LMFDB - Embedded newform 630.2.cd.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.66709 - 0.469915i) q^{3} +1.00000i q^{4} +(0.917891 + 2.03899i) q^{5} +(0.846529 + 1.51109i) q^{6} +(-1.29507 - 2.30712i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.55836 + 1.56678i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.66709 - 0.469915i) q^{3} +1.00000i q^{4} +(0.917891 + 2.03899i) q^{5} +(0.846529 + 1.51109i) q^{6} +(-1.29507 - 2.30712i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.55836 + 1.56678i) q^{9} +(0.792736 - 2.09083i) q^{10} +(-2.98627 - 1.72412i) q^{11} +(0.469915 - 1.66709i) q^{12} +(-0.660095 + 0.176872i) q^{13} +(-0.715625 + 2.54713i) q^{14} +(-0.572052 - 3.83050i) q^{15} -1.00000 q^{16} +(-0.346924 + 1.29474i) q^{17} +(-0.701154 - 2.91691i) q^{18} +(3.92228 + 2.26453i) q^{19} +(-2.03899 + 0.917891i) q^{20} +(1.07485 + 4.45474i) q^{21} +(0.892472 + 3.33075i) q^{22} +(6.09817 + 1.63400i) q^{23} +(-1.51109 + 0.846529i) q^{24} +(-3.31495 + 3.74314i) q^{25} +(0.591825 + 0.341690i) q^{26} +(-3.52876 - 3.81417i) q^{27} +(2.30712 - 1.29507i) q^{28} +(3.64800 + 6.31853i) q^{29} +(-2.30407 + 3.11308i) q^{30} +5.83910 q^{31} +(0.707107 + 0.707107i) q^{32} +(4.16818 + 4.27756i) q^{33} +(1.16083 - 0.670205i) q^{34} +(3.51545 - 4.75832i) q^{35} +(-1.56678 + 2.55836i) q^{36} +(-2.37092 - 8.84838i) q^{37} +(-1.17221 - 4.37473i) q^{38} +(1.18355 + 0.0153277i) q^{39} +(2.09083 + 0.792736i) q^{40} +(5.83150 + 3.36682i) q^{41} +(2.38994 - 3.91001i) q^{42} +(2.96558 - 11.0677i) q^{43} +(1.72412 - 2.98627i) q^{44} +(-0.846350 + 6.65460i) q^{45} +(-3.15664 - 5.46747i) q^{46} +(6.44623 + 6.44623i) q^{47} +(1.66709 + 0.469915i) q^{48} +(-3.64558 + 5.97576i) q^{49} +(4.99082 - 0.302773i) q^{50} +(1.18677 - 1.99541i) q^{51} +(-0.176872 - 0.660095i) q^{52} +(6.72766 + 1.80267i) q^{53} +(-0.201817 + 5.19223i) q^{54} +(0.774400 - 7.67153i) q^{55} +(-2.54713 - 0.715625i) q^{56} +(-5.47465 - 5.61831i) q^{57} +(1.88835 - 7.04740i) q^{58} -2.26061 q^{59} +(3.83050 - 0.572052i) q^{60} +7.30460 q^{61} +(-4.12887 - 4.12887i) q^{62} +(0.301485 - 7.93153i) q^{63} -1.00000i q^{64} +(-0.966535 - 1.18358i) q^{65} +(0.0773413 - 5.97204i) q^{66} +(-2.32952 + 2.32952i) q^{67} +(-1.29474 - 0.346924i) q^{68} +(-9.39834 - 5.58964i) q^{69} +(-5.85044 + 0.878837i) q^{70} +9.71446i q^{71} +(2.91691 - 0.701154i) q^{72} +(0.290247 - 1.08322i) q^{73} +(-4.58026 + 7.93324i) q^{74} +(7.28527 - 4.68239i) q^{75} +(-2.26453 + 3.92228i) q^{76} +(-0.110325 + 9.12254i) q^{77} +(-0.826059 - 0.847735i) q^{78} -11.9061i q^{79} +(-0.917891 - 2.03899i) q^{80} +(4.09041 + 8.01677i) q^{81} +(-1.74279 - 6.50420i) q^{82} +(6.92667 + 1.85599i) q^{83} +(-4.45474 + 1.07485i) q^{84} +(-2.95839 + 0.481053i) q^{85} +(-9.92303 + 5.72906i) q^{86} +(-3.11237 - 12.2478i) q^{87} +(-3.33075 + 0.892472i) q^{88} +(3.77839 - 6.54437i) q^{89} +(5.30397 - 4.10705i) q^{90} +(1.26293 + 1.29386i) q^{91} +(-1.63400 + 6.09817i) q^{92} +(-9.73429 - 2.74388i) q^{93} -9.11635i q^{94} +(-1.01713 + 10.0761i) q^{95} +(-0.846529 - 1.51109i) q^{96} +(15.2655 + 4.09038i) q^{97} +(6.80332 - 1.64769i) q^{98} +(-4.93863 - 9.08976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.66709	−	0.469915i	−0.962493	−	0.271306i
$3$	−1.66709	−	0.469915i	−0.962493	−	0.271306i
$4$			1.00000i			0.500000i
$5$	0.917891	+	2.03899i	0.410493	+	0.911864i
$5$	0.917891	+	2.03899i	0.410493	+	0.911864i
$6$	0.846529	+	1.51109i	0.345594	+	0.616899i
$7$	−1.29507	−	2.30712i	−0.489491	−	0.872008i
$7$	−1.29507	−	2.30712i	−0.489491	−	0.872008i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.55836	+	1.56678i	0.852787	+	0.522260i
$10$	0.792736	−	2.09083i	0.250685	−	0.661178i
$11$	−2.98627	−	1.72412i	−0.900395	−	0.519843i	−0.0230664	−	0.999734i	$-0.507343\pi$
$11$	−2.98627	−	1.72412i	−0.900395	−	0.519843i	−0.877328	+	0.479891i	$0.840676\pi$
$12$	0.469915	−	1.66709i	0.135653	−	0.481247i
$13$	−0.660095	+	0.176872i	−0.183077	+	0.0490555i	−0.349193	−	0.937051i	$-0.613544\pi$
$13$	−0.660095	+	0.176872i	−0.183077	+	0.0490555i	0.166115	+	0.986106i	$0.446878\pi$
$14$	−0.715625	+	2.54713i	−0.191259	+	0.680750i
$15$	−0.572052	−	3.83050i	−0.147703	−	0.989032i
$16$	−1.00000			−0.250000
$17$	−0.346924	+	1.29474i	−0.0841413	+	0.314020i	−0.995150	−	0.0983671i	$-0.968638\pi$
$17$	−0.346924	+	1.29474i	−0.0841413	+	0.314020i	0.911009	+	0.412387i	$0.135305\pi$
$18$	−0.701154	−	2.91691i	−0.165263	−	0.687523i
$19$	3.92228	+	2.26453i	0.899833	+	0.519519i	0.877146	−	0.480224i	$-0.159445\pi$
$19$	3.92228	+	2.26453i	0.899833	+	0.519519i	0.0226868	+	0.999743i	$0.492778\pi$
$20$	−2.03899	+	0.917891i	−0.455932	+	0.205247i
$21$	1.07485	+	4.45474i	0.234551	+	0.972104i
$22$	0.892472	+	3.33075i	0.190276	+	0.710119i
$23$	6.09817	+	1.63400i	1.27156	+	0.340712i	0.830627	−	0.556829i	$-0.187982\pi$
$23$	6.09817	+	1.63400i	1.27156	+	0.340712i	0.440929	+	0.897542i	$0.354649\pi$
$24$	−1.51109	+	0.846529i	−0.308450	+	0.172797i
$25$	−3.31495	+	3.74314i	−0.662991	+	0.748628i
$26$	0.591825	+	0.341690i	0.116066	+	0.0670110i
$27$	−3.52876	−	3.81417i	−0.679109	−	0.734037i
$28$	2.30712	−	1.29507i	0.436004	−	0.244745i
$29$	3.64800	+	6.31853i	0.677417	+	1.17332i	0.975756	+	0.218861i	$0.0702341\pi$
$29$	3.64800	+	6.31853i	0.677417	+	1.17332i	−0.298339	+	0.954460i	$0.596433\pi$
$30$	−2.30407	+	3.11308i	−0.420664	+	0.568368i
$31$	5.83910			1.04873			0.524367	−	0.851493i	$-0.324302\pi$
$31$	5.83910			1.04873			0.524367	+	0.851493i	$0.324302\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	4.16818	+	4.27756i	0.725587	+	0.744627i
$34$	1.16083	−	0.670205i	0.199080	−	0.114939i
$35$	3.51545	−	4.75832i	0.594220	−	0.804302i
$36$	−1.56678	+	2.55836i	−0.261130	+	0.426393i
$37$	−2.37092	−	8.84838i	−0.389776	−	1.45467i	−0.830498	−	0.557022i	$-0.811944\pi$
$37$	−2.37092	−	8.84838i	−0.389776	−	1.45467i	0.440722	−	0.897644i	$-0.354723\pi$
$38$	−1.17221	−	4.37473i	−0.190157	−	0.709676i
$39$	1.18355	+	0.0153277i	0.189520	+	0.00245439i
$40$	2.09083	+	0.792736i	0.330589	+	0.125343i
$41$	5.83150	+	3.36682i	0.910728	+	0.525809i	0.880665	−	0.473739i	$-0.157096\pi$
$41$	5.83150	+	3.36682i	0.910728	+	0.525809i	0.0300625	+	0.999548i	$0.490429\pi$
$42$	2.38994	−	3.91001i	0.368776	−	0.603327i
$43$	2.96558	−	11.0677i	0.452247	−	1.68781i	−0.243811	−	0.969823i	$-0.578398\pi$
$43$	2.96558	−	11.0677i	0.452247	−	1.68781i	0.696058	−	0.717985i	$-0.254936\pi$
$44$	1.72412	−	2.98627i	0.259922	−	0.450197i
$45$	−0.846350	+	6.65460i	−0.126166	+	0.992009i
$46$	−3.15664	−	5.46747i	−0.465422	−	0.806134i
$47$	6.44623	+	6.44623i	0.940279	+	0.940279i	0.998315	−	0.0580353i	$-0.0184836\pi$
$47$	6.44623	+	6.44623i	0.940279	+	0.940279i	−0.0580353	+	0.998315i	$0.518484\pi$
$48$	1.66709	+	0.469915i	0.240623	+	0.0678264i
$49$	−3.64558	+	5.97576i	−0.520797	+	0.853680i
$50$	4.99082	−	0.302773i	0.705809	−	0.0428186i
$51$	1.18677	−	1.99541i	0.166181	−	0.279414i
$52$	−0.176872	−	0.660095i	−0.0245277	−	0.0915387i
$53$	6.72766	+	1.80267i	0.924116	+	0.247616i	0.689344	−	0.724434i	$-0.257899\pi$
$53$	6.72766	+	1.80267i	0.924116	+	0.247616i	0.234772	+	0.972050i	$0.424566\pi$
$54$	−0.201817	+	5.19223i	−0.0274639	+	0.706573i
$55$	0.774400	−	7.67153i	0.104420	−	1.03443i
$56$	−2.54713	−	0.715625i	−0.340375	−	0.0956294i
$57$	−5.47465	−	5.61831i	−0.725135	−	0.744163i
$58$	1.88835	−	7.04740i	0.247952	−	0.925369i
$59$	−2.26061			−0.294307			−0.147153	−	0.989114i	$-0.547011\pi$
$59$	−2.26061			−0.294307			−0.147153	+	0.989114i	$0.547011\pi$
$60$	3.83050	−	0.572052i	0.494516	−	0.0738516i
$61$	7.30460			0.935258			0.467629	−	0.883925i	$-0.345108\pi$
$61$	7.30460			0.935258			0.467629	+	0.883925i	$0.345108\pi$
$62$	−4.12887	−	4.12887i	−0.524367	−	0.524367i
$63$	0.301485	−	7.93153i	0.0379836	−	0.999278i
$64$		−	1.00000i		−	0.125000i
$65$	−0.966535	−	1.18358i	−0.119884	−	0.146805i
$66$	0.0773413	−	5.97204i	0.00952006	−	0.735107i
$67$	−2.32952	+	2.32952i	−0.284596	+	0.284596i	−0.834939	−	0.550343i	$-0.814497\pi$
$67$	−2.32952	+	2.32952i	−0.284596	+	0.284596i	0.550343	+	0.834939i	$0.314497\pi$
$68$	−1.29474	−	0.346924i	−0.157010	−	0.0420707i
$69$	−9.39834	−	5.58964i	−1.13143	−	0.672914i
$70$	−5.85044	+	0.878837i	−0.699261	+	0.105041i
$71$			9.71446i			1.15289i	0.817134	+	0.576447i	$0.195561\pi$
$71$			9.71446i			1.15289i	−0.817134	+	0.576447i	$0.804439\pi$
$72$	2.91691	−	0.701154i	0.343762	−	0.0826317i
$73$	0.290247	−	1.08322i	0.0339709	−	0.126781i	−0.946858	−	0.321652i	$-0.895762\pi$
$73$	0.290247	−	1.08322i	0.0339709	−	0.126781i	0.980829	+	0.194871i	$0.0624287\pi$
$74$	−4.58026	+	7.93324i	−0.532444	+	0.922221i
$75$	7.28527	−	4.68239i	0.841231	−	0.540676i
$76$	−2.26453	+	3.92228i	−0.259759	+	0.449916i
$77$	−0.110325	+	9.12254i	−0.0125727	+	1.03961i
$78$	−0.826059	−	0.847735i	−0.0935327	−	0.0959871i
$79$		−	11.9061i		−	1.33954i	−0.742568	−	0.669771i	$-0.766392\pi$
$79$		−	11.9061i		−	1.33954i	0.742568	−	0.669771i	$-0.233608\pi$
$80$	−0.917891	−	2.03899i	−0.102623	−	0.227966i
$81$	4.09041	+	8.01677i	0.454490	+	0.890752i
$82$	−1.74279	−	6.50420i	−0.192459	−	0.718268i
$83$	6.92667	+	1.85599i	0.760300	+	0.203722i	0.618082	−	0.786113i	$-0.287910\pi$
