LMFDB - Embedded newform 483.2.e.a.344.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(344,483)]

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, 0, 1]))

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

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

chi := DirichletCharacter("483.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.e (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			344.48
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.64103i q^{2} +(-1.65834 - 0.499912i) q^{3} -4.97503 q^{4} +2.97721 q^{5} +(1.32028 - 4.37972i) q^{6} -1.00000i q^{7} -7.85715i q^{8} +(2.50018 + 1.65805i) q^{9} +O(q^{10})$	\(q+2.64103i q^{2} +(-1.65834 - 0.499912i) q^{3} -4.97503 q^{4} +2.97721 q^{5} +(1.32028 - 4.37972i) q^{6} -1.00000i q^{7} -7.85715i q^{8} +(2.50018 + 1.65805i) q^{9} +7.86291i q^{10} +5.69716 q^{11} +(8.25029 + 2.48708i) q^{12} +3.06429 q^{13} +2.64103 q^{14} +(-4.93723 - 1.48835i) q^{15} +10.8009 q^{16} -5.87514 q^{17} +(-4.37895 + 6.60304i) q^{18} +0.0296511i q^{19} -14.8117 q^{20} +(-0.499912 + 1.65834i) q^{21} +15.0464i q^{22} +(3.33589 - 3.44555i) q^{23} +(-3.92789 + 13.0298i) q^{24} +3.86380 q^{25} +8.09287i q^{26} +(-3.31726 - 3.99947i) q^{27} +4.97503i q^{28} +8.39999i q^{29} +(3.93076 - 13.0394i) q^{30} +4.36910 q^{31} +12.8112i q^{32} +(-9.44782 - 2.84808i) q^{33} -15.5164i q^{34} -2.97721i q^{35} +(-12.4385 - 8.24885i) q^{36} +6.88542i q^{37} -0.0783095 q^{38} +(-5.08162 - 1.53187i) q^{39} -23.3924i q^{40} -7.13205i q^{41} +(-4.37972 - 1.32028i) q^{42} +3.13957i q^{43} -28.3436 q^{44} +(7.44356 + 4.93636i) q^{45} +(9.09980 + 8.81019i) q^{46} +0.363467i q^{47} +(-17.9115 - 5.39950i) q^{48} -1.00000 q^{49} +10.2044i q^{50} +(9.74297 + 2.93705i) q^{51} -15.2449 q^{52} +3.88569 q^{53} +(10.5627 - 8.76098i) q^{54} +16.9617 q^{55} -7.85715 q^{56} +(0.0148230 - 0.0491716i) q^{57} -22.1846 q^{58} -4.67475i q^{59} +(24.5629 + 7.40457i) q^{60} +15.0345i q^{61} +11.5389i q^{62} +(1.65805 - 2.50018i) q^{63} -12.2329 q^{64} +9.12303 q^{65} +(7.52186 - 24.9520i) q^{66} -5.80252i q^{67} +29.2290 q^{68} +(-7.25451 + 4.04623i) q^{69} +7.86291 q^{70} -6.51952i q^{71} +(13.0275 - 19.6443i) q^{72} +0.133529 q^{73} -18.1846 q^{74} +(-6.40749 - 1.93156i) q^{75} -0.147515i q^{76} -5.69716i q^{77} +(4.04572 - 13.4207i) q^{78} +9.73465i q^{79} +32.1566 q^{80} +(3.50175 + 8.29082i) q^{81} +18.8359 q^{82} -0.210120 q^{83} +(2.48708 - 8.25029i) q^{84} -17.4915 q^{85} -8.29170 q^{86} +(4.19926 - 13.9300i) q^{87} -44.7635i q^{88} -2.19782 q^{89} +(-13.0371 + 19.6586i) q^{90} -3.06429i q^{91} +(-16.5962 + 17.1417i) q^{92} +(-7.24545 - 2.18417i) q^{93} -0.959928 q^{94} +0.0882778i q^{95} +(6.40446 - 21.2453i) q^{96} -2.81310i q^{97} -2.64103i q^{98} +(14.2439 + 9.44617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

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 $

$2$			2.64103i			1.86749i	0.357940	+	0.933745i	$0.383479\pi$
$2$			2.64103i			1.86749i	−0.357940	+	0.933745i	$0.616521\pi$
$3$	−1.65834	−	0.499912i	−0.957442	−	0.288625i
$3$	−1.65834	−	0.499912i	−0.957442	−	0.288625i
$4$	−4.97503			−2.48752
$5$	2.97721			1.33145			0.665725	−	0.746197i	$-0.268122\pi$
$5$	2.97721			1.33145			0.665725	+	0.746197i	$0.268122\pi$
$6$	1.32028	−	4.37972i	0.539003	−	1.78801i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	7.85715i		−	2.77792i
$9$	2.50018	+	1.65805i	0.833392	+	0.552683i
$10$			7.86291i			2.48647i
$11$	5.69716			1.71776			0.858879	−	0.512178i	$-0.171161\pi$
$11$	5.69716			1.71776			0.858879	+	0.512178i	$0.171161\pi$
$12$	8.25029	+	2.48708i	2.38165	+	0.717958i
$13$	3.06429			0.849880			0.424940	−	0.905222i	$-0.360295\pi$
$13$	3.06429			0.849880			0.424940	+	0.905222i	$0.360295\pi$
$14$	2.64103			0.705845
$15$	−4.93723	−	1.48835i	−1.27479	−	0.384289i
$16$	10.8009			2.70022
$17$	−5.87514			−1.42493			−0.712465	−	0.701708i	$-0.752421\pi$
$17$	−5.87514			−1.42493			−0.712465	+	0.701708i	$0.752421\pi$
$18$	−4.37895	+	6.60304i	−1.03213	+	1.55635i
$19$			0.0296511i			0.00680244i	0.999994	+	0.00340122i	$0.00108264\pi$
$19$			0.0296511i			0.00680244i	−0.999994	+	0.00340122i	$0.998917\pi$
$20$	−14.8117			−3.31201
$21$	−0.499912	+	1.65834i	−0.109090	+	0.361879i
$22$			15.0464i			3.20790i
$23$	3.33589	−	3.44555i	0.695582	−	0.718447i
$23$	3.33589	−	3.44555i	0.695582	−	0.718447i
$24$	−3.92789	+	13.0298i	−0.801776	+	2.65970i
$25$	3.86380			0.772760
$26$			8.09287i			1.58714i
$27$	−3.31726	−	3.99947i	−0.638407	−	0.769699i
$28$			4.97503i			0.940193i
$29$			8.39999i			1.55984i	0.625880	+	0.779920i	$0.284740\pi$
$29$			8.39999i			1.55984i	−0.625880	+	0.779920i	$0.715260\pi$
$30$	3.93076	−	13.0394i	0.717656	−	2.38065i
$31$	4.36910			0.784714			0.392357	−	0.919813i	$-0.371660\pi$
$31$	4.36910			0.784714			0.392357	+	0.919813i	$0.371660\pi$
$32$			12.8112i			2.26472i
$33$	−9.44782	−	2.84808i	−1.64466	−	0.495787i
$34$		−	15.5164i		−	2.66104i
$35$		−	2.97721i		−	0.503241i
$36$	−12.4385	−	8.24885i	−2.07308	−	1.37481i
$37$			6.88542i			1.13196i	0.824420	+	0.565978i	$0.191501\pi$
$37$			6.88542i			1.13196i	−0.824420	+	0.565978i	$0.808499\pi$
$38$	−0.0783095			−0.0127035
$39$	−5.08162	−	1.53187i	−0.813711	−	0.245296i
$40$		−	23.3924i		−	3.69867i
$41$		−	7.13205i		−	1.11384i	−0.830567	−	0.556919i	$-0.811983\pi$
$41$		−	7.13205i		−	1.11384i	0.830567	−	0.556919i	$-0.188017\pi$
$42$	−4.37972	−	1.32028i	−0.675806	−	0.203724i
$43$			3.13957i			0.478780i	0.970923	+	0.239390i	$0.0769475\pi$
$43$			3.13957i			0.478780i	−0.970923	+	0.239390i	$0.923053\pi$
$44$	−28.3436			−4.27295
$45$	7.44356	+	4.93636i	1.10962	+	0.735869i
$46$	9.09980	+	8.81019i	1.34169	+	1.29899i
$47$			0.363467i			0.0530172i	0.999649	+	0.0265086i	$0.00843893\pi$
$47$			0.363467i			0.0530172i	−0.999649	+	0.0265086i	$0.991561\pi$
$48$	−17.9115	−	5.39950i	−2.58531	−	0.779351i
$49$	−1.00000			−0.142857
$50$			10.2044i			1.44312i
$51$	9.74297	+	2.93705i	1.36429	+	0.411270i
$52$	−15.2449			−2.11409
$53$	3.88569			0.533741			0.266870	−	0.963732i	$-0.414010\pi$
$53$	3.88569			0.533741			0.266870	+	0.963732i	$0.414010\pi$
$54$	10.5627	−	8.76098i	1.43740	−	1.19222i
$55$	16.9617			2.28711
$56$	−7.85715			−1.04996
$57$	0.0148230	−	0.0491716i	0.00196335	−	0.00651294i
$58$	−22.1846			−2.91298
$59$		−	4.67475i		−	0.608600i	−0.952576	−	0.304300i	$-0.901577\pi$
$59$		−	4.67475i		−	0.608600i	0.952576	−	0.304300i	$-0.0984226\pi$
$60$	24.5629	+	7.40457i	3.17105	+	0.955926i
$61$			15.0345i			1.92497i	0.271333	+	0.962485i	$0.412535\pi$
$61$			15.0345i			1.92497i	−0.271333	+	0.962485i	$0.587465\pi$
$62$			11.5389i			1.46545i
$63$	1.65805	−	2.50018i	0.208894	−	0.314992i
$64$	−12.2329			−1.52911
$65$	9.12303			1.13157
$66$	7.52186	−	24.9520i	0.925878	−	3.07138i
$67$		−	5.80252i		−	0.708890i	−0.935077	−	0.354445i	$-0.884670\pi$
$67$		−	5.80252i		−	0.708890i	0.935077	−	0.354445i	$-0.115330\pi$
$68$	29.2290			3.54454
$69$	−7.25451	+	4.04623i	−0.873341	+	0.487109i
$70$	7.86291			0.939797
$71$		−	6.51952i		−	0.773725i	−0.922137	−	0.386863i	$-0.873559\pi$
$71$		−	6.51952i		−	0.773725i	0.922137	−	0.386863i	$-0.126441\pi$
$72$	13.0275	−	19.6443i	1.53531	−	2.31510i
$73$	0.133529			0.0156284			0.00781421	−	0.999969i	$-0.497513\pi$
$73$	0.133529			0.0156284			0.00781421	+	0.999969i	$0.497513\pi$
