LMFDB - Embedded newform 315.2.bb.b.89.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(89,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("315.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bb (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.11
Character	$\chi$	$=$	315.89
Dual form			315.2.bb.b.269.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28469 - 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(-2.22083 - 0.260635i) q^{5} +(-2.64140 + 0.151755i) q^{7} -6.68468 q^{8} +O(q^{10})$	\(q+(1.28469 - 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(-2.22083 - 0.260635i) q^{5} +(-2.64140 + 0.151755i) q^{7} -6.68468 q^{8} +(-3.43302 + 4.60682i) q^{10} +(4.88189 - 2.81856i) q^{11} -3.53537 q^{13} +(-3.05569 + 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(4.62703 - 2.67142i) q^{17} +(-1.24942 - 0.721351i) q^{19} +(4.07109 + 9.45005i) q^{20} -14.4839i q^{22} +(1.49930 - 2.59686i) q^{23} +(4.86414 + 1.15765i) q^{25} +(-4.54184 + 7.86670i) q^{26} +(6.68220 + 10.1772i) q^{28} -2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(3.55696 + 6.16083i) q^{32} -13.7277i q^{34} +(5.90563 + 0.351419i) q^{35} +(0.946690 + 0.546572i) q^{37} +(-3.21022 + 1.85342i) q^{38} +(14.8455 + 1.74226i) q^{40} -6.52058 q^{41} +0.486125i q^{43} +(-22.4649 - 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(3.68608 + 2.12816i) q^{47} +(6.95394 - 0.801688i) q^{49} +(8.82483 - 9.33618i) q^{50} +(8.13432 + 14.0891i) q^{52} +(2.01102 + 3.48318i) q^{53} +(-11.5764 + 4.98714i) q^{55} +(17.6569 - 1.01443i) q^{56} +(-4.88206 - 2.81866i) q^{58} +(5.70978 + 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} -3.91326i q^{62} +2.33411 q^{64} +(7.85144 + 0.921441i) q^{65} +(-2.15623 + 1.24490i) q^{67} +(-21.2921 - 12.2930i) q^{68} +(8.36885 - 12.6894i) q^{70} -8.13849i q^{71} +(-1.56901 - 2.71761i) q^{73} +(2.43240 - 1.40435i) q^{74} +6.63886i q^{76} +(-12.4673 + 8.18578i) q^{77} +(-6.40252 + 11.0895i) q^{79} +(10.6517 - 14.2938i) q^{80} +(-8.37690 + 14.5092i) q^{82} -6.77241i q^{83} +(-10.9721 + 4.72679i) q^{85} +(1.08170 + 0.624518i) q^{86} +(-32.6339 + 18.8412i) q^{88} +(5.16513 - 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} -13.7986 q^{92} +(9.47093 - 5.46804i) q^{94} +(2.58673 + 1.92764i) q^{95} +14.7321 q^{97} +(7.14976 - 16.5034i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4}+O(q^{10}) $ 24 * q - 24 * q^4	$ 24 q - 24 q^{4} - 12 q^{10} - 36 q^{19} + 12 q^{25} - 60 q^{31} + 96 q^{40} - 24 q^{46} + 36 q^{49} + 48 q^{61} + 48 q^{64} - 48 q^{70} - 60 q^{79} - 72 q^{85} + 60 q^{91} + 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^4 - 12 * q^10 - 36 * q^19 + 12 * q^25 - 60 * q^31 + 96 * q^40 - 24 * q^46 + 36 * q^49 + 48 * q^61 + 48 * q^64 - 48 * q^70 - 60 * q^79 - 72 * q^85 + 60 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.28469	−	2.22514i	0.908411	−	1.57341i	0.0921382	−	0.995746i	$-0.470630\pi$
$2$	1.28469	−	2.22514i	0.908411	−	1.57341i	0.816272	−	0.577667i	$-0.196037\pi$
$3$		0			0
$3$		0			0
$4$	−2.30084	−	3.98517i	−1.15042	−	1.99259i
$5$	−2.22083	−	0.260635i	−0.993184	−	0.116560i
$5$	−2.22083	−	0.260635i	−0.993184	−	0.116560i
$6$		0			0
$7$	−2.64140	+	0.151755i	−0.998354	+	0.0573579i
$7$	−2.64140	+	0.151755i	−0.998354	+	0.0573579i
$8$	−6.68468			−2.36339
$9$		0			0
$10$	−3.43302	+	4.60682i	−1.08561	+	1.45680i
$11$	4.88189	−	2.81856i	1.47195	−	0.849828i	0.472442	−	0.881362i	$-0.343372\pi$
$11$	4.88189	−	2.81856i	1.47195	−	0.849828i	0.999503	+	0.0315336i	$0.0100391\pi$
$12$		0			0
$13$	−3.53537			−0.980535			−0.490267	−	0.871572i	$-0.663101\pi$
$13$	−3.53537			−0.980535			−0.490267	+	0.871572i	$0.663101\pi$
$14$	−3.05569	+	6.07244i	−0.816667	+	1.62293i
$15$		0			0
$16$	−3.98605	+	6.90403i	−0.996512	+	1.72601i
$17$	4.62703	−	2.67142i	1.12222	−	0.647914i	0.180253	−	0.983620i	$-0.442308\pi$
$17$	4.62703	−	2.67142i	1.12222	−	0.647914i	0.941967	+	0.335707i	$0.108975\pi$
$18$		0			0
$19$	−1.24942	−	0.721351i	−0.286636	−	0.165489i	0.349788	−	0.936829i	$-0.386254\pi$
$19$	−1.24942	−	0.721351i	−0.286636	−	0.165489i	−0.636424	+	0.771340i	$0.719587\pi$
$20$	4.07109	+	9.45005i	0.910323	+	2.11310i
$21$		0			0
$22$		−	14.4839i		−	3.08797i
$23$	1.49930	−	2.59686i	0.312626	−	0.541484i	−0.666304	−	0.745680i	$-0.732125\pi$
$23$	1.49930	−	2.59686i	0.312626	−	0.541484i	0.978930	+	0.204196i	$0.0654581\pi$
$24$		0			0
$25$	4.86414	+	1.15765i	0.972828	+	0.231530i
$26$	−4.54184	+	7.86670i	−0.890728	+	1.54279i
$27$		0			0
$28$	6.68220	+	10.1772i	1.26282	+	1.92332i
$29$		−	2.19404i		−	0.407423i	−0.979031	−	0.203712i	$-0.934699\pi$
$29$		−	2.19404i		−	0.407423i	0.979031	−	0.203712i	$-0.0653005\pi$
$30$		0			0
$31$	1.31899	−	0.761520i	0.236898	−	0.136773i	−0.376852	−	0.926273i	$-0.622994\pi$
$31$	1.31899	−	0.761520i	0.236898	−	0.136773i	0.613750	+	0.789500i	$0.289660\pi$
$32$	3.55696	+	6.16083i	0.628787	+	1.08909i
$33$		0			0
$34$		−	13.7277i		−	2.35429i
$35$	5.90563	+	0.351419i	0.998234	+	0.0594007i
$36$		0			0
$37$	0.946690	+	0.546572i	0.155635	+	0.0898558i	0.575795	−	0.817594i	$-0.304693\pi$
$37$	0.946690	+	0.546572i	0.155635	+	0.0898558i	−0.420160	+	0.907450i	$0.638026\pi$
$38$	−3.21022	+	1.85342i	−0.520766	+	0.300665i
$39$		0			0
$40$	14.8455	+	1.74226i	2.34728	+	0.275476i
$41$	−6.52058			−1.01834			−0.509172	−	0.860665i	$-0.670048\pi$
$41$	−6.52058			−1.01834			−0.509172	+	0.860665i	$0.670048\pi$
$42$		0			0
$43$			0.486125i			0.0741333i	0.999313	+	0.0370667i	$0.0118014\pi$
$43$			0.486125i			0.0741333i	−0.999313	+	0.0370667i	$0.988199\pi$
$44$	−22.4649	−	12.9701i	−3.38671	−	1.95532i
$45$		0			0
$46$	−3.85226	−	6.67231i	−0.567985	−	0.983779i
$47$	3.68608	+	2.12816i	0.537671	+	0.310424i	0.744134	−	0.668030i	$-0.232862\pi$
$47$	3.68608	+	2.12816i	0.537671	+	0.310424i	−0.206464	+	0.978454i	$0.566196\pi$
$48$		0			0
$49$	6.95394	−	0.801688i	0.993420	−	0.114527i
$50$	8.82483	−	9.33618i	1.24802	−	1.32034i
$51$		0			0
$52$	8.13432	+	14.0891i	1.12803	+	1.95380i
$53$	2.01102	+	3.48318i	0.276235	+	0.478452i	0.970446	−	0.241319i	$-0.0775800\pi$
$53$	2.01102	+	3.48318i	0.276235	+	0.478452i	−0.694211	+	0.719771i	$0.744247\pi$
$54$		0			0
$55$	−11.5764	+	4.98714i	−1.56097	+	0.672466i
$56$	17.6569	−	1.01443i	2.35950	−	0.135559i
$57$		0			0
$58$	−4.88206	−	2.81866i	−0.641046	−	0.370108i
$59$	5.70978	+	9.88963i	0.743350	+	1.28752i	0.950962	+	0.309309i	$0.100098\pi$
$59$	5.70978	+	9.88963i	0.743350	+	1.28752i	−0.207612	+	0.978211i	$0.566569\pi$
$60$		0			0
$61$	6.06957	+	3.50427i	0.777129	+	0.448676i	0.835412	−	0.549624i	$-0.185229\pi$
$61$	6.06957	+	3.50427i	0.777129	+	0.448676i	−0.0582826	+	0.998300i	$0.518562\pi$
$62$		−	3.91326i		−	0.496984i
$63$		0			0
$64$	2.33411			0.291764
$65$	7.85144	+	0.921441i	0.973851	+	0.114291i
$66$		0			0
$67$	−2.15623	+	1.24490i	−0.263425	+	0.152089i	−0.625896	−	0.779907i	$-0.715267\pi$
$67$	−2.15623	+	1.24490i	−0.263425	+	0.152089i	0.362471	+	0.931995i	$0.381933\pi$
$68$	−21.2921	−	12.2930i	−2.58205	−	1.49075i
$69$		0			0
$70$	8.36885	−	12.6894i	1.00027	−	1.51667i
$71$		−	8.13849i		−	0.965861i	−0.875659	−	0.482930i	$-0.839572\pi$
$71$		−	8.13849i		−	0.965861i	0.875659	−	0.482930i	$-0.160428\pi$
$72$		0			0
$73$	−1.56901	−	2.71761i	−0.183639	−	0.318072i	0.759478	−	0.650533i	$-0.225454\pi$
$73$	−1.56901	−	2.71761i	−0.183639	−	0.318072i	−0.943117	+	0.332461i	$0.892121\pi$
$74$	2.43240	−	1.40435i	0.282761	−	0.163252i
$75$		0			0
