LMFDB - Embedded newform 804.2.ba.b.353.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			353.13
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.354927 + 1.69530i) q^{3} +(-0.606307 - 4.21696i) q^{5} +(-0.295017 + 3.08956i) q^{7} +(-2.74805 + 1.20341i) q^{9} +O(q^{10})$	\(q+(0.354927 + 1.69530i) q^{3} +(-0.606307 - 4.21696i) q^{5} +(-0.295017 + 3.08956i) q^{7} +(-2.74805 + 1.20341i) q^{9} +(-5.34850 - 2.14122i) q^{11} +(1.06287 - 1.11471i) q^{13} +(6.93379 - 2.52458i) q^{15} +(-3.13592 - 1.08535i) q^{17} +(0.373168 - 0.0356332i) q^{19} +(-5.34242 + 0.596426i) q^{21} +(3.36039 + 0.160075i) q^{23} +(-12.6176 + 3.70487i) q^{25} +(-3.01550 - 4.23164i) q^{27} +(-5.55526 - 3.20733i) q^{29} +(-5.06664 - 5.31374i) q^{31} +(1.73167 - 9.82726i) q^{33} +(13.2074 - 0.629146i) q^{35} +(2.92489 + 5.06605i) q^{37} +(2.26700 + 1.40624i) q^{39} +(-10.4018 + 2.00479i) q^{41} +(0.118743 - 0.102891i) q^{43} +(6.74090 + 10.8588i) q^{45} +(2.91118 + 5.64690i) q^{47} +(-2.58483 - 0.498185i) q^{49} +(0.726970 - 5.70153i) q^{51} +(1.39615 - 1.61125i) q^{53} +(-5.78658 + 23.8526i) q^{55} +(0.192856 + 0.619982i) q^{57} +(0.864195 - 2.94318i) q^{59} +(-5.18649 - 12.9552i) q^{61} +(-2.90729 - 8.84530i) q^{63} +(-5.34509 - 3.80622i) q^{65} +(1.49951 - 8.04683i) q^{67} +(0.921319 + 5.75367i) q^{69} +(4.54395 - 1.57268i) q^{71} +(2.76888 - 1.10849i) q^{73} +(-10.7592 - 20.0757i) q^{75} +(8.19331 - 15.8928i) q^{77} +(0.363719 + 0.0882373i) q^{79} +(6.10360 - 6.61408i) q^{81} +(6.94036 + 8.82538i) q^{83} +(-2.67555 + 13.8821i) q^{85} +(3.46566 - 10.5562i) q^{87} +(-1.23838 - 1.92696i) q^{89} +(3.13038 + 3.61265i) q^{91} +(7.21007 - 10.4754i) q^{93} +(-0.376518 - 1.55203i) q^{95} +(-0.393962 + 0.227454i) q^{97} +(17.2747 - 0.552271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{13}{66}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.354927	+	1.69530i	0.204917	+	0.978779i
$3$	0.354927	+	1.69530i	0.204917	+	0.978779i
$4$		0			0
$5$	−0.606307	−	4.21696i	−0.271149	−	1.88588i	−0.436590	−	0.899660i	$-0.643814\pi$
$5$	−0.606307	−	4.21696i	−0.271149	−	1.88588i	0.165442	−	0.986220i	$-0.447095\pi$
$6$		0			0
$7$	−0.295017	+	3.08956i	−0.111506	+	1.16774i	0.750509	+	0.660860i	$0.229808\pi$
$7$	−0.295017	+	3.08956i	−0.111506	+	1.16774i	−0.862015	+	0.506883i	$0.830798\pi$
$8$		0			0
$9$	−2.74805	+	1.20341i	−0.916018	+	0.401137i
$10$		0			0
$11$	−5.34850	−	2.14122i	−1.61263	−	0.645601i	−0.622108	−	0.782931i	$-0.713724\pi$
$11$	−5.34850	−	2.14122i	−1.61263	−	0.645601i	−0.990525	+	0.137330i	$0.956148\pi$
$12$		0			0
$13$	1.06287	−	1.11471i	0.294787	−	0.309164i	−0.559639	−	0.828736i	$-0.689060\pi$
$13$	1.06287	−	1.11471i	0.294787	−	0.309164i	0.854426	+	0.519573i	$0.173909\pi$
$14$		0			0
$15$	6.93379	−	2.52458i	1.79030	−	0.651844i
$16$		0			0
$17$	−3.13592	−	1.08535i	−0.760572	−	0.263236i	−0.0808697	−	0.996725i	$-0.525770\pi$
$17$	−3.13592	−	1.08535i	−0.760572	−	0.263236i	−0.679702	+	0.733488i	$0.737891\pi$
$18$		0			0
$19$	0.373168	−	0.0356332i	0.0856105	−	0.00817481i	−0.0521629	−	0.998639i	$-0.516611\pi$
$19$	0.373168	−	0.0356332i	0.0856105	−	0.00817481i	0.137773	+	0.990464i	$0.456005\pi$
$20$		0			0
$21$	−5.34242	+	0.596426i	−1.16581	+	0.130151i
$22$		0			0
$23$	3.36039	+	0.160075i	0.700690	+	0.0333780i	0.394904	−	0.918722i	$-0.370778\pi$
$23$	3.36039	+	0.160075i	0.700690	+	0.0333780i	0.305786	+	0.952100i	$0.401081\pi$
$24$		0			0
$25$	−12.6176	+	3.70487i	−2.52353	+	0.740975i
$26$		0			0
$27$	−3.01550	−	4.23164i	−0.580333	−	0.814380i
$28$		0			0
$29$	−5.55526	−	3.20733i	−1.03159	−	0.595586i	−0.114147	−	0.993464i	$-0.536414\pi$
$29$	−5.55526	−	3.20733i	−1.03159	−	0.595586i	−0.917438	+	0.397878i	$0.869747\pi$
$30$		0			0
$31$	−5.06664	−	5.31374i	−0.909996	−	0.954376i	0.0891369	−	0.996019i	$-0.471589\pi$
$31$	−5.06664	−	5.31374i	−0.909996	−	0.954376i	−0.999133	+	0.0416434i	$0.986741\pi$
$32$		0			0
$33$	1.73167	−	9.82726i	0.301445	−	1.71071i
$34$		0			0
$35$	13.2074	−	0.629146i	2.23246	−	0.106345i
$36$		0			0
$37$	2.92489	+	5.06605i	0.480848	+	0.832854i	0.999759	−	0.0219750i	$-0.00699543\pi$
$37$	2.92489	+	5.06605i	0.480848	+	0.832854i	−0.518910	+	0.854829i	$0.673662\pi$
$38$		0			0
$39$	2.26700	+	1.40624i	0.363010	+	0.225178i
$40$		0			0
$41$	−10.4018	+	2.00479i	−1.62449	+	0.313095i	−0.918590	−	0.395213i	$-0.870671\pi$
$41$	−10.4018	+	2.00479i	−1.62449	+	0.313095i	−0.705903	+	0.708308i	$0.749459\pi$
$42$		0			0
$43$	0.118743	−	0.102891i	0.0181081	−	0.0156908i	−0.645760	−	0.763541i	$-0.723459\pi$
$43$	0.118743	−	0.102891i	0.0181081	−	0.0156908i	0.663868	+	0.747850i	$0.268914\pi$
$44$		0			0
$45$	6.74090	+	10.8588i	1.00487	+	1.61873i
$46$		0			0
$47$	2.91118	+	5.64690i	0.424639	+	0.823685i	0.999983	+	0.00577368i	$0.00183783\pi$
$47$	2.91118	+	5.64690i	0.424639	+	0.823685i	−0.575344	+	0.817911i	$0.695132\pi$
$48$		0			0
$49$	−2.58483	−	0.498185i	−0.369261	−	0.0711692i
$50$		0			0
$51$	0.726970	−	5.70153i	0.101796	−	0.798374i
$52$		0			0
$53$	1.39615	−	1.61125i	0.191776	−	0.221322i	−0.651716	−	0.758463i	$-0.725950\pi$
$53$	1.39615	−	1.61125i	0.191776	−	0.221322i	0.843492	+	0.537142i	$0.180496\pi$
$54$		0			0
$55$	−5.78658	+	23.8526i	−0.780263	+	3.21629i
$56$		0			0
$57$	0.192856	+	0.619982i	0.0255444	+	0.0821186i
$58$		0			0
$59$	0.864195	−	2.94318i	0.112509	−	0.383169i	−0.883917	−	0.467644i	$-0.845103\pi$
$59$	0.864195	−	2.94318i	0.112509	−	0.383169i	0.996426	+	0.0844747i	$0.0269212\pi$
$60$		0			0
$61$	−5.18649	−	12.9552i	−0.664062	−	1.65875i	−0.749173	−	0.662375i	$-0.769549\pi$
$61$	−5.18649	−	12.9552i	−0.664062	−	1.65875i	0.0851109	−	0.996371i	$-0.472876\pi$
$62$		0			0
$63$	−2.90729	−	8.84530i	−0.366284	−	1.11440i
$64$		0			0
$65$	−5.34509	−	3.80622i	−0.662977	−	0.472104i
$66$		0			0
$67$	1.49951	−	8.04683i	0.183194	−	0.983077i
$67$	1.49951	−	8.04683i	0.183194	−	0.983077i
$68$		0			0
$69$	0.921319	+	5.75367i	0.110914	+	0.692661i
$70$		0			0
$71$	4.54395	−	1.57268i	0.539268	−	0.186642i	−0.0438379	−	0.999039i	$-0.513959\pi$
$71$	4.54395	−	1.57268i	0.539268	−	0.186642i	0.583106	+	0.812396i	$0.301837\pi$
$72$		0			0
$73$	2.76888	−	1.10849i	0.324073	−	0.129739i	−0.203921	−	0.978987i	$-0.565369\pi$
$73$	2.76888	−	1.10849i	0.324073	−	0.129739i	0.527994	+	0.849248i	$0.322944\pi$
$74$		0			0
$75$	−10.7592	−	20.0757i	−1.24237	−	2.31814i
$76$		0			0
$77$	8.19331	−	15.8928i	0.933714	−	1.81115i
$78$		0			0
$79$	0.363719	+	0.0882373i	0.0409216	+	0.00992748i	0.256167	−	0.966632i	$-0.417540\pi$
$79$	0.363719	+	0.0882373i	0.0409216	+	0.00992748i	−0.215246	+	0.976560i	$0.569055\pi$
$80$		0			0
$81$	6.10360	−	6.61408i	0.678178	−	0.734898i
$82$		0			0
$83$	6.94036	+	8.82538i	0.761803	+	0.968712i	0.999997	−	0.00250596i	$-0.000797672\pi$
$83$	6.94036	+	8.82538i	0.761803	+	0.968712i	−0.238194	+	0.971218i	$0.576555\pi$
