LMFDB - Embedded newform 459.2.o.a.208.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(64,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			208.4
Character	$\chi$	$=$	459.208
Dual form			459.2.o.a.64.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.64395 - 0.949132i) q^{2} +(0.801704 + 1.38859i) q^{4} +(2.17864 + 0.583765i) q^{5} +(-1.92618 + 0.516120i) q^{7} +0.752835i q^{8} +(-3.02750 - 3.02750i) q^{10} +(-5.69260 + 1.52533i) q^{11} +(-2.62105 - 4.53979i) q^{13} +(3.65641 + 0.979732i) q^{14} +(2.31795 - 4.01481i) q^{16} +(2.46059 - 3.30840i) q^{17} -1.31278i q^{19} +(0.936014 + 3.49325i) q^{20} +(10.8061 + 2.89547i) q^{22} +(1.24995 - 4.66487i) q^{23} +(0.0755659 + 0.0436280i) q^{25} +9.95088i q^{26} +(-2.26091 - 2.26091i) q^{28} +(-1.64689 - 6.14628i) q^{29} +(-5.87097 - 1.57312i) q^{31} +(-6.31721 + 3.64725i) q^{32} +(-7.18518 + 3.10341i) q^{34} -4.49776 q^{35} +(0.0561633 - 0.0561633i) q^{37} +(-1.24601 + 2.15815i) q^{38} +(-0.439479 + 1.64016i) q^{40} +(0.875143 - 3.26608i) q^{41} +(0.590522 + 0.340938i) q^{43} +(-6.68184 - 6.68184i) q^{44} +(-6.48243 + 6.48243i) q^{46} +(0.445543 - 0.771702i) q^{47} +(-2.61837 + 1.51172i) q^{49} +(-0.0828175 - 0.143444i) q^{50} +(4.20261 - 7.27913i) q^{52} +3.82857i q^{53} -13.2926 q^{55} +(-0.388553 - 1.45010i) q^{56} +(-3.12623 + 11.6673i) q^{58} +(-10.3316 + 5.96494i) q^{59} +(9.62356 - 2.57863i) q^{61} +(8.15845 + 8.15845i) q^{62} +4.57508 q^{64} +(-3.06015 - 11.4206i) q^{65} +(2.54607 + 4.40993i) q^{67} +(6.56668 + 0.764390i) q^{68} +(7.39407 + 4.26897i) q^{70} +(-2.14742 + 2.14742i) q^{71} +(0.612456 - 0.612456i) q^{73} +(-0.145636 + 0.0390230i) q^{74} +(1.82292 - 1.05247i) q^{76} +(10.1777 - 5.87612i) q^{77} +(-0.617312 + 0.165408i) q^{79} +(7.39368 - 7.39368i) q^{80} +(-4.53863 + 4.53863i) q^{82} +(8.24317 + 4.75919i) q^{83} +(7.29206 - 5.77141i) q^{85} +(-0.647191 - 1.12097i) q^{86} +(-1.14832 - 4.28559i) q^{88} -16.7260 q^{89} +(7.39169 + 7.39169i) q^{91} +(7.47969 - 2.00418i) q^{92} +(-1.46490 + 0.845758i) q^{94} +(0.766358 - 2.86009i) q^{95} +(0.491234 + 1.83331i) q^{97} +5.73928 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7} - 16 q^{10} - 4 q^{13} - 16 q^{16} + 8 q^{17} - 18 q^{20} - 4 q^{22} + 8 q^{23} + 10 q^{29} - 2 q^{31} + 20 q^{34} + 128 q^{35} - 8 q^{37} + 24 q^{38} - 20 q^{40} - 32 q^{41}+ \cdots - 208 q^{98}+O(q^{100}) $ 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7 - 16 * q^10 - 4 * q^13 - 16 * q^16 + 8 * q^17 - 18 * q^20 - 4 * q^22 + 8 * q^23 + 10 * q^29 - 2 * q^31 + 20 * q^34 + 128 * q^35 - 8 * q^37 + 24 * q^38 - 20 * q^40 - 32 * q^41 - 20 * q^44 - 40 * q^46 + 64 * q^47 - 48 * q^50 + 36 * q^52 - 16 * q^55 - 12 * q^56 - 10 * q^58 - 2 * q^61 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^67 + 60 * q^68 + 84 * q^71 - 44 * q^73 + 14 * q^74 + 10 * q^79 - 204 * q^80 - 52 * q^82 + 22 * q^85 - 32 * q^86 + 16 * q^88 - 128 * q^89 + 44 * q^91 - 136 * q^92 - 4 * q^95 - 44 * q^97 - 208 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.64395	−	0.949132i	−1.16244	−	0.671138i	−0.210556	−	0.977582i	$-0.567528\pi$
$2$	−1.64395	−	0.949132i	−1.16244	−	0.671138i	−0.951889	+	0.306444i	$0.900861\pi$
$3$		0			0
$3$		0			0
$4$	0.801704	+	1.38859i	0.400852	+	0.694296i
$5$	2.17864	+	0.583765i	0.974318	+	0.261068i	0.710650	−	0.703546i	$-0.248401\pi$
$5$	2.17864	+	0.583765i	0.974318	+	0.261068i	0.263668	+	0.964614i	$0.415068\pi$
$6$		0			0
$7$	−1.92618	+	0.516120i	−0.728029	+	0.195075i	−0.603752	−	0.797173i	$-0.706328\pi$
$7$	−1.92618	+	0.516120i	−0.728029	+	0.195075i	−0.124278	+	0.992247i	$0.539661\pi$
$8$			0.752835i			0.266167i
$9$		0			0
$10$	−3.02750	−	3.02750i	−0.957378	−	0.957378i
$11$	−5.69260	+	1.52533i	−1.71638	+	0.459903i	−0.976975	−	0.213355i	$-0.931561\pi$
$11$	−5.69260	+	1.52533i	−1.71638	+	0.459903i	−0.739408	+	0.673258i	$0.764894\pi$
$12$		0			0
$13$	−2.62105	−	4.53979i	−0.726947	−	1.25911i	−0.958167	−	0.286208i	$-0.907605\pi$
$13$	−2.62105	−	4.53979i	−0.726947	−	1.25911i	0.231220	−	0.972902i	$-0.425728\pi$
$14$	3.65641	+	0.979732i	0.977216	+	0.261844i
$15$		0			0
$16$	2.31795	−	4.01481i	0.579487	−	1.00370i
$17$	2.46059	−	3.30840i	0.596780	−	0.802405i
$17$	2.46059	−	3.30840i	0.596780	−	0.802405i
$18$		0			0
$19$		−	1.31278i		−	0.301173i	−0.988597	−	0.150587i	$-0.951884\pi$
$19$		−	1.31278i		−	0.301173i	0.988597	−	0.150587i	$-0.0481163\pi$
$20$	0.936014	+	3.49325i	0.209299	+	0.781115i
$21$		0			0
$22$	10.8061	+	2.89547i	2.30386	+	0.617317i
$23$	1.24995	−	4.66487i	0.260632	−	0.972693i	−0.704238	−	0.709964i	$-0.748711\pi$
$23$	1.24995	−	4.66487i	0.260632	−	0.972693i	0.964870	−	0.262728i	$-0.0846223\pi$
$24$		0			0
$25$	0.0755659	+	0.0436280i	0.0151132	+	0.00872560i
$26$			9.95088i			1.95153i
$27$		0			0
$28$	−2.26091	−	2.26091i	−0.427272	−	0.427272i
$29$	−1.64689	−	6.14628i	−0.305820	−	1.14134i	−0.932237	−	0.361848i	$-0.882146\pi$
$29$	−1.64689	−	6.14628i	−0.305820	−	1.14134i	0.626417	−	0.779488i	$-0.284521\pi$
$30$		0			0
$31$	−5.87097	−	1.57312i	−1.05446	−	0.282541i	−0.310365	−	0.950618i	$-0.600451\pi$
$31$	−5.87097	−	1.57312i	−1.05446	−	0.282541i	−0.744092	+	0.668077i	$0.767118\pi$
$32$	−6.31721	+	3.64725i	−1.11674	+	0.644748i
$33$		0			0
$34$	−7.18518	+	3.10341i	−1.23225	+	0.532231i
$35$	−4.49776			−0.760260
$36$		0			0
$37$	0.0561633	−	0.0561633i	0.00923320	−	0.00923320i	−0.702475	−	0.711708i	$-0.747922\pi$
$37$	0.0561633	−	0.0561633i	0.00923320	−	0.00923320i	0.711708	+	0.702475i	$0.247922\pi$
$38$	−1.24601	+	2.15815i	−0.202129	+	0.350098i
$39$		0			0
$40$	−0.439479	+	1.64016i	−0.0694877	+	0.259332i
$41$	0.875143	−	3.26608i	0.136674	−	0.510076i	−0.863311	−	0.504672i	$-0.831613\pi$
$41$	0.875143	−	3.26608i	0.136674	−	0.510076i	0.999985	−	0.00540349i	$-0.00171999\pi$
$42$		0			0
$43$	0.590522	+	0.340938i	0.0900538	+	0.0519926i	0.544351	−	0.838858i	$-0.316776\pi$
$43$	0.590522	+	0.340938i	0.0900538	+	0.0519926i	−0.454297	+	0.890850i	$0.650109\pi$
$44$	−6.68184	−	6.68184i	−1.00733	−	1.00733i
$45$		0			0
$46$	−6.48243	+	6.48243i	−0.955782	+	0.955782i
$47$	0.445543	−	0.771702i	0.0649891	−	0.112564i	−0.831700	−	0.555225i	$-0.812632\pi$
$47$	0.445543	−	0.771702i	0.0649891	−	0.112564i	0.896689	+	0.442661i	$0.145965\pi$
$48$		0			0
$49$	−2.61837	+	1.51172i	−0.374053	+	0.215959i
$50$	−0.0828175	−	0.143444i	−0.0117122	−	0.0202861i
$51$		0			0
$52$	4.20261	−	7.27913i	0.582797	−	1.00943i
$53$			3.82857i			0.525894i	0.964810	+	0.262947i	$0.0846945\pi$
$53$			3.82857i			0.525894i	−0.964810	+	0.262947i	$0.915306\pi$
$54$		0			0
$55$	−13.2926			−1.79237
$56$	−0.388553	−	1.45010i	−0.0519226	−	0.193778i
$57$		0			0
$58$	−3.12623	+	11.6673i	−0.410495	+	1.53199i
$59$	−10.3316	+	5.96494i	−1.34506	+	0.776569i	−0.987545	−	0.157339i	$-0.949709\pi$
$59$	−10.3316	+	5.96494i	−1.34506	+	0.776569i	−0.357513	+	0.933908i	$0.616375\pi$
$60$		0			0
$61$	9.62356	−	2.57863i	1.23217	−	0.330159i	0.416746	−	0.909023i	$-0.363170\pi$
$61$	9.62356	−	2.57863i	1.23217	−	0.330159i	0.815424	+	0.578864i	$0.196504\pi$
$62$	8.15845	+	8.15845i	1.03612	+	1.03612i
$63$		0			0
$64$	4.57508			0.571885
$65$	−3.06015	−	11.4206i	−0.379565	−	1.41656i
$66$		0			0
$67$	2.54607	+	4.40993i	0.311052	+	0.538759i	0.978590	−	0.205817i	$-0.0659852\pi$
$67$	2.54607	+	4.40993i	0.311052	+	0.538759i	−0.667538	+	0.744576i	$0.732652\pi$
$68$	6.56668	+	0.764390i	0.796327	+	0.0926960i
$69$		0			0
$70$	7.39407	+	4.26897i	0.883760	+	0.510239i
$71$	−2.14742	+	2.14742i	−0.254852	+	0.254852i	−0.822956	−	0.568105i	$-0.807677\pi$
$71$	−2.14742	+	2.14742i	−0.254852	+	0.254852i	0.568105	+	0.822956i	$0.307677\pi$