$76$			6.63886i			0.761529i
$77$	−12.4673	+	8.18578i	−1.42078	+	0.932856i
$78$		0			0
$79$	−6.40252	+	11.0895i	−0.720340	+	1.24766i	0.240524	+	0.970643i	$0.422681\pi$
$79$	−6.40252	+	11.0895i	−0.720340	+	1.24766i	−0.960864	+	0.277022i	$0.910653\pi$
$80$	10.6517	−	14.2938i	1.19090	−	1.59809i
$81$		0			0
$82$	−8.37690	+	14.5092i	−0.925074	+	1.60228i
$83$		−	6.77241i		−	0.743368i	−0.928359	−	0.371684i	$-0.878780\pi$
$83$		−	6.77241i		−	0.743368i	0.928359	−	0.371684i	$-0.121220\pi$
$84$		0			0
$85$	−10.9721	+	4.72679i	−1.19009	+	0.512692i
$86$	1.08170	+	0.624518i	0.116642	+	0.0673435i
$87$		0			0
$88$	−32.6339	+	18.8412i	−3.47878	+	2.00848i
$89$	5.16513	−	8.94627i	0.547503	−	0.948303i	−0.450942	−	0.892553i	$-0.648912\pi$
$89$	5.16513	−	8.94627i	0.547503	−	0.948303i	0.998445	−	0.0557494i	$-0.0177548\pi$
$90$		0			0
$91$	9.33831	−	0.536509i	0.978921	−	0.0562414i
$92$	−13.7986			−1.43860
$93$		0			0
$94$	9.47093	−	5.46804i	0.976852	−	0.563985i
$95$	2.58673	+	1.92764i	0.265393	+	0.197771i
$96$		0			0
$97$	14.7321			1.49582			0.747908	−	0.663802i	$-0.231058\pi$
$97$	14.7321			1.49582			0.747908	+	0.663802i	$0.231058\pi$
$98$	7.14976	−	16.5034i	0.722235	−	1.66710i
$99$		0			0
$100$	−6.57817	−	22.0480i	−0.657817	−	2.20480i
$101$	−7.46683	−	12.9329i	−0.742977	−	1.28687i	−0.951134	−	0.308779i	$-0.900080\pi$
$101$	−7.46683	−	12.9329i	−0.742977	−	1.28687i	0.208157	−	0.978095i	$-0.433254\pi$
$102$		0			0
$103$	1.95755	−	3.39058i	0.192883	−	0.334084i	−0.753321	−	0.657653i	$-0.771549\pi$
$103$	1.95755	−	3.39058i	0.192883	−	0.334084i	0.946205	+	0.323569i	$0.104883\pi$
$104$	23.6328			2.31739
$105$		0			0
$106$	10.3341			1.00374
$107$	−7.41102	+	12.8363i	−0.716450	+	1.24093i	0.245948	+	0.969283i	$0.420901\pi$
$107$	−7.41102	+	12.8363i	−0.716450	+	1.24093i	−0.962398	+	0.271645i	$0.912432\pi$
$108$		0			0
$109$	−5.51932	−	9.55974i	−0.528655	−	0.915657i	−0.999442	−	0.0334099i	$-0.989363\pi$
$109$	−5.51932	−	9.55974i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$110$	−3.77500	+	32.1662i	−0.359932	+	3.06692i
$111$		0			0
$112$	9.48101	−	18.8412i	0.895871	−	1.78032i
$113$	7.54314			0.709599			0.354799	−	0.934942i	$-0.384549\pi$
$113$	7.54314			0.709599			0.354799	+	0.934942i	$0.384549\pi$
$114$		0			0
$115$	−4.00652	+	5.37641i	−0.373610	+	0.501353i
$116$	−8.74363	+	5.04814i	−0.811826	+	0.468708i
$117$		0			0
$118$	29.3411			2.70107
$119$	−11.8164	+	7.75844i	−1.08321	+	0.711215i
$120$		0			0
$121$	10.3886	−	17.9935i	0.944415	−	1.63577i
$122$	15.5950	−	9.00378i	1.41191	−	0.815164i
$123$		0			0
$124$	−6.06957	−	3.50427i	−0.545064	−	0.314693i
$125$	−10.5007	−	3.83871i	−0.939210	−	0.343344i
$126$		0			0
$127$			3.93715i			0.349366i	0.984625	+	0.174683i	$0.0558900\pi$
$127$			3.93715i			0.349366i	−0.984625	+	0.174683i	$0.944110\pi$
$128$	−4.11531	+	7.12793i	−0.363746	+	0.630026i
$129$		0			0
$130$	12.1370	−	16.2868i	1.06448	−	1.42845i
$131$	1.97399	−	3.41906i	0.172469	−	0.298724i	−0.766814	−	0.641870i	$-0.778159\pi$
$131$	1.97399	−	3.41906i	0.172469	−	0.298724i	0.939282	+	0.343145i	$0.111492\pi$
$132$		0			0
$133$	3.40967	+	1.71577i	0.295656	+	0.148776i
$134$			6.39722i			0.552635i
$135$		0			0
$136$	−30.9302	+	17.8576i	−2.65225	+	1.53127i
$137$	2.83062	+	4.90279i	0.241837	+	0.418873i	0.961237	−	0.275722i	$-0.0889169\pi$
$137$	2.83062	+	4.90279i	0.241837	+	0.418873i	−0.719401	+	0.694595i	$0.755584\pi$
$138$		0			0
$139$			23.3015i			1.97640i	0.153158	+	0.988202i	$0.451056\pi$
$139$			23.3015i			1.97640i	−0.153158	+	0.988202i	$0.548944\pi$
$140$	−12.1874	−	24.3435i	−1.03003	−	2.05740i
$141$		0			0
$142$	−18.1093	−	10.4554i	−1.51970	−	0.877398i
$143$	−17.2593	+	9.96465i	−1.44329	+	0.833286i
$144$		0			0
$145$	−0.571844	+	4.87259i	−0.0474891	+	0.404646i
$146$	−8.06275			−0.667278
$147$		0			0
$148$		−	5.03030i		−	0.413488i
$149$	4.04926	+	2.33784i	0.331728	+	0.191523i	0.656608	−	0.754232i	$-0.271991\pi$
$149$	4.04926	+	2.33784i	0.331728	+	0.191523i	−0.324880	+	0.945755i	$0.605324\pi$
$150$		0			0
$151$	−0.930426	−	1.61155i	−0.0757170	−	0.131146i	0.825681	−	0.564138i	$-0.190791\pi$
$151$	−0.930426	−	1.61155i	−0.0757170	−	0.131146i	−0.901398	+	0.432992i	$0.857458\pi$
$152$	8.35196	+	4.82201i	0.677433	+	0.391116i
$153$		0			0
$154$	2.19799	+	38.2576i	0.177119	+	3.08289i
$155$	−3.12773	+	1.34743i	−0.251225	+	0.108228i
$156$		0			0
$157$	3.28398	+	5.68802i	0.262090	+	0.453953i	0.966797	−	0.255545i	$-0.0822549\pi$
$157$	3.28398	+	5.68802i	0.262090	+	0.453953i	−0.704707	+	0.709498i	$0.748922\pi$
$158$	16.4505	+	28.4930i	1.30873	+	2.26678i
$159$		0			0
$160$	−6.29365	−	14.6092i	−0.497557	−	1.15496i
$161$	−3.56616	+	7.08687i	−0.281053	+	0.558524i
$162$		0			0
$163$	16.2598	+	9.38762i	1.27357	+	0.735295i	0.975658	−	0.219299i	$-0.0703770\pi$
$163$	16.2598	+	9.38762i	1.27357	+	0.735295i	0.297910	+	0.954594i	$0.403710\pi$
$164$	15.0028	+	25.9856i	1.17152	+	2.02914i
$165$		0			0
$166$	−15.0696	−	8.70042i	−1.16963	−	0.675284i
$167$			4.80581i			0.371884i	0.982561	+	0.185942i	$0.0595337\pi$
$167$			4.80581i			0.371884i	−0.982561	+	0.185942i	$0.940466\pi$
$168$		0			0
$169$	−0.501166			−0.0385512
$170$	−3.57793	+	30.4869i	−0.274415	+	2.33824i
$171$		0			0
$172$	1.93729	−	1.11849i	0.147717	−	0.0852844i
$173$	−2.91312	−	1.68189i	−0.221480	−	0.127872i	0.385155	−	0.922852i	$-0.374148\pi$
$173$	−2.91312	−	1.68189i	−0.221480	−	0.127872i	−0.606635	+	0.794980i	$0.707481\pi$
$174$		0			0
$175$	−13.0238	−	2.31966i	−0.984506	−	0.175350i
$176$			44.9396i			3.38745i
$177$		0			0
$178$	−13.2712	−	22.9863i	−0.994715	−	1.72290i
$179$	9.63782	−	5.56440i	0.720365	−	0.415903i	−0.0945223	−	0.995523i	$-0.530132\pi$
$179$	9.63782	−	5.56440i	0.720365	−	0.415903i	0.814887	+	0.579620i	$0.196799\pi$
$180$		0			0
$181$		−	2.19549i		−	0.163190i	−0.996666	−	0.0815949i	$-0.973999\pi$
$181$		−	2.19549i		−	0.163190i	0.996666	−	0.0815949i	$-0.0260014\pi$
$182$	10.8030	−	21.4683i	0.800771	−	1.59134i
$183$		0			0
$184$	−10.0223	+	17.3592i	−0.738857	+	1.27974i
$185$	−1.95998	−	1.46058i	−0.144100	−	0.107384i
$186$		0			0
$187$	15.0591	−	26.0831i	1.10123	−	1.90739i
$188$		−	19.5862i		−	1.42847i
$189$		0			0
$190$	7.61241	−	3.27943i	0.552262	−	0.237915i
$191$	8.62053	+	4.97707i	0.623760	+	0.360128i	0.778331	−	0.627854i	$-0.216066\pi$
$191$	8.62053	+	4.97707i	0.623760	+	0.360128i	−0.154572	+	0.987982i	$0.549400\pi$
$192$		0			0
$193$	−21.6068	+	12.4747i	−1.55529	+	0.897948i	−0.557594	+	0.830114i	$0.688275\pi$
$193$	−21.6068	+	12.4747i	−1.55529	+	0.897948i	−0.997697	+	0.0678339i	$0.978391\pi$
$194$	18.9261	−	32.7810i	1.35882	−	2.35354i
$195$		0			0
$196$	−19.1948	−	25.8681i	−1.37105	−	1.84772i
$197$	19.1023			1.36098			0.680492	−	0.732755i	$-0.261766\pi$
$197$	19.1023			1.36098			0.680492	+	0.732755i	$0.261766\pi$
$198$		0			0
$199$	1.59632	−	0.921633i	0.113160	−	0.0653329i	−0.442352	−	0.896842i	$-0.645856\pi$
$199$	1.59632	−	0.921633i	0.113160	−	0.0653329i	0.555512	+	0.831509i	$0.312522\pi$
$200$	−32.5152	−	7.73853i	−2.29917	−	0.547197i
$201$		0			0
$202$	−38.3701			−2.69971
$203$	0.332956	+	5.79533i	0.0233689	+	0.406753i
$204$		0			0
$205$	14.4811	+	1.69949i	1.01140	+	0.118698i
$206$	−5.02968	−	8.71167i	−0.350435	−	0.606971i
$207$		0			0
$208$	14.0921	−	24.4083i	0.977114	−	1.69241i
$209$	−8.13269			−0.562550
$210$		0			0
$211$	−9.77713			−0.673085			−0.336543	−	0.941668i	$-0.609258\pi$
$211$	−9.77713			−0.673085			−0.336543	+	0.941668i	$0.609258\pi$
