LMFDB - Embedded newform 483.2.d.d.461.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (of order $2$, degree $1$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.6
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.52935i q^{2} +(0.292165 + 1.70723i) q^{3} -4.39759 q^{4} +0.707387 q^{5} +(4.31818 - 0.738987i) q^{6} +(-2.12498 - 1.57622i) q^{7} +6.06435i q^{8} +(-2.82928 + 0.997587i) q^{9} -1.78923i q^{10} -5.52115i q^{11} +(-1.28482 - 7.50771i) q^{12} +1.55101i q^{13} +(-3.98681 + 5.37480i) q^{14} +(0.206674 + 1.20767i) q^{15} +6.54364 q^{16} -4.61936 q^{17} +(2.52324 + 7.15623i) q^{18} -7.93197i q^{19} -3.11080 q^{20} +(2.07013 - 4.08834i) q^{21} -13.9649 q^{22} +1.00000i q^{23} +(-10.3532 + 1.77179i) q^{24} -4.49960 q^{25} +3.92303 q^{26} +(-2.52973 - 4.53877i) q^{27} +(9.34478 + 6.93158i) q^{28} -2.49930i q^{29} +(3.05463 - 0.522750i) q^{30} +5.71523i q^{31} -4.42245i q^{32} +(9.42589 - 1.61309i) q^{33} +11.6840i q^{34} +(-1.50318 - 1.11500i) q^{35} +(12.4420 - 4.38698i) q^{36} -0.902839 q^{37} -20.0627 q^{38} +(-2.64792 + 0.453149i) q^{39} +4.28984i q^{40} +3.75081 q^{41} +(-10.3408 - 5.23608i) q^{42} -9.08177 q^{43} +24.2798i q^{44} +(-2.00140 + 0.705680i) q^{45} +2.52935 q^{46} +9.85490 q^{47} +(1.91182 + 11.1715i) q^{48} +(2.03105 + 6.69887i) q^{49} +11.3811i q^{50} +(-1.34962 - 7.88632i) q^{51} -6.82069i q^{52} -5.71246i q^{53} +(-11.4801 + 6.39856i) q^{54} -3.90559i q^{55} +(9.55875 - 12.8866i) q^{56} +(13.5417 - 2.31745i) q^{57} -6.32158 q^{58} +12.0511 q^{59} +(-0.908867 - 5.31086i) q^{60} -9.47586i q^{61} +14.4558 q^{62} +(7.58457 + 2.33972i) q^{63} +1.90138 q^{64} +1.09716i q^{65} +(-4.08006 - 23.8413i) q^{66} -0.757531 q^{67} +20.3141 q^{68} +(-1.70723 + 0.292165i) q^{69} +(-2.82022 + 3.80207i) q^{70} -2.66408i q^{71} +(-6.04971 - 17.1577i) q^{72} +1.77391i q^{73} +2.28359i q^{74} +(-1.31463 - 7.68186i) q^{75} +34.8816i q^{76} +(-8.70256 + 11.7323i) q^{77} +(1.14617 + 6.69752i) q^{78} +6.58585 q^{79} +4.62889 q^{80} +(7.00964 - 5.64490i) q^{81} -9.48709i q^{82} +7.55664 q^{83} +(-9.10360 + 17.9789i) q^{84} -3.26768 q^{85} +22.9709i q^{86} +(4.26688 - 0.730207i) q^{87} +33.4822 q^{88} -12.1777 q^{89} +(1.78491 + 5.06222i) q^{90} +(2.44473 - 3.29585i) q^{91} -4.39759i q^{92} +(-9.75722 + 1.66979i) q^{93} -24.9265i q^{94} -5.61098i q^{95} +(7.55015 - 1.29209i) q^{96} +0.965637i q^{97} +(16.9438 - 5.13723i) q^{98} +(5.50783 + 15.6209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49}+ \cdots + 4 q^{99}+O(q^{100}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	2.52935i		−	1.78852i	−0.447550	−	0.894259i	$-0.647703\pi$
$2$		−	2.52935i		−	1.78852i	0.447550	−	0.894259i	$-0.352297\pi$
$3$	0.292165	+	1.70723i	0.168682	+	0.985671i
$3$	0.292165	+	1.70723i	0.168682	+	0.985671i
$4$	−4.39759			−2.19880
$5$	0.707387			0.316353			0.158177	−	0.987411i	$-0.449438\pi$
$5$	0.707387			0.316353			0.158177	+	0.987411i	$0.449438\pi$
$6$	4.31818	−	0.738987i	1.76289	−	0.301690i
$7$	−2.12498	−	1.57622i	−0.803166	−	0.595756i
$7$	−2.12498	−	1.57622i	−0.803166	−	0.595756i
$8$			6.06435i			2.14407i
$9$	−2.82928	+	0.997587i	−0.943093	+	0.332529i
$10$		−	1.78923i		−	0.565803i
$11$		−	5.52115i		−	1.66469i	−0.554258	−	0.832345i	$-0.686998\pi$
$11$		−	5.52115i		−	1.66469i	0.554258	−	0.832345i	$-0.313002\pi$
$12$	−1.28482	−	7.50771i	−0.370897	−	2.16729i
$13$			1.55101i			0.430171i	0.976595	+	0.215086i	$0.0690031\pi$
$13$			1.55101i			0.430171i	−0.976595	+	0.215086i	$0.930997\pi$
$14$	−3.98681	+	5.37480i	−1.06552	+	1.43648i
$15$	0.206674	+	1.20767i	0.0533629	+	0.311820i
$16$	6.54364			1.63591
$17$	−4.61936			−1.12036			−0.560180	−	0.828371i	$-0.689268\pi$
$17$	−4.61936			−1.12036			−0.560180	+	0.828371i	$0.689268\pi$
$18$	2.52324	+	7.15623i	0.594734	+	1.68674i
$19$		−	7.93197i		−	1.81972i	−0.414916	−	0.909860i	$-0.636189\pi$
$19$		−	7.93197i		−	1.81972i	0.414916	−	0.909860i	$-0.363811\pi$
$20$	−3.11080			−0.695596
$21$	2.07013	−	4.08834i	0.451740	−	0.892150i
$22$	−13.9649			−2.97733
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−10.3532	+	1.77179i	−2.11335	+	0.361665i
$25$	−4.49960			−0.899921
$26$	3.92303			0.769369
$27$	−2.52973	−	4.53877i	−0.486846	−	0.873488i
$28$	9.34478	+	6.93158i	1.76600	+	1.30995i
$29$		−	2.49930i		−	0.464108i	−0.972703	−	0.232054i	$-0.925455\pi$
$29$		−	2.49930i		−	0.464108i	0.972703	−	0.232054i	$-0.0745445\pi$
$30$	3.05463	−	0.522750i	0.557696	−	0.0954406i
$31$			5.71523i			1.02649i	0.858244	+	0.513243i	$0.171556\pi$
$31$			5.71523i			1.02649i	−0.858244	+	0.513243i	$0.828444\pi$
$32$		−	4.42245i		−	0.781786i
$33$	9.42589	−	1.61309i	1.64084	−	0.280803i
$34$			11.6840i			2.00378i
$35$	−1.50318	−	1.11500i	−0.254084	−	0.188469i
$36$	12.4420	−	4.38698i	2.07367	−	0.731164i
$37$	−0.902839			−0.148426			−0.0742129	−	0.997242i	$-0.523644\pi$
$37$	−0.902839			−0.148426			−0.0742129	+	0.997242i	$0.523644\pi$
$38$	−20.0627			−3.25460
$39$	−2.64792	+	0.453149i	−0.424007	+	0.0725620i
$40$			4.28984i			0.678283i
$41$	3.75081			0.585778			0.292889	−	0.956147i	$-0.405383\pi$
$41$	3.75081			0.585778			0.292889	+	0.956147i	$0.405383\pi$
$42$	−10.3408	−	5.23608i	−1.59563	−	0.807945i
$43$	−9.08177			−1.38496			−0.692479	−	0.721438i	$-0.743481\pi$
$43$	−9.08177			−1.38496			−0.692479	+	0.721438i	$0.743481\pi$
$44$			24.2798i			3.66032i
$45$	−2.00140	+	0.705680i	−0.298350	+	0.105197i
$46$	2.52935			0.372932
$47$	9.85490			1.43749			0.718743	−	0.695276i	$-0.244718\pi$
$47$	9.85490			1.43749			0.718743	+	0.695276i	$0.244718\pi$
$48$	1.91182	+	11.1715i	0.275948	+	1.61247i
$49$	2.03105	+	6.69887i	0.290150	+	0.956981i
$50$			11.3811i			1.60952i
$51$	−1.34962	−	7.88632i	−0.188984	−	1.10431i
$52$		−	6.82069i		−	0.945860i
$53$		−	5.71246i		−	0.784667i	−0.919823	−	0.392333i	$-0.871668\pi$
$53$		−	5.71246i		−	0.784667i	0.919823	−	0.392333i	$-0.128332\pi$
$54$	−11.4801	+	6.39856i	−1.56225	+	0.870734i
$55$		−	3.90559i		−	0.526630i
$56$	9.55875	−	12.8866i	1.27734	−	1.72204i
$57$	13.5417	−	2.31745i	1.79364	−	0.306953i
$58$	−6.32158			−0.830065
$59$	12.0511			1.56892			0.784459	−	0.620180i	$-0.212941\pi$
$59$	12.0511			1.56892			0.784459	+	0.620180i	$0.212941\pi$
$60$	−0.908867	−	5.31086i	−0.117334	−	0.685629i
$61$		−	9.47586i		−	1.21326i	−0.794984	−	0.606630i	$-0.792521\pi$
$61$		−	9.47586i		−	1.21326i	0.794984	−	0.606630i	$-0.207479\pi$
$62$	14.4558			1.83589
$63$	7.58457	+	2.33972i	0.955566	+	0.294777i
$64$	1.90138			0.237672
$65$			1.09716i			0.136086i
$66$	−4.08006	−	23.8413i	−0.502220	−	2.93467i
$67$	−0.757531			−0.0925472			−0.0462736	−	0.998929i	$-0.514735\pi$
$67$	−0.757531			−0.0925472			−0.0462736	+	0.998929i	$0.514735\pi$
$68$	20.3141			2.46344
$69$	−1.70723	+	0.292165i	−0.205527	+	0.0351725i
$70$	−2.82022	+	3.80207i	−0.337081	+	0.454434i
$71$		−	2.66408i		−	0.316168i	−0.987426	−	0.158084i	$-0.949468\pi$
$71$		−	2.66408i		−	0.316168i	0.987426	−	0.158084i	$-0.0505317\pi$
$72$	−6.04971	−	17.1577i	−0.712965	−	2.02206i
$73$			1.77391i			0.207620i	0.994597	+	0.103810i	$0.0331034\pi$
$73$			1.77391i			0.207620i	−0.994597	+	0.103810i	$0.966897\pi$
$74$			2.28359i			0.265462i
$75$	−1.31463	−	7.68186i	−0.151800	−	0.887025i
$76$			34.8816i			4.00119i
$77$	−8.70256	+	11.7323i	−0.991749	+	1.33702i
$78$	1.14617	+	6.69752i	0.129778	+	0.758345i
$79$	6.58585			0.740966			0.370483	−	0.928839i	$-0.379192\pi$
$79$	6.58585			0.740966			0.370483	+	0.928839i	$0.379192\pi$
$80$	4.62889			0.517526