$84$		0			0
$85$	−2.67555	+	13.8821i	−0.290204	+	1.50572i
$86$		0			0
$87$	3.46566	−	10.5562i	0.371558	−	1.13174i
$88$		0			0
$89$	−1.23838	−	1.92696i	−0.131268	−	0.204258i	0.769397	−	0.638771i	$-0.220557\pi$
$89$	−1.23838	−	1.92696i	−0.131268	−	0.204258i	−0.900665	+	0.434513i	$0.856920\pi$
$90$		0			0
$91$	3.13038	+	3.61265i	0.328153	+	0.378709i
$92$		0			0
$93$	7.21007	−	10.4754i	0.747650	−	1.08625i
$94$		0			0
$95$	−0.376518	−	1.55203i	−0.0386299	−	0.159235i
$96$		0			0
$97$	−0.393962	+	0.227454i	−0.0400008	+	0.0230945i	−0.519867	−	0.854247i	$-0.674019\pi$
$97$	−0.393962	+	0.227454i	−0.0400008	+	0.0230945i	0.479866	+	0.877342i	$0.340685\pi$
$98$		0			0
$99$	17.2747	−	0.552271i	1.73618	−	0.0555053i
$100$		0			0
$101$	7.12702	+	10.0085i	0.709165	+	0.995882i	0.999244	+	0.0388797i	$0.0123789\pi$
$101$	7.12702	+	10.0085i	0.709165	+	0.995882i	−0.290079	+	0.957003i	$0.593682\pi$
$102$		0			0
$103$	−13.1880	+	12.5747i	−1.29945	+	1.23902i	−0.345726	+	0.938336i	$0.612367\pi$
$103$	−13.1880	+	12.5747i	−1.29945	+	1.23902i	−0.953723	+	0.300686i	$0.902784\pi$
$104$		0			0
$105$	5.75425	+	22.1671i	0.561557	+	2.16329i
$106$		0			0
$107$	−1.02067	−	0.146751i	−0.0986721	−	0.0141869i	0.0928019	−	0.995685i	$-0.470418\pi$
$107$	−1.02067	−	0.146751i	−0.0986721	−	0.0141869i	−0.191474	+	0.981498i	$0.561327\pi$
$108$		0			0
$109$	−3.29791	−	11.2316i	−0.315882	−	1.07580i	−0.952480	−	0.304601i	$-0.901477\pi$
$109$	−3.29791	−	11.2316i	−0.315882	−	1.07580i	0.636598	−	0.771196i	$-0.280341\pi$
$110$		0			0
$111$	−7.55033	+	6.75662i	−0.716646	+	0.641310i
$112$		0			0
$113$	−7.84294	−	6.16776i	−0.737802	−	0.580214i	0.176955	−	0.984219i	$-0.443375\pi$
$113$	−7.84294	−	6.16776i	−0.737802	−	0.580214i	−0.914757	+	0.404005i	$0.867618\pi$
$114$		0			0
$115$	−1.36240	−	14.2677i	−0.127044	−	1.33047i
$116$		0			0
$117$	−1.57937	+	4.34234i	−0.146013	+	0.401450i
$118$		0			0
$119$	4.27841	−	9.36840i	0.392201	−	0.858800i
$120$		0			0
$121$	16.0606	+	15.3137i	1.46005	+	1.39216i
$122$		0			0
$123$	−7.09060	−	16.9226i	−0.639338	−	1.52586i
$124$		0			0
$125$	14.4244	+	31.5851i	1.29016	+	2.82506i
$126$		0			0
$127$	6.65841	+	0.635801i	0.590839	+	0.0564183i	0.386193	−	0.922418i	$-0.373790\pi$
$127$	6.65841	+	0.635801i	0.590839	+	0.0564183i	0.204645	+	0.978836i	$0.434396\pi$
$128$		0			0
$129$	0.216576	+	0.164785i	0.0190685	+	0.0145085i
$130$		0			0
$131$	−2.72329	+	4.23752i	−0.237935	+	0.370234i	−0.939601	−	0.342272i	$-0.888803\pi$
$131$	−2.72329	+	4.23752i	−0.237935	+	0.370234i	0.701666	+	0.712506i	$0.252440\pi$
$132$		0			0
$133$			1.16343i			0.100883i
$134$		0			0
$135$	−16.0163	+	15.2819i	−1.37847	+	1.31526i
$136$		0			0
$137$	14.7333	+	9.46850i	1.25875	+	0.808948i	0.988112	−	0.153734i	$-0.0491298\pi$
$137$	14.7333	+	9.46850i	1.25875	+	0.808948i	0.270636	+	0.962682i	$0.412766\pi$
$138$		0			0
$139$	8.55641	−	1.23023i	0.725746	−	0.104346i	0.230466	−	0.973080i	$-0.425975\pi$
$139$	8.55641	−	1.23023i	0.725746	−	0.104346i	0.495279	+	0.868734i	$0.335066\pi$
$140$		0			0
$141$	−8.53991	+	6.93955i	−0.719190	+	0.584415i
$142$		0			0
$143$	−8.07158	+	3.68617i	−0.674980	+	0.308253i
$144$		0			0
$145$	−10.1570	+	25.3709i	−0.843491	+	2.10694i
$146$		0			0
$147$	−0.0728546	−	4.55886i	−0.00600894	−	0.376009i
$148$		0			0
$149$	−9.94457	−	4.54153i	−0.814691	−	0.372057i	−0.0359117	−	0.999355i	$-0.511433\pi$
$149$	−9.94457	−	4.54153i	−0.814691	−	0.372057i	−0.778779	+	0.627298i	$0.784161\pi$
$150$		0			0
$151$	3.03650	−	8.77339i	0.247107	−	0.713968i	−0.751426	−	0.659817i	$-0.770634\pi$
$151$	3.03650	−	8.77339i	0.247107	−	0.713968i	0.998533	−	0.0541507i	$-0.0172452\pi$
$152$		0			0
$153$	9.92380	−	0.791196i	0.802291	−	0.0639644i
$154$		0			0
$155$	−19.3359	+	24.5876i	−1.55309	+	1.97492i
$156$		0			0
$157$	−0.126031	+	2.64571i	−0.0100584	+	0.211151i	0.988243	+	0.152891i	$0.0488583\pi$
$157$	−0.126031	+	2.64571i	−0.0100584	+	0.211151i	−0.998301	+	0.0582601i	$0.981445\pi$
$158$		0			0
$159$	3.22707	+	1.79502i	0.255924	+	0.142354i
$160$		0			0
$161$	−1.48593	+	10.3349i	−0.117108	+	0.814504i
$162$		0			0
$163$	7.59768	−	13.1596i	0.595096	−	1.03074i	−0.398437	−	0.917196i	$-0.630447\pi$
$163$	7.59768	−	13.1596i	0.595096	−	1.03074i	0.993533	−	0.113541i	$-0.0362194\pi$
$164$		0			0
$165$	−42.4911	−	1.34403i	−3.30792	−	0.104633i
$166$		0			0
$167$	−9.89558	+	7.04661i	−0.765743	+	0.545283i	−0.894860	−	0.446346i	$-0.852725\pi$
$167$	−9.89558	+	7.04661i	−0.765743	+	0.545283i	0.129117	+	0.991629i	$0.458786\pi$
$168$		0			0
$169$	0.505688	+	10.6157i	0.0388991	+	0.816592i
$170$		0			0
$171$	−0.982603	+	0.546996i	−0.0751415	+	0.0418298i
$172$		0			0
$173$	−6.27092	+	1.52131i	−0.476769	+	0.115663i	−0.466941	−	0.884289i	$-0.654644\pi$
$173$	−6.27092	+	1.52131i	−0.476769	+	0.115663i	−0.00982875	+	0.999952i	$0.503129\pi$
$174$		0			0
$175$	−7.72400	−	40.0759i	−0.583880	−	3.02946i
$176$		0			0
$177$	5.29628	+	0.420453i	0.398093	+	0.0316032i
$178$		0			0
$179$	−19.2913	+	12.3978i	−1.44190	+	0.926653i	−0.442344	+	0.896845i	$0.645853\pi$
$179$	−19.2913	+	12.3978i	−1.44190	+	0.926653i	−0.999556	+	0.0298077i	$0.990511\pi$
$180$		0			0
$181$	−11.7407	+	6.05273i	−0.872677	+	0.449896i	−0.835550	−	0.549414i	$-0.814851\pi$
$181$	−11.7407	+	6.05273i	−0.872677	+	0.449896i	−0.0371268	+	0.999311i	$0.511821\pi$
$182$		0			0
$183$	20.1221	−	13.3908i	1.48747	−	0.989875i
$184$		0			0
$185$	19.5899	−	15.4057i	1.44028	−	1.13265i
$186$		0			0
$187$	14.4485	+	12.5197i	1.05658	+	0.915530i
$188$		0			0
$189$	13.9635	−	8.06814i	1.01570	−	0.586871i
$190$		0			0
$191$	2.68091	+	1.38211i	0.193984	+	0.100006i	0.552482	−	0.833525i	$-0.313681\pi$
$191$	2.68091	+	1.38211i	0.193984	+	0.100006i	−0.358498	+	0.933530i	$0.616711\pi$
$192$		0			0
$193$	6.64319	+	1.95062i	0.478187	+	0.140408i	0.511939	−	0.859022i	$-0.328927\pi$
$193$	6.64319	+	1.95062i	0.478187	+	0.140408i	−0.0337517	+	0.999430i	$0.510746\pi$
$194$		0			0
$195$	4.55555	−	10.4124i	0.326230	−	0.745650i
$196$		0			0
$197$	3.87942	+	11.2088i	0.276397	+	0.798596i	0.994696	+	0.102862i	$0.0327999\pi$
$197$	3.87942	+	11.2088i	0.276397	+	0.798596i	−0.718299	+	0.695735i	$0.755079\pi$
$198$		0			0
$199$	−11.6192	+	16.3169i	−0.823663	+	1.15667i	0.161807	+	0.986822i	$0.448268\pi$
$199$	−11.6192	+	16.3169i	−0.823663	+	1.15667i	−0.985470	+	0.169850i	$0.945672\pi$
$200$		0			0
$201$	14.1740	−	0.313924i	0.999755	−	0.0221425i
$202$		0			0
$203$	11.5481	−	16.2171i	0.810519	−	1.13822i
$204$		0			0
$205$	14.7608	+	42.6485i	1.03094	+	2.97870i
$206$		0			0
$207$	−9.42717	+	3.60404i	−0.655234	+	0.250498i
$208$		0			0
$209$	−2.07219	−	0.608449i	−0.143336	−	0.0420873i
$210$		0			0
$211$	22.8993	+	11.8054i	1.57645	+	0.812718i	0.999990	−	0.00440540i	$-0.00140229\pi$
$211$	22.8993	+	11.8054i	1.57645	+	0.812718i	0.576463	+	0.817123i	$0.304433\pi$