$212$	9.25406	−	16.0285i	0.635571	−	1.10084i
$213$		0			0
$214$	19.0417	+	32.9811i	1.30166	+	2.25454i
$215$	0.126701	−	1.07960i	0.00864094	−	0.0736280i
$216$		0			0
$217$	−3.36841	+	2.21164i	−0.228663	+	0.150136i
$218$	−28.3624			−1.92094
$219$		0			0
$220$	46.5102	+	34.6595i	3.13571	+	2.33674i
$221$	−16.3583	+	9.44444i	−1.10038	+	0.635302i
$222$		0			0
$223$	−7.84782			−0.525529			−0.262765	−	0.964860i	$-0.584634\pi$
$223$	−7.84782			−0.525529			−0.262765	+	0.964860i	$0.584634\pi$
$224$	−10.3303	−	15.7334i	−0.690220	−	1.05123i
$225$		0			0
$226$	9.69057	−	16.7846i	0.644607	−	1.11649i
$227$	−0.475865	+	0.274741i	−0.0315843	+	0.0182352i	−0.515709	−	0.856764i	$-0.672471\pi$
$227$	−0.475865	+	0.274741i	−0.0315843	+	0.0182352i	0.484125	+	0.874999i	$0.339138\pi$
$228$		0			0
$229$	−18.5833	−	10.7291i	−1.22802	−	0.708998i	−0.261406	−	0.965229i	$-0.584186\pi$
$229$	−18.5833	−	10.7291i	−1.22802	−	0.708998i	−0.966616	+	0.256231i	$0.917519\pi$
$230$	6.81617	+	15.8221i	0.449445	+	1.04328i
$231$		0			0
$232$			14.6665i			0.962902i
$233$	9.38319	−	16.2522i	0.614713	−	1.06471i	−0.375722	−	0.926733i	$-0.622605\pi$
$233$	9.38319	−	16.2522i	0.614713	−	1.06471i	0.990435	−	0.137982i	$-0.0440615\pi$
$234$		0			0
$235$	−7.63148	−	5.68700i	−0.497823	−	0.370979i
$236$	26.2746	−	45.5089i	1.71033	−	2.96238i
$237$		0			0
$238$	2.08325	+	36.2604i	0.135037	+	2.35041i
$239$		−	7.35866i		−	0.475992i	−0.971266	−	0.237996i	$-0.923509\pi$
$239$		−	7.35866i		−	0.475992i	0.971266	−	0.237996i	$-0.0764905\pi$
$240$		0			0
$241$	23.8467	−	13.7679i	1.53610	−	0.886868i	0.537040	−	0.843557i	$-0.319543\pi$
$241$	23.8467	−	13.7679i	1.53610	−	0.886868i	0.999062	−	0.0433114i	$-0.0137908\pi$
$242$	−26.6921	−	46.2321i	−1.71583	−	2.97191i
$243$		0			0
$244$		−	32.2511i		−	2.06466i
$245$	−15.6524	−	0.0320301i	−0.999998	−	0.00204633i
$246$		0			0
$247$	4.41715	+	2.55024i	0.281057	+	0.162268i
$248$	−8.81704	+	5.09052i	−0.559883	+	0.323248i
$249$		0			0
$250$	−22.0318	+	18.4340i	−1.39341	+	1.16587i
$251$	−22.4204			−1.41516			−0.707582	−	0.706631i	$-0.750214\pi$
$251$	−22.4204			−1.41516			−0.707582	+	0.706631i	$0.750214\pi$
$252$		0			0
$253$		−	16.9035i		−	1.06271i
$254$	8.76072	+	5.05801i	0.549697	+	0.317368i
$255$		0			0
$256$	12.9079	+	22.3571i	0.806743	+	1.39732i
$257$	−14.8328	−	8.56373i	−0.925246	−	0.534191i	−0.0399409	−	0.999202i	$-0.512717\pi$
$257$	−14.8328	−	8.56373i	−0.925246	−	0.534191i	−0.885305	+	0.465011i	$0.846050\pi$
$258$		0			0
$259$	−2.58353	−	1.30005i	−0.160533	−	0.0807810i
$260$	−14.3928	−	33.4094i	−0.892604	−	2.07196i
$261$		0			0
$262$	−5.07193	−	8.78483i	−0.313345	−	0.542729i
$263$	0.808821	+	1.40092i	0.0498741	+	0.0863844i	0.889885	−	0.456186i	$-0.150785\pi$
$263$	0.808821	+	1.40092i	0.0498741	+	0.0863844i	−0.840011	+	0.542570i	$0.817451\pi$
$264$		0			0
$265$	−3.55828	−	8.25969i	−0.218583	−	0.507389i
$266$	8.19819	−	5.38278i	0.502664	−	0.330040i
$267$		0			0
$268$	9.92226	+	5.72862i	0.606099	+	0.349931i
$269$	5.84048	+	10.1160i	0.356101	+	0.616784i	0.987306	−	0.158832i	$-0.0507727\pi$
$269$	5.84048	+	10.1160i	0.356101	+	0.616784i	−0.631205	+	0.775616i	$0.717439\pi$
$270$		0			0
$271$	5.05562	+	2.91886i	0.307107	+	0.177308i	0.645631	−	0.763649i	$-0.276594\pi$
$271$	5.05562	+	2.91886i	0.307107	+	0.177308i	−0.338524	+	0.940958i	$0.609928\pi$
$272$			42.5936i			2.58261i
$273$		0			0
$274$	14.5459			0.878748
$275$	27.0091	−	8.05835i	1.62871	−	0.485937i
$276$		0			0
$277$	14.3760	−	8.29998i	0.863770	−	0.498698i	−0.00150328	−	0.999999i	$-0.500479\pi$
$277$	14.3760	−	8.29998i	0.863770	−	0.498698i	0.865273	+	0.501301i	$0.167145\pi$
$278$	51.8491	+	29.9351i	3.10970	+	1.79539i
$279$		0			0
$280$	−39.4773	−	2.34913i	−2.35922	−	0.140387i
$281$		−	20.4255i		−	1.21848i	−0.792984	−	0.609242i	$-0.791474\pi$
$281$		−	20.4255i		−	1.21848i	0.792984	−	0.609242i	$-0.208526\pi$
$282$		0			0
$283$	−3.31643	−	5.74423i	−0.197141	−	0.341459i	0.750459	−	0.660917i	$-0.229832\pi$
$283$	−3.31643	−	5.74423i	−0.197141	−	0.341459i	−0.947600	+	0.319458i	$0.896499\pi$
$284$	−32.4333	+	18.7254i	−1.92456	+	1.11115i
$285$		0			0
$286$			51.2058i			3.02786i
$287$	17.2234	−	0.989529i	1.01667	−	0.0584100i
$288$		0			0
$289$	5.77293	−	9.99901i	0.339584	−	0.588177i
$290$	10.1076	+	7.53218i	0.593536	+	0.442305i
$291$		0			0
$292$	−7.22008	+	12.5055i	−0.422523	+	0.731832i
$293$		−	16.3716i		−	0.956437i	−0.878241	−	0.478219i	$-0.841283\pi$
$293$		−	16.3716i		−	0.956437i	0.878241	−	0.478219i	$-0.158717\pi$
$294$		0			0
$295$	−10.1028	−	23.4513i	−0.588210	−	1.36539i
$296$	−6.32832	−	3.65366i	−0.367826	−	0.212365i
$297$		0			0
$298$	10.4040	−	6.00678i	0.602690	−	0.347963i
$299$	−5.30058	+	9.18087i	−0.306540	+	0.530944i
$300$		0			0
$301$	−0.0737717	−	1.28405i	−0.00425213	−	0.0740113i
$302$	−4.78122			−0.275129
$303$		0			0
$304$	9.96047	−	5.75068i	0.571272	−	0.329824i
$305$	−12.5661	−	9.36432i	−0.719535	−	0.536199i
$306$		0			0
$307$	−25.5071			−1.45576			−0.727882	−	0.685702i	$-0.759495\pi$
$307$	−25.5071			−1.45576			−0.727882	+	0.685702i	$0.759495\pi$
$308$	61.3069	+	30.8500i	3.49329	+	1.75784i
$309$		0			0
$310$	−1.01993	+	8.69067i	−0.0579282	+	0.493597i
$311$	15.5180	+	26.8780i	0.879946	+	1.52411i	0.851399	+	0.524519i	$0.175755\pi$
$311$	15.5180	+	26.8780i	0.879946	+	1.52411i	0.0285476	+	0.999592i	$0.490912\pi$
$312$		0			0
$313$	7.52345	−	13.0310i	0.425251	−	0.736556i	−0.571193	−	0.820816i	$-0.693519\pi$
$313$	7.52345	−	13.0310i	0.425251	−	0.736556i	0.996444	+	0.0842599i	$0.0268526\pi$
$314$	16.8755			0.952341
$315$		0			0
$316$	58.9247			3.31477
$317$	−7.79061	+	13.4937i	−0.437564	+	0.757884i	−0.997501	−	0.0706518i	$-0.977492\pi$
$317$	−7.79061	+	13.4937i	−0.437564	+	0.757884i	0.559937	+	0.828535i	$0.310825\pi$
$318$		0			0
$319$	−6.18404	−	10.7111i	−0.346240	−	0.599705i
$320$	−5.18365	−	0.608351i	−0.289775	−	0.0340079i
$321$		0			0
$322$	11.1879	+	17.0396i	0.623477	+	0.949581i
$323$	−7.70812			−0.428891
$324$		0			0
$325$	−17.1965	−	4.09272i	−0.953892	−	0.227023i
$326$	41.7776	−	24.1203i	2.31385	−	1.33590i
$327$		0			0
$328$	43.5880			2.40675
$329$	−10.0594	−	5.06194i	−0.554591	−	0.279074i
$330$		0			0
$331$	−6.83411	+	11.8370i	−0.375637	+	0.650622i	−0.990422	−	0.138073i	$-0.955909\pi$
$331$	−6.83411	+	11.8370i	−0.375637	+	0.650622i	0.614785	+	0.788694i	$0.289243\pi$
$332$	−26.9892	+	15.5822i	−1.48123	+	0.855186i
$333$		0			0
$334$	10.6936	+	6.17395i	0.585128	+	0.337824i
$335$	5.11307	−	2.20271i	0.279357	−	0.120347i
$336$		0			0
$337$			22.8443i			1.24441i	0.782855	+	0.622204i	$0.213763\pi$
$337$			22.8443i			1.24441i	−0.782855	+	0.622204i	$0.786237\pi$
$338$	−0.643841	+	1.11516i	−0.0350203	+	0.0606570i
$339$		0			0
$340$	44.0821	+	32.8501i	2.39069	+	1.78155i
$341$	4.29278	−	7.43531i	0.232467	−	0.402645i
$342$		0			0
$343$	−18.2464	+	3.17287i	−0.985216	+	0.171319i
$344$		−	3.24959i		−	0.175206i
$345$		0			0
$346$	−7.48488	+	4.32140i	−0.402390	+	0.232320i
$347$	9.81241	+	16.9956i	0.526758	+	0.912372i	0.999514	+	0.0311781i	$0.00992591\pi$
$347$	9.81241	+	16.9956i	0.526758	+	0.912372i	−0.472756	+	0.881193i	$0.656741\pi$
$348$		0			0
$349$		−	6.14050i		−	0.328693i	−0.986403	−	0.164347i	$-0.947448\pi$
$349$		−	6.14050i		−	0.328693i	0.986403	−	0.164347i	$-0.0525516\pi$
$350$	−21.8931	+	25.9998i	−1.17023	+	1.38975i
$351$		0			0
$352$	34.7293	+	20.0510i	1.85108	+	1.06872i
$353$	20.7882	−	12.0021i	1.10644	−	0.638805i	0.168537	−	0.985695i	$-0.446096\pi$
