LMFDB - Embedded newform 820.2.j.c.483.65

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.65
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.65

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.219268 + 1.39711i) q^{2} -2.16299i q^{3} +(-1.90384 + 0.612684i) q^{4} +(0.498284 - 2.17984i) q^{5} +(3.02194 - 0.474275i) q^{6} -0.295068 q^{7} +(-1.27344 - 2.52554i) q^{8} -1.67853 q^{9} +(3.15474 + 0.218189i) q^{10} +(0.592458 + 0.592458i) q^{11} +(1.32523 + 4.11800i) q^{12} +5.60783 q^{13} +(-0.0646989 - 0.412242i) q^{14} +(-4.71498 - 1.07778i) q^{15} +(3.24924 - 2.33291i) q^{16} -5.37402 q^{17} +(-0.368048 - 2.34510i) q^{18} +(-2.97295 - 2.97295i) q^{19} +(0.386899 + 4.45537i) q^{20} +0.638229i q^{21} +(-0.697823 + 0.957637i) q^{22} +(0.212568 - 0.212568i) q^{23} +(-5.46272 + 2.75444i) q^{24} +(-4.50343 - 2.17236i) q^{25} +(1.22962 + 7.83477i) q^{26} -2.85832i q^{27} +(0.561762 - 0.180783i) q^{28} +(-2.66637 - 2.66637i) q^{29} +(0.471941 - 6.82368i) q^{30} -4.70570i q^{31} +(3.97179 + 4.02802i) q^{32} +(1.28148 - 1.28148i) q^{33} +(-1.17835 - 7.50810i) q^{34} +(-0.147028 + 0.643201i) q^{35} +(3.19566 - 1.02841i) q^{36} +(2.69046 - 2.69046i) q^{37} +(3.50167 - 4.80541i) q^{38} -12.1297i q^{39} +(-6.13981 + 1.51746i) q^{40} +(-4.98535 - 4.01824i) q^{41} +(-0.891677 + 0.139943i) q^{42} +(-2.01035 - 2.01035i) q^{43} +(-1.49094 - 0.764957i) q^{44} +(-0.836386 + 3.65894i) q^{45} +(0.343591 + 0.250372i) q^{46} +10.3048i q^{47} +(-5.04606 - 7.02807i) q^{48} -6.91294 q^{49} +(2.04758 - 6.76812i) q^{50} +11.6240i q^{51} +(-10.6764 + 3.43583i) q^{52} -3.29257 q^{53} +(3.99340 - 0.626739i) q^{54} +(1.58668 - 0.996252i) q^{55} +(0.375751 + 0.745205i) q^{56} +(-6.43046 + 6.43046i) q^{57} +(3.14057 - 4.30987i) q^{58} +14.2604 q^{59} +(9.63692 - 0.836860i) q^{60} -2.98490i q^{61} +(6.57439 - 1.03181i) q^{62} +0.495280 q^{63} +(-4.75670 + 6.43225i) q^{64} +(2.79430 - 12.2242i) q^{65} +(2.07136 + 1.50938i) q^{66} +3.44881i q^{67} +(10.2313 - 3.29257i) q^{68} +(-0.459783 - 0.459783i) q^{69} +(-0.930862 - 0.0643805i) q^{70} +(-5.63883 - 5.63883i) q^{71} +(2.13751 + 4.23920i) q^{72} +(3.86014 - 3.86014i) q^{73} +(4.34880 + 3.16894i) q^{74} +(-4.69880 + 9.74087i) q^{75} +(7.48150 + 3.83855i) q^{76} +(-0.174815 - 0.174815i) q^{77} +(16.9465 - 2.65965i) q^{78} +(1.35423 - 1.35423i) q^{79} +(-3.46633 - 8.24528i) q^{80} -11.2181 q^{81} +(4.52080 - 7.84617i) q^{82} +(1.25094 - 1.25094i) q^{83} +(-0.391032 - 1.21509i) q^{84} +(-2.67779 + 11.7145i) q^{85} +(2.36787 - 3.24948i) q^{86} +(-5.76734 + 5.76734i) q^{87} +(0.741816 - 2.25073i) q^{88} +(10.3994 + 10.3994i) q^{89} +(-5.29534 - 0.366238i) q^{90} -1.65469 q^{91} +(-0.274460 + 0.534934i) q^{92} -10.1784 q^{93} +(-14.3969 + 2.25951i) q^{94} +(-7.96193 + 4.99919i) q^{95} +(8.71256 - 8.59094i) q^{96} +13.1496 q^{97} +(-1.51579 - 9.65814i) q^{98} +(-0.994459 - 0.994459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.219268	+	1.39711i	0.155046	+	0.987907i
$2$	0.219268	+	1.39711i	0.155046	+	0.987907i
$3$		−	2.16299i		−	1.24880i	−0.781103	−	0.624402i	$-0.785343\pi$
$3$		−	2.16299i		−	1.24880i	0.781103	−	0.624402i	$-0.214657\pi$
$4$	−1.90384	+	0.612684i	−0.951922	+	0.306342i
$5$	0.498284	−	2.17984i	0.222839	−	0.974855i
$5$	0.498284	−	2.17984i	0.222839	−	0.974855i
$6$	3.02194	−	0.474275i	1.23370	−	0.193622i
$7$	−0.295068			−0.111525			−0.0557625	−	0.998444i	$-0.517759\pi$
$7$	−0.295068			−0.111525			−0.0557625	+	0.998444i	$0.517759\pi$
$8$	−1.27344	−	2.52554i	−0.450229	−	0.892913i
$9$	−1.67853			−0.559511
$10$	3.15474	+	0.218189i	0.997617	+	0.0689975i
$11$	0.592458	+	0.592458i	0.178633	+	0.178633i	0.790760	−	0.612127i	$-0.209686\pi$
$11$	0.592458	+	0.592458i	0.178633	+	0.178633i	−0.612127	+	0.790760i	$0.709686\pi$
$12$	1.32523	+	4.11800i	0.382561	+	1.18876i
$13$	5.60783			1.55533			0.777667	−	0.628677i	$-0.216403\pi$
$13$	5.60783			1.55533			0.777667	+	0.628677i	$0.216403\pi$
$14$	−0.0646989	−	0.412242i	−0.0172915	−	0.110176i
$15$	−4.71498	−	1.07778i	−1.21740	−	0.278283i
$16$	3.24924	−	2.33291i	0.812309	−	0.583227i
$17$	−5.37402			−1.30339			−0.651695	−	0.758481i	$-0.725942\pi$
$17$	−5.37402			−1.30339			−0.651695	+	0.758481i	$0.725942\pi$
$18$	−0.368048	−	2.34510i	−0.0867498	−	0.552745i
$19$	−2.97295	−	2.97295i	−0.682041	−	0.682041i	0.278419	−	0.960460i	$-0.410190\pi$
$19$	−2.97295	−	2.97295i	−0.682041	−	0.682041i	−0.960460	+	0.278419i	$0.910190\pi$
$20$	0.386899	+	4.45537i	0.0865133	+	0.996251i
$21$			0.638229i			0.139273i
$22$	−0.697823	+	0.957637i	−0.148776	+	0.204169i
$23$	0.212568	−	0.212568i	0.0443236	−	0.0443236i	−0.684598	−	0.728921i	$-0.740022\pi$
$23$	0.212568	−	0.212568i	0.0443236	−	0.0443236i	0.728921	+	0.684598i	$0.240022\pi$
$24$	−5.46272	+	2.75444i	−1.11507	+	0.562248i
$25$	−4.50343	−	2.17236i	−0.900685	−	0.434472i
$26$	1.22962	+	7.83477i	0.241148	+	1.53652i
$27$		−	2.85832i		−	0.550085i
$28$	0.561762	−	0.180783i	0.106163	−	0.0341648i
$29$	−2.66637	−	2.66637i	−0.495132	−	0.495132i	0.414786	−	0.909919i	$-0.363856\pi$
$29$	−2.66637	−	2.66637i	−0.495132	−	0.495132i	−0.909919	+	0.414786i	$0.863856\pi$
$30$	0.471941	−	6.82368i	0.0861643	−	1.24583i
$31$		−	4.70570i		−	0.845169i	−0.906323	−	0.422585i	$-0.861123\pi$
$31$		−	4.70570i		−	0.845169i	0.906323	−	0.422585i	$-0.138877\pi$
$32$	3.97179	+	4.02802i	0.702119	+	0.712059i
$33$	1.28148	−	1.28148i	0.223077	−	0.223077i
$34$	−1.17835	−	7.50810i	−0.202085	−	1.28763i
$35$	−0.147028	+	0.643201i	−0.0248522	+	0.108721i
$36$	3.19566	−	1.02841i	0.532610	−	0.171402i
$37$	2.69046	−	2.69046i	0.442308	−	0.442308i	−0.450479	−	0.892787i	$-0.648747\pi$
$37$	2.69046	−	2.69046i	0.442308	−	0.442308i	0.892787	+	0.450479i	$0.148747\pi$
$38$	3.50167	−	4.80541i	0.568046	−	0.779541i
$39$		−	12.1297i		−	1.94231i
$40$	−6.13981	+	1.51746i	−0.970790	+	0.239932i
$41$	−4.98535	−	4.01824i	−0.778581	−	0.627544i
$41$	−4.98535	−	4.01824i	−0.778581	−	0.627544i
$42$	−0.891677	+	0.139943i	−0.137589	+	0.0215937i
$43$	−2.01035	−	2.01035i	−0.306575	−	0.306575i	0.537004	−	0.843579i	$-0.319556\pi$
$43$	−2.01035	−	2.01035i	−0.306575	−	0.306575i	−0.843579	+	0.537004i	$0.819556\pi$
$44$	−1.49094	−	0.764957i	−0.224767	−	0.115322i
$45$	−0.836386	+	3.65894i	−0.124681	+	0.545442i
$46$	0.343591	+	0.250372i	0.0506598	+	0.0369154i
$47$			10.3048i			1.50311i	0.659672	+	0.751554i	$0.270695\pi$
$47$			10.3048i			1.50311i	−0.659672	+	0.751554i	$0.729305\pi$
$48$	−5.04606	−	7.02807i	−0.728336	−	1.01441i
$49$	−6.91294			−0.987562
$50$	2.04758	−	6.76812i	0.289571	−	0.957157i
$51$			11.6240i			1.62768i
$52$	−10.6764	+	3.43583i	−1.48056	+	0.476464i
$53$	−3.29257			−0.452269			−0.226135	−	0.974096i	$-0.572609\pi$
$53$	−3.29257			−0.452269			−0.226135	+	0.974096i	$0.572609\pi$
$54$	3.99340	−	0.626739i	0.543433	−	0.0852884i
$55$	1.58668	−	0.996252i	0.213947	−	0.134335i
$56$	0.375751	+	0.745205i	0.0502118	+	0.0995822i
$57$	−6.43046	+	6.43046i	−0.851735	+	0.851735i
$58$	3.14057	−	4.30987i	0.412377	−	0.565913i
$59$	14.2604			1.85655			0.928275	−	0.371893i	$-0.121291\pi$
$59$	14.2604			1.85655			0.928275	+	0.371893i	$0.121291\pi$
$60$	9.63692	−	0.836860i	1.24412	−	0.108038i
$61$		−	2.98490i		−	0.382177i	−0.981573	−	0.191089i	$-0.938798\pi$
$61$		−	2.98490i		−	0.382177i	0.981573	−	0.191089i	$-0.0612018\pi$
$62$	6.57439	−	1.03181i	0.834949	−	0.131040i
$63$	0.495280			0.0623995
$64$	−4.75670	+	6.43225i	−0.594588	+	0.804031i
$65$	2.79430	−	12.2242i	0.346590	−	1.51622i
$66$	2.07136	+	1.50938i	0.254967	+	0.185792i
$67$			3.44881i			0.421339i	0.977557	+	0.210670i	$0.0675644\pi$
$67$			3.44881i			0.421339i	−0.977557	+	0.210670i	$0.932436\pi$
$68$	10.2313	−	3.29257i	1.24073	−	0.399283i
$69$	−0.459783	−	0.459783i	−0.0553514	−	0.0553514i
$70$	−0.930862	−	0.0643805i	−0.111259	−	0.00769495i
$71$	−5.63883	−	5.63883i	−0.669206	−	0.669206i	0.288326	−	0.957532i	$-0.406901\pi$
$71$	−5.63883	−	5.63883i	−0.669206	−	0.669206i	−0.957532	+	0.288326i	$0.906901\pi$
$72$	2.13751	+	4.23920i	0.251908	+	0.499595i
$73$	3.86014	−	3.86014i	0.451795	−	0.451795i	−0.444155	−	0.895950i	$-0.646496\pi$
$73$	3.86014	−	3.86014i	0.451795	−	0.451795i	0.895950	+	0.444155i	$0.146496\pi$
$74$	4.34880	+	3.16894i	0.505538	+	0.368382i
$75$	−4.69880	+	9.74087i	−0.542571	+	1.12478i
$76$	7.48150	+	3.83855i	0.858187	+	0.440312i
$77$	−0.174815	−	0.174815i	−0.0199220	−	0.0199220i
$78$	16.9465	−	2.65965i	1.91882	−	0.301147i
$79$	1.35423	−	1.35423i	0.152363	−	0.152363i	−0.626810	−	0.779173i	$-0.715640\pi$
$79$	1.35423	−	1.35423i	0.152363	−	0.152363i	0.779173	+	0.626810i	$0.215640\pi$
$80$	−3.46633	−	8.24528i	−0.387547	−	0.921850i
$81$	−11.2181			−1.24646
$82$	4.52080	−	7.84617i	0.499239	−	0.866464i
