LMFDB - Embedded newform 1170.2.cu.d.1151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("1170.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.cu (of order $12$, degree $4$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1151.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1170.1151
Dual form			1170.2.cu.d.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.500000 + 0.133975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.500000 + 0.133975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(5.01910 - 1.34486i) q^{11} +(0.232051 - 3.59808i) q^{13} +0.517638i q^{14} +(0.500000 - 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-0.232051 + 0.866025i) q^{19} +(0.258819 - 0.965926i) q^{20} +(2.59808 + 4.50000i) q^{22} +(1.22474 - 2.12132i) q^{23} -1.00000i q^{25} +(3.53553 - 0.707107i) q^{26} +(-0.500000 + 0.133975i) q^{28} +(6.69213 + 3.86370i) q^{29} +(0.732051 + 0.732051i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-2.00000 + 2.00000i) q^{34} +(-0.448288 + 0.258819i) q^{35} +(-0.696152 - 2.59808i) q^{37} -0.896575 q^{38} +1.00000 q^{40} +(2.31079 + 8.62398i) q^{41} +(-0.464102 + 0.267949i) q^{43} +(-3.67423 + 3.67423i) q^{44} +(2.36603 + 0.633975i) q^{46} +(4.57081 + 4.57081i) q^{47} +(-5.83013 - 3.36603i) q^{49} +(0.965926 - 0.258819i) q^{50} +(1.59808 + 3.23205i) q^{52} +1.27551i q^{53} +(-2.59808 + 4.50000i) q^{55} +(-0.258819 - 0.448288i) q^{56} +(-2.00000 + 7.46410i) q^{58} +(-0.896575 + 3.34607i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-0.517638 + 0.896575i) q^{62} +1.00000i q^{64} +(2.38014 + 2.70831i) q^{65} +(9.46410 - 2.53590i) q^{67} +(-2.44949 - 1.41421i) q^{68} +(-0.366025 - 0.366025i) q^{70} +(-1.93185 - 0.517638i) q^{71} +(-9.46410 + 9.46410i) q^{73} +(2.32937 - 1.34486i) q^{74} +(-0.232051 - 0.866025i) q^{76} +2.68973 q^{77} -0.928203 q^{79} +(0.258819 + 0.965926i) q^{80} +(-7.73205 + 4.46410i) q^{82} +(8.48528 - 8.48528i) q^{83} +(-2.73205 - 0.732051i) q^{85} +(-0.378937 - 0.378937i) q^{86} +(-4.50000 - 2.59808i) q^{88} +(12.4183 - 3.32748i) q^{89} +(0.598076 - 1.76795i) q^{91} +2.44949i q^{92} +(-3.23205 + 5.59808i) q^{94} +(-0.448288 - 0.776457i) q^{95} +(2.00000 - 7.46410i) q^{97} +(1.74238 - 6.50266i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 12 q^{13} + 4 q^{16} + 12 q^{19} - 4 q^{28} - 8 q^{31} - 16 q^{34} + 36 q^{37} + 8 q^{40} + 24 q^{43} + 12 q^{46} - 12 q^{49} - 8 q^{52} - 16 q^{58} + 16 q^{61} + 48 q^{67} + 4 q^{70} - 48 q^{73} + 12 q^{76} + 48 q^{79} - 48 q^{82} - 8 q^{85} - 36 q^{88} - 16 q^{91} - 12 q^{94} + 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 12 * q^13 + 4 * q^16 + 12 * q^19 - 4 * q^28 - 8 * q^31 - 16 * q^34 + 36 * q^37 + 8 * q^40 + 24 * q^43 + 12 * q^46 - 12 * q^49 - 8 * q^52 - 16 * q^58 + 16 * q^61 + 48 * q^67 + 4 * q^70 - 48 * q^73 + 12 * q^76 + 48 * q^79 - 48 * q^82 - 8 * q^85 - 36 * q^88 - 16 * q^91 - 12 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	0.500000	+	0.133975i	0.188982	+	0.0506376i	0.352069	−	0.935974i	$-0.385478\pi$
$7$	0.500000	+	0.133975i	0.188982	+	0.0506376i	−0.163087	+	0.986612i	$0.552145\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	5.01910	−	1.34486i	1.51331	−	0.405492i	0.595780	−	0.803147i	$-0.296843\pi$
$11$	5.01910	−	1.34486i	1.51331	−	0.405492i	0.917535	+	0.397656i	$0.130176\pi$
$12$		0			0
$13$	0.232051	−	3.59808i	0.0643593	−	0.997927i
$13$	0.232051	−	3.59808i	0.0643593	−	0.997927i
$14$			0.517638i			0.138345i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	0.984988	−	0.172624i	$-0.0552245\pi$
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	−0.641991	+	0.766712i	$0.721891\pi$
$18$		0			0
$19$	−0.232051	+	0.866025i	−0.0532361	+	0.198680i	−0.987422	−	0.158107i	$-0.949461\pi$
$19$	−0.232051	+	0.866025i	−0.0532361	+	0.198680i	0.934186	+	0.356787i	$0.116128\pi$
$20$	0.258819	−	0.965926i	0.0578737	−	0.215988i
$21$		0			0
$22$	2.59808	+	4.50000i	0.553912	+	0.959403i
$23$	1.22474	−	2.12132i	0.255377	−	0.442326i	−0.709621	−	0.704584i	$-0.751134\pi$
$23$	1.22474	−	2.12132i	0.255377	−	0.442326i	0.964998	+	0.262258i	$0.0844671\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	3.53553	−	0.707107i	0.693375	−	0.138675i
$27$		0			0
$28$	−0.500000	+	0.133975i	−0.0944911	+	0.0253188i
$29$	6.69213	+	3.86370i	1.24270	+	0.717472i	0.969643	−	0.244527i	$-0.0786326\pi$
$29$	6.69213	+	3.86370i	1.24270	+	0.717472i	0.273055	+	0.961998i	$0.411966\pi$
$30$		0			0
$31$	0.732051	+	0.732051i	0.131480	+	0.131480i	0.769784	−	0.638304i	$-0.220364\pi$
$31$	0.732051	+	0.732051i	0.131480	+	0.131480i	−0.638304	+	0.769784i	$0.720364\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	−2.00000	+	2.00000i	−0.342997	+	0.342997i
$35$	−0.448288	+	0.258819i	−0.0757745	+	0.0437484i
$36$		0			0
$37$	−0.696152	−	2.59808i	−0.114447	−	0.427121i	0.884798	−	0.465974i	$-0.154296\pi$
$37$	−0.696152	−	2.59808i	−0.114447	−	0.427121i	−0.999245	+	0.0388534i	$0.987629\pi$
$38$	−0.896575			−0.145444
$39$		0			0
$40$	1.00000			0.158114
$41$	2.31079	+	8.62398i	0.360885	+	1.34684i	0.872915	+	0.487872i	$0.162227\pi$
$41$	2.31079	+	8.62398i	0.360885	+	1.34684i	−0.512030	+	0.858967i	$0.671106\pi$
$42$		0			0
$43$	−0.464102	+	0.267949i	−0.0707748	+	0.0408619i	−0.534970	−	0.844871i	$-0.679677\pi$
$43$	−0.464102	+	0.267949i	−0.0707748	+	0.0408619i	0.464195	+	0.885733i	$0.346344\pi$
$44$	−3.67423	+	3.67423i	−0.553912	+	0.553912i
$45$		0			0
$46$	2.36603	+	0.633975i	0.348851	+	0.0934745i
$47$	4.57081	+	4.57081i	0.666721	+	0.666721i	0.956956	−	0.290234i	$-0.0937333\pi$
$47$	4.57081	+	4.57081i	0.666721	+	0.666721i	−0.290234	+	0.956956i	$0.593733\pi$
$48$		0			0
$49$	−5.83013	−	3.36603i	−0.832875	−	0.480861i
$50$	0.965926	−	0.258819i	0.136603	−	0.0366025i
$51$		0			0
$52$	1.59808	+	3.23205i	0.221613	+	0.448205i
$53$			1.27551i			0.175205i	0.996156	+	0.0876026i	$0.0279206\pi$
$53$			1.27551i			0.175205i	−0.996156	+	0.0876026i	$0.972079\pi$
$54$		0			0
$55$	−2.59808	+	4.50000i	−0.350325	+	0.606780i
$56$	−0.258819	−	0.448288i	−0.0345861	−	0.0599050i
$57$		0			0
$58$	−2.00000	+	7.46410i	−0.262613	+	0.980085i
$59$	−0.896575	+	3.34607i	−0.116724	+	0.435621i	−0.999410	−	0.0343428i	$-0.989066\pi$
$59$	−0.896575	+	3.34607i	−0.116724	+	0.435621i	0.882686	+	0.469963i	$0.155733\pi$
$60$		0			0
$61$	3.73205	+	6.46410i	0.477840	+	0.827643i	0.999677	−	0.0254017i	$-0.00808648\pi$
$61$	3.73205	+	6.46410i	0.477840	+	0.827643i	−0.521837	+	0.853045i	$0.674753\pi$
$62$	−0.517638	+	0.896575i	−0.0657401	+	0.113865i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	2.38014	+	2.70831i	0.295220	+	0.335924i
$66$		0			0
$67$	9.46410	−	2.53590i	1.15622	−	0.309809i	0.370767	−	0.928726i	$-0.379095\pi$
$67$	9.46410	−	2.53590i	1.15622	−	0.309809i	0.785457	+	0.618917i	$0.212428\pi$
$68$	−2.44949	−	1.41421i	−0.297044	−	0.171499i
$69$		0			0
$70$	−0.366025	−	0.366025i	−0.0437484	−	0.0437484i
$71$	−1.93185	−	0.517638i	−0.229269	−	0.0614323i	0.142356	−	0.989816i	$-0.454532\pi$
$71$	−1.93185	−	0.517638i	−0.229269	−	0.0614323i	−0.371624	+	0.928383i	$0.621199\pi$
$72$		0			0
$73$	−9.46410	+	9.46410i	−1.10769	+	1.10769i	−0.114236	+	0.993454i	$0.536442\pi$
$73$	−9.46410	+	9.46410i	−1.10769	+	1.10769i	−0.993454	+	0.114236i	$0.963558\pi$
$74$	2.32937	−	1.34486i	0.270784	−	0.156337i
$75$		0			0
$76$	−0.232051	−	0.866025i	−0.0266181	−	0.0993399i
$77$	2.68973			0.306523
$78$		0			0
$79$	−0.928203			−0.104431			−0.0522155	−	0.998636i	$-0.516628\pi$
