LMFDB - Embedded newform 693.2.m.k.190.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.7
Character	$\chi$	$=$	693.190
Dual form			693.2.m.k.631.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70216 - 1.23669i) q^{2} +(0.749912 - 2.30799i) q^{4} +(3.03419 + 2.20447i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.277470 - 0.853964i) q^{8} +O(q^{10})$	\(q+(1.70216 - 1.23669i) q^{2} +(0.749912 - 2.30799i) q^{4} +(3.03419 + 2.20447i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.277470 - 0.853964i) q^{8} +7.89093 q^{10} +(1.33588 + 3.03569i) q^{11} +(-2.80385 + 2.03712i) q^{13} +(-0.650168 - 2.00101i) q^{14} +(2.39820 + 1.74239i) q^{16} +(-1.23523 - 0.897450i) q^{17} +(-1.59455 - 4.90753i) q^{19} +(7.36326 - 5.34972i) q^{20} +(6.02811 + 3.51516i) q^{22} -4.87487 q^{23} +(2.80154 + 8.62225i) q^{25} +(-2.25332 + 6.93501i) q^{26} +(-1.96329 - 1.42642i) q^{28} +(3.31493 - 10.2023i) q^{29} +(-6.57516 + 4.77714i) q^{31} +8.03275 q^{32} -3.21244 q^{34} +(3.03419 - 2.20447i) q^{35} +(2.86103 - 8.80533i) q^{37} +(-8.78330 - 6.38144i) q^{38} +(1.04064 - 3.20276i) q^{40} +(-3.36746 - 10.3640i) q^{41} -0.137677 q^{43} +(8.00814 - 0.806704i) q^{44} +(-8.29782 + 6.02872i) q^{46} +(-0.843708 - 2.59667i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(15.4318 + 11.2118i) q^{50} +(2.59901 + 7.99893i) q^{52} +(2.26034 - 1.64224i) q^{53} +(-2.63876 + 12.1558i) q^{55} -0.897910 q^{56} +(-6.97458 - 21.4656i) q^{58} +(-1.49714 + 4.60772i) q^{59} +(0.240947 + 0.175058i) q^{61} +(-5.28414 + 16.2629i) q^{62} +(8.87665 - 6.44926i) q^{64} -12.9982 q^{65} +0.816899 q^{67} +(-2.99762 + 2.17790i) q^{68} +(2.43843 - 7.50472i) q^{70} +(-4.63563 - 3.36798i) q^{71} +(-0.764866 + 2.35402i) q^{73} +(-6.01957 - 18.5263i) q^{74} -12.5223 q^{76} +(3.29992 - 0.332419i) q^{77} +(-9.24242 + 6.71501i) q^{79} +(3.43554 + 10.5735i) q^{80} +(-18.5490 - 13.4766i) q^{82} +(8.61276 + 6.25754i) q^{83} +(-1.76953 - 5.44606i) q^{85} +(-0.234348 + 0.170264i) q^{86} +(2.22170 - 1.98311i) q^{88} +8.91589 q^{89} +(1.07098 + 3.29613i) q^{91} +(-3.65572 + 11.2512i) q^{92} +(-4.64741 - 3.37654i) q^{94} +(5.98031 - 18.4055i) q^{95} +(-6.54067 + 4.75207i) q^{97} -2.10399 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.70216	−	1.23669i	1.20361	−	0.874474i	0.208975	−	0.977921i	$-0.432987\pi$
$2$	1.70216	−	1.23669i	1.20361	−	0.874474i	0.994635	+	0.103447i	$0.0329871\pi$
$3$		0			0
$3$		0			0
$4$	0.749912	−	2.30799i	0.374956	−	1.15400i
$5$	3.03419	+	2.20447i	1.35693	+	0.985867i	0.998634	+	0.0522596i	$0.0166423\pi$
$5$	3.03419	+	2.20447i	1.35693	+	0.985867i	0.358297	+	0.933608i	$0.383358\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.277470	−	0.853964i	−0.0981003	−	0.301922i
$9$		0			0
$10$	7.89093			2.49533
$11$	1.33588	+	3.03569i	0.402784	+	0.915295i
$11$	1.33588	+	3.03569i	0.402784	+	0.915295i
$12$		0			0
$13$	−2.80385	+	2.03712i	−0.777649	+	0.564995i	−0.904272	−	0.426956i	$-0.859586\pi$
$13$	−2.80385	+	2.03712i	−0.777649	+	0.564995i	0.126624	+	0.991951i	$0.459586\pi$
$14$	−0.650168	−	2.00101i	−0.173765	−	0.534793i
$15$		0			0
$16$	2.39820	+	1.74239i	0.599550	+	0.435599i
$17$	−1.23523	−	0.897450i	−0.299588	−	0.217664i	0.427828	−	0.903860i	$-0.359279\pi$
$17$	−1.23523	−	0.897450i	−0.299588	−	0.217664i	−0.727416	+	0.686197i	$0.759279\pi$
$18$		0			0
$19$	−1.59455	−	4.90753i	−0.365816	−	1.12587i	−0.949469	−	0.313862i	$-0.898377\pi$
$19$	−1.59455	−	4.90753i	−0.365816	−	1.12587i	0.583653	−	0.812003i	$-0.301623\pi$
$20$	7.36326	−	5.34972i	1.64648	−	1.19623i
$21$		0			0
$22$	6.02811	+	3.51516i	1.28520	+	0.749435i
$23$	−4.87487			−1.01648			−0.508240	−	0.861215i	$-0.669704\pi$
$23$	−4.87487			−1.01648			−0.508240	+	0.861215i	$0.669704\pi$
$24$		0			0
$25$	2.80154	+	8.62225i	0.560308	+	1.72445i
$26$	−2.25332	+	6.93501i	−0.441913	+	1.36007i
$27$		0			0
$28$	−1.96329	−	1.42642i	−0.371028	−	0.269568i
$29$	3.31493	−	10.2023i	0.615568	−	1.89452i	0.222907	−	0.974840i	$-0.428445\pi$
$29$	3.31493	−	10.2023i	0.615568	−	1.89452i	0.392661	−	0.919683i	$-0.371555\pi$
$30$		0			0
$31$	−6.57516	+	4.77714i	−1.18093	+	0.857999i	−0.992277	−	0.124044i	$-0.960414\pi$
$31$	−6.57516	+	4.77714i	−1.18093	+	0.857999i	−0.188658	+	0.982043i	$0.560414\pi$
$32$	8.03275			1.42000
$33$		0			0
$34$	−3.21244			−0.550929
$35$	3.03419	−	2.20447i	0.512871	−	0.372623i
$36$		0			0
$37$	2.86103	−	8.80533i	0.470350	−	1.44759i	−0.381778	−	0.924254i	$-0.624688\pi$
$37$	2.86103	−	8.80533i	0.470350	−	1.44759i	0.852128	−	0.523334i	$-0.175312\pi$
$38$	−8.78330	−	6.38144i	−1.42484	−	1.03521i
$39$		0			0
$40$	1.04064	−	3.20276i	0.164540	−	0.506401i
$41$	−3.36746	−	10.3640i	−0.525908	−	1.61858i	−0.762513	−	0.646973i	$-0.776035\pi$
$41$	−3.36746	−	10.3640i	−0.525908	−	1.61858i	0.236605	−	0.971606i	$-0.423965\pi$
$42$		0			0
$43$	−0.137677			−0.0209955			−0.0104978	−	0.999945i	$-0.503342\pi$
$43$	−0.137677			−0.0209955			−0.0104978	+	0.999945i	$0.503342\pi$
$44$	8.00814	−	0.806704i	1.20727	−	0.121615i
$45$		0			0
$46$	−8.29782	+	6.02872i	−1.22345	+	0.888886i
$47$	−0.843708	−	2.59667i	−0.123068	−	0.378763i	0.870477	−	0.492210i	$-0.163811\pi$
$47$	−0.843708	−	2.59667i	−0.123068	−	0.378763i	−0.993544	+	0.113447i	$0.963811\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	15.4318	+	11.2118i	2.18238	+	1.58559i
$51$		0			0
$52$	2.59901	+	7.99893i	0.360418	+	1.10925i
$53$	2.26034	−	1.64224i	0.310482	−	0.225579i	−0.421621	−	0.906772i	$-0.638539\pi$
$53$	2.26034	−	1.64224i	0.310482	−	0.225579i	0.732103	+	0.681194i	$0.238539\pi$
$54$		0			0
$55$	−2.63876	+	12.1558i	−0.355811	+	1.63908i
$56$	−0.897910			−0.119988
$57$		0			0
$58$	−6.97458	−	21.4656i	−0.915808	−	2.81857i
$59$	−1.49714	+	4.60772i	−0.194911	+	0.599875i	0.805067	+	0.593185i	$0.202130\pi$
$59$	−1.49714	+	4.60772i	−0.194911	+	0.599875i	−0.999978	+	0.00669015i	$0.997870\pi$
$60$		0			0
$61$	0.240947	+	0.175058i	0.0308501	+	0.0224139i	0.603103	−	0.797663i	$-0.293931\pi$
$61$	0.240947	+	0.175058i	0.0308501	+	0.0224139i	−0.572253	+	0.820077i	$0.693931\pi$
$62$	−5.28414	+	16.2629i	−0.671087	+	2.06539i
$63$		0			0
$64$	8.87665	−	6.44926i	1.10958	−	0.806158i
$65$	−12.9982			−1.61223
$66$		0			0
$67$	0.816899			0.0998001			0.0499001	−	0.998754i	$-0.484110\pi$
$67$	0.816899			0.0998001			0.0499001	+	0.998754i	$0.484110\pi$
$68$	−2.99762	+	2.17790i	−0.363515	+	0.264109i
$69$		0			0
$70$	2.43843	−	7.50472i	0.291448	−	0.896986i
$71$	−4.63563	−	3.36798i	−0.550148	−	0.399706i	0.277692	−	0.960670i	$-0.410430\pi$
$71$	−4.63563	−	3.36798i	−0.550148	−	0.399706i	−0.827840	+	0.560964i	$0.810430\pi$
$72$		0			0
$73$	−0.764866	+	2.35402i	−0.0895208	+	0.275517i	−0.985787	−	0.168000i	$-0.946269\pi$
$73$	−0.764866	+	2.35402i	−0.0895208	+	0.275517i	0.896266	+	0.443516i	$0.146269\pi$
$74$	−6.01957	−	18.5263i	−0.699760	−	2.15364i
$75$		0			0
$76$	−12.5223			−1.43641
$77$	3.29992	−	0.332419i	0.376061	−	0.0378827i
$78$		0			0
$79$	−9.24242	+	6.71501i	−1.03985	+	0.755497i	−0.970257	−	0.242078i	$-0.922171\pi$
$79$	−9.24242	+	6.71501i	−1.03985	+	0.755497i	−0.0695961	+	0.997575i	$0.522171\pi$
$80$	3.43554	+	10.5735i	0.384105	+	1.18215i
$81$		0			0
$82$	−18.5490	−	13.4766i	−2.04839	−	1.48825i
$83$	8.61276	+	6.25754i	0.945373	+	0.686854i	0.949708	−	0.313137i	$-0.101380\pi$