$212$		0			0
$213$	4.27892	+	7.14516i	0.293187	+	0.489578i
$214$		0			0
$215$	−0.505882	−	0.438350i	−0.0345009	−	0.0298952i
$216$		0			0
$217$	17.9118	−	14.0860i	1.21594	−	0.956222i
$218$		0			0
$219$	2.86197	+	4.30063i	0.193394	+	0.290610i
$220$		0			0
$221$	−4.54292	+	2.34204i	−0.305590	+	0.157543i
$222$		0			0
$223$	−11.7753	+	7.56750i	−0.788530	+	0.506757i	−0.871854	−	0.489765i	$-0.837083\pi$
$223$	−11.7753	+	7.56750i	−0.788530	+	0.506757i	0.0833246	+	0.996522i	$0.473446\pi$
$224$		0			0
$225$	30.2155	−	25.3654i	2.01436	−	1.69103i
$226$		0			0
$227$	−4.97463	−	25.8108i	−0.330178	−	1.71312i	−0.645177	−	0.764033i	$-0.723216\pi$
$227$	−4.97463	−	25.8108i	−0.330178	−	1.71312i	0.314999	−	0.949092i	$-0.397996\pi$
$228$		0			0
$229$	6.42665	−	1.55909i	0.424685	−	0.103027i	−0.0177199	−	0.999843i	$-0.505641\pi$
$229$	6.42665	−	1.55909i	0.424685	−	0.103027i	0.442405	+	0.896816i	$0.354126\pi$
$230$		0			0
$231$	29.8510	+	8.24930i	1.96405	+	0.542764i
$232$		0			0
$233$	−0.980955	−	20.5928i	−0.0642645	−	1.34908i	−0.768837	−	0.639445i	$-0.779164\pi$
$233$	−0.980955	−	20.5928i	−0.0642645	−	1.34908i	0.704572	−	0.709632i	$-0.251139\pi$
$234$		0			0
$235$	22.0477	−	15.7001i	1.43823	−	1.02416i
$236$		0			0
$237$	−0.0204946	+	0.647929i	−0.00133127	+	0.0420875i
$238$		0			0
$239$	3.37469	−	5.84513i	0.218290	−	0.378090i	−0.735995	−	0.676987i	$-0.763285\pi$
$239$	3.37469	−	5.84513i	0.218290	−	0.378090i	0.954285	+	0.298897i	$0.0966186\pi$
$240$		0			0
$241$	3.90362	−	27.1503i	0.251454	−	1.74890i	−0.338042	−	0.941131i	$-0.609765\pi$
$241$	3.90362	−	27.1503i	0.251454	−	1.74890i	0.589496	−	0.807771i	$-0.299326\pi$
$242$		0			0
$243$	13.3792	+	7.99989i	0.858273	+	0.513193i
$244$		0			0
$245$	−0.533624	+	11.2022i	−0.0340920	+	0.715679i
$246$		0			0
$247$	0.356908	−	0.453845i	0.0227095	−	0.0288775i
$248$		0			0
$249$	−12.4983	+	14.8983i	−0.792048	+	0.944143i
$250$		0			0
$251$	−3.62965	+	10.4872i	−0.229101	+	0.661945i	0.770595	+	0.637325i	$0.219959\pi$
$251$	−3.62965	+	10.4872i	−0.229101	+	0.661945i	−0.999697	+	0.0246205i	$0.992162\pi$
$252$		0			0
$253$	−17.6303	−	8.05149i	−1.10841	−	0.506193i
$254$		0			0
$255$	−24.4839	+	0.391273i	−1.53324	+	0.0245025i
$256$		0			0
$257$	7.02930	−	17.5583i	0.438475	−	1.09526i	−0.530408	−	0.847742i	$-0.677961\pi$
$257$	7.02930	−	17.5583i	0.438475	−	1.09526i	0.968884	−	0.247516i	$-0.0796144\pi$
$258$		0			0
$259$	−16.5147	+	7.54203i	−1.02618	+	0.468639i
$260$		0			0
$261$	19.1259	+	2.12865i	1.18386	+	0.131760i
$262$		0			0
$263$	−13.9779	+	2.00973i	−0.861917	+	0.123925i	−0.559076	−	0.829116i	$-0.688844\pi$
$263$	−13.9779	+	2.00973i	−0.861917	+	0.123925i	−0.302841	+	0.953041i	$0.597935\pi$
$264$		0			0
$265$	−7.64106	−	4.91061i	−0.469386	−	0.301656i
$266$		0			0
$267$	2.82724	−	2.78336i	0.173024	−	0.170339i
$268$		0			0
$269$		−	16.1978i		−	0.987597i	−0.869576	−	0.493799i	$-0.835608\pi$
$269$		−	16.1978i		−	0.987597i	0.869576	−	0.493799i	$-0.164392\pi$
$270$		0			0
$271$	2.88664	−	4.49170i	0.175351	−	0.272851i	−0.742442	−	0.669910i	$-0.766333\pi$
$271$	2.88664	−	4.49170i	0.175351	−	0.272851i	0.917793	+	0.397059i	$0.129969\pi$
$272$		0			0
$273$	−5.01346	+	6.58915i	−0.303428	+	0.398794i
$274$		0			0
$275$	75.4184	+	7.20158i	4.54790	+	0.434272i
$276$		0			0
$277$	−10.0366	−	21.9772i	−0.603043	−	1.32048i	−0.927232	−	0.374487i	$-0.877819\pi$
$277$	−10.0366	−	21.9772i	−0.603043	−	1.32048i	0.324189	−	0.945992i	$-0.394909\pi$
$278$		0			0
$279$	20.3180	+	8.50519i	1.21641	+	0.509192i
$280$		0			0
$281$	−13.0301	−	12.4242i	−0.777312	−	0.741166i	0.193476	−	0.981105i	$-0.438024\pi$
$281$	−13.0301	−	12.4242i	−0.777312	−	0.741166i	−0.970788	+	0.239939i	$0.922872\pi$
$282$		0			0
$283$	1.76612	−	3.86727i	0.104985	−	0.229885i	−0.849848	−	0.527028i	$-0.823306\pi$
$283$	1.76612	−	3.86727i	0.104985	−	0.229885i	0.954833	+	0.297142i	$0.0960336\pi$
$284$		0			0
$285$	2.49751	−	1.18916i	0.147940	−	0.0704400i
$286$		0			0
$287$	−3.12519	−	32.7285i	−0.184474	−	1.93190i
$288$		0			0
$289$	−4.70691	−	3.70155i	−0.276877	−	0.217738i
$290$		0			0
$291$	−0.525430	−	0.587153i	−0.0308012	−	0.0344195i
$292$		0			0
$293$	−2.18836	−	7.45288i	−0.127845	−	0.435402i	0.870547	−	0.492086i	$-0.163765\pi$
$293$	−2.18836	−	7.45288i	−0.127845	−	0.435402i	−0.998392	+	0.0566841i	$0.981947\pi$
$294$		0			0
$295$	−12.9352	−	1.85980i	−0.753117	−	0.108282i
$296$		0			0
$297$	7.06753	+	29.0898i	0.410100	+	1.68796i
$298$		0			0
$299$	3.75010	−	3.57571i	0.216874	−	0.206789i
$300$		0			0
$301$	0.282857	+	0.397217i	0.0163036	+	0.0228952i
$302$		0			0
$303$	−14.4378	+	15.6347i	−0.829429	+	0.898189i
$304$		0			0
$305$	−51.4870	+	29.7260i	−2.94814	+	1.70211i
$306$		0			0
$307$	1.30583	+	5.38272i	0.0745279	+	0.307208i	0.996859	−	0.0791913i	$-0.0252338\pi$
$307$	1.30583	+	5.38272i	0.0745279	+	0.307208i	−0.922332	+	0.386399i	$0.873719\pi$
$308$		0			0
$309$	−25.9986	−	17.8944i	−1.47901	−	1.01798i
$310$		0			0
$311$	−7.91488	−	9.13426i	−0.448812	−	0.517956i	0.485586	−	0.874189i	$-0.338606\pi$
$311$	−7.91488	−	9.13426i	−0.448812	−	0.517956i	−0.934397	+	0.356233i	$0.884061\pi$
$312$		0			0
$313$	−15.9193	−	24.7709i	−0.899813	−	1.40014i	−0.916396	−	0.400274i	$-0.868915\pi$
$313$	−15.9193	−	24.7709i	−0.899813	−	1.40014i	0.0165828	−	0.999862i	$-0.494721\pi$
$314$		0			0
$315$	−35.5375	+	17.6229i	−2.00231	+	0.992936i
$316$		0			0
$317$	−2.77787	+	14.4130i	−0.156021	+	0.809514i	0.816616	+	0.577182i	$0.195848\pi$
$317$	−2.77787	+	14.4130i	−0.156021	+	0.809514i	−0.972637	+	0.232332i	$0.925364\pi$
$318$		0			0
$319$	22.8447	+	29.0494i	1.27906	+	1.62646i
$320$		0			0
$321$	−0.113479	−	1.78243i	−0.00633376	−	0.0994854i
$322$		0			0
$323$	−1.20890	−	0.293275i	−0.0672649	−	0.0163183i
$324$		0			0
$325$	−9.28107	+	18.0028i	−0.514821	+	0.998613i
$326$		0			0
$327$	17.8704	−	9.57734i	0.988238	−	0.529628i
$328$		0			0
$329$	−18.3053	+	7.32832i	−1.00920	+	0.404024i
$330$		0			0
$331$	4.93615	−	1.70842i	0.271315	−	0.0939031i	−0.188023	−	0.982165i	$-0.560208\pi$
$331$	4.93615	−	1.70842i	0.271315	−	0.0939031i	0.459338	+	0.888262i	$0.348087\pi$
$332$		0			0
$333$	−14.1343	−	10.4019i	−0.774554	−	0.570023i
$334$		0			0
$335$	−34.8423	−	1.44452i	−1.90364	−	0.0789226i
$336$		0			0
$337$	15.9342	+	11.3467i	0.867990	+	0.618093i	0.924868	−	0.380288i	$-0.124175\pi$
$337$	15.9342	+	11.3467i	0.867990	+	0.618093i	−0.0568779	+	0.998381i	$0.518115\pi$
$338$		0			0
$339$	7.67250	−	15.4852i	0.416713	−	0.841041i
$340$		0			0
$341$	15.7211	+	39.2693i	0.851343	+	2.12655i
$342$		0			0
$343$	−3.81898	+	13.0062i	−0.206206	+	0.702271i
$344$		0			0
$345$	23.7044	−	7.37365i	1.27620	−	0.396984i
$346$		0			0
$347$	1.90110	−	7.83645i	0.102056	−	0.420683i	−0.897747	−	0.440512i	$-0.854797\pi$
$347$	1.90110	−	7.83645i	0.102056	−	0.420683i	0.999803	+	0.0198291i	$0.00631220\pi$
