LMFDB - Embedded newform 819.2.fd.a.557.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(422,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 5]))

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

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

chi := DirichletCharacter("819.422");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fd (of order $12$, degree $4$, 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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.17
Character	$\chi$	$=$	819.557
Dual form			819.2.fd.a.422.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.117431 - 0.438260i) q^{2} +(1.55377 - 0.897069i) q^{4} +(3.41884 + 0.916074i) q^{5} +(-2.33620 + 1.24184i) q^{7} +(-1.21727 - 1.21727i) q^{8} +O(q^{10})$	\(q+(-0.117431 - 0.438260i) q^{2} +(1.55377 - 0.897069i) q^{4} +(3.41884 + 0.916074i) q^{5} +(-2.33620 + 1.24184i) q^{7} +(-1.21727 - 1.21727i) q^{8} -1.60591i q^{10} +(1.81075 + 1.81075i) q^{11} +(1.13882 + 3.42098i) q^{13} +(0.818592 + 0.878032i) q^{14} +(1.40360 - 2.43111i) q^{16} +(-2.75782 - 4.77669i) q^{17} +(6.13346 + 6.13346i) q^{19} +(6.13386 - 1.64356i) q^{20} +(0.580942 - 1.00622i) q^{22} +(1.46355 - 2.53494i) q^{23} +(6.51912 + 3.76382i) q^{25} +(1.36554 - 0.900829i) q^{26} +(-2.51590 + 4.02527i) q^{28} +(5.48217 - 3.16513i) q^{29} +(-9.29796 + 2.49138i) q^{31} +(-4.55592 - 1.22076i) q^{32} +(-1.76958 + 1.76958i) q^{34} +(-9.12470 + 2.10551i) q^{35} +(-0.210749 - 0.786526i) q^{37} +(1.96779 - 3.40831i) q^{38} +(-3.04653 - 5.27675i) q^{40} +(-4.03703 - 1.08172i) q^{41} +(2.87345 + 1.65899i) q^{43} +(4.43787 + 1.18912i) q^{44} +(-1.28283 - 0.343733i) q^{46} +(-1.03163 + 3.85009i) q^{47} +(3.91567 - 5.80237i) q^{49} +(0.883980 - 3.29906i) q^{50} +(4.83832 + 4.29381i) q^{52} +(-3.83716 - 2.21539i) q^{53} +(4.53189 + 7.84946i) q^{55} +(4.35543 + 1.33213i) q^{56} +(-2.03093 - 2.03093i) q^{58} +(2.61310 - 9.75222i) q^{59} -2.74069 q^{61} +(2.18374 + 3.78236i) q^{62} -3.47438i q^{64} +(0.759565 + 12.7390i) q^{65} +(-7.81072 - 7.81072i) q^{67} +(-8.57004 - 4.94791i) q^{68} +(1.99429 + 3.75174i) q^{70} +(0.823385 + 3.07291i) q^{71} +(1.36681 + 5.10099i) q^{73} +(-0.319954 + 0.184726i) q^{74} +(15.0321 + 4.02785i) q^{76} +(-6.47895 - 1.98162i) q^{77} +(-1.45971 - 2.52829i) q^{79} +(7.02577 - 7.02577i) q^{80} +1.89629i q^{82} +(0.639916 - 0.639916i) q^{83} +(-5.05274 - 18.8571i) q^{85} +(0.389634 - 1.45413i) q^{86} -4.40835i q^{88} +(12.3996 - 3.32246i) q^{89} +(-6.90882 - 6.57786i) q^{91} -5.25161i q^{92} +1.80849 q^{94} +(15.3506 + 26.5880i) q^{95} +(-3.12540 + 0.837450i) q^{97} +(-3.00277 - 1.03470i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} + 88 q^{16} + 4 q^{19} + 16 q^{28} - 16 q^{31} + 48 q^{34} - 8 q^{37} - 40 q^{40} + 72 q^{43} - 72 q^{46} - 28 q^{49} - 64 q^{52} + 16 q^{55} + 16 q^{58} + 64 q^{61} - 124 q^{67} - 40 q^{70} - 4 q^{73} - 72 q^{76} - 16 q^{79} - 88 q^{85} - 4 q^{91} + 16 q^{94} - 140 q^{97}+O(q^{100}) $ 152 * q + 8 * q^7 + 88 * q^16 + 4 * q^19 + 16 * q^28 - 16 * q^31 + 48 * q^34 - 8 * q^37 - 40 * q^40 + 72 * q^43 - 72 * q^46 - 28 * q^49 - 64 * q^52 + 16 * q^55 + 16 * q^58 + 64 * q^61 - 124 * q^67 - 40 * q^70 - 4 * q^73 - 72 * q^76 - 16 * q^79 - 88 * q^85 - 4 * q^91 + 16 * q^94 - 140 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.117431	−	0.438260i	−0.0830365	−	0.309897i	0.911899	−	0.410416i	$-0.134616\pi$
$2$	−0.117431	−	0.438260i	−0.0830365	−	0.309897i	−0.994935	+	0.100519i	$0.967950\pi$
$3$		0			0
$3$		0			0
$4$	1.55377	−	0.897069i	0.776885	−	0.448535i
$5$	3.41884	+	0.916074i	1.52895	+	0.409681i	0.922676	−	0.385575i	$-0.125997\pi$
$5$	3.41884	+	0.916074i	1.52895	+	0.409681i	0.606274	+	0.795256i	$0.292664\pi$
$6$		0			0
$7$	−2.33620	+	1.24184i	−0.883001	+	0.469371i
$7$	−2.33620	+	1.24184i	−0.883001	+	0.469371i
$8$	−1.21727	−	1.21727i	−0.430369	−	0.430369i
$9$		0			0
$10$		−	1.60591i		−	0.507835i
$11$	1.81075	+	1.81075i	0.545963	+	0.545963i	0.925271	−	0.379308i	$-0.123838\pi$
$11$	1.81075	+	1.81075i	0.545963	+	0.545963i	−0.379308	+	0.925271i	$0.623838\pi$
$12$		0			0
$13$	1.13882	+	3.42098i	0.315852	+	0.948809i
$13$	1.13882	+	3.42098i	0.315852	+	0.948809i
$14$	0.818592	+	0.878032i	0.218778	+	0.234664i
$15$		0			0
$16$	1.40360	−	2.43111i	0.350901	−	0.607778i
$17$	−2.75782	−	4.77669i	−0.668870	−	1.15852i	−0.978220	−	0.207569i	$-0.933445\pi$
$17$	−2.75782	−	4.77669i	−0.668870	−	1.15852i	0.309351	−	0.950948i	$-0.399888\pi$
$18$		0			0
$19$	6.13346	+	6.13346i	1.40711	+	1.40711i	0.774326	+	0.632786i	$0.218089\pi$
$19$	6.13346	+	6.13346i	1.40711	+	1.40711i	0.632786	+	0.774326i	$0.281911\pi$
$20$	6.13386	−	1.64356i	1.37157	−	0.367512i
$21$		0			0
$22$	0.580942	−	1.00622i	0.123857	−	0.214527i
$23$	1.46355	−	2.53494i	0.305171	−	0.528571i	−0.672129	−	0.740434i	$-0.734620\pi$
$23$	1.46355	−	2.53494i	0.305171	−	0.528571i	0.977299	+	0.211863i	$0.0679531\pi$
$24$		0			0
$25$	6.51912	+	3.76382i	1.30382	+	0.752763i
$26$	1.36554	−	0.900829i	0.267805	−	0.176667i
$27$		0			0
$28$	−2.51590	+	4.02527i	−0.475461	+	0.760704i
$29$	5.48217	−	3.16513i	1.01801	−	0.587750i	0.104485	−	0.994526i	$-0.466681\pi$
$29$	5.48217	−	3.16513i	1.01801	−	0.587750i	0.913528	+	0.406777i	$0.133347\pi$
$30$		0			0
$31$	−9.29796	+	2.49138i	−1.66996	+	0.447465i	−0.965101	−	0.261879i	$-0.915658\pi$
$31$	−9.29796	+	2.49138i	−1.66996	+	0.447465i	−0.704862	+	0.709344i	$0.748991\pi$
$32$	−4.55592	−	1.22076i	−0.805381	−	0.215801i
$33$		0			0
$34$	−1.76958	+	1.76958i	−0.303480	+	0.303480i
$35$	−9.12470	+	2.10551i	−1.54236	+	0.355897i
$36$		0			0
$37$	−0.210749	−	0.786526i	−0.0346469	−	0.129304i	0.946436	−	0.322891i	$-0.104655\pi$
$37$	−0.210749	−	0.786526i	−0.0346469	−	0.129304i	−0.981083	+	0.193587i	$0.937988\pi$
$38$	1.96779	−	3.40831i	0.319218	−	0.552901i
$39$		0			0
$40$	−3.04653	−	5.27675i	−0.481699	−	0.834327i
$41$	−4.03703	−	1.08172i	−0.630478	−	0.168936i	−0.0705913	−	0.997505i	$-0.522489\pi$
$41$	−4.03703	−	1.08172i	−0.630478	−	0.168936i	−0.559886	+	0.828569i	$0.689155\pi$
$42$		0			0
$43$	2.87345	+	1.65899i	0.438197	+	0.252993i	0.702832	−	0.711355i	$-0.251918\pi$
$43$	2.87345	+	1.65899i	0.438197	+	0.252993i	−0.264636	+	0.964348i	$0.585252\pi$
$44$	4.43787	+	1.18912i	0.669034	+	0.179267i
$45$		0			0
$46$	−1.28283	−	0.343733i	−0.189143	−	0.0506806i
$47$	−1.03163	+	3.85009i	−0.150479	+	0.561594i	0.848972	+	0.528439i	$0.177222\pi$
$47$	−1.03163	+	3.85009i	−0.150479	+	0.561594i	−0.999450	+	0.0331554i	$0.989444\pi$
$48$		0			0
$49$	3.91567	−	5.80237i	0.559381	−	0.828911i
$50$	0.883980	−	3.29906i	0.125014	−	0.466557i
$51$		0			0
$52$	4.83832	+	4.29381i	0.670954	+	0.595444i
$53$	−3.83716	−	2.21539i	−0.527075	−	0.304307i	0.212750	−	0.977107i	$-0.431758\pi$
$53$	−3.83716	−	2.21539i	−0.527075	−	0.304307i	−0.739824	+	0.672800i	$0.765091\pi$
$54$		0			0
$55$	4.53189	+	7.84946i	0.611080	+	1.05842i
$56$	4.35543	+	1.33213i	0.582019	+	0.178013i
$57$		0			0
$58$	−2.03093	−	2.03093i	−0.266674	−	0.266674i
$59$	2.61310	−	9.75222i	0.340197	−	1.26963i	−0.557928	−	0.829890i	$-0.688403\pi$
$59$	2.61310	−	9.75222i	0.340197	−	1.26963i	0.898124	−	0.439742i	$-0.144930\pi$
$60$		0			0
$61$	−2.74069			−0.350909			−0.175455	−	0.984488i	$-0.556139\pi$
$61$	−2.74069			−0.350909			−0.175455	+	0.984488i	$0.556139\pi$
$62$	2.18374	+	3.78236i	0.277336	+	0.480360i
$63$		0			0
$64$		−	3.47438i		−	0.434298i
$65$	0.759565	+	12.7390i	0.0942125	+	1.58008i
$66$		0			0
$67$	−7.81072	−	7.81072i	−0.954231	−	0.954231i	0.0447664	−	0.998997i	$-0.485746\pi$
$67$	−7.81072	−	7.81072i	−0.954231	−	0.954231i	−0.998997	+	0.0447664i	$0.985746\pi$
