LMFDB - Embedded newform 637.2.g.m.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$-0.756863 + 1.31093i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.m.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21605 - 2.10626i) q^{2} +0.753592 q^{3} +(-1.95755 + 3.39058i) q^{4} +(-0.170769 + 0.295780i) q^{5} +(-0.916405 - 1.58726i) q^{6} +4.65773 q^{8} -2.43210 q^{9} +O(q^{10})$	\(q+(-1.21605 - 2.10626i) q^{2} +0.753592 q^{3} +(-1.95755 + 3.39058i) q^{4} +(-0.170769 + 0.295780i) q^{5} +(-0.916405 - 1.58726i) q^{6} +4.65773 q^{8} -2.43210 q^{9} +0.830652 q^{10} -2.43210 q^{11} +(-1.47520 + 2.55511i) q^{12} +(2.50139 + 2.59674i) q^{13} +(-0.128690 + 0.222897i) q^{15} +(-1.74892 - 3.02922i) q^{16} +(0.974117 - 1.68722i) q^{17} +(2.95755 + 5.12263i) q^{18} -6.29039 q^{19} +(-0.668577 - 1.15801i) q^{20} +(2.95755 + 5.12263i) q^{22} +(1.84474 + 3.19518i) q^{23} +3.51003 q^{24} +(2.44168 + 4.22911i) q^{25} +(2.42760 - 8.42634i) q^{26} -4.09359 q^{27} +(-2.22068 + 3.84632i) q^{29} +0.625973 q^{30} +(0.987661 + 1.71068i) q^{31} +(0.404180 - 0.700061i) q^{32} -1.83281 q^{33} -4.73830 q^{34} +(4.76096 - 8.24623i) q^{36} +(4.81433 + 8.33867i) q^{37} +(7.64942 + 13.2492i) q^{38} +(1.88503 + 1.95688i) q^{39} +(-0.795393 + 1.37766i) q^{40} +(-6.26793 + 10.8564i) q^{41} +(4.20368 + 7.28099i) q^{43} +(4.76096 - 8.24623i) q^{44} +(0.415326 - 0.719366i) q^{45} +(4.48659 - 7.77100i) q^{46} +(4.50265 - 7.79882i) q^{47} +(-1.31797 - 2.28279i) q^{48} +(5.93840 - 10.2856i) q^{50} +(0.734087 - 1.27148i) q^{51} +(-13.7011 + 3.39790i) q^{52} +(-0.746129 - 1.29233i) q^{53} +(4.97800 + 8.62216i) q^{54} +(0.415326 - 0.719366i) q^{55} -4.74039 q^{57} +10.8018 q^{58} +(-0.313495 + 0.542990i) q^{59} +(-0.503834 - 0.872666i) q^{60} -1.14319 q^{61} +(2.40209 - 4.16054i) q^{62} -8.96169 q^{64} +(-1.19522 + 0.296418i) q^{65} +(2.22879 + 3.86037i) q^{66} -5.59199 q^{67} +(3.81377 + 6.60564i) q^{68} +(1.39018 + 2.40786i) q^{69} +(-4.74859 - 8.22481i) q^{71} -11.3280 q^{72} +(-5.95934 - 10.3219i) q^{73} +(11.7089 - 20.2805i) q^{74} +(1.84003 + 3.18702i) q^{75} +(12.3138 - 21.3281i) q^{76} +(1.82942 - 6.35002i) q^{78} +(-2.23583 + 3.87258i) q^{79} +1.19464 q^{80} +4.21140 q^{81} +30.4885 q^{82} +1.41231 q^{83} +(0.332697 + 0.576248i) q^{85} +(10.2238 - 17.7081i) q^{86} +(-1.67348 + 2.89856i) q^{87} -11.3280 q^{88} +(-6.22219 - 10.7771i) q^{89} -2.02023 q^{90} -14.4447 q^{92} +(0.744294 + 1.28915i) q^{93} -21.9018 q^{94} +(1.07420 - 1.86057i) q^{95} +(0.304587 - 0.527560i) q^{96} +(-5.13850 - 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.21605	−	2.10626i	−0.859877	−	1.48935i	−0.872046	−	0.489424i	$-0.837207\pi$
$2$	−1.21605	−	2.10626i	−0.859877	−	1.48935i	0.0121689	−	0.999926i	$-0.496126\pi$
$3$	0.753592			0.435087			0.217543	−	0.976051i	$-0.430196\pi$
$3$	0.753592			0.435087			0.217543	+	0.976051i	$0.430196\pi$
$4$	−1.95755	+	3.39058i	−0.978776	+	1.69529i
$5$	−0.170769	+	0.295780i	−0.0763700	+	0.132277i	−0.901681	−	0.432401i	$-0.857666\pi$
$5$	−0.170769	+	0.295780i	−0.0763700	+	0.132277i	0.825311	+	0.564678i	$0.191000\pi$
$6$	−0.916405	−	1.58726i	−0.374121	−	0.647996i
$7$		0			0
$7$		0			0
$8$	4.65773			1.64675
$9$	−2.43210			−0.810700
$10$	0.830652			0.262675
$11$	−2.43210			−0.733305			−0.366653	−	0.930358i	$-0.619496\pi$
$11$	−2.43210			−0.733305			−0.366653	+	0.930358i	$0.619496\pi$
$12$	−1.47520	+	2.55511i	−0.425852	+	0.737598i
$13$	2.50139	+	2.59674i	0.693760	+	0.720206i
$13$	2.50139	+	2.59674i	0.693760	+	0.720206i
$14$		0			0
$15$	−0.128690	+	0.222897i	−0.0332276	+	0.0575518i
$16$	−1.74892	−	3.02922i	−0.437230	−	0.757304i
$17$	0.974117	−	1.68722i	0.236258	−	0.409211i	−0.723379	−	0.690451i	$-0.757412\pi$
$17$	0.974117	−	1.68722i	0.236258	−	0.409211i	0.959638	+	0.281240i	$0.0907456\pi$
$18$	2.95755	+	5.12263i	0.697102	+	1.20742i
$19$	−6.29039			−1.44311			−0.721557	−	0.692355i	$-0.756573\pi$
$19$	−6.29039			−1.44311			−0.721557	+	0.692355i	$0.756573\pi$
$20$	−0.668577	−	1.15801i	−0.149498	−	0.258939i
$21$		0			0
$22$	2.95755	+	5.12263i	0.630552	+	1.09215i
$23$	1.84474	+	3.19518i	0.384655	+	0.666242i	0.991721	−	0.128409i	$-0.0409872\pi$
$23$	1.84474	+	3.19518i	0.384655	+	0.666242i	−0.607066	+	0.794651i	$0.707654\pi$
$24$	3.51003			0.716481
$25$	2.44168	+	4.22911i	0.488335	+	0.845821i
$26$	2.42760	−	8.42634i	0.476091	−	1.65254i
$27$	−4.09359			−0.787811
$28$		0			0
$29$	−2.22068	+	3.84632i	−0.412369	+	0.714244i	−0.995148	−	0.0983864i	$-0.968632\pi$
$29$	−2.22068	+	3.84632i	−0.412369	+	0.714244i	0.582779	+	0.812631i	$0.301965\pi$
$30$	0.625973			0.114286
$31$	0.987661	+	1.71068i	0.177389	+	0.307247i	0.940986	−	0.338447i	$-0.109902\pi$
$31$	0.987661	+	1.71068i	0.177389	+	0.307247i	−0.763596	+	0.645694i	$0.776568\pi$
$32$	0.404180	−	0.700061i	0.0714496	−	0.123754i
$33$	−1.83281			−0.319051
$34$	−4.73830			−0.812611
$35$		0			0
$36$	4.76096	−	8.24623i	0.793494	−	1.37437i
$37$	4.81433	+	8.33867i	0.791472	+	1.37087i	0.925056	+	0.379832i	$0.124018\pi$
$37$	4.81433	+	8.33867i	0.791472	+	1.37087i	−0.133584	+	0.991037i	$0.542649\pi$
$38$	7.64942	+	13.2492i	1.24090	+	2.14930i
$39$	1.88503	+	1.95688i	0.301846	+	0.313352i
$40$	−0.795393	+	1.37766i	−0.125763	+	0.217827i
$41$	−6.26793	+	10.8564i	−0.978887	+	1.69548i	−0.312426	+	0.949942i	$0.601141\pi$
$41$	−6.26793	+	10.8564i	−0.978887	+	1.69548i	−0.666461	+	0.745540i	$0.732192\pi$
$42$		0			0
$43$	4.20368	+	7.28099i	0.641055	+	1.11034i	0.985198	+	0.171423i	$0.0548365\pi$
$43$	4.20368	+	7.28099i	0.641055	+	1.11034i	−0.344142	+	0.938918i	$0.611830\pi$
$44$	4.76096	−	8.24623i	0.717742	−	1.24317i
$45$	0.415326	−	0.719366i	0.0619131	−	0.107237i
$46$	4.48659	−	7.77100i	0.661511	−	1.14577i
$47$	4.50265	−	7.79882i	0.656779	−	1.13757i	−0.324666	−	0.945829i	$-0.605252\pi$
$47$	4.50265	−	7.79882i	0.656779	−	1.13757i	0.981445	−	0.191745i	$-0.0614148\pi$
$48$	−1.31797	−	2.28279i	−0.190233	−	0.329493i
$49$		0			0
$50$	5.93840	−	10.2856i	0.839816	−	1.45460i
$51$	0.734087	−	1.27148i	0.102793	−	0.178042i
$52$	−13.7011	+	3.39790i	−1.89999	+	0.471204i
$53$	−0.746129	−	1.29233i	−0.102489	−	0.177516i	0.810221	−	0.586125i	$-0.199347\pi$
$53$	−0.746129	−	1.29233i	−0.102489	−	0.177516i	−0.912709	+	0.408609i	$0.866014\pi$
$54$	4.97800	+	8.62216i	0.677421	+	1.17333i
$55$	0.415326	−	0.719366i	0.0560025	−	0.0969993i
$56$		0			0
$57$	−4.74039			−0.627879
$58$	10.8018			1.41835
$59$	−0.313495	+	0.542990i	−0.0408136	+	0.0706913i	−0.885711	−	0.464238i	$-0.846328\pi$
$59$	−0.313495	+	0.542990i	−0.0408136	+	0.0706913i	0.844897	+	0.534929i	$0.179662\pi$
$60$	−0.503834	−	0.872666i	−0.0650447	−	0.112661i
$61$	−1.14319			−0.146371			−0.0731855	−	0.997318i	$-0.523317\pi$
$61$	−1.14319			−0.146371			−0.0731855	+	0.997318i	$0.523317\pi$
$62$	2.40209	−	4.16054i	0.305066	−	0.528389i
$63$		0			0
$64$	−8.96169			−1.12021
$65$	−1.19522	+	0.296418i	−0.148249	+	0.0367662i
$66$	2.22879	+	3.86037i	0.274345	+	0.475179i
$67$	−5.59199			−0.683170			−0.341585	−	0.939851i	$-0.610964\pi$
$67$	−5.59199			−0.683170			−0.341585	+	0.939851i	$0.610964\pi$
$68$	3.81377	+	6.60564i	0.462488	+	0.801052i
$69$	1.39018	+	2.40786i	0.167358	+	0.289873i
$70$		0			0
$71$	−4.74859	−	8.22481i	−0.563554	−	0.976105i	−0.997183	−	0.0750130i	$-0.976100\pi$
$71$	−4.74859	−	8.22481i	−0.563554	−	0.976105i	0.433628	−	0.901092i	$-0.357233\pi$
$72$	−11.3280			−1.33502
$73$	−5.95934	−	10.3219i	−0.697488	−	1.20808i	−0.969335	−	0.245744i	$-0.920968\pi$
$73$	−5.95934	−	10.3219i	−0.697488	−	1.20808i	0.271847	−	0.962340i	$-0.412366\pi$
$74$	11.7089	−	20.2805i	1.36114	−	2.35756i
$75$	1.84003	+	3.18702i	0.212468	+	0.368006i
$76$	12.3138	−	21.3281i	1.41249	−	2.44650i
$77$		0			0
$78$	1.82942	−	6.35002i	0.207141	−	0.718998i
$79$	−2.23583	+	3.87258i	−0.251551	+	0.435699i	−0.963953	−	0.266073i	$-0.914274\pi$
