LMFDB - Embedded newform 756.2.bj.b.523.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(451,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bj (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			523.27
Character	$\chi$	$=$	756.523
Dual form			756.2.bj.b.451.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.412858 - 1.35261i) q^{2} +(-1.65910 - 1.11687i) q^{4} +(-0.514884 + 0.297269i) q^{5} +(-1.74201 + 1.99133i) q^{7} +(-2.19566 + 1.78300i) q^{8} +(0.189514 + 0.819166i) q^{10} +(-2.63566 - 1.52170i) q^{11} +(6.21148 + 3.58620i) q^{13} +(1.97428 + 3.17840i) q^{14} +(1.50521 + 3.70599i) q^{16} +(-2.28182 + 1.31741i) q^{17} +(-1.15636 + 2.00287i) q^{19} +(1.18625 + 0.0818611i) q^{20} +(-3.14642 + 2.93677i) q^{22} +(1.34481 - 0.776425i) q^{23} +(-2.32326 + 4.02401i) q^{25} +(7.41518 - 6.92111i) q^{26} +(5.11422 - 1.35821i) q^{28} +(3.50068 + 6.06335i) q^{29} +5.91792 q^{31} +(5.63419 - 0.505907i) q^{32} +(0.839873 + 3.63032i) q^{34} +(0.304976 - 1.54315i) q^{35} +(-2.74961 + 4.76246i) q^{37} +(2.23169 + 2.39100i) q^{38} +(0.600480 - 1.57074i) q^{40} +(3.27676 + 1.89184i) q^{41} +(-2.52490 + 1.45775i) q^{43} +(2.67328 + 5.46834i) q^{44} +(-0.494984 - 2.13955i) q^{46} -9.67847 q^{47} +(-0.930778 - 6.93784i) q^{49} +(4.48373 + 4.80381i) q^{50} +(-6.30013 - 12.8873i) q^{52} +(-4.10505 - 7.11016i) q^{53} +1.80941 q^{55} +(0.274327 - 7.47828i) q^{56} +(9.64661 - 2.23174i) q^{58} -3.77001 q^{59} +2.67699i q^{61} +(2.44326 - 8.00462i) q^{62} +(1.64182 - 7.82971i) q^{64} -4.26426 q^{65} +8.92572i q^{67} +(5.25714 + 0.362785i) q^{68} +(-1.96136 - 1.04961i) q^{70} +8.75743i q^{71} +(-1.30083 + 0.751036i) q^{73} +(5.30655 + 5.68536i) q^{74} +(4.15546 - 2.03146i) q^{76} +(7.62156 - 2.59765i) q^{77} -6.73276i q^{79} +(-1.87668 - 1.46071i) q^{80} +(3.91175 - 3.65111i) q^{82} +(-4.99378 - 8.64947i) q^{83} +(0.783250 - 1.35663i) q^{85} +(0.929343 + 4.01705i) q^{86} +(8.50020 - 1.35825i) q^{88} +(13.7577 + 7.94299i) q^{89} +(-17.9618 + 6.12189i) q^{91} +(-3.09833 - 0.213810i) q^{92} +(-3.99583 + 13.0912i) q^{94} -1.37500i q^{95} +(1.20110 - 0.693454i) q^{97} +(-9.76846 - 1.60536i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.412858	−	1.35261i	0.291935	−	0.956438i
$2$	0.412858	−	1.35261i	0.291935	−	0.956438i
$3$		0			0
$3$		0			0
$4$	−1.65910	−	1.11687i	−0.829548	−	0.558435i
$5$	−0.514884	+	0.297269i	−0.230263	+	0.132943i	−0.610693	−	0.791867i	$-0.709109\pi$
$5$	−0.514884	+	0.297269i	−0.230263	+	0.132943i	0.380430	+	0.924810i	$0.375776\pi$
$6$		0			0
$7$	−1.74201	+	1.99133i	−0.658419	+	0.752651i
$7$	−1.74201	+	1.99133i	−0.658419	+	0.752651i
$8$	−2.19566	+	1.78300i	−0.776282	+	0.630386i
$9$		0			0
$10$	0.189514	+	0.819166i	0.0599296	+	0.259043i
$11$	−2.63566	−	1.52170i	−0.794682	−	0.458810i	0.0469262	−	0.998898i	$-0.485057\pi$
$11$	−2.63566	−	1.52170i	−0.794682	−	0.458810i	−0.841608	+	0.540088i	$0.818391\pi$
$12$		0			0
$13$	6.21148	+	3.58620i	1.72275	+	0.994633i	0.913110	+	0.407712i	$0.133673\pi$
$13$	6.21148	+	3.58620i	1.72275	+	0.994633i	0.809644	+	0.586921i	$0.199660\pi$
$14$	1.97428	+	3.17840i	0.527649	+	0.849462i
$15$		0			0
$16$	1.50521	+	3.70599i	0.376301	+	0.926497i
$17$	−2.28182	+	1.31741i	−0.553423	+	0.319519i	−0.750502	−	0.660869i	$-0.770188\pi$
$17$	−2.28182	+	1.31741i	−0.553423	+	0.319519i	0.197078	+	0.980388i	$0.436855\pi$
$18$		0			0
$19$	−1.15636	+	2.00287i	−0.265287	+	0.459490i	−0.967639	−	0.252340i	$-0.918800\pi$
$19$	−1.15636	+	2.00287i	−0.265287	+	0.459490i	0.702352	+	0.711830i	$0.252133\pi$
$20$	1.18625	+	0.0818611i	0.265254	+	0.0183047i
$21$		0			0
$22$	−3.14642	+	2.93677i	−0.670819	+	0.626122i
$23$	1.34481	−	0.776425i	0.280412	−	0.161896i	−0.353198	−	0.935549i	$-0.614906\pi$
$23$	1.34481	−	0.776425i	0.280412	−	0.161896i	0.633610	+	0.773653i	$0.281573\pi$
$24$		0			0
$25$	−2.32326	+	4.02401i	−0.464653	+	0.804802i
$26$	7.41518	−	6.92111i	1.45424	−	1.35734i
$27$		0			0
$28$	5.11422	−	1.35821i	0.966497	−	0.256677i
$29$	3.50068	+	6.06335i	0.650059	+	1.12594i	0.983108	+	0.183026i	$0.0585892\pi$
$29$	3.50068	+	6.06335i	0.650059	+	1.12594i	−0.333049	+	0.942910i	$0.608077\pi$
$30$		0			0
$31$	5.91792			1.06289			0.531445	−	0.847093i	$-0.321649\pi$
$31$	5.91792			1.06289			0.531445	+	0.847093i	$0.321649\pi$
$32$	5.63419	−	0.505907i	0.995993	−	0.0894325i
$33$		0			0
$34$	0.839873	+	3.63032i	0.144037	+	0.622594i
$35$	0.304976	−	1.54315i	0.0515503	−	0.260840i
$36$		0			0
$37$	−2.74961	+	4.76246i	−0.452033	+	0.782944i	−0.998512	−	0.0545287i	$-0.982634\pi$
$37$	−2.74961	+	4.76246i	−0.452033	+	0.782944i	0.546479	+	0.837473i	$0.315968\pi$
$38$	2.23169	+	2.39100i	0.362028	+	0.387872i
$39$		0			0
$40$	0.600480	−	1.57074i	0.0949442	−	0.248356i
$41$	3.27676	+	1.89184i	0.511744	+	0.295456i	0.733550	−	0.679635i	$-0.237862\pi$
$41$	3.27676	+	1.89184i	0.511744	+	0.295456i	−0.221806	+	0.975091i	$0.571195\pi$
$42$		0			0
$43$	−2.52490	+	1.45775i	−0.385044	+	0.222305i	−0.680011	−	0.733202i	$-0.738025\pi$
$43$	−2.52490	+	1.45775i	−0.385044	+	0.222305i	0.294967	+	0.955508i	$0.404691\pi$
$44$	2.67328	+	5.46834i	0.403012	+	0.824383i
$45$		0			0
$46$	−0.494984	−	2.13955i	−0.0729815	−	0.315459i
$47$	−9.67847			−1.41175			−0.705875	−	0.708336i	$-0.749446\pi$
$47$	−9.67847			−1.41175			−0.705875	+	0.708336i	$0.749446\pi$
$48$		0			0
$49$	−0.930778	−	6.93784i	−0.132968	−	0.991120i
$50$	4.48373	+	4.80381i	0.634095	+	0.679361i
$51$		0			0
$52$	−6.30013	−	12.8873i	−0.873671	−	1.78714i
$53$	−4.10505	−	7.11016i	−0.563872	−	0.976655i	−0.997154	−	0.0753965i	$-0.975978\pi$
$53$	−4.10505	−	7.11016i	−0.563872	−	0.976655i	0.433282	−	0.901259i	$-0.357356\pi$
$54$		0			0
$55$	1.80941			0.243981
$56$	0.274327	−	7.47828i	0.0366585	−	0.999328i
$57$		0			0
$58$	9.64661	−	2.23174i	1.26666	−	0.293042i
$59$	−3.77001			−0.490814			−0.245407	−	0.969420i	$-0.578922\pi$
$59$	−3.77001			−0.490814			−0.245407	+	0.969420i	$0.578922\pi$
$60$		0			0
$61$			2.67699i			0.342754i	0.985206	+	0.171377i	$0.0548216\pi$
$61$			2.67699i			0.342754i	−0.985206	+	0.171377i	$0.945178\pi$
$62$	2.44326	−	8.00462i	0.310294	−	1.01659i
$63$		0			0
$64$	1.64182	−	7.82971i	0.205228	−	0.978714i
$65$	−4.26426			−0.528916
$66$		0			0
$67$			8.92572i			1.09045i	0.838290	+	0.545225i	$0.183556\pi$
$67$			8.92572i			1.09045i	−0.838290	+	0.545225i	$0.816444\pi$
$68$	5.25714	+	0.362785i	0.637522	+	0.0439942i
$69$		0			0
$70$	−1.96136	−	1.04961i	−0.234428	−	0.125453i
$71$			8.75743i			1.03932i	0.854374	+	0.519658i	$0.173941\pi$
$71$			8.75743i			1.03932i	−0.854374	+	0.519658i	$0.826059\pi$
$72$		0			0
$73$	−1.30083	+	0.751036i	−0.152251	+	0.0879022i	−0.574190	−	0.818722i	$-0.694683\pi$
$73$	−1.30083	+	0.751036i	−0.152251	+	0.0879022i	0.421939	+	0.906624i	$0.361350\pi$
$74$	5.30655	+	5.68536i	0.616874	+	0.660910i
$75$		0			0
$76$	4.15546	−	2.03146i	0.476664	−	0.233024i
$77$	7.62156	−	2.59765i	0.868558	−	0.296029i
$78$		0			0
$79$		−	6.73276i		−	0.757495i	−0.925500	−	0.378747i	$-0.876355\pi$
$79$		−	6.73276i		−	0.757495i	0.925500	−	0.378747i	$-0.123645\pi$
$80$	−1.87668	−	1.46071i	−0.209819	−	0.163312i
$81$		0			0
$82$	3.91175	−	3.65111i	0.431981	−	0.403198i
$83$	−4.99378	−	8.64947i	−0.548138	−	0.949403i	−0.998402	−	0.0565077i	$-0.982003\pi$
$83$	−4.99378	−	8.64947i	−0.548138	−	0.949403i	0.450264	−	0.892895i	$-0.351330\pi$
$84$		0			0
$85$	0.783250	−	1.35663i	0.0849554	−	0.147147i
$86$	0.929343	+	4.01705i	0.100214	+	0.433169i
