LMFDB - Embedded newform 637.2.bb.a.423.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			423.2
Character	$\chi$	$=$	637.423
Dual form			637.2.bb.a.509.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42500 - 1.42500i) q^{2} +(-1.25027 + 0.721843i) q^{3} +2.06123i q^{4} +(-3.16920 - 0.849184i) q^{5} +(2.81025 + 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 + 0.793083i) q^{9} +O(q^{10})$	\(q+(-1.42500 - 1.42500i) q^{2} +(-1.25027 + 0.721843i) q^{3} +2.06123i q^{4} +(-3.16920 - 0.849184i) q^{5} +(2.81025 + 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 + 0.793083i) q^{9} +(3.30601 + 5.72618i) q^{10} +(-5.74323 - 1.53889i) q^{11} +(-1.48788 - 2.57709i) q^{12} +(-2.81021 - 2.25892i) q^{13} +(4.57532 - 1.22595i) q^{15} +3.87379 q^{16} +0.628578 q^{17} +(1.78263 - 0.477654i) q^{18} +(0.191033 + 0.712944i) q^{19} +(1.75036 - 6.53244i) q^{20} +(5.99117 + 10.3770i) q^{22} +4.54665i q^{23} +(-0.0461069 + 0.172073i) q^{24} +(4.99256 + 2.88246i) q^{25} +(0.785596 + 7.22349i) q^{26} -5.65314i q^{27} +(-1.33622 + 2.31439i) q^{29} +(-8.26680 - 4.77284i) q^{30} +(0.285936 + 1.06713i) q^{31} +(-5.69464 - 5.69464i) q^{32} +(8.29142 - 2.22168i) q^{33} +(-0.895721 - 0.895721i) q^{34} +(-1.63473 - 0.943810i) q^{36} +(1.79007 - 1.79007i) q^{37} +(0.743721 - 1.28816i) q^{38} +(5.14410 + 0.795719i) q^{39} +(-0.350617 + 0.202429i) q^{40} +(0.746755 + 2.78693i) q^{41} +(3.49297 - 2.01667i) q^{43} +(3.17202 - 11.8381i) q^{44} +(2.12461 - 2.12461i) q^{45} +(6.47896 - 6.47896i) q^{46} +(1.90459 - 7.10802i) q^{47} +(-4.84328 + 2.79627i) q^{48} +(-3.00689 - 11.2219i) q^{50} +(-0.785891 + 0.453734i) q^{51} +(4.65615 - 5.79250i) q^{52} +(3.89042 - 6.73840i) q^{53} +(-8.05571 + 8.05571i) q^{54} +(16.8946 + 9.75412i) q^{55} +(-0.753475 - 0.753475i) q^{57} +(5.20211 - 1.39390i) q^{58} +(-0.673419 - 0.673419i) q^{59} +(2.52697 + 9.43079i) q^{60} +(0.943178 + 0.544544i) q^{61} +(1.11320 - 1.92811i) q^{62} +8.48212i q^{64} +(6.98788 + 9.54534i) q^{65} +(-14.9811 - 8.64936i) q^{66} +(-1.39678 + 5.21286i) q^{67} +1.29564i q^{68} +(-3.28197 - 5.68453i) q^{69} +(0.590023 - 2.20200i) q^{71} +(0.0292470 + 0.109151i) q^{72} +(5.94515 - 1.59300i) q^{73} -5.10168 q^{74} -8.32273 q^{75} +(-1.46954 + 0.393762i) q^{76} +(-6.19643 - 8.46422i) q^{78} +(-6.08299 - 10.5361i) q^{79} +(-12.2768 - 3.28956i) q^{80} +(2.70702 + 4.68870i) q^{81} +(2.90724 - 5.03549i) q^{82} +(-3.59152 + 3.59152i) q^{83} +(-1.99209 - 0.533778i) q^{85} +(-7.85121 - 2.10373i) q^{86} -3.85815i q^{87} +(-0.635390 + 0.366843i) q^{88} +(2.88817 + 2.88817i) q^{89} -6.05511 q^{90} -9.37170 q^{92} +(-1.12779 - 1.12779i) q^{93} +(-12.8429 + 7.41487i) q^{94} -2.42168i q^{95} +(11.2305 + 3.00919i) q^{96} +(-8.41780 - 2.25554i) q^{97} +(3.85022 - 3.85022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.42500	−	1.42500i	−1.00762	−	1.00762i	−0.999971	−	0.00765404i	$-0.997564\pi$
