LMFDB - Embedded newform 484.2.i.a.89.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(45,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([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("484.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.i (of order $11$, degree $10$, 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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			89.8
Character	$\chi$	$=$	484.89
Dual form			484.2.i.a.397.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.38825 q^{3} +(0.974029 + 2.13282i) q^{5} +(-1.64826 + 1.05927i) q^{7} -1.07277 q^{9} +(1.39726 + 3.00793i) q^{11} +(2.25948 + 0.663443i) q^{13} +(1.35219 + 2.96089i) q^{15} +(-0.722940 + 0.834317i) q^{17} +(1.82848 + 2.11018i) q^{19} +(-2.28819 + 1.47053i) q^{21} +(1.88355 + 1.21048i) q^{23} +(-0.325907 + 0.376117i) q^{25} -5.65401 q^{27} +(-6.49221 - 7.49241i) q^{29} +(8.08103 - 2.37280i) q^{31} +(1.93974 + 4.17576i) q^{33} +(-3.86469 - 2.48369i) q^{35} +(1.98865 - 0.583919i) q^{37} +(3.13672 + 0.921024i) q^{39} +(-0.281637 + 1.95883i) q^{41} +(1.69094 - 3.70265i) q^{43} +(-1.04490 - 2.28802i) q^{45} +(0.335781 + 2.33541i) q^{47} +(-1.31320 + 2.87551i) q^{49} +(-1.00362 + 1.15824i) q^{51} +(9.49972 - 6.10510i) q^{53} +(-5.05443 + 5.90992i) q^{55} +(2.53838 + 2.92945i) q^{57} +(0.257354 + 1.78994i) q^{59} +(-1.26332 - 8.78655i) q^{61} +(1.76820 - 1.13635i) q^{63} +(0.785790 + 5.46529i) q^{65} +(0.359515 - 2.50048i) q^{67} +(2.61483 + 1.68045i) q^{69} +(8.82298 + 10.1823i) q^{71} +(-5.47129 - 3.51619i) q^{73} +(-0.452440 + 0.522143i) q^{75} +(-5.48927 - 3.47778i) q^{77} +(-5.37517 - 11.7700i) q^{79} -4.63087 q^{81} +(-8.65111 + 5.55973i) q^{83} +(-2.48362 - 0.729255i) q^{85} +(-9.01280 - 10.4013i) q^{87} +(-0.0361963 + 0.0417727i) q^{89} +(-4.42698 + 1.29988i) q^{91} +(11.2185 - 3.29404i) q^{93} +(-2.71965 + 5.95520i) q^{95} +(3.93249 - 8.61096i) q^{97} +(-1.49893 - 3.22681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{3} + 2 q^{5} - 2 q^{7} + 112 q^{9} - 10 q^{11} - 29 q^{13} - 18 q^{15} - 6 q^{17} - 8 q^{19} - 2 q^{21} + 4 q^{23} - 17 q^{25} + 4 q^{27} - 28 q^{31} + q^{33} + 6 q^{35} - 31 q^{37} + 4 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) $ 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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			0
$2$		0			0
$3$	1.38825			0.801506			0.400753	−	0.916186i	$-0.368749\pi$
$3$	1.38825			0.801506			0.400753	+	0.916186i	$0.368749\pi$
$4$		0			0
$5$	0.974029	+	2.13282i	0.435599	+	0.953828i	0.992385	+	0.123173i	$0.0393069\pi$
$5$	0.974029	+	2.13282i	0.435599	+	0.953828i	−0.556786	+	0.830656i	$0.687966\pi$
$6$		0			0
$7$	−1.64826	+	1.05927i	−0.622984	+	0.400367i	−0.813706	−	0.581277i	$-0.802553\pi$
$7$	−1.64826	+	1.05927i	−0.622984	+	0.400367i	0.190722	+	0.981644i	$0.438917\pi$
$8$		0			0
$9$	−1.07277			−0.357589
$10$		0			0
$11$	1.39726	+	3.00793i	0.421290	+	0.906926i
$11$	1.39726	+	3.00793i	0.421290	+	0.906926i
$12$		0			0
$13$	2.25948	+	0.663443i	0.626667	+	0.184006i	0.579620	−	0.814887i	$-0.303201\pi$
$13$	2.25948	+	0.663443i	0.626667	+	0.184006i	0.0470468	+	0.998893i	$0.485019\pi$
$14$		0			0
$15$	1.35219	+	2.96089i	0.349135	+	0.764499i
$16$		0			0
$17$	−0.722940	+	0.834317i	−0.175339	+	0.202352i	−0.836616	−	0.547790i	$-0.815469\pi$
$17$	−0.722940	+	0.834317i	−0.175339	+	0.202352i	0.661277	+	0.750142i	$0.270015\pi$
$18$		0			0
$19$	1.82848	+	2.11018i	0.419482	+	0.484108i	0.925679	−	0.378310i	$-0.123495\pi$
$19$	1.82848	+	2.11018i	0.419482	+	0.484108i	−0.506197	+	0.862418i	$0.668949\pi$
$20$		0			0
$21$	−2.28819	+	1.47053i	−0.499325	+	0.320897i
$22$		0			0
$23$	1.88355	+	1.21048i	0.392747	+	0.252403i	0.722078	−	0.691811i	$-0.243187\pi$
$23$	1.88355	+	1.21048i	0.392747	+	0.252403i	−0.329332	+	0.944214i	$0.606823\pi$
$24$		0			0
$25$	−0.325907	+	0.376117i	−0.0651814	+	0.0752233i
$26$		0			0
$27$	−5.65401			−1.08812
$28$		0			0
$29$	−6.49221	−	7.49241i	−1.20557	−	1.39131i	−0.898125	−	0.439740i	$-0.855071\pi$
$29$	−6.49221	−	7.49241i	−1.20557	−	1.39131i	−0.307448	−	0.951565i	$-0.599475\pi$
$30$		0			0
$31$	8.08103	−	2.37280i	1.45139	−	0.426168i	0.541392	−	0.840770i	$-0.317897\pi$
$31$	8.08103	−	2.37280i	1.45139	−	0.426168i	0.910003	+	0.414602i	$0.136079\pi$
$32$		0			0
$33$	1.93974	+	4.17576i	0.337666	+	0.726906i
$34$		0			0
$35$	−3.86469	−	2.48369i	−0.653253	−	0.419820i
$36$		0			0
$37$	1.98865	−	0.583919i	0.326931	−	0.0959957i	−0.114148	−	0.993464i	$-0.536414\pi$
$37$	1.98865	−	0.583919i	0.326931	−	0.0959957i	0.441079	+	0.897468i	$0.354596\pi$
$38$		0			0
$39$	3.13672	+	0.921024i	0.502277	+	0.147482i
$40$		0			0
$41$	−0.281637	+	1.95883i	−0.0439843	+	0.305917i	0.955939	+	0.293564i	$0.0948414\pi$
$41$	−0.281637	+	1.95883i	−0.0439843	+	0.305917i	−0.999924	+	0.0123533i	$0.996068\pi$
$42$		0			0
$43$	1.69094	−	3.70265i	0.257866	−	0.564648i	−0.735777	−	0.677224i	$-0.763183\pi$
$43$	1.69094	−	3.70265i	0.257866	−	0.564648i	0.993643	+	0.112576i	$0.0359101\pi$
$44$		0			0
$45$	−1.04490	−	2.28802i	−0.155765	−	0.341078i
$46$		0			0
$47$	0.335781	+	2.33541i	0.0489787	+	0.340654i	0.999546	+	0.0301351i	$0.00959374\pi$
$47$	0.335781	+	2.33541i	0.0489787	+	0.340654i	−0.950567	+	0.310519i	$0.899497\pi$
$48$		0			0
$49$	−1.31320	+	2.87551i	−0.187600	+	0.410787i
$50$		0			0
$51$	−1.00362	+	1.15824i	−0.140535	+	0.162186i
$52$		0			0
$53$	9.49972	−	6.10510i	1.30489	−	0.838600i	0.311151	−	0.950360i	$-0.399285\pi$
$53$	9.49972	−	6.10510i	1.30489	−	0.838600i	0.993735	+	0.111761i	$0.0356490\pi$
$54$		0			0
$55$	−5.05443	+	5.90992i	−0.681539	+	0.796894i
$56$		0			0
$57$	2.53838	+	2.92945i	0.336217	+	0.388015i
$58$		0			0
$59$	0.257354	+	1.78994i	0.0335046	+	0.233030i	0.999692	−	0.0248105i	$-0.00789822\pi$
$59$	0.257354	+	1.78994i	0.0335046	+	0.233030i	−0.966188	+	0.257840i	$0.916989\pi$
$60$		0			0
$61$	−1.26332	−	8.78655i	−0.161751	−	1.12500i	−0.895332	−	0.445400i	$-0.853061\pi$
$61$	−1.26332	−	8.78655i	−0.161751	−	1.12500i	0.733581	−	0.679602i	$-0.237848\pi$
$62$		0			0
$63$	1.76820	−	1.13635i	0.222772	−	0.143167i
$64$		0			0
$65$	0.785790	+	5.46529i	0.0974653	+	0.677886i
$66$		0			0
$67$	0.359515	−	2.50048i	0.0439217	−	0.305482i	−0.956005	−	0.293351i	$-0.905229\pi$
$67$	0.359515	−	2.50048i	0.0439217	−	0.305482i	0.999926	−	0.0121310i	$-0.00386150\pi$
$68$		0			0
$69$	2.61483	+	1.68045i	0.314789	+	0.202302i
$70$		0			0
$71$	8.82298	+	10.1823i	1.04710	+	1.20841i	0.977521	+	0.210836i	$0.0676186\pi$
$71$	8.82298	+	10.1823i	1.04710	+	1.20841i	0.0695742	+	0.997577i	$0.477836\pi$
$72$		0			0
$73$	−5.47129	−	3.51619i	−0.640367	−	0.411539i	0.179768	−	0.983709i	$-0.442465\pi$
$73$	−5.47129	−	3.51619i	−0.640367	−	0.411539i	−0.820135	+	0.572170i	$0.806102\pi$
$74$		0			0
