LMFDB - Embedded newform 441.2.u.e.379.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			379.6
Character	$\chi$	$=$	441.379
Dual form			441.2.u.e.64.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.131442 + 0.575886i) q^{2} +(1.48757 - 0.716376i) q^{4} +(-1.01472 - 1.27242i) q^{5} +(2.21270 + 1.45050i) q^{7} +(1.34467 + 1.68616i) q^{8} +O(q^{10})$	\(q+(0.131442 + 0.575886i) q^{2} +(1.48757 - 0.716376i) q^{4} +(-1.01472 - 1.27242i) q^{5} +(2.21270 + 1.45050i) q^{7} +(1.34467 + 1.68616i) q^{8} +(0.599392 - 0.751614i) q^{10} +(-1.34004 - 5.87109i) q^{11} +(0.430296 + 1.88525i) q^{13} +(-0.544483 + 1.46492i) q^{14} +(1.26457 - 1.58572i) q^{16} +(5.24693 + 2.52679i) q^{17} -1.43943 q^{19} +(-2.42100 - 1.16589i) q^{20} +(3.20494 - 1.54342i) q^{22} +(-0.615561 + 0.296439i) q^{23} +(0.523209 - 2.29233i) q^{25} +(-1.02913 + 0.495603i) q^{26} +(4.33065 + 0.572602i) q^{28} +(-1.77848 - 0.856469i) q^{29} +1.60503 q^{31} +(4.96561 + 2.39131i) q^{32} +(-0.765473 + 3.35376i) q^{34} +(-0.399623 - 4.28735i) q^{35} +(-2.43336 - 1.17185i) q^{37} +(-0.189202 - 0.828948i) q^{38} +(0.781041 - 3.42196i) q^{40} +(2.74509 + 3.44223i) q^{41} +(3.73601 - 4.68481i) q^{43} +(-6.19931 - 7.77369i) q^{44} +(-0.251625 - 0.315528i) q^{46} +(2.60349 + 11.4066i) q^{47} +(2.79208 + 6.41906i) q^{49} +1.38889 q^{50} +(1.99064 + 2.49619i) q^{52} +(-10.9470 + 5.27178i) q^{53} +(-6.11074 + 7.66263i) q^{55} +(0.529563 + 5.68140i) q^{56} +(0.259462 - 1.13678i) q^{58} +(-5.38363 + 6.75085i) q^{59} +(-11.0773 - 5.33453i) q^{61} +(0.210968 + 0.924313i) q^{62} +(0.178210 - 0.780789i) q^{64} +(1.96220 - 2.46052i) q^{65} +1.47235 q^{67} +9.61530 q^{68} +(2.41649 - 0.793675i) q^{70} +(0.575382 - 0.277090i) q^{71} +(-2.60092 + 11.3954i) q^{73} +(0.355003 - 1.55537i) q^{74} +(-2.14126 + 1.03117i) q^{76} +(5.55094 - 14.9347i) q^{77} -12.3614 q^{79} -3.30090 q^{80} +(-1.62151 + 2.03331i) q^{82} +(2.03882 - 8.93264i) q^{83} +(-2.10904 - 9.24030i) q^{85} +(3.18898 + 1.53573i) q^{86} +(8.09768 - 10.1542i) q^{88} +(3.61486 - 15.8378i) q^{89} +(-1.78245 + 4.79564i) q^{91} +(-0.703329 + 0.881947i) q^{92} +(-6.22671 + 2.99863i) q^{94} +(1.46062 + 1.83156i) q^{95} -11.2648 q^{97} +(-3.32965 + 2.45165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) $ 60 * q - 12 * q^4 - 2 * q^7	$ 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) $ 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	0.131442	+	0.575886i	0.0929436	+	0.407213i	0.999902	−	0.0140078i	$-0.00445898\pi$
$2$	0.131442	+	0.575886i	0.0929436	+	0.407213i	−0.906958	+	0.421221i	$0.861602\pi$
$3$		0			0
$3$		0			0
$4$	1.48757	−	0.716376i	0.743785	−	0.358188i
$5$	−1.01472	−	1.27242i	−0.453798	−	0.569044i	0.501323	−	0.865260i	$-0.332847\pi$
$5$	−1.01472	−	1.27242i	−0.453798	−	0.569044i	−0.955121	+	0.296216i	$0.904275\pi$
$6$		0			0
$7$	2.21270	+	1.45050i	0.836322	+	0.548239i
$7$	2.21270	+	1.45050i	0.836322	+	0.548239i
$8$	1.34467	+	1.68616i	0.475411	+	0.596147i
$9$		0			0
$10$	0.599392	−	0.751614i	0.189545	−	0.237681i
$11$	−1.34004	−	5.87109i	−0.404037	−	1.77020i	−0.610775	−	0.791805i	$-0.709142\pi$
$11$	−1.34004	−	5.87109i	−0.404037	−	1.77020i	0.206738	−	0.978396i	$-0.433715\pi$
$12$		0			0
$13$	0.430296	+	1.88525i	0.119343	+	0.522874i	0.998892	+	0.0470662i	$0.0149872\pi$
$13$	0.430296	+	1.88525i	0.119343	+	0.522874i	−0.879549	+	0.475808i	$0.842156\pi$
$14$	−0.544483	+	1.46492i	−0.145519	+	0.391516i
$15$		0			0
$16$	1.26457	−	1.58572i	0.316143	−	0.396431i
$17$	5.24693	+	2.52679i	1.27257	+	0.612836i	0.943469	−	0.331460i	$-0.107541\pi$
$17$	5.24693	+	2.52679i	1.27257	+	0.612836i	0.329098	+	0.944296i	$0.393255\pi$
$18$		0			0
$19$	−1.43943			−0.330228			−0.165114	−	0.986274i	$-0.552799\pi$
$19$	−1.43943			−0.330228			−0.165114	+	0.986274i	$0.552799\pi$
$20$	−2.42100	−	1.16589i	−0.541353	−	0.260702i
$21$		0			0
$22$	3.20494	−	1.54342i	0.683296	−	0.329058i
$23$	−0.615561	+	0.296439i	−0.128353	+	0.0618117i	−0.496958	−	0.867774i	$-0.665550\pi$
$23$	−0.615561	+	0.296439i	−0.128353	+	0.0618117i	0.368605	+	0.929586i	$0.379836\pi$
$24$		0			0
$25$	0.523209	−	2.29233i	0.104642	−	0.458466i
$26$	−1.02913	+	0.495603i	−0.201829	+	0.0971957i
$27$		0			0
$28$	4.33065	+	0.572602i	0.818416	+	0.108212i
$29$	−1.77848	−	0.856469i	−0.330255	−	0.159042i	0.261407	−	0.965229i	$-0.415814\pi$
$29$	−1.77848	−	0.856469i	−0.330255	−	0.159042i	−0.591662	+	0.806186i	$0.701528\pi$
$30$		0			0
$31$	1.60503			0.288272			0.144136	−	0.989558i	$-0.453960\pi$
$31$	1.60503			0.288272			0.144136	+	0.989558i	$0.453960\pi$
$32$	4.96561	+	2.39131i	0.877804	+	0.422728i
$33$		0			0
$34$	−0.765473	+	3.35376i	−0.131278	+	0.575165i
$35$	−0.399623	−	4.28735i	−0.0675486	−	0.724694i
$36$		0			0
$37$	−2.43336	−	1.17185i	−0.400042	−	0.192650i	0.223035	−	0.974810i	$-0.428404\pi$
$37$	−2.43336	−	1.17185i	−0.400042	−	0.192650i	−0.623077	+	0.782160i	$0.714118\pi$
$38$	−0.189202	−	0.828948i	−0.0306926	−	0.134473i
$39$		0			0
$40$	0.781041	−	3.42196i	0.123493	−	0.541060i
$41$	2.74509	+	3.44223i	0.428710	+	0.537586i	0.948529	−	0.316691i	$-0.102572\pi$
$41$	2.74509	+	3.44223i	0.428710	+	0.537586i	−0.519818	+	0.854277i	$0.674000\pi$
$42$		0			0
$43$	3.73601	−	4.68481i	0.569736	−	0.714427i	−0.410588	−	0.911821i	$-0.634676\pi$
$43$	3.73601	−	4.68481i	0.569736	−	0.714427i	0.980324	+	0.197394i	$0.0632479\pi$
$44$	−6.19931	−	7.77369i	−0.934581	−	1.17193i
$45$		0			0
$46$	−0.251625	−	0.315528i	−0.0371002	−	0.0465221i
$47$	2.60349	+	11.4066i	0.379758	+	1.66383i	0.698212	+	0.715891i	$0.253979\pi$
$47$	2.60349	+	11.4066i	0.379758	+	1.66383i	−0.318454	+	0.947938i	$0.603164\pi$
$48$		0			0
$49$	2.79208	+	6.41906i	0.398868	+	0.917008i
$50$	1.38889			0.196419
$51$		0			0
$52$	1.99064	+	2.49619i	0.276053	+	0.346159i
$53$	−10.9470	+	5.27178i	−1.50368	+	0.724134i	−0.990927	−	0.134402i	$-0.957089\pi$
$53$	−10.9470	+	5.27178i	−1.50368	+	0.724134i	−0.512753	+	0.858536i	$0.671374\pi$
$54$		0			0
$55$	−6.11074	+	7.66263i	−0.823972	+	1.03323i
$56$	0.529563	+	5.68140i	0.0707658	+	0.759209i
$57$		0			0
$58$	0.259462	−	1.13678i	0.0340690	−	0.149266i
$59$	−5.38363	+	6.75085i	−0.700889	+	0.878886i	−0.997090	−	0.0762392i	$-0.975709\pi$
$59$	−5.38363	+	6.75085i	−0.700889	+	0.878886i	0.296201	+	0.955126i	$0.404280\pi$
$60$		0			0
$61$	−11.0773	−	5.33453i	−1.41830	−	0.683017i	−0.441517	−	0.897253i	$-0.645559\pi$
$61$	−11.0773	−	5.33453i	−1.41830	−	0.683017i	−0.976782	+	0.214237i	$0.931274\pi$
$62$	0.210968	+	0.924313i	0.0267930	+	0.117388i
$63$		0			0
$64$	0.178210	−	0.780789i	0.0222762	−	0.0975986i
$65$	1.96220	−	2.46052i	0.243381	−	0.305191i
$66$		0			0
$67$	1.47235			0.179876			0.0899380	−	0.995947i	$-0.471333\pi$
$67$	1.47235			0.179876			0.0899380	+	0.995947i	$0.471333\pi$
$68$	9.61530			1.16603
$69$		0			0
$70$	2.41649	−	0.793675i	0.288826	−	0.0948623i
$71$	0.575382	−	0.277090i	0.0682853	−	0.0328845i	−0.399429	−	0.916764i	$-0.630792\pi$
$71$	0.575382	−	0.277090i	0.0682853	−	0.0328845i	0.467715	+	0.883879i	$0.345077\pi$
$72$		0			0
$73$	−2.60092	+	11.3954i	−0.304415	+	1.33373i	0.558973	+	0.829186i	$0.311196\pi$
$73$	−2.60092	+	11.3954i	−0.304415	+	1.33373i	−0.863387	+	0.504542i	$0.831662\pi$
$74$	0.355003	−	1.55537i	0.0412682	−	0.180808i
$75$		0			0
$76$	−2.14126	+	1.03117i	−0.245619	+	0.118284i
$77$	5.55094	−	14.9347i	0.632588	−	1.70197i
$78$		0			0
$79$	−12.3614			−1.39077			−0.695383	−	0.718640i	$-0.744765\pi$
$79$	−12.3614			−1.39077			−0.695383	+	0.718640i	$0.744765\pi$
