LMFDB - Embedded newform 819.2.bm.h.478.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			478.8
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.h.550.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.411691i q^{2} +1.83051 q^{4} +(1.54520 + 0.892120i) q^{5} +(2.44833 - 1.00283i) q^{7} -1.57699i q^{8} +O(q^{10})$	\(q-0.411691i q^{2} +1.83051 q^{4} +(1.54520 + 0.892120i) q^{5} +(2.44833 - 1.00283i) q^{7} -1.57699i q^{8} +(0.367278 - 0.636145i) q^{10} +(4.35580 + 2.51482i) q^{11} +(-0.0961009 + 3.60427i) q^{13} +(-0.412855 - 1.00796i) q^{14} +3.01179 q^{16} -7.92679 q^{17} +(2.74013 - 1.58202i) q^{19} +(2.82850 + 1.63304i) q^{20} +(1.03533 - 1.79324i) q^{22} -7.89207 q^{23} +(-0.908242 - 1.57312i) q^{25} +(1.48385 + 0.0395639i) q^{26} +(4.48170 - 1.83568i) q^{28} +(2.23275 + 3.86723i) q^{29} +(-4.24013 + 2.44804i) q^{31} -4.39390i q^{32} +3.26339i q^{34} +(4.67780 + 0.634645i) q^{35} -8.26714i q^{37} +(-0.651302 - 1.12809i) q^{38} +(1.40686 - 2.43676i) q^{40} +(-2.53740 + 1.46497i) q^{41} +(-1.50434 + 2.60560i) q^{43} +(7.97333 + 4.60340i) q^{44} +3.24910i q^{46} +(-0.196058 - 0.113194i) q^{47} +(4.98868 - 4.91050i) q^{49} +(-0.647641 + 0.373916i) q^{50} +(-0.175914 + 6.59765i) q^{52} +(-2.51579 - 4.35748i) q^{53} +(4.48704 + 7.77179i) q^{55} +(-1.58144 - 3.86099i) q^{56} +(1.59210 - 0.919202i) q^{58} -1.21619i q^{59} +(-0.128466 - 0.222510i) q^{61} +(1.00784 + 1.74563i) q^{62} +4.21464 q^{64} +(-3.36394 + 5.48358i) q^{65} +(5.55676 + 3.20820i) q^{67} -14.5101 q^{68} +(0.261278 - 1.92581i) q^{70} +(3.64365 + 2.10366i) q^{71} +(-4.59263 + 2.65156i) q^{73} -3.40351 q^{74} +(5.01584 - 2.89590i) q^{76} +(13.1864 + 1.78902i) q^{77} +(5.43814 - 9.41913i) q^{79} +(4.65381 + 2.68688i) q^{80} +(0.603114 + 1.04462i) q^{82} -14.0461i q^{83} +(-12.2485 - 7.07165i) q^{85} +(1.07270 + 0.619325i) q^{86} +(3.96584 - 6.86904i) q^{88} -5.98692i q^{89} +(3.37917 + 8.92083i) q^{91} -14.4465 q^{92} +(-0.0466011 + 0.0807154i) q^{94} +5.64539 q^{95} +(-3.99191 - 2.30473i) q^{97} +(-2.02161 - 2.05380i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) $ 36 * q - 44 * q^4 + 8 * q^7	$ 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) $ 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	0.411691i		−	0.291110i	−0.989350	−	0.145555i	$-0.953503\pi$
$2$		−	0.411691i		−	0.291110i	0.989350	−	0.145555i	$-0.0464967\pi$
$3$		0			0
$3$		0			0
$4$	1.83051			0.915255
$5$	1.54520	+	0.892120i	0.691034	+	0.398968i	0.803999	−	0.594631i	$-0.202702\pi$
$5$	1.54520	+	0.892120i	0.691034	+	0.398968i	−0.112966	+	0.993599i	$0.536035\pi$
$6$		0			0
$7$	2.44833	−	1.00283i	0.925383	−	0.379032i
$7$	2.44833	−	1.00283i	0.925383	−	0.379032i
$8$		−	1.57699i		−	0.557549i
$9$		0			0
$10$	0.367278	−	0.636145i	0.116144	−	0.201167i
$11$	4.35580	+	2.51482i	1.31332	+	0.758247i	0.982645	−	0.185497i	$-0.0593896\pi$
$11$	4.35580	+	2.51482i	1.31332	+	0.758247i	0.330677	+	0.943744i	$0.392723\pi$
$12$		0			0
$13$	−0.0961009	+	3.60427i	−0.0266536	+	0.999645i
$13$	−0.0961009	+	3.60427i	−0.0266536	+	0.999645i
$14$	−0.412855	−	1.00796i	−0.110340	−	0.269388i
$15$		0			0
$16$	3.01179			0.752947
$17$	−7.92679			−1.92253			−0.961264	−	0.275630i	$-0.911114\pi$
$17$	−7.92679			−1.92253			−0.961264	+	0.275630i	$0.911114\pi$
$18$		0			0
$19$	2.74013	−	1.58202i	0.628629	−	0.362939i	−0.151592	−	0.988443i	$-0.548440\pi$
$19$	2.74013	−	1.58202i	0.628629	−	0.362939i	0.780221	+	0.625504i	$0.215107\pi$
$20$	2.82850	+	1.63304i	0.632472	+	0.365158i
$21$		0			0
$22$	1.03533	−	1.79324i	0.220733	−	0.382321i
$23$	−7.89207			−1.64561			−0.822805	−	0.568324i	$-0.807592\pi$
$23$	−7.89207			−1.64561			−0.822805	+	0.568324i	$0.807592\pi$
$24$		0			0
$25$	−0.908242	−	1.57312i	−0.181648	−	0.314624i
$26$	1.48385	+	0.0395639i	0.291006	+	0.00775912i
$27$		0			0
$28$	4.48170	−	1.83568i	0.846962	−	0.346911i
$29$	2.23275	+	3.86723i	0.414611	+	0.718126i	0.995387	−	0.0959363i	$-0.0305845\pi$
$29$	2.23275	+	3.86723i	0.414611	+	0.718126i	−0.580777	+	0.814063i	$0.697251\pi$
$30$		0			0
$31$	−4.24013	+	2.44804i	−0.761550	+	0.439681i	−0.829852	−	0.557984i	$-0.811575\pi$
$31$	−4.24013	+	2.44804i	−0.761550	+	0.439681i	0.0683019	+	0.997665i	$0.478242\pi$
$32$		−	4.39390i		−	0.776740i
$33$		0			0
$34$			3.26339i			0.559667i
$35$	4.67780	+	0.634645i	0.790693	+	0.107275i
$36$		0			0
$37$		−	8.26714i		−	1.35911i	−0.733624	−	0.679555i	$-0.762173\pi$
$37$		−	8.26714i		−	1.35911i	0.733624	−	0.679555i	$-0.237827\pi$
$38$	−0.651302	−	1.12809i	−0.105655	−	0.183000i
$39$		0			0
$40$	1.40686	−	2.43676i	0.222445	−	0.385285i
$41$	−2.53740	+	1.46497i	−0.396275	+	0.228789i	−0.684875	−	0.728660i	$-0.740143\pi$
$41$	−2.53740	+	1.46497i	−0.396275	+	0.228789i	0.288601	+	0.957450i	$0.406810\pi$
$42$		0			0
$43$	−1.50434	+	2.60560i	−0.229410	+	0.397350i	−0.957633	−	0.287990i	$-0.907013\pi$
$43$	−1.50434	+	2.60560i	−0.229410	+	0.397350i	0.728223	+	0.685340i	$0.240346\pi$
$44$	7.97333	+	4.60340i	1.20202	+	0.693989i
$45$		0			0
$46$			3.24910i			0.479053i
$47$	−0.196058	−	0.113194i	−0.0285980	−	0.0165111i	0.485633	−	0.874163i	$-0.338589\pi$
$47$	−0.196058	−	0.113194i	−0.0285980	−	0.0165111i	−0.514231	+	0.857652i	$0.671923\pi$
$48$		0			0
$49$	4.98868	−	4.91050i	0.712669	−	0.701501i
$50$	−0.647641	+	0.373916i	−0.0915902	+	0.0528796i
$51$		0			0
$52$	−0.175914	+	6.59765i	−0.0243948	+	0.914930i
$53$	−2.51579	−	4.35748i	−0.345571	−	0.598546i	0.639887	−	0.768469i	$-0.278981\pi$
$53$	−2.51579	−	4.35748i	−0.345571	−	0.598546i	−0.985457	+	0.169924i	$0.945648\pi$
$54$		0			0
$55$	4.48704	+	7.77179i	0.605033	+	1.04795i
$56$	−1.58144	−	3.86099i	−0.211329	−	0.515947i
$57$		0			0
$58$	1.59210	−	0.919202i	0.209054	−	0.120697i
$59$		−	1.21619i		−	0.158335i	−0.996861	−	0.0791675i	$-0.974774\pi$
$59$		−	1.21619i		−	0.158335i	0.996861	−	0.0791675i	$-0.0252262\pi$
$60$		0			0
$61$	−0.128466	−	0.222510i	−0.0164484	−	0.0284895i	0.857684	−	0.514177i	$-0.171903\pi$
$61$	−0.128466	−	0.222510i	−0.0164484	−	0.0284895i	−0.874132	+	0.485688i	$0.838569\pi$
$62$	1.00784	+	1.74563i	0.127995	+	0.221695i
$63$		0			0
$64$	4.21464			0.526831
$65$	−3.36394	+	5.48358i	−0.417245	+	0.680154i
$66$		0			0
$67$	5.55676	+	3.20820i	0.678867	+	0.391944i	0.799428	−	0.600762i	$-0.205136\pi$
$67$	5.55676	+	3.20820i	0.678867	+	0.391944i	−0.120561	+	0.992706i	$0.538469\pi$
$68$	−14.5101			−1.75960
$69$		0			0
$70$	0.261278	−	1.92581i	0.0312287	−	0.230178i
$71$	3.64365	+	2.10366i	0.432422	+	0.249659i	0.700378	−	0.713772i	$-0.253015\pi$
$71$	3.64365	+	2.10366i	0.432422	+	0.249659i	−0.267956	+	0.963431i	$0.586348\pi$
$72$		0			0
$73$	−4.59263	+	2.65156i	−0.537527	+	0.310341i	−0.744076	−	0.668095i	$-0.767110\pi$
$73$	−4.59263	+	2.65156i	−0.537527	+	0.310341i	0.206549	+	0.978436i	$0.433777\pi$
$74$	−3.40351			−0.395650
$75$		0			0
$76$	5.01584	−	2.89590i	0.575356	−	0.332182i
$77$	13.1864	+	1.78902i	1.50273	+	0.203877i
$78$		0			0
$79$	5.43814	−	9.41913i	0.611839	−	1.05974i	−0.379092	−	0.925359i	$-0.623764\pi$
$79$	5.43814	−	9.41913i	0.611839	−	1.05974i	0.990930	−	0.134376i	$-0.0429031\pi$
$80$	4.65381	+	2.68688i	0.520312	+	0.300402i
$81$		0			0
