LMFDB - Embedded newform 570.2.k.a.77.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.7
Character	$\chi$	$=$	570.77
Dual form			570.2.k.a.533.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.43759 + 0.966096i) q^{3} -1.00000i q^{4} +(-1.74702 - 1.39568i) q^{5} +(-1.69966 + 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.13332 + 2.77770i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.43759 + 0.966096i) q^{3} -1.00000i q^{4} +(-1.74702 - 1.39568i) q^{5} +(-1.69966 + 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.13332 + 2.77770i) q^{9} +(2.22222 - 0.248430i) q^{10} +4.73487i q^{11} +(0.966096 - 1.43759i) q^{12} +(3.07524 - 3.07524i) q^{13} -0.524733 q^{14} +(-1.16313 - 3.69420i) q^{15} -1.00000 q^{16} +(-2.77446 + 2.77446i) q^{17} +(-2.76550 - 1.16275i) q^{18} +1.00000i q^{19} +(-1.39568 + 1.74702i) q^{20} +(0.174943 + 0.891868i) q^{21} +(-3.34806 - 3.34806i) q^{22} +(5.62880 + 5.62880i) q^{23} +(0.333395 + 1.69966i) q^{24} +(1.10414 + 4.87656i) q^{25} +4.34904i q^{26} +(-1.05428 + 5.08807i) q^{27} +(0.371042 - 0.371042i) q^{28} +4.06253 q^{29} +(3.43465 + 1.78974i) q^{30} +3.53345 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.57434 + 6.80679i) q^{33} -3.92368i q^{34} +(-0.130360 - 1.16607i) q^{35} +(2.77770 - 1.13332i) q^{36} +(2.20796 + 2.20796i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(7.39190 - 1.44995i) q^{39} +(-0.248430 - 2.22222i) q^{40} -6.41083i q^{41} +(-0.754350 - 0.506942i) q^{42} +(-6.80047 + 6.80047i) q^{43} +4.73487 q^{44} +(1.89686 - 6.43443i) q^{45} -7.96032 q^{46} +(-5.86781 + 5.86781i) q^{47} +(-1.43759 - 0.966096i) q^{48} -6.72466i q^{49} +(-4.22899 - 2.66751i) q^{50} +(-6.66893 + 1.30814i) q^{51} +(-3.07524 - 3.07524i) q^{52} +(-6.65823 - 6.65823i) q^{53} +(-2.85232 - 4.34330i) q^{54} +(6.60838 - 8.27189i) q^{55} +0.524733i q^{56} +(-0.966096 + 1.43759i) q^{57} +(-2.87264 + 2.87264i) q^{58} +6.00225 q^{59} +(-3.69420 + 1.16313i) q^{60} -3.00545 q^{61} +(-2.49852 + 2.49852i) q^{62} +(-0.610134 + 1.45115i) q^{63} +1.00000i q^{64} +(-9.66455 + 1.08043i) q^{65} +(-1.57858 - 8.04767i) q^{66} +(4.01127 + 4.01127i) q^{67} +(2.77446 + 2.77446i) q^{68} +(2.65393 + 13.5299i) q^{69} +(0.916717 + 0.732361i) q^{70} -3.67498i q^{71} +(-1.16275 + 2.76550i) q^{72} +(7.51659 - 7.51659i) q^{73} -3.12253 q^{74} +(-3.12394 + 8.07719i) q^{75} +1.00000 q^{76} +(-1.75684 + 1.75684i) q^{77} +(-4.20159 + 6.25213i) q^{78} -7.93390i q^{79} +(1.74702 + 1.39568i) q^{80} +(-6.43119 + 6.29602i) q^{81} +(4.53314 + 4.53314i) q^{82} +(-7.74087 - 7.74087i) q^{83} +(0.891868 - 0.174943i) q^{84} +(8.71931 - 0.974762i) q^{85} -9.61732i q^{86} +(5.84025 + 3.92480i) q^{87} +(-3.34806 + 3.34806i) q^{88} +7.13257 q^{89} +(3.20855 + 5.89111i) q^{90} +2.28209 q^{91} +(5.62880 - 5.62880i) q^{92} +(5.07964 + 3.41365i) q^{93} -8.29833i q^{94} +(1.39568 - 1.74702i) q^{95} +(1.69966 - 0.333395i) q^{96} +(5.01544 + 5.01544i) q^{97} +(4.75505 + 4.75505i) q^{98} +(-13.1520 + 5.36611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.43759	+	0.966096i	0.829992	+	0.557776i
$3$	1.43759	+	0.966096i	0.829992	+	0.557776i
$4$		−	1.00000i		−	0.500000i
$5$	−1.74702	−	1.39568i	−0.781290	−	0.624169i
$5$	−1.74702	−	1.39568i	−0.781290	−	0.624169i
$6$	−1.69966	+	0.333395i	−0.693884	+	0.136108i
$7$	0.371042	+	0.371042i	0.140241	+	0.140241i	0.773742	−	0.633501i	$-0.218383\pi$
$7$	0.371042	+	0.371042i	0.140241	+	0.140241i	−0.633501	+	0.773742i	$0.718383\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.13332	+	2.77770i	0.377772	+	0.925899i
$10$	2.22222	−	0.248430i	0.702729	−	0.0785605i
$11$			4.73487i			1.42762i	0.700341	+	0.713808i	$0.253031\pi$
$11$			4.73487i			1.42762i	−0.700341	+	0.713808i	$0.746969\pi$
$12$	0.966096	−	1.43759i	0.278888	−	0.414996i
$13$	3.07524	−	3.07524i	0.852917	−	0.852917i	−0.137574	−	0.990491i	$-0.543931\pi$
$13$	3.07524	−	3.07524i	0.852917	−	0.852917i	0.990491	+	0.137574i	$0.0439305\pi$
$14$	−0.524733			−0.140241
$15$	−1.16313	−	3.69420i	−0.300318	−	0.953839i
$16$	−1.00000			−0.250000
$17$	−2.77446	+	2.77446i	−0.672906	+	0.672906i	−0.958385	−	0.285479i	$-0.907847\pi$
$17$	−2.77446	+	2.77446i	−0.672906	+	0.672906i	0.285479	+	0.958385i	$0.407847\pi$
$18$	−2.76550	−	1.16275i	−0.651835	−	0.274063i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.39568	+	1.74702i	−0.312084	+	0.390645i
$21$	0.174943	+	0.891868i	0.0381758	+	0.194622i
$22$	−3.34806	−	3.34806i	−0.713808	−	0.713808i
$23$	5.62880	+	5.62880i	1.17369	+	1.17369i	0.981324	+	0.192362i	$0.0616146\pi$
$23$	5.62880	+	5.62880i	1.17369	+	1.17369i	0.192362	+	0.981324i	$0.438385\pi$
$24$	0.333395	+	1.69966i	0.0680540	+	0.346942i
$25$	1.10414	+	4.87656i	0.220827	+	0.975313i
$26$			4.34904i			0.852917i
$27$	−1.05428	+	5.08807i	−0.202896	+	0.979200i
$28$	0.371042	−	0.371042i	0.0701204	−	0.0701204i
$29$	4.06253			0.754393			0.377197	−	0.926133i	$-0.376888\pi$
$29$	4.06253			0.754393			0.377197	+	0.926133i	$0.376888\pi$
$30$	3.43465	+	1.78974i	0.627078	+	0.326761i
$31$	3.53345			0.634625			0.317313	−	0.948321i	$-0.397220\pi$
$31$	3.53345			0.634625			0.317313	+	0.948321i	$0.397220\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.57434	+	6.80679i	−0.796290	+	1.18491i
$34$		−	3.92368i		−	0.672906i
$35$	−0.130360	−	1.16607i	−0.0220348	−	0.197103i
$36$	2.77770	−	1.13332i	0.462949	−	0.188886i
$37$	2.20796	+	2.20796i	0.362987	+	0.362987i	0.864911	−	0.501925i	$-0.167375\pi$
$37$	2.20796	+	2.20796i	0.362987	+	0.362987i	−0.501925	+	0.864911i	$0.667375\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$	7.39190	−	1.44995i	1.18365	−	0.232178i
$40$	−0.248430	−	2.22222i	−0.0392803	−	0.351365i
$41$		−	6.41083i		−	1.00120i	−0.865678	−	0.500601i	$-0.833112\pi$
$41$		−	6.41083i		−	1.00120i	0.865678	−	0.500601i	$-0.166888\pi$
$42$	−0.754350	−	0.506942i	−0.116399	−	0.0782229i
$43$	−6.80047	+	6.80047i	−1.03706	+	1.03706i	−0.0377764	+	0.999286i	$0.512027\pi$
$43$	−6.80047	+	6.80047i	−1.03706	+	1.03706i	−0.999286	+	0.0377764i	$0.987973\pi$
$44$	4.73487			0.713808
$45$	1.89686	−	6.43443i	0.282767	−	0.959189i
$46$	−7.96032			−1.17369
$47$	−5.86781	+	5.86781i	−0.855908	+	0.855908i	−0.990853	−	0.134945i	$-0.956914\pi$
$47$	−5.86781	+	5.86781i	−0.855908	+	0.855908i	0.134945	+	0.990853i	$0.456914\pi$
$48$	−1.43759	−	0.966096i	−0.207498	−	0.139444i
$49$		−	6.72466i		−	0.960665i
$50$	−4.22899	−	2.66751i	−0.598070	−	0.377243i
$51$	−6.66893	+	1.30814i	−0.933837	+	0.183176i
$52$	−3.07524	−	3.07524i	−0.426459	−	0.426459i
$53$	−6.65823	−	6.65823i	−0.914579	−	0.914579i	0.0820496	−	0.996628i	$-0.473853\pi$
$53$	−6.65823	−	6.65823i	−0.914579	−	0.914579i	−0.996628	+	0.0820496i	$0.973853\pi$
$54$	−2.85232	−	4.34330i	−0.388152	−	0.591048i
$55$	6.60838	−	8.27189i	0.891073	−	1.11538i
$56$			0.524733i			0.0701204i
$57$	−0.966096	+	1.43759i	−0.127963	+	0.190413i
$58$	−2.87264	+	2.87264i	−0.377197	+	0.377197i
$59$	6.00225			0.781426			0.390713	−	0.920513i	$-0.372228\pi$
$59$	6.00225			0.781426			0.390713	+	0.920513i	$0.372228\pi$
$60$	−3.69420	+	1.16313i	−0.476920	+	0.150159i
$61$	−3.00545			−0.384809			−0.192404	−	0.981316i	$-0.561628\pi$
$61$	−3.00545			−0.384809			−0.192404	+	0.981316i	$0.561628\pi$
$62$	−2.49852	+	2.49852i	−0.317313	+	0.317313i
$63$	−0.610134	+	1.45115i	−0.0768696	+	0.182828i
$64$			1.00000i			0.125000i
$65$	−9.66455	+	1.08043i	−1.19874	+	0.134011i
$66$	−1.57858	−	8.04767i	−0.194310	−	0.990600i
$67$	4.01127	+	4.01127i	0.490055	+	0.490055i	0.908323	−	0.418269i	$-0.137363\pi$
$67$	4.01127	+	4.01127i	0.490055	+	0.490055i	−0.418269	+	0.908323i	$0.637363\pi$
$68$	2.77446	+	2.77446i	0.336453	+	0.336453i
$69$	2.65393	+	13.5299i	0.319496	+	1.62880i
$70$	0.916717	+	0.732361i	0.109569	+	0.0875339i
$71$		−	3.67498i		−	0.436140i	−0.975933	−	0.218070i	$-0.930024\pi$
$71$		−	3.67498i		−	0.436140i	0.975933	−	0.218070i	$-0.0699762\pi$
$72$	−1.16275	+	2.76550i	−0.137032	+	0.325918i
$73$	7.51659	−	7.51659i	0.879750	−	0.879750i	−0.113758	−	0.993508i	$-0.536289\pi$
$73$	7.51659	−	7.51659i	0.879750	−	0.879750i	0.993508	+	0.113758i	$0.0362890\pi$
$74$	−3.12253			−0.362987
$75$	−3.12394	+	8.07719i	−0.360721	+	0.932674i
$76$	1.00000			0.114708
$77$	−1.75684	+	1.75684i	−0.200210	+	0.200210i
$78$	−4.20159	+	6.25213i	−0.475737	+	0.707914i
$79$		−	7.93390i		−	0.892633i	−0.894875	−	0.446317i	$-0.852735\pi$
$79$		−	7.93390i		−	0.892633i	0.894875	−	0.446317i	$-0.147265\pi$
$80$	1.74702	+	1.39568i	0.195322	+	0.156042i
