LMFDB - Embedded newform 819.2.dx.a.503.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(503,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("819.503");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dx (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.11
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14474 - 0.660916i) q^{2} +(-0.126381 - 0.218898i) q^{4} -1.30928 q^{5} +(2.62751 + 0.310174i) q^{7} +2.97777i q^{8} +O(q^{10})$	\(q+(-1.14474 - 0.660916i) q^{2} +(-0.126381 - 0.218898i) q^{4} -1.30928 q^{5} +(2.62751 + 0.310174i) q^{7} +2.97777i q^{8} +(1.49878 + 0.865323i) q^{10} +(-2.91784 - 1.68462i) q^{11} +(-2.43576 - 2.65840i) q^{13} +(-2.80281 - 2.09163i) q^{14} +(1.71529 - 2.97098i) q^{16} +(3.28870 + 5.69619i) q^{17} +(-0.0563295 + 0.0325218i) q^{19} +(0.165468 + 0.286598i) q^{20} +(2.22678 + 3.85689i) q^{22} +(-4.45220 - 2.57048i) q^{23} -3.28579 q^{25} +(1.03133 + 4.65301i) q^{26} +(-0.264170 - 0.614356i) q^{28} +(-6.80855 - 3.93092i) q^{29} +6.51216i q^{31} +(1.23052 - 0.710441i) q^{32} -8.69420i q^{34} +(-3.44014 - 0.406104i) q^{35} +(-0.139690 + 0.241950i) q^{37} +0.0859768 q^{38} -3.89873i q^{40} +(-3.70861 + 6.42351i) q^{41} +(1.47922 + 2.56209i) q^{43} +0.851612i q^{44} +(3.39774 + 5.88506i) q^{46} -0.756319 q^{47} +(6.80758 + 1.62997i) q^{49} +(3.76137 + 2.17163i) q^{50} +(-0.274086 + 0.869153i) q^{52} +7.81904i q^{53} +(3.82026 + 2.20563i) q^{55} +(-0.923627 + 7.82411i) q^{56} +(5.19601 + 8.99975i) q^{58} +(-0.590438 - 1.02267i) q^{59} +(2.48105 - 1.43244i) q^{61} +(4.30399 - 7.45473i) q^{62} -8.73934 q^{64} +(3.18908 + 3.48059i) q^{65} +(-5.60820 + 9.71368i) q^{67} +(0.831256 - 1.43978i) q^{68} +(3.66966 + 2.73852i) q^{70} +(-5.31936 + 3.07113i) q^{71} +15.1338i q^{73} +(0.319817 - 0.184646i) q^{74} +(0.0142379 + 0.00822027i) q^{76} +(-7.14412 - 5.33137i) q^{77} -9.20483 q^{79} +(-2.24580 + 3.88984i) q^{80} +(8.49079 - 4.90216i) q^{82} +14.3917 q^{83} +(-4.30582 - 7.45790i) q^{85} -3.91056i q^{86} +(5.01640 - 8.68866i) q^{88} +(3.32454 - 5.75827i) q^{89} +(-5.57540 - 7.74047i) q^{91} +1.29944i q^{92} +(0.865789 + 0.499863i) q^{94} +(0.0737510 - 0.0425801i) q^{95} +(-16.2545 + 9.38452i) q^{97} +(-6.71564 - 6.36513i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^7	$ 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.14474	−	0.660916i	−0.809453	−	0.467338i	0.0373128	−	0.999304i	$-0.488120\pi$
$2$	−1.14474	−	0.660916i	−0.809453	−	0.467338i	−0.846766	+	0.531966i	$0.821454\pi$
$3$		0			0
$3$		0			0
$4$	−0.126381	−	0.218898i	−0.0631904	−	0.109449i
$5$	−1.30928			−0.585527			−0.292764	−	0.956185i	$-0.594575\pi$
$5$	−1.30928			−0.585527			−0.292764	+	0.956185i	$0.594575\pi$
$6$		0			0
$7$	2.62751	+	0.310174i	0.993104	+	0.117235i
$7$	2.62751	+	0.310174i	0.993104	+	0.117235i
$8$			2.97777i			1.05280i
$9$		0			0
$10$	1.49878	+	0.865323i	0.473957	+	0.273639i
$11$	−2.91784	−	1.68462i	−0.879761	−	0.507931i	−0.00918173	−	0.999958i	$-0.502923\pi$
$11$	−2.91784	−	1.68462i	−0.879761	−	0.507931i	−0.870580	+	0.492027i	$0.836256\pi$
$12$		0			0
$13$	−2.43576	−	2.65840i	−0.675557	−	0.737308i
$13$	−2.43576	−	2.65840i	−0.675557	−	0.737308i
$14$	−2.80281	−	2.09163i	−0.749083	−	0.559011i
$15$		0			0
$16$	1.71529	−	2.97098i	0.428824	−	0.742744i
$17$	3.28870	+	5.69619i	0.797626	+	1.38153i	0.921158	+	0.389188i	$0.127244\pi$
$17$	3.28870	+	5.69619i	0.797626	+	1.38153i	−0.123532	+	0.992341i	$0.539422\pi$
$18$		0			0
$19$	−0.0563295	+	0.0325218i	−0.0129229	+	0.00746102i	−0.506448	−	0.862271i	$-0.669042\pi$
$19$	−0.0563295	+	0.0325218i	−0.0129229	+	0.00746102i	0.493525	+	0.869732i	$0.335708\pi$
$20$	0.165468	+	0.286598i	0.0369997	+	0.0640853i
$21$		0			0
$22$	2.22678	+	3.85689i	0.474750	+	0.822292i
$23$	−4.45220	−	2.57048i	−0.928349	−	0.535982i	−0.0420597	−	0.999115i	$-0.513392\pi$
$23$	−4.45220	−	2.57048i	−0.928349	−	0.535982i	−0.886289	+	0.463133i	$0.846725\pi$
$24$		0			0
$25$	−3.28579			−0.657158
$26$	1.03133	+	4.65301i	0.202260	+	0.912530i
$27$		0			0
$28$	−0.264170	−	0.614356i	−0.0499234	−	0.116102i
$29$	−6.80855	−	3.93092i	−1.26432	−	0.729953i	−0.290409	−	0.956903i	$-0.593791\pi$
$29$	−6.80855	−	3.93092i	−1.26432	−	0.729953i	−0.973907	+	0.226950i	$0.927125\pi$
$30$		0			0
$31$			6.51216i			1.16962i	0.811171	+	0.584810i	$0.198831\pi$
$31$			6.51216i			1.16962i	−0.811171	+	0.584810i	$0.801169\pi$
$32$	1.23052	−	0.710441i	0.217527	−	0.125589i
$33$		0			0
$34$		−	8.69420i		−	1.49104i
$35$	−3.44014	−	0.406104i	−0.581489	−	0.0686441i
$36$		0			0
$37$	−0.139690	+	0.241950i	−0.0229648	+	0.0397763i	−0.877279	−	0.479980i	$-0.840644\pi$
$37$	−0.139690	+	0.241950i	−0.0229648	+	0.0397763i	0.854315	+	0.519756i	$0.173977\pi$
$38$	0.0859768			0.0139473
$39$		0			0
$40$		−	3.89873i		−	0.616444i
$41$	−3.70861	+	6.42351i	−0.579188	+	1.00318i	0.416385	+	0.909189i	$0.363297\pi$
$41$	−3.70861	+	6.42351i	−0.579188	+	1.00318i	−0.995573	+	0.0939945i	$0.970036\pi$
$42$		0			0
$43$	1.47922	+	2.56209i	0.225579	+	0.390715i	0.956493	−	0.291755i	$-0.0942392\pi$
$43$	1.47922	+	2.56209i	0.225579	+	0.390715i	−0.730914	+	0.682470i	$0.760906\pi$
$44$			0.851612i			0.128385i
$45$		0			0
$46$	3.39774	+	5.88506i	0.500970	+	0.867705i
$47$	−0.756319			−0.110321			−0.0551603	−	0.998478i	$-0.517567\pi$
$47$	−0.756319			−0.110321			−0.0551603	+	0.998478i	$0.517567\pi$
$48$		0			0
$49$	6.80758	+	1.62997i	0.972512	+	0.232853i
$50$	3.76137	+	2.17163i	0.531939	+	0.307115i
$51$		0			0
$52$	−0.274086	+	0.869153i	−0.0380088	+	0.120530i
$53$			7.81904i			1.07403i	0.843573	+	0.537014i	$0.180448\pi$
$53$			7.81904i			1.07403i	−0.843573	+	0.537014i	$0.819552\pi$
$54$		0			0
$55$	3.82026	+	2.20563i	0.515124	+	0.297407i
$56$	−0.923627	+	7.82411i	−0.123425	+	1.04554i
$57$		0			0
$58$	5.19601	+	8.99975i	0.682270	+	1.18173i
$59$	−0.590438	−	1.02267i	−0.0768685	−	0.133140i	0.825029	−	0.565091i	$-0.191159\pi$
$59$	−0.590438	−	1.02267i	−0.0768685	−	0.133140i	−0.901897	+	0.431951i	$0.857826\pi$
$60$		0			0
$61$	2.48105	−	1.43244i	0.317666	−	0.183405i	−0.332685	−	0.943038i	$-0.607955\pi$
$61$	2.48105	−	1.43244i	0.317666	−	0.183405i	0.650352	+	0.759633i	$0.274621\pi$
$62$	4.30399	−	7.45473i	0.546607	−	0.946752i
$63$		0			0
$64$	−8.73934			−1.09242
$65$	3.18908	+	3.48059i	0.395557	+	0.431714i
$66$		0			0
$67$	−5.60820	+	9.71368i	−0.685150	+	1.18672i	0.288239	+	0.957558i	$0.406930\pi$
$67$	−5.60820	+	9.71368i	−0.685150	+	1.18672i	−0.973390	+	0.229157i	$0.926403\pi$
$68$	0.831256	−	1.43978i	0.100805	−	0.174599i
$69$		0			0
$70$	3.66966	+	2.73852i	0.438609	+	0.327316i
$71$	−5.31936	+	3.07113i	−0.631291	+	0.364476i	−0.781252	−	0.624216i	$-0.785419\pi$
$71$	−5.31936	+	3.07113i	−0.631291	+	0.364476i	0.149961	+	0.988692i	$0.452085\pi$
$72$		0			0
$73$			15.1338i			1.77128i	0.464372	+	0.885640i	$0.346280\pi$
$73$			15.1338i			1.77128i	−0.464372	+	0.885640i	$0.653720\pi$
$74$	0.319817	−	0.184646i	0.0371779	−	0.0214647i
$75$		0			0
$76$	0.0142379	+	0.00822027i	0.00163320	+	0.000942929i
$77$	−7.14412	−	5.33137i	−0.814148	−	0.607567i
$78$		0			0
$79$	−9.20483			−1.03562			−0.517812	−	0.855494i	$-0.673253\pi$
$79$	−9.20483			−1.03562			−0.517812	+	0.855494i	$0.673253\pi$
$80$	−2.24580	+	3.88984i	−0.251088	+	0.434897i