$83$	6.92667	+	1.85599i	0.760300	+	0.203722i	0.142218	+	0.989835i	$0.454577\pi$
$84$	−4.45474	+	1.07485i	−0.486052	+	0.117275i
$85$	−2.95839	+	0.481053i	−0.320883	+	0.0521775i
$86$	−9.92303	+	5.72906i	−1.07003	+	0.617781i
$87$	−3.11237	−	12.2478i	−0.333681	−	1.31310i
$88$	−3.33075	+	0.892472i	−0.355059	+	0.0951379i
$89$	3.77839	−	6.54437i	0.400509	−	0.693702i	−0.593278	−	0.804997i	$-0.702167\pi$
$89$	3.77839	−	6.54437i	0.400509	−	0.693702i	0.993787	+	0.111296i	$0.0355000\pi$
$90$	5.30397	−	4.10705i	0.559088	−	0.432921i
$91$	1.26293	+	1.29386i	0.132392	+	0.135633i
$92$	−1.63400	+	6.09817i	−0.170356	+	0.635778i
$93$	−9.73429	−	2.74388i	−1.00940	−	0.284527i
$94$		−	9.11635i		−	0.940279i
$95$	−1.01713	+	10.0761i	−0.104355	+	1.03378i
$96$	−0.846529	−	1.51109i	−0.0863985	−	0.154225i
$97$	15.2655	+	4.09038i	1.54998	+	0.415315i	0.929473	−	0.368890i	$-0.120262\pi$
$97$	15.2655	+	4.09038i	1.54998	+	0.415315i	0.620502	+	0.784205i	$0.286929\pi$
$98$	6.80332	−	1.64769i	0.687239	−	0.166441i
$99$	−4.93863	−	9.08976i	−0.496351	−	0.913555i
$100$	−3.74314	−	3.31495i	−0.374314	−	0.331495i
$101$	−0.330469	−	0.190796i	−0.0328829	−	0.0189849i	0.483468	−	0.875362i	$-0.339377\pi$
$101$	−0.330469	−	0.190796i	−0.0328829	−	0.0189849i	−0.516351	+	0.856377i	$0.672710\pi$
$102$	−2.25014	+	0.571799i	−0.222797	+	0.0566165i
$103$	−5.13815	+	19.1759i	−0.506277	+	1.88945i	−0.0518814	+	0.998653i	$0.516522\pi$
$103$	−5.13815	+	19.1759i	−0.506277	+	1.88945i	−0.454396	+	0.890800i	$0.650145\pi$
$104$	−0.341690	+	0.591825i	−0.0335055	+	0.0580332i
$105$	−8.09657	+	6.28057i	−0.790145	+	0.612920i
$106$	−3.48249	−	6.03186i	−0.338250	−	0.585866i
$107$	−0.202568	+	0.0542780i	−0.0195830	+	0.00524726i	−0.268597	−	0.963253i	$-0.586560\pi$
$107$	−0.202568	+	0.0542780i	−0.0195830	+	0.00524726i	0.249014	+	0.968500i	$0.419893\pi$
$108$	3.81417	−	3.52876i	0.367019	−	0.339555i
$109$	−0.714728	+	0.412648i	−0.0684585	+	0.0395245i	−0.533839	−	0.845586i	$-0.679251\pi$
$109$	−0.714728	+	0.412648i	−0.0684585	+	0.0395245i	0.465380	+	0.885111i	$0.345918\pi$
$110$	−5.97218	+	4.87701i	−0.569425	+	0.465004i
$111$	−0.205463	+	15.8652i	−0.0195017	+	1.50585i
$112$	1.29507	+	2.30712i	0.122373	+	0.218002i
$113$	0.310324	+	1.15814i	0.0291928	+	0.108949i	0.978985	−	0.203933i	$-0.0653723\pi$
$113$	0.310324	+	1.15814i	0.0291928	+	0.108949i	−0.949792	+	0.312882i	$0.898706\pi$
$114$	−0.101583	+	7.84390i	−0.00951412	+	0.734649i
$115$	2.26575	+	13.9339i	0.211282	+	1.29935i
$116$	−6.31853	+	3.64800i	−0.586660	+	0.338709i
$117$	−1.96588	−	0.581721i	−0.181746	−	0.0537801i
$118$	1.59849	+	1.59849i	0.147153	+	0.147153i
$119$	3.43640	−	0.876382i	0.315014	−	0.0803378i
$120$	−3.11308	−	2.30407i	−0.284184	−	0.210332i
$121$	0.445209	+	0.771124i	0.0404735	+	0.0701022i
$122$	−5.16513	−	5.16513i	−0.467629	−	0.467629i
$123$	−8.13951	−	8.35309i	−0.733914	−	0.753173i
$124$			5.83910i			0.524367i
$125$	−10.6750	−	3.32336i	−0.954800	−	0.297250i
$126$	−5.82162	+	5.39525i	−0.518631	+	0.480647i
$127$	−10.6034	+	10.6034i	−0.940895	+	0.940895i	−0.998348	−	0.0574529i	$-0.981702\pi$
$127$	−10.6034	+	10.6034i	−0.940895	+	0.940895i	0.0574529	+	0.998348i	$0.481702\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−10.1448	+	17.0572i	−0.893196	+	1.50181i
$130$	−0.153472	+	1.52036i	−0.0134604	+	0.133344i
$131$	1.83677	−	1.06046i	0.160479	−	0.0926526i	−0.417610	−	0.908626i	$-0.637132\pi$
$131$	1.83677	−	1.06046i	0.160479	−	0.0926526i	0.578089	+	0.815974i	$0.303799\pi$
$132$	−4.27756	+	4.16818i	−0.372314	+	0.362794i
$133$	0.144904	−	11.9819i	0.0125648	−	1.03896i
$134$	3.29444			0.284596
$135$	4.53804	−	10.6961i	0.390572	−	0.920572i
$136$	0.670205	+	1.16083i	0.0574696	+	0.0995402i
$137$	−9.78797	+	2.62268i	−0.836243	+	0.224071i	−0.651435	−	0.758704i	$-0.725833\pi$
$137$	−9.78797	+	2.62268i	−0.836243	+	0.224071i	−0.184807	+	0.982775i	$0.559166\pi$
$138$	2.69316	+	10.5981i	0.229257	+	0.902170i
$139$	−1.59111	−	0.918626i	−0.134956	−	0.0779168i	0.431002	−	0.902351i	$-0.358160\pi$
$139$	−1.59111	−	0.918626i	−0.134956	−	0.0779168i	−0.565958	+	0.824434i	$0.691494\pi$
$140$	4.75832	+	3.51545i	0.402151	+	0.297110i
$141$	−7.71725	−	13.7756i	−0.649909	−	1.16012i
$142$	6.86916	−	6.86916i	0.576447	−	0.576447i
$143$	2.27617	+	0.609898i	0.190343	+	0.0510023i
$144$	−2.55836	−	1.56678i	−0.213197	−	0.130565i
$145$	−9.53494	+	13.2380i	−0.791834	+	1.09935i
$146$	−0.971186	+	0.560714i	−0.0803759	+	0.0464051i
$147$	8.88560	−	8.24900i	0.732872	−	0.680366i
$148$	8.84838	−	2.37092i	0.727333	−	0.194888i
$149$	−0.00829922	−	0.0143747i	−0.000679899	−	0.00117762i	0.865685	−	0.500589i	$-0.166883\pi$
$149$	−0.00829922	−	0.0143747i	−0.000679899	−	0.00117762i	−0.866365	+	0.499411i	$0.833550\pi$
$150$	−8.46242	−	1.84051i	−0.690953	−	0.150277i
$151$	−1.76191	+	3.05171i	−0.143382	+	0.248345i	−0.928768	−	0.370661i	$-0.879131\pi$
$151$	−1.76191	+	3.05171i	−0.143382	+	0.248345i	0.785386	+	0.619006i	$0.212464\pi$
$152$	4.37473	−	1.17221i	0.354838	−	0.0950785i
$153$	−2.91612	+	2.76885i	−0.235754	+	0.223848i
$154$	6.52862	−	6.37260i	0.526091	−	0.513519i
$155$	5.35966	+	11.9059i	0.430498	+	0.956302i
$156$	−0.0153277	+	1.18355i	−0.00122719	+	0.0947599i
$157$	5.05920	−	5.05920i	0.403768	−	0.403768i	−0.475791	−	0.879559i	$-0.657838\pi$
$157$	5.05920	−	5.05920i	0.403768	−	0.403768i	0.879559	+	0.475791i	$0.157838\pi$
$158$	−8.41889	+	8.41889i	−0.669771	+	0.669771i
$159$	−10.3685	−	6.16664i	−0.822275	−	0.489046i
$160$	−0.792736	+	2.09083i	−0.0626713	+	0.165295i
$161$	−4.12773	−	16.1853i	−0.325311	−	1.27558i
$162$	2.77635	−	8.56107i	0.218131	−	0.672621i
$163$	−6.03317	+	1.61658i	−0.472554	+	0.126621i	−0.487234	−	0.873272i	$-0.661994\pi$
$163$	−6.03317	+	1.61658i	−0.472554	+	0.126621i	0.0146792	+	0.999892i	$0.495327\pi$
$164$	−3.36682	+	5.83150i	−0.262904	+	0.455364i
$165$	−4.89596	+	12.4252i	−0.381150	+	0.967301i
$166$	−3.58551	−	6.21028i	−0.278289	−	0.482011i
$167$	−14.4756	+	3.87872i	−1.12015	+	0.300144i	−0.770945	−	0.636901i	$-0.780216\pi$
$167$	−14.4756	+	3.87872i	−1.12015	+	0.300144i	−0.349208	+	0.937045i	$0.613549\pi$
$168$	3.91001	+	2.38994i	0.301664	+	0.184388i
$169$	−10.8539	+	6.26650i	−0.834914	+	0.482038i
$170$	2.43205	+	1.75174i	0.186530	+	0.134353i
$171$	6.48659	+	11.9388i	0.496042	+	0.912985i
$172$	11.0677	+	2.96558i	0.843904	+	0.226123i
$173$	4.26550	−	4.26550i	0.324300	−	0.324300i	−0.526114	−	0.850414i	$-0.676352\pi$
$173$	4.26550	−	4.26550i	0.324300	−	0.324300i	0.850414	+	0.526114i	$0.176352\pi$
$174$	−6.45972	+	10.8613i	−0.489710	+	0.823391i
$175$	12.9290	+	2.80036i	0.977338	+	0.211687i
$176$	2.98627	+	1.72412i	0.225099	+	0.129961i
$177$	3.76864	+	1.06230i	0.283268	+	0.0798470i
$178$	−7.29930	+	1.95584i	−0.547105	+	0.146596i
$179$	−10.7312	−	18.5870i	−0.802089	−	1.38926i	−0.918239	−	0.396027i	$-0.870389\pi$
$179$	−10.7312	−	18.5870i	−0.802089	−	1.38926i	0.116150	−	0.993232i	$-0.462945\pi$
$180$	−6.65460	−	0.846350i	−0.496005	−	0.0630832i
$181$	15.1316			1.12473			0.562363	−	0.826890i	$-0.309892\pi$
$181$	15.1316			1.12473			0.562363	+	0.826890i	$0.309892\pi$
$182$	0.0218644	−	1.80792i	0.00162069	−	0.134012i
$183$	−12.1774	−	3.43254i	−0.900179	−	0.253741i
$184$	5.46747	−	3.15664i	0.403067	−	0.232711i
$185$	15.8655	−	12.9561i	1.16646	−	0.952553i
$186$	4.94297	+	8.82340i	0.362436	+	0.646963i
$187$	3.26829	−	3.26829i	0.239001	−	0.239001i
$188$	−6.44623	+	6.44623i	−0.470140	+	0.470140i
$189$	−4.22975	+	13.0809i	−0.307669	+	0.951494i
$190$	7.84408	−	6.40564i	0.569069	−	0.464714i
$191$		−	3.91285i		−	0.283124i	−0.989929	−	0.141562i	$-0.954788\pi$
$191$		−	3.91285i		−	0.283124i	0.989929	−	0.141562i	$-0.0452124\pi$
$192$	−0.469915	+	1.66709i	−0.0339132	+	0.120312i
$193$	3.24570	+	3.24570i	0.233630	+	0.233630i	0.814206	−	0.580576i	$-0.197173\pi$
$193$	3.24570	+	3.24570i	0.233630	+	0.233630i	−0.580576	+	0.814206i	$0.697173\pi$
$194$	−7.90200	−	13.6867i	−0.567330	−	0.982645i
$195$	1.05512	+	2.42732i	0.0755585	+	0.173824i
$196$	−5.97576	−	3.64558i	−0.426840	−	0.260399i
$197$	−16.5738	−	16.5738i	−1.18083	−	1.18083i	−0.979529	−	0.201304i	$-0.935482\pi$
$197$	−16.5738	−	16.5738i	−1.18083	−	1.18083i	−0.201304	−	0.979529i	$-0.564518\pi$
$198$	−2.93529	+	9.91957i	−0.208602	+	0.704953i
$199$	4.91498	−	2.83766i	0.348414	−	0.201157i	−0.315573	−	0.948901i	$-0.602197\pi$
$199$	4.91498	−	2.83766i	0.348414	−	0.201157i	0.663986	+	0.747745i	$0.268863\pi$
$200$	0.302773	+	4.99082i	0.0214093	+	0.352905i
$201$	4.97819	−	2.78883i	0.351134	−	0.196709i
$202$	0.0987634	+	0.368590i	0.00694897	+	0.0259339i
$203$	9.85316	−	16.5993i	0.691556	−	1.16504i
$204$	1.99541	+	1.18677i	0.139707	+	0.0830904i
$205$	−1.51223	+	14.9807i	−0.105618	+	1.04630i
$206$	17.1926	−	9.92615i	1.19787	−	0.691588i
$207$	13.0412	+	13.7348i	0.906426	+	0.954637i
$208$	0.660095	−	0.176872i	0.0457694	−	0.0122639i
$209$	−7.80866	−	13.5250i	−0.540136	−	0.935543i
$210$	10.1662	+	1.28411i	0.701533	+	0.0886121i
$211$	11.4417	−	19.8177i	0.787681	−	1.36430i	−0.139703	−	0.990193i	$-0.544615\pi$
$211$	11.4417	−	19.8177i	0.787681	−	1.36430i	0.927384	−	0.374111i	$-0.122052\pi$
$212$	−1.80267	+	6.72766i	−0.123808	+	0.462058i
$213$	4.56497	−	16.1948i	0.312787	−	1.10965i
$214$	0.181618	+	0.104857i	0.0124151	+	0.00716789i