$83$	8.61276	+	6.25754i	0.945373	+	0.686854i	−0.00433474	+	0.999991i	$0.501380\pi$
$84$		0			0
$85$	−1.76953	−	5.44606i	−0.191933	−	0.590708i
$86$	−0.234348	+	0.170264i	−0.0252704	+	0.0183600i
$87$		0			0
$88$	2.22170	−	1.98311i	0.236834	−	0.211400i
$89$	8.91589			0.945082			0.472541	−	0.881309i	$-0.343337\pi$
$89$	8.91589			0.945082			0.472541	+	0.881309i	$0.343337\pi$
$90$		0			0
$91$	1.07098	+	3.29613i	0.112269	+	0.345528i
$92$	−3.65572	+	11.2512i	−0.381135	+	1.17301i
$93$		0			0
$94$	−4.64741	−	3.37654i	−0.479344	−	0.348264i
$95$	5.98031	−	18.4055i	0.613567	−	1.88837i
$96$		0			0
$97$	−6.54067	+	4.75207i	−0.664104	+	0.482500i	−0.868046	−	0.496483i	$-0.834625\pi$
$97$	−6.54067	+	4.75207i	−0.664104	+	0.482500i	0.203942	+	0.978983i	$0.434625\pi$
$98$	−2.10399			−0.212535
$99$		0			0
$100$	22.0010			2.20010
$101$	1.39311	−	1.01215i	0.138619	−	0.100713i	−0.516315	−	0.856399i	$-0.672696\pi$
$101$	1.39311	−	1.01215i	0.138619	−	0.100713i	0.654934	+	0.755686i	$0.272696\pi$
$102$		0			0
$103$	−0.832485	+	2.56213i	−0.0820272	+	0.252454i	−0.983656	−	0.180056i	$-0.942372\pi$
$103$	−0.832485	+	2.56213i	−0.0820272	+	0.252454i	0.901629	+	0.432510i	$0.142372\pi$
$104$	2.51761	+	1.82915i	0.246872	+	0.179363i
$105$		0			0
$106$	1.81653	−	5.59070i	0.176437	−	0.543017i
$107$	−1.53889	−	4.73620i	−0.148770	−	0.457866i	0.848707	−	0.528864i	$-0.177382\pi$
$107$	−1.53889	−	4.73620i	−0.148770	−	0.457866i	−0.997476	+	0.0709975i	$0.977382\pi$
$108$		0			0
$109$	11.2061			1.07335			0.536676	−	0.843788i	$-0.319680\pi$
$109$	11.2061			1.07335			0.536676	+	0.843788i	$0.319680\pi$
$110$	10.5414	+	23.9544i	1.00508	+	2.28396i
$111$		0			0
$112$	2.39820	−	1.74239i	0.226609	−	0.164641i
$113$	5.07595	+	15.6222i	0.477505	+	1.46961i	0.842549	+	0.538620i	$0.181054\pi$
$113$	5.07595	+	15.6222i	0.477505	+	1.46961i	−0.365044	+	0.930990i	$0.618946\pi$
$114$		0			0
$115$	−14.7913	−	10.7465i	−1.37929	−	1.00212i
$116$	−21.0610	−	15.3017i	−1.95546	−	1.42073i
$117$		0			0
$118$	3.14997	+	9.69460i	0.289978	+	0.892460i
$119$	−1.23523	+	0.897450i	−0.113234	+	0.0822691i
$120$		0			0
$121$	−7.43084	+	8.11065i	−0.675531	+	0.737332i
$122$	0.626624			0.0567318
$123$		0			0
$124$	6.09480	+	18.7579i	0.547329	+	1.68450i
$125$	−4.71228	+	14.5029i	−0.421479	+	1.29718i
$126$		0			0
$127$	15.8614	+	11.5240i	1.40747	+	1.02259i	0.993684	+	0.112213i	$0.0357939\pi$
$127$	15.8614	+	11.5240i	1.40747	+	1.02259i	0.413786	+	0.910374i	$0.364206\pi$
$128$	2.16922	−	6.67618i	0.191734	−	0.590096i
$129$		0			0
$130$	−22.1250	+	16.0748i	−1.94049	+	1.40985i
$131$	−13.3659			−1.16778			−0.583891	−	0.811832i	$-0.698470\pi$
$131$	−13.3659			−1.16778			−0.583891	+	0.811832i	$0.698470\pi$
$132$		0			0
$133$	−5.16008			−0.447436
$134$	1.39050	−	1.01025i	0.120120	−	0.0872726i
$135$		0			0
$136$	−0.423650	+	1.30386i	−0.0363277	+	0.111805i
$137$	−4.27145	−	3.10339i	−0.364935	−	0.265141i	0.390173	−	0.920742i	$-0.372415\pi$
$137$	−4.27145	−	3.10339i	−0.364935	−	0.265141i	−0.755107	+	0.655601i	$0.772415\pi$
$138$		0			0
$139$	−6.60545	+	20.3295i	−0.560267	+	1.72432i	0.121344	+	0.992610i	$0.461280\pi$
$139$	−6.60545	+	20.3295i	−0.560267	+	1.72432i	−0.681611	+	0.731714i	$0.738720\pi$
$140$	−2.81252	−	8.65604i	−0.237701	−	0.731569i
$141$		0			0
$142$	−12.0557			−1.01170
$143$	−9.92968	−	5.79028i	−0.830362	−	0.484208i
$144$		0			0
$145$	32.5488	−	23.6481i	2.70303	−	1.96387i
$146$	1.60927	+	4.95282i	0.133184	+	0.409898i
$147$		0			0
$148$	−18.1771	−	13.2064i	−1.49415	−	1.08556i
$149$	−8.89641	−	6.46362i	−0.728822	−	0.529520i	0.160369	−	0.987057i	$-0.448732\pi$
$149$	−8.89641	−	6.46362i	−0.728822	−	0.529520i	−0.889191	+	0.457537i	$0.848732\pi$
$150$		0			0
$151$	−1.09444	−	3.36836i	−0.0890647	−	0.274113i	0.896597	−	0.442848i	$-0.146032\pi$
$151$	−1.09444	−	3.36836i	−0.0890647	−	0.274113i	−0.985661	+	0.168735i	$0.946032\pi$
$152$	−3.74841	+	2.72338i	−0.304036	+	0.220895i
$153$		0			0
$154$	5.20590	−	4.64682i	0.419504	−	0.374452i
$155$	−30.4813			−2.44832
$156$		0			0
$157$	3.94277	+	12.1346i	0.314667	+	0.968446i	0.975891	+	0.218257i	$0.0700372\pi$
$157$	3.94277	+	12.1346i	0.314667	+	0.968446i	−0.661224	+	0.750188i	$0.729963\pi$
$158$	−7.42768	+	22.8601i	−0.590915	+	1.81865i
$159$		0			0
$160$	24.3729	+	17.7079i	1.92685	+	1.39994i
$161$	−1.50642	+	4.63628i	−0.118722	+	0.365390i
$162$		0			0
$163$	13.1748	−	9.57207i	1.03193	−	0.749742i	0.0632373	−	0.997999i	$-0.479858\pi$
$163$	13.1748	−	9.57207i	1.03193	−	0.749742i	0.968694	+	0.248256i	$0.0798575\pi$
$164$	−26.4452			−2.06503
$165$		0			0
$166$	22.3990			1.73850
$167$	4.58131	−	3.32851i	0.354512	−	0.257568i	−0.396247	−	0.918144i	$-0.629688\pi$
$167$	4.58131	−	3.32851i	0.354512	−	0.257568i	0.750760	+	0.660576i	$0.229688\pi$
$168$		0			0
$169$	−0.305480	+	0.940172i	−0.0234985	+	0.0723209i
$170$	−9.74714	−	7.08171i	−0.747572	−	0.543143i
$171$		0			0
$172$	−0.103245	+	0.317757i	−0.00787239	+	0.0242287i
$173$	4.14744	+	12.7645i	0.315324	+	0.970467i	0.975621	+	0.219462i	$0.0704303\pi$
$173$	4.14744	+	12.7645i	0.315324	+	0.970467i	−0.660297	+	0.751004i	$0.729570\pi$
$174$		0			0
$175$	9.06597			0.685323
$176$	−2.08566	+	9.60783i	−0.157212	+	0.724217i
$177$		0			0
$178$	15.1763	−	11.0262i	1.13751	−	0.826450i
$179$	1.17687	+	3.62202i	0.0879631	+	0.270722i	0.985356	−	0.170510i	$-0.0545415\pi$
$179$	1.17687	+	3.62202i	0.0879631	+	0.270722i	−0.897393	+	0.441232i	$0.854541\pi$
$180$		0			0
$181$	7.91914	+	5.75359i	0.588625	+	0.427661i	0.841823	−	0.539753i	$-0.181483\pi$
$181$	7.91914	+	5.75359i	0.588625	+	0.427661i	−0.253198	+	0.967414i	$0.581483\pi$
$182$	5.89927	+	4.28607i	0.437283	+	0.317705i
$183$		0			0
$184$	1.35263	+	4.16296i	0.0997171	+	0.306898i
$185$	28.0920	−	20.4100i	2.06536	−	1.50057i
$186$		0			0
$187$	1.07425	−	4.94867i	0.0785572	−	0.361883i
$188$	−6.62579			−0.483236
$189$		0			0
$190$	−12.5825	−	38.7250i	−0.912831	−	2.80941i
$191$	2.77796	−	8.54967i	0.201006	−	0.618632i	−0.798848	−	0.601533i	$-0.794557\pi$
$191$	2.77796	−	8.54967i	0.201006	−	0.618632i	0.999854	−	0.0170994i	$-0.00544316\pi$
$192$		0			0
$193$	4.73227	+	3.43819i	0.340636	+	0.247487i	0.744930	−	0.667142i	$-0.232483\pi$
$193$	4.73227	+	3.43819i	0.340636	+	0.247487i	−0.404294	+	0.914629i	$0.632483\pi$
$194$	−5.25642	+	16.1776i	−0.377389	+	1.16148i
$195$		0			0
$196$	−1.96329	+	1.42642i	−0.140235	+	0.101887i
$197$	6.19555			0.441414			0.220707	−	0.975340i	$-0.429163\pi$
$197$	6.19555			0.441414			0.220707	+	0.975340i	$0.429163\pi$
$198$		0			0
$199$	−18.8634			−1.33719			−0.668596	−	0.743626i	$-0.733105\pi$
$199$	−18.8634			−1.33719			−0.668596	+	0.743626i	$0.733105\pi$
$200$	6.58575	−	4.78482i	0.465683	−	0.338338i
$201$		0			0
$202$	1.11957	−	3.44569i	0.0787729	−	0.242438i
$203$	−8.67861	−	6.30538i	−0.609119	−	0.442551i
$204$		0			0
$205$	12.6295	−	38.8697i	0.882084	−	2.71477i
$206$	1.75154	+	5.39068i	0.122036	+	0.375587i
$207$		0			0
$208$	−10.2737			−0.712351
$209$	12.7676	−	11.3965i	0.883154	−	0.788309i
$210$		0			0
$211$	−0.517917	+	0.376288i	−0.0356549	+	0.0259048i	−0.605470	−	0.795868i	$-0.707015\pi$
$211$	−0.517917	+	0.376288i	−0.0356549	+	0.0259048i	0.569815	+	0.821773i	$0.307015\pi$
$212$	−2.09521	−	6.44839i	−0.143900	−	0.442877i
$213$		0			0
