LMFDB - Embedded newform 819.2.fd.a.422.17

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			422.17
Character	$\chi$	$=$	819.422
Dual form			819.2.fd.a.557.17

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$

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	−0.994935	−	0.100519i	$-0.967950\pi$
$2$	−0.117431	+	0.438260i	−0.0830365	+	0.309897i	0.911899	+	0.410416i	$0.134616\pi$
$3$		0			0
$3$		0			0
$4$	1.55377	+	0.897069i	0.776885	+	0.448535i
$5$	3.41884	−	0.916074i	1.52895	−	0.409681i	0.606274	−	0.795256i	$-0.292664\pi$
$5$	3.41884	−	0.916074i	1.52895	−	0.409681i	0.922676	+	0.385575i	$0.125997\pi$
$6$		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	−0.379308	−	0.925271i	$-0.623838\pi$
$11$	1.81075	−	1.81075i	0.545963	−	0.545963i	0.925271	+	0.379308i	$0.123838\pi$
$12$		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	0.309351	+	0.950948i	$0.399888\pi$
$17$	−2.75782	+	4.77669i	−0.668870	+	1.15852i	−0.978220	+	0.207569i	$0.933445\pi$
$18$		0			0
$19$	6.13346	−	6.13346i	1.40711	−	1.40711i	0.632786	−	0.774326i	$-0.281911\pi$
$19$	6.13346	−	6.13346i	1.40711	−	1.40711i	0.774326	−	0.632786i	$-0.218089\pi$
$20$	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	0.977299	−	0.211863i	$-0.0679531\pi$
$23$	1.46355	+	2.53494i	0.305171	+	0.528571i	−0.672129	+	0.740434i	$0.734620\pi$
$24$		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	0.913528	−	0.406777i	$-0.133347\pi$
$29$	5.48217	+	3.16513i	1.01801	+	0.587750i	0.104485	+	0.994526i	$0.466681\pi$
$30$		0			0
$31$	−9.29796	−	2.49138i	−1.66996	−	0.447465i	−0.704862	−	0.709344i	$-0.748991\pi$
$31$	−9.29796	−	2.49138i	−1.66996	−	0.447465i	−0.965101	+	0.261879i	$0.915658\pi$
$32$	−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	−0.981083	−	0.193587i	$-0.937988\pi$
$37$	−0.210749	+	0.786526i	−0.0346469	+	0.129304i	0.946436	+	0.322891i	$0.104655\pi$
$38$	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	−0.559886	−	0.828569i	$-0.689155\pi$
$41$	−4.03703	+	1.08172i	−0.630478	+	0.168936i	−0.0705913	+	0.997505i	$0.522489\pi$
$42$		0			0
$43$	2.87345	−	1.65899i	0.438197	−	0.252993i	−0.264636	−	0.964348i	$-0.585252\pi$
$43$	2.87345	−	1.65899i	0.438197	−	0.252993i	0.702832	+	0.711355i	$0.251918\pi$
$44$	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	−0.999450	−	0.0331554i	$-0.989444\pi$
$47$	−1.03163	−	3.85009i	−0.150479	−	0.561594i	0.848972	−	0.528439i	$-0.177222\pi$
$48$		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	−0.739824	−	0.672800i	$-0.765091\pi$
$53$	−3.83716	+	2.21539i	−0.527075	+	0.304307i	0.212750	+	0.977107i	$0.431758\pi$
$54$		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	0.898124	+	0.439742i	$0.144930\pi$
$59$	2.61310	+	9.75222i	0.340197	+	1.26963i	−0.557928	+	0.829890i	$0.688403\pi$
$60$		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	−0.998997	−	0.0447664i	$-0.985746\pi$
$67$	−7.81072	+	7.81072i	−0.954231	+	0.954231i	0.0447664	+	0.998997i	$0.485746\pi$
$68$	−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	−0.899700	−	0.436509i	$-0.856215\pi$
$71$	0.823385	−	3.07291i	0.0977178	−	0.364688i	0.997417	+	0.0718216i	$0.0228812\pi$
$72$		0			0
$73$	1.36681	−	5.10099i	0.159972	−	0.597025i	−0.838656	−	0.544662i	$-0.816658\pi$
$73$	1.36681	−	5.10099i	0.159972	−	0.597025i	0.998628	−	0.0523633i	$-0.0166754\pi$
$74$	−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	−0.936382	−	0.350983i	$-0.885847\pi$
$79$	−1.45971	+	2.52829i	−0.164230	+	0.284455i	0.772151	+	0.635439i	$0.219181\pi$