$215$	25.2890	−	4.11215i	1.72470	−	0.280446i
$216$	−5.19223	−	0.201817i	−0.353287	−	0.0137319i
$217$	−7.56205	−	13.4715i	−0.513345	−	0.914504i
$218$	0.797175	+	0.213603i	0.0539915	+	0.0144670i
$219$	−0.992887	+	1.66943i	−0.0670931	+	0.112809i
$220$	7.67153	+	0.774400i	0.517215	+	0.0522100i
$221$		−	0.916010i		−	0.0616175i
$222$	11.3636	−	11.0731i	0.762678	−	0.743176i
$223$	4.78883	−	17.8722i	0.320684	−	1.19681i	−0.597896	−	0.801573i	$-0.703997\pi$
$223$	4.78883	−	17.8722i	0.320684	−	1.19681i	0.918580	−	0.395235i	$-0.129337\pi$
$224$	0.715625	−	2.54713i	0.0478147	−	0.170187i
$225$	−14.3455	+	4.38250i	−0.956367	+	0.292166i
$226$	0.599499	−	1.03836i	0.0398781	−	0.0690709i
$227$	−18.7727	+	5.03013i	−1.24599	+	0.333861i	−0.820785	−	0.571237i	$-0.806464\pi$
$227$	−18.7727	+	5.03013i	−1.24599	+	0.333861i	−0.425202	+	0.905099i	$0.639797\pi$
$228$	5.61831	−	5.47465i	0.372081	−	0.362567i
$229$	−10.0283	+	5.78983i	−0.662688	+	0.382603i	−0.793300	−	0.608831i	$-0.791639\pi$
$229$	−10.0283	+	5.78983i	−0.662688	+	0.382603i	0.130613	+	0.991433i	$0.458306\pi$
$230$	8.25065	−	11.4549i	0.544032	−	0.755314i
$231$	4.47074	−	15.1562i	0.294153	−	0.997207i
$232$	7.04740	+	1.88835i	0.462685	+	0.123976i
$233$	4.96006	+	18.5112i	0.324944	+	1.21271i	0.914368	+	0.404885i	$0.132688\pi$
$233$	4.96006	+	18.5112i	0.324944	+	1.21271i	−0.589423	+	0.807824i	$0.700645\pi$
$234$	0.978748	+	1.80143i	0.0639828	+	0.117763i
$235$	−7.22686	+	19.0607i	−0.471428	+	1.24338i
$236$		−	2.26061i		−	0.147153i
$237$	−5.59486	+	19.8485i	−0.363425	+	1.28930i
$238$	−3.04960	−	1.81021i	−0.197676	−	0.117338i
$239$	−0.403640	+	0.699125i	−0.0261093	+	0.0452226i	−0.878785	−	0.477218i	$-0.841645\pi$
$239$	−0.403640	+	0.699125i	−0.0261093	+	0.0452226i	0.852676	+	0.522441i	$0.174978\pi$
$240$	0.572052	+	3.83050i	0.0369258	+	0.247258i
$241$	−2.13386	+	3.69595i	−0.137454	+	0.238077i	−0.926532	−	0.376215i	$-0.877225\pi$
$241$	−2.13386	+	3.69595i	−0.137454	+	0.238077i	0.789078	+	0.614293i	$0.210559\pi$
$242$	0.230457	−	0.860077i	0.0148143	−	0.0552879i
$243$	−3.05187	−	15.2868i	−0.195777	−	0.980648i
$244$			7.30460i			0.467629i
$245$	−15.5308	−	1.94821i	−0.992224	−	0.124466i
$246$	−0.151030	+	11.6620i	−0.00962931	+	0.743544i
$247$	−2.98961	−	0.801063i	−0.190224	−	0.0509704i
$248$	4.12887	−	4.12887i	0.262183	−	0.262183i
$249$	−10.6752	−	6.34905i	−0.676513	−	0.402355i
$250$	5.19838	+	9.89832i	0.328775	+	0.626025i
$251$			17.5709i			1.10907i	0.832162	+	0.554533i	$0.187103\pi$
$251$			17.5709i			1.10907i	−0.832162	+	0.554533i	$0.812897\pi$
$252$	7.93153	+	0.301485i	0.499639	+	0.0189918i
$253$	−15.3936	−	15.3936i	−0.967785	−	0.967785i
$254$	14.9954			0.940895
$255$	5.15795	+	0.588235i	0.323003	+	0.0368367i
$256$	1.00000			0.0625000
$257$	0.374599	−	1.39802i	0.0233668	−	0.0872062i	−0.953258	−	0.302158i	$-0.902293\pi$
$257$	0.374599	−	1.39802i	0.0233668	−	0.0872062i	0.976625	+	0.214952i	$0.0689595\pi$
$258$	19.2347	−	4.88787i	1.19750	−	0.304305i
$259$	−17.3438	+	16.9293i	−1.07769	+	1.05193i
$260$	1.18358	−	0.966535i	0.0734024	−	0.0599420i
$261$	−0.566829	+	21.8807i	−0.0350859	+	1.35438i
$262$	−2.04865	−	0.548933i	−0.126566	−	0.0339132i
$263$	−0.485480	−	1.81184i	−0.0299360	−	0.111723i	0.949341	−	0.314247i	$-0.101752\pi$
$263$	−0.485480	−	1.81184i	−0.0299360	−	0.111723i	−0.979277	+	0.202525i	$0.935085\pi$
$264$	5.97204	+	0.0773413i	0.367554	+	0.00476003i
$265$	2.49963	+	15.3723i	0.153551	+	0.944312i
$266$	−8.57494	+	8.37001i	−0.525763	+	0.513198i
$267$	−9.37421	+	9.13451i	−0.573692	+	0.559023i
$268$	−2.32952	−	2.32952i	−0.142298	−	0.142298i
$269$	6.81683	+	11.8071i	0.415629	+	0.719891i	0.995494	−	0.0948214i	$-0.0302280\pi$
$269$	6.81683	+	11.8071i	0.415629	+	0.719891i	−0.579865	+	0.814713i	$0.696895\pi$
$270$	−10.7721	+	4.35440i	−0.655572	+	0.265000i
$271$	10.5680	−	18.3043i	0.641960	−	1.11191i	−0.343035	−	0.939323i	$-0.611455\pi$
$271$	10.5680	−	18.3043i	0.641960	−	1.11191i	0.984995	−	0.172584i	$-0.0552116\pi$
$272$	0.346924	−	1.29474i	0.0210353	−	0.0785049i
$273$	−1.49742	−	2.75044i	−0.0906280	−	0.166464i
$274$	8.77565	+	5.06662i	0.530157	+	0.306086i
$275$	16.3530	−	5.46263i	0.986122	−	0.329409i
$276$	5.58964	−	9.39834i	0.336457	−	0.565713i
$277$	0.0691447	+	0.258052i	0.00415450	+	0.0155048i	0.967972	−	0.251058i	$-0.0807786\pi$
$277$	0.0691447	+	0.258052i	0.00415450	+	0.0155048i	−0.963817	+	0.266563i	$0.914112\pi$
$278$	0.475516	+	1.77465i	0.0285195	+	0.106436i
$279$	14.9385	+	9.14858i	0.894346	+	0.547711i
$280$	−0.878837	−	5.85044i	−0.0525206	−	0.349631i
$281$	12.6201	−	7.28624i	0.752854	−	0.434661i	−0.0738700	−	0.997268i	$-0.523535\pi$
$281$	12.6201	−	7.28624i	0.752854	−	0.434661i	0.826724	+	0.562607i	$0.190202\pi$
$282$	−4.28391	+	15.1977i	−0.255103	+	0.905012i
$283$	−15.7458	−	15.7458i	−0.935993	−	0.935993i	0.0620784	−	0.998071i	$-0.480227\pi$
$283$	−15.7458	−	15.7458i	−0.935993	−	0.935993i	−0.998071	+	0.0620784i	$0.980227\pi$
$284$	−9.71446			−0.576447
$285$	6.43054	−	16.3197i	0.380912	−	0.966698i
$286$	−1.17823	−	2.04076i	−0.0696704	−	0.120673i
$287$	0.215439	−	17.8142i	0.0127169	−	1.05154i
$288$	0.701154	+	2.91691i	0.0413159	+	0.171881i
$289$	13.1664	+	7.60165i	0.774497	+	0.447156i
$290$	16.1029	−	2.61843i	0.945593	−	0.153759i
$291$	−23.5268	−	13.9925i	−1.37916	−	0.820255i
$292$	1.08322	+	0.290247i	0.0633905	+	0.0169854i
$293$	3.41571	+	12.7476i	0.199548	+	0.744724i	0.991042	+	0.133547i	$0.0426368\pi$
$293$	3.41571	+	12.7476i	0.199548	+	0.744724i	−0.791494	+	0.611177i	$0.790697\pi$
$294$	−12.1160	−	0.450146i	−0.706619	−	0.0262530i
$295$	−2.07499	−	4.60936i	−0.120811	−	0.268367i
$296$	−7.93324	−	4.58026i	−0.461110	−	0.266222i
$297$	3.96172	+	17.4742i	0.229882	+	1.01395i
$298$	−0.00429599	+	0.0160329i	−0.000248860	+	0.000928759i
$299$	−4.31438			−0.249507
$300$	4.68239	+	7.28527i	0.270338	+	0.420615i
$301$	−29.3751	+	7.49151i	−1.69315	+	0.431804i
$302$	3.40374	−	0.912031i	0.195863	−	0.0524815i
$303$	0.461262	+	0.473366i	0.0264988	+	0.0271942i
$304$	−3.92228	−	2.26453i	−0.224958	−	0.129880i
$305$	6.70482	+	14.8940i	0.383917	+	0.852828i
$306$	4.01988	+	0.104137i	0.229801	+	0.00595311i
$307$	−10.6557	+	10.6557i	−0.608152	+	0.608152i	−0.942463	−	0.334311i	$-0.891496\pi$
$307$	−10.6557	+	10.6557i	−0.608152	+	0.608152i	0.334311	+	0.942463i	$0.391496\pi$
$308$	−9.12254	−	0.110325i	−0.519805	−	0.00628633i
$309$	17.5768	−	29.5533i	0.999908	−	1.68123i
$310$	4.62887	−	12.2086i	0.262902	−	0.693400i
$311$			22.8076i			1.29330i	0.762786	+	0.646651i	$0.223831\pi$
$311$			22.8076i			1.29330i	−0.762786	+	0.646651i	$0.776169\pi$
$312$	0.847735	−	0.826059i	0.0479936	−	0.0467664i
$313$	21.4805	+	21.4805i	1.21415	+	1.21415i	0.969649	+	0.244502i	$0.0786243\pi$
$313$	21.4805	+	21.4805i	1.21415	+	1.21415i	0.244502	+	0.969649i	$0.421376\pi$
$314$	−7.15479			−0.403768
$315$	16.4490	−	6.66555i	0.926798	−	0.375561i
$316$	11.9061			0.669771
$317$	−8.52005	−	8.52005i	−0.478534	−	0.478534i	0.426129	−	0.904662i	$-0.359877\pi$
$317$	−8.52005	−	8.52005i	−0.478534	−	0.478534i	−0.904662	+	0.426129i	$0.859877\pi$
$318$	2.97116	+	11.6921i	0.166614	+	0.655661i
$319$		−	25.1584i		−	1.40860i
$320$	2.03899	−	0.917891i	0.113983	−	0.0513117i
$321$	0.363205	+	0.00470371i	0.0202721	+	0.000262536i
$322$	−8.52601	+	14.3635i	−0.475136	+	0.800447i
$323$	−4.29270	+	4.29270i	−0.238852	+	0.238852i
$324$	−8.01677	+	4.09041i	−0.445376	+	0.227245i
$325$	1.52613	−	3.05715i	0.0846544	−	0.169580i
$326$	5.40919	+	3.12300i	0.299587	+	0.172967i
$327$	1.38542	−	0.352059i	0.0766141	−	0.0194689i
$328$	6.50420	−	1.74279i	0.359134	−	0.0962297i
$329$	6.52388	−	23.2205i	0.359673	−	1.28019i
$330$	12.2479	−	5.32398i	0.674226	−	0.293076i
$331$	2.66188			0.146310			0.0731550	−	0.997321i	$-0.476693\pi$
$331$	2.66188			0.146310			0.0731550	+	0.997321i	$0.476693\pi$
$332$	−1.85599	+	6.92667i	−0.101861	+	0.380150i
$333$	7.79780	−	26.3521i	0.427317	−	1.44408i
$334$	12.9784	+	7.49311i	0.710149	+	0.410005i
$335$	−6.88811	−	2.61162i	−0.376337	−	0.142688i
$336$	−1.07485	−	4.45474i	−0.0586377	−	0.243026i
$337$	0.276415	+	1.03160i	0.0150573	+	0.0561946i	0.973046	−	0.230612i	$-0.0740729\pi$
$337$	0.276415	+	1.03160i	0.0150573	+	0.0561946i	−0.957988	+	0.286807i	$0.907406\pi$
$338$	12.1059	+	3.24378i	0.658476	+	0.176438i
$339$	0.0268925	−	2.07655i	0.00146060	−	0.112783i
$340$	−0.481053	−	2.95839i	−0.0260888	−	0.160441i
$341$	−17.4371	−	10.0673i	−0.944274	−	0.545177i
$342$	3.85532	−	13.0287i	0.208472	−	0.704513i
$343$	18.5081	+	0.671751i	0.999342	+	0.0362712i
$344$	−5.72906	−	9.92303i	−0.308890	−	0.535014i
$345$	2.77057	−	24.2938i	0.149162	−	1.30793i
$346$	−6.03233			−0.324300
$347$	25.5768	+	25.5768i	1.37303	+	1.37303i	0.855914	+	0.517118i	$0.172995\pi$
$347$	25.5768	+	25.5768i	1.37303	+	1.37303i	0.517118	+	0.855914i	$0.327005\pi$
$348$	12.2478	−	3.11237i	0.656550	−	0.166840i
$349$	23.3688	−	13.4920i	1.25090	−	0.722208i	0.279613	−	0.960113i	$-0.409794\pi$
$349$	23.3688	−	13.4920i	1.25090	−	0.722208i	0.971288	+	0.237905i	$0.0764606\pi$
$350$	−7.16200	−	11.1223i	−0.382825	−	0.594512i
$351$	3.00393	+	1.89358i	0.160338	+	0.101072i
$352$	−0.892472	−	3.33075i	−0.0475689	−	0.177530i
