LMFDB - Embedded newform 462.2.bc.b.95.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, 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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(1.38347 + 1.04212i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.333330 - 0.748672i) q^{5} +(-1.18102 + 1.26696i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.827988 + 2.88348i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(1.38347 + 1.04212i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.333330 - 0.748672i) q^{5} +(-1.18102 + 1.26696i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.827988 + 2.88348i) q^{9} +(0.709728 + 0.409762i) q^{10} +(3.26863 - 0.562216i) q^{11} +(-1.13657 - 1.30698i) q^{12} +(-3.17222 + 4.36618i) q^{13} +(-1.50072 - 2.17895i) q^{14} +(1.24136 - 0.688398i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.578545 + 5.50449i) q^{17} +(-2.95423 + 0.522047i) q^{18} +(-0.283650 - 1.33447i) q^{19} +(-0.481704 + 0.663008i) q^{20} +(-4.57370 + 0.285126i) q^{21} +(0.217472 + 3.30949i) q^{22} +(-1.94955 + 1.12557i) q^{23} +(1.41863 - 0.993728i) q^{24} +(2.89625 + 3.21661i) q^{25} +(-4.01068 - 3.61123i) q^{26} +(-1.85942 + 4.85207i) q^{27} +(2.32388 - 1.26474i) q^{28} +(-1.93527 - 5.95615i) q^{29} +(0.554870 + 1.30651i) q^{30} +(5.27750 - 2.34969i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.10795 + 2.62848i) q^{33} -5.53481 q^{34} +(0.617869 + 2.07836i) q^{35} +(-0.210386 - 2.99261i) q^{36} +(4.14442 - 4.60285i) q^{37} +(1.35681 - 0.142606i) q^{38} +(-8.93874 + 2.73467i) q^{39} +(-0.609025 - 0.548368i) q^{40} +(3.35806 - 10.3350i) q^{41} +(0.194518 - 4.57845i) q^{42} +7.89449i q^{43} +(-3.31409 - 0.129655i) q^{44} +(2.43477 + 0.341258i) q^{45} +(-0.915622 - 2.05652i) q^{46} +(0.101280 + 0.476484i) q^{47} +(0.839998 + 1.51473i) q^{48} +(1.08140 - 6.91597i) q^{49} +(-3.50173 + 2.54416i) q^{50} +(-4.93592 + 8.21822i) q^{51} +(4.01068 - 3.61123i) q^{52} +(-5.29538 - 11.8936i) q^{53} +(-4.63113 - 2.35641i) q^{54} +(0.668616 - 2.63453i) q^{55} +(1.01490 + 2.44336i) q^{56} +(0.998249 - 2.14180i) q^{57} +(6.12582 - 1.30208i) q^{58} +(-0.606629 + 2.85396i) q^{59} +(-1.35736 + 0.415262i) q^{60} +(-1.10861 + 2.48998i) q^{61} +(1.78517 + 5.49419i) q^{62} +(-6.62471 - 4.37186i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.21144 + 3.83033i) q^{65} +(-3.14800 + 4.80521i) q^{66} +(2.35441 - 4.07795i) q^{67} +(0.578545 - 5.50449i) q^{68} +(-3.87012 - 0.474458i) q^{69} +(-2.13156 + 0.397236i) q^{70} +(2.12867 + 2.92987i) q^{71} +(2.99821 + 0.103579i) q^{72} +(0.719776 - 3.38628i) q^{73} +(4.14442 + 4.60285i) q^{74} +(0.654798 + 7.46833i) q^{75} +1.36428i q^{76} +(-5.60327 + 6.75303i) q^{77} +(-1.78534 - 9.17563i) q^{78} +(10.1418 + 1.06594i) q^{79} +(0.609025 - 0.548368i) q^{80} +(-7.62887 + 4.77497i) q^{81} +(9.92741 + 4.41997i) q^{82} +(-7.40963 + 5.38341i) q^{83} +(4.53303 + 0.672030i) q^{84} +(4.31390 + 1.40167i) q^{85} +(-7.85124 - 0.825199i) q^{86} +(3.52961 - 10.2569i) q^{87} +(0.475362 - 3.28238i) q^{88} +(5.82848 - 3.36507i) q^{89} +(-0.593892 + 2.38576i) q^{90} +(-1.13435 - 14.2337i) q^{91} +(2.14096 - 0.695641i) q^{92} +(9.74992 + 2.24903i) q^{93} +(-0.484461 + 0.0509189i) q^{94} +(-1.09363 - 0.232458i) q^{95} +(-1.59423 + 0.677064i) q^{96} +(4.17913 + 3.03631i) q^{97} +(6.76504 + 1.79839i) q^{98} +(4.32752 + 8.95950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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
$3$	1.38347	+	1.04212i	0.798748	+	0.601666i
$3$	1.38347	+	1.04212i	0.798748	+	0.601666i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	0.333330	−	0.748672i	0.149070	−	0.334816i	−0.823541	−	0.567257i	$-0.808005\pi$
$5$	0.333330	−	0.748672i	0.149070	−	0.334816i	0.972611	+	0.232441i	$0.0746712\pi$
$6$	−1.18102	+	1.26696i	−0.482149	+	0.517235i
$7$	−2.01015	+	1.72026i	−0.759765	+	0.650198i
$7$	−2.01015	+	1.72026i	−0.759765	+	0.650198i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.827988	+	2.88348i	0.275996	+	0.961159i
$10$	0.709728	+	0.409762i	0.224436	+	0.129578i
$11$	3.26863	−	0.562216i	0.985528	−	0.169514i
$11$	3.26863	−	0.562216i	0.985528	−	0.169514i
$12$	−1.13657	−	1.30698i	−0.328100	−	0.377294i
$13$	−3.17222	+	4.36618i	−0.879815	+	1.21096i	0.0966573	+	0.995318i	$0.469185\pi$
$13$	−3.17222	+	4.36618i	−0.879815	+	1.21096i	−0.976472	+	0.215644i	$0.930815\pi$
$14$	−1.50072	−	2.17895i	−0.401084	−	0.582350i
$15$	1.24136	−	0.688398i	0.320517	−	0.177744i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.578545	+	5.50449i	0.140318	+	1.33503i	0.807380	+	0.590032i	$0.200885\pi$
$17$	0.578545	+	5.50449i	0.140318	+	1.33503i	−0.667062	+	0.745002i	$0.732448\pi$
$18$	−2.95423	+	0.522047i	−0.696318	+	0.123048i
$19$	−0.283650	−	1.33447i	−0.0650738	−	0.306148i	0.933559	−	0.358424i	$-0.116686\pi$
$19$	−0.283650	−	1.33447i	−0.0650738	−	0.306148i	−0.998633	+	0.0522760i	$0.983352\pi$
$20$	−0.481704	+	0.663008i	−0.107712	+	0.148253i
$21$	−4.57370	+	0.285126i	−0.998062	+	0.0622195i
$22$	0.217472	+	3.30949i	0.0463651	+	0.705585i
$23$	−1.94955	+	1.12557i	−0.406508	+	0.234698i	−0.689288	−	0.724487i	$-0.742077\pi$
$23$	−1.94955	+	1.12557i	−0.406508	+	0.234698i	0.282780	+	0.959185i	$0.408743\pi$
$24$	1.41863	−	0.993728i	0.289576	−	0.202844i
$25$	2.89625	+	3.21661i	0.579250	+	0.643323i
$26$	−4.01068	−	3.61123i	−0.786559	−	0.708221i
$27$	−1.85942	+	4.85207i	−0.357845	+	0.933781i
$28$	2.32388	−	1.26474i	0.439173	−	0.239013i
$29$	−1.93527	−	5.95615i	−0.359371	−	1.10603i	−0.953432	−	0.301610i	$-0.902476\pi$
$29$	−1.93527	−	5.95615i	−0.359371	−	1.10603i	0.594061	−	0.804420i	$-0.297524\pi$
$30$	0.554870	+	1.30651i	0.101305	+	0.238536i
$31$	5.27750	−	2.34969i	0.947866	−	0.422017i	0.126212	−	0.992003i	$-0.459718\pi$
$31$	5.27750	−	2.34969i	0.947866	−	0.422017i	0.821654	+	0.569986i	$0.193051\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.10795	+	2.62848i	0.889179	+	0.457559i
$34$	−5.53481			−0.949212
$35$	0.617869	+	2.07836i	0.104439	+	0.351306i
$36$	−0.210386	−	2.99261i	−0.0350644	−	0.498769i
$37$	4.14442	−	4.60285i	0.681338	−	0.756703i	−0.298951	−	0.954268i	$-0.596637\pi$
$37$	4.14442	−	4.60285i	0.681338	−	0.756703i	0.980290	+	0.197565i	$0.0633035\pi$
$38$	1.35681	−	0.142606i	0.220103	−	0.0231338i
$39$	−8.93874	+	2.73467i	−1.43134	+	0.437898i
$40$	−0.609025	−	0.548368i	−0.0962952	−	0.0867046i
$41$	3.35806	−	10.3350i	0.524440	−	1.61406i	−0.240979	−	0.970530i	$-0.577469\pi$
$41$	3.35806	−	10.3350i	0.524440	−	1.61406i	0.765420	−	0.643531i	$-0.222531\pi$
$42$	0.194518	−	4.57845i	0.0300147	−	0.706469i
$43$			7.89449i			1.20390i	0.798534	+	0.601949i	$0.205609\pi$
$43$			7.89449i			1.20390i	−0.798534	+	0.601949i	$0.794391\pi$
$44$	−3.31409	−	0.129655i	−0.499618	−	0.0195463i
$45$	2.43477	+	0.341258i	0.362954	+	0.0508718i
$46$	−0.915622	−	2.05652i	−0.135001	−	0.303217i
$47$	0.101280	+	0.476484i	0.0147732	+	0.0695024i	0.984917	−	0.173029i	$-0.0553555\pi$
$47$	0.101280	+	0.476484i	0.0147732	+	0.0695024i	−0.970144	+	0.242532i	$0.922022\pi$
$48$	0.839998	+	1.51473i	0.121243	+	0.218632i
$49$	1.08140	−	6.91597i	0.154485	−	0.987995i
$50$	−3.50173	+	2.54416i	−0.495220	+	0.359798i
$51$	−4.93592	+	8.21822i	−0.691166	+	1.15078i
$52$	4.01068	−	3.61123i	0.556181	−	0.500788i
$53$	−5.29538	−	11.8936i	−0.727377	−	1.63371i	−0.772723	−	0.634743i	$-0.781106\pi$
$53$	−5.29538	−	11.8936i	−0.727377	−	1.63371i	0.0453466	−	0.998971i	$-0.485561\pi$
$54$	−4.63113	−	2.35641i	−0.630216	−	0.320667i
$55$	0.668616	−	2.63453i	0.0901562	−	0.355240i
$56$	1.01490	+	2.44336i	0.135621	+	0.326507i
$57$	0.998249	−	2.14180i	0.132221	−	0.283688i
$58$	6.12582	−	1.30208i	0.804359	−	0.170972i
$59$	−0.606629	+	2.85396i	−0.0789764	+	0.371555i	−0.999832	−	0.0183500i	$-0.994159\pi$
$59$	−0.606629	+	2.85396i	−0.0789764	+	0.371555i	0.920855	+	0.389905i	$0.127492\pi$
$60$	−1.35736	+	0.415262i	−0.175234	+	0.0536101i
$61$	−1.10861	+	2.48998i	−0.141943	+	0.318809i	−0.970502	−	0.241092i	$-0.922494\pi$
$61$	−1.10861	+	2.48998i	−0.141943	+	0.318809i	0.828559	+	0.559901i	$0.189161\pi$
$62$	1.78517	+	5.49419i	0.226717	+	0.697763i
$63$	−6.62471	−	4.37186i	−0.834636	−	0.550803i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.21144	+	3.83033i	0.274296	+	0.475094i
$66$	−3.14800	+	4.80521i	−0.387492	+	0.591481i
$67$	2.35441	−	4.07795i	0.287636	−	0.498201i	−0.685609	−	0.727970i	$-0.740464\pi$
$67$	2.35441	−	4.07795i	0.287636	−	0.498201i	0.973245	+	0.229769i	$0.0737972\pi$
$68$	0.578545	−	5.50449i	0.0701589	−	0.667517i
$69$	−3.87012	−	0.474458i	−0.465907	−	0.0571180i
$70$	−2.13156	+	0.397236i	−0.254770	+	0.0474788i
$71$	2.12867	+	2.92987i	0.252627	+	0.347711i	0.916429	−	0.400197i	$-0.131058\pi$
$71$	2.12867	+	2.92987i	0.252627	+	0.347711i	−0.663802	+	0.747908i	$0.731058\pi$
$72$	2.99821	+	0.103579i	0.353343	+	0.0122070i
$73$	0.719776	−	3.38628i	0.0842435	−	0.396334i	−0.915742	−	0.401767i	$-0.868396\pi$
$73$	0.719776	−	3.38628i	0.0842435	−	0.396334i	0.999985	+	0.00543304i	$0.00172940\pi$
$74$	4.14442	+	4.60285i	0.481779	+	0.535070i
$75$	0.654798	+	7.46833i	0.0756096	+	0.862368i
$76$			1.36428i			0.156494i
$77$	−5.60327	+	6.75303i	−0.638551	+	0.769579i
$78$	−1.78534	−	9.17563i	−0.202150	−	1.03894i
$79$	10.1418	+	1.06594i	1.14104	+	0.119928i	0.656137	−	0.754642i	$-0.272189\pi$
$79$	10.1418	+	1.06594i	1.14104	+	0.119928i	0.484900	+	0.874570i	$0.338856\pi$