$353$	20.7882	−	12.0021i	1.10644	−	0.638805i	0.937906	+	0.346890i	$0.112762\pi$
$354$		0			0
$355$	−2.12118	+	18.0742i	−0.112580	+	0.959277i
$356$	−47.5366			−2.51943
$357$		0			0
$358$		−	28.5940i		−	1.51124i
$359$	14.6798	+	8.47541i	0.774773	+	0.447315i	0.834575	−	0.550895i	$-0.185714\pi$
$359$	14.6798	+	8.47541i	0.774773	+	0.447315i	−0.0598018	+	0.998210i	$0.519047\pi$
$360$		0			0
$361$	−8.45930	−	14.6519i	−0.445227	−	0.771155i
$362$	−4.88529	−	2.82052i	−0.256765	−	0.148243i
$363$		0			0
$364$	−23.6240	−	35.9803i	−1.23824	−	1.88588i
$365$	2.77620	+	6.44427i	0.145313	+	0.337308i
$366$		0			0
$367$	17.5018	+	30.3140i	0.913587	+	1.58238i	0.808956	+	0.587869i	$0.200033\pi$
$367$	17.5018	+	30.3140i	0.913587	+	1.58238i	0.104631	+	0.994511i	$0.466634\pi$
$368$	11.9526	+	20.7024i	0.623070	+	1.07919i
$369$		0			0
$370$	−5.76796	+	2.48484i	−0.299862	+	0.129181i
$371$	−5.84048	−	8.89529i	−0.303223	−	0.461820i
$372$		0			0
$373$	5.18881	+	2.99576i	0.268667	+	0.155115i	0.628282	−	0.777986i	$-0.283759\pi$
$373$	5.18881	+	2.99576i	0.268667	+	0.155115i	−0.359615	+	0.933101i	$0.617092\pi$
$374$	−38.6924	−	67.0173i	−2.00074	−	3.46538i
$375$		0			0
$376$	−24.6403	−	14.2261i	−1.27073	−	0.733655i
$377$			7.75675i			0.399493i
$378$		0			0
$379$	−3.12842			−0.160696			−0.0803481	−	0.996767i	$-0.525603\pi$
$379$	−3.12842			−0.160696			−0.0803481	+	0.996767i	$0.525603\pi$
$380$	1.73032	−	14.7437i	0.0887635	−	0.756338i
$381$		0			0
$382$	22.1494	−	12.7879i	1.13326	−	0.654288i
$383$	−14.6929	−	8.48295i	−0.750772	−	0.433459i	0.0752006	−	0.997168i	$-0.476040\pi$
$383$	−14.6929	−	8.48295i	−0.750772	−	0.433459i	−0.825973	+	0.563710i	$0.809374\pi$
$384$		0			0
$385$	29.8211	−	14.9298i	1.51983	−	0.760893i
$386$			64.1043i			3.26282i
$387$		0			0
$388$	−33.8961	−	58.7099i	−1.72082	−	2.98054i
$389$	−0.389255	+	0.224737i	−0.0197360	+	0.0113946i	−0.509836	−	0.860272i	$-0.670294\pi$
$389$	−0.389255	+	0.224737i	−0.0197360	+	0.0113946i	0.490100	+	0.871666i	$0.336960\pi$
$390$		0			0
$391$		−	16.0210i		−	0.810218i
$392$	−46.4849	+	5.35903i	−2.34784	+	0.270672i
$393$		0			0
$394$	24.5405	−	42.5054i	1.23633	−	2.14139i
$395$	17.1092	−	22.9591i	0.860857	−	1.15520i
$396$		0			0
$397$	11.3663	−	19.6870i	0.570459	−	0.988064i	−0.426060	−	0.904695i	$-0.640099\pi$
$397$	11.3663	−	19.6870i	0.570459	−	0.988064i	0.996519	−	0.0833689i	$-0.0265680\pi$
$398$		−	4.73604i		−	0.237396i
$399$		0			0
$400$	−27.3811	+	28.9677i	−1.36906	+	1.44839i
$401$	8.41308	+	4.85729i	0.420129	+	0.242562i	0.695132	−	0.718882i	$-0.255346\pi$
$401$	8.41308	+	4.85729i	0.420129	+	0.242562i	−0.275004	+	0.961443i	$0.588679\pi$
$402$		0			0
$403$	−4.66312	+	2.69225i	−0.232287	+	0.134111i
$404$	−34.3599	+	59.5132i	−1.70947	+	2.96089i
$405$		0			0
$406$	13.3232	+	6.70431i	0.661219	+	0.332729i
$407$	6.16218			0.305448
$408$		0			0
$409$	3.51628	−	2.03013i	0.173869	−	0.100383i	−0.410540	−	0.911843i	$-0.634660\pi$
$409$	3.51628	−	2.03013i	0.173869	−	0.100383i	0.584409	+	0.811459i	$0.301326\pi$
$410$	22.3853	−	30.0391i	1.10553	−	1.48353i
$411$		0			0
$412$	−18.0161			−0.887587
$413$	−16.5826	−	25.2559i	−0.815976	−	1.24276i
$414$		0			0
$415$	−1.76513	+	15.0403i	−0.0866467	+	0.738301i
$416$	−12.5752	−	21.7808i	−0.616548	−	1.06789i
$417$		0			0
$418$	−10.4480	+	18.0964i	−0.511026	+	0.885124i
$419$	−20.9314			−1.02257			−0.511283	−	0.859412i	$-0.670830\pi$
$419$	−20.9314			−1.02257			−0.511283	+	0.859412i	$0.670830\pi$
$420$		0			0
$421$	−19.7795			−0.963992			−0.481996	−	0.876173i	$-0.660088\pi$
$421$	−19.7795			−0.963992			−0.481996	+	0.876173i	$0.660088\pi$
$422$	−12.5605	+	21.7555i	−0.611438	+	1.05904i
$423$		0			0
$424$	−13.4430	−	23.2840i	−0.652851	−	1.13077i
$425$	25.5991	−	7.63766i	1.24174	−	0.370481i
$426$		0			0
$427$	−16.5639	−	8.33508i	−0.801585	−	0.403363i
$428$	68.2062			3.29687
$429$		0			0
$430$	−2.23949	−	1.66887i	−0.107998	−	0.0804802i
$431$	9.23148	−	5.32980i	0.444665	−	0.256727i	−0.260910	−	0.965363i	$-0.584022\pi$
$431$	9.23148	−	5.32980i	0.444665	−	0.256727i	0.705574	+	0.708636i	$0.250689\pi$
$432$		0			0
$433$	21.2351			1.02050			0.510248	−	0.860028i	$-0.329554\pi$
$433$	21.2351			1.02050			0.510248	+	0.860028i	$0.329554\pi$
$434$	0.593855	+	10.3365i	0.0285060	+	0.496166i
$435$		0			0
$436$	−25.3981	+	43.9908i	−1.21635	+	2.10678i
$437$	−3.74650	+	2.16304i	−0.179220	+	0.103472i
$438$		0			0
$439$	18.5707	+	10.7218i	0.886333	+	0.511725i	0.872741	−	0.488183i	$-0.162340\pi$
$439$	18.5707	+	10.7218i	0.886333	+	0.511725i	0.0135918	+	0.999908i	$0.495673\pi$
$440$	77.3849	−	33.3375i	3.68918	−	1.58930i
$441$		0			0
$442$			48.5326i			2.30846i
$443$	0.0854851	−	0.148064i	0.00406152	−	0.00703475i	−0.863988	−	0.503513i	$-0.832041\pi$
$443$	0.0854851	−	0.148064i	0.00406152	−	0.00703475i	0.868049	+	0.496478i	$0.165374\pi$
$444$		0			0
$445$	−13.8026	+	18.5219i	−0.654305	+	0.878022i
$446$	−10.0820	+	17.4625i	−0.477396	+	0.826874i
$447$		0			0
$448$	−6.16531	+	0.354212i	−0.291283	+	0.0167350i
$449$		−	9.38752i		−	0.443025i	−0.975158	−	0.221512i	$-0.928901\pi$
$449$		−	9.38752i		−	0.443025i	0.975158	−	0.221512i	$-0.0710993\pi$
$450$		0			0
$451$	−31.8328	+	18.3786i	−1.49895	+	0.865417i
$452$	−17.3556	−	30.0607i	−0.816337	−	1.41394i
$453$		0			0
$454$			1.41182i			0.0662602i
$455$	−20.8786	−	1.24240i	−0.978804	−	0.0582445i
$456$		0			0
$457$	−14.6293	−	8.44623i	−0.684330	−	0.395098i	0.117155	−	0.993114i	$-0.462623\pi$
$457$	−14.6293	−	8.44623i	−0.684330	−	0.395098i	−0.801484	+	0.598016i	$0.795956\pi$
$458$	−47.7475	+	27.5670i	−2.23110	+	1.28812i
$459$		0			0
$460$	30.6443	+	3.59640i	1.42880	+	0.167683i
$461$	31.0360			1.44549			0.722746	−	0.691113i	$-0.242880\pi$
$461$	31.0360			1.44549			0.722746	+	0.691113i	$0.242880\pi$
$462$		0			0
$463$			11.9434i			0.555055i	0.960718	+	0.277528i	$0.0895150\pi$
$463$			11.9434i			0.555055i	−0.960718	+	0.277528i	$0.910485\pi$
$464$	15.1477	+	8.74555i	0.703216	+	0.406002i
$465$		0			0
$466$	−24.1089	−	41.7579i	−1.11682	−	1.93440i
$467$	−29.9304	−	17.2803i	−1.38501	−	0.799638i	−0.392265	−	0.919852i	$-0.628308\pi$
$467$	−29.9304	−	17.2803i	−1.38501	−	0.799638i	−0.992748	+	0.120215i	$0.961642\pi$
$468$		0			0
$469$	5.50653	−	3.61549i	0.254268	−	0.166948i
$470$	−22.4584	+	9.67512i	−1.03593	+	0.446280i
$471$		0			0
$472$	−38.1681	−	66.1090i	−1.75683	−	3.04292i
$473$	1.37017	+	2.37321i	0.0630006	+	0.109120i
$474$		0			0
$475$	−5.24227	−	4.95514i	−0.240532	−	0.227357i
$476$	58.1064	+	29.2395i	2.66330	+	1.34019i
$477$		0			0
$478$	−16.3741	−	9.45357i	−0.748932	−	0.432396i
$479$	−1.48615	−	2.57409i	−0.0679040	−	0.117613i	0.830074	−	0.557653i	$-0.188298\pi$
$479$	−1.48615	−	2.57409i	−0.0679040	−	0.117613i	−0.897978	+	0.440039i	$0.854964\pi$
$480$		0			0
$481$	−3.34690	−	1.93233i	−0.152605	−	0.0881068i
$482$		−	70.7498i		−	3.22256i
$483$		0			0
$484$	−95.6097			−4.34589
$485$	−32.7174	−	3.83970i	−1.48562	−	0.174352i
$486$		0			0
$487$	19.6695	−	11.3562i	0.891310	−	0.514598i	0.0169394	−	0.999857i	$-0.494608\pi$
$487$	19.6695	−	11.3562i	0.891310	−	0.514598i	0.874371	+	0.485258i	$0.161274\pi$
$488$	−40.5732	−	23.4249i	−1.83666	−	1.06040i
$489$		0			0
$490$	−20.1798	+	34.7878i	−0.911628	+	1.57155i
$491$			13.0036i			0.586846i	0.955983	+	0.293423i	$0.0947944\pi$
$491$			13.0036i			0.586846i	−0.955983	+	0.293423i	$0.905206\pi$
$492$		0			0
$493$	−5.86120	−	10.1519i	−0.263975	−	0.457219i