$79$	−2.23583	+	3.87258i	−0.251551	+	0.435699i	0.712402	+	0.701772i	$0.247607\pi$
$80$	1.19464			0.133565
$81$	4.21140			0.467934
$82$	30.4885			3.36689
$83$	1.41231			0.155021			0.0775104	−	0.996992i	$-0.475303\pi$
$83$	1.41231			0.155021			0.0775104	+	0.996992i	$0.475303\pi$
$84$		0			0
$85$	0.332697	+	0.576248i	0.0360861	+	0.0625029i
$86$	10.2238	−	17.7081i	1.10246	−	1.90951i
$87$	−1.67348	+	2.89856i	−0.179416	+	0.310758i
$88$	−11.3280			−1.20757
$89$	−6.22219	−	10.7771i	−0.659551	−	1.14238i	−0.980732	−	0.195357i	$-0.937413\pi$
$89$	−6.22219	−	10.7771i	−0.659551	−	1.14238i	0.321182	−	0.947018i	$-0.395920\pi$
$90$	−2.02023			−0.212951
$91$		0			0
$92$	−14.4447			−1.50596
$93$	0.744294	+	1.28915i	0.0771797	+	0.133679i
$94$	−21.9018			−2.25900
$95$	1.07420	−	1.86057i	0.110211	−	0.190890i
$96$	0.304587	−	0.527560i	0.0310868	−	0.0538439i
$97$	−5.13850	−	8.90014i	−0.521736	−	0.903673i	−0.999680	−	0.0252826i	$-0.991951\pi$
$97$	−5.13850	−	8.90014i	−0.521736	−	0.903673i	0.477945	−	0.878390i	$-0.341382\pi$
$98$		0			0
$99$	5.91511			0.594490
$100$	−19.1188			−1.91188
$101$	15.0537			1.49790			0.748948	−	0.662629i	$-0.230559\pi$
$101$	15.0537			1.49790			0.748948	+	0.662629i	$0.230559\pi$
$102$	−3.57074			−0.353556
$103$	−8.80880	+	15.2573i	−0.867957	+	1.50335i	−0.00387687	+	0.999992i	$0.501234\pi$
$103$	−8.80880	+	15.2573i	−0.867957	+	1.50335i	−0.864080	+	0.503354i	$0.832099\pi$
$104$	11.6508	+	12.0949i	1.14245	+	1.18600i
$105$		0			0
$106$	−1.81466	+	3.14308i	−0.176255	+	0.305283i
$107$	−3.19227	−	5.52917i	−0.308608	−	0.534525i	0.669450	−	0.742857i	$-0.266530\pi$
$107$	−3.19227	−	5.52917i	−0.308608	−	0.534525i	−0.978058	+	0.208332i	$0.933197\pi$
$108$	8.01341	−	13.8796i	0.771091	−	1.33557i
$109$	4.08736	+	7.07951i	0.391498	+	0.678095i	0.992647	−	0.121042i	$-0.0386236\pi$
$109$	4.08736	+	7.07951i	0.391498	+	0.678095i	−0.601149	+	0.799137i	$0.705290\pi$
$110$	−2.02023			−0.192621
$111$	3.62804	+	6.28396i	0.344359	+	0.596447i
$112$		0			0
$113$	4.81083	+	8.33259i	0.452564	+	0.783865i	0.998545	−	0.0539336i	$-0.0171759\pi$
$113$	4.81083	+	8.33259i	0.452564	+	0.783865i	−0.545980	+	0.837798i	$0.683843\pi$
$114$	5.76454	+	9.98448i	0.539899	+	0.935133i
$115$	−1.26009			−0.117504
$116$	−8.69418	−	15.0588i	−0.807234	−	1.39817i
$117$	−6.08362	−	6.31553i	−0.562431	−	0.583871i
$118$	1.52490			0.140379
$119$		0			0
$120$	−0.599402	+	1.03819i	−0.0547177	+	0.0947738i
$121$	−5.08489			−0.462263
$122$	1.39018	+	2.40786i	0.125861	+	0.217998i
$123$	−4.72347	+	8.18128i	−0.425901	+	0.737681i
$124$	−7.73360			−0.694497
$125$	−3.37553			−0.301917
$126$		0			0
$127$	−4.50988	+	7.81134i	−0.400187	+	0.693145i	−0.993748	−	0.111644i	$-0.964388\pi$
$127$	−4.50988	+	7.81134i	−0.400187	+	0.693145i	0.593561	+	0.804789i	$0.297722\pi$
$128$	10.0895	+	17.4755i	0.891794	+	1.54463i
$129$	3.16786	+	5.48690i	0.278915	+	0.483094i
$130$	2.07778	+	2.15699i	0.182234	+	0.189180i
$131$	0.0962416	−	0.166695i	0.00840867	−	0.0145642i	−0.861790	−	0.507264i	$-0.830657\pi$
$131$	0.0962416	−	0.166695i	0.00840867	−	0.0145642i	0.870199	+	0.492700i	$0.163990\pi$
$132$	3.58782	−	6.21429i	0.312280	−	0.540885i
$133$		0			0
$134$	6.80013	+	11.7782i	0.587442	+	1.01748i
$135$	0.699056	−	1.21080i	0.0601651	−	0.104209i
$136$	4.53717	−	7.85861i	0.389059	−	0.673870i
$137$	−2.43840	+	4.22343i	−0.208326	+	0.360832i	−0.951187	−	0.308614i	$-0.900135\pi$
$137$	−2.43840	+	4.22343i	−0.208326	+	0.360832i	0.742861	+	0.669446i	$0.233468\pi$
$138$	3.38106	−	5.85616i	0.287815	−	0.498510i
$139$	5.53701	+	9.59038i	0.469643	+	0.813446i	0.999398	−	0.0347054i	$-0.0110493\pi$
$139$	5.53701	+	9.59038i	0.469643	+	0.813446i	−0.529755	+	0.848151i	$0.677716\pi$
$140$		0			0
$141$	3.39316	−	5.87713i	0.285756	−	0.494943i
$142$	−11.5491	+	20.0035i	−0.969175	+	1.67866i
$143$	−6.08362	−	6.31553i	−0.508738	−	0.528131i
$144$	4.25355	+	7.36736i	0.354462	+	0.613946i
$145$	−0.758443	−	1.31366i	−0.0629853	−	0.109094i
$146$	−14.4937	+	25.1038i	−1.19951	+	2.07761i
$147$		0			0
$148$	−37.6973			−3.09869
$149$	15.9087			1.30329			0.651646	−	0.758524i	$-0.274079\pi$
$149$	15.9087			1.30329			0.651646	+	0.758524i	$0.274079\pi$
$150$	4.47513	−	7.75115i	0.365393	−	0.632879i
$151$	5.29518	+	9.17152i	0.430916	+	0.746368i	0.996952	−	0.0780122i	$-0.0248573\pi$
$151$	5.29518	+	9.17152i	0.430916	+	0.746368i	−0.566037	+	0.824380i	$0.691524\pi$
$152$	−29.2989			−2.37645
$153$	−2.36915	+	4.10349i	−0.191534	+	0.331747i
$154$		0			0
$155$	−0.674646			−0.0541889
$156$	−10.3250	+	2.56063i	−0.826662	+	0.205014i
$157$	−4.56194	−	7.90151i	−0.364082	−	0.630609i	0.624546	−	0.780988i	$-0.285284\pi$
$157$	−4.56194	−	7.90151i	−0.364082	−	0.630609i	−0.988628	+	0.150379i	$0.951951\pi$
$158$	10.8755			0.865211
$159$	−0.562277	−	0.973892i	−0.0445915	−	0.0772347i
$160$	0.138043	+	0.239097i	0.0109132	+	0.0189023i
$161$		0			0
$162$	−5.12127	−	8.87031i	−0.402365	−	0.696917i
$163$	−10.9639			−0.858761			−0.429380	−	0.903124i	$-0.641268\pi$
$163$	−10.9639			−0.858761			−0.429380	+	0.903124i	$0.641268\pi$
$164$	−24.5396	−	42.5039i	−1.91622	−	3.31900i
$165$	0.312986	−	0.542108i	0.0243660	−	0.0422031i
$166$	−1.71744	−	2.97469i	−0.133299	−	0.230880i
$167$	9.13884	−	15.8289i	0.707185	−	1.22488i	−0.258713	−	0.965954i	$-0.583298\pi$
$167$	9.13884	−	15.8289i	0.707185	−	1.22488i	0.965897	−	0.258925i	$-0.0833683\pi$
$168$		0			0
$169$	−0.486122	+	12.9909i	−0.0373940	+	0.999301i
$170$	0.809152	−	1.40149i	0.0620591	−	0.107490i
$171$	15.2988			1.16993
$172$	−32.9157			−2.50980
$173$	−8.19835			−0.623309			−0.311655	−	0.950195i	$-0.600883\pi$
$173$	−8.19835			−0.623309			−0.311655	+	0.950195i	$0.600883\pi$
$174$	8.14015			0.617104
$175$		0			0
$176$	4.25355	+	7.36736i	0.320623	+	0.555335i
$177$	−0.236248	+	0.409193i	−0.0177575	+	0.0307568i
$178$	−15.1330	+	26.2111i	−1.13426	+	1.96460i
$179$	−15.5537			−1.16254			−0.581268	−	0.813712i	$-0.697443\pi$
$179$	−15.5537			−1.16254			−0.581268	+	0.813712i	$0.697443\pi$
$180$	1.62605	+	2.81639i	0.121198	+	0.209922i
$181$	−6.67302			−0.496001			−0.248001	−	0.968760i	$-0.579774\pi$
$181$	−6.67302			−0.496001			−0.248001	+	0.968760i	$0.579774\pi$
$182$		0			0
$183$	−0.861502			−0.0636841
$184$	8.59229	+	14.8823i	0.633432	+	1.09714i
$185$	−3.28855			−0.241779
$186$	1.81020	−	3.13535i	0.132730	−	0.229895i
$187$	−2.36915	+	4.10349i	−0.173249	+	0.300077i
$188$	17.6283	+	30.5332i	1.28568	+	2.22686i
$189$		0			0
$190$	−5.22512			−0.379070
$191$	−18.7459			−1.35641			−0.678204	−	0.734874i	$-0.737241\pi$
$191$	−18.7459			−1.35641			−0.678204	+	0.734874i	$0.737241\pi$
$192$	−6.75346			−0.487389
$193$	−8.17309			−0.588312			−0.294156	−	0.955757i	$-0.595039\pi$
$193$	−8.17309			−0.588312			−0.294156	+	0.955757i	$0.595039\pi$
$194$	−12.4973	+	21.6460i	−0.897257	+	1.55409i
$195$	−0.900710	+	0.223378i	−0.0645012	+	0.0159965i
$196$		0			0
$197$	−4.36006	+	7.55184i	−0.310641	+	0.538047i	−0.978501	−	0.206240i	$-0.933877\pi$
$197$	−4.36006	+	7.55184i	−0.310641	+	0.538047i	0.667860	+	0.744287i	$0.267210\pi$
$198$	−7.19306	−	12.4587i	−0.511189	−	0.885405i
$199$	8.73332	−	15.1266i	0.619089	−	1.07229i	−0.370563	−	0.928807i	$-0.620835\pi$
$199$	8.73332	−	15.1266i	0.619089	−	1.07229i	0.989652	−	0.143486i	$-0.0458313\pi$
$200$	11.3727	+	19.6980i	0.804168	+	1.39286i
$201$	−4.21408			−0.297238
$202$	−18.3060	−	31.7069i	−1.28801	−	2.23089i
$203$		0			0
$204$	2.87403	+	4.97796i	0.201222	+	0.348527i
$205$	−2.14073	−	3.70786i	−0.149515	−	0.258968i
$206$	42.8478			2.98535
$207$	−4.48659	−	7.77100i	−0.311839	−	0.540122i
$208$	3.49137	−	12.1187i	0.242083	−	0.840283i
$209$	15.2988			1.05824
$210$		0			0
$211$	11.6284	−	20.1410i	0.800535	−	1.38657i	−0.118730	−	0.992927i	$-0.537882\pi$
$211$	11.6284	−	20.1410i	0.800535	−	1.38657i	0.919265	−	0.393640i	$-0.128784\pi$
$212$	5.84235			0.401254
