LMFDB - Embedded newform 585.2.bs.b.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.b.334.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16430 + 0.672211i) q^{2} +(-0.0962645 + 0.166735i) q^{4} +(0.868136 - 2.06066i) q^{5} +(3.39681 + 1.96115i) q^{7} -2.94768i q^{8} +O(q^{10})$	\(q+(-1.16430 + 0.672211i) q^{2} +(-0.0962645 + 0.166735i) q^{4} +(0.868136 - 2.06066i) q^{5} +(3.39681 + 1.96115i) q^{7} -2.94768i q^{8} +(0.374428 + 2.98281i) q^{10} +(1.37576 + 2.38289i) q^{11} +(-1.14795 - 3.41792i) q^{13} -5.27322 q^{14} +(1.78894 + 3.09853i) q^{16} +(-4.09295 - 2.36307i) q^{17} +(1.85142 - 3.20675i) q^{19} +(0.260014 + 0.343117i) q^{20} +(-3.20361 - 1.84960i) q^{22} +(4.57432 - 2.64098i) q^{23} +(-3.49268 - 3.57787i) q^{25} +(3.63413 + 3.20784i) q^{26} +(-0.653984 + 0.377578i) q^{28} +(1.31107 + 2.27085i) q^{29} +4.71963 q^{31} +(0.939806 + 0.542597i) q^{32} +6.35392 q^{34} +(6.99016 - 5.29714i) q^{35} +(3.66040 - 2.11333i) q^{37} +4.97818i q^{38} +(-6.07419 - 2.55899i) q^{40} +(0.408805 + 0.708072i) q^{41} +(4.85491 + 2.80298i) q^{43} -0.529747 q^{44} +(-3.55060 + 6.14981i) q^{46} +8.36266i q^{47} +(4.19221 + 7.26111i) q^{49} +(6.47163 + 1.81791i) q^{50} +(0.680394 + 0.137621i) q^{52} +7.01335i q^{53} +(6.10468 - 0.766311i) q^{55} +(5.78085 - 10.0127i) q^{56} +(-3.05297 - 1.76264i) q^{58} +(-1.09316 + 1.89340i) q^{59} +(6.41847 - 11.1171i) q^{61} +(-5.49508 + 3.17259i) q^{62} -8.61471 q^{64} +(-8.03977 - 0.601683i) q^{65} +(-10.8821 + 6.28278i) q^{67} +(0.788011 - 0.454959i) q^{68} +(-4.57787 + 10.8663i) q^{70} +(6.08542 - 10.5403i) q^{71} +0.955441i q^{73} +(-2.84121 + 4.92112i) q^{74} +(0.356452 + 0.617393i) q^{76} +10.7923i q^{77} +11.1009 q^{79} +(7.93807 - 0.996455i) q^{80} +(-0.951947 - 0.549607i) q^{82} -11.7889i q^{83} +(-8.42273 + 6.38274i) q^{85} -7.53678 q^{86} +(7.02400 - 4.05531i) q^{88} +(5.60164 + 9.70232i) q^{89} +(2.80369 - 13.8613i) q^{91} +1.01693i q^{92} +(-5.62147 - 9.73668i) q^{94} +(-5.00076 - 6.59905i) q^{95} +(-1.52806 - 0.882226i) q^{97} +(-9.76200 - 5.63610i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) $ 24 * q + 8 * q^4 - 4 * q^5	$ 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) $ 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.16430	+	0.672211i	−0.823287	+	0.475325i	−0.851549	−	0.524276i	$-0.824336\pi$
$2$	−1.16430	+	0.672211i	−0.823287	+	0.475325i	0.0282616	+	0.999601i	$0.491003\pi$
$3$		0			0
$3$		0			0
$4$	−0.0962645	+	0.166735i	−0.0481322	+	0.0833675i
$5$	0.868136	−	2.06066i	0.388242	−	0.921557i
$5$	0.868136	−	2.06066i	0.388242	−	0.921557i
$6$		0			0
$7$	3.39681	+	1.96115i	1.28387	+	0.741244i	0.977554	−	0.210684i	$-0.0675693\pi$
$7$	3.39681	+	1.96115i	1.28387	+	0.741244i	0.306319	+	0.951929i	$0.400903\pi$
$8$		−	2.94768i		−	1.04216i
$9$		0			0
$10$	0.374428	+	2.98281i	0.118404	+	0.943248i
$11$	1.37576	+	2.38289i	0.414807	+	0.718467i	0.995408	−	0.0957210i	$-0.0305157\pi$
$11$	1.37576	+	2.38289i	0.414807	+	0.718467i	−0.580601	+	0.814188i	$0.697182\pi$
$12$		0			0
$13$	−1.14795	−	3.41792i	−0.318384	−	0.947962i
$13$	−1.14795	−	3.41792i	−0.318384	−	0.947962i
$14$	−5.27322			−1.40933
$15$		0			0
$16$	1.78894	+	3.09853i	0.447234	+	0.774633i
$17$	−4.09295	−	2.36307i	−0.992686	−	0.573128i	−0.0866102	−	0.996242i	$-0.527603\pi$
$17$	−4.09295	−	2.36307i	−0.992686	−	0.573128i	−0.906076	+	0.423115i	$0.860937\pi$
$18$		0			0
$19$	1.85142	−	3.20675i	0.424745	−	0.735680i	−0.571652	−	0.820496i	$-0.693697\pi$
$19$	1.85142	−	3.20675i	0.424745	−	0.735680i	0.996397	+	0.0848167i	$0.0270305\pi$
$20$	0.260014	+	0.343117i	0.0581409	+	0.0767234i
$21$		0			0
$22$	−3.20361	−	1.84960i	−0.683011	−	0.394337i
$23$	4.57432	−	2.64098i	0.953811	−	0.550683i	0.0595484	−	0.998225i	$-0.481034\pi$
$23$	4.57432	−	2.64098i	0.953811	−	0.550683i	0.894263	+	0.447542i	$0.147701\pi$
$24$		0			0
$25$	−3.49268	−	3.57787i	−0.698536	−	0.715575i
$26$	3.63413	+	3.20784i	0.712711	+	0.629109i
$27$		0			0
$28$	−0.653984	+	0.377578i	−0.123591	+	0.0713555i
$29$	1.31107	+	2.27085i	0.243460	+	0.421685i	0.961698	−	0.274113i	$-0.0883842\pi$
$29$	1.31107	+	2.27085i	0.243460	+	0.421685i	−0.718237	+	0.695798i	$0.755051\pi$
$30$		0			0
$31$	4.71963			0.847670			0.423835	−	0.905739i	$-0.360684\pi$
$31$	4.71963			0.847670			0.423835	+	0.905739i	$0.360684\pi$
$32$	0.939806	+	0.542597i	0.166136	+	0.0959186i
$33$		0			0
$34$	6.35392			1.08969
$35$	6.99016	−	5.29714i	1.18155	−	0.895380i
$36$		0			0
$37$	3.66040	−	2.11333i	0.601765	−	0.347429i	−0.167970	−	0.985792i	$-0.553721\pi$
$37$	3.66040	−	2.11333i	0.601765	−	0.347429i	0.769736	+	0.638363i	$0.220388\pi$
$38$			4.97818i			0.807568i
$39$		0			0
$40$	−6.07419	−	2.55899i	−0.960414	−	0.404612i
$41$	0.408805	+	0.708072i	0.0638447	+	0.110582i	0.896181	−	0.443689i	$-0.146330\pi$
$41$	0.408805	+	0.708072i	0.0638447	+	0.110582i	−0.832336	+	0.554271i	$0.812997\pi$
$42$		0			0
$43$	4.85491	+	2.80298i	0.740367	+	0.427451i	0.822203	−	0.569195i	$-0.192745\pi$
$43$	4.85491	+	2.80298i	0.740367	+	0.427451i	−0.0818360	+	0.996646i	$0.526078\pi$
$44$	−0.529747			−0.0798624
$45$		0			0
$46$	−3.55060	+	6.14981i	−0.523507	+	0.906741i
$47$			8.36266i			1.21982i	0.792471	+	0.609910i	$0.208794\pi$
$47$			8.36266i			1.21982i	−0.792471	+	0.609910i	$0.791206\pi$
$48$		0			0
$49$	4.19221	+	7.26111i	0.598887	+	1.03730i
$50$	6.47163	+	1.81791i	0.915226	+	0.257092i
$51$		0			0
$52$	0.680394	+	0.137621i	0.0943537	+	0.0190846i
$53$			7.01335i			0.963358i	0.876348	+	0.481679i	$0.159973\pi$
$53$			7.01335i			0.963358i	−0.876348	+	0.481679i	$0.840027\pi$
$54$		0			0
$55$	6.10468	−	0.766311i	0.823154	−	0.103329i
$56$	5.78085	−	10.0127i	0.772498	−	1.33801i
$57$		0			0
$58$	−3.05297	−	1.76264i	−0.400875	−	0.231445i
$59$	−1.09316	+	1.89340i	−0.142317	+	0.246500i	−0.928369	−	0.371661i	$-0.878789\pi$
$59$	−1.09316	+	1.89340i	−0.142317	+	0.246500i	0.786052	+	0.618161i	$0.212122\pi$
$60$		0			0
$61$	6.41847	−	11.1171i	0.821801	−	1.42340i	−0.0825394	−	0.996588i	$-0.526303\pi$
$61$	6.41847	−	11.1171i	0.821801	−	1.42340i	0.904340	−	0.426813i	$-0.140364\pi$
$62$	−5.49508	+	3.17259i	−0.697876	+	0.402919i
$63$		0			0
$64$	−8.61471			−1.07684
$65$	−8.03977	−	0.601683i	−0.997211	−	0.0746296i
$66$		0			0
$67$	−10.8821	+	6.28278i	−1.32946	+	0.767563i	−0.985216	−	0.171318i	$-0.945198\pi$
$67$	−10.8821	+	6.28278i	−1.32946	+	0.767563i	−0.344243	+	0.938881i	$0.611864\pi$
$68$	0.788011	−	0.454959i	0.0955604	−	0.0551718i
$69$		0			0
$70$	−4.57787	+	10.8663i	−0.547161	+	1.29878i
$71$	6.08542	−	10.5403i	0.722206	−	1.25090i	−0.237908	−	0.971288i	$-0.576462\pi$
$71$	6.08542	−	10.5403i	0.722206	−	1.25090i	0.960114	−	0.279610i	$-0.0902051\pi$
$72$		0			0
$73$			0.955441i			0.111826i	0.998436	+	0.0559129i	$0.0178069\pi$
$73$			0.955441i			0.111826i	−0.998436	+	0.0559129i	$0.982193\pi$
$74$	−2.84121	+	4.92112i	−0.330284	+	0.572068i
$75$		0			0
$76$	0.356452	+	0.617393i	0.0408878	+	0.0708198i
$77$			10.7923i			1.22989i
$78$		0			0
$79$	11.1009			1.24895			0.624475	−	0.781045i	$-0.285313\pi$
$79$	11.1009			1.24895			0.624475	+	0.781045i	$0.285313\pi$
$80$	7.93807	−	0.996455i	0.887504	−	0.111407i
$81$		0			0
$82$	−0.951947	−	0.549607i	−0.105125	−	0.0606939i