$494$	11.3493	−	6.55253i	0.510630	−	0.294812i
$495$		0			0
$496$			12.1418i			0.545184i
$497$	1.23505	+	21.4970i	0.0553997	+	0.964271i
$498$		0			0
$499$	10.8039	−	18.7129i	0.483648	−	0.837702i	−0.516176	−	0.856483i	$-0.672645\pi$
$499$	10.8039	−	18.7129i	0.483648	−	0.837702i	0.999824	+	0.0187802i	$0.00597826\pi$
$500$	8.86249	+	50.6793i	0.396343	+	2.26645i
$501$		0			0
$502$	−28.8032	+	49.8886i	−1.28555	+	2.22664i
$503$			32.4125i			1.44520i	0.691265	+	0.722601i	$0.257054\pi$
$503$			32.4125i			1.44520i	−0.691265	+	0.722601i	$0.742946\pi$
$504$		0			0
$505$	13.2118	+	30.6679i	0.587915	+	1.36470i
$506$	−37.6126	−	21.7157i	−1.67209	−	0.965379i
$507$		0			0
$508$	15.6902	−	9.05875i	0.696141	−	0.401917i
$509$	−18.2802	+	31.6622i	−0.810255	+	1.40340i	0.102430	+	0.994740i	$0.467338\pi$
$509$	−18.2802	+	31.6622i	−0.810255	+	1.40340i	−0.912685	+	0.408663i	$0.865995\pi$
$510$		0			0
$511$	4.55679	+	6.94017i	0.201580	+	0.307015i
$512$	49.8691			2.20392
$513$		0			0
$514$	−38.1110	+	22.0034i	−1.68101	+	0.970529i
$515$	−5.23109	+	7.01968i	−0.230509	+	0.309324i
$516$		0			0
$517$	23.9934			1.05523
$518$	−6.21181	+	4.07856i	−0.272931	+	0.179202i
$519$		0			0
$520$	−52.4844	−	6.15954i	−2.30159	−	0.270114i
$521$	−9.43608	−	16.3438i	−0.413402	−	0.716033i	0.581857	−	0.813291i	$-0.302326\pi$
$521$	−9.43608	−	16.3438i	−0.413402	−	0.716033i	−0.995259	+	0.0972577i	$0.968993\pi$
$522$		0			0
$523$	−14.1124	+	24.4434i	−0.617092	+	1.06884i	0.372921	+	0.927863i	$0.378356\pi$
$523$	−14.1124	+	24.4434i	−0.617092	+	1.06884i	−0.990014	+	0.140972i	$0.954977\pi$
$524$	−18.1674			−0.793645
$525$		0			0
$526$	4.15633			0.181225
$527$	4.06867	−	7.04715i	0.177234	−	0.306979i
$528$		0			0
$529$	7.00420	+	12.1316i	0.304530	+	0.527462i
$530$	−22.9503	−	2.69343i	−0.996896	−	0.116995i
$531$		0			0
$532$	−1.00748	−	17.5358i	−0.0436797	−	0.760275i
$533$	23.0527			0.998521
$534$		0			0
$535$	19.8042	−	26.5755i	0.856208	−	1.14896i
$536$	14.4137	−	8.32175i	0.622577	−	0.359445i
$537$		0			0
$538$	30.0128			1.29394
$539$	31.6888	−	23.5139i	1.36493	−	1.01281i
$540$		0			0
$541$	−14.2269	+	24.6417i	−0.611661	+	1.05943i	0.379299	+	0.925274i	$0.376165\pi$
$541$	−14.2269	+	24.6417i	−0.611661	+	1.05943i	−0.990960	+	0.134154i	$0.957168\pi$
$542$	12.9898	−	7.49965i	0.557959	−	0.322138i
$543$		0			0
$544$	32.9163	+	19.0042i	1.41127	+	0.814799i
$545$	9.76584	+	22.6690i	0.418323	+	0.971035i
$546$		0			0
$547$		−	21.9338i		−	0.937820i	−0.883246	−	0.468910i	$-0.844647\pi$
$547$		−	21.9338i		−	0.937820i	0.883246	−	0.468910i	$-0.155353\pi$
$548$	13.0256	−	22.5610i	0.556427	−	0.963760i
$549$		0			0
$550$	16.7673	−	70.4515i	0.714958	−	3.00406i
$551$	−1.58268	+	2.74127i	−0.0674242	+	0.116782i
$552$		0			0
$553$	15.2287	−	30.2633i	0.647590	−	1.28693i
$554$		−	42.6515i		−	1.81209i
$555$		0			0
$556$	92.8603	−	53.6129i	3.93815	−	2.27369i
$557$	12.2168	+	21.1601i	0.517643	+	0.896583i	0.999790	+	0.0204933i	$0.00652367\pi$
$557$	12.2168	+	21.1601i	0.517643	+	0.896583i	−0.482147	+	0.876090i	$0.660143\pi$
$558$		0			0
$559$		−	1.71863i		−	0.0726903i
$560$	−25.9663	+	39.3719i	−1.09728	+	1.66377i
$561$		0			0
$562$	−45.4497	−	26.2404i	−1.91718	−	1.10688i
$563$	−18.4585	+	10.6570i	−0.777932	+	0.449139i	−0.835697	−	0.549191i	$-0.814936\pi$
$563$	−18.4585	+	10.6570i	−0.777932	+	0.449139i	0.0577647	+	0.998330i	$0.481603\pi$
$564$		0			0
$565$	−16.7520	−	1.96601i	−0.704762	−	0.0827105i
$566$	−17.0423			−0.716341
$567$		0			0
$568$			54.4032i			2.28271i
$569$	−24.1707	−	13.9549i	−1.01329	−	0.585022i	−0.101135	−	0.994873i	$-0.532247\pi$
$569$	−24.1707	−	13.9549i	−1.01329	−	0.585022i	−0.912152	+	0.409851i	$0.865581\pi$
$570$		0			0
$571$	23.1936	+	40.1725i	0.970622	+	1.68117i	0.693685	+	0.720279i	$0.255986\pi$
$571$	23.1936	+	40.1725i	0.970622	+	1.68117i	0.276937	+	0.960888i	$0.410681\pi$
$572$	79.4217	+	45.8541i	3.32079	+	1.91726i
$573$		0			0
$574$	19.9249	−	39.5958i	0.831648	−	1.65270i
$575$	10.2991	−	10.8958i	0.429501	−	0.454388i
$576$		0			0
$577$	16.2167	+	28.0881i	0.675108	+	1.16932i	0.976437	+	0.215801i	$0.0692364\pi$
$577$	16.2167	+	28.0881i	0.675108	+	1.16932i	−0.301329	+	0.953520i	$0.597430\pi$
$578$	−14.8328	−	25.6912i	−0.616964	−	1.06861i
$579$		0			0
$580$	20.7338	−	8.93214i	0.860925	−	0.370887i
$581$	1.02774	+	17.8886i	0.0426380	+	0.742145i
$582$		0			0
$583$	19.6351	+	11.3363i	0.813204	+	0.469504i
$584$	10.4883	+	18.1663i	0.434011	+	0.751728i
$585$		0			0
$586$	−36.4291	−	21.0323i	−1.50487	−	0.868838i
$587$		−	0.790380i		−	0.0326225i	−0.999867	−	0.0163112i	$-0.994808\pi$
$587$		−	0.790380i		−	0.0326225i	0.999867	−	0.0163112i	$-0.00519226\pi$
$588$		0			0
$589$	−2.19729			−0.0905379
$590$	−65.1615	−	7.64732i	−2.68266	−	0.314835i
$591$		0			0
$592$	−7.54710	+	4.35732i	−0.310184	+	0.179085i
$593$	17.5672	+	10.1424i	0.721397	+	0.416499i	0.815267	−	0.579086i	$-0.196590\pi$
$593$	17.5672	+	10.1424i	0.721397	+	0.416499i	−0.0938695	+	0.995585i	$0.529924\pi$
$594$		0			0
$595$	28.2643	−	14.1504i	1.15872	−	0.580109i
$596$		−	21.5160i		−	0.881328i
$597$		0			0
$598$	13.6192	+	23.5891i	0.556929	+	0.964630i
$599$	8.77781	−	5.06787i	0.358652	−	0.207068i	−0.309837	−	0.950790i	$-0.600275\pi$
$599$	8.77781	−	5.06787i	0.358652	−	0.207068i	0.668489	+	0.743722i	$0.266941\pi$
$600$		0			0
$601$			35.6657i			1.45483i	0.686196	+	0.727417i	$0.259279\pi$
$601$			35.6657i			1.45483i	−0.686196	+	0.727417i	$0.740721\pi$
$602$	−2.95196	−	1.48545i	−0.120313	−	0.0605423i
$603$		0			0
$604$	−4.28152	+	7.41581i	−0.174213	+	0.301745i
$605$	−27.7609	+	37.2529i	−1.12864	+	1.51454i
$606$		0			0
$607$	13.1333	−	22.7475i	0.533063	−	0.923292i	−0.466192	−	0.884684i	$-0.654374\pi$
$607$	13.1333	−	22.7475i	0.533063	−	0.923292i	0.999254	−	0.0386080i	$-0.0122924\pi$
$608$		−	10.2633i		−	0.416230i
$609$		0			0
$610$	−36.9805	+	15.9312i	−1.49730	+	0.645036i
$611$	−13.0317	−	7.52384i	−0.527205	−	0.304382i
$612$		0			0
$613$	−22.4144	+	12.9410i	−0.905310	+	0.522681i	−0.878919	−	0.476971i	$-0.841735\pi$
$613$	−22.4144	+	12.9410i	−0.905310	+	0.522681i	−0.0263906	+	0.999652i	$0.508401\pi$
$614$	−32.7686	+	56.7568i	−1.32243	+	2.29052i
$615$		0			0
$616$	83.3398	−	54.7194i	3.35786	−	2.20471i
$617$	−16.1754			−0.651198			−0.325599	−	0.945508i	$-0.605566\pi$
$617$	−16.1754			−0.651198			−0.325599	+	0.945508i	$0.605566\pi$
$618$		0			0
$619$	5.29108	−	3.05481i	0.212667	−	0.122783i	−0.389883	−	0.920864i	$-0.627485\pi$
$619$	5.29108	−	3.05481i	0.212667	−	0.122783i	0.602550	+	0.798081i	$0.294151\pi$
$620$	12.5661	+	9.36432i	0.504668	+	0.376080i
$621$		0			0
$622$	79.7432			3.19741
$623$	−12.2855	+	24.4145i	−0.492209	+	0.978145i
$624$		0			0
$625$	22.3197	+	11.2619i	0.892788	+	0.450478i
$626$	−19.3306	−	33.4815i	−0.772605	−	1.33819i
$627$		0			0
$628$	15.1118	−	26.1744i	0.603027	−	1.04447i
$629$	5.84048			0.232875
$630$		0			0
$631$	1.89949			0.0756174			0.0378087	−	0.999285i	$-0.487962\pi$
$631$	1.89949			0.0756174			0.0378087	+	0.999285i	$0.487962\pi$
$632$	42.7988	−	74.1297i	1.70245	−	2.94872i
$633$		0			0
$634$	20.0170	+	34.6704i	0.794976	+	1.37694i
$635$	1.02616	−	8.74373i	0.0407219	−	0.346984i
$636$		0			0
$637$	−24.5847	+	2.83426i	−0.974083	+	0.112298i
$638$	−31.7782			−1.25811
$639$		0			0
$640$	10.9972	−	14.7573i	0.434702	−	0.583333i
$641$	−9.82533	+	5.67266i	−0.388077	+	0.224057i	−0.681327	−	0.731979i	$-0.738597\pi$
$641$	−9.82533	+	5.67266i	−0.388077	+	0.224057i	0.293249	+	0.956036i	$0.405263\pi$