$74$	−18.1846			−2.11392
$75$	−6.40749	−	1.93156i	−0.739873	−	0.223037i
$76$		−	0.147515i		−	0.0169212i
$77$		−	5.69716i		−	0.649252i
$78$	4.04572	−	13.4207i	0.458088	−	1.51960i
$79$			9.73465i			1.09523i	0.836729	+	0.547617i	$0.184465\pi$
$79$			9.73465i			1.09523i	−0.836729	+	0.547617i	$0.815535\pi$
$80$	32.1566			3.59521
$81$	3.50175	+	8.29082i	0.389084	+	0.921202i
$82$	18.8359			2.08008
$83$	−0.210120			−0.0230637			−0.0115318	−	0.999934i	$-0.503671\pi$
$83$	−0.210120			−0.0230637			−0.0115318	+	0.999934i	$0.503671\pi$
$84$	2.48708	−	8.25029i	0.271363	−	0.900181i
$85$	−17.4915			−1.89722
$86$	−8.29170			−0.894117
$87$	4.19926	−	13.9300i	0.450208	−	1.49346i
$88$		−	44.7635i		−	4.77180i
$89$	−2.19782			−0.232968			−0.116484	−	0.993193i	$-0.537162\pi$
$89$	−2.19782			−0.232968			−0.116484	+	0.993193i	$0.537162\pi$
$90$	−13.0371	+	19.6586i	−1.37423	+	2.07220i
$91$		−	3.06429i		−	0.321224i
$92$	−16.5962	+	17.1417i	−1.73027	+	1.78715i
$93$	−7.24545	−	2.18417i	−0.751318	−	0.226488i
$94$	−0.959928			−0.0990090
$95$			0.0882778i			0.00905711i
$96$	6.40446	−	21.2453i	0.653653	−	2.16834i
$97$		−	2.81310i		−	0.285627i	−0.989750	−	0.142814i	$-0.954385\pi$
$97$		−	2.81310i		−	0.285627i	0.989750	−	0.142814i	$-0.0456150\pi$
$98$		−	2.64103i		−	0.266784i
$99$	14.2439	+	9.44617i	1.43157	+	0.949376i
$100$	−19.2225			−1.92225
$101$			0.0848816i			0.00844603i	0.999991	+	0.00422302i	$0.00134423\pi$
$101$			0.0848816i			0.00844603i	−0.999991	+	0.00422302i	$0.998656\pi$
$102$	−7.75684	+	25.7315i	−0.768042	+	2.54779i
$103$		−	12.4127i		−	1.22306i	−0.791222	−	0.611529i	$-0.790555\pi$
$103$		−	12.4127i		−	1.22306i	0.791222	−	0.611529i	$-0.209445\pi$
$104$		−	24.0766i		−	2.36090i
$105$	−1.48835	+	4.93723i	−0.145248	+	0.481824i
$106$			10.2622i			0.996755i
$107$	0.528479			0.0510900			0.0255450	−	0.999674i	$-0.491868\pi$
$107$	0.528479			0.0510900			0.0255450	+	0.999674i	$0.491868\pi$
$108$	16.5035	+	19.8975i	1.58805	+	1.91464i
$109$			1.57761i			0.151108i	0.997142	+	0.0755539i	$0.0240725\pi$
$109$			1.57761i			0.151108i	−0.997142	+	0.0755539i	$0.975928\pi$
$110$			44.7962i			4.27115i
$111$	3.44211	−	11.4184i	0.326710	−	1.08378i
$112$		−	10.8009i		−	1.02059i
$113$	−3.00594			−0.282775			−0.141387	−	0.989954i	$-0.545156\pi$
$113$	−3.00594			−0.282775			−0.141387	+	0.989954i	$0.545156\pi$
$114$	0.129864	+	0.0391479i	0.0121628	+	0.00366654i
$115$	9.93167	−	10.2581i	0.926133	−	0.956576i
$116$		−	41.7902i		−	3.88013i
$117$	7.66125	+	5.08073i	0.708283	+	0.469714i
$118$	12.3461			1.13655
$119$			5.87514i			0.538573i
$120$	−11.6942	+	38.7925i	−1.06753	+	3.54126i
$121$	21.4576			1.95070
$122$	−39.7066			−3.59486
$123$	−3.56540	+	11.8273i	−0.321481	+	1.06644i
$124$	−21.7364			−1.95199
$125$	−3.38271			−0.302559
$126$	6.60304	+	4.37895i	0.588245	+	0.390108i
$127$	−5.12591			−0.454851			−0.227426	−	0.973795i	$-0.573031\pi$
$127$	−5.12591			−0.454851			−0.227426	+	0.973795i	$0.573031\pi$
$128$		−	6.68508i		−	0.590883i
$129$	1.56951	−	5.20647i	0.138188	−	0.458404i
$130$			24.0942i			2.11320i
$131$		−	4.55170i		−	0.397684i	−0.980032	−	0.198842i	$-0.936282\pi$
$131$		−	4.55170i		−	0.397684i	0.980032	−	0.198842i	$-0.0637181\pi$
$132$	47.0032	+	14.1693i	4.09111	+	1.23328i
$133$	0.0296511			0.00257108
$134$	15.3246			1.32384
$135$	−9.87619	−	11.9073i	−0.850007	−	1.02482i
$136$			46.1618i			3.95834i
$137$	7.73358			0.660725			0.330362	−	0.943854i	$-0.392829\pi$
$137$	7.73358			0.660725			0.330362	+	0.943854i	$0.392829\pi$
$138$	−10.6862	−	19.1594i	−0.909672	−	1.63096i
$139$	−2.87063			−0.243484			−0.121742	−	0.992562i	$-0.538848\pi$
$139$	−2.87063			−0.243484			−0.121742	+	0.992562i	$0.538848\pi$
$140$			14.8117i			1.25182i
$141$	0.181702	−	0.602752i	0.0153021	−	0.0507609i
$142$	17.2183			1.44492
$143$	17.4577			1.45989
$144$	27.0041	+	17.9084i	2.25034	+	1.49237i
$145$			25.0086i			2.07685i
$146$			0.352655i			0.0291859i
$147$	1.65834	+	0.499912i	0.136777	+	0.0412321i
$148$		−	34.2552i		−	2.81576i
$149$	1.46976			0.120407			0.0602036	−	0.998186i	$-0.480825\pi$
$149$	1.46976			0.120407			0.0602036	+	0.998186i	$0.480825\pi$
$150$	5.10131	−	16.9224i	0.416520	−	1.38171i
$151$	−7.69797			−0.626452			−0.313226	−	0.949679i	$-0.601410\pi$
$151$	−7.69797			−0.626452			−0.313226	+	0.949679i	$0.601410\pi$
$152$	0.232973			0.0188966
$153$	−14.6889	−	9.74126i	−1.18752	−	0.787534i
$154$	15.0464			1.21247
$155$	13.0078			1.04481
$156$	25.2813	+	7.62113i	2.02412	+	0.610178i
$157$		−	6.13186i		−	0.489376i	−0.969602	−	0.244688i	$-0.921314\pi$
$157$		−	6.13186i		−	0.489376i	0.969602	−	0.244688i	$-0.0786856\pi$
$158$	−25.7095			−2.04534
$159$	−6.44379	−	1.94250i	−0.511026	−	0.154051i
$160$			38.1416i			3.01536i
$161$	−3.44555	−	3.33589i	−0.271547	−	0.262905i
$162$	−21.8963	+	9.24823i	−1.72034	+	0.726610i
$163$	−22.4375			−1.75744			−0.878719	−	0.477339i	$-0.841602\pi$
$163$	−22.4375			−1.75744			−0.878719	+	0.477339i	$0.841602\pi$
$164$			35.4822i			2.77069i
$165$	−28.1282	−	8.47935i	−2.18978	−	0.660116i
$166$		−	0.554933i		−	0.0430711i
$167$		−	20.4472i		−	1.58225i	−0.611652	−	0.791127i	$-0.709495\pi$
$167$		−	20.4472i		−	1.58225i	0.611652	−	0.791127i	$-0.290505\pi$
$168$	13.0298	+	3.92789i	1.00527	+	0.303043i
$169$	−3.61015			−0.277704
$170$		−	46.1956i		−	3.54304i
$171$	−0.0491630	+	0.0741330i	−0.00375959	+	0.00566909i
$172$		−	15.6195i		−	1.19097i
$173$		−	10.1055i		−	0.768305i	−0.923270	−	0.384152i	$-0.874494\pi$
$173$		−	10.1055i		−	0.768305i	0.923270	−	0.384152i	$-0.125506\pi$
$174$	36.7896	+	11.0904i	2.78901	+	0.840758i
$175$		−	3.86380i		−	0.292076i
$176$	61.5344			4.63833
$177$	−2.33696	+	7.75232i	−0.175657	+	0.582700i
$178$		−	5.80450i		−	0.435066i
$179$		−	15.2793i		−	1.14203i	−0.820941	−	0.571014i	$-0.806550\pi$
$179$		−	15.2793i		−	1.14203i	0.820941	−	0.571014i	$-0.193450\pi$
$180$	−37.0319	−	24.5586i	−2.76020	−	1.83049i
$181$		−	2.97839i		−	0.221382i	−0.993855	−	0.110691i	$-0.964694\pi$
$181$		−	2.97839i		−	0.221382i	0.993855	−	0.110691i	$-0.0353064\pi$
$182$	8.09287			0.599883
$183$	7.51593	−	24.9323i	0.555594	−	1.84305i
$184$	−27.0722	−	26.2106i	−1.99579	−	1.93227i
$185$			20.4994i			1.50714i
$186$	5.76845	−	19.1355i	0.422963	−	1.40308i
$187$	−33.4716			−2.44769
$188$		−	1.80826i		−	0.131881i
$189$	−3.99947	+	3.31726i	−0.290919	+	0.241295i
$190$	−0.233144			−0.0169141
$191$	−22.0883			−1.59825			−0.799126	−	0.601163i	$-0.794704\pi$
$191$	−22.0883			−1.59825			−0.799126	+	0.601163i	$0.794704\pi$
$192$	20.2863	+	6.11537i	1.46404	+	0.441339i
$193$	−4.41676			−0.317925			−0.158963	−	0.987285i	$-0.550815\pi$
$193$	−4.41676			−0.317925			−0.158963	+	0.987285i	$0.550815\pi$
$194$	7.42949			0.533406
$195$	−15.1291	−	4.56072i	−1.08342	−	0.326600i
$196$	4.97503			0.355360
$197$		−	5.43432i		−	0.387179i	−0.981083	−	0.193590i	$-0.937987\pi$
$197$		−	5.43432i		−	0.387179i	0.981083	−	0.193590i	$-0.0620130\pi$
$198$	−24.9476	+	37.6186i	−1.77295	+	2.67343i
$199$			17.1622i			1.21660i	0.793709	+	0.608298i	$0.208148\pi$
$199$			17.1622i			1.21660i	−0.793709	+	0.608298i	$0.791852\pi$
$200$		−	30.3585i		−	2.14667i
$201$	−2.90075	+	9.62254i	−0.204603	+	0.678721i
$202$	−0.224175			−0.0157729
$203$	8.39999			0.589564
$204$	−48.4716	−	14.6119i	−3.39369	−	1.02304i
$205$		−	21.2336i		−	1.48302i
