LMFDB - Embedded newform 462.2.s.a.125.18

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			125.18
Character	$\chi$	$=$	462.125
Dual form			462.2.s.a.377.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-1.65754 - 0.502567i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(3.26960 - 2.37551i) q^{5} +(-1.38086 + 1.04557i) q^{6} +(1.78115 + 1.95640i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.49485 + 1.66605i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-1.65754 - 0.502567i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(3.26960 - 2.37551i) q^{5} +(-1.38086 + 1.04557i) q^{6} +(1.78115 + 1.95640i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.49485 + 1.66605i) 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} +(-6.61333 + 2.29429i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.169874 - 0.123420i) q^{17} +(2.81430 - 1.03910i) q^{18} +(-4.28096 - 1.39097i) q^{19} +(-3.26960 - 2.37551i) q^{20} +(-1.96910 - 4.13795i) q^{21} +(2.21440 - 2.46909i) q^{22} +3.57303i q^{23} +(1.42111 + 0.990177i) q^{24} +(3.50219 - 10.7786i) q^{25} +(-0.232890 - 0.716762i) q^{26} +(-3.29801 - 4.01536i) q^{27} +(1.31024 - 2.29854i) q^{28} +(-3.08562 + 1.00258i) q^{29} +(-2.03110 + 6.69885i) q^{30} +(1.09670 - 1.50948i) q^{31} +1.00000i q^{32} +(-5.29746 - 2.22192i) q^{33} -0.209975i q^{34} +(10.4711 + 2.16551i) q^{35} +(0.813552 - 2.88758i) q^{36} +(-2.05160 - 6.31417i) q^{37} +(-3.64161 + 2.64578i) q^{38} +(-1.04068 + 0.787994i) q^{39} +(-3.84365 + 1.24888i) q^{40} +(-0.333365 + 1.02599i) q^{41} +(-4.50508 - 0.839189i) 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} +(1.63638 - 0.567690i) q^{48} +(-0.654994 + 6.96929i) q^{49} +(-6.66156 - 9.16885i) q^{50} +(-0.343599 + 0.119201i) 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} +(6.39680 + 4.45705i) q^{57} +(-1.00258 + 3.08562i) q^{58} +(-1.60917 - 4.95252i) q^{59} +(4.22563 + 5.58068i) q^{60} +(4.82176 + 6.63658i) q^{61} +(-0.576570 - 1.77450i) q^{62} +(1.18426 + 7.84841i) q^{63} +(0.809017 + 0.587785i) q^{64} -3.04583i q^{65} +(-4.91134 + 2.97973i) q^{66} +10.5693 q^{67} +(-0.169874 - 0.123420i) q^{68} +(1.79569 - 5.92242i) q^{69} +(7.90669 - 7.19844i) q^{70} +(5.35632 + 7.37234i) q^{71} +(-1.85791 - 2.35546i) q^{72} +(-9.89230 + 3.21420i) q^{73} +(-6.31417 - 2.05160i) q^{74} +(-11.2220 + 16.1059i) 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} +(3.44858 + 8.31308i) q^{81} +(0.634098 + 0.872761i) q^{82} +(-11.7821 + 8.56017i) q^{83} +(-3.32694 + 3.15142i) 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} +(6.73324 - 10.0828i) q^{90} +(1.98186 - 0.219342i) q^{91} +(3.39815 - 1.10413i) q^{92} +(-2.57643 + 1.95085i) q^{93} +(7.16372 + 9.86001i) q^{94} +(-17.3013 + 5.62153i) q^{95} +(0.502567 - 1.65754i) q^{96} +(2.66417 - 3.66691i) q^{97} +(5.25328 + 4.62635i) q^{98} +(7.66407 + 6.34524i) 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
$3$	−1.65754	−	0.502567i	−0.956979	−	0.290157i
$3$	−1.65754	−	0.502567i	−0.956979	−	0.290157i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	3.26960	−	2.37551i	1.46221	−	1.06236i	0.479430	−	0.877580i	$-0.340843\pi$
$5$	3.26960	−	2.37551i	1.46221	−	1.06236i	0.982780	−	0.184778i	$-0.0591567\pi$
$6$	−1.38086	+	1.04557i	−0.563734	+	0.426854i
$7$	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
$9$	2.49485	+	1.66605i	0.831618	+	0.555349i
$10$		−	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
$15$	−6.61333	+	2.29429i	−1.70756	+	0.592383i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.169874	−	0.123420i	0.0412004	−	0.0299338i	−0.566994	−	0.823722i	$-0.691894\pi$
$17$	0.169874	−	0.123420i	0.0412004	−	0.0299338i	0.608195	+	0.793788i	$0.291894\pi$
$18$	2.81430	−	1.03910i	0.663336	−	0.244918i
$19$	−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
$21$	−1.96910	−	4.13795i	−0.429693	−	0.902975i
$22$	2.21440	−	2.46909i	0.472112	−	0.526412i
$23$			3.57303i			0.745028i	0.928027	+	0.372514i	$0.121504\pi$
$23$			3.57303i			0.745028i	−0.928027	+	0.372514i	$0.878496\pi$
$24$	1.42111	+	0.990177i	0.290083	+	0.202119i
$25$	3.50219	−	10.7786i	0.700438	−	2.15573i
$26$	−0.232890	−	0.716762i	−0.0456735	−	0.140569i
$27$	−3.29801	−	4.01536i	−0.634702	−	0.772757i
$28$	1.31024	−	2.29854i	0.247612	−	0.434383i
$29$	−3.08562	+	1.00258i	−0.572986	+	0.186174i	−0.581156	−	0.813792i	$-0.697399\pi$
$29$	−3.08562	+	1.00258i	−0.572986	+	0.186174i	0.00816997	+	0.999967i	$0.497399\pi$
$30$	−2.03110	+	6.69885i	−0.370826	+	1.22304i
$31$	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
$33$	−5.29746	−	2.22192i	−0.922169	−	0.386786i
$34$		−	0.209975i		−	0.0360105i
$35$	10.4711	+	2.16551i	1.76994	+	0.366038i
$36$	0.813552	−	2.88758i	0.135592	−	0.481264i
$37$	−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
$39$	−1.04068	+	0.787994i	−0.166643	+	0.126180i
$40$	−3.84365	+	1.24888i	−0.607734	+	0.197465i
$41$	−0.333365	+	1.02599i	−0.0520629	+	0.160233i	−0.973707	−	0.227802i	$-0.926846\pi$
$41$	−0.333365	+	1.02599i	−0.0520629	+	0.160233i	0.921645	+	0.388035i	$0.126846\pi$
$42$	−4.50508	−	0.839189i	−0.695149	−	0.129490i
$43$	−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	$0.448513\pi$
$47$	−3.76619	+	11.5911i	−0.549355	+	1.69074i	−0.710403	+	0.703795i	$0.751487\pi$
$48$	1.63638	−	0.567690i	0.236191	−	0.0819390i
$49$	−0.654994	+	6.96929i	−0.0935706	+	0.995613i
$50$	−6.66156	−	9.16885i	−0.942087	−	1.29667i
$51$	−0.343599	+	0.119201i	−0.0481134	+	0.0166915i
$52$	−0.716762	−	0.232890i	−0.0993970	−	0.0322960i
$53$	4.39833	−	6.05378i	0.604157	−	0.831551i	−0.391924	−	0.919998i	$-0.628190\pi$
$53$	4.39833	−	6.05378i	0.604157	−	0.831551i	0.996081	+	0.0884470i	$0.0281904\pi$
$54$	−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
$57$	6.39680	+	4.45705i	0.847276	+	0.590351i
$58$	−1.00258	+	3.08562i	−0.131645	+	0.405162i
$59$	−1.60917	−	4.95252i	−0.209496	−	0.644763i	−0.999499	−	0.0316594i	$-0.989921\pi$
$59$	−1.60917	−	4.95252i	−0.209496	−	0.644763i	0.790003	−	0.613104i	$-0.210079\pi$
$60$	4.22563	+	5.58068i	0.545527	+	0.720463i
$61$	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
$63$	1.18426	+	7.84841i	0.149203	+	0.988807i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		−	3.04583i		−	0.377789i
$66$	−4.91134	+	2.97973i	−0.604544	+	0.366779i
$67$	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
$69$	1.79569	−	5.92242i	0.216175	−	0.712976i
$70$	7.90669	−	7.19844i	0.945030	−	0.860378i
$71$	5.35632	+	7.37234i	0.635678	+	0.874936i	0.998376	−	0.0569707i	$-0.0181442\pi$
$71$	5.35632	+	7.37234i	0.635678	+	0.874936i	−0.362697	+	0.931907i	$0.618144\pi$