$80$	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	0.741354	−	0.671114i	$-0.234184\pi$
$83$	0.639916	+	0.639916i	0.0702399	+	0.0702399i	−0.671114	+	0.741354i	$0.734184\pi$
$84$		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	0.846861	−	0.531815i	$-0.178490\pi$
$89$	12.3996	+	3.32246i	1.31436	+	0.352181i	0.467495	+	0.883996i	$0.345157\pi$
$90$		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	0.0966349	−	0.995320i	$-0.469192\pi$
$97$	−3.12540	−	0.837450i	−0.317337	−	0.0850301i	−0.413972	+	0.910290i	$0.635859\pi$
$98$	−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	0.695305	−	0.718715i	$-0.255269\pi$
$103$	4.26794	+	2.46410i	0.420533	+	0.242795i	−0.274772	+	0.961509i	$0.588603\pi$
$104$	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	−0.556514	−	0.830838i	$-0.687861\pi$
$107$	−1.19209	+	0.688252i	−0.115243	+	0.0665359i	0.441270	+	0.897374i	$0.354528\pi$
$108$		0			0
$109$	−7.39990	−	1.98280i	−0.708782	−	0.189917i	−0.113621	−	0.993524i	$-0.536245\pi$
$109$	−7.39990	−	1.98280i	−0.708782	−	0.189917i	−0.595161	+	0.803607i	$0.702912\pi$
$110$	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	−0.999066	−	0.0432171i	$-0.986239\pi$
$113$	−15.5325	+	8.96767i	−1.46117	+	0.843608i	−0.462106	+	0.886825i	$0.652906\pi$
$114$		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	0.560112	−	0.828417i	$-0.310758\pi$
$127$	1.38318	+	0.798578i	0.122737	+	0.0708624i	−0.437374	+	0.899279i	$0.644092\pi$
$128$	−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	−0.973085	−	0.230446i	$-0.925981\pi$
$131$	−18.9904	−	10.9641i	−1.65920	−	0.957940i	−0.686115	−	0.727493i	$-0.740685\pi$
$132$		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	0.998676	−	0.0514454i	$-0.0163828\pi$
$137$	1.26498	+	4.72097i	0.108074	+	0.403339i	−0.890601	+	0.454785i	$0.849716\pi$
$138$		0			0
$139$	−7.20599	−	12.4811i	−0.611204	−	1.05864i	−0.991038	−	0.133582i	$-0.957352\pi$
$139$	−7.20599	−	12.4811i	−0.611204	−	1.05864i	0.379833	−	0.925055i	$-0.375981\pi$
$140$	−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	0.872673	−	0.488305i	$-0.162385\pi$
$149$	4.69181	+	4.69181i	0.384368	+	0.384368i	−0.488305	+	0.872673i	$0.662385\pi$
$150$		0			0
$151$	3.05544	−	11.4030i	0.248648	−	0.927967i	−0.722867	−	0.690987i	$-0.757176\pi$
$151$	3.05544	−	11.4030i	0.248648	−	0.927967i	0.971515	−	0.236979i	$-0.0761573\pi$
$152$			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	0.685395	−	0.728171i	$-0.259629\pi$
$157$	−3.60759	−	6.24853i	−0.287917	−	0.498687i	−0.973312	+	0.229484i	$0.926296\pi$
$158$	−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	0.149015	−	0.988835i	$-0.452390\pi$
$163$	−10.7221	−	10.7221i	−0.839820	−	0.839820i	−0.988835	+	0.149015i	$0.952390\pi$
$164$	−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	0.912333	−	0.409449i	$-0.134279\pi$
$167$	−1.06607	−	3.97864i	−0.0824953	−	0.307877i	−0.994828	+	0.101573i	$0.967613\pi$
$168$		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	$0.203799\pi$
$181$			16.0744i			1.19480i	−0.801944	+	0.597399i	$0.796201\pi$
$182$	−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	$-0.912417\pi$
$191$		−	7.50968i		−	0.543381i	0.962385	−	0.271691i	$-0.0875827\pi$
$192$		0			0
$193$	13.3496	+	13.3496i	0.960922	+	0.960922i	0.999265	−	0.0383422i	$-0.0122077\pi$
$193$	13.3496	+	13.3496i	0.960922	+	0.960922i	−0.0383422	+	0.999265i	$0.512208\pi$
$194$	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	−0.961121	−	0.276126i	$-0.910949\pi$
$197$	−23.2348	+	6.22576i	−1.65541	+	0.443567i	−0.694292	+	0.719693i	$0.744283\pi$
