LMFDB - Embedded newform 315.2.bb.b.89.1

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			89.1
Character	$\chi$	$=$	315.89
Dual form			315.2.bb.b.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28469 + 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(1.33613 + 1.79297i) q^{5} +(2.64140 - 0.151755i) q^{7} +6.68468 q^{8} +O(q^{10})$	\(q+(-1.28469 + 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(1.33613 + 1.79297i) q^{5} +(2.64140 - 0.151755i) q^{7} +6.68468 q^{8} +(-5.70613 + 0.669669i) q^{10} +(4.88189 - 2.81856i) q^{11} +3.53537 q^{13} +(-3.05569 + 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(-4.62703 + 2.67142i) q^{17} +(-1.24942 - 0.721351i) q^{19} +(4.07109 - 9.45005i) q^{20} +14.4839i q^{22} +(-1.49930 + 2.59686i) q^{23} +(-1.42951 + 4.79129i) q^{25} +(-4.54184 + 7.86670i) q^{26} +(-6.68220 - 10.1772i) q^{28} -2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(-3.55696 - 6.16083i) q^{32} -13.7277i q^{34} +(3.80134 + 4.53319i) q^{35} +(-0.946690 - 0.546572i) q^{37} +(3.21022 - 1.85342i) q^{38} +(8.93161 + 11.9855i) q^{40} -6.52058 q^{41} -0.486125i q^{43} +(-22.4649 - 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(-3.68608 - 2.12816i) q^{47} +(6.95394 - 0.801688i) q^{49} +(-8.82483 - 9.33618i) q^{50} +(-8.13432 - 14.0891i) q^{52} +(-2.01102 - 3.48318i) q^{53} +(11.5764 + 4.98714i) q^{55} +(17.6569 - 1.01443i) q^{56} +(4.88206 + 2.81866i) q^{58} +(5.70978 + 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} +3.91326i q^{62} +2.33411 q^{64} +(4.72371 + 6.33883i) q^{65} +(2.15623 - 1.24490i) q^{67} +(21.2921 + 12.2930i) q^{68} +(-14.9705 + 2.63479i) q^{70} -8.13849i q^{71} +(1.56901 + 2.71761i) q^{73} +(2.43240 - 1.40435i) q^{74} +6.63886i q^{76} +(12.4673 - 8.18578i) q^{77} +(-6.40252 + 11.0895i) q^{79} +(-17.7046 + 2.07781i) q^{80} +(8.37690 - 14.5092i) q^{82} +6.77241i q^{83} +(-10.9721 - 4.72679i) q^{85} +(1.08170 + 0.624518i) q^{86} +(32.6339 - 18.8412i) q^{88} +(5.16513 - 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} +13.7986 q^{92} +(9.47093 - 5.46804i) q^{94} +(-0.376019 - 3.20399i) q^{95} -14.7321 q^{97} +(-7.14976 + 16.5034i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.529370\pi$
$2$	−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
$5$	1.33613	+	1.79297i	0.597535	+	0.801843i
$5$	1.33613	+	1.79297i	0.597535	+	0.801843i
$6$		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
$10$	−5.70613	+	0.669669i	−1.80444	+	0.211768i
$11$	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	$-0.336899\pi$
$13$	3.53537			0.980535			0.490267	+	0.871572i	$0.336899\pi$
$14$	−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
$25$	−1.42951	+	4.79129i	−0.285903	+	0.958259i
$26$	−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
$35$	3.80134	+	4.53319i	0.642544	+	0.766249i
$36$		0			0
$37$	−0.946690	−	0.546572i	−0.155635	−	0.0898558i	0.420160	−	0.907450i	$-0.361974\pi$
$37$	−0.946690	−	0.546572i	−0.155635	−	0.0898558i	−0.575795	+	0.817594i	$0.695307\pi$
$38$	3.21022	−	1.85342i	0.520766	−	0.300665i