$83$	1.25094	−	1.25094i	0.137309	−	0.137309i	−0.635112	−	0.772420i	$-0.719046\pi$
$83$	1.25094	−	1.25094i	0.137309	−	0.137309i	0.772420	+	0.635112i	$0.219046\pi$
$84$	−0.391032	−	1.21509i	−0.0426651	−	0.132577i
$85$	−2.67779	+	11.7145i	−0.290447	+	1.27062i
$86$	2.36787	−	3.24948i	0.255334	−	0.350401i
$87$	−5.76734	+	5.76734i	−0.618323	+	0.618323i
$88$	0.741816	−	2.25073i	0.0790779	−	0.239929i
$89$	10.3994	+	10.3994i	1.10234	+	1.10234i	0.994128	+	0.108209i	$0.0345116\pi$
$89$	10.3994	+	10.3994i	1.10234	+	1.10234i	0.108209	+	0.994128i	$0.465488\pi$
$90$	−5.29534	−	0.366238i	−0.558177	−	0.0386048i
$91$	−1.65469			−0.173459
$92$	−0.274460	+	0.534934i	−0.0286144	+	0.0557707i
$93$	−10.1784			−1.05545
$94$	−14.3969	+	2.25951i	−1.48493	+	0.233051i
$95$	−7.96193	+	4.99919i	−0.816877	+	0.512906i
$96$	8.71256	−	8.59094i	0.889222	−	0.876809i
$97$	13.1496			1.33514			0.667568	−	0.744549i	$-0.267335\pi$
$97$	13.1496			1.33514			0.667568	+	0.744549i	$0.267335\pi$
$98$	−1.51579	−	9.65814i	−0.153117	−	0.975620i
$99$	−0.994459	−	0.994459i	−0.0999469	−	0.0999469i
$100$	9.90479	+	1.37666i	0.990479	+	0.137666i
$101$	6.43682	+	6.43682i	0.640487	+	0.640487i	0.950675	−	0.310188i	$-0.100392\pi$
$101$	6.43682	+	6.43682i	0.640487	+	0.640487i	−0.310188	+	0.950675i	$0.600392\pi$
$102$	−16.2400	+	2.54876i	−1.60800	+	0.252365i
$103$	6.32443	+	6.32443i	0.623165	+	0.623165i	0.946339	−	0.323175i	$-0.104750\pi$
$103$	6.32443	+	6.32443i	0.623165	+	0.623165i	−0.323175	+	0.946339i	$0.604750\pi$
$104$	−7.14124	−	14.1628i	−0.700256	−	1.38878i
$105$	1.39124	+	0.318019i	0.135771	+	0.0310355i
$106$	−0.721955	−	4.60009i	−0.0701225	−	0.446800i
$107$	6.55946	+	6.55946i	0.634127	+	0.634127i	0.949101	−	0.314973i	$-0.101996\pi$
$107$	6.55946	+	6.55946i	0.634127	+	0.634127i	−0.314973	+	0.949101i	$0.601996\pi$
$108$	1.75125	+	5.44180i	0.168514	+	0.523637i
$109$	6.36154	−	6.36154i	0.609325	−	0.609325i	−0.333445	−	0.942770i	$-0.608211\pi$
$109$	6.36154	−	6.36154i	0.609325	−	0.609325i	0.942770	+	0.333445i	$0.108211\pi$
$110$	1.73978	+	1.99832i	0.165882	+	0.190532i
$111$	−5.81944	−	5.81944i	−0.552356	−	0.552356i
$112$	−0.958744	+	0.688365i	−0.0905928	+	0.0650444i
$113$	−5.99373	−	5.99373i	−0.563843	−	0.563843i	0.366554	−	0.930397i	$-0.380538\pi$
$113$	−5.99373	−	5.99373i	−0.563843	−	0.563843i	−0.930397	+	0.366554i	$0.880538\pi$
$114$	−10.3941	−	7.57408i	−0.973494	−	0.709378i
$115$	−0.357446	−	0.569285i	−0.0333320	−	0.0530861i
$116$	6.70999	+	3.44271i	0.623007	+	0.319647i
$117$	−9.41293			−0.870226
$118$	3.12686	+	19.9234i	0.287851	+	1.83410i
$119$	1.58570			0.145361
$120$	3.28226	+	13.2804i	0.299628	+	1.21233i
$121$		−	10.2980i		−	0.936181i
$122$	4.17024	−	0.654493i	0.377556	−	0.0592550i
$123$	−8.69142	+	10.7833i	−0.783679	+	0.972295i
$124$	2.88311	+	8.95892i	0.258911	+	0.804535i
$125$	−6.97939	+	8.73430i	−0.624256	+	0.781220i
$126$	0.108599	+	0.691962i	0.00967478	+	0.0616449i
$127$	9.71448	+	9.71448i	0.862020	+	0.862020i	0.991573	−	0.129552i	$-0.0413540\pi$
$127$	9.71448	+	9.71448i	0.862020	+	0.862020i	−0.129552	+	0.991573i	$0.541354\pi$
$128$	−10.0296	−	5.23526i	−0.886496	−	0.462736i
$129$	−4.34836	+	4.34836i	−0.382852	+	0.382852i
$130$	17.6913	+	1.22357i	1.55163	+	0.107314i
$131$	7.66395			0.669603			0.334801	−	0.942289i	$-0.391331\pi$
$131$	7.66395			0.669603			0.334801	+	0.942289i	$0.391331\pi$
$132$	−1.65460	+	3.22488i	−0.144014	+	0.280690i
$133$	0.877221	+	0.877221i	0.0760647	+	0.0760647i
$134$	−4.81837	+	0.756213i	−0.416244	+	0.0653269i
$135$	−6.23069	−	1.42426i	−0.536253	−	0.122581i
$136$	6.84349	+	13.5723i	0.586824	+	1.16381i
$137$	10.8159			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$137$	10.8159			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$138$	0.541553	−	0.743185i	0.0461001	−	0.0632641i
$139$	5.79546			0.491565			0.245782	−	0.969325i	$-0.420955\pi$
$139$	5.79546			0.491565			0.245782	+	0.969325i	$0.420955\pi$
$140$	−0.114161	−	1.31463i	−0.00964840	−	0.111107i
$141$	22.2892			1.87709
$142$	6.64166	−	9.11449i	0.557356	−	0.764871i
$143$	3.32240	+	3.32240i	0.277833	+	0.277833i
$144$	−5.45395	+	3.91586i	−0.454496	+	0.326322i
$145$	−7.14088	+	4.48366i	−0.593017	+	0.372347i
$146$	6.23945	+	4.54664i	0.516381	+	0.376283i
$147$			14.9526i			1.23327i
$148$	−3.47381	+	6.77061i	−0.285545	+	0.556541i
$149$	0.492775	−	0.492775i	0.0403697	−	0.0403697i	−0.686634	−	0.727003i	$-0.740912\pi$
$149$	0.492775	−	0.492775i	0.0403697	−	0.0403697i	0.727003	+	0.686634i	$0.240912\pi$
$150$	−14.6394	−	4.42889i	−1.19530	−	0.361617i
$151$	3.76361	+	3.76361i	0.306279	+	0.306279i	0.843464	−	0.537186i	$-0.180513\pi$
$151$	3.76361	+	3.76361i	0.306279	+	0.306279i	−0.537186	+	0.843464i	$0.680513\pi$
$152$	−3.72243	+	11.2942i	−0.301929	+	0.916078i
$153$	9.02046			0.729261
$154$	0.205905	−	0.282568i	0.0165923	−	0.0227699i
$155$	−10.2577	−	2.34478i	−0.823918	−	0.188337i
$156$	7.43167	+	23.0930i	0.595010	+	1.84892i
$157$			0.485792i			0.0387704i	0.999812	+	0.0193852i	$0.00617089\pi$
$157$			0.485792i			0.0387704i	−0.999812	+	0.0193852i	$0.993829\pi$
$158$	2.18895	+	1.59507i	0.174144	+	0.126897i
$159$			7.12180i			0.564795i
$160$	10.7595	−	6.65077i	0.850615	−	0.525790i
$161$	−0.0627220	+	0.0627220i	−0.00494319	+	0.00494319i
$162$	−2.45978	−	15.6730i	−0.193258	−	1.23139i
$163$	−13.5914	+	13.5914i	−1.06456	+	1.06456i	−0.0667960	+	0.997767i	$0.521278\pi$
$163$	−13.5914	+	13.5914i	−1.06456	+	1.06456i	−0.997767	+	0.0667960i	$0.978722\pi$
$164$	11.9532	+	4.59565i	0.933391	+	0.358860i
$165$	−2.15488	−	3.43197i	−0.167758	−	0.267178i
$166$	2.02200	+	1.47341i	0.156937	+	0.114359i
$167$	−11.5521			−0.893929			−0.446964	−	0.894552i	$-0.647495\pi$
$167$	−11.5521			−0.893929			−0.446964	+	0.894552i	$0.647495\pi$
$168$	1.61187	−	0.812746i	0.124359	−	0.0627047i
$169$	18.4478			1.41906
$170$	−16.9536	−	1.17255i	−1.30028	−	0.0899306i
$171$	4.99019	+	4.99019i	0.381609	+	0.381609i
$172$	5.05909	+	2.59568i	0.385752	+	0.197919i
$173$	−11.4707	+	11.4707i	−0.872101	+	0.872101i	−0.992701	−	0.120600i	$-0.961518\pi$
$173$	−11.4707	+	11.4707i	−0.872101	+	0.872101i	0.120600	+	0.992701i	$0.461518\pi$
$174$	−9.32220	−	6.79302i	−0.706715	−	0.514978i
$175$	1.32881	+	0.640994i	0.100449	+	0.0484546i
$176$	3.30718	+	0.542886i	0.249288	+	0.0409216i
$177$		−	30.8452i		−	2.31847i
$178$	−12.2489	+	16.8094i	−0.918094	+	1.25992i
$179$	3.60813	+	3.60813i	0.269684	+	0.269684i	0.828973	−	0.559289i	$-0.188926\pi$
$179$	3.60813	+	3.60813i	0.269684	+	0.269684i	−0.559289	+	0.828973i	$0.688926\pi$
$180$	−0.649423	−	7.47848i	−0.0484051	−	0.557413i
$181$	−7.71931	−	7.71931i	−0.573772	−	0.573772i	0.359409	−	0.933180i	$-0.382978\pi$
$181$	−7.71931	−	7.71931i	−0.573772	−	0.573772i	−0.933180	+	0.359409i	$0.882978\pi$
$182$	−0.362820	−	2.31179i	−0.0268940	−	0.171361i
$183$	−6.45631			−0.477264
$184$	−0.807543	−	0.266157i	−0.0595328	−	0.0196213i
$185$	−4.52416	−	7.20539i	−0.332623	−	0.529750i
$186$	−2.23180	−	14.2204i	−0.163643	−	1.04269i
$187$	−3.18388	−	3.18388i	−0.232828	−	0.232828i
$188$	−6.31357	−	19.6187i	−0.460465	−	1.43084i
$189$			0.843398i			0.0613482i
$190$	−8.73022	−	10.0275i	−0.633357	−	0.727475i
$191$	15.8707	−	15.8707i	1.14836	−	1.14836i	0.161488	−	0.986875i	$-0.448371\pi$
$191$	15.8707	−	15.8707i	1.14836	−	1.14836i	0.986875	−	0.161488i	$-0.0516293\pi$
$192$	13.9129	+	10.2887i	1.00408	+	0.742523i
$193$	11.8917			0.855982			0.427991	−	0.903783i	$-0.359221\pi$
$193$	11.8917			0.855982			0.427991	+	0.903783i	$0.359221\pi$
$194$	2.88328	+	18.3714i	0.207007	+	1.31899i
$195$	−26.4408	−	6.04404i	−1.89347	−	0.432822i
$196$	13.1611	−	4.23544i	0.940082	−	0.302532i
$197$	−18.9229	−	18.9229i	−1.34820	−	1.34820i	−0.887617	−	0.460583i	$-0.847640\pi$
$197$	−18.9229	−	18.9229i	−1.34820	−	1.34820i	−0.460583	−	0.887617i	$-0.652360\pi$
$198$	1.17132	−	1.60742i	0.0832419	−	0.114235i
$199$	−13.1786	−	13.1786i	−0.934207	−	0.934207i	0.0637586	−	0.997965i	$-0.479691\pi$
$199$	−13.1786	−	13.1786i	−0.934207	−	0.934207i	−0.997965	+	0.0637586i	$0.979691\pi$
$200$	0.248454	+	14.1400i	0.0175683	+	0.999846i
$201$	7.45974			0.526170
$202$	−7.58157	+	10.4043i	−0.533437	+	0.732047i
$203$	0.786759	+	0.786759i	0.0552197	+	0.0552197i
$204$	−7.12181	−	22.1302i	−0.498626	−	1.54942i
$205$	−11.2433	+	8.86506i	−0.785263	+	0.619162i
$206$	−7.44919	+	10.2227i	−0.519010	+	0.712248i
$207$	−0.356803	+	0.356803i	−0.0247995	+	0.0247995i
$208$	18.2212	−	13.0826i	1.26341	−	0.907112i
$209$		−	3.52269i		−	0.243670i
$210$	−0.139255	+	2.01345i	−0.00960948	+	0.138941i
$211$	15.3564	−	15.3564i	1.05718	−	1.05718i	0.0589138	−	0.998263i	$-0.481236\pi$
$211$	15.3564	−	15.3564i	1.05718	−	1.05718i	0.998263	−	0.0589138i	$-0.0187637\pi$
