LMFDB - Embedded newform 820.2.k.c.83.8

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			83.8
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35150 + 0.416481i) 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} +(-1.76529 + 2.20992i) q^{8} -6.73806i q^{9} +(-3.12770 - 0.466377i) q^{10} +1.16859i q^{11} +(1.16363 - 6.13174i) 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} +(2.80627 + 9.10647i) q^{18} -7.04724 q^{19} +(4.42131 - 0.672320i) q^{20} +10.9674 q^{21} +(-0.486696 - 1.57935i) 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} +(6.90582 + 1.31052i) q^{28} -3.06400i q^{29} +(-7.93064 + 5.87244i) q^{30} +10.5463i q^{31} +(-0.430370 + 5.64046i) 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} +(9.52432 - 2.93504i) q^{38} +6.07784 q^{39} +(-5.69538 + 2.75003i) q^{40} +1.00000 q^{41} +(-14.8224 + 4.56772i) 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} +(-4.97920 - 11.4462i) q^{48} +5.35196i q^{49} +(-5.85601 - 3.96323i) q^{50} -4.88142i q^{51} +(3.82702 + 0.726256i) 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} +(1.27610 + 4.14098i) q^{58} +8.18051 q^{59} +(8.27248 - 11.2395i) q^{60} +6.87387 q^{61} +(-4.39233 - 14.2533i) 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} +(0.583293 - 3.07367i) q^{68} -15.2769i q^{69} +(-6.61379 - 8.93182i) q^{70} -8.05271i q^{71} +(14.8906 + 11.8946i) 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} +(-8.21418 + 2.53130i) q^{78} -0.336653 q^{79} +(6.55195 - 6.08867i) q^{80} -16.1873 q^{81} +(-1.35150 + 0.416481i) 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} +(-2.58250 - 2.06290i) q^{88} +8.32204i q^{89} +(-3.14248 + 21.0746i) q^{90} +6.84512i q^{91} +(1.82547 - 9.61936i) 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} +(-2.22899 - 7.23315i) 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 $

$2$	−1.35150	+	0.416481i	−0.955653	+	0.294497i
$2$	−1.35150	+	0.416481i	−0.955653	+	0.294497i
$3$	2.20659	−	2.20659i	1.27397	−	1.27397i	0.329990	−	0.943985i	$-0.392955\pi$
$3$	2.20659	−	2.20659i	1.27397	−	1.27397i	0.943985	−	0.329990i	$-0.107045\pi$
$4$	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	0.998260	−	0.0589612i	$-0.0187788\pi$
$7$	2.48515	+	2.48515i	0.939299	+	0.939299i	−0.0589612	+	0.998260i	$0.518779\pi$
$8$	−1.76529	+	2.20992i	−0.624124	+	0.781325i
$9$		−	6.73806i		−	2.24602i
$10$	−3.12770	−	0.466377i	−0.989065	−	0.147481i
$11$			1.16859i			0.352344i	0.984359	+	0.176172i	$0.0563714\pi$
$11$			1.16859i			0.352344i	−0.984359	+	0.176172i	$0.943629\pi$
$12$	1.16363	−	6.13174i	0.335910	−	1.77008i
$13$	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	$0.189250\pi$
$18$	2.80627	+	9.10647i	0.661445	+	2.14641i
$19$	−7.04724			−1.61675			−0.808374	−	0.588670i	$-0.799652\pi$
$19$	−7.04724			−1.61675			−0.808374	+	0.588670i	$0.799652\pi$
$20$	4.42131	−	0.672320i	0.988635	−	0.150335i
$21$	10.9674			2.39329
$22$	−0.486696	−	1.57935i	−0.103764	−	0.336718i
$23$	3.46165	−	3.46165i	0.721805	−	0.721805i	−0.247168	−	0.968973i	$-0.579500\pi$
$23$	3.46165	−	3.46165i	0.721805	−	0.721805i	0.968973	+	0.247168i	$0.0794999\pi$
$24$	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
$28$	6.90582	+	1.31052i	1.30508	+	0.247666i
$29$		−	3.06400i		−	0.568970i	−0.958680	−	0.284485i	$-0.908177\pi$
$29$		−	3.06400i		−	0.568970i	0.958680	−	0.284485i	$-0.0918226\pi$
$30$	−7.93064	+	5.87244i	−1.44793	+	1.07216i
$31$			10.5463i			1.89417i	0.320985	+	0.947084i	$0.395986\pi$
$31$			10.5463i			1.89417i	−0.320985	+	0.947084i	$0.604014\pi$
$32$	−0.430370	+	5.64046i	−0.0760794	+	0.997102i
$33$	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	$0.269101\pi$
$38$	9.52432	−	2.93504i	1.54505	−	0.476126i
$39$	6.07784			0.973233
$40$	−5.69538	+	2.75003i	−0.900518	+	0.434818i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−14.8224	+	4.56772i	−2.28715	+	0.704814i
$43$	−4.53072	+	4.53072i	−0.690929	+	0.690929i	−0.962436	−	0.271508i	$-0.912478\pi$
$43$	−4.53072	+	4.53072i	−0.690929	+	0.690929i	0.271508	+	0.962436i	$0.412478\pi$
$44$	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	$-0.972277\pi$
$47$	−7.42600	−	7.42600i	−1.08319	−	1.08319i	−0.0869839	−	0.996210i	$-0.527723\pi$
$48$	−4.97920	−	11.4462i	−0.718686	−	1.65212i
$49$			5.35196i			0.764565i
$50$	−5.85601	−	3.96323i	−0.828165	−	0.560485i
$51$		−	4.88142i		−	0.683536i
$52$	3.82702	+	0.726256i	0.530712	+	0.100714i
$53$	−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
$58$	1.27610	+	4.14098i	0.167560	+	0.543738i
$59$	8.18051			1.06501			0.532506	−	0.846426i	$-0.321251\pi$
$59$	8.18051			1.06501			0.532506	+	0.846426i	$0.321251\pi$
$60$	8.27248	−	11.2395i	1.06797	−	1.45102i
$61$	6.87387			0.880109			0.440055	−	0.897971i	$-0.354959\pi$
$61$	6.87387			0.880109			0.440055	+	0.897971i	$0.354959\pi$
$62$	−4.39233	−	14.2533i	−0.557826	−	1.81017i
$63$	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	$-0.916778\pi$
$67$	−10.0229	−	10.0229i	−1.22450	−	1.22450i	−0.258482	−	0.966016i	$-0.583222\pi$
$68$	0.583293	−	3.07367i	0.0707347	−	0.372737i
$69$		−	15.2769i		−	1.83912i
$70$	−6.61379	−	8.93182i	−0.790499	−	1.06756i
$71$		−	8.05271i		−	0.955680i	−0.878447	−	0.477840i	$-0.841420\pi$
$71$		−	8.05271i		−	0.955680i	0.878447	−	0.477840i	$-0.158580\pi$
$72$	14.8906	+	11.8946i	1.75487	+	1.40180i
$73$	−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
$78$	−8.21418	+	2.53130i	−0.930073	+	0.286614i
$79$	−0.336653			−0.0378764			−0.0189382	−	0.999821i	$-0.506029\pi$
$79$	−0.336653			−0.0378764			−0.0189382	+	0.999821i	$0.506029\pi$