$353$	−3.28017	−	12.2417i	−0.174586	−	0.651563i	−0.996622	−	0.0821273i	$-0.973829\pi$
$353$	−3.28017	−	12.2417i	−0.174586	−	0.651563i	0.822036	−	0.569435i	$-0.192838\pi$
$354$	−1.91367	−	3.41599i	−0.101711	−	0.181558i
$355$	−19.8077	+	8.91681i	−1.05128	+	0.473255i
$356$	6.54437	+	3.77839i	0.346851	+	0.200254i
$357$	−6.14060	−	0.153811i	−0.324995	−	0.00814052i
$358$	−5.55489	+	20.7311i	−0.293585	+	1.09567i
$359$	17.1139	−	29.6421i	0.903237	−	1.56445i	0.0799695	−	0.996797i	$-0.474518\pi$
$359$	17.1139	−	29.6421i	0.903237	−	1.56445i	0.823267	−	0.567654i	$-0.192149\pi$
$360$	4.10705	+	5.30397i	0.216461	+	0.279544i
$361$	0.756185	+	1.30975i	0.0397992	+	0.0689343i
$362$	−10.6997	−	10.6997i	−0.562363	−	0.562363i
$363$	−0.379839	−	1.49474i	−0.0199364	−	0.0784536i
$364$	−1.29386	+	1.26293i	−0.0678164	+	0.0661958i
$365$	2.47508	−	0.402464i	0.129552	−	0.0210659i
$366$	6.18355	+	11.0379i	0.323219	+	0.576960i
$367$	−3.87641	−	14.4670i	−0.202347	−	0.755170i	−0.990242	−	0.139360i	$-0.955496\pi$
$367$	−3.87641	−	14.4670i	−0.202347	−	0.755170i	0.787895	−	0.615810i	$-0.211171\pi$
$368$	−6.09817	−	1.63400i	−0.317889	−	0.0851781i
$369$	9.64402	+	17.7502i	0.502048	+	0.924039i
$370$	−20.3800	−	2.05725i	−1.05950	−	0.106951i
$371$	−4.55383	−	17.8561i	−0.236423	−	0.927042i
$372$	2.74388	−	9.73429i	0.142264	−	0.504699i
$373$	−0.837104	+	3.12412i	−0.0433436	+	0.161761i	−0.984205	−	0.177030i	$-0.943351\pi$
$373$	−0.837104	+	3.12412i	−0.0433436	+	0.161761i	0.940862	+	0.338790i	$0.110018\pi$
$374$	−4.62207			−0.239001
$375$	16.2344	+	10.5567i	0.838342	+	0.545144i
$376$	9.11635			0.470140
$377$	−3.52560	−	3.52560i	−0.181578	−	0.181578i
$378$	12.2405	−	6.25869i	0.629581	−	0.321912i
$379$			16.7640i			0.861107i	0.902565	+	0.430554i	$0.141682\pi$
$379$			16.7640i			0.861107i	−0.902565	+	0.430554i	$0.858318\pi$
$380$	−10.0761	−	1.01713i	−0.516892	−	0.0521775i
$381$	22.6594	−	12.6940i	1.16088	−	0.650335i
$382$	−2.76680	+	2.76680i	−0.141562	+	0.141562i
$383$	−7.37202	−	1.97533i	−0.376693	−	0.100935i	0.0655047	−	0.997852i	$-0.479134\pi$
$383$	−7.37202	−	1.97533i	−0.376693	−	0.100935i	−0.442197	+	0.896918i	$0.645801\pi$
$384$	1.51109	−	0.846529i	0.0771124	−	0.0431992i
$385$	−18.7020	+	8.14855i	−0.953144	+	0.415288i
$386$		−	4.59011i		−	0.233630i
$387$	24.9277	−	23.6687i	1.26714	−	1.20315i
$388$	−4.09038	+	15.2655i	−0.207657	+	0.774988i
$389$	5.50016	−	9.52655i	0.278869	−	0.483015i	−0.692235	−	0.721672i	$-0.743374\pi$
$389$	5.50016	−	9.52655i	0.278869	−	0.483015i	0.971104	+	0.238657i	$0.0767071\pi$
$390$	0.970291	−	2.46245i	0.0491326	−	0.124691i
$391$	−4.23120	+	7.32865i	−0.213981	+	0.370626i
$392$	1.64769	+	6.80332i	0.0832207	+	0.343619i
$393$	−3.56037	+	0.904751i	−0.179597	+	0.0456387i
$394$			23.4389i			1.18083i
$395$	24.2764	−	10.9285i	1.22148	−	0.549873i
$396$	9.08976	−	4.93863i	0.456777	−	0.248176i
$397$	6.74019	+	25.1547i	0.338280	+	1.26248i	0.900269	+	0.435334i	$0.143370\pi$
$397$	6.74019	+	25.1547i	0.338280	+	1.26248i	−0.561989	+	0.827145i	$0.689964\pi$
$398$	−5.48195	−	1.46888i	−0.274785	−	0.0736285i
$399$	−5.87204	+	19.9068i	−0.293970	+	0.996584i
$400$	3.31495	−	3.74314i	0.165748	−	0.187157i
$401$	18.0271	−	10.4079i	0.900230	−	0.519748i	0.0229551	−	0.999736i	$-0.492693\pi$
$401$	18.0271	−	10.4079i	0.900230	−	0.519748i	0.877275	+	0.479989i	$0.159359\pi$
$402$	−5.49211	−	1.54811i	−0.273922	−	0.0772125i
$403$	−3.85436	+	1.03277i	−0.191999	+	0.0514461i
$404$	0.190796	−	0.330469i	0.00949247	−	0.0164414i
$405$	−12.5916	+	15.6988i	−0.625679	+	0.780080i
$406$	−18.7047	+	4.77025i	−0.928300	+	0.236744i
$407$	−8.17551	+	30.5114i	−0.405245	+	1.51240i
$408$	−0.571799	−	2.25014i	−0.0283083	−	0.111399i
$409$			6.45572i			0.319215i	0.987181	+	0.159607i	$0.0510228\pi$
$409$			6.45572i			0.319215i	−0.987181	+	0.159607i	$0.948977\pi$
$410$	11.6623	−	9.52368i	0.575960	−	0.470341i
$411$	17.5498	+	0.227280i	0.865669	+	0.0112109i
$412$	−19.1759	−	5.13815i	−0.944727	−	0.253139i
$413$	2.92765	+	5.21550i	0.144060	+	0.256638i
$414$	0.490482	−	18.9335i	0.0241059	−	0.930531i
$415$	2.57357	+	15.8270i	0.126332	+	0.776917i
$416$	−0.591825	−	0.341690i	−0.0290166	−	0.0167527i
$417$	2.22084	+	2.27911i	0.108755	+	0.111609i
$418$	−4.04206	+	15.0852i	−0.197704	+	0.737840i
$419$	9.02628	−	15.6340i	0.440963	−	0.763770i	−0.556798	−	0.830648i	$-0.687970\pi$
$419$	9.02628	−	15.6340i	0.440963	−	0.763770i	0.997761	+	0.0668777i	$0.0213037\pi$
$420$	−6.28057	−	8.09657i	−0.306460	−	0.395072i
$421$	−11.0117	−	19.0728i	−0.536677	−	0.929552i	−0.999080	−	0.0428823i	$-0.986346\pi$
$421$	−11.0117	−	19.0728i	−0.536677	−	0.929552i	0.462403	−	0.886670i	$-0.346987\pi$
$422$	−22.1037	+	5.92268i	−1.07599	+	0.288311i
$423$	6.39196	+	26.5916i	0.310788	+	1.29293i
$424$	6.03186	−	3.48249i	0.292933	−	0.169125i
$425$	−3.69634	−	5.59057i	−0.179299	−	0.271183i
$426$	−14.6794	+	8.22357i	−0.711220	+	0.398433i
$427$	−9.45997	−	16.8526i	−0.457800	−	0.815553i
$428$	−0.0542780	−	0.202568i	−0.00262363	−	0.00979151i
$429$	−3.50798	−	2.08636i	−0.169367	−	0.100730i
$430$	−20.7897	−	14.9743i	−1.00257	−	0.722124i
$431$	−10.4875	+	6.05495i	−0.505164	+	0.291657i	−0.730844	−	0.682545i	$-0.760873\pi$
$431$	−10.4875	+	6.05495i	−0.505164	+	0.291657i	0.225679	+	0.974202i	$0.427540\pi$
$432$	3.52876	+	3.81417i	0.169777	+	0.183509i
$433$	20.2629	+	20.2629i	0.973774	+	0.973774i	0.999665	−	0.0258906i	$-0.00824214\pi$
$433$	20.2629	+	20.2629i	0.973774	+	0.973774i	−0.0258906	+	0.999665i	$0.508242\pi$
$434$	−4.17861	+	14.8730i	−0.200580	+	0.713925i
$435$	22.1163	−	17.5882i	1.06039	−	0.843290i
$436$	−0.412648	−	0.714728i	−0.0197623	−	0.0342293i
$437$	20.2185	+	20.2185i	0.967181	+	0.967181i
$438$	1.88254	−	0.478385i	0.0899512	−	0.0228581i
$439$			22.8338i			1.08980i	0.838501	+	0.544900i	$0.183432\pi$
$439$			22.8338i			1.08980i	−0.838501	+	0.544900i	$0.816568\pi$
$440$	−4.87701	−	5.97218i	−0.232502	−	0.284712i
$441$	−18.6894	+	9.57633i	−0.889972	+	0.456016i
$442$	−0.647717	+	0.647717i	−0.0308088	+	0.0308088i
$443$	−24.4723	+	24.4723i	−1.16271	+	1.16271i	−0.178835	+	0.983879i	$0.557233\pi$
$443$	−24.4723	+	24.4723i	−1.16271	+	1.16271i	−0.983879	+	0.178835i	$0.942767\pi$
$444$	−15.8652	−	0.205463i	−0.752927	−	0.00975083i
$445$	16.8121	+	1.69709i	0.796968	+	0.0804496i
$446$	−16.0237	+	9.25131i	−0.758746	+	0.438062i
$447$	0.00708065	+	0.0278638i	0.000334903	+	0.00131791i
$448$	−2.30712	+	1.29507i	−0.109001	+	0.0611864i
$449$	−31.4440			−1.48393			−0.741967	−	0.670437i	$-0.766107\pi$
$449$	−31.4440			−1.48393			−0.741967	+	0.670437i	$0.766107\pi$
$450$	13.2427	+	7.04492i	0.624267	+	0.332100i
$451$	−11.6096	−	20.1085i	−0.546676	−	0.946871i
$452$	−1.15814	+	0.310324i	−0.0544745	+	0.0145964i
$453$	4.37130	−	4.25953i	0.205382	−	0.200130i
$454$	16.8311	+	9.71746i	0.789924	+	0.456063i
$455$	−1.47892	+	3.76273i	−0.0693329	+	0.176399i
$456$	−7.84390	−	0.101583i	−0.367324	−	0.00475706i
$457$	22.9299	−	22.9299i	1.07261	−	1.07261i	0.0754655	−	0.997148i	$-0.475956\pi$
$457$	22.9299	−	22.9299i	1.07261	−	1.07261i	0.997148	−	0.0754655i	$-0.0240443\pi$
$458$	11.1851	+	2.99704i	0.522645	+	0.140042i
$459$	6.16255	−	3.24558i	0.287643	−	0.151491i
$460$	−13.9339	+	2.26575i	−0.649673	+	0.105641i
$461$	−2.68367	+	1.54942i	−0.124991	+	0.0721636i	−0.561192	−	0.827686i	$-0.689657\pi$
$461$	−2.68367	+	1.54942i	−0.124991	+	0.0721636i	0.436201	+	0.899849i	$0.356324\pi$
$462$	−13.8784	+	7.55578i	−0.645680	+	0.351527i
$463$	21.7138	−	5.81821i	1.00913	−	0.270395i	0.283863	−	0.958865i	$-0.408384\pi$
$463$	21.7138	−	5.81821i	1.00913	−	0.270395i	0.725265	+	0.688470i	$0.241717\pi$
$464$	−3.64800	−	6.31853i	−0.169354	−	0.293330i
$465$	−3.34027	−	22.3667i	−0.154901	−	1.03723i
$466$	9.58210	−	16.5967i	0.443882	−	0.768827i
$467$	−27.6065	+	7.39714i	−1.27748	+	0.342299i	−0.832891	−	0.553437i	$-0.813316\pi$
$467$	−27.6065	+	7.39714i	−1.27748	+	0.342299i	−0.444586	+	0.895736i	$0.646649\pi$
$468$	0.581721	−	1.96588i	0.0268901	−	0.0908728i
$469$	8.39136	+	2.35758i	0.387477	+	0.108863i
$470$	18.5881	−	8.36781i	0.857406	−	0.385978i
$471$	−10.8115	+	6.05673i	−0.498168	+	0.279079i
$472$	−1.59849	+	1.59849i	−0.0735766	+	0.0735766i
$473$	−27.9381	+	27.9381i	−1.28460	+	1.28460i
$474$	17.9912	−	10.0789i	0.826363	−	0.462937i
$475$	−21.4786	+	7.17483i	−0.985507	+	0.329204i
$476$	0.876382	+	3.43640i	0.0401689	+	0.157507i
$477$	14.3874	+	15.1526i	0.658754	+	0.693792i
$478$	0.779772	−	0.208939i	0.0356659	−	0.00955666i
$479$	15.1360	−	26.2163i	0.691581	−	1.19785i	−0.279739	−	0.960076i	$-0.590248\pi$
$479$	15.1360	−	26.2163i	0.691581	−	1.19785i	0.971320	−	0.237777i	$-0.0764187\pi$
$480$	2.30407	−	3.11308i	0.105166	−	0.142092i
$481$	3.13006	+	5.42143i	0.142719	+	0.247196i
$482$	4.12230	−	1.10457i	0.187766	−	0.0503117i
$483$	−0.724443	+	28.9221i	−0.0329633	+	1.31600i
$484$	−0.771124	+	0.445209i	−0.0350511	+	0.0202368i
$485$	5.67182	+	34.8807i	0.257544	+	1.58385i
$486$	−8.65140	+	12.9674i	−0.392435	+	0.588213i
$487$	−34.5084	−	9.24650i	−1.56373	−	0.418999i	−0.629885	−	0.776689i	$-0.716898\pi$
$487$	−34.5084	−	9.24650i	−1.56373	−	0.418999i	−0.933841	+	0.357690i	$0.883565\pi$
$488$	5.16513	−	5.16513i	0.233814	−	0.233814i
$489$	10.8175	+	0.140092i	0.489183	+	0.00633520i
