+	1.03182i	−0.428437	+	0.903572i	$0.640936\pi$
$163$	−18.1316	+	13.1734i	−1.42018	+	1.03182i	−0.991742	+	0.128249i	$0.959064\pi$
$164$	6.39226	−	0.671854i	0.499152	−	0.0524630i
$165$	4.29420	−	4.56381i	0.334303	−	0.355292i
$166$	2.95082	+	6.62766i	0.229028	+	0.514406i
$167$	5.16142	−	1.09709i	0.399402	−	0.0848956i	−0.00383121	−	0.999993i	$-0.501220\pi$
$167$	5.16142	−	1.09709i	0.399402	−	0.0848956i	0.403234	+	0.915097i	$0.367886\pi$
$168$	0.892930	−	7.01248i	0.0688910	−	0.541025i
$169$	9.77217	+	4.35085i	0.751706	+	0.334681i
$170$	−0.281284	−	0.865702i	−0.0215735	−	0.0663963i
$171$	8.49198	+	16.3222i	0.649398	+	1.24819i
$172$	−4.04923	+	9.09472i	−0.308751	+	0.693466i
$173$	1.25640	−	5.91088i	0.0955221	−	0.449396i	−0.904228	−	0.427050i	$-0.859553\pi$
$173$	1.25640	−	5.91088i	0.0955221	−	0.449396i	0.999750	−	0.0223465i	$-0.00711370\pi$
$174$	−0.379083	−	1.26009i	−0.0287382	−	0.0955270i
$175$	3.72850	−	1.66003i	0.281848	−	0.125487i
$176$	2.42088	+	2.68865i	0.182480	+	0.202665i
$177$	14.6372	−	2.77719i	1.10020	−	0.208746i
$178$	3.69320	+	5.08325i	0.276817	+	0.381005i
$179$	1.37631	−	13.0947i	0.102870	−	0.978747i	−0.814352	−	0.580371i	$-0.802907\pi$
$179$	1.37631	−	13.0947i	0.102870	−	0.978747i	0.917222	−	0.398375i	$-0.130426\pi$
$180$	2.31532	−	1.90770i	0.172574	−	0.142191i
$181$	−17.2702	−	9.97095i	−1.28368	−	0.741135i	−0.306163	−	0.951979i	$-0.599045\pi$
$181$	−17.2702	−	9.97095i	−1.28368	−	0.741135i	−0.977520	+	0.210845i	$0.932379\pi$
$182$	5.01084	+	3.64059i	0.371428	+	0.269859i
$183$	14.9542	+	11.3742i	1.10545	+	0.840803i
$184$	−5.99297	−	1.94723i	−0.441808	−	0.143552i
$185$	7.52148			0.552990
$186$	9.03966	+	3.35925i	0.662820	+	0.246312i
$187$	−3.29324			−0.240826
$188$	9.32882	+	3.03112i	0.680374	+	0.221067i
$189$	−9.88099	+	18.7648i	−0.718736	+	1.36494i
$190$	−4.96174	−	3.60491i	−0.359962	−	0.261528i
$191$	−3.61957	−	2.08976i	−0.261903	−	0.151210i	0.363299	−	0.931673i	$-0.381650\pi$
$191$	−3.61957	−	2.08976i	−0.261903	−	0.151210i	−0.625202	+	0.780463i	$0.714984\pi$
$192$	0.987098	+	1.42325i	0.0712376	+	0.102714i
$193$	−0.312514	+	2.97337i	−0.0224952	+	0.214028i	0.977500	+	0.210936i	$0.0676510\pi$
$193$	−0.312514	+	2.97337i	−0.0224952	+	0.214028i	−0.999995	+	0.00309239i	$0.999016\pi$
$194$	7.32599	+	10.0834i	0.525975	+	0.723943i
$195$	0.489980	+	2.58244i	0.0350882	+	0.184932i
$196$	−6.46208	−	7.17686i	−0.461577	−	0.512633i
$197$	1.85500	−	0.825899i	0.132163	−	0.0588429i	−0.339590	−	0.940574i	$-0.610288\pi$
$197$	1.85500	−	0.825899i	0.132163	−	0.0588429i	0.471753	+	0.881731i	$0.343621\pi$
$198$	−3.97559	−	10.0995i	−0.282533	−	0.717741i
$199$	−2.85520	+	13.4327i	−0.202400	+	0.952216i	0.753255	+	0.657728i	$0.228482\pi$
$199$	−2.85520	+	13.4327i	−0.202400	+	0.952216i	−0.955655	+	0.294488i	$0.904851\pi$
$200$	−0.406737	+	0.913545i	−0.0287606	+	0.0645974i
$201$	4.25515	+	10.1507i	0.300135	+	0.715974i
$202$	−2.47592	−	7.62009i	−0.174205	−	0.536147i
$203$	−2.83262	−	1.26116i	−0.198811	−	0.0885162i
$204$	−1.56398	−	0.199148i	−0.109500	−	0.0139431i
$205$	6.28702	−	1.33635i	0.439104	−	0.0933345i
$206$	−6.86291	−	15.4144i	−0.478162	−	1.07397i
$207$	14.7918	+	11.7715i	1.02810	+	0.818179i
$208$	−1.50926	+	0.158629i	−0.104648	+	0.0109990i
$209$	−17.9513	+	13.0424i	−1.24172	+	0.902160i
$210$	0.155034	−	7.06741i	0.0106984	−	0.487697i
$211$	1.52165	+	2.63558i	0.104755	+	0.181440i	0.913638	−	0.406529i	$-0.133261\pi$
$211$	1.52165	+	2.63558i	0.104755	+	0.181440i	−0.808883	+	0.587969i	$0.799928\pi$
$212$	5.25254	−	9.09767i	0.360746	−	0.624831i
$213$	2.43885	−	4.01804i	0.167107	−	0.275311i
$214$	−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
$219$	−18.2885	−	4.30862i	−1.23582	−	0.291150i
$220$	2.68865	+	2.42088i	0.181269	+	0.163215i
$221$	0.811951	−	1.11756i	0.0546178	−	0.0751749i
$222$	5.55853	−	11.7822i	0.373064	−	0.790771i
$223$	9.66341	−	5.57917i	0.647110	−	0.373609i	−0.140238	−	0.990118i	$-0.544787\pi$
$223$	9.66341	−	5.57917i	0.647110	−	0.373609i	0.787348	+	0.616509i	$0.211453\pi$
$224$	4.05899	+	0.426617i	0.271203	+	0.0285046i
$225$	2.10323	−	2.13926i	0.140215	−	0.142617i
$226$	−2.00601	−	19.0859i	−0.133438	−	1.26958i
$227$	13.3073	−	11.9820i	0.883237	−	0.795270i	−0.0965472	−	0.995328i	$-0.530780\pi$
$227$	13.3073	−	11.9820i	0.883237	−	0.795270i	0.979784	+	0.200058i	$0.0641132\pi$
$228$	−9.31384	+	5.10834i	−0.616824	+	0.338308i
$229$	1.48170	+	6.97085i	0.0979134	+	0.460647i	0.999601	+	0.0282577i	$0.00899589\pi$
$229$	1.48170	+	6.97085i	0.0979134	+	0.460647i	−0.901687	+	0.432389i	$0.857671\pi$
$230$	−6.16368	−	1.31013i	−0.406421	−	0.0863875i
$231$	−24.1447	−	8.43485i	−1.58860	−	0.554972i
$232$	0.722537	−	0.234766i	0.0474369	−	0.0154132i
$233$	1.68590	−	0.547783i	0.110447	−	0.0358865i	−0.253272	−	0.967395i	$-0.581507\pi$
$233$	1.68590	−	0.547783i	0.110447	−	0.0358865i	0.363719	+	0.931509i	$0.381507\pi$
$234$	4.40744	+	1.14093i	0.288123	+	0.0745852i
$235$	9.59456	+	2.03939i	0.625880	+	0.133035i
$236$	1.78836	+	8.41357i	0.116412	+	0.547677i
$237$	10.9009	+	19.8751i	0.708087	+	1.29103i
$238$	−2.76083	+	2.48586i	−0.178958	+	0.161134i
$239$	−0.545577	−	5.19082i	−0.0352904	−	0.335766i	−0.997895	−	0.0648547i	$-0.979342\pi$
$239$	−0.545577	−	5.19082i	−0.0352904	−	0.335766i	0.962604	−	0.270911i	$-0.0873251\pi$
$240$	1.13046	+	1.31227i	0.0729709	+	0.0847068i
$241$	1.83884	+	0.193270i	0.118450	+	0.0124496i	0.163568	−	0.986532i	$-0.447700\pi$
$241$	1.83884	+	0.193270i	0.118450	+	0.0124496i	−0.0451178	+	0.998982i	$0.514366\pi$
$242$	1.80956	−	1.04475i	0.116323	−	0.0671592i
$243$	−1.70608	+	15.4948i	−0.109445	+	0.993993i
$244$	−6.37595	+	8.77575i	−0.408179	+	0.561810i
$245$	−7.17686	−	6.46208i	−0.458513	−	0.412847i
$246$	2.55288	−	10.8361i	0.162766	−	0.690881i
$247$		−	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	$-0.852704\pi$
$251$	−5.66127	+	6.28748i	−0.357336	+	0.396862i	0.537495	+	0.843267i	$0.319371\pi$
$252$	−10.9564	−	5.46582i	−0.690185	−	0.344314i
$253$	−11.3990	+	19.7437i	−0.716650	+	1.24127i
$254$	2.12150	+	3.67455i	0.133115	+	0.230562i
$255$	−1.57623	−	0.0345768i	−0.0987070	−	0.00216529i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−28.2834	+	2.97271i	−1.76427	+	0.185432i	−0.930405	−	0.366534i	$-0.880544\pi$
$257$	−28.2834	+	2.97271i	−1.76427	+	0.185432i	−0.833866	+	0.551967i	$0.813878\pi$
$258$	12.5581	+	11.8163i	0.781835	+	0.735648i
$259$	−12.4859	−	28.0438i	−0.775837	−	1.74256i
$260$	−1.48441	+	0.315521i	−0.0920591	+	0.0195678i
$261$	−2.27697	−	0.0999455i	−0.140941	−	0.00618647i
$262$	−1.64452	−	0.732189i	−0.101599	−	0.0452348i
$263$	2.42838	+	7.47379i	0.149740	+	0.460854i	0.997590	−	0.0693831i	$-0.0221031\pi$
$263$	2.42838	+	7.47379i	0.149740	+	0.460854i	−0.847850	+	0.530237i	$0.822103\pi$
$264$	5.77922	−	2.42264i	0.355686	−	0.149103i
$265$	4.27280	−	9.59687i	0.262476	−	0.589531i
$266$	−5.20426	+	24.4841i	−0.319094	+	1.50122i
$267$	10.4215	−	3.13520i	0.637786	−	0.191871i
$268$	−5.80521	+	2.58465i	−0.354610	+	0.157882i
$269$	−16.8556	−	18.7200i	−1.02770	−	1.14138i	−0.989853	−	0.142095i	$-0.954616\pi$