$198$		0			0
$199$	3.60590	+	2.08186i	0.255615	+	0.147579i	0.622333	−	0.782753i	$-0.286185\pi$
$199$	3.60590	+	2.08186i	0.255615	+	0.147579i	−0.366718	+	0.930332i	$0.619518\pi$
$200$	−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	−0.810626	−	0.585565i	$-0.800873\pi$
$211$	1.47875	−	2.56127i	0.101801	−	0.176325i	0.912427	+	0.409240i	$0.134206\pi$
$212$	−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	0.999324	+	0.0367571i	$0.0117028\pi$
$223$	2.27377	+	8.48581i	0.152263	+	0.568252i	−0.847062	+	0.531495i	$0.821631\pi$
$224$	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	0.724564	−	0.689207i	$-0.242041\pi$
$227$	25.5627	−	6.84952i	1.69666	−	0.454618i	0.972095	+	0.234589i	$0.0753743\pi$
$228$		0			0
$229$	−17.2016	+	4.60916i	−1.13672	+	0.304582i	−0.777630	−	0.628723i	$-0.783578\pi$
$229$	−17.2016	+	4.60916i	−1.13672	+	0.304582i	−0.359086	+	0.933305i	$0.616911\pi$
$230$	−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	−0.653534	−	0.756897i	$-0.726714\pi$
$233$	5.01778	−	8.69105i	0.328726	−	0.569370i	0.982259	+	0.187528i	$0.0600475\pi$
$234$		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	−0.982786	−	0.184748i	$-0.940853\pi$
$239$	−18.0496	−	18.0496i	−1.16753	−	1.16753i	−0.184748	−	0.982786i	$-0.559147\pi$
$240$		0			0
$241$	19.3287	−	5.17911i	1.24507	−	0.333616i	0.424640	−	0.905362i	$-0.360401\pi$
$241$	19.3287	−	5.17911i	1.24507	−	0.333616i	0.820430	+	0.571747i	$0.193734\pi$
$242$	−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	0.720679	−	0.693269i	$-0.243830\pi$
$251$	−3.80309	−	6.58714i	−0.240049	−	0.415777i	−0.960728	+	0.277492i	$0.910497\pi$
$252$		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	0.999996	+	0.00265094i	$0.000843820\pi$
$257$	8.05239	+	13.9471i	0.502294	+	0.869999i	−0.497702	+	0.867348i	$0.665823\pi$
$258$		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	$0.000644077\pi$
$263$			0.0656289i			0.00404685i	−0.999998	+	0.00202343i	$0.999356\pi$
$264$		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	0.597922	−	0.801554i	$-0.295993\pi$
$269$	3.32480	+	1.91957i	0.202716	+	0.117038i	−0.395205	+	0.918593i	$0.629327\pi$
$270$		0			0
$271$	2.56064	−	9.55645i	0.155548	−	0.580513i	−0.843510	−	0.537114i	$-0.819515\pi$
$271$	2.56064	−	9.55645i	0.155548	−	0.580513i	0.999058	−	0.0433992i	$-0.0138187\pi$
$272$	−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	0.355579	−	0.934646i	$-0.384284\pi$
$277$	−4.59453	−	2.65265i	−0.276059	−	0.159382i	−0.631638	+	0.775264i	$0.717617\pi$
$278$	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	−0.967636	−	0.252352i	$-0.918796\pi$
$281$	−11.9903	+	11.9903i	−0.715284	+	0.715284i	0.252352	+	0.967636i	$0.418796\pi$
$282$		0			0
$283$			3.68762i			0.219206i	0.993975	+	0.109603i	$0.0349580\pi$
$283$			3.68762i			0.219206i	−0.993975	+	0.109603i	$0.965042\pi$
$284$	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	0.713175	−	0.700986i	$-0.247257\pi$
$293$	16.7802	+	4.49624i	0.980309	+	0.262673i	0.267134	+	0.963659i	$0.413923\pi$
$294$		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	0.869270	−	0.494338i	$-0.164590\pi$
$307$	6.56933	+	6.56933i	0.374932	+	0.374932i	−0.494338	+	0.869270i	$0.664590\pi$
$308$	−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	0.929711	−	0.368291i	$-0.120057\pi$
$311$	2.57308	+	4.45670i	0.145906	+	0.252716i	−0.783805	+	0.621007i	$0.786724\pi$
$312$		0			0
$313$	4.59918	−	7.96602i	0.259961	−	0.450266i	−0.706270	−	0.707942i	$-0.749624\pi$