$490$	9.60432	+	12.3595i	0.433879	+	0.558345i
$491$	−5.91999	−	3.41791i	−0.267166	−	0.154248i	0.360433	−	0.932785i	$-0.382629\pi$
$491$	−5.91999	−	3.41791i	−0.267166	−	0.154248i	−0.627599	+	0.778537i	$0.715962\pi$
$492$	8.35309	−	8.13951i	0.376587	−	0.366957i
$493$	−9.44640	+	2.53116i	−0.425445	+	0.113998i
$494$	1.54754	+	2.68041i	0.0696269	+	0.120597i
$495$	14.0008	−	18.4132i	0.629289	−	0.827613i
$496$	−5.83910			−0.262183
$497$	22.4124	−	12.5809i	1.00533	−	0.564331i
$498$	3.05905	+	12.0380i	0.137079	+	0.539434i
$499$	−5.45973	+	3.15217i	−0.244411	+	0.141111i	−0.617202	−	0.786804i	$-0.711734\pi$
$499$	−5.45973	+	3.15217i	−0.244411	+	0.141111i	0.372791	+	0.927915i	$0.378401\pi$
$500$	3.32336	−	10.6750i	0.148625	−	0.477400i
$501$	25.9547	+	0.336128i	1.15957	+	0.0150171i
$502$	12.4245	−	12.4245i	0.554533	−	0.554533i
$503$	23.0371	−	23.0371i	1.02718	−	1.02718i	0.0275550	−	0.999620i	$-0.491228\pi$
$503$	23.0371	−	23.0371i	1.02718	−	1.02718i	0.999620	−	0.0275550i	$-0.00877213\pi$
$504$	−5.39525	−	5.82162i	−0.240324	−	0.259315i
$505$	0.0856972	−	0.848952i	0.00381347	−	0.0377779i
$506$			21.7698i			0.967785i
$507$	21.0391	−	5.34639i	0.934379	−	0.237441i
$508$	−10.6034	−	10.6034i	−0.470448	−	0.470448i
$509$	−14.8604	−	25.7389i	−0.658673	−	1.14086i	−0.980959	−	0.194214i	$-0.937785\pi$
$509$	−14.8604	−	25.7389i	−0.658673	−	1.14086i	0.322286	−	0.946642i	$-0.395549\pi$
$510$	−3.23128	−	4.06317i	−0.143083	−	0.179920i
$511$	−2.87500	+	0.733209i	−0.127182	+	0.0324352i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.20347	−	22.9512i	−0.229739	−	1.01332i
$514$	−1.25343	+	0.723670i	−0.0552865	+	0.0319197i
$515$	−43.8156	+	7.12470i	−1.93075	+	0.313952i
$516$	−17.0572	−	10.1448i	−0.750903	−	0.446598i
$517$	−8.13609	−	30.3643i	−0.357825	−	1.33542i
$518$	24.2347	+	0.293085i	1.06481	+	0.0128774i
$519$	−9.11538	+	5.10654i	−0.400121	+	0.224152i
$520$	−1.52036	−	0.153472i	−0.0666722	−	0.00673020i
$521$	−18.7870	+	10.8467i	−0.823072	+	0.475201i	−0.851475	−	0.524396i	$-0.824291\pi$
$521$	−18.7870	+	10.8467i	−0.823072	+	0.475201i	0.0284028	+	0.999597i	$0.490958\pi$
$522$	15.8728	−	15.0712i	0.694733	−	0.659647i
$523$	−20.8076	+	5.57538i	−0.909854	+	0.243795i	−0.683243	−	0.730191i	$-0.739431\pi$
$523$	−20.8076	+	5.57538i	−0.909854	+	0.243795i	−0.226610	+	0.973985i	$0.572764\pi$
$524$	1.06046	+	1.83677i	0.0463263	+	0.0802395i
$525$	−20.2378	−	10.7440i	−0.883249	−	0.468904i
$526$	−0.937875	+	1.62445i	−0.0408933	+	0.0708293i
$527$	−2.02572	+	7.56010i	−0.0882418	+	0.329323i
$528$	−4.16818	−	4.27756i	−0.181397	−	0.186157i
$529$	14.5991	+	8.42881i	0.634744	+	0.366470i
$530$	9.10234	−	12.6374i	0.395380	−	0.548932i
$531$	−5.78346	−	3.54188i	−0.250981	−	0.153704i
$532$	11.9819	+	0.144904i	0.519481	+	0.00628241i
$533$	−4.44484	−	1.19099i	−0.192528	−	0.0515876i
$534$	13.0876	+	0.169492i	0.566358	+	0.00733465i
$535$	−0.296608	−	0.363213i	−0.0128235	−	0.0157031i
$536$			3.29444i			0.142298i
$537$	9.15556	+	36.0289i	0.395091	+	1.55476i
$538$	3.52865	−	13.1691i	0.152131	−	0.567760i
$539$	21.1897	−	11.5598i	0.912703	−	0.497916i
$540$	10.6961	+	4.53804i	0.460286	+	0.195286i
$541$	−9.54979	+	16.5407i	−0.410577	+	0.711141i	−0.994953	−	0.100342i	$-0.968006\pi$
$541$	−9.54979	+	16.5407i	−0.410577	+	0.711141i	0.584376	+	0.811483i	$0.301340\pi$
$542$	−20.4158	+	5.47039i	−0.876933	+	0.234974i
$543$	−25.2258	−	7.11059i	−1.08254	−	0.305145i
$544$	−1.16083	+	0.670205i	−0.0497701	+	0.0287348i
$545$	−1.49743	−	1.07856i	−0.0641428	−	0.0462003i
$546$	−0.886020	+	3.00369i	−0.0379182	+	0.128546i
$547$	9.50115	+	2.54582i	0.406240	+	0.108852i	0.456152	−	0.889902i	$-0.349227\pi$
$547$	9.50115	+	2.54582i	0.406240	+	0.108852i	−0.0499121	+	0.998754i	$0.515894\pi$
$548$	−2.62268	−	9.78797i	−0.112035	−	0.418121i
$549$	18.6878	+	11.4447i	0.797575	+	0.488447i
$550$	−15.4260	−	7.70064i	−0.657766	−	0.328356i
$551$			33.0440i			1.40772i
$552$	−10.5981	+	2.69316i	−0.451085	+	0.114628i
$553$	−27.4688	+	15.4193i	−1.16809	+	0.655693i
$554$	0.133577	−	0.231363i	0.00567516	−	0.00982966i
$555$	−32.5375	+	14.1435i	−1.38114	+	0.600360i
$556$	0.918626	−	1.59111i	0.0389584	−	0.0674779i
$557$	6.78289	−	25.3141i	0.287400	−	1.07259i	−0.659667	−	0.751558i	$-0.729303\pi$
$557$	6.78289	−	25.3141i	0.287400	−	1.07259i	0.947067	−	0.321035i	$-0.104031\pi$
$558$	−4.09411	−	17.0322i	−0.173317	−	0.721028i
$559$			7.83026i			0.331185i
$560$	−3.51545	+	4.75832i	−0.148555	+	0.201076i
$561$	−6.98435	+	3.91271i	−0.294880	+	0.165195i
$562$	−14.0759	−	3.77164i	−0.593757	−	0.159097i
$563$	−3.29272	+	3.29272i	−0.138772	+	0.138772i	−0.773080	−	0.634308i	$-0.781285\pi$
$563$	−3.29272	+	3.29272i	−0.138772	+	0.138772i	0.634308	+	0.773080i	$0.281285\pi$
$564$	13.7756	−	7.71725i	0.580058	−	0.324955i
$565$	−2.07660	+	1.69580i	−0.0873632	+	0.0713427i
$566$			22.2680i			0.935993i
$567$	13.1983	−	19.8193i	0.554275	−	0.832334i
$568$	6.86916	+	6.86916i	0.288224	+	0.288224i
$569$	−27.7240			−1.16225			−0.581125	−	0.813815i	$-0.697387\pi$
$569$	−27.7240			−1.16225			−0.581125	+	0.813815i	$0.697387\pi$
$570$	−16.0869	+	6.99272i	−0.673805	+	0.292893i
$571$	17.7907			0.744519			0.372259	−	0.928129i	$-0.378583\pi$
$571$	17.7907			0.744519			0.372259	+	0.928129i	$0.378583\pi$
$572$	−0.609898	+	2.27617i	−0.0255011	+	0.0951715i
$573$	−1.83871	+	6.52306i	−0.0768130	+	0.272505i
$574$	−12.7489	+	12.4442i	−0.532129	+	0.519412i
$575$	−26.3314	+	17.4097i	−1.09810	+	0.726033i
$576$	1.56678	−	2.55836i	0.0652824	−	0.106598i
$577$	−20.7148	−	5.55051i	−0.862368	−	0.231071i	−0.199583	−	0.979881i	$-0.563959\pi$
$577$	−20.7148	−	5.55051i	−0.862368	−	0.231071i	−0.662785	+	0.748810i	$0.730626\pi$
$578$	−3.93490	−	14.6853i	−0.163670	−	0.610826i
$579$	−3.88566	−	6.93606i	−0.161482	−	0.288253i
$580$	−13.2380	−	9.53494i	−0.549676	−	0.395917i
$581$	−4.68853	−	18.3843i	−0.194513	−	0.762708i
$582$	6.74175	+	26.5301i	0.279455	+	1.09971i
$583$	−16.9826	−	16.9826i	−0.703347	−	0.703347i
$584$	−0.560714	−	0.971186i	−0.0232025	−	0.0401880i
$585$	−0.618341	−	4.54236i	−0.0255652	−	0.187804i
$586$	6.59865	−	11.4292i	0.272588	−	0.472136i
$587$	8.61850	−	32.1647i	0.355724	−	1.32758i	−0.523848	−	0.851812i	$-0.675504\pi$
$587$	8.61850	−	32.1647i	0.355724	−	1.32758i	0.879571	−	0.475767i	$-0.157829\pi$
$588$	8.24900	+	8.88560i	0.340183	+	0.366436i
$589$	22.9026	+	13.2228i	0.943685	+	0.544837i
$590$	−1.79207	+	4.72655i	−0.0737783	+	0.194589i
$591$	19.8417	+	35.4182i	0.816177	+	1.45691i
$592$	2.37092	+	8.84838i	0.0974441	+	0.363666i
$593$	−1.60690	−	5.99704i	−0.0659875	−	0.246269i	0.925051	−	0.379842i	$-0.124022\pi$
$593$	−1.60690	−	5.99704i	−0.0659875	−	0.246269i	−0.991039	+	0.133573i	$0.957355\pi$
$594$	9.55473	−	15.1575i	0.392035	−	0.621918i
$595$	4.94117	+	6.20236i	0.202568	+	0.254272i
$596$	0.0143747	−	0.00829922i	0.000588810	−	0.000339949i
$597$	−9.52716	+	2.42101i	−0.389921	+	0.0990854i
$598$	3.05073	+	3.05073i	0.124754	+	0.124754i
$599$	−2.03324			−0.0830758			−0.0415379	−	0.999137i	$-0.513226\pi$
$599$	−2.03324			−0.0830758			−0.0415379	+	0.999137i	$0.513226\pi$
$600$	1.84051	−	8.46242i	0.0751387	−	0.345477i
$601$	16.6194	+	28.7857i	0.677920	+	1.17419i	0.975606	+	0.219528i	$0.0704516\pi$
$601$	16.6194	+	28.7857i	0.677920	+	1.17419i	−0.297687	+	0.954664i	$0.596215\pi$
$602$	26.0686	+	15.4740i	1.06248	+	0.630675i
$603$	−9.60958	+	2.30991i	−0.391333	+	0.0940666i
$604$	−3.05171	−	1.76191i	−0.124172	−	0.0716910i
$605$	−1.16366	+	1.61558i	−0.0473095	+	0.0656828i
$606$	0.00855880	−	0.660882i	0.000347677	−	0.0268465i
$607$	−25.1476	−	6.73829i	−1.02071	−	0.273499i	−0.290613	−	0.956841i	$-0.593859\pi$
$607$	−25.1476	−	6.73829i	−1.02071	−	0.273499i	−0.730098	+	0.683342i	$0.760526\pi$
$608$	1.17221	+	4.37473i	0.0475393	+	0.177419i
$609$	−24.2263	+	23.0424i	−0.981701	+	0.933723i
$610$	5.79062	−	15.2727i	0.234455	−	0.618372i
$611$	−5.39528	−	3.11497i	−0.218270	−	0.126018i
$612$	−2.76885	−	2.91612i	−0.111924	−	0.117877i
$613$	−10.1885	+	38.0240i	−0.411510	+	1.53577i	0.380216	+	0.924898i	$0.375850\pi$
$613$	−10.1885	+	38.0240i	−0.411510	+	1.53577i	−0.791726	+	0.610877i	$0.790817\pi$
$614$	15.0694			0.608152
$615$	9.56069	−	24.2636i	0.385524	−	0.978402i
$616$	6.37260	+	6.52862i	0.256759	+	0.263046i
$617$	33.7783	−	9.05087i	1.35986	−	0.364374i	0.496097	−	0.868267i	$-0.334766\pi$
$617$	33.7783	−	9.05087i	1.35986	−	0.364374i	0.863766	+	0.503892i	$0.168099\pi$
$618$	−33.3260	+	8.46870i	−1.34057	+	0.340661i
$619$	−17.2786	−	9.97583i	−0.694488	−	0.400963i	0.110803	−	0.993842i	$-0.464658\pi$
$619$	−17.2786	−	9.97583i	−0.694488	−	0.400963i	−0.805291	+	0.592880i	$0.797991\pi$
$620$	−11.9059	+	5.35966i	−0.478151	+	0.215249i
$621$	−15.2866	−	29.0254i	−0.613430	−	1.16475i
$622$	16.1274	−	16.1274i	0.646651	−	0.646651i
$623$	−19.9919	−	0.241775i	−0.800959	−	0.00968650i
$624$	−1.18355	−	0.0153277i	−0.0473800	−	0.000613597i
$625$	−3.02217	−	24.8167i	−0.120887	−	0.992666i
$626$		−	30.3780i		−	1.21415i
$627$	6.66212	+	26.2168i	0.266059	+	1.04700i
$628$	5.05920	+	5.05920i	0.201884	+	0.201884i
$629$	12.2789			0.489590
$630$	−16.3445	−	6.91796i	−0.651179	−	0.275618i
$631$	18.4543			0.734655			0.367328	−	0.930092i	$-0.380273\pi$