$269$	−16.8556	−	18.7200i	−1.02770	−	1.14138i	−0.0378492	−	0.999283i	$-0.512051\pi$
$270$	−1.79678	−	4.87561i	−0.109348	−	0.296720i
$271$	−6.39274	−	8.79886i	−0.388332	−	0.534493i	0.569436	−	0.822036i	$-0.307162\pi$
$271$	−6.39274	−	8.79886i	−0.388332	−	0.534493i	−0.957768	+	0.287543i	$0.907162\pi$
$272$	0.0951473	−	0.905266i	0.00576915	−	0.0548898i
$273$	8.81524	−	6.11383i	0.533522	−	0.370026i
$274$	3.95027	+	2.28069i	0.238644	+	0.137781i
$275$	2.92698	+	2.12657i	0.176503	+	0.128237i
$276$	−6.60738	+	8.68704i	−0.397717	+	0.522899i
$277$	−10.7453	−	3.49136i	−0.645622	−	0.209775i	−0.0321394	−	0.999483i	$-0.510232\pi$
$277$	−10.7453	−	3.49136i	−0.645622	−	0.209775i	−0.613483	+	0.789708i	$0.710232\pi$
$278$	−1.05380			−0.0632029
$279$	10.6566	−	12.8622i	0.637993	−	0.770042i
$280$	4.08135			0.243907
$281$	6.38416	+	2.07434i	0.380847	+	0.123745i	0.493183	−	0.869926i	$-0.335833\pi$
$281$	6.38416	+	2.07434i	0.380847	+	0.123745i	−0.112336	+	0.993670i	$0.535833\pi$
$282$	10.2852	−	13.5225i	0.612477	−	0.805253i
$283$	−12.0044	−	8.72171i	−0.713588	−	0.518452i	0.170742	−	0.985316i	$-0.445384\pi$
$283$	−12.0044	−	8.72171i	−0.713588	−	0.518452i	−0.884329	+	0.466864i	$0.845384\pi$
$284$	2.35014	+	1.35685i	0.139455	+	0.0805144i
$285$	−8.72885	+	6.05392i	−0.517053	+	0.358603i
$286$	−0.573912	+	5.46041i	−0.0339361	+	0.322881i
$287$	−15.4192	−	21.2228i	−0.910169	−	1.25274i
$288$	2.89108	−	0.801042i	0.170358	−	0.0472019i
$289$	−10.8208	−	12.0177i	−0.636518	−	0.706925i
$290$	0.694039	−	0.309006i	0.0407554	−	0.0181455i
$291$	20.6726	−	6.21911i	1.21185	−	0.364571i
$292$	2.25542	−	10.6109i	0.131988	−	0.620956i
$293$	2.17429	−	4.88353i	0.127023	−	0.285299i	−0.838828	−	0.544397i	$-0.816759\pi$
$293$	2.17429	−	4.88353i	0.127023	−	0.285299i	0.965851	+	0.259098i	$0.0834252\pi$
$294$	−15.4265	+	6.46678i	−0.899694	+	0.377150i
$295$	2.65802	+	8.18055i	0.154756	+	0.476290i
$296$	6.87121	+	3.05926i	0.399381	+	0.177816i
$297$	−18.7851	+	0.731503i	−1.09002	+	0.0424461i
$298$	−22.9382	+	4.87567i	−1.32878	+	0.282440i
$299$	−3.88954	−	8.73605i	−0.224938	−	0.505219i
$300$	1.26144	+	1.18692i	0.0728291	+	0.0685268i
$301$	40.4089	−	4.24715i	2.32913	−	0.244802i
$302$	1.04368	−	0.758279i	0.0600571	−	0.0436340i
$303$	−13.8743	−	0.304352i	−0.797055	−	0.0174846i
$304$	−3.06652	−	5.31137i	−0.175877	−	0.304628i
$305$	−5.42371	+	9.39414i	−0.310561	+	0.537907i
$306$	−1.21903	+	2.44357i	−0.0696871	+	0.139689i
$307$	0.251142	−	0.278921i	0.0143334	−	0.0159189i	−0.735935	−	0.677052i	$-0.763257\pi$
$307$	0.251142	−	0.278921i	0.0143334	−	0.0159189i	0.750269	+	0.661133i	$0.229924\pi$
$308$	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	$-0.00281408\pi$
$312$	−0.602754	+	2.55847i	−0.0341242	+	0.144845i
$313$	17.5610	+	15.8120i	0.992607	+	0.893747i	0.994339	−	0.106251i	$-0.0338848\pi$
$313$	17.5610	+	15.8120i	0.992607	+	0.893747i	−0.00173241	+	0.999998i	$0.500551\pi$
$314$	7.30961	−	10.0608i	0.412505	−	0.567765i
$315$	−11.4677	−	4.29063i	−0.646130	−	0.241749i
$316$	−11.3341	+	6.54376i	−0.637595	+	0.368115i
$317$	4.06266	+	0.427003i	0.228182	+	0.0239829i	0.217929	−	0.975965i	$-0.430070\pi$
$317$	4.06266	+	0.427003i	0.228182	+	0.0239829i	0.0102524	+	0.999947i	$0.496736\pi$
$318$	−11.8756	−	13.7855i	−0.665950	−	0.773055i
$319$	−0.287309	−	2.73357i	−0.0160862	−	0.153050i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	13.0887	+	23.8642i	0.730543	+	1.33197i
$322$	5.34710	+	25.1561i	0.297982	+	1.40190i
$323$	5.46063	+	1.16069i	0.303837	+	0.0645827i
$324$	−8.96539	−	0.788574i	−0.498077	−	0.0438097i
$325$	−1.44330	+	0.468955i	−0.0800597	+	0.0260130i
$326$	−21.3150	+	6.92567i	−1.18053	+	0.383577i
$327$	13.7365	+	4.79878i	0.759628	+	0.265373i
$328$	6.28702	+	1.33635i	0.347142	+	0.0737874i
$329$	−8.32345	−	39.1588i	−0.458887	−	2.15889i
$330$	5.49432	−	3.01346i	0.302453	−	0.165885i
$331$	−9.95997	+	8.96800i	−0.547449	+	0.492926i	−0.895811	−	0.444434i	$-0.853405\pi$
$331$	−9.95997	+	8.96800i	−0.547449	+	0.492926i	0.348362	+	0.937360i	$0.386738\pi$
$332$	0.758341	+	7.21513i	0.0416194	+	0.395982i
$333$	−16.0904	−	15.8194i	−0.881749	−	0.866896i
$334$	5.24782	+	0.551568i	0.287148	+	0.0301805i
$335$	−5.50324	+	3.17730i	−0.300674	+	0.173594i
$336$	3.01620	−	6.39334i	0.164547	−	0.348785i
$337$	15.8462	−	21.8104i	0.863197	−	1.18809i	−0.117601	−	0.993061i	$-0.537520\pi$
$337$	15.8462	−	21.8104i	0.863197	−	1.18809i	0.980798	−	0.195027i	$-0.0624795\pi$
$338$	7.94940	+	7.15767i	0.432390	+	0.389326i
$339$	−32.3541	−	7.62235i	−1.75723	−	0.413989i
$340$		−	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
$345$	−5.66314	+	9.33012i	−0.304893	+	0.502317i
$346$	3.02147	−	5.23334i	0.162435	−	0.281346i
$347$	13.8284	+	23.9514i	0.742346	+	1.28578i	0.951425	+	0.307882i	$0.0996201\pi$
$347$	13.8284	+	23.9514i	0.742346	+	1.28578i	−0.209079	+	0.977899i	$0.567047\pi$
$348$	0.0288587	−	1.31556i	0.00154699	−	0.0705213i
$349$	−16.3863	+	11.9053i	−0.877139	+	0.637278i	−0.932493	−	0.361188i	$-0.882371\pi$
$349$	−16.3863	+	11.9053i	−0.877139	+	0.637278i	0.0553543	+	0.998467i	$0.482371\pi$
$350$	4.05899	−	0.426617i	0.216962	−	0.0228037i
$351$	4.38326	−	6.55505i	0.233961	−	0.349883i
$352$	1.47155	+	3.30515i	0.0784339	+	0.176165i
$353$	16.3938	−	3.48461i	0.872554	−	0.185467i	0.250192	−	0.968196i	$-0.419506\pi$
$353$	16.3938	−	3.48461i	0.872554	−	0.185467i	0.622362	+	0.782729i	$0.286173\pi$
$354$	14.7790	+	1.88187i	0.785493	+	0.100020i
$355$	2.47909	+	1.10376i	0.131577	+	0.0585817i
$356$	1.94163	+	5.97572i	0.102906	+	0.316712i
$357$	2.48767	+	5.93435i	0.131661	+	0.314079i
$358$	5.35545	−	12.0285i	0.283044	−	0.635728i
$359$	1.47596	−	6.94385i	0.0778982	−	0.366482i	−0.921882	−	0.387472i	$-0.873348\pi$
$359$	1.47596	−	6.94385i	0.0778982	−	0.366482i	0.999780	+	0.0209898i	$0.00668174\pi$
$360$	2.79151	−	1.09885i	0.147125	−	0.0579147i
$361$	17.0050	−	7.57110i	0.894998	−	0.398479i
$362$	−13.3437	−	14.8197i	−0.701331	−	0.778907i
$363$	−0.674641	−	3.55569i	−0.0354095	−	0.186626i
$364$	3.64059	+	5.01084i	0.190819	+	0.262640i
$365$	1.13392	−	10.7885i	0.0593521	−	0.564697i
$366$	10.7075	+	15.4386i	0.559688	+	0.806987i
$367$	−15.3589	−	8.86747i	−0.801729	−	0.462878i	0.0423466	−	0.999103i	$-0.486517\pi$
$367$	−15.3589	−	8.86747i	−0.801729	−	0.462878i	−0.844075	+	0.536225i	$0.819850\pi$
$368$	−5.09792	−	3.70386i	−0.265748	−	0.193077i
$369$	−16.2602	−	10.3642i	−0.846473	−	0.539540i
$370$	7.15335	+	2.32426i	0.371885	+	0.120833i
$371$	−42.8749			−2.22596
$372$	7.55916	+	5.98824i	0.391924	+	0.310476i
$373$	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
$375$	1.37859	+	1.04856i	0.0711903	+	0.0541474i
$376$	7.93557	+	5.76553i	0.409246	+	0.297335i
$377$	0.998467	+	0.576465i	0.0514237	+	0.0296895i
$378$	−15.1960	+	14.7930i	−0.781598	+	0.760868i
$379$	−1.53231	+	14.5790i	−0.0787096	+	0.748872i	0.881988	+	0.471273i	$0.156205\pi$
$379$	−1.53231	+	14.5790i	−0.0787096	+	0.748872i	−0.960697	+	0.277599i	$0.910461\pi$
$380$	−3.60491	−	4.96174i	−0.184928	−	0.254532i