$39$		0			0
$40$	8.93161	+	11.9855i	1.41221	+	1.89507i
$41$	−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	$-0.988199\pi$
$43$		−	0.486125i		−	0.0741333i	0.999313	−	0.0370667i	$-0.0118014\pi$
$44$	−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	$0.100098\pi$
$59$	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
$65$	4.72371	+	6.33883i	0.585904	+	0.786235i
$66$		0			0
$67$	2.15623	−	1.24490i	0.263425	−	0.152089i	−0.362471	−	0.931995i	$-0.618067\pi$
$67$	2.15623	−	1.24490i	0.263425	−	0.152089i	0.625896	+	0.779907i	$0.284733\pi$
$68$	21.2921	+	12.2930i	2.58205	+	1.49075i
$69$		0			0
$70$	−14.9705	+	2.63479i	−1.78932	+	0.314918i
$71$		−	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	0.943117	−	0.332461i	$-0.107879\pi$
$73$	1.56901	+	2.71761i	0.183639	+	0.318072i	−0.759478	+	0.650533i	$0.774546\pi$
$74$	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	$0.910653\pi$
$80$	−17.7046	+	2.07781i	−1.97944	+	0.232306i
$81$		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	$-0.648912\pi$
$89$	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
$95$	−0.376019	−	3.20399i	−0.0385787	−	0.328723i
$96$		0			0
$97$	−14.7321			−1.49582			−0.747908	−	0.663802i	$-0.768942\pi$
$97$	−14.7321			−1.49582			−0.747908	+	0.663802i	$0.768942\pi$
$98$	−7.14976	+	16.5034i	−0.722235	+	1.66710i
$99$		0			0
$100$	22.3832	−	5.32714i	2.23832	−	0.532714i
$101$	−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	−0.946205	−	0.323569i	$-0.895117\pi$
$103$	−1.95755	+	3.39058i	−0.192883	+	0.334084i	0.753321	+	0.657653i	$0.228451\pi$
$104$	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	$-0.343970\pi$
$110$	−25.9692	+	19.3523i	−2.47607	+	1.84517i
$111$		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
$115$	−6.65937	+	0.781540i	−0.620990	+	0.0728790i
$116$	−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	$-0.944110\pi$
$127$		−	3.93715i		−	0.349366i	0.984625	−	0.174683i	$-0.0558900\pi$
$128$	4.11531	−	7.12793i	0.363746	−	0.630026i
$129$		0			0
$130$	−20.1733	+	2.36753i	−1.76931	+	0.207646i
$131$	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	0.719401	−	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	$0.548944\pi$
$140$	9.31927	−	25.5791i	0.787622	−	2.16183i
$141$		0			0
$142$	18.1093	+	10.4554i	1.51970	+	0.877398i
$143$	17.2593	−	9.96465i	1.44329	−	0.833286i
$144$		0			0
$145$	3.93386	−	2.93153i	0.326689	−	0.243450i
$146$	−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	0.704707	−	0.709498i	$-0.251078\pi$
$157$	−3.28398	−	5.68802i	−0.262090	−	0.453953i	−0.966797	+	0.255545i	$0.917745\pi$
$158$	−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	−0.297910	−	0.954594i	$-0.596290\pi$
$163$	−16.2598	−	9.38762i	−1.27357	−	0.735295i	−0.975658	+	0.219299i	$0.929623\pi$
$164$	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
$170$	24.6135	−	18.3420i	1.88777	−	1.40677i
$171$		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
$175$	−3.04881	+	12.8726i	−0.230469	+	0.973080i
$176$			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
