LMFDB - Embedded newform 495.2.n.f.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.f.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0756511 + 0.0549637i) q^{2} +(-0.615332 - 1.89380i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.39815 + 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +O(q^{10})$	\(q+(0.0756511 + 0.0549637i) q^{2} +(-0.615332 - 1.89380i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.39815 + 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +0.0935099 q^{10} +(2.39815 + 2.29104i) q^{11} +(0.924349 + 0.671579i) q^{13} +(-0.130741 + 0.402380i) q^{14} +(-3.19369 + 2.32035i) q^{16} +(2.72899 - 1.98273i) q^{17} +(1.88030 - 5.78696i) q^{19} +(-1.61096 - 1.17043i) q^{20} +(0.0554990 + 0.305131i) q^{22} +5.45258 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.0330155 + 0.101611i) q^{26} +(7.28883 - 5.29564i) q^{28} +(-1.02619 - 3.15830i) q^{29} +(-1.44887 - 1.05267i) q^{31} -1.11558 q^{32} +0.315430 q^{34} +(3.66042 + 2.65945i) q^{35} +(0.460067 + 1.41594i) q^{37} +(0.460319 - 0.334441i) q^{38} +(-0.115332 - 0.354955i) q^{40} +(0.539933 - 1.66174i) q^{41} -0.263041 q^{43} +(2.86310 - 5.95137i) q^{44} +(0.412494 + 0.299694i) q^{46} +(-2.13986 + 6.58580i) q^{47} +(-10.8985 + 7.91824i) q^{49} +(0.0756511 - 0.0549637i) q^{50} +(0.703052 - 2.16377i) q^{52} +(-1.16479 - 0.846269i) q^{53} +(3.28679 + 0.443888i) q^{55} +1.68865 q^{56} +(0.0959593 - 0.295332i) q^{58} +(2.18416 + 6.72216i) q^{59} +(-2.02452 + 1.47090i) q^{61} +(-0.0517503 - 0.159271i) q^{62} +(6.30297 + 4.57938i) q^{64} +1.14256 q^{65} -0.516598 q^{67} +(-5.43413 - 3.94812i) q^{68} +(0.130741 + 0.402380i) q^{70} +(-8.68098 + 6.30710i) q^{71} +(-1.75560 - 5.40317i) q^{73} +(-0.0430208 + 0.132404i) q^{74} -12.1163 q^{76} +(-6.50552 + 13.5227i) q^{77} +(9.14460 + 6.64394i) q^{79} +(-1.21988 + 3.75440i) q^{80} +(0.132182 - 0.0960360i) q^{82} +(3.62511 - 2.63380i) q^{83} +(1.04238 - 3.20812i) q^{85} +(-0.0198994 - 0.0144577i) q^{86} +(1.08980 - 0.587008i) q^{88} -13.2676 q^{89} +(-1.59747 + 4.91652i) q^{91} +(-3.35515 - 10.3261i) q^{92} +(-0.523863 + 0.380608i) q^{94} +(-1.88030 - 5.78696i) q^{95} +(2.71551 + 1.97293i) q^{97} -1.25970 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8	$ 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 6 q^{10} + 5 q^{11} + 4 q^{13} - 16 q^{14} - 20 q^{16} - q^{17} - q^{19} + q^{20} + 33 q^{22} + 18 q^{23} - 2 q^{25} + 14 q^{26} + 4 q^{28} - 19 q^{29} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 4 q^{37} + 6 q^{38} - 2 q^{40} + 4 q^{41} + 42 q^{43} + 28 q^{44} - 41 q^{46} - 4 q^{47} - 15 q^{49} + 4 q^{50} - 26 q^{52} - 3 q^{53} + 5 q^{55} - 30 q^{56} - 6 q^{58} + 19 q^{59} - 2 q^{61} + 38 q^{62} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} + 16 q^{70} - 40 q^{71} - 23 q^{73} - 48 q^{74} + 16 q^{76} + 28 q^{77} + 17 q^{79} - 15 q^{80} + 2 q^{82} + 25 q^{83} - 4 q^{85} + 31 q^{86} + 22 q^{88} - 12 q^{91} - 81 q^{92} + 33 q^{94} + q^{95} + 12 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 + 6 * q^10 + 5 * q^11 + 4 * q^13 - 16 * q^14 - 20 * q^16 - q^17 - q^19 + q^20 + 33 * q^22 + 18 * q^23 - 2 * q^25 + 14 * q^26 + 4 * q^28 - 19 * q^29 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 4 * q^37 + 6 * q^38 - 2 * q^40 + 4 * q^41 + 42 * q^43 + 28 * q^44 - 41 * q^46 - 4 * q^47 - 15 * q^49 + 4 * q^50 - 26 * q^52 - 3 * q^53 + 5 * q^55 - 30 * q^56 - 6 * q^58 + 19 * q^59 - 2 * q^61 + 38 * q^62 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 + 16 * q^70 - 40 * q^71 - 23 * q^73 - 48 * q^74 + 16 * q^76 + 28 * q^77 + 17 * q^79 - 15 * q^80 + 2 * q^82 + 25 * q^83 - 4 * q^85 + 31 * q^86 + 22 * q^88 - 12 * q^91 - 81 * q^92 + 33 * q^94 + q^95 + 12 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	0.0756511	+	0.0549637i	0.0534934	+	0.0388652i	0.614211	−	0.789142i	$-0.289475\pi$
$2$	0.0756511	+	0.0549637i	0.0534934	+	0.0388652i	−0.560717	+	0.828007i	$0.689475\pi$
$3$		0			0
$3$		0			0
$4$	−0.615332	−	1.89380i	−0.307666	−	0.946898i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	1.39815	+	4.30308i	0.528453	+	1.62641i	0.757385	+	0.652968i	$0.226477\pi$
$7$	1.39815	+	4.30308i	0.528453	+	1.62641i	−0.228932	+	0.973442i	$0.573523\pi$
$8$	0.115332	−	0.354955i	0.0407760	−	0.125496i
$9$		0			0
$10$	0.0935099			0.0295704
$11$	2.39815	+	2.29104i	0.723071	+	0.690774i
$11$	2.39815	+	2.29104i	0.723071	+	0.690774i
$12$		0			0
$13$	0.924349	+	0.671579i	0.256368	+	0.186262i	0.708544	−	0.705666i	$-0.249352\pi$
$13$	0.924349	+	0.671579i	0.256368	+	0.186262i	−0.452176	+	0.891929i	$0.649352\pi$
$14$	−0.130741	+	0.402380i	−0.0349421	+	0.107541i
$15$		0			0
$16$	−3.19369	+	2.32035i	−0.798421	+	0.580087i
$17$	2.72899	−	1.98273i	0.661878	−	0.480883i	−0.205418	−	0.978674i	$-0.565856\pi$
$17$	2.72899	−	1.98273i	0.661878	−	0.480883i	0.867297	+	0.497792i	$0.165856\pi$
$18$		0			0
$19$	1.88030	−	5.78696i	0.431369	−	1.32762i	−0.465392	−	0.885105i	$-0.654087\pi$
$19$	1.88030	−	5.78696i	0.431369	−	1.32762i	0.896762	−	0.442514i	$-0.145913\pi$
$20$	−1.61096	−	1.17043i	−0.360222	−	0.261716i
$21$		0			0
$22$	0.0554990	+	0.305131i	0.0118324	+	0.0650542i
$23$	5.45258			1.13694			0.568471	−	0.822703i	$-0.307535\pi$
$23$	5.45258			1.13694			0.568471	+	0.822703i	$0.307535\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.0330155	+	0.101611i	0.00647488	+	0.0199276i
$27$		0			0
$28$	7.28883	−	5.29564i	1.37746	−	1.00078i
$29$	−1.02619	−	3.15830i	−0.190559	−	0.586482i	0.809440	−	0.587202i	$-0.199771\pi$
$29$	−1.02619	−	3.15830i	−0.190559	−	0.586482i	−1.00000		0.000720503i	$0.999771\pi$
$30$		0			0
$31$	−1.44887	−	1.05267i	−0.260225	−	0.189065i	0.450021	−	0.893018i	$-0.351416\pi$
$31$	−1.44887	−	1.05267i	−0.260225	−	0.189065i	−0.710246	+	0.703953i	$0.751416\pi$
$32$	−1.11558			−0.197209
$33$		0			0
$34$	0.315430			0.0540957
$35$	3.66042	+	2.65945i	0.618723	+	0.449529i
$36$		0			0
$37$	0.460067	+	1.41594i	0.0756345	+	0.232779i	0.981725	−	0.190305i	$-0.0609476\pi$
$37$	0.460067	+	1.41594i	0.0756345	+	0.232779i	−0.906091	+	0.423084i	$0.860948\pi$
$38$	0.460319	−	0.334441i	0.0746736	−	0.0542536i
$39$		0			0
$40$	−0.115332	−	0.354955i	−0.0182356	−	0.0561233i
$41$	0.539933	−	1.66174i	0.0843234	−	0.259521i	−0.900001	−	0.435888i	$-0.856434\pi$
$41$	0.539933	−	1.66174i	0.0843234	−	0.259521i	0.984325	+	0.176367i	$0.0564345\pi$
$42$		0			0
$43$	−0.263041			−0.0401134			−0.0200567	−	0.999799i	$-0.506385\pi$
$43$	−0.263041			−0.0401134			−0.0200567	+	0.999799i	$0.506385\pi$
$44$	2.86310	−	5.95137i	0.431628	−	0.897202i
$45$		0			0
$46$	0.412494	+	0.299694i	0.0608189	+	0.0441875i
$47$	−2.13986	+	6.58580i	−0.312130	+	0.960638i	0.664790	+	0.747031i	$0.268521\pi$
$47$	−2.13986	+	6.58580i	−0.312130	+	0.960638i	−0.976920	+	0.213607i	$0.931479\pi$
$48$		0			0
$49$	−10.8985	+	7.91824i	−1.55693	+	1.13118i
$50$	0.0756511	−	0.0549637i	0.0106987	−	0.00777305i
$51$		0			0
$52$	0.703052	−	2.16377i	0.0974958	−	0.300061i
$53$	−1.16479	−	0.846269i	−0.159996	−	0.116244i	0.504907	−	0.863174i	$-0.331527\pi$
$53$	−1.16479	−	0.846269i	−0.159996	−	0.116244i	−0.664903	+	0.746930i	$0.731527\pi$
$54$		0			0
$55$	3.28679	+	0.443888i	0.443190	+	0.0598539i
$56$	1.68865			0.225656
$57$		0			0
$58$	0.0959593	−	0.295332i	0.0126001	−	0.0387790i
$59$	2.18416	+	6.72216i	0.284354	+	0.875150i	0.986592	+	0.163208i	$0.0521842\pi$
$59$	2.18416	+	6.72216i	0.284354	+	0.875150i	−0.702238	+	0.711942i	$0.747816\pi$
$60$		0			0
$61$	−2.02452	+	1.47090i	−0.259214	+	0.188330i	−0.709800	−	0.704403i	$-0.751215\pi$
$61$	−2.02452	+	1.47090i	−0.259214	+	0.188330i	0.450587	+	0.892733i	$0.351215\pi$
$62$	−0.0517503	−	0.159271i	−0.00657229	−	0.0202274i
$63$		0			0
$64$	6.30297	+	4.57938i	0.787872	+	0.572422i
$65$	1.14256			0.141717
$66$		0			0
$67$	−0.516598			−0.0631124			−0.0315562	−	0.999502i	$-0.510046\pi$
$67$	−0.516598			−0.0631124			−0.0315562	+	0.999502i	$0.510046\pi$
