LMFDB - Embedded newform 637.2.g.m.263.2

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			263.2
Root			$-0.756863 - 1.31093i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.m.373.2

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	0.0121689	+	0.999926i	$0.496126\pi$
$2$	−1.21605	+	2.10626i	−0.859877	+	1.48935i	−0.872046	+	0.489424i	$0.837207\pi$
$3$	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	0.825311	−	0.564678i	$-0.191000\pi$
$5$	−0.170769	−	0.295780i	−0.0763700	−	0.132277i	−0.901681	+	0.432401i	$0.857666\pi$
$6$	−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	0.959638	−	0.281240i	$-0.0907456\pi$
$17$	0.974117	+	1.68722i	0.236258	+	0.409211i	−0.723379	+	0.690451i	$0.757412\pi$
$18$	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	−0.607066	−	0.794651i	$-0.707654\pi$
$23$	1.84474	−	3.19518i	0.384655	−	0.666242i	0.991721	+	0.128409i	$0.0409872\pi$
$24$	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	0.582779	−	0.812631i	$-0.301965\pi$
$29$	−2.22068	−	3.84632i	−0.412369	−	0.714244i	−0.995148	+	0.0983864i	$0.968632\pi$
$30$	0.625973			0.114286
$31$	0.987661	−	1.71068i	0.177389	−	0.307247i	−0.763596	−	0.645694i	$-0.776568\pi$
$31$	0.987661	−	1.71068i	0.177389	−	0.307247i	0.940986	+	0.338447i	$0.109902\pi$
$32$	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	−0.133584	−	0.991037i	$-0.542649\pi$
$37$	4.81433	−	8.33867i	0.791472	−	1.37087i	0.925056	−	0.379832i	$-0.124018\pi$
$38$	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	−0.666461	−	0.745540i	$-0.732192\pi$
$41$	−6.26793	−	10.8564i	−0.978887	−	1.69548i	−0.312426	−	0.949942i	$-0.601141\pi$
$42$		0			0
$43$	4.20368	−	7.28099i	0.641055	−	1.11034i	−0.344142	−	0.938918i	$-0.611830\pi$
$43$	4.20368	−	7.28099i	0.641055	−	1.11034i	0.985198	−	0.171423i	$-0.0548365\pi$
$44$	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	0.981445	+	0.191745i	$0.0614148\pi$
$47$	4.50265	+	7.79882i	0.656779	+	1.13757i	−0.324666	+	0.945829i	$0.605252\pi$
$48$	−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	−0.912709	−	0.408609i	$-0.866014\pi$
$53$	−0.746129	+	1.29233i	−0.102489	+	0.177516i	0.810221	+	0.586125i	$0.199347\pi$
$54$	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	0.844897	−	0.534929i	$-0.179662\pi$
$59$	−0.313495	−	0.542990i	−0.0408136	−	0.0706913i	−0.885711	+	0.464238i	$0.846328\pi$
$60$	−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	0.433628	+	0.901092i	$0.357233\pi$
$71$	−4.74859	+	8.22481i	−0.563554	+	0.976105i	−0.997183	+	0.0750130i	$0.976100\pi$
$72$	−11.3280			−1.33502
$73$	−5.95934	+	10.3219i	−0.697488	+	1.20808i	0.271847	+	0.962340i	$0.412366\pi$
$73$	−5.95934	+	10.3219i	−0.697488	+	1.20808i	−0.969335	+	0.245744i	$0.920968\pi$
$74$	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	0.712402	−	0.701772i	$-0.247607\pi$
$79$	−2.23583	−	3.87258i	−0.251551	−	0.435699i	−0.963953	+	0.266073i	$0.914274\pi$
$80$	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	0.321182	+	0.947018i	$0.395920\pi$
$89$	−6.22219	+	10.7771i	−0.659551	+	1.14238i	−0.980732	+	0.195357i	$0.937413\pi$