$381$	7.22028	−	1.36994i	0.369906	−	0.0701843i
$382$	−2.79665	−	3.10599i	−0.143089	−	0.158916i
$383$	18.5617	−	8.26419i	0.948458	−	0.422281i	0.126588	−	0.991955i	$-0.459598\pi$
$383$	18.5617	−	8.26419i	0.948458	−	0.422281i	0.821870	+	0.569675i	$0.192931\pi$
$384$	0.498978	+	1.65862i	0.0254633	+	0.0846411i
$385$	3.07004	−	14.4434i	0.156464	−	0.736105i
$386$	−1.21604	+	2.73127i	−0.0618948	+	0.139018i
$387$	26.4949	−	13.7845i	1.34681	−	0.700707i
$388$	3.85150	+	11.8537i	0.195530	+	0.601780i
$389$	19.6680	+	8.75676i	0.997207	+	0.443985i	0.839417	−	0.543488i	$-0.182897\pi$
$389$	19.6680	+	8.75676i	0.997207	+	0.443985i	0.157790	+	0.987473i	$0.449563\pi$
$390$	−0.332019	+	2.60746i	−0.0168124	+	0.132034i
$391$	5.61051	−	1.19255i	0.283736	−	0.0603099i
$392$	−3.92803	−	8.82249i	−0.198395	−	0.445603i
$393$	−2.13664	+	2.27078i	−0.107779	+	0.114546i
$394$	2.01943	−	0.212250i	0.101737	−	0.0106930i
$395$	−10.5880	+	7.69266i	−0.532742	+	0.387060i
$396$	−0.660089	−	10.8337i	−0.0331707	−	0.544416i
$397$	−15.9955	−	27.7050i	−0.802790	−	1.39047i	−0.917773	−	0.397105i	$-0.870015\pi$
$397$	−15.9955	−	27.7050i	−0.802790	−	1.39047i	0.114984	−	0.993367i	$-0.463318\pi$
$398$	−6.86638	+	11.8929i	−0.344180	+	0.596138i
$399$	37.0622	+	22.4958i	1.85543	+	1.12620i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	−3.66934	+	11.2931i	−0.183238	+	0.563949i	−0.999914	−	0.0131485i	$-0.995815\pi$
$401$	−3.66934	+	11.2931i	−0.183238	+	0.563949i	0.816676	+	0.577097i	$0.195815\pi$
$402$	0.910151	+	10.9688i	0.0453942	+	0.547073i
$403$	−7.78520	+	3.28395i	−0.387809	+	0.163585i
$404$		−	8.01223i		−	0.398624i
$405$	−8.99870	+	0.152884i	−0.447149	+	0.00759685i
$406$	−2.30426	−	2.07476i	−0.114358	−	0.102969i
$407$	15.9950	−	22.0152i	0.792841	−	1.09125i
$408$	−1.42589	−	0.672696i	−0.0705921	−	0.0333034i
$409$	−17.2967	+	9.98626i	−0.855267	+	0.493789i	−0.862425	−	0.506185i	$-0.831055\pi$
$409$	−17.2967	+	9.98626i	−0.855267	+	0.493789i	0.00715718	+	0.999974i	$0.497722\pi$
$410$	6.39226	+	0.671854i	0.315691	+	0.0331805i
$411$	5.98577	−	5.15645i	0.295256	−	0.254349i
$412$	−1.76372	−	16.7807i	−0.0868923	−	0.826725i
$413$	26.0888	−	23.4904i	1.28374	−	1.15589i
$414$	10.4302	+	15.7663i	0.512618	+	0.774873i
$415$	1.50837	+	7.09634i	0.0740431	+	0.348345i
$416$	−1.48441	−	0.315521i	−0.0727791	−	0.0154697i
$417$	−0.601965	+	1.72312i	−0.0294783	+	0.0843815i
$418$	−21.1030	+	6.85678i	−1.03218	+	0.335376i
$419$	−1.39230	+	0.452387i	−0.0680185	+	0.0221006i	−0.342829	−	0.939398i	$-0.611385\pi$
$419$	−1.39230	+	0.452387i	−0.0680185	+	0.0221006i	0.274810	+	0.961499i	$0.411385\pi$
$420$	2.33139	−	6.67359i	0.113760	−	0.325638i
$421$	3.89011	+	0.826869i	0.189593	+	0.0402991i	0.301729	−	0.953394i	$-0.402436\pi$
$421$	3.89011	+	0.826869i	0.189593	+	0.0402991i	−0.112137	+	0.993693i	$0.535769\pi$
$422$	0.632738	+	2.97680i	0.0308012	+	0.144908i
$423$	−16.2360	−	24.5423i	−0.789421	−	1.19329i
$424$	7.80680	−	7.02928i	0.379132	−	0.341372i
$425$	−0.0951473	−	0.905266i	−0.00461532	−	0.0439119i
$426$	3.56112	−	3.06774i	0.172537	−	0.148632i
$427$	44.0296	+	4.62770i	2.13074	+	0.223950i
$428$	−13.6090	+	7.85714i	−0.657814	+	0.379789i
$429$	8.60072	+	4.05758i	0.415247	+	0.195902i
$430$	−5.85164	+	8.05410i	−0.282191	+	0.388403i
$431$	−21.8945	−	19.7139i	−1.05462	−	0.949584i	−0.0558144	−	0.998441i	$-0.517775\pi$
$431$	−21.8945	−	19.7139i	−1.05462	−	0.949584i	−0.998806	+	0.0488569i	$0.984442\pi$
$432$	0.341654	−	5.18491i	0.0164379	−	0.249459i
$433$		−	24.6658i		−	1.18536i	−0.805438	−	0.592680i	$-0.798070\pi$
$433$		−	24.6658i		−	1.18536i	0.805438	−	0.592680i	$-0.201930\pi$
$434$	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
$438$	−16.0620	−	9.74920i	−0.767471	−	0.465835i
$439$	3.75883	−	6.51048i	0.179399	−	0.310728i	−0.762276	−	0.647252i	$-0.775918\pi$
$439$	3.75883	−	6.51048i	0.179399	−	0.310728i	0.941675	+	0.336524i	$0.109251\pi$
$440$	1.80897	+	3.13323i	0.0862393	+	0.149371i
$441$	1.76198	+	28.9186i	0.0839040	+	1.37708i
$442$	1.11756	−	0.811951i	0.0531567	−	0.0386206i
$443$	21.9356	−	2.30552i	1.04219	−	0.109539i	0.432064	−	0.901843i	$-0.357785\pi$
$443$	21.9356	−	2.30552i	1.04219	−	0.109539i	0.610126	+	0.792304i	$0.291119\pi$
$444$	8.92738	−	9.48787i	0.423675	−	0.450275i
$445$	2.55562	+	5.74002i	0.121148	+	0.272103i
$446$	10.9145	−	2.31995i	0.516817	−	0.109853i
$447$	−5.13061	+	40.2924i	−0.242669	+	1.90577i
$448$	3.72850	+	1.66003i	0.176155	+	0.0784293i
$449$	−3.36491	−	10.3561i	−0.158800	−	0.488737i	0.839726	−	0.543010i	$-0.182716\pi$
$449$	−3.36491	−	10.3561i	−0.158800	−	0.488737i	−0.998526	+	0.0542738i	$0.982716\pi$
$450$	2.66135	−	1.38463i	0.125457	−	0.0652719i
$451$	9.45835	−	21.2438i	0.445376	−	1.00033i
$452$	3.99004	−	18.7717i	0.187676	−	0.882945i
$453$	−0.643711	−	2.13972i	−0.0302442	−	0.100533i
$454$	16.3586	−	7.28333i	0.767748	−	0.341824i
$455$	4.14442	+	4.60285i	0.194294	+	0.215785i
$456$	−10.4366	+	1.98018i	−0.488736	+	0.0927306i
$457$	13.5484	+	18.6478i	0.633768	+	0.872307i	0.998264	−	0.0588978i	$-0.0187586\pi$
$457$	13.5484	+	18.6478i	0.633768	+	0.872307i	−0.364496	+	0.931205i	$0.618759\pi$
$458$	−0.744930	+	7.08754i	−0.0348083	+	0.331179i
$459$	3.29924	+	3.38913i	0.153995	+	0.158191i
$460$	−5.45716	−	3.15069i	−0.254441	−	0.146902i
$461$	19.7483	+	14.3480i	0.919769	+	0.668251i	0.943466	−	0.331468i	$-0.107544\pi$
$461$	19.7483	+	14.3480i	0.919769	+	0.668251i	−0.0236977	+	0.999719i	$0.507544\pi$
$462$	−20.3564	−	15.4831i	−0.947067	−	0.720341i
$463$	−9.07616	−	2.94902i	−0.421805	−	0.137053i	0.0904208	−	0.995904i	$-0.471179\pi$
$463$	−9.07616	−	2.94902i	−0.421805	−	0.137053i	−0.512226	+	0.858851i	$0.671179\pi$
$464$	0.759720			0.0352691
$465$	8.14369	+	5.16529i	0.377655	+	0.239535i
$466$	1.77266			0.0821171
$467$	−8.35410	−	2.71441i	−0.386582	−	0.125608i	0.109277	−	0.994011i	$-0.465147\pi$
$467$	−8.35410	−	2.71441i	−0.386582	−	0.125608i	−0.495858	+	0.868403i	$0.665147\pi$
$468$	3.83915	+	2.44707i	0.177465	+	0.113116i
$469$	20.9821	+	15.2444i	0.968864	+	0.703921i
$470$	8.49476	+	4.90445i	0.391834	+	0.226226i
$471$	−12.2754	−	17.6993i	−0.565621	−	0.815541i
$472$	−0.899105	+	8.55442i	−0.0413847	+	0.393749i
$473$	21.1709	+	29.1393i	0.973440	+	1.33982i
$474$	4.22558	+	22.2709i	0.194088	+	1.02294i
$475$	−4.10381	−	4.55774i	−0.188296	−	0.209123i
$476$	−3.39388	+	1.51105i	−0.155558	+	0.0692589i
$477$	−29.3250	+	11.5436i	−1.34270	+	0.528543i
$478$	1.08518	−	5.10535i	0.0496348	−	0.233513i
$479$	7.12197	−	15.9962i	0.325411	−	0.730885i	−0.674562	−	0.738218i	$-0.735668\pi$
$479$	7.12197	−	15.9962i	0.325411	−	0.730885i	0.999973	+	0.00733307i	$0.00233421\pi$
$480$	0.669617	+	1.59738i	0.0305637	+	0.0729099i
$481$	3.52724	+	10.8557i	0.160828	+	0.494978i
$482$	1.68912	+	0.752045i	0.0769373	+	0.0342547i
$483$	44.1883	+	5.62669i	2.01064	+	0.256023i
$484$	2.04384	−	0.434433i	0.0929020	−	0.0197469i
$485$	5.06945	+	11.3862i	0.230192	+	0.517019i
$486$	−6.41074	+	14.2092i	−0.290797	+	0.644544i
$487$	21.8795	−	2.29963i	0.991455	−	0.104206i	0.405111	−	0.914268i	$-0.367233\pi$