$72$		0			0
$73$	0.612456	−	0.612456i	0.0716826	−	0.0716826i	−0.670357	−	0.742039i	$-0.733859\pi$
$73$	0.612456	−	0.612456i	0.0716826	−	0.0716826i	0.742039	+	0.670357i	$0.233859\pi$
$74$	−0.145636	+	0.0390230i	−0.0169298	+	0.00453633i
$75$		0			0
$76$	1.82292	−	1.05247i	0.209104	−	0.120726i
$77$	10.1777	−	5.87612i	1.15986	−	0.669646i
$78$		0			0
$79$	−0.617312	+	0.165408i	−0.0694530	+	0.0186099i	−0.293378	−	0.955996i	$-0.594780\pi$
$79$	−0.617312	+	0.165408i	−0.0694530	+	0.0186099i	0.223925	+	0.974606i	$0.428113\pi$
$80$	7.39368	−	7.39368i	0.826639	−	0.826639i
$81$		0			0
$82$	−4.53863	+	4.53863i	−0.501208	+	0.501208i
$83$	8.24317	+	4.75919i	0.904805	+	0.522389i	0.878756	−	0.477271i	$-0.158374\pi$
$83$	8.24317	+	4.75919i	0.904805	+	0.522389i	0.0260490	+	0.999661i	$0.491707\pi$
$84$		0			0
$85$	7.29206	−	5.77141i	0.790935	−	0.625998i
$86$	−0.647191	−	1.12097i	−0.0697884	−	0.120877i
$87$		0			0
$88$	−1.14832	−	4.28559i	−0.122411	−	0.456845i
$89$	−16.7260			−1.77295			−0.886477	−	0.462773i	$-0.846855\pi$
$89$	−16.7260			−1.77295			−0.886477	+	0.462773i	$0.846855\pi$
$90$		0			0
$91$	7.39169	+	7.39169i	0.774860	+	0.774860i
$92$	7.47969	−	2.00418i	0.779812	−	0.208950i
$93$		0			0
$94$	−1.46490	+	0.845758i	−0.151092	+	0.0872332i
$95$	0.766358	−	2.86009i	0.0786266	−	0.293439i
$96$		0			0
$97$	0.491234	+	1.83331i	0.0498773	+	0.186144i	0.986370	−	0.164543i	$-0.0526148\pi$
$97$	0.491234	+	1.83331i	0.0498773	+	0.186144i	−0.936493	+	0.350687i	$0.885948\pi$
$98$	5.73928			0.579754
$99$		0			0
$100$			0.139907i			0.0139907i
$101$	1.60224	−	2.77517i	0.159429	−	0.276140i	−0.775234	−	0.631674i	$-0.782368\pi$
$101$	1.60224	−	2.77517i	0.159429	−	0.276140i	0.934663	+	0.355535i	$0.115701\pi$
$102$		0			0
$103$	3.20194	+	5.54592i	0.315496	+	0.546455i	0.979543	−	0.201236i	$-0.0644957\pi$
$103$	3.20194	+	5.54592i	0.315496	+	0.546455i	−0.664047	+	0.747691i	$0.731162\pi$
$104$	3.41771	−	1.97322i	0.335134	−	0.193490i
$105$		0			0
$106$	3.63382	−	6.29396i	0.352948	−	0.611323i
$107$	9.50783	−	9.50783i	0.919157	−	0.919157i	−0.0778113	−	0.996968i	$-0.524793\pi$
$107$	9.50783	−	9.50783i	0.919157	−	0.919157i	0.996968	+	0.0778113i	$0.0247932\pi$
$108$		0			0
$109$	1.78834	+	1.78834i	0.171292	+	0.171292i	0.787547	−	0.616255i	$-0.211351\pi$
$109$	1.78834	+	1.78834i	0.171292	+	0.171292i	−0.616255	+	0.787547i	$0.711351\pi$
$110$	21.8522	+	12.6164i	2.08353	+	1.20293i
$111$		0			0
$112$	−2.39268	+	8.92960i	−0.226087	+	0.843767i
$113$	−1.92202	+	7.17308i	−0.180808	+	0.674786i	0.814681	+	0.579910i	$0.196912\pi$
$113$	−1.92202	+	7.17308i	−0.180808	+	0.674786i	−0.995489	+	0.0948765i	$0.969754\pi$
$114$		0			0
$115$	5.44638	−	9.43340i	0.507877	−	0.879669i
$116$	7.21436	−	7.21436i	0.669837	−	0.669837i
$117$		0			0
$118$	22.6461			2.08474
$119$	−3.03201	+	7.64255i	−0.277944	+	0.700591i
$120$		0			0
$121$	20.5528	−	11.8661i	1.86843	−	1.07874i
$122$	−18.2681	−	4.89491i	−1.65391	−	0.443165i
$123$		0			0
$124$	−2.52236	−	9.41356i	−0.226514	−	0.845363i
$125$	−7.83522	−	7.83522i	−0.700803	−	0.700803i
$126$		0			0
$127$		−	4.87460i		−	0.432551i	−0.976332	−	0.216276i	$-0.930609\pi$
$127$		−	4.87460i		−	0.432551i	0.976332	−	0.216276i	$-0.0693910\pi$
$128$	5.11325	+	2.95213i	0.451952	+	0.260934i
$129$		0			0
$130$	−5.80897	+	21.6794i	−0.509481	+	1.90141i
$131$	13.6726	+	3.66357i	1.19458	+	0.320088i	0.800696	−	0.599071i	$-0.204463\pi$
$131$	13.6726	+	3.66357i	1.19458	+	0.320088i	0.393888	+	0.919159i	$0.371130\pi$
$132$		0			0
$133$	0.677554	+	2.52867i	0.0587514	+	0.219263i
$134$		−	9.66624i		−	0.835036i
$135$		0			0
$136$	2.49068	+	1.85241i	0.213574	+	0.158843i
$137$	−4.17247	+	7.22692i	−0.356478	+	0.617438i	−0.987370	−	0.158433i	$-0.949356\pi$
$137$	−4.17247	+	7.22692i	−0.356478	+	0.617438i	0.630892	+	0.775871i	$0.282689\pi$
$138$		0			0
$139$	−11.2919	−	3.02565i	−0.957764	−	0.256632i	−0.254110	−	0.967175i	$-0.581783\pi$
$139$	−11.2919	−	3.02565i	−0.957764	−	0.256632i	−0.703653	+	0.710543i	$0.748449\pi$
$140$	−3.60587	−	6.24555i	−0.304752	−	0.527846i
$141$		0			0
$142$	5.56842	−	1.49205i	0.467291	−	0.125210i
$143$	21.8452	+	21.8452i	1.82679	+	1.82679i
$144$		0			0
$145$		−	14.3519i		−	1.19186i
$146$	−1.58815	+	0.425543i	−0.131436	+	0.0352182i
$147$		0			0
$148$	0.123014	+	0.0329616i	0.0101117	+	0.00270943i
$149$	−4.36926	−	7.56778i	−0.357944	−	0.619977i	0.629673	−	0.776860i	$-0.283189\pi$
$149$	−4.36926	−	7.56778i	−0.357944	−	0.619977i	−0.987617	+	0.156883i	$0.949855\pi$
$150$		0			0
$151$	−17.8387	−	10.2992i	−1.45169	−	0.838133i	−0.453112	−	0.891454i	$-0.649686\pi$
$151$	−17.8387	−	10.2992i	−1.45169	−	0.838133i	−0.998577	+	0.0533208i	$0.983019\pi$
$152$	0.988310			0.0801625
$153$		0			0
$154$	−22.3089			−1.79770
$155$	−11.8724	−	6.85453i	−0.953614	−	0.550569i
$156$		0			0
$157$	−2.89582	−	5.01570i	−0.231111	−	0.400296i	0.727024	−	0.686612i	$-0.240903\pi$
$157$	−2.89582	−	5.01570i	−0.231111	−	0.400296i	−0.958135	+	0.286315i	$0.907569\pi$
$158$	1.17182	+	0.313988i	0.0932251	+	0.0249796i
$159$		0			0
$160$	−15.8921	+	4.25827i	−1.25638	+	0.336646i
$161$			9.63052i			0.758992i
$162$		0			0
$163$	−4.43622	−	4.43622i	−0.347471	−	0.347471i	0.511695	−	0.859167i	$-0.329018\pi$
$163$	−4.43622	−	4.43622i	−0.347471	−	0.347471i	−0.859167	+	0.511695i	$0.829018\pi$
$164$	5.23686	−	1.40321i	0.408930	−	0.109572i
$165$		0			0
$166$	−9.03421	−	15.6477i	−0.701191	−	1.21450i
$167$	2.52239	+	0.675874i	0.195189	+	0.0523007i	0.355089	−	0.934833i	$-0.384451\pi$
$167$	2.52239	+	0.675874i	0.195189	+	0.0523007i	−0.159900	+	0.987133i	$0.551117\pi$
$168$		0			0
$169$	−7.23977	+	12.5396i	−0.556905	+	0.964588i
$170$	−17.4656	+	2.56676i	−1.33955	+	0.196862i
$171$		0			0
$172$			1.09333i			0.0833653i
$173$	2.83417	+	10.5773i	0.215478	+	0.804174i	0.985998	+	0.166758i	$0.0533299\pi$
$173$	2.83417	+	10.5773i	0.215478	+	0.804174i	−0.770520	+	0.637416i	$0.780003\pi$
$174$		0			0
$175$	−0.168071	−	0.0450346i	−0.0127050	−	0.00340429i
$176$	−7.07126	+	26.3903i	−0.533016	+	1.98924i
$177$		0			0
$178$	27.4967	+	15.8752i	2.06096	+	1.18990i
$179$		−	0.534388i		−	0.0399421i	−0.999801	−	0.0199710i	$-0.993643\pi$
$179$		−	0.534388i		−	0.0399421i	0.999801	−	0.0199710i	$-0.00635740\pi$
$180$		0			0
$181$	13.4383	+	13.4383i	0.998858	+	0.998858i	0.999999	−	0.00114159i	$-0.000363378\pi$
$181$	13.4383	+	13.4383i	0.998858	+	0.998858i	−0.00114159	+	0.999999i	$0.500363\pi$
$182$	−5.13584	−	19.1672i	−0.380694	−	1.42077i
$183$		0			0
$184$	3.51188	+	0.941005i	0.258899	+	0.0693718i
$185$	0.155146	−	0.0895735i	0.0114066	−	0.00658558i
$186$		0			0
$187$	−8.96073	+	22.5866i	−0.655273	+	1.65170i
$188$	1.42877			0.104204
$189$		0			0
$190$	−3.97445	+	3.97445i	−0.288337	+	0.288337i
$191$	−3.59850	+	6.23278i	−0.260378	+	0.450988i	−0.966342	−	0.257259i	$-0.917181\pi$
$191$	−3.59850	+	6.23278i	−0.260378	+	0.450988i	0.705964	+	0.708247i	$0.250514\pi$
$192$		0			0
$193$	6.45452	−	24.0886i	0.464606	−	1.73394i	−0.193584	−	0.981084i	$-0.562011\pi$
$193$	6.45452	−	24.0886i	0.464606	−	1.73394i	0.658191	−	0.752851i	$-0.271322\pi$
$194$	0.932492	−	3.48011i	0.0669490	−	0.249857i
$195$		0			0
$196$	−4.19832	−	2.42390i	−0.299880	−	0.173136i
$197$	−12.4512	−	12.4512i	−0.887112	−	0.887112i	0.107133	−	0.994245i	$-0.465833\pi$
$197$	−12.4512	−	12.4512i	−0.887112	−	0.887112i	−0.994245	+	0.107133i	$0.965833\pi$
$198$		0			0
$199$	13.8641	−	13.8641i	0.982802	−	0.982802i	−0.0170529	−	0.999855i	$-0.505428\pi$
$199$	13.8641	−	13.8641i	0.982802	−	0.982802i	0.999855	+	0.0170529i	$0.00542837\pi$