$83$		−	11.7889i		−	1.29400i	−0.762489	−	0.647002i	$-0.776023\pi$
$83$		−	11.7889i		−	1.29400i	0.762489	−	0.647002i	$-0.223977\pi$
$84$		0			0
$85$	−8.42273	+	6.38274i	−0.913573	+	0.692305i
$86$	−7.53678			−0.812712
$87$		0			0
$88$	7.02400	−	4.05531i	0.748761	−	0.432297i
$89$	5.60164	+	9.70232i	0.593772	+	1.02844i	0.993719	+	0.111906i	$0.0356954\pi$
$89$	5.60164	+	9.70232i	0.593772	+	1.02844i	−0.399946	+	0.916539i	$0.630971\pi$
$90$		0			0
$91$	2.80369	−	13.8613i	0.293907	−	1.45306i
$92$			1.01693i			0.106022i
$93$		0			0
$94$	−5.62147	−	9.73668i	−0.579811	−	1.00426i
$95$	−5.00076	−	6.59905i	−0.513067	−	0.677049i
$96$		0			0
$97$	−1.52806	−	0.882226i	−0.155151	−	0.0895765i	0.420414	−	0.907332i	$-0.361885\pi$
$97$	−1.52806	−	0.882226i	−0.155151	−	0.0895765i	−0.575565	+	0.817756i	$0.695218\pi$
$98$	−9.76200	−	5.63610i	−0.986111	−	0.569332i
$99$		0			0
$100$	0.932778	−	0.237930i	0.0932778	−	0.0237930i
$101$	0.435567	+	0.754425i	0.0433406	+	0.0750681i	0.886882	−	0.461996i	$-0.152867\pi$
$101$	0.435567	+	0.754425i	0.0433406	+	0.0750681i	−0.843541	+	0.537064i	$0.819533\pi$
$102$		0			0
$103$			10.7473i			1.05896i	0.848321	+	0.529482i	$0.177614\pi$
$103$			10.7473i			1.05896i	−0.848321	+	0.529482i	$0.822386\pi$
$104$	−10.0750	+	3.38379i	−0.987932	+	0.331808i
$105$		0			0
$106$	−4.71445	−	8.16567i	−0.457908	−	0.793120i
$107$	11.4966	−	6.63759i	1.11142	−	0.641680i	0.172225	−	0.985058i	$-0.444904\pi$
$107$	11.4966	−	6.63759i	1.11142	−	0.641680i	0.939197	+	0.343378i	$0.111571\pi$
$108$		0			0
$109$	−6.89467			−0.660390			−0.330195	−	0.943913i	$-0.607114\pi$
$109$	−6.89467			−0.660390			−0.330195	+	0.943913i	$0.607114\pi$
$110$	−6.59258	+	4.99585i	−0.628577	+	0.476336i
$111$		0			0
$112$			14.0335i			1.32604i
$113$	−2.15933	−	1.24669i	−0.203133	−	0.117279i	0.394983	−	0.918688i	$-0.370750\pi$
$113$	−2.15933	−	1.24669i	−0.203133	−	0.117279i	−0.598116	+	0.801410i	$0.704084\pi$
$114$		0			0
$115$	−1.47105	−	11.7189i	−0.137176	−	1.09279i
$116$	−0.504839			−0.0468731
$117$		0			0
$118$		−	2.93933i		−	0.270587i
$119$	−9.26865	−	16.0538i	−0.849656	−	1.47165i
$120$		0			0
$121$	1.71457	−	2.96972i	0.155870	−	0.269975i
$122$			17.2583i			1.56249i
$123$		0			0
$124$	−0.454333	+	0.786927i	−0.0408003	+	0.0706681i
$125$	−10.4049	+	4.09116i	−0.930645	+	0.365925i
$126$		0			0
$127$	−13.8796	+	8.01342i	−1.23162	+	0.711076i	−0.967367	−	0.253378i	$-0.918458\pi$
$127$	−13.8796	+	8.01342i	−1.23162	+	0.711076i	−0.264252	+	0.964454i	$0.585125\pi$
$128$	8.15053	−	4.70571i	0.720412	−	0.415930i
$129$		0			0
$130$	9.76520	−	4.70388i	0.856465	−	0.412558i
$131$	−15.2522			−1.33259			−0.666293	−	0.745690i	$-0.732120\pi$
$131$	−15.2522			−1.33259			−0.666293	+	0.745690i	$0.732120\pi$
$132$		0			0
$133$	12.5778	−	7.26182i	1.09064	−	0.629680i
$134$	8.44670	−	14.6301i	0.729684	−	1.26385i
$135$		0			0
$136$	−6.96557	+	12.0647i	−0.597293	+	1.03454i
$137$	−13.3206	−	7.69065i	−1.13806	−	0.657057i	−0.192108	−	0.981374i	$-0.561532\pi$
$137$	−13.3206	−	7.69065i	−1.13806	−	0.657057i	−0.945948	+	0.324317i	$0.894866\pi$
$138$		0			0
$139$	−7.49948	+	12.9895i	−0.636098	+	1.10175i	0.350183	+	0.936681i	$0.386119\pi$
$139$	−7.49948	+	12.9895i	−0.636098	+	1.10175i	−0.986281	+	0.165073i	$0.947214\pi$
$140$	0.210314	+	1.67543i	0.0177748	+	0.141600i
$141$		0			0
$142$			16.3627i			1.37313i
$143$	6.56522	−	7.43768i	0.549011	−	0.621970i
$144$		0			0
$145$	5.81764	−	0.730280i	0.483129	−	0.0606464i
$146$	−0.642258	−	1.11242i	−0.0531536	−	0.0920648i
$147$		0			0
$148$			0.813754i			0.0668902i
$149$	2.57394	−	4.45819i	0.210865	−	0.365229i	−0.741120	−	0.671372i	$-0.765705\pi$
$149$	2.57394	−	4.45819i	0.210865	−	0.365229i	0.951985	+	0.306143i	$0.0990386\pi$
$150$		0			0
$151$	−12.2598			−0.997685			−0.498843	−	0.866693i	$-0.666241\pi$
$151$	−12.2598			−0.997685			−0.498843	+	0.866693i	$0.666241\pi$
$152$	−9.45250	−	5.45740i	−0.766699	−	0.442654i
$153$		0			0
$154$	−7.25469	−	12.5655i	−0.584600	−	1.01256i
$155$	4.09728	−	9.72557i	0.329101	−	0.781177i
$156$		0			0
$157$		−	19.3492i		−	1.54424i	−0.635478	−	0.772119i	$-0.719197\pi$
$157$		−	19.3492i		−	1.54424i	0.635478	−	0.772119i	$-0.280803\pi$
$158$	−12.9248	+	7.46215i	−1.02824	+	0.593657i
$159$		0			0
$160$	1.93399	−	1.46558i	0.152895	−	0.115864i
$161$	20.7174			1.63276
$162$		0			0
$163$	−12.8326	−	7.40888i	−1.00512	−	0.580308i	−0.0953634	−	0.995443i	$-0.530401\pi$
$163$	−12.8326	−	7.40888i	−1.00512	−	0.580308i	−0.909760	+	0.415134i	$0.863735\pi$
$164$	−0.157414			−0.0122919
$165$		0			0
$166$	7.92465	+	13.7259i	0.615072	+	1.06534i
$167$	−4.52871	+	2.61465i	−0.350442	+	0.202328i	−0.664880	−	0.746950i	$-0.731517\pi$
$167$	−4.52871	+	2.61465i	−0.350442	+	0.202328i	0.314438	+	0.949278i	$0.398184\pi$
$168$		0			0
$169$	−10.3644	+	7.84721i	−0.797263	+	0.603632i
$170$	5.51606	−	13.0933i	0.423063	−	1.00421i
$171$		0			0
$172$	−0.934710	+	0.539655i	−0.0712710	+	0.0411483i
$173$	15.9393	+	9.20255i	1.21184	+	0.699657i	0.963160	−	0.268928i	$-0.0866695\pi$
$173$	15.9393	+	9.20255i	1.21184	+	0.699657i	0.248681	+	0.968585i	$0.420003\pi$
$174$		0			0
$175$	−4.84722	−	19.0030i	−0.366416	−	1.43649i
$176$	−4.92230	+	8.52567i	−0.371032	+	0.642646i
$177$		0			0
$178$	−13.0440	−	7.53097i	−0.977690	−	0.564470i
$179$	5.40617	+	9.36377i	0.404076	+	0.699881i	0.994213	−	0.107422i	$-0.0342597\pi$
$179$	5.40617	+	9.36377i	0.404076	+	0.699881i	−0.590137	+	0.807303i	$0.700926\pi$
$180$		0			0
$181$	11.9606			0.889021			0.444511	−	0.895774i	$-0.353378\pi$
$181$	11.9606			0.889021			0.444511	+	0.895774i	$0.353378\pi$
$182$	6.05340	+	18.0235i	0.448708	+	1.33599i
$183$		0			0
$184$	−7.78479	−	13.4836i	−0.573902	−	0.994028i
$185$	−1.17714	−	9.37751i	−0.0865454	−	0.689448i
$186$		0			0
$187$		−	13.0040i		−	0.950950i
$188$	−1.39435	−	0.805027i	−0.101693	−	0.0587126i
$189$		0			0
$190$	10.2584	+	4.32174i	0.744220	+	0.313532i
$191$	−11.4643	+	19.8567i	−0.829524	+	1.43678i	0.0688880	+	0.997624i	$0.478055\pi$
$191$	−11.4643	+	19.8567i	−0.829524	+	1.43678i	−0.898412	+	0.439153i	$0.855278\pi$
$192$		0			0
$193$	−20.1831	+	11.6527i	−1.45281	+	0.838779i	−0.998640	−	0.0521363i	$-0.983397\pi$
$193$	−20.1831	+	11.6527i	−1.45281	+	0.838779i	−0.454169	+	0.890916i	$0.650064\pi$
$194$	2.37217			0.170312
$195$		0			0
$196$	−1.61424			−0.115303
$197$	−11.3025	+	6.52551i	−0.805271	+	0.464924i	−0.845311	−	0.534275i	$-0.820585\pi$
$197$	−11.3025	+	6.52551i	−0.805271	+	0.464924i	0.0400398	+	0.999198i	$0.487252\pi$
$198$		0			0
$199$	1.44768	−	2.50746i	0.102624	−	0.177749i	−0.810141	−	0.586235i	$-0.800610\pi$
$199$	1.44768	−	2.50746i	0.102624	−	0.177749i	0.912765	+	0.408485i	$0.133943\pi$
$200$	−10.5464	+	10.2953i	−0.745746	+	0.727989i
$201$		0			0
$202$	−1.01427	−	0.585586i	−0.0713635	−	0.0412017i
$203$			10.2848i			0.721854i
$204$		0			0
$205$	1.81400	−	0.227708i	0.126695	−	0.0159038i
$206$	−7.22446	−	12.5131i	−0.503352	−	0.871831i
$207$		0			0
$208$	8.53693	−	9.67141i	0.591930	−	0.670592i
$209$	10.1884			0.704749
$210$		0			0
$211$	−5.63964	−	9.76814i	−0.388249	−	0.672466i	0.603965	−	0.797010i	$-0.293586\pi$
$211$	−5.63964	−	9.76814i	−0.388249	−	0.672466i	−0.992214	+	0.124544i	$0.960253\pi$
$212$	−1.16937	−	0.675137i	−0.0803127	−	0.0463686i
$213$		0			0
