LMFDB - Embedded newform 666.2.bs.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.2
Character	$\chi$	$=$	666.143
Dual form			666.2.bs.a.503.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(0.411306 - 0.587405i) q^{5} +(0.509688 + 2.89058i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(0.411306 - 0.587405i) q^{5} +(0.509688 + 2.89058i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.358545 + 0.621018i) q^{10} +(0.176961 - 0.306506i) q^{11} +(-0.334949 + 3.82848i) q^{13} +(-2.83516 - 0.759679i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-0.259854 - 2.97014i) q^{17} +(0.904974 - 0.421996i) q^{19} +(-0.714361 + 0.0624985i) q^{20} +(0.203002 + 0.289916i) q^{22} +(0.280029 - 1.04508i) q^{23} +(1.53423 + 4.21526i) q^{25} +(-3.32823 - 1.92155i) q^{26} +(1.88669 - 2.24847i) q^{28} +(1.56402 + 5.83701i) q^{29} +(5.91180 + 5.91180i) q^{31} +(-0.819152 - 0.573576i) q^{32} +(2.80168 + 1.01973i) q^{34} +(1.90758 + 0.889519i) q^{35} +(-3.92842 + 4.64408i) q^{37} +0.998529i q^{38} +(0.245259 - 0.673844i) q^{40} +(-7.99625 + 6.70965i) q^{41} +(0.277330 - 0.277330i) q^{43} +(-0.348546 + 0.0614580i) q^{44} +(0.828820 + 0.695463i) q^{46} +(1.67066 - 0.964554i) q^{47} +(-1.51784 + 0.552447i) q^{49} +(-4.46871 - 0.390962i) q^{50} +(3.14809 - 2.20432i) q^{52} +(4.92279 + 0.868021i) q^{53} +(-0.107258 - 0.230016i) q^{55} +(1.24046 + 2.66017i) q^{56} +(-5.95112 - 1.04934i) q^{58} +(-4.60774 + 3.22637i) q^{59} +(0.0965990 + 0.00845132i) q^{61} +(-7.85635 + 2.85948i) q^{62} +(0.866025 - 0.500000i) q^{64} +(2.11111 + 1.77143i) q^{65} +(0.627637 - 0.110669i) q^{67} +(-2.10823 + 2.10823i) q^{68} +(-1.61236 + 1.35293i) q^{70} +(1.76347 - 4.84509i) q^{71} -7.35072i q^{73} +(-2.54875 - 5.52303i) q^{74} +(-0.904974 - 0.421996i) q^{76} +(0.976176 + 0.355299i) q^{77} +(0.786387 + 0.550634i) q^{79} +(0.507059 + 0.507059i) q^{80} +(-2.70165 - 10.0827i) q^{82} +(5.39243 - 6.42645i) q^{83} +(-1.85156 - 1.06900i) q^{85} +(0.134141 + 0.368551i) q^{86} +(0.0916019 - 0.341863i) q^{88} +(0.458772 + 0.655195i) q^{89} +(-11.2373 + 0.983133i) q^{91} +(-0.980578 + 0.457251i) q^{92} +(0.168133 + 1.92177i) q^{94} +(0.124338 - 0.705156i) q^{95} +(-13.7207 - 3.67644i) q^{97} +(0.140778 - 1.60910i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{5}{36}\right)$

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 $

$2$	−0.422618	+	0.906308i	−0.298836	+	0.640856i
$2$	−0.422618	+	0.906308i	−0.298836	+	0.640856i
$3$		0			0
$3$		0			0
$4$	−0.642788	−	0.766044i	−0.321394	−	0.383022i
$5$	0.411306	−	0.587405i	0.183941	−	0.262696i	−0.716582	−	0.697503i	$-0.754295\pi$
$5$	0.411306	−	0.587405i	0.183941	−	0.262696i	0.900524	+	0.434807i	$0.143183\pi$
$6$		0			0
$7$	0.509688	+	2.89058i	0.192644	+	1.09254i	0.915734	+	0.401784i	$0.131610\pi$
$7$	0.509688	+	2.89058i	0.192644	+	1.09254i	−0.723091	+	0.690753i	$0.757279\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$		0			0
$10$	0.358545	+	0.621018i	0.113382	+	0.196383i
$11$	0.176961	−	0.306506i	0.0533559	−	0.0924150i	−0.838114	−	0.545495i	$-0.816342\pi$
$11$	0.176961	−	0.306506i	0.0533559	−	0.0924150i	0.891470	+	0.453080i	$0.149675\pi$
$12$		0			0
$13$	−0.334949	+	3.82848i	−0.0928981	+	1.06183i	0.796482	+	0.604662i	$0.206692\pi$
$13$	−0.334949	+	3.82848i	−0.0928981	+	1.06183i	−0.889380	+	0.457168i	$0.848864\pi$
$14$	−2.83516	−	0.759679i	−0.757729	−	0.203033i
$15$		0			0
$16$	−0.173648	+	0.984808i	−0.0434120	+	0.246202i
$17$	−0.259854	−	2.97014i	−0.0630238	−	0.720366i	−0.960313	−	0.278923i	$-0.910023\pi$
$17$	−0.259854	−	2.97014i	−0.0630238	−	0.720366i	0.897290	−	0.441442i	$-0.145533\pi$
$18$		0			0
$19$	0.904974	−	0.421996i	0.207615	−	0.0968126i	−0.316029	−	0.948749i	$-0.602350\pi$
$19$	0.904974	−	0.421996i	0.207615	−	0.0968126i	0.523645	+	0.851937i	$0.324572\pi$
$20$	−0.714361	+	0.0624985i	−0.159736	+	0.0139751i
$21$		0			0
$22$	0.203002	+	0.289916i	0.0432801	+	0.0618104i
$23$	0.280029	−	1.04508i	0.0583900	−	0.217915i	−0.930566	−	0.366124i	$-0.880684\pi$
$23$	0.280029	−	1.04508i	0.0583900	−	0.217915i	0.988956	+	0.148210i	$0.0473511\pi$
$24$		0			0
$25$	1.53423	+	4.21526i	0.306846	+	0.843051i
$26$	−3.32823	−	1.92155i	−0.652719	−	0.376848i
$27$		0			0
$28$	1.88669	−	2.24847i	0.356552	−	0.424922i
$29$	1.56402	+	5.83701i	0.290432	+	1.08391i	0.944778	+	0.327711i	$0.106277\pi$
$29$	1.56402	+	5.83701i	0.290432	+	1.08391i	−0.654346	+	0.756195i	$0.727056\pi$
$30$		0			0
$31$	5.91180	+	5.91180i	1.06179	+	1.06179i	0.997961	+	0.0638301i	$0.0203316\pi$
$31$	5.91180	+	5.91180i	1.06179	+	1.06179i	0.0638301	+	0.997961i	$0.479668\pi$
$32$	−0.819152	−	0.573576i	−0.144807	−	0.101395i
$33$		0			0
$34$	2.80168	+	1.01973i	0.480485	+	0.174882i
$35$	1.90758	+	0.889519i	0.322440	+	0.150356i
$36$		0			0
$37$	−3.92842	+	4.64408i	−0.645828	+	0.763483i
$37$	−3.92842	+	4.64408i	−0.645828	+	0.763483i
$38$			0.998529i			0.161983i
$39$		0			0
$40$	0.245259	−	0.673844i	0.0387789	−	0.106544i
$41$	−7.99625	+	6.70965i	−1.24881	+	1.04787i	−0.252022	+	0.967721i	$0.581096\pi$
$41$	−7.99625	+	6.70965i	−1.24881	+	1.04787i	−0.996783	+	0.0801505i	$0.974460\pi$
$42$		0			0
$43$	0.277330	−	0.277330i	0.0422924	−	0.0422924i	−0.685644	−	0.727937i	$-0.740479\pi$
$43$	0.277330	−	0.277330i	0.0422924	−	0.0422924i	0.727937	+	0.685644i	$0.240479\pi$
$44$	−0.348546	+	0.0614580i	−0.0525453	+	0.00926515i
$45$		0			0
$46$	0.828820	+	0.695463i	0.122203	+	0.102540i
$47$	1.67066	−	0.964554i	0.243690	−	0.140695i	−0.373181	−	0.927758i	$-0.621733\pi$
$47$	1.67066	−	0.964554i	0.243690	−	0.140695i	0.616872	+	0.787064i	$0.288400\pi$
$48$		0			0
$49$	−1.51784	+	0.552447i	−0.216834	+	0.0789210i
$50$	−4.46871	−	0.390962i	−0.631971	−	0.0552903i
$51$		0			0
$52$	3.14809	−	2.20432i	0.436562	−	0.305684i
$53$	4.92279	+	0.868021i	0.676197	+	0.119232i	0.501193	−	0.865336i	$-0.332895\pi$
$53$	4.92279	+	0.868021i	0.676197	+	0.119232i	0.175005	+	0.984568i	$0.444006\pi$
$54$		0			0
$55$	−0.107258	−	0.230016i	−0.0144627	−	0.0310153i
$56$	1.24046	+	2.66017i	0.165763	+	0.355480i
$57$		0			0
$58$	−5.95112	−	1.04934i	−0.781420	−	0.137785i
$59$	−4.60774	+	3.22637i	−0.599876	+	0.420038i	−0.833681	−	0.552246i	$-0.813771\pi$
$59$	−4.60774	+	3.22637i	−0.599876	+	0.420038i	0.233805	+	0.972283i	$0.424882\pi$
$60$		0			0
$61$	0.0965990	+	0.00845132i	0.0123682	+	0.00108208i	0.0933382	−	0.995634i	$-0.470246\pi$
$61$	0.0965990	+	0.00845132i	0.0123682	+	0.00108208i	−0.0809699	+	0.996717i	$0.525802\pi$
$62$	−7.85635	+	2.85948i	−0.997757	+	0.363154i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	2.11111	+	1.77143i	0.261850	+	0.219719i
$66$		0			0
$67$	0.627637	−	0.110669i	0.0766780	−	0.0135204i	−0.135178	−	0.990821i	$-0.543160\pi$
$67$	0.627637	−	0.110669i	0.0766780	−	0.0135204i	0.211856	+	0.977301i	$0.432049\pi$
$68$	−2.10823	+	2.10823i	−0.255661	+	0.255661i
$69$		0			0
$70$	−1.61236	+	1.35293i	−0.192713	+	0.161706i
$71$	1.76347	−	4.84509i	0.209285	−	0.575006i	−0.789988	−	0.613122i	$-0.789913\pi$
$71$	1.76347	−	4.84509i	0.209285	−	0.575006i	0.999273	+	0.0381158i	$0.0121356\pi$
$72$		0			0
$73$		−	7.35072i		−	0.860337i	−0.902749	−	0.430168i	$-0.858454\pi$
$73$		−	7.35072i		−	0.860337i	0.902749	−	0.430168i	$-0.141546\pi$
$74$	−2.54875	−	5.52303i	−0.296286	−	0.642039i
$75$		0			0
$76$	−0.904974	−	0.421996i	−0.103808	−	0.0484063i
$77$	0.976176	+	0.355299i	0.111246	+	0.0404901i
$78$		0			0
$79$	0.786387	+	0.550634i	0.0884755	+	0.0619512i	0.616977	−	0.786981i	$-0.288357\pi$
$79$	0.786387	+	0.550634i	0.0884755	+	0.0619512i	−0.528502	+	0.848932i	$0.677246\pi$
$80$	0.507059	+	0.507059i	0.0566909	+	0.0566909i
$81$		0			0
$82$	−2.70165	−	10.0827i	−0.298347	−	1.11345i