$82$	0.603114	+	1.04462i	0.0666028	+	0.115359i
$83$		−	14.0461i		−	1.54176i	−0.636979	−	0.770881i	$-0.719816\pi$
$83$		−	14.0461i		−	1.54176i	0.636979	−	0.770881i	$-0.280184\pi$
$84$		0			0
$85$	−12.2485	−	7.07165i	−1.32853	−	0.767028i
$86$	1.07270	+	0.619325i	0.115672	+	0.0667835i
$87$		0			0
$88$	3.96584	−	6.86904i	0.422760	−	0.732242i
$89$		−	5.98692i		−	0.634612i	−0.948323	−	0.317306i	$-0.897222\pi$
$89$		−	5.98692i		−	0.634612i	0.948323	−	0.317306i	$-0.102778\pi$
$90$		0			0
$91$	3.37917	+	8.92083i	0.354233	+	0.935157i
$92$	−14.4465			−1.50615
$93$		0			0
$94$	−0.0466011	+	0.0807154i	−0.00480653	+	0.00832516i
$95$	5.64539			0.579205
$96$		0			0
$97$	−3.99191	−	2.30473i	−0.405317	−	0.234010i	0.283459	−	0.958984i	$-0.408518\pi$
$97$	−3.99191	−	2.30473i	−0.405317	−	0.234010i	−0.688776	+	0.724975i	$0.741851\pi$
$98$	−2.02161	−	2.05380i	−0.204214	−	0.207465i
$99$		0			0
$100$	−1.66255	−	2.87962i	−0.166255	−	0.287962i
$101$	7.10416	−	12.3048i	0.706890	−	1.22437i	−0.259114	−	0.965847i	$-0.583431\pi$
$101$	7.10416	−	12.3048i	0.706890	−	1.22437i	0.966005	−	0.258524i	$-0.0832360\pi$
$102$		0			0
$103$	−5.20207	+	9.01025i	−0.512575	+	0.887807i	0.487318	+	0.873224i	$0.337975\pi$
$103$	−5.20207	+	9.01025i	−0.512575	+	0.887807i	−0.999894	+	0.0145822i	$0.995358\pi$
$104$	5.68389	+	0.151550i	0.557351	+	0.0148607i
$105$		0			0
$106$	−1.79394	+	1.03573i	−0.174243	+	0.100599i
$107$	16.7163			1.61603			0.808013	−	0.589165i	$-0.200543\pi$
$107$	16.7163			1.61603			0.808013	+	0.589165i	$0.200543\pi$
$108$		0			0
$109$	−3.65179	+	2.10836i	−0.349778	+	0.201945i	−0.664588	−	0.747210i	$-0.731393\pi$
$109$	−3.65179	+	2.10836i	−0.349778	+	0.201945i	0.314809	+	0.949155i	$0.398059\pi$
$110$	3.19958	−	1.84728i	0.305068	−	0.176131i
$111$		0			0
$112$	7.37386	−	3.02030i	0.696765	−	0.285391i
$113$	−1.47762	+	2.55931i	−0.139003	+	0.240759i	−0.927119	−	0.374766i	$-0.877723\pi$
$113$	−1.47762	+	2.55931i	−0.139003	+	0.240759i	0.788117	+	0.615526i	$0.211056\pi$
$114$		0			0
$115$	−12.1948	−	7.04068i	−1.13717	−	0.656546i
$116$	4.08706	+	7.07900i	0.379474	+	0.657269i
$117$		0			0
$118$	−0.500697			−0.0460929
$119$	−19.4074	+	7.94918i	−1.77908	+	0.728700i
$120$		0			0
$121$	7.14863	+	12.3818i	0.649876	+	1.12562i
$122$	−0.0916055	+	0.0528885i	−0.00829357	+	0.00478830i
$123$		0			0
$124$	−7.76160	+	4.48116i	−0.697013	+	0.402420i
$125$		−	12.1623i		−	1.08782i
$126$		0			0
$127$	−10.0266	−	17.3666i	−0.889718	−	1.54104i	−0.840209	−	0.542263i	$-0.817568\pi$
$127$	−10.0266	−	17.3666i	−0.889718	−	1.54104i	−0.0495095	−	0.998774i	$-0.515766\pi$
$128$		−	10.5229i		−	0.930105i
$129$		0			0
$130$	2.25754	+	1.38490i	0.197999	+	0.121464i
$131$	2.00994	−	3.48132i	0.175609	−	0.304164i	−0.764763	−	0.644312i	$-0.777144\pi$
$131$	2.00994	−	3.48132i	0.175609	−	0.304164i	0.940372	+	0.340148i	$0.110477\pi$
$132$		0			0
$133$	5.12227	−	6.62118i	0.444157	−	0.574129i
$134$	1.32079	−	2.28767i	0.114099	−	0.197625i
$135$		0			0
$136$			12.5004i			1.07190i
$137$			13.5016i			1.15352i	0.816913	+	0.576760i	$0.195683\pi$
$137$			13.5016i			1.15352i	−0.816913	+	0.576760i	$0.804317\pi$
$138$		0			0
$139$	−6.80652	+	11.7892i	−0.577321	+	0.999950i	0.418464	+	0.908233i	$0.362569\pi$
$139$	−6.80652	+	11.7892i	−0.577321	+	0.999950i	−0.995785	+	0.0917163i	$0.970765\pi$
$140$	8.56276	+	1.16172i	0.723686	+	0.0981836i
$141$		0			0
$142$	0.866059	−	1.50006i	0.0726781	−	0.125882i
$143$	−9.48269	+	15.4578i	−0.792982	+	1.29265i
$144$		0			0
$145$			7.96751i			0.661666i
$146$	1.09162	+	1.89075i	0.0903434	+	0.156479i
$147$		0			0
$148$		−	15.1331i		−	1.24393i
$149$	−9.39848	+	5.42622i	−0.769954	+	0.444533i	−0.832858	−	0.553486i	$-0.813297\pi$
$149$	−9.39848	+	5.42622i	−0.769954	+	0.444533i	0.0629043	+	0.998020i	$0.479964\pi$
$150$		0			0
$151$	−12.9759	+	7.49166i	−1.05597	+	0.609663i	−0.924314	−	0.381633i	$-0.875362\pi$
$151$	−12.9759	+	7.49166i	−1.05597	+	0.609663i	−0.131653	+	0.991296i	$0.542028\pi$
$152$	−2.49482	−	4.32115i	−0.202357	−	0.350492i
$153$		0			0
$154$	0.736523	−	5.42871i	0.0593507	−	0.437458i
$155$	−8.73579			−0.701676
$156$		0			0
$157$	6.81038	+	11.7959i	0.543528	+	0.941417i	0.998698	+	0.0510131i	$0.0162450\pi$
$157$	6.81038	+	11.7959i	0.543528	+	0.941417i	−0.455170	+	0.890404i	$0.650422\pi$
$158$	−3.87778	−	2.23884i	−0.308499	−	0.178112i
$159$		0			0
$160$	3.91989	−	6.78945i	0.309895	−	0.536753i
$161$	−19.3224	+	7.91437i	−1.52282	+	0.623740i
$162$		0			0
$163$	−5.07160	+	2.92809i	−0.397238	+	0.229346i	−0.685292	−	0.728269i	$-0.740325\pi$
$163$	−5.07160	+	2.92809i	−0.397238	+	0.229346i	0.288054	+	0.957614i	$0.406992\pi$
$164$	−4.64473	+	2.68163i	−0.362692	+	0.209400i
$165$		0			0
$166$	−5.78267			−0.448822
$167$	−15.4219	+	8.90386i	−1.19339	+	0.689002i	−0.959073	−	0.283160i	$-0.908617\pi$
$167$	−15.4219	+	8.90386i	−1.19339	+	0.689002i	−0.234313	+	0.972161i	$0.575284\pi$
$168$		0			0
$169$	−12.9815	−	0.692747i	−0.998579	−	0.0532883i
$170$	−2.91134	+	5.04258i	−0.223289	+	0.386748i
$171$		0			0
$172$	−2.75372	+	4.76958i	−0.209969	+	0.363677i
$173$	12.4511	+	21.5659i	0.946638	+	1.63963i	0.752438	+	0.658663i	$0.228878\pi$
$173$	12.4511	+	21.5659i	0.946638	+	1.63963i	0.194200	+	0.980962i	$0.437789\pi$
$174$		0			0
$175$	−3.80125	−	2.94072i	−0.287347	−	0.222298i
$176$	13.1187	+	7.57410i	0.988862	+	0.570920i
$177$		0			0
$178$	−2.46476			−0.184742
$179$	5.22356	−	9.04748i	0.390427	−	0.676240i	−0.602078	−	0.798437i	$-0.705661\pi$
$179$	5.22356	−	9.04748i	0.390427	−	0.676240i	0.992506	+	0.122197i	$0.0389939\pi$
$180$		0			0
$181$	0.962937			0.0715745			0.0357873	−	0.999359i	$-0.488606\pi$
$181$	0.962937			0.0715745			0.0357873	+	0.999359i	$0.488606\pi$
$182$	3.67263	−	1.39117i	0.272233	−	0.103121i
$183$		0			0
$184$			12.4457i			0.917509i
$185$	7.37529	−	12.7744i	0.542242	−	0.939191i
$186$		0			0
$187$	−34.5275	−	19.9344i	−2.52490	−	1.45775i
$188$	−0.358886	−	0.207203i	−0.0261745	−	0.0151118i
$189$		0			0
$190$		−	2.32416i		−	0.168612i
$191$	−6.65369	−	11.5245i	−0.481444	−	0.833886i	0.518329	−	0.855181i	$-0.326554\pi$
$191$	−6.65369	−	11.5245i	−0.481444	−	0.833886i	−0.999773	+	0.0212953i	$0.993221\pi$
$192$		0			0
$193$	0.624034	+	0.360286i	0.0449189	+	0.0259340i	0.522291	−	0.852767i	$-0.325077\pi$
$193$	0.624034	+	0.360286i	0.0449189	+	0.0259340i	−0.477372	+	0.878701i	$0.658411\pi$
$194$	−0.948838	+	1.64343i	−0.0681226	+	0.117992i
$195$		0			0
$196$	9.13183	−	8.98873i	0.652274	−	0.642052i
$197$	18.8084	−	10.8591i	1.34005	−	0.773676i	0.353232	−	0.935536i	$-0.385083\pi$
$197$	18.8084	−	10.8591i	1.34005	−	0.773676i	0.986814	+	0.161860i	$0.0517493\pi$
$198$		0			0
$199$	−11.7513			−0.833031			−0.416515	−	0.909129i	$-0.636749\pi$
$199$	−11.7513			−0.833031			−0.416515	+	0.909129i	$0.636749\pi$
$200$	−2.48079	+	1.43229i	−0.175419	+	0.101278i
$201$		0			0
$202$	−5.06577	−	2.92472i	−0.356426	−	0.205783i
$203$	9.34466	+	7.22922i	0.655867	+	0.507391i
$204$		0			0
$205$	−5.22770			−0.365119
$206$	3.70944	+	2.14165i	0.258449	+	0.149216i
$207$		0			0
$208$	−0.289436	+	10.8553i	−0.0200688	+	0.752680i
$209$	15.9139			1.10079
$210$		0			0
$211$	−4.02079	−	6.96421i	−0.276802	−	0.479436i	0.693786	−	0.720181i	$-0.255941\pi$