$81$	−6.43119	+	6.29602i	−0.714576	+	0.699558i
$82$	4.53314	+	4.53314i	0.500601	+	0.500601i
$83$	−7.74087	−	7.74087i	−0.849671	−	0.849671i	0.140421	−	0.990092i	$-0.455154\pi$
$83$	−7.74087	−	7.74087i	−0.849671	−	0.849671i	−0.990092	+	0.140421i	$0.955154\pi$
$84$	0.891868	−	0.174943i	0.0973108	−	0.0190879i
$85$	8.71931	−	0.974762i	0.945742	−	0.105728i
$86$		−	9.61732i		−	1.03706i
$87$	5.84025	+	3.92480i	0.626140	+	0.420782i
$88$	−3.34806	+	3.34806i	−0.356904	+	0.356904i
$89$	7.13257			0.756051			0.378026	−	0.925795i	$-0.376603\pi$
$89$	7.13257			0.756051			0.378026	+	0.925795i	$0.376603\pi$
$90$	3.20855	+	5.89111i	0.338211	+	0.620978i
$91$	2.28209			0.239228
$92$	5.62880	−	5.62880i	0.586843	−	0.586843i
$93$	5.07964	+	3.41365i	0.526734	+	0.353979i
$94$		−	8.29833i		−	0.855908i
$95$	1.39568	−	1.74702i	0.143194	−	0.179240i
$96$	1.69966	−	0.333395i	0.173471	−	0.0340270i
$97$	5.01544	+	5.01544i	0.509241	+	0.509241i	0.914293	−	0.405053i	$-0.132747\pi$
$97$	5.01544	+	5.01544i	0.509241	+	0.509241i	−0.405053	+	0.914293i	$0.632747\pi$
$98$	4.75505	+	4.75505i	0.480333	+	0.480333i
$99$	−13.1520	+	5.36611i	−1.32183	+	0.539314i
$100$	4.87656	−	1.10414i	0.487656	−	0.110414i
$101$		−	14.1063i		−	1.40363i	−0.712361	−	0.701813i	$-0.752374\pi$
$101$		−	14.1063i		−	1.40363i	0.712361	−	0.701813i	$-0.247626\pi$
$102$	3.79066	−	5.64064i	0.375331	−	0.558507i
$103$	−5.16485	+	5.16485i	−0.508907	+	0.508907i	−0.914191	−	0.405284i	$-0.867173\pi$
$103$	−5.16485	+	5.16485i	−0.508907	+	0.508907i	0.405284	+	0.914191i	$0.367173\pi$
$104$	4.34904			0.426459
$105$	0.939137	−	1.80227i	0.0916503	−	0.175884i
$106$	9.41616			0.914579
$107$	−5.85663	+	5.85663i	−0.566182	+	0.566182i	−0.931057	−	0.364875i	$-0.881112\pi$
$107$	−5.85663	+	5.85663i	−0.566182	+	0.566182i	0.364875	+	0.931057i	$0.381112\pi$
$108$	5.08807	+	1.05428i	0.489600	+	0.101448i
$109$			10.5464i			1.01016i	0.863073	+	0.505079i	$0.168537\pi$
$109$			10.5464i			1.01016i	−0.863073	+	0.505079i	$0.831463\pi$
$110$	1.17628	+	10.5219i	0.112154	+	1.00323i
$111$	1.04104	+	5.30724i	0.0988107	+	0.503741i
$112$	−0.371042	−	0.371042i	−0.0350602	−	0.0350602i
$113$	−11.6877	−	11.6877i	−1.09948	−	1.09948i	−0.994471	−	0.105011i	$-0.966512\pi$
$113$	−11.6877	−	11.6877i	−1.09948	−	1.09948i	−0.105011	−	0.994471i	$-0.533488\pi$
$114$	−0.333395	−	1.69966i	−0.0312253	−	0.159188i
$115$	−1.97758	−	17.6896i	−0.184411	−	1.64957i
$116$		−	4.06253i		−	0.377197i
$117$	12.0273	+	5.05685i	1.11192	+	0.467506i
$118$	−4.24423	+	4.24423i	−0.390713	+	0.390713i
$119$	−2.05889			−0.188738
$120$	1.78974	−	3.43465i	0.163380	−	0.313539i
$121$	−11.4190			−1.03809
$122$	2.12517	−	2.12517i	0.192404	−	0.192404i
$123$	6.19347	−	9.21612i	0.558447	−	0.830990i
$124$		−	3.53345i		−	0.317313i
$125$	4.87720	−	10.0605i	0.436230	−	0.899835i
$126$	−0.594689	−	1.45755i	−0.0529791	−	0.129849i
$127$	11.5688	+	11.5688i	1.02656	+	1.02656i	0.999637	+	0.0269261i	$0.00857187\pi$
$127$	11.5688	+	11.5688i	1.02656	+	1.02656i	0.0269261	+	0.999637i	$0.491428\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−16.3462	+	3.20637i	−1.43920	+	0.282305i
$130$	6.06989	−	7.59785i	0.532364	−	0.666376i
$131$		−	12.1137i		−	1.05838i	−0.848505	−	0.529188i	$-0.822497\pi$
$131$		−	12.1137i		−	1.05838i	0.848505	−	0.529188i	$-0.177503\pi$
$132$	6.80679	+	4.57434i	0.592455	+	0.398145i
$133$	−0.371042	+	0.371042i	−0.0321734	+	0.0321734i
$134$	−5.67279			−0.490055
$135$	8.94318	−	7.41751i	0.769707	−	0.638398i
$136$	−3.92368			−0.336453
$137$	−1.08854	+	1.08854i	−0.0930002	+	0.0930002i	−0.752076	−	0.659076i	$-0.770948\pi$
$137$	−1.08854	+	1.08854i	−0.0930002	+	0.0930002i	0.659076	+	0.752076i	$0.270948\pi$
$138$	−11.4437	−	7.69044i	−0.974149	−	0.654653i
$139$		−	6.34474i		−	0.538154i	−0.963119	−	0.269077i	$-0.913281\pi$
$139$		−	6.34474i		−	0.538154i	0.963119	−	0.269077i	$-0.0867185\pi$
$140$	−1.16607	+	0.130360i	−0.0985513	+	0.0110174i
$141$	−14.1044	+	2.76662i	−1.18780	+	0.232992i
$142$	2.59861	+	2.59861i	0.218070	+	0.218070i
$143$	14.5608	+	14.5608i	1.21764	+	1.21764i
$144$	−1.13332	−	2.77770i	−0.0944431	−	0.231475i
$145$	−7.09731	−	5.67001i	−0.589400	−	0.470869i
$146$			10.6301i			0.879750i
$147$	6.49666	−	9.66728i	0.535836	−	0.797344i
$148$	2.20796	−	2.20796i	0.181493	−	0.181493i
$149$	19.2260			1.57506			0.787529	−	0.616278i	$-0.211360\pi$
$149$	19.2260			1.57506			0.787529	+	0.616278i	$0.211360\pi$
$150$	−3.50248	−	7.92039i	−0.285976	−	0.646697i
$151$	5.62170			0.457487			0.228744	−	0.973487i	$-0.426538\pi$
$151$	5.62170			0.457487			0.228744	+	0.973487i	$0.426538\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$	−10.8510	−	4.56227i	−0.877248	−	0.368838i
$154$		−	2.48454i		−	0.200210i
$155$	−6.17299	−	4.93157i	−0.495826	−	0.396113i
$156$	−1.44995	−	7.39190i	−0.116089	−	0.591825i
$157$	−10.3090	−	10.3090i	−0.822747	−	0.822747i	0.163754	−	0.986501i	$-0.447640\pi$
$157$	−10.3090	−	10.3090i	−0.822747	−	0.822747i	−0.986501	+	0.163754i	$0.947640\pi$
$158$	5.61011	+	5.61011i	0.446317	+	0.446317i
$159$	−3.13930	−	16.0043i	−0.248963	−	1.26922i
$160$	−2.22222	+	0.248430i	−0.175682	+	0.0196401i
$161$			4.17704i			0.329197i
$162$	0.0955769	−	8.99949i	0.00750923	−	0.707067i
$163$	15.8628	−	15.8628i	1.24247	−	1.24247i	0.283497	−	0.958973i	$-0.408505\pi$
$163$	15.8628	−	15.8628i	1.24247	−	1.24247i	0.958973	−	0.283497i	$-0.0914947\pi$
$164$	−6.41083			−0.500601
$165$	17.4916	−	5.50725i	1.36172	−	0.428738i
$166$	10.9472			0.849671
$167$	16.9172	−	16.9172i	1.30910	−	1.30910i	0.387027	−	0.922068i	$-0.373502\pi$
$167$	16.9172	−	16.9172i	1.30910	−	1.30910i	0.922068	−	0.387027i	$-0.126498\pi$
$168$	−0.506942	+	0.754350i	−0.0391115	+	0.0581993i
$169$		−	5.91417i		−	0.454936i
$170$	−5.47622	+	6.85474i	−0.420007	+	0.525735i
$171$	−2.77770	+	1.13332i	−0.212416	+	0.0866669i
$172$	6.80047	+	6.80047i	0.518531	+	0.518531i
$173$	6.04290	+	6.04290i	0.459433	+	0.459433i	0.898469	−	0.439036i	$-0.144680\pi$
$173$	6.04290	+	6.04290i	0.459433	+	0.459433i	−0.439036	+	0.898469i	$0.644680\pi$
$174$	−6.90493	+	1.35443i	−0.523461	+	0.102679i
$175$	−1.39973	+	2.21909i	−0.105810	+	0.167748i
$176$		−	4.73487i		−	0.356904i
$177$	8.62876	+	5.79875i	0.648577	+	0.435861i
$178$	−5.04349	+	5.04349i	−0.378026	+	0.378026i
$179$	7.72862			0.577664			0.288832	−	0.957380i	$-0.406733\pi$
$179$	7.72862			0.577664			0.288832	+	0.957380i	$0.406733\pi$
$180$	−6.43443	−	1.89686i	−0.479594	−	0.141384i
$181$	−15.5179			−1.15343			−0.576717	−	0.816944i	$-0.695666\pi$
$181$	−15.5179			−1.15343			−0.576717	+	0.816944i	$0.695666\pi$
$182$	−1.61368	+	1.61368i	−0.119614	+	0.119614i
$183$	−4.32060	−	2.90355i	−0.319388	−	0.214637i
$184$			7.96032i			0.586843i
$185$	−0.775731	−	6.93896i	−0.0570328	−	0.510163i
$186$	−6.00566	+	1.17803i	−0.440356	+	0.0863776i
$187$	−13.1367	−	13.1367i	−0.960652	−	0.960652i
$188$	5.86781	+	5.86781i	0.427954	+	0.427954i
$189$	−2.27907	+	1.49671i	−0.165778	+	0.108870i
$190$	0.248430	+	2.22222i	0.0180230	+	0.161217i
$191$		−	13.5080i		−	0.977402i	−0.872451	−	0.488701i	$-0.837471\pi$
$191$		−	13.5080i		−	0.977402i	0.872451	−	0.488701i	$-0.162529\pi$
$192$	−0.966096	+	1.43759i	−0.0697220	+	0.103749i
$193$	−2.95772	+	2.95772i	−0.212901	+	0.212901i	−0.805499	−	0.592597i	$-0.798103\pi$
$193$	−2.95772	+	2.95772i	−0.212901	+	0.212901i	0.592597	+	0.805499i	$0.298103\pi$
$194$	−7.09290			−0.509241
$195$	−14.9374	−	7.78366i	−1.06969	−	0.557400i
$196$	−6.72466			−0.480333
$197$	−14.5718	+	14.5718i	−1.03820	+	1.03820i	−0.0389574	+	0.999241i	$0.512404\pi$
$197$	−14.5718	+	14.5718i	−1.03820	+	1.03820i	−0.999241	+	0.0389574i	$0.987596\pi$
$198$	5.50547	−	13.0943i	0.391257	−	0.930571i
$199$		−	5.90849i		−	0.418842i	−0.977826	−	0.209421i	$-0.932842\pi$
$199$		−	5.90849i		−	0.418842i	0.977826	−	0.209421i	$-0.0671578\pi$
$200$	−2.66751	+	4.22899i	−0.188621	+	0.299035i
$201$	1.89128	+	9.64183i	0.133401	+	0.680082i
$202$	9.97464	+	9.97464i	0.701813	+	0.701813i
$203$	1.50737	+	1.50737i	0.105797	+	0.105797i
$204$	1.30814	+	6.66893i	0.0915879	+	0.466919i
$205$	−8.94748	+	11.1998i	−0.624919	+	0.782229i
$206$		−	7.30419i		−	0.508907i
$207$	−9.25588	+	22.0143i	−0.643328	+	1.53010i
$208$	−3.07524	+	3.07524i	−0.213229	+	0.213229i
$209$	−4.73487			−0.327518
$210$	0.610330	+	1.93847i	0.0421168	+	0.133767i
$211$	−6.45326			−0.444261			−0.222130	−	0.975017i	$-0.571301\pi$
$211$	−6.45326			−0.444261			−0.222130	+	0.975017i	$0.571301\pi$
$212$	−6.65823	+	6.65823i	−0.457289	+	0.457289i