$80$	6.55195	−	6.08867i	0.732530	−	0.680734i
$81$	−16.1873			−1.79859
$82$	−1.35150	+	0.416481i	−0.149248	+	0.0459926i
$83$	−5.15865	+	5.15865i	−0.566235	+	0.566235i	−0.931072	−	0.364836i	$-0.881125\pi$
$83$	−5.15865	+	5.15865i	−0.566235	+	0.566235i	0.364836	+	0.931072i	$0.381125\pi$
$84$	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
$88$	−2.58250	−	2.06290i	−0.275295	−	0.219906i
$89$			8.32204i			0.882134i	0.897474	+	0.441067i	$0.145400\pi$
$89$			8.32204i			0.882134i	−0.897474	+	0.441067i	$0.854600\pi$
$90$	−3.14248	+	21.0746i	−0.331246	+	2.22146i
$91$			6.84512i			0.717563i
$92$	1.82547	−	9.61936i	0.190319	−	1.00289i
$93$	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	$0.148760\pi$
$98$	−2.22899	−	7.23315i	−0.225162	−	0.730659i
$99$	7.87404			0.791371
$100$	9.56499	+	2.91737i	0.956499	+	0.291737i
$101$	0.807335			0.0803329			0.0401664	−	0.999193i	$-0.487211\pi$
$101$	0.807335			0.0803329			0.0401664	+	0.999193i	$0.487211\pi$
$102$	2.03302	+	6.59723i	0.201299	+	0.653223i
$103$	−7.04746	+	7.04746i	−0.694407	+	0.694407i	−0.963198	−	0.268791i	$-0.913376\pi$
$103$	−7.04746	+	7.04746i	−0.694407	+	0.694407i	0.268791	+	0.963198i	$0.413376\pi$
$104$	−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	0.515629	−	0.856812i	$-0.327558\pi$
$107$	−3.52922	−	3.52922i	−0.341182	−	0.341182i	−0.856812	+	0.515629i	$0.827558\pi$
$108$	−22.9208	−	4.34970i	−2.20556	−	0.418550i
$109$			12.0909i			1.15810i	0.815291	+	0.579051i	$0.196577\pi$
$109$			12.0909i			1.15810i	−0.815291	+	0.579051i	$0.803423\pi$
$110$	0.545004	−	3.65500i	0.0519641	−	0.348491i
$111$			2.27672i			0.216096i
$112$	12.8912	−	5.60779i	1.21811	−	0.529886i
$113$	−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
$118$	−11.0559	+	3.40703i	−1.01778	+	0.313642i
$119$	5.49766			0.503970
$120$	−6.49917	+	18.6355i	−0.593290	+	1.70118i
$121$	9.63439			0.875854
$122$	−9.29002	+	2.86284i	−0.841079	+	0.259189i
$123$	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	0.748933	−	0.662645i	$-0.230566\pi$
$127$	0.972418	+	0.972418i	0.0862882	+	0.0862882i	−0.662645	+	0.748933i	$0.730566\pi$
$128$	5.63828	+	9.80866i	0.498359	+	0.866971i
$129$			19.9949i			1.76045i
$130$	−3.66518	−	4.94977i	−0.321457	−	0.434124i
$131$			7.25966i			0.634280i	0.948379	+	0.317140i	$0.102722\pi$
$131$			7.25966i			0.634280i	−0.948379	+	0.317140i	$0.897278\pi$
$132$	7.16550	+	1.35980i	0.623677	+	0.118356i
$133$	−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	$0.0356820\pi$
$138$	6.36253	+	20.6467i	0.541615	+	1.75756i
$139$	−18.3797			−1.55895			−0.779473	−	0.626436i	$-0.784513\pi$
$139$	−18.3797			−1.55895			−0.779473	+	0.626436i	$0.784513\pi$
$140$	12.6584	+	9.31681i	1.06983	+	0.787414i
$141$	−32.7722			−2.75992
$142$	3.35380	+	10.8832i	0.281445	+	0.913298i
$143$	−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
$148$	−0.272051	+	1.43357i	−0.0223624	+	0.117839i
$149$		−	21.3079i		−	1.74561i	−0.488065	−	0.872807i	$-0.662297\pi$
$149$		−	21.3079i		−	1.74561i	0.488065	−	0.872807i	$-0.337703\pi$
$150$	−21.6670	+	4.17659i	−1.76910	+	0.341017i
$151$		−	2.40553i		−	0.195759i	−0.995198	−	0.0978795i	$-0.968794\pi$
$151$		−	2.40553i		−	0.195759i	0.995198	−	0.0978795i	$-0.0312060\pi$
$152$	12.4404	−	15.5738i	1.00905	−	1.26320i
$153$	−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	$0.357455\pi$
$158$	0.454985	−	0.140210i	0.0361967	−	0.0111545i
$159$	−21.3926			−1.69654
$160$	−6.31912	+	10.9576i	−0.499570	+	0.866273i
$161$	17.2055			1.35598
$162$	21.8770	−	6.74169i	1.71882	−	0.529677i
$163$	10.3392	−	10.3392i	0.809830	−	0.809830i	−0.174778	−	0.984608i	$-0.555921\pi$
$163$	10.3392	−	10.3392i	0.809830	−	0.809830i	0.984608	+	0.174778i	$0.0559208\pi$
$164$	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	0.159228	−	0.987242i	$-0.449099\pi$
$167$	−10.7003	−	10.7003i	−0.828013	−	0.828013i	−0.987242	+	0.159228i	$0.949099\pi$
$168$	−19.3607	+	24.2371i	−1.49371	+	1.86993i
$169$		−	9.20662i		−	0.708202i
$170$	−3.97541	+	2.94369i	−0.304900	+	0.225771i
$171$			47.4847i			3.63125i
$172$	−2.38924	+	12.5901i	−0.182178	+	0.959988i
$173$	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
$178$	−3.46597	−	11.2472i	−0.259785	−	0.843014i
$179$	−23.5700			−1.76170			−0.880851	−	0.473393i	$-0.843029\pi$
$179$	−23.5700			−1.76170			−0.880851	+	0.473393i	$0.843029\pi$
$180$	−4.53013	−	29.7911i	−0.337656	−	2.22049i
$181$	−7.81117			−0.580600			−0.290300	−	0.956936i	$-0.593755\pi$
$181$	−7.81117			−0.580600			−0.290300	+	0.956936i	$0.593755\pi$
$182$	−2.85086	−	9.25115i	−0.211320	−	0.685741i
$183$	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
$188$	−20.6356	−	3.91604i	−1.50501	−	0.285607i
$189$		−	40.9968i		−	2.98208i
$190$	22.0416	+	3.28667i	1.59907	+	0.238440i
$191$		−	14.2310i		−	1.02972i	−0.857275	−	0.514859i	$-0.827844\pi$
$191$		−	14.2310i		−	1.02972i	0.857275	−	0.514859i	$-0.172156\pi$
$192$	−21.1166	−	13.3163i	−1.52396	−	0.961023i
$193$	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	$0.254113\pi$
$198$	−10.6417	+	3.27939i	−0.756276	+	0.233056i
$199$	1.11303			0.0789007			0.0394503	−	0.999222i	$-0.487439\pi$
$199$	1.11303			0.0789007			0.0394503	+	0.999222i	$0.487439\pi$
$200$	−14.1421	+	0.0408163i	−0.999996	+	0.00288615i
$201$	−44.2330			−3.11996
$202$	−1.09111	+	0.336240i	−0.0767703	+	0.0236578i
$203$	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
$208$	7.14397	−	3.10768i	0.495345	−	0.215479i
$209$		−	8.23534i		−	0.569651i
$210$	−34.3027	−	5.11495i	−2.36711	−	0.352965i
$211$			13.4800i			0.928001i	0.885835	+	0.464000i	$0.153586\pi$