$487$	21.8795	−	2.29963i	0.991455	−	0.104206i	0.586345	+	0.810062i	$0.300566\pi$
$488$	−8.77575	+	6.37595i	−0.397259	+	0.288626i
$489$	−0.851339	+	38.8093i	−0.0384989	+	1.75502i
$490$	−4.82871	−	8.36357i	−0.218139	−	0.377828i
$491$	1.16691	−	2.02115i	0.0526619	−	0.0912131i	−0.838493	−	0.544913i	$-0.816563\pi$
$491$	1.16691	−	2.02115i	0.0526619	−	0.0912131i	0.891155	+	0.453700i	$0.149896\pi$
$492$	5.77646	−	9.51681i	0.260423	−	0.429051i
$493$	−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
$498$	12.2310	+	2.88151i	0.548083	+	0.129124i
$499$	−2.81885	−	2.53810i	−0.126189	−	0.113621i	0.603620	−	0.797272i	$-0.293724\pi$
$499$	−2.81885	−	2.53810i	−0.126189	−	0.113621i	−0.729809	+	0.683651i	$0.760391\pi$
$500$	−0.587785	+	0.809017i	−0.0262866	+	0.0361803i
$501$	3.89961	−	8.26587i	0.174222	−	0.369292i
$502$	−7.32713	+	4.23032i	−0.327026	+	0.188808i
$503$	−15.8829	−	1.66936i	−0.708184	−	0.0744331i	−0.256413	−	0.966567i	$-0.582541\pi$
$503$	−15.8829	−	1.66936i	−0.708184	−	0.0744331i	−0.451771	+	0.892134i	$0.649207\pi$
$504$	−8.73108	−	8.58400i	−0.388913	−	0.382362i
$505$	−0.837506	−	7.96834i	−0.0372685	−	0.354587i
$506$	−16.9422	+	15.2549i	−0.753174	+	0.678161i
$507$	16.2448	−	8.90973i	0.721456	−	0.395695i
$508$	0.882170	+	4.15028i	0.0391400	+	0.184139i
$509$	−24.1466	−	5.13251i	−1.07028	−	0.227494i	−0.361102	−	0.932526i	$-0.617599\pi$
$509$	−24.1466	−	5.13251i	−1.07028	−	0.227494i	−0.709176	+	0.705032i	$0.750933\pi$
$510$	−1.48839	−	0.519965i	−0.0659072	−	0.0230244i
$511$	−42.1073	+	13.6815i	−1.86272	+	0.605234i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	31.4060	+	5.40783i	1.38661	+	0.238762i
$514$	−27.8177	−	5.91284i	−1.22699	−	0.260804i
$515$	−3.50812	−	16.5044i	−0.154586	−	0.727271i
$516$	8.29207	+	15.1186i	0.365038	+	0.665560i
$517$	26.3728	−	23.7461i	1.15987	−	1.04435i
$518$	−3.20879	−	30.5296i	−0.140986	−	1.34139i
$519$	−6.83130	−	7.92998i	−0.299861	−	0.348087i
$520$	−1.50926	−	0.158629i	−0.0661854	−	0.00695636i
$521$	−28.8955	+	16.6828i	−1.26593	+	0.730887i	−0.974216	−	0.225617i	$-0.927560\pi$
$521$	−28.8955	+	16.6828i	−1.26593	+	0.730887i	−0.291718	+	0.956504i	$0.594227\pi$
$522$	−2.13464	−	0.798676i	−0.0934307	−	0.0349571i
$523$	14.0585	−	19.3498i	0.614733	−	0.846108i	−0.382223	−	0.924070i	$-0.624841\pi$
$523$	14.0585	−	19.3498i	0.614733	−	0.846108i	0.996956	+	0.0779624i	$0.0248414\pi$
$524$	−1.33778	−	1.20454i	−0.0584410	−	0.0526205i
$525$	1.62104	−	6.88073i	0.0707481	−	0.300300i
$526$			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
$531$	11.5193	−	23.0908i	0.499897	−	1.00205i
$532$	−12.5156	+	21.6776i	−0.542618	+	0.939842i
$533$	4.87708	+	8.44734i	0.211250	+	0.365895i
$534$	10.8803	+	0.238675i	0.470835	+	0.0103285i
$535$	−12.7131	+	9.23662i	−0.549636	+	0.399334i
$536$	−6.31978	+	0.664236i	−0.272973	+	0.0286906i
$537$	−16.6092	−	15.6280i	−0.716739	−	0.674398i
$538$	−10.2458	−	23.0124i	−0.441728	−	0.992137i
$539$	−34.1765	+	7.26443i	−1.47208	+	0.312901i
$540$	−0.202188	−	5.19222i	−0.00870077	−	0.223437i
$541$	−22.8778	−	10.1858i	−0.983592	−	0.437924i	−0.149027	−	0.988833i	$-0.547614\pi$
$541$	−22.8778	−	10.1858i	−0.983592	−	0.437924i	−0.834565	+	0.550910i	$0.814281\pi$
$542$	−3.36086	−	10.3437i	−0.144361	−	0.444299i
$543$	−31.8547	+	13.3534i	−1.36702	+	0.573051i
$544$	0.370233	−	0.831557i	0.0158736	−	0.0356527i
$545$	−1.74662	+	8.21719i	−0.0748169	+	0.351986i
$546$	10.2731	−	3.09054i	0.439647	−	0.132263i
$547$	−35.4599	+	15.7878i	−1.51616	+	0.675036i	−0.985050	−	0.172269i	$-0.944890\pi$
$547$	−35.4599	+	15.7878i	−1.51616	+	0.675036i	−0.531106	+	0.847305i	$0.678223\pi$
$548$	3.05215	+	3.38976i	0.130382	+	0.144803i
$549$	31.3607	−	8.68924i	1.33844	−	0.370848i
$550$	2.12657	+	2.92698i	0.0906774	+	0.124807i
$551$	−0.487040	+	4.63387i	−0.0207486	+	0.197410i
$552$	−8.96843	+	6.22008i	−0.381722	+	0.264744i
$553$	46.2586	+	26.7074i	1.96711	+	1.13571i
$554$	−9.14050	−	6.64096i	−0.388342	−	0.282147i
$555$	7.88672	−	10.3691i	0.334773	−	0.440142i
$556$	−1.00223	−	0.325643i	−0.0425038	−	0.0138103i
$557$	30.8934			1.30900			0.654499	−	0.756063i	$-0.272880\pi$
$557$	30.8934			1.30900			0.654499	+	0.756063i	$0.272880\pi$
$558$	14.1097	−	8.93964i	0.597310	−	0.378445i
$559$	−15.1081			−0.639003
$560$	3.88159	+	1.26121i	0.164027	+	0.0532957i
$561$	−3.45316	+	4.54004i	−0.145793	+	0.191681i
$562$	5.43069	+	3.94563i	0.229080	+	0.166436i
$563$	16.1560	+	9.32770i	0.680896	+	0.393116i	0.800193	−	0.599743i	$-0.204731\pi$
$563$	16.1560	+	9.32770i	0.680896	+	0.393116i	−0.119296	+	0.992859i	$0.538064\pi$
$564$	13.9605	−	9.68235i	0.587844	−	0.407700i
$565$	2.00601	−	19.0859i	0.0843934	−	0.802950i
$566$	−8.72171	−	12.0044i	−0.366601	−	0.504583i
$567$	15.5082	+	33.2979i	0.651282	+	1.39838i
$568$	1.81582	+	2.01668i	0.0761903	+	0.0846179i
$569$	32.4767	−	14.4596i	1.36149	−	0.606176i	0.409505	−	0.912308i	$-0.365702\pi$
$569$	32.4767	−	14.4596i	1.36149	−	0.606176i	0.951989	+	0.306132i	$0.0990349\pi$
$570$	−10.1724	+	3.06025i	−0.426075	+	0.128180i
$571$	−4.71064	+	22.1618i	−0.197134	+	0.927443i	0.762673	+	0.646784i	$0.223886\pi$
$571$	−4.71064	+	22.1618i	−0.197134	+	0.927443i	−0.959808	+	0.280659i	$0.909447\pi$
$572$	−2.23318	+	5.01581i	−0.0933740	+	0.209722i
$573$	−6.67628	+	2.79868i	−0.278905	+	0.116917i
$574$	−8.10637	−	24.9488i	−0.338353	−	1.04134i
$575$	−5.75660	−	2.56300i	−0.240067	−	0.106885i
$576$	2.99711	+	0.131556i	0.124880	+	0.00548148i
$577$	−36.0102	+	7.65420i	−1.49912	+	0.318649i	−0.883140	−	0.469110i	$-0.844575\pi$
$577$	−36.0102	+	7.65420i	−1.49912	+	0.318649i	−0.615984	+	0.787759i	$0.711241\pi$
$578$	−6.57752	−	14.7733i	−0.273589	−	0.614490i
$579$	3.77138	+	3.54859i	0.156733	+	0.147474i
$580$	0.755558	−	0.0794124i	0.0313729	−	0.00329742i
$581$	23.9547	−	17.4041i	0.993810	−	0.722045i
$582$	21.5826	+	0.473446i	0.894627	+	0.0196250i
$583$	−19.0034	−	32.9149i	−0.787040	−	1.36319i
$584$	5.42398	−	9.39460i	0.224446	−	0.388751i
$585$	4.07391	+	2.03236i	0.168435	+	0.0840277i
$586$	3.57697	−	3.97262i	0.147763	−	0.164108i
$587$	5.36028	−	16.4972i	0.221242	−	0.680914i	−0.777409	−	0.628995i	$-0.783466\pi$
$587$	5.36028	−	16.4972i	0.221242	−	0.680914i	0.998651	−	0.0519183i	$-0.0165336\pi$
$588$	−16.6699	+	1.38321i	−0.687453	+	0.0570424i
$589$	−24.9213	−	23.3446i	−1.02686	−	0.961898i
$590$			8.60154i			0.354120i
$591$	0.806500	−	3.42330i	0.0331750	−	0.140816i
$592$	5.58955	+	5.03285i	0.229729	+	0.206849i
$593$	9.32275	−	12.8317i	0.382839	−	0.526933i	−0.573495	−	0.819209i	$-0.694413\pi$
$593$	9.32275	−	12.8317i	0.382839	−	0.526933i	0.956334	+	0.292276i	$0.0944126\pi$
$594$	−18.0918	−	5.10923i	−0.742315	−	0.209634i
$595$	−3.21734	+	1.85753i	−0.131898	+	0.0761513i
$596$	−23.3222	−	2.45126i	−0.955315	−	0.100408i
$597$	15.5243	+	18.0211i	0.635369	+	0.737555i
$598$	−0.999584	−	9.51041i	−0.0408760	−	0.388910i
$599$	−25.1003	+	22.6004i	−1.02557	+	0.923426i	−0.997095	−	0.0761685i	$-0.975731\pi$
$599$	−25.1003	+	22.6004i	−1.02557	+	0.923426i	−0.0284735	+	0.999595i	$0.509065\pi$
