LMFDB - Embedded newform 720.2.cf.a.11.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.34
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.619561 + 1.27128i) q^{2} +(-1.55612 + 0.760585i) q^{3} +(-1.23229 - 1.57527i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-0.00280357 - 2.44949i) q^{6} +(-0.926852 + 1.60536i) q^{7} +(2.76608 - 0.590608i) q^{8} +(1.84302 - 2.36712i) q^{9} +(0.927480 - 1.06760i) q^{10} +(2.65868 - 0.712391i) q^{11} +(3.11571 + 1.51404i) q^{12} +(3.98711 + 1.06834i) q^{13} +(-1.46661 - 2.17290i) q^{14} +(1.69995 - 0.331915i) q^{15} +(-0.962927 + 3.88237i) q^{16} +0.0754433i q^{17} +(1.86741 + 3.80957i) q^{18} +(-0.963668 - 0.963668i) q^{19} +(0.782591 + 1.84053i) q^{20} +(0.221284 - 3.20308i) q^{21} +(-0.741567 + 3.82129i) q^{22} +(1.38637 - 0.800421i) q^{23} +(-3.85514 + 3.02289i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-3.82842 + 4.40682i) q^{26} +(-1.06756 + 5.08530i) q^{27} +(3.67101 - 0.518223i) q^{28} +(1.22272 - 0.327626i) q^{29} +(-0.631266 + 2.36675i) q^{30} +(-9.02548 + 5.21086i) q^{31} +(-4.33897 - 3.62951i) q^{32} +(-3.59539 + 3.13072i) q^{33} +(-0.0959094 - 0.0467417i) q^{34} +(1.31077 - 1.31077i) q^{35} +(-5.99998 + 0.0137346i) q^{36} +(3.33700 + 3.33700i) q^{37} +(1.82214 - 0.628038i) q^{38} +(-7.01699 + 1.37007i) q^{39} +(-2.82469 - 0.145430i) q^{40} +(-3.45662 - 5.98705i) q^{41} +(3.93490 + 2.26581i) q^{42} +(3.06600 + 11.4425i) q^{43} +(-4.39847 - 3.31025i) q^{44} +(-2.39288 + 1.80946i) q^{45} +(0.158616 + 2.25837i) q^{46} +(-4.61814 + 7.99886i) q^{47} +(-1.45444 - 6.77382i) q^{48} +(1.78189 + 3.08632i) q^{49} +(-1.17219 + 0.791178i) q^{50} +(-0.0573811 - 0.117399i) q^{51} +(-3.23035 - 7.59727i) q^{52} +(1.71109 - 1.71109i) q^{53} +(-5.80341 - 4.50782i) q^{54} -2.75247 q^{55} +(-1.61561 + 4.98794i) q^{56} +(2.23254 + 0.766632i) q^{57} +(-0.341043 + 1.75739i) q^{58} +(2.08898 - 7.79617i) q^{59} +(-2.61769 - 2.26886i) q^{60} +(1.47021 + 5.48691i) q^{61} +(-1.03262 - 14.7023i) q^{62} +(2.09187 + 5.15268i) q^{63} +(7.30237 - 3.26733i) q^{64} +(-3.57475 - 2.06388i) q^{65} +(-1.75245 - 6.51040i) q^{66} +(-0.946129 + 3.53100i) q^{67} +(0.118843 - 0.0929680i) q^{68} +(-1.54857 + 2.30000i) q^{69} +(0.854248 + 2.47845i) q^{70} +3.80166i q^{71} +(3.69989 - 7.63615i) q^{72} -5.57176i q^{73} +(-6.30972 + 2.17477i) q^{74} +(-1.72793 - 0.119374i) q^{75} +(-0.330516 + 2.70555i) q^{76} +(-1.32056 + 4.92840i) q^{77} +(2.60572 - 9.76938i) q^{78} +(13.2001 + 7.62111i) q^{79} +(1.93495 - 3.50085i) q^{80} +(-2.20655 - 8.72531i) q^{81} +(9.75278 - 0.684986i) q^{82} +(2.26335 + 8.44696i) q^{83} +(-5.31838 + 3.59853i) q^{84} +(0.0195262 - 0.0728727i) q^{85} +(-16.4461 - 3.19157i) q^{86} +(-1.65350 + 1.43980i) q^{87} +(6.93337 - 3.54076i) q^{88} -11.0501 q^{89} +(-0.817789 - 4.16308i) q^{90} +(-5.41054 + 5.41054i) q^{91} +(-2.96929 - 1.19755i) q^{92} +(10.0814 - 14.9734i) q^{93} +(-7.30754 - 10.8267i) q^{94} +(0.681416 + 1.18025i) q^{95} +(9.51251 + 2.34779i) q^{96} +(-6.26748 + 10.8556i) q^{97} +(-5.02756 + 0.353110i) q^{98} +(3.21368 - 7.60637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64}+ \cdots - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.619561	+	1.27128i	−0.438096	+	0.898928i
$2$	−0.619561	+	1.27128i	−0.438096	+	0.898928i
$3$	−1.55612	+	0.760585i	−0.898426	+	0.439124i
$3$	−1.55612	+	0.760585i	−0.898426	+	0.439124i
$4$	−1.23229	−	1.57527i	−0.616145	−	0.787633i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−0.00280357	−	2.44949i	−0.00114455	−	0.999999i
$7$	−0.926852	+	1.60536i	−0.350317	+	0.606767i	−0.986305	−	0.164932i	$-0.947260\pi$
$7$	−0.926852	+	1.60536i	−0.350317	+	0.606767i	0.635988	+	0.771699i	$0.280593\pi$
$8$	2.76608	−	0.590608i	0.977956	−	0.208811i
$9$	1.84302	−	2.36712i	0.614340	−	0.789041i
$10$	0.927480	−	1.06760i	0.293295	−	0.337606i
$11$	2.65868	−	0.712391i	0.801622	−	0.214794i	0.165326	−	0.986239i	$-0.447132\pi$
$11$	2.65868	−	0.712391i	0.801622	−	0.214794i	0.636296	+	0.771445i	$0.280466\pi$
$12$	3.11571	+	1.51404i	0.899429	+	0.437066i
$13$	3.98711	+	1.06834i	1.10583	+	0.296305i	0.765135	−	0.643870i	$-0.222672\pi$
$13$	3.98711	+	1.06834i	1.10583	+	0.296305i	0.340691	+	0.940175i	$0.389339\pi$
$14$	−1.46661	−	2.17290i	−0.391968	−	0.580732i
$15$	1.69995	−	0.331915i	0.438925	−	0.0857002i
$16$	−0.962927	+	3.88237i	−0.240732	+	0.970592i
$17$			0.0754433i			0.0182977i	0.999958	+	0.00914885i	$0.00291221\pi$
$17$			0.0754433i			0.0182977i	−0.999958	+	0.00914885i	$0.997088\pi$
$18$	1.86741	+	3.80957i	0.440152	+	0.897923i
$19$	−0.963668	−	0.963668i	−0.221081	−	0.221081i	0.587873	−	0.808953i	$-0.299966\pi$
$19$	−0.963668	−	0.963668i	−0.221081	−	0.221081i	−0.808953	+	0.587873i	$0.799966\pi$
$20$	0.782591	+	1.84053i	0.174993	+	0.411555i
$21$	0.221284	−	3.20308i	0.0482881	−	0.698968i
$22$	−0.741567	+	3.82129i	−0.158103	+	0.814701i
$23$	1.38637	−	0.800421i	0.289078	−	0.166899i	−0.348448	−	0.937328i	$-0.613291\pi$
$23$	1.38637	−	0.800421i	0.289078	−	0.166899i	0.637526	+	0.770429i	$0.279958\pi$
$24$	−3.85514	+	3.02289i	−0.786927	+	0.617046i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−3.82842	+	4.40682i	−0.750815	+	0.864249i
$27$	−1.06756	+	5.08530i	−0.205452	+	0.978667i
$28$	3.67101	−	0.518223i	0.693756	−	0.0979349i
$29$	1.22272	−	0.327626i	0.227053	−	0.0608385i	−0.143499	−	0.989650i	$-0.545835\pi$
$29$	1.22272	−	0.327626i	0.227053	−	0.0608385i	0.370551	+	0.928812i	$0.379169\pi$
$30$	−0.631266	+	2.36675i	−0.115253	+	0.432107i
$31$	−9.02548	+	5.21086i	−1.62102	+	0.935898i	−0.634377	+	0.773024i	$0.718743\pi$
$31$	−9.02548	+	5.21086i	−1.62102	+	0.935898i	−0.986647	+	0.162874i	$0.947923\pi$
$32$	−4.33897	−	3.62951i	−0.767029	−	0.641612i
$33$	−3.59539	+	3.13072i	−0.625877	+	0.544988i
$34$	−0.0959094	−	0.0467417i	−0.0164483	−	0.00801614i
$35$	1.31077	−	1.31077i	0.221560	−	0.221560i
$36$	−5.99998	+	0.0137346i	−0.999997	+	0.00228911i
$37$	3.33700	+	3.33700i	0.548599	+	0.548599i	0.926035	−	0.377437i	$-0.123194\pi$
$37$	3.33700	+	3.33700i	0.548599	+	0.548599i	−0.377437	+	0.926035i	$0.623194\pi$
$38$	1.82214	−	0.628038i	0.295590	−	0.101881i
$39$	−7.01699	+	1.37007i	−1.12362	+	0.219387i
$40$	−2.82469	−	0.145430i	−0.446622	−	0.0229945i
$41$	−3.45662	−	5.98705i	−0.539834	−	0.935019i	−0.998913	−	0.0466239i	$-0.985154\pi$
$41$	−3.45662	−	5.98705i	−0.539834	−	0.935019i	0.459079	−	0.888396i	$-0.348180\pi$
$42$	3.93490	+	2.26581i	0.607168	+	0.349623i
$43$	3.06600	+	11.4425i	0.467561	+	1.74496i	0.648256	+	0.761422i	$0.275499\pi$
$43$	3.06600	+	11.4425i	0.467561	+	1.74496i	−0.180695	+	0.983539i	$0.557835\pi$
$44$	−4.39847	−	3.31025i	−0.663094	−	0.499040i
$45$	−2.39288	+	1.80946i	−0.356709	+	0.269738i
$46$	0.158616	+	2.25837i	0.0233867	+	0.332978i
$47$	−4.61814	+	7.99886i	−0.673626	+	1.16675i	0.303243	+	0.952913i	$0.401931\pi$
$47$	−4.61814	+	7.99886i	−0.673626	+	1.16675i	−0.976869	+	0.213840i	$0.931403\pi$
$48$	−1.45444	−	6.77382i	−0.209931	−	0.977716i
$49$	1.78189	+	3.08632i	0.254556	+	0.440903i
$50$	−1.17219	+	0.791178i	−0.165773	+	0.111889i
$51$	−0.0573811	−	0.117399i	−0.00803496	−	0.0164391i
$52$	−3.23035	−	7.59727i	−0.447969	−	1.05355i
$53$	1.71109	−	1.71109i	0.235036	−	0.235036i	−0.579755	−	0.814791i	$-0.696852\pi$
$53$	1.71109	−	1.71109i	0.235036	−	0.235036i	0.814791	+	0.579755i	$0.196852\pi$
$54$	−5.80341	−	4.50782i	−0.789744	−	0.613437i
$55$	−2.75247			−0.371142
$56$	−1.61561	+	4.98794i	−0.215895	+	0.666542i
$57$	2.23254	+	0.766632i	0.295707	+	0.101543i
$58$	−0.341043	+	1.75739i	−0.0447812	+	0.230757i
$59$	2.08898	−	7.79617i	0.271962	−	1.01497i	−0.685889	−	0.727706i	$-0.740586\pi$
$59$	2.08898	−	7.79617i	0.271962	−	1.01497i	0.957850	−	0.287268i	$-0.0927470\pi$
$60$	−2.61769	−	2.26886i	−0.337942	−	0.292908i
$61$	1.47021	+	5.48691i	0.188241	+	0.702527i	0.993913	+	0.110165i	$0.0351378\pi$
$61$	1.47021	+	5.48691i	0.188241	+	0.702527i	−0.805672	+	0.592362i	$0.798196\pi$
$62$	−1.03262	−	14.7023i	−0.131142	−	1.86720i
$63$	2.09187	+	5.15268i	0.263551	+	0.649176i
$64$	7.30237	−	3.26733i	0.912796	−	0.408417i
$65$	−3.57475	−	2.06388i	−0.443393	−	0.255993i
$66$	−1.75245	−	6.51040i	−0.215711	−	0.801375i
$67$	−0.946129	+	3.53100i	−0.115588	+	0.431380i	−0.999330	−	0.0365936i	$-0.988349\pi$
$67$	−0.946129	+	3.53100i	−0.115588	+	0.431380i	0.883742	+	0.467974i	$0.155016\pi$
$68$	0.118843	−	0.0929680i	0.0144119	−	0.0112740i
$69$	−1.54857	+	2.30000i	−0.186426	+	0.276888i
$70$	0.854248	+	2.47845i	0.102102	+	0.296231i
$71$			3.80166i			0.451174i	0.974223	+	0.225587i	$0.0724301\pi$
$71$			3.80166i			0.451174i	−0.974223	+	0.225587i	$0.927570\pi$
$72$	3.69989	−	7.63615i	0.436037	−	0.899929i
$73$		−	5.57176i		−	0.652126i	−0.945348	−	0.326063i	$-0.894278\pi$
$73$		−	5.57176i		−	0.652126i	0.945348	−	0.326063i	$-0.105722\pi$
$74$	−6.30972	+	2.17477i	−0.733490	+	0.252812i
$75$	−1.72793	−	0.119374i	−0.199524	−	0.0137841i
$76$	−0.330516	+	2.70555i	−0.0379128	+	0.310348i
$77$	−1.32056	+	4.92840i	−0.150492	+	0.561644i
$78$	2.60572	−	9.76938i	0.295039	−	1.10616i
$79$	13.2001	+	7.62111i	1.48513	+	0.857442i	0.999857	−	0.0169198i	$-0.00538600\pi$
$79$	13.2001	+	7.62111i	1.48513	+	0.857442i	0.485275	+	0.874361i	$0.338719\pi$
$80$	1.93495	−	3.50085i	0.216334	−	0.391407i
