LMFDB - Embedded newform 637.2.f.l.393.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	16.0.468066644398978174550016.2
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			393.1
Root			$0.756863 - 1.31093i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.l.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21605 - 2.10626i) q^{2} +(-0.376796 - 0.652630i) q^{3} +(-1.95755 + 3.39058i) q^{4} +0.341537 q^{5} +(-0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +(-0.415326 - 0.719366i) q^{10} +(1.21605 + 2.10626i) q^{11} +2.95039 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} -5.91511 q^{18} +(3.14519 - 5.44764i) q^{19} +(-0.668577 + 1.15801i) q^{20} +(2.95755 - 5.12263i) q^{22} +(1.84474 + 3.19518i) q^{23} +(-1.75501 - 3.03977i) q^{24} -4.88335 q^{25} +(-8.51122 - 2.11081i) q^{26} -4.09359 q^{27} +(-2.22068 - 3.84632i) q^{29} +(-0.312986 + 0.542108i) q^{30} -1.97532 q^{31} +(0.404180 - 0.700061i) q^{32} +(0.916405 - 1.58726i) q^{33} -4.73830 q^{34} +(4.76096 + 8.24623i) q^{36} +(4.81433 + 8.33867i) q^{37} -15.2988 q^{38} +(-2.63722 - 0.654039i) q^{39} +1.59079 q^{40} +(-6.26793 - 10.8564i) q^{41} +(4.20368 - 7.28099i) q^{43} -9.52192 q^{44} +(0.415326 - 0.719366i) q^{45} +(4.48659 - 7.77100i) q^{46} -9.00530 q^{47} +(-1.31797 + 2.28279i) q^{48} +(5.93840 + 10.2856i) q^{50} -1.46817 q^{51} +(3.90786 + 13.5644i) q^{52} +1.49226 q^{53} +(4.97800 + 8.62216i) q^{54} +(0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 + 9.35464i) q^{58} +(-0.313495 + 0.542990i) q^{59} +1.00767 q^{60} +(0.571597 - 0.990035i) q^{61} +(2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.854317 - 0.886883i) q^{65} -4.45758 q^{66} +(2.79599 + 4.84280i) q^{67} +(3.81377 + 6.60564i) q^{68} +(1.39018 - 2.40786i) q^{69} +(-4.74859 + 8.22481i) q^{71} +(5.66402 - 9.81038i) q^{72} +11.9187 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} +4.47167 q^{79} +(-0.597321 - 1.03459i) q^{80} +(-2.10570 - 3.64718i) q^{81} +(-15.2442 + 26.4038i) q^{82} +1.41231 q^{83} +(0.332697 - 0.576248i) q^{85} -20.4475 q^{86} +(-1.67348 + 2.89856i) q^{87} +(5.66402 + 9.81038i) q^{88} +(-6.22219 - 10.7771i) q^{89} -2.02023 q^{90} -14.4447 q^{92} +(0.744294 + 1.28915i) q^{93} +(10.9509 + 18.9675i) q^{94} +(1.07420 - 1.86057i) q^{95} -0.609174 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} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−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	$-0.496126\pi$
$3$	−0.376796	−	0.652630i	−0.217543	−	0.376796i	0.736513	−	0.676423i	$-0.236471\pi$
$3$	−0.376796	−	0.652630i	−0.217543	−	0.376796i	−0.954056	+	0.299627i	$0.903138\pi$
$4$	−1.95755	+	3.39058i	−0.978776	+	1.69529i
$5$	0.341537			0.152740			0.0763700	−	0.997080i	$-0.475667\pi$
$5$	0.341537			0.152740			0.0763700	+	0.997080i	$0.475667\pi$
$6$	−0.916405	+	1.58726i	−0.374121	+	0.647996i
$7$		0			0
$7$		0			0
$8$	4.65773			1.64675
$9$	1.21605	−	2.10626i	0.405350	−	0.702086i
$10$	−0.415326	−	0.719366i	−0.131338	−	0.227483i
$11$	1.21605	+	2.10626i	0.366653	+	0.635061i	0.989040	−	0.147648i	$-0.0471704\pi$
$11$	1.21605	+	2.10626i	0.366653	+	0.635061i	−0.622387	+	0.782710i	$0.713837\pi$
$12$	2.95039			0.851705
$13$	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	$0.0907456\pi$
$18$	−5.91511			−1.39420
$19$	3.14519	−	5.44764i	0.721557	−	1.24977i	−0.238819	−	0.971064i	$-0.576760\pi$
$19$	3.14519	−	5.44764i	0.721557	−	1.24977i	0.960376	−	0.278709i	$-0.0899065\pi$
$20$	−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	$0.707654\pi$
$24$	−1.75501	−	3.03977i	−0.358240	−	0.620491i
$25$	−4.88335			−0.976670
$26$	−8.51122	−	2.11081i	−1.66919	−	0.413963i
$27$	−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	$0.968632\pi$
$30$	−0.312986	+	0.542108i	−0.0571432	+	0.0989750i
$31$	−1.97532			−0.354778			−0.177389	−	0.984141i	$-0.556765\pi$
$31$	−1.97532			−0.354778			−0.177389	+	0.984141i	$0.556765\pi$
$32$	0.404180	−	0.700061i	0.0714496	−	0.123754i
$33$	0.916405	−	1.58726i	0.159526	−	0.276307i
$34$	−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	$0.542649\pi$
$38$	−15.2988			−2.48180
$39$	−2.63722	−	0.654039i	−0.422294	−	0.104730i
$40$	1.59079			0.251525
$41$	−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	$-0.0548365\pi$
$44$	−9.52192			−1.43548
$45$	0.415326	−	0.719366i	0.0619131	−	0.107237i
$46$	4.48659	−	7.77100i	0.661511	−	1.14577i
$47$	−9.00530			−1.31356			−0.656779	−	0.754083i	$-0.728081\pi$
$47$	−9.00530			−1.31356			−0.656779	+	0.754083i	$0.728081\pi$
$48$	−1.31797	+	2.28279i	−0.190233	+	0.329493i
$49$		0			0
$50$	5.93840	+	10.2856i	0.839816	+	1.45460i
$51$	−1.46817			−0.205585
$52$	3.90786	+	13.5644i	0.541923	+	1.88105i
$53$	1.49226			0.204977			0.102489	−	0.994734i	$-0.467319\pi$
$53$	1.49226			0.204977			0.102489	+	0.994734i	$0.467319\pi$
$54$	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
$58$	−5.40090	+	9.35464i	−0.709173	+	1.22832i
$59$	−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	$0.179662\pi$
$60$	1.00767			0.130089
$61$	0.571597	−	0.990035i	0.0731855	−	0.126761i	−0.827110	−	0.562040i	$-0.810017\pi$
$61$	0.571597	−	0.990035i	0.0731855	−	0.126761i	0.900296	+	0.435279i	$0.143350\pi$
$62$	2.40209	+	4.16054i	0.305066	+	0.528389i
$63$		0			0
$64$	−8.96169			−1.12021
$65$	0.854317	−	0.886883i	0.105965	−	0.110004i
$66$	−4.45758			−0.548690
$67$	2.79599	+	4.84280i	0.341585	+	0.591642i	0.984727	−	0.174104i	$-0.0557030\pi$