$87$		0			0
$88$	8.50020	−	1.35825i	0.906125	−	0.144790i
$89$	13.7577	+	7.94299i	1.45831	+	0.841955i	0.998928	−	0.0462839i	$-0.0147379\pi$
$89$	13.7577	+	7.94299i	1.45831	+	0.841955i	0.459381	+	0.888239i	$0.348071\pi$
$90$		0			0
$91$	−17.9618	+	6.12189i	−1.88291	+	0.641748i
$92$	−3.09833	−	0.213810i	−0.323023	−	0.0222912i
$93$		0			0
$94$	−3.99583	+	13.0912i	−0.412139	+	1.35025i
$95$		−	1.37500i		−	0.141072i
$96$		0			0
$97$	1.20110	−	0.693454i	0.121953	−	0.0704096i	−0.437783	−	0.899081i	$-0.644236\pi$
$97$	1.20110	−	0.693454i	0.121953	−	0.0704096i	0.559736	+	0.828671i	$0.310903\pi$
$98$	−9.76846	−	1.60536i	−0.986763	−	0.162166i
$99$		0			0
$100$	8.34881	−	4.08144i	0.834881	−	0.408144i
$101$	−6.87010	−	3.96646i	−0.683601	−	0.394677i	0.117610	−	0.993060i	$-0.462477\pi$
$101$	−6.87010	−	3.96646i	−0.683601	−	0.394677i	−0.801210	+	0.598383i	$0.795810\pi$
$102$		0			0
$103$	−4.75698	−	8.23933i	−0.468719	−	0.811846i	0.530641	−	0.847596i	$-0.321951\pi$
$103$	−4.75698	−	8.23933i	−0.468719	−	0.811846i	−0.999361	+	0.0357508i	$0.988618\pi$
$104$	−20.0325	+	3.20100i	−1.96435	+	0.313884i
$105$		0			0
$106$	−11.3121	+	2.61704i	−1.09872	+	0.254190i
$107$	11.8104	+	6.81874i	1.14176	+	0.659193i	0.946865	−	0.321632i	$-0.104231\pi$
$107$	11.8104	+	6.81874i	1.14176	+	0.659193i	0.194891	+	0.980825i	$0.437565\pi$
$108$		0			0
$109$	−4.57329	−	7.92116i	−0.438041	−	0.758710i	0.559497	−	0.828832i	$-0.310994\pi$
$109$	−4.57329	−	7.92116i	−0.438041	−	0.758710i	−0.997538	+	0.0701225i	$0.977661\pi$
$110$	0.747031	−	2.44743i	0.0712266	−	0.233353i
$111$		0			0
$112$	−10.0019	−	3.45852i	−0.945094	−	0.326800i
$113$	−3.57459	+	6.19136i	−0.336269	+	0.582435i	−0.983728	−	0.179666i	$-0.942498\pi$
$113$	−3.57459	+	6.19136i	−0.336269	+	0.582435i	0.647459	+	0.762100i	$0.275832\pi$
$114$		0			0
$115$	−0.461613	+	0.799538i	−0.0430457	+	0.0745573i
$116$	0.964007	−	13.9695i	0.0895058	−	1.29703i
$117$		0			0
$118$	−1.55648	+	5.09935i	−0.143285	+	0.469433i
$119$	1.35157	−	6.83881i	0.123898	−	0.626912i
$120$		0			0
$121$	−0.868856	−	1.50490i	−0.0789869	−	0.136809i
$122$	3.62092	+	1.10522i	0.327823	+	0.100062i
$123$		0			0
$124$	−9.81840	−	6.60954i	−0.881718	−	0.593554i
$125$		−	5.73522i		−	0.512973i
$126$		0			0
$127$			11.0990i			0.984879i	0.870347	+	0.492439i	$0.163895\pi$
$127$			11.0990i			0.984879i	−0.870347	+	0.492439i	$0.836105\pi$
$128$	−9.91269	−	5.45330i	−0.876167	−	0.482008i
$129$		0			0
$130$	−1.76053	+	5.76787i	−0.154409	+	0.505876i
$131$	2.49572	+	4.32271i	0.218052	+	0.377677i	0.954212	−	0.299130i	$-0.0966965\pi$
$131$	2.49572	+	4.32271i	0.218052	+	0.377677i	−0.736160	+	0.676807i	$0.763363\pi$
$132$		0			0
$133$	−1.97398	−	5.79172i	−0.171166	−	0.502206i
$134$	12.0730	+	3.68505i	1.04295	+	0.318340i
$135$		0			0
$136$	2.66116	−	6.96107i	0.228192	−	0.596907i
$137$	−3.15468	+	5.46407i	−0.269523	+	0.466827i	−0.968739	−	0.248084i	$-0.920199\pi$
$137$	−3.15468	+	5.46407i	−0.269523	+	0.466827i	0.699216	+	0.714911i	$0.253533\pi$
$138$		0			0
$139$	−3.37429	+	5.84444i	−0.286203	+	0.495719i	−0.972900	−	0.231225i	$-0.925727\pi$
$139$	−3.37429	+	5.84444i	−0.286203	+	0.495719i	0.686697	+	0.726944i	$0.259060\pi$
$140$	−2.22948	+	2.21962i	−0.188426	+	0.187592i
$141$		0			0
$142$	11.8454	+	3.61557i	0.994042	+	0.303412i
$143$	−10.9142	−	18.9040i	−0.912695	−	1.58083i
$144$		0			0
$145$	−3.60489	−	2.08128i	−0.299369	−	0.172841i
$146$	0.478799	+	2.06959i	0.0396257	+	0.171280i
$147$		0			0
$148$	9.88092	−	4.83043i	0.812206	−	0.397059i
$149$	−2.73106	−	4.73034i	−0.223737	−	0.387525i	0.732202	−	0.681087i	$-0.238492\pi$
$149$	−2.73106	−	4.73034i	−0.223737	−	0.387525i	−0.955940	+	0.293562i	$0.905159\pi$
$150$		0			0
$151$	11.9298	+	6.88770i	0.970837	+	0.560513i	0.899491	−	0.436939i	$-0.143937\pi$
$151$	11.9298	+	6.88770i	0.970837	+	0.560513i	0.0713457	+	0.997452i	$0.477271\pi$
$152$	−1.03215	−	6.45941i	−0.0837186	−	0.523927i
$153$		0			0
$154$	−0.366976	−	11.3814i	−0.0295718	−	0.917143i
$155$	−3.04704	+	1.75921i	−0.244744	+	0.141303i
$156$		0			0
$157$		−	11.7945i		−	0.941303i	−0.882319	−	0.470652i	$-0.844019\pi$
$157$		−	11.7945i		−	0.941303i	0.882319	−	0.470652i	$-0.155981\pi$
$158$	−9.10678	−	2.77967i	−0.724497	−	0.221139i
$159$		0			0
$160$	−2.75056	+	1.93535i	−0.217451	+	0.153003i
$161$	−0.796555	+	4.03050i	−0.0627774	+	0.317648i
$162$		0			0
$163$	2.95281	+	1.70481i	0.231282	+	0.133531i	0.611163	−	0.791505i	$-0.290702\pi$
$163$	2.95281	+	1.70481i	0.231282	+	0.133531i	−0.379881	+	0.925035i	$0.624035\pi$
$164$	−3.32353	−	6.79846i	−0.259524	−	0.530870i
$165$		0			0
$166$	−13.7611	+	3.18362i	−1.06807	+	0.247097i
$167$	−6.47738	+	11.2191i	−0.501235	+	0.868164i	0.498764	+	0.866738i	$0.333787\pi$
$167$	−6.47738	+	11.2191i	−0.501235	+	0.868164i	−0.999999	+	0.00142608i	$0.999546\pi$
$168$		0			0
$169$	19.2217	+	33.2929i	1.47859	+	2.56099i
$170$	−1.51162	−	1.61952i	−0.115936	−	0.124212i
$171$		0			0
$172$	5.81718	+	0.401432i	0.443556	+	0.0306089i
$173$		−	1.24744i		−	0.0948408i	−0.998875	−	0.0474204i	$-0.984900\pi$
$173$		−	1.24744i		−	0.0948408i	0.998875	−	0.0474204i	$-0.0151000\pi$
$174$		0			0
$175$	−3.96597	−	11.6363i	−0.299799	−	0.879618i
$176$	1.67219	−	12.0582i	0.126046	−	0.908922i
$177$		0			0
$178$	16.4237	−	15.3294i	1.23101	−	1.14899i
$179$	−0.0914691	+	0.0528097i	−0.00683672	+	0.00394718i	−0.503414	−	0.864045i	$-0.667923\pi$
$179$	−0.0914691	+	0.0528097i	−0.00683672	+	0.00394718i	0.496578	+	0.867992i	$0.334590\pi$
$180$		0			0
$181$		−	22.3860i		−	1.66394i	−0.554821	−	0.831970i	$-0.687213\pi$
$181$		−	22.3860i		−	1.66394i	0.554821	−	0.831970i	$-0.312787\pi$
$182$	0.864855	+	26.8227i	0.0641073	+	1.98823i
$183$		0			0
$184$	−1.56837	+	4.10255i	−0.115622	+	0.302444i
$185$		−	3.26949i		−	0.240378i
$186$		0			0
$187$	8.01882			0.586394
$188$	16.0575	+	10.8096i	1.17111	+	0.788370i
$189$		0			0
$190$	−1.85983	−	0.567678i	−0.134926	−	0.0411837i
$191$			21.6364i			1.56555i	0.622302	+	0.782777i	$0.286198\pi$
$191$			21.6364i			1.56555i	−0.622302	+	0.782777i	$0.713802\pi$
$192$		0			0
$193$	1.91328			0.137721			0.0688605	−	0.997626i	$-0.478064\pi$
$193$	1.91328			0.137721			0.0688605	+	0.997626i	$0.478064\pi$
$194$	−0.442089	−	1.91091i	−0.0317402	−	0.137196i
$195$		0			0
$196$	−6.20441	+	12.5501i	−0.443172	+	0.896436i
$197$	−17.4136			−1.24067			−0.620334	−	0.784337i	$-0.713003\pi$
$197$	−17.4136			−1.24067			−0.620334	+	0.784337i	$0.713003\pi$
$198$		0			0
$199$	−1.77704	−	3.07792i	−0.125971	−	0.218188i	0.796141	−	0.605111i	$-0.206871\pi$
$199$	−1.77704	−	3.07792i	−0.125971	−	0.218188i	−0.922112	+	0.386923i	$0.873538\pi$
$200$	−2.07372	−	12.9777i	−0.146634	−	0.917664i
$201$		0			0
$202$	−8.20143	+	7.65497i	−0.577051	+	0.538602i
$203$	−18.1723	−	3.59144i	−1.27545	−	0.252070i
$204$		0			0
$205$	−2.24954			−0.157114
$206$	−13.1085	+	3.03266i	−0.913316	+	0.211295i
$207$		0			0
$208$	−3.94086	+	28.4177i	−0.273250	+	1.97041i
$209$	6.09554	−	3.51926i	0.421638	−	0.243433i
$210$		0			0
$211$	−2.88477	−	1.66552i	−0.198596	−	0.114659i	0.397405	−	0.917643i	$-0.369911\pi$
$211$	−2.88477	−	1.66552i	−0.198596	−	0.114659i	−0.596000	+	0.802984i	$0.703244\pi$
$212$	−1.13044	+	16.3812i	−0.0776389	+	1.12507i
$213$		0			0
$214$	14.0991	−	13.1597i	0.963795	−	0.899577i
$215$	0.866688	−	1.50115i	0.0591076	−	0.102377i
$216$		0			0
$217$	−10.3091	+	11.7845i	−0.699827	+	0.799985i
