LMFDB - Embedded newform 666.2.bs.a.35.5

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			35.5
Character	$\chi$	$=$	666.35
Dual form			666.2.bs.a.647.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.567891 - 1.21785i) q^{5} +(-0.300852 + 0.109501i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.567891 - 1.21785i) q^{5} +(-0.300852 + 0.109501i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.671872 - 1.16372i) q^{10} +(-0.282618 - 0.489509i) q^{11} +(4.64189 - 3.25029i) q^{13} +(-0.309251 + 0.0828636i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.15390 + 1.50818i) q^{17} +(0.251816 + 2.87827i) q^{19} +(0.770740 - 1.10073i) q^{20} +(-0.238879 - 0.512278i) q^{22} +(-2.16883 - 8.09420i) q^{23} +(2.05329 + 2.44702i) q^{25} +(4.90751 - 2.83335i) q^{26} +(-0.315296 + 0.0555953i) q^{28} +(0.626757 - 2.33909i) q^{29} +(1.25519 - 1.25519i) q^{31} +(0.906308 + 0.422618i) q^{32} +(2.01426 + 1.69016i) q^{34} +(-0.0374956 + 0.428576i) q^{35} +(1.50742 + 5.89302i) q^{37} +2.88926i q^{38} +(0.863742 - 1.02937i) q^{40} +(-0.936762 + 5.31264i) q^{41} +(0.271805 + 0.271805i) q^{43} +(-0.193322 - 0.531149i) q^{44} +(-1.45513 - 8.25243i) q^{46} +(-8.86683 - 5.11926i) q^{47} +(-5.28379 + 4.43363i) q^{49} +(1.83221 + 2.61666i) q^{50} +(5.13578 - 2.39485i) q^{52} +(1.41455 - 3.88644i) q^{53} +(-0.756643 + 0.0661977i) q^{55} +(-0.318942 + 0.0279038i) q^{56} +(0.828238 - 2.27556i) q^{58} +(-2.87343 + 1.33990i) q^{59} +(-1.12444 - 1.60587i) q^{61} +(1.35981 - 1.14102i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-1.32226 - 7.49891i) q^{65} +(3.00284 + 8.25023i) q^{67} +(1.85929 + 1.85929i) q^{68} +(-0.0747058 + 0.423678i) q^{70} +(-2.58354 + 3.07894i) q^{71} +2.39008i q^{73} +(0.988069 + 6.00198i) q^{74} +(-0.251816 + 2.87827i) q^{76} +(0.138628 + 0.116323i) q^{77} +(8.72743 + 4.06967i) q^{79} +(0.950170 - 0.950170i) q^{80} +(-1.39623 + 5.21078i) q^{82} +(-10.5661 + 1.86309i) q^{83} +(3.05991 - 1.76664i) q^{85} +(0.247081 + 0.294460i) q^{86} +(-0.146294 - 0.545977i) q^{88} +(-0.359487 - 0.770922i) q^{89} +(-1.04061 + 1.48615i) q^{91} +(-0.730342 - 8.34784i) q^{92} +(-8.38691 - 5.87258i) q^{94} +(3.64829 + 1.32787i) q^{95} +(0.0722709 - 0.0193649i) q^{97} +(-5.65010 + 3.95624i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{19}{36}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	0.567891	−	1.21785i	0.253968	−	0.544637i	−0.737444	−	0.675408i	$-0.763968\pi$
$5$	0.567891	−	1.21785i	0.253968	−	0.544637i	0.991413	+	0.130771i	$0.0417453\pi$
$6$		0			0
$7$	−0.300852	+	0.109501i	−0.113712	+	0.0413876i	−0.398249	−	0.917277i	$-0.630382\pi$
$7$	−0.300852	+	0.109501i	−0.113712	+	0.0413876i	0.284538	+	0.958665i	$0.408160\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	0.671872	−	1.16372i	0.212465	−	0.367999i
$11$	−0.282618	−	0.489509i	−0.0852126	−	0.147593i	0.820269	−	0.571978i	$-0.193824\pi$
$11$	−0.282618	−	0.489509i	−0.0852126	−	0.147593i	−0.905482	+	0.424385i	$0.860490\pi$
$12$		0			0
$13$	4.64189	−	3.25029i	1.28743	−	0.901468i	0.288991	−	0.957332i	$-0.406680\pi$
$13$	4.64189	−	3.25029i	1.28743	−	0.901468i	0.998438	+	0.0558642i	$0.0177914\pi$
$14$	−0.309251	+	0.0828636i	−0.0826509	+	0.0221462i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	2.15390	+	1.50818i	0.522397	+	0.365787i	0.804835	−	0.593499i	$-0.202254\pi$
$17$	2.15390	+	1.50818i	0.522397	+	0.365787i	−0.282437	+	0.959286i	$0.591143\pi$
$18$		0			0
$19$	0.251816	+	2.87827i	0.0577705	+	0.660320i	0.968778	+	0.247930i	$0.0797503\pi$
$19$	0.251816	+	2.87827i	0.0577705	+	0.660320i	−0.911007	+	0.412390i	$0.864694\pi$
$20$	0.770740	−	1.10073i	0.172343	−	0.246131i
$21$		0			0
$22$	−0.238879	−	0.512278i	−0.0509292	−	0.109218i
$23$	−2.16883	−	8.09420i	−0.452233	−	1.68776i	−0.696097	−	0.717948i	$-0.745082\pi$
$23$	−2.16883	−	8.09420i	−0.452233	−	1.68776i	0.243864	−	0.969810i	$-0.421585\pi$
$24$		0			0
$25$	2.05329	+	2.44702i	0.410658	+	0.489403i
$26$	4.90751	−	2.83335i	0.962442	−	0.555666i
$27$		0			0
$28$	−0.315296	+	0.0555953i	−0.0595854	+	0.0105065i
$29$	0.626757	−	2.33909i	0.116386	−	0.434358i	−0.883001	−	0.469371i	$-0.844481\pi$
$29$	0.626757	−	2.33909i	0.116386	−	0.434358i	0.999387	+	0.0350131i	$0.0111473\pi$
$30$		0			0
$31$	1.25519	−	1.25519i	0.225439	−	0.225439i	−0.585345	−	0.810784i	$-0.699041\pi$
$31$	1.25519	−	1.25519i	0.225439	−	0.225439i	0.810784	+	0.585345i	$0.199041\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	2.01426	+	1.69016i	0.345442	+	0.289861i
$35$	−0.0374956	+	0.428576i	−0.00633791	+	0.0724426i
$36$		0			0
$37$	1.50742	+	5.89302i	0.247818	+	0.968807i
$37$	1.50742	+	5.89302i	0.247818	+	0.968807i
$38$			2.88926i			0.468700i
$39$		0			0
$40$	0.863742	−	1.02937i	0.136570	−	0.162757i
$41$	−0.936762	+	5.31264i	−0.146298	+	0.829695i	0.820018	+	0.572337i	$0.193963\pi$
$41$	−0.936762	+	5.31264i	−0.146298	+	0.829695i	−0.966316	+	0.257358i	$0.917148\pi$
$42$		0			0
$43$	0.271805	+	0.271805i	0.0414499	+	0.0414499i	0.727528	−	0.686078i	$-0.240669\pi$
$43$	0.271805	+	0.271805i	0.0414499	+	0.0414499i	−0.686078	+	0.727528i	$0.740669\pi$
$44$	−0.193322	−	0.531149i	−0.0291444	−	0.0800737i
$45$		0			0
$46$	−1.45513	−	8.25243i	−0.214547	−	1.21675i
$47$	−8.86683	−	5.11926i	−1.29336	−	0.746722i	−0.314111	−	0.949386i	$-0.601707\pi$
$47$	−8.86683	−	5.11926i	−1.29336	−	0.746722i	−0.979248	+	0.202665i	$0.935040\pi$
$48$		0			0
$49$	−5.28379	+	4.43363i	−0.754827	+	0.633375i
$50$	1.83221	+	2.61666i	0.259113	+	0.370052i
$51$		0			0
$52$	5.13578	−	2.39485i	0.712204	−	0.332106i
$53$	1.41455	−	3.88644i	0.194303	−	0.533844i	−0.803834	−	0.594854i	$-0.797210\pi$
$53$	1.41455	−	3.88644i	0.194303	−	0.533844i	0.998137	+	0.0610101i	$0.0194322\pi$
$54$		0			0
$55$	−0.756643	+	0.0661977i	−0.102026	+	0.00892609i
$56$	−0.318942	+	0.0279038i	−0.0426204	+	0.00372880i
$57$		0			0
$58$	0.828238	−	2.27556i	0.108753	−	0.298796i
$59$	−2.87343	+	1.33990i	−0.374089	+	0.174441i	−0.600565	−	0.799576i	$-0.705057\pi$
$59$	−2.87343	+	1.33990i	−0.374089	+	0.174441i	0.226475	+	0.974017i	$0.427280\pi$
$60$		0			0
$61$	−1.12444	−	1.60587i	−0.143970	−	0.205611i	0.740690	−	0.671847i	$-0.234499\pi$
$61$	−1.12444	−	1.60587i	−0.143970	−	0.205611i	−0.884660	+	0.466236i	$0.845610\pi$
$62$	1.35981	−	1.14102i	0.172696	−	0.144909i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−1.32226	−	7.49891i	−0.164006	−	0.930126i
$66$		0			0
$67$	3.00284	+	8.25023i	0.366855	+	1.00793i	0.976550	+	0.215290i	$0.0690696\pi$
$67$	3.00284	+	8.25023i	0.366855	+	1.00793i	−0.609695	+	0.792636i	$0.708708\pi$
$68$	1.85929	+	1.85929i	0.225471	+	0.225471i
$69$		0			0
$70$	−0.0747058	+	0.423678i	−0.00892905	+	0.0506392i
$71$	−2.58354	+	3.07894i	−0.306610	+	0.365404i	−0.897243	−	0.441537i	$-0.854434\pi$
$71$	−2.58354	+	3.07894i	−0.306610	+	0.365404i	0.590633	+	0.806940i	$0.298878\pi$
$72$		0			0
$73$			2.39008i			0.279738i	0.990170	+	0.139869i	$0.0446681\pi$
$73$			2.39008i			0.279738i	−0.990170	+	0.139869i	$0.955332\pi$
$74$	0.988069	+	6.00198i	0.114861	+	0.697716i
$75$		0			0
$76$	−0.251816	+	2.87827i	−0.0288853	+	0.330160i
$77$	0.138628	+	0.116323i	0.0157982	+	0.0132562i
$78$		0			0
$79$	8.72743	+	4.06967i	0.981913	+	0.457873i	0.846195	−	0.532874i	$-0.178888\pi$
$79$	8.72743	+	4.06967i	0.981913	+	0.457873i	0.135718	+	0.990747i	$0.456666\pi$
$80$	0.950170	−	0.950170i	0.106232	−	0.106232i
$81$		0			0
$82$	−1.39623	+	5.21078i	−0.154187	+	0.575435i
$83$	−10.5661	+	1.86309i	−1.15978	+	0.204501i	−0.720243	−	0.693722i	$-0.755970\pi$
$83$	−10.5661	+	1.86309i	−1.15978	+	0.204501i	−0.439540	+	0.898223i	$0.644859\pi$
$84$		0			0
$85$	3.05991	−	1.76664i	0.331893	−	0.191619i
