LMFDB - Embedded newform 912.2.bn.m.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.4
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.m.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57313 - 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(1.57313 - 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(1.94949 - 2.28024i) q^{9} +5.27792i q^{11} +(-0.232051 + 0.133975i) q^{13} +(2.43916 + 0.224745i) q^{15} +(4.24264 + 2.44949i) q^{17} +(-1.73205 + 4.00000i) q^{19} +(0.421519 - 0.194195i) q^{21} +(4.57081 - 2.63896i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(1.41421 - 5.00000i) q^{27} +(1.03528 + 1.79315i) q^{29} -2.46410i q^{31} +(3.82514 + 8.30286i) q^{33} +(0.328169 + 0.189469i) q^{35} -7.73205i q^{37} +(-0.267949 + 0.378937i) q^{39} +(-2.82843 + 4.89898i) q^{41} +(2.86603 - 4.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(0.656339 - 0.378937i) q^{47} -6.92820 q^{49} +(8.44949 + 0.778539i) q^{51} +(-5.46739 - 9.46979i) q^{53} +(-3.73205 + 6.46410i) q^{55} +(0.174235 + 7.54782i) q^{57} +(-5.60609 + 9.71003i) q^{59} +(5.23205 + 9.06218i) q^{61} +(0.522364 - 0.610988i) q^{63} -0.378937 q^{65} +(0.866025 - 0.500000i) q^{67} +(5.27792 - 7.46410i) q^{69} +(6.69213 - 11.5911i) q^{71} +(1.50000 - 2.59808i) q^{73} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(-9.06218 - 5.23205i) q^{79} +(-1.39898 - 8.89060i) q^{81} -2.07055i q^{83} +(3.46410 + 6.00000i) q^{85} +(2.92820 + 2.07055i) q^{87} +(3.67423 + 6.36396i) q^{89} +(-0.0621778 + 0.0358984i) q^{91} +(-1.78585 - 3.87636i) q^{93} +(-4.94975 + 3.67423i) q^{95} +(-0.464102 - 0.267949i) q^{97} +(12.0349 + 10.2892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 16 * q^7 - 4 * q^9	$ 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) $ 8 * q + 16 * q^7 - 4 * q^9 + 12 * q^13 - 12 * q^21 - 12 * q^25 + 24 * q^33 - 16 * q^39 + 16 * q^43 + 32 * q^45 + 48 * q^51 - 16 * q^55 - 28 * q^57 + 28 * q^61 - 8 * q^63 + 12 * q^73 - 24 * q^79 + 28 * q^81 - 32 * q^87 + 48 * q^91 - 4 * q^93 + 24 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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			0
$2$		0			0
$3$	1.57313	−	0.724745i	0.908248	−	0.418432i
$3$	1.57313	−	0.724745i	0.908248	−	0.418432i
$4$		0			0
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	0.748203	−	0.663470i	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$		0			0
$7$	0.267949			0.101275			0.0506376	−	0.998717i	$-0.483875\pi$
$7$	0.267949			0.101275			0.0506376	+	0.998717i	$0.483875\pi$
$8$		0			0
$9$	1.94949	−	2.28024i	0.649830	−	0.760080i
$10$		0			0
$11$			5.27792i			1.59135i	0.605723	+	0.795676i	$0.292884\pi$
$11$			5.27792i			1.59135i	−0.605723	+	0.795676i	$0.707116\pi$
$12$		0			0
$13$	−0.232051	+	0.133975i	−0.0643593	+	0.0371579i	−0.531834	−	0.846848i	$-0.678497\pi$
$13$	−0.232051	+	0.133975i	−0.0643593	+	0.0371579i	0.467475	+	0.884006i	$0.345164\pi$
$14$		0			0
$15$	2.43916	+	0.224745i	0.629788	+	0.0580289i
$16$		0			0
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.916696	−	0.399586i	$-0.130846\pi$
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.112296	+	0.993675i	$0.464180\pi$
$18$		0			0
$19$	−1.73205	+	4.00000i	−0.397360	+	0.917663i
$19$	−1.73205	+	4.00000i	−0.397360	+	0.917663i
$20$		0			0
$21$	0.421519	−	0.194195i	0.0919831	−	0.0423768i
$22$		0			0
$23$	4.57081	−	2.63896i	0.953080	−	0.550261i	0.0590435	−	0.998255i	$-0.481195\pi$
$23$	4.57081	−	2.63896i	0.953080	−	0.550261i	0.894036	+	0.447995i	$0.147862\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		0			0
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$		0			0
$29$	1.03528	+	1.79315i	0.192246	+	0.332980i	0.945994	−	0.324184i	$-0.105090\pi$
$29$	1.03528	+	1.79315i	0.192246	+	0.332980i	−0.753748	+	0.657163i	$0.771756\pi$
$30$		0			0
$31$		−	2.46410i		−	0.442566i	−0.975210	−	0.221283i	$-0.928976\pi$
$31$		−	2.46410i		−	0.442566i	0.975210	−	0.221283i	$-0.0710244\pi$
$32$		0			0
$33$	3.82514	+	8.30286i	0.665872	+	1.44534i
$34$		0			0
$35$	0.328169	+	0.189469i	0.0554708	+	0.0320261i
$36$		0			0
$37$		−	7.73205i		−	1.27114i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$		−	7.73205i		−	1.27114i	0.772043	−	0.635571i	$-0.219235\pi$
$38$		0			0
$39$	−0.267949	+	0.378937i	−0.0429062	+	0.0606785i
$40$		0			0
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	−0.997818	−	0.0660290i	$-0.978967\pi$
$41$	−2.82843	+	4.89898i	−0.441726	+	0.765092i	0.556092	+	0.831121i	$0.312300\pi$
$42$		0			0
$43$	2.86603	−	4.96410i	0.437065	−	0.757018i	−0.560397	−	0.828224i	$-0.689351\pi$
$43$	2.86603	−	4.96410i	0.437065	−	0.757018i	0.997462	+	0.0712058i	$0.0226847\pi$
$44$		0			0
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		0			0
$47$	0.656339	−	0.378937i	0.0957369	−	0.0552737i	−0.451367	−	0.892338i	$-0.649064\pi$
$47$	0.656339	−	0.378937i	0.0957369	−	0.0552737i	0.547104	+	0.837065i	$0.315730\pi$
$48$		0			0
$49$	−6.92820			−0.989743
$50$		0			0
$51$	8.44949	+	0.778539i	1.18317	+	0.109017i
$52$		0			0
$53$	−5.46739	−	9.46979i	−0.751003	−	1.30078i	−0.947337	−	0.320239i	$-0.896237\pi$
$53$	−5.46739	−	9.46979i	−0.751003	−	1.30078i	0.196334	−	0.980537i	$-0.437096\pi$
$54$		0			0
$55$	−3.73205	+	6.46410i	−0.503230	+	0.871619i
$56$		0			0
$57$	0.174235	+	7.54782i	0.0230779	+	0.999734i
$58$		0			0
$59$	−5.60609	+	9.71003i	−0.729850	+	1.26414i	0.227096	+	0.973872i	$0.427077\pi$
$59$	−5.60609	+	9.71003i	−0.729850	+	1.26414i	−0.956946	+	0.290265i	$0.906256\pi$
$60$		0			0
$61$	5.23205	+	9.06218i	0.669895	+	1.16029i	0.977933	+	0.208919i	$0.0669944\pi$
$61$	5.23205	+	9.06218i	0.669895	+	1.16029i	−0.308038	+	0.951374i	$0.599672\pi$
$62$		0			0
$63$	0.522364	−	0.610988i	0.0658117	−	0.0769773i
$64$		0			0
$65$	−0.378937			−0.0470014
$66$		0			0
$67$	0.866025	−	0.500000i	0.105802	−	0.0610847i	−0.446165	−	0.894951i	$-0.647211\pi$
$67$	0.866025	−	0.500000i	0.105802	−	0.0610847i	0.551967	+	0.833866i	$0.313877\pi$
$68$		0			0
$69$	5.27792	−	7.46410i	0.635387	−	0.898572i
$70$		0			0
$71$	6.69213	−	11.5911i	0.794210	−	1.37561i	−0.129130	−	0.991628i	$-0.541218\pi$
$71$	6.69213	−	11.5911i	0.794210	−	1.37561i	0.923340	−	0.383984i	$-0.125448\pi$
$72$		0			0
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$		0			0
$75$	−4.24264	−	3.00000i	−0.489898	−	0.346410i
$76$		0			0
$77$			1.41421i			0.161165i
$78$		0			0
$79$	−9.06218	−	5.23205i	−1.01957	−	0.588652i	−0.105594	−	0.994409i	$-0.533674\pi$
$79$	−9.06218	−	5.23205i	−1.01957	−	0.588652i	−0.913981	+	0.405758i	$0.867008\pi$
$80$		0			0
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$		0			0