$213$	−3.57850	−	6.19815i	−0.245195	−	0.424690i
$214$	−7.76391	+	13.4475i	−0.530730	+	0.919252i
$215$	−2.87143			−0.195830
$216$	−19.0668			−1.29733
$217$		0			0
$218$	9.94086	−	17.2181i	0.673280	−	1.16616i
$219$	−4.49091	−	7.77848i	−0.303468	−	0.525621i
$220$	1.62605	+	2.81639i	0.109628	+	0.189881i
$221$	6.81792	−	1.69086i	0.458623	−	0.113740i
$222$	8.82376	−	15.2832i	0.592212	−	1.02574i
$223$	14.6364	−	25.3510i	0.980128	−	1.69763i	0.318272	−	0.947999i	$-0.396897\pi$
$223$	14.6364	−	25.3510i	0.980128	−	1.69763i	0.661855	−	0.749632i	$-0.269769\pi$
$224$		0			0
$225$	−5.93840	−	10.2856i	−0.395893	−	0.685707i
$226$	11.7004	−	20.2657i	0.778299	−	1.34805i
$227$	−9.90551	+	17.1569i	−0.657452	+	1.13874i	0.323821	+	0.946118i	$0.395032\pi$
$227$	−9.90551	+	17.1569i	−0.657452	+	1.13874i	−0.981273	+	0.192622i	$0.938301\pi$
$228$	9.27956	−	16.0727i	0.614554	−	1.06444i
$229$	0.664107	−	1.15027i	0.0438855	−	0.0760118i	−0.843248	−	0.537524i	$-0.819360\pi$
$229$	0.664107	−	1.15027i	0.0438855	−	0.0760118i	0.887134	+	0.461512i	$0.152693\pi$
$230$	1.53234	+	2.65408i	0.101039	+	0.175005i
$231$		0			0
$232$	−10.3433	+	17.9151i	−0.679071	+	1.17618i
$233$	−0.758171	+	1.31319i	−0.0496695	+	0.0860300i	−0.889791	−	0.456368i	$-0.849150\pi$
$233$	−0.758171	+	1.31319i	−0.0496695	+	0.0860300i	0.840122	+	0.542398i	$0.182483\pi$
$234$	−5.90416	+	20.4937i	−0.385967	+	1.33971i
$235$	1.53782	+	2.66358i	0.100316	+	0.173753i
$236$	−1.22737	−	2.12586i	−0.0798948	−	0.138382i
$237$	−1.68491	+	2.91834i	−0.109446	+	0.189567i
$238$		0			0
$239$	22.4793			1.45406			0.727032	−	0.686603i	$-0.240899\pi$
$239$	22.4793			1.45406			0.727032	+	0.686603i	$0.240899\pi$
$240$	0.900273			0.0581123
$241$	−6.65528	+	11.5273i	−0.428704	+	0.742538i	−0.996758	−	0.0804535i	$-0.974363\pi$
$241$	−6.65528	+	11.5273i	−0.428704	+	0.742538i	0.568054	+	0.822991i	$0.307696\pi$
$242$	6.18348	+	10.7101i	0.397489	+	0.688472i
$243$	15.4544			0.991403
$244$	2.23786	−	3.87609i	0.143265	−	0.248141i
$245$		0			0
$246$	22.9759			1.46489
$247$	−15.7347	−	16.3345i	−1.00117	−	1.03934i
$248$	4.60026	+	7.96788i	0.292116	+	0.505961i
$249$	1.06430			0.0674475
$250$	4.10481	+	7.10974i	0.259611	+	0.449660i
$251$	−7.95169	−	13.7727i	−0.501906	−	0.869327i	−0.999998	−	0.00220260i	$-0.999299\pi$
$251$	−7.95169	−	13.7727i	−0.501906	−	0.869327i	0.498091	−	0.867125i	$-0.334034\pi$
$252$		0			0
$253$	−4.48659	−	7.77100i	−0.282069	−	0.488559i
$254$	21.9370			1.37645
$255$	0.250718	+	0.434256i	0.0157006	+	0.0271942i
$256$	15.5770	−	26.9801i	0.973561	−	1.68626i
$257$	14.6198	+	25.3223i	0.911960	+	1.57956i	0.811292	+	0.584641i	$0.198764\pi$
$257$	14.6198	+	25.3223i	0.911960	+	1.57956i	0.100667	+	0.994920i	$0.467902\pi$
$258$	7.70455	−	13.3447i	0.479664	−	0.830803i
$259$		0			0
$260$	1.33468	−	4.63275i	0.0827733	−	0.287311i
$261$	5.40090	−	9.35464i	0.334307	−	0.579037i
$262$	−0.468138			−0.0289217
$263$	−1.70435			−0.105095			−0.0525475	−	0.998618i	$-0.516734\pi$
$263$	−1.70435			−0.105095			−0.0525475	+	0.998618i	$0.516734\pi$
$264$	−8.53673			−0.525399
$265$	0.509661			0.0313083
$266$		0			0
$267$	−4.68899	−	8.12157i	−0.286962	−	0.497032i
$268$	10.9466	−	18.9601i	0.668670	−	1.15817i
$269$	−4.18937	+	7.25620i	−0.255430	+	0.442418i	−0.965012	−	0.262205i	$-0.915550\pi$
$269$	−4.18937	+	7.25620i	−0.255430	+	0.442418i	0.709582	+	0.704623i	$0.248884\pi$
$270$	−3.40035			−0.206938
$271$	6.07877	+	10.5287i	0.369259	+	0.639575i	0.989450	−	0.144876i	$-0.0462782\pi$
$271$	6.07877	+	10.5287i	0.369259	+	0.639575i	−0.620191	+	0.784451i	$0.712945\pi$
$272$	−6.81461			−0.413196
$273$		0			0
$274$	11.8609			0.716540
$275$	−5.93840	−	10.2856i	−0.358099	−	0.620245i
$276$	−10.8854			−0.655225
$277$	−5.15907	+	8.93578i	−0.309979	+	0.536899i	−0.978357	−	0.206922i	$-0.933655\pi$
$277$	−5.15907	+	8.93578i	−0.309979	+	0.536899i	0.668379	+	0.743821i	$0.266989\pi$
$278$	13.4666	−	23.3248i	0.807670	−	1.39893i
$279$	−2.40209	−	4.16054i	−0.143809	−	0.249085i
$280$		0			0
$281$	−2.59677			−0.154910			−0.0774551	−	0.996996i	$-0.524679\pi$
$281$	−2.59677			−0.154910			−0.0774551	+	0.996996i	$0.524679\pi$
$282$	−16.5050			−0.982859
$283$	4.60368			0.273660			0.136830	−	0.990595i	$-0.456309\pi$
$283$	4.60368			0.273660			0.136830	+	0.990595i	$0.456309\pi$
$284$	37.1825			2.20637
$285$	0.809509	−	1.40211i	0.0479512	−	0.0830539i
$286$	−5.90416	+	20.4937i	−0.349120	+	1.21182i
$287$		0			0
$288$	−0.983006	+	1.70262i	−0.0579242	+	0.100328i
$289$	6.60219	+	11.4353i	0.388364	+	0.672667i
$290$	−1.84461	+	3.19496i	−0.108319	+	0.187614i
$291$	−3.87233	−	6.70708i	−0.227000	−	0.393176i
$292$	46.6629			2.73074
$293$	0.980596	+	1.69844i	0.0572870	+	0.0992241i	0.893247	−	0.449567i	$-0.148422\pi$
$293$	0.980596	+	1.69844i	0.0572870	+	0.0992241i	−0.835960	+	0.548791i	$0.815088\pi$
$294$		0			0
$295$	−0.107070	−	0.185451i	−0.00623388	−	0.0107974i
$296$	22.4238	+	38.8392i	1.30336	+	2.25749i
$297$	9.95601			0.577706
$298$	−19.3458	−	33.5078i	−1.12067	−	1.94106i
$299$	−3.68265	+	12.7827i	−0.212973	+	0.739242i
$300$	−14.4078			−0.831835
$301$		0			0
$302$	12.8784	−	22.3060i	0.741069	−	1.28357i
$303$	11.3443			0.651714
$304$	11.0014	+	19.0550i	0.630972	+	1.09288i
$305$	0.195222	−	0.338134i	0.0111784	−	0.0193615i
$306$	11.5240			0.658784
$307$	7.37658			0.421004			0.210502	−	0.977593i	$-0.432490\pi$
$307$	7.37658			0.421004			0.210502	+	0.977593i	$0.432490\pi$
$308$		0			0
$309$	−6.63825	+	11.4978i	−0.377637	+	0.654086i
$310$	0.820403	+	1.42098i	0.0465957	+	0.0807062i
$311$	−7.08088	−	12.2644i	−0.401520	−	0.695453i	0.592390	−	0.805652i	$-0.298185\pi$
$311$	−7.08088	−	12.2644i	−0.401520	−	0.695453i	−0.993910	+	0.110199i	$0.964851\pi$
$312$	8.77993	+	9.11462i	0.497066	+	0.516014i
$313$	13.3576	−	23.1361i	0.755017	−	1.30773i	−0.190349	−	0.981716i	$-0.560962\pi$
$313$	13.3576	−	23.1361i	0.755017	−	1.30773i	0.945366	−	0.326011i	$-0.105705\pi$
$314$	−11.0951	+	19.2173i	−0.626132	+	1.08449i
$315$		0			0
$316$	−8.75352	−	15.1615i	−0.492424	−	0.852904i
$317$	−10.7181	+	18.5643i	−0.601989	+	1.04268i	0.390530	+	0.920590i	$0.372292\pi$
$317$	−10.7181	+	18.5643i	−0.601989	+	1.04268i	−0.992520	+	0.122086i	$0.961042\pi$
$318$	−1.36751	+	2.36860i	−0.0766863	+	0.132825i
$319$	5.40090	−	9.35464i	0.302392	−	0.523759i
$320$	1.53037	−	2.65069i	0.0855506	−	0.148178i
$321$	−2.40567	−	4.16674i	−0.134271	−	0.232565i
$322$		0			0
$323$	−6.12757	+	10.6133i	−0.340947	+	0.590538i
$324$	−8.24404	+	14.2791i	−0.458002	+	0.793283i
$325$	−4.87432	+	16.9190i	−0.270378	+	0.938499i
$326$	13.3327	+	23.0929i	0.738429	+	1.27900i
$327$	3.08020	+	5.33507i	0.170336	+	0.295030i
$328$	−29.1943	+	50.5660i	−1.61199	+	2.79204i
$329$		0			0
$330$	−1.52243			−0.0838069
$331$	10.6138			0.583389			0.291695	−	0.956512i	$-0.405781\pi$
$331$	10.6138			0.583389			0.291695	+	0.956512i	$0.405781\pi$
$332$	−2.76467	+	4.78854i	−0.151731	+	0.262805i
$333$	−11.7089	−	20.2805i	−0.641646	−	1.11136i
$334$	−44.4531			−2.43237
$335$	0.954935	−	1.65400i	0.0521737	−	0.0903675i
$336$		0			0
$337$	6.75587			0.368016			0.184008	−	0.982925i	$-0.441093\pi$
$337$	6.75587			0.368016			0.184008	+	0.982925i	$0.441093\pi$
$338$	27.9534	−	14.7737i	1.52046	−	0.803583i
$339$	3.62540	+	6.27938i	0.196905	+	0.341049i
$340$	−2.60509			−0.141281
$341$	−2.40209	−	4.16054i	−0.130080	−	0.225306i
$342$	−18.6042	−	32.2233i	−1.00600	−	1.74244i
$343$		0			0
$344$	19.5796	+	33.9129i	1.05566	+	1.82846i
$345$	−0.949597			−0.0511246
$346$	9.96960	+	17.2679i	0.535969	+	0.928326i
$347$	8.01021	−	13.8741i	0.430010	−	0.744800i	−0.566863	−	0.823812i	$-0.691843\pi$
$347$	8.01021	−	13.8741i	0.430010	−	0.744800i	0.996874	+	0.0790120i	$0.0251765\pi$
$348$	−6.55186	−	11.3482i	−0.351217	−	0.608325i
$349$	−8.01922	+	13.8897i	−0.429259	+	0.743498i	−0.996808	−	0.0798418i	$-0.974558\pi$