$80$	−3.30090			−0.369052
$81$		0			0
$82$	−1.62151	+	2.03331i	−0.179066	+	0.224541i
$83$	2.03882	−	8.93264i	0.223789	−	0.980485i	−0.730807	−	0.682584i	$-0.760856\pi$
$83$	2.03882	−	8.93264i	0.223789	−	0.980485i	0.954597	−	0.297901i	$-0.0962866\pi$
$84$		0			0
$85$	−2.10904	−	9.24030i	−0.228757	−	1.00225i
$86$	3.18898	+	1.53573i	0.343877	+	0.165602i
$87$		0			0
$88$	8.09768	−	10.1542i	0.863216	−	1.08244i
$89$	3.61486	−	15.8378i	0.383175	−	1.67880i	−0.304289	−	0.952580i	$-0.598419\pi$
$89$	3.61486	−	15.8378i	0.383175	−	1.67880i	0.687463	−	0.726219i	$-0.258724\pi$
$90$		0			0
$91$	−1.78245	+	4.79564i	−0.186851	+	0.502719i
$92$	−0.703329	+	0.881947i	−0.0733271	+	0.0919493i
$93$		0			0
$94$	−6.22671	+	2.99863i	−0.642236	+	0.309285i
$95$	1.46062	+	1.83156i	0.149857	+	0.187914i
$96$		0			0
$97$	−11.2648			−1.14377			−0.571886	−	0.820333i	$-0.693788\pi$
$97$	−11.2648			−1.14377			−0.571886	+	0.820333i	$0.693788\pi$
$98$	−3.32965	+	2.45165i	−0.336345	+	0.247654i
$99$		0			0
$100$	−0.863859	−	3.78481i	−0.0863859	−	0.378481i
$101$	−2.74572	−	3.44303i	−0.273210	−	0.342594i	0.626230	−	0.779638i	$-0.284597\pi$
$101$	−2.74572	−	3.44303i	−0.273210	−	0.342594i	−0.899440	+	0.437044i	$0.856025\pi$
$102$		0			0
$103$	−8.37551	−	10.5026i	−0.825264	−	1.03485i	−0.998749	−	0.0500116i	$-0.984074\pi$
$103$	−8.37551	−	10.5026i	−0.825264	−	1.03485i	0.173485	−	0.984837i	$-0.444497\pi$
$104$	−2.60022	+	3.26058i	−0.254973	+	0.319726i
$105$		0			0
$106$	−4.47483	−	5.61126i	−0.434634	−	0.545014i
$107$	−1.30703	+	5.72649i	−0.126356	+	0.553601i	0.871630	+	0.490164i	$0.163063\pi$
$107$	−1.30703	+	5.72649i	−0.126356	+	0.553601i	−0.997986	+	0.0634364i	$0.979794\pi$
$108$		0			0
$109$	2.20584	+	9.66440i	0.211281	+	0.925681i	0.963698	+	0.266995i	$0.0860306\pi$
$109$	2.20584	+	9.66440i	0.211281	+	0.925681i	−0.752417	+	0.658687i	$0.771112\pi$
$110$	−5.21601	−	2.51190i	−0.497327	−	0.239500i
$111$		0			0
$112$	5.09822	−	1.67446i	0.481736	−	0.158222i
$113$	−2.64758	+	11.5998i	−0.249063	+	1.09122i	0.683426	+	0.730020i	$0.260489\pi$
$113$	−2.64758	+	11.5998i	−0.249063	+	1.09122i	−0.932489	+	0.361198i	$0.882368\pi$
$114$		0			0
$115$	1.00182	+	0.482451i	0.0934201	+	0.0449888i
$116$	−3.25916			−0.302606
$117$		0			0
$118$	−4.59536	−	2.21301i	−0.423037	−	0.203724i
$119$	7.94476	+	13.2017i	0.728295	+	1.21020i
$120$		0			0
$121$	−22.7634	+	10.9623i	−2.06940	+	0.996569i
$122$	1.61606	−	7.08042i	0.146311	−	0.641031i
$123$		0			0
$124$	2.38759	−	1.14980i	0.214412	−	0.103256i
$125$	−10.7793	+	5.19104i	−0.964130	+	0.464301i
$126$		0			0
$127$	−2.43988	−	1.17499i	−0.216504	−	0.104263i	0.322488	−	0.946573i	$-0.395481\pi$
$127$	−2.43988	−	1.17499i	−0.216504	−	0.104263i	−0.538993	+	0.842310i	$0.681195\pi$
$128$	11.4959			1.01610
$129$		0			0
$130$	1.67490	+	0.806588i	0.146898	+	0.0707424i
$131$	−2.77914	+	3.48494i	−0.242815	+	0.304480i	−0.888273	−	0.459315i	$-0.848095\pi$
$131$	−2.77914	+	3.48494i	−0.242815	+	0.304480i	0.645458	+	0.763795i	$0.276666\pi$
$132$		0			0
$133$	−3.18503	−	2.08790i	−0.276177	−	0.181044i
$134$	0.193529	+	0.847904i	0.0167183	+	0.0732478i
$135$		0			0
$136$	2.79480	+	12.2448i	0.239652	+	1.04999i
$137$	2.48800	−	3.11986i	0.212564	−	0.266547i	−0.664106	−	0.747638i	$-0.731188\pi$
$137$	2.48800	−	3.11986i	0.212564	−	0.266547i	0.876671	+	0.481091i	$0.159759\pi$
$138$		0			0
$139$	5.92524	+	7.43001i	0.502572	+	0.630205i	0.966807	−	0.255507i	$-0.0822423\pi$
$139$	5.92524	+	7.43001i	0.502572	+	0.630205i	−0.464235	+	0.885712i	$0.653671\pi$
$140$	−3.66582	−	6.09145i	−0.309818	−	0.514822i
$141$		0			0
$142$	0.235201	+	0.294933i	0.0197377	+	0.0247503i
$143$	10.4919	−	5.05262i	0.877374	−	0.422521i
$144$		0			0
$145$	0.714870	+	3.13205i	0.0593667	+	0.260103i
$146$	−6.90430			−0.571404
$147$		0			0
$148$	−4.45928			−0.366551
$149$	−1.02435	−	4.48799i	−0.0839184	−	0.367671i	0.915480	−	0.402364i	$-0.131812\pi$
$149$	−1.02435	−	4.48799i	−0.0839184	−	0.367671i	−0.999398	+	0.0346938i	$0.988954\pi$
$150$		0			0
$151$	16.4464	−	7.92018i	1.33839	−	0.644535i	0.378681	−	0.925527i	$-0.376378\pi$
$151$	16.4464	−	7.92018i	1.33839	−	0.644535i	0.959710	+	0.280992i	$0.0906635\pi$
$152$	−1.93555	−	2.42711i	−0.156994	−	0.196864i
$153$		0			0
$154$	9.33030	+	1.23366i	0.751857	+	0.0994111i
$155$	−1.62866	−	2.04227i	−0.130817	−	0.164039i
$156$		0			0
$157$	−2.16634	+	2.71651i	−0.172893	+	0.216801i	−0.860727	−	0.509067i	$-0.829990\pi$
$157$	−2.16634	+	2.71651i	−0.172893	+	0.216801i	0.687834	+	0.725868i	$0.258562\pi$
$158$	−1.62481	−	7.11875i	−0.129263	−	0.566337i
$159$		0			0
$160$	−1.99596	−	8.74487i	−0.157794	−	0.691343i
$161$	−1.79204	−	0.236944i	−0.141232	−	0.0186738i
$162$		0			0
$163$	−3.32595	+	4.17061i	−0.260509	+	0.326668i	−0.894834	−	0.446398i	$-0.852706\pi$
$163$	−3.32595	+	4.17061i	−0.260509	+	0.326668i	0.634326	+	0.773066i	$0.281278\pi$
$164$	6.54944	+	3.15404i	0.511425	+	0.246289i
$165$		0			0
$166$	5.41217			0.420066
$167$	−8.11365	−	3.90733i	−0.627853	−	0.302358i	0.0927676	−	0.995688i	$-0.470429\pi$
$167$	−8.11365	−	3.90733i	−0.627853	−	0.302358i	−0.720620	+	0.693330i	$0.756143\pi$
$168$		0			0
$169$	8.34358	−	4.01806i	0.641814	−	0.309081i
$170$	5.04414	−	2.42913i	0.386868	−	0.186306i
$171$		0			0
$172$	2.20149	−	9.64537i	0.167862	−	0.735453i
$173$	0.131925	−	0.0635316i	0.0100301	−	0.00483022i	−0.428862	−	0.903370i	$-0.641085\pi$
$173$	0.131925	−	0.0635316i	0.0100301	−	0.00483022i	0.438892	+	0.898540i	$0.355371\pi$
$174$		0			0
$175$	4.48274	−	4.31332i	0.338863	−	0.326056i
$176$	−11.0045	−	5.29949i	−0.829496	−	0.399464i
$177$		0			0
$178$	9.59588			0.719242
$179$	15.2866	+	7.36166i	1.14258	+	0.550236i	0.906796	−	0.421570i	$-0.138521\pi$
$179$	15.2866	+	7.36166i	1.14258	+	0.550236i	0.235781	+	0.971806i	$0.424235\pi$
$180$		0			0
$181$	−3.78727	+	16.5931i	−0.281505	+	1.23335i	0.614359	+	0.789027i	$0.289415\pi$
$181$	−3.78727	+	16.5931i	−0.281505	+	1.23335i	−0.895864	+	0.444328i	$0.853442\pi$
$182$	−2.99603	−	0.396137i	−0.222080	−	0.0293636i
$183$		0			0
$184$	−1.32757	−	0.639322i	−0.0978695	−	0.0471315i
$185$	0.978106	+	4.28536i	0.0719118	+	0.315066i
$186$		0			0
$187$	7.80392	−	34.1912i	0.570679	−	2.50031i
$188$	12.0443	+	15.1031i	0.878422	+	1.10151i
$189$		0			0
$190$	−0.862784	+	1.08190i	−0.0625929	+	0.0784891i
$191$	5.92491	+	7.42960i	0.428711	+	0.537587i	0.948529	−	0.316690i	$-0.102572\pi$
$191$	5.92491	+	7.42960i	0.428711	+	0.537587i	−0.519818	+	0.854277i	$0.674000\pi$
$192$		0			0
$193$	13.8155	+	17.3241i	0.994462	+	1.24702i	0.968928	+	0.247342i	$0.0795571\pi$
$193$	13.8155	+	17.3241i	0.994462	+	1.24702i	0.0255338	+	0.999674i	$0.491871\pi$
$194$	−1.48068	−	6.48727i	−0.106306	−	0.465759i
$195$		0			0
$196$	8.75187	+	7.54863i	0.625134	+	0.539188i
$197$	1.43284			0.102086			0.0510429	−	0.998696i	$-0.483745\pi$
$197$	1.43284			0.102086			0.0510429	+	0.998696i	$0.483745\pi$
$198$		0			0
$199$	11.7051	+	14.6777i	0.829753	+	1.04048i	0.998496	+	0.0548172i	$0.0174576\pi$
$199$	11.7051	+	14.6777i	0.829753	+	1.04048i	−0.168744	+	0.985660i	$0.553971\pi$
$200$	4.56877	−	2.20020i	0.323061	−	0.155578i
$201$		0			0
$202$	1.62189	−	2.03378i	0.114116	−	0.143096i
$203$	−2.69292	−	4.47480i	−0.189006	−	0.314069i
$204$		0			0
$205$	1.59447	−	6.98581i	0.111362	−	0.487910i
$206$	4.94738	−	6.20382i	0.344700	−	0.432240i
$207$		0			0
$208$	3.53363	+	1.70171i	0.245013	+	0.117992i
$209$	1.92889	+	8.45103i	0.133424	+	0.584570i
$210$		0			0