$600$	0.832920	+	1.51863i	0.0340038	+	0.0619979i
$601$	−2.64159	−	12.4277i	−0.107753	−	0.506937i	−0.998613	−	0.0526588i	$-0.983230\pi$
$601$	−2.64159	−	12.4277i	−0.107753	−	0.506937i	0.890860	−	0.454278i	$-0.150103\pi$
$602$	39.7436	+	8.44777i	1.61983	+	0.344305i
$603$	18.4554	+	4.77749i	0.751564	+	0.194554i
$604$	1.22692	−	0.398651i	0.0499227	−	0.0162209i
$605$	1.98724	−	0.645693i	0.0807927	−	0.0262511i
$606$	−13.1012	−	4.57684i	−0.532198	−	0.185921i
$607$	−30.1846	−	6.41593i	−1.22515	−	0.260415i	−0.450487	−	0.892783i	$-0.648750\pi$
$607$	−30.1846	−	6.41593i	−1.22515	−	0.260415i	−0.774668	+	0.632368i	$0.782083\pi$
$608$	−1.27513	−	5.99902i	−0.0517134	−	0.243293i
$609$	−4.70880	+	2.58262i	−0.190810	+	0.104653i
$610$	−8.06120	+	7.25834i	−0.326389	+	0.293882i
$611$	1.55598	+	14.8042i	0.0629483	+	0.598913i
$612$	−1.91447	+	1.94727i	−0.0773877	+	0.0787137i
$613$	32.8955	+	3.45746i	1.32864	+	0.139646i	0.742107	−	0.670281i	$-0.233826\pi$
$613$	32.8955	+	3.45746i	1.32864	+	0.139646i	0.586531	+	0.809927i	$0.300493\pi$
$614$	0.325041	−	0.187663i	0.0131176	−	0.00757345i
$615$	4.75004	−	10.0685i	0.191540	−	0.406000i
$616$	8.67929	−	11.9460i	0.349699	−	0.481319i
$617$	−12.0771	−	10.8743i	−0.486206	−	0.437782i	0.389212	−	0.921148i	$-0.372747\pi$
$617$	−12.0771	−	10.8743i	−0.486206	−	0.437782i	−0.875418	+	0.483366i	$0.839414\pi$
$618$	−28.4463	−	6.70171i	−1.14428	−	0.269582i
$619$			15.9164i			0.639735i	0.947462	+	0.319868i	$0.103638\pi$
$619$			15.9164i			0.639735i	−0.947462	+	0.319868i	$0.896362\pi$
$620$	−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
$624$	−1.36386	+	2.24699i	−0.0545982	+	0.0899515i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.8153	+	20.4648i	0.472236	+	0.817936i
$627$	−0.842871	+	38.4232i	−0.0336610	+	1.53448i
$628$	10.0608	−	7.30961i	0.401470	−	0.291685i
$629$	−6.80894	+	0.715649i	−0.271490	+	0.0285348i
$630$	−9.58052	−	7.62433i	−0.381697	−	0.303761i
$631$	−9.57691	−	21.5101i	−0.381251	−	0.856303i	−0.997627	−	0.0688515i	$-0.978067\pi$
$631$	−9.57691	−	21.5101i	−0.381251	−	0.856303i	0.616376	−	0.787452i	$-0.288600\pi$
$632$	−12.8015	+	2.72105i	−0.509218	+	0.108238i
$633$	5.22893	+	0.665822i	0.207831	+	0.0264641i
$634$	3.73187	+	1.66153i	0.148211	+	0.0659879i
$635$	1.31116	+	4.03534i	0.0520318	+	0.160137i
$636$	−7.03439	−	16.7806i	−0.278932	−	0.665393i
$637$	5.96106	−	13.3888i	0.236186	−	0.530482i
$638$	0.571471	−	2.68856i	0.0226248	−	0.106441i
$639$	−2.98197	−	7.57533i	−0.117965	−	0.299676i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	14.0213	+	15.5722i	0.553806	+	0.615064i	0.953430	−	0.301615i	$-0.0975258\pi$
$641$	14.0213	+	15.5722i	0.553806	+	0.615064i	−0.399623	+	0.916679i	$0.630859\pi$
$642$	5.07369	+	26.7409i	0.200242	+	1.05538i
$643$	3.56059	+	4.90072i	0.140416	+	0.193266i	0.873433	−	0.486944i	$-0.161889\pi$
$643$	3.56059	+	4.90072i	0.140416	+	0.193266i	−0.733017	+	0.680210i	$0.761889\pi$
$644$	−2.68828	+	25.5773i	−0.105933	+	1.00789i
$645$	9.82697	+	14.1690i	0.386936	+	0.557905i
$646$	4.83469	+	2.79131i	0.190218	+	0.109823i
$647$	−21.4776	−	15.6044i	−0.844371	−	0.613471i	0.0792172	−	0.996857i	$-0.474758\pi$
$647$	−21.4776	−	15.6044i	−0.844371	−	0.613471i	−0.923588	+	0.383386i	$0.874758\pi$
$648$	−8.28291	−	3.52044i	−0.325383	−	0.138296i
$649$	29.5967	+	9.61657i	1.16177	+	0.377483i
$650$	−1.51757			−0.0595241
$651$	5.73997	−	38.9383i	0.224967	−	1.52611i
$652$	−22.4119			−0.877719
$653$	−11.4812	−	3.73046i	−0.449293	−	0.145984i	0.0756261	−	0.997136i	$-0.475904\pi$
$653$	−11.4812	−	3.73046i	−0.449293	−	0.145984i	−0.524919	+	0.851152i	$0.675904\pi$
$654$	11.5812	+	8.80871i	0.452863	+	0.344448i
$655$	−1.45636	−	1.05811i	−0.0569046	−	0.0413436i
$656$	5.56636	+	3.21374i	0.217330	+	0.125475i
$657$	−25.1165	+	20.6946i	−0.979886	+	0.807373i
$658$	4.18465	−	39.8143i	0.163135	−	1.55212i
$659$	17.3549	+	23.8870i	0.676053	+	0.930507i	0.999878	−	0.0156102i	$-0.00496909\pi$
$659$	17.3549	+	23.8870i	0.676053	+	0.930507i	−0.323826	+	0.946117i	$0.604969\pi$
$660$	6.15662	−	1.16813i	0.239646	−	0.0454694i
$661$	−31.1022	−	34.5425i	−1.20974	−	1.34355i	−0.922648	−	0.385644i	$-0.873979\pi$
$661$	−31.1022	−	34.5425i	−1.20974	−	1.34355i	−0.287088	−	0.957904i	$-0.592687\pi$
$662$	−12.2438	+	5.45127i	−0.475867	+	0.211870i
$663$	−0.689275	−	2.29118i	−0.0267692	−	0.0889819i
$664$	−1.50837	+	7.09634i	−0.0585362	+	0.275391i
$665$	−10.1811	+	22.8671i	−0.394805	+	0.886746i
$666$	−10.4144	−	20.0173i	−0.403551	−	0.775655i
$667$	1.47935	+	4.55298i	0.0572808	+	0.176292i
$668$	4.82053	+	2.14624i	0.186512	+	0.0830404i
$669$	2.44126	−	19.1720i	0.0943844	−	0.741233i
$670$	−6.21573	+	1.32119i	−0.240135	+	0.0510422i
$671$	15.9625	+	35.8524i	0.616226	+	1.38407i
$672$	4.84423	−	5.14837i	0.186870	−	0.198603i
$673$	−25.8039	+	2.71210i	−0.994669	+	0.104544i	−0.587854	−	0.808967i	$-0.700027\pi$
$673$	−25.8039	+	2.71210i	−0.994669	+	0.104544i	−0.406814	+	0.913511i	$0.633360\pi$
$674$	21.8104	−	15.8462i	0.840105	−	0.610372i
$675$	−0.743814	−	5.14264i	−0.0286294	−	0.197940i
$676$	5.34849	+	9.26385i	0.205711	+	0.356302i
$677$	11.0710	−	19.1756i	0.425494	−	0.736977i	−0.570972	−	0.820969i	$-0.693434\pi$
$677$	11.0710	−	19.1756i	0.425494	−	0.736977i	0.996466	+	0.0839919i	$0.0267670\pi$
$678$	−28.4151	−	17.2472i	−1.09128	−	0.662376i
$679$	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	$-0.0134474\pi$
$684$	−2.72380	+	18.1964i	−0.104147	+	0.695757i
$685$	3.38976	+	3.05215i	0.129516	+	0.116617i
$686$	−6.37504	+	8.77449i	−0.243400	+	0.335012i
$687$	11.1636	+	5.26669i	0.425919	+	0.200937i
$688$	−8.62164	+	4.97771i	−0.328697	+	0.189773i
$689$	15.8549	+	1.66642i	0.604023	+	0.0634854i
$690$	−8.26913	+	7.12346i	−0.314800	+	0.271186i
$691$	−5.20613	−	49.5330i	−0.198050	−	1.88432i	−0.417467	−	0.908692i	$-0.637082\pi$
$691$	−5.20613	−	49.5330i	−0.198050	−	1.88432i	0.219417	−	0.975631i	$-0.429585\pi$
$692$	4.49078	−	4.04351i	0.170714	−	0.153711i
$693$	−36.9454	+	24.4413i	−1.40344	+	0.928447i
$694$	5.75016	+	27.0524i	0.218273	+	1.02689i
$695$	−1.03077	−	0.219098i	−0.0390995	−	0.00831086i
$696$	0.433976	−	1.24225i	0.0164498	−	0.0470874i
$697$	−5.56428	+	1.80794i	−0.210762	+	0.0684807i
$698$	−19.2633	+	6.25901i	−0.729125	+	0.236907i
$699$	1.01260	−	2.89856i	0.0383001	−	0.109634i
$700$	3.99216	+	0.848560i	0.150890	+	0.0320726i
$701$	−1.33306	−	6.27154i	−0.0503489	−	0.236873i	0.945776	−	0.324818i	$-0.105303\pi$
$701$	−1.33306	−	6.27154i	−0.0503489	−	0.236873i	−0.996125	+	0.0879456i	$0.971970\pi$
$702$	6.19435	−	4.87972i	0.233791	−	0.184173i
$703$	−34.2809	+	30.8667i	−1.29293	+	1.16416i
$704$	0.378178	+	3.59812i	0.0142531	+	0.135609i
$705$	12.8720	−	11.0886i	0.484786	−	0.417620i
$706$	16.6682	+	1.75190i	0.627317	+	0.0659337i
$707$	−28.3197	+	16.3504i	−1.06507	+	0.614919i
$708$	13.4741	+	6.35672i	0.506388	+	0.238900i
$709$	3.87884	−	5.33877i	0.145673	−	0.200502i	−0.729945	−	0.683506i	$-0.760454\pi$
$709$	3.87884	−	5.33877i	0.145673	−	0.200502i	0.875618	+	0.483004i	$0.160454\pi$