$313$	4.59918	−	7.96602i	0.259961	−	0.450266i	0.966231	+	0.257677i	$0.0829569\pi$
$314$	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	−0.845683	−	0.533686i	$-0.820807\pi$
$317$	−23.3457	+	6.25545i	−1.31122	+	0.351341i	−0.465540	+	0.885027i	$0.654140\pi$
$318$		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	−0.979359	−	0.202129i	$-0.935214\pi$
$331$	−14.1404	+	14.1404i	−0.777229	+	0.777229i	0.202129	+	0.979359i	$0.435214\pi$
$332$	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	$-0.916649\pi$
$337$		−	9.50458i		−	0.517747i	0.965911	−	0.258874i	$-0.0833513\pi$
$338$	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	0.887186	−	0.461412i	$-0.152657\pi$
$347$	17.3461	+	10.0148i	0.931185	+	0.537620i	0.0439990	+	0.999032i	$0.485990\pi$
$348$		0			0
$349$	14.1285	−	3.78572i	0.756282	−	0.202645i	0.139979	−	0.990154i	$-0.455296\pi$
$349$	14.1285	−	3.78572i	0.756282	−	0.202645i	0.616303	+	0.787509i	$0.288630\pi$
$350$	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	0.0931824	−	0.995649i	$-0.470296\pi$
$353$	−16.9558	−	16.9558i	−0.902467	−	0.902467i	−0.995649	+	0.0931824i	$0.970296\pi$
$354$		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	−0.998922	−	0.0464242i	$-0.985217\pi$
$359$	−2.97553	−	11.1048i	−0.157042	−	0.586090i	0.841880	−	0.539665i	$-0.181449\pi$
$360$		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	0.991736	−	0.128293i	$-0.0409499\pi$
$379$	1.33785	+	4.99292i	0.0687207	+	0.256469i	−0.923016	+	0.384763i	$0.874283\pi$
$380$	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	−0.896078	−	0.443897i	$-0.853596\pi$
$383$	−26.2238	−	26.2238i	−1.33997	−	1.33997i	−0.443897	−	0.896078i	$-0.646404\pi$
$384$		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	0.874553	−	0.484930i	$-0.161155\pi$
$389$	0.341507	+	0.591507i	0.0173151	+	0.0299906i	−0.857238	+	0.514920i	$0.827821\pi$
$390$		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	0.801522	−	0.597965i	$-0.204024\pi$
$397$	4.05586	+	4.05586i	0.203558	+	0.203558i	−0.597965	+	0.801522i	$0.704024\pi$
$398$	−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	0.741332	−	0.671138i	$-0.234194\pi$
$401$	20.9817	+	5.62203i	1.04778	+	0.280751i	0.306444	+	0.951889i	$0.400861\pi$
$402$		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	0.982224	+	0.187711i	$0.0601068\pi$
$409$	4.55941	+	17.0160i	0.225449	+	0.841385i	−0.756776	+	0.653675i	$0.773227\pi$
$410$	−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	0.996761	+	0.0804205i	$0.0256263\pi$
$419$	32.0304	+	18.4928i	1.56479	+	0.903431i	0.568027	+	0.823010i	$0.307707\pi$
$420$		0			0
$421$	23.9589	−	23.9589i	1.16769	−	1.16769i	0.184935	−	0.982751i	$-0.440792\pi$
$421$	23.9589	−	23.9589i	1.16769	−	1.16769i	0.982751	−	0.184935i	$-0.0592076\pi$
$422$	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	0.983564	−	0.180558i	$-0.0577903\pi$
$431$	16.6708	+	16.6708i	0.803007	+	0.803007i	−0.180558	+	0.983564i	$0.557790\pi$
$432$		0			0
$433$	−3.43344	+	1.98230i	−0.165001	+	0.0952632i	−0.580226	−	0.814455i	$-0.697036\pi$
$433$	−3.43344	+	1.98230i	−0.165001	+	0.0952632i	0.415226	+	0.909718i	$0.363703\pi$
$434$	−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	−0.765050	−	0.643971i	$-0.777286\pi$
$439$	−12.3593	+	7.13567i	−0.589879	+	0.340567i	0.175171	+	0.984538i	$0.443952\pi$
$440$	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	0.679835	−	0.733365i	$-0.262051\pi$
$443$	8.09574	+	4.67407i	0.384640	+	0.222072i	−0.295195	+	0.955437i	$0.595385\pi$