$212$	6.26854	−	2.01730i	0.430525	−	0.138549i
$213$	−12.1967	+	12.1967i	−0.835707	+	0.835707i
$214$	−7.72603	+	10.6026i	−0.528140	+	0.724778i
$215$	−5.38396	+	3.38051i	−0.367183	+	0.230549i
$216$	−7.21881	+	3.63990i	−0.491178	+	0.247664i
$217$			1.38850i			0.0942576i
$218$	10.2827	+	7.49290i	0.696430	+	0.507483i
$219$	−8.34945	−	8.34945i	−0.564204	−	0.564204i
$220$	−2.41040	+	2.86884i	−0.162509	+	0.193417i
$221$	−30.1366			−2.02721
$222$	6.85439	−	9.40642i	0.460036	−	0.631318i
$223$	6.06023	−	6.06023i	0.405823	−	0.405823i	−0.474456	−	0.880279i	$-0.657355\pi$
$223$	6.06023	−	6.06023i	0.405823	−	0.405823i	0.880279	+	0.474456i	$0.157355\pi$
$224$	−1.17195	−	1.18854i	−0.0783039	−	0.0794124i
$225$	7.55915	+	3.64638i	0.503943	+	0.243092i
$226$	7.05968	−	9.68815i	0.469603	−	0.644446i
$227$			22.9523i			1.52340i	0.647933	+	0.761698i	$0.275634\pi$
$227$			22.9523i			1.52340i	−0.647933	+	0.761698i	$0.724366\pi$
$228$	8.30275	−	16.1824i	0.549863	−	1.07171i
$229$	8.25822	−	8.25822i	0.545719	−	0.545719i	−0.379481	−	0.925200i	$-0.623897\pi$
$229$	8.25822	−	8.25822i	0.545719	−	0.545719i	0.925200	+	0.379481i	$0.123897\pi$
$230$	0.716978	−	0.624218i	0.0472761	−	0.0411597i
$231$	−0.378123	+	0.378123i	−0.0248787	+	0.0248787i
$232$	−3.33856	+	10.1295i	−0.219187	+	0.665033i
$233$	1.24661			0.0816681			0.0408341	−	0.999166i	$-0.486998\pi$
$233$	1.24661			0.0816681			0.0408341	+	0.999166i	$0.486998\pi$
$234$	−2.06395	−	13.1509i	−0.134925	−	0.859702i
$235$	22.4628	+	5.13471i	1.46531	+	0.334952i
$236$	−27.1496	+	8.73714i	−1.76729	+	0.568739i
$237$	−2.92919	−	2.92919i	−0.190271	−	0.190271i
$238$	0.347693	+	2.21540i	0.0225376	+	0.143603i
$239$	16.3808	−	16.3808i	1.05959	−	1.05959i	0.0614786	−	0.998108i	$-0.480418\pi$
$239$	16.3808	−	16.3808i	1.05959	−	1.05959i	0.998108	−	0.0614786i	$-0.0195816\pi$
$240$	−17.8345	+	7.49764i	−1.15121	+	0.483970i
$241$			0.184499i			0.0118846i	0.999982	+	0.00594232i	$0.00189151\pi$
$241$			0.184499i			0.0118846i	−0.999982	+	0.00594232i	$0.998108\pi$
$242$	14.3874	−	2.25802i	0.924860	−	0.145151i
$243$			15.6897i			1.00650i
$244$	1.82880	+	5.68278i	0.117077	+	0.363803i
$245$	−3.44461	+	15.0691i	−0.220068	+	0.962730i
$246$	−16.9712	−	9.77846i	−1.08204	−	0.623452i
$247$	−16.6718	−	16.6718i	−1.06080	−	1.06080i
$248$	−11.8844	+	5.99243i	−0.754663	+	0.380520i
$249$	−2.70578	−	2.70578i	−0.171472	−	0.171472i
$250$	−13.7332	−	7.83584i	−0.868561	−	0.495582i
$251$	−22.1113			−1.39566			−0.697828	−	0.716265i	$-0.745850\pi$
$251$	−22.1113			−1.39566			−0.697828	+	0.716265i	$0.745850\pi$
$252$	−0.942936	+	0.303450i	−0.0593994	+	0.0191156i
$253$	0.251875			0.0158353
$254$	−11.4421	+	15.7023i	−0.717944	+	0.985249i
$255$	25.3384	+	5.79203i	1.58675	+	0.362711i
$256$	5.11508	−	15.1603i	0.319693	−	0.947521i
$257$			12.2412i			0.763582i	0.924249	+	0.381791i	$0.124693\pi$
$257$			12.2412i			0.763582i	−0.924249	+	0.381791i	$0.875307\pi$
$258$	−7.02860	−	5.12169i	−0.437582	−	0.318863i
$259$	−0.793867	+	0.793867i	−0.0493285	+	0.0493285i
$260$	2.16967	+	24.9850i	0.134557	+	1.54950i
$261$	4.47559	+	4.47559i	0.277032	+	0.277032i
$262$	1.68046	+	10.7074i	0.103819	+	0.661505i
$263$	11.8229			0.729030			0.364515	−	0.931197i	$-0.381235\pi$
$263$	11.8229			0.729030			0.364515	+	0.931197i	$0.381235\pi$
$264$	−4.86832	−	1.60454i	−0.299624	−	0.0987528i
$265$	−1.64064	+	7.17728i	−0.100783	+	0.440897i
$266$	−1.03323	+	1.41792i	−0.0633513	+	0.0869384i
$267$	22.4939	−	22.4939i	1.37660	−	1.37660i
$268$	−2.11303	−	6.56599i	−0.129074	−	0.401082i
$269$			8.55896i			0.521849i	0.965359	+	0.260925i	$0.0840274\pi$
$269$			8.55896i			0.521849i	−0.965359	+	0.260925i	$0.915973\pi$
$270$	0.623655	−	9.01727i	0.0379544	−	0.548774i
$271$		−	12.5928i		−	0.764957i	−0.923964	−	0.382479i	$-0.875071\pi$
$271$		−	12.5928i		−	0.764957i	0.923964	−	0.382479i	$-0.124929\pi$
$272$	−17.4615	+	12.5371i	−1.05876	+	0.760172i
$273$			3.57908i			0.216616i
$274$	2.37157	+	15.1110i	0.143272	+	0.912887i
$275$	−1.38106	−	3.95512i	−0.0832808	−	0.238503i
$276$	1.15706	+	0.593654i	0.0696467	+	0.0357338i
$277$	−9.15817	+	9.15817i	−0.550261	+	0.550261i	−0.926516	−	0.376255i	$-0.877212\pi$
$277$	−9.15817	+	9.15817i	−0.550261	+	0.550261i	0.376255	+	0.926516i	$0.377212\pi$
$278$	1.27076	+	8.09691i	0.0762151	+	0.485620i
$279$			7.89868i			0.472881i
$280$	1.81166	−	0.447754i	0.108267	−	0.0267584i
$281$	21.4286	+	21.4286i	1.27832	+	1.27832i	0.941606	+	0.336716i	$0.109316\pi$
$281$	21.4286	+	21.4286i	1.27832	+	1.27832i	0.336716	+	0.941606i	$0.390684\pi$
$282$	4.88730	+	31.1404i	0.291034	+	1.85439i
$283$	11.0847	−	11.0847i	0.658917	−	0.658917i	−0.296207	−	0.955124i	$-0.595722\pi$
$283$	11.0847	−	11.0847i	0.658917	−	0.658917i	0.955124	+	0.296207i	$0.0957218\pi$
$284$	14.1903	+	7.28063i	0.842037	+	0.432026i
$285$	10.8132	+	17.2216i	0.640518	+	1.02012i
$286$	−3.91327	+	5.37027i	−0.231397	+	0.317551i
$287$	1.47102	+	1.18565i	0.0868313	+	0.0699868i
$288$	−6.66677	−	6.76115i	−0.392843	−	0.398405i
$289$	11.8800			0.698826
$290$	−7.82993	−	8.99348i	−0.459790	−	0.528115i
$291$		−	28.4424i		−	1.66732i
$292$	−4.98406	+	9.71415i	−0.291670	+	0.568477i
$293$			24.2894i			1.41900i	0.704705	+	0.709501i	$0.251079\pi$
$293$			24.2894i			1.41900i	−0.704705	+	0.709501i	$0.748921\pi$
$294$	−20.8905	+	3.27863i	−1.21836	+	0.191214i
$295$	7.10575	−	31.0855i	0.413713	−	1.80987i
$296$	−10.2210	−	3.36872i	−0.594083	−	0.195803i
$297$	1.69344	−	1.69344i	0.0982631	−	0.0982631i
$298$	0.796511	+	0.580412i	0.0461406	+	0.0336223i
$299$	1.19205	−	1.19205i	0.0689379	−	0.0689379i
$300$	2.97771	−	21.4240i	0.171918	−	1.23691i
$301$	0.593188	+	0.593188i	0.0341908	+	0.0341908i
$302$	−4.43295	+	6.08343i	−0.255088	+	0.350062i
$303$	13.9228	−	13.9228i	0.799843	−	0.799843i
$304$	−16.5954	−	2.72420i	−0.951813	−	0.156244i
$305$	−6.50661	−	1.48733i	−0.372567	−	0.0851641i
$306$	1.97790	+	12.6026i	0.113069	+	0.720442i
$307$	10.1386	−	10.1386i	0.578638	−	0.578638i	−0.355890	−	0.934528i	$-0.615822\pi$
$307$	10.1386	−	10.1386i	0.578638	−	0.578638i	0.934528	+	0.355890i	$0.115822\pi$
$308$	0.439927	+	0.225714i	0.0250672	+	0.0128613i
$309$	13.6797	−	13.6797i	0.778210	−	0.778210i
$310$	1.02673	−	14.8453i	0.0583145	−	0.843155i
$311$	−16.2293	+	16.2293i	−0.920279	+	0.920279i	−0.997049	−	0.0767695i	$-0.975539\pi$
$311$	−16.2293	+	16.2293i	−0.920279	+	0.920279i	0.0767695	+	0.997049i	$0.475539\pi$
$312$	−30.6340	+	15.4464i	−1.73431	+	0.874482i
$313$			10.5559i			0.596657i	0.954463	+	0.298328i	$0.0964290\pi$
$313$			10.5559i			0.596657i	−0.954463	+	0.298328i	$0.903571\pi$
$314$	−0.678706	+	0.106519i	−0.0383016	+	0.00601119i
$315$	0.246790	−	1.07963i	0.0139051	−	0.0608304i
$316$	−1.74853	+	3.40796i	−0.0983624	+	0.191713i
$317$		−	8.92147i		−	0.501080i	−0.968106	−	0.250540i	$-0.919392\pi$
$317$		−	8.92147i		−	0.501080i	0.968106	−	0.250540i	$-0.0806082\pi$
$318$	−9.94995	+	1.56158i	−0.557966	+	0.0875692i
$319$		−	3.15942i		−	0.176894i
$320$	11.6511	+	13.5739i	0.651316	+	0.758807i
$321$	14.1881	−	14.1881i	0.791901	−	0.791901i
$322$	−0.101383	−	0.0738767i	−0.00564983	−	0.00411699i
$323$	15.9767	+	15.9767i	0.888966	+	0.888966i
$324$	21.3576	−	6.87316i	1.18653	−	0.381842i
$325$	−25.2545	−	12.1822i	−1.40087	−	0.675749i
$326$	−21.9689	−	16.0086i	−1.21675	−	0.886633i
$327$	−13.7600	−	13.7600i	−0.760927	−	0.760927i
$328$	−3.79968	+	17.7077i	−0.209802	+	0.977744i
$329$		−	3.04061i		−	0.167634i
$330$	4.32235	−	3.76314i	0.237937	−	0.207154i
$331$	14.1620	+	14.1620i	0.778415	+	0.778415i	0.979561	−	0.201146i	$-0.0644666\pi$
$331$	14.1620	+	14.1620i	0.778415	+	0.778415i	−0.201146	+	0.979561i	$0.564467\pi$
$332$	−1.61517	+	3.14803i	−0.0886437	+	0.172771i
$333$	−4.51602	+	4.51602i	−0.247476	+	0.247476i
$334$	−2.53301	−	16.1396i	−0.138600	−	0.883119i
$335$	7.51786	+	1.71849i	0.410745	+	0.0938910i
$336$	1.48893	+	2.07376i	0.0812277	+	0.113133i
$337$	9.81602	+	9.81602i	0.534713	+	0.534713i	0.921971	−	0.387258i	$-0.126578\pi$
$337$	9.81602	+	9.81602i	0.534713	+	0.534713i	−0.387258	+	0.921971i	$0.626578\pi$
$338$	4.04501	+	25.7736i	0.220020	+	1.40190i
$339$	−12.9644	+	12.9644i	−0.704129	+	0.704129i
$340$	−2.07920	−	23.9432i	−0.112761	−	1.29850i
$341$	2.78793	−	2.78793i	0.150975	−	0.150975i
$342$	−5.87766	+	8.06604i	−0.317828	+	0.436162i
$343$	4.10526			0.221663
$344$	−2.51715	+	7.63726i	−0.135716	+	0.411774i
$345$	−1.23136	+	0.773153i	−0.0662941	+	0.0416251i
$346$	−18.5410	−	13.5107i	−0.996771	−	0.726339i
$347$			29.6855i			1.59360i	0.604241	+	0.796801i	$0.293476\pi$
$347$			29.6855i			1.59360i	−0.604241	+	0.796801i	$0.706524\pi$
$348$	7.44655	−	14.5137i	0.399177	−	0.778014i
$349$	11.0175			0.589753			0.294876	−	0.955535i	$-0.404722\pi$