$214$	−8.92372	+	15.4563i	−0.610013	+	1.05657i
$215$	9.99073	−	7.57097i	0.681362	−	0.516336i
$216$		0			0
$217$	16.0317	+	9.25589i	1.08830	+	0.628331i
$218$	8.02749	−	4.63467i	0.543690	−	0.313900i
$219$		0			0
$220$	−0.459893	+	1.09163i	−0.0310060	+	0.0735978i
$221$	−3.37828	+	16.7021i	−0.227248	+	1.12350i
$222$		0			0
$223$	−13.3465	+	7.70559i	−0.893746	+	0.516004i	−0.875166	−	0.483823i	$-0.839248\pi$
$223$	−13.3465	+	7.70559i	−0.893746	+	0.516004i	−0.0185799	+	0.999827i	$0.505915\pi$
$224$	2.12823	+	3.68620i	0.142198	+	0.246295i
$225$		0			0
$226$	3.35216			0.222982
$227$	−2.11918	−	1.22351i	−0.140655	−	0.0812070i	0.428021	−	0.903769i	$-0.359211\pi$
$227$	−2.11918	−	1.22351i	−0.140655	−	0.0812070i	−0.568676	+	0.822562i	$0.692544\pi$
$228$		0			0
$229$	−7.41584			−0.490053			−0.245026	−	0.969516i	$-0.578797\pi$
$229$	−7.41584			−0.490053			−0.245026	+	0.969516i	$0.578797\pi$
$230$	9.59031	+	12.6555i	0.632366	+	0.834477i
$231$		0			0
$232$	6.69374	−	3.86463i	0.439465	−	0.253725i
$233$		−	3.81094i		−	0.249663i	−0.992178	−	0.124831i	$-0.960161\pi$
$233$		−	3.81094i		−	0.249663i	0.992178	−	0.124831i	$-0.0398390\pi$
$234$		0			0
$235$	17.2326	+	7.25993i	1.12413	+	0.473585i
$236$	−0.210464	−	0.364535i	−0.0137001	−	0.0237292i
$237$		0			0
$238$	21.5830	+	12.4610i	1.39902	+	0.807725i
$239$	13.4385			0.869264			0.434632	−	0.900608i	$-0.356878\pi$
$239$	13.4385			0.869264			0.434632	+	0.900608i	$0.356878\pi$
$240$		0			0
$241$	−6.80023	+	11.7783i	−0.438041	+	0.758710i	−0.997538	−	0.0701227i	$-0.977661\pi$
$241$	−6.80023	+	11.7783i	−0.438041	+	0.758710i	0.559497	+	0.828832i	$0.310994\pi$
$242$			4.61021i			0.296355i
$243$		0			0
$244$	1.23574	+	2.14037i	0.0791102	+	0.137023i
$245$	18.6021	−	2.33510i	1.18845	−	0.149184i
$246$		0			0
$247$	−13.0858	−	2.64682i	−0.832628	−	0.168413i
$248$		−	13.9120i		−	0.883411i
$249$		0			0
$250$	9.36437	−	11.7577i	0.592255	−	0.743620i
$251$	5.46883	−	9.47230i	0.345190	−	0.597886i	−0.640198	−	0.768210i	$-0.721148\pi$
$251$	5.46883	−	9.47230i	0.345190	−	0.597886i	0.985388	+	0.170323i	$0.0544812\pi$
$252$		0			0
$253$	12.5863	+	7.26672i	0.791296	+	0.456855i
$254$	10.7734	−	18.6601i	0.675984	−	1.17084i
$255$		0			0
$256$	2.28825	−	3.96337i	0.143016	−	0.247710i
$257$	−7.60629	+	4.39149i	−0.474467	+	0.273934i	−0.718108	−	0.695932i	$-0.754992\pi$
$257$	−7.60629	+	4.39149i	−0.474467	+	0.273934i	0.243641	+	0.969866i	$0.421658\pi$
$258$		0			0
$259$	16.5782			1.03012
$260$	0.874266	−	1.28259i	0.0542197	−	0.0795429i
$261$		0			0
$262$	17.7581	−	10.2527i	1.09710	−	0.633412i
$263$	−15.9657	+	9.21780i	−0.984487	+	0.568394i	−0.903622	−	0.428331i	$-0.859102\pi$
$263$	−15.9657	+	9.21780i	−0.984487	+	0.568394i	−0.0808652	+	0.996725i	$0.525768\pi$
$264$		0			0
$265$	14.4522	+	6.08854i	0.887790	+	0.374016i
$266$	−9.76295	+	16.9099i	−0.598605	+	1.03681i
$267$		0			0
$268$		−	2.41923i		−	0.147778i
$269$	7.95679	−	13.7816i	0.485134	−	0.840277i	−0.514720	−	0.857358i	$-0.672104\pi$
$269$	7.95679	−	13.7816i	0.485134	−	0.840277i	0.999854	+	0.0170813i	$0.00543740\pi$
$270$		0			0
$271$	−0.755492	−	1.30855i	−0.0458929	−	0.0794888i	0.842166	−	0.539218i	$-0.181280\pi$
$271$	−0.755492	−	1.30855i	−0.0458929	−	0.0794888i	−0.888059	+	0.459729i	$0.847947\pi$
$272$		−	16.9095i		−	1.02529i
$273$		0			0
$274$	20.6790			1.24926
$275$	3.72058	−	13.2450i	0.224359	−	0.798701i
$276$		0			0
$277$	12.2058	+	7.04702i	0.733375	+	0.423414i	0.819656	−	0.572857i	$-0.194165\pi$
$277$	12.2058	+	7.04702i	0.733375	+	0.423414i	−0.0862805	+	0.996271i	$0.527498\pi$
$278$		−	20.1649i		−	1.20941i
$279$		0			0
$280$	−15.6143	−	20.6048i	−0.933133	−	1.23137i
$281$	4.85007			0.289331			0.144665	−	0.989481i	$-0.453789\pi$
$281$	4.85007			0.289331			0.144665	+	0.989481i	$0.453789\pi$
$282$		0			0
$283$	19.9720	−	11.5309i	1.18721	−	0.685438i	0.229542	−	0.973299i	$-0.426277\pi$
$283$	19.9720	−	11.5309i	1.18721	−	0.685438i	0.957672	+	0.287860i	$0.0929439\pi$
$284$	1.17162	+	2.02930i	0.0695228	+	0.120417i
$285$		0			0
$286$	−2.64422	+	13.0729i	−0.156356	+	0.773019i
$287$			3.20691i			0.189298i
$288$		0			0
$289$	2.66816	+	4.62139i	0.156951	+	0.271847i
$290$	−6.28260	+	4.76095i	−0.368927	+	0.279573i
$291$		0			0
$292$	−0.159305	−	0.0919750i	−0.00932264	−	0.00538243i
$293$	24.2589	+	14.0059i	1.41722	+	0.818233i	0.996054	−	0.0887498i	$-0.0282871\pi$
$293$	24.2589	+	14.0059i	1.41722	+	0.818233i	0.421167	+	0.906983i	$0.361620\pi$
$294$		0			0
$295$	2.95266	+	3.89636i	0.171910	+	0.226855i
$296$	−6.22943	−	10.7897i	−0.362078	−	0.627138i
$297$		0			0
$298$			6.92091i			0.400918i
$299$	−14.2778	−	12.6030i	−0.825705	−	0.728848i
$300$		0			0
$301$	10.9941	+	19.0424i	0.633691	+	1.09759i
$302$	14.2741	−	8.24115i	0.821381	−	0.474225i
$303$		0			0
$304$	13.2483			0.759842
$305$	−17.3365	−	22.8775i	−0.992688	−	1.30996i
$306$		0			0
$307$			18.4662i			1.05392i	0.849889	+	0.526961i	$0.176669\pi$
$307$			18.4662i			1.05392i	−0.849889	+	0.526961i	$0.823331\pi$
$308$	−1.79945	−	1.03891i	−0.102533	−	0.0591976i
$309$		0			0
$310$	1.76716	+	14.0778i	0.100368	+	0.799563i
$311$	−9.53182			−0.540500			−0.270250	−	0.962790i	$-0.587106\pi$
$311$	−9.53182			−0.540500			−0.270250	+	0.962790i	$0.587106\pi$
$312$		0			0
$313$		−	20.0605i		−	1.13389i	−0.823756	−	0.566945i	$-0.808125\pi$
$313$		−	20.0605i		−	1.13389i	0.823756	−	0.566945i	$-0.191875\pi$
$314$	13.0068	+	22.5284i	0.734015	+	1.27135i
$315$		0			0
$316$	−1.06862	+	1.85091i	−0.0601147	+	0.104122i
$317$			3.43508i			0.192933i	0.995336	+	0.0964667i	$0.0307541\pi$
$317$			3.43508i			0.192933i	−0.995336	+	0.0964667i	$0.969246\pi$
$318$		0			0
$319$	−3.60744	+	6.24828i	−0.201978	+	0.349836i
$320$	−7.47874	+	17.7520i	−0.418074	+	0.992369i
$321$		0			0
$322$	−24.1214	+	13.9265i	−1.34423	+	0.776093i
$323$	−15.1555	+	8.75006i	−0.843277	+	0.486866i
$324$		0			0
$325$	−8.21949	+	16.0449i	−0.455935	+	0.890013i
$326$	19.9213			1.10334
$327$		0			0
$328$	2.08717	−	1.20503i	0.115245	−	0.0665366i
$329$	−16.4004	+	28.4064i	−0.904184	+	1.56609i
$330$		0			0
$331$	6.22159	−	10.7761i	0.341970	−	0.592309i	−0.642829	−	0.766010i	$-0.722239\pi$
$331$	6.22159	−	10.7761i	0.341970	−	0.592309i	0.984798	+	0.173701i	$0.0555726\pi$
$332$	1.96563	+	1.13486i	0.107878	+	0.0622833i
$333$		0			0
$334$	3.51520	−	6.08850i	0.192343	−	0.333148i
$335$	3.49956	+	27.8786i	0.191202	+	1.52317i
$336$		0			0
$337$			12.9346i			0.704593i	0.935888	+	0.352297i	$0.114599\pi$
$337$			12.9346i			0.704593i	−0.935888	+	0.352297i	$0.885401\pi$
$338$	6.79235	−	16.1036i	0.369455	−	0.875921i
$339$		0			0
$340$	−0.253416	−	2.01879i	−0.0137434	−	0.109484i
$341$	6.49308	+	11.2463i	0.351620	+	0.609023i
$342$		0			0
$343$			5.43008i			0.293197i
$344$	8.26231	−	14.3107i	0.445474	−	0.771583i
$345$		0			0
$346$	−24.7442			−1.33026
$347$	−9.54712	−	5.51203i	−0.512516	−	0.295901i	0.221351	−	0.975194i	$-0.428953\pi$
$347$	−9.54712	−	5.51203i	−0.512516	−	0.295901i	−0.733867	+	0.679293i	$0.762287\pi$
$348$		0			0
$349$	4.21143	+	7.29441i	0.225433	+	0.390461i	0.956449	−	0.291899i	$-0.0942871\pi$
$349$	4.21143	+	7.29441i	0.225433	+	0.390461i	−0.731017	+	0.682360i	$0.760954\pi$
$350$	18.4177	+	18.8669i	0.984466	+	1.00848i
$351$		0			0