$218$	−12.6023	+	2.91555i	−0.853539	+	0.197466i
$219$		0			0
$220$	−3.00199	−	2.02088i	−0.202394	−	0.136248i
$221$	−18.8980			−1.27122
$222$		0			0
$223$	−6.52029	−	11.2935i	−0.436631	−	0.756267i	0.560796	−	0.827954i	$-0.310495\pi$
$223$	−6.52029	−	11.2935i	−0.436631	−	0.756267i	−0.997427	+	0.0716868i	$0.977162\pi$
$224$	−8.80740	+	12.1008i	−0.588469	+	0.808520i
$225$		0			0
$226$	6.89869	+	7.39117i	0.458894	+	0.491653i
$227$	4.72639	−	8.18636i	0.313702	−	0.543347i	−0.665459	−	0.746435i	$-0.731764\pi$
$227$	4.72639	−	8.18636i	0.313702	−	0.543347i	0.979161	+	0.203087i	$0.0650974\pi$
$228$		0			0
$229$	12.2899	−	7.09560i	0.812142	−	0.468890i	−0.0355574	−	0.999368i	$-0.511321\pi$
$229$	12.2899	−	7.09560i	0.812142	−	0.468890i	0.847699	+	0.530477i	$0.177987\pi$
$230$	0.890880	+	0.954477i	0.0587429	+	0.0629364i
$231$		0			0
$232$	−18.4972	−	7.07133i	−1.21440	−	0.464256i
$233$	12.9100	−	22.3607i	0.845761	−	1.46490i	−0.0391981	−	0.999231i	$-0.512480\pi$
$233$	12.9100	−	22.3607i	0.845761	−	1.46490i	0.884959	−	0.465669i	$-0.154186\pi$
$234$		0			0
$235$	4.98329	−	2.87710i	0.325074	−	0.187682i
$236$	6.25482	+	4.21061i	0.407154	+	0.274087i
$237$		0			0
$238$	−8.69222	−	4.65160i	−0.563433	−	0.301518i
$239$	18.8003	+	10.8544i	1.21609	+	0.702110i	0.964079	−	0.265614i	$-0.0855746\pi$
$239$	18.8003	+	10.8544i	1.21609	+	0.702110i	0.252011	+	0.967724i	$0.418908\pi$
$240$		0			0
$241$	−3.26469	−	1.88487i	−0.210297	−	0.121415i	0.391152	−	0.920326i	$-0.372077\pi$
$241$	−3.26469	−	1.88487i	−0.210297	−	0.121415i	−0.601450	+	0.798911i	$0.705410\pi$
$242$	−2.39426	+	0.553911i	−0.153909	+	0.0356067i
$243$		0			0
$244$	2.98985	−	4.44139i	0.191406	−	0.284331i
$245$	2.54165	+	3.29549i	0.162380	+	0.210541i
$246$		0			0
$247$	−14.3654	+	8.29387i	−0.914049	+	0.527726i
$248$	−12.9937	+	10.5516i	−0.825102	+	0.670030i
$249$		0			0
$250$	−7.75750	−	2.36783i	−0.490627	−	0.149755i
$251$	13.8993			0.877316			0.438658	−	0.898654i	$-0.355454\pi$
$251$	13.8993			0.877316			0.438658	+	0.898654i	$0.355454\pi$
$252$		0			0
$253$	−4.72594			−0.297118
$254$	15.0126	+	4.58232i	0.941976	+	0.287520i
$255$		0			0
$256$	−11.4687	+	11.1566i	−0.716795	+	0.697284i
$257$	−3.71735	+	2.14621i	−0.231882	+	0.133877i	−0.611440	−	0.791291i	$-0.709409\pi$
$257$	−3.71735	+	2.14621i	−0.231882	+	0.133877i	0.379558	+	0.925168i	$0.376076\pi$
$258$		0			0
$259$	−4.69377	−	13.7716i	−0.291657	−	0.855728i
$260$	7.07482	+	4.76262i	0.438762	+	0.295365i
$261$		0			0
$262$	6.87731	−	1.59106i	0.424882	−	0.0982962i
$263$	15.1754	+	8.76154i	0.935758	+	0.540260i	0.888628	−	0.458629i	$-0.151659\pi$
$263$	15.1754	+	8.76154i	0.935758	+	0.540260i	0.0471298	+	0.998889i	$0.484993\pi$
$264$		0			0
$265$	4.22725	+	2.44061i	0.259678	+	0.149925i
$266$	−8.64890	+	0.278870i	−0.530298	+	0.0170986i
$267$		0			0
$268$	9.96886	−	14.8086i	0.608945	−	0.904581i
$269$	−3.89531	+	2.24896i	−0.237501	+	0.137122i	−0.614028	−	0.789284i	$-0.710452\pi$
$269$	−3.89531	+	2.24896i	−0.237501	+	0.137122i	0.376526	+	0.926406i	$0.377118\pi$
$270$		0			0
$271$	10.3784	−	17.9759i	0.630442	−	1.09196i	−0.357019	−	0.934097i	$-0.616207\pi$
$271$	10.3784	−	17.9759i	0.630442	−	1.09196i	0.987461	−	0.157861i	$-0.0504598\pi$
$272$	−8.31693	−	6.47344i	−0.504288	−	0.392510i
$273$		0			0
$274$	6.08831	+	6.52293i	0.367808	+	0.394065i
$275$	12.2467	−	7.07062i	0.738502	−	0.426374i
$276$		0			0
$277$	6.85236	−	11.8686i	0.411718	−	0.713117i	−0.583359	−	0.812214i	$-0.698262\pi$
$277$	6.85236	−	11.8686i	0.411718	−	0.713117i	0.995078	+	0.0990971i	$0.0315954\pi$
$278$	6.51213	+	6.97701i	0.390572	+	0.418453i
$279$		0			0
$280$	2.08181	+	3.93200i	0.124412	+	0.234982i
$281$	1.27529	+	2.20886i	0.0760773	+	0.131770i	0.901554	−	0.432666i	$-0.142427\pi$
$281$	1.27529	+	2.20886i	0.0760773	+	0.131770i	−0.825477	+	0.564436i	$0.809094\pi$
$282$		0			0
$283$	8.59795			0.511095			0.255547	−	0.966797i	$-0.417744\pi$
$283$	8.59795			0.511095			0.255547	+	0.966797i	$0.417744\pi$
$284$	9.78091	−	14.5294i	0.580390	−	0.862163i
$285$		0			0
$286$	−30.0758	+	6.95802i	−1.77842	+	0.411436i
$287$	−9.47543	+	3.22950i	−0.559317	+	0.190631i
$288$		0			0
$289$	−5.02886	+	8.71023i	−0.295815	+	0.512367i
$290$	−4.30346	+	4.01672i	−0.252708	+	0.235870i
$291$		0			0
$292$	2.99702	+	0.206819i	0.175387	+	0.0121031i
$293$	17.2244	+	9.94449i	1.00626	+	0.580963i	0.910094	−	0.414402i	$-0.136009\pi$
$293$	17.2244	+	9.94449i	1.00626	+	0.580963i	0.0961641	+	0.995365i	$0.469343\pi$
$294$		0			0
$295$	1.94112	−	1.12071i	0.113016	−	0.0652500i
$296$	−2.45427	−	15.3593i	−0.142652	−	0.892740i
$297$		0			0
$298$	−7.52584	+	1.74110i	−0.435960	+	0.100859i
$299$	11.1377			0.644107
$300$		0			0
$301$	1.49555	−	7.56733i	0.0862020	−	0.436174i
$302$	14.2417	−	13.2928i	0.819517	−	0.764913i
$303$		0			0
$304$	−9.16318	−	1.27072i	−0.525545	−	0.0728807i
$305$	−0.795786	−	1.37834i	−0.0455665	−	0.0789236i
$306$		0			0
$307$	26.7987			1.52948			0.764742	−	0.644337i	$-0.222867\pi$
$307$	26.7987			1.52948			0.764742	+	0.644337i	$0.222867\pi$
$308$	−15.5461	−	4.20254i	−0.885824	−	0.239462i
$309$		0			0
$310$	1.12153	+	4.84776i	0.0636985	+	0.275334i
$311$	−4.79353			−0.271816			−0.135908	−	0.990721i	$-0.543395\pi$
$311$	−4.79353			−0.271816			−0.135908	+	0.990721i	$0.543395\pi$
$312$		0			0
$313$			8.81253i			0.498113i	0.968489	+	0.249057i	$0.0801206\pi$
$313$			8.81253i			0.498113i	−0.968489	+	0.249057i	$0.919879\pi$
$314$	−15.9533	−	4.86945i	−0.900299	−	0.274799i
$315$		0			0
$316$	−7.51961	+	11.1703i	−0.423011	+	0.628378i
$317$	−18.1124			−1.01729			−0.508646	−	0.860976i	$-0.669854\pi$
$317$	−18.1124			−1.01729			−0.508646	+	0.860976i	$0.669854\pi$
$318$		0			0
$319$		−	21.3079i		−	1.19301i
$320$	1.48218	+	4.51946i	0.0828563	+	0.252645i
$321$		0			0
$322$	5.12282	+	2.74145i	0.285483	+	0.152775i
$323$		−	6.09360i		−	0.339057i
$324$		0			0
$325$	−28.8618	+	16.6634i	−1.60096	+	0.924318i
$326$	3.52502	−	3.29015i	0.195233	−	0.182225i
$327$		0			0
$328$	−10.5678	+	1.68863i	−0.583509	+	0.0932392i
$329$	16.8600	−	19.2730i	0.929523	−	1.06256i
$330$		0			0
$331$			7.76983i			0.427068i	0.976936	+	0.213534i	$0.0684975\pi$
$331$			7.76983i			0.427068i	−0.976936	+	0.213534i	$0.931503\pi$
$332$	−1.37517	+	19.9277i	−0.0754725	+	1.09368i
$333$		0			0
$334$	12.5009	+	13.3933i	0.684017	+	0.732847i
$335$	−2.65334	−	4.59571i	−0.144967	−	0.251091i
$336$		0			0
$337$	3.96613	−	6.86954i	0.216049	−	0.374208i	−0.737548	−	0.675295i	$-0.764016\pi$
$337$	3.96613	−	6.86954i	0.216049	−	0.374208i	0.953597	+	0.301087i	$0.0973496\pi$
$338$	52.9681	−	12.2541i	2.88108	−	0.666538i
$339$		0			0
$340$	−2.81466	+	1.37599i	−0.152647	+	0.0746236i
$341$	−15.5976	−	9.00530i	−0.844659	−	0.487664i
$342$		0			0
$343$	15.4370	+	10.2323i	0.833517	+	0.552494i
$344$	2.94465	−	7.70262i	0.158765	−	0.415298i
$345$		0			0
$346$	−1.68729	−	0.515014i	−0.0907094	−	0.0276873i
$347$		−	0.835385i		−	0.0448458i	−0.999749	−	0.0224229i	$-0.992862\pi$
$347$		−	0.835385i		−	0.0448458i	0.999749	−	0.0224229i	$-0.00713803\pi$
$348$		0			0
$349$	13.8892	−	8.01895i	0.743473	−	0.429244i	−0.0798577	−	0.996806i	$-0.525447\pi$
$349$	13.8892	−	8.01895i	0.743473	−	0.429244i	0.823331	+	0.567562i	$0.192113\pi$
$350$	−17.3767	+	0.560283i	−0.928822	+	0.0299484i
$351$		0			0
$352$	−15.6197	−	7.24014i	−0.832530	−	0.385901i
$353$	11.2880	+	6.51711i	0.600798	+	0.346871i	0.769355	−	0.638821i	$-0.220578\pi$