$710$	2.01668	+	1.81582i	0.0756845	+	0.0681467i
$711$	38.8300	+	5.81242i	1.45624	+	0.217983i
$712$			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
$717$	−7.72810	−	4.69076i	−0.288611	−	0.175180i
$718$	3.54949	−	6.14789i	0.132466	−	0.229437i
$719$	−7.51176	−	13.0108i	−0.280141	−	0.485219i	0.691278	−	0.722589i	$-0.257048\pi$
$719$	−7.51176	−	13.0108i	−0.280141	−	0.485219i	−0.971419	+	0.237370i	$0.923715\pi$
$720$	2.99445	−	0.182449i	0.111596	−	0.00679947i
$721$	−55.7130	+	40.4779i	−2.07486	+	1.50748i
$722$	18.5123	−	1.94572i	0.688955	−	0.0724121i
$723$	2.19458	−	2.33236i	0.0816173	−	0.0867415i
$724$	−8.11110	−	18.2178i	−0.301447	−	0.677060i
$725$	0.743119	−	0.157955i	0.0275987	−	0.00586629i
$726$	0.457148	−	3.59014i	0.0169664	−	0.133243i
$727$	−4.39587	−	1.95717i	−0.163034	−	0.0725874i	0.323597	−	0.946195i	$-0.395108\pi$
$727$	−4.39587	−	1.95717i	−0.163034	−	0.0725874i	−0.486631	+	0.873608i	$0.661774\pi$
$728$	1.91397	+	5.89060i	0.0709365	+	0.218320i
$729$	19.5721	+	18.5992i	0.724894	+	0.688861i
$730$	4.41226	−	9.91010i	0.163305	−	0.366789i
$731$	1.88408	−	8.86392i	0.0696854	−	0.327844i
$732$	5.41262	+	17.9917i	0.200056	+	0.664994i
$733$	−1.31670	+	0.586235i	−0.0486336	+	0.0216531i	−0.430909	−	0.902395i	$-0.641807\pi$
$733$	−1.31670	+	0.586235i	−0.0486336	+	0.0216531i	0.382276	+	0.924048i	$0.375140\pi$
$734$	−11.8670	−	13.1796i	−0.438019	−	0.486469i
$735$	−16.4340	+	3.11810i	−0.606175	+	0.115013i
$736$	−3.70386	−	5.09792i	−0.136526	−	0.187912i
$737$	−2.40317	+	22.8646i	−0.0885218	+	0.842229i
$738$	−12.2617	−	14.8816i	−0.451358	−	0.547801i
$739$	40.1286	+	23.1682i	1.47615	+	0.852258i	0.999638	−	0.0269081i	$-0.00856615\pi$
$739$	40.1286	+	23.1682i	1.47615	+	0.852258i	0.476516	+	0.879166i	$0.341899\pi$
$740$	6.08500	+	4.42101i	0.223689	+	0.162520i
$741$	−12.8310	−	9.75930i	−0.471360	−	0.358517i
$742$	−40.7765	−	13.2491i	−1.49695	−	0.486389i
$743$	1.55250			0.0569556			0.0284778	−	0.999594i	$-0.490934\pi$
$743$	1.55250			0.0569556			0.0284778	+	0.999594i	$0.490934\pi$
$744$	5.33872	+	8.03107i	0.195727	+	0.294433i
$745$	−23.4507			−0.859166
$746$	18.7490	+	6.09192i	0.686450	+	0.223041i
$747$	11.6984	−	18.3534i	0.428022	−	0.671515i
$748$	−2.66429	−	1.93572i	−0.0974161	−	0.0707769i
$749$	55.5430	+	32.0677i	2.02950	+	1.17173i
$750$	0.987098	+	1.42325i	0.0360437	+	0.0519697i
$751$	2.22312	−	21.1516i	0.0811229	−	0.771833i	−0.876031	−	0.482254i	$-0.839818\pi$
$751$	2.22312	−	21.1516i	0.0811229	−	0.771833i	0.957154	−	0.289579i	$-0.0935152\pi$
$752$	5.76553	+	7.93557i	0.210247	+	0.289381i
$753$	2.73169	+	14.3974i	0.0995485	+	0.524670i
$754$	0.771461	+	0.856794i	0.0280949	+	0.0312026i
$755$	1.17853	−	0.524715i	0.0428911	−	0.0190963i
$756$	−19.0235	+	9.37312i	−0.691879	+	0.340897i
$757$	1.50186	−	7.06571i	0.0545862	−	0.256808i	−0.942390	−	0.334516i	$-0.891427\pi$
$757$	1.50186	−	7.06571i	0.0545862	−	0.256808i	0.996976	+	0.0777086i	$0.0247604\pi$
$758$	−5.96247	+	13.3919i	−0.216567	+	0.486416i
$759$	15.2660	+	36.4170i	0.554119	+	1.32186i
$760$	−1.89522	−	5.83287i	−0.0687467	−	0.211581i
$761$	24.2538	+	10.7985i	0.879199	+	0.391445i	0.796149	−	0.605101i	$-0.206867\pi$
$761$	24.2538	+	10.7985i	0.879199	+	0.391445i	0.0830503	+	0.996545i	$0.473534\pi$
$762$	7.29023	+	0.928297i	0.264097	+	0.0336286i
$763$	33.5372	−	7.12856i	1.21413	−	0.258071i
$764$	−1.69997	−	3.81819i	−0.0615026	−	0.138137i
$765$	−1.70043	+	2.13672i	−0.0614793	+	0.0772532i
$766$	20.2070	−	2.12384i	0.730108	−	0.0767375i
$767$	−10.5605	+	7.67263i	−0.381316	+	0.277042i
$768$	−0.0379860	+	1.73163i	−0.00137070	+	0.0624850i
$769$	−11.1980	−	19.3954i	−0.403808	−	0.699417i	0.590374	−	0.807130i	$-0.298980\pi$
$769$	−11.1980	−	19.3954i	−0.403808	−	0.699417i	−0.994182	+	0.107713i	$0.965647\pi$
$770$	7.38304	−	12.7878i	0.266066	−	0.460841i
$771$	−25.5587	+	42.1084i	−0.920474	+	1.51650i
$772$	−2.00053	+	2.22182i	−0.0720007	+	0.0799649i
$773$	−5.07522	+	15.6199i	−0.182543	+	0.561809i	−0.999897	−	0.0143259i	$-0.995440\pi$
$773$	−5.07522	+	15.6199i	−0.182543	+	0.561809i	0.817355	+	0.576135i	$0.195440\pi$
$774$	29.4578	−	4.92250i	1.05884	−	0.176935i
$775$	−2.36440	+	5.04080i	−0.0849316	+	0.181071i
$776$			12.4637i			0.447421i
$777$	−51.7533	−	12.1926i	−1.85664	−	0.437408i
$778$	15.9994	+	14.4059i	0.573606	+	0.516477i
$779$	−23.1705	+	31.8914i	−0.830169	+	1.14263i
$780$	−1.12152	+	2.37724i	−0.0401568	+	0.0851189i
$781$	8.50267	−	4.90902i	0.304249	−	0.175658i
$782$	5.70443	+	0.599560i	0.203990	+	0.0214402i
$783$	−2.52532	+	3.03422i	−0.0902477	+	0.108434i
$784$	−1.00948	−	9.60452i	−0.0360527	−	0.343018i
$785$	9.24164	−	8.32121i	0.329848	−	0.296997i
$786$	−2.73377	+	1.49939i	−0.0975105	+	0.0534813i
$787$	5.21614	+	24.5400i	0.185935	+	0.874756i	0.967881	+	0.251410i	$0.0808941\pi$
$787$	5.21614	+	24.5400i	0.185935	+	0.874756i	−0.781946	+	0.623347i	$0.785773\pi$
$788$	1.98618	+	0.422175i	0.0707547	+	0.0150394i
$789$	12.8496	+	4.48897i	0.457459	+	0.159811i
$790$	−12.4470	+	4.04427i	−0.442844	+	0.143889i
$791$	−74.4918	+	24.2039i	−2.64862	+	0.860590i
$792$	2.72003	−	10.5075i	0.0966519	−	0.373367i
$793$	−16.1020	−	3.42259i	−0.571799	−	0.121540i
$794$	−6.65129	−	31.2919i	−0.236045	−	1.11051i
$795$	−8.74990	−	15.9534i	−0.310327	−	0.565808i
$796$	−10.2054	+	9.18901i	−0.361722	+	0.325696i
$797$	−5.01908	−	47.7534i	−0.177785	−	1.69151i	−0.612125	−	0.790761i	$-0.709685\pi$
$797$	−5.01908	−	47.7534i	−0.177785	−	1.69151i	0.434340	−	0.900749i	$-0.356982\pi$
$798$	28.2967	+	32.8476i	1.00169	+	1.16279i
$799$	−8.87967	−	0.933291i	−0.314140	−	0.0330175i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	6.60542	−	17.6545i	0.233391	−	0.623790i
$802$	−6.97950	+	9.60645i	−0.246455	+	0.339216i
$803$	−29.1664	−	26.2615i	−1.02926	−	0.926750i
$804$	−2.52394	+	10.7132i	−0.0890124	+	0.377825i
$805$			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	$-0.586466\pi$
$809$	20.4160	−	22.6742i	0.717787	−	0.797184i	0.986101	+	0.166148i	$0.0531329\pi$
$810$	−8.60552	−	2.63535i	−0.302367	−	0.0925968i
$811$	5.64396	−	9.77563i	0.198186	−	0.343269i	−0.749754	−	0.661717i	$-0.769828\pi$
$811$	5.64396	−	9.77563i	0.198186	−	0.343269i	0.947940	+	0.318448i	$0.103162\pi$
$812$	−1.55034	−	2.68527i	−0.0544064	−	0.0942346i
$813$	−18.8332	−	0.413135i	−0.660510	−	0.0144893i
$814$	22.0152	−	15.9950i	0.771632	−	0.560623i
$815$	−22.2892	+	2.34268i	−0.780755	+	0.0820607i
$816$	−1.14823	−	1.08040i	−0.0401960	−	0.0378214i
$817$	−24.8341	−	55.7783i	−0.868836	−	1.95144i
$818$	−19.5361	+	4.15252i	−0.683063	+	0.145190i
$819$	0.814822	−	18.5634i	0.0284722	−	0.648656i
$820$	5.87179	+	2.61429i	0.205052	+	0.0912949i
$821$	5.40345	+	16.6301i	0.188582	+	0.580394i	0.999992	−	0.00408290i	$-0.00129963\pi$
$821$	5.40345	+	16.6301i	0.188582	+	0.580394i	−0.811410	+	0.584477i	$0.801300\pi$
$822$	7.28623	−	3.05437i	0.254137	−	0.106534i
$823$	3.95567	−	8.88459i	0.137886	−	0.309697i	−0.831383	−	0.555700i	$-0.812450\pi$
$823$	3.95567	−	8.88459i	0.137886	−	0.309697i	0.969269	+	0.246002i	$0.0791171\pi$
$824$	3.50812	−	16.5044i	0.122211	−	0.574958i