$68$	−8.57004	−	4.94791i	−1.03927	−	0.600023i
$69$		0			0
$70$	1.99429	+	3.75174i	0.238363	+	0.448419i
$71$	0.823385	+	3.07291i	0.0977178	+	0.364688i	0.997417	−	0.0718216i	$-0.0228812\pi$
$71$	0.823385	+	3.07291i	0.0977178	+	0.364688i	−0.899700	+	0.436509i	$0.856215\pi$
$72$		0			0
$73$	1.36681	+	5.10099i	0.159972	+	0.597025i	0.998628	+	0.0523633i	$0.0166754\pi$
$73$	1.36681	+	5.10099i	0.159972	+	0.597025i	−0.838656	+	0.544662i	$0.816658\pi$
$74$	−0.319954	+	0.184726i	−0.0371939	+	0.0214739i
$75$		0			0
$76$	15.0321	+	4.02785i	1.72430	+	0.462026i
$77$	−6.47895	−	1.98162i	−0.738345	−	0.225826i
$78$		0			0
$79$	−1.45971	−	2.52829i	−0.164230	−	0.284455i	0.772151	−	0.635439i	$-0.219181\pi$
$79$	−1.45971	−	2.52829i	−0.164230	−	0.284455i	−0.936382	+	0.350983i	$0.885847\pi$
$80$	7.02577	−	7.02577i	0.785505	−	0.785505i
$81$		0			0
$82$			1.89629i			0.209411i
$83$	0.639916	−	0.639916i	0.0702399	−	0.0702399i	−0.671114	−	0.741354i	$-0.734184\pi$
$83$	0.639916	−	0.639916i	0.0702399	−	0.0702399i	0.741354	+	0.671114i	$0.234184\pi$
$84$		0			0
$85$	−5.05274	−	18.8571i	−0.548046	−	2.04534i
$86$	0.389634	−	1.45413i	0.0420153	−	0.156803i
$87$		0			0
$88$		−	4.40835i		−	0.469931i
$89$	12.3996	−	3.32246i	1.31436	−	0.352181i	0.467495	−	0.883996i	$-0.345157\pi$
$89$	12.3996	−	3.32246i	1.31436	−	0.352181i	0.846861	+	0.531815i	$0.178490\pi$
$90$		0			0
$91$	−6.90882	−	6.57786i	−0.724241	−	0.689547i
$92$		−	5.25161i		−	0.547519i
$93$		0			0
$94$	1.80849			0.186531
$95$	15.3506	+	26.5880i	1.57494	+	2.72787i
$96$		0			0
$97$	−3.12540	+	0.837450i	−0.317337	+	0.0850301i	−0.413972	−	0.910290i	$-0.635859\pi$
$97$	−3.12540	+	0.837450i	−0.317337	+	0.0850301i	0.0966349	+	0.995320i	$0.469192\pi$
$98$	−3.00277	−	1.03470i	−0.303326	−	0.104520i
$99$		0			0
$100$	13.5056			1.35056
$101$	12.7848			1.27214			0.636068	−	0.771633i	$-0.280560\pi$
$101$	12.7848			1.27214			0.636068	+	0.771633i	$0.280560\pi$
$102$		0			0
$103$	4.26794	−	2.46410i	0.420533	−	0.242795i	−0.274772	−	0.961509i	$-0.588603\pi$
$103$	4.26794	−	2.46410i	0.420533	−	0.242795i	0.695305	+	0.718715i	$0.255269\pi$
$104$	2.77800	−	5.55049i	0.272405	−	0.544271i
$105$		0			0
$106$	−0.520312	+	1.94183i	−0.0505371	+	0.188607i
$107$	−1.19209	−	0.688252i	−0.115243	−	0.0665359i	0.441270	−	0.897374i	$-0.354528\pi$
$107$	−1.19209	−	0.688252i	−0.115243	−	0.0665359i	−0.556514	+	0.830838i	$0.687861\pi$
$108$		0			0
$109$	−7.39990	+	1.98280i	−0.708782	+	0.189917i	−0.595161	−	0.803607i	$-0.702912\pi$
$109$	−7.39990	+	1.98280i	−0.708782	+	0.189917i	−0.113621	+	0.993524i	$0.536245\pi$
$110$	2.90792	−	2.90792i	0.277259	−	0.277259i
$111$		0			0
$112$	−0.260048	+	7.42262i	−0.0245722	+	0.701372i
$113$	−15.5325	−	8.96767i	−1.46117	−	0.843608i	−0.462106	−	0.886825i	$-0.652906\pi$
$113$	−15.5325	−	8.96767i	−1.46117	−	0.843608i	−0.999066	+	0.0432171i	$0.986239\pi$
$114$		0			0
$115$	7.32582	−	7.32582i	0.683136	−	0.683136i
$116$	5.67868	−	9.83576i	0.527252	−	0.913228i
$117$		0			0
$118$	−4.58087			−0.421703
$119$	12.3747	+	7.73453i	1.13439	+	0.709023i
$120$		0			0
$121$		−	4.44234i		−	0.403849i
$122$	0.321843	+	1.20113i	0.0291383	+	0.108745i
$123$		0			0
$124$	−12.2119	+	12.2119i	−1.09666	+	1.09666i
$125$	6.32606	+	6.32606i	0.565820	+	0.565820i
$126$		0			0
$127$	1.38318	−	0.798578i	0.122737	−	0.0708624i	−0.437374	−	0.899279i	$-0.644092\pi$
$127$	1.38318	−	0.798578i	0.122737	−	0.0708624i	0.560112	+	0.828417i	$0.310758\pi$
$128$	−10.6345	+	2.84951i	−0.939969	+	0.251864i
$129$		0			0
$130$	5.49380	−	1.82885i	0.481838	−	0.160400i
$131$	−18.9904	+	10.9641i	−1.65920	+	0.957940i	−0.686115	+	0.727493i	$0.740685\pi$
$131$	−18.9904	+	10.9641i	−1.65920	+	0.957940i	−0.973085	+	0.230446i	$0.925981\pi$
$132$		0			0
$133$	−21.9458	−	6.71222i	−1.90294	−	0.582024i
$134$	−2.50590	+	4.34035i	−0.216477	+	0.374949i
$135$		0			0
$136$	−2.45750	+	9.17151i	−0.210729	+	0.786451i
$137$	1.26498	−	4.72097i	0.108074	−	0.403339i	−0.890601	−	0.454785i	$-0.849716\pi$
$137$	1.26498	−	4.72097i	0.108074	−	0.403339i	0.998676	+	0.0514454i	$0.0163828\pi$
$138$		0			0
$139$	−7.20599	+	12.4811i	−0.611204	+	1.05864i	0.379833	+	0.925055i	$0.375981\pi$
$139$	−7.20599	+	12.4811i	−0.611204	+	1.05864i	−0.991038	+	0.133582i	$0.957352\pi$
$140$	−12.2889	+	11.4570i	−1.03860	+	0.968291i
$141$		0			0
$142$	1.25004	−	0.721713i	0.104901	−	0.0605648i
$143$	−4.13243	+	8.25667i	−0.345571	+	0.690458i
$144$		0			0
$145$	21.6421	−	5.79899i	1.79728	−	0.481580i
$146$	2.07505	−	1.19803i	0.171733	−	0.0991498i
$147$		0			0
$148$	−1.03302	−	1.03302i	−0.0849140	−	0.0849140i
$149$	4.69181	−	4.69181i	0.384368	−	0.384368i	−0.488305	−	0.872673i	$-0.662385\pi$
$149$	4.69181	−	4.69181i	0.384368	−	0.384368i	0.872673	+	0.488305i	$0.162385\pi$
$150$		0			0
$151$	3.05544	+	11.4030i	0.248648	+	0.927967i	0.971515	+	0.236979i	$0.0761573\pi$
$151$	3.05544	+	11.4030i	0.248648	+	0.927967i	−0.722867	+	0.690987i	$0.757176\pi$
$152$		−	14.9321i		−	1.21116i
$153$		0			0
$154$	−0.107632	+	3.07217i	−0.00867322	+	0.247562i
$155$	−34.0705			−2.73661
$156$		0			0
$157$	−3.60759	+	6.24853i	−0.287917	+	0.498687i	−0.973312	−	0.229484i	$-0.926296\pi$
$157$	−3.60759	+	6.24853i	−0.287917	+	0.498687i	0.685395	+	0.728171i	$0.259629\pi$
$158$	−0.936633	+	0.936633i	−0.0745145	+	0.0745145i
$159$		0			0
$160$	−14.4577	−	8.34713i	−1.14298	−	0.659898i
$161$	−0.271154	+	7.73962i	−0.0213699	+	0.609967i
$162$		0			0
$163$	−10.7221	+	10.7221i	−0.839820	+	0.839820i	−0.988835	−	0.149015i	$-0.952390\pi$
$163$	−10.7221	+	10.7221i	−0.839820	+	0.839820i	0.149015	+	0.988835i	$0.452390\pi$
$164$	−7.24299	+	1.94075i	−0.565582	+	0.151547i
$165$		0			0
$166$	−0.355596	−	0.205303i	−0.0275996	−	0.0159346i
$167$	−1.06607	+	3.97864i	−0.0824953	+	0.307877i	−0.994828	−	0.101573i	$-0.967613\pi$
$167$	−1.06607	+	3.97864i	−0.0824953	+	0.307877i	0.912333	+	0.409449i	$0.134279\pi$
$168$		0			0
$169$	−10.4062	+	7.79175i	−0.800476	+	0.599365i
$170$	−7.67095	+	4.42883i	−0.588335	+	0.339675i
$171$		0			0
$172$	5.95290			0.453904
$173$	−16.3236			−1.24106			−0.620531	−	0.784182i	$-0.713083\pi$
$173$	−16.3236			−1.24106			−0.620531	+	0.784182i	$0.713083\pi$
$174$		0			0
$175$	−19.9040	−	0.697327i	−1.50460	−	0.0527130i
$176$	6.94373	−	1.86057i	0.523404	−	0.140246i
$177$		0			0
$178$	−2.91221	−	5.04409i	−0.218279	−	0.378070i
$179$	−9.41900			−0.704009			−0.352005	−	0.935998i	$-0.614500\pi$
$179$	−9.41900			−0.704009			−0.352005	+	0.935998i	$0.614500\pi$
$180$		0			0
$181$		−	16.0744i		−	1.19480i	−0.801944	−	0.597399i	$-0.796201\pi$
$181$		−	16.0744i		−	1.19480i	0.801944	−	0.597399i	$-0.203799\pi$
$182$	−2.07150	+	3.80030i	−0.153550	+	0.281697i
$183$		0			0
$184$	−4.86723	+	1.30417i	−0.358817	+	0.0961447i
$185$		−	2.88206i		−	0.211894i
$186$		0			0
$187$	3.65567	−	13.6431i	0.267329	−	0.997686i
$188$	1.85089	+	6.90760i	0.134990	+	0.503789i
$189$		0			0
$190$	9.84982	−	9.84982i	0.714581	−	0.714581i
$191$			7.50968i			0.543381i	0.962385	+	0.271691i	$0.0875827\pi$
$191$			7.50968i			0.543381i	−0.962385	+	0.271691i	$0.912417\pi$
$192$		0			0
$193$	13.3496	−	13.3496i	0.960922	−	0.960922i	−0.0383422	−	0.999265i	$-0.512208\pi$
$193$	13.3496	−	13.3496i	0.960922	−	0.960922i	0.999265	+	0.0383422i	$0.0122077\pi$
$194$	0.734041	+	1.27140i	0.0527011	+	0.0912810i
$195$		0			0
$196$	0.878915	−	12.5282i	0.0627797	−	0.894870i
$197$	−23.2348	−	6.22576i	−1.65541	−	0.443567i	−0.694292	−	0.719693i	$-0.744283\pi$
$197$	−23.2348	−	6.22576i	−1.65541	−	0.443567i	−0.961121	+	0.276126i	$0.910949\pi$
$198$		0			0
$199$	3.60590	−	2.08186i	0.255615	−	0.147579i	−0.366718	−	0.930332i	$-0.619518\pi$
$199$	3.60590	−	2.08186i	0.255615	−	0.147579i	0.622333	+	0.782753i	$0.286185\pi$