$352$			2.98594i			0.159151i
$353$	−11.9633	+	6.90700i	−0.636741	+	0.367623i	−0.783358	−	0.621571i	$-0.786495\pi$
$353$	−11.9633	+	6.90700i	−0.636741	+	0.367623i	0.146617	+	0.989193i	$0.453162\pi$
$354$		0			0
$355$	−16.4370	−	21.6904i	−0.872383	−	1.15121i
$356$	−2.15695			−0.114318
$357$		0			0
$358$	−12.5889	−	7.26818i	−0.665342	−	0.384135i
$359$	−1.30027			−0.0686258			−0.0343129	−	0.999411i	$-0.510924\pi$
$359$	−1.30027			−0.0686258			−0.0343129	+	0.999411i	$0.510924\pi$
$360$		0			0
$361$	2.64449	+	4.58039i	0.139184	+	0.241073i
$362$	−13.9257	+	8.04002i	−0.731920	+	0.422574i
$363$		0			0
$364$	2.04127	+	1.80183i	0.106992	+	0.0944414i
$365$	1.96884	+	0.829452i	0.103054	+	0.0434155i
$366$		0			0
$367$	14.0757	−	8.12662i	0.734747	−	0.424206i	−0.0854093	−	0.996346i	$-0.527220\pi$
$367$	14.0757	−	8.12662i	0.734747	−	0.424206i	0.820156	+	0.572140i	$0.193886\pi$
$368$	16.3663	+	9.44911i	0.853154	+	0.492569i
$369$		0			0
$370$	7.67422	+	10.1270i	0.398964	+	0.526476i
$371$	−13.7542	+	23.8230i	−0.714084	+	1.23683i
$372$		0			0
$373$	8.29759	+	4.79061i	0.429633	+	0.248049i	0.699190	−	0.714936i	$-0.253544\pi$
$373$	8.29759	+	4.79061i	0.429633	+	0.248049i	−0.269557	+	0.962984i	$0.586877\pi$
$374$	8.74147	+	15.1407i	0.452010	+	0.782905i
$375$		0			0
$376$	24.6505			1.27125
$377$	6.25653	−	7.08797i	0.322228	−	0.365049i
$378$		0			0
$379$	11.7836	+	20.4099i	0.605285	+	1.04838i	0.992006	+	0.126188i	$0.0402743\pi$
$379$	11.7836	+	20.4099i	0.605285	+	1.04838i	−0.386721	+	0.922197i	$0.626392\pi$
$380$	1.58169	−	0.198547i	0.0811389	−	0.0101852i
$381$		0			0
$382$		−	30.8256i		−	1.57717i
$383$	−5.26755	−	3.04122i	−0.269159	−	0.155399i	0.359346	−	0.933204i	$-0.383000\pi$
$383$	−5.26755	−	3.04122i	−0.269159	−	0.155399i	−0.628506	+	0.777805i	$0.716333\pi$
$384$		0			0
$385$	22.2393	+	9.36917i	1.13342	+	0.477497i
$386$	15.6661	−	27.1346i	0.797386	−	1.38111i
$387$		0			0
$388$	0.294196	−	0.169854i	0.0149355	−	0.00862303i
$389$	−0.960817			−0.0487153			−0.0243577	−	0.999703i	$-0.507754\pi$
$389$	−0.960817			−0.0487153			−0.0243577	+	0.999703i	$0.507754\pi$
$390$		0			0
$391$	−24.9633			−1.26245
$392$	21.4035	−	12.3573i	1.08104	−	0.624138i
$393$		0			0
$394$	8.77304	−	15.1954i	0.441980	−	0.765531i
$395$	9.63710	−	22.8752i	0.484895	−	1.15098i
$396$		0			0
$397$	−25.7780	−	14.8829i	−1.29376	−	0.746952i	−0.314440	−	0.949277i	$-0.601817\pi$
$397$	−25.7780	−	14.8829i	−1.29376	−	0.746952i	−0.979318	+	0.202325i	$0.935150\pi$
$398$			3.89260i			0.195118i
$399$		0			0
$400$	4.83797	−	17.2228i	0.241898	−	0.861138i
$401$	−18.4114	−	31.8895i	−0.919423	−	1.59249i	−0.800294	−	0.599608i	$-0.795323\pi$
$401$	−18.4114	−	31.8895i	−0.919423	−	1.59249i	−0.119129	−	0.992879i	$-0.538010\pi$
$402$		0			0
$403$	−5.41790	−	16.1313i	−0.269885	−	0.803559i
$404$	−0.167719			−0.00834431
$405$		0			0
$406$	−6.91358	−	11.9747i	−0.343115	−	0.594293i
$407$	10.0717	+	5.81487i	0.499233	+	0.288232i
$408$		0			0
$409$	3.97360	−	6.88248i	0.196482	−	0.340317i	−0.750903	−	0.660412i	$-0.770382\pi$
$409$	3.97360	−	6.88248i	0.196482	−	0.340317i	0.947385	+	0.320095i	$0.103715\pi$
$410$	−1.95898	+	1.48451i	−0.0967469	+	0.0733148i
$411$		0			0
$412$	−1.79195	−	1.03458i	−0.0882831	−	0.0509703i
$413$	−7.42649	+	4.28768i	−0.365434	+	0.210983i
$414$		0			0
$415$	−24.2930	−	10.2344i	−1.19250	−	0.502387i
$416$	0.775707	−	3.83506i	0.0380321	−	0.188029i
$417$		0			0
$418$	−11.8624	+	6.84878i	−0.580211	+	0.334985i
$419$	−10.3784	−	17.9760i	−0.507020	−	0.878184i	−0.999967	−	0.00812497i	$-0.997414\pi$
$419$	−10.3784	−	17.9760i	−0.507020	−	0.878184i	0.492947	−	0.870059i	$-0.335920\pi$
$420$		0			0
$421$	−39.1986			−1.91042			−0.955212	−	0.295922i	$-0.904373\pi$
$421$	−39.1986			−1.91042			−0.955212	+	0.295922i	$0.904373\pi$
$422$	13.1325	+	7.58205i	0.639280	+	0.369089i
$423$		0			0
$424$	20.6731			1.00398
$425$	5.84061	+	22.8975i	0.283311	+	1.11069i
$426$		0			0
$427$	43.6046	−	25.1751i	2.11018	−	1.21831i
$428$			2.55586i			0.123542i
$429$		0			0
$430$	−6.54295	+	15.5308i	−0.315529	+	0.748961i
$431$	7.33512	+	12.7048i	0.353321	+	0.611969i	0.986829	−	0.161767i	$-0.0517192\pi$
$431$	7.33512	+	12.7048i	0.353321	+	0.611969i	−0.633509	+	0.773736i	$0.718386\pi$
$432$		0			0
$433$	15.3950	+	8.88833i	0.739839	+	0.427146i	0.822011	−	0.569472i	$-0.192852\pi$
$433$	15.3950	+	8.88833i	0.739839	+	0.427146i	−0.0821720	+	0.996618i	$0.526186\pi$
$434$	−24.8877			−1.19465
$435$		0			0
$436$	0.663712	−	1.14958i	0.0317860	−	0.0550550i
$437$		−	19.5583i		−	0.935599i
$438$		0			0
$439$	−10.9923	−	19.0393i	−0.524635	−	0.908694i	−0.999589	−	0.0286834i	$-0.990869\pi$
$439$	−10.9923	−	19.0393i	−0.524635	−	0.908694i	0.474954	−	0.880011i	$-0.342465\pi$
$440$	−2.25884	−	17.9947i	−0.107686	−	0.857862i
$441$		0			0
$442$	−7.29398	−	21.7172i	−0.346939	−	1.03298i
$443$		−	0.861429i		−	0.0409277i	−0.999791	−	0.0204639i	$-0.993486\pi$
$443$		−	0.861429i		−	0.0409277i	0.999791	−	0.0204639i	$-0.00651430\pi$
$444$		0			0
$445$	24.8562	−	3.12016i	1.17830	−	0.147910i
$446$	10.3596	−	17.9433i	0.490540	−	0.849639i
$447$		0			0
$448$	−29.2625	−	16.8947i	−1.38252	−	0.798201i
$449$	−17.2864	+	29.9409i	−0.815795	+	1.41300i	0.0929602	+	0.995670i	$0.470367\pi$
$449$	−17.2864	+	29.9409i	−0.815795	+	1.41300i	−0.908755	+	0.417329i	$0.862966\pi$
$450$		0			0
$451$	−1.12484	+	1.94827i	−0.0529665	+	0.0917406i
$452$	0.415734	−	0.240024i	0.0195545	−	0.0112898i
$453$		0			0
$454$	3.28982			0.154399
$455$	−26.1296	−	17.8110i	−1.22497	−	0.834992i
$456$		0			0
$457$	−16.7071	+	9.64584i	−0.781524	+	0.451213i	−0.836970	−	0.547248i	$-0.815675\pi$
$457$	−16.7071	+	9.64584i	−0.781524	+	0.451213i	0.0554459	+	0.998462i	$0.482342\pi$
$458$	8.63429	−	4.98501i	0.403454	−	0.232934i
$459$		0			0
$460$	2.09556	+	0.882835i	0.0977058	+	0.0411624i
$461$	3.85847	−	6.68306i	0.179707	−	0.311261i	−0.762073	−	0.647491i	$-0.775818\pi$
$461$	3.85847	−	6.68306i	0.179707	−	0.311261i	0.941780	+	0.336229i	$0.109152\pi$
$462$		0			0
$463$			34.8030i			1.61743i	0.588198	+	0.808717i	$0.299837\pi$
$463$			34.8030i			1.61743i	−0.588198	+	0.808717i	$0.700163\pi$
$464$	−4.69086	+	8.12480i	−0.217767	+	0.377184i
$465$		0			0
$466$	2.56176	+	4.43709i	0.118671	+	0.205544i
$467$		−	6.87588i		−	0.318178i	−0.987264	−	0.159089i	$-0.949144\pi$
$467$		−	6.87588i		−	0.318178i	0.987264	−	0.159089i	$-0.0508556\pi$
$468$		0			0
$469$	−49.2858			−2.27581
$470$	−24.9442	+	3.13121i	−1.15059	+	0.144432i
$471$		0			0
$472$	5.58115	+	3.22228i	0.256893	+	0.148317i
$473$			15.4249i			0.709239i
$474$		0			0
$475$	−17.9398	+	4.57601i	−0.823134	+	0.209962i
$476$	3.56897			0.163583
$477$		0			0
$478$	−15.6465	+	9.03351i	−0.715654	+	0.413183i
$479$	−4.04666	−	7.00902i	−0.184897	−	0.320250i	0.758645	−	0.651504i	$-0.225862\pi$
$479$	−4.04666	−	7.00902i	−0.184897	−	0.320250i	−0.943542	+	0.331254i	$0.892528\pi$
$480$		0			0
$481$	−11.4252	−	10.0850i	−0.520942	−	0.459835i
$482$		−	18.2848i		−	0.832848i
$483$		0			0
$484$	0.330104	+	0.571757i	0.0150047	+	0.0259890i
$485$	−3.14454	+	2.38293i	−0.142786	+	0.108203i
$486$		0			0
$487$	−15.6456	−	9.03299i	−0.708970	−	0.409324i	0.101710	−	0.994814i	$-0.467569\pi$
$487$	−15.6456	−	9.03299i	−0.708970	−	0.409324i	−0.810679	+	0.585490i	$0.800902\pi$
