LMFDB - Embedded newform 819.2.dx.a.503.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.503");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			503.2
Character	$\chi$	$=$	819.503
Dual form			819.2.dx.a.692.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27480 - 1.31336i) q^{2} +(2.44981 + 4.24319i) q^{4} +1.43978 q^{5} +(2.32410 - 1.26434i) q^{7} -7.61644i q^{8} +O(q^{10})$	\(q+(-2.27480 - 1.31336i) q^{2} +(2.44981 + 4.24319i) q^{4} +1.43978 q^{5} +(2.32410 - 1.26434i) q^{7} -7.61644i q^{8} +(-3.27522 - 1.89095i) q^{10} +(-2.00154 - 1.15559i) q^{11} +(-3.25793 + 1.54463i) q^{13} +(-6.94739 - 0.176260i) q^{14} +(-5.10349 + 8.83950i) q^{16} +(-3.11770 - 5.40001i) q^{17} +(0.988087 - 0.570472i) q^{19} +(3.52719 + 6.10928i) q^{20} +(3.03540 + 5.25746i) q^{22} +(0.221135 + 0.127672i) q^{23} -2.92702 q^{25} +(9.43979 + 0.765103i) q^{26} +(11.0584 + 6.76422i) q^{28} +(0.385601 + 0.222627i) q^{29} -5.95469i q^{31} +(10.0267 - 5.78894i) q^{32} +16.3786i q^{34} +(3.34621 - 1.82037i) q^{35} +(4.71851 - 8.17269i) q^{37} -2.99693 q^{38} -10.9660i q^{40} +(-1.63145 + 2.82576i) q^{41} +(-3.43583 - 5.95104i) q^{43} -11.3239i q^{44} +(-0.335358 - 0.580857i) q^{46} +5.29613 q^{47} +(3.80290 - 5.87690i) q^{49} +(6.65838 + 3.84422i) q^{50} +(-14.5355 - 10.0400i) q^{52} -8.94138i q^{53} +(-2.88178 - 1.66380i) q^{55} +(-9.62975 - 17.7014i) q^{56} +(-0.584777 - 1.01286i) q^{58} +(6.44296 + 11.1595i) q^{59} +(0.869760 - 0.502156i) q^{61} +(-7.82063 + 13.5457i) q^{62} -9.99782 q^{64} +(-4.69072 + 2.22393i) q^{65} +(6.55732 - 11.3576i) q^{67} +(15.2755 - 26.4580i) q^{68} +(-10.0027 - 0.253776i) q^{70} +(-7.67870 + 4.43330i) q^{71} +15.5891i q^{73} +(-21.4673 + 12.3942i) q^{74} +(4.84124 + 2.79509i) q^{76} +(-6.11283 - 0.155087i) q^{77} -8.43513 q^{79} +(-7.34792 + 12.7270i) q^{80} +(7.42245 - 4.28535i) q^{82} -10.2199 q^{83} +(-4.48881 - 7.77485i) q^{85} +18.0499i q^{86} +(-8.80148 + 15.2446i) q^{88} +(8.74839 - 15.1527i) q^{89} +(-5.61883 + 7.70900i) q^{91} +1.25109i q^{92} +(-12.0476 - 6.95571i) q^{94} +(1.42263 - 0.821357i) q^{95} +(6.46193 - 3.73080i) q^{97} +(-16.3693 + 8.37420i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^7	$ 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.27480	−	1.31336i	−1.60853	−	0.928683i	−0.989700	−	0.143154i	$-0.954276\pi$
$2$	−2.27480	−	1.31336i	−1.60853	−	0.928683i	−0.618825	−	0.785529i	$-0.712391\pi$
$3$		0			0
$3$		0			0
$4$	2.44981	+	4.24319i	1.22490	+	2.12159i
$5$	1.43978			0.643891			0.321946	−	0.946758i	$-0.395663\pi$
$5$	1.43978			0.643891			0.321946	+	0.946758i	$0.395663\pi$
$6$		0			0
$7$	2.32410	−	1.26434i	0.878428	−	0.477875i
$7$	2.32410	−	1.26434i	0.878428	−	0.477875i
$8$		−	7.61644i		−	2.69282i
$9$		0			0
$10$	−3.27522	−	1.89095i	−1.03572	−	0.597971i
$11$	−2.00154	−	1.15559i	−0.603487	−	0.348423i	0.166925	−	0.985970i	$-0.446616\pi$
$11$	−2.00154	−	1.15559i	−0.603487	−	0.348423i	−0.770412	+	0.637546i	$0.779949\pi$
$12$		0			0
$13$	−3.25793	+	1.54463i	−0.903588	+	0.428403i
$13$	−3.25793	+	1.54463i	−0.903588	+	0.428403i
$14$	−6.94739	−	0.176260i	−1.85677	−	0.0471075i
$15$		0			0
$16$	−5.10349	+	8.83950i	−1.27587	+	2.20987i
$17$	−3.11770	−	5.40001i	−0.756153	−	1.30969i	−0.944799	−	0.327650i	$-0.893743\pi$
$17$	−3.11770	−	5.40001i	−0.756153	−	1.30969i	0.188647	−	0.982045i	$-0.439590\pi$
$18$		0			0
$19$	0.988087	−	0.570472i	0.226683	−	0.130875i	−0.382358	−	0.924014i	$-0.624888\pi$
$19$	0.988087	−	0.570472i	0.226683	−	0.130875i	0.609041	+	0.793139i	$0.291555\pi$
$20$	3.52719	+	6.10928i	0.788704	+	1.36608i
$21$		0			0
$22$	3.03540	+	5.25746i	0.647149	+	1.12090i
$23$	0.221135	+	0.127672i	0.0461098	+	0.0266215i	0.522878	−	0.852408i	$-0.324858\pi$
$23$	0.221135	+	0.127672i	0.0461098	+	0.0266215i	−0.476768	+	0.879029i	$0.658192\pi$
$24$		0			0
$25$	−2.92702			−0.585404
$26$	9.43979	+	0.765103i	1.85129	+	0.150049i
$27$		0			0
$28$	11.0584	+	6.76422i	2.08985	+	1.27832i
$29$	0.385601	+	0.222627i	0.0716043	+	0.0413408i	0.535375	−	0.844615i	$-0.320170\pi$
$29$	0.385601	+	0.222627i	0.0716043	+	0.0413408i	−0.463770	+	0.885955i	$0.653504\pi$
$30$		0			0
$31$		−	5.95469i		−	1.06949i	−0.845012	−	0.534747i	$-0.820407\pi$
$31$		−	5.95469i		−	1.06949i	0.845012	−	0.534747i	$-0.179593\pi$
$32$	10.0267	−	5.78894i	1.77249	−	1.02335i
$33$		0			0
$34$			16.3786i			2.80890i
$35$	3.34621	−	1.82037i	0.565612	−	0.307699i
$36$		0			0
$37$	4.71851	−	8.17269i	0.775718	−	1.34358i	−0.158672	−	0.987331i	$-0.550721\pi$
$37$	4.71851	−	8.17269i	0.775718	−	1.34358i	0.934390	−	0.356251i	$-0.115945\pi$
$38$	−2.99693			−0.486166
$39$		0			0
$40$		−	10.9660i		−	1.73388i
$41$	−1.63145	+	2.82576i	−0.254790	+	0.441309i	−0.964838	−	0.262844i	$-0.915340\pi$
$41$	−1.63145	+	2.82576i	−0.254790	+	0.441309i	0.710048	+	0.704153i	$0.248673\pi$
$42$		0			0
$43$	−3.43583	−	5.95104i	−0.523960	−	0.907525i	−0.999611	−	0.0278908i	$-0.991121\pi$
$43$	−3.43583	−	5.95104i	−0.523960	−	0.907525i	0.475651	−	0.879634i	$-0.342212\pi$
$44$		−	11.3239i		−	1.70714i
$45$		0			0
$46$	−0.335358	−	0.580857i	−0.0494458	−	0.0856427i
$47$	5.29613			0.772521			0.386260	−	0.922390i	$-0.373767\pi$
$47$	5.29613			0.772521			0.386260	+	0.922390i	$0.373767\pi$
$48$		0			0
$49$	3.80290	−	5.87690i	0.543272	−	0.839557i
$50$	6.65838	+	3.84422i	0.941638	+	0.543655i
$51$		0			0
$52$	−14.5355	−	10.0400i	−2.01570	−	1.39229i
$53$		−	8.94138i		−	1.22819i	−0.789231	−	0.614097i	$-0.789520\pi$
$53$		−	8.94138i		−	1.22819i	0.789231	−	0.614097i	$-0.210480\pi$
$54$		0			0
$55$	−2.88178	−	1.66380i	−0.388580	−	0.224347i
$56$	−9.62975	−	17.7014i	−1.28683	−	2.36545i
$57$		0			0
$58$	−0.584777	−	1.01286i	−0.0767849	−	0.132995i
$59$	6.44296	+	11.1595i	0.838802	+	1.45285i	0.890897	+	0.454206i	$0.150077\pi$
$59$	6.44296	+	11.1595i	0.838802	+	1.45285i	−0.0520942	+	0.998642i	$0.516590\pi$
$60$		0			0
$61$	0.869760	−	0.502156i	0.111361	−	0.0642945i	−0.443285	−	0.896381i	$-0.646187\pi$
$61$	0.869760	−	0.502156i	0.111361	−	0.0642945i	0.554646	+	0.832086i	$0.312854\pi$
$62$	−7.82063	+	13.5457i	−0.993221	+	1.72031i
$63$		0			0
$64$	−9.99782			−1.24973
$65$	−4.69072	+	2.22393i	−0.581812	+	0.275845i
$66$		0			0
$67$	6.55732	−	11.3576i	0.801104	−	1.38755i	−0.117786	−	0.993039i	$-0.537580\pi$
$67$	6.55732	−	11.3576i	0.801104	−	1.38755i	0.918890	−	0.394514i	$-0.129087\pi$
$68$	15.2755	−	26.4580i	1.85243	−	3.20850i
$69$		0			0
$70$	−10.0027	−	0.253776i	−1.19556	−	0.0303321i
$71$	−7.67870	+	4.43330i	−0.911294	+	0.526136i	−0.880847	−	0.473400i	$-0.843026\pi$
$71$	−7.67870	+	4.43330i	−0.911294	+	0.526136i	−0.0304469	+	0.999536i	$0.509693\pi$
$72$		0			0
$73$			15.5891i			1.82457i	0.409554	+	0.912286i	$0.365684\pi$
$73$			15.5891i			1.82457i	−0.409554	+	0.912286i	$0.634316\pi$
$74$	−21.4673	+	12.3942i	−2.49552	+	1.44079i
$75$		0			0
$76$	4.84124	+	2.79509i	0.555329	+	0.320619i
$77$	−6.11283	−	0.155087i	−0.696622	−	0.0176738i
$78$		0			0
$79$	−8.43513			−0.949026			−0.474513	−	0.880248i	$-0.657376\pi$
$79$	−8.43513			−0.949026			−0.474513	+	0.880248i	$0.657376\pi$
$80$	−7.34792	+	12.7270i	−0.821523	+	1.42292i
$81$		0			0
$82$	7.42245	−	4.28535i	0.819673	−	0.473238i