$90$	−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	0.477945	+	0.878390i	$0.341382\pi$
$97$	−5.13850	+	8.90014i	−0.521736	+	0.903673i	−0.999680	+	0.0252826i	$0.991951\pi$
$98$		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	−0.864080	−	0.503354i	$-0.832099\pi$
$103$	−8.80880	−	15.2573i	−0.867957	−	1.50335i	−0.00387687	−	0.999992i	$-0.501234\pi$
$104$	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	−0.978058	−	0.208332i	$-0.933197\pi$
$107$	−3.19227	+	5.52917i	−0.308608	+	0.534525i	0.669450	+	0.742857i	$0.266530\pi$
$108$	8.01341	+	13.8796i	0.771091	+	1.33557i
$109$	4.08736	−	7.07951i	0.391498	−	0.678095i	−0.601149	−	0.799137i	$-0.705290\pi$
$109$	4.08736	−	7.07951i	0.391498	−	0.678095i	0.992647	+	0.121042i	$0.0386236\pi$
$110$	−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	−0.545980	−	0.837798i	$-0.683843\pi$
$113$	4.81083	−	8.33259i	0.452564	−	0.783865i	0.998545	+	0.0539336i	$0.0171759\pi$
$114$	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	0.593561	−	0.804789i	$-0.297722\pi$
$127$	−4.50988	−	7.81134i	−0.400187	−	0.693145i	−0.993748	+	0.111644i	$0.964388\pi$
$128$	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	0.870199	−	0.492700i	$-0.163990\pi$
$131$	0.0962416	+	0.166695i	0.00840867	+	0.0145642i	−0.861790	+	0.507264i	$0.830657\pi$
$132$	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	0.742861	−	0.669446i	$-0.233468\pi$
$137$	−2.43840	−	4.22343i	−0.208326	−	0.360832i	−0.951187	+	0.308614i	$0.900135\pi$
$138$	3.38106	+	5.85616i	0.287815	+	0.498510i
$139$	5.53701	−	9.59038i	0.469643	−	0.813446i	−0.529755	−	0.848151i	$-0.677716\pi$
$139$	5.53701	−	9.59038i	0.469643	−	0.813446i	0.999398	+	0.0347054i	$0.0110493\pi$
$140$		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	−0.566037	−	0.824380i	$-0.691524\pi$
$151$	5.29518	−	9.17152i	0.430916	−	0.746368i	0.996952	+	0.0780122i	$0.0248573\pi$
$152$	−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	−0.988628	−	0.150379i	$-0.951951\pi$
$157$	−4.56194	+	7.90151i	−0.364082	+	0.630609i	0.624546	+	0.780988i	$0.285284\pi$
$158$	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	0.965897	+	0.258925i	$0.0833683\pi$
$167$	9.13884	+	15.8289i	0.707185	+	1.22488i	−0.258713	+	0.965954i	$0.583298\pi$
$168$		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	0.667860	−	0.744287i	$-0.267210\pi$
$197$	−4.36006	−	7.55184i	−0.310641	−	0.538047i	−0.978501	+	0.206240i	$0.933877\pi$
$198$	−7.19306	+	12.4587i	−0.511189	+	0.885405i
$199$	8.73332	+	15.1266i	0.619089	+	1.07229i	0.989652	+	0.143486i	$0.0458313\pi$
$199$	8.73332	+	15.1266i	0.619089	+	1.07229i	−0.370563	+	0.928807i	$0.620835\pi$
$200$	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	0.919265	+	0.393640i	$0.128784\pi$
$211$	11.6284	+	20.1410i	0.800535	+	1.38657i	−0.118730	+	0.992927i	$0.537882\pi$
$212$	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	0.661855	+	0.749632i	$0.269769\pi$
$223$	14.6364	+	25.3510i	0.980128	+	1.69763i	0.318272	+	0.947999i	$0.396897\pi$
$224$		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	−0.981273	−	0.192622i	$-0.938301\pi$
