LMFDB - Embedded newform 462.2.s.a.125.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(125,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 2]))

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

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

chi := DirichletCharacter("462.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.s (of order $10$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			125.3
Character	$\chi$	$=$	462.125
Dual form			462.2.s.a.377.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.63638 - 0.567690i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-3.26960 + 2.37551i) q^{5} +(1.42111 - 0.990177i) q^{6} +(1.78115 + 1.95640i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.35546 + 1.85791i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.63638 - 0.567690i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-3.26960 + 2.37551i) q^{5} +(1.42111 - 0.990177i) q^{6} +(1.78115 + 1.95640i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.35546 + 1.85791i) q^{9} -4.04145i q^{10} +(-3.29913 - 0.340193i) q^{11} +(-0.0342372 + 1.73171i) q^{12} +(0.442983 - 0.609714i) q^{13} +(-2.62970 + 0.291040i) q^{14} +(6.69885 - 2.03110i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.169874 + 0.123420i) q^{17} +(-2.88758 + 0.813552i) q^{18} +(-4.28096 - 1.39097i) q^{19} +(3.26960 + 2.37551i) q^{20} +(-1.80401 - 4.21255i) q^{21} +(2.21440 - 2.46909i) q^{22} -3.57303i q^{23} +(-1.38086 - 1.04557i) q^{24} +(3.50219 - 10.7786i) q^{25} +(0.232890 + 0.716762i) q^{26} +(-2.79970 - 4.37741i) q^{27} +(1.31024 - 2.29854i) q^{28} +(3.08562 - 1.00258i) q^{29} +(-2.29429 + 6.61333i) q^{30} +(1.09670 - 1.50948i) q^{31} -1.00000i q^{32} +(5.20550 + 2.42957i) q^{33} -0.209975i q^{34} +(-10.4711 - 2.16551i) q^{35} +(1.03910 - 2.81430i) q^{36} +(-2.05160 - 6.31417i) q^{37} +(3.64161 - 2.64578i) q^{38} +(-1.07102 + 0.746244i) q^{39} +(-3.84365 + 1.24888i) q^{40} +(0.333365 - 1.02599i) q^{41} +(4.46839 + 1.01660i) q^{42} -8.73301 q^{43} +(0.695945 + 3.24279i) q^{44} +(-12.1149 - 0.479227i) q^{45} +(2.89064 + 2.10017i) q^{46} +(3.76619 - 11.5911i) q^{47} +(1.65754 - 0.502567i) q^{48} +(-0.654994 + 6.96929i) q^{49} +(6.66156 + 9.16885i) q^{50} +(0.348042 - 0.105527i) q^{51} +(-0.716762 - 0.232890i) q^{52} +(-4.39833 + 6.05378i) q^{53} +(5.18702 + 0.307974i) q^{54} +(11.5950 - 6.72481i) q^{55} +(1.08942 + 2.41105i) q^{56} +(6.21563 + 4.70641i) q^{57} +(-1.00258 + 3.08562i) q^{58} +(1.60917 + 4.95252i) q^{59} +(-4.00175 - 5.74334i) q^{60} +(4.82176 + 6.63658i) q^{61} +(0.576570 + 1.77450i) q^{62} +(0.560613 + 7.91743i) q^{63} +(0.809017 + 0.587785i) q^{64} +3.04583i q^{65} +(-5.02528 + 2.78327i) q^{66} +10.5693 q^{67} +(0.169874 + 0.123420i) q^{68} +(-2.02837 + 5.84682i) q^{69} +(7.90669 - 7.19844i) q^{70} +(-5.35632 - 7.37234i) q^{71} +(1.66605 + 2.49485i) q^{72} +(-9.89230 + 3.21420i) q^{73} +(6.31417 + 2.05160i) q^{74} +(-11.8498 + 15.6497i) q^{75} +4.50127i q^{76} +(-5.21070 - 7.06035i) q^{77} +(0.0258028 - 1.30510i) q^{78} +(-1.07577 - 0.781596i) q^{79} +(1.24888 - 3.84365i) q^{80} +(2.09635 + 8.75245i) q^{81} +(0.634098 + 0.872761i) q^{82} +(11.7821 - 8.56017i) q^{83} +(-3.44890 + 3.01746i) q^{84} +(0.262233 - 0.807071i) q^{85} +(5.13314 - 7.06515i) q^{86} +(-5.61840 - 0.111080i) q^{87} +(-3.03254 - 1.34303i) q^{88} -5.55137 q^{89} +(7.50865 - 9.51946i) q^{90} +(1.98186 - 0.219342i) q^{91} +(-3.39815 + 1.10413i) q^{92} +(-2.65153 + 1.84749i) q^{93} +(7.16372 + 9.86001i) q^{94} +(17.3013 - 5.62153i) q^{95} +(-0.567690 + 1.63638i) q^{96} +(2.66417 - 3.66691i) q^{97} +(-5.25328 - 4.62635i) q^{98} +(-7.13891 - 6.93080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) $ 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9	$ 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) $ 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9 + 12 * q^15 - 32 * q^16 - 16 * q^18 - 20 * q^21 - 36 * q^25 - 6 * q^28 + 8 * q^36 - 16 * q^37 + 60 * q^39 + 4 * q^42 - 64 * q^43 - 8 * q^46 - 40 * q^49 - 28 * q^51 + 88 * q^57 + 92 * q^58 + 8 * q^60 - 42 * q^63 + 32 * q^64 - 64 * q^67 - 26 * q^70 - 24 * q^72 - 64 * q^78 + 136 * q^79 - 116 * q^81 - 28 * q^85 - 40 * q^91 - 76 * q^93 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.63638	−	0.567690i	−0.944762	−	0.327756i
$3$	−1.63638	−	0.567690i	−0.944762	−	0.327756i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−3.26960	+	2.37551i	−1.46221	+	1.06236i	−0.479430	+	0.877580i	$0.659157\pi$
$5$	−3.26960	+	2.37551i	−1.46221	+	1.06236i	−0.982780	+	0.184778i	$0.940843\pi$
$6$	1.42111	−	0.990177i	0.580165	−	0.404238i
$7$	1.78115	+	1.95640i	0.673212	+	0.739449i
$7$	1.78115	+	1.95640i	0.673212	+	0.739449i
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	2.35546	+	1.85791i	0.785152	+	0.619303i
$10$		−	4.04145i		−	1.27802i
$11$	−3.29913	−	0.340193i	−0.994726	−	0.102572i
$11$	−3.29913	−	0.340193i	−0.994726	−	0.102572i
$12$	−0.0342372	+	1.73171i	−0.00988343	+	0.499902i
$13$	0.442983	−	0.609714i	0.122861	−	0.169104i	−0.743156	−	0.669118i	$-0.766672\pi$
$13$	0.442983	−	0.609714i	0.122861	−	0.169104i	0.866017	+	0.500014i	$0.166672\pi$
$14$	−2.62970	+	0.291040i	−0.702816	+	0.0777837i
$15$	6.69885	−	2.03110i	1.72964	−	0.524428i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.169874	+	0.123420i	−0.0412004	+	0.0299338i	−0.608195	−	0.793788i	$-0.708106\pi$
$17$	−0.169874	+	0.123420i	−0.0412004	+	0.0299338i	0.566994	+	0.823722i	$0.308106\pi$
$18$	−2.88758	+	0.813552i	−0.680610	+	0.191756i
$19$	−4.28096	−	1.39097i	−0.982120	−	0.319110i	−0.226421	−	0.974029i	$-0.572703\pi$
$19$	−4.28096	−	1.39097i	−0.982120	−	0.319110i	−0.755699	+	0.654919i	$0.772703\pi$
$20$	3.26960	+	2.37551i	0.731105	+	0.531179i
$21$	−1.80401	−	4.21255i	−0.393667	−	0.919253i
$22$	2.21440	−	2.46909i	0.472112	−	0.526412i
$23$		−	3.57303i		−	0.745028i	−0.928027	−	0.372514i	$-0.878496\pi$
$23$		−	3.57303i		−	0.745028i	0.928027	−	0.372514i	$-0.121504\pi$
$24$	−1.38086	−	1.04557i	−0.281867	−	0.213427i
$25$	3.50219	−	10.7786i	0.700438	−	2.15573i
$26$	0.232890	+	0.716762i	0.0456735	+	0.140569i
$27$	−2.79970	−	4.37741i	−0.538802	−	0.842433i
$28$	1.31024	−	2.29854i	0.247612	−	0.434383i
$29$	3.08562	−	1.00258i	0.572986	−	0.186174i	−0.00816997	−	0.999967i	$-0.502601\pi$
$29$	3.08562	−	1.00258i	0.572986	−	0.186174i	0.581156	+	0.813792i	$0.302601\pi$
$30$	−2.29429	+	6.61333i	−0.418878	+	1.20742i
$31$	1.09670	−	1.50948i	0.196973	−	0.271110i	−0.699093	−	0.715031i	$-0.746413\pi$
$31$	1.09670	−	1.50948i	0.196973	−	0.271110i	0.896066	+	0.443920i	$0.146413\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.20550	+	2.42957i	0.906161	+	0.422934i
$34$		−	0.209975i		−	0.0360105i
$35$	−10.4711	−	2.16551i	−1.76994	−	0.366038i
$36$	1.03910	−	2.81430i	0.173183	−	0.469050i
$37$	−2.05160	−	6.31417i	−0.337281	−	1.03804i	−0.965588	−	0.260078i	$-0.916252\pi$
$37$	−2.05160	−	6.31417i	−0.337281	−	1.03804i	0.628307	−	0.777966i	$-0.283748\pi$
$38$	3.64161	−	2.64578i	0.590746	−	0.429202i
$39$	−1.07102	+	0.746244i	−0.171500	+	0.119495i
$40$	−3.84365	+	1.24888i	−0.607734	+	0.197465i
$41$	0.333365	−	1.02599i	0.0520629	−	0.160233i	−0.921645	−	0.388035i	$-0.873154\pi$
$41$	0.333365	−	1.02599i	0.0520629	−	0.160233i	0.973707	+	0.227802i	$0.0731539\pi$
$42$	4.46839	+	1.01660i	0.689488	+	0.156865i
$43$	−8.73301			−1.33177			−0.665886	−	0.746054i	$-0.731946\pi$
$43$	−8.73301			−1.33177			−0.665886	+	0.746054i	$0.731946\pi$
$44$	0.695945	+	3.24279i	0.104918	+	0.488868i
$45$	−12.1149	−	0.479227i	−1.80598	−	0.0714389i
$46$	2.89064	+	2.10017i	0.426201	+	0.309654i
$47$	3.76619	−	11.5911i	0.549355	−	1.69074i	−0.161048	−	0.986947i	$-0.551487\pi$
$47$	3.76619	−	11.5911i	0.549355	−	1.69074i	0.710403	−	0.703795i	$-0.248513\pi$
$48$	1.65754	−	0.502567i	0.239245	−	0.0725393i
$49$	−0.654994	+	6.96929i	−0.0935706	+	0.995613i
$50$	6.66156	+	9.16885i	0.942087	+	1.29667i
$51$	0.348042	−	0.105527i	0.0487356	−	0.0147767i
$52$	−0.716762	−	0.232890i	−0.0993970	−	0.0322960i
$53$	−4.39833	+	6.05378i	−0.604157	+	0.831551i	−0.996081	−	0.0884470i	$-0.971810\pi$
$53$	−4.39833	+	6.05378i	−0.604157	+	0.831551i	0.391924	+	0.919998i	$0.371810\pi$
$54$	5.18702	+	0.307974i	0.705864	+	0.0419100i
$55$	11.5950	−	6.72481i	1.56347	−	0.906773i
$56$	1.08942	+	2.41105i	0.145579	+	0.322190i
$57$	6.21563	+	4.70641i	0.823280	+	0.623379i
$58$	−1.00258	+	3.08562i	−0.131645	+	0.405162i
$59$	1.60917	+	4.95252i	0.209496	+	0.644763i	0.999499	+	0.0316594i	$0.0100792\pi$
$59$	1.60917	+	4.95252i	0.209496	+	0.644763i	−0.790003	+	0.613104i	$0.789921\pi$
$60$	−4.00175	−	5.74334i	−0.516624	−	0.741462i
$61$	4.82176	+	6.63658i	0.617363	+	0.849727i	0.997158	−	0.0753436i	$-0.0240054\pi$
$61$	4.82176	+	6.63658i	0.617363	+	0.849727i	−0.379795	+	0.925071i	$0.624005\pi$
$62$	0.576570	+	1.77450i	0.0732244	+	0.225362i
$63$	0.560613	+	7.91743i	0.0706306	+	0.997503i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$			3.04583i			0.377789i
$66$	−5.02528	+	2.78327i	−0.618569	+	0.342597i
$67$	10.5693			1.29125			0.645625	−	0.763654i	$-0.276597\pi$
$67$	10.5693			1.29125			0.645625	+	0.763654i	$0.276597\pi$
$68$	0.169874	+	0.123420i	0.0206002	+	0.0149669i
$69$	−2.02837	+	5.84682i	−0.244187	+	0.703874i
$70$	7.90669	−	7.19844i	0.945030	−	0.860378i
$71$	−5.35632	−	7.37234i	−0.635678	−	0.874936i	0.362697	−	0.931907i	$-0.381856\pi$