$83$	−10.2199			−1.12178			−0.560889	−	0.827891i	$-0.689541\pi$
$83$	−10.2199			−1.12178			−0.560889	+	0.827891i	$0.689541\pi$
$84$		0			0
$85$	−4.48881	−	7.77485i	−0.486880	−	0.843301i
$86$			18.0499i			1.94637i
$87$		0			0
$88$	−8.80148	+	15.2446i	−0.938241	+	1.62508i
$89$	8.74839	−	15.1527i	0.927328	−	1.60618i	0.139554	−	0.990214i	$-0.455433\pi$
$89$	8.74839	−	15.1527i	0.927328	−	1.60618i	0.787774	−	0.615965i	$-0.211234\pi$
$90$		0			0
$91$	−5.61883	+	7.70900i	−0.589014	+	0.808123i
$92$			1.25109i			0.130435i
$93$		0			0
$94$	−12.0476	−	6.95571i	−1.24262	−	0.717427i
$95$	1.42263	−	0.821357i	0.145959	−	0.0842694i
$96$		0			0
$97$	6.46193	−	3.73080i	0.656109	−	0.378805i	−0.134684	−	0.990889i	$-0.543002\pi$
$97$	6.46193	−	3.73080i	0.656109	−	0.378805i	0.790793	+	0.612084i	$0.209668\pi$
$98$	−16.3693	+	8.37420i	−1.65355	+	0.845922i
$99$		0			0
$100$	−7.17063	−	12.4199i	−0.717063	−	1.24199i
$101$	−4.82373	+	8.35495i	−0.479979	+	0.831348i	−0.999736	−	0.0229657i	$-0.992689\pi$
$101$	−4.82373	+	8.35495i	−0.479979	+	0.831348i	0.519757	+	0.854314i	$0.326022\pi$
$102$		0			0
$103$			3.25458i			0.320683i	0.987062	+	0.160342i	$0.0512596\pi$
$103$			3.25458i			0.320683i	−0.987062	+	0.160342i	$0.948740\pi$
$104$	11.7646	+	24.8139i	1.15361	+	2.43320i
$105$		0			0
$106$	−11.7432	+	20.3398i	−1.14060	+	1.97558i
$107$	−2.59677	−	1.49924i	−0.251039	−	0.144937i	0.369201	−	0.929350i	$-0.379631\pi$
$107$	−2.59677	−	1.49924i	−0.251039	−	0.144937i	−0.620240	+	0.784412i	$0.712965\pi$
$108$		0			0
$109$	−6.19590			−0.593460			−0.296730	−	0.954961i	$-0.595896\pi$
$109$	−6.19590			−0.593460			−0.296730	+	0.954961i	$0.595896\pi$
$110$	4.37032	+	7.56961i	0.416694	+	0.721734i
$111$		0			0
$112$	−0.684918	+	26.9964i	−0.0647187	+	2.55092i
$113$	4.98453	−	2.87782i	0.468906	−	0.270723i	−0.246876	−	0.969047i	$-0.579404\pi$
$113$	4.98453	−	2.87782i	0.468906	−	0.270723i	0.715781	+	0.698324i	$0.246071\pi$
$114$		0			0
$115$	0.318386	+	0.183820i	0.0296897	+	0.0171413i
$116$			2.18157i			0.202554i
$117$		0			0
$118$		−	33.8476i		−	3.11592i
$119$	−14.0733	−	8.60835i	−1.29010	−	0.789127i
$120$		0			0
$121$	−2.82923	−	4.90037i	−0.257203	−	0.445488i
$122$	−2.63804			−0.238837
$123$		0			0
$124$	25.2669	−	14.5878i	2.26903	−	1.31003i
$125$	−11.4132			−1.02083
$126$		0			0
$127$	6.24024	−	10.8084i	0.553732	−	0.959091i	−0.444269	−	0.895893i	$-0.646537\pi$
$127$	6.24024	−	10.8084i	0.553732	−	0.959091i	0.998001	−	0.0631980i	$-0.0201300\pi$
$128$	2.68953	+	1.55280i	0.237724	+	0.137250i
$129$		0			0
$130$	13.5913	+	1.10158i	1.19203	+	0.0966152i
$131$	−1.60913			−0.140590			−0.0702951	−	0.997526i	$-0.522394\pi$
$131$	−1.60913			−0.140590			−0.0702951	+	0.997526i	$0.522394\pi$
$132$		0			0
$133$	1.57515	−	2.57511i	0.136582	−	0.223290i
$134$	−29.8332	+	17.2242i	−2.57719	+	1.48794i
$135$		0			0
$136$	−41.1289	+	23.7458i	−3.52677	+	2.03618i
$137$	11.9072	−	6.87464i	1.01730	−	0.587340i	0.103981	−	0.994579i	$-0.466842\pi$
$137$	11.9072	−	6.87464i	1.01730	−	0.587340i	0.913322	+	0.407239i	$0.133508\pi$
$138$		0			0
$139$	0.786440	−	0.454051i	0.0667050	−	0.0385121i	−0.466277	−	0.884639i	$-0.654405\pi$
$139$	0.786440	−	0.454051i	0.0667050	−	0.0385121i	0.532982	+	0.846127i	$0.321072\pi$
$140$	15.9217	+	9.73902i	1.34563	+	0.823098i
$141$		0			0
$142$	23.2900			1.95445
$143$	8.30583	+	0.673195i	0.694569	+	0.0562954i
$144$		0			0
$145$	0.555182	+	0.320535i	0.0461054	+	0.0266190i
$146$	20.4741	−	35.4622i	1.69445	−	2.93487i
$147$		0			0
$148$	46.2377			3.80072
$149$	4.51878	−	2.60892i	0.370193	−	0.213731i	−0.303350	−	0.952879i	$-0.598105\pi$
$149$	4.51878	−	2.60892i	0.370193	−	0.213731i	0.673543	+	0.739148i	$0.264772\pi$
$150$		0			0
$151$	−14.9049			−1.21295			−0.606474	−	0.795104i	$-0.707416\pi$
$151$	−14.9049			−1.21295			−0.606474	+	0.795104i	$0.707416\pi$
$152$	−4.34497	−	7.52571i	−0.352424	−	0.610416i
$153$		0			0
$154$	13.7018	+	8.38112i	1.10412	+	0.675370i
$155$		−	8.57347i		−	0.688638i
$156$		0			0
$157$		−	13.4979i		−	1.07725i	−0.842546	−	0.538625i	$-0.818944\pi$
$157$		−	13.4979i		−	1.07725i	0.842546	−	0.538625i	$-0.181056\pi$
$158$	19.1882	+	11.0783i	1.52653	+	0.881344i
$159$		0			0
$160$	14.4363	−	8.33483i	1.14129	−	0.658926i
$161$	0.675361	+	0.0171344i	0.0532259	+	0.00135038i
$162$		0			0
$163$	8.76069	+	15.1740i	0.686190	+	1.18852i	0.973061	+	0.230547i	$0.0740516\pi$
$163$	8.76069	+	15.1740i	0.686190	+	1.18852i	−0.286871	+	0.957969i	$0.592615\pi$
$164$	−15.9870			−1.24837
$165$		0			0
$166$	23.2482	+	13.4223i	1.80441	+	1.04178i
$167$	−1.08752	+	1.88364i	−0.0841550	+	0.145761i	−0.905031	−	0.425346i	$-0.860152\pi$
$167$	−1.08752	+	1.88364i	−0.0841550	+	0.145761i	0.820876	+	0.571107i	$0.193486\pi$
$168$		0			0
$169$	8.22824	−	10.0646i	0.632942	−	0.774199i
$170$			23.5816i			1.80863i
$171$		0			0
$172$	16.8342	−	29.1578i	1.28360	−	2.22326i
$173$	4.17248	+	7.22695i	0.317228	+	0.549454i	0.979909	−	0.199447i	$-0.0639147\pi$
$173$	4.17248	+	7.22695i	0.317228	+	0.549454i	−0.662681	+	0.748902i	$0.730581\pi$
$174$		0			0
$175$	−6.80270	+	3.70074i	−0.514235	+	0.279750i
$176$	20.4297	−	11.7951i	1.53994	−	0.889087i
$177$		0			0
$178$	−39.8017	+	22.9795i	−2.98326	+	1.72239i
$179$	−8.48345	−	4.89792i	−0.634083	−	0.366088i	0.148249	−	0.988950i	$-0.452636\pi$
$179$	−8.48345	−	4.89792i	−0.634083	−	0.366088i	−0.782332	+	0.622862i	$0.785970\pi$
$180$		0			0
$181$		−	6.84143i		−	0.508520i	−0.967136	−	0.254260i	$-0.918168\pi$
$181$		−	6.84143i		−	0.508520i	0.967136	−	0.254260i	$-0.0818318\pi$
$182$	22.9064	−	10.1569i	1.69793	−	0.752879i
$183$		0			0
$184$	0.972408	−	1.68426i	0.0716869	−	0.124165i
$185$	6.79363	−	11.7669i	0.499478	−	0.865121i
$186$		0			0
$187$			14.4111i			1.05384i
$188$	12.9745	+	22.4725i	0.946263	+	1.63898i
$189$		0			0
$190$	−4.31494			−0.313038
$191$	20.7658	−	11.9892i	1.50256	−	0.867505i	0.502568	−	0.864538i	$-0.332389\pi$
$191$	20.7658	−	11.9892i	1.50256	−	0.867505i	0.999996	−	0.00296733i	$-0.000944530\pi$
$192$		0			0
$193$	−2.71390	+	4.70061i	−0.195351	+	0.338357i	−0.947015	−	0.321188i	$-0.895918\pi$
$193$	−2.71390	+	4.70061i	−0.195351	+	0.338357i	0.751665	+	0.659545i	$0.229251\pi$
$194$	−19.5994			−1.40716
$195$		0			0
$196$	34.2532	+	1.73917i	2.44665	+	0.124227i
$197$	14.3153	+	8.26492i	1.01992	+	0.588851i	0.914081	−	0.405532i	$-0.132914\pi$
$197$	14.3153	+	8.26492i	1.01992	+	0.588851i	0.105839	+	0.994383i	$0.466247\pi$
$198$		0			0
$199$	−19.1790	+	11.0730i	−1.35956	+	0.784945i	−0.989565	−	0.144087i	$-0.953976\pi$
$199$	−19.1790	+	11.0730i	−1.35956	+	0.784945i	−0.370000	+	0.929032i	$0.620642\pi$
$200$			22.2935i			1.57639i
$201$		0			0
$202$	21.9460	−	12.6706i	1.54412	−	0.891497i
$203$	1.17765	+	0.0298778i	0.0826550	+	0.00209701i
$204$		0			0
$205$	−2.34894	+	4.06848i	−0.164057	+	0.284155i
$206$	4.27442	−	7.40352i	0.297813	−	0.515828i
$207$		0			0
$208$	2.97307	−	36.6815i	0.206145	−	2.54340i
$209$	−2.63693			−0.182400
$210$		0			0
$211$	−8.92921	+	15.4658i	−0.614712	+	1.06471i	0.375723	+	0.926732i	$0.377395\pi$
$211$	−8.92921	+	15.4658i	−0.614712	+	1.06471i	−0.990435	+	0.137981i	$0.955939\pi$
$212$	37.9400	−	21.9047i	2.60573	−	1.50442i
$213$		0			0
$214$	3.93808	+	6.82096i	0.269202	+	0.466271i