$68$	−5.43413	−	3.94812i	−0.658984	−	0.478780i
$69$		0			0
$70$	0.130741	+	0.402380i	0.0156266	+	0.0480937i
$71$	−8.68098	+	6.30710i	−1.03024	+	0.748515i	−0.968357	−	0.249568i	$-0.919711\pi$
$71$	−8.68098	+	6.30710i	−1.03024	+	0.748515i	−0.0618853	+	0.998083i	$0.519711\pi$
$72$		0			0
$73$	−1.75560	−	5.40317i	−0.205477	−	0.632393i	−0.999693	−	0.0247584i	$-0.992118\pi$
$73$	−1.75560	−	5.40317i	−0.205477	−	0.632393i	0.794216	−	0.607635i	$-0.207882\pi$
$74$	−0.0430208	+	0.132404i	−0.00500106	+	0.0153917i
$75$		0			0
$76$	−12.1163			−1.38984
$77$	−6.50552	+	13.5227i	−0.741373	+	1.54105i
$78$		0			0
$79$	9.14460	+	6.64394i	1.02885	+	0.747502i	0.968078	−	0.250650i	$-0.0806444\pi$
$79$	9.14460	+	6.64394i	1.02885	+	0.747502i	0.0607700	+	0.998152i	$0.480644\pi$
$80$	−1.21988	+	3.75440i	−0.136387	+	0.419755i
$81$		0			0
$82$	0.132182	−	0.0960360i	0.0145971	−	0.0106054i
$83$	3.62511	−	2.63380i	0.397907	−	0.289097i	−0.370781	−	0.928720i	$-0.620910\pi$
$83$	3.62511	−	2.63380i	0.397907	−	0.289097i	0.768688	+	0.639624i	$0.220910\pi$
$84$		0			0
$85$	1.04238	−	3.20812i	0.113062	−	0.347970i
$86$	−0.0198994	−	0.0144577i	−0.00214580	−	0.00155902i
$87$		0			0
$88$	1.08980	−	0.587008i	0.116173	−	0.0625752i
$89$	−13.2676			−1.40637			−0.703183	−	0.711009i	$-0.748238\pi$
$89$	−13.2676			−1.40637			−0.703183	+	0.711009i	$0.748238\pi$
$90$		0			0
$91$	−1.59747	+	4.91652i	−0.167461	+	0.515391i
$92$	−3.35515	−	10.3261i	−0.349798	−	1.07657i
$93$		0			0
$94$	−0.523863	+	0.380608i	−0.0540323	+	0.0392568i
$95$	−1.88030	−	5.78696i	−0.192914	−	0.593729i
$96$		0			0
$97$	2.71551	+	1.97293i	0.275718	+	0.200321i	0.717048	−	0.697024i	$-0.245493\pi$
$97$	2.71551	+	1.97293i	0.275718	+	0.200321i	−0.441330	+	0.897345i	$0.645493\pi$
$98$	−1.25970			−0.127249
$99$		0			0
$100$	−1.99126			−0.199126
$101$	−7.55216	−	5.48696i	−0.751468	−	0.545973i	0.144814	−	0.989459i	$-0.453742\pi$
$101$	−7.55216	−	5.48696i	−0.751468	−	0.545973i	−0.896282	+	0.443486i	$0.853742\pi$
$102$		0			0
$103$	−4.30027	−	13.2349i	−0.423718	−	1.30407i	−0.904216	−	0.427075i	$-0.859544\pi$
$103$	−4.30027	−	13.2349i	−0.423718	−	1.30407i	0.480498	−	0.876996i	$-0.340456\pi$
$104$	0.344987	−	0.250648i	0.0338288	−	0.0245781i
$105$		0			0
$106$	−0.0416035	−	0.128042i	−0.00404089	−	0.0124366i
$107$	5.18787	−	15.9666i	0.501531	−	1.54355i	−0.304996	−	0.952354i	$-0.598655\pi$
$107$	5.18787	−	15.9666i	0.501531	−	1.54355i	0.806526	−	0.591198i	$-0.201345\pi$
$108$		0			0
$109$	−3.65293			−0.349888			−0.174944	−	0.984578i	$-0.555974\pi$
$109$	−3.65293			−0.349888			−0.174944	+	0.984578i	$0.555974\pi$
$110$	0.224251	+	0.214235i	0.0213815	+	0.0204265i
$111$		0			0
$112$	−14.4499	−	10.4985i	−1.36539	−	0.992012i
$113$	3.67802	−	11.3198i	0.345999	−	1.06488i	−0.615047	−	0.788490i	$-0.710863\pi$
$113$	3.67802	−	11.3198i	0.345999	−	1.06488i	0.961047	−	0.276386i	$-0.0891369\pi$
$114$		0			0
$115$	4.41123	−	3.20495i	0.411350	−	0.298863i
$116$	−5.34973	+	3.88681i	−0.496710	+	0.360881i
$117$		0			0
$118$	−0.204241	+	0.628588i	−0.0188019	+	0.0578662i
$119$	12.3474	+	8.97091i	1.13188	+	0.822362i
$120$		0			0
$121$	0.502293	+	10.9885i	0.0456630	+	0.998957i
$122$	−0.234004			−0.0211857
$123$		0			0
$124$	−1.10200	+	3.39161i	−0.0989626	+	0.304576i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−15.9883	+	11.6162i	−1.41873	+	1.03077i	−0.426756	+	0.904367i	$0.640344\pi$
$127$	−15.9883	+	11.6162i	−1.41873	+	1.03077i	−0.991979	+	0.126404i	$0.959656\pi$
$128$	0.914596	+	2.81484i	0.0808397	+	0.248799i
$129$		0			0
$130$	0.0864358	+	0.0627993i	0.00758092	+	0.00550786i
$131$	1.93479			0.169043			0.0845215	−	0.996422i	$-0.473064\pi$
$131$	1.93479			0.169043			0.0845215	+	0.996422i	$0.473064\pi$
$132$		0			0
$133$	27.5307			2.38721
$134$	−0.0390812	−	0.0283941i	−0.00337610	−	0.00245288i
$135$		0			0
$136$	−0.389040	−	1.19734i	−0.0333599	−	0.102671i
$137$	−10.1413	+	7.36808i	−0.866429	+	0.629498i	−0.929626	−	0.368503i	$-0.879870\pi$
$137$	−10.1413	+	7.36808i	−0.866429	+	0.629498i	0.0631970	+	0.998001i	$0.479870\pi$
$138$		0			0
$139$	−3.47491	−	10.6947i	−0.294738	−	0.907111i	−0.983309	−	0.181942i	$-0.941762\pi$
$139$	−3.47491	−	10.6947i	−0.294738	−	0.907111i	0.688571	−	0.725169i	$-0.258238\pi$
$140$	2.78408	−	8.56853i	0.235298	−	0.724173i
$141$		0			0
$142$	−1.00339			−0.0842024
$143$	0.678120	+	3.72827i	0.0567072	+	0.311773i
$144$		0			0
$145$	−2.68661	−	1.95194i	−0.223111	−	0.162100i
$146$	0.164166	−	0.505250i	0.0135864	−	0.0418148i
$147$		0			0
$148$	2.39841	−	1.74255i	0.197148	−	0.143236i
$149$	−14.0232	+	10.1885i	−1.14883	+	0.834672i	−0.988325	−	0.152363i	$-0.951312\pi$
$149$	−14.0232	+	10.1885i	−1.14883	+	0.834672i	−0.160503	+	0.987035i	$0.551312\pi$
$150$		0			0
$151$	−0.00166997	+	0.00513965i	−0.000135901	+	0.000418259i	−0.951124	−	0.308808i	$-0.900070\pi$
$151$	−0.00166997	+	0.00513965i	−0.000135901	+	0.000418259i	0.950989	+	0.309226i	$0.100070\pi$
$152$	−1.83725	−	1.33484i	−0.149021	−	0.108270i
$153$		0			0
$154$	−1.23541	+	0.665437i	−0.0995519	+	0.0536225i
$155$	−1.79091			−0.143849
$156$		0			0
$157$	0.171454	−	0.527682i	0.0136835	−	0.0421136i	−0.943982	−	0.329998i	$-0.892952\pi$
$157$	0.171454	−	0.527682i	0.0136835	−	0.0421136i	0.957665	+	0.287884i	$0.0929519\pi$
$158$	0.326623	+	1.00524i	0.0259847	+	0.0799728i
$159$		0			0
$160$	−0.902527	+	0.655724i	−0.0713510	+	0.0518395i
$161$	7.62356	+	23.4629i	0.600820	+	1.84914i
$162$		0			0
$163$	6.44324	+	4.68129i	0.504673	+	0.366667i	0.810799	−	0.585324i	$-0.199033\pi$
$163$	6.44324	+	4.68129i	0.504673	+	0.366667i	−0.306126	+	0.951991i	$0.599033\pi$
$164$	−3.47924			−0.271683
$165$		0			0
$166$	0.419007			0.0325212
$167$	2.77204	+	2.01400i	0.214507	+	0.155848i	0.689850	−	0.723952i	$-0.257676\pi$
$167$	2.77204	+	2.01400i	0.214507	+	0.155848i	−0.475344	+	0.879800i	$0.657676\pi$
$168$		0			0
$169$	−3.61382	−	11.1222i	−0.277986	−	0.855553i
$170$	0.255188	−	0.185405i	0.0195720	−	0.0142199i
$171$		0			0
$172$	0.161858	+	0.498147i	0.0123415	+	0.0379834i
$173$	−6.35552	+	19.5603i	−0.483201	+	1.48714i	0.351368	+	0.936237i	$0.385717\pi$
$173$	−6.35552	+	19.5603i	−0.483201	+	1.48714i	−0.834569	+	0.550903i	$0.814283\pi$
$174$		0			0
$175$	4.52452			0.342022
$176$	−12.9750	−	1.75230i	−0.978024	−	0.132084i
$177$		0			0
$178$	−1.00371	−	0.729238i	−0.0752313	−	0.0546587i
$179$	0.792419	−	2.43882i	0.0592282	−	0.182286i	−0.917065	−	0.398738i	$-0.869448\pi$
$179$	0.792419	−	2.43882i	0.0592282	−	0.182286i	0.976293	+	0.216452i	$0.0694484\pi$
$180$		0			0
$181$	−10.8545	+	7.88624i	−0.806807	+	0.586179i	−0.912903	−	0.408177i	$-0.866165\pi$
$181$	−10.8545	+	7.88624i	−0.806807	+	0.586179i	0.106096	+	0.994356i	$0.466165\pi$
$182$	−0.391081	+	0.284137i	−0.0289888	+	0.0210616i
$183$		0			0
$184$	0.628857	−	1.93542i	0.0463599	−	0.142681i
$185$	1.20447	+	0.875099i	0.0885544	+	0.0643385i
$186$		0			0
$187$	11.0871	+	1.49733i	0.810766	+	0.109496i
$188$	13.7889			1.00566
$189$		0			0
$190$	0.175826	−	0.541138i	0.0127558	−	0.0392583i
$191$	−5.62097	−	17.2996i	−0.406719	−	1.25175i	−0.919452	−	0.393203i	$-0.871367\pi$
$191$	−5.62097	−	17.2996i	−0.406719	−	1.25175i	0.512733	−	0.858548i	$-0.328633\pi$
$192$		0			0
$193$	−12.6924	+	9.22156i	−0.913618	+	0.663782i	−0.941927	−	0.335817i	$-0.890988\pi$
$193$	−12.6924	+	9.22156i	−0.913618	+	0.663782i	0.0283094	+	0.999599i	$0.490988\pi$
$194$	0.0969914	+	0.298509i	0.00696358	+	0.0214317i
$195$		0			0
$196$	21.7018	+	15.7672i	1.55013	+	1.12623i
$197$	21.8486			1.55665			0.778325	−	0.627862i	$-0.216070\pi$
$197$	21.8486			1.55665			0.778325	+	0.627862i	$0.216070\pi$
$198$		0			0
$199$	−4.55200			−0.322683			−0.161341	−	0.986899i	$-0.551582\pi$
$199$	−4.55200			−0.322683			−0.161341	+	0.986899i	$0.551582\pi$
$200$	−0.301943	−	0.219374i	−0.0213506	−	0.0155121i
$201$		0			0
$202$	−0.269745	−	0.830190i	−0.0189792	−	0.0584119i