$211$	−4.02079	−	6.96421i	−0.276802	−	0.479436i	−0.970588	+	0.240745i	$0.922608\pi$
$212$	−4.60518	−	7.97641i	−0.316285	−	0.547822i
$213$		0			0
$214$		−	6.88196i		−	0.470441i
$215$	−4.64902	+	2.68411i	−0.317060	+	0.183055i
$216$		0			0
$217$	−7.92630	+	10.2457i	−0.538072	+	0.695526i
$218$	0.867995	+	1.50341i	0.0587880	+	0.101824i
$219$		0			0
$220$	8.21358	+	14.2263i	0.553759	+	0.959139i
$221$	0.761771	−	28.5703i	0.0512423	−	1.92184i
$222$		0			0
$223$	−9.56217	+	5.52072i	−0.640330	+	0.369695i	−0.784742	−	0.619823i	$-0.787204\pi$
$223$	−9.56217	+	5.52072i	−0.640330	+	0.369695i	0.144412	+	0.989518i	$0.453871\pi$
$224$	−4.40632	−	10.7577i	−0.294409	−	0.718782i
$225$		0			0
$226$	1.05364	+	0.608322i	0.0700874	+	0.0404650i
$227$			21.8266i			1.44869i	0.689440	+	0.724343i	$0.257857\pi$
$227$			21.8266i			1.44869i	−0.689440	+	0.724343i	$0.742143\pi$
$228$		0			0
$229$	4.35045	+	2.51173i	0.287486	+	0.165980i	0.636807	−	0.771023i	$-0.280255\pi$
$229$	4.35045	+	2.51173i	0.287486	+	0.165980i	−0.349322	+	0.937003i	$0.613588\pi$
$230$	−2.89859	+	5.02050i	−0.191127	+	0.331042i
$231$		0			0
$232$	6.09857	−	3.52101i	0.400391	−	0.231166i
$233$	8.16195	−	14.1369i	0.534707	−	0.926140i	−0.464470	−	0.885589i	$-0.653755\pi$
$233$	8.16195	−	14.1369i	0.534707	−	0.926140i	0.999177	−	0.0405512i	$-0.0129114\pi$
$234$		0			0
$235$	−0.201966	−	0.349815i	−0.0131748	−	0.0228194i
$236$		−	2.22626i		−	0.144917i
$237$		0			0
$238$	3.27261	+	7.98987i	0.212132	+	0.517906i
$239$		−	12.0986i		−	0.782594i	−0.920264	−	0.391297i	$-0.872027\pi$
$239$		−	12.0986i		−	0.782594i	0.920264	−	0.391297i	$-0.127973\pi$
$240$		0			0
$241$			13.2691i			0.854737i	0.904077	+	0.427369i	$0.140559\pi$
$241$			13.2691i			0.854737i	−0.904077	+	0.427369i	$0.859441\pi$
$242$	5.09748	−	2.94303i	0.327678	−	0.189185i
$243$		0			0
$244$	−0.235159	−	0.407307i	−0.0150545	−	0.0260752i
$245$	12.0893	−	3.13720i	0.772355	−	0.200428i
$246$		0			0
$247$	5.43868	+	10.0282i	0.346055	+	0.638080i
$248$	3.86053	+	6.68664i	0.245144	+	0.424602i
$249$		0			0
$250$	−5.00709			−0.316676
$251$	−8.53935	+	14.7906i	−0.538999	+	0.933573i	0.459960	+	0.887940i	$0.347864\pi$
$251$	−8.53935	+	14.7906i	−0.538999	+	0.933573i	−0.998958	+	0.0456333i	$0.985469\pi$
$252$		0			0
$253$	−34.3762	−	19.8471i	−2.16122	−	1.24778i
$254$	−7.14968	+	4.12787i	−0.448611	+	0.259006i
$255$		0			0
$256$	4.09709			0.256068
$257$	−11.6546			−0.726996			−0.363498	−	0.931595i	$-0.618418\pi$
$257$	−11.6546			−0.726996			−0.363498	+	0.931595i	$0.618418\pi$
$258$		0			0
$259$	−8.29050	−	20.2407i	−0.515147	−	1.25770i
$260$	−6.15772	+	10.0377i	−0.381886	+	0.622514i
$261$		0			0
$262$	−1.43323	−	0.827474i	−0.0885451	−	0.0511215i
$263$	−5.72547	+	9.91681i	−0.353048	+	0.611497i	−0.986782	−	0.162054i	$-0.948188\pi$
$263$	−5.72547	+	9.91681i	−0.353048	+	0.611497i	0.633734	+	0.773551i	$0.281521\pi$
$264$		0			0
$265$		−	8.97756i		−	0.551487i
$266$	−2.72588	−	2.10880i	−0.167135	−	0.129299i
$267$		0			0
$268$	10.1717	+	5.87264i	0.621336	+	0.358729i
$269$	9.13095			0.556724			0.278362	−	0.960476i	$-0.410209\pi$
$269$	9.13095			0.556724			0.278362	+	0.960476i	$0.410209\pi$
$270$		0			0
$271$		−	8.16146i		−	0.495773i	−0.968789	−	0.247887i	$-0.920264\pi$
$271$		−	8.16146i		−	0.495773i	0.968789	−	0.247887i	$-0.0797361\pi$
$272$	−23.8738			−1.44756
$273$		0			0
$274$	5.55850			0.335801
$275$		−	9.13626i		−	0.550937i
$276$		0			0
$277$	0.634028			0.0380951			0.0190475	−	0.999819i	$-0.493937\pi$
$277$	0.634028			0.0380951			0.0190475	+	0.999819i	$0.493937\pi$
$278$	4.85353	+	2.80218i	0.291095	+	0.168064i
$279$		0			0
$280$	1.00083	−	7.37684i	0.0598109	−	0.440850i
$281$			4.48885i			0.267782i	0.990996	+	0.133891i	$0.0427473\pi$
$281$			4.48885i			0.267782i	−0.990996	+	0.133891i	$0.957253\pi$
$282$		0			0
$283$	−7.72367	+	13.3778i	−0.459124	+	0.795227i	−0.998915	−	0.0465726i	$-0.985170\pi$
$283$	−7.72367	+	13.3778i	−0.459124	+	0.795227i	0.539791	+	0.841799i	$0.318503\pi$
$284$	6.66974	+	3.85077i	0.395776	+	0.228501i
$285$		0			0
$286$	6.36384	+	3.90394i	0.376302	+	0.230845i
$287$	−4.74329	+	6.13129i	−0.279987	+	0.361919i
$288$		0			0
$289$	45.8339			2.69611
$290$	3.28016			0.192617
$291$		0			0
$292$	−8.40686	+	4.85371i	−0.491975	+	0.284042i
$293$	18.4020	+	10.6244i	1.07506	+	0.620684i	0.929558	−	0.368675i	$-0.120188\pi$
$293$	18.4020	+	10.6244i	1.07506	+	0.620684i	0.145497	+	0.989359i	$0.453522\pi$
$294$		0			0
$295$	1.08499	−	1.87926i	0.0631707	−	0.109415i
$296$	−13.0372			−0.757771
$297$		0			0
$298$	2.23393	+	3.86927i	0.129408	+	0.224141i
$299$	0.758435	−	28.4452i	0.0438614	−	1.64503i
$300$		0			0
$301$	−1.07017	+	7.88797i	−0.0616838	+	0.454655i
$302$	3.08425	+	5.34208i	0.177479	+	0.307402i
$303$		0			0
$304$	8.25270	−	4.76470i	0.473325	−	0.273274i
$305$		−	0.458430i		−	0.0262496i
$306$		0			0
$307$			2.38473i			0.136104i	0.997682	+	0.0680520i	$0.0216784\pi$
$307$			2.38473i			0.136104i	−0.997682	+	0.0680520i	$0.978322\pi$
$308$	24.1378	+	3.27481i	1.37538	+	0.186600i
$309$		0			0
$310$			3.59645i			0.204265i
$311$	2.08542	+	3.61205i	0.118253	+	0.204820i	0.919075	−	0.394082i	$-0.128937\pi$
$311$	2.08542	+	3.61205i	0.118253	+	0.204820i	−0.800822	+	0.598902i	$0.795604\pi$
$312$		0			0
$313$	15.6128	−	27.0421i	0.882485	−	1.52851i	0.0339160	−	0.999425i	$-0.489202\pi$
$313$	15.6128	−	27.0421i	0.882485	−	1.52851i	0.848569	−	0.529084i	$-0.177465\pi$
$314$	4.85628	−	2.80378i	0.274056	−	0.158226i
$315$		0			0
$316$	9.95457	−	17.2418i	0.559988	−	0.969928i
$317$	5.72998	+	3.30821i	0.321828	+	0.185807i	0.652207	−	0.758041i	$-0.273843\pi$
$317$	5.72998	+	3.30821i	0.321828	+	0.185807i	−0.330379	+	0.943848i	$0.607177\pi$
$318$		0			0
$319$			22.4598i			1.25751i
$320$	6.51246	+	3.75997i	0.364058	+	0.210189i
$321$		0			0
$322$	3.25828	+	7.95488i	0.181577	+	0.443308i
$323$	−21.7204	+	12.5403i	−1.20856	+	0.697761i
$324$		0			0
$325$	5.75724	−	3.12237i	0.319354	−	0.173198i
$326$	1.20547	+	2.08793i	0.0667647	+	0.115640i
$327$		0			0
$328$	2.31023	+	4.00144i	0.127561	+	0.220943i
$329$	−0.593530	−	0.0805252i	−0.0327224	−	0.00443950i
$330$		0			0
$331$	3.12774	−	1.80580i	0.171916	−	0.0992559i	−0.411573	−	0.911377i	$-0.635020\pi$
$331$	3.12774	−	1.80580i	0.171916	−	0.0992559i	0.583489	+	0.812121i	$0.301687\pi$
$332$		−	25.7116i		−	1.41111i
$333$		0			0
$334$	3.66564	+	6.34908i	0.200575	+	0.347406i
$335$	5.72420	+	9.91460i	0.312746	+	0.541693i
$336$		0			0
$337$	18.5941			1.01288			0.506442	−	0.862274i	$-0.330960\pi$
$337$	18.5941			1.01288			0.506442	+	0.862274i	$0.330960\pi$
$338$	−0.285198	+	5.34438i	−0.0155127	+	0.290696i
$339$		0			0
$340$	−22.4209	−	12.9447i	−1.21594	−	0.702026i
$341$	−24.6255			−1.33355
$342$		0			0
$343$	7.28958	−	17.0253i	0.393600	−	0.919282i
$344$	4.10900	+	2.37233i	0.221542	+	0.127908i
$345$		0			0
$346$	8.87850	−	5.12600i	0.477311	−	0.275576i
$347$	−3.76725			−0.202237			−0.101118	−	0.994874i	$-0.532242\pi$
$347$	−3.76725			−0.202237			−0.101118	+	0.994874i	$0.532242\pi$
$348$		0			0
$349$	27.1541	−	15.6774i	1.45353	−	0.839194i	0.454847	−	0.890569i	$-0.349694\pi$
$349$	27.1541	−	15.6774i	1.45353	−	0.839194i	0.998679	+	0.0513752i	$0.0163604\pi$