$200$	−3.35394	−	12.5171i	−0.237160	−	0.885091i
$201$		0			0
$202$	−1.50134	−	5.60307i	−0.105634	−	0.394231i
$203$	−8.87686	+	14.2024i	−0.623033	+	0.996810i
$204$		0			0
$205$	−12.8110	−	7.39643i	−0.894759	−	0.516589i
$206$	−1.58111	−	1.58111i	−0.110161	−	0.110161i
$207$		0			0
$208$	9.91524	+	2.03310i	0.687498	+	0.140970i
$209$			22.2124i			1.53646i
$210$		0			0
$211$	1.47875	+	2.56127i	0.101801	+	0.176325i	0.912427	−	0.409240i	$-0.134206\pi$
$211$	1.47875	+	2.56127i	0.101801	+	0.176325i	−0.810626	+	0.585565i	$0.800873\pi$
$212$	−7.94942			−0.545968
$213$		0			0
$214$	−0.161645	+	0.603267i	−0.0110498	+	0.0412385i
$215$	8.30409	+	8.30409i	0.566335	+	0.566335i
$216$		0			0
$217$	18.6280	−	17.3669i	1.26455	−	1.17894i
$218$	1.73796	+	3.01024i	0.117710	+	0.203879i
$219$		0			0
$220$	14.0830	+	8.13083i	0.949477	+	0.548181i
$221$	13.2003	−	14.8742i	0.887947	−	1.00055i
$222$		0			0
$223$	2.27377	−	8.48581i	0.152263	−	0.568252i	−0.847062	−	0.531495i	$-0.821631\pi$
$223$	2.27377	−	8.48581i	0.152263	−	0.568252i	0.999324	−	0.0367571i	$-0.0117028\pi$
$224$	12.1595	−	2.80580i	0.812443	−	0.187470i
$225$		0			0
$226$	−2.10617	+	7.86034i	−0.140101	+	0.522862i
$227$	25.5627	+	6.84952i	1.69666	+	0.454618i	0.972095	−	0.234589i	$-0.0753743\pi$
$227$	25.5627	+	6.84952i	1.69666	+	0.454618i	0.724564	+	0.689207i	$0.242041\pi$
$228$		0			0
$229$	−17.2016	−	4.60916i	−1.13672	−	0.304582i	−0.359086	−	0.933305i	$-0.616911\pi$
$229$	−17.2016	−	4.60916i	−1.13672	−	0.304582i	−0.777630	+	0.628723i	$0.783578\pi$
$230$	−4.07089	−	2.35033i	−0.268427	−	0.154976i
$231$		0			0
$232$	−10.5261	−	2.82045i	−0.691071	−	0.185172i
$233$	5.01778	+	8.69105i	0.328726	+	0.569370i	0.982259	−	0.187528i	$-0.0600475\pi$
$233$	5.01778	+	8.69105i	0.328726	+	0.569370i	−0.653534	+	0.756897i	$0.726714\pi$
$234$		0			0
$235$	−7.05395	+	12.2178i	−0.460149	+	0.797001i
$236$	−4.68826	−	17.4968i	−0.305180	−	1.13895i
$237$		0			0
$238$	1.93655	−	6.33161i	0.125528	−	0.410417i
$239$	−18.0496	+	18.0496i	−1.16753	+	1.16753i	−0.184748	+	0.982786i	$0.559147\pi$
$239$	−18.0496	+	18.0496i	−1.16753	+	1.16753i	−0.982786	+	0.184748i	$0.940853\pi$
$240$		0			0
$241$	19.3287	+	5.17911i	1.24507	+	0.333616i	0.820430	−	0.571747i	$-0.193734\pi$
$241$	19.3287	+	5.17911i	1.24507	+	0.333616i	0.424640	+	0.905362i	$0.360401\pi$
$242$	−1.94690	+	0.521670i	−0.125151	+	0.0335342i
$243$		0			0
$244$	−4.25840	+	2.45859i	−0.272616	+	0.157395i
$245$	18.7024	−	16.2503i	1.19485	−	1.03819i
$246$		0			0
$247$	−13.9975	+	27.9673i	−0.890642	+	1.77952i
$248$	14.3508	+	8.28543i	0.911276	+	0.526125i
$249$		0			0
$250$	2.02958	−	3.51533i	0.128362	−	0.222329i
$251$	−3.80309	+	6.58714i	−0.240049	+	0.415777i	−0.960728	−	0.277492i	$-0.910497\pi$
$251$	−3.80309	+	6.58714i	−0.240049	+	0.415777i	0.720679	+	0.693269i	$0.243830\pi$
$252$		0			0
$253$	7.24028	−	1.94003i	0.455192	−	0.121968i
$254$	−0.512413	−	0.512413i	−0.0321517	−	0.0321517i
$255$		0			0
$256$	−0.976728	−	1.69174i	−0.0610455	−	0.105734i
$257$	8.05239	−	13.9471i	0.502294	−	0.869999i	−0.497702	−	0.867348i	$-0.665823\pi$
$257$	8.05239	−	13.9471i	0.502294	−	0.869999i	0.999996	−	0.00265094i	$-0.000843820\pi$
$258$		0			0
$259$	1.46909	+	1.57577i	0.0912849	+	0.0979133i
$260$	12.6080	+	19.1121i	0.781912	+	1.18528i
$261$		0			0
$262$	7.03520	+	7.03520i	0.434636	+	0.434636i
$263$		−	0.0656289i		−	0.00404685i	−0.999998	−	0.00202343i	$-0.999356\pi$
$263$		−	0.0656289i		−	0.00404685i	0.999998	−	0.00202343i	$-0.000644077\pi$
$264$		0			0
$265$	−11.0892	−	11.0892i	−0.681202	−	0.681202i
$266$	−0.364575	+	10.4062i	−0.0223535	+	0.638044i
$267$		0			0
$268$	−19.1428	−	5.12930i	−1.16933	−	0.313322i
$269$	3.32480	−	1.91957i	0.202716	−	0.117038i	−0.395205	−	0.918593i	$-0.629327\pi$
$269$	3.32480	−	1.91957i	0.202716	−	0.117038i	0.597922	+	0.801554i	$0.295993\pi$
$270$		0			0
$271$	2.56064	+	9.55645i	0.155548	+	0.580513i	0.999058	+	0.0433992i	$0.0138187\pi$
$271$	2.56064	+	9.55645i	0.155548	+	0.580513i	−0.843510	+	0.537114i	$0.819515\pi$
$272$	−15.4836			−0.938829
$273$		0			0
$274$	−2.21756			−0.133968
$275$	4.98918	+	18.6199i	0.300859	+	1.12282i
$276$		0			0
$277$	−4.59453	+	2.65265i	−0.276059	+	0.159382i	−0.631638	−	0.775264i	$-0.717617\pi$
$277$	−4.59453	+	2.65265i	−0.276059	+	0.159382i	0.355579	+	0.934646i	$0.384284\pi$
$278$	6.31619	+	1.69242i	0.378820	+	0.101505i
$279$		0			0
$280$	13.6702	+	8.54424i	0.816949	+	0.510616i
$281$	−11.9903	−	11.9903i	−0.715284	−	0.715284i	0.252352	−	0.967636i	$-0.418796\pi$
$281$	−11.9903	−	11.9903i	−0.715284	−	0.715284i	−0.967636	+	0.252352i	$0.918796\pi$
$282$		0			0
$283$		−	3.68762i		−	0.219206i	−0.993975	−	0.109603i	$-0.965042\pi$
$283$		−	3.68762i		−	0.219206i	0.993975	−	0.109603i	$-0.0349580\pi$
$284$	4.03597	+	4.03597i	0.239491	+	0.239491i
$285$		0			0
$286$	4.10385	+	0.841486i	0.242665	+	0.0497581i
$287$	10.7746	−	2.48623i	0.636006	−	0.146758i
$288$		0			0
$289$	−6.71116	+	11.6241i	−0.394774	+	0.683769i
$290$	−5.08293	−	8.80389i	−0.298480	−	0.516982i
$291$		0			0
$292$	6.69964	+	6.69964i	0.392067	+	0.392067i
$293$	16.7802	−	4.49624i	0.980309	−	0.262673i	0.267134	−	0.963659i	$-0.413923\pi$
$293$	16.7802	−	4.49624i	0.980309	−	0.262673i	0.713175	+	0.700986i	$0.247257\pi$
$294$		0			0
$295$	17.8675	−	30.9475i	1.04029	−	1.80183i
$296$	−0.700875	+	1.21395i	−0.0407375	+	0.0705594i
$297$		0			0
$298$	−2.60720	−	1.50527i	−0.151031	−	0.0871977i
$299$	10.3387	+	2.11993i	0.597902	+	0.122599i
$300$		0			0
$301$	−8.77315	−	0.307363i	−0.505676	−	0.0177161i
$302$	4.63869	−	2.67815i	0.266927	−	0.154110i
$303$		0			0
$304$	23.5201	−	6.30219i	1.34897	−	0.361455i
$305$	−9.36996	−	2.51067i	−0.536522	−	0.143761i
$306$		0			0
$307$	6.56933	−	6.56933i	0.374932	−	0.374932i	−0.494338	−	0.869270i	$-0.664590\pi$
$307$	6.56933	−	6.56933i	0.374932	−	0.374932i	0.869270	+	0.494338i	$0.164590\pi$
$308$	−11.8444	+	2.73309i	−0.674900	+	0.155732i
$309$		0			0
$310$	4.00094	+	14.9317i	0.227238	+	0.848065i
$311$	2.57308	−	4.45670i	0.145906	−	0.252716i	−0.783805	−	0.621007i	$-0.786724\pi$
$311$	2.57308	−	4.45670i	0.145906	−	0.252716i	0.929711	+	0.368291i	$0.120057\pi$
$312$		0			0
$313$	4.59918	+	7.96602i	0.259961	+	0.450266i	0.966231	−	0.257677i	$-0.0829569\pi$
$313$	4.59918	+	7.96602i	0.259961	+	0.450266i	−0.706270	+	0.707942i	$0.749624\pi$
$314$	3.16213	+	0.847289i	0.178449	+	0.0478153i
$315$		0			0
$316$	−4.53611	−	2.61892i	−0.255176	−	0.147326i
$317$	−23.3457	−	6.25545i	−1.31122	−	0.351341i	−0.465540	−	0.885027i	$-0.654140\pi$
$317$	−23.3457	−	6.25545i	−1.31122	−	0.351341i	−0.845683	+	0.533686i	$0.820807\pi$
$318$		0			0
$319$	15.6581	+	4.19558i	0.876687	+	0.234908i
$320$	3.18279	−	11.8783i	0.177924	−	0.664020i
$321$		0			0
$322$	3.42381	−	0.790038i	0.190801	−	0.0440271i
$323$	12.3826	−	46.2126i	0.688988	−	2.57134i
$324$		0			0
$325$	−5.45183	+	26.5881i	−0.302413	+	1.47484i
$326$	5.95818	+	3.43996i	0.329993	+	0.190522i
$327$		0			0
$328$	3.59740	+	6.23088i	0.198633	+	0.344043i
$329$	−2.37111	−	10.2757i	−0.130723	−	0.566518i
$330$		0			0
$331$	−14.1404	−	14.1404i	−0.777229	−	0.777229i	0.202129	−	0.979359i	$-0.435214\pi$
$331$	−14.1404	−	14.1404i	−0.777229	−	0.777229i	−0.979359	+	0.202129i	$0.935214\pi$
$332$	0.420233	−	1.56833i	0.0230633	−	0.0860733i
$333$		0			0
$334$	1.86887			0.102260
$335$	−19.5484	−	33.8588i	−1.06804	−	1.84990i
$336$		0			0
$337$			9.50458i			0.517747i	0.965911	+	0.258874i	$0.0833513\pi$
$337$			9.50458i			0.517747i	−0.965911	+	0.258874i	$0.916649\pi$
$338$	4.63682	+	3.64562i	0.252210	+	0.198295i
$339$		0			0
$340$	−24.7669	−	24.7669i	−1.34317	−	1.34317i