$81$		0			0
$82$	8.49079	−	4.90216i	0.937651	−	0.541353i
$83$	14.3917			1.57970			0.789849	−	0.613302i	$-0.210159\pi$
$83$	14.3917			1.57970			0.789849	+	0.613302i	$0.210159\pi$
$84$		0			0
$85$	−4.30582	−	7.45790i	−0.467032	−	0.808923i
$86$		−	3.91056i		−	0.421687i
$87$		0			0
$88$	5.01640	−	8.68866i	0.534750	−	0.926214i
$89$	3.32454	−	5.75827i	0.352400	−	0.610375i	−0.634269	−	0.773112i	$-0.718699\pi$
$89$	3.32454	−	5.75827i	0.352400	−	0.610375i	0.986669	+	0.162737i	$0.0520322\pi$
$90$		0			0
$91$	−5.57540	−	7.74047i	−0.584461	−	0.811422i
$92$			1.29944i			0.135476i
$93$		0			0
$94$	0.865789	+	0.499863i	0.0892993	+	0.0515570i
$95$	0.0737510	−	0.0425801i	0.00756669	−	0.00436863i
$96$		0			0
$97$	−16.2545	+	9.38452i	−1.65039	+	0.952854i	−0.673481	+	0.739204i	$0.735202\pi$
$97$	−16.2545	+	9.38452i	−1.65039	+	0.952854i	−0.976910	+	0.213650i	$0.931465\pi$
$98$	−6.71564	−	6.36513i	−0.678382	−	0.642975i
$99$		0			0
$100$	0.415261	+	0.719253i	0.0415261	+	0.0719253i
$101$	−2.65527	+	4.59906i	−0.264209	+	0.457624i	−0.967356	−	0.253421i	$-0.918444\pi$
$101$	−2.65527	+	4.59906i	−0.264209	+	0.457624i	0.703147	+	0.711045i	$0.251778\pi$
$102$		0			0
$103$		−	10.5416i		−	1.03870i	−0.854563	−	0.519348i	$-0.826175\pi$
$103$		−	10.5416i		−	1.03870i	0.854563	−	0.519348i	$-0.173825\pi$
$104$	7.91611	−	7.25312i	0.776238	−	0.711227i
$105$		0			0
$106$	5.16773	−	8.95077i	0.501934	−	0.869376i
$107$	−2.63681	−	1.52236i	−0.254910	−	0.147172i	0.367100	−	0.930181i	$-0.380351\pi$
$107$	−2.63681	−	1.52236i	−0.254910	−	0.147172i	−0.622011	+	0.783009i	$0.713684\pi$
$108$		0			0
$109$	−11.6917			−1.11986			−0.559929	−	0.828541i	$-0.689172\pi$
$109$	−11.6917			−1.11986			−0.559929	+	0.828541i	$0.689172\pi$
$110$	−2.91547	−	5.04974i	−0.277979	−	0.481474i
$111$		0			0
$112$	5.42847	−	7.27422i	0.512942	−	0.687349i
$113$	9.42522	−	5.44165i	0.886650	−	0.511908i	0.0138048	−	0.999905i	$-0.495606\pi$
$113$	9.42522	−	5.44165i	0.886650	−	0.511908i	0.872845	+	0.487997i	$0.162272\pi$
$114$		0			0
$115$	5.82917	+	3.36548i	0.543573	+	0.313832i
$116$			1.98717i			0.184504i
$117$		0			0
$118$			1.56092i			0.143694i
$119$	6.87426	+	15.9868i	0.630163	+	1.46551i
$120$		0			0
$121$	0.175855	+	0.304591i	0.0159869	+	0.0276901i
$122$	−3.78688			−0.342848
$123$		0			0
$124$	1.42550	−	0.823012i	0.128014	−	0.0739087i
$125$	10.8484			0.970311
$126$		0			0
$127$	−4.98854	+	8.64041i	−0.442661	+	0.766712i	−0.997886	−	0.0649883i	$-0.979299\pi$
$127$	−4.98854	+	8.64041i	−0.442661	+	0.766712i	0.555225	+	0.831700i	$0.312632\pi$
$128$	7.54323	+	4.35509i	0.666734	+	0.384939i
$129$		0			0
$130$	−1.35030	−	6.09208i	−0.118429	−	0.534311i
$131$	−13.6703			−1.19438			−0.597188	−	0.802101i	$-0.703715\pi$
$131$	−13.6703			−1.19438			−0.597188	+	0.802101i	$0.703715\pi$
$132$		0			0
$133$	−0.158093	+	0.0679794i	−0.0137084	+	0.00589456i
$134$	12.8398	−	7.41309i	1.10919	−	0.640394i
$135$		0			0
$136$	−16.9619	+	9.79298i	−1.45447	+	0.839742i
$137$	0.0968515	−	0.0559172i	0.00827458	−	0.00477733i	−0.495857	−	0.868404i	$-0.665146\pi$
$137$	0.0968515	−	0.0559172i	0.00827458	−	0.00477733i	0.504132	+	0.863627i	$0.331813\pi$
$138$		0			0
$139$	−5.29234	+	3.05553i	−0.448890	+	0.259167i	−0.707361	−	0.706852i	$-0.750115\pi$
$139$	−5.29234	+	3.05553i	−0.448890	+	0.259167i	0.258471	+	0.966019i	$0.416781\pi$
$140$	0.345872	+	0.804363i	0.0292315	+	0.0679811i
$141$		0			0
$142$	8.11904			0.681335
$143$	2.62876	+	11.8601i	0.219828	+	0.991791i
$144$		0			0
$145$	8.91429	+	5.14667i	0.740291	+	0.427407i
$146$	10.0022	−	17.3243i	0.827787	−	1.43377i
$147$		0			0
$148$	0.0706164			0.00580463
$149$	6.74537	−	3.89444i	0.552603	−	0.319045i	−0.197568	−	0.980289i	$-0.563304\pi$
$149$	6.74537	−	3.89444i	0.552603	−	0.319045i	0.750171	+	0.661244i	$0.229971\pi$
$150$		0			0
$151$	13.9319			1.13376			0.566880	−	0.823800i	$-0.308150\pi$
$151$	13.9319			1.13376			0.566880	+	0.823800i	$0.308150\pi$
$152$	−0.0968426	−	0.167736i	−0.00785497	−	0.0136052i
$153$		0			0
$154$	4.65457	+	10.8247i	0.375076	+	0.872279i
$155$		−	8.52624i		−	0.684844i
$156$		0			0
$157$			2.41830i			0.193001i	0.995333	+	0.0965007i	$0.0307650\pi$
$157$			2.41830i			0.193001i	−0.995333	+	0.0965007i	$0.969235\pi$
$158$	10.5371	+	6.08362i	0.838289	+	0.483987i
$159$		0			0
$160$	−1.61109	+	0.930165i	−0.127368	+	0.0735360i
$161$	−10.9009	−	8.13491i	−0.859111	−	0.641121i
$162$		0			0
$163$	−6.45952	−	11.1882i	−0.505949	−	0.876329i	−0.999976	−	0.00688296i	$-0.997809\pi$
$163$	−6.45952	−	11.1882i	−0.505949	−	0.876329i	0.494027	−	0.869446i	$-0.335524\pi$
$164$	1.87479			0.146396
$165$		0			0
$166$	−16.4748	−	9.51172i	−1.27869	−	0.738253i
$167$	8.10077	−	14.0309i	0.626857	−	1.08575i	−0.361322	−	0.932441i	$-0.617675\pi$
$167$	8.10077	−	14.0309i	0.626857	−	1.08575i	0.988179	−	0.153306i	$-0.0489922\pi$
$168$		0			0
$169$	−1.13418	+	12.9504i	−0.0872450	+	0.996187i
$170$			11.3831i			0.873047i
$171$		0			0
$172$	0.373890	−	0.647597i	0.0285089	−	0.0493788i
$173$	−12.0709	−	20.9074i	−0.917733	−	1.58956i	−0.802850	−	0.596181i	$-0.796684\pi$
$173$	−12.0709	−	20.9074i	−0.917733	−	1.58956i	−0.114883	−	0.993379i	$-0.536649\pi$
$174$		0			0
$175$	−8.63344	−	1.01917i	−0.652626	−	0.0770417i
$176$	−10.0099	+	5.77922i	−0.754525	+	0.435625i
$177$		0			0
$178$	−7.61146	+	4.39448i	−0.570503	+	0.329380i
$179$	−1.11559	−	0.644084i	−0.0833829	−	0.0481411i	0.457729	−	0.889092i	$-0.348663\pi$
$179$	−1.11559	−	0.644084i	−0.0833829	−	0.0481411i	−0.541112	+	0.840951i	$0.681996\pi$
$180$		0			0
$181$		−	20.5194i		−	1.52520i	−0.646873	−	0.762598i	$-0.723924\pi$
$181$		−	20.5194i		−	1.52520i	0.646873	−	0.762598i	$-0.276076\pi$
$182$	1.26658	+	12.5457i	0.0938852	+	0.929949i
$183$		0			0
$184$	7.65430	−	13.2576i	0.564283	−	0.977366i
$185$	0.182893	−	0.316779i	0.0134465	−	0.0232901i
$186$		0			0
$187$		−	22.1607i		−	1.62055i
$188$	0.0955842	+	0.165557i	0.00697120	+	0.0120745i
$189$		0			0
$190$	−0.112568			−0.00816651
$191$	−14.4453	+	8.34001i	−1.04523	+	0.603462i	−0.921309	−	0.388830i	$-0.872879\pi$
$191$	−14.4453	+	8.34001i	−1.04523	+	0.603462i	−0.123918	+	0.992292i	$0.539546\pi$
$192$		0			0
$193$	9.88608	−	17.1232i	0.711616	−	1.23255i	−0.252634	−	0.967562i	$-0.581297\pi$
$193$	9.88608	−	17.1232i	0.711616	−	1.23255i	0.964250	−	0.264993i	$-0.0853697\pi$
$194$	24.8095			1.78122
$195$		0			0
$196$	−0.503551	−	1.69616i	−0.0359679	−	0.121154i
$197$	−1.02639	−	0.592587i	−0.0731273	−	0.0422200i	0.462991	−	0.886363i	$-0.346776\pi$
$197$	−1.02639	−	0.592587i	−0.0731273	−	0.0422200i	−0.536118	+	0.844143i	$0.680110\pi$
$198$		0			0
$199$	1.37964	−	0.796537i	0.0978003	−	0.0564650i	−0.450302	−	0.892876i	$-0.648684\pi$
$199$	1.37964	−	0.796537i	0.0978003	−	0.0564650i	0.548102	+	0.836411i	$0.315350\pi$
$200$		−	9.78433i		−	0.691857i
$201$		0			0
$202$	6.07918	−	3.50982i	0.427730	−	0.246950i
$203$	−16.6702	−	12.4403i	−1.17002	−	0.873141i
$204$		0			0
$205$	4.85561	−	8.41016i	0.339130	−	0.587391i
$206$	−6.96712	+	12.0674i	−0.485422	+	0.840776i
$207$		0			0
$208$	−12.0761	+	2.67664i	−0.837326	+	0.185591i
$209$	0.219147			0.0151587
$210$		0			0
$211$	11.2007	−	19.4002i	0.771090	−	1.33557i	−0.165875	−	0.986147i	$-0.553045\pi$