$488$	−32.7697	−	18.9196i	−1.48342	−	0.856451i
$489$		0			0
$490$	−20.0889	+	15.2233i	−0.907522	+	0.687720i
$491$	−6.48160	−	11.2265i	−0.292511	−	0.506643i	0.681892	−	0.731453i	$-0.261157\pi$
$491$	−6.48160	−	11.2265i	−0.292511	−	0.506643i	−0.974403	+	0.224810i	$0.927824\pi$
$492$		0			0
$493$		−	12.3926i		−	0.558135i
$494$	17.0150	−	5.71470i	0.765543	−	0.257117i
$495$		0			0
$496$	8.44312	+	14.6239i	0.379107	+	0.656633i
$497$	41.3420	−	23.8688i	1.85444	−	1.07066i
$498$		0			0
$499$	13.9318			0.623673			0.311836	−	0.950136i	$-0.399056\pi$
$499$	13.9318			0.623673			0.311836	+	0.950136i	$0.399056\pi$
$500$	0.319485	−	2.12870i	0.0142878	−	0.0951982i
$501$		0			0
$502$			14.7048i			0.656309i
$503$	−3.16948	−	1.82990i	−0.141320	−	0.0815911i	0.427673	−	0.903934i	$-0.359333\pi$
$503$	−3.16948	−	1.82990i	−0.141320	−	0.0815911i	−0.568993	+	0.822342i	$0.692667\pi$
$504$		0			0
$505$	1.93275	−	0.242615i	0.0860062	−	0.0107962i
$506$	−19.5391			−0.868618
$507$		0			0
$508$		−	3.08563i		−	0.136903i
$509$	−3.50399	−	6.06909i	−0.155312	−	0.269008i	0.777861	−	0.628437i	$-0.216305\pi$
$509$	−3.50399	−	6.06909i	−0.155312	−	0.269008i	−0.933172	+	0.359429i	$0.882971\pi$
$510$		0			0
$511$	−1.87376	+	3.24545i	−0.0828903	+	0.143570i
$512$			24.9756i			1.10378i
$513$		0			0
$514$	5.90402	−	10.2261i	0.260415	−	0.451052i
$515$	22.1466	+	9.33012i	0.975896	+	0.411134i
$516$		0			0
$517$	−19.9273	+	11.5050i	−0.876400	+	0.505990i
$518$	−19.3021	+	11.1441i	−0.848085	+	0.489642i
$519$		0			0
$520$	−1.77357	+	23.6987i	−0.0777763	+	1.03926i
$521$	−28.9937			−1.27024			−0.635119	−	0.772415i	$-0.719049\pi$
$521$	−28.9937			−1.27024			−0.635119	+	0.772415i	$0.719049\pi$
$522$		0			0
$523$	10.2802	−	5.93530i	0.449524	−	0.259533i	−0.258105	−	0.966117i	$-0.583098\pi$
$523$	10.2802	−	5.93530i	0.449524	−	0.259533i	0.707629	+	0.706584i	$0.249765\pi$
$524$	1.46824	−	2.54307i	0.0641404	−	0.111094i
$525$		0			0
$526$	12.3926	−	21.4646i	0.540344	−	0.935903i
$527$	−19.3172	−	11.1528i	−0.841471	−	0.485823i
$528$		0			0
$529$	2.44959	−	4.24281i	0.106504	−	0.184470i
$530$	−20.9195	+	2.62599i	−0.908685	+	0.114066i
$531$		0			0
$532$			2.79622i			0.121232i
$533$	1.95085	−	2.21010i	0.0845006	−	0.0957299i
$534$		0			0
$535$	−3.69720	−	29.4530i	−0.159844	−	1.27337i
$536$	18.5196	+	32.0770i	0.799927	+	1.38551i
$537$		0			0
$538$			21.3946i			0.922386i
$539$	−11.5349	+	19.9791i	−0.496845	+	0.860561i
$540$		0			0
$541$	23.9074			1.02786			0.513930	−	0.857832i	$-0.328189\pi$
$541$	23.9074			1.02786			0.513930	+	0.857832i	$0.328189\pi$
$542$	1.75925	+	1.01570i	0.0755661	+	0.0436281i
$543$		0			0
$544$	−2.56439	−	4.44165i	−0.109947	−	0.190434i
$545$	−5.98551	+	14.2076i	−0.256391	+	0.608587i
$546$		0			0
$547$			19.8266i			0.847725i	0.905727	+	0.423862i	$0.139326\pi$
$547$			19.8266i			0.847725i	−0.905727	+	0.423862i	$0.860674\pi$
$548$	2.56460	−	1.48067i	0.109554	−	0.0632512i
$549$		0			0
$550$	4.57152	+	17.9222i	0.194930	+	0.764204i
$551$	9.70939			0.413634
$552$		0			0
$553$	37.7077	+	21.7705i	1.60349	+	0.925777i
$554$	−18.9483			−0.805038
$555$		0			0
$556$	−1.44387	−	2.50085i	−0.0612336	−	0.106060i
$557$	15.4032	−	8.89306i	0.652656	−	0.376811i	−0.136817	−	0.990596i	$-0.543687\pi$
$557$	15.4032	−	8.89306i	0.652656	−	0.376811i	0.789473	+	0.613785i	$0.210354\pi$
$558$		0			0
$559$	4.00719	−	19.8114i	0.169486	−	0.837933i
$560$	28.9183	+	12.1830i	1.22202	+	0.514825i
$561$		0			0
$562$	−5.64695	+	3.26027i	−0.238202	+	0.137526i
$563$	27.4498	+	15.8482i	1.15687	+	0.667920i	0.950552	−	0.310565i	$-0.100518\pi$
$563$	27.4498	+	15.8482i	1.15687	+	0.667920i	0.206319	+	0.978485i	$0.433851\pi$
$564$		0			0
$565$	−4.44360	+	3.36736i	−0.186944	+	0.141666i
$566$	−15.5023	+	26.8508i	−0.651612	+	1.12863i
$567$		0			0
$568$	−31.0693	−	17.9379i	−1.30364	−	0.752657i
$569$	0.801035	+	1.38743i	0.0335811	+	0.0581642i	0.882328	−	0.470636i	$-0.155975\pi$
$569$	0.801035	+	1.38743i	0.0335811	+	0.0581642i	−0.848746	+	0.528800i	$0.822642\pi$
$570$		0			0
$571$	−30.3459			−1.26994			−0.634969	−	0.772538i	$-0.718987\pi$
$571$	−30.3459			−1.26994			−0.634969	+	0.772538i	$0.718987\pi$
$572$	0.608123	+	1.81064i	0.0254269	+	0.0757065i
$573$		0			0
$574$	−2.15572	−	3.73382i	−0.0899781	−	0.155847i
$575$	−25.4257	−	7.14223i	−1.06033	−	0.297851i
$576$		0			0
$577$		−	4.59201i		−	0.191168i	−0.995421	−	0.0955840i	$-0.969528\pi$
$577$		−	4.59201i		−	0.191168i	0.995421	−	0.0955840i	$-0.0304719\pi$
$578$	−6.21311	−	3.58714i	−0.258431	−	0.149205i
$579$		0			0
$580$	−0.438269	+	1.04030i	−0.0181981	+	0.0431963i
$581$	23.1198	−	40.0447i	0.959173	−	1.66134i
$582$		0			0
$583$	−16.7120	+	9.64869i	−0.692141	+	0.399608i
$584$	2.81634			0.116541
$585$		0			0
$586$	−37.6597			−1.55571
$587$	2.59899	−	1.50053i	0.107272	−	0.0619335i	−0.445404	−	0.895330i	$-0.646940\pi$
$587$	2.59899	−	1.50053i	0.107272	−	0.0619335i	0.552676	+	0.833396i	$0.313607\pi$
$588$		0			0
$589$	8.73801	−	15.1347i	0.360044	−	0.623614i
$590$	−6.05697	−	2.55174i	−0.249361	−	0.105053i
$591$		0			0
$592$	13.0964	+	7.56123i	0.538260	+	0.310765i
$593$			1.33065i			0.0546431i	0.999627	+	0.0273215i	$0.00869780\pi$
$593$			1.33065i			0.0546431i	−0.999627	+	0.0273215i	$0.991302\pi$
$594$		0			0
$595$	−41.1279	+	5.16272i	−1.68608	+	0.211651i
$596$	0.495557	+	0.858330i	0.0202988	+	0.0351586i
$597$		0			0
$598$	25.0955	+	5.07599i	1.02623	+	0.207573i
$599$	−17.9203			−0.732205			−0.366103	−	0.930574i	$-0.619308\pi$
$599$	−17.9203			−0.732205			−0.366103	+	0.930574i	$0.619308\pi$
$600$		0			0
$601$	7.78973	+	13.4922i	0.317750	+	0.550359i	0.980018	−	0.198908i	$-0.0637395\pi$
$601$	7.78973	+	13.4922i	0.317750	+	0.550359i	−0.662268	+	0.749267i	$0.730406\pi$
$602$	−25.6010	−	14.7808i	−1.04342	−	0.602419i
$603$		0			0
$604$	1.18018	−	2.04413i	0.0480208	−	0.0831745i
$605$	−4.63112	−	6.11127i	−0.188282	−	0.248459i
$606$		0			0
$607$	18.6893	+	10.7902i	0.758574	+	0.437963i	0.828783	−	0.559570i	$-0.189034\pi$
$607$	18.6893	+	10.7902i	0.758574	+	0.437963i	−0.0702098	+	0.997532i	$0.522367\pi$
$608$	3.47995	−	2.00915i	0.141131	−	0.0814819i
$609$		0			0
$610$	35.5635	+	14.9825i	1.43992	+	0.606624i
$611$	28.5829	−	9.59992i	1.15634	−	0.388371i
$612$		0			0
$613$	−7.73293	+	4.46461i	−0.312330	+	0.180324i	−0.647969	−	0.761667i	$-0.724381\pi$
$613$	−7.73293	+	4.46461i	−0.312330	+	0.180324i	0.335639	+	0.941991i	$0.391048\pi$
$614$	−12.4132	−	21.5003i	−0.500956	−	0.867681i
$615$		0			0
$616$	31.8122			1.28175
$617$	6.48679	+	3.74515i	0.261149	+	0.150774i	0.624858	−	0.780738i	$-0.285157\pi$
$617$	6.48679	+	3.74515i	0.261149	+	0.150774i	−0.363710	+	0.931512i	$0.618490\pi$
$618$		0			0
$619$	−9.13983			−0.367361			−0.183680	−	0.982986i	$-0.558801\pi$
$619$	−9.13983			−0.367361			−0.183680	+	0.982986i	$0.558801\pi$
$620$	1.22717	+	1.61939i	0.0492844	+	0.0650361i
$621$		0			0
$622$	11.0979	−	6.40740i	0.444987	−	0.256913i
$623$			43.9426i			1.76052i
$624$		0			0
$625$	−0.602375	+	24.9927i	−0.0240950	+	0.999710i
$626$	13.4849	+	23.3566i	0.538966	+	0.933516i
$627$		0			0
$628$	3.22620	+	1.86265i	0.128739	+	0.0743276i
$629$	−19.9758			−0.796486
$630$		0			0
$631$	13.6160	−	23.5836i	0.542043	−	0.938847i	−0.456743	−	0.889599i	$-0.650984\pi$