$185$	−0.284911	−	2.42768i	−0.0209471	−	0.178487i
$186$		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	$-0.311725\pi$
$193$	21.6068	−	12.4747i	1.55529	−	0.897948i	0.997697	−	0.0678339i	$-0.0216088\pi$
$194$	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	$0.312522\pi$
$200$	−9.55586	+	32.0283i	−0.675701	+	2.26474i
$201$		0			0
$202$	38.3701			2.69971
$203$	−0.332956	−	5.79533i	−0.0233689	−	0.406753i
$204$		0			0
$205$	−8.71234	−	11.6912i	−0.608496	−	0.816551i
$206$	−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
$215$	0.871609	−	0.649526i	0.0594432	−	0.0442973i
$216$		0			0
$217$	3.36841	−	2.21164i	0.228663	−	0.150136i
$218$	28.3624			1.92094
$219$		0			0
$220$	−6.76093	−	57.6087i	−0.455822	−	3.88398i
$221$	−16.3583	+	9.44444i	−1.10038	+	0.635302i
$222$		0			0
$223$	7.84782			0.525529			0.262765	−	0.964860i	$-0.415366\pi$
$223$	7.84782			0.525529			0.262765	+	0.964860i	$0.415366\pi$
$224$	−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
$235$	−1.10935	−	9.45256i	−0.0723658	−	0.616617i
$236$	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
$245$	10.7288	+	11.3971i	0.685436	+	0.728133i
$246$		0			0
$247$	−4.41715	−	2.55024i	−0.281057	−	0.162268i
$248$	8.81704	−	5.09052i	0.559883	−	0.323248i
$249$		0			0
$250$	4.94842	−	28.2970i	0.312966	−	1.78966i
$251$	−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	0.885305	−	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	0.987306	−	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
$275$	6.52581	+	27.4197i	0.393521	+	1.65347i
$276$		0			0
$277$	−14.3760	+	8.29998i	−0.863770	+	0.498698i	−0.865273	−	0.501301i	$-0.832855\pi$
$277$	−14.3760	+	8.29998i	−0.863770	+	0.498698i	0.00150328	+	0.999999i	$0.499521\pi$
$278$	−51.8491	−	29.9351i	−3.10970	−	1.79539i
$279$		0			0
$280$	25.4108	+	30.3030i	1.51858	+	1.81095i
$281$		−	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	0.947600	−	0.319458i	$-0.103501\pi$
$283$	3.31643	+	5.74423i	0.197141	+	0.341459i	−0.750459	+	0.660917i	$0.770168\pi$
$284$	−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
$290$	1.46928	+	12.5195i	0.0862792	+	0.735170i
$291$		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
$305$	1.82667	+	15.5648i	0.104595	+	0.891235i
$306$		0			0
$307$	25.5071			1.45576			0.727882	−	0.685702i	$-0.240505\pi$
$307$	25.5071			1.45576			0.727882	+	0.685702i	$0.240505\pi$
$308$	−61.3069	−	30.8500i	−3.49329	−	1.75784i
$309$		0			0
$310$	−7.01637	+	5.22862i	−0.398503	+	0.296966i
$311$	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	−0.996444	−	0.0842599i	$-0.973147\pi$
$313$	−7.52345	+	13.0310i	−0.425251	+	0.736556i	0.571193	+	0.820816i	$0.306481\pi$
$314$	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
$320$	3.11867	+	4.18500i	0.174339	+	0.233949i
$321$		0			0
$322$	−11.1879	−	17.0396i	−0.623477	−	0.949581i
$323$	7.70812			0.428891
$324$		0			0
$325$	−5.05386	+	16.9390i	−0.280338	+	0.939606i
$326$	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	$-0.786237\pi$
$337$		−	22.8443i		−	1.24441i	0.782855	−	0.622204i	$-0.213763\pi$