$214$	−8.47667	−	6.15866i	−0.579453	−	0.420997i
$215$	−0.417737	−	0.303504i	−0.0284894	−	0.0206988i
$216$		0			0
$217$	2.51149	+	7.72957i	0.170491	+	0.524717i
$218$	19.0746	−	13.8585i	1.29190	−	0.938618i
$219$		0			0
$220$	26.0766	+	15.2060i	1.75808	+	1.02519i
$221$	5.29163			0.355953
$222$		0			0
$223$	−5.16437	−	15.8943i	−0.345832	−	1.06436i	−0.961137	−	0.276072i	$-0.910967\pi$
$223$	−5.16437	−	15.8943i	−0.345832	−	1.06436i	0.615305	−	0.788289i	$-0.289033\pi$
$224$	2.48226	−	7.63960i	0.165853	−	0.510443i
$225$		0			0
$226$	27.9599	+	20.3141i	1.85987	+	1.35127i
$227$	2.88200	−	8.86988i	0.191285	−	0.588714i	−0.808715	−	0.588201i	$-0.799836\pi$
$227$	2.88200	−	8.86988i	0.191285	−	0.588714i	1.00000		0.000513716i	$-0.000163521\pi$
$228$		0			0
$229$	−17.2900	+	12.5619i	−1.14256	+	0.830115i	−0.987473	−	0.157786i	$-0.949564\pi$
$229$	−17.2900	+	12.5619i	−1.14256	+	0.830115i	−0.155083	+	0.987902i	$0.549564\pi$
$230$	−38.4672			−2.53646
$231$		0			0
$232$	−9.63220			−0.632385
$233$	13.8475	−	10.0608i	0.907177	−	0.659103i	−0.0331221	−	0.999451i	$-0.510545\pi$
$233$	13.8475	−	10.0608i	0.907177	−	0.659103i	0.940299	+	0.340348i	$0.110545\pi$
$234$		0			0
$235$	3.16430	−	9.73870i	0.206416	−	0.635283i
$236$	9.51187	+	6.91078i	0.619170	+	0.449853i
$237$		0			0
$238$	−0.992698	+	3.05521i	−0.0643470	+	0.198040i
$239$	1.04152	+	3.20548i	0.0673706	+	0.207345i	0.979074	−	0.203503i	$-0.0652326\pi$
$239$	1.04152	+	3.20548i	0.0673706	+	0.207345i	−0.911704	+	0.410848i	$0.865233\pi$
$240$		0			0
$241$	5.77583			0.372054			0.186027	−	0.982545i	$-0.440439\pi$
$241$	5.77583			0.372054			0.186027	+	0.982545i	$0.440439\pi$
$242$	−2.61811	+	22.9953i	−0.168298	+	1.47819i
$243$		0			0
$244$	0.584721	−	0.424825i	0.0374330	−	0.0271966i
$245$	−1.15896	−	3.56690i	−0.0740430	−	0.227881i
$246$		0			0
$247$	14.4681	+	10.5117i	0.920584	+	0.668844i
$248$	5.90391	+	4.28944i	0.374899	+	0.272380i
$249$		0			0
$250$	9.91459	+	30.5140i	0.627054	+	1.92987i
$251$	−9.51530	+	6.91327i	−0.600600	+	0.436362i	−0.846092	−	0.533037i	$-0.821051\pi$
$251$	−9.51530	+	6.91327i	−0.600600	+	0.436362i	0.245492	+	0.969399i	$0.421051\pi$
$252$		0			0
$253$	−6.51225	−	14.7986i	−0.409422	−	0.930380i
$254$	41.2503			2.58827
$255$		0			0
$256$	2.21714	+	6.82366i	0.138571	+	0.426479i
$257$	−4.40845	+	13.5678i	−0.274991	+	0.846336i	0.714230	+	0.699911i	$0.246777\pi$
$257$	−4.40845	+	13.5678i	−0.274991	+	0.846336i	−0.989222	+	0.146426i	$0.953223\pi$
$258$		0			0
$259$	−7.49026	−	5.44200i	−0.465422	−	0.338149i
$260$	−9.74749	+	29.9997i	−0.604514	+	1.86050i
$261$		0			0
$262$	−22.7509	+	16.5295i	−1.40555	+	1.02119i
$263$	−4.85285			−0.299239			−0.149620	−	0.988744i	$-0.547805\pi$
$263$	−4.85285			−0.299239			−0.149620	+	0.988744i	$0.547805\pi$
$264$		0			0
$265$	10.4786			0.643693
$266$	−8.78330	+	6.38144i	−0.538539	+	0.391271i
$267$		0			0
$268$	0.612603	−	1.88540i	0.0374207	−	0.115169i
$269$	5.14102	+	3.73517i	0.313453	+	0.227737i	0.733377	−	0.679822i	$-0.237943\pi$
$269$	5.14102	+	3.73517i	0.313453	+	0.227737i	−0.419923	+	0.907560i	$0.637943\pi$
$270$		0			0
$271$	−4.70183	+	14.4708i	−0.285616	+	0.879036i	0.700597	+	0.713557i	$0.252917\pi$
$271$	−4.70183	+	14.4708i	−0.285616	+	0.879036i	−0.986213	+	0.165479i	$0.947083\pi$
$272$	−1.39863	−	4.30453i	−0.0848042	−	0.261000i
$273$		0			0
$274$	−11.1086			−0.671098
$275$	−22.4320	+	20.0229i	−1.35270	+	1.20743i
$276$		0			0
$277$	0.306857	−	0.222945i	0.0184372	−	0.0133954i	−0.578528	−	0.815662i	$-0.696373\pi$
$277$	0.306857	−	0.222945i	0.0184372	−	0.0133954i	0.596966	+	0.802267i	$0.296373\pi$
$278$	13.8978	+	42.7730i	0.833534	+	2.56535i
$279$		0			0
$280$	−2.72443	−	1.97941i	−0.162816	−	0.118293i
$281$	−4.08025	−	2.96448i	−0.243407	−	0.176846i	0.459393	−	0.888233i	$-0.348067\pi$
$281$	−4.08025	−	2.96448i	−0.243407	−	0.176846i	−0.702800	+	0.711387i	$0.748067\pi$
$282$		0			0
$283$	−9.93028	−	30.5623i	−0.590294	−	1.81674i	−0.576881	−	0.816828i	$-0.695730\pi$
$283$	−9.93028	−	30.5623i	−0.590294	−	1.81674i	−0.0134127	−	0.999910i	$-0.504270\pi$
$284$	−11.2496	+	8.17330i	−0.667540	+	0.484996i
$285$		0			0
$286$	−24.0627	+	2.42397i	−1.42286	+	0.143332i
$287$	−10.8973			−0.643248
$288$		0			0
$289$	−4.53290	−	13.9508i	−0.266641	−	0.820638i
$290$	26.1579	−	80.5058i	1.53605	−	4.72746i
$291$		0			0
$292$	4.85947	+	3.53061i	0.284379	+	0.206613i
$293$	8.28925	−	25.5117i	0.484263	−	1.49041i	−0.348783	−	0.937204i	$-0.613405\pi$
$293$	8.28925	−	25.5117i	0.484263	−	1.49041i	0.833046	−	0.553204i	$-0.186595\pi$
$294$		0			0
$295$	−14.7002	+	10.6803i	−0.855878	+	0.621832i
$296$	−8.31328			−0.483200
$297$		0			0
$298$	−23.1366			−1.34027
$299$	13.6684	−	9.93069i	0.790465	−	0.574306i
$300$		0			0
$301$	−0.0425445	+	0.130938i	−0.00245222	+	0.00754716i
$302$	−6.02854	−	4.37999i	−0.346904	−	0.252040i
$303$		0			0
$304$	4.72680	−	14.5476i	0.271100	−	0.834361i
$305$	0.345168	+	1.06232i	0.0197643	+	0.0608282i
$306$		0			0
$307$	−5.75200			−0.328284			−0.164142	−	0.986437i	$-0.552486\pi$
$307$	−5.75200			−0.328284			−0.164142	+	0.986437i	$0.552486\pi$
$308$	1.70743	−	7.86548i	0.0972899	−	0.448177i
$309$		0			0
$310$	−51.8841	+	37.6960i	−2.94682	+	2.14099i
$311$	5.52543	+	17.0055i	0.313319	+	0.964295i	0.976441	+	0.215784i	$0.0692309\pi$
$311$	5.52543	+	17.0055i	0.313319	+	0.964295i	−0.663122	+	0.748511i	$0.730769\pi$
$312$		0			0
$313$	−15.7763	−	11.4621i	−0.891727	−	0.647877i	0.0446010	−	0.999005i	$-0.485798\pi$
$313$	−15.7763	−	11.4621i	−0.891727	−	0.647877i	−0.936328	+	0.351128i	$0.885798\pi$
$314$	21.7180	+	15.7790i	1.22562	+	0.890463i
$315$		0			0
$316$	8.56718	+	26.3671i	0.481942	+	1.48326i
$317$	14.1666	−	10.2926i	0.795675	−	0.578091i	−0.113967	−	0.993484i	$-0.536356\pi$
$317$	14.1666	−	10.2926i	0.795675	−	0.578091i	0.909642	+	0.415393i	$0.136356\pi$
$318$		0			0
$319$	35.3994	−	3.56598i	1.98199	−	0.199657i
$320$	41.1506			2.30039
$321$		0			0
$322$	3.16948	+	9.75467i	0.176628	+	0.543607i
$323$	−2.43462	+	7.49298i	−0.135466	+	0.416921i
$324$		0			0
$325$	−25.4196	−	18.4685i	−1.41003	−	1.02445i
$326$	10.5880	−	32.5864i	0.586413	−	1.80480i
$327$		0			0
$328$	−7.91608	+	5.75137i	−0.437092	+	0.317566i
$329$	−2.73030			−0.150526
$330$		0			0
$331$	−17.6231			−0.968652			−0.484326	−	0.874888i	$-0.660935\pi$
$331$	−17.6231			−0.968652			−0.484326	+	0.874888i	$0.660935\pi$
$332$	20.9012	−	15.1856i	1.14710	−	0.833417i
$333$		0			0
$334$	3.68178	−	11.3313i	0.201458	−	0.620023i
$335$	2.47863	+	1.80083i	0.135422	+	0.0983897i
$336$		0			0
$337$	0.494763	−	1.52272i	0.0269515	−	0.0829481i	−0.936676	−	0.350197i	$-0.886115\pi$
$337$	0.494763	−	1.52272i	0.0269515	−	0.0829481i	0.963628	+	0.267249i	$0.0861146\pi$
$338$	0.642727	+	1.97811i	0.0349598	+	0.107595i
$339$		0			0
$340$	−13.8965			−0.753641
$341$	−23.2856	−	13.5785i	−1.26098	−	0.735316i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.0382011	+	0.117571i	0.00205967	+	0.00633900i
$345$		0			0
$346$	22.8454	+	16.5981i	1.22817	+	0.892321i
$347$	−2.78676	−	2.02470i	−0.149601	−	0.108691i	0.510467	−	0.859897i	$-0.329473\pi$
$347$	−2.78676	−	2.02470i	−0.149601	−	0.108691i	−0.660068	+	0.751206i	$0.729473\pi$
$348$		0			0
$349$	1.04987	+	3.23117i	0.0561983	+	0.172961i	0.975216	−	0.221257i	$-0.0710158\pi$