$72$	−1.85791	−	2.35546i	−0.218957	−	0.277593i
$73$	−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
$75$	−11.2220	+	16.1059i	−1.29580	+	1.85975i
$76$			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
$81$	3.44858	+	8.31308i	0.383176	+	0.923676i
$82$	0.634098	+	0.872761i	0.0700244	+	0.0963803i
$83$	−11.7821	+	8.56017i	−1.29325	+	0.939601i	−0.999866	−	0.0163936i	$-0.994782\pi$
$83$	−11.7821	+	8.56017i	−1.29325	+	0.939601i	−0.293384	+	0.955995i	$0.594782\pi$
$84$	−3.32694	+	3.15142i	−0.362999	+	0.343849i
$85$	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	$-0.404940\pi$
$89$	5.55137			0.588444			0.294222	+	0.955737i	$0.404940\pi$
$90$	6.73324	−	10.0828i	0.709746	−	1.06282i
$91$	1.98186	−	0.219342i	0.207756	−	0.0229932i
$92$	3.39815	−	1.10413i	0.354282	−	0.115113i
$93$	−2.57643	+	1.95085i	−0.267164	+	0.202294i
$94$	7.16372	+	9.86001i	0.738881	+	1.01698i
$95$	−17.3013	+	5.62153i	−1.77508	+	0.576757i
$96$	0.502567	−	1.65754i	0.0512930	−	0.169172i
$97$	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
$99$	7.66407	+	6.34524i	0.770268	+	0.637720i
$100$	−11.3333			−1.13333
$101$	−6.60680	−	4.80012i	−0.657401	−	0.477630i	0.208383	−	0.978047i	$-0.433180\pi$
$101$	−6.60680	−	4.80012i	−0.657401	−	0.477630i	−0.865784	+	0.500418i	$0.833180\pi$
$102$	−0.105527	+	0.348042i	−0.0104487	+	0.0344613i
$103$	−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
$105$	−16.2679	−	8.85184i	−1.58758	−	0.863851i
$106$	−2.31234	−	7.11664i	−0.224594	−	0.691230i
$107$	6.98309	+	2.26894i	0.675081	+	0.219347i	0.626440	−	0.779469i	$-0.284511\pi$
$107$	6.98309	+	2.26894i	0.675081	+	0.219347i	0.0486404	+	0.998816i	$0.484511\pi$
$108$	−2.79970	+	4.37741i	−0.269401	+	0.421216i
$109$	−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	0.908660	−	0.417538i	$-0.137107\pi$
$113$	14.8648	+	4.82985i	1.39836	+	0.454354i	0.489699	+	0.871892i	$0.337107\pi$
$114$	7.36577	−	2.55533i	0.689868	−	0.239328i
$115$	8.48774	+	11.6824i	0.791486	+	1.08939i
$116$	1.90702	+	2.62479i	0.177062	+	0.243706i
$117$	2.12099	−	0.783116i	0.196086	−	0.0723991i
$118$	−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
$123$	1.06819	−	1.53308i	0.0963158	−	0.138233i
$124$	−1.77450	−	0.576570i	−0.159355	−	0.0517775i
$125$	−7.90954	−	24.3431i	−0.707451	−	2.17731i
$126$	7.04559	+	3.65509i	0.627671	+	0.325621i
$127$	−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
$129$	14.4753	+	4.38892i	1.27448	+	0.386423i
$130$	−2.46413	−	1.79029i	−0.216118	−	0.157019i
$131$	13.0907			1.14374			0.571868	−	0.820346i	$-0.306219\pi$
$131$	13.0907			1.14374			0.571868	+	0.820346i	$0.306219\pi$
$132$	−0.476164	+	5.72479i	−0.0414447	+	0.498279i
$133$	−4.90376	−	10.8528i	−0.425210	−	0.941057i
$134$	6.21250	−	8.55078i	0.536678	−	0.738675i
$135$	−20.3217	−	5.29420i	−1.74901	−	0.455652i
$136$	−0.199698	+	0.0648859i	−0.0171240	+	0.00556392i
$137$	−5.71572	−	7.86701i	−0.488327	−	0.672124i	0.491752	−	0.870735i	$-0.336357\pi$
$137$	−5.71572	−	7.86701i	−0.488327	−	0.672124i	−0.980078	+	0.198612i	$0.936357\pi$
$138$	−3.73586	−	4.93385i	−0.318018	−	0.419997i
$139$	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
$141$	12.0679	−	17.3200i	1.01630	−	1.45860i
$142$	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
$147$	4.58821	−	11.2227i	0.378429	−	0.925630i
$148$	−5.37116	+	3.90237i	−0.441506	+	0.320773i
$149$	5.05977	+	6.96418i	0.414513	+	0.570528i	0.964312	−	0.264769i	$-0.0852958\pi$
$149$	5.05977	+	6.96418i	0.414513	+	0.570528i	−0.549799	+	0.835297i	$0.685296\pi$
$150$	6.43382	+	18.5456i	0.525319	+	1.51424i
$151$	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
$156$	1.07102	+	0.746244i	0.0857499	+	0.0597474i
$157$	−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
$159$	−10.3328	+	7.82390i	−0.819446	+	0.620476i
$160$	2.37551	+	3.26960i	0.187800	+	0.258485i
$161$	−6.99027	+	6.36410i	−0.550910	+	0.501562i
$162$	8.75245	+	2.09635i	0.687657	+	0.164704i
$163$	−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
$165$	−22.5988	+	5.31936i	−1.75931	+	0.414111i
$166$			14.5634i			1.13034i
$167$	10.1342	+	7.36290i	0.784205	+	0.569758i	0.906238	−	0.422768i	$-0.138941\pi$
$167$	10.1342	+	7.36290i	0.784205	+	0.569758i	−0.122033	+	0.992526i	$0.538941\pi$
$168$	0.594031	+	4.54391i	0.0458305	+	0.350570i
$169$	3.84170	+	11.8235i	0.295516	+	0.909504i
$170$	−0.498797	−	0.686536i	−0.0382560	−	0.0526549i
$171$	−8.36295	−	10.6025i	−0.639531	−	0.810797i
$172$	2.69865	+	8.30559i	0.205770	+	0.633295i
$173$	1.48178	−	4.56044i	0.112657	−	0.346724i	−0.878794	−	0.477202i	$-0.841651\pi$
$173$	1.48178	−	4.56044i	0.112657	−	0.346724i	0.991451	+	0.130478i	$0.0416511\pi$
$174$	3.21255	−	4.61067i	0.243542	−	0.349534i
$175$	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	−0.110707	−	0.993853i	$-0.535311\pi$
$179$	−10.4951	−	3.41007i	−0.784443	−	0.254881i	−0.673736	+	0.738972i	$0.735311\pi$
$180$	−4.19947	−	11.3738i	−0.313010	−	0.847756i
$181$	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
$183$	−4.65691	−	13.4236i	−0.344249	−	0.992303i
$184$	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
$189$	1.98140	−	13.6042i	0.144125	−	0.989559i
$190$	−5.62153	+	17.3013i	−0.407829	+	1.25517i
$191$	17.9262	−	5.82457i	1.29709	−	0.421451i	0.422523	−	0.906352i	$-0.361144\pi$
$191$	17.9262	−	5.82457i	1.29709	−	0.421451i	0.874569	+	0.484901i	$0.161144\pi$
$192$	−1.04557	−	1.38086i	−0.0754578	−	0.0996550i
$193$	−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
$195$	−1.53073	+	5.04858i	−0.109618	+	0.361536i
$196$	6.83059	−	1.53069i	0.487899	−	0.109335i
$197$			21.2226i			1.51205i	0.654543	+	0.756025i	$0.272861\pi$
$197$			21.2226i			1.51205i	−0.654543	+	0.756025i	$0.727139\pi$
$198$	9.63823	−	2.47073i	0.684959	−	0.175587i
$199$		−	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
$201$	−17.5191	−	5.31180i	−1.23570	−	0.374666i
$202$	−7.76676	+	2.52357i	−0.546467	+	0.177558i
$203$	−7.45741	−	4.25096i	−0.523408	−	0.298359i
$204$	0.219545	+	0.289947i	0.0153712	+	0.0203003i
$205$	1.34728	+	4.14650i	0.0940980	+	0.289604i
$206$	−4.20169	+	12.9315i	−0.292746	+	0.900978i
$207$	−5.95283	+	8.91417i	−0.413750	+	0.619578i
$208$			0.753648i			0.0522561i
$209$	−13.6503	−	6.04535i	−0.944208	−	0.418165i
$210$	−16.7233	+	7.95803i	−1.15402	+	0.549156i
$211$	−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
$213$	−5.17320	−	14.9118i	−0.354462	−	1.02174i
$214$	5.94017	−	4.31579i	0.406062	−	0.295021i
$215$	−28.5535	+	20.7453i	−1.94733	+	1.41482i
$216$	1.89578	+	4.83798i	0.128991	+	0.329183i