$81$	7.00964	−	5.64490i	0.778849	−	0.627211i
$82$		−	9.48709i		−	1.04767i
$83$	7.55664			0.829449			0.414725	−	0.909947i	$-0.363878\pi$
$83$	7.55664			0.829449			0.414725	+	0.909947i	$0.363878\pi$
$84$	−9.10360	+	17.9789i	−0.993284	+	1.96166i
$85$	−3.26768			−0.354429
$86$			22.9709i			2.47702i
$87$	4.26688	−	0.730207i	0.457457	−	0.0782864i
$88$	33.4822			3.56921
$89$	−12.1777			−1.29083			−0.645417	−	0.763830i	$-0.723316\pi$
$89$	−12.1777			−1.29083			−0.645417	+	0.763830i	$0.723316\pi$
$90$	1.78491	+	5.06222i	0.188146	+	0.533605i
$91$	2.44473	−	3.29585i	0.256277	−	0.345499i
$92$		−	4.39759i		−	0.458481i
$93$	−9.75722	+	1.66979i	−1.01178	+	0.173149i
$94$		−	24.9265i		−	2.57097i
$95$		−	5.61098i		−	0.575674i
$96$	7.55015	−	1.29209i	0.770584	−	0.131873i
$97$			0.965637i			0.0980455i	0.998798	+	0.0490228i	$0.0156107\pi$
$97$			0.965637i			0.0980455i	−0.998798	+	0.0490228i	$0.984389\pi$
$98$	16.9438	−	5.13723i	1.71158	−	0.518939i
$99$	5.50783	+	15.6209i	0.553558	+	1.56996i
$100$	19.7874			1.97874
$101$	−1.40753			−0.140054			−0.0700271	−	0.997545i	$-0.522309\pi$
$101$	−1.40753			−0.140054			−0.0700271	+	0.997545i	$0.522309\pi$
$102$	−19.9472	+	3.41365i	−1.97507	+	0.338001i
$103$			16.3750i			1.61348i	0.590909	+	0.806738i	$0.298769\pi$
$103$			16.3750i			1.61348i	−0.590909	+	0.806738i	$0.701231\pi$
$104$	−9.40583			−0.922318
$105$	1.46438	−	2.89204i	0.142909	−	0.282234i
$106$	−14.4488			−1.40339
$107$		−	0.250085i		−	0.0241766i	−0.999927	−	0.0120883i	$-0.996152\pi$
$107$		−	0.250085i		−	0.0241766i	0.999927	−	0.0120883i	$-0.00384792\pi$
$108$	11.1247	+	19.9597i	1.07048	+	1.92062i
$109$	−5.31325			−0.508917			−0.254458	−	0.967084i	$-0.581897\pi$
$109$	−5.31325			−0.508917			−0.254458	+	0.967084i	$0.581897\pi$
$110$	−9.87860			−0.941887
$111$	−0.263778	−	1.54136i	−0.0250367	−	0.146299i
$112$	−13.9051	−	10.3142i	−1.31391	−	0.974603i
$113$		−	17.3070i		−	1.62811i	−0.580788	−	0.814055i	$-0.697255\pi$
$113$		−	17.3070i		−	1.62811i	0.580788	−	0.814055i	$-0.302745\pi$
$114$	−5.86162	−	34.2517i	−0.548991	−	3.20797i
$115$			0.707387i			0.0659642i
$116$			10.9909i			1.02048i
$117$	−1.54726	−	4.38823i	−0.143044	−	0.405692i
$118$		−	30.4814i		−	2.80604i
$119$	9.81603	+	7.28114i	0.899834	+	0.667461i
$120$	−7.32375	+	1.25334i	−0.668564	+	0.114414i
$121$	−19.4831			−1.77119
$122$	−23.9677			−2.16994
$123$	1.09585	+	6.40350i	0.0988099	+	0.577384i
$124$		−	25.1333i		−	2.25703i
$125$	−6.71990			−0.601046
$126$	5.91797	−	19.1840i	0.527215	−	1.70905i
$127$	0.813212			0.0721609			0.0360805	−	0.999349i	$-0.488513\pi$
$127$	0.813212			0.0721609			0.0360805	+	0.999349i	$0.488513\pi$
$128$		−	13.6541i		−	1.20687i
$129$	−2.65338	−	15.5047i	−0.233617	−	1.36511i
$130$	2.77510			0.243392
$131$	−0.402916			−0.0352029			−0.0176015	−	0.999845i	$-0.505603\pi$
$131$	−0.402916			−0.0352029			−0.0176015	+	0.999845i	$0.505603\pi$
$132$	−41.4512	+	7.09371i	−3.60787	+	0.617428i
$133$	−12.5026	+	16.8553i	−1.08411	+	1.46154i
$134$			1.91606i			0.165522i
$135$	−1.78950	−	3.21067i	−0.154015	−	0.276331i
$136$		−	28.0134i		−	2.40213i
$137$			0.400246i			0.0341953i	0.999854	+	0.0170977i	$0.00544262\pi$
$137$			0.400246i			0.0341953i	−0.999854	+	0.0170977i	$0.994557\pi$
$138$	0.738987	+	4.31818i	0.0629067	+	0.367588i
$139$		−	9.97089i		−	0.845720i	−0.906195	−	0.422860i	$-0.861026\pi$
$139$		−	9.97089i		−	0.845720i	0.906195	−	0.422860i	$-0.138974\pi$
$140$	6.61038	+	4.90331i	0.558679	+	0.414406i
$141$	2.87926	+	16.8246i	0.242477	+	1.41689i
$142$	−6.73839			−0.565473
$143$	8.56334			0.716102
$144$	−18.5138	+	6.52785i	−1.54282	+	0.543988i
$145$		−	1.76797i		−	0.146822i
$146$	4.48682			0.371332
$147$	−10.8431	+	5.42465i	−0.894325	+	0.447418i
$148$	3.97032			0.326358
$149$		−	6.66349i		−	0.545894i	−0.962029	−	0.272947i	$-0.912002\pi$
$149$		−	6.66349i		−	0.545894i	0.962029	−	0.272947i	$-0.0879984\pi$
$150$	−19.4301	+	3.32515i	−1.58646	+	0.271497i
$151$	3.28477			0.267311			0.133655	−	0.991028i	$-0.457329\pi$
$151$	3.28477			0.267311			0.133655	+	0.991028i	$0.457329\pi$
$152$	48.1022			3.90161
$153$	13.0695	−	4.60821i	1.05660	−	0.372552i
$154$	29.6751	+	22.0118i	2.39129	+	1.77376i
$155$			4.04288i			0.324732i
$156$	11.6445	−	1.99277i	0.932306	−	0.159549i
$157$			13.0633i			1.04257i	0.853384	+	0.521283i	$0.174547\pi$
$157$			13.0633i			1.04257i	−0.853384	+	0.521283i	$0.825453\pi$
$158$		−	16.6579i		−	1.32523i
$159$	9.75249	−	1.66898i	0.773423	−	0.132359i
$160$		−	3.12839i		−	0.247321i
$161$	1.57622	−	2.12498i	0.124224	−	0.167472i
$162$	−14.2779	−	17.7298i	−1.12178	−	1.39299i
$163$	0.510051			0.0399503			0.0199751	−	0.999800i	$-0.493641\pi$
$163$	0.510051			0.0399503			0.0199751	+	0.999800i	$0.493641\pi$
$164$	−16.4945			−1.28801
$165$	6.66775	−	1.14108i	0.519084	−	0.0888328i
$166$		−	19.1134i		−	1.48349i
$167$	0.102981			0.00796894			0.00398447	−	0.999992i	$-0.498732\pi$
$167$	0.102981			0.00796894			0.00398447	+	0.999992i	$0.498732\pi$
$168$	24.7931	+	12.5540i	1.91283	+	0.968562i
$169$	10.5944			0.814953
$170$			8.26509i			0.633903i
$171$	7.91283	+	22.4418i	0.605109	+	1.71617i
$172$	39.9379			3.04524
$173$	−4.16159			−0.316400			−0.158200	−	0.987407i	$-0.550569\pi$
$173$	−4.16159			−0.316400			−0.158200	+	0.987407i	$0.550569\pi$
$174$	−1.84695	−	10.7924i	−0.140017	−	0.818170i
$175$	9.56155	+	7.09237i	0.722785	+	0.536133i
$176$		−	36.1285i		−	2.72329i
$177$	3.52091	+	20.5740i	0.264648	+	1.54644i
$178$			30.8016i			2.30868i
$179$			9.47344i			0.708078i	0.935231	+	0.354039i	$0.115192\pi$
$179$			9.47344i			0.708078i	−0.935231	+	0.354039i	$0.884808\pi$
$180$	8.80133	−	3.10329i	0.656012	−	0.231306i
$181$		−	9.81326i		−	0.729414i	−0.931122	−	0.364707i	$-0.881169\pi$
$181$		−	9.81326i		−	0.729414i	0.931122	−	0.364707i	$-0.118831\pi$
$182$	−8.33635	−	6.18356i	−0.617931	−	0.458356i
$183$	16.1775	−	2.76852i	1.19587	−	0.204655i
$184$	−6.06435			−0.447069
$185$	−0.638657			−0.0469550
$186$	4.22348	+	24.6794i	0.309680	+	1.80958i
$187$			25.5042i			1.86505i
$188$	−43.3379			−3.16074
$189$	−1.77850	+	13.6322i	−0.129367	+	0.991597i
$190$	−14.1921			−1.02960
$191$		−	18.3642i		−	1.32879i	−0.747384	−	0.664393i	$-0.768690\pi$
$191$		−	18.3642i		−	1.32879i	0.747384	−	0.664393i	$-0.231310\pi$
$192$	0.555516	+	3.24609i	0.0400909	+	0.234266i
$193$	2.26270			0.162872			0.0814362	−	0.996679i	$-0.474049\pi$
$193$	2.26270			0.162872			0.0814362	+	0.996679i	$0.474049\pi$
$194$	2.44243			0.175356
$195$	−1.87311	+	0.320552i	−0.134136	+	0.0229552i
$196$	−8.93174	−	29.4589i	−0.637981	−	2.10421i
$197$		−	24.9037i		−	1.77431i	−0.461468	−	0.887157i	$-0.652677\pi$
$197$		−	24.9037i		−	1.77431i	0.461468	−	0.887157i	$-0.347323\pi$
$198$	39.5106	−	13.9312i	2.80790	−	0.990048i
$199$			15.5526i			1.10250i	0.834341	+	0.551249i	$0.185849\pi$
$199$			15.5526i			1.10250i	−0.834341	+	0.551249i	$0.814151\pi$
$200$		−	27.2871i		−	1.92949i
$201$	−0.221324	−	1.29328i	−0.0156110	−	0.0912211i
$202$			3.56012i			0.250489i
$203$	−3.93944	+	5.31094i	−0.276495	+	0.372755i
$204$	5.93506	+	34.6808i	0.415537	+	2.42814i
$205$	2.65327			0.185313
$206$	41.4180			2.88573
$207$	−0.997587	−	2.82928i	−0.0693371	−	0.196648i
$208$			10.1492i			0.703722i
$209$	−43.7936			−3.02927
$210$	−7.31498	−	3.70394i	−0.504781	−	0.255596i
$211$	−16.0941			−1.10796			−0.553980	−	0.832530i	$-0.686892\pi$
$211$	−16.0941			−1.10796			−0.553980	+	0.832530i	$0.686892\pi$
$212$			25.1211i			1.72532i