$211$	4.25437	−	18.6396i	0.292883	−	1.28321i	−0.587609	−	0.809145i	$-0.699931\pi$
$211$	4.25437	−	18.6396i	0.292883	−	1.28321i	0.880492	−	0.474060i	$-0.157212\pi$
$212$	−12.5078	+	15.6843i	−0.859039	+	1.07720i
$213$		0			0
$214$	−3.46960			−0.237177
$215$	−9.75207			−0.665086
$216$		0			0
$217$	3.55145	+	2.32810i	0.241088	+	0.158042i
$218$	−5.27565	+	2.54062i	−0.357312	+	0.172072i
$219$		0			0
$220$	−3.60083	+	15.7763i	−0.242768	+	1.06364i
$221$	−2.50589	+	10.9790i	−0.168565	+	0.738530i
$222$		0			0
$223$	12.6312	−	6.08289i	0.845851	−	0.407340i	0.0398149	−	0.999207i	$-0.487323\pi$
$223$	12.6312	−	6.08289i	0.845851	−	0.407340i	0.806036	+	0.591867i	$0.201609\pi$
$224$	7.51880	+	12.4939i	0.502371	+	0.834783i
$225$		0			0
$226$	−7.02816			−0.467507
$227$	−20.4290			−1.35592			−0.677961	−	0.735098i	$-0.737136\pi$
$227$	−20.4290			−1.35592			−0.677961	+	0.735098i	$0.737136\pi$
$228$		0			0
$229$	−7.26076	+	9.10470i	−0.479804	+	0.601656i	−0.961541	−	0.274660i	$-0.911435\pi$
$229$	−7.26076	+	9.10470i	−0.479804	+	0.601656i	0.481737	+	0.876316i	$0.340006\pi$
$230$	−0.146155	+	0.640348i	−0.00963719	+	0.0422233i
$231$		0			0
$232$	−0.947314	−	4.15046i	−0.0621942	−	0.272491i
$233$	−11.5582	−	5.56613i	−0.757203	−	0.364650i	0.0151153	−	0.999886i	$-0.495188\pi$
$233$	−11.5582	−	5.56613i	−0.757203	−	0.364650i	−0.772318	+	0.635236i	$0.780903\pi$
$234$		0			0
$235$	11.8722	−	14.8873i	0.774459	−	0.971141i
$236$	−3.17237	+	13.8991i	−0.206504	+	0.904753i
$237$		0			0
$238$	−6.55840	+	6.31053i	−0.425118	+	0.409051i
$239$	17.6388	−	22.1183i	1.14096	−	1.43072i	0.255006	−	0.966939i	$-0.417922\pi$
$239$	17.6388	−	22.1183i	1.14096	−	1.43072i	0.885952	−	0.463777i	$-0.153506\pi$
$240$		0			0
$241$	3.16423	−	1.52381i	0.203826	−	0.0981575i	−0.329186	−	0.944265i	$-0.606774\pi$
$241$	3.16423	−	1.52381i	0.203826	−	0.0981575i	0.533012	+	0.846108i	$0.321060\pi$
$242$	−9.30507	−	11.6682i	−0.598153	−	0.750060i
$243$		0			0
$244$	−20.2997			−1.29956
$245$	5.33457	−	10.0663i	0.340813	−	0.643110i
$246$		0			0
$247$	−0.619381	−	2.71369i	−0.0394103	−	0.172668i
$248$	2.15823	+	2.70633i	0.137048	+	0.171852i
$249$		0			0
$250$	−4.40630	−	5.52533i	−0.278679	−	0.349452i
$251$	17.1108	−	21.4562i	1.08002	−	1.35430i	0.149210	−	0.988805i	$-0.452327\pi$
$251$	17.1108	−	21.4562i	1.08002	−	1.35430i	0.930812	−	0.365499i	$-0.119102\pi$
$252$		0			0
$253$	2.56529	+	3.21678i	0.161279	+	0.202237i
$254$	0.355954	−	1.55954i	0.0223345	−	0.0978540i
$255$		0			0
$256$	1.15463	+	5.05874i	0.0721641	+	0.316171i
$257$	15.0660	+	7.25540i	0.939791	+	0.452580i	0.840096	−	0.542438i	$-0.182499\pi$
$257$	15.0660	+	7.25540i	0.939791	+	0.452580i	0.0996956	+	0.995018i	$0.468213\pi$
$258$		0			0
$259$	−3.68453	−	6.12254i	−0.228946	−	0.380436i
$260$	1.15625	−	5.06588i	0.0717078	−	0.314172i
$261$		0			0
$262$	−2.37222	−	1.14240i	−0.146556	−	0.0705778i
$263$	−12.3120			−0.759187			−0.379594	−	0.925153i	$-0.623936\pi$
$263$	−12.3120			−0.759187			−0.379594	+	0.925153i	$0.623936\pi$
$264$		0			0
$265$	17.8161	+	8.57976i	1.09443	+	0.527050i
$266$	0.783745	−	2.10865i	0.0480545	−	0.129290i
$267$		0			0
$268$	2.19022	−	1.05475i	0.133789	−	0.0644294i
$269$	−6.03994	+	26.4627i	−0.368262	+	1.61346i	0.363291	+	0.931676i	$0.381653\pi$
$269$	−6.03994	+	26.4627i	−0.368262	+	1.61346i	−0.731553	+	0.681785i	$0.761204\pi$
$270$		0			0
$271$	3.99782	−	1.92525i	0.242850	−	0.116950i	−0.308500	−	0.951224i	$-0.599827\pi$
$271$	3.99782	−	1.92525i	0.242850	−	0.116950i	0.551350	+	0.834274i	$0.314113\pi$
$272$	10.6419	−	5.12487i	0.645261	−	0.310741i
$273$		0			0
$274$	2.12371	+	1.02272i	0.128298	+	0.0617851i
$275$	−14.1596			−0.853855
$276$		0			0
$277$	−3.82521	−	1.84212i	−0.229834	−	0.110682i	0.315423	−	0.948951i	$-0.397854\pi$
$277$	−3.82521	−	1.84212i	−0.229834	−	0.110682i	−0.545257	+	0.838269i	$0.683568\pi$
$278$	−3.50001	+	4.38887i	−0.209917	+	0.263227i
$279$		0			0
$280$	6.69178	−	6.43888i	0.399911	−	0.384796i
$281$	0.185881	+	0.814396i	0.0110887	+	0.0485828i	0.980170	−	0.198160i	$-0.0634967\pi$
$281$	0.185881	+	0.814396i	0.0110887	+	0.0485828i	−0.969081	+	0.246743i	$0.920640\pi$
$282$		0			0
$283$	−3.79241	−	16.6156i	−0.225435	−	0.987697i	−0.953312	−	0.301988i	$-0.902350\pi$
$283$	−3.79241	−	16.6156i	−0.225435	−	0.987697i	0.727876	−	0.685709i	$-0.240508\pi$
$284$	0.657422	−	0.824381i	0.0390108	−	0.0489180i
$285$		0			0
$286$	4.28880	+	5.37799i	0.253602	+	0.318007i
$287$	1.08108	+	11.5984i	0.0638143	+	0.684630i
$288$		0			0
$289$	10.5463	+	13.2246i	0.620369	+	0.777918i
$290$	−1.70974	+	0.823367i	−0.100399	+	0.0483498i
$291$		0			0
$292$	4.29432	+	18.8147i	0.251306	+	1.10104i
$293$	16.1902			0.945839			0.472920	−	0.881106i	$-0.343200\pi$
$293$	16.1902			0.945839			0.472920	+	0.881106i	$0.343200\pi$
$294$		0			0
$295$	14.0528			0.818187
$296$	−1.29614	−	5.67877i	−0.0753368	−	0.330072i
$297$		0			0
$298$	2.44993	−	1.17982i	0.141920	−	0.0683453i
$299$	−0.823735	−	1.03293i	−0.0476378	−	0.0597359i
$300$		0			0
$301$	15.0620	−	4.94698i	0.868160	−	0.285139i
$302$	6.72287	+	8.43021i	0.386858	+	0.485104i
$303$		0			0
$304$	−1.82027	+	2.28254i	−0.104399	+	0.130913i
$305$	4.45258	+	19.5080i	0.254954	+	1.11703i
$306$		0			0
$307$	−5.39836	−	23.6518i	−0.308101	−	1.34988i	−0.857571	−	0.514365i	$-0.828028\pi$
$307$	−5.39836	−	23.6518i	−0.308101	−	1.34988i	0.549471	−	0.835513i	$-0.314829\pi$
$308$	−2.44144	−	26.1930i	−0.139114	−	1.49248i
$309$		0			0
$310$	0.962042	−	1.20636i	0.0546403	−	0.0685168i
$311$	−22.7157	−	10.9393i	−1.28809	−	0.620311i	−0.340632	−	0.940197i	$-0.610641\pi$
$311$	−22.7157	−	10.9393i	−1.28809	−	0.620311i	−0.947456	+	0.319886i	$0.896355\pi$
$312$		0			0
$313$	−12.5097			−0.707092			−0.353546	−	0.935417i	$-0.615024\pi$
$313$	−12.5097			−0.707092			−0.353546	+	0.935417i	$0.615024\pi$
$314$	−1.84915	−	0.890503i	−0.104353	−	0.0502540i
$315$		0			0
$316$	−18.3884	+	8.85541i	−1.03443	+	0.498156i
$317$	3.36738	−	1.62164i	0.189131	−	0.0910806i	−0.336922	−	0.941533i	$-0.609386\pi$
$317$	3.36738	−	1.62164i	0.189131	−	0.0910806i	0.526053	+	0.850452i	$0.323672\pi$
$318$		0			0
$319$	−2.64518	+	11.5893i	−0.148102	+	0.648876i
$320$	−1.17433	+	0.565526i	−0.0656468	+	0.0316139i
$321$		0			0
$322$	−0.0990963	−	1.06315i	−0.00552242	−	0.0592472i
$323$	−7.55259	−	3.63714i	−0.420237	−	0.202376i
$324$		0			0
$325$	4.54675			0.252208
$326$	−2.83897	−	1.36717i	−0.157236	−	0.0757208i
$327$		0			0
$328$	−2.11292	+	9.25729i	−0.116666	+	0.511148i
$329$	−10.7846	+	29.0158i	−0.594576	+	1.59969i
$330$		0			0
$331$	17.5865	+	8.46923i	0.966643	+	0.465511i	0.849491	−	0.527603i	$-0.176909\pi$
$331$	17.5865	+	8.46923i	0.966643	+	0.465511i	0.117152	+	0.993114i	$0.462623\pi$
$332$	−3.36625	−	14.7485i	−0.184747	−	0.809429i
$333$		0			0
$334$	1.18370	−	5.18612i	0.0647691	−	0.283772i
$335$	−1.49402	−	1.87345i	−0.0816273	−	0.102357i
$336$		0			0
$337$	11.6671	−	14.6300i	0.635545	−	0.796948i	−0.354893	−	0.934907i	$-0.615483\pi$
$337$	11.6671	−	14.6300i	0.635545	−	0.796948i	0.990438	+	0.137959i	$0.0440542\pi$
$338$	3.41064	+	4.27681i	0.185514	+	0.232628i
$339$		0			0
$340$	−9.75687	−	12.2347i	−0.529141	−	0.663521i
$341$	−2.15080	−	9.42327i	−0.116472	−	0.510299i
$342$		0			0
$343$	−3.13285	+	18.2534i	−0.169158	+	0.985589i
$344$	12.9230			0.696762
$345$		0			0
$346$	0.0539274	+	0.0676228i	0.00289916	+	0.00363543i
$347$	24.9112	−	11.9966i	1.33730	−	0.644010i	0.377845	−	0.925869i	$-0.376665\pi$
$347$	24.9112	−	11.9966i	1.33730	−	0.644010i	0.959456	+	0.281858i	$0.0909508\pi$