$81$	−2.20655	−	8.72531i	−0.245173	−	0.969479i
$82$	9.75278	−	0.684986i	1.07701	−	0.0756440i
$83$	2.26335	+	8.44696i	0.248435	+	0.927174i	0.971625	+	0.236525i	$0.0760084\pi$
$83$	2.26335	+	8.44696i	0.248435	+	0.927174i	−0.723190	+	0.690649i	$0.757325\pi$
$84$	−5.31838	+	3.59853i	−0.580283	+	0.392632i
$85$	0.0195262	−	0.0728727i	0.00211791	−	0.00790415i
$86$	−16.4461	−	3.19157i	−1.77343	−	0.344156i
$87$	−1.65350	+	1.43980i	−0.177274	+	0.154363i
$88$	6.93337	−	3.54076i	0.739099	−	0.377447i
$89$	−11.0501			−1.17131			−0.585656	−	0.810560i	$-0.699163\pi$
$89$	−11.0501			−1.17131			−0.585656	+	0.810560i	$0.699163\pi$
$90$	−0.817789	−	4.16308i	−0.0862025	−	0.438827i
$91$	−5.41054	+	5.41054i	−0.567178	+	0.567178i
$92$	−2.96929	−	1.19755i	−0.309569	−	0.124853i
$93$	10.0814	−	14.9734i	1.04539	−	1.55267i
$94$	−7.30754	−	10.8267i	−0.753716	−	1.11669i
$95$	0.681416	+	1.18025i	0.0699118	+	0.121091i
$96$	9.51251	+	2.34779i	0.970867	+	0.239621i
$97$	−6.26748	+	10.8556i	−0.636366	+	1.10222i	0.349857	+	0.936803i	$0.386230\pi$
$97$	−6.26748	+	10.8556i	−0.636366	+	1.10222i	−0.986224	+	0.165416i	$0.947103\pi$
$98$	−5.02756	+	0.353110i	−0.507860	+	0.0356695i
$99$	3.21368	−	7.60637i	0.322987	−	0.764469i
$100$	−0.279561	−	1.98037i	−0.0279561	−	0.198037i
$101$	1.73884	+	6.48945i	0.173021	+	0.645724i	0.996880	+	0.0789292i	$0.0251501\pi$
$101$	1.73884	+	6.48945i	0.173021	+	0.645724i	−0.823859	+	0.566795i	$0.808183\pi$
$102$	0.184798		0.000211511i	0.0182977		2.09427e-5i
$103$	−7.25324	−	12.5630i	−0.714683	−	1.23787i	−0.963082	−	0.269209i	$-0.913238\pi$
$103$	−7.25324	−	12.5630i	−0.714683	−	1.23787i	0.248399	−	0.968658i	$-0.420096\pi$
$104$	11.6596	+	0.600302i	1.14332	+	0.0588644i
$105$	−1.04276	+	3.03666i	−0.101763	+	0.296348i
$106$	1.11515	+	3.23540i	0.108313	+	0.314249i
$107$	−0.369195	−	0.369195i	−0.0356915	−	0.0356915i	0.689036	−	0.724727i	$-0.258034\pi$
$107$	−0.369195	−	0.369195i	−0.0356915	−	0.0356915i	−0.724727	+	0.689036i	$0.758034\pi$
$108$	9.32625	−	4.58487i	0.897419	−	0.441180i
$109$	3.10489	−	3.10489i	0.297395	−	0.297395i	−0.542598	−	0.839993i	$-0.682559\pi$
$109$	3.10489	−	3.10489i	0.297395	−	0.297395i	0.839993	+	0.542598i	$0.182559\pi$
$110$	1.70532	−	3.49915i	0.162596	−	0.333631i
$111$	−7.73084	−	2.65470i	−0.733779	−	0.251973i
$112$	−5.34009	−	5.14422i	−0.504591	−	0.486083i
$113$	4.87401	−	2.81401i	0.458508	−	0.264720i	−0.252909	−	0.967490i	$-0.581387\pi$
$113$	4.87401	−	2.81401i	0.458508	−	0.264720i	0.711417	+	0.702770i	$0.248054\pi$
$114$	−2.35779	+	2.36320i	−0.220827	+	0.221334i
$115$	−1.54630	+	0.414329i	−0.144193	+	0.0386363i
$116$	−2.02284	−	1.52237i	−0.187816	−	0.141349i
$117$	9.87723	−	7.46901i	0.913150	−	0.690511i
$118$	8.61684	+	7.48586i	0.793244	+	0.689130i
$119$	−0.121113	−	0.0699248i	−0.0111024	−	0.00641000i
$120$	4.50616	−	1.92211i	0.411354	−	0.175464i
$121$	−2.96521	+	1.71196i	−0.269564	+	0.155633i
$122$	−7.88626	−	1.53043i	−0.713989	−	0.138558i
$123$	9.93258	+	6.68751i	0.895590	+	0.602992i
$124$	19.3305	+	7.79624i	1.73593	+	0.700123i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−7.84652	−	0.533052i	−0.699023	−	0.0474881i
$127$			21.0168i			1.86494i	0.361248	+	0.932470i	$0.382351\pi$
$127$			21.0168i			1.86494i	−0.361248	+	0.932470i	$0.617649\pi$
$128$	−0.370574	+	11.3076i	−0.0327544	+	0.999463i
$129$	−13.4740	−	15.4739i	−1.18632	−	1.36240i
$130$	4.83854	−	3.26579i	0.424368	−	0.286429i
$131$	13.2899	+	3.56102i	1.16114	+	0.311128i	0.787423	−	0.616414i	$-0.211415\pi$
$131$	13.2899	+	3.56102i	1.16114	+	0.311128i	0.373721	+	0.927541i	$0.378082\pi$
$132$	9.36227	+	1.80575i	0.814881	+	0.157170i
$133$	2.44021	−	0.653852i	0.211593	−	0.0566961i
$134$	−3.90270	−	3.39046i	−0.337142	−	0.292891i
$135$	2.34736	−	4.63572i	0.202028	−	0.398979i
$136$	0.0445574	+	0.208682i	0.00382077	+	0.0178943i
$137$	0.0254123	−	0.0440153i	0.00217112	−	0.00376048i	−0.864938	−	0.501879i	$-0.832642\pi$
$137$	0.0254123	−	0.0440153i	0.00217112	−	0.00376048i	0.867109	+	0.498119i	$0.165976\pi$
$138$	−1.96451	−	3.39365i	−0.167230	−	0.288887i
$139$	11.4705	+	3.07351i	0.972914	+	0.260692i	0.710058	−	0.704143i	$-0.248669\pi$
$139$	11.4705	+	3.07351i	0.972914	+	0.260692i	0.262857	+	0.964835i	$0.415335\pi$
$140$	−3.68005	−	0.449563i	−0.311021	−	0.0379950i
$141$	1.10257	−	15.9597i	0.0928533	−	1.34405i
$142$	−4.83297	−	2.35536i	−0.405573	−	0.197657i
$143$	11.3615			0.950099
$144$	7.41535	+	9.43465i	0.617946	+	0.786221i
$145$	−1.26585			−0.105123
$146$	7.08325	+	3.45205i	0.586214	+	0.285693i
$147$	−5.12025	−	3.44741i	−0.422311	−	0.284338i
$148$	1.14451	−	9.36880i	0.0940784	−	0.770111i
$149$	14.1499	+	3.79146i	1.15921	+	0.310608i	0.786649	−	0.617401i	$-0.211814\pi$
$149$	14.1499	+	3.79146i	1.15921	+	0.310608i	0.372557	+	0.928009i	$0.378481\pi$
$150$	1.22232	−	2.12272i	0.0998017	−	0.173319i
$151$	−0.519232	+	0.899336i	−0.0422545	+	0.0731869i	−0.886379	−	0.462960i	$-0.846787\pi$
$151$	−0.519232	+	0.899336i	−0.0422545	+	0.0731869i	0.844125	+	0.536147i	$0.180121\pi$
$152$	−3.23473	−	2.09643i	−0.262371	−	0.170043i
$153$	0.178584	+	0.139044i	0.0144376	+	0.0112410i
$154$	−5.44720	−	4.73224i	−0.438948	−	0.381335i
$155$	10.0666	−	2.69734i	0.808570	−	0.216656i
$156$	10.8052	+	9.36531i	0.865107	+	0.749825i
$157$	11.4147	+	3.05855i	0.910989	+	0.244099i	0.683729	−	0.729736i	$-0.260357\pi$
$157$	11.4147	+	3.05855i	0.910989	+	0.244099i	0.227259	+	0.973834i	$0.427024\pi$
$158$	−17.8668	+	12.0593i	−1.42141	+	0.959386i
$159$	−1.36123	+	3.96410i	−0.107953	+	0.314373i
$160$	3.25174	+	4.62884i	0.257073	+	0.365942i
$161$			2.96749i			0.233871i
$162$	12.4594	+	2.60072i	0.978902	+	0.204332i
$163$	−9.61601	−	9.61601i	−0.753184	−	0.753184i	0.221888	−	0.975072i	$-0.428778\pi$
$163$	−9.61601	−	9.61601i	−0.753184	−	0.753184i	−0.975072	+	0.221888i	$0.928778\pi$
$164$	−5.17163	+	12.8229i	−0.403837	+	1.00130i
$165$	4.28317	−	2.09349i	0.333444	−	0.162978i
$166$	−12.1407	−	2.35605i	−0.942301	−	0.182865i
$167$	3.10414	−	1.79217i	0.240205	−	0.138683i	−0.375066	−	0.926998i	$-0.622380\pi$
$167$	3.10414	−	1.79217i	0.240205	−	0.138683i	0.615271	+	0.788316i	$0.289047\pi$
$168$	−1.27967	−	8.99065i	−0.0987289	−	0.693643i
$169$	3.49738	+	2.01922i	0.269030	+	0.155324i
$170$	0.0805437	+	0.0699722i	0.00617742	+	0.00536662i
$171$	−4.05718	+	0.505063i	−0.310260	+	0.0386231i
$172$	14.2467	−	18.9302i	1.08630	−	1.44342i
$173$	16.6490	−	4.46108i	1.26580	−	0.339169i	0.437378	−	0.899278i	$-0.355907\pi$
$173$	16.6490	−	4.46108i	1.26580	−	0.339169i	0.828419	+	0.560108i	$0.189241\pi$
$174$	−0.805943	−	2.99411i	−0.0610984	−	0.226983i
$175$	−1.60536	+	0.926852i	−0.121353	+	0.0700634i
$176$	0.205650	+	11.0079i	0.0155014	+	0.829755i
$177$	2.67895	+	13.7206i	0.201362	+	1.03130i
$178$	6.84622	−	14.0478i	0.513146	−	1.05292i
$179$	−16.6023	+	16.6023i	−1.24091	+	1.24091i	−0.281288	+	0.959623i	$0.590762\pi$
$179$	−16.6023	+	16.6023i	−1.24091	+	1.24091i	−0.959623	+	0.281288i	$0.909238\pi$
$180$	5.79909	+	1.53964i	0.432239	+	0.114758i
$181$	4.81894	+	4.81894i	0.358189	+	0.358189i	0.863145	−	0.504956i	$-0.168491\pi$
$181$	4.81894	+	4.81894i	0.358189	+	0.358189i	−0.504956	+	0.863145i	$0.668491\pi$
$182$	−3.52613	−	10.2304i	−0.261374	−	0.758331i
$183$	−6.46109	−	7.42007i	−0.477617	−	0.548507i
$184$	3.36207	−	3.03283i	0.247855	−	0.223583i
$185$	−2.35961	−	4.08697i	−0.173482	−	0.300480i
$186$	12.7892	+	22.0932i	0.937753	+	1.61995i
$187$	0.0537451	+	0.200580i	0.00393023	+	0.0146678i
$188$	18.2912	−	2.58210i	1.33402	−	0.188319i
$189$	−7.17425	−	6.42714i	−0.521850	−	0.467506i
$190$	−1.92260	+	0.135034i	−0.139480	+	0.00979637i
$191$	−0.856274	+	1.48311i	−0.0619578	+	0.107314i	−0.895340	−	0.445382i	$-0.853068\pi$
$191$	−0.856274	+	1.48311i	−0.0619578	+	0.107314i	0.833383	+	0.552696i	$0.186401\pi$
$192$	−8.87827	+	10.6384i	−0.640734	+	0.767763i
$193$	1.41943	+	2.45853i	0.102173	+	0.176969i	0.912580	−	0.408899i	$-0.134087\pi$
$193$	1.41943	+	2.45853i	0.102173	+	0.176969i	−0.810407	+	0.585868i	$0.800754\pi$
$194$	−9.91738	−	14.6934i	−0.712027	−	1.05493i
$195$	7.13250	+	0.492747i	0.510769	+	0.0352864i
$196$	2.66598	−	6.61019i	0.190427	−	0.472157i
$197$	−13.7464	+	13.7464i	−0.979393	+	0.979393i	−0.999792	−	0.0203992i	$-0.993506\pi$
$197$	−13.7464	+	13.7464i	−0.979393	+	0.979393i	0.0203992	+	0.999792i	$0.493506\pi$
$198$	7.67873	+	8.79809i	0.545704	+	0.625253i
$199$	−11.3779			−0.806559			−0.403279	−	0.915077i	$-0.632130\pi$
$199$	−11.3779			−0.806559			−0.403279	+	0.915077i	$0.632130\pi$
$200$	2.69080	+	0.871557i	0.190268	+	0.0616284i
$201$	−1.21334	−	6.21427i	−0.0855822	−	0.438321i
$202$	−9.32720	−	1.81006i	−0.656259	−	0.127355i
$203$	−0.607321	+	2.26655i	−0.0426256	+	0.159081i
$204$	−0.114224	+	0.235060i	−0.00799731	+	0.0164575i
$205$	1.78928	+	6.67768i	0.124969	+	0.466390i
$206$	20.4648	−	1.43735i	1.42585	−	0.100145i
$207$	0.660412	−	4.75690i	0.0459018	−	0.330628i
$208$	−7.98700	+	14.4507i	−0.553799	+	1.00198i
$209$	−3.24859	−	1.87558i	−0.224710	−	0.129736i
$210$	−3.21438	−	3.20703i	−0.221814	−	0.221306i
$211$	3.39645	−	12.6757i	0.233821	−	0.872632i	−0.744856	−	0.667225i	$-0.767482\pi$
$211$	3.39645	−	12.6757i	0.233821	−	0.872632i	0.978677	−	0.205406i	$-0.0658516\pi$