$80$	0.609025	−	0.548368i	0.0680910	−	0.0613094i
$81$	−7.62887	+	4.77497i	−0.847652	+	0.530552i
$82$	9.92741	+	4.41997i	1.09630	+	0.488104i
$83$	−7.40963	+	5.38341i	−0.813312	+	0.590906i	−0.914789	−	0.403932i	$-0.867643\pi$
$83$	−7.40963	+	5.38341i	−0.813312	+	0.590906i	0.101477	+	0.994838i	$0.467643\pi$
$84$	4.53303	+	0.672030i	0.494594	+	0.0733245i
$85$	4.31390	+	1.40167i	0.467908	+	0.152033i
$86$	−7.85124	−	0.825199i	−0.846621	−	0.0889835i
$87$	3.52961	−	10.2569i	0.378414	−	1.09966i
$88$	0.475362	−	3.28238i	0.0506737	−	0.349903i
$89$	5.82848	−	3.36507i	0.617818	−	0.356697i	−0.158201	−	0.987407i	$-0.550569\pi$
$89$	5.82848	−	3.36507i	0.617818	−	0.356697i	0.776019	+	0.630710i	$0.217236\pi$
$90$	−0.593892	+	2.38576i	−0.0626017	+	0.251481i
$91$	−1.13435	−	14.2337i	−0.118912	−	1.49210i
$92$	2.14096	−	0.695641i	0.223211	−	0.0725256i
$93$	9.74992	+	2.24903i	1.01102	+	0.233214i
$94$	−0.484461	+	0.0509189i	−0.0499683	+	0.00525188i
$95$	−1.09363	−	0.232458i	−0.112204	−	0.0238497i
$96$	−1.59423	+	0.677064i	−0.162711	+	0.0691025i
$97$	4.17913	+	3.03631i	0.424326	+	0.308291i	0.779376	−	0.626556i	$-0.215536\pi$
$97$	4.17913	+	3.03631i	0.424326	+	0.308291i	−0.355050	+	0.934847i	$0.615536\pi$
$98$	6.76504	+	1.79839i	0.683372	+	0.181665i
$99$	4.32752	+	8.95950i	0.434932	+	0.900463i
$100$	−2.16419	−	3.74849i	−0.216419	−	0.374849i
$101$	13.9380	−	6.20560i	1.38688	−	0.617480i	0.428650	−	0.903471i	$-0.358989\pi$
$101$	13.9380	−	6.20560i	1.38688	−	0.617480i	0.958232	+	0.285991i	$0.0923227\pi$
$102$	−7.65725	−	5.76791i	−0.758181	−	0.571109i
$103$	−1.48077	+	1.64456i	−0.145905	+	0.162044i	−0.811667	−	0.584120i	$-0.801440\pi$
$103$	−1.48077	+	1.64456i	−0.145905	+	0.162044i	0.665763	+	0.746164i	$0.268106\pi$
$104$	3.17222	+	4.36618i	0.311062	+	0.428139i
$105$	−1.31109	+	3.51924i	−0.127949	+	0.343443i
$106$	12.3820	−	4.02315i	1.20264	−	0.390763i
$107$	11.5667	−	2.45858i	1.11820	−	0.237680i	0.388499	−	0.921449i	$-0.372994\pi$
$107$	11.5667	−	2.45858i	1.11820	−	0.237680i	0.729699	+	0.683769i	$0.239660\pi$
$108$	2.82759	−	4.35944i	0.272085	−	0.419488i
$109$	−6.24870	−	3.60769i	−0.598517	−	0.345554i	0.169941	−	0.985454i	$-0.445642\pi$
$109$	−6.24870	−	3.60769i	−0.598517	−	0.345554i	−0.768458	+	0.639900i	$0.778976\pi$
$110$	2.55021	+	0.940337i	0.243153	+	0.0896576i
$111$	10.5304	−	2.04894i	0.999500	−	0.194477i
$112$	−2.53606	+	0.753936i	−0.239635	+	0.0712403i
$113$	−11.7571	−	3.82011i	−1.10601	−	0.359365i	−0.301599	−	0.953435i	$-0.597520\pi$
$113$	−11.7571	−	3.82011i	−1.10601	−	0.359365i	−0.804414	+	0.594069i	$0.797520\pi$
$114$	2.02572	+	1.21666i	0.189726	+	0.113951i
$115$	0.192841	+	1.83476i	0.0179825	+	0.171092i
$116$	0.654627	+	6.22836i	0.0607806	+	0.578289i
$117$	−15.2163	−	5.53187i	−1.40675	−	0.511421i
$118$	−2.77492	−	0.901626i	−0.255452	−	0.0830014i
$119$	−10.6321	−	10.0696i	−0.974645	−	0.923078i
$120$	−0.271105	−	1.39333i	−0.0247484	−	0.127193i
$121$	10.3678	−	3.67535i	0.942530	−	0.334122i
$122$	−2.36046	−	1.36281i	−0.213706	−	0.123383i
$123$	15.4161	−	10.7987i	1.39002	−	0.973690i
$124$	−5.65070	+	1.20109i	−0.507448	+	0.107861i
$125$	7.27066	−	2.36238i	0.650308	−	0.211298i
$126$	5.04038	−	6.13144i	0.449033	−	0.546232i
$127$	−3.83348	−	5.27633i	−0.340166	−	0.468198i	0.604324	−	0.796739i	$-0.293443\pi$
$127$	−3.83348	−	5.27633i	−0.340166	−	0.468198i	−0.944490	+	0.328540i	$0.893443\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−8.22698	+	10.9218i	−0.724345	+	0.961611i
$130$	−4.04051	+	1.79895i	−0.354376	+	0.157778i
$131$	10.9098	+	18.8963i	0.953193	+	1.65098i	0.738450	+	0.674308i	$0.235558\pi$
$131$	10.9098	+	18.8963i	0.953193	+	1.65098i	0.214743	+	0.976671i	$0.431109\pi$
$132$	−4.44983	−	3.63304i	−0.387308	−	0.316216i
$133$	2.86581	+	2.19453i	0.248498	+	0.190290i
$134$	3.80951	+	2.76777i	0.329091	+	0.239099i
$135$	3.01281	+	3.00944i	0.259301	+	0.259011i
$136$	5.41386	+	1.15075i	0.464235	+	0.0986761i
$137$	7.20162	−	0.756920i	0.615276	−	0.0646681i	0.208236	−	0.978079i	$-0.433228\pi$
$137$	7.20162	−	0.756920i	0.615276	−	0.0646681i	0.407040	+	0.913411i	$0.366561\pi$
$138$	0.876396	−	3.79932i	0.0746038	−	0.323420i
$139$	−20.5836	+	6.68803i	−1.74588	+	0.567271i	−0.995588	−	0.0938343i	$-0.970088\pi$
$139$	−20.5836	+	6.68803i	−1.74588	+	0.567271i	−0.750293	+	0.661105i	$0.770088\pi$
$140$	−0.172252	−	2.16140i	−0.0145579	−	0.182672i
$141$	−0.356434	+	0.764748i	−0.0300172	+	0.0644034i
$142$	−3.13632	+	1.81076i	−0.263195	+	0.151955i
$143$	−7.91405	+	16.0549i	−0.661806	+	1.34258i
$144$	−0.416411	+	2.97096i	−0.0347009	+	0.247580i
$145$	−5.10429	−	0.536482i	−0.423888	−	0.0445524i
$146$	3.29249	+	1.06980i	0.272489	+	0.0885370i
$147$	8.70332	−	8.44110i	0.717838	−	0.696210i
$148$	−5.01084	+	3.64059i	−0.411889	+	0.299255i
$149$	−6.03743	−	2.68804i	−0.494606	−	0.220213i	0.144247	−	0.989542i	$-0.453924\pi$
$149$	−6.03743	−	2.68804i	−0.494606	−	0.220213i	−0.638853	+	0.769329i	$0.720591\pi$
$150$	−7.49586	−	0.129441i	−0.612034	−	0.0105689i
$151$	13.4063	−	12.0711i	1.09099	−	0.982330i	0.0910788	−	0.995844i	$-0.470968\pi$
$151$	13.4063	−	12.0711i	1.09099	−	0.982330i	0.999909	+	0.0135142i	$0.00430182\pi$
$152$	−1.35681	−	0.142606i	−0.110052	−	0.0115669i
$153$	−15.3930	+	6.22587i	−1.24445	+	0.503332i
$154$	−6.13034	−	6.27845i	−0.493997	−	0.505932i
$155$		−	4.73434i		−	0.380271i
$156$	9.31198	−	0.816444i	0.745555	−	0.0653678i
$157$	9.03791	+	10.0376i	0.721304	+	0.801089i	0.986614	−	0.163074i	$-0.0521409\pi$
$157$	9.03791	+	10.0376i	0.721304	+	0.801089i	−0.265310	+	0.964163i	$0.585474\pi$
$158$	−2.12020	+	9.97477i	−0.168674	+	0.793550i
$159$	5.06852	−	21.9729i	0.401960	−	1.74256i
$160$	0.481704	+	0.663008i	0.0380820	+	0.0524154i
$161$	1.98260	−	5.61629i	0.156251	−	0.442626i
$162$	−3.95138	−	8.08620i	−0.310450	−	0.635312i
$163$	0.747732	−	7.11419i	0.0585669	−	0.557227i	−0.925415	−	0.378956i	$-0.876283\pi$
$163$	0.747732	−	7.11419i	0.0585669	−	0.557227i	0.983982	−	0.178270i	$-0.0570502\pi$
$164$	−5.43345	+	9.41101i	−0.424281	+	0.734877i
$165$	3.67050	−	2.94802i	0.285748	−	0.229503i
$166$	−4.57940	−	7.93176i	−0.355431	−	0.615624i
$167$	0.591761	+	0.429939i	0.0457918	+	0.0332697i	0.610446	−	0.792058i	$-0.290990\pi$
$167$	0.591761	+	0.429939i	0.0457918	+	0.0332697i	−0.564654	+	0.825328i	$0.690990\pi$
$168$	−1.14218	+	4.43795i	−0.0881211	+	0.342396i
$169$	−4.98337	−	15.3372i	−0.383336	−	1.17979i
$170$	−1.84492	+	4.14376i	−0.141499	+	0.317812i
$171$	3.61305	−	1.92282i	0.276297	−	0.147042i
$172$	1.64136	−	7.72198i	0.125152	−	0.588795i
$173$	−16.0384	+	3.40908i	−1.21938	+	0.259187i	−0.772272	−	0.635292i	$-0.780880\pi$
$173$	−16.0384	+	3.40908i	−1.21938	+	0.259187i	−0.447109	+	0.894480i	$0.647546\pi$
$174$	9.83181	+	4.58242i	0.745348	+	0.347392i
$175$	−11.3553	−	1.48356i	−0.858381	−	0.112147i
$176$	3.21471	+	0.815860i	0.242318	+	0.0614978i
$177$	−3.81342	+	3.31620i	−0.286634	+	0.249261i
$178$	2.73740	+	6.14830i	0.205177	+	0.460834i
$179$	18.7330	−	16.8672i	1.40017	−	1.26072i	0.475618	−	0.879652i	$-0.342224\pi$
$179$	18.7330	−	16.8672i	1.40017	−	1.26072i	0.924549	−	0.381064i	$-0.124442\pi$
$180$	−2.31061	−	0.840018i	−0.172223	−	0.0626113i
$181$	6.22315	−	4.52139i	0.462563	−	0.336072i	−0.331973	−	0.943289i	$-0.607714\pi$
$181$	6.22315	−	4.52139i	0.462563	−	0.336072i	0.794536	+	0.607217i	$0.207714\pi$
$182$	14.2743	+	0.359694i	1.05808	+	0.0266623i
$183$	−4.12858	+	2.28952i	−0.305193	+	0.169246i
$184$	0.468039	+	2.20195i	0.0345043	+	0.162330i
$185$	−2.06456	−	4.63708i	−0.151789	−	0.340925i
$186$	−3.25585	+	9.46142i	−0.238731	+	0.693745i
$187$	4.98576	+	17.6668i	0.364595	+	1.29193i
$188$		−	0.487129i		−	0.0355275i
$189$	−4.60912	−	12.9521i	−0.335264	−	0.942124i
$190$	0.345500	−	1.06334i	0.0250652	−	0.0771427i
$191$	−6.46030	−	5.81688i	−0.467451	−	0.420895i	0.401450	−	0.915881i	$-0.368506\pi$
$191$	−6.46030	−	5.81688i	−0.467451	−	0.420895i	−0.868901	+	0.494986i	$0.835173\pi$
$192$	−0.506712	−	1.65627i	−0.0365688	−	0.119531i
$193$	2.61720	−	0.275079i	0.188390	−	0.0198006i	−0.00986337	−	0.999951i	$-0.503140\pi$
$193$	2.61720	−	0.275079i	0.188390	−	0.0198006i	0.198254	+	0.980151i	$0.436473\pi$
$194$	−3.45652	+	3.83885i	−0.248163	+	0.275613i
$195$	−0.932181	+	7.60373i	−0.0667549	+	0.544515i
$196$	−2.49568	+	6.54000i	−0.178263	+	0.467143i
$197$	−14.5091			−1.03373			−0.516866	−	0.856066i	$-0.672901\pi$
$197$	−14.5091			−1.03373			−0.516866	+	0.856066i	$0.672901\pi$
$198$	−9.36276	+	3.36729i	−0.665383	+	0.239303i
$199$	−5.00511	+	8.66910i	−0.354803	+	0.614536i	−0.987084	−	0.160202i	$-0.948785\pi$
$199$	−5.00511	+	8.66910i	−0.354803	+	0.614536i	0.632281	+	0.774739i	$0.282119\pi$
$200$	3.95417	−	1.76051i	0.279602	−	0.124487i
$201$	7.50695	−	3.18817i	0.529500	−	0.224876i
$202$	4.71468	+	14.5103i	0.331724	+	1.02094i
$203$	14.1363	+	8.64358i	0.992176	+	0.606660i
$204$	6.53672	−	7.01239i	0.457662	−	0.490966i
$205$	−6.61821	−	5.95906i	−0.462236	−	0.416199i
$206$	−1.48077	−	1.64456i	−0.103170	−	0.114582i
$207$	−4.85976	−	4.68951i	−0.337777	−	0.325943i
$208$	−4.67385	+	2.69845i	−0.324073	+	0.187104i
$209$	−1.67740	−	4.20240i	−0.116029	−	0.290686i
$210$	−3.36291	−	1.67176i	−0.232063	−	0.115363i
$211$	−14.1618	+	19.4920i	−0.974938	+	1.34189i	−0.0354260	+	0.999372i	$0.511279\pi$
$211$	−14.1618	+	19.4920i	−0.974938	+	1.34189i	−0.939512	+	0.342515i	$0.888721\pi$
$212$	2.70684	+	12.7347i	0.185907	+	0.874622i