$217$	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
$222$	9.43490	+	6.57389i	0.633229	+	0.441211i
$223$	−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
$225$	26.6951	−	21.0563i	1.77968	−	1.40375i
$226$	12.6447	−	9.18692i	0.841114	−	0.611105i
$227$	3.78474	+	11.6482i	0.251202	+	0.773120i	0.994554	+	0.104220i	$0.0332347\pi$
$227$	3.78474	+	11.6482i	0.251202	+	0.773120i	−0.743352	+	0.668900i	$0.766765\pi$
$228$	2.26219	−	7.46102i	0.149817	−	0.494118i
$229$	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
$231$	−5.08863	−	14.3215i	−0.334807	−	0.942287i
$232$	3.24442			0.213006
$233$	−2.59330	+	3.56937i	−0.169893	+	0.233838i	−0.885470	−	0.464696i	$-0.846164\pi$
$233$	−2.59330	+	3.56937i	−0.169893	+	0.233838i	0.715577	+	0.698533i	$0.246164\pi$
$234$	0.613132	−	2.17622i	0.0400817	−	0.142264i
$235$	15.2209	+	46.8450i	0.992900	+	3.05583i
$236$	−4.21286	+	3.06082i	−0.274234	+	0.199243i
$237$	1.39033	+	1.83617i	0.0903117	+	0.119272i
$238$	0.410795	−	0.373998i	0.0266279	−	0.0242427i
$239$	−17.3868	−	5.64931i	−1.12466	−	0.365423i	−0.313114	−	0.949715i	$-0.601372\pi$
$239$	−17.3868	−	5.64931i	−1.12466	−	0.365423i	−0.811543	+	0.584292i	$0.801372\pi$
$240$	4.00175	−	5.74334i	0.258312	−	0.370731i
$241$			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
$246$	−0.612419	−	1.76531i	−0.0390464	−	0.112552i
$247$	−2.74449	+	1.99399i	−0.174628	+	0.126874i
$248$	−1.50948	+	1.09670i	−0.0958520	+	0.0696405i
$249$	23.8313	−	8.26752i	1.51024	−	0.523933i
$250$	−24.3431	−	7.90954i	−1.53959	−	0.500243i
$251$	3.74043	+	2.71758i	0.236094	+	0.171532i	0.699541	−	0.714592i	$-0.253388\pi$
$251$	3.74043	+	2.71758i	0.236094	+	0.171532i	−0.463448	+	0.886124i	$0.653388\pi$
$252$	7.09832	−	3.55159i	0.447152	−	0.223729i
$253$	−1.21552	+	11.7879i	−0.0764190	+	0.741098i
$254$			9.78286i			0.613831i
$255$	−0.840268	+	1.20596i	−0.0526196	+	0.0755201i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.75229	+	5.39299i	0.109305	+	0.336406i	0.990717	−	0.135943i	$-0.0434064\pi$
$257$	1.75229	+	5.39299i	0.109305	+	0.336406i	−0.881412	+	0.472348i	$0.843406\pi$
$258$	12.0591	−	9.13100i	0.750765	−	0.568472i
$259$	8.69883	−	15.2602i	0.540519	−	0.948226i
$260$	−2.89676	+	0.941214i	−0.179649	+	0.0583716i
$261$	−9.36852	−	2.63950i	−0.579897	−	0.163381i
$262$	7.69450	−	10.5906i	0.475368	−	0.654287i
$263$		−	12.4117i		−	0.765339i	−0.923885	−	0.382669i	$-0.875005\pi$
$263$		−	12.4117i		−	0.765339i	0.923885	−	0.382669i	$-0.124995\pi$
$264$	4.35157	+	3.75017i	0.267821	+	0.230807i
$265$		−	30.2417i		−	1.85773i
$266$	−11.6625	−	2.41189i	−0.715071	−	0.147883i
$267$	−9.20159	−	2.78993i	−0.563128	−	0.170741i
$268$	−3.26611	−	10.0520i	−0.199509	−	0.614026i
$269$	8.28375	−	6.01850i	0.505069	−	0.366954i	−0.305881	−	0.952070i	$-0.598951\pi$
$269$	8.28375	−	6.01850i	0.505069	−	0.366954i	0.810950	+	0.585116i	$0.198951\pi$
$270$	−16.2279	+	13.3287i	−0.987598	+	0.811161i
$271$	−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
$273$	−3.39525	−	0.632453i	−0.205490	−	0.0382778i
$274$	−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
$279$	5.25097	−	1.93877i	0.314367	−	0.116071i
$280$	−9.28942	−	5.29527i	−0.555149	−	0.316453i
$281$	−11.7169	−	16.1270i	−0.698974	−	0.962056i	−0.999964	−	0.00842829i	$-0.997317\pi$
$281$	−11.7169	−	16.1270i	−0.698974	−	0.962056i	0.300990	−	0.953627i	$-0.402683\pi$
$282$	−6.91881	−	19.9436i	−0.412009	−	1.18762i
$283$	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
$288$	−1.66605	+	2.49485i	−0.0981727	+	0.147011i
$289$	−5.23966	+	16.1260i	−0.308216	+	0.948590i
$290$	4.05188	+	12.4704i	0.237934	+	0.732287i
$291$	−6.25882	+	4.73912i	−0.366899	+	0.277812i
$292$	6.11378	+	8.41489i	0.357782	+	0.492444i
$293$	6.91828	+	21.2923i	0.404170	+	1.24391i	0.921586	+	0.388174i	$0.126894\pi$
$293$	6.91828	+	21.2923i	0.404170	+	1.24391i	−0.517416	+	0.855734i	$0.673106\pi$
$294$	−6.38245	−	10.3085i	−0.372232	−	0.601202i
$295$	−17.0261	−	12.3702i	−0.991297	−	0.720219i
$296$			6.63911i			0.385891i
$297$	−9.51457	−	14.3692i	−0.552091	−	0.833784i
$298$	8.60820			0.498659
$299$	2.17852	+	1.58279i	0.125987	+	0.0915351i
$300$	18.7854	+	5.69575i	1.08458	+	0.328845i
$301$	−15.5548	−	17.0853i	−0.896565	−	0.984778i
$302$	−13.6719	−	18.8177i	−0.786727	−	1.08284i
$303$	8.53862	+	11.2767i	0.490531	+	0.647831i
$304$	4.28096	−	1.39097i	0.245530	−	0.0797776i
$305$	31.5305	+	10.2449i	1.80543	+	0.586620i
$306$	0.349828	−	0.523857i	0.0199984	−	0.0299469i
$307$		−	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	$-0.748167\pi$
$311$	5.00394	−	15.4005i	0.283748	−	0.873285i	0.986771	−	0.162119i	$-0.0518327\pi$
$312$	1.23325	−	0.427838i	0.0698191	−	0.0242216i
$313$	−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
$315$	22.5160	+	22.8480i	1.26863	+	1.28734i
$316$	−0.410909	+	1.26465i	−0.0231155	+	0.0711421i
$317$	−9.34020	+	12.8557i	−0.524598	+	0.722047i	−0.986295	−	0.164990i	$-0.947241\pi$
$317$	−9.34020	+	12.8557i	−0.524598	+	0.722047i	0.461697	+	0.887038i	$0.347241\pi$
$318$	0.256193	+	12.9582i	0.0143666	+	0.726660i
$319$	−10.5210	+	2.25794i	−0.589060	+	0.126420i
$320$	4.04145			0.225924
$321$	−10.4344	−	7.27033i	−0.582393	−	0.405790i
$322$	1.03989	+	9.39597i	0.0579510	+	0.523617i
$323$	−0.898896	+	0.292069i	−0.0500159	+	0.0162512i
$324$	6.84054	−	5.84868i	0.380030	−	0.324927i
$325$	−5.02047	−	6.91009i	−0.278486	−	0.383303i
$326$	−14.2333	+	4.62468i	−0.788310	+	0.256137i
$327$	20.6074	+	6.24820i	1.13959	+	0.345526i
$328$	0.634098	−	0.872761i	0.0350122	−	0.0481902i
$329$	−29.3851	+	13.2774i	−1.62005	+	0.732008i
$330$	−8.97977	+	21.4094i	−0.494320	+	1.17855i
$331$	−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
$333$	5.40127	−	19.1710i	0.295988	−	1.05056i
$334$	11.9134	−	3.87091i	0.651874	−	0.211807i
$335$	34.5575	−	25.1075i	1.88808	−	1.37177i
$336$	4.02526	+	2.19026i	0.219596	+	0.119489i
$337$	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
$339$	−22.2115	−	15.4762i	−1.20637	−	0.840551i
$340$	−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
$345$	−8.19756	−	23.6296i	−0.441342	−	1.27218i
$346$	−2.81851	−	3.87934i	−0.151524	−	0.208555i
$347$	−2.53612	−	3.49067i	−0.136146	−	0.187389i	0.735500	−	0.677525i	$-0.236947\pi$
$347$	−2.53612	−	3.49067i	−0.136146	−	0.187389i	−0.871646	+	0.490136i	$0.836947\pi$
$348$	−1.84182	−	5.30909i	−0.0987321	−	0.284597i
$349$	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	$-0.383772\pi$
$353$	13.4179			0.714164			0.357082	+	0.934073i	$0.383772\pi$
$354$	7.40026	+	5.15623i	0.393319	+	0.274051i
$355$	35.0261	+	11.3807i	1.85899	+	0.604023i