$341$	−21.3476	−	12.3250i	−1.15604	−	0.667439i
$342$		0			0
$343$	−1.94217	+	18.4181i	−0.104867	+	0.994486i
$344$	−1.47833	−	5.51719i	−0.0797060	−	0.297467i
$345$		0			0
$346$	1.91691	+	7.15399i	0.103053	+	0.384601i
$347$	17.3461	−	10.0148i	0.931185	−	0.537620i	0.0439990	−	0.999032i	$-0.485990\pi$
$347$	17.3461	−	10.0148i	0.931185	−	0.537620i	0.887186	+	0.461412i	$0.152657\pi$
$348$		0			0
$349$	14.1285	+	3.78572i	0.756282	+	0.202645i	0.616303	−	0.787509i	$-0.288630\pi$
$349$	14.1285	+	3.78572i	0.756282	+	0.202645i	0.139979	+	0.990154i	$0.455296\pi$
$350$	2.03175	+	8.80502i	0.108601	+	0.470648i
$351$		0			0
$352$	−6.03917	−	10.4601i	−0.321889	−	0.557528i
$353$	−16.9558	+	16.9558i	−0.902467	+	0.902467i	−0.995649	−	0.0931824i	$-0.970296\pi$
$353$	−16.9558	+	16.9558i	−0.902467	+	0.902467i	0.0931824	+	0.995649i	$0.470296\pi$
$354$		0			0
$355$			11.2601i			0.597623i
$356$	16.2856	−	16.2856i	0.863138	−	0.863138i
$357$		0			0
$358$	1.10609	+	4.12797i	0.0584585	+	0.218170i
$359$	−2.97553	+	11.1048i	−0.157042	+	0.586090i	0.841880	+	0.539665i	$0.181449\pi$
$359$	−2.97553	+	11.1048i	−0.157042	+	0.586090i	−0.998922	+	0.0464242i	$0.985217\pi$
$360$		0			0
$361$			56.2387i			2.95993i
$362$	−7.04475	+	1.88763i	−0.370264	+	0.0992119i
$363$		0			0
$364$	−16.6355	−	4.02279i	−0.871937	−	0.210852i
$365$			18.6915i			0.978359i
$366$		0			0
$367$	−7.88549			−0.411619			−0.205810	−	0.978592i	$-0.565983\pi$
$367$	−7.88549			−0.411619			−0.205810	+	0.978592i	$0.565983\pi$
$368$	−4.10848	−	7.11610i	−0.214169	−	0.370952i
$369$		0			0
$370$	−1.26309	+	0.338445i	−0.0656651	+	0.0175949i
$371$	11.7155	+	0.410448i	0.608240	+	0.0213094i
$372$		0			0
$373$	−0.966919			−0.0500651			−0.0250326	−	0.999687i	$-0.507969\pi$
$373$	−0.966919			−0.0500651			−0.0250326	+	0.999687i	$0.507969\pi$
$374$	−6.40853			−0.331377
$375$		0			0
$376$	5.94236	−	3.43083i	0.306454	−	0.176931i
$377$	17.0710	+	15.1499i	0.879203	+	0.780258i
$378$		0			0
$379$	1.33785	−	4.99292i	0.0687207	−	0.256469i	−0.923016	−	0.384763i	$-0.874283\pi$
$379$	1.33785	−	4.99292i	0.0687207	−	0.256469i	0.991736	+	0.128293i	$0.0409499\pi$
$380$	47.7026	+	27.5411i	2.44709	+	1.41283i
$381$		0			0
$382$	3.29119	−	0.881872i	0.168392	−	0.0451205i
$383$	−26.2238	+	26.2238i	−1.33997	+	1.33997i	−0.443897	+	0.896078i	$0.646404\pi$
$383$	−26.2238	+	26.2238i	−1.33997	+	1.33997i	−0.896078	+	0.443897i	$0.853596\pi$
$384$		0			0
$385$	−20.3352	−	12.7100i	−1.03638	−	0.647763i
$386$	−7.41823	−	4.28292i	−0.377578	−	0.217995i
$387$		0			0
$388$	−4.10491	+	4.10491i	−0.208395	+	0.208395i
$389$	0.341507	−	0.591507i	0.0173151	−	0.0299906i	−0.857238	−	0.514920i	$-0.827821\pi$
$389$	0.341507	−	0.591507i	0.0173151	−	0.0299906i	0.874553	+	0.484930i	$0.161155\pi$
$390$		0			0
$391$	−16.1448			−0.816478
$392$	−11.8295	+	2.29663i	−0.597478	+	0.115997i
$393$		0			0
$394$			10.9140i			0.549839i
$395$	−2.67441	−	9.98102i	−0.134564	−	0.502200i
$396$		0			0
$397$	4.05586	−	4.05586i	0.203558	−	0.203558i	−0.597965	−	0.801522i	$-0.704024\pi$
$397$	4.05586	−	4.05586i	0.203558	−	0.203558i	0.801522	+	0.597965i	$0.204024\pi$
$398$	−1.33584	−	1.33584i	−0.0669598	−	0.0669598i
$399$		0			0
$400$	18.3005	−	10.5658i	0.915026	−	0.528291i
$401$	20.9817	−	5.62203i	1.04778	−	0.280751i	0.306444	−	0.951889i	$-0.400861\pi$
$401$	20.9817	−	5.62203i	1.04778	−	0.280751i	0.741332	+	0.671138i	$0.234194\pi$
$402$		0			0
$403$	−19.1117	−	28.9709i	−0.952019	−	1.44314i
$404$	19.8646	−	11.4689i	0.988303	−	0.570597i
$405$		0			0
$406$	7.26674	+	2.22257i	0.360642	+	0.110304i
$407$	1.04259	−	1.80582i	0.0516793	−	0.0895112i
$408$		0			0
$409$	4.55941	−	17.0160i	0.225449	−	0.841385i	−0.756776	−	0.653675i	$-0.773227\pi$
$409$	4.55941	−	17.0160i	0.225449	−	0.841385i	0.982224	−	0.187711i	$-0.0601068\pi$
$410$	−1.73715	+	6.48312i	−0.0857916	+	0.320179i
$411$		0			0
$412$	4.42093	−	7.65728i	0.217804	−	0.377247i
$413$	6.00597	+	26.0282i	0.295534	+	1.28076i
$414$		0			0
$415$	2.77398	−	1.60156i	0.136169	−	0.0786173i
$416$	−1.01219	−	16.9759i	−0.0496268	−	0.832314i
$417$		0			0
$418$	9.73480	−	2.60843i	0.476145	−	0.127583i
$419$	32.0304	−	18.4928i	1.56479	−	0.903431i	0.568027	−	0.823010i	$-0.307707\pi$
$419$	32.0304	−	18.4928i	1.56479	−	0.903431i	0.996761	−	0.0804205i	$-0.0256263\pi$
$420$		0			0
$421$	23.9589	+	23.9589i	1.16769	+	1.16769i	0.982751	+	0.184935i	$0.0592076\pi$
$421$	23.9589	+	23.9589i	1.16769	+	1.16769i	0.184935	+	0.982751i	$0.440792\pi$
$422$	0.948849	−	0.948849i	0.0461892	−	0.0461892i
$423$		0			0
$424$	1.97413	+	7.36757i	0.0958725	+	0.357801i
$425$		−	41.5197i		−	2.01400i
$426$		0			0
$427$	6.40280	−	3.40349i	0.309853	−	0.164707i
$428$	−2.46964			−0.119375
$429$		0			0
$430$	2.66419	−	4.61451i	0.128479	−	0.222532i
$431$	16.6708	−	16.6708i	0.803007	−	0.803007i	−0.180558	−	0.983564i	$-0.557790\pi$
$431$	16.6708	−	16.6708i	0.803007	−	0.803007i	0.983564	+	0.180558i	$0.0577903\pi$
$432$		0			0
$433$	−3.43344	−	1.98230i	−0.165001	−	0.0952632i	0.415226	−	0.909718i	$-0.363703\pi$
$433$	−3.43344	−	1.98230i	−0.165001	−	0.0952632i	−0.580226	+	0.814455i	$0.697036\pi$
$434$	−9.79875	−	6.12448i	−0.470355	−	0.293985i
$435$		0			0
$436$	−9.71903	+	9.71903i	−0.465457	+	0.465457i
$437$	24.5246	−	6.57134i	1.17317	−	0.314350i
$438$		0			0
$439$	−12.3593	−	7.13567i	−0.589879	−	0.340567i	0.175171	−	0.984538i	$-0.443952\pi$
$439$	−12.3593	−	7.13567i	−0.589879	−	0.340567i	−0.765050	+	0.643971i	$0.777286\pi$
$440$	4.03837	−	15.0714i	0.192522	−	0.718501i
$441$		0			0
$442$	−8.06890	−	4.03845i	−0.383799	−	0.192090i
$443$	8.09574	−	4.67407i	0.384640	−	0.222072i	−0.295195	−	0.955437i	$-0.595385\pi$
$443$	8.09574	−	4.67407i	0.384640	−	0.222072i	0.679835	+	0.733365i	$0.262051\pi$
$444$		0			0
$445$	45.4358			2.15387
$446$	−3.98600			−0.188743
$447$		0			0
$448$	4.31463	+	8.11686i	0.203847	+	0.383485i
$449$	−15.7860	+	4.22986i	−0.744989	+	0.199619i	−0.611294	−	0.791403i	$-0.709351\pi$
$449$	−15.7860	+	4.22986i	−0.744989	+	0.199619i	−0.133695	+	0.991023i	$0.542684\pi$
$450$		0			0
$451$	−5.35134	−	9.26879i	−0.251985	−	0.436450i
$452$	−32.1785			−1.51355
$453$		0			0
$454$		−	12.0075i		−	0.563539i
$455$	−17.5943	−	28.8176i	−0.824833	−	1.35099i
$456$		0			0
$457$	4.54075	−	1.21669i	0.212407	−	0.0569143i	−0.151046	−	0.988527i	$-0.548264\pi$
$457$	4.54075	−	1.21669i	0.212407	−	0.0569143i	0.363453	+	0.931612i	$0.381598\pi$
$458$			8.08004i			0.377556i
$459$		0			0
$460$	4.81087	−	17.9544i	0.224308	−	0.837128i
$461$	9.00144	+	33.5938i	0.419239	+	1.56462i	0.776191	+	0.630498i	$0.217149\pi$
$461$	9.00144	+	33.5938i	0.419239	+	1.56462i	−0.356952	+	0.934123i	$0.616184\pi$
$462$		0			0
$463$	9.30270	−	9.30270i	0.432333	−	0.432333i	−0.457088	−	0.889421i	$-0.651108\pi$
$463$	9.30270	−	9.30270i	0.432333	−	0.432333i	0.889421	+	0.457088i	$0.151108\pi$
$464$		−	17.7704i		−	0.824968i
$465$		0			0
$466$	3.21969	−	3.21969i	0.149149	−	0.149149i
$467$	15.3498	+	26.5866i	0.710303	+	1.23028i	0.964743	+	0.263193i	$0.0847755\pi$
$467$	15.3498	+	26.5866i	0.710303	+	1.23028i	−0.254440	+	0.967089i	$0.581891\pi$
$468$		0			0
$469$	27.9471	+	8.54775i	1.29048	+	0.394698i
$470$	6.18292	+	1.65671i	0.285197	+	0.0764183i
$471$		0			0
$472$	−15.0519	+	8.69022i	−0.692820	+	0.400000i
$473$	2.19909	+	8.20713i	0.101114	+	0.377364i
$474$		0			0
$475$	16.8996	+	63.0700i	0.775405	+	2.89385i
$476$	26.1658	+	0.916707i	1.19931	+	0.0420172i
$477$		0			0
$478$	10.0300	+	5.79084i	0.458763	+	0.264867i
$479$	−14.9193	−	14.9193i	−0.681680	−	0.681680i	0.278699	−	0.960379i	$-0.410097\pi$
$479$	−14.9193	−	14.9193i	−0.681680	−	0.681680i	−0.960379	+	0.278699i	$0.910097\pi$