$211$			13.4800i			0.928001i	−0.885835	+	0.464000i	$0.846414\pi$
$212$	−13.4702	−	2.55625i	−0.925137	−	0.175564i
$213$	−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
$218$	−5.03565	−	16.3409i	−0.341057	−	1.10674i
$219$	−25.4677			−1.72095
$220$	0.785667	+	5.16671i	0.0529697	+	0.348339i
$221$	3.04665			0.204940
$222$	−0.948209	−	3.07698i	−0.0636397	−	0.206513i
$223$	0.484616	−	0.484616i	0.0324523	−	0.0324523i	−0.690694	−	0.723147i	$-0.742695\pi$
$223$	0.484616	−	0.484616i	0.0324523	−	0.0324523i	0.723147	+	0.690694i	$0.242695\pi$
$224$	−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	$0.0565429\pi$
$227$	17.4917	+	17.4917i	1.16097	+	1.16097i	0.176702	+	0.984264i	$0.443457\pi$
$228$	−8.20034	+	43.2118i	−0.543081	+	2.86177i
$229$			23.1172i			1.52763i	0.645435	+	0.763815i	$0.276676\pi$
$229$			23.1172i			1.52763i	−0.645435	+	0.763815i	$0.723324\pi$
$230$	−12.4414	+	9.21257i	−0.820365	+	0.607459i
$231$			12.8164i			0.843259i
$232$	6.77119	+	5.40885i	0.444551	+	0.355108i
$233$	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
$238$	−7.43007	+	2.28967i	−0.481620	+	0.148417i
$239$	6.19313			0.400601			0.200300	−	0.979735i	$-0.435808\pi$
$239$	6.19313			0.400601			0.200300	+	0.979735i	$0.435808\pi$
$240$	1.02226	−	27.8926i	0.0659866	−	1.80046i
$241$	20.2939			1.30725			0.653624	−	0.756820i	$-0.273248\pi$
$241$	20.2939			1.30725			0.653624	+	0.756820i	$0.273248\pi$
$242$	−13.0209	+	4.01254i	−0.837012	+	0.257936i
$243$	−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
$248$	−23.3064	−	18.6172i	−1.47996	−	1.18220i
$249$			22.7660i			1.44274i
$250$	−7.97783	−	13.6512i	−0.504563	−	0.863375i
$251$			7.27720i			0.459333i	0.973269	+	0.229666i	$0.0737635\pi$
$251$			7.27720i			0.459333i	−0.973269	+	0.229666i	$0.926237\pi$
$252$	8.83039	−	46.5318i	0.556262	−	2.93123i
$253$	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	$0.333025\pi$
$258$	−8.32749	−	27.0230i	−0.518447	−	1.68238i
$259$	−2.56413			−0.159328
$260$	7.01496	+	5.16312i	0.435050	+	0.320203i
$261$	−20.6454			−1.27792
$262$	−3.02351	−	9.81141i	−0.186793	−	0.606151i
$263$	−9.87638	+	9.87638i	−0.609004	+	0.609004i	−0.942686	−	0.333682i	$-0.891709\pi$
$263$	−9.87638	+	9.87638i	−0.609004	+	0.609004i	0.333682	+	0.942686i	$0.391709\pi$
$264$	−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
$268$	−27.8521	−	5.28552i	−1.70134	−	0.322864i
$269$			22.0676i			1.34548i	0.739878	+	0.672741i	$0.234883\pi$
$269$			22.0676i			1.34548i	−0.739878	+	0.672741i	$0.765117\pi$
$270$	21.9515	+	29.6452i	1.33593	+	1.80415i
$271$			24.9607i			1.51626i	0.652106	+	0.758128i	$0.273886\pi$
$271$			24.9607i			1.51626i	−0.652106	+	0.758128i	$0.726114\pi$
$272$	−2.49594	−	5.73769i	−0.151338	−	0.347898i
$273$	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	$0.0924575\pi$
$278$	24.8401	−	7.65479i	1.48981	−	0.459104i
$279$	71.0615			4.25434
$280$	−20.9881	−	7.31964i	−1.25428	−	0.437432i
$281$	−10.3845			−0.619486			−0.309743	−	0.950820i	$-0.600243\pi$
$281$	−10.3845			−0.619486			−0.309743	+	0.950820i	$0.600243\pi$
$282$	44.2916	−	13.6490i	2.63753	−	0.812787i
$283$	−4.98737	+	4.98737i	−0.296468	+	0.296468i	−0.839629	−	0.543161i	$-0.817227\pi$
$283$	−4.98737	+	4.98737i	−0.296468	+	0.296468i	0.543161	+	0.839629i	$0.317227\pi$
$284$	−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
$288$	38.0058	+	2.89986i	2.23951	+	0.170876i
$289$			14.5531i			0.856063i
$290$	−1.42898	+	9.58326i	−0.0839125	+	0.562748i
$291$		−	19.2223i		−	1.12683i
$292$	−16.0362	−	3.04320i	−0.938446	−	0.178090i
$293$	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
$298$	8.87435	+	28.7976i	0.514077	+	1.66820i
$299$	9.53480			0.551412
$300$	27.5434	−	14.6685i	1.59022	−	0.846889i
$301$	−22.5191			−1.29798
$302$	1.00186	+	3.25106i	0.0576504	+	0.187078i
$303$	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	$0.149628\pi$
$307$	23.5573	+	23.5573i	1.34448	+	1.34448i	0.452948	+	0.891537i	$0.350372\pi$
$308$	−1.53147	+	8.07008i	−0.0872634	+	0.459836i
$309$			31.1017i			1.76931i
$310$	4.91854	−	32.9856i	0.279354	−	1.87346i
$311$		−	1.12898i		−	0.0640187i	−0.999488	−	0.0320094i	$-0.989809\pi$
$311$		−	1.12898i		−	0.0640187i	0.999488	−	0.0320094i	$-0.0101906\pi$
$312$	−10.7292	+	13.4315i	−0.607419	+	0.760411i
$313$	−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	$0.314818\pi$
$318$	28.9120	−	8.90960i	1.62130	−	0.499626i
$319$	3.58056			0.200473
$320$	3.97665	−	17.4409i	0.222301	−	0.974978i
$321$	−15.5751			−0.869315
$322$	−23.2531	+	7.16575i	−1.29585	+	0.399332i
$323$	−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
$328$	−1.76529	+	2.20992i	−0.0974718	+	0.122022i
$329$		−	36.9095i		−	2.03489i
$330$	−6.86248	−	9.26768i	−0.377767	−	0.510169i
$331$			25.3181i			1.39161i	0.718231	+	0.695804i	$0.244952\pi$
$331$			25.3181i			1.39161i	−0.718231	+	0.695804i	$0.755048\pi$
$332$	−2.72037	+	14.3350i	−0.149300	+	0.786736i
$333$	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	$0.224887\pi$
$338$	3.83438	+	12.4427i	0.208563	+	0.676795i
$339$	−33.7996			−1.83574
$340$	4.14677	−	5.63407i	0.224890	−	0.305551i
$341$	−12.3243			−0.667398
$342$	−19.7765	−	64.1754i	−1.06939	−	3.47021i
$343$	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	0.503540	−	0.863972i	$-0.332031\pi$
$347$	−6.71409	−	6.71409i	−0.360431	−	0.360431i	−0.863972	+	0.503540i	$0.832031\pi$
$348$	−18.7876	−	3.56535i	−1.00712	−	0.191123i
$349$		−	19.3438i		−	1.03545i	−0.855547	−	0.517725i	$-0.826779\pi$
$349$		−	19.3438i		−	1.03545i	0.855547	−	0.517725i	$-0.173221\pi$
