LMFDB - Embedded newform 315.2.bb.b.89.2

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			89.2
Character	$\chi$	$=$	315.89
Dual form			315.2.bb.b.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$0.529370\pi$
$2$	−1.28469	+	2.22514i	−0.908411	+	1.57341i	−0.816272	+	0.577667i	$0.803963\pi$
$3$		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	−0.999503	−	0.0315336i	$-0.989961\pi$
$11$	−4.88189	+	2.81856i	−1.47195	+	0.849828i	−0.472442	+	0.881362i	$0.656628\pi$
$12$		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	−0.941967	−	0.335707i	$-0.891025\pi$
$17$	−4.62703	+	2.67142i	−1.12222	+	0.647914i	−0.180253	+	0.983620i	$0.557692\pi$
$18$		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	−0.978930	−	0.204196i	$-0.934542\pi$
$23$	−1.49930	+	2.59686i	−0.312626	+	0.541484i	0.666304	+	0.745680i	$0.267875\pi$
$24$		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	$0.0653005\pi$
$29$			2.19404i			0.407423i	−0.979031	+	0.203712i	$0.934699\pi$
$30$		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	$-0.329952\pi$
$41$	6.52058			1.01834			0.509172	+	0.860665i	$0.329952\pi$
$42$		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	0.206464	−	0.978454i	$-0.433804\pi$
$47$	−3.68608	−	2.12816i	−0.537671	−	0.310424i	−0.744134	+	0.668030i	$0.767138\pi$
$48$		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	0.694211	−	0.719771i	$-0.255753\pi$
$53$	−2.01102	−	3.48318i	−0.276235	−	0.478452i	−0.970446	+	0.241319i	$0.922420\pi$
$54$		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	$-0.899902\pi$
$59$	−5.70978	−	9.88963i	−0.743350	−	1.28752i	0.207612	−	0.978211i	$-0.433431\pi$
$60$		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	$0.160428\pi$
$71$			8.13849i			0.965861i	−0.875659	+	0.482930i	$0.839572\pi$
$72$		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	$0.121220\pi$
$83$			6.77241i			0.743368i	−0.928359	+	0.371684i	$0.878780\pi$
$84$		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	$0.351088\pi$
$89$	−5.16513	+	8.94627i	−0.547503	+	0.948303i	−0.998445	+	0.0557494i	$0.982245\pi$
$90$		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	$0.0999202\pi$
$101$	7.46683	+	12.9329i	0.742977	+	1.28687i	−0.208157	+	0.978095i	$0.566746\pi$
$102$		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	$-0.579099\pi$
$107$	7.41102	−	12.8363i	0.716450	−	1.24093i	0.962398	−	0.271645i	$-0.0875675\pi$
$108$		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	$-0.615451\pi$
$113$	−7.54314			−0.709599			−0.354799	+	0.934942i	$0.615451\pi$
$114$		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	−0.939282	−	0.343145i	$-0.888508\pi$
$131$	−1.97399	+	3.41906i	−0.172469	+	0.298724i	0.766814	+	0.641870i	$0.221841\pi$
$132$		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	0.719401	−	0.694595i	$-0.244416\pi$
$137$	−2.83062	−	4.90279i	−0.241837	−	0.418873i	−0.961237	+	0.275722i	$0.911083\pi$
$138$		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	0.324880	−	0.945755i	$-0.394676\pi$
$149$	−4.04926	−	2.33784i	−0.331728	−	0.191523i	−0.656608	+	0.754232i	$0.728009\pi$
$150$		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	$-0.940466\pi$
$167$		−	4.80581i		−	0.371884i	0.982561	−	0.185942i	$-0.0595337\pi$
$168$		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	0.606635	−	0.794980i	$-0.292519\pi$
$173$	2.91312	+	1.68189i	0.221480	+	0.127872i	−0.385155	+	0.922852i	$0.625852\pi$
$174$		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	−0.814887	−	0.579620i	$-0.803201\pi$
$179$	−9.63782	+	5.56440i	−0.720365	+	0.415903i	0.0945223	+	0.995523i	$0.469868\pi$
$180$		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	0.154572	−	0.987982i	$-0.450600\pi$
$191$	−8.62053	−	4.97707i	−0.623760	−	0.360128i	−0.778331	+	0.627854i	$0.783934\pi$
$192$		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	$-0.738234\pi$
$197$	−19.1023			−1.36098			−0.680492	+	0.732755i	$0.738234\pi$
