LMFDB - Embedded newform 810.2.m.g.377.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(53,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("810.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	810.377
Dual form			810.2.m.g.593.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(1.48356 + 1.67303i) q^{5} +(1.13397 - 4.23205i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.00000i) q^{10} +(1.22474 - 0.707107i) q^{11} +(-1.50000 - 5.59808i) q^{13} +(2.19067 - 3.79435i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.38134 - 4.38134i) q^{17} +3.19615i q^{19} +(0.448288 + 2.19067i) q^{20} +(1.36603 - 0.366025i) q^{22} +(-4.82963 + 1.29410i) q^{23} +(-0.598076 + 4.96410i) q^{25} -5.79555i q^{26} +(3.09808 - 3.09808i) q^{28} +(2.82843 + 4.89898i) q^{29} +(-3.09808 + 5.36603i) q^{31} +(0.258819 + 0.965926i) q^{32} +(5.36603 - 3.09808i) q^{34} +(8.76268 - 4.38134i) q^{35} +(5.19615 + 5.19615i) q^{37} +(-0.827225 + 3.08725i) q^{38} +(-0.133975 + 2.23205i) q^{40} +(1.10463 + 0.637756i) q^{41} +(-7.09808 - 1.90192i) q^{43} +1.41421 q^{44} -5.00000 q^{46} +(0.776457 + 0.208051i) q^{47} +(-10.5622 - 6.09808i) q^{49} +(-1.86250 + 4.64016i) q^{50} +(1.50000 - 5.59808i) q^{52} +(2.26002 + 2.26002i) q^{53} +(3.00000 + 1.00000i) q^{55} +(3.79435 - 2.19067i) q^{56} +(1.46410 + 5.46410i) q^{58} +(1.48356 - 2.56961i) q^{59} +(-1.90192 - 3.29423i) q^{61} +(-4.38134 + 4.38134i) q^{62} +1.00000i q^{64} +(7.14042 - 10.8147i) q^{65} +(-5.73205 + 1.53590i) q^{67} +(5.98502 - 1.60368i) q^{68} +(9.59808 - 1.96410i) q^{70} +10.1769i q^{71} +(4.00000 - 4.00000i) q^{73} +(3.67423 + 6.36396i) q^{74} +(-1.59808 + 2.76795i) q^{76} +(-1.60368 - 5.98502i) q^{77} +(-1.90192 + 1.09808i) q^{79} +(-0.707107 + 2.12132i) q^{80} +(0.901924 + 0.901924i) q^{82} +(-3.67423 + 13.7124i) q^{83} +(13.8301 + 0.830127i) q^{85} +(-6.36396 - 3.67423i) q^{86} +(1.36603 + 0.366025i) q^{88} -1.69161 q^{89} -25.3923 q^{91} +(-4.82963 - 1.29410i) q^{92} +(0.696152 + 0.401924i) q^{94} +(-5.34727 + 4.74170i) q^{95} +(-2.19615 + 8.19615i) q^{97} +(-8.62398 - 8.62398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7} + 8 q^{10} - 12 q^{13} + 4 q^{16} + 4 q^{22} + 16 q^{25} + 4 q^{28} - 4 q^{31} + 36 q^{34} - 8 q^{40} - 36 q^{43} - 40 q^{46} - 36 q^{49} + 12 q^{52} + 24 q^{55} - 16 q^{58} - 36 q^{61} - 32 q^{67}+ \cdots + 24 q^{97}+O(q^{100}) $ 8 * q + 16 * q^7 + 8 * q^10 - 12 * q^13 + 4 * q^16 + 4 * q^22 + 16 * q^25 + 4 * q^28 - 4 * q^31 + 36 * q^34 - 8 * q^40 - 36 * q^43 - 40 * q^46 - 36 * q^49 + 12 * q^52 + 24 * q^55 - 16 * q^58 - 36 * q^61 - 32 * q^67 + 56 * q^70 + 32 * q^73 + 8 * q^76 - 36 * q^79 + 28 * q^82 + 76 * q^85 + 4 * q^88 - 120 * q^91 - 36 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.48356	+	1.67303i	0.663470	+	0.748203i
$5$	1.48356	+	1.67303i	0.663470	+	0.748203i
$6$		0			0
$7$	1.13397	−	4.23205i	0.428602	−	1.59956i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	1.13397	−	4.23205i	0.428602	−	1.59956i	0.755929	−	0.654654i	$-0.227186\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$	1.22474	−	0.707107i	0.369274	−	0.213201i	−0.303867	−	0.952714i	$-0.598278\pi$
$11$	1.22474	−	0.707107i	0.369274	−	0.213201i	0.673141	+	0.739514i	$0.264945\pi$
$12$		0			0
$13$	−1.50000	−	5.59808i	−0.416025	−	1.55263i	−0.782773	−	0.622307i	$-0.786196\pi$
$13$	−1.50000	−	5.59808i	−0.416025	−	1.55263i	0.366748	−	0.930320i	$-0.380471\pi$
$14$	2.19067	−	3.79435i	0.585481	−	1.01408i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.38134	−	4.38134i	1.06263	−	1.06263i	0.0647285	−	0.997903i	$-0.479382\pi$
$17$	4.38134	−	4.38134i	1.06263	−	1.06263i	0.997903	−	0.0647285i	$-0.0206181\pi$
$18$		0			0
$19$			3.19615i			0.733248i	0.930369	+	0.366624i	$0.119486\pi$
$19$			3.19615i			0.733248i	−0.930369	+	0.366624i	$0.880514\pi$
$20$	0.448288	+	2.19067i	0.100240	+	0.489849i
$21$		0			0
$22$	1.36603	−	0.366025i	0.291238	−	0.0780369i
$23$	−4.82963	+	1.29410i	−1.00705	+	0.269838i	−0.724395	−	0.689385i	$-0.757881\pi$
$23$	−4.82963	+	1.29410i	−1.00705	+	0.269838i	−0.282652	+	0.959222i	$0.591214\pi$
$24$		0			0
$25$	−0.598076	+	4.96410i	−0.119615	+	0.992820i
$26$		−	5.79555i		−	1.13660i
$27$		0			0
$28$	3.09808	−	3.09808i	0.585481	−	0.585481i
$29$	2.82843	+	4.89898i	0.525226	+	0.909718i	0.999568	+	0.0293774i	$0.00935245\pi$
$29$	2.82843	+	4.89898i	0.525226	+	0.909718i	−0.474343	+	0.880340i	$0.657314\pi$
$30$		0			0
$31$	−3.09808	+	5.36603i	−0.556431	+	0.963767i	0.441360	+	0.897330i	$0.354496\pi$
$31$	−3.09808	+	5.36603i	−0.556431	+	0.963767i	−0.997791	+	0.0664364i	$0.978837\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	5.36603	−	3.09808i	0.920266	−	0.531316i
$35$	8.76268	−	4.38134i	1.48116	−	0.740582i
$36$		0			0
$37$	5.19615	+	5.19615i	0.854242	+	0.854242i	0.990652	−	0.136410i	$-0.0435565\pi$
$37$	5.19615	+	5.19615i	0.854242	+	0.854242i	−0.136410	+	0.990652i	$0.543557\pi$
$38$	−0.827225	+	3.08725i	−0.134194	+	0.500817i
$39$		0			0
$40$	−0.133975	+	2.23205i	−0.0211832	+	0.352918i
$41$	1.10463	+	0.637756i	0.172514	+	0.0996008i	0.583771	−	0.811919i	$-0.301577\pi$
$41$	1.10463	+	0.637756i	0.172514	+	0.0996008i	−0.411257	+	0.911519i	$0.634910\pi$
$42$		0			0
$43$	−7.09808	−	1.90192i	−1.08245	−	0.290041i	−0.326849	−	0.945077i	$-0.605987\pi$
$43$	−7.09808	−	1.90192i	−1.08245	−	0.290041i	−0.755598	+	0.655036i	$0.772653\pi$
$44$	1.41421			0.213201
$45$		0			0
$46$	−5.00000			−0.737210
$47$	0.776457	+	0.208051i	0.113258	+	0.0303474i	0.315003	−	0.949091i	$-0.397995\pi$
$47$	0.776457	+	0.208051i	0.113258	+	0.0303474i	−0.201745	+	0.979438i	$0.564661\pi$
$48$		0			0
$49$	−10.5622	−	6.09808i	−1.50888	−	0.871154i
$50$	−1.86250	+	4.64016i	−0.263397	+	0.656218i
$51$		0			0
$52$	1.50000	−	5.59808i	0.208013	−	0.776313i
$53$	2.26002	+	2.26002i	0.310438	+	0.310438i	0.845079	−	0.534641i	$-0.179553\pi$
$53$	2.26002	+	2.26002i	0.310438	+	0.310438i	−0.534641	+	0.845079i	$0.679553\pi$
$54$		0			0
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$	3.79435	−	2.19067i	0.507042	−	0.292741i
$57$		0			0
$58$	1.46410	+	5.46410i	0.192246	+	0.717472i
$59$	1.48356	−	2.56961i	0.193144	−	0.334534i	−0.753147	−	0.657852i	$-0.771465\pi$
$59$	1.48356	−	2.56961i	0.193144	−	0.334534i	0.946290	+	0.323318i	$0.104798\pi$
$60$		0			0
$61$	−1.90192	−	3.29423i	−0.243516	−	0.421783i	0.718197	−	0.695840i	$-0.244968\pi$
$61$	−1.90192	−	3.29423i	−0.243516	−	0.421783i	−0.961713	+	0.274057i	$0.911634\pi$
$62$	−4.38134	+	4.38134i	−0.556431	+	0.556431i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	7.14042	−	10.8147i	0.885660	−	1.34139i
$66$		0			0
$67$	−5.73205	+	1.53590i	−0.700281	+	0.187640i	−0.591357	−	0.806410i	$-0.701407\pi$
$67$	−5.73205	+	1.53590i	−0.700281	+	0.187640i	−0.108925	+	0.994050i	$0.534741\pi$
$68$	5.98502	−	1.60368i	0.725791	−	0.194475i
$69$		0			0
$70$	9.59808	−	1.96410i	1.14719	−	0.234755i
$71$			10.1769i			1.20778i	0.797069	+	0.603888i	$0.206382\pi$
$71$			10.1769i			1.20778i	−0.797069	+	0.603888i	$0.793618\pi$
$72$		0			0
$73$	4.00000	−	4.00000i	0.468165	−	0.468165i	−0.433155	−	0.901319i	$-0.642600\pi$
$73$	4.00000	−	4.00000i	0.468165	−	0.468165i	0.901319	+	0.433155i	$0.142600\pi$
$74$	3.67423	+	6.36396i	0.427121	+	0.739795i
$75$		0			0
$76$	−1.59808	+	2.76795i	−0.183312	+	0.317506i
$77$	−1.60368	−	5.98502i	−0.182757	−	0.682057i
$78$		0			0
$79$	−1.90192	+	1.09808i	−0.213983	+	0.123543i	−0.603161	−	0.797619i	$-0.706092\pi$