$200$	−0.0328447	+	0.0568887i	−0.00232247	+	0.00402264i
$201$		0			0
$202$	−5.26801	+	3.04148i	−0.370656	+	0.213998i
$203$	6.34443	+	10.9889i	0.445292	+	0.771268i
$204$		0			0
$205$	3.81324	−	6.60473i	0.266329	−	0.461295i
$206$		−	12.1562i		−	0.846966i
$207$		0			0
$208$	−24.3018			−1.68503
$209$	2.00243	+	7.47315i	0.138511	+	0.516929i
$210$		0			0
$211$	−2.71000	+	10.1139i	−0.186564	+	0.696267i	0.807726	+	0.589558i	$0.200698\pi$
$211$	−2.71000	+	10.1139i	−0.186564	+	0.696267i	−0.994290	+	0.106709i	$0.965969\pi$
$212$	−5.31632	+	3.06938i	−0.365126	+	0.210806i
$213$		0			0
$214$	−24.6545	+	6.60617i	−1.68535	+	0.451588i
$215$	1.08751	+	1.08751i	0.0741674	+	0.0741674i
$216$		0			0
$217$	12.1205			0.822792
$218$	−1.24256	−	4.63731i	−0.0841570	−	0.314078i
$219$		0			0
$220$	−10.6567	−	18.4579i	−0.718475	−	1.24443i
$221$	−21.4687	−	2.49905i	−1.44414	−	0.168105i
$222$		0			0
$223$	12.5294	+	7.23383i	0.839028	+	0.484413i	0.856934	−	0.515427i	$-0.172366\pi$
$223$	12.5294	+	7.23383i	0.839028	+	0.484413i	−0.0179056	+	0.999840i	$0.505700\pi$
$224$	10.2857	−	10.2857i	0.687243	−	0.687243i
$225$		0			0
$226$	9.96790	−	9.96790i	0.663055	−	0.663055i
$227$	14.8717	−	3.98485i	0.987067	−	0.264484i	0.271049	−	0.962566i	$-0.412629\pi$
$227$	14.8717	−	3.98485i	0.987067	−	0.264484i	0.716018	+	0.698082i	$0.245963\pi$
$228$		0			0
$229$	−17.3484	+	10.0161i	−1.14642	+	0.661884i	−0.948011	−	0.318236i	$-0.896909\pi$
$229$	−17.3484	+	10.0161i	−1.14642	+	0.661884i	−0.198405	+	0.980120i	$0.563576\pi$
$230$	−17.9071	+	10.3387i	−1.18076	+	0.681711i
$231$		0			0
$232$	4.62713	−	1.23984i	0.303786	−	0.0813993i
$233$	−1.40190	+	1.40190i	−0.0918418	+	0.0918418i	−0.751535	−	0.659693i	$-0.770686\pi$
$233$	−1.40190	+	1.40190i	−0.0918418	+	0.0918418i	0.659693	+	0.751535i	$0.270686\pi$
$234$		0			0
$235$	1.42117	−	1.42117i	0.0927069	−	0.0927069i
$236$	−16.5658	−	9.56424i	−1.07834	−	0.622579i
$237$		0			0
$238$	12.2382	−	9.68615i	0.793288	−	0.627860i
$239$	−10.0805	−	17.4599i	−0.652052	−	1.12939i	−0.982624	−	0.185606i	$-0.940575\pi$
$239$	−10.0805	−	17.4599i	−0.652052	−	1.12939i	0.330573	−	0.943781i	$-0.392758\pi$
$240$		0			0
$241$	4.72441	+	17.6317i	0.304326	+	1.13576i	0.933524	+	0.358515i	$0.116717\pi$
$241$	4.72441	+	17.6317i	0.304326	+	1.13576i	−0.629198	+	0.777245i	$0.716616\pi$
$242$	−45.0502			−2.89593
$243$		0			0
$244$	11.2959	+	11.2959i	0.723147	+	0.723147i
$245$	−6.58697	+	1.76497i	−0.420826	+	0.112760i
$246$		0			0
$247$	−5.95976	+	3.44087i	−0.379211	+	0.218937i
$248$	1.18430	−	4.41987i	0.0752032	−	0.280662i
$249$		0			0
$250$	5.44401	+	20.3173i	0.344309	+	1.28498i
$251$	−12.6084			−0.795835			−0.397917	−	0.917421i	$-0.630267\pi$
$251$	−12.6084			−0.795835			−0.397917	+	0.917421i	$0.630267\pi$
$252$		0			0
$253$			28.4618i			1.78938i
$254$	−4.62664	+	8.01358i	−0.290301	+	0.502817i
$255$		0			0
$256$	−10.1790	−	17.6306i	−0.636188	−	1.10191i
$257$	16.6738	−	9.62661i	1.04008	−	0.600492i	0.120225	−	0.992747i	$-0.461638\pi$
$257$	16.6738	−	9.62661i	1.04008	−	0.600492i	0.919856	+	0.392255i	$0.128305\pi$
$258$		0			0
$259$	−0.0791940	+	0.137168i	−0.00492087	+	0.00852320i
$260$	13.4053	−	13.4053i	0.831360	−	0.831360i
$261$		0			0
$262$	−18.9999	−	18.9999i	−1.17381	−	1.17381i
$263$	−16.2155	−	9.36203i	−0.999891	−	0.577287i	−0.0916751	−	0.995789i	$-0.529222\pi$
$263$	−16.2155	−	9.36203i	−0.999891	−	0.577287i	−0.908216	+	0.418502i	$0.862555\pi$
$264$		0			0
$265$	−2.23498	+	8.34107i	−0.137294	+	0.512388i
$266$	1.28618	−	4.80008i	0.0788606	−	0.294312i
$267$		0			0
$268$	−4.08240	+	7.07092i	−0.249372	+	0.431925i
$269$	2.67436	−	2.67436i	0.163059	−	0.163059i	−0.620862	−	0.783920i	$-0.713217\pi$
$269$	2.67436	−	2.67436i	0.163059	−	0.163059i	0.783920	+	0.620862i	$0.213217\pi$
$270$		0			0
$271$	−14.8066			−0.899435			−0.449717	−	0.893171i	$-0.648475\pi$
$271$	−14.8066			−0.899435			−0.449717	+	0.893171i	$0.648475\pi$
$272$	−7.57908	−	17.5475i	−0.459549	−	1.06397i
$273$		0			0
$274$	13.7186	−	7.92045i	0.828772	−	0.478492i
$275$	−0.496713	−	0.133094i	−0.0299530	−	0.00802587i
$276$		0			0
$277$	−0.224755	−	0.838796i	−0.0135042	−	0.0503984i	0.958845	−	0.283930i	$-0.0916384\pi$
$277$	−0.224755	−	0.838796i	−0.0135042	−	0.0503984i	−0.972349	+	0.233532i	$0.924972\pi$
$278$	15.6915	+	15.6915i	0.941112	+	0.941112i
$279$		0			0
$280$		−	3.38607i		−	0.202356i
$281$	1.82873	+	1.05582i	0.109093	+	0.0629847i	0.553554	−	0.832814i	$-0.313271\pi$
$281$	1.82873	+	1.05582i	0.109093	+	0.0629847i	−0.444461	+	0.895798i	$0.646605\pi$
$282$		0			0
$283$	7.82835	−	29.2158i	0.465347	−	1.73670i	−0.190389	−	0.981709i	$-0.560975\pi$
$283$	7.82835	−	29.2158i	0.465347	−	1.73670i	0.655736	−	0.754990i	$-0.272358\pi$
$284$	−4.70348	−	1.26029i	−0.279100	−	0.0747847i
$285$		0			0
$286$	−15.1783	−	56.6463i	−0.897514	−	3.34957i
$287$			6.74275i			0.398012i
$288$		0			0
$289$	−4.89104	−	16.2812i	−0.287708	−	0.957718i
$290$	−13.6219	+	23.5938i	−0.799905	+	1.38548i
$291$		0			0
$292$	1.34146	+	0.359444i	0.0785031	+	0.0210348i
$293$	6.50970	+	11.2751i	0.380301	+	0.658700i	0.991105	−	0.133081i	$-0.0424872\pi$
$293$	6.50970	+	11.2751i	0.380301	+	0.658700i	−0.610804	+	0.791781i	$0.709154\pi$
$294$		0			0
$295$	−25.9909	+	6.96425i	−1.51325	+	0.405474i
$296$	0.0422817	+	0.0422817i	0.00245757	+	0.00245757i
$297$		0			0
$298$			16.5880i			0.960919i
$299$	−24.4537	+	6.55234i	−1.41419	+	0.378932i
$300$		0			0
$301$	−1.31342	−	0.351930i	−0.0757042	−	0.0202849i
$302$	19.5505	+	33.8625i	1.12501	+	1.94857i
$303$		0			0
$304$	−5.27058	−	3.04297i	−0.302288	−	0.174526i
$305$	22.4716			1.28672
$306$		0			0
$307$	7.13616			0.407282			0.203641	−	0.979046i	$-0.434722\pi$
$307$	7.13616			0.407282			0.203641	+	0.979046i	$0.434722\pi$
$308$	16.3191	+	9.42183i	0.929866	+	0.536858i
$309$		0			0
$310$	13.0117	+	22.5369i	0.739016	+	1.28001i
$311$	12.6600	+	3.39224i	0.717884	+	0.192356i	0.599227	−	0.800579i	$-0.295475\pi$
$311$	12.6600	+	3.39224i	0.717884	+	0.192356i	0.118657	+	0.992935i	$0.462141\pi$
$312$		0			0
$313$	0.891295	−	0.238822i	0.0503790	−	0.0134990i	−0.233542	−	0.972347i	$-0.575031\pi$
$313$	0.891295	−	0.238822i	0.0503790	−	0.0134990i	0.283921	+	0.958848i	$0.408365\pi$
$314$			10.9940i			0.620430i
$315$		0			0
$316$	−0.724586	−	0.724586i	−0.0407612	−	0.0407612i
$317$	31.0198	−	8.31174i	1.74225	−	0.466834i	0.759303	−	0.650737i	$-0.225540\pi$
$317$	31.0198	−	8.31174i	1.74225	−	0.466834i	0.982944	+	0.183904i	$0.0588734\pi$
$318$		0			0
$319$	18.7502	+	32.4763i	1.04981	+	1.81832i
$320$	9.96745	+	2.67077i	0.557198	+	0.149301i
$321$		0			0
$322$	9.14064	−	15.8321i	0.509388	−	0.882286i
$323$	−4.34322	−	3.23022i	−0.241663	−	0.179734i
$324$		0			0
$325$		−	0.457404i		−	0.0253722i
$326$	3.08234	+	11.5035i	0.170715	+	0.637118i
$327$		0			0
$328$	2.45882	+	0.658838i	0.135766	+	0.0363783i
$329$	−0.459907	+	1.71639i	−0.0253555	+	0.0946279i
$330$		0			0
$331$	−12.7084	−	7.33718i	−0.698515	−	0.403288i	0.108279	−	0.994121i	$-0.465466\pi$
$331$	−12.7084	−	7.33718i	−0.698515	−	0.403288i	−0.806794	+	0.590833i	$0.798799\pi$
$332$			15.2619i			0.837604i
$333$		0			0
$334$	−3.50519	−	3.50519i	−0.191795	−	0.191795i
$335$	2.97262	+	11.0940i	0.162411	+	0.606128i
$336$		0			0
$337$	−19.2763	−	5.16507i	−1.05005	−	0.281359i	−0.307776	−	0.951459i	$-0.599585\pi$
$337$	−19.2763	−	5.16507i	−1.05005	−	0.281359i	−0.742271	+	0.670099i	$0.766251\pi$
$338$	23.8036	−	13.7430i	1.29474	−	0.747520i
$339$		0			0
$340$	13.8602	+	5.49873i	0.751676	+	0.298211i
$341$	35.8206			1.93979
$342$		0			0
$343$	14.1337	−	14.1337i	0.763148	−	0.763148i
$344$	−0.256670	+	0.444566i	−0.0138387	+	0.0239694i