$349$	1.04987	+	3.23117i	0.0561983	+	0.172961i	−0.919017	+	0.394217i	$0.871016\pi$
$350$	15.4318	−	11.2118i	0.824862	−	0.599297i
$351$		0			0
$352$	10.7308	+	24.3850i	0.571954	+	1.29972i
$353$	10.4083			0.553977			0.276989	−	0.960873i	$-0.410664\pi$
$353$	10.4083			0.553977			0.276989	+	0.960873i	$0.410664\pi$
$354$		0			0
$355$	−6.64076	−	20.4382i	−0.352455	−	1.08475i
$356$	6.68613	−	20.5778i	0.354364	−	1.09062i
$357$		0			0
$358$	6.48254	+	4.70984i	0.342613	+	0.248923i
$359$	7.10580	−	21.8694i	0.375030	−	1.15422i	−0.568429	−	0.822732i	$-0.692449\pi$
$359$	7.10580	−	21.8694i	0.375030	−	1.15422i	0.943459	−	0.331490i	$-0.107551\pi$
$360$		0			0
$361$	−6.16995	+	4.48273i	−0.324734	+	0.235933i
$362$	20.5951			1.08245
$363$		0			0
$364$	8.41057			0.440834
$365$	−7.51010	+	5.45640i	−0.393096	+	0.285601i
$366$		0			0
$367$	6.06776	−	18.6747i	0.316735	−	0.974809i	−0.658300	−	0.752756i	$-0.728724\pi$
$367$	6.06776	−	18.6747i	0.316735	−	0.974809i	0.975035	−	0.222053i	$-0.0712759\pi$
$368$	−11.6909	−	8.49395i	−0.609431	−	0.442778i
$369$		0			0
$370$	22.5762	−	69.4823i	1.17368	−	3.61221i
$371$	−0.863375	−	2.65719i	−0.0448242	−	0.137955i
$372$		0			0
$373$	−31.9047			−1.65196			−0.825981	−	0.563698i	$-0.809378\pi$
$373$	−31.9047			−1.65196			−0.825981	+	0.563698i	$0.809378\pi$
$374$	−4.29144	−	9.75197i	−0.221905	−	0.504262i
$375$		0			0
$376$	−1.98336	+	1.44099i	−0.102284	+	0.0743135i
$377$	11.4887	+	35.3587i	0.591700	+	1.82107i
$378$		0			0
$379$	1.39117	+	1.01074i	0.0714594	+	0.0519183i	0.622941	−	0.782268i	$-0.285937\pi$
$379$	1.39117	+	1.01074i	0.0714594	+	0.0519183i	−0.551482	+	0.834187i	$0.685937\pi$
$380$	−37.9951	−	27.6050i	−1.94911	−	1.41611i
$381$		0			0
$382$	−5.84479	−	17.9884i	−0.299045	−	0.920367i
$383$	−7.02258	+	5.10220i	−0.358837	+	0.260710i	−0.752567	−	0.658516i	$-0.771185\pi$
$383$	−7.02258	+	5.10220i	−0.358837	+	0.260710i	0.393730	+	0.919226i	$0.371185\pi$
$384$		0			0
$385$	10.7454	+	6.26595i	0.547636	+	0.319342i
$386$	12.3071			0.626414
$387$		0			0
$388$	6.06282	+	18.6594i	0.307793	+	0.947290i
$389$	−8.28220	+	25.4900i	−0.419924	+	1.29239i	0.487847	+	0.872929i	$0.337782\pi$
$389$	−8.28220	+	25.4900i	−0.419924	+	1.29239i	−0.907771	+	0.419465i	$0.862218\pi$
$390$		0			0
$391$	6.02160	+	4.37495i	0.304526	+	0.221251i
$392$	−0.277470	+	0.853964i	−0.0140143	+	0.0431317i
$393$		0			0
$394$	10.5458	−	7.66199i	0.531291	−	0.386005i
$395$	−42.8462			−2.15583
$396$		0			0
$397$	−17.8714			−0.896938			−0.448469	−	0.893798i	$-0.648031\pi$
$397$	−17.8714			−0.896938			−0.448469	+	0.893798i	$0.648031\pi$
$398$	−32.1086	+	23.3283i	−1.60946	+	1.16934i
$399$		0			0
$400$	−8.30471	+	25.5593i	−0.415236	+	1.27796i
$401$	23.3916	+	16.9950i	1.16812	+	0.848689i	0.990783	−	0.135462i	$-0.0432518\pi$
$401$	23.3916	+	16.9950i	1.16812	+	0.848689i	0.177337	+	0.984150i	$0.443252\pi$
$402$		0			0
$403$	8.70420	−	26.7888i	0.433587	−	1.33444i
$404$	−1.29133	−	3.97430i	−0.0642461	−	0.197729i
$405$		0			0
$406$	−22.5702			−1.12014
$407$	30.5523	−	3.07770i	1.51442	−	0.152556i
$408$		0			0
$409$	−22.3760	+	16.2571i	−1.10642	+	0.803864i	−0.982097	−	0.188378i	$-0.939677\pi$
$409$	−22.3760	+	16.2571i	−1.10642	+	0.803864i	−0.124327	+	0.992241i	$0.539677\pi$
$410$	−26.5724	−	81.7813i	−1.31232	−	4.03889i
$411$		0			0
$412$	5.28908	+	3.84274i	0.260574	+	0.189318i
$413$	3.91956	+	2.84773i	0.192869	+	0.140128i
$414$		0			0
$415$	12.3382	+	37.9731i	0.605659	+	1.86403i
$416$	−22.5227	+	16.3637i	−1.10426	+	0.802295i
$417$		0			0
$418$	7.63863	−	35.1882i	0.373618	−	1.72111i
$419$	−4.51003			−0.220330			−0.110165	−	0.993913i	$-0.535138\pi$
$419$	−4.51003			−0.220330			−0.110165	+	0.993913i	$0.535138\pi$
$420$		0			0
$421$	11.1075	+	34.1853i	0.541345	+	1.66609i	0.729526	+	0.683953i	$0.239741\pi$
$421$	11.1075	+	34.1853i	0.541345	+	1.66609i	−0.188181	+	0.982134i	$0.560259\pi$
$422$	−0.416225	+	1.28101i	−0.0202615	+	0.0623585i
$423$		0			0
$424$	−2.02959	−	1.47458i	−0.0985655	−	0.0716120i
$425$	4.27748	−	13.1647i	0.207488	−	0.638583i
$426$		0			0
$427$	0.240947	−	0.175058i	0.0116602	−	0.00847165i
$428$	−12.0851			−0.584158
$429$		0			0
$430$	−1.08640			−0.0523907
$431$	17.9771	−	13.0611i	0.865927	−	0.629133i	−0.0635640	−	0.997978i	$-0.520247\pi$
$431$	17.9771	−	13.0611i	0.865927	−	0.629133i	0.929491	+	0.368845i	$0.120247\pi$
$432$		0			0
$433$	7.87661	−	24.2417i	0.378526	−	1.16498i	−0.562544	−	0.826768i	$-0.690177\pi$
$433$	7.87661	−	24.2417i	0.378526	−	1.16498i	0.941069	−	0.338214i	$-0.109823\pi$
$434$	13.8341	+	10.0510i	0.664056	+	0.482465i
$435$		0			0
$436$	8.40360	−	25.8636i	0.402460	−	1.23864i
$437$	7.77324	+	23.9236i	0.371845	+	1.14442i
$438$		0			0
$439$	11.1407			0.531715			0.265857	−	0.964012i	$-0.414345\pi$
$439$	11.1407			0.531715			0.265857	+	0.964012i	$0.414345\pi$
$440$	11.1128	−	1.11945i	0.529780	−	0.0533676i
$441$		0			0
$442$	9.00720	−	6.54412i	0.428429	−	0.311272i
$443$	4.28027	+	13.1733i	0.203362	+	0.625883i	0.999777	+	0.0211325i	$0.00672717\pi$
$443$	4.28027	+	13.1733i	0.203362	+	0.625883i	−0.796415	+	0.604751i	$0.793273\pi$
$444$		0			0
$445$	27.0525	+	19.6548i	1.28241	+	0.931726i
$446$	−28.4470	−	20.6679i	−1.34700	−	0.978655i
$447$		0			0
$448$	−3.39058	−	10.4351i	−0.160190	−	0.493013i
$449$	−8.64664	+	6.28215i	−0.408060	+	0.296473i	−0.772816	−	0.634630i	$-0.781152\pi$
$449$	−8.64664	+	6.28215i	−0.408060	+	0.296473i	0.364756	+	0.931103i	$0.381152\pi$
$450$		0			0
$451$	26.9633	−	24.0676i	1.26965	−	1.13330i
$452$	39.8624			1.87497
$453$		0			0
$454$	−6.06369	−	18.6621i	−0.284583	−	0.875857i
$455$	−4.01666	+	12.3620i	−0.188304	+	0.579540i
$456$		0			0
$457$	−25.3852	−	18.4434i	−1.18747	−	0.862746i	−0.194473	−	0.980908i	$-0.562300\pi$
$457$	−25.3852	−	18.4434i	−1.18747	−	0.862746i	−0.992994	+	0.118162i	$0.962300\pi$
$458$	−13.8951	+	42.7649i	−0.649278	+	1.99827i
$459$		0			0
$460$	−35.8950	+	26.0792i	−1.67361	+	1.21595i
$461$	41.1844			1.91815			0.959075	−	0.283151i	$-0.0913797\pi$
$461$	41.1844			1.91815			0.959075	+	0.283151i	$0.0913797\pi$
$462$		0			0
$463$	35.6274			1.65575			0.827874	−	0.560915i	$-0.189550\pi$
$463$	35.6274			1.65575			0.827874	+	0.560915i	$0.189550\pi$
$464$	25.7263	−	18.6913i	1.19432	−	0.867721i
$465$		0			0
$466$	11.1285	−	34.2501i	0.515520	−	1.58661i
$467$	−5.22581	−	3.79677i	−0.241821	−	0.175694i	0.460273	−	0.887777i	$-0.347752\pi$
$467$	−5.22581	−	3.79677i	−0.241821	−	0.175694i	−0.702094	+	0.712084i	$0.747752\pi$
$468$		0			0
$469$	0.252436	−	0.776917i	0.0116564	−	0.0358747i
$470$	−6.65764	−	20.4901i	−0.307094	−	0.945139i
$471$		0			0
$472$	4.35024			0.200236
$473$	−0.183920	−	0.417944i	−0.00845665	−	0.0192171i
$474$		0			0
$475$	37.8468	−	27.4973i	1.73653	−	1.26166i
$476$	1.14499	+	3.52392i	0.0524805	+	0.161518i
$477$		0			0
$478$	5.73704	+	4.16820i	0.262406	+	0.190649i
$479$	5.50379	+	3.99874i	0.251475	+	0.182707i	0.706380	−	0.707833i	$-0.250327\pi$
$479$	5.50379	+	3.99874i	0.251475	+	0.182707i	−0.454905	+	0.890540i	$0.650327\pi$
$480$		0			0
$481$	9.91561	+	30.5171i	0.452113	+	1.39146i
$482$	9.83139	−	7.14293i	0.447808	−	0.325351i
$483$		0			0
$484$	13.1468	+	23.2326i	0.597584	+	1.05603i
$485$	−30.3214			−1.37682
$486$		0			0
$487$	8.25829	+	25.4164i	0.374219	+	1.15173i	0.944004	+	0.329933i	$0.107026\pi$