$213$	−0.108302	+	6.27171i	−0.00742076	+	0.429731i
$214$	1.23606	+	11.7604i	0.0844956	+	0.803922i
$215$	5.91038	+	2.63147i	0.403085	+	0.179465i
$216$	4.04000	+	3.26778i	0.274887	+	0.222345i
$217$	−6.56646	+	13.8019i	−0.445761	+	0.936934i
$218$	4.24109	−	5.83736i	0.287243	−	0.395356i
$219$	4.52469	−	3.93473i	0.305750	−	0.265885i
$220$	−1.20176	+	2.43795i	−0.0810223	+	0.164366i
$221$	−25.8689	−	14.9354i	−1.74013	−	1.00466i
$222$	0.936990	+	10.6869i	0.0628866	+	0.717256i
$223$	−5.39133	+	16.5928i	−0.361030	+	1.11114i	0.591400	+	0.806378i	$0.298575\pi$
$223$	−5.39133	+	16.5928i	−0.361030	+	1.11114i	−0.952430	+	0.304758i	$0.901425\pi$
$224$	−0.484716	−	2.60097i	−0.0323865	−	0.173785i
$225$	−6.87697	+	11.0146i	−0.458465	+	0.734306i
$226$	5.02813	−	11.2934i	0.334466	−	0.751223i
$227$	−13.5237	−	2.87456i	−0.897601	−	0.190791i	−0.264065	−	0.964505i	$-0.585064\pi$
$227$	−13.5237	−	2.87456i	−0.897601	−	0.190791i	−0.633535	+	0.773714i	$0.718397\pi$
$228$	−1.42174	+	1.88744i	−0.0941570	+	0.124999i
$229$	−1.22865	+	11.6898i	−0.0811915	+	0.772486i	0.875860	+	0.482566i	$0.160295\pi$
$229$	−1.22865	+	11.6898i	−0.0811915	+	0.772486i	−0.957051	+	0.289920i	$0.906371\pi$
$230$	−1.84486			−0.121647
$231$	−14.7894	+	3.50337i	−0.973071	+	0.230505i
$232$	−6.26267			−0.411164
$233$	2.01977	−	19.2169i	0.132320	−	1.25894i	−0.703802	−	0.710396i	$-0.748516\pi$
$233$	2.01977	−	19.2169i	0.132320	−	1.25894i	0.836122	−	0.548543i	$-0.184817\pi$
$234$	7.09210	−	14.5548i	0.463625	−	0.951474i
$235$	0.390490	+	0.0830012i	0.0254728	+	0.00541440i
$236$	1.18675	−	2.66547i	0.0772505	−	0.173508i
$237$	12.9200	+	12.0436i	0.839244	+	0.782315i
$238$	11.1258	−	9.52132i	0.721178	−	0.617176i
$239$	−3.70446	+	11.4011i	−0.239621	+	0.737479i	0.756853	+	0.653585i	$0.226736\pi$
$239$	−3.70446	+	11.4011i	−0.239621	+	0.737479i	−0.996475	+	0.0838939i	$0.973264\pi$
$240$	1.41403	−	0.123978i	0.0912754	−	0.00800272i
$241$	9.19652	+	5.30961i	0.592400	+	0.342022i	0.766046	−	0.642786i	$-0.222222\pi$
$241$	9.19652	+	5.30961i	0.592400	+	0.342022i	−0.173646	+	0.984808i	$0.555555\pi$
$242$	2.57148	+	10.6952i	0.165301	+	0.687514i
$243$	−15.5304	−	1.34413i	−0.996276	−	0.0862262i
$244$	1.60208	−	2.20507i	0.102563	−	0.141165i
$245$	−4.81733	−	3.11491i	−0.307768	−	0.199004i
$246$	9.12817	+	16.4604i	0.581991	+	1.04948i
$247$	6.72633	+	2.99476i	0.427986	+	0.190552i
$248$	−0.603854	−	5.74529i	−0.0383448	−	0.364826i
$249$	−15.8612	−	0.273897i	−1.00516	−	0.0173575i
$250$	1.58945	+	7.47777i	0.100526	+	0.472936i
$251$	0.290555	−	0.399915i	0.0183397	−	0.0252424i	−0.799749	−	0.600335i	$-0.795034\pi$
$251$	0.290555	−	0.399915i	0.0183397	−	0.0252424i	0.818088	+	0.575093i	$0.195034\pi$
$252$	5.57099	+	5.65368i	0.350939	+	0.356148i
$253$	−5.73952	+	4.77514i	−0.360841	+	0.300210i
$254$	5.64813	−	3.26095i	0.354395	−	0.204610i
$255$	4.50746	+	6.43476i	0.282268	+	0.402960i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−4.50621	−	4.05741i	−0.281090	−	0.253095i	0.516510	−	0.856281i	$-0.327231\pi$
$257$	−4.50621	−	4.05741i	−0.281090	−	0.253095i	−0.797600	+	0.603186i	$0.793897\pi$
$258$	−10.0020	−	9.32355i	−0.622699	−	0.580459i
$259$	−0.412802	+	16.3819i	−0.0256502	+	1.01792i
$260$	−1.36675	−	4.20641i	−0.0847620	−	0.260871i
$261$	15.5720	−	10.5119i	0.963885	−	0.650672i
$262$	−19.9332	+	8.87483i	−1.23148	+	0.548289i
$263$	−7.85828	+	13.6109i	−0.484562	+	0.839287i	−0.999843	−	0.0177350i	$-0.994354\pi$
$263$	−7.85828	+	13.6109i	−0.484562	+	0.839287i	0.515280	+	0.857022i	$0.327688\pi$
$264$	4.07827	−	4.04570i	0.251000	−	0.248996i
$265$	−10.6695			−0.655424
$266$	−2.48206	+	2.62072i	−0.152185	+	0.160687i
$267$	11.5703	+	1.41847i	0.708093	+	0.0868088i
$268$	−3.15081	+	3.49933i	−0.192466	+	0.213756i
$269$	−19.3123	+	2.02980i	−1.17749	+	0.123759i	−0.672989	−	0.739652i	$-0.734990\pi$
$269$	−19.3123	+	2.02980i	−1.17749	+	0.123759i	−0.504501	+	0.863411i	$0.668323\pi$
$270$	−3.30787	+	2.68173i	−0.201311	+	0.163205i
$271$	0.997419	+	0.898080i	0.0605889	+	0.0545545i	0.698869	−	0.715250i	$-0.253687\pi$
$271$	0.997419	+	0.898080i	0.0605889	+	0.0545545i	−0.638280	+	0.769804i	$0.720354\pi$
$272$	−1.71035	+	5.26392i	−0.103705	+	0.319172i
$273$	13.2639	−	20.8741i	0.802765	−	1.26336i
$274$			7.24129i			0.437462i
$275$	11.2752	+	8.88559i	0.679920	+	0.535821i
$276$	3.68690	+	1.26873i	0.221925	+	0.0763687i
$277$	−4.26795	−	9.58596i	−0.256436	−	0.575965i	0.738749	−	0.673981i	$-0.235417\pi$
$277$	−4.26795	−	9.58596i	−0.256436	−	0.575965i	−0.995185	+	0.0980161i	$0.968750\pi$
$278$	−4.49981	−	21.1700i	−0.269881	−	1.26969i
$279$	11.1450	+	13.2720i	0.667233	+	0.794575i
$280$	2.16757	+	0.0546198i	0.129537	+	0.00326416i
$281$	−2.46866	+	1.79359i	−0.147268	+	0.106997i	−0.658980	−	0.752161i	$-0.729012\pi$
$281$	−2.46866	+	1.79359i	−0.147268	+	0.106997i	0.511712	+	0.859157i	$0.329012\pi$
$282$	−0.723301	−	0.434419i	−0.0430719	−	0.0258693i
$283$	−1.18492	+	1.06691i	−0.0704363	+	0.0634211i	−0.703597	−	0.710599i	$-0.748424\pi$
$283$	−1.18492	+	1.06691i	−0.0704363	+	0.0634211i	0.633161	+	0.774020i	$0.281757\pi$
$284$	−1.47300	−	3.30842i	−0.0874067	−	0.196319i
$285$	−1.27076	−	1.46129i	−0.0752731	−	0.0865591i
$286$	−15.1397	−	9.54889i	−0.895229	−	0.564638i
$287$	11.0288	+	26.5517i	0.651008	+	1.56730i
$288$	−2.91116	−	0.724679i	−0.171542	−	0.0427021i
$289$	−13.3362	+	2.83469i	−0.784481	+	0.166747i
$290$	1.06709	−	5.02025i	0.0626615	−	0.294799i
$291$	2.61751	+	8.55579i	0.153441	+	0.501549i
$292$	−1.40810	+	3.16263i	−0.0824025	+	0.185079i
$293$	−4.76787	−	14.6740i	−0.278542	−	0.857264i	−0.988260	−	0.152779i	$-0.951178\pi$
$293$	−4.76787	−	14.6740i	−0.278542	−	0.857264i	0.709718	−	0.704486i	$-0.248822\pi$
$294$	7.48512	+	9.53798i	0.436541	+	0.556266i
$295$	1.93448	+	1.40548i	0.112630	+	0.0818301i
$296$	−3.09687	−	5.36394i	−0.180002	−	0.311772i
$297$	−3.34983	+	16.9050i	−0.194377	+	0.980927i
$298$	3.30440	−	5.72338i	0.191418	−	0.331547i
$299$	1.26994	−	12.0826i	0.0734423	−	0.698757i
$300$	0.912263	−	7.44127i	0.0526695	−	0.429622i
$301$	−13.5806	−	15.8691i	−0.782772	−	0.914680i
$302$	10.6036	+	14.5946i	0.610169	+	0.839825i
$303$	25.7498	+	5.93974i	1.47929	+	0.341229i
$304$	0.283650	−	1.33447i	0.0162684	−	0.0765370i
$305$	1.49464	+	1.65997i	0.0855831	+	0.0950496i
$306$	−4.58276	−	15.9595i	−0.261979	−	0.912343i
$307$		−	22.7875i		−	1.30055i	−0.759699	−	0.650275i	$-0.774654\pi$
$307$		−	22.7875i		−	1.30055i	0.759699	−	0.650275i	$-0.225346\pi$
$308$	6.88485	−	5.44048i	0.392301	−	0.310000i
$309$	−3.76243	+	0.732071i	−0.214037	+	0.0416461i
$310$	4.70840	+	0.494873i	0.267419	+	0.0281069i
$311$	−7.79971	+	7.02289i	−0.442281	+	0.398231i	−0.859959	−	0.510364i	$-0.829511\pi$
$311$	−7.79971	+	7.02289i	−0.442281	+	0.398231i	0.417678	+	0.908595i	$0.362844\pi$
$312$	−0.161396	+	9.34631i	−0.00913724	+	0.529131i
$313$	−20.1622	−	8.97678i	−1.13963	−	0.507398i	−0.251899	−	0.967753i	$-0.581055\pi$
$313$	−20.1622	−	8.97678i	−1.13963	−	0.507398i	−0.887735	+	0.460356i	$0.847722\pi$
$314$	−10.9274	+	7.93919i	−0.616666	+	0.448034i
$315$	−5.48131	+	3.50246i	−0.308837	+	0.197342i
$316$	−9.69851	−	3.15124i	−0.545584	−	0.177271i
$317$	−23.8951	−	2.51147i	−1.34208	−	0.141058i	−0.593893	−	0.804544i	$-0.702410\pi$
$317$	−23.8951	−	2.51147i	−1.34208	−	0.141058i	−0.748189	+	0.663486i	$0.769076\pi$
$318$	21.3227	+	7.33755i	1.19572	+	0.411469i
$319$	−9.67432	−	18.3804i	−0.541658	−	1.02910i
$320$	−0.709728	+	0.409762i	−0.0396750	+	0.0229064i
$321$	18.5644	+	8.65249i	1.03616	+	0.482935i
$322$	5.37829	+	2.55880i	0.299720	+	0.142596i
$323$	7.18146	−	2.33340i	0.399587	−	0.129834i
$324$	8.45493	−	3.08449i	0.469719	−	0.171361i
$325$	−23.2319	+	2.44177i	−1.28867	+	0.135445i
$326$	6.99706	+	1.48727i	0.387531	+	0.0823723i
$327$	−4.88527	−	11.5030i	−0.270156	−	0.636118i
$328$	−8.79151	−	6.38740i	−0.485430	−	0.352685i
$329$	−1.02327	−	0.783576i	−0.0564144	−	0.0432000i
$330$	2.54820	+	3.95854i	0.140274	+	0.217911i
$331$	−1.32492	−	2.29483i	−0.0728242	−	0.126135i	0.827314	−	0.561740i	$-0.189868\pi$
$331$	−1.32492	−	2.29483i	−0.0728242	−	0.126135i	−0.900138	+	0.435605i	$0.856535\pi$
$332$	8.36698	−	3.72522i	0.459198	−	0.204448i
$333$	16.7037	+	8.13924i	0.915359	+	0.446027i
$334$	−0.489440	+	0.543578i	−0.0267810	+	0.0297433i
$335$	−2.26825	−	3.12198i	−0.123928	−	0.170572i
$336$	−4.29425	−	1.59981i	−0.234271	−	0.0872771i
$337$	11.2086	−	3.64189i	0.610570	−	0.198386i	0.0126209	−	0.999920i	$-0.495983\pi$
$337$	11.2086	−	3.64189i	0.610570	−	0.198386i	0.597949	+	0.801534i	$0.295983\pi$
$338$	15.7741	−	3.35289i	0.857999	−	0.182373i
$339$	−12.2846	−	17.5373i	−0.667208	−	0.952493i
$340$	−3.92821	−	2.26795i	−0.213037	−	0.122997i
$341$	15.9291	−	10.6474i	0.862610	−	0.576587i
$342$	1.53462	+	3.79425i	0.0829829	+	0.205169i
$343$	9.72351	+	15.7624i	0.525020	+	0.851090i
$344$	7.50811	+	2.43953i	0.404810	+	0.131531i
$345$	−1.64524	+	2.73930i	−0.0885767	+	0.147479i
$346$	−1.71393	−	16.3069i	−0.0921413	−	0.876666i
$347$	−1.08634	−	10.3358i	−0.0583177	−	0.554856i	−0.984202	−	0.177049i	$-0.943345\pi$
$347$	−1.08634	−	10.3358i	−0.0583177	−	0.554856i	0.925884	−	0.377807i	$-0.123322\pi$
$348$	−5.58502	+	9.29896i	−0.299388	+	0.498477i
$349$	5.57527	+	1.81152i	0.298438	+	0.0969682i	0.454409	−	0.890793i	$-0.349851\pi$
$349$	5.57527	+	1.81152i	0.298438	+	0.0969682i	−0.155971	+	0.987762i	$0.549851\pi$
$350$	2.66239	−	11.1380i	0.142311	−	0.595353i