$348$		0			0
$349$	−10.4476	+	13.1009i	−0.559250	+	0.701277i	−0.978419	−	0.206631i	$-0.933750\pi$
$349$	−10.4476	+	13.1009i	−0.559250	+	0.701277i	0.419169	+	0.907908i	$0.362321\pi$
$350$	3.07320	+	2.01459i	0.164269	+	0.107684i
$351$		0			0
$352$	7.38550	−	32.3580i	0.393649	−	1.72469i
$353$	19.5130	−	24.4685i	1.03857	−	1.30233i	0.0865656	−	0.996246i	$-0.472411\pi$
$353$	19.5130	−	24.4685i	1.03857	−	1.30233i	0.952006	−	0.306081i	$-0.0990178\pi$
$354$		0			0
$355$	−0.936429	−	0.450960i	−0.0497005	−	0.0239345i
$356$	−5.96843	−	26.1494i	−0.316326	−	1.38591i
$357$		0			0
$358$	−2.23017	+	9.77099i	−0.117868	+	0.516413i
$359$	8.80129	−	11.0365i	0.464514	−	0.582483i	−0.493304	−	0.869857i	$-0.664211\pi$
$359$	8.80129	−	11.0365i	0.464514	−	0.582483i	0.957818	+	0.287374i	$0.0927824\pi$
$360$		0			0
$361$	−16.9280			−0.890949
$362$	−10.0535			−0.528402
$363$		0			0
$364$	0.783965	+	8.41075i	0.0410909	+	0.440843i
$365$	17.1389	−	8.25368i	0.897093	−	0.432017i
$366$		0			0
$367$	6.73184	−	29.4941i	0.351399	−	1.53958i	−0.422554	−	0.906338i	$-0.638866\pi$
$367$	6.73184	−	29.4941i	0.351399	−	1.53958i	0.773953	−	0.633243i	$-0.218276\pi$
$368$	−0.308352	+	1.35098i	−0.0160740	+	0.0704246i
$369$		0			0
$370$	−2.33931	+	1.12655i	−0.121615	+	0.0585668i
$371$	−31.8691	−	4.21375i	−1.65456	−	0.218767i
$372$		0			0
$373$	−26.3362			−1.36364			−0.681818	−	0.731522i	$-0.738811\pi$
$373$	−26.3362			−1.36364			−0.681818	+	0.731522i	$0.738811\pi$
$374$	20.7160			1.07120
$375$		0			0
$376$	−15.7326	+	19.7280i	−0.811345	+	1.01739i
$377$	0.849387	−	3.72141i	0.0437457	−	0.191662i
$378$		0			0
$379$	5.08350	+	22.2723i	0.261122	+	1.14405i	0.920037	+	0.391832i	$0.128158\pi$
$379$	5.08350	+	22.2723i	0.261122	+	1.14405i	−0.658915	+	0.752217i	$0.728984\pi$
$380$	3.48487	+	1.67822i	0.178770	+	0.0860911i
$381$		0			0
$382$	−3.49982	+	4.38863i	−0.179066	+	0.224542i
$383$	−3.70325	+	16.2250i	−0.189227	+	0.829058i	0.787798	+	0.615934i	$0.211221\pi$
$383$	−3.70325	+	16.2250i	−0.189227	+	0.829058i	−0.977025	+	0.213125i	$0.931636\pi$
$384$		0			0
$385$	−24.6359	+	8.09143i	−1.25556	+	0.412378i
$386$	−8.16076	+	10.2333i	−0.415372	+	0.520860i
$387$		0			0
$388$	−16.7573	+	8.06987i	−0.850721	+	0.409686i
$389$	−2.14021	−	2.68374i	−0.108513	−	0.136071i	0.724609	−	0.689160i	$-0.242020\pi$
$389$	−2.14021	−	2.68374i	−0.108513	−	0.136071i	−0.833122	+	0.553089i	$0.813449\pi$
$390$		0			0
$391$	−3.97884			−0.201219
$392$	−7.06914	+	13.3394i	−0.357045	+	0.673740i
$393$		0			0
$394$	0.188336	+	0.825153i	0.00948822	+	0.0415706i
$395$	12.5434	+	15.7289i	0.631126	+	0.791407i
$396$		0			0
$397$	−4.04680	−	5.07453i	−0.203103	−	0.254683i	0.669840	−	0.742506i	$-0.266363\pi$
$397$	−4.04680	−	5.07453i	−0.203103	−	0.254683i	−0.872943	+	0.487822i	$0.837791\pi$
$398$	−6.91415	+	8.67008i	−0.346575	+	0.434592i
$399$		0			0
$400$	−2.97336	−	3.72848i	−0.148668	−	0.186424i
$401$	0.515415	−	2.25818i	0.0257386	−	0.112768i	−0.960427	−	0.278533i	$-0.910152\pi$
$401$	0.515415	−	2.25818i	0.0257386	−	0.112768i	0.986165	+	0.165764i	$0.0530091\pi$
$402$		0			0
$403$	0.690638	+	3.02588i	0.0344031	+	0.150730i
$404$	−6.55096	−	3.15478i	−0.325923	−	0.156956i
$405$		0			0
$406$	2.22301	−	2.13899i	0.110326	−	0.106156i
$407$	−3.61921	+	15.8568i	−0.179398	+	0.785993i
$408$		0			0
$409$	−20.1308	−	9.69449i	−0.995405	−	0.479362i	−0.136028	−	0.990705i	$-0.543434\pi$
$409$	−20.1308	−	9.69449i	−0.995405	−	0.479362i	−0.859377	+	0.511343i	$0.829148\pi$
$410$	4.23261			0.209034
$411$		0			0
$412$	−19.9830	−	9.62328i	−0.984489	−	0.474105i
$413$	−21.7045	+	7.12864i	−1.06801	+	0.350777i
$414$		0			0
$415$	−13.4349	+	6.46992i	−0.659495	+	0.317596i
$416$	−2.37154	+	10.3904i	−0.116274	+	0.509431i
$417$		0			0
$418$	−4.61329	+	2.22164i	−0.225643	+	0.108664i
$419$	−20.3367	+	9.79362i	−0.993511	+	0.478450i	−0.858732	−	0.512426i	$-0.828747\pi$
$419$	−20.3367	+	9.79362i	−0.993511	+	0.478450i	−0.134780	+	0.990876i	$0.543033\pi$
$420$		0			0
$421$	3.10000	+	1.49288i	0.151085	+	0.0727585i	0.507898	−	0.861417i	$-0.330423\pi$
$421$	3.10000	+	1.49288i	0.151085	+	0.0727585i	−0.356814	+	0.934176i	$0.616137\pi$
$422$	11.2935			0.549759
$423$		0			0
$424$	−23.6090	−	11.3695i	−1.14656	−	0.552152i
$425$	8.53746	−	10.7056i	0.414128	−	0.519300i
$426$		0			0
$427$	−16.7729	−	27.8713i	−0.811697	−	1.34879i
$428$	2.15802	+	9.45488i	0.104312	+	0.457019i
$429$		0			0
$430$	−1.28183	−	5.61608i	−0.0618155	−	0.270831i
$431$	14.3314	−	17.9710i	0.690320	−	0.865634i	−0.305939	−	0.952051i	$-0.598970\pi$
$431$	14.3314	−	17.9710i	0.690320	−	0.865634i	0.996259	+	0.0864172i	$0.0275418\pi$
$432$		0			0
$433$	17.4746	+	21.9124i	0.839774	+	1.05304i	0.997845	+	0.0656156i	$0.0209011\pi$
$433$	17.4746	+	21.9124i	0.839774	+	1.05304i	−0.158071	+	0.987428i	$0.550527\pi$
$434$	−0.873910	+	2.35124i	−0.0419490	+	0.112863i
$435$		0			0
$436$	10.2047	+	12.7963i	0.488716	+	0.612830i
$437$	0.886058	−	0.426703i	0.0423859	−	0.0204120i
$438$		0			0
$439$	1.96954	+	8.62910i	0.0940008	+	0.411845i	0.999933	−	0.0115783i	$-0.00368558\pi$
$439$	1.96954	+	8.62910i	0.0940008	+	0.411845i	−0.905932	+	0.423423i	$0.860828\pi$
$440$	−21.1373			−1.00768
$441$		0			0
$442$	−6.65205			−0.316406
$443$	3.86749	+	16.9446i	0.183750	+	0.805061i	0.979824	+	0.199862i	$0.0640494\pi$
$443$	3.86749	+	16.9446i	0.183750	+	0.805061i	−0.796074	+	0.605199i	$0.793093\pi$
$444$		0			0
$445$	−23.8204	+	11.4713i	−1.12920	+	0.543792i
$446$	5.16332	+	6.47460i	0.244491	+	0.306581i
$447$		0			0
$448$	1.52686	−	1.46916i	0.0721374	−	0.0694111i
$449$	−15.2272	−	19.0943i	−0.718616	−	0.901116i	0.279643	−	0.960104i	$-0.409784\pi$
$449$	−15.2272	−	19.0943i	−0.718616	−	0.901116i	−0.998259	+	0.0589881i	$0.981213\pi$
$450$		0			0
$451$	16.5311	−	20.7294i	0.778420	−	0.976108i
$452$	4.37136	+	19.1522i	0.205612	+	0.900843i
$453$		0			0
$454$	−2.68523	−	11.7648i	−0.126024	−	0.552148i
$455$	7.91077	−	2.59822i	0.370862	−	0.121806i
$456$		0			0
$457$	11.4826	−	14.3987i	0.537133	−	0.673543i	−0.437015	−	0.899454i	$-0.643964\pi$
$457$	11.4826	−	14.3987i	0.537133	−	0.673543i	0.974148	+	0.225911i	$0.0725359\pi$
$458$	−6.19764	−	2.98462i	−0.289597	−	0.139462i
$459$		0			0
$460$	1.83589			0.0855989
$461$	24.0392	+	11.5767i	1.11962	+	0.539179i	0.899774	−	0.436356i	$-0.143731\pi$
$461$	24.0392	+	11.5767i	1.11962	+	0.539179i	0.219843	+	0.975535i	$0.429446\pi$
$462$		0			0
$463$	7.14174	−	3.43928i	0.331905	−	0.159837i	−0.260508	−	0.965472i	$-0.583890\pi$
$463$	7.14174	−	3.43928i	0.331905	−	0.159837i	0.592412	+	0.805635i	$0.298176\pi$
$464$	−3.60714	+	1.73711i	−0.167457	+	0.0806431i
$465$		0			0
$466$	1.68622	−	7.38783i	0.0781128	−	0.342234i
$467$	10.3365	−	4.97779i	0.478316	−	0.230345i	−0.179161	−	0.983820i	$-0.557338\pi$
$467$	10.3365	−	4.97779i	0.478316	−	0.230345i	0.657476	+	0.753475i	$0.271624\pi$
$468$		0			0
$469$	3.25786	+	2.13565i	0.150434	+	0.0986150i
$470$	10.1339	+	4.88023i	0.467442	+	0.225108i
$471$		0			0
$472$	−18.6222			−0.857155
$473$	−32.5114	−	15.6566i	−1.49487	−	0.719893i
$474$		0			0
$475$	−0.753123	+	3.29965i	−0.0345557	+	0.151398i
$476$	21.2758	+	13.9470i	0.975174	+	0.639261i
$477$		0			0
$478$	15.0561	+	7.25064i	0.688651	+	0.331637i
$479$	−6.48045	−	28.3927i	−0.296099	−	1.29730i	−0.875882	−	0.482525i	$-0.839720\pi$
$479$	−6.48045	−	28.3927i	−0.296099	−	1.29730i	0.579783	−	0.814771i	$-0.303137\pi$
$480$		0			0
$481$	1.16216	−	5.09174i	0.0529897	−	0.232163i