$71$	−5.35632	−	7.37234i	−0.635678	−	0.874936i	−0.998376	+	0.0569707i	$0.981856\pi$
$72$	1.66605	+	2.49485i	0.196345	+	0.294021i
$73$	−9.89230	+	3.21420i	−1.15781	+	0.376194i	−0.824078	−	0.566476i	$-0.808307\pi$
$73$	−9.89230	+	3.21420i	−1.15781	+	0.376194i	−0.333727	+	0.942670i	$0.608307\pi$
$74$	6.31417	+	2.05160i	0.734008	+	0.238494i
$75$	−11.8498	+	15.6497i	−1.36830	+	1.80708i
$76$			4.50127i			0.516331i
$77$	−5.21070	−	7.06035i	−0.593815	−	0.804602i
$78$	0.0258028	−	1.30510i	0.00292159	−	0.147774i
$79$	−1.07577	−	0.781596i	−0.121034	−	0.0879364i	0.525621	−	0.850719i	$-0.323833\pi$
$79$	−1.07577	−	0.781596i	−0.121034	−	0.0879364i	−0.646656	+	0.762782i	$0.723833\pi$
$80$	1.24888	−	3.84365i	0.139629	−	0.429733i
$81$	2.09635	+	8.75245i	0.232927	+	0.972494i
$82$	0.634098	+	0.872761i	0.0700244	+	0.0963803i
$83$	11.7821	−	8.56017i	1.29325	−	0.939601i	0.293384	−	0.955995i	$-0.405218\pi$
$83$	11.7821	−	8.56017i	1.29325	−	0.939601i	0.999866	+	0.0163936i	$0.00521847\pi$
$84$	−3.44890	+	3.01746i	−0.376306	+	0.329232i
$85$	0.262233	−	0.807071i	0.0284432	−	0.0875391i
$86$	5.13314	−	7.06515i	0.553520	−	0.761855i
$87$	−5.61840	−	0.111080i	−0.602355	−	0.0119090i
$88$	−3.03254	−	1.34303i	−0.323269	−	0.143168i
$89$	−5.55137			−0.588444			−0.294222	−	0.955737i	$-0.595060\pi$
$89$	−5.55137			−0.588444			−0.294222	+	0.955737i	$0.595060\pi$
$90$	7.50865	−	9.51946i	0.791481	−	1.00344i
$91$	1.98186	−	0.219342i	0.207756	−	0.0229932i
$92$	−3.39815	+	1.10413i	−0.354282	+	0.115113i
$93$	−2.65153	+	1.84749i	−0.274951	+	0.191576i
$94$	7.16372	+	9.86001i	0.738881	+	1.01698i
$95$	17.3013	−	5.62153i	1.77508	−	0.576757i
$96$	−0.567690	+	1.63638i	−0.0579396	+	0.167012i
$97$	2.66417	−	3.66691i	0.270505	−	0.372318i	−0.652055	−	0.758172i	$-0.726093\pi$
$97$	2.66417	−	3.66691i	0.270505	−	0.372318i	0.922560	+	0.385853i	$0.126093\pi$
$98$	−5.25328	−	4.62635i	−0.530661	−	0.467332i
$99$	−7.13891	−	6.93080i	−0.717488	−	0.696571i
$100$	−11.3333			−1.13333
$101$	6.60680	+	4.80012i	0.657401	+	0.477630i	0.865784	−	0.500418i	$-0.166820\pi$
$101$	6.60680	+	4.80012i	0.657401	+	0.477630i	−0.208383	+	0.978047i	$0.566820\pi$
$102$	−0.119201	+	0.343599i	−0.0118026	+	0.0340213i
$103$	−12.9315	+	4.20169i	−1.27418	+	0.414005i	−0.866525	−	0.499133i	$-0.833652\pi$
$103$	−12.9315	+	4.20169i	−1.27418	+	0.414005i	−0.407650	+	0.913138i	$0.633652\pi$
$104$	0.609714	−	0.442983i	0.0597874	−	0.0434381i
$105$	15.9053	+	9.48793i	1.55220	+	0.925927i
$106$	−2.31234	−	7.11664i	−0.224594	−	0.691230i
$107$	−6.98309	−	2.26894i	−0.675081	−	0.219347i	−0.0486404	−	0.998816i	$-0.515489\pi$
$107$	−6.98309	−	2.26894i	−0.675081	−	0.219347i	−0.626440	+	0.779469i	$0.715489\pi$
$108$	−3.29801	+	4.01536i	−0.317351	+	0.386378i
$109$	−12.4326			−1.19082			−0.595412	−	0.803421i	$-0.703011\pi$
$109$	−12.4326			−1.19082			−0.595412	+	0.803421i	$0.703011\pi$
$110$	−1.37487	+	13.3333i	−0.131089	+	1.27128i
$111$	−0.227305	+	11.4970i	−0.0215748	+	1.09125i
$112$	−2.59092	−	0.535825i	−0.244819	−	0.0506307i
$113$	−14.8648	−	4.82985i	−1.39836	−	0.454354i	−0.489699	−	0.871892i	$-0.662893\pi$
$113$	−14.8648	−	4.82985i	−1.39836	−	0.454354i	−0.908660	+	0.417538i	$0.862893\pi$
$114$	−7.46102	+	2.26219i	−0.698789	+	0.211874i
$115$	8.48774	+	11.6824i	0.791486	+	1.08939i
$116$	−1.90702	−	2.62479i	−0.177062	−	0.243706i
$117$	2.17622	−	0.613132i	0.201192	−	0.0566841i
$118$	−4.95252	−	1.60917i	−0.455916	−	0.148136i
$119$	−0.544030	−	0.112510i	−0.0498712	−	0.0103138i
$120$	6.99863	+	0.138368i	0.638885	+	0.0126312i
$121$	10.7685	+	2.24468i	0.978958	+	0.204062i
$122$	−8.20327			−0.742689
$123$	−1.12796	+	1.48966i	−0.101704	+	0.134318i
$124$	−1.77450	−	0.576570i	−0.159355	−	0.0517775i
$125$	7.90954	+	24.3431i	0.707451	+	2.17731i
$126$	−6.73486	−	4.20020i	−0.599989	−	0.374184i
$127$	−7.91450	+	5.75022i	−0.702298	+	0.510249i	−0.880680	−	0.473712i	$-0.842914\pi$
$127$	−7.91450	+	5.75022i	−0.702298	+	0.510249i	0.178382	+	0.983961i	$0.442914\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	14.2905	+	4.95764i	1.25821	+	0.436496i
$130$	−2.46413	−	1.79029i	−0.216118	−	0.157019i
$131$	−13.0907			−1.14374			−0.571868	−	0.820346i	$-0.693781\pi$
$131$	−13.0907			−1.14374			−0.571868	+	0.820346i	$0.693781\pi$
$132$	0.702070	−	5.70150i	0.0611073	−	0.496252i
$133$	−4.90376	−	10.8528i	−0.425210	−	0.941057i
$134$	−6.21250	+	8.55078i	−0.536678	+	0.738675i
$135$	19.5524	+	7.66169i	1.68281	+	0.659413i
$136$	−0.199698	+	0.0648859i	−0.0171240	+	0.00556392i
$137$	5.71572	+	7.86701i	0.488327	+	0.672124i	0.980078	−	0.198612i	$-0.0636432\pi$
$137$	5.71572	+	7.86701i	0.488327	+	0.672124i	−0.491752	+	0.870735i	$0.663643\pi$
$138$	−3.53793	−	5.07766i	−0.301168	−	0.432239i
$139$	20.4721	−	6.65179i	1.73642	−	0.564197i	0.742068	−	0.670325i	$-0.233845\pi$
$139$	20.4721	−	6.65179i	1.73642	−	0.564197i	0.994353	+	0.106128i	$0.0338452\pi$
$140$	1.17622	+	10.6278i	0.0994090	+	0.898212i
$141$	−12.7431	+	16.8294i	−1.07316	+	1.41729i
$142$	9.11272			0.764722
$143$	−1.66888	+	1.86083i	−0.139559	+	0.155610i
$144$	−2.99766	−	0.118578i	−0.249805	−	0.00988150i
$145$	−7.70713	+	10.6080i	−0.640042	+	0.880943i
$146$	3.21420	−	9.89230i	0.266009	−	0.818692i
$147$	5.02821	−	11.0325i	0.414720	−	0.909949i
$148$	−5.37116	+	3.90237i	−0.441506	+	0.320773i
$149$	−5.05977	−	6.96418i	−0.414513	−	0.570528i	0.549799	−	0.835297i	$-0.314704\pi$
$149$	−5.05977	−	6.96418i	−0.414513	−	0.570528i	−0.964312	+	0.264769i	$0.914704\pi$
$150$	−5.69575	−	18.7854i	−0.465056	−	1.53382i
$151$	7.18772	−	22.1215i	0.584928	−	1.80022i	−0.0146307	−	0.999893i	$-0.504657\pi$
$151$	7.18772	−	22.1215i	0.584928	−	1.80022i	0.599559	−	0.800331i	$-0.295343\pi$
$152$	−3.64161	−	2.64578i	−0.295373	−	0.214601i
$153$	−0.629434	−	0.0248984i	−0.0508867	−	0.00201292i
$154$	8.77472	−	0.0655745i	0.707087	−	0.00528414i
$155$			7.54061i			0.605677i
$156$	1.04068	+	0.787994i	0.0833213	+	0.0630900i
$157$	−15.6548	−	5.08655i	−1.24939	−	0.405951i	−0.391687	−	0.920098i	$-0.628108\pi$
$157$	−15.6548	−	5.08655i	−1.24939	−	0.405951i	−0.857702	+	0.514147i	$0.828108\pi$
$158$	1.26465	−	0.410909i	0.100610	−	0.0326902i
$159$	10.6340	−	7.40938i	0.843330	−	0.587602i
$160$	2.37551	+	3.26960i	0.187800	+	0.258485i
$161$	6.99027	−	6.36410i	0.550910	−	0.501562i
$162$	−8.31308	−	3.44858i	−0.653137	−	0.270946i
$163$	−12.1076	−	8.79666i	−0.948338	−	0.689008i	0.00207519	−	0.999998i	$-0.499339\pi$
$163$	−12.1076	−	8.79666i	−0.948338	−	0.689008i	−0.950413	+	0.310990i	$0.899339\pi$
$164$	−1.07879			−0.0842395
$165$	−22.7914	+	4.42196i	−1.77430	+	0.344249i
$166$			14.5634i			1.13034i
$167$	−10.1342	−	7.36290i	−0.784205	−	0.569758i	0.122033	−	0.992526i	$-0.461059\pi$
$167$	−10.1342	−	7.36290i	−0.784205	−	0.569758i	−0.906238	+	0.422768i	$0.861059\pi$
$168$	−0.413964	−	4.56384i	−0.0319380	−	0.352108i
$169$	3.84170	+	11.8235i	0.295516	+	0.909504i
$170$	0.498797	+	0.686536i	0.0382560	+	0.0526549i
$171$	−7.49933	−	11.2300i	−0.573488	−	0.858780i
$172$	2.69865	+	8.30559i	0.205770	+	0.633295i
$173$	−1.48178	+	4.56044i	−0.112657	+	0.346724i	−0.991451	−	0.130478i	$-0.958349\pi$
$173$	−1.48178	+	4.56044i	−0.112657	+	0.346724i	0.878794	+	0.477202i	$0.158349\pi$
$174$	3.39228	−	4.48009i	0.257168	−	0.339635i
$175$	27.3252	−	12.3467i	2.06559	−	0.933323i
$176$	2.86901	−	1.66396i	0.216260	−	0.125426i
$177$	0.178286	−	9.01769i	0.0134008	−	0.677811i
$178$	3.26301	−	4.49115i	0.244573	−	0.336626i
$179$	10.4951	+	3.41007i	0.784443	+	0.254881i	0.673736	−	0.738972i	$-0.264689\pi$
$179$	10.4951	+	3.41007i	0.784443	+	0.254881i	0.110707	+	0.993853i	$0.464689\pi$
$180$	3.28793	+	11.6700i	0.245068	+	0.869832i
$181$	1.42845	+	1.96610i	0.106176	+	0.146139i	0.858799	−	0.512314i	$-0.171211\pi$
$181$	1.42845	+	1.96610i	0.106176	+	0.146139i	−0.752622	+	0.658452i	$0.771211\pi$
$182$	−0.987459	+	1.73229i	−0.0731954	+	0.128406i
$183$	−4.12269	−	13.5972i	−0.304758	−	1.00513i
$184$	1.10413	−	3.39815i	0.0813972	−	0.250515i
$185$	21.7073	+	15.7712i	1.59595	+	1.15953i
$186$	0.0638804	−	3.23106i	0.00468394	−	0.236913i
$187$	0.602422	−	0.349390i	0.0440535	−	0.0255499i
$188$	−12.1876			−0.888875
$189$	3.57727	−	13.2742i	0.260208	−	0.965553i
$190$	−5.62153	+	17.3013i	−0.407829	+	1.25517i
$191$	−17.9262	+	5.82457i	−1.29709	+	0.421451i	−0.874569	−	0.484901i	$-0.838856\pi$
$191$	−17.9262	+	5.82457i	−1.29709	+	0.421451i	−0.422523	+	0.906352i	$0.638856\pi$
$192$	−0.990177	−	1.42111i	−0.0714598	−	0.102560i
$193$	−6.68286	+	4.85538i	−0.481043	+	0.349498i	−0.801729	−	0.597687i	$-0.796086\pi$
$193$	−6.68286	+	4.85538i	−0.481043	+	0.349498i	0.320686	+	0.947185i	$0.396086\pi$
$194$	1.40064	+	4.31071i	0.100560	+	0.309491i
$195$	1.72909	−	4.98413i	0.123823	−	0.356921i
$196$	6.83059	−	1.53069i	0.487899	−	0.109335i
$197$		−	21.2226i		−	1.51205i	−0.654543	−	0.756025i	$-0.727139\pi$
$197$		−	21.2226i		−	1.51205i	0.654543	−	0.756025i	$-0.272861\pi$
$198$	9.80328	−	1.70168i	0.696689	−	0.120933i
$199$		−	1.36947i		−	0.0970789i	−0.998821	−	0.0485395i	$-0.984543\pi$
$199$		−	1.36947i		−	0.0970789i	0.998821	−	0.0485395i	$-0.0154567\pi$
$200$	6.66156	−	9.16885i	0.471043	−	0.648336i
$201$	−17.2954	−	6.00011i	−1.21992	−	0.423215i
$202$	−7.76676	+	2.52357i	−0.546467	+	0.177558i
$203$	7.45741	+	4.25096i	0.523408	+	0.298359i
$204$	−0.207913	−	0.298398i	−0.0145568	−	0.0208920i