$83$	5.39243	−	6.42645i	0.591896	−	0.705394i	−0.384073	−	0.923303i	$-0.625479\pi$
$83$	5.39243	−	6.42645i	0.591896	−	0.705394i	0.975969	+	0.217908i	$0.0699234\pi$
$84$		0			0
$85$	−1.85156	−	1.06900i	−0.200830	−	0.115949i
$86$	0.134141	+	0.368551i	0.0144648	+	0.0397418i
$87$		0			0
$88$	0.0916019	−	0.341863i	0.00976480	−	0.0364427i
$89$	0.458772	+	0.655195i	0.0486298	+	0.0694505i	0.842731	−	0.538336i	$-0.180947\pi$
$89$	0.458772	+	0.655195i	0.0486298	+	0.0694505i	−0.794101	+	0.607786i	$0.792058\pi$
$90$		0			0
$91$	−11.2373	+	0.983133i	−1.17799	+	0.103060i
$92$	−0.980578	+	0.457251i	−0.102232	+	0.0476717i
$93$		0			0
$94$	0.168133	+	1.92177i	0.0173416	+	0.198215i
$95$	0.124338	−	0.705156i	0.0127568	−	0.0723475i
$96$		0			0
$97$	−13.7207	−	3.67644i	−1.39312	−	0.373286i	−0.517252	−	0.855833i	$-0.673045\pi$
$97$	−13.7207	−	3.67644i	−1.39312	−	0.373286i	−0.875870	+	0.482547i	$0.839712\pi$
$98$	0.140778	−	1.60910i	0.0142207	−	0.162544i
$99$		0			0
$100$	2.24289	−	3.88480i	0.224289	−	0.388480i
$101$	5.57742	+	9.66037i	0.554974	+	0.961242i	0.997906	+	0.0646872i	$0.0206050\pi$
$101$	5.57742	+	9.66037i	0.554974	+	0.961242i	−0.442932	+	0.896555i	$0.646062\pi$
$102$		0			0
$103$	3.78309	−	1.01368i	0.372759	−	0.0998804i	−0.0675759	−	0.997714i	$-0.521526\pi$
$103$	3.78309	−	1.01368i	0.372759	−	0.0998804i	0.440335	+	0.897834i	$0.354860\pi$
$104$	0.667349	+	3.78472i	0.0654389	+	0.371123i
$105$		0			0
$106$	−2.86715	+	4.09472i	−0.278483	+	0.397714i
$107$	−6.71020	−	7.99690i	−0.648699	−	0.773090i	0.337018	−	0.941498i	$-0.390582\pi$
$107$	−6.71020	−	7.99690i	−0.648699	−	0.773090i	−0.985717	+	0.168408i	$0.946137\pi$
$108$		0			0
$109$	−1.18061	+	2.53182i	−0.113082	+	0.242504i	−0.954701	−	0.297567i	$-0.903825\pi$
$109$	−1.18061	+	2.53182i	−0.113082	+	0.242504i	0.841619	+	0.540071i	$0.181603\pi$
$110$	0.253794			0.0241983
$111$		0			0
$112$	−2.93517			−0.277348
$113$	4.26384	−	9.14383i	0.401108	−	0.860180i	−0.597203	−	0.802090i	$-0.703721\pi$
$113$	4.26384	−	9.14383i	0.401108	−	0.860180i	0.998311	−	0.0580894i	$-0.0185009\pi$
$114$		0			0
$115$	−0.498709	−	0.594338i	−0.0465049	−	0.0554223i
$116$	3.46608	−	4.95007i	0.321817	−	0.459603i
$117$		0			0
$118$	−0.976772	−	5.53955i	−0.0899192	−	0.509957i
$119$	8.45300	−	2.26497i	0.774885	−	0.207630i
$120$		0			0
$121$	5.43737	+	9.41780i	0.494306	+	0.856164i
$122$	−0.0484840	+	0.0839768i	−0.00438954	+	0.00760290i
$123$		0			0
$124$	0.728670	−	8.32874i	0.0654365	−	0.747943i
$125$	6.57038	+	1.76053i	0.587672	+	0.157466i
$126$		0			0
$127$	3.20909	−	18.1997i	0.284761	−	1.61496i	−0.421376	−	0.906886i	$-0.638453\pi$
$127$	3.20909	−	18.1997i	0.284761	−	1.61496i	0.706137	−	0.708075i	$-0.250436\pi$
$128$	0.0871557	+	0.996195i	0.00770355	+	0.0880520i
$129$		0			0
$130$	−2.49765	+	1.16467i	−0.219058	+	0.102149i
$131$	−5.15158	+	0.450705i	−0.450096	+	0.0393783i	−0.309951	−	0.950753i	$-0.600312\pi$
$131$	−5.15158	+	0.450705i	−0.450096	+	0.0393783i	−0.140145	+	0.990131i	$0.544757\pi$
$132$		0			0
$133$	1.68107	+	2.40082i	0.145767	+	0.208177i
$134$	−0.164950	+	0.615603i	−0.0142495	+	0.0531800i
$135$		0			0
$136$	−1.01973	−	2.80168i	−0.0874411	−	0.240242i
$137$	10.8732	+	6.27767i	0.928964	+	0.536338i	0.886484	−	0.462760i	$-0.153141\pi$
$137$	10.8732	+	6.27767i	0.928964	+	0.536338i	0.0424802	+	0.999097i	$0.486474\pi$
$138$		0			0
$139$	12.9897	−	15.4805i	1.10177	−	1.31304i	0.156166	−	0.987731i	$-0.450087\pi$
$139$	12.9897	−	15.4805i	1.10177	−	1.31304i	0.945607	−	0.325311i	$-0.105469\pi$
$140$	−0.544758	−	2.03306i	−0.0460404	−	0.171825i
$141$		0			0
$142$	3.64587	+	3.64587i	0.305954	+	0.305954i
$143$	1.11418	+	0.780157i	0.0931724	+	0.0652400i
$144$		0			0
$145$	4.07198	+	1.48208i	0.338160	+	0.123080i
$146$	6.66202	+	3.10655i	0.551352	+	0.257100i
$147$		0			0
$148$	6.08271	+	0.0241840i	0.499996	+	0.00198791i
$149$		−	2.47276i		−	0.202576i	−0.994857	−	0.101288i	$-0.967704\pi$
$149$		−	2.47276i		−	0.202576i	0.994857	−	0.101288i	$-0.0322964\pi$
$150$		0			0
$151$	−0.502144	+	1.37963i	−0.0408639	+	0.112273i	−0.958446	−	0.285273i	$-0.907916\pi$
$151$	−0.502144	+	1.37963i	−0.0408639	+	0.112273i	0.917582	+	0.397546i	$0.130138\pi$
$152$	0.764917	−	0.641842i	0.0620430	−	0.0520603i
$153$		0			0
$154$	−0.734560	+	0.734560i	−0.0591925	+	0.0591925i
$155$	5.90418	−	1.04107i	0.474235	−	0.0836205i
$156$		0			0
$157$	−1.70522	−	1.43085i	−0.136091	−	0.114194i	0.572201	−	0.820113i	$-0.306090\pi$
$157$	−1.70522	−	1.43085i	−0.136091	−	0.114194i	−0.708292	+	0.705919i	$0.750534\pi$
$158$	−0.831386	+	0.480001i	−0.0661415	+	0.0381868i
$159$		0			0
$160$	−0.673844	+	0.245259i	−0.0532720	+	0.0193894i
$161$	3.16362	+	0.276781i	0.249328	+	0.0218134i
$162$		0			0
$163$	11.9168	−	8.34427i	0.933400	−	0.653573i	−0.00468149	−	0.999989i	$-0.501490\pi$
$163$	11.9168	−	8.34427i	0.933400	−	0.653573i	0.938081	+	0.346416i	$0.112601\pi$
$164$	10.2798	+	1.81260i	0.802716	+	0.141541i
$165$		0			0
$166$	3.54540	+	7.60314i	0.275176	+	0.590118i
$167$	−7.29368	−	15.6414i	−0.564402	−	1.21036i	−0.956848	−	0.290589i	$-0.906149\pi$
$167$	−7.29368	−	15.6414i	−0.564402	−	1.21036i	0.392446	−	0.919775i	$-0.371629\pi$
$168$		0			0
$169$	−1.74260	−	0.307267i	−0.134046	−	0.0236359i
$170$	1.75134	−	1.22630i	0.134322	−	0.0940531i
$171$		0			0
$172$	−0.390711	−	0.0341828i	−0.0297914	−	0.00260641i
$173$	19.5760	−	7.12510i	1.48834	−	0.541711i	0.535328	−	0.844644i	$-0.320188\pi$
$173$	19.5760	−	7.12510i	1.48834	−	0.541711i	0.953012	+	0.302933i	$0.0979659\pi$
$174$		0			0
$175$	−11.4026	+	6.58328i	−0.861953	+	0.497649i
$176$	0.271120	+	0.227497i	0.0204365	+	0.0171482i
$177$		0			0
$178$	−0.787694	+	0.138892i	−0.0590401	+	0.0104104i
$179$	−14.4715	+	14.4715i	−1.08165	+	1.08165i	−0.0852924	+	0.996356i	$0.527182\pi$
$179$	−14.4715	+	14.4715i	−1.08165	+	1.08165i	−0.996356	+	0.0852924i	$0.972818\pi$
$180$		0			0
$181$	−8.10282	+	6.79907i	−0.602278	+	0.505371i	−0.892177	−	0.451686i	$-0.850823\pi$
$181$	−8.10282	+	6.79907i	−0.602278	+	0.505371i	0.289899	+	0.957057i	$0.406378\pi$
$182$	3.85805	−	10.5999i	0.285978	−	0.785718i
$183$		0			0
$184$		−	1.08195i		−	0.0797623i
$185$	1.11218	+	4.21771i	0.0817690	+	0.310092i
$186$		0			0
$187$	−0.956351	−	0.445954i	−0.0699353	−	0.0326114i
$188$	−1.81277	−	0.659794i	−0.132210	−	0.0481204i
$189$		0			0
$190$	0.586541	+	0.410700i	0.0425522	+	0.0297953i
$191$	−4.13161	−	4.13161i	−0.298953	−	0.298953i	0.541651	−	0.840604i	$-0.317800\pi$
$191$	−4.13161	−	4.13161i	−0.298953	−	0.298953i	−0.840604	+	0.541651i	$0.817800\pi$
$192$		0			0
$193$	−6.29375	−	23.4886i	−0.453034	−	1.69075i	−0.693805	−	0.720163i	$-0.744067\pi$
$193$	−6.29375	−	23.4886i	−0.453034	−	1.69075i	0.240771	−	0.970582i	$-0.422600\pi$
$194$	9.13059	−	10.8814i	0.655538	−	0.781240i
$195$		0			0
$196$	1.39885	+	0.807624i	0.0999175	+	0.0576874i
$197$	−1.68021	−	4.61633i	−0.119710	−	0.328900i	0.865336	−	0.501192i	$-0.167105\pi$
$197$	−1.68021	−	4.61633i	−0.119710	−	0.328900i	−0.985046	+	0.172292i	$0.944883\pi$
$198$		0			0
$199$	2.99186	−	11.1658i	0.212088	−	0.791522i	−0.775084	−	0.631858i	$-0.782292\pi$
$199$	2.99186	−	11.1658i	0.212088	−	0.791522i	0.987171	−	0.159664i	$-0.0510409\pi$
$200$	2.57294	+	3.67454i	0.181934	+	0.259829i
$201$		0			0
$202$	−11.1124	+	0.972208i	−0.781865	+	0.0684043i
$203$	−16.0752	+	7.49599i	−1.12826	+	0.526115i
$204$		0			0
$205$	0.652382	+	7.45676i	0.0455643	+	0.520803i
$206$	−0.680100	+	3.85704i	−0.0473848	+	0.268733i
$207$		0			0
$208$	−3.71216	−	0.994670i	−0.257392	−	0.0689679i
$209$	0.0308010	−	0.352057i	0.00213055	−	0.0243523i
$210$		0			0
$211$	−2.05598	+	3.56107i	−0.141540	+	0.245154i	−0.928077	−	0.372389i	$-0.878539\pi$