$83$		−	2.07055i		−	0.227273i	−0.993522	−	0.113636i	$-0.963750\pi$
$83$		−	2.07055i		−	0.227273i	0.993522	−	0.113636i	$-0.0362499\pi$
$84$		0			0
$85$	3.46410	+	6.00000i	0.375735	+	0.650791i
$86$		0			0
$87$	2.92820	+	2.07055i	0.313936	+	0.221987i
$88$		0			0
$89$	3.67423	+	6.36396i	0.389468	+	0.674579i	0.992378	−	0.123231i	$-0.0393255\pi$
$89$	3.67423	+	6.36396i	0.389468	+	0.674579i	−0.602910	+	0.797809i	$0.705992\pi$
$90$		0			0
$91$	−0.0621778	+	0.0358984i	−0.00651801	+	0.00376317i
$92$		0			0
$93$	−1.78585	−	3.87636i	−0.185184	−	0.401960i
$94$		0			0
$95$	−4.94975	+	3.67423i	−0.507833	+	0.376969i
$96$		0			0
$97$	−0.464102	−	0.267949i	−0.0471224	−	0.0272061i	0.476254	−	0.879308i	$-0.341994\pi$
$97$	−0.464102	−	0.267949i	−0.0471224	−	0.0272061i	−0.523376	+	0.852102i	$0.675328\pi$
$98$		0			0
$99$	12.0349	+	10.2892i	1.20955	+	1.03411i
$100$		0			0
$101$	−1.79315	+	1.03528i	−0.178425	+	0.103014i	−0.586553	−	0.809911i	$-0.699515\pi$
$101$	−1.79315	+	1.03528i	−0.178425	+	0.103014i	0.408127	+	0.912925i	$0.366182\pi$
$102$		0			0
$103$		−	3.53590i		−	0.348402i	−0.984710	−	0.174201i	$-0.944266\pi$
$103$		−	3.53590i		−	0.348402i	0.984710	−	0.174201i	$-0.0557343\pi$
$104$		0			0
$105$	0.653570	+	0.0602202i	0.0637819	+	0.00587689i
$106$		0			0
$107$	−4.89898			−0.473602			−0.236801	−	0.971558i	$-0.576099\pi$
$107$	−4.89898			−0.473602			−0.236801	+	0.971558i	$0.576099\pi$
$108$		0			0
$109$	−5.53590	−	3.19615i	−0.530243	−	0.306136i	0.210872	−	0.977514i	$-0.432370\pi$
$109$	−5.53590	−	3.19615i	−0.530243	−	0.306136i	−0.741115	+	0.671378i	$0.765703\pi$
$110$		0			0
$111$	−5.60376	−	12.1635i	−0.531886	−	1.15451i
$112$		0			0
$113$	3.96524			0.373018			0.186509	−	0.982453i	$-0.440283\pi$
$113$	3.96524			0.373018			0.186509	+	0.982453i	$0.440283\pi$
$114$		0			0
$115$	7.46410			0.696031
$116$		0			0
$117$	−0.146887	+	0.790313i	−0.0135797	+	0.0730645i
$118$		0			0
$119$	1.13681	+	0.656339i	0.104211	+	0.0601665i
$120$		0			0
$121$	−16.8564			−1.53240
$122$		0			0
$123$	−0.898979	+	9.75663i	−0.0810583	+	0.879726i
$124$		0			0
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	−17.1962	+	9.92820i	−1.52591	+	0.880986i	−0.526384	+	0.850247i	$0.676453\pi$
$127$	−17.1962	+	9.92820i	−1.52591	+	0.880986i	−0.999527	+	0.0307388i	$0.990214\pi$
$128$		0			0
$129$	0.910930	−	9.88633i	0.0802029	−	0.870442i
$130$		0			0
$131$	10.9348	+	6.31319i	0.955375	+	0.551586i	0.894747	−	0.446574i	$-0.147356\pi$
$131$	10.9348	+	6.31319i	0.955375	+	0.551586i	0.0606288	+	0.998160i	$0.480689\pi$
$132$		0			0
$133$	−0.464102	+	1.07180i	−0.0402427	+	0.0929366i
$134$		0			0
$135$	5.26758	−	5.12372i	0.453362	−	0.440980i
$136$		0			0
$137$	9.14162	−	5.27792i	0.781021	−	0.450923i	−0.0557708	−	0.998444i	$-0.517762\pi$
$137$	9.14162	−	5.27792i	0.781021	−	0.450923i	0.836792	+	0.547521i	$0.184428\pi$
$138$		0			0
$139$	1.40192	+	2.42820i	0.118910	+	0.205958i	0.919336	−	0.393474i	$-0.128727\pi$
$139$	1.40192	+	2.42820i	0.118910	+	0.205958i	−0.800426	+	0.599431i	$0.795393\pi$
$140$		0			0
$141$	0.757875	−	1.07180i	0.0638246	−	0.0902616i
$142$		0			0
$143$	−0.707107	−	1.22474i	−0.0591312	−	0.102418i
$144$		0			0
$145$			2.92820i			0.243174i
$146$		0			0
$147$	−10.8990	+	5.02118i	−0.898933	+	0.414140i
$148$		0			0
$149$	2.36156	+	1.36345i	0.193466	+	0.111698i	0.593604	−	0.804757i	$-0.297704\pi$
$149$	2.36156	+	1.36345i	0.193466	+	0.111698i	−0.400138	+	0.916455i	$0.631038\pi$
$150$		0			0
$151$			2.00000i			0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$			2.00000i			0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$		0			0
$153$	13.8564	−	4.89898i	1.12022	−	0.396059i
$154$		0			0
$155$	1.74238	−	3.01790i	0.139952	−	0.242403i
$156$		0			0
$157$	−5.23205	+	9.06218i	−0.417563	+	0.723241i	−0.995694	−	0.0927037i	$-0.970449\pi$
$157$	−5.23205	+	9.06218i	−0.417563	+	0.723241i	0.578131	+	0.815944i	$0.303782\pi$
$158$		0			0
$159$	−15.4641	−	10.9348i	−1.22638	−	0.867184i
$160$		0			0
$161$	1.22474	−	0.707107i	0.0965234	−	0.0557278i
$162$		0			0
$163$	5.19615			0.406994			0.203497	−	0.979076i	$-0.434769\pi$
$163$	5.19615			0.406994			0.203497	+	0.979076i	$0.434769\pi$
$164$		0			0
$165$	−1.18618	+	12.8737i	−0.0923444	+	1.00221i
$166$		0			0
$167$	−10.8840	−	18.8516i	−0.842229	−	1.45878i	−0.888006	−	0.459832i	$-0.847909\pi$
$167$	−10.8840	−	18.8516i	−0.842229	−	1.45878i	0.0457762	−	0.998952i	$-0.485424\pi$
$168$		0			0
$169$	−6.46410	+	11.1962i	−0.497239	+	0.861242i
$170$		0			0
$171$	5.74434	+	11.7474i	0.439281	+	0.898350i
$172$		0			0
$173$	−8.76268	+	15.1774i	−0.666214	+	1.15392i	0.312740	+	0.949839i	$0.398753\pi$
$173$	−8.76268	+	15.1774i	−0.666214	+	1.15392i	−0.978955	+	0.204079i	$0.934580\pi$
$174$		0			0
$175$	−0.401924	−	0.696152i	−0.0303826	−	0.0526242i
$176$		0			0
$177$	−1.78182	+	19.3381i	−0.133930	+	1.45354i
$178$		0			0
$179$	−1.41421			−0.105703			−0.0528516	−	0.998602i	$-0.516831\pi$
$179$	−1.41421			−0.105703			−0.0528516	+	0.998602i	$0.516831\pi$
$180$		0			0
$181$	−3.00000	+	1.73205i	−0.222988	+	0.128742i	−0.607333	−	0.794447i	$-0.707761\pi$
$181$	−3.00000	+	1.73205i	−0.222988	+	0.128742i	0.384345	+	0.923190i	$0.374427\pi$
$182$		0			0
$183$	14.7985	+	10.4641i	1.09393	+	0.773529i
$184$		0			0
$185$	5.46739	−	9.46979i	0.401970	−	0.696233i
$186$		0			0
$187$	−12.9282	+	22.3923i	−0.945404	+	1.63749i
$188$		0			0
$189$	0.378937	−	1.33975i	0.0275636	−	0.0974522i
$190$		0			0
$191$			13.0053i			0.941032i	0.882391	+	0.470516i	$0.155932\pi$
$191$			13.0053i			0.941032i	−0.882391	+	0.470516i	$0.844068\pi$
$192$		0			0
$193$	−2.42820	−	1.40192i	−0.174786	−	0.100913i	0.410055	−	0.912061i	$-0.365510\pi$
$193$	−2.42820	−	1.40192i	−0.174786	−	0.100913i	−0.584841	+	0.811148i	$0.698843\pi$
$194$		0			0
$195$	−0.596119	+	0.274633i	−0.0426889	+	0.0196669i
$196$		0			0
$197$			0.656339i			0.0467622i	0.999727	+	0.0233811i	$0.00744311\pi$
$197$			0.656339i			0.0467622i	−0.999727	+	0.0233811i	$0.992557\pi$
$198$		0			0
$199$	−11.5981	−	20.0885i	−0.822166	−	1.42403i	−0.904066	−	0.427392i	$-0.859432\pi$
$199$	−11.5981	−	20.0885i	−0.822166	−	1.42403i	0.0819004	−	0.996641i	$-0.473901\pi$
$200$		0			0
$201$	1.00000	−	1.41421i	0.0705346	−	0.0997509i
$202$		0			0
$203$	0.277401	+	0.480473i	0.0194698	+	0.0337226i
$204$		0			0
$205$	−6.92820	+	4.00000i	−0.483887	+	0.279372i
$206$		0			0
$207$	2.89329	−	15.5672i	0.201098	−	1.08199i
$208$		0			0
$209$	−21.1117	−	9.14162i	−1.46032	−	0.632339i
$210$		0			0
$211$	−9.52628	−	5.50000i	−0.655816	−	0.378636i	0.134865	−	0.990864i	$-0.456940\pi$