$206$	32.7823			2.28405
$207$	14.0532	−	3.08341i	0.976765	−	0.214312i
$208$	33.0970			2.29487
$209$			0.168927i			0.0116849i
$210$	−13.0394	−	3.93076i	−0.899802	−	0.271248i
$211$	25.9380			1.78565			0.892824	−	0.450406i	$-0.148721\pi$
$211$	25.9380			1.78565			0.892824	+	0.450406i	$0.148721\pi$
$212$	−19.3314			−1.32769
$213$	−3.25919	+	10.8116i	−0.223316	+	0.740797i
$214$			1.39573i			0.0954100i
$215$			9.34718i			0.637472i
$216$	−31.4245	+	26.0642i	−2.13816	+	1.77344i
$217$		−	4.36910i		−	0.296594i
$218$	−4.16652			−0.282192
$219$	−0.221437	−	0.0667530i	−0.0149633	−	0.00451075i
$220$	−84.3849			−5.68923
$221$	−18.0031			−1.21102
$222$	30.1562	+	9.09070i	2.02395	+	0.610128i
$223$	−1.52846			−0.102353			−0.0511767	−	0.998690i	$-0.516297\pi$
$223$	−1.52846			−0.102353			−0.0511767	+	0.998690i	$0.516297\pi$
$224$	12.8112			0.855983
$225$	9.66018	+	6.40636i	0.644012	+	0.427091i
$226$		−	7.93877i		−	0.528079i
$227$	−6.68116			−0.443444			−0.221722	−	0.975110i	$-0.571168\pi$
$227$	−6.68116			−0.443444			−0.221722	+	0.975110i	$0.571168\pi$
$228$	−0.0737448	+	0.244631i	−0.00488387	+	0.0162011i
$229$			0.166695i			0.0110155i	0.999985	+	0.00550777i	$0.00175319\pi$
$229$			0.166695i			0.0110155i	−0.999985	+	0.00550777i	$0.998247\pi$
$230$	27.0920	+	26.2298i	1.78640	+	1.72954i
$231$	−2.84808	+	9.44782i	−0.187390	+	0.621621i
$232$	66.0000			4.33311
$233$		−	0.0170024i		−	0.00111386i	−1.00000		0.000556932i	$-0.999823\pi$
$233$		−	0.0170024i		−	0.00111386i	1.00000		0.000556932i	$-0.000177277\pi$
$234$	−13.4184	+	20.2336i	−0.877186	+	1.32271i
$235$			1.08212i			0.0705897i
$236$			23.2570i			1.51390i
$237$	4.86647	−	16.1433i	0.316111	−	1.04862i
$238$	−15.5164			−1.00578
$239$			17.5776i			1.13700i	0.822682	+	0.568501i	$0.192477\pi$
$239$			17.5776i			1.13700i	−0.822682	+	0.568501i	$0.807523\pi$
$240$	−53.3265	−	16.0755i	−3.44221	−	1.03767i
$241$		−	8.77557i		−	0.565284i	−0.959225	−	0.282642i	$-0.908789\pi$
$241$		−	8.77557i		−	0.565284i	0.959225	−	0.282642i	$-0.0912109\pi$
$242$			56.6703i			3.64290i
$243$	−1.66241	−	15.4996i	−0.106644	−	0.994297i
$244$		−	74.7972i		−	4.78840i
$245$	−2.97721			−0.190207
$246$	−31.2364	−	9.41632i	−1.99156	−	0.600362i
$247$			0.0908596i			0.00578125i
$248$		−	34.3287i		−	2.17987i
$249$	0.348450	+	0.105042i	0.0220821	+	0.00665674i
$250$		−	8.93384i		−	0.565026i
$251$	16.8897			1.06607			0.533034	−	0.846094i	$-0.321052\pi$
$251$	16.8897			1.06607			0.533034	+	0.846094i	$0.321052\pi$
$252$	−8.24885	+	12.4385i	−0.519628	+	0.783549i
$253$	19.0051	−	19.6299i	1.19484	−	1.23412i
$254$		−	13.5377i		−	0.849430i
$255$	29.0069	+	8.74423i	1.81648	+	0.547585i
$256$	−6.81030			−0.425644
$257$		−	21.2188i		−	1.32359i	−0.749683	−	0.661797i	$-0.769794\pi$
$257$		−	21.2188i		−	1.32359i	0.749683	−	0.661797i	$-0.230206\pi$
$258$	13.7504	+	4.14512i	0.856066	+	0.258064i
$259$	6.88542			0.427839
$260$	−45.3874			−2.81481
$261$	−13.9276	+	21.0015i	−0.862096	+	1.29996i
$262$	12.0212			0.742671
$263$	−2.63161			−0.162272			−0.0811359	−	0.996703i	$-0.525855\pi$
$263$	−2.63161			−0.162272			−0.0811359	+	0.996703i	$0.525855\pi$
$264$	−22.3778	+	74.2330i	−1.37726	+	4.56872i
$265$	11.5685			0.710649
$266$			0.0783095i			0.00480146i
$267$	3.64473	+	1.09872i	0.223054	+	0.0672403i
$268$			28.8677i			1.76338i
$269$			0.857217i			0.0522655i	0.999658	+	0.0261327i	$0.00831925\pi$
$269$			0.857217i			0.0522655i	−0.999658	+	0.0261327i	$0.991681\pi$
$270$	31.4475	−	26.0833i	1.91383	−	1.58738i
$271$	−21.4367			−1.30218			−0.651092	−	0.758999i	$-0.725689\pi$
$271$	−21.4367			−1.30218			−0.651092	+	0.758999i	$0.725689\pi$
$272$	−63.4567			−3.84763
$273$	−1.53187	+	5.08162i	−0.0927132	+	0.307554i
$274$			20.4246i			1.23390i
$275$	22.0127			1.32741
$276$	36.0915	−	20.1302i	2.17245	−	1.21169i
$277$	−20.3796			−1.22449			−0.612245	−	0.790668i	$-0.709733\pi$
$277$	−20.3796			−1.22449			−0.612245	+	0.790668i	$0.709733\pi$
$278$		−	7.58143i		−	0.454704i
$279$	10.9235	+	7.24418i	0.653974	+	0.433698i
$280$	−23.3924			−1.39796
$281$	−21.9750			−1.31092			−0.655459	−	0.755231i	$-0.727525\pi$
$281$	−21.9750			−1.31092			−0.655459	+	0.755231i	$0.727525\pi$
$282$	1.59189	+	0.479880i	0.0947954	+	0.0285764i
$283$		−	1.20966i		−	0.0719069i	−0.999353	−	0.0359534i	$-0.988553\pi$
$283$		−	1.20966i		−	0.0719069i	0.999353	−	0.0359534i	$-0.0114468\pi$
$284$			32.4349i			1.92465i
$285$	0.0441311	−	0.146394i	0.00261410	−	0.00867166i
$286$			46.1064i			2.72633i
$287$	−7.13205			−0.420991
$288$	−21.2415	+	32.0302i	−1.25167	+	1.88740i
$289$	17.5172			1.03042
$290$	−66.0483			−3.87849
$291$	−1.40631	+	4.66508i	−0.0824391	+	0.273472i
$292$	−0.664313			−0.0388760
$293$	−4.83884			−0.282688			−0.141344	−	0.989961i	$-0.545142\pi$
$293$	−4.83884			−0.282688			−0.141344	+	0.989961i	$0.545142\pi$
$294$	−1.32028	+	4.37972i	−0.0770005	+	0.255431i
$295$		−	13.9177i		−	0.810321i
$296$	54.0998			3.14449
$297$	−18.8990	−	22.7856i	−1.09663	−	1.32216i
$298$			3.88167i			0.224859i
$299$	10.2221	−	10.5581i	0.591161	−	0.610594i
$300$	31.8775	+	9.60958i	1.84045	+	0.554809i
$301$	3.13957			0.180962
$302$		−	20.3306i		−	1.16989i
$303$	0.0424333	−	0.140762i	0.00243773	−	0.00808659i
$304$			0.320259i			0.0183681i
$305$			44.7609i			2.56300i
$306$	25.7269	−	38.7937i	1.47071	−	2.21769i
$307$	−16.0756			−0.917481			−0.458740	−	0.888570i	$-0.651699\pi$
$307$	−16.0756			−0.917481			−0.458740	+	0.888570i	$0.651699\pi$
$308$			28.3436i			1.61502i
$309$	−6.20526	+	20.5845i	−0.353005	+	1.17101i
$310$			34.3538i			1.95117i
$311$		−	13.0394i		−	0.739398i	−0.929152	−	0.369699i	$-0.879461\pi$
$311$		−	13.0394i		−	0.739398i	0.929152	−	0.369699i	$-0.120539\pi$
$312$	−12.0362	+	39.9271i	−0.681414	+	2.26043i
$313$			26.2250i			1.48233i	0.671325	+	0.741163i	$0.265725\pi$
$313$			26.2250i			1.48233i	−0.671325	+	0.741163i	$0.734275\pi$
$314$	16.1944			0.913905
$315$	4.93636	−	7.44356i	0.278133	−	0.419397i
$316$		−	48.4302i		−	2.72441i
$317$			9.84289i			0.552832i	0.961038	+	0.276416i	$0.0891467\pi$
$317$			9.84289i			0.552832i	−0.961038	+	0.276416i	$0.910853\pi$
$318$	5.13021	−	17.0182i	0.287688	−	0.954335i
$319$			47.8561i			2.67943i
$320$	−36.4199			−2.03594
$321$	−0.876397	−	0.264193i	−0.0489157	−	0.0147458i
$322$	8.81019	−	9.09980i	0.490973	−	0.507112i
$323$		−	0.174204i		−	0.00969299i
$324$	−17.4213	−	41.2471i	−0.967852	−	2.29151i
$325$	11.8398			0.656753
$326$		−	59.2580i		−	3.28200i
$327$	0.788668	−	2.61621i	0.0436134	−	0.144677i
$328$	−56.0376			−3.09416
$329$	0.363467			0.0200386
$330$	22.3942	−	74.2874i	1.23276	−	4.08938i
$331$	−9.80156			−0.538742			−0.269371	−	0.963036i	$-0.586816\pi$
$331$	−9.80156			−0.538742			−0.269371	+	0.963036i	$0.586816\pi$
$332$	1.04535			0.0573712
$333$	−11.4164	+	17.2148i	−0.625613	+	0.943363i
$334$	54.0017			2.95484
$335$		−	17.2753i		−	0.943852i
$336$	−5.39950	+	17.9115i	−0.294567	+	0.977155i
$337$		−	32.2535i		−	1.75696i	−0.477779	−	0.878480i	$-0.658558\pi$
$337$		−	32.2535i		−	1.75696i	0.477779	−	0.878480i	$-0.341442\pi$
$338$		−	9.53452i		−	0.518609i
$339$	4.98486	+	1.50270i	0.270740	+	0.0816157i
$340$	87.0210			4.71937
$341$	24.8915			1.34795
$342$	−0.195787	−	0.129841i	−0.0105870	−	0.00702099i
$343$			1.00000i			0.0539949i
$344$	24.6681			1.33001