$211$	−2.05598	+	3.56107i	−0.141540	+	0.245154i	0.786537	+	0.617543i	$0.211872\pi$
$212$	−2.49937	−	4.32903i	−0.171657	−	0.297319i
$213$		0			0
$214$	10.0835	−	2.70187i	0.689294	−	0.184696i
$215$	−0.0488377	−	0.276972i	−0.00333070	−	0.0188893i
$216$		0			0
$217$	−14.0754	+	20.1017i	−0.955499	+	1.36459i
$218$	−1.79566	−	2.13998i	−0.121617	−	0.144938i
$219$		0			0
$220$	−0.107258	+	0.230016i	−0.00723134	+	0.0155077i
$221$	11.4582			0.770761
$222$		0			0
$223$	−5.25613			−0.351976			−0.175988	−	0.984392i	$-0.556312\pi$
$223$	−5.25613			−0.351976			−0.175988	+	0.984392i	$0.556312\pi$
$224$	1.24046	−	2.66017i	0.0828816	−	0.177740i
$225$		0			0
$226$	6.48515	+	7.72870i	0.431386	+	0.514106i
$227$	2.38349	−	3.40398i	0.158198	−	0.225930i	−0.732226	−	0.681061i	$-0.761519\pi$
$227$	2.38349	−	3.40398i	0.158198	−	0.225930i	0.890424	+	0.455131i	$0.150408\pi$
$228$		0			0
$229$	−3.01828	−	17.1175i	−0.199454	−	1.13116i	−0.905932	−	0.423423i	$-0.860828\pi$
$229$	−3.01828	−	17.1175i	−0.199454	−	1.13116i	0.706478	−	0.707735i	$-0.250283\pi$
$230$	0.749417	−	0.200806i	0.0494151	−	0.0132407i
$231$		0			0
$232$	3.02146	+	5.23332i	0.198369	+	0.343585i
$233$	−4.80714	+	8.32621i	−0.314926	+	0.545468i	−0.979422	−	0.201824i	$-0.935313\pi$
$233$	−4.80714	+	8.32621i	−0.314926	+	0.545468i	0.664496	+	0.747292i	$0.268646\pi$
$234$		0			0
$235$	0.120566	−	1.37808i	0.00786488	−	0.0898959i
$236$	5.43334	+	1.45586i	0.353680	+	0.0947683i
$237$		0			0
$238$	−1.51963	+	8.61824i	−0.0985029	+	0.558637i
$239$	−2.61700	−	29.9124i	−0.169280	−	1.93487i	−0.322272	−	0.946647i	$-0.604447\pi$
$239$	−2.61700	−	29.9124i	−0.169280	−	1.93487i	0.152993	−	0.988227i	$-0.451109\pi$
$240$		0			0
$241$	13.6986	−	6.38776i	0.882405	−	0.411472i	0.0720426	−	0.997402i	$-0.477048\pi$
$241$	13.6986	−	6.38776i	0.882405	−	0.411472i	0.810362	+	0.585929i	$0.199270\pi$
$242$	−10.8334	+	0.947796i	−0.696395	+	0.0609266i
$243$		0			0
$244$	−0.0556186	−	0.0794315i	−0.00356061	−	0.00508508i
$245$	−0.299784	+	1.11881i	−0.0191525	+	0.0714781i
$246$		0			0
$247$	1.31249	+	3.60603i	0.0835115	+	0.229446i
$248$	7.24045	+	4.18027i	0.459769	+	0.265448i
$249$		0			0
$250$	−4.37234	+	5.21075i	−0.276531	+	0.329557i
$251$	2.52633	+	9.42839i	0.159460	+	0.595115i	0.998682	+	0.0513249i	$0.0163444\pi$
$251$	2.52633	+	9.42839i	0.159460	+	0.595115i	−0.839222	+	0.543790i	$0.816989\pi$
$252$		0			0
$253$	−0.270770	−	0.270770i	−0.0170231	−	0.0170231i
$254$	15.1383	+	10.5999i	0.949861	+	0.665100i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−6.47149	−	3.01770i	−0.403680	−	0.188239i	0.210164	−	0.977666i	$-0.432600\pi$
$257$	−6.47149	−	3.01770i	−0.403680	−	0.188239i	−0.613845	+	0.789427i	$0.710378\pi$
$258$		0			0
$259$	−15.4264	−	8.98839i	−0.958548	−	0.558511i
$260$		−	2.75585i		−	0.170911i
$261$		0			0
$262$	1.76867	−	4.85939i	0.109269	−	0.300214i
$263$	−11.9434	+	10.0217i	−0.736462	+	0.617965i	−0.931885	−	0.362754i	$-0.881836\pi$
$263$	−11.9434	+	10.0217i	−0.736462	+	0.617965i	0.195423	+	0.980719i	$0.437392\pi$
$264$		0			0
$265$	2.53465	−	2.53465i	0.155702	−	0.155702i
$266$	−2.88633	+	0.508938i	−0.176972	+	0.0312050i
$267$		0			0
$268$	−0.488215	−	0.409661i	−0.0298225	−	0.0250240i
$269$	−23.0934	+	13.3330i	−1.40803	+	0.812927i	−0.995198	−	0.0978797i	$-0.968794\pi$
$269$	−23.0934	+	13.3330i	−1.40803	+	0.812927i	−0.412833	+	0.910807i	$0.635461\pi$
$270$		0			0
$271$	11.7729	−	4.28497i	0.715150	−	0.260293i	0.0412845	−	0.999147i	$-0.486855\pi$
$271$	11.7729	−	4.28497i	0.715150	−	0.260293i	0.673865	+	0.738854i	$0.264633\pi$
$272$	2.97014	+	0.259854i	0.180091	+	0.0157560i
$273$		0			0
$274$	−10.2847	+	7.20145i	−0.621323	+	0.435055i
$275$	1.56350	+	0.275687i	0.0942826	+	0.0166246i
$276$		0			0
$277$	8.19196	+	17.5677i	0.492207	+	1.05554i	0.982888	+	0.184202i	$0.0589701\pi$
$277$	8.19196	+	17.5677i	0.492207	+	1.05554i	−0.490681	+	0.871339i	$0.663252\pi$
$278$	8.54044	+	18.3150i	0.512222	+	1.09846i
$279$		0			0
$280$	2.07281	+	0.365492i	0.123874	+	0.0218423i
$281$	3.47745	−	2.43494i	0.207447	−	0.145256i	−0.465236	−	0.885187i	$-0.654031\pi$
$281$	3.47745	−	2.43494i	0.207447	−	0.145256i	0.672683	+	0.739930i	$0.265142\pi$
$282$		0			0
$283$	23.1502	+	2.02538i	1.37614	+	0.120396i	0.751094	−	0.660195i	$-0.229526\pi$
$283$	23.1502	+	2.02538i	1.37614	+	0.120396i	0.625042	+	0.780591i	$0.285082\pi$
$284$	−4.84509	+	1.76347i	−0.287503	+	0.104643i
$285$		0			0
$286$	−1.17794	+	0.680082i	−0.0696528	+	0.0402141i
$287$	−23.4704	−	19.6940i	−1.38541	−	1.16250i
$288$		0			0
$289$	7.98750	−	1.40841i	0.469853	−	0.0828478i
$290$	−3.06412	+	3.06412i	−0.179931	+	0.179931i
$291$		0			0
$292$	−5.63098	+	4.72495i	−0.329528	+	0.276507i
$293$	−7.74759	+	21.2863i	−0.452619	+	1.24356i	0.478255	+	0.878221i	$0.341270\pi$
$293$	−7.74759	+	21.2863i	−0.452619	+	1.24356i	−0.930874	+	0.365340i	$0.880953\pi$
$294$		0			0
$295$			4.03363i			0.234847i
$296$	−2.59258	+	5.50259i	−0.150691	+	0.319832i
$297$		0			0
$298$	2.24108	+	1.04503i	0.129822	+	0.0605371i
$299$	3.90728	+	1.42213i	0.225964	+	0.0822442i
$300$		0			0
$301$	0.942996	+	0.660293i	0.0543534	+	0.0380587i
$302$	−1.03815	−	1.03815i	−0.0597391	−	0.0597391i
$303$		0			0
$304$	0.258438	+	0.964505i	0.0148224	+	0.0553181i
$305$	0.0446961	−	0.0532667i	0.00255929	−	0.00305004i
$306$		0			0
$307$	−4.41626	−	2.54973i	−0.252049	−	0.145521i	0.368653	−	0.929567i	$-0.379819\pi$
$307$	−4.41626	−	2.54973i	−0.252049	−	0.145521i	−0.620702	+	0.784046i	$0.713152\pi$
$308$	−0.355299	−	0.976176i	−0.0202450	−	0.0556228i
$309$		0			0
$310$	−1.55169	+	5.79098i	−0.0881299	+	0.328905i
$311$	−6.77813	−	9.68018i	−0.384353	−	0.548912i	0.579629	−	0.814880i	$-0.303197\pi$
$311$	−6.77813	−	9.68018i	−0.384353	−	0.548912i	−0.963982	+	0.265968i	$0.914308\pi$
$312$		0			0
$313$	−1.42120	+	0.124339i	−0.0803308	+	0.00702804i	−0.127250	−	0.991871i	$-0.540615\pi$
$313$	−1.42120	+	0.124339i	−0.0803308	+	0.00702804i	0.0469195	+	0.998899i	$0.485060\pi$
$314$	2.01745	−	0.940752i	0.113851	−	0.0530897i
$315$		0			0
$316$	−0.0836696	−	0.956348i	−0.00470679	−	0.0537988i
$317$	−2.44687	+	13.8769i	−0.137430	+	0.779405i	0.835706	+	0.549177i	$0.185059\pi$
$317$	−2.44687	+	13.8769i	−0.137430	+	0.779405i	−0.973137	+	0.230229i	$0.926053\pi$
$318$		0			0
$319$	2.06585	+	0.553543i	0.115665	+	0.0309925i
$320$	0.0624985	−	0.714361i	0.00349377	−	0.0399340i
$321$		0			0
$322$	−1.58785	+	2.75024i	−0.0884876	+	0.153265i
$323$	−1.48855	−	2.57825i	−0.0828252	−	0.143457i
$324$		0			0
$325$	−16.6519	+	4.46187i	−0.923683	+	0.247500i
$326$	2.52620	+	14.3268i	0.139913	+	0.793487i
$327$		0			0
$328$	−5.98720	+	8.55061i	−0.330588	+	0.472129i
$329$	3.63964	+	4.33755i	0.200660	+	0.239137i
$330$		0			0
$331$	−2.83554	+	6.08084i	−0.155856	+	0.334233i	−0.968695	−	0.248255i	$-0.920143\pi$
$331$	−2.83554	+	6.08084i	−0.155856	+	0.334233i	0.812839	+	0.582488i	$0.197921\pi$
$332$	−8.38913			−0.460413
$333$		0			0
$334$	17.2583			0.944334
$335$	0.193143	−	0.414196i	0.0105525	−	0.0226299i
$336$		0			0
$337$	2.95363	+	3.52000i	0.160895	+	0.191747i	0.840469	−	0.541860i	$-0.182280\pi$
$337$	2.95363	+	3.52000i	0.160895	+	0.191747i	−0.679574	+	0.733607i	$0.737835\pi$
$338$	1.01493	−	1.44947i	0.0552050	−	0.0788409i
$339$		0			0
$340$	0.371259	+	2.10551i	0.0201343	+	0.114187i
$341$	2.85816	−	0.765842i	0.154778	−	0.0414727i
$342$		0			0
$343$	7.90259	+	13.6877i	0.426700	+	0.739066i
$344$	0.196102	−	0.339658i	0.0105731	−	0.0183131i
$345$		0			0
$346$	−1.81566	+	20.7531i	−0.0976107	+	1.11569i
$347$	−34.3430	−	9.20219i	−1.84363	−	0.493999i	−0.844495	−	0.535564i	$-0.820099\pi$
$347$	−34.3430	−	9.20219i	−1.84363	−	0.493999i	−0.999136	+	0.0415645i	$0.986766\pi$
$348$		0			0