$348$		0			0
$349$	3.25401	−	3.75533i	0.174183	−	0.201018i	−0.661945	−	0.749553i	$-0.730269\pi$
$349$	3.25401	−	3.75533i	0.174183	−	0.201018i	0.836128	+	0.548535i	$0.184814\pi$
$350$		0			0
$351$	−7.92211	−	1.13629i	−0.422851	−	0.0606507i
$352$		0			0
$353$	26.5842	+	5.12369i	1.41493	+	0.272706i	0.838707	−	0.544583i	$-0.183312\pi$
$353$	26.5842	+	5.12369i	1.41493	+	0.272706i	0.576228	+	0.817289i	$0.304524\pi$
$354$		0			0
$355$	−9.38694	−	18.2081i	−0.498207	−	0.966387i
$356$		0			0
$357$	17.4007	+	3.92806i	0.920944	+	0.207895i
$358$		0			0
$359$	15.4265	−	13.3671i	0.814177	−	0.705489i	−0.144649	−	0.989483i	$-0.546205\pi$
$359$	15.4265	−	13.3671i	0.814177	−	0.705489i	0.958826	+	0.283995i	$0.0916597\pi$
$360$		0			0
$361$	−18.5187	+	3.56918i	−0.974666	+	0.187852i
$362$		0			0
$363$	−20.2610	+	32.6627i	−1.06342	+	1.71435i
$364$		0			0
$365$	−6.35325	−	11.0041i	−0.332544	−	0.575984i
$366$		0			0
$367$	−17.2173	+	0.820159i	−0.898734	+	0.0428120i	−0.491862	−	0.870673i	$-0.663684\pi$
$367$	−17.2173	+	0.820159i	−0.898734	+	0.0428120i	−0.406872	+	0.913485i	$0.633381\pi$
$368$		0			0
$369$	26.1722	−	18.0270i	1.36247	−	0.938446i
$370$		0			0
$371$	4.56615	+	4.78884i	0.237063	+	0.248624i
$372$		0			0
$373$	−6.10626	−	3.52545i	−0.316170	−	0.182541i	0.333514	−	0.942745i	$-0.391765\pi$
$373$	−6.10626	−	3.52545i	−0.316170	−	0.182541i	−0.649684	+	0.760204i	$0.725099\pi$
$374$		0			0
$375$	−48.4265	+	35.6641i	−2.50073	+	1.84169i
$376$		0			0
$377$	−9.47974	+	2.78350i	−0.488232	+	0.143358i
$378$		0			0
$379$	−0.768266	−	0.0365970i	−0.0394632	−	0.00187986i	0.0278410	−	0.999612i	$-0.491137\pi$
$379$	−0.768266	−	0.0365970i	−0.0394632	−	0.00187986i	−0.0673042	+	0.997732i	$0.521440\pi$
$380$		0			0
$381$	1.28538	+	11.5136i	0.0658520	+	0.589862i
$382$		0			0
$383$	−7.47379	+	0.713661i	−0.381893	+	0.0364663i	−0.284237	−	0.958754i	$-0.591740\pi$
$383$	−7.47379	+	0.713661i	−0.381893	+	0.0364663i	−0.0976555	+	0.995220i	$0.531134\pi$
$384$		0			0
$385$	−71.9869	−	24.9149i	−3.66879	−	1.26978i
$386$		0			0
$387$	−0.202491	+	0.425647i	−0.0102932	+	0.0216369i
$388$		0			0
$389$	11.1481	−	11.6917i	0.565229	−	0.592795i	−0.377643	−	0.925951i	$-0.623265\pi$
$389$	11.1481	−	11.6917i	0.565229	−	0.592795i	0.942872	+	0.333156i	$0.108114\pi$
$390$		0			0
$391$	−10.3642	−	4.14919i	−0.524139	−	0.209834i
$392$		0			0
$393$	−8.15041	−	3.11277i	−0.411134	−	0.157018i
$394$		0			0
$395$	0.151568	−	1.58729i	0.00762619	−	0.0798651i
$396$		0			0
$397$	3.11736	+	21.6817i	0.156456	+	1.08818i	0.905099	+	0.425202i	$0.139797\pi$
$397$	3.11736	+	21.6817i	0.156456	+	1.08818i	−0.748643	+	0.662974i	$0.769294\pi$
$398$		0			0
$399$	−1.97237	+	0.412934i	−0.0987418	+	0.0206726i
$400$		0			0
$401$	−27.5475			−1.37566			−0.687829	−	0.725873i	$-0.741436\pi$
$401$	−27.5475			−1.37566			−0.687829	+	0.725873i	$0.741436\pi$
$402$		0			0
$403$	−11.3084			−0.563313
$404$		0			0
$405$	−31.5919	−	21.7284i	−1.56982	−	1.07970i
$406$		0			0
$407$	−4.79624	−	33.3586i	−0.237741	−	1.65352i
$408$		0			0
$409$	2.08694	−	21.8554i	0.103193	−	1.08068i	−0.784464	−	0.620175i	$-0.787062\pi$
$409$	2.08694	−	21.8554i	0.103193	−	1.08068i	0.887656	−	0.460507i	$-0.152332\pi$
$410$		0			0
$411$	−10.8227	+	28.3379i	−0.533843	+	1.39780i
$412$		0			0
$413$	8.83816	+	3.53827i	0.434897	+	0.174107i
$414$		0			0
$415$	33.0083	−	34.6181i	1.62031	−	1.69933i
$416$		0			0
$417$	5.12250	+	14.0690i	0.250850	+	0.688962i
$418$		0			0
$419$	20.6175	+	7.13577i	1.00723	+	0.348605i	0.780367	−	0.625322i	$-0.215032\pi$
$419$	20.6175	+	7.13577i	1.00723	+	0.348605i	0.226862	+	0.973927i	$0.427153\pi$
$420$		0			0
$421$	9.37835	−	0.895524i	0.457073	−	0.0436452i	0.136019	−	0.990706i	$-0.456569\pi$
$421$	9.37835	−	0.895524i	0.457073	−	0.0436452i	0.321054	+	0.947061i	$0.395963\pi$
$422$		0			0
$423$	−14.7956	−	12.0146i	−0.719388	−	0.584172i
$424$		0			0
$425$	43.5890	+	2.07640i	2.11438	+	0.100720i
$426$		0			0
$427$	41.5560	−	12.2019i	2.01104	−	0.590493i
$428$		0			0
$429$	−9.11397	−	12.3754i	−0.440027	−	0.597490i
$430$		0			0
$431$	23.2702	+	13.4351i	1.12089	+	0.647144i	0.941627	−	0.336657i	$-0.109296\pi$
$431$	23.2702	+	13.4351i	1.12089	+	0.647144i	0.179260	+	0.983802i	$0.442630\pi$
$432$		0			0
$433$	−23.0976	−	24.2241i	−1.11000	−	1.16414i	−0.985103	−	0.171967i	$-0.944988\pi$
$433$	−23.0976	−	24.2241i	−1.11000	−	1.16414i	−0.124899	−	0.992169i	$-0.539861\pi$
$434$		0			0
$435$	−46.6162	−	8.21426i	−2.23507	−	0.393844i
$436$		0			0
$437$	1.25969	−	0.0600066i	0.0602593	−	0.00287050i
$438$		0			0
$439$	−7.23239	−	12.5269i	−0.345183	−	0.597875i	0.640204	−	0.768205i	$-0.278850\pi$
$439$	−7.23239	−	12.5269i	−0.345183	−	0.597875i	−0.985387	+	0.170330i	$0.945517\pi$
$440$		0			0
$441$	7.70276	−	1.74157i	0.366798	−	0.0829321i
$442$		0			0
$443$	−36.6488	+	7.06347i	−1.74124	+	0.335596i	−0.958139	−	0.286304i	$-0.907573\pi$
$443$	−36.6488	+	7.06347i	−1.74124	+	0.335596i	−0.783097	+	0.621900i	$0.786361\pi$
$444$		0			0
$445$	−7.37508	+	6.39054i	−0.349612	+	0.302941i
$446$		0			0
$447$	4.16964	−	18.4709i	0.197217	−	0.873643i
$448$		0			0
$449$	−2.78293	−	5.39814i	−0.131335	−	0.254754i	0.813994	−	0.580874i	$-0.197289\pi$
$449$	−2.78293	−	5.39814i	−0.131335	−	0.254754i	−0.945328	+	0.326120i	$0.894259\pi$
$450$		0			0
$451$	59.9269	+	11.5500i	2.82185	+	0.543866i
$452$		0			0
$453$	15.9512	+	2.03385i	0.749454	+	0.0955587i
$454$		0			0
$455$	13.3364	−	15.3911i	0.625221	−	0.721544i
$456$		0			0
$457$	−2.94610	+	12.1440i	−0.137813	+	0.568073i	0.860470	+	0.509501i	$0.170170\pi$
$457$	−2.94610	+	12.1440i	−0.137813	+	0.568073i	−0.998283	+	0.0585720i	$0.981345\pi$
$458$		0			0
$459$	4.86353	+	16.5430i	0.227010	+	0.772159i
$460$		0			0
$461$	−3.50252	+	11.9285i	−0.163129	+	0.555566i	0.836838	+	0.547450i	$0.184401\pi$
$461$	−3.50252	+	11.9285i	−0.163129	+	0.555566i	−0.999967	+	0.00811540i	$0.997417\pi$
$462$		0			0
$463$	7.60634	+	18.9997i	0.353497	+	0.882992i	0.993417	+	0.114551i	$0.0365429\pi$
$463$	7.60634	+	18.9997i	0.353497	+	0.882992i	−0.639921	+	0.768441i	$0.721033\pi$
$464$		0			0
$465$	−48.5460	−	24.0532i	−2.25127	−	1.11544i
$466$		0			0
$467$	−7.51464	−	5.35115i	−0.347736	−	0.247622i	0.392821	−	0.919615i	$-0.371499\pi$
$467$	−7.51464	−	5.35115i	−0.347736	−	0.247622i	−0.740557	+	0.671993i	$0.765438\pi$
$468$		0			0
$469$	24.4188	+	7.00677i	1.12755	+	0.323543i
$470$		0			0
$471$	−4.53000	+	0.725375i	−0.208731	+	0.0334235i
$472$		0			0
$473$	−0.855409	+	0.296060i	−0.0393317	+	0.0136128i
$474$		0			0
$475$	−4.57648	+	1.83215i	−0.209983	+	0.0840646i
$476$		0			0
$477$	−1.89771	+	6.10794i	−0.0868902	+	0.279663i
$478$		0			0
$479$	8.80975	−	17.0885i	0.402528	−	0.780795i	−0.597246	−	0.802058i	$-0.703738\pi$
$479$	8.80975	−	17.0885i	0.402528	−	0.780795i	0.999774	+	0.0212630i	$0.00676873\pi$