$350$	−4.70385	−	24.4023i	−0.251431	−	1.30436i
$351$		−	22.7193i		−	1.21267i
$352$	−6.59139	−	0.502927i	−0.351322	−	0.0268061i
$353$	−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
$358$	31.8547	−	9.81644i	1.68358	−	0.518815i
$359$	6.70187			0.353711			0.176856	−	0.984237i	$-0.443407\pi$
$359$	6.70187			0.353711			0.176856	+	0.984237i	$0.443407\pi$
$360$	18.5299	+	38.3758i	0.976610	+	2.02258i
$361$	30.6636			1.61387
$362$	10.5568	−	3.25320i	0.554852	−	0.170985i
$363$	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	0.999998	−	0.00182896i	$-0.000582175\pi$
$367$	19.1222	+	19.1222i	0.998169	+	0.998169i	−0.00182896	+	0.999998i	$0.500582\pi$
$368$	−7.81128	−	17.9567i	−0.407191	−	0.936055i
$369$		−	6.73806i		−	0.350769i
$370$	1.85415	−	1.37295i	0.0963927	−	0.0713763i
$371$		−	24.0932i		−	1.25086i
$372$	64.6670	+	12.2719i	3.35283	+	0.636270i
$373$	−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
$378$	17.0744	+	55.4071i	0.878213	+	2.84983i
$379$	−9.79958			−0.503370			−0.251685	−	0.967809i	$-0.580985\pi$
$379$	−9.79958			−0.503370			−0.251685	+	0.967809i	$0.580985\pi$
$380$	−31.1580	+	4.73800i	−1.59837	+	0.243054i
$381$	4.29145			0.219858
$382$	5.92694	+	19.2331i	0.303249	+	0.984054i
$383$	1.83690	−	1.83690i	0.0938611	−	0.0938611i	−0.658617	−	0.752478i	$-0.728858\pi$
$383$	1.83690	−	1.83690i	0.0938611	−	0.0938611i	0.752478	+	0.658617i	$0.228858\pi$
$384$	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
$388$	2.29692	−	12.1036i	0.116608	−	0.614470i
$389$		−	9.12214i		−	0.462511i	−0.972893	−	0.231256i	$-0.925717\pi$
$389$		−	9.12214i		−	0.462511i	0.972893	−	0.231256i	$-0.0742833\pi$
$390$	−19.0096	−	2.83456i	−0.962591	−	0.143534i
$391$		−	7.65789i		−	0.387276i
$392$	−11.8274	−	9.44776i	−0.597374	−	0.477184i
$393$	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	$0.170864\pi$
$398$	−1.50426	+	0.463556i	−0.0754016	+	0.0232360i
$399$	−77.2899			−3.86934
$400$	19.0960	−	5.94507i	0.954799	−	0.297253i
$401$	6.22557			0.310890			0.155445	−	0.987845i	$-0.450319\pi$
$401$	6.22557			0.310890			0.155445	+	0.987845i	$0.450319\pi$
$402$	59.7808	−	18.4222i	2.98160	−	0.918817i
$403$	−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
$408$	10.7876	+	8.61713i	0.534064	+	0.426611i
$409$			9.55377i			0.472403i	0.971704	+	0.236202i	$0.0759026\pi$
$409$			9.55377i			0.472403i	−0.971704	+	0.236202i	$0.924097\pi$
$410$	−3.12770	−	0.466377i	−0.154466	−	0.0230327i
$411$		−	45.5524i		−	2.24693i
$412$	−3.71642	+	19.5837i	−0.183095	+	0.964821i
$413$	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
$418$	3.42986	+	11.1300i	0.167760	+	0.544388i
$419$	22.6553			1.10678			0.553392	−	0.832921i	$-0.313333\pi$
$419$	22.6553			1.10678			0.553392	+	0.832921i	$0.313333\pi$
$420$	48.4903	−	7.37361i	2.36609	−	0.359795i
$421$	32.7772			1.59746			0.798731	−	0.601689i	$-0.205505\pi$
$421$	32.7772			1.59746			0.798731	+	0.601689i	$0.205505\pi$
$422$	−5.61416	−	18.2182i	−0.273293	−	0.886846i
$423$	−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
$428$	−9.80710	−	1.86110i	−0.474044	−	0.0899598i
$429$			7.10251i			0.342913i
$430$	16.2838	−	12.0577i	0.785272	−	0.581474i
$431$		−	7.88569i		−	0.379840i	−0.981800	−	0.189920i	$-0.939177\pi$
$431$		−	7.88569i		−	0.379840i	0.981800	−	0.189920i	$-0.0608229\pi$
$432$	−42.7867	+	18.6126i	−2.05858	+	0.895497i
$433$	−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
$438$	34.4195	−	10.6068i	1.64463	−	0.506813i
$439$	26.2772			1.25414			0.627070	−	0.778963i	$-0.284254\pi$
$439$	26.2772			1.25414			0.627070	+	0.778963i	$0.284254\pi$
$440$	−3.21366	−	6.65557i	−0.153205	−	0.317292i
$441$	36.0618			1.71723
$442$	−4.11754	+	1.26887i	−0.195852	+	0.0603542i
$443$	−10.4659	+	10.4659i	−0.497250	+	0.497250i	−0.910581	−	0.413331i	$-0.864365\pi$
$443$	−10.4659	+	10.4659i	−0.497250	+	0.497250i	0.413331	+	0.910581i	$0.364365\pi$
$444$	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
$448$	14.9974	−	23.7824i	0.708561	−	1.12361i
$449$			14.8142i			0.699127i	0.936913	+	0.349564i	$0.113670\pi$
$449$			14.8142i			0.699127i	−0.936913	+	0.349564i	$0.886330\pi$
$450$	−26.7045	+	39.4581i	−1.25886	+	1.86007i
$451$			1.16859i			0.0550268i
$452$	−21.2825	−	4.03880i	−1.00104	−	0.189969i
$453$	−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	$0.311645\pi$
$458$	−9.62789	−	31.2429i	−0.449882	−	1.45988i
$459$	−18.2471			−0.851699
$460$	12.9777	−	17.6324i	0.605089	−	0.822114i
$461$	3.11512			0.145086			0.0725428	−	0.997365i	$-0.476889\pi$
$461$	3.11512			0.145086			0.0725428	+	0.997365i	$0.476889\pi$
$462$	−5.33780	−	17.3214i	−0.248337	−	0.805862i
$463$	−6.95566	+	6.95566i	−0.323257	+	0.323257i	−0.850015	−	0.526758i	$-0.823407\pi$
$463$	−6.95566	+	6.95566i	−0.323257	+	0.323257i	0.526758	+	0.850015i	$0.323407\pi$
$464$	−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	0.810874	−	0.585220i	$-0.198992\pi$
$467$	4.87643	+	4.87643i	0.225654	+	0.225654i	−0.585220	+	0.810874i	$0.698992\pi$
$468$	4.89356	−	25.7867i	0.226205	−	1.19199i
$469$		−	49.8171i		−	2.30034i
$470$	19.7630	+	26.6896i	0.911598	+	1.23110i
$471$			25.9007i			1.19344i
$472$	−14.4410	+	18.0783i	−0.664699	+	0.832120i
$473$	−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
$478$	−8.37000	+	2.57932i	−0.382835	+	0.117975i
$479$	−27.9650			−1.27775			−0.638876	−	0.769310i	$-0.720600\pi$
$479$	−27.9650			−1.27775			−0.638876	+	0.769310i	$0.720600\pi$
$480$	10.2352	+	38.1226i	0.467170	+	1.74005i
$481$	−1.42097			−0.0647908
$482$	−27.4272	+	8.45204i	−1.24927	+	0.384980i
$483$	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	0.867462	−	0.497503i	$-0.165750\pi$