$213$	3.55039	−	5.28311i	0.243268	−	0.361993i
$214$		−	8.28252i		−	0.566182i
$215$	21.3719	−	2.38923i	1.45755	−	0.162944i
$216$	−4.34330	+	2.85232i	−0.295524	+	0.194076i
$217$	1.31106	+	1.31106i	0.0890004	+	0.0890004i
$218$	−7.45740	−	7.45740i	−0.505079	−	0.505079i
$219$	18.0675	−	3.54401i	1.22089	−	0.239482i
$220$	−8.27189	−	6.60838i	−0.557691	−	0.445537i
$221$			17.0643i			1.14787i
$222$	−4.48891	−	3.01666i	−0.301276	−	0.202465i
$223$	−12.4934	+	12.4934i	−0.836618	+	0.836618i	−0.988412	−	0.151794i	$-0.951495\pi$
$223$	−12.4934	+	12.4934i	−0.836618	+	0.836618i	0.151794	+	0.988412i	$0.451495\pi$
$224$	0.524733			0.0350602
$225$	−12.2943	+	8.59365i	−0.819618	+	0.572910i
$226$	16.5288			1.09948
$227$	−3.12326	+	3.12326i	−0.207298	+	0.207298i	−0.803118	−	0.595820i	$-0.796827\pi$
$227$	−3.12326	+	3.12326i	−0.207298	+	0.207298i	0.595820	+	0.803118i	$0.296827\pi$
$228$	1.43759	+	0.966096i	0.0952066	+	0.0639813i
$229$			4.46088i			0.294783i	0.989078	+	0.147392i	$0.0470878\pi$
$229$			4.46088i			0.294783i	−0.989078	+	0.147392i	$0.952912\pi$
$230$	13.9068	+	11.1101i	0.916989	+	0.732578i
$231$	−4.22288	+	0.828333i	−0.277845	+	0.0545003i
$232$	2.87264	+	2.87264i	0.188598	+	0.188598i
$233$	2.29263	+	2.29263i	0.150195	+	0.150195i	0.778205	−	0.628010i	$-0.216130\pi$
$233$	2.29263	+	2.29263i	0.150195	+	0.150195i	−0.628010	+	0.778205i	$0.716130\pi$
$234$	−12.0803	+	4.92884i	−0.789715	+	0.322209i
$235$	18.4408	−	2.06156i	1.20294	−	0.134481i
$236$		−	6.00225i		−	0.390713i
$237$	7.66491	−	11.4057i	0.497889	−	0.740878i
$238$	1.45585	−	1.45585i	0.0943689	−	0.0943689i
$239$	−4.10728			−0.265678			−0.132839	−	0.991138i	$-0.542409\pi$
$239$	−4.10728			−0.265678			−0.132839	+	0.991138i	$0.542409\pi$
$240$	1.16313	+	3.69420i	0.0750794	+	0.238460i
$241$	25.0963			1.61659			0.808297	−	0.588776i	$-0.200390\pi$
$241$	25.0963			1.61659			0.808297	+	0.588776i	$0.200390\pi$
$242$	8.07443	−	8.07443i	0.519044	−	0.519044i
$243$	−15.3280	+	2.83794i	−0.983289	+	0.182054i
$244$			3.00545i			0.192404i
$245$	−9.38549	+	11.7481i	−0.599617	+	0.750558i
$246$	2.13734	+	10.8962i	0.136272	+	0.694718i
$247$	3.07524	+	3.07524i	0.195673	+	0.195673i
$248$	2.49852	+	2.49852i	0.158656	+	0.158656i
$249$	−3.64976	−	18.6066i	−0.231294	−	1.17915i
$250$	3.66512	+	10.5625i	0.231803	+	0.668033i
$251$		−	21.3779i		−	1.34936i	−0.738110	−	0.674681i	$-0.764281\pi$
$251$		−	21.3779i		−	1.34936i	0.738110	−	0.674681i	$-0.235719\pi$
$252$	1.45115	+	0.610134i	0.0914139	+	0.0384348i
$253$	−26.6516	+	26.6516i	−1.67557	+	1.67557i
$254$	−16.3607			−1.02656
$255$	13.4765	+	7.02238i	0.843930	+	0.439759i
$256$	1.00000			0.0625000
$257$	−7.08612	+	7.08612i	−0.442020	+	0.442020i	−0.892690	−	0.450670i	$-0.851185\pi$
$257$	−7.08612	+	7.08612i	−0.442020	+	0.442020i	0.450670	+	0.892690i	$0.351185\pi$
$258$	9.29126	−	13.8257i	0.578448	−	0.860753i
$259$			1.63849i			0.101811i
$260$	1.08043	+	9.66455i	0.0670056	+	0.599370i
$261$	4.60414	+	11.2845i	0.284989	+	0.698492i
$262$	8.56565	+	8.56565i	0.529188	+	0.529188i
$263$	10.3710	+	10.3710i	0.639500	+	0.639500i	0.950432	−	0.310932i	$-0.100641\pi$
$263$	10.3710	+	10.3710i	0.639500	+	0.639500i	−0.310932	+	0.950432i	$0.600641\pi$
$264$	−8.04767	+	1.57858i	−0.495300	+	0.0971549i
$265$	2.33926	+	20.9248i	0.143700	+	1.28540i
$266$		−	0.524733i		−	0.0321734i
$267$	10.2537	+	6.89075i	0.627516	+	0.421707i
$268$	4.01127	−	4.01127i	0.245027	−	0.245027i
$269$	−13.9150			−0.848410			−0.424205	−	0.905566i	$-0.639446\pi$
$269$	−13.9150			−0.848410			−0.424205	+	0.905566i	$0.639446\pi$
$270$	−1.07881	+	11.5688i	−0.0656544	+	0.704052i
$271$	9.79499			0.595003			0.297502	−	0.954721i	$-0.403847\pi$
$271$	9.79499			0.595003			0.297502	+	0.954721i	$0.403847\pi$
$272$	2.77446	−	2.77446i	0.168227	−	0.168227i
$273$	3.28070	+	2.20471i	0.198557	+	0.133435i
$274$		−	1.53943i		−	0.0930002i
$275$	−23.0899	+	5.22793i	−1.39237	+	0.315256i
$276$	13.5299	−	2.65393i	0.814401	−	0.159748i
$277$	−4.58635	−	4.58635i	−0.275567	−	0.275567i	0.555770	−	0.831336i	$-0.312424\pi$
$277$	−4.58635	−	4.58635i	−0.275567	−	0.275567i	−0.831336	+	0.555770i	$0.812424\pi$
$278$	4.48641	+	4.48641i	0.269077	+	0.269077i
$279$	4.00451	+	9.81484i	0.239744	+	0.587599i
$280$	0.732361	−	0.916717i	0.0437669	−	0.0547843i
$281$			12.1098i			0.722412i	0.932486	+	0.361206i	$0.117635\pi$
$281$			12.1098i			0.722412i	−0.932486	+	0.361206i	$0.882365\pi$
$282$	8.01699	−	11.9296i	0.477405	−	0.710396i
$283$	−1.32735	+	1.32735i	−0.0789029	+	0.0789029i	−0.745457	−	0.666554i	$-0.767769\pi$
$283$	−1.32735	+	1.32735i	−0.0789029	+	0.0789029i	0.666554	+	0.745457i	$0.267769\pi$
$284$	−3.67498			−0.218070
$285$	3.69420	−	1.16313i	0.218826	−	0.0688976i
$286$	−20.5921			−1.21764
$287$	2.37869	−	2.37869i	0.140409	−	0.140409i
$288$	2.76550	+	1.16275i	0.162959	+	0.0685158i
$289$			1.60471i			0.0943944i
$290$	9.02786	−	1.00926i	0.530134	−	0.0592655i
$291$	2.36474	+	12.0555i	0.138623	+	0.706708i
$292$	−7.51659	−	7.51659i	−0.439875	−	0.439875i
$293$	−12.6506	−	12.6506i	−0.739057	−	0.739057i	0.233339	−	0.972395i	$-0.425035\pi$
$293$	−12.6506	−	12.6506i	−0.739057	−	0.739057i	−0.972395	+	0.233339i	$0.925035\pi$
$294$	2.24197	+	11.4296i	0.130754	+	0.666590i
$295$	−10.4860	−	8.37724i	−0.610520	−	0.487742i
$296$			3.12253i			0.181493i
$297$	−24.0914	−	4.99187i	−1.39792	−	0.289657i
$298$	−13.5949	+	13.5949i	−0.787529	+	0.787529i
$299$	34.6198			2.00211
$300$	8.07719	+	3.12394i	0.466337	+	0.180361i
$301$	−5.04653			−0.290877
$302$	−3.97514	+	3.97514i	−0.228744	+	0.228744i
$303$	13.6280	−	20.2790i	0.782909	−	1.16500i
$304$		−	1.00000i		−	0.0573539i
$305$	5.25057	+	4.19466i	0.300647	+	0.240185i
$306$	10.8988	−	4.44678i	0.623043	−	0.254205i
$307$	−16.4288	−	16.4288i	−0.937644	−	0.937644i	0.0605232	−	0.998167i	$-0.480723\pi$
$307$	−16.4288	−	16.4288i	−0.937644	−	0.937644i	−0.998167	+	0.0605232i	$0.980723\pi$
$308$	1.75684	+	1.75684i	0.100105	+	0.100105i
$309$	−12.4147	+	2.43518i	−0.706245	+	0.138533i
$310$	7.85211	−	0.877815i	0.445970	−	0.0498565i
$311$			6.49385i			0.368232i	0.982904	+	0.184116i	$0.0589423\pi$
$311$			6.49385i			0.368232i	−0.982904	+	0.184116i	$0.941058\pi$
$312$	6.25213	+	4.20159i	0.353957	+	0.237868i
$313$	−15.5616	+	15.5616i	−0.879591	+	0.879591i	−0.993492	−	0.113901i	$-0.963665\pi$
$313$	−15.5616	+	15.5616i	−0.879591	+	0.879591i	0.113901	+	0.993492i	$0.463665\pi$
$314$	14.5791			0.822747
$315$	3.09126	−	1.68363i	0.174173	−	0.0948619i
$316$	−7.93390			−0.446317
$317$	21.8274	−	21.8274i	1.22595	−	1.22595i	0.260466	−	0.965483i	$-0.416124\pi$
$317$	21.8274	−	21.8274i	1.22595	−	1.22595i	0.965483	−	0.260466i	$-0.0838762\pi$
$318$	13.5366	+	9.09692i	0.759093	+	0.510130i
$319$			19.2355i			1.07698i
$320$	1.39568	−	1.74702i	0.0780211	−	0.0976612i
$321$	−14.0775	+	2.76135i	−0.785728	+	0.154124i
$322$	−2.95362	−	2.95362i	−0.164599	−	0.164599i
$323$	−2.77446	−	2.77446i	−0.154375	−	0.154375i
$324$	6.29602	+	6.43119i	0.349779	+	0.357288i
$325$	18.3921	+	11.6011i	1.02021	+	0.643514i
$326$			22.4334i			1.24247i
$327$	−10.1888	+	15.1613i	−0.563442	+	0.838422i
$328$	4.53314	−	4.53314i	0.250301	−	0.250301i
$329$	−4.35441			−0.240066
$330$	−8.47419	+	16.2626i	−0.466489	+	0.895227i
$331$	−10.9575			−0.602276			−0.301138	−	0.953581i	$-0.597367\pi$
$331$	−10.9575			−0.602276			−0.301138	+	0.953581i	$0.597367\pi$
$332$	−7.74087	+	7.74087i	−0.424836	+	0.424836i
$333$	−3.63072	+	8.63536i	−0.198962	+	0.473215i
$334$			23.9246i			1.30910i
$335$	−1.40929	−	12.6062i	−0.0769979	−	0.688752i
$336$	−0.174943	−	0.891868i	−0.00954394	−	0.0486554i
$337$	−9.98105	−	9.98105i	−0.543702	−	0.543702i	0.380910	−	0.924612i	$-0.375611\pi$
$337$	−9.98105	−	9.98105i	−0.543702	−	0.543702i	−0.924612	+	0.380910i	$0.875611\pi$
$338$	4.18195	+	4.18195i	0.227468	+	0.227468i
$339$	−5.51063	−	28.0934i	−0.299296	−	1.52583i
$340$	−0.974762	−	8.71931i	−0.0528639	−	0.472871i
$341$			16.7304i			0.906002i
$342$	1.16275	−	2.76550i	0.0628744	−	0.149541i
$343$	5.09243	−	5.09243i	0.274965	−	0.274965i
$344$	−9.61732			−0.518531
$345$	14.2469	−	27.3409i	0.767029	−	1.47199i
$346$	−8.54595			−0.459433
$347$	−6.53710	+	6.53710i	−0.350930	+	0.350930i	−0.860456	−	0.509526i	$-0.829821\pi$
$347$	−6.53710	+	6.53710i	−0.350930	+	0.350930i	0.509526	+	0.860456i	$0.329821\pi$
$348$	3.92480	−	5.84025i	0.210391	−	0.313070i
$349$		−	16.6692i		−	0.892280i	−0.894963	−	0.446140i	$-0.852798\pi$
$349$		−	16.6692i		−	0.892280i	0.894963	−	0.446140i	$-0.147202\pi$