$338$	0.643841	−	1.11516i	0.0350203	−	0.0606570i
$339$		0			0
$340$	6.40797	+	54.6012i	0.347521	+	2.96117i
$341$	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	$-0.0525516\pi$
$350$	−24.7267	−	23.3213i	−1.32170	−	1.24658i
$351$		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
$355$	14.5921	−	10.8741i	0.774468	−	0.577136i
$356$	−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	$-0.799967\pi$
$367$	−17.5018	−	30.3140i	−0.913587	−	1.58238i	−0.104631	−	0.994511i	$-0.533366\pi$
$368$	−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	0.359615	−	0.933101i	$-0.382908\pi$
$373$	−5.18881	−	2.99576i	−0.268667	−	0.155115i	−0.628282	+	0.777986i	$0.716241\pi$
$374$	−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	$0.525603\pi$
$380$	−11.9033	+	8.87037i	−0.610626	+	0.455040i
$381$		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
$385$	31.3348	+	11.4162i	1.59697	+	0.581825i
$386$			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
$395$	−28.4378	+	3.33744i	−1.43086	+	0.167925i
$396$		0			0
$397$	−11.3663	+	19.6870i	−0.570459	+	0.988064i	0.426060	+	0.904695i	$0.359901\pi$
$397$	−11.3663	+	19.6870i	−0.570459	+	0.988064i	−0.996519	+	0.0833689i	$0.973432\pi$
$398$			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	$0.301326\pi$
$410$	37.2073	−	4.36663i	1.83754	−	0.215652i
$411$		0			0
$412$	18.0161			0.887587
$413$	16.5826	+	25.2559i	0.815976	+	1.24276i
$414$		0			0
$415$	−12.1428	+	9.04882i	−0.596064	+	0.444189i
$416$	−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
$425$	−6.18513	−	25.9883i	−0.300023	−	1.26062i
$426$		0			0
$427$	16.5639	+	8.33508i	0.801585	+	0.403363i
$428$	−68.2062			−3.29687
$429$		0			0
$430$	0.325542	+	2.77389i	0.0156991	+	0.133769i
$431$	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	$-0.670446\pi$
$433$	−21.2351			−1.02050			−0.510248	+	0.860028i	$0.670446\pi$
$434$	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
$445$	22.9417	−	2.69243i	1.08754	−	0.127633i
$446$	−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
$455$	13.4391	+	16.0265i	0.630036	+	0.751334i
$456$		0			0
$457$	14.6293	+	8.44623i	0.684330	+	0.395098i	0.801484	−	0.598016i	$-0.204044\pi$
$457$	14.6293	+	8.44623i	0.684330	+	0.395098i	−0.117155	+	0.993114i	$0.537377\pi$
$458$	47.7475	−	27.5670i	2.23110	−	1.28812i
$459$		0			0
$460$	18.4367	+	24.7405i	0.859616	+	1.15353i
$461$	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	$-0.910485\pi$
$463$		−	11.9434i		−	0.555055i	0.960718	−	0.277528i	$-0.0895150\pi$
$464$	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	0.830074	−	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
$485$	−19.6840	−	26.4142i	−0.893803	−	1.19941i
$486$		0			0
$487$	−19.6695	+	11.3562i	−0.891310	+	0.514598i	−0.874371	−	0.485258i	$-0.838726\pi$
$487$	−19.6695	+	11.3562i	−0.891310	+	0.514598i	−0.0169394	+	0.999857i	$0.505392\pi$
$488$	40.5732	+	23.4249i	1.83666	+	1.06040i
$489$		0			0
$490$	−39.1432	+	9.23138i	−1.76831	+	0.417031i
$491$			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	$0.00597826\pi$