$211$	−9.52628	−	5.50000i	−0.655816	−	0.378636i	−0.790681	+	0.612228i	$0.790273\pi$
$212$		0			0
$213$	2.12701	−	23.0844i	0.145740	−	1.58172i
$214$		0			0
$215$	7.02030	−	4.05317i	0.478780	−	0.276424i
$216$		0			0
$217$		−	0.660254i		−	0.0448210i
$218$		0			0
$219$	0.476756	−	5.17423i	0.0322162	−	0.349642i
$220$		0			0
$221$	−1.31268			−0.0883003
$222$		0			0
$223$	9.86603	+	5.69615i	0.660678	+	0.381443i	0.792535	−	0.609826i	$-0.208761\pi$
$223$	9.86603	+	5.69615i	0.660678	+	0.381443i	−0.131857	+	0.991269i	$0.542094\pi$
$224$		0			0
$225$	−8.84847	−	1.64456i	−0.589898	−	0.109638i
$226$		0			0
$227$	−4.79744			−0.318418			−0.159209	−	0.987245i	$-0.550894\pi$
$227$	−4.79744			−0.318418			−0.159209	+	0.987245i	$0.550894\pi$
$228$		0			0
$229$	−11.3923			−0.752825			−0.376412	−	0.926452i	$-0.622842\pi$
$229$	−11.3923			−0.752825			−0.376412	+	0.926452i	$0.622842\pi$
$230$		0			0
$231$	1.02494	+	2.22474i	0.0674364	+	0.146377i
$232$		0			0
$233$	−11.5911	−	6.69213i	−0.759359	−	0.438416i	0.0697066	−	0.997568i	$-0.477794\pi$
$233$	−11.5911	−	6.69213i	−0.759359	−	0.438416i	−0.829066	+	0.559151i	$0.811127\pi$
$234$		0			0
$235$	1.07180			0.0699163
$236$		0			0
$237$	−18.0479	−	1.66294i	−1.17234	−	0.108020i
$238$		0			0
$239$		−	15.2789i		−	0.988313i	−0.869373	−	0.494156i	$-0.835477\pi$
$239$		−	15.2789i		−	0.988313i	0.869373	−	0.494156i	$-0.164523\pi$
$240$		0			0
$241$	9.82051	−	5.66987i	0.632595	−	0.365229i	−0.149162	−	0.988813i	$-0.547657\pi$
$241$	9.82051	−	5.66987i	0.632595	−	0.365229i	0.781756	+	0.623584i	$0.214324\pi$
$242$		0			0
$243$	−8.64420	−	12.9722i	−0.554526	−	0.832167i
$244$		0			0
$245$	−8.48528	−	4.89898i	−0.542105	−	0.312984i
$246$		0			0
$247$	−0.133975	−	1.16025i	−0.00852460	−	0.0738252i
$248$		0			0
$249$	−1.50062	−	3.25725i	−0.0950981	−	0.206420i
$250$		0			0
$251$	−12.7279	+	7.34847i	−0.803379	+	0.463831i	−0.844651	−	0.535317i	$-0.820192\pi$
$251$	−12.7279	+	7.34847i	−0.803379	+	0.463831i	0.0412721	+	0.999148i	$0.486859\pi$
$252$		0			0
$253$	13.9282	+	24.1244i	0.875659	+	1.51669i
$254$		0			0
$255$	9.79796	+	6.92820i	0.613572	+	0.433861i
$256$		0			0
$257$	−4.05317	−	7.02030i	−0.252830	−	0.437914i	0.711474	−	0.702713i	$-0.248028\pi$
$257$	−4.05317	−	7.02030i	−0.252830	−	0.437914i	−0.964304	+	0.264798i	$0.914695\pi$
$258$		0			0
$259$		−	2.07180i		−	0.128735i
$260$		0			0
$261$	6.10707	+	1.13505i	0.378018	+	0.0702580i
$262$		0			0
$263$	−24.9754	−	14.4195i	−1.54005	−	0.889147i	−0.998835	−	0.0482609i	$-0.984632\pi$
$263$	−24.9754	−	14.4195i	−1.54005	−	0.889147i	−0.541213	−	0.840886i	$-0.682035\pi$
$264$		0			0
$265$		−	15.4641i		−	0.949952i
$266$		0			0
$267$	10.3923	+	7.34847i	0.635999	+	0.449719i
$268$		0			0
$269$	−5.46739	+	9.46979i	−0.333352	+	0.577383i	−0.983167	−	0.182710i	$-0.941513\pi$
$269$	−5.46739	+	9.46979i	−0.333352	+	0.577383i	0.649815	+	0.760093i	$0.274847\pi$
$270$		0			0
$271$	3.46410	−	6.00000i	0.210429	−	0.364474i	−0.741420	−	0.671042i	$-0.765847\pi$
$271$	3.46410	−	6.00000i	0.210429	−	0.364474i	0.951849	+	0.306568i	$0.0991805\pi$
$272$		0			0
$273$	−0.0717968	+	0.101536i	−0.00434534	+	0.00614524i
$274$		0			0
$275$	13.7124	−	7.91688i	0.826891	−	0.477406i
$276$		0			0
$277$	17.8564			1.07289			0.536444	−	0.843936i	$-0.319767\pi$
$277$	17.8564			1.07289			0.536444	+	0.843936i	$0.319767\pi$
$278$		0			0
$279$	−5.61874	−	4.80374i	−0.336385	−	0.287592i
$280$		0			0
$281$	−4.70951	−	8.15711i	−0.280946	−	0.486613i	0.690672	−	0.723168i	$-0.257315\pi$
$281$	−4.70951	−	8.15711i	−0.280946	−	0.486613i	−0.971618	+	0.236556i	$0.923981\pi$
$282$		0			0
$283$	2.92820	−	5.07180i	0.174064	−	0.301487i	−0.765773	−	0.643111i	$-0.777643\pi$
$283$	2.92820	−	5.07180i	0.174064	−	0.301487i	0.939837	+	0.341624i	$0.110977\pi$
$284$		0			0
$285$	−5.12372	+	9.36736i	−0.303503	+	0.554875i
$286$		0			0
$287$	−0.757875	+	1.31268i	−0.0447359	+	0.0774849i
$288$		0			0
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$		0			0
$291$	−0.924288	−	0.0851642i	−0.0541827	−	0.00499242i
$292$		0			0
$293$	13.9391			0.814329			0.407164	−	0.913355i	$-0.366518\pi$
$293$	13.9391			0.814329			0.407164	+	0.913355i	$0.366518\pi$
$294$		0			0
$295$	−13.7321	+	7.92820i	−0.799511	+	0.461598i
$296$		0			0
$297$	26.3896	+	7.46410i	1.53128	+	0.433111i
$298$		0			0
$299$	−0.707107	+	1.22474i	−0.0408930	+	0.0708288i
$300$		0			0
$301$	0.767949	−	1.33013i	0.0442639	−	0.0766672i
$302$		0			0
$303$	−2.07055	+	2.92820i	−0.118950	+	0.168221i
$304$		0			0
$305$			14.7985i			0.847358i
$306$		0			0
$307$	12.0000	+	6.92820i	0.684876	+	0.395413i	0.801690	−	0.597740i	$-0.203935\pi$
$307$	12.0000	+	6.92820i	0.684876	+	0.395413i	−0.116814	+	0.993154i	$0.537268\pi$
$308$		0			0
$309$	−2.56262	−	5.56244i	−0.145783	−	0.316436i
$310$		0			0
$311$			12.4505i			0.706004i	0.935623	+	0.353002i	$0.114839\pi$
$311$			12.4505i			0.706004i	−0.935623	+	0.353002i	$0.885161\pi$
$312$		0			0
$313$	−8.39230	−	14.5359i	−0.474361	−	0.821618i	0.525208	−	0.850974i	$-0.323988\pi$
$313$	−8.39230	−	14.5359i	−0.474361	−	0.821618i	−0.999569	+	0.0293564i	$0.990654\pi$
$314$		0			0
$315$	1.07180	−	0.378937i	0.0603889	−	0.0213507i
$316$		0			0
$317$	4.43211	+	7.67664i	0.248932	+	0.431163i	0.963230	−	0.268679i	$-0.0865871\pi$
$317$	4.43211	+	7.67664i	0.248932	+	0.431163i	−0.714298	+	0.699842i	$0.753254\pi$
$318$		0			0
$319$	−9.46410	+	5.46410i	−0.529888	+	0.305931i
$320$		0			0
$321$	−7.70674	+	3.55051i	−0.430148	+	0.198170i
$322$		0			0
$323$	−17.1464	+	12.7279i	−0.954053	+	0.708201i
$324$		0			0
$325$	0.696152	+	0.401924i	0.0386156	+	0.0222947i
$326$		0			0
$327$	−11.0251	−	1.01586i	−0.609689	−	0.0561770i
$328$		0			0
$329$	0.175865	−	0.101536i	0.00969578	−	0.00559786i
$330$		0			0
$331$			18.0718i			0.993316i	0.867946	+	0.496658i	$0.165440\pi$
$331$			18.0718i			0.993316i	−0.867946	+	0.496658i	$0.834560\pi$
$332$		0			0
$333$	−17.6309	−	15.0736i	−0.966169	−	0.826026i
$334$		0			0
$335$	1.41421			0.0772667
$336$		0			0
$337$	−21.3564	−	12.3301i	−1.16336	−	0.671665i	−0.211251	−	0.977432i	$-0.567754\pi$
$337$	−21.3564	−	12.3301i	−1.16336	−	0.671665i	−0.952106	+	0.305767i	$0.901087\pi$
$338$		0			0
$339$	6.23785	−	2.87379i	0.338793	−	0.156083i
$340$		0			0
$341$	13.0053			0.704278
$342$		0			0
$343$	−3.73205			−0.201512
$344$		0			0
$345$	11.7420	−	5.40957i	0.632169	−	0.291241i
$346$		0			0
$347$	16.6424	+	9.60849i	0.893410	+	0.515811i	0.875057	−	0.484021i	$-0.160824\pi$
$347$	16.6424	+	9.60849i	0.893410	+	0.515811i	0.0183540	+	0.999832i	$0.494157\pi$
$348$		0			0
$349$	9.39230			0.502759			0.251379	−	0.967889i	$-0.419116\pi$