$353$	11.2880	+	6.51711i	0.600798	+	0.346871i	−0.168558	+	0.985692i	$0.553911\pi$
$354$		0			0
$355$	−2.60331	−	4.50906i	−0.138169	−	0.239316i
$356$	−13.9540	−	28.5437i	−0.739561	−	1.51281i
$357$		0			0
$358$	0.0336671	+	0.145525i	0.00177936	+	0.00769122i
$359$	−6.68926	−	3.86205i	−0.353046	−	0.203831i	0.312980	−	0.949760i	$-0.398673\pi$
$359$	−6.68926	−	3.86205i	−0.353046	−	0.203831i	−0.666026	+	0.745929i	$0.732006\pi$
$360$		0			0
$361$	6.82567	+	11.8224i	0.359246	+	0.622232i
$362$	−30.2795	−	9.24224i	−1.59146	−	0.485761i
$363$		0			0
$364$	36.6377	+	9.90416i	1.92034	+	0.519119i
$365$	0.446519	−	0.773394i	0.0233719	−	0.0404813i
$366$		0			0
$367$	0.426271	−	0.738323i	0.0222512	−	0.0385402i	−0.854685	−	0.519146i	$-0.826250\pi$
$367$	0.426271	−	0.738323i	0.0222512	−	0.0385402i	0.876937	+	0.480606i	$0.159583\pi$
$368$	4.90163	+	3.81516i	0.255515	+	0.198879i
$369$		0			0
$370$	−4.42234	−	1.34983i	−0.229906	−	0.0701745i
$371$	21.3097	+	4.21148i	1.10635	+	0.218649i
$372$		0			0
$373$	1.16495	+	2.01776i	0.0603190	+	0.104476i	0.894608	−	0.446852i	$-0.147455\pi$
$373$	1.16495	+	2.01776i	0.0603190	+	0.104476i	−0.834289	+	0.551327i	$0.814122\pi$
$374$	3.31063	−	10.8463i	0.171189	−	0.560850i
$375$		0			0
$376$	21.2506	−	17.2567i	1.09592	−	0.889947i
$377$			50.2165i			2.58628i
$378$		0			0
$379$		−	28.9056i		−	1.48478i	−0.669968	−	0.742390i	$-0.733692\pi$
$379$		−	28.9056i		−	1.48478i	0.669968	−	0.742390i	$-0.266308\pi$
$380$	−1.53569	+	2.28125i	−0.0787793	+	0.117026i
$381$		0			0
$382$	29.2656	+	8.93275i	1.49736	+	0.457039i
$383$	8.89994	+	15.4151i	0.454766	+	0.787677i	0.998675	−	0.0514671i	$-0.0163897\pi$
$383$	8.89994	+	15.4151i	0.454766	+	0.787677i	−0.543909	+	0.839144i	$0.683056\pi$
$384$		0			0
$385$	−3.15202	+	3.60314i	−0.160642	+	0.183633i
$386$	0.789913	−	2.58792i	0.0402055	−	0.131722i
$387$		0			0
$388$	−2.76724	−	0.190962i	−0.140485	−	0.00969462i
$389$	12.8152	−	22.1966i	0.649757	−	1.12541i	−0.333424	−	0.942777i	$-0.608204\pi$
$389$	12.8152	−	22.1966i	0.649757	−	1.12541i	0.983181	−	0.182635i	$-0.0584627\pi$
$390$		0			0
$391$	−2.04574	+	3.54333i	−0.103458	+	0.179194i
$392$	14.4138	+	13.5735i	0.728009	+	0.685568i
$393$		0			0
$394$	−7.18935	+	23.5538i	−0.362194	+	1.18662i
$395$	2.00144	+	3.46659i	0.100703	+	0.174423i
$396$		0			0
$397$	5.33703	+	3.08134i	0.267858	+	0.154648i	0.627914	−	0.778283i	$-0.283909\pi$
$397$	5.33703	+	3.08134i	0.267858	+	0.154648i	−0.360056	+	0.932931i	$0.617242\pi$
$398$	−4.89689	+	1.13289i	−0.245459	+	0.0567868i
$399$		0			0
$400$	−18.4099	−	2.55303i	−0.920496	−	0.127651i
$401$	0.135983	+	0.235529i	0.00679066	+	0.0117618i	0.869401	−	0.494108i	$-0.164505\pi$
$401$	0.135983	+	0.235529i	0.00679066	+	0.0117618i	−0.862610	+	0.505869i	$0.831172\pi$
$402$		0			0
$403$	36.7590	+	21.2228i	1.83110	+	1.05718i
$404$	6.96815	+	14.2537i	0.346679	+	0.709150i
$405$		0			0
$406$	−12.3604	+	23.0973i	−0.613436	+	1.14630i
$407$	14.4941	−	8.36816i	0.718445	−	0.414794i
$408$		0			0
$409$		−	6.53526i		−	0.323148i	−0.986861	−	0.161574i	$-0.948343\pi$
$409$		−	6.53526i		−	0.323148i	0.986861	−	0.161574i	$-0.0516570\pi$
$410$	−0.928738	+	3.04274i	−0.0458671	+	0.150270i
$411$		0			0
$412$	−1.30997	+	18.9828i	−0.0645374	+	0.935214i
$413$	6.56741	−	7.50733i	0.323161	−	0.369412i
$414$		0			0
$415$	5.14243	+	2.96899i	0.252432	+	0.145742i
$416$	36.8109	+	17.0629i	1.80480	+	0.836577i
$417$		0			0
$418$	−2.24359	−	9.69784i	−0.109738	−	0.474337i
$419$	18.6788	−	32.3526i	0.912519	−	1.58053i	0.102026	−	0.994782i	$-0.467468\pi$
$419$	18.6788	−	32.3526i	0.912519	−	1.58053i	0.810493	−	0.585748i	$-0.199199\pi$
$420$		0			0
$421$	8.81289	+	15.2644i	0.429514	+	0.743940i	0.996830	−	0.0795601i	$-0.0253516\pi$
$421$	8.81289	+	15.2644i	0.429514	+	0.743940i	−0.567316	+	0.823500i	$0.692018\pi$
$422$	−3.44379	+	3.21434i	−0.167641	+	0.156471i
$423$		0			0
$424$	21.6907	+	8.29216i	1.05339	+	0.402703i
$425$		−	12.2428i		−	0.593862i
$426$		0			0
$427$	−5.33077	−	4.66336i	−0.257974	−	0.225676i
$428$	−11.9790	−	24.5036i	−0.579025	−	1.18443i
$429$		0			0
$430$	−1.67265	−	1.79205i	−0.0806621	−	0.0864203i
$431$	26.8406	−	15.4964i	1.29286	−	0.746436i	0.313703	−	0.949521i	$-0.398430\pi$
$431$	26.8406	−	15.4964i	1.29286	−	0.746436i	0.979161	+	0.203085i	$0.0650969\pi$
$432$		0			0
$433$		−	20.1669i		−	0.969161i	−0.874747	−	0.484581i	$-0.838972\pi$
$433$		−	20.1669i		−	0.969161i	0.874747	−	0.484581i	$-0.161028\pi$
$434$	11.6836	+	18.8095i	0.560833	+	0.902884i
$435$		0			0
$436$	−1.25938	+	18.2497i	−0.0603134	+	0.874004i
$437$			3.59130i			0.171795i
$438$		0			0
$439$	−1.31016			−0.0625304			−0.0312652	−	0.999511i	$-0.509954\pi$
$439$	−1.31016			−0.0625304			−0.0312652	+	0.999511i	$0.509954\pi$
$440$	−3.97285	+	3.22619i	−0.189398	+	0.153802i
$441$		0			0
$442$	−7.80219	+	25.5616i	−0.371112	+	1.21584i
$443$		−	2.54555i		−	0.120943i	−0.998170	−	0.0604713i	$-0.980740\pi$
$443$		−	2.54555i		−	0.120943i	0.998170	−	0.0604713i	$-0.0192604\pi$
$444$		0			0
$445$	−9.44481			−0.447727
$446$	−17.9676	+	4.15680i	−0.850790	+	0.196830i
$447$		0			0
$448$	12.7315	+	16.9089i	0.601505	+	0.798869i
$449$	30.0500			1.41815			0.709073	−	0.705135i	$-0.249114\pi$
$449$	30.0500			1.41815			0.709073	+	0.705135i	$0.249114\pi$
$450$		0			0
$451$	−5.75762	−	9.97249i	−0.271116	−	0.469586i
$452$	12.8455	−	6.27973i	0.604203	−	0.295374i
$453$		0			0
$454$	−9.12160	−	9.77276i	−0.428098	−	0.458658i
$455$	7.42839	−	8.49154i	0.348249	−	0.398089i
$456$		0			0
$457$	−38.3846			−1.79556			−0.897779	−	0.440447i	$-0.854820\pi$
$457$	−38.3846			−1.79556			−0.897779	+	0.440447i	$0.854820\pi$
$458$	−4.52357	−	19.5529i	−0.211372	−	0.913649i
$459$		0			0
$460$	1.65884	−	0.810949i	0.0773438	−	0.0378107i
$461$	29.8694	−	17.2451i	1.39116	−	0.803186i	0.397715	−	0.917509i	$-0.369803\pi$
$461$	29.8694	−	17.2451i	1.39116	−	0.803186i	0.993444	+	0.114323i	$0.0364699\pi$
$462$		0			0
$463$	23.3117	+	13.4590i	1.08339	+	0.625493i	0.931808	−	0.362952i	$-0.118231\pi$
$463$	23.3117	+	13.4590i	1.08339	+	0.625493i	0.151578	+	0.988445i	$0.451565\pi$
$464$	−17.2015	+	22.1000i	−0.798558	+	1.02597i
$465$		0			0
$466$	−24.9153	−	26.6939i	−1.15418	−	1.23657i
$467$	−10.1757	+	17.6248i	−0.470874	+	0.815577i	−0.999445	−	0.0333119i	$-0.989395\pi$
$467$	−10.1757	+	17.6248i	−0.470874	+	0.815577i	0.528571	+	0.848889i	$0.322728\pi$
$468$		0			0
$469$	−17.7740	−	15.5487i	−0.820729	−	0.717973i
$470$	−1.83420	−	7.92827i	−0.0846055	−	0.365704i
$471$		0			0
$472$	8.27766	−	6.72193i	0.381010	−	0.309402i
$473$	8.87305			0.407983
$474$		0			0
$475$	−5.37305	−	9.30640i	−0.246533	−	0.427007i
$476$	−9.88044	+	9.83672i	−0.452869	+	0.450865i
$477$		0			0
$478$	22.4436	−	20.9481i	1.02654	−	0.958146i
$479$	1.09961	−	1.90458i	0.0502424	−	0.0870225i	−0.839810	−	0.542880i	$-0.817334\pi$
$479$	1.09961	−	1.90458i	0.0502424	−	0.0870225i	0.890053	+	0.455857i	$0.150667\pi$
$480$		0			0
$481$	−34.1583	+	19.7213i	−1.55748	+	0.899214i
$482$	−3.89734	+	3.63766i	−0.177519	+	0.165691i
$483$		0			0
$484$	−0.239263	+	3.46718i	−0.0108756	+	0.157599i
$485$	−0.412284	+	0.714098i	−0.0187209	+	0.0324255i
$486$		0			0
$487$	−16.7601	+	9.67646i	−0.759473	+	0.438482i	−0.829107	−	0.559090i	$-0.811150\pi$
$487$	−16.7601	+	9.67646i	−0.759473	+	0.438482i	0.0696332	+	0.997573i	$0.477817\pi$
$488$	−4.77308	−	5.87776i	−0.216067	−	0.266074i
$489$		0			0
$490$	5.50685	−	2.07728i	0.248774	−	0.0938419i