$349$	1.58015	−	8.96148i	0.0845835	−	0.479697i	−0.912862	−	0.408268i	$-0.866133\pi$
$349$	1.58015	−	8.96148i	0.0845835	−	0.479697i	0.997446	−	0.0714291i	$-0.0227560\pi$
$350$	−1.14754	−	13.1165i	−0.0613386	−	0.701104i
$351$		0			0
$352$	−0.320763	+	0.149574i	−0.0170967	+	0.00797233i
$353$	−19.2447	+	1.68369i	−1.02429	+	0.0896137i	−0.586901	−	0.809659i	$-0.699652\pi$
$353$	−19.2447	+	1.68369i	−1.02429	+	0.0896137i	−0.437389	+	0.899273i	$0.644097\pi$
$354$		0			0
$355$	−2.12071	−	3.02868i	−0.112555	−	0.160746i
$356$	0.207015	−	0.772591i	0.0109718	−	0.0409472i
$357$		0			0
$358$	−6.99970	−	19.2315i	−0.369946	−	1.01642i
$359$	0.129699	+	0.0748819i	0.00684526	+	0.00395211i	0.503419	−	0.864043i	$-0.332075\pi$
$359$	0.129699	+	0.0748819i	0.00684526	+	0.00395211i	−0.496573	+	0.867995i	$0.665409\pi$
$360$		0			0
$361$	−11.5721	+	13.7911i	−0.609056	+	0.725845i
$362$	−2.73765	−	10.2171i	−0.143888	−	0.536997i
$363$		0			0
$364$	7.97630	+	7.97630i	0.418072	+	0.418072i
$365$	−4.31785	−	3.02339i	−0.226007	−	0.158252i
$366$		0			0
$367$	29.9244	+	10.8916i	1.56204	+	0.568537i	0.971203	−	0.238252i	$-0.0765743\pi$
$367$	29.9244	+	10.8916i	1.56204	+	0.568537i	0.590840	+	0.806789i	$0.298797\pi$
$368$	0.980578	+	0.457251i	0.0511162	+	0.0238359i
$369$		0			0
$370$	−4.29257	−	0.774506i	−0.223160	−	0.0402646i
$371$			14.6721i			0.761740i
$372$		0			0
$373$	8.90946	−	24.4785i	0.461314	−	1.26745i	−0.463184	−	0.886262i	$-0.653293\pi$
$373$	8.90946	−	24.4785i	0.461314	−	1.26745i	0.924498	−	0.381188i	$-0.124485\pi$
$374$	0.808343	−	0.678280i	0.0417984	−	0.0350730i
$375$		0			0
$376$	1.36409	−	1.36409i	0.0703473	−	0.0703473i
$377$	−22.8708	+	4.03274i	−1.17791	+	0.207696i
$378$		0			0
$379$	6.80395	+	5.70919i	0.349495	+	0.293261i	0.800587	−	0.599216i	$-0.204521\pi$
$379$	6.80395	+	5.70919i	0.349495	+	0.293261i	−0.451092	+	0.892477i	$0.648965\pi$
$380$	−0.620104	+	0.358017i	−0.0318107	+	0.0183659i
$381$		0			0
$382$	5.49060	−	1.99842i	0.280924	−	0.102248i
$383$	−5.08376	−	0.444772i	−0.259768	−	0.0227268i	−0.0434723	−	0.999055i	$-0.513842\pi$
$383$	−5.08376	−	0.444772i	−0.259768	−	0.0227268i	−0.216296	+	0.976328i	$0.569398\pi$
$384$		0			0
$385$	0.610211	−	0.427274i	0.0310992	−	0.0217759i
$386$	23.9477	+	4.22263i	1.21891	+	0.214926i
$387$		0			0
$388$	6.00315	+	12.8738i	0.304764	+	0.653568i
$389$	14.2041	+	30.4607i	0.720174	+	1.54442i	0.834520	+	0.550978i	$0.185745\pi$
$389$	14.2041	+	30.4607i	0.720174	+	1.54442i	−0.114346	+	0.993441i	$0.536477\pi$
$390$		0			0
$391$	−3.17681	−	0.560157i	−0.160658	−	0.0283284i
$392$	−1.32313	+	0.926468i	−0.0668283	+	0.0467937i
$393$		0			0
$394$	4.89391	+	0.428161i	0.246551	+	0.0215705i
$395$	0.646891	−	0.235449i	0.0325486	−	0.0118467i
$396$		0			0
$397$	−24.0449	+	13.8823i	−1.20678	+	0.696733i	−0.962054	−	0.272859i	$-0.912031\pi$
$397$	−24.0449	+	13.8823i	−1.20678	+	0.696733i	−0.244724	+	0.969593i	$0.578697\pi$
$398$	8.85523	+	7.43042i	0.443872	+	0.372453i
$399$		0			0
$400$	−4.41763	+	0.778948i	−0.220882	+	0.0389474i
$401$	−16.9486	+	16.9486i	−0.846373	+	0.846373i	−0.989678	−	0.143306i	$-0.954227\pi$
$401$	−16.9486	+	16.9486i	−0.846373	+	0.846373i	0.143306	+	0.989678i	$0.454227\pi$
$402$		0			0
$403$	−24.6134	+	20.6531i	−1.22608	+	1.02880i
$404$	3.81518	−	10.4821i	0.189812	−	0.521505i
$405$		0			0
$406$		−	17.7370i		−	0.880274i
$407$	0.728261	+	2.02591i	0.0360986	+	0.100421i
$408$		0			0
$409$	0.724980	+	0.338064i	0.0358480	+	0.0167162i	0.440460	−	0.897772i	$-0.354816\pi$
$409$	0.724980	+	0.338064i	0.0358480	+	0.0167162i	−0.404612	+	0.914489i	$0.632593\pi$
$410$	−7.03383	−	2.56010i	−0.347376	−	0.126435i
$411$		0			0
$412$	−3.20824	−	2.24644i	−0.158059	−	0.110674i
$413$	−11.6746	−	11.6746i	−0.574469	−	0.574469i
$414$		0			0
$415$	−1.55699	−	5.81078i	−0.0764298	−	0.285240i
$416$	2.47030	−	2.94399i	0.121117	−	0.144341i
$417$		0			0
$418$	0.306055	+	0.176701i	0.0149696	+	0.00864273i
$419$	12.2916	+	33.7709i	0.600483	+	1.64981i	0.750298	+	0.661100i	$0.229910\pi$
$419$	12.2916	+	33.7709i	0.600483	+	1.64981i	−0.149815	+	0.988714i	$0.547868\pi$
$420$		0			0
$421$	−3.03192	+	11.3153i	−0.147767	+	0.551473i	0.851850	+	0.523786i	$0.175481\pi$
$421$	−3.03192	+	11.3153i	−0.147767	+	0.551473i	−0.999617	+	0.0276872i	$0.991186\pi$
$422$	−2.35853	−	3.36832i	−0.114811	−	0.163967i
$423$		0			0
$424$	4.97971	−	0.435668i	0.241836	−	0.0211579i
$425$	12.1212	−	5.65223i	0.587967	−	0.274173i
$426$		0			0
$427$	0.0248061	+	0.283535i	0.00120045	+	0.0137212i
$428$	−1.81275	+	10.2806i	−0.0876226	+	0.496933i
$429$		0			0
$430$	0.271662	+	0.0727916i	0.0131007	+	0.00351032i
$431$	3.04127	−	34.7619i	0.146493	−	1.67442i	−0.466643	−	0.884446i	$-0.654537\pi$
$431$	3.04127	−	34.7619i	0.146493	−	1.67442i	0.613136	−	0.789977i	$-0.289908\pi$
$432$		0			0
$433$	−6.55128	+	11.3472i	−0.314834	+	0.545309i	−0.979402	−	0.201919i	$-0.935282\pi$
$433$	−6.55128	+	11.3472i	−0.314834	+	0.545309i	0.664568	+	0.747228i	$0.268616\pi$
$434$	−12.2698	−	21.2520i	−0.588971	−	1.02013i
$435$		0			0
$436$	2.69836	−	0.723024i	0.129228	−	0.0346266i
$437$	−0.187602	−	1.06394i	−0.00897422	−	0.0508953i
$438$		0			0
$439$	9.35123	−	13.3549i	0.446310	−	0.637397i	−0.531459	−	0.847084i	$-0.678356\pi$
$439$	9.35123	−	13.3549i	0.446310	−	0.637397i	0.977768	+	0.209688i	$0.0672447\pi$
$440$	−0.163136	−	0.194418i	−0.00777719	−	0.00926850i
$441$		0			0
$442$	−4.84244	+	10.3846i	−0.230331	+	0.493947i
$443$	18.4470			0.876446			0.438223	−	0.898866i	$-0.355608\pi$
$443$	18.4470			0.876446			0.438223	+	0.898866i	$0.355608\pi$
$444$		0			0
$445$	0.573560			0.0271894
$446$	2.22134	−	4.76367i	0.105183	−	0.225566i
$447$		0			0
$448$	1.88669	+	2.24847i	0.0891379	+	0.106230i
$449$	3.95868	−	5.65358i	0.186822	−	0.266809i	−0.714805	−	0.699324i	$-0.753485\pi$
$449$	3.95868	−	5.65358i	0.186822	−	0.266809i	0.901627	+	0.432515i	$0.142374\pi$
$450$		0			0
$451$	0.641522	+	3.63825i	0.0302081	+	0.171318i
$452$	−9.74533	+	2.61125i	−0.458382	+	0.122823i
$453$		0			0
$454$	2.07775	+	3.59876i	0.0975134	+	0.168898i
$455$	−4.04445	+	7.00520i	−0.189607	+	0.328409i
$456$		0			0
$457$	−0.0824991	+	0.942969i	−0.00385915	+	0.0441102i	−0.997880	−	0.0650793i	$-0.979270\pi$
$457$	−0.0824991	+	0.942969i	−0.00385915	+	0.0441102i	0.994021	+	0.109189i	$0.0348255\pi$
$458$	16.7893	+	4.49869i	0.784514	+	0.210210i
$459$		0			0
$460$	−0.134726	+	0.764067i	−0.00628161	+	0.0356248i
$461$	−1.74742	−	19.9731i	−0.0813856	−	0.930241i	−0.921639	−	0.388048i	$-0.873150\pi$
$461$	−1.74742	−	19.9731i	−0.0813856	−	0.930241i	0.840254	−	0.542193i	$-0.182406\pi$
$462$		0			0
$463$	34.7064	−	16.1839i	1.61294	−	0.752128i	0.613646	−	0.789582i	$-0.289702\pi$
$463$	34.7064	−	16.1839i	1.61294	−	0.752128i	0.999298	+	0.0374534i	$0.0119246\pi$
$464$	−6.01993	+	0.526675i	−0.279468	+	0.0244503i
$465$		0			0
$466$	−5.51452	−	7.87555i	−0.255455	−	0.364828i
$467$	−0.868930	+	3.24289i	−0.0402093	+	0.150063i	−0.983112	−	0.183005i	$-0.941417\pi$
$467$	−0.868930	+	3.24289i	−0.0402093	+	0.150063i	0.942903	+	0.333069i	$0.108084\pi$
$468$		0			0
$469$	0.639798	+	1.75783i	0.0295431	+	0.0811690i
$470$	1.19801	+	0.691671i	0.0552601	+	0.0319044i
$471$		0			0
$472$	−3.61568	+	4.30900i	−0.166425	+	0.198338i
$473$	−0.0359266	−	0.134080i	−0.00165191	−	0.00616500i
$474$		0			0
$475$	3.16726	+	3.16726i	0.145324	+	0.145324i
$476$	−7.16855	−	5.01948i	−0.328570	−	0.230067i
$477$		0			0
$478$	28.2159	+	10.2697i	1.29056	+	0.469727i
$479$	8.25759	+	3.85058i	0.377299	+	0.175937i	0.602011	−	0.798488i	$-0.294366\pi$
$479$	8.25759	+	3.85058i	0.377299	+	0.175937i	−0.224712	+	0.974425i	$0.572144\pi$
$480$		0			0
$481$	−16.4640	−	16.5954i	−0.750693	−	0.756686i
$482$			15.1147i			0.688457i