$79$	−0.928203			−0.104431			−0.0522155	+	0.998636i	$0.516628\pi$
$80$	0.258819	+	0.965926i	0.0289368	+	0.107994i
$81$		0			0
$82$	−7.73205	+	4.46410i	−0.853862	+	0.492978i
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	−0.0664117	−	0.997792i	$-0.521155\pi$
$83$	8.48528	−	8.48528i	0.931381	−	0.931381i	0.997792	+	0.0664117i	$0.0211551\pi$
$84$		0			0
$85$	−2.73205	−	0.732051i	−0.296333	−	0.0794021i
$86$	−0.378937	−	0.378937i	−0.0408619	−	0.0408619i
$87$		0			0
$88$	−4.50000	−	2.59808i	−0.479702	−	0.276956i
$89$	12.4183	−	3.32748i	1.31634	−	0.352712i	0.468735	−	0.883339i	$-0.344710\pi$
$89$	12.4183	−	3.32748i	1.31634	−	0.352712i	0.847606	+	0.530626i	$0.178043\pi$
$90$		0			0
$91$	0.598076	−	1.76795i	0.0626954	−	0.185331i
$92$			2.44949i			0.255377i
$93$		0			0
$94$	−3.23205	+	5.59808i	−0.333361	+	0.577397i
$95$	−0.448288	−	0.776457i	−0.0459934	−	0.0796628i
$96$		0			0
$97$	2.00000	−	7.46410i	0.203069	−	0.757865i	−0.786960	−	0.617004i	$-0.788346\pi$
$97$	2.00000	−	7.46410i	0.203069	−	0.757865i	0.990029	−	0.140861i	$-0.0449870\pi$
$98$	1.74238	−	6.50266i	0.176007	−	0.656868i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	1.41421	−	2.44949i	0.140720	−	0.243733i	−0.787048	−	0.616891i	$-0.788392\pi$
$101$	1.41421	−	2.44949i	0.140720	−	0.243733i	0.927768	+	0.373158i	$0.121725\pi$
$102$		0			0
$103$			3.53590i			0.348402i	0.984710	+	0.174201i	$0.0557343\pi$
$103$			3.53590i			0.348402i	−0.984710	+	0.174201i	$0.944266\pi$
$104$	−2.70831	+	2.38014i	−0.265572	+	0.233392i
$105$		0			0
$106$	−1.23205	+	0.330127i	−0.119667	+	0.0320648i
$107$	−3.34607	−	1.93185i	−0.323476	−	0.186759i	0.329465	−	0.944168i	$-0.393132\pi$
$107$	−3.34607	−	1.93185i	−0.323476	−	0.186759i	−0.652941	+	0.757409i	$0.726465\pi$
$108$		0			0
$109$	−7.26795	−	7.26795i	−0.696143	−	0.696143i	0.267433	−	0.963576i	$-0.413825\pi$
$109$	−7.26795	−	7.26795i	−0.696143	−	0.696143i	−0.963576	+	0.267433i	$0.913825\pi$
$110$	−5.01910	−	1.34486i	−0.478552	−	0.128228i
$111$		0			0
$112$	0.366025	−	0.366025i	0.0345861	−	0.0345861i
$113$	6.69213	−	3.86370i	0.629543	−	0.363467i	−0.151032	−	0.988529i	$-0.548260\pi$
$113$	6.69213	−	3.86370i	0.629543	−	0.363467i	0.780575	+	0.625062i	$0.214926\pi$
$114$		0			0
$115$	0.633975	+	2.36603i	0.0591184	+	0.220633i
$116$	−7.72741			−0.717472
$117$		0			0
$118$	−3.46410			−0.318896
$119$	0.378937	+	1.41421i	0.0347371	+	0.129641i
$120$		0			0
$121$	13.8564	−	8.00000i	1.25967	−	0.727273i
$122$	−5.27792	+	5.27792i	−0.477840	+	0.477840i
$123$		0			0
$124$	−1.00000	−	0.267949i	−0.0898027	−	0.0240625i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−6.52628	−	3.76795i	−0.579114	−	0.334351i	0.181667	−	0.983360i	$-0.441851\pi$
$127$	−6.52628	−	3.76795i	−0.579114	−	0.334351i	−0.760781	+	0.649009i	$0.775184\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	−2.00000	+	3.00000i	−0.175412	+	0.263117i
$131$			19.9377i			1.74196i	0.491315	+	0.870982i	$0.336516\pi$
$131$			19.9377i			1.74196i	−0.491315	+	0.870982i	$0.663484\pi$
$132$		0			0
$133$	−0.232051	+	0.401924i	−0.0201214	+	0.0348512i
$134$	4.89898	+	8.48528i	0.423207	+	0.733017i
$135$		0			0
$136$	0.732051	−	2.73205i	0.0627728	−	0.234271i
$137$	1.41421	−	5.27792i	0.120824	−	0.450923i	−0.878832	−	0.477131i	$-0.841677\pi$
$137$	1.41421	−	5.27792i	0.120824	−	0.450923i	0.999657	+	0.0262083i	$0.00834332\pi$
$138$		0			0
$139$	5.13397	+	8.89230i	0.435458	+	0.754235i	0.997333	−	0.0729868i	$-0.0232531\pi$
$139$	5.13397	+	8.89230i	0.435458	+	0.754235i	−0.561875	+	0.827222i	$0.689920\pi$
$140$	0.258819	−	0.448288i	0.0218742	−	0.0378872i
$141$		0			0
$142$		−	2.00000i		−	0.167836i
$143$	−3.67423	−	18.3712i	−0.307255	−	1.53627i
$144$		0			0
$145$	−7.46410	+	2.00000i	−0.619860	+	0.166091i
$146$	−11.5911	−	6.69213i	−0.959287	−	0.553845i
$147$		0			0
$148$	1.90192	+	1.90192i	0.156337	+	0.156337i
$149$	−16.7303	−	4.48288i	−1.37060	−	0.367252i	−0.502903	−	0.864343i	$-0.667735\pi$
$149$	−16.7303	−	4.48288i	−1.37060	−	0.367252i	−0.867698	+	0.497091i	$0.834401\pi$
$150$		0			0
$151$	−0.196152	+	0.196152i	−0.0159627	+	0.0159627i	−0.715043	−	0.699080i	$-0.753593\pi$
$151$	−0.196152	+	0.196152i	−0.0159627	+	0.0159627i	0.699080	+	0.715043i	$0.253593\pi$
$152$	0.776457	−	0.448288i	0.0629790	−	0.0363609i
$153$		0			0
$154$	0.696152	+	2.59808i	0.0560976	+	0.209359i
$155$	−1.03528			−0.0831554
$156$		0			0
$157$	18.3205			1.46214			0.731068	−	0.682305i	$-0.239022\pi$
$157$	18.3205			1.46214			0.731068	+	0.682305i	$0.239022\pi$
$158$	−0.240237	−	0.896575i	−0.0191122	−	0.0713277i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	0.896575	−	0.896575i	0.0706600	−	0.0706600i
$162$		0			0
$163$	−8.19615	−	2.19615i	−0.641972	−	0.172016i	−0.0768756	−	0.997041i	$-0.524494\pi$
$163$	−8.19615	−	2.19615i	−0.641972	−	0.172016i	−0.565097	+	0.825025i	$0.691161\pi$
$164$	−6.31319	−	6.31319i	−0.492978	−	0.492978i
$165$		0			0
$166$	10.3923	+	6.00000i	0.806599	+	0.465690i
$167$	0.258819	−	0.0693504i	0.0200280	−	0.00536649i	−0.248791	−	0.968557i	$-0.580033\pi$
$167$	0.258819	−	0.0693504i	0.0200280	−	0.00536649i	0.268819	+	0.963191i	$0.413367\pi$
$168$		0			0
$169$	−12.8923	−	1.66987i	−0.991716	−	0.128452i
$170$		−	2.82843i		−	0.216930i
$171$		0			0
$172$	0.267949	−	0.464102i	0.0204309	−	0.0353874i
$173$	−11.9007	−	20.6126i	−0.904793	−	1.56715i	−0.821195	−	0.570648i	$-0.806692\pi$
$173$	−11.9007	−	20.6126i	−0.904793	−	1.56715i	−0.0835987	−	0.996500i	$-0.526641\pi$
$174$		0			0
$175$	0.133975	−	0.500000i	0.0101275	−	0.0377964i
$176$	1.34486	−	5.01910i	0.101373	−	0.378329i
$177$		0			0
$178$	6.42820	+	11.1340i	0.481814	+	0.834527i
$179$	−12.8159	+	22.1977i	−0.957902	+	1.65913i	−0.230319	+	0.973115i	$0.573977\pi$
$179$	−12.8159	+	22.1977i	−0.957902	+	1.65913i	−0.727583	+	0.686020i	$0.759356\pi$
$180$		0			0
$181$		−	16.9282i		−	1.25826i	−0.777299	−	0.629132i	$-0.783411\pi$
$181$		−	16.9282i		−	1.25826i	0.777299	−	0.629132i	$-0.216589\pi$
$182$	1.86250	+	0.120118i	0.138058	+	0.00890376i
$183$		0			0
$184$	−2.36603	+	0.633975i	−0.174426	+	0.0467372i
$185$	2.32937	+	1.34486i	0.171259	+	0.0988763i
$186$		0			0
$187$	10.3923	+	10.3923i	0.759961	+	0.759961i
$188$	−6.24384	−	1.67303i	−0.455379	−	0.122018i
$189$		0			0
$190$	0.633975	−	0.633975i	0.0459934	−	0.0459934i
$191$	−0.416102	+	0.240237i	−0.0301081	+	0.0173829i	−0.514978	−	0.857203i	$-0.672200\pi$
$191$	−0.416102	+	0.240237i	−0.0301081	+	0.0173829i	0.484870	+	0.874586i	$0.338867\pi$
$192$		0			0
$193$	−3.12436	−	11.6603i	−0.224896	−	0.839323i	−0.982446	−	0.186546i	$-0.940271\pi$
$193$	−3.12436	−	11.6603i	−0.224896	−	0.839323i	0.757550	−	0.652777i	$-0.226396\pi$
$194$	7.72741			0.554795
$195$		0			0
$196$	6.73205			0.480861
$197$	−2.75908	−	10.2970i	−0.196576	−	0.733632i	−0.991853	−	0.127386i	$-0.959341\pi$
$197$	−2.75908	−	10.2970i	−0.196576	−	0.733632i	0.795277	−	0.606246i	$-0.207325\pi$
$198$		0			0
$199$	19.3923	−	11.1962i	1.37468	−	0.793674i	0.383170	−	0.923678i	$-0.374832\pi$
$199$	19.3923	−	11.1962i	1.37468	−	0.793674i	0.991514	+	0.130003i	$0.0414988\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$		0			0
$202$	2.73205	+	0.732051i	0.192226	+	0.0515069i
$203$	2.82843	+	2.82843i	0.198517	+	0.198517i
$204$		0			0
$205$	−7.73205	−	4.46410i	−0.540030	−	0.311786i
$206$	−3.41542	+	0.915158i	−0.237963	+	0.0637621i
$207$		0			0
$208$	−3.00000	−	2.00000i	−0.208013	−	0.138675i
$209$			4.65874i			0.322252i
$210$		0			0