$349$	−8.01922	+	13.8897i	−0.429259	+	0.743498i	0.567549	+	0.823340i	$0.307892\pi$
$350$		0			0
$351$	−10.2396	−	10.6300i	−0.546552	−	0.567386i
$352$	−0.983006	+	1.70262i	−0.0523944	+	0.0907498i
$353$	3.84311			0.204548			0.102274	−	0.994756i	$-0.467388\pi$
$353$	3.84311			0.204548			0.102274	+	0.994756i	$0.467388\pi$
$354$	1.14916			0.0610769
$355$	3.24364			0.172155
$356$	48.7210			2.58221
$357$		0			0
$358$	18.9140	+	32.7601i	0.999638	+	1.73142i
$359$	10.5668	−	18.3022i	0.557692	−	0.965952i	−0.439996	−	0.898000i	$-0.645020\pi$
$359$	10.5668	−	18.3022i	0.557692	−	0.965952i	0.997689	−	0.0679519i	$-0.0216465\pi$
$360$	1.93447	−	3.35061i	0.101956	−	0.176593i
$361$	20.5690			1.08258
$362$	8.11472	+	14.0551i	0.426500	+	0.738720i
$363$	−3.83194			−0.201125
$364$		0			0
$365$	4.07067			0.213069
$366$	1.04763	+	1.81455i	0.0547605	+	0.0948479i
$367$	−14.7392			−0.769381			−0.384690	−	0.923046i	$-0.625692\pi$
$367$	−14.7392			−0.769381			−0.384690	+	0.923046i	$0.625692\pi$
$368$	6.45260	−	11.1762i	0.336365	−	0.582601i
$369$	15.2442	−	26.4038i	0.793583	−	1.37453i
$370$	3.99904	+	6.92653i	0.207900	+	0.360093i
$371$		0			0
$372$	−5.82798			−0.302166
$373$	12.9266			0.669314			0.334657	−	0.942340i	$-0.391380\pi$
$373$	12.9266			0.669314			0.334657	+	0.942340i	$0.391380\pi$
$374$	11.5240			0.595892
$375$	−2.54377			−0.131360
$376$	20.9721	−	36.3247i	1.08155	−	1.87331i
$377$	−15.5427	+	3.85463i	−0.800488	+	0.198523i
$378$		0			0
$379$	13.4179	−	23.2405i	0.689231	−	1.19378i	−0.282856	−	0.959162i	$-0.591282\pi$
$379$	13.4179	−	23.2405i	0.689231	−	1.19378i	0.972087	−	0.234621i	$-0.0753848\pi$
$380$	4.20561	+	7.28433i	0.215743	+	0.373678i
$381$	−3.39861	+	5.88657i	−0.174116	+	0.301578i
$382$	22.7960	+	39.4838i	1.16634	+	2.02017i
$383$	−2.90782			−0.148583			−0.0742914	−	0.997237i	$-0.523669\pi$
$383$	−2.90782			−0.148583			−0.0742914	+	0.997237i	$0.523669\pi$
$384$	7.60337	+	13.1694i	0.388008	+	0.672049i
$385$		0			0
$386$	9.93889	+	17.2147i	0.505876	+	0.876203i
$387$	−10.2238	−	17.7081i	−0.519703	−	0.900153i
$388$	40.2355			2.04265
$389$	8.35048	+	14.4635i	0.423386	+	0.733327i	0.996268	−	0.0863114i	$-0.0275080\pi$
$389$	8.35048	+	14.4635i	0.423386	+	0.733327i	−0.572882	+	0.819638i	$0.694175\pi$
$390$	1.56580	+	1.62549i	0.0792874	+	0.0823098i
$391$	7.18797			0.363511
$392$		0			0
$393$	0.0725269	−	0.125620i	0.00365850	−	0.00633671i
$394$	21.2082			1.06845
$395$	−0.763620	−	1.32263i	−0.0384219	−	0.0665487i
$396$	−11.5791	+	20.0556i	−0.581873	+	1.00783i
$397$	−24.0984			−1.20947			−0.604733	−	0.796428i	$-0.706720\pi$
$397$	−24.0984			−1.20947			−0.604733	+	0.796428i	$0.706720\pi$
$398$	−42.4806			−2.12936
$399$		0			0
$400$	8.54059	−	14.7927i	0.427030	−	0.739637i
$401$	−0.922448	−	1.59773i	−0.0460649	−	0.0797867i	0.842074	−	0.539363i	$-0.181335\pi$
$401$	−0.922448	−	1.59773i	−0.0460649	−	0.0797867i	−0.888139	+	0.459576i	$0.848001\pi$
$402$	5.12453	+	8.87594i	0.255588	+	0.442692i
$403$	−1.97167	+	6.84377i	−0.0982157	+	0.340913i
$404$	−29.4683	+	51.0406i	−1.46610	+	2.53937i
$405$	−0.719175	+	1.24565i	−0.0357361	+	0.0618967i
$406$		0			0
$407$	−11.7089	−	20.2805i	−0.580390	−	1.00527i
$408$	3.41918	−	5.92218i	0.169274	−	0.293192i
$409$	12.8351	−	22.2311i	0.634657	−	1.09926i	−0.351931	−	0.936026i	$-0.614475\pi$
$409$	12.8351	−	22.2311i	0.634657	−	1.09926i	0.986588	−	0.163232i	$-0.0521920\pi$
$410$	−5.20647	+	9.01787i	−0.257129	+	0.445361i
$411$	−1.83756	+	3.18274i	−0.0906400	+	0.156993i
$412$	−34.4874	−	59.7339i	−1.69907	−	2.94288i
$413$		0			0
$414$	−10.9118	+	18.8998i	−0.536287	+	0.928876i
$415$	−0.241178	+	0.417732i	−0.0118389	+	0.0205057i
$416$	2.82889	−	0.701572i	0.138698	−	0.0343974i
$417$	4.17265	+	7.22724i	0.204335	+	0.353919i
$418$	−18.6042	−	32.2233i	−0.909959	−	1.57609i
$419$	13.1199	−	22.7244i	0.640950	−	1.11016i	−0.344271	−	0.938870i	$-0.611874\pi$
$419$	13.1199	−	22.7244i	0.640950	−	1.11016i	0.985221	−	0.171288i	$-0.0547928\pi$
$420$		0			0
$421$	23.6637			1.15330			0.576650	−	0.816992i	$-0.304360\pi$
$421$	23.6637			1.15330			0.576650	+	0.816992i	$0.304360\pi$
$422$	−56.5630			−2.75344
$423$	−10.9509	+	18.9675i	−0.532450	+	0.922231i
$424$	−3.47526	−	6.01933i	−0.168774	−	0.292325i
$425$	9.51391			0.461493
$426$	−8.70327	+	15.0745i	−0.421675	+	0.730362i
$427$		0			0
$428$	24.9961			1.20823
$429$	−4.58457	−	4.75933i	−0.221345	−	0.229783i
$430$	3.49180	+	6.04797i	0.168389	+	0.291659i
$431$	−23.0177			−1.10872			−0.554361	−	0.832276i	$-0.687037\pi$
$431$	−23.0177			−1.10872			−0.554361	+	0.832276i	$0.687037\pi$
$432$	7.15935	+	12.4004i	0.344455	+	0.596613i
$433$	12.9304	+	22.3961i	0.621394	+	1.07629i	0.989226	+	0.146394i	$0.0467667\pi$
$433$	12.9304	+	22.3961i	0.621394	+	1.07629i	−0.367832	+	0.929892i	$0.619900\pi$
$434$		0			0
$435$	−0.571557	−	0.989965i	−0.0274040	−	0.0474652i
$436$	−32.0049			−1.53276
$437$	−11.6041	−	20.0989i	−0.555101	−	0.961462i
$438$	−10.9223	+	18.9180i	−0.521890	+	0.903939i
$439$	17.8385	+	30.8973i	0.851387	+	1.47465i	0.879956	+	0.475054i	$0.157572\pi$
$439$	17.8385	+	30.8973i	0.851387	+	1.47465i	−0.0285691	+	0.999592i	$0.509095\pi$
$440$	1.93447	−	3.35061i	0.0922225	−	0.159734i
$441$		0			0
$442$	−11.8523	−	12.3041i	−0.563757	−	0.585248i
$443$	3.42940	−	5.93990i	0.162936	−	0.282213i	−0.772984	−	0.634425i	$-0.781237\pi$
$443$	3.42940	−	5.93990i	0.162936	−	0.282213i	0.935920	+	0.352212i	$0.114570\pi$
$444$	−28.4084			−1.34820
$445$	4.25022			0.201480
$446$	−71.1945			−3.37116
$447$	11.9887			0.567045
$448$		0			0
$449$	4.99075	+	8.64423i	0.235528	+	0.407946i	0.959426	−	0.281961i	$-0.0909847\pi$
$449$	4.99075	+	8.64423i	0.235528	+	0.407946i	−0.723898	+	0.689907i	$0.757651\pi$
$450$	−14.4428	+	25.0156i	−0.680839	+	1.17925i
$451$	15.2442	−	26.4038i	0.717823	−	1.24331i
$452$	−37.6698			−1.77184
$453$	3.99041	+	6.91159i	0.187486	+	0.324735i
$454$	48.1824			2.26131
$455$		0			0
$456$	−22.0794			−1.03396
$457$	4.38656	+	7.59774i	0.205194	+	0.355407i	0.950195	−	0.311657i	$-0.100884\pi$
$457$	4.38656	+	7.59774i	0.205194	+	0.355407i	−0.745000	+	0.667064i	$0.767551\pi$
$458$	−3.23035			−0.150944
$459$	−3.98763	+	6.90678i	−0.186127	+	0.322381i
$460$	2.46670	−	4.27245i	0.115010	−	0.199204i
$461$	−3.44272	−	5.96296i	−0.160343	−	0.277723i	0.774649	−	0.632392i	$-0.217927\pi$
$461$	−3.44272	−	5.96296i	−0.160343	−	0.277723i	−0.934992	+	0.354669i	$0.884593\pi$
$462$		0			0
$463$	−13.9526			−0.648432			−0.324216	−	0.945983i	$-0.605100\pi$
$463$	−13.9526			−0.648432			−0.324216	+	0.945983i	$0.605100\pi$
$464$	15.5351			0.721200
$465$	−0.508408			−0.0235768
$466$	3.68790			0.170838
$467$	14.4056	−	24.9513i	0.666613	−	1.15461i	−0.312232	−	0.950006i	$-0.601077\pi$
$467$	14.4056	−	24.9513i	0.666613	−	1.15461i	0.978845	−	0.204602i	$-0.0655900\pi$
$468$	33.3223	−	8.26403i	1.54032	−	0.382005i
$469$		0			0
$470$	3.74013	−	6.47810i	0.172520	−	0.298813i
$471$	−3.43784	−	5.95452i	−0.158407	−	0.274370i
$472$	−1.46018	+	2.52910i	−0.0672100	+	0.116411i
$473$	−10.2238	−	17.7081i	−0.470089	−	0.814219i
$474$	8.19572			0.376442
$475$	−15.3591	−	26.6027i	−0.704723	−	1.22062i
$476$		0			0
$477$	1.81466	+	3.14308i	0.0830876	+	0.143912i
$478$	−27.3359	−	47.3472i	−1.25032	−	2.16561i
$479$	−24.5871			−1.12341			−0.561707	−	0.827336i	$-0.689855\pi$
$479$	−24.5871			−1.12341			−0.561707	+	0.827336i	$0.689855\pi$
$480$	0.104028	+	0.180181i	0.00474820	+	0.00822412i
$481$	−9.61085	+	33.3598i	−0.438217	+	1.52108i
$482$	32.3726			1.47453
$483$		0			0
$484$	9.95395	−	17.2407i	0.452452	−	0.783670i
$485$	3.50998			0.159380
$486$	−18.7934	−	32.5511i	−0.852484	−	1.47655i
$487$	1.28658	−	2.22842i	0.0583004	−	0.100979i	−0.835402	−	0.549639i	$-0.814765\pi$
$487$	1.28658	−	2.22842i	0.0583004	−	0.100979i	0.893703	+	0.448660i	$0.148099\pi$
$488$	−5.32469			−0.241037
$489$	−8.26233			−0.373635
$490$		0			0