$483$		0			0
$484$	3.71938	−	10.2189i	0.169063	−	0.464496i
$485$	−7.80294	+	6.54745i	−0.354313	+	0.297304i
$486$		0			0
$487$	0.177564	−	0.177564i	0.00804621	−	0.00804621i	−0.703072	−	0.711118i	$-0.748189\pi$
$487$	0.177564	−	0.177564i	0.00804621	−	0.00804621i	0.711118	+	0.703072i	$0.248189\pi$
$488$	0.0954948	−	0.0168383i	0.00432285	−	0.000762235i
$489$		0			0
$490$	−0.887292	−	0.744526i	−0.0400837	−	0.0336343i
$491$	30.8153	−	17.7912i	1.39068	−	0.802907i	0.397286	−	0.917695i	$-0.369952\pi$
$491$	30.8153	−	17.7912i	1.39068	−	0.802907i	0.993390	+	0.114788i	$0.0366189\pi$
$492$		0			0
$493$	16.9304	−	6.16214i	0.762505	−	0.277529i
$494$	−3.82285	−	0.334456i	−0.171998	−	0.0150479i
$495$		0			0
$496$	−6.84856	+	4.79541i	−0.307509	+	0.215320i
$497$	14.9039	+	2.62797i	0.668533	+	0.117880i
$498$		0			0
$499$	6.22085	+	13.3406i	0.278483	+	0.597209i	0.994945	−	0.100417i	$-0.0320175\pi$
$499$	6.22085	+	13.3406i	0.278483	+	0.597209i	−0.716462	+	0.697626i	$0.754240\pi$
$500$	−2.87471	−	6.16485i	−0.128561	−	0.275700i
$501$		0			0
$502$	−9.61270	−	1.69498i	−0.429036	−	0.0756505i
$503$	22.4071	−	15.6896i	0.999084	−	0.699566i	0.0449637	−	0.998989i	$-0.485683\pi$
$503$	22.4071	−	15.6896i	0.999084	−	0.699566i	0.954121	+	0.299422i	$0.0967939\pi$
$504$		0			0
$505$	7.96857	+	0.697160i	0.354597	+	0.0310232i
$506$	0.359833	−	0.130968i	0.0159965	−	0.00582226i
$507$		0			0
$508$	−16.0045	+	9.24022i	−0.710086	+	0.409968i
$509$	−16.4827	−	13.8307i	−0.730585	−	0.613034i	0.199706	−	0.979856i	$-0.436001\pi$
$509$	−16.4827	−	13.8307i	−0.730585	−	0.613034i	−0.930291	+	0.366822i	$0.880446\pi$
$510$		0			0
$511$	21.2479	−	3.74657i	0.939950	−	0.165739i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	5.46994	−	4.58982i	0.241269	−	0.202448i
$515$	0.960567	−	2.63914i	0.0423276	−	0.116294i
$516$		0			0
$517$		−	0.682755i		−	0.0300275i
$518$	14.6657	−	10.1824i	0.644374	−	0.447388i
$519$		0			0
$520$	2.49765	+	1.16467i	0.109529	+	0.0510743i
$521$	29.9855	+	10.9138i	1.31369	+	0.478144i	0.901431	−	0.432923i	$-0.142518\pi$
$521$	29.9855	+	10.9138i	1.31369	+	0.478144i	0.412258	+	0.911067i	$0.364740\pi$
$522$		0			0
$523$	−25.5857	−	17.9153i	−1.11879	−	0.783383i	−0.140385	−	0.990097i	$-0.544834\pi$
$523$	−25.5857	−	17.9153i	−1.11879	−	0.783383i	−0.978401	+	0.206714i	$0.933723\pi$
$524$	3.65663	+	3.65663i	0.159741	+	0.159741i
$525$		0			0
$526$	−4.03525	−	15.0598i	−0.175945	−	0.656636i
$527$	16.0227	−	19.0951i	0.697959	−	0.831796i
$528$		0			0
$529$	18.9048	+	10.9147i	0.821948	+	0.474552i
$530$	1.22598	+	3.36836i	0.0532533	+	0.146312i
$531$		0			0
$532$	0.758561	−	2.83099i	0.0328878	−	0.122739i
$533$	−23.0095	−	32.8609i	−0.996651	−	1.42336i
$534$		0			0
$535$	−7.45736	+	0.652435i	−0.322410	+	0.0282072i
$536$	0.577607	−	0.269343i	0.0249488	−	0.0116338i
$537$		0			0
$538$	−2.32409	−	26.5645i	−0.100199	−	1.14528i
$539$	−0.0992699	+	0.562988i	−0.00427586	+	0.0242496i
$540$		0			0
$541$	−2.27818	−	0.610438i	−0.0979468	−	0.0262448i	0.209513	−	0.977806i	$-0.432812\pi$
$541$	−2.27818	−	0.610438i	−0.0979468	−	0.0262448i	−0.307460	+	0.951561i	$0.599479\pi$
$542$	−1.09192	+	12.4807i	−0.0469021	+	0.536093i
$543$		0			0
$544$	−1.49074	+	2.58205i	−0.0639151	+	0.110704i
$545$	1.00161	+	1.73484i	0.0429044	+	0.0743126i
$546$		0			0
$547$	−36.2895	+	9.72373i	−1.55163	+	0.415757i	−0.930000	−	0.367558i	$-0.880194\pi$
$547$	−36.2895	+	9.72373i	−1.55163	+	0.415757i	−0.621625	+	0.783315i	$0.713527\pi$
$548$	−2.18021	−	12.3646i	−0.0931340	−	0.528189i
$549$		0			0
$550$	−0.910622	+	1.30050i	−0.0388290	+	0.0554536i
$551$	3.87860	+	4.62234i	0.165234	+	0.196918i
$552$		0			0
$553$	−1.19084	+	2.55377i	−0.0506397	+	0.108597i
$554$	−19.3838			−0.823540
$555$		0			0
$556$	−20.2084			−0.857027
$557$	9.68126	−	20.7615i	0.410208	−	0.879694i	−0.587315	−	0.809358i	$-0.699815\pi$
$557$	9.68126	−	20.7615i	0.410208	−	0.879694i	0.997523	−	0.0703357i	$-0.0224071\pi$
$558$		0			0
$559$	0.968861	+	1.15464i	0.0409785	+	0.0488362i
$560$	−1.20725	+	1.72414i	−0.0510158	+	0.0728581i
$561$		0			0
$562$	0.737169	+	4.18069i	0.0310956	+	0.176352i
$563$	2.68254	−	0.718784i	0.113056	−	0.0302931i	−0.201848	−	0.979417i	$-0.564695\pi$
$563$	2.68254	−	0.718784i	0.113056	−	0.0302931i	0.314903	+	0.949124i	$0.398028\pi$
$564$		0			0
$565$	−3.61739	−	6.26551i	−0.152185	−	0.263592i
$566$	−11.6193	+	20.1252i	−0.488396	+	0.845927i
$567$		0			0
$568$	0.449378	−	5.13642i	0.0188555	−	0.215519i
$569$	30.6129	+	8.20271i	1.28336	+	0.343875i	0.835135	−	0.550045i	$-0.185390\pi$
$569$	30.6129	+	8.20271i	1.28336	+	0.343875i	0.448225	+	0.893921i	$0.352056\pi$
$570$		0			0
$571$	4.77860	−	27.1008i	0.199978	−	1.13413i	−0.705170	−	0.709038i	$-0.749129\pi$
$571$	4.77860	−	27.1008i	0.199978	−	1.13413i	0.905149	−	0.425095i	$-0.139759\pi$
$572$	−0.118546	−	1.35499i	−0.00495666	−	0.0566549i
$573$		0			0
$574$	27.7678	−	12.9484i	1.15901	−	0.540454i
$575$	4.83492	−	0.423000i	0.201630	−	0.0176403i
$576$		0			0
$577$	5.48500	+	7.83339i	0.228344	+	0.326108i	0.916932	−	0.399044i	$-0.130658\pi$
$577$	5.48500	+	7.83339i	0.228344	+	0.326108i	−0.688588	+	0.725153i	$0.741769\pi$
$578$	−2.09921	+	7.83436i	−0.0873156	+	0.325866i
$579$		0			0
$580$	−1.48208	−	4.07198i	−0.0615401	−	0.169080i
$581$	21.3246	+	12.3118i	0.884695	+	0.510779i
$582$		0			0
$583$	1.13720	−	1.35526i	0.0470979	−	0.0561291i
$584$	−1.90251	−	7.10025i	−0.0787263	−	0.293811i
$585$		0			0
$586$	−16.0177	−	16.0177i	−0.661685	−	0.661685i
$587$	−10.4571	−	7.32212i	−0.431609	−	0.302216i	0.337509	−	0.941322i	$-0.390416\pi$
$587$	−10.4571	−	7.32212i	−0.431609	−	0.302216i	−0.769119	+	0.639106i	$0.779304\pi$
$588$		0			0
$589$	7.84479	+	2.85527i	0.323239	+	0.117649i
$590$	−3.65571	−	1.70469i	−0.150503	−	0.0701808i
$591$		0			0
$592$	−3.89137	−	4.67517i	−0.159934	−	0.192149i
$593$		−	11.6437i		−	0.478151i	−0.971001	−	0.239075i	$-0.923156\pi$
$593$		−	11.6437i		−	0.478151i	0.971001	−	0.239075i	$-0.0768443\pi$
$594$		0			0
$595$	2.14631	−	5.89693i	0.0879900	−	0.241751i
$596$	−1.89424	+	1.58946i	−0.0775912	+	0.0651068i
$597$		0			0
$598$	−2.94018	+	2.94018i	−0.120233	+	0.120233i
$599$	−3.90488	+	0.688536i	−0.159549	+	0.0281328i	−0.252852	−	0.967505i	$-0.581369\pi$
$599$	−3.90488	+	0.688536i	−0.159549	+	0.0281328i	0.0933030	+	0.995638i	$0.470257\pi$
$600$		0			0
$601$	−22.4152	−	18.8086i	−0.914336	−	0.767219i	0.0586031	−	0.998281i	$-0.481335\pi$
$601$	−22.4152	−	18.8086i	−0.914336	−	0.767219i	−0.972939	+	0.231063i	$0.925780\pi$
$602$	−0.996956	+	0.575593i	−0.0406329	+	0.0234594i
$603$		0			0
$604$	1.37963	−	0.502144i	0.0561364	−	0.0204320i
$605$	7.76849	+	0.679654i	0.315834	+	0.0276319i
$606$		0			0
$607$	−19.2167	+	13.4557i	−0.779982	+	0.546149i	−0.894392	−	0.447284i	$-0.852391\pi$
$607$	−19.2167	+	13.4557i	−0.779982	+	0.546149i	0.114410	+	0.993434i	$0.463502\pi$
$608$	−0.983359	−	0.173393i	−0.0398805	−	0.00703200i
$609$		0			0
$610$	0.0293866	+	0.0630199i	0.00118983	+	0.00255160i
$611$	3.13319	+	6.71916i	0.126755	+	0.271828i
$612$		0			0
$613$	−1.86057	−	0.328069i	−0.0751478	−	0.0132506i	0.135948	−	0.990716i	$-0.456592\pi$
$613$	−1.86057	−	0.328069i	−0.0751478	−	0.0132506i	−0.211096	+	0.977465i	$0.567703\pi$
$614$	4.17723	−	2.92493i	0.168579	−	0.118040i
$615$		0			0
$616$	1.03487	+	0.0905395i	0.0416962	+	0.00364794i
$617$	36.9779	−	13.4589i	1.48868	−	0.541834i	0.535575	−	0.844487i	$-0.320095\pi$
$617$	36.9779	−	13.4589i	1.48868	−	0.541834i	0.953101	+	0.302654i	$0.0978725\pi$
$618$		0			0
$619$	−29.9743	+	17.3057i	−1.20477	+	0.695573i	−0.961612	−	0.274414i	$-0.911516\pi$
$619$	−29.9743	+	17.3057i	−1.20477	+	0.695573i	−0.243157	+	0.969987i	$0.578183\pi$
$620$	−4.59264	−	3.85368i	−0.184445	−	0.154768i