$211$	6.42820	−	11.1340i	0.442536	−	0.766494i	−0.555341	−	0.831623i	$-0.687412\pi$
$211$	6.42820	−	11.1340i	0.442536	−	0.766494i	0.997877	+	0.0651282i	$0.0207456\pi$
$212$	−0.637756	−	1.10463i	−0.0438013	−	0.0758661i
$213$		0			0
$214$	1.00000	−	3.73205i	0.0683586	−	0.255118i
$215$	0.138701	−	0.517638i	0.00945931	−	0.0353026i
$216$		0			0
$217$	0.267949	+	0.464102i	0.0181896	+	0.0315053i
$218$	5.13922	−	8.90138i	0.348072	−	0.602878i
$219$		0			0
$220$		−	5.19615i		−	0.350325i
$221$	9.14162	−	4.52004i	0.614932	−	0.304051i
$222$		0			0
$223$	−26.3564	+	7.06218i	−1.76496	+	0.472918i	−0.987712	−	0.156282i	$-0.950049\pi$
$223$	−26.3564	+	7.06218i	−1.76496	+	0.472918i	−0.777243	+	0.629200i	$0.783382\pi$
$224$	0.448288	+	0.258819i	0.0299525	+	0.0172931i
$225$		0			0
$226$	5.46410	+	5.46410i	0.363467	+	0.363467i
$227$	−20.0764	−	5.37945i	−1.33252	−	0.357047i	−0.478864	−	0.877889i	$-0.658951\pi$
$227$	−20.0764	−	5.37945i	−1.33252	−	0.357047i	−0.853653	+	0.520842i	$0.825618\pi$
$228$		0			0
$229$	5.12436	−	5.12436i	0.338627	−	0.338627i	−0.517223	−	0.855850i	$-0.673034\pi$
$229$	5.12436	−	5.12436i	0.338627	−	0.338627i	0.855850	+	0.517223i	$0.173034\pi$
$230$	−2.12132	+	1.22474i	−0.139876	+	0.0807573i
$231$		0			0
$232$	−2.00000	−	7.46410i	−0.131306	−	0.490042i
$233$	−18.7637			−1.22925			−0.614626	−	0.788819i	$-0.710693\pi$
$233$	−18.7637			−1.22925			−0.614626	+	0.788819i	$0.710693\pi$
$234$		0			0
$235$	−6.46410			−0.421671
$236$	−0.896575	−	3.34607i	−0.0583621	−	0.217810i
$237$		0			0
$238$	−1.26795	+	0.732051i	−0.0821889	+	0.0474518i
$239$	−6.79367	+	6.79367i	−0.439446	+	0.439446i	−0.891825	−	0.452380i	$-0.850575\pi$
$239$	−6.79367	+	6.79367i	−0.439446	+	0.439446i	0.452380	+	0.891825i	$0.350575\pi$
$240$		0			0
$241$	1.96410	+	0.526279i	0.126519	+	0.0339006i	0.321523	−	0.946902i	$-0.395805\pi$
$241$	1.96410	+	0.526279i	0.126519	+	0.0339006i	−0.195004	+	0.980802i	$0.562472\pi$
$242$	11.3137	+	11.3137i	0.727273	+	0.727273i
$243$		0			0
$244$	−6.46410	−	3.73205i	−0.413822	−	0.238920i
$245$	6.50266	−	1.74238i	0.415440	−	0.111317i
$246$		0			0
$247$	3.06218	+	1.03590i	0.194842	+	0.0659126i
$248$		−	1.03528i		−	0.0657401i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	8.17569	+	14.1607i	0.516045	+	0.893817i	0.999826	+	0.0186276i	$0.00592970\pi$
$251$	8.17569	+	14.1607i	0.516045	+	0.893817i	−0.483781	+	0.875189i	$0.660737\pi$
$252$		0			0
$253$	3.29423	−	12.2942i	0.207106	−	0.772932i
$254$	1.95043	−	7.27912i	0.122381	−	0.456733i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.41421	−	2.44949i	0.0882162	−	0.152795i	−0.818541	−	0.574448i	$-0.805217\pi$
$257$	1.41421	−	2.44949i	0.0882162	−	0.152795i	0.906757	+	0.421653i	$0.138550\pi$
$258$		0			0
$259$		−	1.39230i		−	0.0865136i
$260$	−3.41542	−	1.15539i	−0.211815	−	0.0716545i
$261$		0			0
$262$	−19.2583	+	5.16025i	−1.18978	+	0.318802i
$263$	−25.0076	−	14.4381i	−1.54203	−	0.890293i	−0.998710	−	0.0507679i	$-0.983833\pi$
$263$	−25.0076	−	14.4381i	−1.54203	−	0.890293i	−0.543322	−	0.839525i	$-0.682834\pi$
$264$		0			0
$265$	−0.901924	−	0.901924i	−0.0554047	−	0.0554047i
$266$	−0.448288	−	0.120118i	−0.0274863	−	0.00736493i
$267$		0			0
$268$	−6.92820	+	6.92820i	−0.423207	+	0.423207i
$269$	17.1464	−	9.89949i	1.04544	−	0.603583i	0.124068	−	0.992274i	$-0.460406\pi$
$269$	17.1464	−	9.89949i	1.04544	−	0.603583i	0.921368	+	0.388691i	$0.127073\pi$
$270$		0			0
$271$	1.26795	+	4.73205i	0.0770224	+	0.287452i	0.993684	−	0.112212i	$-0.0357936\pi$
$271$	1.26795	+	4.73205i	0.0770224	+	0.287452i	−0.916662	+	0.399664i	$0.869127\pi$
$272$	2.82843			0.171499
$273$		0			0
$274$	5.46410			0.330098
$275$	−1.34486	−	5.01910i	−0.0810983	−	0.302663i
$276$		0			0
$277$	20.5526	−	11.8660i	1.23488	−	0.712960i	0.266840	−	0.963741i	$-0.414021\pi$
$277$	20.5526	−	11.8660i	1.23488	−	0.712960i	0.968044	+	0.250781i	$0.0806873\pi$
$278$	−7.26054	+	7.26054i	−0.435458	+	0.435458i
$279$		0			0
$280$	0.500000	+	0.133975i	0.0298807	+	0.00800651i
$281$	19.7990	+	19.7990i	1.18111	+	1.18111i	0.979457	+	0.201651i	$0.0646308\pi$
$281$	19.7990	+	19.7990i	1.18111	+	1.18111i	0.201651	+	0.979457i	$0.435369\pi$
$282$		0			0
$283$	19.0526	+	11.0000i	1.13256	+	0.653882i	0.944577	−	0.328291i	$-0.106473\pi$
$283$	19.0526	+	11.0000i	1.13256	+	0.653882i	0.187980	+	0.982173i	$0.439806\pi$
$284$	1.93185	−	0.517638i	0.114634	−	0.0307162i
$285$		0			0
$286$	16.7942	−	8.30385i	0.993064	−	0.491017i
$287$			4.62158i			0.272803i
$288$		0			0
$289$	4.50000	−	7.79423i	0.264706	−	0.458484i
$290$	−3.86370	−	6.69213i	−0.226884	−	0.392975i
$291$		0			0
$292$	3.46410	−	12.9282i	0.202721	−	0.756566i
$293$	−1.63587	+	6.10514i	−0.0955684	+	0.356666i	−0.997105	−	0.0760366i	$-0.975773\pi$
$293$	−1.63587	+	6.10514i	−0.0955684	+	0.356666i	0.901537	+	0.432703i	$0.142440\pi$
$294$		0			0
$295$	−1.73205	−	3.00000i	−0.100844	−	0.174667i
$296$	−1.34486	+	2.32937i	−0.0781686	+	0.135392i
$297$		0			0
$298$		−	17.3205i		−	1.00335i
$299$	−7.34847	−	4.89898i	−0.424973	−	0.283315i
$300$		0			0
$301$	−0.267949	+	0.0717968i	−0.0154443	+	0.00413830i
$302$	−0.240237	−	0.138701i	−0.0138241	−	0.00798133i
$303$		0			0
$304$	0.633975	+	0.633975i	0.0363609	+	0.0363609i
$305$	−7.20977	−	1.93185i	−0.412830	−	0.110618i
$306$		0			0
$307$	−11.1244	+	11.1244i	−0.634901	+	0.634901i	−0.949293	−	0.314393i	$-0.898199\pi$
$307$	−11.1244	+	11.1244i	−0.634901	+	0.634901i	0.314393	+	0.949293i	$0.398199\pi$
$308$	−2.32937	+	1.34486i	−0.132728	+	0.0766307i
$309$		0			0
$310$	−0.267949	−	1.00000i	−0.0152185	−	0.0567962i
$311$	1.51575			0.0859503			0.0429751	−	0.999076i	$-0.486316\pi$
$311$	1.51575			0.0859503			0.0429751	+	0.999076i	$0.486316\pi$
$312$		0			0
$313$	−7.46410			−0.421896			−0.210948	−	0.977497i	$-0.567655\pi$
$313$	−7.46410			−0.421896			−0.210948	+	0.977497i	$0.567655\pi$
$314$	4.74170	+	17.6963i	0.267589	+	0.998657i
$315$		0			0
$316$	0.803848	−	0.464102i	0.0452200	−	0.0261078i
$317$	−19.2677	+	19.2677i	−1.08218	+	1.08218i	−0.0858790	+	0.996306i	$0.527370\pi$
$317$	−19.2677	+	19.2677i	−1.08218	+	1.08218i	−0.996306	+	0.0858790i	$0.972630\pi$
$318$		0			0
$319$	38.7846	+	10.3923i	2.17152	+	0.581857i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$		0			0
$322$	1.09808	+	0.633975i	0.0611934	+	0.0353300i
$323$	−2.44949	+	0.656339i	−0.136293	+	0.0365197i
$324$		0			0
$325$	−3.59808	−	0.232051i	−0.199585	−	0.0128719i
$326$		−	8.48528i		−	0.469956i
$327$		0			0
$328$	4.46410	−	7.73205i	0.246489	−	0.426931i
$329$	1.67303	+	2.89778i	0.0922373	+	0.159760i
$330$		0			0
$331$	−0.973721	+	3.63397i	−0.0535205	+	0.199741i	−0.987509	−	0.157561i	$-0.949637\pi$
$331$	−0.973721	+	3.63397i	−0.0535205	+	0.199741i	0.933989	+	0.357303i	$0.116303\pi$
$332$	−3.10583	+	11.5911i	−0.170454	+	0.636145i
$333$		0			0
$334$	0.133975	+	0.232051i	0.00733076	+	0.0126973i
$335$	−4.89898	+	8.48528i	−0.267660	+	0.463600i
$336$		0			0
$337$		−	21.7128i		−	1.18277i	−0.806389	−	0.591386i	$-0.798581\pi$
$337$		−	21.7128i		−	1.18277i	0.806389	−	0.591386i	$-0.201419\pi$
$338$	−1.72380	−	12.8852i	−0.0937624	−	0.700863i
$339$		0			0
$340$	2.73205	−	0.732051i	0.148166	−	0.0397010i
$341$	4.65874	+	2.68973i	0.252285	+	0.145657i
$342$		0			0
$343$	−5.02628	−	5.02628i	−0.271394	−	0.271394i
$344$	0.517638	+	0.138701i	0.0279092	+	0.00747824i
$345$		0			0
$346$	16.8301	−	16.8301i	0.904793	−	0.904793i
$347$	13.3843	−	7.72741i	0.718505	−	0.414829i	−0.0956973	−	0.995410i	$-0.530508\pi$
$347$	13.3843	−	7.72741i	0.718505	−	0.414829i	0.814202	+	0.580582i	$0.197175\pi$