$491$	−20.0539	−	11.5781i	−0.905020	−	0.522514i	−0.0261947	−	0.999657i	$-0.508339\pi$
$491$	−20.0539	−	11.5781i	−0.905020	−	0.522514i	−0.878826	+	0.477143i	$0.841672\pi$
$492$		0			0
$493$	−15.9758	−	9.22366i	−0.719516	−	0.415413i
$494$	5.28749	+	22.8549i	0.237895	+	1.02829i
$495$		0			0
$496$	8.90768	+	21.9317i	0.399967	+	0.984764i
$497$	−17.4389	−	15.2556i	−0.782243	−	0.684306i
$498$		0			0
$499$	4.60461	−	2.65847i	0.206131	−	0.119010i	−0.393381	−	0.919375i	$-0.628695\pi$
$499$	4.60461	−	2.65847i	0.206131	−	0.119010i	0.599512	+	0.800366i	$0.295361\pi$
$500$	−6.40549	+	9.51528i	−0.286462	+	0.425536i
$501$		0			0
$502$	5.73844	−	18.8003i	0.256119	−	0.839099i
$503$	−1.45521			−0.0648844			−0.0324422	−	0.999474i	$-0.510328\pi$
$503$	−1.45521			−0.0648844			−0.0324422	+	0.999474i	$0.510328\pi$
$504$		0			0
$505$	4.71641			0.209877
$506$	−1.95114	+	6.39235i	−0.0867389	+	0.284175i
$507$		0			0
$508$	12.3962	−	18.4144i	0.549990	−	0.817005i
$509$	−37.5080	+	21.6553i	−1.66251	+	0.959853i	−0.691006	+	0.722849i	$0.742832\pi$
$509$	−37.5080	+	21.6553i	−1.66251	+	0.959853i	−0.971508	+	0.237005i	$0.923834\pi$
$510$		0			0
$511$	0.770509	−	3.89870i	0.0340853	−	0.172468i
$512$	10.3555	+	20.1187i	0.457652	+	0.889131i
$513$		0			0
$514$	1.36825	+	5.91420i	0.0603509	+	0.260864i
$515$	4.89859	+	2.82820i	0.215858	+	0.124625i
$516$		0			0
$517$	25.5092	+	14.7277i	1.12189	+	0.647725i
$518$	−20.5655	+	0.663101i	−0.903596	+	0.0291350i
$519$		0			0
$520$	9.36285	−	7.60317i	0.410588	−	0.333421i
$521$	−28.2426	+	16.3059i	−1.23733	+	0.714373i	−0.968548	−	0.248827i	$-0.919955\pi$
$521$	−28.2426	+	16.3059i	−1.23733	+	0.714373i	−0.268783	+	0.963201i	$0.586622\pi$
$522$		0			0
$523$	−13.1872	+	22.8409i	−0.576637	+	0.998765i	0.419224	+	0.907883i	$0.362302\pi$
$523$	−13.1872	+	22.8409i	−0.576637	+	0.998765i	−0.995862	+	0.0908822i	$0.971031\pi$
$524$	0.687265	−	9.95919i	0.0300233	−	0.435069i
$525$		0			0
$526$	18.1162	−	16.9092i	0.789905	−	0.737274i
$527$	−13.5036	+	7.79633i	−0.588228	+	0.339613i
$528$		0			0
$529$	−10.2943	+	17.8303i	−0.447580	+	0.775230i
$530$	5.04644	−	4.71019i	0.219203	−	0.204598i
$531$		0			0
$532$	−3.19357	+	11.8137i	−0.138459	+	0.512189i
$533$	13.5690	+	23.5022i	0.587740	+	1.01799i
$534$		0			0
$535$	−8.10799			−0.350539
$536$	−15.9146	−	19.5978i	−0.687404	−	0.846497i
$537$		0			0
$538$	1.43375	+	6.19733i	0.0618134	+	0.267186i
$539$	−8.10410	+	19.7022i	−0.349068	+	0.848633i
$540$		0			0
$541$	12.4508	−	21.5653i	0.535300	−	0.927166i	−0.463849	−	0.885914i	$-0.653532\pi$
$541$	12.4508	−	21.5653i	0.535300	−	0.927166i	0.999149	−	0.0412520i	$-0.0131346\pi$
$542$	−20.0295	−	21.4594i	−0.860343	−	0.921759i
$543$		0			0
$544$	−12.1897	+	8.57693i	−0.522630	+	0.367733i
$545$	4.70943	+	2.71899i	0.201730	+	0.116469i
$546$		0			0
$547$	−31.0502	+	17.9268i	−1.32761	+	0.766496i	−0.984929	−	0.172957i	$-0.944668\pi$
$547$	−31.0502	+	17.9268i	−1.32761	+	0.766496i	−0.342680	+	0.939452i	$0.611335\pi$
$548$	11.3366	−	5.54205i	0.484275	−	0.236745i
$549$		0			0
$550$	−4.50764	−	19.4841i	−0.192207	−	0.830805i
$551$	−16.1921			−0.689809
$552$		0			0
$553$	13.4071	+	11.7286i	0.570129	+	0.498749i
$554$	−13.2246	−	14.1686i	−0.561858	−	0.601967i
$555$		0			0
$556$	12.1257	−	5.92785i	0.514246	−	0.251397i
$557$	−3.14023	−	5.43904i	−0.133056	−	0.230459i	0.791797	−	0.610784i	$-0.209146\pi$
$557$	−3.14023	−	5.43904i	−0.133056	−	0.230459i	−0.924853	+	0.380325i	$0.875812\pi$
$558$		0			0
$559$	−20.9112			−0.884448
$560$	6.17795	−	1.19252i	0.261066	−	0.0503931i
$561$		0			0
$562$	3.51424	−	0.813018i	0.148239	−	0.0342951i
$563$	−15.5747			−0.656397			−0.328198	−	0.944609i	$-0.606441\pi$
$563$	−15.5747			−0.656397			−0.328198	+	0.944609i	$0.606441\pi$
$564$		0			0
$565$		−	4.25045i		−	0.178818i
$566$	3.54973	−	11.6297i	0.149206	−	0.488831i
$567$		0			0
$568$	−15.6145	−	19.2283i	−0.655170	−	0.806802i
$569$	3.13499			0.131426			0.0657128	−	0.997839i	$-0.479068\pi$
$569$	3.13499			0.131426			0.0657128	+	0.997839i	$0.479068\pi$
$570$		0			0
$571$		−	44.4748i		−	1.86121i	−0.366022	−	0.930606i	$-0.619280\pi$
$571$		−	44.4748i		−	1.86121i	0.366022	−	0.930606i	$-0.380720\pi$
$572$	−3.00554	+	43.5534i	−0.125668	+	1.82106i
$573$		0			0
$574$	0.456239	+	14.1499i	0.0190431	+	0.590604i
$575$			7.21536i			0.300901i
$576$		0			0
$577$	30.5353	−	17.6296i	1.27120	−	0.733929i	0.295988	−	0.955192i	$-0.404351\pi$
$577$	30.5353	−	17.6296i	1.27120	−	0.733929i	0.975214	+	0.221263i	$0.0710179\pi$
$578$	9.70533	+	10.3982i	0.403688	+	0.432506i
$579$		0			0
$580$	3.65633	+	7.47923i	0.151821	+	0.310558i
$581$	25.9232	+	5.12325i	1.07547	+	0.212548i
$582$		0			0
$583$			24.9866i			1.03484i
$584$	1.51709	−	3.96840i	0.0627775	−	0.164214i
$585$		0			0
$586$	20.5622	−	19.1922i	0.849417	−	0.792820i
$587$	19.6358	+	34.0102i	0.810455	+	1.40375i	0.912546	+	0.408974i	$0.134113\pi$
$587$	19.6358	+	34.0102i	0.810455	+	1.40375i	−0.102091	+	0.994775i	$0.532553\pi$
$588$		0			0
$589$	−6.84324	+	11.8528i	−0.281971	+	0.488387i
$590$	−0.714470	−	3.08827i	−0.0294143	−	0.127142i
$591$		0			0
$592$	−21.7884	−	3.02154i	−0.895496	−	0.124184i
$593$	28.1689	+	16.2633i	1.15676	+	0.667855i	0.950525	−	0.310648i	$-0.100546\pi$
$593$	28.1689	+	16.2633i	1.15676	+	0.667855i	0.206234	+	0.978503i	$0.433879\pi$
$594$		0			0
$595$	1.33706	+	3.92297i	0.0548142	+	0.160826i
$596$	−0.752074	+	10.8983i	−0.0308061	+	0.446413i
$597$		0			0
$598$	4.59827	−	15.0649i	0.188037	−	0.616049i
$599$		−	4.39397i		−	0.179533i	−0.995963	−	0.0897663i	$-0.971388\pi$
$599$		−	4.39397i		−	0.179533i	0.995963	−	0.0897663i	$-0.0286120\pi$
$600$		0			0
$601$	14.6174	−	8.43937i	0.596257	−	0.344249i	−0.171311	−	0.985217i	$-0.554800\pi$
$601$	14.6174	−	8.43937i	0.596257	−	0.344249i	0.767568	+	0.640968i	$0.221467\pi$
$602$	−9.61819	−	5.14712i	−0.392008	−	0.209781i
$603$		0			0
$604$	−12.1001	−	24.7514i	−0.492346	−	1.00712i
$605$	0.894720	+	0.516567i	0.0363755	+	0.0210014i
$606$		0			0
$607$	16.7306	+	28.9782i	0.679072	+	1.17619i	0.975261	+	0.221058i	$0.0709511\pi$
$607$	16.7306	+	28.9782i	0.679072	+	1.17619i	−0.296188	+	0.955130i	$0.595716\pi$
$608$	−5.50188	+	11.8696i	−0.223131	+	0.481374i
$609$		0			0
$610$	−2.19290	+	0.507327i	−0.0887880	+	0.0205411i
$611$	−60.1176	−	34.7089i	−2.43210	−	1.40417i
$612$		0			0
$613$	18.0048	+	31.1852i	0.727207	+	1.25956i	0.958059	+	0.286570i	$0.0925152\pi$
$613$	18.0048	+	31.1852i	0.727207	+	1.25956i	−0.230852	+	0.972989i	$0.574151\pi$
$614$	11.0641	−	36.2482i	0.446509	−	1.46286i
$615$		0			0
$616$	−12.1027	+	19.2928i	−0.487633	+	0.777329i
$617$	−17.8922	+	30.9902i	−0.720314	+	1.24762i	0.240560	+	0.970634i	$0.422669\pi$
$617$	−17.8922	+	30.9902i	−0.720314	+	1.24762i	−0.960874	+	0.276986i	$0.910665\pi$
$618$		0			0
$619$	8.72404	−	15.1105i	0.350649	−	0.607341i	−0.635715	−	0.771924i	$-0.719294\pi$
$619$	8.72404	−	15.1105i	0.350649	−	0.607341i	0.986363	+	0.164583i	$0.0526278\pi$
$620$	7.02015	+	0.484447i	0.281936	+	0.0194559i
$621$		0			0
$622$	−1.97905	+	6.48377i	−0.0793526	+	0.259976i
$623$	−39.7831	+	13.5592i	−1.59388	+	0.543239i
$624$		0			0
$625$	−9.91141	−	17.1671i	−0.396457	−	0.686683i
$626$	11.9199	+	3.63832i	0.476415	+	0.145417i
$627$		0			0
$628$	−13.1729	+	19.5682i	−0.525656	+	0.780857i
$629$		−	14.4895i		−	0.577733i
$630$		0			0
$631$		−	17.8634i		−	0.711133i	−0.934651	−	0.355566i	$-0.884288\pi$
$631$		−	17.8634i		−	0.711133i	0.934651	−	0.355566i	$-0.115712\pi$