$79$	−1.90192	+	1.09808i	−0.213983	+	0.123543i	0.389178	+	0.921163i	$0.372759\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$		0			0
$82$	0.901924	+	0.901924i	0.0996008	+	0.0996008i
$83$	−3.67423	+	13.7124i	−0.403300	+	1.50513i	0.403871	+	0.914816i	$0.367665\pi$
$83$	−3.67423	+	13.7124i	−0.403300	+	1.50513i	−0.807170	+	0.590319i	$0.799002\pi$
$84$		0			0
$85$	13.8301	+	0.830127i	1.50009	+	0.0900399i
$86$	−6.36396	−	3.67423i	−0.686244	−	0.396203i
$87$		0			0
$88$	1.36603	+	0.366025i	0.145619	+	0.0390184i
$89$	−1.69161			−0.179311			−0.0896554	−	0.995973i	$-0.528577\pi$
$89$	−1.69161			−0.179311			−0.0896554	+	0.995973i	$0.528577\pi$
$90$		0			0
$91$	−25.3923			−2.66184
$92$	−4.82963	−	1.29410i	−0.503524	−	0.134919i
$93$		0			0
$94$	0.696152	+	0.401924i	0.0718026	+	0.0414553i
$95$	−5.34727	+	4.74170i	−0.548618	+	0.486488i
$96$		0			0
$97$	−2.19615	+	8.19615i	−0.222985	+	0.832193i	0.760216	+	0.649670i	$0.225093\pi$
$97$	−2.19615	+	8.19615i	−0.222985	+	0.832193i	−0.983202	+	0.182523i	$0.941574\pi$
$98$	−8.62398	−	8.62398i	−0.871154	−	0.871154i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	11.5032	−	6.64136i	1.14461	−	0.660840i	0.197041	−	0.980395i	$-0.436867\pi$
$101$	11.5032	−	6.64136i	1.14461	−	0.660840i	0.947568	+	0.319555i	$0.103533\pi$
$102$		0			0
$103$	−1.42820	−	5.33013i	−0.140725	−	0.525193i	−0.999909	−	0.0135254i	$-0.995695\pi$
$103$	−1.42820	−	5.33013i	−0.140725	−	0.525193i	0.859183	−	0.511668i	$-0.170972\pi$
$104$	2.89778	−	5.01910i	0.284150	−	0.492163i
$105$		0			0
$106$	1.59808	+	2.76795i	0.155219	+	0.268847i
$107$	8.62398	−	8.62398i	0.833712	−	0.833712i	−0.154311	−	0.988022i	$-0.549316\pi$
$107$	8.62398	−	8.62398i	0.833712	−	0.833712i	0.988022	+	0.154311i	$0.0493156\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$	2.63896	+	1.74238i	0.251615	+	0.166130i
$111$		0			0
$112$	4.23205	−	1.13397i	0.399891	−	0.107151i
$113$	−3.86370	+	1.03528i	−0.363467	+	0.0973906i	−0.435930	−	0.899980i	$-0.643581\pi$
$113$	−3.86370	+	1.03528i	−0.363467	+	0.0973906i	0.0724636	+	0.997371i	$0.476914\pi$
$114$		0			0
$115$	−9.33013	−	6.16025i	−0.870039	−	0.574447i
$116$			5.65685i			0.525226i
$117$		0			0
$118$	2.09808	−	2.09808i	0.193144	−	0.193144i
$119$	−13.5737	−	23.5104i	−1.24430	−	2.15519i
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$	−0.984508	−	3.67423i	−0.0891332	−	0.332650i
$123$		0			0
$124$	−5.36603	+	3.09808i	−0.481883	+	0.278215i
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$		0			0
$127$	−2.09808	−	2.09808i	−0.186174	−	0.186174i	0.607866	−	0.794040i	$-0.292026\pi$
$127$	−2.09808	−	2.09808i	−0.186174	−	0.186174i	−0.794040	+	0.607866i	$0.792026\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	9.69615	−	8.59808i	0.850409	−	0.754101i
$131$	0.120118	+	0.0693504i	0.0104948	+	0.00605917i	0.505238	−	0.862980i	$-0.331405\pi$
$131$	0.120118	+	0.0693504i	0.0104948	+	0.00605917i	−0.494743	+	0.869039i	$0.664738\pi$
$132$		0			0
$133$	13.5263	+	3.62436i	1.17288	+	0.314271i
$134$	−5.93426			−0.512642
$135$		0			0
$136$	6.19615			0.531316
$137$	−13.7124	−	3.67423i	−1.17153	−	0.313911i	−0.379969	−	0.924999i	$-0.624065\pi$
$137$	−13.7124	−	3.67423i	−1.17153	−	0.313911i	−0.791563	+	0.611088i	$0.790732\pi$
$138$		0			0
$139$	−13.3301	−	7.69615i	−1.13065	−	0.652779i	−0.186549	−	0.982446i	$-0.559730\pi$
$139$	−13.3301	−	7.69615i	−1.13065	−	0.652779i	−0.944097	+	0.329666i	$0.893064\pi$
$140$	9.77938	+	0.586988i	0.826508	+	0.0496096i
$141$		0			0
$142$	−2.63397	+	9.83013i	−0.221038	+	0.824926i
$143$	−5.79555	−	5.79555i	−0.484649	−	0.484649i
$144$		0			0
$145$	−4.00000	+	12.0000i	−0.332182	+	0.996546i
$146$	4.89898	−	2.82843i	0.405442	−	0.234082i
$147$		0			0
$148$	1.90192	+	7.09808i	0.156337	+	0.583458i
$149$	0.568406	−	0.984508i	0.0465656	−	0.0806541i	−0.841803	−	0.539785i	$-0.818506\pi$
$149$	0.568406	−	0.984508i	0.0465656	−	0.0806541i	0.888369	+	0.459131i	$0.151839\pi$
$150$		0			0
$151$	4.29423	+	7.43782i	0.349459	+	0.605281i	0.986154	−	0.165835i	$-0.0530319\pi$
$151$	4.29423	+	7.43782i	0.349459	+	0.605281i	−0.636694	+	0.771116i	$0.719699\pi$
$152$	−2.26002	+	2.26002i	−0.183312	+	0.183312i
$153$		0			0
$154$		−	6.19615i		−	0.499300i
$155$	−13.5737	+	2.77766i	−1.09027	+	0.223107i
$156$		0			0
$157$	4.50000	−	1.20577i	0.359139	−	0.0962310i	−0.0747377	−	0.997203i	$-0.523812\pi$
$157$	4.50000	−	1.20577i	0.359139	−	0.0962310i	0.433877	+	0.900972i	$0.357145\pi$
$158$	−2.12132	+	0.568406i	−0.168763	+	0.0452200i
$159$		0			0
$160$	−1.23205	+	1.86603i	−0.0974022	+	0.147522i
$161$			21.9067i			1.72649i
$162$		0			0
$163$	14.0000	−	14.0000i	1.09656	−	1.09656i	0.101755	−	0.994809i	$-0.467554\pi$
$163$	14.0000	−	14.0000i	1.09656	−	1.09656i	0.994809	−	0.101755i	$-0.0324458\pi$
$164$	0.637756	+	1.10463i	0.0498004	+	0.0862568i
$165$		0			0
$166$	−7.09808	+	12.2942i	−0.550918	+	0.954217i
$167$	5.89709	+	22.0082i	0.456331	+	1.70305i	0.684146	+	0.729345i	$0.260175\pi$
$167$	5.89709	+	22.0082i	0.456331	+	1.70305i	−0.227816	+	0.973704i	$0.573158\pi$
$168$		0			0
$169$	−17.8301	+	10.2942i	−1.37155	+	0.791864i
$170$	13.1440	+	4.38134i	1.00810	+	0.336034i
$171$		0			0
$172$	−5.19615	−	5.19615i	−0.396203	−	0.396203i
$173$	−3.51695	+	13.1254i	−0.267389	+	0.997909i	0.693383	+	0.720569i	$0.256119\pi$
$173$	−3.51695	+	13.1254i	−0.267389	+	0.997909i	−0.960772	+	0.277340i	$0.910547\pi$
$174$		0			0
$175$	20.3301	+	8.16025i	1.53681	+	0.616857i
$176$	1.22474	+	0.707107i	0.0923186	+	0.0533002i
$177$		0			0
$178$	−1.63397	−	0.437822i	−0.122472	−	0.0328162i
$179$	−24.4577			−1.82806			−0.914028	−	0.405650i	$-0.867045\pi$
$179$	−24.4577			−1.82806			−0.914028	+	0.405650i	$0.867045\pi$
$180$		0			0
$181$	4.19615			0.311898			0.155949	−	0.987765i	$-0.450157\pi$
$181$	4.19615			0.311898			0.155949	+	0.987765i	$0.450157\pi$
$182$	−24.5271	−	6.57201i	−1.81807	−	0.487150i
$183$		0			0
$184$	−4.33013	−	2.50000i	−0.319221	−	0.184302i
$185$	−0.984508	+	16.4022i	−0.0723825	+	1.20591i
$186$		0			0
$187$	2.26795	−	8.46410i	0.165849	−	0.618956i
$188$	0.568406	+	0.568406i	0.0414553	+	0.0414553i
$189$		0			0
$190$	−6.39230	+	3.19615i	−0.463747	+	0.231873i
$191$	−8.57321	+	4.94975i	−0.620336	+	0.358151i	−0.777000	−	0.629501i	$-0.783259\pi$
$191$	−8.57321	+	4.94975i	−0.620336	+	0.358151i	0.156664	+	0.987652i	$0.449926\pi$
$192$		0			0
$193$	−1.60770	−	6.00000i	−0.115724	−	0.431889i	0.883616	−	0.468213i	$-0.155102\pi$
$193$	−1.60770	−	6.00000i	−0.115724	−	0.431889i	−0.999340	+	0.0363235i	$0.988435\pi$
$194$	−4.24264	+	7.34847i	−0.304604	+	0.527589i
$195$		0			0
$196$	−6.09808	−	10.5622i	−0.435577	−	0.754441i
$197$	−9.46979	+	9.46979i	−0.674695	+	0.674695i	−0.958795	−	0.284100i	$-0.908305\pi$
$197$	−9.46979	+	9.46979i	−0.674695	+	0.674695i	0.284100	+	0.958795i	$0.408305\pi$
$198$		0			0
$199$		−	12.5885i		−	0.892372i	−0.894940	−	0.446186i	$-0.852782\pi$
$199$		−	12.5885i		−	0.892372i	0.894940	−	0.446186i	$-0.147218\pi$
$200$	−3.93305	+	3.08725i	−0.278109	+	0.218301i
$201$		0			0
$202$	12.8301	−	3.43782i	0.902725	−	0.241884i
$203$	23.9401	−	6.41473i	1.68027	−	0.450226i
$204$		0			0
$205$	0.571797	+	2.79423i	0.0399360	+	0.195157i
$206$		−	5.51815i		−	0.384468i
$207$		0			0
$208$	4.09808	−	4.09808i	0.284150	−	0.284150i
$209$	2.26002	+	3.91447i	0.156329	+	0.270770i
$210$		0			0
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	−0.328135	−	0.944631i	$-0.606420\pi$
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	0.982142	−	0.188142i	$-0.0602466\pi$