$500$	39.4583	+	33.0148i	1.76463	+	1.47647i
$501$		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	$0.467338\pi$
$509$	−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
$515$	−8.69477	+	1.02041i	−0.383137	+	0.0449648i
$516$		0			0
$517$	−23.9934			−1.05523
$518$	6.21181	−	4.07856i	0.272931	−	0.179202i
$519$		0			0
$520$	31.5765	+	42.3731i	1.38472	+	1.85818i
$521$	−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	$-0.621644\pi$
$523$	14.1124	−	24.4434i	0.617092	−	1.06884i	0.990014	−	0.140972i	$-0.0450229\pi$
$524$	−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
$530$	13.8077	+	18.5288i	0.599769	+	0.804839i
$531$		0			0
$532$	1.00748	+	17.5358i	0.0436797	+	0.760275i
$533$	−23.0527			−0.998521
$534$		0			0
$535$	32.9172	−	3.86314i	1.42313	−	0.167018i
$536$	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	$0.155353\pi$
$547$			21.9338i			0.937820i	−0.883246	+	0.468910i	$0.844647\pi$
$548$	−13.0256	+	22.5610i	−0.556427	+	0.963760i
$549$		0			0
$550$	−69.3965	−	20.7049i	−2.95907	−	0.882860i
$551$	−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
$560$	−46.4496	+	8.17507i	−1.96285	+	0.345460i
$561$		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
$565$	−10.0786	−	13.5247i	−0.424010	−	0.568987i
$566$	−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	$-0.930764\pi$
$577$	−16.2167	−	28.0881i	−0.675108	−	1.16932i	0.301329	−	0.953520i	$-0.402570\pi$
$578$	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
$590$	−39.2035	−	52.6079i	−1.61398	−	2.16583i
$591$		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
$595$	−29.6989	−	10.8202i	−1.21754	−	0.443587i
$596$		−	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
$605$	46.1424	−	5.41525i	1.87596	−	0.220161i
$606$		0			0
$607$	−13.1333	+	22.7475i	−0.533063	+	0.923292i	0.466192	+	0.884684i	$0.345626\pi$
$607$	−13.1333	+	22.7475i	−0.533063	+	0.923292i	−0.999254	+	0.0386080i	$0.987708\pi$
$608$			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	0.0263906	−	0.999652i	$-0.491599\pi$
$613$	22.4144	−	12.9410i	0.905310	−	0.522681i	0.878919	+	0.476971i	$0.158265\pi$
$614$	−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	$0.294151\pi$
$620$	−1.82667	−	15.5648i	−0.0733609	−	0.625095i
$621$		0			0
$622$	−79.7432			−3.19741
$623$	12.2855	−	24.4145i	0.492209	−	0.978145i
$624$		0			0
$625$	−20.9130	−	13.6984i	−0.836519	−	0.547938i
$626$	−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
$635$	7.05921	−	5.26055i	0.280136	−	0.208758i
$636$		0			0
$637$	24.5847	−	2.83426i	0.974083	−	0.112298i
$638$	31.7782			1.25811
$639$		0			0
$640$	18.2788	−	2.14519i	0.722532	−	0.0847960i
$641$	−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	$-0.382991\pi$
$643$	18.2255			0.718742			0.359371	+	0.933195i	$0.382991\pi$
$644$	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
$655$	8.76779	−	1.02898i	0.342586	−	0.0402057i
$656$	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
$665$	−1.47944	−	8.40595i	−0.0573700	−	0.325969i
$666$		0			0