$75$	−0.452440	+	0.522143i	−0.0522433	+	0.0602919i
$76$		0			0
$77$	−5.48927	−	3.47778i	−0.625560	−	0.396330i
$78$		0			0
$79$	−5.37517	−	11.7700i	−0.604754	−	1.32423i	−0.926105	−	0.377267i	$-0.876864\pi$
$79$	−5.37517	−	11.7700i	−0.604754	−	1.32423i	0.321350	−	0.946960i	$-0.395863\pi$
$80$		0			0
$81$	−4.63087			−0.514542
$82$		0			0
$83$	−8.65111	+	5.55973i	−0.949582	+	0.610259i	−0.921096	−	0.389335i	$-0.872705\pi$
$83$	−8.65111	+	5.55973i	−0.949582	+	0.610259i	−0.0284859	+	0.999594i	$0.509069\pi$
$84$		0			0
$85$	−2.48362	−	0.729255i	−0.269386	−	0.0790989i
$86$		0			0
$87$	−9.01280	−	10.4013i	−0.966273	−	1.11514i
$88$		0			0
$89$	−0.0361963	+	0.0417727i	−0.00383680	+	0.00442790i	−0.757665	−	0.652644i	$-0.773660\pi$
$89$	−0.0361963	+	0.0417727i	−0.00383680	+	0.00442790i	0.753828	+	0.657072i	$0.228205\pi$
$90$		0			0
$91$	−4.42698	+	1.29988i	−0.464074	+	0.136264i
$92$		0			0
$93$	11.2185	−	3.29404i	1.16330	−	0.341576i
$94$		0			0
$95$	−2.71965	+	5.95520i	−0.279030	+	0.610990i
$96$		0			0
$97$	3.93249	−	8.61096i	0.399284	−	0.874310i	−0.598058	−	0.801453i	$-0.704061\pi$
$97$	3.93249	−	8.61096i	0.399284	−	0.874310i	0.997342	−	0.0728578i	$-0.0232119\pi$
$98$		0			0
$99$	−1.49893	−	3.22681i	−0.150648	−	0.324307i
$100$		0			0
$101$	−1.67285	−	11.6349i	−0.166455	−	1.15772i	−0.886139	−	0.463419i	$-0.846623\pi$
$101$	−1.67285	−	11.6349i	−0.166455	−	1.15772i	0.719684	−	0.694301i	$-0.244287\pi$
$102$		0			0
$103$	−1.09595	+	7.62249i	−0.107987	+	0.751066i	0.861824	+	0.507208i	$0.169322\pi$
$103$	−1.09595	+	7.62249i	−0.107987	+	0.751066i	−0.969811	+	0.243858i	$0.921587\pi$
$104$		0			0
$105$	−5.36516	−	3.44798i	−0.523586	−	0.336488i
$106$		0			0
$107$	4.07494	+	8.92287i	0.393939	+	0.862607i	0.997849	+	0.0655539i	$0.0208814\pi$
$107$	4.07494	+	8.92287i	0.393939	+	0.862607i	−0.603910	+	0.797053i	$0.706391\pi$
$108$		0			0
$109$	−6.29697	−	1.84896i	−0.603140	−	0.177098i	−0.0341148	−	0.999418i	$-0.510861\pi$
$109$	−6.29697	−	1.84896i	−0.603140	−	0.177098i	−0.569025	+	0.822320i	$0.692679\pi$
$110$		0			0
$111$	2.76073	−	0.810625i	0.262037	−	0.0769411i
$112$		0			0
$113$	5.90907	−	12.9391i	0.555879	−	1.21720i	−0.398103	−	0.917341i	$-0.630331\pi$
$113$	5.90907	−	12.9391i	0.555879	−	1.21720i	0.953982	−	0.299864i	$-0.0969413\pi$
$114$		0			0
$115$	−0.747118	+	5.19632i	−0.0696691	+	0.484559i
$116$		0			0
$117$	−2.42389	−	0.711720i	−0.224089	−	0.0657985i
$118$		0			0
$119$	0.307824	−	2.14096i	0.0282182	−	0.196262i
$120$		0			0
$121$	−7.09533	+	8.40573i	−0.645030	+	0.764157i
$122$		0			0
$123$	−0.390982	+	2.71934i	−0.0352536	+	0.245194i
$124$		0			0
$125$	10.1290	+	2.97415i	0.905969	+	0.266016i
$126$		0			0
$127$	2.85145	−	19.8322i	0.253025	−	1.75983i	−0.326808	−	0.945091i	$-0.605973\pi$
$127$	2.85145	−	19.8322i	0.253025	−	1.75983i	0.579832	−	0.814736i	$-0.303118\pi$
$128$		0			0
$129$	2.34745	−	5.14019i	0.206681	−	0.452569i
$130$		0			0
$131$	−0.866647	+	0.254470i	−0.0757193	+	0.0222332i	−0.319373	−	0.947629i	$-0.603472\pi$
$131$	−0.866647	+	0.254470i	−0.0757193	+	0.0222332i	0.243654	+	0.969862i	$0.421654\pi$
$132$		0			0
$133$	−5.24906	−	1.54126i	−0.455151	−	0.133644i
$134$		0			0
$135$	−5.50717	−	12.0590i	−0.473982	−	1.03787i
$136$		0			0
$137$	−4.33057	−	2.78309i	−0.369985	−	0.237775i	0.342415	−	0.939549i	$-0.388755\pi$
$137$	−4.33057	−	2.78309i	−0.369985	−	0.237775i	−0.712400	+	0.701774i	$0.752392\pi$
$138$		0			0
$139$	−0.763727	+	5.31184i	−0.0647785	+	0.450544i	0.931457	+	0.363852i	$0.118539\pi$
$139$	−0.763727	+	5.31184i	−0.0647785	+	0.450544i	−0.996235	+	0.0866920i	$0.972370\pi$
$140$		0			0
$141$	0.466147	+	3.24212i	0.0392567	+	0.273036i
$142$		0			0
$143$	1.16149	+	7.72337i	0.0971285	+	0.645861i
$144$		0			0
$145$	9.65640	−	21.1446i	0.801920	−	1.75596i
$146$		0			0
$147$	−1.82305	+	3.99192i	−0.150363	+	0.329248i
$148$		0			0
$149$	1.17394	−	0.344700i	0.0961729	−	0.0282389i	−0.233292	−	0.972407i	$-0.574950\pi$
$149$	1.17394	−	0.344700i	0.0961729	−	0.0282389i	0.329465	+	0.944168i	$0.393132\pi$
$150$		0			0
$151$	9.13152	−	2.68126i	0.743112	−	0.218197i	0.111805	−	0.993730i	$-0.464337\pi$
$151$	9.13152	−	2.68126i	0.743112	−	0.218197i	0.631307	+	0.775533i	$0.282519\pi$
$152$		0			0
$153$	0.775545	−	0.895027i	0.0626991	−	0.0723586i
$154$		0			0
$155$	12.9319	+	14.9242i	1.03872	+	1.19874i
$156$		0			0
$157$	−18.5108	−	5.43526i	−1.47732	−	0.433781i	−0.558851	−	0.829268i	$-0.688758\pi$
$157$	−18.5108	−	5.43526i	−1.47732	−	0.433781i	−0.918472	+	0.395487i	$0.870576\pi$
$158$		0			0
$159$	13.1880	−	8.47539i	1.04587	−	0.672142i
$160$		0			0
$161$	−4.38681			−0.345729
$162$		0			0
$163$	3.57101	+	7.81943i	0.279703	+	0.612465i	0.996387	−	0.0849339i	$-0.0270679\pi$
$163$	3.57101	+	7.81943i	0.279703	+	0.612465i	−0.716683	+	0.697399i	$0.754341\pi$
$164$		0			0
$165$	−7.01680	+	8.20444i	−0.546257	+	0.638715i
$166$		0			0
$167$	−7.26289	+	8.38182i	−0.562019	+	0.648605i	−0.963641	−	0.267201i	$-0.913901\pi$
$167$	−7.26289	+	8.38182i	−0.562019	+	0.648605i	0.401622	+	0.915806i	$0.368447\pi$
$168$		0			0
$169$	−6.27120	−	4.03025i	−0.482400	−	0.310020i
$170$		0			0
$171$	−1.96153	−	2.26373i	−0.150002	−	0.173111i
$172$		0			0
$173$	4.13951	+	2.66030i	0.314721	+	0.202259i	0.688459	−	0.725275i	$-0.258288\pi$
$173$	4.13951	+	2.66030i	0.314721	+	0.202259i	−0.373738	+	0.927534i	$0.621924\pi$
$174$		0			0
$175$	0.138769	−	0.965162i	0.0104900	−	0.0729594i
$176$		0			0
$177$	0.357271	+	2.48488i	0.0268542	+	0.186775i
$178$		0			0
$179$	−11.8303	+	7.60285i	−0.884235	+	0.568263i	−0.902076	−	0.431577i	$-0.857957\pi$
$179$	−11.8303	+	7.60285i	−0.884235	+	0.568263i	0.0178407	+	0.999841i	$0.494321\pi$
$180$		0			0
$181$	−2.93599	−	20.4203i	−0.218230	−	1.51783i	−0.744566	−	0.667549i	$-0.767344\pi$
$181$	−2.93599	−	20.4203i	−0.218230	−	1.51783i	0.526336	−	0.850277i	$-0.323565\pi$
$182$		0			0
$183$	−1.75380	−	12.1979i	−0.129644	−	0.901696i
$184$		0			0
$185$	3.18239	+	3.67268i	0.233974	+	0.270021i
$186$		0			0
$187$	−3.51970	−	1.00880i	−0.257386	−	0.0737706i
$188$		0			0
$189$	9.31928	−	5.98914i	0.677878	−	0.435646i
$190$		0			0
$191$	−2.76577	+	3.19187i	−0.200124	+	0.230956i	−0.846937	−	0.531693i	$-0.821556\pi$
$191$	−2.76577	+	3.19187i	−0.200124	+	0.230956i	0.646813	+	0.762649i	$0.276101\pi$
$192$		0			0
$193$	−3.65725	+	8.00825i	−0.263254	+	0.576447i	−0.994389	−	0.105787i	$-0.966264\pi$
$193$	−3.65725	+	8.00825i	−0.263254	+	0.576447i	0.731134	+	0.682233i	$0.238991\pi$
$194$		0			0
$195$	1.09087	+	7.58718i	0.0781190	+	0.543329i
$196$		0			0
$197$	4.04027	+	8.84696i	0.287858	+	0.630320i	0.997219	−	0.0745246i	$-0.0237439\pi$
$197$	4.04027	+	8.84696i	0.287858	+	0.630320i	−0.709362	+	0.704845i	$0.751017\pi$
$198$		0			0
$199$	−3.43044	+	7.51162i	−0.243178	+	0.532485i	−0.991385	−	0.130980i	$-0.958188\pi$