$213$	4.54820	−	0.778352i	0.311638	−	0.0533318i
$214$	−0.632551			−0.0432403
$215$	−6.42433			−0.438136
$216$	27.5247	−	15.3411i	1.87282	−	1.04383i
$217$	9.00847	−	12.1447i	0.611535	−	0.824438i
$218$			13.4390i			0.910207i
$219$	−3.02847	+	0.518273i	−0.204645	+	0.0350217i
$220$			17.1752i			1.15795i
$221$		−	7.16465i		−	0.481947i
$222$	−3.89862	+	0.667186i	−0.261658	+	0.0447786i
$223$		−	4.41080i		−	0.295369i	−0.989035	−	0.147684i	$-0.952818\pi$
$223$		−	4.41080i		−	0.295369i	0.989035	−	0.147684i	$-0.0471820\pi$
$224$	−6.97076	+	9.39760i	−0.465754	+	0.627904i
$225$	12.7306	−	4.48874i	0.848709	−	0.299250i
$226$	−43.7755			−2.91190
$227$	13.4489			0.892637			0.446319	−	0.894874i	$-0.352735\pi$
$227$	13.4489			0.892637			0.446319	+	0.894874i	$0.352735\pi$
$228$	−59.5510	+	10.1912i	−3.94386	+	0.674928i
$229$		−	15.6363i		−	1.03328i	−0.856204	−	0.516638i	$-0.827183\pi$
$229$		−	15.6363i		−	1.03328i	0.856204	−	0.516638i	$-0.172817\pi$
$230$	1.78923			0.117978
$231$	−22.5724	−	11.4295i	−1.48515	−	0.752007i
$232$	15.1566			0.995079
$233$			26.1148i			1.71084i	0.517938	+	0.855418i	$0.326700\pi$
$233$			26.1148i			1.71084i	−0.517938	+	0.855418i	$0.673300\pi$
$234$	−11.0993	+	3.91356i	−0.725587	+	0.255838i
$235$	6.97123			0.454753
$236$	−52.9958			−3.44973
$237$	1.92415	+	11.2436i	0.124987	+	0.730348i
$238$	18.4165	−	24.8281i	1.19377	−	1.60937i
$239$		−	8.62392i		−	0.557835i	−0.960315	−	0.278918i	$-0.910024\pi$
$239$		−	8.62392i		−	0.557835i	0.960315	−	0.278918i	$-0.0899756\pi$
$240$	1.35240	+	7.90259i	0.0872970	+	0.510110i
$241$			1.62968i			0.104977i	0.998622	+	0.0524883i	$0.0167152\pi$
$241$			1.62968i			0.104977i	−0.998622	+	0.0524883i	$0.983285\pi$
$242$			49.2796i			3.16781i
$243$	11.6851	+	10.3178i	0.749601	+	0.661890i
$244$			41.6710i			2.66771i
$245$	1.43674	+	4.73869i	0.0917899	+	0.302744i
$246$	16.1967	−	2.77180i	1.03266	−	0.176723i
$247$	12.3025			0.782791
$248$	−34.6591			−2.20086
$249$	2.20779	+	12.9009i	0.139913	+	0.817564i
$250$			16.9969i			1.07498i
$251$	21.6454			1.36625			0.683124	−	0.730302i	$-0.260621\pi$
$251$	21.6454			1.36625			0.683124	+	0.730302i	$0.260621\pi$
$252$	−33.3539	−	10.2891i	−2.10110	−	0.648155i
$253$	5.52115			0.347112
$254$		−	2.05690i		−	0.129061i
$255$	−0.954701	−	5.57868i	−0.0597857	−	0.349351i
$256$	−30.7333			−1.92083
$257$	8.71434			0.543585			0.271793	−	0.962356i	$-0.412383\pi$
$257$	8.71434			0.543585			0.271793	+	0.962356i	$0.412383\pi$
$258$	−39.2167	+	6.71131i	−2.44153	+	0.417828i
$259$	1.91851	+	1.42307i	0.119211	+	0.0884255i
$260$		−	4.82487i		−	0.299226i
$261$	2.49326	+	7.07121i	0.154329	+	0.437697i
$262$			1.01911i			0.0629611i
$263$		−	23.7871i		−	1.46678i	−0.679810	−	0.733388i	$-0.737938\pi$
$263$		−	23.7871i		−	1.46678i	0.679810	−	0.733388i	$-0.262062\pi$
$264$	9.78232	+	57.1618i	0.602060	+	3.51807i
$265$		−	4.04092i		−	0.248232i
$266$	42.6328	+	31.6233i	2.61398	+	1.93895i
$267$	−3.55790	−	20.7902i	−0.217740	−	1.27234i
$268$	3.33132			0.203492
$269$	−7.11368			−0.433729			−0.216865	−	0.976202i	$-0.569583\pi$
$269$	−7.11368			−0.433729			−0.216865	+	0.976202i	$0.569583\pi$
$270$	−8.12090	+	4.52626i	−0.494222	+	0.275459i
$271$			15.4136i			0.936311i	0.883646	+	0.468156i	$0.155081\pi$
$271$			15.4136i			0.936311i	−0.883646	+	0.468156i	$0.844919\pi$
$272$	−30.2274			−1.83281
$273$	6.34104	+	3.21078i	0.383777	+	0.194326i
$274$	1.01236			0.0611589
$275$			24.8430i			1.49809i
$276$	7.50771	−	1.28482i	0.451911	−	0.0773373i
$277$	24.0893			1.44739			0.723693	−	0.690122i	$-0.242443\pi$
$277$	24.0893			1.44739			0.723693	+	0.690122i	$0.242443\pi$
$278$	−25.2198			−1.51258
$279$	−5.70144	−	16.1700i	−0.341336	−	0.968071i
$280$	6.76174	−	9.11581i	0.404091	−	0.544774i
$281$			20.7041i			1.23510i	0.786531	+	0.617551i	$0.211875\pi$
$281$			20.7041i			1.23510i	−0.786531	+	0.617551i	$0.788125\pi$
$282$	42.5552	−	7.28264i	2.53413	−	0.433675i
$283$			0.699318i			0.0415701i	0.999784	+	0.0207851i	$0.00661657\pi$
$283$			0.699318i			0.0415701i	−0.999784	+	0.0207851i	$0.993383\pi$
$284$			11.7156i			0.695190i
$285$	9.57924	−	1.63933i	0.567425	−	0.0971056i
$286$		−	21.6596i		−	1.28076i
$287$	−7.97038	−	5.91210i	−0.470476	−	0.348980i
$288$	4.41178	+	12.5123i	0.259967	+	0.737297i
$289$	4.33849			0.255205
$290$	−4.47181			−0.262594
$291$	−1.64857	+	0.282125i	−0.0966406	+	0.0165385i
$292$		−	7.80092i		−	0.456514i
$293$	−14.4273			−0.842850			−0.421425	−	0.906863i	$-0.638470\pi$
$293$	−14.4273			−0.842850			−0.421425	+	0.906863i	$0.638470\pi$
$294$	13.7208	+	27.4260i	0.800214	+	1.59952i
$295$	8.52479			0.496332
$296$		−	5.47513i		−	0.318235i
$297$	−25.0593	+	13.9670i	−1.45409	+	0.810448i
$298$	−16.8543			−0.976342
$299$	−1.55101			−0.0896969
$300$	5.78119	+	33.7817i	0.333777	+	1.95039i
$301$	19.2986	+	14.3149i	1.11235	+	0.825096i
$302$		−	8.30831i		−	0.478090i
$303$	−0.411230	−	2.40297i	−0.0236246	−	0.138047i
$304$		−	51.9040i		−	2.97690i
$305$		−	6.70310i		−	0.383819i
$306$	−11.6558	−	33.0572i	−0.666316	−	1.88975i
$307$		−	17.9470i		−	1.02429i	−0.858900	−	0.512144i	$-0.828852\pi$
$307$		−	17.9470i		−	1.02429i	0.858900	−	0.512144i	$-0.171148\pi$
$308$	38.2703	−	51.5940i	2.18065	−	2.93984i
$309$	−27.9559	+	4.78420i	−1.59036	+	0.272164i
$310$	10.2258			0.580789
$311$	−25.6401			−1.45392			−0.726959	−	0.686681i	$-0.759067\pi$
$311$	−25.6401			−1.45392			−0.726959	+	0.686681i	$0.759067\pi$
$312$	−2.74805	−	16.0579i	−0.155578	−	0.909101i
$313$			11.7075i			0.661746i	0.943675	+	0.330873i	$0.107343\pi$
$313$			11.7075i			0.661746i	−0.943675	+	0.330873i	$0.892657\pi$
$314$	33.0417			1.86465
$315$	5.36523	+	1.65509i	0.302296	+	0.0932537i
$316$	−28.9619			−1.62923
$317$		−	16.9113i		−	0.949832i	−0.880031	−	0.474916i	$-0.842478\pi$
$317$		−	16.9113i		−	0.949832i	0.880031	−	0.474916i	$-0.157522\pi$
$318$	−4.22143	−	24.6674i	−0.236726	−	1.38328i
$319$	−13.7990			−0.772595
$320$	1.34501			0.0751883
$321$	0.426953	−	0.0730661i	0.0238302	−	0.00407815i
$322$	−5.37480	−	3.98681i	−0.299526	−	0.222176i
$323$			36.6407i			2.03874i
$324$	−30.8256	+	24.8240i	−1.71253	+	1.37911i
$325$		−	6.97891i		−	0.387120i
$326$		−	1.29010i		−	0.0714518i
$327$	−1.55235	−	9.07095i	−0.0858449	−	0.501624i
$328$			22.7462i			1.25595i
$329$	−20.9414	−	15.5335i	−1.15454	−	0.856390i
$330$	−2.88618	−	16.8651i	−0.158879	−	0.928391i
$331$	−8.75479			−0.481207			−0.240603	−	0.970624i	$-0.577345\pi$
$331$	−8.75479			−0.481207			−0.240603	+	0.970624i	$0.577345\pi$
$332$	−33.2310			−1.82379
$333$	2.55438	−	0.900660i	0.139979	−	0.0493559i
$334$		−	0.260476i		−	0.0142526i
$335$	−0.535868			−0.0292776
$336$	13.5462	−	26.7527i	0.739006	−	1.45948i
$337$	−17.2965			−0.942200			−0.471100	−	0.882080i	$-0.656143\pi$
$337$	−17.2965			−0.942200			−0.471100	+	0.882080i	$0.656143\pi$
$338$		−	26.7969i		−	1.45756i
$339$	29.5471	−	5.05651i	1.60478	−	0.274632i
$340$	14.3699			0.779318
$341$	31.5547			1.70878
$342$	56.7630	−	20.0143i	3.06939	−	1.08225i
$343$	6.24297	−	17.4363i	0.337088	−	0.941473i
$344$		−	55.0750i		−	2.96945i
$345$	−1.20767	+	0.206674i	−0.0650190	+	0.0111269i
$346$			10.5261i			0.565887i
$347$			10.2305i			0.549203i	0.961558	+	0.274602i	$0.0885460\pi$
$347$			10.2305i			0.549203i	−0.961558	+	0.274602i	$0.911454\pi$
$348$	−18.7640	+	3.21115i	−1.00586	+	0.172136i
$349$		−	34.2212i		−	1.83182i	−0.401382	−	0.915911i	$-0.631470\pi$
$349$		−	34.2212i		−	1.83182i	0.401382	−	0.915911i	$-0.368530\pi$
$350$	17.9391	−	24.1845i	0.958883	−	1.29271i