$621$		0			0
$622$	11.6378	−	2.05205i	0.466632	−	0.0822799i
$623$	−1.66006	+	1.66006i	−0.0665090	+	0.0665090i
$624$		0			0
$625$	−13.4450	+	11.2817i	−0.537799	+	0.451267i
$626$	0.487935	−	1.34059i	0.0195018	−	0.0535808i
$627$		0			0
$628$			2.22601i			0.0888274i
$629$	14.8144	+	10.4612i	0.590689	+	0.417115i
$630$		0			0
$631$	5.40115	+	2.51860i	0.215016	+	0.100264i	0.527142	−	0.849777i	$-0.323263\pi$
$631$	5.40115	+	2.51860i	0.215016	+	0.100264i	−0.312126	+	0.950041i	$0.601041\pi$
$632$	0.902106	+	0.328340i	0.0358839	+	0.0130607i
$633$		0			0
$634$	−11.5427	−	8.08226i	−0.458418	−	0.320988i
$635$	−9.37067	−	9.37067i	−0.371864	−	0.371864i
$636$		0			0
$637$	−1.60664	−	5.99605i	−0.0636573	−	0.237572i
$638$	−1.37475	+	1.63836i	−0.0544268	+	0.0648633i
$639$		0			0
$640$	0.621018	+	0.358545i	0.0245479	+	0.0141727i
$641$	5.61599	+	15.4298i	0.221818	+	0.609440i	0.999823	−	0.0188181i	$-0.00599034\pi$
$641$	5.61599	+	15.4298i	0.221818	+	0.609440i	−0.778005	+	0.628258i	$0.783768\pi$
$642$		0			0
$643$	8.51457	−	31.7768i	0.335782	−	1.25315i	−0.567237	−	0.823554i	$-0.691988\pi$
$643$	8.51457	−	31.7768i	0.335782	−	1.25315i	0.903019	−	0.429600i	$-0.141346\pi$
$644$	−1.82151	−	2.60139i	−0.0717776	−	0.102509i
$645$		0			0
$646$	2.96577	−	0.259472i	0.116687	−	0.0102088i
$647$	−33.2412	+	15.5006i	−1.30685	+	0.609393i	−0.946283	−	0.323340i	$-0.895194\pi$
$647$	−33.2412	+	15.5006i	−1.30685	+	0.609393i	−0.360566	+	0.932734i	$0.617416\pi$
$648$		0			0
$649$	0.173511	+	1.98324i	0.00681091	+	0.0778490i
$650$	2.99358	−	16.9774i	0.117418	−	0.665910i
$651$		0			0
$652$	−14.0521	−	3.76524i	−0.550322	−	0.147458i
$653$	2.48638	−	28.4195i	0.0972998	−	1.11214i	−0.777903	−	0.628385i	$-0.783716\pi$
$653$	2.48638	−	28.4195i	0.0972998	−	1.11214i	0.875203	−	0.483757i	$-0.160728\pi$
$654$		0			0
$655$	−1.85413	+	3.21144i	−0.0724468	+	0.125481i
$656$	−5.21918	−	9.03989i	−0.203775	−	0.352948i
$657$		0			0
$658$	−5.46933	+	1.46550i	−0.213217	+	0.0571312i
$659$	6.89718	+	39.1159i	0.268676	+	1.52374i	0.758359	+	0.651837i	$0.226002\pi$
$659$	6.89718	+	39.1159i	0.268676	+	1.52374i	−0.489683	+	0.871901i	$0.662887\pi$
$660$		0			0
$661$	−6.62005	+	9.45441i	−0.257490	+	0.367734i	−0.926995	−	0.375074i	$-0.877617\pi$
$661$	−6.62005	+	9.45441i	−0.257490	+	0.367734i	0.669505	+	0.742808i	$0.266506\pi$
$662$	−4.31276	−	5.13975i	−0.167620	−	0.199762i
$663$		0			0
$664$	3.54540	−	7.60314i	0.137588	−	0.295059i
$665$	2.10169			0.0814999
$666$		0			0
$667$	6.53813			0.253157
$668$	−7.29368	+	15.6414i	−0.282201	+	0.605182i
$669$		0			0
$670$	0.293763	+	0.350094i	0.0113491	+	0.0135253i
$671$	0.0196847	−	0.0281126i	0.000759918	−	0.00108528i
$672$		0			0
$673$	−2.21581	−	12.5665i	−0.0854132	−	0.484403i	−0.997267	−	0.0738866i	$-0.976460\pi$
$673$	−2.21581	−	12.5665i	−0.0854132	−	0.484403i	0.911853	−	0.410516i	$-0.134651\pi$
$674$	−4.43847	+	1.18928i	−0.170963	+	0.0458095i
$675$		0			0
$676$	0.884740	+	1.53241i	0.0340284	+	0.0589390i
$677$	−1.28758	+	2.23015i	−0.0494857	+	0.0857118i	−0.889707	−	0.456532i	$-0.849092\pi$
$677$	−1.28758	+	2.23015i	−0.0494857	+	0.0857118i	0.840222	+	0.542243i	$0.182425\pi$
$678$		0			0
$679$	3.63380	−	41.5345i	0.139452	−	1.59395i
$680$	−2.06514	−	0.553354i	−0.0791946	−	0.0212201i
$681$		0			0
$682$	−0.513823	+	2.91403i	−0.0196753	+	0.111584i
$683$	3.28236	+	37.5175i	0.125596	+	1.43557i	0.753588	+	0.657347i	$0.228322\pi$
$683$	3.28236	+	37.5175i	0.125596	+	1.43557i	−0.627992	+	0.778220i	$0.716123\pi$
$684$		0			0
$685$	8.15976	−	3.80496i	0.311769	−	0.145380i
$686$	−15.7450	+	1.37751i	−0.601149	+	0.0525937i
$687$		0			0
$688$	0.224959	+	0.321274i	0.00857647	+	0.0122485i
$689$	−4.97209	+	18.5561i	−0.189421	+	0.706930i
$690$		0			0
$691$	−17.1844	−	47.2136i	−0.653724	−	1.79609i	−0.603513	−	0.797353i	$-0.706233\pi$
$691$	−17.1844	−	47.2136i	−0.653724	−	1.79609i	−0.0502105	−	0.998739i	$-0.515989\pi$
$692$	−18.0414	−	10.4162i	−0.685831	−	0.395964i
$693$		0			0
$694$	22.8540	−	27.2363i	0.867526	−	1.03388i
$695$	−3.75061	−	13.9975i	−0.142269	−	0.530954i
$696$		0			0
$697$	22.0065	+	22.0065i	0.833555	+	0.833555i
$698$	7.45406	+	5.21939i	0.282140	+	0.197557i
$699$		0			0
$700$	12.3725	+	4.50323i	0.467637	+	0.170206i
$701$	21.8880	+	10.2066i	0.826700	+	0.385496i	0.789454	−	0.613810i	$-0.210364\pi$
$701$	21.8880	+	10.2066i	0.826700	+	0.385496i	0.0372456	+	0.999306i	$0.488142\pi$
$702$		0			0
$703$	−1.59533	+	5.86056i	−0.0601691	+	0.221035i
$704$		−	0.353923i		−	0.0133390i
$705$		0			0
$706$	6.60720	−	18.1531i	0.248665	−	0.683202i
$707$	−25.0813	+	21.0457i	−0.943281	+	0.791507i
$708$		0			0
$709$	35.2539	−	35.2539i	1.32399	−	1.32399i	0.413469	−	0.910518i	$-0.364317\pi$
$709$	35.2539	−	35.2539i	1.32399	−	1.32399i	0.910518	−	0.413469i	$-0.135683\pi$
$710$	3.64117	−	0.642036i	0.136651	−	0.0240952i
$711$		0			0
$712$	0.612717	+	0.514130i	0.0229625	+	0.0192679i
$713$	7.83379	−	4.52284i	0.293378	−	0.169382i
$714$		0			0
$715$	0.916537	−	0.333592i	0.0342765	−	0.0124756i
$716$	20.3879	+	1.78371i	0.761930	+	0.0666603i
$717$		0			0
$718$	−0.122679	+	0.0859009i	−0.00457835	+	0.00320579i
$719$	36.2636	+	6.39426i	1.35240	+	0.238465i	0.802445	−	0.596726i	$-0.203532\pi$
$719$	36.2636	+	6.39426i	1.35240	+	0.238465i	0.549960	+	0.835191i	$0.314643\pi$
$720$		0			0
$721$	4.85830	+	10.4187i	0.180933	+	0.388011i
$722$	−7.60837	−	16.3162i	−0.283154	−	0.607226i
$723$		0			0
$724$	10.4168	+	1.83676i	0.387137	+	0.0682626i
$725$	−22.2049	+	15.5481i	−0.824671	+	0.577441i
$726$		0			0
$727$	−40.9391	−	3.58171i	−1.51835	−	0.132838i	−0.702741	−	0.711445i	$-0.748041\pi$
$727$	−40.9391	−	3.58171i	−1.51835	−	0.132838i	−0.815606	+	0.578607i	$0.803596\pi$
$728$	−10.5999	+	3.85805i	−0.392859	+	0.142989i
$729$		0			0
$730$	4.56493	−	2.63556i	0.168956	−	0.0975465i
$731$	−0.895774	−	0.751644i	−0.0331314	−	0.0278006i
$732$		0			0
$733$	32.0966	−	5.65949i	1.18551	−	0.209038i	0.454086	−	0.890958i	$-0.349966\pi$
$733$	32.0966	−	5.65949i	1.18551	−	0.209038i	0.731427	+	0.681920i	$0.238855\pi$
$734$	−22.5178	+	22.5178i	−0.831146	+	0.831146i
$735$		0			0
$736$	−0.828820	+	0.695463i	−0.0305507	+	0.0256351i
$737$	0.0771466	−	0.211959i	0.00284173	−	0.00780760i
$738$		0			0
$739$			45.6503i			1.67927i	0.543148	+	0.839637i	$0.317232\pi$
$739$			45.6503i			1.67927i	−0.543148	+	0.839637i	$0.682768\pi$
$740$	2.51606	−	3.56307i	0.0924922	−	0.130981i
$741$		0			0
$742$	−13.2975	−	6.20072i	−0.488166	−	0.227635i
$743$	37.4233	+	13.6210i	1.37293	+	0.499705i	0.920027	−	0.391855i	$-0.128167\pi$
$743$	37.4233	+	13.6210i	1.37293	+	0.499705i	0.452902	+	0.891560i	$0.350389\pi$
$744$		0			0
$745$	−1.45251	−	1.01706i	−0.0532159	−	0.0372622i
$746$	18.4198	+	18.4198i	0.674396	+	0.674396i
$747$		0			0
$748$	0.273110	+	1.01926i	0.00998590	+	0.0372679i
$749$	19.6956	−	23.4723i	0.719662	−	0.857659i
$750$		0			0
$751$	33.6353	+	19.4194i	1.22737	+	0.708623i	0.966479	−	0.256746i	$-0.0826503\pi$
$751$	33.6353	+	19.4194i	1.22737	+	0.708623i	0.260891	+	0.965368i	$0.415984\pi$
$752$	0.659794	+	1.81277i	0.0240602	+	0.0661049i
$753$		0			0
$754$	6.01071	−	22.4323i	0.218897	−	0.816935i
$755$	0.603867	+	0.862412i	0.0219770	+	0.0313864i
$756$		0			0
$757$	−24.6656	+	2.15796i	−0.896485	+	0.0784323i	−0.526077	−	0.850437i	$-0.676338\pi$
$757$	−24.6656	+	2.15796i	−0.896485	+	0.0784323i	−0.370408	+	0.928869i	$0.620782\pi$
$758$	−8.04975	+	3.75366i	−0.292380	+	0.136339i
$759$		0			0
$760$	−0.0624065	−	0.713310i	−0.00226372	−	0.0258745i
$761$	4.95688	−	28.1119i	0.179687	−	1.01905i	−0.752907	−	0.658127i	$-0.771349\pi$
$761$	4.95688	−	28.1119i	0.179687	−	1.01905i	0.932594	−	0.360927i	$-0.117540\pi$
$762$		0			0