$350$	−1.21067	+	1.56494i	−0.0647130	+	0.0836496i
$351$		0			0
$352$	11.0499	−	19.1389i	0.588960	−	1.02011i
$353$	−14.1364	−	8.16168i	−0.752407	−	0.434402i	0.0741562	−	0.997247i	$-0.476374\pi$
$353$	−14.1364	−	8.16168i	−0.752407	−	0.434402i	−0.826563	+	0.562844i	$0.809707\pi$
$354$		0			0
$355$	3.75344	+	6.50115i	0.199212	+	0.345045i
$356$		−	10.9591i		−	0.580832i
$357$		0			0
$358$	−3.72477	−	2.15050i	−0.196860	−	0.113657i
$359$	2.12555	+	1.22719i	0.112182	+	0.0647684i	0.555041	−	0.831823i	$-0.312702\pi$
$359$	2.12555	+	1.22719i	0.112182	+	0.0647684i	−0.442859	+	0.896591i	$0.646036\pi$
$360$		0			0
$361$	−4.49445	+	7.78462i	−0.236550	+	0.409717i
$362$		−	0.396433i		−	0.0208360i
$363$		0			0
$364$	6.18560	+	16.3297i	0.324214	+	0.855907i
$365$	−9.46204			−0.495266
$366$		0			0
$367$	−11.1282	+	19.2746i	−0.580889	+	1.00613i	0.414486	+	0.910056i	$0.363961\pi$
$367$	−11.1282	+	19.2746i	−0.580889	+	1.00613i	−0.995374	+	0.0960726i	$0.969372\pi$
$368$	−23.7692			−1.23906
$369$		0			0
$370$	−5.25910	−	3.03634i	−0.273408	−	0.157852i
$371$	−10.5293	−	8.14567i	−0.546653	−	0.422902i
$372$		0			0
$373$	18.0452	+	31.2552i	0.934344	+	1.61833i	0.775799	+	0.630980i	$0.217347\pi$
$373$	18.0452	+	31.2552i	0.934344	+	1.61833i	0.158545	+	0.987352i	$0.449320\pi$
$374$	−8.20683	+	14.2147i	−0.424365	+	0.735022i
$375$		0			0
$376$	−0.178506	+	0.309181i	−0.00920574	+	0.0159448i
$377$	−14.1531	+	7.67578i	−0.728922	+	0.395323i
$378$		0			0
$379$	−20.5619	+	11.8714i	−1.05619	+	0.609792i	−0.924376	−	0.381482i	$-0.875414\pi$
$379$	−20.5619	+	11.8714i	−1.05619	+	0.609792i	−0.131815	+	0.991274i	$0.542081\pi$
$380$	10.3340			0.530121
$381$		0			0
$382$	−4.74455	+	2.73927i	−0.242752	+	0.140153i
$383$	16.5563	−	9.55877i	0.845986	−	0.488430i	−0.0133083	−	0.999911i	$-0.504236\pi$
$383$	16.5563	−	9.55877i	0.845986	−	0.488430i	0.859295	+	0.511481i	$0.170903\pi$
$384$		0			0
$385$	18.7795	+	14.5282i	0.957093	+	0.740426i
$386$	0.148327	−	0.256909i	0.00754963	−	0.0130763i
$387$		0			0
$388$	−7.30723	−	4.21883i	−0.370969	−	0.214179i
$389$	−3.35966	−	5.81911i	−0.170342	−	0.295040i	0.768198	−	0.640213i	$-0.221154\pi$
$389$	−3.35966	−	5.81911i	−0.170342	−	0.295040i	−0.938539	+	0.345172i	$0.887820\pi$
$390$		0			0
$391$	62.5587			3.16373
$392$	−7.74381	−	7.86709i	−0.391121	−	0.397348i
$393$		0			0
$394$	−4.47058	−	7.74327i	−0.225225	−	0.390100i
$395$	16.8060	−	9.70295i	0.845602	−	0.488208i
$396$		0			0
$397$	15.3887	−	8.88469i	0.772339	−	0.445910i	−0.0613695	−	0.998115i	$-0.519547\pi$
$397$	15.3887	−	8.88469i	0.772339	−	0.445910i	0.833708	+	0.552205i	$0.186213\pi$
$398$			4.83793i			0.242503i
$399$		0			0
$400$	−2.73543	−	4.73791i	−0.136772	−	0.236895i
$401$			18.1443i			0.906084i	0.891489	+	0.453042i	$0.149661\pi$
$401$			18.1443i			0.906084i	−0.891489	+	0.453042i	$0.850339\pi$
$402$		0			0
$403$	−8.41592	−	15.5178i	−0.419227	−	0.772999i
$404$	13.0042	−	22.5240i	0.646985	−	1.12061i
$405$		0			0
$406$	2.97621	−	3.84712i	0.147707	−	0.190929i
$407$	20.7904	−	36.0100i	1.03054	−	1.78495i
$408$		0			0
$409$			9.43935i			0.466746i	0.972387	+	0.233373i	$0.0749763\pi$
$409$			9.43935i			0.466746i	−0.972387	+	0.233373i	$0.925024\pi$
$410$			2.15220i			0.106290i
$411$		0			0
$412$	−9.52245	+	16.4934i	−0.469137	+	0.812570i
$413$	−1.21963	−	2.97765i	−0.0600141	−	0.146521i
$414$		0			0
$415$	12.5308	−	21.7040i	0.615115	−	1.06541i
$416$	15.8368	+	0.422258i	0.776464	+	0.0207029i
$417$		0			0
$418$		−	6.55163i		−	0.320451i
$419$	−9.35129	−	16.1969i	−0.456841	−	0.791271i	0.541951	−	0.840410i	$-0.317686\pi$
$419$	−9.35129	−	16.1969i	−0.456841	−	0.791271i	−0.998792	+	0.0491388i	$0.984352\pi$
$420$		0			0
$421$		−	5.31288i		−	0.258934i	−0.991584	−	0.129467i	$-0.958673\pi$
$421$		−	5.31288i		−	0.258934i	0.991584	−	0.129467i	$-0.0413266\pi$
$422$	−2.86710	+	1.65532i	−0.139568	+	0.0805799i
$423$		0			0
$424$	−6.87169	+	3.96737i	−0.333719	+	0.192673i
$425$	7.19944	+	12.4698i	0.349224	+	0.604874i
$426$		0			0
$427$	−0.537667	−	0.415950i	−0.0260195	−	0.0201292i
$428$	30.5994			1.47908
$429$		0			0
$430$	1.10503	+	1.91396i	0.0532890	+	0.0922993i
$431$	29.9610	+	17.2980i	1.44317	+	0.833214i	0.998060	−	0.0622622i	$-0.0198315\pi$
$431$	29.9610	+	17.2980i	1.44317	+	0.833214i	0.445109	+	0.895476i	$0.353165\pi$
$432$		0			0
$433$	−4.21904	+	7.30758i	−0.202754	+	0.351180i	−0.949415	−	0.314025i	$-0.898322\pi$
$433$	−4.21904	+	7.30758i	−0.202754	+	0.351180i	0.746661	+	0.665205i	$0.231656\pi$
$434$	4.21808	+	3.26319i	0.202474	+	0.156638i
$435$		0			0
$436$	−6.68464	+	3.85938i	−0.320136	+	0.184831i
$437$	−21.6253	+	12.4854i	−1.03448	+	0.597257i
$438$		0			0
$439$	−29.0234			−1.38521			−0.692606	−	0.721316i	$-0.743538\pi$
$439$	−29.0234			−1.38521			−0.692606	+	0.721316i	$0.743538\pi$
$440$	12.2560	−	7.07601i	0.584283	−	0.337336i
$441$		0			0
$442$	−11.7621	−	0.313615i	−0.559468	−	0.0149171i
$443$	−0.652088	+	1.12945i	−0.0309817	+	0.0536618i	−0.881100	−	0.472929i	$-0.843197\pi$
$443$	−0.652088	+	1.12945i	−0.0309817	+	0.0536618i	0.850119	+	0.526591i	$0.176530\pi$
$444$		0			0
$445$	5.34105	−	9.25098i	0.253190	−	0.438538i
$446$	2.27283	+	3.93666i	0.107622	+	0.186406i
$447$		0			0
$448$	10.3189	−	4.22655i	0.487520	−	0.199686i
$449$	−24.4502	−	14.1164i	−1.15388	−	0.666192i	−0.204049	−	0.978961i	$-0.565410\pi$
$449$	−24.4502	−	14.1164i	−1.15388	−	0.666192i	−0.949829	+	0.312769i	$0.898744\pi$
$450$		0			0
$451$	−14.7365			−0.693915
$452$	−2.70479	+	4.68484i	−0.127223	+	0.220356i
$453$		0			0
$454$	8.98584			0.421726
$455$	−2.73697	+	16.7991i	−0.128311	+	0.787553i
$456$		0			0
$457$		−	11.1214i		−	0.520237i	−0.965577	−	0.260118i	$-0.916238\pi$
$457$		−	11.1214i		−	0.520237i	0.965577	−	0.260118i	$-0.0837616\pi$
$458$	1.03406	−	1.79104i	0.0483184	−	0.0836898i
$459$		0			0
$460$	−22.3227	−	12.8880i	−1.04080	−	0.600907i
$461$	−16.6179	−	9.59437i	−0.773974	−	0.446854i	0.0603162	−	0.998179i	$-0.480789\pi$
$461$	−16.6179	−	9.59437i	−0.773974	−	0.446854i	−0.834291	+	0.551325i	$0.814122\pi$
$462$		0			0
$463$		−	6.57466i		−	0.305550i	−0.988261	−	0.152775i	$-0.951179\pi$
$463$		−	6.57466i		−	0.305550i	0.988261	−	0.152775i	$-0.0488211\pi$
$464$	6.72456	+	11.6473i	0.312180	+	0.540711i
$465$		0			0
$466$	−5.82004	−	3.36020i	−0.269608	−	0.155658i
$467$	−6.56821	+	11.3765i	−0.303941	+	0.526440i	−0.977025	−	0.213125i	$-0.931636\pi$
$467$	−6.56821	+	11.3765i	−0.303941	+	0.526440i	0.673084	+	0.739566i	$0.264969\pi$
$468$		0			0
$469$	16.8221	+	2.28228i	0.776771	+	0.105386i
$470$	−0.144016	+	0.0831476i	−0.00664295	+	0.00383531i
$471$		0			0
$472$	−1.91792			−0.0882796
$473$	−13.1052	+	7.56630i	−0.602579	+	0.347899i
$474$		0			0
$475$	−4.97741	−	2.87371i	−0.228379	−	0.131855i
$476$	−35.5255	+	14.5511i	−1.62831	+	0.666947i
$477$		0			0
$478$	−4.98089			−0.227821
$479$	−21.0813	−	12.1713i	−0.963229	−	0.556120i	−0.0660635	−	0.997815i	$-0.521044\pi$
$479$	−21.0813	−	12.1713i	−0.963229	−	0.556120i	−0.897165	+	0.441695i	$0.854377\pi$
$480$		0			0
$481$	29.7970	+	0.794480i	1.35863	+	0.0362252i
$482$	5.46277			0.248822
$483$		0			0
$484$	13.0856	+	22.6650i	0.594802	+	1.03023i
