LMFDB - Embedded newform 820.2.k.c.83.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] 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, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.18
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.416481 + 1.35150i) q^{2} +(-2.20659 + 2.20659i) q^{3} +(-1.65309 - 1.12575i) q^{4} +(2.01642 + 0.966467i) q^{5} +(-2.06319 - 3.90120i) q^{6} +(-2.48515 - 2.48515i) q^{7} +(2.20992 - 1.76529i) q^{8} -6.73806i q^{9} +(-2.14598 + 2.32267i) q^{10} -1.16859i q^{11} +(6.13174 - 1.16363i) q^{12} +(1.37720 + 1.37720i) q^{13} +(4.39369 - 2.32366i) q^{14} +(-6.58200 + 2.31681i) q^{15} +(1.46539 + 3.72191i) q^{16} +(1.10610 - 1.10610i) q^{17} +(9.10647 + 2.80627i) q^{18} +7.04724 q^{19} +(-2.24532 - 3.86763i) q^{20} +10.9674 q^{21} +(1.57935 + 0.486696i) q^{22} +(-3.46165 + 3.46165i) q^{23} +(-0.981117 + 8.77165i) q^{24} +(3.13188 + 3.89760i) q^{25} +(-2.43486 + 1.28771i) q^{26} +(8.24836 + 8.24836i) q^{27} +(1.31052 + 6.90582i) q^{28} -3.06400i q^{29} +(-0.389884 - 9.86046i) q^{30} -10.5463i q^{31} +(-5.64046 + 0.430370i) q^{32} +(2.57860 + 2.57860i) q^{33} +(1.03422 + 1.95556i) q^{34} +(-2.60929 - 7.41292i) q^{35} +(-7.58534 + 11.1386i) q^{36} +(-0.515891 + 0.515891i) q^{37} +(-2.93504 + 9.52432i) q^{38} -6.07784 q^{39} +(6.16222 - 1.42375i) q^{40} +1.00000 q^{41} +(-4.56772 + 14.8224i) q^{42} +(4.53072 - 4.53072i) q^{43} +(-1.31554 + 1.93178i) q^{44} +(6.51211 - 13.5867i) q^{45} +(-3.23670 - 6.12013i) q^{46} +(7.42600 + 7.42600i) q^{47} +(-11.4462 - 4.97920i) q^{48} +5.35196i q^{49} +(-6.57197 + 2.60945i) q^{50} +4.88142i q^{51} +(-0.726256 - 3.82702i) q^{52} +(-4.84743 - 4.84743i) q^{53} +(-14.5829 + 7.71235i) q^{54} +(1.12941 - 2.35637i) q^{55} +(-9.87900 - 1.10497i) q^{56} +(-15.5503 + 15.5503i) q^{57} +(4.14098 + 1.27610i) q^{58} -8.18051 q^{59} +(13.4888 + 3.57977i) q^{60} +6.87387 q^{61} +(14.2533 + 4.39233i) q^{62} +(-16.7451 + 16.7451i) q^{63} +(1.76750 - 7.80230i) q^{64} +(1.44600 + 4.10804i) q^{65} +(-4.55891 + 2.41103i) q^{66} +(10.0229 + 10.0229i) q^{67} +(-3.07367 + 0.583293i) q^{68} -15.2769i q^{69} +(11.1053 - 0.439103i) q^{70} +8.05271i q^{71} +(-11.8946 - 14.8906i) q^{72} +(-5.77083 - 5.77083i) q^{73} +(-0.482366 - 0.912084i) q^{74} +(-15.5112 - 1.68963i) q^{75} +(-11.6497 - 7.93340i) q^{76} +(-2.90413 + 2.90413i) q^{77} +(2.53130 - 8.21418i) q^{78} +0.336653 q^{79} +(-0.642257 + 8.92118i) q^{80} -16.1873 q^{81} +(-0.416481 + 1.35150i) q^{82} +(5.15865 - 5.15865i) q^{83} +(-18.1301 - 12.3465i) q^{84} +(3.29937 - 1.16135i) q^{85} +(4.23630 + 8.01022i) q^{86} +(6.76098 + 6.76098i) q^{87} +(-2.06290 - 2.58250i) q^{88} +8.32204i q^{89} +(15.6503 + 14.4597i) q^{90} -6.84512i q^{91} +(9.61936 - 1.82547i) q^{92} +(23.2713 + 23.2713i) q^{93} +(-13.1290 + 6.94343i) q^{94} +(14.2102 + 6.81092i) q^{95} +(11.4965 - 13.3958i) q^{96} +(4.35566 - 4.35566i) q^{97} +(-7.23315 - 2.22899i) q^{98} -7.87404 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

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

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

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 $

$2$	−0.416481	+	1.35150i	−0.294497	+	0.955653i
$2$	−0.416481	+	1.35150i	−0.294497	+	0.955653i
$3$	−2.20659	+	2.20659i	−1.27397	+	1.27397i	−0.329990	+	0.943985i	$0.607045\pi$
$3$	−2.20659	+	2.20659i	−1.27397	+	1.27397i	−0.943985	+	0.329990i	$0.892955\pi$
$4$	−1.65309	−	1.12575i	−0.826544	−	0.562873i
$5$	2.01642	+	0.966467i	0.901770	+	0.432217i
$5$	2.01642	+	0.966467i	0.901770	+	0.432217i
$6$	−2.06319	−	3.90120i	−0.842296	−	1.59266i
$7$	−2.48515	−	2.48515i	−0.939299	−	0.939299i	0.0589612	−	0.998260i	$-0.481221\pi$
$7$	−2.48515	−	2.48515i	−0.939299	−	0.939299i	−0.998260	+	0.0589612i	$0.981221\pi$
$8$	2.20992	−	1.76529i	0.781325	−	0.624124i
$9$		−	6.73806i		−	2.24602i
$10$	−2.14598	+	2.32267i	−0.678617	+	0.734492i
$11$		−	1.16859i		−	0.352344i	−0.984359	−	0.176172i	$-0.943629\pi$
$11$		−	1.16859i		−	0.352344i	0.984359	−	0.176172i	$-0.0563714\pi$
$12$	6.13174	−	1.16363i	1.77008	−	0.335910i
$13$	1.37720	+	1.37720i	0.381967	+	0.381967i	0.871811	−	0.489843i	$-0.162946\pi$
$13$	1.37720	+	1.37720i	0.381967	+	0.381967i	−0.489843	+	0.871811i	$0.662946\pi$
$14$	4.39369	−	2.32366i	1.17426	−	0.621023i
$15$	−6.58200	+	2.31681i	−1.69946	+	0.598198i
$16$	1.46539	+	3.72191i	0.366348	+	0.930478i
$17$	1.10610	−	1.10610i	0.268269	−	0.268269i	−0.560133	−	0.828402i	$-0.689250\pi$
$17$	1.10610	−	1.10610i	0.268269	−	0.268269i	0.828402	+	0.560133i	$0.189250\pi$
$18$	9.10647	+	2.80627i	2.14641	+	0.661445i
$19$	7.04724			1.61675			0.808374	−	0.588670i	$-0.200348\pi$
$19$	7.04724			1.61675			0.808374	+	0.588670i	$0.200348\pi$
$20$	−2.24532	−	3.86763i	−0.502069	−	0.864828i
$21$	10.9674			2.39329
$22$	1.57935	+	0.486696i	0.336718	+	0.103764i
$23$	−3.46165	+	3.46165i	−0.721805	+	0.721805i	−0.968973	−	0.247168i	$-0.920500\pi$
$23$	−3.46165	+	3.46165i	−0.721805	+	0.721805i	0.247168	+	0.968973i	$0.420500\pi$
$24$	−0.981117	+	8.77165i	−0.200270	+	1.79051i
$25$	3.13188	+	3.89760i	0.626377	+	0.779520i
$26$	−2.43486	+	1.28771i	−0.477516	+	0.252540i
$27$	8.24836	+	8.24836i	1.58740	+	1.58740i
$28$	1.31052	+	6.90582i	0.247666	+	1.30508i
$29$		−	3.06400i		−	0.568970i	−0.958680	−	0.284485i	$-0.908177\pi$
$29$		−	3.06400i		−	0.568970i	0.958680	−	0.284485i	$-0.0918226\pi$
$30$	−0.389884	−	9.86046i	−0.0711827	−	1.80026i
$31$		−	10.5463i		−	1.89417i	−0.320985	−	0.947084i	$-0.604014\pi$
$31$		−	10.5463i		−	1.89417i	0.320985	−	0.947084i	$-0.395986\pi$
$32$	−5.64046	+	0.430370i	−0.997102	+	0.0760794i
$33$	2.57860	+	2.57860i	0.448877	+	0.448877i
$34$	1.03422	+	1.95556i	0.177368	+	0.335376i
$35$	−2.60929	−	7.41292i	−0.441050	−	1.25301i
$36$	−7.58534	+	11.1386i	−1.26422	+	1.85643i
$37$	−0.515891	+	0.515891i	−0.0848119	+	0.0848119i	−0.748240	−	0.663428i	$-0.769101\pi$
$37$	−0.515891	+	0.515891i	−0.0848119	+	0.0848119i	0.663428	+	0.748240i	$0.269101\pi$
$38$	−2.93504	+	9.52432i	−0.476126	+	1.54505i
$39$	−6.07784			−0.973233
$40$	6.16222	−	1.42375i	0.974332	−	0.225114i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−4.56772	+	14.8224i	−0.704814	+	2.28715i
$43$	4.53072	−	4.53072i	0.690929	−	0.690929i	−0.271508	−	0.962436i	$-0.587522\pi$
$43$	4.53072	−	4.53072i	0.690929	−	0.690929i	0.962436	+	0.271508i	$0.0875222\pi$
$44$	−1.31554	+	1.93178i	−0.198325	+	0.291227i
$45$	6.51211	−	13.5867i	0.970768	−	2.02539i
$46$	−3.23670	−	6.12013i	−0.477226	−	0.902364i
$47$	7.42600	+	7.42600i	1.08319	+	1.08319i	0.996210	+	0.0869839i	$0.0277229\pi$
$47$	7.42600	+	7.42600i	1.08319	+	1.08319i	0.0869839	+	0.996210i	$0.472277\pi$
$48$	−11.4462	−	4.97920i	−1.65212	−	0.718686i
$49$			5.35196i			0.764565i
$50$	−6.57197	+	2.60945i	−0.929417	+	0.369032i
$51$			4.88142i			0.683536i
$52$	−0.726256	−	3.82702i	−0.100714	−	0.530712i
$53$	−4.84743	−	4.84743i	−0.665846	−	0.665846i	0.290906	−	0.956752i	$-0.406043\pi$
$53$	−4.84743	−	4.84743i	−0.665846	−	0.665846i	−0.956752	+	0.290906i	$0.906043\pi$
$54$	−14.5829	+	7.71235i	−1.98448	+	1.04952i
$55$	1.12941	−	2.35637i	0.152289	−	0.317733i
$56$	−9.87900	−	1.10497i	−1.32014	−	0.147658i
$57$	−15.5503	+	15.5503i	−2.05969	+	2.05969i
$58$	4.14098	+	1.27610i	0.543738	+	0.167560i
$59$	−8.18051			−1.06501			−0.532506	−	0.846426i	$-0.678749\pi$
$59$	−8.18051			−1.06501			−0.532506	+	0.846426i	$0.678749\pi$
$60$	13.4888	+	3.57977i	1.74139	+	0.462146i
$61$	6.87387			0.880109			0.440055	−	0.897971i	$-0.354959\pi$
$61$	6.87387			0.880109			0.440055	+	0.897971i	$0.354959\pi$
$62$	14.2533	+	4.39233i	1.81017	+	0.557826i
$63$	−16.7451	+	16.7451i	−2.10968	+	2.10968i
$64$	1.76750	−	7.80230i	0.220938	−	0.975288i
$65$	1.44600	+	4.10804i	0.179354	+	0.509539i
$66$	−4.55891	+	2.41103i	−0.561163	+	0.296778i
$67$	10.0229	+	10.0229i	1.22450	+	1.22450i	0.966016	+	0.258482i	$0.0832222\pi$
$67$	10.0229	+	10.0229i	1.22450	+	1.22450i	0.258482	+	0.966016i	$0.416778\pi$
$68$	−3.07367	+	0.583293i	−0.372737	+	0.0707347i
$69$		−	15.2769i		−	1.83912i
$70$	11.1053	−	0.439103i	1.32733	−	0.0524829i
$71$			8.05271i			0.955680i	0.878447	+	0.477840i	$0.158580\pi$
$71$			8.05271i			0.955680i	−0.878447	+	0.477840i	$0.841420\pi$
$72$	−11.8946	−	14.8906i	−1.40180	−	1.75487i
$73$	−5.77083	−	5.77083i	−0.675424	−	0.675424i	0.283537	−	0.958961i	$-0.408492\pi$
$73$	−5.77083	−	5.77083i	−0.675424	−	0.675424i	−0.958961	+	0.283537i	$0.908492\pi$
$74$	−0.482366	−	0.912084i	−0.0560739	−	0.106028i
$75$	−15.5112	−	1.68963i	−1.79108	−	0.195101i
$76$	−11.6497	−	7.93340i	−1.33631	−	0.910023i
$77$	−2.90413	+	2.90413i	−0.330956	+	0.330956i