$198$		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	−0.484125	−	0.874999i	$-0.660862\pi$
$227$	0.475865	−	0.274741i	0.0315843	−	0.0182352i	0.515709	+	0.856764i	$0.327529\pi$
$228$		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	$0.377395\pi$
$233$	−9.38319	+	16.2522i	−0.614713	+	1.06471i	−0.990435	+	0.137982i	$0.955939\pi$
$234$		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	$0.0764905\pi$
$239$			7.35866i			0.475992i	−0.971266	+	0.237996i	$0.923509\pi$
$240$		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	$-0.249786\pi$
$251$	22.4204			1.41516			0.707582	+	0.706631i	$0.249786\pi$
$252$		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	0.885305	−	0.465011i	$-0.153950\pi$
$257$	14.8328	+	8.56373i	0.925246	+	0.534191i	0.0399409	+	0.999202i	$0.487283\pi$
$258$		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	0.840011	−	0.542570i	$-0.182549\pi$
$263$	−0.808821	−	1.40092i	−0.0498741	−	0.0863844i	−0.889885	+	0.456186i	$0.849215\pi$
$264$		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	0.631205	−	0.775616i	$-0.282561\pi$
$269$	−5.84048	−	10.1160i	−0.356101	−	0.616784i	−0.987306	+	0.158832i	$0.949227\pi$
$270$		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	$0.208526\pi$
$281$			20.4255i			1.21848i	−0.792984	+	0.609242i	$0.791474\pi$
$282$		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	$0.158717\pi$
$293$			16.3716i			0.956437i	−0.878241	+	0.478219i	$0.841283\pi$
$294$		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	$-0.824245\pi$
$311$	−15.5180	−	26.8780i	−0.879946	−	1.52411i	−0.0285476	−	0.999592i	$-0.509088\pi$
$312$		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	−0.559937	−	0.828535i	$-0.689175\pi$
$317$	7.79061	−	13.4937i	0.437564	−	0.757884i	0.997501	+	0.0706518i	$0.0225079\pi$
$318$		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	$-0.990074\pi$
$347$	−9.81241	−	16.9956i	−0.526758	−	0.912372i	0.472756	−	0.881193i	$-0.343259\pi$
$348$		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	−0.937906	−	0.346890i	$-0.887238\pi$
$353$	−20.7882	+	12.0021i	−1.10644	+	0.638805i	−0.168537	+	0.985695i	$0.553904\pi$
$354$		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	0.0598018	−	0.998210i	$-0.480953\pi$
$359$	−14.6798	−	8.47541i	−0.774773	−	0.447315i	−0.834575	+	0.550895i	$0.814286\pi$
$360$		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	0.825973	−	0.563710i	$-0.190626\pi$
$383$	14.6929	+	8.48295i	0.750772	+	0.433459i	−0.0752006	+	0.997168i	$0.523960\pi$
$384$		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	−0.490100	−	0.871666i	$-0.663040\pi$
$389$	0.389255	−	0.224737i	0.0197360	−	0.0113946i	0.509836	+	0.860272i	$0.329706\pi$
$390$		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	0.275004	−	0.961443i	$-0.411321\pi$
$401$	−8.41308	−	4.85729i	−0.420129	−	0.242562i	−0.695132	+	0.718882i	$0.744654\pi$
$402$		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	$-0.329170\pi$
$419$	20.9314			1.02257			0.511283	+	0.859412i	$0.329170\pi$
$420$		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	−0.705574	−	0.708636i	$-0.749311\pi$
$431$	−9.23148	+	5.32980i	−0.444665	+	0.256727i	0.260910	+	0.965363i	$0.415978\pi$
$432$		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	−0.868049	−	0.496478i	$-0.834626\pi$
$443$	−0.0854851	+	0.148064i	−0.00406152	+	0.00703475i	0.863988	+	0.503513i	$0.167959\pi$
$444$		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	$0.0710993\pi$
$449$			9.38752i			0.443025i	−0.975158	+	0.221512i	$0.928901\pi$
$450$		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	$-0.757120\pi$
$461$	−31.0360			−1.44549			−0.722746	+	0.691113i	$0.757120\pi$
$462$		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	0.992748	−	0.120215i	$-0.0383583\pi$
$467$	29.9304	+	17.2803i	1.38501	+	0.799638i	0.392265	+	0.919852i	$0.371692\pi$