$86$	0.247081	+	0.294460i	0.0266435	+	0.0317524i
$87$		0			0
$88$	−0.146294	−	0.545977i	−0.0155950	−	0.0582013i
$89$	−0.359487	−	0.770922i	−0.0381055	−	0.0817175i	0.886334	−	0.463047i	$-0.153244\pi$
$89$	−0.359487	−	0.770922i	−0.0381055	−	0.0817175i	−0.924439	+	0.381330i	$0.875466\pi$
$90$		0			0
$91$	−1.04061	+	1.48615i	−0.109086	+	0.155791i
$92$	−0.730342	−	8.34784i	−0.0761434	−	0.870323i
$93$		0			0
$94$	−8.38691	−	5.87258i	−0.865044	−	0.605710i
$95$	3.64829	+	1.32787i	0.374307	+	0.136236i
$96$		0			0
$97$	0.0722709	−	0.0193649i	0.00733800	−	0.00196621i	−0.255148	−	0.966902i	$-0.582124\pi$
$97$	0.0722709	−	0.0193649i	0.00733800	−	0.00196621i	0.262486	+	0.964936i	$0.415458\pi$
$98$	−5.65010	+	3.95624i	−0.570746	+	0.399641i
$99$		0			0
$100$	1.59718	+	2.76639i	0.159718	+	0.276639i
$101$	−7.21194	+	12.4915i	−0.717615	+	1.24295i	0.244327	+	0.969693i	$0.421433\pi$
$101$	−7.21194	+	12.4915i	−0.717615	+	1.24295i	−0.961942	+	0.273253i	$0.911900\pi$
$102$		0			0
$103$	−4.10162	−	1.09903i	−0.404145	−	0.108290i	0.0510196	−	0.998698i	$-0.483753\pi$
$103$	−4.10162	−	1.09903i	−0.404145	−	0.108290i	−0.455165	+	0.890407i	$0.650420\pi$
$104$	5.32496	−	1.93813i	0.522155	−	0.190049i
$105$		0			0
$106$	1.74789	−	3.74836i	0.169770	−	0.364073i
$107$	−2.50511	−	0.441719i	−0.242178	−	0.0427026i	0.0512414	−	0.998686i	$-0.483682\pi$
$107$	−2.50511	−	0.441719i	−0.242178	−	0.0427026i	−0.293420	+	0.955984i	$0.594793\pi$
$108$		0			0
$109$	−17.6611	−	1.54515i	−1.69163	−	0.147998i	−0.799767	−	0.600311i	$-0.795043\pi$
$109$	−17.6611	−	1.54515i	−1.69163	−	0.147998i	−0.891859	+	0.452313i	$0.850599\pi$
$110$	−0.759533			−0.0724186
$111$		0			0
$112$	−0.320160			−0.0302523
$113$	7.22139	+	0.631790i	0.679332	+	0.0594338i	0.421599	−	0.906782i	$-0.361469\pi$
$113$	7.22139	+	0.631790i	0.679332	+	0.0594338i	0.257733	+	0.966216i	$0.417025\pi$
$114$		0			0
$115$	−11.0891	−	1.95532i	−1.03407	−	0.182334i
$116$	1.02341	−	2.19472i	0.0950216	−	0.203775i
$117$		0			0
$118$	−2.97928	+	1.08437i	−0.274265	+	0.0998243i
$119$	−0.813153	−	0.217884i	−0.0745416	−	0.0199734i
$120$		0			0
$121$	5.34025	−	9.24959i	0.485478	−	0.840872i
$122$	−0.980205	−	1.69776i	−0.0887436	−	0.153708i
$123$		0			0
$124$	1.45408	−	1.01816i	0.130580	−	0.0914333i
$125$	10.6359	−	2.84988i	0.951305	−	0.254901i
$126$		0			0
$127$	−16.9264	−	6.16071i	−1.50198	−	0.546674i	−0.545404	−	0.838173i	$-0.683624\pi$
$127$	−16.9264	−	6.16071i	−1.50198	−	0.546674i	−0.956571	+	0.291499i	$0.905846\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	−0.663656	−	7.58562i	−0.0582065	−	0.665303i
$131$	−2.71167	+	3.87266i	−0.236919	+	0.338356i	−0.919951	−	0.392032i	$-0.871772\pi$
$131$	−2.71167	+	3.87266i	−0.236919	+	0.338356i	0.683032	+	0.730389i	$0.260661\pi$
$132$		0			0
$133$	−0.390934	−	0.838360i	−0.0338982	−	0.0726950i
$134$	2.27236	+	8.48055i	0.196302	+	0.732608i
$135$		0			0
$136$	1.69016	+	2.01426i	0.144930	+	0.172721i
$137$	−6.69048	+	3.86275i	−0.571606	+	0.330017i	−0.757791	−	0.652498i	$-0.773721\pi$
$137$	−6.69048	+	3.86275i	−0.571606	+	0.330017i	0.186184	+	0.982515i	$0.440388\pi$
$138$		0			0
$139$	4.00842	−	0.706792i	0.339989	−	0.0599493i	−0.00104680	−	0.999999i	$-0.500333\pi$
$139$	4.00842	−	0.706792i	0.339989	−	0.0599493i	0.341036	+	0.940050i	$0.389222\pi$
$140$	−0.111347	+	0.415554i	−0.00941058	+	0.0351208i
$141$		0			0
$142$	−2.84206	+	2.84206i	−0.238500	+	0.238500i
$143$	−2.90293	−	1.35366i	−0.242755	−	0.113199i
$144$		0			0
$145$	−2.49272	−	2.09164i	−0.207009	−	0.173701i
$146$	−0.208309	+	2.38099i	−0.0172398	+	0.197052i
$147$		0			0
$148$	0.461202	+	6.06525i	0.0379106	+	0.498561i
$149$			8.63606i			0.707494i	0.935341	+	0.353747i	$0.115093\pi$
$149$			8.63606i			0.707494i	−0.935341	+	0.353747i	$0.884907\pi$
$150$		0			0
$151$	−8.17184	+	9.73881i	−0.665015	+	0.792533i	−0.988096	−	0.153838i	$-0.950837\pi$
$151$	−8.17184	+	9.73881i	−0.665015	+	0.792533i	0.323082	+	0.946371i	$0.395281\pi$
$152$	−0.501715	+	2.84537i	−0.0406945	+	0.230790i
$153$		0			0
$154$	0.127963	+	0.127963i	0.0103115	+	0.0103115i
$155$	−0.815816	−	2.24144i	−0.0655279	−	0.180036i
$156$		0			0
$157$	−0.282457	−	1.60189i	−0.0225425	−	0.127845i	0.971460	−	0.237204i	$-0.0762311\pi$
$157$	−0.282457	−	1.60189i	−0.0225425	−	0.127845i	−0.994002	+	0.109360i	$0.965120\pi$
$158$	8.33953	+	4.81483i	0.663457	+	0.383047i
$159$		0			0
$160$	1.02937	−	0.863742i	0.0813786	−	0.0682848i
$161$	1.53882	+	2.19767i	0.121276	+	0.173201i
$162$		0			0
$163$	−14.1614	+	6.60357i	−1.10921	+	0.517231i	−0.888855	−	0.458189i	$-0.848498\pi$
$163$	−14.1614	+	6.60357i	−1.10921	+	0.517231i	−0.220352	+	0.975420i	$0.570721\pi$
$164$	−1.84506	+	5.06927i	−0.144075	+	0.395843i
$165$		0			0
$166$	−10.6883	+	0.935105i	−0.829573	+	0.0725782i
$167$	10.6911	−	0.935349i	0.827301	−	0.0723794i	0.334363	−	0.942444i	$-0.391479\pi$
$167$	10.6911	−	0.935349i	0.827301	−	0.0723794i	0.492937	+	0.870065i	$0.335923\pi$
$168$		0			0
$169$	6.53653	−	17.9590i	0.502810	−	1.38146i
$170$	3.20223	−	1.49323i	0.245600	−	0.114525i
$171$		0			0
$172$	0.220477	+	0.314874i	0.0168112	+	0.0240089i
$173$	−2.06272	+	1.73082i	−0.156825	+	0.131592i	−0.717824	−	0.696225i	$-0.754862\pi$
$173$	−2.06272	+	1.73082i	−0.156825	+	0.131592i	0.560999	+	0.827817i	$0.310417\pi$
$174$		0			0
$175$	−0.885689	−	0.511353i	−0.0669518	−	0.0386546i
$176$	−0.0981523	−	0.556649i	−0.00739851	−	0.0419590i
$177$		0			0
$178$	−0.290929	−	0.799319i	−0.0218060	−	0.0599115i
$179$	−0.0370180	−	0.0370180i	−0.00276686	−	0.00276686i	0.705722	−	0.708489i	$-0.250623\pi$
$179$	−0.0370180	−	0.0370180i	−0.00276686	−	0.00276686i	−0.708489	+	0.705722i	$0.750623\pi$
$180$		0			0
$181$	2.49707	−	14.1616i	0.185606	−	1.05262i	−0.739569	−	0.673081i	$-0.764971\pi$
$181$	2.49707	−	14.1616i	0.185606	−	1.05262i	0.925175	−	0.379542i	$-0.123918\pi$
$182$	−1.16618	+	1.38980i	−0.0864430	+	0.103019i
$183$		0			0
$184$		−	8.37973i		−	0.617762i
$185$	8.03283	+	1.51079i	0.590586	+	0.111076i
$186$		0			0
$187$	0.129535	−	1.48059i	0.00947254	−	0.108272i
$188$	−7.84317	−	6.58120i	−0.572022	−	0.479983i
$189$		0			0
$190$	3.51868	+	1.64079i	0.255272	+	0.119035i
$191$	−10.1724	+	10.1724i	−0.736048	+	0.736048i	−0.971811	−	0.235763i	$-0.924241\pi$
$191$	−10.1724	+	10.1724i	−0.736048	+	0.736048i	0.235763	+	0.971811i	$0.424241\pi$
$192$		0			0
$193$	0.883727	−	3.29811i	0.0636120	−	0.237403i	−0.926798	−	0.375559i	$-0.877451\pi$
$193$	0.883727	−	3.29811i	0.0636120	−	0.237403i	0.990411	+	0.138156i	$0.0441174\pi$
$194$	0.0736837	−	0.0129924i	0.00529018	−	0.000932801i
$195$		0			0
$196$	−5.97341	+	3.44875i	−0.426672	+	0.246339i
$197$	15.4444	+	18.4059i	1.10036	+	1.31136i	0.946295	+	0.323303i	$0.104793\pi$
$197$	15.4444	+	18.4059i	1.10036	+	1.31136i	0.154069	+	0.988060i	$0.450762\pi$
$198$		0			0
$199$	−4.53278	−	16.9166i	−0.321321	−	1.19918i	−0.917959	−	0.396675i	$-0.870164\pi$
$199$	−4.53278	−	16.9166i	−0.321321	−	1.19918i	0.596639	−	0.802510i	$-0.296503\pi$
$200$	1.34999	+	2.89507i	0.0954589	+	0.204712i
$201$		0			0
$202$	−8.27320	+	11.8154i	−0.582100	+	0.831325i
$203$	0.0675720	+	0.772352i	0.00474263	+	0.0542085i
$204$		0			0
$205$	5.93800	+	4.15783i	0.414728	+	0.290396i
$206$	−3.99023	−	1.45232i	−0.278012	−	0.101188i
$207$		0			0
$208$	5.47362	−	1.46665i	0.379527	−	0.101694i
$209$	1.33777	−	0.936718i	0.0925356	−	0.0647941i
$210$		0			0
$211$	8.36729	+	14.4926i	0.576028	+	0.997709i	0.995929	+	0.0901396i	$0.0287313\pi$
$211$	8.36729	+	14.4926i	0.576028	+	0.997709i	−0.419901	+	0.907570i	$0.637935\pi$
$212$	2.06793	−	3.58176i	0.142026	−	0.245996i
$213$		0			0
$214$	−2.45708	−	0.658373i	−0.167963	−	0.0450054i
