LMFDB - Embedded newform 483.2.e.a.344.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(344,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			344.1
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.47

$q$-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} +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} +(3.80957 - 7.38154i) 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} + 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}+ \cdots - 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

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	$-0.616521\pi$
$2$		−	2.64103i		−	1.86749i	0.357940	−	0.933745i	$-0.383479\pi$
$3$	−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	$-0.731878\pi$
$5$	−2.97721			−1.33145			−0.665725	+	0.746197i	$0.731878\pi$
$6$	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	$-0.828839\pi$
$11$	−5.69716			−1.71776			−0.858879	+	0.512178i	$0.828839\pi$
$12$	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	$-0.247579\pi$
$17$	5.87514			1.42493			0.712465	+	0.701708i	$0.247579\pi$
$18$	−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	$-0.715260\pi$
$29$		−	8.39999i		−	1.55984i	0.625880	−	0.779920i	$-0.284740\pi$
$30$	−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	$0.188017\pi$
$41$			7.13205i			1.11384i	−0.830567	+	0.556919i	$0.811983\pi$
$42$	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	$-0.991561\pi$
$47$		−	0.363467i		−	0.0530172i	0.999649	−	0.0265086i	$-0.00843893\pi$
$48$	−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	$-0.585990\pi$
$53$	−3.88569			−0.533741			−0.266870	+	0.963732i	$0.585990\pi$
$54$	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	$0.0984226\pi$
$59$			4.67475i			0.608600i	−0.952576	+	0.304300i	$0.901577\pi$
$60$	−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
$69$	3.80957	−	7.38154i	0.458618	−	0.888633i
$70$	7.86291			0.939797
$71$			6.51952i			0.773725i	0.922137	+	0.386863i	$0.126441\pi$
$71$			6.51952i			0.773725i	−0.922137	+	0.386863i	$0.873559\pi$
$72$	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	$-0.496329\pi$
$83$	0.210120			0.0230637			0.0115318	+	0.999934i	$0.496329\pi$
$84$	−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	$-0.462838\pi$
$89$	2.19782			0.232968			0.116484	+	0.993193i	$0.462838\pi$
$90$	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	$-0.998656\pi$
$101$		−	0.0848816i		−	0.00844603i	0.999991	−	0.00422302i	$-0.00134423\pi$
$102$	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	$-0.508132\pi$
$107$	−0.528479			−0.0510900			−0.0255450	+	0.999674i	$0.508132\pi$
$108$	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	$-0.454844\pi$
$113$	3.00594			0.282775			0.141387	+	0.989954i	$0.454844\pi$
$114$	−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	$0.0637181\pi$
$131$			4.55170i			0.397684i	−0.980032	+	0.198842i	$0.936282\pi$
$132$	−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	$-0.607171\pi$
$137$	−7.73358			−0.660725			−0.330362	+	0.943854i	$0.607171\pi$
$138$	−19.4949	−	10.0612i	−1.65951	−	0.856465i
$139$	−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	$-0.519175\pi$
$149$	−1.46976			−0.120407			−0.0602036	+	0.998186i	$0.519175\pi$
$150$	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	$0.290505\pi$
$167$			20.4472i			1.58225i	−0.611652	+	0.791127i	$0.709495\pi$
$168$	−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	$0.125506\pi$
$173$			10.1055i			0.768305i	−0.923270	+	0.384152i	$0.874494\pi$
$174$	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	$0.193450\pi$
$179$			15.2793i			1.14203i	−0.820941	+	0.571014i	$0.806550\pi$
$180$	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	$-0.205296\pi$
$191$	22.0883			1.59825			0.799126	+	0.601163i	$0.205296\pi$
$192$	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	$0.0620130\pi$
$197$			5.43432i			0.387179i	−0.981083	+	0.193590i	$0.937987\pi$
$198$	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
$207$	−2.62743	+	14.1456i	−0.182619	+	0.983184i
$208$	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	$-0.428832\pi$
$227$	6.68116			0.443444			0.221722	+	0.975110i	$0.428832\pi$
$228$	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	$0.000177277\pi$
$233$			0.0170024i			0.00111386i	−1.00000		0.000556932i	$0.999823\pi$
$234$	−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	$-0.807523\pi$
$239$		−	17.5776i		−	1.13700i	0.822682	−	0.568501i	$-0.192477\pi$
$240$	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	$-0.678948\pi$
$251$	−16.8897			−1.06607			−0.533034	+	0.846094i	$0.678948\pi$
$252$	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	$0.230206\pi$
$257$			21.2188i			1.32359i	−0.749683	+	0.661797i	$0.769794\pi$
$258$	−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	$-0.474145\pi$
$263$	2.63161			0.162272			0.0811359	+	0.996703i	$0.474145\pi$
$264$	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	$-0.991681\pi$