$349$	9.39230			0.502759			0.251379	+	0.967889i	$0.419116\pi$
$350$		0			0
$351$	0.341704	+	1.34972i	0.0182388	+	0.0720429i
$352$		0			0
$353$			2.17209i			0.115609i	0.998328	+	0.0578043i	$0.0184099\pi$
$353$			2.17209i			0.115609i	−0.998328	+	0.0578043i	$0.981590\pi$
$354$		0			0
$355$	16.3923	−	9.46410i	0.870013	−	0.502302i
$356$		0			0
$357$	2.26403	+	0.208609i	0.119825	+	0.0110408i
$358$		0			0
$359$	6.21166	+	3.58630i	0.327839	+	0.189278i	0.654881	−	0.755732i	$-0.272719\pi$
$359$	6.21166	+	3.58630i	0.327839	+	0.189278i	−0.327042	+	0.945010i	$0.606052\pi$
$360$		0			0
$361$	−13.0000	−	13.8564i	−0.684211	−	0.729285i
$362$		0			0
$363$	−26.5174	+	12.2166i	−1.39180	+	0.641205i
$364$		0			0
$365$	3.67423	−	2.12132i	0.192318	−	0.111035i
$366$		0			0
$367$	10.5263	+	18.2321i	0.549467	+	0.951705i	0.998311	+	0.0580950i	$0.0185026\pi$
$367$	10.5263	+	18.2321i	0.549467	+	0.951705i	−0.448844	+	0.893610i	$0.648164\pi$
$368$		0			0
$369$	5.65685	+	16.0000i	0.294484	+	0.832927i
$370$		0			0
$371$	−1.46498	−	2.53742i	−0.0760581	−	0.131736i
$372$		0			0
$373$		−	19.4641i		−	1.00781i	−0.863758	−	0.503906i	$-0.831896\pi$
$373$		−	19.4641i		−	1.00781i	0.863758	−	0.503906i	$-0.168104\pi$
$374$		0			0
$375$	−8.19955	−	17.7980i	−0.423423	−	0.919083i
$376$		0			0
$377$	−0.480473	−	0.277401i	−0.0247456	−	0.0142869i
$378$		0			0
$379$		−	23.7846i		−	1.22173i	−0.791733	−	0.610867i	$-0.790821\pi$
$379$		−	23.7846i		−	1.22173i	0.791733	−	0.610867i	$-0.209179\pi$
$380$		0			0
$381$	−19.8564	+	28.0812i	−1.01727	+	1.43864i
$382$		0			0
$383$	−6.26243	+	10.8468i	−0.319995	+	0.554248i	−0.980487	−	0.196586i	$-0.937015\pi$
$383$	−6.26243	+	10.8468i	−0.319995	+	0.554248i	0.660492	+	0.750833i	$0.270348\pi$
$384$		0			0
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$		0			0
$387$	−5.73205	−	16.2127i	−0.291377	−	0.824137i
$388$		0			0
$389$	12.8159	−	7.39924i	0.649790	−	0.375156i	−0.138586	−	0.990350i	$-0.544256\pi$
$389$	12.8159	−	7.39924i	0.649790	−	0.375156i	0.788376	+	0.615194i	$0.210922\pi$
$390$		0			0
$391$	25.8564			1.30761
$392$		0			0
$393$	21.7773	+	2.00657i	1.09852	+	0.101218i
$394$		0			0
$395$	−7.39924	−	12.8159i	−0.372296	−	0.644836i
$396$		0			0
$397$	13.1603	−	22.7942i	0.660494	−	1.14401i	−0.319992	−	0.947420i	$-0.603680\pi$
$397$	13.1603	−	22.7942i	0.660494	−	1.14401i	0.980486	−	0.196589i	$-0.0629865\pi$
$398$		0			0
$399$	0.0466860	+	2.02243i	0.00233722	+	0.101248i
$400$		0			0
$401$	−11.4016	+	19.7482i	−0.569371	+	0.986179i	0.427257	+	0.904130i	$0.359480\pi$
$401$	−11.4016	+	19.7482i	−0.569371	+	0.986179i	−0.996628	+	0.0820492i	$0.973854\pi$
$402$		0			0
$403$	0.330127	+	0.571797i	0.0164448	+	0.0284832i
$404$		0			0
$405$	4.57321	−	11.8780i	0.227245	−	0.590220i
$406$		0			0
$407$	40.8091			2.02283
$408$		0			0
$409$	17.5359	−	10.1244i	0.867094	−	0.500617i	0.000712791	−	1.00000i	$-0.499773\pi$
$409$	17.5359	−	10.1244i	0.867094	−	0.500617i	0.866382	+	0.499383i	$0.166440\pi$
$410$		0			0
$411$	10.5558	−	14.9282i	0.520681	−	0.736354i
$412$		0			0
$413$	−1.50215	+	2.60179i	−0.0739158	+	0.128026i
$414$		0			0
$415$	1.46410	−	2.53590i	0.0718699	−	0.124482i
$416$		0			0
$417$	3.96524	+	2.80385i	0.194179	+	0.137305i
$418$		0			0
$419$		−	7.55154i		−	0.368917i	−0.982840	−	0.184458i	$-0.940947\pi$
$419$		−	7.55154i		−	0.368917i	0.982840	−	0.184458i	$-0.0590531\pi$
$420$		0			0
$421$	24.7128	+	14.2679i	1.20443	+	0.695377i	0.961537	−	0.274676i	$-0.0885706\pi$
$421$	24.7128	+	14.2679i	1.20443	+	0.695377i	0.242892	+	0.970053i	$0.421904\pi$
$422$		0			0
$423$	0.415458	−	2.23534i	0.0202003	−	0.108686i
$424$		0			0
$425$		−	14.6969i		−	0.712906i
$426$		0			0
$427$	1.40192	+	2.42820i	0.0678438	+	0.117509i
$428$		0			0
$429$	−2.00000	−	1.41421i	−0.0965609	−	0.0682789i
$430$		0			0
$431$	12.7279	+	22.0454i	0.613082	+	1.06189i	0.990718	+	0.135935i	$0.0434040\pi$
$431$	12.7279	+	22.0454i	0.613082	+	1.06189i	−0.377635	+	0.925954i	$0.623263\pi$
$432$		0			0
$433$	−17.8923	+	10.3301i	−0.859849	+	0.496434i	−0.863962	−	0.503557i	$-0.832024\pi$
$433$	−17.8923	+	10.3301i	−0.859849	+	0.496434i	0.00411252	+	0.999992i	$0.498691\pi$
$434$		0			0
$435$	2.12220	+	4.60645i	0.101752	+	0.220862i
$436$		0			0
$437$	2.63896	+	22.8541i	0.126239	+	1.09326i
$438$		0			0
$439$	13.4545	+	7.76795i	0.642147	+	0.370744i	0.785441	−	0.618936i	$-0.212436\pi$
$439$	13.4545	+	7.76795i	0.642147	+	0.370744i	−0.143294	+	0.989680i	$0.545769\pi$
$440$		0			0
$441$	−13.5065	+	15.7980i	−0.643165	+	0.752284i
$442$		0			0
$443$	−8.96575	+	5.17638i	−0.425976	+	0.245937i	−0.697631	−	0.716457i	$-0.745762\pi$
$443$	−8.96575	+	5.17638i	−0.425976	+	0.245937i	0.271655	+	0.962395i	$0.412429\pi$
$444$		0			0
$445$			10.3923i			0.492642i
$446$		0			0
$447$	4.70319	+	0.433354i	0.222453	+	0.0204969i
$448$		0			0
$449$	5.10205			0.240781			0.120390	−	0.992727i	$-0.461585\pi$
$449$	5.10205			0.240781			0.120390	+	0.992727i	$0.461585\pi$
$450$		0			0
$451$	−25.8564	−	14.9282i	−1.21753	−	0.702942i
$452$		0			0
$453$	1.44949	+	3.14626i	0.0681030	+	0.147824i
$454$		0			0
$455$	−0.101536			−0.00476008
$456$		0			0
$457$	34.7128			1.62380			0.811898	−	0.583799i	$-0.198434\pi$
$457$	34.7128			1.62380			0.811898	+	0.583799i	$0.198434\pi$
$458$		0			0
$459$	18.2474	−	17.7491i	0.851718	−	0.828457i
$460$		0			0
$461$	30.9232	+	17.8535i	1.44024	+	0.831522i	0.997865	−	0.0653090i	$-0.0208033\pi$
$461$	30.9232	+	17.8535i	1.44024	+	0.831522i	0.442373	+	0.896831i	$0.354137\pi$
$462$		0			0
$463$	−1.58846			−0.0738219			−0.0369109	−	0.999319i	$-0.511752\pi$
$463$	−1.58846			−0.0738219			−0.0369109	+	0.999319i	$0.511752\pi$
$464$		0			0
$465$	0.553794	−	6.01033i	0.0256816	−	0.278722i
$466$		0			0
$467$			22.6274i			1.04707i	0.852004	+	0.523536i	$0.175387\pi$
$467$			22.6274i			1.04707i	−0.852004	+	0.523536i	$0.824613\pi$
$468$		0			0
$469$	0.232051	−	0.133975i	0.0107151	−	0.00618637i
$470$		0			0
$471$	−1.66294	+	18.0479i	−0.0766243	+	0.831604i
$472$		0			0
$473$	26.2001	+	15.1266i	1.20468	+	0.695524i
$474$		0			0
$475$	12.9904	−	1.50000i	0.596040	−	0.0688247i
$476$		0			0
$477$	−32.2520	−	5.99431i	−1.47672	−	0.274461i
$478$		0			0
$479$	15.1774	−	8.76268i	0.693474	−	0.400377i	−0.111438	−	0.993771i	$-0.535546\pi$
$479$	15.1774	−	8.76268i	0.693474	−	0.400377i	0.804912	+	0.593394i	$0.202212\pi$
$480$		0			0
$481$	1.03590	+	1.79423i	0.0472329	+	0.0818098i
$482$		0			0
$483$	1.41421	−	2.00000i	0.0643489	−	0.0910032i
$484$		0			0
$485$	−0.378937	−	0.656339i	−0.0172067	−	0.0298028i
$486$		0			0