$491$	−7.01897	+	12.1572i	−0.316762	+	0.548647i	−0.979810	−	0.199929i	$-0.935929\pi$
$491$	−7.01897	+	12.1572i	−0.316762	+	0.548647i	0.663049	+	0.748576i	$0.269262\pi$
$492$	−18.4929	−	32.0306i	−0.833723	−	1.44405i
$493$	4.32639	+	7.49354i	0.194851	+	0.337492i
$494$	−15.2705	+	53.0049i	−0.687054	+	2.38480i
$495$	−1.01011	+	1.74957i	−0.0454012	+	0.0786373i
$496$	3.45468	−	5.98368i	0.155120	−	0.268675i
$497$		0			0
$498$	−1.29425	−	2.24170i	−0.0579965	−	0.100453i
$499$	−6.76726	+	11.7212i	−0.302944	+	0.524715i	−0.976801	−	0.214147i	$-0.931303\pi$
$499$	−6.76726	+	11.7212i	−0.302944	+	0.524715i	0.673857	+	0.738862i	$0.264636\pi$
$500$	6.60778	−	11.4450i	0.295509	−	0.511836i
$501$	6.88696	−	11.9286i	0.307687	−	0.532929i
$502$	−19.3393	+	33.4966i	−0.863155	+	1.49503i
$503$	4.13877	+	7.16856i	0.184539	+	0.319630i	0.943421	−	0.331597i	$-0.107588\pi$
$503$	4.13877	+	7.16856i	0.184539	+	0.319630i	−0.758882	+	0.651228i	$0.774254\pi$
$504$		0			0
$505$	−2.57069	+	4.45257i	−0.114394	+	0.198137i
$506$	−10.9118	+	18.8998i	−0.485090	+	0.840200i
$507$	−0.366338	+	9.78985i	−0.0162696	+	0.434782i
$508$	−17.6567	−	30.5822i	−0.783388	−	1.35687i
$509$	0.0831091	+	0.143949i	0.00368375	+	0.00638044i	0.867861	−	0.496806i	$-0.165494\pi$
$509$	0.0831091	+	0.143949i	0.00368375	+	0.00638044i	−0.864178	+	0.503187i	$0.832161\pi$
$510$	0.609771	−	1.05615i	0.0270011	−	0.0467673i
$511$		0			0
$512$	−35.4115			−1.56498
$513$	25.7502			1.13690
$514$	35.5569	−	61.5863i	1.56835	−	2.71646i
$515$	−3.00853	−	5.21093i	−0.132572	−	0.229621i
$516$	−24.8050			−1.09198
$517$	−10.9509	+	18.9675i	−0.481619	+	0.834189i
$518$		0			0
$519$	−6.17821			−0.271193
$520$	−5.56701	+	1.38063i	−0.244130	+	0.0605448i
$521$	3.53090	+	6.11569i	0.154691	+	0.267933i	0.932947	−	0.360015i	$-0.117228\pi$
$521$	3.53090	+	6.11569i	0.154691	+	0.267933i	−0.778255	+	0.627948i	$0.783895\pi$
$522$	−26.2711			−1.14985
$523$	−11.6956	−	20.2574i	−0.511414	−	0.885795i	−0.999912	−	0.0132299i	$-0.995789\pi$
$523$	−11.6956	−	20.2574i	−0.511414	−	0.885795i	0.488499	−	0.872565i	$-0.337545\pi$
$524$	0.376796	+	0.652630i	0.0164604	+	0.0285103i
$525$		0			0
$526$	2.07258	+	3.58981i	0.0903687	+	0.156523i
$527$	3.84839			0.167639
$528$	3.20544	+	5.55198i	0.139499	+	0.241619i
$529$	4.69387	−	8.13003i	0.204081	−	0.353479i
$530$	−0.619774	−	1.07348i	−0.0269212	−	0.0466290i
$531$	0.762452	−	1.32061i	0.0330876	−	0.0573094i
$532$		0			0
$533$	−43.8697	+	10.8798i	−1.90021	+	0.471257i
$534$	−11.4041	+	19.7525i	−0.493503	+	0.854773i
$535$	2.18056			0.0942737
$536$	−26.0459			−1.12501
$537$	−11.7211			−0.505804
$538$	20.3779			0.878554
$539$		0			0
$540$	2.73688	+	4.74041i	0.117776	+	0.203995i
$541$	−13.1540	+	22.7833i	−0.565533	+	0.979532i	0.431467	+	0.902129i	$0.357996\pi$
$541$	−13.1540	+	22.7833i	−0.565533	+	0.979532i	−0.997000	+	0.0774030i	$0.975337\pi$
$542$	14.7842	−	25.6069i	0.635035	−	1.09991i
$543$	−5.02873			−0.215804
$544$	−0.787438	−	1.36388i	−0.0337611	−	0.0584760i
$545$	−2.79197			−0.119595
$546$		0			0
$547$	41.7636			1.78568			0.892841	−	0.450371i	$-0.148708\pi$
$547$	41.7636			1.78568			0.892841	+	0.450371i	$0.148708\pi$
$548$	−9.54659	−	16.5352i	−0.407810	−	0.706348i
$549$	2.78036			0.118663
$550$	−14.4428	+	25.0156i	−0.615842	+	1.06667i
$551$	13.9689	−	24.1949i	0.595095	−	1.03074i
$552$	6.47508	+	11.2152i	0.275598	+	0.477349i
$553$		0			0
$554$	25.0948			1.06617
$555$	−2.47822			−0.105195
$556$	−43.3560			−1.83870
$557$	7.30987			0.309729			0.154865	−	0.987936i	$-0.450506\pi$
$557$	7.30987			0.309729			0.154865	+	0.987936i	$0.450506\pi$
$558$	−5.84212	+	10.1188i	−0.247317	+	0.428365i
$559$	−8.39181	+	29.1284i	−0.354936	+	1.23200i
$560$		0			0
$561$	−1.78537	+	3.09235i	−0.0753785	+	0.130559i
$562$	3.15780	+	5.46947i	0.133204	+	0.230716i
$563$	−22.3868	+	38.7751i	−0.943493	+	1.63418i	−0.184751	+	0.982785i	$0.559148\pi$
$563$	−22.3868	+	38.7751i	−0.943493	+	1.63418i	−0.758741	+	0.651392i	$0.774185\pi$
$564$	13.2846	+	23.0096i	0.559382	+	0.968878i
$565$	−3.28615			−0.138249
$566$	−5.59830	−	9.69654i	−0.235314	−	0.407576i
$567$		0			0
$568$	−22.1176	−	38.3089i	−0.928036	−	1.60741i
$569$	21.2563	+	36.8171i	0.891112	+	1.54345i	0.838544	+	0.544834i	$0.183407\pi$
$569$	21.2563	+	36.8171i	0.891112	+	1.54345i	0.0525679	+	0.998617i	$0.483259\pi$
$570$	−3.93761			−0.164928
$571$	20.4324	+	35.3899i	0.855069	+	1.48102i	0.876581	+	0.481254i	$0.159818\pi$
$571$	20.4324	+	35.3899i	0.855069	+	1.48102i	−0.0215128	+	0.999769i	$0.506848\pi$
$572$	33.3223	−	8.26403i	1.39328	−	0.345536i
$573$	−14.1268			−0.590155
$574$		0			0
$575$	−9.00851	+	15.6032i	−0.375681	+	0.650698i
$576$	21.7957			0.908155
$577$	10.8640	+	18.8170i	0.452275	+	0.783363i	0.998527	−	0.0542578i	$-0.0172793\pi$
$577$	10.8640	+	18.8170i	0.452275	+	0.783363i	−0.546252	+	0.837621i	$0.683946\pi$
$578$	16.0572	−	27.8119i	0.667891	−	1.15682i
$579$	−6.15918			−0.255967
$580$	5.93877			0.246594
$581$		0			0
$582$	−9.41790	+	16.3123i	−0.390384	+	0.676166i
$583$	1.81466	+	3.14308i	0.0751555	+	0.130173i
$584$	−27.7570	−	48.0765i	−1.14859	−	1.98942i
$585$	2.90690	−	0.720919i	0.120185	−	0.0298063i
$586$	2.38491	−	4.13078i	0.0985196	−	0.170641i
$587$	−10.2408	+	17.7376i	−0.422683	+	0.732108i	−0.996201	−	0.0870851i	$-0.972245\pi$
$587$	−10.2408	+	17.7376i	−0.422683	+	0.732108i	0.573518	+	0.819193i	$0.305578\pi$
$588$		0			0
$589$	−6.21277	−	10.7608i	−0.255993	−	0.443393i
$590$	−0.260406	+	0.451036i	−0.0107207	+	0.0185688i
$591$	−3.28571	+	5.69101i	−0.135156	+	0.234097i
$592$	16.8398	−	29.1673i	0.692110	−	1.19877i
$593$	2.81930	−	4.88318i	0.115775	−	0.200528i	−0.802314	−	0.596902i	$-0.796398\pi$
$593$	2.81930	−	4.88318i	0.115775	−	0.200528i	0.918089	+	0.396374i	$0.129732\pi$
$594$	−12.1070	−	20.9699i	−0.496756	−	0.860407i
$595$		0			0
$596$	−31.1421	+	53.9397i	−1.27563	+	2.20946i
$597$	6.58136	−	11.3993i	0.269357	−	0.466541i
$598$	31.4020	−	7.78777i	1.28412	−	0.318466i
$599$	−19.8359	−	34.3568i	−0.810474	−	1.40378i	−0.912533	−	0.409004i	$-0.865876\pi$
$599$	−19.8359	−	34.3568i	−0.810474	−	1.40378i	0.102058	−	0.994778i	$-0.467457\pi$
$600$	8.57035	+	14.8443i	0.349883	+	0.606015i
$601$	−8.41334	+	14.5723i	−0.343187	+	0.594418i	−0.985023	−	0.172425i	$-0.944840\pi$
$601$	−8.41334	+	14.5723i	−0.343187	+	0.594418i	0.641836	+	0.766842i	$0.278173\pi$
$602$		0			0
$603$	13.6003			0.553845
$604$	−41.4624			−1.68708
$605$	0.868340	−	1.50401i	0.0353030	−	0.0611467i
$606$	−13.7953	−	23.8941i	−0.560394	−	0.970631i
$607$	22.4980			0.913164			0.456582	−	0.889681i	$-0.349073\pi$
$607$	22.4980			0.913164			0.456582	+	0.889681i	$0.349073\pi$
$608$	−2.54245	+	4.40365i	−0.103110	+	0.178592i
$609$		0			0
$610$	−0.949597			−0.0384480
$611$	31.5144	−	7.81565i	1.27493	−	0.316187i
$612$	−9.27547	−	16.0656i	−0.374939	−	0.649413i
$613$	27.4269			1.10776			0.553882	−	0.832595i	$-0.313146\pi$
$613$	27.4269			1.10776			0.553882	+	0.832595i	$0.313146\pi$
$614$	−8.97028	−	15.5370i	−0.362011	−	0.627022i
$615$	−1.61324	−	2.79421i	−0.0650521	−	0.112673i
$616$		0			0
$617$	−5.31896	−	9.21271i	−0.214133	−	0.370890i	0.738871	−	0.673847i	$-0.235359\pi$
$617$	−5.31896	−	9.21271i	−0.214133	−	0.370890i	−0.953004	+	0.302957i	$0.902026\pi$
$618$	32.2897			1.29888
$619$	22.7339	+	39.3762i	0.913751	+	1.58266i	0.808719	+	0.588195i	$0.200161\pi$
$619$	22.7339	+	39.3762i	0.913751	+	1.58266i	0.105032	+	0.994469i	$0.466505\pi$
$620$	1.32065	−	2.28744i	0.0530388	−	0.0918659i
$621$	−7.55160	−	13.0798i	−0.303035	−	0.524873i
$622$	−17.2214	+	29.8283i	−0.690515	+	1.19601i
$623$		0			0
$624$	2.63107	−	9.13258i	0.105327	−	0.365596i
$625$	−11.6319	+	20.1471i	−0.465278	+	0.805885i
$626$	−64.9741			−2.59689
$627$	11.5291			0.460427
$628$	35.7210			1.42542
$629$	18.7589			0.747966
$630$		0			0
$631$	−14.7992	−	25.6329i	−0.589146	−	1.02043i	−0.994345	−	0.106202i	$-0.966131\pi$
