LMFDB - Embedded newform 637.2.h.l.471.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.2
Root			$1.16700 + 2.02131i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.l.165.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90556 q^{2} +(0.214224 - 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})$	\(q-1.90556 q^{2} +(0.214224 - 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +(1.40357 - 2.43105i) q^{10} +(2.19681 - 3.80498i) q^{11} +(0.349433 - 0.605236i) q^{12} +(-2.69752 - 2.39236i) q^{13} +(0.315580 + 0.546600i) q^{15} -4.60164 q^{16} +1.20271 q^{17} +(-2.68344 - 4.64786i) q^{18} +(1.62105 + 2.80773i) q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} -4.43710 q^{23} +(0.150567 - 0.260790i) q^{24} +(1.41494 + 2.45075i) q^{25} +(5.14029 + 4.55878i) q^{26} +2.49204 q^{27} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 - 1.04158i) q^{30} +(2.62272 + 4.54268i) q^{31} +7.36300 q^{32} +(-0.941217 - 1.63024i) q^{33} -2.29184 q^{34} +(2.29702 + 3.97856i) q^{36} +7.05055 q^{37} +(-3.08900 - 5.35031i) q^{38} +(-1.46555 + 0.488407i) q^{39} +(-0.517694 + 0.896672i) q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} -4.14897 q^{45} +8.45516 q^{46} +(5.84178 - 10.1183i) q^{47} +(-0.985780 + 1.70742i) q^{48} +(-2.69626 - 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(-4.40009 - 3.90231i) q^{52} +(0.0708929 + 0.122790i) q^{53} -4.74873 q^{54} +(3.23618 + 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} +5.34354 q^{59} +(0.514760 + 0.891591i) q^{60} +(5.77287 + 9.99891i) q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(5.03899 - 1.67929i) q^{65} +(1.79355 + 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} +1.96181 q^{68} +(-0.950533 + 1.64637i) q^{69} +(4.98486 - 8.63403i) q^{71} +(0.989763 + 1.71432i) q^{72} +(7.62080 + 13.1996i) q^{73} -13.4352 q^{74} +1.21246 q^{75} +(2.64418 + 4.57986i) q^{76} +(2.79269 - 0.930689i) q^{78} +(-0.387251 + 0.670738i) q^{79} +(3.38941 - 5.87062i) q^{80} +(-3.69080 + 6.39265i) q^{81} +(-4.92006 - 8.52179i) q^{82} +16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} +(0.0216761 - 0.0375441i) q^{86} -0.0717913 q^{87} +(1.54402 - 2.67433i) q^{88} -6.55760 q^{89} +7.90611 q^{90} -7.23762 q^{92} +2.24739 q^{93} +(-11.1319 + 19.2809i) q^{94} -4.77602 q^{95} +(1.57733 - 2.73202i) q^{96} +(1.74583 - 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.90556			−1.34743			−0.673717	−	0.738989i	$-0.735303\pi$
$2$	−1.90556			−1.34743			−0.673717	+	0.738989i	$0.735303\pi$
$3$	0.214224	−	0.371047i	0.123682	−	0.214224i	−0.797535	−	0.603273i	$-0.793863\pi$
$3$	0.214224	−	0.371047i	0.123682	−	0.214224i	0.921217	+	0.389049i	$0.127196\pi$
$4$	1.63116			0.815580
$5$	−0.736565	+	1.27577i	−0.329402	+	0.570541i	−0.982393	−	0.186825i	$-0.940180\pi$
$5$	−0.736565	+	1.27577i	−0.329402	+	0.570541i	0.652991	+	0.757365i	$0.273514\pi$
$6$	−0.408216	+	0.707051i	−0.166654	+	0.288653i
$7$		0			0
$7$		0			0
$8$	0.702849			0.248495
$9$	1.40822	+	2.43910i	0.469405	+	0.813034i
$10$	1.40357	−	2.43105i	0.443847	−	0.768766i
$11$	2.19681	−	3.80498i	0.662362	−	1.14725i	−0.317631	−	0.948214i	$-0.602887\pi$
$11$	2.19681	−	3.80498i	0.662362	−	1.14725i	0.979993	−	0.199031i	$-0.0637794\pi$
$12$	0.349433	−	0.605236i	0.100873	−	0.174717i
$13$	−2.69752	−	2.39236i	−0.748158	−	0.663520i
$13$	−2.69752	−	2.39236i	−0.748158	−	0.663520i
$14$		0			0
$15$	0.315580	+	0.546600i	0.0814823	+	0.141131i
$16$	−4.60164			−1.15041
$17$	1.20271			0.291700			0.145850	−	0.989307i	$-0.453408\pi$
$17$	1.20271			0.291700			0.145850	+	0.989307i	$0.453408\pi$
$18$	−2.68344	−	4.64786i	−0.632493	−	1.09551i
$19$	1.62105	+	2.80773i	0.371893	+	0.644138i	0.989857	−	0.142068i	$-0.0453753\pi$
$19$	1.62105	+	2.80773i	0.371893	+	0.644138i	−0.617963	+	0.786207i	$0.712042\pi$
$20$	−1.20145	+	2.08098i	−0.268653	+	0.465321i
$21$		0			0
$22$	−4.18615	+	7.25062i	−0.892490	+	1.54584i
$23$	−4.43710			−0.925200			−0.462600	−	0.886567i	$-0.653083\pi$
$23$	−4.43710			−0.925200			−0.462600	+	0.886567i	$0.653083\pi$
$24$	0.150567	−	0.260790i	0.0307343	−	0.0532334i
$25$	1.41494	+	2.45075i	0.282989	+	0.490151i
$26$	5.14029	+	4.55878i	1.00809	+	0.894050i
$27$	2.49204			0.479593
$28$		0			0
$29$	−0.0837807	−	0.145112i	−0.0155577	−	0.0269467i	0.858142	−	0.513413i	$-0.171619\pi$
$29$	−0.0837807	−	0.145112i	−0.0155577	−	0.0269467i	−0.873699	+	0.486466i	$0.838286\pi$
$30$	−0.601356	−	1.04158i	−0.109792	−	0.190165i
$31$	2.62272	+	4.54268i	0.471054	+	0.815889i	0.999452	−	0.0331076i	$-0.0105404\pi$
$31$	2.62272	+	4.54268i	0.471054	+	0.815889i	−0.528398	+	0.848997i	$0.677207\pi$
$32$	7.36300			1.30161
$33$	−0.941217	−	1.63024i	−0.163845	−	0.283788i
$34$	−2.29184			−0.393047
$35$		0			0
$36$	2.29702	+	3.97856i	0.382837	+	0.663094i
$37$	7.05055			1.15910			0.579552	−	0.814936i	$-0.303228\pi$
$37$	7.05055			1.15910			0.579552	+	0.814936i	$0.303228\pi$
$38$	−3.08900	−	5.35031i	−0.501102	−	0.867934i
$39$	−1.46555	+	0.488407i	−0.234676	+	0.0782077i
$40$	−0.517694	+	0.896672i	−0.0818546	+	0.141776i
$41$	2.58195	+	4.47206i	0.403233	+	0.698419i	0.994114	−	0.108339i	$-0.0345533\pi$
$41$	2.58195	+	4.47206i	0.403233	+	0.698419i	−0.590881	+	0.806758i	$0.701220\pi$
$42$		0			0
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	−0.866891	−	0.498497i	$-0.833886\pi$
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	0.865157	+	0.501502i	$0.167219\pi$
$44$	3.58334	−	6.20653i	0.540209	−	0.935670i
$45$	−4.14897			−0.618492
$46$	8.45516			1.24665
$47$	5.84178	−	10.1183i	0.852111	−	1.47590i	−0.0271891	−	0.999630i	$-0.508656\pi$
$47$	5.84178	−	10.1183i	0.852111	−	1.47590i	0.879300	−	0.476269i	$-0.158011\pi$
$48$	−0.985780	+	1.70742i	−0.142285	+	0.246445i
$49$		0			0
$50$	−2.69626	−	4.67006i	−0.381309	−	0.660446i
$51$	0.257649	−	0.446262i	0.0360781	−	0.0624892i
$52$	−4.40009	−	3.90231i	−0.610183	−	0.541154i
$53$	0.0708929	+	0.122790i	0.00973788	+	0.0168665i	0.870853	−	0.491543i	$-0.163567\pi$
$53$	0.0708929	+	0.122790i	0.00973788	+	0.0168665i	−0.861115	+	0.508410i	$0.830234\pi$
$54$	−4.74873			−0.646220
$55$	3.23618	+	5.60523i	0.436367	+	0.755809i
$56$		0			0
$57$	1.38907			0.183986
$58$	0.159649	+	0.276520i	0.0209630	+	0.0363089i
$59$	5.34354			0.695670			0.347835	−	0.937556i	$-0.386917\pi$