$199$	−3.43044	+	7.51162i	−0.243178	+	0.532485i	0.748207	+	0.663465i	$0.230915\pi$
$200$		0			0
$201$	0.499096	−	3.47129i	0.0352035	−	0.244846i
$202$		0			0
$203$	18.6373	+	5.47242i	1.30809	+	0.384088i
$204$		0			0
$205$	−4.45216	+	1.30727i	−0.310952	+	0.0913038i
$206$		0			0
$207$	−2.02061	−	1.29856i	−0.140442	−	0.0902565i
$208$		0			0
$209$	−3.79241	+	8.44841i	−0.262327	+	0.584389i
$210$		0			0
$211$	7.24713	−	2.12795i	0.498913	−	0.146494i	−0.0225876	−	0.999745i	$-0.507190\pi$
$211$	7.24713	−	2.12795i	0.498913	−	0.146494i	0.521501	+	0.853251i	$0.325372\pi$
$212$		0			0
$213$	12.2485	+	14.1355i	0.839253	+	0.968550i
$214$		0			0
$215$	9.54412			0.650904
$216$		0			0
$217$	−10.8062	+	12.4710i	−0.733572	+	0.846587i
$218$		0			0
$219$	−7.59552	−	4.88134i	−0.513257	−	0.329851i
$220$		0			0
$221$	−2.18699	+	1.40549i	−0.147113	+	0.0945437i
$222$		0			0
$223$	1.69332	+	1.95419i	0.113393	+	0.130862i	0.809608	−	0.586971i	$-0.199680\pi$
$223$	1.69332	+	1.95419i	0.113393	+	0.130862i	−0.696215	+	0.717833i	$0.745134\pi$
$224$		0			0
$225$	0.349622	−	0.403485i	0.0233081	−	0.0268990i
$226$		0			0
$227$	10.1824	+	22.2964i	0.675833	+	1.47987i	0.866999	+	0.498310i	$0.166046\pi$
$227$	10.1824	+	22.2964i	0.675833	+	1.47987i	−0.191166	+	0.981558i	$0.561227\pi$
$228$		0			0
$229$	9.23563	+	2.71182i	0.610307	+	0.179202i	0.572258	−	0.820073i	$-0.306067\pi$
$229$	9.23563	+	2.71182i	0.610307	+	0.179202i	0.0380491	+	0.999276i	$0.487886\pi$
$230$		0			0
$231$	−7.62047	−	4.82802i	−0.501390	−	0.317660i
$232$		0			0
$233$	13.8455			0.907049			0.453524	−	0.891244i	$-0.350166\pi$
$233$	13.8455			0.907049			0.453524	+	0.891244i	$0.350166\pi$
$234$		0			0
$235$	−4.65395	+	2.99091i	−0.303590	+	0.195106i
$236$		0			0
$237$	−7.46208	−	16.3397i	−0.484714	−	1.06138i
$238$		0			0
$239$	3.25776			0.210727			0.105363	−	0.994434i	$-0.466399\pi$
$239$	3.25776			0.210727			0.105363	+	0.994434i	$0.466399\pi$
$240$		0			0
$241$	−5.12234			−0.329959			−0.164980	−	0.986297i	$-0.552756\pi$
$241$	−5.12234			−0.329959			−0.164980	+	0.986297i	$0.552756\pi$
$242$		0			0
$243$	10.5332			0.675707
$244$		0			0
$245$	−7.41206			−0.473539
$246$		0			0
$247$	2.73143	+	5.98100i	0.173797	+	0.380562i
$248$		0			0
$249$	−12.0099	+	7.71828i	−0.761095	+	0.489126i
$250$		0			0
$251$	−9.97508			−0.629621			−0.314811	−	0.949155i	$-0.601941\pi$
$251$	−9.97508			−0.629621			−0.314811	+	0.949155i	$0.601941\pi$
$252$		0			0
$253$	−1.00925	+	7.35694i	−0.0634507	+	0.462527i
$254$		0			0
$255$	−3.44788	−	1.01239i	−0.215914	−	0.0633982i
$256$		0			0
$257$	10.4228	+	22.8227i	0.650154	+	1.42364i	0.891420	+	0.453179i	$0.149710\pi$
$257$	10.4228	+	22.8227i	0.650154	+	1.42364i	−0.241266	+	0.970459i	$0.577563\pi$
$258$		0			0
$259$	−2.65927	+	3.06897i	−0.165239	+	0.190696i
$260$		0			0
$261$	6.96462	+	8.03760i	0.431099	+	0.497515i
$262$		0			0
$263$	21.9428	−	14.1018i	1.35305	−	0.869553i	0.355182	−	0.934797i	$-0.384419\pi$
$263$	21.9428	−	14.1018i	1.35305	−	0.869553i	0.997869	+	0.0652437i	$0.0207825\pi$
$264$		0			0
$265$	22.2741	+	14.3147i	1.36829	+	0.879345i
$266$		0			0
$267$	−0.0502494	+	0.0579909i	−0.00307521	+	0.00354899i
$268$		0			0
$269$	12.9994			0.792590			0.396295	−	0.918123i	$-0.370296\pi$
$269$	12.9994			0.792590			0.396295	+	0.918123i	$0.370296\pi$
$270$		0			0
$271$	12.8550	+	14.8355i	0.780888	+	0.901193i	0.997173	−	0.0751375i	$-0.0239396\pi$
$271$	12.8550	+	14.8355i	0.780888	+	0.901193i	−0.216285	+	0.976330i	$0.569394\pi$
$272$		0			0
$273$	−6.14575	+	1.80455i	−0.371958	+	0.109217i
$274$		0			0
$275$	−1.58671	−	0.454774i	−0.0956823	−	0.0274239i
$276$		0			0
$277$	7.92555	+	5.09344i	0.476200	+	0.306035i	0.756635	−	0.653838i	$-0.226842\pi$
$277$	7.92555	+	5.09344i	0.476200	+	0.306035i	−0.280435	+	0.959873i	$0.590479\pi$
$278$		0			0
$279$	−8.66905	+	2.54546i	−0.519002	+	0.152393i
$280$		0			0
$281$	2.46090	+	0.722584i	0.146805	+	0.0431057i	0.354309	−	0.935128i	$-0.384716\pi$
$281$	2.46090	+	0.722584i	0.146805	+	0.0431057i	−0.207505	+	0.978234i	$0.566534\pi$
$282$		0			0
$283$	−1.01094	+	7.03128i	−0.0600944	+	0.417966i	0.937461	+	0.348090i	$0.113170\pi$
$283$	−1.01094	+	7.03128i	−0.0600944	+	0.417966i	−0.997556	+	0.0698763i	$0.977740\pi$
$284$		0			0
$285$	−3.77555	+	8.26729i	−0.223644	+	0.489712i
$286$		0			0
$287$	−1.61072	−	3.52699i	−0.0950778	−	0.208191i
$288$		0			0
$289$	2.24591	+	15.6206i	0.132112	+	0.918861i
$290$		0			0
$291$	5.45928	−	11.9542i	0.320029	−	0.700765i
$292$		0			0
$293$	−21.2594	+	24.5346i	−1.24199	+	1.43333i	−0.381098	+	0.924535i	$0.624454\pi$
$293$	−21.2594	+	24.5346i	−1.24199	+	1.43333i	−0.860889	+	0.508794i	$0.830092\pi$
$294$		0			0
$295$	−3.56695	+	2.29234i	−0.207676	+	0.133465i
$296$		0			0
$297$	−7.90012	−	17.0069i	−0.458412	−	0.986840i
$298$		0			0
$299$	3.45275	+	3.98469i	0.199678	+	0.230441i
$300$		0			0
$301$	1.13500	+	7.89409i	0.0654202	+	0.455008i
$302$		0			0
$303$	−2.32233	−	16.1522i	−0.133415	−	0.927919i
$304$		0			0
$305$	17.5097	−	11.2528i	1.00260	−	0.644332i
$306$		0			0
$307$	−3.58729	−	24.9502i	−0.204738	−	1.42398i	−0.789985	−	0.613126i	$-0.789912\pi$
$307$	−3.58729	−	24.9502i	−0.204738	−	1.42398i	0.585247	−	0.810855i	$-0.300997\pi$
$308$		0			0
$309$	−1.52145	+	10.5819i	−0.0865522	+	0.601984i
$310$		0			0
$311$	−26.4341	−	16.9882i	−1.49894	−	0.963310i	−0.995032	−	0.0995522i	$-0.968259\pi$
$311$	−26.4341	−	16.9882i	−1.49894	−	0.963310i	−0.503907	−	0.863758i	$-0.668105\pi$
$312$		0			0
$313$	10.1577	+	11.7226i	0.574145	+	0.662599i	0.966336	−	0.257285i	$-0.0828279\pi$
$313$	10.1577	+	11.7226i	0.574145	+	0.662599i	−0.392190	+	0.919884i	$0.628282\pi$
$314$		0			0
$315$	4.14591	+	2.66442i	0.233596	+	0.150123i
$316$		0			0
$317$	7.43991	−	8.58611i	0.417867	−	0.482244i	−0.507319	−	0.861758i	$-0.669363\pi$
$317$	7.43991	−	8.58611i	0.417867	−	0.482244i	0.925186	+	0.379514i	$0.123909\pi$
$318$		0			0
$319$	13.4654	−	29.9970i	0.753916	−	1.67951i
$320$		0			0
$321$	5.65703	+	12.3872i	0.315745	+	0.691384i
$322$		0			0
$323$	−3.08244			−0.171511
$324$		0			0
$325$	−0.985913	+	0.633608i	−0.0546886	+	0.0351462i
$326$		0			0
$327$	−8.74176	−	2.56681i	−0.483420	−	0.141945i
$328$		0			0
$329$	−3.02729	−	3.49367i	−0.166900	−	0.192612i
$330$		0			0
$331$	8.02554	−	9.26197i	0.441124	−	0.509084i	−0.491032	−	0.871142i	$-0.663380\pi$
$331$	8.02554	−	9.26197i	0.441124	−	0.509084i	0.932156	+	0.362058i	$0.117926\pi$
$332$		0			0
$333$	−2.13335	+	0.626408i	−0.116907	+	0.0343270i
$334$		0			0
$335$	5.68327	−	1.66876i	0.310510	−	0.0911740i
$336$		0			0
$337$	9.12380	−	19.9783i	0.497005	−	1.08829i	−0.480426	−	0.877035i	$-0.659518\pi$
$337$	9.12380	−	19.9783i	0.497005	−	1.08829i	0.977431	−	0.211254i	$-0.0677547\pi$
$338$		0			0
$339$	8.20326	−	17.9626i	0.445540	−	0.975596i
$340$		0			0