$356$	−1.71547	−	5.27966i	−0.0909196	−	0.279822i
$357$	−0.845206	−	0.459901i	−0.0447330	−	0.0243405i
$358$	−8.92769	+	6.48634i	−0.471843	+	0.342814i
$359$	−11.0362	+	3.58589i	−0.582470	+	0.189256i	−0.585407	−	0.810740i	$-0.699065\pi$
$359$	−11.0362	+	3.58589i	−0.582470	+	0.189256i	0.00293703	+	0.999996i	$0.499065\pi$
$360$	−11.6700	−	3.28793i	−0.615064	−	0.173289i
$361$	1.02053	+	0.741459i	0.0537121	+	0.0390241i
$362$	2.43023			0.127730
$363$	−16.7211	−	9.13256i	−0.877632	−	0.479335i
$364$	−0.821036	−	1.81708i	−0.0430340	−	0.0952411i
$365$	−24.7085	+	34.0084i	−1.29330	+	1.78008i
$366$	−13.5972	−	4.12269i	−0.710738	−	0.215497i
$367$	−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
$369$	−2.54105	+	2.00430i	−0.132282	+	0.104340i
$370$	−25.5184	+	8.29144i	−1.32664	+	0.431051i
$371$	19.6777	−	2.17782i	1.02162	−	0.113067i
$372$	2.65153	+	1.84749i	0.137475	+	0.0957879i
$373$	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
$378$	−9.84139	−	9.59933i	−0.506186	−	0.493736i
$379$	−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
$381$	16.0084	−	5.55363i	0.820137	−	0.284521i
$382$	5.82457	−	17.9262i	0.298011	−	0.917183i
$383$	−9.39339	−	6.82469i	−0.479980	−	0.348726i	0.321338	−	0.946965i	$-0.395867\pi$
$383$	−9.39339	−	6.82469i	−0.479980	−	0.348726i	−0.801318	+	0.598239i	$0.795867\pi$
$384$	−1.73171	+	0.0342372i	−0.0883711	+	0.00174716i
$385$	33.8088	+	10.7065i	1.72306	+	0.545654i
$386$			8.26047i			0.420447i
$387$	−21.7876	−	14.5496i	−1.10752	−	0.739598i
$388$	−4.31071	−	1.40064i	−0.218843	−	0.0711065i
$389$	21.9079	−	7.11830i	1.11077	−	0.360912i	0.304534	−	0.952501i	$-0.401499\pi$
$389$	21.9079	−	7.11830i	1.11077	−	0.360912i	0.806239	+	0.591589i	$0.201499\pi$
$390$	3.18464	+	4.20587i	0.161261	+	0.212972i
$391$	0.440984	+	0.606963i	0.0223015	+	0.0306954i
$392$	2.77657	−	6.42578i	0.140238	−	0.324551i
$393$	−21.6982	−	6.57893i	−1.09453	−	0.331863i
$394$	17.1695	+	12.4743i	0.864985	+	0.628449i
$395$	−5.37404			−0.270397
$396$	3.66635	−	9.24975i	0.184241	−	0.464817i
$397$			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
$399$	2.67389	+	20.4534i	0.133862	+	1.02395i
$400$	3.50219	+	10.7786i	0.175109	+	0.538932i
$401$	3.09923	+	4.26572i	0.154768	+	0.213020i	0.879359	−	0.476159i	$-0.157971\pi$
$401$	3.09923	+	4.26572i	0.154768	+	0.213020i	−0.724591	+	0.689179i	$0.757971\pi$
$402$	−14.5948	+	11.0510i	−0.727922	+	0.551175i
$403$	−0.434530	−	1.33735i	−0.0216455	−	0.0666180i
$404$	−2.52357	+	7.76676i	−0.125552	+	0.386411i
$405$	31.0232	+	18.9883i	1.54156	+	0.943538i
$406$	−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
$411$	5.52031	+	15.9124i	0.272297	+	0.784900i
$412$	7.99209	+	11.0002i	0.393742	+	0.541939i
$413$	6.82292	−	11.9694i	0.335734	−	0.588974i
$414$	3.71273	+	10.0556i	0.182471	+	0.494204i
$415$	−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	$-0.192731\pi$
$419$	33.6612			1.64446			0.822228	+	0.569159i	$0.192731\pi$
$420$	−3.39154	+	18.2071i	−0.165490	+	0.888414i
$421$	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
$423$	−28.7075	+	22.6435i	−1.39580	+	1.10097i
$424$	−6.05378	+	4.39833i	−0.293998	+	0.213602i
$425$	−0.735373	−	2.26325i	−0.0356708	−	0.109784i
$426$	−15.1047	−	4.57975i	−0.731823	−	0.221890i
$427$	−4.39552	+	21.2540i	−0.212714	+	1.02856i
$428$		−	7.34246i		−	0.354911i
$429$	−3.70142	+	2.24566i	−0.178706	+	0.108422i
$430$			35.2940i			1.70203i
$431$	8.09674	−	11.1442i	0.390006	−	0.536798i	−0.568194	−	0.822894i	$-0.692358\pi$
$431$	8.09674	−	11.1442i	0.390006	−	0.536798i	0.958201	+	0.286097i	$0.0923579\pi$
$432$	5.02832	+	1.30998i	0.241925	+	0.0630262i
$433$	−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
$435$	18.1061	−	13.7097i	0.868119	−	0.657331i
$436$	3.84187	+	11.8241i	0.183992	+	0.566270i
$437$	4.96997	−	15.2960i	0.237746	−	0.731707i
$438$	10.2992	−	14.7815i	0.492115	−	0.706287i
$439$		−	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
$441$	−13.2453	+	16.2961i	−0.630727	+	0.776005i
$442$	−0.128025	−	0.0930155i	−0.00608952	−	0.00442430i
$443$	−26.0214	−	8.45486i	−1.23631	−	0.401702i	−0.383315	−	0.923617i	$-0.625218\pi$
$443$	−26.0214	−	8.45486i	−1.23631	−	0.401702i	−0.852997	+	0.521915i	$0.825218\pi$
$444$	10.8641	−	3.76896i	0.515587	−	0.178867i
$445$	18.1508	−	13.1873i	0.860429	−	0.625138i
$446$	−13.8280	+	10.0467i	−0.654776	+	0.475723i
$447$	−4.88679	−	14.0862i	−0.231137	−	0.666257i
$448$	0.291040	+	2.62970i	0.0137503	+	0.124241i
$449$	14.0557	−	19.3461i	0.663331	−	0.912997i	−0.336255	−	0.941771i	$-0.609160\pi$
$449$	14.0557	−	19.3461i	0.663331	−	0.912997i	0.999586	+	0.0287738i	$0.00916025\pi$
$450$	−1.34388	−	33.9734i	−0.0633512	−	1.60152i
$451$	−1.44885	+	3.27147i	−0.0682237	+	0.154048i
$452$		−	15.6297i		−	0.735160i
$453$	−23.0314	+	33.0549i	−1.08211	+	1.55306i
$454$	11.6482	+	3.78474i	0.546679	+	0.177627i
$455$	5.95886	−	5.42509i	0.279356	−	0.254332i
$456$	−4.70641	−	6.21563i	−0.220398	−	0.291073i
$457$	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
$459$	−1.05582	−	0.275062i	−0.0492816	−	0.0128388i
$460$	8.48774	−	11.6824i	0.395743	−	0.544694i
$461$	9.63919			0.448942			0.224471	−	0.974481i	$-0.427935\pi$
$461$	9.63919			0.448942			0.224471	+	0.974481i	$0.427935\pi$
$462$	−14.5774	−	4.30119i	−0.678201	−	0.200110i
$463$	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
$465$	−3.78966	+	12.4988i	−0.175741	+	0.579620i
$466$	1.36338	+	4.19605i	0.0631574	+	0.194378i
$467$	−5.53908	+	4.02438i	−0.256318	+	0.186226i	−0.708522	−	0.705688i	$-0.750638\pi$
$467$	−5.53908	+	4.02438i	−0.256318	+	0.186226i	0.452204	+	0.891914i	$0.350638\pi$
$468$	−1.40021	−	1.77518i	−0.0647247	−	0.0820579i
$469$	18.8256	+	20.6778i	0.869286	+	0.954814i
$470$	46.8450	+	15.2209i	2.16080	+	0.702086i
$471$	23.3921	+	16.2987i	1.07785	+	0.751006i
$472$			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
$477$	21.0591	−	7.77547i	0.964228	−	0.356014i
$478$	−14.7901	+	10.7456i	−0.676483	+	0.491493i
$479$	15.9277	−	11.5722i	0.727756	−	0.528746i	−0.161097	−	0.986939i	$-0.551503\pi$
$479$	15.9277	−	11.5722i	0.727756	−	0.528746i	0.888853	+	0.458193i	$0.151503\pi$
$480$	−2.29429	−	6.61333i	−0.104720	−	0.301856i
$481$	−4.75866	−	1.54618i	−0.216976	−	0.0704999i
$482$	14.9625	+	10.8709i	0.681522	+	0.495155i
$483$	14.7850	−	7.03566i	0.672741	−	0.320133i
$484$	−1.19284	−	10.9351i	−0.0542200	−	0.497051i
$485$		−	18.3181i		−	0.831781i
$486$	−13.4539	−	7.87346i	−0.610283	−	0.357147i
$487$	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
$489$	15.6478	+	20.6657i	0.707619	+	0.934533i
$490$	28.1660	+	2.64713i	1.27241	+	0.119585i