$212$	−4.80398	−	0.586865i	−0.329939	−	0.0403060i
$213$	−2.89149	−	5.91584i	−0.198122	−	0.405347i
$214$	0.698088	−	0.240611i	0.0477203	−	0.0164478i
$215$		−	11.8461i		−	0.807899i
$216$	0.0504642	+	14.6969i	0.00343365	+	0.999994i
$217$		−	19.3188i		−	1.31145i
$218$	2.02351	+	5.87084i	0.137049	+	0.397624i
$219$	4.23780	+	8.67033i	0.286364	+	0.585887i
$220$	3.39183	+	4.33587i	0.228677	+	0.292324i
$221$	−0.0805994	+	0.300801i	−0.00542170	+	0.0202341i
$222$	8.16458	−	8.18329i	0.547971	−	0.549226i
$223$	8.33688	+	4.81330i	0.558279	+	0.322322i	0.752454	−	0.658644i	$-0.228870\pi$
$223$	8.33688	+	4.81330i	0.558279	+	0.322322i	−0.194176	+	0.980967i	$0.562203\pi$
$224$	9.84823	−	3.60157i	0.658013	−	0.240640i
$225$	2.77966	−	1.12848i	0.185311	−	0.0752320i
$226$	0.557642	+	7.93966i	0.0370938	+	0.528138i
$227$	−5.92626	−	22.1171i	−0.393339	−	1.46796i	−0.824590	−	0.565730i	$-0.808594\pi$
$227$	−5.92626	−	22.1171i	−0.393339	−	1.46796i	0.431251	−	0.902232i	$-0.358072\pi$
$228$	−1.54348	−	4.46155i	−0.102219	−	0.295473i
$229$	−2.15462	+	8.04115i	−0.142381	+	0.531374i	0.857477	+	0.514523i	$0.172031\pi$
$229$	−2.15462	+	8.04115i	−0.142381	+	0.531374i	−0.999858	+	0.0168516i	$0.994636\pi$
$230$	0.431297	−	2.22247i	0.0284389	−	0.146545i
$231$	−1.69352	−	8.67359i	−0.111425	−	0.570680i
$232$	3.18863	−	1.62838i	0.209344	−	0.106909i
$233$	14.1686			0.928213			0.464106	−	0.885780i	$-0.346376\pi$
$233$	14.1686			0.928213			0.464106	+	0.885780i	$0.346376\pi$
$234$	3.37564	+	17.1842i	0.220672	+	1.12337i
$235$	6.53104	−	6.53104i	0.426038	−	0.426038i
$236$	−14.8553	+	6.31644i	−0.966995	+	0.411165i
$237$	−26.3375	−	1.81952i	−1.71081	−	0.118191i
$238$	0.163931	−	0.110646i	0.0106261	−	0.00717211i
$239$	−5.63527	−	9.76058i	−0.364516	−	0.631359i	0.624183	−	0.781278i	$-0.285432\pi$
$239$	−5.63527	−	9.76058i	−0.364516	−	0.631359i	−0.988698	+	0.149919i	$0.952099\pi$
$240$	−0.348310	+	6.91944i	−0.0224833	+	0.446648i
$241$	13.4213	−	23.2464i	0.864545	−	1.49744i	−0.00295378	−	0.999996i	$-0.500940\pi$
$241$	13.4213	−	23.2464i	0.864545	−	1.49744i	0.867499	−	0.497440i	$-0.165726\pi$
$242$	−0.339254	−	4.83027i	−0.0218080	−	0.310501i
$243$	10.0700	+	11.8994i	0.645991	+	0.763345i
$244$	6.83161	−	9.07743i	0.437349	−	0.581123i
$245$	−0.922374	−	3.44235i	−0.0589283	−	0.219923i
$246$	−14.6555	+	8.48374i	−0.934401	+	0.540904i
$247$	−2.81273	−	4.87178i	−0.178969	−	0.309984i
$248$	−21.8876	+	19.7442i	−1.38986	+	1.25376i
$249$	−9.94668	−	11.4230i	−0.630345	−	0.723903i
$250$	1.33702	−	0.460833i	0.0845608	−	0.0291456i
$251$	−10.3917	−	10.3917i	−0.655916	−	0.655916i	0.298495	−	0.954411i	$-0.403515\pi$
$251$	−10.3917	−	10.3917i	−0.655916	−	0.655916i	−0.954411	+	0.298495i	$0.903515\pi$
$252$	5.53905	−	9.64484i	0.348927	−	0.607568i
$253$	3.11570	−	3.11570i	0.195882	−	0.195882i
$254$	−26.7182	−	13.0212i	−1.67645	−	0.817022i
$255$	0.0250408	+	0.128250i	0.00156812	+	0.00803132i
$256$	−14.1455	−	7.47687i	−0.884097	−	0.467304i
$257$	−19.6128	+	11.3235i	−1.22341	+	0.706339i	−0.965644	−	0.259868i	$-0.916321\pi$
$257$	−19.6128	+	11.3235i	−1.22341	+	0.706339i	−0.257770	+	0.966206i	$0.582988\pi$
$258$	28.0196	−	7.54222i	1.74443	−	0.469558i
$259$	−8.44997	+	2.26416i	−0.525055	+	0.140688i
$260$	1.15396	+	8.17448i	0.0715656	+	0.506960i
$261$	1.47796	−	3.49814i	0.0914833	−	0.216529i
$262$	−12.7609	+	14.6889i	−0.788373	+	0.907482i
$263$	3.06455	+	1.76932i	0.188968	+	0.109101i	0.591500	−	0.806305i	$-0.298536\pi$
$263$	3.06455	+	1.76932i	0.188968	+	0.109101i	−0.402531	+	0.915406i	$0.631869\pi$
$264$	−8.09610	+	10.7833i	−0.498280	+	0.663664i
$265$	−2.09565	+	1.20992i	−0.128735	+	0.0743251i
$266$	−0.680630	+	3.50728i	−0.0417321	+	0.215045i
$267$	17.1953	−	8.40456i	1.05234	−	0.514351i
$268$	6.72817	−	2.86081i	0.410988	−	0.174752i
$269$	1.15456	+	1.15456i	0.0703946	+	0.0703946i	0.741428	−	0.671033i	$-0.234149\pi$
$269$	1.15456	+	1.15456i	0.0703946	+	0.0703946i	−0.671033	+	0.741428i	$0.734149\pi$
$270$	4.43895	+	5.85625i	0.270146	+	0.356400i
$271$			8.70991i			0.529090i	0.964373	+	0.264545i	$0.0852217\pi$
$271$			8.70991i			0.529090i	−0.964373	+	0.264545i	$0.914778\pi$
$272$	−0.292899	−	0.0726464i	−0.0177596	−	0.00440484i
$273$	4.30427	−	12.5346i	0.260506	−	0.758630i
$274$	0.0402112	+	0.0595762i	0.00242925	+	0.00359913i
$275$	2.65868	+	0.712391i	0.160324	+	0.0429588i
$276$	5.53141	−	0.394861i	0.332951	−	0.0237678i
$277$	−31.4766	+	8.43413i	−1.89125	+	0.506758i	−0.892837	+	0.450381i	$0.851288\pi$
$277$	−31.4766	+	8.43413i	−1.89125	+	0.506758i	−0.998410	+	0.0563770i	$0.982045\pi$
$278$	−11.0139	+	12.6779i	−0.660573	+	0.760373i
$279$	−4.29938	+	30.9681i	−0.257397	+	1.85401i
$280$	2.85153	−	4.39983i	0.170412	−	0.262940i
$281$	0.986125	−	1.70802i	0.0588273	−	0.101892i	−0.835112	−	0.550080i	$-0.814597\pi$
$281$	0.986125	−	1.70802i	0.0588273	−	0.101892i	0.893939	+	0.448188i	$0.147931\pi$
$282$	19.6061	+	11.2897i	1.16752	+	0.672290i
$283$	−16.4325	−	4.40309i	−0.976813	−	0.261736i	−0.265111	−	0.964218i	$-0.585409\pi$
$283$	−16.4325	−	4.40309i	−0.976813	−	0.261736i	−0.711702	+	0.702482i	$0.752075\pi$
$284$	5.98863	−	4.68475i	0.355360	−	0.277989i
$285$	−1.95804	−	1.31833i	−0.115985	−	0.0780912i
$286$	−7.03916	+	14.4436i	−0.416234	+	0.854071i
$287$	12.8151			0.756452
$288$	−16.5883	+	3.58163i	−0.977475	+	0.211049i
$289$	16.9943			0.999665
$290$	0.784270	−	1.60924i	0.0460539	−	0.0944980i
$291$	1.49635	−	21.6596i	0.0877175	−	1.26971i
$292$	−8.77701	+	6.86602i	−0.513636	+	0.401804i
$293$	7.77052	+	2.08210i	0.453959	+	0.121638i	0.478551	−	0.878060i	$-0.341162\pi$
$293$	7.77052	+	2.08210i	0.453959	+	0.121638i	−0.0245924	+	0.999698i	$0.507829\pi$
$294$	7.55492	−	4.37337i	0.440612	−	0.255060i
$295$	−4.03559	+	6.98985i	−0.234961	+	0.406965i
$296$	11.2012	+	7.25953i	0.651059	+	0.421952i
$297$	0.784423	+	14.2807i	0.0455168	+	0.828651i
$298$	−13.5867	+	15.6394i	−0.787058	+	0.905967i
$299$	6.38274	−	1.71025i	0.369123	−	0.0989063i
$300$	1.94127	+	2.86906i	0.112079	+	0.165645i
$301$	−21.2110	−	5.68346i	−1.22258	−	0.327589i
$302$	−0.821609	−	1.21728i	−0.0472783	−	0.0700466i
$303$	−7.64162	−	8.77582i	−0.439000	−	0.504158i
$304$	4.66925	−	2.81337i	0.267800	−	0.161358i
$305$		−	5.68047i		−	0.325262i
$306$	−0.287406	+	0.140883i	−0.0164299	+	0.00805377i
$307$	−3.74012	−	3.74012i	−0.213460	−	0.213460i	0.592276	−	0.805735i	$-0.298230\pi$
$307$	−3.74012	−	3.74012i	−0.213460	−	0.213460i	−0.805735	+	0.592276i	$0.798230\pi$
$308$	9.39086	−	3.99298i	0.535094	−	0.227521i
$309$	20.8421	+	14.0328i	1.18567	+	0.798298i
$310$	−2.80781	+	14.4686i	−0.159473	+	0.821762i
$311$	19.7122	−	11.3809i	1.11778	−	0.645350i	0.176946	−	0.984221i	$-0.443378\pi$
$311$	19.7122	−	11.3809i	1.11778	−	0.645350i	0.940833	+	0.338871i	$0.110045\pi$
$312$	−18.6004	+	7.93401i	−1.05304	+	0.449175i
$313$	−5.16024	−	2.97927i	−0.291674	−	0.168398i	0.347023	−	0.937857i	$-0.387193\pi$
$313$	−5.16024	−	2.97927i	−0.291674	−	0.168398i	−0.638697	+	0.769459i	$0.720526\pi$
$314$	−10.9603	+	12.6162i	−0.618527	+	0.711975i
$315$	−0.686979	−	5.51852i	−0.0387069	−	0.310933i
$316$	−4.26112	−	30.1851i	−0.239707	−	1.69805i
$317$	21.8096	−	5.84387i	1.22495	−	0.328224i	0.412339	−	0.911031i	$-0.364712\pi$
$317$	21.8096	−	5.84387i	1.22495	−	0.328224i	0.812611	+	0.582806i	$0.198045\pi$
$318$	−4.19610	−	4.18650i	−0.235305	−	0.234767i
$319$	3.01741	−	1.74210i	0.168942	−	0.0975390i
$320$	−7.89919	+	1.26601i	−0.441578	+	0.0707721i
$321$	0.855317	+	0.293708i	0.0477391	+	0.0163932i
$322$	−3.77250	−	1.83854i	−0.210233	−	0.102458i
$323$	0.0727023	−	0.0727023i	0.00404527	−	0.00404527i
$324$	−11.0256	+	14.2280i	−0.612532	+	0.790446i
$325$	2.91877	+	2.91877i	0.161904	+	0.161904i
$326$	18.1823	−	6.26691i	1.00702	−	0.347092i
$327$	−2.47005	+	7.19312i	−0.136594	+	0.397780i
$328$	−13.0973	−	14.5191i	−0.723176	−	0.801684i
$329$	−8.56067	−	14.8275i	−0.471965	−	0.817468i
$330$	0.00771674	+	6.74213i	0.000424792	+	0.371142i
$331$	−3.64318	−	13.5965i	−0.200247	−	0.747334i	−0.990846	−	0.134999i	$-0.956897\pi$
$331$	−3.64318	−	13.5965i	−0.200247	−	0.747334i	0.790598	−	0.612335i	$-0.209770\pi$
$332$	10.5171	−	13.9745i	0.577201	−	0.766949i
$333$	14.0492	−	1.74893i	0.769893	−	0.0958410i
$334$	0.355148	+	5.05658i	0.0194329	+	0.276684i
$335$	1.82778	−	3.16581i	0.0998623	−	0.172967i
$336$	12.2224	+	3.94343i	0.666789	+	0.215132i
$337$	8.97705	+	15.5487i	0.489011	+	0.846992i	0.999920	−	0.0126426i	$-0.00402437\pi$
$337$	8.97705	+	15.5487i	0.489011	+	0.846992i	−0.510909	+	0.859635i	$0.670691\pi$
$338$	−4.73382	+	3.19512i	−0.257486	+	0.173791i
$339$	−5.44425	+	8.08604i	−0.295691	+	0.439173i
$340$	−0.138856	+	0.0590413i	−0.00753051	+	0.00320196i
$341$	−20.2837	+	20.2837i	−1.09842	+	1.09842i
$342$	1.87160	−	5.47072i	0.101204	−	0.295823i
$343$	−19.5821			−1.05734
$344$	15.2388	+	29.8400i	0.821622	+	1.60886i
$345$	2.09109	−	1.82083i	0.112580	−	0.0980304i
$346$	−4.64378	+	23.9293i	−0.249651	+	1.28645i
$347$	8.00879	−	29.8892i	0.429935	−	1.60454i	−0.322971	−	0.946409i	$-0.604682\pi$
$347$	8.00879	−	29.8892i	0.429935	−	1.60454i	0.752905	−	0.658129i	$-0.228652\pi$
$348$	4.30567	+	0.830455i	0.230808	+	0.0445171i
$349$	−0.563262	−	2.10212i	−0.0301507	−	0.112524i	0.949211	−	0.314642i	$-0.101884\pi$