$345$	−21.5982	+	12.0465i	−1.16281	+	0.648562i
$346$	26.6888			1.43480
$347$			30.2615i			1.62452i	0.583295	+	0.812260i	$0.301763\pi$
$347$			30.2615i			1.62452i	−0.583295	+	0.812260i	$0.698237\pi$
$348$	−20.8915	+	69.3024i	−1.11990	+	3.71500i
$349$	28.6110			1.53151			0.765756	−	0.643131i	$-0.222365\pi$
$349$	28.6110			1.53151			0.765756	+	0.643131i	$0.222365\pi$
$350$	10.2044			0.545448
$351$	−10.1650	−	12.2555i	−0.542569	−	0.654152i
$352$			72.9873i			3.89024i
$353$		−	15.6893i		−	0.835057i	−0.908664	−	0.417529i	$-0.862896\pi$
$353$		−	15.6893i		−	0.835057i	0.908664	−	0.417529i	$-0.137104\pi$
$354$	−20.4741	−	6.17199i	−1.08819	−	0.328038i
$355$		−	19.4100i		−	1.03018i
$356$	10.9342			0.579512
$357$	2.93705	−	9.74297i	0.155445	−	0.515652i
$358$	40.3530			2.13272
$359$	29.8665			1.57629			0.788146	−	0.615488i	$-0.211041\pi$
$359$	29.8665			1.57629			0.788146	+	0.615488i	$0.211041\pi$
$360$	38.7857	−	58.4851i	2.04419	−	3.08244i
$361$	18.9991			0.999954
$362$	7.86602			0.413429
$363$	−35.5841	−	10.7269i	−1.86768	−	0.563018i
$364$			15.2449i			0.799051i
$365$	0.397545			0.0208085
$366$	65.8469	+	19.8498i	3.44187	+	1.03757i
$367$			33.1989i			1.73297i	0.499206	+	0.866483i	$0.333625\pi$
$367$			33.1989i			1.73297i	−0.499206	+	0.866483i	$0.666375\pi$
$368$	36.0306	−	37.2150i	1.87823	−	1.93997i
$369$	11.8253	−	17.8314i	0.615599	−	0.928264i
$370$	−54.1394			−2.81457
$371$		−	3.88569i		−	0.201735i
$372$	36.0464	+	10.8663i	1.86892	+	0.563392i
$373$			22.9230i			1.18691i	0.804867	+	0.593455i	$0.202237\pi$
$373$			22.9230i			1.18691i	−0.804867	+	0.593455i	$0.797763\pi$
$374$		−	88.3995i		−	4.57103i
$375$	5.60968	+	1.69106i	0.289683	+	0.0873259i
$376$	2.85582			0.147278
$377$			25.7400i			1.32568i
$378$	−8.76098	−	10.5627i	−0.450616	−	0.543288i
$379$			33.3674i			1.71397i	0.515343	+	0.856984i	$0.327664\pi$
$379$			33.3674i			1.71397i	−0.515343	+	0.856984i	$0.672336\pi$
$380$		−	0.439185i		−	0.0225297i
$381$	8.50050	+	2.56251i	0.435494	+	0.131281i
$382$		−	58.3358i		−	2.98472i
$383$	−19.1911			−0.980621			−0.490310	−	0.871548i	$-0.663117\pi$
$383$	−19.1911			−0.980621			−0.490310	+	0.871548i	$0.663117\pi$
$384$	−3.34195	+	11.0861i	−0.170543	+	0.565736i
$385$		−	16.9617i		−	0.864446i
$386$		−	11.6648i		−	0.593722i
$387$	−5.20556	+	7.84948i	−0.264614	+	0.399012i
$388$			13.9953i			0.710503i
$389$	21.5710			1.09369			0.546847	−	0.837233i	$-0.315828\pi$
$389$	21.5710			1.09369			0.546847	+	0.837233i	$0.315828\pi$
$390$	12.0450	−	39.9563i	0.609921	−	2.02327i
$391$	−19.5988	+	20.2431i	−0.991155	+	1.02374i
$392$			7.85715i			0.396846i
$393$	−2.27545	+	7.54827i	−0.114781	+	0.380760i
$394$	14.3522			0.723053
$395$			28.9821i			1.45825i
$396$	−70.8639	−	46.9950i	−3.56104	−	2.36159i
$397$	2.24566			0.112707			0.0563533	−	0.998411i	$-0.482053\pi$
$397$	2.24566			0.112707			0.0563533	+	0.998411i	$0.482053\pi$
$398$	−45.3259			−2.27198
$399$	−0.0491716	−	0.0148230i	−0.00246166	−	0.000742077i
$400$	41.7325			2.08662
$401$	−19.2521			−0.961402			−0.480701	−	0.876885i	$-0.659618\pi$
$401$	−19.2521			−0.961402			−0.480701	+	0.876885i	$0.659618\pi$
$402$	−25.4134	−	7.66096i	−1.26751	−	0.382094i
$403$	13.3882			0.666913
$404$		−	0.422289i		−	0.0210096i
$405$	10.4255	+	24.6835i	0.518046	+	1.22654i
$406$			22.1846i			1.10100i
$407$			39.2273i			1.94443i
$408$	23.0769	−	76.5520i	1.14248	−	3.78989i
$409$	6.21653			0.307388			0.153694	−	0.988119i	$-0.450883\pi$
$409$	6.21653			0.307388			0.153694	+	0.988119i	$0.450883\pi$
$410$	56.0786			2.76952
$411$	−12.8249	−	3.86611i	−0.632606	−	0.190701i
$412$			61.7536i			3.04238i
$413$	−4.67475			−0.230029
$414$	8.14336	+	37.1149i	0.400225	+	1.82410i
$415$	−0.625572			−0.0307081
$416$			39.2571i			1.92474i
$417$	4.76048	+	1.43507i	0.233122	+	0.0702754i
$418$	−0.446142			−0.0218215
$419$	−25.0065			−1.22165			−0.610825	−	0.791766i	$-0.709162\pi$
$419$	−25.0065			−1.22165			−0.610825	+	0.791766i	$0.709162\pi$
$420$	7.40457	−	24.5629i	0.361306	−	1.19855i
$421$			12.4454i			0.606551i	0.952903	+	0.303275i	$0.0980802\pi$
$421$			12.4454i			0.606551i	−0.952903	+	0.303275i	$0.901920\pi$
$422$			68.5031i			3.33468i
$423$	−0.602646	+	0.908732i	−0.0293017	+	0.0441841i
$424$		−	30.5305i		−	1.48269i
$425$	−22.7003			−1.10113
$426$	−28.5537	−	8.60762i	−1.38343	−	0.417040i
$427$	15.0345			0.727571
$428$	−2.62920			−0.127087
$429$	−28.9508	−	8.72733i	−1.39776	−	0.421360i
$430$	−24.6862			−1.19047
$431$	−22.8900			−1.10257			−0.551286	−	0.834317i	$-0.685863\pi$
$431$	−22.8900			−1.10257			−0.551286	+	0.834317i	$0.685863\pi$
$432$	−35.8294	−	43.1979i	−1.72384	−	2.07836i
$433$			5.67879i			0.272905i	0.990647	+	0.136453i	$0.0435702\pi$
$433$			5.67879i			0.272905i	−0.990647	+	0.136453i	$0.956430\pi$
$434$	11.5389			0.553886
$435$	12.5021	−	41.4727i	0.599429	−	1.98846i
$436$		−	7.84867i		−	0.375883i
$437$	0.102164	+	0.0989130i	0.00488719	+	0.00473165i
$438$	0.176296	−	0.584821i	0.00842377	−	0.0279438i
$439$	−28.9362			−1.38105			−0.690524	−	0.723309i	$-0.742620\pi$
$439$	−28.9362			−1.38105			−0.690524	+	0.723309i	$0.742620\pi$
$440$		−	133.270i		−	6.35342i
$441$	−2.50018	−	1.65805i	−0.119056	−	0.0789547i
$442$		−	47.5467i		−	2.26157i
$443$		−	1.01974i		−	0.0484494i	−0.999707	−	0.0242247i	$-0.992288\pi$
$443$		−	1.01974i		−	0.0484494i	0.999707	−	0.0242247i	$-0.00771172\pi$
$444$	−17.1246	+	56.8067i	−0.812697	+	2.69593i
$445$	−6.54337			−0.310186
$446$		−	4.03671i		−	0.191144i
$447$	−2.43735	−	0.734749i	−0.115283	−	0.0347525i
$448$			12.2329i			0.577950i
$449$		−	14.8374i		−	0.700218i	−0.936709	−	0.350109i	$-0.886145\pi$
$449$		−	14.8374i		−	0.700218i	0.936709	−	0.350109i	$-0.113855\pi$
$450$	−16.9194	+	25.5128i	−0.797588	+	1.20269i
$451$		−	40.6324i		−	1.91331i
$452$	14.9546			0.703407
$453$	12.7658	+	3.84831i	0.599792	+	0.180809i
$454$		−	17.6451i		−	0.828128i
$455$		−	9.12303i		−	0.427694i
$456$	−0.386349	−	0.116466i	−0.0180924	−	0.00545403i
$457$		−	2.01671i		−	0.0943375i	−0.998887	−	0.0471688i	$-0.984980\pi$
$457$		−	2.01671i		−	0.0943375i	0.998887	−	0.0471688i	$-0.0150199\pi$
$458$	−0.440247			−0.0205714
$459$	19.4893	+	23.4975i	0.909685	+	1.09677i
$460$	−49.4104	+	51.0346i	−2.30377	+	2.37950i
$461$		−	4.85676i		−	0.226202i	−0.993583	−	0.113101i	$-0.963922\pi$
$461$		−	4.85676i		−	0.226202i	0.993583	−	0.113101i	$-0.0360784\pi$
$462$	−24.9520	−	7.52186i	−1.16087	−	0.349949i
$463$	5.71042			0.265386			0.132693	−	0.991157i	$-0.457638\pi$
$463$	5.71042			0.265386			0.132693	+	0.991157i	$0.457638\pi$
$464$			90.7274i			4.21192i
$465$	−21.5713	−	6.50274i	−1.00034	−	0.301557i
$466$	0.0449038			0.00208013
$467$	−9.07635			−0.420003			−0.210002	−	0.977701i	$-0.567347\pi$
$467$	−9.07635			−0.420003			−0.210002	+	0.977701i	$0.567347\pi$
$468$	−38.1150	−	25.2768i	−1.76187	−	1.16842i
$469$	−5.80252			−0.267935
$470$	−2.85791			−0.131826
$471$	−3.06539	+	10.1687i	−0.141246	+	0.468549i
$472$	−36.7302			−1.69064
$473$			17.8866i			0.822429i
$474$	42.6351	+	12.8525i	1.95829	+	0.590335i
$475$			0.114566i			0.00525665i
$476$		−	29.2290i		−	1.33971i
$477$	9.71491	+	6.44266i	0.444815	+	0.294989i
$478$	−46.4230			−2.12334
$479$	33.9453			1.55100			0.775500	−	0.631348i	$-0.217498\pi$
$479$	33.9453			1.55100			0.775500	+	0.631348i	$0.217498\pi$
$480$	19.0675	−	63.2517i	0.870306	−	2.88703i
