LMFDB - Embedded newform 637.2.f.l.295.2

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			295.2
Root			$-0.756863 - 1.31093i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.l.393.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21605 + 2.10626i) q^{2} +(0.376796 - 0.652630i) q^{3} +(-1.95755 - 3.39058i) q^{4} -0.341537 q^{5} +(0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 + 2.10626i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.0121689	+	0.999926i	$0.496126\pi$
$2$	−1.21605	+	2.10626i	−0.859877	+	1.48935i	−0.872046	+	0.489424i	$0.837207\pi$
$3$	0.376796	−	0.652630i	0.217543	−	0.376796i	−0.736513	−	0.676423i	$-0.763529\pi$
$3$	0.376796	−	0.652630i	0.217543	−	0.376796i	0.954056	+	0.299627i	$0.0968623\pi$
$4$	−1.95755	−	3.39058i	−0.978776	−	1.69529i
$5$	−0.341537			−0.152740			−0.0763700	−	0.997080i	$-0.524333\pi$
$5$	−0.341537			−0.152740			−0.0763700	+	0.997080i	$0.524333\pi$
$6$	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	−0.622387	−	0.782710i	$-0.713837\pi$
$11$	1.21605	−	2.10626i	0.366653	−	0.635061i	0.989040	+	0.147648i	$0.0471704\pi$
$12$	−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	$-0.242588\pi$
$17$	−0.974117	−	1.68722i	−0.236258	−	0.409211i	−0.959638	+	0.281240i	$0.909254\pi$
$18$	−5.91511			−1.39420
$19$	−3.14519	−	5.44764i	−0.721557	−	1.24977i	−0.960376	−	0.278709i	$-0.910093\pi$
$19$	−3.14519	−	5.44764i	−0.721557	−	1.24977i	0.238819	−	0.971064i	$-0.423240\pi$
$20$	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	$0.0409872\pi$
$24$	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	−0.995148	−	0.0983864i	$-0.968632\pi$
$29$	−2.22068	+	3.84632i	−0.412369	+	0.714244i	0.582779	+	0.812631i	$0.301965\pi$
$30$	−0.312986	−	0.542108i	−0.0571432	−	0.0989750i
$31$	1.97532			0.354778			0.177389	−	0.984141i	$-0.443235\pi$
$31$	1.97532			0.354778			0.177389	+	0.984141i	$0.443235\pi$
$32$	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	−0.133584	−	0.991037i	$-0.542649\pi$
$37$	4.81433	−	8.33867i	0.791472	−	1.37087i	0.925056	−	0.379832i	$-0.124018\pi$
$38$	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	0.312426	−	0.949942i	$-0.398859\pi$
$41$	6.26793	−	10.8564i	0.978887	−	1.69548i	0.666461	−	0.745540i	$-0.267808\pi$
$42$		0			0
$43$	4.20368	+	7.28099i	0.641055	+	1.11034i	0.985198	+	0.171423i	$0.0548365\pi$
$43$	4.20368	+	7.28099i	0.641055	+	1.11034i	−0.344142	+	0.938918i	$0.611830\pi$
$44$	−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	$-0.271919\pi$
$47$	9.00530			1.31356			0.656779	+	0.754083i	$0.271919\pi$
$48$	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	$-0.153672\pi$
$59$	0.313495	+	0.542990i	0.0408136	+	0.0706913i	−0.844897	+	0.534929i	$0.820338\pi$
$60$	1.00767			0.130089
$61$	−0.571597	−	0.990035i	−0.0731855	−	0.126761i	0.827110	−	0.562040i	$-0.189983\pi$
$61$	−0.571597	−	0.990035i	−0.0731855	−	0.126761i	−0.900296	+	0.435279i	$0.856650\pi$
$62$	−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	−0.643142	−	0.765747i	$-0.722370\pi$
$67$	2.79599	−	4.84280i	0.341585	−	0.591642i	0.984727	+	0.174104i	$0.0557030\pi$
$68$	−3.81377	+	6.60564i	−0.462488	+	0.801052i
$69$	−1.39018	−	2.40786i	−0.167358	−	0.289873i
$70$		0			0
$71$	−4.74859	−	8.22481i	−0.563554	−	0.976105i	−0.997183	−	0.0750130i	$-0.976100\pi$
$71$	−4.74859	−	8.22481i	−0.563554	−	0.976105i	0.433628	−	0.901092i	$-0.357233\pi$
$72$	5.66402	+	9.81038i	0.667512	+	1.15616i
$73$	−11.9187			−1.39498			−0.697488	−	0.716597i	$-0.745699\pi$
$73$	−11.9187			−1.39498			−0.697488	+	0.716597i	$0.745699\pi$