$345$		0			0
$346$	5.38000	−	20.0784i	0.289231	−	1.07942i
$347$	−0.741206	+	2.76622i	−0.0397900	+	0.148498i	−0.982963	−	0.183804i	$-0.941159\pi$
$347$	−0.741206	+	2.76622i	−0.0397900	+	0.148498i	0.943173	+	0.332302i	$0.107825\pi$
$348$		0			0
$349$	−4.47762	−	2.58516i	−0.239682	−	0.138380i	0.375349	−	0.926884i	$-0.377523\pi$
$349$	−4.47762	−	2.58516i	−0.239682	−	0.138380i	−0.615030	+	0.788503i	$0.710856\pi$
$350$	0.233556	+	0.233556i	0.0124841	+	0.0124841i
$351$		0			0
$352$	30.3981	−	30.3981i	1.62023	−	1.62023i
$353$	9.51485	−	16.4802i	0.506424	−	0.877153i	−0.493548	−	0.869719i	$-0.664300\pi$
$353$	9.51485	−	16.4802i	0.506424	−	0.877153i	0.999972	−	0.00743409i	$-0.00236637\pi$
$354$		0			0
$355$	−5.93204	+	3.42486i	−0.314840	+	0.181773i
$356$	−13.4093	−	23.2256i	−0.710693	−	1.23096i
$357$		0			0
$358$	−0.507205	+	0.878505i	−0.0268066	+	0.0464305i
$359$			16.3446i			0.862636i	0.902200	+	0.431318i	$0.141951\pi$
$359$			16.3446i			0.862636i	−0.902200	+	0.431318i	$0.858049\pi$
$360$		0			0
$361$	17.2766			0.909295
$362$	−9.33708	−	34.8464i	−0.490746	−	1.83149i
$363$		0			0
$364$	−4.33810	+	16.1900i	−0.227378	+	0.848587i
$365$	1.69185	−	0.976792i	0.0885556	−	0.0511276i
$366$		0			0
$367$	−7.31943	+	1.96123i	−0.382071	+	0.102376i	−0.444742	−	0.895659i	$-0.646705\pi$
$367$	−7.31943	+	1.96123i	−0.382071	+	0.102376i	0.0626713	+	0.998034i	$0.480038\pi$
$368$	−15.8312	−	15.8312i	−0.825260	−	0.825260i
$369$		0			0
$370$	−0.340069			−0.0176793
$371$	−1.97600	−	7.37453i	−0.102589	−	0.382866i
$372$		0			0
$373$	11.7350	+	20.3256i	0.607616	+	1.05242i	0.991632	+	0.129095i	$0.0412073\pi$
$373$	11.7350	+	20.3256i	0.607616	+	1.05242i	−0.384016	+	0.923326i	$0.625459\pi$
$374$	36.1686	−	28.6262i	1.87023	−	1.48023i
$375$		0			0
$376$	0.580964	+	0.335420i	0.0299610	+	0.0172980i
$377$	−23.5862	+	23.5862i	−1.21475	+	1.21475i
$378$		0			0
$379$	−2.92624	+	2.92624i	−0.150311	+	0.150311i	−0.778257	−	0.627946i	$-0.783896\pi$
$379$	−2.92624	+	2.92624i	−0.150311	+	0.150311i	0.627946	+	0.778257i	$0.283896\pi$
$380$	4.58589	−	1.22878i	0.235251	−	0.0630353i
$381$		0			0
$382$	11.8315	−	6.83090i	0.605350	−	0.349499i
$383$	5.45172	−	3.14755i	0.278570	−	0.160832i	−0.354206	−	0.935167i	$-0.615249\pi$
$383$	5.45172	−	3.14755i	0.278570	−	0.160832i	0.632776	+	0.774335i	$0.281915\pi$
$384$		0			0
$385$	25.6039	−	6.86055i	1.30490	−	0.349646i
$386$	−33.4741	+	33.4741i	−1.70379	+	1.70379i
$387$		0			0
$388$	−2.15190	+	2.15190i	−0.109246	+	0.109246i
$389$	8.39131	+	4.84472i	0.425456	+	0.245637i	0.697409	−	0.716673i	$-0.254336\pi$
$389$	8.39131	+	4.84472i	0.425456	+	0.245637i	−0.271953	+	0.962311i	$0.587669\pi$
$390$		0			0
$391$	−12.3577	−	15.6136i	−0.624954	−	0.789616i
$392$	−1.13807	−	1.97120i	−0.0574814	−	0.0995606i
$393$		0			0
$394$	8.65127	+	32.2870i	0.435844	+	1.62659i
$395$	−1.44146			−0.0725277
$396$		0			0
$397$	13.1234	+	13.1234i	0.658644	+	0.658644i	0.955059	−	0.296415i	$-0.0957912\pi$
$397$	13.1234	+	13.1234i	0.658644	+	0.658644i	−0.296415	+	0.955059i	$0.595791\pi$
$398$	−35.9508	+	9.63298i	−1.80205	+	0.482857i
$399$		0			0
$400$	0.350316	−	0.202255i	0.0175158	−	0.0101128i
$401$	0.963549	−	3.59601i	0.0481173	−	0.179576i	−0.937685	−	0.347487i	$-0.887035\pi$
$401$	0.963549	−	3.59601i	0.0481173	−	0.179576i	0.985802	+	0.167910i	$0.0537019\pi$
$402$		0			0
$403$	8.24645	+	30.7762i	0.410785	+	1.53307i
$404$	5.13811			0.255630
$405$		0			0
$406$		−	24.0868i		−	1.19541i
$407$	−0.234048	+	0.405383i	−0.0116013	+	0.0200941i
$408$		0			0
$409$	−11.6145	−	20.1169i	−0.574300	−	0.994716i	−0.996117	−	0.0880356i	$-0.971941\pi$
$409$	−11.6145	−	20.1169i	−0.574300	−	0.994716i	0.421818	−	0.906681i	$-0.361392\pi$
$410$	−12.5375	+	7.23855i	−0.619185	+	0.357486i
$411$		0			0
$412$	−5.13401	+	8.89237i	−0.252935	+	0.438096i
$413$	16.8219	−	16.8219i	0.827752	−	0.827752i
$414$		0			0
$415$	15.1806	+	15.1806i	0.745189	+	0.745189i
$416$	33.1154	+	19.1192i	1.62362	+	0.937396i
$417$		0			0
$418$	3.80113	−	14.1860i	0.185920	−	0.693861i
$419$	0.483059	−	1.80280i	0.0235990	−	0.0880727i	−0.953122	−	0.302586i	$-0.902150\pi$
$419$	0.483059	−	1.80280i	0.0235990	−	0.0880727i	0.976721	+	0.214514i	$0.0688166\pi$
$420$		0			0
$421$	4.54349	−	7.86955i	0.221436	−	0.383539i	−0.733808	−	0.679357i	$-0.762259\pi$
$421$	4.54349	−	7.86955i	0.221436	−	0.383539i	0.955244	+	0.295818i	$0.0955922\pi$
$422$	14.0545	−	14.0545i	0.684162	−	0.684162i
$423$		0			0
$424$	−2.88228			−0.139976
$425$	0.330275	−	0.142652i	0.0160207	−	0.00691964i
$426$		0			0
$427$	−17.2059	+	9.93382i	−0.832651	+	0.480731i
$428$	20.8250	+	5.58004i	1.00661	+	0.269721i
$429$		0			0
$430$	−0.755615	−	2.81999i	−0.0364390	−	0.135992i
$431$	23.2645	+	23.2645i	1.12061	+	1.12061i	0.991650	+	0.128961i	$0.0411641\pi$
$431$	23.2645	+	23.2645i	1.12061	+	1.12061i	0.128961	+	0.991650i	$0.458836\pi$
$432$		0			0
$433$			39.0956i			1.87882i	0.342802	+	0.939408i	$0.388624\pi$
$433$			39.0956i			1.87882i	−0.342802	+	0.939408i	$0.611376\pi$
$434$	−19.9254	−	11.5039i	−0.956451	−	0.552207i
$435$		0			0
$436$	−1.04956	+	3.91700i	−0.0502647	+	0.187590i
$437$	−6.12397	−	1.64091i	−0.292949	−	0.0784955i
$438$		0			0
$439$	−3.49320	−	13.0368i	−0.166721	−	0.622212i	−0.997814	−	0.0660790i	$-0.978951\pi$
$439$	−3.49320	−	13.0368i	−0.166721	−	0.622212i	0.831093	−	0.556133i	$-0.187716\pi$
$440$		−	10.0071i		−	0.477070i
$441$		0			0
$442$	32.9215	+	24.4850i	1.56592	+	1.16463i
$443$	13.6564	−	23.6536i	0.648837	−	1.12382i	−0.334564	−	0.942373i	$-0.608589\pi$
$443$	13.6564	−	23.6536i	0.648837	−	1.12382i	0.983401	−	0.181446i	$-0.0580776\pi$
$444$		0			0
$445$	−36.4400	−	9.76406i	−1.72742	−	0.462861i
$446$	−13.7317	−	23.7840i	−0.650216	−	1.12621i
$447$		0			0
$448$	−8.81245	+	2.36129i	−0.416349	+	0.111560i
$449$	−20.8158	−	20.8158i	−0.982358	−	0.982358i	0.0174887	−	0.999847i	$-0.494433\pi$
$449$	−20.8158	−	20.8158i	−0.982358	−	0.982358i	−0.999847	+	0.0174887i	$0.994433\pi$
$450$		0			0
$451$			19.9273i			0.938342i
$452$	−11.5014	+	3.08178i	−0.540979	+	0.144955i
$453$		0			0
$454$	−28.2304	−	7.56430i	−1.32492	−	0.355010i
$455$	11.7888	+	20.4189i	0.552669	+	0.957250i
$456$		0			0
$457$	10.7308	+	6.19545i	0.501967	+	0.289811i	0.729526	−	0.683953i	$-0.239741\pi$
$457$	10.7308	+	6.19545i	0.501967	+	0.289811i	−0.227558	+	0.973764i	$0.573074\pi$
$458$	38.0265			1.77686
$459$		0			0
$460$	17.4655			0.814335
$461$	−4.49683	−	2.59625i	−0.209438	−	0.120919i	0.391612	−	0.920130i	$-0.371918\pi$
$461$	−4.49683	−	2.59625i	−0.209438	−	0.120919i	−0.601050	+	0.799211i	$0.705251\pi$
$462$		0			0
$463$	14.3180	+	24.7996i	0.665416	+	1.15253i	0.979172	+	0.203031i	$0.0650791\pi$
$463$	14.3180	+	24.7996i	0.665416	+	1.15253i	−0.313756	+	0.949503i	$0.601588\pi$
$464$	−28.4935	−	7.63482i	−1.32278	−	0.354438i
$465$		0			0
$466$	3.63525	−	0.974061i	0.168399	−	0.0451225i
$467$			3.20188i			0.148165i	0.997252	+	0.0740826i	$0.0236028\pi$
$467$			3.20188i			0.148165i	−0.997252	+	0.0740826i	$0.976397\pi$
$468$		0			0
$469$	−7.18026	−	7.18026i	−0.331554	−	0.331554i
$470$	−3.68520	+	0.987447i	−0.169986	+	0.0455476i
$471$		0			0
$472$	−4.49062	−	7.77798i	−0.206697	−	0.358010i
$473$	−3.88165	−	1.04008i	−0.178478	−	0.0478231i
$474$		0			0
$475$	0.0572742	−	0.0992018i	0.00262792	−	0.00455169i
$476$	−13.0432	+	1.91684i	−0.597832	+	0.0878581i
$477$		0			0
$478$			38.2708i			1.75047i
$479$	−2.72711	−	10.1777i	−0.124605	−	0.465032i	0.875220	−	0.483724i	$-0.160716\pi$
$479$	−2.72711	−	10.1777i	−0.124605	−	0.465032i	−0.999825	+	0.0186927i	$0.994050\pi$
$480$		0			0