$78$	2.53130	−	8.21418i	0.286614	−	0.930073i
$79$	0.336653			0.0378764			0.0189382	−	0.999821i	$-0.493971\pi$
$79$	0.336653			0.0378764			0.0189382	+	0.999821i	$0.493971\pi$
$80$	−0.642257	+	8.92118i	−0.0718065	+	0.997419i
$81$	−16.1873			−1.79859
$82$	−0.416481	+	1.35150i	−0.0459926	+	0.149248i
$83$	5.15865	−	5.15865i	0.566235	−	0.566235i	−0.364836	−	0.931072i	$-0.618875\pi$
$83$	5.15865	−	5.15865i	0.566235	−	0.566235i	0.931072	+	0.364836i	$0.118875\pi$
$84$	−18.1301	−	12.3465i	−1.97815	−	1.34712i
$85$	3.29937	−	1.16135i	0.357867	−	0.125966i
$86$	4.23630	+	8.01022i	0.456812	+	0.863764i
$87$	6.76098	+	6.76098i	0.724853	+	0.724853i
$88$	−2.06290	−	2.58250i	−0.219906	−	0.275295i
$89$			8.32204i			0.882134i	0.897474	+	0.441067i	$0.145400\pi$
$89$			8.32204i			0.882134i	−0.897474	+	0.441067i	$0.854600\pi$
$90$	15.6503	+	14.4597i	1.64968	+	1.52419i
$91$		−	6.84512i		−	0.717563i
$92$	9.61936	−	1.82547i	1.00289	−	0.190319i
$93$	23.2713	+	23.2713i	2.41312	+	2.41312i
$94$	−13.1290	+	6.94343i	−1.35415	+	0.716160i
$95$	14.2102	+	6.81092i	1.45793	+	0.698786i
$96$	11.4965	−	13.3958i	1.17336	−	1.36720i
$97$	4.35566	−	4.35566i	0.442250	−	0.442250i	−0.450517	−	0.892768i	$-0.648760\pi$
$97$	4.35566	−	4.35566i	0.442250	−	0.442250i	0.892768	+	0.450517i	$0.148760\pi$
$98$	−7.23315	−	2.22899i	−0.730659	−	0.225162i
$99$	−7.87404			−0.791371
$100$	−0.789568	−	9.96878i	−0.0789568	−	0.996878i
$101$	0.807335			0.0803329			0.0401664	−	0.999193i	$-0.487211\pi$
$101$	0.807335			0.0803329			0.0401664	+	0.999193i	$0.487211\pi$
$102$	−6.59723	−	2.03302i	−0.653223	−	0.201299i
$103$	7.04746	−	7.04746i	0.694407	−	0.694407i	−0.268791	−	0.963198i	$-0.586624\pi$
$103$	7.04746	−	7.04746i	0.694407	−	0.694407i	0.963198	+	0.268791i	$0.0866241\pi$
$104$	5.47467	+	0.612347i	0.536836	+	0.0600455i
$105$	22.1149	+	10.5996i	2.15819	+	1.03442i
$106$	8.57015	−	4.53243i	0.832407	−	0.440228i
$107$	3.52922	+	3.52922i	0.341182	+	0.341182i	0.856812	−	0.515629i	$-0.172442\pi$
$107$	3.52922	+	3.52922i	0.341182	+	0.341182i	−0.515629	+	0.856812i	$0.672442\pi$
$108$	−4.34970	−	22.9208i	−0.418550	−	2.20556i
$109$			12.0909i			1.15810i	0.815291	+	0.579051i	$0.196577\pi$
$109$			12.0909i			1.15810i	−0.815291	+	0.579051i	$0.803423\pi$
$110$	2.71425	+	2.50777i	0.258794	+	0.239107i
$111$		−	2.27672i		−	0.216096i
$112$	5.60779	−	12.8912i	0.529886	−	1.21811i
$113$	−7.65879	−	7.65879i	−0.720479	−	0.720479i	0.248224	−	0.968703i	$-0.420153\pi$
$113$	−7.65879	−	7.65879i	−0.720479	−	0.720479i	−0.968703	+	0.248224i	$0.920153\pi$
$114$	−14.5398	−	27.4927i	−1.36178	−	2.57492i
$115$	−10.3257	+	3.63457i	−0.962878	+	0.338925i
$116$	−3.44928	+	5.06506i	−0.320258	+	0.470279i
$117$	9.27968	−	9.27968i	0.857906	−	0.857906i
$118$	3.40703	−	11.0559i	0.313642	−	1.01778i
$119$	−5.49766			−0.503970
$120$	−10.4559	+	16.7391i	−0.954484	+	1.52806i
$121$	9.63439			0.875854
$122$	−2.86284	+	9.29002i	−0.259189	+	0.841079i
$123$	−2.20659	+	2.20659i	−0.198961	+	0.198961i
$124$	−11.8724	+	17.4339i	−1.06618	+	1.56561i
$125$	2.54828	+	10.8861i	0.227925	+	0.973679i
$126$	−15.6569	−	29.6050i	−1.39483	−	2.63742i
$127$	−0.972418	−	0.972418i	−0.0862882	−	0.0862882i	0.662645	−	0.748933i	$-0.269434\pi$
$127$	−0.972418	−	0.972418i	−0.0862882	−	0.0862882i	−0.748933	+	0.662645i	$0.769434\pi$
$128$	9.80866	+	5.63828i	0.866971	+	0.498359i
$129$			19.9949i			1.76045i
$130$	−6.15423	+	0.243339i	−0.539762	+	0.0213423i
$131$		−	7.25966i		−	0.634280i	−0.948379	−	0.317140i	$-0.897278\pi$
$131$		−	7.25966i		−	0.634280i	0.948379	−	0.317140i	$-0.102722\pi$
$132$	−1.35980	−	7.16550i	−0.118356	−	0.623677i
$133$	−17.5135	−	17.5135i	−1.51861	−	1.51861i
$134$	−17.7203	+	9.37161i	−1.53080	+	0.809584i
$135$	8.66037	+	24.6039i	0.745366	+	2.11757i
$136$	0.491807	−	4.39699i	0.0421721	−	0.377039i
$137$	10.3219	−	10.3219i	0.881860	−	0.881860i	−0.111864	−	0.993724i	$-0.535682\pi$
$137$	10.3219	−	10.3219i	0.881860	−	0.881860i	0.993724	+	0.111864i	$0.0356820\pi$
$138$	20.6467	+	6.36253i	1.75756	+	0.541615i
$139$	18.3797			1.55895			0.779473	−	0.626436i	$-0.215487\pi$
$139$	18.3797			1.55895			0.779473	+	0.626436i	$0.215487\pi$
$140$	−4.03168	+	15.1916i	−0.340739	+	1.28392i
$141$	−32.7722			−2.75992
$142$	−10.8832	−	3.35380i	−0.913298	−	0.281445i
$143$	1.60939	−	1.60939i	0.134584	−	0.134584i
$144$	25.0785	−	9.87391i	2.08987	−	0.822826i
$145$	2.96125	−	6.17830i	0.245919	−	0.513080i
$146$	10.2027	−	5.39582i	0.844381	−	0.446561i
$147$	−11.8096	−	11.8096i	−0.974036	−	0.974036i
$148$	1.43357	−	0.272051i	0.117839	−	0.0223624i
$149$		−	21.3079i		−	1.74561i	−0.488065	−	0.872807i	$-0.662297\pi$
$149$		−	21.3079i		−	1.74561i	0.488065	−	0.872807i	$-0.337703\pi$
$150$	8.74363	−	20.2596i	0.713915	−	1.65419i
$151$			2.40553i			0.195759i	0.995198	+	0.0978795i	$0.0312060\pi$
$151$			2.40553i			0.195759i	−0.995198	+	0.0978795i	$0.968794\pi$
$152$	15.5738	−	12.4404i	1.26320	−	1.00905i
$153$	−7.45298	−	7.45298i	−0.602538	−	0.602538i
$154$	−2.71540	−	5.13443i	−0.218814	−	0.413744i
$155$	10.1926	−	21.2657i	0.818692	−	1.70810i
$156$	10.0472	+	6.84210i	0.804420	+	0.547806i
$157$	−5.86895	+	5.86895i	−0.468393	+	0.468393i	−0.901394	−	0.433001i	$-0.857455\pi$
$157$	−5.86895	+	5.86895i	−0.468393	+	0.468393i	0.433001	+	0.901394i	$0.357455\pi$
$158$	−0.140210	+	0.454985i	−0.0111545	+	0.0361967i
$159$	21.3926			1.69654
$160$	−11.7895	−	4.58351i	−0.932039	−	0.362358i
$161$	17.2055			1.35598
$162$	6.74169	−	21.8770i	0.529677	−	1.71882i
$163$	−10.3392	+	10.3392i	−0.809830	+	0.809830i	−0.984608	−	0.174778i	$-0.944079\pi$
$163$	−10.3392	+	10.3392i	−0.809830	+	0.809830i	0.174778	+	0.984608i	$0.444079\pi$
$164$	−1.65309	−	1.12575i	−0.129084	−	0.0879060i
$165$	2.70740	+	7.69167i	0.210771	+	0.598796i
$166$	4.82342	+	9.12038i	0.374370	+	0.707878i
$167$	10.7003	+	10.7003i	0.828013	+	0.828013i	0.987242	−	0.159228i	$-0.0509006\pi$
$167$	10.7003	+	10.7003i	0.828013	+	0.828013i	−0.159228	+	0.987242i	$0.550901\pi$
$168$	24.2371	−	19.3607i	1.86993	−	1.49371i
$169$		−	9.20662i		−	0.708202i
$170$	0.195438	+	4.94278i	0.0149894	+	0.379094i
$171$		−	47.4847i		−	3.63125i
$172$	−12.5901	+	2.38924i	−0.959988	+	0.182178i
$173$	8.32828	+	8.32828i	0.633188	+	0.633188i	0.948866	−	0.315679i	$-0.102232\pi$
$173$	8.32828	+	8.32828i	0.633188	+	0.633188i	−0.315679	+	0.948866i	$0.602232\pi$
$174$	−11.9533	+	6.32162i	−0.906175	+	0.479241i
$175$	1.90293	−	17.4693i	0.143848	−	1.32056i
$176$	4.34939	−	1.71245i	0.327848	−	0.129081i
$177$	18.0510	−	18.0510i	1.35680	−	1.35680i
$178$	−11.2472	−	3.46597i	−0.843014	−	0.259785i
$179$	23.5700			1.76170			0.880851	−	0.473393i	$-0.156971\pi$
$179$	23.5700			1.76170			0.880851	+	0.473393i	$0.156971\pi$
$180$	−26.0603	+	15.1291i	−1.94242	+	1.12766i
$181$	−7.81117			−0.580600			−0.290300	−	0.956936i	$-0.593755\pi$
$181$	−7.81117			−0.580600			−0.290300	+	0.956936i	$0.593755\pi$
$182$	9.25115	+	2.85086i	0.685741	+	0.211320i
$183$	−15.1678	+	15.1678i	−1.12124	+	1.12124i
$184$	−1.53916	+	13.7608i	−0.113468	+	1.01446i
$185$	−1.53884	+	0.541660i	−0.113138	+	0.0398237i
$186$	−41.1431	+	21.7590i	−3.01676	+	1.59545i
$187$	−1.29258	−	1.29258i	−0.0945229	−	0.0945229i
$188$	−3.91604	−	20.6356i	−0.285607	−	1.50501i
$189$		−	40.9968i		−	2.98208i
$190$	−15.1232	+	16.3684i	−1.09715	+	1.18749i
$191$			14.2310i			1.02972i	0.857275	+	0.514859i	$0.172156\pi$
$191$			14.2310i			1.02972i	−0.857275	+	0.514859i	$0.827844\pi$
$192$	13.3163	+	21.1166i	0.961023	+	1.52396i
$193$	5.19851	+	5.19851i	0.374197	+	0.374197i	0.869003	−	0.494806i	$-0.164761\pi$
$193$	5.19851	+	5.19851i	0.374197	+	0.374197i	−0.494806	+	0.869003i	$0.664761\pi$
$194$	4.07261	+	7.70071i	0.292396	+	0.552879i
$195$	−12.2555	−	5.87403i	−0.877632	−	0.420648i
$196$	6.02494	−	8.84725i	0.430353	−	0.631947i
$197$	−0.256469	+	0.256469i	−0.0182727	+	0.0182727i	−0.716184	−	0.697911i	$-0.754113\pi$
$197$	−0.256469	+	0.256469i	−0.0182727	+	0.0182727i	0.697911	+	0.716184i	$0.254113\pi$
$198$	3.27939	−	10.6417i	0.233056	−	0.756276i
$199$	−1.11303			−0.0789007			−0.0394503	−	0.999222i	$-0.512561\pi$
$199$	−1.11303			−0.0789007			−0.0394503	+	0.999222i	$0.512561\pi$
$200$	13.8016	+	3.08471i	0.975922	+	0.218122i
$201$	−44.2330			−3.11996
$202$	−0.336240	+	1.09111i	−0.0236578	+	0.0767703i
$203$	−7.61450	+	7.61450i	−0.534433	+	0.534433i
$204$	5.49524	−	8.06942i	0.384744	−	0.564972i
$205$	2.01642	+	0.966467i	0.140833	+	0.0675010i
$206$	6.58949	+	12.4598i	0.459112	+	0.868113i
$207$	23.3248	+	23.3248i	1.62119	+	1.62119i
$208$	−3.10768	+	7.14397i	−0.215479	+	0.495345i
$209$		−	8.23534i		−	0.569651i