$74$	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	$-0.524697\pi$
$83$	−1.41231			−0.155021			−0.0775104	+	0.996992i	$0.524697\pi$
$84$		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	−0.321182	−	0.947018i	$-0.604080\pi$
$89$	6.22219	−	10.7771i	0.659551	−	1.14238i	0.980732	−	0.195357i	$-0.0625867\pi$
$90$	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	0.999680	+	0.0252826i	$0.00804857\pi$
$97$	5.13850	+	8.90014i	0.521736	+	0.903673i	−0.477945	+	0.878390i	$0.658618\pi$
$98$		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	−0.199380	−	0.979922i	$-0.563893\pi$
$101$	7.52683	−	13.0369i	0.748948	−	1.29722i	0.948328	−	0.317293i	$-0.102774\pi$
$102$	1.78537	−	3.09235i	0.176778	−	0.306189i
$103$	−17.6176			−1.73591			−0.867957	−	0.496639i	$-0.834567\pi$
$103$	−17.6176			−1.73591			−0.867957	+	0.496639i	$0.834567\pi$
$104$	−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
$109$	−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	0.998545	−	0.0539336i	$-0.0171759\pi$
$113$	4.81083	+	8.33259i	0.452564	+	0.783865i	−0.545980	+	0.837798i	$0.683843\pi$
$114$	5.76454	−	9.98448i	0.539899	−	0.935133i
$115$	−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	−0.993748	−	0.111644i	$-0.964388\pi$
$127$	−4.50988	+	7.81134i	−0.400187	+	0.693145i	0.593561	+	0.804789i	$0.297722\pi$
$128$	10.0895	−	17.4755i	0.891794	−	1.54463i
$129$	6.33572			0.557829
$130$	−2.90690	+	0.720919i	−0.254952	+	0.0632287i
$131$	0.192483			0.0168173			0.00840867	−	0.999965i	$-0.497323\pi$
$131$	0.192483			0.0168173			0.00840867	+	0.999965i	$0.497323\pi$
$132$	−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	0.742861	−	0.669446i	$-0.233468\pi$
$137$	−2.43840	−	4.22343i	−0.208326	−	0.360832i	−0.951187	+	0.308614i	$0.900135\pi$
$138$	6.76212			0.575629
$139$	−5.53701	−	9.59038i	−0.469643	−	0.813446i	0.529755	−	0.848151i	$-0.322284\pi$
$139$	−5.53701	−	9.59038i	−0.469643	−	0.813446i	−0.999398	+	0.0347054i	$0.988951\pi$
$140$		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	−0.982723	−	0.185080i	$-0.940746\pi$
$149$	−7.95435	−	13.7773i	−0.651646	−	1.12868i	0.331078	−	0.943603i	$-0.392588\pi$
$150$	−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	$-0.618617\pi$
$157$	−9.12388			−0.728165			−0.364082	+	0.931367i	$0.618617\pi$
$158$	−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	0.996818	−	0.0797075i	$-0.0253986\pi$
$163$	5.48196	+	9.49504i	0.429380	+	0.743709i	−0.567438	+	0.823416i	$0.692065\pi$
$164$	−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	0.258713	+	0.965954i	$0.416702\pi$
$167$	−9.13884	+	15.8289i	−0.707185	+	1.22488i	−0.965897	+	0.258925i	$0.916632\pi$
$168$		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	$-0.267550\pi$
$173$	−4.09918	−	7.09998i	−0.311655	−	0.539802i	−0.978721	+	0.205197i	$0.934217\pi$
$174$	−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	−0.414061	−	0.910249i	$-0.635890\pi$
$179$	7.77684	−	13.4699i	0.581268	−	1.00679i	0.995329	−	0.0965370i	$-0.0307766\pi$
$180$	−1.62605	+	2.81639i	−0.121198	+	0.209922i
$181$	6.67302			0.496001			0.248001	−	0.968760i	$-0.420226\pi$
$181$	6.67302			0.496001			0.248001	+	0.968760i	$0.420226\pi$
$182$		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	0.975521	+	0.219905i	$0.0705746\pi$
$191$	9.37296	+	16.2344i	0.678204	+	1.17468i	−0.297318	+	0.954779i	$0.596092\pi$
$192$	−3.37673	+	5.84867i	−0.243694	+	0.422091i
$193$	4.08655	−	7.07811i	0.294156	−	0.509493i	−0.680632	−	0.732625i	$-0.738295\pi$
$193$	4.08655	−	7.07811i	0.294156	−	0.509493i	0.974788	+	0.223132i	$0.0716281\pi$