$351$	−15.2865	−	23.5104i	−0.815935	−	1.25489i
$352$	−1.14742	+	3.11182i	−0.0611577	+	0.165861i
$353$	24.6487	+	14.2309i	1.31192	+	0.757436i	0.982413	−	0.186719i	$-0.0597853\pi$
$353$	24.6487	+	14.2309i	1.31192	+	0.757436i	0.329503	+	0.944154i	$0.393119\pi$
$354$	−2.89942	−	4.13916i	−0.154103	−	0.219994i
$355$	2.90306	−	0.617065i	0.154078	−	0.0327504i
$356$	−6.40075	+	2.07973i	−0.339239	+	0.110226i
$357$	−4.21556	−	25.0109i	−0.223111	−	1.32372i
$358$	14.8167	+	20.3934i	0.783087	+	1.07783i
$359$	2.01803	−	2.24125i	0.106508	−	0.118289i	−0.687534	−	0.726153i	$-0.741307\pi$
$359$	2.01803	−	2.24125i	0.106508	−	0.118289i	0.794041	+	0.607864i	$0.207973\pi$
$360$	1.07694	−	2.21015i	0.0567598	−	0.116485i
$361$	15.6570	−	6.97095i	0.824053	−	0.366892i
$362$	3.84612	+	6.66168i	0.202148	+	0.350130i
$363$	18.1737	+	5.71974i	0.953874	+	0.300208i
$364$	−1.84980	+	14.1585i	−0.0969557	+	0.742108i
$365$	−2.29529	−	1.66763i	−0.120141	−	0.0872875i
$366$	−1.84542	−	4.34528i	−0.0964616	−	0.227131i
$367$	−10.2044	−	2.16902i	−0.532666	−	0.113222i	−0.0662769	−	0.997801i	$-0.521112\pi$
$367$	−10.2044	−	2.16902i	−0.532666	−	0.113222i	−0.466389	+	0.884580i	$0.654445\pi$
$368$	−2.23881	+	0.235308i	−0.116706	+	0.0122663i
$369$	32.5813	+	1.12559i	1.69611	+	0.0585958i
$370$	4.82748	−	1.56854i	0.250969	−	0.0815447i
$371$	31.1047	+	14.7985i	1.61487	+	0.768300i
$372$	−9.06926	−	4.22700i	−0.470219	−	0.219160i
$373$	28.1083	−	16.2283i	1.45539	−	0.840271i	0.456613	−	0.889666i	$-0.349063\pi$
$373$	28.1083	−	16.2283i	1.45539	−	0.840271i	0.998779	+	0.0493948i	$0.0157293\pi$
$374$	−18.0912	+	3.11176i	−0.935475	+	0.160905i
$375$	12.5206	+	4.30859i	0.646563	+	0.222494i
$376$	0.484461	+	0.0509189i	0.0249841	+	0.00262594i
$377$	32.1448	+	10.4445i	1.65554	+	0.537917i
$378$	13.3629	−	3.23001i	0.687313	−	0.166134i
$379$	21.4569	−	15.5894i	1.10217	−	0.800773i	0.120757	−	0.992682i	$-0.461468\pi$
$379$	21.4569	−	15.5894i	1.10217	−	0.800773i	0.981413	+	0.191909i	$0.0614680\pi$
$380$	1.02140	+	0.454756i	0.0523967	+	0.0233285i
$381$	0.195039	−	11.2946i	0.00999216	−	0.578639i
$382$	6.46030	−	5.81688i	0.330538	−	0.297618i
$383$	4.21706	+	0.443231i	0.215482	+	0.0226481i	0.211654	−	0.977345i	$-0.432115\pi$
$383$	4.21706	+	0.443231i	0.215482	+	0.0226481i	0.00382765	+	0.999993i	$0.498782\pi$
$384$	1.70017	−	0.330808i	0.0867613	−	0.0168815i
$385$	3.18807	+	6.44600i	0.162479	+	0.328518i
$386$			2.63162i			0.133946i
$387$	−22.7636	+	6.53655i	−1.15714	+	0.332271i
$388$	−3.45652	−	3.83885i	−0.175478	−	0.194888i
$389$	3.92933	−	18.4860i	0.199225	−	0.937280i	−0.758962	−	0.651135i	$-0.774293\pi$
$389$	3.92933	−	18.4860i	0.199225	−	0.937280i	0.958187	−	0.286144i	$-0.0923737\pi$
$390$	−7.46464	−	1.72188i	−0.377987	−	0.0871908i
$391$	−7.32359	−	10.0801i	−0.370370	−	0.509771i
$392$	−6.24330	−	3.16562i	−0.315334	−	0.159888i
$393$	−4.59876	+	37.5118i	−0.231977	+	1.89222i
$394$	1.51662	−	14.4296i	0.0764060	−	0.726954i
$395$	4.17859	−	7.23754i	0.210248	−	0.364160i
$396$	−2.37017	−	9.66345i	−0.119105	−	0.485607i
$397$	3.08815	+	5.34884i	0.154990	+	0.268451i	0.933055	−	0.359733i	$-0.117132\pi$
$397$	3.08815	+	5.34884i	0.154990	+	0.268451i	−0.778065	+	0.628183i	$0.783799\pi$
$398$	−8.09844	−	5.88386i	−0.405938	−	0.294931i
$399$	1.67782	+	6.02258i	0.0839961	+	0.301506i
$400$	1.33754	+	4.11654i	0.0668772	+	0.205827i
$401$	3.72705	−	8.37109i	0.186120	−	0.418032i	−0.796253	−	0.604964i	$-0.793188\pi$
$401$	3.72705	−	8.37109i	0.186120	−	0.418032i	0.982373	+	0.186931i	$0.0598542\pi$
$402$	2.38601	+	7.79908i	0.119003	+	0.388983i
$403$	−6.48218	+	30.4962i	−0.322900	+	1.51913i
$404$	−14.9236	+	3.17212i	−0.742478	+	0.157819i
$405$	1.03195	+	7.30316i	0.0512781	+	0.362897i
$406$	−10.0739	+	13.1554i	−0.499958	+	0.652891i
$407$	10.9588	−	17.3750i	0.543206	−	0.861249i
$408$	6.29071	+	7.23390i	0.311436	+	0.358132i
$409$	−2.43028	−	5.45851i	−0.120170	−	0.269906i	0.843438	−	0.537227i	$-0.180528\pi$
$409$	−2.43028	−	5.45851i	−0.120170	−	0.269906i	−0.963607	+	0.267321i	$0.913862\pi$
$410$	6.61821	−	5.95906i	0.326850	−	0.294297i
$411$	10.7520	+	6.45774i	0.530359	+	0.318537i
$412$	1.79034	−	1.30076i	0.0882035	−	0.0640836i
$413$	−3.69015	−	6.78045i	−0.181581	−	0.333644i
$414$	5.17180	−	4.34295i	0.254180	−	0.213444i
$415$	1.56056	+	7.34183i	0.0766046	+	0.360396i
$416$	−2.19512	−	4.93031i	−0.107624	−	0.241728i
$417$	−35.4466	−	12.1978i	−1.73583	−	0.597331i
$418$	4.35472	−	1.22895i	0.212996	−	0.0601097i
$419$		−	3.24937i		−	0.158742i	−0.996845	−	0.0793710i	$-0.974709\pi$
$419$		−	3.24937i		−	0.158742i	0.996845	−	0.0793710i	$-0.0252912\pi$
$420$	2.01413	−	3.16975i	0.0982793	−	0.154668i
$421$	−8.63563	+	26.5777i	−0.420875	+	1.29532i	0.486015	+	0.873951i	$0.338450\pi$
$421$	−8.63563	+	26.5777i	−0.420875	+	1.29532i	−0.906889	+	0.421369i	$0.861550\pi$
$422$	−17.9050	−	16.1217i	−0.871599	−	0.784792i
$423$	−1.29007	+	0.686561i	−0.0627255	+	0.0333818i
$424$	−12.9479	+	1.36088i	−0.628804	+	0.0660900i
$425$	−16.0302	+	17.8033i	−0.777579	+	0.863589i
$426$	−6.22604	−	0.763282i	−0.301652	−	0.0369811i
$427$	−2.05495	−	6.91233i	−0.0994458	−	0.334511i
$428$	−11.8251			−0.571590
$429$	−27.6799	+	13.9641i	−1.33640	+	0.674194i
$430$	−3.23486	+	5.60294i	−0.155999	+	0.270198i
$431$	−16.5278	+	7.35864i	−0.796115	+	0.354453i	−0.764152	−	0.645036i	$-0.776842\pi$
$431$	−16.5278	+	7.35864i	−0.796115	+	0.354453i	−0.0319625	+	0.999489i	$0.510176\pi$
$432$	−3.67218	+	3.67629i	−0.176678	+	0.176876i
$433$	−9.64182	−	29.6745i	−0.463356	−	1.42606i	−0.861038	−	0.508541i	$-0.830185\pi$
$433$	−9.64182	−	29.6745i	−0.463356	−	1.42606i	0.397682	−	0.917523i	$-0.369815\pi$
$434$	−13.0399	−	7.97318i	−0.625936	−	0.382725i
$435$	−6.50256	−	6.06147i	−0.311774	−	0.290625i
$436$	5.36207	+	4.82803i	0.256797	+	0.231221i
$437$	2.05503	+	2.28234i	0.0983053	+	0.109179i
$438$	3.44022	+	4.91119i	0.164380	+	0.234666i
$439$	−12.9943	+	7.50224i	−0.620182	+	0.358062i	−0.776940	−	0.629575i	$-0.783229\pi$
$439$	−12.9943	+	7.50224i	−0.620182	+	0.358062i	0.156758	+	0.987637i	$0.449896\pi$
$440$	−2.29897	−	1.45001i	−0.109599	−	0.0691264i
$441$	20.8374	−	2.60816i	0.992257	−	0.124198i
$442$	17.5576	−	24.1660i	0.835131	−	1.14946i
$443$	1.55941	+	7.33643i	0.0740897	+	0.348564i	0.999541	−	0.0303026i	$-0.00964710\pi$
$443$	1.55941	+	7.33643i	0.0740897	+	0.348564i	−0.925451	+	0.378867i	$0.876314\pi$
$444$	−10.7263	−	0.185226i	−0.509046	−	0.00879041i
$445$	−0.576528	−	5.48530i	−0.0273301	−	0.260028i
$446$	−15.9384	−	7.09621i	−0.754703	−	0.336015i
$447$	−5.55137	−	10.0105i	−0.262571	−	0.473482i
$448$	2.63739	−	0.210185i	0.124605	−	0.00993033i
$449$	−16.1391	+	22.2136i	−0.761653	+	1.04833i	0.235421	+	0.971893i	$0.424353\pi$
$449$	−16.1391	+	22.2136i	−0.761653	+	1.04833i	−0.997075	+	0.0764326i	$0.975647\pi$
$450$	−10.2354	−	7.99063i	−0.482502	−	0.376682i
$451$	5.16571	−	35.6693i	0.243244	−	1.67960i
$452$	10.7059	+	6.18106i	0.503564	+	0.290733i
$453$	31.1267	−	2.72908i	1.46246	−	0.128224i
$454$	4.27242	−	13.1492i	0.200515	−	0.617121i
$455$	−11.0345	−	3.89527i	−0.517305	−	0.182613i
$456$	−1.72849	−	1.61124i	−0.0809441	−	0.0754533i
$457$	−5.73200	+	12.8743i	−0.268132	+	0.602234i	−0.996559	−	0.0828897i	$-0.973585\pi$
$457$	−5.73200	+	12.8743i	−0.268132	+	0.602234i	0.728427	+	0.685123i	$0.240252\pi$
$458$	−11.4974	−	2.44384i	−0.537236	−	0.114193i
$459$	−27.7839	−	7.42801i	−1.29684	−	0.346710i
$460$	0.192841	−	1.83476i	0.00899125	−	0.0855460i
$461$	33.9622			1.58178			0.790890	−	0.611959i	$-0.209618\pi$
$461$	33.9622			1.58178			0.790890	+	0.611959i	$0.209618\pi$
$462$	−1.93827	−	15.0746i	−0.0901765	−	0.701333i
$463$	39.7696			1.84825			0.924124	−	0.382093i	$-0.124797\pi$
$463$	39.7696			1.84825			0.924124	+	0.382093i	$0.124797\pi$
$464$	0.654627	−	6.22836i	0.0303903	−	0.289144i
$465$	4.93373	−	6.54982i	0.228796	−	0.303741i
$466$	18.9005	+	4.01742i	0.875548	+	0.186103i
$467$	−6.24968	+	14.0370i	−0.289201	+	0.649556i	−0.998465	−	0.0553871i	$-0.982361\pi$
$467$	−6.24968	+	14.0370i	−0.289201	+	0.649556i	0.709264	+	0.704943i	$0.249027\pi$
$468$	13.7337	+	8.57464i	0.634840	+	0.396363i
$469$	2.28244	+	12.2475i	0.105393	+	0.565536i
$470$	−0.123364	+	0.379675i	−0.00569035	+	0.0175131i
$471$	2.04333	+	23.3053i	0.0941518	+	1.07385i
$472$	2.52682	+	1.45886i	0.116306	+	0.0671496i
$473$	4.43841	+	25.8041i	0.204078	+	1.18648i
$474$	−13.3281	+	11.5903i	−0.612181	+	0.532361i
$475$	3.47095	−	4.77735i	0.159258	−	0.219200i
$476$	8.30620	+	12.0601i	0.380714	+	0.552773i
$477$	29.9105	−	25.1169i	1.36951	−	1.15002i
$478$	−10.9515	−	4.87591i	−0.500908	−	0.223019i
$479$	0.168090	+	1.59927i	0.00768025	+	0.0730727i	0.997691	−	0.0679216i	$-0.0216368\pi$
$479$	0.168090	+	1.59927i	0.00768025	+	0.0730727i	−0.990010	+	0.140994i	$0.954970\pi$
$480$	−0.0245081	+	1.41924i	−0.00111864	+	0.0647794i
$481$	6.94986	+	32.6965i	0.316886	+	1.49083i
$482$	−6.24182	+	8.59113i	−0.284307	+	0.391315i
$483$	8.59570	−	5.70389i	0.391118	−	0.259536i
$484$	−10.9054	+	1.43944i	−0.495701	+	0.0654291i
$485$	3.66623	−	2.11670i	0.166475	−	0.0961144i
$486$	2.96014	−	15.3048i	0.134275	−	0.694241i
$487$	−0.980414	−	1.08886i	−0.0444268	−	0.0493410i	0.720522	−	0.693432i	$-0.243902\pi$
$487$	−0.980414	−	1.08886i	−0.0444268	−	0.0493410i	−0.764949	+	0.644091i	$0.777236\pi$
$488$	2.02553	+	1.82380i	0.0916915	+	0.0825594i
$489$	8.44828	−	9.06306i	0.382044	−	0.409846i