$631$	18.4543			0.734655			0.367328	+	0.930092i	$0.380273\pi$
$632$	−8.41889	−	8.41889i	−0.334885	−	0.334885i
$633$	−28.3870	+	27.6611i	−1.12828	+	1.09943i
$634$			12.0492i			0.478534i
$635$	−31.3528	−	11.8874i	−1.24420	−	0.471737i
$636$	6.16664	−	10.3685i	0.244523	−	0.411138i
$637$	1.34949	−	4.58937i	0.0534686	−	0.181838i
$638$	−17.7897	+	17.7897i	−0.704301	+	0.704301i
$639$	−15.2204	+	24.8531i	−0.602110	+	0.983173i
$640$	−2.09083	−	0.792736i	−0.0826473	−	0.0313356i
$641$	21.5559	+	12.4453i	0.851407	+	0.491560i	0.861125	−	0.508393i	$-0.169760\pi$
$641$	21.5559	+	12.4453i	0.851407	+	0.491560i	−0.00971853	+	0.999953i	$0.503094\pi$
$642$	−0.253499	−	0.260151i	−0.0100048	−	0.0102673i
$643$	18.4936	−	4.95534i	0.729315	−	0.195419i	0.124991	−	0.992158i	$-0.460110\pi$
$643$	18.4936	−	4.95534i	0.729315	−	0.195419i	0.604324	+	0.796738i	$0.293443\pi$
$644$	16.1853	−	4.12773i	0.637792	−	0.162655i
$645$	−44.0913	−	5.02836i	−1.73609	−	0.197992i
$646$	6.07079			0.238852
$647$	−8.86911	+	33.1000i	−0.348681	+	1.30129i	0.539572	+	0.841939i	$0.318586\pi$
$647$	−8.86911	+	33.1000i	−0.348681	+	1.30129i	−0.888253	+	0.459355i	$0.848081\pi$
$648$	8.56107	+	2.77635i	0.336310	+	0.109066i
$649$	6.75080	+	3.89758i	0.264992	+	0.152993i
$650$	−3.24087	+	1.08260i	−0.127117	+	0.0424629i
$651$	6.27614	+	26.0117i	0.245981	+	1.01948i
$652$	−1.61658	−	6.03317i	−0.0633103	−	0.236277i
$653$	−2.27971	−	0.610846i	−0.0892118	−	0.0239042i	0.213937	−	0.976847i	$-0.431371\pi$
$653$	−2.27971	−	0.610846i	−0.0892118	−	0.0239042i	−0.303149	+	0.952943i	$0.598038\pi$
$654$	−1.22859	−	0.730699i	−0.0480415	−	0.0285726i
$655$	3.84821	+	2.77176i	0.150362	+	0.108302i
$656$	−5.83150	−	3.36682i	−0.227682	−	0.131452i
$657$	2.43972	−	2.31651i	0.0951825	−	0.0903755i
$658$	−21.0325	+	11.8063i	−0.819931	+	0.460258i
$659$	12.5805	+	21.7900i	0.490065	+	0.848817i	0.999935	−	0.0114343i	$-0.00363973\pi$
$659$	12.5805	+	21.7900i	0.490065	+	0.848817i	−0.509870	+	0.860252i	$0.670306\pi$
$660$	−12.4252	−	4.89596i	−0.483651	−	0.190575i
$661$	−17.7531			−0.690517			−0.345259	−	0.938508i	$-0.612209\pi$
$661$	−17.7531			−0.690517			−0.345259	+	0.938508i	$0.612209\pi$
$662$	−1.88223	−	1.88223i	−0.0731550	−	0.0731550i
$663$	−0.430447	+	1.52707i	−0.0167172	+	0.0593064i
$664$	6.21028	−	3.58551i	0.241006	−	0.139145i
$665$	24.5639	−	10.7026i	0.952549	−	0.415029i
$666$	−24.1476	+	13.1198i	−0.935700	+	0.508383i
$667$	11.9217	+	44.4923i	0.461609	+	1.72275i
$668$	−3.87872	−	14.4756i	−0.150072	−	0.560077i
$669$	−16.3818	+	27.5441i	−0.633357	+	1.06492i
$670$	3.02393	+	6.71732i	0.116825	+	0.259513i
$671$	−21.8135	−	12.5940i	−0.842101	−	0.486187i
$672$	−2.38994	+	3.91001i	−0.0921941	+	0.150832i
$673$	11.7857	−	43.9848i	0.454305	−	1.69549i	−0.235819	−	0.971797i	$-0.575777\pi$
$673$	11.7857	−	43.9848i	0.454305	−	1.69549i	0.690124	−	0.723691i	$-0.257556\pi$
$674$	0.533994	−	0.924904i	0.0205687	−	0.0356260i
$675$	25.9746	−	0.564833i	0.999764	−	0.0217404i
$676$	−6.26650	−	10.8539i	−0.241019	−	0.417457i
$677$	−0.809850	−	0.809850i	−0.0311251	−	0.0311251i	0.691373	−	0.722498i	$-0.257006\pi$
$677$	−0.809850	−	0.809850i	−0.0311251	−	0.0311251i	−0.722498	+	0.691373i	$0.757006\pi$
$678$	−1.48736	+	1.44933i	−0.0571217	+	0.0556611i
$679$	−10.3329	−	40.5166i	−0.396541	−	1.55488i
$680$	−1.75174	+	2.43205i	−0.0671763	+	0.0932650i
$681$	33.6594	+	0.435909i	1.28983	+	0.0167041i
$682$	5.21124	+	19.4486i	0.199549	+	0.744725i
$683$	24.3856	+	6.53409i	0.933088	+	0.250020i	0.693171	−	0.720773i	$-0.256213\pi$
$683$	24.3856	+	6.53409i	0.933088	+	0.250020i	0.239917	+	0.970793i	$0.422880\pi$
$684$	−11.9388	+	6.48659i	−0.456492	+	0.248021i
$685$	−14.3319	−	17.5502i	−0.547594	−	0.670560i
$686$	−12.6122	−	13.5622i	−0.481535	−	0.517807i
$687$	19.4388	−	4.93972i	0.741635	−	0.188462i
$688$	−2.96558	+	11.0677i	−0.113062	+	0.421952i
$689$	−4.75974			−0.181332
$690$	−19.1374	+	15.2192i	−0.728548	+	0.579386i
$691$	−27.9845			−1.06458			−0.532290	−	0.846562i	$-0.678668\pi$
$691$	−27.9845			−1.06458			−0.532290	+	0.846562i	$0.678668\pi$
$692$	4.26550	+	4.26550i	0.162150	+	0.162150i
$693$	−14.5753	+	23.1659i	−0.553668	+	0.879999i
$694$		−	36.1710i		−	1.37303i
$695$	0.412606	−	4.08745i	0.0156510	−	0.155046i
$696$	−10.8613	−	6.45972i	−0.411695	−	0.244855i
$697$	−6.38223	+	6.38223i	−0.241744	+	0.241744i
$698$	−26.0645	−	6.98395i	−0.986555	−	0.264347i
$699$	0.429837	−	33.1906i	0.0162579	−	1.25538i
$700$	−2.80036	+	12.9290i	−0.105843	+	0.488669i
$701$		−	41.6390i		−	1.57268i	−0.617791	−	0.786342i	$-0.711972\pi$
$701$		−	41.6390i		−	1.57268i	0.617791	−	0.786342i	$-0.288028\pi$
$702$	−0.785142	−	3.46306i	−0.0296333	−	0.130705i
$703$	10.7380	−	40.0748i	0.404992	−	1.51145i
$704$	−1.72412	+	2.98627i	−0.0649804	+	0.112549i
$705$	21.0047	−	28.3799i	0.791084	−	1.06885i
$706$	−6.33680	+	10.9757i	−0.238488	+	0.413074i
$707$	−0.0122088	+	1.00952i	−0.000459160	+	0.0379671i
$708$	−1.06230	+	3.76864i	−0.0399235	+	0.141634i
$709$		−	17.2080i		−	0.646260i	−0.946355	−	0.323130i	$-0.895265\pi$
$709$		−	17.2080i		−	0.646260i	0.946355	−	0.323130i	$-0.104735\pi$
$710$	20.3113	+	7.70100i	0.762269	+	0.289013i
$711$	18.6542	−	30.4601i	0.699589	−	1.14234i
$712$	−1.95584	−	7.29930i	−0.0732982	−	0.273553i
$713$	35.6078	+	9.54109i	1.33352	+	0.357316i
$714$	4.23330	+	4.45082i	0.158427	+	0.166568i
$715$	0.845701	+	5.20091i	0.0316274	+	0.194503i
$716$	18.5870	−	10.7312i	0.694629	−	0.401044i
$717$	1.00143	−	0.975825i	0.0373992	−	0.0364429i
$718$	−33.0615	+	8.85880i	−1.23384	+	0.330608i
$719$	1.56793	−	2.71573i	0.0584738	−	0.101280i	−0.835307	−	0.549784i	$-0.814710\pi$
$719$	1.56793	−	2.71573i	0.0584738	−	0.101280i	0.893780	+	0.448505i	$0.148043\pi$
$720$	0.846350	−	6.65460i	0.0315416	−	0.248002i
$721$	50.8952	−	12.9798i	1.89544	−	0.483392i
$722$	0.391430	−	1.46084i	0.0145675	−	0.0543667i
$723$	5.29412	−	5.15874i	0.196890	−	0.191856i
$724$			15.1316i			0.562363i
$725$	−35.7441	−	7.29064i	−1.32750	−	0.270767i
$726$	−0.788355	+	1.32553i	−0.0292586	+	0.0491950i
$727$	17.5267	+	4.69627i	0.650030	+	0.174175i	0.568742	−	0.822516i	$-0.307430\pi$
$727$	17.5267	+	4.69627i	0.650030	+	0.174175i	0.0812876	+	0.996691i	$0.474097\pi$
$728$	1.80792	+	0.0218644i	0.0670061	+	0.000810347i
$729$	−2.09576	+	26.9185i	−0.0776209	+	0.996983i
$730$	−2.03473	−	1.46556i	−0.0753088	−	0.0542429i
$731$	13.3009	+	7.67929i	0.491952	+	0.284029i
$732$	3.43254	−	12.1774i	0.126870	−	0.450090i
$733$	−0.548744	+	2.04794i	−0.0202683	+	0.0756424i	−0.975319	−	0.220799i	$-0.929133\pi$
$733$	−0.548744	+	2.04794i	−0.0202683	+	0.0756424i	0.955051	+	0.296442i	$0.0958001\pi$
$734$	−7.48866	+	12.9707i	−0.276411	+	0.478758i
$735$	24.9756	+	10.5460i	0.921240	+	0.388994i
$736$	3.15664	+	5.46747i	0.116355	+	0.201534i
$737$	10.9730	−	2.94019i	0.404194	−	0.108303i
$738$	5.73194	−	19.3706i	0.210996	−	0.713043i
$739$	35.2645	−	20.3600i	1.29723	−	0.748954i	0.317303	−	0.948324i	$-0.397223\pi$
$739$	35.2645	−	20.3600i	1.29723	−	0.748954i	0.979924	+	0.199370i	$0.0638896\pi$
$740$	12.9561	+	15.8655i	0.476277	+	0.583228i
$741$	4.60751	+	2.74031i	0.169261	+	0.100668i
$742$	−9.40613	+	15.8462i	−0.345310	+	0.581733i
$743$	13.0540	+	48.7181i	0.478904	+	1.78729i	0.606068	+	0.795413i	$0.292746\pi$
$743$	13.0540	+	48.7181i	0.478904	+	1.78729i	−0.127164	+	0.991882i	$0.540588\pi$
$744$	−8.82340	+	4.94297i	−0.323482	+	0.181218i
$745$	0.0216920	−	0.0301164i	0.000794734	−	0.00110338i
$746$	2.80101	−	1.61716i	0.102552	−	0.0592085i
$747$	14.8130	+	15.6009i	0.541978	+	0.570805i
$748$	3.26829	+	3.26829i	0.119501	+	0.119501i
$749$	0.387566	+	0.397055i	0.0141614	+	0.0145081i
$750$	−4.01479	−	18.9442i	−0.146599	−	0.691743i
$751$	3.82614	+	6.62708i	0.139618	+	0.241825i	0.927352	−	0.374190i	$-0.122079\pi$
$751$	3.82614	+	6.62708i	0.139618	+	0.241825i	−0.787734	+	0.616015i	$0.788746\pi$
$752$	−6.44623	−	6.44623i	−0.235070	−	0.235070i
$753$	8.25683	−	29.2922i	0.300896	−	1.06747i
$754$			4.98595i			0.181578i
$755$	−7.83965	−	0.791371i	−0.285314	−	0.0288009i
$756$	−13.0809	−	4.22975i	−0.475747	−	0.153834i
$757$	−7.43953	+	7.43953i	−0.270394	+	0.270394i	−0.829259	−	0.558865i	$-0.811237\pi$
$757$	−7.43953	+	7.43953i	−0.270394	+	0.270394i	0.558865	+	0.829259i	$0.311237\pi$
$758$	11.8539	−	11.8539i	0.430554	−	0.430554i
$759$	18.4287	+	32.8961i	0.668921	+	1.19405i
$760$	6.40564	+	7.84408i	0.232357	+	0.284535i
$761$	−31.3653	+	18.1088i	−1.13699	+	0.656442i	−0.945684	−	0.325088i	$-0.894606\pi$
$761$	−31.3653	+	18.1088i	−1.13699	+	0.656442i	−0.191307	+	0.981530i	$0.561273\pi$
$762$	−24.9986	−	7.04657i	−0.905605	−	0.255270i
$763$	1.87765	+	1.11455i	0.0679756	+	0.0403495i
$764$	3.91285			0.141562
$765$	−8.32233	−	3.40444i	−0.300895	−	0.123088i
$766$	3.81604	+	6.60958i	0.137879	+	0.238814i
$767$	1.49222	−	0.399839i	0.0538809	−	0.0144373i
$768$	−1.66709	−	0.469915i	−0.0601558	−	0.0169566i
$769$	22.0309	+	12.7195i	0.794454	+	0.458678i	0.841528	−	0.540213i	$-0.181656\pi$
$769$	22.0309	+	12.7195i	0.794454	+	0.458678i	−0.0470739	+	0.998891i	$0.514990\pi$
$770$	18.9862	+	7.46244i	0.684216	+	0.268928i
$771$	−1.28144	+	2.15460i	−0.0461500	+	0.0775959i
$772$	−3.24570	+	3.24570i	−0.116815	+	0.116815i
$773$	−30.7577	−	8.24150i	−1.10628	−	0.296426i	−0.340959	−	0.940078i	$-0.610752\pi$