$211$	11.2007	−	19.4002i	0.771090	−	1.33557i	0.936966	−	0.349421i	$-0.113622\pi$
$212$	1.71157	−	0.988177i	0.117551	−	0.0678683i
$213$		0			0
$214$	2.01231	+	3.48542i	0.137559	+	0.238258i
$215$	−1.93671	−	3.35448i	−0.132083	−	0.228774i
$216$		0			0
$217$	−2.01990	+	17.1108i	−0.137120	+	1.16155i
$218$	13.3839	+	7.72720i	0.906473	+	0.523352i
$219$		0			0
$220$		−	1.11500i		−	0.0751731i
$221$	7.13229	−	22.6172i	0.479770	−	1.52140i
$222$		0			0
$223$	−14.5415	−	8.39554i	−0.973771	−	0.562207i	−0.0733871	−	0.997304i	$-0.523381\pi$
$223$	−14.5415	−	8.39554i	−0.973771	−	0.562207i	−0.900384	+	0.435097i	$0.856714\pi$
$224$	3.45356	−	1.48501i	0.230751	−	0.0992217i
$225$		0			0
$226$	−14.3859			−0.956936
$227$	1.70372	+	2.95092i	0.113080	+	0.195860i	0.917010	−	0.398863i	$-0.130595\pi$
$227$	1.70372	+	2.95092i	0.113080	+	0.195860i	−0.803931	+	0.594723i	$0.797262\pi$
$228$		0			0
$229$			27.6550i			1.82750i	0.406281	+	0.913748i	$0.366825\pi$
$229$			27.6550i			1.82750i	−0.406281	+	0.913748i	$0.633175\pi$
$230$	−4.44859	−	7.70519i	−0.293331	−	0.508065i
$231$		0			0
$232$	11.7054	−	20.2743i	0.768495	−	1.33107i
$233$		−	18.9462i		−	1.24121i	−0.784123	−	0.620605i	$-0.786887\pi$
$233$		−	18.9462i		−	1.24121i	0.784123	−	0.620605i	$-0.213113\pi$
$234$		0			0
$235$	0.990233			0.0645956
$236$	−0.149240	+	0.258492i	−0.00971471	+	0.0168264i
$237$		0			0
$238$	2.69671	−	22.8441i	0.174802	−	1.48076i
$239$			17.2254i			1.11422i	0.830438	+	0.557111i	$0.188090\pi$
$239$			17.2254i			1.11422i	−0.830438	+	0.557111i	$0.811910\pi$
$240$		0			0
$241$	−1.00859	+	0.582312i	−0.0649693	+	0.0375100i	−0.532133	−	0.846661i	$-0.678609\pi$
$241$	−1.00859	+	0.582312i	−0.0649693	+	0.0375100i	0.467163	+	0.884171i	$0.345276\pi$
$242$		−	0.464903i		−	0.0298851i
$243$		0			0
$244$	−0.627115	−	0.362065i	−0.0401469	−	0.0231788i
$245$	−8.91302	−	2.13408i	−0.569432	−	0.136341i
$246$		0			0
$247$	0.223661	+	0.0705310i	0.0142312	+	0.00448778i
$248$	−19.3917			−1.23138
$249$		0			0
$250$	−12.4186	−	7.16988i	−0.785421	−	0.453463i
$251$	9.50374	+	16.4610i	0.599870	+	1.03901i	0.992840	+	0.119454i	$0.0381146\pi$
$251$	9.50374	+	16.4610i	0.599870	+	1.03901i	−0.392969	+	0.919552i	$0.628552\pi$
$252$		0			0
$253$	8.66054	+	15.0005i	0.544484	+	0.943073i
$254$	11.4212	−	6.59401i	0.716627	−	0.413745i
$255$		0			0
$256$	2.98265	+	5.16611i	0.186416	+	0.322882i
$257$	−2.20103	+	3.81229i	−0.137296	+	0.237804i	−0.926472	−	0.376363i	$-0.877175\pi$
$257$	−2.20103	+	3.81229i	−0.137296	+	0.237804i	0.789176	+	0.614167i	$0.210508\pi$
$258$		0			0
$259$	−0.442082	+	0.592396i	−0.0274696	+	0.0368097i
$260$	0.358854	−	1.13796i	0.0222552	−	0.0705735i
$261$		0			0
$262$	15.6489	+	9.03489i	0.966791	+	0.558177i
$263$	−14.4688	−	8.35354i	−0.892182	−	0.515101i	−0.0175263	−	0.999846i	$-0.505579\pi$
$263$	−14.4688	−	8.35354i	−0.892182	−	0.515101i	−0.874656	+	0.484745i	$0.838912\pi$
$264$		0			0
$265$		−	10.2373i		−	0.628873i
$266$	0.225905	+	0.0266677i	0.0138511	+	0.00163510i
$267$		0			0
$268$	2.83507			0.173180
$269$	−5.81456	−	10.0711i	−0.354520	−	0.614047i	0.632516	−	0.774548i	$-0.282022\pi$
$269$	−5.81456	−	10.0711i	−0.354520	−	0.614047i	−0.987036	+	0.160501i	$0.948689\pi$
$270$		0			0
$271$	19.1167	+	11.0370i	1.16126	+	0.670453i	0.951605	−	0.307323i	$-0.0994332\pi$
$271$	19.1167	+	11.0370i	1.16126	+	0.670453i	0.209653	+	0.977776i	$0.432767\pi$
$272$	22.5643			1.36816
$273$		0			0
$274$	−0.147826			−0.00893051
$275$	9.58740	+	5.53529i	0.578142	+	0.333791i
$276$		0			0
$277$	−14.0108	−	24.2674i	−0.841826	−	1.45809i	−0.888349	−	0.459168i	$-0.848148\pi$
$277$	−14.0108	−	24.2674i	−0.841826	−	1.45809i	0.0465235	−	0.998917i	$-0.485186\pi$
$278$	8.07780			0.484474
$279$		0			0
$280$	1.20928	−	10.2439i	0.0722686	−	0.612193i
$281$			1.14834i			0.0685042i	0.999413	+	0.0342521i	$0.0109049\pi$
$281$			1.14834i			0.0685042i	−0.999413	+	0.0342521i	$0.989095\pi$
$282$		0			0
$283$	−5.49437	−	3.17218i	−0.326606	−	0.188566i	0.327727	−	0.944772i	$-0.393717\pi$
$283$	−5.49437	−	3.17218i	−0.326606	−	0.188566i	−0.654333	+	0.756206i	$0.727051\pi$
$284$	1.34453	+	0.776264i	0.0797831	+	0.0460628i
$285$		0			0
$286$	4.82927	−	15.3141i	0.285561	−	0.905542i
$287$	−11.7368	+	15.7275i	−0.692802	+	0.928364i
$288$		0			0
$289$	−13.1310	+	22.7436i	−0.772415	+	1.33786i
$290$	−6.80302	−	11.7832i	−0.399487	−	0.691932i
$291$		0			0
$292$	3.31276	−	1.91263i	0.193865	−	0.111928i
$293$	−9.42871	−	16.3310i	−0.550831	−	0.954067i	−0.998215	−	0.0597254i	$-0.980978\pi$
$293$	−9.42871	−	16.3310i	−0.550831	−	0.954067i	0.447384	−	0.894342i	$-0.352356\pi$
$294$		0			0
$295$	0.773048	+	1.33896i	0.0450086	+	0.0779572i
$296$	−0.720470	−	0.415964i	−0.0418765	−	0.0241774i
$297$		0			0
$298$	−10.2956			−0.596408
$299$	4.01111	+	18.0968i	0.231969	+	1.04657i
$300$		0			0
$301$	3.09197	+	7.19072i	0.178218	+	0.414466i
$302$	−15.9484	−	9.20780i	−0.917726	−	0.529849i
$303$		0			0
$304$			0.223138i			0.0127978i
$305$	−3.24839	+	1.87546i	−0.186002	+	0.107389i
$306$		0			0
$307$			12.6720i			0.723228i	0.932328	+	0.361614i	$0.117774\pi$
$307$			12.6720i			0.723228i	−0.932328	+	0.361614i	$0.882226\pi$
$308$	−0.264148	+	2.23762i	−0.0150512	+	0.127500i
$309$		0			0
$310$	−5.63512	+	9.76032i	−0.320054	+	0.554349i
$311$	14.7255			0.835006			0.417503	−	0.908675i	$-0.362905\pi$
$311$	14.7255			0.835006			0.417503	+	0.908675i	$0.362905\pi$
$312$		0			0
$313$		−	20.6379i		−	1.16652i	−0.812285	−	0.583261i	$-0.801776\pi$
$313$		−	20.6379i		−	1.16652i	0.812285	−	0.583261i	$-0.198224\pi$
$314$	1.59829	−	2.76833i	0.0901969	−	0.156226i
$315$		0			0
$316$	1.16331	+	2.01492i	0.0654415	+	0.113348i
$317$			12.4579i			0.699705i	0.936805	+	0.349852i	$0.113768\pi$
$317$			12.4579i			0.699705i	−0.936805	+	0.349852i	$0.886232\pi$
$318$		0			0
$319$	13.2442	+	22.9396i	0.741531	+	1.28437i
$320$	11.4422			0.639640
$321$		0			0
$322$	7.10220	+	16.5169i	0.395790	+	0.920453i
$323$	−0.370501	−	0.213909i	−0.0206152	−	0.0119022i
$324$		0			0
$325$	8.00338	+	8.73494i	0.443948	+	0.484528i
$326$			17.0768i			0.945797i
$327$		0			0
$328$	−19.1277	−	11.0434i	−1.05615	−	0.609770i
$329$	−1.98723	−	0.234590i	−0.109560	−	0.0129334i
$330$		0			0
$331$	14.8809	+	25.7746i	0.817931	+	1.41670i	0.907204	+	0.420690i	$0.138212\pi$
$331$	14.8809	+	25.7746i	0.817931	+	1.41670i	−0.0892735	+	0.996007i	$0.528455\pi$
$332$	−1.81884	−	3.15032i	−0.0998217	−	0.172896i
$333$		0			0
$334$	−18.5466	+	10.7079i	−1.01482	+	0.585908i
$335$	7.34269	−	12.7179i	0.401174	−	0.694854i
$336$		0			0
$337$	−19.5283			−1.06377			−0.531887	−	0.846815i	$-0.678517\pi$
$337$	−19.5283			−1.06377			−0.531887	+	0.846815i	$0.678517\pi$
$338$	9.85749	−	14.0753i	0.536177	−	0.765594i
$339$		0			0
$340$	−1.08835	+	1.88507i	−0.0590238	+	0.102232i
$341$	10.9705	−	19.0014i	0.594085	−	1.02899i
$342$		0			0
$343$	17.3814	+	6.39429i	0.938507	+	0.345259i
$344$	−7.62931	+	4.40478i	−0.411345	+	0.237490i
$345$		0			0
$346$			31.9114i			1.71557i
$347$	7.55802	−	4.36362i	0.405736	−	0.234252i	−0.283220	−	0.959055i	$-0.591403\pi$
$347$	7.55802	−	4.36362i	0.405736	−	0.234252i	0.688956	+	0.724803i	$0.258069\pi$
$348$		0			0
$349$	−3.23204	−	1.86602i	−0.173007	−	0.0998856i	0.410996	−	0.911637i	$-0.365181\pi$