$59$	5.34354			0.695670			0.347835	+	0.937556i	$0.386917\pi$
$60$	0.514760	+	0.891591i	0.0664553	+	0.115104i
$61$	5.77287	+	9.99891i	0.739141	+	1.28023i	0.952883	+	0.303339i	$0.0981016\pi$
$61$	5.77287	+	9.99891i	0.739141	+	1.28023i	−0.213742	+	0.976890i	$0.568565\pi$
$62$	−4.99774	−	8.65635i	−0.634714	−	1.09936i
$63$		0			0
$64$	−4.82736			−0.603420
$65$	5.03899	−	1.67929i	0.625010	−	0.208290i
$66$	1.79355	+	3.10651i	0.220770	+	0.382385i
$67$	−2.06773	+	3.58141i	−0.252613	+	0.437539i	−0.964245	−	0.265014i	$-0.914623\pi$
$67$	−2.06773	+	3.58141i	−0.252613	+	0.437539i	0.711631	+	0.702553i	$0.247957\pi$
$68$	1.96181			0.237905
$69$	−0.950533	+	1.64637i	−0.114431	+	0.198200i
$70$		0			0
$71$	4.98486	−	8.63403i	0.591594	−	1.02467i	−0.402424	−	0.915453i	$-0.631832\pi$
$71$	4.98486	−	8.63403i	0.591594	−	1.02467i	0.994018	−	0.109217i	$-0.0348344\pi$
$72$	0.989763	+	1.71432i	0.116645	+	0.202035i
$73$	7.62080	+	13.1996i	0.891947	+	1.54490i	0.837539	+	0.546378i	$0.183994\pi$
$73$	7.62080	+	13.1996i	0.891947	+	1.54490i	0.0544080	+	0.998519i	$0.482673\pi$
$74$	−13.4352			−1.56182
$75$	1.21246			0.140003
$76$	2.64418	+	4.57986i	0.303309	+	0.525346i
$77$		0			0
$78$	2.79269	−	0.930689i	0.316210	−	0.105380i
$79$	−0.387251	+	0.670738i	−0.0435691	+	0.0754639i	−0.886988	−	0.461793i	$-0.847206\pi$
$79$	−0.387251	+	0.670738i	−0.0435691	+	0.0754639i	0.843418	+	0.537257i	$0.180540\pi$
$80$	3.38941	−	5.87062i	0.378947	−	0.656356i
$81$	−3.69080	+	6.39265i	−0.410088	+	0.710294i
$82$	−4.92006	−	8.52179i	−0.543329	−	0.941074i
$83$	16.0186			1.75827			0.879136	−	0.476571i	$-0.158121\pi$
$83$	16.0186			1.75827			0.879136	+	0.476571i	$0.158121\pi$
$84$		0			0
$85$	−0.885875	+	1.53438i	−0.0960866	+	0.166427i
$86$	0.0216761	−	0.0375441i	0.00233740	−	0.00404849i
$87$	−0.0717913			−0.00769683
$88$	1.54402	−	2.67433i	0.164593	−	0.285084i
$89$	−6.55760			−0.695104			−0.347552	−	0.937661i	$-0.612987\pi$
$89$	−6.55760			−0.695104			−0.347552	+	0.937661i	$0.612987\pi$
$90$	7.90611			0.833378
$91$		0			0
$92$	−7.23762			−0.754574
$93$	2.24739			0.233044
$94$	−11.1319	+	19.2809i	−1.14816	+	1.98868i
$95$	−4.77602			−0.490010
$96$	1.57733	−	2.73202i	0.160986	−	0.278835i
$97$	1.74583	−	3.02387i	0.177262	−	0.307027i	−0.763680	−	0.645595i	$-0.776609\pi$
$97$	1.74583	−	3.02387i	0.177262	−	0.307027i	0.940942	+	0.338568i	$0.109943\pi$
$98$		0			0
$99$	12.3743			1.24367
$100$	2.30800	+	3.99757i	0.230800	+	0.399757i
$101$	1.28890	−	2.23244i	0.128250	−	0.222136i	−0.794749	−	0.606939i	$-0.792397\pi$
$101$	1.28890	−	2.23244i	0.128250	−	0.222136i	0.922999	+	0.384803i	$0.125731\pi$
$102$	−0.490966	+	0.850379i	−0.0486129	+	0.0842000i
$103$	−8.43173	+	14.6042i	−0.830803	+	1.43899i	0.0665997	+	0.997780i	$0.478785\pi$
$103$	−8.43173	+	14.6042i	−0.830803	+	1.43899i	−0.897402	+	0.441213i	$0.854548\pi$
$104$	−1.89595	−	1.68146i	−0.185913	−	0.164881i
$105$		0			0
$106$	−0.135091	−	0.233984i	−0.0131212	−	0.0227265i
$107$	8.68265			0.839383			0.419692	−	0.907667i	$-0.362138\pi$
$107$	8.68265			0.839383			0.419692	+	0.907667i	$0.362138\pi$
$108$	4.06491			0.391146
$109$	6.02026	+	10.4274i	0.576637	+	0.998764i	0.995862	+	0.0908816i	$0.0289685\pi$
$109$	6.02026	+	10.4274i	0.576637	+	0.998764i	−0.419225	+	0.907882i	$0.637698\pi$
$110$	−6.16674	−	10.6811i	−0.587976	−	1.01840i
$111$	1.51040	−	2.61608i	0.143360	−	0.248307i
$112$		0			0
$113$	−4.68616	+	8.11667i	−0.440837	+	0.763552i	−0.997752	−	0.0670176i	$-0.978652\pi$
$113$	−4.68616	+	8.11667i	−0.440837	+	0.763552i	0.556915	+	0.830570i	$0.311985\pi$
$114$	−2.64695			−0.247910
$115$	3.26821	−	5.66071i	0.304763	−	0.527864i
$116$	−0.136660	−	0.236701i	−0.0126885	−	0.0219772i
$117$	2.03651	−	9.94849i	0.188275	−	0.919738i
$118$	−10.1824			−0.937369
$119$		0			0
$120$	0.221805	+	0.384177i	0.0202479	+	0.0350704i
$121$	−4.15192	−	7.19134i	−0.377448	−	0.653758i
$122$	−11.0006	−	19.0535i	−0.995944	−	1.72503i
$123$	2.21246			0.199491
$124$	4.27807	+	7.40983i	0.384182	+	0.665423i
$125$	−11.5344			−1.03167
$126$		0			0
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	−0.966764	−	0.255672i	$-0.917703\pi$
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	0.261964	−	0.965078i	$-0.415630\pi$
$128$	−5.52717			−0.488537
$129$	0.00487367	+	0.00844145i	0.000429103	+	0.000743228i
$130$	−9.60210	+	3.19998i	−0.842160	+	0.280657i
$131$	0.928725	−	1.60860i	0.0811430	−	0.140544i	−0.822598	−	0.568623i	$-0.807476\pi$
$131$	0.928725	−	1.60860i	0.0811430	−	0.140544i	0.903741	+	0.428079i	$0.140810\pi$
$132$	−1.53527	−	2.65917i	−0.133628	−	0.231451i
$133$		0			0
$134$	3.94018	−	6.82459i	0.340380	−	0.589555i
$135$	−1.83555	+	3.17926i	−0.157979	+	0.273627i
$136$	0.845324			0.0724859
$137$	−12.8002			−1.09360			−0.546798	−	0.837264i	$-0.684153\pi$
$137$	−12.8002			−1.09360			−0.546798	+	0.837264i	$0.684153\pi$
$138$	1.81130	−	3.13726i	0.154188	−	0.267061i
$139$	−0.169365	+	0.293348i	−0.0143653	+	0.0248815i	−0.873119	−	0.487508i	$-0.837906\pi$
$139$	−0.169365	+	0.293348i	−0.0143653	+	0.0248815i	0.858753	+	0.512389i	$0.171239\pi$
$140$		0			0
$141$	−2.50290	−	4.33514i	−0.210782	−	0.365085i
$142$	−9.49894	+	16.4527i	−0.797134	+	1.38068i
$143$	−15.0288	+	5.00848i	−1.25677	+	0.418830i
$144$	−6.48010	−	11.2239i	−0.540009	−	0.935322i
$145$	0.246840			0.0204989
$146$	−14.5219	−	25.1526i	−1.20184	−	2.08165i
$147$		0			0
$148$	11.5006			0.945341
$149$	−1.96158	−	3.39756i	−0.160699	−	0.278339i	0.774421	−	0.632671i	$-0.218041\pi$
$149$	−1.96158	−	3.39756i	−0.160699	−	0.278339i	−0.935120	+	0.354332i	$0.884708\pi$
$150$	−2.31041			−0.188644
$151$	1.05939	+	1.83492i	0.0862122	+	0.149324i	0.905907	−	0.423476i	$-0.139190\pi$
$151$	1.05939	+	1.83492i	0.0862122	+	0.149324i	−0.819695	+	0.572800i	$0.805857\pi$
$152$	1.13935	+	1.97341i	0.0924135	+	0.160065i
$153$	1.69368	+	2.93354i	0.136926	+	0.237162i
$154$		0			0
$155$	−7.72721			−0.620664
$156$	−2.39054	+	0.796669i	−0.191397	+	0.0637846i
$157$	−11.0564	−	19.1502i	−0.882397	−	1.52836i	−0.848668	−	0.528925i	$-0.822595\pi$
$157$	−11.0564	−	19.1502i	−0.882397	−	1.52836i	−0.0337285	−	0.999431i	$-0.510738\pi$
$158$	0.737929	−	1.27813i	0.0587065	−	0.101683i
$159$	0.0607478			0.00481761
$160$	−5.42333	+	9.39348i	−0.428752	+	0.742620i
$161$		0			0
$162$	7.03303	−	12.1816i	0.552567	−	0.957074i