$215$	−4.94686	−	8.56821i	−0.337373	−	0.584347i
$216$		0			0
$217$	−7.52874	−	13.8393i	−0.511084	−	0.939474i
$218$	14.0944	+	8.13743i	0.954596	+	0.551136i
$219$		0			0
$220$		−	16.3039i		−	1.09921i
$221$	18.4983	+	12.7772i	1.24433	+	0.859486i
$222$		0			0
$223$	−19.6860	−	11.3657i	−1.31827	−	0.761105i	−0.334822	−	0.942281i	$-0.608676\pi$
$223$	−19.6860	−	11.3657i	−1.31827	−	0.761105i	−0.983451	+	0.181177i	$0.942009\pi$
$224$	15.9840	−	26.1313i	1.06798	−	1.74597i
$225$		0			0
$226$	−15.1184			−1.00566
$227$	7.03437	+	12.1839i	0.466888	+	0.808673i	0.999285	−	0.0378215i	$-0.0120418\pi$
$227$	7.03437	+	12.1839i	0.466888	+	0.808673i	−0.532397	+	0.846495i	$0.678709\pi$
$228$		0			0
$229$			14.0069i			0.925605i	0.886461	+	0.462803i	$0.153156\pi$
$229$			14.0069i			0.925605i	−0.886461	+	0.462803i	$0.846844\pi$
$230$	−0.482843	−	0.836309i	−0.0318377	−	0.0551446i
$231$		0			0
$232$	1.69563	−	2.93691i	0.111323	−	0.192818i
$233$			3.75336i			0.245891i	0.992413	+	0.122945i	$0.0392340\pi$
$233$			3.75336i			0.245891i	−0.992413	+	0.122945i	$0.960766\pi$
$234$		0			0
$235$	7.62529			0.497419
$236$	−31.5680	+	54.6774i	−2.05490	+	3.55920i
$237$		0			0
$238$	20.7080	+	38.0655i	1.34230	+	2.46742i
$239$		−	0.109491i		−	0.00708239i	−0.999994	−	0.00354119i	$-0.998873\pi$
$239$		−	0.109491i		−	0.00708239i	0.999994	−	0.00354119i	$-0.00112720\pi$
$240$		0			0
$241$	12.8132	−	7.39771i	0.825372	−	0.476529i	−0.0268936	−	0.999638i	$-0.508562\pi$
$241$	12.8132	−	7.39771i	0.825372	−	0.476529i	0.852265	+	0.523110i	$0.175228\pi$
$242$			14.8631i			0.955438i
$243$		0			0
$244$	4.26148	+	2.46037i	0.272814	+	0.157509i
$245$	5.47536	−	8.46147i	0.349808	−	0.540583i
$246$		0			0
$247$	−2.33795	+	3.38479i	−0.148760	+	0.215369i
$248$	−45.3536			−2.87996
$249$		0			0
$250$	25.9627	+	14.9896i	1.64203	+	0.948025i
$251$	0.789075	+	1.36672i	0.0498060	+	0.0862664i	0.889854	−	0.456246i	$-0.150806\pi$
$251$	0.789075	+	1.36672i	0.0498060	+	0.0862664i	−0.840048	+	0.542513i	$0.817473\pi$
$252$		0			0
$253$	−0.295073	−	0.511082i	−0.0185511	−	0.0321314i
$254$	−28.3906	+	16.3913i	−1.78138	+	1.02848i
$255$		0			0
$256$	5.91905	+	10.2521i	0.369941	+	0.640756i
$257$	11.6304	−	20.1444i	0.725481	−	1.25657i	−0.233294	−	0.972406i	$-0.574951\pi$
$257$	11.6304	−	20.1444i	0.725481	−	1.25657i	0.958776	−	0.284164i	$-0.0917161\pi$
$258$		0			0
$259$	0.633251	−	24.9600i	0.0393483	−	1.55094i
$260$	−20.9279	−	14.4554i	−1.29789	−	0.896486i
$261$		0			0
$262$	3.66044	+	2.11336i	0.226143	+	0.130564i
$263$	−13.1137	−	7.57119i	−0.808624	−	0.466859i	0.0378538	−	0.999283i	$-0.487948\pi$
$263$	−13.1137	−	7.57119i	−0.808624	−	0.466859i	−0.846478	+	0.532424i	$0.821281\pi$
$264$		0			0
$265$		−	12.8737i		−	0.790823i
$266$	−6.96518	+	3.78913i	−0.427062	+	0.232327i
$267$		0			0
$268$	64.2567			3.92510
$269$	9.57859	+	16.5906i	0.584017	+	1.01155i	0.994997	+	0.0999031i	$0.0318533\pi$
$269$	9.57859	+	16.5906i	0.584017	+	1.01155i	−0.410980	+	0.911644i	$0.634813\pi$
$270$		0			0
$271$	24.4217	+	14.0999i	1.48351	+	0.856505i	0.999824	−	0.0187359i	$-0.00596416\pi$
$271$	24.4217	+	14.0999i	1.48351	+	0.856505i	0.483686	+	0.875241i	$0.339297\pi$
$272$	63.6445			3.85902
$273$		0			0
$274$	−36.1154			−2.18181
$275$	5.85855	+	3.38243i	0.353284	+	0.203968i
$276$		0			0
$277$	4.42918	+	7.67157i	0.266124	+	0.460940i	0.967857	−	0.251499i	$-0.0809236\pi$
$277$	4.42918	+	7.67157i	0.266124	+	0.460940i	−0.701734	+	0.712439i	$0.747590\pi$
$278$	−2.38532			−0.143062
$279$		0			0
$280$	−13.8648	−	25.4862i	−0.828578	−	1.52309i
$281$		−	25.2076i		−	1.50376i	−0.659300	−	0.751880i	$-0.729147\pi$
$281$		−	25.2076i		−	1.50376i	0.659300	−	0.751880i	$-0.270853\pi$
$282$		0			0
$283$	21.5964	+	12.4687i	1.28377	+	0.741188i	0.977536	−	0.210767i	$-0.0675962\pi$
$283$	21.5964	+	12.4687i	1.28377	+	0.741188i	0.306238	+	0.951955i	$0.400930\pi$
$284$	−37.6227	−	21.7215i	−2.23249	−	1.28893i
$285$		0			0
$286$	−18.0100	−	12.4399i	−1.06495	−	0.735586i
$287$	−0.218951	+	8.63006i	−0.0129242	+	0.509416i
$288$		0			0
$289$	−10.9401	+	18.9488i	−0.643534	+	1.11463i
$290$	−0.841952	−	1.45830i	−0.0494411	−	0.0856346i
$291$		0			0
$292$	−66.1477	+	38.1904i	−3.87100	+	2.23492i
$293$	6.59919	+	11.4301i	0.385529	+	0.667756i	0.991842	−	0.127470i	$-0.0406856\pi$
$293$	6.59919	+	11.4301i	0.385529	+	0.667756i	−0.606313	+	0.795226i	$0.707352\pi$
$294$		0			0
$295$	9.27648	+	16.0673i	0.540097	+	0.935476i
$296$	−62.2469	−	35.9382i	−3.61803	−	2.08887i
$297$		0			0
$298$	−13.7058			−0.793954
$299$	−0.917648	−	0.0743762i	−0.0530690	−	0.00430129i
$300$		0			0
$301$	−15.5093	−	9.48677i	−0.893944	−	0.546808i
$302$	33.9058	+	19.5755i	1.95106	+	1.12644i
$303$		0			0
$304$			11.6456i			0.667920i
$305$	1.25227	−	0.722996i	0.0717046	−	0.0413986i
$306$		0			0
$307$		−	9.77126i		−	0.557675i	−0.960338	−	0.278838i	$-0.910051\pi$
$307$		−	9.77126i		−	0.557675i	0.960338	−	0.278838i	$-0.0899491\pi$
$308$	−14.3172	−	26.3178i	−0.815798	−	1.49960i
$309$		0			0
$310$	−11.2600	+	19.5029i	−0.639526	+	1.10769i
$311$	−25.7682			−1.46118			−0.730590	−	0.682816i	$-0.760755\pi$
$311$	−25.7682			−1.46118			−0.730590	+	0.682816i	$0.760755\pi$
$312$		0			0
$313$			16.4432i			0.929424i	0.885462	+	0.464712i	$0.153842\pi$
$313$			16.4432i			0.929424i	−0.885462	+	0.464712i	$0.846158\pi$
$314$	−17.7275	+	30.7050i	−1.00042	+	1.73278i
$315$		0			0
$316$	−20.6644	−	35.7918i	−1.16247	−	2.01345i
$317$		−	13.6972i		−	0.769311i	−0.923060	−	0.384655i	$-0.874320\pi$
$317$		−	13.6972i		−	0.769311i	0.923060	−	0.384655i	$-0.125680\pi$
$318$		0			0
$319$	−0.514530	−	0.891193i	−0.0288082	−	0.0498972i
$320$	−14.3947			−0.804688
$321$		0			0
$322$	−1.51381	−	0.925966i	−0.0843611	−	0.0516021i
$323$	−6.16111	−	3.55712i	−0.342813	−	0.197923i
$324$		0			0
$325$	9.53604	−	4.52116i	0.528964	−	0.250789i
$326$		−	46.0236i		−	2.54901i
$327$		0			0
$328$	21.5222	+	12.4259i	1.18837	+	0.686104i
$329$	12.3088	−	6.69610i	0.678604	−	0.369168i
$330$		0			0
$331$	−1.96979	−	3.41177i	−0.108269	−	0.187528i	0.806800	−	0.590825i	$-0.201198\pi$
$331$	−1.96979	−	3.41177i	−0.108269	−	0.187528i	−0.915069	+	0.403297i	$0.867864\pi$
$332$	−25.0367	−	43.3649i	−1.37407	−	2.37996i
$333$		0			0
$334$	4.94779	−	2.85661i	0.270731	−	0.156307i
$335$	9.44113	−	16.3525i	0.515824	−	0.893433i
$336$		0			0
$337$	−3.11809			−0.169853			−0.0849265	−	0.996387i	$-0.527066\pi$
$337$	−3.11809			−0.169853			−0.0849265	+	0.996387i	$0.527066\pi$
$338$	−31.9360	+	12.0883i	−1.73709	+	0.657518i
$339$		0			0
$340$	21.9934	−	38.0937i	1.19276	−	2.06592i
$341$	−6.88118	+	11.9185i	−0.372637	+	0.645426i
$342$		0			0
$343$	1.40795	−	18.4667i	0.0760223	−	0.997106i
$344$	−45.3257	+	26.1688i	−2.44380	+	1.41093i
$345$		0			0
$346$		−	21.9198i		−	1.17842i
$347$	−3.73943	+	2.15896i	−0.200743	+	0.115899i	−0.597002	−	0.802240i	$-0.703642\pi$
$347$	−3.73943	+	2.15896i	−0.200743	+	0.115899i	0.396259	+	0.918139i	$0.370308\pi$
$348$		0			0
$349$	10.9817	+	6.34026i	0.587835	+	0.339387i	0.764241	−	0.644931i	$-0.223114\pi$
$349$	10.9817	+	6.34026i	0.587835	+	0.339387i	−0.176406	+	0.984317i	$0.556447\pi$
$350$	20.3352	+	0.515917i	1.08696	+	0.0275769i
$351$		0			0