$210$	−23.5358	+	25.4736i	−1.62413	+	1.75785i
$211$		−	13.4800i		−	0.928001i	−0.885835	−	0.464000i	$-0.846414\pi$
$211$		−	13.4800i		−	0.928001i	0.885835	−	0.464000i	$-0.153586\pi$
$212$	2.55625	+	13.4702i	0.175564	+	0.925137i
$213$	−17.7690	−	17.7690i	−1.21751	−	1.21751i
$214$	−6.23958	+	3.29987i	−0.426529	+	0.225575i
$215$	13.5146	−	4.75704i	0.921690	−	0.324427i
$216$	32.7890	+	3.66747i	2.23101	+	0.249540i
$217$	−26.2091	+	26.2091i	−1.77919	+	1.77919i
$218$	−16.3409	−	5.03565i	−1.10674	−	0.341057i
$219$	25.4677			1.72095
$220$	−4.51968	+	2.62386i	−0.304717	+	0.176901i
$221$	3.04665			0.204940
$222$	3.07698	+	0.948209i	0.206513	+	0.0636397i
$223$	−0.484616	+	0.484616i	−0.0324523	+	0.0324523i	−0.723147	−	0.690694i	$-0.757305\pi$
$223$	−0.484616	+	0.484616i	−0.0324523	+	0.0324523i	0.690694	+	0.723147i	$0.257305\pi$
$224$	15.0869	+	12.9479i	1.00804	+	0.865115i
$225$	26.2623	−	21.1028i	1.75082	−	1.40685i
$226$	13.5406	−	7.16109i	0.900706	−	0.476349i
$227$	−17.4917	−	17.4917i	−1.16097	−	1.16097i	−0.984264	−	0.176702i	$-0.943457\pi$
$227$	−17.4917	−	17.4917i	−1.16097	−	1.16097i	−0.176702	−	0.984264i	$-0.556543\pi$
$228$	43.2118	−	8.20034i	2.86177	−	0.543081i
$229$			23.1172i			1.52763i	0.645435	+	0.763815i	$0.276676\pi$
$229$			23.1172i			1.52763i	−0.645435	+	0.763815i	$0.723324\pi$
$230$	−0.611642	−	15.4689i	−0.0403305	−	1.01999i
$231$		−	12.8164i		−	0.843259i
$232$	−5.40885	−	6.77119i	−0.355108	−	0.444551i
$233$	7.34176	+	7.34176i	0.480975	+	0.480975i	0.905443	−	0.424468i	$-0.139539\pi$
$233$	7.34176	+	7.34176i	0.480975	+	0.480975i	−0.424468	+	0.905443i	$0.639539\pi$
$234$	8.67664	+	16.4063i	0.567210	+	1.07251i
$235$	7.79694	+	22.1509i	0.508616	+	1.44497i
$236$	13.5231	+	9.20917i	0.880278	+	0.599466i
$237$	−0.742854	+	0.742854i	−0.0482536	+	0.0482536i
$238$	2.28967	−	7.43007i	0.148417	−	0.481620i
$239$	−6.19313			−0.400601			−0.200300	−	0.979735i	$-0.564192\pi$
$239$	−6.19313			−0.400601			−0.200300	+	0.979735i	$0.564192\pi$
$240$	−18.2682	−	21.1026i	−1.17921	−	1.36217i
$241$	20.2939			1.30725			0.653624	−	0.756820i	$-0.273248\pi$
$241$	20.2939			1.30725			0.653624	+	0.756820i	$0.273248\pi$
$242$	−4.01254	+	13.0209i	−0.257936	+	0.837012i
$243$	10.9736	−	10.9736i	0.703955	−	0.703955i
$244$	−11.3631	−	7.73823i	−0.727449	−	0.495390i
$245$	−5.17249	+	10.7918i	−0.330458	+	0.689462i
$246$	−2.06319	−	3.90120i	−0.131544	−	0.248731i
$247$	9.70548	+	9.70548i	0.617545	+	0.617545i
$248$	−18.6172	−	23.3064i	−1.18220	−	1.47996i
$249$			22.7660i			1.44274i
$250$	−15.7738	−	1.08984i	−0.997622	−	0.0689275i
$251$		−	7.27720i		−	0.459333i	−0.973269	−	0.229666i	$-0.926237\pi$
$251$		−	7.27720i		−	0.459333i	0.973269	−	0.229666i	$-0.0737635\pi$
$252$	46.5318	−	8.83039i	2.93123	−	0.556262i
$253$	4.04526	+	4.04526i	0.254323	+	0.254323i
$254$	1.71921	−	0.909227i	0.107873	−	0.0570500i
$255$	−4.71773	+	9.84299i	−0.295436	+	0.616392i
$256$	−11.7052	+	10.9081i	−0.731578	+	0.681758i
$257$	−5.84663	+	5.84663i	−0.364703	+	0.364703i	−0.865541	−	0.500838i	$-0.833025\pi$
$257$	−5.84663	+	5.84663i	−0.364703	+	0.364703i	0.500838	+	0.865541i	$0.333025\pi$
$258$	−27.0230	−	8.32749i	−1.68238	−	0.518447i
$259$	2.56413			0.159328
$260$	2.23425	−	8.41877i	0.138562	−	0.522110i
$261$	−20.6454			−1.27792
$262$	9.81141	+	3.02351i	0.606151	+	0.186793i
$263$	9.87638	−	9.87638i	0.609004	−	0.609004i	−0.333682	−	0.942686i	$-0.608291\pi$
$263$	9.87638	−	9.87638i	0.609004	−	0.609004i	0.942686	+	0.333682i	$0.108291\pi$
$264$	10.2505	+	1.14652i	0.630873	+	0.0705637i
$265$	−5.08957	−	14.4593i	−0.312650	−	0.888230i
$266$	30.9634	−	16.3754i	1.89849	−	1.00404i
$267$	−18.3633	−	18.3633i	−1.12382	−	1.12382i
$268$	−5.28552	−	27.8521i	−0.322864	−	1.70134i
$269$			22.0676i			1.34548i	0.739878	+	0.672741i	$0.234883\pi$
$269$			22.0676i			1.34548i	−0.739878	+	0.672741i	$0.765117\pi$
$270$	−36.8590	+	1.45741i	−2.24317	+	0.0886951i
$271$		−	24.9607i		−	1.51626i	−0.652106	−	0.758128i	$-0.726114\pi$
$271$		−	24.9607i		−	1.51626i	0.652106	−	0.758128i	$-0.273886\pi$
$272$	5.73769	+	2.49594i	0.347898	+	0.151338i
$273$	15.1044	+	15.1044i	0.914157	+	0.914157i
$274$	9.65114	+	18.2489i	0.583047	+	1.10246i
$275$	4.55471	−	3.65989i	0.274659	−	0.220700i
$276$	−17.1979	+	25.2540i	−1.03519	+	1.52011i
$277$	11.1796	−	11.1796i	0.671715	−	0.671715i	−0.286397	−	0.958111i	$-0.592457\pi$
$277$	11.1796	−	11.1796i	0.671715	−	0.671715i	0.958111	+	0.286397i	$0.0924575\pi$
$278$	−7.65479	+	24.8401i	−0.459104	+	1.48981i
$279$	−71.0615			−4.25434
$280$	−18.8523	−	11.7758i	−1.12664	−	0.703740i
$281$	−10.3845			−0.619486			−0.309743	−	0.950820i	$-0.600243\pi$
$281$	−10.3845			−0.619486			−0.309743	+	0.950820i	$0.600243\pi$
$282$	13.6490	−	44.2916i	0.812787	−	2.63753i
$283$	4.98737	−	4.98737i	0.296468	−	0.296468i	−0.543161	−	0.839629i	$-0.682773\pi$
$283$	4.98737	−	4.98737i	0.296468	−	0.296468i	0.839629	+	0.543161i	$0.182773\pi$
$284$	9.06530	−	13.3118i	0.537926	−	0.789911i
$285$	−46.3849	+	16.3271i	−2.74760	+	0.967134i
$286$	1.50480	+	2.84536i	0.0889809	+	0.168250i
$287$	−2.48515	−	2.48515i	−0.146694	−	0.146694i
$288$	2.89986	+	38.0058i	0.170876	+	2.23951i
$289$			14.5531i			0.856063i
$290$	7.11665	+	6.57527i	0.417904	+	0.386113i
$291$			19.2223i			1.12683i
$292$	3.04320	+	16.0362i	0.178090	+	0.938446i
$293$	7.37098	+	7.37098i	0.430617	+	0.430617i	0.888838	−	0.458221i	$-0.151513\pi$
$293$	7.37098	+	7.37098i	0.430617	+	0.430617i	−0.458221	+	0.888838i	$0.651513\pi$
$294$	20.8790	−	11.0421i	1.21769	−	0.643990i
$295$	−16.4953	−	7.90619i	−0.960395	−	0.460316i
$296$	−0.229381	+	2.05078i	−0.0133325	+	0.119199i
$297$	9.63896	−	9.63896i	0.559309	−	0.559309i
$298$	28.7976	+	8.87435i	1.66820	+	0.514077i
$299$	−9.53480			−0.551412
$300$	23.7392	+	20.2547i	1.37059	+	1.16941i
$301$	−22.5191			−1.29798
$302$	−3.25106	−	1.00186i	−0.187078	−	0.0576504i
$303$	−1.78146	+	1.78146i	−0.102342	+	0.102342i
$304$	10.3270	+	26.2292i	0.592293	+	1.50435i
$305$	13.8606	+	6.64337i	0.793656	+	0.380398i
$306$	13.1767	−	6.96865i	0.753262	−	0.398371i
$307$	−23.5573	−	23.5573i	−1.34448	−	1.34448i	−0.891537	−	0.452948i	$-0.850372\pi$
$307$	−23.5573	−	23.5573i	−1.34448	−	1.34448i	−0.452948	−	0.891537i	$-0.649628\pi$
$308$	8.07008	−	1.53147i	0.459836	−	0.0872634i
$309$			31.1017i			1.76931i
$310$	24.4955	+	22.6321i	1.39125	+	1.28542i
$311$			1.12898i			0.0640187i	0.999488	+	0.0320094i	$0.0101906\pi$
$311$			1.12898i			0.0640187i	−0.999488	+	0.0320094i	$0.989809\pi$
$312$	−13.4315	+	10.7292i	−0.760411	+	0.607419i
$313$	−16.1792	−	16.1792i	−0.914504	−	0.914504i	0.0821186	−	0.996623i	$-0.473831\pi$
$313$	−16.1792	−	16.1792i	−0.914504	−	0.914504i	−0.996623	+	0.0821186i	$0.973831\pi$
$314$	−5.48756	−	10.3762i	−0.309681	−	0.585561i
$315$	−49.9487	+	17.5815i	−2.81429	+	0.990608i
$316$	−0.556517	−	0.378985i	−0.0313065	−	0.0213196i
$317$	−5.09193	+	5.09193i	−0.285991	+	0.285991i	−0.835493	−	0.549502i	$-0.814818\pi$
$317$	−5.09193	+	5.09193i	−0.285991	+	0.285991i	0.549502	+	0.835493i	$0.314818\pi$
$318$	−8.90960	+	28.9120i	−0.499626	+	1.62130i
$319$	−3.58056			−0.200473
$320$	11.1047	−	14.0245i	0.620771	−	0.783992i
$321$	−15.5751			−0.869315
$322$	−7.16575	+	23.2531i	−0.399332	+	1.29585i
$323$	7.79496	−	7.79496i	0.433723	−	0.433723i
$324$	26.7590	+	18.2228i	1.48661	+	1.01238i
$325$	−1.05455	+	9.68103i	−0.0584959	+	0.537007i
$326$	−9.66733	−	18.2795i	−0.535424	−	1.01241i
$327$	−26.6797	−	26.6797i	−1.47539	−	1.47539i
$328$	2.20992	−	1.76529i	0.122022	−	0.0974718i
$329$		−	36.9095i		−	2.03489i
$330$	−11.5228	+	0.455615i	−0.634312	+	0.0250808i
$331$		−	25.3181i		−	1.39161i	−0.718231	−	0.695804i	$-0.755048\pi$
$331$		−	25.3181i		−	1.39161i	0.718231	−	0.695804i	$-0.244952\pi$
$332$	−14.3350	+	2.72037i	−0.786736	+	0.149300i
$333$	3.47610	+	3.47610i	0.190489	+	0.190489i
$334$	−18.9179	+	10.0049i	−1.03514	+	0.547446i
$335$	10.5236	+	29.8973i	0.574966	+	1.63346i
$336$	16.0716	+	40.8197i	0.876776	+	2.22690i
$337$	2.04612	−	2.04612i	0.111460	−	0.111460i	−0.649177	−	0.760637i	$-0.724887\pi$
$337$	2.04612	−	2.04612i	0.111460	−	0.111460i	0.760637	+	0.649177i	$0.224887\pi$
$338$	12.4427	+	3.83438i	0.676795	+	0.208563i
$339$	33.7996			1.83574
$340$	−6.76154	−	1.79444i	−0.366696	−	0.0973171i
$341$	−12.3243			−0.667398
$342$	64.1754	+	19.7765i	3.47021	+	1.06939i
$343$	−4.09564	+	4.09564i	−0.221144	+	0.221144i
$344$	2.01450	−	18.0106i	0.108614	−	0.971065i
$345$	14.7646	−	30.8046i	0.794900	−	1.65846i
$346$	−14.7242	+	7.78707i	−0.791579	+	0.418636i
$347$	6.71409	+	6.71409i	0.360431	+	0.360431i	0.863972	−	0.503540i	$-0.167969\pi$
$347$	6.71409	+	6.71409i	0.360431	+	0.360431i	−0.503540	+	0.863972i	$0.667969\pi$