$205$	1.34728	+	4.14650i	0.0940980	+	0.289604i
$206$	4.20169	−	12.9315i	0.292746	−	0.900978i
$207$	6.63836	−	8.41611i	0.461398	−	0.584960i
$208$			0.753648i			0.0522561i
$209$	13.6503	+	6.04535i	0.944208	+	0.418165i
$210$	−17.0248	+	7.29081i	−1.17482	+	0.503113i
$211$	−5.78113	−	4.20023i	−0.397989	−	0.289156i	0.370732	−	0.928740i	$-0.379107\pi$
$211$	−5.78113	−	4.20023i	−0.397989	−	0.289156i	−0.768721	+	0.639584i	$0.779107\pi$
$212$	7.11664	+	2.31234i	0.488773	+	0.158812i
$213$	4.57975	+	15.1047i	0.313799	+	1.03495i
$214$	5.94017	−	4.31579i	0.406062	−	0.295021i
$215$	28.5535	−	20.7453i	1.94733	−	1.41482i
$216$	−1.30998	−	5.02832i	−0.0891326	−	0.342134i
$217$	4.90653	−	0.543027i	0.333077	−	0.0368631i
$218$	7.30768	−	10.0582i	0.494939	−	0.681224i
$219$	18.0122	+	0.356114i	1.21715	+	0.0240640i
$220$	−9.97872	−	8.94940i	−0.672765	−	0.603368i
$221$			0.158247i			0.0106449i
$222$	−9.16769	−	6.94168i	−0.615295	−	0.465895i
$223$	−16.2558	−	5.28184i	−1.08857	−	0.353698i	−0.290877	−	0.956761i	$-0.593947\pi$
$223$	−16.2558	−	5.28184i	−1.08857	−	0.353698i	−0.797694	+	0.603063i	$0.793947\pi$
$224$	1.95640	−	1.78115i	0.130717	−	0.119008i
$225$	28.2750	−	18.8818i	1.88500	−	1.25879i
$226$	12.6447	−	9.18692i	0.841114	−	0.611105i
$227$	−3.78474	−	11.6482i	−0.251202	−	0.773120i	−0.994554	−	0.104220i	$-0.966765\pi$
$227$	−3.78474	−	11.6482i	−0.251202	−	0.773120i	0.743352	−	0.668900i	$-0.233235\pi$
$228$	2.55533	−	7.36577i	0.169231	−	0.487810i
$229$	0.652859	−	0.898584i	0.0431422	−	0.0593801i	−0.786901	−	0.617079i	$-0.788316\pi$
$229$	0.652859	−	0.898584i	0.0431422	−	0.0593801i	0.830043	+	0.557699i	$0.188316\pi$
$230$	−14.4402			−0.952159
$231$	4.51858	+	14.5115i	0.297301	+	0.954784i
$232$	3.24442			0.213006
$233$	2.59330	−	3.56937i	0.169893	−	0.233838i	−0.715577	−	0.698533i	$-0.753836\pi$
$233$	2.59330	−	3.56937i	0.169893	−	0.233838i	0.885470	+	0.464696i	$0.153836\pi$
$234$	−0.783116	+	2.12099i	−0.0511939	+	0.138653i
$235$	15.2209	+	46.8450i	0.992900	+	3.05583i
$236$	4.21286	−	3.06082i	0.274234	−	0.199243i
$237$	1.31667	+	1.88969i	0.0855268	+	0.122749i
$238$	0.410795	−	0.373998i	0.0266279	−	0.0242427i
$239$	17.3868	+	5.64931i	1.12466	+	0.365423i	0.811543	−	0.584292i	$-0.198628\pi$
$239$	17.3868	+	5.64931i	1.12466	+	0.365423i	0.313114	+	0.949715i	$0.398628\pi$
$240$	−4.22563	+	5.58068i	−0.272763	+	0.360231i
$241$			18.4946i			1.19134i	0.803228	+	0.595672i	$0.203114\pi$
$241$			18.4946i			1.19134i	−0.803228	+	0.595672i	$0.796886\pi$
$242$	−8.14557	+	7.39254i	−0.523617	+	0.475210i
$243$	1.53827	−	15.5124i	0.0986799	−	0.995119i
$244$	4.82176	−	6.63658i	0.308681	−	0.424864i
$245$	−14.4140	−	24.3427i	−0.920877	−	1.55520i
$246$	−0.542165	−	1.78814i	−0.0345672	−	0.114007i
$247$	−2.74449	+	1.99399i	−0.174628	+	0.126874i
$248$	1.50948	−	1.09670i	0.0958520	−	0.0696405i
$249$	−24.1394	+	7.31910i	−1.52977	+	0.463829i
$250$	−24.3431	−	7.90954i	−1.53959	−	0.500243i
$251$	−3.74043	−	2.71758i	−0.236094	−	0.171532i	0.463448	−	0.886124i	$-0.346612\pi$
$251$	−3.74043	−	2.71758i	−0.236094	−	0.171532i	−0.699541	+	0.714592i	$0.746612\pi$
$252$	7.35669	−	2.97980i	0.463428	−	0.187709i
$253$	−1.21552	+	11.7879i	−0.0764190	+	0.741098i
$254$		−	9.78286i		−	0.613831i
$255$	−0.887279	+	1.17180i	−0.0555635	+	0.0733813i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.75229	−	5.39299i	−0.109305	−	0.336406i	0.881412	−	0.472348i	$-0.156594\pi$
$257$	−1.75229	−	5.39299i	−0.109305	−	0.336406i	−0.990717	+	0.135943i	$0.956594\pi$
$258$	−12.4106	+	8.64722i	−0.772648	+	0.538353i
$259$	8.69883	−	15.2602i	0.540519	−	0.948226i
$260$	2.89676	−	0.941214i	0.179649	−	0.0583716i
$261$	9.13075	+	3.37128i	0.565180	+	0.208677i
$262$	7.69450	−	10.5906i	0.475368	−	0.654287i
$263$			12.4117i			0.765339i	0.923885	+	0.382669i	$0.124995\pi$
$263$			12.4117i			0.765339i	−0.923885	+	0.382669i	$0.875005\pi$
$264$	4.19994	+	3.91924i	0.258489	+	0.241213i
$265$		−	30.2417i		−	1.85773i
$266$	11.6625	+	2.41189i	0.715071	+	0.147883i
$267$	9.08413	+	3.15146i	0.555940	+	0.192866i
$268$	−3.26611	−	10.0520i	−0.199509	−	0.614026i
$269$	−8.28375	+	6.01850i	−0.505069	+	0.366954i	−0.810950	−	0.585116i	$-0.801049\pi$
$269$	−8.28375	+	6.01850i	−0.505069	+	0.366954i	0.305881	+	0.952070i	$0.401049\pi$
$270$	−17.6911	+	11.3148i	−1.07664	+	0.688599i
$271$	−20.0560	+	6.51658i	−1.21831	+	0.395854i	−0.846468	−	0.532440i	$-0.821275\pi$
$271$	−20.0560	+	6.51658i	−1.21831	+	0.395854i	−0.371847	+	0.928294i	$0.621275\pi$
$272$	0.0648859	−	0.199698i	0.00393429	−	0.0121085i
$273$	−3.36759	−	0.766159i	−0.203816	−	0.0463701i
$274$	−9.72416			−0.587458
$275$	−15.2210	+	34.3687i	−0.917861	+	2.07251i
$276$	6.18745	+	0.122330i	0.372441	+	0.00736343i
$277$	9.29197	+	6.75101i	0.558300	+	0.405629i	0.830836	−	0.556517i	$-0.187862\pi$
$277$	9.29197	+	6.75101i	0.558300	+	0.405629i	−0.272536	+	0.962146i	$0.587862\pi$
$278$	−6.65179	+	20.4721i	−0.398948	+	1.22783i
$279$	5.38770	−	1.51794i	0.322553	−	0.0908767i
$280$	−9.28942	−	5.29527i	−0.555149	−	0.316453i
$281$	11.7169	+	16.1270i	0.698974	+	0.962056i	0.999964	+	0.00842829i	$0.00268284\pi$
$281$	11.7169	+	16.1270i	0.698974	+	0.962056i	−0.300990	+	0.953627i	$0.597317\pi$
$282$	−6.12511	−	20.2015i	−0.364745	−	1.20298i
$283$	5.95701	+	1.93555i	0.354108	+	0.115057i	0.480669	−	0.876902i	$-0.340394\pi$
$283$	5.95701	+	1.93555i	0.354108	+	0.115057i	−0.126561	+	0.991959i	$0.540394\pi$
$284$	−5.35632	+	7.37234i	−0.317839	+	0.437468i
$285$	−31.5027	−	0.622832i	−1.86606	−	0.0368934i
$286$	−0.524497	−	2.44392i	−0.0310142	−	0.144512i
$287$	2.60102	−	1.17525i	0.153534	−	0.0693730i
$288$	1.85791	−	2.35546i	0.109478	−	0.138797i
$289$	−5.23966	+	16.1260i	−0.308216	+	0.948590i
$290$	−4.05188	−	12.4704i	−0.237934	−	0.732287i
$291$	−6.44125	+	4.48803i	−0.377593	+	0.263093i
$292$	6.11378	+	8.41489i	0.357782	+	0.492444i
$293$	−6.91828	−	21.2923i	−0.404170	−	1.24391i	−0.921586	−	0.388174i	$-0.873106\pi$
$293$	−6.91828	−	21.2923i	−0.404170	−	1.24391i	0.517416	−	0.855734i	$-0.326894\pi$
$294$	5.97001	+	10.5527i	0.348178	+	0.615445i
$295$	−17.0261	−	12.3702i	−0.991297	−	0.720219i
$296$		−	6.63911i		−	0.385891i
$297$	7.74740	+	15.3941i	0.449550	+	0.893255i
$298$	8.60820			0.498659
$299$	−2.17852	−	1.58279i	−0.125987	−	0.0915351i
$300$	18.5456	+	6.43382i	1.07073	+	0.371456i
$301$	−15.5548	−	17.0853i	−0.896565	−	0.984778i
$302$	13.6719	+	18.8177i	0.786727	+	1.08284i
$303$	−8.08623	−	11.6054i	−0.464542	−	0.666714i
$304$	4.28096	−	1.39097i	0.245530	−	0.0797776i
$305$	−31.5305	−	10.2449i	−1.80543	−	0.586620i
$306$	0.390115	−	0.494587i	0.0223014	−	0.0282737i
$307$		−	0.171520i		−	0.00978916i	−0.999988	−	0.00489458i	$-0.998442\pi$
$307$		−	0.171520i		−	0.00978916i	0.999988	−	0.00489458i	$-0.00155800\pi$
$308$	−5.10460	+	7.13744i	−0.290862	+	0.406693i
$309$	23.5460	+	0.465522i	1.33949	+	0.0264826i
$310$	−6.10048	−	4.43226i	−0.346484	−	0.251735i
$311$	−5.00394	+	15.4005i	−0.283748	+	0.873285i	0.703024	+	0.711166i	$0.251833\pi$
$311$	−5.00394	+	15.4005i	−0.283748	+	0.873285i	−0.986771	+	0.162119i	$0.948167\pi$
$312$	−1.24920	+	0.378759i	−0.0707220	+	0.0214430i
$313$	−7.67181	−	10.5593i	−0.433636	−	0.596849i	0.535147	−	0.844759i	$-0.320256\pi$
$313$	−7.67181	−	10.5593i	−0.433636	−	0.596849i	−0.968783	+	0.247910i	$0.920256\pi$
$314$	13.3168	−	9.67520i	0.751509	−	0.546003i
$315$	−20.6409	−	24.5551i	−1.16298	−	1.38352i
$316$	−0.410909	+	1.26465i	−0.0231155	+	0.0711421i
$317$	9.34020	−	12.8557i	0.524598	−	0.722047i	−0.461697	−	0.887038i	$-0.652759\pi$
$317$	9.34020	−	12.8557i	0.524598	−	0.722047i	0.986295	+	0.164990i	$0.0527593\pi$
$318$	−0.256193	+	12.9582i	−0.0143666	+	0.726660i
$319$	−10.5210	+	2.25794i	−0.589060	+	0.126420i
$320$	−4.04145			−0.225924
$321$	10.1389	+	7.67708i	0.565899	+	0.428493i
$322$	1.03989	+	9.39597i	0.0579510	+	0.523617i
$323$	0.898896	−	0.292069i	0.0500159	−	0.0162512i
$324$	7.67627	−	4.69840i	0.426459	−	0.261022i
$325$	−5.02047	−	6.91009i	−0.278486	−	0.383303i
$326$	14.2333	−	4.62468i	0.788310	−	0.256137i
$327$	20.3444	+	7.05784i	1.12505	+	0.390300i
$328$	0.634098	−	0.872761i	0.0350122	−	0.0481902i
$329$	29.3851	−	13.2774i	1.62005	−	0.732008i
$330$	9.81898	−	21.0378i	0.540517	−	1.15809i
$331$	−3.75173			−0.206214			−0.103107	−	0.994670i	$-0.532878\pi$
$331$	−3.75173			−0.206214			−0.103107	+	0.994670i	$0.532878\pi$
$332$	−11.7821	−	8.56017i	−0.646625	−	0.469801i
$333$	6.89871	−	18.6844i	0.378047	−	1.02390i
$334$	11.9134	−	3.87091i	0.651874	−	0.211807i
$335$	−34.5575	+	25.1075i	−1.88808	+	1.37177i
$336$	3.93555	+	2.34765i	0.214702	+	0.128075i
$337$	1.70064	+	5.23404i	0.0926400	+	0.285116i	0.986631	−	0.162967i	$-0.0521066\pi$
$337$	1.70064	+	5.23404i	0.0926400	+	0.285116i	−0.893991	+	0.448084i	$0.852107\pi$
$338$	−11.8235	−	3.84170i	−0.643116	−	0.208961i
$339$	21.5825	+	16.3420i	1.17220	+	0.887577i
$340$	−0.848605			−0.0460220
$341$	−4.13167	+	4.60688i	−0.223743	+	0.249476i
$342$	13.4933	+	0.533752i	0.729632	+	0.0288620i
$343$	−14.8014	+	11.1319i	−0.799198	+	0.601068i
$344$	−8.30559	−	2.69865i	−0.447807	−	0.145501i
$345$	−7.25717	−	23.9352i	−0.390713	−	1.28863i
$346$	−2.81851	−	3.87934i	−0.151524	−	0.208555i
$347$	2.53612	+	3.49067i	0.136146	+	0.187389i	0.871646	−	0.490136i	$-0.163053\pi$
$347$	2.53612	+	3.49067i	0.136146	+	0.187389i	−0.735500	+	0.677525i	$0.763053\pi$
$348$	1.63054	+	5.37774i	0.0874060	+	0.288277i