$203$	12.1556	−	8.83159i	0.853158	−	0.619856i
$204$		0			0
$205$	−0.539933	−	1.66174i	−0.0377106	−	0.116061i
$206$	0.402118	−	1.23759i	0.0280169	−	0.0862271i
$207$		0			0
$208$	−4.51038			−0.312738
$209$	17.7674	−	9.57019i	1.22900	−	0.661984i
$210$		0			0
$211$	−15.3393	−	11.1447i	−1.05600	−	0.767230i	−0.0826575	−	0.996578i	$-0.526341\pi$
$211$	−15.3393	−	11.1447i	−1.05600	−	0.767230i	−0.973345	+	0.229348i	$0.926341\pi$
$212$	−0.885929	+	2.72661i	−0.0608459	+	0.187264i
$213$		0			0
$214$	1.27005	−	0.922748i	0.0868191	−	0.0630778i
$215$	−0.212805	+	0.154612i	−0.0145132	+	0.0105444i
$216$		0			0
$217$	2.50396	−	7.70641i	0.169980	−	0.523145i
$218$	−0.276348	−	0.200779i	−0.0187167	−	0.0135985i
$219$		0			0
$220$	−1.18183	−	6.49764i	−0.0796790	−	0.438071i
$221$	3.85410			0.259255
$222$		0			0
$223$	1.50785	−	4.64070i	0.100973	−	0.310764i	−0.887791	−	0.460247i	$-0.847761\pi$
$223$	1.50785	−	4.64070i	0.100973	−	0.310764i	0.988764	+	0.149483i	$0.0477609\pi$
$224$	−1.55976	−	4.80045i	−0.104216	−	0.320743i
$225$		0			0
$226$	0.900424	−	0.654197i	0.0598953	−	0.0435165i
$227$	−5.04404	−	15.5240i	−0.334785	−	1.03036i	−0.966828	−	0.255428i	$-0.917784\pi$
$227$	−5.04404	−	15.5240i	−0.334785	−	1.03036i	0.632043	−	0.774933i	$-0.282216\pi$
$228$		0			0
$229$	3.90890	+	2.83998i	0.258307	+	0.187671i	0.709401	−	0.704806i	$-0.248966\pi$
$229$	3.90890	+	2.83998i	0.258307	+	0.187671i	−0.451093	+	0.892477i	$0.648966\pi$
$230$	0.509871			0.0336199
$231$		0			0
$232$	−1.23941			−0.0813711
$233$	−6.81172	−	4.94900i	−0.446251	−	0.324220i	0.341863	−	0.939750i	$-0.388942\pi$
$233$	−6.81172	−	4.94900i	−0.446251	−	0.324220i	−0.788114	+	0.615530i	$0.788942\pi$
$234$		0			0
$235$	2.13986	+	6.58580i	0.139589	+	0.429610i
$236$	11.3864	−	8.27272i	0.741193	−	0.538508i
$237$		0			0
$238$	0.441019	+	1.35732i	0.0285870	+	0.0879819i
$239$	7.01245	−	21.5821i	0.453598	−	1.39603i	−0.419175	−	0.907905i	$-0.637681\pi$
$239$	7.01245	−	21.5821i	0.453598	−	1.39603i	0.872773	−	0.488126i	$-0.162319\pi$
$240$		0			0
$241$	11.6065			0.747638			0.373819	−	0.927502i	$-0.378048\pi$
$241$	11.6065			0.747638			0.373819	+	0.927502i	$0.378048\pi$
$242$	−0.565971	+	0.858902i	−0.0363820	+	0.0552123i
$243$		0			0
$244$	4.03135	+	2.92894i	0.258080	+	0.187506i
$245$	−4.16287	+	12.8120i	−0.265956	+	0.818528i
$246$		0			0
$247$	5.62445	−	4.08640i	0.357875	−	0.260011i
$248$	−0.540751	+	0.392879i	−0.0343377	+	0.0249478i
$249$		0			0
$250$	0.0288961	−	0.0889332i	0.00182755	−	0.00562463i
$251$	2.68032	+	1.94736i	0.169180	+	0.122917i	0.669153	−	0.743124i	$-0.266657\pi$
$251$	2.68032	+	1.94736i	0.169180	+	0.122917i	−0.499973	+	0.866041i	$0.666657\pi$
$252$		0			0
$253$	13.0761	+	12.4921i	0.822090	+	0.785370i
$254$	−1.84800			−0.115954
$255$		0			0
$256$	4.72952	−	14.5560i	0.295595	−	0.909748i
$257$	8.29606	+	25.5326i	0.517494	+	1.59268i	0.778698	+	0.627399i	$0.215880\pi$
$257$	8.29606	+	25.5326i	0.517494	+	1.59268i	−0.261204	+	0.965284i	$0.584120\pi$
$258$		0			0
$259$	−5.44965	+	3.95940i	−0.338625	+	0.246025i
$260$	−0.703052	−	2.16377i	−0.0436015	−	0.134192i
$261$		0			0
$262$	0.146369	+	0.106343i	0.00904269	+	0.00656990i
$263$	−12.1682			−0.750324			−0.375162	−	0.926959i	$-0.622413\pi$
$263$	−12.1682			−0.750324			−0.375162	+	0.926959i	$0.622413\pi$
$264$		0			0
$265$	−1.43976			−0.0884436
$266$	2.08273	+	1.51319i	0.127700	+	0.0927795i
$267$		0			0
$268$	0.317879	+	0.978331i	0.0194176	+	0.0597611i
$269$	−1.69369	+	1.23053i	−0.103266	+	0.0750270i	−0.638220	−	0.769854i	$-0.720329\pi$
$269$	−1.69369	+	1.23053i	−0.103266	+	0.0750270i	0.534954	+	0.844881i	$0.320329\pi$
$270$		0			0
$271$	4.67938	+	14.4017i	0.284252	+	0.874838i	0.986622	+	0.163026i	$0.0521254\pi$
$271$	4.67938	+	14.4017i	0.284252	+	0.874838i	−0.702370	+	0.711812i	$0.747875\pi$
$272$	−4.11492	+	12.6644i	−0.249504	+	0.767894i
$273$		0			0
$274$	−1.17218			−0.0708138
$275$	2.91998	−	1.57281i	0.176081	−	0.0948441i
$276$		0			0
$277$	−6.69110	−	4.86137i	−0.402029	−	0.292091i	0.368338	−	0.929692i	$-0.379927\pi$
$277$	−6.69110	−	4.86137i	−0.402029	−	0.292091i	−0.770367	+	0.637601i	$0.779927\pi$
$278$	0.324939	−	1.00006i	0.0194885	−	0.0599795i
$279$		0			0
$280$	1.36615	−	0.992564i	0.0816429	−	0.0593171i
$281$	1.97985	−	1.43844i	0.118108	−	0.0858104i	−0.527163	−	0.849764i	$-0.676744\pi$
$281$	1.97985	−	1.43844i	0.118108	−	0.0858104i	0.645271	+	0.763954i	$0.276744\pi$
$282$		0			0
$283$	8.06372	−	24.8176i	0.479339	−	1.47525i	−0.360677	−	0.932691i	$-0.617454\pi$
$283$	8.06372	−	24.8176i	0.479339	−	1.47525i	0.840016	−	0.542562i	$-0.182546\pi$
$284$	17.2860	+	12.5590i	1.02574	+	0.745242i
$285$		0			0
$286$	−0.153619	+	0.319320i	−0.00908369	+	0.0188818i
$287$	7.90553			0.466648
$288$		0			0
$289$	−1.73710	+	5.34624i	−0.102182	+	0.314485i
$290$	−0.0959593	−	0.295332i	−0.00563492	−	0.0173425i
$291$		0			0
$292$	−9.15223	+	6.64949i	−0.535594	+	0.389132i
$293$	−4.15719	−	12.7945i	−0.242866	−	0.747463i	−0.995980	−	0.0895739i	$-0.971449\pi$
$293$	−4.15719	−	12.7945i	−0.242866	−	0.747463i	0.753115	−	0.657889i	$-0.228551\pi$
$294$		0			0
$295$	5.71821	+	4.15452i	0.332927	+	0.241886i
$296$	0.555655			0.0322968
$297$		0			0
$298$	−1.62087			−0.0938944
$299$	5.04009	+	3.66184i	0.291476	+	0.211770i
$300$		0			0
$301$	−0.367773	−	1.13189i	−0.0211981	−	0.0652409i
$302$	−0.000408830	0	0.000297032i	−2.35255e−5	0	1.70923e-5i
$303$		0			0
$304$	7.42268	+	22.8447i	0.425720	+	1.31023i
$305$	−0.773299	+	2.37997i	−0.0442790	+	0.136277i
$306$		0			0
$307$	27.1844			1.55150			0.775748	−	0.631042i	$-0.217373\pi$
$307$	27.1844			1.55150			0.775748	+	0.631042i	$0.217373\pi$
$308$	29.6123	+	3.99921i	1.68731	+	0.227876i
$309$		0			0
$310$	−0.135484	−	0.0984349i	−0.00769497	−	0.00559072i
$311$	4.07872	−	12.5530i	0.231283	−	0.711817i	−0.766310	−	0.642472i	$-0.777909\pi$
$311$	4.07872	−	12.5530i	0.231283	−	0.711817i	0.997593	−	0.0693450i	$-0.0220909\pi$
$312$		0			0
$313$	−13.0833	+	9.50561i	−0.739515	+	0.537289i	−0.892559	−	0.450931i	$-0.851092\pi$
$313$	−13.0833	+	9.50561i	−0.739515	+	0.537289i	0.153044	+	0.988219i	$0.451092\pi$
$314$	0.0419741	−	0.0304959i	0.00236873	−	0.00172099i
$315$		0			0
$316$	6.95531	−	21.4062i	0.391267	−	1.20420i
$317$	−4.35344	−	3.16296i	−0.244514	−	0.177650i	0.458778	−	0.888551i	$-0.348287\pi$
$317$	−4.35344	−	3.16296i	−0.244514	−	0.177650i	−0.703292	+	0.710901i	$0.748287\pi$
$318$		0			0
$319$	4.77481	−	9.92514i	0.267338	−	0.555701i
$320$	7.79091			0.435525
$321$		0			0
$322$	−0.712878	+	2.19401i	−0.0397271	+	0.122268i
$323$	−6.34266	−	19.5207i	−0.352915	−	1.08616i
$324$		0			0
$325$	0.924349	−	0.671579i	0.0512737	−	0.0372525i
$326$	0.230137	+	0.708289i	0.0127461	+	0.0392285i
$327$		0			0
$328$	−0.527573	−	0.383304i	−0.0291304	−	0.0211644i
$329$	−31.3311			−1.72734
$330$		0			0
$331$	−18.5702			−1.02071			−0.510356	−	0.859963i	$-0.670486\pi$
$331$	−18.5702			−1.02071			−0.510356	+	0.859963i	$0.670486\pi$
$332$	−7.21852	−	5.24456i	−0.396168	−	0.287833i
$333$		0			0
$334$	0.0990106	+	0.304723i	0.00541762	+	0.0166737i
$335$	−0.417936	+	0.303648i	−0.0228343	+	0.0165901i
$336$		0			0
$337$	2.78305	+	8.56535i	0.151603	+	0.466585i	0.997801	−	0.0662836i	$-0.0211142\pi$
$337$	2.78305	+	8.56535i	0.151603	+	0.466585i	−0.846198	+	0.532868i	$0.821114\pi$
$338$	0.337928	−	1.04003i	0.0183808	−	0.0565704i
$339$		0			0
$340$	−6.71695			−0.364278
$341$	−1.06292	−	5.84388i	−0.0575604	−	0.316464i
$342$		0			0
$343$	−23.6877	−	17.2101i	−1.27902	−	0.929260i
$344$	−0.0303371	+	0.0933679i	−0.00163567	+	0.00503406i
$345$		0			0
$346$	−1.55591	+	1.13043i	−0.0836461	+	0.0607725i
$347$	8.30939	−	6.03712i	0.446071	−	0.324090i	−0.341971	−	0.939710i	$-0.611095\pi$
$347$	8.30939	−	6.03712i	0.446071	−	0.324090i	0.788043	+	0.615621i	$0.211095\pi$
$348$		0			0
$349$	5.33402	−	16.4164i	0.285524	−	0.878752i	−0.700718	−	0.713439i	$-0.747137\pi$
$349$	5.33402	−	16.4164i	0.285524	−	0.878752i	0.986241	−	0.165313i	$-0.0528633\pi$