$215$	0.485372	−	0.176661i	0.0331021	−	0.0120482i
$216$		0			0
$217$	−0.240182	+	0.515071i	−0.0163046	+	0.0349653i
$218$	−17.4592	−	3.07853i	−1.18249	−	0.208504i
$219$		0			0
$220$	−0.756643	−	0.0661977i	−0.0510128	−	0.00446305i
$221$	14.9002			1.00229
$222$		0			0
$223$	9.00870			0.603267			0.301634	−	0.953424i	$-0.402468\pi$
$223$	9.00870			0.603267			0.301634	+	0.953424i	$0.402468\pi$
$224$	−0.318942	−	0.0279038i	−0.0213102	−	0.00186440i
$225$		0			0
$226$	7.13885	+	1.25877i	0.474869	+	0.0837323i
$227$	7.20810	−	15.4578i	0.478418	−	1.02597i	−0.507945	−	0.861389i	$-0.669595\pi$
$227$	7.20810	−	15.4578i	0.478418	−	1.02597i	0.986363	−	0.164582i	$-0.0526275\pi$
$228$		0			0
$229$	6.36118	−	2.31528i	0.420359	−	0.152998i	−0.123176	−	0.992385i	$-0.539308\pi$
$229$	6.36118	−	2.31528i	0.420359	−	0.152998i	0.543535	+	0.839387i	$0.317086\pi$
$230$	−10.8765	−	2.91436i	−0.717177	−	0.192167i
$231$		0			0
$232$	1.21080	−	2.09717i	0.0794931	−	0.137686i
$233$	12.2642	+	21.2421i	0.803451	+	1.39162i	0.917332	+	0.398124i	$0.130339\pi$
$233$	12.2642	+	21.2421i	0.803451	+	1.39162i	−0.113880	+	0.993494i	$0.536328\pi$
$234$		0			0
$235$	−11.2699	+	7.89124i	−0.735165	+	0.514768i
$236$	−3.06245	+	0.820582i	−0.199349	+	0.0534153i
$237$		0			0
$238$	−0.791069	−	0.287926i	−0.0512774	−	0.0186634i
$239$	−7.65713	−	5.36158i	−0.495298	−	0.346812i	0.299087	−	0.954226i	$-0.403318\pi$
$239$	−7.65713	−	5.36158i	−0.495298	−	0.346812i	−0.794385	+	0.607414i	$0.792207\pi$
$240$		0			0
$241$	−0.471855	−	5.39333i	−0.0303949	−	0.347415i	−0.996130	−	0.0878869i	$-0.971989\pi$
$241$	−0.471855	−	5.39333i	−0.0303949	−	0.347415i	0.965736	−	0.259528i	$-0.0835670\pi$
$242$	6.12609	−	8.74896i	0.393800	−	0.562404i
$243$		0			0
$244$	−0.828505	−	1.77673i	−0.0530396	−	0.113744i
$245$	2.39886	+	8.95265i	0.153257	+	0.571964i
$246$		0			0
$247$	10.5241	+	12.5421i	0.669633	+	0.798037i
$248$	1.53729	−	0.887553i	0.0976178	−	0.0563596i
$249$		0			0
$250$	10.8438	−	1.91206i	0.685824	−	0.120929i
$251$	4.81689	−	17.9769i	0.304039	−	1.13469i	−0.629730	−	0.776814i	$-0.716834\pi$
$251$	4.81689	−	17.9769i	0.304039	−	1.13469i	0.933769	−	0.357876i	$-0.116499\pi$
$252$		0			0
$253$	−3.34923	+	3.34923i	−0.210565	+	0.210565i
$254$	−16.3251	−	7.61250i	−1.02432	−	0.477651i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.61793	−	18.4930i	0.100924	−	1.15356i	−0.761775	−	0.647842i	$-0.775672\pi$
$257$	1.61793	−	18.4930i	0.100924	−	1.15356i	0.862698	−	0.505719i	$-0.168773\pi$
$258$		0			0
$259$	−1.09880	−	1.60787i	−0.0682763	−	0.0999079i
$260$		−	7.61460i		−	0.472237i
$261$		0			0
$262$	−3.03887	+	3.62159i	−0.187742	+	0.223742i
$263$	−1.00848	+	5.71935i	−0.0621853	+	0.352670i	0.937800	+	0.347177i	$0.112860\pi$
$263$	−1.00848	+	5.71935i	−0.0621853	+	0.352670i	−0.999985	+	0.00549322i	$0.998251\pi$
$264$		0			0
$265$	−3.92977	−	3.92977i	−0.241404	−	0.241404i
$266$	−0.316378	−	0.869242i	−0.0193984	−	0.0532966i
$267$		0			0
$268$	1.52458	+	8.64632i	0.0931286	+	0.528158i
$269$	−3.23672	−	1.86872i	−0.197346	−	0.113938i	0.398071	−	0.917355i	$-0.369680\pi$
$269$	−3.23672	−	1.86872i	−0.197346	−	0.113938i	−0.595417	+	0.803417i	$0.703013\pi$
$270$		0			0
$271$	22.7876	−	19.1211i	1.38425	−	1.16152i	0.416642	−	0.909071i	$-0.363207\pi$
$271$	22.7876	−	19.1211i	1.38425	−	1.16152i	0.967609	−	0.252454i	$-0.0812376\pi$
$272$	1.50818	+	2.15390i	0.0914467	+	0.130599i
$273$		0			0
$274$	−7.00168	+	3.26494i	−0.422987	+	0.197242i
$275$	0.617540	−	1.69668i	0.0372390	−	0.102313i
$276$		0			0
$277$	18.3587	−	1.60618i	1.10307	−	0.0965058i	0.478954	−	0.877840i	$-0.341016\pi$
$277$	18.3587	−	1.60618i	1.10307	−	0.0965058i	0.624113	+	0.781334i	$0.285461\pi$
$278$	4.05476	−	0.354746i	0.243189	−	0.0212762i
$279$		0			0
$280$	−0.147142	+	0.404268i	−0.00879340	+	0.0241597i
$281$	3.44017	−	1.60418i	0.205224	−	0.0956973i	−0.317289	−	0.948329i	$-0.602773\pi$
$281$	3.44017	−	1.60418i	0.205224	−	0.0956973i	0.522513	+	0.852632i	$0.324995\pi$
$282$		0			0
$283$	11.6333	+	16.6141i	0.691529	+	0.987605i	0.999346	+	0.0361599i	$0.0115126\pi$
$283$	11.6333	+	16.6141i	0.691529	+	0.987605i	−0.307817	+	0.951445i	$0.599599\pi$
$284$	−3.07894	+	2.58354i	−0.182702	+	0.153305i
$285$		0			0
$286$	−2.77390	−	1.60151i	−0.164024	−	0.0946995i
$287$	−0.299914	−	1.70090i	−0.0177034	−	0.100401i
$288$		0			0
$289$	−3.44966	−	9.47785i	−0.202921	−	0.557521i
$290$	−2.30094	−	2.30094i	−0.135116	−	0.135116i
$291$		0			0
$292$	−0.415033	+	2.35377i	−0.0242880	+	0.137744i
$293$	15.5494	−	18.5311i	0.908407	−	1.08260i	−0.0878476	−	0.996134i	$-0.527999\pi$
$293$	15.5494	−	18.5311i	0.908407	−	1.08260i	0.996255	−	0.0864638i	$-0.0275567\pi$
$294$		0			0
$295$			4.26032i			0.248045i
$296$	−0.0691745	+	6.08237i	−0.00402068	+	0.353531i
$297$		0			0
$298$	−0.752682	+	8.60320i	−0.0436017	+	0.498370i
$299$	−36.3760	−	30.5231i	−2.10368	−	1.76519i
$300$		0			0
$301$	−0.111536	−	0.0520101i	−0.00642884	−	0.00299782i
$302$	−8.98953	+	8.98953i	−0.517289	+	0.517289i
$303$		0			0
$304$	−0.747796	+	2.79081i	−0.0428891	+	0.160064i
$305$	−2.59427	+	0.457439i	−0.148547	+	0.0261929i
$306$		0			0
$307$	−23.2551	+	13.4264i	−1.32724	+	0.766282i	−0.984872	−	0.173284i	$-0.944562\pi$
$307$	−23.2551	+	13.4264i	−1.32724	+	0.766282i	−0.342368	+	0.939566i	$0.611229\pi$
$308$	0.116323	+	0.138628i	0.00662812	+	0.00789908i
$309$		0			0
$310$	−0.617358	−	2.30401i	−0.0350636	−	0.130859i
$311$	8.92059	+	19.1303i	0.505840	+	1.08478i	0.979011	+	0.203807i	$0.0653316\pi$
$311$	8.92059	+	19.1303i	0.505840	+	1.08478i	−0.473171	+	0.880971i	$0.656891\pi$
$312$		0			0
$313$	−2.79327	+	3.98921i	−0.157885	+	0.225483i	−0.890299	−	0.455376i	$-0.849505\pi$
$313$	−2.79327	+	3.98921i	−0.157885	+	0.225483i	0.732414	+	0.680860i	$0.238394\pi$
$314$	−0.141768	−	1.62041i	−0.00800042	−	0.0914453i
$315$		0			0
$316$	7.88815	+	5.52334i	0.443743	+	0.310712i
$317$	−15.3820	−	5.59858i	−0.863938	−	0.314448i	−0.128228	−	0.991745i	$-0.540929\pi$
$317$	−15.3820	−	5.59858i	−0.863938	−	0.314448i	−0.735710	+	0.677297i	$0.763151\pi$
$318$		0			0
$319$	−1.32214	+	0.354266i	−0.0740256	+	0.0198351i
$320$	1.10073	−	0.770740i	0.0615327	−	0.0430857i
$321$		0			0
$322$	1.34143	+	2.32342i	0.0747549	+	0.129479i
$323$	−3.79855	+	6.57929i	−0.211357	+	0.366081i
$324$		0			0
$325$	17.4847	+	4.68500i	0.969875	+	0.259877i
$326$	−14.6831	+	5.34419i	−0.813219	+	0.295987i
$327$		0			0
$328$	−2.27986	+	4.88917i	−0.125884	+	0.269959i
$329$	3.22817	+	0.569214i	0.177975	+	0.0313818i
$330$		0			0
$331$	−5.70439	−	0.499069i	−0.313542	−	0.0274313i	−0.0707010	−	0.997498i	$-0.522524\pi$
$331$	−5.70439	−	0.499069i	−0.313542	−	0.0274313i	−0.242841	+	0.970066i	$0.578079\pi$
$332$	−10.7291			−0.588837
$333$		0			0
$334$	10.7319			0.587225
$335$	11.7528	+	1.02824i	0.642123	+	0.0561785i
$336$		0			0
$337$	32.3095	+	5.69704i	1.76001	+	0.310338i	0.957957	−	0.286912i	$-0.0926288\pi$
$337$	32.3095	+	5.69704i	1.76001	+	0.310338i	0.802055	+	0.597250i	$0.203740\pi$
$338$	8.07688	−	17.3209i	0.439324	−	0.942134i
$339$		0			0
$340$	3.32019	−	1.20845i	0.180063	−	0.0655375i
$341$	−0.969166	−	0.259687i	−0.0524833	−	0.0140629i
$342$		0			0
$343$	2.22471	−	3.85332i	0.120123	−	0.208060i
$344$	0.192195	+	0.332892i	0.0103625	+	0.0179483i
$345$		0			0
$346$	−2.20572	+	1.54446i	−0.118580	+	0.0830307i
$347$	13.0391	−	3.49382i	0.699976	−	0.187558i	0.108756	−	0.994068i	$-0.465313\pi$
$347$	13.0391	−	3.49382i	0.699976	−	0.187558i	0.591220	+	0.806510i	$0.298646\pi$
$348$		0			0
$349$	−33.9025	−	12.3395i	−1.81476	−	0.660518i	−0.996299	−	0.0859552i	$-0.972606\pi$
$349$	−33.9025	−	12.3395i	−1.81476	−	0.660518i	−0.818460	−	0.574563i	$-0.805172\pi$