$631$	−14.7992	−	25.6329i	−0.589146	−	1.02043i	0.405199	−	0.914229i	$-0.367202\pi$
$632$	−10.4139	+	18.0374i	−0.414243	+	0.717489i
$633$	8.76310	−	15.1781i	0.348302	−	0.603277i
$634$	52.1350			2.07055
$635$	−1.54029	−	2.66786i	−0.0611246	−	0.105871i
$636$	4.40275			0.174580
$637$		0			0
$638$	−26.2711			−1.04008
$639$	11.5491	+	20.0035i	0.456873	+	0.791328i
$640$	−6.89188			−0.272425
$641$	21.2823	−	36.8621i	0.840601	−	1.45596i	−0.0487858	−	0.998809i	$-0.515535\pi$
$641$	21.2823	−	36.8621i	0.840601	−	1.45596i	0.889387	−	0.457155i	$-0.151131\pi$
$642$	−5.85082	+	10.1339i	−0.230914	+	0.399954i
$643$	−10.9980	−	19.0492i	−0.433721	−	0.751226i	0.563470	−	0.826137i	$-0.309466\pi$
$643$	−10.9980	−	19.0492i	−0.433721	−	0.751226i	−0.997190	+	0.0749106i	$0.976133\pi$
$644$		0			0
$645$	−2.16388			−0.0852029
$646$	29.8057			1.17269
$647$	34.8051			1.36833			0.684166	−	0.729327i	$-0.260167\pi$
$647$	34.8051			1.36833			0.684166	+	0.729327i	$0.260167\pi$
$648$	19.6156			0.770572
$649$	0.762452	−	1.32061i	0.0299289	−	0.0518383i
$650$	41.5633	−	10.3078i	1.63025	−	0.404306i
$651$		0			0
$652$	21.4625	−	37.1741i	0.840535	−	1.45585i
$653$	25.4084	+	44.0086i	0.994306	+	1.72219i	0.589436	+	0.807815i	$0.299350\pi$
$653$	25.4084	+	44.0086i	0.994306	+	1.72219i	0.404870	+	0.914374i	$0.367317\pi$
$654$	7.49136	−	12.9754i	0.292935	−	0.507379i
$655$	0.0328701	+	0.0569326i	0.00128434	+	0.00222454i
$656$	43.8485			1.71199
$657$	14.4937	+	25.1038i	0.565453	+	0.979394i
$658$		0			0
$659$	7.37203	+	12.7687i	0.287173	+	0.497399i	0.973134	−	0.230240i	$-0.0739511\pi$
$659$	7.37203	+	12.7687i	0.287173	+	0.497399i	−0.685960	+	0.727639i	$0.740618\pi$
$660$	1.22537	+	2.12241i	0.0476976	+	0.0826147i
$661$	−18.1245			−0.704963			−0.352481	−	0.935819i	$-0.614662\pi$
$661$	−18.1245			−0.704963			−0.352481	+	0.935819i	$0.614662\pi$
$662$	−12.9069	−	22.3555i	−0.501643	−	0.868871i
$663$	5.13793	−	1.27422i	0.199541	−	0.0494866i
$664$	6.57814			0.255281
$665$		0			0
$666$	−28.4773	+	49.3241i	−1.10347	+	1.91127i
$667$	−16.3863			−0.634479
$668$	35.7795	+	61.9719i	1.38435	+	2.39777i
$669$	11.0299	−	19.1043i	0.426440	−	0.738616i
$670$	−4.64499			−0.179452
$671$	2.78036			0.107335
$672$		0			0
$673$	−10.4574	+	18.1127i	−0.403102	+	0.698193i	−0.994099	−	0.108481i	$-0.965401\pi$
$673$	−10.4574	+	18.1127i	−0.403102	+	0.698193i	0.590997	+	0.806674i	$0.298735\pi$
$674$	−8.21547	−	14.2296i	−0.316448	−	0.548104i
$675$	−9.99521	−	17.3122i	−0.384716	−	0.666348i
$676$	−43.0951	−	27.0786i	−1.65750	−	1.04149i
$677$	19.1089	−	33.0976i	0.734416	−	1.27205i	−0.220563	−	0.975373i	$-0.570790\pi$
$677$	19.1089	−	33.0976i	0.734416	−	1.27205i	0.954979	−	0.296673i	$-0.0958771\pi$
$678$	8.81733	−	15.2721i	0.338628	−	0.586520i
$679$		0			0
$680$	1.54961	+	2.68401i	0.0594249	+	0.102927i
$681$	−7.46472	+	12.9293i	−0.286049	+	0.495451i
$682$	−5.84212	+	10.1188i	−0.223706	+	0.387471i
$683$	11.9126	−	20.6333i	0.455825	−	0.789511i	−0.542911	−	0.839790i	$-0.682678\pi$
$683$	11.9126	−	20.6333i	0.455825	−	0.789511i	0.998735	+	0.0502792i	$0.0160111\pi$
$684$	−29.9483	+	51.8720i	−1.14510	+	1.98337i
$685$	−0.832803	−	1.44246i	−0.0318198	−	0.0551135i
$686$		0			0
$687$	0.500466	−	0.866833i	0.0190940	−	0.0330717i
$688$	14.7038	−	25.4677i	0.560577	−	0.970948i
$689$	1.48950	−	5.17013i	0.0567453	−	0.196966i
$690$	1.15476	+	2.00010i	0.0439608	+	0.0761424i
$691$	9.57063	+	16.5768i	0.364084	+	0.630612i	0.988629	−	0.150377i	$-0.0480488\pi$
$691$	9.57063	+	16.5768i	0.364084	+	0.630612i	−0.624545	+	0.780989i	$0.714715\pi$
$692$	16.0487	−	27.7972i	0.610080	−	1.05669i
$693$		0			0
$694$	−38.9632			−1.47902
$695$	−3.78219			−0.143467
$696$	−7.79463	+	13.5007i	−0.295455	+	0.511742i
$697$	12.2114	+	21.1508i	0.462540	+	0.801143i
$698$	39.0071			1.47644
$699$	−0.571352	+	0.989611i	−0.0216105	+	0.0374305i
$700$		0			0
$701$	−27.2956			−1.03094			−0.515471	−	0.856907i	$-0.672383\pi$
$701$	−27.2956			−1.03094			−0.515471	+	0.856907i	$0.672383\pi$
$702$	−9.93759	+	34.4939i	−0.375070	+	1.30189i
$703$	−30.2840	−	52.4535i	−1.14218	−	1.97832i
$704$	21.7957			0.821457
$705$	1.15889	+	2.00726i	0.0436463	+	0.0755977i
$706$	−4.67342	−	8.09460i	−0.175886	−	0.304644i
$707$		0			0
$708$	−0.924935	−	1.60203i	−0.0347612	−	0.0602081i
$709$	6.17166			0.231781			0.115891	−	0.993262i	$-0.463028\pi$
$709$	6.17166			0.231781			0.115891	+	0.993262i	$0.463028\pi$
$710$	−3.94443	−	6.83195i	−0.148032	−	0.256399i
$711$	5.43777	−	9.41849i	0.203932	−	0.353221i
$712$	−28.9812	−	50.1970i	−1.08612	−	1.88121i
$713$	−3.64395	+	6.31152i	−0.136467	+	0.236368i
$714$		0			0
$715$	2.90690	−	0.720919i	0.108712	−	0.0269608i
$716$	30.4471	−	52.7360i	1.13786	−	1.97084i
$717$	16.9402			0.632644
$718$	−51.3988			−1.91819
$719$	2.72133			0.101488			0.0507442	−	0.998712i	$-0.483841\pi$
$719$	2.72133			0.101488			0.0507442	+	0.998712i	$0.483841\pi$
$720$	−2.90549			−0.108281
$721$		0			0
$722$	−25.0129	−	43.3236i	−0.930883	−	1.61234i
$723$	−5.01537	+	8.68687i	−0.186524	+	0.323068i
$724$	13.0628	−	22.6254i	0.485475	−	0.840867i
$725$	−21.6887			−0.805497
$726$	4.65982	+	8.07105i	0.172942	+	0.299545i
$727$	−9.47153			−0.351280			−0.175640	−	0.984455i	$-0.556199\pi$
$727$	−9.47153			−0.351280			−0.175640	+	0.984455i	$0.556199\pi$
$728$		0			0
$729$	−0.987863			−0.0365875
$730$	−4.95014	−	8.57389i	−0.183213	−	0.317334i
$731$	16.3795			0.605818
$732$	1.68644	−	2.92099i	0.0623325	−	0.107963i
$733$	−1.74853	+	3.02855i	−0.0645836	+	0.111862i	−0.896509	−	0.443025i	$-0.853905\pi$
$733$	−1.74853	+	3.02855i	−0.0645836	+	0.111862i	0.831926	+	0.554887i	$0.187239\pi$
$734$	17.9236	+	31.0446i	0.661573	+	1.14588i
$735$		0			0
$736$	2.98243			0.109934
$737$	13.6003			0.500972
$738$	−74.1510			−2.72954
$739$	32.0303			1.17825			0.589126	−	0.808041i	$-0.299472\pi$
$739$	32.0303			1.17825			0.589126	+	0.808041i	$0.299472\pi$
$740$	6.43750	−	11.1501i	0.236647	−	0.409885i
$741$	−11.8575	−	12.3096i	−0.435598	−	0.452203i
$742$		0			0
$743$	−17.4593	+	30.2404i	−0.640519	+	1.10941i	0.344798	+	0.938677i	$0.387947\pi$
$743$	−17.4593	+	30.2404i	−0.640519	+	1.10941i	−0.985317	+	0.170734i	$0.945386\pi$
$744$	3.46672	+	6.00453i	0.127096	+	0.220137i
$745$	−2.71670	+	4.70547i	−0.0995324	+	0.172395i
$746$	−15.7194	−	27.2268i	−0.575527	−	0.996842i
$747$	−3.43487			−0.125675
$748$	−9.27547	−	16.0656i	−0.339145	−	0.587416i
$749$		0			0
$750$	3.09335	+	5.35785i	0.112953	+	0.195641i
$751$	−13.4986	−	23.3803i	−0.492571	−	0.853158i	0.507392	−	0.861715i	$-0.330610\pi$
$751$	−13.4986	−	23.3803i	−0.492571	−	0.853158i	−0.999963	+	0.00855684i	$0.997276\pi$
$752$	−31.4991			−1.14865
$753$	−5.99233	−	10.3790i	−0.218373	−	0.378233i
$754$	27.0195	+	28.0495i	0.983992	+	1.02150i
$755$	−3.61700			−0.131636
$756$		0			0
$757$	26.2950	−	45.5442i	0.955707	−	1.65533i	0.222965	−	0.974826i	$-0.428426\pi$
$757$	26.2950	−	45.5442i	0.955707	−	1.65533i	0.732742	−	0.680507i	$-0.238240\pi$
$758$	−65.2673			−2.37062
$759$	−3.38106	−	5.85616i	−0.122725	−	0.212565i
$760$	5.00333	−	8.66602i	0.181490	−	0.314350i
$761$	13.9286			0.504912			0.252456	−	0.967608i	$-0.418762\pi$
$761$	13.9286			0.504912			0.252456	+	0.967608i	$0.418762\pi$
$762$	16.5315			0.598874
$763$		0			0
$764$	36.6961	−	63.5596i	1.32762	−	2.29950i
$765$	−0.809152	−	1.40149i	−0.0292550	−	0.0506711i
$766$	3.53606	+	6.12463i	0.127763	+	0.221292i
$767$	−2.19418	+	0.544162i	−0.0792272	+	0.0196486i
$768$	11.7387	−	20.3320i	0.423583	−	0.733668i
$769$	−6.89545	+	11.9433i	−0.248656	+	0.430685i	−0.963153	−	0.268953i	$-0.913322\pi$
$769$	−6.89545	+	11.9433i	−0.248656	+	0.430685i	0.714497	+	0.699639i	$0.246656\pi$
$770$		0			0
$771$	11.0174	+	19.0827i	0.396781	+	0.687246i
$772$	15.9993	−	27.7115i	0.575826	−	0.997360i
$773$	−25.2435	+	43.7230i	−0.907946	+	1.57261i	−0.0910326	+	0.995848i	$0.529017\pi$