$350$	0.342285	+	0.248685i	0.0182959	+	0.0132928i
$351$		0			0
$352$	−2.67534	−	2.55585i	−0.142596	−	0.136227i
$353$	22.8096			1.21403			0.607017	−	0.794689i	$-0.292366\pi$
$353$	22.8096			1.21403			0.607017	+	0.794689i	$0.292366\pi$
$354$		0			0
$355$	−3.31584	+	10.2051i	−0.175986	+	0.541631i
$356$	8.16399	+	25.1262i	0.432691	+	1.33169i
$357$		0			0
$358$	0.193994	−	0.140945i	0.0102529	−	0.00744916i
$359$	4.96736	+	15.2879i	0.262167	+	0.806867i	0.992333	+	0.123597i	$0.0394429\pi$
$359$	4.96736	+	15.2879i	0.262167	+	0.806867i	−0.730166	+	0.683270i	$0.760557\pi$
$360$		0			0
$361$	−14.5820	−	10.5945i	−0.767475	−	0.557603i
$362$	−1.25461			−0.0659408
$363$		0			0
$364$	10.2939			0.539545
$365$	−4.59621	−	3.33934i	−0.240577	−	0.174789i
$366$		0			0
$367$	6.79759	+	20.9208i	0.354832	+	1.09206i	0.956107	+	0.293017i	$0.0946594\pi$
$367$	6.79759	+	20.9208i	0.354832	+	1.09206i	−0.601276	+	0.799042i	$0.705341\pi$
$368$	−17.4138	+	12.6519i	−0.907759	+	0.659525i
$369$		0			0
$370$	0.0430208	+	0.132404i	0.00223654	+	0.00688337i
$371$	2.01301	−	6.19539i	0.104510	−	0.321649i
$372$		0			0
$373$	−20.2604			−1.04905			−0.524523	−	0.851396i	$-0.675756\pi$
$373$	−20.2604			−1.04905			−0.524523	+	0.851396i	$0.675756\pi$
$374$	0.756449	+	0.722661i	0.0391151	+	0.0373679i
$375$		0			0
$376$	2.09087	+	1.51911i	0.107828	+	0.0783419i
$377$	1.17249	−	3.60854i	0.0603861	−	0.185849i
$378$		0			0
$379$	3.01578	−	2.19109i	0.154910	−	0.112549i	−0.507630	−	0.861575i	$-0.669478\pi$
$379$	3.01578	−	2.19109i	0.154910	−	0.112549i	0.662540	+	0.749026i	$0.269478\pi$
$380$	−9.80231	+	7.12180i	−0.502848	+	0.365341i
$381$		0			0
$382$	0.525616	−	1.61768i	0.0268928	−	0.0827677i
$383$	−8.89708	−	6.46411i	−0.454620	−	0.330301i	0.336797	−	0.941577i	$-0.390656\pi$
$383$	−8.89708	−	6.46411i	−0.454620	−	0.330301i	−0.791417	+	0.611277i	$0.790656\pi$
$384$		0			0
$385$	2.68535	+	14.7639i	0.136858	+	0.752439i
$386$	−1.46704			−0.0746706
$387$		0			0
$388$	2.06539	−	6.35663i	0.104854	−	0.322709i
$389$	−2.89926	−	8.92300i	−0.146998	−	0.452414i	0.850264	−	0.526356i	$-0.176442\pi$
$389$	−2.89926	−	8.92300i	−0.146998	−	0.452414i	−0.997263	+	0.0739418i	$0.976442\pi$
$390$		0			0
$391$	14.8801	−	10.8110i	0.752517	−	0.546736i
$392$	1.55367	+	4.78171i	0.0784723	+	0.241513i
$393$		0			0
$394$	1.65287	+	1.20088i	0.0832705	+	0.0604996i
$395$	11.3033			0.568733
$396$		0			0
$397$	22.3136			1.11989			0.559945	−	0.828530i	$-0.310822\pi$
$397$	22.3136			1.11989			0.559945	+	0.828530i	$0.310822\pi$
$398$	−0.344364	−	0.250195i	−0.0172614	−	0.0125411i
$399$		0			0
$400$	1.21988	+	3.75440i	0.0609940	+	0.187720i
$401$	−19.9683	+	14.5078i	−0.997171	+	0.724487i	−0.961480	−	0.274876i	$-0.911363\pi$
$401$	−19.9683	+	14.5078i	−0.997171	+	0.724487i	−0.0356909	+	0.999363i	$0.511363\pi$
$402$		0			0
$403$	−0.632315	−	1.94606i	−0.0314978	−	0.0969404i
$404$	−5.74411	+	17.6786i	−0.285780	+	0.879541i
$405$		0			0
$406$	1.40500			0.0697292
$407$	−2.14066	+	4.44967i	−0.106109	+	0.220562i
$408$		0			0
$409$	−23.8705	−	17.3429i	−1.18032	−	0.857553i	−0.188113	−	0.982147i	$-0.560237\pi$
$409$	−23.8705	−	17.3429i	−1.18032	−	0.857553i	−0.992208	+	0.124594i	$0.960237\pi$
$410$	0.0504891	−	0.155390i	0.00249348	−	0.00767414i
$411$		0			0
$412$	−22.4181	+	16.2877i	−1.10446	+	0.802437i
$413$	−25.8722	+	18.7972i	−1.27309	+	0.924951i
$414$		0			0
$415$	1.38467	−	4.26157i	0.0679707	−	0.209192i
$416$	−1.03119	−	0.749203i	−0.0505582	−	0.0367327i
$417$		0			0
$418$	1.87013	+	0.252566i	0.0914713	+	0.0123534i
$419$	−9.03564			−0.441420			−0.220710	−	0.975339i	$-0.570837\pi$
$419$	−9.03564			−0.441420			−0.220710	+	0.975339i	$0.570837\pi$
$420$		0			0
$421$	4.39426	−	13.5242i	0.214163	−	0.659127i	−0.785049	−	0.619434i	$-0.787362\pi$
$421$	4.39426	−	13.5242i	0.214163	−	0.659127i	0.999212	−	0.0396928i	$-0.0126379\pi$
$422$	−0.547884	−	1.68621i	−0.0266706	−	0.0820835i
$423$		0			0
$424$	−0.434725	+	0.315846i	−0.0211121	+	0.0153388i
$425$	−1.04238	−	3.20812i	−0.0505630	−	0.155617i
$426$		0			0
$427$	−9.16001	−	6.65514i	−0.443284	−	0.322065i
$428$	−33.4298			−1.61589
$429$		0			0
$430$	−0.0245970			−0.00118617
$431$	−1.40086	−	1.01778i	−0.0674769	−	0.0490248i	0.553535	−	0.832826i	$-0.313278\pi$
$431$	−1.40086	−	1.01778i	−0.0674769	−	0.0490248i	−0.621012	+	0.783801i	$0.713278\pi$
$432$		0			0
$433$	5.70062	+	17.5447i	0.273955	+	0.843145i	0.989494	+	0.144573i	$0.0461809\pi$
$433$	5.70062	+	17.5447i	0.273955	+	0.843145i	−0.715540	+	0.698572i	$0.753819\pi$
$434$	0.613000	−	0.445371i	0.0294250	−	0.0213785i
$435$		0			0
$436$	2.24777	+	6.91791i	0.107649	+	0.331308i
$437$	10.2525	−	31.5539i	0.490442	−	1.50943i
$438$		0			0
$439$	−17.1704			−0.819499			−0.409750	−	0.912198i	$-0.634384\pi$
$439$	−17.1704			−0.819499			−0.409750	+	0.912198i	$0.634384\pi$
$440$	0.536632	−	1.11547i	0.0255829	−	0.0531778i
$441$		0			0
$442$	0.291567	+	0.211836i	0.0138684	+	0.0100760i
$443$	−11.3098	+	34.8079i	−0.537344	+	1.65377i	0.201185	+	0.979553i	$0.435521\pi$
$443$	−11.3098	+	34.8079i	−0.537344	+	1.65377i	−0.738529	+	0.674221i	$0.764479\pi$
$444$		0			0
$445$	−10.7337	+	7.79852i	−0.508828	+	0.369685i
$446$	0.369141	−	0.268196i	0.0174793	−	0.0126995i
$447$		0			0
$448$	−10.8929	+	33.5249i	−0.514641	+	1.58390i
$449$	−13.4320	−	9.75895i	−0.633897	−	0.460553i	0.223851	−	0.974623i	$-0.428137\pi$
$449$	−13.4320	−	9.75895i	−0.633897	−	0.460553i	−0.857748	+	0.514070i	$0.828137\pi$
$450$		0			0
$451$	5.10196	−	2.74811i	0.240242	−	0.129404i
$452$	−23.7006			−1.11478
$453$		0			0
$454$	0.471667	−	1.45164i	0.0221365	−	0.0681290i
$455$	1.59747	+	4.91652i	0.0748907	+	0.230490i
$456$		0			0
$457$	25.6178	−	18.6124i	1.19835	−	0.870651i	0.204227	−	0.978923i	$-0.434532\pi$
$457$	25.6178	−	18.6124i	1.19835	−	0.870651i	0.994121	+	0.108272i	$0.0345318\pi$
$458$	0.139617	+	0.429696i	0.00652385	+	0.0200784i
$459$		0			0
$460$	−8.78389	−	6.38187i	−0.409551	−	0.297556i
$461$	25.4351			1.18463			0.592315	−	0.805706i	$-0.298214\pi$
$461$	25.4351			1.18463			0.592315	+	0.805706i	$0.298214\pi$
$462$		0			0
$463$	−16.3319			−0.759007			−0.379503	−	0.925190i	$-0.623905\pi$
$463$	−16.3319			−0.759007			−0.379503	+	0.925190i	$0.623905\pi$
$464$	10.6057	+	7.70549i	0.492357	+	0.357718i
$465$		0			0
$466$	−0.243298	−	0.748795i	−0.0112706	−	0.0346873i
$467$	6.90020	−	5.01329i	0.319303	−	0.231987i	−0.416575	−	0.909101i	$-0.636770\pi$
$467$	6.90020	−	5.01329i	0.319303	−	0.231987i	0.735878	+	0.677114i	$0.236770\pi$
$468$		0			0
$469$	−0.722284	−	2.22296i	−0.0333520	−	0.102647i
$470$	−0.200098	+	0.615837i	−0.00922982	+	0.0284065i
$471$		0			0
$472$	2.63797			0.121422
$473$	−0.630814	−	0.602638i	−0.0290049	−	0.0277093i
$474$		0			0
$475$	−4.92268	−	3.57654i	−0.225868	−	0.164103i
$476$	9.39133	−	28.9036i	0.430451	−	1.32479i
$477$		0			0
$478$	1.71673	−	1.24728i	0.0785216	−	0.0570493i
$479$	24.2283	−	17.6029i	1.10702	−	0.804296i	0.124827	−	0.992178i	$-0.460162\pi$
$479$	24.2283	−	17.6029i	1.10702	−	0.804296i	0.982192	+	0.187882i	$0.0601623\pi$
$480$		0			0
$481$	−0.525653	+	1.61779i	−0.0239677	+	0.0737650i
$482$	0.878041	+	0.637934i	0.0399937	+	0.0290571i
$483$		0			0
$484$	20.5010	−	7.71283i	0.931862	−	0.350583i
$485$	3.35655			0.152413
$486$		0			0
$487$	−6.05768	+	18.6436i	−0.274500	+	0.844823i	0.714852	+	0.699276i	$0.246494\pi$
$487$	−6.05768	+	18.6436i	−0.274500	+	0.844823i	−0.989351	+	0.145547i	$0.953506\pi$
$488$	0.288612	+	0.888257i	0.0130649	+	0.0402095i
$489$		0			0
$490$	−1.01912	+	0.740434i	−0.0460391	+	0.0334494i
$491$	4.87911	+	15.0163i	0.220191	+	0.677678i	0.998744	+	0.0500997i	$0.0159539\pi$
$491$	4.87911	+	15.0163i	0.220191	+	0.677678i	−0.778553	+	0.627579i	$0.784046\pi$
$492$		0			0
$493$	−9.06253	−	6.58432i	−0.408156	−	0.296543i
$494$	0.650099			0.0292494
$495$		0			0
$496$	7.06980			0.317443
$497$	−39.2773	−	28.5366i	−1.76183	−	1.28004i