$350$	−0.837751	−	0.586600i	−0.0447797	−	0.0313551i
$351$		0			0
$352$	−0.0492636	−	0.563086i	−0.00262576	−	0.0300126i
$353$	7.88954	−	11.2674i	0.419918	−	0.599704i	−0.552340	−	0.833619i	$-0.686265\pi$
$353$	7.88954	−	11.2674i	0.419918	−	0.599704i	0.972257	+	0.233915i	$0.0751537\pi$
$354$		0			0
$355$	2.28251	+	4.89486i	0.121143	+	0.259792i
$356$	−0.220156	−	0.821634i	−0.0116683	−	0.0435465i
$357$		0			0
$358$	−0.0336508	−	0.0401035i	−0.00177850	−	0.00211954i
$359$	−7.22780	+	4.17297i	−0.381469	+	0.220241i	−0.678457	−	0.734640i	$-0.737351\pi$
$359$	−7.22780	+	4.17297i	−0.381469	+	0.220241i	0.296988	+	0.954881i	$0.404018\pi$
$360$		0			0
$361$	10.4903	−	1.84973i	0.552123	−	0.0973541i
$362$	3.72183	−	13.8901i	0.195615	−	0.730046i
$363$		0			0
$364$	−1.28287	+	1.28287i	−0.0672407	+	0.0672407i
$365$	2.91075	+	1.35730i	0.152356	+	0.0710446i
$366$		0			0
$367$	22.9179	+	19.2304i	1.19630	+	1.00382i	0.999728	+	0.0233299i	$0.00742680\pi$
$367$	22.9179	+	19.2304i	1.19630	+	1.00382i	0.196576	+	0.980489i	$0.437018\pi$
$368$	0.730342	−	8.34784i	0.0380717	−	0.435161i
$369$		0			0
$370$	7.87059	+	2.20515i	0.409173	+	0.114640i
$371$			1.32414i			0.0687459i
$372$		0			0
$373$	11.9905	−	14.2897i	0.620845	−	0.739894i	−0.360370	−	0.932809i	$-0.617350\pi$
$373$	11.9905	−	14.2897i	0.620845	−	0.739894i	0.981215	+	0.192915i	$0.0617941\pi$
$374$	0.258084	−	1.46367i	0.0133452	−	0.0756845i
$375$		0			0
$376$	−7.23973	−	7.23973i	−0.373361	−	0.373361i
$377$	−4.69338	−	12.8949i	−0.241721	−	0.664124i
$378$		0			0
$379$	1.47405	+	8.35976i	0.0757170	+	0.429412i	0.998976	+	0.0452351i	$0.0144037\pi$
$379$	1.47405	+	8.35976i	0.0757170	+	0.429412i	−0.923259	+	0.384177i	$0.874485\pi$
$380$	3.36228	+	1.94121i	0.172481	+	0.0995822i
$381$		0			0
$382$	−11.0203	+	9.24709i	−0.563845	+	0.473122i
$383$	17.5903	+	25.1215i	0.898821	+	1.28365i	0.958401	+	0.285426i	$0.0921350\pi$
$383$	17.5903	+	25.1215i	0.898821	+	1.28365i	−0.0595799	+	0.998224i	$0.518976\pi$
$384$		0			0
$385$	0.220389	−	0.102769i	0.0112321	−	0.00523760i
$386$	1.16781	−	3.20854i	0.0594401	−	0.163310i
$387$		0			0
$388$	0.0745356	−	0.00652102i	0.00378397	−	0.000331055i
$389$	−26.5904	+	2.32635i	−1.34818	+	0.117951i	−0.738264	−	0.674512i	$-0.764354\pi$
$389$	−26.5904	+	2.32635i	−1.34818	+	0.117951i	−0.609920	+	0.792463i	$0.708799\pi$
$390$		0			0
$391$	7.53603	−	20.7051i	0.381114	−	1.04710i
$392$	−6.25126	+	2.91501i	−0.315736	+	0.147230i
$393$		0			0
$394$	13.7814	+	19.6819i	0.694297	+	0.991559i
$395$	9.91245	−	8.31754i	0.498750	−	0.418501i
$396$		0			0
$397$	19.6924	+	11.3694i	0.988332	+	0.570614i	0.904775	−	0.425889i	$-0.140039\pi$
$397$	19.6924	+	11.3694i	0.988332	+	0.570614i	0.0835565	+	0.996503i	$0.473372\pi$
$398$	−3.04116	−	17.2473i	−0.152440	−	0.864527i
$399$		0			0
$400$	1.09253	+	3.00171i	0.0546267	+	0.150086i
$401$	23.9897	+	23.9897i	1.19799	+	1.19799i	0.974768	+	0.223219i	$0.0716565\pi$
$401$	23.9897	+	23.9897i	1.19799	+	1.19799i	0.223219	+	0.974768i	$0.428344\pi$
$402$		0			0
$403$	1.74673	−	9.90618i	0.0870106	−	0.493462i
$404$	−9.27149	+	11.0493i	−0.461274	+	0.549725i
$405$		0			0
$406$			0.775302i			0.0384776i
$407$	2.45867	−	2.40337i	0.121872	−	0.119131i
$408$		0			0
$409$	0.173891	−	1.98758i	0.00859835	−	0.0982795i	−0.990683	−	0.136189i	$-0.956514\pi$
$409$	0.173891	−	1.98758i	0.00859835	−	0.0982795i	0.999281	+	0.0379099i	$0.0120700\pi$
$410$	5.55302	+	4.65954i	0.274244	+	0.230118i
$411$		0			0
$412$	−3.84847	−	1.79457i	−0.189600	−	0.0884121i
$413$	0.717758	−	0.717758i	0.0353186	−	0.0353186i
$414$		0			0
$415$	−3.73145	+	13.9259i	−0.183169	+	0.683598i
$416$	5.58061	−	0.984013i	0.273612	−	0.0482452i
$417$		0			0
$418$	1.41432	−	0.816559i	0.0691767	−	0.0399392i
$419$	−9.86964	−	11.7622i	−0.482163	−	0.574620i	0.469043	−	0.883175i	$-0.344599\pi$
$419$	−9.86964	−	11.7622i	−0.482163	−	0.574620i	−0.951206	+	0.308555i	$0.900154\pi$
$420$		0			0
$421$	−2.12716	−	7.93868i	−0.103672	−	0.386908i	0.894519	−	0.447029i	$-0.147518\pi$
$421$	−2.12716	−	7.93868i	−0.103672	−	0.386908i	−0.998191	+	0.0601212i	$0.980851\pi$
$422$	7.07234	+	15.1667i	0.344276	+	0.738302i
$423$		0			0
$424$	2.37223	−	3.38790i	0.115206	−	0.164531i
$425$	0.732049	+	8.36735i	0.0355096	+	0.405876i
$426$		0			0
$427$	0.514137	+	0.360003i	0.0248808	+	0.0174217i
$428$	−2.39035	−	0.870016i	−0.115542	−	0.0420538i
$429$		0			0
$430$	0.498922	−	0.133686i	0.0240601	−	0.00644689i
$431$	16.6780	−	11.6781i	0.803352	−	0.562513i	−0.0982084	−	0.995166i	$-0.531311\pi$
$431$	16.6780	−	11.6781i	0.803352	−	0.562513i	0.901561	+	0.432653i	$0.142422\pi$
$432$		0			0
$433$	−12.7507	−	22.0848i	−0.612758	−	1.06133i	−0.990773	−	0.135529i	$-0.956727\pi$
$433$	−12.7507	−	22.0848i	−0.612758	−	1.06133i	0.378015	−	0.925800i	$-0.376607\pi$
$434$	−0.284159	+	0.492178i	−0.0136401	+	0.0236253i
$435$		0			0
$436$	−17.1245	−	4.58849i	−0.820113	−	0.219749i
$437$	22.7511	−	8.28074i	1.08833	−	0.396121i
$438$		0			0
$439$	8.87287	−	19.0279i	0.423479	−	0.908153i	−0.572613	−	0.819826i	$-0.694070\pi$
$439$	8.87287	−	19.0279i	0.423479	−	0.908153i	0.996092	−	0.0883272i	$-0.0281521\pi$
$440$	−0.747994	−	0.131892i	−0.0356592	−	0.00628768i
$441$		0			0
$442$	14.8435	+	1.29864i	0.706032	+	0.0617698i
$443$	−38.8660			−1.84658			−0.923290	−	0.384102i	$-0.874511\pi$
$443$	−38.8660			−1.84658			−0.923290	+	0.384102i	$0.874511\pi$
$444$		0			0
$445$	−1.14301			−0.0541840
$446$	8.97442	+	0.785160i	0.424951	+	0.0371784i
$447$		0			0
$448$	−0.315296	−	0.0555953i	−0.0148964	−	0.00262663i
$449$	−1.10232	+	2.36393i	−0.0520217	+	0.111561i	−0.930600	−	0.366037i	$-0.880714\pi$
$449$	−1.10232	+	2.36393i	−0.0520217	+	0.111561i	0.878579	+	0.477598i	$0.158492\pi$
$450$		0			0
$451$	2.86533	−	1.04290i	0.134923	−	0.0491081i
$452$	7.00198	+	1.87617i	0.329345	+	0.0882478i
$453$		0			0
$454$	8.52791	−	14.7708i	0.400234	−	0.693226i
$455$	1.21895	+	2.11128i	0.0571451	+	0.0989782i
$456$		0			0
$457$	−25.3523	+	17.7519i	−1.18593	+	0.830399i	−0.988693	−	0.149956i	$-0.952087\pi$
$457$	−25.3523	+	17.7519i	−1.18593	+	0.830399i	−0.197240	+	0.980355i	$0.563198\pi$
$458$	6.53877	−	1.75206i	0.305536	−	0.0818683i
$459$		0			0
$460$	−10.5811	−	3.85122i	−0.493348	−	0.179564i
$461$	11.5515	+	8.08847i	0.538009	+	0.376718i	0.810771	−	0.585364i	$-0.199048\pi$
$461$	11.5515	+	8.08847i	0.538009	+	0.376718i	−0.272762	+	0.962081i	$0.587937\pi$
$462$		0			0
$463$	−3.30542	−	37.7812i	−0.153616	−	1.75584i	−0.547616	−	0.836730i	$-0.684464\pi$
$463$	−3.30542	−	37.7812i	−0.153616	−	1.75584i	0.394000	−	0.919111i	$-0.371091\pi$
$464$	1.38898	−	1.98366i	0.0644816	−	0.0920892i
$465$		0			0
$466$	10.3661	+	22.2302i	0.480201	+	1.02979i
$467$	−7.12829	−	26.6032i	−0.329858	−	1.23105i	−0.909337	−	0.416060i	$-0.863411\pi$
$467$	−7.12829	−	26.6032i	−0.329858	−	1.23105i	0.579479	−	0.814987i	$-0.303256\pi$
$468$		0			0
$469$	−1.80682	−	2.15329i	−0.0834313	−	0.0994295i
$470$	−11.9147	+	6.87898i	−0.549586	+	0.317304i
$471$		0			0
$472$	−3.12232	+	0.550549i	−0.143716	+	0.0253411i
$473$	0.0562340	−	0.209868i	0.00258564	−	0.00964974i
$474$		0			0
$475$	−6.52612	+	6.52612i	−0.299439	+	0.299439i
$476$	−0.762965	−	0.355776i	−0.0349704	−	0.0163070i
$477$		0			0
$478$	−7.16070	−	6.00854i	−0.327523	−	0.274824i
$479$	−2.09024	+	23.8915i	−0.0955054	+	1.09163i	0.785607	+	0.618725i	$0.212351\pi$
$479$	−2.09024	+	23.8915i	−0.0955054	+	1.09163i	−0.881113	+	0.472906i	$0.843205\pi$
$480$		0			0
$481$	26.1513	+	22.4552i	1.19240	+	1.02387i
$482$		−	5.41393i		−	0.246598i
$483$		0			0
$484$	6.86530	−	8.18174i	0.312059	−	0.371897i
$485$	0.0174585	−	0.0990120i	0.000792749	−	0.00449590i
$486$		0			0