$482$	1.29346	+	1.62194i	0.0589153	+	0.0738775i
$483$		0			0
$484$	−26.0090	+	32.6143i	−1.18223	+	1.48247i
$485$	11.4307	+	14.3336i	0.519041	+	0.650857i
$486$		0			0
$487$	−0.0756261	−	0.0948322i	−0.00342695	−	0.00429726i	0.780115	−	0.625636i	$-0.215160\pi$
$487$	−0.0756261	−	0.0948322i	−0.00342695	−	0.00429726i	−0.783542	+	0.621339i	$0.786589\pi$
$488$	−5.90036	−	25.8512i	−0.267097	−	1.17023i
$489$		0			0
$490$	6.49821	+	1.74897i	0.293559	+	0.0790104i
$491$	−17.4454			−0.787300			−0.393650	−	0.919260i	$-0.628788\pi$
$491$	−17.4454			−0.787300			−0.393650	+	0.919260i	$0.628788\pi$
$492$		0			0
$493$	−7.16742	−	8.98766i	−0.322804	−	0.404784i
$494$	1.48136	−	0.713386i	0.0666496	−	0.0320967i
$495$		0			0
$496$	2.02968	−	2.54513i	0.0911352	−	0.114280i
$497$	1.67507	+	0.221479i	0.0751371	+	0.00993468i
$498$		0			0
$499$	7.85595	−	34.4192i	0.351681	−	1.54081i	−0.421619	−	0.906773i	$-0.638538\pi$
$499$	7.85595	−	34.4192i	0.351681	−	1.54081i	0.773300	−	0.634040i	$-0.218605\pi$
$500$	−12.3162	+	15.4441i	−0.550799	+	0.690680i
$501$		0			0
$502$	14.6054	+	7.03359i	0.651871	+	0.313925i
$503$	2.33882	+	10.2470i	0.104283	+	0.456892i	0.999927	+	0.0121204i	$0.00385813\pi$
$503$	2.33882	+	10.2470i	0.104283	+	0.456892i	−0.895644	+	0.444772i	$0.853285\pi$
$504$		0			0
$505$	−1.59484	+	6.98744i	−0.0709694	+	0.310937i
$506$	−1.51531	+	1.90014i	−0.0673637	+	0.0844714i
$507$		0			0
$508$	−4.47123			−0.198379
$509$	−28.5132			−1.26382			−0.631912	−	0.775040i	$-0.717730\pi$
$509$	−28.5132			−1.26382			−0.631912	+	0.775040i	$0.717730\pi$
$510$		0			0
$511$	−22.2841	+	21.4419i	−0.985790	+	0.948533i
$512$	17.9534	−	8.64590i	0.793435	−	0.382098i
$513$		0			0
$514$	−2.19798	+	9.62996i	−0.0969485	+	0.424759i
$515$	−4.86487	+	21.3144i	−0.214372	+	0.939224i
$516$		0			0
$517$	63.4806	−	30.5707i	2.79188	−	1.34450i
$518$	3.04158	−	2.92663i	0.133639	−	0.128589i
$519$		0			0
$520$	6.78734			0.297644
$521$	−9.69799			−0.424877			−0.212438	−	0.977174i	$-0.568140\pi$
$521$	−9.69799			−0.424877			−0.212438	+	0.977174i	$0.568140\pi$
$522$		0			0
$523$	−8.59270	+	10.7749i	−0.375732	+	0.471153i	−0.933362	−	0.358936i	$-0.883140\pi$
$523$	−8.59270	+	10.7749i	−0.375732	+	0.471153i	0.557630	+	0.830090i	$0.311711\pi$
$524$	−1.63765	+	7.17500i	−0.0715409	+	0.313441i
$525$		0			0
$526$	−1.61831	−	7.09028i	−0.0705616	−	0.309151i
$527$	8.42147	+	4.05557i	0.366845	+	0.176663i
$528$		0			0
$529$	−14.0492	+	17.6172i	−0.610836	+	0.765964i
$530$	−2.59918	+	11.3878i	−0.112901	+	0.494652i
$531$		0			0
$532$	−6.23368	−	0.824221i	−0.270264	−	0.0357345i
$533$	−5.30826	+	6.65635i	−0.229926	+	0.288318i
$534$		0			0
$535$	8.61279	−	4.14770i	0.372363	−	0.179321i
$536$	1.97982	+	2.48261i	0.0855150	+	0.107232i
$537$		0			0
$538$	−16.0334			−0.691249
$539$	33.9454	−	24.9943i	1.46213	−	1.07658i
$540$		0			0
$541$	2.52029	+	11.0421i	0.108356	+	0.474738i	0.999768	+	0.0215440i	$0.00685820\pi$
$541$	2.52029	+	11.0421i	0.108356	+	0.474738i	−0.891412	+	0.453194i	$0.850285\pi$
$542$	1.63420	+	2.04923i	0.0701951	+	0.0880219i
$543$		0			0
$544$	20.0119	+	25.0941i	0.858002	+	1.07590i
$545$	10.0589	−	12.6134i	0.430875	−	0.540300i
$546$		0			0
$547$	10.5558	+	13.2366i	0.451335	+	0.565957i	0.954491	−	0.298239i	$-0.0963992\pi$
$547$	10.5558	+	13.2366i	0.451335	+	0.565957i	−0.503156	+	0.864196i	$0.667828\pi$
$548$	1.46609	−	6.42335i	0.0626282	−	0.274392i
$549$		0			0
$550$	−1.86117	−	8.15431i	−0.0793604	−	0.347701i
$551$	2.55999	+	1.23283i	0.109059	+	0.0525202i
$552$		0			0
$553$	−27.3520	−	17.9303i	−1.16313	−	0.762472i
$554$	0.558058	−	2.44501i	0.0237096	−	0.103879i
$555$		0			0
$556$	14.1369	+	6.80797i	0.599538	+	0.288722i
$557$	16.7810			0.711036			0.355518	−	0.934669i	$-0.384305\pi$
$557$	16.7810			0.711036			0.355518	+	0.934669i	$0.384305\pi$
$558$		0			0
$559$	10.4396	+	5.02746i	0.441549	+	0.212639i
$560$	−7.30390	−	4.78797i	−0.308646	−	0.202329i
$561$		0			0
$562$	−0.444567	+	0.214092i	−0.0187529	+	0.00903093i
$563$	1.70285	−	7.46068i	0.0717666	−	0.314430i	−0.926285	−	0.376824i	$-0.877016\pi$
$563$	1.70285	−	7.46068i	0.0717666	−	0.314430i	0.998052	+	0.0623936i	$0.0198734\pi$
$564$		0			0
$565$	17.4464	−	8.40175i	0.733976	−	0.353464i
$566$	9.07022	−	4.36799i	0.381250	−	0.183600i
$567$		0			0
$568$	1.24091	+	0.597593i	0.0520676	+	0.0250744i
$569$	−38.0070			−1.59334			−0.796669	−	0.604416i	$-0.793406\pi$
$569$	−38.0070			−1.59334			−0.796669	+	0.604416i	$0.793406\pi$
$570$		0			0
$571$	3.61147	+	1.73919i	0.151135	+	0.0727829i	0.507923	−	0.861403i	$-0.330414\pi$
$571$	3.61147	+	1.73919i	0.151135	+	0.0727829i	−0.356787	+	0.934186i	$0.616128\pi$
$572$	11.9878	−	15.0322i	0.501236	−	0.628530i
$573$		0			0
$574$	−6.53724	+	2.14709i	−0.272859	+	0.0896180i
$575$	0.357468	+	1.56617i	0.0149074	+	0.0653137i
$576$		0			0
$577$	−7.20053	−	31.5476i	−0.299762	−	1.31334i	−0.870483	−	0.492199i	$-0.836193\pi$
$577$	−7.20053	−	31.5476i	−0.299762	−	1.31334i	0.570721	−	0.821144i	$-0.306664\pi$
$578$	−6.22964	+	7.81172i	−0.259119	+	0.324925i
$579$		0			0
$580$	3.30715	+	4.14703i	0.137322	+	0.172196i
$581$	17.4681	−	16.8079i	0.724700	−	0.697311i
$582$		0			0
$583$	45.6204	+	57.2062i	1.88941	+	2.36924i
$584$	−22.7118	+	10.9374i	−0.939819	+	0.452593i
$585$		0			0
$586$	2.12807	+	9.32368i	0.0879097	+	0.385158i
$587$	11.7445			0.484746			0.242373	−	0.970183i	$-0.422074\pi$
$587$	11.7445			0.484746			0.242373	+	0.970183i	$0.422074\pi$
$588$		0			0
$589$	−2.31033			−0.0951954
$590$	1.84713	+	8.09282i	0.0760453	+	0.333176i
$591$		0			0
$592$	−4.93539	+	2.37676i	−0.202843	+	0.0976841i
$593$	12.0645	+	15.1284i	0.495429	+	0.621248i	0.965191	−	0.261545i	$-0.0842319\pi$
$593$	12.0645	+	15.1284i	0.495429	+	0.621248i	−0.469763	+	0.882793i	$0.655660\pi$
$594$		0			0
$595$	8.73642	−	23.5052i	0.358158	−	0.963618i
$596$	−4.73889	−	5.94238i	−0.194113	−	0.243409i
$597$		0			0
$598$	0.486576	−	0.610148i	0.0198976	−	0.0249508i
$599$	−2.19834	−	9.63156i	−0.0898217	−	0.393535i	0.909954	−	0.414709i	$-0.136117\pi$
$599$	−2.19834	−	9.63156i	−0.0898217	−	0.393535i	−0.999776	+	0.0211743i	$0.993260\pi$
$600$		0			0
$601$	−6.50291	−	28.4911i	−0.265259	−	1.16218i	−0.915458	−	0.402413i	$-0.868172\pi$
$601$	−6.50291	−	28.4911i	−0.265259	−	1.16218i	0.650199	−	0.759764i	$-0.274686\pi$
$602$	4.82868	+	8.02375i	0.196802	+	0.327024i
$603$		0			0
$604$	18.7914	−	23.5636i	0.764611	−	0.958791i
$605$	37.0471	+	17.8410i	1.50618	+	0.725338i
$606$		0			0
$607$	−0.0838630			−0.00340389			−0.00170195	−	0.999999i	$-0.500542\pi$
$607$	−0.0838630			−0.00340389			−0.00170195	+	0.999999i	$0.500542\pi$
$608$	−7.14765	−	3.44213i	−0.289876	−	0.139597i
$609$		0			0
$610$	−10.6491	+	5.12835i	−0.431171	+	0.207641i
$611$	−20.3841	+	9.81646i	−0.824652	+	0.397132i
$612$		0			0
$613$	−5.15917	+	22.6038i	−0.208377	+	0.912959i	0.757270	+	0.653102i	$0.226533\pi$
$613$	−5.15917	+	22.6038i	−0.208377	+	0.912959i	−0.965647	+	0.259857i	$0.916325\pi$
$614$	12.9111	−	6.21768i	0.521051	−	0.250925i
$615$		0			0
$616$	32.6464	−	10.7224i	1.31536	−	0.432018i
$617$	−38.8434	−	18.7060i	−1.56378	−	0.753076i	−0.566310	−	0.824192i	$-0.691630\pi$
$617$	−38.8434	−	18.7060i	−1.56378	−	0.753076i	−0.997468	+	0.0711164i	$0.977344\pi$
$618$		0			0
$619$	22.2804			0.895523			0.447762	−	0.894153i	$-0.352221\pi$
$619$	22.2804			0.895523			0.447762	+	0.894153i	$0.352221\pi$
$620$	−3.88578	−	1.87129i	−0.156057	−	0.0751530i
$621$		0			0
$622$	3.31399	−	14.5195i	0.132879	−	0.582180i