$348$		0			0
$349$	1.80385	+	6.73205i	0.0965577	+	0.360358i	0.997251	−	0.0740971i	$-0.0236075\pi$
$349$	1.80385	+	6.73205i	0.0965577	+	0.360358i	−0.900693	+	0.434456i	$0.856941\pi$
$350$	0.517638			0.0276689
$351$		0			0
$352$	5.19615			0.276956
$353$	−2.55103	−	9.52056i	−0.135777	−	0.506728i	−0.999993	−	0.00360735i	$-0.998852\pi$
$353$	−2.55103	−	9.52056i	−0.135777	−	0.506728i	0.864216	−	0.503121i	$-0.167815\pi$
$354$		0			0
$355$	1.73205	−	1.00000i	0.0919277	−	0.0530745i
$356$	−9.09085	+	9.09085i	−0.481814	+	0.481814i
$357$		0			0
$358$	−24.7583	−	6.63397i	−1.30852	−	0.350616i
$359$	−22.8033	−	22.8033i	−1.20351	−	1.20351i	−0.973091	−	0.230420i	$-0.925990\pi$
$359$	−22.8033	−	22.8033i	−1.20351	−	1.20351i	−0.230420	−	0.973091i	$-0.574010\pi$
$360$		0			0
$361$	15.7583	+	9.09808i	0.829386	+	0.478846i
$362$	16.3514	−	4.38134i	0.859410	−	0.230278i
$363$		0			0
$364$	0.366025	+	1.83013i	0.0191849	+	0.0959247i
$365$		−	13.3843i		−	0.700564i
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	−1.22474	−	2.12132i	−0.0638442	−	0.110581i
$369$		0			0
$370$	−0.696152	+	2.59808i	−0.0361912	+	0.135068i
$371$	−0.170886	+	0.637756i	−0.00887198	+	0.0331107i
$372$		0			0
$373$	−2.07180	−	3.58846i	−0.107274	−	0.185803i	0.807391	−	0.590016i	$-0.200879\pi$
$373$	−2.07180	−	3.58846i	−0.107274	−	0.185803i	−0.914665	+	0.404213i	$0.867545\pi$
$374$	−7.34847	+	12.7279i	−0.379980	+	0.658145i
$375$		0			0
$376$		−	6.46410i		−	0.333361i
$377$	15.4548	−	23.1822i	0.795963	−	1.19395i
$378$		0			0
$379$	−26.0885	+	6.99038i	−1.34007	+	0.359072i	−0.856462	−	0.516211i	$-0.827342\pi$
$379$	−26.0885	+	6.99038i	−1.34007	+	0.359072i	−0.483612	+	0.875282i	$0.660676\pi$
$380$	0.776457	+	0.448288i	0.0398314	+	0.0229967i
$381$		0			0
$382$	−0.339746	−	0.339746i	−0.0173829	−	0.0173829i
$383$	11.0735	+	2.96713i	0.565828	+	0.151613i	0.530382	−	0.847758i	$-0.322048\pi$
$383$	11.0735	+	2.96713i	0.565828	+	0.151613i	0.0354455	+	0.999372i	$0.488715\pi$
$384$		0			0
$385$	−1.90192	+	1.90192i	−0.0969310	+	0.0969310i
$386$	10.4543	−	6.03579i	0.532110	−	0.307214i
$387$		0			0
$388$	2.00000	+	7.46410i	0.101535	+	0.378932i
$389$	19.7990			1.00385			0.501924	−	0.864912i	$-0.332626\pi$
$389$	19.7990			1.00385			0.501924	+	0.864912i	$0.332626\pi$
$390$		0			0
$391$	6.92820			0.350374
$392$	1.74238	+	6.50266i	0.0880036	+	0.328434i
$393$		0			0
$394$	9.23205	−	5.33013i	0.465104	−	0.268528i
$395$	0.656339	−	0.656339i	0.0330240	−	0.0330240i
$396$		0			0
$397$	−16.3301	−	4.37564i	−0.819586	−	0.219607i	−0.175420	−	0.984494i	$-0.556128\pi$
$397$	−16.3301	−	4.37564i	−0.819586	−	0.219607i	−0.644165	+	0.764886i	$0.722795\pi$
$398$	15.8338	+	15.8338i	0.793674	+	0.793674i
$399$		0			0
$400$	−0.866025	−	0.500000i	−0.0433013	−	0.0250000i
$401$	−17.1278	+	4.58939i	−0.855324	+	0.229183i	−0.659731	−	0.751502i	$-0.729330\pi$
$401$	−17.1278	+	4.58939i	−0.855324	+	0.229183i	−0.195593	+	0.980685i	$0.562663\pi$
$402$		0			0
$403$	2.80385	−	2.46410i	0.139670	−	0.122746i
$404$			2.82843i			0.140720i
$405$		0			0
$406$	−2.00000	+	3.46410i	−0.0992583	+	0.171920i
$407$	−6.98811	−	12.1038i	−0.346388	−	0.599962i
$408$		0			0
$409$	0.892305	−	3.33013i	0.0441216	−	0.164664i	−0.940350	−	0.340209i	$-0.889502\pi$
$409$	0.892305	−	3.33013i	0.0441216	−	0.164664i	0.984471	+	0.175545i	$0.0561688\pi$
$410$	2.31079	−	8.62398i	0.114122	−	0.425908i
$411$		0			0
$412$	−1.76795	−	3.06218i	−0.0871006	−	0.150863i
$413$	−0.896575	+	1.55291i	−0.0441176	+	0.0764139i
$414$		0			0
$415$			12.0000i			0.589057i
$416$	1.15539	−	3.41542i	0.0566479	−	0.167455i
$417$		0			0
$418$	−4.50000	+	1.20577i	−0.220102	+	0.0589762i
$419$	−27.0967	−	15.6443i	−1.32376	−	0.764273i	−0.339434	−	0.940630i	$-0.610235\pi$
$419$	−27.0967	−	15.6443i	−1.32376	−	0.764273i	−0.984326	+	0.176357i	$0.943569\pi$
$420$		0			0
$421$	−18.9282	−	18.9282i	−0.922504	−	0.922504i	0.0747017	−	0.997206i	$-0.476200\pi$
$421$	−18.9282	−	18.9282i	−0.922504	−	0.922504i	−0.997206	+	0.0747017i	$0.976200\pi$
$422$	12.4183	+	3.32748i	0.604515	+	0.161979i
$423$		0			0
$424$	0.901924	−	0.901924i	0.0438013	−	0.0438013i
$425$	2.44949	−	1.41421i	0.118818	−	0.0685994i
$426$		0			0
$427$	1.00000	+	3.73205i	0.0483934	+	0.180607i
$428$	3.86370			0.186759
$429$		0			0
$430$	0.535898			0.0258433
$431$	3.76217	+	14.0406i	0.181217	+	0.676312i	0.995409	+	0.0957155i	$0.0305139\pi$
$431$	3.76217	+	14.0406i	0.181217	+	0.676312i	−0.814192	+	0.580596i	$0.802819\pi$
$432$		0			0
$433$	−1.26795	+	0.732051i	−0.0609337	+	0.0351801i	−0.530157	−	0.847899i	$-0.677867\pi$
$433$	−1.26795	+	0.732051i	−0.0609337	+	0.0351801i	0.469224	+	0.883079i	$0.344534\pi$
$434$	−0.378937	+	0.378937i	−0.0181896	+	0.0181896i
$435$		0			0
$436$	9.92820	+	2.66025i	0.475475	+	0.127403i
$437$	1.55291	+	1.55291i	0.0742860	+	0.0742860i
$438$		0			0
$439$	−22.8564	−	13.1962i	−1.09088	−	0.629818i	−0.157067	−	0.987588i	$-0.550204\pi$
$439$	−22.8564	−	13.1962i	−1.09088	−	0.629818i	−0.933810	+	0.357770i	$0.883537\pi$
$440$	5.01910	−	1.34486i	0.239276	−	0.0641138i
$441$		0			0
$442$	6.73205	+	7.66025i	0.320211	+	0.364361i
$443$			15.7322i			0.747460i	0.927538	+	0.373730i	$0.121921\pi$
$443$			15.7322i			0.747460i	−0.927538	+	0.373730i	$0.878079\pi$
$444$		0			0
$445$	−6.42820	+	11.1340i	−0.304726	+	0.527801i
$446$	−13.6431	−	23.6305i	−0.646019	−	1.11894i
$447$		0			0
$448$	−0.133975	+	0.500000i	−0.00632970	+	0.0236228i
$449$	1.57150	−	5.86491i	0.0741635	−	0.276782i	−0.918879	−	0.394540i	$-0.870904\pi$
$449$	1.57150	−	5.86491i	0.0741635	−	0.276782i	0.993042	+	0.117758i	$0.0375707\pi$
$450$		0			0
$451$	23.1962	+	40.1769i	1.09226	+	1.89186i
$452$	−3.86370	+	6.69213i	−0.181733	+	0.314771i
$453$		0			0
$454$		−	20.7846i		−	0.975470i
$455$	0.827225	+	1.67303i	0.0387809	+	0.0784330i
$456$		0			0
$457$	−11.1962	+	3.00000i	−0.523734	+	0.140334i	−0.510993	−	0.859585i	$-0.670722\pi$
$457$	−11.1962	+	3.00000i	−0.523734	+	0.140334i	−0.0127407	+	0.999919i	$0.504056\pi$
$458$	6.27603	+	3.62347i	0.293260	+	0.169313i
$459$		0			0
$460$	−1.73205	−	1.73205i	−0.0807573	−	0.0807573i
$461$	−4.62158	−	1.23835i	−0.215248	−	0.0576756i	0.149583	−	0.988749i	$-0.452207\pi$
$461$	−4.62158	−	1.23835i	−0.215248	−	0.0576756i	−0.364832	+	0.931074i	$0.618873\pi$
$462$		0			0
$463$	−29.0526	+	29.0526i	−1.35019	+	1.35019i	−0.464739	+	0.885448i	$0.653852\pi$
$463$	−29.0526	+	29.0526i	−1.35019	+	1.35019i	−0.885448	+	0.464739i	$0.846148\pi$
$464$	6.69213	−	3.86370i	0.310674	−	0.179368i
$465$		0			0
$466$	−4.85641	−	18.1244i	−0.224969	−	0.839595i
$467$	−28.0812			−1.29944			−0.649721	−	0.760172i	$-0.725114\pi$
$467$	−28.0812			−1.29944			−0.649721	+	0.760172i	$0.725114\pi$
$468$		0			0
$469$	5.07180			0.234194
$470$	−1.67303	−	6.24384i	−0.0771712	−	0.288007i
$471$		0			0
$472$	3.00000	−	1.73205i	0.138086	−	0.0797241i
$473$	−1.96902	+	1.96902i	−0.0905355	+	0.0905355i
$474$		0			0
$475$	0.866025	+	0.232051i	0.0397360	+	0.0106472i
$476$	−1.03528	−	1.03528i	−0.0474518	−	0.0474518i
$477$		0			0
$478$	−8.32051	−	4.80385i	−0.380571	−	0.219723i
$479$	29.8744	−	8.00481i	1.36499	−	0.365749i	0.499346	−	0.866403i	$-0.333574\pi$
$479$	29.8744	−	8.00481i	1.36499	−	0.365749i	0.865648	+	0.500654i	$0.166907\pi$
$480$		0			0
$481$	−9.50962	+	1.90192i	−0.433601	+	0.0867203i
$482$			2.03339i			0.0926183i
$483$		0			0
$484$	−8.00000	+	13.8564i	−0.363636	+	0.629837i
$485$	3.86370	+	6.69213i	0.175442	+	0.303874i
$486$		0			0