$480$		0			0
$481$	2.45068	−	1.61668i	0.111742	−	0.0737142i
$482$		−	9.07918i		−	0.413545i
$483$		0			0
$484$	−3.98508	−	6.90236i	−0.181140	−	0.313744i
$485$	−11.4524			−0.520027
$486$		0			0
$487$	3.31612	−	12.3759i	0.150268	−	0.560807i	−0.849196	−	0.528077i	$-0.822913\pi$
$487$	3.31612	−	12.3759i	0.150268	−	0.560807i	0.999464	−	0.0327301i	$-0.0104202\pi$
$488$	3.33615	+	3.33615i	0.151020	+	0.151020i
$489$		0			0
$490$	−9.31812	−	6.28823i	−0.420950	−	0.284073i
$491$	−6.25756	−	10.8384i	−0.282400	−	0.489131i	0.689575	−	0.724214i	$-0.257797\pi$
$491$	−6.25756	−	10.8384i	−0.282400	−	0.489131i	−0.971975	+	0.235083i	$0.924464\pi$
$492$		0			0
$493$	−30.2377	−	17.4577i	−1.36184	−	0.786257i
$494$	13.9007	+	2.85031i	0.625423	+	0.128242i
$495$		0			0
$496$	−6.99382	+	26.1013i	−0.314032	+	1.17198i
$497$	−5.73966	−	6.15643i	−0.257459	−	0.276154i
$498$		0			0
$499$	9.64287	−	35.9877i	0.431674	−	1.61103i	−0.317228	−	0.948349i	$-0.602752\pi$
$499$	9.64287	−	35.9877i	0.431674	−	1.61103i	0.748902	−	0.662680i	$-0.230581\pi$
$500$	15.5041	+	4.15432i	0.693366	+	0.185787i
$501$		0			0
$502$	3.33348	+	0.893203i	0.148781	+	0.0398656i
$503$	−23.7586	−	13.7170i	−1.05934	−	0.611613i	−0.134094	−	0.990969i	$-0.542812\pi$
$503$	−23.7586	−	13.7170i	−1.05934	−	0.611613i	−0.925251	+	0.379356i	$0.876146\pi$
$504$		0			0
$505$	43.7092	+	11.7118i	1.94503	+	0.521170i
$506$	−1.70047	−	2.94530i	−0.0755952	−	0.130935i
$507$		0			0
$508$	1.43276	−	2.48161i	0.0635685	−	0.110104i
$509$	−0.456329	−	1.70304i	−0.0202264	−	0.0754860i	0.955075	−	0.296364i	$-0.0957743\pi$
$509$	−0.456329	−	1.70304i	−0.0202264	−	0.0754860i	−0.975301	+	0.220878i	$0.929108\pi$
$510$		0			0
$511$	−9.52774	−	10.2196i	−0.421482	−	0.452087i
$512$	−16.1968	+	16.1968i	−0.715802	+	0.715802i
$513$		0			0
$514$	−7.05808	−	1.89121i	−0.311318	−	0.0834175i
$515$	16.8487	−	4.51459i	0.742442	−	0.198937i
$516$		0			0
$517$	−8.83960	+	5.10355i	−0.388765	+	0.224454i
$518$	0.518078	−	0.828888i	0.0227630	−	0.0364192i
$519$		0			0
$520$	14.5822	−	16.4314i	0.639471	−	0.720563i
$521$	−6.81645	−	3.93548i	−0.298634	−	0.172416i	0.343195	−	0.939264i	$-0.388491\pi$
$521$	−6.81645	−	3.93548i	−0.298634	−	0.172416i	−0.641829	+	0.766848i	$0.721824\pi$
$522$		0			0
$523$	−9.98176	+	17.2889i	−0.436472	+	0.755991i	−0.997414	−	0.0718633i	$-0.977105\pi$
$523$	−9.98176	+	17.2889i	−0.436472	+	0.755991i	0.560943	+	0.827855i	$0.310439\pi$
$524$	−19.6711	+	34.0714i	−0.859338	+	1.48842i
$525$		0			0
$526$	−0.0287625	+	0.00770690i	−0.00125411	+	0.000336037i
$527$	37.5427	+	37.5427i	1.63538	+	1.63538i
$528$		0			0
$529$	7.21606	+	12.4986i	0.313742	+	0.543416i
$530$	−3.55772	+	6.16215i	−0.154538	+	0.267667i
$531$		0			0
$532$	−40.1200	+	9.25763i	−1.73942	+	0.401369i
$533$	−0.896909	−	15.0425i	−0.0388495	−	0.651561i
$534$		0			0
$535$	−3.44506	−	3.44506i	−0.148943	−	0.148943i
$536$			19.0155i			0.821343i
$537$		0			0
$538$	−1.23171	−	1.23171i	−0.0531027	−	0.0531027i
$539$	17.5970	−	3.41636i	0.757956	−	0.147153i
$540$		0			0
$541$	32.8889	+	8.81257i	1.41401	+	0.378882i	0.883353	−	0.468708i	$-0.155280\pi$
$541$	32.8889	+	8.81257i	1.41401	+	0.378882i	0.530653	+	0.847589i	$0.321947\pi$
$542$	3.88751	−	2.24445i	0.166983	−	0.0964076i
$543$		0			0
$544$	6.73325	+	25.1288i	0.288686	+	1.07739i
$545$	−27.1154			−1.16150
$546$		0			0
$547$	−24.2699			−1.03771			−0.518854	−	0.854863i	$-0.673641\pi$
$547$	−24.2699			−1.03771			−0.518854	+	0.854863i	$0.673641\pi$
$548$	−2.26955	−	8.47007i	−0.0969503	−	0.361823i
$549$		0			0
$550$	7.57446	−	4.37311i	0.322976	−	0.186470i
$551$	53.0379	+	14.2115i	2.25949	+	0.605428i
$552$		0			0
$553$	6.54991	+	4.09387i	0.278531	+	0.174089i
$554$	1.70209	+	1.70209i	0.0723150	+	0.0723150i
$555$		0			0
$556$			25.8571i			1.09659i
$557$	−30.2007	−	30.2007i	−1.27964	−	1.27964i	−0.940867	−	0.338776i	$-0.889987\pi$
$557$	−30.2007	−	30.2007i	−1.27964	−	1.27964i	−0.338776	−	0.940867i	$-0.610013\pi$
$558$		0			0
$559$	−2.40302	+	11.7193i	−0.101637	+	0.495673i
$560$	−7.68873	+	25.1385i	−0.324908	+	1.06230i
$561$		0			0
$562$	−3.84684	+	6.66293i	−0.162269	+	0.281059i
$563$	−3.88594	−	6.73065i	−0.163773	−	0.283663i	0.772446	−	0.635081i	$-0.219033\pi$
$563$	−3.88594	−	6.73065i	−0.163773	−	0.283663i	−0.936219	+	0.351418i	$0.885700\pi$
$564$		0			0
$565$	−44.8879	−	44.8879i	−1.88845	−	1.88845i
$566$	−1.61613	+	0.433042i	−0.0679312	+	0.0182021i
$567$		0			0
$568$	2.73828	−	4.74284i	0.114896	−	0.199005i
$569$	7.38166	−	12.7854i	0.309455	−	0.535992i	−0.668788	−	0.743453i	$-0.733187\pi$
$569$	7.38166	−	12.7854i	0.309455	−	0.535992i	0.978243	+	0.207461i	$0.0665200\pi$
$570$		0			0
$571$	−17.8099	−	10.2826i	−0.745323	−	0.430312i	0.0786786	−	0.996900i	$-0.474930\pi$
$571$	−17.8099	−	10.2826i	−0.745323	−	0.430312i	−0.824001	+	0.566588i	$0.808263\pi$
$572$	0.985964	+	16.5360i	0.0412252	+	0.691407i
$573$		0			0
$574$	−2.35489	−	4.43013i	−0.0982914	−	0.184910i
$575$	19.0821	−	11.0170i	0.795778	−	0.459443i
$576$		0			0
$577$	44.6707	−	11.9695i	1.85966	−	0.498295i	0.859741	−	0.510730i	$-0.170625\pi$
$577$	44.6707	−	11.9695i	1.85966	−	0.498295i	0.999923	+	0.0124345i	$0.00395814\pi$
$578$	5.88246	+	1.57620i	0.244678	+	0.0655613i
$579$		0			0
$580$	28.4248	−	28.4248i	1.18027	−	1.18027i
$581$	−0.700299	+	2.28964i	−0.0290533	+	0.0949905i
$582$		0			0
$583$	−2.93664	−	10.9597i	−0.121623	−	0.453904i
$584$	4.54550	−	7.87303i	0.188094	−	0.325788i
$585$		0			0
$586$	−3.94104	−	6.82609i	−0.162803	−	0.281983i
$587$	27.6725	+	7.41484i	1.14217	+	0.306043i	0.779822	−	0.626001i	$-0.215309\pi$
$587$	27.6725	+	7.41484i	1.14217	+	0.306043i	0.362346	+	0.932044i	$0.381976\pi$
$588$		0			0
$589$	−72.3095	−	41.7479i	−2.97946	−	1.72019i
$590$	−15.6612	−	4.19642i	−0.644763	−	0.172764i
$591$		0			0
$592$	−2.20794	−	0.591616i	−0.0907458	−	0.0243153i
$593$	0.584753	−	2.18233i	0.0240129	−	0.0896174i	−0.952879	−	0.303349i	$-0.901895\pi$
$593$	0.584753	−	2.18233i	0.0240129	−	0.0896174i	0.976892	+	0.213732i	$0.0685618\pi$
$594$		0			0
$595$	35.2217	+	37.7792i	1.44395	+	1.54880i
$596$	3.08111	−	11.4989i	0.126207	−	0.471012i
$597$		0			0
$598$	−0.285007	−	4.77998i	−0.0116548	−	0.195468i
$599$	−6.35409	−	3.66854i	−0.259621	−	0.149892i	0.364541	−	0.931188i	$-0.381226\pi$
$599$	−6.35409	−	3.66854i	−0.259621	−	0.149892i	−0.624162	+	0.781295i	$0.714559\pi$
$600$		0			0
$601$	12.2600	+	21.2349i	0.500094	+	0.866188i	1.00000		0.000108542i	$3.45499e-5\pi$
$601$	12.2600	+	21.2349i	0.500094	+	0.866188i	−0.499906	+	0.866080i	$0.666632\pi$
$602$	0.895538	+	3.88101i	0.0364994	+	0.158178i
$603$		0			0
$604$	14.9768	+	14.9768i	0.609396	+	0.609396i
$605$	4.06951	−	15.1876i	0.165449	−	0.617464i
$606$		0			0
$607$	16.4984			0.669651			0.334826	−	0.942280i	$-0.391323\pi$
$607$	16.4984			0.669651			0.334826	+	0.942280i	$0.391323\pi$
$608$	−20.4561	−	35.4310i	−0.829605	−	1.43692i
$609$		0			0
$610$			4.40131i			0.178204i
$611$	−14.3459	+	0.855378i	−0.580374	+	0.0346049i
$612$		0			0
$613$	13.8780	+	13.8780i	0.560527	+	0.560527i	0.929457	−	0.368930i	$-0.120276\pi$
$613$	13.8780	+	13.8780i	0.560527	+	0.560527i	−0.368930	+	0.929457i	$0.620276\pi$
$614$	−3.65052	−	2.10763i	−0.147323	−	0.0850570i
$615$		0			0
$616$	5.47446	+	10.2988i	0.220572	+	0.414950i
$617$	−1.55373	−	5.79859i	−0.0625507	−	0.233442i	0.927572	−	0.373644i	$-0.121892\pi$
$617$	−1.55373	−	5.79859i	−0.0625507	−	0.233442i	−0.990123	+	0.140201i	$0.955225\pi$
$618$		0			0
$619$	2.57543	+	9.61163i	0.103515	+	0.386324i	0.998172	−	0.0604291i	$-0.0192469\pi$
$619$	2.57543	+	9.61163i	0.103515	+	0.386324i	−0.894657	+	0.446753i	$0.852580\pi$
$620$	−52.9377	+	30.5636i	−2.12603	+	1.22746i