$349$	−0.563262	−	2.10212i	−0.0301507	−	0.112524i	−0.979361	+	0.202118i	$0.935218\pi$
$350$	−0.183671	−	2.61509i	−0.00981762	−	0.139783i
$351$	−9.68934	+	19.1352i	−0.517179	+	1.02136i
$352$	−14.1216	−	6.55865i	−0.752682	−	0.349577i
$353$	−26.7400	−	15.4383i	−1.42323	−	0.821700i	−0.426652	−	0.904416i	$-0.640307\pi$
$353$	−26.7400	−	15.4383i	−1.42323	−	0.821700i	−0.996573	+	0.0827162i	$0.973641\pi$
$354$	−19.1025	−	5.09507i	−1.01528	−	0.270800i
$355$	0.983943	−	3.67212i	0.0522223	−	0.194896i
$356$	13.6170	+	17.4069i	0.721697	+	0.922563i
$357$	0.241651	+	0.0166944i	0.0127895	+	0.000883561i
$358$	−10.8200	−	31.3922i	−0.571853	−	1.65913i
$359$		−	1.90422i		−	0.100501i	−0.998737	−	0.0502505i	$-0.983998\pi$
$359$		−	1.90422i		−	0.100501i	0.998737	−	0.0502505i	$-0.0160020\pi$
$360$	−5.55020	+	6.41835i	−0.292521	+	0.338277i
$361$		−	17.1427i		−	0.902247i
$362$	−9.11182	+	3.14058i	−0.478907	+	0.165065i
$363$	3.31213	−	4.91932i	0.173842	−	0.258197i
$364$	15.1904	+	1.85569i	0.796192	+	0.0972645i
$365$	−1.44208	+	5.38191i	−0.0754818	+	0.281702i
$366$	13.4360	−	3.61665i	0.702311	−	0.189045i
$367$	−20.6805	−	11.9399i	−1.07951	−	0.623258i	−0.148749	−	0.988875i	$-0.547525\pi$
$367$	−20.6805	−	11.9399i	−1.07951	−	0.623258i	−0.930765	+	0.365617i	$0.880858\pi$
$368$	1.77256	+	6.15314i	0.0924009	+	0.320755i
$369$	−20.5427	−	2.85199i	−1.06941	−	0.148469i
$370$	6.65759	−	0.467596i	0.346112	−	0.0243091i
$371$	1.16098	+	4.33284i	0.0602751	+	0.224950i
$372$	−36.0103	+	2.57060i	−1.86705	+	0.133279i
$373$	−2.05702	+	7.67690i	−0.106508	+	0.397495i	−0.998512	−	0.0545337i	$-0.982633\pi$
$373$	−2.05702	+	7.67690i	−0.106508	+	0.397495i	0.892004	+	0.452028i	$0.149299\pi$
$374$	−0.288291	−	0.0559463i	−0.0149071	−	0.00289291i
$375$	1.63816	+	0.562528i	0.0845941	+	0.0290488i
$376$	−8.04995	+	24.8530i	−0.415145	+	1.28169i
$377$	5.22512			0.269107
$378$	12.6156	−	5.13845i	0.648874	−	0.264293i
$379$	22.2920	−	22.2920i	1.14506	−	1.14506i	0.157551	−	0.987511i	$-0.449640\pi$
$379$	22.2920	−	22.2920i	1.14506	−	1.14506i	0.987511	−	0.157551i	$-0.0503597\pi$
$380$	1.01950	−	2.52782i	0.0522994	−	0.129674i
$381$	−15.9851	−	32.7047i	−0.818940	−	1.67551i
$382$	−1.35493	−	2.00744i	−0.0693243	−	0.102709i
$383$	1.35878	+	2.35347i	0.0694302	+	0.120257i	0.898651	−	0.438665i	$-0.144549\pi$
$383$	1.35878	+	2.35347i	0.0694302	+	0.120257i	−0.829220	+	0.558922i	$0.811215\pi$
$384$	−8.02377	−	17.8779i	−0.409461	−	0.912328i
$385$	2.55113	−	4.41869i	0.130018	−	0.225197i
$386$	−4.00489	+	0.281283i	−0.203844	+	0.0143169i
$387$	32.7365	+	13.8311i	1.66409	+	0.703075i
$388$	24.8238	−	3.50428i	1.26024	−	0.177903i
$389$	5.72620	+	21.3705i	0.290330	+	1.08353i	0.944856	+	0.327486i	$0.106201\pi$
$389$	5.72620	+	21.3705i	0.290330	+	1.08353i	−0.654526	+	0.756039i	$0.727132\pi$
$390$	−5.04543	+	8.76209i	−0.255485	+	0.443686i
$391$	0.0603865	+	0.104592i	0.00305387	+	0.00528947i
$392$	6.75165	+	7.48461i	0.341010	+	0.378030i
$393$	−23.3891	+	4.56673i	−1.17983	+	0.230361i
$394$	−8.95877	−	25.9923i	−0.451336	−	1.30947i
$395$	−10.7779	−	10.7779i	−0.542294	−	0.542294i
$396$	−15.9422	+	4.31085i	−0.801128	+	0.216628i
$397$	−24.6208	+	24.6208i	−1.23568	+	1.23568i	−0.273931	+	0.961749i	$0.588324\pi$
$397$	−24.6208	+	24.6208i	−1.23568	+	1.23568i	−0.961749	+	0.273931i	$0.911676\pi$
$398$	7.04930	−	14.4645i	0.353350	−	0.725038i
$399$	−3.29995	+	2.87346i	−0.165204	+	0.143853i
$400$	−2.77510	+	2.88076i	−0.138755	+	0.144038i
$401$	−3.09543	+	1.78715i	−0.154578	+	0.0892458i	−0.575294	−	0.817947i	$-0.695112\pi$
$401$	−3.09543	+	1.78715i	−0.154578	+	0.0892458i	0.420716	+	0.907193i	$0.361779\pi$
$402$	8.65180	+	2.30763i	0.431512	+	0.115094i
$403$	−41.5526	+	11.1340i	−2.06988	+	0.554623i
$404$	8.07985	−	10.7360i	0.401987	−	0.534137i
$405$	−0.126910	+	8.99911i	−0.00630619	+	0.447169i
$406$	−2.50514	−	2.17634i	−0.124328	−	0.108010i
$407$	11.2492	+	6.49476i	0.557604	+	0.321933i
$408$	−0.228057	−	0.290845i	−0.0112905	−	0.0143990i
$409$	14.0960	−	8.13833i	0.697002	−	0.402414i	−0.109228	−	0.994017i	$-0.534838\pi$
$409$	14.0960	−	8.13833i	0.697002	−	0.402414i	0.806230	+	0.591602i	$0.201504\pi$
$410$	−9.59775	−	1.86256i	−0.473999	−	0.0919853i
$411$	−0.00606712	+	0.0878214i	−0.000299269	+	0.00433191i
$412$	−10.8519	+	26.9070i	−0.534637	+	1.32561i
$413$	10.5794	+	10.5794i	0.520580	+	0.520580i
$414$	5.63818	+	3.78676i	0.277101	+	0.186109i
$415$		−	8.74493i		−	0.429272i
$416$	−13.4224	−	19.1068i	−0.658088	−	0.936787i
$417$	−20.1871	+	3.94154i	−0.988568	+	0.193018i
$418$	4.39708	−	2.96783i	0.215068	−	0.145161i
$419$	30.3044	+	8.12004i	1.48047	+	0.396690i	0.906506	−	0.422193i	$-0.138740\pi$
$419$	30.3044	+	8.12004i	1.48047	+	0.396690i	0.573961	+	0.818883i	$0.305406\pi$
$420$	6.06853	−	2.09942i	0.296114	−	0.102441i
$421$	29.3412	−	7.86194i	1.43000	−	0.383168i	0.540981	−	0.841035i	$-0.318053\pi$
$421$	29.3412	−	7.86194i	1.43000	−	0.383168i	0.889021	+	0.457867i	$0.151386\pi$
$422$	14.0100	+	12.1712i	0.681998	+	0.592484i
$423$	10.4230	+	25.6738i	0.506782	+	1.24830i
$424$	3.72243	−	5.74359i	0.180777	−	0.278934i
$425$	−0.0377217	+	0.0653359i	−0.00182977	+	0.00316925i
$426$	9.31213	−	0.0106582i	0.451174	−	0.000516393i
$427$	−10.1711	−	2.72534i	−0.492214	−	0.131888i
$428$	−0.126626	+	1.03654i	−0.00612068	+	0.0501029i
$429$	−17.6799	+	8.64141i	−0.853594	+	0.417211i
$430$	15.0597	+	7.33939i	0.726243	+	0.353937i
$431$	1.76930			0.0852241			0.0426121	−	0.999092i	$-0.486432\pi$
$431$	1.76930			0.0852241			0.0426121	+	0.999092i	$0.486432\pi$
$432$	−18.7150	−	9.04144i	−0.900427	−	0.435006i
$433$	4.06395			0.195301			0.0976506	−	0.995221i	$-0.468867\pi$
$433$	4.06395			0.195301			0.0976506	+	0.995221i	$0.468867\pi$
$434$	24.5595	+	11.9692i	1.17890	+	0.574538i
$435$	1.96981	−	0.962785i	0.0944452	−	0.0461620i
$436$	−8.71715	−	1.06491i	−0.417476	−	0.0509997i
$437$	−2.10734	−	0.564660i	−0.100808	−	0.0270114i
$438$	−13.6480	+	0.0156208i	−0.652125	+	0.000746393i
$439$	−15.7390	+	27.2607i	−0.751181	+	1.30108i	0.196069	+	0.980590i	$0.437182\pi$
$439$	−15.7390	+	27.2607i	−0.751181	+	1.30108i	−0.947251	+	0.320494i	$0.896151\pi$
$440$	−7.61353	+	1.62563i	−0.362961	+	0.0774988i
$441$	10.5898	+	1.47020i	0.504275	+	0.0700096i
$442$	−0.332465	−	0.288829i	−0.0158138	−	0.0137382i
$443$	−15.9180	+	4.26523i	−0.756289	+	0.202647i	−0.616306	−	0.787507i	$-0.711371\pi$
$443$	−15.9180	+	4.26523i	−0.756289	+	0.202647i	−0.139983	+	0.990154i	$0.544705\pi$
$444$	5.34477	+	15.4495i	0.253652	+	0.733200i
$445$	10.6736	+	2.85998i	0.505977	+	0.135576i
$446$	−11.2842	+	7.61635i	−0.534324	+	0.360645i
$447$	−24.9027	+	4.86225i	−1.17786	+	0.229977i
$448$	−1.52298	+	14.7512i	−0.0719542	+	0.696930i
$449$		−	3.64945i		−	0.172228i	−0.996285	−	0.0861141i	$-0.972555\pi$
$449$		−	3.64945i		−	0.172228i	0.996285	−	0.0861141i	$-0.0274450\pi$
$450$	−0.287561	+	4.23288i	−0.0135557	+	0.199540i
$451$	−13.4552	−	13.4552i	−0.633579	−	0.633579i
$452$	−10.4390	−	4.21019i	−0.491009	−	0.198030i
$453$	0.123965	−	1.79439i	0.00582441	−	0.0843080i
$454$	31.7886	+	6.16897i	1.49191	+	0.289524i
$455$	6.62653	−	3.82583i	0.310656	−	0.179358i
$456$	6.62814	+	0.802010i	0.310391	+	0.0375575i
$457$	14.1813	+	8.18758i	0.663373	+	0.382999i	0.793561	−	0.608491i	$-0.208225\pi$
$457$	14.1813	+	8.18758i	0.663373	+	0.382999i	−0.130188	+	0.991489i	$0.541558\pi$
$458$	−8.88762	−	7.72110i	−0.415291	−	0.360783i
$459$	−0.383652	−	0.0805404i	−0.0179074	−	0.00375930i
$460$	2.55816	+	1.92525i	0.119275	+	0.0897654i
$461$	−18.1014	+	4.85026i	−0.843067	+	0.225899i	−0.654406	−	0.756143i	$-0.727081\pi$
$461$	−18.1014	+	4.85026i	−0.843067	+	0.225899i	−0.188661	+	0.982042i	$0.560415\pi$
$462$	12.0758	+	3.22088i	0.561816	+	0.149849i
$463$	−24.2984	+	14.0287i	−1.12924	+	0.651968i	−0.943744	−	0.330677i	$-0.892723\pi$
$463$	−24.2984	+	14.0287i	−1.12924	+	0.651968i	−0.185498	+	0.982645i	$0.559390\pi$
$464$	0.0945774	+	5.06251i	0.00439065	+	0.235021i
$465$	−13.6133	+	11.8539i	−0.631302	+	0.549712i
$466$	−8.77828	+	18.0121i	−0.406646	+	0.834397i
$467$	−14.0970	+	14.0970i	−0.652333	+	0.652333i	−0.953554	−	0.301221i	$-0.902606\pi$
$467$	−14.0970	+	14.0970i	−0.652333	+	0.652333i	0.301221	+	0.953554i	$0.402606\pi$
$468$	−23.9373	−	6.35528i	−1.10650	−	0.293773i
$469$	−4.79159	−	4.79159i	−0.221255	−	0.221255i
$470$	4.25639	+	12.3491i	0.196332	+	0.569623i
$471$	−20.0889	+	3.92235i	−0.925646	+	0.180732i
$472$	1.17379	−	22.7986i	0.0540283	−	1.04939i
$473$	16.3030	+	28.2377i	0.749614	+	1.29837i
$474$	18.6308	−	32.3550i	0.855741	−	1.48611i
$475$	−0.352727	−	1.31640i	−0.0161842	−	0.0604004i
$476$	0.0390965	+	0.276953i	0.00179198	+	0.0126941i
$477$	−0.896790	−	7.20394i	−0.0410612	−	0.329846i
$478$	15.8998	−	1.11672i	0.727240	−	0.0510776i
$479$	8.27320	−	14.3296i	0.378012	−	0.654736i	−0.612761	−	0.790268i	$-0.709941\pi$
$479$	8.27320	−	14.3296i	0.378012	−	0.654736i	0.990773	+	0.135532i	$0.0432744\pi$
$480$	−8.58073	−	4.72981i	−0.391655	−	0.215885i
$481$	9.73992	+	16.8700i	0.444102	+	0.769208i
$482$	21.2373	+	31.4648i	0.967334	+	1.43318i
$483$	−2.25703	−	4.61777i	−0.102698	−	0.210116i
$484$	6.35079	+	2.56136i	0.288672	+	0.116425i
$485$	8.86356	−	8.86356i	0.402473	−	0.402473i
$486$	−21.3664	+	5.42939i	−0.969198	+	0.246282i
