LMFDB - Embedded newform 370.2.ba.a.113.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(17,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("370.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.ba (of order $36$, degree $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.6
Character	$\chi$	$=$	370.113
Dual form			370.2.ba.a.167.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.745094 - 0.0651873i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.94515 + 1.10290i) q^{5} +(0.528874 - 0.528874i) q^{6} +(1.28313 - 2.75168i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.40351 + 0.423803i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.745094 - 0.0651873i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.94515 + 1.10290i) q^{5} +(0.528874 - 0.528874i) q^{6} +(1.28313 - 2.75168i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.40351 + 0.423803i) q^{9} +(2.19900 - 0.405444i) q^{10} +(1.52322 - 0.879430i) q^{11} +(0.0651873 - 0.745094i) q^{12} +(-0.645446 + 3.66051i) q^{13} +(-0.785810 - 2.93268i) q^{14} +(1.52121 + 0.694968i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.460215 - 0.0811484i) q^{17} +(-1.56878 + 1.86960i) q^{18} +(-0.211508 - 2.41755i) q^{19} +(1.42392 - 1.72408i) q^{20} +(0.776677 - 2.13390i) q^{21} +(0.601565 - 1.65279i) q^{22} +(-0.888156 + 1.53833i) q^{23} +(-0.429001 - 0.612677i) q^{24} +(2.56721 + 4.29062i) q^{25} +(1.85849 + 3.21900i) q^{26} +(-3.93058 + 1.05320i) q^{27} +(-2.48706 - 1.74146i) q^{28} +(3.50408 + 0.938915i) q^{29} +(1.61204 - 0.445441i) q^{30} +(-0.755831 - 0.755831i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(1.07761 - 0.754553i) q^{33} +(0.300384 - 0.357984i) q^{34} +(5.53071 - 3.93725i) q^{35} +2.44058i q^{36} +(-5.49716 - 2.60408i) q^{37} +(-1.71600 - 1.71600i) q^{38} +(-0.242300 + 2.76950i) q^{39} +(-0.0174317 - 2.23600i) q^{40} +(-6.02913 - 1.06310i) q^{41} +(-0.776677 - 2.13390i) q^{42} -0.539434 q^{43} +(-0.601565 - 1.65279i) q^{44} +(-5.14259 - 1.82648i) q^{45} +(0.308453 + 1.74933i) q^{46} +(1.22537 + 4.57313i) q^{47} +(-0.722455 - 0.193581i) q^{48} +(-1.42579 - 1.69919i) q^{49} +(4.72455 + 1.63664i) q^{50} +(0.337614 - 0.0904634i) q^{51} +(3.49282 + 1.27128i) q^{52} +(-1.54628 - 3.31600i) q^{53} +(-2.33402 + 3.33332i) q^{54} +(3.93281 - 0.0306600i) q^{55} +(-3.02458 + 0.264617i) q^{56} +(-0.315187 - 1.78752i) q^{57} +(3.28780 - 1.53313i) q^{58} +(2.77453 + 5.95000i) q^{59} +(0.948566 - 1.37742i) q^{60} +(-11.1701 + 7.82136i) q^{61} +(-1.06484 - 0.0931613i) q^{62} +(-1.91784 + 7.15746i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.29268 + 6.40837i) q^{65} +(0.340482 - 1.27070i) q^{66} +(-5.47990 - 2.55532i) q^{67} -0.467315i q^{68} +(-0.561480 + 1.20410i) q^{69} +(1.70595 - 6.57118i) q^{70} +(7.04380 + 5.91045i) q^{71} +(1.56878 + 1.86960i) q^{72} +(-2.93388 + 2.93388i) q^{73} +(-5.88494 + 1.53867i) q^{74} +(2.19251 + 3.02957i) q^{75} +(-2.41755 - 0.211508i) q^{76} +(-0.465424 - 5.31982i) q^{77} +(1.59459 + 2.27731i) q^{78} +(7.25157 + 3.38146i) q^{79} +(-1.45063 - 1.70167i) q^{80} +(4.02020 - 1.46323i) q^{81} +(-5.30193 + 3.06107i) q^{82} +(-1.85084 + 2.64327i) q^{83} +(-1.96661 - 1.13543i) q^{84} +(0.984686 + 0.349728i) q^{85} +(-0.413230 + 0.346741i) q^{86} +(2.67207 + 0.471159i) q^{87} +(-1.52322 - 0.879430i) q^{88} +(9.94463 - 4.63726i) q^{89} +(-5.11349 + 1.90643i) q^{90} +(9.24434 + 6.47296i) q^{91} +(1.36073 + 1.14179i) q^{92} +(-0.612436 - 0.513895i) q^{93} +(3.87824 + 2.71557i) q^{94} +(2.25491 - 4.93577i) q^{95} +(-0.677864 + 0.316093i) q^{96} +(0.199055 + 0.114924i) q^{97} +(-2.18444 - 0.385175i) q^{98} +(-3.28836 + 2.75926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.745094	−	0.0651873i	0.430180	−	0.0376359i	0.129990	−	0.991515i	$-0.458505\pi$
$3$	0.745094	−	0.0651873i	0.430180	−	0.0376359i	0.300190	+	0.953879i	$0.402950\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.94515	+	1.10290i	0.869897	+	0.493234i
$5$	1.94515	+	1.10290i	0.869897	+	0.493234i
$6$	0.528874	−	0.528874i	0.215912	−	0.215912i
$7$	1.28313	−	2.75168i	0.484977	−	1.04004i	−0.499789	−	0.866147i	$-0.666589\pi$
$7$	1.28313	−	2.75168i	0.484977	−	1.04004i	0.984765	−	0.173888i	$-0.0556332\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.40351	+	0.423803i	−0.801169	+	0.141268i
$10$	2.19900	−	0.405444i	0.695386	−	0.128213i
$11$	1.52322	−	0.879430i	0.459267	−	0.265158i	−0.252469	−	0.967605i	$-0.581243\pi$
$11$	1.52322	−	0.879430i	0.459267	−	0.265158i	0.711736	+	0.702447i	$0.247909\pi$
$12$	0.0651873	−	0.745094i	0.0188180	−	0.215090i
$13$	−0.645446	+	3.66051i	−0.179015	+	1.01524i	0.754393	+	0.656424i	$0.227932\pi$
$13$	−0.645446	+	3.66051i	−0.179015	+	1.01524i	−0.933407	+	0.358819i	$0.883180\pi$
$14$	−0.785810	−	2.93268i	−0.210017	−	0.783793i
$15$	1.52121	+	0.694968i	0.392776	+	0.179440i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.460215	−	0.0811484i	0.111619	−	0.0196814i	−0.117560	−	0.993066i	$-0.537507\pi$
$17$	0.460215	−	0.0811484i	0.111619	−	0.0196814i	0.229178	+	0.973384i	$0.426396\pi$
$18$	−1.56878	+	1.86960i	−0.369764	+	0.440668i
$19$	−0.211508	−	2.41755i	−0.0485233	−	0.554624i	−0.981080	−	0.193601i	$-0.937983\pi$
$19$	−0.211508	−	2.41755i	−0.0485233	−	0.554624i	0.932557	−	0.361023i	$-0.117572\pi$
$20$	1.42392	−	1.72408i	0.318398	−	0.385516i
$21$	0.776677	−	2.13390i	0.169485	−	0.465656i
$22$	0.601565	−	1.65279i	0.128254	−	0.352375i
$23$	−0.888156	+	1.53833i	−0.185193	+	0.320764i	−0.943642	−	0.330969i	$-0.892624\pi$
$23$	−0.888156	+	1.53833i	−0.185193	+	0.320764i	0.758448	+	0.651733i	$0.225958\pi$
$24$	−0.429001	−	0.612677i	−0.0875695	−	0.125062i
$25$	2.56721	+	4.29062i	0.513441	+	0.858125i
$26$	1.85849	+	3.21900i	0.364480	+	0.631297i
$27$	−3.93058	+	1.05320i	−0.756440	+	0.202688i
$28$	−2.48706	−	1.74146i	−0.470010	−	0.329104i
$29$	3.50408	+	0.938915i	0.650691	+	0.174352i	0.569041	−	0.822309i	$-0.307314\pi$
$29$	3.50408	+	0.938915i	0.650691	+	0.174352i	0.0816497	+	0.996661i	$0.473981\pi$
$30$	1.61204	−	0.445441i	0.294316	−	0.0813261i
$31$	−0.755831	−	0.755831i	−0.135751	−	0.135751i	0.635966	−	0.771717i	$-0.280602\pi$
$31$	−0.755831	−	0.755831i	−0.135751	−	0.135751i	−0.771717	+	0.635966i	$0.780602\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	1.07761	−	0.754553i	0.187588	−	0.131351i
$34$	0.300384	−	0.357984i	0.0515155	−	0.0613937i
$35$	5.53071	−	3.93725i	0.934860	−	0.665517i
$36$			2.44058i			0.406764i
$37$	−5.49716	−	2.60408i	−0.903728	−	0.428108i
$37$	−5.49716	−	2.60408i	−0.903728	−	0.428108i
$38$	−1.71600	−	1.71600i	−0.278371	−	0.278371i
$39$	−0.242300	+	2.76950i	−0.0387990	+	0.443475i
$40$	−0.0174317	−	2.23600i	−0.00275620	−	0.353543i
$41$	−6.02913	−	1.06310i	−0.941592	−	0.166028i	−0.318276	−	0.947998i	$-0.603104\pi$
$41$	−6.02913	−	1.06310i	−0.941592	−	0.166028i	−0.623316	+	0.781970i	$0.714215\pi$
$42$	−0.776677	−	2.13390i	−0.119844	−	0.329268i
$43$	−0.539434			−0.0822629			−0.0411314	−	0.999154i	$-0.513096\pi$
$43$	−0.539434			−0.0822629			−0.0411314	+	0.999154i	$0.513096\pi$
$44$	−0.601565	−	1.65279i	−0.0906894	−	0.249167i
$45$	−5.14259	−	1.82648i	−0.766612	−	0.272275i
$46$	0.308453	+	1.74933i	0.0454790	+	0.257924i
$47$	1.22537	+	4.57313i	0.178738	+	0.667060i	0.995885	+	0.0906299i	$0.0288880\pi$
$47$	1.22537	+	4.57313i	0.178738	+	0.667060i	−0.817146	+	0.576430i	$0.804445\pi$
$48$	−0.722455	−	0.193581i	−0.104277	−	0.0279411i
$49$	−1.42579	−	1.69919i	−0.203684	−	0.242741i
$50$	4.72455	+	1.63664i	0.668153	+	0.231456i
$51$	0.337614	−	0.0904634i	0.0472754	−	0.0126674i
$52$	3.49282	+	1.27128i	0.484367	+	0.176295i
$53$	−1.54628	−	3.31600i	−0.212397	−	0.455487i	0.771028	−	0.636801i	$-0.219743\pi$
$53$	−1.54628	−	3.31600i	−0.212397	−	0.455487i	−0.983425	+	0.181314i	$0.941965\pi$
$54$	−2.33402	+	3.33332i	−0.317619	+	0.453608i
$55$	3.93281	−	0.0306600i	0.530300	−	0.00413419i
$56$	−3.02458	+	0.264617i	−0.404177	+	0.0353609i
$57$	−0.315187	−	1.78752i	−0.0417476	−	0.236762i
$58$	3.28780	−	1.53313i	0.431710	−	0.201310i
$59$	2.77453	+	5.95000i	0.361213	+	0.774623i	0.999986	+	0.00522855i	$0.00166431\pi$
$59$	2.77453	+	5.95000i	0.361213	+	0.774623i	−0.638774	+	0.769395i	$0.720558\pi$
$60$	0.948566	−	1.37742i	0.122459	−	0.177825i
$61$	−11.1701	+	7.82136i	−1.43018	+	1.00142i	−0.435308	+	0.900281i	$0.643361\pi$
$61$	−11.1701	+	7.82136i	−1.43018	+	1.00142i	−0.994872	+	0.101142i	$0.967750\pi$
$62$	−1.06484	−	0.0931613i	−0.135235	−	0.0118315i
$63$	−1.91784	+	7.15746i	−0.241625	+	0.901756i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−5.29268	+	6.40837i	−0.656476	+	0.794860i
$66$	0.340482	−	1.27070i	0.0419105	−	0.156412i
$67$	−5.47990	−	2.55532i	−0.669476	−	0.312182i	0.0579981	−	0.998317i	$-0.481528\pi$
$67$	−5.47990	−	2.55532i	−0.669476	−	0.312182i	−0.727474	+	0.686135i	$0.759306\pi$
$68$		−	0.467315i		−	0.0566703i
$69$	−0.561480	+	1.20410i	−0.0675943	+	0.144956i
$70$	1.70595	−	6.57118i	0.203900	−	0.785406i
$71$	7.04380	+	5.91045i	0.835945	+	0.701441i	0.956648	−	0.291247i	$-0.0940703\pi$
$71$	7.04380	+	5.91045i	0.835945	+	0.701441i	−0.120702	+	0.992689i	$0.538515\pi$
$72$	1.56878	+	1.86960i	0.184882	+	0.220334i
$73$	−2.93388	+	2.93388i	−0.343385	+	0.343385i	−0.857638	−	0.514254i	$-0.828069\pi$
$73$	−2.93388	+	2.93388i	−0.343385	+	0.343385i	0.514254	+	0.857638i	$0.328069\pi$
$74$	−5.88494	+	1.53867i	−0.684110	+	0.178866i
$75$	2.19251	+	3.02957i	0.253169	+	0.349825i