$163$	−1.92607	−	3.33605i	−0.150861	−	0.261299i	0.780683	−	0.624927i	$-0.214871\pi$
$163$	−1.92607	−	3.33605i	−0.150861	−	0.261299i	−0.931544	+	0.363628i	$0.881538\pi$
$164$	4.21157	+	7.29465i	0.328868	+	0.569616i
$165$	2.77307			0.215883
$166$	−30.5244			−2.36916
$167$	1.06947	+	1.85238i	0.0827582	+	0.143341i	0.904434	−	0.426614i	$-0.140294\pi$
$167$	1.06947	+	1.85238i	0.0827582	+	0.143341i	−0.821676	+	0.569956i	$0.806960\pi$
$168$		0			0
$169$	1.55326	+	12.9069i	0.119482	+	0.992836i
$170$	1.68809	−	2.92385i	0.129470	−	0.224249i
$171$	−4.56557	+	7.90779i	−0.349138	+	0.604724i
$172$	−0.0185547	+	0.0321378i	−0.00141479	+	0.00245048i
$173$	−8.30664	−	14.3875i	−0.631542	−	1.09386i	−0.987237	−	0.159260i	$-0.949089\pi$
$173$	−8.30664	−	14.3875i	−0.631542	−	1.09386i	0.355695	−	0.934602i	$-0.384244\pi$
$174$	0.136803			0.0103710
$175$		0			0
$176$	−10.1089	+	17.5091i	−0.761988	+	1.31980i
$177$	1.14471	−	1.98270i	0.0860419	−	0.149029i
$178$	12.4959			0.936607
$179$	0.269748	−	0.467217i	0.0201619	−	0.0349214i	−0.855768	−	0.517359i	$-0.826915\pi$
$179$	0.269748	−	0.467217i	0.0201619	−	0.0349214i	0.875930	+	0.482438i	$0.160248\pi$
$180$	−6.76763			−0.504430
$181$	−2.77164			−0.206014			−0.103007	−	0.994681i	$-0.532846\pi$
$181$	−2.77164			−0.206014			−0.103007	+	0.994681i	$0.532846\pi$
$182$		0			0
$183$	4.94675			0.365674
$184$	−3.11861			−0.229907
$185$	−5.19319	+	8.99486i	−0.381811	+	0.661316i
$186$	−4.28254			−0.314011
$187$	2.64213	−	4.57629i	0.193211	−	0.334652i
$188$	9.52887	−	16.5045i	0.694964	−	1.20371i
$189$		0			0
$190$	9.10100			0.660256
$191$	10.1204	+	17.5290i	0.732284	+	1.26835i	0.955905	+	0.293677i	$0.0948790\pi$
$191$	10.1204	+	17.5290i	0.732284	+	1.26835i	−0.223621	+	0.974676i	$0.571788\pi$
$192$	−1.03414	+	1.79118i	−0.0746323	+	0.129267i
$193$	8.18856	−	14.1830i	0.589425	−	1.02091i	−0.404882	−	0.914369i	$-0.632688\pi$
$193$	8.18856	−	14.1830i	0.589425	−	1.02091i	0.994308	−	0.106546i	$-0.0339791\pi$
$194$	−3.32678	+	5.76216i	−0.238849	+	0.413699i
$195$	0.456378	−	2.22944i	0.0326819	−	0.159654i
$196$		0			0
$197$	−9.86676	−	17.0897i	−0.702977	−	1.21759i	−0.967417	−	0.253190i	$-0.918520\pi$
$197$	−9.86676	−	17.0897i	−0.702977	−	1.21759i	0.264439	−	0.964402i	$-0.414813\pi$
$198$	−23.5800			−1.67576
$199$	14.1175			1.00076			0.500380	−	0.865806i	$-0.333194\pi$
$199$	14.1175			1.00076			0.500380	+	0.865806i	$0.333194\pi$
$200$	0.994491	+	1.72251i	0.0703212	+	0.121800i
$201$	0.885913	+	1.53445i	0.0624875	+	0.108232i
$202$	−2.45607	+	4.25404i	−0.172809	+	0.299313i
$203$		0			0
$204$	0.420267	−	0.727924i	0.0294246	−	0.0509649i
$205$	−7.60709			−0.531302
$206$	16.0672	−	27.8291i	1.11945	−	1.93895i
$207$	−6.24840	−	10.8225i	−0.434294	−	0.752219i
$208$	12.4130	+	11.0088i	0.860688	+	0.763320i
$209$	14.2445			0.985313
$210$		0			0
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	0.934597	−	0.355709i	$-0.115761\pi$
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	−0.775352	+	0.631530i	$0.782427\pi$
$212$	0.115638	+	0.200290i	0.00794202	+	0.0137560i
$213$	−2.13575	−	3.69923i	−0.146339	−	0.253467i
$214$	−16.5453			−1.13101
$215$	−0.0167571	−	0.0290242i	−0.00114283	−	0.00197943i
$216$	1.75152			0.119176
$217$		0			0
$218$	−11.4720	−	19.8700i	−0.776980	−	1.34577i
$219$	6.53022			0.441272
$220$	5.27873	+	9.14303i	0.355892	+	0.616423i
$221$	−3.24434	−	2.87731i	−0.218238	−	0.193549i
$222$	−2.87815	+	4.98510i	−0.193169	+	0.334578i
$223$	−10.6761	−	18.4916i	−0.714926	−	1.23829i	−0.962988	−	0.269545i	$-0.913127\pi$
$223$	−10.6761	−	18.4916i	−0.714926	−	1.23829i	0.248061	−	0.968744i	$-0.420207\pi$
$224$		0			0
$225$	−3.98509	+	6.90239i	−0.265673	+	0.460159i
$226$	8.92976	−	15.4668i	0.593999	−	1.02884i
$227$	10.4490			0.693526			0.346763	−	0.937953i	$-0.387281\pi$
$227$	10.4490			0.693526			0.346763	+	0.937953i	$0.387281\pi$
$228$	2.26579			0.150056
$229$	7.22901	−	12.5210i	0.477706	−	0.827412i	−0.521967	−	0.852966i	$-0.674802\pi$
$229$	7.22901	−	12.5210i	0.477706	−	0.827412i	0.999673	+	0.0255538i	$0.00813493\pi$
$230$	−6.22778	+	10.7868i	−0.410648	+	0.711262i
$231$		0			0
$232$	−0.0588852	−	0.101992i	−0.00386600	−	0.00669611i
$233$	4.64413	−	8.04388i	0.304247	−	0.526972i	−0.672846	−	0.739783i	$-0.734928\pi$
$233$	4.64413	−	8.04388i	0.304247	−	0.526972i	0.977093	+	0.212811i	$0.0682617\pi$
$234$	−3.88068	+	18.9574i	−0.253688	+	1.23929i
$235$	8.60570	+	14.9055i	0.561374	+	0.972328i
$236$	8.71616			0.567374
$237$	0.165917	+	0.287376i	0.0107774	+	0.0186671i
$238$		0			0
$239$	19.6332			1.26997			0.634983	−	0.772526i	$-0.281007\pi$
$239$	19.6332			1.26997			0.634983	+	0.772526i	$0.281007\pi$
$240$	−1.45218	−	2.51525i	−0.0937380	−	0.162359i
$241$	−7.31105			−0.470946			−0.235473	−	0.971881i	$-0.575664\pi$
$241$	−7.31105			−0.470946			−0.235473	+	0.971881i	$0.575664\pi$
$242$	7.91174	+	13.7035i	0.508586	+	0.880897i
$243$	5.31937	+	9.21341i	0.341238	+	0.591041i
$244$	9.41648	+	16.3098i	0.602828	+	1.04413i
$245$		0			0
$246$	−4.21597			−0.268801
$247$	2.34429	−	11.4520i	0.149164	−	0.728676i
$248$	1.84337	+	3.19282i	0.117054	+	0.202744i
$249$	3.43157	−	5.94365i	0.217467	−	0.376664i
$250$	21.9796			1.39011
$251$	−5.93191	+	10.2744i	−0.374419	+	0.648512i	−0.990240	−	0.139374i	$-0.955491\pi$
$251$	−5.93191	+	10.2744i	−0.374419	+	0.648512i	0.615821	+	0.787886i	$0.288824\pi$
$252$		0			0
$253$	−9.74746	+	16.8831i	−0.612817	+	1.06143i
$254$	15.1353	+	26.2151i	0.949672	+	1.64488i
$255$	0.379551	+	0.657402i	0.0237684	+	0.0411681i
$256$	20.1871			1.26169
$257$	15.1722			0.946413			0.473206	−	0.880952i	$-0.343096\pi$
$257$	15.1722			0.946413			0.473206	+	0.880952i	$0.343096\pi$
$258$	−0.00928708	−	0.0160857i	−0.000578188	−	0.00100145i
$259$		0			0
$260$	8.21940	−	2.73919i	0.509745	−	0.169877i
$261$	0.235963	−	0.408699i	0.0146057	−	0.0252979i
$262$	−1.76974	+	3.06528i	−0.109335	+	0.189374i
$263$	−8.59820	+	14.8925i	−0.530187	+	0.918312i	0.469192	+	0.883096i	$0.344545\pi$
$263$	−8.59820	+	14.8925i	−0.530187	+	0.918312i	−0.999380	+	0.0352156i	$0.988788\pi$
$264$	−0.661533	−	1.14581i	−0.0407145	−	0.0705196i
$265$	−0.208869			−0.0128307
$266$		0			0
$267$	−1.40479	+	2.43317i	−0.0859719	+	0.148908i
$268$	−3.37279	+	5.84185i	−0.206026	+	0.356848i
$269$	−18.9220			−1.15370			−0.576849	−	0.816851i	$-0.695718\pi$
$269$	−18.9220			−1.15370			−0.576849	+	0.816851i	$0.695718\pi$