$487$	39.7043			1.79917			0.899587	−	0.436742i	$-0.143868\pi$
$487$	39.7043			1.79917			0.899587	+	0.436742i	$0.143868\pi$
$488$	7.30733	+	14.3089i	0.330787	+	0.647733i
$489$	22.2775	+	7.64987i	1.00742	+	0.345939i
$490$	4.94764	+	0.960150i	0.223512	+	0.0433752i
$491$	0.604415	−	2.25571i	0.0272769	−	0.101799i	−0.950945	−	0.309359i	$-0.899886\pi$
$491$	0.604415	−	2.25571i	0.0272769	−	0.101799i	0.978222	+	0.207560i	$0.0665523\pi$
$492$	−1.70521	−	23.8874i	−0.0768767	−	1.07693i
$493$	0.0247172	+	0.0922457i	0.00111321	+	0.00415454i
$494$	7.93604	−	0.557387i	0.357059	−	0.0250780i
$495$	−5.07285	+	6.51543i	−0.228008	+	0.292847i
$496$	−11.5396	−	40.0579i	−0.518143	−	1.79865i
$497$	−6.10302	−	3.52358i	−0.273758	−	0.158054i
$498$	20.6844	−	5.56774i	0.926889	−	0.249497i
$499$	8.46721	−	31.6001i	0.379044	−	1.41461i	−0.468300	−	0.883569i	$-0.655133\pi$
$499$	8.46721	−	31.6001i	0.379044	−	1.41461i	0.847345	−	0.531043i	$-0.178200\pi$
$500$	−0.242521	+	1.98524i	−0.0108459	+	0.0887827i
$501$	−3.46731	+	5.14980i	−0.154908	+	0.230076i
$502$	19.6489	−	6.77241i	0.876975	−	0.302268i
$503$		−	15.9929i		−	0.713087i	−0.934279	−	0.356543i	$-0.883955\pi$
$503$		−	15.9929i		−	0.713087i	0.934279	−	0.356543i	$-0.116045\pi$
$504$	8.82948	+	13.0172i	0.393296	+	0.579833i
$505$		−	6.71837i		−	0.298963i
$506$	2.03055	+	5.89128i	0.0902690	+	0.261899i
$507$	−6.97814	−	0.482083i	−0.309910	−	0.0214101i
$508$	33.1070	−	25.8988i	1.46889	−	1.14907i
$509$	1.05993	−	3.95573i	0.0469808	−	0.175335i	−0.938449	−	0.345418i	$-0.887737\pi$
$509$	1.05993	−	3.95573i	0.0469808	−	0.175335i	0.985430	+	0.170083i	$0.0544037\pi$
$510$	−0.178555	−	0.0476248i	−0.00790657	−	0.00210886i
$511$	8.94466	+	5.16420i	0.395688	+	0.228451i
$512$	18.2692	−	13.3505i	0.807392	−	0.590016i
$513$	5.92932	−	3.87177i	0.261786	−	0.170943i
$514$	−2.24393	−	31.9489i	−0.0989755	−	1.40921i
$515$	3.75455	+	14.0122i	0.165445	+	0.617450i
$516$	−7.77161	+	40.2935i	−0.342126	+	1.77382i
$517$	−6.57985	+	24.5563i	−0.289381	+	1.07999i
$518$	2.35689	−	12.1450i	0.103556	−	0.533622i
$519$	−22.5148	+	19.6049i	−0.988288	+	0.860561i
$520$	−11.1070	−	3.59758i	−0.487073	−	0.157764i
$521$	24.4443			1.07092			0.535462	−	0.844559i	$-0.320137\pi$
$521$	24.4443			1.07092			0.535462	+	0.844559i	$0.320137\pi$
$522$	3.53142	+	4.04620i	0.154566	+	0.177098i
$523$	−2.73613	+	2.73613i	−0.119643	+	0.119643i	−0.764393	−	0.644751i	$-0.776961\pi$
$523$	−2.73613	+	2.73613i	−0.119643	+	0.119643i	0.644751	+	0.764393i	$0.276961\pi$
$524$	−10.7674	−	25.3233i	−0.470378	−	1.10625i
$525$	1.79318	−	2.66330i	0.0782606	−	0.116236i
$526$	−4.14797	+	2.79969i	−0.180860	+	0.122072i
$527$	−0.393125	−	0.680912i	−0.0171248	−	0.0296610i
$528$	−8.69250	−	16.9733i	−0.378292	−	0.738667i
$529$	−10.2187	+	17.6992i	−0.444289	+	0.769531i
$530$	−0.239766	−	3.41377i	−0.0104148	−	0.148285i
$531$	−14.6045	−	19.3134i	−0.633780	−	0.838128i
$532$	−4.03703	−	3.03824i	−0.175028	−	0.131724i
$533$	−7.38572	−	27.5639i	−0.319911	−	1.19392i
$534$	0.0309798	+	27.0672i	0.00134063	+	1.17131i
$535$	0.261061	+	0.452170i	0.0112866	+	0.0195490i
$536$	−0.531629	+	10.3258i	−0.0229629	+	0.446007i
$537$	13.2077	−	38.4626i	0.569953	−	1.65978i
$538$	−2.18308	+	0.752444i	−0.0941193	+	0.0324402i
$539$	6.93614	+	6.93614i	0.298761	+	0.298761i
$540$	−10.1951	+	2.01484i	−0.438728	+	0.0867047i
$541$	20.7984	−	20.7984i	0.894194	−	0.894194i	−0.100721	−	0.994915i	$-0.532115\pi$
$541$	20.7984	−	20.7984i	0.894194	−	0.894194i	0.994915	+	0.100721i	$0.0321148\pi$
$542$	−11.0727	−	5.39632i	−0.475614	−	0.231792i
$543$	−11.1641	−	3.83363i	−0.479095	−	0.164517i
$544$	0.273822	−	0.327346i	0.0117400	−	0.0140349i
$545$	−3.80270	+	2.19549i	−0.162890	+	0.0940444i
$546$	13.2682	+	13.2379i	0.567827	+	0.566529i
$547$	17.1501	−	4.59535i	0.733284	−	0.196483i	0.127193	−	0.991878i	$-0.459403\pi$
$547$	17.1501	−	4.59535i	0.733284	−	0.196483i	0.606091	+	0.795395i	$0.292737\pi$
$548$	−0.100651	+	0.0142085i	−0.00429960	+	0.000606959i
$549$	15.6978	+	6.63231i	0.669967	+	0.283060i
$550$	−2.55286	+	2.93855i	−0.108854	+	0.125300i
$551$	−1.49401	−	0.862569i	−0.0636471	−	0.0367467i
$552$	−2.92506	+	7.27659i	−0.124499	+	0.309712i
$553$	−24.4692	+	14.1273i	−1.04053	+	0.600753i
$554$	8.77955	−	45.2409i	0.373007	−	1.92210i
$555$	6.78033	+	4.56513i	0.287809	+	0.193779i
$556$	−9.29337	−	21.8565i	−0.394127	−	0.926923i
$557$	24.4025	+	24.4025i	1.03396	+	1.03396i	0.999403	+	0.0345625i	$0.0110038\pi$
$557$	24.4025	+	24.4025i	1.03396	+	1.03396i	0.0345625	+	0.999403i	$0.488996\pi$
$558$	−36.7054	−	24.6523i	−1.55386	−	1.04362i
$559$			48.8980i			2.06817i
$560$	3.82671	+	6.35105i	0.161708	+	0.268381i
$561$	−0.236192	−	0.271248i	−0.00997202	−	0.0114521i
$562$	1.56040	+	2.31186i	0.0658215	+	0.0975199i
$563$	15.3201	+	4.10502i	0.645667	+	0.173006i	0.566769	−	0.823877i	$-0.308193\pi$
$563$	15.3201	+	4.10502i	0.645667	+	0.173006i	0.0788978	+	0.996883i	$0.474860\pi$
$564$	−26.4994	+	17.9301i	−1.11583	+	0.754993i
$565$	−5.43625	+	1.45664i	−0.228705	+	0.0612812i
$566$	15.7785	−	18.1623i	0.663220	−	0.763420i
$567$	16.0524	+	4.54477i	0.674137	+	0.190863i
$568$	2.24529	+	10.5157i	0.0942103	+	0.441229i
$569$	−1.99661	+	3.45823i	−0.0837022	+	0.144976i	−0.904837	−	0.425757i	$-0.860008\pi$
$569$	−1.99661	+	3.45823i	−0.0837022	+	0.144976i	0.821135	+	0.570734i	$0.193341\pi$
$570$	2.88909	−	1.67243i	0.121011	−	0.0700504i
$571$	−18.0074	−	4.82507i	−0.753587	−	0.201923i	−0.138479	−	0.990365i	$-0.544221\pi$
$571$	−18.0074	−	4.82507i	−0.753587	−	0.201923i	−0.615109	+	0.788442i	$0.710888\pi$
$572$	−14.0007	−	17.8974i	−0.585398	−	0.748329i
$573$	0.204434	−	2.95917i	0.00854034	−	0.123621i
$574$	−7.93974	+	16.2916i	−0.331398	+	0.679996i
$575$	1.60084			0.0667597
$576$	5.72422	−	23.3074i	0.238509	−	0.971140i
$577$	−1.06381			−0.0442868			−0.0221434	−	0.999755i	$-0.507049\pi$
$577$	−1.06381			−0.0442868			−0.0221434	+	0.999755i	$0.507049\pi$
$578$	−10.5290	+	21.6045i	−0.437949	+	0.898627i
$579$	−4.07873	−	2.74617i	−0.169506	−	0.114127i
$580$	1.55989	+	1.99405i	0.0647709	+	0.0827983i
$581$	−15.6582	−	4.19559i	−0.649610	−	0.174062i
$582$	26.6082	+	15.3217i	1.10295	+	0.635105i
$583$	3.33028	−	5.76821i	0.137926	−	0.238895i
$584$	−3.29073	−	15.4119i	−0.136171	−	0.637750i
$585$	−11.4738	+	4.65810i	−0.474383	+	0.192589i
$586$	−7.46124	+	8.58849i	−0.308221	+	0.354787i
$587$	10.4133	−	2.79024i	0.429804	−	0.115166i	−0.0374300	−	0.999299i	$-0.511917\pi$
$587$	10.4133	−	2.79024i	0.429804	−	0.115166i	0.467234	+	0.884134i	$0.345250\pi$
$588$	0.879035	+	12.3140i	0.0362508	+	0.507819i
$589$	13.7191	+	3.67602i	0.565286	+	0.151468i
$590$	−6.38574	−	9.46099i	−0.262897	−	0.389503i
$591$	10.9358	−	31.8464i	0.449837	−	1.30999i
$592$	−16.1687	+	9.74216i	−0.664531	+	0.400400i
$593$		−	29.4717i		−	1.21026i	−0.796128	−	0.605129i	$-0.793122\pi$
$593$		−	29.4717i		−	1.21026i	0.796128	−	0.605129i	$-0.206878\pi$
$594$	−18.6407	−	7.85055i	−0.764838	−	0.322112i
$595$	0.0988886	+	0.0988886i	0.00405404	+	0.00405404i
$596$	−11.4642	−	26.9621i	−0.469593	−	1.10441i
$597$	17.7054	−	8.65387i	0.724634	−	0.354179i
$598$	−1.78029	+	9.17383i	−0.0728016	+	0.375146i
$599$	0.785935	−	0.453760i	0.0321124	−	0.0185401i	−0.483858	−	0.875147i	$-0.660765\pi$
$599$	0.785935	−	0.453760i	0.0321124	−	0.0185401i	0.515970	+	0.856606i	$0.327431\pi$
$600$	−4.85010	+	0.690333i	−0.198004	+	0.0281827i
$601$	33.1893	+	19.1618i	1.35382	+	0.781628i	0.988782	−	0.149365i	$-0.0477229\pi$
$601$	33.1893	+	19.1618i	1.35382	+	0.781628i	0.365037	+	0.930993i	$0.381056\pi$
$602$	20.3667	−	23.4438i	0.830086	−	0.955497i
$603$	6.61458	+	8.74731i	0.269367	+	0.356218i
$604$	2.05654	−	0.290314i	0.0836793	−	0.0118127i
$605$	3.30726	−	0.886178i	0.134459	−	0.0360283i
$606$	15.8909	−	4.27747i	0.645526	−	0.173760i
$607$	28.6858	−	16.5618i	1.16432	−	0.672221i	0.211985	−	0.977273i	$-0.432007\pi$
$607$	28.6858	−	16.5618i	1.16432	−	0.672221i	0.952336	+	0.305052i	$0.0986738\pi$
$608$	0.683687	+	7.67897i	0.0277272	+	0.311423i
$609$	−0.778842	−	3.98895i	−0.0315603	−	0.161640i
$610$	7.22144	+	3.51939i	0.292388	+	0.142496i
$611$	−26.9586	+	26.9586i	−1.09063	+	1.09063i
$612$	−0.00103619	−	0.452659i	−4.18854e−5	−	0.0182977i
$613$	−33.0637	−	33.0637i	−1.33543	−	1.33543i	−0.900430	−	0.435002i	$-0.856748\pi$
$613$	−33.0637	−	33.0637i	−1.33543	−	1.33543i	−0.435002	−	0.900430i	$-0.643252\pi$
$614$	7.07195	−	2.43749i	0.285401	−	0.0983693i
$615$	−7.86328	−	9.03038i	−0.317078	−	0.364140i
$616$	−0.742023	+	14.4123i	−0.0298969	+	0.580687i
$617$	18.7298	+	32.4410i	0.754034	+	1.30602i	0.945853	+	0.324595i	$0.105228\pi$
$617$	18.7298	+	32.4410i	0.754034	+	1.30602i	−0.191819	+	0.981430i	$0.561439\pi$
$618$	−30.7525	+	17.8019i	−1.23705	+	0.716099i
$619$	−1.77666	−	6.63057i	−0.0714098	−	0.266505i	0.920985	−	0.389597i	$-0.127386\pi$
$619$	−1.77666	−	6.63057i	−0.0714098	−	0.266505i	−0.992395	+	0.123092i	$0.960719\pi$
$620$	−16.6540	−	12.5337i	−0.668841	−	0.503365i
$621$	2.59035	+	7.90461i	0.103947	+	0.317201i
$622$	2.25530	+	32.1108i	0.0904294	+	1.28753i
$623$	10.2418	−	17.7394i	0.410330	−	0.710713i
$624$	1.43774	−	28.5618i	0.0575558	−	1.14339i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	6.98455	−	4.71426i	0.279159	−	0.188420i
$627$	6.48173	+	0.447789i	0.258856	+	0.0178830i