$212$	0.827225	+	3.08725i	0.0568141	+	0.212033i
$213$		0			0
$214$	10.5622	−	6.09808i	0.722016	−	0.416856i
$215$	−7.34847	−	14.6969i	−0.501161	−	1.00232i
$216$		0			0
$217$	19.1962	+	19.1962i	1.30312	+	1.30312i
$218$	2.58819	−	9.65926i	0.175294	−	0.654208i
$219$		0			0
$220$	2.09808	+	2.36603i	0.141452	+	0.159517i
$221$	−31.0991	−	17.9551i	−2.09195	−	1.20779i
$222$		0			0
$223$	−23.4904	−	6.29423i	−1.57303	−	0.421493i	−0.636272	−	0.771465i	$-0.719524\pi$
$223$	−23.4904	−	6.29423i	−1.57303	−	0.421493i	−0.936760	+	0.349972i	$0.886191\pi$
$224$	4.38134			0.292741
$225$		0			0
$226$	−4.00000			−0.266076
$227$	11.7806	+	3.15660i	0.781904	+	0.209511i	0.627624	−	0.778516i	$-0.284027\pi$
$227$	11.7806	+	3.15660i	0.781904	+	0.209511i	0.154280	+	0.988027i	$0.450694\pi$
$228$		0			0
$229$	19.3923	+	11.1962i	1.28148	+	0.739863i	0.977119	−	0.212694i	$-0.0682238\pi$
$229$	19.3923	+	11.1962i	1.28148	+	0.739863i	0.304361	+	0.952557i	$0.401557\pi$
$230$	−7.41782	−	8.36516i	−0.489117	−	0.551583i
$231$		0			0
$232$	−1.46410	+	5.46410i	−0.0961230	+	0.358736i
$233$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		0			0
$235$	0.803848	+	1.60770i	0.0524372	+	0.104874i
$236$	2.56961	−	1.48356i	0.167267	−	0.0965718i
$237$		0			0
$238$	−7.02628	−	26.2224i	−0.455446	−	1.69975i
$239$	8.48528	−	14.6969i	0.548867	−	0.950666i	−0.449485	−	0.893288i	$-0.648393\pi$
$239$	8.48528	−	14.6969i	0.548867	−	0.950666i	0.998353	−	0.0573782i	$-0.0182741\pi$
$240$		0			0
$241$	15.1962	+	26.3205i	0.978870	+	1.69545i	0.666522	+	0.745485i	$0.267782\pi$
$241$	15.1962	+	26.3205i	0.978870	+	1.69545i	0.312348	+	0.949968i	$0.398884\pi$
$242$	−6.36396	+	6.36396i	−0.409091	+	0.409091i
$243$		0			0
$244$		−	3.80385i		−	0.243516i
$245$	−5.46739	−	26.7178i	−0.349298	−	1.70693i
$246$		0			0
$247$	17.8923	−	4.79423i	1.13846	−	0.305049i
$248$	−5.98502	+	1.60368i	−0.380049	+	0.101834i
$249$		0			0
$250$	−10.5263	+	3.76795i	−0.665740	+	0.238306i
$251$		−	5.79555i		−	0.365812i	−0.983130	−	0.182906i	$-0.941450\pi$
$251$		−	5.79555i		−	0.365812i	0.983130	−	0.182906i	$-0.0585504\pi$
$252$		0			0
$253$	−5.00000	+	5.00000i	−0.314347	+	0.314347i
$254$	−1.48356	−	2.56961i	−0.0930871	−	0.161232i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.86181	−	18.1445i	−0.303272	−	1.13183i	−0.934423	−	0.356165i	$-0.884084\pi$
$257$	−4.86181	−	18.1445i	−0.303272	−	1.13183i	0.631151	−	0.775660i	$-0.282583\pi$
$258$		0			0
$259$	27.8827	−	16.0981i	1.73255	−	1.00029i
$260$	11.5911	−	5.79555i	0.718850	−	0.359425i
$261$		0			0
$262$	0.0980762	+	0.0980762i	0.00605917	+	0.00605917i
$263$	0.258819	−	0.965926i	0.0159595	−	0.0595615i	−0.957487	−	0.288477i	$-0.906851\pi$
$263$	0.258819	−	0.965926i	0.0159595	−	0.0595615i	0.973446	+	0.228915i	$0.0735179\pi$
$264$		0			0
$265$	−0.428203	+	7.13397i	−0.0263043	+	0.438237i
$266$	12.1273	+	7.00172i	0.743574	+	0.429303i
$267$		0			0
$268$	−5.73205	−	1.53590i	−0.350141	−	0.0938199i
$269$	3.96524			0.241765			0.120882	−	0.992667i	$-0.461428\pi$
$269$	3.96524			0.241765			0.120882	+	0.992667i	$0.461428\pi$
$270$		0			0
$271$	−32.7846			−1.99152			−0.995762	−	0.0919719i	$-0.970683\pi$
$271$	−32.7846			−1.99152			−0.995762	+	0.0919719i	$0.970683\pi$
$272$	5.98502	+	1.60368i	0.362895	+	0.0972375i
$273$		0			0
$274$	−12.2942	−	7.09808i	−0.742722	−	0.428810i
$275$	2.77766	+	6.50266i	0.167499	+	0.392125i
$276$		0			0
$277$	2.30385	−	8.59808i	0.138425	−	0.516608i	−0.861536	−	0.507697i	$-0.830497\pi$
$277$	2.30385	−	8.59808i	0.138425	−	0.516608i	0.999960	−	0.00891102i	$-0.00283650\pi$
$278$	−10.8840	−	10.8840i	−0.652779	−	0.652779i
$279$		0			0
$280$	9.29423	+	3.09808i	0.555436	+	0.185145i
$281$	−13.3521	+	7.70882i	−0.796518	+	0.459870i	−0.842252	−	0.539084i	$-0.818771\pi$
$281$	−13.3521	+	7.70882i	−0.796518	+	0.459870i	0.0457341	+	0.998954i	$0.485437\pi$
$282$		0			0
$283$	−1.97372	−	7.36603i	−0.117326	−	0.437865i	0.882125	−	0.471016i	$-0.156112\pi$
$283$	−1.97372	−	7.36603i	−0.117326	−	0.437865i	−0.999450	+	0.0331509i	$0.989446\pi$
$284$	−5.08845	+	8.81345i	−0.301944	+	0.522982i
$285$		0			0
$286$	−4.09808	−	7.09808i	−0.242324	−	0.419718i
$287$	3.95164	−	3.95164i	0.233258	−	0.233258i
$288$		0			0
$289$		−	21.3923i		−	1.25837i
$290$	−6.96953	+	10.5558i	−0.409265	+	0.619860i
$291$		0			0
$292$	5.46410	−	1.46410i	0.319762	−	0.0856801i
$293$	7.14042	−	1.91327i	0.417148	−	0.111774i	−0.0441393	−	0.999025i	$-0.514055\pi$
$293$	7.14042	−	1.91327i	0.417148	−	0.111774i	0.461287	+	0.887251i	$0.347388\pi$
$294$		0			0
$295$	6.50000	−	1.33013i	0.378445	−	0.0774430i
$296$			7.34847i			0.427121i
$297$		0			0
$298$	0.803848	−	0.803848i	0.0465656	−	0.0465656i
$299$	14.4889	+	25.0955i	0.837914	+	1.45131i
$300$		0			0
$301$	−16.0981	+	27.8827i	−0.927878	+	1.60713i
$302$	2.22286	+	8.29581i	0.127911	+	0.477370i
$303$		0			0
$304$	−2.76795	+	1.59808i	−0.158753	+	0.0916560i
$305$	2.68973	−	8.06918i	0.154013	−	0.462040i
$306$		0			0
$307$	−0.803848	−	0.803848i	−0.0458780	−	0.0458780i	0.683796	−	0.729674i	$-0.260328\pi$
$307$	−0.803848	−	0.803848i	−0.0458780	−	0.0458780i	−0.729674	+	0.683796i	$0.760328\pi$
$308$	1.60368	−	5.98502i	0.0913783	−	0.341028i
$309$		0			0
$310$	−13.8301	−	0.830127i	−0.785498	−	0.0471480i
$311$	14.9372	+	8.62398i	0.847009	+	0.489021i	0.859641	−	0.510899i	$-0.170687\pi$
$311$	14.9372	+	8.62398i	0.847009	+	0.489021i	−0.0126312	+	0.999920i	$0.504021\pi$
$312$		0			0
$313$	10.0981	+	2.70577i	0.570777	+	0.152939i	0.532653	−	0.846334i	$-0.321195\pi$
$313$	10.0981	+	2.70577i	0.570777	+	0.152939i	0.0381241	+	0.999273i	$0.487862\pi$
$314$	4.65874			0.262908
$315$		0			0
$316$	−2.19615			−0.123543
$317$	26.0800	+	6.98811i	1.46480	+	0.392492i	0.901144	−	0.433519i	$-0.142728\pi$
$317$	26.0800	+	6.98811i	1.46480	+	0.392492i	0.563654	+	0.826011i	$0.309395\pi$
$318$		0			0
$319$	6.92820	+	4.00000i	0.387905	+	0.223957i
$320$	−1.67303	+	1.48356i	−0.0935254	+	0.0829337i
$321$		0			0
$322$	−5.66987	+	21.1603i	−0.315970	+	1.17921i
$323$	14.0034	+	14.0034i	0.779172	+	0.779172i
$324$		0			0
$325$	28.6865	−	4.09808i	1.59124	−	0.227320i
$326$	17.1464	−	9.89949i	0.949653	−	0.548282i
$327$		0			0
$328$	0.330127	+	1.23205i	0.0182282	+	0.0680286i
$329$	1.76097	−	3.05008i	0.0970852	−	0.168156i
$330$		0			0
$331$	−5.80385	−	10.0526i	−0.319008	−	0.552539i	0.661273	−	0.750145i	$-0.270016\pi$
$331$	−5.80385	−	10.0526i	−0.319008	−	0.552539i	−0.980281	+	0.197607i	$0.936683\pi$
$332$	−10.0382	+	10.0382i	−0.550918	+	0.550918i
$333$		0			0
$334$			22.7846i			1.24672i
$335$	−11.0735	−	7.31130i	−0.605008	−	0.399459i
$336$		0			0
$337$	−12.2942	+	3.29423i	−0.669709	+	0.179448i	−0.577624	−	0.816303i	$-0.696020\pi$
$337$	−12.2942	+	3.29423i	−0.669709	+	0.179448i	−0.0920854	+	0.995751i	$0.529353\pi$
$338$	−19.8869	+	5.32868i	−1.08171	+	0.289842i
$339$		0			0
$340$	11.5622	+	7.63397i	0.627047	+	0.414010i
$341$			8.76268i			0.474526i
$342$		0			0
$343$	−16.0981	+	16.0981i	−0.869214	+	0.869214i
$344$	−3.67423	−	6.36396i	−0.198101	−	0.343122i
$345$		0			0
$346$	−6.79423	+	11.7679i	−0.365260	+	0.632649i
$347$	1.45138	+	5.41662i	0.0779141	+	0.290779i	0.993878	−	0.110481i	$-0.0352390\pi$
$347$	1.45138	+	5.41662i	0.0779141	+	0.290779i	−0.915964	+	0.401260i	$0.868572\pi$
$348$		0			0
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$	17.5254	+	13.1440i	0.936770	+	0.702578i
$351$		0			0
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	2.12132	−	7.91688i	0.112906	−	0.421373i	−0.886215	−	0.463274i	$-0.846675\pi$