$487$	8.25829	+	25.4164i	0.374219	+	1.15173i	−0.569786	+	0.821793i	$0.692974\pi$
$488$	0.0826378	−	0.254333i	0.00374084	−	0.0115131i
$489$		0			0
$490$	−6.38390	−	4.63817i	−0.288395	−	0.209531i
$491$	−1.88271	+	5.79438i	−0.0849654	+	0.261497i	−0.984509	−	0.175335i	$-0.943899\pi$
$491$	−1.88271	+	5.79438i	−0.0849654	+	0.261497i	0.899544	+	0.436831i	$0.143899\pi$
$492$		0			0
$493$	−13.2508	+	9.62726i	−0.596785	+	0.433590i
$494$	37.6268			1.69291
$495$		0			0
$496$	−24.0922			−1.08177
$497$	−4.63563	+	3.36798i	−0.207936	+	0.151075i
$498$		0			0
$499$	0.462142	−	1.42233i	0.0206883	−	0.0636721i	−0.940179	−	0.340680i	$-0.889343\pi$
$499$	0.462142	−	1.42233i	0.0206883	−	0.0636721i	0.960868	+	0.277008i	$0.0893428\pi$
$500$	29.9388	+	21.7518i	1.33890	+	0.972771i
$501$		0			0
$502$	−7.64699	+	23.5350i	−0.341302	+	1.05042i
$503$	4.44469	+	13.6793i	0.198179	+	0.609932i	0.999925	+	0.0122669i	$0.00390477\pi$
$503$	4.44469	+	13.6793i	0.198179	+	0.609932i	−0.801746	+	0.597665i	$0.796095\pi$
$504$		0			0
$505$	6.45820			0.287386
$506$	−29.3862	−	17.1360i	−1.30638	−	0.761786i
$507$		0			0
$508$	38.4919	−	27.9660i	1.70780	−	1.24079i
$509$	−0.860293	−	2.64771i	−0.0381318	−	0.117358i	0.930179	−	0.367107i	$-0.119652\pi$
$509$	−0.860293	−	2.64771i	−0.0381318	−	0.117358i	−0.968310	+	0.249749i	$0.919652\pi$
$510$		0			0
$511$	2.00245	+	1.45486i	0.0885830	+	0.0643593i
$512$	23.5709	+	17.1253i	1.04170	+	0.756837i
$513$		0			0
$514$	9.27532	+	28.5465i	0.409117	+	1.25913i
$515$	−8.17404	+	5.93879i	−0.360191	+	0.261694i
$516$		0			0
$517$	6.75558	−	6.03008i	0.297110	−	0.265203i
$518$	−19.4797			−0.855890
$519$		0			0
$520$	3.60660	+	11.1000i	0.158160	+	0.486766i
$521$	12.5241	−	38.5453i	0.548691	−	1.68870i	−0.163356	−	0.986567i	$-0.552232\pi$
$521$	12.5241	−	38.5453i	0.548691	−	1.68870i	0.712047	−	0.702131i	$-0.247768\pi$
$522$		0			0
$523$	−0.724294	−	0.526231i	−0.0316712	−	0.0230105i	0.571837	−	0.820367i	$-0.306231\pi$
$523$	−0.724294	−	0.526231i	−0.0316712	−	0.0230105i	−0.603508	+	0.797357i	$0.706231\pi$
$524$	−10.0232	+	30.8483i	−0.437867	+	1.34762i
$525$		0			0
$526$	−8.26033	+	6.00148i	−0.360168	+	0.261677i
$527$	12.4091			0.540549
$528$		0			0
$529$	0.764354			0.0332328
$530$	17.8362	−	12.9588i	0.774756	−	0.562893i
$531$		0			0
$532$	−3.86961	+	11.9094i	−0.167769	+	0.516339i
$533$	30.5545	+	22.1991i	1.32346	+	0.961551i
$534$		0			0
$535$	5.77154	−	17.7630i	0.249525	−	0.767960i
$536$	−0.226665	−	0.697602i	−0.00979042	−	0.0301318i
$537$		0			0
$538$	13.3701			0.576426
$539$	0.703583	−	3.24114i	0.0303055	−	0.139606i
$540$		0			0
$541$	2.31464	−	1.68169i	0.0995144	−	0.0723014i	−0.536915	−	0.843636i	$-0.680411\pi$
$541$	2.31464	−	1.68169i	0.0995144	−	0.0723014i	0.636430	+	0.771335i	$0.280411\pi$
$542$	9.89260	+	30.4463i	0.424924	+	1.30778i
$543$		0			0
$544$	−9.92233	−	7.20899i	−0.425416	−	0.309083i
$545$	34.0015	+	24.7035i	1.45646	+	1.05818i
$546$		0			0
$547$	8.25667	+	25.4114i	0.353030	+	1.08651i	0.957143	+	0.289615i	$0.0935273\pi$
$547$	8.25667	+	25.4114i	0.353030	+	1.08651i	−0.604114	+	0.796898i	$0.706473\pi$
$548$	−10.3658	+	7.53120i	−0.442806	+	0.321717i
$549$		0			0
$550$	−13.4206	+	61.8237i	−0.572258	+	2.63617i
$551$	−55.3540			−2.35816
$552$		0			0
$553$	3.53029	+	10.8651i	0.150123	+	0.462031i
$554$	0.246606	−	0.758976i	0.0104773	−	0.0322458i
$555$		0			0
$556$	41.9668	+	30.4907i	1.77979	+	1.29309i
$557$	−3.53536	+	10.8807i	−0.149798	+	0.461031i	−0.997597	−	0.0692874i	$-0.977927\pi$
$557$	−3.53536	+	10.8807i	−0.149798	+	0.461031i	0.847799	+	0.530318i	$0.177927\pi$
$558$		0			0
$559$	0.386025	−	0.280464i	0.0163271	−	0.0118624i
$560$	11.1176			0.469806
$561$		0			0
$562$	−10.6114			−0.447615
$563$	−9.88153	+	7.17935i	−0.416457	+	0.302574i	−0.776211	−	0.630474i	$-0.782861\pi$
$563$	−9.88153	+	7.17935i	−0.416457	+	0.302574i	0.359754	+	0.933047i	$0.382861\pi$
$564$		0			0
$565$	−19.0372	+	58.5904i	−0.800900	+	2.46492i
$566$	−54.6991	−	39.7412i	−2.29917	−	1.67045i
$567$		0			0
$568$	−1.58989	+	4.89317i	−0.0667102	+	0.205313i
$569$	6.29680	+	19.3796i	0.263976	+	0.812433i	0.991928	+	0.126805i	$0.0404723\pi$
$569$	6.29680	+	19.3796i	0.263976	+	0.812433i	−0.727952	+	0.685628i	$0.759528\pi$
$570$		0			0
$571$	−20.3621			−0.852129			−0.426065	−	0.904693i	$-0.640100\pi$
$571$	−20.3621			−0.852129			−0.426065	+	0.904693i	$0.640100\pi$
$572$	−20.8103	+	18.5754i	−0.870123	+	0.776677i
$573$		0			0
$574$	−18.5490	+	13.4766i	−0.774220	+	0.562504i
$575$	−13.6571	−	42.0323i	−0.569542	−	1.75287i
$576$		0			0
$577$	−4.89034	−	3.55304i	−0.203588	−	0.147915i	0.481320	−	0.876545i	$-0.340157\pi$
$577$	−4.89034	−	3.55304i	−0.203588	−	0.147915i	−0.684908	+	0.728630i	$0.740157\pi$
$578$	−24.9686	−	18.1408i	−1.03856	−	0.754557i
$579$		0			0
$580$	−30.1709	−	92.8564i	−1.25278	−	3.85565i
$581$	8.61276	−	6.25754i	0.357318	−	0.259606i
$582$		0			0
$583$	8.00488	+	4.66787i	0.331528	+	0.193324i
$584$	2.22247			0.0919665
$585$		0			0
$586$	−17.4405	−	53.6763i	−0.720459	−	2.21735i
$587$	11.2920	−	34.7533i	0.466072	−	1.43442i	−0.391557	−	0.920154i	$-0.628064\pi$
$587$	11.2920	−	34.7533i	0.466072	−	1.43442i	0.857629	−	0.514268i	$-0.171936\pi$
$588$		0			0
$589$	33.9284	+	24.6504i	1.39800	+	1.01570i
$590$	−11.8138	+	36.3592i	−0.486368	+	1.49689i
$591$		0			0
$592$	22.2037	−	16.1319i	0.912566	−	0.663018i
$593$	15.6666			0.643349			0.321675	−	0.946850i	$-0.395754\pi$
$593$	15.6666			0.643349			0.321675	+	0.946850i	$0.395754\pi$
$594$		0			0
$595$	−5.72633			−0.234757
$596$	−21.5895	+	15.6857i	−0.884340	+	0.642511i
$597$		0			0
$598$	10.9847	−	33.8073i	0.449196	−	1.38248i
$599$	−22.9983	−	16.7092i	−0.939683	−	0.682720i	0.00866125	−	0.999962i	$-0.497243\pi$
$599$	−22.9983	−	16.7092i	−0.939683	−	0.682720i	−0.948344	+	0.317243i	$0.897243\pi$
$600$		0			0
$601$	−3.80479	+	11.7099i	−0.155201	+	0.477658i	−0.998181	−	0.0602858i	$-0.980799\pi$
$601$	−3.80479	+	11.7099i	−0.155201	+	0.477658i	0.842981	+	0.537944i	$0.180799\pi$
$602$	0.0895130	+	0.275493i	0.00364828	+	0.0112282i
$603$		0			0
$604$	−8.59487			−0.349720
$605$	−40.4262	+	8.22820i	−1.64356	+	0.334524i
$606$		0			0
$607$	27.1485	−	19.7245i	1.10192	−	0.800594i	0.120550	−	0.992707i	$-0.461534\pi$
$607$	27.1485	−	19.7245i	1.10192	−	0.800594i	0.981373	+	0.192113i	$0.0615342\pi$
$608$	−12.8087	−	39.4210i	−0.519460	−	1.59873i
$609$		0			0
$610$	1.90129	+	1.38137i	0.0769811	+	0.0559301i
$611$	7.65535	+	5.56194i	0.309702	+	0.225012i
$612$		0			0
$613$	−1.66265	−	5.11712i	−0.0671540	−	0.206679i	0.911849	−	0.410527i	$-0.134655\pi$
$613$	−1.66265	−	5.11712i	−0.0671540	−	0.206679i	−0.979003	+	0.203848i	$0.934655\pi$
$614$	−9.79083	+	7.11346i	−0.395126	+	0.287076i
$615$		0			0
$616$	−1.19950	−	2.72578i	−0.0483293	−	0.109825i
$617$	−29.3058			−1.17981			−0.589904	−	0.807473i	$-0.700834\pi$
$617$	−29.3058			−1.17981			−0.589904	+	0.807473i	$0.700834\pi$
$618$		0			0
$619$	1.03779	+	3.19399i	0.0417123	+	0.128377i	0.969744	−	0.244124i	$-0.0785003\pi$
$619$	1.03779	+	3.19399i	0.0417123	+	0.128377i	−0.928032	+	0.372501i	$0.878500\pi$
$620$	−22.8583	+	70.3506i	−0.918012	+	2.82535i
$621$		0			0
$622$	30.4358	+	22.1129i	1.22036	+	0.886647i
$623$	2.75516	−	8.47951i	0.110383	−	0.339724i
$624$		0			0