$487$	8.16428	+	8.16428i	0.369959	+	0.369959i	−0.497503	+	0.867462i	$0.665750\pi$
$488$	−12.1344	+	15.1907i	−0.549298	+	0.687651i
$489$		−	45.6288i		−	2.06340i
$490$	2.49603	−	16.7393i	0.112759	−	0.756205i
$491$		−	18.5654i		−	0.837843i	−0.908022	−	0.418922i	$-0.862408\pi$
$491$		−	18.5654i		−	0.837843i	0.908022	−	0.418922i	$-0.137592\pi$
$492$	1.16363	−	6.13174i	0.0524603	−	0.276440i
$493$	−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
$498$	−9.48162	−	30.7682i	−0.424881	−	1.37876i
$499$	24.1427			1.08078			0.540388	−	0.841416i	$-0.318277\pi$
$499$	24.1427			1.08078			0.540388	+	0.841416i	$0.318277\pi$
$500$	16.4675	+	15.1269i	0.736447	+	0.676495i
$501$	−47.2223			−2.10974
$502$	−3.03082	−	9.83511i	−0.135272	−	0.438962i
$503$	12.5723	−	12.5723i	0.560572	−	0.560572i	−0.368898	−	0.929470i	$-0.620265\pi$
$503$	12.5723	−	12.5723i	0.560572	−	0.560572i	0.929470	+	0.368898i	$0.120265\pi$
$504$	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
$508$	2.70219	+	0.512797i	0.119890	+	0.0227517i
$509$			37.3491i			1.65547i	0.561120	+	0.827734i	$0.310371\pi$
$509$			37.3491i			1.65547i	−0.561120	+	0.827734i	$0.689629\pi$
$510$	−2.27658	+	15.2676i	−0.100809	+	0.676061i
$511$		−	28.6828i		−	1.26885i
$512$	20.3626	+	9.86729i	0.899909	+	0.436077i
$513$	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
$518$	3.46542	−	1.06791i	0.152262	−	0.0469214i
$519$	36.7542			1.61333
$520$	−11.6310	−	4.05634i	−0.510055	−	0.177882i
$521$	33.2508			1.45674			0.728372	−	0.685182i	$-0.240277\pi$
$521$	33.2508			1.45674			0.728372	+	0.685182i	$0.240277\pi$
$522$	27.9022	−	8.59842i	1.22125	−	0.376343i
$523$	−9.43538	+	9.43538i	−0.412580	+	0.412580i	−0.882636	−	0.470056i	$-0.844234\pi$
$523$	−9.43538	+	9.43538i	−0.412580	+	0.412580i	0.470056	+	0.882636i	$0.344234\pi$
$524$	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
$528$	13.3760	−	5.81866i	0.582115	−	0.253224i
$529$		−	0.966102i		−	0.0420045i
$530$	12.9006	+	17.4220i	0.560365	+	0.756765i
$531$		−	55.1207i		−	2.39204i
$532$	−48.6670	−	9.23557i	−2.10998	−	0.400413i
$533$	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
$538$	−9.19072	−	29.8242i	−0.396240	−	1.28581i
$539$	−6.25425			−0.269390
$540$	−42.0141	−	30.9230i	−1.80800	−	1.33071i
$541$	8.69130			0.373668			0.186834	−	0.982391i	$-0.440177\pi$
$541$	8.69130			0.373668			0.186834	+	0.982391i	$0.440177\pi$
$542$	−10.3957	−	33.7343i	−0.446532	−	1.44901i
$543$	−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	0.897358	−	0.441303i	$-0.145484\pi$
$547$	10.6662	+	10.6662i	0.456055	+	0.456055i	−0.441303	+	0.897358i	$0.645484\pi$
$548$	5.44317	−	28.6828i	0.232521	−	1.22527i
$549$		−	46.3166i		−	1.97674i
$550$	4.63139	−	6.84328i	0.197483	−	0.291799i
$551$			21.5927i			0.919881i
$552$	33.7607	+	26.9681i	1.43695	+	1.14784i
$553$	−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	$0.0615577\pi$
$558$	−96.0394	+	29.5958i	−4.06567	+	1.25289i
$559$	−12.4795			−0.527825
$560$	31.4139	+	1.15131i	1.32748	+	0.0486518i
$561$	5.70439			0.240840
$562$	14.0346	−	4.32494i	0.592013	−	0.182436i
$563$	2.21476	−	2.21476i	0.0933412	−	0.0933412i	−0.658894	−	0.752236i	$-0.728976\pi$
$563$	2.21476	−	2.21476i	0.0933412	−	0.0933412i	0.752236	+	0.658894i	$0.228976\pi$
$564$	−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
$568$	17.7958	+	14.2154i	0.746697	+	0.596463i
$569$			17.8205i			0.747076i	0.927615	+	0.373538i	$0.121855\pi$
$569$			17.8205i			0.747076i	−0.927615	+	0.373538i	$0.878145\pi$
$570$	55.8891	−	41.3845i	2.34094	−	1.73340i
$571$		−	11.5700i		−	0.484190i	−0.970252	−	0.242095i	$-0.922165\pi$
$571$		−	11.5700i		−	0.484190i	0.970252	−	0.242095i	$-0.0778346\pi$
$572$	−0.848697	+	4.47222i	−0.0354858	+	0.186993i
$573$	−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	$0.0561409\pi$
$578$	−6.06108	−	19.6684i	−0.252108	−	0.818099i
$579$	22.9420			0.953435
$580$	−2.05999	−	13.5469i	−0.0855363	−	0.562504i
$581$	−25.6400			−1.06373
$582$	8.00572	+	25.9789i	0.331848	+	1.07686i
$583$	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	0.901534	−	0.432708i	$-0.142442\pi$
$587$	11.3588	+	11.3588i	0.468826	+	0.468826i	−0.432708	+	0.901534i	$0.642442\pi$
$588$	32.8168	+	6.22767i	1.35334	+	0.256825i
$589$		−	74.3222i		−	3.06239i
$590$	−25.5862	−	3.81520i	−1.05337	−	0.157069i
$591$			1.13184i			0.0465578i
$592$	1.16412	+	2.67608i	0.0478449	+	0.109986i
$593$	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
$598$	−12.8863	+	3.97106i	−0.526958	+	0.162389i
$599$	38.6463			1.57904			0.789522	−	0.613723i	$-0.210329\pi$
$599$	38.6463			1.57904			0.789522	+	0.613723i	$0.210329\pi$
$600$	−31.1157	+	31.2958i	−1.27029	+	1.27765i
$601$	−16.6688			−0.679934			−0.339967	−	0.940437i	$-0.610416\pi$
$601$	−16.6688			−0.679934			−0.339967	+	0.940437i	$0.610416\pi$
$602$	30.4344	−	9.37876i	1.24042	−	0.382250i
$603$	−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	0.360011	−	0.932948i	$-0.382773\pi$
$607$	−14.1157	−	14.1157i	−0.572938	−	0.572938i	−0.932948	+	0.360011i	$0.882773\pi$
$608$	3.03292	−	39.7497i	0.123001	−	1.61206i
$609$		−	33.6041i		−	1.36171i
$610$	−21.4994	−	3.20582i	−0.870485	−	0.129800i
$611$		−	20.4542i		−	0.827489i
$612$	−20.7106	−	3.93027i	−0.837176	−	0.158872i
$613$	−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	$0.431430\pi$
$618$	−12.9533	−	42.0338i	−0.521057	−	1.69085i
$619$	−43.3562			−1.74263			−0.871317	−	0.490720i	$-0.836734\pi$
$619$	−43.3562			−1.74263			−0.871317	+	0.490720i	$0.836734\pi$
$620$	7.09048	+	46.6284i	0.284760	+	1.87264i