$487$	3.17949	−	11.8660i	0.144077	−	0.537701i	−0.855718	−	0.517442i	$-0.826884\pi$
$487$	3.17949	−	11.8660i	0.144077	−	0.537701i	0.999795	−	0.0202589i	$-0.00644904\pi$
$488$	1.93185	−	7.20977i	0.0874508	−	0.326371i
$489$		0			0
$490$	3.36603	+	5.83013i	0.152062	+	0.263378i
$491$	−19.0089	+	32.9244i	−0.857861	+	1.48586i	0.0161042	+	0.999870i	$0.494874\pi$
$491$	−19.0089	+	32.9244i	−0.857861	+	1.48586i	−0.873965	+	0.485988i	$0.838460\pi$
$492$		0			0
$493$			21.8564i			0.984363i
$494$	−0.208051	+	3.22595i	−0.00936066	+	0.145142i
$495$		0			0
$496$	1.00000	−	0.267949i	0.0449013	−	0.0120313i
$497$	−0.896575	−	0.517638i	−0.0402169	−	0.0232192i
$498$		0			0
$499$	19.7321	+	19.7321i	0.883328	+	0.883328i	0.993871	−	0.110543i	$-0.0352591\pi$
$499$	19.7321	+	19.7321i	0.883328	+	0.883328i	−0.110543	+	0.993871i	$0.535259\pi$
$500$	−0.965926	−	0.258819i	−0.0431975	−	0.0115747i
$501$		0			0
$502$	−11.5622	+	11.5622i	−0.516045	+	0.516045i
$503$	16.9384	−	9.77938i	0.755245	−	0.436041i	−0.0723410	−	0.997380i	$-0.523047\pi$
$503$	16.9384	−	9.77938i	0.755245	−	0.436041i	0.827586	+	0.561339i	$0.189714\pi$
$504$		0			0
$505$	0.732051	+	2.73205i	0.0325758	+	0.121575i
$506$	12.7279			0.565825
$507$		0			0
$508$	7.53590			0.334351
$509$	8.72552	+	32.5641i	0.386752	+	1.44338i	0.835387	+	0.549662i	$0.185244\pi$
$509$	8.72552	+	32.5641i	0.386752	+	1.44338i	−0.448635	+	0.893715i	$0.648090\pi$
$510$		0			0
$511$	−6.00000	+	3.46410i	−0.265424	+	0.153243i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	2.73205	+	0.732051i	0.120506	+	0.0322894i
$515$	−2.50026	−	2.50026i	−0.110175	−	0.110175i
$516$		0			0
$517$	29.0885	+	16.7942i	1.27931	+	0.738609i
$518$	1.34486	−	0.360355i	0.0590899	−	0.0158331i
$519$		0			0
$520$	0.232051	−	3.59808i	0.0101761	−	0.157786i
$521$			15.9725i			0.699766i	0.936793	+	0.349883i	$0.113779\pi$
$521$			15.9725i			0.699766i	−0.936793	+	0.349883i	$0.886221\pi$
$522$		0			0
$523$	−15.9282	+	27.5885i	−0.696492	+	1.20636i	0.273184	+	0.961962i	$0.411923\pi$
$523$	−15.9282	+	27.5885i	−0.696492	+	1.20636i	−0.969675	+	0.244397i	$0.921410\pi$
$524$	−9.96885	−	17.2665i	−0.435491	−	0.754293i
$525$		0			0
$526$	7.47372	−	27.8923i	0.325870	−	1.21616i
$527$	−0.757875	+	2.82843i	−0.0330135	+	0.123208i
$528$		0			0
$529$	8.50000	+	14.7224i	0.369565	+	0.640106i
$530$	0.637756	−	1.10463i	0.0277024	−	0.0479819i
$531$		0			0
$532$		−	0.464102i		−	0.0201214i
$533$	31.5660	−	6.31319i	1.36727	−	0.273455i
$534$		0			0
$535$	3.73205	−	1.00000i	0.161351	−	0.0432338i
$536$	−8.48528	−	4.89898i	−0.366508	−	0.211604i
$537$		0			0
$538$	14.0000	+	14.0000i	0.603583	+	0.603583i
$539$	−33.7888	−	9.05369i	−1.45539	−	0.389970i
$540$		0			0
$541$	−23.6603	+	23.6603i	−1.01723	+	1.01723i	−0.0173849	+	0.999849i	$0.505534\pi$
$541$	−23.6603	+	23.6603i	−1.01723	+	1.01723i	−0.999849	+	0.0173849i	$0.994466\pi$
$542$	−4.24264	+	2.44949i	−0.182237	+	0.105215i
$543$		0			0
$544$	0.732051	+	2.73205i	0.0313864	+	0.117136i
$545$	10.2784			0.440280
$546$		0			0
$547$	13.6077			0.581823			0.290912	−	0.956750i	$-0.406041\pi$
$547$	13.6077			0.581823			0.290912	+	0.956750i	$0.406041\pi$
$548$	1.41421	+	5.27792i	0.0604122	+	0.225461i
$549$		0			0
$550$	4.50000	−	2.59808i	0.191881	−	0.110782i
$551$	−4.89898	+	4.89898i	−0.208704	+	0.208704i
$552$		0			0
$553$	−0.464102	−	0.124356i	−0.0197356	−	0.00528814i
$554$	16.7811	+	16.7811i	0.712960	+	0.712960i
$555$		0			0
$556$	−8.89230	−	5.13397i	−0.377118	−	0.217729i
$557$	4.88040	−	1.30770i	0.206789	−	0.0554090i	−0.153937	−	0.988081i	$-0.549195\pi$
$557$	4.88040	−	1.30770i	0.206789	−	0.0554090i	0.360727	+	0.932672i	$0.382529\pi$
$558$		0			0
$559$	0.856406	+	1.73205i	0.0362221	+	0.0732579i
$560$			0.517638i			0.0218742i
$561$		0			0
$562$	−14.0000	+	24.2487i	−0.590554	+	1.02287i
$563$	−2.72689	−	4.72311i	−0.114925	−	0.199056i	0.802825	−	0.596215i	$-0.203329\pi$
$563$	−2.72689	−	4.72311i	−0.114925	−	0.199056i	−0.917750	+	0.397159i	$0.869996\pi$
$564$		0			0
$565$	−2.00000	+	7.46410i	−0.0841406	+	0.314017i
$566$	−5.69402	+	21.2504i	−0.239337	+	0.893220i
$567$		0			0
$568$	1.00000	+	1.73205i	0.0419591	+	0.0726752i
$569$	13.3149	−	23.0621i	0.558190	−	0.966814i	−0.439458	−	0.898263i	$-0.644829\pi$
$569$	13.3149	−	23.0621i	0.558190	−	0.966814i	0.997648	−	0.0685502i	$-0.0218373\pi$
$570$		0			0
$571$			43.5885i			1.82412i	0.410057	+	0.912060i	$0.365509\pi$
$571$			43.5885i			1.82412i	−0.410057	+	0.912060i	$0.634491\pi$
$572$	12.3676	+	14.0728i	0.517114	+	0.588413i
$573$		0			0
$574$	−4.46410	+	1.19615i	−0.186328	+	0.0499264i
$575$	−2.12132	−	1.22474i	−0.0884652	−	0.0510754i
$576$		0			0
$577$	−26.5885	−	26.5885i	−1.10689	−	1.10689i	−0.993557	−	0.113335i	$-0.963847\pi$
$577$	−26.5885	−	26.5885i	−1.10689	−	1.10689i	−0.113335	−	0.993557i	$-0.536153\pi$
$578$	8.69333	+	2.32937i	0.361595	+	0.0968891i
$579$		0			0
$580$	5.46410	−	5.46410i	0.226884	−	0.226884i
$581$	5.37945	−	3.10583i	0.223177	−	0.128851i
$582$		0			0
$583$	1.71539	+	6.40192i	0.0710442	+	0.265141i
$584$	13.3843			0.553845
$585$		0			0
$586$	−6.32051			−0.261098
$587$	8.79985	+	32.8415i	0.363209	+	1.35551i	0.869833	+	0.493346i	$0.164226\pi$
$587$	8.79985	+	32.8415i	0.363209	+	1.35551i	−0.506625	+	0.862167i	$0.669107\pi$
$588$		0			0
$589$	−0.803848	+	0.464102i	−0.0331220	+	0.0191230i
$590$	2.44949	−	2.44949i	0.100844	−	0.100844i
$591$		0			0
$592$	−2.59808	−	0.696152i	−0.106780	−	0.0286117i
$593$	−6.96953	−	6.96953i	−0.286204	−	0.286204i	0.549373	−	0.835577i	$-0.314867\pi$
$593$	−6.96953	−	6.96953i	−0.286204	−	0.286204i	−0.835577	+	0.549373i	$0.814867\pi$
$594$		0			0
$595$	−1.26795	−	0.732051i	−0.0519808	−	0.0300112i
$596$	16.7303	−	4.48288i	0.685301	−	0.183626i
$597$		0			0
$598$	2.83013	−	8.36603i	0.115733	−	0.342112i
$599$		−	17.4510i		−	0.713030i	−0.934290	−	0.356515i	$-0.883965\pi$
$599$		−	17.4510i		−	0.713030i	0.934290	−	0.356515i	$-0.116035\pi$
$600$		0			0
$601$	2.89230	−	5.00962i	0.117980	−	0.204347i	−0.800987	−	0.598681i	$-0.795692\pi$
$601$	2.89230	−	5.00962i	0.117980	−	0.204347i	0.918967	+	0.394335i	$0.129025\pi$
$602$	−0.138701	−	0.240237i	−0.00565302	−	0.00979132i
$603$		0			0
$604$	0.0717968	−	0.267949i	0.00292137	−	0.0109027i
$605$	−4.14110	+	15.4548i	−0.168360	+	0.628328i
$606$		0			0
$607$	5.69615	+	9.86603i	0.231200	+	0.400450i	0.958161	−	0.286228i	$-0.0924016\pi$
$607$	5.69615	+	9.86603i	0.231200	+	0.400450i	−0.726962	+	0.686678i	$0.759068\pi$
$608$	−0.448288	+	0.776457i	−0.0181805	+	0.0314895i
$609$		0			0
$610$		−	7.46410i		−	0.302213i
$611$	17.5068	−	15.3855i	0.708249	−	0.622429i
$612$		0			0
$613$	−26.1865	+	7.01666i	−1.05766	+	0.283400i	−0.745415	−	0.666600i	$-0.767749\pi$
$613$	−26.1865	+	7.01666i	−1.05766	+	0.283400i	−0.312249	+	0.950000i	$0.601082\pi$
$614$	−13.6245	−	7.86611i	−0.549840	−	0.317450i
$615$		0			0
$616$	−1.90192	−	1.90192i	−0.0766307	−	0.0766307i
$617$	−26.9072	−	7.20977i	−1.08324	−	0.290254i	−0.327320	−	0.944914i	$-0.606145\pi$
$617$	−26.9072	−	7.20977i	−1.08324	−	0.290254i	−0.755924	+	0.654659i	$0.772812\pi$
$618$		0			0
$619$	3.95448	−	3.95448i	0.158944	−	0.158944i	−0.623155	−	0.782099i	$-0.714149\pi$
$619$	3.95448	−	3.95448i	0.158944	−	0.158944i	0.782099	+	0.623155i	$0.214149\pi$
$620$	0.896575	−	0.517638i	0.0360073	−	0.0207888i
$621$		0			0
$622$	0.392305	+	1.46410i	0.0157300	+	0.0587051i
$623$	6.65497			0.266626
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−1.93185	−	7.20977i	−0.0772123	−	0.288160i