$348$	−3.56535	−	18.7876i	−0.191123	−	1.00712i
$349$		−	19.3438i		−	1.03545i	−0.855547	−	0.517725i	$-0.826779\pi$
$349$		−	19.3438i		−	1.03545i	0.855547	−	0.517725i	$-0.173221\pi$
$350$	22.8172	+	9.84745i	1.21963	+	0.526368i
$351$			22.7193i			1.21267i
$352$	0.502927	+	6.59139i	0.0268061	+	0.351322i
$353$	−16.7495	−	16.7495i	−0.891487	−	0.891487i	0.103176	−	0.994663i	$-0.467100\pi$
$353$	−16.7495	−	16.7495i	−0.891487	−	0.891487i	−0.994663	+	0.103176i	$0.967100\pi$
$354$	16.8780	+	31.9138i	0.897054	+	1.69620i
$355$	−7.78267	+	16.2376i	−0.413061	+	0.861803i
$356$	9.36850	−	13.7571i	0.496529	−	0.729122i
$357$	12.1311	−	12.1311i	0.642045	−	0.642045i
$358$	−9.81644	+	31.8547i	−0.518815	+	1.68358i
$359$	−6.70187			−0.353711			−0.176856	−	0.984237i	$-0.556593\pi$
$359$	−6.70187			−0.353711			−0.176856	+	0.984237i	$0.556593\pi$
$360$	−9.59330	−	41.5214i	−0.505611	−	2.18837i
$361$	30.6636			1.61387
$362$	3.25320	−	10.5568i	0.170985	−	0.554852i
$363$	−21.2591	+	21.2591i	−1.11582	+	1.11582i
$364$	−7.70586	+	11.3156i	−0.403897	+	0.593097i
$365$	−6.05909	−	17.2137i	−0.317147	−	0.901007i
$366$	−14.1821	−	26.8163i	−0.741312	−	1.40171i
$367$	−19.1222	−	19.1222i	−0.998169	−	0.998169i	0.00182896	−	0.999998i	$-0.499418\pi$
$367$	−19.1222	−	19.1222i	−0.998169	−	0.998169i	−0.999998	+	0.00182896i	$0.999418\pi$
$368$	−17.9567	−	7.81128i	−0.936055	−	0.407191i
$369$		−	6.73806i		−	0.350769i
$370$	−0.0911532	−	2.30533i	−0.00473883	−	0.119849i
$371$			24.0932i			1.25086i
$372$	−12.2719	−	64.6670i	−0.636270	−	3.35283i
$373$	−15.6103	−	15.6103i	−0.808273	−	0.808273i	0.176099	−	0.984372i	$-0.443652\pi$
$373$	−15.6103	−	15.6103i	−0.808273	−	0.808273i	−0.984372	+	0.176099i	$0.943652\pi$
$374$	2.28526	−	1.20858i	0.118168	−	0.0624944i
$375$	−29.6441	−	18.3980i	−1.53081	−	0.950070i
$376$	29.5199	+	3.30183i	1.52237	+	0.170279i
$377$	4.21975	−	4.21975i	0.217328	−	0.217328i
$378$	55.4071	+	17.0744i	2.84983	+	0.878213i
$379$	9.79958			0.503370			0.251685	−	0.967809i	$-0.419015\pi$
$379$	9.79958			0.503370			0.251685	+	0.967809i	$0.419015\pi$
$380$	−15.8233	−	27.2561i	−0.811718	−	1.39821i
$381$	4.29145			0.219858
$382$	−19.2331	−	5.92694i	−0.984054	−	0.303249i
$383$	−1.83690	+	1.83690i	−0.0938611	+	0.0938611i	−0.752478	−	0.658617i	$-0.771142\pi$
$383$	−1.83690	+	1.83690i	−0.0938611	+	0.0938611i	0.658617	+	0.752478i	$0.271142\pi$
$384$	−34.0850	+	9.20230i	−1.73939	+	0.469603i
$385$	−8.66268	+	3.04919i	−0.441491	+	0.155401i
$386$	−9.19086	+	4.86069i	−0.467802	+	0.247403i
$387$	−30.5283	−	30.5283i	−1.55184	−	1.55184i
$388$	−12.1036	+	2.29692i	−0.614470	+	0.116608i
$389$		−	9.12214i		−	0.462511i	−0.972893	−	0.231256i	$-0.925717\pi$
$389$		−	9.12214i		−	0.462511i	0.972893	−	0.231256i	$-0.0742833\pi$
$390$	13.0429	−	14.1168i	0.660453	−	0.714832i
$391$			7.65789i			0.387276i
$392$	9.44776	+	11.8274i	0.477184	+	0.597374i
$393$	16.0191	+	16.0191i	0.808056	+	0.808056i
$394$	−0.239802	−	0.453431i	−0.0120811	−	0.0228435i
$395$	0.678833	+	0.325364i	0.0341558	+	0.0163708i
$396$	13.0165	+	8.86417i	0.654103	+	0.445441i
$397$	6.93346	−	6.93346i	0.347980	−	0.347980i	−0.511377	−	0.859357i	$-0.670864\pi$
$397$	6.93346	−	6.93346i	0.347980	−	0.347980i	0.859357	+	0.511377i	$0.170864\pi$
$398$	0.463556	−	1.50426i	0.0232360	−	0.0754016i
$399$	77.2899			3.86934
$400$	−9.91708	+	17.3681i	−0.495854	+	0.868406i
$401$	6.22557			0.310890			0.155445	−	0.987845i	$-0.450319\pi$
$401$	6.22557			0.310890			0.155445	+	0.987845i	$0.450319\pi$
$402$	18.4222	−	59.7808i	0.918817	−	2.98160i
$403$	14.5244	−	14.5244i	0.723511	−	0.723511i
$404$	−1.33460	−	0.908854i	−0.0663986	−	0.0452172i
$405$	−32.6403	−	15.6445i	−1.62191	−	0.777380i
$406$	−7.11968	−	13.4623i	−0.353344	−	0.668121i
$407$	0.602866	+	0.602866i	0.0298829	+	0.0298829i
$408$	8.61713	+	10.7876i	0.426611	+	0.534064i
$409$			9.55377i			0.472403i	0.971704	+	0.236202i	$0.0759026\pi$
$409$			9.55377i			0.472403i	−0.971704	+	0.236202i	$0.924097\pi$
$410$	−2.14598	+	2.32267i	−0.105982	+	0.114708i
$411$			45.5524i			2.24693i
$412$	−19.5837	+	3.71642i	−0.964821	+	0.183095i
$413$	20.3298	+	20.3298i	1.00036	+	1.00036i
$414$	−41.2378	+	21.8091i	−2.02673	+	1.07186i
$415$	15.3877	−	5.41633i	0.755350	−	0.265877i
$416$	−8.36076	−	7.17535i	−0.409920	−	0.351801i
$417$	−40.5564	+	40.5564i	−1.98606	+	1.98606i
$418$	11.1300	+	3.42986i	0.544388	+	0.167760i
$419$	−22.6553			−1.10678			−0.553392	−	0.832921i	$-0.686667\pi$
$419$	−22.6553			−1.10678			−0.553392	+	0.832921i	$0.686667\pi$
$420$	−24.6253	−	42.4179i	−1.20159	−	2.06978i
$421$	32.7772			1.59746			0.798731	−	0.601689i	$-0.205505\pi$
$421$	32.7772			1.59746			0.798731	+	0.601689i	$0.205505\pi$
$422$	18.2182	+	5.61416i	0.886846	+	0.273293i
$423$	50.0368	−	50.0368i	2.43287	−	2.43287i
$424$	−19.2696	−	2.15532i	−0.935813	−	0.104671i
$425$	7.77533	+	0.846963i	0.377159	+	0.0410837i
$426$	31.4152	−	16.6143i	1.52207	−	0.804965i
$427$	−17.0826	−	17.0826i	−0.826686	−	0.826686i
$428$	−1.86110	−	9.80710i	−0.0899598	−	0.474044i
$429$			7.10251i			0.342913i
$430$	0.800537	+	20.2462i	0.0386053	+	0.976358i
$431$			7.88569i			0.379840i	0.981800	+	0.189920i	$0.0608229\pi$
$431$			7.88569i			0.379840i	−0.981800	+	0.189920i	$0.939177\pi$
$432$	−18.6126	+	42.7867i	−0.895497	+	2.05858i
$433$	−17.7773	−	17.7773i	−0.854322	−	0.854322i	0.136340	−	0.990662i	$-0.456466\pi$
$433$	−17.7773	−	17.7773i	−0.854322	−	0.854322i	−0.990662	+	0.136340i	$0.956466\pi$
$434$	−24.5059	−	46.3371i	−1.17632	−	2.22425i
$435$	7.09870	+	20.1672i	0.340357	+	0.966945i
$436$	13.6113	−	19.9874i	0.651865	−	0.957222i
$437$	−24.3951	+	24.3951i	−1.16698	+	1.16698i
$438$	−10.6068	+	34.4195i	−0.506813	+	1.64463i
$439$	−26.2772			−1.25414			−0.627070	−	0.778963i	$-0.715746\pi$
$439$	−26.2772			−1.25414			−0.627070	+	0.778963i	$0.715746\pi$
$440$	−1.66378	−	7.20112i	−0.0793176	−	0.343300i
$441$	36.0618			1.71723
$442$	−1.26887	+	4.11754i	−0.0603542	+	0.195852i
$443$	10.4659	−	10.4659i	0.497250	−	0.497250i	−0.413331	−	0.910581i	$-0.635635\pi$
$443$	10.4659	−	10.4659i	0.497250	−	0.497250i	0.910581	+	0.413331i	$0.135635\pi$
$444$	−2.56300	+	3.76361i	−0.121635	+	0.178613i
$445$	−8.04297	+	16.7807i	−0.381273	+	0.795482i
$446$	−0.453124	−	0.856790i	−0.0214560	−	0.0405702i
$447$	47.0178	+	47.0178i	2.22387	+	2.22387i
$448$	−23.7824	+	14.9974i	−1.12361	+	0.708561i
$449$			14.8142i			0.699127i	0.936913	+	0.349564i	$0.113670\pi$
$449$			14.8142i			0.699127i	−0.936913	+	0.349564i	$0.886330\pi$
$450$	17.5827	+	44.2823i	0.828854	+	2.08749i
$451$		−	1.16859i		−	0.0550268i
$452$	4.03880	+	21.2825i	0.189969	+	1.00104i
$453$	−5.30801	−	5.30801i	−0.249392	−	0.249392i
$454$	30.9250	−	16.3550i	1.45138	−	0.767580i
$455$	6.61558	−	13.8026i	0.310143	−	0.647077i
$456$	−6.91416	+	61.8159i	−0.323785	+	2.89480i
$457$	−5.81837	+	5.81837i	−0.272172	+	0.272172i	−0.829974	−	0.557802i	$-0.811645\pi$
$457$	−5.81837	+	5.81837i	−0.272172	+	0.272172i	0.557802	+	0.829974i	$0.311645\pi$
$458$	−31.2429	−	9.62789i	−1.45988	−	0.449882i
$459$	18.2471			0.851699
$460$	21.1609	+	5.61587i	0.986632	+	0.261841i
$461$	3.11512			0.145086			0.0725428	−	0.997365i	$-0.476889\pi$
$461$	3.11512			0.145086			0.0725428	+	0.997365i	$0.476889\pi$
$462$	17.3214	+	5.33780i	0.805862	+	0.248337i
$463$	6.95566	−	6.95566i	0.323257	−	0.323257i	−0.526758	−	0.850015i	$-0.676593\pi$
$463$	6.95566	−	6.95566i	0.323257	−	0.323257i	0.850015	+	0.526758i	$0.176593\pi$
$464$	11.4039	−	4.48996i	0.529414	−	0.208441i
$465$	24.4337	+	69.4156i	1.13309	+	3.21907i
$466$	−12.9801	+	6.86466i	−0.601290	+	0.317999i
$467$	−4.87643	−	4.87643i	−0.225654	−	0.225654i	0.585220	−	0.810874i	$-0.301008\pi$
$467$	−4.87643	−	4.87643i	−0.225654	−	0.225654i	−0.810874	+	0.585220i	$0.801008\pi$
$468$	−25.7867	+	4.89356i	−1.19199	+	0.226205i
$469$		−	49.8171i		−	2.30034i
$470$	−33.1842	+	1.31211i	−1.53067	+	0.0605229i
$471$		−	25.9007i		−	1.19344i
$472$	−18.0783	+	14.4410i	−0.832120	+	0.664699i
$473$	−5.29456	−	5.29456i	−0.243444	−	0.243444i
$474$	−0.694580	−	1.31335i	−0.0319031	−	0.0603242i
$475$	22.0711	+	27.4673i	1.01269	+	1.26029i
$476$	9.08811	+	6.18897i	0.416553	+	0.283671i
$477$	−32.6623	+	32.6623i	−1.49550	+	1.49550i
$478$	2.57932	−	8.37000i	0.117975	−	0.382835i
$479$	27.9650			1.27775			0.638876	−	0.769310i	$-0.279400\pi$
$479$	27.9650			1.27775			0.638876	+	0.769310i	$0.279400\pi$
$480$	36.1284	−	15.9006i	1.64903	−	0.725758i
$481$	−1.42097			−0.0647908
$482$	−8.45204	+	27.4272i	−0.384980	+	1.24927i
$483$	−37.9654	+	37.9654i	−1.72748	+	1.72748i
$484$	−15.9265	−	10.8459i	−0.723931	−	0.492994i