$351$	7.03966	−	3.92362i	0.375749	−	0.209427i
$352$	−24.4170			−1.30143
$353$	−23.8812			−1.27107			−0.635535	−	0.772072i	$-0.719220\pi$
$353$	−23.8812			−1.27107			−0.635535	+	0.772072i	$0.719220\pi$
$354$	52.0388	−	8.90560i	2.76583	−	0.473327i
$355$		−	1.88454i		−	0.100021i
$356$	53.5526			2.83828
$357$	−9.56268	+	18.8855i	−0.506111	+	0.999528i
$358$	23.9616			1.26641
$359$		−	6.24006i		−	0.329338i	−0.986349	−	0.164669i	$-0.947344\pi$
$359$		−	6.24006i		−	0.329338i	0.986349	−	0.164669i	$-0.0526555\pi$
$360$	−4.27949	−	12.1372i	−0.225549	−	0.639684i
$361$	−43.9162			−2.31138
$362$	−24.8211			−1.30457
$363$	−5.69229	−	33.2622i	−0.298768	−	1.74581i
$364$	−10.7509	+	14.4938i	−0.563501	+	0.759682i
$365$			1.25484i			0.0656812i
$366$	−7.00253	−	40.9185i	−0.366028	−	2.13884i
$367$			9.80997i			0.512076i	0.966667	+	0.256038i	$0.0824172\pi$
$367$			9.80997i			0.512076i	−0.966667	+	0.256038i	$0.917583\pi$
$368$			6.54364i			0.341111i
$369$	−10.6121	+	3.74176i	−0.552443	+	0.194788i
$370$			1.61538i			0.0839798i
$371$	−9.00410	+	12.1388i	−0.467470	+	0.630217i
$372$	42.9083	−	7.34306i	2.22469	−	0.380720i
$373$	8.10091			0.419449			0.209725	−	0.977760i	$-0.432743\pi$
$373$	8.10091			0.419449			0.209725	+	0.977760i	$0.432743\pi$
$374$	64.5089			3.33568
$375$	−1.96332	−	11.4724i	−0.101385	−	0.592433i
$376$			59.7635i			3.08207i
$377$	3.87642			0.199646
$378$	34.4806	+	4.49845i	1.77349	+	0.231375i
$379$	−10.5506			−0.541947			−0.270974	−	0.962587i	$-0.587346\pi$
$379$	−10.5506			−0.541947			−0.270974	+	0.962587i	$0.587346\pi$
$380$			24.6748i			1.26579i
$381$	0.237592	+	1.38834i	0.0121722	+	0.0711269i
$382$	−46.4494			−2.37656
$383$	21.0606			1.07615			0.538073	−	0.842899i	$-0.319153\pi$
$383$	21.0606			1.07615			0.538073	+	0.842899i	$0.319153\pi$
$384$	23.3108	−	3.98926i	1.18957	−	0.203576i
$385$	−6.15608	+	8.29929i	−0.313743	+	0.422971i
$386$		−	5.72314i		−	0.291300i
$387$	25.6949	−	9.05986i	1.30614	−	0.460538i
$388$		−	4.24648i		−	0.215582i
$389$		−	1.62714i		−	0.0824995i	−0.999149	−	0.0412497i	$-0.986866\pi$
$389$		−	1.62714i		−	0.0824995i	0.999149	−	0.0412497i	$-0.0131339\pi$
$390$	0.810787	+	4.73774i	0.0410558	+	0.239905i
$391$		−	4.61936i		−	0.233611i
$392$	−40.6243	+	12.3170i	−2.05183	+	0.622102i
$393$	−0.117718	−	0.687871i	−0.00593809	−	0.0346985i
$394$	−62.9901			−3.17339
$395$	4.65874			0.234407
$396$	−24.2212	−	68.6943i	−1.21716	−	3.45202i
$397$			16.8597i			0.846166i	0.906091	+	0.423083i	$0.139052\pi$
$397$			16.8597i			0.846166i	−0.906091	+	0.423083i	$0.860948\pi$
$398$	39.3380			1.97184
$399$	−32.4286	−	16.4202i	−1.62346	−	0.822040i
$400$	−29.4438			−1.47219
$401$		−	0.736308i		−	0.0367694i	−0.999831	−	0.0183847i	$-0.994148\pi$
$401$		−	0.736308i		−	0.0367694i	0.999831	−	0.0183847i	$-0.00585237\pi$
$402$	−3.27116	+	0.559806i	−0.163150	+	0.0279206i
$403$	−8.86435			−0.441565
$404$	6.18973			0.307951
$405$	4.95853	−	3.99313i	0.246391	−	0.198420i
$406$	13.4332	+	9.96422i	0.666679	+	0.494516i
$407$			4.98471i			0.247083i
$408$	47.8254	−	8.18454i	2.36771	−	0.405195i
$409$		−	26.6312i		−	1.31683i	−0.752655	−	0.658415i	$-0.771227\pi$
$409$		−	26.6312i		−	1.31683i	0.752655	−	0.658415i	$-0.228773\pi$
$410$		−	6.71105i		−	0.331435i
$411$	−0.683313	+	0.116938i	−0.0337053	+	0.00576812i
$412$		−	72.0106i		−	3.54771i
$413$	−25.6083	−	18.9952i	−1.26010	−	0.934692i
$414$	−7.15623	+	2.52324i	−0.351709	+	0.124011i
$415$	5.34547			0.262399
$416$	6.85924			0.336302
$417$	17.0226	−	2.91314i	0.833601	−	0.142657i
$418$			110.769i			5.41790i
$419$	−12.9173			−0.631050			−0.315525	−	0.948917i	$-0.602181\pi$
$419$	−12.9173			−0.631050			−0.315525	+	0.948917i	$0.602181\pi$
$420$	−6.43977	+	12.7180i	−0.314229	+	0.620576i
$421$	−12.7138			−0.619632			−0.309816	−	0.950797i	$-0.600267\pi$
$421$	−12.7138			−0.619632			−0.309816	+	0.950797i	$0.600267\pi$
$422$			40.7074i			1.98161i
$423$	−27.8823	+	9.83112i	−1.35568	+	0.478005i
$424$	34.6423			1.68238
$425$	20.7853			1.00823
$426$	−1.96872	−	11.5040i	−0.0953848	−	0.557370i
$427$	−14.9361	+	20.1360i	−0.722806	+	0.974448i
$428$			1.09977i			0.0531595i
$429$	2.50191	+	14.6196i	0.120793	+	0.705841i
$430$			16.2494i			0.783613i
$431$		−	30.9946i		−	1.49296i	−0.665411	−	0.746478i	$-0.731744\pi$
$431$		−	30.9946i		−	1.49296i	0.665411	−	0.746478i	$-0.268256\pi$
$432$	−16.5536	−	29.7001i	−0.796437	−	1.42895i
$433$			27.7026i			1.33130i	0.746263	+	0.665652i	$0.231846\pi$
$433$			27.7026i			1.33130i	−0.746263	+	0.665652i	$0.768154\pi$
$434$	−30.7182	−	22.7855i	−1.47452	−	1.09374i
$435$	3.01833	−	0.516539i	0.144718	−	0.0247661i
$436$	23.3655			1.11901
$437$	7.93197			0.379438
$438$	1.31089	+	7.66005i	0.0626369	+	0.366011i
$439$		−	34.6102i		−	1.65186i	−0.563775	−	0.825928i	$-0.690652\pi$
$439$		−	34.6102i		−	1.65186i	0.563775	−	0.825928i	$-0.309348\pi$
$440$	23.6849			1.12913
$441$	−12.4291	−	16.9268i	−0.591862	−	0.806039i
$442$	−18.1219			−0.861970
$443$		−	13.8423i		−	0.657669i	−0.944388	−	0.328835i	$-0.893344\pi$
$443$		−	13.8423i		−	0.657669i	0.944388	−	0.328835i	$-0.106656\pi$
$444$	1.15999	+	6.77825i	0.0550506	+	0.321682i
$445$	−8.61435			−0.408359
$446$	−11.1564			−0.528273
$447$	11.3761	−	1.94684i	0.538072	−	0.0920823i
$448$	−4.04038	−	2.99699i	−0.190890	−	0.141594i
$449$			18.3320i			0.865141i	0.901600	+	0.432571i	$0.142393\pi$
$449$			18.3320i			0.865141i	−0.901600	+	0.432571i	$0.857607\pi$
$450$	−11.3536	−	32.2002i	−0.535213	−	1.51793i
$451$		−	20.7088i		−	0.975138i
$452$			76.1094i			3.57988i
$453$	0.959694	+	5.60786i	0.0450904	+	0.263480i
$454$		−	34.0170i		−	1.59650i
$455$	1.72937	−	2.33144i	0.0810741	−	0.109300i
$456$	14.0538	+	82.1217i	0.658129	+	3.84570i
$457$	25.0486			1.17172			0.585861	−	0.810411i	$-0.300756\pi$
$457$	25.0486			1.17172			0.585861	+	0.810411i	$0.300756\pi$
$458$	−39.5497			−1.84803
$459$	11.6857	+	20.9662i	0.545443	+	0.978620i
$460$		−	3.11080i		−	0.145042i
$461$	31.9680			1.48890			0.744449	−	0.667679i	$-0.232712\pi$
$461$	31.9680			1.48890			0.744449	+	0.667679i	$0.232712\pi$
$462$	−28.9092	+	57.0934i	−1.34498	+	2.65622i
$463$	−25.1651			−1.16952			−0.584761	−	0.811206i	$-0.698812\pi$
$463$	−25.1651			−1.16952			−0.584761	+	0.811206i	$0.698812\pi$
$464$		−	16.3545i		−	0.759239i
$465$	−6.90213	+	1.18119i	−0.320079	+	0.0547763i
$466$	66.0534			3.05986
$467$	−19.0033			−0.879367			−0.439683	−	0.898153i	$-0.644909\pi$
$467$	−19.0033			−0.879367			−0.439683	+	0.898153i	$0.644909\pi$
$468$	6.80423	+	19.2976i	0.314526	+	0.892034i
$469$	1.60974	+	1.19404i	0.0743307	+	0.0551355i
$470$		−	17.6327i		−	0.813334i
$471$	−22.3021	+	3.81665i	−1.02763	+	0.175862i
$472$			73.0820i			3.36387i
$473$			50.1419i			2.30552i
$474$	28.4389	−	4.86685i	1.30624	−	0.223542i
$475$			35.6907i			1.63760i
$476$	−43.1669	−	32.0195i	−1.97855	−	1.46761i
$477$	5.69868	+	16.1621i	0.260924	+	0.740014i
$478$	−21.8129			−0.997698
$479$	8.26084			0.377448			0.188724	−	0.982030i	$-0.439565\pi$
$479$	8.26084			0.377448			0.188724	+	0.982030i	$0.439565\pi$
$480$	5.34088	−	0.914005i	0.243777	−	0.0417184i
$481$		−	1.40031i		−	0.0638485i
$482$	4.12202			0.187753
$483$	4.08834	+	2.07013i	0.186026	+	0.0941942i
$484$	85.6789			3.89450
$485$			0.683079i			0.0310170i
$486$	26.0974	−	29.5557i	1.18380	−	1.34068i
$487$	1.63769			0.0742108			0.0371054	−	0.999311i	$-0.488186\pi$
$487$	1.63769			0.0742108			0.0371054	+	0.999311i	$0.488186\pi$
$488$	57.4649			2.60131