$491$	0.277777	−	0.0902552i	0.0125359	−	0.00407316i	−0.302742	−	0.953072i	$-0.597902\pi$
$491$	0.277777	−	0.0902552i	0.0125359	−	0.00407316i	0.315278	+	0.948999i	$0.397902\pi$
$492$	−1.78814	−	0.542165i	−0.0806154	−	0.0244427i
$493$	−0.400427	+	0.551141i	−0.0180343	+	0.0248221i
$494$			3.39237i			0.152630i
$495$	40.1316	+	2.54037i	1.80378	+	0.114181i
$496$			1.86582i			0.0837777i
$497$	−4.88282	+	23.6104i	−0.219025	+	1.05907i
$498$	7.31910	−	24.1394i	0.327977	−	1.08171i
$499$	−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
$501$	−13.0974	−	17.2974i	−0.585148	−	0.772790i
$502$	4.39713	−	1.42872i	0.196254	−	0.0637667i
$503$	−4.60004	+	14.1575i	−0.205106	+	0.631251i	0.794603	+	0.607129i	$0.207679\pi$
$503$	−4.60004	+	14.1575i	−0.205106	+	0.631251i	−0.999709	+	0.0241216i	$0.992321\pi$
$504$	1.29899	−	7.83024i	0.0578617	−	0.348786i
$505$	−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	−0.992301	−	0.123848i	$-0.960476\pi$
$509$	−2.63324	+	8.10429i	−0.116717	+	0.359217i	0.875585	+	0.483065i	$0.160476\pi$
$510$	0.481744	+	1.38864i	0.0213320	+	0.0614899i
$511$	−23.9080	−	13.6283i	−1.05763	−	0.602880i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	8.53341	+	21.7771i	0.376759	+	0.961480i
$514$	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
$519$	−4.74803	+	6.81441i	−0.208415	+	0.299119i
$520$	−0.941214	+	2.89676i	−0.0412749	+	0.127031i
$521$	9.64872	+	29.6957i	0.422718	+	1.30099i	0.905163	+	0.425066i	$0.139749\pi$
$521$	9.64872	+	29.6957i	0.422718	+	1.30099i	−0.482445	+	0.875926i	$0.660251\pi$
$522$	−7.64208	+	6.02783i	−0.334485	+	0.263831i
$523$	−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
$525$	−51.4976	+	6.73234i	−2.24754	+	0.293823i
$526$	−10.0413	−	7.29542i	−0.437821	−	0.318095i
$527$		−	0.391776i		−	0.0170660i
$528$	5.59175	−	1.31620i	0.243349	−	0.0572803i
$529$	10.2335			0.444934
$530$	−24.4661	−	17.7756i	−1.06274	−	0.772124i
$531$	4.23648	−	15.0368i	0.183848	−	0.652540i
$532$	−8.80628	+	8.01745i	−0.381801	+	0.347601i
$533$	0.477887	+	0.657754i	0.0206996	+	0.0284905i
$534$	−7.66567	+	5.80436i	−0.331726	+	0.251179i
$535$	28.2218	−	9.16982i	1.22014	−	0.396446i
$536$	−10.0520	−	3.26611i	−0.434182	−	0.141074i
$537$	15.6823	+	10.9268i	0.676739	+	0.471527i
$538$		−	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
$543$	−1.37962	−	3.97677i	−0.0592050	−	0.170660i
$544$	0.123420	+	0.169874i	0.00529160	+	0.00728327i
$545$	−40.6495	+	29.5336i	−1.74124	+	1.26508i
$546$	−2.50734	+	2.37506i	−0.107304	+	0.101643i
$547$	−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
$552$	−3.53793	+	5.07766i	−0.150584	+	0.216120i
$553$	−0.387005	−	3.49679i	−0.0164571	−	0.148698i
$554$	10.9234	−	3.54922i	0.464089	−	0.150792i
$555$	28.0545	+	37.0508i	1.19085	+	1.57272i
$556$	−12.6525	−	17.4146i	−0.536583	−	0.738544i
$557$	−13.1297	+	4.26610i	−0.556324	+	0.180761i	−0.573666	−	0.819089i	$-0.694479\pi$
$557$	−13.1297	+	4.26610i	−0.556324	+	0.180761i	0.0173425	+	0.999850i	$0.494479\pi$
$558$	1.51794	−	5.38770i	0.0642595	−	0.228080i
$559$	−3.86858	+	5.32464i	−0.163623	+	0.225208i
$560$	−9.74415	+	4.40282i	−0.411765	+	0.186053i
$561$	−1.17413	+	0.276369i	−0.0495717	+	0.0116683i
$562$	−19.9341			−0.840867
$563$	−12.9928	−	9.43979i	−0.547579	−	0.397840i	0.279313	−	0.960200i	$-0.409893\pi$
$563$	−12.9928	−	9.43979i	−0.547579	−	0.397840i	−0.826892	+	0.562360i	$0.809893\pi$
$564$	−20.2015	−	6.12511i	−0.850635	−	0.257914i
$565$	60.0752	−	19.5196i	2.52738	−	0.821196i
$566$	5.06734	−	3.68164i	0.212996	−	0.154751i
$567$	−10.1213	+	21.5537i	−0.425053	+	0.905169i
$568$	−2.81598	−	8.66671i	−0.118156	−	0.363647i
$569$	−17.9164	−	5.82140i	−0.751096	−	0.244046i	−0.0916431	−	0.995792i	$-0.529212\pi$
$569$	−17.9164	−	5.82140i	−0.751096	−	0.244046i	−0.659453	+	0.751746i	$0.729212\pi$
$570$	18.0130	−	25.8523i	0.754480	−	1.08284i
$571$	−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
$576$	1.03910	+	2.81430i	0.0432959	+	0.117262i
$577$	−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
$579$	13.5172	−	4.68939i	0.561757	−	0.194884i
$580$	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
$585$	5.07449	−	7.59890i	0.209805	−	0.314176i
$586$	21.2923	+	6.91828i	0.879575	+	0.285791i
$587$	−9.69466	−	29.8371i	−0.400141	−	1.23151i	−0.924885	−	0.380248i	$-0.875839\pi$
$587$	−9.69466	−	29.8371i	−0.400141	−	1.23151i	0.524743	−	0.851261i	$-0.324161\pi$
$588$	−12.0912	−	0.895653i	−0.498634	−	0.0369361i
$589$	−6.79457	+	4.93655i	−0.279966	+	0.203407i
$590$	−20.0154	+	6.50338i	−0.824019	+	0.267740i
$591$	10.6658	−	35.1773i	0.438732	−	1.44700i
$592$	5.37116	+	3.90237i	0.220753	+	0.160387i
$593$	−5.23814			−0.215104			−0.107552	−	0.994199i	$-0.534301\pi$
$593$	−5.23814			−0.215104			−0.107552	+	0.994199i	$0.534301\pi$
$594$	−17.2174	−	0.748540i	−0.706439	−	0.0307130i
$595$	2.04603	−	0.924483i	0.0838791	−	0.0379001i
$596$	5.05977	−	6.96418i	0.207256	−	0.285264i
$597$	−0.688249	+	2.26994i	−0.0281682	+	0.0929025i
$598$	2.56101	−	0.832122i	0.104727	−	0.0340280i
$599$	2.29221	+	3.15496i	0.0936573	+	0.128908i	0.853274	−	0.521463i	$-0.174613\pi$
$599$	2.29221	+	3.15496i	0.0936573	+	0.128908i	−0.759617	+	0.650371i	$0.774613\pi$
$600$	15.6497	−	11.8498i	0.638898	−	0.483767i
$601$	−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
$603$	26.3689	+	17.6090i	1.07383	+	0.717094i
$604$	−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
$609$	10.2245	+	10.7940i	0.414319	+	0.437394i
$610$	26.8214	−	19.4869i	1.08597	−	0.789002i
$611$	5.39892	+	7.43098i	0.218417	+	0.300625i
$612$	−0.218185	−	0.590933i	−0.00881963	−	0.0238870i
$613$	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	$-0.798634\pi$
$617$		−	29.3727i		−	1.18250i	0.806488	−	0.591251i	$-0.201366\pi$
$618$	13.4634	−	19.3228i	0.541577	−	0.777275i
$619$	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
$621$	14.3470	−	11.7839i	0.575725	−	0.472871i
$622$	−9.51806	−	13.1005i	−0.381640	−	0.525282i
$623$	9.88783	+	10.8607i	0.396148	+	0.435124i
$624$	0.378759	−	1.24920i	0.0151625	−	0.0500080i
$625$	−37.8439	−	27.4952i	−1.51375	−	1.09981i
$626$	−13.0521			−0.521665
$627$	19.5876	+	16.8806i	0.782254	+	0.674144i
$628$			16.4604i			0.656843i
$629$	−1.12781	−	0.819402i	−0.0449687	−	0.0326717i
$630$	31.7190	−	4.78613i	1.26371	−	0.190684i
$631$	−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
$633$	7.47153	+	9.86744i	0.296966	+	0.392196i
$634$	4.91043	+	15.1128i	0.195018	+	0.600204i
$635$	−12.2176	+	37.6019i	−0.484840	+	1.49218i
$636$	10.6340	+	7.40938i	0.421665	+	0.293801i