$498$		0			0
$499$	3.46350	+	10.6596i	0.155048	+	0.477188i	0.998166	−	0.0605408i	$-0.0192825\pi$
$499$	3.46350	+	10.6596i	0.155048	+	0.477188i	−0.843118	+	0.537729i	$0.819283\pi$
$500$	−1.61096	+	1.17043i	−0.0720443	+	0.0523433i
$501$		0			0
$502$	0.0957345	+	0.294640i	0.00427284	+	0.0131504i
$503$	0.105965	−	0.326125i	0.00472473	−	0.0145412i	−0.948666	−	0.316279i	$-0.897567\pi$
$503$	0.105965	−	0.326125i	0.00472473	−	0.0145412i	0.953391	+	0.301737i	$0.0975666\pi$
$504$		0			0
$505$	−9.33498			−0.415401
$506$	0.302613	+	1.66375i	0.0134528	+	0.0739628i
$507$		0			0
$508$	31.8368	+	23.1308i	1.41253	+	1.02626i
$509$	6.04518	−	18.6052i	0.267948	−	0.824659i	−0.723052	−	0.690794i	$-0.757261\pi$
$509$	6.04518	−	18.6052i	0.267948	−	0.824659i	0.991000	−	0.133865i	$-0.0427389\pi$
$510$		0			0
$511$	20.7957	−	15.1089i	0.919946	−	0.668380i
$512$	5.94673	−	4.32055i	0.262811	−	0.190943i
$513$		0			0
$514$	−0.775763	+	2.38755i	−0.0342175	+	0.105311i
$515$	−11.2583	−	8.17961i	−0.496098	−	0.360436i
$516$		0			0
$517$	−20.2200	+	10.8913i	−0.889275	+	0.478998i
$518$	−0.629896			−0.0276760
$519$		0			0
$520$	0.131773	−	0.405557i	0.00577865	−	0.0177848i
$521$	−12.9869	−	39.9695i	−0.568966	−	1.75110i	−0.655864	−	0.754879i	$-0.727695\pi$
$521$	−12.9869	−	39.9695i	−0.568966	−	1.75110i	0.0868981	−	0.996217i	$-0.472305\pi$
$522$		0			0
$523$	−24.2790	+	17.6398i	−1.06165	+	0.771333i	−0.974393	−	0.224853i	$-0.927810\pi$
$523$	−24.2790	+	17.6398i	−1.06165	+	0.771333i	−0.0872555	+	0.996186i	$0.527810\pi$
$524$	−1.19054	−	3.66409i	−0.0520088	−	0.160067i
$525$		0			0
$526$	−0.920538	−	0.668810i	−0.0401374	−	0.0291615i
$527$	−6.04112			−0.263155
$528$		0			0
$529$	6.73067			0.292638
$530$	−0.108919	−	0.0791345i	−0.00473115	−	0.00343738i
$531$		0			0
$532$	−16.9405	−	52.1375i	−0.734464	−	2.26045i
$533$	1.61508	−	1.17342i	0.0699568	−	0.0508266i
$534$		0			0
$535$	−5.18787	−	15.9666i	−0.224291	−	0.690298i
$536$	−0.0595802	+	0.183369i	−0.00257347	+	0.00792033i
$537$		0			0
$538$	−0.195764			−0.00843998
$539$	−44.2773	−	5.97976i	−1.90716	−	0.257567i
$540$		0			0
$541$	8.35196	+	6.06806i	0.359079	+	0.260886i	0.752668	−	0.658400i	$-0.228767\pi$
$541$	8.35196	+	6.06806i	0.359079	+	0.260886i	−0.393589	+	0.919287i	$0.628767\pi$
$542$	−0.437568	+	1.34670i	−0.0187952	+	0.0578456i
$543$		0			0
$544$	−3.04442	+	2.21190i	−0.130529	+	0.0948346i
$545$	−2.95529	+	2.14714i	−0.126591	+	0.0919734i
$546$		0			0
$547$	12.9221	−	39.7702i	0.552510	−	1.70045i	−0.149921	−	0.988698i	$-0.547902\pi$
$547$	12.9221	−	39.7702i	0.552510	−	1.70045i	0.702431	−	0.711752i	$-0.252098\pi$
$548$	20.1939	+	14.6717i	0.862641	+	0.626746i
$549$		0			0
$550$	0.307347	+	0.0415079i	0.0131053	+	0.00176990i
$551$	−20.2065			−0.860826
$552$		0			0
$553$	−15.8038	+	48.6392i	−0.672047	+	2.06835i
$554$	−0.238990	−	0.735536i	−0.0101537	−	0.0312499i
$555$		0			0
$556$	−18.1153	+	13.1616i	−0.768261	+	0.558174i
$557$	11.8918	+	36.5993i	0.503874	+	1.55076i	0.802656	+	0.596442i	$0.203420\pi$
$557$	11.8918	+	36.5993i	0.503874	+	1.55076i	−0.298782	+	0.954321i	$0.596580\pi$
$558$		0			0
$559$	−0.243142	−	0.176653i	−0.0102838	−	0.00747163i
$560$	−17.8611			−0.754768
$561$		0			0
$562$	0.228840			0.00965303
$563$	24.8258	+	18.0370i	1.04628	+	0.760170i	0.971502	−	0.237030i	$-0.0761740\pi$
$563$	24.8258	+	18.0370i	1.04628	+	0.760170i	0.0747817	+	0.997200i	$0.476174\pi$
$564$		0			0
$565$	−3.67802	−	11.3198i	−0.154736	−	0.476227i
$566$	1.97410	−	1.43427i	0.0829775	−	0.0602867i
$567$		0			0
$568$	1.23754	+	3.80877i	0.0519262	+	0.159812i
$569$	−4.03220	+	12.4098i	−0.169039	+	0.520247i	−0.999311	−	0.0371104i	$-0.988185\pi$
$569$	−4.03220	+	12.4098i	−0.169039	+	0.520247i	0.830273	+	0.557357i	$0.188185\pi$
$570$		0			0
$571$	16.1300			0.675018			0.337509	−	0.941322i	$-0.390416\pi$
$571$	16.1300			0.675018			0.337509	+	0.941322i	$0.390416\pi$
$572$	6.64331	−	3.57834i	0.277771	−	0.149618i
$573$		0			0
$574$	0.598062	+	0.434517i	0.0249626	+	0.0181364i
$575$	1.68494	−	5.18572i	0.0702669	−	0.216259i
$576$		0			0
$577$	11.7885	−	8.56487i	0.490763	−	0.356560i	−0.314715	−	0.949186i	$-0.601909\pi$
$577$	11.7885	−	8.56487i	0.490763	−	0.356560i	0.805478	+	0.592626i	$0.201909\pi$
$578$	−0.425263	+	0.308972i	−0.0176886	+	0.0128515i
$579$		0			0
$580$	−2.04341	+	6.28898i	−0.0848482	+	0.261136i
$581$	16.4019	+	11.9167i	0.680465	+	0.494387i
$582$		0			0
$583$	−0.854511	−	4.69806i	−0.0353902	−	0.194574i
$584$	−2.12036			−0.0877411
$585$		0			0
$586$	0.388738	−	1.19641i	0.0160586	−	0.0494234i
$587$	8.61360	+	26.5099i	0.355521	+	1.09418i	0.955707	+	0.294321i	$0.0950936\pi$
$587$	8.61360	+	26.5099i	0.355521	+	1.09418i	−0.600185	+	0.799861i	$0.704906\pi$
$588$		0			0
$589$	−8.81605	+	6.40524i	−0.363259	+	0.263923i
$590$	0.204241	+	0.628588i	0.00840846	+	0.0258786i
$591$		0			0
$592$	−4.75478	−	3.45455i	−0.195420	−	0.141981i
$593$	−15.1037			−0.620236			−0.310118	−	0.950698i	$-0.600369\pi$
$593$	−15.1037			−0.620236			−0.310118	+	0.950698i	$0.600369\pi$
$594$		0			0
$595$	15.2622			0.625690
$596$	27.9238	+	20.2878i	1.14380	+	0.831023i
$597$		0			0
$598$	0.180020	+	0.554044i	0.00736156	+	0.0226566i
$599$	−20.9339	+	15.2093i	−0.855334	+	0.621437i	−0.926612	−	0.376020i	$-0.877292\pi$
$599$	−20.9339	+	15.2093i	−0.855334	+	0.621437i	0.0712774	+	0.997457i	$0.477292\pi$
$600$		0			0
$601$	−14.5321	−	44.7252i	−0.592776	−	1.82438i	−0.565498	−	0.824750i	$-0.691316\pi$
$601$	−14.5321	−	44.7252i	−0.592776	−	1.82438i	−0.0272781	−	0.999628i	$-0.508684\pi$
$602$	0.0343904	−	0.105843i	0.00140165	−	0.00431383i
$603$		0			0
$604$	0.0107610			0.000437861
$605$	6.86526	+	8.59466i	0.279112	+	0.349423i
$606$		0			0
$607$	28.4967	+	20.7041i	1.15665	+	0.840353i	0.989350	−	0.145553i	$-0.0464963\pi$
$607$	28.4967	+	20.7041i	1.15665	+	0.840353i	0.167297	+	0.985907i	$0.446496\pi$
$608$	−2.09763	+	6.45584i	−0.0850701	+	0.261819i
$609$		0			0
$610$	−0.189313	+	0.137544i	−0.00766506	+	0.00556899i
$611$	−6.40086	+	4.65049i	−0.258951	+	0.188139i
$612$		0			0
$613$	−7.23461	+	22.2658i	−0.292203	+	0.899309i	0.691943	+	0.721952i	$0.256755\pi$
$613$	−7.23461	+	22.2658i	−0.292203	+	0.899309i	−0.984147	+	0.177357i	$0.943245\pi$
$614$	2.05653	+	1.49416i	0.0829948	+	0.0602993i
$615$		0			0
$616$	4.04965	+	3.86876i	0.163165	+	0.155877i
$617$	−22.8910			−0.921557			−0.460778	−	0.887515i	$-0.652430\pi$
$617$	−22.8910			−0.921557			−0.460778	+	0.887515i	$0.652430\pi$
$618$		0			0
$619$	0.657441	−	2.02339i	0.0264248	−	0.0813271i	−0.936974	−	0.349398i	$-0.886386\pi$
$619$	0.657441	−	2.02339i	0.0264248	−	0.0813271i	0.963399	+	0.268071i	$0.0863861\pi$
$620$	1.10200	+	3.39161i	0.0442574	+	0.136210i
$621$		0			0
$622$	0.998521	−	0.725468i	0.0400370	−	0.0290886i
$623$	−18.5502	−	57.0916i	−0.743198	−	2.28733i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−1.51223			−0.0604410
$627$		0			0
$628$	−1.10482			−0.0440873
$629$	4.06294	+	2.95190i	0.162000	+	0.117700i
$630$		0			0
$631$	4.77702	+	14.7022i	0.190170	+	0.585284i	0.999999	−	0.00138227i	$-0.000439991\pi$
$631$	4.77702	+	14.7022i	0.190170	+	0.585284i	−0.809829	+	0.586666i	$0.800440\pi$
$632$	3.41296	−	2.47966i	0.135760	−	0.0986357i
$633$		0			0
$634$	−0.155494	−	0.478563i	−0.00617547	−	0.0190062i
$635$	−6.10700	+	18.7954i	−0.242349	+	0.745873i
$636$		0			0
$637$	−15.3918			−0.609844
$638$	0.906743	−	0.488406i	0.0358983	−	0.0193362i
$639$		0			0
$640$	2.39444	+	1.73967i	0.0946487	+	0.0687663i
$641$	−4.38201	+	13.4864i	−0.173079	+	0.532682i	−0.999541	−	0.0303108i	$-0.990350\pi$
$641$	−4.38201	+	13.4864i	−0.173079	+	0.532682i	0.826461	+	0.562993i	$0.190350\pi$
$642$		0			0
$643$	10.0270	−	7.28504i	0.395426	−	0.287294i	−0.372249	−	0.928133i	$-0.621413\pi$
$643$	10.0270	−	7.28504i	0.395426	−	0.287294i	0.767675	+	0.640839i	$0.221413\pi$
$644$	39.7429	−	28.8749i	1.56609	−	1.13783i
$645$		0			0
$646$	0.593101	−	1.82538i	0.0233352	−	0.0718185i