$621$	−57.1059			−2.29158
$622$	0.470200	+	1.52582i	0.0188533	+	0.0611797i
$623$	−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
$628$	−3.09494	+	16.3088i	−0.123502	+	0.650793i
$629$			1.14126i			0.0455048i
$630$	−60.1831	+	44.5641i	−2.39775	+	1.77548i
$631$			2.64123i			0.105146i	0.998617	+	0.0525728i	$0.0167421\pi$
$631$			2.64123i			0.105146i	−0.998617	+	0.0525728i	$0.983258\pi$
$632$	0.594290	−	0.743976i	0.0236396	−	0.0295938i
$633$	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
$638$	−4.83912	+	1.49124i	−0.191583	+	0.0590386i
$639$	−54.2596			−2.14648
$640$	1.88939	+	25.2276i	0.0746849	+	0.997207i
$641$	2.72244			0.107530			0.0537649	−	0.998554i	$-0.482878\pi$
$641$	2.72244			0.107530			0.0537649	+	0.998554i	$0.482878\pi$
$642$	21.0496	−	6.48671i	0.830763	−	0.256010i
$643$	20.3630	−	20.3630i	0.803038	−	0.803038i	−0.180531	−	0.983569i	$-0.557782\pi$
$643$	20.3630	−	20.3630i	0.803038	−	0.803038i	0.983569	+	0.180531i	$0.0577817\pi$
$644$	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	$-0.989688\pi$
$647$	−26.2467	−	26.2467i	−1.03187	−	1.03187i	−0.0323902	−	0.999475i	$-0.510312\pi$
$648$	28.5752	−	35.7726i	1.12254	−	1.40528i
$649$			9.55967i			0.375250i
$650$	−2.60674	−	13.5231i	−0.102245	−	0.530419i
$651$			115.665i			4.53328i
$652$	5.45230	−	28.7309i	0.213528	−	1.12519i
$653$	−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
$658$	15.3721	+	49.8830i	0.599267	+	1.94464i
$659$	−47.8782			−1.86507			−0.932535	−	0.361080i	$-0.882408\pi$
$659$	−47.8782			−1.86507			−0.932535	+	0.361080i	$0.882408\pi$
$660$	13.1344	+	9.66715i	0.511257	+	0.376293i
$661$	−36.3419			−1.41353			−0.706767	−	0.707446i	$-0.749847\pi$
$661$	−36.3419			−1.41353			−0.706767	+	0.707446i	$0.749847\pi$
$662$	−10.5445	−	34.2173i	−0.409824	−	1.32989i
$663$	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
$668$	−29.7343	−	5.64271i	−1.15046	−	0.218323i
$669$		−	2.13870i		−	0.0826867i
$670$	26.6743	+	36.0232i	1.03052	+	1.39170i
$671$			8.03275i			0.310101i
$672$	−4.72004	+	61.8612i	−0.182080	+	2.38635i
$673$	−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	$0.186185\pi$
$678$	45.6801	−	14.0769i	1.75433	−	0.540620i
$679$	21.6489			0.830810
$680$	−3.25786	+	9.34148i	−0.124933	+	0.358229i
$681$	77.1940			2.95808
$682$	16.6562	−	5.13284i	0.637801	−	0.196546i
$683$	12.8608	−	12.8608i	0.492105	−	0.492105i	−0.416864	−	0.908969i	$-0.636871\pi$
$683$	12.8608	−	12.8608i	0.492105	−	0.492105i	0.908969	+	0.416864i	$0.136871\pi$
$684$	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
$688$	10.2237	+	23.5022i	0.389773	+	0.896014i
$689$		−	13.3518i		−	0.508663i
$690$	−7.12479	+	47.7815i	−0.271236	+	1.81901i
$691$			14.4383i			0.549261i	0.961550	+	0.274630i	$0.0885555\pi$
$691$			14.4383i			0.549261i	−0.961550	+	0.274630i	$0.911445\pi$
$692$	23.1429	+	4.39185i	0.879761	+	0.166953i
$693$	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
$698$	8.05633	+	26.1431i	0.304936	+	0.989530i
$699$	32.4005			1.22550
$700$	16.5203	+	31.0206i	0.624410	+	1.17247i
$701$	−34.5991			−1.30679			−0.653395	−	0.757017i	$-0.726656\pi$
$701$	−34.5991			−1.30679			−0.653395	+	0.757017i	$0.726656\pi$
$702$	9.46217	+	30.7051i	0.357127	+	1.15889i
$703$	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
$708$	9.51905	−	50.1607i	0.357748	−	1.88516i
$709$		−	21.0190i		−	0.789383i	−0.918814	−	0.394692i	$-0.870851\pi$
$709$		−	21.0190i		−	0.789383i	0.918814	−	0.394692i	$-0.129149\pi$
$710$	−3.75560	+	25.1864i	−0.140945	+	0.945230i
$711$			2.26839i			0.0850712i
$712$	−18.3910	−	14.6908i	−0.689234	−	0.550561i
$713$	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
$718$	−9.05756	+	2.79120i	−0.338025	+	0.104167i
$719$	43.9045			1.63736			0.818681	−	0.574248i	$-0.194706\pi$
$719$	43.9045			1.63736			0.818681	+	0.574248i	$0.194706\pi$
$720$	−41.0259	−	44.1474i	−1.52894	−	1.64528i
$721$	−35.0280			−1.30451
$722$	−41.4417	+	12.7708i	−1.54230	+	0.475280i
$723$	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	0.250915	−	0.968009i	$-0.419269\pi$
$727$	−19.3350	−	19.3350i	−0.717094	−	0.717094i	−0.968009	+	0.250915i	$0.919269\pi$
$728$	−15.1272	−	12.0836i	−0.560650	−	0.447849i
$729$		−	0.133533i		−	0.00494568i
$730$	15.3580	+	20.7408i	0.568426	+	0.767651i
$731$			10.0229i			0.370710i
$732$	7.99861	−	42.1488i	0.295637	−	1.55786i
$733$	−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
$738$	2.80627	+	9.10647i	0.103300	+	0.335214i
$739$	17.0990			0.628997			0.314498	−	0.949258i	$-0.398164\pi$
$739$	17.0990			0.628997			0.314498	+	0.949258i	$0.398164\pi$
$740$	−1.93407	+	2.62776i	−0.0710978	+	0.0965983i
$741$	−42.8320			−1.57347
$742$	10.0344	+	32.5619i	0.368373	+	1.19538i
$743$	27.4332	−	27.4332i	1.00642	−	1.00642i	0.00644563	−	0.999979i	$-0.497948\pi$
$743$	27.4332	−	27.4332i	1.00642	−	1.00642i	0.999979	−	0.00644563i	$-0.00205172\pi$
$744$	−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
$748$	3.59187	+	0.681632i	0.131332	+	0.0249229i
$749$		−	17.5413i		−	0.640944i
$750$	−47.7263	−	12.5187i	−1.74272	−	0.457118i
$751$		−	24.4933i		−	0.893773i	−0.894591	−	0.446887i	$-0.852533\pi$
$751$		−	24.4933i		−	0.893773i	0.894591	−	0.446887i	$-0.147467\pi$
$752$	−38.5209	+	16.7569i	−1.40471	+	0.611061i
$753$	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	$0.0886603\pi$
$758$	13.2441	−	4.08134i	0.481047	−	0.148241i
$759$	17.8524			0.648003
$760$	40.1367	−	19.3801i	1.45591	−	0.702991i
$761$	14.8149			0.537041			0.268521	−	0.963274i	$-0.413465\pi$
$761$	14.8149			0.537041			0.268521	+	0.963274i	$0.413465\pi$