$490$	3.60140	−	4.46534i	0.162694	−	0.201724i
$491$	−3.58459	−	11.0322i	−0.161770	−	0.497878i	0.837014	−	0.547182i	$-0.184300\pi$
$491$	−3.58459	−	11.0322i	−0.161770	−	0.497878i	−0.998784	+	0.0493045i	$0.984300\pi$
$492$	−17.3244	+	7.35758i	−0.781044	+	0.331706i
$493$	31.6659	−	14.0986i	1.42616	−	0.634968i
$494$	−3.68144	+	6.37645i	−0.165636	+	0.286890i
$495$	8.15022	−	0.253422i	0.366325	−	0.0113905i
$496$	5.77694			0.259392
$497$	−9.31909	−	2.22759i	−0.418018	−	0.0999212i
$498$	1.93034	−	15.7456i	0.0865005	−	0.705579i
$499$	−20.6887	+	22.9772i	−0.926155	+	1.02860i	0.0733553	+	0.997306i	$0.476629\pi$
$499$	−20.6887	+	22.9772i	−0.926155	+	1.02860i	−0.999510	+	0.0312934i	$0.990037\pi$
$500$	−7.60295	+	0.799102i	−0.340014	+	0.0357369i
$501$	0.370638	+	1.21149i	0.0165589	+	0.0541255i
$502$	0.367353	+	0.330766i	0.0163958	+	0.0147628i
$503$	2.45888	−	7.56765i	0.109636	−	0.337425i	−0.881155	−	0.472828i	$-0.843233\pi$
$503$	2.45888	−	7.56765i	0.109636	−	0.337425i	0.990791	+	0.135403i	$0.0432330\pi$
$504$	−6.20503	+	4.94950i	−0.276394	+	0.220468i
$505$		−	12.5035i		−	0.556398i
$506$	−4.14903	−	6.20722i	−0.184447	−	0.275944i
$507$	9.08882	−	26.4119i	0.403649	−	1.17299i
$508$	2.65270	+	5.95805i	0.117694	+	0.264346i
$509$	−0.0146057	−	0.0687144i	−0.000647386	−	0.00304571i	0.977823	−	0.209434i	$-0.0671622\pi$
$509$	−0.0146057	−	0.0687144i	−0.000647386	−	0.00304571i	−0.978470	+	0.206389i	$0.933829\pi$
$510$	−6.87067	+	3.81015i	−0.304238	+	0.168716i
$511$	4.37843	+	8.04513i	0.193691	+	0.355896i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	7.00235	+	1.10505i	0.309162	+	0.0487890i
$514$	4.50621	−	4.05741i	0.198761	−	0.178965i
$515$	0.737652	+	1.65679i	0.0325048	+	0.0730071i
$516$	10.3180	−	8.97265i	0.454223	−	0.394999i
$517$	0.598933	+	1.50051i	0.0263410	+	0.0659922i
$518$	−16.2490	−	2.12291i	−0.713940	−	0.0932755i
$519$	−25.7414	−	11.9976i	−1.12992	−	0.526634i
$520$	4.32623	−	0.919570i	0.189718	−	0.0403258i
$521$	−1.08172	+	5.08908i	−0.0473909	+	0.222957i	−0.995470	−	0.0950787i	$-0.969690\pi$
$521$	−1.08172	+	5.08908i	−0.0473909	+	0.222957i	0.948079	+	0.318035i	$0.103023\pi$
$522$	8.82663	+	16.5855i	0.386331	+	0.725929i
$523$	11.1632	−	25.0729i	0.488132	−	1.09636i	−0.486731	−	0.873552i	$-0.661811\pi$
$523$	11.1632	−	25.0729i	0.488132	−	1.09636i	0.974862	−	0.222809i	$-0.0715227\pi$
$524$	−6.74262	−	20.7517i	−0.294553	−	0.906540i
$525$	−14.1637	−	13.8860i	−0.618155	−	0.606036i
$526$	−12.7150	−	9.23796i	−0.554399	−	0.402794i
$527$	15.9871	+	27.6905i	0.696410	+	1.20622i
$528$	3.59724	+	4.47882i	0.156550	+	0.194916i
$529$	−8.96618	+	15.5299i	−0.389834	+	0.675212i
$530$	1.11527	−	10.6111i	0.0484442	−	0.460916i
$531$	−8.73162	+	0.613849i	−0.378920	+	0.0266388i
$532$	−2.34692	−	2.74241i	−0.101752	−	0.118898i
$533$	34.4722	+	47.4469i	1.49316	+	2.05515i
$534$	−2.62013	+	11.3587i	−0.113384	+	0.491538i
$535$	2.01487	−	9.47921i	0.0871103	−	0.409822i
$536$	−3.15081	−	3.49933i	−0.136094	−	0.151148i
$537$	43.4941	−	3.81342i	1.87691	−	0.164561i
$538$		−	19.4186i		−	0.837197i
$539$	−0.353586	−	23.2137i	−0.0152300	−	0.999884i
$540$	−2.32127	−	3.57007i	−0.0998917	−	0.153631i
$541$	−11.7909	−	1.23927i	−0.506930	−	0.0532805i	−0.152388	−	0.988321i	$-0.548696\pi$
$541$	−11.7909	−	1.23927i	−0.506930	−	0.0532805i	−0.354542	+	0.935040i	$0.615363\pi$
$542$	−0.997419	+	0.898080i	−0.0428428	+	0.0385758i
$543$	13.3214	+	0.230039i	0.571675	+	0.00987190i
$544$	−5.05630	−	2.25121i	−0.216787	−	0.0965198i
$545$	−4.78386	+	3.47568i	−0.204918	+	0.148882i
$546$	19.3733	+	15.3731i	0.829100	+	0.657909i
$547$	−14.9485	−	4.85707i	−0.639153	−	0.207673i	−0.0285276	−	0.999593i	$-0.509082\pi$
$547$	−14.9485	−	4.85707i	−0.639153	−	0.207673i	−0.610625	+	0.791920i	$0.709082\pi$
$548$	−7.20162	−	0.756920i	−0.307638	−	0.0323340i
$549$	−8.09771	−	1.13498i	−0.345602	−	0.0484397i
$550$	−10.0155	+	10.2846i	−0.427062	+	0.438538i
$551$	−7.39936	+	4.27202i	−0.315223	+	0.181994i
$552$	−1.64717	+	3.53408i	−0.0701081	+	0.150421i
$553$	−22.2201	+	15.3038i	−0.944896	+	0.650783i
$554$	9.97957	−	3.24256i	0.423991	−	0.137763i
$555$	1.97611	−	8.56678i	0.0838813	−	0.363639i
$556$	21.5243	−	2.26230i	0.912836	−	0.0959429i
$557$	−17.4054	−	3.69964i	−0.737492	−	0.156759i	−0.176174	−	0.984359i	$-0.556372\pi$
$557$	−17.4054	−	3.69964i	−0.737492	−	0.156759i	−0.561318	+	0.827600i	$0.689705\pi$
$558$	−14.3643	+	9.69663i	−0.608088	+	0.410491i
$559$	−34.4688	−	25.0430i	−1.45787	−	1.05921i
$560$	−0.280893	+	2.14998i	−0.0118699	+	0.0908534i
$561$	−11.5132	+	29.6373i	−0.486090	+	1.25129i
$562$	−1.52572	−	2.64262i	−0.0643585	−	0.111472i
$563$	16.6751	−	7.42424i	0.702773	−	0.312895i	−0.0240586	−	0.999711i	$-0.507659\pi$
$563$	16.6751	−	7.42424i	0.702773	−	0.312895i	0.726831	+	0.686816i	$0.240992\pi$
$564$	0.507645	−	0.673929i	0.0213757	−	0.0283775i
$565$	−6.77900	+	7.52884i	−0.285195	+	0.316741i
$566$	−0.937205	−	1.28995i	−0.0393937	−	0.0542207i
$567$	7.12097	−	22.7221i	0.299052	−	0.954237i
$568$	3.44427	−	1.11911i	0.144518	−	0.0469568i
$569$	15.0281	−	3.19431i	0.630009	−	0.133913i	0.118169	−	0.992993i	$-0.462298\pi$
$569$	15.0281	−	3.19431i	0.630009	−	0.133913i	0.511840	+	0.859081i	$0.328964\pi$
$570$	1.58611	−	1.11105i	0.0664349	−	0.0465367i
$571$	33.4687	+	19.3232i	1.40062	+	0.808649i	0.994456	−	0.105150i	$-0.0335323\pi$
$571$	33.4687	+	19.3232i	1.40062	+	0.808649i	0.406165	+	0.913800i	$0.366866\pi$
$572$	11.0791	−	14.0586i	0.463241	−	0.587821i
$573$	−2.87578	−	14.7799i	−0.120137	−	0.617438i
$574$	−27.5591	+	8.19295i	−1.15029	+	0.341967i
$575$	−9.26690	−	3.01100i	−0.386457	−	0.125567i
$576$	1.02501	−	2.81946i	0.0427087	−	0.117478i
$577$	−0.243104	−	2.31298i	−0.0101206	−	0.0962907i	0.988296	−	0.152551i	$-0.0487489\pi$
$577$	−0.243104	−	2.31298i	−0.0101206	−	0.0962907i	−0.998416	+	0.0562606i	$0.982082\pi$
$578$	−1.42515	−	13.5594i	−0.0592786	−	0.563998i
$579$	3.90749	+	2.34686i	0.162390	+	0.0975324i
$580$	4.88121	+	1.58600i	0.202681	+	0.0658551i
$581$	5.63358	−	23.5680i	0.233720	−	0.977764i
$582$	−8.78252	+	1.70885i	−0.364047	+	0.0708341i
$583$	−23.9954	−	35.8986i	−0.993788	−	1.48677i
$584$	−2.99812	−	1.73097i	−0.124063	−	0.0716279i
$585$	−9.21362	+	9.54811i	−0.380936	+	0.394766i
$586$	15.0920	−	3.20790i	0.623444	−	0.132517i
$587$	−40.4542	+	13.1444i	−1.66972	+	0.542526i	−0.982875	−	0.184273i	$-0.941007\pi$
$587$	−40.4542	+	13.1444i	−1.66972	+	0.542526i	−0.686850	+	0.726800i	$0.741007\pi$
$588$	−10.2681	+	6.44712i	−0.423451	+	0.265875i
$589$	−4.63255	−	6.37616i	−0.190881	−	0.262725i
$590$	−1.59999	+	1.77697i	−0.0658704	+	0.0731565i
$591$	−20.0730	−	15.1202i	−0.825691	−	0.621961i
$592$	5.65826	−	2.51922i	0.232553	−	0.103539i
$593$	17.3843	+	30.1104i	0.713886	+	1.23649i	0.963388	+	0.268112i	$0.0863998\pi$
$593$	17.3843	+	30.1104i	0.713886	+	1.23649i	−0.249502	+	0.968374i	$0.580267\pi$
$594$	−16.4622	−	5.09853i	−0.675453	−	0.209195i
$595$	−11.0828	+	4.60347i	−0.454352	+	0.188724i
$596$	5.34662	+	3.88455i	0.219006	+	0.159117i
$597$	−15.9586	+	6.77755i	−0.653144	+	0.277387i
$598$	11.8837	+	2.52596i	0.485960	+	0.103294i
$599$	12.0970	−	1.27144i	0.494270	−	0.0519498i	0.145885	−	0.989302i	$-0.453397\pi$
$599$	12.0970	−	1.27144i	0.494270	−	0.0519498i	0.348384	+	0.937352i	$0.386730\pi$
$600$	7.30514	+	1.68509i	0.298231	+	0.0687935i
$601$	−22.3148	+	7.25051i	−0.910239	+	0.295755i	−0.726457	−	0.687212i	$-0.758834\pi$
$601$	−22.3148	+	7.25051i	−0.910239	+	0.295755i	−0.183783	+	0.982967i	$0.558834\pi$
$602$	17.2017	−	11.8474i	0.701090	−	0.482865i
$603$	13.7081	+	3.41238i	0.558237	+	0.138963i
$604$	−15.6230	+	9.01996i	−0.635692	+	0.367017i
$605$	0.704281	−	8.98720i	0.0286331	−	0.365382i
$606$	−8.59879	+	24.9878i	−0.349302	+	1.01506i
$607$	20.8756	+	2.19411i	0.847314	+	0.0890563i	0.518227	−	0.855243i	$-0.326592\pi$
$607$	20.8756	+	2.19411i	0.847314	+	0.0890563i	0.329087	+	0.944299i	$0.393259\pi$
$608$	1.29751	+	0.421586i	0.0526209	+	0.0170976i
$609$	10.5496	+	26.6898i	0.427491	+	1.08153i
$610$	−1.80711	+	1.31294i	−0.0731677	+	0.0531595i
$611$	−2.40170	−	1.06931i	−0.0971623	−	0.0432595i
$612$	16.3511	−	2.88943i	0.660954	−	0.116798i
$613$	25.4857	−	22.9475i	1.02936	−	0.926839i	0.0320013	−	0.999488i	$-0.489812\pi$
$613$	25.4857	−	22.9475i	1.02936	−	0.926839i	0.997358	+	0.0726490i	$0.0231453\pi$
$614$	22.6627	+	2.38194i	0.914590	+	0.0961273i
$615$	−2.94607	−	15.1411i	−0.118797	−	0.610550i
$616$	4.69101	+	7.41582i	0.189006	+	0.298792i
$617$		−	30.7003i		−	1.23595i	−0.786199	−	0.617973i	$-0.787954\pi$
$617$		−	30.7003i		−	1.23595i	0.786199	−	0.617973i	$-0.212046\pi$
$618$	−0.334780	−	3.81834i	−0.0134668	−	0.153596i
$619$	9.60052	+	10.6625i	0.385877	+	0.428560i	0.904520	−	0.426431i	$-0.140229\pi$
$619$	9.60052	+	10.6625i	0.385877	+	0.428560i	−0.518643	+	0.854991i	$0.673563\pi$
$620$	−0.984324	+	4.63088i	−0.0395314	+	0.185981i
$621$	−1.83632	−	11.5522i	−0.0736892	−	0.463575i
$622$	−6.16912	−	8.49107i	−0.247359	−	0.340461i
$623$	−5.92730	+	16.7908i	−0.237472	+	0.672710i
$624$	−9.27824	−	1.13747i	−0.371427	−	0.0455351i
$625$	−1.60731	+	15.2926i	−0.0642925	+	0.611702i
$626$	11.0351	−	19.1134i	0.441052	−	0.763925i
$627$	2.05875	−	7.56196i	0.0822186	−	0.301996i
$628$	−6.75347	−	11.6974i	−0.269493	−	0.466776i
$629$	27.7340	+	20.1500i	1.10583	+	0.803432i
$630$	−2.91033	−	5.81739i	−0.115950	−	0.231770i
$631$	−0.104217	−	0.320748i	−0.00414882	−	0.0127688i	0.948961	−	0.315394i	$-0.102137\pi$