$763$	−7.92017	−	2.12220i	−0.286729	−	0.0768289i
$764$	−0.509249	+	5.82074i	−0.0184240	+	0.210587i
$765$		0			0
$766$	2.55159	−	4.41948i	0.0921927	−	0.159682i
$767$	−10.8088	−	18.7213i	−0.390281	−	0.675987i
$768$		0			0
$769$	−48.4646	+	12.9861i	−1.74768	+	0.468289i	−0.984128	−	0.177459i	$-0.943212\pi$
$769$	−48.4646	+	12.9861i	−1.74768	+	0.468289i	−0.763550	+	0.645748i	$0.776545\pi$
$770$	0.129356	+	0.733613i	0.00466166	+	0.0264376i
$771$		0			0
$772$	−13.9478	+	19.9195i	−0.501991	+	0.716917i
$773$	−13.2829	−	15.8300i	−0.477753	−	0.569364i	0.472306	−	0.881435i	$-0.343422\pi$
$773$	−13.2829	−	15.8300i	−0.477753	−	0.569364i	−0.950059	+	0.312071i	$0.898977\pi$
$774$		0			0
$775$	−15.8497	+	33.9898i	−0.569338	+	1.22095i
$776$	−14.2047			−0.509918
$777$		0			0
$778$	−33.6097			−1.20496
$779$	−4.40495	+	9.44646i	−0.157824	+	0.338454i
$780$		0			0
$781$	−1.17298	−	1.39791i	−0.0419726	−	0.0500211i
$782$	1.85025	−	2.64243i	0.0661649	−	0.0944932i
$783$		0			0
$784$	−0.280485	−	1.59071i	−0.0100173	−	0.0568110i
$785$	−1.54186	+	0.413139i	−0.0550312	+	0.0147456i
$786$		0			0
$787$	−17.0372	−	29.5092i	−0.607309	−	1.05189i	−0.991682	−	0.128712i	$-0.958916\pi$
$787$	−17.0372	−	29.5092i	−0.607309	−	1.05189i	0.384373	−	0.923178i	$-0.374418\pi$
$788$	−2.45630	+	4.25444i	−0.0875021	+	0.151558i
$789$		0			0
$790$	−0.0599986	+	0.685787i	−0.00213465	+	0.0243992i
$791$	28.6042	+	7.66448i	1.01705	+	0.272518i
$792$		0			0
$793$	−0.0647115	+	0.366997i	−0.00229797	+	0.0130324i
$794$	−2.41985	−	27.6590i	−0.0858772	−	0.981580i
$795$		0			0
$796$	−10.4766	+	4.88533i	−0.371334	+	0.173156i
$797$	−20.6757	+	1.80889i	−0.732372	+	0.0640743i	−0.447240	−	0.894414i	$-0.647593\pi$
$797$	−20.6757	+	1.80889i	−0.732372	+	0.0640743i	−0.285132	+	0.958488i	$0.592037\pi$
$798$		0			0
$799$	−3.29899	−	4.71145i	−0.116710	−	0.166679i
$800$	1.16101	−	4.33293i	0.0410478	−	0.153192i
$801$		0			0
$802$	−8.19786	−	22.5234i	−0.289477	−	0.795330i
$803$	−2.25304	−	1.30079i	−0.0795081	−	0.0459040i
$804$		0			0
$805$	1.46380	−	1.74449i	0.0515921	−	0.0614851i
$806$	−8.31598	−	31.0357i	−0.292918	−	1.09319i
$807$		0			0
$808$	7.88766	+	7.88766i	0.277487	+	0.277487i
$809$	2.32118	+	1.62531i	0.0816083	+	0.0571427i	0.613669	−	0.789564i	$-0.289693\pi$
$809$	2.32118	+	1.62531i	0.0816083	+	0.0571427i	−0.532060	+	0.846706i	$0.678582\pi$
$810$		0			0
$811$	19.2953	+	7.02293i	0.677551	+	0.246609i	0.657796	−	0.753196i	$-0.271489\pi$
$811$	19.2953	+	7.02293i	0.677551	+	0.246609i	0.0197555	+	0.999805i	$0.493711\pi$
$812$	16.0752	+	7.49599i	0.564129	+	0.263058i
$813$		0			0
$814$	−2.14387	−	0.196157i	−0.0751427	−	0.00687528i
$815$		−	10.4321i		−	0.365419i
$816$		0			0
$817$	0.133944	−	0.368008i	0.00468611	−	0.0128750i
$818$	−0.612780	+	0.514183i	−0.0214253	+	0.0179780i
$819$		0			0
$820$	5.29287	−	5.29287i	0.184835	−	0.184835i
$821$	−40.9079	+	7.21316i	−1.42769	+	0.251741i	−0.833473	−	0.552560i	$-0.813651\pi$
$821$	−40.9079	+	7.21316i	−1.42769	+	0.251741i	−0.594222	+	0.804301i	$0.702540\pi$
$822$		0			0
$823$	26.7188	+	22.4197i	0.931357	+	0.781502i	0.976061	−	0.217499i	$-0.0697898\pi$
$823$	26.7188	+	22.4197i	0.931357	+	0.781502i	−0.0447033	+	0.999000i	$0.514234\pi$
$824$	3.39182	−	1.95827i	0.118160	−	0.0682196i
$825$		0			0
$826$	15.5147	−	5.64688i	0.539825	−	0.196480i
$827$	−34.6137	−	3.02831i	−1.20364	−	0.105305i	−0.532364	−	0.846515i	$-0.678696\pi$
$827$	−34.6137	−	3.02831i	−1.20364	−	0.105305i	−0.671272	+	0.741211i	$0.734252\pi$
$828$		0			0
$829$	−7.75897	+	5.43289i	−0.269480	+	0.188692i	−0.700504	−	0.713649i	$-0.747041\pi$
$829$	−7.75897	+	5.43289i	−0.269480	+	0.188692i	0.431024	+	0.902341i	$0.358152\pi$
$830$	5.92436	+	1.04463i	0.205638	+	0.0362595i
$831$		0			0
$832$	1.62417	+	3.48304i	0.0563079	+	0.120753i
$833$	2.03526	+	4.36464i	0.0705177	+	0.151226i
$834$		0			0
$835$	−12.1877	−	2.14903i	−0.421774	−	0.0743702i
$836$	−0.289490	+	0.202703i	−0.0100122	+	0.00701063i
$837$		0			0
$838$	−35.8014	−	3.13222i	−1.23674	−	0.108201i
$839$	36.2394	−	13.1901i	1.25112	−	0.455372i	0.370343	−	0.928895i	$-0.379240\pi$
$839$	36.2394	−	13.1901i	1.25112	−	0.455372i	0.880781	+	0.473523i	$0.157018\pi$
$840$		0			0
$841$	−6.50983	+	3.75845i	−0.224477	+	0.129602i
$842$	−8.97379	−	7.52990i	−0.309257	−	0.259498i
$843$		0			0
$844$	4.04949	−	0.714035i	0.139389	−	0.0245781i
$845$	−0.897230	+	0.897230i	−0.0308656	+	0.0308656i
$846$		0			0
$847$	−24.4516	+	20.5173i	−0.840166	+	0.704983i
$848$	−1.70967	+	4.69727i	−0.0587102	+	0.161305i
$849$		0			0
$850$			13.3743i			0.458735i
$851$	3.75338	+	5.40600i	0.128664	+	0.185315i
$852$		0			0
$853$	−0.702945	−	0.327789i	−0.0240684	−	0.0112233i	0.410547	−	0.911840i	$-0.365338\pi$
$853$	−0.702945	−	0.327789i	−0.0240684	−	0.0112233i	−0.434615	+	0.900616i	$0.643116\pi$
$854$	−0.267453	−	0.0973451i	−0.00915207	−	0.00333108i
$855$		0			0
$856$	−8.55130	−	5.98769i	−0.292278	−	0.204655i
$857$	−39.7846	−	39.7846i	−1.35901	−	1.35901i	−0.875134	−	0.483880i	$-0.839227\pi$
$857$	−39.7846	−	39.7846i	−1.35901	−	1.35901i	−0.483880	−	0.875134i	$-0.660773\pi$
$858$		0			0
$859$	−3.64096	−	13.5883i	−0.124228	−	0.463626i	0.875583	−	0.483068i	$-0.160478\pi$
$859$	−3.64096	−	13.5883i	−0.124228	−	0.463626i	−0.999811	+	0.0194424i	$0.993811\pi$
$860$	−0.180781	+	0.215446i	−0.00616457	+	0.00734665i
$861$		0			0
$862$	30.2197	+	17.4474i	1.02929	+	0.594259i
$863$	−3.99648	−	10.9802i	−0.136042	−	0.373772i	0.852900	−	0.522074i	$-0.174841\pi$
$863$	−3.99648	−	10.9802i	−0.136042	−	0.373772i	−0.988942	+	0.148302i	$0.952619\pi$
$864$		0			0
$865$	3.86642	−	14.4297i	0.131462	−	0.490623i
$866$	−7.51532	−	10.7330i	−0.255381	−	0.364722i
$867$		0			0
$868$	24.4463	−	2.13877i	0.829761	−	0.0725947i
$869$	0.307933	−	0.143591i	0.0104459	−	0.00487101i
$870$		0			0
$871$	0.213469	+	2.43997i	0.00723313	+	0.0826751i
$872$	−0.485095	+	2.75111i	−0.0164274	+	0.0931644i
$873$		0			0
$874$	1.04354	+	0.279617i	0.0352984	+	0.00945818i
$875$	−1.74011	+	19.8895i	−0.0588264	+	0.672389i
$876$		0			0
$877$	−3.90872	+	6.77011i	−0.131988	+	0.228610i	−0.924443	−	0.381321i	$-0.875469\pi$
$877$	−3.90872	+	6.77011i	−0.131988	+	0.228610i	0.792455	+	0.609931i	$0.208803\pi$
$878$	8.15169	+	14.1191i	0.275106	+	0.476498i
$879$		0			0
$880$	0.245146	−	0.0656868i	0.00826388	−	0.00221430i
$881$	4.82843	+	27.3834i	0.162674	+	0.922570i	0.951430	+	0.307864i	$0.0996142\pi$
$881$	4.82843	+	27.3834i	0.162674	+	0.922570i	−0.788756	+	0.614706i	$0.789275\pi$
$882$		0			0
$883$	−27.7675	+	39.6560i	−0.934450	+	1.33453i	0.00792366	+	0.999969i	$0.497478\pi$
$883$	−27.7675	+	39.6560i	−0.934450	+	1.33453i	−0.942373	+	0.334564i	$0.891411\pi$
$884$	−7.36518	−	8.77748i	−0.247718	−	0.295219i
$885$		0			0
$886$	−7.79606	+	16.7187i	−0.261914	+	0.561676i
$887$	41.4136			1.39053			0.695266	−	0.718753i	$-0.255287\pi$
$887$	41.4136			1.39053			0.695266	+	0.718753i	$0.255287\pi$
$888$		0			0
$889$	54.2433			1.81926
$890$	−0.242397	+	0.519822i	−0.00812517	+	0.0174245i
$891$		0			0
$892$	3.37857	+	4.02643i	0.113123	+	0.134815i
$893$	1.10486	−	1.57791i	0.0369728	−	0.0528027i
$894$		0			0
$895$	2.54842	+	14.4528i	0.0851843	+	0.483104i
$896$	−2.83516	+	0.759679i	−0.0947161	+	0.0253791i
$897$		0			0
$898$	3.45087	+	5.97709i	0.115157	+	0.199458i
$899$	−25.2611	+	43.7535i	−0.842504	+	1.45926i
$900$		0			0
$901$	1.29894	−	14.8469i	0.0432740	−	0.494624i
$902$	−3.56849	−	0.956175i	−0.118818	−	0.0318371i
$903$		0			0
$904$	1.75195	−	9.93583i	0.0582691	−	0.330461i
$905$	0.661076	+	7.55613i	0.0219749	+	0.251174i
$906$		0			0
$907$	−4.35607	+	2.03127i	−0.144641	+	0.0674472i	−0.493591	−	0.869694i	$-0.664316\pi$
$907$	−4.35607	+	2.03127i	−0.144641	+	0.0674472i	0.348950	+	0.937141i	$0.386538\pi$