$270$	3.49774	−	6.05827i	0.212866	−	0.368695i
$271$	−32.1334			−1.95196			−0.975982	−	0.217853i	$-0.930095\pi$
$271$	−32.1334			−1.95196			−0.975982	+	0.217853i	$0.930095\pi$
$272$	−5.53444			−0.335575
$273$		0			0
$274$	24.3916			1.47355
$275$	12.4334			0.749764
$276$	−1.55047	+	2.68549i	−0.0933273	+	0.161648i
$277$	18.4054			1.10587			0.552936	−	0.833224i	$-0.313507\pi$
$277$	18.4054			1.10587			0.552936	+	0.833224i	$0.313507\pi$
$278$	0.322734	−	0.558992i	0.0193563	−	0.0335261i
$279$	−7.38671	+	12.7942i	−0.442231	+	0.765966i
$280$		0			0
$281$	−14.2252			−0.848603			−0.424302	−	0.905521i	$-0.639480\pi$
$281$	−14.2252			−0.848603			−0.424302	+	0.905521i	$0.639480\pi$
$282$	4.76942	+	8.26087i	0.284015	+	0.491928i
$283$	−5.71446	+	9.89773i	−0.339689	+	0.588359i	−0.984374	−	0.176089i	$-0.943655\pi$
$283$	−5.71446	+	9.89773i	−0.339689	+	0.588359i	0.644685	+	0.764448i	$0.276989\pi$
$284$	8.13109	−	14.0835i	0.482492	−	0.835700i
$285$	−1.02314	+	1.77213i	−0.0606055	+	0.104972i
$286$	28.6383	−	9.54396i	1.69342	−	0.564346i
$287$		0			0
$288$	10.3687	+	17.9591i	0.610981	+	1.05825i
$289$	−15.5535			−0.914911
$290$	−0.470368			−0.0276210
$291$	−0.747997	−	1.29557i	−0.0438483	−	0.0759476i
$292$	12.4307	+	21.5307i	0.727453	+	1.25999i
$293$	−6.60231	+	11.4355i	−0.385711	+	0.668071i	−0.991868	−	0.127274i	$-0.959377\pi$
$293$	−6.60231	+	11.4355i	−0.385711	+	0.668071i	0.606156	+	0.795345i	$0.292711\pi$
$294$		0			0
$295$	−3.93586	+	6.81712i	−0.229155	+	0.396908i
$296$	4.95547			0.288031
$297$	5.47452	−	9.48215i	0.317664	−	0.550210i
$298$	3.73791	+	6.47425i	0.216531	+	0.375043i
$299$	11.9692	+	10.6151i	0.692196	+	0.613889i
$300$	1.97771			0.114183
$301$		0			0
$302$	−2.01874	−	3.49656i	−0.116165	−	0.201204i
$303$	−0.552225	−	0.956482i	−0.0317245	−	0.0549484i
$304$	−7.45947	−	12.9202i	−0.427830	−	0.741023i
$305$	−17.0084			−0.973898
$306$	−3.22740	−	5.59003i	−0.184498	−	0.319561i
$307$	6.65903			0.380051			0.190026	−	0.981779i	$-0.439143\pi$
$307$	6.65903			0.380051			0.190026	+	0.981779i	$0.439143\pi$
$308$		0			0
$309$	3.61255	+	6.25713i	0.205511	+	0.355955i
$310$	14.7247			0.836304
$311$	−1.02298	−	1.77186i	−0.0580081	−	0.100473i	0.835563	−	0.549395i	$-0.185142\pi$
$311$	−1.02298	−	1.77186i	−0.0580081	−	0.100473i	−0.893571	+	0.448922i	$0.851808\pi$
$312$	−1.03006	+	0.343276i	−0.0583156	+	0.0194342i
$313$	4.70883	−	8.15594i	0.266159	−	0.461001i	−0.701708	−	0.712465i	$-0.747579\pi$
$313$	4.70883	−	8.15594i	0.266159	−	0.461001i	0.967867	+	0.251464i	$0.0809120\pi$
$314$	21.0686	+	36.4919i	1.18897	+	2.05936i
$315$		0			0
$316$	−0.631667	+	1.09408i	−0.0355341	+	0.0615468i
$317$	16.6856	−	28.9004i	0.937159	−	1.62321i	0.166421	−	0.986055i	$-0.446779\pi$
$317$	16.6856	−	28.9004i	0.937159	−	1.62321i	0.770738	−	0.637153i	$-0.219888\pi$
$318$	−0.115758			−0.00649141
$319$	−0.736200			−0.0412193
$320$	3.55567	−	6.15860i	0.198768	−	0.344276i
$321$	1.86003	−	3.22167i	0.103817	−	0.179816i
$322$		0			0
$323$	1.94965	+	3.37689i	0.108481	+	0.187895i
$324$	−6.02027	+	10.4274i	−0.334460	+	0.579301i
$325$	2.04624	−	9.99602i	0.113505	−	0.554479i
$326$	3.67024	+	6.35704i	0.203276	+	0.352084i
$327$	5.15873			0.285279
$328$	1.81472	+	3.14318i	0.100201	+	0.173553i
$329$		0			0
$330$	−5.28425			−0.290888
$331$	−9.53298	−	16.5116i	−0.523980	−	0.907560i	−0.999610	−	0.0279144i	$-0.991113\pi$
$331$	−9.53298	−	16.5116i	−0.523980	−	0.907560i	0.475631	−	0.879645i	$-0.342220\pi$
$332$	26.1289			1.43401
$333$	9.92870	+	17.1970i	0.544089	+	0.942390i
$334$	−2.03794	−	3.52982i	−0.111511	−	0.193143i
$335$	−3.04603	−	5.27588i	−0.166423	−	0.288252i
$336$		0			0
$337$	−31.2849			−1.70420			−0.852098	−	0.523382i	$-0.824670\pi$
$337$	−31.2849			−1.70420			−0.852098	+	0.523382i	$0.824670\pi$
$338$	−2.95983	−	24.5948i	−0.160994	−	1.33778i
$339$	2.00777	+	3.47757i	0.109047	+	0.188876i
$340$	−1.44500	+	2.50282i	−0.0783663	+	0.135734i
$341$	23.0464			1.24803
$342$	8.69996	−	15.0688i	0.470440	−	0.814826i
$343$		0			0
$344$	−0.00799504	+	0.0138478i	−0.000431064	+	0.000746624i
$345$	−1.40026	−	2.42532i	−0.0753874	−	0.130575i
$346$	15.8288	+	27.4163i	0.850961	+	1.47391i
$347$	11.6752			0.626757			0.313378	−	0.949628i	$-0.398539\pi$
$347$	11.6752			0.626757			0.313378	+	0.949628i	$0.398539\pi$
$348$	−0.117103			−0.00627738
$349$	11.9952	+	20.7763i	0.642089	+	1.11213i	0.984966	+	0.172750i	$0.0552652\pi$
$349$	11.9952	+	20.7763i	0.642089	+	1.11213i	−0.342877	+	0.939380i	$0.611401\pi$
$350$		0			0
$351$	−6.72233	−	5.96184i	−0.358811	−	0.318219i
$352$	16.1751	−	28.0161i	0.862135	−	1.49326i
$353$	6.39668	−	11.0794i	0.340461	−	0.589696i	−0.644057	−	0.764977i	$-0.722750\pi$
$353$	6.39668	−	11.0794i	0.340461	−	0.589696i	0.984518	+	0.175282i	$0.0560836\pi$
$354$	−2.18132	+	3.77816i	−0.115936	+	0.200807i
$355$	7.34334	+	12.7190i	0.389744	+	0.675057i
$356$	−10.6965			−0.566912
$357$		0			0
$358$	−0.514021	+	0.890310i	−0.0271668	+	0.0470544i
$359$	−6.16986	+	10.6865i	−0.325633	+	0.564012i	−0.981640	−	0.190742i	$-0.938911\pi$
$359$	−6.16986	+	10.6865i	−0.325633	+	0.564012i	0.656008	+	0.754754i	$0.272244\pi$
$360$	−2.91610			−0.153692
$361$	4.24442	−	7.35155i	0.223390	−	0.386924i
$362$	5.28152			0.277591
$363$	−3.55776			−0.186734
$364$		0			0
$365$	−22.4528			−1.17524
$366$	−9.42633			−0.492722
$367$	1.01538	−	1.75870i	0.0530026	−	0.0918032i	−0.838307	−	0.545199i	$-0.816454\pi$
$367$	1.01538	−	1.75870i	0.0530026	−	0.0918032i	0.891309	+	0.453396i	$0.149788\pi$
$368$	20.4179			1.06436
$369$	−7.27188	+	12.5953i	−0.378559	+	0.655684i
$370$	9.89593	−	17.1403i	0.514465	−	0.891079i
$371$		0			0
$372$	3.66586			0.190066
$373$	1.93700	+	3.35498i	0.100294	+	0.173714i	0.911806	−	0.410622i	$-0.134688\pi$
$373$	1.93700	+	3.35498i	0.100294	+	0.173714i	−0.811512	+	0.584336i	$0.801355\pi$
$374$	−5.03473	+	8.72040i	−0.260340	+	0.450921i
$375$	−2.47095	+	4.27981i	−0.127599	+	0.221009i
$376$	4.10588	−	7.11160i	0.211745	−	0.366753i
$377$	−0.121160	+	0.591877i	−0.00624007	+	0.0304832i
$378$		0			0
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	0.990200	−	0.139659i	$-0.0446006\pi$
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	−0.616048	+	0.787709i	$0.711267\pi$
$380$	−7.79045			−0.399642
$381$	−6.80606			−0.348685
$382$	−19.2850	−	33.4025i	−0.986705	−	1.70902i
