LMFDB - Embedded newform 462.2.y.d.235.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.4
Character	$\chi$	$=$	462.235
Dual form			462.2.y.d.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.363254 + 0.161731i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-1.41564 - 2.23517i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.363254 + 0.161731i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-1.41564 - 2.23517i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.198815 + 0.344358i) q^{10} +(-0.820550 + 3.21352i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.60680 - 1.89395i) q^{13} +(2.37090 - 1.17425i) q^{14} +(-0.122875 - 0.378169i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.654675 - 6.22881i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-4.92136 + 1.04607i) q^{19} +(-0.321690 - 0.233721i) q^{20} +(-0.713804 + 2.54764i) q^{21} +(-3.11014 - 1.15196i) q^{22} +(-3.00849 - 5.21086i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-3.23986 - 3.59823i) q^{25} +(2.15606 - 2.39455i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.919987 + 2.48065i) q^{28} +(1.61120 + 4.95877i) q^{29} +(0.388941 - 0.0826720i) q^{30} +(-0.289038 + 0.128688i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.93716 - 1.54048i) q^{33} +6.26312 q^{34} +(-0.152741 - 1.04088i) q^{35} +(0.309017 - 0.951057i) q^{36} +(2.18654 - 2.42840i) q^{37} +(-0.525915 - 5.00375i) q^{38} +(0.336810 + 3.20453i) q^{39} +(0.266067 - 0.295497i) q^{40} +(2.86189 - 8.80800i) q^{41} +(-2.45907 - 0.976195i) q^{42} -2.62440 q^{43} +(1.47075 - 2.97269i) q^{44} +(-0.198815 + 0.344358i) q^{45} +(5.49679 - 2.44733i) q^{46} +(-7.69721 + 1.63609i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-2.99193 + 6.32838i) q^{49} +(3.91717 - 2.84599i) q^{50} +(-4.19085 + 4.65441i) q^{51} +(2.15606 + 2.39455i) q^{52} +(10.6680 - 4.74971i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.817793 + 1.03461i) q^{55} +(-2.56323 + 0.655649i) q^{56} +(4.07042 + 2.95733i) q^{57} +(-5.10003 + 1.08404i) q^{58} +(7.74742 + 1.64676i) q^{59} +(0.0415637 + 0.395452i) q^{60} +(-3.35599 - 1.49418i) q^{61} +(-0.0977705 - 0.300907i) q^{62} +(2.37090 - 1.17425i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.640620 - 1.10959i) q^{65} +(1.22502 + 3.08210i) q^{66} +(-7.15234 + 12.3882i) q^{67} +(-0.654675 + 6.22881i) q^{68} +(-1.85935 + 5.72249i) q^{69} +(1.05115 - 0.0431018i) q^{70} +(-4.67285 + 3.39502i) q^{71} +(0.913545 + 0.406737i) q^{72} +(-8.02696 - 1.70618i) q^{73} +(2.18654 + 2.42840i) q^{74} +(-0.506115 + 4.81537i) q^{75} +5.03131 q^{76} +(8.34435 - 2.71512i) q^{77} -3.22219 q^{78} +(0.0695906 - 0.662110i) q^{79} +(0.266067 + 0.295497i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(8.46060 + 3.76690i) q^{82} +(7.09793 - 5.15695i) q^{83} +(1.22789 - 2.34356i) q^{84} +(0.769579 - 2.36852i) q^{85} +(0.274325 - 2.61002i) q^{86} +(2.60698 - 4.51542i) q^{87} +(2.80267 + 1.77342i) q^{88} +(2.97452 + 5.15202i) q^{89} +(-0.321690 - 0.233721i) q^{90} +(-0.543007 + 8.50779i) q^{91} +(1.85935 + 5.72249i) q^{92} +(0.289038 + 0.128688i) q^{93} +(-0.822552 - 7.82606i) q^{94} +(-1.95688 - 0.415949i) q^{95} +(0.978148 - 0.207912i) q^{96} +(12.7158 + 9.23855i) q^{97} +(-5.98097 - 3.63704i) q^{98} +(-3.11014 - 1.15196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	0.363254	+	0.161731i	0.162452	+	0.0723283i	0.486352	−	0.873763i	$-0.338327\pi$
$5$	0.363254	+	0.161731i	0.162452	+	0.0723283i	−0.323900	+	0.946091i	$0.604994\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−1.41564	−	2.23517i	−0.535061	−	0.844813i
$7$	−1.41564	−	2.23517i	−0.535061	−	0.844813i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−0.198815	+	0.344358i	−0.0628709	+	0.108896i
$11$	−0.820550	+	3.21352i	−0.247405	+	0.968912i
$11$	−0.820550	+	3.21352i	−0.247405	+	0.968912i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.60680	−	1.89395i	−0.722997	−	0.525288i	0.164343	−	0.986403i	$-0.447450\pi$
$13$	−2.60680	−	1.89395i	−0.722997	−	0.525288i	−0.887340	+	0.461115i	$0.847450\pi$
$14$	2.37090	−	1.17425i	0.633649	−	0.313830i
$15$	−0.122875	−	0.378169i	−0.0317261	−	0.0976429i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.654675	−	6.22881i	−0.158782	−	1.51071i	−0.726317	−	0.687360i	$-0.758770\pi$
$17$	−0.654675	−	6.22881i	−0.158782	−	1.51071i	0.567535	−	0.823349i	$-0.307897\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	−4.92136	+	1.04607i	−1.12904	+	0.239984i	−0.734311	−	0.678814i	$-0.762494\pi$
$19$	−4.92136	+	1.04607i	−1.12904	+	0.239984i	−0.394728	+	0.918798i	$0.629161\pi$
$20$	−0.321690	−	0.233721i	−0.0719321	−	0.0522617i
$21$	−0.713804	+	2.54764i	−0.155765	+	0.555941i
$22$	−3.11014	−	1.15196i	−0.663085	−	0.245598i
$23$	−3.00849	−	5.21086i	−0.627314	−	1.08654i	−0.988089	−	0.153887i	$-0.950821\pi$
$23$	−3.00849	−	5.21086i	−0.627314	−	1.08654i	0.360775	−	0.932653i	$-0.382512\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	−3.23986	−	3.59823i	−0.647971	−	0.719645i
$26$	2.15606	−	2.39455i	0.422839	−	0.469610i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.919987	+	2.48065i	0.173861	+	0.468799i
$29$	1.61120	+	4.95877i	0.299193	+	0.920821i	0.981781	+	0.190018i	$0.0608545\pi$
$29$	1.61120	+	4.95877i	0.299193	+	0.920821i	−0.682588	+	0.730804i	$0.739146\pi$
$30$	0.388941	−	0.0826720i	0.0710107	−	0.0150938i
$31$	−0.289038	+	0.128688i	−0.0519128	+	0.0231131i	−0.432529	−	0.901620i	$-0.642379\pi$
$31$	−0.289038	+	0.128688i	−0.0519128	+	0.0231131i	0.380616	+	0.924733i	$0.375712\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.93716	−	1.54048i	0.511295	−	0.268162i
$34$	6.26312			1.07412
$35$	−0.152741	−	1.04088i	−0.0258179	−	0.175942i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	2.18654	−	2.42840i	0.359465	−	0.399227i	−0.536102	−	0.844153i	$-0.680104\pi$
$37$	2.18654	−	2.42840i	0.359465	−	0.399227i	0.895567	+	0.444927i	$0.146770\pi$
$38$	−0.525915	−	5.00375i	−0.0853147	−	0.811715i
$39$	0.336810	+	3.20453i	0.0539328	+	0.513136i
$40$	0.266067	−	0.295497i	0.0420689	−	0.0467222i
$41$	2.86189	−	8.80800i	0.446952	−	1.37558i	−0.433376	−	0.901213i	$-0.642678\pi$
$41$	2.86189	−	8.80800i	0.446952	−	1.37558i	0.880328	−	0.474365i	$-0.157322\pi$
$42$	−2.45907	−	0.976195i	−0.379443	−	0.150630i
$43$	−2.62440			−0.400218			−0.200109	−	0.979774i	$-0.564130\pi$
$43$	−2.62440			−0.400218			−0.200109	+	0.979774i	$0.564130\pi$
$44$	1.47075	−	2.97269i	0.221723	−	0.448150i
$45$	−0.198815	+	0.344358i	−0.0296376	+	0.0513339i
$46$	5.49679	−	2.44733i	0.810457	−	0.360839i
$47$	−7.69721	+	1.63609i	−1.12275	+	0.238649i	−0.731638	−	0.681693i	$-0.761244\pi$
$47$	−7.69721	+	1.63609i	−1.12275	+	0.238649i	−0.391115	+	0.920342i	$0.627911\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	−2.99193	+	6.32838i	−0.427419	+	0.904054i
$50$	3.91717	−	2.84599i	0.553972	−	0.402484i
$51$	−4.19085	+	4.65441i	−0.586836	+	0.651747i
$52$	2.15606	+	2.39455i	0.298992	+	0.332064i
$53$	10.6680	−	4.74971i	1.46537	−	0.652423i	0.489742	−	0.871868i	$-0.337091\pi$
$53$	10.6680	−	4.74971i	1.46537	−	0.652423i	0.975625	+	0.219444i	$0.0704244\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−0.817793	+	1.03461i	−0.110271	+	0.139507i
$56$	−2.56323	+	0.655649i	−0.342525	+	0.0876147i
$57$	4.07042	+	2.95733i	0.539140	+	0.391708i
$58$	−5.10003	+	1.08404i	−0.669666	+	0.142342i
$59$	7.74742	+	1.64676i	1.00863	+	0.214390i	0.682461	−	0.730922i	$-0.260910\pi$
$59$	7.74742	+	1.64676i	1.00863	+	0.214390i	0.326167	+	0.945312i	$0.394243\pi$
$60$	0.0415637	+	0.395452i	0.00536585	+	0.0510527i
$61$	−3.35599	−	1.49418i	−0.429691	−	0.191311i	0.180483	−	0.983578i	$-0.442234\pi$
$61$	−3.35599	−	1.49418i	−0.429691	−	0.191311i	−0.610174	+	0.792267i	$0.708901\pi$
$62$	−0.0977705	−	0.300907i	−0.0124169	−	0.0382152i
$63$	2.37090	−	1.17425i	0.298705	−	0.147941i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.640620	−	1.10959i	−0.0794591	−	0.137627i
$66$	1.22502	+	3.08210i	0.150790	+	0.379380i
$67$	−7.15234	+	12.3882i	−0.873797	+	1.51346i	−0.0157579	+	0.999876i	$0.505016\pi$
$67$	−7.15234	+	12.3882i	−0.873797	+	1.51346i	−0.858039	+	0.513585i	$0.828317\pi$
$68$	−0.654675	+	6.22881i	−0.0793910	+	0.755355i
$69$	−1.85935	+	5.72249i	−0.223839	+	0.688907i
$70$	1.05115	−	0.0431018i	0.125636	−	0.00515165i
$71$	−4.67285	+	3.39502i	−0.554565	+	0.402915i	−0.829466	−	0.558558i	$-0.811355\pi$
$71$	−4.67285	+	3.39502i	−0.554565	+	0.402915i	0.274901	+	0.961473i	$0.411355\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	−8.02696	−	1.70618i	−0.939484	−	0.199694i	−0.287375	−	0.957818i	$-0.592783\pi$
$73$	−8.02696	−	1.70618i	−0.939484	−	0.199694i	−0.652110	+	0.758125i	$0.726116\pi$
$74$	2.18654	+	2.42840i	0.254180	+	0.282296i
$75$	−0.506115	+	4.81537i	−0.0584412	+	0.556031i
$76$	5.03131			0.577131
$77$	8.34435	−	2.71512i	0.950927	−	0.309416i
$78$	−3.22219			−0.364841
$79$	0.0695906	−	0.662110i	0.00782955	−	0.0744932i	−0.989909	−	0.141702i	$-0.954743\pi$
$79$	0.0695906	−	0.662110i	0.00782955	−	0.0744932i	0.997739	+	0.0672085i	$0.0214093\pi$
$80$	0.266067	+	0.295497i	0.0297472	+	0.0330376i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	8.46060	+	3.76690i	0.934317	+	0.415985i
$83$	7.09793	−	5.15695i	0.779100	−	0.566049i	−0.125609	−	0.992080i	$-0.540089\pi$