$625$	−9.59653	+	6.97229i	−0.383861	+	0.278891i
$626$	−41.0289			−1.63984
$627$		0			0
$628$	30.9633			1.23557
$629$	−11.4364	+	8.30902i	−0.455998	+	0.331302i
$630$		0			0
$631$	−9.62320	+	29.6172i	−0.383093	+	1.17904i	0.554761	+	0.832010i	$0.312810\pi$
$631$	−9.62320	+	29.6172i	−0.383093	+	1.17904i	−0.937854	+	0.347030i	$0.887190\pi$
$632$	8.29886	+	6.02948i	0.330111	+	0.239840i
$633$		0			0
$634$	11.3850	−	35.0394i	0.452156	−	1.39159i
$635$	22.7222	+	69.9318i	0.901704	+	2.77516i
$636$		0			0
$637$	3.46575			0.137318
$638$	55.8456	−	49.8481i	2.21095	−	1.97351i
$639$		0			0
$640$	21.2992	−	15.4748i	0.841926	−	0.611695i
$641$	6.57985	+	20.2507i	0.259888	+	0.799855i	0.992827	+	0.119560i	$0.0381483\pi$
$641$	6.57985	+	20.2507i	0.259888	+	0.799855i	−0.732939	+	0.680295i	$0.761852\pi$
$642$		0			0
$643$	−18.4098	−	13.3755i	−0.726011	−	0.527478i	0.162288	−	0.986743i	$-0.448113\pi$
$643$	−18.4098	−	13.3755i	−0.726011	−	0.527478i	−0.888299	+	0.459265i	$0.848113\pi$
$644$	9.57081	+	6.95360i	0.377143	+	0.274010i
$645$		0			0
$646$	5.12241	+	15.7651i	0.201538	+	0.620271i
$647$	−34.8543	+	25.3232i	−1.37027	+	0.995556i	−0.372549	+	0.928013i	$0.621516\pi$
$647$	−34.8543	+	25.3232i	−1.37027	+	0.995556i	−0.997716	+	0.0675433i	$0.978484\pi$
$648$		0			0
$649$	−15.9876	+	1.61052i	−0.627569	+	0.0632185i
$650$	−66.1082			−2.59298
$651$		0			0
$652$	−12.2123	−	37.5856i	−0.478270	−	1.47197i
$653$	11.0514	−	34.0126i	0.432473	−	1.33102i	−0.463181	−	0.886264i	$-0.653292\pi$
$653$	11.0514	−	34.0126i	0.432473	−	1.33102i	0.895654	−	0.444752i	$-0.146708\pi$
$654$		0			0
$655$	−40.5546	−	29.4646i	−1.58460	−	1.15128i
$656$	9.98228	−	30.7223i	0.389743	−	1.19950i
$657$		0			0
$658$	−4.64741	+	3.37654i	−0.181175	+	0.131631i
$659$	16.6988			0.650495			0.325247	−	0.945629i	$-0.394552\pi$
$659$	16.6988			0.650495			0.325247	+	0.945629i	$0.394552\pi$
$660$		0			0
$661$	36.5422			1.42133			0.710664	−	0.703532i	$-0.248395\pi$
$661$	36.5422			1.42133			0.710664	+	0.703532i	$0.248395\pi$
$662$	−29.9973	+	21.7943i	−1.16588	+	0.847061i
$663$		0			0
$664$	2.95393	−	9.09126i	0.114635	−	0.352809i
$665$	−15.6567	−	11.3752i	−0.607139	−	0.441113i
$666$		0			0
$667$	−16.1599	+	49.7350i	−0.625713	+	1.92575i
$668$	−4.24661	−	13.0697i	−0.164306	−	0.505682i
$669$		0			0
$670$	6.44609			0.249034
$671$	−0.209546	+	0.965297i	−0.00808942	+	0.0372649i
$672$		0			0
$673$	−23.1936	+	16.8512i	−0.894049	+	0.649564i	−0.936930	−	0.349516i	$-0.886346\pi$
$673$	−23.1936	+	16.8512i	−0.894049	+	0.649564i	0.0428818	+	0.999080i	$0.486346\pi$
$674$	−1.04098	−	3.20379i	−0.0400969	−	0.123405i
$675$		0			0
$676$	1.94083	+	1.41009i	0.0746472	+	0.0542343i
$677$	−8.88350	−	6.45424i	−0.341421	−	0.248057i	0.403840	−	0.914829i	$-0.367675\pi$
$677$	−8.88350	−	6.45424i	−0.341421	−	0.248057i	−0.745261	+	0.666773i	$0.767675\pi$
$678$		0			0
$679$	2.49831	+	7.68902i	0.0958764	+	0.295077i
$680$	−4.15975	+	3.02223i	−0.159519	+	0.115897i
$681$		0			0
$682$	−56.4282	+	5.68432i	−2.16075	+	0.217664i
$683$	25.3941			0.971679			0.485840	−	0.874048i	$-0.338514\pi$
$683$	25.3941			0.971679			0.485840	+	0.874048i	$0.338514\pi$
$684$		0			0
$685$	−6.11906	−	18.8325i	−0.233797	−	0.719554i
$686$	−0.650168	+	2.00101i	−0.0248235	+	0.0763990i
$687$		0			0
$688$	−0.330176	−	0.239887i	−0.0125879	−	0.00914562i
$689$	−2.99224	+	9.20918i	−0.113995	+	0.350842i
$690$		0			0
$691$	21.5170	−	15.6330i	0.818545	−	0.594708i	−0.0977502	−	0.995211i	$-0.531165\pi$
$691$	21.5170	−	15.6330i	0.818545	−	0.594708i	0.916295	+	0.400503i	$0.131165\pi$
$692$	32.5706			1.23815
$693$		0			0
$694$	−7.24744			−0.275109
$695$	−64.8579	+	47.1220i	−2.46020	+	1.78744i
$696$		0			0
$697$	−5.14154	+	15.8240i	−0.194750	+	0.599378i
$698$	5.78302	+	4.20161i	0.218890	+	0.159033i
$699$		0			0
$700$	6.79868	−	20.9242i	0.256966	−	0.790860i
$701$	−13.9546	−	42.9477i	−0.527057	−	1.62211i	−0.760213	−	0.649674i	$-0.774905\pi$
$701$	−13.9546	−	42.9477i	−0.527057	−	1.62211i	0.233156	−	0.972439i	$-0.425095\pi$
$702$		0			0
$703$	−47.7745			−1.80185
$704$	31.4361	+	18.3313i	1.18479	+	0.690887i
$705$		0			0
$706$	17.7166	−	12.8719i	0.666773	−	0.484439i
$707$	−0.532120	−	1.63770i	−0.0200124	−	0.0615919i
$708$		0			0
$709$	−34.5641	−	25.1123i	−1.29808	−	0.943111i	−0.298146	−	0.954520i	$-0.596368\pi$
$709$	−34.5641	−	25.1123i	−1.29808	−	0.943111i	−0.999935	+	0.0114097i	$0.996368\pi$
$710$	−36.5794	−	26.5765i	−1.37280	−	0.997398i
$711$		0			0
$712$	−2.47389	−	7.61384i	−0.0927128	−	0.285341i
$713$	32.0531	−	23.2879i	1.20040	−	0.872139i
$714$		0			0
$715$	−17.3640	−	39.4584i	−0.649378	−	1.47566i
$716$	9.24214			0.345395
$717$		0			0
$718$	−14.9505	−	46.0130i	−0.557948	−	1.71719i
$719$	−4.77125	+	14.6844i	−0.177938	+	0.547636i	−0.999755	−	0.0221144i	$-0.992960\pi$
$719$	−4.77125	+	14.6844i	−0.177938	+	0.547636i	0.821818	+	0.569751i	$0.192960\pi$
$720$		0			0
$721$	2.17947	+	1.58348i	0.0811679	+	0.0589719i
$722$	−4.95849	+	15.2607i	−0.184536	+	0.567943i
$723$		0			0
$724$	19.2179	−	13.9626i	0.714227	−	0.518917i
$725$	97.2539			3.61192
$726$		0			0
$727$	14.8932			0.552357			0.276178	−	0.961106i	$-0.410932\pi$
$727$	14.8932			0.552357			0.276178	+	0.961106i	$0.410932\pi$
$728$	2.51761	−	1.82915i	0.0933088	−	0.0677928i
$729$		0			0
$730$	−6.03550	+	18.5754i	−0.223384	+	0.687505i
$731$	0.170063	+	0.123558i	0.00629001	+	0.00456996i
$732$		0			0
$733$	−2.28260	+	7.02511i	−0.0843096	+	0.259478i	−0.984321	−	0.176389i	$-0.943558\pi$
$733$	−2.28260	+	7.02511i	−0.0843096	+	0.259478i	0.900011	+	0.435867i	$0.143558\pi$
$734$	−12.7665	−	39.2913i	−0.471220	−	1.45027i
$735$		0			0
$736$	−39.1586			−1.44341
$737$	1.09128	+	2.47985i	0.0401979	+	0.0913466i
$738$		0			0
$739$	−28.1984	+	20.4874i	−1.03730	+	0.753640i	−0.969756	−	0.244077i	$-0.921515\pi$
$739$	−28.1984	+	20.4874i	−1.03730	+	0.753640i	−0.0675401	+	0.997717i	$0.521515\pi$
$740$	−26.0396	−	80.1417i	−0.957235	−	2.94607i
$741$		0			0
$742$	−4.75574	−	3.45525i	−0.174589	−	0.126846i
$743$	2.69669	+	1.95926i	0.0989321	+	0.0718783i	0.636152	−	0.771564i	$-0.280525\pi$
$743$	2.69669	+	1.95926i	0.0989321	+	0.0718783i	−0.537219	+	0.843442i	$0.680525\pi$
$744$		0			0
$745$	−12.7445	−	39.2237i	−0.466924	−	1.43704i
$746$	−54.3069	+	39.4563i	−1.98832	+	1.44460i
$747$		0			0
$748$	−10.6159	−	6.19044i	−0.388156	−	0.226345i
$749$	−4.97994			−0.181963
$750$		0			0
$751$	15.8399	+	48.7501i	0.578005	+	1.77892i	0.625711	+	0.780055i	$0.284809\pi$
$751$	15.8399	+	48.7501i	0.578005	+	1.77892i	−0.0477057	+	0.998861i	$0.515191\pi$
$752$	2.50104	−	7.69740i	0.0912034	−	0.280695i
$753$		0			0
$754$	63.2836	+	45.9782i	2.30465	+	1.67443i
$755$	4.10467	−	12.6329i	0.149384	−	0.459758i
$756$		0			0
$757$	−3.29614	+	2.39479i	−0.119800	+	0.0870401i	−0.646072	−	0.763276i	$-0.723589\pi$
$757$	−3.29614	+	2.39479i	−0.119800	+	0.0870401i	0.526272	+	0.850316i	$0.323589\pi$
$758$	3.61797			0.131411
$759$		0			0
$760$	−17.3770			−0.630330
$761$	−4.86330	+	3.53339i	−0.176294	+	0.128085i	−0.672433	−	0.740158i	$-0.734751\pi$
$761$	−4.86330	+	3.53339i	−0.176294	+	0.128085i	0.496139	+	0.868243i	$0.334751\pi$
$762$		0			0
$763$	3.46288	−	10.6577i	0.125365	−	0.385833i
$764$	−17.6493	−	12.8230i	−0.638531	−	0.463920i
$765$		0			0
$766$	−5.64371	+	17.3696i	−0.203916	+	0.627588i