$489$	0.149019	+	0.870775i	0.00673887	+	0.0393778i
$490$	11.9858	−	3.63401i	0.541463	−	0.164168i
$491$		−	35.8851i		−	1.61947i	−0.586795	−	0.809735i	$-0.699611\pi$
$491$		−	35.8851i		−	1.61947i	0.586795	−	0.809735i	$-0.300389\pi$
$492$	−4.81912	−	28.1600i	−0.217263	−	1.26955i
$493$			11.5451i			0.519967i
$494$		−	31.1174i		−	1.40004i
$495$	3.89617	+	11.0500i	0.175120	+	0.496661i
$496$			37.3984i			1.67924i
$497$	−4.19918	+	5.66111i	−0.188359	+	0.253936i
$498$	32.6309	−	5.58426i	1.46223	−	0.250237i
$499$	31.9673			1.43105			0.715526	−	0.698586i	$-0.246187\pi$
$499$	31.9673			1.43105			0.715526	+	0.698586i	$0.246187\pi$
$500$	29.5514			1.32158
$501$	0.0300876	+	0.175813i	0.00134421	+	0.00785475i
$502$		−	54.7488i		−	2.44356i
$503$	−10.9788			−0.489520			−0.244760	−	0.969584i	$-0.578709\pi$
$503$	−10.9788			−0.489520			−0.244760	+	0.969584i	$0.578709\pi$
$504$	−14.1889	+	45.9955i	−0.632023	+	2.04880i
$505$	−0.995667			−0.0443066
$506$		−	13.9649i		−	0.620816i
$507$	3.09531	+	18.0871i	0.137467	+	0.803275i
$508$	−3.57618			−0.158667
$509$	−12.1025			−0.536435			−0.268218	−	0.963358i	$-0.586435\pi$
$509$	−12.1025			−0.536435			−0.268218	+	0.963358i	$0.586435\pi$
$510$	−14.1104	+	2.41477i	−0.624820	+	0.106928i
$511$	2.79607	−	3.76951i	0.123691	−	0.166753i
$512$			50.4269i			2.22857i
$513$	−36.0014	+	20.0657i	−1.58950	+	0.885924i
$514$		−	22.0416i		−	0.972212i
$515$			11.5835i			0.510428i
$516$	11.6685	+	68.1833i	0.513676	+	3.00160i
$517$		−	54.4104i		−	2.39297i
$518$	3.59945	−	4.85258i	0.158151	−	0.213210i
$519$	−1.21587	−	7.10480i	−0.0533708	−	0.311866i
$520$	−6.65356			−0.291778
$521$	−31.9112			−1.39805			−0.699027	−	0.715096i	$-0.746383\pi$
$521$	−31.9112			−1.39805			−0.699027	+	0.715096i	$0.746383\pi$
$522$	17.8855	−	6.30633i	0.782828	−	0.276021i
$523$		−	12.6035i		−	0.551113i	−0.961285	−	0.275557i	$-0.911138\pi$
$523$		−	12.6035i		−	0.551113i	0.961285	−	0.275557i	$-0.0888622\pi$
$524$	1.77186			0.0774041
$525$	−9.31477	+	18.3959i	−0.406530	+	0.802864i
$526$	−60.1659			−2.62336
$527$		−	26.4007i		−	1.15003i
$528$	61.6796	−	10.5555i	2.68426	−	0.459368i
$529$	−1.00000			−0.0434783
$530$	−10.2209			−0.443967
$531$	−34.0959	+	12.0220i	−1.47964	+	0.521711i
$532$	54.9811	−	74.1226i	2.38373	−	3.21362i
$533$			5.81752i			0.251985i
$534$	−52.5855	+	8.99916i	−2.27560	+	0.389432i
$535$		−	0.176907i		−	0.00764835i
$536$		−	4.59393i		−	0.198428i
$537$	−16.1734	+	2.76781i	−0.697932	+	0.119440i
$538$			17.9930i			0.775732i
$539$	36.9855	−	11.2137i	1.59308	−	0.483010i
$540$	7.86948	+	14.1192i	0.338649	+	0.607595i
$541$	12.4235			0.534127			0.267063	−	0.963679i	$-0.413947\pi$
$541$	12.4235			0.534127			0.267063	+	0.963679i	$0.413947\pi$
$542$	38.9864			1.67461
$543$	16.7535	−	2.86709i	0.718962	−	0.123039i
$544$			20.4289i			0.875882i
$545$	−3.75852			−0.160997
$546$	8.12119	−	16.0387i	0.347555	−	0.686393i
$547$	−35.9969			−1.53912			−0.769559	−	0.638576i	$-0.779524\pi$
$547$	−35.9969			−1.53912			−0.769559	+	0.638576i	$0.779524\pi$
$548$		−	1.76012i		−	0.0751886i
$549$	9.45299	+	26.8099i	0.403444	+	1.14422i
$550$	62.8366			2.67936
$551$	−19.8244			−0.844546
$552$	−1.77179	−	10.3532i	−0.0754124	−	0.440663i
$553$	−13.9948	−	10.3808i	−0.595118	−	0.441435i
$554$		−	60.9302i		−	2.58868i
$555$	−0.186593	−	1.09033i	−0.00792044	−	0.0462821i
$556$			43.8479i			1.85957i
$557$			20.9709i			0.888566i	0.895887	+	0.444283i	$0.146541\pi$
$557$			20.9709i			0.888566i	−0.895887	+	0.444283i	$0.853459\pi$
$558$	−40.8995	+	14.4209i	−1.73141	+	0.610486i
$559$		−	14.0859i		−	0.595769i
$560$	−9.83628	−	7.29616i	−0.415659	−	0.308319i
$561$	−43.5416	+	7.45143i	−1.83833	+	0.314600i
$562$	52.3678			2.20900
$563$	−22.5239			−0.949269			−0.474634	−	0.880183i	$-0.657420\pi$
$563$	−22.5239			−0.949269			−0.474634	+	0.880183i	$0.657420\pi$
$564$	−12.6618	−	73.9878i	−0.533158	−	3.11545i
$565$		−	12.2428i		−	0.515058i
$566$	1.76882			0.0743490
$567$	−23.7929	+	0.946538i	−0.999210	+	0.0397509i
$568$	16.1559			0.677887
$569$			4.71133i			0.197509i	0.995112	+	0.0987547i	$0.0314859\pi$
$569$			4.71133i			0.197509i	−0.995112	+	0.0987547i	$0.968514\pi$
$570$	−4.14644	−	24.2292i	−0.173675	−	1.01485i
$571$	30.6560			1.28291			0.641457	−	0.767159i	$-0.278330\pi$
$571$	30.6560			1.28291			0.641457	+	0.767159i	$0.278330\pi$
$572$	−37.6581			−1.57456
$573$	31.3519	−	5.36537i	1.30974	−	0.224142i
$574$	−14.9538	+	20.1598i	−0.624158	+	0.841456i
$575$		−	4.49960i		−	0.187646i
$576$	−5.37952	+	1.89679i	−0.224147	+	0.0790328i
$577$			39.0475i			1.62557i	0.582564	+	0.812785i	$0.302049\pi$
$577$			39.0475i			1.62557i	−0.582564	+	0.812785i	$0.697951\pi$
$578$		−	10.9735i		−	0.456439i
$579$	0.661081	+	3.86295i	0.0274736	+	0.160539i
$580$			7.77481i			0.322832i
$581$	−16.0577	−	11.9109i	−0.666185	−	0.494149i
$582$	0.713593	+	4.16979i	0.0295794	+	0.172843i
$583$	−31.5394			−1.30623
$584$	−10.7576			−0.445152
$585$	−1.09451	−	3.10418i	−0.0452526	−	0.128342i
$586$			36.4916i			1.50745i
$587$	26.9464			1.11220			0.556098	−	0.831116i	$-0.312298\pi$
$587$	26.9464			1.11220			0.556098	+	0.831116i	$0.312298\pi$
$588$	47.6836	−	23.8554i	1.96644	−	0.983780i
$589$	45.3331			1.86792
$590$		−	21.5621i		−	0.887699i
$591$	42.5164	−	7.27599i	1.74889	−	0.299294i
$592$	−5.90786			−0.242811
$593$	36.0389			1.47994			0.739970	−	0.672640i	$-0.234840\pi$
$593$	36.0389			1.47994			0.739970	+	0.672640i	$0.234840\pi$
$594$	35.3274	+	63.3836i	1.44950	+	2.60066i
$595$	6.94374	+	5.15058i	0.284665	+	0.211153i
$596$			29.3033i			1.20031i
$597$	−26.5520	+	4.54394i	−1.08670	+	0.185971i
$598$			3.92303i			0.160425i
$599$		−	2.58866i		−	0.105770i	−0.998601	−	0.0528850i	$-0.983158\pi$
$599$		−	2.58866i		−	0.105770i	0.998601	−	0.0528850i	$-0.0168417\pi$
$600$	46.5855	−	7.97235i	1.90184	−	0.325470i
$601$		−	1.95680i		−	0.0798195i	−0.999203	−	0.0399097i	$-0.987293\pi$
$601$		−	1.95680i		−	0.0798195i	0.999203	−	0.0399097i	$-0.0127070\pi$
$602$	36.2073	−	48.8127i	1.47570	−	1.98946i
$603$	2.14327	−	0.755703i	0.0872806	−	0.0307746i
$604$	−14.4451			−0.587762
$605$	−13.7821			−0.560323
$606$	−6.07796	+	1.04014i	−0.246900	+	0.0422530i
$607$		−	5.96093i		−	0.241947i	−0.992656	−	0.120973i	$-0.961398\pi$
$607$		−	5.96093i		−	0.241947i	0.992656	−	0.120973i	$-0.0386016\pi$
$608$	−35.0788			−1.42263
$609$	−10.2180	−	5.17387i	−0.414053	−	0.209656i
$610$	−16.9545			−0.686466
$611$			15.2850i			0.618365i
$612$	−57.4742	+	20.2650i	−2.32326	+	0.819166i
$613$	−0.985569			−0.0398068			−0.0199034	−	0.999802i	$-0.506336\pi$
$613$	−0.985569			−0.0398068			−0.0199034	+	0.999802i	$0.506336\pi$
$614$	−45.3941			−1.83196
$615$	0.775194	+	4.52975i	0.0312588	+	0.182657i
$616$	−71.1488	−	52.7753i	−2.86667	−	2.12638i
$617$		−	43.9650i		−	1.76997i	−0.465624	−	0.884983i	$-0.654170\pi$
$617$		−	43.9650i		−	1.76997i	0.465624	−	0.884983i	$-0.345830\pi$
$618$	12.1009	+	70.7102i	0.486770	+	2.84438i
$619$			11.5732i			0.465165i	0.972577	+	0.232582i	$0.0747175\pi$
$619$			11.5732i			0.465165i	−0.972577	+	0.232582i	$0.925282\pi$
$620$		−	17.7789i		−	0.714020i
$621$	4.53877	−	2.52973i	0.182135	−	0.101514i
$622$			64.8528i			2.60036i
$623$	25.8773	+	19.1948i	1.03675	+	0.769022i
$624$	−17.3271	+	2.96525i	−0.693638	+	0.118705i
$625$	17.7444			0.709778
$626$	29.6123			1.18355
$627$	−12.7950	−	74.7659i	−0.510982	−	2.98586i
$628$		−	57.4472i		−	2.29239i
$629$	4.17054			0.166290
$630$	4.18630	−	13.5705i	0.166786	−	0.540662i