$647$	26.8970	+	19.5418i	1.05743	+	0.768267i	0.973611	−	0.228214i	$-0.0732885\pi$
$647$	26.8970	+	19.5418i	1.05743	+	0.768267i	0.0838181	+	0.996481i	$0.473289\pi$
$648$		0			0
$649$	−10.1628	+	21.1248i	−0.398923	+	0.829220i
$650$	0.106840			0.00419063
$651$		0			0
$652$	4.90068	−	15.0827i	0.191925	−	0.590685i
$653$	10.7558	+	33.1030i	0.420908	+	1.29542i	0.906858	+	0.421435i	$0.138474\pi$
$653$	10.7558	+	33.1030i	0.420908	+	1.29542i	−0.485951	+	0.873986i	$0.661526\pi$
$654$		0			0
$655$	1.56528	−	1.13724i	0.0611604	−	0.0444356i
$656$	2.13145	+	6.55992i	0.0832191	+	0.256122i
$657$		0			0
$658$	−2.37023	−	1.72207i	−0.0924011	−	0.0671334i
$659$	34.4953			1.34375			0.671873	−	0.740666i	$-0.265490\pi$
$659$	34.4953			1.34375			0.671873	+	0.740666i	$0.265490\pi$
$660$		0			0
$661$	1.77827			0.0691668			0.0345834	−	0.999402i	$-0.488990\pi$
$661$	1.77827			0.0691668			0.0345834	+	0.999402i	$0.488990\pi$
$662$	−1.40486	−	1.02069i	−0.0546014	−	0.0396702i
$663$		0			0
$664$	−0.516788	−	1.59051i	−0.0200553	−	0.0617238i
$665$	22.2728	−	16.1821i	0.863701	−	0.627516i
$666$		0			0
$667$	−5.59541	−	17.2209i	−0.216655	−	0.666796i
$668$	2.10839	−	6.48896i	0.0815761	−	0.251065i
$669$		0			0
$670$	−0.0483070			−0.00186626
$671$	−8.22502	−	1.11081i	−0.317523	−	0.0428823i
$672$		0			0
$673$	−15.6111	−	11.3422i	−0.601765	−	0.437208i	0.244740	−	0.969589i	$-0.421297\pi$
$673$	−15.6111	−	11.3422i	−0.601765	−	0.437208i	−0.846505	+	0.532381i	$0.821297\pi$
$674$	−0.260243	+	0.800945i	−0.0100242	+	0.0308513i
$675$		0			0
$676$	−18.8395	+	13.6877i	−0.724595	+	0.526449i
$677$	−13.6805	+	9.93949i	−0.525786	+	0.382006i	−0.818779	−	0.574109i	$-0.805349\pi$
$677$	−13.6805	+	9.93949i	−0.525786	+	0.382006i	0.292993	+	0.956114i	$0.405349\pi$
$678$		0			0
$679$	−4.69298	+	14.4435i	−0.180100	+	0.554291i
$680$	−1.01852	−	0.739998i	−0.0390585	−	0.0283776i
$681$		0			0
$682$	0.240791	−	0.500518i	0.00922035	−	0.0191658i
$683$	−4.14018			−0.158420			−0.0792098	−	0.996858i	$-0.525240\pi$
$683$	−4.14018			−0.158420			−0.0792098	+	0.996858i	$0.525240\pi$
$684$		0			0
$685$	−3.87363	+	11.9218i	−0.148004	+	0.455509i
$686$	−0.846069	−	2.60393i	−0.0323031	−	0.0994186i
$687$		0			0
$688$	0.840072	−	0.610348i	0.0320274	−	0.0232693i
$689$	−0.508335	−	1.56450i	−0.0193660	−	0.0596025i
$690$		0			0
$691$	37.4996	+	27.2450i	1.42655	+	1.03645i	0.990646	+	0.136457i	$0.0435714\pi$
$691$	37.4996	+	27.2450i	1.42655	+	1.03645i	0.435904	+	0.899993i	$0.356429\pi$
$692$	40.9539			1.55684
$693$		0			0
$694$	0.960437			0.0364577
$695$	−9.09743	−	6.60967i	−0.345085	−	0.250719i
$696$		0			0
$697$	−1.82132	−	5.60543i	−0.0689872	−	0.212321i
$698$	1.30583	−	0.948743i	0.0494265	−	0.0359105i
$699$		0			0
$700$	−2.78408	−	8.56853i	−0.105228	−	0.323860i
$701$	14.0465	−	43.2306i	0.530528	−	1.63280i	−0.222591	−	0.974912i	$-0.571452\pi$
$701$	14.0465	−	43.2306i	0.530528	−	1.63280i	0.753119	−	0.657884i	$-0.228548\pi$
$702$		0			0
$703$	9.05904			0.341668
$704$	4.62398	+	25.4224i	0.174273	+	0.958143i
$705$		0			0
$706$	1.72557	+	1.25370i	0.0649428	+	0.0471837i
$707$	13.0518	−	40.1692i	0.490862	−	1.51072i
$708$		0			0
$709$	11.3458	−	8.24318i	0.426099	−	0.309579i	−0.353988	−	0.935250i	$-0.615175\pi$
$709$	11.3458	−	8.24318i	0.426099	−	0.309579i	0.780087	+	0.625671i	$0.215175\pi$
$710$	−0.811757	+	0.589776i	−0.0304647	+	0.0221339i
$711$		0			0
$712$	−1.53018	+	4.70941i	−0.0573460	+	0.176493i
$713$	−7.90010	−	5.73976i	−0.295861	−	0.214956i
$714$		0			0
$715$	2.74003	+	2.61764i	0.102471	+	0.0978943i
$716$	−5.10622			−0.190829
$717$		0			0
$718$	−0.464497	+	1.42957i	−0.0173349	+	0.0533512i
$719$	−4.05999	−	12.4954i	−0.151412	−	0.465998i	0.846368	−	0.532599i	$-0.178785\pi$
$719$	−4.05999	−	12.4954i	−0.151412	−	0.465998i	−0.997780	+	0.0666007i	$0.978785\pi$
$720$		0			0
$721$	50.9383	−	37.0088i	1.89704	−	1.37828i
$722$	−0.520835	−	1.60297i	−0.0193835	−	0.0596562i
$723$		0			0
$724$	21.6140	+	15.7035i	0.803279	+	0.583616i
$725$	−3.32083			−0.123333
$726$		0			0
$727$	−18.3635			−0.681063			−0.340532	−	0.940233i	$-0.610607\pi$
$727$	−18.3635			−0.681063			−0.340532	+	0.940233i	$0.610607\pi$
$728$	1.56090	+	1.13406i	0.0578509	+	0.0420312i
$729$		0			0
$730$	−0.164166	−	0.505250i	−0.00607604	−	0.0187001i
$731$	−0.717839	+	0.521540i	−0.0265502	+	0.0192899i
$732$		0			0
$733$	−11.4329	−	35.1869i	−0.422284	−	1.29966i	−0.905571	−	0.424195i	$-0.860557\pi$
$733$	−11.4329	−	35.1869i	−0.422284	−	1.29966i	0.483287	−	0.875462i	$-0.339443\pi$
$734$	−0.635642	+	1.95631i	−0.0234620	+	0.0722086i
$735$		0			0
$736$	−6.08282			−0.224216
$737$	−1.23888	−	1.18354i	−0.0456348	−	0.0435964i
$738$		0			0
$739$	−7.96909	−	5.78988i	−0.293148	−	0.212984i	0.431484	−	0.902121i	$-0.357990\pi$
$739$	−7.96909	−	5.78988i	−0.293148	−	0.212984i	−0.724632	+	0.689136i	$0.757990\pi$
$740$	0.916110	−	2.81950i	0.0336769	−	0.103647i
$741$		0			0
$742$	0.492808	−	0.358046i	0.0180915	−	0.0131443i
$743$	22.2052	−	16.1330i	0.814629	−	0.591862i	−0.100540	−	0.994933i	$-0.532057\pi$
$743$	22.2052	−	16.1330i	0.814629	−	0.591862i	0.915169	+	0.403071i	$0.132057\pi$
$744$		0			0
$745$	−5.35640	+	16.4853i	−0.196243	+	0.603974i
$746$	−1.53272	−	1.11359i	−0.0561170	−	0.0407714i
$747$		0			0
$748$	−3.98658	−	21.9180i	−0.145764	−	0.801401i
$749$	75.9591			2.77549
$750$		0			0
$751$	4.24232	−	13.0565i	0.154804	−	0.476439i	−0.843337	−	0.537385i	$-0.819412\pi$
$751$	4.24232	−	13.0565i	0.154804	−	0.476439i	0.998141	+	0.0609469i	$0.0194120\pi$
$752$	−8.44732	−	25.9982i	−0.308042	−	0.948056i
$753$		0			0
$754$	0.287039	−	0.208546i	0.0104533	−	0.00759479i
$755$	0.00166997	+	0.00513965i	6.07766e−5	+	0.000187051i
$756$		0			0
$757$	18.5507	+	13.4779i	0.674236	+	0.489861i	0.871440	−	0.490501i	$-0.163186\pi$
$757$	18.5507	+	13.4779i	0.674236	+	0.489861i	−0.197205	+	0.980362i	$0.563186\pi$
$758$	0.348578			0.0126609
$759$		0			0
$760$	−2.27097			−0.0823767
$761$	−16.7319	−	12.1565i	−0.606533	−	0.440672i	0.241659	−	0.970361i	$-0.422308\pi$
$761$	−16.7319	−	12.1565i	−0.606533	−	0.440672i	−0.848192	+	0.529689i	$0.822308\pi$
$762$		0			0
$763$	−5.10737	−	15.7189i	−0.184899	−	0.569061i
$764$	−29.3031	+	21.2899i	−1.06015	+	0.770243i
$765$		0			0
$766$	−0.317783	−	0.978034i	−0.0114819	−	0.0353378i
$767$	−2.49553	+	7.68046i	−0.0901084	+	0.277325i
$768$		0			0
$769$	38.4306			1.38584			0.692922	−	0.721013i	$-0.256323\pi$
$769$	38.4306			1.38584			0.692922	+	0.721013i	$0.256323\pi$
$770$	−0.608331	+	1.26450i	−0.0219227	+	0.0455696i
$771$		0			0
$772$	25.2738	+	18.3625i	0.909624	+	0.660880i
$773$	−15.4325	+	47.4964i	−0.555069	+	1.70833i	0.140693	+	0.990053i	$0.455067\pi$
$773$	−15.4325	+	47.4964i	−0.555069	+	1.70833i	−0.695762	+	0.718272i	$0.744933\pi$
$774$		0			0
$775$	−1.44887	+	1.05267i	−0.0520451	+	0.0378129i
$776$	1.01349	−	0.736341i	0.0363821	−	0.0264331i
$777$		0			0
$778$	0.271109	−	0.834389i	0.00971975	−	0.0299143i
$779$	−8.60121	−	6.24914i	−0.308170	−	0.223899i
$780$		0			0
$781$	−35.2681	−	4.76305i	−1.26199	−	0.170435i
$782$	1.71991			0.0615037
$783$		0			0
$784$	16.4334	−	50.5767i	0.586906	−	1.80631i
$785$	−0.171454	−	0.527682i	−0.00611946	−	0.0188338i
$786$		0			0
$787$	12.5834	−	9.14241i	0.448551	−	0.325892i	−0.340472	−	0.940255i	$-0.610587\pi$
$787$	12.5834	−	9.14241i	0.448551	−	0.325892i	0.789024	+	0.614363i	$0.210587\pi$
$788$	−13.4442	−	41.3769i	−0.478928	−	1.47399i
$789$		0			0
$790$	0.855110	+	0.621274i	0.0304235	+	0.0221039i
$791$	53.8524			1.91477
$792$		0			0
$793$	−2.85919			−0.101533
$794$	1.68805	+	1.22644i	0.0599067	+	0.0435248i
$795$		0			0
$796$	2.80099	+	8.62057i	0.0992786	+	0.305548i
$797$	37.3012	−	27.1009i	1.32127	−	0.959962i	0.321359	−	0.946957i	$-0.395860\pi$
$797$	37.3012	−	27.1009i	1.32127	−	0.959962i	0.999915	−	0.0130049i	$-0.00413972\pi$
$798$		0			0
$799$	7.21821	+	22.2154i	0.255362	+	0.785923i