$383$	−13.3909	−	23.1937i	−0.684243	−	1.18514i	−0.973674	−	0.227945i	$-0.926799\pi$
$383$	−13.3909	−	23.1937i	−0.684243	−	1.18514i	0.289430	−	0.957199i	$-0.406534\pi$
$384$	−1.18405	+	2.05084i	−0.0604234	+	0.104656i
$385$		0			0
$386$	−15.6038	+	27.0266i	−0.794212	+	1.37562i
$387$	−0.0640749			−0.00325711
$388$	2.84773	−	4.93241i	0.144571	−	0.250405i
$389$	−6.00738	−	10.4051i	−0.304586	−	0.527559i	0.672583	−	0.740022i	$-0.265185\pi$
$389$	−6.00738	−	10.4051i	−0.304586	−	0.527559i	−0.977169	+	0.212463i	$0.931852\pi$
$390$	−0.869656	+	4.24834i	−0.0440368	+	0.215123i
$391$	−5.33655			−0.269881
$392$		0			0
$393$	−0.397910	−	0.689200i	−0.0200719	−	0.0347655i
$394$	18.8017	+	32.5655i	0.947216	+	1.64063i
$395$	−0.570470	−	0.988084i	−0.0287035	−	0.0497159i
$396$	20.1845			1.01431
$397$	−0.828825	−	1.43557i	−0.0415975	−	0.0720491i	0.844477	−	0.535592i	$-0.179911\pi$
$397$	−0.828825	−	1.43557i	−0.0415975	−	0.0720491i	−0.886075	+	0.463543i	$0.846578\pi$
$398$	−26.9017			−1.34846
$399$		0			0
$400$	−6.51106	−	11.2775i	−0.325553	−	0.563874i
$401$	−20.4828			−1.02286			−0.511430	−	0.859325i	$-0.670884\pi$
$401$	−20.4828			−1.02286			−0.511430	+	0.859325i	$0.670884\pi$
$402$	−1.68816	−	2.92398i	−0.0841978	−	0.145835i
$403$	3.79287	−	18.5285i	0.188936	−	0.922968i
$404$	2.10240	−	3.64146i	0.104598	−	0.181169i
$405$	−5.43702	−	9.41720i	−0.270168	−	0.467944i
$406$		0			0
$407$	15.4887	−	26.8272i	0.767746	−	1.32978i
$408$	0.181089	−	0.313655i	0.00896522	−	0.0155282i
$409$	−14.8659			−0.735070			−0.367535	−	0.930010i	$-0.619798\pi$
$409$	−14.8659			−0.735070			−0.367535	+	0.930010i	$0.619798\pi$
$410$	14.4958			0.715895
$411$	−2.74211	+	4.74948i	−0.135258	+	0.234274i
$412$	−13.7535	+	23.8217i	−0.677586	+	1.17361i
$413$		0			0
$414$	11.9067	+	20.6230i	0.585182	+	1.01357i
$415$	−11.7988	+	20.4360i	−0.579178	+	1.00317i
$416$	−19.8619	−	17.6149i	−0.973808	−	0.863643i
$417$	0.0725639	+	0.125684i	0.00355347	+	0.00615479i
$418$	−27.1438			−1.32764
$419$	−11.8087	−	20.4533i	−0.576895	−	0.999211i	−0.995833	−	0.0911962i	$-0.970931\pi$
$419$	−11.8087	−	20.4533i	−0.576895	−	0.999211i	0.418938	−	0.908015i	$-0.362402\pi$
$420$		0			0
$421$	26.0822			1.27117			0.635585	−	0.772031i	$-0.280759\pi$
$421$	26.0822			1.27117			0.635585	+	0.772031i	$0.280759\pi$
$422$	−4.40788	−	7.63467i	−0.214572	−	0.371650i
$423$	32.9059			1.59994
$424$	0.0498269	+	0.0863028i	0.00241981	+	0.00419123i
$425$	1.70177	+	2.94755i	0.0825479	+	0.142977i
$426$	4.06980	+	7.04910i	0.197182	+	0.341530i
$427$		0			0
$428$	14.1628			0.684584
$429$	−1.36115	+	6.64932i	−0.0657169	+	0.321032i
$430$	0.0319317	+	0.0553074i	0.00153988	+	0.00266716i
$431$	6.65859	−	11.5330i	0.320733	−	0.555526i	−0.659906	−	0.751348i	$-0.729404\pi$
$431$	6.65859	−	11.5330i	0.320733	−	0.555526i	0.980640	+	0.195822i	$0.0627374\pi$
$432$	−11.4675			−0.551728
$433$	10.2110	−	17.6860i	0.490711	−	0.849937i	−0.509232	−	0.860629i	$-0.670070\pi$
$433$	10.2110	−	17.6860i	0.490711	−	0.849937i	0.999943	+	0.0106929i	$0.00340371\pi$
$434$		0			0
$435$	0.0528790	−	0.0915890i	0.00253535	−	0.00439136i
$436$	9.82001	+	17.0087i	0.470293	+	0.814571i
$437$	−7.19275	−	12.4582i	−0.344076	−	0.595957i
$438$	−12.4437			−0.594585
$439$	9.77074			0.466332			0.233166	−	0.972437i	$-0.425091\pi$
$439$	9.77074			0.466332			0.233166	+	0.972437i	$0.425091\pi$
$440$	2.27455	+	3.93963i	0.108435	+	0.187814i
$441$		0			0
$442$	6.18229	+	5.48290i	0.294061	+	0.260795i
$443$	−10.5819	+	18.3285i	−0.502763	+	0.870811i	0.497232	+	0.867618i	$0.334350\pi$
$443$	−10.5819	+	18.3285i	−0.502763	+	0.870811i	−0.999995	+	0.00319331i	$0.998984\pi$
$444$	2.46370	−	4.26725i	0.116922	−	0.202514i
$445$	4.83010	−	8.36597i	0.228968	−	0.396585i
$446$	20.3440	+	35.2368i	0.963317	+	1.66851i
$447$	−1.68087			−0.0795023
$448$		0			0
$449$	9.07320	−	15.7152i	0.428191	−	0.741648i	−0.568522	−	0.822668i	$-0.692484\pi$
$449$	9.07320	−	15.7152i	0.428191	−	0.741648i	0.996712	+	0.0810200i	$0.0258178\pi$
$450$	7.59384	−	13.1529i	0.357977	−	0.620034i
$451$	22.6882			1.06834
$452$	−7.64387	+	13.2396i	−0.359538	+	0.622737i
$453$	0.907789			0.0426517
$454$	−19.9112			−0.934480
$455$		0			0
$456$	0.976304			0.0457196
$457$	−18.0198			−0.842932			−0.421466	−	0.906844i	$-0.638484\pi$
$457$	−18.0198			−0.842932			−0.421466	+	0.906844i	$0.638484\pi$
$458$	−13.7753	+	23.8595i	−0.643678	+	1.11488i
$459$	2.99720			0.139897
$460$	5.33098	−	9.23352i	0.248558	−	0.430515i
$461$	−14.8873	+	25.7855i	−0.693370	+	1.20095i	0.277357	+	0.960767i	$0.410542\pi$
$461$	−14.8873	+	25.7855i	−0.693370	+	1.20095i	−0.970727	+	0.240185i	$0.922792\pi$
$462$		0			0
$463$	17.7067			0.822900			0.411450	−	0.911432i	$-0.365023\pi$
$463$	17.7067			0.822900			0.411450	+	0.911432i	$0.365023\pi$
$464$	0.385529	+	0.667755i	0.0178977	+	0.0309997i
$465$	−1.65535	+	2.86715i	−0.0767651	+	0.132961i
$466$	−8.84968	+	15.3281i	−0.409953	+	0.710060i
$467$	−2.91461	+	5.04825i	−0.134872	+	0.233605i	−0.925549	−	0.378629i	$-0.876396\pi$
$467$	−2.91461	+	5.04825i	−0.134872	+	0.233605i	0.790677	+	0.612234i	$0.209729\pi$
$468$	3.32186	−	16.2276i	0.153553	−	0.750120i
$469$		0			0
$470$	−16.3987	−	28.4033i	−0.756414	−	1.31015i
$471$	−9.47418			−0.436547
$472$	3.75570			0.172870
$473$	0.0499782	+	0.0865648i	0.00229800	+	0.00398025i
$474$	−0.316164	−	0.547612i	−0.0145219	−	0.0251527i
$475$	−4.58738	+	7.94557i	−0.210483	+	0.364568i
$476$		0			0
$477$	−0.199665	+	0.345830i	−0.00914203	+	0.0158345i
$478$	−37.4122			−1.71120
$479$	7.24565	−	12.5498i	0.331062	−	0.573417i	−0.651658	−	0.758513i	$-0.725926\pi$
$479$	7.24565	−	12.5498i	0.331062	−	0.573417i	0.982720	+	0.185096i	$0.0592596\pi$
$480$	2.32361	+	4.02461i	0.106058	+	0.183698i
$481$	−19.0190	−	16.8674i	−0.867193	−	0.769088i
$482$	13.9316			0.634569
$483$		0			0
$484$	−6.77245	−	11.7302i	−0.307839	−	0.533192i
$485$	2.57183	+	4.45455i	0.116781	+	0.202271i
$486$	−10.1364	−	17.5567i	−0.459795	−	0.796389i
$487$	−17.9601			−0.813851			−0.406926	−	0.913461i	$-0.633399\pi$
$487$	−17.9601			−0.813851			−0.406926	+	0.913461i	$0.633399\pi$
$488$	4.05746	+	7.02772i	0.183672	+	0.318130i
$489$	−1.65044			−0.0746354
$490$		0			0
$491$	18.1505	+	31.4375i	0.819119	+	1.41876i	0.906332	+	0.422566i	$0.138870\pi$
$491$	18.1505	+	31.4375i	0.819119	+	1.41876i	−0.0872134	+	0.996190i	$0.527796\pi$