$487$	−3.99266	−	3.99266i	−0.180925	−	0.180925i	0.610834	−	0.791759i	$-0.290834\pi$
$487$	−3.99266	−	3.99266i	−0.180925	−	0.180925i	−0.791759	+	0.610834i	$0.790834\pi$
$488$	−0.670499	−	1.84218i	−0.0303521	−	0.0833917i
$489$		0			0
$490$	1.60945	+	9.12766i	0.0727077	+	0.412346i
$491$	1.20206	+	0.694012i	0.0542484	+	0.0313203i	0.526879	−	0.849940i	$-0.323362\pi$
$491$	1.20206	+	0.694012i	0.0542484	+	0.0313203i	−0.472631	+	0.881261i	$0.656695\pi$
$492$		0			0
$493$	4.87774	−	4.09291i	0.219682	−	0.184335i
$494$	9.39094	+	13.4116i	0.422518	+	0.603419i
$495$		0			0
$496$	1.60879	−	0.750192i	0.0722369	−	0.0336846i
$497$	0.440116	−	1.20921i	0.0197419	−	0.0542404i
$498$		0			0
$499$	−20.2000	+	1.76727i	−0.904275	+	0.0791138i	−0.529799	−	0.848123i	$-0.677733\pi$
$499$	−20.2000	+	1.76727i	−0.904275	+	0.0791138i	−0.374476	+	0.927237i	$0.622177\pi$
$500$	10.9692	−	0.959681i	0.490558	−	0.0429183i
$501$		0			0
$502$	6.36535	−	17.4887i	0.284099	−	0.780557i
$503$	3.11463	−	1.45238i	0.138875	−	0.0647583i	−0.351939	−	0.936023i	$-0.614477\pi$
$503$	3.11463	−	1.45238i	0.138875	−	0.0647583i	0.490813	+	0.871265i	$0.336700\pi$
$504$		0			0
$505$	11.1171	+	15.8768i	0.494703	+	0.706509i
$506$	−3.62839	+	3.04458i	−0.161302	+	0.135348i
$507$		0			0
$508$	−15.5995	−	9.00635i	−0.692114	−	0.399592i
$509$	−7.26120	−	41.1803i	−0.321847	−	1.82529i	−0.530963	−	0.847395i	$-0.678170\pi$
$509$	−7.26120	−	41.1803i	−0.321847	−	1.82529i	0.209116	−	0.977891i	$-0.432941\pi$
$510$		0			0
$511$	−0.261717	−	0.719062i	−0.0115777	−	0.0318094i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	3.22354	−	18.2816i	0.142184	−	0.806368i
$515$	−3.66772	+	4.37102i	−0.161619	+	0.192610i
$516$		0			0
$517$			5.78719i			0.254520i
$518$	−0.954487	−	1.69751i	−0.0419378	−	0.0745845i
$519$		0			0
$520$	0.663656	−	7.58562i	0.0291032	−	0.332651i
$521$	−8.39229	−	7.04197i	−0.367673	−	0.308514i	0.440167	−	0.897916i	$-0.354919\pi$
$521$	−8.39229	−	7.04197i	−0.367673	−	0.308514i	−0.807840	+	0.589402i	$0.799364\pi$
$522$		0			0
$523$	26.3212	+	12.2738i	1.15095	+	0.536695i	0.901963	−	0.431813i	$-0.142126\pi$
$523$	26.3212	+	12.2738i	1.15095	+	0.536695i	0.248983	+	0.968508i	$0.419904\pi$
$524$	−3.34295	+	3.34295i	−0.146037	+	0.146037i
$525$		0			0
$526$	−1.50311	+	5.60969i	−0.0655388	+	0.244594i
$527$	4.59660	−	0.810504i	0.200231	−	0.0353061i
$528$		0			0
$529$	−40.8936	+	23.6100i	−1.77798	+	1.02652i
$530$	−3.57232	−	4.25732i	−0.155172	−	0.184926i
$531$		0			0
$532$	−0.239415	−	0.893508i	−0.0103799	−	0.0387385i
$533$	12.9193	+	27.7055i	0.559596	+	1.20006i
$534$		0			0
$535$	−1.96057	+	2.79999i	−0.0847630	+	0.121054i
$536$	0.765202	+	8.74630i	0.0330517	+	0.377783i
$537$		0			0
$538$	−3.06153	−	2.14371i	−0.131992	−	0.0924219i
$539$	3.66360	+	1.33344i	0.157802	+	0.0574353i
$540$		0			0
$541$	−23.7252	+	6.35716i	−1.02003	+	0.273316i	−0.729814	−	0.683646i	$-0.760393\pi$
$541$	−23.7252	+	6.35716i	−1.02003	+	0.273316i	−0.290214	+	0.956962i	$0.593727\pi$
$542$	24.3674	−	17.0623i	1.04667	−	0.732887i
$543$		0			0
$544$	1.31471	+	2.27715i	0.0563679	+	0.0976320i
$545$	−11.9113	+	20.6310i	−0.510225	+	0.883735i
$546$		0			0
$547$	−7.51774	−	2.01437i	−0.321435	−	0.0861283i	0.0944936	−	0.995525i	$-0.469877\pi$
$547$	−7.51774	−	2.01437i	−0.321435	−	0.0861283i	−0.415929	+	0.909397i	$0.636543\pi$
$548$	−7.25960	+	2.64228i	−0.310115	+	0.112872i
$549$		0			0
$550$	0.763065	−	1.63640i	0.0325372	−	0.0697762i
$551$	6.89036	+	1.21496i	0.293539	+	0.0517589i
$552$		0			0
$553$	−3.07130	−	0.268704i	−0.130605	−	0.0114265i
$554$	18.4288			0.782965
$555$		0			0
$556$	4.07025			0.172617
$557$	13.6665	+	1.19566i	0.579067	+	0.0506618i	0.372927	−	0.927861i	$-0.378354\pi$
$557$	13.6665	+	1.19566i	0.579067	+	0.0506618i	0.206140	+	0.978523i	$0.433910\pi$
$558$		0			0
$559$	2.14513	+	0.378245i	0.0907294	+	0.0159980i
$560$	−0.181816	+	0.389906i	−0.00768313	+	0.0164765i
$561$		0			0
$562$	3.56690	−	1.29824i	0.150460	−	0.0547631i
$563$	−31.9455	−	8.55978i	−1.34634	−	0.360752i	−0.487559	−	0.873090i	$-0.662113\pi$
$563$	−31.9455	−	8.55978i	−1.34634	−	0.360752i	−0.858784	+	0.512338i	$0.828779\pi$
$564$		0			0
$565$	4.87038	−	8.43575i	0.204899	−	0.354895i
$566$	10.1410	+	17.5648i	0.426259	+	0.738303i
$567$		0			0
$568$	−3.29240	+	2.30536i	−0.138146	+	0.0967309i
$569$	11.2532	−	3.01527i	0.471757	−	0.126407i	−0.0151049	−	0.999886i	$-0.504808\pi$
$569$	11.2532	−	3.01527i	0.471757	−	0.126407i	0.486862	+	0.873479i	$0.338142\pi$
$570$		0			0
$571$	−33.5074	−	12.1957i	−1.40224	−	0.510374i	−0.473398	−	0.880849i	$-0.656973\pi$
$571$	−33.5074	−	12.1957i	−1.40224	−	0.510374i	−0.928842	+	0.370475i	$0.879195\pi$
$572$	−2.62377	−	1.83718i	−0.109705	−	0.0768164i
$573$		0			0
$574$	−0.150530	−	1.72056i	−0.00628300	−	0.0718150i
$575$	15.3534	−	21.9269i	0.640281	−	0.914416i
$576$		0			0
$577$	−0.734870	−	1.57593i	−0.0305930	−	0.0656070i	0.890417	−	0.455145i	$-0.150413\pi$
$577$	−0.734870	−	1.57593i	−0.0305930	−	0.0656070i	−0.921010	+	0.389538i	$0.872635\pi$
$578$	−2.61048	−	9.74244i	−0.108582	−	0.405232i
$579$		0			0
$580$	−2.09164	−	2.49272i	−0.0868507	−	0.103505i
$581$	2.97483	−	1.71752i	0.123417	−	0.0712548i
$582$		0			0
$583$	−2.30223	+	0.405945i	−0.0953484	+	0.0168125i
$584$	−0.618599	+	2.30864i	−0.0255978	+	0.0955323i
$585$		0			0
$586$	17.1053	−	17.1053i	0.706615	−	0.706615i
$587$	3.70691	+	1.72856i	0.153001	+	0.0713454i	0.497610	−	0.867401i	$-0.334211\pi$
$587$	3.70691	+	1.72856i	0.153001	+	0.0713454i	−0.344610	+	0.938746i	$0.611989\pi$
$588$		0			0
$589$	3.92885	+	3.29669i	0.161885	+	0.135838i
$590$	−0.371311	+	4.24411i	−0.0152866	+	0.174727i
$591$		0			0
$592$	−0.599025	+	6.05319i	−0.0246198	+	0.248785i
$593$			29.7574i			1.22199i	0.791634	+	0.610995i	$0.209231\pi$
$593$			29.7574i			1.22199i	−0.791634	+	0.610995i	$0.790769\pi$
$594$		0			0
$595$	−0.727131	+	0.866561i	−0.0298095	+	0.0355255i
$596$	−1.49964	+	8.50486i	−0.0614275	+	0.348373i
$597$		0			0
$598$	−33.5773	−	33.5773i	−1.37308	−	1.37308i
$599$	9.28681	+	25.5153i	0.379449	+	1.04253i	0.971585	+	0.236689i	$0.0760624\pi$
$599$	9.28681	+	25.5153i	0.379449	+	1.04253i	−0.592137	+	0.805838i	$0.701715\pi$
$600$		0			0
$601$	−6.25074	−	35.4497i	−0.254973	−	1.44602i	−0.796142	−	0.605110i	$-0.793129\pi$
$601$	−6.25074	−	35.4497i	−0.254973	−	1.44602i	0.541169	−	0.840914i	$-0.317982\pi$
$602$	−0.106579	−	0.0615332i	−0.00434382	−	0.00250791i
$603$		0			0
$604$	−9.73881	+	8.17184i	−0.396267	+	0.332507i
$605$	−8.23189	−	11.7564i	−0.334674	−	0.477964i
$606$		0			0
$607$	−15.8759	+	7.40307i	−0.644385	+	0.300481i	−0.717204	−	0.696864i	$-0.754578\pi$
$607$	−15.8759	+	7.40307i	−0.644385	+	0.300481i	0.0728190	+	0.997345i	$0.476800\pi$
$608$	−0.988186	+	2.71502i	−0.0400762	+	0.110109i
$609$		0			0
$610$	−2.62426	+	0.229593i	−0.106253	+	0.00929596i
$611$	−57.7979	+	5.05666i	−2.33825	+	0.204571i
$612$		0			0
$613$	10.3470	−	28.4280i	0.417910	−	1.14820i	−0.534976	−	0.844867i	$-0.679679\pi$
$613$	10.3470	−	28.4280i	0.417910	−	1.14820i	0.952885	−	0.303330i	$-0.0980985\pi$
$614$	−24.3368	+	11.3484i	−0.982154	+	0.457986i
$615$		0			0
$616$	0.103798	+	0.148239i	0.00418214	+	0.00597272i
$617$	−9.22456	+	7.74032i	−0.371367	+	0.311614i	−0.809302	−	0.587393i	$-0.800154\pi$
$617$	−9.22456	+	7.74032i	−0.371367	+	0.311614i	0.437935	+	0.899006i	$0.355710\pi$
$618$		0			0
$619$	−26.4238	−	15.2558i	−1.06206	−	0.613181i	−0.136059	−	0.990701i	$-0.543444\pi$
$619$	−26.4238	−	15.2558i	−1.06206	−	0.613181i	−0.926002	+	0.377520i	$0.876777\pi$
$620$	−0.414201	−	2.34905i	−0.0166347	−	0.0943401i
$621$		0			0
$622$	7.21933	+	19.8350i	0.289469	+	0.795309i