$444$		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	−0.133695	−	0.991023i	$-0.542684\pi$
$449$	−15.7860	−	4.22986i	−0.744989	−	0.199619i	−0.611294	+	0.791403i	$0.709351\pi$
$450$		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	0.363453	−	0.931612i	$-0.381598\pi$
$457$	4.54075	+	1.21669i	0.212407	+	0.0569143i	−0.151046	+	0.988527i	$0.548264\pi$
$458$		−	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	−0.356952	−	0.934123i	$-0.616184\pi$
$461$	9.00144	−	33.5938i	0.419239	−	1.56462i	0.776191	−	0.630498i	$-0.217149\pi$
$462$		0			0
$463$	9.30270	+	9.30270i	0.432333	+	0.432333i	0.889421	−	0.457088i	$-0.151108\pi$
$463$	9.30270	+	9.30270i	0.432333	+	0.432333i	−0.457088	+	0.889421i	$0.651108\pi$
$464$			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	−0.254440	−	0.967089i	$-0.581891\pi$
$467$	15.3498	−	26.5866i	0.710303	−	1.23028i	0.964743	−	0.263193i	$-0.0847755\pi$
$468$		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	−0.960379	−	0.278699i	$-0.910097\pi$
$479$	−14.9193	+	14.9193i	−0.681680	+	0.681680i	0.278699	+	0.960379i	$0.410097\pi$
$480$		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	0.999464	+	0.0327301i	$0.0104202\pi$
$487$	3.31612	+	12.3759i	0.150268	+	0.560807i	−0.849196	+	0.528077i	$0.822913\pi$
$488$	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	−0.971975	−	0.235083i	$-0.924464\pi$
$491$	−6.25756	+	10.8384i	−0.282400	+	0.489131i	0.689575	+	0.724214i	$0.257797\pi$
$492$		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	0.748902	+	0.662680i	$0.230581\pi$
$499$	9.64287	+	35.9877i	0.431674	+	1.61103i	−0.317228	+	0.948349i	$0.602752\pi$
$500$	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	−0.925251	−	0.379356i	$-0.876146\pi$
$503$	−23.7586	+	13.7170i	−1.05934	+	0.611613i	−0.134094	+	0.990969i	$0.542812\pi$
$504$		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	−0.975301	−	0.220878i	$-0.929108\pi$
$509$	−0.456329	+	1.70304i	−0.0202264	+	0.0754860i	0.955075	+	0.296364i	$0.0957743\pi$
$510$		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	−0.641829	−	0.766848i	$-0.721824\pi$
$521$	−6.81645	+	3.93548i	−0.298634	+	0.172416i	0.343195	+	0.939264i	$0.388491\pi$
$522$		0			0
$523$	−9.98176	−	17.2889i	−0.436472	−	0.755991i	0.560943	−	0.827855i	$-0.310439\pi$
$523$	−9.98176	−	17.2889i	−0.436472	−	0.755991i	−0.997414	+	0.0718633i	$0.977105\pi$
$524$	−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	0.530653	−	0.847589i	$-0.321947\pi$
$541$	32.8889	−	8.81257i	1.41401	−	0.378882i	0.883353	+	0.468708i	$0.155280\pi$
$542$	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	−0.338776	+	0.940867i	$0.610013\pi$
$557$	−30.2007	+	30.2007i	−1.27964	+	1.27964i	−0.940867	+	0.338776i	$0.889987\pi$
$558$		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	−0.936219	−	0.351418i	$-0.885700\pi$
$563$	−3.88594	+	6.73065i	−0.163773	+	0.283663i	0.772446	+	0.635081i	$0.219033\pi$
$564$		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	0.978243	−	0.207461i	$-0.0665200\pi$
$569$	7.38166	+	12.7854i	0.309455	+	0.535992i	−0.668788	+	0.743453i	$0.733187\pi$
$570$		0			0
$571$	−17.8099	+	10.2826i	−0.745323	+	0.430312i	−0.824001	−	0.566588i	$-0.808263\pi$
$571$	−17.8099	+	10.2826i	−0.745323	+	0.430312i	0.0786786	+	0.996900i	$0.474930\pi$
$572$	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	0.999923	−	0.0124345i	$-0.00395814\pi$
$577$	44.6707	+	11.9695i	1.85966	+	0.498295i	0.859741	+	0.510730i	$0.170625\pi$
$578$	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	0.362346	−	0.932044i	$-0.381976\pi$