$621$		0			0
$622$	−2.25535	−	0.604320i	−0.0904315	−	0.0242310i
$623$	−24.8420	+	23.1603i	−0.995274	+	0.927897i
$624$		0			0
$625$	−2.98647	−	5.17271i	−0.119459	−	0.206908i
$626$	2.95110	−	2.95110i	0.117950	−	0.117950i
$627$		0			0
$628$			12.9450i			0.516563i
$629$	−3.17578	+	3.17578i	−0.126627	+	0.126627i
$630$		0			0
$631$	0.0376954	+	0.140681i	0.00150063	+	0.00560043i	0.966672	−	0.256018i	$-0.0824106\pi$
$631$	0.0376954	+	0.140681i	0.00150063	+	0.00560043i	−0.965171	+	0.261618i	$0.915744\pi$
$632$	−1.30075	+	4.85447i	−0.0517411	+	0.193100i
$633$		0			0
$634$			10.9661i			0.435518i
$635$	5.46042	−	1.46311i	0.216690	−	0.0580619i
$636$		0			0
$637$	24.3090	+	6.78756i	0.963159	+	0.268933i
$638$		−	7.35502i		−	0.291188i
$639$		0			0
$640$	−38.9681			−1.54035
$641$	−2.36955	−	4.10418i	−0.0935916	−	0.162105i	0.815428	−	0.578858i	$-0.196501\pi$
$641$	−2.36955	−	4.10418i	−0.0935916	−	0.162105i	−0.909020	+	0.416753i	$0.863168\pi$
$642$		0			0
$643$	−19.4102	+	5.20095i	−0.765464	+	0.205105i	−0.620367	−	0.784312i	$-0.713016\pi$
$643$	−19.4102	+	5.20095i	−0.765464	+	0.205105i	−0.145097	+	0.989417i	$0.546349\pi$
$644$	6.52166	+	12.2688i	0.256989	+	0.483459i
$645$		0			0
$646$	−21.7072			−0.854060
$647$	27.0621			1.06392			0.531961	−	0.846769i	$-0.321455\pi$
$647$	27.0621			1.06392			0.531961	+	0.846769i	$0.321455\pi$
$648$		0			0
$649$	22.3906	−	12.9272i	0.878907	−	0.507437i
$650$	12.2927	−	0.732954i	0.482159	−	0.0287488i
$651$		0			0
$652$	−7.04121	+	26.2781i	−0.275755	+	1.02913i
$653$	−13.1748	−	7.60647i	−0.515569	−	0.297664i	0.219551	−	0.975601i	$-0.429541\pi$
$653$	−13.1748	−	7.60647i	−0.515569	−	0.297664i	−0.735120	+	0.677937i	$0.762874\pi$
$654$		0			0
$655$	−74.9690	+	20.0879i	−2.92928	+	0.784899i
$656$	−8.29617	+	8.29617i	−0.323911	+	0.323911i
$657$		0			0
$658$	−4.22499	+	2.24585i	−0.164707	+	0.0875524i
$659$	22.4492	+	12.9610i	0.874496	+	0.504891i	0.868840	−	0.495093i	$-0.164866\pi$
$659$	22.4492	+	12.9610i	0.874496	+	0.504891i	0.00565642	+	0.999984i	$0.498199\pi$
$660$		0			0
$661$	−25.2194	+	25.2194i	−0.980921	+	0.980921i	−0.999821	−	0.0189001i	$-0.993984\pi$
$661$	−25.2194	+	25.2194i	−0.980921	+	0.980921i	0.0189001	+	0.999821i	$0.493984\pi$
$662$	−4.53666	+	7.85772i	−0.176322	+	0.305399i
$663$		0			0
$664$	−1.55790			−0.0604582
$665$	−68.8801	−	43.0520i	−2.67106	−	1.66948i
$666$		0			0
$667$		−	18.5293i		−	0.717456i
$668$	1.91268	+	7.13824i	0.0740040	+	0.276187i
$669$		0			0
$670$	−12.5433	+	12.5433i	−0.484592	+	0.484592i
$671$	−4.96271	−	4.96271i	−0.191583	−	0.191583i
$672$		0			0
$673$	29.6825	−	17.1372i	1.14418	−	0.660590i	0.196714	−	0.980461i	$-0.436973\pi$
$673$	29.6825	−	17.1372i	1.14418	−	0.660590i	0.947461	+	0.319871i	$0.103640\pi$
$674$	4.16547	−	1.11614i	0.160448	−	0.0429919i
$675$		0			0
$676$	−9.17907	+	21.4416i	−0.353041	+	0.824679i
$677$	12.5430	−	7.24170i	0.482066	−	0.278321i	−0.239211	−	0.970968i	$-0.576889\pi$
$677$	12.5430	−	7.24170i	0.482066	−	0.278321i	0.721277	+	0.692646i	$0.243555\pi$
$678$		0			0
$679$	6.26159	−	5.83770i	0.240298	−	0.224030i
$680$	−16.8036	+	29.1046i	−0.644388	+	1.11611i
$681$		0			0
$682$	−2.89469	+	10.8031i	−0.110844	+	0.413674i
$683$	−4.40704	+	16.4473i	−0.168631	+	0.629338i	0.828919	+	0.559369i	$0.188957\pi$
$683$	−4.40704	+	16.4473i	−0.168631	+	0.629338i	−0.997549	+	0.0699686i	$0.977710\pi$
$684$		0			0
$685$	8.64951	−	14.9814i	0.330481	−	0.572410i
$686$	8.30000	−	1.31169i	0.316896	−	0.0500807i
$687$		0			0
$688$	8.06637	−	4.65712i	0.307527	−	0.177551i
$689$	3.20896	−	15.6498i	0.122251	−	0.596209i
$690$		0			0
$691$	30.4205	−	8.15114i	1.15725	−	0.310084i	0.371382	−	0.928480i	$-0.378884\pi$
$691$	30.4205	−	8.15114i	1.15725	−	0.310084i	0.785866	+	0.618396i	$0.212217\pi$
$692$	−25.3631	+	14.6434i	−0.964162	+	0.556659i
$693$		0			0
$694$	−6.42604	−	6.42604i	−0.243929	−	0.243929i
$695$	−36.0698	+	36.0698i	−1.36820	+	1.36820i
$696$		0			0
$697$	5.96637	+	22.2668i	0.225992	+	0.843415i
$698$		−	6.63652i		−	0.251196i
$699$		0			0
$700$	−31.5518	+	16.7718i	−1.19255	+	0.633914i
$701$	33.4863			1.26476			0.632380	−	0.774659i	$-0.282078\pi$
$701$	33.4863			1.26476			0.632380	+	0.774659i	$0.282078\pi$
$702$		0			0
$703$	3.53151	−	6.11675i	0.133193	−	0.230697i
$704$	6.29125	−	6.29125i	0.237111	−	0.237111i
$705$		0			0
$706$	9.42219	+	5.43991i	0.354609	+	0.204734i
$707$	−29.8679	+	15.8767i	−1.12330	+	0.597104i
$708$		0			0
$709$	34.1594	−	34.1594i	1.28288	−	1.28288i	0.343864	−	0.939020i	$-0.388264\pi$
$709$	34.1594	−	34.1594i	1.28288	−	1.28288i	0.939020	−	0.343864i	$-0.111736\pi$
$710$	4.93484	−	1.32229i	0.185201	−	0.0496245i
$711$		0			0
$712$	−19.1380	−	11.0493i	−0.717226	−	0.414090i
$713$	−7.29251	+	27.2160i	−0.273107	+	1.01925i
$714$		0			0
$715$	−21.6918	+	24.4426i	−0.811228	+	0.914101i
$716$	−14.6350	+	8.44949i	−0.546934	+	0.315772i
$717$		0			0
$718$	5.21622			0.194667
$719$	−14.2773			−0.532453			−0.266227	−	0.963910i	$-0.585777\pi$
$719$	−14.2773			−0.532453			−0.266227	+	0.963910i	$0.585777\pi$
$720$		0			0
$721$	−6.91075	+	11.0567i	−0.257370	+	0.411774i
$722$	24.6472	−	6.60419i	0.917273	−	0.245783i
$723$		0			0
$724$	−14.4198	−	24.9758i	−0.535908	−	0.928220i
$725$	47.6519			1.76975
$726$		0			0
$727$			12.4740i			0.462634i	0.972878	+	0.231317i	$0.0743034\pi$
$727$			12.4740i			0.462634i	−0.972878	+	0.231317i	$0.925697\pi$
$728$	0.402861	+	16.4169i	0.0149310	+	0.608451i
$729$		0			0
$730$	8.19175	−	2.19497i	0.303190	−	0.0812396i
$731$		−	18.3008i		−	0.676878i
$732$		0			0
$733$	−1.05756	+	3.94686i	−0.0390618	+	0.145781i	−0.982703	−	0.185191i	$-0.940710\pi$
$733$	−1.05756	+	3.94686i	−0.0390618	+	0.145781i	0.943641	+	0.330971i	$0.107376\pi$
$734$	0.926004	+	3.45589i	0.0341794	+	0.127559i
$735$		0			0
$736$	−9.76235	+	9.76235i	−0.359845	+	0.359845i
$737$		−	28.2866i		−	1.04195i
$738$		0			0
$739$	26.9099	−	26.9099i	0.989897	−	0.989897i	−0.0100526	−	0.999949i	$-0.503200\pi$
$739$	26.9099	−	26.9099i	0.989897	−	0.989897i	0.999949	+	0.0100526i	$0.00319990\pi$
$740$	−2.58541	−	4.47806i	−0.0950416	−	0.164617i
$741$		0			0
$742$	−1.19589	−	5.18265i	−0.0439025	−	0.190261i
$743$	3.73336	+	1.00035i	0.136964	+	0.0366993i	0.326650	−	0.945146i	$-0.394080\pi$
$743$	3.73336	+	1.00035i	0.136964	+	0.0366993i	−0.189686	+	0.981845i	$0.560747\pi$
$744$		0			0
$745$	20.3386	−	11.7425i	0.745147	−	0.430211i
$746$	0.113547	+	0.423762i	0.00415724	+	0.0155150i
$747$		0			0
$748$	−6.55878	−	24.4777i	−0.239813	−	0.894993i
$749$	3.63966	+	0.127513i	0.132990	+	0.00465924i
$750$		0			0
$751$	−18.0118	−	10.3991i	−0.657262	−	0.379470i	0.133971	−	0.990985i	$-0.457227\pi$
$751$	−18.0118	−	10.3991i	−0.657262	−	0.379470i	−0.791233	+	0.611515i	$0.790560\pi$
$752$	7.91202	+	7.91202i	0.288522	+	0.288522i
$753$		0			0
$754$	4.63490	−	9.26062i	0.168793	−	0.337252i
$755$			41.7841i			1.52068i
$756$		0			0
$757$	14.0844	+	24.3949i	0.511906	+	0.886647i	0.999905	+	0.0138025i	$0.00439361\pi$
$757$	14.0844	+	24.3949i	0.511906	+	0.886647i	−0.487999	+	0.872844i	$0.662273\pi$
$758$	−2.34530			−0.0851853
$759$		0			0
$760$	13.6789	−	51.0505i	0.496187	−	1.85180i
$761$	−18.4128	−	18.4128i	−0.667463	−	0.667463i	0.289665	−	0.957128i	$-0.406456\pi$
$761$	−18.4128	−	18.4128i	−0.667463	−	0.667463i	−0.957128	+	0.289665i	$0.906456\pi$
$762$		0			0
$763$	14.8253	−	13.8217i	0.536713	−	0.500379i
$764$	6.73670	+	11.6683i	0.243725	+	0.422144i
$765$		0			0
$766$	14.5723	+	8.41335i	0.526520	+	0.303987i
$767$	36.3380	−	2.16666i	1.31209	−	0.0782335i
$768$		0			0
$769$	5.15161	−	19.2261i	0.185772	−	0.693309i	−0.808692	−	0.588232i	$-0.799824\pi$