$767$	−5.18872	−	15.9692i	−0.187354	−	0.576616i
$768$		0			0
$769$	43.2310			1.55895			0.779474	−	0.626434i	$-0.215486\pi$
$769$	43.2310			1.55895			0.779474	+	0.626434i	$0.215486\pi$
$770$	26.0395	−	2.62310i	0.938397	−	0.0945299i
$771$		0			0
$772$	11.4841	−	8.34369i	0.413322	−	0.300296i
$773$	−2.98056	−	9.17322i	−0.107203	−	0.329938i	0.883038	−	0.469302i	$-0.155494\pi$
$773$	−2.98056	−	9.17322i	−0.107203	−	0.329938i	−0.990241	+	0.139364i	$0.955494\pi$
$774$		0			0
$775$	−59.6102	−	43.3094i	−2.14126	−	1.55572i
$776$	5.87293	+	4.26694i	0.210826	+	0.153174i
$777$		0			0
$778$	17.4257	+	53.6307i	0.624740	+	1.92275i
$779$	−45.4919	+	33.0518i	−1.62992	+	1.18420i
$780$		0			0
$781$	4.03150	−	18.5716i	0.144258	−	0.664542i
$782$	15.6602			0.560008
$783$		0			0
$784$	−0.916031	−	2.81925i	−0.0327154	−	0.100688i
$785$	−14.7872	+	45.5103i	−0.527778	+	1.62433i
$786$		0			0
$787$	19.5129	+	14.1769i	0.695558	+	0.505353i	0.878483	−	0.477774i	$-0.158556\pi$
$787$	19.5129	+	14.1769i	0.695558	+	0.505353i	−0.182924	+	0.983127i	$0.558556\pi$
$788$	4.64611	−	14.2993i	0.165511	−	0.509390i
$789$		0			0
$790$	−72.9312	+	52.9876i	−2.59478	+	1.88522i
$791$	16.4261			0.584046
$792$		0			0
$793$	−1.03219			−0.0366543
$794$	−30.4200	+	22.1014i	−1.07956	+	0.784349i
$795$		0			0
$796$	−14.1459	+	43.5366i	−0.501388	+	1.54311i
$797$	34.3079	+	24.9262i	1.21525	+	0.882931i	0.995697	−	0.0926701i	$-0.0295402\pi$
$797$	34.3079	+	24.9262i	1.21525	+	0.882931i	0.219553	+	0.975601i	$0.429540\pi$
$798$		0			0
$799$	−1.28820	+	3.96468i	−0.0455733	+	0.140260i
$800$	22.5041	+	69.2604i	0.795639	+	2.44873i
$801$		0			0
$802$	60.8338			2.14812
$803$	−8.16783	+	0.822790i	−0.288237	+	0.0290356i
$804$		0			0
$805$	−14.7913	+	10.7465i	−0.521324	+	0.378764i
$806$	−18.3135	−	56.3633i	−0.645067	−	1.98531i
$807$		0			0
$808$	−1.25089	−	0.908821i	−0.0440060	−	0.0319722i
$809$	2.80108	+	2.03510i	0.0984806	+	0.0715503i	0.635936	−	0.771742i	$-0.280614\pi$
$809$	2.80108	+	2.03510i	0.0984806	+	0.0715503i	−0.537455	+	0.843292i	$0.680614\pi$
$810$		0			0
$811$	4.86848	+	14.9837i	0.170956	+	0.526147i	0.999426	−	0.0338861i	$-0.0107883\pi$
$811$	4.86848	+	14.9837i	0.170956	+	0.526147i	−0.828470	+	0.560033i	$0.810788\pi$
$812$	−21.0610	+	15.3017i	−0.739095	+	0.536984i
$813$		0			0
$814$	48.1987	−	43.0225i	1.68937	−	1.50794i
$815$	61.0762			2.13941
$816$		0			0
$817$	0.219533	+	0.675653i	0.00768049	+	0.0236381i
$818$	−17.9825	+	55.3446i	−0.628745	+	1.93508i
$819$		0			0
$820$	−80.2398	−	58.2976i	−2.80210	−	2.03584i
$821$	2.45096	−	7.54328i	0.0855391	−	0.263262i	−0.899134	−	0.437674i	$-0.855802\pi$
$821$	2.45096	−	7.54328i	0.0855391	−	0.263262i	0.984673	+	0.174412i	$0.0558024\pi$
$822$		0			0
$823$	−26.6492	+	19.3618i	−0.928932	+	0.674908i	−0.945731	−	0.324950i	$-0.894652\pi$
$823$	−26.6492	+	19.3618i	−0.928932	+	0.674908i	0.0167992	+	0.999859i	$0.494652\pi$
$824$	2.41895			0.0842682
$825$		0			0
$826$	10.1935			0.354677
$827$	−24.4141	+	17.7379i	−0.848962	+	0.616807i	−0.924860	−	0.380309i	$-0.875818\pi$
$827$	−24.4141	+	17.7379i	−0.848962	+	0.616807i	0.0758980	+	0.997116i	$0.475818\pi$
$828$		0			0
$829$	−6.73188	+	20.7186i	−0.233808	+	0.719587i	0.763469	+	0.645844i	$0.223494\pi$
$829$	−6.73188	+	20.7186i	−0.233808	+	0.719587i	−0.997277	+	0.0737429i	$0.976506\pi$
$830$	67.9627	+	49.3778i	2.35902	+	1.71393i
$831$		0			0
$832$	−11.7509	+	36.1656i	−0.407389	+	1.25382i
$833$	0.471817	+	1.45210i	0.0163475	+	0.0503124i
$834$		0			0
$835$	21.2381			0.734976
$836$	−16.7283	−	38.0139i	−0.578562	−	1.31474i
$837$		0			0
$838$	−7.67681	+	5.57753i	−0.265191	+	0.192672i
$839$	−4.17093	−	12.8368i	−0.143996	−	0.443175i	0.852884	−	0.522100i	$-0.174851\pi$
$839$	−4.17093	−	12.8368i	−0.143996	−	0.443175i	−0.996881	+	0.0789248i	$0.974851\pi$
$840$		0			0
$841$	−69.6370	−	50.5943i	−2.40128	−	1.74463i
$842$	61.1834	+	44.4523i	2.10852	+	1.53193i
$843$		0			0
$844$	0.480079	+	1.47753i	0.0165250	+	0.0508587i
$845$	−2.99946	+	2.17924i	−0.103185	+	0.0749681i
$846$		0			0
$847$	5.41743	+	9.57348i	0.186145	+	0.328949i
$848$	8.28218			0.284411
$849$		0			0
$850$	−8.99977	−	27.6984i	−0.308690	−	0.950049i
$851$	−13.9471	+	42.9249i	−0.478101	+	1.47145i
$852$		0			0
$853$	−18.2167	−	13.2352i	−0.623729	−	0.453165i	0.230493	−	0.973074i	$-0.425966\pi$
$853$	−18.2167	−	13.2352i	−0.623729	−	0.453165i	−0.854222	+	0.519909i	$0.825966\pi$
$854$	0.193637	−	0.595955i	0.00662613	−	0.0203931i
$855$		0			0
$856$	−3.61755	+	2.62831i	−0.123645	+	0.0898336i
$857$	12.2772			0.419383			0.209691	−	0.977768i	$-0.432754\pi$
$857$	12.2772			0.419383			0.209691	+	0.977768i	$0.432754\pi$
$858$		0			0
$859$	−46.4901			−1.58622			−0.793110	−	0.609078i	$-0.791540\pi$
$859$	−46.4901			−1.58622			−0.793110	+	0.609078i	$0.791540\pi$
$860$	−1.01375	+	0.736533i	−0.0345686	+	0.0251156i
$861$		0			0
$862$	14.4473	−	44.4643i	0.492078	−	1.51446i
$863$	−44.0606	−	32.0119i	−1.49984	−	1.08970i	−0.970445	−	0.241324i	$-0.922419\pi$
$863$	−44.0606	−	32.0119i	−1.49984	−	1.08970i	−0.529396	−	0.848375i	$-0.677581\pi$
$864$		0			0
$865$	−15.5548	+	47.8728i	−0.528879	+	1.62772i
$866$	−16.5723	−	51.0043i	−0.563149	−	1.73320i
$867$		0			0
$868$	19.7232			0.669448
$869$	−32.7315	−	19.0867i	−1.11034	−	0.647470i
$870$		0			0
$871$	−2.29047	+	1.66412i	−0.0776095	+	0.0563866i
$872$	−3.10936	−	9.56962i	−0.105296	−	0.324068i
$873$		0			0
$874$	42.8174	+	31.1087i	1.44832	+	1.05227i
$875$	12.3369	+	8.96329i	0.417064	+	0.303015i
$876$		0			0
$877$	−9.10275	−	28.0154i	−0.307378	−	0.946013i	−0.978779	−	0.204918i	$-0.934307\pi$
$877$	−9.10275	−	28.0154i	−0.307378	−	0.946013i	0.671401	−	0.741094i	$-0.265693\pi$
$878$	18.9632	−	13.7776i	0.639977	−	0.464971i
$879$		0			0
$880$	−27.5084	+	24.5542i	−0.927309	+	0.827722i
$881$	−29.9763			−1.00993			−0.504964	−	0.863141i	$-0.668494\pi$
$881$	−29.9763			−1.00993			−0.504964	+	0.863141i	$0.668494\pi$
$882$		0			0
$883$	9.34912	+	28.7736i	0.314623	+	0.968310i	0.975909	+	0.218176i	$0.0700108\pi$
$883$	9.34912	+	28.7736i	0.314623	+	0.968310i	−0.661286	+	0.750134i	$0.729989\pi$
$884$	3.96825	−	12.2130i	0.133467	−	0.410769i
$885$		0			0
$886$	23.5771	+	17.1297i	0.792087	+	0.575485i
$887$	14.6213	−	44.9998i	0.490936	−	1.51095i	−0.332259	−	0.943188i	$-0.607811\pi$
$887$	14.6213	−	44.9998i	0.490936	−	1.51095i	0.823195	−	0.567759i	$-0.192189\pi$
$888$		0			0
$889$	15.8614	−	11.5240i	0.531974	−	0.386502i
$890$	70.3546			2.35829
$891$		0			0
$892$	−40.5567			−1.35794
$893$	−11.3979	+	8.28105i	−0.381416	+	0.277115i
$894$		0			0
$895$	−4.41379	+	13.5842i	−0.147537	+	0.454071i
$896$	−5.67910	−	4.12610i	−0.189725	−	0.137843i
$897$		0			0
$898$	−6.94889	+	21.3865i	−0.231887	+	0.713676i
$899$	26.9416	+	82.9178i	0.898554	+	2.76546i
$900$		0			0
$901$	−4.26588			−0.142117
$902$	16.1316	−	74.3122i	0.537124	−	2.47433i
$903$		0			0
$904$	11.9323	−	8.66935i	0.396864	−	0.288338i
$905$	11.3446	+	34.9149i	0.377106	+	1.16061i
$906$		0			0
$907$	40.1660	+	29.1823i	1.33369	+	0.968982i	0.999651	+	0.0264221i	$0.00841141\pi$
$907$	40.1660	+	29.1823i	1.33369	+	0.968982i	0.334038	+	0.942560i	$0.391589\pi$
$908$	−18.3104	−	13.3033i	−0.607651	−	0.441484i
$909$		0			0
$910$	8.45100	+	26.0095i	0.280148	+	0.862207i