$76$	−2.41755	−	0.211508i	−0.277312	−	0.0242617i
$77$	−0.465424	−	5.31982i	−0.0530400	−	0.606250i
$78$	1.59459	+	2.27731i	0.180552	+	0.257854i
$79$	7.25157	+	3.38146i	0.815866	+	0.380444i	0.785321	−	0.619089i	$-0.212498\pi$
$79$	7.25157	+	3.38146i	0.815866	+	0.380444i	0.0305449	+	0.999533i	$0.490276\pi$
$80$	−1.45063	−	1.70167i	−0.162185	−	0.190253i
$81$	4.02020	−	1.46323i	0.446689	−	0.162582i
$82$	−5.30193	+	3.06107i	−0.585500	+	0.338038i
$83$	−1.85084	+	2.64327i	−0.203156	+	0.290137i	−0.907782	−	0.419442i	$-0.862226\pi$
$83$	−1.85084	+	2.64327i	−0.203156	+	0.290137i	0.704626	+	0.709579i	$0.251115\pi$
$84$	−1.96661	−	1.13543i	−0.214575	−	0.123885i
$85$	0.984686	+	0.349728i	0.106804	+	0.0379333i
$86$	−0.413230	+	0.346741i	−0.0445598	+	0.0373901i
$87$	2.67207	+	0.471159i	0.286476	+	0.0505135i
$88$	−1.52322	−	0.879430i	−0.162375	−	0.0937475i
$89$	9.94463	−	4.63726i	1.05413	−	0.491548i	0.183260	−	0.983064i	$-0.441335\pi$
$89$	9.94463	−	4.63726i	1.05413	−	0.491548i	0.870868	+	0.491516i	$0.163557\pi$
$90$	−5.11349	+	1.90643i	−0.539009	+	0.200956i
$91$	9.24434	+	6.47296i	0.969070	+	0.678550i
$92$	1.36073	+	1.14179i	0.141866	+	0.119040i
$93$	−0.612436	−	0.513895i	−0.0635066	−	0.0532884i
$94$	3.87824	+	2.71557i	0.400010	+	0.280090i
$95$	2.25491	−	4.93577i	0.231349	−	0.506399i
$96$	−0.677864	+	0.316093i	−0.0691842	+	0.0322611i
$97$	0.199055	+	0.114924i	0.0202110	+	0.0116688i	0.510071	−	0.860132i	$-0.329619\pi$
$97$	0.199055	+	0.114924i	0.0202110	+	0.0116688i	−0.489860	+	0.871801i	$0.662952\pi$
$98$	−2.18444	−	0.385175i	−0.220661	−	0.0389085i
$99$	−3.28836	+	2.75926i	−0.330492	+	0.277316i
$100$	4.67123	−	1.78315i	0.467123	−	0.178315i
$101$	−13.1108	−	7.56952i	−1.30457	−	0.753195i	−0.323388	−	0.946267i	$-0.604822\pi$
$101$	−13.1108	−	7.56952i	−1.30457	−	0.753195i	−0.981185	+	0.193071i	$0.938155\pi$
$102$	0.200479	−	0.286313i	0.0198503	−	0.0283492i
$103$	−10.5316	+	6.08041i	−1.03771	+	0.599120i	−0.919183	−	0.393831i	$-0.871150\pi$
$103$	−10.5316	+	6.08041i	−1.03771	+	0.599120i	−0.118524	+	0.992951i	$0.537816\pi$
$104$	3.49282	−	1.27128i	0.342499	−	0.124659i
$105$	3.86424	−	3.29416i	0.377111	−	0.321477i
$106$	−3.31600	−	1.54628i	−0.322078	−	0.150188i
$107$	−10.1397	−	14.4811i	−0.980246	−	1.39994i	−0.915628	−	0.402026i	$-0.868306\pi$
$107$	−10.1397	−	14.4811i	−0.980246	−	1.39994i	−0.0646180	−	0.997910i	$-0.520583\pi$
$108$	0.354657	+	4.05375i	0.0341269	+	0.390072i
$109$	15.8304	+	1.38498i	1.51628	+	0.132657i	0.814679	−	0.579912i	$-0.196913\pi$
$109$	15.8304	+	1.38498i	1.51628	+	0.132657i	0.701602	+	0.712569i	$0.252469\pi$
$110$	2.99300	−	2.55145i	0.285371	−	0.243271i
$111$	−4.26566	−	1.58194i	−0.404878	−	0.150151i
$112$	−2.14687	+	2.14687i	−0.202861	+	0.202861i
$113$	−2.87358	−	3.42460i	−0.270324	−	0.322160i	0.613756	−	0.789496i	$-0.289658\pi$
$113$	−2.87358	−	3.42460i	−0.270324	−	0.322160i	−0.884079	+	0.467337i	$0.845214\pi$
$114$	−1.39044	−	1.16672i	−0.130227	−	0.109273i
$115$	−3.42423	+	2.01273i	−0.319311	+	0.187688i
$116$	1.53313	−	3.28780i	0.142347	−	0.305265i
$117$		−	9.07160i		−	0.838670i
$118$	5.95000	+	2.77453i	0.547741	+	0.255416i
$119$	0.367221	−	1.37049i	0.0336631	−	0.125632i
$120$	−0.158747	−	1.66489i	−0.0144916	−	0.151983i
$121$	−3.95321	+	6.84715i	−0.359382	+	0.622469i
$122$	−3.52929	+	13.1715i	−0.319527	+	1.19249i
$123$	−4.56157	−	0.399086i	−0.411303	−	0.0359843i
$124$	−0.875597	+	0.613099i	−0.0786309	+	0.0550579i
$125$	0.261455	+	11.1773i	0.0233853	+	0.999727i
$126$	3.13158	+	6.71570i	0.278983	+	0.598282i
$127$	9.97130	−	4.64969i	0.884810	−	0.412593i	0.0735581	−	0.997291i	$-0.476565\pi$
$127$	9.97130	−	4.64969i	0.884810	−	0.412593i	0.811251	+	0.584697i	$0.198787\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.401929	+	0.0351642i	−0.0353879	+	0.00309604i
$130$	0.0647934	+	8.31116i	0.00568276	+	0.728937i
$131$	10.6369	−	15.1911i	0.929354	−	1.32725i	−0.0155405	−	0.999879i	$-0.504947\pi$
$131$	10.6369	−	15.1911i	0.929354	−	1.32725i	0.944894	−	0.327376i	$-0.106164\pi$
$132$	−0.555964	−	1.19227i	−0.0483904	−	0.103774i
$133$	−6.92370	−	2.52002i	−0.600361	−	0.218514i
$134$	−5.84037	+	1.56492i	−0.504532	+	0.135189i
$135$	−8.80713	−	2.28643i	−0.757997	−	0.196784i
$136$	−0.300384	−	0.357984i	−0.0257577	−	0.0306969i
$137$	−9.15303	−	2.45255i	−0.781996	−	0.209535i	−0.154332	−	0.988019i	$-0.549322\pi$
$137$	−9.15303	−	2.45255i	−0.781996	−	0.209535i	−0.627665	+	0.778484i	$0.715989\pi$
$138$	0.343861	+	1.28331i	0.0292714	+	0.109242i
$139$	2.56515	+	14.5477i	0.217573	+	1.23392i	0.876385	+	0.481612i	$0.159949\pi$
$139$	2.56515	+	14.5477i	0.217573	+	1.23392i	−0.658811	+	0.752308i	$0.728940\pi$
$140$	−2.91704	−	6.13038i	−0.246535	−	0.518112i
$141$	1.21112	+	3.32754i	0.101995	+	0.280229i
$142$	9.19503			0.771630
$143$	2.23601	+	6.14337i	0.186984	+	0.513735i
$144$	2.40351	+	0.423803i	0.200292	+	0.0353169i
$145$	5.78042	+	5.69099i	0.480038	+	0.472611i
$146$	−0.361621	+	4.13334i	−0.0299279	+	0.342078i
$147$	−1.17311	−	1.17311i	−0.0967567	−	0.0967567i
$148$	−3.51909	+	4.96145i	−0.289267	+	0.407829i
$149$		−	13.9753i		−	1.14490i	−0.819938	−	0.572452i	$-0.805992\pi$
$149$		−	13.9753i		−	1.14490i	0.819938	−	0.572452i	$-0.194008\pi$
$150$	3.62693	+	0.911470i	0.296137	+	0.0744212i
$151$	7.39855	−	8.81725i	0.602086	−	0.717538i	−0.375795	−	0.926703i	$-0.622630\pi$
$151$	7.39855	−	8.81725i	0.602086	−	0.717538i	0.977880	+	0.209165i	$0.0670746\pi$
$152$	−1.98791	+	1.39195i	−0.161240	+	0.112902i
$153$	−1.07174	+	0.390081i	−0.0866450	+	0.0315362i
$154$	−3.77605	−	3.77605i	−0.304283	−	0.304283i
$155$	−0.636595	−	2.30381i	−0.0511325	−	0.185047i
$156$	2.68535	+	0.719537i	0.215000	+	0.0576091i
$157$	−3.55710	−	2.49071i	−0.283887	−	0.198780i	0.422956	−	0.906150i	$-0.360993\pi$
$157$	−3.55710	−	2.49071i	−0.283887	−	0.198780i	−0.706843	+	0.707370i	$0.749881\pi$
$158$	7.72859	−	2.07087i	0.614854	−	0.164750i
$159$	−1.36828	−	2.36993i	−0.108512	−	0.187948i
$160$	−2.20506	−	0.371110i	−0.174325	−	0.0293389i
$161$	3.09337	+	4.41779i	0.243792	+	0.348171i
$162$	2.13910	−	3.70504i	0.168064	−	0.291095i
$163$	−0.537308	+	1.47624i	−0.0420852	+	0.115628i	−0.958955	−	0.283558i	$-0.908485\pi$
$163$	−0.537308	+	1.47624i	−0.0420852	+	0.115628i	0.916870	+	0.399186i	$0.130707\pi$
$164$	−2.09389	+	5.75293i	−0.163506	+	0.449228i
$165$	2.92832	−	0.279214i	0.227969	−	0.0217368i
$166$	0.281238	+	3.21456i	0.0218283	+	0.249498i
$167$	6.69895	−	7.98349i	0.518380	−	0.617781i	−0.441817	−	0.897105i	$-0.645666\pi$
$167$	6.69895	−	7.98349i	0.518380	−	0.617781i	0.960197	+	0.279324i	$0.0901104\pi$
$168$	−2.23635	+	0.394329i	−0.172538	+	0.0304232i
$169$	−0.766719	−	0.279063i	−0.0589784	−	0.0214664i
$170$	0.979114	−	0.365037i	0.0750946	−	0.0279971i
$171$	1.53293	+	5.72096i	0.117226	+	0.437493i
$172$	−0.0936717	+	0.531239i	−0.00714240	+	0.0405066i
$173$	1.85417	−	21.1933i	0.140970	−	1.61130i	−0.515462	−	0.856912i	$-0.672380\pi$
$173$	1.85417	−	21.1933i	0.140970	−	1.61130i	0.656432	−	0.754385i	$-0.272065\pi$
$174$	2.34978	−	1.35665i	0.178137	−	0.102847i
$175$	15.1005	−	1.55870i	1.14149	−	0.117827i
$176$	−1.73214	+	0.305423i	−0.130565	+	0.0230221i
$177$	2.45515	+	4.25244i	0.184540	+	0.319633i
$178$	4.63726	−	9.94463i	0.347577	−	0.745381i
$179$	9.27493	−	9.27493i	0.693241	−	0.693241i	−0.269703	−	0.962944i	$-0.586925\pi$
$179$	9.27493	−	9.27493i	0.693241	−	0.693241i	0.962944	+	0.269703i	$0.0869254\pi$
$180$	−2.69173	+	4.74730i	−0.200630	+	0.353843i
$181$	−1.96177	+	11.1258i	−0.145818	+	0.826972i	0.820890	+	0.571087i	$0.193478\pi$
$181$	−1.96177	+	11.1258i	−0.145818	+	0.826972i	−0.966707	+	0.255885i	$0.917633\pi$
$182$	11.2423	−	0.983575i	0.833336	−	0.0729074i
$183$	−7.81290	+	6.55580i	−0.577546	+	0.484619i
$184$	1.77631			0.130951
$185$	−7.82075	−	11.1282i	−0.574993	−	0.818158i
$186$	−0.799478			−0.0586206
$187$	0.629644	−	0.528334i	0.0460441	−	0.0386356i
$188$	4.71644	−	0.412635i	0.343982	−	0.0300945i
$189$	−2.14538	+	12.1671i	−0.156054	+	0.885023i
$190$	−1.44529	−	5.23044i	−0.104852	−	0.379456i
$191$	1.61258	−	1.61258i	0.116682	−	0.116682i	−0.646355	−	0.763037i	$-0.723707\pi$
$191$	1.61258	−	1.61258i	0.116682	−	0.116682i	0.763037	+	0.646355i	$0.223707\pi$
$192$	−0.316093	+	0.677864i	−0.0228121	+	0.0489206i
$193$	−2.47874	−	4.29330i	−0.178424	−	0.309039i	0.762917	−	0.646496i	$-0.223766\pi$
$193$	−2.47874	−	4.29330i	−0.178424	−	0.309039i	−0.941341	+	0.337457i	$0.890433\pi$
$194$	0.226357	−	0.0399128i	0.0162515	−	0.00286557i
$195$	−3.52580	+	5.11986i	−0.252488	+	0.366640i
$196$	−1.92096	+	1.10907i	−0.137211	+	0.0792191i
$197$	2.31539	−	26.4650i	0.164964	−	1.88555i	−0.239351	−	0.970933i	$-0.576935\pi$
$197$	2.31539	−	26.4650i	0.164964	−	1.88555i	0.404316	−	0.914619i	$-0.367510\pi$
$198$	−0.745410	+	4.22743i	−0.0529740	+	0.300430i
$199$	−3.34781	−	12.4942i	−0.237320	−	0.885689i	−0.977089	−	0.212829i	$-0.931732\pi$
$199$	−3.34781	−	12.4942i	−0.237320	−	0.885689i	0.739770	−	0.672860i	$-0.234934\pi$
$200$	2.43219	−	4.36858i	0.171981	−	0.308905i
$201$	−4.24962	−	1.54673i	−0.299745	−	0.109098i
$202$	−14.9090	+	2.62887i	−1.04900	+	0.184966i
$203$	7.07977	−	8.43734i	0.496902	−	0.592185i
$204$	−0.0304630	−	0.348194i	−0.00213284	−	0.0243784i
$205$	−10.5551	−	8.71743i	−0.737197	−	0.608852i
$206$	−4.15924	+	11.4274i	−0.289788	+	0.796186i
$207$	1.48274	−	4.07379i	0.103057	−	0.283148i
$208$	1.85849	−	3.21900i	0.128863	−	0.223197i