$667$	5.69763	+	3.28953i	0.220613	+	0.127371i
$668$	−19.1520	+	11.0574i	−0.741011	+	0.427823i
$669$		0			0
$670$	−11.4700	+	8.54751i	−0.443127	+	0.330219i
$671$	39.5080			1.52519
$672$		0			0
$673$		−	36.0634i		−	1.39014i	−0.718941	−	0.695071i	$-0.755373\pi$
$673$		−	36.0634i		−	1.39014i	0.718941	−	0.695071i	$-0.244627\pi$
$674$	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
$695$	−41.7789	+	31.1338i	−1.58476	+	1.18097i
$696$		0			0
$697$	30.1709	−	17.4192i	1.14280	−	0.659799i
$698$	13.6635	+	7.88861i	0.517170	+	0.298588i
$699$		0			0
$700$	58.3145	−	17.4678i	2.20408	−	0.660222i
$701$			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	$0.942637\pi$
$710$	5.45009	+	46.4393i	0.204538	+	1.74284i
$711$		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
$725$	10.5123	+	3.13642i	0.390417	+	0.116484i
$726$		0			0
$727$	−10.4196			−0.386442			−0.193221	−	0.981155i	$-0.561894\pi$
$727$	−10.4196			−0.386442			−0.193221	+	0.981155i	$0.561894\pi$
$728$	62.4236	−	3.58639i	2.31357	−	0.132921i
$729$		0			0
$730$	−10.7729	−	14.4563i	−0.398722	−	0.535052i
$731$	1.29864	+	2.24931i	0.0480320	+	0.0831938i
$732$		0			0
$733$	−11.3541	+	19.6659i	−0.419374	+	0.726377i	−0.995877	−	0.0907181i	$-0.971084\pi$
$733$	−11.3541	+	19.6659i	−0.419374	+	0.726377i	0.576503	+	0.817095i	$0.304417\pi$
$734$	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	$-0.351174\pi$
$740$	−9.01919	+	6.72113i	−0.331552	+	0.247074i
$741$		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
$745$	1.21865	+	10.3839i	0.0446477	+	0.380435i
$746$	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	$-0.984599\pi$
$757$		−	2.66139i		−	0.0967300i	0.998830	−	0.0483650i	$-0.0154011\pi$
$758$	4.01904	−	6.96118i	0.145978	−	0.252842i
$759$		0			0
$760$	−2.51357	−	21.4177i	−0.0911767	−	0.776901i
$761$	−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	$0.933515\pi$
$770$	−65.6581	+	55.0581i	−2.36615	+	1.98416i
$771$		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
$775$	1.76315	+	7.40828i	0.0633341	+	0.266113i
$776$	−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	0.569026	−	0.822319i	$-0.307320\pi$
$787$	−11.9967	−	20.7789i	−0.427636	−	0.740688i	−0.996663	+	0.0816315i	$0.973987\pi$
$788$	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
$800$	34.6031	−	8.23542i	1.22340	−	0.291166i
$801$		0			0
$802$	−21.6163	+	12.4802i	−0.763299	+	0.440691i
$803$	15.3195	+	8.84470i	0.540612	+	0.312123i
$804$		0			0
$805$	−17.4714	+	3.07495i	−0.615787	+	0.108378i
$806$			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
$815$	−4.89348	−	41.6965i	−0.171411	−	1.46057i
$816$		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	−0.993514	−	0.113713i	$-0.963725\pi$
$823$	−39.9277	+	23.0523i	−1.39179	+	0.803551i	−0.398278	+	0.917265i	$0.630392\pi$
$824$	−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	$0.294055\pi$
$830$	−4.53527	−	38.6443i	−0.157422	−	1.34136i
$831$		0			0
$832$	8.25194			0.286085
$833$	−30.0344	+	22.2863i	−1.04063	+	0.772175i
$834$		0			0
$835$	8.61669	−	6.42118i	0.298193	−	0.222214i