$825$	6.00079	−	1.80527i	0.208921	−	0.0628515i
$826$	32.0708	−	14.2789i	1.11589	−	0.496825i
$827$	29.6184	+	32.8946i	1.02993	+	1.14386i	0.989479	+	0.144675i	$0.0462135\pi$
$827$	29.6184	+	32.8946i	1.02993	+	1.14386i	0.0404533	+	0.999181i	$0.487120\pi$
$828$	5.04767	+	18.2178i	0.175419	+	0.633112i
$829$	−3.36160	−	4.62684i	−0.116753	−	0.160697i	0.746641	−	0.665228i	$-0.231666\pi$
$829$	−3.36160	−	4.62684i	−0.116753	−	0.160697i	−0.863394	+	0.504531i	$0.831666\pi$
$830$	−0.758341	+	7.21513i	−0.0263224	+	0.250441i
$831$	−16.0803	+	11.1525i	−0.557818	+	0.386876i
$832$	−1.31426	−	0.758786i	−0.0455636	−	0.0263062i
$833$	7.11182	+	5.16704i	0.246410	+	0.179027i
$834$	−1.10498	+	1.45277i	−0.0382622	+	0.0503052i
$835$	5.01847	+	1.63060i	0.173671	+	0.0564292i
$836$	−22.1890			−0.767423
$837$	−6.55772	−	28.1779i	−0.226668	−	0.973972i
$838$	−1.46396			−0.0505715
$839$	19.8627	+	6.45378i	0.685736	+	0.222809i	0.631105	−	0.775697i	$-0.282602\pi$
$839$	19.8627	+	6.45378i	0.685736	+	0.222809i	0.0546313	+	0.998507i	$0.482602\pi$
$840$	4.27954	−	5.62652i	0.147658	−	0.194134i
$841$	22.9945	+	16.7065i	0.792915	+	0.576087i
$842$	3.44420	+	1.98851i	0.118695	+	0.0685286i
$843$	9.55385	−	6.62609i	0.329052	−	0.228215i
$844$	−0.318111	+	3.02663i	−0.0109498	+	0.104181i
$845$	6.28752	+	8.65404i	0.216297	+	0.297708i
$846$	−7.85735	−	28.3583i	−0.270141	−	0.974979i
$847$	−5.70635	−	6.33754i	−0.196072	−	0.217761i
$848$	9.59687	−	4.27280i	0.329558	−	0.146729i
$849$	−24.6110	+	7.40396i	−0.844648	+	0.254103i
$850$	0.189252	−	0.890362i	0.00649130	−	0.0305392i
$851$	−19.2776	+	43.2981i	−0.660826	+	1.48424i
$852$	4.33481	−	1.81714i	0.148508	−	0.0622543i
$853$	−8.55122	−	26.3179i	−0.292788	−	0.901109i	−0.983955	−	0.178414i	$-0.942903\pi$
$853$	−8.55122	−	26.3179i	−0.292788	−	0.901109i	0.691167	−	0.722695i	$-0.257097\pi$
$854$	40.4446	+	18.0071i	1.38399	+	0.616190i
$855$	−0.806837	+	18.3814i	−0.0275932	+	0.628632i
$856$	−15.3709	+	3.26718i	−0.525366	+	0.111670i
$857$	1.91825	+	4.30847i	0.0655263	+	0.147174i	0.943340	−	0.331828i	$-0.107665\pi$
$857$	1.91825	+	4.30847i	0.0655263	+	0.147174i	−0.877814	+	0.479002i	$0.840999\pi$
$858$	6.92591	+	6.51676i	0.236447	+	0.222479i
$859$	35.8092	−	3.76369i	1.22179	−	0.128416i	0.528413	−	0.848988i	$-0.322787\pi$
$859$	35.8092	−	3.76369i	1.22179	−	0.128416i	0.693380	+	0.720572i	$0.256121\pi$
$860$	−8.05410	+	5.85164i	−0.274642	+	0.199539i
$861$	−45.4256	−	0.996477i	−1.54810	−	0.0339599i
$862$	−14.7310	−	25.5148i	−0.501739	−	0.869037i
$863$	−20.7560	+	35.9505i	−0.706543	+	1.22377i	0.259589	+	0.965719i	$0.416413\pi$
$863$	−20.7560	+	35.9505i	−0.706543	+	1.22377i	−0.966132	+	0.258049i	$0.916920\pi$
$864$	1.92716	−	4.82556i	0.0655632	−	0.164169i
$865$	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
$870$	0.301748	−	1.28081i	0.0102302	−	0.0434235i
$871$	−7.16656	−	6.45280i	−0.242830	−	0.218645i
$872$	−4.93785	+	6.79636i	−0.167217	+	0.230154i
$873$	13.1028	−	35.0202i	0.443463	−	1.18525i
$874$	33.4690	−	19.3233i	1.13211	−	0.653621i
$875$	4.05899	+	0.426617i	0.137219	+	0.0144223i
$876$	−12.2632	−	14.2355i	−0.414334	−	0.480972i
$877$	4.58158	+	43.5909i	0.154709	+	1.47196i	0.746240	+	0.665677i	$0.231857\pi$
$877$	4.58158	+	43.5909i	0.154709	+	1.47196i	−0.591531	+	0.806282i	$0.701476\pi$
$878$	5.58671	−	5.03029i	0.188542	−	0.169764i
$879$	−4.45254	−	8.11814i	−0.150180	−	0.273818i
$880$	0.752212	+	3.53888i	0.0253571	+	0.119296i
$881$	26.9008	+	5.71795i	0.906312	+	0.192643i	0.637410	−	0.770525i	$-0.280006\pi$
$881$	26.9008	+	5.71795i	0.906312	+	0.192643i	0.268902	+	0.963167i	$0.413339\pi$
$882$	−7.26060	+	28.0477i	−0.244477	+	0.944417i
$883$	−7.88334	+	2.56145i	−0.265296	+	0.0861998i	−0.438644	−	0.898661i	$-0.644541\pi$
$883$	−7.88334	+	2.56145i	−0.265296	+	0.0861998i	0.173349	+	0.984860i	$0.444541\pi$
$884$	1.31376	−	0.426868i	0.0441867	−	0.0143571i
$885$	14.0647	+	4.91347i	0.472781	+	0.165164i
$886$	21.5744	+	4.58578i	0.724806	+	0.154062i
$887$	−1.79158	−	8.42873i	−0.0601554	−	0.283009i	0.937780	−	0.347229i	$-0.112877\pi$
$887$	−1.79158	−	8.42873i	−0.0601554	−	0.283009i	−0.997936	+	0.0642201i	$0.979544\pi$
$888$	11.4224	−	6.26479i	0.383309	−	0.210233i
$889$	12.8692	−	11.5875i	0.431618	−	0.388631i
$890$	0.656777	+	6.24882i	0.0220152	+	0.209461i
$891$	−18.6889	+	26.6641i	−0.626102	+	0.893281i
$892$	11.0972	+	1.16637i	0.371562	+	0.0390528i
$893$	−52.0988	+	30.0792i	−1.74342	+	1.00656i
$894$	−17.3305	+	36.7349i	−0.579620	+	1.22860i
$895$	7.73929	−	10.6522i	0.258696	−	0.356064i
$896$	3.03303	+	2.73096i	0.101327	+	0.0912349i
$897$	−16.1219	−	3.79818i	−0.538294	−	0.126818i
$898$		−	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
$903$	36.5161	−	60.1609i	1.21518	−	2.00203i
$904$	9.59551	−	16.6199i	0.319142	−	0.552770i
$905$	−9.97095	−	17.2702i	−0.331445	−	0.574080i
$906$	0.0490042	−	2.23391i	0.00162806	−	0.0742168i
$907$	31.3940	−	22.8091i	1.04242	−	0.757363i	0.0716646	−	0.997429i	$-0.477169\pi$
$907$	31.3940	−	22.8091i	1.04242	−	0.757363i	0.970757	+	0.240065i	$0.0771689\pi$
$908$	17.8086	−	1.87176i	0.591001	−	0.0621167i
$909$	−14.9676	+	18.8078i	−0.496443	+	0.623817i
$910$	2.51922	+	5.65826i	0.0835114	+	0.187570i
$911$	−19.4928	+	4.14333i	−0.645826	+	0.137275i	−0.519168	−	0.854672i	$-0.673758\pi$
$911$	−19.4928	+	4.14333i	−0.645826	+	0.137275i	−0.126658	+	0.991947i	$0.540425\pi$
$912$	−10.5377	−	1.34181i	−0.348937	−	0.0444316i
$913$	23.9785	+	10.6759i	0.793572	+	0.353321i
$914$	7.12283	+	21.9218i	0.235602	+	0.725109i
$915$	7.26362	+	17.3274i	0.240128	+	0.572827i
$916$	−2.89864	+	6.51045i	−0.0957738	+	0.215111i
$917$	−1.52754	+	7.18652i	−0.0504439	+	0.237320i
$918$	2.09046	+	4.24277i	0.0689955	+	0.140032i
$919$	−53.7487	+	23.9305i	−1.77301	+	0.789393i	−0.788272	+	0.615327i	$0.789024\pi$
$919$	−53.7487	+	23.9305i	−1.77301	+	0.789393i	−0.984734	+	0.174066i	$0.944309\pi$
$920$	−4.21645	−	4.68284i	−0.139012	−	0.154389i
$921$	−0.121182	−	0.638688i	−0.00399307	−	0.0210455i
$922$	14.3480	+	19.7483i	0.472525	+	0.650375i
$923$	−0.430474	+	4.09568i	−0.0141692	+	0.134811i
$924$	−14.5756	−	21.0158i	−0.479501	−	0.691370i
$925$	6.51379	+	3.76074i	0.214172	+	0.123652i
$926$	−7.72064	−	5.60937i	−0.253716	−	0.184335i
$927$	−27.2077	+	42.6856i	−0.893618	+	1.40198i
$928$	0.722537	+	0.234766i	0.0237184	+	0.00770659i
$929$	−23.8745			−0.783297			−0.391648	−	0.920115i	$-0.628095\pi$
$929$	−23.8745			−0.783297			−0.391648	+	0.920115i	$0.628095\pi$
$930$	6.14895	+	7.42903i	0.201632	+	0.243607i
$931$	59.2294			1.94117
$932$	1.68590	+	0.547783i	0.0552236	+	0.0179432i
$933$	−0.429860	−	0.326952i	−0.0140730	−	0.0107039i
$934$	−7.10642	−	5.16312i	−0.232529	−	0.168942i
$935$	−2.85203	−	1.64662i	−0.0932714	−	0.0538503i
$936$	2.89507	+	3.51366i	0.0946282	+	0.114848i
$937$	−2.12343	+	20.2031i	−0.0693694	+	0.660006i	0.903490	+	0.428609i	$0.140996\pi$
$937$	−2.12343	+	20.2031i	−0.0693694	+	0.660006i	−0.972859	+	0.231397i	$0.925670\pi$
$938$	15.2444	+	20.9821i	0.497747	+	0.685091i
$939$	40.2121	−	7.62966i	1.31227	−	0.248985i