$481$	−0.402176	−	0.107763i	−0.0183377	−	0.00491356i
$482$	8.96818	−	33.4697i	0.408489	−	1.52450i
$483$		0			0
$484$	32.9545	+	19.0263i	1.49793	+	0.864831i
$485$			4.28089i			0.194385i
$486$		0			0
$487$	−24.6742	−	24.6742i	−1.11809	−	1.11809i	−0.992021	−	0.126073i	$-0.959763\pi$
$487$	−24.6742	−	24.6742i	−1.11809	−	1.11809i	−0.126073	−	0.992021i	$-0.540237\pi$
$488$	1.94128	+	7.24495i	0.0878776	+	0.327964i
$489$		0			0
$490$	12.5038	+	3.35039i	0.564865	+	0.151355i
$491$	−24.0866	+	13.9064i	−1.08701	+	0.627587i	−0.932780	−	0.360447i	$-0.882624\pi$
$491$	−24.0866	+	13.9064i	−1.08701	+	0.627587i	−0.154234	+	0.988034i	$0.549291\pi$
$492$		0			0
$493$	−24.3867	−	9.67487i	−1.09832	−	0.435734i
$494$	13.0634			0.587748
$495$		0			0
$496$	−19.9244	+	19.9244i	−0.894631	+	0.894631i
$497$	3.02800	−	5.24465i	0.135824	−	0.235255i
$498$		0			0
$499$	4.42000	−	16.4956i	0.197866	−	0.738447i	−0.793640	−	0.608388i	$-0.791817\pi$
$499$	4.42000	−	16.4956i	0.197866	−	0.738447i	0.991506	−	0.130059i	$-0.0415167\pi$
$500$	4.59840	−	17.1615i	0.205647	−	0.767483i
$501$		0			0
$502$	20.7275	+	11.9670i	0.925114	+	0.534115i
$503$	−5.39636	−	5.39636i	−0.240612	−	0.240612i	0.576491	−	0.817103i	$-0.304421\pi$
$503$	−5.39636	−	5.39636i	−0.240612	−	0.240612i	−0.817103	+	0.576491i	$0.804421\pi$
$504$		0			0
$505$	5.11076	−	5.11076i	0.227426	−	0.227426i
$506$	27.0140	−	46.7897i	1.20092	−	2.08005i
$507$		0			0
$508$	6.76884	−	3.90799i	0.300319	−	0.173389i
$509$	−14.3762	−	24.9003i	−0.637214	−	1.10369i	−0.986041	−	0.166500i	$-0.946753\pi$
$509$	−14.3762	−	24.9003i	−0.637214	−	1.10369i	0.348827	−	0.937187i	$-0.386580\pi$
$510$		0			0
$511$	−0.863603	+	1.49581i	−0.0382036	+	0.0661705i
$512$			26.8364i			1.18601i
$513$		0			0
$514$	−36.5477			−1.61205
$515$	3.73836	+	13.9517i	0.164732	+	0.614787i
$516$		0			0
$517$	−1.35920	+	5.07259i	−0.0597774	+	0.223092i
$518$	0.260381	−	0.150331i	0.0114405	−	0.00660517i
$519$		0			0
$520$	8.59785	−	2.30379i	0.377041	−	0.101028i
$521$	−11.0656	−	11.0656i	−0.484792	−	0.484792i	0.421866	−	0.906658i	$-0.361375\pi$
$521$	−11.0656	−	11.0656i	−0.484792	−	0.484792i	−0.906658	+	0.421866i	$0.861375\pi$
$522$		0			0
$523$	−25.0456			−1.09517			−0.547585	−	0.836750i	$-0.684453\pi$
$523$	−25.0456			−1.09517			−0.547585	+	0.836750i	$0.684453\pi$
$524$	5.87420	+	21.9228i	0.256616	+	0.957703i
$525$		0			0
$526$	17.7716	+	30.7813i	0.774879	+	1.34213i
$527$	−19.6505	+	15.5527i	−0.855991	+	0.677487i
$528$		0			0
$529$	−0.280057	−	0.161691i	−0.0121764	−	0.00703004i
$530$	11.5910	−	11.5910i	0.503480	−	0.503480i
$531$		0			0
$532$	−2.96809	+	2.96809i	−0.128683	+	0.128683i
$533$	−17.1211	+	4.58758i	−0.741597	+	0.198710i
$534$		0			0
$535$	26.2645	−	15.1638i	1.13551	−	0.655589i
$536$	−3.31995	+	1.91677i	−0.143400	+	0.0827920i
$537$		0			0
$538$	−6.93482	+	1.85818i	−0.298981	+	0.0801118i
$539$	12.5995	−	12.5995i	0.542697	−	0.542697i
$540$		0			0
$541$	18.4736	−	18.4736i	0.794242	−	0.794242i	−0.187939	−	0.982181i	$-0.560181\pi$
$541$	18.4736	−	18.4736i	0.794242	−	0.794242i	0.982181	+	0.187939i	$0.0601806\pi$
$542$	24.3412	+	14.0534i	1.04554	+	0.603645i
$543$		0			0
$544$	−3.47749	+	29.8742i	−0.149096	+	1.28085i
$545$	2.85218	+	4.94013i	0.122174	+	0.211612i
$546$		0			0
$547$	−8.23746	−	30.7426i	−0.352208	−	1.31446i	−0.883961	−	0.467560i	$-0.845133\pi$
$547$	−8.23746	−	30.7426i	−0.352208	−	1.31446i	0.531753	−	0.846899i	$-0.321533\pi$
$548$	−13.3803			−0.571580
$549$		0			0
$550$	0.690246	+	0.690246i	0.0294322	+	0.0294322i
$551$	−8.06874	+	2.16201i	−0.343740	+	0.0921049i
$552$		0			0
$553$	1.10369	−	0.637213i	0.0469335	−	0.0270971i
$554$	−0.426644	+	1.59226i	−0.0181264	+	0.0676485i
$555$		0			0
$556$	−4.85135	−	18.1055i	−0.205743	−	0.767843i
$557$	−18.3168			−0.776109			−0.388054	−	0.921636i	$-0.626853\pi$
$557$	−18.3168			−0.776109			−0.388054	+	0.921636i	$0.626853\pi$
$558$		0			0
$559$		−	3.57446i		−	0.151183i
$560$	−10.4256	+	18.0576i	−0.440561	+	0.763074i
$561$		0			0
$562$	−2.00422	−	3.47141i	−0.0845429	−	0.146433i
$563$	−32.8350	+	18.9573i	−1.38383	+	0.798954i	−0.992610	−	0.121344i	$-0.961279\pi$
$563$	−32.8350	+	18.9573i	−1.38383	+	0.798954i	−0.391218	+	0.920298i	$0.627946\pi$
$564$		0			0
$565$	−8.37478	+	14.5056i	−0.352330	+	0.610253i
$566$	−40.5990	+	40.5990i	−1.70650	+	1.70650i
$567$		0			0
$568$	−1.61665	−	1.61665i	−0.0678331	−	0.0678331i
$569$	12.1507	+	7.01522i	0.509384	+	0.294093i	0.732581	−	0.680680i	$-0.238316\pi$
$569$	12.1507	+	7.01522i	0.509384	+	0.294093i	−0.223196	+	0.974774i	$0.571649\pi$
$570$		0			0
$571$	−8.01644	+	29.9178i	−0.335478	+	1.25202i	0.567873	+	0.823116i	$0.307767\pi$
$571$	−8.01644	+	29.9178i	−0.335478	+	1.25202i	−0.903350	+	0.428903i	$0.858900\pi$
$572$	−12.8207	+	47.8475i	−0.536061	+	2.00061i
$573$		0			0
$574$	6.39976	−	11.0847i	0.267121	−	0.462667i
$575$	0.297973	−	0.297973i	0.0124263	−	0.0124263i
$576$		0			0
$577$	−38.0720			−1.58496			−0.792479	−	0.609899i	$-0.791210\pi$
$577$	−38.0720			−1.58496			−0.792479	+	0.609899i	$0.791210\pi$
$578$	−7.41241	+	31.4077i	−0.308316	+	1.30639i
$579$		0			0
$580$	19.9290	−	11.5060i	0.827506	−	0.477761i
$581$	−18.3342	−	4.91263i	−0.760630	−	0.203810i
$582$		0			0
$583$	−5.83982	−	21.7945i	−0.241860	−	0.902636i
$584$	0.461079	+	0.461079i	0.0190796	+	0.0190796i
$585$		0			0
$586$		−	24.7143i		−	1.02094i
$587$	−7.39465	−	4.26930i	−0.305210	−	0.176213i	0.339571	−	0.940580i	$-0.389718\pi$
$587$	−7.39465	−	4.26930i	−0.305210	−	0.176213i	−0.644781	+	0.764367i	$0.723051\pi$
$588$		0			0
$589$	−2.06517	+	7.70732i	−0.0850938	+	0.317574i
$590$	49.3377	+	13.2200i	2.03120	+	0.544258i
$591$		0			0
$592$	−0.0953011	−	0.355669i	−0.00391685	−	0.0146179i
$593$		−	25.3743i		−	1.04200i	−0.853558	−	0.520998i	$-0.825560\pi$
$593$		−	25.3743i		−	1.04200i	0.853558	−	0.520998i	$-0.174440\pi$
$594$		0			0
$595$	−11.0671	+	14.8804i	−0.453707	+	0.610036i
$596$	7.00571	−	12.1342i	0.286965	−	0.497038i
$597$		0			0
$598$	46.4196	+	12.4381i	1.89824	+	0.508631i
$599$	12.5835	+	21.7952i	0.514146	+	0.890527i	0.999865	+	0.0164122i	$0.00522440\pi$
$599$	12.5835	+	21.7952i	0.514146	+	0.890527i	−0.485719	+	0.874115i	$0.661442\pi$
$600$		0			0
$601$	−23.9794	+	6.42527i	−0.978141	+	0.262092i	−0.712261	−	0.701914i	$-0.752329\pi$
$601$	−23.9794	+	6.42527i	−0.978141	+	0.262092i	−0.265879	+	0.964006i	$0.585662\pi$
$602$	1.82516	+	1.82516i	0.0743881	+	0.0743881i
$603$		0			0
$604$		−	33.0275i		−	1.34387i
$605$	51.7041	−	13.8541i	2.10207	−	0.563248i
$606$		0			0
$607$	−21.2255	−	5.68736i	−0.861517	−	0.230843i	−0.199101	−	0.979979i	$-0.563802\pi$
$607$	−21.2255	−	5.68736i	−0.861517	−	0.230843i	−0.662416	+	0.749136i	$0.730469\pi$
$608$	4.78805	+	8.29314i	0.194181	+	0.336331i
$609$		0			0
$610$	−36.9421	−	21.3285i	−1.49574	−	0.863566i
$611$	−4.67115			−0.188975
$612$		0			0
$613$	28.5467			1.15299			0.576495	−	0.817100i	$-0.304420\pi$
$613$	28.5467			1.15299			0.576495	+	0.817100i	$0.304420\pi$
$614$	−11.7315	−	6.77316i	−0.473443	−	0.273342i
$615$		0			0
$616$	4.42375	+	7.66216i	0.178238	+	0.308717i
$617$	12.8125	+	3.43310i	0.515812	+	0.138211i	0.507329	−	0.861753i	$-0.330633\pi$
$617$	12.8125	+	3.43310i	0.515812	+	0.138211i	0.00848330	+	0.999964i	$0.497300\pi$
$618$		0			0
$619$	15.4344	−	4.13562i	0.620359	−	0.166225i	0.0650681	−	0.997881i	$-0.479274\pi$
$619$	15.4344	−	4.13562i	0.620359	−	0.166225i	0.555291	+	0.831656i	$0.312607\pi$
$620$		−	21.9812i		−	0.882787i
$621$		0			0
$622$	−17.5927	−	17.5927i	−0.705403	−	0.705403i
$623$	32.2174	−	8.63262i	1.29076	−	0.345859i
$624$		0			0
$625$	−12.7143	−	22.0219i	−0.508573	−	0.880875i