$637$	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	0.219439	−	0.975626i	$-0.429577\pi$
$641$	−4.46839	−	1.45187i	−0.176491	−	0.0573453i	−0.395929	+	0.918281i	$0.629577\pi$
$642$	−12.0150	+	4.16824i	−0.474195	+	0.164507i
$643$	−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
$645$	57.7543	−	20.0361i	2.27407	−	0.788920i
$646$	−0.292069	+	0.898896i	−0.0114913	+	0.0353666i
$647$	7.14257	+	5.18938i	0.280803	+	0.204016i	0.719268	−	0.694733i	$-0.244477\pi$
$647$	7.14257	+	5.18938i	0.280803	+	0.204016i	−0.438464	+	0.898749i	$0.644477\pi$
$648$	−0.710912	−	8.97188i	−0.0279273	−	0.352449i
$649$	−3.62405	−	16.8864i	−0.142257	−	0.662851i
$650$	−8.54134			−0.335019
$651$	−8.40566	−	1.56577i	−0.329444	−	0.0613675i
$652$	−4.62468	+	14.2333i	−0.181116	+	0.557419i
$653$	−23.2278	+	7.54717i	−0.908974	+	0.295343i	−0.725936	−	0.687762i	$-0.758593\pi$
$653$	−23.2278	+	7.54717i	−0.908974	+	0.295343i	−0.183038	+	0.983106i	$0.558593\pi$
$654$	17.1676	−	12.9992i	0.671308	−	0.508307i
$655$	42.8012	−	31.0969i	1.67238	−	1.21506i
$656$	−0.333365	−	1.02599i	−0.0130157	−	0.0400583i
$657$	−30.0348	−	8.46206i	−1.17177	−	0.330137i
$658$	−6.53045	+	31.5773i	−0.254583	+	1.23101i
$659$			1.23662i			0.0481720i	0.999710	+	0.0240860i	$0.00766756\pi$
$659$			1.23662i			0.0481720i	−0.999710	+	0.0240860i	$0.992332\pi$
$660$	12.0424	+	19.8489i	0.468750	+	0.772619i
$661$		−	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
$663$	−0.0795299	+	0.262301i	−0.00308869	+	0.0101869i
$664$	13.8507	−	4.50035i	0.537509	−	0.174647i
$665$	−41.8142	−	23.8354i	−1.62149	−	0.924299i
$666$	−12.3349	−	15.6381i	−0.477967	−	0.605966i
$667$	−3.58225	−	11.0250i	−0.138705	−	0.426890i
$668$	3.87091	−	11.9134i	0.149770	−	0.460944i
$669$	24.2901	+	16.9245i	0.939111	+	0.654338i
$670$		−	42.7155i		−	1.65024i
$671$	13.6499	+	23.5353i	0.526948	+	0.908570i
$672$	4.13795	−	1.96910i	0.159625	−	0.0759598i
$673$	−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
$675$	−54.8304	+	21.4855i	−2.11042	+	0.826976i
$676$	10.0577	−	7.30735i	0.386835	−	0.281052i
$677$	42.0204	−	30.5296i	1.61497	−	1.17335i	0.771352	−	0.636408i	$-0.219581\pi$
$677$	42.0204	−	30.5296i	1.61497	−	1.17335i	0.843621	−	0.536939i	$-0.180419\pi$
$678$	−25.5761	+	8.87284i	−0.982245	+	0.340759i
$679$	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	$-0.722406\pi$
$683$		−	40.0206i		−	1.53135i	0.643230	−	0.765673i	$-0.277594\pi$
$684$	−7.49933	+	11.2300i	−0.286744	+	0.429390i
$685$	−37.3762	−	12.1443i	−1.42807	−	0.464009i
$686$	0.305905	+	18.5177i	0.0116795	+	0.707010i
$687$	−1.53374	+	1.16133i	−0.0585157	+	0.0443075i
$688$	7.06515	−	5.13314i	0.269356	−	0.195699i
$689$	−1.74269	−	5.36344i	−0.0663912	−	0.204331i
$690$	−23.9352	−	7.25717i	−0.911196	−	0.276276i
$691$	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
$693$	1.23706	+	26.2958i	0.0469919	+	0.998895i
$694$	−4.31470			−0.163784
$695$	51.1343	−	70.3803i	1.93963	−	2.66968i
$696$	−5.37774	−	1.63054i	−0.203843	−	0.0618054i
$697$	0.0699984	+	0.215433i	0.00265138	+	0.00816010i
$698$	18.5117	−	13.4496i	0.700679	−	0.509073i
$699$	6.09234	−	4.61306i	0.230434	−	0.174482i
$700$	−20.1864	−	22.1725i	−0.762973	−	0.838042i
$701$	3.77072	+	1.22518i	0.142418	+	0.0462744i	0.379359	−	0.925250i	$-0.376145\pi$
$701$	3.77072	+	1.22518i	0.142418	+	0.0462744i	−0.236941	+	0.971524i	$0.576145\pi$
$702$	−2.10999	+	3.29902i	−0.0796363	+	0.124514i
$703$			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
$708$	8.52124	−	2.95618i	0.320248	−	0.111100i
$709$	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
$711$	−1.38172	−	3.74226i	−0.0518187	−	0.140346i
$712$	−5.27966	−	1.71547i	−0.197864	−	0.0642898i
$713$	5.39341	+	3.91854i	0.201985	+	0.146750i
$714$	−0.868867	+	0.413463i	−0.0325165	+	0.0154735i
$715$	1.03617	−	10.0486i	0.0387506	−	0.375796i
$716$			11.0352i			0.412406i
$717$	25.9801	+	18.1020i	0.970243	+	0.676030i
$718$	−3.58589	+	11.0362i	−0.133824	+	0.411868i
$719$	−8.86126	−	27.2722i	−0.330469	−	1.01708i	−0.968911	−	0.247410i	$-0.920421\pi$
$719$	−8.86126	−	27.2722i	−0.330469	−	1.01708i	0.638442	−	0.769670i	$-0.279579\pi$
$720$	−9.51946	+	7.50865i	−0.354769	+	0.279831i
$721$	−31.2531	−	17.8153i	−1.16393	−	0.663475i
$722$	1.19971	−	0.389808i	0.0446484	−	0.0145072i
$723$	9.29480	−	30.6555i	0.345677	−	1.14009i
$724$	1.42845	−	1.96610i	0.0530880	−	0.0730694i
$725$			36.7700i			1.36560i
$726$	−17.2168	+	8.15970i	−0.638977	+	0.302835i
$727$			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
$729$	−5.24628	+	26.4854i	−0.194306	+	0.980941i
$730$	12.9900	+	39.9792i	0.480783	+	1.47970i
$731$	−1.48351	+	1.07783i	−0.0548695	+	0.0398650i
$732$	−11.3276	+	8.57712i	−0.418679	+	0.317019i
$733$	−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
$735$	−11.6579	−	47.5930i	−0.430007	−	1.75549i
$736$	−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
$741$	5.55120	−	1.92582i	0.203928	−	0.0707467i
$742$	9.80437	−	17.1997i	0.359930	−	0.631420i
$743$	21.7768	+	29.9732i	0.798913	+	1.09961i	0.992940	+	0.118614i	$0.0378451\pi$
$743$	21.7768	+	29.9732i	0.798913	+	1.09961i	−0.194027	+	0.980996i	$0.562155\pi$
$744$	3.05318	−	1.05921i	0.111935	−	0.0388324i
$745$	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
$750$	36.3744	+	25.3444i	1.32821	+	0.925446i
$751$	−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
$753$	−4.83413	−	6.38430i	−0.176165	−	0.232657i
$754$	1.43722	+	1.97817i	0.0523405	+	0.0720406i
$755$	−29.0488	−	89.4030i	−1.05719	−	3.25371i
$756$	−13.5506	+	2.31951i	−0.492832	+	0.0843597i
$757$	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
$759$	7.93897	−	18.9280i	0.288166	−	0.687042i
$760$	18.1917			0.659881
$761$	−1.03966	−	0.755358i	−0.0376877	−	0.0273817i	0.568782	−	0.822488i	$-0.307415\pi$
$761$	−1.03966	−	0.755358i	−0.0376877	−	0.0273817i	−0.606470	+	0.795107i	$0.707415\pi$
$762$	4.91654	−	16.2154i	0.178107	−	0.587423i
$763$	−22.1443	−	24.3231i	−0.801677	−	0.880554i
$764$	−11.0790	−	15.2489i	−0.400824	−	0.551686i
$765$	1.99885	−	1.57663i	0.0722686	−	0.0570032i
$766$	−11.0426	+	3.58795i	−0.398985	+	0.129638i
$767$	−3.73245	−	1.21275i	−0.134771	−	0.0437898i
$768$	−0.990177	+	1.42111i	−0.0357299	+	0.0512798i
$769$			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	$0.262622\pi$
$773$	−8.40178	+	25.8580i	−0.302191	+	0.930048i	−0.980711	+	0.195466i	$0.937378\pi$
$774$	−24.5773	+	9.07448i	−0.883412	+	0.326175i
$775$	−12.4293	−	17.1074i	−0.446472	−	0.614516i
$776$	−3.66691	+	2.66417i	−0.131634	+	0.0956380i
$777$	−22.0879	+	20.9227i	−0.792400	+	0.750596i
$778$	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