$352$	−26.7586			−1.42624
$353$	−12.6218	+	21.8616i	−0.671790	+	1.16358i	0.305606	+	0.952158i	$0.401141\pi$
$353$	−12.6218	+	21.8616i	−0.671790	+	1.16358i	−0.977396	+	0.211417i	$0.932192\pi$
$354$		0			0
$355$	−11.0557	+	6.38300i	−0.586774	+	0.338774i
$356$	85.7275			4.54355
$357$		0			0
$358$	12.8654	+	22.2836i	0.679959	+	1.17772i
$359$			17.6272i			0.930327i	0.885225	+	0.465164i	$0.154004\pi$
$359$			17.6272i			0.930327i	−0.885225	+	0.465164i	$0.845996\pi$
$360$		0			0
$361$	−8.84912	+	15.3271i	−0.465743	+	0.806691i
$362$	−8.98523	+	15.5629i	−0.472253	+	0.817967i
$363$		0			0
$364$	−46.4758	−	4.95622i	−2.43599	−	0.259776i
$365$			22.4450i			1.17483i
$366$		0			0
$367$	14.3140	+	8.26420i	0.747185	+	0.431387i	0.824676	−	0.565606i	$-0.191358\pi$
$367$	14.3140	+	8.26420i	0.747185	+	0.431387i	−0.0774908	+	0.996993i	$0.524691\pi$
$368$	−2.25712	+	1.30315i	−0.117660	+	0.0679312i
$369$		0			0
$370$	−30.9083	+	17.8449i	−1.60685	+	0.927713i
$371$	−11.3049	−	20.7807i	−0.586922	−	1.07888i
$372$		0			0
$373$	−3.60764	−	6.24862i	−0.186797	−	0.323541i	0.757384	−	0.652970i	$-0.226477\pi$
$373$	−3.60764	−	6.24862i	−0.186797	−	0.323541i	−0.944180	+	0.329429i	$0.893144\pi$
$374$	18.9269	−	32.7824i	0.978687	−	1.69514i
$375$		0			0
$376$		−	40.3377i		−	2.08026i
$377$	−1.60014	−	0.129693i	−0.0824113	−	0.00667951i
$378$		0			0
$379$	−15.2100	+	26.3445i	−0.781285	+	1.35323i	0.149908	+	0.988700i	$0.452102\pi$
$379$	−15.2100	+	26.3445i	−0.781285	+	1.35323i	−0.931193	+	0.364526i	$0.881231\pi$
$380$	6.97034	+	4.02433i	0.357571	+	0.206444i
$381$		0			0
$382$	−62.9841			−3.22255
$383$	−11.6641	−	20.2027i	−0.596005	−	1.03231i	−0.993404	−	0.114666i	$-0.963420\pi$
$383$	−11.6641	−	20.2027i	−0.596005	−	1.03231i	0.397399	−	0.917646i	$-0.369913\pi$
$384$		0			0
$385$	−8.80116	−	0.223292i	−0.448549	−	0.0113800i
$386$	12.3471	−	7.12863i	0.628453	−	0.362837i
$387$		0			0
$388$	31.6609	+	18.2795i	1.60734	+	0.927999i
$389$			28.8092i			1.46069i	0.683081	+	0.730343i	$0.260640\pi$
$389$			28.8092i			1.46069i	−0.683081	+	0.730343i	$0.739360\pi$
$390$		0			0
$391$		−	1.59217i		−	0.0805197i
$392$	−44.7611	−	28.9646i	−2.26078	−	1.46293i
$393$		0			0
$394$	−21.7096	−	37.6021i	−1.09371	−	1.89436i
$395$	−12.1448			−0.611070
$396$		0			0
$397$	−11.1686	+	6.44817i	−0.560533	+	0.323624i	−0.753360	−	0.657609i	$-0.771568\pi$
$397$	−11.1686	+	6.44817i	−0.560533	+	0.323624i	0.192826	+	0.981233i	$0.438235\pi$
$398$	58.1712			2.91586
$399$		0			0
$400$	14.9380	−	25.8734i	0.746901	−	1.29367i
$401$	24.3074	+	14.0339i	1.21385	+	0.700819i	0.963597	−	0.267360i	$-0.0861512\pi$
$401$	24.3074	+	14.0339i	1.21385	+	0.700819i	0.250258	+	0.968179i	$0.419485\pi$
$402$		0			0
$403$	9.19779	+	19.4000i	0.458175	+	0.966382i
$404$	−47.2688			−2.35171
$405$		0			0
$406$	−2.63968	−	1.61464i	−0.131005	−	0.0801333i
$407$	−18.8885	+	10.9053i	−0.936271	+	0.540556i
$408$		0			0
$409$	8.49992	−	4.90743i	0.420294	−	0.242657i	−0.274909	−	0.961470i	$-0.588648\pi$
$409$	8.49992	−	4.90743i	0.420294	−	0.242657i	0.695203	+	0.718813i	$0.255314\pi$
$410$	10.6867	−	6.16999i	0.527780	−	0.304714i
$411$		0			0
$412$	−13.8098	+	7.97309i	−0.680360	+	0.392806i
$413$	29.0835	+	17.7898i	1.43111	+	0.875380i
$414$		0			0
$415$	−14.7144			−0.722303
$416$	−23.7247	+	34.3476i	−1.16320	+	1.68403i
$417$		0			0
$418$	5.99847	+	3.46322i	0.293395	+	0.169392i
$419$	−9.74649	+	16.8814i	−0.476147	+	0.824711i	−0.999627	−	0.0273272i	$-0.991300\pi$
$419$	−9.74649	+	16.8814i	−0.476147	+	0.824711i	0.523479	+	0.852038i	$0.324634\pi$
$420$		0			0
$421$	26.7861			1.30547			0.652737	−	0.757585i	$-0.273621\pi$
$421$	26.7861			1.30547			0.652737	+	0.757585i	$0.273621\pi$
$422$	40.6243	−	23.4545i	1.97756	−	1.14175i
$423$		0			0
$424$	−68.1015			−3.30730
$425$	9.12557	+	15.8059i	0.442655	+	0.766701i
$426$		0			0
$427$	1.38652	−	2.26673i	0.0670982	−	0.109695i
$428$		−	14.6914i		−	0.710137i
$429$		0			0
$430$			25.9879i			1.25325i
$431$	−4.00419	−	2.31182i	−0.192875	−	0.111356i	0.400453	−	0.916317i	$-0.368853\pi$
$431$	−4.00419	−	2.31182i	−0.192875	−	0.111356i	−0.593328	+	0.804961i	$0.702186\pi$
$432$		0			0
$433$	−19.0918	+	11.0226i	−0.917493	+	0.529715i	−0.882834	−	0.469685i	$-0.844368\pi$
$433$	−19.0918	+	11.0226i	−0.917493	+	0.529715i	−0.0346584	+	0.999399i	$0.511034\pi$
$434$	−1.04957	+	41.3696i	−0.0503812	+	1.98580i
$435$		0			0
$436$	−15.1788	−	26.2904i	−0.726931	−	1.25908i
$437$	0.291334			0.0139364
$438$		0			0
$439$	−7.20007	−	4.15696i	−0.343641	−	0.198401i	0.318240	−	0.948010i	$-0.396908\pi$
$439$	−7.20007	−	4.15696i	−0.343641	−	0.198401i	−0.661881	+	0.749609i	$0.730242\pi$
$440$	−12.6722	+	21.9489i	−0.604125	+	1.04637i
$441$		0			0
$442$	−25.2988	−	53.3603i	−1.20334	−	2.53809i
$443$		−	21.8119i		−	1.03631i	−0.855286	−	0.518157i	$-0.826618\pi$
$443$		−	21.8119i		−	1.03631i	0.855286	−	0.518157i	$-0.173382\pi$
$444$		0			0
$445$	12.5958	−	21.8166i	0.597098	−	1.03420i
$446$	29.8545	+	51.7095i	1.41365	+	2.44851i
$447$		0			0
$448$	−23.2360	+	12.6406i	−1.09780	+	0.597213i
$449$	29.9196	−	17.2741i	1.41199	−	0.815215i	0.416417	−	0.909174i	$-0.363286\pi$
$449$	29.9196	−	17.2741i	1.41199	−	0.815215i	0.995576	+	0.0939592i	$0.0299523\pi$
$450$		0			0
$451$	6.53083	−	3.77058i	0.307525	−	0.177550i
$452$	24.4223	+	14.1002i	1.14873	+	0.663218i
$453$		0			0
$454$		−	36.9545i		−	1.73436i
$455$	−8.08991	+	11.0993i	−0.379261	+	0.520343i
$456$		0			0
$457$	7.75923	−	13.4394i	0.362961	−	0.628668i	−0.625485	−	0.780236i	$-0.715099\pi$
$457$	7.75923	−	13.4394i	0.362961	−	0.628668i	0.988447	+	0.151568i	$0.0484324\pi$
$458$	18.3961	−	31.8630i	0.859593	−	1.48886i
$459$		0			0
$460$			1.80130i			0.0839859i
$461$	−8.22049	−	14.2383i	−0.382867	−	0.663144i	0.608604	−	0.793474i	$-0.291730\pi$
$461$	−8.22049	−	14.2383i	−0.382867	−	0.663144i	−0.991471	+	0.130330i	$0.958396\pi$
$462$		0			0
$463$	−11.3808			−0.528908			−0.264454	−	0.964398i	$-0.585192\pi$
$463$	−11.3808			−0.528908			−0.264454	+	0.964398i	$0.585192\pi$
$464$	−3.93582	+	2.27235i	−0.182716	+	0.105491i
$465$		0			0
$466$	4.92949	−	8.53813i	0.228354	−	0.395521i
$467$	20.9907			0.971332			0.485666	−	0.874145i	$-0.338577\pi$
$467$	20.9907			0.971332			0.485666	+	0.874145i	$0.338577\pi$
$468$		0			0
$469$	0.880031	−	34.6869i	0.0406361	−	1.60169i
$470$	−17.3460	−	10.0147i	−0.800111	−	0.461945i
$471$		0			0
$472$	84.9960	−	49.0725i	3.91226	−	2.25874i
$473$			15.8816i			0.730239i
$474$		0			0
$475$	−2.89215	+	1.66978i	−0.132701	+	0.0766150i
$476$	2.05006	−	80.8044i	0.0939645	−	3.70366i
$477$		0			0
$478$	−0.143801	+	0.249070i	−0.00657729	+	0.0113922i
$479$	20.0062	−	34.6518i	0.914109	−	1.58328i	0.105908	−	0.994376i	$-0.466225\pi$
$479$	20.0062	−	34.6518i	0.914109	−	1.58328i	0.808201	−	0.588907i	$-0.200441\pi$
$480$		0			0
$481$	−2.74879	+	33.9144i	−0.125334	+	1.54636i
$482$	−38.8633			−1.77018
$483$		0			0
$484$	13.8621	−	24.0099i	0.630096	−	1.09136i
$485$	9.30378	−	5.37154i	0.422463	−	0.243909i
$486$		0			0
$487$	9.74368	+	16.8766i	0.441528	+	0.764750i	0.997803	−	0.0662489i	$-0.0211031\pi$
$487$	9.74368	+	16.8766i	0.441528	+	0.764750i	−0.556275	+	0.830998i	$0.687770\pi$
$488$	−3.82464	−	6.62448i	−0.173133	−	0.299876i