$485$	−4.11219	−	7.12253i	−0.186725	−	0.323417i
$486$		0			0
$487$			28.9709i			1.31280i	0.754414	+	0.656399i	$0.227921\pi$
$487$			28.9709i			1.31280i	−0.754414	+	0.656399i	$0.772079\pi$
$488$	−0.350896	+	0.202590i	−0.0158843	+	0.00917081i
$489$		0			0
$490$	−1.29156	−	4.97704i	−0.0583466	−	0.224840i
$491$	10.1324	+	17.5498i	0.457267	+	0.792010i	0.998815	−	0.0486596i	$-0.0154950\pi$
$491$	10.1324	+	17.5498i	0.457267	+	0.792010i	−0.541548	+	0.840670i	$0.682162\pi$
$492$		0			0
$493$	−17.6985	−	30.6547i	−0.797100	−	1.38062i
$494$	4.12853	−	2.23906i	0.185751	−	0.100740i
$495$		0			0
$496$	−12.7704	+	7.37298i	−0.573407	+	0.331057i
$497$	11.0305	+	1.49652i	0.494784	+	0.0671282i
$498$		0			0
$499$	−10.6581	−	6.15344i	−0.477121	−	0.275466i	0.242095	−	0.970253i	$-0.422165\pi$
$499$	−10.6581	−	6.15344i	−0.477121	−	0.275466i	−0.719216	+	0.694787i	$0.755499\pi$
$500$		−	22.2631i		−	0.995637i
$501$		0			0
$502$	6.08915	+	3.51557i	0.271772	+	0.156908i
$503$	17.7156	−	30.6842i	0.789898	−	1.36814i	−0.136132	−	0.990691i	$-0.543467\pi$
$503$	17.7156	−	30.6842i	0.789898	−	1.36814i	0.926029	−	0.377452i	$-0.123200\pi$
$504$		0			0
$505$	21.9547	−	12.6755i	0.976970	−	0.564054i
$506$	−8.17089	+	14.1524i	−0.363240	+	0.629151i
$507$		0			0
$508$	−18.3538	−	31.7897i	−0.814319	−	1.41044i
$509$			31.5235i			1.39725i	0.715486	+	0.698627i	$0.246205\pi$
$509$			31.5235i			1.39725i	−0.715486	+	0.698627i	$0.753795\pi$
$510$		0			0
$511$	−8.58525	+	11.0975i	−0.379789	+	0.490925i
$512$		−	22.7326i		−	1.00465i
$513$		0			0
$514$			4.79811i			0.211636i
$515$	−16.0765	+	9.28175i	−0.708414	+	0.409003i
$516$		0			0
$517$	−0.569326	−	0.986102i	−0.0250389	−	0.0433687i
$518$	−8.33294	+	3.41313i	−0.366128	+	0.149964i
$519$		0			0
$520$	8.64754	+	5.30489i	0.379220	+	0.232635i
$521$	−0.472864	−	0.819025i	−0.0207166	−	0.0358821i	0.855481	−	0.517834i	$-0.173261\pi$
$521$	−0.472864	−	0.819025i	−0.0207166	−	0.0358821i	−0.876198	+	0.481952i	$0.839928\pi$
$522$		0			0
$523$	−1.51457			−0.0662274			−0.0331137	−	0.999452i	$-0.510542\pi$
$523$	−1.51457			−0.0662274			−0.0331137	+	0.999452i	$0.510542\pi$
$524$	3.67921	−	6.37258i	0.160727	−	0.278388i
$525$		0			0
$526$	4.08267	+	2.35713i	0.178013	+	0.102776i
$527$	33.6106	−	19.4051i	1.46410	−	0.845299i
$528$		0			0
$529$	39.2848			1.70803
$530$	−3.69598			−0.160543
$531$		0			0
$532$	9.37637	−	12.1201i	0.406517	−	0.525474i
$533$	−5.03629	−	9.28624i	−0.218146	−	0.402232i
$534$		0			0
$535$	25.8300	+	14.9130i	1.11673	+	0.644743i
$536$	5.05929	−	8.76295i	0.218528	−	0.378502i
$537$		0			0
$538$		−	3.75913i		−	0.162068i
$539$	34.0787	−	8.84351i	1.46787	−	0.380917i
$540$		0			0
$541$	16.8059	+	9.70288i	0.722541	+	0.417159i	0.815687	−	0.578493i	$-0.196359\pi$
$541$	16.8059	+	9.70288i	0.722541	+	0.417159i	−0.0931461	+	0.995652i	$0.529692\pi$
$542$	−3.36000			−0.144324
$543$		0			0
$544$			34.8295i			1.49330i
$545$	−7.52365			−0.322278
$546$		0			0
$547$	19.5957			0.837854			0.418927	−	0.908020i	$-0.362406\pi$
$547$	19.5957			0.837854			0.418927	+	0.908020i	$0.362406\pi$
$548$			24.7148i			1.05577i
$549$		0			0
$550$	−3.76132			−0.160383
$551$	12.2360	+	7.06448i	0.521273	+	0.300957i
$552$		0			0
$553$	3.86864	−	28.5147i	0.164511	−	1.21257i
$554$		−	0.261024i		−	0.0110898i
$555$		0			0
$556$	−12.4594	+	21.5803i	−0.528396	+	0.915209i
$557$	1.06983	+	0.617669i	0.0453303	+	0.0261715i	0.522494	−	0.852643i	$-0.325002\pi$
$557$	1.06983	+	0.617669i	0.0453303	+	0.0261715i	−0.477164	+	0.878815i	$0.658335\pi$
$558$		0			0
$559$	−9.24671	−	5.67246i	−0.391094	−	0.239920i
$560$	14.0885	+	1.91142i	0.595350	+	0.0807721i
$561$		0			0
$562$	1.84802			0.0779541
$563$	10.0091			0.421832			0.210916	−	0.977504i	$-0.432355\pi$
$563$	10.0091			0.421832			0.210916	+	0.977504i	$0.432355\pi$
$564$		0			0
$565$	−4.56642	+	2.63642i	−0.192111	+	0.110915i
$566$	5.50752	+	3.17977i	0.231498	+	0.133656i
$567$		0			0
$568$	3.31745	−	5.74599i	0.139197	−	0.241096i
$569$	35.0482			1.46930			0.734649	−	0.678448i	$-0.237347\pi$
$569$	35.0482			1.46930			0.734649	+	0.678448i	$0.237347\pi$
$570$		0			0
$571$	19.9323	+	34.5237i	0.834140	+	1.44477i	0.894729	+	0.446610i	$0.147369\pi$
$571$	19.9323	+	34.5237i	0.834140	+	1.44477i	−0.0605890	+	0.998163i	$0.519298\pi$
$572$	−17.3582	+	28.2956i	−0.725781	+	1.18310i
$573$		0			0
$574$	2.52420	+	1.95277i	0.105358	+	0.0815070i
$575$	7.16791	+	12.4152i	0.298923	+	0.517749i
$576$		0			0
$577$	21.5772	−	12.4576i	0.898271	−	0.518617i	0.0216320	−	0.999766i	$-0.493114\pi$
$577$	21.5772	−	12.4576i	0.898271	−	0.518617i	0.876639	+	0.481149i	$0.159780\pi$
$578$		−	18.8694i		−	0.784865i
$579$		0			0
$580$			14.5846i			0.605593i
$581$	−14.0858	−	34.3896i	−0.584378	−	1.42672i
$582$		0			0
$583$		−	25.3070i		−	1.04811i
$584$	4.18148	+	7.24253i	0.173031	+	0.299698i
$585$		0			0
$586$	4.37397	−	7.57594i	0.180687	−	0.312959i
$587$	16.8894	−	9.75109i	0.697099	−	0.402470i	−0.109167	−	0.994023i	$-0.534818\pi$
$587$	16.8894	−	9.75109i	0.697099	−	0.402470i	0.806266	+	0.591553i	$0.201485\pi$
$588$		0			0
$589$	−7.74568	+	13.4159i	−0.319155	+	0.552793i
$590$	−0.773676	−	0.446682i	−0.0318517	−	0.0183896i
$591$		0			0
$592$		−	24.8989i		−	1.02334i
$593$	9.27492	+	5.35488i	0.380875	+	0.219898i	0.678199	−	0.734878i	$-0.262761\pi$
$593$	9.27492	+	5.35488i	0.380875	+	0.219898i	−0.297324	+	0.954777i	$0.596094\pi$
$594$		0			0
$595$	−37.0799	−	5.03070i	−1.52013	−	0.206238i
$596$	−17.2040	+	9.93275i	−0.704704	+	0.406861i
$597$		0			0
$598$	−11.7106	−	0.312241i	−0.478883	−	0.0127685i
$599$	7.20554	+	12.4804i	0.294411	+	0.509934i	0.974848	−	0.222873i	$-0.0715434\pi$
$599$	7.20554	+	12.4804i	0.294411	+	0.509934i	−0.680437	+	0.732807i	$0.738210\pi$
$600$		0			0
$601$	12.5931	+	21.8120i	0.513685	+	0.889729i	0.999874	+	0.0158749i	$0.00505336\pi$
$601$	12.5931	+	21.8120i	0.513685	+	0.889729i	−0.486189	+	0.873854i	$0.661613\pi$
$602$	3.24741	+	0.440581i	0.132355	+	0.0179568i
$603$		0			0
$604$	−23.7526	+	13.7136i	−0.966479	+	0.557997i
$605$			25.5098i			1.03712i
$606$		0			0
$607$	5.88500	+	10.1931i	0.238865	+	0.413726i	0.960389	−	0.278664i	$-0.0898914\pi$
$607$	5.88500	+	10.1931i	0.238865	+	0.413726i	−0.721524	+	0.692389i	$0.756558\pi$
$608$	−6.95122	−	12.0399i	−0.281909	−	0.488281i
$609$		0			0
$610$	−0.188731			−0.00764151
$611$	0.426824	−	0.695768i	0.0172674	−	0.0281478i
$612$		0			0
$613$	7.80746	+	4.50764i	0.315340	+	0.182062i	0.649314	−	0.760521i	$-0.275056\pi$
$613$	7.80746	+	4.50764i	0.315340	+	0.182062i	−0.333973	+	0.942583i	$0.608390\pi$
$614$	0.981774			0.0396212
$615$		0			0
$616$	2.82126	−	20.7947i	0.113672	−	0.837844i
$617$	−16.6581	−	9.61754i	−0.670629	−	0.387188i	0.125686	−	0.992070i	$-0.459887\pi$
$617$	−16.6581	−	9.61754i	−0.670629	−	0.387188i	−0.796315	+	0.604882i	$0.793220\pi$
$618$		0			0
$619$	−3.28531	+	1.89678i	−0.132048	+	0.0762379i	−0.564569	−	0.825386i	$-0.690957\pi$
$619$	−3.28531	+	1.89678i	−0.132048	+	0.0762379i	0.432521	+	0.901624i	$0.357624\pi$
$620$	−15.9910			−0.642212
$621$		0			0
$622$	1.48705	−	0.858548i	0.0596252	−	0.0344246i
$623$	−6.00384	−	14.6580i	−0.240539	−	0.587260i
$624$		0			0
$625$	6.30898	−	10.9275i	0.252359	−	0.437099i