$485$	12.9924	−	4.57323i	0.589956	−	0.207660i
$486$	10.2605	+	19.4010i	0.465424	+	0.880048i
$487$	−8.16428	−	8.16428i	−0.369959	−	0.369959i	0.497503	−	0.867462i	$-0.334250\pi$
$487$	−8.16428	−	8.16428i	−0.369959	−	0.369959i	−0.867462	+	0.497503i	$0.834250\pi$
$488$	15.1907	−	12.1344i	0.687651	−	0.549298i
$489$		−	45.6288i		−	2.06340i
$490$	−12.4308	−	11.4852i	−0.561567	−	0.518847i
$491$			18.5654i			0.837843i	0.908022	+	0.418922i	$0.137592\pi$
$491$			18.5654i			0.837843i	−0.908022	+	0.418922i	$0.862408\pi$
$492$	6.13174	−	1.16363i	0.276440	−	0.0524603i
$493$	−3.38909	−	3.38909i	−0.152637	−	0.152637i
$494$	−17.1591	+	9.07477i	−0.772023	+	0.408293i
$495$	−15.8774	−	7.61000i	−0.713634	−	0.342044i
$496$	39.2523	−	15.4545i	1.76248	−	0.693926i
$497$	20.0122	−	20.0122i	0.897670	−	0.897670i
$498$	−30.7682	−	9.48162i	−1.37876	−	0.424881i
$499$	−24.1427			−1.08078			−0.540388	−	0.841416i	$-0.681723\pi$
$499$	−24.1427			−1.08078			−0.540388	+	0.841416i	$0.681723\pi$
$500$	8.04240	−	20.8643i	0.359667	−	0.933081i
$501$	−47.2223			−2.10974
$502$	9.83511	+	3.03082i	0.438962	+	0.135272i
$503$	−12.5723	+	12.5723i	−0.560572	+	0.560572i	−0.929470	−	0.368898i	$-0.879735\pi$
$503$	−12.5723	+	12.5723i	−0.560572	+	0.560572i	0.368898	+	0.929470i	$0.379735\pi$
$504$	−7.44539	+	66.5653i	−0.331644	+	2.96505i
$505$	1.62793	+	0.780263i	0.0724417	+	0.0347212i
$506$	−7.15193	+	3.78238i	−0.317942	+	0.168147i
$507$	20.3152	+	20.3152i	0.902231	+	0.902231i
$508$	0.512797	+	2.70219i	0.0227517	+	0.119890i
$509$			37.3491i			1.65547i	0.561120	+	0.827734i	$0.310371\pi$
$509$			37.3491i			1.65547i	−0.561120	+	0.827734i	$0.689629\pi$
$510$	−11.3379	−	10.4754i	−0.502052	−	0.463859i
$511$			28.6828i			1.26885i
$512$	−9.86729	−	20.3626i	−0.436077	−	0.899909i
$513$	58.1281	+	58.1281i	2.56642	+	2.56642i
$514$	−5.46669	−	10.3367i	−0.241125	−	0.455933i
$515$	21.0218	−	7.39949i	0.926330	−	0.326061i
$516$	22.5091	−	33.0533i	0.990910	−	1.45509i
$517$	8.67796	−	8.67796i	0.381656	−	0.381656i
$518$	−1.06791	+	3.46542i	−0.0469214	+	0.152262i
$519$	−36.7542			−1.61333
$520$	10.4474	+	6.52584i	0.458150	+	0.286177i
$521$	33.2508			1.45674			0.728372	−	0.685182i	$-0.240277\pi$
$521$	33.2508			1.45674			0.728372	+	0.685182i	$0.240277\pi$
$522$	8.59842	−	27.9022i	0.376343	−	1.22125i
$523$	9.43538	−	9.43538i	0.412580	−	0.412580i	−0.470056	−	0.882636i	$-0.655766\pi$
$523$	9.43538	−	9.43538i	0.412580	−	0.412580i	0.882636	+	0.470056i	$0.155766\pi$
$524$	−8.17254	+	12.0009i	−0.357019	+	0.524260i
$525$	34.3487	+	42.7466i	1.49910	+	1.86561i
$526$	9.23457	+	17.4612i	0.402646	+	0.761346i
$527$	−11.6653	−	11.6653i	−0.508147	−	0.508147i
$528$	−5.81866	+	13.3760i	−0.253224	+	0.582115i
$529$		−	0.966102i		−	0.0420045i
$530$	21.6614	−	0.856497i	0.940913	−	0.0372038i
$531$			55.1207i			2.39204i
$532$	9.23557	+	48.6670i	0.400413	+	2.10998i
$533$	1.37720	+	1.37720i	0.0596533	+	0.0596533i
$534$	32.4659	−	17.1700i	1.40494	−	0.743018i
$535$	3.70550	+	10.5272i	0.160203	+	0.455133i
$536$	39.8433	+	4.45651i	1.72097	+	0.192492i
$537$	−52.0092	+	52.0092i	−2.24436	+	2.24436i
$538$	−29.8242	−	9.19072i	−1.28581	−	0.396240i
$539$	6.25425			0.269390
$540$	13.3814	−	50.4218i	0.575843	−	2.16981i
$541$	8.69130			0.373668			0.186834	−	0.982391i	$-0.440177\pi$
$541$	8.69130			0.373668			0.186834	+	0.982391i	$0.440177\pi$
$542$	33.7343	+	10.3957i	1.44901	+	0.446532i
$543$	17.2360	−	17.2360i	0.739669	−	0.739669i
$544$	−5.76289	+	6.71496i	−0.247082	+	0.287901i
$545$	−11.6855	+	24.3804i	−0.500552	+	1.04434i
$546$	−26.7042	+	14.1228i	−1.14283	+	0.604400i
$547$	−10.6662	−	10.6662i	−0.456055	−	0.456055i	0.441303	−	0.897358i	$-0.354516\pi$
$547$	−10.6662	−	10.6662i	−0.456055	−	0.456055i	−0.897358	+	0.441303i	$0.854516\pi$
$548$	−28.6828	+	5.44317i	−1.22527	+	0.232521i
$549$		−	46.3166i		−	1.97674i
$550$	3.04939	+	7.67995i	0.130026	+	0.327474i
$551$		−	21.5927i		−	0.919881i
$552$	−26.9681	−	33.7607i	−1.14784	−	1.43695i
$553$	−0.836633	−	0.836633i	−0.0355773	−	0.0355773i
$554$	10.4531	+	19.7652i	0.444108	+	0.839743i
$555$	2.20037	−	4.59081i	0.0934006	−	0.194869i
$556$	−30.3832	−	20.6909i	−1.28854	−	0.877488i
$557$	18.6251	−	18.6251i	0.789172	−	0.789172i	−0.192186	−	0.981359i	$-0.561558\pi$
$557$	18.6251	−	18.6251i	0.789172	−	0.789172i	0.981359	+	0.192186i	$0.0615577\pi$
$558$	29.5958	−	96.0394i	1.25289	−	4.06567i
$559$	12.4795			0.527825
$560$	23.7666	−	20.5744i	1.00432	−	0.869427i
$561$	5.70439			0.240840
$562$	4.32494	−	14.0346i	0.182436	−	0.592013i
$563$	−2.21476	+	2.21476i	−0.0933412	+	0.0933412i	−0.752236	−	0.658894i	$-0.771024\pi$
$563$	−2.21476	+	2.21476i	−0.0933412	+	0.0933412i	0.658894	+	0.752236i	$0.271024\pi$
$564$	54.1754	+	36.8932i	2.28120	+	1.55348i
$565$	−8.04136	−	22.8453i	−0.338303	−	0.961109i
$566$	4.66327	+	8.81756i	0.196012	+	0.370630i
$567$	40.2278	+	40.2278i	1.68941	+	1.68941i
$568$	14.2154	+	17.7958i	0.596463	+	0.746697i
$569$			17.8205i			0.747076i	0.927615	+	0.373538i	$0.121855\pi$
$569$			17.8205i			0.747076i	−0.927615	+	0.373538i	$0.878145\pi$
$570$	−2.74760	−	69.4890i	−0.115084	−	2.91057i
$571$			11.5700i			0.484190i	0.970252	+	0.242095i	$0.0778346\pi$
$571$			11.5700i			0.484190i	−0.970252	+	0.242095i	$0.922165\pi$
$572$	−4.47222	+	0.848697i	−0.186993	+	0.0354858i
$573$	−31.4019	−	31.4019i	−1.31184	−	1.31184i
$574$	4.39369	−	2.32366i	0.183389	−	0.0969875i
$575$	−24.3337	−	2.65065i	−1.01478	−	0.110540i
$576$	−52.5724	−	11.9095i	−2.19052	−	0.496230i
$577$	19.4335	−	19.4335i	0.809028	−	0.809028i	−0.175459	−	0.984487i	$-0.556141\pi$
$577$	19.4335	−	19.4335i	0.809028	−	0.809028i	0.984487	+	0.175459i	$0.0561409\pi$
$578$	−19.6684	−	6.06108i	−0.818099	−	0.252108i
$579$	−22.9420			−0.953435
$580$	−11.8504	+	6.87965i	−0.492061	+	0.285662i
$581$	−25.6400			−1.06373
$582$	−25.9789	−	8.00572i	−1.07686	−	0.331848i
$583$	−5.66467	+	5.66467i	−0.234607	+	0.234607i
$584$	−22.9403	−	2.56589i	−0.949275	−	0.106177i
$585$	27.6802	−	9.74321i	1.14444	−	0.402832i
$586$	−13.0317	+	6.89199i	−0.538336	+	0.284705i
$587$	−11.3588	−	11.3588i	−0.468826	−	0.468826i	0.432708	−	0.901534i	$-0.357558\pi$
$587$	−11.3588	−	11.3588i	−0.468826	−	0.468826i	−0.901534	+	0.432708i	$0.857558\pi$
$588$	6.22767	+	32.8168i	0.256825	+	1.35334i
$589$		−	74.3222i		−	3.06239i
$590$	17.5552	−	19.0006i	0.722735	−	0.782242i
$591$		−	1.13184i		−	0.0465578i
$592$	−2.67608	−	1.16412i	−0.109986	−	0.0478449i
$593$	11.3896	+	11.3896i	0.467715	+	0.467715i	0.901173	−	0.433459i	$-0.142707\pi$
$593$	11.3896	+	11.3896i	0.467715	+	0.467715i	−0.433459	+	0.901173i	$0.642707\pi$
$594$	9.01258	+	17.0415i	0.369791	+	0.699220i
$595$	−11.0856	−	5.31331i	−0.454465	−	0.217824i
$596$	−23.9873	+	35.2239i	−0.982559	+	1.44283i
$597$	2.45600	−	2.45600i	0.100517	−	0.100517i
$598$	3.97106	−	12.8863i	0.162389	−	0.526958i
$599$	−38.6463			−1.57904			−0.789522	−	0.613723i	$-0.789671\pi$
$599$	−38.6463			−1.57904			−0.789522	+	0.613723i	$0.789671\pi$
$600$	−37.2612	+	23.6478i	−1.52118	+	0.965417i
$601$	−16.6688			−0.679934			−0.339967	−	0.940437i	$-0.610416\pi$
$601$	−16.6688			−0.679934			−0.339967	+	0.940437i	$0.610416\pi$
$602$	9.37876	−	30.4344i	0.382250	−	1.24042i
$603$	67.5352	−	67.5352i	2.75025	−	2.75025i
$604$	2.70801	−	3.97655i	0.110187	−	0.161803i
$605$	19.4270	+	9.31132i	0.789818	+	0.378559i
$606$	−1.66569	−	3.14958i	−0.0676640	−	0.127943i
$607$	14.1157	+	14.1157i	0.572938	+	0.572938i	0.932948	−	0.360011i	$-0.117227\pi$
$607$	14.1157	+	14.1157i	0.572938	+	0.572938i	−0.360011	+	0.932948i	$0.617227\pi$
$608$	−39.7497	+	3.03292i	−1.61206	+	0.123001i
$609$		−	33.6041i		−	1.36171i
$610$	−14.7512	+	15.9657i	−0.597258	+	0.646433i
$611$			20.4542i			0.827489i
$612$	3.93027	+	20.7106i	0.158872	+	0.837176i
$613$	−7.45901	−	7.45901i	−0.301266	−	0.301266i	0.540243	−	0.841509i	$-0.318332\pi$
$613$	−7.45901	−	7.45901i	−0.301266	−	0.301266i	−0.841509	+	0.540243i	$0.818332\pi$
$614$	41.6487	−	22.0264i	1.68081	−	0.888914i
$615$	−6.58200	+	2.31681i	−0.265412	+	0.0934228i
$616$	−1.29126	+	11.5445i	−0.0520265	+	0.465142i
$617$	−18.9558	+	18.9558i	−0.763132	+	0.763132i	−0.976887	−	0.213756i	$-0.931430\pi$
$617$	−18.9558	+	18.9558i	−0.763132	+	0.763132i	0.213756	+	0.976887i	$0.431430\pi$
$618$	−42.0338	−	12.9533i	−1.69085	−	0.521057i
$619$	43.3562			1.74263			0.871317	−	0.490720i	$-0.163266\pi$
$619$	43.3562			1.74263			0.871317	+	0.490720i	$0.163266\pi$
$620$	−40.7891	+	23.6798i	−1.63813	+	0.951002i
$621$	−57.1059			−2.29158
$622$	−1.52582	−	0.470200i	−0.0611797	−	0.0188533i
$623$	20.6815	−	20.6815i	0.828588	−	0.828588i
$624$	−8.90643	−	22.6212i	−0.356542	−	0.905572i