$631$	40.8618			1.62668			0.813342	−	0.581786i	$-0.197646\pi$
$631$	40.8618			1.62668			0.813342	+	0.581786i	$0.197646\pi$
$632$			39.9388i			1.58868i
$633$	−4.70212	−	27.4763i	−0.186893	−	1.09208i
$634$	−42.7745			−1.69879
$635$	0.575256			0.0228283
$636$	−42.8875	+	7.33950i	−1.70060	+	0.291030i
$637$	−10.3900	+	3.15017i	−0.411666	+	0.124814i
$638$			34.9024i			1.38180i
$639$	2.65765	+	7.53743i	0.105135	+	0.298176i
$640$		−	9.65876i		−	0.381796i
$641$			38.2129i			1.50932i	0.656117	+	0.754660i	$0.272198\pi$
$641$			38.2129i			1.50932i	−0.656117	+	0.754660i	$0.727802\pi$
$642$	−0.184809	−	1.07991i	−0.00729384	−	0.0426207i
$643$		−	0.405655i		−	0.0159975i	−0.999968	−	0.00799874i	$-0.997454\pi$
$643$		−	0.405655i		−	0.0159975i	0.999968	−	0.00799874i	$-0.00254610\pi$
$644$	−6.93158	+	9.34478i	−0.273143	+	0.368236i
$645$	−1.87696	−	10.9678i	−0.0739054	−	0.431857i
$646$	92.6769			3.64632
$647$	21.5798			0.848388			0.424194	−	0.905571i	$-0.360557\pi$
$647$	21.5798			0.848388			0.424194	+	0.905571i	$0.360557\pi$
$648$	34.2326	+	42.5089i	1.34479	+	1.66991i
$649$		−	66.5359i		−	2.61176i
$650$	−17.6521			−0.692371
$651$	23.3658	+	11.8313i	0.915779	+	0.463704i
$652$	−2.24300			−0.0878425
$653$			20.3500i			0.796358i	0.917308	+	0.398179i	$0.130358\pi$
$653$			20.3500i			0.796358i	−0.917308	+	0.398179i	$0.869642\pi$
$654$	−22.9436	+	3.92642i	−0.897164	+	0.153535i
$655$	−0.285018			−0.0111366
$656$	24.5439			0.958280
$657$	−1.76963	−	5.01888i	−0.0690396	−	0.195805i
$658$	−39.2896	+	52.9682i	−1.53167	+	2.06491i
$659$		−	4.79473i		−	0.186776i	−0.995630	−	0.0933880i	$-0.970230\pi$
$659$		−	4.79473i		−	0.186776i	0.995630	−	0.0933880i	$-0.0297697\pi$
$660$	−29.3221	+	5.01800i	−1.14136	+	0.195325i
$661$		−	33.3449i		−	1.29697i	−0.761229	−	0.648483i	$-0.775404\pi$
$661$		−	33.3449i		−	1.29697i	0.761229	−	0.648483i	$-0.224596\pi$
$662$			22.1439i			0.860647i
$663$	12.2317	−	2.09326i	0.475041	−	0.0812955i
$664$			45.8261i			1.77840i
$665$	−8.84414	+	11.9232i	−0.342961	+	0.462362i
$666$	−2.27808	−	6.46092i	−0.0882739	−	0.250356i
$667$	2.49930			0.0967731
$668$	−0.452871			−0.0175221
$669$	7.53025	−	1.28868i	0.291136	−	0.0498233i
$670$			1.35540i			0.0523635i
$671$	−52.3177			−2.01970
$672$	−18.0805	−	9.15505i	−0.697470	−	0.353164i
$673$	6.03676			0.232700			0.116350	−	0.993208i	$-0.462881\pi$
$673$	6.03676			0.232700			0.116350	+	0.993208i	$0.462881\pi$
$674$			43.7488i			1.68514i
$675$	11.3828	+	20.4227i	0.438123	+	0.786070i
$676$	−46.5898			−1.79192
$677$	−3.11583			−0.119751			−0.0598756	−	0.998206i	$-0.519070\pi$
$677$	−3.11583			−0.119751			−0.0598756	+	0.998206i	$0.519070\pi$
$678$	−12.7897	−	74.7349i	−0.491185	−	2.87018i
$679$	1.52206	−	2.05196i	0.0584112	−	0.0787468i
$680$		−	19.8163i		−	0.759921i
$681$	3.92931	+	22.9605i	0.150571	+	0.879846i
$682$		−	79.8127i		−	3.05618i
$683$		−	4.64852i		−	0.177871i	−0.996037	−	0.0889354i	$-0.971654\pi$
$683$		−	4.64852i		−	0.177871i	0.996037	−	0.0889354i	$-0.0283465\pi$
$684$	−34.7974	−	98.6898i	−1.33051	−	3.77350i
$685$			0.283129i			0.0108178i
$686$	−44.1025	−	15.7906i	−1.68384	−	0.602889i
$687$	26.6948	−	4.56838i	1.01847	−	0.174295i
$688$	−59.4279			−2.26567
$689$	8.86006			0.337541
$690$	0.522750	+	3.05463i	0.0199007	+	0.116288i
$691$		−	37.5491i		−	1.42843i	−0.699924	−	0.714217i	$-0.746783\pi$
$691$		−	37.5491i		−	1.42843i	0.699924	−	0.714217i	$-0.253217\pi$
$692$	18.3010			0.695699
$693$	12.9180	−	41.8756i	0.490713	−	1.59072i
$694$	25.8765			0.982260
$695$		−	7.05328i		−	0.267546i
$696$	4.42823	+	25.8758i	0.167851	+	0.980820i
$697$	−17.3263			−0.656281
$698$	−86.5574			−3.27625
$699$	−44.5840	+	7.62983i	−1.68632	+	0.288587i
$700$	−42.0478	−	31.1894i	−1.58926	−	1.17885i
$701$			4.28835i			0.161969i	0.996715	+	0.0809844i	$0.0258064\pi$
$701$			4.28835i			0.161969i	−0.996715	+	0.0809844i	$0.974194\pi$
$702$	−9.92420	−	17.8057i	−0.374565	−	0.672035i
$703$			7.16130i			0.270093i
$704$		−	10.4978i		−	0.395650i
$705$	2.03675	+	11.9015i	0.0767085	+	0.448237i
$706$			60.4039i			2.27333i
$707$	2.99096	+	2.21857i	0.112487	+	0.0834381i
$708$	−15.4835	−	90.4761i	−0.581906	−	3.40030i
$709$	−19.1320			−0.718518			−0.359259	−	0.933238i	$-0.616971\pi$
$709$	−19.1320			−0.718518			−0.359259	+	0.933238i	$0.616971\pi$
$710$	−4.76665			−0.178889
$711$	−18.6332	+	6.56995i	−0.698800	+	0.246392i
$712$		−	73.8498i		−	2.76764i
$713$	−5.71523			−0.214037
$714$	47.7681	+	24.1873i	1.78767	+	0.905188i
$715$	6.05759			0.226541
$716$		−	41.6603i		−	1.55692i
$717$	14.7230	−	2.51961i	0.549842	−	0.0940965i
$718$	−15.7833			−0.589026
$719$	47.5269			1.77246			0.886228	−	0.463250i	$-0.153317\pi$
$719$	47.5269			1.77246			0.886228	+	0.463250i	$0.153317\pi$
$720$	−13.0964	+	4.61772i	−0.488075	+	0.172092i
$721$	25.8106	−	34.7965i	0.961238	−	1.29589i
$722$			111.079i			4.13395i
$723$	−2.78223	+	0.476134i	−0.103472	+	0.0177076i
$724$			43.1548i			1.60383i
$725$			11.2458i			0.417660i
$726$	−84.1317	+	14.3978i	−3.12242	+	0.534352i
$727$		−	25.5163i		−	0.946348i	−0.880969	−	0.473174i	$-0.843108\pi$
$727$		−	25.5163i		−	0.946348i	0.880969	−	0.473174i	$-0.156892\pi$
$728$	19.9872	+	14.8257i	0.740774	+	0.549476i
$729$	−14.2010	+	22.9637i	−0.525961	+	0.850509i
$730$	3.17392			0.117472
$731$	41.9520			1.55165
$732$	−71.1420	+	12.1748i	−2.62948	+	0.449994i
$733$			37.8948i			1.39967i	0.714302	+	0.699837i	$0.246744\pi$
$733$			37.8948i			1.39967i	−0.714302	+	0.699837i	$0.753256\pi$
$734$	24.8128			0.915857
$735$	−7.67028	+	3.83733i	−0.282923	+	0.141542i
$736$	4.42245			0.163014
$737$			4.18245i			0.154062i
$738$	9.46420	+	26.8416i	0.348382	+	0.988054i
$739$	8.18752			0.301183			0.150591	−	0.988596i	$-0.451882\pi$
$739$	8.18752			0.301183			0.150591	+	0.988596i	$0.451882\pi$
$740$	2.80855			0.103244
$741$	3.59437	+	21.0033i	0.132042	+	0.771575i
$742$	30.7033	+	22.7745i	1.12716	+	0.836078i
$743$			0.427222i			0.0156733i	0.999969	+	0.00783663i	$0.00249450\pi$
$743$			0.427222i			0.0156733i	−0.999969	+	0.00783663i	$0.997505\pi$
$744$	−10.1262	−	59.1711i	−0.371244	−	2.16932i
$745$		−	4.71367i		−	0.172695i
$746$		−	20.4900i		−	0.750192i
$747$	−21.3799	+	7.53841i	−0.782248	+	0.275816i
$748$		−	112.157i		−	4.10087i
$749$	−0.394189	+	0.531424i	−0.0144034	+	0.0194178i
$750$	−29.0177	+	4.96591i	−1.05958	+	0.181330i
$751$	43.1819			1.57573			0.787865	−	0.615848i	$-0.211186\pi$
$751$	43.1819			1.57573			0.787865	+	0.615848i	$0.211186\pi$
$752$	64.4870			2.35160
$753$	6.32404	+	36.9538i	0.230461	+	1.34667i
$754$		−	9.80481i		−	0.357070i
$755$	2.32360			0.0845645
$756$	7.82113	−	59.9489i	0.284452	−	2.18032i
$757$	−13.2294			−0.480829			−0.240415	−	0.970670i	$-0.577283\pi$
$757$	−13.2294			−0.480829			−0.240415	+	0.970670i	$0.577283\pi$
$758$			26.6861i			0.969283i
$759$	1.61309	+	9.42589i	0.0585514	+	0.342138i
$760$	34.0269			1.23429
$761$	−22.7780			−0.825702			−0.412851	−	0.910799i	$-0.635467\pi$
$761$	−22.7780			−0.825702			−0.412851	+	0.910799i	$0.635467\pi$
$762$	3.51160	−	0.600953i	0.127212	−	0.0217702i
$763$	11.2905	+	8.37486i	0.408745	+	0.303190i
$764$			80.7582i			2.92173i
$765$	9.24517	−	3.25979i	0.334260	−	0.117858i
$766$		−	53.2695i		−	1.92471i
$767$			18.6913i			0.674904i
$768$	−8.97920	−	52.4689i	−0.324009	−	1.89331i
$769$			7.62443i			0.274944i	0.990506	+	0.137472i	$0.0438977\pi$
$769$			7.62443i			0.274944i	−0.990506	+	0.137472i	$0.956102\pi$
$770$	20.9918	+	15.5709i	0.756492	+	0.561135i
$771$	2.54602	+	14.8774i	0.0916928	+	0.535796i