$209$	−2.44824	−	3.49645i	−0.169348	−	0.241854i
$210$	0.842736	−	5.00736i	0.0581543	−	0.345540i
$211$	4.71596	+	8.16829i	0.324660	+	0.562328i	0.981444	−	0.191751i	$-0.0614167\pi$
$211$	4.71596	+	8.16829i	0.324660	+	0.562328i	−0.656783	+	0.754079i	$0.728083\pi$
$212$	−3.53413	+	0.946967i	−0.242725	+	0.0650379i
$213$	5.63358	+	3.94468i	0.386007	+	0.270285i
$214$	−17.0757	−	4.57543i	−1.16727	−	0.312770i
$215$	−1.04928	−	0.594943i	−0.0715602	−	0.0405748i
$216$	2.87738	+	2.87738i	0.195781	+	0.195781i
$217$	−3.04963	+	1.10997i	−0.207022	+	0.0753499i
$218$	13.0171	−	9.11465i	0.881627	−	0.617322i
$219$	−1.99477	+	2.37727i	−0.134794	+	0.160641i
$220$	0.652731	−	3.87839i	0.0440071	−	0.261481i
$221$			1.73700i			0.116843i
$222$	−4.28453	+	1.53008i	−0.287559	+	0.102692i
$223$	−17.6658	−	17.6658i	−1.18299	−	1.18299i	−0.978966	−	0.204022i	$-0.934599\pi$
$223$	−17.6658	−	17.6658i	−1.18299	−	1.18299i	−0.204022	−	0.978966i	$-0.565401\pi$
$224$	−0.264617	+	3.02458i	−0.0176805	+	0.202089i
$225$	−7.98868	−	9.22455i	−0.532579	−	0.614970i
$226$	−4.40258	−	0.776294i	−0.292856	−	0.0516383i
$227$	4.43597	+	12.1877i	0.294426	+	0.808928i	0.995406	+	0.0957471i	$0.0305240\pi$
$227$	4.43597	+	12.1877i	0.294426	+	0.808928i	−0.700980	+	0.713181i	$0.747254\pi$
$228$	−1.81509			−0.120207
$229$	6.43623	+	17.6834i	0.425318	+	1.16855i	0.948624	+	0.316406i	$0.102476\pi$
$229$	6.43623	+	17.6834i	0.425318	+	1.16855i	−0.523306	+	0.852145i	$0.675301\pi$
$230$	−1.32935	+	3.74289i	−0.0876547	+	0.246799i
$231$	−0.693570	−	3.93343i	−0.0456335	−	0.258801i
$232$	−0.938915	−	3.50408i	−0.0616428	−	0.230054i
$233$	17.0044	+	4.55632i	1.11400	+	0.298494i	0.768452	−	0.639908i	$-0.221028\pi$
$233$	17.0044	+	4.55632i	1.11400	+	0.298494i	0.345545	+	0.938402i	$0.387694\pi$
$234$	−5.83111	−	6.94925i	−0.381192	−	0.454287i
$235$	−2.66020	+	10.2469i	−0.173533	+	0.668433i
$236$	6.34139	−	1.69917i	0.412790	−	0.110607i
$237$	5.62354	+	2.04680i	0.365288	+	0.132954i
$238$	−0.599625	−	1.28590i	−0.0388679	−	0.0833525i
$239$	16.3440	−	23.3417i	1.05721	−	1.50985i	0.210640	−	0.977564i	$-0.432445\pi$
$239$	16.3440	−	23.3417i	1.05721	−	1.50985i	0.846566	−	0.532283i	$-0.178666\pi$
$240$	−1.19178	−	1.17334i	−0.0769291	−	0.0757390i
$241$	17.5907	−	1.53899i	1.13312	−	0.0991348i	0.494870	−	0.868967i	$-0.335216\pi$
$241$	17.5907	−	1.53899i	1.13312	−	0.0991348i	0.638246	+	0.769833i	$0.279660\pi$
$242$	1.37293	+	7.78630i	0.0882555	+	0.500522i
$243$	13.9640	−	6.51151i	0.895790	−	0.417714i
$244$	5.76288	+	12.3585i	0.368930	+	0.791174i
$245$	−0.899330	−	4.87768i	−0.0574561	−	0.311624i
$246$	−3.75089	+	2.62640i	−0.239148	+	0.167453i
$247$	8.98598	+	0.786171i	0.571764	+	0.0500229i
$248$	−0.276653	+	1.03248i	−0.0175675	+	0.0655628i
$249$	−1.20674	+	2.09014i	−0.0764742	+	0.132457i
$250$	7.38490	+	8.39423i	0.467062	+	0.530898i
$251$	0.462964	−	1.72780i	0.0292220	−	0.109058i	−0.949774	−	0.312935i	$-0.898688\pi$
$251$	0.462964	−	1.72780i	0.0292220	−	0.109058i	0.978996	+	0.203877i	$0.0653544\pi$
$252$	6.71570	+	3.13158i	0.423049	+	0.197271i
$253$			3.12428i			0.196422i
$254$	4.64969	−	9.97130i	0.291748	−	0.625655i
$255$	0.756482	+	0.196391i	0.0473727	+	0.0122985i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.02327	+	1.21949i	0.0638299	+	0.0760695i	0.797015	−	0.603960i	$-0.206411\pi$
$257$	1.02327	+	1.21949i	0.0638299	+	0.0760695i	−0.733185	+	0.680030i	$0.761967\pi$
$258$	−0.285292	+	0.285292i	−0.0177615	+	0.0177615i
$259$	−14.2191	+	11.7850i	−0.883534	+	0.732287i
$260$	5.39195	+	6.32507i	0.334394	+	0.392264i
$261$	−8.81999	−	0.771649i	−0.545944	−	0.0477639i
$262$	−1.61630	−	18.4744i	−0.0998552	−	1.14135i
$263$	14.0685	+	20.0920i	0.867503	+	1.23892i	0.969734	+	0.244162i	$0.0785129\pi$
$263$	14.0685	+	20.0920i	0.867503	+	1.23892i	−0.102231	+	0.994761i	$0.532598\pi$
$264$	−1.19227	−	0.555964i	−0.0733790	−	0.0342172i
$265$	0.649491	−	8.15550i	0.0398979	−	0.500988i
$266$	−6.92370	+	2.52002i	−0.424519	+	0.154512i
$267$	7.10740	−	4.10346i	0.434966	−	0.251128i
$268$	−3.46807	+	4.95292i	−0.211846	+	0.302548i
$269$	11.2601	+	6.50101i	0.686539	+	0.396374i	0.802314	−	0.596902i	$-0.203602\pi$
$269$	11.2601	+	6.50101i	0.686539	+	0.396374i	−0.115775	+	0.993275i	$0.536935\pi$
$270$	−8.21634	+	3.90961i	−0.500031	+	0.237931i
$271$	15.1832	−	12.7402i	0.922315	−	0.773914i	−0.0521065	−	0.998642i	$-0.516594\pi$
$271$	15.1832	−	12.7402i	0.922315	−	0.773914i	0.974422	+	0.224727i	$0.0721491\pi$
$272$	−0.460215	−	0.0811484i	−0.0279047	−	0.00492034i
$273$	7.30986	+	4.22035i	0.442413	+	0.255427i
$274$	−8.58810	+	4.00469i	−0.518826	+	0.241932i
$275$	7.68372	+	4.27787i	0.463346	+	0.257965i
$276$	1.08831	+	0.762040i	0.0655083	+	0.0458694i
$277$	−13.0131	−	10.9193i	−0.781880	−	0.656076i	0.161841	−	0.986817i	$-0.448257\pi$
$277$	−13.0131	−	10.9193i	−0.781880	−	0.656076i	−0.943721	+	0.330741i	$0.892701\pi$
$278$	11.3161	+	9.49534i	0.678695	+	0.569493i
$279$	2.13697	+	1.49632i	0.127937	+	0.0895824i
$280$	−6.17511	−	2.82111i	−0.369034	−	0.168593i
$281$	−23.1231	+	10.7825i	−1.37941	+	0.643228i	−0.963876	−	0.266351i	$-0.914182\pi$
$281$	−23.1231	+	10.7825i	−1.37941	+	0.643228i	−0.415531	+	0.909579i	$0.636404\pi$
$282$	3.06668	+	1.77055i	0.182618	+	0.105434i
$283$	14.8747	+	2.62280i	0.884207	+	0.155909i	0.597270	−	0.802040i	$-0.296252\pi$
$283$	14.8747	+	2.62280i	0.884207	+	0.155909i	0.286936	+	0.957950i	$0.407363\pi$
$284$	7.04380	−	5.91045i	0.417973	−	0.350721i
$285$	1.35837	−	3.82460i	0.0804630	−	0.226550i
$286$	5.66176	+	3.26882i	0.334787	+	0.193289i
$287$	−10.6614	+	15.2261i	−0.629325	+	0.898769i
$288$	2.11361	−	1.22029i	0.124546	−	0.0719064i
$289$	−15.7696	+	5.73965i	−0.927621	+	0.337627i
$290$	8.08616	+	0.643969i	0.474835	+	0.0378151i
$291$	0.155806	+	0.0726537i	0.00913353	+	0.00425904i
$292$	2.37984	+	3.39877i	0.139270	+	0.198898i
$293$	0.967570	+	11.0594i	0.0565260	+	0.646096i	0.970624	+	0.240602i	$0.0773448\pi$
$293$	0.967570	+	11.0594i	0.0565260	+	0.646096i	−0.914098	+	0.405494i	$0.867100\pi$
$294$	−1.65272	−	0.144594i	−0.0963885	−	0.00843291i
$295$	−1.16540	+	14.6337i	−0.0678523	+	0.852005i
$296$	0.493383	+	6.06272i	0.0286773	+	0.352388i
$297$	−5.06091	+	5.06091i	−0.293664	+	0.293664i
$298$	−8.98317	−	10.7057i	−0.520381	−	0.620166i
$299$	−5.05782	−	4.24401i	−0.292501	−	0.245438i
$300$	3.36427	−	1.63312i	0.194236	−	0.0942881i
$301$	−0.692162	+	1.48435i	−0.0398956	+	0.0855563i
$302$		−	11.5101i		−	0.662332i
$303$	−10.2622	−	4.78535i	−0.589549	−	0.274911i
$304$	−0.628098	+	2.34409i	−0.0360239	+	0.134443i
$305$	−30.3536	+	2.89421i	−1.73804	+	0.165722i
$306$	−0.570261	+	0.987721i	−0.0325996	+	0.0564642i
$307$	−7.57029	+	28.2527i	−0.432059	+	1.61247i	0.315948	+	0.948776i	$0.397677\pi$
$307$	−7.57029	+	28.2527i	−0.432059	+	1.61247i	−0.748007	+	0.663690i	$0.768989\pi$
$308$	−5.31982	−	0.465424i	−0.303125	−	0.0265200i
$309$	−7.45065	+	5.21700i	−0.423853	+	0.296785i
$310$	−1.96852	−	1.35563i	−0.111804	−	0.0769944i
$311$	−8.95742	−	19.2092i	−0.507929	−	1.08926i	−0.978377	−	0.206829i	$-0.933686\pi$
$311$	−8.95742	−	19.2092i	−0.507929	−	1.08926i	0.470448	−	0.882427i	$-0.344092\pi$
$312$	2.51961	−	1.17491i	0.142645	−	0.0665163i
$313$	−2.17804	−	12.3523i	−0.123110	−	0.698192i	−0.982412	−	0.186724i	$-0.940213\pi$
$313$	−2.17804	−	12.3523i	−0.123110	−	0.698192i	0.859302	−	0.511468i	$-0.170898\pi$
$314$	−4.32589	+	0.378466i	−0.244124	+	0.0213581i
$315$	−11.6245	+	11.8071i	−0.654965	+	0.665257i
$316$	4.58931	−	6.55422i	0.258169	−	0.368704i
$317$	12.0373	+	25.8140i	0.676079	+	1.44986i	0.881981	+	0.471284i	$0.156209\pi$
$317$	12.0373	+	25.8140i	0.676079	+	1.44986i	−0.205902	+	0.978573i	$0.566013\pi$
$318$	−2.57153	−	0.935960i	−0.144204	−	0.0524860i
$319$	6.16318	−	1.65142i	0.345072	−	0.0924617i
$320$	−1.92772	+	1.13310i	−0.107763	+	0.0633420i
$321$	−8.49905	−	10.1288i	−0.474371	−	0.565333i
$322$	5.20936	+	1.39584i	0.290306	+	0.0777873i
$323$	−0.293520	−	1.09543i	−0.0163319	−	0.0609513i
$324$	−0.742903	−	4.21321i	−0.0412724	−	0.234067i
$325$	−17.3629	+	6.62792i	−0.963118	+	0.367651i
$326$	0.537308	+	1.47624i	0.0297587	+	0.0817614i
$327$	11.8855			0.657267
$328$	2.09389	+	5.75293i	0.115616	+	0.317652i
$329$	14.1561	+	2.49610i	0.780450	+	0.137614i
$330$	2.06375	−	2.09618i	0.113605	−	0.115391i
$331$	0.450411	−	5.14822i	0.0247568	−	0.282972i	−0.973718	−	0.227758i	$-0.926860\pi$
$331$	0.450411	−	5.14822i	0.0247568	−	0.282972i	0.998475	−	0.0552136i	$-0.0175840\pi$
$332$	2.28172	+	2.28172i	0.125226	+	0.125226i
$333$	14.3161	+	3.92920i	0.784516	+	0.215319i
$334$		−	10.4217i		−	0.570251i
$335$	−7.84095	−	11.0143i	−0.428397	−	0.601774i
$336$	−1.45967	+	1.73957i	−0.0796318	+	0.0949015i
$337$	−21.3698	+	14.9633i	−1.16409	+	0.815103i	−0.985642	−	0.168846i	$-0.945996\pi$
$337$	−21.3698	+	14.9633i	−1.16409	+	0.815103i	−0.178446	+	0.983950i	$0.557107\pi$
$338$	−0.766719	+	0.279063i	−0.0417040	+	0.0151790i
$339$	−2.36433	−	2.36433i	−0.128413	−	0.128413i
$340$	0.515403	−	0.908997i	0.0279517	−	0.0492973i
$341$	−1.81599	−	0.486594i	−0.0983416	−	0.0263506i
$342$	4.85165	+	3.39716i	0.262347	+	0.183698i
$343$	14.0237	−	3.75764i	0.757209	−	0.202893i
$344$	0.269717	+	0.467163i	0.0145422	+	0.0251878i
$345$	−2.42017	+	1.72289i	−0.130297	+	0.0927574i
$346$	−12.2024	−	17.4269i	−0.656006	−	0.936873i
$347$	−16.5600	+	28.6827i	−0.888985	+	1.53977i	−0.0479084	+	0.998852i	$0.515256\pi$
$347$	−16.5600	+	28.6827i	−0.888985	+	1.53977i	−0.841077	+	0.540916i	$0.818078\pi$