$349$	11.0175			0.589753			0.294876	+	0.955535i	$0.404722\pi$
$350$	−0.604173	+	1.99705i	−0.0322944	+	0.106747i
$351$		−	16.0290i		−	0.855565i
$352$	−0.0333130	+	4.73954i	−0.00177559	+	0.252619i
$353$	11.9989	+	11.9989i	0.638635	+	0.638635i	0.950219	−	0.311584i	$-0.100859\pi$
$353$	11.9989	+	11.9989i	0.638635	+	0.638635i	−0.311584	+	0.950219i	$0.600859\pi$
$354$	43.0942	−	6.76337i	2.29043	−	0.359469i
$355$	−15.1015	+	9.48202i	−0.801504	+	0.503253i
$356$	−26.1704	−	13.4273i	−1.38703	−	0.711647i
$357$		−	3.42985i		−	0.181527i
$358$	−4.24981	+	5.83211i	−0.224610	+	0.308236i
$359$	−29.8748			−1.57673			−0.788367	−	0.615206i	$-0.789073\pi$
$359$	−29.8748			−1.57673			−0.788367	+	0.615206i	$0.789073\pi$
$360$	10.3059	−	2.54711i	0.543167	−	0.134244i
$361$		−	1.32316i		−	0.0696398i
$362$	9.09214	−	12.4773i	0.477872	−	0.655794i
$363$	−22.2745			−1.16911
$364$	3.15027	−	1.01380i	0.165119	−	0.0531376i
$365$	−6.49105	−	10.3379i	−0.339757	−	0.541113i
$366$	−1.41566	−	9.02019i	−0.0739978	−	0.471493i
$367$	−3.28211	+	3.28211i	−0.171324	+	0.171324i	−0.787561	−	0.616237i	$-0.788657\pi$
$367$	−3.28211	+	3.28211i	−0.171324	+	0.171324i	0.616237	+	0.787561i	$0.288657\pi$
$368$	0.194783	−	1.18659i	0.0101537	−	0.0618551i
$369$	8.36808	+	6.74475i	0.435625	+	0.351117i
$370$	9.07473	−	7.90067i	0.471773	−	0.410736i
$371$	0.971530			0.0504393
$372$	19.3781	−	6.23614i	1.00471	−	0.323329i
$373$	0.510894	+	0.510894i	0.0264531	+	0.0264531i	0.720210	−	0.693757i	$-0.244046\pi$
$373$	0.510894	+	0.510894i	0.0264531	+	0.0264531i	−0.693757	+	0.720210i	$0.744046\pi$
$374$	3.75011	−	5.14636i	0.193914	−	0.266112i
$375$	18.8922	+	15.0964i	0.975590	+	0.779573i
$376$	26.0251	−	13.1225i	1.34214	−	0.676742i
$377$	−14.9526	−	14.9526i	−0.770096	−	0.770096i
$378$	−1.17832	+	0.184930i	−0.0606063	+	0.00951179i
$379$	32.1666			1.65229			0.826144	−	0.563459i	$-0.190530\pi$
$379$	32.1666			1.65229			0.826144	+	0.563459i	$0.190530\pi$
$380$	12.0953	−	14.3958i	0.620478	−	0.738490i
$381$	21.0123	−	21.0123i	1.07649	−	1.07649i
$382$	25.6531	+	18.6932i	1.31252	+	0.956427i
$383$	12.3819			0.632684			0.316342	−	0.948645i	$-0.397545\pi$
$383$	12.3819			0.632684			0.316342	+	0.948645i	$0.397545\pi$
$384$	−11.3238	+	21.6939i	−0.577866	+	1.10706i
$385$	−0.468177	+	0.293962i	−0.0238605	+	0.0149817i
$386$	2.60747	+	16.6140i	0.132717	+	0.845631i
$387$	3.37443	+	3.37443i	0.171532	+	0.171532i
$388$	−25.0347	+	8.05653i	−1.27094	+	0.409008i
$389$	4.79811			0.243274			0.121637	−	0.992575i	$-0.461186\pi$
$389$	4.79811			0.243274			0.121637	+	0.992575i	$0.461186\pi$
$390$	2.64657	−	38.2661i	0.134014	−	1.93768i
$391$	−1.14235	+	1.14235i	−0.0577709	+	0.0577709i
$392$	8.80321	+	17.4589i	0.444629	+	0.881807i
$393$		−	16.5771i		−	0.836202i
$394$	22.2882	−	30.5866i	1.12286	−	1.54093i
$395$	−2.27722	−	3.62680i	−0.114579	−	0.182484i
$396$	2.50258	+	1.28401i	0.125760	+	0.0645237i
$397$		−	12.9178i		−	0.648327i	−0.946001	−	0.324163i	$-0.894917\pi$
$397$		−	12.9178i		−	0.648327i	0.946001	−	0.324163i	$-0.105083\pi$
$398$	15.5223	−	21.3016i	0.778065	−	1.06775i
$399$	1.89742	−	1.89742i	0.0949898	−	0.0949898i
$400$	−19.7006	+	3.44756i	−0.985031	+	0.172378i
$401$		−	35.5877i		−	1.77716i	−0.458719	−	0.888581i	$-0.651691\pi$
$401$		−	35.5877i		−	1.77716i	0.458719	−	0.888581i	$-0.348309\pi$
$402$	1.63568	+	10.4221i	0.0815805	+	0.519807i
$403$		−	26.3888i		−	1.31452i
$404$	−16.1984	−	8.31096i	−0.805902	−	0.413486i
$405$	−5.58982	+	24.4537i	−0.277760	+	1.21512i
$406$	−0.926679	+	1.27170i	−0.0459903	+	0.0631135i
$407$	3.18796			0.158022
$408$	29.3568	−	14.8024i	1.45338	−	0.732828i
$409$			28.3999i			1.40429i	0.712036	+	0.702143i	$0.247773\pi$
$409$			28.3999i			1.40429i	−0.712036	+	0.702143i	$0.752227\pi$
$410$	−14.8508	−	13.7643i	−0.733427	−	0.679768i
$411$		−	23.3946i		−	1.15397i
$412$	−15.9156	−	8.16585i	−0.784105	−	0.402302i
$413$	−4.20779			−0.207052
$414$	−0.576729	−	0.420258i	−0.0283447	−	0.0206546i
$415$	−2.10353	−	3.35018i	−0.103258	−	0.164454i
$416$	22.2731	+	22.5884i	1.09203	+	1.10749i
$417$		−	12.5355i		−	0.613868i
$418$	4.92160	−	0.772414i	0.240723	−	0.0377800i
$419$		−	19.6389i		−	0.959424i	−0.877426	−	0.479712i	$-0.840741\pi$
$419$		−	19.6389i		−	0.959424i	0.877426	−	0.479712i	$-0.159259\pi$
$420$	−2.84354	+	0.246930i	−0.138751	+	0.0120490i
$421$	−13.1860	+	13.1860i	−0.642647	+	0.642647i	−0.951205	−	0.308558i	$-0.900154\pi$
$421$	−13.1860	+	13.1860i	−0.642647	+	0.642647i	0.308558	+	0.951205i	$0.400154\pi$
$422$	24.8217	+	18.0874i	1.20830	+	0.880482i
$423$		−	17.2969i		−	0.841005i
$424$	4.19289	+	8.31552i	0.203625	+	0.403837i
$425$	24.2015	+	11.6743i	1.17394	+	0.566287i
$426$	−19.7146	−	14.3659i	−0.955174	−	0.696028i
$427$			0.880747i			0.0426223i
$428$	−16.5071	−	8.46931i	−0.797899	−	0.409380i
$429$	7.18633	−	7.18633i	0.346959	−	0.346959i
$430$	−5.90349	−	6.78076i	−0.284691	−	0.326997i
$431$	−35.2396			−1.69743			−0.848716	−	0.528850i	$-0.822624\pi$
$431$	−35.2396			−1.69743			−0.848716	+	0.528850i	$0.822624\pi$
$432$	−6.66821	−	9.28737i	−0.320824	−	0.446839i
$433$	0.610511	+	0.610511i	0.0293393	+	0.0293393i	0.721624	−	0.692285i	$-0.243396\pi$
$433$	0.610511	+	0.610511i	0.0293393	+	0.0293393i	−0.692285	+	0.721624i	$0.743396\pi$
$434$	−1.93989	+	0.304454i	−0.0931177	+	0.0146142i
$435$	9.69811	+	15.4457i	0.464989	+	0.740562i
$436$	−8.21376	+	16.0090i	−0.393368	+	0.766691i
$437$	−1.26391			−0.0604610
$438$	9.83435	−	13.4959i	0.469903	−	0.644858i
$439$	22.5528	−	22.5528i	1.07639	−	1.07639i	0.0795578	−	0.996830i	$-0.474649\pi$
$439$	22.5528	−	22.5528i	1.07639	−	1.07639i	0.996830	−	0.0795578i	$-0.0253508\pi$
$440$	−4.53661	−	2.73855i	−0.216274	−	0.130555i
$441$	11.6036			0.552552
$442$	−6.60799	−	42.1042i	−0.314310	−	2.00269i
$443$	16.8925	+	16.8925i	0.802587	+	0.802587i	0.983499	−	0.180913i	$-0.0579051\pi$
$443$	16.8925	+	16.8925i	0.802587	+	0.802587i	−0.180913	+	0.983499i	$0.557905\pi$
$444$	14.6448	+	7.51382i	0.695010	+	0.356590i
$445$	27.8510	−	17.4872i	1.32026	−	0.828975i
$446$	9.79564	+	7.13801i	0.463837	+	0.337994i
$447$	−1.06587	−	1.06587i	−0.0504138	−	0.0504138i
$448$	1.40355	−	1.89795i	0.0663114	−	0.0896696i
$449$	−8.55502			−0.403736			−0.201868	−	0.979413i	$-0.564701\pi$
$449$	−8.55502			−0.403736			−0.201868	+	0.979413i	$0.564701\pi$
$450$	−3.43692	+	11.3605i	−0.162018	+	0.535539i
$451$	−0.572973	−	5.33425i	−0.0269802	−	0.251180i
$452$	15.0834	+	7.73886i	0.709463	+	0.364006i
$453$	8.14066	−	8.14066i	0.382482	−	0.382482i
$454$	−32.0669	+	5.03270i	−1.50497	+	0.236196i
$455$	−0.824506	+	3.60696i	−0.0386534	+	0.169097i
$456$	24.4292	+	8.05158i	1.14400	+	0.377050i
$457$	28.2440			1.32120			0.660599	−	0.750739i	$-0.270303\pi$
$457$	28.2440			1.32120			0.660599	+	0.750739i	$0.270303\pi$
$458$	13.3484	+	9.72690i	0.623731	+	0.454508i
$459$			15.3607i			0.716975i
$460$	1.02931	+	0.864828i	0.0479920	+	0.0403228i
$461$	26.8598			1.25098			0.625492	−	0.780231i	$-0.284898\pi$
$461$	26.8598			1.25098			0.625492	+	0.780231i	$0.284898\pi$
$462$	−0.611191	−	0.445370i	−0.0284352	−	0.0207205i
$463$		−	18.4162i		−	0.855873i	−0.903809	−	0.427936i	$-0.859241\pi$
$463$		−	18.4162i		−	0.855873i	0.903809	−	0.427936i	$-0.140759\pi$
$464$	−14.8841	−	2.44327i	−0.690975	−	0.113426i
$465$	−5.07174	+	22.1873i	−0.235196	+	1.02891i
$466$	0.273342	+	1.74165i	0.0126623	+	0.0806806i
$467$	−23.2022	−	23.2022i	−1.07367	−	1.07367i	−0.997061	−	0.0766098i	$-0.975590\pi$
$467$	−23.2022	−	23.2022i	−1.07367	−	1.07367i	−0.0766098	−	0.997061i	$-0.524410\pi$
$468$	17.9207	−	5.76715i	0.828387	−	0.266587i
$469$		−	1.01763i		−	0.0469899i
$470$	−2.24839	+	32.5089i	−0.103711	+	1.49952i
$471$	1.05076			0.0484166
$472$	−18.1598	−	36.0153i	−0.835873	−	1.65774i
$473$		−	2.38209i		−	0.109529i
$474$	3.45013	−	4.73469i	0.158470	−	0.217471i
$475$	6.93013	+	19.8468i	0.317976	+	0.910632i
$476$	−3.01892	+	0.971531i	−0.138372	+	0.0445301i
$477$	5.52668			0.253049
$478$	26.4776	+	19.2940i	1.21106	+	0.882489i
$479$	5.93689	−	5.93689i	0.271264	−	0.271264i	−0.558345	−	0.829609i	$-0.688564\pi$
$479$	5.93689	−	5.93689i	0.271264	−	0.271264i	0.829609	+	0.558345i	$0.188564\pi$
$480$	−14.3856	−	23.2727i	−0.656608	−	1.06225i
$481$	15.0876	−	15.0876i	0.687937	−	0.687937i
$482$	−0.257766	+	0.0404548i	−0.0117409	+	0.00184266i
$483$	0.135667	+	0.135667i	0.00617307	+	0.00617307i
$484$	6.30941	+	19.6058i	0.286791	+	0.891171i
$485$	6.55222	−	28.6640i	0.297521	−	1.30156i
$486$	−21.9203	+	3.44026i	−0.994326	+	0.156053i
$487$	−15.9947	+	15.9947i	−0.724790	+	0.724790i	−0.969577	−	0.244787i	$-0.921282\pi$
$487$	−15.9947	+	15.9947i	−0.724790	+	0.724790i	0.244787	+	0.969577i	$0.421282\pi$
$488$	−7.53848	+	3.80109i	−0.341251	+	0.172067i
