LMFDB - Embedded newform 483.2.d.d.461.5

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			461.5
Character	$\chi$	$=$	483.461
Dual form			483.2.d.d.461.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52935i q^{2} +(-0.292165 - 1.70723i) q^{3} -4.39759 q^{4} -0.707387 q^{5} +(-4.31818 + 0.738987i) q^{6} +(-2.12498 + 1.57622i) q^{7} +6.06435i q^{8} +(-2.82928 + 0.997587i) q^{9} +O(q^{10})$	\(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} +(3.31182 + 3.16731i) 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} +(8.01122 - 8.37674i) 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} +(4.43973 - 6.57942i) 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} +(-14.5640 - 13.9285i) 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}+O(q^{10}) $ 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.550562\pi$
$5$	−0.707387			−0.316353			−0.158177	+	0.987411i	$0.550562\pi$
$6$	−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	$-0.930997\pi$
$13$		−	1.55101i		−	0.430171i	0.976595	−	0.215086i	$-0.0690031\pi$
$14$	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	$-0.310732\pi$
$17$	4.61936			1.12036			0.560180	+	0.828371i	$0.310732\pi$
$18$	2.52324	+	7.15623i	0.594734	+	1.68674i
$19$			7.93197i			1.81972i	0.414916	+	0.909860i	$0.363811\pi$
$19$			7.93197i			1.81972i	−0.414916	+	0.909860i	$0.636189\pi$
$20$	3.11080			0.695596
$21$	3.31182	+	3.16731i	0.722698	+	0.691164i
$22$	−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	$-0.828444\pi$
$31$		−	5.71523i		−	1.02649i	0.858244	−	0.513243i	$-0.171556\pi$
$32$		−	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	$-0.594617\pi$
$41$	−3.75081			−0.585778			−0.292889	+	0.956147i	$0.594617\pi$
$42$	8.01122	−	8.37674i	1.23616	−	1.29256i
$43$	−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	$-0.755282\pi$
$47$	−9.85490			−1.43749			−0.718743	+	0.695276i	$0.755282\pi$
$48$	−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	$-0.787059\pi$
$59$	−12.0511			−1.56892			−0.784459	+	0.620180i	$0.787059\pi$
$60$	−0.908867	−	5.31086i	−0.117334	−	0.685629i
$61$			9.47586i			1.21326i	0.794984	+	0.606630i	$0.207479\pi$
$61$			9.47586i			1.21326i	−0.794984	+	0.606630i	$0.792521\pi$
$62$	−14.4558			−1.83589
$63$	4.43973	−	6.57942i	0.559354	−	0.828929i
$64$	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	$-0.966897\pi$
$73$		−	1.77391i		−	0.207620i	0.994597	−	0.103810i	$-0.0331034\pi$
$74$			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	$-0.636122\pi$
$83$	−7.55664			−0.829449			−0.414725	+	0.909947i	$0.636122\pi$
$84$	−14.5640	−	13.9285i	−1.58907	−	1.51973i
$85$	−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	$-0.276684\pi$
$89$	12.1777			1.29083			0.645417	+	0.763830i	$0.276684\pi$
$90$	−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	$-0.984389\pi$
$97$		−	0.965637i		−	0.0980455i	0.998798	−	0.0490228i	$-0.0156107\pi$
$98$	−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	$-0.477691\pi$
$101$	1.40753			0.140054			0.0700271	+	0.997545i	$0.477691\pi$
$102$	−19.9472	+	3.41365i	−1.97507	+	0.338001i
$103$		−	16.3750i		−	1.61348i	−0.590909	−	0.806738i	$-0.701231\pi$
$103$		−	16.3750i		−	1.61348i	0.590909	−	0.806738i	$-0.298769\pi$
$104$	9.40583			0.922318
$105$	−2.34274	−	2.24051i	−0.228628	−	0.218652i
$106$	−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
$126$	−16.6416	−	11.2296i	−1.48255	−	1.00041i
$127$	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	$-0.494397\pi$
$131$	0.402916			0.0352029			0.0176015	+	0.999845i	$0.494397\pi$
$132$	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	$0.138974\pi$
$139$			9.97089i			0.845720i	−0.906195	+	0.422860i	$0.861026\pi$
$140$	−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