$2$	−1.42500	−	1.42500i	−1.00762	−	1.00762i	−0.00765404	−	0.999971i	$-0.502436\pi$
$3$	−1.25027	+	0.721843i	−0.721843	+	0.416756i	−0.815430	−	0.578855i	$-0.803500\pi$
$3$	−1.25027	+	0.721843i	−0.721843	+	0.416756i	0.0935879	+	0.995611i	$0.470166\pi$
$4$			2.06123i			1.03062i
$5$	−3.16920	−	0.849184i	−1.41731	−	0.379766i	−0.532780	−	0.846254i	$-0.678853\pi$
$5$	−3.16920	−	0.849184i	−1.41731	−	0.379766i	−0.884528	+	0.466487i	$0.845519\pi$
$6$	2.81025	+	0.753004i	1.14728	+	0.307413i
$7$		0			0
$7$		0			0
$8$	0.0872533	−	0.0872533i	0.0308487	−	0.0308487i
$9$	−0.457887	+	0.793083i	−0.152629	+	0.264361i
$10$	3.30601	+	5.72618i	1.04545	+	1.81078i
$11$	−5.74323	−	1.53889i	−1.73165	−	0.463994i	−0.751088	−	0.660202i	$-0.770471\pi$
$11$	−5.74323	−	1.53889i	−1.73165	−	0.463994i	−0.980562	+	0.196208i	$0.937137\pi$
$12$	−1.48788	−	2.57709i	−0.429515	−	0.743942i
$13$	−2.81021	−	2.25892i	−0.779413	−	0.626511i
$13$	−2.81021	−	2.25892i	−0.779413	−	0.626511i
$14$		0			0
$15$	4.57532	−	1.22595i	1.18134	−	0.316540i
$16$	3.87379			0.968447
$17$	0.628578			0.152452			0.0762262	−	0.997091i	$-0.475713\pi$
$17$	0.628578			0.152452			0.0762262	+	0.997091i	$0.475713\pi$
$18$	1.78263	−	0.477654i	0.420169	−	0.112584i
$19$	0.191033	+	0.712944i	0.0438259	+	0.163561i	0.984371	−	0.176109i	$-0.0563513\pi$
$19$	0.191033	+	0.712944i	0.0438259	+	0.163561i	−0.940545	+	0.339670i	$0.889685\pi$
$20$	1.75036	−	6.53244i	0.391393	−	1.46070i
$21$		0			0
$22$	5.99117	+	10.3770i	1.27732	+	2.21239i
$23$			4.54665i			0.948043i	0.880513	+	0.474021i	$0.157198\pi$
$23$			4.54665i			0.948043i	−0.880513	+	0.474021i	$0.842802\pi$
$24$	−0.0461069	+	0.172073i	−0.00941153	+	0.0351243i
$25$	4.99256	+	2.88246i	0.998513	+	0.576492i
$26$	0.785596	+	7.22349i	0.154068	+	1.41664i
$27$		−	5.65314i		−	1.08795i
$28$		0			0
$29$	−1.33622	+	2.31439i	−0.248129	+	0.429772i	−0.963007	−	0.269477i	$-0.913149\pi$
$29$	−1.33622	+	2.31439i	−0.248129	+	0.429772i	0.714878	+	0.699250i	$0.246482\pi$
$30$	−8.26680	−	4.77284i	−1.50930	−	0.871397i
$31$	0.285936	+	1.06713i	0.0513556	+	0.191662i	0.986838	−	0.161711i	$-0.0517013\pi$
$31$	0.285936	+	1.06713i	0.0513556	+	0.191662i	−0.935482	+	0.353373i	$0.885035\pi$
$32$	−5.69464	−	5.69464i	−1.00668	−	1.00668i
$33$	8.29142	−	2.22168i	1.44335	−	0.386745i
$34$	−0.895721	−	0.895721i	−0.153615	−	0.153615i
$35$		0			0
$36$	−1.63473	−	0.943810i	−0.272454	−	0.157302i
$37$	1.79007	−	1.79007i	0.294285	−	0.294285i	−0.544485	−	0.838770i	$-0.683275\pi$
$37$	1.79007	−	1.79007i	0.294285	−	0.294285i	0.838770	+	0.544485i	$0.183275\pi$
$38$	0.743721	−	1.28816i	0.120648	−	0.208968i
$39$	5.14410	+	0.795719i	0.823715	+	0.127417i
$40$	−0.350617	+	0.202429i	−0.0554374	+	0.0320068i
$41$	0.746755	+	2.78693i	0.116624	+	0.435245i	0.999403	−	0.0345422i	$-0.0109973\pi$
$41$	0.746755	+	2.78693i	0.116624	+	0.435245i	−0.882780	+	0.469787i	$0.844331\pi$