$350$	−0.579376	−	2.55889i	−0.0309690	−	0.136779i
$351$	12.4049	+	18.8892i	0.662123	+	1.00823i
$352$	3.34806	+	3.34806i	0.178452	+	0.178452i
$353$	18.7729	+	18.7729i	0.999178	+	0.999178i	1.00000		0.000821466i	$-0.000261481\pi$
$353$	18.7729	+	18.7729i	0.999178	+	0.999178i	−0.000821466		1.00000i	$0.500261\pi$
$354$	−10.2018	+	2.00112i	−0.542219	+	0.106358i
$355$	−5.12911	+	6.42026i	−0.272225	+	0.340752i
$356$		−	7.13257i		−	0.378026i
$357$	−2.95983	−	1.98908i	−0.156651	−	0.105273i
$358$	−5.46496	+	5.46496i	−0.288832	+	0.288832i
$359$	−31.0918			−1.64096			−0.820480	−	0.571675i	$-0.806294\pi$
$359$	−31.0918			−1.64096			−0.820480	+	0.571675i	$0.806294\pi$
$360$	5.89111	−	3.20855i	0.310489	−	0.169105i
$361$	−1.00000			−0.0526316
$362$	10.9728	−	10.9728i	0.576717	−	0.576717i
$363$	−16.4158	−	11.0318i	−0.861604	−	0.579020i
$364$		−	2.28209i		−	0.119614i
$365$	−23.6224	+	2.64083i	−1.23645	+	0.138227i
$366$	5.10825	−	1.00200i	0.267012	−	0.0523755i
$367$	−0.761107	−	0.761107i	−0.0397295	−	0.0397295i	0.686963	−	0.726692i	$-0.258943\pi$
$367$	−0.761107	−	0.761107i	−0.0397295	−	0.0397295i	−0.726692	+	0.686963i	$0.758943\pi$
$368$	−5.62880	−	5.62880i	−0.293421	−	0.293421i
$369$	17.8073	−	7.26550i	0.927012	−	0.378227i
$370$	5.45511	+	4.35806i	0.283598	+	0.226565i
$371$		−	4.94097i		−	0.256522i
$372$	3.41365	−	5.07964i	0.176989	−	0.263367i
$373$	8.01035	−	8.01035i	0.414760	−	0.414760i	−0.468633	−	0.883393i	$-0.655253\pi$
$373$	8.01035	−	8.01035i	0.414760	−	0.414760i	0.883393	+	0.468633i	$0.155253\pi$
$374$	18.5781			0.960652
$375$	16.7308	−	9.75096i	0.863973	−	0.503537i
$376$	−8.29833			−0.427954
$377$	12.4932	−	12.4932i	0.643435	−	0.643435i
$378$	0.553214	−	2.66988i	0.0284543	−	0.137324i
$379$		−	15.0607i		−	0.773616i	−0.922160	−	0.386808i	$-0.873578\pi$
$379$		−	15.0607i		−	0.773616i	0.922160	−	0.386808i	$-0.126422\pi$
$380$	−1.74702	−	1.39568i	−0.0896201	−	0.0715970i
$381$	5.45459	+	27.8077i	0.279447	+	1.42463i
$382$	9.55157	+	9.55157i	0.488701	+	0.488701i
$383$	−21.4822	−	21.4822i	−1.09769	−	1.09769i	−0.994680	−	0.103010i	$-0.967153\pi$
$383$	−21.4822	−	21.4822i	−1.09769	−	1.09769i	−0.103010	−	0.994680i	$-0.532847\pi$
$384$	−0.333395	−	1.69966i	−0.0170135	−	0.0867355i
$385$	5.52121	−	0.617235i	0.281387	−	0.0314572i
$386$		−	4.18285i		−	0.212901i
$387$	−26.5967	−	11.1826i	−1.35199	−	0.568441i
$388$	5.01544	−	5.01544i	0.254620	−	0.254620i
$389$	11.7608			0.596296			0.298148	−	0.954520i	$-0.403631\pi$
$389$	11.7608			0.596296			0.298148	+	0.954520i	$0.403631\pi$
$390$	16.0662	−	5.05848i	0.813546	−	0.256146i
$391$	−31.2338			−1.57956
$392$	4.75505	−	4.75505i	0.240166	−	0.240166i
$393$	11.7030	−	17.4144i	0.590336	−	0.878443i
$394$		−	20.6076i		−	1.03820i
$395$	−11.0732	+	13.8607i	−0.557154	+	0.697405i
$396$	5.36611	+	13.1520i	0.269657	+	0.660914i
$397$	6.27425	+	6.27425i	0.314895	+	0.314895i	0.846803	−	0.531907i	$-0.178524\pi$
$397$	6.27425	+	6.27425i	0.314895	+	0.314895i	−0.531907	+	0.846803i	$0.678524\pi$
$398$	4.17793	+	4.17793i	0.209421	+	0.209421i
$399$	−0.891868	+	0.174943i	−0.0446493	+	0.00875812i
$400$	−1.10414	−	4.87656i	−0.0552068	−	0.243828i
$401$			28.8320i			1.43980i	0.694076	+	0.719901i	$0.255813\pi$
$401$			28.8320i			1.43980i	−0.694076	+	0.719901i	$0.744187\pi$
$402$	−8.15514	−	5.48046i	−0.406741	−	0.273341i
$403$	10.8662	−	10.8662i	0.541283	−	0.541283i
$404$	−14.1063			−0.701813
$405$	20.0226	−	2.02335i	0.994933	−	0.100541i
$406$	−2.13174			−0.105797
$407$	−10.4544	+	10.4544i	−0.518206	+	0.518206i
$408$	−5.64064	−	3.79066i	−0.279253	−	0.187665i
$409$			18.6400i			0.921687i	0.887482	+	0.460843i	$0.152453\pi$
$409$			18.6400i			0.921687i	−0.887482	+	0.460843i	$0.847547\pi$
$410$	−1.59264	−	14.2463i	−0.0786550	−	0.703574i
$411$	−2.61650	+	0.513237i	−0.129063	+	0.0253161i
$412$	5.16485	+	5.16485i	0.254454	+	0.254454i
$413$	2.22709	+	2.22709i	0.109588	+	0.109588i
$414$	−9.02157	−	22.1114i	−0.443386	−	1.08671i
$415$	2.71963	+	24.3272i	0.133501	+	1.19418i
$416$		−	4.34904i		−	0.213229i
$417$	6.12962	−	9.12112i	0.300169	−	0.446663i
$418$	3.34806	−	3.34806i	0.163759	−	0.163759i
$419$	33.3598			1.62974			0.814868	−	0.579647i	$-0.196810\pi$
$419$	33.3598			1.62974			0.814868	+	0.579647i	$0.196810\pi$
$420$	−1.80227	−	0.939137i	−0.0879420	−	0.0458252i
$421$	−14.3797			−0.700824			−0.350412	−	0.936596i	$-0.613959\pi$
$421$	−14.3797			−0.700824			−0.350412	+	0.936596i	$0.613959\pi$
$422$	4.56315	−	4.56315i	0.222130	−	0.222130i
$423$	−22.9491	−	9.64890i	−1.11582	−	0.469145i
$424$		−	9.41616i		−	0.457289i
$425$	−16.5932	−	10.4665i	−0.804890	−	0.507698i
$426$	1.22522	+	6.24623i	0.0593622	+	0.302631i
$427$	−1.11515	−	1.11515i	−0.0539658	−	0.0539658i
$428$	5.85663	+	5.85663i	0.283091	+	0.283091i
$429$	6.86532	+	34.9997i	0.331461	+	1.68980i
$430$	−13.4227	+	16.8016i	−0.647302	+	0.810246i
$431$		−	13.4317i		−	0.646980i	−0.946232	−	0.323490i	$-0.895144\pi$
$431$		−	13.4317i		−	0.646980i	0.946232	−	0.323490i	$-0.104856\pi$
$432$	1.05428	−	5.08807i	0.0507240	−	0.244800i
$433$	4.59824	−	4.59824i	0.220977	−	0.220977i	−0.587933	−	0.808910i	$-0.700058\pi$
$433$	4.59824	−	4.59824i	0.220977	−	0.220977i	0.808910	+	0.587933i	$0.200058\pi$
$434$	−1.85411			−0.0890004
$435$	−4.72524	−	15.0078i	−0.226558	−	0.719570i
$436$	10.5464			0.505079
$437$	−5.62880	+	5.62880i	−0.269262	+	0.269262i
$438$	−10.2697	+	15.2816i	−0.490703	+	0.730185i
$439$		−	8.50450i		−	0.405898i	−0.979189	−	0.202949i	$-0.934948\pi$
$439$		−	8.50450i		−	0.405898i	0.979189	−	0.202949i	$-0.0650525\pi$
$440$	10.5219	−	1.17628i	0.501614	−	0.0560771i
$441$	18.6790	−	7.62117i	0.889478	−	0.362913i
$442$	−12.0663	−	12.0663i	−0.573933	−	0.573933i
$443$	21.4192	+	21.4192i	1.01766	+	1.01766i	0.999841	+	0.0178169i	$0.00567159\pi$
$443$	21.4192	+	21.4192i	1.01766	+	1.01766i	0.0178169	+	0.999841i	$0.494328\pi$
$444$	5.30724	−	1.04104i	0.251871	−	0.0494054i
$445$	−12.4607	−	9.95481i	−0.590695	−	0.471903i
$446$		−	17.6683i		−	0.836618i
$447$	27.6391	+	18.5742i	1.30728	+	0.878529i
$448$	−0.371042	+	0.371042i	−0.0175301	+	0.0175301i
$449$	−33.6163			−1.58645			−0.793226	−	0.608927i	$-0.791600\pi$
$449$	−33.6163			−1.58645			−0.793226	+	0.608927i	$0.791600\pi$
$450$	2.61674	−	14.7700i	0.123354	−	0.696264i
$451$	30.3544			1.42933
$452$	−11.6877	+	11.6877i	−0.549741	+	0.549741i
$453$	8.08168	+	5.43110i	0.379710	+	0.255175i
$454$		−	4.41695i		−	0.207298i
$455$	−3.98684	−	3.18507i	−0.186906	−	0.149318i
$456$	−1.69966	+	0.333395i	−0.0795939	+	0.0156127i
$457$	−14.7287	−	14.7287i	−0.688978	−	0.688978i	0.273028	−	0.962006i	$-0.411975\pi$
$457$	−14.7287	−	14.7287i	−0.688978	−	0.688978i	−0.962006	+	0.273028i	$0.911975\pi$
$458$	−3.15432	−	3.15432i	−0.147392	−	0.147392i
$459$	−11.1916	−	17.0417i	−0.522380	−	0.795440i
$460$	−17.6896	+	1.97758i	−0.824783	+	0.0922054i
$461$			1.22359i			0.0569885i	0.999594	+	0.0284942i	$0.00907123\pi$
$461$			1.22359i			0.0569885i	−0.999594	+	0.0284942i	$0.990929\pi$
$462$	2.40030	−	3.57174i	0.111672	−	0.166173i
$463$	12.9428	−	12.9428i	0.601501	−	0.601501i	−0.339209	−	0.940711i	$-0.610160\pi$
$463$	12.9428	−	12.9428i	0.601501	−	0.601501i	0.940711	+	0.339209i	$0.110160\pi$
$464$	−4.06253			−0.188598
$465$	−4.10984	−	13.0533i	−0.190589	−	0.605331i
$466$	−3.24227			−0.150195
$467$	−8.23017	+	8.23017i	−0.380847	+	0.380847i	−0.871407	−	0.490560i	$-0.836792\pi$
$467$	−8.23017	+	8.23017i	−0.380847	+	0.380847i	0.490560	+	0.871407i	$0.336792\pi$
$468$	5.05685	−	12.0273i	0.233753	−	0.555962i
$469$			2.97670i			0.137451i
$470$	−11.5818	+	14.4973i	−0.534231	+	0.668712i
$471$	−4.86060	−	24.7796i	−0.223965	−	1.14178i
$472$	4.24423	+	4.24423i	0.195357	+	0.195357i
$473$	−32.1993	−	32.1993i	−1.48053	−	1.48053i
$474$	2.64512	+	13.4849i	0.121494	+	0.619384i
$475$	−4.87656	+	1.10414i	−0.223752	+	0.0506612i
$476$			2.05889i			0.0943689i
$477$	10.9487	−	26.0404i	0.501304	−	1.19231i
$478$	2.90428	−	2.90428i	0.132839	−	0.132839i
$479$	23.7395			1.08469			0.542344	−	0.840157i	$-0.317537\pi$
$479$	23.7395			1.08469			0.542344	+	0.840157i	$0.317537\pi$
$480$	−3.43465	−	1.78974i	−0.156770	−	0.0816902i
$481$	13.5800			0.619195
$482$	−17.7457	+	17.7457i	−0.808297	+	0.808297i
$483$	−4.03543	+	6.00487i	−0.183618	+	0.273231i
$484$			11.4190i			0.519044i
$485$	−1.76209	−	15.7620i	−0.0800125	−	0.715717i
$486$	8.83177	−	12.8452i	0.400617	−	0.582671i
$487$	27.2107	+	27.2107i	1.23303	+	1.23303i	0.962793	+	0.270239i	$0.0871028\pi$