$348$	0.928002	−	2.54966i	0.0497461	−	0.136676i
$349$	3.30065	−	9.06845i	0.176680	−	0.485423i	−0.819467	−	0.573126i	$-0.805730\pi$
$349$	3.30065	−	9.06845i	0.176680	−	0.485423i	0.996147	+	0.0877031i	$0.0279527\pi$
$350$	10.5657	−	10.9004i	0.564761	−	0.582652i
$351$	−1.31825	−	15.0677i	−0.0703631	−	0.804254i
$352$	−1.13057	+	1.34736i	−0.0602598	+	0.0718148i
$353$	−10.9712	+	1.93452i	−0.583937	+	0.102964i	−0.457810	−	0.889050i	$-0.651366\pi$
$353$	−10.9712	+	1.93452i	−0.583937	+	0.102964i	−0.126128	+	0.992014i	$0.540255\pi$
$354$	4.61417	+	1.67942i	0.245241	+	0.0892602i
$355$	7.18258	+	19.2653i	0.381212	+	1.02250i
$356$	−2.83994	−	10.5988i	−0.150516	−	0.561735i
$357$	0.184276	−	1.04508i	0.00975291	−	0.0553115i
$358$	1.14320	−	13.0668i	0.0604199	−	0.690603i
$359$	4.01803	−	2.31981i	0.212064	−	0.122435i	−0.390206	−	0.920727i	$-0.627596\pi$
$359$	4.01803	−	2.31981i	0.212064	−	0.122435i	0.602270	+	0.798292i	$0.294263\pi$
$360$	0.989521	+	5.36685i	0.0521523	+	0.282858i
$361$	12.9115	−	2.27665i	0.679555	−	0.119824i
$362$	5.64870	+	9.78384i	0.296889	+	0.514227i
$363$	−2.49916	+	5.35948i	−0.131172	+	0.281300i
$364$	7.97988	−	7.97988i	0.418259	−	0.418259i
$365$	−8.94262	+	2.47105i	−0.468078	+	0.129340i
$366$	−1.77104	+	10.0441i	−0.0925738	+	0.525012i
$367$	0.658763	−	0.0576343i	0.0343872	−	0.00300849i	−0.0699492	−	0.997551i	$-0.522284\pi$
$367$	0.658763	−	0.0576343i	0.0343872	−	0.00300849i	0.104336	+	0.994542i	$0.466728\pi$
$368$	1.36073	−	1.14179i	0.0709331	−	0.0595200i
$369$	14.9416			0.777828
$370$	−13.1441	−	3.49758i	−0.683328	−	0.181831i
$371$	−11.1086			−0.576731
$372$	−0.612436	+	0.513895i	−0.0317533	+	0.0266442i
$373$	−33.3514	+	2.91787i	−1.72687	+	0.151082i	−0.906906	−	0.421333i	$-0.861562\pi$
$373$	−33.3514	+	2.91787i	−1.72687	+	0.151082i	−0.819964	+	0.572415i	$0.806007\pi$
$374$	0.142729	−	0.809454i	0.00738032	−	0.0418559i
$375$	0.923426	+	8.31109i	0.0476855	+	0.429183i
$376$	3.34777	−	3.34777i	0.172648	−	0.172648i
$377$	−5.69860	+	12.2207i	−0.293493	+	0.629398i
$378$	6.17738	+	10.6995i	0.317730	+	0.550325i
$379$	−31.4688	+	5.54879i	−1.61644	+	0.285022i	−0.907439	−	0.420184i	$-0.861966\pi$
$379$	−31.4688	+	5.54879i	−1.61644	+	0.285022i	−0.709002	+	0.705206i	$0.750855\pi$
$380$	−4.46922	−	3.07774i	−0.229266	−	0.157885i
$381$	7.12646	−	4.11446i	0.365099	−	0.210790i
$382$	0.198762	−	2.27185i	0.0101695	−	0.116238i
$383$	2.15248	−	12.2073i	0.109987	−	0.623765i	−0.879124	−	0.476593i	$-0.841872\pi$
$383$	2.15248	−	12.2073i	0.109987	−	0.623765i	0.989111	−	0.147172i	$-0.0470172\pi$
$384$	0.193581	+	0.722455i	0.00987865	+	0.0368676i
$385$	4.96193	−	10.8612i	0.252883	−	0.553536i
$386$	−4.65851	−	1.69556i	−0.237112	−	0.0863016i
$387$	1.29653	−	0.228614i	0.0659065	−	0.0116211i
$388$	0.147744	−	0.176074i	0.00750057	−	0.00893883i
$389$	−0.598139	−	6.83676i	−0.0303269	−	0.346638i	−0.996165	−	0.0874922i	$-0.972115\pi$
$389$	−0.598139	−	6.83676i	−0.0303269	−	0.346638i	0.965838	−	0.259145i	$-0.0834408\pi$
$390$	0.590060	+	6.18838i	0.0298788	+	0.313361i
$391$	−0.283910	+	0.780036i	−0.0143579	+	0.0394481i
$392$	−0.758646	+	2.08436i	−0.0383174	+	0.105276i
$393$	6.93526	−	12.0122i	0.349837	−	0.605936i
$394$	−15.2377	−	21.7617i	−0.767663	−	1.09634i
$395$	10.3760	+	14.5752i	0.522071	+	0.733360i
$396$	2.14632	+	3.71754i	0.107857	+	0.186813i
$397$	36.1107	−	9.67583i	1.81234	−	0.485616i	0.816553	−	0.577271i	$-0.195882\pi$
$397$	36.1107	−	9.67583i	1.81234	−	0.485616i	0.995791	+	0.0916550i	$0.0292157\pi$
$398$	−10.5957	−	7.41917i	−0.531113	−	0.371889i
$399$	−5.32309	−	1.42632i	−0.266488	−	0.0714051i
$400$	−0.944906	−	4.90990i	−0.0472453	−	0.245495i
$401$	−0.547394	−	0.547394i	−0.0273356	−	0.0273356i	0.693307	−	0.720642i	$-0.256153\pi$
$401$	−0.547394	−	0.547394i	−0.0273356	−	0.0273356i	−0.720642	+	0.693307i	$0.756153\pi$
$402$	−4.24962	+	1.54673i	−0.211952	+	0.0771441i
$403$	3.25457	−	2.27888i	0.162122	−	0.113519i
$404$	−9.73119	+	11.5972i	−0.484145	+	0.576981i
$405$	9.43369	+	1.58769i	0.468764	+	0.0788928i
$406$		−	11.0142i		−	0.546624i
$407$	−10.6635	+	0.867791i	−0.528569	+	0.0430148i
$408$	−0.247151	−	0.247151i	−0.0122358	−	0.0122358i
$409$	−2.55732	+	29.2303i	−0.126451	+	1.44534i	0.622449	+	0.782661i	$0.286138\pi$
$409$	−2.55732	+	29.2303i	−0.126451	+	1.44534i	−0.748900	+	0.662683i	$0.769418\pi$
$410$	−13.6891	+	0.106720i	−0.676056	+	0.00527050i
$411$	−6.97975	−	1.23072i	−0.344286	−	0.0607068i
$412$	4.15924	+	11.4274i	0.204911	+	0.562989i
$413$	19.9325			0.980816
$414$	−1.48274	−	4.07379i	−0.0728726	−	0.200216i
$415$	−6.51544	+	3.10026i	−0.319830	+	0.152186i
$416$	−0.645446	−	3.66051i	−0.0316456	−	0.179471i
$417$	2.85961	+	10.6722i	0.140036	+	0.522620i
$418$	−4.12293	−	1.10474i	−0.201659	−	0.0540344i
$419$	−25.2606	−	30.1044i	−1.23406	−	1.47070i	−0.831708	−	0.555213i	$-0.812637\pi$
$419$	−25.2606	−	30.1044i	−1.23406	−	1.47070i	−0.402354	−	0.915484i	$-0.631808\pi$
$420$	−2.57309	−	4.37756i	−0.125554	−	0.213603i
$421$	−11.6967	+	3.13413i	−0.570063	+	0.152748i	−0.532326	−	0.846540i	$-0.678682\pi$
$421$	−11.6967	+	3.13413i	−0.570063	+	0.152748i	−0.0377377	+	0.999288i	$0.512015\pi$
$422$	8.86311	+	3.22591i	0.431449	+	0.157035i
$423$	−4.88329	−	10.4722i	−0.237434	−	0.509178i
$424$	−2.09860	+	2.99711i	−0.101917	+	0.145553i
$425$	1.52965	+	1.76629i	0.0741987	+	0.0856775i
$426$	6.85116	−	0.599399i	0.331940	−	0.0290410i
$427$	7.18924	+	40.7722i	0.347912	+	1.97311i
$428$	−16.0218	+	7.47109i	−0.774443	+	0.361129i
$429$	2.06651	+	4.43164i	0.0997718	+	0.213961i
$430$	−1.18622	+	0.218710i	−0.0572044	+	0.0105471i
$431$	29.9046	−	20.9394i	1.44045	−	1.00862i	0.446981	−	0.894544i	$-0.352499\pi$
$431$	29.9046	−	20.9394i	1.44045	−	1.00862i	0.993472	−	0.114072i	$-0.0363896\pi$
$432$	4.05375	+	0.354657i	0.195036	+	0.0170634i
$433$	−2.08354	+	7.77586i	−0.100128	+	0.373684i	−0.997747	−	0.0670888i	$-0.978629\pi$
$433$	−2.08354	+	7.77586i	−0.100128	+	0.373684i	0.897619	+	0.440773i	$0.145296\pi$
$434$	−1.62267	+	2.81055i	−0.0778908	+	0.134911i
$435$	4.67794	+	3.86351i	0.224290	+	0.185241i
$436$	4.11287	−	15.3494i	0.196971	−	0.735105i
$437$	3.90684	+	1.82179i	0.186890	+	0.0871481i
$438$			3.10330i			0.148282i
$439$	−13.8848	+	29.7760i	−0.662683	+	1.42113i	0.231234	+	0.972898i	$0.425724\pi$
$439$	−13.8848	+	29.7760i	−0.662683	+	1.42113i	−0.893918	+	0.448231i	$0.852054\pi$
$440$	−1.99296	−	3.39058i	−0.0950105	−	0.161640i
$441$	4.14702	+	3.47976i	0.197477	+	0.165703i
$442$	1.11652	+	1.33062i	0.0531075	+	0.0632911i
$443$	−26.6048	+	26.6048i	−1.26403	+	1.26403i	−0.314913	+	0.949121i	$0.601975\pi$
$443$	−26.6048	+	26.6048i	−1.26403	+	1.26403i	−0.949121	+	0.314913i	$0.898025\pi$
$444$	−2.29863	+	3.92615i	−0.109088	+	0.186327i
$445$	24.4582	+	1.94781i	1.15943	+	0.0923352i
$446$	−24.8881	−	2.17743i	−1.17849	−	0.103104i
$447$	−0.911014	−	10.4129i	−0.0430895	−	0.492515i
$448$	1.74146	+	2.48706i	0.0822761	+	0.117502i
$449$	−14.3688	−	6.70030i	−0.678107	−	0.316207i	0.0528769	−	0.998601i	$-0.483161\pi$
$449$	−14.3688	−	6.70030i	−0.678107	−	0.316207i	−0.730984	+	0.682394i	$0.760939\pi$
$450$	−12.0491	−	1.93139i	−0.568001	−	0.0910467i
$451$	−10.1186	+	3.68287i	−0.476466	+	0.173419i
$452$	−3.87157	+	2.23525i	−0.182103	+	0.105137i
$453$	4.93785	−	7.05198i	0.232000	−	0.331331i
$454$	11.2323	+	6.48496i	0.527157	+	0.304354i
$455$	10.8426	+	22.7865i	0.508308	+	1.06825i
$456$	−1.39044	+	1.16672i	−0.0651133	+	0.0546366i
$457$	−7.13291	−	1.25772i	−0.333663	−	0.0588339i	0.00430666	−	0.999991i	$-0.498629\pi$
$457$	−7.13291	−	1.25772i	−0.333663	−	0.0588339i	−0.337970	+	0.941157i	$0.609740\pi$
$458$	16.2971	+	9.40914i	0.761514	+	0.439660i
$459$	−1.72345	+	0.803657i	−0.0804436	+	0.0375115i
$460$	1.38754	+	3.72171i	0.0646946	+	0.173526i
$461$	19.5263	+	13.6725i	0.909430	+	0.636790i	0.931805	−	0.362960i	$-0.118234\pi$
$461$	19.5263	+	13.6725i	0.909430	+	0.636790i	−0.0223745	+	0.999750i	$0.507123\pi$
$462$	−3.05966	−	2.56736i	−0.142348	−	0.119445i
$463$	−16.7847	−	14.0840i	−0.780049	−	0.654539i	0.163212	−	0.986591i	$-0.447815\pi$
$463$	−16.7847	−	14.0840i	−0.780049	−	0.654539i	−0.943261	+	0.332052i	$0.892259\pi$
$464$	−2.97163	−	2.08076i	−0.137954	−	0.0965967i
$465$	−0.624502	−	1.67506i	−0.0289606	−	0.0776790i
$466$	15.9549	−	7.43988i	0.739096	−	0.344646i
$467$	−5.89546	−	3.40375i	−0.272810	−	0.157507i	0.357354	−	0.933969i	$-0.383679\pi$
$467$	−5.89546	−	3.40375i	−0.272810	−	0.157507i	−0.630164	+	0.776462i	$0.717012\pi$
$468$	−8.93378	−	1.57527i	−0.412964	−	0.0728167i
$469$	−14.0628	+	11.8001i	−0.649361	+	0.544878i
$470$	4.54874	+	9.55952i	0.209818	+	0.440948i
$471$	−2.81274	−	1.62393i	−0.129604	−	0.0748270i
$472$	3.76558	−	5.37781i	0.173325	−	0.247534i
$473$	−0.821675	+	0.474394i	−0.0377806	+	0.0218127i
$474$	5.62354	−	2.04680i	0.258298	−	0.0940126i
$475$	9.82981	−	7.11385i	0.451023	−	0.326406i
$476$	−1.28590	−	0.599625i	−0.0589391	−	0.0274837i
$477$	5.12181	+	7.31471i	0.234512	+	0.334917i
$478$	−2.48350	−	28.3865i	−0.113592	−	1.29837i
$479$	9.41592	+	0.823786i	0.430224	+	0.0376397i	0.300212	−	0.953873i	$-0.402943\pi$
$479$	9.41592	+	0.823786i	0.430224	+	0.0376397i	0.130013	+	0.991512i	$0.458498\pi$
$480$	−1.66717	−	0.132771i	−0.0760954	−	0.00606012i
$481$	13.0804	−	18.4416i	0.596414	−	0.840865i
$482$	12.4860	−	12.4860i	0.568722	−	0.568722i
$483$	2.59284	+	3.09002i	0.117978	+	0.140601i