$623$	0.192569	+	0.192569i	0.00771513	+	0.00771513i
$624$		0			0
$625$	−0.204151	+	1.15780i	−0.00816604	+	0.0463119i
$626$	−3.13033	+	3.73058i	−0.125113	+	0.149104i
$627$		0			0
$628$		−	1.62660i		−	0.0649086i
$629$	−5.64090	+	14.9664i	−0.224917	+	0.596751i
$630$		0			0
$631$	0.0923775	−	1.05588i	0.00367749	−	0.0420339i	−0.994134	−	0.108153i	$-0.965506\pi$
$631$	0.0923775	−	1.05588i	0.00367749	−	0.0420339i	0.997812	+	0.0661194i	$0.0210618\pi$
$632$	7.37674	+	6.18982i	0.293431	+	0.246218i
$633$		0			0
$634$	−14.8355	−	6.91790i	−0.589193	−	0.274745i
$635$	−17.1151	+	17.1151i	−0.679193	+	0.679193i
$636$		0			0
$637$	−10.1162	+	37.7542i	−0.400819	+	1.49588i
$638$	−1.34798	+	0.237686i	−0.0533672	+	0.00941008i
$639$		0			0
$640$	1.16372	−	0.671872i	0.0459999	−	0.0265581i
$641$	8.94400	+	10.6590i	0.353267	+	0.421007i	0.913188	−	0.407539i	$-0.133613\pi$
$641$	8.94400	+	10.6590i	0.353267	+	0.421007i	−0.559921	+	0.828546i	$0.689169\pi$
$642$		0			0
$643$	5.41944	+	20.2256i	0.213722	+	0.797621i	0.986613	+	0.163082i	$0.0521435\pi$
$643$	5.41944	+	20.2256i	0.213722	+	0.797621i	−0.772891	+	0.634539i	$0.781190\pi$
$644$	1.13383	+	2.43150i	0.0446790	+	0.0958144i
$645$		0			0
$646$	−4.35752	+	6.22318i	−0.171444	+	0.244848i
$647$	0.421540	+	4.81822i	0.0165724	+	0.189424i	0.999968	+	0.00795095i	$0.00253089\pi$
$647$	0.421540	+	4.81822i	0.0165724	+	0.189424i	−0.983396	+	0.181473i	$0.941914\pi$
$648$		0			0
$649$	1.46798	+	1.02789i	0.0576233	+	0.0403483i
$650$	17.0098	+	6.19106i	0.667179	+	0.242833i
$651$		0			0
$652$	−15.0930	+	4.04414i	−0.591086	+	0.158381i
$653$	−41.1655	+	28.8244i	−1.61093	+	1.12799i	−0.701051	+	0.713111i	$0.747285\pi$
$653$	−41.1655	+	28.8244i	−1.61093	+	1.12799i	−0.909879	+	0.414874i	$0.863826\pi$
$654$		0			0
$655$	3.17637	+	5.50164i	0.124111	+	0.214967i
$656$	−2.69730	+	4.67186i	−0.105312	+	0.182405i
$657$		0			0
$658$	3.16628	+	0.848402i	0.123434	+	0.0330741i
$659$	1.80489	−	0.656927i	0.0703086	−	0.0255902i	−0.306626	−	0.951830i	$-0.599200\pi$
$659$	1.80489	−	0.656927i	0.0703086	−	0.0255902i	0.376935	+	0.926240i	$0.376978\pi$
$660$		0			0
$661$	−0.336726	+	0.722112i	−0.0130971	+	0.0280869i	−0.912748	−	0.408524i	$-0.866044\pi$
$661$	−0.336726	+	0.722112i	−0.0130971	+	0.0280869i	0.899650	+	0.436611i	$0.143821\pi$
$662$	−5.63919	−	0.994340i	−0.219173	−	0.0386461i
$663$		0			0
$664$	−10.6883	−	0.935105i	−0.414787	−	0.0362891i
$665$	−1.24300			−0.0482015
$666$		0			0
$667$	−20.2924			−0.785725
$668$	10.6911	+	0.935349i	0.413650	+	0.0361897i
$669$		0			0
$670$	11.6184	+	2.04865i	0.448860	+	0.0791461i
$671$	−0.468301	+	1.00428i	−0.0180786	+	0.0387696i
$672$		0			0
$673$	−17.1155	+	6.22952i	−0.659753	+	0.240130i	−0.650130	−	0.759823i	$-0.725285\pi$
$673$	−17.1155	+	6.22952i	−0.659753	+	0.240130i	−0.00962308	+	0.999954i	$0.503063\pi$
$674$	31.6901	+	8.49132i	1.22066	+	0.327074i
$675$		0			0
$676$	9.55577	−	16.5511i	0.367529	−	0.636580i
$677$	−8.66748	−	15.0125i	−0.333118	−	0.576978i	0.650003	−	0.759932i	$-0.274768\pi$
$677$	−8.66748	−	15.0125i	−0.333118	−	0.576978i	−0.983122	+	0.182953i	$0.941434\pi$
$678$		0			0
$679$	−0.0196224	+	0.0137397i	−0.000753038	+	0.000527283i
$680$	3.41288	−	0.914479i	0.130878	−	0.0350687i
$681$		0			0
$682$	−0.942845	−	0.343167i	−0.0361034	−	0.0131406i
$683$	35.2204	+	24.6616i	1.34767	+	0.943649i	0.999982	+	0.00603844i	$0.00192211\pi$
$683$	35.2204	+	24.6616i	1.34767	+	0.943649i	0.347688	+	0.937610i	$0.386967\pi$
$684$		0			0
$685$	0.904772	+	10.3416i	0.0345696	+	0.395132i
$686$	2.55209	−	3.64476i	0.0974392	−	0.139158i
$687$		0			0
$688$	0.162450	+	0.348376i	0.00619336	+	0.0132817i
$689$	−6.06587	−	22.6381i	−0.231091	−	0.862444i
$690$		0			0
$691$	11.0444	+	13.1622i	0.420149	+	0.500714i	0.934053	−	0.357134i	$-0.116246\pi$
$691$	11.0444	+	13.1622i	0.420149	+	0.500714i	−0.513905	+	0.857847i	$0.671801\pi$
$692$	−2.33193	+	1.34634i	−0.0886468	+	0.0511802i
$693$		0			0
$694$	13.2940	−	2.34409i	0.504634	−	0.0889805i
$695$	1.41558	−	5.28301i	0.0536960	−	0.200396i
$696$		0			0
$697$	−10.0301	+	10.0301i	−0.379917	+	0.379917i
$698$	−32.6980	−	15.2473i	−1.23764	−	0.577120i
$699$		0			0
$700$	−0.783438	−	0.657382i	−0.0296112	−	0.0248467i
$701$	0.0362584	−	0.414435i	0.00136946	−	0.0156530i	−0.995479	−	0.0949796i	$-0.969721\pi$
$701$	0.0362584	−	0.414435i	0.00136946	−	0.0156530i	0.996849	+	0.0793266i	$0.0252770\pi$
$702$		0			0
$703$	−16.5821	+	5.82270i	−0.625406	+	0.219607i
$704$		−	0.565237i		−	0.0213032i
$705$		0			0
$706$	8.84153	−	10.5369i	0.332756	−	0.396563i
$707$	0.801900	−	4.54780i	0.0301585	−	0.171038i
$708$		0			0
$709$	−27.8967	−	27.8967i	−1.04768	−	1.04768i	−0.998805	−	0.0488765i	$-0.984436\pi$
$709$	−27.8967	−	27.8967i	−1.04768	−	1.04768i	−0.0488765	−	0.998805i	$-0.515564\pi$
$710$	1.84721	+	5.07516i	0.0693245	+	0.190468i
$711$		0			0
$712$	−0.147708	−	0.837695i	−0.00553560	−	0.0313940i
$713$	−12.8820	−	7.43745i	−0.482436	−	0.278535i
$714$		0			0
$715$	−3.29709	+	2.76659i	−0.123304	+	0.103465i
$716$	−0.0300275	−	0.0428838i	−0.00112218	−	0.00160264i
$717$		0			0
$718$	−7.56400	+	3.52715i	−0.282286	+	0.131632i
$719$	−0.340840	+	0.936449i	−0.0127112	+	0.0349236i	−0.945886	−	0.324499i	$-0.894804\pi$
$719$	−0.340840	+	0.936449i	−0.0127112	+	0.0349236i	0.933175	+	0.359423i	$0.117026\pi$
$720$		0			0
$721$	1.35433	−	0.118488i	0.0504378	−	0.00441274i
$722$	10.6116	−	0.928397i	0.394924	−	0.0345513i
$723$		0			0
$724$	4.91827	−	13.5128i	0.182786	−	0.502200i
$725$	7.01071	−	3.26915i	0.260371	−	0.121413i
$726$		0			0
$727$	18.6950	+	26.6993i	0.693360	+	0.990221i	0.999272	+	0.0381610i	$0.0121500\pi$
$727$	18.6950	+	26.6993i	0.693360	+	0.990221i	−0.305911	+	0.952060i	$0.598961\pi$
$728$	−1.38980	+	1.16618i	−0.0515094	+	0.0432215i
$729$		0			0
$730$	2.78138	+	1.60583i	0.102943	+	0.0594344i
$731$	0.175511	+	0.995370i	0.00649150	+	0.0368151i
$732$		0			0
$733$	7.08822	+	19.4747i	0.261809	+	0.719315i	0.999046	+	0.0436803i	$0.0139083\pi$
$733$	7.08822	+	19.4747i	0.261809	+	0.719315i	−0.737236	+	0.675635i	$0.763869\pi$
$734$	21.1546	+	21.1546i	0.780832	+	0.780832i
$735$		0			0
$736$	1.45513	−	8.25243i	0.0536366	−	0.304188i
$737$	3.18991	−	3.80158i	0.117502	−	0.140033i
$738$		0			0
$739$			20.5449i			0.755757i	0.925855	+	0.377879i	$0.123346\pi$
$739$			20.5449i			0.755757i	−0.925855	+	0.377879i	$0.876654\pi$
$740$	7.64845	+	2.88273i	0.281163	+	0.105971i
$741$		0			0
$742$	−0.115406	+	1.31910i	−0.00423670	+	0.0484257i
$743$	−41.5683	−	34.8799i	−1.52499	−	1.27962i	−0.824289	−	0.566169i	$-0.808425\pi$
$743$	−41.5683	−	34.8799i	−1.52499	−	1.27962i	−0.700704	−	0.713452i	$-0.747130\pi$
$744$		0			0
$745$	10.5174	+	4.90434i	0.385327	+	0.179681i
$746$	13.1903	−	13.1903i	0.482932	−	0.482932i
$747$		0			0
$748$	0.384669	−	1.43561i	0.0140649	−	0.0524909i
$749$	0.802037	−	0.141421i	0.0293058	−	0.00516740i
$750$		0			0
$751$	−10.3895	+	5.99836i	−0.379117	+	0.218883i	−0.677434	−	0.735584i	$-0.736908\pi$
$751$	−10.3895	+	5.99836i	−0.379117	+	0.218883i	0.298317	+	0.954467i	$0.403575\pi$
$752$	−6.58120	−	7.84317i	−0.239992	−	0.286011i
$753$		0			0
$754$	−3.55165	−	13.2549i	−0.129343	−	0.482716i
$755$	7.21966	+	15.4826i	0.262750	+	0.563470i
$756$		0			0
$757$	−12.9138	+	18.4428i	−0.469359	+	0.670314i	−0.982128	−	0.188212i	$-0.939731\pi$
$757$	−12.9138	+	18.4428i	−0.469359	+	0.670314i	0.512769	+	0.858526i	$0.328620\pi$
$758$	0.739841	+	8.45643i	0.0268722	+	0.307151i
$759$		0			0
$760$	3.18030	+	2.22687i	0.115362	+	0.0807771i
$761$	−48.9755	−	17.8256i	−1.77536	−	0.646178i	−0.999891	−	0.0147925i	$-0.995291\pi$
$761$	−48.9755	−	17.8256i	−1.77536	−	0.646178i	−0.775469	−	0.631386i	$-0.782487\pi$