$349$	21.7618	+	7.07085i	1.16489	+	0.378494i	0.826731	−	0.562597i	$-0.190198\pi$
$349$	21.7618	+	7.07085i	1.16489	+	0.378494i	0.338154	+	0.941091i	$0.390198\pi$
$350$	−6.07268	+	29.3638i	−0.324598	+	1.56956i
$351$	−3.90919	−	0.232104i	−0.208657	−	0.0123888i
$352$	−0.340193	+	3.29913i	−0.0181324	+	0.175844i
$353$	−13.4179			−0.714164			−0.357082	−	0.934073i	$-0.616228\pi$
$353$	−13.4179			−0.714164			−0.357082	+	0.934073i	$0.616228\pi$
$354$	7.19067	+	5.44470i	0.382180	+	0.289383i
$355$	35.0261	+	11.3807i	1.85899	+	0.604023i
$356$	1.71547	+	5.27966i	0.0909196	+	0.279822i
$357$	0.826367	+	0.492949i	0.0437360	+	0.0260896i
$358$	−8.92769	+	6.48634i	−0.471843	+	0.342814i
$359$	11.0362	−	3.58589i	0.582470	−	0.189256i	−0.00293703	−	0.999996i	$-0.500935\pi$
$359$	11.0362	−	3.58589i	0.582470	−	0.189256i	0.585407	+	0.810740i	$0.300935\pi$
$360$	−11.3738	−	4.19947i	−0.599454	−	0.221332i
$361$	1.02053	+	0.741459i	0.0537121	+	0.0390241i
$362$	−2.43023			−0.127730
$363$	−16.3471	−	9.78634i	−0.858000	−	0.513650i
$364$	−0.821036	−	1.81708i	−0.0430340	−	0.0952411i
$365$	24.7085	−	34.0084i	1.29330	−	1.78008i
$366$	13.4236	+	4.65691i	0.701664	+	0.243421i
$367$	−19.6124	+	6.37245i	−1.02376	+	0.332639i	−0.772319	−	0.635234i	$-0.780904\pi$
$367$	−19.6124	+	6.37245i	−1.02376	+	0.332639i	−0.251438	+	0.967873i	$0.580904\pi$
$368$	2.10017	+	2.89064i	0.109479	+	0.150685i
$369$	2.69143	−	1.79732i	0.140110	−	0.0935646i
$370$	−25.5184	+	8.29144i	−1.32664	+	0.431051i
$371$	−19.6777	+	2.17782i	−1.02162	+	0.113067i
$372$	2.57643	+	1.95085i	0.133582	+	0.101147i
$373$	2.30251			0.119220			0.0596098	−	0.998222i	$-0.481014\pi$
$373$	2.30251			0.119220			0.0596098	+	0.998222i	$0.481014\pi$
$374$	−0.0714321	+	0.692736i	−0.00369367	+	0.0358205i
$375$	0.876329	−	44.3246i	0.0452534	−	2.28891i
$376$	7.16372	−	9.86001i	0.369441	−	0.508491i
$377$	0.755592	−	2.32547i	0.0389150	−	0.119768i
$378$	8.63635	+	10.6964i	0.444206	+	0.550165i
$379$	−23.6432	+	17.1778i	−1.21447	+	0.882364i	−0.995629	−	0.0933963i	$-0.970228\pi$
$379$	−23.6432	+	17.1778i	−1.21447	+	0.882364i	−0.218841	+	0.975761i	$0.570228\pi$
$380$	−10.6928	−	14.7174i	−0.548529	−	0.754985i
$381$	16.2154	−	4.91654i	0.830742	−	0.251882i
$382$	5.82457	−	17.9262i	0.298011	−	0.917183i
$383$	9.39339	+	6.82469i	0.479980	+	0.348726i	0.801318	−	0.598239i	$-0.204133\pi$
$383$	9.39339	+	6.82469i	0.479980	+	0.348726i	−0.321338	+	0.946965i	$0.604133\pi$
$384$	1.73171	+	0.0342372i	0.0883711	+	0.00174716i
$385$	33.8088	+	10.7065i	1.72306	+	0.545654i
$386$		−	8.26047i		−	0.420447i
$387$	−20.5702	−	16.2251i	−1.04564	−	0.824770i
$388$	−4.31071	−	1.40064i	−0.218843	−	0.0711065i
$389$	−21.9079	+	7.11830i	−1.11077	+	0.360912i	−0.806239	−	0.591589i	$-0.798501\pi$
$389$	−21.9079	+	7.11830i	−1.11077	+	0.360912i	−0.304534	+	0.952501i	$0.598501\pi$
$390$	3.01591	+	4.32846i	0.152717	+	0.219180i
$391$	0.440984	+	0.606963i	0.0223015	+	0.0306954i
$392$	−2.77657	+	6.42578i	−0.140238	+	0.324551i
$393$	21.4212	+	7.43144i	1.08056	+	0.374866i
$394$	17.1695	+	12.4743i	0.864985	+	0.628449i
$395$	5.37404			0.270397
$396$	−4.38554	+	8.93124i	−0.220381	+	0.448812i
$397$			14.4836i			0.726910i	0.931612	+	0.363455i	$0.118403\pi$
$397$			14.4836i			0.726910i	−0.931612	+	0.363455i	$0.881597\pi$
$398$	1.10792	+	0.804952i	0.0555351	+	0.0403486i
$399$	1.86336	+	20.5431i	0.0932849	+	1.02844i
$400$	3.50219	+	10.7786i	0.175109	+	0.538932i
$401$	−3.09923	−	4.26572i	−0.154768	−	0.213020i	0.724591	−	0.689179i	$-0.242029\pi$
$401$	−3.09923	−	4.26572i	−0.154768	−	0.213020i	−0.879359	+	0.476159i	$0.842029\pi$
$402$	15.0202	−	10.4655i	0.749139	−	0.521972i
$403$	−0.434530	−	1.33735i	−0.0216455	−	0.0666180i
$404$	2.52357	−	7.76676i	0.125552	−	0.386411i
$405$	−27.6457	−	23.6371i	−1.37373	−	1.17454i
$406$	−7.82246	+	3.53452i	−0.388222	+	0.175415i
$407$	4.62046	+	21.5292i	0.229028	+	1.06716i
$408$	0.363617	+	0.00718896i	0.0180017	+	0.000355907i
$409$	14.5054	−	19.9649i	0.717245	−	0.987203i	−0.282366	−	0.959307i	$-0.591119\pi$
$409$	14.5054	−	19.9649i	0.717245	−	0.987203i	0.999611	−	0.0278959i	$-0.00888069\pi$
$410$	−4.14650	−	1.34728i	−0.204781	−	0.0665373i
$411$	−4.88704	−	16.1181i	−0.241060	−	0.795049i
$412$	7.99209	+	11.0002i	0.393742	+	0.541939i
$413$	−6.82292	+	11.9694i	−0.335734	+	0.588974i
$414$	2.90684	+	10.3174i	0.142864	+	0.507073i
$415$	−18.1879	+	55.9767i	−0.892811	+	2.74779i
$416$	−0.609714	−	0.442983i	−0.0298937	−	0.0217190i
$417$	−37.2762	−	0.736977i	−1.82542	−	0.0360899i
$418$	−12.9142	+	7.48993i	−0.631655	+	0.366344i
$419$	−33.6612			−1.64446			−0.822228	−	0.569159i	$-0.807269\pi$
$419$	−33.6612			−1.64446			−0.822228	+	0.569159i	$0.807269\pi$
$420$	4.10854	−	18.0588i	0.200476	−	0.881178i
$421$	4.03873	−	12.4299i	0.196836	−	0.605798i	−0.803115	−	0.595824i	$-0.796825\pi$
$421$	4.03873	−	12.4299i	0.196836	−	0.605798i	0.999950	−	0.00997316i	$-0.00317461\pi$
$422$	6.79612	−	2.20819i	0.330830	−	0.107493i
$423$	30.4064	−	20.3052i	1.47841	−	0.987272i
$424$	−6.05378	+	4.39833i	−0.293998	+	0.213602i
$425$	0.735373	+	2.26325i	0.0356708	+	0.109784i
$426$	−14.9118	−	5.17320i	−0.722481	−	0.250642i
$427$	−4.39552	+	21.2540i	−0.212714	+	1.02856i
$428$			7.34246i			0.354911i
$429$	3.78729	−	2.09761i	0.182852	−	0.101273i
$430$			35.2940i			1.70203i
$431$	−8.09674	+	11.1442i	−0.390006	+	0.536798i	−0.958201	−	0.286097i	$-0.907642\pi$
$431$	−8.09674	+	11.1442i	−0.390006	+	0.536798i	0.568194	+	0.822894i	$0.307642\pi$
$432$	4.83798	+	1.89578i	0.232767	+	0.0912106i
$433$	−0.304169	+	0.0988303i	−0.0146174	+	0.00474948i	−0.316317	−	0.948654i	$-0.602446\pi$
$433$	−0.304169	+	0.0988303i	−0.0146174	+	0.00474948i	0.301699	+	0.953403i	$0.402446\pi$
$434$	−2.44467	+	4.28865i	−0.117348	+	0.205862i
$435$	18.6338	−	12.9833i	0.893422	−	0.622504i
$436$	3.84187	+	11.8241i	0.183992	+	0.566270i
$437$	−4.96997	+	15.2960i	−0.237746	+	0.731707i
$438$	−10.8754	+	14.3629i	−0.519647	+	0.686284i
$439$		−	12.3431i		−	0.589104i	−0.955635	−	0.294552i	$-0.904830\pi$
$439$		−	12.3431i		−	0.589104i	0.955635	−	0.294552i	$-0.0951705\pi$
$440$	13.1056	−	2.81263i	0.624783	−	0.134087i
$441$	−14.4911	+	15.1989i	−0.690053	+	0.723759i
$442$	−0.128025	−	0.0930155i	−0.00608952	−	0.00442430i
$443$	26.0214	+	8.45486i	1.23631	+	0.401702i	0.852997	−	0.521915i	$-0.174782\pi$
$443$	26.0214	+	8.45486i	1.23631	+	0.401702i	0.383315	+	0.923617i	$0.374782\pi$
$444$	11.0046	−	3.33660i	0.522254	−	0.158348i
$445$	18.1508	−	13.1873i	0.860429	−	0.625138i
$446$	13.8280	−	10.0467i	0.654776	−	0.475723i
$447$	4.32620	+	14.2684i	0.204622	+	0.674872i
$448$	0.291040	+	2.62970i	0.0137503	+	0.124241i
$449$	−14.0557	+	19.3461i	−0.663331	+	0.912997i	−0.999586	−	0.0287738i	$-0.990840\pi$
$449$	−14.0557	+	19.3461i	−0.663331	+	0.912997i	0.336255	+	0.941771i	$0.390840\pi$
$450$	−1.34388	+	33.9734i	−0.0633512	+	1.60152i
$451$	−1.44885	+	3.27147i	−0.0682237	+	0.154048i
$452$			15.6297i			0.735160i
$453$	−24.3200	+	32.1187i	−1.14265	+	1.50907i
$454$	11.6482	+	3.78474i	0.546679	+	0.177627i
$455$	−5.95886	+	5.42509i	−0.279356	+	0.254332i
$456$	4.45705	+	6.39680i	0.208721	+	0.299557i
$457$	9.34537	−	6.78981i	0.437158	−	0.317614i	−0.347347	−	0.937737i	$-0.612917\pi$
$457$	9.34537	−	6.78981i	0.437158	−	0.317614i	0.784505	+	0.620123i	$0.212917\pi$
$458$	0.343229	+	1.05635i	0.0160380	+	0.0493599i
$459$	1.01586	+	0.398066i	0.0474161	+	0.0185801i
$460$	8.48774	−	11.6824i	0.395743	−	0.544694i
$461$	−9.63919			−0.448942			−0.224471	−	0.974481i	$-0.572065\pi$
$461$	−9.63919			−0.448942			−0.224471	+	0.974481i	$0.572065\pi$
$462$	−14.3960	−	4.87402i	−0.669761	−	0.226760i
$463$	13.7066			0.636998			0.318499	−	0.947923i	$-0.396821\pi$
$463$	13.7066			0.636998			0.318499	+	0.947923i	$0.396821\pi$
$464$	−1.90702	+	2.62479i	−0.0885312	+	0.121853i
$465$	4.28073	−	12.3393i	0.198514	−	0.572220i
$466$	1.36338	+	4.19605i	0.0631574	+	0.194378i
$467$	5.53908	−	4.02438i	0.256318	−	0.186226i	−0.452204	−	0.891914i	$-0.649362\pi$
$467$	5.53908	−	4.02438i	0.256318	−	0.186226i	0.708522	+	0.705688i	$0.249362\pi$
$468$	−1.25561	−	1.88024i	−0.0580407	−	0.0869142i
$469$	18.8256	+	20.6778i	0.869286	+	0.954814i
$470$	−46.8450	−	15.2209i	−2.16080	−	0.702086i
$471$	22.7296	+	17.2106i	1.04732	+	0.793022i
$472$			5.20739i			0.239689i
$473$	28.8114	+	2.97091i	1.32475	+	0.136603i
$474$	−2.30271	−	0.0455263i	−0.105767	−	0.00209109i
$475$	−29.9855	+	41.2715i	−1.37583	+	1.89367i
$476$	0.0611112	+	0.552171i	0.00280103	+	0.0253087i
$477$	−21.6074	+	6.08772i	−0.989337	+	0.278737i
$478$	−14.7901	+	10.7456i	−0.676483	+	0.491493i
$479$	−15.9277	+	11.5722i	−0.727756	+	0.528746i	−0.888853	−	0.458193i	$-0.848497\pi$
$479$	−15.9277	+	11.5722i	−0.727756	+	0.528746i	0.161097	+	0.986939i	$0.448497\pi$
$480$	−2.03110	−	6.69885i	−0.0927066	−	0.305759i
$481$	−4.75866	−	1.54618i	−0.216976	−	0.0704999i
$482$	−14.9625	−	10.8709i	−0.681522	−	0.495155i
$483$	−15.0515	+	6.44577i	−0.684869	+	0.293292i
$484$	−1.19284	−	10.9351i	−0.0542200	−	0.497051i
$485$			18.3181i			0.831781i
$486$	11.6456	+	10.3624i	0.528255	+	0.470049i
$487$	11.2465	−	34.6131i	0.509627	−	1.56847i	−0.283224	−	0.959054i	$-0.591404\pi$
$487$	11.2465	−	34.6131i	0.509627	−	1.56847i	0.792851	−	0.609416i	$-0.208596\pi$
$488$	2.53495	+	7.80177i	0.114752	+	0.353170i
$489$	14.8188	+	21.2680i	0.670128	+	0.961772i