$626$	−1.69191	−	0.453347i	−0.0676225	−	0.0181194i
$627$		0			0
$628$	4.64318	−	8.04222i	0.185283	−	0.320919i
$629$	−0.0476162	−	0.324006i	−0.00189858	−	0.0129189i
$630$		0			0
$631$			12.9668i			0.516200i	0.966118	+	0.258100i	$0.0830964\pi$
$631$			12.9668i			0.516200i	−0.966118	+	0.258100i	$0.916904\pi$
$632$	−0.124525	−	0.464734i	−0.00495334	−	0.0184861i
$633$		0			0
$634$	−58.8838	−	15.7779i	−2.33858	−	0.626620i
$635$	2.84562	−	10.6200i	0.112925	−	0.421442i
$636$		0			0
$637$	13.7257	+	7.92456i	0.543833	+	0.313982i
$638$		−	71.1856i		−	2.81826i
$639$		0			0
$640$	9.41658	+	9.41658i	0.372223	+	0.372223i
$641$	1.88100	+	7.02000i	0.0742951	+	0.277273i	0.993073	−	0.117503i	$-0.0374889\pi$
$641$	1.88100	+	7.02000i	0.0742951	+	0.277273i	−0.918777	+	0.394776i	$0.870822\pi$
$642$		0			0
$643$	16.4649	+	4.41175i	0.649311	+	0.173982i	0.568417	−	0.822740i	$-0.307556\pi$
$643$	16.4649	+	4.41175i	0.649311	+	0.173982i	0.0808938	+	0.996723i	$0.474223\pi$
$644$	−13.3729	+	7.72083i	−0.526965	+	0.304243i
$645$		0			0
$646$	4.07411	+	9.43259i	0.160294	+	0.371120i
$647$	−20.9417			−0.823304			−0.411652	−	0.911341i	$-0.635048\pi$
$647$	−20.9417			−0.823304			−0.411652	+	0.911341i	$0.635048\pi$
$648$		0			0
$649$	49.7151	−	49.7151i	1.95149	−	1.95149i
$650$	−0.434137	+	0.751948i	−0.0170283	+	0.0294938i
$651$		0			0
$652$	2.60357	−	9.71664i	0.101963	−	0.380533i
$653$	6.01663	−	22.4544i	0.235449	−	0.878708i	−0.742497	−	0.669850i	$-0.766359\pi$
$653$	6.01663	−	22.4544i	0.235449	−	0.878708i	0.977946	−	0.208858i	$-0.0669747\pi$
$654$		0			0
$655$	27.6491	+	15.9632i	1.08034	+	0.623734i
$656$	−11.0841	−	11.0841i	−0.432763	−	0.432763i
$657$		0			0
$658$	2.38515	−	2.38515i	0.0929827	−	0.0929827i
$659$	−4.09976	+	7.10100i	−0.159704	+	0.276616i	−0.934762	−	0.355275i	$-0.884387\pi$
$659$	−4.09976	+	7.10100i	−0.159704	+	0.276616i	0.775058	+	0.631890i	$0.217721\pi$
$660$		0			0
$661$	42.4508	−	24.5090i	1.65114	−	0.953288i	0.674540	−	0.738238i	$-0.264342\pi$
$661$	42.4508	−	24.5090i	1.65114	−	0.953288i	0.976603	−	0.215050i	$-0.0689913\pi$
$662$	13.9279	+	24.1238i	0.541323	+	0.937600i
$663$		0			0
$664$	−3.58289	+	6.20574i	−0.139043	+	0.240830i
$665$			5.90459i			0.228970i
$666$		0			0
$667$	−30.7301			−1.18988
$668$	1.08370	+	4.04443i	0.0419297	+	0.156484i
$669$		0			0
$670$	5.64281	−	21.0593i	0.218001	−	0.813591i
$671$	−50.8498	+	29.3582i	−1.96304	+	1.13336i
$672$		0			0
$673$	−33.0571	+	8.85763i	−1.27426	+	0.341436i	−0.831661	−	0.555284i	$-0.812610\pi$
$673$	−33.0571	+	8.85763i	−1.27426	+	0.341436i	−0.442597	+	0.896720i	$0.645943\pi$
$674$	26.7869	+	26.7869i	1.03179	+	1.03179i
$675$		0			0
$676$	−23.2166			−0.892947
$677$	4.44594	+	16.5925i	0.170871	+	0.637701i	0.997218	+	0.0745390i	$0.0237485\pi$
$677$	4.44594	+	16.5925i	0.170871	+	0.637701i	−0.826347	+	0.563162i	$0.809585\pi$
$678$		0			0
$679$	−1.89241	−	3.27776i	−0.0726242	−	0.125789i
$680$	4.34492	+	5.48972i	0.166620	+	0.210521i
$681$		0			0
$682$	−58.8871	−	33.9985i	−2.25490	−	1.30187i
$683$	20.2575	−	20.2575i	0.775131	−	0.775131i	−0.203867	−	0.978999i	$-0.565351\pi$
$683$	20.2575	−	20.2575i	0.775131	−	0.775131i	0.978999	+	0.203867i	$0.0653511\pi$
$684$		0			0
$685$	−13.3091	+	13.3091i	−0.508516	+	0.508516i
$686$	−36.6498	+	9.82027i	−1.39929	+	0.374940i
$687$		0			0
$688$	2.73760	−	1.58055i	0.104370	−	0.0602581i
$689$	17.3809	−	10.0349i	0.662159	−	0.382297i
$690$		0			0
$691$	26.2108	−	7.02316i	0.997106	−	0.267174i	0.276873	−	0.960906i	$-0.410702\pi$
$691$	26.2108	−	7.02316i	0.997106	−	0.267174i	0.720232	+	0.693733i	$0.244035\pi$
$692$	−12.4153	+	12.4153i	−0.471960	+	0.471960i
$693$		0			0
$694$	3.84401	−	3.84401i	0.145917	−	0.145917i
$695$	−22.8347	−	13.1836i	−0.866168	−	0.500082i
$696$		0			0
$697$	−8.65214	−	10.9318i	−0.327723	−	0.414071i
$698$	4.90731	+	8.49972i	0.185745	+	0.321719i
$699$		0			0
$700$	−0.0722088	−	0.269487i	−0.00272924	−	0.0101856i
$701$	48.1083			1.81703			0.908513	−	0.417856i	$-0.137218\pi$
$701$	48.1083			1.81703			0.908513	+	0.417856i	$0.137218\pi$
$702$		0			0
$703$	−0.0737304	−	0.0737304i	−0.00278079	−	0.00278079i
$704$	−26.0441	+	6.97849i	−0.981573	+	0.263012i
$705$		0			0
$706$	−31.2838	+	18.0617i	−1.17738	+	0.679761i
$707$	−1.65390	+	6.17244i	−0.0622013	+	0.232138i
$708$		0			0
$709$	5.20083	+	19.4098i	0.195321	+	0.728949i	0.992183	+	0.124788i	$0.0398249\pi$
$709$	5.20083	+	19.4098i	0.195321	+	0.728949i	−0.796862	+	0.604161i	$0.793508\pi$
$710$	13.0026			0.487979
$711$		0			0
$712$		−	12.5919i		−	0.471902i
$713$	−14.6768	+	25.4210i	−0.549651	+	0.952023i
$714$		0			0
$715$	34.8404	+	60.3453i	1.30296	+	2.25679i
$716$	0.742048	−	0.428422i	0.0277316	−	0.0160109i
$717$		0			0
$718$	15.5132	−	26.8697i	0.578948	−	1.00277i
$719$	26.3520	−	26.3520i	0.982762	−	0.982762i	−0.0170917	−	0.999854i	$-0.505441\pi$
$719$	26.3520	−	26.3520i	0.982762	−	0.982762i	0.999854	+	0.0170917i	$0.00544073\pi$
$720$		0			0
$721$	−9.02988	−	9.02988i	−0.336290	−	0.336290i
$722$	−28.4018	−	16.3978i	−1.05700	−	0.610262i
$723$		0			0
$724$	−7.88676	+	29.4338i	−0.293109	+	1.09390i
$725$	0.143701	−	0.536300i	0.00533693	−	0.0199177i
$726$		0			0
$727$	13.5933	−	23.5443i	0.504148	−	0.873210i	−0.495840	−	0.868414i	$-0.665140\pi$
$727$	13.5933	−	23.5443i	0.504148	−	0.873210i	0.999988	−	0.00479665i	$-0.00152683\pi$
$728$	−5.56472	+	5.56472i	−0.206242	+	0.206242i
$729$		0			0
$730$	−3.70842			−0.137255
$731$	2.58099	−	1.11478i	0.0954614	−	0.0412315i
$732$		0			0
$733$	15.1340	−	8.73761i	0.558987	−	0.322731i	−0.193752	−	0.981051i	$-0.562066\pi$
$733$	15.1340	−	8.73761i	0.558987	−	0.322731i	0.752739	+	0.658319i	$0.228732\pi$
$734$	13.8942	+	3.72294i	0.512845	+	0.137416i
$735$		0			0
$736$	9.11774	+	34.0279i	0.336084	+	1.25428i
$737$	−21.2204	−	21.2204i	−0.781662	−	0.781662i
$738$		0			0
$739$		−	29.7131i		−	1.09301i	−0.837454	−	0.546507i	$-0.815957\pi$
$739$		−	29.7131i		−	1.09301i	0.837454	−	0.546507i	$-0.184043\pi$
$740$	0.248762	+	0.143623i	0.00914468	+	0.00527969i
$741$		0			0
$742$	−3.75097	+	13.9988i	−0.137702	+	0.513912i
$743$	12.3139	+	3.29950i	0.451753	+	0.121047i	0.477520	−	0.878621i	$-0.341536\pi$
$743$	12.3139	+	3.29950i	0.451753	+	0.121047i	−0.0257664	+	0.999668i	$0.508203\pi$
$744$		0			0
$745$	−5.10124	−	19.0381i	−0.186895	−	0.697502i
$746$		−	44.5523i		−	1.63118i
$747$		0			0
$748$	−38.5474	+	5.66497i	−1.40943	+	0.207132i
$749$	−13.4067	+	23.2210i	−0.489869	+	0.848478i
$750$		0			0
$751$	−1.11670	−	0.299220i	−0.0407491	−	0.0109187i	0.238387	−	0.971170i	$-0.423381\pi$
$751$	−1.11670	−	0.299220i	−0.0407491	−	0.0109187i	−0.279136	+	0.960252i	$0.590048\pi$
$752$	−2.06549	−	3.57753i	−0.0753207	−	0.130459i
$753$		0			0
$754$	61.1609	−	16.3880i	2.22735	−	0.596816i
$755$	−32.8517	−	32.8517i	−1.19560	−	1.19560i
$756$		0			0
$757$			16.1102i			0.585534i	0.956184	+	0.292767i	$0.0945760\pi$
$757$			16.1102i			0.585534i	−0.956184	+	0.292767i	$0.905424\pi$
$758$	7.58796	−	2.03319i	0.275607	−	0.0738487i
$759$		0			0
$760$	2.15317	+	0.576941i	0.0781038	+	0.0209278i
$761$	1.86930	+	3.23773i	0.0677622	+	0.117368i	0.897916	−	0.440167i	$-0.145081\pi$
$761$	1.86930	+	3.23773i	0.0677622	+	0.117368i	−0.830154	+	0.557535i	$0.811747\pi$
$762$		0			0
$763$	−4.36768	−	2.52168i	−0.158120	−	0.0912909i
$764$	−11.5397			−0.417492
$765$		0			0
$766$	−11.9498			−0.431763
$767$	54.1591	+	31.2688i	1.95557	+	1.12905i
$768$		0			0
$769$	19.7133	+	34.1444i	0.710879	+	1.23128i	0.964527	+	0.263983i	$0.0850362\pi$
$769$	19.7133	+	34.1444i	0.710879	+	1.23128i	−0.253648	+	0.967297i	$0.581630\pi$