$642$		0			0
$643$	−18.2255			−0.718742			−0.359371	−	0.933195i	$-0.617009\pi$
$643$	−18.2255			−0.718742			−0.359371	+	0.933195i	$0.617009\pi$
$644$	36.4476	−	2.09400i	1.43623	−	0.0825152i
$645$		0			0
$646$	−9.90252	+	17.1517i	−0.389609	+	0.674823i
$647$	21.2533	−	12.2706i	0.835552	−	0.482406i	−0.0201980	−	0.999796i	$-0.506430\pi$
$647$	21.2533	−	12.2706i	0.835552	−	0.482406i	0.855750	+	0.517390i	$0.173096\pi$
$648$		0			0
$649$	55.7490	+	32.1867i	2.18834	+	1.26344i
$650$	−31.1990	+	33.0069i	−1.22373	+	1.29464i
$651$		0			0
$652$		−	86.3976i		−	3.38359i
$653$	−4.37656	+	7.58043i	−0.171268	+	0.296645i	−0.938863	−	0.344290i	$-0.888120\pi$
$653$	−4.37656	+	7.58043i	−0.171268	+	0.296645i	0.767595	+	0.640935i	$0.221453\pi$
$654$		0			0
$655$	−5.27502	+	7.07864i	−0.206112	+	0.276585i
$656$	25.9913	−	45.0183i	1.01479	−	1.75767i
$657$		0			0
$658$	−24.1867	+	15.8805i	−0.942894	+	0.619087i
$659$			2.51324i			0.0979020i	0.998801	+	0.0489510i	$0.0155878\pi$
$659$			2.51324i			0.0979020i	−0.998801	+	0.0489510i	$0.984412\pi$
$660$		0			0
$661$	−34.5393	+	19.9413i	−1.34342	+	0.775626i	−0.987308	−	0.158815i	$-0.949233\pi$
$661$	−34.5393	+	19.9413i	−1.34342	+	0.775626i	−0.356116	+	0.934442i	$0.615899\pi$
$662$	17.5594	+	30.4137i	0.682465	+	1.18206i
$663$		0			0
$664$			45.2714i			1.75687i
$665$	−7.12510	−	4.69911i	−0.276300	−	0.182224i
$666$		0			0
$667$	−5.69763	−	3.28953i	−0.220613	−	0.127371i
$668$	19.1520	−	11.0574i	0.741011	−	0.427823i
$669$		0			0
$670$	1.66734	−	14.2071i	0.0644149	−	0.548868i
$671$	39.5080			1.52519
$672$		0			0
$673$			36.0634i			1.39014i	0.718941	+	0.695071i	$0.244627\pi$
$673$			36.0634i			1.39014i	−0.718941	+	0.695071i	$0.755373\pi$
$674$	50.8318	+	29.3478i	1.95797	+	1.13043i
$675$		0			0
$676$	1.15310	+	1.99723i	0.0443501	+	0.0768166i
$677$	−6.84487	−	3.95189i	−0.263070	−	0.151883i	0.362664	−	0.931920i	$-0.381867\pi$
$677$	−6.84487	−	3.95189i	−0.263070	−	0.151883i	−0.625734	+	0.780036i	$0.715200\pi$
$678$		0			0
$679$	−38.9132	+	2.23566i	−1.49335	+	0.0857968i
$680$	73.3450	−	31.5971i	2.81265	−	1.21169i
$681$		0			0
$682$	−11.0298	−	19.1041i	−0.422351	−	0.731534i
$683$	12.6430	+	21.8984i	0.483772	+	0.837918i	0.999826	−	0.0186377i	$-0.00593291\pi$
$683$	12.6430	+	21.8984i	0.483772	+	0.837918i	−0.516054	+	0.856556i	$0.672600\pi$
$684$		0			0
$685$	−5.00849	−	11.6260i	−0.191365	−	0.444206i
$686$	−16.3809	+	44.6771i	−0.625425	+	1.70578i
$687$		0			0
$688$	−3.35622	−	1.93772i	−0.127955	−	0.0738747i
$689$	−7.10969	−	12.3143i	−0.270858	−	0.469139i
$690$		0			0
$691$	−13.1380	−	7.58522i	−0.499792	−	0.288555i	0.228835	−	0.973465i	$-0.426508\pi$
$691$	−13.1380	−	7.58522i	−0.499792	−	0.288555i	−0.728628	+	0.684910i	$0.759842\pi$
$692$			15.4790i			0.588424i
$693$		0			0
$694$	50.4235			1.91405
$695$	6.07317	−	51.7485i	0.230369	−	1.96293i
$696$		0			0
$697$	−30.1709	+	17.4192i	−1.14280	+	0.659799i
$698$	−13.6635	−	7.88861i	−0.517170	−	0.298588i
$699$		0			0
$700$	20.7214	+	57.2392i	0.783196	+	2.16344i
$701$			34.6815i			1.30990i	0.755671	+	0.654951i	$0.227311\pi$
$701$			34.6815i			1.30990i	−0.755671	+	0.654951i	$0.772689\pi$
$702$		0			0
$703$	−0.788541	−	1.36579i	−0.0297404	−	0.0515118i
$704$	11.3949	−	6.57883i	0.429460	−	0.247949i
$705$		0			0
$706$		−	61.6755i		−	2.32119i
$707$	21.6855	+	33.0278i	0.815566	+	1.24214i
$708$		0			0
$709$	−17.2311	+	29.8451i	−0.647126	+	1.12086i	0.336680	+	0.941619i	$0.390696\pi$
$709$	−17.2311	+	29.8451i	−0.647126	+	1.12086i	−0.983806	+	0.179237i	$0.942637\pi$
$710$	37.4926	+	27.9396i	1.40707	+	1.04855i
$711$		0			0
$712$	−34.5273	+	59.8030i	−1.29396	+	2.24121i
$713$		−	4.56699i		−	0.171035i
$714$		0			0
$715$	40.9270	−	17.6314i	1.53058	−	0.659376i
$716$	−44.3502	−	25.6056i	−1.65744	−	0.956925i
$717$		0			0
$718$	37.7180	−	21.7765i	1.40762	−	0.812692i
$719$	13.4825	−	23.3523i	0.502812	−	0.870895i	−0.497183	−	0.867646i	$-0.665632\pi$
$719$	13.4825	−	23.3523i	0.502812	−	0.870895i	0.999995	−	0.00324951i	$-0.00103435\pi$
$720$		0			0
$721$	−4.65613	+	9.25293i	−0.173403	+	0.344597i
$722$	−43.4702			−1.61779
$723$		0			0
$724$	−8.74942	+	5.05148i	−0.325170	+	0.187737i
$725$	2.53993	−	10.6721i	0.0943308	−	0.396353i
$726$		0			0
$727$	10.4196			0.386442			0.193221	−	0.981155i	$-0.438106\pi$
$727$	10.4196			0.386442			0.193221	+	0.981155i	$0.438106\pi$
$728$	−62.4236	+	3.58639i	−2.31357	+	0.132921i
$729$		0			0
$730$	17.9060	+	2.10143i	0.662729	+	0.0777776i
$731$	1.29864	+	2.24931i	0.0480320	+	0.0831938i
$732$		0			0
$733$	11.3541	−	19.6659i	0.419374	−	0.726377i	−0.576503	−	0.817095i	$-0.695583\pi$
$733$	11.3541	−	19.6659i	0.419374	−	0.726377i	0.995877	+	0.0907181i	$0.0289162\pi$
$734$	89.9374			3.31965
$735$		0			0
$736$	21.3318			0.786300
$737$	−7.01764	+	12.1549i	−0.258498	+	0.447732i
$738$		0			0
$739$	−14.8897	−	25.7898i	−0.547728	−	0.948692i	−0.998430	−	0.0560176i	$-0.982160\pi$
$739$	−14.8897	−	25.7898i	−0.547728	−	0.948692i	0.450702	−	0.892674i	$-0.351174\pi$
$740$	−1.31107	+	11.1714i	−0.0481959	+	0.410669i
$741$		0			0
$742$	−27.2965	+	1.56825i	−1.00209	+	0.0575723i
$743$	−34.8044			−1.27685			−0.638424	−	0.769684i	$-0.720414\pi$
$743$	−34.8044			−1.27685			−0.638424	+	0.769684i	$0.720414\pi$
$744$		0			0
$745$	−8.38337	−	6.24731i	−0.307143	−	0.228884i
$746$	13.3320	−	7.69723i	0.488119	−	0.281816i
$747$		0			0
$748$	−138.594			−5.06751
$749$	17.6275	−	35.0303i	0.644093	−	1.27998i
$750$		0			0
$751$	−3.74522	+	6.48691i	−0.136665	+	0.236711i	−0.926232	−	0.376953i	$-0.876972\pi$
$751$	−3.74522	+	6.48691i	−0.136665	+	0.236711i	0.789567	+	0.613664i	$0.210305\pi$
$752$	−29.3858	+	16.9659i	−1.07159	+	0.618683i
$753$		0			0
$754$	17.2599	+	9.96499i	0.628568	+	0.362904i
$755$	1.64629	+	3.82146i	0.0599146	+	0.139077i
$756$		0			0
$757$			2.66139i			0.0967300i	0.998830	+	0.0483650i	$0.0154011\pi$
$757$			2.66139i			0.0967300i	−0.998830	+	0.0483650i	$0.984599\pi$
$758$	−4.01904	+	6.96118i	−0.145978	+	0.252842i
$759$		0			0
$760$	−17.2915	−	12.8857i	−0.627228	−	0.467412i
$761$	−2.78479	+	4.82340i	−0.100949	+	0.174848i	−0.912076	−	0.410022i	$-0.865521\pi$
$761$	−2.78479	+	4.82340i	−0.100949	+	0.174848i	0.811127	+	0.584870i	$0.198854\pi$
$762$		0			0
$763$	16.0294	+	24.4135i	0.580304	+	0.883827i
$764$		−	45.8057i		−	1.65719i
$765$		0			0
$766$	−37.7516	+	21.7959i	−1.36402	+	0.787517i
$767$	−20.1862	−	34.9635i	−0.728881	−	1.26246i
$768$		0			0
$769$			11.5002i			0.414709i	0.978266	+	0.207355i	$0.0664854\pi$
$769$			11.5002i			0.414709i	−0.978266	+	0.207355i	$0.933515\pi$
$770$	5.08991	−	85.5364i	0.183428	−	3.08252i
$771$		0			0
$772$	99.4275	+	57.4045i	3.57847	+	2.06603i
$773$	21.9748	−	12.6872i	0.790378	−	0.456325i	−0.0497174	−	0.998763i	$-0.515832\pi$
$773$	21.9748	−	12.6872i	0.790378	−	0.456325i	0.840096	+	0.542438i	$0.182499\pi$
$774$		0			0
$775$	7.29733	−	2.17721i	0.262128	−	0.0782076i
$776$	−98.4793			−3.53520
$777$		0			0
$778$			1.15486i			0.0414039i
$779$	8.14692	+	4.70363i	0.291894	+	0.168525i
$780$		0			0
$781$	−22.9388	−	39.7312i	−0.820816	−	1.42169i
$782$	−35.6491	−	20.5820i	−1.27481	−	0.736011i
$783$		0			0
$784$	−22.1838	+	51.2058i	−0.792280	+	1.82878i
$785$	−5.81065	−	13.4880i	−0.207391	−	0.481408i
$786$		0			0
$787$	11.9967	+	20.7789i	0.427636	+	0.740688i	0.996663	−	0.0816315i	$-0.0260130\pi$
$787$	11.9967	+	20.7789i	0.427636	+	0.740688i	−0.569026	+	0.822319i	$0.692680\pi$
$788$	−43.9514	−	76.1260i	−1.56570	−	2.71188i