$341$	18.4285	+	20.9918i	0.997961	+	1.13677i
$342$		0			0
$343$	−2.83330	−	19.7061i	−0.152984	−	1.06403i
$344$		0			0
$345$	−1.03719	+	7.21378i	−0.0558402	+	0.388377i
$346$		0			0
$347$	5.59601	+	3.59634i	0.300410	+	0.193062i	0.682158	−	0.731205i	$-0.261042\pi$
$347$	5.59601	+	3.59634i	0.300410	+	0.193062i	−0.381748	+	0.924266i	$0.624678\pi$
$348$		0			0
$349$	8.44770	+	18.4979i	0.452195	+	0.990169i	0.989198	+	0.146588i	$0.0468293\pi$
$349$	8.44770	+	18.4979i	0.452195	+	0.990169i	−0.537003	+	0.843581i	$0.680443\pi$
$350$		0			0
$351$	−12.7751	−	3.75112i	−0.681886	−	0.200220i
$352$		0			0
$353$	−10.0479	+	2.95031i	−0.534793	+	0.157029i	−0.537968	−	0.842966i	$-0.680808\pi$
$353$	−10.0479	+	2.95031i	−0.534793	+	0.157029i	0.00317447	+	0.999995i	$0.498990\pi$
$354$		0			0
$355$	−13.1232	+	28.7357i	−0.696505	+	1.52513i
$356$		0			0
$357$	0.427336	−	2.97219i	0.0226170	−	0.157305i
$358$		0			0
$359$	−22.8014	−	6.69508i	−1.20341	−	0.353353i	−0.382254	−	0.924057i	$-0.624852\pi$
$359$	−22.8014	−	6.69508i	−1.20341	−	0.353353i	−0.821156	+	0.570704i	$0.806670\pi$
$360$		0			0
$361$	1.59447	−	11.0898i	0.0839195	−	0.583673i
$362$		0			0
$363$	−9.85008	+	11.6692i	−0.516995	+	0.612476i
$364$		0			0
$365$	2.17022	−	15.0942i	0.113594	−	0.790066i
$366$		0			0
$367$	−24.1162	−	7.08114i	−1.25885	−	0.369633i	−0.416786	−	0.909005i	$-0.636843\pi$
$367$	−24.1162	−	7.08114i	−1.25885	−	0.369633i	−0.842068	+	0.539372i	$0.818662\pi$
$368$		0			0
$369$	0.302130	−	2.10136i	0.0157283	−	0.109393i
$370$		0			0
$371$	−9.19104	+	20.1256i	−0.477175	+	1.04487i
$372$		0			0
$373$	−30.4413	+	8.93837i	−1.57619	+	0.462811i	−0.948796	−	0.315891i	$-0.897697\pi$
$373$	−30.4413	+	8.93837i	−1.57619	+	0.462811i	−0.627394	+	0.778702i	$0.715878\pi$
$374$		0			0
$375$	14.0616	+	4.12887i	0.726139	+	0.213214i
$376$		0			0
$377$	−9.69823	−	21.2362i	−0.499484	−	1.09372i
$378$		0			0
$379$	−26.8442	−	17.2517i	−1.37889	−	0.886162i	−0.379654	−	0.925128i	$-0.623957\pi$
$379$	−26.8442	−	17.2517i	−1.37889	−	0.886162i	−0.999241	+	0.0389665i	$0.987593\pi$
$380$		0			0
$381$	3.95852	−	27.5321i	0.202801	−	1.41051i
$382$		0			0
$383$	−3.02892	−	21.0666i	−0.154771	−	1.07645i	−0.908083	−	0.418791i	$-0.862454\pi$
$383$	−3.02892	−	21.0666i	−0.154771	−	1.07645i	0.753312	−	0.657663i	$-0.228455\pi$
$384$		0			0
$385$	2.07079	−	15.0951i	0.105537	−	0.769318i
$386$		0			0
$387$	−1.81398	+	3.97207i	−0.0922100	+	0.201912i
$388$		0			0
$389$	−3.73562	+	8.17988i	−0.189404	+	0.414736i	−0.980382	−	0.197108i	$-0.936845\pi$
$389$	−3.73562	+	8.17988i	−0.189404	+	0.414736i	0.790978	+	0.611845i	$0.209572\pi$
$390$		0			0
$391$	−2.37162	+	0.696370i	−0.119938	+	0.0352169i
$392$		0			0
$393$	−1.20312	+	0.353268i	−0.0606894	+	0.0178200i
$394$		0			0
$395$	19.8678	−	22.9286i	0.999655	−	1.15366i
$396$		0			0
$397$	2.52616	+	2.91534i	0.126784	+	0.146317i	0.815592	−	0.578627i	$-0.196411\pi$
$397$	2.52616	+	2.91534i	0.126784	+	0.146317i	−0.688808	+	0.724944i	$0.741866\pi$
$398$		0			0
$399$	−7.28700	−	2.13966i	−0.364806	−	0.107117i
$400$		0			0
$401$	−7.25857	+	4.66480i	−0.362476	+	0.232949i	−0.709183	−	0.705024i	$-0.750936\pi$
$401$	−7.25857	+	4.66480i	−0.362476	+	0.232949i	0.346707	+	0.937973i	$0.387300\pi$
$402$		0			0
$403$	19.8331			0.987959
$404$		0			0
$405$	−4.51060	−	9.87685i	−0.224134	−	0.490784i
$406$		0			0
$407$	4.53504	+	5.16583i	0.224794	+	0.256061i
$408$		0			0
$409$	−13.1369	+	15.1608i	−0.649577	+	0.749652i	−0.981038	−	0.193817i	$-0.937913\pi$
$409$	−13.1369	+	15.1608i	−0.649577	+	0.749652i	0.331461	+	0.943469i	$0.392459\pi$
$410$		0			0
$411$	−6.01190	−	3.86361i	−0.296545	−	0.190578i
$412$		0			0
$413$	−2.32022	−	2.67767i	−0.114170	−	0.131760i
$414$		0			0
$415$	−20.2843	−	13.0360i	−0.995720	−	0.639910i
$416$		0			0
$417$	−1.06024	+	7.37415i	−0.0519203	+	0.361114i
$418$		0			0
$419$	3.48798	+	24.2595i	0.170399	+	1.18515i	0.878043	+	0.478583i	$0.158849\pi$
$419$	3.48798	+	24.2595i	0.170399	+	1.18515i	−0.707643	+	0.706570i	$0.750242\pi$
$420$		0			0
$421$	−18.5899	+	11.9470i	−0.906015	+	0.582260i	−0.908568	−	0.417736i	$-0.862824\pi$
$421$	−18.5899	+	11.9470i	−0.906015	+	0.582260i	0.00255345	+	0.999997i	$0.499187\pi$
$422$		0			0
$423$	−0.360214	−	2.50535i	−0.0175142	−	0.121814i
$424$		0			0
$425$	−0.0781894	−	0.543819i	−0.00379274	−	0.0263791i
$426$		0			0
$427$	11.3896	+	13.1443i	0.551183	+	0.636099i
$428$		0			0
$429$	1.61243	+	10.7220i	0.0778490	+	0.517661i
$430$		0			0
$431$	0.0599547	−	0.0385305i	0.00288792	−	0.00185595i	−0.539196	−	0.842180i	$-0.681272\pi$
$431$	0.0599547	−	0.0385305i	0.00288792	−	0.00185595i	0.542084	+	0.840324i	$0.317635\pi$
$432$		0			0
$433$	19.4770	−	22.4776i	0.936003	−	1.08020i	−0.0606259	−	0.998161i	$-0.519310\pi$
$433$	19.4770	−	22.4776i	0.936003	−	1.08020i	0.996629	−	0.0820443i	$-0.0261449\pi$
$434$		0			0
$435$	13.4055	−	29.3539i	0.642744	−	1.40741i
$436$		0			0
$437$	0.889694	+	6.18796i	0.0425598	+	0.296010i
$438$		0			0
$439$	−1.65352	−	3.62071i	−0.0789182	−	0.172807i	0.866060	−	0.499940i	$-0.166645\pi$
$439$	−1.65352	−	3.62071i	−0.0789182	−	0.172807i	−0.944978	+	0.327133i	$0.893917\pi$
$440$		0			0
$441$	1.40876	−	3.08475i	0.0670837	−	0.146893i
$442$		0			0
$443$	−0.901491	+	6.27001i	−0.0428311	+	0.297897i	0.957135	+	0.289643i	$0.0935365\pi$
$443$	−0.901491	+	6.27001i	−0.0428311	+	0.297897i	−0.999966	+	0.00825427i	$0.997373\pi$
$444$		0			0
$445$	−0.124350	−	0.0365125i	−0.00589476	−	0.00173086i
$446$		0			0
$447$	1.62972	−	0.478529i	0.0770831	−	0.0226336i
$448$		0			0
$449$	20.7649	+	13.3448i	0.979954	+	0.629778i	0.929451	−	0.368946i	$-0.120281\pi$
$449$	20.7649	+	13.3448i	0.979954	+	0.629778i	0.0505032	+	0.998724i	$0.483917\pi$
$450$		0			0
$451$	−6.28554	+	1.88984i	−0.295975	+	0.0889893i
$452$		0			0
$453$	12.6768	−	3.72225i	0.595609	−	0.174886i
$454$		0			0
$455$	−7.08442	−	8.17585i	−0.332123	−	0.383290i
$456$		0			0
$457$	−1.62470			−0.0760004			−0.0380002	−	0.999278i	$-0.512099\pi$
$457$	−1.62470			−0.0760004			−0.0380002	+	0.999278i	$0.512099\pi$
$458$		0			0
$459$	4.08751	−	4.71724i	0.190789	−	0.220182i
$460$		0			0
$461$	−26.8575	−	17.2603i	−1.25088	−	0.803891i	−0.263870	−	0.964558i	$-0.584999\pi$
$461$	−26.8575	−	17.2603i	−1.25088	−	0.803891i	−0.987009	+	0.160667i	$0.948635\pi$
$462$		0			0
$463$	29.5488	−	18.9898i	1.37325	−	0.882533i	0.374252	−	0.927327i	$-0.377899\pi$
$463$	29.5488	−	18.9898i	1.37325	−	0.882533i	0.998996	+	0.0447939i	$0.0142631\pi$
$464$		0			0
$465$	17.9527	+	20.7185i	0.832538	+	0.960800i
$466$		0			0
$467$	4.25581	−	4.91146i	0.196935	−	0.227275i	−0.648690	−	0.761053i	$-0.724683\pi$
$467$	4.25581	−	4.91146i	0.196935	−	0.227275i	0.845625	+	0.533778i	$0.179228\pi$
$468$		0			0
$469$	2.05612	+	4.50227i	0.0949426	+	0.207895i
$470$		0			0