$489$	29.3981	+	29.3981i	1.32943	+	1.32943i
$490$	−21.8085	−	1.50833i	−0.985209	−	0.0681393i
$491$		−	14.0574i		−	0.634404i	−0.948358	−	0.317202i	$-0.897257\pi$
$491$		−	14.0574i		−	0.634404i	0.948358	−	0.317202i	$-0.102743\pi$
$492$	9.94036	−	25.8548i	0.448146	−	1.16562i
$493$	14.3291	+	14.3291i	0.645351	+	0.645351i
$494$	19.6368	−	26.9480i	0.883500	−	1.21245i
$495$	−2.66329	+	1.67224i	−0.119706	+	0.0751617i
$496$	−10.9780	−	15.2899i	−0.492926	−	0.686539i
$497$	1.66384	+	1.66384i	0.0746332	+	0.0746332i
$498$	3.18698	−	4.37356i	0.142812	−	0.195984i
$499$	−28.5996	+	28.5996i	−1.28029	+	1.28029i	−0.339796	+	0.940499i	$0.610358\pi$
$499$	−28.5996	+	28.5996i	−1.28029	+	1.28029i	−0.940499	+	0.339796i	$0.889642\pi$
$500$	7.93630	−	20.9049i	0.354922	−	0.934896i
$501$			24.9871i			1.11634i
$502$	−4.84831	−	30.8920i	−0.216391	−	1.37878i
$503$			14.2373i			0.634808i	0.948290	+	0.317404i	$0.102811\pi$
$503$			14.2373i			0.634808i	−0.948290	+	0.317404i	$0.897189\pi$
$504$	−0.630710	−	1.25085i	−0.0280940	−	0.0557173i
$505$	17.2386	−	10.8239i	0.767108	−	0.481657i
$506$	0.0552282	+	0.351898i	0.00245519	+	0.0156438i
$507$		−	39.9024i		−	1.77213i
$508$	−24.4467	−	12.5429i	−1.08465	−	0.556503i
$509$	−13.8837	+	13.8837i	−0.615384	+	0.615384i	−0.944344	−	0.328960i	$-0.893302\pi$
$509$	−13.8837	+	13.8837i	−0.615384	+	0.615384i	0.328960	+	0.944344i	$0.393302\pi$
$510$	−2.53622	+	36.6706i	−0.112306	+	1.62380i
$511$	−1.13900	+	1.13900i	−0.0503865	+	0.0503865i
$512$	22.3023	+	3.82216i	0.985630	+	0.168917i
$513$	−8.49765	+	8.49765i	−0.375180	+	0.375180i
$514$	−17.1023	+	2.68409i	−0.754348	+	0.118390i
$515$	16.9376	−	10.6349i	0.746361	−	0.468630i
$516$	5.61443	−	10.9428i	0.247161	−	0.481729i
$517$	−6.10515	+	6.10515i	−0.268504	+	0.268504i
$518$	−1.28319	−	0.935051i	−0.0563801	−	0.0410838i
$519$	24.8110	+	24.8110i	1.08908	+	1.08908i
$520$	−34.4311	+	8.50967i	−1.50990	+	0.373174i
$521$	−27.1602	+	27.1602i	−1.18991	+	1.18991i	−0.212821	+	0.977091i	$0.568265\pi$
$521$	−27.1602	+	27.1602i	−1.18991	+	1.18991i	−0.977091	+	0.212821i	$0.931735\pi$
$522$	−5.27154	+	7.23425i	−0.230729	+	0.316635i
$523$	12.5127	−	12.5127i	0.547141	−	0.547141i	−0.378472	−	0.925613i	$-0.623550\pi$
$523$	12.5127	−	12.5127i	0.547141	−	0.547141i	0.925613	+	0.378472i	$0.123550\pi$
$524$	−14.5910	+	4.69558i	−0.637409	+	0.205127i
$525$	1.38646	−	2.87421i	0.0605102	−	0.125441i
$526$	2.59238	+	16.5179i	0.113033	+	0.720214i
$527$			25.2885i			1.10159i
$528$	1.17426	−	7.15341i	0.0511030	−	0.311312i
$529$			22.9096i			0.996071i
$530$	−10.3872	−	0.718403i	−0.451191	−	0.0312054i
$531$	−23.9366			−1.03876
$532$	−2.20755	−	1.13263i	−0.0957094	−	0.0491058i
$533$	−27.9570	−	22.5336i	−1.21095	−	0.976040i
$534$	36.3587	+	26.4943i	1.57339	+	1.14652i
$535$	17.5671	−	11.0301i	0.759491	−	0.476874i
$536$	8.71010	−	4.39185i	0.376219	−	0.189699i
$537$	7.80435	−	7.80435i	0.336783	−	0.336783i
$538$	−11.9578	+	1.87671i	−0.515539	+	0.0809106i
$539$	−4.09562	−	4.09562i	−0.176411	−	0.176411i
$540$	12.7349	−	1.10588i	0.548022	−	0.0475896i
$541$		−	10.8226i		−	0.465301i	−0.972560	−	0.232650i	$-0.925260\pi$
$541$		−	10.8226i		−	0.465301i	0.972560	−	0.232650i	$-0.0747397\pi$
$542$	17.5935	−	2.76119i	0.755707	−	0.118603i
$543$	−16.6968	+	16.6968i	−0.716528	+	0.716528i
$544$	−21.3444	−	21.6466i	−0.915136	−	0.928091i
$545$	−10.6973	−	17.0370i	−0.458222	−	0.729785i
$546$	−5.00037	+	0.784778i	−0.213996	+	0.0335854i
$547$		−	39.0177i		−	1.66828i	−0.551554	−	0.834139i	$-0.685965\pi$
$547$		−	39.0177i		−	1.66828i	0.551554	−	0.834139i	$-0.314035\pi$
$548$	−20.5917	+	6.62671i	−0.879634	+	0.283079i
$549$			5.01025i			0.213832i
$550$	5.22293	−	2.79672i	0.222706	−	0.119253i
$551$			15.8540i			0.675401i
$552$	−0.575695	+	1.74671i	−0.0245032	+	0.0743448i
$553$	−0.399590	+	0.399590i	−0.0169923	+	0.0169923i
$554$	−14.8031	−	10.7869i	−0.628922	−	0.458291i
$555$	−15.5852	+	9.78572i	−0.661554	+	0.415381i
$556$	−11.0336	+	3.55079i	−0.467931	+	0.150587i
$557$	35.3386			1.49734			0.748672	−	0.662941i	$-0.230692\pi$
$557$	35.3386			1.49734			0.748672	+	0.662941i	$0.230692\pi$
$558$	−11.0353	+	1.73193i	−0.467163	+	0.0733183i
$559$	−11.2737	−	11.2737i	−0.476826	−	0.476826i
$560$	1.02280	+	2.43291i	0.0432212	+	0.102809i
$561$	−6.88670	+	6.88670i	−0.290757	+	0.290757i
$562$	−25.2395	+	34.6367i	−1.06467	+	1.46106i
$563$		−	12.9105i		−	0.544114i	−0.962281	−	0.272057i	$-0.912296\pi$
$563$		−	12.9105i		−	0.544114i	0.962281	−	0.272057i	$-0.0877039\pi$
$564$	−42.4351	+	13.6562i	−1.78684	+	0.575030i
$565$	−16.0520	+	10.0788i	−0.675312	+	0.424019i
$566$	17.9171	+	13.0560i	0.753111	+	0.548786i
$567$	3.31010			0.139011
$568$	−7.06038	+	21.4218i	−0.296247	+	0.898839i
$569$	25.8383			1.08320			0.541599	−	0.840637i	$-0.317819\pi$
$569$	25.8383			1.08320			0.541599	+	0.840637i	$0.317819\pi$
$570$	−21.6895	+	18.8834i	−0.908473	+	0.790938i
$571$	−6.86766	−	6.86766i	−0.287403	−	0.287403i	0.548650	−	0.836052i	$-0.315142\pi$
$571$	−6.86766	−	6.86766i	−0.287403	−	0.287403i	−0.836052	+	0.548650i	$0.815142\pi$
$572$	−8.36092	−	4.28975i	−0.349588	−	0.179364i
$573$	−34.3282	−	34.3282i	−1.43408	−	1.43408i
$574$	−1.33394	+	2.31515i	−0.0556777	+	0.0966325i
$575$	−1.41906	+	0.495510i	−0.0591789	+	0.0206642i
$576$	7.98428	−	10.7967i	0.332678	−	0.449864i
$577$			24.7568i			1.03064i	0.856998	+	0.515320i	$0.172327\pi$
$577$			24.7568i			1.03064i	−0.856998	+	0.515320i	$0.827673\pi$
$578$	2.60491	+	16.5978i	0.108350	+	0.690376i
$579$		−	25.7216i		−	1.06895i
$580$	10.8480	−	12.9113i	0.450441	−	0.536112i
$581$	−0.369112	+	0.369112i	−0.0153134	+	0.0153134i
$582$	39.7372	−	6.23651i	1.64716	−	0.258512i
$583$	−1.95071	−	1.95071i	−0.0807901	−	0.0807901i
$584$	−14.6646	−	4.83328i	−0.606825	−	0.200003i
$585$	−4.69031	+	20.5187i	−0.193921	+	0.848344i
$586$	−33.9350	+	5.32589i	−1.40184	+	0.220010i
$587$	−15.4873			−0.639230			−0.319615	−	0.947548i	$-0.603553\pi$
$587$	−15.4873			−0.639230			−0.319615	+	0.947548i	$0.603553\pi$
$588$	−9.16123	−	28.4674i	−0.377803	−	1.17398i
$589$	−13.9898	+	13.9898i	−0.576440	+	0.576440i
$590$	44.9880	+	3.11147i	1.85213	+	0.128097i
$591$	−40.9300	+	40.9300i	−1.68364	+	1.68364i
$592$	2.46534	−	15.0185i	0.101325	−	0.617257i
$593$		−	11.8002i		−	0.484577i	−0.970204	−	0.242289i	$-0.922102\pi$
$593$		−	11.8002i		−	0.484577i	0.970204	−	0.242289i	$-0.0778981\pi$
$594$	2.73724	+	1.99460i	0.112310	+	0.0818396i
$595$	0.790128	−	3.45657i	0.0323921	−	0.141706i
$596$	−0.636251	+	1.24008i	−0.0260618	+	0.0507957i
$597$	−28.5052	+	28.5052i	−1.16664	+	1.16664i
$598$	1.92680	+	1.40405i	0.0787928	+	0.0574157i
$599$	−30.5031			−1.24632			−0.623162	−	0.782093i	$-0.714152\pi$
$599$	−30.5031			−1.24632			−0.623162	+	0.782093i	$0.714152\pi$
$600$	30.5846	−	0.537404i	1.24861	−	0.0219394i
$601$	6.76101	+	6.76101i	0.275787	+	0.275787i	0.831425	−	0.555637i	$-0.187526\pi$
$601$	6.76101	+	6.76101i	0.275787	+	0.275787i	−0.555637	+	0.831425i	$0.687526\pi$
$602$	−0.698683	+	0.958817i	−0.0284762	+	0.0390785i
$603$		−	5.78894i		−	0.235744i
$604$	−9.47124	−	4.85942i	−0.385379	−	0.197727i
$605$	−22.4480	−	5.13133i	−0.912641	−	0.208618i
$606$	22.5045	+	16.3989i	0.914183	+	0.666158i
$607$	−11.3825	+	11.3825i	−0.462002	+	0.462002i	−0.899311	−	0.437309i	$-0.855932\pi$
$607$	−11.3825	+	11.3825i	−0.462002	+	0.462002i	0.437309	+	0.899311i	$0.355932\pi$
$608$	0.167164	−	23.7830i	0.00677940	−	0.964528i
$609$	1.70175	−	1.70175i	0.0689585	−	0.0689585i
$610$	0.651272	−	9.41658i	0.0263693	−	0.381266i
$611$			57.7875i			2.33783i
$612$	−17.1735	+	5.52669i	−0.694199	+	0.223403i
$613$	21.0461	−	21.0461i	0.850044	−	0.850044i	−0.140094	−	0.990138i	$-0.544740\pi$
$613$	21.0461	−	21.0461i	0.850044	−	0.850044i	0.990138	+	0.140094i	$0.0447405\pi$
$614$	16.3878	+	11.9416i	0.661356	+	0.481925i
$615$	19.1750	+	24.3191i	0.773212	+	0.980639i
$616$	−0.218886	+	0.664119i	−0.00881916	+	0.0267581i
$617$	−21.9292	−	21.9292i	−0.882838	−	0.882838i	0.110985	−	0.993822i	$-0.464600\pi$
$617$	−21.9292	−	21.9292i	−0.882838	−	0.882838i	−0.993822	+	0.110985i	$0.964600\pi$
$618$	22.1116	+	16.1125i	0.889458	+	0.648141i
$619$	17.6974			0.711319			0.355660	−	0.934616i	$-0.384256\pi$
$619$	17.6974			0.711319			0.355660	+	0.934616i	$0.384256\pi$
$620$	20.9656	−	1.82063i	0.842001	−	0.0731184i
$621$	−0.607589	−	0.607589i	−0.0243817	−	0.0243817i
$622$	−26.2327	−	19.1156i	−1.05184	−	0.766465i
$623$	−3.06853	−	3.06853i	−0.122938	−	0.122938i
$624$	−28.2975	−	39.4123i	−1.13281	−	1.57775i
$625$	15.5617	+	19.5661i	0.622467	+	0.782646i
$626$	−14.7478	+	2.31458i	−0.589441	+	0.0925091i
$627$	−7.61955			−0.304296
$628$	−0.297637	−	0.924872i	−0.0118770	−	0.0369064i