$83$	7.09793	−	5.15695i	0.779100	−	0.566049i	0.904709	+	0.426031i	$0.140089\pi$
$84$	1.22789	−	2.34356i	0.133974	−	0.255704i
$85$	0.769579	−	2.36852i	0.0834725	−	0.256902i
$86$	0.274325	−	2.61002i	0.0295812	−	0.281446i
$87$	2.60698	−	4.51542i	0.279498	−	0.484104i
$88$	2.80267	+	1.77342i	0.298766	+	0.189047i
$89$	2.97452	+	5.15202i	0.315298	+	0.546113i	0.979501	−	0.201440i	$-0.0645621\pi$
$89$	2.97452	+	5.15202i	0.315298	+	0.546113i	−0.664202	+	0.747553i	$0.731229\pi$
$90$	−0.321690	−	0.233721i	−0.0339091	−	0.0246364i
$91$	−0.543007	+	8.50779i	−0.0569226	+	0.891859i
$92$	1.85935	+	5.72249i	0.193851	+	0.596611i
$93$	0.289038	+	0.128688i	0.0299719	+	0.0133443i
$94$	−0.822552	−	7.82606i	−0.0848397	−	0.807196i
$95$	−1.95688	−	0.415949i	−0.200772	−	0.0426754i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	12.7158	+	9.23855i	1.29109	+	0.938033i	0.999827	−	0.0186093i	$-0.00592386\pi$
$97$	12.7158	+	9.23855i	1.29109	+	0.938033i	0.291265	+	0.956642i	$0.405924\pi$
$98$	−5.98097	−	3.63704i	−0.604169	−	0.367396i
$99$	−3.11014	−	1.15196i	−0.312581	−	0.115776i
$100$	2.42094	+	4.19320i	0.242094	+	0.419320i
$101$	12.7243	−	5.66521i	1.26611	−	0.563710i	0.339811	−	0.940494i	$-0.389637\pi$
$101$	12.7243	−	5.66521i	1.26611	−	0.563710i	0.926301	+	0.376784i	$0.122970\pi$
$102$	−4.19085	−	4.65441i	−0.414956	−	0.460855i
$103$	5.31111	−	5.89859i	0.523320	−	0.581205i	−0.422310	−	0.906452i	$-0.638781\pi$
$103$	5.31111	−	5.89859i	0.523320	−	0.581205i	0.945629	+	0.325246i	$0.105447\pi$
$104$	−2.60680	+	1.89395i	−0.255618	+	0.185717i
$105$	−0.671325	+	0.809996i	−0.0655146	+	0.0790475i
$106$	3.60858	+	11.1061i	0.350496	+	1.07872i
$107$	−5.70098	+	1.21178i	−0.551135	+	0.117147i	−0.475058	−	0.879955i	$-0.657573\pi$
$107$	−5.70098	+	1.21178i	−0.551135	+	0.117147i	−0.0760772	+	0.997102i	$0.524240\pi$
$108$	−0.913545	+	0.406737i	−0.0879060	+	0.0391383i
$109$	−6.50107	+	11.2602i	−0.622690	+	1.07853i	0.366293	+	0.930500i	$0.380627\pi$
$109$	−6.50107	+	11.2602i	−0.622690	+	1.07853i	−0.988983	+	0.148031i	$0.952706\pi$
$110$	−0.943463	−	0.921460i	−0.0899557	−	0.0878577i
$111$	−3.26774			−0.310160
$112$	−0.384127	−	2.61772i	−0.0362966	−	0.247351i
$113$	−3.90848	+	12.0291i	−0.367679	+	1.13160i	0.580607	+	0.814184i	$0.302815\pi$
$113$	−3.90848	+	12.0291i	−0.367679	+	1.13160i	−0.948286	+	0.317416i	$0.897185\pi$
$114$	−3.36660	+	3.73899i	−0.315311	+	0.350189i
$115$	−0.250088	−	2.37943i	−0.0233208	−	0.221883i
$116$	−0.545008	−	5.18540i	−0.0506027	−	0.481452i
$117$	2.15606	−	2.39455i	0.199328	−	0.221376i
$118$	−2.44757	+	7.53284i	−0.225317	+	0.693454i
$119$	−12.9956	+	10.2811i	−1.19131	+	0.942463i
$120$	−0.397631			−0.0362985
$121$	−9.65340	−	5.27370i	−0.877581	−	0.479428i
$122$	1.83680	−	3.18142i	0.166296	−	0.288033i
$123$	−8.46060	+	3.76690i	−0.762866	+	0.339650i
$124$	0.309478	−	0.0657816i	0.0277919	−	0.00590736i
$125$	−1.20932	−	3.72190i	−0.108165	−	0.332897i
$126$	0.919987	+	2.48065i	0.0819590	+	0.220994i
$127$	6.02970	−	4.38083i	0.535049	−	0.388736i	−0.287194	−	0.957872i	$-0.592722\pi$
$127$	6.02970	−	4.38083i	0.535049	−	0.388736i	0.822243	+	0.569137i	$0.192722\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	1.75607	+	1.95031i	0.154613	+	0.171715i
$130$	1.17047	−	0.521127i	0.102657	−	0.0457059i
$131$	−2.74662	−	4.75728i	−0.239973	−	0.415646i	0.720733	−	0.693213i	$-0.243805\pi$
$131$	−2.74662	−	4.75728i	−0.239973	−	0.415646i	−0.960706	+	0.277567i	$0.910472\pi$
$132$	−3.19326	+	0.896142i	−0.277938	+	0.0779992i
$133$	9.30501	+	9.51921i	0.806847	+	0.825420i
$134$	−11.5727	−	8.40807i	−0.999731	−	0.726347i
$135$	0.388941	−	0.0826720i	0.0334747	−	0.00711528i
$136$	−6.12626	−	1.30218i	−0.525322	−	0.111661i
$137$	2.00790	+	19.1039i	0.171547	+	1.63216i	0.654183	+	0.756336i	$0.273013\pi$
$137$	2.00790	+	19.1039i	0.171547	+	1.63216i	−0.482636	+	0.875821i	$0.660321\pi$
$138$	−5.49679	−	2.44733i	−0.467918	−	0.208330i
$139$	−3.89057	−	11.9740i	−0.329994	−	1.01562i	−0.969136	−	0.246528i	$-0.920710\pi$
$139$	−3.89057	−	11.9740i	−0.329994	−	1.01562i	0.639142	−	0.769089i	$-0.279290\pi$
$140$	−0.0670092	+	1.04990i	−0.00566331	+	0.0887324i
$141$	6.36629	+	4.62538i	0.536138	+	0.389527i
$142$	−2.88798	−	5.00213i	−0.242354	−	0.419769i
$143$	8.22526	−	6.82293i	0.687831	−	0.570562i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.216712	+	2.06187i	−0.0179969	+	0.171229i
$146$	2.53588	−	7.80464i	0.209871	−	0.645917i
$147$	6.70489	−	2.01107i	0.553010	−	0.165870i
$148$	−2.64365	+	1.92073i	−0.217307	+	0.157883i
$149$	−9.11932	−	4.06018i	−0.747083	−	0.332623i	−0.00236090	−	0.999997i	$-0.500751\pi$
$149$	−9.11932	−	4.06018i	−0.747083	−	0.332623i	−0.744723	+	0.667374i	$0.767418\pi$
$150$	−4.73608	−	1.00669i	−0.386700	−	0.0821955i
$151$	2.98282	+	3.31276i	0.242739	+	0.269589i	0.852187	−	0.523237i	$-0.175276\pi$
$151$	2.98282	+	3.31276i	0.242739	+	0.269589i	−0.609449	+	0.792826i	$0.708609\pi$
$152$	−0.525915	+	5.00375i	−0.0426573	+	0.405858i
$153$	6.26312			0.506344
$154$	1.82802	+	8.58244i	0.147306	+	0.691593i
$155$	−0.125807			−0.0101051
$156$	0.336810	−	3.20453i	0.0269664	−	0.256568i
$157$	−7.89609	−	8.76950i	−0.630177	−	0.699882i	0.340507	−	0.940242i	$-0.389401\pi$
$157$	−7.89609	−	8.76950i	−0.630177	−	0.699882i	−0.970684	+	0.240360i	$0.922735\pi$
$158$	0.651209	+	0.138419i	0.0518074	+	0.0110120i
$159$	−10.6680	−	4.74971i	−0.846030	−	0.376677i
$160$	−0.321690	+	0.233721i	−0.0254318	+	0.0184773i
$161$	−7.38820	+	14.1012i	−0.582272	+	1.11133i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	2.12577	−	20.2254i	0.166503	−	1.58417i	−0.518140	−	0.855296i	$-0.673375\pi$
$163$	2.12577	−	20.2254i	0.166503	−	1.58417i	0.684643	−	0.728878i	$-0.259958\pi$
$164$	−4.63064	+	8.02050i	−0.361592	+	0.626296i
$165$	1.31608	−	0.0845532i	0.102457	−	0.00658246i
$166$	4.38677	+	7.59810i	0.340479	+	0.589727i
$167$	1.76999	+	1.28597i	0.136966	+	0.0995113i	0.654158	−	0.756358i	$-0.273023\pi$
$167$	1.76999	+	1.28597i	0.136966	+	0.0995113i	−0.517193	+	0.855869i	$0.673023\pi$
$168$	2.20237	+	1.46613i	0.169917	+	0.113115i
$169$	−0.808858	−	2.48941i	−0.0622199	−	0.191493i
$170$	2.27510	+	1.01294i	0.174492	+	0.0776890i
$171$	−0.525915	−	5.00375i	−0.0402177	−	0.382646i
$172$	2.56705	+	0.545644i	0.195736	+	0.0416049i
$173$	5.85846	−	1.24525i	0.445410	−	0.0946749i	0.0202541	−	0.999795i	$-0.493552\pi$
$173$	5.85846	−	1.24525i	0.445410	−	0.0946749i	0.425156	+	0.905120i	$0.360219\pi$
$174$	4.21819	+	3.06469i	0.319780	+	0.232334i
$175$	−3.45616	+	12.3354i	−0.261261	+	0.932469i
$176$	−2.05667	+	2.60195i	−0.155027	+	0.196129i
$177$	−3.96025	−	6.85935i	−0.297671	−	0.515581i
$178$	−5.43472	+	2.41969i	−0.407349	+	0.181364i
$179$	0.909531	+	1.01014i	0.0679815	+	0.0755011i	0.776176	−	0.630516i	$-0.217157\pi$
$179$	0.909531	+	1.01014i	0.0679815	+	0.0755011i	−0.708195	+	0.706017i	$0.750490\pi$
$180$	0.266067	−	0.295497i	0.0198314	−	0.0220251i
$181$	20.5349	−	14.9195i	1.52635	−	1.10896i	0.568126	−	0.822942i	$-0.307669\pi$
$181$	20.5349	−	14.9195i	1.52635	−	1.10896i	0.958225	−	0.286017i	$-0.0923313\pi$
$182$	−8.40442	−	1.42934i	−0.622977	−	0.105950i
$183$	1.13520	+	3.49379i	0.0839166	+	0.258269i
$184$	−5.88550	+	1.25100i	−0.433885	+	0.0922250i
$185$	1.18702	−	0.528494i	0.0872712	−	0.0388557i
$186$	−0.158196	+	0.274003i	−0.0115995	+	0.0200909i
$187$	20.5536	+	3.00724i	1.50303	+	0.219911i
$188$	7.86917			0.573918
$189$	−2.45907	−	0.976195i	−0.178871	−	0.0710078i
$190$	0.618220	−	1.90269i	0.0448504	−	0.138035i
$191$	12.4390	−	13.8150i	0.900058	−	0.999616i	−0.0999315	−	0.994994i	$-0.531862\pi$
$191$	12.4390	−	13.8150i	0.900058	−	0.999616i	0.999989	−	0.00462119i	$-0.00147098\pi$
$192$	0.104528	+	0.994522i	0.00754369	+	0.0717734i
$193$	−2.10973	−	20.0727i	−0.151861	−	1.44487i	−0.759425	−	0.650594i	$-0.774520\pi$
$193$	−2.10973	−	20.0727i	−0.151861	−	1.44487i	0.607564	−	0.794271i	$-0.292147\pi$
$194$	−10.5171	+	11.6804i	−0.755084	+	0.838606i
$195$	−0.395925	+	1.21853i	−0.0283528	+	0.0872608i
$196$	4.24229	−	5.56803i	0.303021	−	0.397716i
$197$	13.3412			0.950520			0.475260	−	0.879845i	$-0.342354\pi$
$197$	13.3412			0.950520			0.475260	+	0.879845i	$0.342354\pi$
$198$	1.47075	−	2.97269i	0.104521	−	0.211260i
$199$	−9.47838	+	16.4170i	−0.671904	+	1.16377i	0.305459	+	0.952205i	$0.401190\pi$
$199$	−9.47838	+	16.4170i	−0.671904	+	1.16377i	−0.977363	+	0.211567i	$0.932143\pi$
$200$	−4.42329	+	1.96937i	−0.312774	+	0.139256i
$201$	13.9921	−	2.97411i	0.986925	−	0.209777i
$202$	4.30413	+	13.2467i	0.302837	+	0.932038i
$203$	8.80280	−	10.6211i	0.617835	−	0.745458i
$204$	5.06697	−	3.68137i	0.354759	−	0.257748i
$205$	2.46412	−	2.73668i	0.172101	−	0.191138i
$206$	5.31111	+	5.89859i	0.370043	+	0.410974i
$207$	5.49679	−	2.44733i	0.382053	−	0.170101i
$208$	−1.61109	−	2.79049i	−0.111709	−	0.193486i
$209$	0.676665	−	16.6732i	0.0468059	−	1.15331i
$210$	−0.735386	−	0.752315i	−0.0507465	−	0.0519146i
$211$	−7.03436	−	5.11076i	−0.484265	−	0.351839i	0.318709	−	0.947852i	$-0.396751\pi$
$211$	−7.03436	−	5.11076i	−0.484265	−	0.351839i	−0.802975	+	0.596013i	$0.796751\pi$
$212$	−11.4224	+	2.42791i	−0.784496	+	0.166750i
$213$	5.64974	+	1.20089i	0.387114	+	0.0822836i
$214$	−0.609228	−	5.79642i	−0.0416460	−	0.396235i