$471$	−25.6976	−	7.54549i	−1.18408	−	0.347678i
$472$		0			0
$473$	13.5000	−	0.0873173i	0.620731	−	0.00401485i
$474$		0			0
$475$	−1.38959			−0.0637586
$476$		0			0
$477$	−10.1910	+	6.54934i	−0.466613	+	0.299874i
$478$		0			0
$479$	−0.441518	−	0.966790i	−0.0201735	−	0.0441738i	0.899277	−	0.437379i	$-0.144093\pi$
$479$	−0.441518	−	0.966790i	−0.0201735	−	0.0441738i	−0.919451	+	0.393206i	$0.871366\pi$
$480$		0			0
$481$	4.88070			0.222541
$482$		0			0
$483$	−6.08998			−0.277104
$484$		0			0
$485$	22.1960			1.00787
$486$		0			0
$487$	28.9973			1.31399			0.656996	−	0.753894i	$-0.271827\pi$
$487$	28.9973			1.31399			0.656996	+	0.753894i	$0.271827\pi$
$488$		0			0
$489$	4.95745	+	10.8553i	0.224184	+	0.490894i
$490$		0			0
$491$	−17.2433	+	11.0816i	−0.778180	+	0.500106i	−0.868429	−	0.495813i	$-0.834870\pi$
$491$	−17.2433	+	11.0816i	−0.778180	+	0.500106i	0.0902493	+	0.995919i	$0.471234\pi$
$492$		0			0
$493$	10.9445			0.492916
$494$		0			0
$495$	5.42222	−	6.33997i	0.243710	−	0.284960i
$496$		0			0
$497$	−25.3284	−	7.43708i	−1.13613	−	0.333599i
$498$		0			0
$499$	−4.97648	−	10.8970i	−0.222778	−	0.487816i	0.764933	−	0.644110i	$-0.222772\pi$
$499$	−4.97648	−	10.8970i	−0.222778	−	0.487816i	−0.987710	+	0.156295i	$0.950045\pi$
$500$		0			0
$501$	−10.0827	+	11.6360i	−0.450461	+	0.519860i
$502$		0			0
$503$	3.06146	+	3.53312i	0.136504	+	0.157534i	0.819886	−	0.572527i	$-0.194037\pi$
$503$	3.06146	+	3.53312i	0.136504	+	0.157534i	−0.683382	+	0.730061i	$0.739491\pi$
$504$		0			0
$505$	23.1859	−	14.9007i	1.03176	−	0.663071i
$506$		0			0
$507$	−8.70598	−	5.59500i	−0.386646	−	0.248482i
$508$		0			0
$509$	23.7745	−	27.4373i	1.05379	−	1.21614i	0.0781060	−	0.996945i	$-0.475113\pi$
$509$	23.7745	−	27.4373i	1.05379	−	1.21614i	0.975682	−	0.219191i	$-0.0703418\pi$
$510$		0			0
$511$	12.7427			0.563705
$512$		0			0
$513$	−10.3382	−	11.9310i	−0.456444	−	0.526765i
$514$		0			0
$515$	−17.3249	+	5.08705i	−0.763427	+	0.224162i
$516$		0			0
$517$	−6.55558	+	4.27318i	−0.288314	+	0.187934i
$518$		0			0
$519$	5.74667	+	3.69316i	0.252251	+	0.162112i
$520$		0			0
$521$	−35.2852	+	10.3607i	−1.54587	+	0.453909i	−0.939864	−	0.341549i	$-0.889049\pi$
$521$	−35.2852	+	10.3607i	−1.54587	+	0.453909i	−0.606009	+	0.795458i	$0.707230\pi$
$522$		0			0
$523$	14.8783	+	4.36865i	0.650581	+	0.191028i	0.590338	−	0.807156i	$-0.298994\pi$
$523$	14.8783	+	4.36865i	0.650581	+	0.191028i	0.0602429	+	0.998184i	$0.480812\pi$
$524$		0			0
$525$	0.192646	−	1.33989i	0.00840778	−	0.0584774i
$526$		0			0
$527$	−3.86242	+	8.45753i	−0.168250	+	0.368416i
$528$		0			0
$529$	−7.47206	−	16.3615i	−0.324872	−	0.711371i
$530$		0			0
$531$	−0.276081	−	1.92018i	−0.0119809	−	0.0833289i
$532$		0			0
$533$	−1.93592	+	4.23908i	−0.0838542	+	0.183615i
$534$		0			0
$535$	−15.0618	+	17.3823i	−0.651179	+	0.751501i
$536$		0			0
$537$	−16.4233	+	10.5546i	−0.708720	+	0.455466i
$538$		0			0
$539$	−10.4842	+	0.0678115i	−0.451588	+	0.00292085i
$540$		0			0
$541$	−14.0465	−	16.2106i	−0.603908	−	0.696947i	0.368660	−	0.929564i	$-0.379817\pi$
$541$	−14.0465	−	16.2106i	−0.603908	−	0.696947i	−0.972568	+	0.232617i	$0.925271\pi$
$542$		0			0
$543$	−4.07588	−	28.3484i	−0.174913	−	1.21655i
$544$		0			0
$545$	−2.18993	−	15.2313i	−0.0938061	−	0.652436i
$546$		0			0
$547$	−14.4211	+	9.26786i	−0.616601	+	0.396265i	−0.811327	−	0.584592i	$-0.801254\pi$
$547$	−14.4211	+	9.26786i	−0.616601	+	0.396265i	0.194727	+	0.980858i	$0.437618\pi$
$548$		0			0
$549$	1.35524	+	9.42591i	0.0578403	+	0.402288i
$550$		0			0
$551$	3.93944	−	27.3994i	0.167826	−	1.16725i
$552$		0			0
$553$	21.3273	+	13.7062i	0.906929	+	0.582848i
$554$		0			0
$555$	4.41795	+	5.09859i	0.187532	+	0.216423i
$556$		0			0
$557$	−7.72239	−	4.96288i	−0.327208	−	0.210284i	0.366714	−	0.930334i	$-0.380483\pi$
$557$	−7.72239	−	4.96288i	−0.327208	−	0.210284i	−0.693923	+	0.720050i	$0.744119\pi$
$558$		0			0
$559$	6.27715	−	7.24421i	0.265495	−	0.306398i
$560$		0			0
$561$	−4.88622	−	1.40046i	−0.206297	−	0.0591275i
$562$		0			0
$563$	19.0901	+	41.8015i	0.804553	+	1.76172i	0.629239	+	0.777212i	$0.283367\pi$
$563$	19.0901	+	41.8015i	0.804553	+	1.76172i	0.175314	+	0.984513i	$0.443906\pi$
$564$		0			0
$565$	33.3524			1.40314
$566$		0			0
$567$	7.63289	−	4.90536i	0.320551	−	0.206006i
$568$		0			0
$569$	−32.4878	−	9.53928i	−1.36196	−	0.399907i	−0.482506	−	0.875893i	$-0.660273\pi$
$569$	−32.4878	−	9.53928i	−1.36196	−	0.399907i	−0.879453	+	0.475985i	$0.842092\pi$
$570$		0			0
$571$	−20.9110	−	24.1326i	−0.875099	−	1.00992i	−0.999843	−	0.0177294i	$-0.994356\pi$
$571$	−20.9110	−	24.1326i	−0.875099	−	1.00992i	0.124744	−	0.992189i	$-0.460189\pi$
$572$		0			0
$573$	−3.83958	+	4.43111i	−0.160401	+	0.185112i
$574$		0			0
$575$	−1.06914	+	0.313929i	−0.0445864	+	0.0130917i
$576$		0			0
$577$	−33.0184	+	9.69507i	−1.37457	+	0.403611i	−0.883877	−	0.467719i	$-0.845076\pi$
$577$	−33.0184	+	9.69507i	−1.37457	+	0.403611i	−0.490697	+	0.871331i	$0.663258\pi$
$578$		0			0
$579$	−5.07717	+	11.1174i	−0.211000	+	0.462025i
$580$		0			0
$581$	8.37000	−	18.3278i	0.347246	−	0.760363i
$582$		0			0
$583$	31.6373	+	20.0441i	1.31028	+	0.830142i
$584$		0			0
$585$	−0.842969	−	5.86298i	−0.0348525	−	0.242404i
$586$		0			0
$587$	2.80576	−	19.5145i	0.115806	−	0.805450i	−0.846287	−	0.532728i	$-0.821167\pi$
$587$	2.80576	−	19.5145i	0.115806	−	0.805450i	0.962093	−	0.272722i	$-0.0879240\pi$
$588$		0			0
$589$	19.7830	+	12.7138i	0.815145	+	0.523862i
$590$		0			0
$591$	5.60890	+	12.2818i	0.230719	+	0.505205i
$592$		0			0
$593$	16.9622	+	4.98056i	0.696556	+	0.204527i	0.610795	−	0.791789i	$-0.290850\pi$
$593$	16.9622	+	4.98056i	0.696556	+	0.204527i	0.0857604	+	0.996316i	$0.472668\pi$
$594$		0			0
$595$	4.86612	−	1.42882i	0.199492	−	0.0585760i
$596$		0			0
$597$	−4.76231	+	10.4280i	−0.194908	+	0.426790i
$598$		0			0
$599$	1.06124	−	7.38110i	0.0433611	−	0.301583i	−0.956587	−	0.291445i	$-0.905864\pi$
$599$	1.06124	−	7.38110i	0.0433611	−	0.301583i	0.999949	−	0.0101380i	$-0.00322708\pi$
$600$		0			0
$601$	−10.0991	−	2.96535i	−0.411950	−	0.120959i	0.0691896	−	0.997604i	$-0.477959\pi$
$601$	−10.0991	−	2.96535i	−0.411950	−	0.120959i	−0.481139	+	0.876644i	$0.659777\pi$
$602$		0			0
$603$	−0.385675	+	2.68243i	−0.0157059	+	0.109237i
$604$		0			0
$605$	−24.8390	−	6.94568i	−1.00985	−	0.282382i
$606$		0			0
$607$	−1.64136	+	11.4159i	−0.0666206	+	0.463357i	0.929016	+	0.370040i	$0.120656\pi$
$607$	−1.64136	+	11.4159i	−0.0666206	+	0.463357i	−0.995636	+	0.0933167i	$0.970253\pi$
$608$		0			0
$609$	25.8733	+	7.59708i	1.04844	+	0.307849i
$610$		0			0
$611$	−0.790720	+	5.49958i	−0.0319891	+	0.222489i
$612$		0			0
$613$	−7.24501	+	15.8644i	−0.292623	+	0.640756i	−0.997657	−	0.0684184i	$-0.978205\pi$
$613$	−7.24501	+	15.8644i	−0.292623	+	0.640756i	0.705033	+	0.709174i	$0.250932\pi$
$614$		0			0