$623$	30.9713	−	29.8008i	1.24084	−	1.19394i
$624$		0			0
$625$	6.95105	+	3.34745i	0.278042	+	0.133898i
$626$	−1.64431	−	7.20418i	−0.0657197	−	0.287937i
$627$		0			0
$628$	−1.27655	+	5.59292i	−0.0509398	+	0.223182i
$629$	−9.80667	−	12.2972i	−0.391018	−	0.490321i
$630$		0			0
$631$	−0.707412	+	0.887066i	−0.0281616	+	0.0353136i	−0.795713	−	0.605674i	$-0.792904\pi$
$631$	−0.707412	+	0.887066i	−0.0281616	+	0.0353136i	0.767551	+	0.640988i	$0.221475\pi$
$632$	−16.6219	−	20.8433i	−0.661185	−	0.829100i
$633$		0			0
$634$	1.37650	+	1.72607i	0.0546677	+	0.0685511i
$635$	0.980727	+	4.29684i	0.0389189	+	0.170515i
$636$		0			0
$637$	−10.9001	+	8.02586i	−0.431878	+	0.317996i
$638$	−7.02180			−0.277996
$639$		0			0
$640$	−11.6651	−	14.6276i	−0.461105	−	0.578208i
$641$	−8.10980	+	3.90548i	−0.320318	+	0.154257i	−0.587132	−	0.809491i	$-0.699743\pi$
$641$	−8.10980	+	3.90548i	−0.320318	+	0.154257i	0.266814	+	0.963748i	$0.414029\pi$
$642$		0			0
$643$	16.2240	−	20.3443i	0.639814	−	0.802301i	−0.351166	−	0.936313i	$-0.614215\pi$
$643$	16.2240	−	20.3443i	0.639814	−	0.802301i	0.990980	+	0.134012i	$0.0427862\pi$
$644$	−2.83552	+	0.931301i	−0.111735	+	0.0366984i
$645$		0			0
$646$	1.10185	−	4.82750i	0.0433515	−	0.189936i
$647$	−8.38509	+	10.5146i	−0.329652	+	0.413370i	−0.918843	−	0.394623i	$-0.870875\pi$
$647$	−8.38509	+	10.5146i	−0.329652	+	0.413370i	0.589191	+	0.807994i	$0.299447\pi$
$648$		0			0
$649$	46.8492	+	22.5614i	1.83899	+	0.885611i
$650$	0.597634	+	2.61841i	0.0234411	+	0.102702i
$651$		0			0
$652$	−1.95986	+	8.58671i	−0.0767541	+	0.336282i
$653$	19.3244	−	24.2321i	0.756223	−	0.948274i	−0.243543	−	0.969890i	$-0.578310\pi$
$653$	19.3244	−	24.2321i	0.756223	−	0.948274i	0.999766	+	0.0216163i	$0.00688121\pi$
$654$		0			0
$655$	7.25437			0.283452
$656$	8.92979			0.348650
$657$		0			0
$658$	−18.1274	−	2.39681i	−0.706678	−	0.0934375i
$659$	−13.5371	+	6.51915i	−0.527332	+	0.253950i	−0.678555	−	0.734550i	$-0.737393\pi$
$659$	−13.5371	+	6.51915i	−0.527332	+	0.253950i	0.151222	+	0.988500i	$0.451679\pi$
$660$		0			0
$661$	3.79723	−	16.6367i	0.147695	−	0.647095i	−0.845827	−	0.533457i	$-0.820893\pi$
$661$	3.79723	−	16.6367i	0.147695	−	0.647095i	0.993522	−	0.113638i	$-0.0362503\pi$
$662$	−2.56570	+	11.2410i	−0.0997186	+	0.436896i
$663$		0			0
$664$	17.8034	−	8.57365i	0.690905	−	0.332722i
$665$	0.575230	+	6.17134i	0.0223064	+	0.239314i
$666$		0			0
$667$	1.34865			0.0522200
$668$	−14.8687			−0.575289
$669$		0			0
$670$	0.882514	−	1.10664i	0.0340945	−	0.0427531i
$671$	−16.4756	+	72.1841i	−0.636032	+	2.78664i
$672$		0			0
$673$	4.99224	+	21.8724i	0.192437	+	0.843120i	0.975293	+	0.220917i	$0.0709050\pi$
$673$	4.99224	+	21.8724i	0.192437	+	0.843120i	−0.782856	+	0.622203i	$0.786238\pi$
$674$	9.95876	+	4.79589i	0.383597	+	0.184731i
$675$		0			0
$676$	9.53323	−	11.9543i	0.366663	−	0.459780i
$677$	−2.24684	+	9.84405i	−0.0863531	+	0.378337i	−0.999576	−	0.0291232i	$-0.990728\pi$
$677$	−2.24684	+	9.84405i	−0.0863531	+	0.378337i	0.913223	+	0.407461i	$0.133586\pi$
$678$		0			0
$679$	−24.9257	−	16.3397i	−0.956561	−	0.627061i
$680$	12.7446	−	15.9813i	0.488735	−	0.612854i
$681$		0			0
$682$	5.14402	−	2.47723i	0.196975	−	0.0948581i
$683$	16.6423	+	20.8687i	0.636798	+	0.798520i	0.990599	−	0.136801i	$-0.0436822\pi$
$683$	16.6423	+	20.8687i	0.636798	+	0.798520i	−0.353800	+	0.935321i	$0.615111\pi$
$684$		0			0
$685$	−6.49441			−0.248139
$686$	−10.9236	+	0.595100i	−0.417066	+	0.0227210i
$687$		0			0
$688$	−2.70436	−	11.8486i	−0.103103	−	0.451722i
$689$	−14.6490	−	18.3693i	−0.558084	−	0.699816i
$690$		0			0
$691$	−22.3641	−	28.0436i	−0.850769	−	1.06683i	−0.996986	−	0.0775782i	$-0.975281\pi$
$691$	−22.3641	−	28.0436i	−0.850769	−	1.06683i	0.146217	−	0.989253i	$-0.453290\pi$
$692$	0.150735	−	0.189015i	0.00573008	−	0.00718529i
$693$		0			0
$694$	10.1830	+	12.7691i	0.386543	+	0.484709i
$695$	3.44164	−	15.0788i	0.130549	−	0.571972i
$696$		0			0
$697$	5.70549	+	24.9974i	0.216111	+	0.946843i
$698$	−8.91790	−	4.29463i	−0.337547	−	0.162554i
$699$		0			0
$700$	3.57843	−	9.62769i	0.135252	−	0.363892i
$701$	2.06504	−	9.04753i	0.0779955	−	0.341720i	−0.920841	−	0.389937i	$-0.872497\pi$
$701$	2.06504	−	9.04753i	0.0779955	−	0.341720i	0.998837	+	0.0482168i	$0.0153538\pi$
$702$		0			0
$703$	3.50266	+	1.68679i	0.132105	+	0.0636185i
$704$	−4.82289			−0.181770
$705$		0			0
$706$	16.6559	+	8.02105i	0.626853	+	0.301876i
$707$	−1.08133	−	11.6011i	−0.0406678	−	0.436303i
$708$		0			0
$709$	−21.5065	+	10.3570i	−0.807693	+	0.388965i	−0.791702	−	0.610907i	$-0.790805\pi$
$709$	−21.5065	+	10.3570i	−0.807693	+	0.388965i	−0.0159915	+	0.999872i	$0.505090\pi$
$710$	0.136615	−	0.598551i	0.00512708	−	0.0224632i
$711$		0			0
$712$	31.5657	−	15.2013i	1.18298	−	0.569691i
$713$	−0.987994	+	0.475793i	−0.0370007	+	0.0178186i
$714$		0			0
$715$	−17.0754	−	8.22308i	−0.638584	−	0.307526i
$716$	28.0137			1.04692
$717$		0			0
$718$	7.51261	+	3.61788i	0.280368	+	0.135018i
$719$	−4.95697	+	6.21584i	−0.184864	+	0.231812i	−0.865624	−	0.500694i	$-0.833078\pi$
$719$	−4.95697	+	6.21584i	−0.184864	+	0.231812i	0.680760	+	0.732506i	$0.261649\pi$
$720$		0			0
$721$	−3.29848	−	35.3877i	−0.122842	−	1.31791i
$722$	−2.22506	−	9.74862i	−0.0828081	−	0.362806i
$723$		0			0
$724$	6.25307	+	27.3965i	0.232394	+	1.01818i
$725$	−2.89382	+	3.62874i	−0.107474	+	0.134768i
$726$		0			0
$727$	0.163500	+	0.205022i	0.00606387	+	0.00760385i	0.784854	−	0.619681i	$-0.212738\pi$
$727$	0.163500	+	0.205022i	0.00606387	+	0.00760385i	−0.778790	+	0.627284i	$0.784166\pi$
$728$	−10.4830	+	3.44304i	−0.388526	+	0.127608i
$729$		0			0
$730$	7.00595	+	8.78519i	0.259302	+	0.325154i
$731$	31.4401	−	15.1408i	1.16285	−	0.560001i
$732$		0			0
$733$	11.7531	+	51.4937i	0.434110	+	1.90196i	0.431810	+	0.901965i	$0.357875\pi$
$733$	11.7531	+	51.4937i	0.434110	+	1.90196i	0.00230080	+	0.999997i	$0.499268\pi$
$734$	17.8701			0.659597
$735$		0			0
$736$	−3.76551			−0.138799
$737$	−1.97300	−	8.64429i	−0.0726765	−	0.318416i
$738$		0			0
$739$	−12.4370	+	5.98935i	−0.457503	+	0.220322i	−0.648418	−	0.761285i	$-0.724569\pi$
$739$	−12.4370	+	5.98935i	−0.457503	+	0.220322i	0.190915	+	0.981607i	$0.438855\pi$
$740$	4.52493	+	5.67409i	0.166340	+	0.208584i
$741$		0			0
$742$	−1.76230	−	18.9068i	−0.0646960	−	0.694090i
$743$	27.4573	+	34.4304i	1.00731	+	1.26313i	0.964510	+	0.264046i	$0.0850569\pi$
$743$	27.4573	+	34.4304i	1.00731	+	1.26313i	0.0428017	+	0.999084i	$0.486372\pi$
$744$		0			0
$745$	−4.67118	+	5.85748i	−0.171139	+	0.214601i
$746$	−3.46169	−	15.1666i	−0.126741	−	0.555290i
$747$		0			0
$748$	−12.8849	−	56.4523i	−0.471118	−	2.06410i
$749$	−11.1984	+	10.7751i	−0.409179	+	0.393715i
$750$		0			0
$751$	−5.12514	+	6.42672i	−0.187019	+	0.234514i	−0.866498	−	0.499181i	$-0.833634\pi$
$751$	−5.12514	+	6.42672i	−0.187019	+	0.234514i	0.679479	+	0.733695i	$0.262206\pi$
$752$	21.3801	+	10.2961i	0.779652	+	0.375460i
$753$		0			0
$754$	2.25475			0.0821132
$755$	−26.7664	−	12.8900i	−0.974128	−	0.469115i
$756$		0			0
$757$	5.97694	−	2.87834i	0.217236	−	0.104615i	−0.322101	−	0.946705i	$-0.604389\pi$
$757$	5.97694	−	2.87834i	0.217236	−	0.104615i	0.539337	+	0.842090i	$0.318675\pi$
$758$	−12.1581	+	5.85503i	−0.441602	+	0.212664i
$759$		0			0
$760$	−1.12425	+	4.92568i	−0.0407810	+	0.178673i
$761$	−9.86305	+	4.74979i	−0.357535	+	0.172180i	−0.604025	−	0.796966i	$-0.706437\pi$
$761$	−9.86305	+	4.74979i	−0.357535	+	0.172180i	0.246489	+	0.969145i	$0.420723\pi$
$762$		0			0