$487$		−	11.0718i		−	0.501711i	−0.968025	−	0.250856i	$-0.919288\pi$
$487$		−	11.0718i		−	0.501711i	0.968025	−	0.250856i	$-0.0807119\pi$
$488$		0			0
$489$	8.17423	−	3.76588i	0.369652	−	0.170299i
$490$		0			0
$491$	25.6317	+	14.7985i	1.15674	+	0.667846i	0.950521	−	0.310660i	$-0.100550\pi$
$491$	25.6317	+	14.7985i	1.15674	+	0.667846i	0.206222	+	0.978505i	$0.433883\pi$
$492$		0			0
$493$			10.1436i			0.456844i
$494$		0			0
$495$	7.46410	+	21.1117i	0.335486	+	0.948899i
$496$		0			0
$497$	1.79315	−	3.10583i	0.0804338	−	0.139315i
$498$		0			0
$499$	4.06218	−	7.03590i	0.181848	−	0.314970i	−0.760662	−	0.649148i	$-0.775125\pi$
$499$	4.06218	−	7.03590i	0.181848	−	0.314970i	0.942510	+	0.334178i	$0.108459\pi$
$500$		0			0
$501$	−30.7846	−	21.7680i	−1.37535	−	0.972523i
$502$		0			0
$503$	1.13681	−	0.656339i	0.0506879	−	0.0292647i	−0.474442	−	0.880287i	$-0.657350\pi$
$503$	1.13681	−	0.656339i	0.0506879	−	0.0292647i	0.525130	+	0.851022i	$0.324017\pi$
$504$		0			0
$505$	−2.92820			−0.130303
$506$		0			0
$507$	−2.05453	+	22.2979i	−0.0912450	+	0.990282i
$508$		0			0
$509$	−21.4906	−	37.2228i	−0.952554	−	1.64987i	−0.739868	−	0.672752i	$-0.765112\pi$
$509$	−21.4906	−	37.2228i	−0.952554	−	1.64987i	−0.212686	−	0.977121i	$-0.568221\pi$
$510$		0			0
$511$	0.401924	−	0.696152i	0.0177801	−	0.0307960i
$512$		0			0
$513$	17.5505	+	14.3171i	0.774874	+	0.632116i
$514$		0			0
$515$	2.50026	−	4.33057i	0.110175	−	0.190828i
$516$		0			0
$517$	2.00000	+	3.46410i	0.0879599	+	0.152351i
$518$		0			0
$519$	−2.78511	+	30.2268i	−0.122253	+	1.32681i
$520$		0			0
$521$	10.1769			0.445858			0.222929	−	0.974835i	$-0.428438\pi$
$521$	10.1769			0.445858			0.222929	+	0.974835i	$0.428438\pi$
$522$		0			0
$523$	9.40192	−	5.42820i	0.411117	−	0.237359i	−0.280152	−	0.959956i	$-0.590385\pi$
$523$	9.40192	−	5.42820i	0.411117	−	0.237359i	0.691270	+	0.722597i	$0.257052\pi$
$524$		0			0
$525$	−1.13681	−	0.803848i	−0.0496145	−	0.0350828i
$526$		0			0
$527$	6.03579	−	10.4543i	0.262923	−	0.455396i
$528$		0			0
$529$	2.42820	−	4.20577i	0.105574	−	0.182860i
$530$		0			0
$531$	11.2122	+	31.7128i	0.486567	+	1.37622i
$532$		0			0
$533$		−	1.51575i		−	0.0656544i
$534$		0			0
$535$	−6.00000	−	3.46410i	−0.259403	−	0.149766i
$536$		0			0
$537$	−2.22474	+	1.02494i	−0.0960048	+	0.0442296i
$538$		0			0
$539$		−	36.5665i		−	1.57503i
$540$		0			0
$541$	12.2321	+	21.1865i	0.525897	+	0.910880i	0.999545	+	0.0301660i	$0.00960358\pi$
$541$	12.2321	+	21.1865i	0.525897	+	0.910880i	−0.473648	+	0.880714i	$0.657063\pi$
$542$		0			0
$543$	−3.46410	+	4.89898i	−0.148659	+	0.210235i
$544$		0			0
$545$	−4.52004	−	7.82894i	−0.193617	−	0.335355i
$546$		0			0
$547$	12.8660	−	7.42820i	0.550112	−	0.317607i	−0.199055	−	0.979988i	$-0.563787\pi$
$547$	12.8660	−	7.42820i	0.550112	−	0.317607i	0.749167	+	0.662381i	$0.230454\pi$
$548$		0			0
$549$	30.8638	+	5.73630i	1.31723	+	0.244819i
$550$		0			0
$551$	−8.96575	+	1.03528i	−0.381954	+	0.0441042i
$552$		0			0
$553$	−2.42820	−	1.40192i	−0.103258	−	0.0596159i
$554$		0			0
$555$	1.73774	−	18.8597i	0.0737629	−	0.800549i
$556$		0			0
$557$	−22.5259	+	13.0053i	−0.954452	+	0.551053i	−0.894461	−	0.447146i	$-0.852441\pi$
$557$	−22.5259	+	13.0053i	−0.954452	+	0.551053i	−0.0599911	+	0.998199i	$0.519107\pi$
$558$		0			0
$559$			1.53590i			0.0649616i
$560$		0			0
$561$	−4.10906	+	44.5957i	−0.173485	+	1.88283i
$562$		0			0
$563$	26.0106			1.09622			0.548109	−	0.836407i	$-0.315348\pi$
$563$	26.0106			1.09622			0.548109	+	0.836407i	$0.315348\pi$
$564$		0			0
$565$	4.85641	+	2.80385i	0.204311	+	0.117959i
$566$		0			0
$567$	−0.374855	−	2.38223i	−0.0157424	−	0.100044i
$568$		0			0
$569$	25.2528			1.05865			0.529326	−	0.848419i	$-0.322445\pi$
$569$	25.2528			1.05865			0.529326	+	0.848419i	$0.322445\pi$
$570$		0			0
$571$	−14.8038			−0.619522			−0.309761	−	0.950814i	$-0.600249\pi$
$571$	−14.8038			−0.619522			−0.309761	+	0.950814i	$0.600249\pi$
$572$		0			0
$573$	9.42554	+	20.4591i	0.393758	+	0.854691i
$574$		0			0
$575$	−13.7124	−	7.91688i	−0.571848	−	0.330157i
$576$		0			0
$577$	29.0718			1.21027			0.605137	−	0.796121i	$-0.293118\pi$
$577$	29.0718			1.21027			0.605137	+	0.796121i	$0.293118\pi$
$578$		0			0
$579$	−4.83592	−	0.445584i	−0.200974	−	0.0185178i
$580$		0			0
$581$		−	0.554803i		−	0.0230171i
$582$		0			0
$583$	49.9808	−	28.8564i	2.06999	−	1.19511i
$584$		0			0
$585$	−0.738735	+	0.864068i	−0.0305429	+	0.0357248i
$586$		0			0
$587$	−28.8898	−	16.6796i	−1.19241	−	0.688439i	−0.233559	−	0.972343i	$-0.575037\pi$
$587$	−28.8898	−	16.6796i	−1.19241	−	0.688439i	−0.958853	+	0.283904i	$0.908370\pi$
$588$		0			0
$589$	9.85641	+	4.26795i	0.406126	+	0.175858i
$590$		0			0
$591$	0.475678	+	1.03251i	0.0195668	+	0.0424717i
$592$		0			0
$593$	−29.1301	+	16.8183i	−1.19623	+	0.690643i	−0.959712	−	0.280984i	$-0.909339\pi$
$593$	−29.1301	+	16.8183i	−1.19623	+	0.690643i	−0.236517	+	0.971627i	$0.576006\pi$
$594$		0			0
$595$	0.928203	+	1.60770i	0.0380526	+	0.0659091i
$596$		0			0
$597$	−32.8043	−	23.1962i	−1.34259	−	0.949355i
$598$		0			0
$599$	−1.36345	−	2.36156i	−0.0557089	−	0.0964906i	0.836826	−	0.547469i	$-0.184409\pi$
$599$	−1.36345	−	2.36156i	−0.0557089	−	0.0964906i	−0.892535	+	0.450978i	$0.851075\pi$
$600$		0			0
$601$		−	28.3731i		−	1.15736i	−0.815554	−	0.578681i	$-0.803568\pi$
$601$		−	28.3731i		−	1.15736i	0.815554	−	0.578681i	$-0.196432\pi$
$602$		0			0
$603$	0.548188	−	2.94949i	0.0223239	−	0.120113i
$604$		0			0
$605$	−20.6448	−	11.9193i	−0.839330	−	0.484588i
$606$		0			0
$607$		−	35.2487i		−	1.43070i	−0.698766	−	0.715351i	$-0.746267\pi$
$607$		−	35.2487i		−	1.43070i	0.698766	−	0.715351i	$-0.253733\pi$
$608$		0			0
$609$	0.784610	+	0.554803i	0.0317940	+	0.0224817i
$610$		0			0
$611$	−0.101536	+	0.175865i	−0.00410771	+	0.00711475i
$612$		0			0
$613$	23.3205	−	40.3923i	0.941906	−	1.63143i	0.180077	−	0.983653i	$-0.442365\pi$
$613$	23.3205	−	40.3923i	0.941906	−	1.63143i	0.761830	−	0.647777i	$-0.224301\pi$
$614$		0			0
$615$	−8.00000	+	11.3137i	−0.322591	+	0.456213i
$616$		0			0
$617$	19.9885	−	11.5403i	0.804705	−	0.464597i	−0.0404087	−	0.999183i	$-0.512866\pi$
$617$	19.9885	−	11.5403i	0.804705	−	0.464597i	0.845114	+	0.534587i	$0.179533\pi$
$618$		0			0
$619$	−13.1962			−0.530398			−0.265199	−	0.964194i	$-0.585438\pi$
$619$	−13.1962			−0.530398			−0.265199	+	0.964194i	$0.585438\pi$
$620$		0			0
$621$	−6.73069	−	26.5861i	−0.270093	−	1.06686i
$622$		0			0
$623$	0.984508	+	1.70522i	0.0394435	+	0.0683181i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$		0			0
$627$	−39.8368	+	0.919596i	−1.59093	+	0.0367251i
$628$		0			0