$42$		0			0
$43$	3.49297	−	2.01667i	0.532673	−	0.307539i	−0.209431	−	0.977823i	$-0.567161\pi$
$43$	3.49297	−	2.01667i	0.532673	−	0.307539i	0.742104	+	0.670285i	$0.233828\pi$
$44$	3.17202	−	11.8381i	0.478200	−	1.78467i
$45$	2.12461	−	2.12461i	0.316718	−	0.316718i
$46$	6.47896	−	6.47896i	0.955271	−	0.955271i
$47$	1.90459	−	7.10802i	0.277813	−	1.03681i	−0.676120	−	0.736791i	$-0.736340\pi$
$47$	1.90459	−	7.10802i	0.277813	−	1.03681i	0.953933	−	0.300020i	$-0.0969934\pi$
$48$	−4.84328	+	2.79627i	−0.699067	+	0.403606i
$49$		0			0
$50$	−3.00689	−	11.2219i	−0.425239	−	1.58701i
$51$	−0.785891	+	0.453734i	−0.110047	+	0.0635355i
$52$	4.65615	−	5.79250i	0.645691	−	0.803275i
$53$	3.89042	−	6.73840i	0.534390	−	0.925590i	−0.464803	−	0.885414i	$-0.653875\pi$
$53$	3.89042	−	6.73840i	0.534390	−	0.925590i	0.999193	−	0.0401759i	$-0.0127918\pi$
$54$	−8.05571	+	8.05571i	−1.09624	+	1.09624i
$55$	16.8946	+	9.75412i	2.27807	+	1.31525i
$56$		0			0
$57$	−0.753475	−	0.753475i	−0.0998002	−	0.0998002i
$58$	5.20211	−	1.39390i	0.683070	−	0.183028i
$59$	−0.673419	−	0.673419i	−0.0876717	−	0.0876717i	0.661911	−	0.749583i	$-0.269746\pi$
$59$	−0.673419	−	0.673419i	−0.0876717	−	0.0876717i	−0.749583	+	0.661911i	$0.769746\pi$
$60$	2.52697	+	9.43079i	0.326231	+	1.21751i
$61$	0.943178	+	0.544544i	0.120762	+	0.0697217i	0.559164	−	0.829057i	$-0.311122\pi$
$61$	0.943178	+	0.544544i	0.120762	+	0.0697217i	−0.438402	+	0.898779i	$0.644456\pi$
$62$	1.11320	−	1.92811i	0.141376	−	0.244870i
$63$		0			0
$64$			8.48212i			1.06026i
$65$	6.98788	+	9.54534i	0.866740	+	1.18395i
$66$	−14.9811	−	8.64936i	−1.84405	−	1.06466i
$67$	−1.39678	+	5.21286i	−0.170644	+	0.636852i	0.826609	+	0.562777i	$0.190267\pi$
$67$	−1.39678	+	5.21286i	−0.170644	+	0.636852i	−0.997253	+	0.0740750i	$0.976400\pi$
$68$			1.29564i			0.157120i
$69$	−3.28197	−	5.68453i	−0.395102	−	0.684338i
$70$		0			0
$71$	0.590023	−	2.20200i	0.0700229	−	0.261329i	−0.922036	−	0.387105i	$-0.873475\pi$
$71$	0.590023	−	2.20200i	0.0700229	−	0.261329i	0.992059	+	0.125776i	$0.0401419\pi$
$72$	0.0292470	+	0.109151i	0.00344679	+	0.0128636i
$73$	5.94515	−	1.59300i	0.695827	−	0.186446i	0.106466	−	0.994316i	$-0.466046\pi$
$73$	5.94515	−	1.59300i	0.695827	−	0.186446i	0.589361	+	0.807870i	$0.299380\pi$
$74$	−5.10168			−0.593058
$75$	−8.32273			−0.961026
$76$	−1.46954	+	0.393762i	−0.168568	+	0.0451677i
$77$		0			0
$78$	−6.19643	−	8.46422i	−0.701608	−	0.958385i
$79$	−6.08299	−	10.5361i	−0.684390	−	1.18540i	−0.973628	−	0.228141i	$-0.926735\pi$
$79$	−6.08299	−	10.5361i	−0.684390	−	1.18540i	0.289238	−	0.957257i	$-0.406598\pi$
$80$	−12.2768	−	3.28956i	−1.37259	−	0.367784i
$81$	2.70702	+	4.68870i	0.300780	+	0.520966i
$82$	2.90724	−	5.03549i	0.321051	−	0.556076i
$83$	−3.59152	+	3.59152i	−0.394220	+	0.394220i	−0.876189	−	0.481968i	$-0.839922\pi$
$83$	−3.59152	+	3.59152i	−0.394220	+	0.394220i	0.481968	+	0.876189i	$0.339922\pi$