$763$	−9.13740	+	24.5840i	−0.330796	+	0.890000i
$764$	14.1361	+	6.80759i	0.511427	+	0.246290i
$765$		0			0
$766$	−9.83051			−0.355191
$767$	−15.0436	−	7.24462i	−0.543193	−	0.261588i
$768$		0			0
$769$	−2.77664	+	12.1653i	−0.100128	+	0.438691i	0.899868	+	0.436161i	$0.143662\pi$
$769$	−2.77664	+	12.1653i	−0.100128	+	0.438691i	−0.999997	+	0.00252948i	$0.999195\pi$
$770$	−7.89794	−	13.1239i	−0.284622	−	0.472953i
$771$		0			0
$772$	32.9621	+	15.8737i	1.18633	+	0.571308i
$773$	0.512299	+	2.24453i	0.0184261	+	0.0807301i	0.983305	−	0.181965i	$-0.0582458\pi$
$773$	0.512299	+	2.24453i	0.0184261	+	0.0807301i	−0.964879	+	0.262695i	$0.915389\pi$
$774$		0			0
$775$	0.839766	−	3.67925i	0.0301653	−	0.132163i
$776$	−15.1475	−	18.9943i	−0.543762	−	0.681856i
$777$		0			0
$778$	1.26421	−	1.58527i	0.0453242	−	0.0568347i
$779$	−3.95136	−	4.95485i	−0.141572	−	0.177526i
$780$		0			0
$781$	−2.39785	−	3.00681i	−0.0858019	−	0.107592i
$782$	−0.522988	−	2.29136i	−0.0187020	−	0.0819388i
$783$		0			0
$784$	13.7096	+	3.68991i	0.489630	+	0.131782i
$785$	5.65478			0.201828
$786$		0			0
$787$	−14.2211	−	17.8327i	−0.506929	−	0.635669i	0.460848	−	0.887479i	$-0.347545\pi$
$787$	−14.2211	−	17.8327i	−0.506929	−	0.635669i	−0.967777	+	0.251811i	$0.918974\pi$
$788$	2.13145	−	1.02645i	0.0759299	−	0.0365659i
$789$		0			0
$790$	−7.40932	+	9.29100i	−0.263612	+	0.330559i
$791$	−22.6839	+	21.8266i	−0.806545	+	0.776063i
$792$		0			0
$793$	5.29042	−	23.1788i	0.187868	−	0.823105i
$794$	2.39043	−	2.99750i	0.0848331	−	0.106377i
$795$		0			0
$796$	27.9269	+	13.4489i	0.989844	+	0.476684i
$797$	−8.04742	−	35.2581i	−0.285054	−	1.24890i	−0.891222	−	0.453568i	$-0.850151\pi$
$797$	−8.04742	−	35.2581i	−0.285054	−	1.24890i	0.606168	−	0.795337i	$-0.292706\pi$
$798$		0			0
$799$	−15.1618	+	66.4283i	−0.536387	+	2.35006i
$800$	8.07972	−	10.1317i	0.285661	−	0.358208i
$801$		0			0
$802$	1.36820			0.0483128
$803$	70.3886			2.48396
$804$		0			0
$805$	1.51693	+	2.52066i	0.0534647	+	0.0888416i
$806$	−1.65178	+	0.795457i	−0.0581816	+	0.0280188i
$807$		0			0
$808$	2.11341	−	9.25945i	0.0743495	−	0.325746i
$809$	12.5044	−	54.7854i	0.439632	−	1.92615i	0.0682602	−	0.997668i	$-0.478255\pi$
$809$	12.5044	−	54.7854i	0.439632	−	1.92615i	0.371371	−	0.928484i	$-0.378888\pi$
$810$		0			0
$811$	40.2690	−	19.3926i	1.41404	−	0.680965i	0.438082	−	0.898935i	$-0.355658\pi$
$811$	40.2690	−	19.3926i	1.41404	−	0.680965i	0.975955	+	0.217970i	$0.0699436\pi$
$812$	−7.21155	−	4.72743i	−0.253076	−	0.165900i
$813$		0			0
$814$	−9.60743			−0.336740
$815$	8.68170			0.304107
$816$		0			0
$817$	−5.37773	+	6.74346i	−0.188143	+	0.235924i
$818$	2.93688	−	12.8673i	0.102686	−	0.449895i
$819$		0			0
$820$	−2.63259	−	11.5341i	−0.0919340	−	0.402789i
$821$	20.5267	+	9.88513i	0.716386	+	0.344993i	0.756314	−	0.654209i	$-0.226998\pi$
$821$	20.5267	+	9.88513i	0.716386	+	0.344993i	−0.0399274	+	0.999203i	$0.512713\pi$
$822$		0			0
$823$	−30.1025	+	37.7473i	−1.04931	+	1.31579i	−0.102238	+	0.994760i	$0.532600\pi$
$823$	−30.1025	+	37.7473i	−1.04931	+	1.31579i	−0.947069	+	0.321030i	$0.895971\pi$
$824$	6.44671	−	28.2449i	0.224582	−	0.983957i
$825$		0			0
$826$	−6.95817	−	11.5623i	−0.242106	−	0.402304i
$827$	−18.9024	+	23.7029i	−0.657302	+	0.824231i	−0.993047	−	0.117722i	$-0.962441\pi$
$827$	−18.9024	+	23.7029i	−0.657302	+	0.824231i	0.335744	+	0.941953i	$0.391012\pi$
$828$		0			0
$829$	18.8200	−	9.06321i	0.653644	−	0.314778i	−0.0775091	−	0.996992i	$-0.524697\pi$
$829$	18.8200	−	9.06321i	0.653644	−	0.314778i	0.731153	+	0.682213i	$0.238982\pi$
$830$	−5.49185	−	6.88656i	−0.190625	−	0.239036i
$831$		0			0
$832$	1.54866			0.0536903
$833$	−1.56978	+	40.7353i	−0.0543895	+	1.41140i
$834$		0			0
$835$	3.26133	+	14.2888i	0.112863	+	0.494486i
$836$	8.92348	+	11.1897i	0.308625	+	0.387004i
$837$		0			0
$838$	−8.31310	−	10.4243i	−0.287171	−	0.360102i
$839$	−3.45449	+	4.33179i	−0.119262	+	0.149550i	−0.837879	−	0.545857i	$-0.816204\pi$
$839$	−3.45449	+	4.33179i	−0.119262	+	0.149550i	0.718616	+	0.695407i	$0.244776\pi$
$840$		0			0
$841$	−15.6518	−	19.6267i	−0.539716	−	0.676783i
$842$	−0.452258	+	1.98147i	−0.0155858	+	0.0682860i
$843$		0			0
$844$	−7.02431	−	30.7755i	−0.241787	−	1.05934i
$845$	−13.5791	−	6.53934i	−0.467135	−	0.224960i
$846$		0			0
$847$	−66.2693	−	8.76217i	−2.27704	−	0.301072i
$848$	−5.48364	+	24.0254i	−0.188309	+	0.825036i
$849$		0			0
$850$	7.28741	+	3.50943i	0.249956	+	0.120373i
$851$	1.84526			0.0632548
$852$		0			0
$853$	30.2797	+	14.5820i	1.03676	+	0.499277i	0.873254	−	0.487266i	$-0.162006\pi$
$853$	30.2797	+	14.5820i	1.03676	+	0.499277i	0.163505	+	0.986543i	$0.447720\pi$
$854$	13.8460	−	13.3227i	0.473802	−	0.455895i
$855$		0			0
$856$	−11.4133	+	5.49635i	−0.390098	+	0.187861i
$857$	−7.16022	+	31.3710i	−0.244588	+	1.07161i	0.692197	+	0.721708i	$0.256643\pi$
$857$	−7.16022	+	31.3710i	−0.244588	+	1.07161i	−0.936786	+	0.349904i	$0.886214\pi$
$858$		0			0
$859$	34.3291	−	16.5320i	1.17129	−	0.564065i	0.255931	−	0.966695i	$-0.417618\pi$
$859$	34.3291	−	16.5320i	1.17129	−	0.564065i	0.915363	+	0.402630i	$0.131904\pi$
$860$	−14.5069	+	6.98615i	−0.494681	+	0.238226i
$861$		0			0
$862$	12.2330	+	5.89111i	0.416658	+	0.200652i
$863$	−16.2596			−0.553482			−0.276741	−	0.960945i	$-0.589254\pi$
$863$	−16.2596			−0.553482			−0.276741	+	0.960945i	$0.589254\pi$
$864$		0			0
$865$	−0.214706	−	0.103397i	−0.00730023	−	0.00351560i
$866$	−10.3222	+	12.9436i	−0.350761	+	0.439840i
$867$		0			0
$868$	6.95082	+	0.919043i	0.235926	+	0.0311943i
$869$	16.5647	+	72.5749i	0.561920	+	2.46193i
$870$		0			0
$871$	0.633545	+	2.77574i	0.0214669	+	0.0940525i
$872$	−13.3296	+	16.7148i	−0.451397	+	0.566034i
$873$		0			0
$874$	0.362198	+	0.454181i	0.0122515	+	0.0153629i
$875$	−31.3810	−	4.14922i	−1.06087	−	0.140269i
$876$		0			0
$877$	4.28046	+	5.36753i	0.144541	+	0.181249i	0.848832	−	0.528663i	$-0.177306\pi$
$877$	4.28046	+	5.36753i	0.144541	+	0.181249i	−0.704291	+	0.709911i	$0.748735\pi$
$878$	−4.71050	+	2.26846i	−0.158972	+	0.0765567i
$879$		0			0
$880$	4.42334	+	19.3799i	0.149111	+	0.653296i
$881$	−12.9955			−0.437830			−0.218915	−	0.975744i	$-0.570252\pi$
$881$	−12.9955			−0.437830			−0.218915	+	0.975744i	$0.570252\pi$
$882$		0			0
$883$	−22.3685			−0.752759			−0.376380	−	0.926466i	$-0.622831\pi$
$883$	−22.3685			−0.752759			−0.376380	+	0.926466i	$0.622831\pi$
$884$	4.13743	+	18.1273i	0.139157	+	0.609686i
$885$		0			0
$886$	−9.24979	+	4.45447i	−0.310753	+	0.149651i
$887$	−28.6447	−	35.9193i	−0.961795	−	1.20605i	−0.978511	−	0.206192i	$-0.933893\pi$
$887$	−28.6447	−	35.9193i	−0.961795	−	1.20605i	0.0167167	−	0.999860i	$-0.494679\pi$
$888$		0			0
$889$	−3.69440	−	6.13895i	−0.123906	−	0.205894i
$890$	−9.73716	−	12.2100i	−0.326390	−	0.409281i
$891$		0			0
$892$	14.4322	−	18.0974i	0.483227	−	0.605947i
$893$	−3.74755	−	16.4191i	−0.125407	−	0.549443i
$894$		0			0
$895$	−6.14457	−	26.9211i	−0.205390	−	0.899873i
$896$	25.4370	+	16.6748i	0.849789	+	0.557067i
$897$		0			0
$898$	8.99464	−	11.2789i	0.300155	−	0.376383i
$899$	−2.85451	−	1.37466i	−0.0952031	−	0.0458474i
$900$		0			0
$901$	−70.7585			−2.35731
$902$	14.1106	+	6.79532i	0.469833	+	0.226259i
$903$		0			0
$904$	−23.1192	+	11.1336i	−0.768933	+	0.370299i
$905$	24.9564	−	12.0184i	0.829580	−	0.399505i
$906$		0			0
$907$	2.24133	−	9.81992i	0.0744223	−	0.326065i	−0.923989	−	0.382420i	$-0.875091\pi$
$907$	2.24133	−	9.81992i	0.0744223	−	0.326065i	0.998411	+	0.0563549i	$0.0179478\pi$