$587$	27.6725	−	7.41484i	1.14217	−	0.306043i	0.779822	+	0.626001i	$0.215309\pi$
$588$		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	0.976892	−	0.213732i	$-0.0685618\pi$
$593$	0.584753	+	2.18233i	0.0240129	+	0.0896174i	−0.952879	+	0.303349i	$0.901895\pi$
$594$		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	−0.624162	−	0.781295i	$-0.714559\pi$
$599$	−6.35409	+	3.66854i	−0.259621	+	0.149892i	0.364541	+	0.931188i	$0.381226\pi$
$600$		0			0
$601$	12.2600	−	21.2349i	0.500094	−	0.866188i	−0.499906	−	0.866080i	$-0.666632\pi$
$601$	12.2600	−	21.2349i	0.500094	−	0.866188i	1.00000		0.000108542i	$-3.45499e-5\pi$
$602$	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	−0.368930	−	0.929457i	$-0.620276\pi$
$613$	13.8780	−	13.8780i	0.560527	−	0.560527i	0.929457	+	0.368930i	$0.120276\pi$
$614$	−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	−0.990123	−	0.140201i	$-0.955225\pi$
$617$	−1.55373	+	5.79859i	−0.0625507	+	0.233442i	0.927572	+	0.373644i	$0.121892\pi$
$618$		0			0
$619$	2.57543	−	9.61163i	0.103515	−	0.386324i	−0.894657	−	0.446753i	$-0.852580\pi$
$619$	2.57543	−	9.61163i	0.103515	−	0.386324i	0.998172	+	0.0604291i	$0.0192469\pi$
$620$	−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	−0.965171	−	0.261618i	$-0.915744\pi$
$631$	0.0376954	−	0.140681i	0.00150063	−	0.00560043i	0.966672	+	0.256018i	$0.0824106\pi$
$632$	−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	−0.909020	−	0.416753i	$-0.863168\pi$
$641$	−2.36955	+	4.10418i	−0.0935916	+	0.162105i	0.815428	+	0.578858i	$0.196501\pi$
$642$		0			0
$643$	−19.4102	−	5.20095i	−0.765464	−	0.205105i	−0.145097	−	0.989417i	$-0.546349\pi$
$643$	−19.4102	−	5.20095i	−0.765464	−	0.205105i	−0.620367	+	0.784312i	$0.713016\pi$
$644$	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	−0.735120	−	0.677937i	$-0.762874\pi$
$653$	−13.1748	+	7.60647i	−0.515569	+	0.297664i	0.219551	+	0.975601i	$0.429541\pi$
$654$		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	0.00565642	−	0.999984i	$-0.498199\pi$
$659$	22.4492	−	12.9610i	0.874496	−	0.504891i	0.868840	+	0.495093i	$0.164866\pi$
$660$		0			0
$661$	−25.2194	−	25.2194i	−0.980921	−	0.980921i	0.0189001	−	0.999821i	$-0.493984\pi$
$661$	−25.2194	−	25.2194i	−0.980921	−	0.980921i	−0.999821	+	0.0189001i	$0.993984\pi$
$662$	−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	0.947461	−	0.319871i	$-0.103640\pi$
$673$	29.6825	+	17.1372i	1.14418	+	0.660590i	0.196714	+	0.980461i	$0.436973\pi$
$674$	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	0.721277	−	0.692646i	$-0.243555\pi$
$677$	12.5430	+	7.24170i	0.482066	+	0.278321i	−0.239211	+	0.970968i	$0.576889\pi$
$678$		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	−0.997549	−	0.0699686i	$-0.977710\pi$
$683$	−4.40704	−	16.4473i	−0.168631	−	0.629338i	0.828919	−	0.559369i	$-0.188957\pi$
$684$		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	0.785866	−	0.618396i	$-0.212217\pi$
$691$	30.4205	+	8.15114i	1.15725	+	0.310084i	0.371382	+	0.928480i	$0.378884\pi$
$692$	−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	0.939020	+	0.343864i	$0.111736\pi$
$709$	34.1594	+	34.1594i	1.28288	+	1.28288i	0.343864	+	0.939020i	$0.388264\pi$
$710$	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	$-0.925697\pi$
$727$		−	12.4740i		−	0.462634i	0.972878	−	0.231317i	$-0.0743034\pi$
$728$	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	0.943641	−	0.330971i	$-0.107376\pi$
$733$	−1.05756	−	3.94686i	−0.0390618	−	0.145781i	−0.982703	+	0.185191i	$0.940710\pi$