$84$		0			0
$85$	−1.99209	−	0.533778i	−0.216072	−	0.0578963i
$86$	−7.85121	−	2.10373i	−0.846618	−	0.226851i
$87$		−	3.85815i		−	0.413637i
$88$	−0.635390	+	0.366843i	−0.0677328	+	0.0391055i
$89$	2.88817	+	2.88817i	0.306146	+	0.306146i	0.843412	−	0.537267i	$-0.180543\pi$
$89$	2.88817	+	2.88817i	0.306146	+	0.306146i	−0.537267	+	0.843412i	$0.680543\pi$
$90$	−6.05511			−0.638265
$91$		0			0
$92$	−9.37170			−0.977067
$93$	−1.12779	−	1.12779i	−0.116947	−	0.116947i
$94$	−12.8429	+	7.41487i	−1.32465	+	0.764786i
$95$		−	2.42168i		−	0.248459i
$96$	11.2305	+	3.00919i	1.14620	+	0.307125i
$97$	−8.41780	−	2.25554i	−0.854698	−	0.229016i	−0.195239	−	0.980756i	$-0.562548\pi$
$97$	−8.41780	−	2.25554i	−0.854698	−	0.229016i	−0.659460	+	0.751740i	$0.729215\pi$
$98$		0			0
$99$	3.85022	−	3.85022i	0.386962	−	0.386962i
$100$	−5.94141	+	10.2908i	−0.594141	+	1.02908i
$101$	8.58758	+	14.8741i	0.854496	+	1.48003i	0.877112	+	0.480286i	$0.159467\pi$
$101$	8.58758	+	14.8741i	0.854496	+	1.48003i	−0.0226160	+	0.999744i	$0.507200\pi$
$102$	1.76646	+	0.473322i	0.174906	+	0.0468658i
$103$	7.19481	+	12.4618i	0.708926	+	1.22790i	0.965256	+	0.261306i	$0.0841532\pi$
$103$	7.19481	+	12.4618i	0.708926	+	1.22790i	−0.256330	+	0.966589i	$0.582513\pi$
$104$	−0.442298	+	0.0481025i	−0.0433709	+	0.00471684i
$105$		0			0
$106$	−15.1460	+	4.05836i	−1.47111	+	0.394183i
$107$	3.12072			0.301691			0.150846	−	0.988557i	$-0.451800\pi$
$107$	3.12072			0.301691			0.150846	+	0.988557i	$0.451800\pi$
$108$	11.6524			1.12126
$109$	−9.17711	+	2.45900i	−0.879008	+	0.235529i	−0.669979	−	0.742380i	$-0.733697\pi$
$109$	−9.17711	+	2.45900i	−0.879008	+	0.235529i	−0.209029	+	0.977909i	$0.567030\pi$
$110$	−10.1752	−	37.9744i	−0.970168	−	3.62071i
$111$	−0.945917	+	3.53021i	−0.0897825	+	0.335073i
$112$		0			0
$113$	1.34080	+	2.32234i	0.126132	+	0.218467i	0.922175	−	0.386773i	$-0.126410\pi$
$113$	1.34080	+	2.32234i	0.126132	+	0.218467i	−0.796043	+	0.605240i	$0.793077\pi$
$114$			2.14740i			0.201122i
$115$	3.86094	−	14.4092i	0.360035	−	1.34367i
$116$	−4.77050	−	2.75425i	−0.442930	−	0.255726i
$117$	3.07827	−	1.19440i	0.284586	−	0.110423i
$118$			1.91924i			0.176680i
$119$		0			0
$120$	0.292243	−	0.506181i	0.0266781	−	0.0462077i
$121$	21.0903	+	12.1765i	1.91730	+	1.10695i
$122$	−0.568052	−	2.12000i	−0.0514290	−	0.191936i
$123$	−2.94537	−	2.94537i	−0.265575	−	0.265575i
$124$	−2.19960	+	0.589380i	−0.197530	+	0.0529279i
$125$	−1.77462	−	1.77462i	−0.158727	−	0.158727i
$126$		0			0
$127$	−4.93218	−	2.84760i	−0.437661	−	0.252683i	0.264944	−	0.964264i	$-0.414646\pi$
$127$	−4.93218	−	2.84760i	−0.437661	−	0.252683i	−0.702605	+	0.711580i	$0.747980\pi$
$128$	0.697699	−	0.697699i	0.0616685	−	0.0616685i
$129$	−2.91143	+	5.04275i	−0.256337	+	0.443989i
$130$	3.64436	−	23.5598i	0.319632	−	2.06633i
$131$	−15.1645	+	8.75520i	−1.32492	+	0.764946i	−0.984510	−	0.175329i	$-0.943901\pi$