$908$	−4.13968	+	0.362175i	−0.137380	+	0.0120192i
$909$		0			0
$910$	−4.63961	−	6.62604i	−0.153801	−	0.219651i
$911$	14.8159	−	55.2936i	0.490872	−	1.83196i	−0.0611485	−	0.998129i	$-0.519476\pi$
$911$	14.8159	−	55.2936i	0.490872	−	1.83196i	0.552021	−	0.833831i	$-0.313857\pi$
$912$		0			0
$913$	−1.01549	−	2.79005i	−0.0336079	−	0.0923370i
$914$	−0.819755	−	0.473286i	−0.0271151	−	0.0156549i
$915$		0			0
$916$	−11.1727	+	13.3151i	−0.369155	+	0.439942i
$917$	−3.92850	−	14.6613i	−0.129730	−	0.484160i
$918$		0			0
$919$	34.4940	+	34.4940i	1.13785	+	1.13785i	0.988835	+	0.149017i	$0.0476108\pi$
$919$	34.4940	+	34.4940i	1.13785	+	1.13785i	0.149017	+	0.988835i	$0.452389\pi$
$920$	−0.635542	−	0.445011i	−0.0209532	−	0.0146716i
$921$		0			0
$922$	18.8403	+	6.85730i	0.620472	+	0.225833i
$923$	17.9587	+	8.37427i	0.591117	+	0.275642i
$924$		0			0
$925$	−25.6031	−	9.43421i	−0.841825	−	0.310195i
$926$			38.2943i			1.25843i
$927$		0			0
$928$	2.06680	−	5.67849i	0.0678461	−	0.186406i
$929$	−10.6185	+	8.91000i	−0.348382	+	0.292328i	−0.800140	−	0.599813i	$-0.795242\pi$
$929$	−10.6185	+	8.91000i	−0.348382	+	0.292328i	0.451758	+	0.892141i	$0.350797\pi$
$930$		0			0
$931$	−1.14047	+	1.14047i	−0.0373775	+	0.0373775i
$932$	9.46821	−	1.66950i	0.310142	−	0.0546863i
$933$		0			0
$934$	−2.57183	−	2.15802i	−0.0841529	−	0.0706127i
$935$	−0.655308	+	0.378342i	−0.0214309	+	0.0123731i
$936$		0			0
$937$	28.1480	−	10.2450i	0.919555	−	0.334691i	0.161493	−	0.986874i	$-0.448369\pi$
$937$	28.1480	−	10.2450i	0.919555	−	0.334691i	0.758061	+	0.652183i	$0.226147\pi$
$938$	−1.86352	−	0.163037i	−0.0608462	−	0.00532336i
$939$		0			0
$940$	−1.13317	+	0.793453i	−0.0369599	+	0.0258796i
$941$	7.25349	+	1.27899i	0.236457	+	0.0416937i	0.290621	−	0.956838i	$-0.406138\pi$
$941$	7.25349	+	1.27899i	0.236457	+	0.0416937i	−0.0541638	+	0.998532i	$0.517249\pi$
$942$		0			0
$943$	4.77295	+	10.2356i	0.155429	+	0.333318i
$944$	−2.37723	−	5.09799i	−0.0773723	−	0.165925i
$945$		0			0
$946$	0.136701	+	0.0241041i	0.00444453	+	0.000783690i
$947$	−7.71306	+	5.40074i	−0.250641	+	0.175501i	−0.692145	−	0.721759i	$-0.743334\pi$
$947$	−7.71306	+	5.40074i	−0.250641	+	0.175501i	0.441504	+	0.897259i	$0.354445\pi$
$948$		0			0
$949$	28.1421	+	2.46212i	0.913532	+	0.0799237i
$950$	−4.20906	+	1.53197i	−0.136560	+	0.0497037i
$951$		0			0
$952$	7.57875	−	4.37559i	0.245629	−	0.141814i
$953$	−1.46763	−	1.23149i	−0.0475412	−	0.0398918i	0.618707	−	0.785621i	$-0.287657\pi$
$953$	−1.46763	−	1.23149i	−0.0475412	−	0.0398918i	−0.666249	+	0.745730i	$0.732101\pi$
$954$		0			0
$955$	−4.12628	+	0.727575i	−0.133523	+	0.0235438i
$956$	−21.2321	+	21.2321i	−0.686694	+	0.686694i
$957$		0			0
$958$	−6.97962	+	5.85659i	−0.225501	+	0.189218i
$959$	−12.6042	+	34.6297i	−0.407010	+	1.11825i
$960$		0			0
$961$			38.8988i			1.25480i
$962$	21.9985	−	7.90791i	0.709261	−	0.254961i
$963$		0			0
$964$	−13.6986	−	6.38776i	−0.441202	−	0.205736i
$965$	−16.3860	−	5.96400i	−0.527483	−	0.191988i
$966$		0			0
$967$	41.2541	+	28.8864i	1.32664	+	0.928924i	0.999869	−	0.0161788i	$-0.00515009\pi$
$967$	41.2541	+	28.8864i	1.32664	+	0.928924i	0.326772	+	0.945103i	$0.394039\pi$
$968$	7.68960	+	7.68960i	0.247153	+	0.247153i
$969$		0			0
$970$	−2.63634	−	9.83894i	−0.0846476	−	0.315909i
$971$	21.7435	−	25.9129i	0.697783	−	0.831586i	−0.294490	−	0.955654i	$-0.595150\pi$
$971$	21.7435	−	25.9129i	0.697783	−	0.831586i	0.992274	+	0.124069i	$0.0395943\pi$
$972$		0			0
$973$	51.3685	+	29.6576i	1.64680	+	0.950779i
$974$	0.0858860	+	0.235970i	0.00275197	+	0.00756096i
$975$		0			0
$976$	−0.0250972	+	0.0936639i	−0.000803341	+	0.00299811i
$977$	−14.4227	−	20.5977i	−0.461422	−	0.658979i	0.519253	−	0.854620i	$-0.326210\pi$
$977$	−14.4227	−	20.5977i	−0.461422	−	0.658979i	−0.980676	+	0.195641i	$0.937321\pi$
$978$		0			0
$979$	0.282006	−	0.0246723i	0.00901295	−	0.000788531i
$980$	1.04976	−	0.489509i	0.0335332	−	0.0156368i
$981$		0			0
$982$	3.10122	+	35.4471i	0.0989638	+	1.13116i
$983$	−5.74667	+	32.5910i	−0.183290	+	1.03949i	0.744842	+	0.667241i	$0.232525\pi$
$983$	−5.74667	+	32.5910i	−0.183290	+	1.03949i	−0.928132	+	0.372250i	$0.878586\pi$
$984$		0			0
$985$	−3.40274	−	0.911761i	−0.108420	−	0.0290511i
$986$	−1.57028	+	17.9483i	−0.0500078	+	0.571592i
$987$		0			0
$988$	1.91873	−	3.32333i	0.0610428	−	0.105729i
$989$	−0.212172	−	0.367493i	−0.00674667	−	0.0116856i
$990$		0			0
$991$	28.6950	−	7.68879i	0.911526	−	0.244243i	0.227566	−	0.973763i	$-0.426923\pi$
$991$	28.6950	−	7.68879i	0.911526	−	0.244243i	0.683959	+	0.729520i	$0.260257\pi$
$992$	−1.45179	−	8.23353i	−0.0460945	−	0.261415i
$993$		0			0
$994$	−8.68043	+	12.3969i	−0.275326	+	0.393207i
$995$	−5.32827	−	6.34999i	−0.168918	−	0.201308i
$996$		0			0
$997$	−2.61838	+	5.61513i	−0.0829249	+	0.177833i	−0.943398	−	0.331663i	$-0.892390\pi$
$997$	−2.61838	+	5.61513i	−0.0829249	+	0.177833i	0.860473	+	0.509496i	$0.170168\pi$
$998$	−14.7198			−0.465946
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.143.2	✓	72
3.2	odd	2	inner	666.2.bs.a.143.5	yes	72
37.22	odd	36	inner	666.2.bs.a.503.5	yes	72
111.59	even	36	inner	666.2.bs.a.503.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.143.2	✓	72	1.1	even	1	trivial
666.2.bs.a.143.5	yes	72	3.2	odd	2	inner
666.2.bs.a.503.2	yes	72	111.59	even	36	inner
666.2.bs.a.503.5	yes	72	37.22	odd	36	inner

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(0.411306 - 0.587405i) q^{5} +(0.509688 + 2.89058i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.422618 + 0.906308i) q^{2} +(-0.642788 - 0.766044i) q^{4} +(0.411306 - 0.587405i) q^{5} +(0.509688 + 2.89058i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.358545 + 0.621018i) q^{10} +(0.176961 - 0.306506i) q^{11} +(-0.334949 + 3.82848i) q^{13} +(-2.83516 - 0.759679i) q^{14} +(-0.173648 + 0.984808i) q^{16} +(-0.259854 - 2.97014i) q^{17} +(0.904974 - 0.421996i) q^{19} +(-0.714361 + 0.0624985i) q^{20} +(0.203002 + 0.289916i) q^{22} +(0.280029 - 1.04508i) q^{23} +(1.53423 + 4.21526i) q^{25} +(-3.32823 - 1.92155i) q^{26} +(1.88669 - 2.24847i) q^{28} +(1.56402 + 5.83701i) q^{29} +(5.91180 + 5.91180i) q^{31} +(-0.819152 - 0.573576i) q^{32} +(2.80168 + 1.01973i) q^{34} +(1.90758 + 0.889519i) q^{35} +(-3.92842 + 4.64408i) q^{37} +0.998529i q^{38} +(0.245259 - 0.673844i) q^{40} +(-7.99625 + 6.70965i) q^{41} +(0.277330 - 0.277330i) q^{43} +(-0.348546 + 0.0614580i) q^{44} +(0.828820 + 0.695463i) q^{46} +(1.67066 - 0.964554i) q^{47} +(-1.51784 + 0.552447i) q^{49} +(-4.46871 - 0.390962i) q^{50} +(3.14809 - 2.20432i) q^{52} +(4.92279 + 0.868021i) q^{53} +(-0.107258 - 0.230016i) q^{55} +(1.24046 + 2.66017i) q^{56} +(-5.95112 - 1.04934i) q^{58} +(-4.60774 + 3.22637i) q^{59} +(0.0965990 + 0.00845132i) q^{61} +(-7.85635 + 2.85948i) q^{62} +(0.866025 - 0.500000i) q^{64} +(2.11111 + 1.77143i) q^{65} +(0.627637 - 0.110669i) q^{67} +(-2.10823 + 2.10823i) q^{68} +(-1.61236 + 1.35293i) q^{70} +(1.76347 - 4.84509i) q^{71} -7.35072i q^{73} +(-2.54875 - 5.52303i) q^{74} +(-0.904974 - 0.421996i) q^{76} +(0.976176 + 0.355299i) q^{77} +(0.786387 + 0.550634i) q^{79} +(0.507059 + 0.507059i) q^{80} +(-2.70165 - 10.0827i) q^{82} +(5.39243 - 6.42645i) q^{83} +(-1.85156 - 1.06900i) q^{85} +(0.134141 + 0.368551i) q^{86} +(0.0916019 - 0.341863i) q^{88} +(0.458772 + 0.655195i) q^{89} +(-11.2373 + 0.983133i) q^{91} +(-0.980578 + 0.457251i) q^{92} +(0.168133 + 1.92177i) q^{94} +(0.124338 - 0.705156i) q^{95} +(-13.7207 - 3.67644i) q^{97} +(0.140778 - 1.60910i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

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Database

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