$67$	2.79599	+	4.84280i	0.341585	+	0.591642i	−0.643142	+	0.765747i	$0.722370\pi$
$68$	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	$0.976100\pi$
$72$	5.66402	−	9.81038i	0.667512	−	1.15616i
$73$	11.9187			1.39498			0.697488	−	0.716597i	$-0.254301\pi$
$73$	11.9187			1.39498			0.697488	+	0.716597i	$0.254301\pi$
$74$	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
$79$	4.47167			0.503102			0.251551	−	0.967844i	$-0.419059\pi$
$79$	4.47167			0.503102			0.251551	+	0.967844i	$0.419059\pi$
$80$	−0.597321	−	1.03459i	−0.0667825	−	0.115671i
$81$	−2.10570	−	3.64718i	−0.233967	−	0.405242i
$82$	−15.2442	+	26.4038i	−1.68344	+	2.91581i
$83$	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
$86$	−20.4475			−2.20491
$87$	−1.67348	+	2.89856i	−0.179416	+	0.310758i
$88$	5.66402	+	9.81038i	0.603787	+	1.04579i
$89$	−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
$94$	10.9509	+	18.9675i	1.12950	+	1.95635i
$95$	1.07420	−	1.86057i	0.110211	−	0.190890i
$96$	−0.609174			−0.0621736
$97$	−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
$100$	9.55942	−	16.5574i	0.955942	−	1.65574i
$101$	−7.52683	−	13.0369i	−0.748948	−	1.29722i	−0.948328	−	0.317293i	$-0.897226\pi$
$101$	−7.52683	−	13.0369i	−0.748948	−	1.29722i	0.199380	−	0.979922i	$-0.436107\pi$
$102$	1.78537	+	3.09235i	0.176778	+	0.306189i
$103$	17.6176			1.73591			0.867957	−	0.496639i	$-0.165433\pi$
$103$	17.6176			1.73591			0.867957	+	0.496639i	$0.165433\pi$
$104$	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
$109$	−8.17472			−0.782996			−0.391498	−	0.920179i	$-0.628043\pi$
$109$	−8.17472			−0.782996			−0.391498	+	0.920179i	$0.628043\pi$
$110$	1.01011	−	1.74957i	0.0963106	−	0.166815i
$111$	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
$115$	0.630047	+	1.09127i	0.0587522	+	0.101762i
$116$	17.3884			1.61447
$117$	−2.42760	−	8.42634i	−0.224432	−	0.779015i
$118$	1.52490			0.140379
$119$		0			0
$120$	−0.599402	−	1.03819i	−0.0547177	−	0.0947738i
$121$	2.54245	−	4.40365i	0.231132	−	0.400332i
$122$	−2.78036			−0.251722
$123$	−4.72347	+	8.18128i	−0.425901	+	0.737681i
$124$	3.86680	−	6.69749i	0.347249	−	0.601452i
$125$	−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
$129$	−6.33572			−0.557829
$130$	−2.90690	−	0.720919i	−0.254952	−	0.0632287i
$131$	−0.192483			−0.0168173			−0.00840867	−	0.999965i	$-0.502677\pi$
$131$	−0.192483			−0.0168173			−0.00840867	+	0.999965i	$0.502677\pi$
$132$	3.58782	+	6.21429i	0.312280	+	0.540885i
$133$		0			0
$134$	6.80013	−	11.7782i	0.587442	−	1.01748i
$135$	−1.39811			−0.120330
$136$	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	$0.233468\pi$
$138$	−6.76212			−0.575629
$139$	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
$142$	23.0981			1.93835
$143$	8.51122	+	2.11081i	0.711744	+	0.176514i
$144$	−8.50709			−0.708924
$145$	−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
$149$	−7.95435	+	13.7773i	−0.651646	+	1.12868i	0.331078	+	0.943603i	$0.392588\pi$
$149$	−7.95435	+	13.7773i	−0.651646	+	1.12868i	−0.982723	+	0.185080i	$0.940746\pi$
$150$	4.47513	−	7.75115i	0.365393	−	0.632879i
$151$	−10.5904			−0.861831			−0.430916	−	0.902392i	$-0.641809\pi$
$151$	−10.5904			−0.861831			−0.430916	+	0.902392i	$0.641809\pi$
$152$	14.6494	−	25.3736i	1.18823	−	2.05807i
$153$	−2.36915	−	4.10349i	−0.191534	−	0.331747i
$154$		0			0
$155$	−0.674646			−0.0541889
$156$	7.38007	−	7.66140i	0.590879	−	0.613403i
$157$	9.12388			0.728165			0.364082	−	0.931367i	$-0.381383\pi$
$157$	9.12388			0.728165			0.364082	+	0.931367i	$0.381383\pi$
$158$	−5.43777	−	9.41849i	−0.432606	−	0.749295i
$159$	−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
$163$	5.48196	−	9.49504i	0.429380	−	0.743709i	−0.567438	−	0.823416i	$-0.692065\pi$
$163$	5.48196	−	9.49504i	0.429380	−	0.743709i	0.996818	+	0.0797075i	$0.0253986\pi$
$164$	49.0792			3.83245
$165$	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
$170$	−1.61830			−0.124118
$171$	−7.64942	−	13.2492i	−0.584966	−	1.01319i
$172$	16.4579	+	28.5058i	1.25490	+	2.17355i
$173$	4.09918	−	7.09998i	0.311655	−	0.539802i	−0.667066	−	0.744999i	$-0.732450\pi$
$173$	4.09918	−	7.09998i	0.311655	−	0.539802i	0.978721	+	0.205197i	$0.0657835\pi$
$174$	8.14015			0.617104
$175$		0			0
$176$	4.25355	−	7.36736i	0.320623	−	0.555335i
$177$	0.472495			0.0355149
$178$	−15.1330	+	26.2111i	−1.13426	+	1.96460i
$179$	7.77684	+	13.4699i	0.581268	+	1.00679i	0.995329	+	0.0965370i	$0.0307766\pi$
$179$	7.77684	+	13.4699i	0.581268	+	1.00679i	−0.414061	+	0.910249i	$0.635890\pi$
$180$	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
$185$	1.64427	+	2.84797i	0.120889	+	0.209387i
$186$	1.81020	−	3.13535i	0.132730	−	0.229895i
$187$	4.73830			0.346499
$188$	17.6283	−	30.5332i	1.28568	−	2.22686i
$189$		0			0
$190$	−5.22512			−0.379070
$191$	9.37296	−	16.2344i	0.678204	−	1.17468i	−0.297318	−	0.954779i	$-0.596092\pi$
$191$	9.37296	−	16.2344i	0.678204	−	1.17468i	0.975521	−	0.219905i	$-0.0705746\pi$
$192$	3.37673	+	5.84867i	0.243694	+	0.422091i
$193$	4.08655	+	7.07811i	0.294156	+	0.509493i	0.974788	−	0.223132i	$-0.0716281\pi$
$193$	4.08655	+	7.07811i	0.294156	+	0.509493i	−0.680632	+	0.732625i	$0.738295\pi$
$194$	24.9947			1.79451
$195$	−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	−0.370563	−	0.928807i	$-0.620835\pi$
$199$	8.73332	−	15.1266i	0.619089	−	1.07229i	0.989652	−	0.143486i	$-0.0458313\pi$
$200$	−22.7453			−1.60834
$201$	2.10704	−	3.64950i	0.148619	−	0.257416i