$631$	−0.104217	−	0.320748i	−0.00414882	−	0.0127688i	−0.953109	+	0.302626i	$0.902137\pi$
$632$	4.14774	−	9.31599i	0.164988	−	0.370570i
$633$	−39.9054	+	12.2085i	−1.58610	+	0.485242i
$634$	4.99543	−	23.5017i	0.198394	−	0.933370i
$635$	−5.22805	+	1.11126i	−0.207469	+	0.0440989i
$636$	−9.52618	+	20.4389i	−0.377738	+	0.810456i
$637$	26.7659	+	26.6605i	1.06051	+	1.05633i
$638$	19.2909	−	7.70005i	0.763736	−	0.304848i
$639$	−6.68569	+	8.56388i	−0.264482	+	0.338782i
$640$	−0.333330	−	0.748672i	−0.0131760	−	0.0295939i
$641$	−18.8990	+	17.0167i	−0.746465	+	0.672120i	−0.951851	−	0.306561i	$-0.900822\pi$
$641$	−18.8990	+	17.0167i	−0.746465	+	0.672120i	0.205386	+	0.978681i	$0.434155\pi$
$642$	−10.5456	+	17.5582i	−0.416202	+	0.692969i
$643$	−3.27731	+	2.38111i	−0.129244	+	0.0939016i	−0.650529	−	0.759481i	$-0.725453\pi$
$643$	−3.27731	+	2.38111i	−0.129244	+	0.0939016i	0.521285	+	0.853383i	$0.325453\pi$
$644$	−3.10697	+	5.08136i	−0.122432	+	0.200234i
$645$	5.43455	+	9.79987i	0.213985	+	0.385870i
$646$	1.56995	+	7.38603i	0.0617688	+	0.290599i
$647$	14.9973	+	33.6845i	0.589606	+	1.32428i	0.924198	+	0.381913i	$0.124735\pi$
$647$	14.9973	+	33.6845i	0.589606	+	1.32428i	−0.334593	+	0.942363i	$0.608599\pi$
$648$	2.18381	+	8.73103i	0.0857884	+	0.342987i
$649$	−0.378298	+	9.66960i	−0.0148495	+	0.379565i
$650$		−	23.3598i		−	0.916248i
$651$	−23.4677	+	12.2515i	−0.919772	+	0.480175i
$652$	−2.21052	+	6.80327i	−0.0865705	+	0.266437i
$653$	−12.2670	−	11.0453i	−0.480045	−	0.432235i	0.393246	−	0.919433i	$-0.371352\pi$
$653$	−12.2670	−	11.0453i	−0.480045	−	0.432235i	−0.873291	+	0.487199i	$0.838019\pi$
$654$	11.9506	−	3.65612i	0.467307	−	0.142965i
$655$	17.7837	−	1.86914i	0.694867	−	0.0730334i
$656$	7.27138	−	8.07568i	0.283900	−	0.315302i
$657$	10.3602	−	0.728343i	0.404191	−	0.0284154i
$658$	0.886244	−	0.935754i	0.0345494	−	0.0364795i
$659$	−36.2251			−1.41113			−0.705565	−	0.708646i	$-0.749307\pi$
$659$	−36.2251			−1.41113			−0.705565	+	0.708646i	$0.749307\pi$
$660$	−4.20322	+	2.12046i	−0.163610	+	0.0825389i
$661$	−6.22054	+	10.7743i	−0.241951	+	0.419071i	−0.961270	−	0.275609i	$-0.911121\pi$
$661$	−6.22054	+	10.7743i	−0.241951	+	0.419071i	0.719319	+	0.694680i	$0.244454\pi$
$662$	2.42075	−	1.07779i	0.0940851	−	0.0418894i
$663$	−20.2244	−	47.6211i	−0.785452	−	1.84945i
$664$	2.83023	+	8.71054i	0.109834	+	0.338035i
$665$	2.59824	−	1.41405i	0.100756	−	0.0548346i
$666$	−9.84066	+	15.7614i	−0.381318	+	0.610743i
$667$	10.4770	+	9.43351i	0.405670	+	0.365267i
$668$	−0.489440	−	0.543578i	−0.0189370	−	0.0210317i
$669$	−24.7504	+	17.3373i	−0.956905	+	0.670298i
$670$	3.34198	−	1.92949i	0.129112	−	0.0745427i
$671$	−2.22373	+	8.76209i	−0.0858460	+	0.338257i
$672$	2.03992	−	4.10350i	0.0786917	−	0.158296i
$673$	10.2158	−	14.0609i	0.393792	−	0.542008i	−0.565381	−	0.824830i	$-0.691271\pi$
$673$	10.2158	−	14.0609i	0.393792	−	0.542008i	0.959172	+	0.282822i	$0.0912707\pi$
$674$	2.45032	+	11.5279i	0.0943828	+	0.444036i
$675$	−20.9926	+	8.07178i	−0.808005	+	0.310683i
$676$	1.68568	+	16.0382i	0.0648339	+	0.616853i
$677$	−40.3007	−	17.9430i	−1.54888	−	0.689607i	−0.558698	−	0.829371i	$-0.688699\pi$
$677$	−40.3007	−	17.9430i	−1.54888	−	0.689607i	−0.990185	+	0.139764i	$0.955366\pi$
$678$	18.7253	−	10.3842i	0.719140	−	0.398801i
$679$	−13.6239	+	1.08575i	−0.522838	+	0.0416673i
$680$	2.66614	−	3.66963i	0.102242	−	0.140724i
$681$	−15.7141	−	18.0702i	−0.602164	−	0.692450i
$682$	8.92398	+	16.9548i	0.341717	+	0.649233i
$683$	1.82174	+	1.05178i	0.0697069	+	0.0402453i	0.534448	−	0.845201i	$-0.320519\pi$
$683$	1.82174	+	1.05178i	0.0697069	+	0.0402453i	−0.464741	+	0.885446i	$0.653853\pi$
$684$	−3.93387	+	1.12961i	−0.150415	+	0.0431917i
$685$	1.83383	−	5.64395i	0.0700671	−	0.215644i
$686$	−16.6924	+	8.02262i	−0.637320	+	0.306305i
$687$	−13.8820	+	14.8922i	−0.529630	+	0.568171i
$688$	−3.21098	+	7.21198i	−0.122417	+	0.274954i
$689$	68.7278	+	14.6086i	2.61832	+	0.556541i
$690$	−2.55232	−	1.92256i	−0.0971650	−	0.0731907i
$691$	0.477462	−	4.54275i	0.0181635	−	0.172814i	−0.981679	−	0.190540i	$-0.938976\pi$
$691$	0.477462	−	4.54275i	0.0181635	−	0.172814i	0.999843	+	0.0177261i	$0.00564268\pi$
$692$	16.3968			0.623311
$693$	−24.1116	−	10.5655i	−0.915926	−	0.401348i
$694$	10.3928			0.394503
$695$	−1.85401	+	17.6397i	−0.0703265	+	0.669112i
$696$	−8.66423	−	6.52643i	−0.328417	−	0.247384i
$697$	58.8319	+	12.5051i	2.22842	+	0.473665i
$698$	−2.38437	+	5.35538i	−0.0902496	+	0.202704i
$699$	22.8205	−	24.4812i	0.863151	−	0.925962i
$700$	10.7987	+	3.81204i	0.408154	+	0.144082i
$701$	6.74430	−	20.7568i	0.254729	−	0.783974i	−0.739154	−	0.673536i	$-0.764775\pi$
$701$	6.74430	−	20.7568i	0.254729	−	0.783974i	0.993883	−	0.110438i	$-0.0352254\pi$
$702$	24.9795	−	12.7453i	0.942789	−	0.481040i
$703$	−7.31792	−	4.22500i	−0.276000	−	0.159349i
$704$	−2.97484	−	1.46641i	−0.112118	−	0.0552673i
$705$	0.453735	+	0.521766i	0.0170886	+	0.0196508i
$706$	−16.7295	+	23.0261i	−0.629621	+	0.866599i
$707$	−17.3422	+	36.4512i	−0.652220	+	1.37089i
$708$	4.41956	−	2.45088i	0.166097	−	0.0921097i
$709$	−9.01963	−	4.01580i	−0.338739	−	0.150817i	0.230316	−	0.973116i	$-0.426024\pi$
$709$	−9.01963	−	4.01580i	−0.338739	−	0.150817i	−0.569055	+	0.822299i	$0.692691\pi$
$710$	0.310232	+	2.95166i	0.0116428	+	0.110774i
$711$	5.32364	+	30.1261i	0.199652	+	1.12982i
$712$	−1.39928	−	6.58308i	−0.0524401	−	0.246711i
$713$	−7.64397	+	10.5210i	−0.286269	+	0.394016i
$714$	25.3145	−	1.57812i	0.947373	−	0.0590595i
$715$	9.38185	+	11.2766i	0.350861	+	0.421721i
$716$	−21.8305	+	12.6038i	−0.815844	+	0.471028i
$717$	−17.0063	+	11.9127i	−0.635113	+	0.444887i
$718$	2.01803	+	2.24125i	0.0753123	+	0.0836428i
$719$	12.8719	+	11.5899i	0.480042	+	0.432232i	0.873290	−	0.487201i	$-0.161982\pi$
$719$	12.8719	+	11.5899i	0.480042	+	0.432232i	−0.393248	+	0.919432i	$0.628649\pi$
$720$	2.08547	+	1.30207i	0.0777210	+	0.0485251i
$721$	0.147491	−	5.85313i	0.00549285	−	0.217982i
$722$	5.29616	+	16.2999i	0.197103	+	0.606620i
$723$	7.18989	+	16.9295i	0.267395	+	0.629616i
$724$	−7.02721	+	3.12872i	−0.261164	+	0.116278i
$725$	13.5536	−	23.4755i	0.503369	−	0.871860i
$726$	−7.58808	+	17.4763i	−0.281620	+	0.648606i
$727$	32.9051			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$727$	32.9051			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$728$	−13.8876	−	3.31963i	−0.514709	−	0.123034i
$729$	−20.0851	−	18.0440i	−0.743894	−	0.668298i
$730$	1.89841	−	2.10840i	0.0702635	−	0.0780355i
$731$	−43.4551	+	4.56732i	−1.60725	+	0.168928i
$732$	4.51438	−	1.38110i	0.166856	−	0.0510471i
$733$	−14.3093	−	12.8841i	−0.528526	−	0.475887i	0.361132	−	0.932515i	$-0.382390\pi$
$733$	−14.3093	−	12.8841i	−0.528526	−	0.475887i	−0.889658	+	0.456628i	$0.849057\pi$
$734$	3.22378	−	9.92179i	0.118992	−	0.366220i
$735$	−3.41854	−	9.32961i	−0.126095	−	0.344128i
$736$		−	2.25114i		−	0.0829782i
$737$	5.40298	−	14.6530i	0.199021	−	0.539749i
$738$	−4.52509	+	32.2851i	−0.166571	+	1.18843i
$739$	−0.433453	−	0.973551i	−0.0159448	−	0.0358126i	0.905398	−	0.424565i	$-0.139573\pi$
$739$	−0.433453	−	0.973551i	−0.0159448	−	0.0358126i	−0.921342	+	0.388752i	$0.872906\pi$
$740$	1.05534	+	4.96499i	0.0387951	+	0.182517i
$741$	6.18481	+	11.1528i	0.227205	+	0.409708i
$742$	−17.9688	+	29.3874i	−0.659654	+	1.07885i
$743$	−11.4625	+	8.32797i	−0.420517	+	0.305524i	−0.777846	−	0.628455i	$-0.783688\pi$
$743$	−11.4625	+	8.32797i	−0.420517	+	0.305524i	0.357329	+	0.933979i	$0.383688\pi$
$744$	5.15184	−	8.57773i	0.188876	−	0.314475i
$745$	−4.02492	+	3.62405i	−0.147462	+	0.132775i
$746$	13.2013	+	29.6506i	0.483334	+	1.08559i
$747$	−21.6580	−	16.9081i	−0.792426	−	0.618635i
$748$	−1.20366	−	18.3174i	−0.0440103	−	0.669750i
$749$	−19.0214	+	24.8399i	−0.695028	+	0.907631i
$750$	−5.59375	+	12.0017i	−0.204255	+	0.438239i
$751$	−44.5286	+	9.46484i	−1.62487	+	0.345377i	−0.928219	−	0.372033i	$-0.878661\pi$
$751$	−44.5286	+	9.46484i	−1.62487	+	0.345377i	−0.696651	+	0.717410i	$0.745327\pi$
$752$	−0.101280	+	0.476484i	−0.00369330	+	0.0173756i
$753$	0.818733	−	0.250479i	0.0298363	−	0.00912795i
$754$	−13.7473	+	30.8769i	−0.500647	+	1.12447i
$755$	−4.56855	−	14.0606i	−0.166267	−	0.511716i
$756$	1.81551	+	13.6273i	0.0660296	+	0.495621i
$757$	6.54374	+	4.75430i	0.237836	+	0.172798i	0.700319	−	0.713830i	$-0.253041\pi$
$757$	6.54374	+	4.75430i	0.237836	+	0.172798i	−0.462483	+	0.886628i	$0.653041\pi$
$758$	13.2611	+	22.9689i	0.481666	+	0.834269i
$759$	−12.9167	+	0.625018i	−0.468847	+	0.0226867i
$760$	−0.559030	+	0.968269i	−0.0202782	+	0.0351228i
$761$	−1.81333	+	17.2527i	−0.0657333	+	0.625411i	0.911214	+	0.411932i	$0.135146\pi$
$761$	−1.81333	+	17.2527i	−0.0657333	+	0.625411i	−0.976948	+	0.213478i	$0.931521\pi$
$762$	11.2123	+	1.37458i	0.406179	+	0.0497956i
$763$	18.7670	−	3.49741i	0.679411	−	0.126615i
$764$	5.10973	+	7.03294i	0.184864	+	0.254443i
$765$	−0.469827	+	13.5996i	−0.0169866	+	0.491695i
$766$	−0.881606	+	4.14763i	−0.0318537	+	0.149860i
$767$	−10.5366	−	11.7020i	−0.380454	−	0.422537i
$768$	0.151280	+	1.72543i	0.00545885	+	0.0622612i
$769$			19.5906i			0.706455i	0.935537	+	0.353228i	$0.114916\pi$
$769$			19.5906i			0.706455i	−0.935537	+	0.353228i	$0.885084\pi$
$770$	−6.74393	+	2.49681i	−0.243034	+	0.0899789i
$771$	−2.00592	−	10.3093i	−0.0722416	−	0.371281i
$772$	−2.61720	−	0.275079i	−0.0941952	−	0.00990031i
$773$	20.3417	−	18.3157i	0.731640	−	0.658772i	−0.216624	−	0.976255i	$-0.569505\pi$