$227$	−9.90551	−	17.1569i	−0.657452	−	1.13874i	0.323821	−	0.946118i	$-0.395032\pi$
$228$	9.27956	+	16.0727i	0.614554	+	1.06444i
$229$	0.664107	+	1.15027i	0.0438855	+	0.0760118i	0.887134	−	0.461512i	$-0.152693\pi$
$229$	0.664107	+	1.15027i	0.0438855	+	0.0760118i	−0.843248	+	0.537524i	$0.819360\pi$
$230$	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	0.840122	−	0.542398i	$-0.182483\pi$
$233$	−0.758171	−	1.31319i	−0.0496695	−	0.0860300i	−0.889791	+	0.456368i	$0.849150\pi$
$234$	−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	0.568054	−	0.822991i	$-0.307696\pi$
$241$	−6.65528	−	11.5273i	−0.428704	−	0.742538i	−0.996758	+	0.0804535i	$0.974363\pi$
$242$	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	0.498091	+	0.867125i	$0.334034\pi$
$251$	−7.95169	+	13.7727i	−0.501906	+	0.869327i	−0.999998	+	0.00220260i	$0.999299\pi$
$252$		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	0.100667	−	0.994920i	$-0.467902\pi$
$257$	14.6198	−	25.3223i	0.911960	−	1.57956i	0.811292	−	0.584641i	$-0.198764\pi$
$258$	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	0.709582	−	0.704623i	$-0.248884\pi$
$269$	−4.18937	−	7.25620i	−0.255430	−	0.442418i	−0.965012	+	0.262205i	$0.915550\pi$
$270$	−3.40035			−0.206938
$271$	6.07877	−	10.5287i	0.369259	−	0.639575i	−0.620191	−	0.784451i	$-0.712945\pi$
$271$	6.07877	−	10.5287i	0.369259	−	0.639575i	0.989450	+	0.144876i	$0.0462782\pi$
$272$	−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	0.668379	−	0.743821i	$-0.266989\pi$
$277$	−5.15907	−	8.93578i	−0.309979	−	0.536899i	−0.978357	+	0.206922i	$0.933655\pi$
$278$	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	−0.835960	−	0.548791i	$-0.815088\pi$
$293$	0.980596	−	1.69844i	0.0572870	−	0.0992241i	0.893247	+	0.449567i	$0.148422\pi$
$294$		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	−0.993910	−	0.110199i	$-0.964851\pi$
$311$	−7.08088	+	12.2644i	−0.401520	+	0.695453i	0.592390	+	0.805652i	$0.298185\pi$
$312$	8.77993	−	9.11462i	0.497066	−	0.516014i
$313$	13.3576	+	23.1361i	0.755017	+	1.30773i	0.945366	+	0.326011i	$0.105705\pi$
$313$	13.3576	+	23.1361i	0.755017	+	1.30773i	−0.190349	+	0.981716i	$0.560962\pi$
$314$	−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	−0.992520	−	0.122086i	$-0.961042\pi$
$317$	−10.7181	−	18.5643i	−0.601989	−	1.04268i	0.390530	−	0.920590i	$-0.372292\pi$
$318$	−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	0.996874	−	0.0790120i	$-0.0251765\pi$
$347$	8.01021	+	13.8741i	0.430010	+	0.744800i	−0.566863	+	0.823812i	$0.691843\pi$
$348$	−6.55186	+	11.3482i	−0.351217	+	0.608325i
$349$	−8.01922	−	13.8897i	−0.429259	−	0.743498i	0.567549	−	0.823340i	$-0.307892\pi$
$349$	−8.01922	−	13.8897i	−0.429259	−	0.743498i	−0.996808	+	0.0798418i	$0.974558\pi$
$350$		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	0.997689	+	0.0679519i	$0.0216465\pi$
$359$	10.5668	+	18.3022i	0.557692	+	0.965952i	−0.439996	+	0.898000i	$0.645020\pi$
$360$	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	0.972087	+	0.234621i	$0.0753848\pi$