$349$	−3.23204	−	1.86602i	−0.173007	−	0.0998856i	−0.584003	+	0.811752i	$0.698514\pi$
$350$	9.20945	+	6.87265i	0.492266	+	0.367359i
$351$		0			0
$352$	−4.78728			−0.255163
$353$	−15.4362	+	26.7362i	−0.821584	+	1.42303i	0.0829179	+	0.996556i	$0.473576\pi$
$353$	−15.4362	+	26.7362i	−0.821584	+	1.42303i	−0.904502	+	0.426469i	$0.859757\pi$
$354$		0			0
$355$	6.96452	−	4.02097i	0.369638	−	0.213411i
$356$	−1.68063			−0.0890733
$357$		0			0
$358$	0.851371	+	1.47462i	0.0449964	+	0.0779360i
$359$			6.82463i			0.360190i	0.983649	+	0.180095i	$0.0576405\pi$
$359$			6.82463i			0.360190i	−0.983649	+	0.180095i	$0.942359\pi$
$360$		0			0
$361$	−9.49788	+	16.4508i	−0.499889	+	0.865833i
$362$	−13.5616	+	23.4894i	−0.712782	+	1.23457i
$363$		0			0
$364$	−0.989750	+	2.19869i	−0.0518770	+	0.115243i
$365$		−	19.8144i		−	1.03713i
$366$		0			0
$367$	16.7082	+	9.64648i	0.872161	+	0.503542i	0.868066	−	0.496449i	$-0.165363\pi$
$367$	16.7082	+	9.64648i	0.872161	+	0.503542i	0.00409495	+	0.999992i	$0.498697\pi$
$368$	−15.2737	+	8.81826i	−0.796195	+	0.459684i
$369$		0			0
$370$	−0.418729	+	0.241753i	−0.0217687	+	0.0125682i
$371$	−2.42526	+	20.5446i	−0.125913	+	1.06662i
$372$		0			0
$373$	−3.51227	−	6.08342i	−0.181858	−	0.314988i	0.760655	−	0.649156i	$-0.224878\pi$
$373$	−3.51227	−	6.08342i	−0.181858	−	0.314988i	−0.942513	+	0.334169i	$0.891545\pi$
$374$	−14.6464	+	25.3683i	−0.757347	+	1.31176i
$375$		0			0
$376$		−	2.25215i		−	0.116146i
$377$	6.13401	+	27.6746i	0.315918	+	1.42531i
$378$		0			0
$379$	−0.414538	+	0.718001i	−0.0212934	+	0.0368812i	−0.876476	−	0.481446i	$-0.840112\pi$
$379$	−0.414538	+	0.718001i	−0.0212934	+	0.0368812i	0.855182	+	0.518327i	$0.173445\pi$
$380$	−0.0186414	−	0.0107626i	−0.000956284	−	0.000552111i
$381$		0			0
$382$	22.0482			1.12808
$383$	−4.27638	−	7.40690i	−0.218513	−	0.378475i	0.735841	−	0.677155i	$-0.236787\pi$
$383$	−4.27638	−	7.40690i	−0.218513	−	0.378475i	−0.954353	+	0.298680i	$0.903454\pi$
$384$		0			0
$385$	9.35364	+	6.98025i	0.476706	+	0.355747i
$386$	−22.6340	+	13.0677i	−1.15204	+	0.665130i
$387$		0			0
$388$	4.10851	+	2.37205i	0.208578	+	0.120422i
$389$			10.3501i			0.524771i	0.964963	+	0.262385i	$0.0845092\pi$
$389$			10.3501i			0.524771i	−0.964963	+	0.262385i	$0.915491\pi$
$390$		0			0
$391$		−	33.8141i		−	1.71005i
$392$	−4.85367	+	20.2714i	−0.245147	+	1.02386i
$393$		0			0
$394$	0.783300	+	1.35671i	0.0394621	+	0.0683503i
$395$	12.0517			0.606386
$396$		0			0
$397$	−8.41998	+	4.86128i	−0.422587	+	0.243981i	−0.696184	−	0.717864i	$-0.745120\pi$
$397$	−8.41998	+	4.86128i	−0.422587	+	0.243981i	0.273597	+	0.961845i	$0.411787\pi$
$398$	−2.10578			−0.105553
$399$		0			0
$400$	−5.63610	+	9.76201i	−0.281805	+	0.488100i
$401$	−7.87854	−	4.54868i	−0.393435	−	0.227150i	0.290212	−	0.956962i	$-0.406274\pi$
$401$	−7.87854	−	4.54868i	−0.393435	−	0.227150i	−0.683648	+	0.729812i	$0.739607\pi$
$402$		0			0
$403$	17.3119	−	15.8620i	0.862369	−	0.790145i
$404$	1.34230			0.0667819
$405$		0			0
$406$	10.8611	+	25.2586i	0.539026	+	1.25356i
$407$	0.815184	−	0.470647i	0.0404072	−	0.0233291i
$408$		0			0
$409$	11.4905	−	6.63403i	0.568167	−	0.328031i	−0.188250	−	0.982121i	$-0.560281\pi$
$409$	11.4905	−	6.63403i	0.568167	−	0.328031i	0.756417	+	0.654090i	$0.226948\pi$
$410$	−11.1168	+	6.41829i	−0.549020	+	0.316977i
$411$		0			0
$412$	−2.30754	+	1.33226i	−0.113684	+	0.0656356i
$413$	−1.23418	−	2.87021i	−0.0607298	−	0.141234i
$414$		0			0
$415$	−18.8428			−0.924956
$416$	−4.88588	−	1.54075i	−0.239550	−	0.0755417i
$417$		0			0
$418$	−0.250866	−	0.144838i	−0.0122703	−	0.00708425i
$419$	11.3849	−	19.7193i	0.556191	−	0.963351i	−0.441619	−	0.897203i	$-0.645596\pi$
$419$	11.3849	−	19.7193i	0.556191	−	0.963351i	0.997810	−	0.0661483i	$-0.0210710\pi$
$420$		0			0
$421$	−24.2167			−1.18025			−0.590124	−	0.807312i	$-0.700921\pi$
$421$	−24.2167			−1.18025			−0.590124	+	0.807312i	$0.700921\pi$
$422$	−25.6439	+	14.8055i	−1.24832	+	0.720720i
$423$		0			0
$424$	−23.2833			−1.13074
$425$	−10.8060	−	18.7165i	−0.524166	−	0.907883i
$426$		0			0
$427$	6.96329	−	2.99418i	0.336977	−	0.144899i
$428$			0.769590i			0.0371995i
$429$		0			0
$430$			5.12002i			0.246909i
$431$	11.7531	+	6.78565i	0.566126	+	0.326853i	0.755601	−	0.655032i	$-0.227345\pi$
$431$	11.7531	+	6.78565i	0.566126	+	0.326853i	−0.189474	+	0.981886i	$0.560678\pi$
$432$		0			0
$433$	0.579129	−	0.334360i	0.0278311	−	0.0160683i	−0.486020	−	0.873948i	$-0.661552\pi$
$433$	0.579129	−	0.334360i	0.0278311	−	0.0160683i	0.513851	+	0.857879i	$0.328218\pi$
$434$	13.6210	−	18.2524i	0.653830	−	0.876142i
$435$		0			0
$436$	1.47760	+	2.55928i	0.0707643	+	0.122567i
$437$	0.334387			0.0159959
$438$		0			0
$439$	27.3223	+	15.7745i	1.30402	+	0.752877i	0.981091	−	0.193546i	$-0.0619989\pi$
$439$	27.3223	+	15.7745i	1.30402	+	0.752877i	0.322930	+	0.946423i	$0.395332\pi$
$440$	−6.56786	+	11.3759i	−0.313111	+	0.542323i
$441$		0			0
$442$	−23.1127	+	21.1770i	−1.09936	+	1.00729i
$443$			0.791020i			0.0375825i	0.999823	+	0.0187913i	$0.00598179\pi$
$443$			0.791020i			0.0375825i	−0.999823	+	0.0187913i	$0.994018\pi$
$444$		0			0
$445$	−4.35275	+	7.53918i	−0.206340	+	0.357391i
$446$	11.0975	+	19.2214i	0.525481	+	0.910160i
$447$		0			0
$448$	−22.9627	−	2.71072i	−1.08488	−	0.128069i
$449$	14.2261	−	8.21344i	0.671371	−	0.387616i	−0.125225	−	0.992128i	$-0.539965\pi$
$449$	14.2261	−	8.21344i	0.671371	−	0.387616i	0.796596	+	0.604512i	$0.206632\pi$
$450$		0			0
$451$	21.6423	−	12.4952i	1.01909	−	0.588375i
$452$	−2.38233	−	1.37544i	−0.112056	−	0.0646953i
$453$		0			0
$454$		−	4.50405i		−	0.211386i
$455$	7.29975	+	10.1344i	0.342218	+	0.475110i
$456$		0			0
$457$	9.30367	−	16.1144i	0.435207	−	0.753801i	−0.562105	−	0.827066i	$-0.690008\pi$
$457$	9.30367	−	16.1144i	0.435207	−	0.753801i	0.997313	+	0.0732646i	$0.0233418\pi$
$458$	18.2776	−	31.6578i	0.854058	−	1.47927i
$459$		0			0
$460$		−	1.70133i		−	0.0793247i
$461$	−6.90102	−	11.9529i	−0.321413	−	0.556703i	0.659367	−	0.751821i	$-0.270824\pi$
$461$	−6.90102	−	11.9529i	−0.321413	−	0.556703i	−0.980780	+	0.195118i	$0.937491\pi$
$462$		0			0
$463$	22.5162			1.04642			0.523209	−	0.852205i	$-0.324735\pi$
$463$	22.5162			1.04642			0.523209	+	0.852205i	$0.324735\pi$
$464$	−23.3573	+	13.4854i	−1.08434	+	0.626042i
$465$		0			0
$466$	−12.5219	+	21.6885i	−0.580064	+	1.00470i
$467$	18.1874			0.841613			0.420806	−	0.907150i	$-0.361747\pi$
$467$	18.1874			0.841613			0.420806	+	0.907150i	$0.361747\pi$
$468$		0			0
$469$	−17.7485	+	23.7832i	−0.819550	+	1.09821i
$470$	−1.13356	−	0.654460i	−0.0522872	−	0.0301880i
$471$		0			0
$472$	3.04528	−	1.75819i	0.140170	−	0.0809273i
$473$		−	9.96767i		−	0.458314i
$474$		0			0
$475$	0.185087	−	0.106860i	0.00849236	−	0.00490307i
$476$	2.63071	−	3.52519i	0.120578	−	0.161577i
$477$		0			0
$478$	11.3846	−	19.7187i	0.520718	−	0.901910i
$479$	−10.2154	+	17.6936i	−0.466753	+	0.808439i	−0.999279	−	0.0379744i	$-0.987909\pi$
$479$	−10.2154	+	17.6936i	−0.466753	+	0.808439i	0.532526	+	0.846414i	$0.321243\pi$
$480$		0			0
$481$	0.983449	−	0.217979i	0.0448414	−	0.00993899i
$482$	1.53944			0.0701195
$483$		0			0
$484$	0.0444495	−	0.0769888i	0.00202043	−	0.00349949i
$485$	21.2816	−	12.2870i	0.966349	−	0.557922i