$202$	−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
$206$	−21.4239	−	37.1073i	−1.49267	−	2.58539i
$207$	8.97318			0.623679
$208$	−12.2408	−	3.03576i	−0.848748	−	0.210492i
$209$	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	$0.537882\pi$
$212$	−2.92117	+	5.05962i	−0.200627	+	0.347496i
$213$	7.15701			0.490390
$214$	−7.76391	+	13.4475i	−0.530730	+	0.919252i
$215$	1.43571	−	2.48673i	0.0979148	−	0.169593i
$216$	−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
$220$	−3.25209			−0.219256
$221$	−1.94463	−	6.74992i	−0.130810	−	0.454049i
$222$	−17.6475			−1.18442
$223$	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
$226$	−23.4008			−1.55660
$227$	−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
$229$	−1.32821			−0.0877709			−0.0438855	−	0.999037i	$-0.513974\pi$
$229$	−1.32821			−0.0877709			−0.0438855	+	0.999037i	$0.513974\pi$
$230$	1.53234	−	2.65408i	0.101039	−	0.175005i
$231$		0			0
$232$	−10.3433	−	17.9151i	−0.679071	−	1.17618i
$233$	1.51634			0.0993389			0.0496695	−	0.998766i	$-0.484183\pi$
$233$	1.51634			0.0993389			0.0496695	+	0.998766i	$0.484183\pi$
$234$	−14.7960	+	15.3600i	−0.967243	+	1.00411i
$235$	−3.07564			−0.200633
$236$	−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	$0.240899\pi$
$240$	−0.450136	+	0.779659i	−0.0290562	+	0.0503268i
$241$	−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	$0.307696\pi$
$242$	−12.3670			−0.794979
$243$	−7.72722	+	13.3839i	−0.495701	+	0.858580i
$244$	2.23786	+	3.87609i	0.143265	+	0.248141i
$245$		0			0
$246$	22.9759			1.46489
$247$	−6.27875	−	21.7939i	−0.399507	−	1.38671i
$248$	−9.20051			−0.584233
$249$	−0.532152	−	0.921714i	−0.0337238	−	0.0584113i
$250$	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
$254$	−10.9685	+	18.9980i	−0.688224	+	1.19204i
$255$	−0.501436			−0.0314011
$256$	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
$261$	−10.8018			−0.668615
$262$	0.234069	+	0.405420i	0.0144608	+	0.0250469i
$263$	0.852177	+	1.47601i	0.0525475	+	0.0910149i	0.891103	−	0.453802i	$-0.149933\pi$
$263$	0.852177	+	1.47601i	0.0525475	+	0.0910149i	−0.838555	+	0.544817i	$0.816599\pi$
$264$	4.26836	−	7.39302i	0.262700	−	0.455009i
$265$	0.509661			0.0313083
$266$		0			0
$267$	−4.68899	+	8.12157i	−0.286962	+	0.497032i
$268$	−21.8932			−1.33734
$269$	−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	$0.248884\pi$
$270$	1.70017	+	2.94479i	0.103469	+	0.179214i
$271$	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
$276$	5.44270	+	9.42704i	0.327612	+	0.567441i
$277$	−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	$0.266989\pi$
$278$	−26.9331			−1.61534
$279$	−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	$0.524679\pi$
$282$	8.25250	−	14.2938i	0.491429	−	0.851181i
$283$	−2.30184	−	3.98690i	−0.136830	−	0.236997i	0.789465	−	0.613796i	$-0.210358\pi$
$283$	−2.30184	−	3.98690i	−0.136830	−	0.236997i	−0.926295	+	0.376799i	$0.877025\pi$
$284$	−18.5912	−	32.2010i	−1.10319	−	1.91078i
$285$	−1.61902			−0.0959023
$286$	−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
$291$	7.74466			0.454000
$292$	−23.3314	+	40.4112i	−1.36537	+	2.36489i
$293$	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
$297$	−4.97800	−	8.62216i	−0.288853	−	0.500308i
$298$	38.6915			2.24134
$299$	12.9115	+	3.20208i	0.746689	+	0.185181i
$300$	−14.4078			−0.831835
$301$		0			0
$302$	12.8784	+	22.3060i	0.741069	+	1.28357i
$303$	−5.67216	+	9.82447i	−0.325857	+	0.564401i
$304$	−22.0028			−1.26194
$305$	0.195222	−	0.338134i	0.0111784	−	0.0193615i
$306$	−5.76200	+	9.98008i	−0.329392	+	0.570523i
$307$	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
$311$	14.1618			0.803040			0.401520	−	0.915850i	$-0.368482\pi$
$311$	14.1618			0.803040			0.401520	+	0.915850i	$0.368482\pi$
$312$	−12.2835	−	3.04633i	−0.695414	−	0.172465i
$313$	−26.7152			−1.51003			−0.755017	−	0.655705i	$-0.772371\pi$
$313$	−26.7152			−1.51003			−0.755017	+	0.655705i	$0.772371\pi$
$314$	−11.0951	−	19.2173i	−0.626132	−	1.08449i
$315$		0			0
$316$	−8.75352	+	15.1615i	−0.492424	+	0.852904i
$317$	21.4362			1.20398			0.601989	−	0.798504i	$-0.294375\pi$
$317$	21.4362			1.20398			0.601989	+	0.798504i	$0.294375\pi$
$318$	−1.36751	+	2.36860i	−0.0766863	+	0.132825i
$319$	5.40090	−	9.35464i	0.302392	−	0.523759i
$320$	−3.06075			−0.171101
$321$	−2.40567	+	4.16674i	−0.134271	+	0.232565i
$322$		0			0
$323$	−6.12757	−	10.6133i	−0.340947	−	0.590538i
$324$	16.4881			0.916005
$325$	−12.2152	+	12.6808i	−0.677575	+	0.703404i
$326$	−26.6654			−1.47686
$327$	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
$331$	−5.30692	+	9.19185i	−0.291695	+	0.505230i	−0.974211	−	0.225641i	$-0.927552\pi$
$331$	−5.30692	+	9.19185i	−0.291695	+	0.505230i	0.682516	+	0.730871i	$0.260886\pi$
$332$	−2.76467	+	4.78854i	−0.151731	+	0.262805i
$333$	23.4179			1.28329
$334$	22.2266	−	38.4975i	1.21618	−	2.10649i
$335$	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	$0.441093\pi$
$338$	−26.7711	+	16.8215i	−1.45615	+	0.914968i
$339$	−7.25080			−0.393809
$340$	1.30254	+	2.25607i	0.0706404	+	0.122353i
$341$	−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
$345$	0.474798	−	0.822375i	0.0255623	−	0.0442752i
$346$	−19.9392			−1.07194
$347$	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	0.567549	−	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
$352$	1.96601			0.104789
$353$	−1.92156	−	3.32823i	−0.102274	−	0.177144i	0.810347	−	0.585950i	$-0.199279\pi$