$194$	−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	−0.978501	−	0.206240i	$-0.933877\pi$
$197$	−4.36006	+	7.55184i	−0.310641	+	0.538047i	0.667860	+	0.744287i	$0.267210\pi$
$198$	−7.19306	+	12.4587i	−0.511189	+	0.885405i
$199$	−8.73332	−	15.1266i	−0.619089	−	1.07229i	−0.989652	−	0.143486i	$-0.954169\pi$
$199$	−8.73332	−	15.1266i	−0.619089	−	1.07229i	0.370563	−	0.928807i	$-0.379165\pi$
$200$	−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	−0.118730	−	0.992927i	$-0.537882\pi$
$211$	11.6284	−	20.1410i	0.800535	−	1.38657i	0.919265	−	0.393640i	$-0.128784\pi$
$212$	−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	−0.318272	+	0.947999i	$0.603103\pi$
$223$	−14.6364	+	25.3510i	−0.980128	+	1.69763i	−0.661855	+	0.749632i	$0.730231\pi$
$224$		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	0.981273	+	0.192622i	$0.0616991\pi$
$227$	9.90551	+	17.1569i	0.657452	+	1.13874i	−0.323821	+	0.946118i	$0.604968\pi$
$228$	9.27956	+	16.0727i	0.614554	+	1.06444i
$229$	1.32821			0.0877709			0.0438855	−	0.999037i	$-0.486026\pi$
$229$	1.32821			0.0877709			0.0438855	+	0.999037i	$0.486026\pi$
$230$	−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	$-0.0256369\pi$
$241$	6.65528	+	11.5273i	0.428704	+	0.742538i	−0.568054	+	0.822991i	$0.692304\pi$
$242$	−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	0.999998	+	0.00220260i	$0.000701110\pi$
$251$	7.95169	+	13.7727i	0.501906	+	0.869327i	−0.498091	+	0.867125i	$0.665966\pi$
$252$		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	−0.100667	+	0.994920i	$0.532098\pi$
$257$	−14.6198	+	25.3223i	−0.911960	+	1.57956i	−0.811292	+	0.584641i	$0.801236\pi$
$258$	−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	−0.838555	−	0.544817i	$-0.816599\pi$
$263$	0.852177	−	1.47601i	0.0525475	−	0.0910149i	0.891103	+	0.453802i	$0.149933\pi$
$264$	−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	$-0.0844495\pi$
$269$	4.18937	+	7.25620i	0.255430	+	0.442418i	−0.709582	+	0.704623i	$0.751116\pi$
$270$	1.70017	−	2.94479i	0.103469	−	0.179214i
$271$	−6.07877	+	10.5287i	−0.369259	+	0.639575i	−0.989450	−	0.144876i	$-0.953722\pi$
$271$	−6.07877	+	10.5287i	−0.369259	+	0.639575i	0.620191	+	0.784451i	$0.287055\pi$
$272$	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	0.668379	−	0.743821i	$-0.266989\pi$
$277$	−5.15907	−	8.93578i	−0.309979	−	0.536899i	−0.978357	+	0.206922i	$0.933655\pi$
$278$	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	$-0.789642\pi$
$283$	2.30184	−	3.98690i	0.136830	−	0.236997i	0.926295	+	0.376799i	$0.122975\pi$
$284$	−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	$-0.184912\pi$
$293$	−0.980596	−	1.69844i	−0.0572870	−	0.0992241i	−0.893247	+	0.449567i	$0.851578\pi$
$294$		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	$-0.567510\pi$
$307$	−7.37658			−0.421004			−0.210502	+	0.977593i	$0.567510\pi$
$308$		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	$-0.631518\pi$
$311$	−14.1618			−0.803040			−0.401520	+	0.915850i	$0.631518\pi$
$312$	−12.2835	+	3.04633i	−0.695414	+	0.172465i
$313$	26.7152			1.51003			0.755017	−	0.655705i	$-0.227629\pi$
$313$	26.7152			1.51003			0.755017	+	0.655705i	$0.227629\pi$
$314$	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	0.682516	−	0.730871i	$-0.260886\pi$
$331$	−5.30692	−	9.19185i	−0.291695	−	0.505230i	−0.974211	+	0.225641i	$0.927552\pi$
$332$	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	0.996874	−	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	$-0.692108\pi$