$215$	−0.953323	−	0.424447i	−0.0650161	−	0.0289470i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	0.696814	+	0.463873i	0.0473028	+	0.0314897i
$218$	−10.5190	−	7.64247i	−0.712434	−	0.517613i
$219$	4.10314	+	7.10685i	0.277265	+	0.480237i
$220$	1.01503	−	0.841976i	0.0684333	−	0.0567660i
$221$	−10.0905	+	17.4772i	−0.678759	+	1.17564i
$222$	0.341571	−	3.24984i	0.0229248	−	0.218115i
$223$	−4.25602	+	13.0987i	−0.285004	+	0.877154i	0.701393	+	0.712775i	$0.252562\pi$
$223$	−4.25602	+	13.0987i	−0.285004	+	0.877154i	−0.986397	+	0.164379i	$0.947438\pi$
$224$	2.64353	−	0.108397i	0.176628	−	0.00724255i
$225$	3.91717	−	2.84599i	0.261145	−	0.189733i
$226$	−11.5546	−	5.14445i	−0.768603	−	0.342204i
$227$	−15.9575	−	3.39186i	−1.05913	−	0.225126i	−0.354762	−	0.934957i	$-0.615438\pi$
$227$	−15.9575	−	3.39186i	−1.05913	−	0.225126i	−0.704372	+	0.709831i	$0.748771\pi$
$228$	−3.36660	−	3.73899i	−0.222959	−	0.247621i
$229$	2.17453	−	20.6893i	0.143697	−	1.36719i	−0.650491	−	0.759514i	$-0.725437\pi$
$229$	2.17453	−	20.6893i	0.143697	−	1.36719i	0.794188	−	0.607672i	$-0.207896\pi$
$230$	2.39254			0.157759
$231$	−7.60118	−	4.38429i	−0.500121	−	0.288465i
$232$	5.21396			0.342313
$233$	0.530821	−	5.05042i	0.0347752	−	0.330864i	−0.963279	−	0.268504i	$-0.913471\pi$
$233$	0.530821	−	5.05042i	0.0347752	−	0.330864i	0.998054	−	0.0623599i	$-0.0198627\pi$
$234$	2.15606	+	2.39455i	0.140946	+	0.156537i
$235$	−3.06064	−	0.650560i	−0.199654	−	0.0424379i
$236$	−7.23574	−	3.22156i	−0.471006	−	0.209706i
$237$	−0.538609	+	0.391322i	−0.0349864	+	0.0254191i
$238$	−8.86632	−	13.9991i	−0.574718	−	0.907428i
$239$	5.78426	−	17.8021i	0.374153	−	1.15152i	−0.569896	−	0.821717i	$-0.693016\pi$
$239$	5.78426	−	17.8021i	0.374153	−	1.15152i	0.944049	−	0.329807i	$-0.106984\pi$
$240$	0.0415637	−	0.395452i	0.00268293	−	0.0255263i
$241$	6.18350	−	10.7101i	0.398314	−	0.689901i	−0.595204	−	0.803575i	$-0.702929\pi$
$241$	6.18350	−	10.7101i	0.398314	−	0.689901i	0.993518	+	0.113674i	$0.0362619\pi$
$242$	6.25387	−	9.04926i	0.402014	−	0.581709i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	2.97200	+	2.15928i	0.190263	+	0.138234i
$245$	−2.11032	+	1.81492i	−0.134824	+	0.115951i
$246$	−2.86189	−	8.80800i	−0.182468	−	0.561577i
$247$	14.8102	+	6.59394i	0.942352	+	0.419562i
$248$	0.0330720	+	0.314659i	0.00210007	+	0.0199809i
$249$	−8.58181	−	1.82412i	−0.543850	−	0.115599i
$250$	3.82792	−	0.813649i	0.242099	−	0.0514597i
$251$	−6.61755	−	4.80793i	−0.417696	−	0.303474i	0.359014	−	0.933332i	$-0.383113\pi$
$251$	−6.61755	−	4.80793i	−0.417696	−	0.303474i	−0.776710	+	0.629858i	$0.783113\pi$
$252$	−2.56323	+	0.655649i	−0.161468	+	0.0413020i
$253$	19.2138	−	5.39207i	1.20796	−	0.338997i
$254$	3.72656	+	6.45459i	0.233825	+	0.404997i
$255$	−2.27510	+	1.01294i	−0.142472	+	0.0634328i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−4.30487	+	4.78104i	−0.268531	+	0.298233i	−0.862296	−	0.506405i	$-0.830974\pi$
$257$	−4.30487	+	4.78104i	−0.268531	+	0.298233i	0.593765	+	0.804638i	$0.297641\pi$
$258$	−2.12319	+	1.54258i	−0.132184	+	0.0960371i
$259$	−8.52324	−	1.44954i	−0.529608	−	0.0900703i
$260$	0.395925	+	1.21853i	0.0245542	+	0.0755701i
$261$	−5.10003	+	1.08404i	−0.315684	+	0.0671006i
$262$	5.01832	−	2.23430i	0.310033	−	0.138035i
$263$	−12.9098	+	22.3605i	−0.796054	+	1.37881i	0.126114	+	0.992016i	$0.459749\pi$
$263$	−12.9098	+	22.3605i	−0.796054	+	1.37881i	−0.922168	+	0.386790i	$0.873584\pi$
$264$	−0.557446	−	3.26944i	−0.0343084	−	0.201220i
$265$	4.64338			0.285240
$266$	−10.4397	+	8.25901i	−0.640099	+	0.506392i
$267$	1.83835	−	5.65787i	0.112505	−	0.346256i
$268$	9.57169	−	10.6304i	0.584684	−	0.649358i
$269$	1.28577	+	12.2333i	0.0783948	+	0.745877i	0.961147	+	0.276038i	$0.0890215\pi$
$269$	1.28577	+	12.2333i	0.0783948	+	0.745877i	−0.882752	+	0.469839i	$0.844312\pi$
$270$	0.0415637	+	0.395452i	0.00252949	+	0.0240665i
$271$	3.11684	−	3.46161i	0.189335	−	0.210278i	−0.641002	−	0.767539i	$-0.721481\pi$
$271$	3.11684	−	3.46161i	0.189335	−	0.210278i	0.830337	+	0.557261i	$0.188148\pi$
$272$	1.93541	−	5.95658i	0.117352	−	0.361171i
$273$	6.68586	−	5.28929i	0.404647	−	0.320122i
$274$	−19.2091			−1.16047
$275$	14.2214	−	7.45882i	0.857584	−	0.449783i
$276$	3.00849	−	5.21086i	0.181090	−	0.313657i
$277$	6.00459	−	2.67341i	0.360781	−	0.160630i	−0.218338	−	0.975873i	$-0.570064\pi$
$277$	6.00459	−	2.67341i	0.360781	−	0.160630i	0.579119	+	0.815243i	$0.303397\pi$
$278$	12.3150	−	2.61764i	0.738607	−	0.156996i
$279$	−0.0977705	−	0.300907i	−0.00585337	−	0.0180148i
$280$	−1.03714	−	0.176386i	−0.0619809	−	0.0105411i
$281$	11.7993	−	8.57267i	0.703885	−	0.511403i	−0.177310	−	0.984155i	$-0.556740\pi$
$281$	11.7993	−	8.57267i	0.703885	−	0.511403i	0.881195	+	0.472752i	$0.156740\pi$
$282$	−5.26550	+	5.84793i	−0.313556	+	0.348239i
$283$	−7.20735	−	8.00458i	−0.428433	−	0.475823i	0.489817	−	0.871825i	$-0.337064\pi$
$283$	−7.20735	−	8.00458i	−0.428433	−	0.475823i	−0.918249	+	0.396003i	$0.870397\pi$
$284$	5.27660	−	2.34929i	0.313109	−	0.139405i
$285$	1.00030	+	1.73257i	0.0592527	+	0.102629i
$286$	5.92577	+	8.89340i	0.350398	+	0.525877i
$287$	−23.7387	+	6.07214i	−1.40125	+	0.358427i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	−21.7410	+	4.62119i	−1.27888	+	0.271835i
$290$	−2.02793	−	0.431049i	−0.119084	−	0.0253121i
$291$	−1.64293	−	15.6315i	−0.0963105	−	0.916333i
$292$	7.49682	+	3.33780i	0.438718	+	0.195330i
$293$	−3.41332	−	10.5051i	−0.199408	−	0.613715i	−0.999897	−	0.0143673i	$-0.995427\pi$
$293$	−3.41332	−	10.5051i	−0.199408	−	0.613715i	0.800489	−	0.599348i	$-0.204573\pi$
$294$	1.29920	+	6.87838i	0.0757710	+	0.401155i
$295$	2.54794	+	1.85119i	0.148347	+	0.107780i
$296$	−1.63387	−	2.82994i	−0.0949667	−	0.164487i
$297$	1.22502	+	3.08210i	0.0710829	+	0.178841i
$298$	4.99117	−	8.64495i	0.289131	−	0.500789i
$299$	−2.02658	+	19.2816i	−0.117200	+	1.11509i
$300$	1.49623	−	4.60491i	0.0863847	−	0.265865i
$301$	3.71521	+	5.86597i	0.214141	+	0.338109i
$302$	−3.60640	+	2.62020i	−0.207525	+	0.150776i
$303$	−12.7243	−	5.66521i	−0.730990	−	0.325458i
$304$	−4.92136	−	1.04607i	−0.282260	−	0.0599961i
$305$	−0.977421	−	1.08554i	−0.0559670	−	0.0621576i
$306$	−0.654675	+	6.22881i	−0.0374253	+	0.356078i
$307$	−8.80164			−0.502336			−0.251168	−	0.967944i	$-0.580815\pi$
$307$	−8.80164			−0.502336			−0.251168	+	0.967944i	$0.580815\pi$
$308$	−8.72651	+	0.920898i	−0.497239	+	0.0524730i
$309$	−7.93734			−0.451539
$310$	0.0131504	−	0.125118i	0.000746894	−	0.00710622i
$311$	−7.53270	−	8.36591i	−0.427140	−	0.474387i	0.490705	−	0.871326i	$-0.336739\pi$
$311$	−7.53270	−	8.36591i	−0.427140	−	0.474387i	−0.917845	+	0.396939i	$0.870073\pi$
$312$	3.15177	+	0.669930i	0.178434	+	0.0379273i
$313$	−22.2728	−	9.91648i	−1.25893	−	0.560513i	−0.334693	−	0.942327i	$-0.608633\pi$
$313$	−22.2728	−	9.91648i	−1.25893	−	0.560513i	−0.924239	+	0.381815i	$0.875299\pi$
$314$	9.54682	−	6.93617i	0.538758	−	0.391431i
$315$	1.05115	−	0.0431018i	0.0592255	−	0.00242851i
$316$	−0.205730	+	0.633173i	−0.0115732	+	0.0356188i
$317$	−2.92312	+	27.8117i	−0.164179	+	1.56206i	0.533595	+	0.845740i	$0.320841\pi$
$317$	−2.92312	+	27.8117i	−0.164179	+	1.56206i	−0.697774	+	0.716318i	$0.745826\pi$
$318$	5.83881	−	10.1131i	0.327424	−	0.567115i
$319$	−17.2572	+	1.10871i	−0.966217	+	0.0620759i
$320$	−0.198815	−	0.344358i	−0.0111141	−	0.0192502i
$321$	4.71523	+	3.42582i	0.263179	+	0.191210i
$322$	−13.2517	−	8.82170i	−0.738486	−	0.491614i
$323$	9.73766	+	29.9694i	0.541818	+	1.66754i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	1.63080	+	15.5160i	0.0904604	+	0.860673i
$326$	19.8924	+	4.22826i	1.10174	+	0.234182i
$327$	12.7180	−	2.70330i	0.703308	−	0.149493i
$328$	−7.49253	−	5.44364i	−0.413706	−	0.300575i
$329$	14.5534	+	14.8884i	0.802355	+	0.820825i
$330$	−0.0534776	+	1.31771i	−0.00294385	+	0.0725374i
$331$	−2.05987	−	3.56780i	−0.113221	−	0.196104i	0.803846	−	0.594837i	$-0.202783\pi$
$331$	−2.05987	−	3.56780i	−0.113221	−	0.196104i	−0.917067	+	0.398733i	$0.869450\pi$
$332$	−8.01502	+	3.56852i	−0.439881	+	0.195848i
$333$	2.18654	+	2.42840i	0.119822	+	0.133076i
$334$	−1.46394	+	1.62587i	−0.0801032	+	0.0889636i
$335$	−4.60167	+	3.34331i	−0.251416	+	0.182664i
$336$	−1.68831	+	2.03706i	−0.0921050	+	0.111131i
$337$	−10.8990	−	33.5435i	−0.593704	−	1.82723i	−0.561076	−	0.827764i	$-0.689612\pi$
$337$	−10.8990	−	33.5435i	−0.593704	−	1.82723i	−0.0326280	−	0.999468i	$-0.510388\pi$
$338$	2.56032	−	0.544213i	0.139263	−	0.0296013i
$339$	11.5546	−	5.14445i	0.627561	−	0.279408i
$340$	−1.24520	+	2.15676i	−0.0675307	+	0.116967i
$341$	−0.176371	−	1.03443i	−0.00955105	−	0.0560173i
$342$	5.03131			0.272062
$343$	18.3805	−	2.27123i	0.992452	−	0.122635i
$344$	−0.810985	+	2.49595i	−0.0437254	+	0.134573i
$345$	−1.60092	+	1.77800i	−0.0861906	+	0.0957244i
$346$	0.626057	+	5.95653i	0.0336570	+	0.320225i
$347$	1.51854	+	14.4480i	0.0815196	+	0.775607i	0.956556	+	0.291550i	$0.0941708\pi$
$347$	1.51854	+	14.4480i	0.0815196	+	0.775607i	−0.875036	+	0.484058i	$0.839162\pi$
$348$	−3.48882	+	3.87473i	−0.187021	+	0.207707i
$349$	−9.60127	+	29.5497i	−0.513944	+	1.58176i	0.271250	+	0.962509i	$0.412563\pi$
$349$	−9.60127	+	29.5497i	−0.513944	+	1.58176i	−0.785195	+	0.619249i	$0.787437\pi$
$350$	−11.9066	−	4.72663i	−0.636433	−	0.252649i