$629$	−14.4586	+	14.4586i	−0.576501	+	0.576501i
$630$	1.56248	+	0.108065i	0.0622508	+	0.00430541i
$631$		−	32.8381i		−	1.30726i	−0.756812	−	0.653632i	$-0.773244\pi$
$631$		−	32.8381i		−	1.30726i	0.756812	−	0.653632i	$-0.226756\pi$
$632$	−5.14470	−	1.69563i	−0.204645	−	0.0674487i
$633$	−33.2157	−	33.2157i	−1.32021	−	1.32021i
$634$	12.4643	−	1.95619i	0.495021	−	0.0776904i
$635$	26.0166	−	16.3355i	1.03244	−	0.648253i
$636$	−4.36341	−	13.5588i	−0.173021	−	0.537641i
$637$	−38.7666			−1.53599
$638$	4.41407	−	0.692760i	0.174755	−	0.0274266i
$639$	9.46496	+	9.46496i	0.374428	+	0.374428i
$640$	−16.4096	+	19.2542i	−0.648647	+	0.761090i
$641$	−34.3455	−	34.3455i	−1.35657	−	1.35657i	−0.878112	−	0.478455i	$-0.841197\pi$
$641$	−34.3455	−	34.3455i	−1.35657	−	1.35657i	−0.478455	−	0.878112i	$-0.658803\pi$
$642$	22.9333	+	16.7113i	0.905105	+	0.659543i
$643$		−	4.81618i		−	0.189932i	−0.995481	−	0.0949658i	$-0.969726\pi$
$643$		−	4.81618i		−	0.189932i	0.995481	−	0.0949658i	$-0.0302742\pi$
$644$	0.0809841	−	0.157842i	0.00319122	−	0.00621983i
$645$	7.31202	+	11.6455i	0.287911	+	0.458540i
$646$	−18.8180	+	25.8244i	−0.740385	+	1.01605i
$647$	−3.59621	+	3.59621i	−0.141381	+	0.141381i	−0.774255	−	0.632874i	$-0.781875\pi$
$647$	−3.59621	+	3.59621i	−0.141381	+	0.141381i	0.632874	+	0.774255i	$0.281875\pi$
$648$	14.2856	+	28.3318i	0.561192	+	1.11298i
$649$	8.44871	+	8.44871i	0.331641	+	0.331641i
$650$	11.4825	−	37.9545i	0.450379	−	1.48870i
$651$	3.00331			0.117709
$652$	17.5487	−	34.2032i	0.687260	−	1.33950i
$653$	−35.9169			−1.40554			−0.702769	−	0.711418i	$-0.748053\pi$
$653$	−35.9169			−1.40554			−0.702769	+	0.711418i	$0.748053\pi$
$654$	16.2071	−	22.2413i	0.633747	−	0.869704i
$655$	3.81883	−	16.7062i	0.149214	−	0.652766i
$656$	−25.5728	−	1.42585i	−0.998449	−	0.0556700i
$657$	−6.47937	+	6.47937i	−0.252784	+	0.252784i
$658$	4.24807	−	0.666708i	0.165607	−	0.0259910i
$659$	−17.7691	+	17.7691i	−0.692185	+	0.692185i	−0.962712	−	0.270527i	$-0.912802\pi$
$659$	−17.7691	+	17.7691i	−0.692185	+	0.692185i	0.270527	+	0.962712i	$0.412802\pi$
$660$	6.20527	+	5.21367i	0.241540	+	0.202942i
$661$			30.6829i			1.19343i	0.802454	+	0.596714i	$0.203527\pi$
$661$			30.6829i			1.19343i	−0.802454	+	0.596714i	$0.796473\pi$
$662$	−16.6807	+	22.8912i	−0.648312	+	0.889692i
$663$			65.1852i			2.53158i
$664$	−4.75230	−	1.56630i	−0.184425	−	0.0607844i
$665$	2.34931	−	1.47510i	0.0911022	−	0.0572018i
$666$	−7.29960	−	5.31917i	−0.282854	−	0.206113i
$667$	−1.13357			−0.0438921
$668$	21.9934	−	7.07779i	0.850950	−	0.273848i
$669$	−13.1082	−	13.1082i	−0.506793	−	0.506793i
$670$	−0.752493	+	10.8801i	−0.0290713	+	0.420335i
$671$	1.76843	−	1.76843i	0.0682693	−	0.0682693i
$672$	−2.57079	+	2.53491i	−0.0991706	+	0.0977862i
$673$		−	26.1544i		−	1.00818i	−0.863652	−	0.504089i	$-0.831828\pi$
$673$		−	26.1544i		−	1.00818i	0.863652	−	0.504089i	$-0.168172\pi$
$674$	−11.5617	+	15.8664i	−0.445342	+	0.611152i
$675$	−6.20931	+	12.8722i	−0.238997	+	0.495453i
$676$	−35.1217	+	11.3027i	−1.35083	+	0.434718i
$677$	13.8939	+	13.8939i	0.533984	+	0.533984i	0.921756	−	0.387771i	$-0.126755\pi$
$677$	13.8939	+	13.8939i	0.533984	+	0.533984i	−0.387771	+	0.921756i	$0.626755\pi$
$678$	−20.9554	−	15.2700i	−0.804787	−	0.586442i
$679$	−3.88001			−0.148901
$680$	32.9955	−	8.15486i	1.26532	−	0.312725i
$681$	49.6456			1.90242
$682$	4.50636	+	3.28375i	0.172557	+	0.125741i
$683$	−9.79987			−0.374982			−0.187491	−	0.982266i	$-0.560035\pi$
$683$	−9.79987			−0.374982			−0.187491	+	0.982266i	$0.560035\pi$
$684$	−12.5579	−	6.44313i	−0.480165	−	0.246359i
$685$	5.38938	−	23.5769i	0.205917	−	0.900827i
$686$	0.900151	+	5.73550i	0.0343679	+	0.218982i
$687$	−17.8625	−	17.8625i	−0.681496	−	0.681496i
$688$	−11.2220	−	1.84214i	−0.427836	−	0.0702309i
$689$	−18.4642			−0.703429
$690$	−1.35018	−	1.55082i	−0.0514004	−	0.0590386i
$691$	−7.23522	+	7.23522i	−0.275241	+	0.275241i	−0.831206	−	0.555965i	$-0.812349\pi$
$691$	−7.23522	+	7.23522i	−0.275241	+	0.275241i	0.555965	+	0.831206i	$0.312349\pi$
$692$	14.8105	−	28.8663i	0.563011	−	1.09733i
$693$	0.293433	+	0.293433i	0.0111466	+	0.0111466i
$694$	−41.4740	+	6.50909i	−1.57433	+	0.247082i
$695$	2.88779	−	12.6332i	0.109540	−	0.479204i
$696$	21.9100	+	7.22128i	0.830496	+	0.273722i
$697$	26.7914	+	21.5941i	1.01480	+	0.817934i
$698$	2.41578	+	15.3927i	0.0914388	+	0.582621i
$699$		−	2.69641i		−	0.101987i
$700$	−2.92258	−	0.406208i	−0.110463	−	0.0153532i
$701$	−0.962763			−0.0363630			−0.0181815	−	0.999835i	$-0.505788\pi$
$701$	−0.962763			−0.0363630			−0.0181815	+	0.999835i	$0.505788\pi$
$702$	22.3943	−	3.51465i	0.845219	−	0.132652i
$703$	−15.9972			−0.603345
$704$	−6.62898	+	0.992689i	−0.249839	+	0.0374134i
$705$	11.1063	−	48.5869i	0.418289	−	1.82989i
$706$	−14.1328	+	19.3947i	−0.531894	+	0.729930i
$707$	−1.89930	−	1.89930i	−0.0714304	−	0.0714304i
$708$	18.8984	+	58.7244i	0.710244	+	2.20700i
$709$	6.53364	+	6.53364i	0.245376	+	0.245376i	0.819070	−	0.573694i	$-0.194490\pi$
$709$	6.53364	+	6.53364i	0.245376	+	0.245376i	−0.573694	+	0.819070i	$0.694490\pi$
$710$	−16.5587	−	19.0194i	−0.621438	−	0.713785i
$711$	−2.27312	+	2.27312i	−0.0852487	+	0.0852487i
$712$	13.0211	−	39.5072i	0.487987	−	1.48060i
$713$	−1.00028	−	1.00028i	−0.0374609	−	0.0374609i
$714$	4.79189	−	0.752057i	0.179332	−	0.0281450i
$715$	8.89782	−	5.58682i	0.332760	−	0.208935i
$716$	−9.07995	−	4.65867i	−0.339334	−	0.174103i
$717$	−35.4316	−	35.4316i	−1.32322	−	1.32322i
$718$	−6.55060	−	41.7385i	−0.244466	−	1.55767i
$719$	−26.9605	−	26.9605i	−1.00546	−	1.00546i	−0.999985	−	0.00547208i	$-0.998258\pi$
$719$	−26.9605	−	26.9605i	−1.00546	−	1.00546i	−0.00547208	−	0.999985i	$-0.501742\pi$
$720$	5.81834	+	13.8400i	0.216837	+	0.515785i
$721$	−1.86613	−	1.86613i	−0.0694985	−	0.0694985i
$722$	1.84860	−	0.290126i	0.0687977	−	0.0107974i
$723$	0.399070			0.0148416
$724$	19.4258	+	9.96685i	0.721956	+	0.370415i
$725$	6.21548	+	17.8001i	0.230837	+	0.661080i
$726$	−4.88408	−	31.1199i	−0.181265	−	1.15497i
$727$	−30.5494			−1.13302			−0.566508	−	0.824056i	$-0.691706\pi$
$727$	−30.5494			−1.13302			−0.566508	+	0.824056i	$0.691706\pi$
$728$	2.10715	+	4.17898i	0.0780961	+	0.154883i
$729$	0.282400			0.0104592
$730$	13.0200	−	11.3355i	0.481891	−	0.419546i
$731$	10.8036	+	10.8036i	0.399587	+	0.399587i
$732$	12.2918	−	3.95568i	0.454318	−	0.146206i
$733$	4.41040	−	4.41040i	0.162902	−	0.162902i	−0.620949	−	0.783851i	$-0.713253\pi$
$733$	4.41040	−	4.41040i	0.162902	−	0.162902i	0.783851	+	0.620949i	$0.213253\pi$
$734$	−5.30513	−	3.86581i	−0.195816	−	0.142690i
$735$	32.5944	+	7.45066i	1.20226	+	0.274822i
$736$	1.70050	+	0.0119524i	0.0626814	+	0.000440571i
$737$	−2.04327	+	2.04327i	−0.0752649	+	0.0752649i
$738$	−7.58831	+	13.1700i	−0.279330	+	0.484796i
$739$	−5.37329			−0.197660			−0.0988299	−	0.995104i	$-0.531510\pi$
$739$	−5.37329			−0.197660			−0.0988299	+	0.995104i	$0.531510\pi$
$740$	13.0279	+	10.9460i	0.478916	+	0.402385i
$741$	−36.0610	+	36.0610i	−1.32473	+	1.32473i
$742$	0.213026	+	1.35734i	0.00782041	+	0.0498294i
$743$	24.3657	+	24.3657i	0.893892	+	0.893892i	0.994887	−	0.100995i	$-0.0322025\pi$
$743$	24.3657	+	24.3657i	0.893892	+	0.893892i	−0.100995	+	0.994887i	$0.532202\pi$
$744$	12.9616	+	25.7059i	0.475194	+	0.942426i
$745$	−0.828629	−	1.31971i	−0.0303586	−	0.0483505i
$746$	−0.601753	+	0.825798i	−0.0220317	+	0.0302346i
$747$	−2.09975	+	2.09975i	−0.0768257	+	0.0768257i
$748$	8.01231	+	4.11089i	0.292959	+	0.150309i
$749$	−1.93549	−	1.93549i	−0.0707211	−	0.0707211i
$750$	−16.9489	+	29.7047i	−0.618885	+	1.08466i
$751$	28.5669	+	28.5669i	1.04242	+	1.04242i	0.999059	+	0.0433622i	$0.0138070\pi$
$751$	28.5669	+	28.5669i	1.04242	+	1.04242i	0.0433622	+	0.999059i	$0.486193\pi$
$752$	24.0401	+	33.4827i	0.876653	+	1.22099i
$753$			47.8267i			1.74290i
$754$	17.6118	−	24.1690i	0.641383	−	0.880184i
$755$	10.0794	−	6.32874i	0.366828	−	0.230326i
$756$	−0.516737	−	1.60570i	−0.0187935	−	0.0583987i
$757$	6.18605			0.224836			0.112418	−	0.993661i	$-0.464140\pi$
$757$	6.18605			0.224836			0.112418	+	0.993661i	$0.464140\pi$
$758$	7.05311	+	44.9404i	0.256181	+	1.63231i
$759$		−	0.544805i		−	0.0197752i
$760$	22.7647	+	13.7420i	0.825762	+	0.498475i
$761$	3.98484			0.144450			0.0722251	−	0.997388i	$-0.476990\pi$
$761$	3.98484			0.144450			0.0722251	+	0.997388i	$0.476990\pi$
$762$	33.9639	+	24.7492i	1.23038	+	0.896571i
$763$	−1.87708	+	1.87708i	−0.0679550	+	0.0679550i
$764$	−20.4916	+	39.9390i	−0.741359	+	1.44494i
$765$	4.49475	−	19.6632i	0.162508	−	0.710924i
$766$	2.71495	+	17.2988i	0.0980950	+	0.625033i
$767$	79.9702			2.88756
$768$	−32.7917	−	11.0639i	−1.18327	−	0.399233i
$769$			16.5226i			0.595822i	0.954594	+	0.297911i	$0.0962898\pi$