$269$		−	0.857217i		−	0.0522655i	0.999658	−	0.0261327i	$-0.00831925\pi$
$270$	−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
$276$	−18.9527	+	36.7234i	−1.14082	+	2.21049i
$277$	−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	$-0.272475\pi$
$281$	21.9750			1.31092			0.655459	+	0.755231i	$0.272475\pi$
$282$	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	$-0.454858\pi$
$293$	4.83884			0.282688			0.141344	+	0.989961i	$0.454858\pi$
$294$	−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	$0.120539\pi$
$311$			13.0394i			0.739398i	−0.929152	+	0.369699i	$0.879461\pi$
$312$	−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	$-0.910853\pi$
$317$		−	9.84289i		−	0.552832i	0.961038	−	0.276416i	$-0.0891467\pi$
$318$	−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
$345$	−11.3419	+	21.9764i	−0.610627	+	1.18317i
$346$	26.6888			1.43480
$347$		−	30.2615i		−	1.62452i	−0.583295	−	0.812260i	$-0.698237\pi$
$347$		−	30.2615i		−	1.62452i	0.583295	−	0.812260i	$-0.301763\pi$
$348$	−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	$0.137104\pi$
$353$			15.6893i			0.835057i	−0.908664	+	0.417529i	$0.862896\pi$
$354$	−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	$-0.788959\pi$
$359$	−29.8665			−1.57629			−0.788146	+	0.615488i	$0.788959\pi$
$360$	−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	$-0.336883\pi$
$383$	19.1911			0.980621			0.490310	+	0.871548i	$0.336883\pi$
$384$	−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	$-0.684172\pi$
$389$	−21.5710			−1.09369			−0.546847	+	0.837233i	$0.684172\pi$
$390$	−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	$-0.340382\pi$
$401$	19.2521			0.961402			0.480701	+	0.876885i	$0.340382\pi$
$402$	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
$414$	37.3588	+	6.93913i	1.83609	+	0.341039i
$415$	−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	$-0.290838\pi$
$419$	25.0065			1.22165			0.610825	+	0.791766i	$0.290838\pi$
$420$	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	$-0.314137\pi$
$431$	22.8900			1.10257			0.551286	+	0.834317i	$0.314137\pi$
$432$	−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	$0.00771172\pi$
$443$			1.01974i			0.0484494i	−0.999707	+	0.0242247i	$0.992288\pi$
$444$	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	$0.113855\pi$
$449$			14.8374i			0.700218i	−0.936709	+	0.350109i	$0.886145\pi$
$450$	−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	$0.0360784\pi$
$461$			4.85676i			0.226202i	−0.993583	+	0.113101i	$0.963922\pi$
$462$	−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	$-0.432653\pi$
$467$	9.07635			0.420003			0.210002	+	0.977701i	$0.432653\pi$
$468$	−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	$-0.782502\pi$
$479$	−33.9453			−1.55100			−0.775500	+	0.631348i	$0.782502\pi$
$480$	−19.0675	−	63.2517i	−0.870306	−	2.88703i
$481$			21.0989i			0.962027i
$482$	−23.1765			−1.05566
$483$	−7.38154	−	3.80957i	−0.335872	−	0.173341i
$484$	−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	$0.0593713\pi$
$491$			8.21819i			0.370882i	−0.982655	+	0.185441i	$0.940629\pi$
$492$	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	$-0.417651\pi$
$503$	11.4754			0.511662			0.255831	+	0.966721i	$0.417651\pi$
$504$	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	$0.229257\pi$
$509$			29.7606i			1.31912i	−0.751653	+	0.659559i	$0.770743\pi$
$510$	−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	$-0.244723\pi$
$521$	32.8107			1.43746			0.718732	+	0.695287i	$0.244723\pi$
$522$	−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
$552$	57.9979	+	29.9324i	2.46855	+	1.27401i
$553$	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	$-0.781228\pi$
$557$	−36.4853			−1.54593			−0.772966	+	0.634447i	$0.781228\pi$
$558$	−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	$-0.588136\pi$
$563$	−12.9726			−0.546728			−0.273364	+	0.961911i	$0.588136\pi$
$564$	−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	$-0.425000\pi$
$569$	11.1370			0.466889			0.233444	+	0.972370i	$0.425000\pi$
$570$	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	$0.106492\pi$
$587$			15.9105i			0.656697i	−0.944557	+	0.328348i	$0.893508\pi$
$588$	−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	$-0.778759\pi$
$593$		−	31.1906i		−	1.28085i	0.768023	−	0.640423i	$-0.221241\pi$
$594$	−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	$0.189821\pi$
$599$			27.4906i			1.12324i	−0.827396	+	0.561618i	$0.810179\pi$
$600$	−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	$-0.596810\pi$
$617$	−14.8774			−0.598940			−0.299470	+	0.954106i	$0.596810\pi$
$618$	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
$621$	−2.71436	−	24.7716i	−0.108924	−	0.994050i
$622$	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	$-0.760521\pi$
$641$	−36.9687			−1.46018			−0.730088	+	0.683353i	$0.760521\pi$
$642$	−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	$-0.586036\pi$
$647$		−	49.0254i		−	1.92739i	0.267012	−	0.963693i	$-0.413964\pi$