$789$		0			0
$790$	−29.1073	−	67.5656i	−1.03559	−	2.40388i
$791$	−19.9244	+	1.14471i	−0.708431	+	0.0407011i
$792$		0			0
$793$	−21.4582	−	12.3889i	−0.762002	−	0.439942i
$794$	−29.2043	−	50.5833i	−1.03642	−	1.79514i
$795$		0			0
$796$	−7.34573	−	4.24106i	−0.260363	−	0.150320i
$797$		−	28.1188i		−	0.996020i	−0.867171	−	0.498010i	$-0.834064\pi$
$797$		−	28.1188i		−	0.996020i	0.867171	−	0.498010i	$-0.165936\pi$
$798$		0			0
$799$	22.7408			0.804513
$800$	10.1694	+	34.0848i	0.359544	+	1.20508i
$801$		0			0
$802$	21.6163	−	12.4802i	0.763299	−	0.440691i
$803$	−15.3195	−	8.84470i	−0.540612	−	0.312123i
$804$		0			0
$805$	9.76691	−	14.8092i	0.344238	−	0.521957i
$806$			13.8348i			0.487310i
$807$		0			0
$808$	49.9134	+	86.4525i	1.75595	+	3.04139i
$809$	24.2977	−	14.0283i	0.854263	−	0.493209i	−0.00782425	−	0.999969i	$-0.502491\pi$
$809$	24.2977	−	14.0283i	0.854263	−	0.493209i	0.862087	+	0.506761i	$0.169157\pi$
$810$		0			0
$811$		−	43.4980i		−	1.52742i	−0.645559	−	0.763710i	$-0.723376\pi$
$811$		−	43.4980i		−	1.52742i	0.645559	−	0.763710i	$-0.276624\pi$
$812$	22.3293	−	14.6610i	0.783605	−	0.514501i
$813$		0			0
$814$	7.91647	−	13.7117i	0.277472	−	0.480596i
$815$	−33.6635	−	25.0861i	−1.17918	−	0.878729i
$816$		0			0
$817$	0.350667	−	0.607373i	0.0122683	−	0.0212493i
$818$		−	10.4323i		−	0.364757i
$819$		0			0
$820$	−26.5459	−	61.6198i	−0.927022	−	2.15186i
$821$	31.5875	+	18.2371i	1.10241	+	0.636477i	0.936853	−	0.349723i	$-0.113724\pi$
$821$	31.5875	+	18.2371i	1.10241	+	0.636477i	0.165558	+	0.986200i	$0.447058\pi$
$822$		0			0
$823$	39.9277	−	23.0523i	1.39179	−	0.803551i	0.398278	−	0.917265i	$-0.369608\pi$
$823$	39.9277	−	23.0523i	1.39179	−	0.803551i	0.993514	+	0.113713i	$0.0362745\pi$
$824$	−13.0856	+	22.6650i	−0.455859	+	0.789571i
$825$		0			0
$826$	−77.5015	+	4.45265i	−2.69662	+	0.154928i
$827$	−20.1533			−0.700800			−0.350400	−	0.936600i	$-0.613954\pi$
$827$	−20.1533			−0.700800			−0.350400	+	0.936600i	$0.613954\pi$
$828$		0			0
$829$	6.13818	−	3.54388i	0.213188	−	0.123084i	−0.389604	−	0.920982i	$-0.627388\pi$
$829$	6.13818	−	3.54388i	0.213188	−	0.123084i	0.602792	+	0.797898i	$0.294055\pi$
$830$	31.1993	+	23.2498i	1.08294	+	0.807012i
$831$		0			0
$832$	−8.25194			−0.286085
$833$	30.0344	−	22.2863i	1.04063	−	0.772175i
$834$		0			0
$835$	1.25256	−	10.6729i	0.0433467	−	0.369350i
$836$	18.7120	+	32.4102i	0.647169	+	1.12093i
$837$		0			0
$838$	−26.8903	+	46.5754i	−0.928911	+	1.60892i
$839$	−33.0805			−1.14206			−0.571032	−	0.820928i	$-0.693457\pi$
$839$	−33.0805			−1.14206			−0.571032	+	0.820928i	$0.693457\pi$
$840$		0			0
$841$	24.1862			0.834006
$842$	−25.4104	+	44.0121i	−0.875701	+	1.51676i
$843$		0			0
$844$	22.4956	+	38.9635i	0.774331	+	1.34118i
$845$	1.11300	+	0.130621i	0.0382884	+	0.00449351i
$846$		0			0
$847$	−24.7097	+	49.1045i	−0.849036	+	1.68725i
$848$	−32.0640			−1.10108
$849$		0			0
$850$	15.8919	−	66.7736i	0.545088	−	2.29032i
$851$	2.83875	−	1.63895i	0.0973109	−	0.0561825i
$852$		0			0
$853$	−38.1187			−1.30516			−0.652580	−	0.757719i	$-0.726314\pi$
$853$	−38.1187			−1.30516			−0.652580	+	0.757719i	$0.726314\pi$
$854$	−39.8262	+	26.1492i	−1.36282	+	0.894806i
$855$		0			0
$856$	49.5403	−	85.8063i	1.69325	−	2.93280i
$857$	6.09347	−	3.51807i	0.208149	−	0.120175i	−0.392302	−	0.919837i	$-0.628321\pi$
$857$	6.09347	−	3.51807i	0.208149	−	0.120175i	0.600451	+	0.799662i	$0.294988\pi$
$858$		0			0
$859$	22.2343	+	12.8370i	0.758624	+	0.437992i	0.828802	−	0.559543i	$-0.189023\pi$
$859$	22.2343	+	12.8370i	0.758624	+	0.437992i	−0.0701772	+	0.997535i	$0.522356\pi$
$860$	−4.59390	+	1.97906i	−0.156651	+	0.0674853i
$861$		0			0
$862$		−	27.3885i		−	0.932855i
$863$	25.4929	−	44.1550i	0.867788	−	1.50305i	0.00353683	−	0.999994i	$-0.498874\pi$
$863$	25.4929	−	44.1550i	0.867788	−	1.50305i	0.864252	−	0.503060i	$-0.167792\pi$
$864$		0			0
$865$	6.03116	+	4.49444i	0.205066	+	0.152816i
$866$	27.2805	−	47.2512i	0.927029	−	1.60566i
$867$		0			0
$868$	16.5639	+	8.33508i	0.562217	+	0.282911i
$869$			72.1835i			2.44866i
$870$		0			0
$871$	7.62306	−	4.40117i	0.258297	−	0.149128i
$872$	36.8949	+	63.9038i	1.24942	+	2.16406i
$873$		0			0
$874$			11.1153i			0.375982i
$875$	28.3190	+	8.54601i	0.957357	+	0.288908i
$876$		0			0
$877$	−33.3881	−	19.2766i	−1.12743	−	0.650925i	−0.184146	−	0.982899i	$-0.558952\pi$
$877$	−33.3881	−	19.2766i	−1.12743	−	0.650925i	−0.943289	+	0.331974i	$0.892285\pi$
$878$	47.7152	−	27.5484i	1.61031	−	0.929712i
$879$		0			0
$880$	11.7128	−	99.8032i	0.394840	−	3.36436i
$881$	34.4764			1.16154			0.580770	−	0.814068i	$-0.302752\pi$
$881$	34.4764			1.16154			0.580770	+	0.814068i	$0.302752\pi$
$882$		0			0
$883$		−	25.5869i		−	0.861068i	−0.902574	−	0.430534i	$-0.858325\pi$
$883$		−	25.5869i		−	0.861068i	0.902574	−	0.430534i	$-0.141675\pi$
$884$	75.2754	+	43.4603i	2.53179	+	1.46173i
$885$		0			0
$886$	−0.219643	−	0.380433i	−0.00737905	−	0.0127809i
$887$	20.6076	+	11.8978i	0.691936	+	0.399489i	0.804337	−	0.594174i	$-0.202521\pi$
$887$	20.6076	+	11.8978i	0.691936	+	0.399489i	−0.112401	+	0.993663i	$0.535854\pi$
$888$		0			0
$889$	−0.597481	−	10.3996i	−0.0200389	−	0.348791i
$890$	23.4819	+	54.5075i	0.787114	+	1.82710i
$891$		0			0
$892$	18.0566	+	31.2749i	0.604579	+	1.04716i
$893$	−3.07031	−	5.31792i	−0.102744	−	0.177958i
$894$		0			0
$895$	−22.8542	+	9.84561i	−0.763932	+	0.329102i
$896$	9.78847	−	19.4522i	0.327010	−	0.649852i
$897$		0			0
$898$	−20.8886	−	12.0600i	−0.697061	−	0.402448i
$899$	−1.67081	−	2.89392i	−0.0557245	−	0.0965177i
$900$		0			0
$901$	18.6101	+	10.7445i	0.619991	+	0.357952i
$902$			94.4432i			3.14461i
$903$		0			0
$904$	−50.4235			−1.67706
$905$	−0.572223	+	4.87581i	−0.0190213	+	0.162077i
$906$		0			0
$907$	−33.5806	+	19.3878i	−1.11503	+	0.643760i	−0.940126	−	0.340826i	$-0.889293\pi$
$907$	−33.5806	+	19.3878i	−1.11503	+	0.643760i	−0.174899	+	0.984586i	$0.555960\pi$
$908$	2.18978	+	1.26427i	0.0726704	+	0.0419563i
$909$		0			0
$910$	−29.5870	+	44.8618i	−0.980798	+	1.48715i
$911$			31.4438i			1.04178i	0.853624	+	0.520889i	$0.174400\pi$
$911$			31.4438i			1.04178i	−0.853624	+	0.520889i	$0.825600\pi$
$912$		0			0
$913$	−19.0884	−	33.0622i	−0.631735	−	1.09420i
$914$	−37.5881	+	21.7015i	−1.24330	+	0.717822i
$915$		0			0
$916$			98.7437i			3.26258i
$917$	−4.69524	+	9.33064i	−0.155050	+	0.308125i
$918$		0			0
$919$	−13.9872	+	24.2266i	−0.461396	+	0.799161i	−0.999031	−	0.0440170i	$-0.985984\pi$
$919$	−13.9872	+	24.2266i	−0.461396	+	0.799161i	0.537635	+	0.843178i	$0.319318\pi$
$920$	26.7823	−	35.9396i	0.882987	−	1.18489i
$921$		0			0
$922$	39.8716	−	69.0596i	1.31310	−	2.27436i
$923$			28.7726i			0.947060i
$924$		0			0
$925$	3.97209	+	3.75454i	0.130602	+	0.123448i
$926$	26.5757	+	15.3435i	0.873332	+	0.504218i
$927$		0			0
$928$	13.5171	−	7.80411i	0.443721	−	0.256183i
$929$	11.2452	−	19.4772i	0.368943	−	0.639027i	−0.620458	−	0.784240i	$-0.713053\pi$
$929$	11.2452	−	19.4772i	0.368943	−	0.639027i	0.989400	+	0.145212i	$0.0463866\pi$
$930$		0			0
$931$	−9.26667	−	4.01459i	−0.303703	−	0.131573i
$932$	−86.3568			−2.82871
$933$		0			0
$934$	−76.9023	+	44.3996i	−2.51632	+	1.45280i
$935$	−40.2418	+	54.0012i	−1.31605	+	1.76603i
$936$		0			0
$937$	32.0994			1.04864			0.524321	−	0.851521i	$-0.324319\pi$
$937$	32.0994			1.04864			0.524321	+	0.851521i	$0.324319\pi$
$938$	−0.970808	−	16.8976i	−0.0316980	−	0.551725i
$939$		0			0
$940$	−5.10486	+	43.4976i	−0.166502	+	1.41874i