$487$	27.2107	+	27.2107i	1.23303	+	1.23303i	0.270239	+	0.962793i	$0.412897\pi$
$488$	−2.12517	−	2.12517i	−0.0962021	−	0.0962021i
$489$	38.1292	−	7.47918i	1.72426	−	0.338220i
$490$	−1.67061	−	14.9437i	−0.0754704	−	0.675087i
$491$		−	40.4871i		−	1.82716i	−0.406662	−	0.913579i	$-0.633307\pi$
$491$		−	40.4871i		−	1.82716i	0.406662	−	0.913579i	$-0.366693\pi$
$492$	−9.21612	−	6.19347i	−0.415495	−	0.279223i
$493$	−11.2713	+	11.2713i	−0.507636	+	0.507636i
$494$	−4.34904			−0.195673
$495$	30.4662	+	8.98138i	1.36935	+	0.403683i
$496$	−3.53345			−0.158656
$497$	1.36357	−	1.36357i	0.0611646	−	0.0611646i
$498$	15.7376	+	10.5761i	0.705220	+	0.473926i
$499$			5.75646i			0.257695i	0.991664	+	0.128847i	$0.0411277\pi$
$499$			5.75646i			0.257695i	−0.991664	+	0.128847i	$0.958872\pi$
$500$	−10.0605	−	4.87720i	−0.449918	−	0.218115i
$501$	40.6637	−	7.97634i	1.81672	−	0.356357i
$502$	15.1165	+	15.1165i	0.674681	+	0.674681i
$503$	25.9616	+	25.9616i	1.15757	+	1.15757i	0.984997	+	0.172573i	$0.0552081\pi$
$503$	25.9616	+	25.9616i	1.15757	+	1.15757i	0.172573	+	0.984997i	$0.444792\pi$
$504$	−1.45755	+	0.594689i	−0.0649244	+	0.0264895i
$505$	−19.6879	+	24.6439i	−0.876100	+	1.09664i
$506$		−	37.6911i		−	1.67557i
$507$	5.71365	−	8.50213i	0.253752	−	0.377593i
$508$	11.5688	−	11.5688i	0.513282	−	0.513282i
$509$	−5.27569			−0.233841			−0.116920	−	0.993141i	$-0.537302\pi$
$509$	−5.27569			−0.233841			−0.116920	+	0.993141i	$0.537302\pi$
$510$	−14.4949	+	4.56374i	−0.641844	+	0.202086i
$511$	5.57794			0.246754
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−5.08807	−	1.05428i	−0.224644	−	0.0465475i
$514$		−	10.0213i		−	0.442020i
$515$	16.2316	−	1.81458i	0.715248	−	0.0799601i
$516$	3.20637	+	16.3462i	0.141152	+	0.719601i
$517$	−27.7833	−	27.7833i	−1.22191	−	1.22191i
$518$	−1.15859	−	1.15859i	−0.0509055	−	0.0509055i
$519$	2.84918	+	14.5252i	0.125065	+	0.637586i
$520$	−7.59785	−	6.06989i	−0.333188	−	0.266182i
$521$		−	1.12070i		−	0.0490988i	−0.999699	−	0.0245494i	$-0.992185\pi$
$521$		−	1.12070i		−	0.0490988i	0.999699	−	0.0245494i	$-0.00781510\pi$
$522$	−11.2349	−	4.72371i	−0.491740	−	0.206751i
$523$	−3.66564	+	3.66564i	−0.160287	+	0.160287i	−0.782694	−	0.622407i	$-0.786155\pi$
$523$	−3.66564	+	3.66564i	−0.160287	+	0.160287i	0.622407	+	0.782694i	$0.286155\pi$
$524$	−12.1137			−0.529188
$525$	−4.15609	+	1.83787i	−0.181387	+	0.0802110i
$526$	−14.6667			−0.639500
$527$	−9.80341	+	9.80341i	−0.427043	+	0.427043i
$528$	4.57434	−	6.80679i	0.199072	−	0.296227i
$529$			40.3668i			1.75508i
$530$	−16.4502	−	13.1420i	−0.714551	−	0.570851i
$531$	6.80245	+	16.6724i	0.295201	+	0.723521i
$532$	0.371042	+	0.371042i	0.0160867	+	0.0160867i
$533$	−19.7148	−	19.7148i	−0.853943	−	0.853943i
$534$	−12.1230	+	2.37796i	−0.524612	+	0.102905i
$535$	18.4056	−	2.05763i	0.795745	−	0.0889591i
$536$			5.67279i			0.245027i
$537$	11.1106	+	7.46659i	0.479456	+	0.322207i
$538$	9.83936	−	9.83936i	0.424205	−	0.424205i
$539$	31.8403			1.37146
$540$	−7.41751	−	8.94318i	−0.319199	−	0.384853i
$541$	35.1833			1.51265			0.756324	−	0.654197i	$-0.226993\pi$
$541$	35.1833			1.51265			0.756324	+	0.654197i	$0.226993\pi$
$542$	−6.92611	+	6.92611i	−0.297502	+	0.297502i
$543$	−22.3083	−	14.9917i	−0.957340	−	0.643357i
$544$			3.92368i			0.168227i
$545$	14.7194	−	18.4247i	0.630509	−	0.789226i
$546$	−3.87877	+	0.760836i	−0.165996	+	0.0325608i
$547$	−11.8492	−	11.8492i	−0.506635	−	0.506635i	0.406857	−	0.913492i	$-0.366625\pi$
$547$	−11.8492	−	11.8492i	−0.506635	−	0.506635i	−0.913492	+	0.406857i	$0.866625\pi$
$548$	1.08854	+	1.08854i	0.0465001	+	0.0465001i
$549$	−3.40613	−	8.34823i	−0.145370	−	0.356294i
$550$	12.6303	−	20.0237i	0.538558	−	0.853814i
$551$			4.06253i			0.173070i
$552$	−7.69044	+	11.4437i	−0.327327	+	0.487075i
$553$	2.94381	−	2.94381i	0.125184	−	0.125184i
$554$	6.48607			0.275567
$555$	5.58852	−	10.7248i	0.237220	−	0.455242i
$556$	−6.34474			−0.269077
$557$	10.8257	−	10.8257i	0.458701	−	0.458701i	−0.439528	−	0.898229i	$-0.644854\pi$
$557$	10.8257	−	10.8257i	0.458701	−	0.458701i	0.898229	+	0.439528i	$0.144854\pi$
$558$	−9.77176	−	4.10852i	−0.413671	−	0.173927i
$559$			41.8261i			1.76906i
$560$	0.130360	+	1.16607i	0.00550869	+	0.0492756i
$561$	−6.19385	−	31.5765i	−0.261505	−	1.33316i
$562$	−8.56294	−	8.56294i	−0.361206	−	0.361206i
$563$	15.9790	+	15.9790i	0.673433	+	0.673433i	0.958506	−	0.285073i	$-0.0920179\pi$
$563$	15.9790	+	15.9790i	0.673433	+	0.673433i	−0.285073	+	0.958506i	$0.592018\pi$
$564$	2.76662	+	14.1044i	0.116496	+	0.593900i
$565$	4.10626	+	36.7308i	0.172752	+	1.54528i
$566$		−	1.87716i		−	0.0789029i
$567$	−4.72233	−	0.0501524i	−0.198319	−	0.00210620i
$568$	2.59861	−	2.59861i	0.109035	−	0.109035i
$569$	−18.1067			−0.759073			−0.379536	−	0.925177i	$-0.623916\pi$
$569$	−18.1067			−0.759073			−0.379536	+	0.925177i	$0.623916\pi$
$570$	−1.78974	+	3.43465i	−0.0749640	+	0.143862i
$571$	−19.9248			−0.833826			−0.416913	−	0.908946i	$-0.636888\pi$
$571$	−19.9248			−0.833826			−0.416913	+	0.908946i	$0.636888\pi$
$572$	14.5608	−	14.5608i	0.608819	−	0.608819i
$573$	13.0500	−	19.4189i	0.545171	−	0.811235i
$574$			3.36397i			0.140409i
$575$	−21.2342	+	33.6642i	−0.885529	+	1.40389i
$576$	−2.77770	+	1.13332i	−0.115737	+	0.0472215i
$577$	−9.32107	−	9.32107i	−0.388041	−	0.388041i	0.485947	−	0.873988i	$-0.338475\pi$
$577$	−9.32107	−	9.32107i	−0.388041	−	0.388041i	−0.873988	+	0.485947i	$0.838475\pi$
$578$	−1.13470	−	1.13470i	−0.0471972	−	0.0471972i
$579$	−7.10943	+	1.39454i	−0.295458	+	0.0579552i
$580$	−5.67001	+	7.09731i	−0.235434	+	0.294700i
$581$		−	5.74438i		−	0.238317i
$582$	−10.1967	−	6.85243i	−0.422666	−	0.284042i
$583$	31.5258	−	31.5258i	1.30567	−	1.30567i
$584$	10.6301			0.439875
$585$	−13.9541	−	25.6207i	−0.576932	−	1.05929i
$586$	17.8907			0.739057
$587$	−29.1721	+	29.1721i	−1.20406	+	1.20406i	−0.231141	+	0.972920i	$0.574246\pi$
$587$	−29.1721	+	29.1721i	−1.20406	+	1.20406i	−0.972920	+	0.231141i	$0.925754\pi$
$588$	−9.66728	−	6.49666i	−0.398672	−	0.267918i
$589$			3.53345i			0.145593i
$590$	13.3383	−	1.49114i	0.549131	−	0.0613893i
$591$	−35.0260	+	6.87049i	−1.44078	+	0.282614i
$592$	−2.20796	−	2.20796i	−0.0907467	−	0.0907467i
$593$	3.55825	+	3.55825i	0.146120	+	0.146120i	0.776382	−	0.630262i	$-0.217053\pi$
$593$	3.55825	+	3.55825i	0.146120	+	0.146120i	−0.630262	+	0.776382i	$0.717053\pi$
$594$	20.5649	−	13.5054i	0.843790	−	0.554132i
$595$	3.59691	+	2.87355i	0.147459	+	0.117804i
$596$		−	19.2260i		−	0.787529i
$597$	5.70817	−	8.49397i	0.233620	−	0.347635i
$598$	−24.4799	+	24.4799i	−1.00106	+	1.00106i
$599$	30.7070			1.25466			0.627328	−	0.778755i	$-0.284149\pi$
$599$	30.7070			1.25466			0.627328	+	0.778755i	$0.284149\pi$
$600$	−7.92039	+	3.50248i	−0.323349	+	0.142988i
$601$	40.1017			1.63578			0.817891	−	0.575373i	$-0.195143\pi$
$601$	40.1017			1.63578			0.817891	+	0.575373i	$0.195143\pi$
$602$	3.56843	−	3.56843i	0.145438	−	0.145438i
$603$	−6.59605	+	15.6881i	−0.268612	+	0.638870i
$604$		−	5.62170i		−	0.228744i
$605$	19.9491	+	15.9373i	0.811047	+	0.647942i
$606$	4.70296	+	23.9759i	0.191045	+	0.973954i
$607$	−19.8610	−	19.8610i	−0.806134	−	0.806134i	0.177912	−	0.984046i	$-0.443066\pi$
$607$	−19.8610	−	19.8610i	−0.806134	−	0.806134i	−0.984046	+	0.177912i	$0.943066\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$	0.710713	+	3.62324i	0.0287995	+	0.146821i
$610$	−6.67879	+	0.746645i	−0.270416	+	0.0302308i
$611$			36.0898i			1.46004i
$612$	−4.56227	+	10.8510i	−0.184419	+	0.438624i
$613$	22.6569	−	22.6569i	0.915102	−	0.915102i	−0.0815658	−	0.996668i	$-0.525992\pi$
$613$	22.6569	−	22.6569i	0.915102	−	0.915102i	0.996668	+	0.0815658i	$0.0259921\pi$
$614$	23.2339			0.937644
$615$	−23.6829	+	7.45660i	−0.954986	+	0.300679i
$616$	−2.48454			−0.100105
$617$	−15.5110	+	15.5110i	−0.624451	+	0.624451i	−0.946666	−	0.322215i	$-0.895573\pi$
$617$	−15.5110	+	15.5110i	−0.624451	+	0.624451i	0.322215	+	0.946666i	$0.395573\pi$
$618$	7.05655	−	10.5004i	0.283856	−	0.422389i
$619$			15.5862i			0.626463i	0.949677	+	0.313232i	$0.101412\pi$
$619$			15.5862i			0.626463i	−0.949677	+	0.313232i	$0.898588\pi$
$620$	−4.93157	+	6.17299i	−0.198057	+	0.247913i
$621$	−34.5741	+	22.7054i	−1.38741	+	0.911137i
$622$	−4.59184	−	4.59184i	−0.184116	−	0.184116i
$623$	2.64649	+	2.64649i	0.106029	+	0.106029i
$624$	−7.39190	+	1.44995i	−0.295913	+	0.0580444i
$625$	−22.5618	+	10.7688i	−0.902471	+	0.430751i
$626$		−	22.0074i		−	0.879591i
$627$	−6.80679	−	4.57434i	−0.271837	−	0.182681i