$349$	8.01922	−	13.8897i	0.429259	−	0.743498i	0.996808	+	0.0798418i	$0.0254415\pi$
$350$		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	$-0.800721\pi$
$353$	1.92156	−	3.32823i	0.102274	−	0.177144i	0.912621	+	0.408806i	$0.134055\pi$
$354$	−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	$-0.959025\pi$
$367$	−7.36961	+	12.7645i	−0.384690	+	0.666303i	0.607036	+	0.794674i	$0.292358\pi$
$368$	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	0.648762	−	0.760991i	$-0.275287\pi$
$373$	−6.46330	−	11.1948i	−0.334657	−	0.579643i	−0.983419	+	0.181349i	$0.941954\pi$
$374$	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	−0.282856	−	0.959162i	$-0.591282\pi$
$379$	13.4179	−	23.2405i	0.689231	−	1.19378i	0.972087	−	0.234621i	$-0.0753848\pi$
$380$	4.20561	−	7.28433i	0.215743	−	0.373678i
$381$	3.39861	+	5.88657i	0.174116	+	0.301578i
$382$	−45.5919			−2.33269
$383$	−1.45391	−	2.51825i	−0.0742914	−	0.128677i	0.826487	−	0.562957i	$-0.190336\pi$
$383$	−1.45391	−	2.51825i	−0.0742914	−	0.128677i	−0.900778	+	0.434280i	$0.857003\pi$
$384$	−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	−0.992094	−	0.125500i	$-0.959946\pi$
$397$	−12.0492	−	20.8699i	−0.604733	−	1.04743i	0.387360	−	0.921928i	$-0.373387\pi$
$398$	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	$0.181335\pi$
$402$	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	−0.986588	−	0.163232i	$-0.947808\pi$
$409$	−12.8351	−	22.2311i	−0.634657	−	1.09926i	0.351931	−	0.936026i	$-0.385525\pi$
$410$	−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	0.344271	+	0.938870i	$0.388126\pi$
$419$	−13.1199	+	22.7244i	−0.640950	+	1.11016i	−0.985221	+	0.171288i	$0.945207\pi$
$420$		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	−0.443592	−	0.896229i	$-0.646296\pi$
$431$	11.5088	−	19.9339i	0.554361	−	0.960182i	0.997953	−	0.0639528i	$-0.0203707\pi$
$432$	−7.15935	+	12.4004i	−0.344455	+	0.596613i
$433$	−12.9304	−	22.3961i	−0.621394	−	1.07629i	−0.989226	−	0.146394i	$-0.953233\pi$
$433$	−12.9304	−	22.3961i	−0.621394	−	1.07629i	0.367832	−	0.929892i	$-0.380100\pi$
$434$		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	0.0285691	+	0.999592i	$0.490905\pi$
$439$	−17.8385	+	30.8973i	−0.851387	+	1.47465i	−0.879956	+	0.475054i	$0.842428\pi$
$440$	−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	0.959426	−	0.281961i	$-0.0909847\pi$
$449$	4.99075	+	8.64423i	0.235528	+	0.407946i	−0.723898	+	0.689907i	$0.757651\pi$
$450$	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	−0.745000	−	0.667064i	$-0.767551\pi$
$457$	4.38656	−	7.59774i	0.205194	−	0.355407i	0.950195	+	0.311657i	$0.100884\pi$
$458$	−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	$-0.115407\pi$
$461$	3.44272	+	5.96296i	0.160343	+	0.277723i	−0.774649	+	0.632392i	$0.782073\pi$
$462$		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	$-0.267743\pi$
$467$	28.8113			1.33323			0.666613	+	0.745404i	$0.267743\pi$
$468$	−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	0.435640	+	0.900121i	$0.356522\pi$
$479$	−12.2936	+	21.2931i	−0.561707	+	0.972906i	−0.997348	+	0.0727849i	$0.976811\pi$
$480$	−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	0.893703	−	0.448660i	$-0.148099\pi$
$487$	1.28658	+	2.22842i	0.0583004	+	0.100979i	−0.835402	+	0.549639i	$0.814765\pi$
$488$	−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	−0.979810	−	0.199929i	$-0.935929\pi$
$491$	−7.01897	+	12.1572i	−0.316762	+	0.548647i	0.663049	+	0.748576i	$0.269262\pi$
$492$	−18.4929	+	32.0306i	−0.833723	+	1.44405i
$493$	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	$-0.225746\pi$