$353$	−1.92156	−	3.32823i	−0.102274	−	0.177144i	−0.912621	+	0.408806i	$0.865945\pi$
$354$	−0.574578	−	0.995198i	−0.0305385	−	0.0528942i
$355$	−1.62182	+	2.80908i	−0.0860773	+	0.149090i
$356$	48.7210			2.58221
$357$		0			0
$358$	18.9140	−	32.7601i	0.999638	−	1.73142i
$359$	−21.1335			−1.11538			−0.557692	−	0.830048i	$-0.688313\pi$
$359$	−21.1335			−1.11538			−0.557692	+	0.830048i	$0.688313\pi$
$360$	1.93447	−	3.35061i	0.101956	−	0.176593i
$361$	−10.2845	−	17.8133i	−0.541289	−	0.937540i
$362$	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
$367$	7.36961	+	12.7645i	0.384690	+	0.666303i	0.991726	−	0.128371i	$-0.0409749\pi$
$367$	7.36961	+	12.7645i	0.384690	+	0.666303i	−0.607036	+	0.794674i	$0.707642\pi$
$368$	6.45260	−	11.1762i	0.336365	−	0.582601i
$369$	−30.4885			−1.58717
$370$	3.99904	−	6.92653i	0.207900	−	0.360093i
$371$		0			0
$372$	−5.82798			−0.302166
$373$	−6.46330	+	11.1948i	−0.334657	+	0.579643i	−0.983419	−	0.181349i	$-0.941954\pi$
$373$	−6.46330	+	11.1948i	−0.334657	+	0.579643i	0.648762	+	0.760991i	$0.275287\pi$
$374$	−5.76200	−	9.98008i	−0.297946	−	0.516058i
$375$	1.27189	+	2.20297i	0.0656800	+	0.113761i
$376$	−41.9442			−2.16311
$377$	−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
$382$	−45.5919			−2.33269
$383$	1.45391	−	2.51825i	0.0742914	−	0.128677i	−0.826487	−	0.562957i	$-0.809664\pi$
$383$	1.45391	−	2.51825i	0.0742914	−	0.128677i	0.900778	+	0.434280i	$0.142997\pi$
$384$	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
$388$	−20.1178	−	34.8450i	−1.02132	−	1.76899i
$389$	−16.7010			−0.846773			−0.423386	−	0.905949i	$-0.639159\pi$
$389$	−16.7010			−0.846773			−0.423386	+	0.905949i	$0.639159\pi$
$390$	0.624814	+	2.16877i	0.0316387	+	0.109820i
$391$	7.18797			0.363511
$392$		0			0
$393$	0.0725269	+	0.125620i	0.00365850	+	0.00633671i
$394$	−10.6041	+	18.3668i	−0.534227	+	0.925308i
$395$	1.52724			0.0768438
$396$	−11.5791	+	20.0556i	−0.581873	+	1.00783i
$397$	12.0492	−	20.8699i	0.604733	−	1.04743i	−0.387360	−	0.921928i	$-0.626613\pi$
$397$	12.0492	−	20.8699i	0.604733	−	1.04743i	0.992094	−	0.125500i	$-0.0400536\pi$
$398$	−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	$0.848001\pi$
$402$	−10.2491			−0.511176
$403$	−4.94105	+	5.12940i	−0.246131	+	0.255514i
$404$	58.9367			2.93221
$405$	−0.719175	−	1.24565i	−0.0357361	−	0.0618967i
$406$		0			0
$407$	−11.7089	+	20.2805i	−0.580390	+	1.00527i
$408$	−6.83835			−0.338549
$409$	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
$411$	3.67512			0.181280
$412$	−34.4874	+	59.7339i	−1.69907	+	2.94288i
$413$		0			0
$414$	−10.9118	−	18.8998i	−0.536287	−	0.928876i
$415$	0.482355			0.0236779
$416$	−0.806865	−	2.80067i	−0.0395598	−	0.137314i
$417$	−8.34529			−0.408671
$418$	−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	$0.304360\pi$
$422$	28.2815	−	48.9850i	1.37672	−	2.38455i
$423$	−10.9509	+	18.9675i	−0.532450	+	0.922231i
$424$	6.95053			0.337548
$425$	−4.75696	+	8.23929i	−0.230746	+	0.399664i
$426$	−8.70327	−	15.0745i	−0.421675	−	0.730362i
$427$		0			0
$428$	24.9961			1.20823
$429$	−1.82942	−	6.35002i	−0.0883252	−	0.306582i
$430$	−6.98359			−0.336779
$431$	11.5088	+	19.9339i	0.554361	+	0.960182i	0.997953	+	0.0639528i	$0.0203707\pi$
$431$	11.5088	+	19.9339i	0.554361	+	0.960182i	−0.443592	+	0.896229i	$0.646296\pi$
$432$	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
$436$	16.0024	−	27.7170i	0.766378	−	1.32741i
$437$	23.2082			1.11020
$438$	−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
$443$	−6.85881			−0.325872			−0.162936	−	0.986637i	$-0.552096\pi$
$443$	−6.85881			−0.325872			−0.162936	+	0.986637i	$0.552096\pi$
$444$	14.2042	+	24.6024i	0.674100	+	1.16758i
$445$	−2.12511	−	3.68079i	−0.100740	−	0.174486i
$446$	35.5972	−	61.6562i	1.68558	−	2.91951i
$447$	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	$0.0909847\pi$
$450$	28.8855			1.36168
$451$	15.2442	−	26.4038i	0.717823	−	1.24331i
$452$	18.8349	+	32.6230i	0.885919	+	1.53446i
$453$	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	$0.767551\pi$
$458$	1.61518	+	2.79757i	0.0754722	+	0.130722i
$459$	−3.98763	+	6.90678i	−0.186127	+	0.322381i
$460$	−4.93340			−0.230021
$461$	−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	$0.605100\pi$
$464$	−7.76757	+	13.4538i	−0.360600	+	0.624578i
$465$	0.254204	+	0.440294i	0.0117884	+	0.0204181i
$466$	−1.84395	−	3.19381i	−0.0854192	−	0.147950i
$467$	−28.8113			−1.33323			−0.666613	−	0.745404i	$-0.732257\pi$
$467$	−28.8113			−1.33323			−0.666613	+	0.745404i	$0.732257\pi$
$468$	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
$473$	20.4475			0.940179
$474$	−4.09786	+	7.09770i	−0.188221	+	0.326008i
$475$	−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
$479$	12.2936	+	21.2931i	0.561707	+	0.972906i	0.997348	+	0.0727849i	$0.0231887\pi$
$479$	12.2936	+	21.2931i	0.561707	+	0.972906i	−0.435640	+	0.900121i	$0.643478\pi$
$480$	−0.208056			−0.00949639
$481$	33.6959	+	8.35667i	1.53640	+	0.381031i
$482$	32.3726			1.47453
$483$		0			0
$484$	9.95395	+	17.2407i	0.452452	+	0.783670i
$485$	−1.75499	+	3.03973i	−0.0796899	+	0.138027i
$486$	37.5867			1.70497
$487$	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	$0.148099\pi$
$488$	2.66234	−	4.61131i	0.120519	−	0.208744i
$489$	−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
$493$	−8.65279			−0.389702
$494$	−38.2683	+	39.7271i	−1.72177	+	1.78741i
$495$	2.02023			0.0908025