$772$	−9.95042			−0.358123
$773$	−33.5539			−1.20685			−0.603424	−	0.797420i	$-0.706198\pi$
$773$	−33.5539			−1.20685			−0.603424	+	0.797420i	$0.706198\pi$
$774$	−22.9155	−	64.9912i	−0.823681	−	2.33606i
$775$		−	25.7163i		−	0.923755i
$776$	−5.85595			−0.210216
$777$	−1.86900	+	3.69112i	−0.0670498	+	0.132418i
$778$	−4.11561			−0.147552
$779$		−	29.7513i		−	1.06595i
$780$	8.23717	−	1.40966i	0.294938	−	0.0504739i
$781$	−14.7088			−0.526322
$782$	−11.6840			−0.417818
$783$	−11.3437	+	6.32254i	−0.405392	+	0.225949i
$784$	13.2905	+	43.8350i	0.474660	+	1.56554i
$785$			9.24083i			0.329819i
$786$	−1.73986	+	0.297750i	−0.0620589	+	0.0106204i
$787$			4.37933i			0.156106i	0.996949	+	0.0780532i	$0.0248704\pi$
$787$			4.37933i			0.156106i	−0.996949	+	0.0780532i	$0.975130\pi$
$788$			109.516i			3.90136i
$789$	40.6101	−	6.94976i	1.44576	−	0.247418i
$790$		−	11.7836i		−	0.419241i
$791$	−27.2797	+	36.7771i	−0.969956	+	1.30764i
$792$	−94.7304	+	33.4014i	−3.36610	+	1.18687i
$793$	14.6971			0.521910
$794$	42.6441			1.51338
$795$	6.89879	−	1.18062i	0.244675	−	0.0418721i
$796$		−	68.3942i		−	2.42417i
$797$	−17.8688			−0.632947			−0.316473	−	0.948601i	$-0.602499\pi$
$797$	−17.8688			−0.632947			−0.316473	+	0.948601i	$0.602499\pi$
$798$	−41.5325	+	82.0233i	−1.47023	+	2.90359i
$799$	−45.5233			−1.61050
$800$			19.8993i			0.703546i
$801$	34.4541	−	12.1483i	1.21738	−	0.429240i
$802$	−1.86238			−0.0657628
$803$	9.79401			0.345623
$804$	0.973294	+	5.68733i	0.0343254	+	0.200577i
$805$	1.11500	−	1.50318i	0.0392986	−	0.0529802i
$806$			22.4210i			0.789746i
$807$	−2.07837	−	12.1447i	−0.0731621	−	0.427514i
$808$		−	8.53573i		−	0.300286i
$809$			31.5292i			1.10851i	0.832348	+	0.554254i	$0.186996\pi$
$809$			31.5292i			1.10851i	−0.832348	+	0.554254i	$0.813004\pi$
$810$	−10.1000	−	12.5418i	−0.354878	−	0.440675i
$811$			3.97582i			0.139610i	0.997561	+	0.0698050i	$0.0222377\pi$
$811$			3.97582i			0.139610i	−0.997561	+	0.0698050i	$0.977762\pi$
$812$	17.3241	−	23.3554i	0.607956	−	0.819613i
$813$	−26.3146	+	4.50332i	−0.922894	+	0.157938i
$814$	12.6081			0.441912
$815$	0.360803			0.0126384
$816$	−8.83140	−	51.6053i	−0.309161	−	1.80655i
$817$			72.0364i			2.52023i
$818$	−67.3596			−2.35517
$819$	−3.62892	+	11.7637i	−0.126805	+	0.411057i
$820$	−11.6680			−0.407465
$821$		−	19.2303i		−	0.671142i	−0.942015	−	0.335571i	$-0.891071\pi$
$821$		−	19.2303i		−	0.671142i	0.942015	−	0.335571i	$-0.108929\pi$
$822$	0.295776	+	1.72833i	0.0103164	+	0.0602826i
$823$	−14.2818			−0.497833			−0.248916	−	0.968525i	$-0.580074\pi$
$823$	−14.2818			−0.497833			−0.248916	+	0.968525i	$0.580074\pi$
$824$	−99.3036			−3.45941
$825$	−42.4128	+	7.25826i	−1.47662	+	0.252700i
$826$	−48.0454	+	64.7722i	−1.67171	+	2.25371i
$827$			2.12977i			0.0740593i	0.999314	+	0.0370296i	$0.0117896\pi$
$827$			2.12977i			0.0740593i	−0.999314	+	0.0370296i	$0.988210\pi$
$828$	4.38698	+	12.4420i	0.152458	+	0.432390i
$829$			27.7261i			0.962966i	0.876455	+	0.481483i	$0.159902\pi$
$829$			27.7261i			0.962966i	−0.876455	+	0.481483i	$0.840098\pi$
$830$		−	13.5206i		−	0.469305i
$831$	7.03805	+	41.1260i	0.244147	+	1.42665i
$832$			2.94904i			0.102240i
$833$	−9.38216	−	30.9445i	−0.325072	−	1.07216i
$834$	−7.36835	−	43.0561i	−0.255145	−	1.49091i
$835$	0.0728478			0.00252100
$836$	192.587			6.66075
$837$	25.9401	−	14.4580i	0.896622	−	0.499741i
$838$			32.6722i			1.12864i
$839$	−27.3015			−0.942552			−0.471276	−	0.881986i	$-0.656206\pi$
$839$	−27.3015			−0.942552			−0.471276	+	0.881986i	$0.656206\pi$
$840$	17.5383	+	8.88053i	0.605130	+	0.306408i
$841$	22.7535			0.784604
$842$			32.1576i			1.10822i
$843$	−35.3467	+	6.04901i	−1.21740	+	0.208339i
$844$	70.7751			2.43618
$845$	7.49433			0.257813
$846$	24.8663	+	70.5239i	0.854921	+	2.42466i
$847$	41.4012	+	30.7097i	1.42256	+	1.05520i
$848$		−	37.3803i		−	1.28365i
$849$	−1.19390	+	0.204316i	−0.0409745	+	0.00701212i
$850$		−	52.5732i		−	1.80325i
$851$		−	0.902839i		−	0.0309489i
$852$	−20.0012	+	3.42287i	−0.685228	+	0.117266i
$853$			4.15254i			0.142180i	0.997470	+	0.0710902i	$0.0226478\pi$
$853$			4.15254i			0.142180i	−0.997470	+	0.0710902i	$0.977352\pi$
$854$	50.9309	+	37.7785i	1.74282	+	1.29275i
$855$	5.59744	+	15.8750i	0.191428	+	0.542914i
$856$	1.51660			0.0518364
$857$	54.4094			1.85859			0.929295	−	0.369337i	$-0.120415\pi$
$857$	54.4094			1.85859			0.929295	+	0.369337i	$0.120415\pi$
$858$	36.9780	−	6.32819i	1.26241	−	0.216041i
$859$			18.6678i			0.636936i	0.947934	+	0.318468i	$0.103168\pi$
$859$			18.6678i			0.636936i	−0.947934	+	0.318468i	$0.896832\pi$
$860$	28.2516			0.963371
$861$	7.76466	−	15.3346i	0.264619	−	0.522601i
$862$	−78.3960			−2.67018
$863$		−	35.6312i		−	1.21290i	−0.795122	−	0.606450i	$-0.792593\pi$
$863$		−	35.6312i		−	1.21290i	0.795122	−	0.606450i	$-0.207407\pi$
$864$	−20.0725	+	11.1876i	−0.682881	+	0.380610i
$865$	−2.94385			−0.100094
$866$	70.0695			2.38106
$867$	1.26756	+	7.40681i	0.0430484	+	0.251548i
$868$	−39.6156	+	53.4076i	−1.34464	+	1.81277i
$869$		−	36.3615i		−	1.23348i
$870$	−1.30651	−	7.63441i	−0.0442947	−	0.258831i
$871$		−	1.17494i		−	0.0398112i
$872$		−	32.2214i		−	1.09115i
$873$	−0.963306	−	2.73206i	−0.0326030	−	0.0924661i
$874$		−	20.0627i		−	0.678631i
$875$	14.2796	+	10.5920i	0.482739	+	0.358077i
$876$	13.3180	−	2.27916i	0.449973	−	0.0770055i
$877$	23.1339			0.781176			0.390588	−	0.920566i	$-0.372272\pi$
$877$	23.1339			0.781176			0.390588	+	0.920566i	$0.372272\pi$
$878$	−87.5413			−2.95438
$879$	−4.21515	−	24.6307i	−0.142173	−	0.830773i
$880$		−	25.5568i		−	0.861520i
$881$	−9.43397			−0.317838			−0.158919	−	0.987292i	$-0.550801\pi$
$881$	−9.43397			−0.317838			−0.158919	+	0.987292i	$0.550801\pi$
$882$	−42.8138	+	31.4375i	−1.44162	+	1.05856i
$883$	38.4009			1.29229			0.646147	−	0.763213i	$-0.276379\pi$
$883$	38.4009			1.29229			0.646147	+	0.763213i	$0.276379\pi$
$884$			31.5072i			1.05970i
$885$	2.49065	+	14.5538i	0.0837221	+	0.489220i
$886$	−35.0121			−1.17625
$887$	9.00623			0.302400			0.151200	−	0.988503i	$-0.451686\pi$
$887$	9.00623			0.302400			0.151200	+	0.988503i	$0.451686\pi$
$888$	9.34731	−	1.59964i	0.313675	−	0.0536804i
$889$	−1.72806	−	1.28180i	−0.0579572	−	0.0429903i
$890$			21.7887i			0.730358i
$891$	−31.1664	−	38.7013i	−1.04411	−	1.29654i
$892$			19.3969i			0.649456i
$893$		−	78.1688i		−	2.61582i
$894$	−4.92423	−	28.7742i	−0.164691	−	0.962352i
$895$			6.70139i			0.224003i
$896$	−21.5220	+	29.0147i	−0.718998	+	0.969314i
$897$	−0.453149	−	2.64792i	−0.0151302	−	0.0884116i
$898$	46.3680			1.54732
$899$	14.2840			0.476400
$900$	−55.9842	+	19.7397i	−1.86614	+	0.657989i
$901$			26.3879i			0.879109i
$902$	−52.3797			−1.74405
$903$	−18.8005	+	37.1294i	−0.625640	+	1.23559i
$904$	104.956			3.49078
$905$		−	6.94178i		−	0.230752i
$906$	14.1842	−	2.42740i	0.471239	−	0.0806449i
$907$	−17.9779			−0.596945			−0.298472	−	0.954418i	$-0.596477\pi$
$907$	−17.9779			−0.596945			−0.298472	+	0.954418i	$0.596477\pi$
$908$	−59.1430			−1.96273
$909$	3.98229	−	1.40413i	0.132084	−	0.0465721i
$910$	−5.89702	−	4.37417i	−0.195484	−	0.145002i
$911$		−	5.25487i		−	0.174102i	−0.996204	−	0.0870509i	$-0.972256\pi$
$911$		−	5.25487i		−	0.174102i	0.996204	−	0.0870509i	$-0.0277443\pi$
$912$	88.6122	−	15.1645i	2.93424	−	0.502148i
$913$		−	41.7214i		−	1.38078i
$914$		−	63.3565i		−	2.09565i
$915$	11.4437	−	1.95841i	0.378319	−	0.0647431i
$916$			68.7622i			2.27197i
$917$	0.856187	+	0.635085i	0.0282738	+	0.0209724i