$800$	−0.344735	+	1.06098i	−0.0121882	+	0.0375114i
$801$		0			0
$802$	−2.30803			−0.0814994
$803$	8.16868	−	16.9798i	0.288266	−	0.599203i
$804$		0			0
$805$	19.9587	+	14.5009i	0.703453	+	0.511088i
$806$	0.0591277	−	0.181976i	0.00208268	−	0.00640984i
$807$		0			0
$808$	−2.81863	+	2.04786i	−0.0991591	+	0.0720433i
$809$	−30.3700	+	22.0651i	−1.06775	+	0.775767i	−0.975507	−	0.219969i	$-0.929404\pi$
$809$	−30.3700	+	22.0651i	−1.06775	+	0.775767i	−0.0922454	+	0.995736i	$0.529404\pi$
$810$		0			0
$811$	2.22661	−	6.85281i	0.0781870	−	0.240635i	−0.904322	−	0.426852i	$-0.859623\pi$
$811$	2.22661	−	6.85281i	0.0781870	−	0.240635i	0.982509	+	0.186217i	$0.0596227\pi$
$812$	−24.2050	−	17.5859i	−0.849428	−	0.617146i
$813$		0			0
$814$	−0.406514	+	0.218964i	−0.0142483	+	0.00767468i
$815$	7.96428			0.278977
$816$		0			0
$817$	−0.494596	+	1.52221i	−0.0173037	+	0.0532554i
$818$	−0.852597	−	2.62402i	−0.0298104	−	0.0917469i
$819$		0			0
$820$	−2.81477	+	2.04505i	−0.0982960	+	0.0714162i
$821$	2.66807	+	8.21147i	0.0931163	+	0.286582i	0.986758	−	0.162198i	$-0.0518584\pi$
$821$	2.66807	+	8.21147i	0.0931163	+	0.286582i	−0.893642	+	0.448781i	$0.851858\pi$
$822$		0			0
$823$	20.2352	+	14.7017i	0.705354	+	0.512470i	0.881672	−	0.471864i	$-0.156419\pi$
$823$	20.2352	+	14.7017i	0.705354	+	0.512470i	−0.176318	+	0.984333i	$0.556419\pi$
$824$	−5.19375			−0.180933
$825$		0			0
$826$	−2.99042			−0.104050
$827$	39.5387	+	28.7265i	1.37489	+	0.998919i	0.997337	+	0.0729332i	$0.0232360\pi$
$827$	39.5387	+	28.7265i	1.37489	+	0.998919i	0.377558	+	0.925986i	$0.376764\pi$
$828$		0			0
$829$	1.63522	+	5.03270i	0.0567937	+	0.174793i	0.975429	−	0.220313i	$-0.0707079\pi$
$829$	1.63522	+	5.03270i	0.0567937	+	0.174793i	−0.918636	+	0.395106i	$0.870708\pi$
$830$	0.338983	−	0.246286i	0.0117663	−	0.00854871i
$831$		0			0
$832$	2.75073	+	8.46589i	0.0953645	+	0.293502i
$833$	−14.0423	+	43.2177i	−0.486536	+	1.49740i
$834$		0			0
$835$	3.42643			0.118576
$836$	−29.0568	−	27.7590i	−1.00495	−	0.960064i
$837$		0			0
$838$	−0.683556	−	0.496633i	−0.0236131	−	0.0171559i
$839$	4.09196	−	12.5938i	0.141270	−	0.434785i	−0.855242	−	0.518228i	$-0.826592\pi$
$839$	4.09196	−	12.5938i	0.141270	−	0.434785i	0.996513	+	0.0834435i	$0.0265918\pi$
$840$		0			0
$841$	14.5397	−	10.5637i	0.501369	−	0.364266i
$842$	1.07577	−	0.781592i	0.0370734	−	0.0269354i
$843$		0			0
$844$	−11.6670	+	35.9072i	−0.401593	+	1.23598i
$845$	−9.46110	−	6.87389i	−0.325472	−	0.236469i
$846$		0			0
$847$	−46.5822	+	17.5251i	−1.60058	+	0.602168i
$848$	5.68361			0.195176
$849$		0			0
$850$	0.0974731	−	0.299991i	0.00334330	−	0.0102896i
$851$	2.50855	+	7.72053i	0.0859920	+	0.264656i
$852$		0			0
$853$	−1.79509	+	1.30421i	−0.0614626	+	0.0446552i	−0.618092	−	0.786106i	$-0.712094\pi$
$853$	−1.79509	+	1.30421i	−0.0614626	+	0.0446552i	0.556630	+	0.830761i	$0.312094\pi$
$854$	−0.327174	−	1.00694i	−0.0111956	−	0.0344567i
$855$		0			0
$856$	−5.06911	−	3.68292i	−0.173259	−	0.125880i
$857$	−31.4625			−1.07474			−0.537368	−	0.843348i	$-0.680582\pi$
$857$	−31.4625			−1.07474			−0.537368	+	0.843348i	$0.680582\pi$
$858$		0			0
$859$	9.07676			0.309695			0.154848	−	0.987938i	$-0.450511\pi$
$859$	9.07676			0.309695			0.154848	+	0.987938i	$0.450511\pi$
$860$	0.423749	+	0.307872i	0.0144497	+	0.0104983i
$861$		0			0
$862$	−0.0500352	−	0.153993i	−0.00170421	−	0.00524501i
$863$	34.3704	−	24.9716i	1.16998	−	0.850042i	0.178976	−	0.983853i	$-0.442721\pi$
$863$	34.3704	−	24.9716i	1.16998	−	0.850042i	0.991007	+	0.133811i	$0.0427215\pi$
$864$		0			0
$865$	6.35552	+	19.5603i	0.216094	+	0.665069i
$866$	−0.533065	+	1.64060i	−0.0181143	+	0.0557500i
$867$		0			0
$868$	−16.1351			−0.547662
$869$	6.70865	+	36.8838i	0.227575	+	1.25120i
$870$		0			0
$871$	−0.477516	−	0.346936i	−0.0161800	−	0.0117555i
$872$	−0.421300	+	1.29663i	−0.0142670	+	0.0439094i
$873$		0			0
$874$	2.50993	−	1.82357i	0.0848996	−	0.0616832i
$875$	3.66042	−	2.65945i	0.123745	−	0.0899058i
$876$		0			0
$877$	−9.67537	+	29.7777i	−0.326714	+	1.00552i	0.643947	+	0.765070i	$0.277296\pi$
$877$	−9.67537	+	29.7777i	−0.326714	+	1.00552i	−0.970661	+	0.240452i	$0.922704\pi$
$878$	−1.29896	−	0.943750i	−0.0438378	−	0.0318500i
$879$		0			0
$880$	−11.5269	+	6.20885i	−0.388573	+	0.209300i
$881$	−21.5189			−0.724990			−0.362495	−	0.931986i	$-0.618075\pi$
$881$	−21.5189			−0.724990			−0.362495	+	0.931986i	$0.618075\pi$
$882$		0			0
$883$	−0.201650	+	0.620614i	−0.00678605	+	0.0208853i	−0.954392	−	0.298556i	$-0.903495\pi$
$883$	−0.201650	+	0.620614i	−0.00678605	+	0.0208853i	0.947606	+	0.319441i	$0.103495\pi$
$884$	−2.37155	−	7.29889i	−0.0797639	−	0.245488i
$885$		0			0
$886$	−2.76877	+	2.01163i	−0.0930187	+	0.0675820i
$887$	4.52593	+	13.9294i	0.151966	+	0.467702i	0.997841	−	0.0656786i	$-0.0209212\pi$
$887$	4.52593	+	13.9294i	0.151966	+	0.467702i	−0.845875	+	0.533381i	$0.820921\pi$
$888$		0			0
$889$	−72.3396	−	52.5578i	−2.42619	−	1.76273i
$890$	−1.24065			−0.0415868
$891$		0			0
$892$	−9.71637			−0.325328
$893$	34.0882	+	24.7665i	1.14072	+	0.828780i
$894$		0			0
$895$	−0.792419	−	2.43882i	−0.0264877	−	0.0815206i
$896$	−10.8337	+	7.87116i	−0.361929	+	0.262957i
$897$		0			0
$898$	−0.479760	−	1.47655i	−0.0160098	−	0.0492731i
$899$	−1.83782	+	5.65622i	−0.0612946	+	0.188645i
$900$		0			0
$901$	−4.85662			−0.161798
$902$	0.537016	+	0.0725252i	0.0178807	+	0.00241483i
$903$		0			0
$904$	−3.59382	−	2.61107i	−0.119529	−	0.0868428i
$905$	−4.14604	+	12.7602i	−0.137819	+	0.424163i
$906$		0			0
$907$	−23.2552	+	16.8959i	−0.772175	+	0.561018i	−0.902620	−	0.430437i	$-0.858359\pi$
$907$	−23.2552	+	16.8959i	−0.772175	+	0.561018i	0.130445	+	0.991456i	$0.458359\pi$
$908$	−26.2955	+	19.1048i	−0.872645	+	0.634014i
$909$		0			0
$910$	−0.149380	+	0.459743i	−0.00495188	+	0.0152403i
$911$	13.9813	+	10.1580i	0.463222	+	0.336550i	0.794794	−	0.606880i	$-0.207579\pi$
$911$	13.9813	+	10.1580i	0.463222	+	0.336550i	−0.331572	+	0.943430i	$0.607579\pi$
$912$		0			0
$913$	14.7277	+	1.98901i	0.487416	+	0.0658266i
$914$	2.96102			0.0979418
$915$		0			0
$916$	2.97308	−	9.15020i	0.0982333	−	0.302331i
$917$	2.70513	+	8.32554i	0.0893313	+	0.274933i
$918$		0			0
$919$	1.77859	−	1.29222i	0.0586701	−	0.0426263i	−0.558064	−	0.829798i	$-0.688456\pi$
$919$	1.77859	−	1.29222i	0.0586701	−	0.0426263i	0.616734	+	0.787172i	$0.288456\pi$
$920$	−0.628857	−	1.93542i	−0.0207328	−	0.0638090i
$921$		0			0
$922$	1.92419	+	1.39801i	0.0633699	+	0.0460409i
$923$	−12.2600			−0.403542
$924$		0			0
$925$	1.48881			0.0489517
$926$	−1.23552	−	0.897661i	−0.0406019	−	0.0294990i
$927$		0			0
$928$	1.14481	+	3.52335i	0.0375801	+	0.115660i
$929$	19.5866	−	14.2305i	0.642616	−	0.466888i	−0.218132	−	0.975919i	$-0.569996\pi$
$929$	19.5866	−	14.2305i	0.642616	−	0.466888i	0.860748	+	0.509031i	$0.169996\pi$
$930$		0			0
$931$	25.3301	+	77.9579i	0.830159	+	2.55497i
$932$	−5.18094	+	15.9453i	−0.169707	+	0.522305i
$933$		0			0
$934$	0.797556			0.0260968
$935$	9.84973	−	5.30544i	0.322121	−	0.173506i
$936$		0			0
$937$	16.8459	+	12.2393i	0.550333	+	0.399840i	0.827908	−	0.560864i	$-0.189531\pi$
$937$	16.8459	+	12.2393i	0.550333	+	0.399840i	−0.277575	+	0.960704i	$0.589531\pi$
$938$	0.0675407	−	0.207869i	0.00220528	−	0.00678716i
$939$		0			0
$940$	11.1554	−	8.10491i	0.363851	−	0.264353i
$941$	27.6787	−	20.1098i	0.902301	−	0.655560i	−0.0367552	−	0.999324i	$-0.511702\pi$
$941$	27.6787	−	20.1098i	0.902301	−	0.655560i	0.939056	+	0.343764i	$0.111702\pi$
$942$		0			0
$943$	2.94403	−	9.06080i	0.0958709	−	0.295060i
$944$	−22.5733	−	16.4004i	−0.734697	−	0.533789i
$945$		0			0
$946$	−0.0145986	−	0.0802621i	−0.000474640	−	0.00260955i
$947$	−33.8128			−1.09877			−0.549383	−	0.835570i	$-0.685137\pi$
$947$	−33.8128			−1.09877			−0.549383	+	0.835570i	$0.685137\pi$
$948$		0			0
$949$	2.00587	−	6.17344i	0.0651133	−	0.200398i
$950$	−0.175826	−	0.541138i	−0.00570456	−	0.0175568i
$951$		0			0
$952$	4.60832	−	3.34814i	0.149356	−	0.108514i