$836$	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
$845$	−0.669622	−	0.898577i	−0.0230357	−	0.0309120i
$846$		0			0
$847$	24.7097	−	49.1045i	0.849036	−	1.68725i
$848$	32.0640			1.10108
$849$		0			0
$850$	65.7736	+	19.6240i	2.25602	+	0.673098i
$851$	2.83875	−	1.63895i	0.0973109	−	0.0561825i
$852$		0			0
$853$	38.1187			1.30516			0.652580	−	0.757719i	$-0.273686\pi$
$853$	38.1187			1.30516			0.652580	+	0.757719i	$0.273686\pi$
$854$	−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
$865$	0.876718	+	7.47036i	0.0298093	+	0.254000i
$866$	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
$875$	−27.1539	+	11.7331i	−0.917970	+	0.396650i
$876$		0			0
$877$	33.3881	+	19.2766i	1.12743	+	0.650925i	0.943289	−	0.331974i	$-0.107715\pi$
$877$	33.3881	+	19.2766i	1.12743	+	0.650925i	0.184146	+	0.982899i	$0.441048\pi$
$878$	−47.7152	+	27.5484i	−1.61031	+	0.929712i
$879$		0			0
$880$	−80.5756	+	60.0452i	−2.71620	+	2.02412i
$881$	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	$0.141675\pi$
$883$			25.5869i			0.861068i	−0.902574	+	0.430534i	$0.858325\pi$
$884$	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
$905$	3.93646	−	2.93346i	0.130852	−	0.0975116i
$906$		0			0
$907$	33.5806	−	19.3878i	1.11503	−	0.643760i	0.174899	−	0.984586i	$-0.444040\pi$
$907$	33.5806	−	19.3878i	1.11503	−	0.643760i	0.940126	+	0.340826i	$0.110707\pi$
$908$	−2.18978	−	1.26427i	−0.0726704	−	0.0419563i
$909$		0			0
$910$	−52.9263	+	9.31496i	−1.75449	+	0.308788i
$911$			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	$0.319318\pi$
$920$	−44.5158	+	5.22435i	−1.46764	+	0.172242i
$921$		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
$935$	−66.8873	+	7.84986i	−2.18745	+	0.256718i
$936$		0			0
$937$	−32.0994			−1.04864			−0.524321	−	0.851521i	$-0.675681\pi$
$937$	−32.0994			−1.04864			−0.524321	+	0.851521i	$0.675681\pi$
$938$	0.970808	+	16.8976i	0.0316980	+	0.551725i
$939$		0			0
$940$	−35.1176	+	26.1698i	−1.14541	+	0.853563i
$941$	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	−0.937483	−	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
$950$	4.29123	+	18.0306i	0.139226	+	0.584990i
$951$		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
$955$	2.59440	+	22.1064i	0.0839527	+	0.715346i
$956$	−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	$-0.978379\pi$
$967$		−	4.22117i		−	0.135744i	0.997694	−	0.0678719i	$-0.0216209\pi$
$968$	69.4443	−	120.281i	2.23202	−	3.86598i
$969$		0			0
$970$	84.0632	−	9.86561i	2.69911	−	0.316766i
$971$	−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	$0.0928900\pi$
$977$	22.7556	+	39.4138i	0.728015	+	1.26096i	−0.229707	+	0.973260i	$0.573777\pi$
$978$		0			0
$979$		−	58.2329i		−	1.86113i
$980$	20.7341	−	68.9788i	0.662327	−	2.20345i
$981$		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
$985$	−25.5232	−	34.2500i	−0.813236	−	1.09130i
$986$	−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	$0.0446623\pi$
$997$	19.4567	+	33.7000i	0.616201	+	1.06729i	−0.373972	+	0.927440i	$0.622004\pi$
$998$	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.89.1	✓	24