$770$	−48.6030	−	13.0231i	−1.75153	−	0.469321i
$771$		0			0
$772$	38.6239	−	10.3492i	1.39010	−	0.372477i
$773$			21.4324i			0.770869i	0.922735	+	0.385435i	$0.125948\pi$
$773$			21.4324i			0.770869i	−0.922735	+	0.385435i	$0.874052\pi$
$774$		0			0
$775$	−0.375013	−	0.375013i	−0.0134709	−	0.0134709i
$776$	−1.38018	+	0.369818i	−0.0495456	+	0.0132757i
$777$		0			0
$778$	−9.19657	−	15.9289i	−0.329713	−	0.571080i
$779$	−4.28766	−	1.14887i	−0.153621	−	0.0411627i
$780$		0			0
$781$	8.94887	−	15.4999i	0.320216	−	0.554630i
$782$	5.49591	+	37.3970i	0.196533	+	1.33731i
$783$		0			0
$784$			14.0163i			0.500583i
$785$	−3.38095	−	12.6179i	−0.120671	−	0.450351i
$786$		0			0
$787$	5.06817	+	1.35801i	0.180661	+	0.0484079i	0.348015	−	0.937489i	$-0.386856\pi$
$787$	5.06817	+	1.35801i	0.180661	+	0.0484079i	−0.167354	+	0.985897i	$0.553522\pi$
$788$	7.30747	−	27.2719i	0.260318	−	0.971520i
$789$		0			0
$790$	2.36968	+	1.36814i	0.0843095	+	0.0486761i
$791$		−	14.8087i		−	0.526536i
$792$		0			0
$793$	−36.9302	−	36.9302i	−1.31143	−	1.31143i
$794$	−9.11830	−	34.0300i	−0.323596	−	1.20768i
$795$		0			0
$796$	30.3666	+	8.13669i	1.07631	+	0.288397i
$797$	−4.68437	+	2.70452i	−0.165929	+	0.0957990i	−0.580665	−	0.814143i	$-0.697207\pi$
$797$	−4.68437	+	2.70452i	−0.165929	+	0.0957990i	0.414736	+	0.909942i	$0.363874\pi$
$798$		0			0
$799$	−1.45681	−	3.37287i	−0.0515381	−	0.119324i
$800$	−0.636488			−0.0225033
$801$		0			0
$802$	−4.99711	+	4.99711i	−0.176454	+	0.176454i
$803$	−2.55227	+	4.42066i	−0.0900677	+	0.156002i
$804$		0			0
$805$	−5.62196	+	20.9815i	−0.198148	+	0.739499i
$806$	15.6539	−	58.4213i	0.551386	−	2.05780i
$807$		0			0
$808$	2.08924	+	1.20623i	0.0734993	+	0.0424349i
$809$	16.8399	+	16.8399i	0.592061	+	0.592061i	0.938188	−	0.346127i	$-0.112503\pi$
$809$	16.8399	+	16.8399i	0.592061	+	0.592061i	−0.346127	+	0.938188i	$0.612503\pi$
$810$		0			0
$811$	−17.8632	+	17.8632i	−0.627261	+	0.627261i	−0.947378	−	0.320117i	$-0.896278\pi$
$811$	−17.8632	+	17.8632i	−0.627261	+	0.627261i	0.320117	+	0.947378i	$0.396278\pi$
$812$	−10.1727	+	17.6197i	−0.356992	+	0.618329i
$813$		0			0
$814$	0.769524	−	0.444285i	0.0269718	−	0.0155722i
$815$	−7.07522	−	12.2546i	−0.247834	−	0.429261i
$816$		0			0
$817$	0.447578	−	0.775228i	0.0156588	−	0.0271218i
$818$			44.0948i			1.54174i
$819$		0			0
$820$	12.2284			0.427034
$821$	11.3496	+	42.3571i	0.396102	+	1.47827i	0.819895	+	0.572515i	$0.194032\pi$
$821$	11.3496	+	42.3571i	0.396102	+	1.47827i	−0.423792	+	0.905759i	$0.639301\pi$
$822$		0			0
$823$	3.10278	−	11.5797i	0.108156	−	0.403644i	−0.890528	−	0.454929i	$-0.849665\pi$
$823$	3.10278	−	11.5797i	0.108156	−	0.403644i	0.998684	+	0.0512842i	$0.0163314\pi$
$824$	−4.17516	+	2.41053i	−0.145449	+	0.0839748i
$825$		0			0
$826$	−43.6205	+	11.6881i	−1.51775	+	0.406681i
$827$	−24.2979	−	24.2979i	−0.844920	−	0.844920i	0.144574	−	0.989494i	$-0.453819\pi$
$827$	−24.2979	−	24.2979i	−0.844920	−	0.844920i	−0.989494	+	0.144574i	$0.953819\pi$
$828$		0			0
$829$	33.7417			1.17190			0.585949	−	0.810348i	$-0.300722\pi$
$829$	33.7417			1.17190			0.585949	+	0.810348i	$0.300722\pi$
$830$	−10.5477	−	39.3646i	−0.366116	−	1.36636i
$831$		0			0
$832$	−11.9915	−	20.7699i	−0.415730	−	0.720066i
$833$	−1.44136	+	12.3823i	−0.0499400	+	0.429022i
$834$		0			0
$835$	5.10084	+	2.94497i	0.176522	+	0.101915i
$836$	−8.77182	+	8.77182i	−0.303380	+	0.303380i
$837$		0			0
$838$	−2.50522	+	2.50522i	−0.0865414	+	0.0865414i
$839$	−6.62393	+	1.77488i	−0.228684	+	0.0612756i	−0.371341	−	0.928497i	$-0.621102\pi$
$839$	−6.62393	+	1.77488i	−0.228684	+	0.0612756i	0.142657	+	0.989772i	$0.454435\pi$
$840$		0			0
$841$	−9.94978	+	5.74451i	−0.343096	+	0.198086i
$842$	−14.9385	+	8.62474i	−0.514815	+	0.297228i
$843$		0			0
$844$	−16.2167	+	4.34524i	−0.558201	+	0.149569i
$845$	−23.0931	+	23.0931i	−0.794425	+	0.794425i
$846$		0			0
$847$	−33.4641	+	33.4641i	−1.14984	+	1.14984i
$848$	15.3710	+	8.87442i	0.527841	+	0.304749i
$849$		0			0
$850$	−0.678351	−	0.0789629i	−0.0232672	−	0.00270841i
$851$	−0.191793	−	0.332196i	−0.00657459	−	0.0113875i
$852$		0			0
$853$	7.02438	+	26.2153i	0.240510	+	0.897596i	0.975587	+	0.219612i	$0.0704792\pi$
$853$	7.02438	+	26.2153i	0.240510	+	0.897596i	−0.735077	+	0.677983i	$0.762854\pi$
$854$	37.7140			1.29055
$855$		0			0
$856$	7.15783	+	7.15783i	0.244650	+	0.244650i
$857$	−43.3437	+	11.6139i	−1.48059	+	0.396723i	−0.906548	−	0.422102i	$-0.861292\pi$
$857$	−43.3437	+	11.6139i	−1.48059	+	0.396723i	−0.574043	+	0.818825i	$0.694626\pi$
$858$		0			0
$859$	43.7116	−	25.2369i	1.49142	−	0.861072i	0.491469	−	0.870895i	$-0.336460\pi$
$859$	43.7116	−	25.2369i	1.49142	−	0.861072i	0.999952	+	0.00982325i	$0.00312689\pi$
$860$	−0.638246	+	2.38196i	−0.0217640	+	0.0812243i
$861$		0			0
$862$	−16.1645	−	60.3266i	−0.550564	−	2.05473i
$863$	−20.8391			−0.709371			−0.354686	−	0.934986i	$-0.615412\pi$
$863$	−20.8391			−0.709371			−0.354686	+	0.934986i	$0.615412\pi$
$864$		0			0
$865$			24.6985i			0.839775i
$866$	37.1069	−	64.2711i	1.26094	−	2.18402i
$867$		0			0
$868$	9.71705	+	16.8304i	0.329818	+	0.571262i
$869$	3.26181	−	1.88320i	0.110649	−	0.0638833i
$870$		0			0
$871$	13.3468	−	23.1173i	0.452238	−	0.783298i
$872$	−1.34633	+	1.34633i	−0.0455924	+	0.0455924i
$873$		0			0
$874$	8.51003	+	8.51003i	0.287856	+	0.287856i
$875$	19.1360	+	11.0482i	0.646914	+	0.373496i
$876$		0			0
$877$	4.03997	−	15.0774i	0.136420	−	0.509127i	−0.863568	−	0.504232i	$-0.831775\pi$
$877$	4.03997	−	15.0774i	0.136420	−	0.509127i	0.999988	−	0.00489414i	$-0.00155786\pi$
$878$	−6.63102	+	24.7473i	−0.223786	+	0.835181i
$879$		0			0
$880$	−30.8115	+	53.3670i	−1.03865	+	1.79900i
$881$	10.8259	−	10.8259i	0.364732	−	0.364732i	−0.500819	−	0.865552i	$-0.666968\pi$
$881$	10.8259	−	10.8259i	0.364732	−	0.364732i	0.865552	+	0.500819i	$0.166968\pi$
$882$		0			0
$883$	−26.3119			−0.885467			−0.442733	−	0.896653i	$-0.645991\pi$
$883$	−26.3119			−0.885467			−0.442733	+	0.896653i	$0.645991\pi$
$884$	−13.7414	−	31.8148i	−0.462174	−	1.07005i
$885$		0			0
$886$	−44.9009	+	25.9235i	−1.50847	+	0.870918i
$887$	−1.31918	−	0.353474i	−0.0442938	−	0.0118685i	0.236604	−	0.971606i	$-0.423966\pi$
$887$	−1.31918	−	0.353474i	−0.0442938	−	0.0118685i	−0.280898	+	0.959738i	$0.590632\pi$
$888$		0			0
$889$	2.51588	+	9.38939i	0.0843799	+	0.314910i
$890$	50.6379	+	50.6379i	1.69739	+	1.69739i
$891$		0			0
$892$			23.1976i			0.776712i
$893$	−1.01308	−	0.584901i	−0.0339014	−	0.0195730i
$894$		0			0
$895$	0.311957	−	1.16424i	0.0104276	−	0.0389163i
$896$	−11.3727	−	3.04731i	−0.379936	−	0.101803i
$897$		0			0
$898$	14.4631	+	53.9770i	0.482640	+	1.80124i
$899$			38.6754i			1.28990i
$900$		0			0
$901$	12.6664	+	9.42052i	0.421980	+	0.313843i
$902$	18.9137	−	32.7595i	0.629757	−	1.09077i
$903$		0			0
$904$	−5.40014	−	1.44696i	−0.179606	−	0.0481253i
$905$	21.4323	+	37.1219i	0.712435	+	1.23397i
$906$		0			0
$907$	−19.0980	+	5.11728i	−0.634137	+	0.169917i	−0.561546	−	0.827445i	$-0.689793\pi$
$907$	−19.0980	+	5.11728i	−0.634137	+	0.169917i	−0.0725907	+	0.997362i	$0.523127\pi$
$908$	17.4560	+	17.4560i	0.579298	+	0.579298i
$909$		0			0
$910$		−	44.7566i		−	1.48367i
$911$	−29.7583	+	7.97372i	−0.985937	+	0.264181i	−0.715543	−	0.698569i	$-0.753821\pi$
$911$	−29.7583	+	7.97372i	−0.985937	+	0.264181i	−0.270394	+	0.962750i	$0.587154\pi$
$912$		0			0
$913$	−54.1843	−	14.5187i	−1.79324	−	0.480497i
$914$	−11.7606	−	20.3700i	−0.389006	−	0.673779i
$915$		0			0
$916$	−27.8166	−	16.0599i	−0.919087	−	0.530635i
$917$	−28.2269			−0.932133
$918$		0			0
$919$	−7.87734			−0.259850			−0.129925	−	0.991524i	$-0.541474\pi$