$503$	−4.13877	−	7.16856i	−0.184539	−	0.319630i	−0.943421	+	0.331597i	$0.892412\pi$
$504$		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	$-0.834506\pi$
$509$	−0.0831091	+	0.143949i	−0.00368375	+	0.00638044i	0.864178	+	0.503187i	$0.167839\pi$
$510$	−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	$-0.450562\pi$
$521$	7.06180			0.309383			0.154691	+	0.987963i	$0.450562\pi$
$522$	13.1355	−	22.7514i	0.574926	−	0.995802i
$523$	11.6956	−	20.2574i	0.511414	−	0.885795i	−0.488499	−	0.872565i	$-0.662455\pi$
$523$	11.6956	−	20.2574i	0.511414	−	0.885795i	0.999912	−	0.0132299i	$-0.00421135\pi$
$524$	−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	−0.933010	−	0.359851i	$-0.882827\pi$
$557$	−3.65494	+	6.33053i	−0.154865	+	0.268233i	0.778145	+	0.628085i	$0.216161\pi$
$558$	−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	0.758741	+	0.651392i	$0.225815\pi$
$563$	22.3868	+	38.7751i	0.943493	+	1.63418i	0.184751	+	0.982785i	$0.440852\pi$
$564$	−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	0.0525679	−	0.998617i	$-0.483259\pi$
$569$	21.2563	−	36.8171i	0.891112	−	1.54345i	0.838544	−	0.544834i	$-0.183407\pi$
$570$	−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	$-0.350613\pi$
$577$	21.7280			0.904550			0.452275	+	0.891879i	$0.350613\pi$
$578$	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	$-0.694422\pi$
$587$	10.2408	−	17.7376i	0.422683	−	0.732108i	0.996201	+	0.0870851i	$0.0277552\pi$
$588$		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	$-0.463065\pi$
$593$	5.63861			0.231550			0.115775	+	0.993275i	$0.463065\pi$
$594$	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	$-0.721827\pi$
$601$	8.41334	−	14.5723i	0.343187	−	0.594418i	0.985023	+	0.172425i	$0.0551602\pi$
$602$		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	$-0.0157402\pi$
$607$	11.2490	+	19.4838i	0.456582	+	0.790823i	−0.542196	+	0.840252i	$0.682407\pi$
$608$	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	0.444108	+	0.895973i	$0.353521\pi$
$613$	−13.7135	+	23.7524i	−0.553882	+	0.959351i	−0.997990	+	0.0633780i	$0.979813\pi$
$614$	8.97028	−	15.5370i	0.362011	−	0.627022i
$615$	1.61324	+	2.79421i	0.0650521	+	0.112673i
$616$		0			0
$617$	−5.31896	−	9.21271i	−0.214133	−	0.370890i	0.738871	−	0.673847i	$-0.235359\pi$
$617$	−5.31896	−	9.21271i	−0.214133	−	0.370890i	−0.953004	+	0.302957i	$0.902026\pi$
$618$	−16.1449	−	27.9637i	−0.649442	−	1.12487i
$619$	45.4677			1.82750			0.913751	−	0.406274i	$-0.133172\pi$
$619$	45.4677			1.82750			0.913751	+	0.406274i	$0.133172\pi$
$620$	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	−0.994345	−	0.106202i	$-0.966131\pi$
$631$	−14.7992	−	25.6329i	−0.589146	−	1.02043i	0.405199	−	0.914229i	$-0.367202\pi$
$632$	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	0.889387	+	0.457155i	$0.151131\pi$
$641$	21.2823	+	36.8621i	0.840601	+	1.45596i	−0.0487858	+	0.998809i	$0.515535\pi$
$642$	−11.7016			−0.461827
$643$	10.9980	+	19.0492i	0.433721	+	0.751226i	0.997190	−	0.0749106i	$-0.0238671\pi$
$643$	10.9980	+	19.0492i	0.433721	+	0.751226i	−0.563470	+	0.826137i	$0.690534\pi$
$644$		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	−0.289533	−	0.957168i	$-0.593500\pi$
$647$	17.4026	−	30.1421i	0.684166	−	1.18501i	0.973698	−	0.227841i	$-0.0731668\pi$
$648$	−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	0.404870	−	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
$655$	−0.0657402			−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	0.973134	−	0.230240i	$-0.0739511\pi$