$628$	−10.3090	+	10.3090i	−0.411374	+	0.411374i
$629$	−12.2518			−0.488512
$630$	−0.995345	+	3.37636i	−0.0396555	+	0.134517i
$631$	25.8671			1.02975			0.514876	−	0.857264i	$-0.327838\pi$
$631$	25.8671			1.02975			0.514876	+	0.857264i	$0.327838\pi$
$632$	5.61011	−	5.61011i	0.223158	−	0.223158i
$633$	−9.27713	−	6.23447i	−0.368733	−	0.247798i
$634$			30.8686i			1.22595i
$635$	−4.06450	−	36.3572i	−0.161295	−	1.44279i
$636$	−16.0043	+	3.13930i	−0.634611	+	0.124481i
$637$	−20.6799	−	20.6799i	−0.819368	−	0.819368i
$638$	−13.6016	−	13.6016i	−0.538492	−	0.538492i
$639$	10.2080	−	4.16492i	0.403822	−	0.164762i
$640$	0.248430	+	2.22222i	0.00982007	+	0.0878411i
$641$			1.67735i			0.0662515i	0.999451	+	0.0331258i	$0.0105462\pi$
$641$			1.67735i			0.0662515i	−0.999451	+	0.0331258i	$0.989454\pi$
$642$	8.00171	−	11.9069i	0.315802	−	0.469926i
$643$	−23.1508	+	23.1508i	−0.912978	+	0.912978i	−0.996505	−	0.0835277i	$-0.973381\pi$
$643$	−23.1508	+	23.1508i	−0.912978	+	0.912978i	0.0835277	+	0.996505i	$0.473381\pi$
$644$	4.17704			0.164599
$645$	33.0321	+	17.2125i	1.30064	+	0.677743i
$646$	3.92368			0.154375
$647$	1.87972	−	1.87972i	0.0738993	−	0.0738993i	−0.669191	−	0.743090i	$-0.733359\pi$
$647$	1.87972	−	1.87972i	0.0738993	−	0.0738993i	0.743090	+	0.669191i	$0.233359\pi$
$648$	−8.99949	−	0.0955769i	−0.353533	−	0.00375462i
$649$			28.4198i			1.11558i
$650$	−21.2084	+	4.80193i	−0.831861	+	0.188347i
$651$	0.618153	+	3.15137i	0.0242273	+	0.123512i
$652$	−15.8628	−	15.8628i	−0.621235	−	0.621235i
$653$	−4.68423	−	4.68423i	−0.183308	−	0.183308i	0.609488	−	0.792796i	$-0.291375\pi$
$653$	−4.68423	−	4.68423i	−0.183308	−	0.183308i	−0.792796	+	0.609488i	$0.791375\pi$
$654$	−3.51610	−	17.9252i	−0.137490	−	0.700932i
$655$	−16.9068	+	21.1628i	−0.660605	+	0.826898i
$656$			6.41083i			0.250301i
$657$	29.3975	+	12.3601i	1.14690	+	0.482214i
$658$	3.07903	−	3.07903i	0.120033	−	0.120033i
$659$	29.9598			1.16707			0.583533	−	0.812089i	$-0.301670\pi$
$659$	29.9598			1.16707			0.583533	+	0.812089i	$0.301670\pi$
$660$	−5.50725	−	17.4916i	−0.214369	−	0.680858i
$661$	25.1252			0.977257			0.488629	−	0.872492i	$-0.337497\pi$
$661$	25.1252			0.977257			0.488629	+	0.872492i	$0.337497\pi$
$662$	7.74809	−	7.74809i	0.301138	−	0.301138i
$663$	−16.4857	+	24.5314i	−0.640252	+	0.952720i
$664$		−	10.9472i		−	0.424836i
$665$	1.16607	−	0.130360i	0.0452184	−	0.00505513i
$666$	−3.53882	−	8.67343i	−0.137126	−	0.336089i
$667$	22.8672	+	22.8672i	0.885421	+	0.885421i
$668$	−16.9172	−	16.9172i	−0.654548	−	0.654548i
$669$	−30.0301	+	5.89052i	−1.16103	+	0.227741i
$670$	9.91047	+	7.91742i	0.382875	+	0.305877i
$671$		−	14.2304i		−	0.549359i
$672$	0.754350	+	0.506942i	0.0290997	+	0.0195557i
$673$	31.2587	−	31.2587i	1.20493	−	1.20493i	0.232285	−	0.972648i	$-0.425380\pi$
$673$	31.2587	−	31.2587i	1.20493	−	1.20493i	0.972648	−	0.232285i	$-0.0746201\pi$
$674$	14.1153			0.543702
$675$	−25.9764	+	0.476668i	−0.999832	+	0.0183470i
$676$	−5.91417			−0.227468
$677$	23.6302	−	23.6302i	0.908182	−	0.908182i	−0.0879438	−	0.996125i	$-0.528030\pi$
$677$	23.6302	−	23.6302i	0.908182	−	0.908182i	0.996125	+	0.0879438i	$0.0280296\pi$
$678$	23.7617	+	15.9684i	0.912561	+	0.613265i
$679$			3.72188i			0.142833i
$680$	6.85474	+	5.47622i	0.262867	+	0.210003i
$681$	−7.50733	+	1.47259i	−0.287681	+	0.0564298i
$682$	−11.8302	−	11.8302i	−0.453001	−	0.453001i
$683$	−18.9685	−	18.9685i	−0.725809	−	0.725809i	0.243973	−	0.969782i	$-0.421549\pi$
$683$	−18.9685	−	18.9685i	−0.725809	−	0.725809i	−0.969782	+	0.243973i	$0.921549\pi$
$684$	1.13332	+	2.77770i	0.0433335	+	0.106208i
$685$	3.42095	−	0.382440i	0.130708	−	0.0146123i
$686$			7.20178i			0.274965i
$687$	−4.30964	+	6.41291i	−0.164423	+	0.244668i
$688$	6.80047	−	6.80047i	0.259266	−	0.259266i
$689$	−40.9513			−1.56012
$690$	9.25886	+	29.4071i	0.352479	+	1.11951i
$691$	4.36817			0.166173			0.0830866	−	0.996542i	$-0.473522\pi$
$691$	4.36817			0.166173			0.0830866	+	0.996542i	$0.473522\pi$
$692$	6.04290	−	6.04290i	0.229717	−	0.229717i
$693$	−6.87101	−	2.88890i	−0.261008	−	0.109740i
$694$		−	9.24486i		−	0.350930i
$695$	−8.85524	+	11.0844i	−0.335899	+	0.420454i
$696$	1.35443	+	6.90493i	0.0513395	+	0.261731i
$697$	17.7866	+	17.7866i	0.673716	+	0.673716i
$698$	11.7869	+	11.7869i	0.446140	+	0.446140i
$699$	1.08096	+	5.51077i	0.0408856	+	0.208436i
$700$	2.21909	+	1.39973i	0.0838738	+	0.0529048i
$701$		−	20.9191i		−	0.790102i	−0.918659	−	0.395051i	$-0.870727\pi$
$701$		−	20.9191i		−	0.790102i	0.918659	−	0.395051i	$-0.129273\pi$
$702$	−22.1282	−	4.58510i	−0.835177	−	0.173053i
$703$	−2.20796	+	2.20796i	−0.0832748	+	0.0832748i
$704$	−4.73487			−0.178452
$705$	28.5019	+	14.8519i	1.07344	+	0.559354i
$706$	−26.5488			−0.999178
$707$	5.23402	−	5.23402i	0.196846	−	0.196846i
$708$	5.79875	−	8.62876i	0.217930	−	0.324289i
$709$		−	46.0079i		−	1.72786i	−0.503610	−	0.863931i	$-0.667995\pi$
$709$		−	46.0079i		−	1.72786i	0.503610	−	0.863931i	$-0.332005\pi$
$710$	−0.912977	−	8.16664i	−0.0342634	−	0.306488i
$711$	22.0380	−	8.99162i	0.826488	−	0.337212i
$712$	5.04349	+	5.04349i	0.189013	+	0.189013i
$713$	19.8891	+	19.8891i	0.744851	+	0.744851i
$714$	3.49941	−	0.686422i	0.130962	−	0.0256887i
$715$	−5.11571	−	45.7604i	−0.191317	−	1.71134i
$716$		−	7.72862i		−	0.288832i
$717$	−5.90457	−	3.96803i	−0.220510	−	0.148189i
$718$	21.9852	−	21.9852i	0.820480	−	0.820480i
$719$	−25.7542			−0.960468			−0.480234	−	0.877140i	$-0.659448\pi$
$719$	−25.7542			−0.960468			−0.480234	+	0.877140i	$0.659448\pi$
$720$	−1.89686	+	6.43443i	−0.0706918	+	0.239797i
$721$	−3.83275			−0.142739
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	36.0781	+	24.2454i	1.34176	+	0.901697i
$724$			15.5179i			0.576717i
$725$	4.48559	+	19.8112i	0.166590	+	0.735770i
$726$	19.4084	−	3.80703i	0.720312	−	0.141292i
$727$	−11.1708	−	11.1708i	−0.414302	−	0.414302i	0.468932	−	0.883234i	$-0.344639\pi$
$727$	−11.1708	−	11.1708i	−0.414302	−	0.414302i	−0.883234	+	0.468932i	$0.844639\pi$
$728$	1.61368	+	1.61368i	0.0598069	+	0.0598069i
$729$	−24.7770	−	10.7285i	−0.917667	−	0.397351i
$730$	14.8362	−	18.5709i	0.549112	−	0.687340i
$731$		−	37.7353i		−	1.39569i
$732$	−2.90355	+	4.32060i	−0.107318	+	0.159694i
$733$	9.70478	−	9.70478i	0.358454	−	0.358454i	−0.504789	−	0.863243i	$-0.668430\pi$
$733$	9.70478	−	9.70478i	0.358454	−	0.358454i	0.863243	+	0.504789i	$0.168430\pi$
$734$	1.07637			0.0397295
$735$	−24.8422	+	7.82162i	−0.916320	+	0.288505i
$736$	7.96032			0.293421
$737$	−18.9928	+	18.9928i	−0.699610	+	0.699610i
$738$	−7.45420	+	17.7292i	−0.274393	+	0.652619i
$739$			31.4666i			1.15752i	0.815499	+	0.578759i	$0.196463\pi$
$739$			31.4666i			1.15752i	−0.815499	+	0.578759i	$0.803537\pi$
$740$	−6.93896	+	0.775731i	−0.255081	+	0.0285164i
$741$	1.44995	+	7.39190i	0.0532652	+	0.271548i
$742$	3.49379	+	3.49379i	0.128261	+	0.128261i
$743$	0.387245	+	0.387245i	0.0142066	+	0.0142066i	0.714174	−	0.699968i	$-0.246802\pi$
$743$	0.387245	+	0.387245i	0.0142066	+	0.0142066i	−0.699968	+	0.714174i	$0.746802\pi$
$744$	1.17803	+	6.00566i	0.0431888	+	0.220178i
$745$	−33.5882	−	26.8334i	−1.23058	−	0.983101i
$746$			11.3284i			0.414760i
$747$	12.7289	−	30.2747i	0.465727	−	1.10769i
$748$	−13.1367	+	13.1367i	−0.480326	+	0.480326i
$749$	−4.34611			−0.158803
$750$	−4.93547	+	18.7254i	−0.180218	+	0.683755i
$751$	8.65270			0.315742			0.157871	−	0.987460i	$-0.449537\pi$
$751$	8.65270			0.315742			0.157871	+	0.987460i	$0.449537\pi$
$752$	5.86781	−	5.86781i	0.213977	−	0.213977i
$753$	20.6531	−	30.7326i	0.752641	−	1.11996i
$754$			17.6681i			0.643435i
$755$	−9.82120	−	7.84611i	−0.357430	−	0.285549i
$756$	1.49671	+	2.27907i	0.0544348	+	0.0828890i
$757$	−2.24043	−	2.24043i	−0.0814299	−	0.0814299i	0.665219	−	0.746649i	$-0.268338\pi$
$757$	−2.24043	−	2.24043i	−0.0814299	−	0.0814299i	−0.746649	+	0.665219i	$0.768338\pi$
$758$	10.6495	+	10.6495i	0.386808	+	0.386808i
$759$	−64.0621	+	12.5660i	−2.32531	+	0.456117i
$760$	2.22222	−	0.248430i	0.0806086	−	0.00901151i
$761$			9.75042i			0.353452i	0.984260	+	0.176726i	$0.0565507\pi$
$761$			9.75042i			0.353452i	−0.984260	+	0.176726i	$0.943449\pi$
$762$	−23.5200	−	15.8060i	−0.852039	−	0.572592i
$763$	−3.91314	+	3.91314i	−0.141665	+	0.141665i
$764$	−13.5080			−0.488701
$765$	12.5893	+	23.1149i	0.455168	+	0.835720i
$766$	30.3805			1.09769
$767$	18.4583	−	18.4583i	0.666492	−	0.666492i
$768$	1.43759	+	0.966096i	0.0518745	+	0.0348610i
$769$		−	49.3395i		−	1.77923i	−0.456714	−	0.889614i	$-0.650974\pi$