$351$	−3.22219			−0.171988
$352$	−2.37271	−	2.31738i	−0.126466	−	0.123517i
$353$	−4.14946	+	7.18708i	−0.220854	+	0.382530i	−0.955067	−	0.296389i	$-0.904218\pi$
$353$	−4.14946	+	7.18708i	−0.220854	+	0.382530i	0.734214	+	0.678918i	$0.237551\pi$
$354$	7.23574	−	3.22156i	0.384575	−	0.171224i
$355$	−2.24651	+	0.477510i	−0.119232	+	0.0253436i
$356$	−1.83835	−	5.65787i	−0.0974326	−	0.299867i
$357$	16.3361	+	2.77828i	0.864598	+	0.147042i
$358$	−1.09967	+	0.798960i	−0.0581196	+	0.0422264i
$359$	−10.2322	+	11.3640i	−0.540037	+	0.599772i	−0.949969	−	0.312344i	$-0.898886\pi$
$359$	−10.2322	+	11.3640i	−0.540037	+	0.599772i	0.409932	+	0.912116i	$0.365552\pi$
$360$	0.266067	+	0.295497i	0.0140230	+	0.0155741i
$361$	5.76820	−	2.56817i	0.303589	−	0.135167i
$362$	12.6913	+	21.9820i	0.667040	+	1.15535i
$363$	2.54026	+	10.7027i	0.133329	+	0.561744i
$364$	2.30001	−	8.20898i	0.120553	−	0.430267i
$365$	−2.63988	−	1.91798i	−0.138178	−	0.100392i
$366$	−3.59331	+	0.763783i	−0.187826	+	0.0399236i
$367$	18.1206	+	3.85165i	0.945886	+	0.201054i	0.654936	−	0.755684i	$-0.272695\pi$
$367$	18.1206	+	3.85165i	0.945886	+	0.201054i	0.290950	+	0.956738i	$0.406029\pi$
$368$	−0.628946	−	5.98402i	−0.0327861	−	0.311939i
$369$	8.46060	+	3.76690i	0.440441	+	0.196097i
$370$	0.401522	+	1.23576i	0.0208741	+	0.0642440i
$371$	−25.7185	−	17.1209i	−1.33524	−	0.888875i
$372$	−0.255966	−	0.185971i	−0.0132712	−	0.00964212i
$373$	−8.67070	−	15.0181i	−0.448952	−	0.777607i	0.549366	−	0.835582i	$-0.314869\pi$
$373$	−8.67070	−	15.0181i	−0.448952	−	0.777607i	−0.998318	+	0.0579743i	$0.981536\pi$
$374$	−5.13920	+	20.1267i	−0.265742	+	1.04072i
$375$	−1.95672	+	3.38914i	−0.101044	+	0.175014i
$376$	−0.822552	+	7.82606i	−0.0424199	+	0.403598i
$377$	5.19160	−	15.9781i	0.267381	−	0.822914i
$378$	1.22789	−	2.34356i	0.0631559	−	0.120540i
$379$	15.9478	−	11.5868i	0.819183	−	0.595172i	−0.0972951	−	0.995256i	$-0.531019\pi$
$379$	15.9478	−	11.5868i	0.819183	−	0.595172i	0.916478	+	0.400084i	$0.131019\pi$
$380$	1.82764	+	0.813718i	0.0937560	+	0.0417429i
$381$	−7.29024	−	1.54959i	−0.373491	−	0.0793879i
$382$	12.4390	+	13.8150i	0.636437	+	0.706835i
$383$	1.86363	−	17.7313i	0.0952271	−	0.906025i	−0.837741	−	0.546067i	$-0.816124\pi$
$383$	1.86363	−	17.7313i	0.0952271	−	0.906025i	0.932969	−	0.359958i	$-0.117209\pi$
$384$	−1.00000			−0.0510310
$385$	3.47023	+	0.363263i	0.176859	+	0.0185136i
$386$	20.1833			1.02730
$387$	0.274325	−	2.61002i	0.0139447	−	0.132675i
$388$	−10.5171	−	11.6804i	−0.533925	−	0.592984i
$389$	25.6110	+	5.44379i	1.29853	+	0.276011i	0.804770	−	0.593587i	$-0.202289\pi$
$389$	25.6110	+	5.44379i	1.29853	+	0.276011i	0.493760	+	0.869598i	$0.335622\pi$
$390$	−1.17047	−	0.521127i	−0.0592691	−	0.0263883i
$391$	−30.4879	+	22.1508i	−1.54184	+	1.12021i
$392$	5.09409	+	4.80107i	0.257290	+	0.242491i
$393$	−1.69750	+	5.22438i	−0.0856277	+	0.263535i
$394$	−1.39453	+	13.2681i	−0.0702556	+	0.668437i
$395$	0.132363	−	0.229259i	0.00665989	−	0.0115353i
$396$	2.80267	+	1.77342i	0.140840	+	0.0891178i
$397$	−6.48629	−	11.2346i	−0.325538	−	0.563848i	0.656083	−	0.754688i	$-0.272212\pi$
$397$	−6.48629	−	11.2346i	−0.325538	−	0.563848i	−0.981621	+	0.190841i	$0.938879\pi$
$398$	−15.3363	−	11.1425i	−0.768741	−	0.558523i
$399$	0.847883	−	13.2846i	0.0424472	−	0.665060i
$400$	−1.49623	−	4.60491i	−0.0748113	−	0.230246i
$401$	−11.1988	−	4.98604i	−0.559243	−	0.248991i	0.107594	−	0.994195i	$-0.465685\pi$
$401$	−11.1988	−	4.98604i	−0.559243	−	0.248991i	−0.666837	+	0.745204i	$0.732352\pi$
$402$	1.49525	+	14.2263i	0.0745761	+	0.709544i
$403$	0.997196	+	0.211960i	0.0496739	+	0.0105585i
$404$	−13.6241	+	2.89589i	−0.677823	+	0.144076i
$405$	−0.321690	−	0.233721i	−0.0159849	−	0.0116137i
$406$	9.64281	+	9.86479i	0.478565	+	0.489581i
$407$	6.00955	+	9.01912i	0.297882	+	0.447061i
$408$	3.13156	+	5.42402i	0.155035	+	0.268529i
$409$	−25.3731	+	11.2968i	−1.25462	+	0.558592i	−0.922992	−	0.384820i	$-0.874264\pi$
$409$	−25.3731	+	11.2968i	−1.25462	+	0.558592i	−0.331625	+	0.943411i	$0.607597\pi$
$410$	2.46412	+	2.73668i	0.121694	+	0.135155i
$411$	12.8534	−	14.2752i	0.634013	−	0.704142i
$412$	−6.42144	+	4.66545i	−0.316362	+	0.229850i
$413$	−7.28676	−	19.6480i	−0.358558	−	0.966814i
$414$	1.85935	+	5.72249i	0.0913821	+	0.281245i
$415$	3.41239	−	0.725326i	0.167508	−	0.0356048i
$416$	2.94361	−	1.31058i	0.144323	−	0.0642565i
$417$	−6.29508	+	10.9034i	−0.308271	+	0.533942i
$418$	16.5112	+	2.41579i	0.807588	+	0.118160i
$419$	−6.13229			−0.299582			−0.149791	−	0.988718i	$-0.547860\pi$
$419$	−6.13229			−0.299582			−0.149791	+	0.988718i	$0.547860\pi$
$420$	0.825062	−	0.652720i	0.0402589	−	0.0318495i
$421$	−7.70987	+	23.7285i	−0.375756	+	1.15646i	0.567211	+	0.823572i	$0.308022\pi$
$421$	−7.70987	+	23.7285i	−0.375756	+	1.15646i	−0.942967	+	0.332886i	$0.891978\pi$
$422$	5.81805	−	6.46160i	0.283218	−	0.314546i
$423$	−0.822552	−	7.82606i	−0.0399938	−	0.380516i
$424$	−1.22064	−	11.6136i	−0.0592797	−	0.564008i
$425$	−20.2916	+	22.5361i	−0.984288	+	1.09316i
$426$	−1.78487	+	5.49326i	−0.0864772	+	0.266149i
$427$	1.41113	+	9.61643i	0.0682891	+	0.465371i
$428$	5.82835			0.281724
$429$	−10.5742	−	1.54713i	−0.510527	−	0.0746963i
$430$	0.521771	−	0.903734i	0.0251620	−	0.0435819i
$431$	6.95476	−	3.09646i	0.334999	−	0.149151i	−0.232342	−	0.972634i	$-0.574639\pi$
$431$	6.95476	−	3.09646i	0.334999	−	0.149151i	0.567341	+	0.823483i	$0.307972\pi$
$432$	0.978148	−	0.207912i	0.0470611	−	0.0100032i
$433$	7.51787	+	23.1376i	0.361286	+	1.11192i	0.952274	+	0.305243i	$0.0987378\pi$
$433$	7.51787	+	23.1376i	0.361286	+	1.11192i	−0.590989	+	0.806680i	$0.701262\pi$
$434$	−0.534168	+	0.644508i	−0.0256409	+	0.0309374i
$435$	1.67728	−	1.21861i	0.0804194	−	0.0584281i
$436$	8.70014	−	9.66248i	0.416661	−	0.462749i
$437$	20.2568	+	22.4975i	0.969014	+	1.07620i
$438$	−7.49682	+	3.33780i	−0.358212	+	0.159486i
$439$	0.970029	+	1.68014i	0.0462970	+	0.0801887i	0.888245	−	0.459370i	$-0.151925\pi$
$439$	0.970029	+	1.68014i	0.0462970	+	0.0801887i	−0.841948	+	0.539558i	$0.818591\pi$
$440$	0.731264	+	1.09748i	0.0348617	+	0.0523203i
$441$	−5.98097	−	3.63704i	−0.284808	−	0.173192i
$442$	−16.3267	−	11.8621i	−0.776583	−	0.564221i
$443$	21.2857	−	4.52441i	1.01131	−	0.214961i	0.327682	−	0.944788i	$-0.393733\pi$
$443$	21.2857	−	4.52441i	1.01131	−	0.214961i	0.683632	+	0.729827i	$0.260399\pi$
$444$	3.19633	+	0.679401i	0.151691	+	0.0322429i
$445$	0.247264	+	2.35256i	0.0117214	+	0.111522i
$446$	−12.5821	−	5.60190i	−0.595778	−	0.265257i
$447$	3.08471	+	9.49376i	0.145902	+	0.449040i
$448$	−0.168521	+	2.64038i	−0.00796188	+	0.124746i
$449$	−10.2057	−	7.41489i	−0.481638	−	0.349930i	0.320322	−	0.947309i	$-0.396209\pi$
$449$	−10.2057	−	7.41489i	−0.481638	−	0.349930i	−0.801959	+	0.597378i	$0.796209\pi$
$450$	2.42094	+	4.19320i	0.114124	+	0.197669i
$451$	25.9563	+	16.4241i	1.22224	+	0.773383i
$452$	6.32406	−	10.9536i	0.297459	−	0.515214i
$453$	0.465962	−	4.43334i	0.0218928	−	0.208296i
$454$	5.04129	−	15.5155i	0.236600	−	0.728179i
$455$	−1.57322	+	3.00266i	−0.0737538	+	0.140767i
$456$	4.07042	−	2.95733i	0.190615	−	0.138490i
$457$	−19.3507	−	8.61547i	−0.905186	−	0.403015i	−0.0992809	−	0.995059i	$-0.531654\pi$
$457$	−19.3507	−	8.61547i	−0.905186	−	0.403015i	−0.805905	+	0.592045i	$0.798321\pi$
$458$	20.3486	+	4.32523i	0.950829	+	0.202105i
$459$	−4.19085	−	4.65441i	−0.195612	−	0.217249i
$460$	−0.250088	+	2.37943i	−0.0116604	+	0.110942i
$461$	−22.6341			−1.05417			−0.527087	−	0.849811i	$-0.676716\pi$
$461$	−22.6341			−1.05417			−0.527087	+	0.849811i	$0.676716\pi$
$462$	5.15481	−	7.10126i	0.239824	−	0.330381i
$463$	17.5540			0.815804			0.407902	−	0.913026i	$-0.366261\pi$
$463$	17.5540			0.815804			0.407902	+	0.913026i	$0.366261\pi$
$464$	−0.545008	+	5.18540i	−0.0253013	+	0.240726i
$465$	0.0841814	+	0.0934929i	0.00390382	+	0.00433563i
$466$	4.96727	+	1.05583i	0.230104	+	0.0489102i
$467$	−12.9077	−	5.74688i	−0.597297	−	0.265934i	0.0857400	−	0.996318i	$-0.472675\pi$
$467$	−12.9077	−	5.74688i	−0.597297	−	0.265934i	−0.683037	+	0.730384i	$0.739341\pi$
$468$	−2.60680	+	1.89395i	−0.120500	+	0.0875480i
$469$	37.8148	−	1.55058i	1.74613	−	0.0715990i
$470$	0.966921	−	2.97588i	0.0446007	−	0.137267i
$471$	−1.23349	+	11.7359i	−0.0568362	+	0.540761i
$472$	3.96025	−	6.85935i	0.182285	−	0.315727i
$473$	2.15345	−	8.43356i	0.0990158	−	0.387776i
$474$	−0.332879	−	0.576563i	−0.0152896	−	0.0264824i
$475$	19.7085	+	14.3191i	0.904288	+	0.657004i
$476$	14.8492	−	7.35445i	0.680613	−	0.337090i
$477$	3.60858	+	11.1061i	0.165226	+	0.508512i
$478$	17.1000	+	7.61340i	0.782135	+	0.348229i
$479$	−0.292342	−	2.78145i	−0.0133574	−	0.127088i	0.985811	−	0.167859i	$-0.0536852\pi$
$479$	−0.292342	−	2.78145i	−0.0133574	−	0.127088i	−0.999169	+	0.0407711i	$0.987019\pi$
$480$	0.388941	+	0.0826720i	0.0177527	+	0.00377345i
$481$	−10.2992	+	2.18916i	−0.469601	+	0.0998169i
$482$	10.0051	+	7.26914i	0.455721	+	0.331100i
$483$	15.4229	−	3.94503i	0.701766	−	0.179505i
$484$	8.34598	+	7.16551i	0.379363	+	0.325705i
$485$	3.12489	+	5.41247i	0.141894	+	0.245768i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−10.0688	−	11.1826i	−0.456262	−	0.506730i	0.470490	−	0.882406i	$-0.344077\pi$
$487$	−10.0688	−	11.1826i	−0.456262	−	0.506730i	−0.926751	+	0.375676i	$0.877411\pi$