$734$	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	0.999949	−	0.0100526i	$-0.00319990\pi$
$739$	26.9099	+	26.9099i	0.989897	+	0.989897i	−0.0100526	+	0.999949i	$0.503200\pi$
$740$	−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	−0.189686	−	0.981845i	$-0.560747\pi$
$743$	3.73336	−	1.00035i	0.136964	−	0.0366993i	0.326650	+	0.945146i	$0.394080\pi$
$744$		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	−0.791233	−	0.611515i	$-0.790560\pi$
$751$	−18.0118	+	10.3991i	−0.657262	+	0.379470i	0.133971	+	0.990985i	$0.457227\pi$
$752$	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	−0.487999	−	0.872844i	$-0.662273\pi$
$757$	14.0844	−	24.3949i	0.511906	−	0.886647i	0.999905	−	0.0138025i	$-0.00439361\pi$
$758$	−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	−0.957128	−	0.289665i	$-0.906456\pi$
$761$	−18.4128	+	18.4128i	−0.667463	+	0.667463i	0.289665	+	0.957128i	$0.406456\pi$
$762$		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	0.994464	+	0.105078i	$0.0335091\pi$
$769$	5.15161	+	19.2261i	0.185772	+	0.693309i	−0.808692	+	0.588232i	$0.799824\pi$
$770$	−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	−0.553163	−	0.833073i	$-0.686579\pi$
$773$	−17.1176	+	4.58666i	−0.615679	+	0.164971i	−0.0625162	+	0.998044i	$0.519913\pi$
$774$		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	−0.176739	−	0.984258i	$-0.556555\pi$
$787$	4.55393	−	1.22022i	0.162330	−	0.0434962i	0.339069	+	0.940762i	$0.389888\pi$
$788$	−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	0.945095	+	0.326795i	$0.105969\pi$
$797$	21.3304	+	36.9453i	0.755560	+	1.30867i	−0.189535	+	0.981874i	$0.560698\pi$
$798$		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	$-0.799992\pi$
$809$		−	33.4379i		−	1.17561i	0.809001	−	0.587807i	$-0.200008\pi$
$810$		0			0
$811$	−36.3145	+	36.3145i	−1.27517	+	1.27517i	−0.331836	+	0.943337i	$0.607668\pi$
$811$	−36.3145	+	36.3145i	−1.27517	+	1.27517i	−0.943337	+	0.331836i	$0.892332\pi$
$812$	−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	−0.928022	−	0.372527i	$-0.878492\pi$
$821$	1.77454	−	6.62268i	0.0619319	−	0.231133i	0.989953	+	0.141393i	$0.0451582\pi$
$822$		0			0
$823$	29.7340	+	17.1669i	1.03646	+	0.598402i	0.918829	−	0.394655i	$-0.129136\pi$
$823$	29.7340	+	17.1669i	1.03646	+	0.598402i	0.117633	+	0.993057i	$0.462469\pi$
$824$	−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	−0.258428	−	0.966031i	$-0.583204\pi$
$827$	20.3490	−	20.3490i	0.707603	−	0.707603i	0.966031	+	0.258428i	$0.0832043\pi$
$828$		0			0
$829$			37.3445i			1.29703i	0.761202	+	0.648514i	$0.224609\pi$
$829$			37.3445i			1.29703i	−0.761202	+	0.648514i	$0.775391\pi$
$830$	−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	0.492930	−	0.870069i	$-0.335926\pi$
$839$	14.0421	+	3.76256i	0.484786	+	0.129898i	−0.00814453	+	0.999967i	$0.502593\pi$
$840$		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	0.395439	−	0.918492i	$-0.370592\pi$
$853$	−15.2764	−	15.2764i	−0.523053	−	0.523053i	−0.918492	+	0.395439i	$0.870592\pi$
$854$	−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	0.822981	−	0.568068i	$-0.192309\pi$
$857$	−2.35575	−	4.08028i	−0.0804710	−	0.139380i	−0.903452	+	0.428689i	$0.858976\pi$
$858$		0			0
$859$	9.15975	−	15.8652i	0.312527	−	0.541312i	−0.666382	−	0.745610i	$-0.732158\pi$
$859$	9.15975	−	15.8652i	0.312527	−	0.541312i	0.978909	+	0.204299i	$0.0654913\pi$
$860$	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	−0.0789379	−	0.996880i	$-0.525153\pi$
$863$	10.3154	−	2.76400i	0.351140	−	0.0940876i	0.430078	+	0.902792i	$0.358486\pi$