$492$	3.60887			0.162701
$493$	−0.100764	−	0.174528i	−0.00453818	−	0.00786036i
$494$	−4.46719	+	21.8226i	−0.200988	+	0.981844i
$495$	−9.11449	+	15.7868i	−0.409666	+	0.709562i
$496$	−12.0688	−	20.9038i	−0.541905	−	0.938607i
$497$		0			0
$498$	−6.53906	+	11.3260i	−0.293022	+	0.507530i
$499$	−11.8538	+	20.5314i	−0.530649	+	0.919112i	0.468711	+	0.883352i	$0.344719\pi$
$499$	−11.8538	+	20.5314i	−0.530649	+	0.919112i	−0.999360	+	0.0357602i	$0.988615\pi$
$500$	−18.8145			−0.841410
$501$	0.916426			0.0409429
$502$	11.3036	−	19.5784i	0.504505	−	0.873828i
$503$	13.8876	−	24.0540i	0.619217	−	1.07252i	−0.370411	−	0.928868i	$-0.620783\pi$
$503$	13.8876	−	24.0540i	0.619217	−	1.07252i	0.989629	−	0.143648i	$-0.0458834\pi$
$504$		0			0
$505$	1.89871	+	3.28867i	0.0844916	+	0.146344i
$506$	18.5744	−	32.1717i	0.825731	−	1.43021i
$507$	5.12180	+	2.18863i	0.227467	+	0.0972003i
$508$	−12.9558	−	22.4401i	−0.574820	−	0.995618i
$509$	−8.70416			−0.385805			−0.192902	−	0.981218i	$-0.561790\pi$
$509$	−8.70416			−0.385805			−0.192902	+	0.981218i	$0.561790\pi$
$510$	−0.723257	−	1.25272i	−0.0320264	−	0.0554713i
$511$		0			0
$512$	−27.4134			−1.21151
$513$	4.03971	+	6.99698i	0.178357	+	0.308924i
$514$	−28.9114			−1.27523
$515$	−12.4210	−	21.5139i	−0.547336	−	0.948014i
$516$	0.00794974	+	0.0137693i	0.000349968	+	0.000606162i
$517$	−25.6665	−	44.4557i	−1.12881	−	1.95516i
$518$		0			0
$519$	−7.11792			−0.312442
$520$	3.54165	−	1.18028i	0.155312	−	0.0517589i
$521$	−4.28573	−	7.42310i	−0.187761	−	0.325212i	0.756742	−	0.653713i	$-0.226790\pi$
$521$	−4.28573	−	7.42310i	−0.187761	−	0.325212i	−0.944504	+	0.328501i	$0.893456\pi$
$522$	−0.449641	+	0.778801i	−0.0196803	+	0.0340872i
$523$	−29.9493			−1.30959			−0.654796	−	0.755806i	$-0.727245\pi$
$523$	−29.9493			−1.30959			−0.654796	+	0.755806i	$0.727245\pi$
$524$	1.51490	−	2.62388i	0.0661786	−	0.114625i
$525$		0			0
$526$	16.3844	−	28.3786i	0.714393	−	1.23736i
$527$	3.15437	+	5.46353i	0.137407	+	0.237995i
$528$	4.33114	+	7.50175i	0.188489	+	0.326472i
$529$	−3.31212			−0.144005
$530$	0.398012			0.0172885
$531$	7.52486	+	13.0334i	0.326551	+	0.565603i
$532$		0			0
$533$	3.73391	−	18.2404i	0.161734	−	0.790081i
$534$	2.67692	−	4.63656i	0.115842	−	0.200643i
$535$	−6.39534	+	11.0770i	−0.276494	+	0.478902i
$536$	−1.45330	+	2.51719i	−0.0627730	+	0.108726i
$537$	−0.115573	−	0.200178i	−0.00498734	−	0.00863832i
$538$	36.0571			1.55453
$539$		0			0
$540$	−2.99407	+	5.18588i	−0.128844	+	0.223165i
$541$	−5.24095	+	9.07760i	−0.225326	+	0.390276i	−0.956417	−	0.292003i	$-0.905678\pi$
$541$	−5.24095	+	9.07760i	−0.225326	+	0.390276i	0.731091	+	0.682280i	$0.239011\pi$
$542$	61.2321			2.63014
$543$	−0.593751	+	1.02841i	−0.0254803	+	0.0441331i
$544$	8.85557			0.379679
$545$	−17.7373			−0.759781
$546$		0			0
$547$	15.2216			0.650829			0.325415	−	0.945571i	$-0.394496\pi$
$547$	15.2216			0.650829			0.325415	+	0.945571i	$0.394496\pi$
$548$	−20.8792			−0.891915
$549$	−16.2589	+	28.1613i	−0.693914	+	1.20189i
$550$	−23.6927			−1.01026
$551$	0.271625	−	0.470468i	0.0115716	−	0.0200426i
$552$	−0.668081	+	1.15715i	−0.0284354	+	0.0492516i
$553$		0			0
$554$	−35.0726			−1.49009
$555$	2.22501	+	3.85383i	0.0944464	+	0.163586i
$556$	−0.276261	+	0.478497i	−0.0117161	+	0.0202928i
$557$	−5.92986	+	10.2708i	−0.251256	+	0.435189i	−0.963872	−	0.266366i	$-0.914177\pi$
$557$	−5.92986	+	10.2708i	−0.251256	+	0.435189i	0.712616	+	0.701555i	$0.247510\pi$
$558$	14.0758	−	24.3800i	0.595877	−	1.03209i
$559$	0.0778200	−	0.0259342i	0.00329144	−	0.00109690i
$560$		0			0
$561$	−1.13201	−	1.96070i	−0.0477936	−	0.0827809i
$562$	27.1069			1.14344
$563$	−7.69349			−0.324242			−0.162121	−	0.986771i	$-0.551834\pi$
$563$	−7.69349			−0.324242			−0.162121	+	0.986771i	$0.551834\pi$
$564$	−4.08262	−	7.07131i	−0.171909	−	0.297756i
$565$	−6.90332	−	11.9569i	−0.290425	−	0.503031i
$566$	10.8892	−	18.8607i	0.457709	−	0.792775i
$567$		0			0
$568$	3.50360	−	6.06841i	0.147008	−	0.254625i
$569$	37.4196			1.56871			0.784355	−	0.620312i	$-0.212994\pi$
$569$	37.4196			1.56871			0.784355	+	0.620312i	$0.212994\pi$
$570$	1.94965	−	3.37689i	0.0816619	−	0.141443i
$571$	−7.08285	−	12.2679i	−0.296408	−	0.513394i	0.678903	−	0.734228i	$-0.262456\pi$
$571$	−7.08285	−	12.2679i	−0.296408	−	0.513394i	−0.975311	+	0.220834i	$0.929122\pi$
$572$	−24.5144	+	8.16963i	−1.02500	+	0.341589i
$573$	8.67209			0.362282
$574$		0			0
$575$	−6.27825	−	10.8742i	−0.261821	−	0.453488i
$576$	−6.79797	−	11.7744i	−0.283249	−	0.490601i
$577$	−7.48776	−	12.9692i	−0.311720	−	0.539914i	0.667015	−	0.745044i	$-0.267572\pi$
$577$	−7.48776	−	12.9692i	−0.311720	−	0.539914i	−0.978735	+	0.205130i	$0.934238\pi$
$578$	29.6381			1.23278
$579$	−3.50837	−	6.07667i	−0.145803	−	0.252538i
$580$	0.402635			0.0167185
$581$		0			0
$582$	1.42535	+	2.46878i	0.0590828	+	0.102334i
$583$	0.622952			0.0258000
$584$	5.35627	+	9.27732i	0.221644	+	0.383898i
$585$	11.1919	+	9.92582i	0.462730	+	0.410382i
$586$	12.5811	−	21.7911i	0.519720	−	0.900182i
$587$	−6.58821	−	11.4111i	−0.271925	−	0.470987i	0.697430	−	0.716653i	$-0.254327\pi$
$587$	−6.58821	−	11.4111i	−0.271925	−	0.470987i	−0.969355	+	0.245666i	$0.920993\pi$
$588$		0			0
$589$	−8.50309	+	14.7278i	−0.350364	+	0.606848i
$590$	7.50003	−	12.9904i	0.308771	−	0.534807i
$591$	−8.45478			−0.347783
$592$	−32.4441			−1.33344
$593$	−22.0663	+	38.2200i	−0.906156	+	1.56951i	−0.0867989	+	0.996226i	$0.527664\pi$
$593$	−22.0663	+	38.2200i	−0.906156	+	1.56951i	−0.819357	+	0.573283i	$0.805670\pi$
$594$	−10.4320	+	18.0688i	−0.428032	+	0.741372i
$595$		0			0
$596$	−3.19965	−	5.54195i	−0.131063	−	0.227007i
$597$	3.02429	−	5.23823i	0.123776	−	0.214387i
$598$	−22.8080	−	20.2278i	−0.932689	−	0.827175i
$599$	3.01349	+	5.21952i	0.123128	+	0.213264i	0.921000	−	0.389564i	$-0.127374\pi$
$599$	3.01349	+	5.21952i	0.123128	+	0.213264i	−0.797872	+	0.602827i	$0.794041\pi$
$600$	0.852175			0.0347899
$601$	1.86260	+	3.22612i	0.0759770	+	0.131596i	0.901511	−	0.432757i	$-0.142459\pi$
$601$	1.86260	+	3.22612i	0.0759770	+	0.131596i	−0.825534	+	0.564353i	$0.809126\pi$
$602$		0			0
$603$	−11.6472			−0.474312
$604$	1.72804	+	2.99305i	0.0703129	+	0.121786i
$605$	12.2326			0.497328
$606$	1.05230	+	1.82263i	0.0427467	+	0.0740394i