$632$	12.0045	+	14.7828i	0.477514	+	0.588030i
$633$		0			0
$634$	−7.47783	+	24.4989i	−0.296983	+	0.972977i
$635$	−3.29939	−	5.71471i	−0.130932	−	0.226781i
$636$		0			0
$637$	19.0990	−	46.4322i	0.756729	−	1.83971i
$638$	−28.8213	−	8.79714i	−1.14104	−	0.348282i
$639$		0			0
$640$	6.72498	−	0.138913i	0.265828	−	0.00549101i
$641$	−23.5403	+	40.7730i	−0.929786	+	1.61044i	−0.146108	+	0.989269i	$0.546675\pi$
$641$	−23.5403	+	40.7730i	−0.929786	+	1.61044i	−0.783678	+	0.621168i	$0.786659\pi$
$642$		0			0
$643$	−11.4838	+	19.8904i	−0.452875	+	0.784403i	−0.998563	−	0.0535856i	$-0.982935\pi$
$643$	−11.4838	+	19.8904i	−0.452875	+	0.784403i	0.545688	+	0.837988i	$0.316268\pi$
$644$	5.82310	−	5.79733i	0.229462	−	0.228447i
$645$		0			0
$646$	−8.24225	−	2.51579i	−0.324287	−	0.0989825i
$647$	17.5968	+	30.4785i	0.691800	+	1.19823i	0.971248	+	0.238072i	$0.0765153\pi$
$647$	17.5968	+	30.4785i	0.691800	+	1.19823i	−0.279448	+	0.960161i	$0.590151\pi$
$648$		0			0
$649$	9.93648	+	5.73683i	0.390041	+	0.225190i
$650$	10.6232	+	45.9183i	0.416676	+	1.80106i
$651$		0			0
$652$	−2.99495	−	6.12634i	−0.117291	−	0.239926i
$653$	−18.4253	−	31.9135i	−0.721036	−	1.24887i	−0.960585	−	0.277987i	$-0.910333\pi$
$653$	−18.4253	−	31.9135i	−0.721036	−	1.24887i	0.239549	−	0.970884i	$-0.423001\pi$
$654$		0			0
$655$	−2.57001	−	1.48380i	−0.100419	−	0.0579767i
$656$	−2.07894	+	14.9912i	−0.0811688	+	0.585310i
$657$		0			0
$658$	−19.1080	−	30.7620i	−0.744909	−	1.19923i
$659$	−6.21863	+	3.59033i	−0.242244	+	0.139859i	−0.616207	−	0.787584i	$-0.711332\pi$
$659$	−6.21863	+	3.59033i	−0.242244	+	0.139859i	0.373964	+	0.927443i	$0.377998\pi$
$660$		0			0
$661$			2.24017i			0.0871324i	0.999051	+	0.0435662i	$0.0138719\pi$
$661$			2.24017i			0.0871324i	−0.999051	+	0.0435662i	$0.986128\pi$
$662$	10.5095	+	3.20783i	0.408464	+	0.124676i
$663$		0			0
$664$	26.3866	+	10.0874i	1.02400	+	0.391466i
$665$	2.73807	+	2.39526i	0.106178	+	0.0928843i
$666$		0			0
$667$	9.41547	+	5.43602i	0.364568	+	0.210484i
$668$	23.2769	−	11.3793i	0.900611	−	0.440277i
$669$		0			0
$670$	−7.31165	+	1.69155i	−0.282474	+	0.0653502i
$671$	4.07358	−	7.05565i	0.157259	−	0.272380i
$672$		0			0
$673$	7.99088	+	13.8406i	0.308026	+	0.533516i	0.977930	−	0.208931i	$-0.0669984\pi$
$673$	7.99088	+	13.8406i	0.308026	+	0.533516i	−0.669905	+	0.742447i	$0.733665\pi$
$674$	−7.65435	−	8.20077i	−0.294835	−	0.315882i
$675$		0			0
$676$	5.29321	−	76.7042i	0.203585	−	2.95016i
$677$		−	16.6132i		−	0.638498i	−0.947671	−	0.319249i	$-0.896569\pi$
$677$		−	16.6132i		−	0.638498i	0.947671	−	0.319249i	$-0.103431\pi$
$678$		0			0
$679$	−0.711434	+	3.59979i	−0.0273023	+	0.138147i
$680$	0.699120	+	4.37523i	0.0268100	+	0.167782i
$681$		0			0
$682$	−18.6202	+	17.3796i	−0.713006	+	0.665498i
$683$	−24.9863	+	14.4258i	−0.956073	+	0.551989i	−0.894962	−	0.446142i	$-0.852798\pi$
$683$	−24.9863	+	14.4258i	−0.956073	+	0.551989i	−0.0611106	+	0.998131i	$0.519464\pi$
$684$		0			0
$685$		−	3.75115i		−	0.143324i
$686$	20.2136	−	16.6556i	0.771759	−	0.635916i
$687$		0			0
$688$	−9.20291	−	7.16304i	−0.350858	−	0.273088i
$689$		−	58.8861i		−	2.24338i
$690$		0			0
$691$	−31.5172			−1.19897			−0.599485	−	0.800386i	$-0.704628\pi$
$691$	−31.5172			−1.19897			−0.599485	+	0.800386i	$0.704628\pi$
$692$	−1.39322	+	2.06962i	−0.0529624	+	0.0786750i
$693$		0			0
$694$	−1.12995	−	0.344895i	−0.0428922	−	0.0130920i
$695$		−	4.01228i		−	0.152194i
$696$		0			0
$697$	−9.96932			−0.377615
$698$	−5.11222	−	22.0974i	−0.193500	−	0.836397i
$699$		0			0
$700$	−6.41625	+	23.7351i	−0.242512	+	0.897104i
$701$	−38.3817			−1.44966			−0.724829	−	0.688929i	$-0.758081\pi$
$701$	−38.3817			−1.44966			−0.724829	+	0.688929i	$0.758081\pi$
$702$		0			0
$703$	−6.35907	−	11.0142i	−0.239837	−	0.415410i
$704$	−16.2418	+	18.1381i	−0.612135	+	0.683606i
$705$		0			0
$706$	13.4754	−	12.5776i	0.507154	−	0.473362i
$707$	19.8663	−	6.77101i	0.747150	−	0.254650i
$708$		0			0
$709$	−10.5603			−0.396602			−0.198301	−	0.980141i	$-0.563542\pi$
$709$	−10.5603			−0.396602			−0.198301	+	0.980141i	$0.563542\pi$
$710$	−7.17379	+	1.65965i	−0.269228	+	0.0622857i
$711$		0			0
$712$	−44.3695	+	7.08982i	−1.66282	+	0.265702i
$713$	7.95846	−	4.59482i	0.298047	−	0.172077i
$714$		0			0
$715$	11.2391	+	6.48892i	0.420320	+	0.242672i
$716$	0.210738	+	0.0145426i	0.00787564	+	0.000543483i
$717$		0			0
$718$	−7.98555	+	7.45348i	−0.298018	+	0.278161i
$719$	17.7183	−	30.6890i	0.660782	−	1.14451i	−0.319629	−	0.947543i	$-0.603558\pi$
$719$	17.7183	−	30.6890i	0.660782	−	1.14451i	0.980411	−	0.196965i	$-0.0631084\pi$
$720$		0			0
$721$	24.6939	+	4.88032i	0.919651	+	0.181752i
$722$	18.8091	−	4.35148i	0.700003	−	0.161945i
$723$		0			0
$724$	−25.0023	+	37.1406i	−0.929201	+	1.38032i
$725$	−32.5320			−1.20821
$726$		0			0
$727$	−16.3858	−	28.3811i	−0.607717	−	1.05260i	−0.991616	−	0.129222i	$-0.958752\pi$
$727$	−16.3858	−	28.3811i	−0.607717	−	1.05260i	0.383898	−	0.923375i	$-0.374581\pi$
$728$	28.5226	−	45.4674i	1.05712	−	1.68514i
$729$		0			0
$730$	−0.861750	−	0.923267i	−0.0318948	−	0.0341716i
$731$	3.84092	−	6.65267i	0.142062	−	0.246058i
$732$		0			0
$733$	4.86739	−	2.81019i	0.179781	−	0.103797i	−0.407409	−	0.913246i	$-0.633568\pi$
$733$	4.86739	−	2.81019i	0.179781	−	0.103797i	0.587190	+	0.809449i	$0.300234\pi$
$734$	−0.822673	−	0.881400i	−0.0303654	−	0.0325331i
$735$		0			0
$736$	7.18410	−	5.05487i	0.264809	−	0.186325i
$737$	13.5823	−	23.5252i	0.500309	−	0.866561i
$738$		0			0
$739$	−37.9429	+	21.9063i	−1.39575	+	0.805838i	−0.993944	−	0.109886i	$-0.964951\pi$
$739$	−37.9429	+	21.9063i	−1.39575	+	0.805838i	−0.401808	+	0.915724i	$0.631618\pi$
$740$	−3.65159	+	5.42440i	−0.134235	+	0.199405i
$741$		0			0
$742$	14.4944	−	27.0849i	0.532105	−	0.994320i
$743$	9.43980	+	5.45007i	0.346313	+	0.199944i	0.663060	−	0.748566i	$-0.269257\pi$
$743$	9.43980	+	5.45007i	0.346313	+	0.199944i	−0.316747	+	0.948510i	$0.602591\pi$
$744$		0			0
$745$	2.81236	+	1.62372i	0.103037	+	0.0594885i
$746$	3.21019	−	0.742678i	0.117534	−	0.0271914i
$747$		0			0
$748$	−13.3040	−	8.95598i	−0.486442	−	0.327463i
$749$	−34.1522	+	11.6401i	−1.24790	+	0.425319i
$750$		0			0
$751$	−8.29441	+	4.78878i	−0.302667	+	0.174745i	−0.643641	−	0.765328i	$-0.722577\pi$
$751$	−8.29441	+	4.78878i	−0.302667	+	0.174745i	0.340973	+	0.940073i	$0.389243\pi$
$752$	−14.5681	−	35.8683i	−0.531243	−	1.30798i
$753$		0			0
$754$	67.9232	+	20.7323i	2.47362	+	0.755025i
$755$	−8.18999			−0.298064
$756$		0			0
$757$	−1.91601			−0.0696384			−0.0348192	−	0.999394i	$-0.511086\pi$
$757$	−1.91601			−0.0696384			−0.0348192	+	0.999394i	$0.511086\pi$
$758$	−39.0979	−	11.9339i	−1.42010	−	0.433459i
$759$		0			0
$760$	2.45162	+	3.01902i	0.0889295	+	0.109511i
$761$	0.552623	−	0.319057i	0.0200326	−	0.0115658i	−0.489950	−	0.871750i	$-0.662985\pi$
$761$	0.552623	−	0.319057i	0.0200326	−	0.0115658i	0.509983	+	0.860185i	$0.329652\pi$
$762$		0			0
$763$	23.7404	+	4.69186i	0.859459	+	0.169857i
$764$	24.1650	−	35.8969i	0.874260	−	1.29870i
$765$		0			0
$766$	24.5251	−	5.67387i	0.886126	−	0.205005i
$767$	−23.4174	−	13.5200i	−0.845552	−	0.488180i
$768$		0			0
$769$	4.56501	+	2.63561i	0.164618	+	0.0950425i	0.580046	−	0.814584i	$-0.303035\pi$
$769$	4.56501	+	2.63561i	0.164618	+	0.0950425i	−0.415427	+	0.909626i	$0.636368\pi$
$770$	3.57230	+	5.75104i	0.128737	+	0.207253i
$771$		0			0
$772$	−3.17432	−	2.13689i	−0.114246	−	0.0769082i