$131$	−15.1645	+	8.75520i	−1.32492	+	0.764946i	−0.340415	+	0.940275i	$0.610568\pi$
$132$	4.57939	+	17.0905i	0.398585	+	1.48754i
$133$		0			0
$134$	9.41872	−	5.43790i	0.813653	−	0.469763i
$135$	−4.80056	+	17.9159i	−0.413166	+	1.54196i
$136$	0.0548455	−	0.0548455i	0.00470296	−	0.00470296i
$137$	10.3658	−	10.3658i	0.885611	−	0.885611i	−0.108487	−	0.994098i	$-0.534600\pi$
$137$	10.3658	−	10.3658i	0.885611	−	0.885611i	0.994098	+	0.108487i	$0.0346005\pi$
$138$	−3.42365	+	12.7772i	−0.291440	+	1.08767i
$139$	−3.10457	+	1.79243i	−0.263327	+	0.152032i	−0.625851	−	0.779943i	$-0.715248\pi$
$139$	−3.10457	+	1.79243i	−0.263327	+	0.152032i	0.362525	+	0.931974i	$0.381915\pi$
$140$		0			0
$141$	2.74963	+	10.2617i	0.231560	+	0.864195i
$142$	−3.97862	+	2.29706i	−0.333878	+	0.192765i
$143$	12.6635	+	17.2981i	1.05897	+	1.44654i
$144$	−1.77376	+	3.07224i	−0.147813	+	0.256020i
$145$	6.20008	−	6.20008i	0.514888	−	0.514888i
$146$	−10.7418	−	6.20180i	−0.889001	−	0.513265i
$147$		0			0
$148$	3.68974	+	3.68974i	0.303295	+	0.303295i
$149$	−13.8632	+	3.71462i	−1.13571	+	0.304314i	−0.777226	−	0.629221i	$-0.783374\pi$
$149$	−13.8632	+	3.71462i	−1.13571	+	0.304314i	−0.358487	+	0.933535i	$0.616707\pi$
$150$	11.8599	+	11.8599i	0.968353	+	0.968353i
$151$	6.15509	+	22.9711i	0.500894	+	1.86936i	0.494134	+	0.869386i	$0.335485\pi$
$151$	6.15509	+	22.9711i	0.500894	+	1.86936i	0.00676075	+	0.999977i	$0.497848\pi$
$152$	0.0788749	+	0.0455385i	0.00639760	+	0.00369366i
$153$	−0.287817	+	0.498514i	−0.0232687	+	0.0403025i
$154$		0			0
$155$		−	3.62475i		−	0.291147i
$156$	−1.64016	+	10.6032i	−0.131318	+	0.848934i
$157$	−6.58929	−	3.80433i	−0.525882	−	0.303618i	0.213456	−	0.976953i	$-0.431528\pi$
$157$	−6.58929	−	3.80433i	−0.525882	−	0.303618i	−0.739338	+	0.673334i	$0.764861\pi$
$158$	−6.34560	+	23.6821i	−0.504829	+	1.88405i
$159$			11.2331i			0.890840i
$160$	13.2116	+	22.8832i	1.04447	+	1.80908i
$161$		0			0
$162$	2.82388	−	10.5389i	0.221865	−	0.828012i
$163$	−0.665670	−	2.48431i	−0.0521393	−	0.194586i	0.934944	−	0.354796i	$-0.115450\pi$
$163$	−0.665670	−	2.48431i	−0.0521393	−	0.194586i	−0.987083	+	0.160210i	$0.948783\pi$
$164$	−5.74450	+	1.53923i	−0.448570	+	0.120194i
$165$	−28.1638			−2.19255
$166$	10.2358			0.794452
$167$	−3.28638	+	0.880582i	−0.254308	+	0.0681415i	−0.383720	−	0.923449i	$-0.625357\pi$
$167$	−3.28638	+	0.880582i	−0.254308	+	0.0681415i	0.129413	+	0.991591i	$0.458691\pi$
$168$		0			0
$169$	2.79460	+	12.6961i	0.214969	+	0.976621i
$170$	2.07808	+	3.59935i	0.159382	+	0.276057i
$171$	−0.652895	−	0.174943i	−0.0499281	−	0.0133782i
$172$	4.15682	+	7.19982i	0.316954	+	0.548981i
$173$	7.02517	−	12.1680i	0.534114	−	0.925113i	−0.465092	−	0.885263i	$-0.653979\pi$
$173$	7.02517	−	12.1680i	0.534114	−	0.925113i	0.999206	−	0.0398501i	$-0.0126880\pi$
$174$	−5.49785	+	5.49785i	−0.416791	+	0.416791i
$175$		0			0
$176$	−22.2481	−	5.96136i	−1.67701	−	0.449354i