$607$	−3.00825	−	5.21045i	−0.122101	−	0.211486i	0.798495	−	0.602002i	$-0.205630\pi$
$607$	−3.00825	−	5.21045i	−0.122101	−	0.211486i	−0.920596	+	0.390516i	$0.872297\pi$
$608$	11.9358	+	20.6733i	0.484059	+	0.838415i
$609$		0			0
$610$	32.4105			1.31226
$611$	−39.9648	+	13.3186i	−1.61680	+	0.538813i
$612$	2.76266	+	4.78506i	0.111674	+	0.193425i
$613$	−4.90413	+	8.49420i	−0.198076	+	0.343077i	−0.947904	−	0.318555i	$-0.896803\pi$
$613$	−4.90413	+	8.49420i	−0.198076	+	0.343077i	0.749829	+	0.661632i	$0.230136\pi$
$614$	−12.6892			−0.512094
$615$	−1.62962	+	2.82258i	−0.0657126	+	0.113818i
$616$		0			0
$617$	−16.8838	+	29.2436i	−0.679716	+	1.17730i	0.295350	+	0.955389i	$0.404564\pi$
$617$	−16.8838	+	29.2436i	−0.679716	+	1.17730i	−0.975066	+	0.221914i	$0.928770\pi$
$618$	−6.88394	−	11.9233i	−0.276913	−	0.479627i
$619$	2.04671	+	3.54501i	0.0822644	+	0.142486i	0.904222	−	0.427062i	$-0.140451\pi$
$619$	2.04671	+	3.54501i	0.0822644	+	0.142486i	−0.821958	+	0.569548i	$0.807118\pi$
$620$	−12.6043			−0.506201
$621$	−11.0574			−0.443719
$622$	1.94936	+	3.37639i	0.0781621	+	0.135381i
$623$		0			0
$624$	6.74393	−	2.24747i	0.269973	−	0.0899709i
$625$	1.42115	−	2.46150i	0.0568459	−	0.0984599i
$626$	−8.97297	+	15.5416i	−0.358632	+	0.621169i
$627$	3.05151	−	5.28537i	0.121866	−	0.211077i
$628$	−18.0347	−	31.2371i	−0.719665	−	1.24650i
$629$	8.47978			0.338111
$630$		0			0
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	−0.466340	−	0.884605i	$-0.654428\pi$
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	0.999261	−	0.0384402i	$-0.0122389\pi$
$632$	−0.272179	+	0.471427i	−0.0108267	+	0.0187524i
$633$	1.98214			0.0787831
$634$	−31.7955	+	55.0714i	−1.26276	+	2.18717i
$635$	23.4012			0.928650
$636$	0.0990892			0.00392914
$637$		0			0
$638$	1.40287			0.0555403
$639$	28.0790			1.11079
$640$	4.07112	−	7.05139i	0.160925	−	0.278731i
$641$	−18.5722			−0.733558			−0.366779	−	0.930308i	$-0.619539\pi$
$641$	−18.5722			−0.733558			−0.366779	+	0.930308i	$0.619539\pi$
$642$	−3.54440	+	6.13908i	−0.139886	+	0.242290i
$643$	−1.96695	+	3.40686i	−0.0775690	+	0.134353i	−0.902201	−	0.431317i	$-0.858049\pi$
$643$	−1.96695	+	3.40686i	−0.0775690	+	0.134353i	0.824632	+	0.565670i	$0.191382\pi$
$644$		0			0
$645$	−0.0143591			−0.000565389
$646$	−3.71518	−	6.43487i	−0.146172	−	0.253177i
$647$	−0.0985378	+	0.170672i	−0.00387392	+	0.00670983i	−0.867956	−	0.496641i	$-0.834566\pi$
$647$	−0.0985378	+	0.170672i	−0.00387392	+	0.00670983i	0.864082	+	0.503351i	$0.167900\pi$
$648$	−2.59407	+	4.49306i	−0.101905	+	0.176504i
$649$	11.7387	−	20.3321i	0.460785	−	0.798104i
$650$	−3.89922	+	19.0480i	−0.152940	+	0.747125i
$651$		0			0
$652$	−3.14172	−	5.44163i	−0.123039	−	0.213110i
$653$	−14.4673			−0.566148			−0.283074	−	0.959098i	$-0.591354\pi$
$653$	−14.4673			−0.566148			−0.283074	+	0.959098i	$0.591354\pi$
$654$	−9.83028			−0.384394
$655$	1.36813	+	2.36967i	0.0534573	+	0.0925908i
$656$	−11.8812	−	20.5788i	−0.463883	−	0.803468i
$657$	−21.4635	+	37.1758i	−0.837369	+	1.45037i
$658$		0			0
$659$	11.7066	−	20.2764i	0.456024	−	0.789857i	−0.542722	−	0.839912i	$-0.682606\pi$
$659$	11.7066	−	20.2764i	0.456024	−	0.789857i	0.998746	+	0.0500552i	$0.0159397\pi$
$660$	4.52332			0.176070
$661$	−2.02409	+	3.50582i	−0.0787278	+	0.136361i	−0.902701	−	0.430268i	$-0.858419\pi$
$661$	−2.02409	+	3.50582i	−0.0787278	+	0.136361i	0.823973	+	0.566628i	$0.191752\pi$
$662$	18.1657	+	31.4638i	0.706028	+	1.22288i
$663$	−1.76263	+	0.587412i	−0.0684550	+	0.0228132i
$664$	11.2587			0.436921
$665$		0			0
$666$	−18.9197	−	32.7699i	−0.733125	−	1.26981i
$667$	0.371744	+	0.643879i	0.0143940	+	0.0249311i
$668$	1.74448	+	3.02153i	0.0674959	+	0.116906i
$669$	−9.14832			−0.353695
$670$	5.80440	+	10.0535i	0.224243	+	0.388401i
$671$	50.7276			1.95832
$672$		0			0
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	0.787133	−	0.616783i	$-0.211564\pi$
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	−0.927716	+	0.373286i	$0.878231\pi$
$674$	59.6152			2.29629
$675$	3.52609	+	6.10737i	0.135719	+	0.235073i
$676$	2.53362	+	21.0532i	0.0974468	+	0.809737i
$677$	−7.87553	+	13.6408i	−0.302681	+	0.524259i	−0.976742	−	0.214416i	$-0.931215\pi$
$677$	−7.87553	+	13.6408i	−0.302681	+	0.524259i	0.674061	+	0.738676i	$0.264548\pi$
$678$	−3.82593	−	6.62671i	−0.146934	−	0.254497i
$679$		0			0
$680$	−0.622636	+	1.07844i	−0.0238770	+	0.0413562i
$681$	2.23843	−	3.87707i	0.0857767	−	0.148570i
$682$	−43.9163			−1.68164
$683$	41.4854			1.58739			0.793697	−	0.608314i	$-0.208154\pi$
$683$	41.4854			1.58739			0.793697	+	0.608314i	$0.208154\pi$
$684$	−7.44717	+	12.8989i	−0.284750	+	0.493201i
$685$	9.42819	−	16.3301i	0.360233	−	0.623941i
$686$		0			0
$687$	−3.09725	−	5.36460i	−0.118168	−	0.204672i
$688$	0.0523445	−	0.0906634i	0.00199562	−	0.00345651i
$689$	0.102522	−	0.500830i	0.00390579	−	0.0190801i
$690$	2.66828	+	4.62159i	0.101580	+	0.175941i
$691$	46.8216			1.78118			0.890589	−	0.454809i	$-0.150292\pi$
$691$	46.8216			1.78118			0.890589	+	0.454809i	$0.150292\pi$
$692$	−13.5494	−	23.4683i	−0.515073	−	0.892132i
$693$		0			0
$694$	−22.2478			−0.844514
$695$	−0.249496	−	0.432140i	−0.00946392	−	0.0163920i
$696$	−0.0504584			−0.00191262
$697$	3.10534	+	5.37860i	0.117623	+	0.203729i
$698$	−22.8576	−	39.5905i	−0.865172	−	1.49852i
$699$	−1.98977	−	3.44638i	−0.0752600	−	0.130354i
$700$		0			0
$701$	29.8626			1.12790			0.563948	−	0.825810i	$-0.309282\pi$
$701$	29.8626			1.12790			0.563948	+	0.825810i	$0.309282\pi$
$702$	12.8098	+	11.3606i	0.483475	+	0.428780i
$703$	11.4293	+	19.7961i	0.431063	+	0.746623i
$704$	−10.6048	+	18.3680i	−0.399683	+	0.692271i
$705$	7.37418			0.277728
$706$	−12.1893	+	21.1124i	−0.458749	+	0.794576i
$707$		0			0
$708$	1.86721	−	3.23410i	0.0701740	−	0.121545i
$709$	−13.4666	−	23.3249i	−0.505750	−	0.875984i	−0.999978	−	0.00665185i	$-0.997883\pi$
$709$	−13.4666	−	23.3249i	−0.505750	−	0.875984i	0.494228	−	0.869332i	$-0.335451\pi$
$710$	−13.9932	−	24.2369i	−0.525155	−	0.909595i
$711$	−2.18133			−0.0818063
$712$	−4.60900			−0.172729
$713$	−11.6373	−	20.1563i	−0.435819	−	0.754861i
$714$		0			0
$715$	4.68004	−	22.8623i	0.175023	−	0.855003i
$716$	0.440002	−	0.762105i	0.0164436	−	0.0284812i
$717$	4.20590	−	7.28483i	0.157072	−	0.272057i
$718$	11.7570	−	20.3638i	0.438769	−	0.759969i
$719$	−7.24938	−	12.5563i	−0.270356	−	0.468271i	0.698597	−	0.715516i	$-0.253808\pi$