$773$	−25.2435	+	43.7230i	−0.907946	+	1.57261i	−0.816913	+	0.576760i	$0.804317\pi$
$774$	−24.8652	+	43.0678i	−0.893762	+	1.54804i
$775$	−4.82310	+	8.35385i	−0.173251	+	0.300079i
$776$	−23.9337	−	41.4544i	−0.859170	−	1.48813i
$777$		0			0
$778$	20.3092	−	35.1766i	0.728120	−	1.26114i
$779$	39.4277	−	68.2908i	1.41265	−	2.44677i
$780$	1.00580	−	3.49120i	0.0360136	−	0.125005i
$781$	11.5491	+	20.0035i	0.413258	+	0.715783i
$782$	−8.74092	−	15.1397i	−0.312575	−	0.541395i
$783$	9.09053	−	15.7453i	0.324869	−	0.562690i
$784$		0			0
$785$	3.11614			0.111220
$786$	−0.352785			−0.0125834
$787$	−5.43189	+	9.40831i	−0.193626	+	0.335370i	−0.946449	−	0.322853i	$-0.895358\pi$
$787$	−5.43189	+	9.40831i	−0.193626	+	0.335370i	0.752823	+	0.658223i	$0.228691\pi$
$788$	−17.0701	−	29.5663i	−0.608097	−	1.05325i
$789$	−1.28439			−0.0457254
$790$	−1.85720	+	3.21676i	−0.0660762	+	0.114447i
$791$		0			0
$792$	27.5509			0.978980
$793$	−2.85957	−	2.96858i	−0.101546	−	0.105417i
$794$	29.3049	+	50.7576i	1.03999	+	1.80132i
$795$	0.384077			0.0136218
$796$	34.1919	+	59.2221i	1.21190	+	2.09907i
$797$	3.95840	+	6.85616i	0.140214	+	0.242858i	0.927577	−	0.373632i	$-0.121888\pi$
$797$	3.95840	+	6.85616i	0.140214	+	0.242858i	−0.787363	+	0.616489i	$0.788554\pi$
$798$		0			0
$799$	−8.77221	−	15.1939i	−0.310339	−	0.537522i
$800$	3.94751			0.139566
$801$	15.1330	+	26.2111i	0.534697	+	0.926123i
$802$	−2.24349	+	3.88583i	−0.0792202	+	0.137213i
$803$	14.4937	+	25.1038i	0.511472	+	0.885895i
$804$	8.24928	−	14.2882i	0.290930	−	0.503905i
$805$		0			0
$806$	16.8124	−	4.16952i	0.592192	−	0.146865i
$807$	−3.15707	+	5.46821i	−0.111134	+	0.192490i
$808$	70.1158			2.46667
$809$	−29.6389			−1.04205			−0.521023	−	0.853542i	$-0.674450\pi$
$809$	−29.6389			−1.04205			−0.521023	+	0.853542i	$0.674450\pi$
$810$	3.49821			0.122915
$811$	15.8344			0.556022			0.278011	−	0.960578i	$-0.410325\pi$
$811$	15.8344			0.556022			0.278011	+	0.960578i	$0.410325\pi$
$812$		0			0
$813$	4.58091	+	7.93438i	0.160660	+	0.278271i
$814$	−28.4773	+	49.3241i	−0.998129	+	1.72881i
$815$	1.87229	−	3.24291i	0.0655836	−	0.113594i
$816$	−5.13544			−0.179776
$817$	−26.4428	−	45.8002i	−0.925116	−	1.60235i
$818$	−62.4327			−2.18291
$819$		0			0
$820$	16.7624			0.585368
$821$	−8.86971	−	15.3628i	−0.309555	−	0.536165i	0.668710	−	0.743523i	$-0.266847\pi$
$821$	−8.86971	−	15.3628i	−0.309555	−	0.536165i	−0.978265	+	0.207358i	$0.933513\pi$
$822$	8.93824			0.311757
$823$	4.34100	−	7.51883i	0.151318	−	0.262090i	−0.780394	−	0.625288i	$-0.784982\pi$
$823$	4.34100	−	7.51883i	0.151318	−	0.262090i	0.931712	+	0.363198i	$0.118315\pi$
$824$	−41.0290	+	71.0643i	−1.42931	+	2.47564i
$825$	−4.47513	−	7.75115i	−0.155804	−	0.269860i
$826$		0			0
$827$	14.3121			0.497681			0.248840	−	0.968545i	$-0.419951\pi$
$827$	14.3121			0.497681			0.248840	+	0.968545i	$0.419951\pi$
$828$	35.1309			1.22088
$829$	25.3066			0.878933			0.439467	−	0.898259i	$-0.355167\pi$
$829$	25.3066			0.878933			0.439467	+	0.898259i	$0.355167\pi$
$830$	1.17314			0.0407201
$831$	−3.88784	+	6.73393i	−0.134868	+	0.233597i
$832$	−22.4167	−	23.2712i	−0.777158	−	0.806783i
$833$		0			0
$834$	10.1483	−	17.5774i	0.351407	−	0.608654i
$835$	3.12125	+	5.40617i	0.108015	+	0.187088i
$836$	−29.9483	+	51.8720i	−1.03578	+	1.79403i
$837$	−4.04308	−	7.00281i	−0.139749	−	0.242053i
$838$	−63.8179			−2.20455
$839$	−6.52129	−	11.2952i	−0.225140	−	0.389954i	0.731222	−	0.682140i	$-0.238951\pi$
$839$	−6.52129	−	11.2952i	−0.225140	−	0.389954i	−0.956361	+	0.292186i	$0.905617\pi$
$840$		0			0
$841$	4.63720	+	8.03187i	0.159904	+	0.276961i
$842$	−28.7763	−	49.8419i	−0.991695	−	1.71767i
$843$	−1.95690			−0.0673994
$844$	45.5266	+	78.8543i	1.56709	+	2.71428i
$845$	−3.75943	−	2.36222i	−0.129328	−	0.0812630i
$846$	53.2673			1.83137
$847$		0			0
$848$	−2.60984	+	4.52037i	−0.0896223	+	0.155230i
$849$	3.46930			0.119066
$850$	−11.5694	−	20.0388i	−0.396827	−	0.687324i
$851$	−17.7624	+	30.7653i	−0.608887	+	1.05462i
$852$	28.0204			0.959964
$853$	18.8926			0.646869			0.323435	−	0.946251i	$-0.395162\pi$
$853$	18.8926			0.646869			0.323435	+	0.946251i	$0.395162\pi$
$854$		0			0
$855$	−2.61256	+	4.52509i	−0.0893477	+	0.154755i
$856$	−14.8687	−	25.7534i	−0.508202	−	0.880232i
$857$	−12.3219	−	21.3422i	−0.420909	−	0.729036i	0.575119	−	0.818069i	$-0.304956\pi$
$857$	−12.3219	−	21.3422i	−0.420909	−	0.729036i	−0.996029	+	0.0890333i	$0.971622\pi$
$858$	−4.44933	+	15.4439i	−0.151898	+	0.527245i
$859$	−1.28571	+	2.22691i	−0.0438677	+	0.0759811i	−0.887126	−	0.461528i	$-0.847301\pi$
$859$	−1.28571	+	2.22691i	−0.0438677	+	0.0759811i	0.843258	+	0.537509i	$0.180635\pi$
$860$	5.62097	−	9.73580i	0.191673	−	0.331988i
$861$		0			0
$862$	27.9906	+	48.4812i	0.953365	+	1.65128i
$863$	−19.7704	+	34.2433i	−0.672991	+	1.16565i	0.304061	+	0.952653i	$0.401657\pi$
$863$	−19.7704	+	34.2433i	−0.672991	+	1.16565i	−0.977052	+	0.213002i	$0.931676\pi$
$864$	−1.65455	+	2.86576i	−0.0562888	+	0.0974951i
$865$	1.40002	−	2.42491i	0.0476021	−	0.0824493i
$866$	31.4479	−	54.4694i	1.06864	−	1.85095i
$867$	4.97536	+	8.61758i	0.168972	+	0.292668i
$868$		0			0
$869$	5.43777	−	9.41849i	0.184464	−	0.319500i
$870$	−1.39008	+	2.40769i	−0.0471282	+	0.0816284i
$871$	−13.9877	−	14.5209i	−0.473956	−	0.492023i
$872$	19.0378	+	32.9744i	0.644701	+	1.11666i
$873$	12.4973	+	21.6460i	0.422971	+	0.732607i
$874$	−28.2224	+	48.8826i	−0.954636	+	1.65348i
$875$		0			0
$876$	35.1648			1.18811
$877$	21.0455			0.710655			0.355328	−	0.934742i	$-0.384369\pi$
$877$	21.0455			0.710655			0.355328	+	0.934742i	$0.384369\pi$
$878$	43.3851	−	75.1452i	1.46418	−	2.53603i
$879$	0.738970	+	1.27993i	0.0249248	+	0.0431711i
$880$	−2.90549			−0.0979439
$881$	2.50592	−	4.34038i	0.0844266	−	0.146231i	−0.820720	−	0.571330i	$-0.806427\pi$
$881$	2.50592	−	4.34038i	0.0844266	−	0.146231i	0.905147	+	0.425099i	$0.139761\pi$
$882$		0			0
$883$	−7.13079			−0.239970			−0.119985	−	0.992776i	$-0.538285\pi$
$883$	−7.13079			−0.239970			−0.119985	+	0.992776i	$0.538285\pi$
$884$	−7.61343	+	26.4266i	−0.256067	+	0.888824i
$885$	−0.0806874	−	0.139755i	−0.00271228	−	0.00469780i
$886$	−16.6813			−0.560419
$887$	−3.36301	−	5.82491i	−0.112919	−	0.195581i	0.804027	−	0.594593i	$-0.202687\pi$
$887$	−3.36301	−	5.82491i	−0.112919	−	0.195581i	−0.916946	+	0.399011i	$0.869353\pi$
$888$	16.8984	+	29.2689i	0.567074	+	0.982202i
$889$		0			0
$890$	−5.16847	−	8.95206i	−0.173248	−	0.300074i
$891$	−10.2425			−0.343138
$892$	57.3032	+	99.2520i	1.91865	+	3.32320i
$893$	−28.3234	+	49.0576i	−0.947807	+	1.64165i
$894$	−14.5788	−	25.2512i	−0.487588	−	0.844528i
$895$	2.65608	−	4.60046i	0.0887829	−	0.153777i
$896$		0			0
$897$	−2.77522	+	9.63294i	−0.0926618	+	0.321635i
$898$	12.1380	−	21.0236i	0.405050	−	0.701567i
$899$	−8.77310			−0.292599
$900$	46.4989			1.54996
$901$	−2.90727			−0.0968551
$902$	−74.1510			−2.46896
$903$		0			0
$904$	22.4075	+	38.8109i	0.745263	+	1.29083i
$905$	1.13954	−	1.97374i	0.0378796	−	0.0656095i
$906$	9.70506	−	16.8097i	0.322429	−	0.558464i
$907$	29.5725			0.981938			0.490969	−	0.871177i	$-0.336643\pi$
$907$	29.5725			0.981938			0.490969	+	0.871177i	$0.336643\pi$
$908$	−38.7811	−	67.1709i	−1.28700	−	2.22914i
$909$	−36.6120			−1.21434
$910$		0			0
$911$	−20.6132			−0.682947			−0.341473	−	0.939891i	$-0.610926\pi$
$911$	−20.6132			−0.682947			−0.341473	+	0.939891i	$0.610926\pi$
$912$	8.29055	+	14.3597i	0.274528	+	0.475496i
$913$	−3.43487			−0.113678
$914$	10.6685	−	18.4785i	0.352884	−	0.611213i
$915$	0.147117	−	0.254815i	0.00486355	−	0.00842392i
$916$	2.60005	+	4.50342i	0.0859081	+	0.148797i
$917$		0			0
$918$	19.3966			0.640184
$919$	−4.17904			−0.137854			−0.0689269	−	0.997622i	$-0.521958\pi$
$919$	−4.17904			−0.137854			−0.0689269	+	0.997622i	$0.521958\pi$
$920$	−5.86917			−0.193501
$921$	5.55893			0.183173
$922$	−8.37303	+	14.5025i	−0.275751	+	0.477615i