$615$	−6.18070	+	1.81482i	−0.249230	+	0.0731805i
$616$		0			0
$617$	−36.3279	−	10.6668i	−1.46250	−	0.429430i	−0.548850	−	0.835921i	$-0.684934\pi$
$617$	−36.3279	−	10.6668i	−1.46250	−	0.429430i	−0.913655	+	0.406491i	$0.866752\pi$
$618$		0			0
$619$	−13.0672	−	28.6131i	−0.525214	−	1.15006i	−0.967427	−	0.253149i	$-0.918534\pi$
$619$	−13.0672	−	28.6131i	−0.525214	−	1.15006i	0.442213	−	0.896910i	$-0.354194\pi$
$620$		0			0
$621$	−10.6496	−	6.84408i	−0.427354	−	0.274644i
$622$		0			0
$623$	0.0154122	−	0.107194i	0.000617476	−	0.00429464i
$624$		0			0
$625$	3.87675	+	26.9634i	0.155070	+	1.07854i
$626$		0			0
$627$	−5.26481	+	11.7285i	−0.210256	+	0.468391i
$628$		0			0
$629$	−0.950497	+	2.08130i	−0.0378988	+	0.0829868i
$630$		0			0
$631$	−7.57110	+	16.5784i	−0.301401	+	0.659975i	−0.998367	−	0.0571287i	$-0.981805\pi$
$631$	−7.57110	+	16.5784i	−0.301401	+	0.659975i	0.696966	+	0.717104i	$0.254533\pi$
$632$		0			0
$633$	10.0608	−	2.95412i	0.399882	−	0.117416i
$634$		0			0
$635$	45.0761	−	13.2355i	1.78879	−	0.525236i
$636$		0			0
$637$	−4.87489	+	5.62593i	−0.193150	+	0.222907i
$638$		0			0
$639$	−9.46500	−	10.9232i	−0.374430	−	0.432115i
$640$		0			0
$641$	−19.9380	−	5.85433i	−0.787504	−	0.231232i	−0.136836	−	0.990594i	$-0.543693\pi$
$641$	−19.9380	−	5.85433i	−0.787504	−	0.231232i	−0.650669	+	0.759362i	$0.725511\pi$
$642$		0			0
$643$	16.5281	−	10.6220i	0.651806	−	0.418891i	−0.172519	−	0.985006i	$-0.555191\pi$
$643$	16.5281	−	10.6220i	0.651806	−	0.418891i	0.824326	+	0.566116i	$0.191554\pi$
$644$		0			0
$645$	13.2496			0.521703
$646$		0			0
$647$	−0.720012	−	1.57661i	−0.0283066	−	0.0619828i	0.894951	−	0.446165i	$-0.147211\pi$
$647$	−0.720012	−	1.57661i	−0.0283066	−	0.0619828i	−0.923257	+	0.384182i	$0.874483\pi$
$648$		0			0
$649$	−5.02442	+	3.27511i	−0.197226	+	0.128559i
$650$		0			0
$651$	−15.0017	+	17.3129i	−0.587962	+	0.678544i
$652$		0			0
$653$	0.841825	+	0.541008i	0.0329431	+	0.0211713i	0.557009	−	0.830507i	$-0.311949\pi$
$653$	0.841825	+	0.541008i	0.0329431	+	0.0211713i	−0.524066	+	0.851678i	$0.675585\pi$
$654$		0			0
$655$	−1.38688	−	1.60054i	−0.0541899	−	0.0625384i
$656$		0			0
$657$	5.86942	+	3.77205i	0.228988	+	0.147162i
$658$		0			0
$659$	−4.82000	+	33.5238i	−0.187761	+	1.30590i	0.650029	+	0.759910i	$0.274757\pi$
$659$	−4.82000	+	33.5238i	−0.187761	+	1.30590i	−0.837789	+	0.545994i	$0.816152\pi$
$660$		0			0
$661$	0.352327	+	2.45049i	0.0137039	+	0.0953129i	0.995525	−	0.0944934i	$-0.0301231\pi$
$661$	0.352327	+	2.45049i	0.0137039	+	0.0953129i	−0.981822	+	0.189806i	$0.939214\pi$
$662$		0			0
$663$	−3.03609	+	1.95117i	−0.117912	+	0.0757773i
$664$		0			0
$665$	−1.82549	−	12.6966i	−0.0707895	−	0.492352i
$666$		0			0
$667$	−3.15895	−	21.9710i	−0.122315	−	0.850721i
$668$		0			0
$669$	2.35074	+	2.71290i	0.0908850	+	0.104887i
$670$		0			0
$671$	24.6642	−	16.0771i	0.952150	−	0.620648i
$672$		0			0
$673$	17.0898	−	10.9830i	0.658765	−	0.423362i	−0.168095	−	0.985771i	$-0.553761\pi$
$673$	17.0898	−	10.9830i	0.658765	−	0.423362i	0.826860	+	0.562408i	$0.190125\pi$
$674$		0			0
$675$	1.84268	−	2.12657i	0.0709249	−	0.0818516i
$676$		0			0
$677$	−14.0908	+	30.8546i	−0.541554	+	1.18584i	0.419062	+	0.907957i	$0.362359\pi$
$677$	−14.0908	+	30.8546i	−0.541554	+	1.18584i	−0.960616	+	0.277880i	$0.910368\pi$
$678$		0			0
$679$	2.63958	+	18.3587i	0.101298	+	0.704542i
$680$		0			0
$681$	14.1358	+	30.9530i	0.541684	+	1.18612i
$682$		0			0
$683$	−8.22772	+	18.0162i	−0.314825	+	0.689370i	−0.999210	−	0.0397507i	$-0.987344\pi$
$683$	−8.22772	+	18.0162i	−0.314825	+	0.689370i	0.684385	+	0.729121i	$0.260071\pi$
$684$		0			0
$685$	1.71774	−	11.9471i	0.0656315	−	0.456477i
$686$		0			0
$687$	12.8213	+	3.76469i	0.489165	+	0.143632i
$688$		0			0
$689$	25.5148	−	7.49183i	0.972037	−	0.285416i
$690$		0			0
$691$	8.12911	+	5.22426i	0.309246	+	0.198740i	0.686053	−	0.727551i	$-0.259342\pi$
$691$	8.12911	+	5.22426i	0.309246	+	0.198740i	−0.376807	+	0.926292i	$0.622978\pi$
$692$		0			0
$693$	5.88870	+	3.73084i	0.223693	+	0.141723i
$694$		0			0
$695$	−12.0731	+	3.54499i	−0.457959	+	0.134469i
$696$		0			0
$697$	−1.43068	−	1.65109i	−0.0541907	−	0.0625394i
$698$		0			0
$699$	19.2210			0.727005
$700$		0			0
$701$	13.8056	−	15.9325i	0.521431	−	0.601764i	−0.432557	−	0.901606i	$-0.642389\pi$
$701$	13.8056	−	15.9325i	0.521431	−	0.601764i	0.953989	+	0.299843i	$0.0969342\pi$
$702$		0			0
$703$	4.86837	+	3.12871i	0.183614	+	0.118002i
$704$		0			0
$705$	−6.46084	+	4.15213i	−0.243329	+	0.156378i
$706$		0			0
$707$	15.0819	+	17.4054i	0.567212	+	0.654598i
$708$		0			0
$709$	−23.3337	+	26.9285i	−0.876315	+	1.01132i	0.123505	+	0.992344i	$0.460587\pi$
$709$	−23.3337	+	26.9285i	−0.876315	+	1.01132i	−0.999820	+	0.0189777i	$0.993959\pi$
$710$		0			0
$711$	5.76630	+	12.6264i	0.216253	+	0.473529i
$712$		0			0
$713$	18.0932	+	5.31265i	0.677597	+	0.198960i
$714$		0			0
$715$	−15.3413	+	10.0000i	−0.573731	+	0.373980i
$716$		0			0
$717$	4.52258			0.168899
$718$		0			0
$719$	14.2288	−	9.14429i	0.530644	−	0.341024i	−0.247726	−	0.968830i	$-0.579683\pi$
$719$	14.2288	−	9.14429i	0.530644	−	0.341024i	0.778370	+	0.627806i	$0.216047\pi$
$720$		0			0
$721$	−6.26788	−	13.7247i	−0.233428	−	0.511136i
$722$		0			0
$723$	−7.11109			−0.264464
$724$		0			0
$725$	4.93387			0.183240
$726$		0			0
$727$	7.85553			0.291346			0.145673	−	0.989333i	$-0.453465\pi$
$727$	7.85553			0.291346			0.145673	+	0.989333i	$0.453465\pi$
$728$		0			0
$729$	28.5154			1.05612
$730$		0			0
$731$	1.86673	+	4.08757i	0.0690435	+	0.151184i
$732$		0			0
$733$	42.5049	−	27.3163i	1.56996	−	1.00895i	0.590561	−	0.806993i	$-0.298907\pi$
$733$	42.5049	−	27.3163i	1.56996	−	1.00895i	0.979395	−	0.201956i	$-0.0647298\pi$
$734$		0			0
$735$	−10.2898			−0.379544
$736$		0			0
$737$	8.02362	−	2.41242i	0.295554	−	0.0888628i
$738$		0			0
$739$	−38.1750	−	11.2092i	−1.40429	−	0.412337i	−0.510135	−	0.860094i	$-0.670404\pi$
$739$	−38.1750	−	11.2092i	−1.40429	−	0.412337i	−0.894155	+	0.447758i	$0.852223\pi$
$740$		0			0
$741$	3.79190	+	8.30311i	0.139299	+	0.305022i
$742$		0			0
$743$	3.63445	−	4.19438i	0.133335	−	0.153877i	−0.685155	−	0.728397i	$-0.740266\pi$
$743$	3.63445	−	4.19438i	0.133335	−	0.153877i	0.818491	+	0.574520i	$0.194811\pi$
$744$		0			0
$745$	1.87863	+	2.16806i	0.0688278	+	0.0794316i
$746$		0			0
$747$	9.28061	−	5.96429i	0.339560	−	0.218222i
$748$		0			0
$749$	−16.1683	−	10.3907i	−0.590777	−	0.379669i
$750$		0			0
$751$	−17.3136	+	19.9810i	−0.631783	+	0.729116i	−0.977900	−	0.209075i	$-0.932955\pi$
$751$	−17.3136	+	19.9810i	−0.631783	+	0.729116i	0.346117	+	0.938191i	$0.387500\pi$
$752$		0			0
$753$	−13.8479			−0.504645
$754$		0			0
$755$	14.6130	+	16.8643i	0.531822	+	0.613755i
$756$		0			0
$757$	14.1024	−	4.14084i	0.512561	−	0.150502i	−0.0152163	−	0.999884i	$-0.504844\pi$