$769$		−	49.3395i		−	1.77923i	0.456714	−	0.889614i	$-0.349026\pi$
$770$	−3.46763	+	4.34053i	−0.124965	+	0.156422i
$771$	−17.0328	+	3.34105i	−0.613421	+	0.120325i
$772$	2.95772	+	2.95772i	0.106451	+	0.106451i
$773$	22.1512	+	22.1512i	0.796725	+	0.796725i	0.982578	−	0.185853i	$-0.0595048\pi$
$773$	22.1512	+	22.1512i	0.796725	+	0.796725i	−0.185853	+	0.982578i	$0.559505\pi$
$774$	26.7140	−	10.8995i	0.960215	−	0.391774i
$775$	3.90140	+	17.2311i	0.140143	+	0.618958i
$776$			7.09290i			0.254620i
$777$	−1.58294	+	2.35548i	−0.0567877	+	0.0845023i
$778$	−8.31614	+	8.31614i	−0.298148	+	0.298148i
$779$	6.41083			0.229692
$780$	−7.78366	+	14.9374i	−0.278700	+	0.534846i
$781$	17.4006			0.622641
$782$	22.0856	−	22.0856i	0.789780	−	0.789780i
$783$	−4.28304	+	20.6705i	−0.153063	+	0.738702i
$784$			6.72466i			0.240166i
$785$	3.62189	+	32.3981i	0.129271	+	1.15634i
$786$	4.03863	+	20.5891i	0.144053	+	0.734389i
$787$	−9.86758	−	9.86758i	−0.351741	−	0.351741i	0.509016	−	0.860757i	$-0.330009\pi$
$787$	−9.86758	−	9.86758i	−0.351741	−	0.351741i	−0.860757	+	0.509016i	$0.830009\pi$
$788$	14.5718	+	14.5718i	0.519099	+	0.519099i
$789$	4.88982	+	24.9285i	0.174082	+	0.887478i
$790$	−1.97102	−	17.6309i	−0.0701258	−	0.627280i
$791$		−	8.67323i		−	0.308384i
$792$	−13.0943	−	5.50547i	−0.465285	−	0.195628i
$793$	−9.24247	+	9.24247i	−0.328210	+	0.328210i
$794$	−8.87312			−0.314895
$795$	−16.8525	+	32.3412i	−0.597697	+	1.14703i
$796$	−5.90849			−0.209421
$797$	−3.60992	+	3.60992i	−0.127870	+	0.127870i	−0.768145	−	0.640275i	$-0.778820\pi$
$797$	−3.60992	+	3.60992i	−0.127870	+	0.127870i	0.640275	+	0.768145i	$0.278820\pi$
$798$	0.506942	−	0.754350i	0.0179456	−	0.0267037i
$799$		−	32.5600i		−	1.15189i
$800$	4.22899	+	2.66751i	0.149518	+	0.0943107i
$801$	8.08347	+	19.8121i	0.285615	+	0.700027i
$802$	−20.3873	−	20.3873i	−0.719901	−	0.719901i
$803$	35.5900	+	35.5900i	1.25595	+	1.25595i
$804$	9.64183	−	1.89128i	0.340041	−	0.0667003i
$805$	5.82983	−	7.29737i	0.205475	−	0.257198i
$806$			15.3671i			0.541283i
$807$	−20.0040	−	13.4432i	−0.704173	−	0.473223i
$808$	9.97464	−	9.97464i	0.350907	−	0.350907i
$809$	−5.63069			−0.197964			−0.0989822	−	0.995089i	$-0.531559\pi$
$809$	−5.63069			−0.197964			−0.0989822	+	0.995089i	$0.531559\pi$
$810$	−12.7274	+	15.5889i	−0.447196	+	0.547737i
$811$	−4.93429			−0.173266			−0.0866332	−	0.996240i	$-0.527611\pi$
$811$	−4.93429			−0.173266			−0.0866332	+	0.996240i	$0.527611\pi$
$812$	1.50737	−	1.50737i	0.0528983	−	0.0528983i
$813$	14.0812	+	9.46290i	0.493848	+	0.331879i
$814$		−	14.7848i		−	0.518206i
$815$	−49.8520	+	5.57313i	−1.74624	+	0.195218i
$816$	6.66893	−	1.30814i	0.233459	−	0.0457939i
$817$	−6.80047	−	6.80047i	−0.237918	−	0.237918i
$818$	−13.1804	−	13.1804i	−0.460843	−	0.460843i
$819$	2.58633	+	6.33894i	0.0903736	+	0.221500i
$820$	11.1998	+	8.94748i	0.391115	+	0.312460i
$821$		−	33.4852i		−	1.16864i	−0.811522	−	0.584321i	$-0.801361\pi$
$821$		−	33.4852i		−	1.16864i	0.811522	−	0.584321i	$-0.198639\pi$
$822$	1.48723	−	2.21306i	0.0518733	−	0.0771894i
$823$	−1.29986	+	1.29986i	−0.0453102	+	0.0453102i	−0.729399	−	0.684089i	$-0.760200\pi$
$823$	−1.29986	+	1.29986i	−0.0453102	+	0.0453102i	0.684089	+	0.729399i	$0.260200\pi$
$824$	−7.30419			−0.254454
$825$	−38.2444	−	14.7914i	−1.33150	−	0.514972i
$826$	−3.14958			−0.109588
$827$	10.5401	−	10.5401i	0.366514	−	0.366514i	−0.499690	−	0.866204i	$-0.666553\pi$
$827$	10.5401	−	10.5401i	0.366514	−	0.366514i	0.866204	+	0.499690i	$0.166553\pi$
$828$	22.0143	+	9.25588i	0.765050	+	0.321664i
$829$		−	26.4052i		−	0.917089i	−0.888671	−	0.458545i	$-0.848371\pi$
$829$		−	26.4052i		−	0.917089i	0.888671	−	0.458545i	$-0.151629\pi$
$830$	−19.1250	−	15.2789i	−0.663839	−	0.530338i
$831$	−2.16242	−	11.0241i	−0.0750137	−	0.382423i
$832$	3.07524	+	3.07524i	0.106615	+	0.106615i
$833$	18.6573	+	18.6573i	0.646437	+	0.646437i
$834$	2.11530	+	10.7839i	0.0732470	+	0.373416i
$835$	−53.1658	+	5.94359i	−1.83988	+	0.205686i
$836$			4.73487i			0.163759i
$837$	−3.72523	+	17.9784i	−0.128763	+	0.621425i
$838$	−23.5890	+	23.5890i	−0.814868	+	0.814868i
$839$	16.4354			0.567412			0.283706	−	0.958911i	$-0.408436\pi$
$839$	16.4354			0.567412			0.283706	+	0.958911i	$0.408436\pi$
$840$	1.93847	−	0.610330i	0.0668836	−	0.0210584i
$841$	−12.4958			−0.430891
$842$	10.1680	−	10.1680i	0.350412	−	0.350412i
$843$	−11.6993	+	17.4089i	−0.402944	+	0.599596i
$844$			6.45326i			0.222130i
$845$	−8.25431	+	10.3322i	−0.283957	+	0.355437i
$846$	23.0502	−	9.40464i	0.792484	−	0.323338i
$847$	−4.23692	−	4.23692i	−0.145582	−	0.145582i
$848$	6.65823	+	6.65823i	0.228645	+	0.228645i
$849$	−3.19054	+	0.625836i	−0.109499	+	0.0214786i
$850$	19.1341	−	4.33228i	0.656294	−	0.148596i
$851$			24.8563i			0.852064i
$852$	−5.28311	−	3.55039i	−0.180996	−	0.121634i
$853$	−0.541057	+	0.541057i	−0.0185254	+	0.0185254i	−0.716309	−	0.697783i	$-0.754170\pi$
$853$	−0.541057	+	0.541057i	−0.0185254	+	0.0185254i	0.697783	+	0.716309i	$0.254170\pi$
$854$	1.57706			0.0539658
$855$	6.43443	+	1.89686i	0.220053	+	0.0648712i
$856$	−8.28252			−0.283091
$857$	−12.6475	+	12.6475i	−0.432029	+	0.432029i	−0.889318	−	0.457289i	$-0.848820\pi$
$857$	−12.6475	+	12.6475i	−0.432029	+	0.432029i	0.457289	+	0.889318i	$0.348820\pi$
$858$	−29.6030	−	19.8940i	−1.01063	−	0.679169i
$859$		−	4.30216i		−	0.146788i	−0.997303	−	0.0733939i	$-0.976617\pi$
$859$		−	4.30216i		−	0.146788i	0.997303	−	0.0733939i	$-0.0233830\pi$
$860$	−2.38923	−	21.3719i	−0.0814722	−	0.728774i
$861$	5.71761	−	1.12153i	0.194856	−	0.0382217i
$862$	9.49762	+	9.49762i	0.323490	+	0.323490i
$863$	29.8424	+	29.8424i	1.01585	+	1.01585i	0.999872	+	0.0159756i	$0.00508541\pi$
$863$	29.8424	+	29.8424i	1.01585	+	1.01585i	0.0159756	+	0.999872i	$0.494915\pi$
$864$	2.85232	+	4.34330i	0.0970381	+	0.147762i
$865$	−2.12307	−	18.9910i	−0.0721866	−	0.645714i
$866$			6.50290i			0.220977i
$867$	−1.55030	+	2.30690i	−0.0526509	+	0.0783466i
$868$	1.31106	−	1.31106i	0.0445002	−	0.0445002i
$869$	37.5660			1.27434
$870$	13.9534	+	7.27088i	0.473064	+	0.246506i
$871$	24.6712			0.835952
$872$	−7.45740	+	7.45740i	−0.252539	+	0.252539i
$873$	−8.24728	+	19.6155i	−0.279128	+	0.663882i
$874$		−	7.96032i		−	0.269262i
$875$	5.54250	−	1.92321i	0.187371	−	0.0650164i
$876$	−3.54401	−	18.0675i	−0.119741	−	0.610444i
$877$	30.6993	+	30.6993i	1.03664	+	1.03664i	0.999303	+	0.0373388i	$0.0118881\pi$
$877$	30.6993	+	30.6993i	1.03664	+	1.03664i	0.0373388	+	0.999303i	$0.488112\pi$
$878$	6.01359	+	6.01359i	0.202949	+	0.202949i
$879$	−5.96466	−	30.4081i	−0.201183	−	1.02564i
$880$	−6.60838	+	8.27189i	−0.222768	+	0.278845i
$881$			27.9951i			0.943179i	0.881818	+	0.471590i	$0.156320\pi$
$881$			27.9951i			0.943179i	−0.881818	+	0.471590i	$0.843680\pi$
$882$	−7.81910	+	18.5971i	−0.263283	+	0.626196i
$883$	16.3149	−	16.3149i	0.549041	−	0.549041i	−0.377123	−	0.926163i	$-0.623086\pi$
$883$	16.3149	−	16.3149i	0.549041	−	0.549041i	0.926163	+	0.377123i	$0.123086\pi$
$884$	17.0643			0.573933
$885$	−6.98137	−	22.1735i	−0.234676	−	0.745355i
$886$	−30.2914			−1.01766
$887$	6.91467	−	6.91467i	0.232172	−	0.232172i	−0.581427	−	0.813599i	$-0.697505\pi$
$887$	6.91467	−	6.91467i	0.232172	−	0.232172i	0.813599	+	0.581427i	$0.197505\pi$
$888$	−3.01666	+	4.48891i	−0.101233	+	0.150638i
$889$			8.58501i			0.287932i
$890$	15.8502	−	1.77195i	0.531299	−	0.0593958i
$891$	−29.8108	−	30.4508i	−0.998700	−	1.02014i
$892$	12.4934	+	12.4934i	0.418309	+	0.418309i
$893$	−5.86781	−	5.86781i	−0.196359	−	0.196359i
$894$	−32.6777	+	6.40986i	−1.09291	+	0.214378i
$895$	−13.5020	−	10.7867i	−0.451323	−	0.360560i
$896$		−	0.524733i		−	0.0175301i
$897$	49.7690	+	33.4460i	1.66174	+	1.11673i
$898$	23.7703	−	23.7703i	0.793226	−	0.793226i
$899$	14.3547			0.478757
$900$	8.59365	+	12.2943i	0.286455	+	0.409809i
$901$	36.9460			1.23085
$902$	−21.4638	+	21.4638i	−0.714667	+	0.714667i
$903$	−7.25482	−	4.87543i	−0.241425	−	0.162244i
$904$		−	16.5288i		−	0.549741i
$905$	27.1100	+	21.6580i	0.901165	+	0.719937i
$906$	−9.55498	+	1.87425i	−0.317443	+	0.0622676i
$907$	−30.4082	−	30.4082i	−1.00969	−	1.00969i	−0.999953	−	0.00973481i	$-0.996901\pi$
$907$	−30.4082	−	30.4082i	−1.00969	−	1.00969i	−0.00973481	−	0.999953i	$-0.503099\pi$
$908$	3.12326	+	3.12326i	0.103649	+	0.103649i
$909$	39.1829	−	15.9869i	1.29962	−	0.530251i
$910$	5.07131	−	0.566939i	0.168112	−	0.0187938i
$911$			23.5754i			0.781089i	0.920584	+	0.390544i	$0.127713\pi$
$911$			23.5754i			0.781089i	−0.920584	+	0.390544i	$0.872287\pi$