$783$	14.2021	+	9.08338i	0.507543	+	0.324614i
$784$	−3.56654	−	6.02327i	−0.127377	−	0.215117i
$785$	−63.2681	+	20.5571i	−2.25814	+	0.733713i
$786$	−18.0764	+	13.6872i	−0.644763	+	0.488208i
$787$	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
$789$	−6.23771	+	20.5729i	−0.222069	+	0.732413i
$790$	−3.15878	+	4.34769i	−0.112384	+	0.154684i
$791$	17.0273	+	37.6841i	0.605420	+	1.33989i
$792$	−5.32818	−	8.40301i	−0.189329	−	0.298588i
$793$	6.18237			0.219543
$794$	11.7175	+	8.51323i	0.415837	+	0.302123i
$795$	−15.1985	+	50.1267i	−0.539035	+	1.77781i
$796$	−1.30244	+	0.423189i	−0.0461638	+	0.0149995i
$797$	3.37013	−	2.44855i	0.119376	−	0.0867319i	−0.526495	−	0.850178i	$-0.676494\pi$
$797$	3.37013	−	2.44855i	0.119376	−	0.0867319i	0.645871	+	0.763446i	$0.276494\pi$
$798$	18.1188	+	9.85897i	0.641399	+	0.349004i
$799$	0.790807	+	2.43385i	0.0279767	+	0.0861035i
$800$	10.7786	+	3.50219i	0.381082	+	0.123821i
$801$	13.8498	+	9.24884i	0.489360	+	0.326792i
$802$	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
$807$	−16.7553	+	5.81274i	−0.589815	+	0.204618i
$808$	4.80012	+	6.60680i	0.168868	+	0.232426i
$809$	1.91969	+	2.64222i	0.0674926	+	0.0928955i	0.841429	−	0.540368i	$-0.181715\pi$
$809$	1.91969	+	2.64222i	0.0674926	+	0.0928955i	−0.773936	+	0.633263i	$0.781715\pi$
$810$	33.5969	−	13.9373i	1.18047	−	0.489706i
$811$	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
$816$	0.207913	−	0.298398i	0.00727840	−	0.0104460i
$817$	37.3857	+	12.1474i	1.30796	+	0.424982i
$818$	−7.62593	−	23.4702i	−0.266634	−	0.820616i
$819$	5.30989	+	2.75465i	0.185543	+	0.0962553i
$820$	3.52722	−	2.56268i	0.123176	−	0.0894925i
$821$	−40.1303	+	13.0391i	−1.40056	+	0.455068i	−0.909371	−	0.415987i	$-0.863436\pi$
$821$	−40.1303	+	13.0391i	−1.40056	+	0.455068i	−0.491185	+	0.871055i	$0.663436\pi$
$822$	16.1181	+	4.88704i	0.562185	+	0.170455i
$823$	−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
$825$	−42.5019	+	49.3178i	−1.47973	+	1.71703i
$826$	−5.67301	−	12.5553i	−0.197389	−	0.436854i
$827$	−26.9639	+	37.1126i	−0.937627	+	1.29053i	0.0191818	+	0.999816i	$0.493894\pi$
$827$	−26.9639	+	37.1126i	−0.937627	+	1.29053i	−0.956809	+	0.290717i	$0.906106\pi$
$828$	10.3174	+	2.90684i	0.358555	+	0.101020i
$829$	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
$831$	−12.0089	−	15.8599i	−0.416585	−	0.550173i
$832$	0.716762	−	0.232890i	0.0248492	−	0.00807401i
$833$	0.748886	+	1.26474i	0.0259474	+	0.0438206i
$834$	−21.3142	+	30.5903i	−0.738050	+	1.05925i
$835$	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	−0.932301	−	0.361684i	$-0.882202\pi$
$839$	1.00043	−	3.07901i	0.0345387	−	0.106299i	0.966840	+	0.255384i	$0.0822020\pi$
$840$	12.7363	+	13.4457i	0.439445	+	0.463919i
$841$	−14.9456	+	10.8586i	−0.515365	+	0.374435i
$842$	−7.68212	−	10.5735i	−0.264743	−	0.364388i
$843$	11.3164	+	32.6196i	0.389756	+	1.12348i
$844$	−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
$849$	−8.90122	−	6.20205i	−0.305489	−	0.212854i
$850$	−2.26325	−	0.735373i	−0.0776287	−	0.0252231i
$851$	22.5607	−	7.33042i	0.773371	−	0.251283i
$852$	−12.5834	+	9.52802i	−0.431100	+	0.326424i
$853$	−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
$855$	−52.5299	−	14.7999i	−1.79649	−	0.506145i
$856$	−5.94017	−	4.31579i	−0.203031	−	0.147511i
$857$	−44.7221			−1.52768			−0.763839	−	0.645407i	$-0.776688\pi$
$857$	−44.7221			−1.52768			−0.763839	+	0.645407i	$0.776688\pi$
$858$	−0.358860	+	4.31448i	−0.0122513	+	0.147294i
$859$			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
$861$	4.90193	−	0.640835i	0.167057	−	0.0218396i
$862$	−4.25671	−	13.1008i	−0.144984	−	0.446215i
$863$	−2.90881	−	4.00364i	−0.0990171	−	0.136285i	0.756634	−	0.653839i	$-0.226843\pi$
$863$	−2.90881	−	4.00364i	−0.0990171	−	0.136285i	−0.855651	+	0.517554i	$0.826843\pi$
$864$	4.01536	−	3.29801i	0.136605	−	0.112201i
$865$	−5.98853	−	18.4308i	−0.203616	−	0.626666i
$866$	−0.0988303	+	0.304169i	−0.00335839	+	0.0103361i
$867$	16.7893	−	24.0962i	0.570196	−	0.818350i
$868$	−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
$873$	12.7559	−	4.70978i	0.431723	−	0.159402i
$874$	−9.45345	−	13.0116i	−0.319768	−	0.440122i
$875$	33.5367	−	58.8329i	1.13375	−	1.98892i
$876$	−5.90476	−	17.0206i	−0.199503	−	0.575072i
$877$	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	$-0.864281\pi$
$881$	−54.0486			−1.82094			−0.910471	+	0.413572i	$0.864281\pi$
$882$	5.39845	+	20.2943i	0.181775	+	0.683343i
$883$	−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
$885$	22.0045	+	29.0608i	0.739673	+	0.976867i
$886$	−22.1351	+	16.0821i	−0.743643	+	0.540289i
$887$	−13.4288	−	41.3297i	−0.450896	−	1.38771i	−0.875887	−	0.482517i	$-0.839723\pi$
$887$	−13.4288	−	41.3297i	−0.450896	−	1.38771i	0.424991	−	0.905198i	$-0.360277\pi$
$888$	3.33660	−	11.0046i	0.111969	−	0.369289i
$889$	−25.3466	−	5.24190i	−0.850099	−	0.175808i
$890$		−	22.4356i		−	0.752042i
$891$	8.54927	+	28.5991i	0.286411	+	0.958107i
$892$			17.0924i			0.572295i
$893$	32.2458	−	44.3826i	1.07907	−	1.48521i
$894$	−14.2684	−	4.32620i	−0.477207	−	0.144690i
$895$	−42.4155	+	13.7816i	−1.41779	+	0.460669i
$896$	2.29854	+	1.31024i	0.0767887	+	0.0437720i
$897$	−2.81552	−	3.71839i	−0.0940076	−	0.124153i
$898$	−7.38954	−	22.7427i	−0.246592	−	0.758933i
$899$	−1.87063	+	5.75721i	−0.0623891	+	0.192014i
$900$	−28.2750	−	18.8818i	−0.942499	−	0.629395i
$901$		−	1.57122i		−	0.0523449i
$902$	1.79506	+	3.09507i	0.0597691	+	0.103055i
$903$	17.1962	+	36.1368i	0.572253	+	1.20256i
$904$	−12.6447	−	9.18692i	−0.420557	−	0.305552i
$905$	9.34095	+	3.03506i	0.310504	+	0.100889i
$906$	13.2044	+	38.0620i	0.438688	+	1.26453i
$907$	−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
$909$	−8.48576	−	22.9828i	−0.281455	−	0.762292i
$910$	−0.886458	−	8.00961i	−0.0293858	−	0.265516i
$911$	23.3173	−	32.0935i	0.772538	−	1.06331i	−0.223529	−	0.974697i	$-0.571758\pi$
$911$	23.3173	−	32.0935i	0.772538	−	1.06331i	0.996066	−	0.0886094i	$-0.0282423\pi$
$912$	−7.79491	+	0.154111i	−0.258115	+	0.00510312i
$913$	−41.7827	+	24.2330i	−1.38281	+	0.801994i
$914$		−	11.5515i		−	0.382090i
$915$	−47.1142	−	32.8274i	−1.55755	−	1.08524i
$916$	−1.05635	−	0.343229i	−0.0349027	−	0.0113406i
$917$	23.3165	+	25.6105i	0.769977	+	0.845735i
$918$	−0.843127	+	0.692500i	−0.0278273	+	0.0228559i
$919$	−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
$921$	−0.0862003	+	0.284301i	−0.00284040	+	0.00936802i
$922$	5.66577	−	7.79827i	0.186592	−	0.256822i
$923$	6.86778			0.226056
$924$	−12.0481	+	9.26516i	−0.396353	+	0.304801i
$925$	−75.2432			−2.47398
$926$	8.05651	−	11.0888i	0.264753	−	0.364402i