$353$	2.12132	−	7.91688i	0.112906	−	0.421373i	0.999122	+	0.0419009i	$0.0133414\pi$
$354$		0			0
$355$	−17.0263	+	15.0981i	−0.903661	+	0.801323i
$356$	−1.46498	−	0.845807i	−0.0776439	−	0.0448277i
$357$		0			0
$358$	−23.6244	−	6.33013i	−1.24859	−	0.334558i
$359$	11.8685			0.626396			0.313198	−	0.949688i	$-0.398600\pi$
$359$	11.8685			0.626396			0.313198	+	0.949688i	$0.398600\pi$
$360$		0			0
$361$	8.78461			0.462348
$362$	4.05317	+	1.08604i	0.213030	+	0.0570812i
$363$		0			0
$364$	−21.9904	−	12.6962i	−1.15261	−	0.665459i
$365$	12.6264	+	0.757875i	0.660895	+	0.0396690i
$366$		0			0
$367$	5.63397	−	21.0263i	0.294091	−	1.09756i	−0.647845	−	0.761772i	$-0.724330\pi$
$367$	5.63397	−	21.0263i	0.294091	−	1.09756i	0.941937	−	0.335791i	$-0.109004\pi$
$368$	−3.53553	−	3.53553i	−0.184302	−	0.184302i
$369$		0			0
$370$	−5.19615	+	15.5885i	−0.270135	+	0.810405i
$371$	12.1273	−	7.00172i	0.629620	−	0.363511i
$372$		0			0
$373$	−7.83013	−	29.2224i	−0.405429	−	1.51308i	−0.803264	−	0.595623i	$-0.796905\pi$
$373$	−7.83013	−	29.2224i	−0.405429	−	1.51308i	0.397835	−	0.917457i	$-0.369762\pi$
$374$	4.38134	−	7.58871i	0.226554	−	0.392403i
$375$		0			0
$376$	0.401924	+	0.696152i	0.0207276	+	0.0359013i
$377$	23.1822	−	23.1822i	1.19395	−	1.19395i
$378$		0			0
$379$		−	11.0000i		−	0.565032i	−0.959263	−	0.282516i	$-0.908831\pi$
$379$		−	11.0000i		−	0.565032i	0.959263	−	0.282516i	$-0.0911690\pi$
$380$	−7.00172	+	1.43280i	−0.359181	+	0.0735009i
$381$		0			0
$382$	−9.56218	+	2.56218i	−0.489244	+	0.131092i
$383$	10.8147	−	2.89778i	0.552603	−	0.148070i	0.0282971	−	0.999600i	$-0.490992\pi$
$383$	10.8147	−	2.89778i	0.552603	−	0.148070i	0.524306	+	0.851530i	$0.324325\pi$
$384$		0			0
$385$	7.63397	−	11.5622i	0.389063	−	0.589263i
$386$		−	6.21166i		−	0.316165i
$387$		0			0
$388$	−6.00000	+	6.00000i	−0.304604	+	0.304604i
$389$	13.7124	+	23.7506i	0.695248	+	1.20420i	0.970097	+	0.242717i	$0.0780387\pi$
$389$	13.7124	+	23.7506i	0.695248	+	1.20420i	−0.274849	+	0.961487i	$0.588628\pi$
$390$		0			0
$391$	−15.4904	+	26.8301i	−0.783382	+	1.35686i
$392$	−3.15660	−	11.7806i	−0.159432	−	0.595009i
$393$		0			0
$394$	−11.5981	+	6.69615i	−0.584303	+	0.337347i
$395$	−4.65874	−	1.55291i	−0.234407	−	0.0781356i
$396$		0			0
$397$	3.19615	+	3.19615i	0.160410	+	0.160410i	0.782748	−	0.622338i	$-0.213817\pi$
$397$	3.19615	+	3.19615i	0.160410	+	0.160410i	−0.622338	+	0.782748i	$0.713817\pi$
$398$	3.25813	−	12.1595i	0.163315	−	0.609501i
$399$		0			0
$400$	−4.59808	+	1.96410i	−0.229904	+	0.0982051i
$401$	−11.3831	−	6.57201i	−0.568443	−	0.328191i	0.188084	−	0.982153i	$-0.439772\pi$
$401$	−11.3831	−	6.57201i	−0.568443	−	0.328191i	−0.756527	+	0.653962i	$0.773106\pi$
$402$		0			0
$403$	34.6865	+	9.29423i	1.72786	+	0.462979i
$404$	13.2827			0.660840
$405$		0			0
$406$	24.7846			1.23004
$407$	10.0382	+	2.68973i	0.497575	+	0.133325i
$408$		0			0
$409$	21.9904	+	12.6962i	1.08735	+	0.627784i	0.932871	−	0.360211i	$-0.117295\pi$
$409$	21.9904	+	12.6962i	1.08735	+	0.627784i	0.154484	+	0.987995i	$0.450629\pi$
$410$	−0.170886	+	2.84701i	−0.00843947	+	0.140604i
$411$		0			0
$412$	1.42820	−	5.33013i	0.0703625	−	0.262597i
$413$	−9.19239	−	9.19239i	−0.452328	−	0.452328i
$414$		0			0
$415$	−28.3923	+	14.1962i	−1.39372	+	0.696862i
$416$	5.01910	−	2.89778i	0.246082	−	0.142075i
$417$		0			0
$418$	1.16987	+	4.36603i	0.0572204	+	0.213549i
$419$	−9.05369	+	15.6814i	−0.442302	+	0.766089i	−0.997860	−	0.0653888i	$-0.979171\pi$
$419$	−9.05369	+	15.6814i	−0.442302	+	0.766089i	0.555558	+	0.831478i	$0.312505\pi$
$420$		0			0
$421$	−2.09808	−	3.63397i	−0.102254	−	0.177109i	0.810359	−	0.585934i	$-0.199272\pi$
$421$	−2.09808	−	3.63397i	−0.102254	−	0.177109i	−0.912613	+	0.408825i	$0.865939\pi$
$422$	13.4350	−	13.4350i	0.654007	−	0.654007i
$423$		0			0
$424$			3.19615i			0.155219i
$425$	19.1290	+	24.3698i	0.927895	+	1.18211i
$426$		0			0
$427$	−16.0981	+	4.31347i	−0.779041	+	0.208743i
$428$	11.7806	−	3.15660i	0.569436	−	0.152580i
$429$		0			0
$430$	−3.29423	−	16.0981i	−0.158862	−	0.776318i
$431$		−	24.0416i		−	1.15804i	−0.815312	−	0.579022i	$-0.803434\pi$
$431$		−	24.0416i		−	1.15804i	0.815312	−	0.579022i	$-0.196566\pi$
$432$		0			0
$433$	8.00000	−	8.00000i	0.384455	−	0.384455i	−0.488249	−	0.872704i	$-0.662364\pi$
$433$	8.00000	−	8.00000i	0.384455	−	0.384455i	0.872704	+	0.488249i	$0.162364\pi$
$434$	13.5737	+	23.5104i	0.651560	+	1.12853i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−4.13613	−	15.4362i	−0.197858	−	0.738415i
$438$		0			0
$439$	−8.15064	+	4.70577i	−0.389009	+	0.224594i	−0.681730	−	0.731603i	$-0.738772\pi$
$439$	−8.15064	+	4.70577i	−0.389009	+	0.224594i	0.292722	+	0.956198i	$0.405439\pi$
$440$	1.41421	+	2.82843i	0.0674200	+	0.134840i
$441$		0			0
$442$	−25.3923	−	25.3923i	−1.20779	−	1.20779i
$443$	−3.10583	+	11.5911i	−0.147562	+	0.550710i	0.852066	+	0.523435i	$0.175350\pi$
$443$	−3.10583	+	11.5911i	−0.147562	+	0.550710i	−0.999628	+	0.0272752i	$0.991317\pi$
$444$		0			0
$445$	−2.50962	−	2.83013i	−0.118967	−	0.134161i
$446$	−21.0609	−	12.1595i	−0.997262	−	0.575770i
$447$		0			0
$448$	4.23205	+	1.13397i	0.199946	+	0.0535753i
$449$	−19.9377			−0.940918			−0.470459	−	0.882422i	$-0.655912\pi$
$449$	−19.9377			−0.940918			−0.470459	+	0.882422i	$0.655912\pi$
$450$		0			0
$451$	1.80385			0.0849399
$452$	−3.86370	−	1.03528i	−0.181733	−	0.0486953i
$453$		0			0
$454$	10.5622	+	6.09808i	0.495708	+	0.286197i
$455$	−37.6711	−	42.4822i	−1.76605	−	1.99159i
$456$		0			0
$457$	4.09808	−	15.2942i	0.191700	−	0.715434i	−0.801397	−	0.598133i	$-0.795909\pi$
$457$	4.09808	−	15.2942i	0.191700	−	0.715434i	0.993096	−	0.117300i	$-0.0374240\pi$
$458$	15.8338	+	15.8338i	0.739863	+	0.739863i
$459$		0			0
$460$	−5.00000	−	10.0000i	−0.233126	−	0.466252i
$461$	−7.10823	+	4.10394i	−0.331063	+	0.191140i	−0.656313	−	0.754489i	$-0.727885\pi$
$461$	−7.10823	+	4.10394i	−0.331063	+	0.191140i	0.325250	+	0.945628i	$0.394552\pi$
$462$		0			0
$463$	9.33013	+	34.8205i	0.433608	+	1.61825i	0.744376	+	0.667761i	$0.232747\pi$
$463$	9.33013	+	34.8205i	0.433608	+	1.61825i	−0.310768	+	0.950486i	$0.600586\pi$
$464$	−2.82843	+	4.89898i	−0.131306	+	0.227429i
$465$		0			0
$466$		0			0
$467$	17.5254	−	17.5254i	0.810977	−	0.810977i	−0.173803	−	0.984780i	$-0.555606\pi$
$467$	17.5254	−	17.5254i	0.810977	−	0.810977i	0.984780	+	0.173803i	$0.0556057\pi$
$468$		0			0
$469$			26.0000i			1.20057i
$470$	0.360355	+	1.76097i	0.0166219	+	0.0812273i
$471$		0			0
$472$	2.86603	−	0.767949i	0.131920	−	0.0353477i
$473$	−10.0382	+	2.68973i	−0.461557	+	0.123674i
$474$		0			0
$475$	−15.8660	−	1.91154i	−0.727983	−	0.0877076i
$476$		−	27.1475i		−	1.24430i
$477$		0			0
$478$	12.0000	−	12.0000i	0.548867	−	0.548867i
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	0.773879	−	0.633333i	$-0.218314\pi$
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	−0.935422	+	0.353533i	$0.884980\pi$
$480$		0			0
$481$	21.2942	−	36.8827i	0.970933	−	1.68171i
$482$	7.86611	+	29.3567i	0.358291	+	1.33716i
$483$		0			0
$484$	−7.79423	+	4.50000i	−0.354283	+	0.204545i
$485$	−16.9706	+	8.48528i	−0.770594	+	0.385297i
$486$		0			0
$487$	4.90192	+	4.90192i	0.222127	+	0.222127i	0.809394	−	0.587266i	$-0.199796\pi$
$487$	4.90192	+	4.90192i	0.222127	+	0.222127i	−0.587266	+	0.809394i	$0.699796\pi$
$488$	0.984508	−	3.67423i	0.0445666	−	0.166325i
$489$		0			0
$490$	1.63397	−	27.2224i	0.0738154	−	1.22978i