$489$		0			0
$490$	−23.5683	+	12.0570i	−1.06471	+	0.544681i
$491$	2.76077	+	1.59393i	0.124592	+	0.0719330i	0.561001	−	0.827815i	$-0.310417\pi$
$491$	2.76077	+	1.59393i	0.124592	+	0.0719330i	−0.436409	+	0.899748i	$0.643750\pi$
$492$		0			0
$493$		−	2.77633i		−	0.125040i
$494$	9.76380	−	4.62915i	0.439294	−	0.208275i
$495$		0			0
$496$	52.6365	+	30.3897i	2.36345	+	1.36454i
$497$	−12.2409	+	20.0119i	−0.549079	+	0.897657i
$498$		0			0
$499$	6.60755			0.295795			0.147897	−	0.989003i	$-0.452750\pi$
$499$	6.60755			0.295795			0.147897	+	0.989003i	$0.452750\pi$
$500$	−27.9601	−	48.4284i	−1.25041	−	2.16578i
$501$		0			0
$502$		−	4.14534i		−	0.185016i
$503$	7.57935	+	13.1278i	0.337947	+	0.585341i	0.984046	−	0.177912i	$-0.0569343\pi$
$503$	7.57935	+	13.1278i	0.337947	+	0.585341i	−0.646100	+	0.763253i	$0.723601\pi$
$504$		0			0
$505$	−6.94513	+	12.0293i	−0.309054	+	0.535298i
$506$			1.55014i			0.0689123i
$507$		0			0
$508$	61.1495			2.71307
$509$	16.6526	−	28.8432i	0.738114	−	1.27845i	−0.215229	−	0.976564i	$-0.569050\pi$
$509$	16.6526	−	28.8432i	0.738114	−	1.27845i	0.953343	−	0.301888i	$-0.0976168\pi$
$510$		0			0
$511$	19.7099	+	36.2308i	0.871916	+	1.60275i
$512$		−	37.3065i		−	1.64873i
$513$		0			0
$514$	−52.9134	+	30.5496i	−2.33391	+	1.34748i
$515$			4.68590i			0.206485i
$516$		0			0
$517$	−10.6004	−	6.12015i	−0.466206	−	0.269164i
$518$	−34.2218	+	55.9472i	−1.50362	+	2.45818i
$519$		0			0
$520$	16.9385	+	35.7266i	0.742801	+	1.56672i
$521$	6.27887			0.275082			0.137541	−	0.990496i	$-0.456080\pi$
$521$	6.27887			0.275082			0.137541	+	0.990496i	$0.456080\pi$
$522$		0			0
$523$	16.5000	+	9.52630i	0.721496	+	0.416556i	0.815303	−	0.579034i	$-0.196570\pi$
$523$	16.5000	+	9.52630i	0.721496	+	0.416556i	−0.0938068	+	0.995590i	$0.529904\pi$
$524$	−3.94205	−	6.82784i	−0.172209	−	0.298276i
$525$		0			0
$526$	19.8873	+	34.4458i	0.867128	+	1.50191i
$527$	−32.1554	+	18.5649i	−1.40071	+	0.808701i
$528$		0			0
$529$	−11.4674	−	19.8621i	−0.498583	−	0.863570i
$530$	−16.9077	+	29.2850i	−0.734424	+	1.27206i
$531$		0			0
$532$	14.7855	+	0.375118i	0.641032	+	0.0162634i
$533$	0.950412	−	11.7261i	0.0411669	−	0.507915i
$534$		0			0
$535$	−3.73878	−	2.15859i	−0.161642	−	0.0933239i
$536$	−86.5046	−	49.9435i	−3.73643	−	2.15723i
$537$		0			0
$538$		−	50.3204i		−	2.16947i
$539$	−14.4029	+	7.36825i	−0.620378	+	0.317373i
$540$		0			0
$541$	45.0612			1.93733			0.968667	−	0.248364i	$-0.0798930\pi$
$541$	45.0612			1.93733			0.968667	+	0.248364i	$0.0798930\pi$
$542$	−37.0363	−	64.1487i	−1.59084	−	2.75542i
$543$		0			0
$544$	−62.5207	−	36.0963i	−2.68055	−	1.54762i
$545$	−8.92077			−0.382124
$546$		0			0
$547$	−22.5836			−0.965606			−0.482803	−	0.875729i	$-0.660381\pi$
$547$	−22.5836			−0.965606			−0.482803	+	0.875729i	$0.660381\pi$
$548$	58.3408	+	33.6831i	2.49220	+	1.43887i
$549$		0			0
$550$	−8.88468	−	15.3887i	−0.378844	−	0.656177i
$551$	0.508010			0.0216419
$552$		0			0
$553$	−19.6041	+	10.6648i	−0.833651	+	0.453516i
$554$		−	23.2684i		−	0.988579i
$555$		0			0
$556$	3.85325	+	2.22468i	0.163414	+	0.0943472i
$557$	9.72083	+	5.61232i	0.411885	+	0.237802i	0.691599	−	0.722281i	$-0.256906\pi$
$557$	9.72083	+	5.61232i	0.411885	+	0.237802i	−0.279715	+	0.960083i	$0.590240\pi$
$558$		0			0
$559$	20.3859	+	14.0810i	0.862230	+	0.595562i
$560$	−0.986134	+	38.8690i	−0.0416718	+	1.64252i
$561$		0			0
$562$	−33.1066	+	57.3422i	−1.39652	+	2.41884i
$563$	15.3448	+	26.5780i	0.646708	+	1.12013i	0.983904	+	0.178696i	$0.0571879\pi$
$563$	15.3448	+	26.5780i	0.646708	+	1.12013i	−0.337197	+	0.941434i	$0.609479\pi$
$564$		0			0
$565$	7.17665	−	4.14344i	0.301924	−	0.174316i
$566$	−32.7517	−	56.7276i	−1.37666	−	2.38444i
$567$		0			0
$568$	33.7660	+	58.4844i	1.41679	+	2.45395i
$569$	−35.8042	−	20.6716i	−1.50099	−	0.866598i	−0.999999	−	0.00114561i	$-0.999635\pi$
$569$	−35.8042	−	20.6716i	−1.50099	−	0.866598i	−0.500992	−	0.865452i	$-0.667031\pi$
$570$		0			0
$571$	7.66204			0.320646			0.160323	−	0.987065i	$-0.448746\pi$
$571$	7.66204			0.320646			0.160323	+	0.987065i	$0.448746\pi$
$572$	17.4912	+	36.8924i	0.731343	+	1.54255i
$573$		0			0
$574$	11.8324	−	19.3441i	0.493875	−	0.807406i
$575$	−0.647266	−	0.373699i	−0.0269929	−	0.0155843i
$576$		0			0
$577$			8.12580i			0.338282i	0.985592	+	0.169141i	$0.0540992\pi$
$577$			8.12580i			0.338282i	−0.985592	+	0.169141i	$0.945901\pi$
$578$	49.7729	−	28.7364i	2.07028	−	1.19528i
$579$		0			0
$580$			3.14099i			0.130423i
$581$	−23.7521	+	12.9214i	−0.985401	+	0.536069i
$582$		0			0
$583$	−10.3326	+	17.8965i	−0.427931	+	0.741198i
$584$	118.734			4.91324
$585$		0			0
$586$		−	34.6684i		−	1.43214i
$587$	−0.489478	+	0.847801i	−0.0202029	+	0.0349925i	−0.875950	−	0.482402i	$-0.839765\pi$
$587$	−0.489478	+	0.847801i	−0.0202029	+	0.0349925i	0.855747	+	0.517394i	$0.173098\pi$
$588$		0			0
$589$	−3.39699	−	5.88375i	−0.139970	−	0.242436i
$590$		−	48.7333i		−	2.00632i
$591$		0			0
$592$	48.1617	+	83.4185i	1.97943	+	3.42848i
$593$	41.8839			1.71997			0.859983	−	0.510322i	$-0.170474\pi$
$593$	41.8839			1.71997			0.859983	+	0.510322i	$0.170474\pi$
$594$		0			0
$595$	−20.2625	−	12.3942i	−0.830681	−	0.508112i
$596$	22.1403	+	12.7827i	0.906901	+	0.523600i
$597$		0			0
$598$	1.98978	+	1.37439i	0.0813683	+	0.0562030i
$599$			9.44112i			0.385754i	0.981223	+	0.192877i	$0.0617818\pi$
$599$			9.44112i			0.385754i	−0.981223	+	0.192877i	$0.938218\pi$
$600$		0			0
$601$	−28.3950	−	16.3939i	−1.15826	−	0.668719i	−0.207370	−	0.978263i	$-0.566490\pi$
$601$	−28.3950	−	16.3939i	−1.15826	−	0.668719i	−0.950885	+	0.309543i	$0.899824\pi$
$602$	22.8211	+	41.9498i	0.930120	+	1.70975i
$603$		0			0
$604$	−36.5142	−	63.2445i	−1.48574	−	2.57338i
$605$	−4.07348	−	7.05547i	−0.165610	−	0.286846i
$606$		0			0
$607$	−19.2583	+	11.1188i	−0.781671	+	0.451298i	−0.837022	−	0.547169i	$-0.815706\pi$
$607$	−19.2583	+	11.1188i	−0.781671	+	0.451298i	0.0553510	+	0.998467i	$0.482372\pi$
$608$	6.60486	−	11.4400i	0.267863	−	0.463952i
$609$		0			0
$610$	−3.79820			−0.153785
$611$	−17.2544	+	8.18056i	−0.698040	+	0.330950i
$612$		0			0
$613$	−6.14938	+	10.6510i	−0.248371	+	0.430191i	−0.963074	−	0.269237i	$-0.913229\pi$
$613$	−6.14938	+	10.6510i	−0.248371	+	0.430191i	0.714703	+	0.699428i	$0.246562\pi$
$614$	−12.8331	+	22.2276i	−0.517903	+	0.897035i
$615$		0			0
$616$	−1.18121	+	46.5581i	−0.0475923	+	1.87588i
$617$	−16.9634	+	9.79383i	−0.682921	+	0.394285i	−0.800955	−	0.598725i	$-0.795674\pi$
$617$	−16.9634	+	9.79383i	−0.682921	+	0.394285i	0.118034	+	0.993010i	$0.462341\pi$
$618$		0			0
$619$			39.2803i			1.57881i	0.613874	+	0.789404i	$0.289610\pi$
$619$			39.2803i			1.57881i	−0.613874	+	0.789404i	$0.710390\pi$
$620$	36.3789	−	21.0033i	1.46101	−	0.843515i
$621$		0			0
$622$	58.6175	+	33.8428i	2.35035	+	1.35697i
$623$	1.17409	−	46.2773i	0.0470388	−	1.85406i
$624$		0			0
$625$	−1.79744			−0.0718977
$626$	21.5958	−	37.4050i	0.863140	−	1.49500i
$627$		0			0
$628$	57.2741	−	33.0672i	2.28549	−	1.31953i
$629$	−58.8435			−2.34624
$630$		0			0
$631$	6.57597	+	11.3899i	0.261785	+	0.453425i	0.966716	−	0.255850i	$-0.0823555\pi$
$631$	6.57597	+	11.3899i	0.261785	+	0.453425i	−0.704931	+	0.709276i	$0.749022\pi$