$496$	3.45468	+	5.98368i	0.155120	+	0.268675i
$497$		0			0
$498$	−1.29425	+	2.24170i	−0.0579965	+	0.100453i
$499$	13.5345			0.605888			0.302944	−	0.953008i	$-0.402030\pi$
$499$	13.5345			0.605888			0.302944	+	0.953008i	$0.402030\pi$
$500$	6.60778	−	11.4450i	0.295509	−	0.511836i
$501$	6.88696	−	11.9286i	0.307687	−	0.532929i
$502$	38.6786			1.72631
$503$	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
$506$	21.8237			0.970180
$507$	−8.29509	+	5.21218i	−0.368398	+	0.231481i
$508$	35.3133			1.56678
$509$	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
$513$	−12.8751	+	22.3004i	−0.568451	+	0.984585i
$514$	35.5569	−	61.5863i	1.56835	−	2.71646i
$515$	6.01707			0.265144
$516$	12.4025	−	21.4818i	0.545990	−	0.945683i
$517$	−10.9509	−	18.9675i	−0.481619	−	0.834189i
$518$		0			0
$519$	−6.17821			−0.271193
$520$	3.97917	−	4.13086i	0.174498	−	0.181150i
$521$	−7.06180			−0.309383			−0.154691	−	0.987963i	$-0.549438\pi$
$521$	−7.06180			−0.309383			−0.154691	+	0.987963i	$0.549438\pi$
$522$	13.1355	+	22.7514i	0.574926	+	0.995802i
$523$	−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
$527$	−1.92420	+	3.33280i	−0.0838193	+	0.145179i
$528$	−6.41088			−0.278998
$529$	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
$534$	22.8082			0.987006
$535$	−1.09028	−	1.88842i	−0.0471368	−	0.0816434i
$536$	13.0230	+	22.5564i	0.562507	+	0.974290i
$537$	5.86056	−	10.1508i	0.252902	−	0.438039i
$538$	20.3779			0.878554
$539$		0			0
$540$	2.73688	−	4.74041i	0.117776	−	0.203995i
$541$	26.3079			1.13107			0.565533	−	0.824726i	$-0.308671\pi$
$541$	26.3079			1.13107			0.565533	+	0.824726i	$0.308671\pi$
$542$	14.7842	−	25.6069i	0.635035	−	1.09991i
$543$	2.51437	+	4.35501i	0.107902	+	0.186891i
$544$	−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
$549$	−1.39018	−	2.40786i	−0.0593315	−	0.102765i
$550$	−14.4428	+	25.0156i	−0.615842	+	1.06667i
$551$	−27.9378			−1.19019
$552$	6.47508	−	11.2152i	0.275598	−	0.477349i
$553$		0			0
$554$	25.0948			1.06617
$555$	1.23911	−	2.14620i	0.0525974	−	0.0911013i
$556$	21.6780	+	37.5474i	0.919351	+	1.59236i
$557$	−3.65494	−	6.33053i	−0.154865	−	0.268233i	0.778145	−	0.628085i	$-0.216161\pi$
$557$	−3.65494	−	6.33053i	−0.154865	−	0.268233i	−0.933010	+	0.359851i	$0.882827\pi$
$558$	11.6842			0.494633
$559$	−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	$0.774185\pi$
$564$	−26.5692			−1.11876
$565$	1.64308	−	2.84589i	0.0691247	−	0.119727i
$566$	−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	$0.483259\pi$
$570$	1.96881	+	3.41007i	0.0824642	+	0.142832i
$571$	−40.8648			−1.71014			−0.855069	−	0.518515i	$-0.826485\pi$
$571$	−40.8648			−1.71014			−0.855069	+	0.518515i	$0.826485\pi$
$572$	−23.8180	+	24.7260i	−0.995881	+	1.03384i
$573$	−14.1268			−0.590155
$574$		0			0
$575$	−9.00851	−	15.6032i	−0.375681	−	0.650698i
$576$	−10.8979	+	18.8756i	−0.454077	+	0.786485i
$577$	−21.7280			−0.904550			−0.452275	−	0.891879i	$-0.649387\pi$
$577$	−21.7280			−0.904550			−0.452275	+	0.891879i	$0.649387\pi$
$578$	16.0572	−	27.8119i	0.667891	−	1.15682i
$579$	3.07959	−	5.33400i	0.127983	−	0.221674i
$580$	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
$584$	55.5139			2.29718
$585$	−0.829115	−	2.87791i	−0.0342797	−	0.118987i
$586$	−4.76981			−0.197039
$587$	−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
$590$	0.520811			0.0214415
$591$	−3.28571	+	5.69101i	−0.135156	+	0.234097i
$592$	16.8398	−	29.1673i	0.692110	−	1.19877i
$593$	−5.63861			−0.231550			−0.115775	−	0.993275i	$-0.536935\pi$
$593$	−5.63861			−0.231550			−0.115775	+	0.993275i	$0.536935\pi$
$594$	−12.1070	+	20.9699i	−0.496756	+	0.860407i
$595$		0			0
$596$	−31.1421	−	53.9397i	−1.27563	−	2.20946i
$597$	−13.1627			−0.538715
$598$	−8.95657	−	31.0888i	−0.366261	−	1.27131i
$599$	39.6719			1.62095			0.810474	−	0.585774i	$-0.199209\pi$
$599$	39.6719			1.62095			0.810474	+	0.585774i	$0.199209\pi$
$600$	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
$604$	20.7312	−	35.9075i	0.843540	−	1.46105i
$605$	0.868340	−	1.50401i	0.0353030	−	0.0611467i
$606$	27.5905			1.12079
$607$	−11.2490	+	19.4838i	−0.456582	+	0.790823i	−0.998778	−	0.0494290i	$-0.984260\pi$
$607$	−11.2490	+	19.4838i	−0.456582	+	0.790823i	0.542196	+	0.840252i	$0.317593\pi$
$608$	−2.54245	−	4.40365i	−0.103110	−	0.178592i
$609$		0			0
$610$	−0.949597			−0.0384480
$611$	−22.5257	+	23.3844i	−0.911294	+	0.946032i
$612$	18.5509			0.749877
$613$	−13.7135	−	23.7524i	−0.553882	−	0.959351i	−0.997990	−	0.0633780i	$-0.979813\pi$
$613$	−13.7135	−	23.7524i	−0.553882	−	0.959351i	0.444108	−	0.895973i	$-0.353521\pi$
$614$	−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	$0.235359\pi$
$618$	−16.1449	+	27.9637i	−0.649442	+	1.12487i
$619$	−45.4677			−1.82750			−0.913751	−	0.406274i	$-0.866828\pi$
$619$	−45.4677			−1.82750			−0.913751	+	0.406274i	$0.866828\pi$
$620$	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
$625$	23.2639			0.930556
$626$	32.4870	+	56.2692i	1.29844	+	2.24897i
$627$	−5.76454	−	9.98448i	−0.230214	−	0.398742i
$628$	−17.8605	+	30.9353i	−0.712711	+	1.23445i
$629$	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	$0.966131\pi$
$632$	20.8278			0.828485
$633$	8.76310	−	15.1781i	0.348302	−	0.603277i
$634$	−26.0675	−	45.1503i	−1.03527	−	1.79315i
$635$	−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
$640$	3.44594	+	5.96854i	0.136213	+	0.235927i
$641$	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	$-0.151131\pi$