$480$		0			0
$481$	8.75593	+	2.12417i	0.399236	+	0.0968536i
$482$		0			0
$483$	−18.0481	+	1.14904i	−0.821217	+	0.0522829i
$484$		0			0
$485$	1.19803	+	1.52341i	0.0543995	+	0.0691747i
$486$		0			0
$487$	0.0504807	−	0.261919i	0.00228750	−	0.0118687i	−0.980767	−	0.195182i	$-0.937470\pi$
$487$	0.0504807	−	0.261919i	0.00228750	−	0.0118687i	0.983055	+	0.183313i	$0.0586823\pi$
$488$		0			0
$489$	25.0060	+	8.20963i	1.13081	+	0.371252i
$490$		0			0
$491$	−4.10090	−	6.38112i	−0.185071	−	0.287976i	0.736304	−	0.676651i	$-0.236569\pi$
$491$	−4.10090	−	6.38112i	−0.185071	−	0.287976i	−0.921375	+	0.388675i	$0.872933\pi$
$492$		0			0
$493$	13.9398	+	16.0873i	0.627815	+	0.724537i
$494$		0			0
$495$	−12.8027	−	72.5119i	−0.575438	−	3.25917i
$496$		0			0
$497$	3.51833	+	14.5028i	0.157819	+	0.650538i
$498$		0			0
$499$	−28.5894	+	16.5061i	−1.27984	+	0.738915i	−0.976818	−	0.214070i	$-0.931328\pi$
$499$	−28.5894	+	16.5061i	−1.27984	+	0.738915i	−0.303019	+	0.952984i	$0.597995\pi$
$500$		0			0
$501$	−15.4583	−	14.2749i	−0.690626	−	0.637756i
$502$		0			0
$503$	−12.8092	−	17.9880i	−0.571133	−	0.802045i	0.423457	−	0.905916i	$-0.360816\pi$
$503$	−12.8092	−	17.9880i	−0.571133	−	0.802045i	−0.994591	+	0.103871i	$0.966877\pi$
$504$		0			0
$505$	37.8842	−	36.1225i	1.68583	−	1.60743i
$506$		0			0
$507$	−17.8173	+	4.62509i	−0.791293	+	0.205407i
$508$		0			0
$509$	−11.2173	−	1.61280i	−0.497197	−	0.0714861i	−0.110845	−	0.993838i	$-0.535356\pi$
$509$	−11.2173	−	1.61280i	−0.497197	−	0.0714861i	−0.386352	+	0.922352i	$0.626265\pi$
$510$		0			0
$511$	2.60788	+	8.88163i	0.115366	+	0.392900i
$512$		0			0
$513$	−1.27607	−	1.47166i	−0.0563400	−	0.0649753i
$514$		0			0
$515$	61.0229	+	47.9889i	2.68899	+	2.11465i
$516$		0			0
$517$	−3.47921	−	36.4359i	−0.153015	−	1.60245i
$518$		0			0
$519$	−4.80479	−	10.0911i	−0.210907	−	0.442951i
$520$		0			0
$521$	11.8525	−	25.9534i	0.519269	−	1.13704i	−0.450446	−	0.892804i	$-0.648735\pi$
$521$	11.8525	−	25.9534i	0.519269	−	1.13704i	0.969715	−	0.244238i	$-0.0785377\pi$
$522$		0			0
$523$	−9.57913	−	9.13368i	−0.418866	−	0.399388i	0.451121	−	0.892463i	$-0.351024\pi$
$523$	−9.57913	−	9.13368i	−0.418866	−	0.399388i	−0.869987	+	0.493075i	$0.835873\pi$
$524$		0			0
$525$	65.1991	−	27.3185i	2.84552	−	1.19228i
$526$		0			0
$527$	10.1213	+	22.1625i	0.440890	+	0.965416i
$528$		0			0
$529$	−11.6292	−	1.11046i	−0.505619	−	0.0482808i
$530$		0			0
$531$	1.16700	+	9.12799i	0.0506435	+	0.396121i
$532$		0			0
$533$	−8.82104	+	13.7258i	−0.382082	+	0.594531i
$534$		0			0
$535$			4.39311i			0.189931i
$536$		0			0
$537$	−27.8649	−	28.3042i	−1.20246	−	1.22141i
$538$		0			0
$539$	12.7582	+	8.19921i	0.549536	+	0.353165i
$540$		0			0
$541$	29.6342	−	4.26075i	1.27407	−	0.183184i	0.528112	−	0.849175i	$-0.322900\pi$
$541$	29.6342	−	4.26075i	1.27407	−	0.183184i	0.745960	+	0.665991i	$0.231991\pi$
$542$		0			0
$543$	−14.4283	−	17.7556i	−0.619176	−	0.761967i
$544$		0			0
$545$	−45.3638	+	20.7170i	−1.94317	+	0.887417i
$546$		0			0
$547$	12.9717	−	32.4018i	0.554631	−	1.38540i	−0.340773	−	0.940146i	$-0.610689\pi$
$547$	12.9717	−	32.4018i	0.554631	−	1.38540i	0.895404	−	0.445255i	$-0.146887\pi$
$548$		0			0
$549$	29.8432	+	29.3602i	1.27368	+	1.25306i
$550$		0			0
$551$	−2.18733	−	0.998920i	−0.0931834	−	0.0425554i
$552$		0			0
$553$	−0.379918	+	1.09770i	−0.0161557	+	0.0466789i
$554$		0			0
$555$	33.0702	+	27.7428i	1.40375	+	1.17762i
$556$		0			0
$557$	13.7885	−	17.5335i	0.584238	−	0.742919i	−0.400627	−	0.916241i	$-0.631208\pi$
$557$	13.7885	−	17.5335i	0.584238	−	0.742919i	0.984865	+	0.173322i	$0.0554502\pi$
$558$		0			0
$559$	0.0115147	−	0.241723i	0.000487020	−	0.0102238i
$560$		0			0
$561$	−16.0964	+	28.9380i	−0.679591	+	1.22176i
$562$		0			0
$563$	1.75169	−	12.1833i	0.0738250	−	0.513464i	−0.919035	−	0.394176i	$-0.871030\pi$
$563$	1.75169	−	12.1833i	0.0738250	−	0.513464i	0.992860	−	0.119288i	$-0.0380610\pi$
$564$		0			0
$565$	−21.2539	+	36.8129i	−0.894159	+	1.54873i
$566$		0			0
$567$	18.6339	+	20.8087i	0.782551	+	0.873883i
$568$		0			0
$569$	26.8976	−	19.1537i	1.12761	−	0.802965i	0.145141	−	0.989411i	$-0.453636\pi$
$569$	26.8976	−	19.1537i	1.12761	−	0.802965i	0.982465	+	0.186446i	$0.0596969\pi$
$570$		0			0
$571$	0.0868183	+	1.82254i	0.00363323	+	0.0762710i	0.999956	−	0.00941174i	$-0.00299589\pi$
$571$	0.0868183	+	1.82254i	0.00363323	+	0.0762710i	−0.996322	+	0.0856827i	$0.972693\pi$
$572$		0			0
$573$	−1.39155	+	5.03549i	−0.0581329	+	0.210360i
$574$		0			0
$575$	−42.9933	+	10.4301i	−1.79294	+	0.434963i
$576$		0			0
$577$	−0.209927	−	1.08920i	−0.00873936	−	0.0453441i	0.977297	−	0.211873i	$-0.0679563\pi$
$577$	−0.209927	−	1.08920i	−0.00873936	−	0.0453441i	−0.986037	+	0.166529i	$0.946744\pi$
$578$		0			0
$579$	−0.949025	+	11.9545i	−0.0394401	+	0.496812i
$580$		0			0
$581$	−29.3141	+	18.8390i	−1.21615	+	0.781573i
$582$		0			0
$583$	−10.9174	+	5.62829i	−0.452151	+	0.233100i
$584$		0			0
$585$	19.2690	+	4.02736i	0.796677	+	0.166511i
$586$		0			0
$587$	−14.1258	+	11.1087i	−0.583036	+	0.458505i	−0.865595	−	0.500746i	$-0.833059\pi$
$587$	−14.1258	+	11.1087i	−0.583036	+	0.458505i	0.282559	+	0.959250i	$0.408817\pi$
$588$		0			0
$589$	−2.08005	−	1.80238i	−0.0857070	−	0.0742656i
$590$		0			0
$591$	−17.6254	+	10.5551i	−0.725011	+	0.434178i
$592$		0			0
$593$	−9.58828	−	4.94310i	−0.393744	−	0.202989i	0.249973	−	0.968253i	$-0.419578\pi$
$593$	−9.58828	−	4.94310i	−0.393744	−	0.202989i	−0.643717	+	0.765264i	$0.722608\pi$
$594$		0			0
$595$	−42.1002	−	12.3617i	−1.72594	−	0.506781i
$596$		0			0
$597$	−31.7859	−	13.9067i	−1.30091	−	0.569162i
$598$		0			0
$599$	1.04442	+	3.01765i	0.0426738	+	0.123298i	0.964325	−	0.264722i	$-0.0852803\pi$
$599$	1.04442	+	3.01765i	0.0426738	+	0.123298i	−0.921651	+	0.388020i	$0.873159\pi$
$600$		0			0
$601$	−3.69220	+	5.18497i	−0.150608	+	0.211499i	−0.882986	−	0.469399i	$-0.844471\pi$
$601$	−3.69220	+	5.18497i	−0.150608	+	0.211499i	0.732379	+	0.680898i	$0.238410\pi$
$602$		0			0
$603$	5.56292	+	23.9176i	0.226539	+	0.974002i
$604$		0			0
$605$	54.8397	−	77.0115i	2.22955	−	3.13096i
$606$		0			0
$607$	4.49809	+	12.9964i	0.182572	+	0.527506i	0.998733	−	0.0503174i	$-0.0160233\pi$
$607$	4.49809	+	12.9964i	0.182572	+	0.527506i	−0.816162	+	0.577824i	$0.803902\pi$
$608$		0			0
$609$	31.5915	+	13.8216i	1.28015	+	0.560080i
$610$		0			0
$611$	9.38884	+	2.75681i	0.379832	+	0.111529i
$612$		0			0
$613$	−23.7393	−	12.2385i	−0.958823	−	0.494308i	−0.0935533	−	0.995614i	$-0.529823\pi$
$613$	−23.7393	−	12.2385i	−0.958823	−	0.494308i	−0.865270	+	0.501307i	$0.832853\pi$
$614$		0			0
$615$	−67.0629	+	40.1610i	−2.70424	+	1.61945i
$616$		0			0
$617$	4.81268	+	4.17021i	0.193751	+	0.167886i	0.746334	−	0.665572i	$-0.231812\pi$
$617$	4.81268	+	4.17021i	0.193751	+	0.167886i	−0.552583	+	0.833458i	$0.686358\pi$
$618$		0			0