$628$	−9.24813	−	21.7501i	−0.369041	−	0.867925i
$629$	−0.251754	+	0.251754i	−0.0100381	+	0.0100381i
$630$	7.44119	+	2.54572i	0.296464	+	0.101424i
$631$	34.2067			1.36175			0.680874	−	0.732401i	$-0.261600\pi$
$631$	34.2067			1.36175			0.680874	+	0.732401i	$0.261600\pi$
$632$	41.0137	+	13.2845i	1.63144	+	0.528428i
$633$	4.35568	+	22.3082i	0.173123	+	0.886672i
$634$	−6.08320	+	31.3467i	−0.241595	+	1.24494i
$635$	5.43955	−	20.3007i	0.215862	−	0.805607i
$636$	7.92194	−	2.74061i	0.314125	−	0.108672i
$637$	3.80734	+	14.2092i	0.150852	+	0.562989i
$638$	0.345226	+	4.91530i	0.0136676	+	0.194599i
$639$	8.99901	+	7.00654i	0.355995	+	0.277174i
$640$	3.28458	−	10.8264i	0.129834	−	0.427952i
$641$	−37.9867	−	21.9316i	−1.50038	−	0.866246i	−1.00000		0.000442145i	$-0.999859\pi$
$641$	−37.9867	−	21.9316i	−1.50038	−	0.866246i	−0.500383	−	0.865804i	$-0.666807\pi$
$642$	−0.903305	+	0.905375i	−0.0356506	+	0.0357323i
$643$	4.59953	−	17.1657i	0.181388	−	0.676948i	−0.813987	−	0.580883i	$-0.802707\pi$
$643$	4.59953	−	17.1657i	0.181388	−	0.676948i	0.995375	−	0.0960656i	$-0.0306259\pi$
$644$	4.67458	−	3.65680i	0.184204	−	0.144098i
$645$	9.00999	+	18.4340i	0.354768	+	0.725838i
$646$	0.0473813	+	0.137468i	0.00186419	+	0.00540862i
$647$		−	10.7065i		−	0.420918i	−0.977603	−	0.210459i	$-0.932504\pi$
$647$		−	10.7065i		−	0.420918i	0.977603	−	0.210459i	$-0.0674958\pi$
$648$	−11.2567	−	22.8317i	−0.442206	−	0.896913i
$649$		−	22.2157i		−	0.872041i
$650$	−5.51892	+	1.90221i	−0.216470	+	0.0746108i
$651$	14.6936	+	30.0624i	0.575887	+	1.17824i
$652$	−3.29807	+	26.9975i	−0.129162	+	1.05730i
$653$	−5.50661	+	20.5509i	−0.215490	+	0.804220i	0.770503	+	0.637436i	$0.220005\pi$
$653$	−5.50661	+	20.5509i	−0.215490	+	0.804220i	−0.985993	+	0.166784i	$0.946662\pi$
$654$	−7.61410	−	7.59669i	−0.297735	−	0.297054i
$655$	−11.9154	−	6.87936i	−0.465573	−	0.268799i
$656$	26.5724	−	7.65479i	1.03748	−	0.298869i
$657$	−13.1891	−	10.2689i	−0.514554	−	0.400627i
$658$	24.1537	−	1.69644i	0.941611	−	0.0661340i
$659$	−4.36701	−	16.2979i	−0.170114	−	0.634876i	−0.997332	−	0.0729946i	$-0.976744\pi$
$659$	−4.36701	−	16.2979i	−0.170114	−	0.634876i	0.827218	−	0.561881i	$-0.189922\pi$
$660$	−8.57590	−	4.16735i	−0.333816	−	0.162214i
$661$	2.55095	−	9.52027i	0.0992205	−	0.370296i	−0.898405	−	0.439168i	$-0.855273\pi$
$661$	2.55095	−	9.52027i	0.0992205	−	0.370296i	0.997626	+	0.0688720i	$0.0219400\pi$
$662$	19.5421	+	3.79239i	0.759527	+	0.147395i
$663$	−0.103363	−	0.529386i	−0.00401427	−	0.0205596i
$664$	11.2495	+	22.0282i	0.436563	+	0.854859i
$665$	−2.52629			−0.0979653
$666$	−6.48098	+	18.9440i	−0.251133	+	0.734067i
$667$	1.43290	−	1.43290i	0.0554820	−	0.0554820i
$668$	−6.64835	−	2.68136i	−0.257232	−	0.103745i
$669$	−16.6341	−	1.14916i	−0.643112	−	0.0444293i
$670$	2.89220	+	4.28503i	0.111735	+	0.165545i
$671$	7.81764	+	13.5406i	0.301797	+	0.522727i
$672$	−12.5857	+	13.0949i	−0.485505	+	0.505147i
$673$	3.43679	−	5.95269i	0.132478	−	0.229459i	−0.792153	−	0.610323i	$-0.791040\pi$
$673$	3.43679	−	5.95269i	0.132478	−	0.229459i	0.924631	+	0.380863i	$0.124373\pi$
$674$	−25.3285	+	1.77895i	−0.975619	+	0.0685225i
$675$	−3.46719	+	3.87022i	−0.133452	+	0.148965i
$676$	−1.12899	−	7.99757i	−0.0434226	−	0.307599i
$677$	−0.430496	−	1.60663i	−0.0165453	−	0.0617479i	0.957160	−	0.289561i	$-0.0935092\pi$
$677$	−0.430496	−	1.60663i	−0.0165453	−	0.0617479i	−0.973705	+	0.227813i	$0.926843\pi$
$678$	−6.90655	−	11.9309i	−0.265244	−	0.458205i
$679$	−11.6181	−	20.1231i	−0.445860	−	0.772253i
$680$	0.0109717	−	0.213104i	0.000420747	−	0.00817216i
$681$	26.0439	+	29.9094i	0.998004	+	1.14613i
$682$	−13.2192	−	38.3531i	−0.506189	−	1.46862i
$683$	22.0373	+	22.0373i	0.843235	+	0.843235i	0.989278	−	0.146044i	$-0.0466540\pi$
$683$	22.0373	+	22.0373i	0.843235	+	0.843235i	−0.146044	+	0.989278i	$0.546654\pi$
$684$	5.79523	+	5.76876i	0.221586	+	0.220574i
$685$	−0.0359384	+	0.0359384i	−0.00137313	+	0.00137313i
$686$	12.1323	−	24.8943i	0.463214	−	0.950469i
$687$	−2.76314	−	14.1518i	−0.105420	−	0.539924i
$688$	−47.3762	+	0.885079i	−1.80620	+	0.0337433i
$689$	8.65035	−	4.99428i	0.329552	−	0.190267i
$690$	1.01923	+	3.78647i	0.0388013	+	0.144148i
$691$	−2.41443	+	0.646944i	−0.0918492	+	0.0246109i	−0.304451	−	0.952528i	$-0.598473\pi$
$691$	−2.41443	+	0.646944i	−0.0918492	+	0.0246109i	0.212602	+	0.977139i	$0.431806\pi$
$692$	−27.5437	−	20.7292i	−1.04706	−	0.788006i
$693$	9.23232	+	12.2091i	0.350707	+	0.463785i
$694$	33.0355	+	28.6996i	1.25401	+	1.08942i
$695$	−10.2842	−	5.93756i	−0.390101	−	0.225225i
$696$	−3.72336	+	4.95918i	−0.141134	+	0.187977i
$697$	0.451683	−	0.260779i	0.0171087	−	0.00987772i
$698$	3.02135	+	0.586330i	0.114360	+	0.0221929i
$699$	−22.0480	+	10.7764i	−0.833931	+	0.407601i
$700$	3.43830	+	1.38671i	0.129956	+	0.0524128i
$701$	1.86606	+	1.86606i	0.0704800	+	0.0704800i	0.741468	−	0.670988i	$-0.234130\pi$
$701$	1.86606	+	1.86606i	0.0704800	+	0.0704800i	−0.670988	+	0.741468i	$0.734130\pi$
$702$	−18.3230	−	24.1732i	−0.691555	−	0.912360i
$703$		−	6.43151i		−	0.242569i
$704$	17.0870	−	13.8889i	0.643991	−	0.523459i
$705$	−5.19567	+	15.1305i	−0.195680	+	0.569848i
$706$	36.1934	−	24.4289i	1.36216	−	0.919395i
$707$	−12.0295	−	3.22330i	−0.452416	−	0.121225i
$708$	18.3124	−	21.1278i	0.688221	−	0.794032i
$709$	43.7679	−	11.7276i	1.64374	−	0.440439i	0.685889	−	0.727706i	$-0.259413\pi$
$709$	43.7679	−	11.7276i	1.64374	−	0.440439i	0.957850	+	0.287267i	$0.0927468\pi$
$710$	4.05867	+	3.52597i	0.152319	+	0.132327i
$711$	42.3682	−	17.2005i	1.58893	−	0.645070i
$712$	−30.5655	+	6.52629i	−1.14549	+	0.244583i
$713$	−8.34177	+	14.4484i	−0.312402	+	0.541096i
$714$	−0.170941	+	0.296862i	−0.00639729	+	0.0111098i
$715$	−10.9744	−	2.94058i	−0.410419	−	0.109971i
$716$	46.6118	+	5.69419i	1.74196	+	0.212802i
$717$	16.1929	+	10.9025i	0.604736	+	0.407162i
$718$	2.42079	+	1.17978i	0.0903432	+	0.0440290i
$719$	−14.4041			−0.537184			−0.268592	−	0.963254i	$-0.586558\pi$
$719$	−14.4041			−0.537184			−0.268592	+	0.963254i	$0.586558\pi$
$720$	−4.72081	−	11.0324i	−0.175934	−	0.411153i
$721$	26.8907			1.00146
$722$	21.7931	+	10.6209i	0.811055	+	0.395270i
$723$	−3.20432	+	46.3823i	−0.119170	+	1.72498i
$724$	1.65278	−	13.5294i	0.0614252	−	0.502817i
$725$	1.22272	+	0.327626i	0.0454105	+	0.0121677i
$726$	4.20175	+	7.25845i	0.155942	+	0.269386i
$727$	22.3310	−	38.6784i	0.828211	−	1.43450i	−0.0712289	−	0.997460i	$-0.522692\pi$
$727$	22.3310	−	38.6784i	0.828211	−	1.43450i	0.899440	−	0.437044i	$-0.143975\pi$
$728$	−11.7705	+	18.1615i	−0.436242	+	0.673109i
$729$	−24.7206	−	10.8577i	−0.915579	−	0.402139i
$730$	−5.94844	−	5.16770i	−0.220162	−	0.191265i
$731$	−0.863259	+	0.231309i	−0.0319288	+	0.00855529i
$732$	−3.72665	+	19.3216i	−0.137741	+	0.714147i
$733$	−16.8439	−	4.51330i	−0.622142	−	0.166702i	−0.0660406	−	0.997817i	$-0.521037\pi$
$733$	−16.8439	−	4.51330i	−0.622142	−	0.166702i	−0.556101	+	0.831115i	$0.687703\pi$
$734$	27.9917	−	18.8932i	1.03319	−	0.697359i
$735$	4.05352	+	4.65516i	0.149516	+	0.171708i
$736$	−8.92056	−	1.55884i	−0.328816	−	0.0574595i
$737$			10.0618i			0.370632i
$738$	16.3531	−	24.3485i	0.601967	−	0.896280i
$739$	7.44602	+	7.44602i	0.273906	+	0.273906i	0.830671	−	0.556764i	$-0.187957\pi$
$739$	7.44602	+	7.44602i	0.273906	+	0.273906i	−0.556764	+	0.830671i	$0.687957\pi$
$740$	−3.53034	+	8.75335i	−0.129778	+	0.321779i
$741$	8.08234	+	5.44176i	0.296912	+	0.199908i
$742$	−6.22754	−	1.20853i	−0.228620	−	0.0443665i
$743$	11.8146	−	6.82114i	0.433434	−	0.250243i	−0.267374	−	0.963593i	$-0.586156\pi$
$743$	11.8146	−	6.82114i	0.433434	−	0.250243i	0.700809	+	0.713349i	$0.252823\pi$
$744$	19.0426	−	47.3717i	0.698136	−	1.73673i
$745$	−12.6865	−	7.32453i	−0.464796	−	0.268350i
$746$	−8.48501	−	7.37134i	−0.310658	−	0.269884i
$747$	24.1664	+	10.2103i	0.884202	+	0.373574i
$748$	0.249737	−	0.331835i	0.00913128	−	0.0121331i
$749$	0.934879	−	0.250500i	0.0341597	−	0.00915308i
$750$	−1.73007	+	1.73403i	−0.0631731	+	0.0633179i
$751$	−31.2880	+	18.0641i	−1.14171	+	0.659169i	−0.946854	−	0.321662i	$-0.895758\pi$
$751$	−31.2880	+	18.0641i	−1.14171	+	0.659169i	−0.194860	+	0.980831i	$0.562425\pi$
$752$	−26.6076	−	25.6316i	−0.970278	−	0.934690i
$753$	24.0744	+	8.26693i	0.877321	+	0.301264i
$754$	−3.23728	+	6.64257i	−0.117895	+	0.241908i
$755$	0.734305	−	0.734305i	0.0267241	−	0.0267241i
$756$	−1.28371	+	19.2214i	−0.0466880	+	0.699077i
$757$	−1.22689	−	1.22689i	−0.0445920	−	0.0445920i	0.684459	−	0.729051i	$-0.260038\pi$
$757$	−1.22689	−	1.22689i	−0.0445920	−	0.0445920i	−0.729051	+	0.684459i	$0.760038\pi$
$758$	14.5280	+	42.1505i	0.527682	+	1.53097i
$759$	−2.47865	+	7.21816i	−0.0899692	+	0.262003i
$760$	2.58191	+	2.86221i	0.0936558	+	0.103823i
$761$	−6.10462	−	10.5735i	−0.221292	−	0.383289i	0.733908	−	0.679248i	$-0.237694\pi$
$761$	−6.10462	−	10.5735i	−0.221292	−	0.383289i	−0.955201	+	0.295959i	$0.904361\pi$
$762$	51.4804	−	0.0589221i	1.86494	−	0.00213452i
$763$	2.10668	+	7.86223i	0.0762668	+	0.284632i
$764$	3.39147	−	0.478761i	0.122699	−	0.0173210i
$765$	−0.136512	−	0.180527i	−0.00493559	−	0.00652696i
$766$	−3.83376	+	0.269264i	−0.138519	+	0.00972889i
$767$	16.6580	−	28.8524i	0.601484	−	1.04180i
$768$	27.6990	+	0.876015i	0.999500	+	0.0316105i