$773$	−30.7577	−	8.24150i	−1.10628	−	0.296426i	−0.765319	+	0.643652i	$0.777419\pi$
$774$	−34.3628	−	0.890186i	−1.23515	−	0.0319971i
$775$	−19.3563	+	21.8566i	−0.695300	+	0.785111i
$776$	13.6867	−	7.90200i	0.491323	−	0.283665i
$777$	36.8689	−	20.0725i	1.32266	−	0.720096i
$778$	−10.6255	+	2.84709i	−0.380942	+	0.102073i
$779$	15.2485	+	26.4112i	0.546335	+	0.946280i
$780$	−2.42732	+	1.05512i	−0.0869119	+	0.0377793i
$781$	16.7489	−	29.0100i	0.599324	−	1.03806i
$782$	8.17404	−	2.19023i	0.292303	−	0.0783224i
$783$	11.2270	−	36.2106i	0.401221	−	1.29406i
$784$	3.64558	−	5.97576i	0.130199	−	0.213420i
$785$	14.9594	+	5.67186i	0.533925	+	0.202437i
$786$	3.15732	+	1.87781i	0.112618	+	0.0669793i
$787$	−4.27679	+	4.27679i	−0.152451	+	0.152451i	−0.779212	−	0.626761i	$-0.784380\pi$
$787$	−4.27679	+	4.27679i	−0.152451	+	0.152451i	0.626761	+	0.779212i	$0.284380\pi$
$788$	16.5738	−	16.5738i	0.590416	−	0.590416i
$789$	−0.0420715	+	3.24862i	−0.00149778	+	0.115654i
$790$	−24.8936	−	9.43840i	−0.885676	−	0.335803i
$791$	2.27008	−	2.21583i	0.0807149	−	0.0787859i
$792$	−9.91957	−	2.93529i	−0.352477	−	0.104301i
$793$	−4.82173	+	1.29198i	−0.171225	+	0.0458795i
$794$	13.0210	−	22.5531i	0.462099	−	0.800380i
$795$	3.05657	−	26.8016i	0.108405	−	0.950553i
$796$	2.83766	+	4.91498i	0.100578	+	0.174207i
$797$	−14.3894	+	3.85562i	−0.509698	+	0.136573i	−0.504497	−	0.863413i	$-0.668322\pi$
$797$	−14.3894	+	3.85562i	−0.509698	+	0.136573i	−0.00520091	+	0.999986i	$0.501656\pi$
$798$	18.2284	−	9.92405i	0.645277	−	0.351307i
$799$	−10.5825	+	6.10982i	−0.374382	+	0.216150i
$800$	−4.99082	+	0.302773i	−0.176452	+	0.0107046i
$801$	19.9201	−	10.8229i	0.703841	−	0.382410i
$802$	−20.1066	−	5.38755i	−0.709989	−	0.190241i
$803$	−2.73436	+	2.73436i	−0.0964934	+	0.0964934i
$804$	2.78883	+	4.97819i	0.0983546	+	0.175567i
$805$	29.2129	−	23.2728i	1.02962	−	0.820257i
$806$	3.45573	+	1.99516i	0.121723	+	0.0702767i
$807$	−5.81592	−	22.8868i	−0.204730	−	0.805653i
$808$	−0.368590	+	0.0987634i	−0.0129670	+	0.00347448i
$809$	5.83742	+	10.1107i	0.205233	+	0.355474i	0.950207	−	0.311620i	$-0.100872\pi$
$809$	5.83742	+	10.1107i	0.205233	+	0.355474i	−0.744974	+	0.667093i	$0.767538\pi$
$810$	20.0043	−	2.19717i	0.702880	−	0.0772006i
$811$	0.572865			0.0201160			0.0100580	−	0.999949i	$-0.496798\pi$
$811$	0.572865			0.0201160			0.0100580	+	0.999949i	$0.496798\pi$
$812$	16.5993	+	9.85316i	0.582522	+	0.345778i
$813$	−26.2192	+	25.5488i	−0.919548	+	0.896035i
$814$	27.3558	−	15.7939i	0.958820	−	0.553575i
$815$	−8.83399	−	10.8177i	−0.309441	−	0.378928i
$816$	−1.18677	+	1.99541i	−0.0415452	+	0.0698535i
$817$	36.6950	−	36.6950i	1.28379	−	1.28379i
$818$	4.56488	−	4.56488i	0.159607	−	0.159607i
$819$	1.20386	+	5.28889i	0.0420661	+	0.184809i
$820$	−14.9807	−	1.51223i	−0.523150	−	0.0528092i
$821$		−	9.88805i		−	0.345095i	−0.985001	−	0.172548i	$-0.944800\pi$
$821$		−	9.88805i		−	0.345095i	0.985001	−	0.172548i	$-0.0551999\pi$
$822$	−12.2489	−	12.5703i	−0.427229	−	0.438440i
$823$	−19.3510	−	19.3510i	−0.674533	−	0.674533i	0.284224	−	0.958758i	$-0.408264\pi$
$823$	−19.3510	−	19.3510i	−0.674533	−	0.674533i	−0.958758	+	0.284224i	$0.908264\pi$
$824$	9.92615	+	17.1926i	0.345794	+	0.598933i
$825$	−29.8288	+	1.42218i	−1.03851	+	0.0495138i
$826$	1.61775	−	5.75808i	0.0562887	−	0.200349i
$827$	21.0151	+	21.0151i	0.730766	+	0.730766i	0.970772	−	0.240006i	$-0.0771493\pi$
$827$	21.0151	+	21.0151i	0.730766	+	0.730766i	−0.240006	+	0.970772i	$0.577149\pi$
$828$	−13.7348	+	13.0412i	−0.477319	+	0.453213i
$829$	1.17707	−	0.679584i	0.0408815	−	0.0236029i	−0.479420	−	0.877586i	$-0.659153\pi$
$829$	1.17707	−	0.679584i	0.0408815	−	0.0236029i	0.520301	+	0.853983i	$0.325820\pi$
$830$	9.37159	−	13.0112i	0.325293	−	0.451624i
$831$	0.00599205	−	0.462687i	0.000207862	−	0.0160504i
$832$	0.176872	+	0.660095i	0.00613193	+	0.0228847i
$833$	−6.47230	−	6.79320i	−0.224252	−	0.235370i
$834$	0.0412080	−	3.18195i	0.00142692	−	0.110182i
$835$	−21.1957	−	25.9553i	−0.733506	−	0.898220i
$836$	13.5250	−	7.80866i	0.467772	−	0.270068i
$837$	−20.6048	−	22.2713i	−0.712205	−	0.769809i
$838$	−17.4374	+	4.67235i	−0.602366	+	0.161404i
$839$	−7.37134	−	12.7675i	−0.254487	−	0.440784i	0.710269	−	0.703930i	$-0.248573\pi$
$839$	−7.37134	−	12.7675i	−0.254487	−	0.440784i	−0.964756	+	0.263146i	$0.915240\pi$
$840$	−1.28411	+	10.1662i	−0.0443060	+	0.350766i
$841$	−12.1159	+	20.9853i	−0.417788	+	0.723630i
$842$	−5.70007	+	21.2730i	−0.196437	+	0.733115i
$843$	−24.4628	+	6.21641i	−0.842543	+	0.214104i
$844$	19.8177	+	11.4417i	0.682152	+	0.393841i
$845$	−22.7400	−	16.3790i	−0.782280	−	0.563455i
$846$	14.2833	−	23.3229i	0.491070	−	0.801857i
$847$	1.20250	−	2.02581i	0.0413183	−	0.0696076i
$848$	−6.72766	−	1.80267i	−0.231029	−	0.0619040i
$849$	18.8505	+	33.6489i	0.646947	+	1.15483i
$850$	−1.33942	+	6.56684i	−0.0459418	+	0.225241i
$851$		−	57.8330i		−	1.98249i
$852$	16.1948	+	4.56497i	0.554826	+	0.156393i
$853$	−0.478564	+	1.78602i	−0.0163857	+	0.0611523i	−0.973635	−	0.228113i	$-0.926744\pi$
$853$	−0.478564	+	1.78602i	−0.0163857	+	0.0611523i	0.957249	+	0.289265i	$0.0934110\pi$
$854$	−5.22735	+	18.6058i	−0.178876	+	0.636676i
$855$	−18.3892	+	24.1846i	−0.628896	+	0.827096i
$856$	−0.104857	+	0.181618i	−0.00358394	+	0.00620757i
$857$	39.3105	−	10.5332i	1.34282	−	0.359808i	0.485341	−	0.874325i	$-0.338696\pi$
$857$	39.3105	−	10.5332i	1.34282	−	0.359808i	0.857480	+	0.514518i	$0.172029\pi$
$858$	1.00523	+	3.95579i	0.0343181	+	0.135049i
$859$	−11.4656	+	6.61968i	−0.391202	+	0.225861i	−0.682681	−	0.730717i	$-0.739186\pi$
$859$	−11.4656	+	6.61968i	−0.391202	+	0.225861i	0.291479	+	0.956577i	$0.405853\pi$
$860$	4.11215	+	25.2890i	0.140223	+	0.862348i
$861$	−8.73033	+	29.5966i	−0.297529	+	1.00865i
$862$	11.6973	+	3.13427i	0.398410	+	0.106754i
$863$	0.875636	+	3.26792i	0.0298070	+	0.111241i	0.979227	−	0.202769i	$-0.0649940\pi$
$863$	0.875636	+	3.26792i	0.0298070	+	0.111241i	−0.949420	+	0.314010i	$0.898327\pi$
$864$	0.201817	−	5.19223i	0.00686596	−	0.176643i
$865$	12.6126	+	4.78204i	0.428840	+	0.162594i
$866$		−	28.6561i		−	0.973774i
$867$	−18.3775	−	18.8597i	−0.624132	−	0.640510i
$868$	13.4715	−	7.56205i	0.457252	−	0.256673i
$869$	−20.5276	+	35.5549i	−0.696351	+	1.20612i
$870$	−28.0753	−	3.20183i	−0.951843	−	0.108552i
$871$	1.12568	−	1.94973i	0.0381421	−	0.0660641i
$872$	−0.213603	+	0.797175i	−0.00723349	+	0.0269958i
$873$	32.6459	+	34.3823i	1.10490	+	1.16366i
$874$		−	28.5933i		−	0.967181i
$875$	6.15748	+	28.9324i	0.208161	+	0.978095i
$876$	−1.66943	−	0.992887i	−0.0564047	−	0.0335466i
$877$	−18.2637	−	4.89374i	−0.616721	−	0.165250i	−0.0630844	−	0.998008i	$-0.520094\pi$
$877$	−18.2637	−	4.89374i	−0.616721	−	0.165250i	−0.553637	+	0.832758i	$0.686760\pi$
$878$	16.1460	−	16.1460i	0.544900	−	0.544900i
$879$	0.296004	−	22.8565i	0.00998398	−	0.770930i
$880$	−0.774400	+	7.67153i	−0.0261050	+	0.258607i
$881$			22.9080i			0.771790i	0.922543	+	0.385895i	$0.126107\pi$
$881$			22.9080i			0.771790i	−0.922543	+	0.385895i	$0.873893\pi$
$882$	19.9869	+	6.44392i	0.672994	+	0.216978i
$883$	28.9012	+	28.9012i	0.972602	+	0.972602i	0.999635	−	0.0270324i	$-0.00860573\pi$
$883$	28.9012	+	28.9012i	0.972602	+	0.972602i	−0.0270324	+	0.999635i	$0.508606\pi$
$884$	0.916010			0.0308088
$885$	1.29319	+	8.65928i	0.0434701	+	0.291079i
$886$	34.6091			1.16271
$887$	3.01737	−	11.2610i	0.101313	−	0.378106i	−0.896588	−	0.442866i	$-0.853962\pi$
$887$	3.01737	−	11.2610i	0.101313	−	0.378106i	0.997901	+	0.0647602i	$0.0206282\pi$
$888$	11.0731	+	11.3636i	0.371588	+	0.381339i
$889$	38.1953	+	10.7311i	1.28103	+	0.359909i
$890$	−10.6879	−	13.0879i	−0.358259	−	0.438709i
$891$	1.60684	−	30.9926i	0.0538310	−	1.03829i
$892$	17.8722	+	4.78883i	0.598404	+	0.160342i
$893$	10.6862	+	39.8816i	0.357601	+	1.33459i
$894$	0.0146959	−	0.0247094i	0.000491504	−	0.000826407i
$895$	28.0486	−	38.9417i	0.937562	−	1.30168i
$896$	2.54713	+	0.715625i	0.0850937	+	0.0239074i
$897$	7.19245	+	2.02739i	0.240149	+	0.0676927i
$898$	22.2343	+	22.2343i	0.741967	+	0.741967i
$899$	21.3011	+	36.8945i	0.710430	+	1.23050i
$900$	−4.38250	−	14.3455i	−0.146083	−	0.478184i
$901$	−4.66797	+	8.08516i	−0.155513	+	0.269356i
$902$	−6.00959	+	22.4281i	−0.200097	+	0.746774i
$903$	52.4913	+	1.31481i	1.74680	+	0.0437540i
$904$	1.03836	+	0.599499i	0.0345355	+	0.0199391i
$905$	13.8892	+	30.8533i	0.461693	+	1.02560i
$906$	−6.10292	−	0.0790362i	−0.202756	−	0.00262580i
$907$	10.7498	+	40.1187i	0.356940	+	1.33212i	0.878025	+	0.478614i	$0.158861\pi$
$907$	10.7498	+	40.1187i	0.356940	+	1.33212i	−0.521085	+	0.853505i	$0.674473\pi$
$908$	−5.03013	−	18.7727i	−0.166931	−	0.622993i
$909$	−0.546522	−	1.00590i	−0.0181270	−	0.0333635i
$910$	3.70641	−	1.61490i	0.122866	−	0.0535333i
$911$	−9.44767	+	5.45462i	−0.313015	+	0.180719i	−0.648275	−	0.761406i	$-0.724509\pi$
$911$	−9.44767	+	5.45462i	−0.313015	+	0.180719i	0.335260	+	0.942126i	$0.391176\pi$
$912$	5.47465	+	5.61831i	0.181284	+	0.186041i
$913$	−17.4849	−	17.4849i	−0.578667	−	0.578667i
$914$	−32.4277			−1.07261
$915$	−4.17861	−	27.9803i	−0.138141	−	0.925000i
$916$	−5.78983	−	10.0283i	−0.191301	−	0.331344i
$917$	−4.82534	−	2.86427i	−0.159347	−	0.0945865i