$468$		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	0.897978	−	0.440039i	$-0.145036\pi$
$479$	1.48615	+	2.57409i	0.0679040	+	0.117613i	−0.830074	+	0.557653i	$0.811702\pi$
$480$		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	$-0.905206\pi$
$491$		−	13.0036i		−	0.586846i	0.955983	−	0.293423i	$-0.0947944\pi$
$492$		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	$-0.742946\pi$
$503$		−	32.4125i		−	1.44520i	0.691265	−	0.722601i	$-0.257054\pi$
$504$		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	$-0.532662\pi$
$509$	18.2802	−	31.6622i	0.810255	−	1.40340i	0.912685	−	0.408663i	$-0.134005\pi$
$510$		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	0.995259	−	0.0972577i	$-0.0310071\pi$
$521$	9.43608	+	16.3438i	0.413402	+	0.716033i	−0.581857	+	0.813291i	$0.697674\pi$
$522$		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	$-0.993476\pi$
$557$	−12.2168	−	21.1601i	−0.517643	−	0.896583i	0.482147	−	0.876090i	$-0.339857\pi$
$558$		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	−0.0577647	−	0.998330i	$-0.518397\pi$
$563$	18.4585	−	10.6570i	0.777932	−	0.449139i	0.835697	+	0.549191i	$0.185064\pi$
$564$		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	0.912152	−	0.409851i	$-0.134419\pi$
$569$	24.1707	+	13.9549i	1.01329	+	0.585022i	0.101135	+	0.994873i	$0.467753\pi$
$570$		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	$0.00519226\pi$
$587$			0.790380i			0.0326225i	−0.999867	+	0.0163112i	$0.994808\pi$
$588$		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	0.0938695	−	0.995585i	$-0.470076\pi$
$593$	−17.5672	−	10.1424i	−0.721397	−	0.416499i	−0.815267	+	0.579086i	$0.803410\pi$
$594$		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	−0.668489	−	0.743722i	$-0.733059\pi$
$599$	−8.77781	+	5.06787i	−0.358652	+	0.207068i	0.309837	+	0.950790i	$0.399725\pi$
$600$		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	$-0.394434\pi$
$617$	16.1754			0.651198			0.325599	+	0.945508i	$0.394434\pi$
$618$		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	−0.293249	−	0.956036i	$-0.594737\pi$
$641$	9.82533	−	5.67266i	0.388077	−	0.224057i	0.681327	+	0.731979i	$0.261403\pi$
$642$		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	−0.855750	−	0.517390i	$-0.826904\pi$
$647$	−21.2533	+	12.2706i	−0.835552	+	0.482406i	0.0201980	+	0.999796i	$0.493570\pi$
$648$		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	−0.767595	−	0.640935i	$-0.778547\pi$
$653$	4.37656	−	7.58043i	0.171268	−	0.296645i	0.938863	+	0.344290i	$0.111880\pi$
$654$		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	$-0.984412\pi$
$659$		−	2.51324i		−	0.0979020i	0.998801	−	0.0489510i	$-0.0155878\pi$
$660$		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	0.625734	−	0.780036i	$-0.284800\pi$
$677$	6.84487	+	3.95189i	0.263070	+	0.151883i	−0.362664	+	0.931920i	$0.618133\pi$
$678$		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	0.516054	−	0.856556i	$-0.327400\pi$
$683$	−12.6430	−	21.8984i	−0.483772	−	0.837918i	−0.999826	+	0.0186377i	$0.994067\pi$
$684$		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	$-0.772689\pi$
$701$		−	34.6815i		−	1.30990i	0.755671	−	0.654951i	$-0.227311\pi$
$702$		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	$0.334368\pi$
$719$	−13.4825	+	23.3523i	−0.502812	+	0.870895i	−0.999995	+	0.00324951i	$0.998966\pi$
$720$		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	$-0.279586\pi$
$743$	34.8044			1.27685			0.638424	+	0.769684i	$0.279586\pi$
$744$		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	−0.811127	−	0.584870i	$-0.801146\pi$
$761$	2.78479	−	4.82340i	0.100949	−	0.174848i	0.912076	+	0.410022i	$0.134479\pi$
$762$		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	−0.840096	−	0.542438i	$-0.817501\pi$
$773$	−21.9748	+	12.6872i	−0.790378	+	0.456325i	0.0497174	+	0.998763i	$0.484168\pi$
$774$		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	$0.165936\pi$