$762$	−5.79989	+	1.78731i	−0.210108	+	0.0647474i
$763$	−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
$768$	−49.8984	+	1.75889i	−1.80055	+	0.0634686i
$769$		−	40.8420i		−	1.47280i	−0.676547	−	0.736399i	$-0.736525\pi$
$769$		−	40.8420i		−	1.47280i	0.676547	−	0.736399i	$-0.263475\pi$
$770$	10.4377	−	7.72881i	0.376147	−	0.278527i
$771$			25.8022i			0.929243i
$772$	14.4458	+	2.74139i	0.519916	+	0.0986649i
$773$	−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
$778$	3.79920	+	12.3285i	0.136208	+	0.442000i
$779$	−7.04724			−0.252493
$780$	26.8720	−	4.08625i	0.962172	−	0.146311i
$781$	9.41033			0.336728
$782$	3.18936	+	10.3496i	0.114051	+	0.370101i
$783$	−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	0.0695471	−	0.997579i	$-0.477845\pi$
$787$	−26.0346	−	26.0346i	−0.928032	−	0.928032i	−0.997579	+	0.0695471i	$0.977845\pi$
$788$	−0.135247	+	0.712684i	−0.00481796	+	0.0253883i
$789$			43.5862i			1.55171i
$790$	1.05295	+	0.157007i	0.0374622	+	0.00558606i
$791$		−	38.0665i		−	1.35349i
$792$	−13.9000	+	17.4010i	−0.493914	+	0.618318i
$793$	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	$-0.0105989\pi$
$798$	104.457	−	32.1898i	3.69774	−	1.13951i
$799$	−16.4278			−0.581175
$800$	−23.3321	+	15.9879i	−0.824916	+	0.565256i
$801$	56.0744			1.98129
$802$	−8.41384	+	2.59283i	−0.297103	+	0.0915561i
$803$	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
$808$	−1.42518	+	1.78415i	−0.0501377	+	0.0627661i
$809$			36.7957i			1.29367i	0.762631	+	0.646834i	$0.223907\pi$
$809$			36.7957i			1.29367i	−0.762631	+	0.646834i	$0.776093\pi$
$810$	50.6289	+	7.54937i	1.77892	+	0.265258i
$811$		−	14.8882i		−	0.522795i	−0.965231	−	0.261398i	$-0.915817\pi$
$811$		−	14.8882i		−	0.522795i	0.965231	−	0.261398i	$-0.0841834\pi$
$812$	4.01544	−	21.1594i	0.140914	−	0.742550i
$813$	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
$818$	−3.97896	−	12.9119i	−0.139121	−	0.451453i
$819$	46.1228			1.61166
$820$	4.42131	−	0.672320i	0.154399	−	0.0234784i
$821$	−5.49766			−0.191870			−0.0959349	−	0.995388i	$-0.530584\pi$
$821$	−5.49766			−0.191870			−0.0959349	+	0.995388i	$0.530584\pi$
$822$	18.9717	+	61.5639i	0.661714	+	2.14729i
$823$	17.6094	−	17.6094i	0.613825	−	0.613825i	−0.330115	−	0.943941i	$-0.607088\pi$
$823$	17.6094	−	17.6094i	0.613825	−	0.613825i	0.943941	+	0.330115i	$0.107088\pi$
$824$	−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	0.708842	−	0.705367i	$-0.249218\pi$
$827$	0.0999246	+	0.0999246i	0.00347472	+	0.00347472i	−0.705367	+	0.708842i	$0.749218\pi$
$828$	−64.8158	−	12.3002i	−2.25251	−	0.427460i
$829$			15.7807i			0.548086i	0.961717	+	0.274043i	$0.0883611\pi$
$829$			15.7807i			0.548086i	−0.961717	+	0.274043i	$0.911639\pi$
$830$	18.5406	−	13.7288i	0.643552	−	0.476534i
$831$		−	49.3374i		−	1.71149i
$832$	8.31115	−	13.1796i	0.288137	−	0.456919i
$833$	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
$838$	−30.6186	+	9.43550i	−1.05770	+	0.325944i
$839$	41.4415			1.43072			0.715360	−	0.698757i	$-0.246263\pi$
$839$	41.4415			1.43072			0.715360	+	0.698757i	$0.246263\pi$
$840$	−62.4636	+	30.1607i	−2.15520	+	1.04064i
$841$	19.6119			0.676273
$842$	−44.2982	+	13.6511i	−1.52662	+	0.470447i
$843$	−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
$848$	−25.1451	+	10.9383i	−0.863486	+	0.375623i
$849$			22.0101i			0.755386i
$850$	−10.8611	+	2.09361i	−0.372532	+	0.0718102i
$851$			3.57167i			0.122435i
$852$	−49.3771	−	9.37033i	−1.69163	−	0.321022i
$853$	−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	$0.162233\pi$
$858$	−2.95806	−	9.59902i	−0.100987	−	0.327705i
$859$	−23.4588			−0.800402			−0.400201	−	0.916427i	$-0.631060\pi$
$859$	−23.4588			−0.800402			−0.400201	+	0.916427i	$0.631060\pi$
$860$	−16.9856	+	23.0778i	−0.579205	+	0.786947i
$861$	10.9674			0.373768
$862$	3.28424	+	10.6575i	0.111862	+	0.362995i
$863$	4.17560	−	4.17560i	0.142139	−	0.142139i	−0.632457	−	0.774596i	$-0.717953\pi$
$863$	4.17560	−	4.17560i	0.142139	−	0.142139i	0.774596	+	0.632457i	$0.217953\pi$
$864$	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
$868$	−13.8212	+	72.8307i	−0.469121	+	2.47204i
$869$		−	0.393410i		−	0.0133455i
$870$	17.9931	+	24.2995i	0.610025	+	0.823829i
$871$		−	27.6073i		−	0.935437i
$872$	−26.7200	−	21.3440i	−0.904855	−	0.722800i
$873$	−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	$0.987363\pi$
$878$	−35.5135	+	10.9439i	−1.19852	+	0.369340i
$879$	32.5294			1.09719
$880$	7.11517	+	7.65655i	0.239852	+	0.258102i
$881$	−28.5582			−0.962150			−0.481075	−	0.876679i	$-0.659754\pi$
$881$	−28.5582			−0.962150			−0.481075	+	0.876679i	$0.659754\pi$
$882$	−48.7374	+	15.0191i	−1.64107	+	0.505718i
$883$	12.2146	−	12.2146i	0.411054	−	0.411054i	−0.471052	−	0.882106i	$-0.656125\pi$
$883$	12.2146	−	12.2146i	0.411054	−	0.411054i	0.882106	+	0.471052i	$0.156125\pi$
$884$	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	0.276688	−	0.960960i	$-0.410763\pi$
$887$	−20.3794	−	20.3794i	−0.684272	−	0.684272i	−0.960960	+	0.276688i	$0.910763\pi$
$888$	−5.03136	−	4.01907i	−0.168842	−	0.134871i
$889$			4.83321i			0.162101i
$890$	3.88121	−	26.0288i	0.130098	−	0.872488i
$891$		−	18.9163i		−	0.633720i
$892$	0.255558	−	1.34667i	0.00855672	−	0.0450897i
$893$	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
$898$	−6.16985	−	20.0214i	−0.205891	−	0.668123i
$899$	32.3138			1.07773
$900$	19.6574	−	64.4494i	0.655248	−	2.14831i
$901$	−10.7235			−0.357252
$902$	−0.486696	−	1.57935i	−0.0162052	−	0.0525865i
$903$	−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	0.871251	−	0.490839i	$-0.163309\pi$