$488$	−2.45811	+	2.73001i	−0.111274	+	0.123582i
$489$	−16.4528	+	11.9537i	−0.744022	+	0.540564i
$490$	−1.58439	−	2.28847i	−0.0715753	−	0.103383i
$491$	4.56029	+	14.0351i	0.205803	+	0.633397i	0.999679	+	0.0253176i	$0.00805971\pi$
$491$	4.56029	+	14.0351i	0.205803	+	0.633397i	−0.793876	+	0.608079i	$0.791940\pi$
$492$	9.05890	−	1.92553i	0.408407	−	0.0868095i
$493$	29.8325	−	13.2823i	1.34359	−	0.598203i
$494$	−8.10591	+	14.0398i	−0.364702	+	0.631682i
$495$	−0.943463	−	0.921460i	−0.0424055	−	0.0414165i
$496$	−0.316392			−0.0142064
$497$	14.2035	+	5.63846i	0.637114	+	0.252920i
$498$	2.71117	−	8.34412i	0.121490	−	0.373909i
$499$	3.70540	−	4.11527i	0.165877	−	0.184225i	−0.654476	−	0.756083i	$-0.727111\pi$
$499$	3.70540	−	4.11527i	0.165877	−	0.184225i	0.820352	+	0.571858i	$0.193777\pi$
$500$	0.409066	+	3.89200i	0.0182940	+	0.174055i
$501$	−0.228690	−	2.17584i	−0.0102171	−	0.0972092i
$502$	5.47331	−	6.07873i	0.244286	−	0.271307i
$503$	−1.30086	+	4.00364i	−0.0580026	+	0.178514i	−0.975860	−	0.218396i	$-0.929917\pi$
$503$	−1.30086	+	4.00364i	−0.0580026	+	0.178514i	0.917858	+	0.396910i	$0.129917\pi$
$504$	−0.384127	−	2.61772i	−0.0171104	−	0.116602i
$505$	5.53838			0.246455
$506$	3.35414	+	19.6722i	0.149110	+	0.874535i
$507$	−1.30876	+	2.26684i	−0.0581241	+	0.100674i
$508$	−6.80876	+	3.03145i	−0.302090	+	0.134499i
$509$	32.6879	−	6.94803i	1.44887	−	0.307966i	0.584732	−	0.811227i	$-0.301200\pi$
$509$	32.6879	−	6.94803i	1.44887	−	0.307966i	0.864135	+	0.503261i	$0.167866\pi$
$510$	−0.769579	−	2.36852i	−0.0340775	−	0.104880i
$511$	7.54968	+	20.3569i	0.333978	+	0.900537i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−3.36660	+	3.73899i	−0.148639	+	0.165081i
$514$	−4.30487	−	4.78104i	−0.189880	−	0.210883i
$515$	2.88327	−	1.28371i	0.127052	−	0.0565671i
$516$	−1.31220	−	2.27280i	−0.0577664	−	0.100054i
$517$	1.05833	−	26.0776i	0.0465453	−	1.14689i
$518$	2.33252	−	8.32503i	0.102485	−	0.365781i
$519$	−4.84548	−	3.52045i	−0.212693	−	0.154530i
$520$	−1.25324	+	0.266385i	−0.0549583	+	0.0116817i
$521$	−11.8195	−	2.51231i	−0.517821	−	0.110066i	−0.0584145	−	0.998292i	$-0.518605\pi$
$521$	−11.8195	−	2.51231i	−0.517821	−	0.110066i	−0.459406	+	0.888226i	$0.651938\pi$
$522$	−0.545008	−	5.18540i	−0.0238543	−	0.226959i
$523$	−26.4149	−	11.7607i	−1.15504	−	0.514259i	−0.262373	−	0.964966i	$-0.584505\pi$
$523$	−26.4149	−	11.7607i	−1.15504	−	0.514259i	−0.892672	+	0.450707i	$0.851172\pi$
$524$	1.69750	+	5.22438i	0.0741558	+	0.228228i
$525$	11.4796	−	5.68557i	0.501012	−	0.248139i
$526$	−20.8885	−	15.1764i	−0.910783	−	0.661723i
$527$	0.990801	+	1.71612i	0.0431600	+	0.0747553i
$528$	3.30980	−	0.212643i	0.144041	−	0.00925408i
$529$	−6.60205	+	11.4351i	−0.287045	+	0.497177i
$530$	−0.485365	+	4.61794i	−0.0210829	+	0.200590i
$531$	−2.44757	+	7.53284i	−0.106215	+	0.326898i
$532$	−7.12252	−	11.2458i	−0.308800	−	0.487568i
$533$	−24.1423	+	17.5404i	−1.04572	+	0.759760i
$534$	5.43472	+	2.41969i	0.235183	+	0.104710i
$535$	−2.26689	−	0.481841i	−0.0980060	−	0.0208318i
$536$	9.57169	+	10.6304i	0.413434	+	0.459165i
$537$	0.142083	−	1.35183i	0.00613132	−	0.0583356i
$538$	−12.3007			−0.530320
$539$	−17.8813	−	14.8074i	−0.770203	−	0.637799i
$540$	−0.397631			−0.0171113
$541$	−4.06698	+	38.6947i	−0.174853	+	1.66362i	0.457706	+	0.889104i	$0.348671\pi$
$541$	−4.06698	+	38.6947i	−0.174853	+	1.66362i	−0.632559	+	0.774512i	$0.717995\pi$
$542$	3.11684	+	3.46161i	0.133880	+	0.148689i
$543$	−24.8279	−	5.27734i	−1.06547	−	0.226472i
$544$	5.72165	+	2.54744i	0.245314	+	0.109221i
$545$	−4.18266	+	3.03888i	−0.179165	+	0.130171i
$546$	4.56145	+	7.20212i	0.195212	+	0.308222i
$547$	4.89671	−	15.0705i	0.209368	−	0.644369i	−0.790137	−	0.612930i	$-0.789991\pi$
$547$	4.89671	−	15.0705i	0.209368	−	0.644369i	0.999506	−	0.0314395i	$-0.0100092\pi$
$548$	2.00790	−	19.1039i	0.0857733	−	0.816079i
$549$	1.83680	−	3.18142i	0.0783925	−	0.135780i
$550$	5.93141	+	14.9232i	0.252916	+	0.636326i
$551$	−13.1165	−	22.7185i	−0.558783	−	0.967841i
$552$	4.86784	+	3.53669i	0.207189	+	0.150532i
$553$	−1.57844	+	0.781763i	−0.0671222	+	0.0332439i
$554$	2.03112	+	6.25114i	0.0862940	+	0.265585i
$555$	−1.18702	−	0.528494i	−0.0503861	−	0.0224333i
$556$	1.31603	+	12.5212i	0.0558121	+	0.531017i
$557$	19.7899	+	4.20648i	0.838526	+	0.178234i	0.607107	−	0.794620i	$-0.292330\pi$
$557$	19.7899	+	4.20648i	0.838526	+	0.178234i	0.231419	+	0.972854i	$0.425663\pi$
$558$	0.309478	−	0.0657816i	0.0131013	−	0.00278476i
$559$	6.84130	+	4.97049i	0.289356	+	0.210229i
$560$	0.283830	−	1.01302i	0.0119940	−	0.0428079i
$561$	−11.5182	−	17.2865i	−0.486300	−	0.729838i
$562$	7.29235	+	12.6307i	0.307609	+	0.532795i
$563$	15.4487	−	6.87822i	0.651087	−	0.289882i	−0.0544918	−	0.998514i	$-0.517354\pi$
$563$	15.4487	−	6.87822i	0.651087	−	0.289882i	0.705579	+	0.708632i	$0.250687\pi$
$564$	−5.26550	−	5.84793i	−0.221718	−	0.246242i
$565$	−3.36524	+	3.73748i	−0.141577	+	0.157237i
$566$	8.71410	−	6.33116i	0.366281	−	0.266119i
$567$	0.919987	+	2.48065i	0.0386358	+	0.104178i
$568$	1.78487	+	5.49326i	0.0748914	+	0.230492i
$569$	12.8265	−	2.72636i	0.537715	−	0.114295i	0.0689540	−	0.997620i	$-0.478034\pi$
$569$	12.8265	−	2.72636i	0.537715	−	0.114295i	0.468761	+	0.883325i	$0.344700\pi$
$570$	−1.82764	+	0.813718i	−0.0765515	+	0.0340829i
$571$	9.12708	−	15.8086i	0.381956	−	0.661568i	−0.609385	−	0.792874i	$-0.708584\pi$
$571$	9.12708	−	15.8086i	0.381956	−	0.661568i	0.991342	+	0.131306i	$0.0419171\pi$
$572$	−9.46409	+	4.96370i	−0.395713	+	0.207543i
$573$	−18.5899			−0.776603
$574$	−3.55751	−	24.2434i	−0.148487	−	1.01190i
$575$	−9.00277	+	27.7077i	−0.375441	+	1.15549i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−3.13196	−	29.7986i	−0.130385	−	1.24053i	−0.842587	−	0.538559i	$-0.818969\pi$
$577$	−3.13196	−	29.7986i	−0.130385	−	1.24053i	0.712202	−	0.701974i	$-0.247698\pi$
$578$	−2.32332	−	22.1050i	−0.0966376	−	0.919445i
$579$	−13.5052	+	14.9991i	−0.561259	+	0.623341i
$580$	0.640664	−	1.97176i	0.0266021	−	0.0818729i
$581$	−21.5748	−	8.56468i	−0.895072	−	0.355323i
$582$	15.7176			0.651514
$583$	6.50964	+	38.1793i	0.269602	+	1.58122i
$584$	−4.10314	+	7.10685i	−0.169789	+	0.294084i
$585$	1.17047	−	0.521127i	0.0483930	−	0.0215460i
$586$	10.8044	−	2.29654i	0.446324	−	0.0948690i
$587$	−4.11520	−	12.6653i	−0.169853	−	0.522752i	0.829509	−	0.558494i	$-0.188621\pi$
$587$	−4.11520	−	12.6653i	−0.169853	−	0.522752i	−0.999361	+	0.0357417i	$0.988621\pi$
$588$	−6.97650	+	0.573099i	−0.287706	+	0.0236342i
$589$	1.28785	−	0.935675i	0.0530648	−	0.0385538i
$590$	−2.10738	+	2.34048i	−0.0867595	+	0.0963562i
$591$	−8.92700	−	9.91443i	−0.367208	−	0.407825i
$592$	2.98523	−	1.32911i	0.122692	−	0.0546260i
$593$	−4.66083	−	8.07280i	−0.191397	−	0.331510i	0.754316	−	0.656511i	$-0.227969\pi$
$593$	−4.66083	−	8.07280i	−0.191397	−	0.331510i	−0.945714	+	0.325001i	$0.894635\pi$
$594$	−3.19326	+	0.896142i	−0.131021	+	0.0367692i
$595$	−6.38348	+	1.63283i	−0.261697	+	0.0669397i
$596$	8.07588	+	5.86747i	0.330801	+	0.240341i
$597$	18.5425	−	3.94133i	0.758894	−	0.161308i
$598$	−18.9642	−	4.03096i	−0.775502	−	0.164838i
$599$	−2.98774	−	28.4264i	−0.122076	−	1.16147i	−0.868391	−	0.495880i	$-0.834846\pi$
$599$	−2.98774	−	28.4264i	−0.122076	−	1.16147i	0.746315	−	0.665592i	$-0.231821\pi$
$600$	4.42329	+	1.96937i	0.180580	+	0.0803994i
$601$	−13.3442	−	41.0693i	−0.544323	−	1.67525i	−0.722594	−	0.691272i	$-0.757051\pi$
$601$	−13.3442	−	41.0693i	−0.544323	−	1.67525i	0.178272	−	0.983981i	$-0.442949\pi$
$602$	−6.22218	+	3.08169i	−0.253597	+	0.125600i
$603$	−11.5727	−	8.40807i	−0.471278	−	0.342403i
$604$	−2.22888	−	3.86053i	−0.0906918	−	0.157083i
$605$	−2.65371	−	3.47694i	−0.107889	−	0.141358i
$606$	6.96423	−	12.0624i	0.282902	−	0.490001i
$607$	−1.99466	+	18.9780i	−0.0809609	+	0.770292i	0.876436	+	0.481518i	$0.159914\pi$
$607$	−1.99466	+	18.9780i	−0.0809609	+	0.770292i	−0.957397	+	0.288774i	$0.906752\pi$
$608$	1.55476	−	4.78506i	0.0630539	−	0.194060i
$609$	−13.7833	+	0.565176i	−0.558526	+	0.0229021i
$610$	1.18176	−	0.858597i	0.0478480	−	0.0347636i
$611$	23.1638	+	10.3132i	0.937106	+	0.417227i
$612$	−6.12626	−	1.30218i	−0.247639	−	0.0526374i
$613$	−1.53184	−	1.70128i	−0.0618702	−	0.0687139i	0.711415	−	0.702772i	$-0.248055\pi$
$613$	−1.53184	−	1.70128i	−0.0618702	−	0.0687139i	−0.773285	+	0.634058i	$0.781388\pi$
$614$	0.920022	−	8.75342i	0.0371291	−	0.353259i
$615$	−3.68257			−0.148495
$616$	−0.00368482	−	8.77496i	−0.000148466	−	0.353553i
$617$	−25.5472			−1.02849			−0.514246	−	0.857643i	$-0.671928\pi$
$617$	−25.5472			−1.02849			−0.514246	+	0.857643i	$0.671928\pi$
$618$	0.829678	−	7.89385i	0.0333745	−	0.317537i
$619$	21.9676	+	24.3975i	0.882954	+	0.980620i	0.999922	−	0.0125157i	$-0.00398397\pi$
$619$	21.9676	+	24.3975i	0.882954	+	0.980620i	−0.116967	+	0.993136i	$0.537317\pi$
$620$	0.123058	+	0.0261568i	0.00494213	+	0.00105048i
$621$	−5.49679	−	2.44733i	−0.220579	−	0.0982079i
$622$	9.10746	−	6.61696i	0.365176	−	0.265316i
$623$	7.30477	−	13.9419i	0.292659	−	0.558572i
$624$	−0.995710	+	3.06448i	−0.0398603	+	0.122677i
$625$	−2.36792	+	22.5293i	−0.0947168	+	0.901170i
$626$	12.1903	−	21.1142i	0.487222	−	0.843894i
$627$	−12.8434	+	10.6537i	−0.512916	+	0.425468i
$628$	5.90026	+	10.2196i	0.235446	+	0.407804i
$629$	−16.5575	−	12.0298i	−0.660192	−	0.479658i