$769$	14.7533	+	25.5534i	0.532016	+	0.921479i	0.999301	+	0.0373727i	$0.0118989\pi$
$769$	14.7533	+	25.5534i	0.532016	+	0.921479i	−0.467285	+	0.884107i	$0.654768\pi$
$770$	4.03679	+	5.98084i	0.145476	+	0.215534i
$771$	21.9074	−	32.5379i	0.788977	−	1.17182i
$772$	2.12369	−	5.26560i	0.0764331	−	0.189513i
$773$	−25.1515	+	25.1515i	−0.904638	+	0.904638i	−0.995833	−	0.0911949i	$-0.970931\pi$
$773$	−25.1515	+	25.1515i	−0.904638	+	0.904638i	0.0911949	+	0.995833i	$0.470931\pi$
$774$	−37.8654	+	33.0479i	−1.36104	+	1.18788i
$775$	−10.4217			−0.374359
$776$	−10.9249	+	33.7290i	−0.392183	+	1.21080i
$777$	11.4271	−	9.95023i	0.409944	−	0.356962i
$778$	−30.7155	−	5.96072i	−1.10120	−	0.213702i
$779$	−2.43849	+	9.10056i	−0.0873679	+	0.326061i
$780$	−8.01309	−	11.8428i	−0.286915	−	0.424040i
$781$	2.70827	+	10.1074i	0.0969095	+	0.361671i
$782$	−0.170379	+	0.0119666i	−0.00609274	+	0.000427923i
$783$	0.360753	+	6.56764i	0.0128923	+	0.234708i
$784$	−13.6981	+	3.94605i	−0.489217	+	0.140930i
$785$	−10.2341	−	5.90866i	−0.365271	−	0.210889i
$786$	8.68541	−	32.5634i	0.309798	−	1.16150i
$787$	12.8969	−	48.1320i	0.459726	−	1.71572i	−0.214085	−	0.976815i	$-0.568677\pi$
$787$	12.8969	−	48.1320i	0.459726	−	1.71572i	0.673810	−	0.738904i	$-0.264656\pi$
$788$	38.5939	+	4.71471i	1.37485	+	0.167955i
$789$	−6.11453	−	0.422421i	−0.217683	−	0.0150386i
$790$	20.3792	−	7.02411i	0.725060	−	0.249907i
$791$			10.4327i			0.370944i
$792$	4.39690	−	22.9378i	0.156237	−	0.815061i
$793$			23.4476i			0.832649i
$794$	−16.0457	−	46.5538i	−0.569442	−	1.65213i
$795$	2.34083	−	3.47671i	0.0830208	−	0.123306i
$796$	14.0209	+	17.9232i	0.496957	+	0.635272i
$797$	−10.7303	+	40.0462i	−0.380088	+	1.41851i	0.465678	+	0.884954i	$0.345810\pi$
$797$	−10.7303	+	40.0462i	−0.380088	+	1.41851i	−0.845766	+	0.533554i	$0.820856\pi$
$798$	−1.60844	−	5.97543i	−0.0569383	−	0.211528i
$799$	−0.603461	−	0.348408i	−0.0213489	−	0.0123258i
$800$	−1.94291	−	5.31273i	−0.0686921	−	0.187833i
$801$	−20.3656	+	26.1570i	−0.719583	+	0.924213i
$802$	−0.354152	−	5.04239i	−0.0125055	−	0.178053i
$803$	−3.96927	−	14.8135i	−0.140073	−	0.522758i
$804$	−8.29395	+	9.56911i	−0.292505	+	0.337477i
$805$	0.768043	−	2.86637i	0.0270699	−	0.101026i
$806$	11.5900	−	59.7230i	0.408240	−	2.10365i
$807$	−2.67477	−	0.918491i	−0.0941563	−	0.0323324i
$808$	8.64249	+	16.9233i	0.304042	+	0.595361i
$809$	−14.1637			−0.497970			−0.248985	−	0.968507i	$-0.580097\pi$
$809$	−14.1637			−0.497970			−0.248985	+	0.968507i	$0.580097\pi$
$810$	−11.3617	−	5.73683i	−0.399210	−	0.201572i
$811$	13.1513	−	13.1513i	0.461804	−	0.461804i	−0.437443	−	0.899246i	$-0.644116\pi$
$811$	13.1513	−	13.1513i	0.461804	−	0.461804i	0.899246	+	0.437443i	$0.144116\pi$
$812$	4.31882	−	1.83636i	0.151561	−	0.0644435i
$813$	−6.62463	−	13.5537i	−0.232336	−	0.475348i
$814$	−15.2262	+	10.2770i	−0.533679	+	0.360209i
$815$	6.79954	+	11.7772i	0.238178	+	0.412536i
$816$	0.511039	−	0.109728i	0.0178900	−	0.00384125i
$817$	8.07214	−	13.9814i	0.282408	−	0.489146i
$818$	1.61274	+	22.9621i	0.0563882	+	0.802851i
$819$	2.83569	+	22.7791i	0.0990869	+	0.795968i
$820$	8.31422	−	11.0474i	0.290345	−	0.385793i
$821$	−12.4299	−	46.3891i	−0.433807	−	1.61899i	−0.743904	−	0.668286i	$-0.767028\pi$
$821$	−12.4299	−	46.3891i	−0.433807	−	1.61899i	0.310097	−	0.950705i	$-0.399639\pi$
$822$	−0.107886	−	0.0621237i	−0.00376297	−	0.00216681i
$823$	4.48994	+	7.77680i	0.156509	+	0.271082i	0.933608	−	0.358297i	$-0.116643\pi$
$823$	4.48994	+	7.77680i	0.156509	+	0.271082i	−0.777098	+	0.629379i	$0.783309\pi$
$824$	−27.4828	−	30.4663i	−0.957409	−	1.06135i
$825$	−4.67906	+	0.913586i	−0.162904	+	0.0318070i
$826$	−20.0040	+	6.89479i	−0.696028	+	0.239901i
$827$	−31.6848	−	31.6848i	−1.10179	−	1.10179i	−0.994195	−	0.107595i	$-0.965685\pi$
$827$	−31.6848	−	31.6848i	−1.10179	−	1.10179i	−0.107595	−	0.994195i	$-0.534315\pi$
$828$	−8.30721	+	4.82156i	−0.288695	+	0.167561i
$829$	−35.4807	+	35.4807i	−1.23230	+	1.23230i	−0.269218	+	0.963079i	$0.586765\pi$
$829$	−35.4807	+	35.4807i	−1.23230	+	1.23230i	−0.963079	+	0.269218i	$0.913235\pi$
$830$	11.1172	+	5.41802i	0.385885	+	0.188062i
$831$	42.5665	−	37.0652i	1.47662	−	1.28578i
$832$	32.6060	−	5.22579i	1.13041	−	0.181172i
$833$	−0.232843	+	0.134432i	−0.00806752	+	0.00465778i
$834$	7.49637	−	28.1055i	0.259578	−	0.973212i
$835$	−3.46221	+	0.927698i	−0.119815	+	0.0321043i
$836$	1.04867	+	7.42865i	0.0362692	+	0.256925i
$837$	−16.8636	−	51.4602i	−0.582890	−	1.77872i
$838$	−29.0982	+	33.4944i	−1.00518	+	1.15705i
$839$	−44.3205	−	25.5885i	−1.53011	−	0.883411i	−0.999356	−	0.0358879i	$-0.988574\pi$
$839$	−44.3205	−	25.5885i	−1.53011	−	0.883411i	−0.530758	−	0.847524i	$-0.678093\pi$
$840$	−1.09088	+	9.01550i	−0.0376390	+	0.311064i
$841$	−23.7270	+	13.6988i	−0.818174	+	0.472373i
$842$	−8.18393	+	42.1717i	−0.282037	+	1.45333i
$843$	−0.235435	+	3.40791i	−0.00810882	+	0.117375i
$844$	−24.1530	+	10.2698i	−0.831381	+	0.353502i
$845$	−2.85560	−	2.85560i	−0.0982357	−	0.0982357i
$846$	−39.0961	−	2.65599i	−1.34415	−	0.0913149i
$847$		−	6.34695i		−	0.218084i
$848$	4.99543	+	8.29074i	0.171544	+	0.284705i
$849$	28.9199	−	5.64662i	0.992529	−	0.193791i
$850$	−0.0596891	−	0.0884342i	−0.00204732	−	0.00303327i
$851$	7.29732	+	1.95531i	0.250149	+	0.0670272i
$852$	−5.75588	+	11.8449i	−0.197193	+	0.405799i
$853$	−15.1907	+	4.07033i	−0.520119	+	0.139366i	−0.509322	−	0.860576i	$-0.670104\pi$
$853$	−15.1907	+	4.07033i	−0.520119	+	0.139366i	−0.0107974	+	0.999942i	$0.503437\pi$
$854$	9.76628	−	11.2418i	0.334195	−	0.384686i
$855$	4.04966	+	0.562223i	0.138495	+	0.0192276i
$856$	−1.23927	−	0.803173i	−0.0423575	−	0.0274519i
$857$	−25.9445	+	44.9372i	−0.886248	+	1.53503i	−0.0419705	+	0.999119i	$0.513364\pi$
$857$	−25.9445	+	44.9372i	−0.886248	+	1.53503i	−0.844277	+	0.535907i	$0.819970\pi$
$858$	−0.0318529	−	27.8299i	−0.00108744	−	0.950098i
$859$	26.3889	+	7.07087i	0.900376	+	0.241255i	0.679178	−	0.733974i	$-0.262336\pi$
$859$	26.3889	+	7.07087i	0.900376	+	0.241255i	0.221198	+	0.975229i	$0.429003\pi$
$860$	−18.6608	+	14.5979i	−0.636328	+	0.497783i
$861$	−19.9419	+	9.74699i	−0.679617	+	0.332176i
$862$	−1.09619	+	2.24927i	−0.0373363	+	0.0766104i
$863$	47.9783			1.63320			0.816600	−	0.577205i	$-0.195857\pi$
$863$	47.9783			1.63320			0.816600	+	0.577205i	$0.195857\pi$
$864$	23.0893	−	18.1903i	0.785513	−	0.618845i
$865$	−17.2363			−0.586051
$866$	−2.51787	+	5.16641i	−0.0855606	+	0.175562i
$867$	−26.4452	+	12.9256i	−0.898126	+	0.438977i
$868$	−30.4322	+	23.8063i	−1.03294	+	0.808040i
$869$	40.5241	+	10.8584i	1.37469	+	0.368346i
$870$	0.00354890	+	3.10068i	0.000120319	+	0.105123i
$871$	−7.54465	+	13.0677i	−0.255641	+	0.442783i
$872$	6.75459	−	10.4221i	0.228739	−	0.352938i
$873$	14.1455	+	34.8430i	0.478751	+	1.17926i
$874$	2.02347	−	2.32917i	0.0684447	−	0.0787854i
$875$	1.79054	−	0.479774i	0.0605313	−	0.0162193i
$876$	8.43589	−	17.3600i	0.285022	−	0.586541i
$877$	−1.25998	−	0.337610i	−0.0425464	−	0.0114003i	0.237483	−	0.971392i	$-0.423678\pi$
$877$	−1.25998	−	0.337610i	−0.0425464	−	0.0114003i	−0.280029	+	0.959991i	$0.590344\pi$
$878$	−24.9047	−	36.8983i	−0.840492	−	1.24526i
$879$	−13.6755	+	2.67014i	−0.461263	+	0.0900615i
$880$	2.65042	−	10.6861i	0.0893458	−	0.360228i
$881$			42.5025i			1.43195i	0.698128	+	0.715973i	$0.254017\pi$
$881$			42.5025i			1.43195i	−0.698128	+	0.715973i	$0.745983\pi$
$882$	−8.43004	+	12.5516i	−0.283854	+	0.422636i
$883$	−16.4707	−	16.4707i	−0.554283	−	0.554283i	0.373391	−	0.927674i	$-0.378195\pi$
$883$	−16.4707	−	16.4707i	−0.554283	−	0.554283i	−0.927674	+	0.373391i	$0.878195\pi$
$884$	0.573164	−	0.243708i	0.0192776	−	0.00819680i
$885$	0.963489	−	13.9465i	0.0323873	−	0.468805i
$886$	4.43991	−	22.8788i	0.149162	−	0.768628i
$887$	−29.8851	+	17.2542i	−1.00345	+	0.579339i	−0.909266	−	0.416216i	$-0.863356\pi$
$887$	−29.8851	+	17.2542i	−1.00345	+	0.579339i	−0.0941793	+	0.995555i	$0.530023\pi$
$888$	−22.9520	−	2.77720i	−0.770218	−	0.0931969i
$889$	−33.7394	−	19.4795i	−1.13158	−	0.653320i
$890$	−10.2488	+	11.7972i	−0.343540	+	0.395442i
$891$	−12.0824	−	21.6259i	−0.404774	−	0.724494i
$892$	−2.69122	−	19.0642i	−0.0901086	−	0.638316i
$893$	12.1586	−	3.25789i	0.406872	−	0.109021i
$894$	9.24746	−	34.6707i	0.309281	−	1.15956i
$895$	20.3335	−	11.7396i	0.679675	−	0.392411i
$896$	−17.8093	−	11.0754i	−0.594967	−	0.370004i
$897$	−8.63152	+	7.51597i	−0.288198	+	0.250951i
$898$	4.63946	+	2.26106i	0.154821	+	0.0754524i
$899$	−9.32838	+	9.32838i	−0.311119	+	0.311119i
$900$	−5.20301	−	2.98810i	−0.173434	−	0.0996033i
$901$	0.129090	+	0.129090i	0.00430063	+	0.00430063i
$902$	25.4415	−	8.76895i	0.847110	−	0.291974i
$903$	37.3296	−	7.28860i	1.24225	−	0.242549i
$904$	11.8199	−	10.6624i	0.393124	−	0.354626i
$905$	−3.40750	−	5.90197i	−0.113269	−	0.196188i
$906$	2.20437	+	1.26933i	0.0732352	+	0.0421707i
$907$	−4.27818	−	15.9664i	−0.142055	−	0.530155i	−0.999869	−	0.0161953i	$-0.994845\pi$
$907$	−4.27818	−	15.9664i	−0.142055	−	0.530155i	0.857814	−	0.513960i	$-0.171822\pi$
$908$	−27.5374	+	36.5901i	−0.913862	+	1.21428i
$909$	18.5660	+	7.84412i	0.615797	+	0.260173i
$910$	0.758150	+	10.7945i	0.0251324	+	0.357834i
$911$	19.7130	−	34.1439i	0.653120	−	1.13124i	−0.329242	−	0.944246i	$-0.606793\pi$