$907$	11.4567	+	11.4567i	0.380412	+	0.380412i	−0.490839	+	0.871251i	$0.663309\pi$
$908$	48.6066	+	9.22411i	1.61307	+	0.306113i
$909$		−	5.43987i		−	0.180429i
$910$	3.19240	−	21.4095i	0.105827	−	0.709717i
$911$			35.1701i			1.16524i	0.812745	+	0.582619i	$0.197972\pi$
$911$			35.1701i			1.16524i	−0.812745	+	0.582619i	$0.802028\pi$
$912$	35.0896	+	80.6644i	1.16193	+	2.67107i
$913$	−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
$918$	24.6608	−	7.59955i	0.813929	−	0.250823i
$919$	24.7123			0.815184			0.407592	−	0.913164i	$-0.366369\pi$
$919$	24.7123			0.815184			0.407592	+	0.913164i	$0.366369\pi$
$920$	−10.1958	+	29.2351i	−0.336145	+	0.963852i
$921$	103.962			3.42568
$922$	−4.21007	+	1.29739i	−0.138651	+	0.0427272i
$923$	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
$928$	17.2824	+	1.31865i	0.567321	+	0.0432869i
$929$			15.6421i			0.513201i	0.966518	+	0.256601i	$0.0826025\pi$
$929$			15.6421i			0.513201i	−0.966518	+	0.256601i	$0.917397\pi$
$930$	−61.9324	−	83.6388i	−2.03084	−	2.74262i
$931$		−	37.7165i		−	1.23611i
$932$	20.4015	+	3.87162i	0.668274	+	0.126819i
$933$	−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	$0.955896\pi$
$938$	20.7479	+	67.3276i	0.677442	+	2.19833i
$939$	−71.4018			−2.33011
$940$	−37.8253	−	27.8400i	−1.23373	−	0.908041i
$941$	−48.9972			−1.59726			−0.798632	−	0.601820i	$-0.794443\pi$
$941$	−48.9972			−1.59726			−0.798632	+	0.601820i	$0.794443\pi$
$942$	−10.7871	−	35.0047i	−0.351464	−	1.14051i
$943$	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	$0.00997514\pi$
$947$	31.7225	+	31.7225i	1.03084	+	1.03084i	0.0313327	+	0.999509i	$0.490025\pi$
$948$	−0.391738	+	2.06427i	−0.0127231	+	0.0670443i
$949$		−	15.8952i		−	0.515980i
$950$	41.2687	+	27.9298i	1.33893	+	0.906162i
$951$			22.4716i			0.728691i
$952$	−9.70497	+	12.1494i	−0.314540	+	0.393764i
$953$	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
$958$	37.7946	−	11.6469i	1.22109	−	0.376293i
$959$	51.3030			1.65666
$960$	−29.7101	−	47.2598i	−0.958891	−	1.52530i
$961$	−80.2241			−2.58787
$962$	1.92044	−	0.591808i	0.0619175	−	0.0190807i
$963$	−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	0.494160	−	0.869371i	$-0.335476\pi$
$967$	−11.6678	−	11.6678i	−0.375211	−	0.375211i	−0.869371	+	0.494160i	$0.835476\pi$
$968$	−17.0075	+	21.2912i	−0.546642	+	0.684327i
$969$			34.4005i			1.10510i
$970$	−15.6546	+	11.5918i	−0.502638	+	0.372190i
$971$		−	32.1295i		−	1.03108i	−0.856864	−	0.515542i	$-0.827591\pi$
$971$		−	32.1295i		−	1.03108i	0.856864	−	0.515542i	$-0.172409\pi$
$972$	−5.78682	+	30.4937i	−0.185612	+	0.978086i
$973$	−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	$0.227034\pi$
$978$	19.0035	+	61.6671i	0.607665	+	1.97190i
$979$	−9.72506			−0.310814
$980$	3.59823	+	23.6627i	0.114941	+	0.755876i
$981$	81.4695			2.60112
$982$	7.73212	+	25.0910i	0.246742	+	0.800687i
$983$	26.2666	−	26.2666i	0.837773	−	0.837773i	−0.150792	−	0.988565i	$-0.548182\pi$
$983$	26.2666	−	26.2666i	0.837773	−	0.837773i	0.988565	+	0.150792i	$0.0481824\pi$
$984$	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
$988$	−26.9699	−	5.11810i	−0.858027	−	0.162828i
$989$			31.3676i			0.997431i
$990$	−24.6276	−	3.67227i	−0.782717	−	0.116712i
$991$			54.2806i			1.72428i	0.506671	+	0.862139i	$0.330876\pi$
$991$			54.2806i			1.72428i	−0.506671	+	0.862139i	$0.669124\pi$
$992$	−59.4859	−	4.53880i	−1.88868	−	0.144107i
$993$	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	$0.966434\pi$
$998$	−32.6288	+	10.0550i	−1.03285	+	0.318285i
$999$	8.51051			0.269260

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.8	✓	108	1.1	even	1	trivial
820.2.k.c.83.18	yes	108	4.3	odd	2	inner
820.2.k.c.247.8	yes	108	20.7	even	4	inner
820.2.k.c.247.18	yes	108	5.2	odd	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+(-1.35150 + 0.416481i) 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} +(-1.76529 + 2.20992i) q^{8} -6.73806i q^{9} +(-3.12770 - 0.466377i) q^{10} +1.16859i q^{11} +(1.16363 - 6.13174i) 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} +(2.80627 + 9.10647i) q^{18} -7.04724 q^{19} +(4.42131 - 0.672320i) q^{20} +10.9674 q^{21} +(-0.486696 - 1.57935i) 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} +(6.90582 + 1.31052i) q^{28} -3.06400i q^{29} +(-7.93064 + 5.87244i) q^{30} +10.5463i q^{31} +(-0.430370 + 5.64046i) 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} +(9.52432 - 2.93504i) q^{38} +6.07784 q^{39} +(-5.69538 + 2.75003i) q^{40} +1.00000 q^{41} +(-14.8224 + 4.56772i) 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} +(-4.97920 - 11.4462i) q^{48} +5.35196i q^{49} +(-5.85601 - 3.96323i) q^{50} -4.88142i q^{51} +(3.82702 + 0.726256i) 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} +(1.27610 + 4.14098i) q^{58} +8.18051 q^{59} +(8.27248 - 11.2395i) q^{60} +6.87387 q^{61} +(-4.39233 - 14.2533i) 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} +(0.583293 - 3.07367i) q^{68} -15.2769i q^{69} +(-6.61379 - 8.93182i) q^{70} -8.05271i q^{71} +(14.8906 + 11.8946i) 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} +(-8.21418 + 2.53130i) q^{78} -0.336653 q^{79} +(6.55195 - 6.08867i) q^{80} -16.1873 q^{81} +(-1.35150 + 0.416481i) 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} +(-2.58250 - 2.06290i) q^{88} +8.32204i q^{89} +(-3.14248 + 21.0746i) q^{90} +6.84512i q^{91} +(1.82547 - 9.61936i) 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} +(-2.22899 - 7.23315i) 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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