$147$	−12.0299	−	1.51030i	−0.992211	−	0.124567i
$148$	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	$-0.825453\pi$
$157$		−	13.0633i		−	1.04257i	0.853384	−	0.521283i	$-0.174547\pi$
$158$		−	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	$-0.501268\pi$
$167$	−0.102981			−0.00796894			−0.00398447	+	0.999992i	$0.501268\pi$
$168$	−19.2077	+	20.0840i	−1.48190	+	1.54952i
$169$	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	$-0.449431\pi$
$173$	4.16159			0.316400			0.158200	+	0.987407i	$0.449431\pi$
$174$	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	$0.118831\pi$
$181$			9.81326i			0.729414i	−0.931122	+	0.364707i	$0.881169\pi$
$182$	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
$189$	−12.5297	−	5.65738i	−0.911404	−	0.411514i
$190$	−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	$-0.814151\pi$
$199$		−	15.5526i		−	1.10250i	0.834341	−	0.551249i	$-0.185849\pi$
$200$		−	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
$210$	−5.66704	+	5.92560i	−0.391063	+	0.408905i
$211$	−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	$0.0471820\pi$
$223$			4.41080i			0.295369i	−0.989035	+	0.147684i	$0.952818\pi$
$224$	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	$-0.647265\pi$
$227$	−13.4489			−0.892637			−0.446319	+	0.894874i	$0.647265\pi$
$228$	−59.5510	+	10.1912i	−3.94386	+	0.674928i
$229$			15.6363i			1.03328i	0.856204	+	0.516638i	$0.172817\pi$
$229$			15.6363i			1.03328i	−0.856204	+	0.516638i	$0.827183\pi$
$230$	−1.78923			−0.117978
$231$	17.4872	−	18.2851i	1.15057	−	1.20307i
$232$	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	$-0.983285\pi$
$241$		−	1.62968i		−	0.104977i	0.998622	−	0.0524883i	$-0.0167152\pi$
$242$			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	$-0.739379\pi$
$251$	−21.6454			−1.36625			−0.683124	+	0.730302i	$0.739379\pi$
$252$	−19.5241	+	28.9336i	−1.22991	+	1.82265i
$253$	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	$-0.587617\pi$
$257$	−8.71434			−0.543585			−0.271793	+	0.962356i	$0.587617\pi$
$258$	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	$-0.430417\pi$
$269$	7.11368			0.433729			0.216865	+	0.976202i	$0.430417\pi$
$270$	−8.12090	+	4.52626i	−0.494222	+	0.275459i
$271$		−	15.4136i		−	0.936311i	−0.883646	−	0.468156i	$-0.844919\pi$
$271$		−	15.4136i		−	0.936311i	0.883646	−	0.468156i	$-0.155081\pi$
$272$	30.2274			1.83281
$273$	4.91251	−	5.13665i	0.297319	−	0.310884i
$274$	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	$-0.993383\pi$
$283$		−	0.699318i		−	0.0415701i	0.999784	−	0.0207851i	$-0.00661657\pi$
$284$			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	$-0.361530\pi$
$293$	14.4273			0.842850			0.421425	+	0.906863i	$0.361530\pi$
$294$	−3.82007	+	30.4278i	−0.222791	+	1.77459i
$295$	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	$0.171148\pi$
$307$			17.9470i			1.02429i	−0.858900	+	0.512144i	$0.828852\pi$
$308$	−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	$-0.240933\pi$
$311$	25.6401			1.45392			0.726959	+	0.686681i	$0.240933\pi$
$312$	−2.74805	−	16.0579i	−0.155578	−	0.909101i
$313$		−	11.7075i		−	0.661746i	−0.943675	−	0.330873i	$-0.892657\pi$
$313$		−	11.7075i		−	0.661746i	0.943675	−	0.330873i	$-0.107343\pi$
$314$	−33.0417			−1.86465
$315$	−3.14061	+	4.65420i	−0.176953	+	0.262234i
$316$	−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
$336$	21.6714	+	20.7257i	1.18227	+	1.13068i
$337$	−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	$0.368530\pi$
$349$			34.2212i			1.83182i	−0.401382	+	0.915911i	$0.631470\pi$
$350$	−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	$-0.280780\pi$
$353$	23.8812			1.27107			0.635535	+	0.772072i	$0.280780\pi$
$354$	52.0388	−	8.90560i	2.76583	−	0.473327i
$355$			1.88454i			0.100021i