$762$		0			0
$763$	5.48258	−	1.46905i	0.198483	−	0.0531833i
$764$	−11.7843	+	8.25143i	−0.426339	+	0.298526i
$765$		0			0
$766$	15.3339	+	26.5590i	0.554035	+	0.959616i
$767$	−8.98310	+	15.5592i	−0.324361	+	0.561809i
$768$		0			0
$769$	2.62040	+	0.702134i	0.0944940	+	0.0253196i	0.305756	−	0.952110i	$-0.401091\pi$
$769$	2.62040	+	0.702134i	0.0944940	+	0.0253196i	−0.211262	+	0.977429i	$0.567757\pi$
$770$	0.228507	−	0.0831699i	0.00823483	−	0.00299723i
$771$		0			0
$772$	1.44301	−	3.09455i	0.0519352	−	0.111375i
$773$	−39.4788	−	6.96117i	−1.41995	−	0.250376i	−0.589636	−	0.807669i	$-0.700729\pi$
$773$	−39.4788	−	6.96117i	−1.41995	−	0.250376i	−0.830316	+	0.557293i	$0.811840\pi$
$774$		0			0
$775$	5.64874	+	0.494200i	0.202909	+	0.0177522i
$776$	0.0748204			0.00268589
$777$		0			0
$778$	−26.6919			−0.956952
$779$	−15.5271	−	1.35845i	−0.556316	−	0.0486714i
$780$		0			0
$781$	2.23733	+	0.394501i	0.0800579	+	0.0141164i
$782$	9.31192	−	19.9695i	0.332994	−	0.714107i
$783$		0			0
$784$	−6.48153	+	2.35908i	−0.231483	+	0.0842530i
$785$	−2.11126	−	0.565711i	−0.0753542	−	0.0201911i
$786$		0			0
$787$	20.3172	−	35.1904i	0.724230	−	1.25440i	−0.235060	−	0.971981i	$-0.575529\pi$
$787$	20.3172	−	35.1904i	0.724230	−	1.25440i	0.959290	−	0.282423i	$-0.0911381\pi$
$788$	12.0136	+	20.8081i	0.427966	+	0.741259i
$789$		0			0
$790$	10.5997	−	7.42196i	0.377119	−	0.264061i
$791$	−2.24176	+	0.600677i	−0.0797077	+	0.0213576i
$792$		0			0
$793$	−10.4391	−	3.79952i	−0.370703	−	0.134925i
$794$	18.6265	+	13.0424i	0.661031	+	0.462859i
$795$		0			0
$796$	−1.52639	−	17.4467i	−0.0541014	−	0.618382i
$797$	9.94549	−	14.2036i	0.352287	−	0.503119i	−0.603425	−	0.797419i	$-0.706198\pi$
$797$	9.94549	−	14.2036i	0.352287	−	0.503119i	0.955713	+	0.294301i	$0.0950868\pi$
$798$		0			0
$799$	−11.3775	−	24.3991i	−0.402507	−	0.863179i
$800$	0.826759	+	3.08551i	0.0292304	+	0.109089i
$801$		0			0
$802$	21.8076	+	25.9892i	0.770051	+	0.917711i
$803$	1.16997	−	0.675481i	0.0412872	−	0.0238372i
$804$		0			0
$805$	3.55030	−	0.626015i	0.125132	−	0.0220641i
$806$	2.60346	−	9.71624i	0.0917030	−	0.342240i
$807$		0			0
$808$	−10.1992	+	10.1992i	−0.358808	+	0.358808i
$809$	−32.8694	−	15.3272i	−1.15563	−	0.538877i	−0.252223	−	0.967669i	$-0.581162\pi$
$809$	−32.8694	−	15.3272i	−1.15563	−	0.538877i	−0.903403	+	0.428792i	$0.858939\pi$
$810$		0			0
$811$	0.106839	+	0.0896482i	0.00375161	+	0.00314797i	0.644661	−	0.764468i	$-0.276998\pi$
$811$	0.106839	+	0.0896482i	0.00375161	+	0.00314797i	−0.640910	+	0.767616i	$0.721443\pi$
$812$	−0.0675720	+	0.772352i	−0.00237131	+	0.0271042i
$813$		0			0
$814$	2.65878	−	2.17994i	0.0931901	−	0.0764068i
$815$			20.9965i			0.735475i
$816$		0			0
$817$	−0.713883	+	0.850772i	−0.0249756	+	0.0297648i
$818$	0.346458	−	1.96486i	0.0121136	−	0.0686998i
$819$		0			0
$820$	5.12579	+	5.12579i	0.179000	+	0.179000i
$821$	4.83985	+	13.2974i	0.168912	+	0.464081i	0.995049	−	0.0993881i	$-0.0316885\pi$
$821$	4.83985	+	13.2974i	0.168912	+	0.464081i	−0.826137	+	0.563469i	$0.809466\pi$
$822$		0			0
$823$	−8.64839	−	49.0475i	−0.301464	−	1.70969i	−0.639699	−	0.768626i	$-0.720941\pi$
$823$	−8.64839	−	49.0475i	−0.301464	−	1.70969i	0.338235	−	0.941062i	$-0.390170\pi$
$824$	−3.67742	−	2.12316i	−0.128109	−	0.0739637i
$825$		0			0
$826$	0.777584	−	0.652470i	0.0270556	−	0.0227023i
$827$	−14.9044	−	21.2857i	−0.518277	−	0.740176i	0.471645	−	0.881788i	$-0.343660\pi$
$827$	−14.9044	−	21.2857i	−0.518277	−	0.740176i	−0.989922	+	0.141612i	$0.954771\pi$
$828$		0			0
$829$	−30.4593	+	14.2034i	−1.05790	+	0.493305i	−0.872122	−	0.489288i	$-0.837257\pi$
$829$	−30.4593	+	14.2034i	−1.05790	+	0.493305i	−0.185773	+	0.982593i	$0.559479\pi$
$830$	−4.93097	+	13.5477i	−0.171157	+	0.470249i
$831$		0			0
$832$	5.64514	−	0.493886i	0.195710	−	0.0171224i
$833$	−18.0674	+	1.58070i	−0.626000	+	0.0547679i
$834$		0			0
$835$	4.93226	−	13.5513i	0.170688	−	0.468961i
$836$	1.48011	−	0.690185i	0.0511906	−	0.0238706i
$837$		0			0
$838$	−8.80694	−	12.5776i	−0.304231	−	0.434486i
$839$	33.0205	−	27.7074i	1.13999	−	0.956567i	0.140554	−	0.990073i	$-0.455112\pi$
$839$	33.0205	−	27.7074i	1.13999	−	0.956567i	0.999439	+	0.0335057i	$0.0106672\pi$
$840$		0			0
$841$	20.0362	+	11.5679i	0.690904	+	0.398894i
$842$	−1.42717	−	8.09387i	−0.0491834	−	0.278933i
$843$		0			0
$844$	5.72356	+	15.7254i	0.197013	+	0.541289i
$845$	−18.1592	−	18.1592i	−0.624696	−	0.624696i
$846$		0			0
$847$	−0.593786	+	3.36753i	−0.0204027	+	0.115710i
$848$	2.65848	−	3.16825i	0.0912926	−	0.108798i
$849$		0			0
$850$			8.39932i			0.288094i
$851$	44.4300	−	24.9823i	1.52304	−	0.856383i
$852$		0			0
$853$	−0.993072	+	11.3509i	−0.0340022	+	0.388646i	0.960057	+	0.279805i	$0.0902697\pi$
$853$	−0.993072	+	11.3509i	−0.0340022	+	0.388646i	−0.994059	+	0.108842i	$0.965286\pi$
$854$	0.480804	+	0.403443i	0.0164528	+	0.0138055i
$855$		0			0
$856$	−2.30543	−	1.07504i	−0.0787978	−	0.0367440i
$857$	3.75675	−	3.75675i	0.128328	−	0.128328i	−0.640026	−	0.768354i	$-0.721076\pi$
$857$	3.75675	−	3.75675i	0.128328	−	0.128328i	0.768354	+	0.640026i	$0.221076\pi$
$858$		0			0
$859$	−2.54261	+	9.48914i	−0.0867527	+	0.323765i	−0.995640	−	0.0932757i	$-0.970266\pi$
$859$	−2.54261	+	9.48914i	−0.0867527	+	0.323765i	0.908888	+	0.417041i	$0.136933\pi$
$860$	0.508675	−	0.0896931i	0.0173457	−	0.00305851i
$861$		0			0
$862$	17.6324	−	10.1801i	0.600561	−	0.346734i
$863$	35.6768	+	42.5179i	1.21445	+	1.44733i	0.858492	+	0.512826i	$0.171402\pi$
$863$	35.6768	+	42.5179i	1.21445	+	1.44733i	0.355960	+	0.934501i	$0.384154\pi$
$864$		0			0
$865$	0.936479	+	3.49499i	0.0318412	+	0.118833i
$866$	−10.7773	−	23.1121i	−0.366229	−	0.785380i
$867$		0			0
$868$	−0.325974	+	0.465539i	−0.0110643	+	0.0158014i
$869$	−0.474392	−	5.42232i	−0.0160926	−	0.183940i
$870$		0			0
$871$	40.7545	+	28.5366i	1.38091	+	0.966925i
$872$	−16.6594	−	6.06352i	−0.564158	−	0.205337i
$873$		0			0
$874$	23.3863	−	6.26633i	0.791053	−	0.211962i
$875$	−2.88777	+	2.02204i	−0.0976246	+	0.0683575i
$876$		0			0
$877$	17.7762	+	30.7893i	0.600260	+	1.03968i	0.992781	+	0.119938i	$0.0382695\pi$
$877$	17.7762	+	30.7893i	0.600260	+	1.03968i	−0.392522	+	0.919743i	$0.628397\pi$
$878$	10.4975	−	18.1822i	0.354273	−	0.613619i
$879$		0			0
$880$	−0.733653	−	0.196582i	−0.0247314	−	0.00662677i
$881$	47.7113	−	17.3655i	1.60743	−	0.585058i	0.626503	−	0.779419i	$-0.284486\pi$
$881$	47.7113	−	17.3655i	1.60743	−	0.585058i	0.980930	+	0.194361i	$0.0622634\pi$
$882$		0			0
$883$	18.6533	−	40.0022i	0.627734	−	1.34618i	−0.293046	−	0.956098i	$-0.594669\pi$
$883$	18.6533	−	40.0022i	0.627734	−	1.34618i	0.920780	−	0.390082i	$-0.127553\pi$
$884$	14.6738	+	2.58739i	0.493534	+	0.0870233i
$885$		0			0
$886$	−38.7181	−	3.38740i	−1.30076	−	0.113802i
$887$	44.9585			1.50956			0.754779	−	0.655979i	$-0.227744\pi$
$887$	44.9585			1.50956			0.754779	+	0.655979i	$0.227744\pi$
$888$		0			0
$889$	5.76695			0.193417
$890$	−1.13866	−	0.0996201i	−0.0381681	−	0.00333927i
$891$		0			0
$892$	8.87184	+	1.56434i	0.297051	+	0.0523781i
$893$	12.5018	−	26.8102i	0.418357	−	0.897170i
$894$		0			0
$895$	−0.0661045	+	0.0240601i	−0.00220963	+	0.000804239i
$896$	−0.309251	−	0.0828636i	−0.0103314	−	0.00276828i
$897$		0			0
$898$	−1.30416	+	2.25886i	−0.0435202	+	0.0753793i
$899$	−2.14930	−	3.72270i	−0.0716832	−	0.124159i
$900$		0			0
$901$	8.90824	−	6.23761i	0.296776	−	0.207805i
$902$	2.94533	−	0.789198i	0.0980686	−	0.0262774i
$903$		0			0
$904$	6.81181	+	2.47930i	0.226558	+	0.0824602i
$905$	−15.8286	−	11.0833i	−0.526159	−	0.368421i
$906$		0			0
$907$	1.69659	+	19.3922i	0.0563345	+	0.643906i	0.970903	+	0.239474i	$0.0769751\pi$