$625$	−5.38261	+	24.4137i	−0.215304	+	0.976547i
$626$	28.6045	−	15.1278i	1.14327	−	0.604630i
$627$	18.1720	+	18.1720i	0.725720	+	0.725720i
$628$	16.3088	−	3.09494i	0.650793	−	0.123502i
$629$			1.14126i			0.0455048i
$630$	−2.95871	−	74.8279i	−0.117878	−	2.98121i
$631$		−	2.64123i		−	0.105146i	−0.998617	−	0.0525728i	$-0.983258\pi$
$631$		−	2.64123i		−	0.105146i	0.998617	−	0.0525728i	$-0.0167421\pi$
$632$	0.743976	−	0.594290i	0.0295938	−	0.0236396i
$633$	29.7448	+	29.7448i	1.18225	+	1.18225i
$634$	−4.76103	−	9.00241i	−0.189085	−	0.357532i
$635$	−1.02099	−	2.90061i	−0.0405168	−	0.115107i
$636$	−35.3638	−	24.0826i	−1.40227	−	0.954937i
$637$	−7.37073	+	7.37073i	−0.292039	+	0.292039i
$638$	1.49124	−	4.83912i	0.0590386	−	0.191583i
$639$	54.2596			2.14648
$640$	14.3291	+	20.8489i	0.566409	+	0.824124i
$641$	2.72244			0.107530			0.0537649	−	0.998554i	$-0.482878\pi$
$641$	2.72244			0.107530			0.0537649	+	0.998554i	$0.482878\pi$
$642$	6.48671	−	21.0496i	0.256010	−	0.830763i
$643$	−20.3630	+	20.3630i	−0.803038	+	0.803038i	−0.983569	−	0.180531i	$-0.942218\pi$
$643$	−20.3630	+	20.3630i	−0.803038	+	0.803038i	0.180531	+	0.983569i	$0.442218\pi$
$644$	−28.4421	−	19.3690i	−1.12078	−	0.763245i
$645$	−19.3244	+	40.3180i	−0.760897	+	1.58752i
$646$	7.28841	+	13.7813i	0.286759	+	0.542219i
$647$	26.2467	+	26.2467i	1.03187	+	1.03187i	0.999475	+	0.0323902i	$0.0103119\pi$
$647$	26.2467	+	26.2467i	1.03187	+	1.03187i	0.0323902	+	0.999475i	$0.489688\pi$
$648$	−35.7726	+	28.5752i	−1.40528	+	1.12254i
$649$			9.55967i			0.375250i
$650$	−12.6447	−	5.45719i	−0.495965	−	0.214048i
$651$		−	115.665i		−	4.53328i
$652$	28.7309	−	5.45230i	1.12519	−	0.213528i
$653$	−12.8045	−	12.8045i	−0.501077	−	0.501077i	0.410696	−	0.911772i	$-0.365286\pi$
$653$	−12.8045	−	12.8045i	−0.501077	−	0.501077i	−0.911772	+	0.410696i	$0.865286\pi$
$654$	47.1692	−	24.9460i	1.84446	−	0.975465i
$655$	7.01622	−	14.6385i	0.274147	−	0.571974i
$656$	1.46539	+	3.72191i	0.0572140	+	0.145316i
$657$	−38.8842	+	38.8842i	−1.51702	+	1.51702i
$658$	49.8830	+	15.3721i	1.94464	+	0.599267i
$659$	47.8782			1.86507			0.932535	−	0.361080i	$-0.117592\pi$
$659$	47.8782			1.86507			0.932535	+	0.361080i	$0.117592\pi$
$660$	4.18328	−	15.7628i	0.162834	−	0.613568i
$661$	−36.3419			−1.41353			−0.706767	−	0.707446i	$-0.749847\pi$
$661$	−36.3419			−1.41353			−0.706767	+	0.707446i	$0.749847\pi$
$662$	34.2173	+	10.5445i	1.32989	+	0.409824i
$663$	−6.72271	+	6.72271i	−0.261088	+	0.261088i
$664$	2.29369	−	20.5067i	0.0890126	−	0.795815i
$665$	−18.3883	−	52.2406i	−0.713067	−	2.02580i
$666$	−6.14567	+	3.25021i	−0.238140	+	0.125943i
$667$	10.6065	+	10.6065i	0.410685	+	0.410685i
$668$	−5.64271	−	29.7343i	−0.218323	−	1.15046i
$669$		−	2.13870i		−	0.0826867i
$670$	−44.7890	+	1.77096i	−1.73035	+	0.0684183i
$671$		−	8.03275i		−	0.310101i
$672$	−61.8612	+	4.72004i	−2.38635	+	0.182080i
$673$	−10.3404	−	10.3404i	−0.398592	−	0.398592i	0.479144	−	0.877736i	$-0.340947\pi$
$673$	−10.3404	−	10.3404i	−0.398592	−	0.398592i	−0.877736	+	0.479144i	$0.840947\pi$
$674$	1.91316	+	3.61750i	0.0736921	+	0.139341i
$675$	−6.31592	+	57.9817i	−0.243100	+	2.23172i
$676$	−10.3643	+	15.2194i	−0.398628	+	0.585360i
$677$	7.32775	−	7.32775i	0.281628	−	0.281628i	−0.552130	−	0.833758i	$-0.686185\pi$
$677$	7.32775	−	7.32775i	0.281628	−	0.281628i	0.833758	+	0.552130i	$0.186185\pi$
$678$	−14.0769	+	45.6801i	−0.540620	+	1.75433i
$679$	−21.6489			−0.830810
$680$	5.24123	−	8.39085i	0.200992	−	0.321775i
$681$	77.1940			2.95808
$682$	5.13284	−	16.6562i	0.196546	−	0.637801i
$683$	−12.8608	+	12.8608i	−0.492105	+	0.492105i	−0.908969	−	0.416864i	$-0.863129\pi$
$683$	−12.8608	+	12.8608i	−0.492105	+	0.492105i	0.416864	+	0.908969i	$0.363129\pi$
$684$	−53.4557	+	78.4964i	−2.04393	+	3.00138i
$685$	30.7891	−	10.8375i	1.17639	−	0.414079i
$686$	−3.82948	−	7.24099i	−0.146210	−	0.276462i
$687$	−51.0102	−	51.0102i	−1.94616	−	1.94616i
$688$	23.5022	+	10.2237i	0.896014	+	0.389773i
$689$		−	13.3518i		−	0.508663i
$690$	35.4831	+	32.7838i	1.35082	+	1.24806i
$691$		−	14.4383i		−	0.549261i	−0.961550	−	0.274630i	$-0.911445\pi$
$691$		−	14.4383i		−	0.549261i	0.961550	−	0.274630i	$-0.0885555\pi$
$692$	−4.39185	−	23.1429i	−0.166953	−	0.879761i
$693$	19.5682	+	19.5682i	0.743334	+	0.743334i
$694$	−11.8704	+	6.27778i	−0.450593	+	0.238301i
$695$	37.0611	+	17.7634i	1.40581	+	0.673803i
$696$	26.8763	+	3.00614i	1.01874	+	0.113947i
$697$	1.10610	−	1.10610i	0.0418966	−	0.0418966i
$698$	26.1431	+	8.05633i	0.989530	+	0.304936i
$699$	−32.4005			−1.22550
$700$	−22.8117	+	26.7361i	−0.862202	+	1.01053i
$701$	−34.5991			−1.30679			−0.653395	−	0.757017i	$-0.726656\pi$
$701$	−34.5991			−1.30679			−0.653395	+	0.757017i	$0.726656\pi$
$702$	−30.7051	−	9.46217i	−1.15889	−	0.357127i
$703$	−3.63561	+	3.63561i	−0.137119	+	0.137119i
$704$	−9.11771	−	2.06549i	−0.343637	−	0.0778460i
$705$	−66.0826	−	31.6733i	−2.48881	−	1.19289i
$706$	29.6128	−	15.6611i	1.11449	−	0.589412i
$707$	−2.00635	−	2.00635i	−0.0754566	−	0.0754566i
$708$	−50.1607	+	9.51905i	−1.88516	+	0.357748i
$709$		−	21.0190i		−	0.789383i	−0.918814	−	0.394692i	$-0.870851\pi$
$709$		−	21.0190i		−	0.789383i	0.918814	−	0.394692i	$-0.129149\pi$
$710$	−18.7038	−	17.2809i	−0.701940	−	0.648541i
$711$		−	2.26839i		−	0.0850712i
$712$	14.6908	+	18.3910i	0.550561	+	0.689234i
$713$	36.5076	+	36.5076i	1.36722	+	1.36722i
$714$	11.3427	+	21.4475i	0.424492	+	0.802651i
$715$	4.80062	−	1.68978i	0.179533	−	0.0631942i
$716$	−38.9632	−	26.5338i	−1.45612	−	0.991614i
$717$	13.6657	−	13.6657i	0.510355	−	0.510355i
$718$	2.79120	−	9.05756i	0.104167	−	0.338025i
$719$	−43.9045			−1.63736			−0.818681	−	0.574248i	$-0.805294\pi$
$719$	−43.9045			−1.63736			−0.818681	+	0.574248i	$0.805294\pi$
$720$	60.1115	+	4.32756i	2.24022	+	0.161279i
$721$	−35.0280			−1.30451
$722$	−12.7708	+	41.4417i	−0.475280	+	1.54230i
$723$	−44.7804	+	44.7804i	−1.66540	+	1.66540i
$724$	12.9125	+	8.79339i	0.479891	+	0.326804i
$725$	11.9422	−	9.59609i	0.443524	−	0.356390i
$726$	−19.8776	−	37.5857i	−0.737728	−	1.39494i
$727$	19.3350	+	19.3350i	0.717094	+	0.717094i	0.968009	−	0.250915i	$-0.0807314\pi$
$727$	19.3350	+	19.3350i	0.717094	+	0.717094i	−0.250915	+	0.968009i	$0.580731\pi$
$728$	−12.0836	−	15.1272i	−0.447849	−	0.560650i
$729$		−	0.133533i		−	0.00494568i
$730$	25.7878	−	1.01965i	0.954449	−	0.0377390i
$731$		−	10.0229i		−	0.370710i
$732$	42.1488	−	7.99861i	1.55786	−	0.295637i
$733$	−9.28783	−	9.28783i	−0.343054	−	0.343054i	0.514460	−	0.857514i	$-0.327992\pi$
$733$	−9.28783	−	9.28783i	−0.343054	−	0.343054i	−0.857514	+	0.514460i	$0.827992\pi$
$734$	33.8076	−	17.8795i	1.24786	−	0.659946i
$735$	−12.3995	−	35.2266i	−0.457361	−	1.29935i
$736$	18.0355	−	21.0151i	0.664798	−	0.774627i
$737$	11.7127	−	11.7127i	0.431444	−	0.431444i
$738$	9.10647	+	2.80627i	0.335214	+	0.103300i
$739$	−17.0990			−0.628997			−0.314498	−	0.949258i	$-0.601836\pi$
$739$	−17.0990			−0.628997			−0.314498	+	0.949258i	$0.601836\pi$
$740$	3.15361	+	0.836934i	0.115929	+	0.0307663i
$741$	−42.8320			−1.57347
$742$	−32.5619	−	10.0344i	−1.19538	−	0.368373i
$743$	−27.4332	+	27.4332i	−1.00642	+	1.00642i	−0.00644563	+	0.999979i	$0.502052\pi$
$743$	−27.4332	+	27.4332i	−1.00642	+	1.00642i	−0.999979	+	0.00644563i	$0.997948\pi$
$744$	92.5083	+	10.3471i	3.39152	+	0.379344i
$745$	20.5934	−	42.9657i	0.754484	−	1.57414i
$746$	27.5988	−	14.5959i	1.01046	−	0.534395i
$747$	−34.7593	−	34.7593i	−1.27178	−	1.27178i
$748$	0.681632	+	3.59187i	0.0249229	+	0.131332i
$749$		−	17.5413i		−	0.640944i
$750$	37.2111	−	32.4014i	1.35876	−	1.18313i
$751$			24.4933i			0.893773i	0.894591	+	0.446887i	$0.147467\pi$
$751$			24.4933i			0.893773i	−0.894591	+	0.446887i	$0.852533\pi$
$752$	−16.7569	+	38.5209i	−0.611061	+	1.40471i
$753$	16.0578	+	16.0578i	0.585178	+	0.585178i
$754$	3.94553	+	7.46042i	0.143688	+	0.271692i
$755$	−2.32486	+	4.85055i	−0.0846104	+	0.176530i
$756$	−46.1520	+	67.7714i	−1.67853	+	2.46482i
$757$	18.8885	−	18.8885i	0.686513	−	0.686513i	−0.274947	−	0.961459i	$-0.588660\pi$
$757$	18.8885	−	18.8885i	0.686513	−	0.686513i	0.961459	+	0.274947i	$0.0886603\pi$
$758$	−4.08134	+	13.2441i	−0.148241	+	0.481047i
$759$	−17.8524			−0.648003
$760$	43.4266	−	10.0335i	1.57525	−	0.363953i
$761$	14.8149			0.537041			0.268521	−	0.963274i	$-0.413465\pi$
$761$	14.8149			0.537041			0.268521	+	0.963274i	$0.413465\pi$
$762$	−1.78731	+	5.79989i	−0.0647474	+	0.210108i
$763$	30.0478	−	30.0478i	1.08780	−	1.08780i
$764$	16.0205	−	23.5251i	0.579601	−	0.851108i
$765$	−7.82527	−	22.2314i	−0.282923	−	0.803777i
$766$	−1.71753	−	3.24760i	−0.0620569	−	0.117340i