$486$		0			0
$487$	8.16005	+	14.1336i	0.369767	+	0.640455i	0.989529	−	0.144335i	$-0.0461042\pi$
$487$	8.16005	+	14.1336i	0.369767	+	0.640455i	−0.619762	+	0.784790i	$0.712771\pi$
$488$	4.26547	+	7.38801i	0.193089	+	0.334440i
$489$		0			0
$490$	8.79264	+	8.33373i	0.397211	+	0.376479i
$491$	−0.161853	−	0.0934461i	−0.00730434	−	0.00421716i	0.496343	−	0.868126i	$-0.334676\pi$
$491$	−0.161853	−	0.0934461i	−0.00730434	−	0.00421716i	−0.503648	+	0.863909i	$0.668009\pi$
$492$		0			0
$493$		−	51.7104i		−	2.32892i
$494$	−0.209418	−	0.228561i	−0.00942218	−	0.0102834i
$495$		0			0
$496$	19.3475	+	11.1703i	0.868728	+	0.501560i
$497$	−14.9292	+	6.41949i	−0.669668	+	0.287954i
$498$		0			0
$499$	0.0629706			0.00281895			0.00140947	−	0.999999i	$-0.499551\pi$
$499$	0.0629706			0.00281895			0.00140947	+	0.999999i	$0.499551\pi$
$500$	−1.37103	−	2.37469i	−0.0613143	−	0.106200i
$501$		0			0
$502$		−	25.1247i		−	1.12137i
$503$	5.80083	+	10.0473i	0.258646	+	0.447989i	0.965880	−	0.258992i	$-0.0833902\pi$
$503$	5.80083	+	10.0473i	0.258646	+	0.447989i	−0.707233	+	0.706980i	$0.750057\pi$
$504$		0			0
$505$	3.47649	−	6.02145i	0.154702	−	0.267951i
$506$		−	22.8956i		−	1.01783i
$507$		0			0
$508$	2.52182			0.111888
$509$	0.393807	−	0.682094i	0.0174552	−	0.0302333i	−0.857166	−	0.515040i	$-0.827777\pi$
$509$	0.393807	−	0.682094i	0.0174552	−	0.0302333i	0.874621	+	0.484807i	$0.161110\pi$
$510$		0			0
$511$	−4.69412	+	39.7642i	−0.207656	+	1.75907i
$512$		−	25.3055i		−	1.11835i
$513$		0			0
$514$	5.03921	−	2.90939i	0.222270	−	0.128328i
$515$			13.8019i			0.608185i
$516$		0			0
$517$	2.20682	+	1.27411i	0.0970557	+	0.0560352i
$518$	0.897593	−	0.385960i	0.0394380	−	0.0169581i
$519$		0			0
$520$	−10.3644	+	9.49636i	−0.454509	+	0.416443i
$521$	−24.7302			−1.08345			−0.541725	−	0.840555i	$-0.682229\pi$
$521$	−24.7302			−1.08345			−0.541725	+	0.840555i	$0.682229\pi$
$522$		0			0
$523$	−6.02874	−	3.48069i	−0.263618	−	0.152200i	0.362366	−	0.932036i	$-0.381969\pi$
$523$	−6.02874	−	3.48069i	−0.263618	−	0.152200i	−0.625984	+	0.779836i	$0.715302\pi$
$524$	1.72766	+	2.99239i	0.0754731	+	0.130723i
$525$		0			0
$526$	11.0420	+	19.1253i	0.481453	+	0.833901i
$527$	−37.0945	+	21.4165i	−1.61586	+	0.932919i
$528$		0			0
$529$	1.71474	+	2.97002i	0.0745540	+	0.129131i
$530$	−6.76600	+	11.7190i	−0.293896	+	0.509043i
$531$		0			0
$532$	0.0348605	+	0.0260150i	0.00151140	+	0.00112790i
$533$	26.1095	−	5.78712i	1.13093	−	0.250668i
$534$		0			0
$535$	3.45232	+	1.99320i	0.149257	+	0.0861735i
$536$	−28.9251	−	16.6999i	−1.24937	−	0.721327i
$537$		0			0
$538$			15.3717i			0.662723i
$539$	−17.1176	−	16.2241i	−0.737306	−	0.698823i
$540$		0			0
$541$	25.8850			1.11289			0.556443	−	0.830886i	$-0.312166\pi$
$541$	25.8850			1.11289			0.556443	+	0.830886i	$0.312166\pi$
$542$	−14.5891	−	25.2691i	−0.626656	−	1.08540i
$543$		0			0
$544$	8.09362	+	4.67285i	0.347011	+	0.200347i
$545$	15.3076			0.655707
$546$		0			0
$547$	33.0051			1.41120			0.705599	−	0.708611i	$-0.250678\pi$
$547$	33.0051			1.41120			0.705599	+	0.708611i	$0.250678\pi$
$548$	−0.0244803	−	0.0141337i	−0.00104575	−	0.000603763i
$549$		0			0
$550$	−7.31672	−	12.6729i	−0.311986	−	0.540376i
$551$	0.511362			0.0217848
$552$		0			0
$553$	−24.1858	−	2.85510i	−1.02848	−	0.121411i
$554$			37.0398i			1.57367i
$555$		0			0
$556$	1.33770	+	0.772321i	0.0567311	+	0.0327537i
$557$	−9.14688	−	5.28095i	−0.387566	−	0.223761i	0.293539	−	0.955947i	$-0.405167\pi$
$557$	−9.14688	−	5.28095i	−0.387566	−	0.223761i	−0.681105	+	0.732186i	$0.738500\pi$
$558$		0			0
$559$	3.20803	−	10.1730i	0.135685	−	0.430271i
$560$	−7.10737	+	9.52398i	−0.300341	+	0.402462i
$561$		0			0
$562$	0.758956	−	1.31455i	0.0320146	−	0.0554509i
$563$	9.35498	+	16.2033i	0.394265	+	0.682887i	0.993007	−	0.118055i	$-0.0376658\pi$
$563$	9.35498	+	16.2033i	0.394265	+	0.682887i	−0.598742	+	0.800942i	$0.704332\pi$
$564$		0			0
$565$	−12.3402	+	7.12464i	−0.519158	+	0.299736i
$566$	4.19308	+	7.26263i	0.176248	+	0.305271i
$567$		0			0
$568$	−9.14513	−	15.8398i	−0.383721	−	0.664624i
$569$	−19.3477	−	11.1704i	−0.811096	−	0.468287i	0.0362402	−	0.999343i	$-0.488462\pi$
$569$	−19.3477	−	11.1704i	−0.811096	−	0.468287i	−0.847336	+	0.531057i	$0.821795\pi$
$570$		0			0
$571$	−22.2537			−0.931288			−0.465644	−	0.884972i	$-0.654177\pi$
$571$	−22.2537			−0.931288			−0.465644	+	0.884972i	$0.654177\pi$
$572$	2.26393	−	2.07432i	0.0946595	−	0.0867316i
$573$		0			0
$574$	23.8301	−	10.2468i	0.994651	−	0.427695i
$575$	14.6290	+	8.44606i	0.610072	+	0.352225i
$576$		0			0
$577$		−	30.2165i		−	1.25793i	−0.777434	−	0.628964i	$-0.783479\pi$
$577$		−	30.2165i		−	1.25793i	0.777434	−	0.628964i	$-0.216521\pi$
$578$	30.0633	−	17.3570i	1.25047	−	0.721957i
$579$		0			0
$580$		−	2.60176i		−	0.108032i
$581$	37.8144	+	4.46394i	1.56880	+	0.185195i
$582$		0			0
$583$	13.1721	−	22.8147i	0.545532	−	0.944889i
$584$	−45.0651			−1.86481
$585$		0			0
$586$			24.9263i			1.02970i
$587$	−8.19032	+	14.1861i	−0.338051	+	0.585521i	−0.984066	−	0.177803i	$-0.943101\pi$
$587$	−8.19032	+	14.1861i	−0.338051	+	0.585521i	0.646015	+	0.763324i	$0.276434\pi$
$588$		0			0
$589$	−0.211787	−	0.366827i	−0.00872655	−	0.0151148i
$590$		−	2.04368i		−	0.0841369i
$591$		0			0
$592$	0.479218	+	0.830029i	0.0196957	+	0.0341140i
$593$	−27.8771			−1.14478			−0.572389	−	0.819983i	$-0.693983\pi$
$593$	−27.8771			−1.14478			−0.572389	+	0.819983i	$0.693983\pi$
$594$		0			0
$595$	−9.00032	−	20.9312i	−0.368977	−	0.858097i
$596$	−1.70497	−	0.984366i	−0.0698383	−	0.0403212i
$597$		0			0
$598$	7.36878	−	23.3671i	0.301332	−	0.955553i
$599$			40.8707i			1.66993i	0.550302	+	0.834966i	$0.314513\pi$
$599$			40.8707i			1.66993i	−0.550302	+	0.834966i	$0.685487\pi$
$600$		0			0
$601$	5.50215	+	3.17667i	0.224438	+	0.129579i	0.608003	−	0.793934i	$-0.291971\pi$
$601$	5.50215	+	3.17667i	0.224438	+	0.129579i	−0.383566	+	0.923514i	$0.625304\pi$
$602$	1.21295	−	10.2750i	0.0494363	−	0.418779i
$603$		0			0
$604$	−1.76072	−	3.04966i	−0.0716428	−	0.124089i
$605$	−0.230244	−	0.398794i	−0.00936074	−	0.0162133i
$606$		0			0
$607$	−40.2254	+	23.2241i	−1.63270	+	0.942639i	−0.649441	+	0.760412i	$0.724997\pi$
$607$	−40.2254	+	23.2241i	−1.63270	+	0.942639i	−0.983256	+	0.182227i	$0.941669\pi$
$608$	−0.0462097	+	0.0800375i	−0.00187405	+	0.00324595i
$609$		0			0
$610$	4.95808			0.200747
$611$	1.84221	+	2.01060i	0.0745278	+	0.0813401i
$612$		0			0
$613$	10.0681	−	17.4384i	0.406646	−	0.704331i	−0.587866	−	0.808959i	$-0.700032\pi$
$613$	10.0681	−	17.4384i	0.406646	−	0.704331i	0.994512	+	0.104627i	$0.0333649\pi$
$614$	8.37511	−	14.5061i	0.337992	−	0.585419i
$615$		0			0
$616$	15.8756	−	21.2735i	0.639647	−	0.857136i
$617$	−36.2628	+	20.9363i	−1.45988	+	0.842864i	−0.999005	−	0.0445990i	$-0.985799\pi$
$617$	−36.2628	+	20.9363i	−1.45988	+	0.842864i	−0.460879	+	0.887463i	$0.652466\pi$
$618$		0			0
$619$		−	38.2082i		−	1.53572i	−0.640620	−	0.767858i	$-0.721322\pi$
$619$		−	38.2082i		−	1.53572i	0.640620	−	0.767858i	$-0.278678\pi$
$620$	−1.86638	+	1.07755i	−0.0749554	+	0.0432755i
$621$		0			0
$622$	−16.8569	−	9.73231i	−0.675898	−	0.390230i
$623$	10.5213	−	14.0987i	0.421527	−	0.564853i
$624$		0			0
$625$	2.22536			0.0890146
$626$	−13.6399	+	23.6250i	−0.545160	+	0.944245i