$631$	13.6160	−	23.5836i	0.542043	−	0.938847i	0.998787	−	0.0492482i	$-0.0156825\pi$
$632$		−	32.7220i		−	1.30161i
$633$		0			0
$634$	−2.30910	−	3.99948i	−0.0917061	−	0.158840i
$635$	4.46355	+	35.5580i	0.177131	+	1.41108i
$636$		0			0
$637$	20.0055	−	22.6640i	0.792647	−	0.897982i
$638$		−	9.69985i		−	0.384021i
$639$		0			0
$640$	−2.62112	−	20.8807i	−0.103609	−	0.825382i
$641$	−23.2031	+	40.1890i	−0.916469	+	1.58737i	−0.111733	+	0.993738i	$0.535640\pi$
$641$	−23.2031	+	40.1890i	−0.916469	+	1.58737i	−0.804736	+	0.593633i	$0.797693\pi$
$642$		0			0
$643$	15.0786	+	8.70561i	0.594640	+	0.343316i	0.766930	−	0.641731i	$-0.221783\pi$
$643$	15.0786	+	8.70561i	0.594640	+	0.343316i	−0.172290	+	0.985046i	$0.555117\pi$
$644$	−1.99435	+	3.45432i	−0.0785885	+	0.136119i
$645$		0			0
$646$	11.7638	−	20.3754i	0.462839	−	0.801661i
$647$	33.9246	−	19.5864i	1.33371	−	0.770020i	0.347847	−	0.937551i	$-0.386913\pi$
$647$	33.9246	−	19.5864i	1.33371	−	0.770020i	0.985867	+	0.167531i	$0.0535796\pi$
$648$		0			0
$649$	−6.01568			−0.236136
$650$	−1.21561	−	24.2064i	−0.0476801	−	0.949454i
$651$		0			0
$652$	2.47064	−	1.42642i	0.0967577	−	0.0558631i
$653$	−4.84432	+	2.79687i	−0.189573	+	0.109450i	−0.591783	−	0.806098i	$-0.701576\pi$
$653$	−4.84432	+	2.79687i	−0.189573	+	0.109450i	0.402210	+	0.915548i	$0.368242\pi$
$654$		0			0
$655$	−13.2409	+	31.4296i	−0.517367	+	1.22806i
$656$	−1.46265	+	2.53339i	−0.0571071	+	0.0989123i
$657$		0			0
$658$		−	44.0982i		−	1.71913i
$659$	8.86339	−	15.3518i	0.345268	−	0.598023i	−0.640134	−	0.768263i	$-0.721121\pi$
$659$	8.86339	−	15.3518i	0.345268	−	0.598023i	0.985403	+	0.170241i	$0.0544545\pi$
$660$		0			0
$661$	16.1832	+	28.0302i	0.629455	+	1.09025i	0.987661	+	0.156606i	$0.0500553\pi$
$661$	16.1832	+	28.0302i	0.629455	+	1.09025i	−0.358206	+	0.933643i	$0.616611\pi$
$662$			16.7289i			0.650187i
$663$		0			0
$664$	−34.7500			−1.34856
$665$	−4.04490	−	32.2230i	−0.156855	−	1.24955i
$666$		0			0
$667$	11.9945	+	6.92504i	0.464430	+	0.268139i
$668$		−	1.00679i		−	0.0389540i
$669$		0			0
$670$	−22.8149	−	30.1068i	−0.881416	−	1.16313i
$671$	35.3211			1.36356
$672$		0			0
$673$	−3.54112	+	2.04447i	−0.136500	+	0.0788085i	−0.566695	−	0.823928i	$-0.691778\pi$
$673$	−3.54112	+	2.04447i	−0.136500	+	0.0788085i	0.430195	+	0.902736i	$0.358445\pi$
$674$	−8.69479	−	15.0598i	−0.334911	−	0.580082i
$675$		0			0
$676$	−0.310679	−	2.48352i	−0.0119492	−	0.0955200i
$677$			18.6873i			0.718211i	0.933297	+	0.359105i	$0.116918\pi$
$677$			18.6873i			0.718211i	−0.933297	+	0.359105i	$0.883082\pi$
$678$		0			0
$679$	−3.46035	−	5.99351i	−0.132796	−	0.230010i
$680$	18.8143	+	24.8275i	0.721495	+	0.952093i
$681$		0			0
$682$	−15.1198	−	8.72944i	−0.578968	−	0.334267i
$683$	32.0881	+	18.5261i	1.22782	+	0.708881i	0.966573	−	0.256392i	$-0.0825338\pi$
$683$	32.0881	+	18.5261i	1.22782	+	0.708881i	0.261245	+	0.965273i	$0.415867\pi$
$684$		0			0
$685$	−27.4120	+	20.7728i	−1.04736	+	0.793687i
$686$	−3.65016	−	6.32226i	−0.139364	−	0.241385i
$687$		0			0
$688$			20.0574i			0.764683i
$689$	23.9711	−	8.05098i	0.913226	−	0.306718i
$690$		0			0
$691$	5.58704	+	9.67704i	0.212541	+	0.368132i	0.952509	−	0.304510i	$-0.0984927\pi$
$691$	5.58704	+	9.67704i	0.212541	+	0.368132i	−0.739968	+	0.672642i	$0.765159\pi$
$692$	−3.06877	+	1.77176i	−0.116657	+	0.0673521i
$693$		0			0
$694$	14.8210			0.562598
$695$	20.2564	+	26.7306i	0.768369	+	1.01395i
$696$		0			0
$697$		−	3.86414i		−	0.146365i
$698$	−9.80676	−	5.66194i	−0.371191	−	0.214307i
$699$		0			0
$700$	3.63508	+	1.02111i	0.137393	+	0.0385945i
$701$	−7.22276			−0.272800			−0.136400	−	0.990654i	$-0.543553\pi$
$701$	−7.22276			−0.272800			−0.136400	+	0.990654i	$0.543553\pi$
$702$		0			0
$703$		−	15.6506i		−	0.590275i
$704$	−11.8518	−	20.5279i	−0.446680	−	0.773673i
$705$		0			0
$706$	9.28593	−	16.0837i	0.349481	−	0.605318i
$707$			3.41685i			0.128504i
$708$		0			0
$709$	−10.8945	+	18.8699i	−0.409152	+	0.708672i	−0.994795	−	0.101897i	$-0.967509\pi$
$709$	−10.8945	+	18.8699i	−0.409152	+	0.708672i	0.585643	+	0.810569i	$0.300842\pi$
$710$	33.7181	+	14.2051i	1.26542	+	0.533107i
$711$		0			0
$712$	28.5994	−	16.5119i	1.07181	−	0.618808i
$713$	21.5891	−	12.4645i	0.808517	−	0.466798i
$714$		0			0
$715$	−9.62706	−	19.9856i	−0.360032	−	0.747421i
$716$	−2.08169			−0.0777964
$717$		0			0
$718$	1.51391	−	0.874058i	0.0564988	−	0.0326196i
$719$	−4.27804	+	7.40978i	−0.159544	+	0.276338i	−0.934704	−	0.355426i	$-0.884336\pi$
$719$	−4.27804	+	7.40978i	−0.159544	+	0.276338i	0.775160	+	0.631764i	$0.217669\pi$
$720$		0			0
$721$	−21.0771	+	36.5065i	−0.784951	+	1.35957i
$722$	−6.15797	−	3.55531i	−0.229176	−	0.132315i
$723$		0			0
$724$	−1.15138	+	1.99424i	−0.0427906	+	0.0741155i
$725$	3.54564	−	12.6222i	0.131682	−	0.468776i
$726$		0			0
$727$		−	25.5958i		−	0.949296i	−0.880176	−	0.474648i	$-0.842575\pi$
$727$		−	25.5958i		−	0.949296i	0.880176	−	0.474648i	$-0.157425\pi$
$728$	−40.8589	−	8.26440i	−1.51433	−	0.306299i
$729$		0			0
$730$	−2.84990	+	0.357744i	−0.105479	+	0.0132407i
$731$	−13.2473	−	22.9449i	−0.489968	−	0.848649i
$732$		0			0
$733$			42.3075i			1.56266i	0.624115	+	0.781332i	$0.285460\pi$
$733$			42.3075i			1.56266i	−0.624115	+	0.781332i	$0.714540\pi$
$734$	−10.9256	+	18.9237i	−0.403272	+	0.698487i
$735$		0			0
$736$	5.73196			0.211283
$737$	−29.9423	−	17.2872i	−1.10294	−	0.636782i
$738$		0			0
$739$	17.9425	+	31.0773i	0.660026	+	1.14320i	0.980608	+	0.195977i	$0.0627879\pi$
$739$	17.9425	+	31.0773i	0.660026	+	1.14320i	−0.320583	+	0.947220i	$0.603879\pi$
$740$	1.67688	+	0.706450i	0.0616432	+	0.0259696i
$741$		0			0
$742$		−	36.9830i		−	1.35769i
$743$	−21.4322	+	12.3739i	−0.786271	+	0.453954i	−0.838648	−	0.544673i	$-0.816654\pi$
$743$	−21.4322	+	12.3739i	−0.786271	+	0.453954i	0.0523769	+	0.998627i	$0.483320\pi$
$744$		0			0
$745$	−6.95230	−	9.17433i	−0.254713	−	0.336121i
$746$	−12.8812			−0.471615
$747$		0			0
$748$	2.16823	+	1.25183i	0.0792783	+	0.0457714i
$749$	52.0692			1.90257
$750$		0			0
$751$	−12.4016	−	21.4801i	−0.452539	−	0.783821i	0.546004	−	0.837783i	$-0.316149\pi$
$751$	−12.4016	−	21.4801i	−0.452539	−	0.783821i	−0.998543	+	0.0539615i	$0.982815\pi$
$752$	−25.9120	+	14.9603i	−0.944912	+	0.545545i
$753$		0			0
$754$	−2.51989	+	12.4583i	−0.0917691	+	0.453703i
$755$	−10.6431	+	25.2633i	−0.387344	+	0.919424i
$756$		0			0
$757$	−27.7502	+	16.0216i	−1.00860	+	0.582315i	−0.910781	−	0.412889i	$-0.864520\pi$
$757$	−27.7502	+	16.0216i	−1.00860	+	0.582315i	−0.0978178	+	0.995204i	$0.531186\pi$
$758$	−27.4395	−	15.8422i	−0.996647	−	0.575415i
$759$		0			0
$760$	−19.4519	+	14.7407i	−0.705596	+	0.534700i
$761$	18.8056	−	32.5723i	0.681703	−	1.18074i	−0.292758	−	0.956187i	$-0.594573\pi$
$761$	18.8056	−	32.5723i	0.681703	−	1.18074i	0.974461	−	0.224557i	$-0.0720936\pi$
$762$		0			0
$763$	−23.4199	−	13.5215i	−0.847856	−	0.489510i
$764$	−2.20720	−	3.82298i	−0.0798537	−	0.138311i
$765$		0			0
$766$	8.17738			0.295461
$767$	7.72640	+	1.56280i	0.278984	+	0.0564293i
$768$		0			0
$769$	9.78617	+	16.9501i	0.352898	+	0.611238i	0.986756	−	0.162212i	$-0.0518628\pi$
$769$	9.78617	+	16.9501i	0.352898	+	0.611238i	−0.633858	+	0.773450i	$0.718529\pi$