$627$		0			0
$628$	−15.8660	+	9.16025i	−0.633123	+	0.365534i
$629$	5.37945	−	5.37945i	0.214493	−	0.214493i
$630$		0			0
$631$	−19.1244	−	5.12436i	−0.761329	−	0.203997i	−0.142791	−	0.989753i	$-0.545608\pi$
$631$	−19.1244	−	5.12436i	−0.761329	−	0.203997i	−0.618537	+	0.785755i	$0.712274\pi$
$632$	0.656339	+	0.656339i	0.0261078	+	0.0261078i
$633$		0			0
$634$	−23.5981	−	13.6244i	−0.937199	−	0.541092i
$635$	7.27912	−	1.95043i	0.288863	−	0.0774006i
$636$		0			0
$637$	−13.4641	+	20.1962i	−0.533467	+	0.800201i
$638$			40.1528i			1.58966i
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	7.98623	+	13.8325i	0.315437	+	0.546353i	0.979530	−	0.201297i	$-0.0645156\pi$
$641$	7.98623	+	13.8325i	0.315437	+	0.546353i	−0.664093	+	0.747650i	$0.731182\pi$
$642$		0			0
$643$	3.66025	−	13.6603i	0.144346	−	0.538708i	−0.855437	−	0.517906i	$-0.826712\pi$
$643$	3.66025	−	13.6603i	0.144346	−	0.538708i	0.999784	−	0.0208014i	$-0.00662178\pi$
$644$	−0.328169	+	1.22474i	−0.0129317	+	0.0482617i
$645$		0			0
$646$	−1.26795	−	2.19615i	−0.0498868	−	0.0864065i
$647$	10.2091	−	17.6826i	0.401360	−	0.695177i	−0.592530	−	0.805548i	$-0.701871\pi$
$647$	10.2091	−	17.6826i	0.401360	−	0.695177i	0.993890	+	0.110372i	$0.0352042\pi$
$648$		0			0
$649$			18.0000i			0.706562i
$650$	−0.707107	−	3.53553i	−0.0277350	−	0.138675i
$651$		0			0
$652$	8.19615	−	2.19615i	0.320986	−	0.0860080i
$653$	−12.3676	−	7.14042i	−0.483980	−	0.279426i	0.238093	−	0.971242i	$-0.423478\pi$
$653$	−12.3676	−	7.14042i	−0.483980	−	0.279426i	−0.722074	+	0.691816i	$0.756811\pi$
$654$		0			0
$655$	−14.0981	−	14.0981i	−0.550857	−	0.550857i
$656$	8.62398	+	2.31079i	0.336710	+	0.0902212i
$657$		0			0
$658$	−2.36603	+	2.36603i	−0.0922373	+	0.0922373i
$659$	11.0871	−	6.40113i	0.431891	−	0.249352i	−0.268261	−	0.963346i	$-0.586449\pi$
$659$	11.0871	−	6.40113i	0.431891	−	0.249352i	0.700152	+	0.713994i	$0.253116\pi$
$660$		0			0
$661$	−6.12436	−	22.8564i	−0.238210	−	0.889011i	−0.976676	−	0.214720i	$-0.931116\pi$
$661$	−6.12436	−	22.8564i	−0.238210	−	0.889011i	0.738466	−	0.674291i	$-0.235551\pi$
$662$	−3.76217			−0.146221
$663$		0			0
$664$	−12.0000			−0.465690
$665$	−0.120118	−	0.448288i	−0.00465799	−	0.0173839i
$666$		0			0
$667$	16.3923	−	9.46410i	0.634713	−	0.366451i
$668$	−0.189469	+	0.189469i	−0.00733076	+	0.00733076i
$669$		0			0
$670$	−9.46410	−	2.53590i	−0.365630	−	0.0979703i
$671$	27.4249	+	27.4249i	1.05872	+	1.05872i
$672$		0			0
$673$	−11.0718	−	6.39230i	−0.426786	−	0.246405i	0.271190	−	0.962526i	$-0.412583\pi$
$673$	−11.0718	−	6.39230i	−0.426786	−	0.246405i	−0.697977	+	0.716121i	$0.745916\pi$
$674$	20.9730	−	5.61969i	0.807848	−	0.216462i
$675$		0			0
$676$	12.0000	−	5.00000i	0.461538	−	0.192308i
$677$			13.2827i			0.510497i	0.966876	+	0.255248i	$0.0821572\pi$
$677$			13.2827i			0.510497i	−0.966876	+	0.255248i	$0.917843\pi$
$678$		0			0
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$	1.41421	+	2.44949i	0.0542326	+	0.0939336i
$681$		0			0
$682$	−1.39230	+	5.19615i	−0.0533141	+	0.198971i
$683$	−8.72552	+	32.5641i	−0.333873	+	1.24603i	0.571213	+	0.820802i	$0.306473\pi$
$683$	−8.72552	+	32.5641i	−0.333873	+	1.24603i	−0.905086	+	0.425228i	$0.860194\pi$
$684$		0			0
$685$	2.73205	+	4.73205i	0.104386	+	0.180802i
$686$	3.55412	−	6.15591i	0.135697	−	0.235034i
$687$		0			0
$688$			0.535898i			0.0204309i
$689$	4.58939	+	0.295984i	0.174842	+	0.0112761i
$690$		0			0
$691$	−46.0167	+	12.3301i	−1.75056	+	0.469060i	−0.984745	−	0.174005i	$-0.944329\pi$
$691$	−46.0167	+	12.3301i	−1.75056	+	0.469060i	−0.765811	+	0.643065i	$0.777662\pi$
$692$	20.6126	+	11.9007i	0.783574	+	0.452397i
$693$		0			0
$694$	10.9282	+	10.9282i	0.414829	+	0.414829i
$695$	−9.91808	−	2.65754i	−0.376214	−	0.100806i
$696$		0			0
$697$	−17.8564	+	17.8564i	−0.676360	+	0.676360i
$698$	−6.03579	+	3.48477i	−0.228458	+	0.131900i
$699$		0			0
$700$	0.133975	+	0.500000i	0.00506376	+	0.0188982i
$701$	1.31268			0.0495791			0.0247896	−	0.999693i	$-0.492108\pi$
$701$	1.31268			0.0495791			0.0247896	+	0.999693i	$0.492108\pi$
$702$		0			0
$703$	2.41154			0.0909531
$704$	1.34486	+	5.01910i	0.0506864	+	0.189164i
$705$		0			0
$706$	8.53590	−	4.92820i	0.321253	−	0.185475i
$707$	1.03528	−	1.03528i	0.0389356	−	0.0389356i
$708$		0			0
$709$	15.4641	+	4.14359i	0.580767	+	0.155616i	0.537230	−	0.843436i	$-0.319471\pi$
$709$	15.4641	+	4.14359i	0.580767	+	0.155616i	0.0435367	+	0.999052i	$0.486137\pi$
$710$	1.41421	+	1.41421i	0.0530745	+	0.0530745i
$711$		0			0
$712$	−11.1340	−	6.42820i	−0.417263	−	0.240907i
$713$	2.44949	−	0.656339i	0.0917341	−	0.0245801i
$714$		0			0
$715$	15.5885	+	10.3923i	0.582975	+	0.388650i
$716$		−	25.6317i		−	0.957902i
$717$		0			0
$718$	16.1244	−	27.9282i	0.601756	−	1.04227i
$719$	−8.86422	−	15.3533i	−0.330580	−	0.572581i	0.652046	−	0.758179i	$-0.273911\pi$
$719$	−8.86422	−	15.3533i	−0.330580	−	0.572581i	−0.982626	+	0.185599i	$0.940578\pi$
$720$		0			0
$721$	−0.473721	+	1.76795i	−0.0176423	+	0.0658419i
$722$	−4.70951	+	17.5761i	−0.175270	+	0.654116i
$723$		0			0
$724$	8.46410	+	14.6603i	0.314566	+	0.544844i
$725$	3.86370	−	6.69213i	0.143494	−	0.248539i
$726$		0			0
$727$			45.5885i			1.69078i	0.534148	+	0.845391i	$0.320633\pi$
$727$			45.5885i			1.69078i	−0.534148	+	0.845391i	$0.679367\pi$
$728$	−1.67303	+	0.827225i	−0.0620067	+	0.0306590i
$729$		0			0
$730$	12.9282	−	3.46410i	0.478494	−	0.128212i
$731$	−1.31268	−	0.757875i	−0.0485511	−	0.0280310i
$732$		0			0
$733$	−16.9019	−	16.9019i	−0.624287	−	0.624287i	0.322338	−	0.946625i	$-0.395531\pi$
$733$	−16.9019	−	16.9019i	−0.624287	−	0.624287i	−0.946625	+	0.322338i	$0.895531\pi$
$734$	7.72741	+	2.07055i	0.285224	+	0.0764255i
$735$		0			0
$736$	1.73205	−	1.73205i	0.0638442	−	0.0638442i
$737$	44.0908	−	25.4558i	1.62411	−	0.937678i
$738$		0			0
$739$	−4.59808	−	17.1603i	−0.169143	−	0.631250i	−0.997475	−	0.0710132i	$-0.977377\pi$
$739$	−4.59808	−	17.1603i	−0.169143	−	0.631250i	0.828332	−	0.560237i	$-0.189290\pi$
$740$	−2.68973			−0.0988763
$741$		0			0
$742$	−0.660254			−0.0242387
$743$	13.3199	+	49.7105i	0.488659	+	1.82370i	0.562984	+	0.826467i	$0.309653\pi$
$743$	13.3199	+	49.7105i	0.488659	+	1.82370i	−0.0743251	+	0.997234i	$0.523680\pi$
$744$		0			0
$745$	15.0000	−	8.66025i	0.549557	−	0.317287i
$746$	2.92996	−	2.92996i	0.107274	−	0.107274i
$747$		0			0
$748$	−14.1962	−	3.80385i	−0.519063	−	0.139082i
$749$	−1.41421	−	1.41421i	−0.0516742	−	0.0516742i
$750$		0			0
$751$	−5.66025	−	3.26795i	−0.206546	−	0.119249i	0.393159	−	0.919470i	$-0.371382\pi$
$751$	−5.66025	−	3.26795i	−0.206546	−	0.119249i	−0.599705	+	0.800221i	$0.704715\pi$
$752$	6.24384	−	1.67303i	0.227690	−	0.0610092i
$753$		0			0
$754$	26.3923	+	8.92820i	0.961151	+	0.325146i
$755$		−	0.277401i		−	0.0100957i
$756$		0			0
$757$	9.59808	−	16.6244i	0.348848	−	0.604222i	−0.637197	−	0.770701i	$-0.719906\pi$
$757$	9.59808	−	16.6244i	0.348848	−	0.604222i	0.986045	+	0.166478i	$0.0532396\pi$
$758$	−13.5044	−	23.3903i	−0.490501	−	0.849573i
$759$		0			0
$760$	−0.232051	+	0.866025i	−0.00841737	+	0.0314140i
$761$	5.67544	−	21.1810i	0.205734	−	0.767811i	−0.783490	−	0.621404i	$-0.786562\pi$
$761$	5.67544	−	21.1810i	0.205734	−	0.767811i	0.989224	−	0.146407i	$-0.0467709\pi$
$762$		0			0
$763$	−2.66025	−	4.60770i	−0.0963077	−	0.166810i
$764$	0.240237	−	0.416102i	0.00869146	−	0.0150540i
$765$		0			0
$766$			11.4641i			0.414215i
$767$	11.8313	+	4.00240i	0.427205	+	0.144518i
$768$		0			0
$769$	25.0263	−	6.70577i	0.902471	−	0.241816i	0.222394	−	0.974957i	$-0.428613\pi$