$773$	34.2460	−	19.7719i	1.23174	−	0.711147i	0.264350	−	0.964427i	$-0.414843\pi$
$773$	34.2460	−	19.7719i	1.23174	−	0.711147i	0.967393	+	0.253280i	$0.0815094\pi$
$774$		0			0
$775$	−13.7489	+	23.8138i	−0.493874	+	0.855415i
$776$	−1.40077	+	3.66415i	−0.0502848	+	0.131535i
$777$		0			0
$778$	−24.7324	−	26.4980i	−0.886701	−	0.949999i
$779$	−7.57822	+	4.37529i	−0.271518	+	0.156761i
$780$		0			0
$781$	13.3262	−	23.0816i	0.476848	−	0.825926i
$782$	3.94813	+	4.22998i	0.141185	+	0.151264i
$783$		0			0
$784$	24.3106	−	13.8923i	0.868234	−	0.496155i
$785$	3.50613	+	6.07280i	0.125139	+	0.216748i
$786$		0			0
$787$	−2.01708			−0.0719013			−0.0359506	−	0.999354i	$-0.511446\pi$
$787$	−2.01708			−0.0719013			−0.0359506	+	0.999354i	$0.511446\pi$
$788$	28.8909	+	19.4487i	1.02919	+	0.692832i
$789$		0			0
$790$	5.51525	−	1.27595i	0.196224	−	0.0453963i
$791$	−6.10206	−	17.9036i	−0.216964	−	0.636579i
$792$		0			0
$793$	−9.60023	+	16.6281i	−0.340914	+	0.590481i
$794$	6.37127	−	5.94676i	0.226108	−	0.211042i
$795$		0			0
$796$	−0.489357	+	7.09129i	−0.0173448	+	0.251344i
$797$	−16.7785	−	9.68708i	−0.594326	−	0.343134i	0.172480	−	0.985013i	$-0.444822\pi$
$797$	−16.7785	−	9.68708i	−0.594326	−	0.343134i	−0.766806	+	0.641879i	$0.778155\pi$
$798$		0			0
$799$	22.0846	−	12.7505i	0.781295	−	0.451081i
$800$	−11.0539	+	23.8474i	−0.390815	+	0.843132i
$801$		0			0
$802$	0.374720	−	0.0866915i	0.0132318	−	0.00306118i
$803$	4.57141			0.161322
$804$		0			0
$805$	−0.788006	−	2.31203i	−0.0277735	−	0.0814883i
$806$	43.8824	−	40.9585i	1.54569	−	1.44270i
$807$		0			0
$808$	22.1566	−	3.54041i	0.779466	−	0.124551i
$809$	9.30812	+	16.1221i	0.327256	+	0.566824i	0.981966	−	0.189056i	$-0.0605427\pi$
$809$	9.30812	+	16.1221i	0.327256	+	0.566824i	−0.654710	+	0.755880i	$0.727209\pi$
$810$		0			0
$811$	1.07212			0.0376471			0.0188236	−	0.999823i	$-0.494008\pi$
$811$	1.07212			0.0376471			0.0188236	+	0.999823i	$0.494008\pi$
$812$	26.1385	+	26.2547i	0.917282	+	0.921358i
$813$		0			0
$814$	−5.33485	−	23.0597i	−0.186986	−	0.808241i
$815$	−2.02714			−0.0710076
$816$		0			0
$817$		−	6.74274i		−	0.235899i
$818$	−8.83965	−	2.69813i	−0.309071	−	0.0943380i
$819$		0			0
$820$	3.73220	+	2.51244i	0.130334	+	0.0877381i
$821$	−39.6372			−1.38335			−0.691674	−	0.722209i	$-0.743127\pi$
$821$	−39.6372			−1.38335			−0.691674	+	0.722209i	$0.743127\pi$
$822$		0			0
$823$			21.9087i			0.763690i	0.924226	+	0.381845i	$0.124711\pi$
$823$			21.9087i			0.763690i	−0.924226	+	0.381845i	$0.875289\pi$
$824$	25.1354	+	9.60906i	0.875634	+	0.334747i
$825$		0			0
$826$	−7.44307	−	11.9826i	−0.258978	−	0.416928i
$827$			40.4761i			1.40749i	0.710451	+	0.703746i	$0.248491\pi$
$827$			40.4761i			1.40749i	−0.710451	+	0.703746i	$0.751509\pi$
$828$		0			0
$829$	4.10818	−	2.37186i	0.142683	−	0.0823780i	−0.426959	−	0.904271i	$-0.640415\pi$
$829$	4.10818	−	2.37186i	0.142683	−	0.0823780i	0.569642	+	0.821893i	$0.307082\pi$
$830$	6.13897	−	5.72993i	0.213087	−	0.198889i
$831$		0			0
$832$	38.2771	−	42.7462i	1.32702	−	1.48196i
$833$	11.2639	+	14.6047i	0.390270	+	0.506023i
$834$		0			0
$835$		−	7.70208i		−	0.266542i
$836$	−14.0437	−	0.969126i	−0.485710	−	0.0335179i
$837$		0			0
$838$	−36.0487	−	38.6221i	−1.24528	−	1.33418i
$839$	−28.2350	−	48.9045i	−0.974782	−	1.68837i	−0.680653	−	0.732606i	$-0.738304\pi$
$839$	−28.2350	−	48.9045i	−0.974782	−	1.68837i	−0.294128	−	0.955766i	$-0.595029\pi$
$840$		0			0
$841$	−10.0095	+	17.3369i	−0.345154	+	0.597824i
$842$	24.2852	−	5.61837i	0.836923	−	0.193622i
$843$		0			0
$844$	2.92594	+	5.98517i	0.100715	+	0.206018i
$845$	−19.7939	−	11.4280i	−0.680930	−	0.393135i
$846$		0			0
$847$	4.51031	+	0.891383i	0.154976	+	0.0306283i
$848$	20.1712	−	25.9155i	0.692683	−	0.889943i
$849$		0			0
$850$	−16.5597	−	5.05452i	−0.567992	−	0.173369i
$851$			8.53946i			0.292729i
$852$		0			0
$853$	−8.07503	+	4.66212i	−0.276484	+	0.159628i	−0.631830	−	0.775107i	$-0.717696\pi$
$853$	−8.07503	+	4.66212i	−0.276484	+	0.159628i	0.355347	+	0.934735i	$0.384363\pi$
$854$	−8.50854	+	5.28514i	−0.291156	+	0.180854i
$855$		0			0
$856$	−38.0894	+	6.08633i	−1.30187	+	0.208027i
$857$	14.2780	+	8.24340i	0.487727	+	0.281589i	0.723631	−	0.690187i	$-0.242472\pi$
$857$	14.2780	+	8.24340i	0.487727	+	0.281589i	−0.235904	+	0.971776i	$0.575805\pi$
$858$		0			0
$859$	14.2428	+	24.6693i	0.485959	+	0.841706i	0.999870	−	0.0161374i	$-0.00513693\pi$
$859$	14.2428	+	24.6693i	0.485959	+	0.841706i	−0.513910	+	0.857844i	$0.671804\pi$
$860$	−3.11451	+	1.52257i	−0.106204	+	0.0519193i
$861$		0			0
$862$	−9.87923	−	42.7026i	−0.336488	−	1.45446i
$863$	4.17974	+	2.41317i	0.142280	+	0.0821454i	0.569450	−	0.822026i	$-0.307156\pi$
$863$	4.17974	+	2.41317i	0.142280	+	0.0821454i	−0.427170	+	0.904171i	$0.640489\pi$
$864$		0			0
$865$	0.370823	+	0.642285i	0.0126084	+	0.0218383i
$866$	−27.2780	−	8.32608i	−0.926943	−	0.282932i
$867$		0			0
$868$	30.2655	−	8.03775i	1.02728	−	0.272819i
$869$	−10.2452	+	17.7453i	−0.347546	+	0.601967i
$870$		0			0
$871$	−32.0094	+	55.4419i	−1.08460	+	1.87858i
$872$	24.1648	+	9.23800i	0.818323	+	0.312838i
$873$		0			0
$874$	4.85762	+	1.48270i	0.164312	+	0.0501530i
$875$	11.4207	+	9.99083i	0.386090	+	0.337752i
$876$		0			0
$877$	−11.8885	−	20.5915i	−0.401447	−	0.695327i	0.592454	−	0.805604i	$-0.298159\pi$
$877$	−11.8885	−	20.5915i	−0.401447	−	0.695327i	−0.993901	+	0.110278i	$0.964826\pi$
$878$	−0.540908	+	1.77213i	−0.0182548	+	0.0598064i
$879$		0			0
$880$	2.72354	+	6.70567i	0.0918105	+	0.226048i
$881$		−	15.9241i		−	0.536495i	−0.963350	−	0.268248i	$-0.913555\pi$
$881$		−	15.9241i		−	0.536495i	0.963350	−	0.268248i	$-0.0864445\pi$
$882$		0			0
$883$		−	0.631703i		−	0.0212585i	−0.999944	−	0.0106292i	$-0.996617\pi$
$883$		−	0.631703i		−	0.0212585i	0.999944	−	0.0106292i	$-0.00338346\pi$
$884$	31.3536	+	21.1066i	1.05454	+	0.709892i
$885$		0			0
$886$	−3.44313	−	1.05095i	−0.115674	−	0.0353073i
$887$	−7.53340	−	13.0482i	−0.252947	−	0.438117i	0.711389	−	0.702799i	$-0.248066\pi$
$887$	−7.53340	−	13.0482i	−0.252947	−	0.438117i	−0.964336	+	0.264682i	$0.914733\pi$
$888$		0			0
$889$	−22.1018	−	19.3346i	−0.741270	−	0.648463i
$890$	−3.89936	+	12.7751i	−0.130707	+	0.428223i
$891$		0			0
$892$	−1.79554	+	26.0193i	−0.0601192	+	0.871190i
$893$	11.1918	−	19.3847i	0.374519	−	0.648686i
$894$		0			0
$895$	0.0313973	−	0.0543818i	0.00104950	−	0.00181778i
$896$	28.1274	−	10.2397i	0.939669	−	0.342084i
$897$		0			0
$898$	12.4064	−	40.6459i	0.414006	−	1.35637i
$899$	20.7167	+	35.8824i	0.690941	+	1.19674i
$900$		0			0
$901$	18.7340	+	10.8161i	0.624120	+	0.360336i
$902$	−15.8660	+	3.67058i	−0.528279	+	0.122217i
$903$		0			0
$904$	−3.19063	−	19.9676i	−0.106119	−	0.664113i
$905$	6.65466	+	11.5262i	0.221208	+	0.383144i
$906$		0			0
$907$	−25.5312	−	14.7404i	−0.847748	−	0.489448i	0.0121421	−	0.999926i	$-0.496135\pi$
$907$	−25.5312	−	14.7404i	−0.847748	−	0.489448i	−0.859890	+	0.510479i	$0.829468\pi$
$908$	−16.9846	+	8.30319i	−0.563655	+	0.275551i
$909$		0			0
$910$	−8.41885	−	13.5535i	−0.279082	−	0.449294i
$911$	−14.4832	+	8.36189i	−0.479850	+	0.277042i	−0.720354	−	0.693606i	$-0.756021\pi$
$911$	−14.4832	+	8.36189i	−0.479850	+	0.277042i	0.240504	+	0.970648i	$0.422687\pi$
$912$		0			0
$913$			30.3961i			1.00596i
$914$	−15.8474	+	51.9194i	−0.524185	+	1.71734i
$915$		0			0
$916$	−28.3150	−	1.95397i	−0.935555	−	0.0645609i
$917$	−12.9555	−	2.56043i	−0.427829	−	0.0845527i
$918$		0			0