$923$	9.47961	−	32.9043i	0.312025	−	1.08306i
$924$		0			0
$925$	−23.5101	+	40.7207i	−0.773007	+	1.33889i
$926$	16.9670	+	29.3878i	0.557571	+	0.965742i
$927$	21.4239	−	37.1073i	0.703653	−	1.21876i
$928$	1.79511	+	3.10922i	0.0589273	+	0.102065i
$929$	−48.0912			−1.57782			−0.788910	−	0.614509i	$-0.789354\pi$
$929$	−48.0912			−1.57782			−0.788910	+	0.614509i	$0.789354\pi$
$930$	0.618249	+	1.07084i	0.0202732	+	0.0351142i
$931$		0			0
$932$	−2.96832	−	5.14128i	−0.0972306	−	0.168408i
$933$	−5.33610	−	9.24239i	−0.174696	−	0.302582i
$934$	−70.0718			−2.29282
$935$	−0.809152	−	1.40149i	−0.0264621	−	0.0458337i
$936$	−28.3358	−	29.4160i	−0.926186	−	0.961492i
$937$	12.5441			0.409798			0.204899	−	0.978783i	$-0.434313\pi$
$937$	12.5441			0.409798			0.204899	+	0.978783i	$0.434313\pi$
$938$		0			0
$939$	10.0662	−	17.4352i	0.328498	−	0.568975i
$940$	−12.0415			−0.392749
$941$	15.2944	+	26.4907i	0.498583	+	0.863572i	0.999999	−	0.00163503i	$-0.000520447\pi$
$941$	15.2944	+	26.4907i	0.498583	+	0.863572i	−0.501415	+	0.865207i	$0.667187\pi$
$942$	−8.36117	+	14.4820i	−0.272422	+	0.471848i
$943$	−46.2508			−1.50613
$944$	2.19311			0.0713798
$945$		0			0
$946$	−24.8652	+	43.0678i	−0.808438	+	1.40026i
$947$	3.89174	+	6.74069i	0.126465	+	0.219043i	0.922304	−	0.386464i	$-0.126304\pi$
$947$	3.89174	+	6.74069i	0.126465	+	0.219043i	−0.795840	+	0.605507i	$0.792970\pi$
$948$	−6.59659	−	11.4256i	−0.214247	−	0.371087i
$949$	11.8966	−	41.2939i	0.386181	−	1.34046i
$950$	−37.3548	+	64.7005i	−1.21195	+	2.09916i
$951$	−8.07709	+	13.9899i	−0.261917	+	0.453654i
$952$		0			0
$953$	19.2152	+	33.2817i	0.622442	+	1.07810i	0.989030	+	0.147717i	$0.0471926\pi$
$953$	19.2152	+	33.2817i	0.622442	+	1.07810i	−0.366588	+	0.930383i	$0.619474\pi$
$954$	4.41343	−	7.64429i	0.142890	−	0.247493i
$955$	3.20121	−	5.54467i	0.103589	−	0.179421i
$956$	−44.0044	+	76.2179i	−1.42320	+	2.46506i
$957$	4.07008	−	7.04958i	0.131567	−	0.227881i
$958$	29.8992	+	51.7869i	0.965998	+	1.67316i
$959$		0			0
$960$	1.15328	−	1.99754i	0.0372219	−	0.0644702i
$961$	13.5491	−	23.4676i	0.437066	−	0.757021i
$962$	81.9517	−	20.3243i	2.64223	−	0.655280i
$963$	7.76391	+	13.4475i	0.250189	+	0.433339i
$964$	−26.0561	−	45.1305i	−0.839211	−	1.45356i
$965$	1.39571	−	2.41744i	0.0449294	−	0.0778200i
$966$		0			0
$967$	7.80008			0.250834			0.125417	−	0.992104i	$-0.459973\pi$
$967$	7.80008			0.250834			0.125417	+	0.992104i	$0.459973\pi$
$968$	−23.6840			−0.761234
$969$	−4.61769	+	7.99807i	−0.148342	+	0.256935i
$970$	−4.26830	−	7.39292i	−0.137047	−	0.237372i
$971$	57.7914			1.85462			0.927308	−	0.374300i	$-0.122117\pi$
$971$	57.7914			1.85462			0.927308	+	0.374300i	$0.122117\pi$
$972$	−30.2529	+	52.3995i	−0.970362	+	1.68072i
$973$		0			0
$974$	−6.25817			−0.200525
$975$	−3.67325	+	12.7501i	−0.117638	+	0.408328i
$976$	1.99936	+	3.46298i	0.0639978	+	0.110847i
$977$	8.67414			0.277510			0.138755	−	0.990327i	$-0.455690\pi$
$977$	8.67414			0.277510			0.138755	+	0.990327i	$0.455690\pi$
$978$	10.0474	+	17.4026i	0.321280	+	0.556474i
$979$	15.1330	+	26.2111i	0.483652	+	0.837710i
$980$		0			0
$981$	−9.94086	−	17.2181i	−0.317387	−	0.549731i
$982$	34.1417			1.08950
$983$	−18.5560	−	32.1400i	−0.591846	−	1.02511i	−0.993984	−	0.109528i	$-0.965066\pi$
$983$	−18.5560	−	32.1400i	−0.591846	−	1.02511i	0.402138	−	0.915579i	$-0.368267\pi$
$984$	−22.0006	+	38.1062i	−0.701354	+	1.21478i
$985$	−1.48912	−	2.57924i	−0.0474474	−	0.0821813i
$986$	10.5222	−	18.2250i	0.335096	−	0.580403i
$987$		0			0
$988$	86.1849	−	21.3741i	2.74191	−	0.680001i
$989$	−15.5094	+	26.8631i	−0.493170	+	0.854196i
$990$	4.91339			0.156158
$991$	−45.2637			−1.43785			−0.718924	−	0.695089i	$-0.755365\pi$
$991$	−45.2637			−1.43785			−0.718924	+	0.695089i	$0.755365\pi$
$992$	1.59677			0.0506976
$993$	7.99850			0.253825
$994$		0			0
$995$	2.98275	+	5.16628i	0.0945597	+	0.163782i
$996$	−2.08343	+	3.60861i	−0.0660160	+	0.114343i
$997$	22.1277	−	38.3263i	0.700791	−	1.21381i	−0.267398	−	0.963586i	$-0.586164\pi$
$997$	22.1277	−	38.3263i	0.700791	−	1.21381i	0.968189	−	0.250219i	$-0.0805028\pi$
$998$	32.9173			1.04198
$999$	−19.7079	−	34.1351i	−0.623530	−	1.07999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.m.373.2		16
7.2	even	3		637.2.f.l.295.1	✓	16
7.3	odd	6		637.2.h.m.165.8		16
7.4	even	3		637.2.h.m.165.7		16
7.5	odd	6		637.2.f.l.295.2	yes	16
7.6	odd	2	inner	637.2.g.m.373.1		16
13.3	even	3		637.2.h.m.471.7		16
91.3	odd	6	inner	637.2.g.m.263.1		16
91.9	even	3		8281.2.a.ci.1.8		8
91.16	even	3		637.2.f.l.393.1	yes	16
91.30	even	6		8281.2.a.cl.1.2		8
91.55	odd	6		637.2.h.m.471.8		16
91.61	odd	6		8281.2.a.ci.1.7		8
91.68	odd	6		637.2.f.l.393.2	yes	16
91.81	even	3	inner	637.2.g.m.263.2		16
91.82	odd	6		8281.2.a.cl.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.1	✓	16	7.2	even	3
637.2.f.l.295.2	yes	16	7.5	odd	6
637.2.f.l.393.1	yes	16	91.16	even	3
637.2.f.l.393.2	yes	16	91.68	odd	6
637.2.g.m.263.1		16	91.3	odd	6	inner
637.2.g.m.263.2		16	91.81	even	3	inner
637.2.g.m.373.1		16	7.6	odd	2	inner
637.2.g.m.373.2		16	1.1	even	1	trivial
637.2.h.m.165.7		16	7.4	even	3
637.2.h.m.165.8		16	7.3	odd	6
637.2.h.m.471.7		16	13.3	even	3
637.2.h.m.471.8		16	91.55	odd	6
8281.2.a.ci.1.7		8	91.61	odd	6
8281.2.a.ci.1.8		8	91.9	even	3
8281.2.a.cl.1.1		8	91.82	odd	6
8281.2.a.cl.1.2		8	91.30	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21605 - 2.10626i) q^{2} +0.753592 q^{3} +(-1.95755 + 3.39058i) q^{4} +(-0.170769 + 0.295780i) q^{5} +(-0.916405 - 1.58726i) q^{6} +4.65773 q^{8} -2.43210 q^{9} +O(q^{10})\)	\(q+(-1.21605 - 2.10626i) q^{2} +0.753592 q^{3} +(-1.95755 + 3.39058i) q^{4} +(-0.170769 + 0.295780i) q^{5} +(-0.916405 - 1.58726i) q^{6} +4.65773 q^{8} -2.43210 q^{9} +0.830652 q^{10} -2.43210 q^{11} +(-1.47520 + 2.55511i) q^{12} +(2.50139 + 2.59674i) q^{13} +(-0.128690 + 0.222897i) q^{15} +(-1.74892 - 3.02922i) q^{16} +(0.974117 - 1.68722i) q^{17} +(2.95755 + 5.12263i) q^{18} -6.29039 q^{19} +(-0.668577 - 1.15801i) q^{20} +(2.95755 + 5.12263i) q^{22} +(1.84474 + 3.19518i) q^{23} +3.51003 q^{24} +(2.44168 + 4.22911i) q^{25} +(2.42760 - 8.42634i) q^{26} -4.09359 q^{27} +(-2.22068 + 3.84632i) q^{29} +0.625973 q^{30} +(0.987661 + 1.71068i) q^{31} +(0.404180 - 0.700061i) q^{32} -1.83281 q^{33} -4.73830 q^{34} +(4.76096 - 8.24623i) q^{36} +(4.81433 + 8.33867i) q^{37} +(7.64942 + 13.2492i) q^{38} +(1.88503 + 1.95688i) q^{39} +(-0.795393 + 1.37766i) q^{40} +(-6.26793 + 10.8564i) q^{41} +(4.20368 + 7.28099i) q^{43} +(4.76096 - 8.24623i) q^{44} +(0.415326 - 0.719366i) q^{45} +(4.48659 - 7.77100i) q^{46} +(4.50265 - 7.79882i) q^{47} +(-1.31797 - 2.28279i) q^{48} +(5.93840 - 10.2856i) q^{50} +(0.734087 - 1.27148i) q^{51} +(-13.7011 + 3.39790i) q^{52} +(-0.746129 - 1.29233i) q^{53} +(4.97800 + 8.62216i) q^{54} +(0.415326 - 0.719366i) q^{55} -4.74039 q^{57} +10.8018 q^{58} +(-0.313495 + 0.542990i) q^{59} +(-0.503834 - 0.872666i) q^{60} -1.14319 q^{61} +(2.40209 - 4.16054i) q^{62} -8.96169 q^{64} +(-1.19522 + 0.296418i) q^{65} +(2.22879 + 3.86037i) q^{66} -5.59199 q^{67} +(3.81377 + 6.60564i) q^{68} +(1.39018 + 2.40786i) q^{69} +(-4.74859 - 8.22481i) q^{71} -11.3280 q^{72} +(-5.95934 - 10.3219i) q^{73} +(11.7089 - 20.2805i) q^{74} +(1.84003 + 3.18702i) q^{75} +(12.3138 - 21.3281i) q^{76} +(1.82942 - 6.35002i) q^{78} +(-2.23583 + 3.87258i) q^{79} +1.19464 q^{80} +4.21140 q^{81} +30.4885 q^{82} +1.41231 q^{83} +(0.332697 + 0.576248i) q^{85} +(10.2238 - 17.7081i) q^{86} +(-1.67348 + 2.89856i) q^{87} -11.3280 q^{88} +(-6.22219 - 10.7771i) q^{89} -2.02023 q^{90} -14.4447 q^{92} +(0.744294 + 1.28915i) q^{93} -21.9018 q^{94} +(1.07420 - 1.86057i) q^{95} +(0.304587 - 0.527560i) q^{96} +(-5.13850 - 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

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