$627$		0			0
$628$	0.529361	−	0.305627i	0.0211238	−	0.0121958i
$629$	−1.83759			−0.0732694
$630$		0			0
$631$	−8.66592	−	15.0098i	−0.344985	−	0.597531i	0.640366	−	0.768070i	$-0.278783\pi$
$631$	−8.66592	−	15.0098i	−0.344985	−	0.597531i	−0.985351	+	0.170539i	$0.945449\pi$
$632$		−	27.4099i		−	1.09031i
$633$		0			0
$634$	8.23361	−	14.2610i	0.326999	−	0.566378i
$635$	6.53139	−	11.3127i	0.259190	−	0.448931i
$636$		0			0
$637$	−12.2485	−	22.0675i	−0.485304	−	0.874346i
$638$		−	35.0131i		−	1.38618i
$639$		0			0
$640$	−9.87619	−	5.70202i	−0.390391	−	0.225392i
$641$	−16.6407	+	9.60749i	−0.657267	+	0.379473i	−0.791235	−	0.611513i	$-0.790561\pi$
$641$	−16.6407	+	9.60749i	−0.657267	+	0.379473i	0.133968	+	0.990986i	$0.457228\pi$
$642$		0			0
$643$	−12.3203	+	7.11311i	−0.485864	+	0.280514i	−0.722857	−	0.690998i	$-0.757171\pi$
$643$	−12.3203	+	7.11311i	−0.485864	+	0.280514i	0.236993	+	0.971511i	$0.423838\pi$
$644$	−0.403052	+	3.41428i	−0.0158825	+	0.134542i
$645$		0			0
$646$	0.282751	+	0.489740i	0.0111247	+	0.0192686i
$647$	20.4711	−	35.4570i	0.804802	−	1.39396i	−0.111623	−	0.993751i	$-0.535605\pi$
$647$	20.4711	−	35.4570i	0.804802	−	1.39396i	0.916425	−	0.400207i	$-0.131062\pi$
$648$		0			0
$649$			3.97865i			0.156176i
$650$	−3.38873	−	15.2888i	−0.132917	−	0.599676i
$651$		0			0
$652$	−1.63272	+	2.82795i	−0.0639422	+	0.110751i
$653$	36.9339	+	21.3238i	1.44533	+	0.834464i	0.998198	−	0.0600027i	$-0.0191109\pi$
$653$	36.9339	+	21.3238i	1.44533	+	0.834464i	0.447135	+	0.894466i	$0.352444\pi$
$654$		0			0
$655$	17.8982			0.699340
$656$	12.7227	+	22.0364i	0.496739	+	0.860377i
$657$		0			0
$658$	2.11982	+	1.58194i	0.0826392	+	0.0616704i
$659$	−33.4146	+	19.2919i	−1.30165	+	0.751507i	−0.980687	−	0.195586i	$-0.937339\pi$
$659$	−33.4146	+	19.2919i	−1.30165	+	0.751507i	−0.320961	+	0.947092i	$0.604006\pi$
$660$		0			0
$661$	−10.1613	−	5.86664i	−0.395229	−	0.228186i	0.289194	−	0.957270i	$-0.406613\pi$
$661$	−10.1613	−	5.86664i	−0.395229	−	0.228186i	−0.684424	+	0.729085i	$0.739946\pi$
$662$		−	39.3402i		−	1.52900i
$663$		0			0
$664$			42.8553i			1.66311i
$665$	0.206988	−	0.0890040i	0.00802667	−	0.00345143i
$666$		0			0
$667$	20.2087	+	35.0025i	0.782484	+	1.35530i
$668$	−4.09513			−0.158445
$669$		0			0
$670$	−16.8109	+	9.70580i	−0.649463	+	0.374968i
$671$	−9.65242			−0.372628
$672$		0			0
$673$	0.415228	−	0.719196i	0.0160059	−	0.0277230i	−0.857912	−	0.513797i	$-0.828238\pi$
$673$	0.415228	−	0.719196i	0.0160059	−	0.0277230i	0.873917	+	0.486074i	$0.161572\pi$
$674$	22.3548	+	12.9066i	0.861076	+	0.497142i
$675$		0			0
$676$	2.97816	−	1.38841i	0.114545	−	0.0534006i
$677$	15.2165			0.584818			0.292409	−	0.956293i	$-0.405543\pi$
$677$	15.2165			0.584818			0.292409	+	0.956293i	$0.405543\pi$
$678$		0			0
$679$	−45.6196	+	19.6162i	−1.75072	+	0.752800i
$680$	22.2079	−	12.8217i	0.851635	−	0.491691i
$681$		0			0
$682$	−25.1167	+	14.5011i	−0.961768	+	0.555277i
$683$	38.8161	−	22.4105i	1.48526	−	0.857514i	0.485399	−	0.874293i	$-0.338674\pi$
$683$	38.8161	−	22.4105i	1.48526	−	0.857514i	0.999859	+	0.0167786i	$0.00534106\pi$
$684$		0			0
$685$	−0.126806	+	0.0732112i	−0.00484499	+	0.00279726i
$686$	−15.6711	−	18.8074i	−0.598325	−	0.718071i
$687$		0			0
$688$	10.1492			0.386935
$689$	20.7861	−	19.0453i	0.791889	−	0.725568i
$690$		0			0
$691$	6.33694	+	3.65863i	0.241068	+	0.139181i	0.615668	−	0.788006i	$-0.288886\pi$
$691$	6.33694	+	3.65863i	0.241068	+	0.139181i	−0.374599	+	0.927187i	$0.622220\pi$
$692$	−3.05106	+	5.28459i	−0.115984	+	0.200890i
$693$		0			0
$694$	−11.5359			−0.437899
$695$	6.92915	−	4.00054i	0.262837	−	0.151749i
$696$		0			0
$697$	−48.7860			−1.84790
$698$	2.46656	+	4.27221i	0.0933607	+	0.161705i
$699$		0			0
$700$	0.868007	+	2.01864i	0.0328076	+	0.0762976i
$701$		−	10.0782i		−	0.380649i	−0.981721	−	0.190325i	$-0.939046\pi$
$701$		−	10.0782i		−	0.380649i	0.981721	−	0.190325i	$-0.0609541\pi$
$702$		0			0
$703$		−	0.0181719i		−	0.000685364i
$704$	25.5000	+	14.7224i	0.961067	+	0.554872i
$705$		0			0
$706$	35.3408	−	20.4040i	1.33007	−	0.767915i
$707$	−8.40325	+	11.2605i	−0.316037	+	0.423494i
$708$		0			0
$709$	−12.2179	−	21.1620i	−0.458852	−	0.794755i	0.540048	−	0.841634i	$-0.318406\pi$
$709$	−12.2179	−	21.1620i	−0.458852	−	0.794755i	−0.998901	+	0.0468785i	$0.985073\pi$
$710$	−10.6301			−0.398940
$711$		0			0
$712$	17.1468	+	9.89971i	0.642604	+	0.371007i
$713$	16.7394	−	28.9935i	0.626895	−	1.08581i
$714$		0			0
$715$	−3.44178	−	15.5282i	−0.128715	−	0.580721i
$716$			0.325600i			0.0121682i
$717$		0			0
$718$	4.51050	−	7.81242i	0.168330	−	0.291557i
$719$	10.6404	+	18.4298i	0.396821	+	0.687314i	0.993332	−	0.115291i	$-0.0367800\pi$
$719$	10.6404	+	18.4298i	0.396821	+	0.687314i	−0.596511	+	0.802605i	$0.703447\pi$
$720$		0			0
$721$	3.26973	−	27.6982i	0.121771	−	1.03153i
$722$	21.7452	−	12.5546i	0.809273	−	0.467234i
$723$		0			0
$724$	−4.49166	+	2.59326i	−0.166931	+	0.0963777i
$725$	22.3715	+	12.9162i	0.830855	+	0.479694i
$726$		0			0
$727$		−	14.5929i		−	0.541219i	−0.962689	−	0.270610i	$-0.912775\pi$
$727$		−	14.5929i		−	0.541219i	0.962689	−	0.270610i	$-0.0872253\pi$
$728$	23.0494	−	16.6023i	0.854266	−	0.615321i
$729$		0			0
$730$	−13.0956	+	22.6823i	−0.484692	+	0.839511i
$731$	−9.72942	+	16.8518i	−0.359856	+	0.623288i
$732$		0			0
$733$			35.1769i			1.29929i	0.760238	+	0.649644i	$0.225082\pi$
$733$			35.1769i			1.29929i	−0.760238	+	0.649644i	$0.774918\pi$
$734$	−12.7510	−	22.0854i	−0.470649	−	0.815188i
$735$		0			0
$736$	−7.30470			−0.269255
$737$	32.7276	−	18.8953i	1.20554	−	0.696017i
$738$		0			0
$739$	−5.28004	+	9.14529i	−0.194229	+	0.336415i	−0.946648	−	0.322271i	$-0.895554\pi$
$739$	−5.28004	+	9.14529i	−0.194229	+	0.336415i	0.752418	+	0.658686i	$0.228887\pi$
$740$	−0.0924565			−0.00339877
$741$		0			0
$742$	16.3545	−	21.9153i	0.600394	−	0.804536i
$743$	16.9373	+	9.77874i	0.621368	+	0.358747i	0.777402	−	0.629005i	$-0.216537\pi$
$743$	16.9373	+	9.77874i	0.621368	+	0.358747i	−0.156033	+	0.987752i	$0.549871\pi$
$744$		0			0
$745$	−8.83157	+	5.09891i	−0.323564	+	0.186810i
$746$			9.28525i			0.339957i
$747$		0			0
$748$	−4.85094	+	2.80069i	−0.177368	+	0.102403i
$749$	−6.45604	−	4.81789i	−0.235899	−	0.176042i
$750$		0			0
$751$	10.7724	−	18.6583i	0.393090	−	0.680852i	−0.599765	−	0.800176i	$-0.704739\pi$
$751$	10.7724	−	18.6583i	0.393090	−	0.680852i	0.992855	+	0.119324i	$0.0380726\pi$
$752$	−1.29731	+	2.24701i	−0.0473080	+	0.0819399i
$753$		0			0
$754$	11.2687	−	35.7343i	0.410383	−	1.30137i
$755$	−18.2407			−0.663848
$756$		0			0
$757$	16.1896	−	28.0413i	0.588422	−	1.01918i	−0.406017	−	0.913865i	$-0.633083\pi$
$757$	16.1896	−	28.0413i	0.588422	−	1.01918i	0.994439	−	0.105311i	$-0.0335839\pi$
$758$	0.949076	−	0.547950i	0.0344720	−	0.0199024i
$759$		0			0
$760$	0.126794	+	0.219613i	0.00459930	+	0.00796622i
$761$	−6.81501	−	11.8039i	−0.247044	−	0.427892i	0.715660	−	0.698448i	$-0.246126\pi$
$761$	−6.81501	−	11.8039i	−0.247044	−	0.427892i	−0.962704	+	0.270556i	$0.912792\pi$
$762$		0			0
$763$	−30.7199	−	3.62645i	−1.11214	−	0.131286i
$764$	3.65122	+	2.10803i	0.132097	+	0.0762660i
$765$		0			0
$766$			11.3053i			0.408477i
$767$	−1.28050	+	4.06059i	−0.0462362	+	0.146620i
$768$		0			0