$490$	28.1660	+	2.64713i	1.27241	+	0.119585i
$491$	−0.277777	+	0.0902552i	−0.0125359	+	0.00407316i	−0.315278	−	0.948999i	$-0.602098\pi$
$491$	−0.277777	+	0.0902552i	−0.0125359	+	0.00407316i	0.302742	+	0.953072i	$0.402098\pi$
$492$	1.76531	+	0.612419i	0.0795863	+	0.0276100i
$493$	−0.400427	+	0.551141i	−0.0180343	+	0.0248221i
$494$		−	3.39237i		−	0.152630i
$495$	39.8055	+	5.70243i	1.78913	+	0.256305i
$496$			1.86582i			0.0837777i
$497$	4.88282	−	23.6104i	0.219025	−	1.05907i
$498$	8.26752	−	23.8313i	0.370476	−	1.06790i
$499$	−9.27703	−	28.5518i	−0.415297	−	1.27815i	−0.911985	−	0.410223i	$-0.865451\pi$
$499$	−9.27703	−	28.5518i	−0.415297	−	1.27815i	0.496688	−	0.867929i	$-0.334549\pi$
$500$	20.7074	−	15.0448i	0.926065	−	0.672826i
$501$	12.4035	+	17.8015i	0.554146	+	0.795314i
$502$	4.39713	−	1.42872i	0.196254	−	0.0637667i
$503$	4.60004	−	14.1575i	0.205106	−	0.631251i	−0.794603	−	0.607129i	$-0.792321\pi$
$503$	4.60004	−	14.1575i	0.205106	−	0.631251i	0.999709	−	0.0241216i	$-0.00767889\pi$
$504$	−1.91345	+	7.70316i	−0.0852316	+	0.343126i
$505$	−33.0043			−1.46867
$506$	−8.82213	−	7.91212i	−0.392192	−	0.351737i
$507$	0.425637	−	21.5287i	0.0189032	−	0.956122i
$508$	7.91450	+	5.75022i	0.351149	+	0.255125i
$509$	2.63324	−	8.10429i	0.116717	−	0.359217i	−0.875585	−	0.483065i	$-0.839524\pi$
$509$	2.63324	−	8.10429i	0.116717	−	0.359217i	0.992301	+	0.123848i	$0.0395236\pi$
$510$	−0.426481	−	1.40659i	−0.0188849	−	0.0622850i
$511$	−23.9080	−	13.6283i	−1.05763	−	0.602880i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	5.89656	+	22.6338i	0.260339	+	0.999307i
$514$	5.39299	+	1.75229i	0.237875	+	0.0772902i
$515$	32.2996	−	44.4566i	1.42329	−	1.95899i
$516$	0.298994	−	15.1231i	0.0131625	−	0.665756i
$517$	−16.3684	+	36.9595i	−0.719881	+	1.62548i
$518$	7.23275	+	16.0072i	0.317789	+	0.703318i
$519$	5.01366	−	6.62141i	0.220075	−	0.290648i
$520$	−0.941214	+	2.89676i	−0.0412749	+	0.127031i
$521$	−9.64872	−	29.6957i	−0.422718	−	1.30099i	−0.905163	−	0.425066i	$-0.860251\pi$
$521$	−9.64872	−	29.6957i	−0.422718	−	1.30099i	0.482445	−	0.875926i	$-0.339749\pi$
$522$	−8.09434	+	5.40535i	−0.354280	+	0.236586i
$523$	−20.7834	−	28.6060i	−0.908797	−	1.25085i	−0.967576	−	0.252580i	$-0.918721\pi$
$523$	−20.7834	−	28.6060i	−0.908797	−	1.25085i	0.0587793	−	0.998271i	$-0.481279\pi$
$524$	4.04524	+	12.4500i	0.176717	+	0.543879i
$525$	−51.7235	+	4.69159i	−2.25740	+	0.204758i
$526$	−10.0413	−	7.29542i	−0.437821	−	0.318095i
$527$			0.391776i			0.0170660i
$528$	−5.63940	+	1.09415i	−0.245423	+	0.0476169i
$529$	10.2335			0.444934
$530$	24.4661	+	17.7756i	1.06274	+	0.772124i
$531$	−5.41100	+	14.6551i	−0.234817	+	0.635979i
$532$	−8.80628	+	8.01745i	−0.381801	+	0.347601i
$533$	−0.477887	−	0.657754i	−0.0206996	−	0.0284905i
$534$	−7.88910	+	5.49683i	−0.341395	+	0.237871i
$535$	28.2218	−	9.16982i	1.22014	−	0.396446i
$536$	10.0520	+	3.26611i	0.434182	+	0.141074i
$537$	−15.2381	−	11.5381i	−0.657573	−	0.497908i
$538$		−	10.2393i		−	0.441447i
$539$	4.53182	−	22.7698i	0.195199	−	0.980764i
$540$	1.24466	−	20.9631i	0.0535618	−	0.902107i
$541$	19.1155	+	13.8882i	0.821840	+	0.597102i	0.917239	−	0.398337i	$-0.130413\pi$
$541$	19.1155	+	13.8882i	0.821840	+	0.597102i	−0.0953988	+	0.995439i	$0.530413\pi$
$542$	6.51658	−	20.0560i	0.279911	−	0.861478i
$543$	−1.22135	−	4.02819i	−0.0524133	−	0.172866i
$544$	0.123420	+	0.169874i	0.00529160	+	0.00728327i
$545$	40.6495	−	29.5336i	1.74124	−	1.26508i
$546$	2.59926	−	2.27410i	0.111238	−	0.0973227i
$547$	−4.69479	+	14.4491i	−0.200735	+	0.617798i	0.799127	+	0.601162i	$0.205295\pi$
$547$	−4.69479	+	14.4491i	−0.200735	+	0.617798i	−0.999862	+	0.0166355i	$0.994705\pi$
$548$	5.71572	−	7.86701i	0.244163	−	0.336062i
$549$	−0.972727	+	24.5906i	−0.0415150	+	1.04950i
$550$	−18.8582	−	32.5155i	−0.804116	−	1.38646i
$551$	−14.6040			−0.622151
$552$	−3.73586	+	4.93385i	−0.159009	+	0.209999i
$553$	−0.387005	−	3.49679i	−0.0164571	−	0.148698i
$554$	−10.9234	+	3.54922i	−0.464089	+	0.150792i
$555$	−26.5681	−	38.1307i	−1.12775	−	1.61856i
$556$	−12.6525	−	17.4146i	−0.536583	−	0.738544i
$557$	13.1297	−	4.26610i	0.556324	−	0.180761i	−0.0173425	−	0.999850i	$-0.505521\pi$
$557$	13.1297	−	4.26610i	0.556324	−	0.180761i	0.573666	+	0.819089i	$0.305521\pi$
$558$	−1.93877	+	5.25097i	−0.0820748	+	0.222291i
$559$	−3.86858	+	5.32464i	−0.163623	+	0.225208i
$560$	9.74415	−	4.40282i	0.411765	−	0.186053i
$561$	−1.18413	+	0.229745i	−0.0499942	+	0.00969984i
$562$	−19.9341			−0.840867
$563$	12.9928	+	9.43979i	0.547579	+	0.397840i	0.826892	−	0.562360i	$-0.190107\pi$
$563$	12.9928	+	9.43979i	0.547579	+	0.397840i	−0.279313	+	0.960200i	$0.590107\pi$
$564$	19.9436	+	6.91881i	0.839776	+	0.291334i
$565$	60.0752	−	19.5196i	2.52738	−	0.821196i
$566$	−5.06734	+	3.68164i	−0.212996	+	0.154751i
$567$	−13.3894	+	19.6907i	−0.562301	+	0.826933i
$568$	−2.81598	−	8.66671i	−0.118156	−	0.363647i
$569$	17.9164	+	5.82140i	0.751096	+	0.244046i	0.659453	−	0.751746i	$-0.270788\pi$
$569$	17.9164	+	5.82140i	0.751096	+	0.244046i	0.0916431	+	0.995792i	$0.470788\pi$
$570$	19.0207	−	25.1202i	0.796690	−	1.05217i
$571$	−1.29316			−0.0541172			−0.0270586	−	0.999634i	$-0.508614\pi$
$571$	−1.29316			−0.0541172			−0.0270586	+	0.999634i	$0.508614\pi$
$572$	2.28546	+	1.01217i	0.0955600	+	0.0423210i
$573$	32.6405	+	0.645326i	1.36358	+	0.0269589i
$574$	−0.578044	+	2.79507i	−0.0241271	+	0.116664i
$575$	−38.5123	−	12.5134i	−1.60608	−	0.521846i
$576$	0.813552	+	2.88758i	0.0338980	+	0.120316i
$577$	−20.1952	−	27.7963i	−0.840738	−	1.15718i	−0.985828	−	0.167758i	$-0.946347\pi$
$577$	−20.1952	−	27.7963i	−0.840738	−	1.15718i	0.145091	−	0.989418i	$-0.453653\pi$
$578$	−9.96643	−	13.7176i	−0.414549	−	0.570578i
$579$	13.6920	−	4.15144i	0.569022	−	0.172528i
$580$	12.4704	+	4.05188i	0.517805	+	0.168245i
$581$	37.7328	+	7.80345i	1.56542	+	0.323742i
$582$	0.155182	−	7.84908i	0.00643250	−	0.325355i
$583$	16.5701	−	18.4759i	0.686264	−	0.765195i
$584$	−10.4014			−0.430412
$585$	−5.65888	+	7.17432i	−0.233966	+	0.296622i
$586$	21.2923	+	6.91828i	0.879575	+	0.285791i
$587$	9.69466	+	29.8371i	0.400141	+	1.23151i	0.924885	+	0.380248i	$0.124161\pi$
$587$	9.69466	+	29.8371i	0.400141	+	1.23151i	−0.524743	+	0.851261i	$0.675839\pi$
$588$	−12.0464	−	1.37287i	−0.496784	−	0.0566162i
$589$	−6.79457	+	4.93655i	−0.279966	+	0.203407i
$590$	20.0154	−	6.50338i	0.824019	−	0.267740i
$591$	−12.0479	+	34.7282i	−0.495583	+	1.42853i
$592$	5.37116	+	3.90237i	0.220753	+	0.160387i
$593$	5.23814			0.215104			0.107552	−	0.994199i	$-0.465699\pi$
$593$	5.23814			0.215104			0.107552	+	0.994199i	$0.465699\pi$
$594$	−17.0079	−	2.78064i	−0.697842	−	0.114091i
$595$	2.04603	−	0.924483i	0.0838791	−	0.0379001i
$596$	−5.05977	+	6.96418i	−0.207256	+	0.285264i
$597$	−0.777433	+	2.24096i	−0.0318182	+	0.0917165i
$598$	2.56101	−	0.832122i	0.104727	−	0.0340280i
$599$	−2.29221	−	3.15496i	−0.0936573	−	0.128908i	0.759617	−	0.650371i	$-0.225387\pi$
$599$	−2.29221	−	3.15496i	−0.0936573	−	0.128908i	−0.853274	+	0.521463i	$0.825387\pi$
$600$	−16.1059	+	11.2220i	−0.657520	+	0.458136i
$601$	−0.0323844	+	0.0105223i	−0.00132099	+	0.000429215i	−0.309677	−	0.950842i	$-0.600221\pi$
$601$	−0.0323844	+	0.0105223i	−0.00132099	+	0.000429215i	0.308356	+	0.951271i	$0.400221\pi$
$602$	22.9652	−	2.54165i	0.935990	−	0.103590i
$603$	24.8956	+	19.6369i	1.01383	+	0.799675i
$604$	−23.2599			−0.946434
$605$	−40.5411	+	18.2415i	−1.64823	+	0.741622i
$606$	14.1419	+	0.279596i	0.574477	+	0.0113578i
$607$	16.6399	−	22.9029i	0.675393	−	0.929599i	−0.324474	−	0.945895i	$-0.605187\pi$
$607$	16.6399	−	22.9029i	0.675393	−	0.929599i	0.999867	+	0.0162956i	$0.00518729\pi$
$608$	−1.39097	+	4.28096i	−0.0564113	+	0.173616i
$609$	−9.78990	−	11.1897i	−0.396707	−	0.453429i
$610$	26.8214	−	19.4869i	1.08597	−	0.789002i
$611$	−5.39892	−	7.43098i	−0.218417	−	0.300625i
$612$	0.170826	+	0.606321i	0.00690523	+	0.0245091i
$613$	4.42207	−	13.6097i	0.178606	−	0.549692i	−0.821174	−	0.570678i	$-0.806680\pi$
$613$	4.42207	−	13.6097i	0.178606	−	0.549692i	0.999780	+	0.0209857i	$0.00668045\pi$
$614$	0.138763	+	0.100817i	0.00560000	+	0.00406864i
$615$	0.149270	−	7.55006i	0.00601915	−	0.304448i
$616$	−2.77390	−	8.32499i	−0.111764	−	0.335423i
$617$			29.3727i			1.18250i	0.806488	+	0.591251i	$0.201366\pi$
$617$			29.3727i			1.18250i	−0.806488	+	0.591251i	$0.798634\pi$
$618$	−14.2166	+	18.7755i	−0.571876	+	0.755261i
$619$	13.1444	+	4.27087i	0.528317	+	0.171661i	0.561017	−	0.827805i	$-0.310410\pi$
$619$	13.1444	+	4.27087i	0.528317	+	0.171661i	−0.0326993	+	0.999465i	$0.510410\pi$
$620$	7.17155	−	2.33018i	0.288016	−	0.0935822i
$621$	−15.6406	+	10.0034i	−0.627635	+	0.401422i
$622$	−9.51806	−	13.1005i	−0.381640	−	0.525282i
$623$	−9.88783	−	10.8607i	−0.396148	−	0.435124i
$624$	0.427838	−	1.23325i	0.0171272	−	0.0493696i
$625$	−37.8439	−	27.4952i	−1.51375	−	1.09981i
$626$	13.0521			0.521665
$627$	−18.9051	−	17.6416i	−0.754996	−	0.704537i
$628$			16.4604i			0.656843i
$629$	1.12781	+	0.819402i	0.0449687	+	0.0326717i
$630$	31.9979	−	2.26569i	1.27483	−	0.0902673i
$631$	−4.07051	−	12.5278i	−0.162045	−	0.498722i	0.836762	−	0.547567i	$-0.184446\pi$
$631$	−4.07051	−	12.5278i	−0.162045	−	0.498722i	−0.998806	+	0.0488451i	$0.984446\pi$
$632$	−0.781596	−	1.07577i	−0.0310902	−	0.0427920i
$633$	7.07567	+	10.1551i	0.281233	+	0.403627i
$634$	4.91043	+	15.1128i	0.195018	+	0.600204i