$919$	−7.87734			−0.259850			−0.129925	+	0.991524i	$0.541474\pi$
$920$	7.10179	+	4.10022i	0.234139	+	0.135180i
$921$		0			0
$922$	4.92836	+	8.53618i	0.162307	+	0.281124i
$923$	15.3773	+	4.12033i	0.506150	+	0.135622i
$924$		0			0
$925$	0.00669433	−	0.00179374i	0.000220108	−	5.89778e-5i
$926$		−	54.3589i		−	1.78634i
$927$		0			0
$928$	32.8208	+	32.8208i	1.07739	+	1.07739i
$929$	−25.6481	+	6.87239i	−0.841487	+	0.225476i	−0.653719	−	0.756738i	$-0.726792\pi$
$929$	−25.6481	+	6.87239i	−0.841487	+	0.225476i	−0.187768	+	0.982213i	$0.560125\pi$
$930$		0			0
$931$	1.98456	+	3.43736i	0.0650413	+	0.112655i
$932$	−3.07059	−	0.822761i	−0.100580	−	0.0269504i
$933$		0			0
$934$	3.03900	−	5.26371i	0.0994393	−	0.172234i
$935$	−32.7075	+	43.9771i	−1.06965	+	1.43821i
$936$		0			0
$937$		−	13.3991i		−	0.437730i	−0.975755	−	0.218865i	$-0.929765\pi$
$937$		−	13.3991i		−	0.437730i	0.975755	−	0.218865i	$-0.0702354\pi$
$938$	4.98894	+	18.6190i	0.162895	+	0.607931i
$939$		0			0
$940$	3.11278	+	0.834068i	0.101528	+	0.0272043i
$941$	12.8934	−	48.1188i	0.420312	−	1.56863i	−0.353639	−	0.935382i	$-0.615056\pi$
$941$	12.8934	−	48.1188i	0.420312	−	1.56863i	0.773952	−	0.633245i	$-0.218277\pi$
$942$		0			0
$943$	−14.1419	−	8.16486i	−0.460525	−	0.265884i
$944$			55.3057i			1.80005i
$945$		0			0
$946$	5.39404	+	5.39404i	0.175375	+	0.175375i
$947$	−10.0539	−	37.5215i	−0.326706	−	1.21929i	−0.912585	−	0.408886i	$-0.865917\pi$
$947$	−10.0539	−	37.5215i	−0.326706	−	1.21929i	0.585879	−	0.810399i	$-0.300749\pi$
$948$		0			0
$949$	−4.38570	−	1.17514i	−0.142366	−	0.0381468i
$950$	−0.188311	+	0.108722i	−0.00610963	+	0.00352739i
$951$		0			0
$952$	−5.75358	−	2.28260i	−0.186475	−	0.0739796i
$953$	10.0857			0.326707			0.163354	−	0.986568i	$-0.447769\pi$
$953$	10.0857			0.326707			0.163354	+	0.986568i	$0.447769\pi$
$954$		0			0
$955$	−11.4783	+	11.4783i	−0.371429	+	0.371429i
$956$	16.1631	−	27.9954i	0.522753	−	0.905434i
$957$		0			0
$958$	−5.17678	+	19.3200i	−0.167254	+	0.624201i
$959$	4.30698	−	16.0739i	0.139080	−	0.519053i
$960$		0			0
$961$	5.14676	+	2.97149i	0.166025	+	0.0958544i
$962$	0.558875	+	0.558875i	0.0180188	+	0.0180188i
$963$		0			0
$964$	−20.6957	+	20.6957i	−0.666564	+	0.666564i
$965$	28.1242	−	48.7125i	0.905349	−	1.56811i
$966$		0			0
$967$	22.1131	−	12.7670i	0.711108	−	0.410558i	−0.100363	−	0.994951i	$-0.532001\pi$
$967$	22.1131	−	12.7670i	0.711108	−	0.410558i	0.811471	+	0.584393i	$0.198667\pi$
$968$	8.93325	+	15.4728i	0.287125	+	0.497316i
$969$		0			0
$970$	4.06313	−	7.03755i	0.130459	−	0.225962i
$971$		−	8.11737i		−	0.260499i	−0.991481	−	0.130249i	$-0.958422\pi$
$971$		−	8.11737i		−	0.260499i	0.991481	−	0.130249i	$-0.0415778\pi$
$972$		0			0
$973$	23.3118			0.747343
$974$	17.1439	+	63.9821i	0.549327	+	2.05012i
$975$		0			0
$976$	11.9542	−	44.6138i	0.382646	−	1.42805i
$977$	7.15788	−	4.13260i	0.229001	−	0.132214i	−0.381110	−	0.924530i	$-0.624458\pi$
$977$	7.15788	−	4.13260i	0.229001	−	0.132214i	0.610111	+	0.792316i	$0.291125\pi$
$978$		0			0
$979$	95.2145	−	25.5126i	3.04307	−	0.815387i
$980$	−7.73164	−	7.73164i	−0.246978	−	0.246978i
$981$		0			0
$982$	52.7961			1.68479
$983$	7.11101	+	26.5387i	0.226806	+	0.846452i	0.981673	+	0.190574i	$0.0610348\pi$
$983$	7.11101	+	26.5387i	0.226806	+	0.846452i	−0.754867	+	0.655878i	$0.772299\pi$
$984$		0			0
$985$	−19.8581	−	34.3953i	−0.632733	−	1.09593i
$986$	30.9076	+	39.0511i	0.984300	+	1.24364i
$987$		0			0
$988$	−9.55593	−	5.51712i	−0.304015	−	0.175523i
$989$	2.32855	−	2.32855i	0.0740437	−	0.0740437i
$990$		0			0
$991$	24.8200	−	24.8200i	0.788433	−	0.788433i	−0.192804	−	0.981237i	$-0.561758\pi$
$991$	24.8200	−	24.8200i	0.788433	−	0.788433i	0.981237	+	0.192804i	$0.0617582\pi$
$992$	42.8257	−	11.4751i	1.35972	−	0.364335i
$993$		0			0
$994$	−9.95573	+	5.74794i	−0.315776	+	0.182314i
$995$	38.2983	−	22.1116i	1.21414	−	0.700983i
$996$		0			0
$997$	13.7706	−	3.68983i	0.436120	−	0.116858i	−0.0340775	−	0.999419i	$-0.510849\pi$
$997$	13.7706	−	3.68983i	0.436120	−	0.116858i	0.470198	+	0.882561i	$0.344183\pi$
$998$	−22.9228	+	22.9228i	−0.725608	+	0.725608i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.o.a.208.4		64
3.2	odd	2		153.2.n.a.106.13	yes	64
9.4	even	3	inner	459.2.o.a.361.13		64
9.5	odd	6		153.2.n.a.4.4	✓	64
17.13	even	4	inner	459.2.o.a.370.13		64
51.47	odd	4		153.2.n.a.115.4	yes	64
153.13	even	12	inner	459.2.o.a.64.4		64
153.149	odd	12		153.2.n.a.13.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.4	✓	64	9.5	odd	6
153.2.n.a.13.13	yes	64	153.149	odd	12
153.2.n.a.106.13	yes	64	3.2	odd	2
153.2.n.a.115.4	yes	64	51.47	odd	4
459.2.o.a.64.4		64	153.13	even	12	inner
459.2.o.a.208.4		64	1.1	even	1	trivial
459.2.o.a.361.13		64	9.4	even	3	inner
459.2.o.a.370.13		64	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.64395 - 0.949132i) q^{2} +(0.801704 + 1.38859i) q^{4} +(2.17864 + 0.583765i) q^{5} +(-1.92618 + 0.516120i) q^{7} +0.752835i q^{8} +(-3.02750 - 3.02750i) q^{10} +(-5.69260 + 1.52533i) q^{11} +(-2.62105 - 4.53979i) q^{13} +(3.65641 + 0.979732i) q^{14} +(2.31795 - 4.01481i) q^{16} +(2.46059 - 3.30840i) q^{17} -1.31278i q^{19} +(0.936014 + 3.49325i) q^{20} +(10.8061 + 2.89547i) q^{22} +(1.24995 - 4.66487i) q^{23} +(0.0755659 + 0.0436280i) q^{25} +9.95088i q^{26} +(-2.26091 - 2.26091i) q^{28} +(-1.64689 - 6.14628i) q^{29} +(-5.87097 - 1.57312i) q^{31} +(-6.31721 + 3.64725i) q^{32} +(-7.18518 + 3.10341i) q^{34} -4.49776 q^{35} +(0.0561633 - 0.0561633i) q^{37} +(-1.24601 + 2.15815i) q^{38} +(-0.439479 + 1.64016i) q^{40} +(0.875143 - 3.26608i) q^{41} +(0.590522 + 0.340938i) q^{43} +(-6.68184 - 6.68184i) q^{44} +(-6.48243 + 6.48243i) q^{46} +(0.445543 - 0.771702i) q^{47} +(-2.61837 + 1.51172i) q^{49} +(-0.0828175 - 0.143444i) q^{50} +(4.20261 - 7.27913i) q^{52} +3.82857i q^{53} -13.2926 q^{55} +(-0.388553 - 1.45010i) q^{56} +(-3.12623 + 11.6673i) q^{58} +(-10.3316 + 5.96494i) q^{59} +(9.62356 - 2.57863i) q^{61} +(8.15845 + 8.15845i) q^{62} +4.57508 q^{64} +(-3.06015 - 11.4206i) q^{65} +(2.54607 + 4.40993i) q^{67} +(6.56668 + 0.764390i) q^{68} +(7.39407 + 4.26897i) q^{70} +(-2.14742 + 2.14742i) q^{71} +(0.612456 - 0.612456i) q^{73} +(-0.145636 + 0.0390230i) q^{74} +(1.82292 - 1.05247i) q^{76} +(10.1777 - 5.87612i) q^{77} +(-0.617312 + 0.165408i) q^{79} +(7.39368 - 7.39368i) q^{80} +(-4.53863 + 4.53863i) q^{82} +(8.24317 + 4.75919i) q^{83} +(7.29206 - 5.77141i) q^{85} +(-0.647191 - 1.12097i) q^{86} +(-1.14832 - 4.28559i) q^{88} -16.7260 q^{89} +(7.39169 + 7.39169i) q^{91} +(7.47969 - 2.00418i) q^{92} +(-1.46490 + 0.845758i) q^{94} +(0.766358 - 2.86009i) q^{95} +(0.491234 + 1.83331i) q^{97} +5.73928 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7} - 16 q^{10} - 4 q^{13} - 16 q^{16} + 8 q^{17} - 18 q^{20} - 4 q^{22} + 8 q^{23} + 10 q^{29} - 2 q^{31} + 20 q^{34} + 128 q^{35} - 8 q^{37} + 24 q^{38} - 20 q^{40} - 32 q^{41}+ \cdots - 208 q^{98}+O(q^{100}) \) 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7 - 16 * q^10 - 4 * q^13 - 16 * q^16 + 8 * q^17 - 18 * q^20 - 4 * q^22 + 8 * q^23 + 10 * q^29 - 2 * q^31 + 20 * q^34 + 128 * q^35 - 8 * q^37 + 24 * q^38 - 20 * q^40 - 32 * q^41 - 20 * q^44 - 40 * q^46 + 64 * q^47 - 48 * q^50 + 36 * q^52 - 16 * q^55 - 12 * q^56 - 10 * q^58 - 2 * q^61 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^67 + 60 * q^68 + 84 * q^71 - 44 * q^73 + 14 * q^74 + 10 * q^79 - 204 * q^80 - 52 * q^82 + 22 * q^85 - 32 * q^86 + 16 * q^88 - 128 * q^89 + 44 * q^91 - 136 * q^92 - 4 * q^95 - 44 * q^97 - 208 * q^98

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