$907$	1.69659	+	19.3922i	0.0563345	+	0.643906i	−0.914568	+	0.404432i	$0.867469\pi$
$908$	9.78281	−	13.9713i	0.324654	−	0.463654i
$909$		0			0
$910$	1.03030	+	2.20948i	0.0341540	+	0.0732436i
$911$	3.12019	+	11.6447i	0.103377	+	0.385807i	0.998156	−	0.0607018i	$-0.0193339\pi$
$911$	3.12019	+	11.6447i	0.103377	+	0.385807i	−0.894779	+	0.446509i	$0.852667\pi$
$912$		0			0
$913$	3.89818	+	4.64567i	0.129011	+	0.153749i
$914$	−26.8031	+	15.4747i	−0.886566	+	0.511859i
$915$		0			0
$916$	6.66659	−	1.17550i	0.220270	−	0.0388396i
$917$	0.391750	−	1.46203i	0.0129367	−	0.0482805i
$918$		0			0
$919$	19.8908	−	19.8908i	0.656136	−	0.656136i	−0.298328	−	0.954463i	$-0.596429\pi$
$919$	19.8908	−	19.8908i	0.656136	−	0.656136i	0.954463	+	0.298328i	$0.0964289\pi$
$920$	−10.2052	−	4.75877i	−0.336456	−	0.156892i
$921$		0			0
$922$	10.8026	+	9.06447i	0.355765	+	0.298523i
$923$	−1.98506	+	22.6894i	−0.0653392	+	0.746830i
$924$		0			0
$925$	−11.3252	+	15.7888i	−0.372369	+	0.519131i
$926$		−	37.9255i		−	1.24631i
$927$		0			0
$928$	1.55658	−	1.85506i	0.0510972	−	0.0608952i
$929$	1.68072	−	9.53184i	0.0551426	−	0.312729i	−0.944744	−	0.327810i	$-0.893689\pi$
$929$	1.68072	−	9.53184i	0.0551426	−	0.312729i	0.999886	+	0.0150807i	$0.00480051\pi$
$930$		0			0
$931$	−14.0917	−	14.0917i	−0.461837	−	0.461837i
$932$	8.38917	+	23.0491i	0.274797	+	0.754997i
$933$		0			0
$934$	−4.78255	−	27.1232i	−0.156490	−	0.887498i
$935$	−1.72957	−	0.998568i	−0.0565630	−	0.0326567i
$936$		0			0
$937$	43.4445	−	36.4543i	1.41927	−	1.19091i	0.467540	−	0.883972i	$-0.345140\pi$
$937$	43.4445	−	36.4543i	1.41927	−	1.19091i	0.951730	−	0.306937i	$-0.0993042\pi$
$938$	−1.61227	−	2.30257i	−0.0526426	−	0.0751815i
$939$		0			0
$940$	−12.4689	+	5.81436i	−0.406692	+	0.189644i
$941$	−17.9406	+	49.2914i	−0.584847	+	1.60685i	0.194945	+	0.980814i	$0.437547\pi$
$941$	−17.9406	+	49.2914i	−0.584847	+	1.60685i	−0.779792	+	0.626039i	$0.784675\pi$
$942$		0			0
$943$	45.0333	−	3.93990i	1.46649	−	0.128301i
$944$	−3.15842	+	0.276326i	−0.102798	+	0.00899364i
$945$		0			0
$946$	0.0743112	−	0.204168i	0.00241606	−	0.00663808i
$947$	38.2864	−	17.8533i	1.24414	−	0.580153i	0.314725	−	0.949183i	$-0.398088\pi$
$947$	38.2864	−	17.8533i	1.24414	−	0.580153i	0.929417	+	0.369030i	$0.120310\pi$
$948$		0			0
$949$	7.76845	+	11.0945i	0.252175	+	0.360143i
$950$	−7.07008	+	5.93250i	−0.229384	+	0.192476i
$951$		0			0
$952$	−0.729053	−	0.420919i	−0.0236288	−	0.0136421i
$953$	−5.81738	−	32.9920i	−0.188443	−	1.06872i	−0.921451	−	0.388495i	$-0.872995\pi$
$953$	−5.81738	−	32.9920i	−0.188443	−	1.06872i	0.733007	−	0.680221i	$-0.238116\pi$
$954$		0			0
$955$	6.61159	+	18.1652i	0.213946	+	0.587812i
$956$	−6.60977	−	6.60977i	−0.213775	−	0.213775i
$957$		0			0
$958$	−4.16457	+	23.6184i	−0.134551	+	0.763077i
$959$	1.58987	−	1.89473i	0.0513396	−	0.0611842i
$960$		0			0
$961$			27.8490i			0.898355i
$962$	24.0947	+	24.6490i	0.776843	+	0.794716i
$963$		0			0
$964$	0.471855	−	5.39333i	0.0151974	−	0.173707i
$965$	−3.51473	−	2.94921i	−0.113143	−	0.0949384i
$966$		0			0
$967$	51.4018	+	23.9691i	1.65297	+	0.770793i	0.999909	+	0.0134894i	$0.00429393\pi$
$967$	51.4018	+	23.9691i	1.65297	+	0.770793i	0.653063	+	0.757304i	$0.273484\pi$
$968$	7.55226	−	7.55226i	0.242739	−	0.242739i
$969$		0			0
$970$	0.0260215	−	0.0971136i	0.000835500	−	0.00311813i
$971$	−21.1770	+	3.73407i	−0.679601	+	0.119832i	−0.502784	−	0.864412i	$-0.667691\pi$
$971$	−21.1770	+	3.73407i	−0.679601	+	0.119832i	−0.176817	+	0.984244i	$0.556580\pi$
$972$		0			0
$973$	−1.12855	+	0.651567i	−0.0361796	+	0.0208883i
$974$	−3.62949	−	4.32546i	−0.116296	−	0.138597i
$975$		0			0
$976$	−0.507391	−	1.89361i	−0.0162412	−	0.0606130i
$977$	13.3534	+	28.6365i	0.427213	+	0.916162i	0.995627	+	0.0934187i	$0.0297795\pi$
$977$	13.3534	+	28.6365i	0.427213	+	0.916162i	−0.568414	+	0.822743i	$0.692443\pi$
$978$		0			0
$979$	−0.275776	+	0.393849i	−0.00881383	+	0.0125875i
$980$	0.807800	+	9.23320i	0.0258042	+	0.294944i
$981$		0			0
$982$	1.13700	+	0.796137i	0.0362832	+	0.0254058i
$983$	47.1611	+	17.1652i	1.50421	+	0.547486i	0.957146	−	0.289606i	$-0.0935244\pi$
$983$	47.1611	+	17.1652i	1.50421	+	0.547486i	0.547061	+	0.837093i	$0.315747\pi$
$984$		0			0
$985$	31.1862	−	8.35632i	0.993675	−	0.266254i
$986$	5.21589	−	3.65221i	0.166108	−	0.116310i
$987$		0			0
$988$	8.18630	+	14.1791i	0.260441	+	0.451097i
$989$	1.61054	−	2.78954i	0.0512123	−	0.0887023i
$990$		0			0
$991$	−43.1429	−	11.5601i	−1.37048	−	0.367219i	−0.502826	−	0.864388i	$-0.667706\pi$
$991$	−43.1429	−	11.5601i	−1.37048	−	0.367219i	−0.867654	+	0.497169i	$0.834373\pi$
$992$	1.66805	−	0.607122i	0.0529607	−	0.0192761i
$993$		0			0
$994$	0.543831	−	1.16625i	0.0172493	−	0.0369912i
$995$	−23.1759	−	4.08654i	−0.734726	−	0.129552i
$996$		0			0
$997$	−53.1166	−	4.64710i	−1.68222	−	0.147175i	−0.794409	−	0.607383i	$-0.792219\pi$
$997$	−53.1166	−	4.64710i	−1.68222	−	0.147175i	−0.887811	+	0.460208i	$0.847775\pi$
$998$	−20.2771			−0.641862
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.35.5	yes	72
3.2	odd	2	inner	666.2.bs.a.35.2	✓	72
37.18	odd	36	inner	666.2.bs.a.647.2	yes	72
111.92	even	36	inner	666.2.bs.a.647.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.35.2	✓	72	3.2	odd	2	inner
666.2.bs.a.35.5	yes	72	1.1	even	1	trivial
666.2.bs.a.647.2	yes	72	37.18	odd	36	inner
666.2.bs.a.647.5	yes	72	111.92	even	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)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.567891 - 1.21785i) q^{5} +(-0.300852 + 0.109501i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(0.567891 - 1.21785i) q^{5} +(-0.300852 + 0.109501i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.671872 - 1.16372i) q^{10} +(-0.282618 - 0.489509i) q^{11} +(4.64189 - 3.25029i) q^{13} +(-0.309251 + 0.0828636i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.15390 + 1.50818i) q^{17} +(0.251816 + 2.87827i) q^{19} +(0.770740 - 1.10073i) q^{20} +(-0.238879 - 0.512278i) q^{22} +(-2.16883 - 8.09420i) q^{23} +(2.05329 + 2.44702i) q^{25} +(4.90751 - 2.83335i) q^{26} +(-0.315296 + 0.0555953i) q^{28} +(0.626757 - 2.33909i) q^{29} +(1.25519 - 1.25519i) q^{31} +(0.906308 + 0.422618i) q^{32} +(2.01426 + 1.69016i) q^{34} +(-0.0374956 + 0.428576i) q^{35} +(1.50742 + 5.89302i) q^{37} +2.88926i q^{38} +(0.863742 - 1.02937i) q^{40} +(-0.936762 + 5.31264i) q^{41} +(0.271805 + 0.271805i) q^{43} +(-0.193322 - 0.531149i) q^{44} +(-1.45513 - 8.25243i) q^{46} +(-8.86683 - 5.11926i) q^{47} +(-5.28379 + 4.43363i) q^{49} +(1.83221 + 2.61666i) q^{50} +(5.13578 - 2.39485i) q^{52} +(1.41455 - 3.88644i) q^{53} +(-0.756643 + 0.0661977i) q^{55} +(-0.318942 + 0.0279038i) q^{56} +(0.828238 - 2.27556i) q^{58} +(-2.87343 + 1.33990i) q^{59} +(-1.12444 - 1.60587i) q^{61} +(1.35981 - 1.14102i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-1.32226 - 7.49891i) q^{65} +(3.00284 + 8.25023i) q^{67} +(1.85929 + 1.85929i) q^{68} +(-0.0747058 + 0.423678i) q^{70} +(-2.58354 + 3.07894i) q^{71} +2.39008i q^{73} +(0.988069 + 6.00198i) q^{74} +(-0.251816 + 2.87827i) q^{76} +(0.138628 + 0.116323i) q^{77} +(8.72743 + 4.06967i) q^{79} +(0.950170 - 0.950170i) q^{80} +(-1.39623 + 5.21078i) q^{82} +(-10.5661 + 1.86309i) q^{83} +(3.05991 - 1.76664i) q^{85} +(0.247081 + 0.294460i) q^{86} +(-0.146294 - 0.545977i) q^{88} +(-0.359487 - 0.770922i) q^{89} +(-1.04061 + 1.48615i) q^{91} +(-0.730342 - 8.34784i) q^{92} +(-8.38691 - 5.87258i) q^{94} +(3.64829 + 1.32787i) q^{95} +(0.0722709 - 0.0193649i) q^{97} +(-5.65010 + 3.95624i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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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