$769$	25.0263	−	6.70577i	0.902471	−	0.241816i	0.680077	+	0.733141i	$0.261946\pi$
$770$	−2.32937	−	1.34486i	−0.0839447	−	0.0484655i
$771$		0			0
$772$	8.53590	+	8.53590i	0.307214	+	0.307214i
$773$	−6.10514	−	1.63587i	−0.219587	−	0.0588381i	0.147348	−	0.989085i	$-0.452926\pi$
$773$	−6.10514	−	1.63587i	−0.219587	−	0.0588381i	−0.366935	+	0.930247i	$0.619593\pi$
$774$		0			0
$775$	0.732051	−	0.732051i	0.0262960	−	0.0262960i
$776$	−6.69213	+	3.86370i	−0.240233	+	0.138699i
$777$		0			0
$778$	5.12436	+	19.1244i	0.183717	+	0.685641i
$779$	−8.00481			−0.286802
$780$		0			0
$781$	−10.3923			−0.371866
$782$	1.79315	+	6.69213i	0.0641229	+	0.239310i
$783$		0			0
$784$	−5.83013	+	3.36603i	−0.208219	+	0.120215i
$785$	−12.9546	+	12.9546i	−0.462368	+	0.462368i
$786$		0			0
$787$	39.8564	+	10.6795i	1.42073	+	0.380683i	0.885742	−	0.464178i	$-0.153650\pi$
$787$	39.8564	+	10.6795i	1.42073	+	0.380683i	0.534986	+	0.844861i	$0.320317\pi$
$788$	7.53794	+	7.53794i	0.268528	+	0.268528i
$789$		0			0
$790$	0.803848	+	0.464102i	0.0285996	+	0.0165120i
$791$	3.86370	−	1.03528i	0.137377	−	0.0368102i
$792$		0			0
$793$	24.1244	−	11.9282i	0.856681	−	0.423583i
$794$		−	16.9062i		−	0.599978i
$795$		0			0
$796$	−11.1962	+	19.3923i	−0.396837	+	0.687342i
$797$	−3.15660	−	5.46739i	−0.111812	−	0.193665i	0.804689	−	0.593697i	$-0.202332\pi$
$797$	−3.15660	−	5.46739i	−0.111812	−	0.193665i	−0.916501	+	0.400032i	$0.868999\pi$
$798$		0			0
$799$	−4.73205	+	17.6603i	−0.167408	+	0.624775i
$800$	0.258819	−	0.965926i	0.00915064	−	0.0341506i
$801$		0			0
$802$	−8.86603	−	15.3564i	−0.313070	−	0.542254i
$803$	−34.7733	+	60.2292i	−1.22712	+	2.12544i
$804$		0			0
$805$			1.26795i			0.0446893i
$806$	3.10583	+	2.07055i	0.109398	+	0.0729321i
$807$		0			0
$808$	−2.73205	+	0.732051i	−0.0961132	+	0.0257535i
$809$	−6.60420	−	3.81294i	−0.232191	−	0.134056i	0.379391	−	0.925236i	$-0.376133\pi$
$809$	−6.60420	−	3.81294i	−0.232191	−	0.134056i	−0.611583	+	0.791181i	$0.709467\pi$
$810$		0			0
$811$	1.97372	+	1.97372i	0.0693067	+	0.0693067i	0.740910	−	0.671604i	$-0.234394\pi$
$811$	1.97372	+	1.97372i	0.0693067	+	0.0693067i	−0.671604	+	0.740910i	$0.734394\pi$
$812$	−3.86370	−	1.03528i	−0.135589	−	0.0363311i
$813$		0			0
$814$	9.88269	−	9.88269i	0.346388	−	0.346388i
$815$	7.34847	−	4.24264i	0.257406	−	0.148613i
$816$		0			0
$817$	−0.124356	−	0.464102i	−0.00435065	−	0.0162369i
$818$	3.44760			0.120543
$819$		0			0
$820$	8.92820			0.311786
$821$	8.52245	+	31.8062i	0.297435	+	1.11004i	0.939264	+	0.343196i	$0.111509\pi$
$821$	8.52245	+	31.8062i	0.297435	+	1.11004i	−0.641828	+	0.766848i	$0.721824\pi$
$822$		0			0
$823$	16.7942	−	9.69615i	0.585410	−	0.337987i	−0.177870	−	0.984054i	$-0.556921\pi$
$823$	16.7942	−	9.69615i	0.585410	−	0.337987i	0.763280	+	0.646067i	$0.223587\pi$
$824$	2.50026	−	2.50026i	0.0871006	−	0.0871006i
$825$		0			0
$826$	−1.73205	−	0.464102i	−0.0602658	−	0.0161482i
$827$	−29.2180	−	29.2180i	−1.01601	−	1.01601i	−0.999870	−	0.0161401i	$-0.994862\pi$
$827$	−29.2180	−	29.2180i	−1.01601	−	1.01601i	−0.0161401	−	0.999870i	$-0.505138\pi$
$828$		0			0
$829$	−40.6410	−	23.4641i	−1.41152	−	0.814942i	−0.415989	−	0.909370i	$-0.636565\pi$
$829$	−40.6410	−	23.4641i	−1.41152	−	0.814942i	−0.995532	+	0.0944277i	$0.969898\pi$
$830$	−11.5911	+	3.10583i	−0.402333	+	0.107805i
$831$		0			0
$832$	3.59808	+	0.232051i	0.124741	+	0.00804491i
$833$		−	19.0411i		−	0.659736i
$834$		0			0
$835$	−0.133975	+	0.232051i	−0.00463638	+	0.00803045i
$836$	−2.32937	−	4.03459i	−0.0805630	−	0.139539i
$837$		0			0
$838$	8.09808	−	30.2224i	0.279743	−	1.04402i
$839$	2.86559	−	10.6945i	0.0989312	−	0.369216i	−0.898655	−	0.438656i	$-0.855455\pi$
$839$	2.86559	−	10.6945i	0.0989312	−	0.369216i	0.997586	+	0.0694400i	$0.0221212\pi$
$840$		0			0
$841$	15.3564	+	26.5981i	0.529531	+	0.917175i
$842$	13.3843	−	23.1822i	0.461252	−	0.798912i
$843$		0			0
$844$			12.8564i			0.442536i
$845$	10.2970	−	7.93546i	0.354228	−	0.272988i
$846$		0			0
$847$	8.00000	−	2.14359i	0.274883	−	0.0736547i
$848$	1.10463	+	0.637756i	0.0379330	+	0.0219006i
$849$		0			0
$850$	2.00000	+	2.00000i	0.0685994	+	0.0685994i
$851$	−6.36396	−	1.70522i	−0.218154	−	0.0584541i
$852$		0			0
$853$	26.3205	−	26.3205i	0.901197	−	0.901197i	−0.0943427	−	0.995540i	$-0.530075\pi$
$853$	26.3205	−	26.3205i	0.901197	−	0.901197i	0.995540	+	0.0943427i	$0.0300750\pi$
$854$	−3.34607	+	1.93185i	−0.114500	+	0.0661066i
$855$		0			0
$856$	1.00000	+	3.73205i	0.0341793	+	0.127559i
$857$	−38.9144			−1.32929			−0.664646	−	0.747159i	$-0.731418\pi$
$857$	−38.9144			−1.32929			−0.664646	+	0.747159i	$0.731418\pi$
$858$		0			0
$859$	−10.2154			−0.348545			−0.174272	−	0.984697i	$-0.555757\pi$
$859$	−10.2154			−0.348545			−0.174272	+	0.984697i	$0.555757\pi$
$860$	0.138701	+	0.517638i	0.00472965	+	0.0176513i
$861$		0			0
$862$	−12.5885	+	7.26795i	−0.428765	+	0.247547i
$863$	11.6926	−	11.6926i	0.398022	−	0.398022i	−0.479513	−	0.877535i	$-0.659187\pi$
$863$	11.6926	−	11.6926i	0.398022	−	0.398022i	0.877535	+	0.479513i	$0.159187\pi$
$864$		0			0
$865$	22.9904	+	6.16025i	0.781696	+	0.209455i
$866$	−1.03528	−	1.03528i	−0.0351801	−	0.0351801i
$867$		0			0
$868$	−0.464102	−	0.267949i	−0.0157526	−	0.00909479i
$869$	−4.65874	+	1.24831i	−0.158037	+	0.0423459i
$870$		0			0
$871$	−6.92820	−	34.6410i	−0.234753	−	1.17377i
$872$			10.2784i			0.348072i
$873$		0			0
$874$	−1.09808	+	1.90192i	−0.0371430	+	0.0643335i
$875$	0.258819	+	0.448288i	0.00874968	+	0.0151549i
$876$		0			0
$877$	3.09808	−	11.5622i	0.104615	−	0.390427i	−0.893687	−	0.448692i	$-0.851890\pi$
$877$	3.09808	−	11.5622i	0.104615	−	0.390427i	0.998301	+	0.0582648i	$0.0185568\pi$
$878$	6.83083	−	25.4930i	0.230529	−	0.860347i
$879$		0			0
$880$	2.59808	+	4.50000i	0.0875811	+	0.151695i
$881$	−7.74599	+	13.4164i	−0.260969	+	0.452012i	−0.966500	−	0.256668i	$-0.917375\pi$
$881$	−7.74599	+	13.4164i	−0.260969	+	0.452012i	0.705531	+	0.708679i	$0.250709\pi$
$882$		0			0
$883$			29.7128i			0.999916i	0.866050	+	0.499958i	$0.166651\pi$
$883$			29.7128i			0.999916i	−0.866050	+	0.499958i	$0.833349\pi$
$884$	−5.65685	+	8.48528i	−0.190261	+	0.285391i
$885$		0			0
$886$	−15.1962	+	4.07180i	−0.510525	+	0.136795i
$887$	39.3120	+	22.6968i	1.31997	+	0.762083i	0.983723	−	0.179692i	$-0.0575102\pi$
$887$	39.3120	+	22.6968i	1.31997	+	0.762083i	0.336243	+	0.941775i	$0.390844\pi$
$888$		0			0
$889$	−2.75833	−	2.75833i	−0.0925114	−	0.0925114i
$890$	−12.4183	−	3.32748i	−0.416264	−	0.111537i
$891$		0			0
$892$	19.2942	−	19.2942i	0.646019	−	0.646019i
$893$	−5.01910	+	2.89778i	−0.167958	+	0.0969704i
$894$		0			0
$895$	−6.63397	−	24.7583i	−0.221749	−	0.827580i
$896$	−0.517638			−0.0172931
$897$		0			0
$898$	6.07180			0.202618
$899$	2.07055	+	7.72741i	0.0690568	+	0.257723i
$900$		0			0
$901$	−3.12436	+	1.80385i	−0.104087	+	0.0600949i
$902$	−32.8043	+	32.8043i	−1.09226	+	1.09226i
$903$		0			0
$904$	−7.46410	−	2.00000i	−0.248252	−	0.0665190i
$905$	11.9700	+	11.9700i	0.397898	+	0.397898i
$906$		0			0
$907$	−6.46410	−	3.73205i	−0.214637	−	0.123921i	0.388828	−	0.921311i	$-0.372880\pi$
$907$	−6.46410	−	3.73205i	−0.214637	−	0.123921i	−0.603465	+	0.797390i	$0.706214\pi$
$908$	20.0764	−	5.37945i	0.666258	−	0.178523i
$909$		0			0
$910$	−1.40192	+	1.23205i	−0.0464733	+	0.0408421i
$911$		−	23.7370i		−	0.786443i	−0.919444	−	0.393221i	$-0.871361\pi$
$911$		−	23.7370i		−	0.786443i	0.919444	−	0.393221i	$-0.128639\pi$
$912$		0			0