$773$	20.3417	−	18.3157i	0.731640	−	0.658772i	0.948264	+	0.317484i	$0.102838\pi$
$774$	−4.12130	−	23.3221i	−0.148137	−	0.838297i
$775$	22.8430	+	10.1704i	0.820545	+	0.365330i
$776$	4.17913	−	3.03631i	0.150022	−	0.108997i
$777$	−17.6429	+	22.2337i	−0.632937	+	0.797630i
$778$	17.9740	+	5.84012i	0.644401	+	0.209379i
$779$	−14.7443	−	1.54969i	−0.528269	−	0.0555233i
$780$	2.49272	−	7.24376i	0.0892535	−	0.259368i
$781$	8.60506	+	8.37987i	0.307913	+	0.299855i
$782$	10.7904	−	6.22982i	0.385863	−	0.222778i
$783$	32.4981	+	1.68491i	1.16139	+	0.0602139i
$784$	3.80088	−	5.87821i	0.135746	−	0.209936i
$785$	10.5275	−	3.42059i	0.375742	−	0.122086i
$786$	−36.8256	−	8.49462i	−1.31353	−	0.302993i
$787$	37.0752	−	3.89676i	1.32159	−	0.138904i	0.582675	−	0.812706i	$-0.302006\pi$
$787$	37.0752	−	3.89676i	1.32159	−	0.138904i	0.738913	+	0.673801i	$0.235340\pi$
$788$	14.1921	+	3.01661i	0.505571	+	0.107462i
$789$	−25.0559	+	10.6411i	−0.892013	+	0.378834i
$790$	6.76111	+	4.91223i	0.240549	+	0.174769i
$791$	30.2051	−	12.5463i	1.07397	−	0.446094i
$792$	9.85826	−	1.34708i	0.350298	−	0.0478664i
$793$	−7.35495	−	12.7392i	−0.261182	−	0.452381i
$794$	−5.64234	+	2.51213i	−0.200239	+	0.0891522i
$795$	−14.7610	−	11.1189i	−0.523519	−	0.394346i
$796$	6.69814	−	7.43904i	0.237409	−	0.263670i
$797$	−0.329589	−	0.453640i	−0.0116746	−	0.0160688i	0.803140	−	0.595791i	$-0.203161\pi$
$797$	−0.329589	−	0.453640i	−0.0116746	−	0.0160688i	−0.814814	+	0.579722i	$0.803161\pi$
$798$	−6.16497	+	1.03910i	−0.218237	+	0.0367837i
$799$	−2.56421	+	0.833161i	−0.0907151	+	0.0294751i
$800$	−4.23380	+	0.899921i	−0.149687	+	0.0318170i
$801$	14.5290	+	14.0200i	0.513358	+	0.495374i
$802$	7.93565	+	4.58165i	0.280218	+	0.161784i
$803$	0.448858	−	11.4732i	0.0158398	−	0.404879i
$804$	−8.00576	+	1.55771i	−0.282342	+	0.0549363i
$805$	−3.54390	−	3.35640i	−0.124906	−	0.118297i
$806$	−29.6516	−	9.63439i	−1.04443	−	0.339357i
$807$	−28.8333	−	17.3175i	−1.01498	−	0.609603i
$808$	−1.59479	−	15.1735i	−0.0561047	−	0.533800i
$809$	0.000811612		0.00772197i	2.85348e−5		0.000271490i	0.994536	−	0.104393i	$-0.0332899\pi$
$809$	0.000811612		0.00772197i	2.85348e−5		0.000271490i	−0.994508	+	0.104664i	$0.966623\pi$
$810$	−7.37102	+	0.262911i	−0.258991	+	0.00923774i
$811$	17.5754	+	5.71058i	0.617155	+	0.200526i	0.600877	−	0.799342i	$-0.294818\pi$
$811$	17.5754	+	5.71058i	0.617155	+	0.200526i	0.0162781	+	0.999868i	$0.494818\pi$
$812$	−12.0303	−	11.3938i	−0.422181	−	0.399844i
$813$	0.443997	+	2.28190i	0.0155717	+	0.0800296i
$814$	16.1344	+	12.7149i	0.565509	+	0.445658i
$815$	−5.07695	−	2.93118i	−0.177838	−	0.102675i
$816$	−7.85183	+	5.50010i	−0.274869	+	0.192542i
$817$	10.5349	−	2.23927i	0.368571	−	0.0783422i
$818$	5.68264	−	1.84640i	0.198689	−	0.0645579i
$819$	40.1034	−	15.0562i	1.40133	−	0.526107i
$820$	5.23463	+	7.20485i	0.182801	+	0.251604i
$821$	21.7746	−	24.1831i	0.759939	−	0.843998i	−0.231734	−	0.972779i	$-0.574440\pi$
$821$	21.7746	−	24.1831i	0.759939	−	0.843998i	0.991673	+	0.128782i	$0.0411066\pi$
$822$	−7.54626	+	10.0181i	−0.263206	+	0.349422i
$823$	−0.709226	+	0.315768i	−0.0247221	+	0.0110070i	−0.419060	−	0.907958i	$-0.637640\pi$
$823$	−0.709226	+	0.315768i	−0.0247221	+	0.0110070i	0.394338	+	0.918965i	$0.370974\pi$
$824$	1.10649	+	1.91649i	0.0385464	+	0.0667642i
$825$	6.33910	+	24.0430i	0.220699	+	0.837071i
$826$	7.12904	−	2.96119i	0.248051	−	0.103033i
$827$	−33.5218	−	24.3550i	−1.16567	−	0.846907i	−0.175184	−	0.984536i	$-0.556052\pi$
$827$	−33.5218	−	24.3550i	−1.16567	−	0.846907i	−0.990484	+	0.137629i	$0.956052\pi$
$828$	3.77856	+	5.59743i	0.131314	+	0.194524i
$829$	−45.2020	−	9.60798i	−1.56993	−	0.333699i	−0.660915	−	0.750461i	$-0.729832\pi$
$829$	−45.2020	−	9.60798i	−1.56993	−	0.333699i	−0.909016	+	0.416762i	$0.863165\pi$
$830$	−7.46474	+	0.784575i	−0.259105	+	0.0272330i
$831$	4.08510	−	17.7096i	0.141711	−	0.614339i
$832$	5.13276	−	1.66773i	0.177946	−	0.0578183i
$833$	38.6945	+	1.95134i	1.34068	+	0.0676098i
$834$	15.8362	−	33.9774i	0.548362	−	1.17654i
$835$	0.519135	−	0.299723i	0.0179654	−	0.0103723i
$836$	0.767021	+	4.45932i	0.0265280	+	0.154229i
$837$	1.58779	+	29.9758i	0.0548822	+	1.03612i
$838$	3.23157	+	0.339651i	0.111633	+	0.0117331i
$839$	−27.5617	−	8.95535i	−0.951537	−	0.309173i	−0.208197	−	0.978087i	$-0.566760\pi$
$839$	−27.5617	−	8.95535i	−0.951537	−	0.309173i	−0.743340	+	0.668914i	$0.766760\pi$
$840$	2.94185	+	2.33442i	0.101503	+	0.0805452i
$841$	−8.26899	+	6.00777i	−0.285138	+	0.207165i
$842$	−25.5295	−	11.3665i	−0.879803	−	0.391714i
$843$	−5.28445	−	0.0912540i	−0.182006	−	0.00314296i
$844$	17.9050	−	16.1217i	0.616314	−	0.554931i
$845$	−13.1437	−	1.38145i	−0.452156	−	0.0475235i
$846$	−0.547951	−	1.35477i	−0.0188389	−	0.0465780i
$847$	−14.5183	+	25.2234i	−0.498855	+	0.866685i
$848$		−	13.0192i		−	0.447081i
$849$	−2.75115	+	0.241212i	−0.0944191	+	0.00827836i
$850$	−16.0302	−	17.8033i	−0.549832	−	0.610650i
$851$	−2.89891	+	13.6383i	−0.0993733	+	0.467515i
$852$	1.40990	−	6.11214i	0.0483023	−	0.209399i
$853$	−17.4590	−	24.0303i	−0.597785	−	0.822781i	0.397718	−	0.917508i	$-0.369802\pi$
$853$	−17.4590	−	24.0303i	−0.597785	−	0.822781i	−0.995503	+	0.0947268i	$0.969802\pi$
$854$	7.08926	−	1.32115i	0.242590	−	0.0452089i
$855$	−0.235225	−	3.34592i	−0.00804451	−	0.114428i
$856$	1.23606	−	11.7604i	0.0422478	−	0.401961i
$857$	20.0507	−	34.7289i	0.684920	−	1.18632i	−0.288542	−	0.957467i	$-0.593170\pi$
$857$	20.0507	−	34.7289i	0.684920	−	1.18632i	0.973462	−	0.228849i	$-0.0734963\pi$
$858$	−10.9943	−	28.9879i	−0.375339	−	0.989632i
$859$	−17.3091	−	29.9802i	−0.590578	−	1.02291i	−0.994155	−	0.107966i	$-0.965566\pi$
$859$	−17.3091	−	29.9802i	−0.590578	−	1.02291i	0.403576	−	0.914946i	$-0.367767\pi$
$860$	−5.23411	−	3.80281i	−0.178482	−	0.129675i
$861$	−12.4120	+	48.2268i	−0.422998	+	1.64356i
$862$	−5.59070	−	17.2064i	−0.190420	−	0.586053i
$863$	−19.7117	+	44.2733i	−0.670995	+	1.50708i	0.180973	+	0.983488i	$0.442075\pi$
$863$	−19.7117	+	44.2733i	−0.670995	+	1.50708i	−0.851969	+	0.523592i	$0.824591\pi$
$864$	−3.27230	−	4.03634i	−0.111326	−	0.137319i
$865$	−2.79382	+	13.1439i	−0.0949927	+	0.446905i
$866$	30.5198	−	6.48717i	1.03710	−	0.220443i
$867$	−21.4043	−	9.97613i	−0.726928	−	0.338807i
$868$	9.29255	−	12.1351i	0.315410	−	0.411891i
$869$	33.7489	−	2.21769i	1.14485	−	0.0752301i
$870$	6.70797	−	5.83335i	0.227421	−	0.197769i
$871$	10.3364	+	23.2159i	0.350235	+	0.786641i
$872$	−5.36207	+	4.82803i	−0.181583	+	0.163498i
$873$	−5.29487	+	14.5644i	−0.179204	+	0.492932i
$874$	−2.48464	+	1.80520i	−0.0840444	+	0.0610618i
$875$	−10.5512	+	17.2562i	−0.356696	+	0.583365i
$876$	−5.24389	+	2.90802i	−0.177175	+	0.0982527i
$877$	−6.38077	−	30.0192i	−0.215463	−	1.01368i	−0.944325	−	0.329014i	$-0.893284\pi$
$877$	−6.38077	−	30.0192i	−0.215463	−	1.01368i	0.728862	−	0.684661i	$-0.240050\pi$
$878$	−6.10287	−	13.7073i	−0.205962	−	0.462598i
$879$	8.69580	−	25.2697i	0.293302	−	0.852327i
$880$	1.68237	−	2.13481i	0.0567127	−	0.0719646i
$881$			26.7883i			0.902519i	0.892393	+	0.451260i	$0.149025\pi$
$881$			26.7883i			0.902519i	−0.892393	+	0.451260i	$0.850975\pi$
$882$	0.415768	+	20.9959i	0.0139996	+	0.706968i
$883$	3.00148	−	9.23762i	0.101008	−	0.310871i	−0.887765	−	0.460297i	$-0.847743\pi$
$883$	3.00148	−	9.23762i	0.101008	−	0.310871i	0.988773	+	0.149427i	$0.0477428\pi$
$884$	22.1983	+	19.9875i	0.746611	+	0.672251i
$885$	1.21162	+	3.96039i	0.0407282	+	0.133127i
$886$	−7.45925	+	0.783998i	−0.250598	+	0.0263389i
$887$	19.6086	−	21.7775i	0.658391	−	0.731217i	−0.317793	−	0.948160i	$-0.602942\pi$
$887$	19.6086	−	21.7775i	0.658391	−	0.731217i	0.976184	+	0.216943i	$0.0696084\pi$
$888$	1.30541	−	10.6482i	0.0438067	−	0.357329i
$889$	16.7825	+	4.01162i	0.562868	+	0.134545i
$890$	5.51552			0.184880
$891$	−22.2514	+	19.8967i	−0.745449	+	0.666563i
$892$	8.72335	−	15.1093i	0.292079	−	0.505896i
$893$	0.607125	−	0.270309i	0.0203167	−	0.00904556i
$894$	10.5360	−	4.47457i	0.352375	−	0.149652i
$895$	−6.38376	−	19.6472i	−0.213386	−	0.656733i
$896$	−0.0666482	+	2.64491i	−0.00222656	+	0.0883603i
$897$	14.3484	−	15.3926i	0.479080	−	0.513943i
$898$	−20.4049	−	18.3727i	−0.680922	−	0.613105i
$899$	−24.2085	−	26.8863i	−0.807399	−	0.896708i
$900$	9.01675	−	9.34410i	0.300558	−	0.311470i
$901$	62.4047	−	36.0294i	2.07900	−	1.20031i
$902$	34.9340	+	8.86587i	1.16317	+	0.295201i
$903$	−2.25092	−	36.1070i	−0.0749060	−	1.20157i
$904$	−7.26628	+	10.0012i	−0.241673	+	0.332634i
$905$	−1.31067	−	6.16622i	−0.0435681	−	0.204972i
$906$	−0.539489	+	31.2414i	−0.0179233	+	1.03793i
$907$	−1.86772	−	17.7701i	−0.0620165	−	0.590047i	−0.980763	−	0.195200i	$-0.937464\pi$
$907$	−1.86772	−	17.7701i	−0.0620165	−	0.590047i	0.918747	−	0.394847i	$-0.129202\pi$
$908$	12.6305	+	5.62348i	0.419159	+	0.186622i
$909$	29.4342	+	35.0517i	0.976270	+	1.16259i
$910$	5.02736	−	10.5669i	0.166655	−	0.350289i
$911$	18.8753	−	25.9796i	0.625367	−	0.860744i	−0.372363	−	0.928087i	$-0.621452\pi$
$911$	18.8753	−	25.9796i	0.625367	−	0.860744i	0.997730	+	0.0673435i	$0.0214523\pi$
$912$	1.78309	−	1.55060i	0.0590441	−	0.0513456i
$913$	−21.1927	+	21.7622i	−0.701375	+	0.720223i
$914$	−12.2046	−	7.04633i	−0.403692	−	0.233072i
$915$	0.337916	+	3.85412i	0.0111712	+	0.127413i
$916$	3.63225	−	11.1789i	0.120013	−	0.369362i
$917$	−54.4369	−	19.2167i	−1.79767	−	0.634591i
$918$	10.2915	−	26.8553i	0.339671	−	0.886356i