$908$	−30.3896	+	14.6349i	−1.00851	+	0.485675i
$909$		0			0
$910$	2.53608	+	4.21418i	0.0840704	+	0.139699i
$911$	38.1349	+	18.3648i	1.26347	+	0.608453i	0.941089	−	0.338158i	$-0.109804\pi$
$911$	38.1349	+	18.3648i	1.26347	+	0.608453i	0.322377	+	0.946611i	$0.395518\pi$
$912$		0			0
$913$	−55.1765			−1.82607
$914$	9.80130	+	4.72006i	0.324198	+	0.156126i
$915$		0			0
$916$	−4.27850	+	18.7453i	−0.141365	+	0.619363i
$917$	−11.2043	+	3.67996i	−0.369999	+	0.121523i
$918$		0			0
$919$	27.0022	+	13.0036i	0.890719	+	0.428948i	0.822528	−	0.568724i	$-0.192563\pi$
$919$	27.0022	+	13.0036i	0.890719	+	0.428948i	0.0681912	+	0.997672i	$0.478277\pi$
$920$	0.533624	+	2.33796i	0.0175931	+	0.0770802i
$921$		0			0
$922$	−3.50707	+	15.3655i	−0.115499	+	0.506035i
$923$	0.769968	+	0.965509i	0.0253438	+	0.0317801i
$924$		0			0
$925$	−3.95941	+	4.96494i	−0.130185	+	0.163246i
$926$	2.91936	+	3.66076i	0.0959361	+	0.120300i
$927$		0			0
$928$	−6.78314	−	8.50578i	−0.222667	−	0.279216i
$929$	11.4581	+	50.2011i	0.375927	+	1.64704i	0.709783	+	0.704420i	$0.248793\pi$
$929$	11.4581	+	50.2011i	0.375927	+	1.64704i	−0.333856	+	0.942624i	$0.608350\pi$
$930$		0			0
$931$	−4.01900	−	9.23979i	−0.131717	−	0.302822i
$932$	−21.1811			−0.693809
$933$		0			0
$934$	4.22529	+	5.29835i	0.138256	+	0.173367i
$935$	−51.4244	+	24.7647i	−1.68176	+	0.809892i
$936$		0			0
$937$	−2.92041	+	3.66207i	−0.0954055	+	0.119635i	−0.827243	−	0.561845i	$-0.810092\pi$
$937$	−2.92041	+	3.66207i	−0.0954055	+	0.119635i	0.731837	+	0.681480i	$0.238663\pi$
$938$	−0.801668	+	2.15687i	−0.0261754	+	0.0704243i
$939$		0			0
$940$	6.99587	−	30.6509i	0.228180	−	0.999723i
$941$	−11.5744	+	14.5138i	−0.377314	+	0.473136i	−0.933839	−	0.357694i	$-0.883563\pi$
$941$	−11.5744	+	14.5138i	−0.377314	+	0.473136i	0.556525	+	0.830831i	$0.312134\pi$
$942$		0			0
$943$	−2.71018	−	1.30515i	−0.0882555	−	0.0425016i
$944$	3.89701	+	17.0739i	0.126837	+	0.555708i
$945$		0			0
$946$	4.74307	−	20.7808i	0.154211	−	0.675641i
$947$	−10.4728	+	13.1325i	−0.340321	+	0.426749i	−0.922312	−	0.386446i	$-0.873703\pi$
$947$	−10.4728	+	13.1325i	−0.340321	+	0.426749i	0.581991	+	0.813195i	$0.302274\pi$
$948$		0			0
$949$	−22.6023			−0.733701
$950$	−1.99921			−0.0648630
$951$		0			0
$952$	−11.5771	+	31.1480i	−0.375217	+	1.00951i
$953$	46.3594	−	22.3255i	1.50173	−	0.723195i	0.511068	−	0.859540i	$-0.329250\pi$
$953$	46.3594	−	22.3255i	1.50173	−	0.723195i	0.990661	+	0.136345i	$0.0435356\pi$
$954$		0			0
$955$	3.44145	−	15.0780i	0.111363	−	0.487912i
$956$	10.3939	−	45.5386i	0.336162	−	1.47282i
$957$		0			0
$958$	15.4992	−	7.46400i	0.500755	−	0.241151i
$959$	10.0306	−	3.29445i	0.323904	−	0.106383i
$960$		0			0
$961$	−28.4239			−0.916899
$962$	3.08501			0.0994649
$963$		0			0
$964$	3.61539	−	4.53356i	0.116444	−	0.146016i
$965$	8.02466	−	35.1583i	0.258323	−	1.13179i
$966$		0			0
$967$	2.18635	+	9.57904i	0.0703084	+	0.308041i	0.997839	−	0.0657060i	$-0.0209299\pi$
$967$	2.18635	+	9.57904i	0.0703084	+	0.308041i	−0.927531	+	0.373747i	$0.878073\pi$
$968$	−49.0932	−	23.6420i	−1.57792	−	0.759884i
$969$		0			0
$970$	−6.75206	+	8.46682i	−0.216796	+	0.271853i
$971$	9.22592	−	40.4214i	0.296074	−	1.29718i	−0.579845	−	0.814727i	$-0.696887\pi$
$971$	9.22592	−	40.4214i	0.296074	−	1.29718i	0.875919	−	0.482458i	$-0.160256\pi$
$972$		0			0
$973$	2.33350	+	25.0350i	0.0748087	+	0.802584i
$974$	0.0446720	−	0.0560170i	0.00143138	−	0.00179490i
$975$		0			0
$976$	−22.4671	+	10.8196i	−0.719155	+	0.346327i
$977$	9.12890	+	11.4473i	0.292059	+	0.366231i	0.906115	−	0.423032i	$-0.139034\pi$
$977$	9.12890	+	11.4473i	0.292059	+	0.366231i	−0.614055	+	0.789263i	$0.710463\pi$
$978$		0			0
$979$	−97.8290			−3.12663
$980$	0.724316	−	18.7958i	0.0231374	−	0.600411i
$981$		0			0
$982$	−2.29306	−	10.0466i	−0.0731745	−	0.320598i
$983$	−0.173522	−	0.217589i	−0.00553448	−	0.00694002i	0.779057	−	0.626954i	$-0.215698\pi$
$983$	−0.173522	−	0.217589i	−0.00553448	−	0.00694002i	−0.784591	+	0.620014i	$0.787127\pi$
$984$		0			0
$985$	−1.45394	−	1.82318i	−0.0463263	−	0.0580913i
$986$	4.23376	−	5.30897i	0.134831	−	0.169072i
$987$		0			0
$988$	−2.86539	−	3.59309i	−0.0911603	−	0.114311i
$989$	−0.910985	+	3.99129i	−0.0289676	+	0.126915i
$990$		0			0
$991$	−3.56901	−	15.6369i	−0.113373	−	0.496721i	−0.999449	−	0.0331813i	$-0.989436\pi$
$991$	−3.56901	−	15.6369i	−0.113373	−	0.496721i	0.886076	−	0.463540i	$-0.153421\pi$
$992$	7.96995	+	3.83813i	0.253046	+	0.121861i
$993$		0			0
$994$	0.0926281	+	0.993759i	0.00293799	+	0.0315201i
$995$	6.79884	−	29.7877i	0.215538	−	0.944333i
$996$		0			0
$997$	−28.0106	−	13.4892i	−0.887103	−	0.427206i	−0.0658893	−	0.997827i	$-0.520988\pi$
$997$	−28.0106	−	13.4892i	−0.887103	−	0.427206i	−0.821214	+	0.570621i	$0.806703\pi$
$998$	20.8541			0.660125
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.e.379.6	yes	60
3.2	odd	2	inner	441.2.u.e.379.5	yes	60
49.15	even	7	inner	441.2.u.e.64.6	yes	60
147.113	odd	14	inner	441.2.u.e.64.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.u.e.64.5	✓	60	147.113	odd	14	inner
441.2.u.e.64.6	yes	60	49.15	even	7	inner
441.2.u.e.379.5	yes	60	3.2	odd	2	inner
441.2.u.e.379.6	yes	60	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.131442 + 0.575886i) q^{2} +(1.48757 - 0.716376i) q^{4} +(-1.01472 - 1.27242i) q^{5} +(2.21270 + 1.45050i) q^{7} +(1.34467 + 1.68616i) q^{8} +O(q^{10})\)	\(q+(0.131442 + 0.575886i) q^{2} +(1.48757 - 0.716376i) q^{4} +(-1.01472 - 1.27242i) q^{5} +(2.21270 + 1.45050i) q^{7} +(1.34467 + 1.68616i) q^{8} +(0.599392 - 0.751614i) q^{10} +(-1.34004 - 5.87109i) q^{11} +(0.430296 + 1.88525i) q^{13} +(-0.544483 + 1.46492i) q^{14} +(1.26457 - 1.58572i) q^{16} +(5.24693 + 2.52679i) q^{17} -1.43943 q^{19} +(-2.42100 - 1.16589i) q^{20} +(3.20494 - 1.54342i) q^{22} +(-0.615561 + 0.296439i) q^{23} +(0.523209 - 2.29233i) q^{25} +(-1.02913 + 0.495603i) q^{26} +(4.33065 + 0.572602i) q^{28} +(-1.77848 - 0.856469i) q^{29} +1.60503 q^{31} +(4.96561 + 2.39131i) q^{32} +(-0.765473 + 3.35376i) q^{34} +(-0.399623 - 4.28735i) q^{35} +(-2.43336 - 1.17185i) q^{37} +(-0.189202 - 0.828948i) q^{38} +(0.781041 - 3.42196i) q^{40} +(2.74509 + 3.44223i) q^{41} +(3.73601 - 4.68481i) q^{43} +(-6.19931 - 7.77369i) q^{44} +(-0.251625 - 0.315528i) q^{46} +(2.60349 + 11.4066i) q^{47} +(2.79208 + 6.41906i) q^{49} +1.38889 q^{50} +(1.99064 + 2.49619i) q^{52} +(-10.9470 + 5.27178i) q^{53} +(-6.11074 + 7.66263i) q^{55} +(0.529563 + 5.68140i) q^{56} +(0.259462 - 1.13678i) q^{58} +(-5.38363 + 6.75085i) q^{59} +(-11.0773 - 5.33453i) q^{61} +(0.210968 + 0.924313i) q^{62} +(0.178210 - 0.780789i) q^{64} +(1.96220 - 2.46052i) q^{65} +1.47235 q^{67} +9.61530 q^{68} +(2.41649 - 0.793675i) q^{70} +(0.575382 - 0.277090i) q^{71} +(-2.60092 + 11.3954i) q^{73} +(0.355003 - 1.55537i) q^{74} +(-2.14126 + 1.03117i) q^{76} +(5.55094 - 14.9347i) q^{77} -12.3614 q^{79} -3.30090 q^{80} +(-1.62151 + 2.03331i) q^{82} +(2.03882 - 8.93264i) q^{83} +(-2.10904 - 9.24030i) q^{85} +(3.18898 + 1.53573i) q^{86} +(8.09768 - 10.1542i) q^{88} +(3.61486 - 15.8378i) q^{89} +(-1.78245 + 4.79564i) q^{91} +(-0.703329 + 0.881947i) q^{92} +(-6.22671 + 2.99863i) q^{94} +(1.46062 + 1.83156i) q^{95} -11.2648 q^{97} +(-3.32965 + 2.45165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) \) 60 * q - 12 * q^4 - 2 * q^7	\( 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) \) 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

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