$484$	6.05666	+	5.08214i	0.275303	+	0.231007i
$485$	0.260441	+	0.443084i	0.0118260	+	0.0201194i
$486$	6.51151	−	13.9640i	0.295368	−	0.633419i
$487$		−	13.6520i		−	0.618632i	−0.950959	−	0.309316i	$-0.899900\pi$
$487$		−	13.6520i		−	0.618632i	0.950959	−	0.309316i	$-0.100100\pi$
$488$	12.3585	+	5.76288i	0.559444	+	0.260873i
$489$	−0.304113	+	1.13496i	−0.0137525	+	0.0513249i
$490$	−3.82424	−	3.15844i	−0.172762	−	0.142684i
$491$	2.41488	−	4.18270i	0.108982	−	0.188762i	−0.806376	−	0.591403i	$-0.798574\pi$
$491$	2.41488	−	4.18270i	0.108982	−	0.188762i	0.915358	+	0.402641i	$0.131908\pi$
$492$	−1.18513	+	4.42297i	−0.0534298	+	0.199403i
$493$	1.68882	+	0.147753i	0.0760607	+	0.00665445i
$494$	7.38900	−	5.17383i	0.332447	−	0.232782i
$495$	−9.43954	+	1.74043i	−0.424276	+	0.0782265i
$496$	0.451739	+	0.968758i	0.0202837	+	0.0434985i
$497$	25.3017	−	11.7984i	1.13494	−	0.529230i
$498$	0.419097	+	2.37682i	0.0187802	+	0.106508i
$499$	11.4252	−	0.999572i	0.511460	−	0.0447470i	0.171495	−	0.985185i	$-0.445140\pi$
$499$	11.4252	−	0.999572i	0.511460	−	0.0447470i	0.339965	+	0.940438i	$0.389585\pi$
$500$	11.0529	+	1.68343i	0.494300	+	0.0752854i
$501$	4.47093	−	6.38514i	0.199746	−	0.285267i
$502$	−0.755960	−	1.62116i	−0.0337402	−	0.0723560i
$503$	5.76733	+	2.09914i	0.257153	+	0.0935959i	0.467380	−	0.884057i	$-0.345198\pi$
$503$	5.76733	+	2.09914i	0.257153	+	0.0935959i	−0.210227	+	0.977653i	$0.567420\pi$
$504$	7.15746	−	1.91784i	0.318819	−	0.0854272i
$505$	−17.1540	−	29.1838i	−0.763342	−	1.29866i
$506$	2.00825	+	2.39334i	0.0892776	+	0.106397i
$507$	−0.589470	−	0.157948i	−0.0261793	−	0.00701471i
$508$	−2.84756	−	10.6272i	−0.126340	−	0.471507i
$509$	1.59081	+	9.02193i	0.0705114	+	0.399890i	0.999552	+	0.0299134i	$0.00952316\pi$
$509$	1.59081	+	9.02193i	0.0705114	+	0.399890i	−0.929041	+	0.369977i	$0.879366\pi$
$510$	0.705737	−	0.335813i	0.0312505	−	0.0148701i
$511$	4.30854	+	11.8376i	0.190599	+	0.523666i
$512$	1.00000			0.0441942
$513$	3.37750	+	9.27961i	0.149120	+	0.409705i
$514$	1.56774	+	0.276435i	0.0691502	+	0.0121930i
$515$	−27.1916	+	0.211984i	−1.19820	+	0.00934114i
$516$	−0.0351642	+	0.401929i	−0.00154802	+	0.0176939i
$517$	5.88825	+	5.88825i	0.258965	+	0.258965i
$518$	−3.31721	+	18.1677i	−0.145750	+	0.798245i
$519$		−	15.9119i		−	0.698454i
$520$	8.19615	+	1.37941i	0.359425	+	0.0604911i
$521$	−5.53652	+	6.59817i	−0.242559	+	0.289071i	−0.873565	−	0.486707i	$-0.838198\pi$
$521$	−5.53652	+	6.59817i	−0.242559	+	0.289071i	0.631006	+	0.775778i	$0.282642\pi$
$522$	−7.25251	+	5.07826i	−0.317434	+	0.222270i
$523$	−10.3525	+	3.76801i	−0.452685	+	0.164764i	−0.558293	−	0.829644i	$-0.688543\pi$
$523$	−10.3525	+	3.76801i	−0.452685	+	0.164764i	0.105608	+	0.994408i	$0.466321\pi$
$524$	−13.1133	−	13.1133i	−0.572855	−	0.572855i
$525$	11.1497	−	2.14574i	0.486611	−	0.0936478i
$526$	23.6920	+	6.34825i	1.03302	+	0.276797i
$527$	−0.409179	−	0.286510i	−0.0178241	−	0.0124806i
$528$	−1.27070	+	0.340482i	−0.0553000	+	0.0148176i
$529$	9.92236	+	17.1860i	0.431407	+	0.747219i
$530$	−4.74472	−	6.66496i	−0.206097	−	0.289507i
$531$	−9.19022	−	13.1250i	−0.398822	−	0.569576i
$532$	−3.68403	+	6.38092i	−0.159723	+	0.276648i
$533$	7.78296	−	21.3835i	0.337117	−	0.926222i
$534$	2.80693	−	7.71198i	0.121468	−	0.333730i
$535$	−3.75210	−	39.3510i	−0.162217	−	1.70129i
$536$	0.526979	+	6.02339i	0.0227620	+	0.260171i
$537$	6.30609	−	7.51531i	0.272128	−	0.324310i
$538$	12.8045	−	2.25778i	0.552041	−	0.0973397i
$539$	−3.66610	−	1.33435i	−0.157910	−	0.0574746i
$540$	−3.78103	+	8.27630i	−0.162710	+	0.356155i
$541$	−0.998425	−	3.72617i	−0.0429256	−	0.160201i	0.941136	−	0.338028i	$-0.109760\pi$
$541$	−0.998425	−	3.72617i	−0.0429256	−	0.160201i	−0.984062	+	0.177827i	$0.943093\pi$
$542$	3.44176	−	19.5192i	0.147836	−	0.838420i
$543$	−0.736448	+	8.41764i	−0.0316040	+	0.361235i
$544$	−0.404707	+	0.233657i	−0.0173517	+	0.0100180i
$545$	29.2650	+	20.1534i	1.25358	+	0.863279i
$546$	8.31247	−	1.46571i	0.355741	−	0.0627267i
$547$	−15.5597	−	26.9501i	−0.665284	−	1.15231i	−0.979208	−	0.202857i	$-0.934977\pi$
$547$	−15.5597	−	26.9501i	−0.665284	−	1.15231i	0.313925	−	0.949448i	$-0.398356\pi$
$548$	−4.00469	+	8.58810i	−0.171072	+	0.366865i
$549$	23.5326	−	23.5326i	1.00435	−	1.00435i
$550$	8.63583	−	1.66196i	0.368233	−	0.0708661i
$551$	1.52873	−	8.66987i	0.0651262	−	0.369349i
$552$	1.32352	−	0.115793i	0.0563327	−	0.00492848i
$553$	18.6094	−	15.6151i	0.791352	−	0.664023i
$554$	−16.9874			−0.721724
$555$	−6.55261	−	7.78172i	−0.278143	−	0.330315i
$556$	14.7721			0.626478
$557$	20.2033	−	16.9526i	0.856041	−	0.718304i	−0.105070	−	0.994465i	$-0.533507\pi$
$557$	20.2033	−	16.9526i	0.856041	−	0.718304i	0.961111	+	0.276161i	$0.0890622\pi$
$558$	2.59883	−	0.227368i	0.110017	−	0.00962526i
$559$	0.348176	−	1.97460i	0.0147263	−	0.0835168i
$560$	−6.54378	+	1.80819i	−0.276525	+	0.0764101i
$561$	0.434703	−	0.434703i	0.0183532	−	0.0183532i
$562$	−10.7825	+	23.1231i	−0.454831	+	0.975388i
$563$	19.6354	+	34.0096i	0.827535	+	1.43333i	0.899967	+	0.435959i	$0.143591\pi$
$563$	19.6354	+	34.0096i	0.827535	+	1.43333i	−0.0724318	+	0.997373i	$0.523076\pi$
$564$	3.48729	−	0.614904i	0.146842	−	0.0258921i
$565$	−1.81254	−	9.83065i	−0.0762541	−	0.413578i
$566$	13.0806	−	7.55206i	0.549817	−	0.317437i
$567$	1.13209	−	12.9398i	0.0475432	−	0.543421i
$568$	1.59670	−	9.05534i	0.0669960	−	0.379953i
$569$	−5.05635	−	18.8705i	−0.211973	−	0.791094i	−0.987210	−	0.159424i	$-0.949036\pi$
$569$	−5.05635	−	18.8705i	−0.211973	−	0.791094i	0.775237	−	0.631670i	$-0.217630\pi$
$570$	−1.41784	−	3.80296i	−0.0593866	−	0.159288i
$571$	−6.05300	−	2.20311i	−0.253310	−	0.0921974i	0.212244	−	0.977217i	$-0.431923\pi$
$571$	−6.05300	−	2.20311i	−0.253310	−	0.0921974i	−0.465554	+	0.885019i	$0.654145\pi$
$572$	6.43832	−	1.13525i	0.269200	−	0.0474672i
$573$	1.09640	−	1.30664i	0.0458030	−	0.0545858i
$574$	1.62002	+	18.5169i	0.0676184	+	0.772881i
$575$	−8.88048	+	0.138472i	−0.370342	+	0.00577468i
$576$	0.834729	−	2.29340i	0.0347804	−	0.0955583i
$577$	1.91031	−	5.24855i	0.0795274	−	0.218500i	−0.893557	−	0.448951i	$-0.851798\pi$
$577$	1.91031	−	5.24855i	0.0795274	−	0.218500i	0.973084	+	0.230451i	$0.0740201\pi$
$578$	−8.39081	+	14.5333i	−0.349012	+	0.604506i
$579$	−2.12676	−	3.03733i	−0.0883853	−	0.126227i
$580$	6.60829	−	4.70437i	0.274394	−	0.195338i
$581$	4.89857	+	8.48457i	0.203227	+	0.351999i
$582$	0.166056	−	0.0444944i	0.00688322	−	0.00184435i
$583$	−5.27150	−	3.69114i	−0.218323	−	0.152872i
$584$	4.00775	+	1.07387i	0.165842	+	0.0444372i
$585$	10.0051	−	17.6456i	0.413660	−	0.729556i
$586$	7.85003	+	7.85003i	0.324282	+	0.324282i
$587$	12.9546	−	4.71510i	0.534694	−	0.194613i	−0.0605389	−	0.998166i	$-0.519282\pi$
$587$	12.9546	−	4.71510i	0.534694	−	0.194613i	0.595233	+	0.803553i	$0.297060\pi$
$588$	−1.35900	+	0.951582i	−0.0560442	+	0.0392426i
$589$	−1.66739	+	1.98712i	−0.0687038	+	0.0818779i
$590$	8.51359	+	11.9591i	0.350499	+	0.492350i
$591$		−	19.8699i		−	0.817336i
$592$	4.27499	+	4.32717i	0.175701	+	0.177846i
$593$	14.3975	+	14.3975i	0.591234	+	0.591234i	0.937965	−	0.346731i	$-0.112708\pi$
$593$	14.3975	+	14.3975i	0.591234	+	0.591234i	−0.346731	+	0.937965i	$0.612708\pi$
$594$	−0.623792	+	7.12998i	−0.0255945	+	0.292546i
$595$	2.22581	−	2.26079i	0.0912495	−	0.0926834i
$596$	−13.7630	−	2.42679i	−0.563755	−	0.0994052i
$597$	−3.30889	−	9.09111i	−0.135424	−	0.372074i
$598$	−6.60251			−0.269997
$599$	−12.2453	−	33.6436i	−0.500328	−	1.37464i	−0.890956	−	0.454090i	$-0.849964\pi$
$599$	−12.2453	−	33.6436i	−0.500328	−	1.37464i	0.390628	−	0.920549i	$-0.372258\pi$
$600$	1.52743	−	3.41355i	0.0623571	−	0.139358i
$601$	2.87031	+	16.2783i	0.117082	+	0.664007i	0.985698	+	0.168521i	$0.0538990\pi$
$601$	2.87031	+	16.2783i	0.117082	+	0.664007i	−0.868616	+	0.495486i	$0.834990\pi$
$602$	0.423893	+	1.58199i	0.0172766	+	0.0644770i
$603$	14.2539	+	3.81933i	0.580465	+	0.155535i
$604$	−7.39855	−	8.81725i	−0.301043	−	0.358769i
$605$	−15.2413	+	8.95873i	−0.619648	+	0.364224i
$606$	−10.9373	+	2.93063i	−0.444296	+	0.119049i
$607$	40.3261	+	14.6775i	1.63679	+	0.595741i	0.986473	−	0.163925i	$-0.0524156\pi$
$607$	40.3261	+	14.6775i	1.63679	+	0.595741i	0.650313	+	0.759667i	$0.274638\pi$
$608$	1.02560	+	2.19941i	0.0415937	+	0.0891980i
$609$	4.72509	−	6.74813i	0.191470	−	0.273448i
$610$	−21.3919	+	21.7280i	−0.866132	+	0.879743i
$611$	−17.5309	+	1.53376i	−0.709224	+	0.0620491i
$612$	0.198050	+	1.12319i	0.00800568	+	0.0454025i
$613$	3.23618	−	1.50906i	0.130708	−	0.0609502i	−0.356164	−	0.934423i	$-0.615916\pi$
$613$	3.23618	−	1.50906i	0.130708	−	0.0609502i	0.486872	+	0.873473i	$0.338138\pi$
$614$	12.3613	+	26.5089i	0.498862	+	1.06981i
$615$	−8.43278	−	5.80725i	−0.340043	−	0.234171i
$616$	−4.37439	+	3.06298i	−0.176249	+	0.123411i
$617$	19.6096	+	1.71562i	0.789452	+	0.0690681i	0.474748	−	0.880122i	$-0.342539\pi$
$617$	19.6096	+	1.71562i	0.789452	+	0.0690681i	0.314704	+	0.949190i	$0.398095\pi$
$618$	−2.35411	+	8.78564i	−0.0946960	+	0.353410i
$619$	1.14636	−	1.98555i	0.0460761	−	0.0798062i	−0.842068	−	0.539372i	$-0.818662\pi$
$619$	1.14636	−	1.98555i	0.0460761	−	0.0798062i	0.888144	+	0.459566i	$0.151995\pi$
$620$	−2.37935	+	0.226871i	−0.0955572	+	0.00911134i
$621$	1.87080	−	6.98193i	0.0750727	−	0.280175i
$622$	−19.2092	−	8.95742i	−0.770221	−	0.359160i
$623$		−	33.3146i		−	1.33472i
$624$	1.17491	−	2.51961i	0.0470341	−	0.100865i
$625$	−11.8189	+	22.0298i	−0.472756	+	0.881193i