$919$	11.8116	−	26.5293i	0.389628	−	0.875119i	−0.607125	−	0.794606i	$-0.707677\pi$
$919$	11.8116	−	26.5293i	0.389628	−	0.875119i	0.996754	−	0.0805132i	$-0.0256559\pi$
$920$	1.80455	+	0.383569i	0.0594942	+	0.0126459i
$921$	23.7472	−	31.5258i	0.782497	−	1.03881i
$922$	−3.55002	+	33.7762i	−0.116914	+	1.11236i
$923$	−19.5450			−0.643330
$924$	15.1946	−	0.351928i	0.499866	−	0.0115776i
$925$	26.8089			0.881470
$926$	−4.15705	+	39.5517i	−0.136609	+	1.29975i
$927$	−5.96812	−	2.90809i	−0.196019	−	0.0955142i
$928$	6.12582	+	1.30208i	0.201090	+	0.0427429i
$929$	−16.0860	+	36.1298i	−0.527765	+	1.18538i	0.431304	+	0.902206i	$0.358053\pi$
$929$	−16.0860	+	36.1298i	−0.527765	+	1.18538i	−0.959069	+	0.283172i	$0.908613\pi$
$930$	5.99822	+	5.59134i	0.196690	+	0.183347i
$931$	−9.53587	+	0.518624i	−0.312526	+	0.0169972i
$932$	−5.97105	+	18.3770i	−0.195588	+	0.601959i
$933$	−18.1093	+	1.58777i	−0.592873	+	0.0519812i
$934$	−13.3069	−	7.68272i	−0.435414	−	0.251386i
$935$	14.8886	+	2.15620i	0.486909	+	0.0705151i
$936$	−9.96323	+	12.7622i	−0.325658	+	0.417144i
$937$	24.5557	−	33.7980i	0.802200	−	1.10413i	−0.190280	−	0.981730i	$-0.560940\pi$
$937$	24.5557	−	33.7980i	0.802200	−	1.10413i	0.992480	−	0.122404i	$-0.0390603\pi$
$938$	−12.4190	+	0.989724i	−0.405494	+	0.0323156i
$939$	−18.5390	−	33.4305i	−0.604996	−	1.09096i
$940$	−0.364700	−	0.162375i	−0.0118952	−	0.00529608i
$941$	−2.01602	−	19.1812i	−0.0657205	−	0.625289i	−0.976962	−	0.213415i	$-0.931541\pi$
$941$	−2.01602	−	19.1812i	−0.0657205	−	0.625289i	0.911241	−	0.411874i	$-0.135125\pi$
$942$	−23.3912	−	0.403929i	−0.762128	−	0.0131607i
$943$	5.08613	+	23.9284i	0.165627	+	0.779215i
$944$	−1.71500	+	2.36049i	−0.0558183	+	0.0768273i
$945$	−11.2332	−	0.866595i	−0.365416	−	0.0281904i
$946$	−26.1267	+	1.71683i	−0.849453	+	0.0558189i
$947$	20.0706	−	11.5878i	0.652208	−	0.376552i	−0.137094	−	0.990558i	$-0.543776\pi$
$947$	20.0706	−	11.5878i	0.652208	−	0.376552i	0.789301	+	0.614006i	$0.210443\pi$
$948$	−10.1337	−	14.4666i	−0.329126	−	0.469854i
$949$	12.5018	+	13.8847i	0.405827	+	0.450716i
$950$	4.38837	+	3.95130i	0.142377	+	0.128197i
$951$	−30.4409	−	28.3760i	−0.987114	−	0.920155i
$952$	−12.8623	+	7.00008i	−0.416868	+	0.226874i
$953$	−0.450278	−	1.38581i	−0.0145859	−	0.0448908i	0.943499	−	0.331376i	$-0.107513\pi$
$953$	−0.450278	−	1.38581i	−0.0145859	−	0.0448908i	−0.958085	+	0.286486i	$0.907513\pi$
$954$	21.8528	+	32.3720i	0.707510	+	1.04808i
$955$	−6.50835	+	2.89770i	−0.210605	+	0.0937675i
$956$	5.99394	−	10.3818i	0.193858	−	0.335771i
$957$	5.77035	−	35.5105i	0.186529	−	1.14789i
$958$	−1.60808			−0.0519548
$959$	−13.1742	+	13.9102i	−0.425418	+	0.449184i
$960$	−1.40891	−	0.172725i	−0.0454723	−	0.00557468i
$961$	1.58785	−	1.76349i	0.0512211	−	0.0568868i
$962$	−33.2439	+	3.49407i	−1.07183	+	0.112653i
$963$	16.6664	+	31.3167i	0.537067	+	1.00917i
$964$	−7.89162	−	7.10565i	−0.254172	−	0.228858i
$965$	0.666449	−	2.05112i	0.0214537	−	0.0660278i
$966$	4.77414	+	9.14483i	0.153606	+	0.294230i
$967$			7.66929i			0.246628i	0.992368	+	0.123314i	$0.0393522\pi$
$967$			7.66929i			0.246628i	−0.992368	+	0.123314i	$0.960648\pi$
$968$	−0.291628	−	10.9961i	−0.00937329	−	0.353429i
$969$	12.3670	+	4.25573i	0.397286	+	0.136714i
$970$	1.72188	+	3.86740i	0.0552862	+	0.124175i
$971$	−9.83285	−	46.2599i	−0.315551	−	1.48455i	−0.794799	−	0.606873i	$-0.792424\pi$
$971$	−9.83285	−	46.2599i	−0.315551	−	1.48455i	0.479248	−	0.877680i	$-0.340909\pi$
$972$	14.9116	+	4.54371i	0.478289	+	0.145740i
$973$	29.8710	−	48.8532i	0.957620	−	1.56616i
$974$	1.18538	−	0.861227i	0.0379819	−	0.0275955i
$975$	−34.6852	−	20.8322i	−1.11082	−	0.667164i
$976$	−2.02553	+	1.82380i	−0.0648357	+	0.0583783i
$977$	18.6128	+	41.8050i	0.595475	+	1.33746i	0.920125	+	0.391625i	$0.128087\pi$
$977$	18.6128	+	41.8050i	0.595475	+	1.33746i	−0.324650	+	0.945834i	$0.605246\pi$
$978$	8.13033	+	9.34935i	0.259979	+	0.298959i
$979$	17.1592	−	14.2760i	0.548411	−	0.456264i
$980$	4.06443	+	4.04842i	0.129833	+	0.129322i
$981$	5.22884	−	21.0051i	0.166944	−	0.670641i
$982$	11.3465	−	2.41177i	0.362081	−	0.0769627i
$983$	2.13306	−	10.0352i	0.0680339	−	0.320074i	−0.930950	−	0.365147i	$-0.881019\pi$
$983$	2.13306	−	10.0352i	0.0680339	−	0.320074i	0.998984	+	0.0450728i	$0.0143520\pi$
$984$	−5.50639	−	17.9986i	−0.175537	−	0.573773i
$985$	−4.83633	+	10.8626i	−0.154098	+	0.346110i
$986$	10.7114	+	32.9662i	0.341119	+	1.04986i
$987$	−0.599081	−	2.15042i	−0.0190690	−	0.0684485i
$988$	−5.95670	−	4.32780i	−0.189508	−	0.137686i
$989$	−8.88581	−	15.3907i	−0.282552	−	0.489395i
$990$	−0.599896	+	8.13206i	−0.0190659	+	0.258454i
$991$	4.08317	−	7.07226i	0.129706	−	0.224658i	−0.793857	−	0.608105i	$-0.791930\pi$
$991$	4.08317	−	7.07226i	0.129706	−	0.224658i	0.923563	+	0.383447i	$0.125263\pi$
$992$	−0.603854	+	5.74529i	−0.0191724	+	0.182413i
$993$	0.558488	−	4.55555i	0.0177231	−	0.144566i
$994$	3.18950	−	9.03519i	0.101165	−	0.286579i
$995$	4.82196	+	6.63686i	0.152866	+	0.210403i
$996$	15.4576	+	3.56563i	0.489793	+	0.112981i
$997$	0.773610	−	3.63955i	0.0245005	−	0.115266i	−0.964198	−	0.265183i	$-0.914568\pi$
$997$	0.773610	−	3.63955i	0.0245005	−	0.115266i	0.988698	+	0.149918i	$0.0479009\pi$
$998$	−20.6887	−	22.9772i	−0.654890	−	0.727330i
$999$	14.6271	+	28.6676i	0.462781	+	0.907003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.95.13	yes	128
3.2	odd	2		462.2.bc.a.95.12	✓	128
7.2	even	3	inner	462.2.bc.b.359.3	yes	128
11.8	odd	10		462.2.bc.a.305.1	yes	128
21.2	odd	6		462.2.bc.a.359.1	yes	128
33.8	even	10	inner	462.2.bc.b.305.3	yes	128
77.30	odd	30		462.2.bc.a.107.12	yes	128
231.107	even	30	inner	462.2.bc.b.107.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.12	✓	128	3.2	odd	2
462.2.bc.a.107.12	yes	128	77.30	odd	30
462.2.bc.a.305.1	yes	128	11.8	odd	10
462.2.bc.a.359.1	yes	128	21.2	odd	6
462.2.bc.b.95.13	yes	128	1.1	even	1	trivial
462.2.bc.b.107.13	yes	128	231.107	even	30	inner
462.2.bc.b.305.3	yes	128	33.8	even	10	inner
462.2.bc.b.359.3	yes	128	7.2	even	3	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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(1.38347 + 1.04212i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.333330 - 0.748672i) q^{5} +(-1.18102 + 1.26696i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.827988 + 2.88348i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(1.38347 + 1.04212i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.333330 - 0.748672i) q^{5} +(-1.18102 + 1.26696i) q^{6} +(-2.01015 + 1.72026i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.827988 + 2.88348i) q^{9} +(0.709728 + 0.409762i) q^{10} +(3.26863 - 0.562216i) q^{11} +(-1.13657 - 1.30698i) q^{12} +(-3.17222 + 4.36618i) q^{13} +(-1.50072 - 2.17895i) q^{14} +(1.24136 - 0.688398i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.578545 + 5.50449i) q^{17} +(-2.95423 + 0.522047i) q^{18} +(-0.283650 - 1.33447i) q^{19} +(-0.481704 + 0.663008i) q^{20} +(-4.57370 + 0.285126i) q^{21} +(0.217472 + 3.30949i) q^{22} +(-1.94955 + 1.12557i) q^{23} +(1.41863 - 0.993728i) q^{24} +(2.89625 + 3.21661i) q^{25} +(-4.01068 - 3.61123i) q^{26} +(-1.85942 + 4.85207i) q^{27} +(2.32388 - 1.26474i) q^{28} +(-1.93527 - 5.95615i) q^{29} +(0.554870 + 1.30651i) q^{30} +(5.27750 - 2.34969i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.10795 + 2.62848i) q^{33} -5.53481 q^{34} +(0.617869 + 2.07836i) q^{35} +(-0.210386 - 2.99261i) q^{36} +(4.14442 - 4.60285i) q^{37} +(1.35681 - 0.142606i) q^{38} +(-8.93874 + 2.73467i) q^{39} +(-0.609025 - 0.548368i) q^{40} +(3.35806 - 10.3350i) q^{41} +(0.194518 - 4.57845i) q^{42} +7.89449i q^{43} +(-3.31409 - 0.129655i) q^{44} +(2.43477 + 0.341258i) q^{45} +(-0.915622 - 2.05652i) q^{46} +(0.101280 + 0.476484i) q^{47} +(0.839998 + 1.51473i) q^{48} +(1.08140 - 6.91597i) q^{49} +(-3.50173 + 2.54416i) q^{50} +(-4.93592 + 8.21822i) q^{51} +(4.01068 - 3.61123i) q^{52} +(-5.29538 - 11.8936i) q^{53} +(-4.63113 - 2.35641i) q^{54} +(0.668616 - 2.63453i) q^{55} +(1.01490 + 2.44336i) q^{56} +(0.998249 - 2.14180i) q^{57} +(6.12582 - 1.30208i) q^{58} +(-0.606629 + 2.85396i) q^{59} +(-1.35736 + 0.415262i) q^{60} +(-1.10861 + 2.48998i) q^{61} +(1.78517 + 5.49419i) q^{62} +(-6.62471 - 4.37186i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.21144 + 3.83033i) q^{65} +(-3.14800 + 4.80521i) q^{66} +(2.35441 - 4.07795i) q^{67} +(0.578545 - 5.50449i) q^{68} +(-3.87012 - 0.474458i) q^{69} +(-2.13156 + 0.397236i) q^{70} +(2.12867 + 2.92987i) q^{71} +(2.99821 + 0.103579i) q^{72} +(0.719776 - 3.38628i) q^{73} +(4.14442 + 4.60285i) q^{74} +(0.654798 + 7.46833i) q^{75} +1.36428i q^{76} +(-5.60327 + 6.75303i) q^{77} +(-1.78534 - 9.17563i) q^{78} +(10.1418 + 1.06594i) q^{79} +(0.609025 - 0.548368i) q^{80} +(-7.62887 + 4.77497i) q^{81} +(9.92741 + 4.41997i) q^{82} +(-7.40963 + 5.38341i) q^{83} +(4.53303 + 0.672030i) q^{84} +(4.31390 + 1.40167i) q^{85} +(-7.85124 - 0.825199i) q^{86} +(3.52961 - 10.2569i) q^{87} +(0.475362 - 3.28238i) q^{88} +(5.82848 - 3.36507i) q^{89} +(-0.593892 + 2.38576i) q^{90} +(-1.13435 - 14.2337i) q^{91} +(2.14096 - 0.695641i) q^{92} +(9.74992 + 2.24903i) q^{93} +(-0.484461 + 0.0509189i) q^{94} +(-1.09363 - 0.232458i) q^{95} +(-1.59423 + 0.677064i) q^{96} +(4.17913 + 3.03631i) q^{97} +(6.76504 + 1.79839i) q^{98} +(4.32752 + 8.95950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more