$629$	18.9396	−	32.8043i	0.755170	−	1.30799i
$630$		0			0
$631$	5.47372	+	9.48076i	0.217905	+	0.377423i	0.954167	−	0.299273i	$-0.0967442\pi$
$631$	5.47372	+	9.48076i	0.217905	+	0.377423i	−0.736262	+	0.676697i	$0.763411\pi$
$632$		0			0
$633$	−18.9722	−	1.74810i	−0.754077	−	0.0694809i
$634$		0			0
$635$	−28.0812			−1.11437
$636$		0			0
$637$	1.60770	−	0.928203i	0.0636992	−	0.0367768i
$638$		0			0
$639$	−13.3843	−	37.8564i	−0.529473	−	1.49758i
$640$		0			0
$641$	−16.2127	+	28.0812i	−0.640363	+	1.10914i	0.344989	+	0.938607i	$0.387883\pi$
$641$	−16.2127	+	28.0812i	−0.640363	+	1.10914i	−0.985352	+	0.170534i	$0.945451\pi$
$642$		0			0
$643$	−6.20577	+	10.7487i	−0.244732	+	0.423888i	−0.962056	−	0.272852i	$-0.912033\pi$
$643$	−6.20577	+	10.7487i	−0.244732	+	0.423888i	0.717324	+	0.696739i	$0.245367\pi$
$644$		0			0
$645$	8.10634	−	11.4641i	0.319187	−	0.451399i
$646$		0			0
$647$			30.3548i			1.19337i	0.802475	+	0.596686i	$0.203516\pi$
$647$			30.3548i			1.19337i	−0.802475	+	0.596686i	$0.796484\pi$
$648$		0			0
$649$	−51.2487	−	29.5885i	−2.01169	−	1.16145i
$650$		0			0
$651$	−0.478516	−	1.03867i	−0.0187545	−	0.0407086i
$652$		0			0
$653$		−	1.86748i		−	0.0730802i	−0.999332	−	0.0365401i	$-0.988366\pi$
$653$		−	1.86748i		−	0.0730802i	0.999332	−	0.0365401i	$-0.0116337\pi$
$654$		0			0
$655$	8.92820	+	15.4641i	0.348854	+	0.604232i
$656$		0			0
$657$	−3.00000	−	8.48528i	−0.117041	−	0.331042i
$658$		0			0
$659$	1.84392	+	3.19376i	0.0718289	+	0.124411i	0.899703	−	0.436503i	$-0.143783\pi$
$659$	1.84392	+	3.19376i	0.0718289	+	0.124411i	−0.827874	+	0.560914i	$0.810450\pi$
$660$		0			0
$661$	−29.3205	+	16.9282i	−1.14044	+	0.658431i	−0.946538	−	0.322591i	$-0.895446\pi$
$661$	−29.3205	+	16.9282i	−1.14044	+	0.658431i	−0.193897	+	0.981022i	$0.562113\pi$
$662$		0			0
$663$	−2.06502	+	0.951356i	−0.0801986	+	0.0369476i
$664$		0			0
$665$	−1.32628	+	0.984508i	−0.0514310	+	0.0381776i
$666$		0			0
$667$	9.46410	+	5.46410i	0.366451	+	0.211571i
$668$		0			0
$669$	19.6488	+	1.81045i	0.759667	+	0.0699960i
$670$		0			0
$671$	−47.8294	+	27.6143i	−1.84643	+	1.06604i
$672$		0			0
$673$			29.9808i			1.15567i	0.816152	+	0.577837i	$0.196103\pi$
$673$			29.9808i			1.15567i	−0.816152	+	0.577837i	$0.803897\pi$
$674$		0			0
$675$	−15.1117	+	3.82577i	−0.581650	+	0.147254i
$676$		0			0
$677$	30.1518			1.15883			0.579413	−	0.815034i	$-0.303282\pi$
$677$	30.1518			1.15883			0.579413	+	0.815034i	$0.303282\pi$
$678$		0			0
$679$	−0.124356	−	0.0717968i	−0.00477233	−	0.00275531i
$680$		0			0
$681$	−7.54701	+	3.47692i	−0.289202	+	0.133236i
$682$		0			0
$683$	26.1122			0.999155			0.499577	−	0.866269i	$-0.333489\pi$
$683$	26.1122			0.999155			0.499577	+	0.866269i	$0.333489\pi$
$684$		0			0
$685$	14.9282			0.570377
$686$		0			0
$687$	−17.9216	+	8.25651i	−0.683752	+	0.315006i
$688$		0			0
$689$	2.53742	+	1.46498i	0.0966681	+	0.0558114i
$690$		0			0
$691$	17.8564			0.679290			0.339645	−	0.940554i	$-0.389693\pi$
$691$	17.8564			0.679290			0.339645	+	0.940554i	$0.389693\pi$
$692$		0			0
$693$	3.22474	+	2.75699i	0.122498	+	0.104730i
$694$		0			0
$695$			3.96524i			0.150410i
$696$		0			0
$697$	−24.0000	+	13.8564i	−0.909065	+	0.524849i
$698$		0			0
$699$	−23.0844	−	2.12701i	−0.873134	−	0.0804508i
$700$		0			0
$701$	−34.2049	−	19.7482i	−1.29190	−	0.745880i	−0.312911	−	0.949782i	$-0.601304\pi$
$701$	−34.2049	−	19.7482i	−1.29190	−	0.745880i	−0.978991	+	0.203902i	$0.934637\pi$
$702$		0			0
$703$	30.9282	+	13.3923i	1.16648	+	0.505100i
$704$		0			0
$705$	1.68608	−	0.776779i	0.0635014	−	0.0292552i
$706$		0			0
$707$	−0.480473	+	0.277401i	−0.0180701	+	0.0104328i
$708$		0			0
$709$	−3.83975	−	6.65064i	−0.144205	−	0.249770i	0.784871	−	0.619659i	$-0.212729\pi$
$709$	−3.83975	−	6.65064i	−0.144205	−	0.249770i	−0.929076	+	0.369889i	$0.879396\pi$
$710$		0			0
$711$	−29.5969	+	10.4641i	−1.10997	+	0.392434i
$712$		0			0
$713$	−6.50266	−	11.2629i	−0.243527	−	0.421800i
$714$		0			0
$715$		−	2.00000i		−	0.0747958i
$716$		0			0
$717$	−11.0733	−	24.0358i	−0.413541	−	0.897634i
$718$		0			0
$719$	−9.46979	−	5.46739i	−0.353164	−	0.203899i	0.312914	−	0.949781i	$-0.398695\pi$
$719$	−9.46979	−	5.46739i	−0.353164	−	0.203899i	−0.666078	+	0.745882i	$0.732028\pi$
$720$		0			0
$721$		−	0.947441i		−	0.0352846i
$722$		0			0
$723$	11.3397	−	16.0368i	0.421730	−	0.596416i
$724$		0			0
$725$	3.10583	−	5.37945i	0.115348	−	0.199788i
$726$		0			0
$727$	8.79423	−	15.2321i	0.326160	−	0.564925i	−0.655587	−	0.755120i	$-0.727579\pi$
$727$	8.79423	−	15.2321i	0.326160	−	0.564925i	0.981746	+	0.190195i	$0.0609119\pi$
$728$		0			0
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		0			0
$731$	24.3190	−	14.0406i	0.899472	−	0.519310i
$732$		0			0
$733$	19.7128			0.728109			0.364055	−	0.931378i	$-0.381392\pi$
$733$	19.7128			0.728109			0.364055	+	0.931378i	$0.381392\pi$
$734$		0			0
$735$	−16.8990	−	1.55708i	−0.623328	−	0.0574337i
$736$		0			0
$737$	2.63896	+	4.57081i	0.0972073	+	0.168368i
$738$		0			0
$739$	−22.5981	+	39.1410i	−0.831284	+	1.43983i	0.0657370	+	0.997837i	$0.479060\pi$
$739$	−22.5981	+	39.1410i	−0.831284	+	1.43983i	−0.897021	+	0.441989i	$0.854273\pi$
$740$		0			0
$741$	−1.05165	−	1.72814i	−0.0386333	−	0.0634846i
$742$		0			0
$743$	−3.53553	+	6.12372i	−0.129706	+	0.224658i	−0.923563	−	0.383447i	$-0.874737\pi$
$743$	−3.53553	+	6.12372i	−0.129706	+	0.224658i	0.793857	+	0.608105i	$0.208070\pi$
$744$		0			0
$745$	1.92820	+	3.33975i	0.0706439	+	0.122359i
$746$		0			0
$747$	−4.72135	−	4.03652i	−0.172745	−	0.147689i
$748$		0			0
$749$	−1.31268			−0.0479642
$750$		0			0
$751$	−25.4545	+	14.6962i	−0.928847	+	0.536270i	−0.886447	−	0.462830i	$-0.846834\pi$
$751$	−25.4545	+	14.6962i	−0.928847	+	0.536270i	−0.0424005	+	0.999101i	$0.513501\pi$
$752$		0			0
$753$	−14.6969	+	20.7846i	−0.535586	+	0.757433i
$754$		0			0
$755$	−1.41421	+	2.44949i	−0.0514685	+	0.0891461i
$756$		0			0
$757$	−12.6962	+	21.9904i	−0.461450	+	0.799254i	−0.999033	−	0.0439562i	$-0.986004\pi$
$757$	−12.6962	+	21.9904i	−0.461450	+	0.799254i	0.537584	+	0.843210i	$0.319337\pi$
$758$		0			0
$759$	39.3949	+	27.8564i	1.42994	+	1.01112i
$760$		0			0
$761$			32.1208i			1.16438i	0.813054	+	0.582188i	$0.197803\pi$
$761$			32.1208i			1.16438i	−0.813054	+	0.582188i	$0.802197\pi$
$762$		0			0
$763$	−1.48334	−	0.856406i	−0.0537005	−	0.0310040i
$764$		0			0
$765$	20.4347	+	3.79796i	0.738817	+	0.137315i
$766$		0			0
$767$		−	3.00429i		−	0.108479i
$768$		0			0
$769$	−13.4282	−	23.2583i	−0.484233	−	0.838717i	0.515603	−	0.856828i	$-0.327568\pi$
$769$	−13.4282	−	23.2583i	−0.484233	−	0.838717i	−0.999836	+	0.0181110i	$0.994235\pi$