$635$	12.2176	−	37.6019i	0.484840	−	1.49218i
$636$	−10.3328	−	7.82390i	−0.409723	−	0.310238i
$637$	3.95912	+	3.48664i	0.156866	+	0.138146i
$638$	4.35735	−	9.83881i	0.172509	−	0.389522i
$639$	1.08057	−	27.3168i	0.0427466	−	1.08064i
$640$	2.37551	−	3.26960i	0.0939001	−	0.129242i
$641$	4.46839	+	1.45187i	0.176491	+	0.0573453i	0.395929	−	0.918281i	$-0.370423\pi$
$641$	4.46839	+	1.45187i	0.176491	+	0.0573453i	−0.219439	+	0.975626i	$0.570423\pi$
$642$	−12.1704	+	3.69008i	−0.480327	+	0.145636i
$643$	−4.69446	−	6.46137i	−0.185131	−	0.254812i	0.706356	−	0.707857i	$-0.250338\pi$
$643$	−4.69446	−	6.46137i	−0.185131	−	0.254812i	−0.891488	+	0.453045i	$0.850338\pi$
$644$	−8.21273	−	4.68152i	−0.323627	−	0.184478i
$645$	−58.5011	+	17.7376i	−2.30348	+	0.698418i
$646$	−0.292069	+	0.898896i	−0.0114913	+	0.0353666i
$647$	−7.14257	−	5.18938i	−0.280803	−	0.204016i	0.438464	−	0.898749i	$-0.355523\pi$
$647$	−7.14257	−	5.18938i	−0.280803	−	0.204016i	−0.719268	+	0.694733i	$0.755523\pi$
$648$	−0.710912	+	8.97188i	−0.0279273	+	0.352449i
$649$	−3.62405	−	16.8864i	−0.142257	−	0.662851i
$650$	8.54134			0.335019
$651$	−8.33721	−	1.89679i	−0.326761	−	0.0743412i
$652$	−4.62468	+	14.2333i	−0.181116	+	0.557419i
$653$	23.2278	−	7.54717i	0.908974	−	0.295343i	0.183038	−	0.983106i	$-0.441407\pi$
$653$	23.2278	−	7.54717i	0.908974	−	0.295343i	0.725936	+	0.687762i	$0.241407\pi$
$654$	−17.6680	+	12.3104i	−0.690875	+	0.481376i
$655$	42.8012	−	31.0969i	1.67238	−	1.21506i
$656$	0.333365	+	1.02599i	0.0130157	+	0.0400583i
$657$	−29.2726	−	10.8081i	−1.14203	−	0.421663i
$658$	−6.53045	+	31.5773i	−0.254583	+	1.23101i
$659$		−	1.23662i		−	0.0481720i	−0.999710	−	0.0240860i	$-0.992332\pi$
$659$		−	1.23662i		−	0.0481720i	0.999710	−	0.0240860i	$-0.00766756\pi$
$660$	11.2485	+	20.3094i	0.437845	+	0.790543i
$661$		−	37.1937i		−	1.44667i	−0.690498	−	0.723334i	$-0.742609\pi$
$661$		−	37.1937i		−	1.44667i	0.690498	−	0.723334i	$-0.257391\pi$
$662$	2.20521	−	3.03521i	0.0857079	−	0.117967i
$663$	0.0898355	−	0.258952i	0.00348892	−	0.0100569i
$664$	13.8507	−	4.50035i	0.537509	−	0.174647i
$665$	41.8142	+	23.8354i	1.62149	+	0.924299i
$666$	11.0611	+	16.5636i	0.428608	+	0.641827i
$667$	−3.58225	−	11.0250i	−0.138705	−	0.426890i
$668$	−3.87091	+	11.9134i	−0.149770	+	0.460944i
$669$	23.6022	+	17.8713i	0.912514	+	0.690946i
$670$		−	42.7155i		−	1.65024i
$671$	−13.6499	−	23.5353i	−0.526948	−	0.908570i
$672$	−4.21255	+	1.80401i	−0.162503	+	0.0695911i
$673$	−15.4860	−	11.2513i	−0.596943	−	0.433704i	0.247850	−	0.968799i	$-0.420276\pi$
$673$	−15.4860	−	11.2513i	−0.596943	−	0.433704i	−0.844792	+	0.535094i	$0.820276\pi$
$674$	−5.23404	−	1.70064i	−0.201608	−	0.0655063i
$675$	−56.9875	+	14.8464i	−2.19345	+	0.571437i
$676$	10.0577	−	7.30735i	0.386835	−	0.281052i
$677$	−42.0204	+	30.5296i	−1.61497	+	1.17335i	−0.771352	+	0.636408i	$0.780419\pi$
$677$	−42.0204	+	30.5296i	−1.61497	+	1.17335i	−0.843621	+	0.536939i	$0.819581\pi$
$678$	−25.9068	+	7.85498i	−0.994946	+	0.301669i
$679$	11.9192	−	1.31915i	0.457418	−	0.0506244i
$680$	0.498797	−	0.686536i	0.0191280	−	0.0263274i
$681$	−0.419326	+	21.2095i	−0.0160686	+	0.812748i
$682$	−1.29851	−	6.05045i	−0.0497224	−	0.231684i
$683$			40.0206i			1.53135i	0.643230	+	0.765673i	$0.277594\pi$
$683$			40.0206i			1.53135i	−0.643230	+	0.765673i	$0.722406\pi$
$684$	−8.36295	+	10.6025i	−0.319766	+	0.405399i
$685$	−37.3762	−	12.1443i	−1.42807	−	0.464009i
$686$	−0.305905	−	18.5177i	−0.0116795	−	0.707010i
$687$	−1.57844	+	1.09980i	−0.0602213	+	0.0419600i
$688$	7.06515	−	5.13314i	0.269356	−	0.195699i
$689$	1.74269	+	5.36344i	0.0663912	+	0.204331i
$690$	23.6296	+	8.19756i	0.899564	+	0.312076i
$691$	4.53356	−	6.23992i	0.172465	−	0.237378i	−0.714031	−	0.700114i	$-0.753132\pi$
$691$	4.53356	−	6.23992i	0.172465	−	0.237378i	0.886496	+	0.462737i	$0.153132\pi$
$692$	4.79513			0.182284
$693$	0.843919	−	26.3114i	0.0320578	−	0.999486i
$694$	−4.31470			−0.163784
$695$	−51.1343	+	70.3803i	−1.93963	+	2.66968i
$696$	−5.30909	−	1.84182i	−0.201240	−	0.0698141i
$697$	0.0699984	+	0.215433i	0.00265138	+	0.00816010i
$698$	−18.5117	+	13.4496i	−0.700679	+	0.509073i
$699$	−6.26992	+	4.36865i	−0.237150	+	0.165237i
$700$	−20.1864	−	22.1725i	−0.762973	−	0.838042i
$701$	−3.77072	−	1.22518i	−0.142418	−	0.0462744i	0.236941	−	0.971524i	$-0.423855\pi$
$701$	−3.77072	−	1.22518i	−0.142418	−	0.0462744i	−0.379359	+	0.925250i	$0.623855\pi$
$702$	2.48554	−	3.02617i	0.0938106	−	0.114215i
$703$			29.8845i			1.12711i
$704$	−2.46909	−	2.21440i	−0.0930574	−	0.0834584i
$705$	1.68638	−	85.2968i	0.0635127	−	3.21246i
$706$	7.88686	−	10.8553i	0.296826	−	0.408546i
$707$	2.37676	+	21.4753i	0.0893873	+	0.807661i
$708$	−8.63143	+	2.61706i	−0.324389	+	0.0983552i
$709$	1.63312	−	1.18653i	0.0613332	−	0.0445612i	−0.556696	−	0.830716i	$-0.687931\pi$
$709$	1.63312	−	1.18653i	0.0613332	−	0.0445612i	0.618029	+	0.786155i	$0.287931\pi$
$710$	−29.7950	+	21.6473i	−1.11819	+	0.812409i
$711$	−1.08181	−	3.83971i	−0.0405709	−	0.144000i
$712$	−5.27966	−	1.71547i	−0.197864	−	0.0642898i
$713$	−5.39341	−	3.91854i	−0.201985	−	0.146750i
$714$	−0.884531	+	0.378797i	−0.0331027	+	0.0141761i
$715$	1.03617	−	10.0486i	0.0387506	−	0.375796i
$716$		−	11.0352i		−	0.412406i
$717$	−25.2443	−	19.1147i	−0.942765	−	0.713852i
$718$	−3.58589	+	11.0362i	−0.133824	+	0.411868i
$719$	8.86126	+	27.2722i	0.330469	+	1.01708i	0.968911	+	0.247410i	$0.0795794\pi$
$719$	8.86126	+	27.2722i	0.330469	+	1.01708i	−0.638442	+	0.769670i	$0.720421\pi$
$720$	10.0828	−	6.73324i	0.375765	−	0.250933i
$721$	−31.2531	−	17.8153i	−1.16393	−	0.663475i
$722$	−1.19971	+	0.389808i	−0.0446484	+	0.0145072i
$723$	10.4992	−	30.2642i	0.390470	−	1.12554i
$724$	1.42845	−	1.96610i	0.0530880	−	0.0730694i
$725$		−	36.7700i		−	1.36560i
$726$	17.5259	−	7.47281i	0.650447	−	0.277342i
$727$			7.72536i			0.286518i	0.989685	+	0.143259i	$0.0457582\pi$
$727$			7.72536i			0.286518i	−0.989685	+	0.143259i	$0.954242\pi$
$728$	1.95265	+	0.403823i	0.0723698	+	0.0149667i
$729$	−11.3234	+	24.5108i	−0.419385	+	0.907808i
$730$	12.9900	+	39.9792i	0.480783	+	1.47970i
$731$	1.48351	−	1.07783i	0.0548695	−	0.0398650i
$732$	−11.6577	+	8.12268i	−0.430882	+	0.300223i
$733$	−3.15094	+	1.02380i	−0.116383	+	0.0378151i	−0.366629	−	0.930367i	$-0.619488\pi$
$733$	−3.15094	+	1.02380i	−0.116383	+	0.0378151i	0.250247	+	0.968182i	$0.419488\pi$
$734$	6.37245	−	19.6124i	0.235211	−	0.723906i
$735$	9.76761	+	48.0166i	0.360284	+	1.77112i
$736$	−3.57303			−0.131704
$737$	−34.8696	−	3.59562i	−1.28444	−	0.132446i
$738$	−0.127921	+	3.23385i	−0.00470883	+	0.119040i
$739$	−11.8630	−	8.61896i	−0.436387	−	0.317054i	0.347811	−	0.937565i	$-0.386925\pi$
$739$	−11.8630	−	8.61896i	−0.436387	−	0.317054i	−0.784198	+	0.620511i	$0.786925\pi$
$740$	8.29144	−	25.5184i	0.304799	−	0.938076i
$741$	5.62298	−	1.70490i	0.206565	−	0.0626309i
$742$	9.80437	−	17.1997i	0.359930	−	0.631420i
$743$	−21.7768	−	29.9732i	−0.798913	−	1.09961i	−0.992940	−	0.118614i	$-0.962155\pi$
$743$	−21.7768	−	29.9732i	−0.798913	−	1.09961i	0.194027	−	0.980996i	$-0.437845\pi$
$744$	−3.09266	+	0.937699i	−0.113382	+	0.0343777i
$745$	33.0869	+	10.7506i	1.21221	+	0.393871i
$746$	−1.35338	+	1.86277i	−0.0495509	+	0.0682010i
$747$	43.6562	+	1.72690i	1.59730	+	0.0631841i
$748$	−0.518448	−	0.464970i	−0.0189564	−	0.0170010i
$749$	−7.99899	−	17.7030i	−0.292277	−	0.646855i
$750$	35.3443	+	26.7623i	1.29059	+	0.977221i
$751$	−0.968450	+	2.98058i	−0.0353392	+	0.108763i	−0.967170	−	0.254130i	$-0.918211\pi$
$751$	−0.968450	+	2.98058i	−0.0353392	+	0.108763i	0.931831	+	0.362893i	$0.118211\pi$
$752$	3.76619	+	11.5911i	0.137339	+	0.422685i
$753$	4.57800	+	6.57038i	0.166832	+	0.239438i
$754$	1.43722	+	1.97817i	0.0523405	+	0.0720406i
$755$	29.0488	+	89.4030i	1.05719	+	3.25371i
$756$	−13.7299	+	0.699750i	−0.499352	+	0.0254497i
$757$	20.8156	+	15.1234i	0.756556	+	0.549670i	0.897852	−	0.440297i	$-0.145127\pi$
$757$	20.8156	+	15.1234i	0.756556	+	0.549670i	−0.141296	+	0.989967i	$0.545127\pi$
$758$		−	29.2246i		−	1.06149i
$759$	8.68091	−	18.5994i	0.315097	−	0.675115i
$760$	18.1917			0.659881
$761$	1.03966	+	0.755358i	0.0376877	+	0.0273817i	0.606470	−	0.795107i	$-0.292585\pi$
$761$	1.03966	+	0.755358i	0.0376877	+	0.0273817i	−0.568782	+	0.822488i	$0.692585\pi$
$762$	−5.55363	+	16.0084i	−0.201187	+	0.579924i
$763$	−22.1443	−	24.3231i	−0.801677	−	0.880554i
$764$	11.0790	+	15.2489i	0.400824	+	0.551686i
$765$	2.11714	−	1.41381i	0.0765455	−	0.0511166i
$766$	−11.0426	+	3.58795i	−0.398985	+	0.129638i
$767$	3.73245	+	1.21275i	0.134771	+	0.0437898i
$768$	−1.04557	+	1.38086i	−0.0377289	+	0.0498275i
$769$			11.7867i			0.425041i	0.977157	+	0.212520i	$0.0681672\pi$
$769$			11.7867i			0.425041i	−0.977157	+	0.212520i	$0.931833\pi$
$770$	−28.5341	+	21.0588i	−1.02830	+	0.758906i
$771$	−0.194143	+	9.81972i	−0.00699189	+	0.353649i
$772$	6.68286	+	4.85538i	0.240522	+	0.174749i
$773$	8.40178	−	25.8580i	0.302191	−	0.930048i	−0.678520	−	0.734582i	$-0.737378\pi$
$773$	8.40178	−	25.8580i	0.302191	−	0.930048i	0.980711	−	0.195466i	$-0.0626218\pi$
$774$	25.2173	−	7.10476i	0.906417	−	0.255375i
$775$	−12.4293	−	17.1074i	−0.446472	−	0.614516i
$776$	3.66691	−	2.66417i	0.131634	−	0.0956380i
$777$	−22.8977	+	20.0333i	−0.821449	+	0.718690i
$778$	7.11830	−	21.9079i	0.255203	−	0.785435i
$779$	−2.85425	+	3.92853i	−0.102264	+	0.140754i