3.2	odd	2	inner	315.2.bb.b.89.12	yes	24
5.2	odd	4		1575.2.bk.i.26.1		24
5.3	odd	4		1575.2.bk.i.26.11		24
5.4	even	2	inner	315.2.bb.b.89.11	yes	24
7.2	even	3		2205.2.g.b.2204.22		24
7.3	odd	6	inner	315.2.bb.b.269.2	yes	24
7.5	odd	6		2205.2.g.b.2204.21		24
15.2	even	4		1575.2.bk.i.26.12		24
15.8	even	4		1575.2.bk.i.26.2		24
15.14	odd	2	inner	315.2.bb.b.89.2	yes	24
21.2	odd	6		2205.2.g.b.2204.4		24
21.5	even	6		2205.2.g.b.2204.3		24
21.17	even	6	inner	315.2.bb.b.269.11	yes	24
35.3	even	12		1575.2.bk.i.1151.2		24
35.9	even	6		2205.2.g.b.2204.2		24
35.17	even	12		1575.2.bk.i.1151.12		24
35.19	odd	6		2205.2.g.b.2204.1		24
35.24	odd	6	inner	315.2.bb.b.269.12	yes	24
105.17	odd	12		1575.2.bk.i.1151.1		24
105.38	odd	12		1575.2.bk.i.1151.11		24
105.44	odd	6		2205.2.g.b.2204.24		24
105.59	even	6	inner	315.2.bb.b.269.1	yes	24
105.89	even	6		2205.2.g.b.2204.23		24

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

\(f(q)\)	\(=\)	\(q+(-1.28469 + 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(1.33613 + 1.79297i) q^{5} +(2.64140 - 0.151755i) q^{7} +6.68468 q^{8} +O(q^{10})\)	\(q+(-1.28469 + 2.22514i) q^{2} +(-2.30084 - 3.98517i) q^{4} +(1.33613 + 1.79297i) q^{5} +(2.64140 - 0.151755i) q^{7} +6.68468 q^{8} +(-5.70613 + 0.669669i) q^{10} +(4.88189 - 2.81856i) q^{11} +3.53537 q^{13} +(-3.05569 + 6.07244i) q^{14} +(-3.98605 + 6.90403i) q^{16} +(-4.62703 + 2.67142i) q^{17} +(-1.24942 - 0.721351i) q^{19} +(4.07109 - 9.45005i) q^{20} +14.4839i q^{22} +(-1.49930 + 2.59686i) q^{23} +(-1.42951 + 4.79129i) q^{25} +(-4.54184 + 7.86670i) q^{26} +(-6.68220 - 10.1772i) q^{28} -2.19404i q^{29} +(1.31899 - 0.761520i) q^{31} +(-3.55696 - 6.16083i) q^{32} -13.7277i q^{34} +(3.80134 + 4.53319i) q^{35} +(-0.946690 - 0.546572i) q^{37} +(3.21022 - 1.85342i) q^{38} +(8.93161 + 11.9855i) q^{40} -6.52058 q^{41} -0.486125i q^{43} +(-22.4649 - 12.9701i) q^{44} +(-3.85226 - 6.67231i) q^{46} +(-3.68608 - 2.12816i) q^{47} +(6.95394 - 0.801688i) q^{49} +(-8.82483 - 9.33618i) q^{50} +(-8.13432 - 14.0891i) q^{52} +(-2.01102 - 3.48318i) q^{53} +(11.5764 + 4.98714i) q^{55} +(17.6569 - 1.01443i) q^{56} +(4.88206 + 2.81866i) q^{58} +(5.70978 + 9.88963i) q^{59} +(6.06957 + 3.50427i) q^{61} +3.91326i q^{62} +2.33411 q^{64} +(4.72371 + 6.33883i) q^{65} +(2.15623 - 1.24490i) q^{67} +(21.2921 + 12.2930i) q^{68} +(-14.9705 + 2.63479i) q^{70} -8.13849i q^{71} +(1.56901 + 2.71761i) q^{73} +(2.43240 - 1.40435i) q^{74} +6.63886i q^{76} +(12.4673 - 8.18578i) q^{77} +(-6.40252 + 11.0895i) q^{79} +(-17.7046 + 2.07781i) q^{80} +(8.37690 - 14.5092i) q^{82} +6.77241i q^{83} +(-10.9721 - 4.72679i) q^{85} +(1.08170 + 0.624518i) q^{86} +(32.6339 - 18.8412i) q^{88} +(5.16513 - 8.94627i) q^{89} +(9.33831 - 0.536509i) q^{91} +13.7986 q^{92} +(9.47093 - 5.46804i) q^{94} +(-0.376019 - 3.20399i) q^{95} -14.7321 q^{97} +(-7.14976 + 16.5034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4}+O(q^{10}) \) 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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