$913$	31.1769	−	54.0000i	1.03181	−	1.78714i
$914$	−5.79555	−	10.0382i	−0.191700	−	0.332034i
$915$		0			0
$916$	−1.87564	+	7.00000i	−0.0619730	+	0.231287i
$917$	−2.67114	+	9.96885i	−0.0882089	+	0.329200i
$918$		0			0
$919$	−21.7846	−	37.7321i	−0.718608	−	1.24467i	−0.961551	−	0.274625i	$-0.911446\pi$
$919$	−21.7846	−	37.7321i	−0.718608	−	1.24467i	0.242943	−	0.970040i	$-0.421887\pi$
$920$	1.22474	−	2.12132i	0.0403786	−	0.0699379i
$921$		0			0
$922$		−	4.78461i		−	0.157573i
$923$	−2.31079	+	6.83083i	−0.0760605	+	0.224840i
$924$		0			0
$925$	−2.59808	+	0.696152i	−0.0854242	+	0.0228894i
$926$	−35.5820	−	20.5433i	−1.16930	−	0.675093i
$927$		0			0
$928$	5.46410	+	5.46410i	0.179368	+	0.179368i
$929$	−5.93426	−	1.59008i	−0.194697	−	0.0521688i	0.160153	−	0.987092i	$-0.448801\pi$
$929$	−5.93426	−	1.59008i	−0.194697	−	0.0521688i	−0.354850	+	0.934923i	$0.615468\pi$
$930$		0			0
$931$	4.26795	−	4.26795i	0.139876	−	0.139876i
$932$	16.2499	−	9.38186i	0.532282	−	0.307313i
$933$		0			0
$934$	−7.26795	−	27.1244i	−0.237815	−	0.887536i
$935$	−14.6969			−0.480641
$936$		0			0
$937$	31.5692			1.03132			0.515661	−	0.856793i	$-0.327547\pi$
$937$	31.5692			1.03132			0.515661	+	0.856793i	$0.327547\pi$
$938$	1.31268	+	4.89898i	0.0428604	+	0.159957i
$939$		0			0
$940$	5.59808	−	3.23205i	0.182589	−	0.105418i
$941$	4.41851	−	4.41851i	0.144039	−	0.144039i	−0.631410	−	0.775449i	$-0.717523\pi$
$941$	4.41851	−	4.41851i	0.144039	−	0.144039i	0.775449	+	0.631410i	$0.217523\pi$
$942$		0			0
$943$	21.1244	+	5.66025i	0.687904	+	0.184323i
$944$	2.44949	+	2.44949i	0.0797241	+	0.0797241i
$945$		0			0
$946$	−2.41154	−	1.39230i	−0.0784060	−	0.0452677i
$947$	−12.1087	+	3.24453i	−0.393481	+	0.105433i	−0.450134	−	0.892961i	$-0.648624\pi$
$947$	−12.1087	+	3.24453i	−0.393481	+	0.105433i	0.0566528	+	0.998394i	$0.481957\pi$
$948$		0			0
$949$	31.8564	+	36.2487i	1.03410	+	1.17668i
$950$			0.896575i			0.0290887i
$951$		0			0
$952$	0.732051	−	1.26795i	0.0237259	−	0.0410945i
$953$	−2.68973	−	4.65874i	−0.0871288	−	0.150911i	0.819168	−	0.573554i	$-0.194436\pi$
$953$	−2.68973	−	4.65874i	−0.0871288	−	0.150911i	−0.906296	+	0.422643i	$0.861102\pi$
$954$		0			0
$955$	0.124356	−	0.464102i	0.00402405	−	0.0150180i
$956$	2.48665	−	9.28032i	0.0804242	−	0.300147i
$957$		0			0
$958$	15.4641	+	26.7846i	0.499622	+	0.865371i
$959$	1.41421	−	2.44949i	0.0456673	−	0.0790981i
$960$		0			0
$961$		−	29.9282i		−	0.965426i
$962$	−4.29839	−	8.69333i	−0.138586	−	0.280284i
$963$		0			0
$964$	−1.96410	+	0.526279i	−0.0632595	+	0.0169503i
$965$	10.4543	+	6.03579i	0.336536	+	0.194299i
$966$		0			0
$967$	−42.3468	−	42.3468i	−1.36178	−	1.36178i	−0.871647	−	0.490134i	$-0.836948\pi$
$967$	−42.3468	−	42.3468i	−1.36178	−	1.36178i	−0.490134	−	0.871647i	$-0.663052\pi$
$968$	−15.4548	−	4.14110i	−0.496737	−	0.133100i
$969$		0			0
$970$	−5.46410	+	5.46410i	−0.175442	+	0.175442i
$971$	28.6174	−	16.5223i	0.918377	−	0.530225i	0.0352599	−	0.999378i	$-0.488774\pi$
$971$	28.6174	−	16.5223i	0.918377	−	0.530225i	0.883117	+	0.469153i	$0.155441\pi$
$972$		0			0
$973$	1.37564	+	5.13397i	0.0441011	+	0.164588i
$974$	12.2846			0.393624
$975$		0			0
$976$	7.46410			0.238920
$977$	−10.4543	−	39.0160i	−0.334463	−	1.24823i	−0.904451	−	0.426578i	$-0.859719\pi$
$977$	−10.4543	−	39.0160i	−0.334463	−	1.24823i	0.569988	−	0.821653i	$-0.306948\pi$
$978$		0			0
$979$	57.8538	−	33.4019i	1.84902	−	1.06753i
$980$	−4.76028	+	4.76028i	−0.152062	+	0.152062i
$981$		0			0
$982$	−36.7224	−	9.83975i	−1.17186	−	0.313999i
$983$	2.84203	+	2.84203i	0.0906467	+	0.0906467i	0.750976	−	0.660329i	$-0.229583\pi$
$983$	2.84203	+	2.84203i	0.0906467	+	0.0906467i	−0.660329	+	0.750976i	$0.729583\pi$
$984$		0			0
$985$	9.23205	+	5.33013i	0.294158	+	0.169832i
$986$	−21.1117	+	5.65685i	−0.672332	+	0.180151i
$987$		0			0
$988$	−3.16987	+	0.633975i	−0.100847	+	0.0201694i
$989$			1.31268i			0.0417407i
$990$		0			0
$991$	−3.92820	+	6.80385i	−0.124783	+	0.216131i	−0.921648	−	0.388026i	$-0.873157\pi$
$991$	−3.92820	+	6.80385i	−0.124783	+	0.216131i	0.796865	+	0.604158i	$0.206490\pi$
$992$	0.517638	+	0.896575i	0.0164350	+	0.0284663i
$993$		0			0
$994$	0.267949	−	1.00000i	0.00849883	−	0.0317181i
$995$	−5.79555	+	21.6293i	−0.183731	+	0.685695i
$996$		0			0
$997$	−1.33013	−	2.30385i	−0.0421255	−	0.0729636i	0.844194	−	0.536038i	$-0.180080\pi$
$997$	−1.33013	−	2.30385i	−0.0421255	−	0.0729636i	−0.886319	+	0.463074i	$0.846746\pi$
$998$	−13.9527	+	24.1667i	−0.441664	+	0.764984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.d.1151.2	yes	8
3.2	odd	2	inner	1170.2.cu.d.1151.1	yes	8
13.2	odd	12	inner	1170.2.cu.d.431.1	✓	8
39.2	even	12	inner	1170.2.cu.d.431.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.d.431.1	✓	8	13.2	odd	12	inner
1170.2.cu.d.431.2	yes	8	39.2	even	12	inner
1170.2.cu.d.1151.1	yes	8	3.2	odd	2	inner
1170.2.cu.d.1151.2	yes	8	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.500000 + 0.133975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.500000 + 0.133975i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(5.01910 - 1.34486i) q^{11} +(0.232051 - 3.59808i) q^{13} +0.517638i q^{14} +(0.500000 - 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-0.232051 + 0.866025i) q^{19} +(0.258819 - 0.965926i) q^{20} +(2.59808 + 4.50000i) q^{22} +(1.22474 - 2.12132i) q^{23} -1.00000i q^{25} +(3.53553 - 0.707107i) q^{26} +(-0.500000 + 0.133975i) q^{28} +(6.69213 + 3.86370i) q^{29} +(0.732051 + 0.732051i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-2.00000 + 2.00000i) q^{34} +(-0.448288 + 0.258819i) q^{35} +(-0.696152 - 2.59808i) q^{37} -0.896575 q^{38} +1.00000 q^{40} +(2.31079 + 8.62398i) q^{41} +(-0.464102 + 0.267949i) q^{43} +(-3.67423 + 3.67423i) q^{44} +(2.36603 + 0.633975i) q^{46} +(4.57081 + 4.57081i) q^{47} +(-5.83013 - 3.36603i) q^{49} +(0.965926 - 0.258819i) q^{50} +(1.59808 + 3.23205i) q^{52} +1.27551i q^{53} +(-2.59808 + 4.50000i) q^{55} +(-0.258819 - 0.448288i) q^{56} +(-2.00000 + 7.46410i) q^{58} +(-0.896575 + 3.34607i) q^{59} +(3.73205 + 6.46410i) q^{61} +(-0.517638 + 0.896575i) q^{62} +1.00000i q^{64} +(2.38014 + 2.70831i) q^{65} +(9.46410 - 2.53590i) q^{67} +(-2.44949 - 1.41421i) q^{68} +(-0.366025 - 0.366025i) q^{70} +(-1.93185 - 0.517638i) q^{71} +(-9.46410 + 9.46410i) q^{73} +(2.32937 - 1.34486i) q^{74} +(-0.232051 - 0.866025i) q^{76} +2.68973 q^{77} -0.928203 q^{79} +(0.258819 + 0.965926i) q^{80} +(-7.73205 + 4.46410i) q^{82} +(8.48528 - 8.48528i) q^{83} +(-2.73205 - 0.732051i) q^{85} +(-0.378937 - 0.378937i) q^{86} +(-4.50000 - 2.59808i) q^{88} +(12.4183 - 3.32748i) q^{89} +(0.598076 - 1.76795i) q^{91} +2.44949i q^{92} +(-3.23205 + 5.59808i) q^{94} +(-0.448288 - 0.776457i) q^{95} +(2.00000 - 7.46410i) q^{97} +(1.74238 - 6.50266i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 12 q^{13} + 4 q^{16} + 12 q^{19} - 4 q^{28} - 8 q^{31} - 16 q^{34} + 36 q^{37} + 8 q^{40} + 24 q^{43} + 12 q^{46} - 12 q^{49} - 8 q^{52} - 16 q^{58} + 16 q^{61} + 48 q^{67} + 4 q^{70} - 48 q^{73} + 12 q^{76} + 48 q^{79} - 48 q^{82} - 8 q^{85} - 36 q^{88} - 16 q^{91} - 12 q^{94} + 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 12 * q^13 + 4 * q^16 + 12 * q^19 - 4 * q^28 - 8 * q^31 - 16 * q^34 + 36 * q^37 + 8 * q^40 + 24 * q^43 + 12 * q^46 - 12 * q^49 - 8 * q^52 - 16 * q^58 + 16 * q^61 + 48 * q^67 + 4 * q^70 - 48 * q^73 + 12 * q^76 + 48 * q^79 - 48 * q^82 - 8 * q^85 - 36 * q^88 - 16 * q^91 - 12 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more