$912$	0.966096	−	1.43759i	0.0319906	−	0.0476033i
$913$	36.6520	−	36.6520i	1.21300	−	1.21300i
$914$	20.8295			0.688978
$915$	3.49572	+	11.1027i	0.115565	+	0.367045i
$916$	4.46088			0.147392
$917$	4.49468	−	4.49468i	0.148427	−	0.148427i
$918$	19.9640	+	4.13665i	0.658910	+	0.136530i
$919$			27.2929i			0.900308i	0.892951	+	0.450154i	$0.148631\pi$
$919$			27.2929i			0.900308i	−0.892951	+	0.450154i	$0.851369\pi$
$920$	11.1101	−	13.9068i	0.366289	−	0.458494i
$921$	−7.74606	−	39.4897i	−0.255241	−	1.30123i
$922$	−0.865212	−	0.865212i	−0.0284942	−	0.0284942i
$923$	−11.3014	−	11.3014i	−0.371992	−	0.371992i
$924$	0.828333	+	4.22288i	0.0272502	+	0.138922i
$925$	−8.32938	+	13.2052i	−0.273868	+	0.434183i
$926$			18.3038i			0.601501i
$927$	−20.1998	−	8.49296i	−0.663448	−	0.278945i
$928$	2.87264	−	2.87264i	0.0942992	−	0.0942992i
$929$	41.8662			1.37359			0.686793	−	0.726853i	$-0.259018\pi$
$929$	41.8662			1.37359			0.686793	+	0.726853i	$0.259018\pi$
$930$	12.1361	+	6.32396i	0.397960	+	0.207371i
$931$	6.72466			0.220392
$932$	2.29263	−	2.29263i	0.0750977	−	0.0750977i
$933$	−6.27368	+	9.33548i	−0.205391	+	0.305630i
$934$		−	11.6392i		−	0.380847i
$935$	4.61537	+	41.2848i	0.150939	+	1.35016i
$936$	4.92884	+	12.0803i	0.161104	+	0.394857i
$937$	30.2246	+	30.2246i	0.987396	+	0.987396i	0.999922	−	0.0125256i	$-0.00398713\pi$
$937$	30.2246	+	30.2246i	0.987396	+	0.987396i	−0.0125256	+	0.999922i	$0.503987\pi$
$938$	−2.10485	−	2.10485i	−0.0687257	−	0.0687257i
$939$	−37.4051	+	7.33715i	−1.22067	+	0.239439i
$940$	−2.06156	−	18.4408i	−0.0672406	−	0.601471i
$941$			26.6531i			0.868868i	0.900704	+	0.434434i	$0.143052\pi$
$941$			26.6531i			0.868868i	−0.900704	+	0.434434i	$0.856948\pi$
$942$	20.9588	+	14.0848i	0.682873	+	0.458908i
$943$	36.0852	−	36.0852i	1.17510	−	1.17510i
$944$	−6.00225			−0.195357
$945$	6.07051	+	0.566088i	0.197474	+	0.0184148i
$946$	45.5367			1.48053
$947$	−8.48716	+	8.48716i	−0.275796	+	0.275796i	−0.831428	−	0.555632i	$-0.812476\pi$
$947$	−8.48716	+	8.48716i	−0.275796	+	0.275796i	0.555632	+	0.831428i	$0.312476\pi$
$948$	−11.4057	−	7.66491i	−0.370439	−	0.248945i
$949$		−	46.2306i		−	1.50071i
$950$	2.66751	−	4.22899i	0.0865455	−	0.137207i
$951$	52.4662	−	10.2914i	1.70133	−	0.333723i
$952$	−1.45585	−	1.45585i	−0.0471844	−	0.0471844i
$953$	−1.79756	−	1.79756i	−0.0582288	−	0.0582288i	0.677393	−	0.735622i	$-0.263110\pi$
$953$	−1.79756	−	1.79756i	−0.0582288	−	0.0582288i	−0.735622	+	0.677393i	$0.763110\pi$
$954$	10.6715	+	26.1552i	0.345502	+	0.846807i
$955$	−18.8528	+	23.5986i	−0.610063	+	0.763634i
$956$			4.10728i			0.132839i
$957$	−18.5834	+	27.6528i	−0.600716	+	0.893888i
$958$	−16.7864	+	16.7864i	−0.542344	+	0.542344i
$959$	−0.807788			−0.0260848
$960$	3.69420	−	1.16313i	0.119230	−	0.0375397i
$961$	−18.5148			−0.597250
$962$	−9.60252	+	9.60252i	−0.309598	+	0.309598i
$963$	−22.9053	−	9.63051i	−0.738114	−	0.310339i
$964$		−	25.0963i		−	0.808297i
$965$	9.29523	−	1.03915i	0.299224	−	0.0334513i
$966$	−1.39261	−	7.09956i	−0.0448063	−	0.228425i
$967$	39.2936	+	39.2936i	1.26360	+	1.26360i	0.949337	+	0.314260i	$0.101757\pi$
$967$	39.2936	+	39.2936i	1.26360	+	1.26360i	0.314260	+	0.949337i	$0.398243\pi$
$968$	−8.07443	−	8.07443i	−0.259522	−	0.259522i
$969$	−1.30814	−	6.66893i	−0.0420234	−	0.214237i
$970$	12.3914	+	9.89945i	0.397865	+	0.317852i
$971$		−	3.89501i		−	0.124997i	−0.998045	−	0.0624984i	$-0.980093\pi$
$971$		−	3.89501i		−	0.124997i	0.998045	−	0.0624984i	$-0.0199068\pi$
$972$	2.83794	+	15.3280i	0.0910269	+	0.491644i
$973$	2.35416	−	2.35416i	0.0754711	−	0.0754711i
$974$	−38.4817			−1.23303
$975$	15.2324	+	34.4461i	0.487828	+	1.10316i
$976$	3.00545			0.0962021
$977$	−38.4514	+	38.4514i	−1.23017	+	1.23017i	−0.266273	+	0.963898i	$0.585792\pi$
$977$	−38.4514	+	38.4514i	−1.23017	+	1.23017i	−0.963898	+	0.266273i	$0.914208\pi$
$978$	−21.6728	+	32.2500i	−0.693020	+	1.03124i
$979$			33.7718i			1.07935i
$980$	11.7481	+	9.38549i	0.375279	+	0.299808i
$981$	−29.2946	+	11.9524i	−0.935304	+	0.381610i
$982$	28.6287	+	28.6287i	0.913579	+	0.913579i
$983$	−4.51390	−	4.51390i	−0.143971	−	0.143971i	0.631448	−	0.775419i	$-0.282461\pi$
$983$	−4.51390	−	4.51390i	−0.143971	−	0.143971i	−0.775419	+	0.631448i	$0.782461\pi$
$984$	10.8962	−	2.13734i	0.347359	−	0.0681358i
$985$	45.7948	−	5.11956i	1.45914	−	0.163123i
$986$		−	15.9401i		−	0.507636i
$987$	−6.25984	−	4.20678i	−0.199253	−	0.133903i
$988$	3.07524	−	3.07524i	0.0978363	−	0.0978363i
$989$	−76.5570			−2.43437
$990$	−27.8936	+	15.1921i	−0.886518	+	0.482835i
$991$	2.37283			0.0753756			0.0376878	−	0.999290i	$-0.488001\pi$
$991$	2.37283			0.0753756			0.0376878	+	0.999290i	$0.488001\pi$
$992$	2.49852	−	2.49852i	0.0793282	−	0.0793282i
$993$	−15.7523	−	10.5860i	−0.499884	−	0.335935i
$994$			1.92838i			0.0611646i
$995$	−8.24638	+	10.3222i	−0.261428	+	0.327237i
$996$	−18.6066	+	3.64976i	−0.589573	+	0.115647i
$997$	−39.9605	−	39.9605i	−1.26556	−	1.26556i	−0.948357	−	0.317206i	$-0.897255\pi$
$997$	−39.9605	−	39.9605i	−1.26556	−	1.26556i	−0.317206	−	0.948357i	$-0.602745\pi$
$998$	−4.07043	−	4.07043i	−0.128847	−	0.128847i
$999$	−13.5621	+	8.90647i	−0.429085	+	0.281788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.77.7	✓	36
3.2	odd	2	inner	570.2.k.a.77.12	yes	36
5.3	odd	4	inner	570.2.k.a.533.12	yes	36
15.8	even	4	inner	570.2.k.a.533.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.7	✓	36	1.1	even	1	trivial
570.2.k.a.77.12	yes	36	3.2	odd	2	inner
570.2.k.a.533.7	yes	36	15.8	even	4	inner
570.2.k.a.533.12	yes	36	5.3	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.43759 + 0.966096i) q^{3} -1.00000i q^{4} +(-1.74702 - 1.39568i) q^{5} +(-1.69966 + 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.13332 + 2.77770i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.43759 + 0.966096i) q^{3} -1.00000i q^{4} +(-1.74702 - 1.39568i) q^{5} +(-1.69966 + 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.13332 + 2.77770i) q^{9} +(2.22222 - 0.248430i) q^{10} +4.73487i q^{11} +(0.966096 - 1.43759i) q^{12} +(3.07524 - 3.07524i) q^{13} -0.524733 q^{14} +(-1.16313 - 3.69420i) q^{15} -1.00000 q^{16} +(-2.77446 + 2.77446i) q^{17} +(-2.76550 - 1.16275i) q^{18} +1.00000i q^{19} +(-1.39568 + 1.74702i) q^{20} +(0.174943 + 0.891868i) q^{21} +(-3.34806 - 3.34806i) q^{22} +(5.62880 + 5.62880i) q^{23} +(0.333395 + 1.69966i) q^{24} +(1.10414 + 4.87656i) q^{25} +4.34904i q^{26} +(-1.05428 + 5.08807i) q^{27} +(0.371042 - 0.371042i) q^{28} +4.06253 q^{29} +(3.43465 + 1.78974i) q^{30} +3.53345 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.57434 + 6.80679i) q^{33} -3.92368i q^{34} +(-0.130360 - 1.16607i) q^{35} +(2.77770 - 1.13332i) q^{36} +(2.20796 + 2.20796i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(7.39190 - 1.44995i) q^{39} +(-0.248430 - 2.22222i) q^{40} -6.41083i q^{41} +(-0.754350 - 0.506942i) q^{42} +(-6.80047 + 6.80047i) q^{43} +4.73487 q^{44} +(1.89686 - 6.43443i) q^{45} -7.96032 q^{46} +(-5.86781 + 5.86781i) q^{47} +(-1.43759 - 0.966096i) q^{48} -6.72466i q^{49} +(-4.22899 - 2.66751i) q^{50} +(-6.66893 + 1.30814i) q^{51} +(-3.07524 - 3.07524i) q^{52} +(-6.65823 - 6.65823i) q^{53} +(-2.85232 - 4.34330i) q^{54} +(6.60838 - 8.27189i) q^{55} +0.524733i q^{56} +(-0.966096 + 1.43759i) q^{57} +(-2.87264 + 2.87264i) q^{58} +6.00225 q^{59} +(-3.69420 + 1.16313i) q^{60} -3.00545 q^{61} +(-2.49852 + 2.49852i) q^{62} +(-0.610134 + 1.45115i) q^{63} +1.00000i q^{64} +(-9.66455 + 1.08043i) q^{65} +(-1.57858 - 8.04767i) q^{66} +(4.01127 + 4.01127i) q^{67} +(2.77446 + 2.77446i) q^{68} +(2.65393 + 13.5299i) q^{69} +(0.916717 + 0.732361i) q^{70} -3.67498i q^{71} +(-1.16275 + 2.76550i) q^{72} +(7.51659 - 7.51659i) q^{73} -3.12253 q^{74} +(-3.12394 + 8.07719i) q^{75} +1.00000 q^{76} +(-1.75684 + 1.75684i) q^{77} +(-4.20159 + 6.25213i) q^{78} -7.93390i q^{79} +(1.74702 + 1.39568i) q^{80} +(-6.43119 + 6.29602i) q^{81} +(4.53314 + 4.53314i) q^{82} +(-7.74087 - 7.74087i) q^{83} +(0.891868 - 0.174943i) q^{84} +(8.71931 - 0.974762i) q^{85} -9.61732i q^{86} +(5.84025 + 3.92480i) q^{87} +(-3.34806 + 3.34806i) q^{88} +7.13257 q^{89} +(3.20855 + 5.89111i) q^{90} +2.28209 q^{91} +(5.62880 - 5.62880i) q^{92} +(5.07964 + 3.41365i) q^{93} -8.29833i q^{94} +(1.39568 - 1.74702i) q^{95} +(1.69966 - 0.333395i) q^{96} +(5.01544 + 5.01544i) q^{97} +(4.75505 + 4.75505i) q^{98} +(-13.1520 + 5.36611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more