$770$	−32.1913	+	4.04093i	−1.16009	+	0.145625i
$771$		0			0
$772$		−	4.48696i		−	0.161489i
$773$	23.9816	+	13.8458i	0.862558	+	0.497998i	0.864868	−	0.501999i	$-0.167402\pi$
$773$	23.9816	+	13.8458i	0.862558	+	0.497998i	−0.00230983	+	0.999997i	$0.500735\pi$
$774$		0			0
$775$	−16.4842	−	16.8862i	−0.592128	−	0.606572i
$776$	−2.60052	+	4.50424i	−0.0933534	+	0.161693i
$777$		0			0
$778$	1.11868	−	0.645872i	0.0401067	−	0.0231556i
$779$	3.02748			0.108471
$780$		0			0
$781$	33.4883			1.19831
$782$	29.0648	−	16.7806i	1.03936	−	0.600073i
$783$		0			0
$784$	−14.9992	+	25.9794i	−0.535685	+	0.927834i
$785$	−39.8723	−	16.7978i	−1.42310	−	0.599538i
$786$		0			0
$787$	−9.61920	−	5.55365i	−0.342888	−	0.197966i	0.318661	−	0.947869i	$-0.396767\pi$
$787$	−9.61920	−	5.55365i	−0.342888	−	0.197966i	−0.661548	+	0.749903i	$0.730100\pi$
$788$		−	2.51270i		−	0.0895112i
$789$		0			0
$790$	4.15649	+	33.1119i	0.147881	+	1.17807i
$791$	−4.88989	−	8.46953i	−0.173864	−	0.301142i
$792$		0			0
$793$	−45.3655	−	9.17595i	−1.61098	−	0.325848i
$794$	40.0178			1.42018
$795$		0			0
$796$	0.278721	+	0.482759i	0.00987901	+	0.0171109i
$797$	9.70287	+	5.60195i	0.343693	+	0.198431i	0.661904	−	0.749589i	$-0.269749\pi$
$797$	9.70287	+	5.60195i	0.343693	+	0.198431i	−0.318211	+	0.948020i	$0.603082\pi$
$798$		0			0
$799$	19.7615	−	34.2280i	0.699112	−	1.21090i
$800$	−1.34110	−	5.25763i	−0.0474149	−	0.185885i
$801$		0			0
$802$	42.8730	+	24.7527i	1.51390	+	0.874049i
$803$	−2.27671	+	1.31446i	−0.0803432	+	0.0463862i
$804$		0			0
$805$	17.9856	−	42.6917i	0.633908	−	1.50469i
$806$	17.1517	+	15.1398i	0.604144	+	0.533277i
$807$		0			0
$808$	2.22381	−	1.28391i	0.0782332	−	0.0451680i
$809$	15.3937	+	26.6627i	0.541215	+	0.937412i	0.998835	+	0.0482640i	$0.0153689\pi$
$809$	15.3937	+	26.6627i	0.541215	+	0.937412i	−0.457619	+	0.889148i	$0.651298\pi$
$810$		0			0
$811$	26.4129			0.927483			0.463741	−	0.885971i	$-0.346507\pi$
$811$	26.4129			0.927483			0.463741	+	0.885971i	$0.346507\pi$
$812$	−1.71484	−	0.990064i	−0.0601791	−	0.0347444i
$813$		0			0
$814$	−15.6353			−0.548016
$815$	−26.4076	+	20.0117i	−0.925019	+	0.700979i
$816$		0			0
$817$	17.9770	−	10.3790i	0.628934	−	0.363115i
$818$			10.6844i			0.373571i
$819$		0			0
$820$	−0.136657	+	0.324377i	−0.00477225	+	0.0113277i
$821$	10.2066	+	17.6784i	0.356214	+	0.616981i	0.987325	−	0.158712i	$-0.0507341\pi$
$821$	10.2066	+	17.6784i	0.356214	+	0.616981i	−0.631111	+	0.775693i	$0.717401\pi$
$822$		0			0
$823$	−4.61082	−	2.66206i	−0.160723	−	0.0927935i	0.417481	−	0.908686i	$-0.362913\pi$
$823$	−4.61082	−	2.66206i	−0.160723	−	0.0927935i	−0.578204	+	0.815892i	$0.696246\pi$
$824$	31.6797			1.10361
$825$		0			0
$826$	5.76446	−	9.98433i	0.200571	−	0.347399i
$827$			1.33819i			0.0465333i	0.999729	+	0.0232667i	$0.00740668\pi$
$827$			1.33819i			0.0465333i	−0.999729	+	0.0232667i	$0.992593\pi$
$828$		0			0
$829$	12.1369	+	21.0217i	0.421532	+	0.730115i	0.996090	−	0.0883491i	$-0.0281591\pi$
$829$	12.1369	+	21.0217i	0.421532	+	0.730115i	−0.574557	+	0.818464i	$0.694826\pi$
$830$	35.1641	−	4.41410i	1.22057	−	0.153216i
$831$		0			0
$832$	9.88926	+	29.4444i	0.342848	+	1.02080i
$833$		−	39.6258i		−	1.37295i
$834$		0			0
$835$	1.45639	+	11.6020i	0.0504003	+	0.401505i
$836$	−0.980785	+	1.69877i	−0.0339211	+	0.0587531i
$837$		0			0
$838$	24.1673	+	13.9530i	0.834846	+	0.481999i
$839$	14.8013	−	25.6366i	0.510997	−	0.885072i	−0.488922	−	0.872327i	$-0.662610\pi$
$839$	14.8013	−	25.6366i	0.510997	−	0.885072i	0.999919	−	0.0127447i	$-0.00405687\pi$
$840$		0			0
$841$	11.0622	−	19.1602i	0.381454	−	0.660698i
$842$	45.6391	−	26.3497i	1.57283	−	0.908072i
$843$		0			0
$844$	2.17159			0.0747491
$845$	7.17275	+	28.1700i	0.246750	+	0.969079i
$846$		0			0
$847$	11.6481	−	6.72505i	0.400234	−	0.231075i
$848$	−21.7311	+	12.5464i	−0.746248	+	0.430847i
$849$		0			0
$850$	−22.1922	−	22.7335i	−0.761186	−	0.779753i
$851$	11.1625	−	19.3341i	0.382647	−	0.662764i
$852$		0			0
$853$		−	45.4759i		−	1.55707i	−0.627603	−	0.778533i	$-0.715964\pi$
$853$		−	45.4759i		−	1.55707i	0.627603	−	0.778533i	$-0.284036\pi$
$854$	−33.8460	+	58.6230i	−1.15819	+	2.00604i
$855$		0			0
$856$	−19.5655	−	33.8885i	−0.668736	−	1.15828i
$857$		−	45.0228i		−	1.53795i	−0.639279	−	0.768975i	$-0.720767\pi$
$857$		−	45.0228i		−	1.53795i	0.639279	−	0.768975i	$-0.279233\pi$
$858$		0			0
$859$	17.8929			0.610498			0.305249	−	0.952273i	$-0.401260\pi$
$859$	17.8929			0.610498			0.305249	+	0.952273i	$0.401260\pi$
$860$	0.300593	+	2.39462i	0.0102501	+	0.0816558i
$861$		0			0
$862$	−17.0806	−	9.86150i	−0.581768	−	0.335884i
$863$			23.0144i			0.783419i	0.920089	+	0.391709i	$0.128116\pi$
$863$			23.0144i			0.783419i	−0.920089	+	0.391709i	$0.871884\pi$
$864$		0			0
$865$	32.8008	−	24.8565i	1.11526	−	0.845145i
$866$	−23.8993			−0.812133
$867$		0			0
$868$	−3.08656	+	1.78203i	−0.104765	+	0.0604859i
$869$	15.2722	+	26.4522i	0.518073	+	0.897329i
$870$		0			0
$871$	33.9661	+	29.9818i	1.15090	+	1.01590i
$872$			20.3233i			0.688234i
$873$		0			0
$874$	13.1473	+	22.7718i	0.444714	+	0.770267i
$875$	−43.3669	−	6.50871i	−1.46607	−	0.220034i
$876$		0			0
$877$	−6.81268	−	3.93330i	−0.230048	−	0.132818i	0.380546	−	0.924762i	$-0.375736\pi$
$877$	−6.81268	−	3.93330i	−0.230048	−	0.132818i	−0.610594	+	0.791944i	$0.709069\pi$
$878$	25.5968	+	14.7783i	0.863850	+	0.498744i
$879$		0			0
$880$	13.2953	+	17.5446i	0.448185	+	0.591430i
$881$	4.29980	+	7.44748i	0.144864	+	0.250912i	0.929322	−	0.369270i	$-0.120392\pi$
$881$	4.29980	+	7.44748i	0.144864	+	0.250912i	−0.784458	+	0.620182i	$0.787059\pi$
$882$		0			0
$883$			32.8388i			1.10511i	0.833475	+	0.552557i	$0.186348\pi$
$883$			32.8388i			1.10511i	−0.833475	+	0.552557i	$0.813652\pi$
$884$	−2.45961	−	2.17109i	−0.0827257	−	0.0730218i
$885$		0			0
$886$	0.579062	+	1.00296i	0.0194540	+	0.0336953i
$887$	20.4337	−	11.7974i	0.686097	−	0.396118i	−0.116051	−	0.993243i	$-0.537024\pi$
$887$	20.4337	−	11.7974i	0.686097	−	0.396118i	0.802148	+	0.597125i	$0.203690\pi$
$888$		0			0
$889$	−62.8620			−2.10832
$890$	−26.8428	+	20.3414i	−0.899772	+	0.681847i
$891$		0			0
$892$		−	2.96710i		−	0.0993458i
$893$	26.8170	+	15.4828i	0.897397	+	0.518112i
$894$		0			0
$895$	23.9889	−	3.01129i	0.801860	−	0.100656i
$896$	36.9144			1.23322
$897$		0			0
$898$		−	46.4804i		−	1.55107i
$899$	6.18778	+	10.7175i	0.206374	+	0.357450i
$900$		0			0
$901$	16.5730	−	28.7053i	0.552127	−	0.956312i
$902$		−	3.02451i		−	0.100705i
$903$		0			0
$904$	−3.67485	+	6.36502i	−0.122224	+	0.211698i
$905$	10.3834	−	24.6467i	0.345156	−	0.819284i
$906$		0			0
$907$	8.55765	−	4.94076i	0.284152	−	0.164055i	−0.351150	−	0.936319i	$-0.614209\pi$
$907$	8.55765	−	4.94076i	0.284152	−	0.164055i	0.635302	+	0.772264i	$0.280876\pi$
$908$	0.408003	−	0.235560i	0.0135400	−	0.00781735i
$909$		0			0
$910$	42.3955	+	3.17281i	1.40540	+	0.105178i
$911$	−19.5822			−0.648788			−0.324394	−	0.945922i	$-0.605160\pi$
$911$	−19.5822			−0.648788			−0.324394	+	0.945922i	$0.605160\pi$
$912$		0			0
$913$	28.0917	−	16.2187i	0.929699	−	0.536762i
$914$	12.9681	−	22.4614i	0.428946	−	0.742956i
$915$		0			0
$916$	0.713882	−	1.23648i	0.0235873	−	0.0408544i
$917$	−51.8087	−	29.9117i	−1.71087	−	0.987773i
$918$		0			0