$356$	−53.5526			−2.83828
$357$	15.2985	+	14.6309i	0.809682	+	0.774352i
$358$	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	$-0.917583\pi$
$367$		−	9.80997i		−	0.512076i	0.966667	−	0.256038i	$-0.0824172\pi$
$368$			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
$378$	−14.3095	+	31.6920i	−0.736000	+	1.63006i
$379$	−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	$-0.680847\pi$
$383$	−21.0606			−1.07615			−0.538073	+	0.842899i	$0.680847\pi$
$384$	−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	$-0.860948\pi$
$397$		−	16.8597i		−	0.846166i	0.906091	−	0.423083i	$-0.139052\pi$
$398$	−39.3380			−1.97184
$399$	−25.1230	+	26.2693i	−1.25772	+	1.31511i
$400$	−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	$0.228773\pi$
$409$			26.6312i			1.31683i	−0.752655	+	0.658415i	$0.771227\pi$
$410$		−	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	$-0.397819\pi$
$419$	12.9173			0.631050			0.315525	+	0.948917i	$0.397819\pi$
$420$	10.3024	+	9.85287i	0.502706	+	0.480771i
$421$	−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	$-0.768154\pi$
$433$		−	27.7026i		−	1.33130i	0.746263	−	0.665652i	$-0.231846\pi$
$434$	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	$0.309348\pi$
$439$			34.6102i			1.65186i	−0.563775	+	0.825928i	$0.690652\pi$
$440$	−23.6849			−1.12913
$441$	0.936292	+	20.9791i	0.0445853	+	0.999006i
$442$	−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	$-0.767288\pi$
$461$	−31.9680			−1.48890			−0.744449	+	0.667679i	$0.767288\pi$
$462$	−46.2493	−	44.2312i	−2.15171	−	2.05782i
$463$	−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	$-0.355091\pi$
$467$	19.0033			0.879367			0.439683	+	0.898153i	$0.355091\pi$
$468$	−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	$-0.560435\pi$
$479$	−8.26084			−0.377448			−0.188724	+	0.982030i	$0.560435\pi$
$480$	5.34088	−	0.914005i	0.243777	−	0.0417184i
$481$			1.40031i			0.0638485i
$482$	−4.12202			−0.187753
$483$	−3.16731	+	3.31182i	−0.144118	+	0.150693i
$484$	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	$-0.421291\pi$
$503$	10.9788			0.489520			0.244760	+	0.969584i	$0.421291\pi$
$504$	39.8999	+	26.9241i	1.77728	+	1.19929i
$505$	−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	$-0.413565\pi$
$509$	12.1025			0.536435			0.268218	+	0.963358i	$0.413565\pi$
$510$	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	$-0.253617\pi$
$521$	31.9112			1.39805			0.699027	+	0.715096i	$0.253617\pi$
$522$	17.8855	−	6.30633i	0.782828	−	0.276021i
$523$			12.6035i			0.551113i	0.961285	+	0.275557i	$0.0888622\pi$
$523$			12.6035i			0.551113i	−0.961285	+	0.275557i	$0.911138\pi$
$524$	−1.77186			−0.0774041
$525$	−14.9019	−	14.2516i	−0.650371	−	0.621993i
$526$	−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
$546$	−12.9924	−	12.4255i	−0.556022	−	0.531760i
$547$	−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	$-0.342580\pi$
$563$	22.5239			0.949269			0.474634	+	0.880183i	$0.342580\pi$
$564$	−12.6618	−	73.9878i	−0.533158	−	3.11545i
$565$			12.2428i			0.515058i
$566$	−1.76882			−0.0743490
$567$	−5.99771	+	23.0440i	−0.251880	+	0.967758i
$568$	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	$-0.697951\pi$
$577$		−	39.0475i		−	1.62557i	0.582564	−	0.812785i	$-0.302049\pi$
$578$		−	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	$-0.687702\pi$
$587$	−26.9464			−1.11220			−0.556098	+	0.831116i	$0.687702\pi$
$588$	52.9027	+	6.64168i	2.18167	+	0.273898i
$589$	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	$-0.765160\pi$
$593$	−36.0389			−1.47994			−0.739970	+	0.672640i	$0.765160\pi$
$594$	−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	$0.0127070\pi$
$601$			1.95680i			0.0798195i	−0.999203	+	0.0399097i	$0.987293\pi$