$619$	−12.7834	+	10.0530i	−0.513809	+	0.404064i	−0.841116	−	0.540854i	$-0.818101\pi$
$619$	−12.7834	+	10.0530i	−0.513809	+	0.404064i	0.327308	+	0.944918i	$0.393859\pi$
$620$		0			0
$621$	−9.45587	−	14.7027i	−0.379451	−	0.589998i
$622$		0			0
$623$	6.31881	−	3.25757i	0.253158	−	0.130512i
$624$		0			0
$625$	69.1337	−	44.4295i	2.76535	−	1.77718i
$626$		0			0
$627$	0.296026	−	3.72892i	0.0118221	−	0.148919i
$628$		0			0
$629$	−3.67376	−	19.0613i	−0.146482	−	0.760022i
$630$		0			0
$631$	34.7069	−	8.41980i	1.38166	−	0.335187i	0.525014	−	0.851093i	$-0.324060\pi$
$631$	34.7069	−	8.41980i	1.38166	−	0.335187i	0.856645	+	0.515906i	$0.172545\pi$
$632$		0			0
$633$	−11.8861	+	43.0111i	−0.472429	+	1.70954i
$634$		0			0
$635$	−1.35589	−	28.4637i	−0.0538070	−	1.12955i
$636$		0			0
$637$	−3.30266	+	2.35182i	−0.130856	+	0.0931823i
$638$		0			0
$639$	−10.5944	+	9.79005i	−0.419110	+	0.387288i
$640$		0			0
$641$	1.91537	−	3.31751i	0.0756524	−	0.131034i	−0.825717	−	0.564084i	$-0.809229\pi$
$641$	1.91537	−	3.31751i	0.0756524	−	0.131034i	0.901370	+	0.433050i	$0.142563\pi$
$642$		0			0
$643$	−4.05839	+	28.2267i	−0.160047	+	1.11315i	0.738492	+	0.674262i	$0.235538\pi$
$643$	−4.05839	+	28.2267i	−0.160047	+	1.11315i	−0.898540	+	0.438892i	$0.855371\pi$
$644$		0			0
$645$	0.563581	−	1.01320i	0.0221910	−	0.0398948i
$646$		0			0
$647$	−1.47317	+	30.9257i	−0.0579164	+	1.21581i	0.763623	+	0.645663i	$0.223419\pi$
$647$	−1.47317	+	30.9257i	−0.0579164	+	1.21581i	−0.821539	+	0.570152i	$0.806884\pi$
$648$		0			0
$649$	−10.9241	+	13.8912i	−0.428809	+	0.545275i
$650$		0			0
$651$	30.2374	+	25.3664i	1.18510	+	0.994186i
$652$		0			0
$653$	4.31635	−	12.4713i	0.168912	−	0.488038i	−0.828496	−	0.559995i	$-0.810803\pi$
$653$	4.31635	−	12.4713i	0.168912	−	0.488038i	0.997408	+	0.0719565i	$0.0229243\pi$
$654$		0			0
$655$	19.5206	+	8.91475i	0.762732	+	0.348328i
$656$		0			0
$657$	−6.27505	+	6.37830i	−0.244813	+	0.248841i
$658$		0			0
$659$	−4.60925	+	11.5134i	−0.179551	+	0.448497i	−0.990653	−	0.136408i	$-0.956444\pi$
$659$	−4.60925	+	11.5134i	−0.179551	+	0.448497i	0.811102	+	0.584905i	$0.198868\pi$
$660$		0			0
$661$	−38.1537	+	17.4242i	−1.48401	+	0.677723i	−0.982300	−	0.187314i	$-0.940022\pi$
$661$	−38.1537	+	17.4242i	−1.48401	+	0.677723i	−0.501707	+	0.865038i	$0.667294\pi$
$662$		0			0
$663$	−5.58285	−	6.87034i	−0.216820	−	0.266822i
$664$		0			0
$665$	4.90615	−	0.705398i	0.190252	−	0.0273542i
$666$		0			0
$667$	−18.1544	−	11.6671i	−0.702942	−	0.451754i
$668$		0			0
$669$	−17.0085	−	17.2766i	−0.657587	−	0.667953i
$670$		0			0
$671$			80.3964i			3.10367i
$672$		0			0
$673$	−3.70299	+	5.76197i	−0.142740	+	0.222107i	−0.905261	−	0.424856i	$-0.860325\pi$
$673$	−3.70299	+	5.76197i	−0.142740	+	0.222107i	0.762521	+	0.646963i	$0.223961\pi$
$674$		0			0
$675$	53.7262	+	42.2213i	2.06792	+	1.62510i
$676$		0			0
$677$	14.1584	+	1.35197i	0.544153	+	0.0519603i	0.363513	−	0.931589i	$-0.381577\pi$
$677$	14.1584	+	1.35197i	0.544153	+	0.0519603i	0.180640	+	0.983549i	$0.442183\pi$
$678$		0			0
$679$	−0.586507	−	1.28427i	−0.0225081	−	0.0492858i
$680$		0			0
$681$	41.9914	−	17.5944i	1.60911	−	0.674220i
$682$		0			0
$683$	−25.8052	−	24.6052i	−0.987407	−	0.941490i	0.0108837	−	0.999941i	$-0.496536\pi$
$683$	−25.8052	−	24.6052i	−0.987407	−	0.941490i	−0.998290	+	0.0584504i	$0.981384\pi$
$684$		0			0
$685$	30.9953	−	67.8703i	1.18427	−	2.59319i
$686$		0			0
$687$	4.92410	+	10.3417i	0.187866	+	0.394561i
$688$		0			0
$689$	−0.312137	−	3.26885i	−0.0118915	−	0.124533i
$690$		0			0
$691$	−19.2125	−	15.1089i	−0.730879	−	0.574770i	0.181854	−	0.983325i	$-0.441790\pi$
$691$	−19.2125	−	15.1089i	−0.730879	−	0.574770i	−0.912733	+	0.408556i	$0.866033\pi$
$692$		0			0
$693$	−3.39007	+	53.5342i	−0.128778	+	2.03360i
$694$		0			0
$695$	−10.3756	−	35.3361i	−0.393570	−	1.34038i
$696$		0			0
$697$	34.7952	+	5.00279i	1.31796	+	0.189494i
$698$		0			0
$699$	34.5627	−	8.97194i	1.30728	−	0.339350i
$700$		0			0
$701$	−18.2783	+	17.4283i	−0.690361	+	0.658258i	−0.951714	−	0.306986i	$-0.900680\pi$
$701$	−18.2783	+	17.4283i	−0.690361	+	0.658258i	0.261353	+	0.965243i	$0.415831\pi$
$702$		0			0
$703$	1.27199	+	1.78626i	0.0479741	+	0.0673702i
$704$		0			0
$705$	34.4416	+	31.8049i	1.29714	+	1.19784i
$706$		0			0
$707$	−33.0244	+	19.0666i	−1.24201	+	0.717075i
$708$		0			0
$709$	−4.47237	−	18.4354i	−0.167964	−	0.692355i	−0.992045	−	0.125884i	$-0.959823\pi$
$709$	−4.47237	−	18.4354i	−0.167964	−	0.692355i	0.824081	−	0.566471i	$-0.191692\pi$
$710$		0			0
$711$	−1.10571	+	0.195223i	−0.0414672	+	0.00732144i
$712$		0			0
$713$	−16.1753	−	18.6673i	−0.605770	−	0.699096i
$714$		0			0
$715$	20.4383	+	31.8026i	0.764348	+	1.18935i
$716$		0			0
$717$	11.1070	+	3.64650i	0.414798	+	0.136181i
$718$		0			0
$719$	−1.18605	+	6.15381i	−0.0442322	+	0.229498i	−0.997317	−	0.0732054i	$-0.976677\pi$
$719$	−1.18605	+	6.15381i	−0.0442322	+	0.229498i	0.953085	+	0.302704i	$0.0978892\pi$
$720$		0			0
$721$	−34.9596	−	44.4547i	−1.30196	−	1.65558i
$722$		0			0
$723$	47.4132	−	3.01857i	1.76332	−	0.112262i
$724$		0			0
$725$	81.9770	+	19.8874i	3.04455	+	0.738600i
$726$		0			0
$727$	21.9554	−	42.5875i	0.814279	−	1.57948i	−0.000705458	−	1.00000i	$-0.500225\pi$
$727$	21.9554	−	42.5875i	0.814279	−	1.57948i	0.814985	−	0.579482i	$-0.196745\pi$
$728$		0			0
$729$	−8.81355	+	25.5210i	−0.326428	+	0.945222i
$730$		0			0
$731$	−0.484041	+	0.193781i	−0.0179029	+	0.00716724i
$732$		0			0
$733$	22.7614	−	7.87781i	0.840713	−	0.290973i	0.127428	−	0.991848i	$-0.459328\pi$
$733$	22.7614	−	7.87781i	0.840713	−	0.290973i	0.713285	+	0.700874i	$0.247207\pi$
$734$		0			0
$735$	−19.1804	+	3.07129i	−0.707478	+	0.113286i
$736$		0			0
$737$	−25.2501	+	39.8277i	−0.930101	+	1.46707i
$738$		0			0
$739$	14.7241	+	10.4850i	0.541635	+	0.385696i	0.817878	−	0.575391i	$-0.195150\pi$
$739$	14.7241	+	10.4850i	0.541635	+	0.385696i	−0.276244	+	0.961088i	$0.589090\pi$
$740$		0			0
$741$	0.896078	+	0.443983i	0.0329183	+	0.0163101i
$742$		0			0
$743$	0.522599	+	1.30539i	0.0191723	+	0.0478901i	0.937645	−	0.347594i	$-0.113001\pi$
$743$	0.522599	+	1.30539i	0.0191723	+	0.0478901i	−0.918473	+	0.395484i	$0.870577\pi$
$744$		0			0
$745$	−13.1220	+	44.6894i	−0.480752	+	1.63729i
$746$		0			0
$747$	−29.6931	−	15.9005i	−1.08641	−	0.581770i
$748$		0			0
$749$	0.754510	−	3.11013i	0.0275692	−	0.113642i
$750$		0			0
$751$	24.2455	−	27.9808i	0.884732	−	1.02104i	−0.114885	−	0.993379i	$-0.536650\pi$
$751$	24.2455	−	27.9808i	0.884732	−	1.02104i	0.999617	−	0.0276568i	$-0.00880456\pi$
$752$		0			0
$753$	−19.0671	−	2.43114i	−0.694845	−	0.0885958i
$754$		0			0
$755$	−38.8380	−	7.48542i	−1.41346	−	0.272422i
$756$		0			0
$757$	3.14182	+	6.09427i	0.114191	+	0.221500i	0.939004	−	0.343905i	$-0.111750\pi$
$757$	3.14182	+	6.09427i	0.114191	+	0.221500i	−0.824813	+	0.565406i	$0.808720\pi$