$630$	−0.0670092	+	1.04990i	−0.00266971	+	0.0418288i
$631$	0.0427691	+	0.131630i	0.00170261	+	0.00524009i	0.951904	−	0.306396i	$-0.0991231\pi$
$631$	0.0427691	+	0.131630i	0.00170261	+	0.00524009i	−0.950202	+	0.311636i	$0.899123\pi$
$632$	−0.608200	−	0.270788i	−0.0241929	−	0.0107714i
$633$	0.908869	+	8.64731i	0.0361243	+	0.343700i
$634$	−27.3538	−	5.81422i	−1.08636	−	0.230912i
$635$	2.89882	−	0.616164i	0.115036	−	0.0244517i
$636$	9.44739	+	6.86393i	0.374613	+	0.272172i
$637$	19.7850	−	10.8303i	0.783911	−	0.429110i
$638$	0.701230	−	17.2785i	0.0277620	−	0.684064i
$639$	−2.88798	−	5.00213i	−0.114247	−	0.197881i
$640$	0.363254	−	0.161731i	0.0143589	−	0.00639298i
$641$	−6.00736	−	6.67185i	−0.237276	−	0.263522i	0.612733	−	0.790290i	$-0.290070\pi$
$641$	−6.00736	−	6.67185i	−0.237276	−	0.263522i	−0.850009	+	0.526768i	$0.823404\pi$
$642$	−3.89993	+	4.33131i	−0.153918	+	0.170943i
$643$	−18.0299	+	13.0995i	−0.711031	+	0.516594i	−0.883506	−	0.468420i	$-0.844823\pi$
$643$	−18.0299	+	13.0995i	−0.711031	+	0.516594i	0.172475	+	0.985014i	$0.444823\pi$
$644$	10.1585	−	12.2569i	0.400303	−	0.482991i
$645$	0.322472	+	0.992468i	0.0126973	+	0.0390784i
$646$	−30.8231	+	6.55165i	−1.21272	+	0.257771i
$647$	15.4802	−	6.89224i	0.608591	−	0.270962i	−0.0792142	−	0.996858i	$-0.525241\pi$
$647$	15.4802	−	6.89224i	0.608591	−	0.270962i	0.687805	+	0.725896i	$0.258574\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−11.6490	+	23.5452i	−0.457265	+	0.924231i
$650$	−15.6015			−0.611940
$651$	−0.121535	−	0.828225i	−0.00476332	−	0.0324607i
$652$	−6.28441	+	19.3414i	−0.246117	+	0.757469i
$653$	3.24709	−	3.60625i	0.127068	−	0.141124i	−0.676253	−	0.736669i	$-0.736397\pi$
$653$	3.24709	−	3.60625i	0.127068	−	0.141124i	0.803321	+	0.595546i	$0.203064\pi$
$654$	1.35909	+	12.9309i	0.0531448	+	0.505639i
$655$	−0.228319	−	2.17231i	−0.00892117	−	0.0848793i
$656$	6.19700	−	6.88247i	0.241952	−	0.268715i
$657$	2.53588	−	7.80464i	0.0989342	−	0.304488i
$658$	−16.3281	+	12.9174i	−0.636536	+	0.503573i
$659$	−1.59901			−0.0622887			−0.0311443	−	0.999515i	$-0.509915\pi$
$659$	−1.59901			−0.0622887			−0.0311443	+	0.999515i	$0.509915\pi$
$660$	−1.30490	−	0.190923i	−0.0507931	−	0.00743165i
$661$	−11.9610	+	20.7170i	−0.465229	+	0.805800i	−0.999212	−	0.0396955i	$-0.987361\pi$
$661$	−11.9610	+	20.7170i	−0.465229	+	0.805800i	0.533983	+	0.845495i	$0.320695\pi$
$662$	3.76357	−	1.67565i	0.146275	−	0.0651260i
$663$	19.7399	−	4.19585i	0.766636	−	0.162953i
$664$	−2.71117	−	8.34412i	−0.105214	−	0.323815i
$665$	1.84053	+	4.96279i	0.0713726	+	0.192449i
$666$	−2.64365	+	1.92073i	−0.102440	+	0.0744267i
$667$	20.9922	−	23.3142i	0.812821	−	0.902729i
$668$	−1.46394	−	1.62587i	−0.0566415	−	0.0629067i
$669$	12.5821	−	5.60190i	0.486451	−	0.216582i
$670$	−2.84399	−	4.92593i	−0.109873	−	0.190305i
$671$	7.55535	−	9.55849i	0.291671	−	0.369001i
$672$	−1.84942	−	1.89199i	−0.0713430	−	0.0729853i
$673$	15.4530	+	11.2273i	0.595669	+	0.432779i	0.844339	−	0.535810i	$-0.179993\pi$
$673$	15.4530	+	11.2273i	0.595669	+	0.432779i	−0.248670	+	0.968588i	$0.579993\pi$
$674$	34.4990	−	7.33299i	1.32885	−	0.282456i
$675$	−4.73608	−	1.00669i	−0.182292	−	0.0387473i
$676$	0.273605	+	2.60318i	0.0105233	+	0.100122i
$677$	−2.28653	−	1.01803i	−0.0878784	−	0.0391260i	0.362327	−	0.932051i	$-0.381982\pi$
$677$	−2.28653	−	1.01803i	−0.0878784	−	0.0391260i	−0.450205	+	0.892925i	$0.648649\pi$
$678$	3.90848	+	12.0291i	0.150104	+	0.461974i
$679$	2.64875	−	41.5003i	0.101650	−	1.59264i
$680$	−2.01478	−	1.46383i	−0.0772634	−	0.0561352i
$681$	8.15698	+	14.1283i	0.312576	+	0.541398i
$682$	1.04719	−	0.0672784i	0.0400991	−	0.00257622i
$683$	12.5142	−	21.6752i	0.478842	−	0.829379i	−0.520863	−	0.853640i	$-0.674390\pi$
$683$	12.5142	−	21.6752i	0.478842	−	0.829379i	0.999706	+	0.0242607i	$0.00772319\pi$
$684$	−0.525915	+	5.00375i	−0.0201089	+	0.191323i
$685$	−2.36032	+	7.26431i	−0.0901830	+	0.277555i
$686$	0.337510	+	18.5172i	0.0128862	+	0.706989i
$687$	−16.8302	+	12.2278i	−0.642111	+	0.466521i
$688$	−2.39751	−	1.06744i	−0.0914042	−	0.0406958i
$689$	−36.8052	−	7.82318i	−1.40217	−	0.298040i
$690$	−1.60092	−	1.77800i	−0.0609460	−	0.0676874i
$691$	−0.819469	+	7.79672i	−0.0311741	+	0.296601i	0.967816	+	0.251660i	$0.0809766\pi$
$691$	−0.819469	+	7.79672i	−0.0311741	+	0.296601i	−0.998990	+	0.0449409i	$0.985690\pi$
$692$	−5.98934			−0.227681
$693$	1.82802	+	8.58244i	0.0694408	+	0.326020i
$694$	−14.5275			−0.551458
$695$	0.523294	−	4.97881i	0.0198497	−	0.188857i
$696$	−3.48882	−	3.87473i	−0.132243	−	0.146871i
$697$	−56.7370	−	12.0598i	−2.14907	−	0.456798i
$698$	−28.3842	−	12.6375i	−1.07436	−	0.478335i
$699$	−4.10838	+	2.98491i	−0.155393	+	0.112900i
$700$	5.94531	−	11.3473i	0.224712	−	0.428887i
$701$	13.8853	−	42.7344i	0.524439	−	1.61406i	−0.240984	−	0.970529i	$-0.577470\pi$
$701$	13.8853	−	42.7344i	0.524439	−	1.61406i	0.765423	−	0.643527i	$-0.222530\pi$
$702$	0.336810	−	3.20453i	0.0127121	−	0.120947i
$703$	−8.22050	+	14.2383i	−0.310042	+	0.537008i
$704$	2.55270	−	2.11748i	0.0962084	−	0.0798057i
$705$	1.56451	+	2.70981i	0.0589229	+	0.102057i
$706$	−6.71397	−	4.87799i	−0.252684	−	0.183585i
$707$	−30.6757	−	20.4210i	−1.15368	−	0.768009i
$708$	2.44757	+	7.53284i	0.0919853	+	0.283102i
$709$	47.1635	+	20.9985i	1.77126	+	0.788617i	0.985409	+	0.170204i	$0.0544427\pi$
$709$	47.1635	+	20.9985i	1.77126	+	0.788617i	0.785853	+	0.618413i	$0.212224\pi$
$710$	−0.240070	−	2.28412i	−0.00900967	−	0.0857213i
$711$	0.651209	+	0.138419i	0.0244222	+	0.00519111i
$712$	5.81904	−	1.23687i	0.218078	−	0.0463538i
$713$	1.54015	+	1.11898i	0.0576789	+	0.0419062i
$714$	−4.47064	+	15.9562i	−0.167310	+	0.597146i
$715$	4.09134	−	1.14817i	0.153007	−	0.0429392i
$716$	−0.679636	−	1.17716i	−0.0253992	−	0.0439927i
$717$	−17.1000	+	7.61340i	−0.638610	+	0.284328i
$718$	−10.2322	−	11.3640i	−0.381864	−	0.424103i
$719$	−13.9430	+	15.4853i	−0.519988	+	0.577505i	−0.944747	−	0.327802i	$-0.893692\pi$
$719$	−13.9430	+	15.4853i	−0.519988	+	0.577505i	0.424759	+	0.905307i	$0.360359\pi$
$720$	−0.321690	+	0.233721i	−0.0119887	+	0.00871028i
$721$	−20.7029	−	3.52095i	−0.771018	−	0.131127i
$722$	1.95116	+	6.00504i	0.0726145	+	0.223485i
$723$	−12.0968	+	2.57125i	−0.449883	+	0.0956256i
$724$	−23.1881	+	10.3240i	−0.861781	+	0.383689i
$725$	12.6227	−	21.8632i	0.468796	−	0.811979i
$726$	−10.9096	+	1.40761i	−0.404892	+	0.0522413i
$727$	29.6889			1.10110			0.550551	−	0.834802i	$-0.314418\pi$
$727$	29.6889			1.10110			0.550551	+	0.834802i	$0.314418\pi$
$728$	7.92359	+	3.14548i	0.293668	+	0.116579i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	2.18342	−	2.42493i	0.0808120	−	0.0897508i
$731$	1.71813	+	16.3469i	0.0635473	+	0.604612i
$732$	−0.383995	−	3.65347i	−0.0141929	−	0.135036i
$733$	24.7577	−	27.4962i	0.914445	−	1.01559i	−0.0853696	−	0.996349i	$-0.527207\pi$
$733$	24.7577	−	27.4962i	0.914445	−	1.01559i	0.999815	−	0.0192449i	$-0.00612622\pi$
$734$	−5.72466	+	17.6187i	−0.211301	+	0.650318i
$735$	2.76083	+	0.353860i	0.101835	+	0.0130523i
$736$	6.01698			0.221789
$737$	−33.9409	−	33.1493i	−1.25023	−	1.22107i
$738$	−4.63064	+	8.02050i	−0.170456	+	0.295239i
$739$	−4.72670	+	2.10446i	−0.173874	+	0.0774138i	−0.491828	−	0.870692i	$-0.663671\pi$
$739$	−4.72670	+	2.10446i	−0.173874	+	0.0774138i	0.317954	+	0.948106i	$0.397004\pi$
$740$	−1.27096	+	0.270150i	−0.0467213	+	0.00993093i
$741$	−5.00973	−	15.4184i	−0.184037	−	0.566407i
$742$	19.7155	−	23.7880i	0.723777	−	0.873284i
$743$	15.4796	−	11.2466i	0.567893	−	0.412598i	−0.266446	−	0.963850i	$-0.585849\pi$
$743$	15.4796	−	11.2466i	0.567893	−	0.412598i	0.834339	+	0.551251i	$0.185849\pi$
$744$	0.211708	−	0.235125i	0.00776158	−	0.00862010i
$745$	−2.65597	−	2.94975i	−0.0973071	−	0.108071i
$746$	15.8422	−	7.05338i	0.580023	−	0.258243i
$747$	4.38677	+	7.59810i	0.160503	+	0.278000i
$748$	−19.4792	−	7.21486i	−0.712230	−	0.263801i
$749$	10.7791	+	11.0272i	0.393859	+	0.402925i
$750$	−3.16604	−	2.30026i	−0.115607	−	0.0839936i
$751$	34.0220	−	7.23160i	1.24148	−	0.263885i	0.460059	−	0.887888i	$-0.347828\pi$
$751$	34.0220	−	7.23160i	1.24148	−	0.263885i	0.781422	+	0.624003i	$0.214495\pi$
$752$	−7.69721	−	1.63609i	−0.280688	−	0.0596621i
$753$	0.855016	+	8.13493i	0.0311585	+	0.296453i
$754$	15.3479	+	6.83332i	0.558937	+	0.248855i
$755$	0.547745	+	1.68579i	0.0199345	+	0.0613520i
$756$	2.20237	+	1.46613i	0.0800996	+	0.0533227i
$757$	−30.6253	−	22.2506i	−1.11310	−	0.808711i	−0.129947	−	0.991521i	$-0.541481\pi$
$757$	−30.6253	−	22.2506i	−1.11310	−	0.808711i	−0.983148	+	0.182810i	$0.941481\pi$
$758$	9.85628	+	17.0716i	0.357996	+	0.620068i
$759$	−16.8636	−	10.6706i	−0.612111	−	0.387320i
$760$	−1.00030	+	1.73257i	−0.0362847	+	0.0628470i
$761$	1.88009	−	17.8879i	0.0681532	−	0.648435i	−0.906113	−	0.423035i	$-0.860965\pi$
$761$	1.88009	−	17.8879i	0.0681532	−	0.648435i	0.974266	−	0.225399i	$-0.0723687\pi$
$762$	2.30314	−	7.08833i	0.0834339	−	0.256783i
$763$	34.3716	−	1.40939i	1.24433	−	0.0510233i
$764$	−15.0395	+	10.9268i	−0.544111	+	0.395319i
$765$	2.27510	+	1.01294i	0.0822565	+	0.0366230i
$766$	17.4393	+	3.70684i	0.630108	+	0.133934i
$767$	−17.0771	−	18.9660i	−0.616618	−	0.684824i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	−15.6386			−0.563942			−0.281971	−	0.959423i	$-0.590988\pi$