$379$	13.4179	+	23.2405i	0.689231	+	1.19378i	−0.282856	+	0.959162i	$0.591282\pi$
$380$	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	−0.572882	−	0.819638i	$-0.694175\pi$
$389$	8.35048	−	14.4635i	0.423386	−	0.733327i	0.996268	+	0.0863114i	$0.0275080\pi$
$390$	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	−0.888139	−	0.459576i	$-0.848001\pi$
$401$	−0.922448	+	1.59773i	−0.0460649	+	0.0797867i	0.842074	+	0.539363i	$0.181335\pi$
$402$	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	0.986588	+	0.163232i	$0.0521920\pi$
$409$	12.8351	+	22.2311i	0.634657	+	1.09926i	−0.351931	+	0.936026i	$0.614475\pi$
$410$	−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	0.985221	+	0.171288i	$0.0547928\pi$
$419$	13.1199	+	22.7244i	0.640950	+	1.11016i	−0.344271	+	0.938870i	$0.611874\pi$
$420$		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	−0.367832	−	0.929892i	$-0.619900\pi$
$433$	12.9304	−	22.3961i	0.621394	−	1.07629i	0.989226	−	0.146394i	$-0.0467667\pi$
$434$		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	−0.0285691	−	0.999592i	$-0.509095\pi$
$439$	17.8385	−	30.8973i	0.851387	−	1.47465i	0.879956	−	0.475054i	$-0.157572\pi$
$440$	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	0.935920	−	0.352212i	$-0.114570\pi$
$443$	3.42940	+	5.93990i	0.162936	+	0.282213i	−0.772984	+	0.634425i	$0.781237\pi$
$444$	−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	−0.723898	−	0.689907i	$-0.757651\pi$
$449$	4.99075	−	8.64423i	0.235528	−	0.407946i	0.959426	+	0.281961i	$0.0909847\pi$
$450$	−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	−0.745000	−	0.667064i	$-0.767551\pi$
$457$	4.38656	−	7.59774i	0.205194	−	0.355407i	0.950195	+	0.311657i	$0.100884\pi$
$458$	−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	−0.934992	−	0.354669i	$-0.884593\pi$
$461$	−3.44272	+	5.96296i	−0.160343	+	0.277723i	0.774649	+	0.632392i	$0.217927\pi$
$462$		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	0.978845	+	0.204602i	$0.0655900\pi$
$467$	14.4056	+	24.9513i	0.666613	+	1.15461i	−0.312232	+	0.950006i	$0.601077\pi$
$468$	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	0.893703	−	0.448660i	$-0.148099\pi$
$487$	1.28658	+	2.22842i	0.0583004	+	0.100979i	−0.835402	+	0.549639i	$0.814765\pi$
$488$	−5.32469			−0.241037
$489$	−8.26233			−0.373635
$490$		0			0
$491$	−7.01897	−	12.1572i	−0.316762	−	0.548647i	0.663049	−	0.748576i	$-0.269262\pi$
$491$	−7.01897	−	12.1572i	−0.316762	−	0.548647i	−0.979810	+	0.199929i	$0.935929\pi$
$492$	−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	0.673857	−	0.738862i	$-0.264636\pi$
$499$	−6.76726	−	11.7212i	−0.302944	−	0.524715i	−0.976801	+	0.214147i	$0.931303\pi$
$500$	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	−0.758882	−	0.651228i	$-0.774254\pi$
$503$	4.13877	−	7.16856i	0.184539	−	0.319630i	0.943421	+	0.331597i	$0.107588\pi$
$504$		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	−0.864178	−	0.503187i	$-0.832161\pi$
$509$	0.0831091	−	0.143949i	0.00368375	−	0.00638044i	0.867861	+	0.496806i	$0.165494\pi$