$758$		0			0
$759$	7.39218	−	32.7463i	0.268319	−	1.18861i
$760$		0			0
$761$	−36.1610	+	31.3337i	−1.31084	+	1.13585i	−0.329371	+	0.944201i	$0.606837\pi$
$761$	−36.1610	+	31.3337i	−1.31084	+	1.13585i	−0.981464	+	0.191645i	$0.938618\pi$
$762$		0			0
$763$	35.6738	−	6.87555i	1.29148	−	0.248912i
$764$		0			0
$765$	−9.35330	−	41.3685i	−0.338169	−	1.49568i
$766$		0			0
$767$	−2.36225	−	4.09154i	−0.0852959	−	0.147737i
$768$		0			0
$769$	−20.6084	+	0.981699i	−0.743158	+	0.0354010i	−0.415746	−	0.909481i	$-0.636479\pi$
$769$	−20.6084	+	0.981699i	−0.743158	+	0.0354010i	−0.327412	+	0.944882i	$0.606176\pi$
$770$		0			0
$771$	32.2614	+	5.68481i	1.16187	+	0.204733i
$772$		0			0
$773$	−28.8887	−	30.2976i	−1.03905	−	1.08973i	−0.995882	−	0.0906604i	$-0.971102\pi$
$773$	−28.8887	−	30.2976i	−1.03905	−	1.08973i	−0.0431718	−	0.999068i	$-0.513746\pi$
$774$		0			0
$775$	83.6158	+	48.2756i	3.00357	+	1.73411i
$776$		0			0
$777$	−18.6475	−	25.3205i	−0.668975	−	0.908368i
$778$		0			0
$779$	−3.81019	+	1.11877i	−0.136514	+	0.0400842i
$780$		0			0
$781$	−27.6708	−	1.31812i	−0.990138	−	0.0471661i
$782$		0			0
$783$	3.17960	+	33.1795i	0.113630	+	1.18574i
$784$		0			0
$785$	11.2333	−	1.07265i	0.400933	−	0.0382844i
$786$		0			0
$787$	13.3927	+	4.63524i	0.477397	+	0.165229i	0.555161	−	0.831743i	$-0.312657\pi$
$787$	13.3927	+	4.63524i	0.477397	+	0.165229i	−0.0777638	+	0.996972i	$0.524778\pi$
$788$		0			0
$789$	−8.36823	−	22.9834i	−0.297917	−	0.818232i
$790$		0			0
$791$	21.3694	−	22.4116i	0.759810	−	0.796865i
$792$		0			0
$793$	−19.9538	−	7.98830i	−0.708581	−	0.283673i
$794$		0			0
$795$	5.61292	−	14.6968i	0.199070	−	0.521240i
$796$		0			0
$797$	0.0339439	−	0.355477i	0.00120236	−	0.0125916i	−0.994851	−	0.101350i	$-0.967684\pi$
$797$	0.0339439	−	0.355477i	0.00120236	−	0.0125916i	0.996053	+	0.0887583i	$0.0282899\pi$
$798$		0			0
$799$	−3.00035	−	20.8679i	−0.106145	−	0.738252i
$800$		0			0
$801$	5.72208	+	3.80511i	0.202180	+	0.134447i
$802$		0			0
$803$	−17.1829			−0.606370
$804$		0			0
$805$	44.4827			1.56781
$806$		0			0
$807$	27.4601	−	5.74903i	0.966640	−	0.202376i
$808$		0			0
$809$	−2.85633	−	19.8662i	−0.100423	−	0.698459i	−0.976379	−	0.216067i	$-0.930677\pi$
$809$	−2.85633	−	19.8662i	−0.100423	−	0.698459i	0.875955	−	0.482392i	$-0.160232\pi$
$810$		0			0
$811$	4.90615	−	51.3796i	0.172278	−	1.80418i	−0.334809	−	0.942286i	$-0.608672\pi$
$811$	4.90615	−	51.3796i	0.172278	−	1.80418i	0.507088	−	0.861894i	$-0.330722\pi$
$812$		0			0
$813$	8.63930	+	3.29948i	0.302994	+	0.115718i
$814$		0			0
$815$	−60.0998	−	24.0603i	−2.10521	−	0.842797i
$816$		0			0
$817$	0.0406446	−	0.0426269i	0.00142198	−	0.00149133i
$818$		0			0
$819$	−12.9500	−	6.16063i	−0.452509	−	0.215270i
$820$		0			0
$821$	21.7404	+	7.52442i	0.758744	+	0.262604i	0.678927	−	0.734206i	$-0.262445\pi$
$821$	21.7404	+	7.52442i	0.758744	+	0.262604i	0.0798172	+	0.996810i	$0.474566\pi$
$822$		0			0
$823$	−31.5999	+	3.01742i	−1.10150	+	0.105181i	−0.629934	−	0.776648i	$-0.716918\pi$
$823$	−31.5999	+	3.01742i	−1.10150	+	0.105181i	−0.471569	+	0.881829i	$0.656312\pi$
$824$		0			0
$825$	14.5592	+	130.413i	0.506886	+	4.54038i
$826$		0			0
$827$	43.2640	+	2.06092i	1.50444	+	0.0716651i	0.783524	−	0.621362i	$-0.213420\pi$
$827$	43.2640	+	2.06092i	1.50444	+	0.0716651i	0.720912	+	0.693027i	$0.243723\pi$
$828$		0			0
$829$	−33.1925	+	9.74620i	−1.15282	+	0.338499i	−0.801640	−	0.597807i	$-0.796039\pi$
$829$	−33.1925	+	9.74620i	−1.15282	+	0.338499i	−0.351183	+	0.936307i	$0.614221\pi$
$830$		0			0
$831$	33.6955	−	24.8153i	1.16888	−	0.860835i
$832$		0			0
$833$	7.56510	+	4.36771i	0.262115	+	0.151332i
$834$		0			0
$835$	35.7150	+	37.4568i	1.23597	+	1.29625i
$836$		0			0
$837$	−7.20739	+	37.4638i	−0.249124	+	1.29494i
$838$		0			0
$839$	−30.6174	+	1.45849i	−1.05703	+	0.0503525i	−0.568890	−	0.822413i	$-0.692627\pi$
$839$	−30.6174	+	1.45849i	−1.05703	+	0.0503525i	−0.488139	+	0.872766i	$0.662324\pi$
$840$		0			0
$841$	6.07393	+	10.5204i	0.209446	+	0.362771i
$842$		0			0
$843$	16.4380	−	26.4996i	0.566153	−	0.912695i
$844$		0			0
$845$	44.4593	−	8.56884i	1.52945	−	0.294777i
$846$		0			0
$847$	−52.0508	+	45.1022i	−1.78849	+	1.54973i
$848$		0			0
$849$	7.18301	+	1.62150i	0.246520	+	0.0556498i
$850$		0			0
$851$	9.01781	+	17.4921i	0.309127	+	0.599622i
$852$		0			0
$853$	8.39092	+	1.61722i	0.287300	+	0.0553725i	0.330865	−	0.943678i	$-0.392660\pi$
$853$	8.39092	+	1.61722i	0.287300	+	0.0553725i	−0.0435653	+	0.999051i	$0.513872\pi$
$854$		0			0
$855$	2.90242	+	3.81195i	0.0992606	+	0.130366i
$856$		0			0
$857$	−29.8887	+	34.4934i	−1.02098	+	1.17827i	−0.0371221	+	0.999311i	$0.511819\pi$
$857$	−29.8887	+	34.4934i	−1.02098	+	1.17827i	−0.983856	+	0.178961i	$0.942726\pi$
$858$		0			0
$859$	2.75206	−	11.3441i	0.0938990	−	0.387057i	−0.905397	−	0.424565i	$-0.860427\pi$
$859$	2.75206	−	11.3441i	0.0938990	−	0.387057i	0.999296	+	0.0375083i	$0.0119421\pi$
$860$		0			0
$861$	54.3752	−	16.9143i	1.85310	−	0.576439i
$862$		0			0
$863$	−4.01477	+	13.6730i	−0.136664	+	0.465436i	−0.999175	−	0.0406022i	$-0.987072\pi$
$863$	−4.01477	+	13.6730i	−0.136664	+	0.465436i	0.862511	+	0.506038i	$0.168891\pi$
$864$		0			0
$865$	10.2174	+	25.5218i	0.347402	+	0.867768i
$866$		0			0
$867$	4.60462	−	9.29338i	0.156381	−	0.315620i
$868$		0			0
$869$	−1.75642	−	1.25074i	−0.0595824	−	0.0424284i
$870$		0			0
$871$	−7.37606	−	10.2242i	−0.249928	−	0.346435i
$872$		0			0
$873$	0.808908	−	1.09915i	0.0273774	−	0.0372008i
$874$		0			0
$875$	−101.840	+	35.2470i	−3.44280	+	1.19157i
$876$		0			0
$877$	−22.8715	+	9.15635i	−0.772314	+	0.309188i	−0.724142	−	0.689651i	$-0.757764\pi$
$877$	−22.8715	+	9.15635i	−0.772314	+	0.309188i	−0.0481723	+	0.998839i	$0.515340\pi$
$878$		0			0
$879$	11.8581	−	6.35515i	0.399965	−	0.214354i
$880$		0			0
$881$	11.0138	−	21.3637i	0.371063	−	0.719762i	−0.627189	−	0.778867i	$-0.715794\pi$
$881$	11.0138	−	21.3637i	0.371063	−	0.719762i	0.998252	+	0.0591053i	$0.0188248\pi$
$882$		0			0
$883$	0.596955	+	0.144820i	0.0200891	+	0.00487357i	0.245791	−	0.969323i	$-0.420952\pi$
$883$	0.596955	+	0.144820i	0.0200891	+	0.00487357i	−0.225702	+	0.974196i	$0.572467\pi$
$884$		0			0
$885$	−1.43814	−	22.5891i	−0.0483425	−	0.759324i
$886$		0			0
$887$	30.6086	+	38.9220i	1.02774	+	1.30687i	0.950790	+	0.309836i	$0.100274\pi$
$887$	30.6086	+	38.9220i	1.02774	+	1.30687i	0.0769450	+	0.997035i	$0.475483\pi$
$888$		0			0
$889$	−3.92869	+	20.3840i	−0.131764	+	0.683657i
$890$		0			0
$891$	−46.8073	+	22.3063i	−1.56810	+	0.747289i
$892$		0			0
$893$	1.28757	+	2.00351i	0.0430871	+	0.0670448i
$894$		0			0
$895$	63.9773	+	73.8337i	2.13853	+	2.46799i
$896$		0			0
$897$	7.39289	+	5.08840i	0.246841	+	0.169897i
$898$		0			0
$899$	11.1036	+	45.7696i	0.370325	+	1.52650i
$900$		0			0
$901$	−6.12699	+	3.53742i	−0.204120	+	0.117849i
$902$		0			0