$481$			21.0989i			0.962027i
$482$	23.1765			1.05566
$483$	4.04623	+	7.25451i	0.184110	+	0.330092i
$484$	−106.753			−4.85239
$485$		−	8.37521i		−	0.380299i
$486$	40.9348	−	4.39047i	1.85684	−	0.199156i
$487$	−20.5818			−0.932651			−0.466325	−	0.884613i	$-0.654422\pi$
$487$	−20.5818			−0.932651			−0.466325	+	0.884613i	$0.654422\pi$
$488$	118.128			5.34742
$489$	37.2089	+	11.2168i	1.68265	+	0.507240i
$490$		−	7.86291i		−	0.355210i
$491$		−	8.21819i		−	0.370882i	−0.982655	−	0.185441i	$-0.940629\pi$
$491$		−	8.21819i		−	0.370882i	0.982655	−	0.185441i	$-0.0593713\pi$
$492$	17.7380	−	58.8415i	0.799690	−	2.65278i
$493$		−	49.3511i		−	2.22266i
$494$	−0.239963			−0.0107964
$495$	42.4071	+	28.1233i	1.90606	+	1.26405i
$496$	47.1902			2.11890
$497$	−6.51952			−0.292441
$498$	−0.277418	+	0.920266i	−0.0124314	+	0.0412381i
$499$	26.1361			1.17001			0.585007	−	0.811028i	$-0.301092\pi$
$499$	26.1361			1.17001			0.585007	+	0.811028i	$0.301092\pi$
$500$	16.8291			0.752621
$501$	−10.2218	+	33.9084i	−0.456677	+	1.51492i
$502$			44.6062i			1.99087i
$503$	−11.4754			−0.511662			−0.255831	−	0.966721i	$-0.582349\pi$
$503$	−11.4754			−0.511662			−0.255831	+	0.966721i	$0.582349\pi$
$504$	−19.6443	−	13.0275i	−0.875025	−	0.580292i
$505$			0.252711i			0.0112455i
$506$	51.8430	+	50.1931i	2.30470	+	2.23135i
$507$	5.98686	+	1.80476i	0.265886	+	0.0801522i
$508$	25.5016			1.13145
$509$		−	29.7606i		−	1.31912i	−0.751653	−	0.659559i	$-0.770743\pi$
$509$		−	29.7606i		−	1.31912i	0.751653	−	0.659559i	$-0.229257\pi$
$510$	−23.0938	+	76.6080i	−1.02261	+	3.39226i
$511$		−	0.133529i		−	0.00590699i
$512$		−	31.3564i		−	1.38577i
$513$	0.118589	−	0.0983605i	0.00523583	−	0.00434272i
$514$	56.0395			2.47180
$515$		−	36.9552i		−	1.62844i
$516$	−7.80837	+	25.9024i	−0.343744	+	1.14029i
$517$			2.07073i			0.0910707i
$518$			18.1846i			0.798985i
$519$	−5.05185	+	16.7583i	−0.221752	+	0.735608i
$520$		−	71.6810i		−	3.14342i
$521$	−32.8107			−1.43746			−0.718732	−	0.695287i	$-0.755277\pi$
$521$	−32.8107			−1.43746			−0.718732	+	0.695287i	$0.755277\pi$
$522$	−55.4654	−	36.7832i	−2.42766	−	1.60996i
$523$			5.82001i			0.254491i	0.991871	+	0.127246i	$0.0406136\pi$
$523$			5.82001i			0.254491i	−0.991871	+	0.127246i	$0.959386\pi$
$524$			22.6449i			0.989246i
$525$	−1.93156	+	6.40749i	−0.0843002	+	0.279646i
$526$		−	6.95015i		−	0.303041i
$527$	−25.6691			−1.11816
$528$	−102.045	−	30.7618i	−4.44094	−	1.33874i
$529$	−0.743624	−	22.9880i	−0.0323315	−	0.999477i
$530$			30.5528i			1.32713i
$531$	7.75096	−	11.6877i	0.336363	−	0.507203i
$532$	−0.147515			−0.00639560
$533$		−	21.8546i		−	0.946629i
$534$	−2.90174	+	9.62583i	−0.125571	+	0.416550i
$535$	1.57340			0.0680238
$536$	−45.5912			−1.96924
$537$	−7.63830	+	25.3382i	−0.329617	+	1.09343i
$538$	−2.26394			−0.0976052
$539$	−5.69716			−0.245394
$540$	49.1344	+	59.2392i	2.11441	+	2.54925i
$541$	−1.64283			−0.0706306			−0.0353153	−	0.999376i	$-0.511244\pi$
$541$	−1.64283			−0.0706306			−0.0353153	+	0.999376i	$0.511244\pi$
$542$		−	56.6148i		−	2.43182i
$543$	−1.48894	+	4.93919i	−0.0638963	+	0.211961i
$544$		−	75.2674i		−	3.22706i
$545$			4.69689i			0.201193i
$546$	−13.4207	−	4.04572i	−0.574354	−	0.173141i
$547$	18.0062			0.769891			0.384946	−	0.922939i	$-0.374220\pi$
$547$	18.0062			0.769891			0.384946	+	0.922939i	$0.374220\pi$
$548$	−38.4748			−1.64356
$549$	−24.9279	+	37.5889i	−1.06390	+	1.60425i
$550$			58.1361i			2.47893i
$551$	−0.249069			−0.0106107
$552$	31.7919	+	56.9998i	1.35315	+	2.42607i
$553$	9.73465			0.413959
$554$		−	53.8231i		−	2.28672i
$555$	10.2479	−	33.9949i	0.434998	−	1.44300i
$556$	14.2815			0.605671
$557$	36.4853			1.54593			0.772966	−	0.634447i	$-0.218772\pi$
$557$	36.4853			1.54593			0.772966	+	0.634447i	$0.218772\pi$
$558$	−19.1321	+	28.8493i	−0.809926	+	1.22129i
$559$			9.62055i			0.406906i
$560$		−	32.1566i		−	1.35886i
$561$	55.5072	+	16.7329i	2.34352	+	0.706462i
$562$		−	58.0366i		−	2.44813i
$563$	12.9726			0.546728			0.273364	−	0.961911i	$-0.411864\pi$
$563$	12.9726			0.546728			0.273364	+	0.961911i	$0.411864\pi$
$564$	−0.903973	+	2.99871i	−0.0380641	+	0.126269i
$565$	−8.94931			−0.376500
$566$	3.19475			0.134285
$567$	8.29082	−	3.50175i	0.348182	−	0.147060i
$568$	−51.2249			−2.14935
$569$	−11.1370			−0.466889			−0.233444	−	0.972370i	$-0.575000\pi$
$569$	−11.1370			−0.466889			−0.233444	+	0.972370i	$0.575000\pi$
$570$	0.386632	+	0.116552i	0.0161942	+	0.00488181i
$571$		−	12.7046i		−	0.531673i	−0.964018	−	0.265836i	$-0.914352\pi$
$571$		−	12.7046i		−	0.531673i	0.964018	−	0.265836i	$-0.0856481\pi$
$572$	−86.8528			−3.63150
$573$	36.6299	+	11.0422i	1.53023	+	0.461295i
$574$		−	18.8359i		−	0.786197i
$575$	12.8892	−	13.3129i	0.537518	−	0.555187i
$576$	−30.5844	−	20.2827i	−1.27435	−	0.845114i
$577$	−29.1662			−1.21421			−0.607103	−	0.794623i	$-0.707668\pi$
$577$	−29.1662			−1.21421			−0.607103	+	0.794623i	$0.707668\pi$
$578$			46.2635i			1.92431i
$579$	7.32448	+	2.20799i	0.304395	+	0.0917610i
$580$		−	124.418i		−	5.16620i
$581$			0.210120i			0.00871724i
$582$	−12.3206	−	3.71409i	−0.510706	−	0.153954i
$583$	22.1374			0.916838
$584$		−	1.04916i		−	0.0434146i
$585$	22.8092	+	15.1264i	0.943044	+	0.625401i
$586$		−	12.7795i		−	0.527917i
$587$		−	15.9105i		−	0.656697i	−0.944557	−	0.328348i	$-0.893508\pi$
$587$		−	15.9105i		−	0.656697i	0.944557	−	0.328348i	$-0.106492\pi$
$588$	−8.25029	−	2.48708i	−0.340236	−	0.102565i
$589$			0.129549i			0.00533797i
$590$	36.7571			1.51327
$591$	−2.71668	+	9.01195i	−0.111749	+	0.370702i
$592$			74.3687i			3.05653i
$593$			31.1906i			1.28085i	0.768023	+	0.640423i	$0.221241\pi$
$593$			31.1906i			1.28085i	−0.768023	+	0.640423i	$0.778759\pi$
$594$	60.1776	−	49.9127i	2.46912	−	2.04794i
$595$			17.4915i			0.717083i
$596$	−7.31209			−0.299515
$597$	8.57960	−	28.4608i	0.351140	−	1.16482i
$598$	27.8844	+	26.9969i	1.14028	+	1.10399i
$599$		−	27.4906i		−	1.12324i	−0.827396	−	0.561618i	$-0.810179\pi$
$599$		−	27.4906i		−	1.12324i	0.827396	−	0.561618i	$-0.189821\pi$
$600$	−15.1766	+	50.3446i	−0.619581	+	2.05531i
$601$	−19.2230			−0.784121			−0.392061	−	0.919939i	$-0.628238\pi$
$601$	−19.2230			−0.784121			−0.392061	+	0.919939i	$0.628238\pi$
$602$			8.29170i			0.337944i
$603$	9.62085	−	14.5073i	0.391791	−	0.590783i
$604$	38.2977			1.55831
$605$	63.8840			2.59725
$606$	0.371758	+	0.112068i	0.0151016	+	0.00455244i
$607$	−27.8547			−1.13059			−0.565294	−	0.824890i	$-0.691237\pi$
$607$	−27.8547			−1.13059			−0.565294	+	0.824890i	$0.691237\pi$
$608$	−0.379866			−0.0154056
$609$	−13.9300	−	4.19926i	−0.564473	−	0.170163i
$610$	−118.215			−4.78638
$611$			1.11377i			0.0450582i
$612$	73.0776	+	48.4631i	2.95399	+	1.95900i
$613$		−	29.3072i		−	1.18371i	−0.806046	−	0.591853i	$-0.798396\pi$
$613$		−	29.3072i		−	1.18371i	0.806046	−	0.591853i	$-0.201604\pi$
$614$		−	42.4560i		−	1.71339i
$615$	−10.6149	+	35.2125i	−0.428036	+	1.41991i
$616$	−44.7635			−1.80357
$617$	14.8774			0.598940			0.299470	−	0.954106i	$-0.403190\pi$
$617$	14.8774			0.598940			0.299470	+	0.954106i	$0.403190\pi$
$618$	−54.3641	−	16.3883i	−2.18685	−	0.659233i
$619$		−	46.4400i		−	1.86658i	−0.359123	−	0.933290i	$-0.616924\pi$
$619$		−	46.4400i		−	1.86658i	0.359123	−	0.933290i	$-0.383076\pi$
$620$	−64.7140			−2.59898
$621$	−24.8464	−	1.91204i	−0.997052	−	0.0767275i