$757$	14.1024	−	4.14084i	0.512561	−	0.150502i	0.527777	+	0.849383i	$0.323025\pi$
$758$		0			0
$759$	−1.40108	+	10.2133i	−0.0508561	+	0.370718i
$760$		0			0
$761$	−42.8495	−	27.5377i	−1.55329	−	0.998242i	−0.984423	−	0.175815i	$-0.943744\pi$
$761$	−42.8495	−	27.5377i	−1.55329	−	0.998242i	−0.568871	−	0.822427i	$-0.692620\pi$
$762$		0			0
$763$	12.3376	−	3.62264i	0.446651	−	0.131148i
$764$		0			0
$765$	2.66434	+	0.782320i	0.0963294	+	0.0282849i
$766$		0			0
$767$	−0.606035	+	4.21507i	−0.0218827	+	0.152197i
$768$		0			0
$769$	9.85738	−	21.5847i	0.355466	−	0.778362i	−0.644440	−	0.764655i	$-0.722909\pi$
$769$	9.85738	−	21.5847i	0.355466	−	0.778362i	0.999906	−	0.0137074i	$-0.00436333\pi$
$770$		0			0
$771$	14.4694	+	31.6835i	0.521102	+	1.14105i
$772$		0			0
$773$	0.577778	+	4.01854i	0.0207812	+	0.144537i	0.997570	−	0.0696666i	$-0.0221936\pi$
$773$	0.577778	+	4.01854i	0.0207812	+	0.144537i	−0.976789	+	0.214203i	$0.931284\pi$
$774$		0			0
$775$	−1.74121	+	3.81272i	−0.0625462	+	0.136957i
$776$		0			0
$777$	−3.69173	+	4.26049i	−0.132440	+	0.152844i
$778$		0			0
$779$	−4.64844	+	2.98737i	−0.166548	+	0.107034i
$780$		0			0
$781$	−18.2996	+	40.7662i	−0.654811	+	1.45873i
$782$		0			0
$783$	36.7070	+	42.3622i	1.31180	+	1.51390i
$784$		0			0
$785$	−6.43759	−	44.7744i	−0.229767	−	1.59807i
$786$		0			0
$787$	5.81566	+	40.4488i	0.207306	+	1.44184i	0.781899	+	0.623405i	$0.214251\pi$
$787$	5.81566	+	40.4488i	0.207306	+	1.44184i	−0.574593	+	0.818439i	$0.694840\pi$
$788$		0			0
$789$	30.4621	−	19.5768i	1.08448	−	0.696952i
$790$		0			0
$791$	3.96630	+	27.5863i	0.141026	+	0.980854i
$792$		0			0
$793$	2.97494	−	20.6912i	0.105643	−	0.734766i
$794$		0			0
$795$	30.9220	+	19.8724i	1.09669	+	0.704800i
$796$		0			0
$797$	18.8014	+	21.6980i	0.665981	+	0.768583i	0.983742	−	0.179588i	$-0.0574765\pi$
$797$	18.8014	+	21.6980i	0.665981	+	0.768583i	−0.317761	+	0.948171i	$0.602931\pi$
$798$		0			0
$799$	−2.19122	−	1.40821i	−0.0775197	−	0.0498189i
$800$		0			0
$801$	0.0388301	−	0.0448124i	0.00137199	−	0.00158337i
$802$		0			0
$803$	2.93164	−	21.3703i	0.103455	−	0.754142i
$804$		0			0
$805$	−4.27287	−	9.35629i	−0.150599	−	0.329766i
$806$		0			0
$807$	18.0465			0.635265
$808$		0			0
$809$	−21.7416	+	13.9725i	−0.764395	+	0.491247i	−0.863822	−	0.503798i	$-0.831936\pi$
$809$	−21.7416	+	13.9725i	−0.764395	+	0.491247i	0.0994262	+	0.995045i	$0.468299\pi$
$810$		0			0
$811$	−41.1729	−	12.0895i	−1.44578	−	0.424518i	−0.537633	−	0.843179i	$-0.680681\pi$
$811$	−41.1729	−	12.0895i	−1.44578	−	0.424518i	−0.908143	+	0.418661i	$0.862500\pi$
$812$		0			0
$813$	17.8460	+	20.5954i	0.625886	+	0.722311i
$814$		0			0
$815$	−13.1992	+	15.2327i	−0.462348	+	0.533578i
$816$		0			0
$817$	10.9051	−	3.20202i	0.381521	−	0.112025i
$818$		0			0
$819$	4.74911	−	1.39447i	0.165947	−	0.0487266i
$820$		0			0
$821$	8.00241	−	17.5228i	0.279286	−	0.611551i	−0.717055	−	0.697016i	$-0.754510\pi$
$821$	8.00241	−	17.5228i	0.279286	−	0.611551i	0.996341	+	0.0854655i	$0.0272377\pi$
$822$		0			0
$823$	−20.2821	+	44.4116i	−0.706990	+	1.54809i	0.124295	+	0.992245i	$0.460333\pi$
$823$	−20.2821	+	44.4116i	−0.706990	+	1.54809i	−0.831285	+	0.555846i	$0.812394\pi$
$824$		0			0
$825$	−2.20275	−	0.631339i	−0.0766899	−	0.0219804i
$826$		0			0
$827$	−2.33475	−	16.2385i	−0.0811872	−	0.564670i	−0.989295	−	0.145932i	$-0.953382\pi$
$827$	−2.33475	−	16.2385i	−0.0811872	−	0.564670i	0.908107	−	0.418737i	$-0.137527\pi$
$828$		0			0
$829$	−6.07343	+	42.2416i	−0.210939	+	1.46711i	0.559092	+	0.829106i	$0.311150\pi$
$829$	−6.07343	+	42.2416i	−0.210939	+	1.46711i	−0.770031	+	0.638007i	$0.779759\pi$
$830$		0			0
$831$	11.0026	+	7.07096i	0.381677	+	0.245289i
$832$		0			0
$833$	−1.44972	−	3.17445i	−0.0502299	−	0.109988i
$834$		0			0
$835$	−24.9512	−	7.32634i	−0.863472	−	0.253538i
$836$		0			0
$837$	−45.6902	+	13.4159i	−1.57928	+	0.463720i
$838$		0			0
$839$	10.3707	−	22.7086i	0.358035	−	0.783987i	−0.641819	−	0.766857i	$-0.721820\pi$
$839$	10.3707	−	22.7086i	0.358035	−	0.783987i	0.999853	−	0.0171301i	$-0.00545296\pi$
$840$		0			0
$841$	−9.86027	+	68.5797i	−0.340009	+	2.36482i
$842$		0			0
$843$	3.41633	+	1.00313i	0.117665	+	0.0345495i
$844$		0			0
$845$	2.48750	−	17.3010i	0.0855726	−	0.595171i
$846$		0			0
$847$	2.79099	−	21.3707i	0.0958996	−	0.734306i
$848$		0			0
$849$	−1.40344	+	9.76116i	−0.0481660	+	0.335002i
$850$		0			0
$851$	4.45253	+	1.30738i	0.152631	+	0.0448164i
$852$		0			0
$853$	−3.82977	+	26.6367i	−0.131129	+	0.912022i	0.812957	+	0.582323i	$0.197856\pi$
$853$	−3.82977	+	26.6367i	−0.131129	+	0.912022i	−0.944086	+	0.329699i	$0.893053\pi$
$854$		0			0
$855$	2.91755	−	6.38853i	0.0997780	−	0.218483i
$856$		0			0
$857$	32.4109	−	9.51669i	1.10713	−	0.325084i	0.323452	−	0.946245i	$-0.395157\pi$
$857$	32.4109	−	9.51669i	1.10713	−	0.325084i	0.783683	+	0.621161i	$0.213339\pi$
$858$		0			0
$859$	1.89850	+	0.557449i	0.0647758	+	0.0190199i	0.313960	−	0.949436i	$-0.398344\pi$
$859$	1.89850	+	0.557449i	0.0647758	+	0.0190199i	−0.249184	+	0.968456i	$0.580162\pi$
$860$		0			0
$861$	−2.23608	−	4.89633i	−0.0762054	−	0.166867i
$862$		0			0
$863$	−27.6831	−	17.7909i	−0.942344	−	0.605608i	−0.0232857	−	0.999729i	$-0.507413\pi$
$863$	−27.6831	−	17.7909i	−0.942344	−	0.605608i	−0.919059	+	0.394121i	$0.871049\pi$
$864$		0			0
$865$	−1.64196	+	11.4201i	−0.0558282	+	0.388294i
$866$		0			0
$867$	3.11788	+	21.6853i	0.105889	+	0.736473i
$868$		0			0
$869$	27.8928	−	32.6139i	0.946199	−	1.10635i
$870$		0			0
$871$	2.47125	−	5.41127i	0.0837349	−	0.183354i
$872$		0			0
$873$	−4.21865	+	9.23755i	−0.142780	+	0.312644i
$874$		0			0
$875$	−19.8457	+	5.82723i	−0.670908	+	0.196996i
$876$		0			0
$877$	45.2476	−	13.2859i	1.52790	−	0.448633i	0.593495	−	0.804838i	$-0.297748\pi$
$877$	45.2476	−	13.2859i	1.52790	−	0.448633i	0.934408	+	0.356205i	$0.115929\pi$
$878$		0			0
$879$	−29.5133	+	34.0602i	−0.995459	+	1.14882i
$880$		0			0
$881$	−37.6292	−	43.4264i	−1.26776	−	1.46307i	−0.823650	−	0.567098i	$-0.808066\pi$
$881$	−37.6292	−	43.4264i	−1.26776	−	1.46307i	−0.444108	−	0.895973i	$-0.646479\pi$
$882$		0			0
$883$	−22.8723	−	6.71591i	−0.769714	−	0.226008i	−0.126781	−	0.991931i	$-0.540465\pi$
$883$	−22.8723	−	6.71591i	−0.769714	−	0.226008i	−0.642933	+	0.765922i	$0.722283\pi$
$884$		0			0
$885$	−4.95182	+	3.18234i	−0.166453	+	0.106973i
$886$		0			0
$887$	20.7675			0.697306			0.348653	−	0.937252i	$-0.386639\pi$
$887$	20.7675			0.697306			0.348653	+	0.937252i	$0.386639\pi$
$888$		0			0
$889$	16.3078	+	35.7091i	0.546947	+	1.19765i
$890$		0			0
$891$	−6.47053	−	13.9294i	−0.216771	−	0.466651i
$892$		0			0
$893$	−4.31415	+	4.97880i	−0.144368	+	0.166609i
$894$		0			0
$895$	−27.7386	−	17.8265i	−0.927198	−	0.595874i
$896$		0			0
$897$	4.79328	+	5.53174i	0.160043	+	0.184699i
$898$		0			0