$177$	1.32806	+	0.355852i	0.0998228	+	0.0267474i
$178$		−	8.23128i		−	0.616960i
$179$	−12.9578	+	7.48119i	−0.968512	+	0.559170i	−0.898782	−	0.438395i	$-0.855547\pi$
$179$	−12.9578	+	7.48119i	−0.968512	+	0.559170i	−0.0697295	+	0.997566i	$0.522214\pi$
$180$	4.37930	+	4.37930i	0.326414	+	0.326414i
$181$	15.4409			1.14772			0.573858	−	0.818955i	$-0.305446\pi$
$181$	15.4409			1.14772			0.573858	+	0.818955i	$0.305446\pi$
$182$		0			0
$183$	−1.57230			−0.116228
$184$	0.396711	+	0.396711i	0.0292459	+	0.0292459i
$185$	−7.19317	+	4.15298i	−0.528852	+	0.305333i
$186$			3.21421i			0.235677i
$187$	−3.61007	−	0.967315i	−0.263994	−	0.0707371i
$188$	14.6513	+	3.92580i	1.06855	+	0.286318i
$189$		0			0
$190$	−3.45089	+	3.45089i	−0.250354	+	0.250354i
$191$	8.57746	−	14.8566i	0.620643	−	1.07499i	−0.368723	−	0.929539i	$-0.620205\pi$
$191$	8.57746	−	14.8566i	0.620643	−	1.07499i	0.989366	−	0.145446i	$-0.0464617\pi$
$192$	−6.12275	−	10.6049i	−0.441872	−	0.765344i
$193$	5.92369	+	1.58725i	0.426396	+	0.114253i	0.465634	−	0.884977i	$-0.345826\pi$
$193$	5.92369	+	1.58725i	0.426396	+	0.114253i	−0.0392377	+	0.999230i	$0.512493\pi$
$194$	8.78120	+	15.2095i	0.630453	+	1.09198i
$195$	−15.6270	−	6.89008i	−1.11907	−	0.493409i
$196$		0			0
$197$	24.7906	−	6.64263i	1.76626	−	0.473268i	0.778288	−	0.627908i	$-0.216089\pi$
$197$	24.7906	−	6.64263i	1.76626	−	0.473268i	0.987971	+	0.154640i	$0.0494219\pi$
$198$	−10.9731			−0.779825
$199$	−8.72738			−0.618667			−0.309334	−	0.950954i	$-0.600106\pi$
$199$	−8.72738			−0.618667			−0.309334	+	0.950954i	$0.600106\pi$
$200$	0.687122	−	0.184114i	0.0485869	−	0.0130188i
$201$	−2.01651	−	7.52573i	−0.142234	−	0.530824i
$202$	8.95830	−	33.4328i	0.630304	−	2.35233i
$203$		0			0
$204$	−0.935251	−	1.61990i	−0.0654806	−	0.113416i
$205$		−	9.46645i		−	0.661166i
$206$	7.50541	−	28.0106i	0.522927	−	1.95159i
$207$	−3.60587	−	2.08185i	−0.250625	−	0.144699i
$208$	−10.8862	−	8.75057i	−0.754820	−	0.606743i
$209$		−	4.38858i		−	0.303565i
$210$		0			0
$211$	−5.41370	+	9.37680i	−0.372694	+	0.645525i	−0.989979	−	0.141214i	$-0.954899\pi$
$211$	−5.41370	+	9.37680i	−0.372694	+	0.645525i	0.617285	+	0.786740i	$0.288233\pi$
$212$	13.8894	+	8.01904i	0.953927	+	0.550750i
$213$	0.851808	+	3.17899i	0.0583649	+	0.217821i
$214$	−4.44701	−	4.44701i	−0.303991	−	0.303991i
$215$	−12.7824	+	3.42504i	−0.871754	+	0.233586i
$216$	−0.493256	−	0.493256i	−0.0335618	−	0.0335618i
$217$		0			0
$218$	16.5814	+	9.57329i	1.12304	+	0.648385i
$219$	−6.28314	+	6.28314i	−0.424575	+	0.424575i
$220$	−20.1055	+	34.8237i	−1.35551	+	2.34782i
$221$	−1.76644	−	1.41990i	−0.118823	−	0.0955131i
$222$	6.37847	−	3.68261i	0.428095	−	0.247161i
$223$	−2.01754	−	7.52957i	−0.135105	−	0.504217i	−0.999997	−	0.00226068i	$-0.999280\pi$
$223$	−2.01754	−	7.52957i	−0.135105	−	0.504217i	0.864893	−	0.501957i	$-0.167386\pi$
$224$		0			0