$602$	−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	$0.0386016\pi$
$607$			5.96093i			0.241947i	−0.992656	+	0.120973i	$0.961398\pi$
$608$	35.0788			1.42263
$609$	7.91604	−	8.27722i	0.320774	−	0.335410i
$610$	−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	$-0.925282\pi$
$619$		−	11.5732i		−	0.465165i	0.972577	−	0.232582i	$-0.0747175\pi$
$620$		−	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
$630$	11.7721	+	7.94369i	0.469011	+	0.316484i
$631$	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	$0.00254610\pi$
$643$			0.405655i			0.0159975i	−0.999968	+	0.00799874i	$0.997454\pi$
$644$	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	$-0.639443\pi$
$647$	−21.5798			−0.848388			−0.424194	+	0.905571i	$0.639443\pi$
$648$	34.2326	+	42.5089i	1.34479	+	1.66991i
$649$			66.5359i			2.61176i
$650$	17.6521			0.692371
$651$	18.1019	−	18.9278i	0.709470	−	0.741839i
$652$	−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	$0.224596\pi$
$661$			33.3449i			1.29697i	−0.761229	+	0.648483i	$0.775404\pi$
$662$			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
$672$	14.0073	−	14.6464i	0.540342	−	0.564996i
$673$	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	$-0.480930\pi$
$677$	3.11583			0.119751			0.0598756	+	0.998206i	$0.480930\pi$
$678$	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	$0.253217\pi$
$691$			37.5491i			1.42843i	−0.699924	+	0.714217i	$0.746783\pi$
$692$	−18.3010			−0.695699
$693$	−36.3260	−	24.5125i	−1.37991	−	0.931151i
$694$	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
$714$	37.0067	−	38.6952i	1.38494	−	1.44813i
$715$	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	$-0.846683\pi$
$719$	−47.5269			−1.77246			−0.886228	+	0.463250i	$0.846683\pi$
$720$	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	$0.156892\pi$
$727$			25.5163i			0.946348i	−0.880969	+	0.473174i	$0.843108\pi$
$728$	−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	$-0.753256\pi$
$733$		−	37.8948i		−	1.39967i	0.714302	−	0.699837i	$-0.246744\pi$
$734$	−24.8128			−0.915857
$735$	8.50981	+	1.06837i	0.313889	+	0.0394073i
$736$	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
$756$	55.1007	+	24.8788i	2.00399	+	0.904835i
$757$	−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	$-0.364533\pi$
$761$	22.7780			0.825702			0.412851	+	0.910799i	$0.364533\pi$
$762$	−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	$-0.956102\pi$
$769$		−	7.62443i		−	0.274944i	0.990506	−	0.137472i	$-0.0438977\pi$
$770$	−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	$-0.293802\pi$
$773$	33.5539			1.20685			0.603424	+	0.797420i	$0.293802\pi$
$774$	−22.9155	−	64.9912i	−0.823681	−	2.33606i
$775$			25.7163i			0.923755i
$776$	5.85595			0.210216
$777$	−2.99004	−	2.85957i	−0.107267	−	0.102587i
$778$	−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	$-0.975130\pi$
$787$		−	4.37933i		−	0.156106i	0.996949	−	0.0780532i	$-0.0248704\pi$
$788$			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	$-0.397501\pi$
$797$	17.8688			0.632947			0.316473	+	0.948601i	$0.397501\pi$
$798$	66.4441	+	63.5448i	2.35209	+	2.24946i
$799$	−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	$-0.977762\pi$
$811$		−	3.97582i		−	0.139610i	0.997561	−	0.0698050i	$-0.0222377\pi$
$812$	−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
$819$	−10.2047	−	6.88605i	−0.356582	−	0.240618i
$820$	−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	$-0.840098\pi$
$829$		−	27.7261i		−	0.962966i	0.876455	−	0.481483i	$-0.159902\pi$
$830$		−	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	$-0.343794\pi$
$839$	27.3015			0.942552			0.471276	+	0.881986i	$0.343794\pi$
$840$	13.5873	−	14.2072i	0.468805	−	0.490194i
$841$	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	$-0.977352\pi$