$911$	19.7130	−	34.1439i	0.653120	−	1.13124i	0.982362	−	0.186991i	$-0.0598735\pi$
$912$	−5.12611	+	7.92931i	−0.169743	+	0.262566i
$913$	12.0351	+	20.8453i	0.398303	+	0.689880i
$914$	−19.1948	+	12.9557i	−0.634909	+	0.428535i
$915$	4.32048	+	8.83949i	0.142831	+	0.292224i
$916$	15.3221	−	6.51493i	0.506256	−	0.215259i
$917$	−18.0345	+	18.0345i	−0.595551	+	0.595551i
$918$	0.340085	−	0.437829i	0.0112245	−	0.0144505i
$919$	−8.56244			−0.282449			−0.141224	−	0.989978i	$-0.545104\pi$
$919$	−8.56244			−0.282449			−0.141224	+	0.989978i	$0.545104\pi$
$920$	−4.03247	+	2.05932i	−0.132946	+	0.0678937i
$921$	8.66475	+	2.97539i	0.285513	+	0.0980425i
$922$	5.04890	−	26.0169i	0.166277	−	0.856822i
$923$	−4.06148	+	15.1577i	−0.133685	+	0.498921i
$924$	−11.5763	+	13.3561i	−0.380833	+	0.439384i
$925$	1.22143	+	4.55842i	0.0401602	+	0.149880i
$926$	−2.78001	−	39.5816i	−0.0913568	−	1.30073i
$927$	−43.1060	−	5.98450i	−1.41579	−	0.196557i
$928$	−6.49445	−	3.01630i	−0.213191	−	0.0990148i
$929$	−42.7491	−	24.6812i	−1.40255	−	0.809765i	−0.407900	−	0.913027i	$-0.633739\pi$
$929$	−42.7491	−	24.6812i	−1.40255	−	0.809765i	−0.994654	+	0.103262i	$0.967072\pi$
$930$	−6.63533	−	24.6505i	−0.217581	−	0.808321i
$931$	1.25704	−	4.69134i	0.0411979	−	0.153753i
$932$	−17.4598	−	22.3192i	−0.571913	−	0.731091i
$933$	−22.0185	+	32.7028i	−0.720853	+	1.07064i
$934$	−9.18726	−	26.6552i	−0.300616	−	0.872185i
$935$		−	0.207655i		−	0.00679105i
$936$	22.9099	−	26.4934i	0.748834	−	0.865965i
$937$			19.2011i			0.627273i	0.949543	+	0.313636i	$0.101547\pi$
$937$			19.2011i			0.627273i	−0.949543	+	0.313636i	$0.898453\pi$
$938$	9.06012	−	3.12276i	0.295823	−	0.101962i
$939$	10.2959	+	0.711293i	0.335995	+	0.0232122i
$940$	−18.3363	−	2.24000i	−0.598063	−	0.0730606i
$941$	−8.81441	+	32.8958i	−0.287341	+	1.07237i	0.659770	+	0.751468i	$0.270654\pi$
$941$	−8.81441	+	32.8958i	−0.287341	+	1.07237i	−0.947111	+	0.320905i	$0.896013\pi$
$942$	7.45987	−	27.9686i	0.243056	−	0.911268i
$943$	−9.58432	−	5.53351i	−0.312108	−	0.180196i
$944$	28.2560	+	15.6173i	0.919656	+	0.508300i
$945$	5.26633	+	8.06497i	0.171314	+	0.262354i
$946$	−45.9986	+	3.23071i	−1.49554	+	0.105039i
$947$	2.16573	+	8.08261i	0.0703767	+	0.262649i	0.992145	−	0.125091i	$-0.0399223\pi$
$947$	2.16573	+	8.08261i	0.0703767	+	0.262649i	−0.921769	+	0.387741i	$0.873256\pi$
$948$	29.5892	+	43.7308i	0.961013	+	1.42031i
$949$	5.95256	−	22.2153i	0.193228	−	0.721138i
$950$	1.89204	+	0.367173i	0.0613858	+	0.0119127i
$951$	−29.4936	+	25.6818i	−0.956396	+	0.832791i
$952$	−0.376307	−	0.121887i	−0.0121962	−	0.00395038i
$953$	−43.1295			−1.39710			−0.698550	−	0.715561i	$-0.746171\pi$
$953$	−43.1295			−1.39710			−0.698550	+	0.715561i	$0.746171\pi$
$954$	9.71382	+	3.32321i	0.314497	+	0.107593i
$955$	1.21095	−	1.21095i	0.0391856	−	0.0391856i
$956$	−8.43123	+	20.9049i	−0.272685	+	0.676113i
$957$	−3.37043	+	5.00592i	−0.108951	+	0.161818i
$958$	13.0911	+	19.3956i	0.422956	+	0.626643i
$959$	0.0471068	+	0.0815914i	0.00152116	+	0.00263473i
$960$	11.3292	−	7.97807i	0.365648	−	0.257491i
$961$	38.8062	−	67.2142i	1.25181	−	2.16820i
$962$	−27.4810	+	1.93012i	−0.886022	+	0.0622297i
$963$	−1.55437	+	0.193497i	−0.0500887	+	0.00623535i
$964$	−53.1583	+	7.50416i	−1.71211	+	0.241693i
$965$	−0.734752	−	2.74213i	−0.0236525	−	0.0882723i
$966$	7.26883	−	0.00831957i	0.233871	−	0.000267678i
$967$	−11.3038	−	19.5788i	−0.363506	−	0.629610i	0.625030	−	0.780601i	$-0.285087\pi$
$967$	−11.3038	−	19.5788i	−0.363506	−	0.629610i	−0.988535	+	0.150991i	$0.951754\pi$
$968$	−7.19090	+	6.48670i	−0.231124	+	0.208490i
$969$	−0.0578373	+	0.168430i	−0.00185800	+	0.00541075i
$970$	5.77652	+	16.7595i	0.185473	+	0.538117i
$971$	19.7492	+	19.7492i	0.633781	+	0.633781i	0.949014	−	0.315233i	$-0.102083\pi$
$971$	19.7492	+	19.7492i	0.633781	+	0.633781i	−0.315233	+	0.949014i	$0.602083\pi$
$972$	6.33550	−	30.5264i	0.203211	−	0.979135i
$973$	−15.5655	+	15.5655i	−0.499008	+	0.499008i
$974$	−24.5992	+	50.4752i	−0.788210	+	1.61733i
$975$	−6.76193	−	2.32198i	−0.216555	−	0.0743630i
$976$	−22.7179	+	0.424414i	−0.727182	+	0.0135852i
$977$	31.0369	−	17.9192i	0.992959	−	0.573285i	0.0868012	−	0.996226i	$-0.472336\pi$
$977$	31.0369	−	17.9192i	0.992959	−	0.573285i	0.906157	+	0.422941i	$0.139002\pi$
$978$	−23.5273	+	23.5813i	−0.752321	+	0.754045i
$979$	−29.3787	+	7.87201i	−0.938948	+	0.251590i
$980$	−4.28598	+	5.69495i	−0.136911	+	0.181919i
$981$	−1.62729	−	13.0720i	−0.0519552	−	0.417358i
$982$	2.49316	+	2.16593i	0.0795598	+	0.0691175i
$983$	−17.5523	−	10.1338i	−0.559832	−	0.323219i	0.193246	−	0.981150i	$-0.438098\pi$
$983$	−17.5523	−	10.1338i	−0.559832	−	0.323219i	−0.753078	+	0.657931i	$0.771432\pi$
$984$	31.4240	+	12.6319i	1.00176	+	0.402690i
$985$	16.8359	−	9.72020i	0.536436	−	0.309711i
$986$	−0.132584	−	0.0257295i	−0.00422232	−	0.000819393i
$987$	24.5990	+	16.5623i	0.782996	+	0.527183i
$988$	−4.20826	+	10.4342i	−0.133883	+	0.331957i
$989$	13.4094	+	13.4094i	0.426395	+	0.426395i
$990$	−5.13998	−	10.4857i	−0.163359	−	0.333257i
$991$			10.3832i			0.329834i	0.986307	+	0.164917i	$0.0527356\pi$
$991$			10.3832i			0.329834i	−0.986307	+	0.164917i	$0.947264\pi$
$992$	58.0742	+	10.1483i	1.84386	+	0.322208i
$993$	16.0106	+	18.3869i	0.508080	+	0.583491i
$994$	8.26064	−	5.57556i	0.262011	−	0.176846i
$995$	10.9902	+	2.94482i	0.348413	+	0.0933571i
$996$	−5.73708	+	29.7451i	−0.181786	+	0.942510i
$997$	9.97267	−	2.67217i	0.315838	−	0.0846284i	−0.0974179	−	0.995244i	$-0.531058\pi$
$997$	9.97267	−	2.67217i	0.315838	−	0.0846284i	0.413255	+	0.910615i	$0.364392\pi$
$998$	34.9265	+	30.3423i	1.10558	+	0.960469i
$999$	−20.5321	+	13.4072i	−0.649606	+	0.424185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.34	✓	384
9.5	odd	6	inner	720.2.cf.a.491.66	yes	384
16.3	odd	4	inner	720.2.cf.a.371.66	yes	384
144.131	even	12	inner	720.2.cf.a.131.34	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.34	✓	384	1.1	even	1	trivial
720.2.cf.a.131.34	yes	384	144.131	even	12	inner
720.2.cf.a.371.66	yes	384	16.3	odd	4	inner
720.2.cf.a.491.66	yes	384	9.5	odd	6	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.619561 + 1.27128i) q^{2} +(-1.55612 + 0.760585i) q^{3} +(-1.23229 - 1.57527i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-0.00280357 - 2.44949i) q^{6} +(-0.926852 + 1.60536i) q^{7} +(2.76608 - 0.590608i) q^{8} +(1.84302 - 2.36712i) q^{9} +(0.927480 - 1.06760i) q^{10} +(2.65868 - 0.712391i) q^{11} +(3.11571 + 1.51404i) q^{12} +(3.98711 + 1.06834i) q^{13} +(-1.46661 - 2.17290i) q^{14} +(1.69995 - 0.331915i) q^{15} +(-0.962927 + 3.88237i) q^{16} +0.0754433i q^{17} +(1.86741 + 3.80957i) q^{18} +(-0.963668 - 0.963668i) q^{19} +(0.782591 + 1.84053i) q^{20} +(0.221284 - 3.20308i) q^{21} +(-0.741567 + 3.82129i) q^{22} +(1.38637 - 0.800421i) q^{23} +(-3.85514 + 3.02289i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-3.82842 + 4.40682i) q^{26} +(-1.06756 + 5.08530i) q^{27} +(3.67101 - 0.518223i) q^{28} +(1.22272 - 0.327626i) q^{29} +(-0.631266 + 2.36675i) q^{30} +(-9.02548 + 5.21086i) q^{31} +(-4.33897 - 3.62951i) q^{32} +(-3.59539 + 3.13072i) q^{33} +(-0.0959094 - 0.0467417i) q^{34} +(1.31077 - 1.31077i) q^{35} +(-5.99998 + 0.0137346i) q^{36} +(3.33700 + 3.33700i) q^{37} +(1.82214 - 0.628038i) q^{38} +(-7.01699 + 1.37007i) q^{39} +(-2.82469 - 0.145430i) q^{40} +(-3.45662 - 5.98705i) q^{41} +(3.93490 + 2.26581i) q^{42} +(3.06600 + 11.4425i) q^{43} +(-4.39847 - 3.31025i) q^{44} +(-2.39288 + 1.80946i) q^{45} +(0.158616 + 2.25837i) q^{46} +(-4.61814 + 7.99886i) q^{47} +(-1.45444 - 6.77382i) q^{48} +(1.78189 + 3.08632i) q^{49} +(-1.17219 + 0.791178i) q^{50} +(-0.0573811 - 0.117399i) q^{51} +(-3.23035 - 7.59727i) q^{52} +(1.71109 - 1.71109i) q^{53} +(-5.80341 - 4.50782i) q^{54} -2.75247 q^{55} +(-1.61561 + 4.98794i) q^{56} +(2.23254 + 0.766632i) q^{57} +(-0.341043 + 1.75739i) q^{58} +(2.08898 - 7.79617i) q^{59} +(-2.61769 - 2.26886i) q^{60} +(1.47021 + 5.48691i) q^{61} +(-1.03262 - 14.7023i) q^{62} +(2.09187 + 5.15268i) q^{63} +(7.30237 - 3.26733i) q^{64} +(-3.57475 - 2.06388i) q^{65} +(-1.75245 - 6.51040i) q^{66} +(-0.946129 + 3.53100i) q^{67} +(0.118843 - 0.0929680i) q^{68} +(-1.54857 + 2.30000i) q^{69} +(0.854248 + 2.47845i) q^{70} +3.80166i q^{71} +(3.69989 - 7.63615i) q^{72} -5.57176i q^{73} +(-6.30972 + 2.17477i) q^{74} +(-1.72793 - 0.119374i) q^{75} +(-0.330516 + 2.70555i) q^{76} +(-1.32056 + 4.92840i) q^{77} +(2.60572 - 9.76938i) q^{78} +(13.2001 + 7.62111i) q^{79} +(1.93495 - 3.50085i) q^{80} +(-2.20655 - 8.72531i) q^{81} +(9.75278 - 0.684986i) q^{82} +(2.26335 + 8.44696i) q^{83} +(-5.31838 + 3.59853i) q^{84} +(0.0195262 - 0.0728727i) q^{85} +(-16.4461 - 3.19157i) q^{86} +(-1.65350 + 1.43980i) q^{87} +(6.93337 - 3.54076i) q^{88} -11.0501 q^{89} +(-0.817789 - 4.16308i) q^{90} +(-5.41054 + 5.41054i) q^{91} +(-2.96929 - 1.19755i) q^{92} +(10.0814 - 14.9734i) q^{93} +(-7.30754 - 10.8267i) q^{94} +(0.681416 + 1.18025i) q^{95} +(9.51251 + 2.34779i) q^{96} +(-6.26748 + 10.8556i) q^{97} +(-5.02756 + 0.353110i) q^{98} +(3.21368 - 7.60637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64}+ \cdots - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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