$510$	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	−0.778255	−	0.627948i	$-0.783895\pi$
$521$	3.53090	−	6.11569i	0.154691	−	0.267933i	0.932947	+	0.360015i	$0.117228\pi$
$522$	−26.2711			−1.14985
$523$	−11.6956	+	20.2574i	−0.511414	+	0.885795i	0.488499	+	0.872565i	$0.337545\pi$
$523$	−11.6956	+	20.2574i	−0.511414	+	0.885795i	−0.999912	+	0.0132299i	$0.995789\pi$
$524$	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	−0.997000	−	0.0774030i	$-0.975337\pi$
$541$	−13.1540	−	22.7833i	−0.565533	−	0.979532i	0.431467	−	0.902129i	$-0.357996\pi$
$542$	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	−0.758741	−	0.651392i	$-0.774185\pi$
$563$	−22.3868	−	38.7751i	−0.943493	−	1.63418i	−0.184751	−	0.982785i	$-0.559148\pi$
$564$	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	0.0525679	−	0.998617i	$-0.483259\pi$
$569$	21.2563	−	36.8171i	0.891112	−	1.54345i	0.838544	−	0.544834i	$-0.183407\pi$
$570$	−3.93761			−0.164928
$571$	20.4324	−	35.3899i	0.855069	−	1.48102i	−0.0215128	−	0.999769i	$-0.506848\pi$
$571$	20.4324	−	35.3899i	0.855069	−	1.48102i	0.876581	−	0.481254i	$-0.159818\pi$
$572$	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	−0.546252	−	0.837621i	$-0.683946\pi$
$577$	10.8640	−	18.8170i	0.452275	−	0.783363i	0.998527	+	0.0542578i	$0.0172793\pi$
$578$	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	0.573518	−	0.819193i	$-0.305578\pi$
$587$	−10.2408	−	17.7376i	−0.422683	−	0.732108i	−0.996201	+	0.0870851i	$0.972245\pi$
$588$		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	0.918089	−	0.396374i	$-0.129732\pi$
$593$	2.81930	+	4.88318i	0.115775	+	0.200528i	−0.802314	+	0.596902i	$0.796398\pi$
$594$	−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	0.102058	+	0.994778i	$0.467457\pi$
$599$	−19.8359	+	34.3568i	−0.810474	+	1.40378i	−0.912533	+	0.409004i	$0.865876\pi$
$600$	8.57035	−	14.8443i	0.349883	−	0.606015i
$601$	−8.41334	−	14.5723i	−0.343187	−	0.594418i	0.641836	−	0.766842i	$-0.278173\pi$
$601$	−8.41334	−	14.5723i	−0.343187	−	0.594418i	−0.985023	+	0.172425i	$0.944840\pi$
$602$		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	−0.953004	−	0.302957i	$-0.902026\pi$
$617$	−5.31896	+	9.21271i	−0.214133	+	0.370890i	0.738871	+	0.673847i	$0.235359\pi$
$618$	32.2897			1.29888
$619$	22.7339	−	39.3762i	0.913751	−	1.58266i	0.105032	−	0.994469i	$-0.466505\pi$
$619$	22.7339	−	39.3762i	0.913751	−	1.58266i	0.808719	−	0.588195i	$-0.200161\pi$
$620$	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	0.405199	+	0.914229i	$0.367202\pi$
$631$	−14.7992	+	25.6329i	−0.589146	+	1.02043i	−0.994345	+	0.106202i	$0.966131\pi$
$632$	−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	0.889387	+	0.457155i	$0.151131\pi$
$641$	21.2823	+	36.8621i	0.840601	+	1.45596i	−0.0487858	+	0.998809i	$0.515535\pi$
$642$	−5.85082	−	10.1339i	−0.230914	−	0.399954i
$643$	−10.9980	+	19.0492i	−0.433721	+	0.751226i	−0.997190	−	0.0749106i	$-0.976133\pi$
$643$	−10.9980	+	19.0492i	−0.433721	+	0.751226i	0.563470	+	0.826137i	$0.309466\pi$
$644$		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	0.404870	−	0.914374i	$-0.367317\pi$