$626$	−11.1330	−	6.42764i	−0.444964	−	0.256900i
$627$		0			0
$628$	12.4665	+	21.5926i	0.497466	+	0.861637i
$629$			65.5319i			2.61293i
$630$		0			0
$631$	−0.830312	−	0.479381i	−0.0330542	−	0.0190839i	0.483382	−	0.875410i	$-0.339408\pi$
$631$	−0.830312	−	0.479381i	−0.0330542	−	0.0190839i	−0.516436	+	0.856326i	$0.672742\pi$
$632$	−14.8539	−	8.57588i	−0.590855	−	0.341130i
$633$		0			0
$634$	1.36196	−	2.35898i	0.0540903	−	0.0936872i
$635$		−	35.7798i		−	1.41988i
$636$		0			0
$637$	17.2194	+	18.4525i	0.682256	+	0.731113i
$638$	9.24651			0.366073
$639$		0			0
$640$	9.38773	−	16.2600i	0.371083	−	0.642734i
$641$	−28.6455			−1.13143			−0.565714	−	0.824602i	$-0.691399\pi$
$641$	−28.6455			−1.13143			−0.565714	+	0.824602i	$0.691399\pi$
$642$		0			0
$643$	−27.0373	−	15.6100i	−1.06625	−	0.615598i	−0.139093	−	0.990279i	$-0.544419\pi$
$643$	−27.0373	−	15.6100i	−1.06625	−	0.615598i	−0.927153	+	0.374682i	$0.877752\pi$
$644$	−35.3699	+	14.4873i	−1.39377	+	0.570881i
$645$		0			0
$646$	5.16273	+	8.94212i	0.203125	+	0.351823i
$647$	4.64171	−	8.03968i	0.182485	−	0.316073i	−0.760241	−	0.649641i	$-0.774919\pi$
$647$	4.64171	−	8.03968i	0.182485	−	0.316073i	0.942726	+	0.333568i	$0.108253\pi$
$648$		0			0
$649$	3.05851	−	5.29750i	0.120057	−	0.207945i
$650$	−1.28545	−	2.37021i	−0.0504196	−	0.0929671i
$651$		0			0
$652$	−9.28361	+	5.35989i	−0.363574	+	0.209910i
$653$	−42.7939			−1.67465			−0.837327	−	0.546703i	$-0.815883\pi$
$653$	−42.7939			−1.67465			−0.837327	+	0.546703i	$0.815883\pi$
$654$		0			0
$655$	6.21151	−	3.58621i	0.242704	−	0.140125i
$656$	−7.64210	+	4.41217i	−0.298374	+	0.172266i
$657$		0			0
$658$	−0.0331515	+	0.244351i	−0.00129238	+	0.00952580i
$659$	−14.4742	+	25.0701i	−0.563835	+	0.976591i	0.433322	+	0.901239i	$0.357341\pi$
$659$	−14.4742	+	25.0701i	−0.563835	+	0.976591i	−0.997157	+	0.0753518i	$0.975992\pi$
$660$		0			0
$661$	15.5930	+	9.00264i	0.606499	+	0.350162i	0.771594	−	0.636115i	$-0.219460\pi$
$661$	15.5930	+	9.00264i	0.606499	+	0.350162i	−0.165095	+	0.986278i	$0.552793\pi$
$662$	−0.743433	−	1.28766i	−0.0288944	−	0.0500465i
$663$		0			0
$664$	−22.1506			−0.859609
$665$	13.8218	−	5.66135i	0.535987	−	0.219538i
$666$		0			0
$667$	−17.6210	−	30.5204i	−0.682287	−	1.18176i
$668$	−28.2300	+	16.2986i	−1.09225	+	0.630612i
$669$		0			0
$670$	4.08176	−	2.35660i	0.157692	−	0.0910435i
$671$		−	1.29228i		−	0.0498878i
$672$		0			0
$673$	−24.5342	−	42.4944i	−0.945723	−	1.63804i	−0.754298	−	0.656533i	$-0.772022\pi$
$673$	−24.5342	−	42.4944i	−0.945723	−	1.63804i	−0.191425	−	0.981507i	$-0.561311\pi$
$674$		−	7.65502i		−	0.294860i
$675$		0			0
$676$	−23.7628	−	1.26808i	−0.913955	−	0.0487724i
$677$	−4.88492	+	8.46094i	−0.187743	+	0.325180i	−0.944497	−	0.328519i	$-0.893451\pi$
$677$	−4.88492	+	8.46094i	−0.187743	+	0.325180i	0.756754	+	0.653699i	$0.226784\pi$
$678$		0			0
$679$	−12.0848	−	1.63956i	−0.463771	−	0.0629206i
$680$	−11.1519	+	19.3157i	−0.427656	+	0.740722i
$681$		0			0
$682$			10.1381i			0.388209i
$683$			20.7857i			0.795344i	0.917528	+	0.397672i	$0.130182\pi$
$683$			20.7857i			0.795344i	−0.917528	+	0.397672i	$0.869818\pi$
$684$		0			0
$685$	−12.0451	+	20.8627i	−0.460218	+	0.797122i
$686$	−7.00918	−	3.00106i	−0.267612	−	0.114581i
$687$		0			0
$688$	−4.53076	+	7.84751i	−0.172734	+	0.299184i
$689$	15.9473	−	8.64884i	0.607544	−	0.329494i
$690$		0			0
$691$		−	17.7010i		−	0.673379i	−0.941616	−	0.336690i	$-0.890693\pi$
$691$		−	17.7010i		−	0.673379i	0.941616	−	0.336690i	$-0.109307\pi$
$692$	22.7918	+	39.4766i	0.866415	+	1.50068i
$693$		0			0
$694$			1.55094i			0.0588730i
$695$	−21.0348	+	12.1445i	−0.797897	+	0.460666i
$696$		0			0
$697$	20.1134	−	11.6125i	0.761849	−	0.439854i
$698$	−6.45427	−	11.1791i	−0.244298	−	0.423136i
$699$		0			0
$700$	−6.95822	−	5.38302i	−0.262996	−	0.203459i
$701$	0.253105			0.00955964			0.00477982	−	0.999989i	$-0.498479\pi$
$701$	0.253105			0.00955964			0.00477982	+	0.999989i	$0.498479\pi$
$702$		0			0
$703$	−13.0788	−	22.6531i	−0.493275	−	0.854377i
$704$	18.3581	+	10.5991i	0.691898	+	0.399467i
$705$		0			0
$706$	−3.36009	+	5.81985i	−0.126459	+	0.219033i
$707$	5.05383	−	37.2504i	0.190069	−	1.40095i
$708$		0			0
$709$	−36.7989	+	21.2459i	−1.38201	+	0.797905i	−0.992398	−	0.123073i	$-0.960725\pi$
$709$	−36.7989	+	21.2459i	−1.38201	+	0.797905i	−0.389615	+	0.920978i	$0.627392\pi$
$710$	2.67647	−	1.54526i	0.100446	−	0.0579925i
$711$		0			0
$712$	−9.44130			−0.353828
$713$	33.4634	−	19.3201i	1.25321	−	0.723544i
$714$		0			0
$715$	−28.4428	+	15.4256i	−1.06370	+	0.576886i
$716$	9.56178	−	16.5615i	0.357341	−	0.618932i
$717$		0			0
$718$	0.505222	−	0.875070i	0.0188547	−	0.0326573i
$719$	8.93894	+	15.4827i	0.333366	+	0.577407i	0.983170	−	0.182695i	$-0.0584822\pi$
$719$	8.93894	+	15.4827i	0.333366	+	0.577407i	−0.649804	+	0.760102i	$0.725149\pi$
$720$		0			0
$721$	−3.70070	+	27.2769i	−0.137821	+	1.01584i
$722$	3.20486	+	1.85033i	0.119273	+	0.0688620i
$723$		0			0
$724$	1.76267			0.0655089
$725$	4.05575	−	7.02476i	0.150627	−	0.260893i
$726$		0			0
$727$	−21.9547			−0.814255			−0.407128	−	0.913371i	$-0.633470\pi$
$727$	−21.9547			−0.814255			−0.407128	+	0.913371i	$0.633470\pi$
$728$	14.0680	−	5.32891i	0.521396	−	0.197502i
$729$		0			0
$730$			3.89544i			0.144177i
$731$	11.9246	−	20.6540i	0.441047	−	0.763917i
$732$		0			0
$733$	−41.7755	−	24.1191i	−1.54302	−	0.890860i	−0.998646	−	0.0520141i	$-0.983436\pi$
$733$	−41.7755	−	24.1191i	−1.54302	−	0.890860i	−0.544369	−	0.838846i	$-0.683231\pi$
$734$	7.93521	+	4.58139i	0.292894	+	0.169102i
$735$		0			0
$736$			34.6770i			1.27821i
$737$	16.1361	+	27.9485i	0.594380	+	1.02950i
$738$		0			0
$739$	36.1769	+	20.8867i	1.33079	+	0.768331i	0.985421	−	0.170136i	$-0.0544208\pi$
$739$	36.1769	+	20.8867i	1.33079	+	0.768331i	0.345368	+	0.938467i	$0.387754\pi$
$740$	13.5005	−	23.3836i	0.496290	−	0.859599i
$741$		0			0
$742$	−3.35350	+	4.33482i	−0.123111	+	0.159136i
$743$	−20.3120	+	11.7272i	−0.745177	+	0.430228i	−0.823948	−	0.566665i	$-0.808233\pi$
$743$	−20.3120	+	11.7272i	−0.745177	+	0.430228i	0.0787719	+	0.996893i	$0.474900\pi$
$744$		0			0
$745$	−19.3634			−0.709419
$746$	12.8675	−	7.42905i	0.471112	−	0.271997i
$747$		0			0
$748$	−63.2029	−	36.4902i	−2.31093	−	1.33421i
$749$	40.9271	−	16.7635i	1.49544	−	0.612526i
$750$		0			0
$751$	−37.2712			−1.36004			−0.680022	−	0.733191i	$-0.738030\pi$
$751$	−37.2712			−1.36004			−0.680022	+	0.733191i	$0.738030\pi$
$752$	−0.590486	−	0.340917i	−0.0215328	−	0.0124320i
$753$		0			0
$754$	3.16005	+	5.82671i	0.115082	+	0.212196i
$755$	−26.7339			−0.972945
$756$		0			0
$757$	13.0417	+	22.5889i	0.474008	+	0.821007i	0.999557	−	0.0297569i	$-0.00947331\pi$
$757$	13.0417	+	22.5889i	0.474008	+	0.821007i	−0.525549	+	0.850763i	$0.676140\pi$
$758$	4.88735	+	8.46514i	0.177517	+	0.307468i
$759$		0			0
$760$		−	8.90272i		−	0.322936i
$761$	33.5335	−	19.3606i	1.21559	−	0.701820i	0.251616	−	0.967827i	$-0.419038\pi$
$761$	33.5335	−	19.3606i	1.21559	−	0.701820i	0.963971	+	0.266007i	$0.0857046\pi$
$762$		0			0
$763$	−6.82649	+	8.82409i	−0.247135	+	0.319453i
$764$	−12.1797	−	21.0958i	−0.440644	−	0.763219i
$765$		0			0
$766$	−3.93526	−	6.81608i	−0.142187	−	0.246275i