$911$	17.4325	−	12.6655i	0.577564	−	0.419625i	−0.260281	−	0.965533i	$-0.583815\pi$
$911$	17.4325	−	12.6655i	0.577564	−	0.419625i	0.837845	+	0.545908i	$0.183815\pi$
$912$		0			0
$913$	−7.49032	+	34.5050i	−0.247893	+	1.14195i
$914$	−66.0185			−2.18370
$915$		0			0
$916$	16.0268	+	49.3255i	0.529542	+	1.62976i
$917$	−4.13028	+	12.7117i	−0.136394	+	0.419777i
$918$		0			0
$919$	−35.7654	−	25.9851i	−1.17979	−	0.857169i	−0.187643	−	0.982237i	$-0.560085\pi$
$919$	−35.7654	−	25.9851i	−1.17979	−	0.857169i	−0.992148	+	0.125069i	$0.960085\pi$
$920$	−5.07298	+	15.6130i	−0.167251	+	0.514746i
$921$		0			0
$922$	70.1026	−	50.9325i	2.30871	−	1.67737i
$923$	19.8586			0.653654
$924$		0			0
$925$	83.9371			2.75983
$926$	60.6437	−	44.0602i	1.99287	−	1.44791i
$927$		0			0
$928$	26.6281	−	81.9527i	0.874109	−	2.69023i
$929$	−1.38218	−	1.00422i	−0.0453480	−	0.0329472i	0.564880	−	0.825173i	$-0.308922\pi$
$929$	−1.38218	−	1.00422i	−0.0453480	−	0.0329472i	−0.610228	+	0.792226i	$0.708922\pi$
$930$		0			0
$931$	−1.59455	+	4.90753i	−0.0522594	+	0.160838i
$932$	−12.8358	−	39.5045i	−0.420450	−	1.29401i
$933$		0			0
$934$	−13.5906			−0.444698
$935$	14.1687	−	12.6471i	0.463365	−	0.413603i
$936$		0			0
$937$	26.9982	−	19.6153i	0.881991	−	0.640804i	−0.0517861	−	0.998658i	$-0.516491\pi$
$937$	26.9982	−	19.6153i	0.881991	−	0.640804i	0.933778	+	0.357854i	$0.116491\pi$
$938$	−0.531122	−	1.63462i	−0.0173417	−	0.0533724i
$939$		0			0
$940$	−20.1039	−	14.6063i	−0.655717	−	0.476406i
$941$	17.9708	+	13.0566i	0.585832	+	0.425632i	0.840822	−	0.541312i	$-0.182072\pi$
$941$	17.9708	+	13.0566i	0.585832	+	0.425632i	−0.254990	+	0.966944i	$0.582072\pi$
$942$		0			0
$943$	16.4159	+	50.5230i	0.534576	+	1.64525i
$944$	−11.6189	+	8.44164i	−0.378164	+	0.274752i
$945$		0			0
$946$	−0.829930	−	0.483956i	−0.0269834	−	0.0157348i
$947$	16.6969			0.542578			0.271289	−	0.962498i	$-0.412550\pi$
$947$	16.6969			0.542578			0.271289	+	0.962498i	$0.412550\pi$
$948$		0			0
$949$	−2.65084	−	8.15844i	−0.0860498	−	0.264834i
$950$	30.4156	−	93.6097i	0.986813	−	3.03710i
$951$		0			0
$952$	1.10913	+	0.805830i	0.0359471	+	0.0261171i
$953$	−5.89802	+	18.1522i	−0.191056	+	0.588009i	0.808944	+	0.587885i	$0.200039\pi$
$953$	−5.89802	+	18.1522i	−0.191056	+	0.588009i	−1.00000		0.000123576i	$0.999961\pi$
$954$		0			0
$955$	27.2763	−	19.8174i	0.882640	−	0.641276i
$956$	8.17927			0.264537
$957$		0			0
$958$	14.3136			0.462450
$959$	−4.27145	+	3.10339i	−0.137932	+	0.100214i
$960$		0			0
$961$	10.8322	−	33.3381i	0.349426	−	1.07542i
$962$	54.6183	+	39.6825i	1.76096	+	1.27942i
$963$		0			0
$964$	4.33136	−	13.3306i	0.139504	−	0.429348i
$965$	6.77921	+	20.8643i	0.218230	+	0.671644i
$966$		0			0
$967$	36.9443			1.18805			0.594024	−	0.804447i	$-0.297538\pi$
$967$	36.9443			1.18805			0.594024	+	0.804447i	$0.297538\pi$
$968$	8.98803	+	4.09521i	0.288886	+	0.131625i
$969$		0			0
$970$	−51.6119	+	37.4983i	−1.65716	+	1.20400i
$971$	−9.67373	−	29.7727i	−0.310445	−	0.955451i	−0.977589	−	0.210522i	$-0.932484\pi$
$971$	−9.67373	−	29.7727i	−0.310445	−	0.955451i	0.667144	−	0.744929i	$-0.267516\pi$
$972$		0			0
$973$	17.2933	+	12.5643i	0.554398	+	0.402793i
$974$	45.4892	+	33.0499i	1.45757	+	1.05899i
$975$		0			0
$976$	0.272818	+	0.839649i	0.00873271	+	0.0268765i
$977$	36.1962	−	26.2981i	1.15802	−	0.841350i	0.168492	−	0.985703i	$-0.446110\pi$
$977$	36.1962	−	26.2981i	1.15802	−	0.841350i	0.989526	+	0.144353i	$0.0461101\pi$
$978$		0			0
$979$	11.9106	+	27.0659i	0.380664	+	0.865029i
$980$	−9.10149			−0.290737
$981$		0			0
$982$	3.96119	+	12.1913i	0.126407	+	0.389040i
$983$	17.6829	−	54.4225i	0.563998	−	1.73581i	−0.106913	−	0.994268i	$-0.534097\pi$
$983$	17.6829	−	54.4225i	0.563998	−	1.73581i	0.670910	−	0.741538i	$-0.265903\pi$
$984$		0			0
$985$	18.7985	+	13.6579i	0.598969	+	0.435176i
$986$	−10.6490	+	32.7743i	−0.339134	+	1.04375i
$987$		0			0
$988$	35.1107	−	25.5094i	1.11702	−	0.811564i
$989$	0.671156			0.0213415
$990$		0			0
$991$	−26.9663			−0.856614			−0.428307	−	0.903633i	$-0.640890\pi$
$991$	−26.9663			−0.856614			−0.428307	+	0.903633i	$0.640890\pi$
$992$	−52.8167	+	38.3736i	−1.67693	+	1.21836i
$993$		0			0
$994$	−3.72543	+	11.4657i	−0.118163	+	0.363670i
$995$	−57.2352	−	41.5838i	−1.81448	−	1.31829i
$996$		0			0
$997$	7.82755	−	24.0907i	0.247901	−	0.762961i	−0.747245	−	0.664549i	$-0.768624\pi$
$997$	7.82755	−	24.0907i	0.247901	−	0.762961i	0.995146	−	0.0984118i	$-0.0313762\pi$
$998$	−0.972341	−	2.99256i	−0.0307789	−	0.0947278i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.190.7	yes	32
3.2	odd	2	inner	693.2.m.k.190.2	✓	32
11.2	odd	10		7623.2.a.db.1.14		16
11.4	even	5	inner	693.2.m.k.631.7	yes	32
11.9	even	5		7623.2.a.dc.1.3		16
33.2	even	10		7623.2.a.db.1.3		16
33.20	odd	10		7623.2.a.dc.1.14		16
33.26	odd	10	inner	693.2.m.k.631.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.190.2	✓	32	3.2	odd	2	inner
693.2.m.k.190.7	yes	32	1.1	even	1	trivial
693.2.m.k.631.2	yes	32	33.26	odd	10	inner
693.2.m.k.631.7	yes	32	11.4	even	5	inner
7623.2.a.db.1.3		16	33.2	even	10
7623.2.a.db.1.14		16	11.2	odd	10
7623.2.a.dc.1.3		16	11.9	even	5
7623.2.a.dc.1.14		16	33.20	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70216 - 1.23669i) q^{2} +(0.749912 - 2.30799i) q^{4} +(3.03419 + 2.20447i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.277470 - 0.853964i) q^{8} +O(q^{10})\)	\(q+(1.70216 - 1.23669i) q^{2} +(0.749912 - 2.30799i) q^{4} +(3.03419 + 2.20447i) q^{5} +(0.309017 - 0.951057i) q^{7} +(-0.277470 - 0.853964i) q^{8} +7.89093 q^{10} +(1.33588 + 3.03569i) q^{11} +(-2.80385 + 2.03712i) q^{13} +(-0.650168 - 2.00101i) q^{14} +(2.39820 + 1.74239i) q^{16} +(-1.23523 - 0.897450i) q^{17} +(-1.59455 - 4.90753i) q^{19} +(7.36326 - 5.34972i) q^{20} +(6.02811 + 3.51516i) q^{22} -4.87487 q^{23} +(2.80154 + 8.62225i) q^{25} +(-2.25332 + 6.93501i) q^{26} +(-1.96329 - 1.42642i) q^{28} +(3.31493 - 10.2023i) q^{29} +(-6.57516 + 4.77714i) q^{31} +8.03275 q^{32} -3.21244 q^{34} +(3.03419 - 2.20447i) q^{35} +(2.86103 - 8.80533i) q^{37} +(-8.78330 - 6.38144i) q^{38} +(1.04064 - 3.20276i) q^{40} +(-3.36746 - 10.3640i) q^{41} -0.137677 q^{43} +(8.00814 - 0.806704i) q^{44} +(-8.29782 + 6.02872i) q^{46} +(-0.843708 - 2.59667i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(15.4318 + 11.2118i) q^{50} +(2.59901 + 7.99893i) q^{52} +(2.26034 - 1.64224i) q^{53} +(-2.63876 + 12.1558i) q^{55} -0.897910 q^{56} +(-6.97458 - 21.4656i) q^{58} +(-1.49714 + 4.60772i) q^{59} +(0.240947 + 0.175058i) q^{61} +(-5.28414 + 16.2629i) q^{62} +(8.87665 - 6.44926i) q^{64} -12.9982 q^{65} +0.816899 q^{67} +(-2.99762 + 2.17790i) q^{68} +(2.43843 - 7.50472i) q^{70} +(-4.63563 - 3.36798i) q^{71} +(-0.764866 + 2.35402i) q^{73} +(-6.01957 - 18.5263i) q^{74} -12.5223 q^{76} +(3.29992 - 0.332419i) q^{77} +(-9.24242 + 6.71501i) q^{79} +(3.43554 + 10.5735i) q^{80} +(-18.5490 - 13.4766i) q^{82} +(8.61276 + 6.25754i) q^{83} +(-1.76953 - 5.44606i) q^{85} +(-0.234348 + 0.170264i) q^{86} +(2.22170 - 1.98311i) q^{88} +8.91589 q^{89} +(1.07098 + 3.29613i) q^{91} +(-3.65572 + 11.2512i) q^{92} +(-4.64741 - 3.37654i) q^{94} +(5.98031 - 18.4055i) q^{95} +(-6.54067 + 4.75207i) q^{97} -2.10399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

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