$632$			64.2457i			2.55556i
$633$		0			0
$634$	−17.9893	+	31.1583i	−0.714446	+	1.23746i
$635$	8.98460	−	15.5618i	0.356543	−	0.617550i
$636$		0			0
$637$	−3.31197	+	25.0206i	−0.131225	+	0.991353i
$638$			2.70305i			0.107015i
$639$		0			0
$640$	3.87235	+	2.23570i	0.153068	+	0.0883739i
$641$	21.7946	−	12.5831i	0.860836	−	0.497004i	−0.00345644	−	0.999994i	$-0.501100\pi$
$641$	21.7946	−	12.5831i	0.860836	−	0.497004i	0.864292	+	0.502990i	$0.167767\pi$
$642$		0			0
$643$	34.8476	−	20.1192i	1.37425	−	0.793426i	0.382793	−	0.923834i	$-0.374962\pi$
$643$	34.8476	−	20.1192i	1.37425	−	0.793426i	0.991460	+	0.130408i	$0.0416288\pi$
$644$	1.58180	+	2.90766i	0.0623316	+	0.114578i
$645$		0			0
$646$	9.34352	+	16.1835i	0.367616	+	0.636730i
$647$	0.873501	−	1.51295i	0.0343409	−	0.0594801i	−0.848344	−	0.529445i	$-0.822400\pi$
$647$	0.873501	−	1.51295i	0.0343409	−	0.0594801i	0.882685	+	0.469965i	$0.155733\pi$
$648$		0			0
$649$		−	29.7817i		−	1.16903i
$650$	−27.6305	−	2.23947i	−1.08376	−	0.0878393i
$651$		0			0
$652$	−42.9240	+	74.3465i	−1.68103	+	2.91163i
$653$	11.5799	+	6.68567i	0.453157	+	0.261630i	0.709163	−	0.705045i	$-0.249073\pi$
$653$	11.5799	+	6.68567i	0.453157	+	0.261630i	−0.256006	+	0.966675i	$0.582407\pi$
$654$		0			0
$655$	−2.31680			−0.0905248
$656$	−16.6522	−	28.8424i	−0.650159	−	1.12611i
$657$		0			0
$658$	−36.7943	−	0.933497i	−1.43439	−	0.0363915i
$659$	−25.9290	+	14.9701i	−1.01005	+	0.583153i	−0.911206	−	0.411950i	$-0.864848\pi$
$659$	−25.9290	+	14.9701i	−1.01005	+	0.583153i	−0.0988436	+	0.995103i	$0.531514\pi$
$660$		0			0
$661$	23.3678	+	13.4914i	0.908901	+	0.524754i	0.880078	−	0.474830i	$-0.157490\pi$
$661$	23.3678	+	13.4914i	0.908901	+	0.524754i	0.0288239	+	0.999585i	$0.490824\pi$
$662$			10.3481i			0.402192i
$663$		0			0
$664$			77.8392i			3.02075i
$665$	2.26787	−	3.70760i	0.0879442	−	0.143775i
$666$		0			0
$667$	0.0568465	+	0.0984611i	0.00220111	+	0.00381243i
$668$	−10.6569			−0.412327
$669$		0			0
$670$	−42.9533	+	24.7991i	−1.65943	+	0.958073i
$671$	−2.32114			−0.0896067
$672$		0			0
$673$	10.2689	−	17.7863i	0.395839	−	0.685613i	−0.597369	−	0.801967i	$-0.703787\pi$
$673$	10.2689	−	17.7863i	0.395839	−	0.685613i	0.993208	+	0.116353i	$0.0371205\pi$
$674$	7.09302	+	4.09516i	0.273213	+	0.157740i
$675$		0			0
$676$	62.8636	+	10.2577i	2.41783	+	0.394526i
$677$	22.1684			0.852002			0.426001	−	0.904723i	$-0.359922\pi$
$677$	22.1684			0.852002			0.426001	+	0.904723i	$0.359922\pi$
$678$		0			0
$679$	10.3012	−	16.8408i	0.395324	−	0.646291i
$680$	−59.2167	+	34.1888i	−2.27086	+	1.31108i
$681$		0			0
$682$	31.3066	−	18.0749i	1.19879	−	0.692122i
$683$	−10.0535	+	5.80441i	−0.384687	+	0.222099i	−0.679856	−	0.733346i	$-0.737958\pi$
$683$	−10.0535	+	5.80441i	−0.384687	+	0.222099i	0.295168	+	0.955445i	$0.404624\pi$
$684$		0			0
$685$	17.1438	−	9.89800i	0.655032	−	0.378183i
$686$	−27.4561	+	40.1588i	−1.04828	+	1.53327i
$687$		0			0
$688$	70.1389			2.67402
$689$	13.8111	+	29.1304i	0.526162	+	1.10978i
$690$		0			0
$691$	−8.51284	−	4.91489i	−0.323844	−	0.186971i	0.329261	−	0.944239i	$-0.393200\pi$
$691$	−8.51284	−	4.91489i	−0.323844	−	0.186971i	−0.653105	+	0.757268i	$0.726534\pi$
$692$	−20.4435	+	35.4092i	−0.777146	+	1.34606i
$693$		0			0
$694$	11.3419			0.430534
$695$	1.13230	−	0.653736i	0.0429507	−	0.0247976i
$696$		0			0
$697$	20.3455			0.770641
$698$	−16.6540	−	28.8457i	−0.630365	−	1.09182i
$699$		0			0
$700$	−32.3682	−	19.7990i	−1.22340	−	0.748333i
$701$			20.3407i			0.768257i	0.923280	+	0.384129i	$0.125498\pi$
$701$			20.3407i			0.768257i	−0.923280	+	0.384129i	$0.874502\pi$
$702$		0			0
$703$		−	10.7671i		−	0.406089i
$704$	20.0110	+	11.5534i	0.754194	+	0.435434i
$705$		0			0
$706$	57.4241	−	33.1538i	2.16118	−	1.24776i
$707$	−0.647373	+	25.5166i	−0.0243470	+	0.959650i
$708$		0			0
$709$	−8.91988	−	15.4497i	−0.334993	−	0.580225i	0.648490	−	0.761223i	$-0.275401\pi$
$709$	−8.91988	−	15.4497i	−0.334993	−	0.580225i	−0.983484	+	0.180998i	$0.942067\pi$
$710$	33.5326			1.25846
$711$		0			0
$712$	−115.409	−	66.6316i	−4.32515	−	2.49713i
$713$	0.760249	−	1.31679i	0.0284715	−	0.0493142i
$714$		0			0
$715$	11.9586	+	0.969256i	0.447227	+	0.0362481i
$716$		−	47.9958i		−	1.79369i
$717$		0			0
$718$	23.1508	−	40.0983i	0.863979	−	1.49645i
$719$	1.72542	+	2.98852i	0.0643474	+	0.111453i	0.896404	−	0.443237i	$-0.146170\pi$
$719$	1.72542	+	2.98852i	0.0643474	+	0.111453i	−0.832057	+	0.554690i	$0.812837\pi$
$720$		0			0
$721$	4.11489	+	7.56398i	0.153246	+	0.281697i
$722$	40.2599	−	23.2441i	1.49832	−	0.865055i
$723$		0			0
$724$	29.0295	−	16.7602i	1.07887	−	0.622887i
$725$	−1.12866	−	0.651634i	−0.0419175	−	0.0242011i
$726$		0			0
$727$		−	44.9752i		−	1.66804i	−0.551735	−	0.834019i	$-0.686034\pi$
$727$		−	44.9752i		−	1.66804i	0.551735	−	0.834019i	$-0.313966\pi$
$728$	58.7152	+	42.7955i	2.17613	+	1.58611i
$729$		0			0
$730$	29.4783	−	51.0579i	1.09104	−	1.88974i
$731$	−21.4238	+	37.1071i	−0.792387	+	1.37245i
$732$		0			0
$733$		−	27.0655i		−	0.999687i	−0.866116	−	0.499843i	$-0.833391\pi$
$733$		−	27.0655i		−	0.999687i	0.866116	−	0.499843i	$-0.166609\pi$
$734$	−21.7077	−	37.5988i	−0.801244	−	1.38780i
$735$		0			0
$736$	2.95635			0.108972
$737$	−26.2495	+	15.1551i	−0.966911	+	0.558247i
$738$		0			0
$739$	14.4209	−	24.9777i	0.530480	−	0.918818i	−0.468888	−	0.883258i	$-0.655345\pi$
$739$	14.4209	−	24.9777i	0.530480	−	0.918818i	0.999368	−	0.0355603i	$-0.0113216\pi$
$740$	66.5723			2.44725
$741$		0			0
$742$	−1.57601	+	62.1193i	−0.0578571	+	2.28047i
$743$	−18.6306	−	10.7564i	−0.683491	−	0.394614i	0.117678	−	0.993052i	$-0.462455\pi$
$743$	−18.6306	−	10.7564i	−0.683491	−	0.394614i	−0.801169	+	0.598438i	$0.795788\pi$
$744$		0			0
$745$	6.50607	−	3.75628i	0.238364	−	0.137620i
$746$			18.9525i			0.693899i
$747$		0			0
$748$	−61.1490	+	35.3044i	−2.23583	+	1.29086i
$749$	−7.93070	−	0.201207i	−0.289781	−	0.00735196i
$750$		0			0
$751$	−2.01437	+	3.48898i	−0.0735052	+	0.127315i	−0.900435	−	0.434990i	$-0.856752\pi$
$751$	−2.01437	+	3.48898i	−0.0735052	+	0.127315i	0.826930	+	0.562305i	$0.190085\pi$
$752$	−27.0288	+	46.8152i	−0.985637	+	1.70717i
$753$		0			0
$754$	3.46966	+	2.39658i	0.126358	+	0.0872781i
$755$	−21.4599			−0.781006
$756$		0			0
$757$	22.3107	−	38.6433i	0.810898	−	1.40452i	−0.101338	−	0.994852i	$-0.532312\pi$
$757$	22.3107	−	38.6433i	0.810898	−	1.40452i	0.912236	−	0.409664i	$-0.134354\pi$
$758$	69.1994	−	39.9523i	2.51343	−	1.45113i
$759$		0			0
$760$	−6.25582	−	10.8354i	−0.226922	−	0.393041i
$761$	−3.07063	−	5.31848i	−0.111310	−	0.192795i	0.804989	−	0.593290i	$-0.202171\pi$
$761$	−3.07063	−	5.31848i	−0.111310	−	0.192795i	−0.916299	+	0.400495i	$0.868838\pi$
$762$		0			0
$763$	−14.3999	+	7.83371i	−0.521312	+	0.283599i
$764$	101.745	+	58.7422i	3.68099	+	2.12522i
$765$		0			0
$766$			61.2762i			2.21400i
$767$	−38.2281	−	26.4050i	−1.38034	−	0.953430i
$768$		0			0
$769$	17.0587	+	9.84883i	0.615152	+	0.355158i	0.774979	−	0.631987i	$-0.217760\pi$
$769$	17.0587	+	9.84883i	0.615152	+	0.355158i	−0.159827	+	0.987145i	$0.551094\pi$
$770$	19.7276	+	12.0670i	0.710934	+	0.434865i
$771$		0			0
$772$	−26.5941			−0.957142
$773$	−15.6721	−	27.1449i	−0.563686	−	0.976333i	−0.997171	−	0.0751716i	$-0.976050\pi$