$626$	−9.60837	−	8.06238i	−0.384028	−	0.322237i
$627$	−2.05209	−	2.44559i	−0.0819527	−	0.0976674i
$628$	−3.07055	+	3.07055i	−0.122528	+	0.122528i
$629$	−2.74119	−	0.752351i	−0.109299	−	0.0299982i
$630$	−1.31538	+	16.5169i	−0.0524059	+	0.658048i
$631$	−4.59243	−	0.401785i	−0.182822	−	0.0159948i	−0.00462280	−	0.999989i	$-0.501471\pi$
$631$	−4.59243	−	0.401785i	−0.182822	−	0.0159948i	−0.178199	+	0.983994i	$0.557027\pi$
$632$	−0.697353	−	7.97078i	−0.0277392	−	0.317061i
$633$	4.04631	+	5.77872i	0.160826	+	0.229684i
$634$	25.8140	+	12.0373i	1.02520	+	0.478060i
$635$	24.5238	+	1.95304i	0.973198	+	0.0775039i
$636$	−2.57153	+	0.935960i	−0.101968	+	0.0371132i
$637$	7.14017	−	4.12238i	0.282904	−	0.163335i
$638$	3.65976	−	5.22668i	0.144891	−	0.206926i
$639$	−19.4347	−	11.2206i	−0.768824	−	0.443881i
$640$	−0.748377	+	2.10711i	−0.0295822	+	0.0832910i
$641$	12.1681	−	10.2103i	0.480612	−	0.403282i	−0.370035	−	0.929018i	$-0.620654\pi$
$641$	12.1681	−	10.2103i	0.480612	−	0.403282i	0.850648	+	0.525736i	$0.176210\pi$
$642$	−13.0213	−	2.29601i	−0.513910	−	0.0906161i
$643$	−34.2613	−	19.7808i	−1.35113	−	0.780077i	−0.362725	−	0.931896i	$-0.618153\pi$
$643$	−34.2613	−	19.7808i	−1.35113	−	0.780077i	−0.988408	+	0.151820i	$0.951487\pi$
$644$	4.88783	−	2.27923i	0.192608	−	0.0898144i
$645$	−0.820595	−	0.374889i	−0.0323109	−	0.0147613i
$646$	−0.928978	−	0.650477i	−0.0365501	−	0.0255927i
$647$	−12.9007	−	10.8250i	−0.507179	−	0.425574i	0.352956	−	0.935640i	$-0.385176\pi$
$647$	−12.9007	−	10.8250i	−0.507179	−	0.425574i	−0.860135	+	0.510066i	$0.829621\pi$
$648$	−3.27730	−	2.74998i	−0.128744	−	0.108029i
$649$	9.45881	+	6.62313i	0.371291	+	0.259981i
$650$	−9.04038	+	16.2379i	−0.354593	+	0.636903i
$651$	−2.19990	+	1.02583i	−0.0862211	+	0.0402055i
$652$	1.36051	+	0.785491i	0.0532817	+	0.0307622i
$653$	6.83272	+	1.20479i	0.267385	+	0.0471472i	0.305733	−	0.952117i	$-0.401098\pi$
$653$	6.83272	+	1.20479i	0.267385	+	0.0471472i	−0.0383480	+	0.999264i	$0.512210\pi$
$654$	9.10478	−	7.63982i	0.356025	−	0.298741i
$655$	37.4448	−	17.8175i	1.46309	−	0.696186i
$656$	5.30193	+	3.06107i	0.207005	+	0.119515i
$657$	5.80821	−	8.29499i	0.226600	−	0.323618i
$658$	12.4486	−	7.18723i	0.485299	−	0.280187i
$659$	−35.9901	+	13.0993i	−1.40198	+	0.510278i	−0.928764	−	0.370671i	$-0.879128\pi$
$659$	−35.9901	+	13.0993i	−1.40198	+	0.510278i	−0.473212	+	0.880948i	$0.656906\pi$
$660$	0.233525	−	2.93231i	0.00908994	−	0.114140i
$661$	0.642026	+	0.299382i	0.0249719	+	0.0116446i	0.435064	−	0.900399i	$-0.356726\pi$
$661$	0.642026	+	0.299382i	0.0249719	+	0.0116446i	−0.410092	+	0.912044i	$0.634503\pi$
$662$	−2.96418	−	4.23328i	−0.115206	−	0.164531i
$663$	0.113230	+	1.29423i	0.00439750	+	0.0502637i
$664$	3.21456	+	0.281238i	0.124749	+	0.0109141i
$665$	−10.6883	−	12.5380i	−0.414474	−	0.486203i
$666$	13.4924	−	6.19225i	0.522820	−	0.239945i
$667$	−4.55653	+	4.55653i	−0.176430	+	0.176430i
$668$	−6.69895	−	7.98349i	−0.259190	−	0.308891i
$669$	−14.3143	−	12.0111i	−0.553421	−	0.464376i
$670$	−13.0864	−	3.39736i	−0.505570	−	0.131252i
$671$	−10.1361	+	21.7369i	−0.391300	+	0.839145i
$672$			2.27085i			0.0876000i
$673$	23.7829	+	11.0901i	0.916762	+	0.427493i	0.822961	−	0.568098i	$-0.192320\pi$
$673$	23.7829	+	11.0901i	0.916762	+	0.427493i	0.0938011	+	0.995591i	$0.470098\pi$
$674$	−6.75200	+	25.1988i	−0.260077	+	0.970622i
$675$	−14.6095	−	14.1609i	−0.562319	−	0.545052i
$676$	−0.407963	+	0.706612i	−0.0156909	+	0.0271774i
$677$	−9.44104	+	35.2344i	−0.362849	+	1.35417i	0.507465	+	0.861672i	$0.330583\pi$
$677$	−9.44104	+	35.2344i	−0.362849	+	1.35417i	−0.870314	+	0.492497i	$0.836084\pi$
$678$	−3.33095	−	0.291420i	−0.127924	−	0.0111919i
$679$	0.571648	−	0.400272i	0.0219378	−	0.0153610i
$680$	−0.189470	−	1.02763i	−0.00726585	−	0.0394077i
$681$	4.09970	+	8.79184i	0.157101	+	0.336904i
$682$	−1.70391	+	0.794546i	−0.0652460	+	0.0304247i
$683$	−0.683488	−	3.87625i	−0.0261529	−	0.148321i	0.968935	−	0.247315i	$-0.0795484\pi$
$683$	−0.683488	−	3.87625i	−0.0261529	−	0.148321i	−0.995088	+	0.0989948i	$0.968437\pi$
$684$	5.90023	−	0.516204i	0.225601	−	0.0197375i
$685$	−15.0991	−	14.8655i	−0.576906	−	0.567981i
$686$	8.32742	−	11.8928i	0.317942	−	0.454069i
$687$	5.94833	+	12.7562i	0.226943	+	0.486681i
$688$	0.506902	+	0.184497i	0.0193255	+	0.00703389i
$689$	13.1363	−	3.51985i	0.500452	−	0.134096i
$690$	−0.746502	+	2.87547i	−0.0284189	+	0.109467i
$691$	15.8809	+	18.9261i	0.604136	+	0.719981i	0.978256	−	0.207399i	$-0.0664997\pi$
$691$	15.8809	+	18.9261i	0.604136	+	0.719981i	−0.374120	+	0.927380i	$0.622055\pi$
$692$	−20.5494	−	5.50618i	−0.781169	−	0.209314i
$693$	3.37321	+	12.5890i	0.128137	+	0.478216i
$694$	5.75121	+	32.6168i	0.218313	+	1.23811i
$695$	−11.0551	+	31.1266i	−0.419344	+	1.18070i
$696$	−0.928002	−	2.54966i	−0.0351758	−	0.0966448i
$697$	−2.86097			−0.108367
$698$	−3.30065	−	9.06845i	−0.124931	−	0.343246i
$699$	12.9669	+	2.28642i	0.490454	+	0.0864802i
$700$	1.08714	−	15.1417i	0.0410901	−	0.572303i
$701$	−2.38140	+	27.2195i	−0.0899442	+	1.02807i	0.808359	+	0.588690i	$0.200356\pi$
$701$	−2.38140	+	27.2195i	−0.0899442	+	1.02807i	−0.898303	+	0.439377i	$0.855199\pi$
$702$	−10.6952	−	10.6952i	−0.403663	−	0.403663i
$703$	−5.13279	+	13.8404i	−0.193587	+	0.522002i
$704$			1.75886i			0.0662895i
$705$	−1.31414	+	7.80831i	−0.0494932	+	0.294078i
$706$	−7.16094	+	8.53407i	−0.269505	+	0.321184i
$707$	−37.6517	+	26.3640i	−1.41604	+	0.991520i
$708$	4.61417	−	1.67942i	0.173411	−	0.0631165i
$709$	−11.1105	−	11.1105i	−0.417264	−	0.417264i	0.466996	−	0.884260i	$-0.345336\pi$
$709$	−11.1105	−	11.1105i	−0.417264	−	0.417264i	−0.884260	+	0.466996i	$0.845336\pi$
$710$	17.8857	+	10.1412i	0.671238	+	0.380594i
$711$	−18.8623	−	5.05413i	−0.707391	−	0.189545i
$712$	−8.98830	−	6.29367i	−0.336851	−	0.235865i
$713$	1.83401	−	0.491422i	0.0686843	−	0.0184039i
$714$	−0.530601	−	0.919028i	−0.0198573	−	0.0343938i
$715$	−2.42619	+	14.4159i	−0.0907343	+	0.539123i
$716$	−7.52345	−	10.7446i	−0.281165	−	0.401545i
$717$	10.6563	−	18.4572i	0.397965	−	0.689296i
$718$	1.58685	−	4.35982i	0.0592205	−	0.162707i
$719$	3.20927	−	8.81740i	0.119686	−	0.328833i	−0.865354	−	0.501161i	$-0.832906\pi$
$719$	3.20927	−	8.81740i	0.119686	−	0.328833i	0.985040	+	0.172327i	$0.0551287\pi$
$720$	4.20776	+	3.47520i	0.156814	+	0.129513i
$721$	3.21796	+	36.7814i	0.119843	+	1.36981i
$722$	8.42741	−	10.0434i	0.313636	−	0.373776i
$723$	13.0064	−	2.29338i	0.483713	−	0.0852917i
$724$	10.6161	+	3.86394i	0.394544	+	0.143602i
$725$	4.96716	+	17.4451i	0.184476	+	0.647894i
$726$	1.53053	+	5.71203i	0.0568034	+	0.211993i
$727$	5.31574	−	30.1471i	0.197150	−	1.11809i	−0.712174	−	0.702003i	$-0.752289\pi$
$727$	5.31574	−	30.1471i	0.197150	−	1.11809i	0.909324	−	0.416089i	$-0.136600\pi$
$728$	0.983575	−	11.2423i	0.0364537	−	0.416668i
$729$	−1.13509	+	0.655347i	−0.0420405	+	0.0242721i
$730$	−5.26209	+	7.64113i	−0.194759	+	0.282811i
$731$	−0.248256	+	0.0437742i	−0.00918207	+	0.00161905i
$732$	5.09951	+	8.83261i	0.188483	+	0.326463i
$733$	−13.6122	+	29.1915i	−0.502778	+	1.07821i	0.477143	+	0.878826i	$0.341672\pi$
$733$	−13.6122	+	29.1915i	−0.502778	+	1.07821i	−0.979921	+	0.199385i	$0.936105\pi$
$734$	0.467595	−	0.467595i	0.0172593	−	0.0172593i
$735$	−0.988049	−	3.57571i	−0.0364447	−	0.131892i
$736$	0.308453	−	1.74933i	0.0113697	−	0.0644810i
$737$	−10.5943	+	0.926881i	−0.390246	+	0.0341421i
$738$	11.4459	−	9.60427i	0.421330	−	0.353538i
$739$	31.4675			1.15755			0.578775	−	0.815487i	$-0.303531\pi$
$739$	31.4675			1.15755			0.578775	+	0.815487i	$0.303531\pi$
$740$	−12.3172	+	5.76955i	−0.452788	+	0.212093i
$741$	6.74665			0.247844
$742$	−8.50970	+	7.14048i	−0.312401	+	0.262135i
$743$	−39.3302	+	3.44095i	−1.44289	+	0.126236i	−0.781545	−	0.623849i	$-0.785568\pi$
$743$	−39.3302	+	3.44095i	−1.44289	+	0.126236i	−0.661341	+	0.750085i	$0.730012\pi$
$744$	−0.138828	+	0.787332i	−0.00508968	+	0.0288650i
$745$	15.4134	−	27.1841i	0.564705	−	0.995948i
$746$	−23.6731	+	23.6731i	−0.866733	+	0.866733i
$747$	3.32828	−	7.13752i	0.121775	−	0.261148i
$748$	−0.410971	−	0.711822i	−0.0150266	−	0.0260268i
$749$	−52.8578	+	9.32025i	−1.93138	+	0.340554i
$750$	6.04965	+	5.77310i	0.220902	+	0.210804i
$751$	−15.4966	+	8.94694i	−0.565477	+	0.326478i	−0.755341	−	0.655332i	$-0.772529\pi$
$751$	−15.4966	+	8.94694i	−0.565477	+	0.326478i	0.189864	+	0.981810i	$0.439195\pi$
$752$	0.412635	−	4.71644i	0.0150472	−	0.171991i
$753$	0.232321	−	1.31756i	0.00846624	−	0.0480144i
$754$	3.48993	+	13.0246i	0.127096	+	0.474327i
$755$	24.1159	−	8.99098i	0.877666	−	0.327215i
$756$	11.6097	+	4.22558i	0.422240	+	0.153683i
$757$	−48.8615	+	8.61560i	−1.77590	+	0.313139i	−0.963048	−	0.269331i	$-0.913198\pi$
$757$	−48.8615	+	8.61560i	−1.77590	+	0.313139i	−0.812852	+	0.582470i	$0.802086\pi$
$758$	−20.5398	+	24.4783i	−0.746038	+	0.889094i
$759$	0.203664	+	2.32789i	0.00739252	+	0.0844969i
$760$	−5.40195	+	0.515074i	−0.195949	+	0.0186837i
$761$	5.25558	−	14.4396i	0.190515	−	0.523435i	−0.807254	−	0.590205i	$-0.799047\pi$
$761$	5.25558	−	14.4396i	0.190515	−	0.523435i	0.997768	+	0.0667697i	$0.0212693\pi$
$762$	2.81446	−	7.73266i	0.101957	−	0.280125i
$763$	24.1235	−	41.7831i	0.873329	−	1.51265i
$764$	−1.30806	−	1.86810i	−0.0473239	−	0.0675856i
$765$	−2.51492	−	0.423259i	−0.0909270	−	0.0153030i
$766$	−6.19782	−	10.7349i	−0.223936	−	0.387869i
$767$	−23.5708	+	6.31578i	−0.851093	+	0.228050i
$768$	0.612677	+	0.429001i	0.0221081	+	0.0154802i