$491$	−5.76337	−	3.32748i	−0.260097	−	0.150167i	0.364282	−	0.931289i	$-0.381315\pi$
$491$	−5.76337	−	3.32748i	−0.260097	−	0.150167i	−0.624379	+	0.781122i	$0.714648\pi$
$492$		0			0
$493$	33.8564	+	9.07180i	1.52482	+	0.408573i
$494$	18.5235			0.833411
$495$		0			0
$496$	−6.19615			−0.278215
$497$	43.0691	+	11.5403i	1.93192	+	0.517655i
$498$		0			0
$499$	−30.8205	−	17.7942i	−1.37972	−	0.796579i	−0.387591	−	0.921832i	$-0.626693\pi$
$499$	−30.8205	−	17.7942i	−1.37972	−	0.796579i	−0.992125	+	0.125253i	$0.960026\pi$
$500$	−11.1428	+	0.915158i	−0.498322	+	0.0409271i
$501$		0			0
$502$	1.50000	−	5.59808i	0.0669483	−	0.249854i
$503$	28.5617	+	28.5617i	1.27350	+	1.27350i	0.944238	+	0.329264i	$0.106801\pi$
$503$	28.5617	+	28.5617i	1.27350	+	1.27350i	0.329264	+	0.944238i	$0.393199\pi$
$504$		0			0
$505$	28.1769	+	9.39230i	1.25386	+	0.417952i
$506$	−6.12372	+	3.53553i	−0.272233	+	0.157174i
$507$		0			0
$508$	−0.767949	−	2.86603i	−0.0340722	−	0.127159i
$509$	0.707107	−	1.22474i	0.0313420	−	0.0542859i	−0.849929	−	0.526897i	$-0.823355\pi$
$509$	0.707107	−	1.22474i	0.0313420	−	0.0542859i	0.881271	+	0.472611i	$0.156689\pi$
$510$		0			0
$511$	−12.3923	−	21.4641i	−0.548203	−	0.949516i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	18.7846i		−	0.828554i
$515$	6.79865	−	10.2970i	0.299584	−	0.453741i
$516$		0			0
$517$	1.09808	−	0.294229i	0.0482933	−	0.0129402i
$518$	31.0991	−	8.33298i	1.36642	−	0.366130i
$519$		0			0
$520$	12.6962	−	2.59808i	0.556763	−	0.113933i
$521$			42.8425i			1.87696i	0.345328	+	0.938482i	$0.387768\pi$
$521$			42.8425i			1.87696i	−0.345328	+	0.938482i	$0.612232\pi$
$522$		0			0
$523$	−7.39230	+	7.39230i	−0.323243	+	0.323243i	−0.850010	−	0.526767i	$-0.823404\pi$
$523$	−7.39230	+	7.39230i	−0.323243	+	0.323243i	0.526767	+	0.850010i	$0.323404\pi$
$524$	0.0693504	+	0.120118i	0.00302958	+	0.00524739i
$525$		0			0
$526$	0.500000	−	0.866025i	0.0218010	−	0.0377605i
$527$	9.93666	+	37.0841i	0.432848	+	1.61541i
$528$		0			0
$529$	1.73205	−	1.00000i	0.0753066	−	0.0434783i
$530$	−2.26002	+	6.78006i	−0.0981690	+	0.294507i
$531$		0			0
$532$	9.90192	+	9.90192i	0.429303	+	0.429303i
$533$	1.91327	−	7.14042i	0.0828729	−	0.309286i
$534$		0			0
$535$	27.2224	+	1.63397i	1.17693	+	0.0706429i
$536$	−5.13922	−	2.96713i	−0.221980	−	0.128160i
$537$		0			0
$538$	3.83013	+	1.02628i	0.165129	+	0.0442460i
$539$	−17.2480			−0.742922
$540$		0			0
$541$	16.0000			0.687894			0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000			0.687894			0.343947	+	0.938989i	$0.388236\pi$
$542$	−31.6675	−	8.48528i	−1.36024	−	0.364474i
$543$		0			0
$544$	5.36603	+	3.09808i	0.230066	+	0.132829i
$545$	16.7303	−	14.8356i	0.716648	−	0.635489i
$546$		0			0
$547$	−1.09808	+	4.09808i	−0.0469503	+	0.175221i	−0.985420	−	0.170142i	$-0.945577\pi$
$547$	−1.09808	+	4.09808i	−0.0469503	+	0.175221i	0.938469	+	0.345363i	$0.112244\pi$
$548$	−10.0382	−	10.0382i	−0.428810	−	0.428810i
$549$		0			0
$550$	1.00000	+	7.00000i	0.0426401	+	0.298481i
$551$	−15.6579	+	9.04008i	−0.667048	+	0.385121i
$552$		0			0
$553$	2.49038	+	9.29423i	0.105902	+	0.395231i
$554$	4.45069	−	7.70882i	0.189092	−	0.327517i
$555$		0			0
$556$	−7.69615	−	13.3301i	−0.326390	−	0.565323i
$557$	12.1595	−	12.1595i	0.515215	−	0.515215i	−0.400905	−	0.916120i	$-0.631304\pi$
$557$	12.1595	−	12.1595i	0.515215	−	0.515215i	0.916120	+	0.400905i	$0.131304\pi$
$558$		0			0
$559$			42.5885i			1.80130i
$560$	8.17569	+	5.39804i	0.345486	+	0.228109i
$561$		0			0
$562$	−14.8923	+	3.99038i	−0.628194	+	0.168324i
$563$	25.8719	−	6.93237i	1.09037	−	0.292164i	0.331534	−	0.943443i	$-0.392434\pi$
$563$	25.8719	−	6.93237i	1.09037	−	0.292164i	0.758839	+	0.651279i	$0.225767\pi$
$564$		0			0
$565$	−7.46410	−	4.92820i	−0.314017	−	0.207331i
$566$		−	7.62587i		−	0.320539i
$567$		0			0
$568$	−7.19615	+	7.19615i	−0.301944	+	0.301944i
$569$	−14.6276	−	25.3357i	−0.613220	−	1.06213i	−0.990694	−	0.136109i	$-0.956540\pi$
$569$	−14.6276	−	25.3357i	−0.613220	−	1.06213i	0.377474	−	0.926020i	$-0.376793\pi$
$570$		0			0
$571$	8.58846	−	14.8756i	0.359416	−	0.622526i	−0.628448	−	0.777852i	$-0.716309\pi$
$571$	8.58846	−	14.8756i	0.359416	−	0.622526i	0.987863	+	0.155326i	$0.0496427\pi$
$572$	−2.12132	−	7.91688i	−0.0886969	−	0.331021i
$573$		0			0
$574$	4.83975	−	2.79423i	0.202007	−	0.116629i
$575$	−3.53553	−	24.7487i	−0.147442	−	1.03209i
$576$		0			0
$577$	−12.3923	−	12.3923i	−0.515898	−	0.515898i	0.400429	−	0.916328i	$-0.368861\pi$
$577$	−12.3923	−	12.3923i	−0.515898	−	0.515898i	−0.916328	+	0.400429i	$0.868861\pi$
$578$	5.53674	−	20.6634i	0.230298	−	0.859483i
$579$		0			0
$580$	−9.46410	+	8.39230i	−0.392975	+	0.348471i
$581$	53.8652	+	31.0991i	2.23471	+	1.29021i
$582$		0			0
$583$	4.36603	+	1.16987i	0.180822	+	0.0484512i
$584$	5.65685			0.234082
$585$		0			0
$586$	7.39230			0.305373
$587$	−7.91688	−	2.12132i	−0.326764	−	0.0875563i	0.0917075	−	0.995786i	$-0.470768\pi$
$587$	−7.91688	−	2.12132i	−0.326764	−	0.0875563i	−0.418472	+	0.908230i	$0.637434\pi$
$588$		0			0
$589$	−17.1506	−	9.90192i	−0.706680	−	0.408002i
$590$	6.62278	+	0.397520i	0.272656	+	0.0163656i
$591$		0			0
$592$	−1.90192	+	7.09808i	−0.0781686	+	0.291729i
$593$	−32.9430	−	32.9430i	−1.35281	−	1.35281i	−0.882506	−	0.470302i	$-0.844145\pi$
$593$	−32.9430	−	32.9430i	−1.35281	−	1.35281i	−0.470302	−	0.882506i	$-0.655855\pi$
$594$		0			0
$595$	19.1962	−	57.5885i	0.786966	−	2.36090i
$596$	0.984508	−	0.568406i	0.0403270	−	0.0232828i
$597$		0			0
$598$	7.50000	+	27.9904i	0.306698	+	1.14461i
$599$	−19.7854	+	34.2693i	−0.808409	+	1.40021i	0.105556	+	0.994413i	$0.466338\pi$
$599$	−19.7854	+	34.2693i	−0.808409	+	1.40021i	−0.913965	+	0.405792i	$0.866996\pi$
$600$		0			0
$601$	−2.79423	−	4.83975i	−0.113979	−	0.197417i	0.803392	−	0.595450i	$-0.203026\pi$
$601$	−2.79423	−	4.83975i	−0.113979	−	0.197417i	−0.917371	+	0.398033i	$0.869693\pi$
$602$	−22.7661	+	22.7661i	−0.927878	+	0.927878i
$603$		0			0
$604$			8.58846i			0.349459i
$605$	−19.7160	+	4.03459i	−0.801571	+	0.164029i
$606$		0			0
$607$	−4.09808	+	1.09808i	−0.166336	+	0.0445695i	−0.341026	−	0.940054i	$-0.610774\pi$
$607$	−4.09808	+	1.09808i	−0.166336	+	0.0445695i	0.174690	+	0.984623i	$0.444108\pi$
$608$	−3.08725	+	0.827225i	−0.125204	+	0.0335484i
$609$		0			0
$610$	4.68653	−	7.09808i	0.189752	−	0.287393i
$611$		−	4.65874i		−	0.188473i
$612$		0			0
$613$	−11.4904	+	11.4904i	−0.464092	+	0.464092i	−0.899994	−	0.435902i	$-0.856429\pi$
$613$	−11.4904	+	11.4904i	−0.464092	+	0.464092i	0.435902	+	0.899994i	$0.356429\pi$
$614$	−0.568406	−	0.984508i	−0.0229390	−	0.0397315i
$615$		0			0
$616$	3.09808	−	5.36603i	0.124825	−	0.216203i
$617$	3.25813	+	12.1595i	0.131167	+	0.489524i	0.999984	−	0.00561003i	$-0.00178574\pi$
$617$	3.25813	+	12.1595i	0.131167	+	0.489524i	−0.868817	+	0.495134i	$0.835119\pi$
$618$		0			0
$619$	−15.4019	+	8.89230i	−0.619056	+	0.357412i	−0.776501	−	0.630116i	$-0.783007\pi$
$619$	−15.4019	+	8.89230i	−0.619056	+	0.357412i	0.157446	+	0.987528i	$0.449674\pi$
$620$	−13.1440	−	4.38134i	−0.527877	−	0.175959i
$621$		0			0
$622$	12.1962	+	12.1962i	0.489021	+	0.489021i
$623$	−1.91825	+	7.15900i	−0.0768530	+	0.286819i
$624$		0			0
$625$	−24.2846	−	5.93782i	−0.971384	−	0.237513i
$626$	9.05369	+	5.22715i	0.361858	+	0.208919i
$627$		0			0
$628$	4.50000	+	1.20577i	0.179570	+	0.0481155i
$629$	45.5322			1.81549
$630$		0			0
$631$	38.3923			1.52837			0.764187	−	0.644995i	$-0.223141\pi$
$631$	38.3923			1.52837			0.764187	+	0.644995i	$0.223141\pi$