$773$	−15.6721	−	27.1449i	−0.563686	−	0.976333i	0.433485	−	0.901161i	$-0.357284\pi$
$774$		0			0
$775$			17.4295i			0.626087i
$776$	−28.4154	−	49.2169i	−1.02005	−	1.76678i
$777$		0			0
$778$	37.8367	−	65.5352i	1.35651	−	2.34955i
$779$			3.72279i			0.133383i
$780$		0			0
$781$	20.4923			0.733272
$782$	−2.09109	+	3.62187i	−0.0747772	+	0.129518i
$783$		0			0
$784$	32.5408	+	63.6084i	1.16217	+	2.27173i
$785$		−	19.4341i		−	0.693631i
$786$		0			0
$787$	24.0624	−	13.8924i	0.857732	−	0.495212i	−0.00552043	−	0.999985i	$-0.501757\pi$
$787$	24.0624	−	13.8924i	0.857732	−	0.495212i	0.863252	+	0.504773i	$0.168424\pi$
$788$			80.9898i			2.88514i
$789$		0			0
$790$	27.6269	+	15.9504i	0.982921	+	0.567490i
$791$	7.94603	−	12.9905i	0.282528	−	0.461888i
$792$		0			0
$793$	−2.05797	+	2.97945i	−0.0730808	+	0.105803i
$794$	33.8749			1.20218
$795$		0			0
$796$	−93.9698	−	54.2535i	−3.33067	−	1.92296i
$797$	6.19054	+	10.7223i	0.219280	+	0.379805i	0.954588	−	0.297929i	$-0.0962958\pi$
$797$	6.19054	+	10.7223i	0.219280	+	0.379805i	−0.735308	+	0.677733i	$0.762962\pi$
$798$		0			0
$799$	−16.5117	−	28.5992i	−0.584144	−	1.01177i
$800$	−29.3485	+	16.9444i	−1.03763	+	0.599074i
$801$		0			0
$802$	−36.8630	−	63.8486i	−1.30168	−	2.25457i
$803$	18.0146	−	31.2023i	0.635723	−	1.10110i
$804$		0			0
$805$	0.972374	+	0.0246698i	0.0342717	+	0.000869496i
$806$	4.55595	−	56.2110i	0.160477	−	1.97995i
$807$		0			0
$808$	63.6350	+	36.7397i	2.23867	+	1.29250i
$809$	−12.5058	−	7.22021i	−0.439679	−	0.253849i	0.263782	−	0.964582i	$-0.415030\pi$
$809$	−12.5058	−	7.22021i	−0.439679	−	0.253849i	−0.703462	+	0.710733i	$0.748363\pi$
$810$		0			0
$811$			8.72019i			0.306207i	0.988210	+	0.153104i	$0.0489269\pi$
$811$			8.72019i			0.306207i	−0.988210	+	0.153104i	$0.951073\pi$
$812$	2.75824	+	5.07019i	0.0967953	+	0.177929i
$813$		0			0
$814$	57.2902			2.00802
$815$	12.6135	+	21.8472i	0.441832	+	0.765275i
$816$		0			0
$817$	−6.78980	−	3.92009i	−0.237545	−	0.137147i
$818$	−25.7808			−0.901405
$819$		0			0
$820$	−23.0178			−0.803816
$821$	24.0646	+	13.8937i	0.839861	+	0.484894i	0.857217	−	0.514956i	$-0.172192\pi$
$821$	24.0646	+	13.8937i	0.839861	+	0.484894i	−0.0173562	+	0.999849i	$0.505525\pi$
$822$		0			0
$823$	−10.3059	−	17.8503i	−0.359239	−	0.622221i	0.628594	−	0.777733i	$-0.283631\pi$
$823$	−10.3059	−	17.8503i	−0.359239	−	0.622221i	−0.987834	+	0.155512i	$0.950297\pi$
$824$	24.7883			0.863543
$825$		0			0
$826$	−42.7948	−	78.6653i	−1.48902	−	2.73712i
$827$		−	1.31265i		−	0.0456454i	−0.999740	−	0.0228227i	$-0.992735\pi$
$827$		−	1.31265i		−	0.0456454i	0.999740	−	0.0228227i	$-0.00726533\pi$
$828$		0			0
$829$	−13.9381	−	8.04714i	−0.484089	−	0.279489i	0.238030	−	0.971258i	$-0.423498\pi$
$829$	−13.9381	−	8.04714i	−0.484089	−	0.279489i	−0.722119	+	0.691769i	$0.756832\pi$
$830$	33.4724	+	19.3253i	1.16184	+	0.670790i
$831$		0			0
$832$	32.5722	−	15.4429i	1.12924	−	0.535387i
$833$	−43.5916	−	2.21332i	−1.51036	−	0.0766871i
$834$		0			0
$835$	−1.56580	+	2.71204i	−0.0541867	+	0.0938540i
$836$	−6.45996	−	11.1890i	−0.223422	−	0.386979i
$837$		0			0
$838$	44.3426	−	25.6012i	1.53179	−	0.884379i
$839$	18.3971	+	31.8647i	0.635139	+	1.10009i	0.986486	+	0.163848i	$0.0523905\pi$
$839$	18.3971	+	31.8647i	0.635139	+	1.10009i	−0.351347	+	0.936245i	$0.614276\pi$
$840$		0			0
$841$	−14.4009	−	24.9430i	−0.496582	−	0.860105i
$842$	−60.9329	−	35.1796i	−2.09989	−	1.21237i
$843$		0			0
$844$	−87.4993			−3.01185
$845$	11.8469	−	14.4908i	0.407546	−	0.498500i
$846$		0			0
$847$	−12.7711	−	7.81186i	−0.438821	−	0.268419i
$848$	79.0374	+	45.6322i	2.71415	+	1.56702i
$849$		0			0
$850$		−	47.9405i		−	1.64434i
$851$	2.08685	−	1.20484i	0.0715364	−	0.0413015i
$852$		0			0
$853$			3.73617i			0.127924i	0.997952	+	0.0639621i	$0.0203737\pi$
$853$			3.73617i			0.127924i	−0.997952	+	0.0639621i	$0.979626\pi$
$854$	−6.13107	+	3.33537i	−0.209801	+	0.114134i
$855$		0			0
$856$	−11.4189	+	19.7781i	−0.390290	+	0.676002i
$857$	3.08398			0.105347			0.0526734	−	0.998612i	$-0.483226\pi$
$857$	3.08398			0.105347			0.0526734	+	0.998612i	$0.483226\pi$
$858$		0			0
$859$			33.2024i			1.13285i	0.824113	+	0.566425i	$0.191674\pi$
$859$			33.2024i			1.13285i	−0.824113	+	0.566425i	$0.808326\pi$
$860$	24.2377	−	41.9809i	0.826498	−	1.43154i
$861$		0			0
$862$	6.07248	+	10.5179i	0.206830	+	0.358239i
$863$			29.7493i			1.01268i	0.862335	+	0.506339i	$0.169001\pi$
$863$			29.7493i			1.01268i	−0.862335	+	0.506339i	$0.830999\pi$
$864$		0			0
$865$	6.00747	+	10.4052i	0.204260	+	0.353789i
$866$	57.9066			1.96775
$867$		0			0
$868$	40.2789	−	65.8495i	1.36715	−	2.23508i
$869$	16.8832	+	9.74754i	0.572725	+	0.330663i
$870$		0			0
$871$	−3.82000	+	47.1310i	−0.129436	+	1.59697i
$872$			47.1908i			1.59808i
$873$		0			0
$874$	−0.662726	−	0.382625i	−0.0224170	−	0.0129425i
$875$	−26.5254	+	14.4301i	−0.896724	+	0.487828i
$876$		0			0
$877$	−11.5078	−	19.9321i	−0.388592	−	0.673061i	0.603669	−	0.797235i	$-0.293705\pi$
$877$	−11.5078	−	19.9321i	−0.388592	−	0.673061i	−0.992260	+	0.124175i	$0.960372\pi$
$878$	10.9191	+	18.9125i	0.368503	+	0.638266i
$879$		0			0
$880$	29.4143	−	16.9824i	0.991556	−	0.572475i
$881$	−14.0559	+	24.3456i	−0.473556	+	0.820222i	−0.999542	−	0.0302707i	$-0.990363\pi$
$881$	−14.0559	+	24.3456i	−0.473556	+	0.820222i	0.525986	+	0.850493i	$0.323696\pi$
$882$		0			0
$883$	−15.5266			−0.522512			−0.261256	−	0.965270i	$-0.584137\pi$
$883$	−15.5266			−0.522512			−0.261256	+	0.965270i	$0.584137\pi$
$884$	−8.89883	+	109.793i	−0.299300	+	3.69275i
$885$		0			0
$886$	−28.6468	+	49.6176i	−0.962407	+	1.66694i
$887$	1.91883	−	3.32351i	0.0644280	−	0.111593i	−0.832012	−	0.554757i	$-0.812811\pi$
$887$	1.91883	−	3.32351i	0.0644280	−	0.111593i	0.896440	+	0.443165i	$0.146144\pi$
$888$		0			0
$889$	0.837477	−	33.0096i	0.0280881	−	1.10711i
$890$	−57.3058	+	33.0855i	−1.92090	+	1.10903i
$891$		0			0
$892$		−	111.375i		−	3.72912i
$893$	5.23304	−	3.02130i	0.175117	−	0.101104i
$894$		0			0
$895$	−12.2143	−	7.05195i	−0.408280	−	0.235721i
$896$	8.21402	+	0.208395i	0.274411	+	0.00696200i
$897$		0			0
$898$	−90.7481			−3.02830
$899$	1.32567	−	2.29614i	0.0442137	−	0.0765804i
$900$		0			0
$901$	−48.2836	+	27.8765i	−1.60856	+	0.928702i
$902$	−19.8084			−0.659549
$903$		0			0
$904$	−21.9188	−	37.9644i	−0.729007	−	1.26268i
$905$		−	9.85019i		−	0.327431i
$906$		0			0
$907$	−13.5687	+	23.5018i	−0.450543	+	0.780363i	−0.998420	−	0.0561960i	$-0.982103\pi$
$907$	−13.5687	+	23.5018i	−0.450543	+	0.780363i	0.547877	+	0.836559i	$0.315436\pi$
$908$	−34.4657	+	59.6964i	−1.14378	+	1.98109i
$909$		0			0
$910$	32.9802	−	14.6237i	1.09328	−	0.484772i
$911$			14.6390i			0.485011i	0.970150	+	0.242506i	$0.0779693\pi$
$911$			14.6390i			0.485011i	−0.970150	+	0.242506i	$0.922031\pi$
$912$		0			0
$913$	20.4555	+	11.8100i	0.676978	+	0.390854i
$914$	−35.3014	+	20.3813i	−1.16767	+	0.674152i
$915$		0			0
$916$	−59.4341	+	34.3143i	−1.96376	+	1.13378i
$917$	−3.73978	+	2.03448i	−0.123498	+	0.0671845i
$918$		0			0
$919$	16.0927	+	27.8733i	0.530848	+	0.919455i	0.999352	+	0.0359939i	$0.0114597\pi$
$919$	16.0927	+	27.8733i	0.530848	+	0.919455i	−0.468504	+	0.883461i	$0.655207\pi$