$769$			16.5226i			0.595822i	−0.954594	+	0.297911i	$0.903710\pi$
$770$	−0.513354	−	0.589639i	−0.0185000	−	0.0212491i
$771$	26.4775			0.953564
$772$	−22.6399	+	7.28584i	−0.814828	+	0.262223i
$773$			35.3417i			1.27115i	0.772038	+	0.635577i	$0.219238\pi$
$773$			35.3417i			1.27115i	−0.772038	+	0.635577i	$0.780762\pi$
$774$	−3.97455	+	5.45436i	−0.142862	+	0.196053i
$775$	−10.2225	+	21.1918i	−0.367203	+	0.761231i
$776$	−16.7452	−	33.2098i	−0.601117	−	1.19216i
$777$	1.71713	+	1.71713i	0.0616016	+	0.0616016i
$778$	1.05207	+	6.70349i	0.0377186	+	0.240332i
$779$	2.87517	+	26.7672i	0.103014	+	0.959035i
$780$	54.0423	−	4.69297i	1.93502	−	0.168035i
$781$		−	6.68154i		−	0.239084i
$782$	−1.84646	−	1.34550i	−0.0660294	−	0.0481152i
$783$	−7.62135	+	7.62135i	−0.272365	+	0.272365i
$784$	−22.4618	+	16.1272i	−0.802206	+	0.575973i
$785$	1.05895	+	0.242062i	0.0377955	+	0.00863958i
$786$	23.1600	−	3.63482i	0.826090	−	0.129650i
$787$	−5.01916	+	5.01916i	−0.178914	+	0.178914i	−0.790882	−	0.611968i	$-0.790378\pi$
$787$	−5.01916	+	5.01916i	−0.178914	+	0.178914i	0.611968	+	0.790882i	$0.290378\pi$
$788$	47.6199	+	24.4325i	1.69639	+	0.870370i
$789$		−	25.5728i		−	0.910416i
$790$	4.56773	−	3.97677i	0.162513	−	0.141487i
$791$	1.76856	+	1.76856i	0.0628826	+	0.0628826i
$792$	−1.24516	+	3.77793i	−0.0442449	+	0.134243i
$793$		−	16.7388i		−	0.594413i
$794$	18.0476	−	2.83246i	0.640487	−	0.100520i
$795$	15.5244	+	3.54868i	0.550594	+	0.125859i
$796$	33.1643	+	17.0157i	1.17548	+	0.603105i
$797$	39.0883	−	39.0883i	1.38458	−	1.38458i	0.548296	−	0.836284i	$-0.315277\pi$
$797$	39.0883	−	39.0883i	1.38458	−	1.38458i	0.836284	−	0.548296i	$-0.184723\pi$
$798$	3.06695	+	2.23487i	0.108569	+	0.0791134i
$799$		−	55.3781i		−	1.95914i
$800$	−9.13634	−	26.7680i	−0.323018	−	0.946393i
$801$	−17.4558	−	17.4558i	−0.616770	−	0.616770i
$802$	49.7199	−	7.80324i	1.75567	−	0.275542i
$803$	4.57394			0.161411
$804$	−14.2022	+	4.57046i	−0.500872	+	0.161188i
$805$	0.105471	+	0.167977i	0.00371735	+	0.00592043i
$806$	36.8681	−	5.78622i	1.29862	−	0.203811i
$807$	18.5130			0.651687
$808$	8.05954	−	24.4533i	0.283534	−	0.860266i
$809$	8.49004	+	8.49004i	0.298494	+	0.298494i	0.840424	−	0.541930i	$-0.182306\pi$
$809$	8.49004	+	8.49004i	0.298494	+	0.298494i	−0.541930	+	0.840424i	$0.682306\pi$
$810$	−35.3903	−	2.44767i	−1.24349	−	0.0860025i
$811$	−11.7840			−0.413791			−0.206895	−	0.978363i	$-0.566336\pi$
$811$	−11.7840			−0.413791			−0.206895	+	0.978363i	$0.566336\pi$
$812$	−1.97990	−	1.01583i	−0.0694809	−	0.0356487i
$813$	−27.2381			−0.955281
$814$	0.699019	+	4.45394i	0.0245006	+	0.156111i
$815$	22.8548	+	36.3996i	0.800568	+	1.27502i
$816$	27.1176	+	37.7690i	0.949306	+	1.32218i
$817$			11.9533i			0.418193i
$818$	−39.6779	+	6.22720i	−1.38730	+	0.217729i
$819$	2.77745			0.0970520
$820$	15.9739	−	23.7662i	0.557833	−	0.829953i
$821$	−32.6457			−1.13934			−0.569672	−	0.821872i	$-0.692930\pi$
$821$	−32.6457			−1.13934			−0.569672	+	0.821872i	$0.692930\pi$
$822$	32.6849	−	5.12969i	1.14002	−	0.178919i
$823$			14.1894i			0.494612i	0.968937	+	0.247306i	$0.0795453\pi$
$823$			14.1894i			0.494612i	−0.968937	+	0.247306i	$0.920455\pi$
$824$	7.91882	−	24.0264i	0.275865	−	0.836999i
$825$	−8.55490	+	2.98721i	−0.297843	+	0.104001i
$826$	−0.922634	−	5.87876i	−0.0321026	−	0.204548i
$827$	−5.63679			−0.196011			−0.0980053	−	0.995186i	$-0.531246\pi$
$827$	−5.63679			−0.196011			−0.0980053	+	0.995186i	$0.531246\pi$
$828$	0.460689	−	0.897904i	0.0160101	−	0.0312043i
$829$	−53.6658			−1.86389			−0.931945	−	0.362601i	$-0.881889\pi$
$829$	−53.6658			−1.86389			−0.931945	+	0.362601i	$0.881889\pi$
$830$	4.21934	−	3.67346i	0.146455	−	0.127508i
$831$	19.8090	+	19.8090i	0.687168	+	0.687168i
$832$	−26.6748	+	36.0710i	−0.924782	+	1.25054i
$833$	37.1502			1.28718
$834$	17.5135	−	2.74864i	0.606444	−	0.0951777i
$835$	−5.75623	+	25.1818i	−0.199203	+	0.871451i
$836$	2.15830	+	6.70665i	0.0746463	+	0.231954i
$837$	−13.4504			−0.464915
$838$	27.4378	−	4.30619i	0.947822	−	0.148755i
$839$	−3.67736	−	3.67736i	−0.126957	−	0.126957i	0.640773	−	0.767730i	$-0.278614\pi$
$839$	−3.67736	−	3.67736i	−0.126957	−	0.126957i	−0.767730	+	0.640773i	$0.778614\pi$
$840$	−0.968487	−	3.91860i	−0.0334160	−	0.135205i
$841$		−	14.7809i		−	0.509688i
$842$	−21.3136	−	15.5311i	−0.734516	−	0.535236i
$843$	46.3498	−	46.3498i	1.59637	−	1.59637i
$844$	−19.8275	+	38.6447i	−0.682492	+	1.33021i
$845$	9.19225	−	40.2133i	0.316223	−	1.38338i
$846$	24.1657	−	3.79266i	0.830835	−	0.130394i
$847$			3.03860i			0.104408i
$848$	−10.6983	+	7.68126i	−0.367382	+	0.263776i
$849$	−23.9761	−	23.9761i	−0.822858	−	0.822858i
$850$	−11.0037	+	36.3720i	−0.377424	+	1.24755i
$851$		−	1.14381i		−	0.0392094i
$852$	15.7479	−	30.6934i	0.539515	−	1.05154i
$853$	3.99055	−	3.99055i	0.136634	−	0.136634i	−0.635482	−	0.772116i	$-0.719199\pi$
$853$	3.99055	−	3.99055i	0.136634	−	0.136634i	0.772116	+	0.635482i	$0.219199\pi$
$854$	−1.23050	+	0.193120i	−0.0421069	+	0.00660842i
$855$	13.3644	−	8.39129i	0.457051	−	0.286976i
$856$	8.21311	−	24.9193i	0.280718	−	0.851723i
$857$	13.7999	−	13.7999i	0.471394	−	0.471394i	−0.430971	−	0.902366i	$-0.641829\pi$
$857$	13.7999	−	13.7999i	0.471394	−	0.471394i	0.902366	+	0.430971i	$0.141829\pi$
$858$	11.6158	+	8.46438i	0.396558	+	0.288969i
$859$			50.0285i			1.70695i	0.521133	+	0.853475i	$0.325509\pi$
$859$			50.0285i			1.70695i	−0.521133	+	0.853475i	$0.674491\pi$
$860$	8.17903	−	9.73463i	0.278903	−	0.331948i
$861$	2.56456	−	3.18179i	0.0873998	−	0.108435i
$862$	−7.72691	−	49.2336i	−0.263180	−	1.67690i
$863$	−16.8897	−	16.8897i	−0.574932	−	0.574932i	0.358571	−	0.933503i	$-0.383264\pi$
$863$	−16.8897	−	16.8897i	−0.574932	−	0.574932i	−0.933503	+	0.358571i	$0.883264\pi$
$864$	11.5134	−	11.3527i	0.391693	−	0.386225i
$865$	19.2886	+	30.7200i	0.655834	+	1.04451i
$866$	−0.719086	+	0.986817i	−0.0244355	+	0.0335334i
$867$		−	25.6964i		−	0.872697i
$868$	−0.850712	−	2.64349i	−0.0288750	−	0.0897258i
$869$	1.60465			0.0544340
$870$	−19.4528	+	16.9361i	−0.659512	+	0.574187i
$871$			19.3403i			0.655323i
$872$	−24.1674	−	7.96528i	−0.818410	−	0.269738i
$873$	−22.0720			−0.747023
$874$	−0.277135	−	1.76582i	−0.00937423	−	0.0597298i
$875$	2.05939	−	2.57721i	0.0696202	−	0.0871256i
$876$	21.0116	+	10.7805i	0.709917	+	0.364238i
$877$	−4.14206	+	4.14206i	−0.139867	+	0.139867i	−0.773574	−	0.633706i	$-0.781533\pi$
$877$	−4.14206	+	4.14206i	−0.139867	+	0.139867i	0.633706	+	0.773574i	$0.281533\pi$
$878$	36.4539	+	26.5637i	1.23026	+	0.896482i
$879$	52.5377			1.77205
$880$	2.83132	−	6.93863i	0.0954439	−	0.233901i
$881$		−	45.0414i		−	1.51748i	−0.651392	−	0.758741i	$-0.725815\pi$
$881$		−	45.0414i		−	1.51748i	0.651392	−	0.758741i	$-0.274185\pi$
$882$	2.54429	+	16.2115i	0.0856709	+	0.545870i
$883$	−41.9659			−1.41226			−0.706132	−	0.708080i	$-0.749562\pi$
$883$	−41.9659			−1.41226			−0.706132	+	0.708080i	$0.749562\pi$
$884$	57.3753	−	18.4642i	1.92974	−	0.621018i
$885$	−67.2377	−	15.3697i	−2.26017	−	0.516646i
$886$	−19.8967	+	27.3047i	−0.668443	+	0.917319i
$887$		−	8.42535i		−	0.282896i	−0.989946	−	0.141448i	$-0.954824\pi$
$887$		−	8.42535i		−	0.282896i	0.989946	−	0.141448i	$-0.0451758\pi$
$888$	−7.28652	+	22.1079i	−0.244519	+	0.741893i
$889$	−2.86643	−	2.86643i	−0.0961369	−	0.0961369i
$890$	30.5385	+	35.0766i	1.02365	+	1.17577i
$891$	−6.64627	−	6.64627i	−0.222658	−	0.222658i
$892$	−7.82472	+	15.2507i	−0.261991	+	0.510632i
$893$	30.6356	−	30.6356i	1.02518	−	1.02518i
$894$	1.25543	−	1.72285i	0.0419877	−	0.0576206i
$895$	9.66303	−	6.06728i	0.322999	−	0.202807i
$896$	2.95940	+	1.54476i	0.0988665	+	0.0516066i
$897$	−2.57839	−	2.57839i	−0.0860899	−	0.0860899i
$898$	−1.87584	−	11.9523i	−0.0625977	−	0.398854i
$899$	−12.5471	+	12.5471i	−0.418471	+	0.418471i
$900$	−16.6255	−	2.31077i	−0.554184	−	0.0770257i
$901$	17.6943			0.589483
$902$	7.32691	−	1.97014i	0.243959	−	0.0655984i
$903$	1.28306	−	1.28306i	0.0426976	−	0.0426976i
$904$	−7.50475	+	22.7701i	−0.249604	+	0.757321i
$905$	−20.6733	+	12.9805i	−0.687203	+	0.431485i
$906$	13.1584	+	9.58843i	0.437159	+	0.318554i
$907$	−12.9621	+	12.9621i	−0.430400	+	0.430400i	−0.888764	−	0.458364i	$-0.848436\pi$
$907$	−12.9621	+	12.9621i	−0.430400	+	0.430400i	0.458364	+	0.888764i	$0.348436\pi$
$908$	−14.0625	−	43.6975i	−0.466680	−	1.45015i
$909$	−10.8044	−	10.8044i	−0.358360	−	0.358360i
$910$	−5.22012	−	0.361035i	−0.173045	−	0.0119682i
$911$	12.1400			0.402215			0.201108	−	0.979569i	$-0.435546\pi$
$911$	12.1400			0.402215			0.201108	+	0.979569i	$0.435546\pi$
$912$	−5.89242	+	35.8958i	−0.195117	+	1.18863i
$913$	1.48226			0.0490557
$914$	6.19300	+	39.4600i	0.204846	+	1.30522i
$915$	−3.21708	+	14.0737i	−0.106353	+	0.465263i