$769$	−15.6386			−0.563942			−0.281971	+	0.959423i	$0.590988\pi$
$770$	−0.724011	+	3.41325i	−0.0260915	+	0.123005i
$771$	6.43353			0.231698
$772$	−2.10973	+	20.0727i	−0.0759307	+	0.722433i
$773$	−7.74538	−	8.60211i	−0.278582	−	0.309396i	0.587574	−	0.809170i	$-0.300083\pi$
$773$	−7.74538	−	8.60211i	−0.278582	−	0.309396i	−0.866156	+	0.499774i	$0.833416\pi$
$774$	2.56705	+	0.545644i	0.0922708	+	0.0196128i
$775$	1.39949	+	0.623094i	0.0502712	+	0.0223822i
$776$	12.7158	−	9.23855i	0.456470	−	0.331645i
$777$	4.62594	+	7.30393i	0.165955	+	0.262027i
$778$	−8.09105	+	24.9017i	−0.290078	+	0.892768i
$779$	−4.87065	+	46.3411i	−0.174509	+	1.66034i
$780$	0.640620	−	1.10959i	0.0229379	−	0.0397296i
$781$	−7.07566	−	17.8021i	−0.253187	−	0.637008i
$782$	−18.8426	−	32.6363i	−0.673808	−	1.16707i
$783$	4.21819	+	3.06469i	0.150746	+	0.109523i
$784$	−5.30725	+	4.56433i	−0.189545	+	0.163012i
$785$	−1.44998	−	4.46259i	−0.0517522	−	0.159277i
$786$	−5.01832	−	2.23430i	−0.178998	−	0.0796948i
$787$	2.34803	+	22.3400i	0.0836982	+	0.796335i	0.953187	+	0.302382i	$0.0977818\pi$
$787$	2.34803	+	22.3400i	0.0836982	+	0.796335i	−0.869489	+	0.493953i	$0.835552\pi$
$788$	−13.0496	−	2.77379i	−0.464874	−	0.0988121i
$789$	25.2554	−	5.36821i	0.899117	−	0.191113i
$790$	0.214167	+	0.155602i	0.00761974	+	0.00553606i
$791$	32.4200	−	8.29272i	1.15272	−	0.294855i
$792$	−2.05667	+	2.60195i	−0.0730804	+	0.0924562i
$793$	5.91850	+	10.2511i	0.210172	+	0.364029i
$794$	11.8510	−	5.27642i	0.420578	−	0.187253i
$795$	−3.10703	−	3.45070i	−0.110195	−	0.122384i
$796$	12.6845	−	14.0876i	0.449592	−	0.499322i
$797$	−3.96008	+	2.87717i	−0.140273	+	0.101915i	−0.655709	−	0.755014i	$-0.727630\pi$
$797$	−3.96008	+	2.87717i	−0.140273	+	0.101915i	0.515436	+	0.856928i	$0.327630\pi$
$798$	13.1232	+	2.23185i	0.464555	+	0.0790067i
$799$	15.2301	+	46.8734i	0.538801	+	1.65826i
$800$	4.73608	−	1.00669i	0.167446	−	0.0355917i
$801$	−5.43472	+	2.41969i	−0.192026	+	0.0854956i
$802$	6.12933	−	10.6163i	0.216434	−	0.374875i
$803$	12.0694	−	24.3948i	0.425919	−	0.860873i
$804$	−14.3047			−0.504487
$805$	−4.96439	+	3.92740i	−0.174972	+	0.138423i
$806$	−0.315035	+	0.969577i	−0.0110966	+	0.0341519i
$807$	8.23076	−	9.14118i	0.289736	−	0.321785i
$808$	−1.45592	−	13.8521i	−0.0512191	−	0.487317i
$809$	5.26577	+	50.1004i	0.185134	+	1.76144i	0.554529	+	0.832164i	$0.312898\pi$
$809$	5.26577	+	50.1004i	0.185134	+	1.76144i	−0.369395	+	0.929273i	$0.620435\pi$
$810$	0.266067	−	0.295497i	0.00934863	−	0.0103827i
$811$	−9.79672	+	30.1512i	−0.344009	+	1.05875i	0.618103	+	0.786097i	$0.287902\pi$
$811$	−9.79672	+	30.1512i	−0.344009	+	1.05875i	−0.962112	+	0.272654i	$0.912098\pi$
$812$	−10.8187	+	8.55884i	−0.379662	+	0.300356i
$813$	−4.65805			−0.163365
$814$	−9.59788	+	5.03387i	−0.336405	+	0.176437i
$815$	4.04327	−	7.00314i	0.141629	−	0.245309i
$816$	−5.72165	+	2.54744i	−0.200298	+	0.0891783i
$817$	12.9156	−	2.74530i	0.451861	−	0.0960460i
$818$	−8.58272	−	26.4149i	−0.300088	−	0.923576i
$819$	−8.40442	−	1.42934i	−0.293674	−	0.0499451i
$820$	−2.97926	+	2.16456i	−0.104040	+	0.0755897i
$821$	18.3112	−	20.3366i	0.639064	−	0.709752i	−0.333405	−	0.942784i	$-0.608198\pi$
$821$	18.3112	−	20.3366i	0.639064	−	0.709752i	0.972469	+	0.233031i	$0.0748644\pi$
$822$	12.8534	+	14.2752i	0.448315	+	0.497904i
$823$	23.1979	−	10.3284i	0.808628	−	0.360024i	0.0395805	−	0.999216i	$-0.487398\pi$
$823$	23.1979	−	10.3284i	0.808628	−	0.360024i	0.769047	+	0.639192i	$0.220731\pi$
$824$	−3.96867	−	6.87394i	−0.138255	−	0.239465i
$825$	−15.0590	−	5.57766i	−0.524286	−	0.194189i
$826$	20.3020	−	5.19306i	0.706398	−	0.180690i
$827$	11.0845	+	8.05334i	0.385445	+	0.280042i	0.763586	−	0.645706i	$-0.223437\pi$
$827$	11.0845	+	8.05334i	0.385445	+	0.280042i	−0.378141	+	0.925748i	$0.623437\pi$
$828$	−5.88550	+	1.25100i	−0.204535	+	0.0434753i
$829$	−42.3558	−	9.00301i	−1.47108	−	0.312687i	−0.598485	−	0.801134i	$-0.704230\pi$
$829$	−42.3558	−	9.00301i	−1.47108	−	0.312687i	−0.872594	+	0.488447i	$0.837564\pi$
$830$	0.364661	+	3.46951i	0.0126576	+	0.120429i
$831$	−6.00459	−	2.67341i	−0.208297	−	0.0927397i
$832$	0.995710	+	3.06448i	0.0345200	+	0.106242i
$833$	41.3770	+	14.4932i	1.43363	+	0.502158i
$834$	−10.1857	−	7.40031i	−0.352700	−	0.256252i
$835$	0.434972	+	0.753394i	0.0150528	+	0.0260723i
$836$	−4.12844	+	16.1682i	−0.142785	+	0.559189i
$837$	−0.158196	+	0.274003i	−0.00546805	+	0.00947095i
$838$	0.640999	−	6.09870i	0.0221429	−	0.210676i
$839$	6.90690	−	21.2573i	0.238453	−	0.733882i	−0.758192	−	0.652032i	$-0.773917\pi$
$839$	6.90690	−	21.2573i	0.238453	−	0.733882i	0.996645	−	0.0818507i	$-0.0260831\pi$
$840$	0.562901	+	0.888770i	0.0194219	+	0.0306655i
$841$	1.46803	−	1.06659i	0.0506217	−	0.0367788i
$842$	−22.7926	−	10.1479i	−0.785486	−	0.349721i
$843$	−14.2660	−	3.03233i	−0.491347	−	0.104439i
$844$	5.81805	+	6.46160i	0.200266	+	0.222418i
$845$	0.108794	−	1.03510i	0.00374262	−	0.0356087i
$846$	7.86917			0.270548
$847$	1.87813	+	29.0426i	0.0645332	+	0.997916i
$848$	11.6776			0.401011
$849$	−1.12590	+	10.7122i	−0.0386408	+	0.367642i
$850$	−20.2916	−	22.5361i	−0.695997	−	0.772983i
$851$	−19.2323	−	4.08794i	−0.659273	−	0.140133i
$852$	−5.27660	−	2.34929i	−0.180773	−	0.0804855i
$853$	6.43021	−	4.67182i	0.220166	−	0.159960i	−0.472235	−	0.881473i	$-0.656553\pi$
$853$	6.43021	−	4.67182i	0.220166	−	0.159960i	0.692401	+	0.721512i	$0.256553\pi$
$854$	−9.71125	+	0.398205i	−0.332312	+	0.0136263i
$855$	0.618220	−	1.90269i	0.0211427	−	0.0650705i
$856$	−0.609228	+	5.79642i	−0.0208230	+	0.198118i
$857$	24.9355	−	43.1896i	0.851782	−	1.47533i	−0.0278164	−	0.999613i	$-0.508855\pi$
$857$	24.9355	−	43.1896i	0.851782	−	1.47533i	0.879599	−	0.475717i	$-0.157811\pi$
$858$	2.64396	−	10.3546i	0.0902634	−	0.353499i
$859$	14.8401	+	25.7038i	0.506338	+	0.877003i	0.999973	+	0.00733380i	$0.00233444\pi$
$859$	14.8401	+	25.7038i	0.506338	+	0.877003i	−0.493635	+	0.869669i	$0.664332\pi$
$860$	0.844244	+	0.613379i	0.0287885	+	0.0209160i
$861$	20.3968	+	13.5783i	0.695121	+	0.462746i
$862$	2.35253	+	7.24033i	0.0801273	+	0.246607i
$863$	30.6893	+	13.6638i	1.04468	+	0.465120i	0.856030	−	0.516925i	$-0.172924\pi$
$863$	30.6893	+	13.6638i	1.04468	+	0.465120i	0.188646	+	0.982045i	$0.439590\pi$
$864$	0.104528	+	0.994522i	0.00355613	+	0.0338343i
$865$	2.32950	+	0.495151i	0.0792055	+	0.0168356i
$866$	−23.7967	+	5.05815i	−0.808645	+	0.171883i
$867$	17.9818	+	13.0645i	0.610694	+	0.443695i
$868$	−0.585142	−	0.598612i	−0.0198610	−	0.0203182i
$869$	2.07060	+	0.766925i	0.0702403	+	0.0260162i
$870$	1.03662	+	1.79547i	0.0351446	+	0.0608722i
$871$	42.1074	−	18.7474i	1.42676	−	0.635232i
$872$	8.70014	+	9.66248i	0.294624	+	0.327213i
$873$	−10.5171	+	11.6804i	−0.355950	+	0.395323i
$874$	−24.4916	+	17.7942i	−0.828441	+	0.601898i
$875$	−6.60710	+	7.97189i	−0.223361	+	0.269499i
$876$	−2.53588	−	7.80464i	−0.0856795	−	0.263694i
$877$	−8.84834	+	1.88077i	−0.298787	+	0.0635092i	−0.354866	−	0.934917i	$-0.615474\pi$
$877$	−8.84834	+	1.88077i	−0.298787	+	0.0635092i	0.0560788	+	0.998426i	$0.482140\pi$
$878$	−1.77233	+	0.789093i	−0.0598133	+	0.0266306i
$879$	−5.52286	+	9.56588i	−0.186282	+	0.322649i
$880$	−1.16791	+	0.612540i	−0.0393701	+	0.0206487i
$881$	3.78457			0.127505			0.0637527	−	0.997966i	$-0.479693\pi$
$881$	3.78457			0.127505			0.0637527	+	0.997966i	$0.479693\pi$
$882$	4.24229	−	5.56803i	0.142845	−	0.187485i
$883$	−8.51736	+	26.2138i	−0.286632	+	0.882163i	0.699273	+	0.714855i	$0.253507\pi$
$883$	−8.51736	+	26.2138i	−0.286632	+	0.882163i	−0.985905	+	0.167308i	$0.946493\pi$
$884$	13.5037	−	14.9974i	0.454178	−	0.504416i
$885$	−0.329205	−	3.13218i	−0.0110661	−	0.105287i
$886$	2.27467	+	21.6420i	0.0764189	+	0.727078i
$887$	4.57810	−	5.08449i	0.153717	−	0.170720i	−0.661367	−	0.750062i	$-0.730024\pi$
$887$	4.57810	−	5.08449i	0.153717	−	0.170720i	0.815085	+	0.579342i	$0.196690\pi$
$888$	−1.00979	+	3.10780i	−0.0338862	+	0.104291i
$889$	−18.3278	−	7.27569i	−0.614693	−	0.244019i
$890$	−2.36552			−0.0792924
$891$	1.47075	−	2.97269i	0.0492719	−	0.0995890i
$892$	6.88639	−	11.9276i	0.230573	−	0.399365i
$893$	36.1693	−	16.1036i	1.21036	−	0.538887i
$894$	−9.76420	+	2.07544i	−0.326564	+	0.0694132i
$895$	0.167020	+	0.514035i	0.00558287	+	0.0171823i
$896$	−2.60830	−	0.443593i	−0.0871372	−	0.0148194i
$897$	15.6851	−	11.3959i	0.523710	−	0.380498i
$898$	8.44106	−	9.37475i	0.281682	−	0.312839i
$899$	−1.10384	−	1.22593i	−0.0368150	−	0.0408872i
$900$	−4.42329	+	1.96937i	−0.147443	+	0.0656458i
$901$	−36.5692	−	63.3397i	−1.21830	−	2.11015i
$902$	−19.0473	+	24.0974i	−0.634207	+	0.802354i
$903$	1.87331	−	6.68604i	0.0623398	−	0.222497i
$904$	10.2325	+	7.43438i	0.340329	+	0.247264i
$905$	9.87234	−	2.09843i	0.328168	−	0.0697542i
$906$	4.36034	+	0.926820i	0.144863	+	0.0307915i
$907$	−1.39850	−	13.3058i	−0.0464363	−	0.441812i	−0.992896	−	0.118989i	$-0.962035\pi$
$907$	−1.39850	−	13.3058i	−0.0464363	−	0.441812i	0.946459	−	0.322823i	$-0.104632\pi$
$908$	14.9036	+	6.63549i	0.494592	+	0.220206i
$909$	4.30413	+	13.2467i	0.142759	+	0.439367i
$910$	−2.82177	−	1.87847i	−0.0935407	−	0.0622706i
$911$	−22.3112	−	16.2101i	−0.739205	−	0.537064i	0.153257	−	0.988186i	$-0.451024\pi$
$911$	−22.3112	−	16.2101i	−0.739205	−	0.537064i	−0.892462	+	0.451123i	$0.851024\pi$