$853$		−	4.15254i		−	0.142180i	0.997470	−	0.0710902i	$-0.0226478\pi$
$854$	−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	$-0.879585\pi$
$857$	−54.4094			−1.85859			−0.929295	+	0.369337i	$0.879585\pi$
$858$	36.9780	−	6.32819i	1.26241	−	0.216041i
$859$		−	18.6678i		−	0.636936i	−0.947934	−	0.318468i	$-0.896832\pi$
$859$		−	18.6678i		−	0.636936i	0.947934	−	0.318468i	$-0.103168\pi$
$860$	−28.2516			−0.963371
$861$	−12.4220	−	11.8800i	−0.423340	−	0.404868i
$862$	−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	$-0.449199\pi$
$881$	9.43397			0.317838			0.158919	+	0.987292i	$0.449199\pi$
$882$	53.0635	−	2.36821i	1.78674	−	0.0797417i
$883$	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	$-0.548314\pi$
$887$	−9.00623			−0.302400			−0.151200	+	0.988503i	$0.548314\pi$
$888$	−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
$903$	−30.0772	−	28.7648i	−1.00091	−	0.957232i
$904$	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
$924$	−76.9016	+	80.4103i	−2.52988	+	2.64530i
$925$	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	$-0.556333\pi$
$929$	−10.7320			−0.352105			−0.176052	+	0.984381i	$0.556333\pi$
$930$	−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	$-0.680979\pi$
$937$		−	51.5894i		−	1.68535i	0.538420	−	0.842676i	$-0.319021\pi$
$938$	−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	$-0.696915\pi$
$941$	−35.5788			−1.15984			−0.579918	+	0.814675i	$0.696915\pi$
$942$	9.65362	+	56.4098i	0.314532	+	1.83793i
$943$		−	3.75081i		−	0.122143i
$944$	−78.8581			−2.56661
$945$	8.86337	+	4.00196i	0.288325	+	0.130184i
$946$	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
$966$	8.37674	+	8.01122i	0.269517	+	0.257757i
$967$	−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	$-0.597591\pi$
$971$	−18.8094			−0.603624			−0.301812	+	0.953368i	$0.597591\pi$
$972$	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	$-0.642354\pi$
$983$	−27.1176			−0.864916			−0.432458	+	0.901654i	$0.642354\pi$
$984$	−38.8330	+	6.64564i	−1.23795	+	0.211855i
$985$			17.6165i			0.561310i
$986$	−29.2017			−0.929971
$987$	−32.6377	−	31.2135i	−1.03887	−	0.993538i
$988$	−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	$-0.701456\pi$
$997$		−	50.9196i		−	1.61264i	0.591479	−	0.806320i	$-0.298544\pi$
$998$		−	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.461.5	✓	44
3.2	odd	2	inner	483.2.d.d.461.40	yes	44
7.6	odd	2	inner	483.2.d.d.461.6	yes	44
21.20	even	2	inner	483.2.d.d.461.39	yes	44

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

\(f(q)\)	\(=\)	\(q-2.52935i q^{2} +(-0.292165 - 1.70723i) q^{3} -4.39759 q^{4} -0.707387 q^{5} +(-4.31818 + 0.738987i) q^{6} +(-2.12498 + 1.57622i) q^{7} +6.06435i q^{8} +(-2.82928 + 0.997587i) q^{9} +O(q^{10})\)	\(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} +(3.31182 + 3.16731i) 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} +(8.01122 - 8.37674i) 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} +(4.43973 - 6.57942i) 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} +(-14.5640 - 13.9285i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 44 * q - 76 * q^4 - 8 * q^7 + 20 * q^9	\( 44 q - 76 q^{4} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 92 q^{16} + 4 q^{18} - 22 q^{21} + 12 q^{22} + 16 q^{25} + 16 q^{28} - 32 q^{30} - 112 q^{37} + 4 q^{39} - 12 q^{42} - 68 q^{43} + 4 q^{46} + 44 q^{49} + 32 q^{51} + 16 q^{57} + 28 q^{58} - 44 q^{60} - 10 q^{63} - 16 q^{64} + 108 q^{67} - 60 q^{70} + 112 q^{72} - 48 q^{78} + 40 q^{79} - 4 q^{81} - 26 q^{84} - 108 q^{85} + 8 q^{88} + 24 q^{91} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) 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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