$780$	−5.27450	−	0.104281i	−0.188858	−	0.00373385i
$781$	15.1632	+	26.1445i	0.542582	+	0.935524i
$782$	−0.750247			−0.0268288
$783$	−13.0275	−	10.7001i	−0.465565	−	0.382391i
$784$	−3.56654	−	6.02327i	−0.127377	−	0.215117i
$785$	63.2681	−	20.5571i	2.25814	−	0.733713i
$786$	−18.6032	+	12.9621i	−0.663556	+	0.462341i
$787$	16.7865	+	23.1046i	0.598374	+	0.823591i	0.995558	−	0.0941475i	$-0.0300125\pi$
$787$	16.7865	+	23.1046i	0.598374	+	0.823591i	−0.397184	+	0.917739i	$0.630013\pi$
$788$	−20.1839	+	6.55815i	−0.719022	+	0.233625i
$789$	7.04600	−	20.3102i	0.250844	−	0.723063i
$790$	−3.15878	+	4.34769i	−0.112384	+	0.154684i
$791$	−17.0273	−	37.6841i	−0.605420	−	1.33989i
$792$	−4.64777	−	8.79762i	−0.165151	−	0.312610i
$793$	6.18237			0.219543
$794$	−11.7175	−	8.51323i	−0.415837	−	0.302123i
$795$	−17.1679	+	49.4868i	−0.608883	+	1.75512i
$796$	−1.30244	+	0.423189i	−0.0461638	+	0.0149995i
$797$	−3.37013	+	2.44855i	−0.119376	+	0.0867319i	−0.645871	−	0.763446i	$-0.723506\pi$
$797$	−3.37013	+	2.44855i	−0.119376	+	0.0867319i	0.526495	+	0.850178i	$0.323506\pi$
$798$	−17.7150	−	10.5674i	−0.627103	−	0.374083i
$799$	0.790807	+	2.43385i	0.0279767	+	0.0861035i
$800$	−10.7786	−	3.50219i	−0.381082	−	0.123821i
$801$	−13.0760	−	10.3139i	−0.462018	−	0.364425i
$802$	5.27272			0.186186
$803$	33.7294	−	7.23878i	1.19029	−	0.255451i
$804$	−0.361865	+	18.3031i	−0.0127620	+	0.645499i
$805$	−7.73743	+	37.4135i	−0.272708	+	1.31865i
$806$	1.33735	+	0.434530i	0.0471060	+	0.0153057i
$807$	16.9720	−	5.14592i	0.597442	−	0.181145i
$808$	4.80012	+	6.60680i	0.168868	+	0.232426i
$809$	−1.91969	−	2.64222i	−0.0674926	−	0.0928955i	0.773936	−	0.633263i	$-0.218285\pi$
$809$	−1.91969	−	2.64222i	−0.0674926	−	0.0928955i	−0.841429	+	0.540368i	$0.818285\pi$
$810$	35.3726	−	8.47228i	1.24287	−	0.297685i
$811$	32.9796	+	10.7157i	1.15807	+	0.376280i	0.824178	−	0.566331i	$-0.191638\pi$
$811$	32.9796	+	10.7157i	1.15807	+	0.376280i	0.333893	+	0.942611i	$0.391638\pi$
$812$	1.73844	−	8.40604i	0.0610073	−	0.294994i
$813$	36.5185	+	0.721998i	1.28076	+	0.0253216i
$814$	−20.1333	−	8.91653i	−0.705673	−	0.312524i
$815$	60.4835			2.11864
$816$	−0.219545	+	0.289947i	−0.00768560	+	0.0101502i
$817$	37.3857	+	12.1474i	1.30796	+	0.424982i
$818$	7.62593	+	23.4702i	0.266634	+	0.820616i
$819$	5.07571	+	3.16547i	0.177360	+	0.110611i
$820$	3.52722	−	2.56268i	0.123176	−	0.0894925i
$821$	40.1303	−	13.0391i	1.40056	−	0.455068i	0.491185	−	0.871055i	$-0.336564\pi$
$821$	40.1303	−	13.0391i	1.40056	−	0.455068i	0.909371	+	0.415987i	$0.136564\pi$
$822$	15.9124	+	5.52031i	0.555008	+	0.192543i
$823$	−23.4742	−	17.0550i	−0.818260	−	0.594500i	0.0979538	−	0.995191i	$-0.468770\pi$
$823$	−23.4742	−	17.0550i	−0.818260	−	0.594500i	−0.916213	+	0.400691i	$0.868770\pi$
$824$	−13.5970			−0.473672
$825$	44.4181	−	47.5993i	1.54644	−	1.65720i
$826$	−5.67301	−	12.5553i	−0.197389	−	0.436854i
$827$	26.9639	−	37.1126i	0.937627	−	1.29053i	−0.0191818	−	0.999816i	$-0.506106\pi$
$827$	26.9639	−	37.1126i	0.937627	−	1.29053i	0.956809	−	0.290717i	$-0.0938939\pi$
$828$	−10.0556	−	3.71273i	−0.349455	−	0.129026i
$829$	17.5892	−	5.71507i	0.610897	−	0.198492i	0.0128024	−	0.999918i	$-0.495925\pi$
$829$	17.5892	−	5.71507i	0.610897	−	0.198492i	0.598094	+	0.801426i	$0.295925\pi$
$830$	−34.5955	−	47.6166i	−1.20083	−	1.65280i
$831$	−11.3727	−	16.3222i	−0.394514	−	0.566209i
$832$	0.716762	−	0.232890i	0.0248492	−	0.00807401i
$833$	−0.748886	−	1.26474i	−0.0259474	−	0.0438206i
$834$	22.5066	−	29.7239i	0.779341	−	1.02925i
$835$	50.6253			1.75196
$836$	1.53130	−	14.8503i	0.0529612	−	0.513608i
$837$	−9.67803	−	0.574624i	−0.334522	−	0.0198619i
$838$	19.7855	−	27.2325i	0.683480	−	0.940730i
$839$	−1.00043	+	3.07901i	−0.0345387	+	0.106299i	−0.966840	−	0.255384i	$-0.917798\pi$
$839$	−1.00043	+	3.07901i	−0.0345387	+	0.106299i	0.932301	+	0.361684i	$0.117798\pi$
$840$	12.1949	+	13.9386i	0.420765	+	0.480926i
$841$	−14.9456	+	10.8586i	−0.515365	+	0.374435i
$842$	7.68212	+	10.5735i	0.264743	+	0.364388i
$843$	−10.0182	−	33.0414i	−0.345045	−	1.13801i
$844$	−2.20819	+	6.79612i	−0.0760092	+	0.233932i
$845$	−40.6477	−	29.5323i	−1.39832	−	1.01594i
$846$	−1.44519	+	36.5344i	−0.0496865	+	1.25608i
$847$	14.7889	+	25.0657i	0.508153	+	0.861267i
$848$		−	7.48288i		−	0.256963i
$849$	−8.64912	−	6.54903i	−0.296837	−	0.224762i
$850$	−2.26325	−	0.735373i	−0.0776287	−	0.0252231i
$851$	−22.5607	+	7.33042i	−0.773371	+	0.251283i
$852$	12.9502	−	9.02320i	0.443665	−	0.309130i
$853$	−19.8402	−	27.3077i	−0.679316	−	0.934998i	0.320610	−	0.947211i	$-0.396112\pi$
$853$	−19.8402	−	27.3077i	−0.679316	−	0.934998i	−0.999925	+	0.0122134i	$0.996112\pi$
$854$	−14.6113	−	16.0489i	−0.499987	−	0.549181i
$855$	51.1968	+	18.9030i	1.75089	+	0.646468i
$856$	−5.94017	−	4.31579i	−0.203031	−	0.147511i
$857$	44.7221			1.52768			0.763839	−	0.645407i	$-0.223312\pi$
$857$	44.7221			1.52768			0.763839	+	0.645407i	$0.223312\pi$
$858$	−0.529113	+	4.29692i	−0.0180636	+	0.146695i
$859$			17.4802i			0.596416i	0.954501	+	0.298208i	$0.0963888\pi$
$859$			17.4802i			0.596416i	−0.954501	+	0.298208i	$0.903611\pi$
$860$	−28.5535	−	20.7453i	−0.973665	−	0.707409i
$861$	−4.92343	+	0.446581i	−0.167790	+	0.0152194i
$862$	−4.25671	−	13.1008i	−0.144984	−	0.446215i
$863$	2.90881	+	4.00364i	0.0990171	+	0.136285i	0.855651	−	0.517554i	$-0.173157\pi$
$863$	2.90881	+	4.00364i	0.0990171	+	0.136285i	−0.756634	+	0.653839i	$0.773157\pi$
$864$	−4.37741	+	2.79970i	−0.148922	+	0.0952476i
$865$	−5.98853	−	18.4308i	−0.203616	−	0.626666i
$866$	0.0988303	−	0.304169i	0.00335839	−	0.0103361i
$867$	17.7287	−	23.4137i	0.602097	−	0.795173i
$868$	−2.03265	−	4.49859i	−0.0689927	−	0.152692i
$869$	3.28323	+	2.94456i	0.111376	+	0.0998873i
$870$	−0.448923	+	22.7065i	−0.0152199	+	0.769822i
$871$	4.68204	−	6.44427i	0.158645	−	0.218356i
$872$	−11.8241	−	3.84187i	−0.400414	−	0.130102i
$873$	13.0881	−	3.68747i	0.442966	−	0.124802i
$874$	−9.45345	−	13.0116i	−0.319768	−	0.440122i
$875$	−33.5367	+	58.8329i	−1.13375	+	1.98892i
$876$	−5.22739	−	17.2407i	−0.176617	−	0.582508i
$877$	9.09203	−	27.9824i	0.307016	−	0.944898i	−0.671901	−	0.740641i	$-0.734522\pi$
$877$	9.09203	−	27.9824i	0.307016	−	0.944898i	0.978917	−	0.204257i	$-0.0654780\pi$
$878$	9.98579	+	7.25510i	0.337004	+	0.244848i
$879$	−0.766503	+	38.7696i	−0.0258535	+	1.30767i
$880$	−5.42779	+	12.2558i	−0.182971	+	0.413144i
$881$	54.0486			1.82094			0.910471	−	0.413572i	$-0.135719\pi$
$881$	54.0486			1.82094			0.910471	+	0.413572i	$0.135719\pi$
$882$	−3.77853	−	20.6573i	−0.127230	−	0.695566i
$883$	−0.185478	+	0.570842i	−0.00624182	+	0.0192104i	−0.954129	−	0.299396i	$-0.903215\pi$
$883$	−0.185478	+	0.570842i	−0.00624182	+	0.0192104i	0.947887	+	0.318606i	$0.103215\pi$
$884$	0.150502	−	0.0489011i	0.00506194	−	0.00164472i
$885$	20.8387	+	29.9078i	0.700484	+	1.00534i
$886$	−22.1351	+	16.0821i	−0.743643	+	0.540289i
$887$	13.4288	+	41.3297i	0.450896	+	1.38771i	0.875887	+	0.482517i	$0.160277\pi$
$887$	13.4288	+	41.3297i	0.450896	+	1.38771i	−0.424991	+	0.905198i	$0.639723\pi$
$888$	−3.76896	+	10.8641i	−0.126478	+	0.364575i
$889$	−25.3466	−	5.24190i	−0.850099	−	0.175808i
$890$			22.4356i			0.752042i
$891$	−3.93860	−	29.5886i	−0.131948	−	0.991257i
$892$			17.0924i			0.572295i
$893$	−32.2458	+	44.3826i	−1.07907	+	1.48521i
$894$	−14.0862	−	4.88679i	−0.471115	−	0.163439i
$895$	−42.4155	+	13.7816i	−1.41779	+	0.460669i
$896$	−2.29854	−	1.31024i	−0.0767887	−	0.0437720i
$897$	2.66635	+	3.82677i	0.0890269	+	0.127772i
$898$	−7.38954	−	22.7427i	−0.246592	−	0.758933i
$899$	1.87063	−	5.75721i	0.0623891	−	0.192014i
$900$	−26.6951	−	21.0563i	−0.889838	−	0.701876i
$901$		−	1.57122i		−	0.0523449i
$902$	−1.79506	−	3.09507i	−0.0597691	−	0.103055i
$903$	15.7544	+	36.7882i	0.524274	+	1.22424i
$904$	−12.6447	−	9.18692i	−0.420557	−	0.305552i
$905$	−9.34095	−	3.03506i	−0.310504	−	0.100889i
$906$	−11.6897	−	38.5542i	−0.388364	−	1.28088i
$907$	−10.3289	+	7.50435i	−0.342964	+	0.249178i	−0.745911	−	0.666045i	$-0.767986\pi$
$907$	−10.3289	+	7.50435i	−0.342964	+	0.249178i	0.402947	+	0.915223i	$0.367986\pi$
$908$	−9.90858	+	7.19900i	−0.328828	+	0.238907i
$909$	6.64383	+	23.5813i	0.220362	+	0.782142i
$910$	−0.886458	−	8.00961i	−0.0293858	−	0.265516i
$911$	−23.3173	+	32.0935i	−0.772538	+	1.06331i	0.223529	+	0.974697i	$0.428242\pi$
$911$	−23.3173	+	32.0935i	−0.772538	+	1.06331i	−0.996066	+	0.0886094i	$0.971758\pi$
$912$	−7.79491	−	0.154111i	−0.258115	−	0.00510312i
$913$	−41.7827	+	24.2330i	−1.38281	+	0.801994i
$914$			11.5515i			0.382090i
$915$	45.7798	+	34.6640i	1.51343	+	1.14596i
$916$	−1.05635	−	0.343229i	−0.0349027	−	0.0113406i
$917$	−23.3165	−	25.6105i	−0.769977	−	0.845735i
$918$	−0.919147	+	0.587867i	−0.0303364	+	0.0194025i
$919$	−22.9653	+	16.6852i	−0.757554	+	0.550395i	−0.898159	−	0.439670i	$-0.855095\pi$
$919$	−22.9653	+	16.6852i	−0.757554	+	0.550395i	0.140605	+	0.990066i	$0.455095\pi$
$920$	4.46227	+	13.7335i	0.147117	+	0.452779i
$921$	−0.0973702	+	0.280671i	−0.00320846	+	0.00924843i
$922$	5.66577	−	7.79827i	0.186592	−	0.256822i
$923$	−6.86778			−0.226056
$924$	12.4049	−	8.78171i	0.408091	−	0.288897i
$925$	−75.2432			−2.47398
$926$	−8.05651	+	11.0888i	−0.264753	+	0.364402i
$927$	−38.2659	−	14.1286i	−1.25682	−	0.464044i
$928$	−1.00258	−	3.08562i	−0.0329113	−	0.101291i
$929$	18.8333	−	13.6832i	0.617899	−	0.448930i	−0.234288	−	0.972167i	$-0.575276\pi$