$719$	−7.24938	−	12.5563i	−0.270356	−	0.468271i	−0.968953	+	0.247245i	$0.920475\pi$
$720$	19.0921			0.711519
$721$		0			0
$722$	−8.08799	+	14.0088i	−0.301004	+	0.521354i
$723$	−1.56620	+	2.71274i	−0.0582476	+	0.100888i
$724$	−4.52098			−0.168021
$725$	0.237090	−	0.410652i	0.00880530	−	0.0152512i
$726$	6.77953			0.251612
$727$	6.26424			0.232328			0.116164	−	0.993230i	$-0.462940\pi$
$727$	6.26424			0.232328			0.116164	+	0.993230i	$0.462940\pi$
$728$		0			0
$729$	−17.5866			−0.651357
$730$	42.7852			1.58355
$731$	−0.0136811	+	0.0236963i	−0.000506013	+	0.000876440i
$732$	8.06893			0.298236
$733$	−5.99189	+	10.3783i	−0.221316	+	0.383330i	−0.955208	−	0.295936i	$-0.904368\pi$
$733$	−5.99189	+	10.3783i	−0.221316	+	0.383330i	0.733892	+	0.679266i	$0.237702\pi$
$734$	−1.93487	+	3.35130i	−0.0714175	+	0.123699i
$735$		0			0
$736$	−32.6704			−1.20425
$737$	9.08480	+	15.7353i	0.334643	+	0.579619i
$738$	13.8570	−	24.0010i	0.510084	−	0.883491i
$739$	−6.76269	+	11.7133i	−0.248770	+	0.430882i	−0.963185	−	0.268840i	$-0.913360\pi$
$739$	−6.76269	+	11.7133i	−0.248770	+	0.430882i	0.714415	+	0.699722i	$0.246693\pi$
$740$	−8.47091	+	14.6721i	−0.311397	+	0.539355i
$741$	−3.74704	−	3.32314i	−0.137651	−	0.122079i
$742$		0			0
$743$	19.2299	+	33.3072i	0.705477	+	1.22192i	0.966519	+	0.256594i	$0.0826003\pi$
$743$	19.2299	+	33.3072i	0.705477	+	1.22192i	−0.261043	+	0.965327i	$0.584066\pi$
$744$	1.57958			0.0579101
$745$	5.77932			0.211738
$746$	−3.69107	−	6.39312i	−0.135140	−	0.234069i
$747$	22.5577	+	39.0710i	0.825342	+	1.42953i
$748$	4.30973	−	7.46466i	0.157579	−	0.272935i
$749$		0			0
$750$	4.70855	−	8.15544i	0.171932	−	0.297795i
$751$	11.7115			0.427357			0.213679	−	0.976904i	$-0.431455\pi$
$751$	11.7115			0.427357			0.213679	+	0.976904i	$0.431455\pi$
$752$	−26.8817	+	46.5605i	−0.980276	+	1.69789i
$753$	2.54151	+	4.40203i	0.0926178	+	0.160419i
$754$	0.230878	−	1.12786i	0.00840809	−	0.0410742i
$755$	−3.12125			−0.113594
$756$		0			0
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	0.768877	−	0.639396i	$-0.220816\pi$
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	−0.938172	+	0.346169i	$0.887482\pi$
$758$	−13.8800	−	24.0409i	−0.504145	−	0.873205i
$759$	4.17627	+	7.23352i	0.151589	+	0.262560i
$760$	−3.35682			−0.121765
$761$	−21.9691	−	38.0515i	−0.796378	−	1.37937i	−0.921960	−	0.387284i	$-0.873413\pi$
$761$	−21.9691	−	38.0515i	−0.796378	−	1.37937i	0.125582	−	0.992083i	$-0.459920\pi$
$762$	12.9693			0.469830
$763$		0			0
$764$	16.5079	+	28.5926i	0.597236	+	1.03444i
$765$	−4.99002			−0.180414
$766$	25.5172	+	44.1971i	0.921973	+	1.59690i
$767$	−14.4143	−	12.7837i	−0.520471	−	0.461591i
$768$	4.32455	−	7.49035i	0.156049	−	0.270285i
$769$	12.6771	+	21.9573i	0.457147	+	0.791802i	0.998809	−	0.0487946i	$-0.0155380\pi$
$769$	12.6771	+	21.9573i	0.457147	+	0.791802i	−0.541662	+	0.840597i	$0.682205\pi$
$770$		0			0
$771$	3.25024	−	5.62957i	0.117054	−	0.202744i
$772$	13.3568	−	23.1347i	0.480723	−	0.832637i
$773$	23.1084			0.831152			0.415576	−	0.909559i	$-0.363580\pi$
$773$	23.1084			0.831152			0.415576	+	0.909559i	$0.363580\pi$
$774$	0.122099			0.00438874
$775$	−7.42200

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.90556 q^{2} +(0.214224 - 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +O(q^{10})\)	\(q-1.90556 q^{2} +(0.214224 - 0.371047i) q^{3} +1.63116 q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 + 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 + 2.43910i) q^{9} +(1.40357 - 2.43105i) q^{10} +(2.19681 - 3.80498i) q^{11} +(0.349433 - 0.605236i) q^{12} +(-2.69752 - 2.39236i) q^{13} +(0.315580 + 0.546600i) q^{15} -4.60164 q^{16} +1.20271 q^{17} +(-2.68344 - 4.64786i) q^{18} +(1.62105 + 2.80773i) q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} -4.43710 q^{23} +(0.150567 - 0.260790i) q^{24} +(1.41494 + 2.45075i) q^{25} +(5.14029 + 4.55878i) q^{26} +2.49204 q^{27} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 - 1.04158i) q^{30} +(2.62272 + 4.54268i) q^{31} +7.36300 q^{32} +(-0.941217 - 1.63024i) q^{33} -2.29184 q^{34} +(2.29702 + 3.97856i) q^{36} +7.05055 q^{37} +(-3.08900 - 5.35031i) q^{38} +(-1.46555 + 0.488407i) q^{39} +(-0.517694 + 0.896672i) q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} -4.14897 q^{45} +8.45516 q^{46} +(5.84178 - 10.1183i) q^{47} +(-0.985780 + 1.70742i) q^{48} +(-2.69626 - 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(-4.40009 - 3.90231i) q^{52} +(0.0708929 + 0.122790i) q^{53} -4.74873 q^{54} +(3.23618 + 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 + 0.276520i) q^{58} +5.34354 q^{59} +(0.514760 + 0.891591i) q^{60} +(5.77287 + 9.99891i) q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(5.03899 - 1.67929i) q^{65} +(1.79355 + 3.10651i) q^{66} +(-2.06773 + 3.58141i) q^{67} +1.96181 q^{68} +(-0.950533 + 1.64637i) q^{69} +(4.98486 - 8.63403i) q^{71} +(0.989763 + 1.71432i) q^{72} +(7.62080 + 13.1996i) q^{73} -13.4352 q^{74} +1.21246 q^{75} +(2.64418 + 4.57986i) q^{76} +(2.79269 - 0.930689i) q^{78} +(-0.387251 + 0.670738i) q^{79} +(3.38941 - 5.87062i) q^{80} +(-3.69080 + 6.39265i) q^{81} +(-4.92006 - 8.52179i) q^{82} +16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} +(0.0216761 - 0.0375441i) q^{86} -0.0717913 q^{87} +(1.54402 - 2.67433i) q^{88} -6.55760 q^{89} +7.90611 q^{90} -7.23762 q^{92} +2.24739 q^{93} +(-11.1319 + 19.2809i) q^{94} -4.77602 q^{95} +(1.57733 - 2.73202i) q^{96} +(1.74583 - 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23} + 11 q^{24} + 7 q^{25} + 16 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} + 26 q^{37} + 17 q^{38} - 20 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} - 14 q^{45} - 32 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} - 41 q^{52} - 2 q^{53} - 36 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} + 26 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 5 q^{65} - 18 q^{66} - 11 q^{67} + 58 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} + 30 q^{73} + 6 q^{74} - 6 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} - 7 q^{86} + 32 q^{87} + 8 q^{89} + 16 q^{90} + 54 q^{92} + 14 q^{93} - 45 q^{94} + 12 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

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