$632$	−2.12132	−	0.568406i	−0.0843816	−	0.0226100i
$633$		0			0
$634$	23.3827	+	13.5000i	0.928645	+	0.536153i
$635$	0.397520	−	6.62278i	0.0157751	−	0.262817i
$636$		0			0
$637$	−18.2942	+	68.2750i	−0.724844	+	2.70515i
$638$	5.65685	+	5.65685i	0.223957	+	0.223957i
$639$		0			0
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	−11.9837	+	6.91876i	−0.473326	+	0.273275i	−0.717631	−	0.696424i	$-0.754773\pi$
$641$	−11.9837	+	6.91876i	−0.473326	+	0.273275i	0.244305	+	0.969698i	$0.421440\pi$
$642$		0			0
$643$	−1.68653	−	6.29423i	−0.0665104	−	0.248220i	0.924664	−	0.380784i	$-0.124346\pi$
$643$	−1.68653	−	6.29423i	−0.0665104	−	0.248220i	−0.991174	+	0.132564i	$0.957679\pi$
$644$	−10.9534	+	18.9718i	−0.431623	+	0.747592i
$645$		0			0
$646$	9.90192	+	17.1506i	0.389586	+	0.674783i
$647$	−18.6622	+	18.6622i	−0.733686	+	0.733686i	−0.971348	−	0.237662i	$-0.923619\pi$
$647$	−18.6622	+	18.6622i	−0.733686	+	0.733686i	0.237662	+	0.971348i	$0.423619\pi$
$648$		0			0
$649$		−	4.19615i		−	0.164713i
$650$	28.7697	+	3.46618i	1.12844	+	0.135955i
$651$		0			0
$652$	19.1244	−	5.12436i	0.748968	−	0.200685i
$653$	−24.3190	+	6.51626i	−0.951677	+	0.255001i	−0.701074	−	0.713089i	$-0.747296\pi$
$653$	−24.3190	+	6.51626i	−0.951677	+	0.255001i	−0.250603	+	0.968090i	$0.580629\pi$
$654$		0			0
$655$	0.0621778	+	0.303848i	0.00242949	+	0.0118723i
$656$			1.27551i			0.0498004i
$657$		0			0
$658$	2.49038	−	2.49038i	0.0970852	−	0.0970852i
$659$	−2.62038	−	4.53862i	−0.102075	−	0.176800i	0.810464	−	0.585788i	$-0.199215\pi$
$659$	−2.62038	−	4.53862i	−0.102075	−	0.176800i	−0.912540	+	0.408988i	$0.865882\pi$
$660$		0			0
$661$	14.2942	−	24.7583i	0.555981	−	0.962987i	−0.441845	−	0.897091i	$-0.645676\pi$
$661$	14.2942	−	24.7583i	0.555981	−	0.962987i	0.997826	−	0.0658962i	$-0.0209906\pi$
$662$	−3.00429	−	11.2122i	−0.116765	−	0.435773i
$663$		0			0
$664$	−12.2942	+	7.09808i	−0.477109	+	0.275459i
$665$	14.0034	+	28.0069i	0.543030	+	1.08606i
$666$		0			0
$667$	−20.0000	−	20.0000i	−0.774403	−	0.774403i
$668$	−5.89709	+	22.0082i	−0.228165	+	0.851524i
$669$		0			0
$670$	−8.80385	−	9.92820i	−0.340122	−	0.383560i
$671$	−4.65874	−	2.68973i	−0.179849	−	0.103836i
$672$		0			0
$673$	−16.6603	−	4.46410i	−0.642206	−	0.172078i	−0.0770033	−	0.997031i	$-0.524535\pi$
$673$	−16.6603	−	4.46410i	−0.642206	−	0.172078i	−0.565202	+	0.824952i	$0.691202\pi$
$674$	−12.7279			−0.490261
$675$		0			0
$676$	−20.5885			−0.791864
$677$	−35.7393	−	9.57630i	−1.37357	−	0.368047i	−0.504789	−	0.863243i	$-0.668430\pi$
$677$	−35.7393	−	9.57630i	−1.37357	−	0.368047i	−0.868782	+	0.495195i	$0.835097\pi$
$678$		0			0
$679$	32.1962	+	18.5885i	1.23557	+	0.713360i
$680$	9.19239	+	10.3664i	0.352512	+	0.397532i
$681$		0			0
$682$	−2.26795	+	8.46410i	−0.0868443	+	0.324107i
$683$	−12.7279	−	12.7279i	−0.487020	−	0.487020i	0.420344	−	0.907365i	$-0.361909\pi$
$683$	−12.7279	−	12.7279i	−0.487020	−	0.487020i	−0.907365	+	0.420344i	$0.861909\pi$
$684$		0			0
$685$	−14.1962	−	28.3923i	−0.542407	−	1.08481i
$686$	−19.7160	+	11.3831i	−0.752762	+	0.434607i
$687$		0			0
$688$	−1.90192	−	7.09808i	−0.0725102	−	0.270612i
$689$	9.26174	−	16.0418i	0.352844	−	0.611144i
$690$		0			0
$691$	3.40192	+	5.89230i	0.129415	+	0.224154i	0.923450	−	0.383718i	$-0.125357\pi$
$691$	3.40192	+	5.89230i	0.129415	+	0.224154i	−0.794035	+	0.607872i	$0.792023\pi$
$692$	−9.60849	+	9.60849i	−0.365260	+	0.365260i
$693$		0			0
$694$			5.60770i			0.212865i
$695$	−6.90018	−	33.7195i	−0.261739	−	1.27905i
$696$		0			0
$697$	7.63397	−	2.04552i	0.289157	−	0.0774795i
$698$	−1.93185	+	0.517638i	−0.0731217	+	0.0195929i
$699$		0			0
$700$	13.5263	+	17.2321i	0.511245	+	0.651310i
$701$		−	22.9048i		−	0.865103i	−0.901609	−	0.432552i	$-0.857613\pi$
$701$		−	22.9048i		−	0.865103i	0.901609	−	0.432552i	$-0.142387\pi$
$702$		0			0
$703$	−16.6077	+	16.6077i	−0.626371	+	0.626371i
$704$	0.707107	+	1.22474i	0.0266501	+	0.0461593i
$705$		0			0
$706$	4.09808	−	7.09808i	0.154233	−	0.267140i
$707$	−15.0623	−	56.2132i	−0.566475	−	2.11411i
$708$		0			0
$709$	−12.6340	+	7.29423i	−0.474479	+	0.273941i	−0.718113	−	0.695927i	$-0.754994\pi$
$709$	−12.6340	+	7.29423i	−0.474479	+	0.273941i	0.243634	+	0.969867i	$0.421660\pi$
$710$	−20.3538	+	10.1769i	−0.763864	+	0.381932i
$711$		0			0
$712$	−1.19615	−	1.19615i	−0.0448277	−	0.0448277i
$713$	8.01841	−	29.9251i	0.300292	−	1.12070i
$714$		0			0
$715$	1.09808	−	18.2942i	0.0410657	−	0.684165i
$716$	−21.1810	−	12.2289i	−0.791572	−	0.457014i
$717$		0			0
$718$	11.4641	+	3.07180i	0.427836	+	0.114638i
$719$	1.69161			0.0630866			0.0315433	−	0.999502i	$-0.489958\pi$
$719$	1.69161			0.0630866			0.0315433	+	0.999502i	$0.489958\pi$
$720$		0			0
$721$	−24.1769			−0.900395
$722$	8.48528	+	2.27362i	0.315789	+	0.0846155i
$723$		0			0
$724$	3.63397	+	2.09808i	0.135056	+	0.0779744i
$725$	−26.0106	+	11.1106i	−0.966011	+	0.412639i
$726$		0			0
$727$	3.99038	−	14.8923i	0.147995	−	0.552325i	−0.851609	−	0.524178i	$-0.824373\pi$
$727$	3.99038	−	14.8923i	0.147995	−	0.552325i	0.999604	−	0.0281471i	$-0.00896067\pi$
$728$	−17.9551	−	17.9551i	−0.665459	−	0.665459i
$729$		0			0
$730$	12.0000	+	4.00000i	0.444140	+	0.148047i
$731$	−39.4321	+	22.7661i	−1.45845	+	0.842035i
$732$		0			0
$733$	−2.63397	−	9.83013i	−0.0972881	−	0.363084i	0.900068	−	0.435749i	$-0.143516\pi$
$733$	−2.63397	−	9.83013i	−0.0972881	−	0.363084i	−0.997356	+	0.0726647i	$0.976850\pi$
$734$	10.8840	−	18.8516i	0.401736	−	0.695827i
$735$		0			0
$736$	−2.50000	−	4.33013i	−0.0921512	−	0.159611i
$737$	−5.93426	+	5.93426i	−0.218591	+	0.218591i
$738$		0			0
$739$		−	20.3923i		−	0.750143i	−0.926996	−	0.375072i	$-0.877618\pi$
$739$		−	20.3923i		−	0.750143i	0.926996	−	0.375072i	$-0.122382\pi$
$740$	−9.05369	+	13.7124i	−0.332820	+	0.504079i
$741$		0			0
$742$	13.5263	−	3.62436i	0.496565	−	0.133054i
$743$	−31.2886	+	8.38375i	−1.14787	+	0.307570i	−0.782110	−	0.623141i	$-0.785856\pi$
$743$	−31.2886	+	8.38375i	−1.14787	+	0.307570i	−0.365756	+	0.930711i	$0.619190\pi$
$744$		0			0
$745$	2.49038	−	0.509619i	0.0912405	−	0.0186710i
$746$		−	30.2533i		−	1.10765i
$747$		0			0
$748$	6.19615	−	6.19615i	0.226554	−	0.226554i
$749$	−26.7178	−	46.2765i	−0.976245	−	1.69091i
$750$		0			0
$751$	13.3923	−	23.1962i	0.488692	−	0.846440i	−0.511223	−	0.859448i	$-0.670807\pi$
$751$	13.3923	−	23.1962i	0.488692	−	0.846440i	0.999915	+	0.0130083i	$0.00414080\pi$
$752$	0.208051	+	0.776457i	0.00758684	+	0.0283145i
$753$		0			0
$754$	28.3923	−	16.3923i	1.03399	−	0.596973i
$755$	−6.07296	+	18.2189i	−0.221018	+	0.663053i
$756$		0			0
$757$	−15.2942	−	15.2942i	−0.555878	−	0.555878i	0.372253	−	0.928131i	$-0.378585\pi$
$757$	−15.2942	−	15.2942i	−0.555878	−	0.555878i	−0.928131	+	0.372253i	$0.878585\pi$
$758$	2.84701	−	10.6252i	0.103408	−	0.385924i
$759$		0			0
$760$	−7.13397	−	0.428203i	−0.258776	−	0.0155326i
$761$	32.9244	+	19.0089i	1.19351	+	0.689073i	0.959101	−	0.283065i	$-0.0913512\pi$
$761$	32.9244	+	19.0089i	1.19351	+	0.689073i	0.234409	+	0.972138i	$0.424685\pi$
$762$		0			0
$763$	−42.3205	−	11.3397i	−1.53211	−	0.410526i
$764$	−9.89949			−0.358151
$765$		0			0
$766$	11.1962			0.404533
$767$	−16.6102	−	4.45069i	−0.599760	−	0.160705i
$768$		0			0
$769$	44.6603	+	25.7846i	1.61049	+	0.929817i	0.989256	+	0.146191i	$0.0467015\pi$
$769$	44.6603	+	25.7846i	1.61049	+	0.929817i	0.621234	+	0.783625i	$0.286632\pi$
$770$	10.3664	−	9.19239i	0.373578	−	0.331271i
$771$		0			0
$772$	1.60770	−	6.00000i	0.0578622	−	0.215945i