$648$	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	$0.119183\pi$
$653$			18.6920i			0.731475i	−0.930718	+	0.365738i	$0.880817\pi$
$654$	−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	$-0.247659\pi$
$659$	36.5702			1.42457			0.712287	+	0.701888i	$0.247659\pi$
$660$	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	$-0.326139\pi$
$677$	27.0311			1.03889			0.519445	+	0.854504i	$0.326139\pi$
$678$	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	$0.222111\pi$
$683$			33.5836i			1.28504i	−0.766269	+	0.642520i	$0.777889\pi$
$684$	−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
$690$	58.0404	+	29.9543i	2.20956	+	1.14034i
$691$	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	$-0.544136\pi$
$701$	−7.31884			−0.276429			−0.138214	+	0.990402i	$0.544136\pi$
$702$	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	$0.106916\pi$
$719$			17.6763i			0.659215i	−0.944118	+	0.329608i	$0.893084\pi$
$720$	−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	$-0.643526\pi$
$743$	−23.7567			−0.871550			−0.435775	+	0.900056i	$0.643526\pi$
$744$	−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
$759$	−21.7037	+	42.0538i	−0.787796	+	1.52646i
$760$	0.693612			0.0251599
$761$		−	5.12460i		−	0.185767i	−0.995677	−	0.0928833i	$-0.970392\pi$
$761$		−	5.12460i		−	0.185767i	0.995677	−	0.0928833i	$-0.0296084\pi$
$762$	−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	$-0.743531\pi$
$773$	−38.5121			−1.38518			−0.692592	+	0.721330i	$0.743531\pi$
$774$	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	$-0.368428\pi$
$797$	22.6796			0.803351			0.401676	+	0.915782i	$0.368428\pi$
$798$	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	$0.173780\pi$
$809$			29.5367i			1.03846i	−0.854636	+	0.519228i	$0.826220\pi$
$810$	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	$-0.961680\pi$
$821$		−	6.88215i		−	0.240189i	0.992762	−	0.120094i	$-0.0383197\pi$
$822$	−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	$-0.706851\pi$
$827$	−34.8002			−1.21012			−0.605061	+	0.796179i	$0.706851\pi$
$828$	13.0716	−	70.3746i	0.454268	−	2.44569i
$829$	−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	$-0.487170\pi$
$839$	2.33429			0.0805886			0.0402943	+	0.999188i	$0.487170\pi$
$840$	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	$-0.659823\pi$
$857$		−	51.3227i		−	1.75315i	0.481265	−	0.876575i	$-0.340177\pi$
$858$	−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	$0.0520819\pi$
$863$			9.57045i			0.325782i	−0.986644	+	0.162891i	$0.947918\pi$
$864$	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	$-0.664827\pi$
$881$	−29.3840			−0.989972			−0.494986	+	0.868901i	$0.664827\pi$
$882$	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	$-0.950628\pi$
$887$		−	9.20195i		−	0.308971i	0.987995	−	0.154486i	$-0.0493720\pi$
$888$	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
$897$	11.6736	−	22.6192i	0.389771	−	0.755232i
$898$	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	$-0.595592\pi$
$911$	−17.8572			−0.591635			−0.295818	+	0.955244i	$0.595592\pi$
$912$	−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	$-0.628970\pi$
$929$		−	56.0235i		−	1.83807i	0.394175	−	0.919035i	$-0.371030\pi$
$930$	−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	$-0.554025\pi$
$941$	−10.3630			−0.337823			−0.168912	+	0.985631i	$0.554025\pi$
$942$	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	$-0.679325\pi$
$947$		−	52.0354i		−	1.69092i	0.534036	−	0.845462i	$-0.320675\pi$
$948$	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	$-0.698162\pi$
$953$	−36.0016			−1.16621			−0.583103	+	0.812398i	$0.698162\pi$
$954$	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
$966$	−10.0612	+	19.4949i	−0.323713	+	0.627237i
$967$	−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	$-0.249082\pi$
$971$	44.1951			1.41829			0.709143	+	0.705064i	$0.249082\pi$
$972$	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	$-0.391857\pi$
$977$	20.8324			0.666486			0.333243	+	0.942841i	$0.391857\pi$
$978$	−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	$-0.575528\pi$
$983$	−14.7395			−0.470118			−0.235059	+	0.971981i	$0.575528\pi$
$984$	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.344.1	✓	48
3.2	odd	2	inner	483.2.e.a.344.48	yes	48
23.22	odd	2	inner	483.2.e.a.344.2	yes	48
69.68	even	2	inner	483.2.e.a.344.47	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.1	✓	48	1.1	even	1	trivial
483.2.e.a.344.2	yes	48	23.22	odd	2	inner
483.2.e.a.344.47	yes	48	69.68	even	2	inner
483.2.e.a.344.48	yes	48	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 $\F_{q}$
Belyi maps

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} +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} +(3.80957 - 7.38154i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54}+ \cdots - 6 q^{96}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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