$622$	34.4375			1.38082
$623$			2.19782i			0.0880537i
$624$	−54.8861	−	16.5456i	−2.19720	−	0.662355i
$625$	−29.3901			−1.17560
$626$	−69.2611			−2.76823
$627$	0.0844488	−	0.280139i	0.00337256	−	0.0111877i
$628$			30.5062i			1.21733i
$629$		−	40.4528i		−	1.61296i
$630$	19.6586	+	13.0371i	0.783219	+	0.519410i
$631$			18.9080i			0.752717i	0.926474	+	0.376359i	$0.122824\pi$
$631$			18.9080i			0.752717i	−0.926474	+	0.376359i	$0.877176\pi$
$632$	76.4866			3.04247
$633$	−43.0140	−	12.9667i	−1.70965	−	0.515382i
$634$	−25.9954			−1.03241
$635$	−15.2609			−0.605612
$636$	32.0581	+	9.66403i	1.27119	+	0.383204i
$637$	−3.06429			−0.121411
$638$	−126.389			−5.00380
$639$	10.8097	−	16.3000i	0.427625	−	0.644816i
$640$		−	19.9029i		−	0.786731i
$641$	36.9687			1.46018			0.730088	−	0.683353i	$-0.239479\pi$
$641$	36.9687			1.46018			0.730088	+	0.683353i	$0.239479\pi$
$642$	0.697742	−	2.31459i	0.0275377	−	0.0913496i
$643$		−	38.9922i		−	1.53770i	−0.639429	−	0.768851i	$-0.720829\pi$
$643$		−	38.9922i		−	1.53770i	0.639429	−	0.768851i	$-0.279171\pi$
$644$	17.1417	+	16.5962i	0.675479	+	0.653981i
$645$	4.67277	−	15.5008i	0.183990	−	0.610343i
$646$	0.460079			0.0181016
$647$			49.0254i			1.92739i	0.267012	+	0.963693i	$0.413964\pi$
$647$			49.0254i			1.92739i	−0.267012	+	0.963693i	$0.586036\pi$
$648$	65.1422	−	27.5138i	2.55903	−	1.08084i
$649$		−	26.6328i		−	1.04543i
$650$			31.2692i			1.22648i
$651$	−2.18417	+	7.24545i	−0.0856043	+	0.283972i
$652$	111.627			4.37166
$653$		−	18.6920i		−	0.731475i	−0.930718	−	0.365738i	$-0.880817\pi$
$653$		−	18.6920i		−	0.731475i	0.930718	−	0.365738i	$-0.119183\pi$
$654$	6.90950	+	2.08289i	0.270183	+	0.0814476i
$655$		−	13.5514i		−	0.529497i
$656$		−	77.0325i		−	3.00761i
$657$	0.333847	+	0.221398i	0.0130246	+	0.00863756i
$658$			0.959928i			0.0374219i
$659$	−36.5702			−1.42457			−0.712287	−	0.701888i	$-0.752341\pi$
$659$	−36.5702			−1.42457			−0.712287	+	0.701888i	$0.752341\pi$
$660$	139.939	+	42.1850i	5.44711	+	1.64205i
$661$			44.3752i			1.72600i	0.505207	+	0.862998i	$0.331416\pi$
$661$			44.3752i			1.72600i	−0.505207	+	0.862998i	$0.668584\pi$
$662$		−	25.8862i		−	1.00610i
$663$	29.8552	+	8.99997i	1.15948	+	0.349530i
$664$			1.65094i			0.0640690i
$665$	0.0882778			0.00342326
$666$	−45.4647	−	30.1509i	−1.76172	−	1.16832i
$667$	28.9426	+	28.0215i	1.12066	+	1.08500i
$668$			101.726i			3.93588i
$669$	2.53471	+	0.764097i	0.0979975	+	0.0295417i
$670$	45.6246			1.76263
$671$			85.6540i			3.30664i
$672$	−21.2453	−	6.40446i	−0.819554	−	0.247058i
$673$	−20.4964			−0.790079			−0.395040	−	0.918664i	$-0.629269\pi$
$673$	−20.4964			−0.790079			−0.395040	+	0.918664i	$0.629269\pi$
$674$	85.1824			3.28110
$675$	−12.8172	−	15.4532i	−0.493335	−	0.594793i
$676$	17.9606			0.690793
$677$	−27.0311			−1.03889			−0.519445	−	0.854504i	$-0.673861\pi$
$677$	−27.0311			−1.03889			−0.519445	+	0.854504i	$0.673861\pi$
$678$	−3.96869	+	13.1652i	−0.152416	+	0.505605i
$679$	−2.81310			−0.107957
$680$			137.434i			5.27034i
$681$	11.0796	+	3.34000i	0.424573	+	0.127989i
$682$			65.7391i			2.51728i
$683$		−	33.5836i		−	1.28504i	−0.766269	−	0.642520i	$-0.777889\pi$
$683$		−	33.5836i		−	1.28504i	0.766269	−	0.642520i	$-0.222111\pi$
$684$	0.244588	−	0.368814i	0.00935204	−	0.0141020i
$685$	23.0245			0.879722
$686$	−2.64103			−0.100835
$687$	0.0833331	−	0.276437i	0.00317936	−	0.0105467i
$688$			33.9102i			1.29281i
$689$	11.9069			0.453615
$690$	−31.8152	−	57.0416i	−1.21118	−	2.17154i
$691$	2.23378			0.0849769			0.0424885	−	0.999097i	$-0.486471\pi$
$691$	2.23378			0.0849769			0.0424885	+	0.999097i	$0.486471\pi$
$692$			50.2751i			1.91117i
$693$	9.44617	−	14.2439i	0.358830	−	0.541081i
$694$	−79.9214			−3.03377
$695$	−8.54649			−0.324187
$696$	−109.450	−	32.9942i	−4.14871	−	1.25064i
$697$			41.9017i			1.58714i
$698$			75.5625i			2.86008i
$699$	−0.00849971	+	0.0281957i	−0.000321489	+	0.00106646i
$700$			19.2225i			0.726543i
$701$	7.31884			0.276429			0.138214	−	0.990402i	$-0.455864\pi$
$701$	7.31884			0.276429			0.138214	+	0.990402i	$0.455864\pi$
$702$	32.3672	−	26.8461i	1.22162	−	1.01324i
$703$	−0.204161			−0.00770006
$704$	−69.6928			−2.62665
$705$	0.540965	−	1.79452i	0.0203739	−	0.0675856i
$706$	41.4359			1.55946
$707$	0.0848816			0.00319230
$708$	11.6265	−	38.5680i	0.436950	−	1.44948i
$709$		−	41.0125i		−	1.54026i	−0.637889	−	0.770128i	$-0.720192\pi$
$709$		−	41.0125i		−	1.54026i	0.637889	−	0.770128i	$-0.279808\pi$
$710$	51.2624			1.92384
$711$	−16.1405	+	24.3383i	−0.605317	+	0.912759i
$712$			17.2686i			0.647168i
$713$	14.5749	−	15.0540i	0.545833	−	0.563775i
$714$	25.7315	+	7.75684i	0.962976	+	0.290292i
$715$	51.9754			1.94377
$716$			76.0150i			2.84081i
$717$	8.78727	−	29.1497i	0.328167	−	1.08861i
$718$			78.8782i			2.94371i
$719$		−	17.6763i		−	0.659215i	−0.944118	−	0.329608i	$-0.893084\pi$
$719$		−	17.6763i		−	0.659215i	0.944118	−	0.329608i	$-0.106916\pi$
$720$	80.3971	+	53.3171i	2.99622	+	1.98701i
$721$	−12.4127			−0.462273
$722$			50.1772i			1.86740i
$723$	−4.38702	+	14.5529i	−0.163155	+	0.541227i
$724$			14.8176i			0.550692i
$725$			32.4559i			1.20538i
$726$	28.3302	−	93.9785i	1.05143	−	3.48787i
$727$		−	11.9348i		−	0.442637i	−0.975202	−	0.221319i	$-0.928964\pi$
$727$		−	11.9348i		−	0.442637i	0.975202	−	0.221319i	$-0.0710361\pi$
$728$	−24.0766			−0.892337
$729$	−4.99158	+	26.5346i	−0.184873	+	0.982762i
$730$			1.04993i			0.0388596i
$731$		−	18.4454i		−	0.682228i
$732$	−37.3920	+	124.039i	−1.38205	+	4.58461i
$733$			27.5737i			1.01846i	0.860631	+	0.509230i	$0.170070\pi$
$733$			27.5737i			1.01846i	−0.860631	+	0.509230i	$0.829930\pi$
$734$	−87.6792			−3.23630
$735$	4.93723	+	1.48835i	0.182112	+	0.0548985i
$736$	44.1415	+	42.7367i	1.62708	+	1.57530i
$737$		−	33.0579i		−	1.21770i
$738$	47.0931	+	31.2309i	1.73352	+	1.14962i
$739$	−2.34767			−0.0863603			−0.0431802	−	0.999067i	$-0.513749\pi$
$739$	−2.34767			−0.0863603			−0.0431802	+	0.999067i	$0.513749\pi$
$740$		−	101.985i		−	3.74904i
$741$	0.0454218	−	0.150676i	0.00166861	−	0.00553522i
$742$	10.2622			0.376738
$743$	23.7567			0.871550			0.435775	−	0.900056i	$-0.356474\pi$
$743$	23.7567			0.871550			0.435775	+	0.900056i	$0.356474\pi$
$744$	−17.1613	+	56.9286i	−0.629165	+	2.08710i
$745$	4.37578			0.160316
$746$	−60.5404			−2.21654
$747$	−0.525337	−	0.348389i	−0.0192211	−	0.0127469i
$748$	166.522			6.08866
$749$		−	0.528479i		−	0.0193102i
$750$	−4.46614	+	14.8153i	−0.163080	+	0.540980i
$751$		−	37.3963i		−	1.36461i	−0.731068	−	0.682305i	$-0.760978\pi$
$751$		−	37.3963i		−	1.36461i	0.731068	−	0.682305i	$-0.239022\pi$
$752$			3.92577i			0.143158i
$753$	−28.0088	−	8.44336i	−1.02070	−	0.307693i
$754$	−67.9800			−2.47569
$755$	−22.9185			−0.834090
$756$	19.8975	−	16.5035i	0.723666	−	0.600226i
$757$			31.8423i			1.15733i	0.815566	+	0.578664i	$0.196426\pi$
$757$			31.8423i			1.15733i	−0.815566	+	0.578664i	$0.803574\pi$
$758$	−88.1242			−3.20082
$759$	−41.3301	+	23.0520i	−1.50019	+	0.836736i
$760$	0.693612			0.0251599
$761$			5.12460i			0.185767i	0.995677	+	0.0928833i	$0.0296084\pi$
$761$			5.12460i			0.185767i	−0.995677	+	0.0928833i	$0.970392\pi$
$762$	−6.76765	+	22.4501i	−0.245166	+	0.813280i
$763$	1.57761			0.0571134
$764$	109.890			3.97568
$765$	−43.7319	−	29.0018i	−1.58113	−	1.04856i
$766$		−	50.6843i		−	1.83130i