$767$	4.38350	+	0.116877i	0.158279	+	0.00422020i
$768$		0			0
$769$	27.8681	−	16.0897i	1.00495	−	0.580208i	0.0952408	−	0.995454i	$-0.469638\pi$
$769$	27.8681	−	16.0897i	1.00495	−	0.580208i	0.909709	+	0.415246i	$0.136305\pi$
$770$	5.98114	−	7.73137i	0.215545	−	0.278619i
$771$		0			0
$772$	1.14230	+	0.659507i	0.0411123	+	0.0237362i
$773$		−	4.62285i		−	0.166272i	−0.996538	−	0.0831361i	$-0.973506\pi$
$773$		−	4.62285i		−	0.166272i	0.996538	−	0.0831361i	$-0.0264936\pi$
$774$		0			0
$775$	7.70213	+	4.44683i	0.276669	+	0.159735i
$776$	−3.63453	+	6.29519i	−0.130472	+	0.225984i
$777$		0			0
$778$	−2.39568	+	1.38314i	−0.0858891	+	0.0495881i
$779$	−4.63520	+	8.02840i	−0.166073	+	0.287647i
$780$		0			0
$781$	10.5807	+	18.3262i	0.378606	+	0.655764i
$782$		−	25.7549i		−	0.920993i
$783$		0			0
$784$	15.0249	−	14.7894i	0.536602	−	0.528193i
$785$			24.3027i			0.867401i
$786$		0			0
$787$			14.8555i			0.529541i	0.964312	+	0.264770i	$0.0852961\pi$
$787$			14.8555i			0.529541i	−0.964312	+	0.264770i	$0.914704\pi$
$788$	34.4290	−	19.8776i	1.22648	−	0.708111i
$789$		0			0
$790$	−3.99462	−	6.91889i	−0.142122	−	0.246163i
$791$	−1.05116	+	7.74783i	−0.0373750	+	0.275481i
$792$		0			0
$793$	0.814332	−	0.441644i	0.0289178	−	0.0156832i
$794$	−3.65775	−	6.33541i	−0.129809	−	0.224835i
$795$		0			0
$796$	−21.5110			−0.762436
$797$	2.56907	−	4.44976i	0.0910011	−	0.157619i	−0.816932	−	0.576735i	$-0.804327\pi$
$797$	2.56907	−	4.44976i	0.0910011	−	0.157619i	0.907933	+	0.419116i	$0.137660\pi$
$798$		0			0
$799$	1.55411	+	0.897266i	0.0549805	+	0.0317430i
$800$	−6.91214	+	3.99073i	−0.244381	+	0.141094i
$801$		0			0
$802$	7.46986			0.263770
$803$	−26.6728			−0.941262
$804$		0			0
$805$	−36.9175	−	5.00866i	−1.30117	−	0.176532i
$806$	−6.38856	+	3.46476i	−0.225027	+	0.122041i
$807$		0			0
$808$	−19.4045	−	11.2032i	−0.682647	−	0.394126i
$809$	2.32457	−	4.02628i	0.0817276	−	0.141556i	−0.822265	−	0.569106i	$-0.807290\pi$
$809$	2.32457	−	4.02628i	0.0817276	−	0.141556i	0.903992	+	0.427549i	$0.140623\pi$
$810$		0			0
$811$			51.6064i			1.81215i	0.423121	+	0.906073i	$0.360934\pi$
$811$			51.6064i			1.81215i	−0.423121	+	0.906073i	$0.639066\pi$
$812$	17.1055	+	13.2332i	0.600286	+	0.464393i
$813$		0			0
$814$	−14.8250	−	8.55922i	−0.519616	−	0.300000i
$815$	−10.4488			−0.366006
$816$		0			0
$817$			9.51958i			0.333048i
$818$	3.88610			0.135874
$819$		0			0
$820$	−9.56936			−0.334177
$821$		−	32.5864i		−	1.13727i	−0.822589	−	0.568637i	$-0.807471\pi$
$821$		−	32.5864i		−	1.13727i	0.822589	−	0.568637i	$-0.192529\pi$
$822$		0			0
$823$	−23.6887			−0.825737			−0.412869	−	0.910791i	$-0.635473\pi$
$823$	−23.6887			−0.825737			−0.412869	+	0.910791i	$0.635473\pi$
$824$	14.2091	+	8.20361i	0.494996	+	0.285786i
$825$		0			0
$826$	−1.22587	+	0.502112i	−0.0426536	+	0.0174707i
$827$			9.92139i			0.345000i	0.985009	+	0.172500i	$0.0551845\pi$
$827$			9.92139i			0.345000i	−0.985009	+	0.172500i	$0.944815\pi$
$828$		0			0
$829$	13.7952	−	23.8940i	0.479128	−	0.829874i	−0.520585	−	0.853810i	$-0.674286\pi$
$829$	13.7952	−	23.8940i	0.479128	−	0.829874i	0.999714	+	0.0239354i	$0.00761962\pi$
$830$	−8.93537	−	5.15884i	−0.310151	−	0.179066i
$831$		0			0
$832$	−0.405031	+	15.1907i	−0.0140419	+	0.526643i
$833$	−39.5442	+	38.9245i	−1.37013	+	1.34865i
$834$		0			0
$835$	−31.7733			−1.09956
$836$	29.1306			1.00750
$837$		0			0
$838$	−6.66813	+	3.84985i	−0.230347	+	0.132991i
$839$	−41.4104	−	23.9083i	−1.42965	−	0.825406i	−0.432553	−	0.901609i	$-0.642387\pi$
$839$	−41.4104	−	23.9083i	−1.42965	−	0.825406i	−0.997092	+	0.0762027i	$0.975720\pi$
$840$		0			0
$841$	4.52969	−	7.84566i	0.156196	−	0.270540i
$842$	−2.18726			−0.0753781
$843$		0			0
$844$	−7.36009	−	12.7481i	−0.253345	−	0.438806i
$845$	−19.4410	−	12.6515i	−0.668791	−	0.435225i
$846$		0			0
$847$	29.9190	+	23.1459i	1.02803	+	0.795304i
$848$	−7.57703	−	13.1238i	−0.260196	−	0.450673i
$849$		0			0
$850$	5.13371	−	2.96395i	0.176085	−	0.101663i
$851$			65.2449i			2.23657i
$852$		0			0
$853$		−	42.9616i		−	1.47098i	−0.677537	−	0.735489i	$-0.736953\pi$
$853$		−	42.9616i		−	1.47098i	0.677537	−	0.735489i	$-0.263047\pi$
$854$	−0.171243	+	0.221353i	−0.00585981	+	0.00757454i
$855$		0			0
$856$		−	26.3614i		−	0.901014i
$857$	16.4002	+	28.4059i	0.560219	+	0.970328i	0.997477	+	0.0709918i	$0.0226164\pi$
$857$	16.4002	+	28.4059i	0.560219	+	0.970328i	−0.437258	+	0.899336i	$0.644050\pi$
$858$		0			0
$859$	12.7375	−	22.0619i	0.434596	−	0.752743i	−0.562666	−	0.826684i	$-0.690224\pi$
$859$	12.7375	−	22.0619i	0.434596	−	0.752743i	0.997263	+	0.0739411i	$0.0235577\pi$
$860$	−8.51007	+	4.91329i	−0.290191	+	0.167542i
$861$		0			0
$862$	7.12143	−	12.3347i	0.242557	−	0.420121i
$863$	−37.4379	−	21.6148i	−1.27440	−	0.735775i	−0.298587	−	0.954382i	$-0.596515\pi$
$863$	−37.4379	−	21.6148i	−1.27440	−	0.735775i	−0.975813	+	0.218607i	$0.929849\pi$
$864$		0			0
$865$			44.4314i			1.51071i
$866$	3.00847	+	1.73694i	0.102232	+	0.0590236i
$867$		0			0
$868$	−14.5092	+	18.7549i	−0.492474	+	0.636584i
$869$	47.3748	−	27.3519i	1.60708	−	0.927849i
$870$		0			0
$871$	−12.0972	+	19.7198i	−0.409899	+	0.668179i
$872$	3.32486	+	5.75883i	0.112594	+	0.195019i
$873$		0			0
$874$	5.14012	+	8.90295i	0.173867	+	0.301147i
$875$	−12.1966	−	29.7773i	−0.412321	−	1.00665i
$876$		0			0
$877$	−32.4966	+	18.7619i	−1.09733	+	0.633545i	−0.935519	−	0.353276i	$-0.885068\pi$
$877$	−32.4966	+	18.7619i	−1.09733	+	0.633545i	−0.161814	+	0.986821i	$0.551734\pi$
$878$			11.9487i			0.403249i
$879$		0			0
$880$	13.5140	+	23.4070i	0.455558	+	0.789049i
$881$	−1.00050	−	1.73292i	−0.0337078	−	0.0583836i	0.848679	−	0.528908i	$-0.177398\pi$
$881$	−1.00050	−	1.73292i	−0.0337078	−	0.0583836i	−0.882387	+	0.470524i	$0.844065\pi$
$882$		0			0
$883$	13.7382			0.462329			0.231164	−	0.972915i	$-0.425746\pi$
$883$	13.7382			0.462329			0.231164	+	0.972915i	$0.425746\pi$
$884$	1.39443	−	52.2982i	0.0468998	−	1.75898i
$885$		0			0
$886$	0.464985	+	0.268459i	0.0156215	+	0.00901906i
$887$	41.0950			1.37983			0.689917	−	0.723888i	$-0.257647\pi$
$887$	41.0950			1.37983			0.689917	+	0.723888i	$0.257647\pi$
$888$		0			0
$889$	−41.9642	−	32.4643i	−1.40743	−	1.08882i
$890$	−3.80855	−	2.19887i	−0.127663	−	0.0737062i
$891$		0			0
$892$	−17.5036	+	10.1057i	−0.586065	+	0.338365i
$893$	−0.716300			−0.0239701
$894$		0			0
$895$	16.1429	−	9.32009i	0.539597	−	0.311536i
$896$	−10.5527	−	25.7637i	−0.352540	−	0.860704i
$897$		0			0
$898$	−5.81158	+	10.0660i	−0.193935	+	0.335905i
$899$	−18.9343	−	10.9317i	−0.631493	−	0.364593i
$900$		0			0
$901$	19.9421	+	34.5408i	0.664369	+	1.15072i
$902$			6.06689i			0.202005i
$903$		0			0
$904$	4.03600	+	2.33018i	0.134235	+	0.0775008i
$905$	1.48793	+	0.859055i	0.0494604	+	0.0285560i
$906$		0			0
$907$	17.1461	−	29.6980i	0.569328	−	0.986104i	−0.427305	−	0.904108i	$-0.640537\pi$
$907$	17.1461	−	29.6980i	0.569328	−	0.986104i	0.996633	−	0.0819968i	$-0.0261297\pi$
$908$			39.9539i			1.32592i
$909$		0			0
$910$	6.91603	+	1.12679i	0.229264	+	0.0373527i
$911$	28.8500			0.955842			0.477921	−	0.878403i	$-0.341390\pi$
$911$	28.8500			0.955842			0.477921	+	0.878403i	$0.341390\pi$
$912$		0			0