$773$	31.6675	+	31.6675i	1.13900	+	1.13900i	0.988630	+	0.150371i	$0.0480469\pi$
$773$	31.6675	+	31.6675i	1.13900	+	1.13900i	0.150371	+	0.988630i	$0.451953\pi$
$774$		0			0
$775$	−24.7846	−	18.5885i	−0.890289	−	0.667717i
$776$	−7.34847	+	4.24264i	−0.263795	+	0.152302i
$777$		0			0
$778$	7.09808	+	26.4904i	0.254478	+	0.949726i
$779$	−2.03837	+	3.53055i	−0.0730321	+	0.126495i
$780$		0			0
$781$	7.19615	+	12.4641i	0.257499	+	0.446001i
$782$	−21.9067	+	21.9067i	−0.783382	+	0.783382i
$783$		0			0
$784$		−	12.1962i		−	0.435577i
$785$	8.69333	+	5.73981i	0.310278	+	0.204863i
$786$		0			0
$787$	−23.7583	+	6.36603i	−0.846893	+	0.226924i	−0.656070	−	0.754700i	$-0.727782\pi$
$787$	−23.7583	+	6.36603i	−0.846893	+	0.226924i	−0.190823	+	0.981624i	$0.561116\pi$
$788$	−12.9360	+	3.46618i	−0.460825	+	0.123478i
$789$		0			0
$790$	−4.09808	−	2.70577i	−0.145803	−	0.0962670i
$791$			17.5254i			0.623130i
$792$		0			0
$793$	−15.5885	+	15.5885i	−0.553562	+	0.553562i
$794$	2.26002	+	3.91447i	0.0802051	+	0.138919i
$795$		0			0
$796$	6.29423	−	10.9019i	0.223093	−	0.386408i
$797$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$797$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$798$		0			0
$799$	4.31347	−	2.49038i	0.152599	−	0.0881033i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		0			0
$802$	−9.29423	−	9.29423i	−0.328191	−	0.328191i
$803$	2.07055	−	7.72741i	0.0730682	−	0.272694i
$804$		0			0
$805$	−36.6506	+	32.5000i	−1.29177	+	1.14547i
$806$	31.0991	+	17.9551i	1.09542	+	0.632440i
$807$		0			0
$808$	12.8301	+	3.43782i	0.451362	+	0.120942i
$809$	−35.2166			−1.23815			−0.619076	−	0.785331i	$-0.712493\pi$
$809$	−35.2166			−1.23815			−0.619076	+	0.785331i	$0.712493\pi$
$810$		0			0
$811$	30.3923			1.06722			0.533609	−	0.845731i	$-0.320835\pi$
$811$	30.3923			1.06722			0.533609	+	0.845731i	$0.320835\pi$
$812$	23.9401	+	6.41473i	0.840133	+	0.225113i
$813$		0			0
$814$	9.00000	+	5.19615i	0.315450	+	0.182125i
$815$	44.1924	+	2.65256i	1.54799	+	0.0929152i
$816$		0			0
$817$	6.07884	−	22.6865i	0.212672	−	0.793701i
$818$	17.9551	+	17.9551i	0.627784	+	0.627784i
$819$		0			0
$820$	−0.901924	+	2.70577i	−0.0314965	+	0.0944896i
$821$	24.9754	−	14.4195i	0.871646	−	0.503245i	0.00375143	−	0.999993i	$-0.498806\pi$
$821$	24.9754	−	14.4195i	0.871646	−	0.503245i	0.867895	+	0.496748i	$0.165473\pi$
$822$		0			0
$823$	2.84936	+	10.6340i	0.0993226	+	0.370677i	0.997639	−	0.0686714i	$-0.0218760\pi$
$823$	2.84936	+	10.6340i	0.0993226	+	0.370677i	−0.898317	+	0.439348i	$0.855209\pi$
$824$	2.75908	−	4.77886i	0.0961170	−	0.166480i
$825$		0			0
$826$	−6.50000	−	11.2583i	−0.226164	−	0.391727i
$827$	−39.4321	+	39.4321i	−1.37119	+	1.37119i	−0.512501	+	0.858687i	$0.671281\pi$
$827$	−39.4321	+	39.4321i	−1.37119	+	1.37119i	−0.858687	+	0.512501i	$0.828719\pi$
$828$		0			0
$829$		−	18.7846i		−	0.652416i	−0.945298	−	0.326208i	$-0.894229\pi$
$829$		−	18.7846i		−	0.652416i	0.945298	−	0.326208i	$-0.105771\pi$
$830$	−31.0991	+	6.36396i	−1.07947	+	0.220896i
$831$		0			0
$832$	5.59808	−	1.50000i	0.194078	−	0.0520031i
$833$	−72.9943	+	19.5588i	−2.52910	+	0.677671i
$834$		0			0
$835$	−28.0718	+	42.5167i	−0.971465	+	1.47135i
$836$			4.52004i			0.156329i
$837$		0			0
$838$	−12.8038	+	12.8038i	−0.442302	+	0.442302i
$839$	5.24075	+	9.07725i	0.180931	+	0.313381i	0.942198	−	0.335057i	$-0.108756\pi$
$839$	5.24075	+	9.07725i	0.180931	+	0.313381i	−0.761267	+	0.648439i	$0.775422\pi$
$840$		0			0
$841$	−1.50000	+	2.59808i	−0.0517241	+	0.0895888i
$842$	−1.08604	−	4.05317i	−0.0374276	−	0.139682i
$843$		0			0
$844$	16.4545	−	9.50000i	0.566387	−	0.327003i
$845$	−43.6747	−	14.5582i	−1.50246	−	0.500819i
$846$		0			0
$847$	27.8827	+	27.8827i	0.958060	+	0.958060i
$848$	−0.827225	+	3.08725i	−0.0284070	+	0.106016i
$849$		0			0
$850$	12.1699	+	28.4904i	0.417423	+	0.977212i
$851$	−31.8198	−	18.3712i	−1.09077	−	0.629756i
$852$		0			0
$853$	−45.3468	−	12.1506i	−1.55264	−	0.416030i	−0.622319	−	0.782764i	$-0.713809\pi$
$853$	−45.3468	−	12.1506i	−1.55264	−	0.416030i	−0.930326	+	0.366734i	$0.880476\pi$
$854$	−16.6660			−0.570297
$855$		0			0
$856$	12.1962			0.416856
$857$	33.2204	+	8.90138i	1.13479	+	0.304065i	0.776854	−	0.629681i	$-0.216815\pi$
$857$	33.2204	+	8.90138i	1.13479	+	0.304065i	0.357934	+	0.933747i	$0.383481\pi$
$858$		0			0
$859$	4.85641	+	2.80385i	0.165698	+	0.0956660i	0.580556	−	0.814220i	$-0.302835\pi$
$859$	4.85641	+	2.80385i	0.165698	+	0.0956660i	−0.414858	+	0.909886i	$0.636169\pi$
$860$	0.984508	−	16.4022i	0.0335715	−	0.559309i
$861$		0			0
$862$	6.22243	−	23.2224i	0.211937	−	0.790959i
$863$	40.2779	+	40.2779i	1.37107	+	1.37107i	0.858853	+	0.512222i	$0.171177\pi$
$863$	40.2779	+	40.2779i	1.37107	+	1.37107i	0.512222	+	0.858853i	$0.328823\pi$
$864$		0			0
$865$	−27.1769	+	13.5885i	−0.924043	+	0.462021i
$866$	9.79796	−	5.65685i	0.332948	−	0.192228i
$867$		0			0
$868$	7.02628	+	26.2224i	0.238487	+	0.890047i
$869$	−1.55291	+	2.68973i	−0.0526790	+	0.0912427i
$870$		0			0
$871$	17.1962	+	29.7846i	0.582669	+	1.00921i
$872$	7.07107	−	7.07107i	0.239457	−	0.239457i
$873$		0			0
$874$		−	15.9808i		−	0.540557i
$875$	16.5087	+	46.1192i	0.558095	+	1.55911i
$876$		0			0
$877$	−4.50000	+	1.20577i	−0.151954	+	0.0407160i	−0.333994	−	0.942575i	$-0.608397\pi$
$877$	−4.50000	+	1.20577i	−0.151954	+	0.0407160i	0.182040	+	0.983291i	$0.441730\pi$
$878$	−9.09085	+	2.43589i	−0.306801	+	0.0822072i
$879$		0			0
$880$	0.633975	+	3.09808i	0.0213713	+	0.104436i
$881$			6.79367i			0.228884i	0.993430	+	0.114442i	$0.0365081\pi$
$881$			6.79367i			0.228884i	−0.993430	+	0.114442i	$0.963492\pi$
$882$		0			0
$883$	26.9808	−	26.9808i	0.907975	−	0.907975i	−0.0881337	−	0.996109i	$-0.528090\pi$
$883$	26.9808	−	26.9808i	0.907975	−	0.907975i	0.996109	+	0.0881337i	$0.0280903\pi$
$884$	−17.9551	−	31.0991i	−0.603894	−	1.04598i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	3.88229	+	14.4889i	0.130354	+	0.486489i	0.999974	−	0.00723339i	$-0.00230248\pi$
$887$	3.88229	+	14.4889i	0.130354	+	0.486489i	−0.869619	+	0.493723i	$0.835636\pi$
$888$		0			0
$889$	−11.2583	+	6.50000i	−0.377592	+	0.218003i
$890$	−1.69161	−	3.38323i	−0.0567031	−	0.113406i
$891$		0			0
$892$	−17.1962	−	17.1962i	−0.575770	−	0.575770i
$893$	−0.664963	+	2.48168i	−0.0222521	+	0.0830461i
$894$		0			0
$895$	−36.2846	−	40.9186i	−1.21286	−	1.36776i
$896$	3.79435	+	2.19067i	0.126760	+	0.0731852i
$897$		0			0
$898$	−19.2583	−	5.16025i	−0.642659	−	0.172200i
$899$	−35.0507			−1.16901
$900$		0			0
$901$	19.8038			0.659762
$902$	1.74238	+	0.466870i	0.0580150	+	0.0155451i
$903$		0			0
$904$	−3.46410	−	2.00000i	−0.115214	−	0.0665190i
$905$	6.22526	+	7.02030i	0.206935	+	0.233363i
$906$		0			0
$907$	1.75833	−	6.56218i	0.0583844	−	0.217894i	−0.930570	−	0.366114i	$-0.880688\pi$
$907$	1.75833	−	6.56218i	0.0583844	−	0.217894i	0.988954	+	0.148221i	$0.0473546\pi$
$908$	8.62398	+	8.62398i	0.286197	+	0.286197i
$909$		0			0
$910$	−25.3923	−	50.7846i	−0.841747	−	1.68349i
$911$	7.82894	−	4.52004i	0.259384	−	0.149756i	−0.364669	−	0.931137i	$-0.618818\pi$
$911$	7.82894	−	4.52004i	0.259384	−	0.149756i	0.624054	+	0.781381i	$0.285485\pi$
$912$		0			0
$913$	5.19615	+	19.3923i	0.171968	+	0.641792i
$914$	7.91688	−	13.7124i	0.261867	−	0.453567i
$915$		0			0
$916$	11.1962	+	19.3923i	0.369931	+	0.640740i
$917$	0.429705	−	0.429705i	0.0141901	−	0.0141901i
$918$		0			0
$919$			47.9615i			1.58210i	0.611748	+	0.791052i	$0.290466\pi$
$919$			47.9615i			1.58210i	−0.611748	+	0.791052i	$0.709534\pi$