$903$	−0.573007	+	0.620510i	−0.0190685	+	0.0206493i
$904$		0			0
$905$	32.6426	+	45.8401i	1.08508	+	1.52378i
$906$		0			0
$907$	−17.6881	+	16.8655i	−0.587323	+	0.560011i	−0.924380	−	0.381473i	$-0.875417\pi$
$907$	−17.6881	+	16.8655i	−0.587323	+	0.560011i	0.337057	+	0.941484i	$0.390568\pi$
$908$		0			0
$909$	−31.6298	−	18.9271i	−1.04909	−	0.627774i
$910$		0			0
$911$	−9.70330	−	1.39512i	−0.321485	−	0.0462225i	−0.0203166	−	0.999794i	$-0.506467\pi$
$911$	−9.70330	−	1.39512i	−0.321485	−	0.0462225i	−0.301168	+	0.953571i	$0.597376\pi$
$912$		0			0
$913$	−18.2235	−	62.0634i	−0.603108	−	2.05400i
$914$		0			0
$915$	−68.6685	−	76.7351i	−2.27011	−	2.53678i
$916$		0			0
$917$	−12.2886	−	9.66389i	−0.405807	−	0.319130i
$918$		0			0
$919$	1.71168	+	17.9255i	0.0564632	+	0.591309i	0.978785	+	0.204888i	$0.0656829\pi$
$919$	1.71168	+	17.9255i	0.0564632	+	0.591309i	−0.922322	+	0.386422i	$0.873711\pi$
$920$		0			0
$921$	−8.66183	+	4.12425i	−0.285417	+	0.135899i
$922$		0			0
$923$	3.07656	−	6.73672i	0.101266	−	0.221742i
$924$		0			0
$925$	−55.6743	−	53.0853i	−1.83056	−	1.74543i
$926$		0			0
$927$	21.1087	−	50.4265i	0.693300	−	1.65622i
$928$		0			0
$929$	22.5808	+	49.4450i	0.740851	+	1.62224i	0.782149	+	0.623091i	$0.214123\pi$
$929$	22.5808	+	49.4450i	0.740851	+	1.62224i	−0.0412978	+	0.999147i	$0.513149\pi$
$930$		0			0
$931$	−0.982326	−	0.0938007i	−0.0321944	−	0.00307419i
$932$		0			0
$933$	12.6761	−	16.6600i	0.414996	−	0.545426i
$934$		0			0
$935$	44.0347	−	68.5194i	1.44009	−	2.24082i
$936$		0			0
$937$		−	46.2095i		−	1.50960i	−0.655956	−	0.754799i	$-0.727734\pi$
$937$		−	46.2095i		−	1.50960i	0.655956	−	0.754799i	$-0.272266\pi$
$938$		0			0
$939$	36.3439	−	35.7798i	1.18604	−	1.16763i
$940$		0			0
$941$	−3.19084	−	2.05063i	−0.104018	−	0.0668485i	0.487597	−	0.873069i	$-0.337873\pi$
$941$	−3.19084	−	2.05063i	−0.104018	−	0.0668485i	−0.591616	+	0.806220i	$0.701510\pi$
$942$		0			0
$943$	−35.2751	+	5.07180i	−1.14872	+	0.165161i
$944$		0			0
$945$	−42.4892	−	53.9918i	−1.38217	−	1.75635i
$946$		0			0
$947$	−19.4327	+	8.87460i	−0.631477	+	0.288386i	−0.705325	−	0.708884i	$-0.749199\pi$
$947$	−19.4327	+	8.87460i	−0.631477	+	0.288386i	0.0738487	+	0.997269i	$0.476472\pi$
$948$		0			0
$949$	1.70731	−	4.26467i	0.0554218	−	0.138437i
$950$		0			0
$951$	−25.4202	+	0.406237i	−0.824307	+	0.0131731i
$952$		0			0
$953$	11.1843	+	5.10770i	0.362295	+	0.165454i	0.588242	−	0.808685i	$-0.299820\pi$
$953$	11.1843	+	5.10770i	0.362295	+	0.165454i	−0.225947	+	0.974140i	$0.572548\pi$
$954$		0			0
$955$	4.20283	−	12.1433i	0.136000	−	0.392947i
$956$		0			0
$957$	−41.1391	+	49.0390i	−1.32984	+	1.58520i
$958$		0			0
$959$	−33.6000	+	42.7259i	−1.08500	+	1.37969i
$960$		0			0
$961$	−1.08994	+	22.8807i	−0.0351595	+	0.738088i
$962$		0			0
$963$	2.98146	−	0.825011i	0.0960763	−	0.0265856i
$964$		0			0
$965$	4.19785	−	29.1967i	0.135134	−	0.939876i
$966$		0			0
$967$	−20.4017	+	35.3368i	−0.656075	+	1.13636i	0.325548	+	0.945526i	$0.394451\pi$
$967$	−20.4017	+	35.3368i	−0.656075	+	1.13636i	−0.981623	+	0.190830i	$0.938882\pi$
$968$		0			0
$969$	0.0681182	−	2.15353i	0.00218827	−	0.0691813i
$970$		0			0
$971$	26.4067	−	18.8041i	0.847432	−	0.603453i	−0.0716902	−	0.997427i	$-0.522839\pi$
$971$	26.4067	−	18.8041i	0.847432	−	0.603453i	0.919122	+	0.393974i	$0.128900\pi$
$972$		0			0
$973$	1.27657	+	26.7985i	0.0409249	+	0.859119i
$974$		0			0
$975$	−33.8141	−	9.34449i	−1.08292	−	0.299263i
$976$		0			0
$977$	9.02418	−	2.18924i	0.288709	−	0.0700401i	−0.0887889	−	0.996050i	$-0.528300\pi$
$977$	9.02418	−	2.18924i	0.288709	−	0.0700401i	0.377498	+	0.926010i	$0.376784\pi$
$978$		0			0
$979$	2.49745	+	12.9580i	0.0798189	+	0.414140i
$980$		0			0
$981$	22.5791	+	26.8964i	0.720896	+	0.858737i
$982$		0			0
$983$	−15.6773	+	10.0752i	−0.500030	+	0.321350i	−0.766228	−	0.642569i	$-0.777869\pi$
$983$	−15.6773	+	10.0752i	−0.500030	+	0.321350i	0.266198	+	0.963918i	$0.414232\pi$
$984$		0			0
$985$	44.9150	−	23.1553i	1.43111	−	0.737790i
$986$		0			0
$987$	−18.9207	−	28.4318i	−0.602253	−	0.904995i
$988$		0			0
$989$	0.415493	−	0.326747i	0.0132119	−	0.0103900i
$990$		0			0
$991$	16.3701	+	14.1848i	0.520015	+	0.450595i	0.874892	−	0.484317i	$-0.160932\pi$
$991$	16.3701	+	14.1848i	0.520015	+	0.450595i	−0.354878	+	0.934913i	$0.615477\pi$
$992$		0			0
$993$	4.64824	+	7.76187i	0.147508	+	0.246315i
$994$		0			0
$995$	75.8523	+	39.1046i	2.40468	+	1.23970i
$996$		0			0
$997$	42.9340	+	12.6066i	1.35973	+	0.399254i	0.878669	−	0.477431i	$-0.158432\pi$
$997$	42.9340	+	12.6066i	1.35973	+	0.399254i	0.481065	+	0.876685i	$0.340250\pi$
$998$		0			0
$999$	12.6177	−	27.6537i	0.399207	−	0.874925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.353.13	yes	440
3.2	odd	2	inner	804.2.ba.b.353.3	yes	440
67.41	odd	66	inner	804.2.ba.b.41.3	✓	440
201.41	even	66	inner	804.2.ba.b.41.13	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.3	✓	440	67.41	odd	66	inner
804.2.ba.b.41.13	yes	440	201.41	even	66	inner
804.2.ba.b.353.3	yes	440	3.2	odd	2	inner
804.2.ba.b.353.13	yes	440	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.354927 + 1.69530i) q^{3} +(-0.606307 - 4.21696i) q^{5} +(-0.295017 + 3.08956i) q^{7} +(-2.74805 + 1.20341i) q^{9} +O(q^{10})\)	\(q+(0.354927 + 1.69530i) q^{3} +(-0.606307 - 4.21696i) q^{5} +(-0.295017 + 3.08956i) q^{7} +(-2.74805 + 1.20341i) q^{9} +(-5.34850 - 2.14122i) q^{11} +(1.06287 - 1.11471i) q^{13} +(6.93379 - 2.52458i) q^{15} +(-3.13592 - 1.08535i) q^{17} +(0.373168 - 0.0356332i) q^{19} +(-5.34242 + 0.596426i) q^{21} +(3.36039 + 0.160075i) q^{23} +(-12.6176 + 3.70487i) q^{25} +(-3.01550 - 4.23164i) q^{27} +(-5.55526 - 3.20733i) q^{29} +(-5.06664 - 5.31374i) q^{31} +(1.73167 - 9.82726i) q^{33} +(13.2074 - 0.629146i) q^{35} +(2.92489 + 5.06605i) q^{37} +(2.26700 + 1.40624i) q^{39} +(-10.4018 + 2.00479i) q^{41} +(0.118743 - 0.102891i) q^{43} +(6.74090 + 10.8588i) q^{45} +(2.91118 + 5.64690i) q^{47} +(-2.58483 - 0.498185i) q^{49} +(0.726970 - 5.70153i) q^{51} +(1.39615 - 1.61125i) q^{53} +(-5.78658 + 23.8526i) q^{55} +(0.192856 + 0.619982i) q^{57} +(0.864195 - 2.94318i) q^{59} +(-5.18649 - 12.9552i) q^{61} +(-2.90729 - 8.84530i) q^{63} +(-5.34509 - 3.80622i) q^{65} +(1.49951 - 8.04683i) q^{67} +(0.921319 + 5.75367i) q^{69} +(4.54395 - 1.57268i) q^{71} +(2.76888 - 1.10849i) q^{73} +(-10.7592 - 20.0757i) q^{75} +(8.19331 - 15.8928i) q^{77} +(0.363719 + 0.0882373i) q^{79} +(6.10360 - 6.61408i) q^{81} +(6.94036 + 8.82538i) q^{83} +(-2.67555 + 13.8821i) q^{85} +(3.46566 - 10.5562i) q^{87} +(-1.23838 - 1.92696i) q^{89} +(3.13038 + 3.61265i) q^{91} +(7.21007 - 10.4754i) q^{93} +(-0.376518 - 1.55203i) q^{95} +(-0.393962 + 0.227454i) q^{97} +(17.2747 - 0.552271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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