$927$	−39.2623	−	11.0618i	−1.28954	−	0.363318i
$928$	−1.00258	−	3.08562i	−0.0329113	−	0.101291i
$929$	−18.8333	+	13.6832i	−0.617899	+	0.448930i	−0.852187	−	0.523237i	$-0.824724\pi$
$929$	−18.8333	+	13.6832i	−0.617899	+	0.448930i	0.234288	+	0.972167i	$0.424724\pi$
$930$	7.88426	+	10.4125i	0.258535	+	0.341440i
$931$	12.4981	−	28.9242i	0.409608	−	0.947952i
$932$	4.19605	+	1.36338i	0.137446	+	0.0446590i
$933$	−16.0340	+	23.0122i	−0.524930	+	0.753384i
$934$			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
$939$	7.40953	+	21.3581i	0.241801	+	0.696995i
$940$	39.8488	−	28.9518i	1.29972	−	0.944304i
$941$	28.8262	−	20.9434i	0.939706	−	0.682736i	−0.00864378	−	0.999963i	$-0.502751\pi$
$941$	28.8262	−	20.9434i	0.939706	−	0.682736i	0.948350	+	0.317226i	$0.102751\pi$
$942$	26.9355	−	9.34442i	0.877605	−	0.304458i
$943$	−3.66590	−	1.19112i	−0.119378	−	0.0387883i
$944$	4.21286	+	3.06082i	0.137117	+	0.0996214i
$945$	−25.8385	−	49.1871i	−0.840525	−	1.60006i
$946$	−19.3384	+	21.5626i	−0.628746	+	0.701061i
$947$		−	42.1847i		−	1.37082i	−0.728158	−	0.685410i	$-0.759623\pi$
$947$		−	42.1847i		−	1.37082i	0.728158	−	0.685410i	$-0.240377\pi$
$948$	1.31667	−	1.88969i	0.0427634	−	0.0613743i
$949$	−2.42238	+	7.45531i	−0.0786337	+	0.242010i
$950$	15.7643	+	48.5175i	0.511462	+	1.57412i
$951$	21.9426	−	16.6147i	0.711536	−	0.538768i
$952$	−0.482636	−	0.275118i	−0.0156423	−	0.00891662i
$953$	−49.8912	+	16.2106i	−1.61614	+	0.525114i	−0.971026	−	0.238976i	$-0.923188\pi$
$953$	−49.8912	+	16.2106i	−1.61614	+	0.525114i	−0.645110	+	0.764090i	$0.723188\pi$
$954$	6.08772	−	21.6074i	0.197097	−	0.699567i
$955$	44.7752	−	61.6277i	1.44889	−	1.99423i
$956$			18.2815i			0.591268i
$957$	18.5736	+	1.54487i	0.600400	+	0.0499387i
$958$		−	19.6877i		−	0.636082i
$959$	5.21045	−	25.1946i	0.168254	−	0.813575i
$960$	−6.69885	−	2.03110i	−0.216204	−	0.0655535i
$961$	8.50375	+	26.1719i	0.274315	+	0.844254i
$962$	−4.04796	+	2.94102i	−0.130511	+	0.0948221i
$963$	13.6416	+	17.2948i	0.439595	+	0.557318i
$964$	17.5894	−	5.71516i	0.566518	−	0.184073i
$965$	−10.3163	+	31.7504i	−0.332094	+	1.02208i
$966$	2.99844	−	16.0968i	0.0964734	−	0.517905i
$967$	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	$-0.789649\pi$
$971$	6.54353	−	20.1389i	0.209992	−	0.646289i	0.999471	−	0.0325117i	$-0.0103506\pi$
$972$	−14.2778	+	6.25657i	−0.457960	+	0.200679i
$973$	49.4775	+	28.2037i	1.58617	+	0.904170i
$974$	−21.3921	−	29.4437i	−0.685446	−	0.943436i
$975$	4.84883	+	13.9768i	0.155287	+	0.447617i
$976$	−7.80177	−	2.53495i	−0.249729	−	0.0811417i
$977$	17.7848	−	24.4787i	0.568986	−	0.783142i	−0.423448	−	0.905920i	$-0.639181\pi$
$977$	17.7848	−	24.4787i	0.568986	−	0.783142i	0.992434	+	0.122779i	$0.0391805\pi$
$978$	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
$981$	−31.0174	−	20.7132i	−0.990310	−	0.661323i
$982$	0.0902552	−	0.277777i	0.00288016	−	0.00886422i
$983$	18.3668	+	56.5273i	0.585811	+	1.80294i	0.595988	+	0.802993i	$0.296761\pi$
$983$	18.3668	+	56.5273i	0.585811	+	1.80294i	−0.0101769	+	0.999948i	$0.503239\pi$
$984$	−1.48966	+	1.12796i	−0.0474887	+	0.0359579i
$985$	50.4145	+	69.3896i	1.60634	+	2.21094i
$986$	0.210517	+	0.647905i	0.00670423	+	0.0206335i
$987$	55.3796	−	7.23984i	1.76275	−	0.230446i
$988$	2.74449	+	1.99399i	0.0873138	+	0.0634372i
$989$		−	31.2033i		−	0.992207i
$990$	25.6440	−	30.9740i	0.815019	−	0.984417i
$991$	−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
$993$	6.21862	+	1.88549i	0.197342	+	0.0598343i
$994$	16.2311	+	17.8281i	0.514820	+	0.565473i
$995$	−3.25318	−	4.47761i	−0.103133	−	0.141950i
$996$	−15.2271	−	20.1101i	−0.482490	−	0.637212i
$997$	−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
$999$	−18.5875	+	29.0621i	−0.588082	+	0.919484i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-1.65754 - 0.502567i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(3.26960 - 2.37551i) q^{5} +(-1.38086 + 1.04557i) q^{6} +(1.78115 + 1.95640i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.49485 + 1.66605i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-1.65754 - 0.502567i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(3.26960 - 2.37551i) q^{5} +(-1.38086 + 1.04557i) q^{6} +(1.78115 + 1.95640i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.49485 + 1.66605i) 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} +(-6.61333 + 2.29429i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.169874 - 0.123420i) q^{17} +(2.81430 - 1.03910i) q^{18} +(-4.28096 - 1.39097i) q^{19} +(-3.26960 - 2.37551i) q^{20} +(-1.96910 - 4.13795i) q^{21} +(2.21440 - 2.46909i) q^{22} +3.57303i q^{23} +(1.42111 + 0.990177i) q^{24} +(3.50219 - 10.7786i) q^{25} +(-0.232890 - 0.716762i) q^{26} +(-3.29801 - 4.01536i) q^{27} +(1.31024 - 2.29854i) q^{28} +(-3.08562 + 1.00258i) q^{29} +(-2.03110 + 6.69885i) q^{30} +(1.09670 - 1.50948i) q^{31} +1.00000i q^{32} +(-5.29746 - 2.22192i) q^{33} -0.209975i q^{34} +(10.4711 + 2.16551i) q^{35} +(0.813552 - 2.88758i) q^{36} +(-2.05160 - 6.31417i) q^{37} +(-3.64161 + 2.64578i) q^{38} +(-1.04068 + 0.787994i) q^{39} +(-3.84365 + 1.24888i) q^{40} +(-0.333365 + 1.02599i) q^{41} +(-4.50508 - 0.839189i) 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} +(1.63638 - 0.567690i) q^{48} +(-0.654994 + 6.96929i) q^{49} +(-6.66156 - 9.16885i) q^{50} +(-0.343599 + 0.119201i) 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} +(6.39680 + 4.45705i) q^{57} +(-1.00258 + 3.08562i) q^{58} +(-1.60917 - 4.95252i) q^{59} +(4.22563 + 5.58068i) q^{60} +(4.82176 + 6.63658i) q^{61} +(-0.576570 - 1.77450i) q^{62} +(1.18426 + 7.84841i) q^{63} +(0.809017 + 0.587785i) q^{64} -3.04583i q^{65} +(-4.91134 + 2.97973i) q^{66} +10.5693 q^{67} +(-0.169874 - 0.123420i) q^{68} +(1.79569 - 5.92242i) q^{69} +(7.90669 - 7.19844i) q^{70} +(5.35632 + 7.37234i) q^{71} +(-1.85791 - 2.35546i) q^{72} +(-9.89230 + 3.21420i) q^{73} +(-6.31417 - 2.05160i) q^{74} +(-11.2220 + 16.1059i) 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} +(3.44858 + 8.31308i) q^{81} +(0.634098 + 0.872761i) q^{82} +(-11.7821 + 8.56017i) q^{83} +(-3.32694 + 3.15142i) 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} +(6.73324 - 10.0828i) q^{90} +(1.98186 - 0.219342i) q^{91} +(3.39815 - 1.10413i) q^{92} +(-2.57643 + 1.95085i) q^{93} +(7.16372 + 9.86001i) q^{94} +(-17.3013 + 5.62153i) q^{95} +(0.502567 - 1.65754i) q^{96} +(2.66417 - 3.66691i) q^{97} +(5.25328 + 4.62635i) q^{98} +(7.66407 + 6.34524i) 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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