$769$	−23.1587	−	6.20537i	−0.835126	−	0.223771i	−0.184177	−	0.982893i	$-0.558962\pi$
$769$	−23.1587	−	6.20537i	−0.835126	−	0.223771i	−0.650949	+	0.759122i	$0.725629\pi$
$770$	−3.18036	−	11.5096i	−0.114612	−	0.414777i
$771$	0.841929	+	0.841929i	0.0303213	+	0.0303213i
$772$	−4.65851	+	1.69556i	−0.167663	+	0.0610245i
$773$	−4.78827	+	3.35278i	−0.172222	+	0.120591i	−0.656509	−	0.754318i	$-0.727968\pi$
$773$	−4.78827	+	3.35278i	−0.172222	+	0.120591i	0.484287	+	0.874909i	$0.339079\pi$
$774$	0.846252	−	1.00852i	0.0304179	−	0.0362506i
$775$	1.30261	−	5.18336i	0.0467912	−	0.186192i
$776$		−	0.229849i		−	0.00825109i
$777$	−9.82636	+	9.70788i	−0.352519	+	0.348268i
$778$	−4.85279	−	4.85279i	−0.173981	−	0.173981i
$779$	−1.29488	+	14.8006i	−0.0463940	+	0.530285i
$780$	4.42982	+	4.36129i	0.158613	+	0.156159i
$781$	15.9271	+	2.80837i	0.569915	+	0.100491i
$782$	0.283910	+	0.780036i	0.0101526	+	0.0278940i
$783$	−14.7619			−0.527548
$784$	0.758646	+	2.08436i	0.0270945	+	0.0744416i
$785$	−4.17208	−	8.76793i	−0.148908	−	0.312941i
$786$	−2.40859	−	13.6598i	−0.0859115	−	0.487229i
$787$	11.5983	+	43.2853i	0.413433	+	1.54295i	0.787954	+	0.615734i	$0.211141\pi$
$787$	11.5983	+	43.2853i	0.413433	+	1.54295i	−0.374521	+	0.927219i	$0.622193\pi$
$788$	−25.6609	−	6.87581i	−0.914130	−	0.244941i
$789$	11.7921	+	14.0533i	0.419811	+	0.500311i
$790$	17.3172	+	4.49574i	0.616119	+	0.159951i
$791$	−13.1106	+	3.51297i	−0.466158	+	0.124907i
$792$	4.03377	+	1.46817i	0.143334	+	0.0521692i
$793$	−21.4205	−	45.9364i	−0.760664	−	1.63125i
$794$	21.4429	−	30.6236i	0.760980	−	1.08679i
$795$	−0.0477031	−	6.11896i	−0.00169185	−	0.217017i
$796$	−12.8857	+	1.12735i	−0.456722	+	0.0399580i
$797$	−2.67769	−	15.1860i	−0.0948488	−	0.537914i	−0.994794	−	0.101910i	$-0.967504\pi$
$797$	−2.67769	−	15.1860i	−0.0948488	−	0.537914i	0.899945	−	0.436004i	$-0.143607\pi$
$798$	−4.99454	+	2.32899i	−0.176805	+	0.0824454i
$799$	0.935035	+	2.00519i	0.0330792	+	0.0709385i
$800$	−3.87987	−	3.15383i	−0.137174	−	0.111505i
$801$	−21.9367	+	15.3602i	−0.775095	+	0.542727i
$802$	−0.771186	−	0.0674701i	−0.0272315	−	0.00238245i
$803$	−1.88879	+	7.04908i	−0.0666541	+	0.248757i
$804$	−2.26117	+	3.91647i	−0.0797455	+	0.138123i
$805$	1.14467	+	12.0050i	0.0403442	+	0.423119i
$806$	1.02831	−	3.83772i	0.0362208	−	0.135178i
$807$	8.81361	+	4.10985i	0.310254	+	0.144674i
$808$			15.1390i			0.532589i
$809$	1.07587	−	2.30721i	0.0378256	−	0.0811173i	−0.886487	−	0.462754i	$-0.846862\pi$
$809$	1.07587	−	2.30721i	0.0378256	−	0.0811173i	0.924313	+	0.381636i	$0.124639\pi$
$810$	8.24718	−	4.84762i	0.289776	−	0.170328i
$811$	−6.09988	−	5.11841i	−0.214196	−	0.179732i	0.529377	−	0.848387i	$-0.322426\pi$
$811$	−6.09988	−	5.11841i	−0.214196	−	0.179732i	−0.743573	+	0.668655i	$0.766870\pi$
$812$	−7.07977	−	8.43734i	−0.248451	−	0.296093i
$813$	10.4824	−	10.4824i	0.367635	−	0.367635i
$814$	−7.61089	+	7.51912i	−0.266762	+	0.263545i
$815$	−2.67330	+	2.27891i	−0.0936414	+	0.0798267i
$816$	−0.348194	−	0.0304630i	−0.0121892	−	0.00106642i
$817$	0.114095	+	1.30411i	0.00399167	+	0.0456250i
$818$	16.8298	+	24.0355i	0.588441	+	0.840381i
$819$	−24.9621	−	11.6400i	−0.872246	−	0.406735i
$820$	−10.4179	+	8.88094i	−0.363807	+	0.310136i
$821$	−35.3912	+	12.8814i	−1.23516	+	0.449562i	−0.875363	−	0.483467i	$-0.839377\pi$
$821$	−35.3912	+	12.8814i	−1.23516	+	0.449562i	−0.359800	+	0.933029i	$0.617155\pi$
$822$	−6.13789	+	3.54371i	−0.214083	+	0.123601i
$823$	24.4987	−	34.9877i	0.853971	−	1.21960i	−0.119967	−	0.992778i	$-0.538279\pi$
$823$	24.4987	−	34.9877i	0.853971	−	1.21960i	0.973937	−	0.226818i	$-0.0728324\pi$
$824$	10.5316	+	6.08041i	0.366885	+	0.211821i
$825$	6.00396	+	2.68654i	0.209031	+	0.0935333i
$826$	15.2692	−	12.8124i	0.531284	−	0.445800i
$827$	14.0307	+	2.47399i	0.487895	+	0.0860291i	0.412184	−	0.911101i	$-0.364766\pi$
$827$	14.0307	+	2.47399i	0.487895	+	0.0860291i	0.0757113	+	0.997130i	$0.475877\pi$
$828$	−3.75443	−	2.16762i	−0.130475	−	0.0753300i
$829$	25.7924	−	12.0272i	0.895806	−	0.417721i	0.0805022	−	0.996754i	$-0.474348\pi$
$829$	25.7924	−	12.0272i	0.895806	−	0.417721i	0.815304	+	0.579033i	$0.196570\pi$
$830$	−2.99830	+	6.56298i	−0.104073	+	0.227804i
$831$	−10.4078	−	7.28760i	−0.361042	−	0.252804i
$832$	−2.84737	−	2.38923i	−0.0987148	−	0.0828316i
$833$	−0.794056	−	0.666292i	−0.0275124	−	0.0230857i
$834$	9.05055	+	6.33726i	0.313395	+	0.219441i
$835$	21.8355	−	8.14079i	0.755648	−	0.281724i
$836$	−3.86846	+	1.80389i	−0.133793	+	0.0623889i
$837$	3.76689	+	2.17481i	0.130203	+	0.0751726i
$838$	−38.7015	−	6.82412i	−1.33692	−	0.235735i
$839$	−12.6620	+	10.6247i	−0.437142	+	0.366806i	−0.834639	−	0.550798i	$-0.814324\pi$
$839$	−12.6620	+	10.6247i	−0.437142	+	0.366806i	0.397497	+	0.917604i	$0.369879\pi$
$840$	−4.78494	−	1.69945i	−0.165096	−	0.0586367i
$841$	−13.7177	−	7.91994i	−0.473025	−	0.273101i
$842$	−6.94563	+	9.91939i	−0.239362	+	0.341845i
$843$	−16.5260	+	9.54129i	−0.569186	+	0.328619i
$844$	8.86311	−	3.22591i	0.305081	−	0.111040i
$845$	−1.18360	−	1.38844i	−0.0407172	−	0.0477637i
$846$	−10.4722	−	4.88329i	−0.360043	−	0.167891i
$847$	13.7687	+	19.6637i	0.473097	+	0.675653i
$848$	0.318885	+	3.64488i	0.0109506	+	0.125166i
$849$	11.2540	+	0.984597i	0.386236	+	0.0337913i
$850$	2.30712	+	0.369817i	0.0791337	+	0.0126846i
$851$	8.88827	−	6.14363i	0.304686	−	0.210601i
$852$	4.86301	−	4.86301i	0.166604	−	0.166604i
$853$	18.3006	+	21.8098i	0.626600	+	0.746752i	0.982190	−	0.187890i	$-0.0601647\pi$
$853$	18.3006	+	21.8098i	0.626600	+	0.746752i	−0.355591	+	0.934642i	$0.615720\pi$
$854$	31.7151	+	26.6122i	1.08527	+	0.910650i
$855$	−3.32790	+	12.8188i	−0.113812	+	0.438393i
$856$	−7.47109	+	16.0218i	−0.255357	+	0.547614i
$857$			9.09625i			0.310722i	0.987858	+	0.155361i	$0.0496541\pi$
$857$			9.09625i			0.310722i	−0.987858	+	0.155361i	$0.950346\pi$
$858$	4.43164	+	2.06651i	0.151294	+	0.0705493i
$859$	−5.79269	+	21.6186i	−0.197644	+	0.737618i	0.793922	+	0.608019i	$0.208036\pi$
$859$	−5.79269	+	21.6186i	−0.197644	+	0.737618i	−0.991567	+	0.129599i	$0.958631\pi$
$860$	−0.768110	+	0.930027i	−0.0261923	+	0.0317137i
$861$	−6.95123	+	12.0399i	−0.236897	+	0.410318i
$862$	9.44864	−	35.2628i	0.321822	−	1.20106i
$863$	−36.4190	−	3.18625i	−1.23972	−	0.108461i	−0.551631	−	0.834088i	$-0.685994\pi$
$863$	−36.4190	−	3.18625i	−1.23972	−	0.108461i	−0.688088	+	0.725627i	$0.741550\pi$
$864$	3.33332	−	2.33402i	0.113402	−	0.0794049i
$865$	26.9808	−	39.1792i	0.917375	−	1.33213i
$866$	3.40215	+	7.29593i	0.115610	+	0.247926i
$867$	−11.3757	+	5.30456i	−0.386338	+	0.180152i
$868$	0.563548	+	3.19604i	0.0191281	+	0.108481i
$869$	14.0195	−	1.22655i	0.475578	−	0.0416077i
$870$	6.06693	−	0.0472975i	0.205688	−	0.00160354i
$871$	12.8908	−	18.4099i	0.436786	−	0.623796i
$872$	−6.71579	−	14.4021i	−0.227425	−	0.487715i
$873$	−0.527135	−	0.191862i	−0.0178408	−	0.00649353i
$874$	4.16384	−	1.11570i	0.140844	−	0.0377390i
$875$	31.0917	+	13.6224i	1.05109	+	0.460522i
$876$	1.99477	+	2.37727i	0.0673969	+	0.0803205i
$877$	−31.6108	−	8.47010i	−1.06742	−	0.286015i	−0.317989	−	0.948095i	$-0.603007\pi$
$877$	−31.6108	−	8.47010i	−1.06742	−	0.286015i	−0.749434	+	0.662080i	$0.769674\pi$
$878$	8.50328	+	31.7347i	0.286972	+	1.07099i
$879$	1.44186	+	8.17721i	0.0486328	+	0.275810i
$880$	−3.70612	−	1.31629i	−0.124933	−	0.0443721i
$881$	14.3034	+	39.2983i	0.481894	+	1.32399i	0.907868	+	0.419257i	$0.137709\pi$
$881$	14.3034	+	39.2983i	0.481894	+	1.32399i	−0.425974	+	0.904735i	$0.640068\pi$
$882$	5.41354			0.182284
$883$	−1.22256	−	3.35896i	−0.0411425	−	0.113038i	0.917420	−	0.397920i	$-0.130268\pi$
$883$	−1.22256	−	3.35896i	−0.0411425	−	0.113038i	−0.958563	+	0.284882i	$0.908046\pi$
$884$	1.71061	+	0.301627i	0.0575341	+	0.0101448i
$885$	0.0855951	+	10.9794i	0.00287725	+	0.369070i
$886$	−3.27923	+	37.4817i	−0.110168	+	1.25922i
$887$	−19.5362	−	19.5362i	−0.655962	−	0.655962i	0.298460	−	0.954422i	$-0.403527\pi$
$887$	−19.5362	−	19.5362i	−0.655962	−	0.655962i	−0.954422	+	0.298460i	$0.903527\pi$
$888$	0.762829	+	4.48514i	0.0255989	+	0.150511i
$889$		−	33.4039i		−	1.12033i
$890$	19.9881	−	14.2293i	0.670003	−	0.476968i
$891$	4.83683	−	5.76431i	0.162040	−	0.193112i
$892$	−20.4650	+	14.3298i	−0.685220	+	0.479796i
$893$	10.7966	−	3.92964i	0.361294	−	0.131500i
$894$	−7.39119	−	7.39119i	−0.247198	−	0.247198i
$895$	28.2705	−	7.81177i	0.944978	−	0.261119i
$896$	2.93268	+	0.785810i	0.0979741	+	0.0262521i
$897$	−4.04521	−	2.83248i	−0.135066	−	0.0945739i
$898$	−15.3140	+	4.10338i	−0.511036	+	0.136932i
$899$	−1.93883	−	3.35815i	−0.0646636	−	0.112001i
$900$	−10.4716	+	6.26549i	−0.349054	+	0.208850i
$901$	−0.980707	−	1.40060i	−0.0326721	−	0.0466606i
$902$	−5.38399	+	9.32534i	−0.179267	+	0.310500i
$903$	−0.418966	+	1.15110i	−0.0139423	+	0.0383062i
$904$	−1.52900	+	4.20090i	−0.0508538	+	0.139720i
$905$	−16.0866	+	19.4776i	−0.534737	+	0.647459i
$906$	−0.750313	−	8.57612i	−0.0249275	−	0.284922i
$907$	−7.59917	+	9.05634i	−0.252326	+	0.300711i	−0.877307	−	0.479929i	$-0.840662\pi$
$907$	−7.59917	+	9.05634i	−0.252326	+	0.300711i	0.624981	+	0.780640i	$0.285107\pi$
$908$	12.7729	−	2.25220i	0.423883	−	0.0747419i
$909$	34.7199	+	12.6370i	1.15159	+	0.419143i
$910$	22.9528	+	10.4860i	0.760877	+	0.347607i
$911$	14.0480	+	52.4279i	0.465431	+	1.73701i	0.655456	+	0.755234i	$0.272477\pi$
$911$	14.0480	+	52.4279i	0.465431	+	1.73701i	−0.190025	+	0.981779i	$0.560857\pi$