$642$	11.7016			0.461827
$643$	−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
$646$	−14.9029	+	25.8125i	−0.586345	+	1.01558i
$647$	−17.4026	−	30.1421i	−0.684166	−	1.18501i	−0.973698	−	0.227841i	$-0.926833\pi$
$647$	−17.4026	−	30.1421i	−0.684166	−	1.18501i	0.289533	−	0.957168i	$-0.406500\pi$
$648$	−9.80778	−	16.9876i	−0.385286	−	0.667335i
$649$	−1.52490			−0.0598577
$650$	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
$655$	−0.0657402			−0.00256868
$656$	−21.9242	+	37.9739i	−0.855997	+	1.48263i
$657$	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
$661$	9.06227	+	15.6963i	0.352481	+	0.610516i	0.986684	−	0.162651i	$-0.0520046\pi$
$661$	9.06227	+	15.6963i	0.352481	+	0.610516i	−0.634202	+	0.773167i	$0.718671\pi$
$662$	25.8139			1.00329
$663$	−3.67247	+	3.81247i	−0.142627	+	0.148064i
$664$	6.57814			0.255281
$665$		0			0
$666$	−28.4773	−	49.3241i	−1.10347	−	1.91127i
$667$	8.19313	−	14.1909i	0.317239	−	0.549475i
$668$	−71.5590			−2.76870
$669$	11.0299	−	19.1043i	0.426440	−	0.738616i
$670$	2.32250	−	4.02268i	0.0897259	−	0.155410i
$671$	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
$675$	19.9904			0.769432
$676$	44.9983	+	23.7821i	1.73071	+	0.914698i
$677$	−38.2179			−1.46883			−0.734416	−	0.678700i	$-0.762544\pi$
$677$	−38.2179			−1.46883			−0.734416	+	0.678700i	$0.762544\pi$
$678$	8.81733	+	15.2721i	0.338628	+	0.586520i
$679$		0			0
$680$	1.54961	−	2.68401i	0.0594249	−	0.102927i
$681$	14.9294			0.572097
$682$	−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	$0.0160111\pi$
$684$	59.8966			2.29020
$685$	−0.832803	+	1.44246i	−0.0318198	+	0.0551135i
$686$		0			0
$687$	0.500466	+	0.866833i	0.0190940	+	0.0330717i
$688$	−29.4076			−1.12115
$689$	3.73272	−	3.87501i	0.142205	−	0.147626i
$690$	−2.30951			−0.0879217
$691$	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
$695$	1.89109	−	3.27547i	0.0717333	−	0.124246i
$696$	−7.79463	+	13.5007i	−0.295455	+	0.511742i
$697$	−24.4228			−0.925080
$698$	−19.5035	+	33.7811i	−0.738219	+	1.27863i
$699$	−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	$0.672383\pi$
$702$	34.8414	+	8.64077i	1.31500	+	0.326125i
$703$	60.5681			2.28437
$704$	−10.8979	−	18.8756i	−0.410729	−	0.711403i
$705$	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
$709$	−3.08583	+	5.34481i	−0.115891	+	0.200729i	−0.918135	−	0.396267i	$-0.870306\pi$
$709$	−3.08583	+	5.34481i	−0.115891	+	0.200729i	0.802245	+	0.596995i	$0.203639\pi$
$710$	7.88886			0.296064
$711$	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
$716$	−60.8943			−2.27573
$717$	−8.47011	−	14.6707i	−0.316322	−	0.547886i
$718$	25.6994	+	44.5127i	0.959094	+	1.66120i
$719$	−1.36066	+	2.35674i	−0.0507442	+	0.0878915i	−0.890282	−	0.455410i	$-0.849493\pi$
$719$	−1.36066	+	2.35674i	−0.0507442	+	0.0878915i	0.839538	+	0.543302i	$0.182826\pi$
$720$	−2.90549			−0.108281
$721$		0			0
$722$	−25.0129	+	43.3236i	−0.930883	+	1.61234i
$723$	10.0307			0.373047
$724$	13.0628	−	22.6254i	0.485475	−	0.840867i
$725$	10.8443	+	18.7829i	0.402749	+	0.697581i
$726$	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
$731$	−8.18976	−	14.1851i	−0.302909	−	0.524654i
$732$	1.68644	−	2.92099i	0.0623325	−	0.107963i
$733$	3.49707			0.129167			0.0645836	−	0.997912i	$-0.479428\pi$
$733$	3.49707			0.129167			0.0645836	+	0.997912i	$0.479428\pi$
$734$	17.9236	−	31.0446i	0.661573	−	1.14588i
$735$		0			0
$736$	2.98243			0.109934
$737$	−6.80013	+	11.7782i	−0.250486	+	0.433855i
$738$	37.0755	+	64.2166i	1.36477	+	2.36385i
$739$	−16.0151	−	27.7390i	−0.589126	−	1.02040i	−0.994347	−	0.106178i	$-0.966139\pi$
$739$	−16.0151	−	27.7390i	−0.589126	−	1.02040i	0.405221	−	0.914219i	$-0.367195\pi$
$740$	−12.8750			−0.473295
$741$	−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
$746$	31.4387			1.15105
$747$	1.71744	−	2.97469i	0.0628377	−	0.108838i
$748$	−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	$0.997276\pi$
$752$	15.7495	+	27.2790i	0.574327	+	0.994763i
$753$	11.9847			0.436745
$754$	10.7818	+	37.4243i	0.392651	+	1.36291i
$755$	−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	$0.428426\pi$
$758$	32.6337	−	56.5231i	1.18531	−	2.05301i
$759$	6.76212			0.245449
$760$	5.00333	−	8.66602i	0.181490	−	0.314350i
$761$	−6.96431	+	12.0625i	−0.252456	+	0.437267i	−0.964201	−	0.265171i	$-0.914572\pi$
$761$	−6.96431	+	12.0625i	−0.252456	+	0.437267i	0.711745	+	0.702437i	$0.247905\pi$
$762$	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
$766$	−7.07211			−0.255526
$767$	0.625831	+	2.17229i	0.0225974	+	0.0784370i
$768$	−23.4774			−0.847166
$769$	−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
$772$	−31.9985			−1.15165
$773$	−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
$775$	9.64620			0.346502
$776$	−23.9337	+	41.4544i	−0.859170	+	1.48813i
$777$		0			0
$778$	20.3092	+	35.1766i	0.728120	+	1.26114i
$779$	−78.8555			−2.82529
$780$	2.52057	−	2.61665i	0.0902509	−	0.0936912i
$781$	−23.0981			−0.826515
$782$	−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
$786$	0.176393	−	0.305521i	0.00629172	−	0.0108976i
$787$	−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	$0.228691\pi$
$788$	34.1402			1.21619
$789$	0.642194	−	1.11231i	0.0228627	−	0.0395994i
$790$	−1.85720	−	3.21676i	−0.0660762	−	0.114447i
$791$		0			0
$792$	27.5509			0.978980
$793$	−1.14108	−	3.96075i	−0.0405209	−	0.140650i
$794$	−58.6098			−2.07998
$795$	−0.192038	−	0.332620i	−0.00681090	−	0.0117968i