$769$	13.1297	+	7.58043i	0.473469	+	0.273357i	0.717691	−	0.696362i	$-0.245199\pi$
$769$	13.1297	+	7.58043i	0.473469	+	0.273357i	−0.244222	+	0.969719i	$0.578533\pi$
$770$	−6.09412	−	14.1725i	−0.219617	−	0.510743i
$771$		0			0
$772$	−4.99764			−0.179869
$773$	−23.4901	−	40.6860i	−0.844879	−	1.46337i	−0.885726	−	0.464209i	$-0.846339\pi$
$773$	−23.4901	−	40.6860i	−0.844879	−	1.46337i	0.0408465	−	0.999165i	$-0.486995\pi$
$774$		0			0
$775$		−	21.3976i		−	0.768625i
$776$	−27.9450	−	48.4021i	−1.00317	−	1.73753i
$777$		0			0
$778$	6.84054	−	11.8482i	0.245245	−	0.424777i
$779$		−	0.482443i		−	0.0172853i
$780$		0			0
$781$	20.6947			0.740515
$782$	−22.3483	+	38.7084i	−0.799173	+	1.38421i
$783$		0			0
$784$	16.5196	−	17.4293i	0.589986	−	0.622475i
$785$		−	3.16623i		−	0.113008i
$786$		0			0
$787$	18.3763	−	10.6096i	0.655045	−	0.378190i	−0.135342	−	0.990799i	$-0.543213\pi$
$787$	18.3763	−	10.6096i	0.655045	−	0.378190i	0.790386	+	0.612609i	$0.209880\pi$
$788$			0.299566i			0.0106716i
$789$		0			0
$790$	−13.7960	−	7.96515i	−0.490841	−	0.283387i
$791$	26.4527	−	11.3745i	0.940549	−	0.404431i
$792$		0			0
$793$	−9.85124	−	3.10657i	−0.349828	−	0.110317i
$794$	12.8516			0.456086
$795$		0			0
$796$	−0.348721	−	0.201334i	−0.0123601	−	0.00713609i
$797$	−1.65800	−	2.87174i	−0.0587293	−	0.101722i	0.835166	−	0.549998i	$-0.185372\pi$
$797$	−1.65800	−	2.87174i	−0.0587293	−	0.101722i	−0.893895	+	0.448276i	$0.852038\pi$
$798$		0			0
$799$	−2.48730	−	4.30814i	−0.0879945	−	0.152411i
$800$	−4.04323	+	2.33436i	−0.142950	+	0.0825321i
$801$		0			0
$802$	6.01258	+	10.4141i	0.212312	+	0.367735i
$803$	25.4947	−	44.1581i	0.899688	−	1.55830i
$804$		0			0
$805$	14.2723	+	10.6509i	0.503033	+	0.375394i
$806$	−30.3011	+	6.71618i	−1.06731	+	0.236567i
$807$		0			0
$808$	−13.6950	−	7.90678i	−0.481787	−	0.278160i
$809$	−25.8620	−	14.9314i	−0.909260	−	0.524961i	−0.0290668	−	0.999577i	$-0.509254\pi$
$809$	−25.8620	−	14.9314i	−0.909260	−	0.524961i	−0.880193	+	0.474616i	$0.842587\pi$
$810$		0			0
$811$		−	10.9186i		−	0.383405i	−0.981453	−	0.191702i	$-0.938599\pi$
$811$		−	10.9186i		−	0.383405i	0.981453	−	0.191702i	$-0.0614008\pi$
$812$	−0.616368	+	5.22130i	−0.0216303	+	0.183232i
$813$		0			0
$814$	−1.24423			−0.0436103
$815$	8.45732	+	14.6485i	0.296247	+	0.513115i
$816$		0			0
$817$	−0.166647	−	0.0962140i	−0.00583026	−	0.00336610i
$818$	−17.5381			−0.613206
$819$		0			0
$820$	−2.45462			−0.0857191
$821$	2.33515	+	1.34820i	0.0814971	+	0.0470524i	0.540195	−	0.841540i	$-0.318351\pi$
$821$	2.33515	+	1.34820i	0.0814971	+	0.0470524i	−0.458698	+	0.888592i	$0.651684\pi$
$822$		0			0
$823$	−18.1312	−	31.4042i	−0.632015	−	1.09468i	−0.987139	−	0.159863i	$-0.948895\pi$
$823$	−18.1312	−	31.4042i	−0.632015	−	1.09468i	0.355125	−	0.934819i	$-0.384438\pi$
$824$	31.3905			1.09354
$825$		0			0
$826$	−0.484157	+	4.10133i	−0.0168460	+	0.142703i
$827$			50.2597i			1.74770i	0.486196	+	0.873850i	$0.338384\pi$
$827$			50.2597i			1.74770i	−0.486196	+	0.873850i	$0.661616\pi$
$828$		0			0
$829$	−5.06100	−	2.92197i	−0.175776	−	0.101484i	0.409531	−	0.912296i	$-0.365692\pi$
$829$	−5.06100	−	2.92197i	−0.175776	−	0.101484i	−0.585306	+	0.810812i	$0.699026\pi$
$830$	21.5701	+	12.4535i	0.748708	+	0.432267i
$831$		0			0
$832$	21.2869	+	23.2327i	0.737991	+	0.805448i
$833$	13.1035	+	44.1378i	0.454008	+	1.52928i
$834$		0			0
$835$	−10.6062	+	18.3704i	−0.367042	+	0.635735i
$836$	−0.0276960	−	0.0479708i	−0.000957885	−	0.00165911i
$837$		0			0
$838$	−26.0656	+	15.0490i	−0.900421	+	0.519858i
$839$	10.8941	+	18.8691i	0.376105	+	0.651432i	0.990492	−	0.137572i	$-0.0439300\pi$
$839$	10.8941	+	18.8691i	0.376105	+	0.651432i	−0.614387	+	0.789005i	$0.710597\pi$
$840$		0			0
$841$	16.4042	+	28.4129i	0.565663	+	0.979757i
$842$	27.7218	+	16.0052i	0.955356	+	0.551575i
$843$		0			0
$844$	−5.66223			−0.194902
$845$	1.48496	−	16.9557i	0.0510843	−	0.583294i
$846$		0			0
$847$	0.367585	+	0.854860i	0.0126304	+	0.0293733i
$848$	23.2302	+	13.4120i	0.797728	+	0.460569i
$849$		0			0
$850$			28.5673i			0.979851i
$851$	1.24385	−	0.718139i	0.0426387	−	0.0246175i
$852$		0			0
$853$			32.2378i			1.10380i	0.833910	+	0.551901i	$0.186097\pi$
$853$			32.2378i			1.10380i	−0.833910	+	0.551901i	$0.813903\pi$
$854$	−9.95006	−	1.17459i	−0.340484	−	0.0401937i
$855$		0			0
$856$	4.53325	−	7.85182i	0.154943	−	0.268370i
$857$	56.6464			1.93500			0.967502	−	0.252863i	$-0.0813722\pi$
$857$	56.6464			1.93500			0.967502	+	0.252863i	$0.0813722\pi$
$858$		0			0
$859$			45.2324i			1.54331i	0.636042	+	0.771655i	$0.280571\pi$
$859$			45.2324i			1.54331i	−0.636042	+	0.771655i	$0.719429\pi$
$860$	−0.489527	+	0.847885i	−0.0166927	+	0.0289126i
$861$		0			0
$862$	−8.96948	−	15.5356i	−0.305502	−	0.529145i
$863$		−	15.6066i		−	0.531255i	−0.964076	−	0.265628i	$-0.914421\pi$
$863$		−	15.6066i		−	0.531255i	0.964076	−	0.265628i	$-0.0855791\pi$
$864$		0			0
$865$	15.8042	+	27.3736i	0.537358	+	0.930731i
$866$	−0.883935			−0.0300373
$867$		0			0
$868$	4.00079	−	1.72032i	0.135796	−	0.0583914i
$869$	26.8582	+	15.5066i	0.911102	+	0.526025i
$870$		0			0
$871$	39.4831	−	8.75133i	1.33783	−	0.296527i
$872$		−	34.8151i		−	1.17899i
$873$		0			0
$874$	−0.382786	−	0.221002i	−0.0129479	−	0.00747549i
$875$	28.5043	+	3.36489i	0.963620	+	0.113754i
$876$		0			0
$877$	−20.8968	−	36.1944i	−0.705635	−	1.22220i	−0.966462	−	0.256811i	$-0.917328\pi$
$877$	−20.8968	−	36.1944i	−0.705635	−	1.22220i	0.260826	−	0.965386i	$-0.416005\pi$
$878$	−20.8513	−	36.1154i	−0.703696	−	1.21884i
$879$		0			0
$880$	13.1058	−	7.56661i	0.441795	−	0.255070i
$881$	−23.9467	+	41.4770i	−0.806786	+	1.39739i	0.108293	+	0.994119i	$0.465462\pi$
$881$	−23.9467	+	41.4770i	−0.806786	+	1.39739i	−0.915079	+	0.403275i	$0.867872\pi$
$882$		0			0
$883$	−12.0821			−0.406595			−0.203298	−	0.979117i	$-0.565166\pi$
$883$	−12.0821			−0.406595			−0.203298	+	0.979117i	$0.565166\pi$
$884$	−5.85224	+	1.29714i	−0.196832	+	0.0436274i
$885$		0			0
$886$	0.522798	−	0.905512i	0.0175637	−	0.0304213i
$887$	−8.55518	+	14.8180i	−0.287255	+	0.497540i	−0.973153	−	0.230157i	$-0.926076\pi$
$887$	−8.55518	+	14.8180i	−0.287255	+	0.497540i	0.685899	+	0.727697i	$0.259409\pi$
$888$		0			0
$889$	−15.7875	+	21.1554i	−0.529494	+	0.709530i
$890$	9.96552	−	5.75360i	0.334045	−	0.192861i
$891$		0			0
$892$			4.24414i			0.142104i
$893$	0.0426031	−	0.0245969i	0.00142566	−	0.000823103i
$894$		0			0
$895$	1.46061	+	0.843286i	0.0488229	+	0.0281879i
$896$	18.4691	+	13.7827i	0.617008	+	0.460449i
$897$		0			0
$898$	−21.7136			−0.724591
$899$	25.5988	−	44.3384i	0.853767	−	1.47877i
$900$		0			0
$901$	−44.5388	+	25.7145i	−1.48380	+	0.856673i
$902$	−33.0330			−1.09988
$903$		0			0
$904$	16.2040	+	28.0661i	0.538937	+	0.933466i
$905$			26.8656i			0.893043i
$906$		0			0
$907$	−24.8450	+	43.0328i	−0.824964	+	1.42888i	0.0769822	+	0.997032i	$0.475472\pi$
$907$	−24.8450	+	43.0328i	−0.824964	+	1.42888i	−0.901947	+	0.431848i	$0.857862\pi$
$908$	0.430634	−	0.745880i	0.0142911	−	0.0247529i
$909$		0			0
$910$	−1.65831	−	16.4258i	−0.0549723	−	0.544510i
$911$		−	44.9034i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$911$		−	44.9034i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$912$		0			0