$767$		−	14.3248i		−	0.517237i
$768$	11.2938	+	3.40455i	0.407530	+	0.122851i
$769$			46.0132i			1.65928i	0.558299	+	0.829639i	$0.311454\pi$
$769$			46.0132i			1.65928i	−0.558299	+	0.829639i	$0.688546\pi$
$770$	44.7962			1.61434
$771$	−10.6076	+	35.1880i	−0.382022	+	1.26726i
$772$	21.9735			0.790844
$773$	38.5121			1.38518			0.692592	−	0.721330i	$-0.256469\pi$
$773$	38.5121			1.38518			0.692592	+	0.721330i	$0.256469\pi$
$774$	−20.7307	−	13.7480i	−0.745150	−	0.494163i
$775$	16.8813			0.606395
$776$	−22.1030			−0.793451
$777$	−11.4184	−	3.44211i	−0.409631	−	0.123485i
$778$			56.9696i			2.04246i
$779$	0.211473			0.00757681
$780$	75.2677	+	22.6897i	2.69502	+	0.812422i
$781$		−	37.1428i		−	1.32907i
$782$	−53.4625	−	51.7611i	−1.91182	−	1.85097i
$783$	33.5955	−	27.8649i	1.20061	−	0.995812i
$784$	−10.8009			−0.385746
$785$		−	18.2559i		−	0.651580i
$786$	−19.9352	−	6.00954i	−0.711065	−	0.214353i
$787$		−	40.2100i		−	1.43333i	−0.697416	−	0.716667i	$-0.745667\pi$
$787$		−	40.2100i		−	1.43333i	0.697416	−	0.716667i	$-0.254333\pi$
$788$			27.0359i			0.963115i
$789$	4.36410	+	1.31557i	0.155366	+	0.0468356i
$790$	−76.5427			−2.72327
$791$			3.00594i			0.106879i
$792$	74.2200	−	111.916i	2.63729	−	3.97678i
$793$			46.0700i			1.63599i
$794$			5.93086i			0.210478i
$795$	−19.1845	−	5.78325i	−0.680406	−	0.205111i
$796$		−	85.3826i		−	3.02630i
$797$	−22.6796			−0.803351			−0.401676	−	0.915782i	$-0.631572\pi$
$797$	−22.6796			−0.803351			−0.401676	+	0.915782i	$0.631572\pi$
$798$	0.0391479	−	0.129864i	0.00138582	−	0.00459712i
$799$		−	2.13542i		−	0.0755457i
$800$			49.4998i			1.75008i
$801$	−5.49493	−	3.64409i	−0.194154	−	0.128758i
$802$		−	50.8452i		−	1.79541i
$803$	0.760738			0.0268459
$804$	14.4313	−	47.8724i	0.508954	−	1.68833i
$805$	−10.2581	−	9.93167i	−0.361552	−	0.350045i
$806$			35.3586i			1.24545i
$807$	0.428533	−	1.42156i	0.0150851	−	0.0500412i
$808$	0.666927			0.0234624
$809$		−	29.5367i		−	1.03846i	−0.854636	−	0.519228i	$-0.826220\pi$
$809$		−	29.5367i		−	1.03846i	0.854636	−	0.519228i	$-0.173780\pi$
$810$	−65.1900	+	27.5340i	−2.29054	+	0.967445i
$811$	−18.1305			−0.636649			−0.318325	−	0.947982i	$-0.603120\pi$
$811$	−18.1305			−0.636649			−0.318325	+	0.947982i	$0.603120\pi$
$812$	−41.7902			−1.46655
$813$	35.5492	+	10.7164i	1.24677	+	0.375842i
$814$	−103.601			−3.63120
$815$	−66.8012			−2.33994
$816$	105.233	+	31.7228i	3.68388	+	1.11052i
$817$	−0.0930919			−0.00325687
$818$			16.4180i			0.574043i
$819$	5.08073	−	7.66125i	0.177535	−	0.267706i
$820$			105.638i			3.68904i
$821$			6.88215i			0.240189i	0.992762	+	0.120094i	$0.0383197\pi$
$821$			6.88215i			0.240189i	−0.992762	+	0.120094i	$0.961680\pi$
$822$	10.2105	−	33.8709i	0.356133	−	1.18138i
$823$	0.984534			0.0343187			0.0171593	−	0.999853i	$-0.494538\pi$
$823$	0.984534			0.0343187			0.0171593	+	0.999853i	$0.494538\pi$
$824$	−97.5284			−3.39756
$825$	−36.5045	−	11.0044i	−1.27092	−	0.383124i
$826$		−	12.3461i		−	0.429577i
$827$	34.8002			1.21012			0.605061	−	0.796179i	$-0.293149\pi$
$827$	34.8002			1.21012			0.605061	+	0.796179i	$0.293149\pi$
$828$	−69.9152	+	15.3401i	−2.42972	+	0.533104i
$829$	−3.76677			−0.130825			−0.0654126	−	0.997858i	$-0.520836\pi$
$829$	−3.76677			−0.130825			−0.0654126	+	0.997858i	$0.520836\pi$
$830$		−	1.65215i		−	0.0573471i
$831$	33.7962	+	10.1880i	1.17238	+	0.353418i
$832$	−37.4851			−1.29956
$833$	5.87514			0.203561
$834$	−3.79005	+	12.5726i	−0.131239	+	0.435353i
$835$		−	60.8758i		−	2.10669i
$836$		−	0.840419i		−	0.0290665i
$837$	−14.4934	−	17.4741i	−0.500967	−	0.603994i
$838$		−	66.0430i		−	2.28142i
$839$	−2.33429			−0.0805886			−0.0402943	−	0.999188i	$-0.512830\pi$
$839$	−2.33429			−0.0805886			−0.0402943	+	0.999188i	$0.512830\pi$
$840$	38.7925	+	11.6942i	1.33847	+	0.403487i
$841$	−41.5599			−1.43310
$842$	−32.8686			−1.13273
$843$	36.4420	+	10.9856i	1.25513	+	0.378363i
$844$	−129.043			−4.44183
$845$	−10.7482			−0.369749
$846$	−2.39999	−	1.59161i	−0.0825133	−	0.0547206i
$847$		−	21.4576i		−	0.737294i
$848$	41.9689			1.44122
$849$	−0.604724	+	2.00603i	−0.0207541	+	0.0688467i
$850$		−	59.9523i		−	2.05635i
$851$	23.7241	+	22.9690i	0.813250	+	0.787368i
$852$	16.2146	−	53.7880i	0.555503	−	1.84275i
$853$	−30.5014			−1.04435			−0.522174	−	0.852839i	$-0.674879\pi$
$853$	−30.5014			−1.04435			−0.522174	+	0.852839i	$0.674879\pi$
$854$			39.7066i			1.35873i
$855$	−0.146369	+	0.220710i	−0.00500571	+	0.00754812i
$856$		−	4.15234i		−	0.141924i
$857$			51.3227i			1.75315i	0.481265	+	0.876575i	$0.340177\pi$
$857$			51.3227i			1.75315i	−0.481265	+	0.876575i	$0.659823\pi$
$858$	23.0491	−	76.4600i	0.786885	−	2.61030i
$859$	29.2077			0.996553			0.498277	−	0.867018i	$-0.333966\pi$
$859$	29.2077			0.996553			0.498277	+	0.867018i	$0.333966\pi$
$860$		−	46.5025i		−	1.58572i
$861$	11.8273	+	3.56540i	0.403075	+	0.121508i
$862$		−	60.4531i		−	2.05904i
$863$		−	9.57045i		−	0.325782i	−0.986644	−	0.162891i	$-0.947918\pi$
$863$		−	9.57045i		−	0.325782i	0.986644	−	0.162891i	$-0.0520819\pi$
$864$	51.2380	−	42.4980i	1.74315	−	1.44581i
$865$		−	30.0861i		−	1.02296i
$866$	−14.9979			−0.509648
$867$	−29.0495	−	8.75707i	−0.986572	−	0.297406i
$868$			21.7364i			0.737783i
$869$			55.4599i			1.88135i
$870$	109.531	+	33.0184i	3.71343	+	1.11943i
$871$		−	17.7806i		−	0.602471i
$872$	12.3955			0.419766
$873$	4.66426	−	7.03325i	0.157861	−	0.238040i
$874$	−0.261232	+	0.269819i	−0.00883631	+	0.00912677i
$875$			3.38271i			0.114357i
$876$	1.10166	+	0.332098i	0.0372215	+	0.0112206i
$877$	−35.5188			−1.19938			−0.599692	−	0.800231i	$-0.704710\pi$
$877$	−35.5188			−1.19938			−0.599692	+	0.800231i	$0.704710\pi$
$878$		−	76.4213i		−	2.57909i
$879$	8.02443	+	2.41899i	0.270657	+	0.0815907i
$880$	183.201			6.17571
$881$	29.3840			0.989972			0.494986	−	0.868901i	$-0.335173\pi$
$881$	29.3840			0.989972			0.494986	+	0.868901i	$0.335173\pi$
$882$	4.37895	−	6.60304i	0.147447	−	0.222336i
$883$	−8.68000			−0.292105			−0.146053	−	0.989277i	$-0.546657\pi$
$883$	−8.68000			−0.292105			−0.146053	+	0.989277i	$0.546657\pi$
$884$	89.5660			3.01243
$885$	−6.95764	+	23.0803i	−0.233879	+	0.775836i
$886$	2.69317			0.0904787
$887$			9.20195i			0.308971i	0.987995	+	0.154486i	$0.0493720\pi$
$887$			9.20195i			0.308971i	−0.987995	+	0.154486i	$0.950628\pi$
$888$	−89.7158	−	27.0451i	−3.01066	−	0.907576i
$889$			5.12591i			0.171918i
$890$		−	17.2812i		−	0.579268i
$891$	19.9501	+	47.2341i	0.668352	+	1.58240i
$892$	7.60415			0.254606
$893$	−0.0107772			−0.000360646
$894$	1.94049	−	6.43712i	0.0648999	−	0.215290i
$895$		−	45.4897i		−	1.52055i
$896$	−6.68508			−0.223333
$897$	−22.2299	+	12.3988i	−0.742235	+	0.413985i
$898$	39.1859			1.30765
$899$			36.7004i			1.22403i
$900$	−48.0597	−	31.8719i	−1.60199	−	1.06240i
$901$	−22.8290			−0.760543
$902$	107.311			3.57308
$903$	−5.20647	−	1.56951i	−0.173261	−	0.0522300i
$904$			23.6181i			0.785526i
$905$		−	8.86731i		−	0.294759i
$906$	−10.1635	+	33.7150i	−0.337660	+	1.12011i
$907$			1.87741i			0.0623383i	0.999514	+	0.0311692i	$0.00992306\pi$
$907$			1.87741i			0.0623383i	−0.999514	+	0.0311692i	$0.990077\pi$
$908$	33.2390			1.10308
$909$	−0.140738	+	0.212219i	−0.00466797	+	0.00703885i
$910$	24.0942			0.798715
$911$	17.8572			0.591635			0.295818	−	0.955244i	$-0.404408\pi$