$796$	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
$800$	−1.97375	+	3.41864i	−0.0697828	+	0.120867i
$801$	−30.2659			−1.06939
$802$	−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
$807$	6.31415			0.222269
$808$	−35.0579	−	60.7221i	−1.23333	−	2.13620i
$809$	14.8194	+	25.6680i	0.521023	+	0.902439i	0.999701	+	0.0244482i	$0.00778287\pi$
$809$	14.8194	+	25.6680i	0.521023	+	0.902439i	−0.478678	+	0.877991i	$0.658884\pi$
$810$	−1.74910	+	3.02954i	−0.0614573	+	0.106447i
$811$	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
$814$	56.9546			1.99626
$815$	1.87229	−	3.24291i	0.0655836	−	0.113594i
$816$	2.56772	+	4.44742i	0.0898881	+	0.155691i
$817$	−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	$0.933513\pi$
$822$	−4.46912	−	7.74075i	−0.155879	−	0.269990i
$823$	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	$0.118315\pi$
$824$	82.0580			2.85863
$825$	−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	$0.419951\pi$
$828$	−17.5655	+	30.4243i	−0.610442	+	1.05732i
$829$	−12.6533	−	21.9161i	−0.439467	−	0.761179i	0.558182	−	0.829719i	$-0.311499\pi$
$829$	−12.6533	−	21.9161i	−0.439467	−	0.761179i	−0.997648	+	0.0685401i	$0.978166\pi$
$830$	−0.586568	−	1.01597i	−0.0203601	−	0.0352647i
$831$	7.77567			0.269735
$832$	−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
$837$	8.08615			0.279498
$838$	31.9090	−	55.2679i	1.10228	−	1.90920i
$839$	−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
$843$	0.978452	+	1.69473i	0.0336997	+	0.0583696i
$844$	−91.0531			−3.13418
$845$	−0.166029	−	4.43688i	−0.00571157	−	0.152633i
$846$	53.2673			1.83137
$847$		0			0
$848$	−2.60984	−	4.52037i	−0.0896223	−	0.155230i
$849$	−1.73465	+	3.00450i	−0.0595330	+	0.103114i
$850$	23.1388			0.793653
$851$	−17.7624	+	30.7653i	−0.608887	+	1.05462i
$852$	−14.0102	+	24.2664i	−0.479982	+	0.831353i
$853$	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
$857$	24.6439			0.841819			0.420909	−	0.907103i	$-0.361711\pi$
$857$	24.6439			0.841819			0.420909	+	0.907103i	$0.361711\pi$
$858$	−11.1501	+	11.5752i	−0.380659	+	0.395170i
$859$	2.57141			0.0877355			0.0438677	−	0.999037i	$-0.486032\pi$
$859$	2.57141			0.0877355			0.0438677	+	0.999037i	$0.486032\pi$
$860$	5.62097	+	9.73580i	0.191673	+	0.331988i
$861$		0			0
$862$	27.9906	−	48.4812i	0.953365	−	1.65128i
$863$	39.5407			1.34598			0.672991	−	0.739651i	$-0.265009\pi$
$863$	39.5407			1.34598			0.672991	+	0.739651i	$0.265009\pi$
$864$	−1.65455	+	2.86576i	−0.0562888	+	0.0974951i
$865$	1.40002	−	2.42491i	0.0476021	−	0.0824493i
$866$	−62.8959			−2.13729
$867$	4.97536	−	8.61758i	0.168972	−	0.292668i
$868$		0			0
$869$	5.43777	+	9.41849i	0.184464	+	0.319500i
$870$	2.78016			0.0942564
$871$	19.5694	+	4.85325i	0.663082	+	0.164446i
$872$	−38.0756			−1.28940
$873$	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
$877$	−10.5227	+	18.2259i	−0.355328	+	0.615445i	−0.987174	−	0.159648i	$-0.948964\pi$
$877$	−10.5227	+	18.2259i	−0.355328	+	0.615445i	0.631846	+	0.775094i	$0.282297\pi$
$878$	43.3851	−	75.1452i	1.46418	−	2.53603i
$879$	−1.47794			−0.0498497
$880$	1.45274	−	2.51623i	0.0489720	−	0.0848219i
$881$	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	$0.538285\pi$
$884$	26.6929	+	6.61990i	0.897778	+	0.222651i
$885$	0.161375			0.00542455
$886$	8.34065	+	14.4464i	0.280210	+	0.485337i
$887$	−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
$891$	5.12127	−	8.87031i	0.171569	−	0.297166i
$892$	−114.606			−3.83730
$893$	−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
$898$	−24.2760			−0.810100
$899$	4.38655	+	7.59773i	0.146300	+	0.253398i
$900$	−23.2495	−	40.2692i	−0.774982	−	1.34231i
$901$	1.45363	−	2.51777i	0.0484276	−	0.0838790i
$902$	−74.1510			−2.46896
$903$		0			0
$904$	22.4075	−	38.8109i	0.745263	−	1.29083i
$905$	−2.27908			−0.0757593
$906$	9.70506	−	16.8097i	0.322429	−	0.558464i
$907$	−14.7862	−	25.6105i	−0.490969	−	0.850383i	0.508977	−	0.860780i	$-0.330024\pi$
$907$	−14.7862	−	25.6105i	−0.490969	−	0.850383i	−0.999946	+	0.0103972i	$0.996690\pi$
$908$	−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
$913$	1.71744	+	2.97469i	0.0568388	+	0.0984477i
$914$	10.6685	−	18.4785i	0.352884	−	0.611213i
$915$	−0.294235			−0.00972711
$916$	2.60005	−	4.50342i	0.0859081	−	0.148797i
$917$		0			0
$918$	19.3966			0.640184
$919$	2.08952	−	3.61916i	0.0689269	−	0.119385i	−0.829502	−	0.558503i	$-0.811376\pi$
$919$	2.08952	−	3.61916i	0.0689269	−	0.119385i	0.898429	+	0.439118i	$0.144709\pi$
$920$	2.93459	+	5.08285i	0.0967504	+	0.167577i
$921$	−2.77947	−	4.81418i	−0.0915865	−	0.158632i
$922$	16.7461			0.551502
$923$	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
$928$	−3.59021			−0.117855
$929$	24.0456	−	41.6482i	0.788910	−	1.36643i	−0.137725	−	0.990470i	$-0.543979\pi$
$929$	24.0456	−	41.6482i	0.788910	−	1.36643i	0.926635	−	0.375962i	$-0.122688\pi$
$930$	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
$934$	35.0359	+	60.6840i	1.14641	+	1.98564i
$935$	1.61830			0.0529242
$936$	−11.3071	−	39.2476i	−0.369584	−	1.28285i
$937$	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
$940$	6.02073	−	10.4282i	0.196375	−	0.340131i
$941$	−30.5888			−0.997167			−0.498583	−	0.866842i	$-0.666146\pi$
$941$	−30.5888			−0.997167			−0.498583	+	0.866842i	$0.666146\pi$
$942$	−8.36117	+	14.4820i	−0.272422	+	0.471848i
$943$	23.1254	−	40.0544i	0.753067	−	1.30435i
$944$	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	$0.792970\pi$