$929$	18.8333	−	13.6832i	0.617899	−	0.448930i	0.852187	+	0.523237i	$0.175276\pi$
$930$	7.46654	+	10.7160i	0.244837	+	0.351392i
$931$	12.4981	−	28.9242i	0.409608	−	0.947952i
$932$	−4.19605	−	1.36338i	−0.137446	−	0.0446590i
$933$	16.9311	−	22.3604i	0.554298	−	0.732047i
$934$			6.84669i			0.224030i
$935$	−1.13970	+	2.57342i	−0.0372722	+	0.0841599i
$936$	2.25918	+	0.0893660i	0.0738435	+	0.00292102i
$937$	−5.95675	+	8.19877i	−0.194599	+	0.267842i	−0.895155	−	0.445755i	$-0.852935\pi$
$937$	−5.95675	+	8.19877i	−0.194599	+	0.267842i	0.700556	+	0.713597i	$0.252935\pi$
$938$	−27.7941	+	3.07610i	−0.907511	+	0.100438i
$939$	6.55954	+	21.6343i	0.214062	+	0.706008i
$940$	39.8488	−	28.9518i	1.29972	−	0.944304i
$941$	−28.8262	+	20.9434i	−0.939706	+	0.682736i	−0.948350	−	0.317226i	$-0.897249\pi$
$941$	−28.8262	+	20.9434i	−0.939706	+	0.682736i	0.00864378	+	0.999963i	$0.497249\pi$
$942$	−27.2838	+	8.27247i	−0.888953	+	0.269532i
$943$	−3.66590	−	1.19112i	−0.119378	−	0.0387883i
$944$	−4.21286	−	3.06082i	−0.137117	−	0.0996214i
$945$	19.8366	+	51.8990i	0.645283	+	1.68828i
$946$	−19.3384	+	21.5626i	−0.628746	+	0.701061i
$947$			42.1847i			1.37082i	0.728158	+	0.685410i	$0.240377\pi$
$947$			42.1847i			1.37082i	−0.728158	+	0.685410i	$0.759623\pi$
$948$	1.39033	−	1.83617i	0.0451559	−	0.0596361i
$949$	−2.42238	+	7.45531i	−0.0786337	+	0.242010i
$950$	−15.7643	−	48.5175i	−0.511462	−	1.57412i
$951$	−22.5821	+	15.7344i	−0.732276	+	0.510223i
$952$	−0.482636	−	0.275118i	−0.0156423	−	0.00891662i
$953$	49.8912	−	16.2106i	1.61614	−	0.525114i	0.645110	−	0.764090i	$-0.276812\pi$
$953$	49.8912	−	16.2106i	1.61614	−	0.525114i	0.971026	+	0.238976i	$0.0768116\pi$
$954$	7.77547	−	21.0591i	0.251740	−	0.681812i
$955$	44.7752	−	61.6277i	1.44889	−	1.99423i
$956$		−	18.2815i		−	0.591268i
$957$	18.4980	+	2.27781i	0.597957	+	0.0736310i
$958$		−	19.6877i		−	0.636082i
$959$	−5.21045	+	25.1946i	−0.168254	+	0.813575i
$960$	6.61333	+	2.29429i	0.213444	+	0.0740479i
$961$	8.50375	+	26.1719i	0.274315	+	0.844254i
$962$	4.04796	−	2.94102i	0.130511	−	0.0948221i
$963$	−12.2329	−	18.3183i	−0.394199	−	0.590300i
$964$	17.5894	−	5.71516i	0.566518	−	0.184073i
$965$	10.3163	−	31.7504i	0.332094	−	1.02208i
$966$	3.63234	−	15.9657i	0.116869	−	0.513687i
$967$	46.2659			1.48781			0.743906	−	0.668284i	$-0.232971\pi$
$967$	46.2659			1.48781			0.743906	+	0.668284i	$0.232971\pi$
$968$	9.54784	+	5.46248i	0.306879	+	0.175571i
$969$	−1.63674	−	0.0323595i	−0.0525796	−	0.00103954i
$970$	−14.8196	−	10.7671i	−0.475830	−	0.345711i
$971$	−6.54353	+	20.1389i	−0.209992	+	0.646289i	0.789479	+	0.613777i	$0.210351\pi$
$971$	−6.54353	+	20.1389i	−0.209992	+	0.646289i	−0.999471	+	0.0325117i	$0.989649\pi$
$972$	−15.2285	+	3.33061i	−0.488454	+	0.106829i
$973$	49.4775	+	28.2037i	1.58617	+	0.904170i
$974$	21.3921	+	29.4437i	0.685446	+	0.943436i
$975$	4.29259	+	14.1576i	0.137473	+	0.453405i
$976$	−7.80177	−	2.53495i	−0.249729	−	0.0811417i
$977$	−17.7848	+	24.4787i	−0.568986	+	0.783142i	−0.992434	−	0.122779i	$-0.960819\pi$
$977$	−17.7848	+	24.4787i	−0.568986	+	0.783142i	0.423448	+	0.905920i	$0.360819\pi$
$978$	−25.9164	−	0.512386i	−0.828716	−	0.0163843i
$979$	18.3147	+	1.88854i	0.585340	+	0.0603579i
$980$	−18.6972	+	21.2309i	−0.597259	+	0.678195i
$981$	−29.2844	−	23.0986i	−0.934978	−	0.737481i
$982$	0.0902552	−	0.277777i	0.00288016	−	0.00886422i
$983$	−18.3668	−	56.5273i	−0.585811	−	1.80294i	−0.595988	−	0.802993i	$-0.703239\pi$
$983$	−18.3668	−	56.5273i	−0.585811	−	1.80294i	0.0101769	−	0.999948i	$-0.496761\pi$
$984$	−1.53308	+	1.06819i	−0.0488728	+	0.0340528i
$985$	50.4145	+	69.3896i	1.60634	+	2.21094i
$986$	−0.210517	−	0.647905i	−0.00670423	−	0.0206335i
$987$	−55.6225	+	5.04525i	−1.77048	+	0.160592i
$988$	2.74449	+	1.99399i	0.0873138	+	0.0634372i
$989$			31.2033i			0.992207i
$990$	−28.0105	+	28.8516i	−0.890231	+	0.916963i
$991$	−49.9948			−1.58814			−0.794068	−	0.607829i	$-0.792041\pi$
$991$	−49.9948			−1.58814			−0.794068	+	0.607829i	$0.792041\pi$
$992$	−1.50948	−	1.09670i	−0.0479260	−	0.0348203i
$993$	6.13924	+	2.12982i	0.194823	+	0.0675877i
$994$	16.2311	+	17.8281i	0.514820	+	0.565473i
$995$	3.25318	+	4.47761i	0.103133	+	0.141950i
$996$	14.4204	+	20.6962i	0.456927	+	0.655785i
$997$	−3.72274	+	1.20959i	−0.117900	+	0.0383081i	−0.367373	−	0.930074i	$-0.619743\pi$
$997$	−3.72274	+	1.20959i	−0.117900	+	0.0383081i	0.249473	+	0.968382i	$0.419743\pi$
$998$	28.5518	+	9.27703i	0.903790	+	0.293659i
$999$	−21.8959	+	26.6584i	−0.692754	+	0.843436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.s.a.125.3	✓	128
3.2	odd	2	inner	462.2.s.a.125.18	yes	128
7.6	odd	2	inner	462.2.s.a.125.14	yes	128
11.3	even	5	inner	462.2.s.a.377.31	yes	128
21.20	even	2	inner	462.2.s.a.125.31	yes	128
33.14	odd	10	inner	462.2.s.a.377.14	yes	128
77.69	odd	10	inner	462.2.s.a.377.18	yes	128
231.146	even	10	inner	462.2.s.a.377.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.s.a.125.3	✓	128	1.1	even	1	trivial
462.2.s.a.125.14	yes	128	7.6	odd	2	inner
462.2.s.a.125.18	yes	128	3.2	odd	2	inner
462.2.s.a.125.31	yes	128	21.20	even	2	inner
462.2.s.a.377.3	yes	128	231.146	even	10	inner
462.2.s.a.377.14	yes	128	33.14	odd	10	inner
462.2.s.a.377.18	yes	128	77.69	odd	10	inner
462.2.s.a.377.31	yes	128	11.3	even	5	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.63638 - 0.567690i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-3.26960 + 2.37551i) q^{5} +(1.42111 - 0.990177i) q^{6} +(1.78115 + 1.95640i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.35546 + 1.85791i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.63638 - 0.567690i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-3.26960 + 2.37551i) q^{5} +(1.42111 - 0.990177i) q^{6} +(1.78115 + 1.95640i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.35546 + 1.85791i) q^{9} -4.04145i q^{10} +(-3.29913 - 0.340193i) q^{11} +(-0.0342372 + 1.73171i) q^{12} +(0.442983 - 0.609714i) q^{13} +(-2.62970 + 0.291040i) q^{14} +(6.69885 - 2.03110i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.169874 + 0.123420i) q^{17} +(-2.88758 + 0.813552i) q^{18} +(-4.28096 - 1.39097i) q^{19} +(3.26960 + 2.37551i) q^{20} +(-1.80401 - 4.21255i) q^{21} +(2.21440 - 2.46909i) q^{22} -3.57303i q^{23} +(-1.38086 - 1.04557i) q^{24} +(3.50219 - 10.7786i) q^{25} +(0.232890 + 0.716762i) q^{26} +(-2.79970 - 4.37741i) q^{27} +(1.31024 - 2.29854i) q^{28} +(3.08562 - 1.00258i) q^{29} +(-2.29429 + 6.61333i) q^{30} +(1.09670 - 1.50948i) q^{31} -1.00000i q^{32} +(5.20550 + 2.42957i) q^{33} -0.209975i q^{34} +(-10.4711 - 2.16551i) q^{35} +(1.03910 - 2.81430i) q^{36} +(-2.05160 - 6.31417i) q^{37} +(3.64161 - 2.64578i) q^{38} +(-1.07102 + 0.746244i) q^{39} +(-3.84365 + 1.24888i) q^{40} +(0.333365 - 1.02599i) q^{41} +(4.46839 + 1.01660i) q^{42} -8.73301 q^{43} +(0.695945 + 3.24279i) q^{44} +(-12.1149 - 0.479227i) q^{45} +(2.89064 + 2.10017i) q^{46} +(3.76619 - 11.5911i) q^{47} +(1.65754 - 0.502567i) q^{48} +(-0.654994 + 6.96929i) q^{49} +(6.66156 + 9.16885i) q^{50} +(0.348042 - 0.105527i) q^{51} +(-0.716762 - 0.232890i) q^{52} +(-4.39833 + 6.05378i) q^{53} +(5.18702 + 0.307974i) q^{54} +(11.5950 - 6.72481i) q^{55} +(1.08942 + 2.41105i) q^{56} +(6.21563 + 4.70641i) q^{57} +(-1.00258 + 3.08562i) q^{58} +(1.60917 + 4.95252i) q^{59} +(-4.00175 - 5.74334i) q^{60} +(4.82176 + 6.63658i) q^{61} +(0.576570 + 1.77450i) q^{62} +(0.560613 + 7.91743i) q^{63} +(0.809017 + 0.587785i) q^{64} +3.04583i q^{65} +(-5.02528 + 2.78327i) q^{66} +10.5693 q^{67} +(0.169874 + 0.123420i) q^{68} +(-2.02837 + 5.84682i) q^{69} +(7.90669 - 7.19844i) q^{70} +(-5.35632 - 7.37234i) q^{71} +(1.66605 + 2.49485i) q^{72} +(-9.89230 + 3.21420i) q^{73} +(6.31417 + 2.05160i) q^{74} +(-11.8498 + 15.6497i) q^{75} +4.50127i q^{76} +(-5.21070 - 7.06035i) q^{77} +(0.0258028 - 1.30510i) q^{78} +(-1.07577 - 0.781596i) q^{79} +(1.24888 - 3.84365i) q^{80} +(2.09635 + 8.75245i) q^{81} +(0.634098 + 0.872761i) q^{82} +(11.7821 - 8.56017i) q^{83} +(-3.44890 + 3.01746i) q^{84} +(0.262233 - 0.807071i) q^{85} +(5.13314 - 7.06515i) q^{86} +(-5.61840 - 0.111080i) q^{87} +(-3.03254 - 1.34303i) q^{88} -5.55137 q^{89} +(7.50865 - 9.51946i) q^{90} +(1.98186 - 0.219342i) q^{91} +(-3.39815 + 1.10413i) q^{92} +(-2.65153 + 1.84749i) q^{93} +(7.16372 + 9.86001i) q^{94} +(17.3013 - 5.62153i) q^{95} +(-0.567690 + 1.63638i) q^{96} +(2.66417 - 3.66691i) q^{97} +(-5.25328 - 4.62635i) q^{98} +(-7.13891 - 6.93080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9	\( 128 q + 32 q^{4} - 4 q^{7} + 12 q^{9} + 12 q^{15} - 32 q^{16} - 16 q^{18} - 20 q^{21} - 36 q^{25} - 6 q^{28} + 8 q^{36} - 16 q^{37} + 60 q^{39} + 4 q^{42} - 64 q^{43} - 8 q^{46} - 40 q^{49} - 28 q^{51} + 88 q^{57} + 92 q^{58} + 8 q^{60} - 42 q^{63} + 32 q^{64} - 64 q^{67} - 26 q^{70} - 24 q^{72} - 64 q^{78} + 136 q^{79} - 116 q^{81} - 28 q^{85} - 40 q^{91} - 76 q^{93} - 160 q^{99}+O(q^{100}) \) 128 * q + 32 * q^4 - 4 * q^7 + 12 * q^9 + 12 * q^15 - 32 * q^16 - 16 * q^18 - 20 * q^21 - 36 * q^25 - 6 * q^28 + 8 * q^36 - 16 * q^37 + 60 * q^39 + 4 * q^42 - 64 * q^43 - 8 * q^46 - 40 * q^49 - 28 * q^51 + 88 * q^57 + 92 * q^58 + 8 * q^60 - 42 * q^63 + 32 * q^64 - 64 * q^67 - 26 * q^70 - 24 * q^72 - 64 * q^78 + 136 * q^79 - 116 * q^81 - 28 * q^85 - 40 * q^91 - 76 * q^93 - 160 * q^99

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