$769$	5.15161	−	19.2261i	0.185772	−	0.693309i	0.994464	−	0.105078i	$-0.0335091\pi$
$770$	−3.18231	+	10.4046i	−0.114683	+	0.374957i
$771$		0			0
$772$	8.76666	−	32.7176i	0.315519	−	1.17753i
$773$	−17.1176	−	4.58666i	−0.615679	−	0.164971i	−0.0625162	−	0.998044i	$-0.519913\pi$
$773$	−17.1176	−	4.58666i	−0.615679	−	0.164971i	−0.553163	+	0.833073i	$0.686579\pi$
$774$		0			0
$775$	−69.9916	−	18.7542i	−2.51417	−	0.673671i
$776$	4.82385	+	2.78505i	0.173166	+	0.0999776i
$777$		0			0
$778$	−0.299337	−	0.0802072i	−0.0107318	−	0.00287557i
$779$	−18.1263	−	31.3956i	−0.649441	−	1.12487i
$780$		0			0
$781$	−4.07335	+	7.05524i	−0.145756	+	0.252456i
$782$	1.89591	+	7.07562i	0.0677975	+	0.253024i
$783$		0			0
$784$	−8.61018	−	17.6637i	−0.307506	−	0.630845i
$785$	−18.0579	+	18.0579i	−0.644514	+	0.644514i
$786$		0			0
$787$	4.55393	+	1.22022i	0.162330	+	0.0434962i	0.339069	−	0.940762i	$-0.389888\pi$
$787$	4.55393	+	1.22022i	0.162330	+	0.0434962i	−0.176739	+	0.984258i	$0.556555\pi$
$788$	−41.6865	+	11.1699i	−1.48502	+	0.397910i
$789$		0			0
$790$	−4.06022	+	2.34417i	−0.144456	+	0.0834018i
$791$	47.4234	+	1.66145i	1.68618	+	0.0590745i
$792$		0			0
$793$	−3.12115	−	9.37583i	−0.110835	−	0.332946i
$794$	−2.25381	−	1.30124i	−0.0799846	−	0.0461791i
$795$		0			0
$796$	3.73515	−	6.46947i	0.132389	−	0.229304i
$797$	21.3304	−	36.9453i	0.755560	−	1.30867i	−0.189535	−	0.981874i	$-0.560698\pi$
$797$	21.3304	−	36.9453i	0.755560	−	1.30867i	0.945095	−	0.326795i	$-0.105969\pi$
$798$		0			0
$799$	21.2357	−	5.69010i	0.751267	−	0.201301i
$800$	−25.1059	−	25.1059i	−0.887628	−	0.887628i
$801$		0			0
$802$	−4.92782	−	8.53523i	−0.174007	−	0.301390i
$803$	−6.76169	+	11.7116i	−0.238615	+	0.413293i
$804$		0			0
$805$	−8.01709	+	26.2121i	−0.282565	+	0.923855i
$806$	−10.4525	+	11.7780i	−0.368173	+	0.414861i
$807$		0			0
$808$	−15.5625	−	15.5625i	−0.547488	−	0.547488i
$809$			33.4379i			1.17561i	0.809001	+	0.587807i	$0.200008\pi$
$809$			33.4379i			1.17561i	−0.809001	+	0.587807i	$0.799992\pi$
$810$		0			0
$811$	−36.3145	−	36.3145i	−1.27517	−	1.27517i	−0.943337	−	0.331836i	$-0.892332\pi$
$811$	−36.3145	−	36.3145i	−1.27517	−	1.27517i	−0.331836	−	0.943337i	$-0.607668\pi$
$812$	−1.05210	+	30.0303i	−0.0369214	+	1.05386i
$813$		0			0
$814$	−0.913851	−	0.244866i	−0.0320305	−	0.00858254i
$815$	−46.4794	+	26.8349i	−1.62810	+	0.939985i
$816$		0			0
$817$	7.44886	+	27.7995i	0.260603	+	0.972582i
$818$	−7.99283			−0.279463
$819$		0			0
$820$	−26.5405			−0.926833
$821$	1.77454	+	6.62268i	0.0619319	+	0.231133i	0.989953	−	0.141393i	$-0.0451582\pi$
$821$	1.77454	+	6.62268i	0.0619319	+	0.231133i	−0.928022	+	0.372527i	$0.878492\pi$
$822$		0			0
$823$	29.7340	−	17.1669i	1.03646	−	0.598402i	0.117633	−	0.993057i	$-0.462469\pi$
$823$	29.7340	−	17.1669i	1.03646	−	0.598402i	0.918829	+	0.394655i	$0.129136\pi$
$824$	−8.19469	−	2.19576i	−0.285476	−	0.0764930i
$825$		0			0
$826$	10.7018	−	5.68870i	0.372364	−	0.197935i
$827$	20.3490	+	20.3490i	0.707603	+	0.707603i	0.966031	−	0.258428i	$-0.0832043\pi$
$827$	20.3490	+	20.3490i	0.707603	+	0.707603i	−0.258428	+	0.966031i	$0.583204\pi$
$828$		0			0
$829$		−	37.3445i		−	1.29703i	−0.761202	−	0.648514i	$-0.775391\pi$
$829$		−	37.3445i		−	1.29703i	0.761202	−	0.648514i	$-0.224609\pi$
$830$	−1.02765	−	1.02765i	−0.0356703	−	0.0356703i
$831$		0			0
$832$	11.8858	−	3.95669i	0.412066	−	0.137174i
$833$	−38.5148	−	2.70201i	−1.33446	−	0.0936192i
$834$		0			0
$835$	−7.28947	+	12.6257i	−0.252262	+	0.436931i
$836$	19.9260	+	34.5129i	0.689157	+	1.19365i
$837$		0			0
$838$	−11.8660	−	11.8660i	−0.409905	−	0.409905i
$839$	14.0421	−	3.76256i	0.484786	−	0.129898i	−0.00814453	−	0.999967i	$-0.502593\pi$
$839$	14.0421	−	3.76256i	0.484786	−	0.129898i	0.492930	+	0.870069i	$0.335926\pi$
$840$		0			0
$841$	5.53610	−	9.58881i	0.190900	−	0.330648i
$842$	7.68670	−	13.3138i	0.264901	−	0.458822i
$843$		0			0
$844$	4.59526	+	2.65308i	0.158176	+	0.0913227i
$845$	−42.7149	+	17.1059i	−1.46944	+	0.588460i
$846$		0			0
$847$	5.51667	+	10.3782i	0.189555	+	0.356599i
$848$	−10.7717	+	6.21905i	−0.369902	+	0.213563i
$849$		0			0
$850$	−18.1964	+	4.87572i	−0.624132	+	0.167236i
$851$	−2.30224	−	0.616882i	−0.0789196	−	0.0211465i
$852$		0			0
$853$	−15.2764	+	15.2764i	−0.523053	+	0.523053i	−0.918492	−	0.395439i	$-0.870592\pi$
$853$	−15.2764	+	15.2764i	−0.523053	+	0.523053i	0.395439	+	0.918492i	$0.370592\pi$
$854$	−2.24350	−	2.40641i	−0.0767711	−	0.0823457i
$855$		0			0
$856$	0.613303	+	2.28888i	0.0209623	+	0.0782322i
$857$	−2.35575	+	4.08028i	−0.0804710	+	0.139380i	−0.903452	−	0.428689i	$-0.858976\pi$
$857$	−2.35575	+	4.08028i	−0.0804710	+	0.139380i	0.822981	+	0.568068i	$0.192309\pi$
$858$		0			0
$859$	9.15975	+	15.8652i	0.312527	+	0.541312i	0.978909	−	0.204299i	$-0.0654913\pi$
$859$	9.15975	+	15.8652i	0.312527	+	0.541312i	−0.666382	+	0.745610i	$0.732158\pi$
$860$	20.3520	+	5.45330i	0.693997	+	0.185956i
$861$		0			0
$862$	−9.26384	−	5.34848i	−0.315528	−	0.182170i
$863$	10.3154	+	2.76400i	0.351140	+	0.0940876i	0.430078	−	0.902792i	$-0.358486\pi$
$863$	10.3154	+	2.76400i	0.351140	+	0.0940876i	−0.0789379	+	0.996880i	$0.525153\pi$
$864$		0			0
$865$	−55.8078	−	14.9537i	−1.89752	−	0.508439i
$866$	−0.465568	+	1.73752i	−0.0158206	+	0.0590435i
$867$		0			0
$868$	13.3643	−	43.6948i	0.453613	−	1.48310i
$869$	1.93494	−	7.22129i	0.0656383	−	0.244966i
$870$		0			0
$871$	17.8253	−	35.6153i	0.603987	−	1.20678i
$872$	11.4212	+	6.59406i	0.386772	+	0.223303i
$873$		0			0
$874$	−5.75991	−	9.97645i	−0.194832	−	0.337459i
$875$	−22.6349	−	6.92299i	−0.765199	−	0.234040i
$876$		0			0
$877$	31.9876	+	31.9876i	1.08014	+	1.08014i	0.996495	+	0.0836487i	$0.0266573\pi$
$877$	31.9876	+	31.9876i	1.08014	+	1.08014i	0.0836487	+	0.996495i	$0.473343\pi$
$878$	−1.67590	+	6.25455i	−0.0565590	+	0.211081i
$879$		0			0
$880$	25.4439			0.857714
$881$	17.8907	+	30.9876i	0.602754	+	1.04400i	0.992402	+	0.123036i	$0.0392632\pi$
$881$	17.8907	+	30.9876i	0.602754	+	1.04400i	−0.389649	+	0.920964i	$0.627404\pi$
$882$		0			0
$883$		−	25.8540i		−	0.870056i	−0.900417	−	0.435028i	$-0.856739\pi$
$883$		−	25.8540i		−	0.870056i	0.900417	−	0.435028i	$-0.143261\pi$
$884$	7.16698	−	34.9527i	0.241052	−	1.17559i
$885$		0			0
$886$	−2.99915	−	2.99915i	−0.100759	−	0.100759i
$887$	−12.9576	−	7.48105i	−0.435072	−	0.251189i	0.266433	−	0.963853i	$-0.414155\pi$
$887$	−12.9576	−	7.48105i	−0.435072	−	0.251189i	−0.701505	+	0.712665i	$0.747488\pi$
$888$		0			0
$889$	−2.23968	+	3.58333i	−0.0751163	+	0.120181i
$890$	−5.33559	−	19.9127i	−0.178850	−	0.667475i
$891$		0			0
$892$	−4.07945	−	15.2247i	−0.136590	−	0.509761i
$893$	−29.9419	+	17.2869i	−1.00197	+	0.578486i
$894$		0			0
$895$	−32.2020	−	8.62850i	−1.07639	−	0.288419i
$896$	21.3058	−	19.8634i	0.711775	−	0.663590i
$897$		0			0
$898$	3.70755	+	6.42167i	0.123723	+	0.214294i
$899$	−43.0874	+	43.0874i	−1.43705	+	1.43705i
$900$		0			0
$901$			24.4386i			0.814166i
$902$	−3.43372	+	3.43372i	−0.114331	+	0.114331i
$903$		0			0
$904$	7.99111	+	29.8232i	0.265780	+	0.991906i
$905$	14.7253	−	54.9556i	0.489486	−	1.82679i
$906$		0			0
$907$			32.3923i			1.07557i	0.843082	+	0.537785i	$0.180739\pi$
$907$			32.3923i			1.07557i	−0.843082	+	0.537785i	$0.819261\pi$
$908$	45.8631	−	12.2890i	1.52202	−	0.407824i
$909$		0			0
$910$	−10.5635	+	11.0950i	−0.350176	+	0.367795i
$911$			32.8653i			1.08888i	0.838801	+	0.544438i	$0.183257\pi$
$911$			32.8653i			1.08888i	−0.838801	+	0.544438i	$0.816743\pi$
$912$		0			0
$913$	2.31746			0.0766968
$914$	−1.06645	−	1.84715i	−0.0352751	−	0.0610983i
$915$		0			0
$916$	−30.8621	+	8.26947i	−1.01971	+	0.273231i
$917$	30.7497	−	49.1974i	1.01545	−	1.62464i
$918$		0			0