$912$	2.51565	+	4.35724i	0.0833017	+	0.144283i
$913$	10.7477	+	27.0409i	0.355699	+	0.894922i
$914$	10.5910	−	18.3441i	0.350318	−	0.606769i
$915$	−0.152688	+	1.45273i	−0.00504771	+	0.0480258i
$916$	−6.42855	+	19.7850i	−0.212405	+	0.653716i
$917$	−6.74509	+	12.8737i	−0.222743	+	0.425128i
$918$	5.06697	−	3.68137i	0.167235	−	0.121503i
$919$	48.8551	+	21.7517i	1.61158	+	0.717522i	0.997429	−	0.0716653i	$-0.0228314\pi$
$919$	48.8551	+	21.7517i	1.61158	+	0.717522i	0.614152	+	0.789187i	$0.289498\pi$
$920$	−2.34025	−	0.497436i	−0.0771559	−	0.0164000i
$921$	5.88945	+	6.54089i	0.194064	+	0.215530i
$922$	2.36591	−	22.5101i	0.0779170	−	0.741330i
$923$	18.6112			0.612595
$924$	6.52353	+	5.86886i	0.214609	+	0.193071i
$925$	−15.8220			−0.520225
$926$	−1.83489	+	17.4578i	−0.0602983	+	0.573700i
$927$	5.31111	+	5.89859i	0.174440	+	0.193735i
$928$	−5.10003	−	1.08404i	−0.167417	−	0.0355855i
$929$	3.77862	+	1.68235i	0.123972	+	0.0551961i	0.467785	−	0.883842i	$-0.345052\pi$
$929$	3.77862	+	1.68235i	0.123972	+	0.0551961i	−0.343813	+	0.939038i	$0.611719\pi$
$930$	−0.101780	+	0.0739476i	−0.00333750	+	0.00242484i
$931$	8.10447	−	34.2740i	0.265613	−	1.12329i
$932$	−1.56926	+	4.82969i	−0.0514029	+	0.158202i
$933$	−1.17672	+	11.1958i	−0.0385242	+	0.366533i
$934$	7.06462	−	12.2363i	0.231161	−	0.400383i
$935$	6.97980	+	4.41654i	0.228264	+	0.144436i
$936$	−1.61109	−	2.79049i	−0.0526602	−	0.0912102i
$937$	−10.9603	−	7.96309i	−0.358056	−	0.260143i	0.394185	−	0.919031i	$-0.371027\pi$
$937$	−10.9603	−	7.96309i	−0.358056	−	0.260143i	−0.752241	+	0.658888i	$0.771027\pi$
$938$	−2.41064	+	37.7698i	−0.0787102	+	1.23323i
$939$	7.53402	+	23.1873i	0.245863	+	0.756690i
$940$	2.85850	+	1.27269i	0.0932341	+	0.0415105i
$941$	5.58834	+	53.1695i	0.182175	+	1.73328i	0.578951	+	0.815362i	$0.303462\pi$
$941$	5.58834	+	53.1695i	0.182175	+	1.73328i	−0.396776	+	0.917915i	$0.629871\pi$
$942$	−11.5427	−	2.45347i	−0.376080	−	0.0799383i
$943$	−54.5072	+	11.5859i	−1.77500	+	0.377288i
$944$	6.40782	+	4.65555i	0.208557	+	0.151525i
$945$	−0.735386	−	0.752315i	−0.0239221	−	0.0244728i
$946$	8.16227	+	3.02320i	0.265378	+	0.0982928i
$947$	−24.9856	−	43.2763i	−0.811922	−	1.40629i	−0.911517	−	0.411263i	$-0.865088\pi$
$947$	−24.9856	−	43.2763i	−0.811922	−	1.40629i	0.0995943	−	0.995028i	$-0.468246\pi$
$948$	0.608200	−	0.270788i	0.0197534	−	0.00879478i
$949$	17.6933	+	19.6504i	0.574348	+	0.637878i
$950$	−16.3007	+	18.1038i	−0.528865	+	0.587364i
$951$	22.6240	−	16.4373i	0.733635	−	0.533017i
$952$	5.76199	+	15.5366i	0.186747	+	0.503545i
$953$	17.7883	+	54.7468i	0.576220	+	1.77342i	0.631986	+	0.774980i	$0.282240\pi$
$953$	17.7883	+	54.7468i	0.576220	+	1.77342i	−0.0557659	+	0.998444i	$0.517760\pi$
$954$	−11.4224	+	2.42791i	−0.369815	+	0.0786066i
$955$	6.75284	−	3.00656i	0.218517	−	0.0972899i
$956$	−9.35913	+	16.2105i	−0.302696	+	0.524285i
$957$	12.3712	+	12.0827i	0.399905	+	0.390579i
$958$	2.79677			0.0903595
$959$	39.8579	−	31.5322i	1.28708	−	1.01823i
$960$	−0.122875	+	0.378169i	−0.00396576	+	0.0122054i
$961$	−20.6761	+	22.9631i	−0.666970	+	0.740745i
$962$	−1.10061	−	10.4716i	−0.0354850	−	0.337617i
$963$	−0.609228	−	5.79642i	−0.0196321	−	0.186787i
$964$	−8.27514	+	9.19048i	−0.266524	+	0.296005i
$965$	2.48001	−	7.63269i	0.0798344	−	0.245705i
$966$	2.31129	+	15.7508i	0.0743644	+	0.506773i
$967$	−38.0100			−1.22232			−0.611160	−	0.791507i	$-0.709297\pi$
$967$	−38.0100			−1.22232			−0.611160	+	0.791507i	$0.709297\pi$
$968$	−7.99865	+	7.55126i	−0.257086	+	0.242707i
$969$	15.7559	−	27.2899i	0.506151	−	0.876679i
$970$	−5.70946	+	2.54202i	−0.183320	+	0.0816192i
$971$	−37.8778	+	8.05118i	−1.21556	+	0.258375i	−0.770683	−	0.637218i	$-0.780085\pi$
$971$	−37.8778	+	8.05118i	−1.21556	+	0.258375i	−0.444874	+	0.895593i	$0.646752\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−21.2561	+	25.6469i	−0.681440	+	0.822201i
$974$	12.1738	−	8.84476i	0.390073	−	0.283404i
$975$	10.4394	−	11.5942i	0.334329	−	0.371310i
$976$	−2.45811	−	2.73001i	−0.0786823	−	0.0873855i
$977$	18.2224	−	8.11315i	0.582987	−	0.259563i	−0.0939822	−	0.995574i	$-0.529960\pi$
$977$	18.2224	−	8.11315i	0.582987	−	0.259563i	0.676969	+	0.736011i	$0.263293\pi$
$978$	−10.1684	−	17.6122i	−0.325149	−	0.563175i
$979$	−18.9968	+	5.33118i	−0.607142	+	0.170385i
$980$	2.44155	−	1.33650i	0.0779925	−	0.0426928i
$981$	−10.5190	−	7.64247i	−0.335845	−	0.244005i
$982$	−14.4349	+	3.06824i	−0.460637	+	0.0979114i
$983$	30.5483	+	6.49323i	0.974338	+	0.207102i	0.667459	−	0.744647i	$-0.267382\pi$
$983$	30.5483	+	6.49323i	0.974338	+	0.207102i	0.306879	+	0.951749i	$0.400715\pi$
$984$	0.968067	+	9.21054i	0.0308609	+	0.293621i
$985$	4.84623	+	2.15768i	0.154414	+	0.0687495i
$986$	10.0912	+	31.0574i	0.321368	+	0.989070i
$987$	1.32612	−	20.7776i	0.0422109	−	0.661358i
$988$	−13.1156	−	9.52906i	−0.417264	−	0.303160i
$989$	7.89549	+	13.6754i	0.251062	+	0.434852i
$990$	1.01503	−	0.841976i	0.0322598	−	0.0267598i
$991$	22.8906	−	39.6477i	0.727145	−	1.25945i	−0.230940	−	0.972968i	$-0.574180\pi$
$991$	22.8906	−	39.6477i	0.727145	−	1.25945i	0.958085	−	0.286484i	$-0.0924865\pi$
$992$	0.0330720	−	0.314659i	0.00105004	−	0.00999043i
$993$	−1.27307	+	3.91811i	−0.0403997	+	0.124337i
$994$	−7.09224	+	13.5363i	−0.224952	+	0.429346i
$995$	−6.09820	+	4.43060i	−0.193326	+	0.140459i
$996$	8.01502	+	3.56852i	0.253966	+	0.113073i
$997$	−11.0051	−	2.33921i	−0.348535	−	0.0740835i	0.0303177	−	0.999540i	$-0.490348\pi$
$997$	−11.0051	−	2.33921i	−0.348535	−	0.0740835i	−0.378853	+	0.925457i	$0.623681\pi$
$998$	3.70540	+	4.11527i	0.117293	+	0.130267i
$999$	0.341571	−	3.24984i	0.0108068	−	0.102820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.235.4	yes	40
7.2	even	3	inner	462.2.y.d.37.2	yes	40
11.3	even	5	inner	462.2.y.d.25.2	✓	40
77.58	even	15	inner	462.2.y.d.289.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.25.2	✓	40	11.3	even	5	inner
462.2.y.d.37.2	yes	40	7.2	even	3	inner
462.2.y.d.235.4	yes	40	1.1	even	1	trivial
462.2.y.d.289.4	yes	40	77.58	even	15	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.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.363254 + 0.161731i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-1.41564 - 2.23517i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.363254 + 0.161731i) q^{5} +(0.809017 - 0.587785i) q^{6} +(-1.41564 - 2.23517i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.198815 + 0.344358i) q^{10} +(-0.820550 + 3.21352i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.60680 - 1.89395i) q^{13} +(2.37090 - 1.17425i) q^{14} +(-0.122875 - 0.378169i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.654675 - 6.22881i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-4.92136 + 1.04607i) q^{19} +(-0.321690 - 0.233721i) q^{20} +(-0.713804 + 2.54764i) q^{21} +(-3.11014 - 1.15196i) q^{22} +(-3.00849 - 5.21086i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-3.23986 - 3.59823i) q^{25} +(2.15606 - 2.39455i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.919987 + 2.48065i) q^{28} +(1.61120 + 4.95877i) q^{29} +(0.388941 - 0.0826720i) q^{30} +(-0.289038 + 0.128688i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.93716 - 1.54048i) q^{33} +6.26312 q^{34} +(-0.152741 - 1.04088i) q^{35} +(0.309017 - 0.951057i) q^{36} +(2.18654 - 2.42840i) q^{37} +(-0.525915 - 5.00375i) q^{38} +(0.336810 + 3.20453i) q^{39} +(0.266067 - 0.295497i) q^{40} +(2.86189 - 8.80800i) q^{41} +(-2.45907 - 0.976195i) q^{42} -2.62440 q^{43} +(1.47075 - 2.97269i) q^{44} +(-0.198815 + 0.344358i) q^{45} +(5.49679 - 2.44733i) q^{46} +(-7.69721 + 1.63609i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(-2.99193 + 6.32838i) q^{49} +(3.91717 - 2.84599i) q^{50} +(-4.19085 + 4.65441i) q^{51} +(2.15606 + 2.39455i) q^{52} +(10.6680 - 4.74971i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.817793 + 1.03461i) q^{55} +(-2.56323 + 0.655649i) q^{56} +(4.07042 + 2.95733i) q^{57} +(-5.10003 + 1.08404i) q^{58} +(7.74742 + 1.64676i) q^{59} +(0.0415637 + 0.395452i) q^{60} +(-3.35599 - 1.49418i) q^{61} +(-0.0977705 - 0.300907i) q^{62} +(2.37090 - 1.17425i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.640620 - 1.10959i) q^{65} +(1.22502 + 3.08210i) q^{66} +(-7.15234 + 12.3882i) q^{67} +(-0.654675 + 6.22881i) q^{68} +(-1.85935 + 5.72249i) q^{69} +(1.05115 - 0.0431018i) q^{70} +(-4.67285 + 3.39502i) q^{71} +(0.913545 + 0.406737i) q^{72} +(-8.02696 - 1.70618i) q^{73} +(2.18654 + 2.42840i) q^{74} +(-0.506115 + 4.81537i) q^{75} +5.03131 q^{76} +(8.34435 - 2.71512i) q^{77} -3.22219 q^{78} +(0.0695906 - 0.662110i) q^{79} +(0.266067 + 0.295497i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(8.46060 + 3.76690i) q^{82} +(7.09793 - 5.15695i) q^{83} +(1.22789 - 2.34356i) q^{84} +(0.769579 - 2.36852i) q^{85} +(0.274325 - 2.61002i) q^{86} +(2.60698 - 4.51542i) q^{87} +(2.80267 + 1.77342i) q^{88} +(2.97452 + 5.15202i) q^{89} +(-0.321690 - 0.233721i) q^{90} +(-0.543007 + 8.50779i) q^{91} +(1.85935 + 5.72249i) q^{92} +(0.289038 + 0.128688i) q^{93} +(-0.822552 - 7.82606i) q^{94} +(-1.95688 - 0.415949i) q^{95} +(0.978148 - 0.207912i) q^{96} +(12.7158 + 9.23855i) q^{97} +(-5.98097 - 3.63704i) q^{98} +(-3.11014 - 1.15196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more