$225$	−4.57206	+	2.63968i	−0.304804	+	0.175979i
$226$	1.39869	−	5.21997i	0.0930392	−	0.347227i
$227$	10.0802	−	10.0802i	0.669045	−	0.669045i	−0.288450	−	0.957495i	$-0.593140\pi$
$227$	10.0802	−	10.0802i	0.669045	−	0.669045i	0.957495	+	0.288450i	$0.0931398\pi$
$228$	1.55309	−	1.55309i	0.102856	−	0.102856i
$229$	−2.95351	+	11.0227i	−0.195174	+	0.728398i	0.797048	+	0.603916i	$0.206394\pi$
$229$	−2.95351	+	11.0227i	−0.195174	+	0.728398i	−0.992222	+	0.124482i	$0.960273\pi$
$230$	−26.0349	+	15.0313i	−1.71669	+	0.991133i
$231$		0			0
$232$	0.0853493	+	0.318528i	0.00560346	+	0.0209124i
$233$	18.9544	−	10.9433i	1.24175	−	0.716922i	0.272297	−	0.962213i	$-0.412217\pi$
$233$	18.9544	−	10.9433i	1.24175	−	0.716922i	0.969450	+	0.245291i	$0.0788835\pi$
$234$	−6.08854	−	2.68450i	−0.398020	−	0.175491i
$235$	−12.0720	+	20.9094i	−0.787492	+	1.36398i
$236$	1.38807	−	1.38807i	0.0903557	−	0.0903557i
$237$	15.2107	+	8.78193i	0.988044	+	0.570448i
$238$		0			0
$239$	3.79044	+	3.79044i	0.245183	+	0.245183i	0.818990	−	0.573807i	$-0.194534\pi$
$239$	3.79044	+	3.79044i	0.245183	+	0.245183i	−0.573807	+	0.818990i	$0.694534\pi$
$240$	17.7238	−	4.74909i	1.14407	−	0.306552i
$241$	11.0392	+	11.0392i	0.711097	+	0.711097i	0.966765	−	0.255668i	$-0.0822953\pi$
$241$	11.0392	+	11.0392i	0.711097	+	0.711097i	−0.255668	+	0.966765i	$0.582295\pi$
$242$	−12.7021	−	47.4050i	−0.816523	−	3.04731i
$243$	7.91830	+	4.57163i	0.507959	+	0.293270i
$244$	−1.12243	+	1.94411i	−0.0718563	+	0.124459i
$245$		0			0
$246$			8.39427i			0.535199i
$247$	1.07364	−	2.43505i	0.0683139	−	0.154939i
$248$	0.118059	+	0.0681616i	0.00749677	+	0.00432826i
$249$	1.89785	−	7.08287i	0.120271	−	0.448858i
$250$			5.05765i			0.319874i
$251$	2.30694	+	3.99573i	0.145612	+	0.252208i	0.929601	−	0.368567i	$-0.120151\pi$
$251$	2.30694	+	3.99573i	0.145612	+	0.252208i	−0.783989	+	0.620775i	$0.786818\pi$
$252$		0			0
$253$	6.99682	−	26.1125i	0.439886	−	1.64168i
$254$	2.97053	+	11.0862i	0.186388	+	0.695608i
$255$	2.87595	−	0.770607i	0.180099	−	0.0482573i
$256$	14.9758			0.935987
$257$	−15.6656			−0.977191			−0.488596	−	0.872510i	$-0.662491\pi$
$257$	−15.6656			−0.977191			−0.488596	+	0.872510i	$0.662491\pi$
$258$	11.3347	−	3.03712i	0.705666	−	0.189083i
$259$		0			0
$260$	−19.6751	+	14.4036i	−1.22020	+	0.893276i
$261$	−1.22367	−	2.11946i	−0.0757434	−	0.131191i
$262$	34.0854	+	9.13317i	2.10581	+	0.564249i
$263$	11.9554	+	20.7074i	0.737203	+	1.27687i	0.953750	+	0.300601i	$0.0971872\pi$
$263$	11.9554	+	20.7074i	0.737203	+	1.27687i	−0.216547	+	0.976272i	$0.569479\pi$
$264$	0.529605	−	0.917303i	0.0325949	−	0.0564561i
$265$	−18.0516	+	18.0516i	−1.10890	+	1.10890i
$266$		0			0
$267$	−5.69580	−	1.52618i	−0.348577	−	0.0934010i
$268$	−10.7449	−	2.87909i	−0.656350	−	0.175868i
$269$		−	13.5339i		−	0.825177i	−0.910918	−	0.412588i	$-0.864625\pi$
$269$		−	13.5339i		−	0.825177i	0.910918	−	0.412588i	$-0.135375\pi$