$770$		0			0
$771$	−11.4641	−	8.10634i	−0.412870	−	0.291943i
$772$		0			0
$773$	20.3538	+	35.2538i	0.732075	+	1.26799i	0.955995	+	0.293384i	$0.0947813\pi$
$773$	20.3538	+	35.2538i	0.732075	+	1.26799i	−0.223920	+	0.974608i	$0.571885\pi$
$774$		0			0
$775$	−6.40192	+	3.69615i	−0.229964	+	0.132770i
$776$		0			0
$777$	−1.50152	−	3.25921i	−0.0538669	−	0.116924i
$778$		0			0
$779$	−14.6969	−	19.7990i	−0.526572	−	0.709372i
$780$		0			0
$781$	61.1769	+	35.3205i	2.18908	+	1.26387i
$782$		0			0
$783$	10.4299	−	2.64048i	0.372733	−	0.0943631i
$784$		0			0
$785$	−12.8159	+	7.39924i	−0.457417	+	0.264090i
$786$		0			0
$787$		−	37.9282i		−	1.35199i	−0.736904	−	0.675997i	$-0.763713\pi$
$787$		−	37.9282i		−	1.35199i	0.736904	−	0.675997i	$-0.236287\pi$
$788$		0			0
$789$	−49.7400	−	4.58307i	−1.77079	−	0.163161i
$790$		0			0
$791$	1.06248			0.0377775
$792$		0			0
$793$	−2.42820	−	1.40192i	−0.0862280	−	0.0497838i
$794$		0			0
$795$	−11.2075	−	24.3271i	−0.397490	−	0.862792i
$796$		0			0
$797$	−54.0918			−1.91603			−0.958016	−	0.286716i	$-0.907437\pi$
$797$	−54.0918			−1.91603			−0.958016	+	0.286716i	$0.907437\pi$
$798$		0			0
$799$	3.71281			0.131350
$800$		0			0
$801$	21.6742	+	4.02834i	0.765821	+	0.142335i
$802$		0			0
$803$	13.7124	+	7.91688i	0.483901	+	0.279380i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$	−1.73774	+	18.8597i	−0.0611713	+	0.663893i
$808$		0			0
$809$			37.0197i			1.30155i	0.759273	+	0.650773i	$0.225555\pi$
$809$			37.0197i			1.30155i	−0.759273	+	0.650773i	$0.774445\pi$
$810$		0			0
$811$	−29.1962	+	16.8564i	−1.02522	+	0.591908i	−0.915610	−	0.402067i	$-0.868292\pi$
$811$	−29.1962	+	16.8564i	−1.02522	+	0.591908i	−0.109605	+	0.993975i	$0.534959\pi$
$812$		0			0
$813$	1.10102	−	11.9494i	0.0386145	−	0.419083i
$814$		0			0
$815$	6.36396	+	3.67423i	0.222920	+	0.128703i
$816$		0			0
$817$	14.8923	+	20.0622i	0.521016	+	0.701887i
$818$		0			0
$819$	−0.0393581	+	0.211764i	−0.00137528	+	0.00739963i
$820$		0			0
$821$	−4.41851	+	2.55103i	−0.154207	+	0.0890314i	−0.575118	−	0.818071i	$-0.695044\pi$
$821$	−4.41851	+	2.55103i	−0.154207	+	0.0890314i	0.420911	+	0.907102i	$0.361710\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$		0			0
$825$	15.8338	−	22.3923i	0.551260	−	0.779600i
$826$		0			0
$827$	−12.2474	−	21.2132i	−0.425886	−	0.737655i	0.570617	−	0.821216i	$-0.306704\pi$
$827$	−12.2474	−	21.2132i	−0.425886	−	0.737655i	−0.996503	+	0.0835608i	$0.973371\pi$
$828$		0			0
$829$		−	21.3397i		−	0.741160i	−0.928801	−	0.370580i	$-0.879159\pi$
$829$		−	21.3397i		−	0.741160i	0.928801	−	0.370580i	$-0.120841\pi$
$830$		0			0
$831$	28.0905	−	12.9413i	0.974448	−	0.448930i
$832$		0			0
$833$	−29.3939	−	16.9706i	−1.01844	−	0.587995i
$834$		0			0
$835$		−	30.7846i		−	1.06535i
$836$		0			0
$837$	−12.3205	−	3.48477i	−0.425859	−	0.120451i
$838$		0			0
$839$	−12.6772	+	21.9575i	−0.437664	+	0.758056i	−0.997509	−	0.0705412i	$-0.977527\pi$
$839$	−12.6772	+	21.9575i	−0.437664	+	0.758056i	0.559845	+	0.828597i	$0.310861\pi$
$840$		0			0
$841$	12.3564	−	21.4019i	0.426083	−	0.737997i
$842$		0			0
$843$	−13.3205	−	9.41902i	−0.458783	−	0.324408i
$844$		0			0
$845$	−15.8338	+	9.14162i	−0.544698	+	0.314481i
$846$		0			0
$847$	−4.51666			−0.155194
$848$		0			0
$849$	0.930692	−	10.1008i	0.0319413	−	0.346659i
$850$		0			0
$851$	−20.4046	−	35.3417i	−0.699459	−	1.21150i
$852$		0			0
$853$	−27.1603	+	47.0429i	−0.929949	+	1.61072i	−0.146548	+	0.989204i	$0.546816\pi$
$853$	−27.1603	+	47.0429i	−0.929949	+	1.61072i	−0.783401	+	0.621516i	$0.786517\pi$
$854$		0			0
$855$	−1.27135	+	18.4495i	−0.0434792	+	0.630959i
$856$		0			0
$857$	21.1117	−	36.5665i	0.721161	−	1.24909i	−0.239374	−	0.970927i	$-0.576942\pi$
$857$	21.1117	−	36.5665i	0.721161	−	1.24909i	0.960535	−	0.278160i	$-0.0897245\pi$
$858$		0			0
$859$	6.33013	+	10.9641i	0.215981	+	0.374090i	0.953576	−	0.301154i	$-0.0973717\pi$
$859$	6.33013	+	10.9641i	0.215981	+	0.374090i	−0.737594	+	0.675244i	$0.764038\pi$
$860$		0			0
$861$	−0.240881	+	2.61428i	−0.00820920	+	0.0890945i
$862$		0			0
$863$	1.31268			0.0446841			0.0223420	−	0.999750i	$-0.492888\pi$
$863$	1.31268			0.0446841			0.0223420	+	0.999750i	$0.492888\pi$
$864$		0			0
$865$	−21.4641	+	12.3923i	−0.729801	+	0.421351i
$866$		0			0
$867$	9.89949	+	7.00000i	0.336204	+	0.237732i
$868$		0			0
$869$	27.6143	−	47.8294i	0.936752	−	1.62250i
$870$		0			0
$871$	−0.133975	+	0.232051i	−0.00453956	+	0.00786274i
$872$		0			0
$873$	−1.51575	+	0.535898i	−0.0513003	+	0.0181374i
$874$		0			0
$875$		−	3.03150i		−	0.102483i
$876$		0			0
$877$	0.232051	+	0.133975i	0.00783580	+	0.00452400i	0.503913	−	0.863755i	$-0.331893\pi$
$877$	0.232051	+	0.133975i	0.00783580	+	0.00452400i	−0.496077	+	0.868279i	$0.665227\pi$
$878$		0			0
$879$	21.9280	−	10.1023i	0.739613	−	0.340741i
$880$		0			0
$881$		−	48.3335i		−	1.62840i	−0.580588	−	0.814198i	$-0.697177\pi$
$881$		−	48.3335i		−	1.62840i	0.580588	−	0.814198i	$-0.302823\pi$
$882$		0			0
$883$	−12.8660	−	22.2846i	−0.432976	−	0.749937i	0.564152	−	0.825671i	$-0.309203\pi$
$883$	−12.8660	−	22.2846i	−0.432976	−	0.749937i	−0.997128	+	0.0757343i	$0.975870\pi$
$884$		0			0
$885$	−15.8564	+	22.4243i	−0.533007	+	0.753786i
$886$		0			0
$887$	1.08604	+	1.88108i	0.0364658	+	0.0631606i	0.883682	−	0.468087i	$-0.155057\pi$
$887$	1.08604	+	1.88108i	0.0364658	+	0.0631606i	−0.847217	+	0.531248i	$0.821723\pi$
$888$		0			0
$889$	−4.60770	+	2.66025i	−0.154537	+	0.0892221i
$890$		0			0
$891$	46.9239	−	7.38370i	1.57201	−	0.247363i
$892$		0			0
$893$	0.378937	+	3.28169i	0.0126807	+	0.109818i
$894$		0			0
$895$	−1.73205	−	1.00000i	−0.0578961	−	0.0334263i
$896$		0			0
$897$	−0.224745	+	2.43916i	−0.00750401	+	0.0814411i
$898$		0			0
$899$	4.41851	−	2.55103i	0.147365	−	0.0850815i
$900$		0			0
$901$		−	53.5692i		−	1.78465i
$902$		0			0
$903$	0.244083	−	2.64903i	0.00812257	−	0.0881543i
$904$		0			0
$905$	−4.89898			−0.162848
$906$		0			0
$907$	23.4449	+	13.5359i	0.778474	+	0.449452i	0.835889	−	0.548898i	$-0.184953\pi$
$907$	23.4449	+	13.5359i	0.778474	+	0.449452i	−0.0574152	+	0.998350i	$0.518286\pi$
$908$		0			0
$909$	−1.13505	+	6.10707i	−0.0376473	+	0.202559i
$910$		0			0
$911$	21.3147			0.706189			0.353094	−	0.935588i	$-0.385129\pi$
$911$	21.3147			0.706189			0.353094	+	0.935588i	$0.385129\pi$
$912$		0			0
$913$	10.9282			0.361671
$914$		0			0
$915$	10.7251	+	23.2800i	0.354561	+	0.769612i
$916$		0			0
$917$	2.92996	+	1.69161i	0.0967559	+	0.0558620i
$918$		0			0
$919$	−19.9808			−0.659105			−0.329552	−	0.944137i	$-0.606898\pi$
$919$	−19.9808			−0.659105			−0.329552	+	0.944137i	$0.606898\pi$