$913$	−41.9927	−	24.2445i	−1.38976	−	0.802377i
$914$	−21.3006	+	12.2979i	−0.704560	+	0.406778i
$915$		0			0
$916$	6.05363	−	3.49506i	0.200018	−	0.115480i
$917$	−35.9187	−	4.24016i	−1.18614	−	0.140022i
$918$		0			0
$919$	−0.601580	−	1.04197i	−0.0198443	−	0.0343713i	0.855933	−	0.517087i	$-0.172984\pi$
$919$	−0.601580	−	1.04197i	−0.0198443	−	0.0343713i	−0.875777	+	0.482716i	$0.839650\pi$
$920$	−10.0216	+	17.3579i	−0.330403	+	0.572275i
$921$		0			0
$922$			18.2440i			0.600833i
$923$	21.1210	+	6.66045i	0.695205	+	0.219231i
$924$		0			0
$925$	0.458991	−	0.794995i	0.0150915	−	0.0261393i
$926$	−25.7752	−	14.8813i	−0.847026	−	0.489031i
$927$		0			0
$928$	−11.1707			−0.366698
$929$	−19.7940	−	34.2843i	−0.649421	−	1.12483i	−0.983261	−	0.182201i	$-0.941678\pi$
$929$	−19.7940	−	34.2843i	−0.649421	−	1.12483i	0.333840	−	0.942630i	$-0.391655\pi$
$930$		0			0
$931$	−0.436477	+	0.129580i	−0.0143050	+	0.00424681i
$932$	−4.14729	+	2.39444i	−0.135849	+	0.0784325i
$933$		0			0
$934$	−20.8198	−	12.0203i	−0.681246	−	0.393318i
$935$			29.0146i			0.948879i
$936$		0			0
$937$			12.2574i			0.400431i	0.979752	+	0.200215i	$0.0641642\pi$
$937$			12.2574i			0.400431i	−0.979752	+	0.200215i	$0.935836\pi$
$938$	36.0361	−	15.4954i	1.17662	−	0.505941i
$939$		0			0
$940$	−0.125146	−	0.216760i	−0.00408182	−	0.00706993i
$941$	−5.02126			−0.163688			−0.0818441	−	0.996645i	$-0.526081\pi$
$941$	−5.02126			−0.163688			−0.0818441	+	0.996645i	$0.526081\pi$
$942$		0			0
$943$	33.0230	−	19.0658i	1.07538	−	0.620869i
$944$	−4.05110			−0.131852
$945$		0			0
$946$	−6.58779	+	11.4104i	−0.214188	+	0.370984i
$947$	−7.04190	−	4.06565i	−0.228831	−	0.132116i	0.381202	−	0.924492i	$-0.375510\pi$
$947$	−7.04190	−	4.06565i	−0.228831	−	0.132116i	−0.610033	+	0.792376i	$0.708844\pi$
$948$		0			0
$949$	40.2318	−	36.8623i	1.30598	−	1.19660i
$950$	−0.282502			−0.00916556
$951$		0			0
$952$	−47.6052	+	20.4700i	−1.54289	+	0.663436i
$953$	15.4674	−	8.93012i	0.501039	−	0.289275i	−0.228103	−	0.973637i	$-0.573252\pi$
$953$	15.4674	−	8.93012i	0.501039	−	0.289275i	0.729143	+	0.684362i	$0.239919\pi$
$954$		0			0
$955$	18.9130	−	10.9194i	0.612009	−	0.353343i
$956$	3.77061	−	2.17697i	0.121950	−	0.0704081i
$957$		0			0
$958$	23.3879	−	13.5030i	0.755629	−	0.436262i
$959$	0.271822	−	0.116882i	0.00877759	−	0.00377432i
$960$		0			0
$961$	−11.4083			−0.368009
$962$	−1.26986	−	0.400447i	−0.0409419	−	0.0129109i
$963$		0			0
$964$	0.254934	+	0.147186i	0.00821087	+	0.00474055i
$965$	−12.9436	+	22.4190i	−0.416670	+	0.721694i
$966$		0			0
$967$	−29.2738			−0.941381			−0.470690	−	0.882298i	$-0.655995\pi$
$967$	−29.2738			−0.941381			−0.470690	+	0.882298i	$0.655995\pi$
$968$	−0.907001	+	0.523657i	−0.0291521	+	0.0168310i
$969$		0			0
$970$	−32.4826			−1.04295
$971$	18.6318	+	32.2712i	0.597922	+	1.03563i	0.993127	+	0.117039i	$0.0373401\pi$
$971$	18.6318	+	32.2712i	0.597922	+	1.03563i	−0.395205	+	0.918593i	$0.629327\pi$
$972$		0			0
$973$	−14.8534	+	6.38689i	−0.476178	+	0.204754i
$974$		−	21.5724i		−	0.691225i
$975$		0			0
$976$		−	9.82821i		−	0.314593i
$977$	14.6851	+	8.47845i	0.469818	+	0.271250i	0.716164	−	0.697932i	$-0.245896\pi$
$977$	14.6851	+	8.47845i	0.469818	+	0.271250i	−0.246345	+	0.969182i	$0.579230\pi$
$978$		0			0
$979$	−19.4009	+	11.2011i	−0.620057	+	0.357990i
$980$	0.659289	+	2.22075i	0.0210602	+	0.0709392i
$981$		0			0
$982$	0.123520	+	0.213943i	0.00394168	+	0.00682719i
$983$	17.0430			0.543587			0.271793	−	0.962356i	$-0.412383\pi$
$983$	17.0430			0.543587			0.271793	+	0.962356i	$0.412383\pi$
$984$		0			0
$985$	1.34383	+	0.775861i	0.0428180	+	0.0247210i
$986$	−34.1762	+	59.1949i	−1.08839	+	1.88515i
$987$		0			0
$988$	−0.0128273	−	0.0578727i	−0.000408092	−	0.00184117i
$989$		−	15.2092i		−	0.483626i
$990$		0			0
$991$	20.8302	−	36.0789i	0.661693	−	1.14609i	−0.318478	−	0.947930i	$-0.603172\pi$
$991$	20.8302	−	36.0789i	0.661693	−	1.14609i	0.980171	−	0.198155i	$-0.0634949\pi$
$992$	4.62651	+	8.01335i	0.146892	+	0.254424i
$993$		0			0
$994$	21.3328	+	2.51831i	0.676636	+	0.0798760i
$995$	−1.80634	+	1.04289i	−0.0572647	+	0.0330618i
$996$		0			0
$997$	26.5207	−	15.3117i	0.839920	−	0.484928i	−0.0173171	−	0.999850i	$-0.505512\pi$
$997$	26.5207	−	15.3117i	0.839920	−	0.484928i	0.857237	+	0.514922i	$0.172179\pi$
$998$	−0.0720849	−	0.0416182i	−0.00228181	−	0.00131740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dx.a.503.11	✓	72
3.2	odd	2	inner	819.2.dx.a.503.26	yes	72
7.6	odd	2	inner	819.2.dx.a.503.12	yes	72
13.3	even	3	inner	819.2.dx.a.692.25	yes	72
21.20	even	2	inner	819.2.dx.a.503.25	yes	72
39.29	odd	6	inner	819.2.dx.a.692.12	yes	72
91.55	odd	6	inner	819.2.dx.a.692.26	yes	72
273.146	even	6	inner	819.2.dx.a.692.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dx.a.503.11	✓	72	1.1	even	1	trivial
819.2.dx.a.503.12	yes	72	7.6	odd	2	inner
819.2.dx.a.503.25	yes	72	21.20	even	2	inner
819.2.dx.a.503.26	yes	72	3.2	odd	2	inner
819.2.dx.a.692.11	yes	72	273.146	even	6	inner
819.2.dx.a.692.12	yes	72	39.29	odd	6	inner
819.2.dx.a.692.25	yes	72	13.3	even	3	inner
819.2.dx.a.692.26	yes	72	91.55	odd	6	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14474 - 0.660916i) q^{2} +(-0.126381 - 0.218898i) q^{4} -1.30928 q^{5} +(2.62751 + 0.310174i) q^{7} +2.97777i q^{8} +O(q^{10})\)	\(q+(-1.14474 - 0.660916i) q^{2} +(-0.126381 - 0.218898i) q^{4} -1.30928 q^{5} +(2.62751 + 0.310174i) q^{7} +2.97777i q^{8} +(1.49878 + 0.865323i) q^{10} +(-2.91784 - 1.68462i) q^{11} +(-2.43576 - 2.65840i) q^{13} +(-2.80281 - 2.09163i) q^{14} +(1.71529 - 2.97098i) q^{16} +(3.28870 + 5.69619i) q^{17} +(-0.0563295 + 0.0325218i) q^{19} +(0.165468 + 0.286598i) q^{20} +(2.22678 + 3.85689i) q^{22} +(-4.45220 - 2.57048i) q^{23} -3.28579 q^{25} +(1.03133 + 4.65301i) q^{26} +(-0.264170 - 0.614356i) q^{28} +(-6.80855 - 3.93092i) q^{29} +6.51216i q^{31} +(1.23052 - 0.710441i) q^{32} -8.69420i q^{34} +(-3.44014 - 0.406104i) q^{35} +(-0.139690 + 0.241950i) q^{37} +0.0859768 q^{38} -3.89873i q^{40} +(-3.70861 + 6.42351i) q^{41} +(1.47922 + 2.56209i) q^{43} +0.851612i q^{44} +(3.39774 + 5.88506i) q^{46} -0.756319 q^{47} +(6.80758 + 1.62997i) q^{49} +(3.76137 + 2.17163i) q^{50} +(-0.274086 + 0.869153i) q^{52} +7.81904i q^{53} +(3.82026 + 2.20563i) q^{55} +(-0.923627 + 7.82411i) q^{56} +(5.19601 + 8.99975i) q^{58} +(-0.590438 - 1.02267i) q^{59} +(2.48105 - 1.43244i) q^{61} +(4.30399 - 7.45473i) q^{62} -8.73934 q^{64} +(3.18908 + 3.48059i) q^{65} +(-5.60820 + 9.71368i) q^{67} +(0.831256 - 1.43978i) q^{68} +(3.66966 + 2.73852i) q^{70} +(-5.31936 + 3.07113i) q^{71} +15.1338i q^{73} +(0.319817 - 0.184646i) q^{74} +(0.0142379 + 0.00822027i) q^{76} +(-7.14412 - 5.33137i) q^{77} -9.20483 q^{79} +(-2.24580 + 3.88984i) q^{80} +(8.49079 - 4.90216i) q^{82} +14.3917 q^{83} +(-4.30582 - 7.45790i) q^{85} -3.91056i q^{86} +(5.01640 - 8.68866i) q^{88} +(3.32454 - 5.75827i) q^{89} +(-5.57540 - 7.74047i) q^{91} +1.29944i q^{92} +(0.865789 + 0.499863i) q^{94} +(0.0737510 - 0.0425801i) q^{95} +(-16.2545 + 9.38452i) q^{97} +(-6.71564 - 6.36513i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^7	\( 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Introduction

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