$653$	25.4084	−	44.0086i	0.994306	−	1.72219i	0.589436	−	0.807815i	$-0.299350\pi$
$654$	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	−0.685960	−	0.727639i	$-0.740618\pi$
$659$	7.37203	−	12.7687i	0.287173	−	0.497399i	0.973134	+	0.230240i	$0.0739511\pi$
$660$	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	0.590997	−	0.806674i	$-0.298735\pi$
$673$	−10.4574	−	18.1127i	−0.403102	−	0.698193i	−0.994099	+	0.108481i	$0.965401\pi$
$674$	−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	0.954979	+	0.296673i	$0.0958771\pi$
$677$	19.1089	+	33.0976i	0.734416	+	1.27205i	−0.220563	+	0.975373i	$0.570790\pi$
$678$	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	0.998735	−	0.0502792i	$-0.0160111\pi$
$683$	11.9126	+	20.6333i	0.455825	+	0.789511i	−0.542911	+	0.839790i	$0.682678\pi$
$684$	−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	−0.624545	−	0.780989i	$-0.714715\pi$
$691$	9.57063	−	16.5768i	0.364084	−	0.630612i	0.988629	+	0.150377i	$0.0480488\pi$
$692$	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	0.831926	−	0.554887i	$-0.187239\pi$
$733$	−1.74853	−	3.02855i	−0.0645836	−	0.111862i	−0.896509	+	0.443025i	$0.853905\pi$
$734$	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	−0.985317	−	0.170734i	$-0.945386\pi$
$743$	−17.4593	−	30.2404i	−0.640519	−	1.10941i	0.344798	−	0.938677i	$-0.387947\pi$
$744$	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	−0.999963	−	0.00855684i	$-0.997276\pi$
$751$	−13.4986	+	23.3803i	−0.492571	+	0.853158i	0.507392	+	0.861715i	$0.330610\pi$
$752$	−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	0.732742	+	0.680507i	$0.238240\pi$
$757$	26.2950	+	45.5442i	0.955707	+	1.65533i	0.222965	+	0.974826i	$0.428426\pi$
$758$	−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	0.714497	−	0.699639i	$-0.246656\pi$
$769$	−6.89545	−	11.9433i	−0.248656	−	0.430685i	−0.963153	+	0.268953i	$0.913322\pi$
$770$		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	−0.816913	−	0.576760i	$-0.804317\pi$
$773$	−25.2435	−	43.7230i	−0.907946	−	1.57261i	−0.0910326	−	0.995848i	$-0.529017\pi$
$774$	−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	0.752823	−	0.658223i	$-0.228691\pi$
$787$	−5.43189	−	9.40831i	−0.193626	−	0.335370i	−0.946449	+	0.322853i	$0.895358\pi$
$788$	−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	−0.787363	−	0.616489i	$-0.788554\pi$
$797$	3.95840	−	6.85616i	0.140214	−	0.242858i	0.927577	+	0.373632i	$0.121888\pi$
$798$		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	−0.978265	−	0.207358i	$-0.933513\pi$
$821$	−8.86971	+	15.3628i	−0.309555	+	0.536165i	0.668710	+	0.743523i	$0.266847\pi$
$822$	8.93824			0.311757
$823$	4.34100	+	7.51883i	0.151318	+	0.262090i	0.931712	−	0.363198i	$-0.118315\pi$
$823$	4.34100	+	7.51883i	0.151318	+	0.262090i	−0.780394	+	0.625288i	$0.784982\pi$
$824$	−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	−0.956361	−	0.292186i	$-0.905617\pi$
$839$	−6.52129	+	11.2952i	−0.225140	+	0.389954i	0.731222	+	0.682140i	$0.238951\pi$
$840$		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	−0.996029	−	0.0890333i	$-0.971622\pi$