$912$	−0.315187	+	1.78752i	−0.0104369	+	0.0591905i
$913$	−0.494658	+	5.65396i	−0.0163708	+	0.187119i
$914$	−6.27257	+	3.62147i	−0.207478	+	0.119788i
$915$	−22.4277	+	4.13513i	−0.741436	+	0.136703i
$916$	18.5324	−	3.26776i	0.612327	−	0.107970i
$917$	−28.1525	−	48.7616i	−0.929677	−	1.61025i
$918$	−0.803657	+	1.72345i	−0.0265246	+	0.0568822i
$919$	25.3658	−	25.3658i	0.836742	−	0.836742i	−0.151687	−	0.988429i	$-0.548471\pi$
$919$	25.3658	−	25.3658i	0.836742	−	0.836742i	0.988429	+	0.151687i	$0.0484705\pi$
$920$	3.45519	+	1.95910i	0.113914	+	0.0645896i
$921$	−3.79886	+	21.5444i	−0.125177	+	0.709913i
$922$	23.7465	−	2.07755i	0.782049	−	0.0684204i
$923$	−26.1817	+	21.9690i	−0.861780	+	0.723119i
$924$	−3.99411			−0.131397
$925$	−2.93923	−	30.2715i	−0.0966414	−	0.995319i
$926$	−21.9108			−0.720034
$927$	22.7358	−	19.0776i	0.746742	−	0.626591i
$928$	−3.61388	+	0.316174i	−0.118632	+	0.0103789i
$929$	−3.74853	+	21.2590i	−0.122985	+	0.697484i	0.859499	+	0.511138i	$0.170776\pi$
$929$	−3.74853	+	21.2590i	−0.122985	+	0.697484i	−0.982484	+	0.186347i	$0.940335\pi$
$930$	−1.55510	−	0.881747i	−0.0509939	−	0.0289136i
$931$	−3.80631	+	3.80631i	−0.124747	+	0.124747i
$932$	7.43988	−	15.9549i	0.243702	−	0.522620i
$933$	−7.92632	−	13.7288i	−0.259496	−	0.449461i
$934$	−6.70407	+	1.18211i	−0.219364	+	0.0386798i
$935$	1.80745	−	0.333251i	0.0591100	−	0.0108985i
$936$	−7.85624	+	4.53580i	−0.256789	+	0.148257i
$937$	1.18660	−	13.5629i	0.0387646	−	0.443082i	−0.951866	−	0.306514i	$-0.900837\pi$
$937$	1.18660	−	13.5629i	0.0387646	−	0.443082i	0.990631	−	0.136568i	$-0.0436071\pi$
$938$	−3.18778	+	18.0788i	−0.104085	+	0.590294i
$939$	−2.42806	−	9.06164i	−0.0792367	−	0.295715i
$940$	9.62927	+	4.39914i	0.314072	+	0.143484i
$941$	19.0488	+	6.93321i	0.620975	+	0.226016i	0.633298	−	0.773908i	$-0.281701\pi$
$941$	19.0488	+	6.93321i	0.620975	+	0.226016i	−0.0123237	+	0.999924i	$0.503923\pi$
$942$	−3.19853	+	0.563987i	−0.104214	+	0.0183757i
$943$	6.99020	−	8.33060i	0.227632	−	0.271282i
$944$	−0.572186	−	6.54011i	−0.0186231	−	0.212862i
$945$	−17.5922	+	21.3006i	−0.572274	+	0.692908i
$946$	−0.324505	+	0.891569i	−0.0105506	+	0.0289874i
$947$	11.8243	−	32.4870i	0.384238	−	1.05569i	−0.585315	−	0.810806i	$-0.699029\pi$
$947$	11.8243	−	32.4870i	0.384238	−	1.05569i	0.969553	−	0.244880i	$-0.0787486\pi$
$948$	2.99222	−	5.18268i	0.0971828	−	0.168326i
$949$	−8.84583	−	12.6332i	−0.287148	−	0.410090i
$950$	2.95737	−	11.7680i	0.0959499	−	0.381805i
$951$	10.6516	+	18.4492i	0.345403	+	0.598255i
$952$	−1.37049	+	0.367221i	−0.0444177	+	0.0119017i
$953$	10.3125	+	7.22089i	0.334054	+	0.233907i	0.728553	−	0.684989i	$-0.240193\pi$
$953$	10.3125	+	7.22089i	0.334054	+	0.233907i	−0.394499	+	0.918896i	$0.629082\pi$
$954$	8.62534	+	2.31115i	0.279256	+	0.0748263i
$955$	4.91523	−	1.35819i	0.159053	−	0.0439499i
$956$	−20.1489	−	20.1489i	−0.651664	−	0.651664i
$957$	4.48450	−	1.63222i	0.144963	−	0.0527623i
$958$	7.74253	−	5.42138i	0.250150	−	0.175157i
$959$	−18.4931	+	22.0392i	−0.597174	+	0.711684i
$960$	−1.36247	+	0.969927i	−0.0439735	+	0.0313042i
$961$		−	29.8574i		−	0.963143i
$962$	−1.83389	−	22.5350i	−0.0591271	−	0.726557i
$963$	30.5081	+	30.5081i	0.983109	+	0.983109i
$964$	1.53899	−	17.5907i	0.0495674	−	0.566558i
$965$	−0.0864176	−	11.0849i	−0.00278188	−	0.356836i
$966$	3.97246	+	0.700451i	0.127812	+	0.0225367i
$967$	4.22775	+	11.6157i	0.135955	+	0.373534i	0.988923	−	0.148430i	$-0.0474218\pi$
$967$	4.22775	+	11.6157i	0.135955	+	0.373534i	−0.852968	+	0.521964i	$0.825200\pi$
$968$	7.90641			0.254122
$969$	−0.290108	−	0.797065i	−0.00931961	−	0.0256054i
$970$	0.484318	+	0.172014i	0.0155505	+	0.00552302i
$971$	6.00393	+	34.0500i	0.192675	+	1.09272i	0.915691	+	0.401884i	$0.131644\pi$
$971$	6.00393	+	34.0500i	0.192675	+	1.09272i	−0.723015	+	0.690832i	$0.757244\pi$
$972$	−3.98777	−	14.8825i	−0.127908	−	0.477358i
$973$	43.3220	+	11.6081i	1.38884	+	0.372138i
$974$	−8.77535	−	10.4581i	−0.281180	−	0.335098i
$975$	−12.5049	+	6.07026i	−0.400478	+	0.194404i
$976$	13.1715	−	3.52929i	0.421609	−	0.112970i
$977$	17.5053	+	6.37142i	0.560045	+	0.203840i	0.606504	−	0.795080i	$-0.292571\pi$
$977$	17.5053	+	6.37142i	0.560045	+	0.203840i	−0.0464587	+	0.998920i	$0.514794\pi$
$978$	0.496577	+	1.06491i	0.0158788	+	0.0340522i
$979$	11.0697	−	15.8092i	0.353789	−	0.505263i
$980$	−4.95975	+	0.0386660i	−0.158433	+	0.00123514i
$981$	−38.6355	+	3.38017i	−1.23354	+	0.107921i
$982$	−0.838679	−	4.75639i	−0.0267633	−	0.151782i
$983$	16.6172	−	7.74874i	0.530007	−	0.247146i	−0.139145	−	0.990272i	$-0.544435\pi$
$983$	16.6172	−	7.74874i	0.530007	−	0.247146i	0.669152	+	0.743126i	$0.266658\pi$
$984$	1.93517	+	4.14998i	0.0616909	+	0.132296i
$985$	33.6921	−	48.9247i	1.07352	−	1.55887i
$986$	1.38869	−	0.972369i	0.0442248	−	0.0309665i
$987$	10.7103	+	0.937033i	0.340914	+	0.0298261i
$988$	2.33463	−	8.71294i	0.0742744	−	0.277196i
$989$	0.479101	−	0.829828i	0.0152345	−	0.0263870i
$990$	−6.11238	+	7.40087i	−0.194264	+	0.235215i
$991$	5.99937	−	22.3900i	0.190576	−	0.711240i	−0.802791	−	0.596260i	$-0.796653\pi$
$991$	5.99937	−	22.3900i	0.190576	−	0.711240i	0.993368	−	0.114980i	$-0.0366805\pi$
$992$	0.968758	+	0.451739i	0.0307581	+	0.0143427i
$993$		−	3.86527i		−	0.122661i
$994$	11.7984	−	25.3017i	0.374222	−	0.802522i
$995$	7.26790	−	27.9953i	0.230408	−	0.887512i
$996$	1.84884	+	1.55136i	0.0585827	+	0.0491567i
$997$	−15.0482	−	17.9337i	−0.476580	−	0.567966i	0.473172	−	0.880970i	$-0.343109\pi$
$997$	−15.0482	−	17.9337i	−0.476580	−	0.567966i	−0.949752	+	0.313004i	$0.898665\pi$
$998$	8.10966	−	8.10966i	0.256707	−	0.256707i
$999$	24.3496	+	4.44595i	0.770388	+	0.140664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.ba.a.113.6	✓	108
5.2	odd	4		370.2.bd.a.187.4	yes	108
37.19	odd	36		370.2.bd.a.93.4	yes	108
185.167	even	36	inner	370.2.ba.a.167.6	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.113.6	✓	108	1.1	even	1	trivial
370.2.ba.a.167.6	yes	108	185.167	even	36	inner
370.2.bd.a.93.4	yes	108	37.19	odd	36
370.2.bd.a.187.4	yes	108	5.2	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.745094 - 0.0651873i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.94515 + 1.10290i) q^{5} +(0.528874 - 0.528874i) q^{6} +(1.28313 - 2.75168i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.40351 + 0.423803i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.745094 - 0.0651873i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.94515 + 1.10290i) q^{5} +(0.528874 - 0.528874i) q^{6} +(1.28313 - 2.75168i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.40351 + 0.423803i) q^{9} +(2.19900 - 0.405444i) q^{10} +(1.52322 - 0.879430i) q^{11} +(0.0651873 - 0.745094i) q^{12} +(-0.645446 + 3.66051i) q^{13} +(-0.785810 - 2.93268i) q^{14} +(1.52121 + 0.694968i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.460215 - 0.0811484i) q^{17} +(-1.56878 + 1.86960i) q^{18} +(-0.211508 - 2.41755i) q^{19} +(1.42392 - 1.72408i) q^{20} +(0.776677 - 2.13390i) q^{21} +(0.601565 - 1.65279i) q^{22} +(-0.888156 + 1.53833i) q^{23} +(-0.429001 - 0.612677i) q^{24} +(2.56721 + 4.29062i) q^{25} +(1.85849 + 3.21900i) q^{26} +(-3.93058 + 1.05320i) q^{27} +(-2.48706 - 1.74146i) q^{28} +(3.50408 + 0.938915i) q^{29} +(1.61204 - 0.445441i) q^{30} +(-0.755831 - 0.755831i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(1.07761 - 0.754553i) q^{33} +(0.300384 - 0.357984i) q^{34} +(5.53071 - 3.93725i) q^{35} +2.44058i q^{36} +(-5.49716 - 2.60408i) q^{37} +(-1.71600 - 1.71600i) q^{38} +(-0.242300 + 2.76950i) q^{39} +(-0.0174317 - 2.23600i) q^{40} +(-6.02913 - 1.06310i) q^{41} +(-0.776677 - 2.13390i) q^{42} -0.539434 q^{43} +(-0.601565 - 1.65279i) q^{44} +(-5.14259 - 1.82648i) q^{45} +(0.308453 + 1.74933i) q^{46} +(1.22537 + 4.57313i) q^{47} +(-0.722455 - 0.193581i) q^{48} +(-1.42579 - 1.69919i) q^{49} +(4.72455 + 1.63664i) q^{50} +(0.337614 - 0.0904634i) q^{51} +(3.49282 + 1.27128i) q^{52} +(-1.54628 - 3.31600i) q^{53} +(-2.33402 + 3.33332i) q^{54} +(3.93281 - 0.0306600i) q^{55} +(-3.02458 + 0.264617i) q^{56} +(-0.315187 - 1.78752i) q^{57} +(3.28780 - 1.53313i) q^{58} +(2.77453 + 5.95000i) q^{59} +(0.948566 - 1.37742i) q^{60} +(-11.1701 + 7.82136i) q^{61} +(-1.06484 - 0.0931613i) q^{62} +(-1.91784 + 7.15746i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.29268 + 6.40837i) q^{65} +(0.340482 - 1.27070i) q^{66} +(-5.47990 - 2.55532i) q^{67} -0.467315i q^{68} +(-0.561480 + 1.20410i) q^{69} +(1.70595 - 6.57118i) q^{70} +(7.04380 + 5.91045i) q^{71} +(1.56878 + 1.86960i) q^{72} +(-2.93388 + 2.93388i) q^{73} +(-5.88494 + 1.53867i) q^{74} +(2.19251 + 3.02957i) q^{75} +(-2.41755 - 0.211508i) q^{76} +(-0.465424 - 5.31982i) q^{77} +(1.59459 + 2.27731i) q^{78} +(7.25157 + 3.38146i) q^{79} +(-1.45063 - 1.70167i) q^{80} +(4.02020 - 1.46323i) q^{81} +(-5.30193 + 3.06107i) q^{82} +(-1.85084 + 2.64327i) q^{83} +(-1.96661 - 1.13543i) q^{84} +(0.984686 + 0.349728i) q^{85} +(-0.413230 + 0.346741i) q^{86} +(2.67207 + 0.471159i) q^{87} +(-1.52322 - 0.879430i) q^{88} +(9.94463 - 4.63726i) q^{89} +(-5.11349 + 1.90643i) q^{90} +(9.24434 + 6.47296i) q^{91} +(1.36073 + 1.14179i) q^{92} +(-0.612436 - 0.513895i) q^{93} +(3.87824 + 2.71557i) q^{94} +(2.25491 - 4.93577i) q^{95} +(-0.677864 + 0.316093i) q^{96} +(0.199055 + 0.114924i) q^{97} +(-2.18444 - 0.385175i) q^{98} +(-3.28836 + 2.75926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more