$941$	5.10912	+	8.84925i	0.166552	+	0.288477i	0.937206	−	0.348778i	$-0.113403\pi$
$941$	5.10912	+	8.84925i	0.166552	+	0.288477i	−0.770653	+	0.637255i	$0.780070\pi$
$942$		0			0
$943$	−9.77631	+	16.9331i	−0.318360	+	0.551416i
$944$	−91.0378			−2.96303
$945$		0			0
$946$	7.04097			0.228922
$947$	5.14953	−	8.91925i	0.167337	−	0.289837i	−0.770146	−	0.637868i	$-0.779816\pi$
$947$	5.14953	−	8.91925i	0.167337	−	0.289837i	0.937483	+	0.348031i	$0.113150\pi$
$948$		0			0
$949$	5.54703	+	9.60774i	0.180064	+	0.311880i
$950$	−17.7606	+	5.29899i	−0.576229	+	0.171922i
$951$		0			0
$952$	78.9890	−	51.8627i	2.56005	−	1.68088i
$953$	−0.930159			−0.0301308			−0.0150654	−	0.999887i	$-0.504796\pi$
$953$	−0.930159			−0.0301308			−0.0150654	+	0.999887i	$0.504796\pi$
$954$		0			0
$955$	−17.8475	−	13.3000i	−0.577532	−	0.430378i
$956$	−29.3255	+	16.9311i	−0.948455	+	0.547591i
$957$		0			0
$958$	−7.63696			−0.246739
$959$	−8.22082	−	12.5206i	−0.265464	−	0.404312i
$960$		0			0
$961$	−14.3402	+	24.8379i	−0.462586	+	0.801223i
$962$	−8.59943	+	4.96488i	−0.277257	+	0.160074i
$963$		0			0
$964$	−109.735	−	63.3555i	−3.53432	−	2.04054i
$965$	51.2363	−	22.0726i	1.64935	−	0.710543i
$966$		0			0
$967$			4.22117i			0.135744i	0.997694	+	0.0678719i	$0.0216209\pi$
$967$			4.22117i			0.135744i	−0.997694	+	0.0678719i	$0.978379\pi$
$968$	−69.4443	+	120.281i	−2.23202	+	3.86598i
$969$		0			0
$970$	−50.5755	+	67.8680i	−1.62388	+	2.17911i
$971$	−2.28935	+	3.96527i	−0.0734688	+	0.127252i	−0.900419	−	0.435023i	$-0.856740\pi$
$971$	−2.28935	+	3.96527i	−0.0734688	+	0.127252i	0.826951	+	0.562275i	$0.190074\pi$
$972$		0			0
$973$	−3.53610	−	61.5483i	−0.113362	−	1.97315i
$974$		−	58.3566i		−	1.86987i
$975$		0			0
$976$	−48.3872	+	27.9364i	−1.54884	+	0.894221i
$977$	−22.7556	−	39.4138i	−0.728015	−	1.26096i	−0.957721	−	0.287698i	$-0.907110\pi$
$977$	−22.7556	−	39.4138i	−0.728015	−	1.26096i	0.229707	−	0.973260i	$-0.426223\pi$
$978$		0			0
$979$		−	58.2329i		−	1.86113i
$980$	35.8861	+	62.4514i	1.14634	+	1.99494i
$981$		0			0
$982$	28.9350	+	16.7056i	0.923351	+	0.533097i
$983$	−9.10765	+	5.25831i	−0.290489	+	0.167714i	−0.638162	−	0.769902i	$-0.720305\pi$
$983$	−9.10765	+	5.25831i	−0.290489	+	0.167714i	0.347673	+	0.937616i	$0.386972\pi$
$984$		0			0
$985$	−42.4229	−	4.97874i	−1.35171	−	0.158636i
$986$	−30.1192			−0.959192
$987$		0			0
$988$		−	23.4708i		−	0.746706i
$989$	1.26240	+	0.728847i	0.0401420	+	0.0231760i
$990$		0			0
$991$	13.9539	+	24.1689i	0.443262	+	0.767752i	0.997929	−	0.0643204i	$-0.0204880\pi$
$991$	13.9539	+	24.1689i	0.443262	+	0.767752i	−0.554668	+	0.832072i	$0.687155\pi$
$992$	9.38319	+	5.41739i	0.297916	+	0.172002i
$993$		0			0
$994$	49.4205	+	24.8687i	1.56752	+	0.788787i
$995$	−3.78535	+	1.63073i	−0.120004	+	0.0516977i
$996$		0			0
$997$	−19.4567	−	33.7000i	−0.616201	−	1.06729i	−0.990173	−	0.139851i	$-0.955338\pi$
$997$	−19.4567	−	33.7000i	−0.616201	−	1.06729i	0.373972	−	0.927440i	$-0.377996\pi$
$998$	−27.7592	−	48.0803i	−0.878701	−	1.52196i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bb.b.89.11	yes	24
3.2	odd	2	inner	315.2.bb.b.89.2	yes	24
5.2	odd	4		1575.2.bk.i.26.11		24
5.3	odd	4		1575.2.bk.i.26.1		24
5.4	even	2	inner	315.2.bb.b.89.1	✓	24
7.2	even	3		2205.2.g.b.2204.2		24
7.3	odd	6	inner	315.2.bb.b.269.12	yes	24
7.5	odd	6		2205.2.g.b.2204.1		24
15.2	even	4		1575.2.bk.i.26.2		24
15.8	even	4		1575.2.bk.i.26.12		24
15.14	odd	2	inner	315.2.bb.b.89.12	yes	24
21.2	odd	6		2205.2.g.b.2204.24		24
21.5	even	6		2205.2.g.b.2204.23		24
21.17	even	6	inner	315.2.bb.b.269.1	yes	24
35.3	even	12		1575.2.bk.i.1151.12		24
35.9	even	6		2205.2.g.b.2204.22		24
35.17	even	12		1575.2.bk.i.1151.2		24
35.19	odd	6		2205.2.g.b.2204.21		24
35.24	odd	6	inner	315.2.bb.b.269.2	yes	24
105.17	odd	12		1575.2.bk.i.1151.11		24
105.38	odd	12		1575.2.bk.i.1151.1		24
105.44	odd	6		2205.2.g.b.2204.4		24
105.59	even	6	inner	315.2.bb.b.269.11	yes	24
105.89	even	6		2205.2.g.b.2204.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bb.b.89.1	✓	24	5.4	even	2	inner
315.2.bb.b.89.2	yes	24	3.2	odd	2	inner
315.2.bb.b.89.11	yes	24	1.1	even	1	trivial
315.2.bb.b.89.12	yes	24	15.14	odd	2	inner
315.2.bb.b.269.1	yes	24	21.17	even	6	inner
315.2.bb.b.269.2	yes	24	35.24	odd	6	inner
315.2.bb.b.269.11	yes	24	105.59	even	6	inner
315.2.bb.b.269.12	yes	24	7.3	odd	6	inner
1575.2.bk.i.26.1		24	5.3	odd	4
1575.2.bk.i.26.2		24	15.2	even	4
1575.2.bk.i.26.11		24	5.2	odd	4
1575.2.bk.i.26.12		24	15.8	even	4
1575.2.bk.i.1151.1		24	105.38	odd	12
1575.2.bk.i.1151.2		24	35.17	even	12
1575.2.bk.i.1151.11		24	105.17	odd	12
1575.2.bk.i.1151.12		24	35.3	even	12
2205.2.g.b.2204.1		24	7.5	odd	6
2205.2.g.b.2204.2		24	7.2	even	3
2205.2.g.b.2204.3		24	105.89	even	6
2205.2.g.b.2204.4		24	105.44	odd	6
2205.2.g.b.2204.21		24	35.19	odd	6
2205.2.g.b.2204.22		24	35.9	even	6
2205.2.g.b.2204.23		24	21.5	even	6
2205.2.g.b.2204.24		24	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28469 - 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(-2.22083 - 0.260635i) q^{5} +(-2.64140 + 0.151755i) q^{7} -6.68468 q^{8} +O(q^{10})\)	\(q+(1.28469 - 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(-2.22083 - 0.260635i) q^{5} +(-2.64140 + 0.151755i) q^{7} -6.68468 q^{8} +(-3.43302 + 4.60682i) q^{10} +(4.88189 - 2.81856i) q^{11} -3.53537 q^{13} +(-3.05569 + 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(4.62703 - 2.67142i) q^{17} +(-1.24942 - 0.721351i) q^{19} +(4.07109 + 9.45005i) q^{20} -14.4839i q^{22} +(1.49930 - 2.59686i) q^{23} +(4.86414 + 1.15765i) q^{25} +(-4.54184 + 7.86670i) q^{26} +(6.68220 + 10.1772i) q^{28} -2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(3.55696 + 6.16083i) q^{32} -13.7277i q^{34} +(5.90563 + 0.351419i) q^{35} +(0.946690 + 0.546572i) q^{37} +(-3.21022 + 1.85342i) q^{38} +(14.8455 + 1.74226i) q^{40} -6.52058 q^{41} +0.486125i q^{43} +(-22.4649 - 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(3.68608 + 2.12816i) q^{47} +(6.95394 - 0.801688i) q^{49} +(8.82483 - 9.33618i) q^{50} +(8.13432 + 14.0891i) q^{52} +(2.01102 + 3.48318i) q^{53} +(-11.5764 + 4.98714i) q^{55} +(17.6569 - 1.01443i) q^{56} +(-4.88206 - 2.81866i) q^{58} +(5.70978 + 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} -3.91326i q^{62} +2.33411 q^{64} +(7.85144 + 0.921441i) q^{65} +(-2.15623 + 1.24490i) q^{67} +(-21.2921 - 12.2930i) q^{68} +(8.36885 - 12.6894i) q^{70} -8.13849i q^{71} +(-1.56901 - 2.71761i) q^{73} +(2.43240 - 1.40435i) q^{74} +6.63886i q^{76} +(-12.4673 + 8.18578i) q^{77} +(-6.40252 + 11.0895i) q^{79} +(10.6517 - 14.2938i) q^{80} +(-8.37690 + 14.5092i) q^{82} -6.77241i q^{83} +(-10.9721 + 4.72679i) q^{85} +(1.08170 + 0.624518i) q^{86} +(-32.6339 + 18.8412i) q^{88} +(5.16513 - 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} -13.7986 q^{92} +(9.47093 - 5.46804i) q^{94} +(2.58673 + 1.92764i) q^{95} +14.7321 q^{97} +(7.14976 - 16.5034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4}+O(q^{10}) \) 24 * q - 24 * q^4	\( 24 q - 24 q^{4} - 12 q^{10} - 36 q^{19} + 12 q^{25} - 60 q^{31} + 96 q^{40} - 24 q^{46} + 36 q^{49} + 48 q^{61} + 48 q^{64} - 48 q^{70} - 60 q^{79} - 72 q^{85} + 60 q^{91} + 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^4 - 12 * q^10 - 36 * q^19 + 12 * q^25 - 60 * q^31 + 96 * q^40 - 24 * q^46 + 36 * q^49 + 48 * q^61 + 48 * q^64 - 48 * q^70 - 60 * q^79 - 72 * q^85 + 60 * q^91 + 48 * q^94

Introduction

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