$920$	1.40006	−	2.42497i	0.0461586	−	0.0799490i
$921$		0			0
$922$			43.1857i			1.42225i
$923$	18.1689	−	26.3041i	0.598036	−	0.865811i
$924$		0			0
$925$	−13.8112	+	23.9216i	−0.454108	+	0.786539i
$926$	25.8889	+	14.9470i	0.850763	+	0.491188i
$927$		0			0
$928$	5.15510			0.169224
$929$	−15.1042	−	26.1612i	−0.495551	−	0.858320i	0.504435	−	0.863449i	$-0.331701\pi$
$929$	−15.1042	−	26.1612i	−0.495551	−	0.858320i	−0.999987	+	0.00512919i	$0.998367\pi$
$930$		0			0
$931$	0.404991	−	7.97634i	0.0132730	−	0.261414i
$932$	−15.9262	+	9.19500i	−0.521680	+	0.301192i
$933$		0			0
$934$	−47.7495	−	27.5682i	−1.56241	−	0.902059i
$935$			20.7489i			0.678561i
$936$		0			0
$937$			11.5497i			0.377312i	0.982043	+	0.188656i	$0.0604131\pi$
$937$			11.5497i			0.377312i	−0.982043	+	0.188656i	$0.939587\pi$
$938$	−47.5581	+	77.7500i	−1.55283	+	2.53863i
$939$		0			0
$940$	18.6805	+	32.3556i	0.609290	+	1.05532i
$941$	42.5552			1.38726			0.693629	−	0.720332i	$-0.256011\pi$
$941$	42.5552			1.38726			0.693629	+	0.720332i	$0.256011\pi$
$942$		0			0
$943$	−0.721542	+	0.416582i	−0.0234966	+	0.0135658i
$944$	−131.526			−4.28082
$945$		0			0
$946$	20.8582	−	36.1275i	0.678160	−	1.17461i
$947$	−50.9351	−	29.4074i	−1.65517	−	0.955611i	−0.974899	−	0.222648i	$-0.928530\pi$
$947$	−50.9351	−	29.4074i	−1.65517	−	0.955611i	−0.680269	−	0.732963i	$-0.738137\pi$
$948$		0			0
$949$	−24.0795	−	50.7884i	−0.781652	−	1.64866i
$950$	8.77208			0.284604
$951$		0			0
$952$	−65.5650	+	107.188i	−2.12498	+	3.47399i
$953$	−30.6703	+	17.7075i	−0.993507	+	0.573601i	−0.906321	−	0.422591i	$-0.861121\pi$
$953$	−30.6703	+	17.7075i	−0.993507	+	0.573601i	−0.0871862	+	0.996192i	$0.527788\pi$
$954$		0			0
$955$	29.8983	−	17.2618i	0.967487	−	0.558579i
$956$	0.464591	−	0.268232i	0.0150259	−	0.00867524i
$957$		0			0
$958$	−91.0204	+	52.5506i	−2.94073	+	1.69783i
$959$	18.9817	−	31.0321i	0.612953	−	1.00208i
$960$		0			0
$961$	−4.45837			−0.143818
$962$	50.7947	−	73.5383i	1.63769	−	2.37097i
$963$		0			0
$964$	62.7798	+	36.2459i	2.02200	+	1.16740i
$965$	−3.90743	+	6.76786i	−0.125785	+	0.217865i
$966$		0			0
$967$	43.5762			1.40132			0.700658	−	0.713498i	$-0.252890\pi$
$967$	43.5762			1.40132			0.700658	+	0.713498i	$0.252890\pi$
$968$	−37.3234	+	21.5487i	−1.19962	+	0.692600i
$969$		0			0
$970$	−28.2190			−0.906057
$971$	12.5067	+	21.6622i	0.401358	+	0.695172i	0.993890	−	0.110375i	$-0.0352052\pi$
$971$	12.5067	+	21.6622i	0.401358	+	0.695172i	−0.592533	+	0.805547i	$0.701872\pi$
$972$		0			0
$973$	1.25369	−	2.04959i	0.0401915	−	0.0657067i
$974$		−	51.1877i		−	1.64016i
$975$		0			0
$976$			10.2510i			0.328126i
$977$	−35.0386	−	20.2295i	−1.12098	−	0.647200i	−0.179332	−	0.983789i	$-0.557394\pi$
$977$	−35.0386	−	20.2295i	−1.12098	−	0.647200i	−0.941652	+	0.336588i	$0.890727\pi$
$978$		0			0
$979$	−35.0205	+	20.2191i	−1.11926	+	0.646205i
$980$	49.3172	+	2.50403i	1.57538	+	0.0799884i
$981$		0			0
$982$	−4.18679	−	7.25174i	−0.133606	−	0.231412i
$983$	−38.8307			−1.23851			−0.619254	−	0.785191i	$-0.712565\pi$
$983$	−38.8307			−1.23851			−0.619254	+	0.785191i	$0.712565\pi$
$984$		0			0
$985$	20.6109	+	11.8997i	0.656717	+	0.379156i
$986$	−3.64631	+	6.31560i	−0.116122	+	0.201130i
$987$		0			0
$988$	−20.0898	−	1.62830i	−0.639142	−	0.0518030i
$989$		−	1.75464i		−	0.0557944i
$990$		0			0
$991$	−8.96919	+	15.5351i	−0.284916	+	0.493489i	−0.972589	−	0.232532i	$-0.925299\pi$
$991$	−8.96919	+	15.5351i	−0.284916	+	0.493489i	0.687673	+	0.726021i	$0.258632\pi$
$992$	−34.4714	−	59.7062i	−1.09447	−	1.89567i
$993$		0			0
$994$	54.1283	−	29.4464i	1.71685	−	0.933984i
$995$	−27.6137	+	15.9428i	−0.875412	+	0.505419i
$996$		0			0
$997$	0.371455	−	0.214460i	0.0117641	−	0.00679201i	−0.494106	−	0.869401i	$-0.664505\pi$
$997$	0.371455	−	0.214460i	0.0117641	−	0.00679201i	0.505871	+	0.862609i	$0.331171\pi$
$998$	−15.0308	−	8.67806i	−0.475793	−	0.274699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dx.a.503.2	yes	72
3.2	odd	2	inner	819.2.dx.a.503.35	yes	72
7.6	odd	2	inner	819.2.dx.a.503.1	✓	72
13.3	even	3	inner	819.2.dx.a.692.36	yes	72
21.20	even	2	inner	819.2.dx.a.503.36	yes	72
39.29	odd	6	inner	819.2.dx.a.692.1	yes	72
91.55	odd	6	inner	819.2.dx.a.692.35	yes	72
273.146	even	6	inner	819.2.dx.a.692.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dx.a.503.1	✓	72	7.6	odd	2	inner
819.2.dx.a.503.2	yes	72	1.1	even	1	trivial
819.2.dx.a.503.35	yes	72	3.2	odd	2	inner
819.2.dx.a.503.36	yes	72	21.20	even	2	inner
819.2.dx.a.692.1	yes	72	39.29	odd	6	inner
819.2.dx.a.692.2	yes	72	273.146	even	6	inner
819.2.dx.a.692.35	yes	72	91.55	odd	6	inner
819.2.dx.a.692.36	yes	72	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.27480 - 1.31336i) q^{2} +(2.44981 + 4.24319i) q^{4} +1.43978 q^{5} +(2.32410 - 1.26434i) q^{7} -7.61644i q^{8} +O(q^{10})\)	\(q+(-2.27480 - 1.31336i) q^{2} +(2.44981 + 4.24319i) q^{4} +1.43978 q^{5} +(2.32410 - 1.26434i) q^{7} -7.61644i q^{8} +(-3.27522 - 1.89095i) q^{10} +(-2.00154 - 1.15559i) q^{11} +(-3.25793 + 1.54463i) q^{13} +(-6.94739 - 0.176260i) q^{14} +(-5.10349 + 8.83950i) q^{16} +(-3.11770 - 5.40001i) q^{17} +(0.988087 - 0.570472i) q^{19} +(3.52719 + 6.10928i) q^{20} +(3.03540 + 5.25746i) q^{22} +(0.221135 + 0.127672i) q^{23} -2.92702 q^{25} +(9.43979 + 0.765103i) q^{26} +(11.0584 + 6.76422i) q^{28} +(0.385601 + 0.222627i) q^{29} -5.95469i q^{31} +(10.0267 - 5.78894i) q^{32} +16.3786i q^{34} +(3.34621 - 1.82037i) q^{35} +(4.71851 - 8.17269i) q^{37} -2.99693 q^{38} -10.9660i q^{40} +(-1.63145 + 2.82576i) q^{41} +(-3.43583 - 5.95104i) q^{43} -11.3239i q^{44} +(-0.335358 - 0.580857i) q^{46} +5.29613 q^{47} +(3.80290 - 5.87690i) q^{49} +(6.65838 + 3.84422i) q^{50} +(-14.5355 - 10.0400i) q^{52} -8.94138i q^{53} +(-2.88178 - 1.66380i) q^{55} +(-9.62975 - 17.7014i) q^{56} +(-0.584777 - 1.01286i) q^{58} +(6.44296 + 11.1595i) q^{59} +(0.869760 - 0.502156i) q^{61} +(-7.82063 + 13.5457i) q^{62} -9.99782 q^{64} +(-4.69072 + 2.22393i) q^{65} +(6.55732 - 11.3576i) q^{67} +(15.2755 - 26.4580i) q^{68} +(-10.0027 - 0.253776i) q^{70} +(-7.67870 + 4.43330i) q^{71} +15.5891i q^{73} +(-21.4673 + 12.3942i) q^{74} +(4.84124 + 2.79509i) q^{76} +(-6.11283 - 0.155087i) q^{77} -8.43513 q^{79} +(-7.34792 + 12.7270i) q^{80} +(7.42245 - 4.28535i) q^{82} -10.2199 q^{83} +(-4.48881 - 7.77485i) q^{85} +18.0499i q^{86} +(-8.80148 + 15.2446i) q^{88} +(8.74839 - 15.1527i) q^{89} +(-5.61883 + 7.70900i) q^{91} +1.25109i q^{92} +(-12.0476 - 6.95571i) q^{94} +(1.42263 - 0.821357i) q^{95} +(6.46193 - 3.73080i) q^{97} +(-16.3693 + 8.37420i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{7}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^7	\( 72 q + 32 q^{4} - 2 q^{7} - 24 q^{16} + 24 q^{22} + 56 q^{25} - 8 q^{28} + 16 q^{37} - 4 q^{43} + 32 q^{46} + 26 q^{49} - 40 q^{58} - 64 q^{64} + 60 q^{67} - 40 q^{70} - 72 q^{79} - 80 q^{85} - 24 q^{88} + 2 q^{91}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^7 - 24 * q^16 + 24 * q^22 + 56 * q^25 - 8 * q^28 + 16 * q^37 - 4 * q^43 + 32 * q^46 + 26 * q^49 - 40 * q^58 - 64 * q^64 + 60 * q^67 - 40 * q^70 - 72 * q^79 - 80 * q^85 - 24 * q^88 + 2 * q^91

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