$864$		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	0.0836487	−	0.996495i	$-0.473343\pi$
$877$	31.9876	−	31.9876i	1.08014	−	1.08014i	0.996495	−	0.0836487i	$-0.0266573\pi$
$878$	−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	−0.389649	−	0.920964i	$-0.627404\pi$
$881$	17.8907	−	30.9876i	0.602754	−	1.04400i	0.992402	−	0.123036i	$-0.0392632\pi$
$882$		0			0
$883$			25.8540i			0.870056i	0.900417	+	0.435028i	$0.143261\pi$
$883$			25.8540i			0.870056i	−0.900417	+	0.435028i	$0.856739\pi$
$884$	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	−0.701505	−	0.712665i	$-0.747488\pi$
$887$	−12.9576	+	7.48105i	−0.435072	+	0.251189i	0.266433	+	0.963853i	$0.414155\pi$
$888$		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	$-0.819261\pi$
$907$		−	32.3923i		−	1.07557i	0.843082	−	0.537785i	$-0.180739\pi$
$908$	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	$-0.816743\pi$
$911$		−	32.8653i		−	1.08888i	0.838801	−	0.544438i	$-0.183257\pi$
$912$		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	−0.968947	−	0.247268i	$-0.920467\pi$
$929$	−37.0696	−	37.0696i	−1.21621	−	1.21621i	−0.247268	−	0.968947i	$-0.579533\pi$
$930$		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	−0.880026	−	0.474926i	$-0.842475\pi$
$941$	3.66765	−	13.6879i	0.119562	−	0.446211i	0.999588	+	0.0287148i	$0.00914146\pi$
$942$		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	0.203364	−	0.979103i	$-0.434813\pi$
$947$	−3.38723	−	0.907604i	−0.110070	−	0.0294932i	−0.313434	+	0.949610i	$0.601479\pi$
$948$		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	0.591161	−	0.806554i	$-0.298670\pi$
$953$	−12.4383	−	21.5437i	−0.402915	−	0.697870i	−0.994076	+	0.108684i	$0.965336\pi$
$954$		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	−0.735672	−	0.677338i	$-0.763133\pi$
$967$	−1.81398	+	1.81398i	−0.0583338	+	0.0583338i	0.677338	+	0.735672i	$0.263133\pi$
$968$	−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	$0.0588345\pi$
$971$			11.4537i			0.367567i	−0.982967	+	0.183783i	$0.941165\pi$
$972$		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	0.830275	−	0.557354i	$-0.188183\pi$
$977$	8.53070	+	8.53070i	0.272921	+	0.272921i	−0.557354	+	0.830275i	$0.688183\pi$
$978$		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	0.171367	−	0.985207i	$-0.445182\pi$
$983$	−5.41864	−	1.45192i	−0.172828	−	0.0463091i	−0.344195	+	0.938898i	$0.611848\pi$
$984$		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	−0.162042	−	0.986784i	$-0.551808\pi$
$997$	24.4254	−	42.3060i	0.773559	−	1.33984i	0.935601	−	0.353059i	$-0.114859\pi$
$998$	−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.422.17	yes	152
3.2	odd	2	inner	819.2.fd.a.422.22	yes	152
7.4	even	3		819.2.ez.a.305.17	✓	152
13.11	odd	12		819.2.ez.a.674.22	yes	152
21.11	odd	6		819.2.ez.a.305.22	yes	152
39.11	even	12		819.2.ez.a.674.17	yes	152
91.11	odd	12	inner	819.2.fd.a.557.22	yes	152
273.11	even	12	inner	819.2.fd.a.557.17	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ez.a.305.17	✓	152	7.4	even	3
819.2.ez.a.305.22	yes	152	21.11	odd	6
819.2.ez.a.674.17	yes	152	39.11	even	12
819.2.ez.a.674.22	yes	152	13.11	odd	12
819.2.fd.a.422.17	yes	152	1.1	even	1	trivial
819.2.fd.a.422.22	yes	152	3.2	odd	2	inner
819.2.fd.a.557.17	yes	152	273.11	even	12	inner
819.2.fd.a.557.22	yes	152	91.11	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
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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