$918$	−6.65256	−	2.06261i	−0.219567	−	0.0680762i
$919$	−10.2090	−	5.89419i	−0.336765	−	0.194431i	0.322076	−	0.946714i	$-0.395620\pi$
$919$	−10.2090	−	5.89419i	−0.336765	−	0.194431i	−0.658841	+	0.752283i	$0.728953\pi$
$920$	11.4549	+	8.25065i	0.377657	+	0.272016i
$921$	22.7712	−	12.7567i	0.750337	−	0.420347i
$922$	2.99325	+	0.802038i	0.0985773	+	0.0264137i
$923$	−1.71822	−	6.41247i	−0.0565557	−	0.211069i
$924$	15.1562	+	4.47074i	0.498603	+	0.147077i
$925$	40.9802	+	20.4573i	1.34742	+	0.672632i
$926$	−19.4681	−	11.2399i	−0.639762	−	0.369367i
$927$	−43.1896	+	41.0084i	−1.41853	+	1.34689i
$928$	−1.88835	+	7.04740i	−0.0619880	+	0.231342i
$929$	−26.2107			−0.859944			−0.429972	−	0.902842i	$-0.641477\pi$
$929$	−26.2107			−0.859944			−0.429972	+	0.902842i	$0.641477\pi$
$930$	−13.4537	+	18.1776i	−0.441165	+	0.596066i
$931$	−27.8313	+	15.1831i	−0.912133	+	0.497605i
$932$	−18.5112	+	4.96006i	−0.606354	+	0.162472i
$933$	10.7176	−	38.0223i	0.350880	−	1.24479i
$934$	24.7513	+	14.2902i	0.809888	+	0.467589i
$935$	9.66395	+	3.66408i	0.316045	+	0.119828i
$936$	−1.80143	+	0.978748i	−0.0588814	+	0.0319914i
$937$	23.6538	−	23.6538i	0.772735	−	0.772735i	−0.205849	−	0.978584i	$-0.565996\pi$
$937$	23.6538	−	23.6538i	0.772735	−	0.772735i	0.978584	+	0.205849i	$0.0659956\pi$
$938$	−4.26653	−	7.60065i	−0.139307	−	0.248170i
$939$	−25.7159	−	45.9039i	−0.839206	−	1.49802i
$940$	−19.0607	−	7.22686i	−0.621692	−	0.235714i
$941$		−	12.1594i		−	0.396384i	−0.980163	−	0.198192i	$-0.936493\pi$
$941$		−	12.1594i		−	0.396384i	0.980163	−	0.198192i	$-0.0635070\pi$
$942$	11.9277	+	3.36214i	0.388624	+	0.109544i
$943$	30.0601	+	30.0601i	0.978892	+	0.978892i
$944$	2.26061			0.0735766
$945$	−30.5542	+	3.38241i	−0.993928	+	0.110030i
$946$	39.5105			1.28460
$947$	12.3787	+	12.3787i	0.402254	+	0.402254i	0.879027	−	0.476772i	$-0.158193\pi$
$947$	12.3787	+	12.3787i	0.402254	+	0.402254i	−0.476772	+	0.879027i	$0.658193\pi$
$948$	−19.8485	−	5.59486i	−0.644650	−	0.181713i
$949$			0.766363i			0.0248772i
$950$	20.2610	+	10.1143i	0.657355	+	0.328151i
$951$	10.2000	+	18.2074i	0.330757	+	0.590414i
$952$	1.81021	−	3.04960i	0.0586691	−	0.0988380i
$953$	−37.1963	+	37.1963i	−1.20491	+	1.20491i	−0.232249	+	0.972656i	$0.574608\pi$
$953$	−37.1963	+	37.1963i	−1.20491	+	1.20491i	−0.972656	+	0.232249i	$0.925392\pi$
$954$	0.541113	−	20.8880i	0.0175192	−	0.676273i
$955$	7.97825	−	3.59157i	0.258170	−	0.116220i
$956$	−0.699125	−	0.403640i	−0.0226113	−	0.0130546i
$957$	−11.8223	+	41.9413i	−0.382162	+	1.35577i
$958$	−29.2405	+	7.83496i	−0.944717	+	0.253136i
$959$	18.7269	+	19.1854i	0.604724	+	0.619530i
$960$	−3.83050	+	0.572052i	−0.123629	+	0.0184629i
$961$	3.09510			0.0998418
$962$	1.62024	−	6.04682i	0.0522386	−	0.194957i
$963$	−0.603285	−	0.178517i	−0.0194406	−	0.00575263i
$964$	−3.69595	−	2.13386i	−0.119039	−	0.0687270i
$965$	−3.63875	+	9.59714i	−0.117135	+	0.308943i
$966$	20.9632	−	19.9387i	0.674481	−	0.641518i
$967$	−3.42416	−	12.7791i	−0.110114	−	0.410949i	0.888761	−	0.458370i	$-0.151567\pi$
$967$	−3.42416	−	12.7791i	−0.110114	−	0.410949i	−0.998875	+	0.0474207i	$0.984900\pi$
$968$	0.860077	+	0.230457i	0.0276439	+	0.00740717i
$969$	9.17351	−	5.13910i	0.294696	−	0.165092i
$970$	20.6538	−	28.6750i	0.663153	−	0.920697i
$971$	−9.36786	−	5.40854i	−0.300629	−	0.173568i	0.342096	−	0.939665i	$-0.388863\pi$
$971$	−9.36786	−	5.40854i	−0.300629	−	0.173568i	−0.642725	+	0.766097i	$0.722196\pi$
$972$	15.2868	−	3.05187i	0.490324	−	0.0978887i
$973$	−0.0587817	+	4.86056i	−0.00188446	+	0.155822i
$974$	17.8629	+	30.9394i	0.572363	+	0.991362i
$975$	−3.98079	+	4.37939i	−0.127487	+	0.140253i
$976$	−7.30460			−0.233814
$977$	−15.8569	−	15.8569i	−0.507307	−	0.507307i	0.406392	−	0.913699i	$-0.366787\pi$
$977$	−15.8569	−	15.8569i	−0.507307	−	0.507307i	−0.913699	+	0.406392i	$0.866787\pi$
$978$	−7.55005	−	7.74817i	−0.241424	−	0.247759i
$979$	−22.5666	+	13.0288i	−0.721232	+	0.416404i
$980$	1.94821	−	15.5308i	0.0622332	−	0.496112i
$981$	−2.47506	−	0.0641176i	−0.0790226	−	0.00204712i
$982$	1.76924	+	6.60289i	0.0564587	+	0.210707i
$983$	6.46931	+	24.1438i	0.206339	+	0.770068i	0.989037	+	0.147666i	$0.0471762\pi$
$983$	6.46931	+	24.1438i	0.206339	+	0.770068i	−0.782698	+	0.622401i	$0.786157\pi$
$984$	−11.6620	−	0.151030i	−0.371772	−	0.00481466i
$985$	18.5808	−	49.0067i	0.592035	−	1.56148i
$986$	8.46941	+	4.88982i	0.269721	+	0.155724i
$987$	−21.7876	+	35.6450i	−0.693506	+	1.13459i
$988$	0.801063	−	2.98961i	0.0254852	−	0.0951121i
$989$	36.1692	−	62.6469i	1.15011	−	1.99206i
$990$	−22.9202	+	3.12006i	−0.728451	+	0.0991621i
$991$	−29.0395	−	50.2979i	−0.922470	−	1.59776i	−0.795581	−	0.605847i	$-0.792834\pi$
$991$	−29.0395	−	50.2979i	−0.922470	−	1.59776i	−0.126888	−	0.991917i	$-0.540499\pi$
$992$	4.12887	+	4.12887i	0.131092	+	0.131092i
$993$	−4.43758	−	1.25086i	−0.140822	−	0.0396947i
$994$	−24.7440	−	6.95191i	−0.784832	−	0.220501i
$995$	10.2974	+	7.41692i	0.326449	+	0.235132i
$996$	6.34905	−	10.6752i	0.201177	−	0.338257i
$997$	−1.75434	−	6.54730i	−0.0555606	−	0.207355i	0.932565	−	0.361001i	$-0.117565\pi$
$997$	−1.75434	−	6.54730i	−0.0555606	−	0.207355i	−0.988126	+	0.153646i	$0.950898\pi$
$998$	6.08953	+	1.63169i	0.192761	+	0.0516501i
$999$	−25.3828	+	40.2669i	−0.803078	+	1.27399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.4	yes	192
5.2	odd	4	inner	630.2.cd.a.527.35	yes	192
7.4	even	3		630.2.bt.a.473.37	yes	192
9.2	odd	6		630.2.bt.a.443.46	yes	192
35.32	odd	12		630.2.bt.a.347.46	yes	192
45.2	even	12		630.2.bt.a.317.37	✓	192
63.11	odd	6	inner	630.2.cd.a.263.35	yes	192
315.137	even	12	inner	630.2.cd.a.137.4	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.37	✓	192	45.2	even	12
630.2.bt.a.347.46	yes	192	35.32	odd	12
630.2.bt.a.443.46	yes	192	9.2	odd	6
630.2.bt.a.473.37	yes	192	7.4	even	3
630.2.cd.a.23.4	yes	192	1.1	even	1	trivial
630.2.cd.a.137.4	yes	192	315.137	even	12	inner
630.2.cd.a.263.35	yes	192	63.11	odd	6	inner
630.2.cd.a.527.35	yes	192	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.66709 - 0.469915i) q^{3} +1.00000i q^{4} +(0.917891 + 2.03899i) q^{5} +(0.846529 + 1.51109i) q^{6} +(-1.29507 - 2.30712i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.55836 + 1.56678i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.66709 - 0.469915i) q^{3} +1.00000i q^{4} +(0.917891 + 2.03899i) q^{5} +(0.846529 + 1.51109i) q^{6} +(-1.29507 - 2.30712i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.55836 + 1.56678i) q^{9} +(0.792736 - 2.09083i) q^{10} +(-2.98627 - 1.72412i) q^{11} +(0.469915 - 1.66709i) q^{12} +(-0.660095 + 0.176872i) q^{13} +(-0.715625 + 2.54713i) q^{14} +(-0.572052 - 3.83050i) q^{15} -1.00000 q^{16} +(-0.346924 + 1.29474i) q^{17} +(-0.701154 - 2.91691i) q^{18} +(3.92228 + 2.26453i) q^{19} +(-2.03899 + 0.917891i) q^{20} +(1.07485 + 4.45474i) q^{21} +(0.892472 + 3.33075i) q^{22} +(6.09817 + 1.63400i) q^{23} +(-1.51109 + 0.846529i) q^{24} +(-3.31495 + 3.74314i) q^{25} +(0.591825 + 0.341690i) q^{26} +(-3.52876 - 3.81417i) q^{27} +(2.30712 - 1.29507i) q^{28} +(3.64800 + 6.31853i) q^{29} +(-2.30407 + 3.11308i) q^{30} +5.83910 q^{31} +(0.707107 + 0.707107i) q^{32} +(4.16818 + 4.27756i) q^{33} +(1.16083 - 0.670205i) q^{34} +(3.51545 - 4.75832i) q^{35} +(-1.56678 + 2.55836i) q^{36} +(-2.37092 - 8.84838i) q^{37} +(-1.17221 - 4.37473i) q^{38} +(1.18355 + 0.0153277i) q^{39} +(2.09083 + 0.792736i) q^{40} +(5.83150 + 3.36682i) q^{41} +(2.38994 - 3.91001i) q^{42} +(2.96558 - 11.0677i) q^{43} +(1.72412 - 2.98627i) q^{44} +(-0.846350 + 6.65460i) q^{45} +(-3.15664 - 5.46747i) q^{46} +(6.44623 + 6.44623i) q^{47} +(1.66709 + 0.469915i) q^{48} +(-3.64558 + 5.97576i) q^{49} +(4.99082 - 0.302773i) q^{50} +(1.18677 - 1.99541i) q^{51} +(-0.176872 - 0.660095i) q^{52} +(6.72766 + 1.80267i) q^{53} +(-0.201817 + 5.19223i) q^{54} +(0.774400 - 7.67153i) q^{55} +(-2.54713 - 0.715625i) q^{56} +(-5.47465 - 5.61831i) q^{57} +(1.88835 - 7.04740i) q^{58} -2.26061 q^{59} +(3.83050 - 0.572052i) q^{60} +7.30460 q^{61} +(-4.12887 - 4.12887i) q^{62} +(0.301485 - 7.93153i) q^{63} -1.00000i q^{64} +(-0.966535 - 1.18358i) q^{65} +(0.0773413 - 5.97204i) q^{66} +(-2.32952 + 2.32952i) q^{67} +(-1.29474 - 0.346924i) q^{68} +(-9.39834 - 5.58964i) q^{69} +(-5.85044 + 0.878837i) q^{70} +9.71446i q^{71} +(2.91691 - 0.701154i) q^{72} +(0.290247 - 1.08322i) q^{73} +(-4.58026 + 7.93324i) q^{74} +(7.28527 - 4.68239i) q^{75} +(-2.26453 + 3.92228i) q^{76} +(-0.110325 + 9.12254i) q^{77} +(-0.826059 - 0.847735i) q^{78} -11.9061i q^{79} +(-0.917891 - 2.03899i) q^{80} +(4.09041 + 8.01677i) q^{81} +(-1.74279 - 6.50420i) q^{82} +(6.92667 + 1.85599i) q^{83} +(-4.45474 + 1.07485i) q^{84} +(-2.95839 + 0.481053i) q^{85} +(-9.92303 + 5.72906i) q^{86} +(-3.11237 - 12.2478i) q^{87} +(-3.33075 + 0.892472i) q^{88} +(3.77839 - 6.54437i) q^{89} +(5.30397 - 4.10705i) q^{90} +(1.26293 + 1.29386i) q^{91} +(-1.63400 + 6.09817i) q^{92} +(-9.73429 - 2.74388i) q^{93} -9.11635i q^{94} +(-1.01713 + 10.0761i) q^{95} +(-0.846529 - 1.51109i) q^{96} +(15.2655 + 4.09038i) q^{97} +(6.80332 - 1.64769i) q^{98} +(-4.93863 - 9.08976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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