$913$	35.3235	−	61.1821i	1.16904	−	2.02483i
$914$	−4.57858			−0.151446
$915$		0			0
$916$	7.96353	+	4.59775i	0.263123	+	0.151914i
$917$	1.42985	−	10.5390i	0.0472178	−	0.348030i
$918$		0			0
$919$	−15.2828	−	26.4706i	−0.504134	−	0.873185i	−0.999989	−	0.00477979i	$-0.998479\pi$
$919$	−15.2828	−	26.4706i	−0.504134	−	0.873185i	0.495855	−	0.868405i	$-0.334855\pi$
$920$	−11.1031	+	19.2311i	−0.366057	+	0.634029i
$921$		0			0
$922$	−3.94992	+	6.84146i	−0.130084	+	0.225311i
$923$	−7.93232	+	12.9305i	−0.261096	+	0.425614i
$924$		0			0
$925$	−13.0052	+	7.50857i	−0.427609	+	0.246880i
$926$	−2.70673			−0.0889487
$927$		0			0
$928$	16.9922	−	9.81047i	0.557797	−	0.322044i
$929$	−44.7928	+	25.8612i	−1.46961	+	0.848477i	−0.999419	−	0.0340897i	$-0.989147\pi$
$929$	−44.7928	+	25.8612i	−1.46961	+	0.848477i	−0.470187	+	0.882567i	$0.655813\pi$
$930$		0			0
$931$	5.90115	−	21.3476i	0.193402	−	0.699639i
$932$	14.9405	−	25.8778i	0.489393	−	0.847654i
$933$		0			0
$934$	4.68360	+	2.70408i	0.153252	+	0.0884800i
$935$	−35.5678	−	61.6053i	−1.16319	−	2.01471i
$936$		0			0
$937$	30.8803			1.00881			0.504407	−	0.863466i	$-0.331711\pi$
$937$	30.8803			1.00881			0.504407	+	0.863466i	$0.331711\pi$
$938$	0.939595	−	6.92550i	0.0306789	−	0.226126i
$939$		0			0
$940$	−0.369700	−	0.640340i	−0.0120583	−	0.0208856i
$941$	−4.82433	+	2.78533i	−0.157269	+	0.0907992i	−0.576569	−	0.817048i	$-0.695609\pi$
$941$	−4.82433	+	2.78533i	−0.157269	+	0.0907992i	0.419300	+	0.907848i	$0.362275\pi$
$942$		0			0
$943$	20.0253	−	11.5616i	0.652113	−	0.376498i
$944$		−	3.66292i		−	0.119218i
$945$		0			0
$946$	3.11498	+	5.39531i	0.101277	+	0.175417i
$947$			59.4165i			1.93078i	0.260814	+	0.965389i	$0.416009\pi$
$947$			59.4165i			1.93078i	−0.260814	+	0.965389i	$0.583991\pi$
$948$		0			0
$949$	−9.11558	−	16.8079i	−0.295904	−	0.545608i
$950$	−1.18308	+	2.04916i	−0.0383842	+	0.0664834i
$951$		0			0
$952$	12.5358	+	30.6053i	0.406286	+	0.991922i
$953$	11.0374	−	19.1174i	0.357538	−	0.619273i	−0.630011	−	0.776586i	$-0.716950\pi$
$953$	11.0374	−	19.1174i	0.357538	−	0.619273i	0.987549	+	0.157313i	$0.0502830\pi$
$954$		0			0
$955$		−	23.7436i		−	0.768324i
$956$		−	22.1466i		−	0.716273i
$957$		0			0
$958$	−5.01081	+	8.67899i	−0.161892	+	0.280405i
$959$	13.5398	+	33.0565i	0.437222	+	1.06745i
$960$		0			0
$961$	−3.51419	+	6.08675i	−0.113361	+	0.196347i
$962$	0.327081	−	12.2672i	0.0105455	−	0.395510i
$963$		0			0
$964$			24.2892i			0.782303i
$965$	0.642837	+	1.11343i	0.0206937	+	0.0358425i
$966$		0			0
$967$			30.4941i			0.980624i	0.871547	+	0.490312i	$0.163117\pi$
$967$			30.4941i			0.980624i	−0.871547	+	0.490312i	$0.836883\pi$
$968$	19.5259	−	11.2733i	0.627588	−	0.362338i
$969$		0			0
$970$	−2.93228	+	1.69295i	−0.0941500	+	0.0543575i
$971$	12.5535	+	21.7433i	0.402861	+	0.697775i	0.994070	−	0.108743i	$-0.0346826\pi$
$971$	12.5535	+	21.7433i	0.402861	+	0.697775i	−0.591209	+	0.806518i	$0.701349\pi$
$972$		0			0
$973$	−4.84209	+	35.6897i	−0.155230	+	1.14416i
$974$	11.9271			0.382168
$975$		0			0
$976$	−0.386913	−	0.670153i	−0.0123848	−	0.0214511i
$977$	−27.5734	−	15.9195i	−0.882151	−	0.509310i	−0.0107840	−	0.999942i	$-0.503433\pi$
$977$	−27.5734	−	15.9195i	−0.882151	−	0.509310i	−0.871367	+	0.490632i	$0.836766\pi$
$978$		0			0
$979$	15.0560	−	26.0778i	0.481193	−	0.833450i
$980$	22.1295	−	5.74267i	0.706902	−	0.183443i
$981$		0			0
$982$	7.22509	−	4.17141i	0.230562	−	0.133115i
$983$	31.7460	−	18.3285i	1.01254	−	0.584589i	0.100605	−	0.994926i	$-0.467922\pi$
$983$	31.7460	−	18.3285i	1.01254	−	0.584589i	0.911934	+	0.410337i	$0.134589\pi$
$984$		0			0
$985$	38.7503			1.23469
$986$	−12.6203	+	7.28632i	−0.401911	+	0.232044i
$987$		0			0
$988$	9.95557	+	18.3567i	0.316729	+	0.584006i
$989$	11.8724	−	20.5636i	0.377520	−	0.653883i
$990$		0			0
$991$	−3.86878	+	6.70093i	−0.122896	+	0.212862i	−0.920909	−	0.389779i	$-0.872551\pi$
$991$	−3.86878	+	6.70093i	−0.122896	+	0.212862i	0.798013	+	0.602641i	$0.205885\pi$
$992$	10.7565	+	18.6307i	0.341518	+	0.591526i
$993$		0			0
$994$	0.616106	−	4.54115i	0.0195417	−	0.144037i
$995$	−18.1582	−	10.4836i	−0.575652	−	0.332353i
$996$		0			0
$997$	52.0374			1.64804			0.824020	−	0.566560i	$-0.191726\pi$
$997$	52.0374			1.64804			0.824020	+	0.566560i	$0.191726\pi$
$998$	−2.53332	+	4.38784i	−0.0801908	+	0.138895i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.h.478.8	✓	36
3.2	odd	2	inner	819.2.bm.h.478.11	yes	36
7.4	even	3		819.2.do.h.361.11	yes	36
13.4	even	6		819.2.do.h.667.11	yes	36
21.11	odd	6		819.2.do.h.361.8	yes	36
39.17	odd	6		819.2.do.h.667.8	yes	36
91.4	even	6	inner	819.2.bm.h.550.11	yes	36
273.95	odd	6	inner	819.2.bm.h.550.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bm.h.478.8	✓	36	1.1	even	1	trivial
819.2.bm.h.478.11	yes	36	3.2	odd	2	inner
819.2.bm.h.550.8	yes	36	273.95	odd	6	inner
819.2.bm.h.550.11	yes	36	91.4	even	6	inner
819.2.do.h.361.8	yes	36	21.11	odd	6
819.2.do.h.361.11	yes	36	7.4	even	3
819.2.do.h.667.8	yes	36	39.17	odd	6
819.2.do.h.667.11	yes	36	13.4	even	6

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.411691i q^{2} +1.83051 q^{4} +(1.54520 + 0.892120i) q^{5} +(2.44833 - 1.00283i) q^{7} -1.57699i q^{8} +O(q^{10})\)	\(q-0.411691i q^{2} +1.83051 q^{4} +(1.54520 + 0.892120i) q^{5} +(2.44833 - 1.00283i) q^{7} -1.57699i q^{8} +(0.367278 - 0.636145i) q^{10} +(4.35580 + 2.51482i) q^{11} +(-0.0961009 + 3.60427i) q^{13} +(-0.412855 - 1.00796i) q^{14} +3.01179 q^{16} -7.92679 q^{17} +(2.74013 - 1.58202i) q^{19} +(2.82850 + 1.63304i) q^{20} +(1.03533 - 1.79324i) q^{22} -7.89207 q^{23} +(-0.908242 - 1.57312i) q^{25} +(1.48385 + 0.0395639i) q^{26} +(4.48170 - 1.83568i) q^{28} +(2.23275 + 3.86723i) q^{29} +(-4.24013 + 2.44804i) q^{31} -4.39390i q^{32} +3.26339i q^{34} +(4.67780 + 0.634645i) q^{35} -8.26714i q^{37} +(-0.651302 - 1.12809i) q^{38} +(1.40686 - 2.43676i) q^{40} +(-2.53740 + 1.46497i) q^{41} +(-1.50434 + 2.60560i) q^{43} +(7.97333 + 4.60340i) q^{44} +3.24910i q^{46} +(-0.196058 - 0.113194i) q^{47} +(4.98868 - 4.91050i) q^{49} +(-0.647641 + 0.373916i) q^{50} +(-0.175914 + 6.59765i) q^{52} +(-2.51579 - 4.35748i) q^{53} +(4.48704 + 7.77179i) q^{55} +(-1.58144 - 3.86099i) q^{56} +(1.59210 - 0.919202i) q^{58} -1.21619i q^{59} +(-0.128466 - 0.222510i) q^{61} +(1.00784 + 1.74563i) q^{62} +4.21464 q^{64} +(-3.36394 + 5.48358i) q^{65} +(5.55676 + 3.20820i) q^{67} -14.5101 q^{68} +(0.261278 - 1.92581i) q^{70} +(3.64365 + 2.10366i) q^{71} +(-4.59263 + 2.65156i) q^{73} -3.40351 q^{74} +(5.01584 - 2.89590i) q^{76} +(13.1864 + 1.78902i) q^{77} +(5.43814 - 9.41913i) q^{79} +(4.65381 + 2.68688i) q^{80} +(0.603114 + 1.04462i) q^{82} -14.0461i q^{83} +(-12.2485 - 7.07165i) q^{85} +(1.07270 + 0.619325i) q^{86} +(3.96584 - 6.86904i) q^{88} -5.98692i q^{89} +(3.37917 + 8.92083i) q^{91} -14.4465 q^{92} +(-0.0466011 + 0.0807154i) q^{94} +5.64539 q^{95} +(-3.99191 - 2.30473i) q^{97} +(-2.02161 - 2.05380i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) \) 36 * q - 44 * q^4 + 8 * q^7	\( 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) \) 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

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