$919$	−7.90392	+	13.6900i	−0.260726	+	0.451591i	−0.966435	−	0.256911i	$-0.917295\pi$
$919$	−7.90392	+	13.6900i	−0.260726	+	0.451591i	0.705709	+	0.708502i	$0.250629\pi$
$920$	−34.5435	+	4.33620i	−1.13887	+	0.142960i
$921$		0			0
$922$			10.3748i			0.341676i
$923$	−43.0115	−	8.69982i	−1.41574	−	0.286358i
$924$		0			0
$925$	−20.3458	−	5.71525i	−0.668966	−	0.187916i
$926$	−23.3950	−	40.5213i	−0.768807	−	1.33161i
$927$		0			0
$928$			2.84554i			0.0934094i
$929$	−16.2739	+	28.1872i	−0.533930	+	0.924794i	0.465284	+	0.885161i	$0.345952\pi$
$929$	−16.2739	+	28.1872i	−0.533930	+	0.924794i	−0.999214	+	0.0396324i	$0.987381\pi$
$930$		0			0
$931$	31.0461			1.01750
$932$	0.635417	+	0.366858i	0.0208138	+	0.0120168i
$933$		0			0
$934$	4.62204	+	8.00561i	0.151238	+	0.261952i
$935$	−26.7970	−	11.2893i	−0.876355	−	0.369199i
$936$		0			0
$937$			43.6682i			1.42658i	0.700871	+	0.713288i	$0.252795\pi$
$937$			43.6682i			1.42658i	−0.700871	+	0.713288i	$0.747205\pi$
$938$	57.3837	−	33.1305i	1.87364	−	1.08175i
$939$		0			0
$940$	−2.86937	+	2.17441i	−0.0935887	+	0.0709215i
$941$	−46.9923			−1.53191			−0.765953	−	0.642896i	$-0.777733\pi$
$941$	−46.9923			−1.53191			−0.765953	+	0.642896i	$0.777733\pi$
$942$		0			0
$943$	3.74001	+	2.15930i	0.121792	+	0.0703164i
$944$	−7.82235			−0.254596
$945$		0			0
$946$	−10.3688	−	17.9593i	−0.337119	−	0.583907i
$947$	7.78128	−	4.49252i	0.252858	−	0.145987i	−0.368214	−	0.929741i	$-0.620031\pi$
$947$	7.78128	−	4.49252i	0.252858	−	0.145987i	0.621072	+	0.783753i	$0.286697\pi$
$948$		0			0
$949$	3.26562	−	1.09680i	0.106007	−	0.0356036i
$950$	17.8113	−	17.3872i	0.577875	−	0.564115i
$951$		0			0
$952$	−47.3214	+	27.3210i	−1.53370	+	0.885480i
$953$	−17.3223	−	10.0010i	−0.561124	−	0.323965i	0.192473	−	0.981302i	$-0.438349\pi$
$953$	−17.3223	−	10.0010i	−0.561124	−	0.323965i	−0.753596	+	0.657337i	$0.771683\pi$
$954$		0			0
$955$	30.9654	+	40.8623i	1.00202	+	1.32227i
$956$	−1.29365	+	2.24067i	−0.0418396	+	0.0724684i
$957$		0			0
$958$	9.42309	+	5.44042i	0.304446	+	0.175772i
$959$	−30.1650	−	52.2474i	−0.974080	−	1.68716i
$960$		0			0
$961$	−8.72511			−0.281455
$962$	20.0816	+	4.06184i	0.647456	+	0.130959i
$963$		0			0
$964$	−1.30924	−	2.26767i	−0.0421678	−	0.0730368i
$965$	6.49066	+	51.7067i	0.208942	+	1.66450i
$966$		0			0
$967$		−	53.7405i		−	1.72818i	−0.503339	−	0.864089i	$-0.667895\pi$
$967$		−	53.7405i		−	1.72818i	0.503339	−	0.864089i	$-0.332105\pi$
$968$	−8.75380	−	5.05401i	−0.281358	−	0.162442i
$969$		0			0
$970$	2.05936	−	4.88824i	0.0661222	−	0.156952i
$971$	11.9812	−	20.7521i	0.384496	−	0.665966i	−0.607204	−	0.794546i	$-0.707709\pi$
$971$	11.9812	−	20.7521i	0.384496	−	0.665966i	0.991699	+	0.128581i	$0.0410421\pi$
$972$		0			0
$973$	−50.9486	+	29.4152i	−1.63334	+	0.943008i
$974$	24.2883			0.778248
$975$		0			0
$976$	45.9290			1.47015
$977$	−37.8755	+	21.8674i	−1.21175	+	0.699601i	−0.963139	−	0.269003i	$-0.913306\pi$
$977$	−37.8755	+	21.8674i	−1.21175	+	0.699601i	−0.248606	+	0.968605i	$0.579972\pi$
$978$		0			0
$979$	−15.4130	+	26.6961i	−0.492602	+	0.853212i
$980$	−1.40138	+	3.32641i	−0.0447655	+	0.106258i
$981$		0			0
$982$	15.0931	+	8.71401i	0.481640	+	0.278075i
$983$		−	25.4305i		−	0.811106i	−0.914072	−	0.405553i	$-0.867079\pi$
$983$		−	25.4305i		−	0.811106i	0.914072	−	0.405553i	$-0.132921\pi$
$984$		0			0
$985$	3.63477	+	28.9557i	0.115813	+	0.922607i
$986$	8.33045	+	14.4288i	0.265296	+	0.459505i
$987$		0			0
$988$	1.70101	−	1.92706i	0.0541164	−	0.0613080i
$989$	29.6105			0.941560
$990$		0			0
$991$	−5.25265	−	9.09786i	−0.166856	−	0.289003i	0.770457	−	0.637492i	$-0.220028\pi$
$991$	−5.25265	−	9.09786i	−0.166856	−	0.289003i	−0.937313	+	0.348489i	$0.886695\pi$
$992$	4.43554	+	2.56086i	0.140828	+	0.0813073i
$993$		0			0
$994$	−32.0898	+	55.5811i	−1.01783	+	1.76293i
$995$	−3.91025	−	5.16001i	−0.123963	−	0.163583i
$996$		0			0
$997$	3.39138	+	1.95801i	0.107406	+	0.0620109i	0.552741	−	0.833353i	$-0.313582\pi$
$997$	3.39138	+	1.95801i	0.107406	+	0.0620109i	−0.445335	+	0.895364i	$0.646915\pi$
$998$	−16.2208	+	9.36511i	−0.513462	+	0.296447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.b.289.4		24
3.2	odd	2		195.2.ba.a.94.9	yes	24
5.4	even	2	inner	585.2.bs.b.289.9		24
13.9	even	3	inner	585.2.bs.b.334.9		24
15.2	even	4		975.2.i.q.601.5		12
15.8	even	4		975.2.i.o.601.2		12
15.14	odd	2		195.2.ba.a.94.4	✓	24
39.35	odd	6		195.2.ba.a.139.4	yes	24
65.9	even	6	inner	585.2.bs.b.334.4		24
195.74	odd	6		195.2.ba.a.139.9	yes	24
195.113	even	12		975.2.i.o.451.2		12
195.152	even	12		975.2.i.q.451.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.4	✓	24	15.14	odd	2
195.2.ba.a.94.9	yes	24	3.2	odd	2
195.2.ba.a.139.4	yes	24	39.35	odd	6
195.2.ba.a.139.9	yes	24	195.74	odd	6
585.2.bs.b.289.4		24	1.1	even	1	trivial
585.2.bs.b.289.9		24	5.4	even	2	inner
585.2.bs.b.334.4		24	65.9	even	6	inner
585.2.bs.b.334.9		24	13.9	even	3	inner
975.2.i.o.451.2		12	195.113	even	12
975.2.i.o.601.2		12	15.8	even	4
975.2.i.q.451.5		12	195.152	even	12
975.2.i.q.601.5		12	15.2	even	4

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16430 + 0.672211i) q^{2} +(-0.0962645 + 0.166735i) q^{4} +(0.868136 - 2.06066i) q^{5} +(3.39681 + 1.96115i) q^{7} -2.94768i q^{8} +O(q^{10})\)	\(q+(-1.16430 + 0.672211i) q^{2} +(-0.0962645 + 0.166735i) q^{4} +(0.868136 - 2.06066i) q^{5} +(3.39681 + 1.96115i) q^{7} -2.94768i q^{8} +(0.374428 + 2.98281i) q^{10} +(1.37576 + 2.38289i) q^{11} +(-1.14795 - 3.41792i) q^{13} -5.27322 q^{14} +(1.78894 + 3.09853i) q^{16} +(-4.09295 - 2.36307i) q^{17} +(1.85142 - 3.20675i) q^{19} +(0.260014 + 0.343117i) q^{20} +(-3.20361 - 1.84960i) q^{22} +(4.57432 - 2.64098i) q^{23} +(-3.49268 - 3.57787i) q^{25} +(3.63413 + 3.20784i) q^{26} +(-0.653984 + 0.377578i) q^{28} +(1.31107 + 2.27085i) q^{29} +4.71963 q^{31} +(0.939806 + 0.542597i) q^{32} +6.35392 q^{34} +(6.99016 - 5.29714i) q^{35} +(3.66040 - 2.11333i) q^{37} +4.97818i q^{38} +(-6.07419 - 2.55899i) q^{40} +(0.408805 + 0.708072i) q^{41} +(4.85491 + 2.80298i) q^{43} -0.529747 q^{44} +(-3.55060 + 6.14981i) q^{46} +8.36266i q^{47} +(4.19221 + 7.26111i) q^{49} +(6.47163 + 1.81791i) q^{50} +(0.680394 + 0.137621i) q^{52} +7.01335i q^{53} +(6.10468 - 0.766311i) q^{55} +(5.78085 - 10.0127i) q^{56} +(-3.05297 - 1.76264i) q^{58} +(-1.09316 + 1.89340i) q^{59} +(6.41847 - 11.1171i) q^{61} +(-5.49508 + 3.17259i) q^{62} -8.61471 q^{64} +(-8.03977 - 0.601683i) q^{65} +(-10.8821 + 6.28278i) q^{67} +(0.788011 - 0.454959i) q^{68} +(-4.57787 + 10.8663i) q^{70} +(6.08542 - 10.5403i) q^{71} +0.955441i q^{73} +(-2.84121 + 4.92112i) q^{74} +(0.356452 + 0.617393i) q^{76} +10.7923i q^{77} +11.1009 q^{79} +(7.93807 - 0.996455i) q^{80} +(-0.951947 - 0.549607i) q^{82} -11.7889i q^{83} +(-8.42273 + 6.38274i) q^{85} -7.53678 q^{86} +(7.02400 - 4.05531i) q^{88} +(5.60164 + 9.70232i) q^{89} +(2.80369 - 13.8613i) q^{91} +1.01693i q^{92} +(-5.62147 - 9.73668i) q^{94} +(-5.00076 - 6.59905i) q^{95} +(-1.52806 - 0.882226i) q^{97} +(-9.76200 - 5.63610i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 24 * q + 8 * q^4 - 4 * q^5	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) \) 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

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