$767$	−11.2662	−	11.2662i	−0.406800	−	0.406800i
$768$	1.75889	−	49.8984i	0.0634686	−	1.80055i
$769$		−	40.8420i		−	1.47280i	−0.676547	−	0.736399i	$-0.736525\pi$
$769$		−	40.8420i		−	1.47280i	0.676547	−	0.736399i	$-0.263475\pi$
$770$	−0.513133	−	12.9775i	−0.0184920	−	0.467677i
$771$		−	25.8022i		−	0.929243i
$772$	−2.74139	−	14.4458i	−0.0986649	−	0.519916i
$773$	−19.1633	−	19.1633i	−0.689256	−	0.689256i	0.272812	−	0.962067i	$-0.412046\pi$
$773$	−19.1633	−	19.1633i	−0.689256	−	0.689256i	−0.962067	+	0.272812i	$0.912046\pi$
$774$	53.9733	−	28.5444i	1.94003	−	1.02601i
$775$	41.1052	−	33.0297i	1.47654	−	1.18646i
$776$	1.93666	−	17.3147i	0.0695220	−	0.621560i
$777$	−5.65799	+	5.65799i	−0.202979	+	0.202979i
$778$	12.3285	+	3.79920i	0.442000	+	0.136208i
$779$	7.04724			0.252493
$780$	13.6467	+	23.5068i	0.488630	+	0.841679i
$781$	9.41033			0.336728
$782$	−10.3496	−	3.18936i	−0.370101	−	0.114051i
$783$	25.2730	−	25.2730i	0.903182	−	0.903182i
$784$	−19.9195	+	7.84273i	−0.711411	+	0.280097i
$785$	−17.5064	+	6.16211i	−0.624830	+	0.219935i
$786$	−28.3214	+	14.9781i	−1.01019	+	0.534251i
$787$	26.0346	+	26.0346i	0.928032	+	0.928032i	0.997579	−	0.0695471i	$-0.0221554\pi$
$787$	26.0346	+	26.0346i	0.928032	+	0.928032i	−0.0695471	+	0.997579i	$0.522155\pi$
$788$	0.712684	−	0.135247i	0.0253883	−	0.00481796i
$789$			43.5862i			1.55171i
$790$	−0.722449	+	0.781933i	−0.0257036	+	0.0278199i
$791$			38.0665i			1.35349i
$792$	−17.4010	+	13.9000i	−0.618318	+	0.493914i
$793$	9.46672	+	9.46672i	0.336173	+	0.336173i
$794$	6.48289	+	12.2582i	0.230069	+	0.435027i
$795$	43.1364	+	20.6752i	1.52989	+	0.733274i
$796$	1.83994	+	1.25299i	0.0652148	+	0.0444110i
$797$	29.1554	−	29.1554i	1.03274	−	1.03274i	0.0332914	−	0.999446i	$-0.489401\pi$
$797$	29.1554	−	29.1554i	1.03274	−	1.03274i	0.999446	−	0.0332914i	$-0.0105989\pi$
$798$	−32.1898	+	104.457i	−1.13951	+	3.69774i
$799$	16.4278			0.581175
$800$	−19.3427	−	20.6364i	−0.683867	−	0.729607i
$801$	56.0744			1.98129
$802$	−2.59283	+	8.41384i	−0.0915561	+	0.297103i
$803$	−6.74374	+	6.74374i	−0.237981	+	0.237981i
$804$	73.1211	+	49.7951i	2.57878	+	1.75614i
$805$	34.6934	+	16.6285i	1.22278	+	0.586078i
$806$	13.5805	+	25.6788i	0.478353	+	0.904496i
$807$	−48.6940	−	48.6940i	−1.71411	−	1.71411i
$808$	1.78415	−	1.42518i	0.0627661	−	0.0501377i
$809$			36.7957i			1.29367i	0.762631	+	0.646834i	$0.223907\pi$
$809$			36.7957i			1.29367i	−0.762631	+	0.646834i	$0.776093\pi$
$810$	34.7375	−	37.5977i	1.22055	−	1.32105i
$811$			14.8882i			0.522795i	0.965231	+	0.261398i	$0.0841834\pi$
$811$			14.8882i			0.522795i	−0.965231	+	0.261398i	$0.915817\pi$
$812$	21.1594	−	4.01544i	0.742550	−	0.140914i
$813$	55.0780	+	55.0780i	1.93167	+	1.93167i
$814$	−1.06585	+	0.563689i	−0.0373581	+	0.0197573i
$815$	−30.8407	+	10.8557i	−1.08030	+	0.380258i
$816$	−18.1682	+	7.15321i	−0.636015	+	0.250412i
$817$	31.9291	−	31.9291i	1.11706	−	1.11706i
$818$	−12.9119	−	3.97896i	−0.451453	−	0.139121i
$819$	−46.1228			−1.61166
$820$	−2.24532	−	3.86763i	−0.0784099	−	0.135063i
$821$	−5.49766			−0.191870			−0.0959349	−	0.995388i	$-0.530584\pi$
$821$	−5.49766			−0.191870			−0.0959349	+	0.995388i	$0.530584\pi$
$822$	−61.5639	−	18.9717i	−2.14729	−	0.661714i
$823$	−17.6094	+	17.6094i	−0.613825	+	0.613825i	−0.943941	−	0.330115i	$-0.892912\pi$
$823$	−17.6094	+	17.6094i	−0.613825	+	0.613825i	0.330115	+	0.943941i	$0.392912\pi$
$824$	3.13352	−	28.0152i	0.109161	−	0.975954i
$825$	−1.97448	+	18.1262i	−0.0687426	+	0.631074i
$826$	−35.9426	+	19.0087i	−1.25060	+	0.661397i
$827$	−0.0999246	−	0.0999246i	−0.00347472	−	0.00347472i	0.705367	−	0.708842i	$-0.250782\pi$
$827$	−0.0999246	−	0.0999246i	−0.00347472	−	0.00347472i	−0.708842	+	0.705367i	$0.750782\pi$
$828$	−12.3002	−	64.8158i	−0.427460	−	2.25251i
$829$			15.7807i			0.548086i	0.961717	+	0.274043i	$0.0883611\pi$
$829$			15.7807i			0.548086i	−0.961717	+	0.274043i	$0.911639\pi$
$830$	0.911486	+	23.0522i	0.0316381	+	0.800152i
$831$			49.3374i			1.71149i
$832$	13.1796	−	8.31115i	0.456919	−	0.288137i
$833$	5.91981	+	5.91981i	0.205109	+	0.205109i
$834$	−37.9209	−	71.7028i	−1.31309	−	2.48287i
$835$	11.2348	+	31.9177i	0.388796	+	1.10456i
$836$	−9.27090	+	13.6137i	−0.320641	+	0.470841i
$837$	86.9895	−	86.9895i	3.00680	−	3.00680i
$838$	9.43550	−	30.6186i	0.325944	−	1.05770i
$839$	−41.4415			−1.43072			−0.715360	−	0.698757i	$-0.753737\pi$
$839$	−41.4415			−1.43072			−0.715360	+	0.698757i	$0.753737\pi$
$840$	67.5836	−	15.6148i	2.33186	−	0.538763i
$841$	19.6119			0.676273
$842$	−13.6511	+	44.2982i	−0.470447	+	1.52662i
$843$	22.9142	−	22.9142i	0.789209	−	0.789209i
$844$	−15.1750	+	22.2836i	−0.522346	+	0.767033i
$845$	8.89790	−	18.5644i	0.306097	−	0.638635i
$846$	46.7852	+	88.4640i	1.60851	+	3.04146i
$847$	−23.9429	−	23.9429i	−0.822689	−	0.822689i
$848$	10.9383	−	25.1451i	0.375623	−	0.863486i
$849$			22.0101i			0.755386i
$850$	−4.38294	+	10.1556i	−0.150334	+	0.348334i
$851$		−	3.57167i		−	0.122435i
$852$	9.37033	+	49.3771i	0.321022	+	1.69163i
$853$	−16.7442	−	16.7442i	−0.573309	−	0.573309i	0.359743	−	0.933052i	$-0.382865\pi$
$853$	−16.7442	−	16.7442i	−0.573309	−	0.573309i	−0.933052	+	0.359743i	$0.882865\pi$
$854$	30.2017	−	15.9725i	1.03348	−	0.546568i
$855$	45.8924	−	95.7490i	1.56949	−	3.27455i
$856$	14.0294	+	1.56920i	0.479514	+	0.0536341i
$857$	11.2712	−	11.2712i	0.385016	−	0.385016i	−0.487890	−	0.872905i	$-0.662233\pi$
$857$	11.2712	−	11.2712i	0.385016	−	0.385016i	0.872905	+	0.487890i	$0.162233\pi$
$858$	−9.59902	−	2.95806i	−0.327705	−	0.100987i
$859$	23.4588			0.800402			0.400201	−	0.916427i	$-0.368940\pi$
$859$	23.4588			0.800402			0.400201	+	0.916427i	$0.368940\pi$
$860$	−27.6961	−	7.35023i	−0.944428	−	0.250641i
$861$	10.9674			0.373768
$862$	−10.6575	−	3.28424i	−0.362995	−	0.111862i
$863$	−4.17560	+	4.17560i	−0.142139	+	0.142139i	−0.774596	−	0.632457i	$-0.782047\pi$
$863$	−4.17560	+	4.17560i	−0.142139	+	0.142139i	0.632457	+	0.774596i	$0.282047\pi$
$864$	−50.0744	−	42.9747i	−1.70356	−	1.46203i
$865$	8.74429	+	24.8423i	0.297315	+	0.844664i
$866$	31.4299	−	16.6221i	1.06803	−	0.564840i
$867$	−32.1126	−	32.1126i	−1.09060	−	1.09060i
$868$	72.8307	−	13.8212i	2.47204	−	0.469121i
$869$		−	0.393410i		−	0.0133455i
$870$	−30.2124	+	1.19460i	−1.02430	+	0.0405008i
$871$			27.6073i			0.935437i
$872$	21.3440	+	26.7200i	0.722800	+	0.904855i
$873$	−29.3487	−	29.3487i	−0.993303	−	0.993303i
$874$	−22.8098	−	43.1300i	−0.771553	−	1.45889i
$875$	20.7206	−	33.3864i	0.700485	−	1.12867i
$876$	−42.1003	−	28.6701i	−1.42244	−	0.968674i
$877$	−30.7662	+	30.7662i	−1.03890	+	1.03890i	−0.0396902	+	0.999212i	$0.512637\pi$
$877$	−30.7662	+	30.7662i	−1.03890	+	1.03890i	−0.999212	+	0.0396902i	$0.987363\pi$
$878$	10.9439	−	35.5135i	0.369340	−	1.19852i
$879$	−32.5294			−1.09719
$880$	10.4252	+	0.750536i	0.351434	+	0.0253006i
$881$	−28.5582			−0.962150			−0.481075	−	0.876679i	$-0.659754\pi$
$881$	−28.5582			−0.962150			−0.481075	+	0.876679i	$0.659754\pi$
$882$	−15.0191	+	48.7374i	−0.505718	+	1.64107i
$883$	−12.2146	+	12.2146i	−0.411054	+	0.411054i	−0.882106	−	0.471052i	$-0.843875\pi$
$883$	−12.2146	+	12.2146i	−0.411054	+	0.411054i	0.471052	+	0.882106i	$0.343875\pi$
$884$	−5.03638	−	3.42976i	−0.169392	−	0.115355i
$885$	53.8441	−	18.9527i	1.80995	−	0.637087i
$886$	9.78578	+	18.5035i	0.328760	+	0.621636i
$887$	20.3794	+	20.3794i	0.684272	+	0.684272i	0.960960	−	0.276688i	$-0.0892369\pi$
$887$	20.3794	+	20.3794i	0.684272	+	0.684272i	−0.276688	+	0.960960i	$0.589237\pi$
$888$	−4.01907	−	5.03136i	−0.134871	−	0.168842i
$889$			4.83321i			0.162101i
$890$	−19.3293	−	17.8589i	−0.647920	−	0.598632i
$891$			18.9163i			0.633720i
$892$	1.34667	−	0.255558i	0.0450897	−	0.00855672i
$893$	52.3328	+	52.3328i	1.75125	+	1.75125i
$894$	−83.1265	+	43.9624i	−2.78017	+	1.47032i
$895$	47.5269	+	22.7796i	1.58865	+	0.761438i
$896$	−10.3640	−	38.3880i	−0.346237	−	1.28245i
$897$	21.0394	−	21.0394i	0.702484	−	0.702484i
$898$	−20.0214	−	6.16985i	−0.668123	−	0.205891i
$899$	−32.3138			−1.07773
$900$	−67.1702	+	5.32016i	−2.23901	+	0.177339i
$901$	−10.7235			−0.357252
$902$	1.57935	+	0.486696i	0.0525865	+	0.0162052i
$903$	49.6903	−	49.6903i	1.65359	−	1.65359i
$904$	−30.4453	−	3.40533i	−1.01260	−	0.113260i
$905$	−15.7506	−	7.54924i	−0.523567	−	0.250945i
$906$	9.38444	−	4.96307i	0.311777	−	0.164887i
$907$	−11.4567	−	11.4567i	−0.380412	−	0.380412i	0.490839	−	0.871251i	$-0.336691\pi$
$907$	−11.4567	−	11.4567i	−0.380412	−	0.380412i	−0.871251	+	0.490839i	$0.836691\pi$
$908$	9.22411	+	48.6066i	0.306113	+	1.61307i
$909$		−	5.43987i		−	0.180429i
$910$	15.8989	+	14.6895i	0.527044	+	0.486951i