$948$	13.1932			0.428494
$949$	29.8132	−	30.9497i	0.967778	−	1.00467i
$950$	74.7096			2.42390
$951$	−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	$-0.0471926\pi$
$954$	−8.82686			−0.285780
$955$	3.20121	−	5.54467i	0.103589	−	0.179421i
$956$	−44.0044	+	76.2179i	−1.42320	+	2.46506i
$957$	−8.14015			−0.263134
$958$	29.8992	−	51.7869i	0.965998	−	1.67316i
$959$		0			0
$960$	1.15328	+	1.99754i	0.0372219	+	0.0644702i
$961$	−27.0981			−0.874132
$962$	−23.3745	−	81.1344i	−0.753625	−	2.61588i
$963$	−15.5278			−0.500377
$964$	−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	$0.459973\pi$
$968$	11.8420	−	20.5110i	0.380617	−	0.659248i
$969$	−4.61769	+	7.99807i	−0.148342	+	0.256935i
$970$	8.53661			0.274094
$971$	−28.8957	+	50.0489i	−0.927308	+	1.60614i	−0.139501	+	0.990222i	$0.544550\pi$
$971$	−28.8957	+	50.0489i	−0.927308	+	1.60614i	−0.787807	+	0.615922i	$0.788784\pi$
$972$	−30.2529	−	52.3995i	−0.970362	−	1.68072i
$973$		0			0
$974$	−6.25817			−0.200525
$975$	12.8785	+	3.19390i	0.412442	+	0.102287i
$976$	−3.99871			−0.127996
$977$	−4.33707	−	7.51203i	−0.138755	−	0.240331i	0.788270	−	0.615329i	$-0.210977\pi$
$977$	−4.33707	−	7.51203i	−0.138755	−	0.240331i	−0.927026	+	0.374998i	$0.877643\pi$
$978$	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
$982$	−17.0708	+	29.5675i	−0.544752	+	0.943538i
$983$	37.1121			1.18369			0.591846	−	0.806051i	$-0.298399\pi$
$983$	37.1121			1.18369			0.591846	+	0.806051i	$0.298399\pi$
$984$	−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
$989$	31.0188			0.986340
$990$	−2.45670	−	4.25512i	−0.0780790	−	0.135237i
$991$	22.6318	+	39.1995i	0.718924	+	1.24521i	0.961426	+	0.275062i	$0.0886984\pi$
$991$	22.6318	+	39.1995i	0.718924	+	1.24521i	−0.242502	+	0.970151i	$0.577968\pi$
$992$	−0.798386	+	1.38285i	−0.0253488	+	0.0439054i
$993$	7.99850			0.253825
$994$		0			0
$995$	2.98275	−	5.16628i	0.0945597	−	0.163782i
$996$	4.16686			0.132032
$997$	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	$-0.0805028\pi$
$998$	−16.4586	−	28.5072i	−0.520989	−	0.902380i
$999$	−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.f.l.393.1	yes	16
7.2	even	3		637.2.g.m.263.2		16
7.3	odd	6		637.2.h.m.471.8		16
7.4	even	3		637.2.h.m.471.7		16
7.5	odd	6		637.2.g.m.263.1		16
7.6	odd	2	inner	637.2.f.l.393.2	yes	16
13.3	even	3		8281.2.a.ci.1.8		8
13.9	even	3	inner	637.2.f.l.295.1	✓	16
13.10	even	6		8281.2.a.cl.1.2		8
91.9	even	3		637.2.h.m.165.7		16
91.48	odd	6	inner	637.2.f.l.295.2	yes	16
91.55	odd	6		8281.2.a.ci.1.7		8
91.61	odd	6		637.2.h.m.165.8		16
91.62	odd	6		8281.2.a.cl.1.1		8
91.74	even	3		637.2.g.m.373.2		16
91.87	odd	6		637.2.g.m.373.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.1	✓	16	13.9	even	3	inner
637.2.f.l.295.2	yes	16	91.48	odd	6	inner
637.2.f.l.393.1	yes	16	1.1	even	1	trivial
637.2.f.l.393.2	yes	16	7.6	odd	2	inner
637.2.g.m.263.1		16	7.5	odd	6
637.2.g.m.263.2		16	7.2	even	3
637.2.g.m.373.1		16	91.87	odd	6
637.2.g.m.373.2		16	91.74	even	3
637.2.h.m.165.7		16	91.9	even	3
637.2.h.m.165.8		16	91.61	odd	6
637.2.h.m.471.7		16	7.4	even	3
637.2.h.m.471.8		16	7.3	odd	6
8281.2.a.ci.1.7		8	91.55	odd	6
8281.2.a.ci.1.8		8	13.3	even	3
8281.2.a.cl.1.1		8	91.62	odd	6
8281.2.a.cl.1.2		8	13.10	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21605 - 2.10626i) q^{2} +(-0.376796 - 0.652630i) q^{3} +(-1.95755 + 3.39058i) q^{4} +0.341537 q^{5} +(-0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +(-0.415326 - 0.719366i) q^{10} +(1.21605 + 2.10626i) q^{11} +2.95039 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} -5.91511 q^{18} +(3.14519 - 5.44764i) q^{19} +(-0.668577 + 1.15801i) q^{20} +(2.95755 - 5.12263i) q^{22} +(1.84474 + 3.19518i) q^{23} +(-1.75501 - 3.03977i) q^{24} -4.88335 q^{25} +(-8.51122 - 2.11081i) q^{26} -4.09359 q^{27} +(-2.22068 - 3.84632i) q^{29} +(-0.312986 + 0.542108i) q^{30} -1.97532 q^{31} +(0.404180 - 0.700061i) q^{32} +(0.916405 - 1.58726i) q^{33} -4.73830 q^{34} +(4.76096 + 8.24623i) q^{36} +(4.81433 + 8.33867i) q^{37} -15.2988 q^{38} +(-2.63722 - 0.654039i) q^{39} +1.59079 q^{40} +(-6.26793 - 10.8564i) q^{41} +(4.20368 - 7.28099i) q^{43} -9.52192 q^{44} +(0.415326 - 0.719366i) q^{45} +(4.48659 - 7.77100i) q^{46} -9.00530 q^{47} +(-1.31797 + 2.28279i) q^{48} +(5.93840 + 10.2856i) q^{50} -1.46817 q^{51} +(3.90786 + 13.5644i) q^{52} +1.49226 q^{53} +(4.97800 + 8.62216i) q^{54} +(0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 + 9.35464i) q^{58} +(-0.313495 + 0.542990i) q^{59} +1.00767 q^{60} +(0.571597 - 0.990035i) q^{61} +(2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.854317 - 0.886883i) q^{65} -4.45758 q^{66} +(2.79599 + 4.84280i) q^{67} +(3.81377 + 6.60564i) q^{68} +(1.39018 - 2.40786i) q^{69} +(-4.74859 + 8.22481i) q^{71} +(5.66402 - 9.81038i) q^{72} +11.9187 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} +4.47167 q^{79} +(-0.597321 - 1.03459i) q^{80} +(-2.10570 - 3.64718i) q^{81} +(-15.2442 + 26.4038i) q^{82} +1.41231 q^{83} +(0.332697 - 0.576248i) q^{85} -20.4475 q^{86} +(-1.67348 + 2.89856i) q^{87} +(5.66402 + 9.81038i) q^{88} +(-6.22219 - 10.7771i) q^{89} -2.02023 q^{90} -14.4447 q^{92} +(0.744294 + 1.28915i) q^{93} +(10.9509 + 18.9675i) q^{94} +(1.07420 - 1.86057i) q^{95} -0.609174 q^{96} +(-5.13850 + 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

L-functions

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