$659$	7.37203	+	12.7687i	0.287173	+	0.497399i	−0.685960	+	0.727639i	$0.740618\pi$
$660$	1.22537	−	2.12241i	0.0476976	−	0.0826147i
$661$	−9.06227	+	15.6963i	−0.352481	+	0.610516i	−0.986684	−	0.162651i	$-0.947995\pi$
$661$	−9.06227	+	15.6963i	−0.352481	+	0.610516i	0.634202	+	0.773167i	$0.281329\pi$
$662$	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	−0.994099	−	0.108481i	$-0.965401\pi$
$673$	−10.4574	+	18.1127i	−0.403102	+	0.698193i	0.590997	+	0.806674i	$0.298735\pi$
$674$	−8.21547	+	14.2296i	−0.316448	+	0.548104i
$675$	−19.9904			−0.769432
$676$	44.9983	−	23.7821i	1.73071	−	0.914698i
$677$	38.2179			1.46883			0.734416	−	0.678700i	$-0.237456\pi$
$677$	38.2179			1.46883			0.734416	+	0.678700i	$0.237456\pi$
$678$	−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	0.998735	−	0.0502792i	$-0.0160111\pi$
$683$	11.9126	+	20.6333i	0.455825	+	0.789511i	−0.542911	+	0.839790i	$0.682678\pi$
$684$	−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	$-0.951951\pi$
$691$	−9.57063	+	16.5768i	−0.364084	+	0.630612i	0.624545	+	0.780989i	$0.285285\pi$
$692$	−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	0.802245	−	0.596995i	$-0.203639\pi$
$709$	−3.08583	−	5.34481i	−0.115891	−	0.200729i	−0.918135	+	0.396267i	$0.870306\pi$
$710$	−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	$-0.150507\pi$
$719$	1.36066	+	2.35674i	0.0507442	+	0.0878915i	−0.839538	+	0.543302i	$0.817174\pi$
$720$	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	$-0.443801\pi$
$727$	9.47153			0.351280			0.175640	+	0.984455i	$0.443801\pi$
$728$		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	$-0.520572\pi$
$733$	−3.49707			−0.129167			−0.0645836	+	0.997912i	$0.520572\pi$
$734$	−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	0.405221	+	0.914219i	$0.367195\pi$
$739$	−16.0151	+	27.7390i	−0.589126	+	1.02040i	−0.994347	+	0.106178i	$0.966139\pi$
$740$	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	0.344798	+	0.938677i	$0.387947\pi$
$743$	−17.4593	+	30.2404i	−0.640519	+	1.10941i	−0.985317	+	0.170734i	$0.945386\pi$
$744$	3.46672	−	6.00453i	0.127096	−	0.220137i
$745$	2.71670	+	4.70547i	0.0995324	+	0.172395i
$746$	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	−0.999963	−	0.00855684i	$-0.997276\pi$
$751$	−13.4986	+	23.3803i	−0.492571	+	0.853158i	0.507392	+	0.861715i	$0.330610\pi$
$752$	−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	0.222965	−	0.974826i	$-0.428426\pi$
$757$	26.2950	−	45.5442i	0.955707	−	1.65533i	0.732742	−	0.680507i	$-0.238240\pi$
$758$	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	$-0.0854284\pi$
$761$	6.96431	+	12.0625i	0.252456	+	0.437267i	−0.711745	+	0.702437i	$0.752095\pi$
$762$	−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	$-0.753344\pi$
$769$	6.89545	−	11.9433i	0.248656	−	0.430685i	0.963153	+	0.268953i	$0.0866777\pi$
$770$		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	0.816913	+	0.576760i	$0.195683\pi$
$773$	25.2435	+	43.7230i	0.907946	+	1.57261i	0.0910326	+	0.995848i	$0.470983\pi$
$774$	−24.8652	−	43.0678i	−0.893762	−	1.54804i
$775$	−9.64620			−0.346502
$776$	23.9337	+	41.4544i	0.859170	+	1.48813i
$777$		0

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)

\(f(q)\)	\(=\)	\(q+(-1.21605 + 2.10626i) q^{2} +(0.376796 - 0.652630i) q^{3} +(-1.95755 - 3.39058i) q^{4} -0.341537 q^{5} +(0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 + 2.10626i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 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

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