$911$		−	35.1701i		−	1.16524i	−0.812745	−	0.582619i	$-0.802028\pi$
$911$		−	35.1701i		−	1.16524i	0.812745	−	0.582619i	$-0.197972\pi$
$912$	−80.6644	−	35.0896i	−2.67107	−	1.16193i
$913$	−6.02835	−	6.02835i	−0.199509	−	0.199509i
$914$	−5.44027	−	10.2867i	−0.179948	−	0.340255i
$915$	−45.2438	+	15.9255i	−1.49571	+	0.526479i
$916$	26.0241	−	38.2148i	0.859861	−	1.26265i
$917$	−18.0414	+	18.0414i	−0.595778	+	0.595778i
$918$	−7.59955	+	24.6608i	−0.250823	+	0.813929i
$919$	−24.7123			−0.815184			−0.407592	−	0.913164i	$-0.633631\pi$
$919$	−24.7123			−0.815184			−0.407592	+	0.913164i	$0.633631\pi$
$920$	−16.4029	+	26.2600i	−0.540789	+	0.865766i
$921$	103.962			3.42568
$922$	−1.29739	+	4.21007i	−0.0427272	+	0.138651i
$923$	−11.0902	+	11.0902i	−0.365039	+	0.365039i
$924$	−14.4280	+	21.1867i	−0.474647	+	0.696990i
$925$	−3.62645	−	0.395027i	−0.119237	−	0.0129884i
$926$	6.50365	+	12.2974i	0.213723	+	0.404119i
$927$	−47.4862	−	47.4862i	−1.55965	−	1.55965i
$928$	1.31865	+	17.2824i	0.0432869	+	0.567321i
$929$			15.6421i			0.513201i	0.966518	+	0.256601i	$0.0826025\pi$
$929$			15.6421i			0.513201i	−0.966518	+	0.256601i	$0.917397\pi$
$930$	−103.991	+	4.11182i	−3.41000	+	0.134832i
$931$			37.7165i			1.23611i
$932$	−3.87162	−	20.4015i	−0.126819	−	0.668274i
$933$	−2.49120	−	2.49120i	−0.0815582	−	0.0815582i
$934$	8.62141	−	4.55954i	0.282101	−	0.149193i
$935$	−1.35715	−	3.85562i	−0.0443835	−	0.126092i
$936$	4.12603	−	36.8887i	0.134863	−	1.20574i
$937$	−34.5448	+	34.5448i	−1.12853	+	1.12853i	−0.138113	+	0.990416i	$0.544104\pi$
$937$	−34.5448	+	34.5448i	−1.12853	+	1.12853i	−0.990416	+	0.138113i	$0.955896\pi$
$938$	67.3276	+	20.7479i	2.19833	+	0.677442i
$939$	71.4018			2.33011
$940$	12.0473	−	45.3947i	0.392938	−	1.48061i
$941$	−48.9972			−1.59726			−0.798632	−	0.601820i	$-0.794443\pi$
$941$	−48.9972			−1.59726			−0.798632	+	0.601820i	$0.794443\pi$
$942$	35.0047	+	10.7871i	1.14051	+	0.351464i
$943$	−3.46165	+	3.46165i	−0.112727	+	0.112727i
$944$	−11.9877	−	30.4471i	−0.390165	−	0.990969i
$945$	39.6221	−	82.6668i	1.28891	−	2.68915i
$946$	9.36067	−	4.95050i	0.304342	−	0.160955i
$947$	−31.7225	−	31.7225i	−1.03084	−	1.03084i	−0.999509	−	0.0313327i	$-0.990025\pi$
$947$	−31.7225	−	31.7225i	−1.03084	−	1.03084i	−0.0313327	−	0.999509i	$-0.509975\pi$
$948$	2.06427	−	0.391738i	0.0670443	−	0.0127231i
$949$		−	15.8952i		−	0.515980i
$950$	−46.3142	+	18.3894i	−1.50263	+	0.596632i
$951$		−	22.4716i		−	0.728691i
$952$	−12.1494	+	9.70497i	−0.393764	+	0.314540i
$953$	20.2579	+	20.2579i	0.656217	+	0.656217i	0.954483	−	0.298266i	$-0.0964081\pi$
$953$	20.2579	+	20.2579i	0.656217	+	0.656217i	−0.298266	+	0.954483i	$0.596408\pi$
$954$	−30.5398	−	57.7462i	−0.988761	−	1.86960i
$955$	−13.7538	+	28.6956i	−0.445062	+	0.928569i
$956$	10.2378	+	6.97189i	0.331114	+	0.225487i
$957$	7.90083	−	7.90083i	0.255397	−	0.255397i
$958$	−11.6469	+	37.7946i	−0.376293	+	1.22109i
$959$	−51.3030			−1.65666
$960$	6.44277	+	55.4497i	0.207939	+	1.78963i
$961$	−80.2241			−2.58787
$962$	0.591808	−	1.92044i	0.0190807	−	0.0619175i
$963$	23.7801	−	23.7801i	0.766302	−	0.766302i
$964$	−33.5476	−	22.8458i	−1.08050	−	0.735814i
$965$	5.45819	+	15.5066i	0.175705	+	0.499174i
$966$	−35.4982	−	67.1220i	−1.14214	−	2.15961i
$967$	11.6678	+	11.6678i	0.375211	+	0.375211i	0.869371	−	0.494160i	$-0.164524\pi$
$967$	11.6678	+	11.6678i	0.375211	+	0.375211i	−0.494160	+	0.869371i	$0.664524\pi$
$968$	21.2912	−	17.0075i	0.684327	−	0.546642i
$969$			34.4005i			1.10510i
$970$	0.769605	+	19.4639i	0.0247105	+	0.624948i
$971$			32.1295i			1.03108i	0.856864	+	0.515542i	$0.172409\pi$
$971$			32.1295i			1.03108i	−0.856864	+	0.515542i	$0.827591\pi$
$972$	−30.4937	+	5.78682i	−0.978086	+	0.185612i
$973$	−45.6763	−	45.6763i	−1.46432	−	1.46432i
$974$	14.4343	−	7.63373i	0.462504	−	0.244601i
$975$	−19.0351	−	23.6890i	−0.609611	−	0.758655i
$976$	10.0729	+	25.5839i	0.322427	+	0.818922i
$977$	3.18653	−	3.18653i	0.101946	−	0.101946i	−0.654294	−	0.756240i	$-0.727034\pi$
$977$	3.18653	−	3.18653i	0.101946	−	0.101946i	0.756240	+	0.654294i	$0.227034\pi$
$978$	61.6671	+	19.0035i	1.97190	+	0.607665i
$979$	9.72506			0.310814
$980$	20.6994	−	12.0169i	0.661217	−	0.383864i
$981$	81.4695			2.60112
$982$	−25.0910	−	7.73212i	−0.800687	−	0.246742i
$983$	−26.2666	+	26.2666i	−0.837773	+	0.837773i	−0.988565	−	0.150792i	$-0.951818\pi$
$983$	−26.2666	+	26.2666i	−0.837773	+	0.837773i	0.150792	+	0.988565i	$0.451818\pi$
$984$	−0.981117	+	8.77165i	−0.0312769	+	0.279630i
$985$	−0.765017	+	0.269280i	−0.0243755	+	0.00857997i
$986$	5.99184	−	3.16886i	0.190819	−	0.100917i
$987$	81.4440	+	81.4440i	2.59239	+	2.59239i
$988$	−5.11810	−	26.9699i	−0.162828	−	0.858027i
$989$			31.3676i			0.997431i
$990$	16.8975	−	18.2888i	0.537038	−	0.581256i
$991$		−	54.2806i		−	1.72428i	−0.506671	−	0.862139i	$-0.669124\pi$
$991$		−	54.2806i		−	1.72428i	0.506671	−	0.862139i	$-0.330876\pi$
$992$	4.53880	+	59.4859i	0.144107	+	1.88868i
$993$	55.8666	+	55.8666i	1.77287	+	1.77287i
$994$	18.7117	+	35.3811i	0.593500	+	1.12222i
$995$	−2.24434	−	1.07571i	−0.0711502	−	0.0341022i
$996$	25.6287	−	37.6342i	0.812078	−	1.19249i
$997$	−34.7234	+	34.7234i	−1.09970	+	1.09970i	−0.105257	+	0.994445i	$0.533566\pi$
$997$	−34.7234	+	34.7234i	−1.09970	+	1.09970i	−0.994445	+	0.105257i	$0.966434\pi$
$998$	10.0550	−	32.6288i	0.318285	−	1.03285i
$999$	−8.51051			−0.269260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.18	yes	108
4.3	odd	2	inner	820.2.k.c.83.8	✓	108
5.2	odd	4	inner	820.2.k.c.247.8	yes	108
20.7	even	4	inner	820.2.k.c.247.18	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.8	✓	108	4.3	odd	2	inner
820.2.k.c.83.18	yes	108	1.1	even	1	trivial
820.2.k.c.247.8	yes	108	5.2	odd	4	inner
820.2.k.c.247.18	yes	108	20.7	even	4	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.416481 + 1.35150i) q^{2} +(-2.20659 + 2.20659i) q^{3} +(-1.65309 - 1.12575i) q^{4} +(2.01642 + 0.966467i) q^{5} +(-2.06319 - 3.90120i) q^{6} +(-2.48515 - 2.48515i) q^{7} +(2.20992 - 1.76529i) q^{8} -6.73806i q^{9} +(-2.14598 + 2.32267i) q^{10} -1.16859i q^{11} +(6.13174 - 1.16363i) q^{12} +(1.37720 + 1.37720i) q^{13} +(4.39369 - 2.32366i) q^{14} +(-6.58200 + 2.31681i) q^{15} +(1.46539 + 3.72191i) q^{16} +(1.10610 - 1.10610i) q^{17} +(9.10647 + 2.80627i) q^{18} +7.04724 q^{19} +(-2.24532 - 3.86763i) q^{20} +10.9674 q^{21} +(1.57935 + 0.486696i) q^{22} +(-3.46165 + 3.46165i) q^{23} +(-0.981117 + 8.77165i) q^{24} +(3.13188 + 3.89760i) q^{25} +(-2.43486 + 1.28771i) q^{26} +(8.24836 + 8.24836i) q^{27} +(1.31052 + 6.90582i) q^{28} -3.06400i q^{29} +(-0.389884 - 9.86046i) q^{30} -10.5463i q^{31} +(-5.64046 + 0.430370i) q^{32} +(2.57860 + 2.57860i) q^{33} +(1.03422 + 1.95556i) q^{34} +(-2.60929 - 7.41292i) q^{35} +(-7.58534 + 11.1386i) q^{36} +(-0.515891 + 0.515891i) q^{37} +(-2.93504 + 9.52432i) q^{38} -6.07784 q^{39} +(6.16222 - 1.42375i) q^{40} +1.00000 q^{41} +(-4.56772 + 14.8224i) q^{42} +(4.53072 - 4.53072i) q^{43} +(-1.31554 + 1.93178i) q^{44} +(6.51211 - 13.5867i) q^{45} +(-3.23670 - 6.12013i) q^{46} +(7.42600 + 7.42600i) q^{47} +(-11.4462 - 4.97920i) q^{48} +5.35196i q^{49} +(-6.57197 + 2.60945i) q^{50} +4.88142i q^{51} +(-0.726256 - 3.82702i) q^{52} +(-4.84743 - 4.84743i) q^{53} +(-14.5829 + 7.71235i) q^{54} +(1.12941 - 2.35637i) q^{55} +(-9.87900 - 1.10497i) q^{56} +(-15.5503 + 15.5503i) q^{57} +(4.14098 + 1.27610i) q^{58} -8.18051 q^{59} +(13.4888 + 3.57977i) q^{60} +6.87387 q^{61} +(14.2533 + 4.39233i) q^{62} +(-16.7451 + 16.7451i) q^{63} +(1.76750 - 7.80230i) q^{64} +(1.44600 + 4.10804i) q^{65} +(-4.55891 + 2.41103i) q^{66} +(10.0229 + 10.0229i) q^{67} +(-3.07367 + 0.583293i) q^{68} -15.2769i q^{69} +(11.1053 - 0.439103i) q^{70} +8.05271i q^{71} +(-11.8946 - 14.8906i) q^{72} +(-5.77083 - 5.77083i) q^{73} +(-0.482366 - 0.912084i) q^{74} +(-15.5112 - 1.68963i) q^{75} +(-11.6497 - 7.93340i) q^{76} +(-2.90413 + 2.90413i) q^{77} +(2.53130 - 8.21418i) q^{78} +0.336653 q^{79} +(-0.642257 + 8.92118i) q^{80} -16.1873 q^{81} +(-0.416481 + 1.35150i) q^{82} +(5.15865 - 5.15865i) q^{83} +(-18.1301 - 12.3465i) q^{84} +(3.29937 - 1.16135i) q^{85} +(4.23630 + 8.01022i) q^{86} +(6.76098 + 6.76098i) q^{87} +(-2.06290 - 2.58250i) q^{88} +8.32204i q^{89} +(15.6503 + 14.4597i) q^{90} -6.84512i q^{91} +(9.61936 - 1.82547i) q^{92} +(23.2713 + 23.2713i) q^{93} +(-13.1290 + 6.94343i) q^{94} +(14.2102 + 6.81092i) q^{95} +(11.4965 - 13.3958i) q^{96} +(4.35566 - 4.35566i) q^{97} +(-7.23315 - 2.22899i) q^{98} -7.87404 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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