$919$	−20.2714			−0.668692			−0.334346	−	0.942450i	$-0.608515\pi$
$919$	−20.2714			−0.668692			−0.334346	+	0.942450i	$0.608515\pi$
$920$	−17.8350			−0.588002
$921$		0			0
$922$	13.6658	−	7.88994i	0.450059	−	0.259841i
$923$	−9.57469	+	6.31628i	−0.315155	+	0.207903i
$924$		0			0
$925$	1.58644	−	5.92068i	0.0521618	−	0.194671i
$926$	−5.16943	−	2.98457i	−0.169878	−	0.0980791i
$927$		0			0
$928$	−28.8402	+	7.72770i	−0.946725	+	0.253674i
$929$	−37.0696	+	37.0696i	−1.21621	+	1.21621i	−0.247268	+	0.968947i	$0.579533\pi$
$929$	−37.0696	+	37.0696i	−1.21621	+	1.21621i	−0.968947	+	0.247268i	$0.920467\pi$
$930$		0			0
$931$	59.6052	−	11.5720i	1.95348	−	0.379258i
$932$	15.5929	+	9.00259i	0.510764	+	0.294890i
$933$		0			0
$934$	9.84929	−	9.84929i	0.322279	−	0.322279i
$935$	24.9963	−	43.2948i	0.817465	−	1.41589i
$936$		0			0
$937$	20.3329			0.664248			0.332124	−	0.943236i	$-0.392235\pi$
$937$	20.3329			0.664248			0.332124	+	0.943236i	$0.392235\pi$
$938$	0.464272	−	13.2519i	0.0151590	−	0.432688i
$939$		0			0
$940$			25.3115i			0.825570i
$941$	3.66765	+	13.6879i	0.119562	+	0.446211i	0.999588	−	0.0287148i	$-0.00914146\pi$
$941$	3.66765	+	13.6879i	0.119562	+	0.446211i	−0.880026	+	0.474926i	$0.842475\pi$
$942$		0			0
$943$	−8.65047	+	8.65047i	−0.281698	+	0.281698i
$944$	−20.0410	−	20.0410i	−0.652279	−	0.652279i
$945$		0			0
$946$	3.33861	−	1.92755i	0.108548	−	0.0626700i
$947$	−3.38723	+	0.907604i	−0.110070	+	0.0294932i	−0.313434	−	0.949610i	$-0.601479\pi$
$947$	−3.38723	+	0.907604i	−0.110070	+	0.0294932i	0.203364	+	0.979103i	$0.434813\pi$
$948$		0			0
$949$	−15.8938	+	10.4849i	−0.515935	+	0.340355i
$950$	25.6565	−	14.8128i	0.832407	−	0.480590i
$951$		0			0
$952$	−5.64834	−	24.4783i	−0.183064	−	0.793347i
$953$	−12.4383	+	21.5437i	−0.402915	+	0.697870i	−0.994076	−	0.108684i	$-0.965336\pi$
$953$	−12.4383	+	21.5437i	−0.402915	+	0.697870i	0.591161	+	0.806554i	$0.298670\pi$
$954$		0			0
$955$	−6.87942	+	25.6743i	−0.222613	+	0.830802i
$956$	−11.8532	+	44.2367i	−0.383360	+	1.43072i
$957$		0			0
$958$	−4.78653	+	8.29052i	−0.154646	+	0.267854i
$959$	2.90744	+	12.6000i	0.0938861	+	0.406876i
$960$		0			0
$961$	53.3983	−	30.8295i	1.72253	−	0.994501i
$962$	−0.996312	−	0.884187i	−0.0321224	−	0.0285073i
$963$		0			0
$964$	34.6783	−	9.29203i	1.11691	−	0.299276i
$965$	57.8692	−	33.4108i	1.86287	−	1.07553i
$966$		0			0
$967$	−1.81398	−	1.81398i	−0.0583338	−	0.0583338i	0.677338	−	0.735672i	$-0.263133\pi$
$967$	−1.81398	−	1.81398i	−0.0583338	−	0.0583338i	−0.735672	+	0.677338i	$0.763133\pi$
$968$	−5.40751	+	5.40751i	−0.173804	+	0.173804i
$969$		0			0
$970$	1.34487	+	5.01913i	0.0431813	+	0.161155i
$971$		−	11.4537i		−	0.367567i	−0.982967	−	0.183783i	$-0.941165\pi$
$971$		−	11.4537i		−	0.367567i	0.982967	−	0.183783i	$-0.0588345\pi$
$972$		0			0
$973$	1.33506	−	38.1071i	0.0428002	−	1.22166i
$974$	−5.81329			−0.186270
$975$		0			0
$976$	−3.84684	+	6.66292i	−0.123134	+	0.213275i
$977$	8.53070	−	8.53070i	0.272921	−	0.272921i	−0.557354	−	0.830275i	$-0.688183\pi$
$977$	8.53070	−	8.53070i	0.272921	−	0.272921i	0.830275	+	0.557354i	$0.188183\pi$
$978$		0			0
$979$	28.4688	+	16.4365i	0.909867	+	0.525312i
$980$	14.4816	−	42.0266i	0.462598	−	1.34249i
$981$		0			0
$982$	−4.01521	+	4.01521i	−0.128131	+	0.128131i
$983$	−5.41864	+	1.45192i	−0.172828	+	0.0463091i	−0.344195	−	0.938898i	$-0.611848\pi$
$983$	−5.41864	+	1.45192i	−0.172828	+	0.0463091i	0.171367	+	0.985207i	$0.445182\pi$
$984$		0			0
$985$	−73.7328	−	42.5697i	−2.34932	−	1.35638i
$986$	−4.10017	+	15.3020i	−0.130576	+	0.487316i
$987$		0			0
$988$	3.33970	+	56.0116i	0.106250	+	1.78197i
$989$	8.41086	−	4.85601i	0.267450	−	0.154412i
$990$		0			0
$991$	16.1378			0.512635			0.256318	−	0.966593i	$-0.417491\pi$
$991$	16.1378			0.512635			0.256318	+	0.966593i	$0.417491\pi$
$992$	45.4022			1.44152
$993$		0			0
$994$	−2.02410	+	3.23842i	−0.0642006	+	0.102716i
$995$	14.2351	−	3.81429i	0.451283	−	0.120921i
$996$		0			0
$997$	24.4254	+	42.3060i	0.773559	+	1.33984i	0.935601	+	0.353059i	$0.114859\pi$
$997$	24.4254	+	42.3060i	0.773559	+	1.33984i	−0.162042	+	0.986784i	$0.551808\pi$
$998$	−16.9043			−0.535097
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fd.a.557.17	yes	152
3.2	odd	2	inner	819.2.fd.a.557.22	yes	152
7.2	even	3		819.2.ez.a.674.17	yes	152
13.6	odd	12		819.2.ez.a.305.22	yes	152
21.2	odd	6		819.2.ez.a.674.22	yes	152
39.32	even	12		819.2.ez.a.305.17	✓	152
91.58	odd	12	inner	819.2.fd.a.422.22	yes	152
273.149	even	12	inner	819.2.fd.a.422.17	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ez.a.305.17	✓	152	39.32	even	12
819.2.ez.a.305.22	yes	152	13.6	odd	12
819.2.ez.a.674.17	yes	152	7.2	even	3
819.2.ez.a.674.22	yes	152	21.2	odd	6
819.2.fd.a.422.17	yes	152	273.149	even	12	inner
819.2.fd.a.422.22	yes	152	91.58	odd	12	inner
819.2.fd.a.557.17	yes	152	1.1	even	1	trivial
819.2.fd.a.557.22	yes	152	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.117431 - 0.438260i) q^{2} +(1.55377 - 0.897069i) q^{4} +(3.41884 + 0.916074i) q^{5} +(-2.33620 + 1.24184i) q^{7} +(-1.21727 - 1.21727i) q^{8} +O(q^{10})\)	\(q+(-0.117431 - 0.438260i) q^{2} +(1.55377 - 0.897069i) q^{4} +(3.41884 + 0.916074i) q^{5} +(-2.33620 + 1.24184i) q^{7} +(-1.21727 - 1.21727i) q^{8} -1.60591i q^{10} +(1.81075 + 1.81075i) q^{11} +(1.13882 + 3.42098i) q^{13} +(0.818592 + 0.878032i) q^{14} +(1.40360 - 2.43111i) q^{16} +(-2.75782 - 4.77669i) q^{17} +(6.13346 + 6.13346i) q^{19} +(6.13386 - 1.64356i) q^{20} +(0.580942 - 1.00622i) q^{22} +(1.46355 - 2.53494i) q^{23} +(6.51912 + 3.76382i) q^{25} +(1.36554 - 0.900829i) q^{26} +(-2.51590 + 4.02527i) q^{28} +(5.48217 - 3.16513i) q^{29} +(-9.29796 + 2.49138i) q^{31} +(-4.55592 - 1.22076i) q^{32} +(-1.76958 + 1.76958i) q^{34} +(-9.12470 + 2.10551i) q^{35} +(-0.210749 - 0.786526i) q^{37} +(1.96779 - 3.40831i) q^{38} +(-3.04653 - 5.27675i) q^{40} +(-4.03703 - 1.08172i) q^{41} +(2.87345 + 1.65899i) q^{43} +(4.43787 + 1.18912i) q^{44} +(-1.28283 - 0.343733i) q^{46} +(-1.03163 + 3.85009i) q^{47} +(3.91567 - 5.80237i) q^{49} +(0.883980 - 3.29906i) q^{50} +(4.83832 + 4.29381i) q^{52} +(-3.83716 - 2.21539i) q^{53} +(4.53189 + 7.84946i) q^{55} +(4.35543 + 1.33213i) q^{56} +(-2.03093 - 2.03093i) q^{58} +(2.61310 - 9.75222i) q^{59} -2.74069 q^{61} +(2.18374 + 3.78236i) q^{62} -3.47438i q^{64} +(0.759565 + 12.7390i) q^{65} +(-7.81072 - 7.81072i) q^{67} +(-8.57004 - 4.94791i) q^{68} +(1.99429 + 3.75174i) q^{70} +(0.823385 + 3.07291i) q^{71} +(1.36681 + 5.10099i) q^{73} +(-0.319954 + 0.184726i) q^{74} +(15.0321 + 4.02785i) q^{76} +(-6.47895 - 1.98162i) q^{77} +(-1.45971 - 2.52829i) q^{79} +(7.02577 - 7.02577i) q^{80} +1.89629i q^{82} +(0.639916 - 0.639916i) q^{83} +(-5.05274 - 18.8571i) q^{85} +(0.389634 - 1.45413i) q^{86} -4.40835i q^{88} +(12.3996 - 3.32246i) q^{89} +(-6.90882 - 6.57786i) q^{91} -5.25161i q^{92} +1.80849 q^{94} +(15.3506 + 26.5880i) q^{95} +(-3.12540 + 0.837450i) q^{97} +(-3.00277 - 1.03470i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} + 88 q^{16} + 4 q^{19} + 16 q^{28} - 16 q^{31} + 48 q^{34} - 8 q^{37} - 40 q^{40} + 72 q^{43} - 72 q^{46} - 28 q^{49} - 64 q^{52} + 16 q^{55} + 16 q^{58} + 64 q^{61} - 124 q^{67} - 40 q^{70} - 4 q^{73} - 72 q^{76} - 16 q^{79} - 88 q^{85} - 4 q^{91} + 16 q^{94} - 140 q^{97}+O(q^{100}) \) 152 * q + 8 * q^7 + 88 * q^16 + 4 * q^19 + 16 * q^28 - 16 * q^31 + 48 * q^34 - 8 * q^37 - 40 * q^40 + 72 * q^43 - 72 * q^46 - 28 * q^49 - 64 * q^52 + 16 * q^55 + 16 * q^58 + 64 * q^61 - 124 * q^67 - 40 * q^70 - 4 * q^73 - 72 * q^76 - 16 * q^79 - 88 * q^85 - 4 * q^91 + 16 * q^94 - 140 * q^97

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