$940$	6.56344	+	7.28944i	0.214076	+	0.237755i
$941$	−3.40473	+	1.51588i	−0.110991	+	0.0494164i	−0.461481	−	0.887150i	$-0.652682\pi$
$941$	−3.40473	+	1.51588i	−0.110991	+	0.0494164i	0.350490	+	0.936567i	$0.386015\pi$
$942$	−6.20521	−	20.6264i	−0.202177	−	0.672043i
$943$	−8.42083	+	39.6169i	−0.274220	+	1.29010i
$944$	−3.49856	+	7.85790i	−0.113868	+	0.255753i
$945$	−17.9396	+	11.3103i	−0.583574	+	0.367923i
$946$	11.1302	+	34.2553i	0.361874	+	1.11373i
$947$	−54.2192	−	24.1399i	−1.76189	−	0.784443i	−0.988633	−	0.150346i	$-0.951961\pi$
$947$	−54.2192	−	24.1399i	−1.76189	−	0.784443i	−0.773254	−	0.634097i	$-0.781372\pi$
$948$	−2.86333	+	22.4867i	−0.0929966	+	0.730334i
$949$	16.1028	−	3.42276i	0.522719	−	0.111107i
$950$	−2.49453	−	5.60282i	−0.0809334	−	0.181779i
$951$	4.84861	−	5.15302i	0.157227	−	0.167098i
$952$	−3.69471	+	0.388330i	−0.119746	+	0.0125858i
$953$	−20.2339	+	14.7008i	−0.655439	+	0.476205i	−0.865120	−	0.501565i	$-0.832758\pi$
$953$	−20.2339	+	14.7008i	−0.655439	+	0.476205i	0.209680	+	0.977770i	$0.432758\pi$
$954$	−31.4569	+	1.91664i	−1.01846	+	0.0620535i
$955$	−2.08976	−	3.61957i	−0.0676231	−	0.117127i
$956$	2.60971	−	4.52014i	0.0844039	−	0.146192i
$957$	−4.06974	−	2.47023i	−0.131556	−	0.0798511i
$958$	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
$963$	46.6234	+	6.97901i	1.50242	+	0.224895i
$964$	1.37405	+	1.23720i	0.0442553	+	0.0398477i
$965$	−1.75733	+	2.41876i	−0.0565705	+	0.0778626i
$966$	40.2869	+	19.0062i	1.29621	+	0.611516i
$967$	8.24683	−	4.76131i	0.265200	−	0.153113i	−0.361504	−	0.932370i	$-0.617737\pi$
$967$	8.24683	−	4.76131i	0.265200	−	0.153113i	0.626704	+	0.779257i	$0.284403\pi$
$968$	2.07806	+	0.218413i	0.0667913	+	0.00702005i
$969$	7.32592	−	6.31093i	0.235343	−	0.202736i
$970$	1.30281	+	12.3954i	0.0418308	+	0.397993i
$971$	34.7046	−	31.2482i	1.11372	−	1.00280i	0.113767	−	0.993507i	$-0.463708\pi$
$971$	34.7046	−	31.2482i	1.11372	−	1.00280i	0.999957	−	0.00929403i	$-0.00295842\pi$
$972$	−10.4879	+	11.5328i	−0.336399	+	0.369913i
$973$	0.894215	+	4.20695i	0.0286672	+	0.134869i
$974$	21.5193	+	4.57406i	0.689522	+	0.146562i
$975$	−0.866884	+	2.48145i	−0.0277625	+	0.0794699i
$976$	−10.3165	+	3.35204i	−0.330223	+	0.107296i
$977$	−10.8165	+	3.51450i	−0.346051	+	0.112439i	−0.476885	−	0.878965i	$-0.658234\pi$
$977$	−10.8165	+	3.51450i	−0.346051	+	0.112439i	0.130835	+	0.991404i	$0.458234\pi$
$978$	−12.8024	+	36.6467i	−0.409375	+	1.17183i
$979$	22.2356	+	4.72633i	0.710654	+	0.151054i
$980$	−2.00789	−	9.44638i	−0.0641397	−	0.301754i
$981$	21.0191	−	13.9052i	0.671088	−	0.443959i
$982$	1.73437	−	1.56163i	0.0553459	−	0.0498336i
$983$	−1.90111	−	18.0878i	−0.0606359	−	0.576912i	−0.982088	−	0.188421i	$-0.939663\pi$
$983$	−1.90111	−	18.0878i	−0.0606359	−	0.576912i	0.921453	−	0.388491i	$-0.127004\pi$
$984$	8.43460	−	7.26600i	0.268885	−	0.231632i
$985$	2.01943	+	0.212250i	0.0643443	+	0.00676286i
$986$	−0.598889	+	0.345769i	−0.0190725	+	0.0110115i
$987$	−62.7117	−	29.5857i	−1.99613	−	0.941722i
$988$	5.47071	−	7.52979i	0.174047	−	0.239555i
$989$	−46.6196	−	41.9765i	−1.48242	−	1.33477i
$990$	1.60680	−	10.7342i	0.0510673	−	0.341156i
$991$		−	5.47667i		−	0.173972i	−0.996210	−	0.0869861i	$-0.972276\pi$
$991$		−	5.47667i		−	0.173972i	0.996210	−	0.0869861i	$-0.0277236\pi$
$992$	−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
$996$	10.7419	+	6.52006i	0.340370	+	0.206596i
$997$	−24.0548	+	41.6642i	−0.761825	+	1.31952i	0.180084	+	0.983651i	$0.442363\pi$
$997$	−24.0548	+	41.6642i	−0.761825	+	1.31952i	−0.941909	+	0.335868i	$0.890970\pi$
$998$	−1.89657	−	3.28495i	−0.0600348	−	0.103983i
$999$	−38.6802	+	5.59458i	−1.22379	+	0.177005i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.2	✓	176	31.11	odd	30	inner
930.2.br.b.11.18	yes	176	93.11	even	30	inner
930.2.br.b.761.2	yes	176	3.2	odd	2	inner
930.2.br.b.761.18	yes	176	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(1.04856 - 1.37859i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.42325 - 0.987098i) q^{6} +(0.426617 - 4.05899i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.801042 - 2.89108i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(1.04856 - 1.37859i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.42325 - 0.987098i) q^{6} +(0.426617 - 4.05899i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.801042 - 2.89108i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.30515 - 1.47155i) q^{11} +(1.65862 - 0.498978i) q^{12} +(-0.315521 + 1.48441i) q^{13} +(1.66003 - 3.72850i) q^{14} +(1.59738 - 0.669617i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.831557 - 0.370233i) q^{17} +(0.131556 - 2.99711i) q^{18} +(-5.99902 + 1.27513i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-5.14837 - 4.84423i) q^{21} +(3.59812 - 0.378178i) q^{22} +(-5.09792 + 3.70386i) q^{23} +(1.73163 + 0.0379860i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.758786 + 1.31426i) q^{26} +(-4.82556 - 1.92716i) 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} +(1.43698 - 6.09947i) q^{33} +(-0.676450 - 0.609078i) q^{34} +(2.39896 - 3.30188i) q^{35} +(1.05128 - 2.80977i) q^{36} +(6.51379 - 3.76074i) q^{37} +(-6.09945 - 0.641078i) q^{38} +(1.71555 + 1.99147i) q^{39} +(0.104528 + 0.994522i) q^{40} +(4.77654 - 4.30082i) q^{41} +(-3.39944 - 6.19807i) q^{42} +(2.06985 + 9.73786i) q^{43} +(3.53888 + 0.752212i) q^{44} +(0.751816 - 2.90427i) q^{45} +(-5.99297 + 1.94723i) q^{46} +(9.32882 - 3.03112i) q^{47} +(1.63514 + 0.571231i) q^{48} +(-9.44638 - 2.00789i) q^{49} +(0.207912 + 0.978148i) q^{50} +(-1.38234 + 0.758168i) q^{51} +(-1.12778 + 1.01545i) q^{52} +(-1.09808 - 10.4475i) q^{53} +(-3.99386 - 3.32402i) q^{54} +(3.59812 + 0.378178i) q^{55} +(3.53455 - 2.04068i) q^{56} +(-4.53245 + 9.60727i) q^{57} +(0.446552 - 0.614627i) q^{58} +(6.39219 + 5.75555i) q^{59} +(1.68590 + 0.397183i) 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} +(3.25149 - 5.35689i) q^{66} +(-3.17730 + 5.50324i) q^{67} +(-0.455126 - 0.788302i) q^{68} +(-0.239364 + 10.9117i) q^{69} +(3.30188 - 2.39896i) q^{70} +(2.69884 - 0.283660i) q^{71} +(1.86809 - 2.34739i) q^{72} +(-4.41226 - 9.91010i) q^{73} +(7.35712 - 1.56380i) q^{74} +(1.71818 + 0.218783i) q^{75} +(-5.60282 - 2.49453i) q^{76} +(-4.56297 - 14.0434i) q^{77} +(1.01619 + 2.42413i) q^{78} +(-5.32318 + 11.9561i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-7.71666 + 4.63175i) q^{81} +(5.87179 - 2.61429i) q^{82} +(4.85446 + 5.39142i) q^{83} +(-1.31775 - 6.94520i) q^{84} +(-0.535033 - 0.736410i) q^{85} +(-1.04062 + 9.90088i) q^{86} +(-0.749918 - 1.08127i) q^{87} +(3.13323 + 1.80897i) q^{88} +(5.08325 + 3.69320i) q^{89} +(1.61249 - 2.52980i) q^{90} +(5.89060 + 1.91397i) q^{91} -6.30138 q^{92} +(9.63529 + 0.401428i) q^{93} +9.80891 q^{94} +(-5.83287 - 1.89522i) q^{95} +(1.37859 + 1.04856i) q^{96} +(10.0834 + 7.32599i) q^{97} +(-8.36357 - 4.82871i) q^{98} +(-6.90193 - 8.37669i) 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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