$797$			28.1188i			0.996020i	−0.867171	+	0.498010i	$0.834064\pi$
$798$		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	−0.862087	−	0.506761i	$-0.830843\pi$
$809$	−24.2977	+	14.0283i	−0.854263	+	0.493209i	0.00782425	+	0.999969i	$0.497509\pi$
$810$		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	−0.165558	−	0.986200i	$-0.552942\pi$
$821$	−31.5875	−	18.2371i	−1.10241	−	0.636477i	−0.936853	+	0.349723i	$0.886276\pi$
$822$		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	$-0.386046\pi$
$827$	20.1533			0.700800			0.350400	+	0.936600i	$0.386046\pi$
$828$		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	$-0.306543\pi$
$839$	33.0805			1.14206			0.571032	+	0.820928i	$0.306543\pi$
$840$		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	−0.600451	−	0.799662i	$-0.705012\pi$
$857$	−6.09347	+	3.51807i	−0.208149	+	0.120175i	0.392302	+	0.919837i	$0.371679\pi$
$858$		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	$0.501126\pi$
$863$	−25.4929	+	44.1550i	−0.867788	+	1.50305i	−0.864252	+	0.503060i	$0.832208\pi$
$864$		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	$-0.697248\pi$
$881$	−34.4764			−1.16154			−0.580770	+	0.814068i	$0.697248\pi$
$882$		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	0.112401	−	0.993663i	$-0.464146\pi$
$887$	−20.6076	−	11.8978i	−0.691936	−	0.399489i	−0.804337	+	0.594174i	$0.797479\pi$
$888$		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	$-0.825600\pi$
$911$		−	31.4438i		−	1.04178i	0.853624	−	0.520889i	$-0.174400\pi$
$912$		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	−0.989400	−	0.145212i	$-0.953613\pi$
$929$	−11.2452	+	19.4772i	−0.368943	+	0.639027i	0.620458	+	0.784240i	$0.286947\pi$
$930$		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	0.770653	−	0.637255i	$-0.219930\pi$
$941$	−5.10912	−	8.84925i	−0.166552	−	0.288477i	−0.937206	+	0.348778i	$0.886597\pi$
$942$		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	−0.937483	−	0.348031i	$-0.886850\pi$
$947$	−5.14953	+	8.91925i	−0.167337	+	0.289837i	0.770146	+	0.637868i	$0.220184\pi$
$948$		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	$-0.495204\pi$
$953$	0.930159			0.0301308			0.0150654	+	0.999887i	$0.495204\pi$
$954$		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	−0.826951	−	0.562275i	$-0.809926\pi$
$971$	2.28935	−	3.96527i	0.0734688	−	0.127252i	0.900419	+	0.435023i	$0.143260\pi$
$972$		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	$0.0928900\pi$
$977$	22.7556	+	39.4138i	0.728015	+	1.26096i	−0.229707	+	0.973260i	$0.573777\pi$
$978$		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	−0.347673	−	0.937616i	$-0.613028\pi$
$983$	9.10765	−	5.25831i	0.290489	−	0.167714i	0.638162	+	0.769902i	$0.279695\pi$
$984$		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.89.2	yes	24
3.2	odd	2	inner	315.2.bb.b.89.11	yes	24
5.2	odd	4		1575.2.bk.i.26.2		24
5.3	odd	4		1575.2.bk.i.26.12		24
5.4	even	2	inner	315.2.bb.b.89.12	yes	24
7.2	even	3		2205.2.g.b.2204.24		24
7.3	odd	6	inner	315.2.bb.b.269.1	yes	24
7.5	odd	6		2205.2.g.b.2204.23		24
15.2	even	4		1575.2.bk.i.26.11		24
15.8	even	4		1575.2.bk.i.26.1		24
15.14	odd	2	inner	315.2.bb.b.89.1	✓	24
21.2	odd	6		2205.2.g.b.2204.2		24
21.5	even	6		2205.2.g.b.2204.1		24
21.17	even	6	inner	315.2.bb.b.269.12	yes	24
35.3	even	12		1575.2.bk.i.1151.1		24
35.9	even	6		2205.2.g.b.2204.4		24
35.17	even	12		1575.2.bk.i.1151.11		24
35.19	odd	6		2205.2.g.b.2204.3		24
35.24	odd	6	inner	315.2.bb.b.269.11	yes	24
105.17	odd	12		1575.2.bk.i.1151.2		24
105.38	odd	12		1575.2.bk.i.1151.12		24
105.44	odd	6		2205.2.g.b.2204.22		24
105.59	even	6	inner	315.2.bb.b.269.2	yes	24
105.89	even	6		2205.2.g.b.2204.21		24

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

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)

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

L-functions

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