$953$	−7.91027	−	24.3453i	−0.256239	−	0.788622i	−0.993583	−	0.113105i	$-0.963920\pi$
$953$	−7.91027	−	24.3453i	−0.256239	−	0.788622i	0.737344	−	0.675517i	$-0.236080\pi$
$954$		0			0
$955$	−14.7159	−	10.6917i	−0.476195	−	0.345976i
$956$	−45.1871			−1.46146
$957$		0			0
$958$	2.80042			0.0904774
$959$	−45.8845	−	33.3371i	−1.48169	−	1.07651i
$960$		0			0
$961$	−8.58840	−	26.4324i	−0.277045	−	0.852658i
$962$	−0.128686	+	0.0934959i	−0.00414901	+	0.00301443i
$963$		0			0
$964$	−7.14182	−	21.9803i	−0.230023	−	0.707937i
$965$	−4.84806	+	14.9208i	−0.156065	+	0.480317i
$966$		0			0
$967$	43.8942			1.41154			0.705772	−	0.708439i	$-0.250600\pi$
$967$	43.8942			1.41154			0.705772	+	0.708439i	$0.250600\pi$
$968$	3.95836	+	1.08904i	0.127227	+	0.0350029i
$969$		0			0
$970$	0.253927	+	0.184489i	0.00815310	+	0.00592357i
$971$	−11.2392	+	34.5906i	−0.360682	+	1.11006i	0.591959	+	0.805968i	$0.298355\pi$
$971$	−11.2392	+	34.5906i	−0.360682	+	1.11006i	−0.952641	+	0.304097i	$0.901645\pi$
$972$		0			0
$973$	41.1616	−	29.9056i	1.31958	−	0.958730i
$974$	−1.48299	+	1.07746i	−0.0475182	+	0.0345240i
$975$		0			0
$976$	3.05269	−	9.39520i	0.0977141	−	0.300733i
$977$	8.37462	+	6.08452i	0.267928	+	0.194661i	0.713635	−	0.700518i	$-0.247048\pi$
$977$	8.37462	+	6.08452i	0.267928	+	0.194661i	−0.445707	+	0.895179i	$0.647048\pi$
$978$		0			0
$979$	−31.8178	−	30.3966i	−1.01690	−	0.971481i
$980$	26.8248			0.856888
$981$		0			0
$982$	−0.456245	+	1.40418i	−0.0145594	+	0.0448091i
$983$	6.83416	+	21.0334i	0.217976	+	0.670861i	0.998929	+	0.0462712i	$0.0147338\pi$
$983$	6.83416	+	21.0334i	0.217976	+	0.670861i	−0.780953	+	0.624590i	$0.785266\pi$
$984$		0			0
$985$	17.6759	−	12.8423i	0.563201	−	0.409190i
$986$	−0.323692	−	0.996222i	−0.0103085	−	0.0317262i
$987$		0			0
$988$	−11.1997	−	8.13707i	−0.356310	−	0.258875i
$989$	−1.43426			−0.0456067
$990$		0			0
$991$	−55.5911			−1.76591			−0.882955	−	0.469457i	$-0.844450\pi$
$991$	−55.5911			−1.76591			−0.882955	+	0.469457i	$0.844450\pi$
$992$	1.61634	+	1.17434i	0.0513189	+	0.0372853i
$993$		0			0
$994$	−1.40289	−	4.31765i	−0.0444970	−	0.136948i
$995$	−3.68265	+	2.67560i	−0.116748	+	0.0848222i
$996$		0			0
$997$	3.33465	+	10.2630i	0.105609	+	0.325032i	0.989873	−	0.141956i	$-0.0453391\pi$
$997$	3.33465	+	10.2630i	0.105609	+	0.325032i	−0.884264	+	0.466988i	$0.845339\pi$
$998$	−0.323872	+	0.996775i	−0.0102520	+	0.0315524i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.f.136.1		8
3.2	odd	2		55.2.g.a.26.2	✓	8
11.3	even	5	inner	495.2.n.f.91.1		8
11.5	even	5		5445.2.a.bg.1.3		4
11.6	odd	10		5445.2.a.bu.1.2		4
12.11	even	2		880.2.bo.e.81.1		8
15.2	even	4		275.2.z.b.224.3		16
15.8	even	4		275.2.z.b.224.2		16
15.14	odd	2		275.2.h.b.26.1		8
33.2	even	10		605.2.g.g.511.2		8
33.5	odd	10		605.2.a.l.1.2		4
33.8	even	10		605.2.g.n.366.1		8
33.14	odd	10		55.2.g.a.36.2	yes	8
33.17	even	10		605.2.a.i.1.3		4
33.20	odd	10		605.2.g.j.511.1		8
33.26	odd	10		605.2.g.j.251.1		8
33.29	even	10		605.2.g.g.251.2		8
33.32	even	2		605.2.g.n.81.1		8
132.47	even	10		880.2.bo.e.641.1		8
132.71	even	10		9680.2.a.cs.1.1		4
132.83	odd	10		9680.2.a.cv.1.1		4
165.14	odd	10		275.2.h.b.201.1		8
165.47	even	20		275.2.z.b.124.2		16
165.104	odd	10		3025.2.a.v.1.3		4
165.113	even	20		275.2.z.b.124.3		16
165.149	even	10		3025.2.a.be.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	3.2	odd	2
55.2.g.a.36.2	yes	8	33.14	odd	10
275.2.h.b.26.1		8	15.14	odd	2
275.2.h.b.201.1		8	165.14	odd	10
275.2.z.b.124.2		16	165.47	even	20
275.2.z.b.124.3		16	165.113	even	20
275.2.z.b.224.2		16	15.8	even	4
275.2.z.b.224.3		16	15.2	even	4
495.2.n.f.91.1		8	11.3	even	5	inner
495.2.n.f.136.1		8	1.1	even	1	trivial
605.2.a.i.1.3		4	33.17	even	10
605.2.a.l.1.2		4	33.5	odd	10
605.2.g.g.251.2		8	33.29	even	10
605.2.g.g.511.2		8	33.2	even	10
605.2.g.j.251.1		8	33.26	odd	10
605.2.g.j.511.1		8	33.20	odd	10
605.2.g.n.81.1		8	33.32	even	2
605.2.g.n.366.1		8	33.8	even	10
880.2.bo.e.81.1		8	12.11	even	2
880.2.bo.e.641.1		8	132.47	even	10
3025.2.a.v.1.3		4	165.104	odd	10
3025.2.a.be.1.2		4	165.149	even	10
5445.2.a.bg.1.3		4	11.5	even	5
5445.2.a.bu.1.2		4	11.6	odd	10
9680.2.a.cs.1.1		4	132.71	even	10
9680.2.a.cv.1.1		4	132.83	odd	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0756511 + 0.0549637i) q^{2} +(-0.615332 - 1.89380i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.39815 + 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +O(q^{10})\)	\(q+(0.0756511 + 0.0549637i) q^{2} +(-0.615332 - 1.89380i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.39815 + 4.30308i) q^{7} +(0.115332 - 0.354955i) q^{8} +0.0935099 q^{10} +(2.39815 + 2.29104i) q^{11} +(0.924349 + 0.671579i) q^{13} +(-0.130741 + 0.402380i) q^{14} +(-3.19369 + 2.32035i) q^{16} +(2.72899 - 1.98273i) q^{17} +(1.88030 - 5.78696i) q^{19} +(-1.61096 - 1.17043i) q^{20} +(0.0554990 + 0.305131i) q^{22} +5.45258 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.0330155 + 0.101611i) q^{26} +(7.28883 - 5.29564i) q^{28} +(-1.02619 - 3.15830i) q^{29} +(-1.44887 - 1.05267i) q^{31} -1.11558 q^{32} +0.315430 q^{34} +(3.66042 + 2.65945i) q^{35} +(0.460067 + 1.41594i) q^{37} +(0.460319 - 0.334441i) q^{38} +(-0.115332 - 0.354955i) q^{40} +(0.539933 - 1.66174i) q^{41} -0.263041 q^{43} +(2.86310 - 5.95137i) q^{44} +(0.412494 + 0.299694i) q^{46} +(-2.13986 + 6.58580i) q^{47} +(-10.8985 + 7.91824i) q^{49} +(0.0756511 - 0.0549637i) q^{50} +(0.703052 - 2.16377i) q^{52} +(-1.16479 - 0.846269i) q^{53} +(3.28679 + 0.443888i) q^{55} +1.68865 q^{56} +(0.0959593 - 0.295332i) q^{58} +(2.18416 + 6.72216i) q^{59} +(-2.02452 + 1.47090i) q^{61} +(-0.0517503 - 0.159271i) q^{62} +(6.30297 + 4.57938i) q^{64} +1.14256 q^{65} -0.516598 q^{67} +(-5.43413 - 3.94812i) q^{68} +(0.130741 + 0.402380i) q^{70} +(-8.68098 + 6.30710i) q^{71} +(-1.75560 - 5.40317i) q^{73} +(-0.0430208 + 0.132404i) q^{74} -12.1163 q^{76} +(-6.50552 + 13.5227i) q^{77} +(9.14460 + 6.64394i) q^{79} +(-1.21988 + 3.75440i) q^{80} +(0.132182 - 0.0960360i) q^{82} +(3.62511 - 2.63380i) q^{83} +(1.04238 - 3.20812i) q^{85} +(-0.0198994 - 0.0144577i) q^{86} +(1.08980 - 0.587008i) q^{88} -13.2676 q^{89} +(-1.59747 + 4.91652i) q^{91} +(-3.35515 - 10.3261i) q^{92} +(-0.523863 + 0.380608i) q^{94} +(-1.88030 - 5.78696i) q^{95} +(2.71551 + 1.97293i) q^{97} -1.25970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8	\( 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 6 q^{10} + 5 q^{11} + 4 q^{13} - 16 q^{14} - 20 q^{16} - q^{17} - q^{19} + q^{20} + 33 q^{22} + 18 q^{23} - 2 q^{25} + 14 q^{26} + 4 q^{28} - 19 q^{29} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 4 q^{37} + 6 q^{38} - 2 q^{40} + 4 q^{41} + 42 q^{43} + 28 q^{44} - 41 q^{46} - 4 q^{47} - 15 q^{49} + 4 q^{50} - 26 q^{52} - 3 q^{53} + 5 q^{55} - 30 q^{56} - 6 q^{58} + 19 q^{59} - 2 q^{61} + 38 q^{62} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} + 16 q^{70} - 40 q^{71} - 23 q^{73} - 48 q^{74} + 16 q^{76} + 28 q^{77} + 17 q^{79} - 15 q^{80} + 2 q^{82} + 25 q^{83} - 4 q^{85} + 31 q^{86} + 22 q^{88} - 12 q^{91} - 81 q^{92} + 33 q^{94} + q^{95} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 + 6 * q^10 + 5 * q^11 + 4 * q^13 - 16 * q^14 - 20 * q^16 - q^17 - q^19 + q^20 + 33 * q^22 + 18 * q^23 - 2 * q^25 + 14 * q^26 + 4 * q^28 - 19 * q^29 + 6 * q^31 - 12 * q^32 - 20 * q^34 + 8 * q^35 + 4 * q^37 + 6 * q^38 - 2 * q^40 + 4 * q^41 + 42 * q^43 + 28 * q^44 - 41 * q^46 - 4 * q^47 - 15 * q^49 + 4 * q^50 - 26 * q^52 - 3 * q^53 + 5 * q^55 - 30 * q^56 - 6 * q^58 + 19 * q^59 - 2 * q^61 + 38 * q^62 + 6 * q^64 - 14 * q^65 - 2 * q^67 - 35 * q^68 + 16 * q^70 - 40 * q^71 - 23 * q^73 - 48 * q^74 + 16 * q^76 + 28 * q^77 + 17 * q^79 - 15 * q^80 + 2 * q^82 + 25 * q^83 - 4 * q^85 + 31 * q^86 + 22 * q^88 - 12 * q^91 - 81 * q^92 + 33 * q^94 + q^95 + 12 * q^97 + 84 * q^98

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