$919$	−0.945149	−	0.545682i	−0.0311776	−	0.0180004i	0.484330	−	0.874885i	$-0.339063\pi$
$919$	−0.945149	−	0.545682i	−0.0311776	−	0.0180004i	−0.515508	+	0.856885i	$0.672397\pi$
$920$	−0.412031	−	2.57857i	−0.0135843	−	0.0850128i
$921$		0			0
$922$	−10.9941	−	47.5214i	−0.362071	−	1.56504i
$923$	−31.4059	+	54.3966i	−1.03374	+	1.79049i
$924$		0			0
$925$	−12.7761	−	22.1289i	−0.420076	−	0.727594i
$926$	27.8292	−	25.9749i	0.914523	−	0.853588i
$927$		0			0
$928$	22.7909	+	32.3910i	0.748149	+	1.06329i
$929$			17.1306i			0.562036i	0.959703	+	0.281018i	$0.0906720\pi$
$929$			17.1306i			0.562036i	−0.959703	+	0.281018i	$0.909328\pi$
$930$		0			0
$931$	14.9719	+	6.15841i	0.490685	+	0.201834i
$932$	−46.3929	+	22.6799i	−1.51965	+	0.742904i
$933$		0			0
$934$	19.6383	+	21.0402i	0.642585	+	0.688457i
$935$	−4.12876	+	2.38374i	−0.135025	+	0.0779567i
$936$		0			0
$937$			17.6461i			0.576474i	0.957559	+	0.288237i	$0.0930692\pi$
$937$			17.6461i			0.576474i	−0.957559	+	0.288237i	$0.906931\pi$
$938$	−28.3695	+	17.6219i	−0.926296	+	0.575375i
$939$		0			0
$940$	−11.4811	−	0.792290i	−0.374473	−	0.0258417i
$941$		−	14.3693i		−	0.468425i	−0.972185	−	0.234212i	$-0.924749\pi$
$941$		−	14.3693i		−	0.468425i	0.972185	−	0.234212i	$-0.0752511\pi$
$942$		0			0
$943$	5.87548			0.191332
$944$	−5.67464	−	13.9716i	−0.184694	−	0.454738i
$945$		0			0
$946$	3.66331	−	12.0018i	0.119104	−	0.390211i
$947$		−	9.85597i		−	0.320276i	−0.987095	−	0.160138i	$-0.948806\pi$
$947$		−	9.85597i		−	0.320276i	0.987095	−	0.160138i	$-0.0511939\pi$
$948$		0			0
$949$	−10.7735			−0.349722
$950$	−14.8062	+	3.42541i	−0.480377	+	0.111135i
$951$		0			0
$952$	9.22601	+	17.4255i	0.299017	+	0.564765i
$953$	−9.71521			−0.314707			−0.157353	−	0.987542i	$-0.550296\pi$
$953$	−9.71521			−0.314707			−0.157353	+	0.987542i	$0.550296\pi$
$954$		0			0
$955$	−6.43182	−	11.1402i	−0.208129	−	0.360490i
$956$	−19.0686	−	39.0059i	−0.616724	−	1.26154i
$957$		0			0
$958$	−2.12217	−	2.27366i	−0.0685641	−	0.0734587i
$959$	−5.38526	−	15.8005i	−0.173899	−	0.510224i
$960$		0			0
$961$	4.02174			0.129734
$962$	12.5727	+	54.3449i	0.405359	+	1.75215i
$963$		0			0
$964$	3.31128	+	6.77342i	0.106649	+	0.218157i
$965$	−0.985119	+	0.568759i	−0.0317121	+	0.0183090i
$966$		0			0
$967$	−19.5928	−	11.3119i	−0.630061	−	0.363766i	0.150715	−	0.988577i	$-0.451842\pi$
$967$	−19.5928	−	11.3119i	−0.630061	−	0.363766i	−0.780776	+	0.624812i	$0.785176\pi$
$968$	4.59095	+	1.75508i	0.147559	+	0.0564104i
$969$		0			0
$970$	0.795679	+	0.852480i	0.0255477	+	0.0273715i
$971$	8.13371	−	14.0880i	0.261023	−	0.452105i	−0.705491	−	0.708719i	$-0.749273\pi$
$971$	8.13371	−	14.0880i	0.261023	−	0.452105i	0.966514	+	0.256614i	$0.0826068\pi$
$972$		0			0
$973$	−5.76014	−	16.9004i	−0.184662	−	0.541802i
$974$	6.16891	+	26.6649i	0.197665	+	0.854398i
$975$		0			0
$976$	−9.92090	+	4.02942i	−0.317560	+	0.128979i
$977$	35.5330			1.13680			0.568400	−	0.822752i	$-0.307563\pi$
$977$	35.5330			1.13680			0.568400	+	0.822752i	$0.307563\pi$
$978$		0			0
$979$	−24.1737	−	41.8701i	−0.772595	−	1.33817i
$980$	−0.536199	−	8.30623i	−0.0171283	−	0.265333i
$981$		0			0
$982$	−23.9401	+	22.3450i	−0.763959	+	0.713056i
$983$	−12.8397	+	22.2390i	−0.409523	+	0.709315i	−0.994836	−	0.101493i	$-0.967638\pi$
$983$	−12.8397	+	22.2390i	−0.409523	+	0.709315i	0.585313	+	0.810807i	$0.300972\pi$
$984$		0			0
$985$	8.96600	−	5.17652i	0.285680	−	0.164938i
$986$	−19.0717	+	17.8010i	−0.607368	+	0.566899i
$987$		0			0
$988$	33.0968	+	2.28395i	1.05295	+	0.0726620i
$989$	−2.26367	+	3.92079i	−0.0719805	+	0.124674i
$990$		0			0
$991$	−20.2815	+	11.7096i	−0.644264	+	0.371966i	−0.786255	−	0.617902i	$-0.787983\pi$
$991$	−20.2815	+	11.7096i	−0.644264	+	0.371966i	0.141991	+	0.989868i	$0.454650\pi$
$992$	33.3426	−	2.99391i	1.05863	−	0.0950569i
$993$		0			0
$994$	−27.8346	+	17.2897i	−0.882860	+	0.548394i
$995$	1.82994	+	1.05652i	0.0580130	+	0.0334938i
$996$		0			0
$997$	−1.36608	−	0.788707i	−0.0432642	−	0.0249786i	0.478212	−	0.878244i	$-0.341285\pi$
$997$	−1.36608	−	0.788707i	−0.0432642	−	0.0249786i	−0.521476	+	0.853266i	$0.674618\pi$
$998$	−1.69482	−	7.32580i	−0.0536487	−	0.231894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.523.27		84
3.2	odd	2		252.2.bj.b.103.16	yes	84
4.3	odd	2	inner	756.2.bj.b.523.28		84
7.3	odd	6		756.2.n.b.199.30		84
9.2	odd	6		252.2.n.b.187.41	yes	84
9.7	even	3		756.2.n.b.19.2		84
12.11	even	2		252.2.bj.b.103.15	yes	84
21.17	even	6		252.2.n.b.31.13	✓	84
28.3	even	6		756.2.n.b.199.2		84
36.7	odd	6		756.2.n.b.19.30		84
36.11	even	6		252.2.n.b.187.13	yes	84
63.38	even	6		252.2.bj.b.115.16	yes	84
63.52	odd	6	inner	756.2.bj.b.451.27		84
84.59	odd	6		252.2.n.b.31.41	yes	84
252.115	even	6	inner	756.2.bj.b.451.28		84
252.227	odd	6		252.2.bj.b.115.15	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.13	✓	84	21.17	even	6
252.2.n.b.31.41	yes	84	84.59	odd	6
252.2.n.b.187.13	yes	84	36.11	even	6
252.2.n.b.187.41	yes	84	9.2	odd	6
252.2.bj.b.103.15	yes	84	12.11	even	2
252.2.bj.b.103.16	yes	84	3.2	odd	2
252.2.bj.b.115.15	yes	84	252.227	odd	6
252.2.bj.b.115.16	yes	84	63.38	even	6
756.2.n.b.19.2		84	9.7	even	3
756.2.n.b.19.30		84	36.7	odd	6
756.2.n.b.199.2		84	28.3	even	6
756.2.n.b.199.30		84	7.3	odd	6
756.2.bj.b.451.27		84	63.52	odd	6	inner
756.2.bj.b.451.28		84	252.115	even	6	inner
756.2.bj.b.523.27		84	1.1	even	1	trivial
756.2.bj.b.523.28		84	4.3	odd	2	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.412858 - 1.35261i) q^{2} +(-1.65910 - 1.11687i) q^{4} +(-0.514884 + 0.297269i) q^{5} +(-1.74201 + 1.99133i) q^{7} +(-2.19566 + 1.78300i) q^{8} +(0.189514 + 0.819166i) q^{10} +(-2.63566 - 1.52170i) q^{11} +(6.21148 + 3.58620i) q^{13} +(1.97428 + 3.17840i) q^{14} +(1.50521 + 3.70599i) q^{16} +(-2.28182 + 1.31741i) q^{17} +(-1.15636 + 2.00287i) q^{19} +(1.18625 + 0.0818611i) q^{20} +(-3.14642 + 2.93677i) q^{22} +(1.34481 - 0.776425i) q^{23} +(-2.32326 + 4.02401i) q^{25} +(7.41518 - 6.92111i) q^{26} +(5.11422 - 1.35821i) q^{28} +(3.50068 + 6.06335i) q^{29} +5.91792 q^{31} +(5.63419 - 0.505907i) q^{32} +(0.839873 + 3.63032i) q^{34} +(0.304976 - 1.54315i) q^{35} +(-2.74961 + 4.76246i) q^{37} +(2.23169 + 2.39100i) q^{38} +(0.600480 - 1.57074i) q^{40} +(3.27676 + 1.89184i) q^{41} +(-2.52490 + 1.45775i) q^{43} +(2.67328 + 5.46834i) q^{44} +(-0.494984 - 2.13955i) q^{46} -9.67847 q^{47} +(-0.930778 - 6.93784i) q^{49} +(4.48373 + 4.80381i) q^{50} +(-6.30013 - 12.8873i) q^{52} +(-4.10505 - 7.11016i) q^{53} +1.80941 q^{55} +(0.274327 - 7.47828i) q^{56} +(9.64661 - 2.23174i) q^{58} -3.77001 q^{59} +2.67699i q^{61} +(2.44326 - 8.00462i) q^{62} +(1.64182 - 7.82971i) q^{64} -4.26426 q^{65} +8.92572i q^{67} +(5.25714 + 0.362785i) q^{68} +(-1.96136 - 1.04961i) q^{70} +8.75743i q^{71} +(-1.30083 + 0.751036i) q^{73} +(5.30655 + 5.68536i) q^{74} +(4.15546 - 2.03146i) q^{76} +(7.62156 - 2.59765i) q^{77} -6.73276i q^{79} +(-1.87668 - 1.46071i) q^{80} +(3.91175 - 3.65111i) q^{82} +(-4.99378 - 8.64947i) q^{83} +(0.783250 - 1.35663i) q^{85} +(0.929343 + 4.01705i) q^{86} +(8.50020 - 1.35825i) q^{88} +(13.7577 + 7.94299i) q^{89} +(-17.9618 + 6.12189i) q^{91} +(-3.09833 - 0.213810i) q^{92} +(-3.99583 + 13.0912i) q^{94} -1.37500i q^{95} +(1.20110 - 0.693454i) q^{97} +(-9.76846 - 1.60536i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37}+ \cdots - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

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