$916$	−10.6627	+	20.7820i	−0.352305	+	0.686658i
$917$	−2.26138			−0.0746775
$918$	−21.4606	+	3.36810i	−0.708305	+	0.111164i
$919$	7.87823	+	7.87823i	0.259879	+	0.259879i	0.825005	−	0.565126i	$-0.191172\pi$
$919$	7.87823	+	7.87823i	0.259879	+	0.259879i	−0.565126	+	0.825005i	$0.691172\pi$
$920$	−0.982566	+	1.62769i	−0.0323942	+	0.0536635i
$921$	−21.9296	−	21.9296i	−0.722606	−	0.722606i
$922$	5.88948	+	37.5261i	0.193960	+	1.23586i
$923$	−31.6216	−	31.6216i	−1.04084	−	1.04084i
$924$	0.488218	−	0.951558i	0.0160612	−	0.0313040i
$925$	−17.9609	+	6.27163i	−0.590551	+	0.206210i
$926$	25.7295	−	4.03808i	0.845523	−	0.132700i
$927$	−10.6158	−	10.6158i	−0.348667	−	0.348667i
$928$	0.149926	−	21.3304i	0.00492155	−	0.700206i
$929$	−20.5130	+	20.5130i	−0.673011	+	0.673011i	−0.958409	−	0.285398i	$-0.907874\pi$
$929$	−20.5130	+	20.5130i	−0.673011	+	0.673011i	0.285398	+	0.958409i	$0.407874\pi$
$930$	−32.1102	−	2.22082i	−1.05294	−	0.0728234i
$931$	20.5518	+	20.5518i	0.673558	+	0.673558i
$932$	−2.37335	+	0.763778i	−0.0777417	+	0.0250184i
$933$	35.1038	+	35.1038i	1.14925	+	1.14925i
$934$	27.3286	−	37.5036i	0.894219	−	1.22716i
$935$	−8.52683	+	5.35387i	−0.278857	+	0.175090i
$936$	11.9868	+	23.7727i	0.391801	+	0.777036i
$937$	−15.7880			−0.515772			−0.257886	−	0.966175i	$-0.583026\pi$
$937$	−15.7880			−0.515772			−0.257886	+	0.966175i	$0.583026\pi$
$938$	1.42174	−	0.223134i	0.0464216	−	0.00728558i
$939$	22.8324			0.745107
$940$	−45.9116	+	3.98691i	−1.49747	+	0.130039i
$941$			9.90115i			0.322768i	0.986892	+	0.161384i	$0.0515958\pi$
$941$			9.90115i			0.322768i	−0.986892	+	0.161384i	$0.948404\pi$
$942$	0.230399	+	1.46803i	0.00750680	+	0.0478311i
$943$	−1.91388	+	0.205577i	−0.0623245	+	0.00669452i
$944$	46.3355	−	33.2683i	1.50809	−	1.08279i
$945$	1.83848	+	0.420252i	0.0598056	+	0.0136708i
$946$	3.32805	−	0.522316i	0.108204	−	0.0169820i
$947$	−32.5623	−	32.5623i	−1.05813	−	1.05813i	−0.998203	−	0.0599306i	$-0.980912\pi$
$947$	−32.5623	−	32.5623i	−1.05813	−	1.05813i	−0.0599306	−	0.998203i	$-0.519088\pi$
$948$	7.37139	+	3.78205i	0.239412	+	0.122835i
$949$	21.6470	−	21.6470i	0.702692	−	0.702692i
$950$	−26.2086	+	14.0339i	−0.850319	+	0.455321i
$951$	−19.2971			−0.625751
$952$	−2.01929	−	4.00474i	−0.0654456	−	0.129794i
$953$	−6.28887	−	6.28887i	−0.203716	−	0.203716i	0.597874	−	0.801590i	$-0.296012\pi$
$953$	−6.28887	−	6.28887i	−0.203716	−	0.203716i	−0.801590	+	0.597874i	$0.796012\pi$
$954$	1.21183	+	7.72140i	0.0392343	+	0.249989i
$955$	−26.6875	−	42.5037i	−0.863587	−	1.37539i
$956$	−21.1502	+	41.2228i	−0.684048	+	1.33324i
$957$	−6.83380			−0.220906
$958$	9.59628	+	6.99273i	0.310042	+	0.225925i
$959$	−3.19141			−0.103056
$960$	29.3603	−	25.2012i	0.947601	−	0.813366i
$961$	8.85635			0.285689
$962$	24.3874	+	17.7709i	0.786280	+	0.572956i
$963$	−11.0103	−	11.0103i	−0.354801	−	0.354801i
$964$	−0.113040	−	0.351257i	−0.00364076	−	0.0113132i
$965$	5.92544	−	25.9220i	0.190747	−	0.834458i
$966$	−0.159795	+	0.219290i	−0.00514131	+	0.00705553i
$967$			37.3230i			1.20023i	0.799914	+	0.600114i	$0.204878\pi$
$967$			37.3230i			1.20023i	−0.799914	+	0.600114i	$0.795122\pi$
$968$	−26.0080	+	13.1139i	−0.835928	+	0.421496i
$969$	34.5574	−	34.5574i	1.11014	−	1.11014i
$970$	41.4835	+	2.86909i	1.33195	+	0.0921210i
$971$	27.7930	+	27.7930i	0.891920	+	0.891920i	0.994704	−	0.102783i	$-0.0327748\pi$
$971$	27.7930	+	27.7930i	0.891920	+	0.891920i	−0.102783	+	0.994704i	$0.532775\pi$
$972$	−9.61285	−	29.8708i	−0.308332	−	0.958107i
$973$	−1.71005			−0.0548218
$974$	−25.8536	−	18.8393i	−0.828401	−	0.603650i
$975$	−26.3501	+	54.6252i	−0.843878	+	1.74941i
$976$	−6.96349	−	9.69864i	−0.222896	−	0.310446i
$977$			20.6029i			0.659144i	0.944130	+	0.329572i	$0.106904\pi$
$977$			20.6029i			0.659144i	−0.944130	+	0.329572i	$0.893096\pi$
$978$	−34.6264	+	47.5186i	−1.10723	+	1.51948i
$979$			12.3224i			0.393827i
$980$	−2.67461	−	30.7997i	−0.0854373	−	0.983859i
$981$	−10.6780	+	10.6780i	−0.340924	+	0.340924i
$982$	19.6398	−	3.08235i	0.626732	−	0.0983617i
$983$	−20.3951	+	20.3951i	−0.650502	+	0.650502i	−0.953114	−	0.302612i	$-0.902141\pi$
$983$	−20.3951	+	20.3951i	−0.650502	+	0.650502i	0.302612	+	0.953114i	$0.402141\pi$
$984$	38.3016	+	8.21868i	1.22101	+	0.262002i
$985$	−50.6779	+	31.8199i	−1.61473	+	1.01387i
$986$	−16.8775	+	23.1613i	−0.537488	+	0.737606i
$987$	−6.57681			−0.209342
$988$	41.9550	+	21.5259i	1.33477	+	0.684832i
$989$	−0.854672			−0.0271770
$990$	−2.92028	−	3.35424i	−0.0928127	−	0.106605i
$991$	−6.36284	−	6.36284i	−0.202122	−	0.202122i	0.598786	−	0.800909i	$-0.295650\pi$
$991$	−6.36284	−	6.36284i	−0.202122	−	0.202122i	−0.800909	+	0.598786i	$0.795650\pi$
$992$	18.9546	−	18.6901i	0.601811	−	0.593410i
$993$	30.6323	−	30.6323i	0.972088	−	0.972088i
$994$	−1.95974	+	2.68939i	−0.0621591	+	0.0853023i
$995$	−35.2940	+	22.1606i	−1.11889	+	0.702538i
$996$	6.80916	+	3.49359i	0.215757	+	0.110699i
$997$			18.1185i			0.573818i	0.957958	+	0.286909i	$0.0926277\pi$
$997$			18.1185i			0.573818i	−0.957958	+	0.286909i	$0.907372\pi$
$998$	−46.2279	−	33.6859i	−1.46332	−	1.06631i
$999$	−7.69020	−	7.69020i	−0.243307	−	0.243307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.65	✓	240
4.3	odd	2	inner	820.2.j.c.483.115	yes	240
5.2	odd	4		820.2.s.c.647.6	yes	240
20.7	even	4		820.2.s.c.647.56	yes	240
41.9	even	4		820.2.s.c.583.56	yes	240
164.91	odd	4		820.2.s.c.583.6	yes	240
205.132	odd	4	inner	820.2.j.c.747.115	yes	240
820.747	even	4	inner	820.2.j.c.747.65	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.65	✓	240	1.1	even	1	trivial
820.2.j.c.483.115	yes	240	4.3	odd	2	inner
820.2.j.c.747.65	yes	240	820.747	even	4	inner
820.2.j.c.747.115	yes	240	205.132	odd	4	inner
820.2.s.c.583.6	yes	240	164.91	odd	4
820.2.s.c.583.56	yes	240	41.9	even	4
820.2.s.c.647.6	yes	240	5.2	odd	4
820.2.s.c.647.56	yes	240	20.7	even	4

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.219268 + 1.39711i) q^{2} -2.16299i q^{3} +(-1.90384 + 0.612684i) q^{4} +(0.498284 - 2.17984i) q^{5} +(3.02194 - 0.474275i) q^{6} -0.295068 q^{7} +(-1.27344 - 2.52554i) q^{8} -1.67853 q^{9} +(3.15474 + 0.218189i) q^{10} +(0.592458 + 0.592458i) q^{11} +(1.32523 + 4.11800i) q^{12} +5.60783 q^{13} +(-0.0646989 - 0.412242i) q^{14} +(-4.71498 - 1.07778i) q^{15} +(3.24924 - 2.33291i) q^{16} -5.37402 q^{17} +(-0.368048 - 2.34510i) q^{18} +(-2.97295 - 2.97295i) q^{19} +(0.386899 + 4.45537i) q^{20} +0.638229i q^{21} +(-0.697823 + 0.957637i) q^{22} +(0.212568 - 0.212568i) q^{23} +(-5.46272 + 2.75444i) q^{24} +(-4.50343 - 2.17236i) q^{25} +(1.22962 + 7.83477i) q^{26} -2.85832i q^{27} +(0.561762 - 0.180783i) q^{28} +(-2.66637 - 2.66637i) q^{29} +(0.471941 - 6.82368i) q^{30} -4.70570i q^{31} +(3.97179 + 4.02802i) q^{32} +(1.28148 - 1.28148i) q^{33} +(-1.17835 - 7.50810i) q^{34} +(-0.147028 + 0.643201i) q^{35} +(3.19566 - 1.02841i) q^{36} +(2.69046 - 2.69046i) q^{37} +(3.50167 - 4.80541i) q^{38} -12.1297i q^{39} +(-6.13981 + 1.51746i) q^{40} +(-4.98535 - 4.01824i) q^{41} +(-0.891677 + 0.139943i) q^{42} +(-2.01035 - 2.01035i) q^{43} +(-1.49094 - 0.764957i) q^{44} +(-0.836386 + 3.65894i) q^{45} +(0.343591 + 0.250372i) q^{46} +10.3048i q^{47} +(-5.04606 - 7.02807i) q^{48} -6.91294 q^{49} +(2.04758 - 6.76812i) q^{50} +11.6240i q^{51} +(-10.6764 + 3.43583i) q^{52} -3.29257 q^{53} +(3.99340 - 0.626739i) q^{54} +(1.58668 - 0.996252i) q^{55} +(0.375751 + 0.745205i) q^{56} +(-6.43046 + 6.43046i) q^{57} +(3.14057 - 4.30987i) q^{58} +14.2604 q^{59} +(9.63692 - 0.836860i) q^{60} -2.98490i q^{61} +(6.57439 - 1.03181i) q^{62} +0.495280 q^{63} +(-4.75670 + 6.43225i) q^{64} +(2.79430 - 12.2242i) q^{65} +(2.07136 + 1.50938i) q^{66} +3.44881i q^{67} +(10.2313 - 3.29257i) q^{68} +(-0.459783 - 0.459783i) q^{69} +(-0.930862 - 0.0643805i) q^{70} +(-5.63883 - 5.63883i) q^{71} +(2.13751 + 4.23920i) q^{72} +(3.86014 - 3.86014i) q^{73} +(4.34880 + 3.16894i) q^{74} +(-4.69880 + 9.74087i) q^{75} +(7.48150 + 3.83855i) q^{76} +(-0.174815 - 0.174815i) q^{77} +(16.9465 - 2.65965i) q^{78} +(1.35423 - 1.35423i) q^{79} +(-3.46633 - 8.24528i) q^{80} -11.2181 q^{81} +(4.52080 - 7.84617i) q^{82} +(1.25094 - 1.25094i) q^{83} +(-0.391032 - 1.21509i) q^{84} +(-2.67779 + 11.7145i) q^{85} +(2.36787 - 3.24948i) q^{86} +(-5.76734 + 5.76734i) q^{87} +(0.741816 - 2.25073i) q^{88} +(10.3994 + 10.3994i) q^{89} +(-5.29534 - 0.366238i) q^{90} -1.65469 q^{91} +(-0.274460 + 0.534934i) q^{92} -10.1784 q^{93} +(-14.3969 + 2.25951i) q^{94} +(-7.96193 + 4.99919i) q^{95} +(8.71256 - 8.59094i) q^{96} +13.1496 q^{97} +(-1.51579 - 9.65814i) q^{98} +(-0.994459 - 0.994459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

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