$920$		0			0
$921$	23.8988	+	2.20204i	0.787491	+	0.0725597i
$922$		0			0
$923$			3.58630i			0.118045i
$924$		0			0
$925$	−20.0885	+	11.5981i	−0.660504	+	0.381342i
$926$		0			0
$927$	−8.06269	−	6.89320i	−0.264814	−	0.226402i
$928$		0			0
$929$	−9.22955	−	5.32868i	−0.302812	−	0.174828i	0.340894	−	0.940102i	$-0.389270\pi$
$929$	−9.22955	−	5.32868i	−0.302812	−	0.174828i	−0.643705	+	0.765273i	$0.722604\pi$
$930$		0			0
$931$	12.0000	−	27.7128i	0.393284	−	0.908251i
$932$		0			0
$933$	9.02345	+	19.5863i	0.295415	+	0.641227i
$934$		0			0
$935$	−31.6675	+	18.2832i	−1.03564	+	0.597926i
$936$		0			0
$937$	17.8923	+	30.9904i	0.584516	+	1.01241i	0.994936	+	0.100515i	$0.0320490\pi$
$937$	17.8923	+	30.9904i	0.584516	+	1.01241i	−0.410419	+	0.911897i	$0.634618\pi$
$938$		0			0
$939$	−23.7370	−	16.7846i	−0.774628	−	0.547745i
$940$		0			0
$941$	12.6264	+	21.8695i	0.411608	+	0.712927i	0.995066	−	0.0992170i	$-0.0316338\pi$
$941$	12.6264	+	21.8695i	0.411608	+	0.712927i	−0.583457	+	0.812144i	$0.698300\pi$
$942$		0			0
$943$			29.8564i			0.972258i
$944$		0			0
$945$	1.41145	−	1.37290i	0.0459143	−	0.0446604i
$946$		0			0
$947$	−4.06678	−	2.34795i	−0.132152	−	0.0762982i	0.432466	−	0.901650i	$-0.357643\pi$
$947$	−4.06678	−	2.34795i	−0.132152	−	0.0762982i	−0.564619	+	0.825352i	$0.690977\pi$
$948$		0			0
$949$			0.803848i			0.0260940i
$950$		0			0
$951$	12.5359	+	8.86422i	0.406504	+	0.287442i
$952$		0			0
$953$	4.15471	−	7.19617i	0.134584	−	0.233107i	−0.790854	−	0.612004i	$-0.790363\pi$
$953$	4.15471	−	7.19617i	0.134584	−	0.233107i	0.925439	+	0.378898i	$0.123697\pi$
$954$		0			0
$955$	−9.19615	+	15.9282i	−0.297581	+	0.515425i
$956$		0			0
$957$	−10.9282	+	15.4548i	−0.353259	+	0.499583i
$958$		0			0
$959$	2.44949	−	1.41421i	0.0790981	−	0.0456673i
$960$		0			0
$961$	24.9282			0.804136
$962$		0			0
$963$	−9.55051	+	11.1708i	−0.307761	+	0.359975i
$964$		0			0
$965$	−1.98262	−	3.43400i	−0.0638228	−	0.110544i
$966$		0			0
$967$	−9.59808	+	16.6244i	−0.308653	+	0.534603i	−0.978068	−	0.208286i	$-0.933212\pi$
$967$	−9.59808	+	16.6244i	−0.308653	+	0.534603i	0.669415	+	0.742889i	$0.266545\pi$
$968$		0			0
$969$	−17.7491	+	32.4495i	−0.570183	+	1.04243i
$970$		0			0
$971$	26.7685	−	46.3644i	0.859043	−	1.48791i	−0.0138004	−	0.999905i	$-0.504393\pi$
$971$	26.7685	−	46.3644i	0.859043	−	1.48791i	0.872843	−	0.488001i	$-0.162274\pi$
$972$		0			0
$973$	0.375644	+	0.650635i	0.0120426	+	0.0208584i
$974$		0			0
$975$	1.38643	+	0.127746i	0.0444014	+	0.00409116i
$976$		0			0
$977$	−9.04008			−0.289218			−0.144609	−	0.989489i	$-0.546192\pi$
$977$	−9.04008			−0.289218			−0.144609	+	0.989489i	$0.546192\pi$
$978$		0			0
$979$	−33.5885	+	19.3923i	−1.07349	+	0.619781i
$980$		0			0
$981$	−18.0802	+	6.39230i	−0.577255	+	0.204091i
$982$		0			0
$983$	−16.2635	+	28.1691i	−0.518724	+	0.898456i	0.481040	+	0.876699i	$0.340259\pi$
$983$	−16.2635	+	28.1691i	−0.518724	+	0.898456i	−0.999763	+	0.0217569i	$0.993074\pi$
$984$		0			0
$985$	−0.464102	+	0.803848i	−0.0147875	+	0.0256127i
$986$		0			0
$987$	0.203072	−	0.287187i	0.00646385	−	0.00914127i
$988$		0			0
$989$		−	30.2533i		−	0.961999i
$990$		0			0
$991$	50.3827	+	29.0885i	1.60046	+	0.924025i	0.991395	+	0.130904i	$0.0417880\pi$
$991$	50.3827	+	29.0885i	1.60046	+	0.924025i	0.609064	+	0.793121i	$0.291545\pi$
$992$		0			0
$993$	13.0974	+	28.4293i	0.415635	+	0.902177i
$994$		0			0
$995$		−	32.8043i		−	1.03997i
$996$		0			0
$997$	6.08846	+	10.5455i	0.192823	+	0.333980i	0.946185	−	0.323627i	$-0.104902\pi$
$997$	6.08846	+	10.5455i	0.192823	+	0.333980i	−0.753361	+	0.657607i	$0.771569\pi$
$998$		0			0
$999$	−38.6603	−	10.9348i	−1.22316	−	0.345961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.m.65.4		8
3.2	odd	2	inner	912.2.bn.m.65.3		8
4.3	odd	2		57.2.f.a.8.2	✓	8
12.11	even	2		57.2.f.a.8.3	yes	8
19.12	odd	6	inner	912.2.bn.m.449.3		8
57.50	even	6	inner	912.2.bn.m.449.4		8
76.11	odd	6		1083.2.d.b.1082.6		8
76.27	even	6		1083.2.d.b.1082.3		8
76.31	even	6		57.2.f.a.50.3	yes	8
228.11	even	6		1083.2.d.b.1082.4		8
228.107	odd	6		57.2.f.a.50.2	yes	8
228.179	odd	6		1083.2.d.b.1082.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.2	✓	8	4.3	odd	2
57.2.f.a.8.3	yes	8	12.11	even	2
57.2.f.a.50.2	yes	8	228.107	odd	6
57.2.f.a.50.3	yes	8	76.31	even	6
912.2.bn.m.65.3		8	3.2	odd	2	inner
912.2.bn.m.65.4		8	1.1	even	1	trivial
912.2.bn.m.449.3		8	19.12	odd	6	inner
912.2.bn.m.449.4		8	57.50	even	6	inner
1083.2.d.b.1082.3		8	76.27	even	6
1083.2.d.b.1082.4		8	228.11	even	6
1083.2.d.b.1082.5		8	228.179	odd	6
1083.2.d.b.1082.6		8	76.11	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.57313 - 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(1.57313 - 0.724745i) q^{3} +(1.22474 + 0.707107i) q^{5} +0.267949 q^{7} +(1.94949 - 2.28024i) q^{9} +5.27792i q^{11} +(-0.232051 + 0.133975i) q^{13} +(2.43916 + 0.224745i) q^{15} +(4.24264 + 2.44949i) q^{17} +(-1.73205 + 4.00000i) q^{19} +(0.421519 - 0.194195i) q^{21} +(4.57081 - 2.63896i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(1.41421 - 5.00000i) q^{27} +(1.03528 + 1.79315i) q^{29} -2.46410i q^{31} +(3.82514 + 8.30286i) q^{33} +(0.328169 + 0.189469i) q^{35} -7.73205i q^{37} +(-0.267949 + 0.378937i) q^{39} +(-2.82843 + 4.89898i) q^{41} +(2.86603 - 4.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(0.656339 - 0.378937i) q^{47} -6.92820 q^{49} +(8.44949 + 0.778539i) q^{51} +(-5.46739 - 9.46979i) q^{53} +(-3.73205 + 6.46410i) q^{55} +(0.174235 + 7.54782i) q^{57} +(-5.60609 + 9.71003i) q^{59} +(5.23205 + 9.06218i) q^{61} +(0.522364 - 0.610988i) q^{63} -0.378937 q^{65} +(0.866025 - 0.500000i) q^{67} +(5.27792 - 7.46410i) q^{69} +(6.69213 - 11.5911i) q^{71} +(1.50000 - 2.59808i) q^{73} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(-9.06218 - 5.23205i) q^{79} +(-1.39898 - 8.89060i) q^{81} -2.07055i q^{83} +(3.46410 + 6.00000i) q^{85} +(2.92820 + 2.07055i) q^{87} +(3.67423 + 6.36396i) q^{89} +(-0.0621778 + 0.0358984i) q^{91} +(-1.78585 - 3.87636i) q^{93} +(-4.94975 + 3.67423i) q^{95} +(-0.464102 - 0.267949i) q^{97} +(12.0349 + 10.2892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 16 * q^7 - 4 * q^9	\( 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) \) 8 * q + 16 * q^7 - 4 * q^9 + 12 * q^13 - 12 * q^21 - 12 * q^25 + 24 * q^33 - 16 * q^39 + 16 * q^43 + 32 * q^45 + 48 * q^51 - 16 * q^55 - 28 * q^57 + 28 * q^61 - 8 * q^63 + 12 * q^73 - 24 * q^79 + 28 * q^81 - 32 * q^87 + 48 * q^91 - 4 * q^93 + 24 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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