$918$	53.0309	−	29.5572i	1.75028	−	0.975535i
$919$	46.4120			1.53099			0.765495	−	0.643441i	$-0.222494\pi$
$919$	46.4120			1.53099			0.765495	+	0.643441i	$0.222494\pi$
$920$	−4.28984			−0.141432
$921$	30.6396	−	5.24348i	1.00961	−	0.172778i
$922$		−	80.8581i		−	2.66292i
$923$	4.13200			0.136007
$924$	99.2641	+	50.2624i	3.26555	+	1.65351i
$925$	4.06242			0.133571
$926$			63.6512i			2.09171i
$927$	−16.3355	−	46.3294i	−0.536528	−	1.52166i
$928$	−11.0530			−0.362833
$929$	10.7320			0.352105			0.176052	−	0.984381i	$-0.443667\pi$
$929$	10.7320			0.352105			0.176052	+	0.984381i	$0.443667\pi$
$930$	2.98763	+	17.4579i	0.0979684	+	0.572467i
$931$	53.1353	−	16.1102i	1.74144	−	0.527992i
$932$		−	114.842i		−	3.76178i
$933$	−7.49115	−	43.7736i	−0.245249	−	1.43308i
$934$			48.0659i			1.57276i
$935$			18.0413i			0.590015i
$936$	26.6117	−	9.38313i	0.869831	−	0.306697i
$937$			51.5894i			1.68535i	0.538420	+	0.842676i	$0.319021\pi$
$937$			51.5894i			1.68535i	−0.538420	+	0.842676i	$0.680979\pi$
$938$	3.02013	−	4.07158i	0.0986109	−	0.132942i
$939$	−19.9874	+	3.42052i	−0.652264	+	0.111624i
$940$	−30.6566			−0.999910
$941$	35.5788			1.15984			0.579918	−	0.814675i	$-0.303085\pi$
$941$	35.5788			1.15984			0.579918	+	0.814675i	$0.303085\pi$
$942$	9.65362	+	56.4098i	0.314532	+	1.83793i
$943$			3.75081i			0.122143i
$944$	78.8581			2.56661
$945$	−1.25809	+	9.64325i	−0.0409257	+	0.313695i
$946$	126.826			4.12347
$947$			22.5855i			0.733931i	0.930235	+	0.366966i	$0.119603\pi$
$947$			22.5855i			0.733931i	−0.930235	+	0.366966i	$0.880397\pi$
$948$	−8.46165	−	49.4446i	−0.274822	−	1.60589i
$949$	−2.75134			−0.0893122
$950$	90.2743			2.92888
$951$	28.8715	−	4.94088i	0.936222	−	0.160219i
$952$	−44.1553	+	59.5278i	−1.43108	+	1.92931i
$953$		−	41.9118i		−	1.35766i	−0.734297	−	0.678829i	$-0.762488\pi$
$953$		−	41.9118i		−	1.35766i	0.734297	−	0.678829i	$-0.237512\pi$
$954$	40.8797	−	14.4139i	1.32353	−	0.466668i
$955$		−	12.9906i		−	0.420365i
$956$			37.9245i			1.22657i
$957$	−4.03158	−	23.5581i	−0.130323	−	0.761525i
$958$		−	20.8945i		−	0.675072i
$959$	0.630876	−	0.850513i	0.0203721	−	0.0274645i
$960$	0.392965	+	2.29624i	0.0126829	+	0.0741109i
$961$	−1.66384			−0.0536724
$962$	−3.54186			−0.114194
$963$	0.249481	+	0.707560i	0.00803942	+	0.0228008i
$964$		−	7.16665i		−	0.230822i
$965$	1.60060			0.0515252
$966$	5.23608	−	10.3408i	0.168468	−	0.332711i
$967$	−15.6160			−0.502176			−0.251088	−	0.967964i	$-0.580788\pi$
$967$	−15.6160			−0.502176			−0.251088	+	0.967964i	$0.580788\pi$
$968$		−	118.152i		−	3.79756i
$969$	−62.5541	+	10.7051i	−2.00953	+	0.343898i
$970$	1.72774			0.0554745
$971$	18.8094			0.603624			0.301812	−	0.953368i	$-0.402409\pi$
$971$	18.8094			0.603624			0.301812	+	0.953368i	$0.402409\pi$
$972$	−51.3864	−	45.3737i	−1.64822	−	1.45536i
$973$	−15.7163	+	21.1879i	−0.503842	+	0.679253i
$974$		−	4.14228i		−	0.132727i
$975$	11.9146	−	2.03899i	0.381573	−	0.0653000i
$976$		−	62.0067i		−	1.98478i
$977$			43.8295i			1.40223i	0.713049	+	0.701114i	$0.247314\pi$
$977$			43.8295i			1.40223i	−0.713049	+	0.701114i	$0.752686\pi$
$978$	2.20249	−	0.376921i	0.0704279	−	0.0120526i
$979$			67.2350i			2.14884i
$980$	−6.31820	−	20.8388i	−0.201827	−	0.665673i
$981$	15.0327	−	5.30043i	0.479956	−	0.169230i
$982$	−90.7658			−2.89645
$983$	27.1176			0.864916			0.432458	−	0.901654i	$-0.357646\pi$
$983$	27.1176			0.864916			0.432458	+	0.901654i	$0.357646\pi$
$984$	−38.8330	+	6.64564i	−1.23795	+	0.211855i
$985$		−	17.6165i		−	0.561310i
$986$	29.2017			0.929971
$987$	20.4009	−	40.2902i	0.649369	−	1.28245i
$988$	−54.1015			−1.72120
$989$		−	9.08177i		−	0.288784i
$990$	27.9493	−	9.85476i	0.888287	−	0.313205i
$991$	−46.3103			−1.47110			−0.735548	−	0.677473i	$-0.763075\pi$
$991$	−46.3103			−1.47110			−0.735548	+	0.677473i	$0.763075\pi$
$992$	25.2753			0.802492
$993$	−2.55784	−	14.9464i	−0.0811707	−	0.474311i
$994$	14.3189	+	10.6212i	0.454168	+	0.336884i
$995$			11.0017i			0.348779i
$996$	−9.70895	−	56.7331i	−0.307640	−	1.79766i
$997$			50.9196i			1.61264i	0.591479	+	0.806320i	$0.298544\pi$
$997$			50.9196i			1.61264i	−0.591479	+	0.806320i	$0.701456\pi$
$998$		−	80.8563i		−	2.55946i
$999$	2.28394	+	4.09778i	0.0722606	+	0.129648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.d.461.6	yes	44
3.2	odd	2	inner	483.2.d.d.461.39	yes	44
7.6	odd	2	inner	483.2.d.d.461.5	✓	44
21.20	even	2	inner	483.2.d.d.461.40	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.d.461.5	✓	44	7.6	odd	2	inner
483.2.d.d.461.6	yes	44	1.1	even	1	trivial
483.2.d.d.461.39	yes	44	3.2	odd	2	inner
483.2.d.d.461.40	yes	44	21.20	even	2	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52935i q^{2} +(0.292165 + 1.70723i) q^{3} -4.39759 q^{4} +0.707387 q^{5} +(4.31818 - 0.738987i) q^{6} +(-2.12498 - 1.57622i) q^{7} +6.06435i q^{8} +(-2.82928 + 0.997587i) q^{9} -1.78923i q^{10} -5.52115i q^{11} +(-1.28482 - 7.50771i) q^{12} +1.55101i q^{13} +(-3.98681 + 5.37480i) q^{14} +(0.206674 + 1.20767i) q^{15} +6.54364 q^{16} -4.61936 q^{17} +(2.52324 + 7.15623i) q^{18} -7.93197i q^{19} -3.11080 q^{20} +(2.07013 - 4.08834i) q^{21} -13.9649 q^{22} +1.00000i q^{23} +(-10.3532 + 1.77179i) q^{24} -4.49960 q^{25} +3.92303 q^{26} +(-2.52973 - 4.53877i) q^{27} +(9.34478 + 6.93158i) q^{28} -2.49930i q^{29} +(3.05463 - 0.522750i) q^{30} +5.71523i q^{31} -4.42245i q^{32} +(9.42589 - 1.61309i) q^{33} +11.6840i q^{34} +(-1.50318 - 1.11500i) q^{35} +(12.4420 - 4.38698i) q^{36} -0.902839 q^{37} -20.0627 q^{38} +(-2.64792 + 0.453149i) q^{39} +4.28984i q^{40} +3.75081 q^{41} +(-10.3408 - 5.23608i) q^{42} -9.08177 q^{43} +24.2798i q^{44} +(-2.00140 + 0.705680i) q^{45} +2.52935 q^{46} +9.85490 q^{47} +(1.91182 + 11.1715i) q^{48} +(2.03105 + 6.69887i) q^{49} +11.3811i q^{50} +(-1.34962 - 7.88632i) q^{51} -6.82069i q^{52} -5.71246i q^{53} +(-11.4801 + 6.39856i) q^{54} -3.90559i q^{55} +(9.55875 - 12.8866i) q^{56} +(13.5417 - 2.31745i) q^{57} -6.32158 q^{58} +12.0511 q^{59} +(-0.908867 - 5.31086i) q^{60} -9.47586i q^{61} +14.4558 q^{62} +(7.58457 + 2.33972i) q^{63} +1.90138 q^{64} +1.09716i q^{65} +(-4.08006 - 23.8413i) q^{66} -0.757531 q^{67} +20.3141 q^{68} +(-1.70723 + 0.292165i) q^{69} +(-2.82022 + 3.80207i) q^{70} -2.66408i q^{71} +(-6.04971 - 17.1577i) q^{72} +1.77391i q^{73} +2.28359i q^{74} +(-1.31463 - 7.68186i) q^{75} +34.8816i q^{76} +(-8.70256 + 11.7323i) q^{77} +(1.14617 + 6.69752i) q^{78} +6.58585 q^{79} +4.62889 q^{80} +(7.00964 - 5.64490i) q^{81} -9.48709i q^{82} +7.55664 q^{83} +(-9.10360 + 17.9789i) q^{84} -3.26768 q^{85} +22.9709i q^{86} +(4.26688 - 0.730207i) q^{87} +33.4822 q^{88} -12.1777 q^{89} +(1.78491 + 5.06222i) q^{90} +(2.44473 - 3.29585i) q^{91} -4.39759i q^{92} +(-9.75722 + 1.66979i) q^{93} -24.9265i q^{94} -5.61098i q^{95} +(7.55015 - 1.29209i) q^{96} +0.965637i q^{97} +(16.9438 - 5.13723i) q^{98} +(5.50783 + 15.6209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49}+ \cdots + 4 q^{99}+O(q^{100}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 92 * q^16 + 4 * q^18 - 22 * q^21 + 12 * q^22 + 16 * q^25 + 16 * q^28 - 32 * q^30 - 112 * q^37 + 4 * q^39 - 12 * q^42 - 68 * q^43 + 4 * q^46 + 44 * q^49 + 32 * q^51 + 16 * q^57 + 28 * q^58 - 44 * q^60 - 10 * q^63 - 16 * q^64 + 108 * q^67 - 60 * q^70 + 112 * q^72 - 48 * q^78 + 40 * q^79 - 4 * q^81 - 26 * q^84 - 108 * q^85 + 8 * q^88 + 24 * q^91 + 4 * q^93 + 4 * q^99

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