$899$	−70.2417	−	45.1416i	−2.34269	−	1.50556i
$900$		0			0
$901$	−1.77414	+	12.3394i	−0.0591051	+	0.411085i
$902$		0			0
$903$	1.57566	+	10.9590i	0.0524347	+	0.364691i
$904$		0			0
$905$	40.6931	−	26.1519i	1.35268	−	0.869317i
$906$		0			0
$907$	−7.57589	−	52.6914i	−0.251553	−	1.74959i	−0.588896	−	0.808209i	$-0.700437\pi$
$907$	−7.57589	−	52.6914i	−0.251553	−	1.74959i	0.337343	−	0.941382i	$-0.390472\pi$
$908$		0			0
$909$	1.79458	+	12.4816i	0.0595224	+	0.413988i
$910$		0			0
$911$	−26.6981	−	30.8113i	−0.884548	−	1.02082i	−0.999623	−	0.0274664i	$-0.991256\pi$
$911$	−26.6981	−	30.8113i	−0.884548	−	1.02082i	0.115074	−	0.993357i	$-0.463289\pi$
$912$		0			0
$913$	−28.8111	−	18.2536i	−0.953509	−	0.604105i
$914$		0			0
$915$	24.3078	−	15.6217i	0.803590	−	0.516436i
$916$		0			0
$917$	1.15891	−	1.33745i	0.0382704	−	0.0441664i
$918$		0			0
$919$	−3.55320	+	7.78042i	−0.117209	+	0.256652i	−0.959139	−	0.282934i	$-0.908692\pi$
$919$	−3.55320	+	7.78042i	−0.117209	+	0.256652i	0.841930	+	0.539587i	$0.181419\pi$
$920$		0			0
$921$	−4.98005	−	34.6370i	−0.164098	−	1.14133i
$922$		0			0
$923$	13.1800	+	28.8602i	0.433825	+	0.949945i
$924$		0			0
$925$	−0.428492	+	0.938266i	−0.0140887	+	0.0308500i
$926$		0			0
$927$	1.17570	−	8.17715i	0.0386149	−	0.268573i
$928$		0			0
$929$	17.6090	+	5.17047i	0.577733	+	0.169638i	0.557528	−	0.830158i	$-0.311750\pi$
$929$	17.6090	+	5.17047i	0.577733	+	0.169638i	0.0202050	+	0.999796i	$0.493568\pi$
$930$		0			0
$931$	−8.46900	+	2.48672i	−0.277560	+	0.0814990i
$932$		0			0
$933$	−36.6971	−	23.5838i	−1.20141	−	0.772098i
$934$		0			0
$935$	−1.27670	−	8.48951i	−0.0417527	−	0.277637i
$936$		0			0
$937$	28.7266	−	8.43488i	0.938456	−	0.275555i	0.223483	−	0.974708i	$-0.428257\pi$
$937$	28.7266	−	8.43488i	0.938456	−	0.275555i	0.714973	+	0.699152i	$0.246439\pi$
$938$		0			0
$939$	14.1014	+	16.2738i	0.460181	+	0.531077i
$940$		0			0
$941$	−40.3125			−1.31415			−0.657075	−	0.753826i	$-0.728206\pi$
$941$	−40.3125			−1.31415			−0.657075	+	0.753826i	$0.728206\pi$
$942$		0			0
$943$	−2.90160	+	3.34863i	−0.0944891	+	0.109046i
$944$		0			0
$945$	21.8510	+	14.0428i	0.710814	+	0.456812i
$946$		0			0
$947$	−2.37554	+	1.52666i	−0.0771946	+	0.0496099i	−0.578669	−	0.815563i	$-0.696428\pi$
$947$	−2.37554	+	1.52666i	−0.0771946	+	0.0496099i	0.501474	+	0.865173i	$0.332791\pi$
$948$		0			0
$949$	−10.0295	−	11.5747i	−0.325571	−	0.375729i
$950$		0			0
$951$	10.3284	−	11.9197i	0.334923	−	0.386522i
$952$		0			0
$953$	−0.467021	−	1.02263i	−0.0151283	−	0.0331264i	0.901917	−	0.431909i	$-0.142160\pi$
$953$	−0.467021	−	1.02263i	−0.0151283	−	0.0331264i	−0.917045	+	0.398783i	$0.869433\pi$
$954$		0			0
$955$	−9.50165	−	2.78993i	−0.307466	−	0.0902802i
$956$		0			0
$957$	18.6933	−	41.6432i	0.604268	−	1.34613i
$958$		0			0
$959$	10.0859			0.325692
$960$		0			0
$961$	33.5939	−	21.5895i	1.08367	−	0.696435i
$962$		0			0
$963$	−4.37146	−	9.57215i	−0.140868	−	0.308458i
$964$		0			0
$965$	−20.6425			−0.664504
$966$		0			0
$967$	40.0271			1.28718			0.643592	−	0.765369i	$-0.277443\pi$
$967$	40.0271			1.28718			0.643592	+	0.765369i	$0.277443\pi$
$968$		0			0
$969$	−4.27919			−0.137467
$970$		0			0
$971$	16.6439			0.534128			0.267064	−	0.963679i	$-0.413947\pi$
$971$	16.6439			0.534128			0.267064	+	0.963679i	$0.413947\pi$
$972$		0			0
$973$	−4.36786	−	9.56428i	−0.140027	−	0.306617i
$974$		0			0
$975$	−1.36869	+	0.879605i	−0.0438332	+	0.0281699i
$976$		0			0
$977$	−27.3750			−0.875803			−0.437901	−	0.899023i	$-0.644278\pi$
$977$	−27.3750			−0.875803			−0.437901	+	0.899023i	$0.644278\pi$
$978$		0			0
$979$	−0.176225	−	0.0505086i	−0.00563218	−	0.00161426i
$980$		0			0
$981$	6.75517	+	1.98350i	0.215676	+	0.0633282i
$982$		0			0
$983$	−1.49320	−	3.26965i	−0.0476257	−	0.104286i	0.884323	−	0.466875i	$-0.154620\pi$
$983$	−1.49320	−	3.26965i	−0.0476257	−	0.104286i	−0.931949	+	0.362589i	$0.881893\pi$
$984$		0			0
$985$	−14.9337	+	17.2344i	−0.475827	+	0.549133i
$986$		0			0
$987$	−4.20262	−	4.85009i	−0.133771	−	0.154380i
$988$		0			0
$989$	7.66696	−	4.92725i	0.243795	−	0.156678i
$990$		0			0
$991$	−17.8891	−	11.4966i	−0.568266	−	0.365202i	0.224738	−	0.974419i	$-0.427847\pi$
$991$	−17.8891	−	11.4966i	−0.568266	−	0.365202i	−0.793004	+	0.609217i	$0.791484\pi$
$992$		0			0
$993$	11.1414	−	12.8579i	0.353563	−	0.408034i
$994$		0			0
$995$	−19.3623			−0.613827
$996$		0			0
$997$	−27.0995	−	31.2745i	−0.858249	−	0.990472i	−1.00000		0.000569640i	$-0.999819\pi$
$997$	−27.0995	−	31.2745i	−0.858249	−	0.990472i	0.141751	−	0.989902i	$-0.454727\pi$
$998$		0			0
$999$	−11.2438	+	3.30148i	−0.355739	+	0.104454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.i.a.89.8	✓	110
121.34	even	11	inner	484.2.i.a.397.8	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
484.2.i.a.89.8	✓	110	1.1	even	1	trivial
484.2.i.a.397.8	yes	110	121.34	even	11	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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+1.38825 q^{3} +(0.974029 + 2.13282i) q^{5} +(-1.64826 + 1.05927i) q^{7} -1.07277 q^{9} +(1.39726 + 3.00793i) q^{11} +(2.25948 + 0.663443i) q^{13} +(1.35219 + 2.96089i) q^{15} +(-0.722940 + 0.834317i) q^{17} +(1.82848 + 2.11018i) q^{19} +(-2.28819 + 1.47053i) q^{21} +(1.88355 + 1.21048i) q^{23} +(-0.325907 + 0.376117i) q^{25} -5.65401 q^{27} +(-6.49221 - 7.49241i) q^{29} +(8.08103 - 2.37280i) q^{31} +(1.93974 + 4.17576i) q^{33} +(-3.86469 - 2.48369i) q^{35} +(1.98865 - 0.583919i) q^{37} +(3.13672 + 0.921024i) q^{39} +(-0.281637 + 1.95883i) q^{41} +(1.69094 - 3.70265i) q^{43} +(-1.04490 - 2.28802i) q^{45} +(0.335781 + 2.33541i) q^{47} +(-1.31320 + 2.87551i) q^{49} +(-1.00362 + 1.15824i) q^{51} +(9.49972 - 6.10510i) q^{53} +(-5.05443 + 5.90992i) q^{55} +(2.53838 + 2.92945i) q^{57} +(0.257354 + 1.78994i) q^{59} +(-1.26332 - 8.78655i) q^{61} +(1.76820 - 1.13635i) q^{63} +(0.785790 + 5.46529i) q^{65} +(0.359515 - 2.50048i) q^{67} +(2.61483 + 1.68045i) q^{69} +(8.82298 + 10.1823i) q^{71} +(-5.47129 - 3.51619i) q^{73} +(-0.452440 + 0.522143i) q^{75} +(-5.48927 - 3.47778i) q^{77} +(-5.37517 - 11.7700i) q^{79} -4.63087 q^{81} +(-8.65111 + 5.55973i) q^{83} +(-2.48362 - 0.729255i) q^{85} +(-9.01280 - 10.4013i) q^{87} +(-0.0361963 + 0.0417727i) q^{89} +(-4.42698 + 1.29988i) q^{91} +(11.2185 - 3.29404i) q^{93} +(-2.71965 + 5.95520i) q^{95} +(3.93249 - 8.61096i) q^{97} +(-1.49893 - 3.22681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{3} + 2 q^{5} - 2 q^{7} + 112 q^{9} - 10 q^{11} - 29 q^{13} - 18 q^{15} - 6 q^{17} - 8 q^{19} - 2 q^{21} + 4 q^{23} - 17 q^{25} + 4 q^{27} - 28 q^{31} + q^{33} + 6 q^{35} - 31 q^{37} + 4 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) \) 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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