$911$	17.8572			0.591635			0.295818	+	0.955244i	$0.404408\pi$
$912$	0.160101	−	0.531098i	0.00530148	−	0.0175864i
$913$	−1.19709			−0.0396178
$914$	5.32618			0.176174
$915$	22.3765	−	74.2288i	0.739745	−	2.45393i
$916$		−	0.829315i		−	0.0274013i
$917$	−4.55170			−0.150310
$918$	−62.0575	+	51.4719i	−2.04820	+	1.69883i
$919$			5.04096i			0.166286i	0.996538	+	0.0831430i	$0.0264958\pi$
$919$			5.04096i			0.166286i	−0.996538	+	0.0831430i	$0.973504\pi$
$920$	−80.5997	−	78.0346i	−2.65729	−	2.57272i
$921$	26.6587	+	8.03637i	0.878435	+	0.264807i
$922$	12.8269			0.422430
$923$		−	19.9777i		−	0.657574i
$924$	14.1693	−	47.0032i	0.466136	−	1.54629i
$925$			26.6039i			0.874730i
$926$			15.0814i			0.495605i
$927$	20.5808	−	31.0339i	0.675964	−	1.01929i
$928$	−107.614			−3.53259
$929$			56.0235i			1.83807i	0.394175	+	0.919035i	$0.371030\pi$
$929$			56.0235i			1.83807i	−0.394175	+	0.919035i	$0.628970\pi$
$930$	17.1739	−	56.9703i	0.563155	−	1.86813i
$931$		−	0.0296511i		−	0.000971777i
$932$			0.0845875i			0.00277076i
$933$	−6.51857	+	21.6238i	−0.213408	+	0.707931i
$934$		−	23.9709i		−	0.784352i
$935$	−99.6521			−3.25897
$936$	39.9201	−	60.1956i	1.30483	−	1.96756i
$937$		−	25.8101i		−	0.843178i	−0.906787	−	0.421589i	$-0.861472\pi$
$937$		−	25.8101i		−	0.843178i	0.906787	−	0.421589i	$-0.138528\pi$
$938$		−	15.3246i		−	0.500366i
$939$	13.1102	−	43.4900i	0.427836	−	1.41924i
$940$		−	5.38358i		−	0.175593i
$941$	10.3630			0.337823			0.168912	−	0.985631i	$-0.445975\pi$
$941$	10.3630			0.337823			0.168912	+	0.985631i	$0.445975\pi$
$942$	−26.8559	−	8.09580i	−0.875011	−	0.263775i
$943$	−24.5738	−	23.7917i	−0.800234	−	0.774766i
$944$		−	50.4915i		−	1.64336i
$945$	−11.9073	+	9.87619i	−0.387344	+	0.321272i
$946$	−47.2392			−1.53588
$947$			52.0354i			1.69092i	0.534036	+	0.845462i	$0.320675\pi$
$947$			52.0354i			1.69092i	−0.534036	+	0.845462i	$0.679325\pi$
$948$	−24.2109	+	80.3137i	−0.786332	+	2.60847i
$949$	0.409172			0.0132823
$950$	−0.302572			−0.00981674
$951$	4.92058	−	16.3229i	0.159561	−	0.529305i
$952$	46.1618			1.49611
$953$	36.0016			1.16621			0.583103	−	0.812398i	$-0.301838\pi$
$953$	36.0016			1.16621			0.583103	+	0.812398i	$0.301838\pi$
$954$	−17.0153	+	25.6574i	−0.550889	+	0.830687i
$955$	−65.7615			−2.12799
$956$		−	87.4493i		−	2.82831i
$957$	23.9239	−	79.3616i	0.773348	−	2.56540i
$958$			89.6505i			2.89648i
$959$		−	7.73358i		−	0.249730i
$960$	60.3966	+	18.2068i	1.94929	+	0.587621i
$961$	−11.9109			−0.384224
$962$	−55.7228			−1.79658
$963$	1.32129	+	0.876244i	0.0425780	+	0.0282366i
$964$			43.6588i			1.40615i
$965$	−13.1496			−0.423301
$966$	−19.1594	+	10.6862i	−0.616443	+	0.343824i
$967$	−49.9446			−1.60611			−0.803055	−	0.595905i	$-0.796793\pi$
$967$	−49.9446			−1.60611			−0.803055	+	0.595905i	$0.796793\pi$
$968$		−	168.596i		−	5.41888i
$969$	−0.0870869	+	0.288890i	−0.00279764	+	0.00928048i
$970$	22.1192			0.710204
$971$	−44.1951			−1.41829			−0.709143	−	0.705064i	$-0.750918\pi$
$971$	−44.1951			−1.41829			−0.709143	+	0.705064i	$0.750918\pi$
$972$	8.27055	+	77.1108i	0.265278	+	2.47333i
$973$			2.87063i			0.0920283i
$974$		−	54.3572i		−	1.74172i
$975$	−19.6344	−	5.91885i	−0.628803	−	0.189555i
$976$			162.386i			5.19785i
$977$	−20.8324			−0.666486			−0.333243	−	0.942841i	$-0.608143\pi$
$977$	−20.8324			−0.666486			−0.333243	+	0.942841i	$0.608143\pi$
$978$	−29.6238	+	98.2699i	−0.947265	+	3.14232i
$979$	−12.5213			−0.400183
$980$	14.8117			0.473144
$981$	−2.61576	+	3.94431i	−0.0835147	+	0.125932i
$982$	21.7045			0.692618
$983$	14.7395			0.470118			0.235059	−	0.971981i	$-0.424472\pi$
$983$	14.7395			0.470118			0.235059	+	0.971981i	$0.424472\pi$
$984$	92.9293	+	28.0139i	2.96248	+	0.893049i
$985$		−	16.1791i		−	0.515510i
$986$	130.338			4.15080
$987$	−0.602752	−	0.181702i	−0.0191858	−	0.00578363i
$988$		−	0.452029i		−	0.0143810i
$989$	10.8176	+	10.4733i	0.343978	+	0.333031i
$990$	−74.2743	+	111.998i	−2.36059	+	3.55955i
$991$	58.9995			1.87418			0.937090	−	0.349088i	$-0.113508\pi$
$991$	58.9995			1.87418			0.937090	+	0.349088i	$0.113508\pi$
$992$			55.9733i			1.77716i
$993$	16.2543	+	4.89992i	0.515815	+	0.155494i
$994$		−	17.2183i		−	0.546130i
$995$			51.0955i			1.61984i
$996$	−1.73355	−	0.522585i	−0.0549296	−	0.0165587i
$997$	52.2984			1.65631			0.828154	−	0.560501i	$-0.189392\pi$
$997$	52.2984			1.65631			0.828154	+	0.560501i	$0.189392\pi$
$998$			69.0263i			2.18499i
$999$	27.5381	−	22.8407i	0.871266	−	0.722649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.e.a.344.48	yes	48
3.2	odd	2	inner	483.2.e.a.344.1	✓	48
23.22	odd	2	inner	483.2.e.a.344.47	yes	48
69.68	even	2	inner	483.2.e.a.344.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.1	✓	48	3.2	odd	2	inner
483.2.e.a.344.2	yes	48	69.68	even	2	inner
483.2.e.a.344.47	yes	48	23.22	odd	2	inner
483.2.e.a.344.48	yes	48	1.1	even	1	trivial

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.64103i q^{2} +(-1.65834 - 0.499912i) q^{3} -4.97503 q^{4} +2.97721 q^{5} +(1.32028 - 4.37972i) q^{6} -1.00000i q^{7} -7.85715i q^{8} +(2.50018 + 1.65805i) q^{9} +O(q^{10})\)	\(q+2.64103i q^{2} +(-1.65834 - 0.499912i) q^{3} -4.97503 q^{4} +2.97721 q^{5} +(1.32028 - 4.37972i) q^{6} -1.00000i q^{7} -7.85715i q^{8} +(2.50018 + 1.65805i) q^{9} +7.86291i q^{10} +5.69716 q^{11} +(8.25029 + 2.48708i) q^{12} +3.06429 q^{13} +2.64103 q^{14} +(-4.93723 - 1.48835i) q^{15} +10.8009 q^{16} -5.87514 q^{17} +(-4.37895 + 6.60304i) q^{18} +0.0296511i q^{19} -14.8117 q^{20} +(-0.499912 + 1.65834i) q^{21} +15.0464i q^{22} +(3.33589 - 3.44555i) q^{23} +(-3.92789 + 13.0298i) q^{24} +3.86380 q^{25} +8.09287i q^{26} +(-3.31726 - 3.99947i) q^{27} +4.97503i q^{28} +8.39999i q^{29} +(3.93076 - 13.0394i) q^{30} +4.36910 q^{31} +12.8112i q^{32} +(-9.44782 - 2.84808i) q^{33} -15.5164i q^{34} -2.97721i q^{35} +(-12.4385 - 8.24885i) q^{36} +6.88542i q^{37} -0.0783095 q^{38} +(-5.08162 - 1.53187i) q^{39} -23.3924i q^{40} -7.13205i q^{41} +(-4.37972 - 1.32028i) q^{42} +3.13957i q^{43} -28.3436 q^{44} +(7.44356 + 4.93636i) q^{45} +(9.09980 + 8.81019i) q^{46} +0.363467i q^{47} +(-17.9115 - 5.39950i) q^{48} -1.00000 q^{49} +10.2044i q^{50} +(9.74297 + 2.93705i) q^{51} -15.2449 q^{52} +3.88569 q^{53} +(10.5627 - 8.76098i) q^{54} +16.9617 q^{55} -7.85715 q^{56} +(0.0148230 - 0.0491716i) q^{57} -22.1846 q^{58} -4.67475i q^{59} +(24.5629 + 7.40457i) q^{60} +15.0345i q^{61} +11.5389i q^{62} +(1.65805 - 2.50018i) q^{63} -12.2329 q^{64} +9.12303 q^{65} +(7.52186 - 24.9520i) q^{66} -5.80252i q^{67} +29.2290 q^{68} +(-7.25451 + 4.04623i) q^{69} +7.86291 q^{70} -6.51952i q^{71} +(13.0275 - 19.6443i) q^{72} +0.133529 q^{73} -18.1846 q^{74} +(-6.40749 - 1.93156i) q^{75} -0.147515i q^{76} -5.69716i q^{77} +(4.04572 - 13.4207i) q^{78} +9.73465i q^{79} +32.1566 q^{80} +(3.50175 + 8.29082i) q^{81} +18.8359 q^{82} -0.210120 q^{83} +(2.48708 - 8.25029i) q^{84} -17.4915 q^{85} -8.29170 q^{86} +(4.19926 - 13.9300i) q^{87} -44.7635i q^{88} -2.19782 q^{89} +(-13.0371 + 19.6586i) q^{90} -3.06429i q^{91} +(-16.5962 + 17.1417i) q^{92} +(-7.24545 - 2.18417i) q^{93} -0.959928 q^{94} +0.0882778i q^{95} +(6.40446 - 21.2453i) q^{96} -2.81310i q^{97} -2.64103i q^{98} +(14.2439 + 9.44617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

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