$857$	−12.3219	+	21.3422i	−0.420909	+	0.729036i	0.575119	+	0.818069i	$0.304956\pi$
$858$	−4.44933	−	15.4439i	−0.151898	−	0.527245i
$859$	−1.28571	−	2.22691i	−0.0438677	−	0.0759811i	0.843258	−	0.537509i	$-0.180635\pi$
$859$	−1.28571	−	2.22691i	−0.0438677	−	0.0759811i	−0.887126	+	0.461528i	$0.847301\pi$
$860$	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	−0.977052	−	0.213002i	$-0.931676\pi$
$863$	−19.7704	−	34.2433i	−0.672991	−	1.16565i	0.304061	−	0.952653i	$-0.401657\pi$
$864$	−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	0.905147	−	0.425099i	$-0.139761\pi$
$881$	2.50592	+	4.34038i	0.0844266	+	0.146231i	−0.820720	+	0.571330i	$0.806427\pi$
$882$		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	−0.916946	−	0.399011i	$-0.869353\pi$
$887$	−3.36301	+	5.82491i	−0.112919	+	0.195581i	0.804027	+	0.594593i	$0.202687\pi$
$888$	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	−0.501415	−	0.865207i	$-0.667187\pi$
$941$	15.2944	−	26.4907i	0.498583	−	0.863572i	0.999999	+	0.00163503i	$0.000520447\pi$
$942$	−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	−0.795840	−	0.605507i	$-0.792970\pi$
$947$	3.89174	−	6.74069i	0.126465	−	0.219043i	0.922304	+	0.386464i	$0.126304\pi$
$948$	−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	−0.366588	−	0.930383i	$-0.619474\pi$
$953$	19.2152	−	33.2817i	0.622442	−	1.07810i	0.989030	−	0.147717i	$-0.0471926\pi$
$954$	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	0.402138	+	0.915579i	$0.368267\pi$
$983$	−18.5560	+	32.1400i	−0.591846	+	1.02511i	−0.993984	+	0.109528i	$0.965066\pi$
$984$	−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	0.968189	+	0.250219i	$0.0805028\pi$
$997$	22.1277	+	38.3263i	0.700791	+	1.21381i	−0.267398	+	0.963586i	$0.586164\pi$
$998$	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.263.2		16
7.2	even	3		637.2.h.m.471.7		16
7.3	odd	6		637.2.f.l.393.2	yes	16
7.4	even	3		637.2.f.l.393.1	yes	16
7.5	odd	6		637.2.h.m.471.8		16
7.6	odd	2	inner	637.2.g.m.263.1		16
13.9	even	3		637.2.h.m.165.7		16
91.3	odd	6		8281.2.a.ci.1.7		8
91.9	even	3	inner	637.2.g.m.373.2		16
91.10	odd	6		8281.2.a.cl.1.1		8
91.48	odd	6		637.2.h.m.165.8		16
91.61	odd	6	inner	637.2.g.m.373.1		16
91.74	even	3		637.2.f.l.295.1	✓	16
91.81	even	3		8281.2.a.ci.1.8		8
91.87	odd	6		637.2.f.l.295.2	yes	16
91.88	even	6		8281.2.a.cl.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.1	✓	16	91.74	even	3
637.2.f.l.295.2	yes	16	91.87	odd	6
637.2.f.l.393.1	yes	16	7.4	even	3
637.2.f.l.393.2	yes	16	7.3	odd	6
637.2.g.m.263.1		16	7.6	odd	2	inner
637.2.g.m.263.2		16	1.1	even	1	trivial
637.2.g.m.373.1		16	91.61	odd	6	inner
637.2.g.m.373.2		16	91.9	even	3	inner
637.2.h.m.165.7		16	13.9	even	3
637.2.h.m.165.8		16	91.48	odd	6
637.2.h.m.471.7		16	7.2	even	3
637.2.h.m.471.8		16	7.5	odd	6
8281.2.a.ci.1.7		8	91.3	odd	6
8281.2.a.ci.1.8		8	91.81	even	3
8281.2.a.cl.1.1		8	91.10	odd	6
8281.2.a.cl.1.2		8	91.88	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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