$920$	−2.24144	−	10.9534i	−0.0738980	−	0.361121i
$921$		0			0
$922$	−7.92820	+	2.12436i	−0.261101	+	0.0699619i
$923$	56.9710	−	15.2653i	1.87522	−	0.502465i
$924$		0			0
$925$	−28.9019	+	22.6865i	−0.950289	+	0.745929i
$926$			36.0488i			1.18464i
$927$		0			0
$928$	−4.00000	+	4.00000i	−0.131306	+	0.131306i
$929$	−17.0957	−	29.6106i	−0.560890	−	0.971491i	−0.997419	−	0.0718003i	$-0.977126\pi$
$929$	−17.0957	−	29.6106i	−0.560890	−	0.971491i	0.436529	−	0.899690i	$-0.356208\pi$
$930$		0			0
$931$	19.4904	−	33.7583i	0.638771	−	1.10638i
$932$		0			0
$933$		0			0
$934$	21.4641	−	12.3923i	0.702327	−	0.405489i
$935$	17.5254	−	8.76268i	0.573141	−	0.286570i
$936$		0			0
$937$	−23.8038	−	23.8038i	−0.777638	−	0.777638i	0.201791	−	0.979429i	$-0.435324\pi$
$937$	−23.8038	−	23.8038i	−0.777638	−	0.777638i	−0.979429	+	0.201791i	$0.935324\pi$
$938$	−6.72930	+	25.1141i	−0.219719	+	0.820004i
$939$		0			0
$940$	−0.107695	+	1.79423i	−0.00351263	+	0.0585213i
$941$	18.1074	+	10.4543i	0.590284	+	0.340800i	0.765210	−	0.643781i	$-0.222635\pi$
$941$	18.1074	+	10.4543i	0.590284	+	0.340800i	−0.174926	+	0.984582i	$0.555969\pi$
$942$		0			0
$943$	−6.16025	−	1.65064i	−0.200605	−	0.0537521i
$944$	2.96713			0.0965718
$945$		0			0
$946$	−10.3923			−0.337883
$947$	−34.5839	−	9.26672i	−1.12382	−	0.301128i	−0.351394	−	0.936228i	$-0.614292\pi$
$947$	−34.5839	−	9.26672i	−1.12382	−	0.301128i	−0.772430	+	0.635100i	$0.780959\pi$
$948$		0			0
$949$	−28.3923	−	16.3923i	−0.921653	−	0.532117i
$950$	−14.8307	−	5.95284i	−0.481170	−	0.193136i
$951$		0			0
$952$	7.02628	−	26.2224i	0.227723	−	0.849874i
$953$	7.76457	+	7.76457i	0.251519	+	0.251519i	0.821593	−	0.570074i	$-0.193086\pi$
$953$	7.76457	+	7.76457i	0.251519	+	0.251519i	−0.570074	+	0.821593i	$0.693086\pi$
$954$		0			0
$955$	−21.0000	−	7.00000i	−0.679544	−	0.226515i
$956$	14.6969	−	8.48528i	0.475333	−	0.274434i
$957$		0			0
$958$	−1.83013	−	6.83013i	−0.0591287	−	0.220671i
$959$	−31.0991	+	53.8652i	−1.00424	+	1.73940i
$960$		0			0
$961$	−3.69615	−	6.40192i	−0.119231	−	0.206514i
$962$	30.1146	−	30.1146i	0.970933	−	0.970933i
$963$		0			0
$964$			30.3923i			0.978870i
$965$	7.65308	−	11.5911i	0.246361	−	0.373131i
$966$		0			0
$967$	−50.5429	+	13.5429i	−1.62535	+	0.435512i	−0.952567	−	0.304327i	$-0.901568\pi$
$967$	−50.5429	+	13.5429i	−1.62535	+	0.435512i	−0.672784	+	0.739839i	$0.734902\pi$
$968$	−8.69333	+	2.32937i	−0.279414	+	0.0748688i
$969$		0			0
$970$	−18.5885	+	3.80385i	−0.596839	+	0.122134i
$971$		−	48.1948i		−	1.54664i	−0.634014	−	0.773322i	$-0.718594\pi$
$971$		−	48.1948i		−	1.54664i	0.634014	−	0.773322i	$-0.281406\pi$
$972$		0			0
$973$	−47.6865	+	47.6865i	−1.52876	+	1.52876i
$974$	3.46618	+	6.00361i	0.111064	+	0.192368i
$975$		0			0
$976$	1.90192	−	3.29423i	0.0608791	−	0.105446i
$977$	−10.4543	−	39.0160i	−0.334463	−	1.24823i	−0.904451	−	0.426578i	$-0.859719\pi$
$977$	−10.4543	−	39.0160i	−0.334463	−	1.24823i	0.569988	−	0.821653i	$-0.306948\pi$
$978$		0			0
$979$	−2.07180	+	1.19615i	−0.0662149	+	0.0382292i
$980$	8.62398	−	25.8719i	0.275483	−	0.826449i
$981$		0			0
$982$	−4.70577	−	4.70577i	−0.150167	−	0.150167i
$983$	11.3781	−	42.4636i	0.362904	−	1.35438i	−0.507335	−	0.861749i	$-0.669369\pi$
$983$	11.3781	−	42.4636i	0.362904	−	1.35438i	0.870240	−	0.492629i	$-0.163964\pi$
$984$		0			0
$985$	−29.8923	−	1.79423i	−0.952448	−	0.0571689i
$986$	30.3548	+	17.5254i	0.966695	+	0.558121i
$987$		0			0
$988$	17.8923	+	4.79423i	0.569230	+	0.152525i
$989$	36.7423			1.16834
$990$		0			0
$991$	20.3923			0.647783			0.323891	−	0.946094i	$-0.395009\pi$
$991$	20.3923			0.647783			0.323891	+	0.946094i	$0.395009\pi$
$992$	−5.98502	−	1.60368i	−0.190025	−	0.0509170i
$993$		0			0
$994$	38.6147	+	22.2942i	1.22479	+	0.707130i
$995$	21.0609	−	18.6758i	0.667675	−	0.592062i
$996$		0			0
$997$	1.57180	−	5.86603i	0.0497793	−	0.185779i	−0.936559	−	0.350509i	$-0.886009\pi$
$997$	1.57180	−	5.86603i	0.0497793	−	0.185779i	0.986339	+	0.164730i	$0.0526753\pi$
$998$	−25.1648	−	25.1648i	−0.796579	−	0.796579i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.m.g.377.2		8
3.2	odd	2	inner	810.2.m.g.377.1		8
5.3	odd	4		810.2.m.b.53.2		8
9.2	odd	6		810.2.m.b.107.2		8
9.4	even	3		810.2.f.a.647.2	yes	8
9.5	odd	6		810.2.f.a.647.4	yes	8
9.7	even	3		810.2.m.b.107.1		8
15.8	even	4		810.2.m.b.53.1		8
45.13	odd	12		810.2.f.a.323.4	yes	8
45.23	even	12		810.2.f.a.323.2	✓	8
45.38	even	12	inner	810.2.m.g.593.2		8
45.43	odd	12	inner	810.2.m.g.593.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.2.f.a.323.2	✓	8	45.23	even	12
810.2.f.a.323.4	yes	8	45.13	odd	12
810.2.f.a.647.2	yes	8	9.4	even	3
810.2.f.a.647.4	yes	8	9.5	odd	6
810.2.m.b.53.1		8	15.8	even	4
810.2.m.b.53.2		8	5.3	odd	4
810.2.m.b.107.1		8	9.7	even	3
810.2.m.b.107.2		8	9.2	odd	6
810.2.m.g.377.1		8	3.2	odd	2	inner
810.2.m.g.377.2		8	1.1	even	1	trivial
810.2.m.g.593.1		8	45.43	odd	12	inner
810.2.m.g.593.2		8	45.38	even	12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(1.48356 + 1.67303i) q^{5} +(1.13397 - 4.23205i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.00000i) q^{10} +(1.22474 - 0.707107i) q^{11} +(-1.50000 - 5.59808i) q^{13} +(2.19067 - 3.79435i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.38134 - 4.38134i) q^{17} +3.19615i q^{19} +(0.448288 + 2.19067i) q^{20} +(1.36603 - 0.366025i) q^{22} +(-4.82963 + 1.29410i) q^{23} +(-0.598076 + 4.96410i) q^{25} -5.79555i q^{26} +(3.09808 - 3.09808i) q^{28} +(2.82843 + 4.89898i) q^{29} +(-3.09808 + 5.36603i) q^{31} +(0.258819 + 0.965926i) q^{32} +(5.36603 - 3.09808i) q^{34} +(8.76268 - 4.38134i) q^{35} +(5.19615 + 5.19615i) q^{37} +(-0.827225 + 3.08725i) q^{38} +(-0.133975 + 2.23205i) q^{40} +(1.10463 + 0.637756i) q^{41} +(-7.09808 - 1.90192i) q^{43} +1.41421 q^{44} -5.00000 q^{46} +(0.776457 + 0.208051i) q^{47} +(-10.5622 - 6.09808i) q^{49} +(-1.86250 + 4.64016i) q^{50} +(1.50000 - 5.59808i) q^{52} +(2.26002 + 2.26002i) q^{53} +(3.00000 + 1.00000i) q^{55} +(3.79435 - 2.19067i) q^{56} +(1.46410 + 5.46410i) q^{58} +(1.48356 - 2.56961i) q^{59} +(-1.90192 - 3.29423i) q^{61} +(-4.38134 + 4.38134i) q^{62} +1.00000i q^{64} +(7.14042 - 10.8147i) q^{65} +(-5.73205 + 1.53590i) q^{67} +(5.98502 - 1.60368i) q^{68} +(9.59808 - 1.96410i) q^{70} +10.1769i q^{71} +(4.00000 - 4.00000i) q^{73} +(3.67423 + 6.36396i) q^{74} +(-1.59808 + 2.76795i) q^{76} +(-1.60368 - 5.98502i) q^{77} +(-1.90192 + 1.09808i) q^{79} +(-0.707107 + 2.12132i) q^{80} +(0.901924 + 0.901924i) q^{82} +(-3.67423 + 13.7124i) q^{83} +(13.8301 + 0.830127i) q^{85} +(-6.36396 - 3.67423i) q^{86} +(1.36603 + 0.366025i) q^{88} -1.69161 q^{89} -25.3923 q^{91} +(-4.82963 - 1.29410i) q^{92} +(0.696152 + 0.401924i) q^{94} +(-5.34727 + 4.74170i) q^{95} +(-2.19615 + 8.19615i) q^{97} +(-8.62398 - 8.62398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7} + 8 q^{10} - 12 q^{13} + 4 q^{16} + 4 q^{22} + 16 q^{25} + 4 q^{28} - 4 q^{31} + 36 q^{34} - 8 q^{40} - 36 q^{43} - 40 q^{46} - 36 q^{49} + 12 q^{52} + 24 q^{55} - 16 q^{58} - 36 q^{61} - 32 q^{67}+ \cdots + 24 q^{97}+O(q^{100}) \) 8 * q + 16 * q^7 + 8 * q^10 - 12 * q^13 + 4 * q^16 + 4 * q^22 + 16 * q^25 + 4 * q^28 - 4 * q^31 + 36 * q^34 - 8 * q^40 - 36 * q^43 - 40 * q^46 - 36 * q^49 + 12 * q^52 + 24 * q^55 - 16 * q^58 - 36 * q^61 - 32 * q^67 + 56 * q^70 + 32 * q^73 + 8 * q^76 - 36 * q^79 + 28 * q^82 + 76 * q^85 + 4 * q^88 - 120 * q^91 - 36 * q^94 + 24 * q^97

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