$270$	32.3709	−	18.6893i	1.97003	−	1.13740i
$271$	−15.3119	−	15.3119i	−0.930129	−	0.930129i	0.0675846	−	0.997714i	$-0.478471\pi$
$271$	−15.3119	−	15.3119i	−0.930129	−	0.930129i	−0.997714	+	0.0675846i	$0.978471\pi$
$272$	2.43498			0.147642
$273$		0			0
$274$	−29.5425			−1.78473
$275$	−24.2377	−	24.2377i	−1.46159	−	1.46159i
$276$	11.7171	−	6.76489i	0.705289	−	0.407199i
$277$		−	21.4166i		−	1.28680i	−0.765531	−	0.643399i	$-0.777524\pi$
$277$		−	21.4166i		−	1.28680i	0.765531	−	0.643399i	$-0.222476\pi$
$278$	6.97821	+	1.86981i	0.418525	+	0.112143i
$279$	−0.977247	−	0.261853i	−0.0585063	−	0.0156767i
$280$		0			0
$281$	0.874765	−	0.874765i	0.0521841	−	0.0521841i	−0.680533	−	0.732717i	$-0.738252\pi$
$281$	0.874765	−	0.874765i	0.0521841	−	0.0521841i	0.732717	+	0.680533i	$0.238252\pi$
$282$	10.7047	−	18.5412i	0.637458	−	1.10411i
$283$	−9.23061	−	15.9879i	−0.548703	−	0.950381i	−0.998364	−	0.0571816i	$-0.981789\pi$
$283$	−9.23061	−	15.9879i	−0.548703	−	0.950381i	0.449661	−	0.893199i	$-0.351545\pi$
$284$	4.53882	+	1.21617i	0.269330	+	0.0721667i
$285$	1.74807	+	3.02775i	0.103547	+	0.179348i
$286$	6.60433	−	42.6952i	0.390522	−	2.52462i
$287$		0			0
$288$	7.12383	−	1.90882i	0.419775	−	0.112479i
$289$	−16.6049			−0.976758
$290$	−17.6702			−1.03763
$291$	12.1527	−	3.25629i	0.712401	−	0.190887i
$292$	3.28354	+	12.2543i	0.192154	+	0.717130i
$293$	3.21602	−	12.0024i	0.187882	−	0.701186i	−0.806113	−	0.591762i	$-0.798433\pi$
$293$	3.21602	−	12.0024i	0.187882	−	0.701186i	0.993995	−	0.109424i	$-0.0349006\pi$
$294$		0			0
$295$	1.56234	+	2.70605i	0.0909629	+	0.157552i
$296$		−	0.312379i		−	0.0181566i
$297$	−8.69959	+	32.4673i	−0.504802	+	1.88395i
$298$	25.0483	+	14.4616i	1.45101	+	0.837739i
$299$	10.2705	−	12.7771i	0.593959	−	0.738917i
$300$		−	17.1551i		−	0.990448i
$301$		0			0
$302$	23.9628	−	41.5048i	1.37890	−	2.38833i
$303$	−21.4735	−	12.3978i	−1.23362	−	0.712233i
$304$	0.740021	+	2.76179i	0.0424431	+	0.158400i
$305$	−2.52670	−	2.52670i	−0.144678	−	0.144678i
$306$	1.12052	−	0.300242i	0.0640559	−	0.0171637i
$307$	−3.51390	−	3.51390i	−0.200549	−	0.200549i	0.599686	−	0.800235i	$-0.295292\pi$
$307$	−3.51390	−	3.51390i	−0.200549	−	0.200549i	−0.800235	+	0.599686i	$0.795292\pi$
$308$		0			0
$309$	−17.9909	−	10.3870i	−1.02347	−	0.590898i
$310$	−5.16526	+	5.16526i	−0.293367	+	0.293367i
$311$	9.18303	−	15.9055i	0.520722	−	0.901916i	−0.478988	−	0.877821i	$-0.658996\pi$
$311$	9.18303	−	15.9055i	0.520722	−	0.901916i	0.999710	−	0.0240949i	$-0.00767040\pi$
$312$	0.518269	−	0.379411i	0.0293412	−	0.0214799i
$313$	−7.78607	+	4.49529i	−0.440095	+	0.254089i	−0.703638	−	0.710559i	$-0.748442\pi$
$313$	−7.78607	+	4.49529i	−0.440095	+	0.254089i	0.263543	+	0.964648i	$0.415109\pi$
$314$	3.96856	+	14.8109i	0.223959	+	0.835825i
$315$		0			0
$316$	21.7172	−	12.5385i	1.22169	−	0.705343i
$317$	3.72880	−	13.9161i	0.209430	−	0.781605i	−0.778623	−	0.627492i	$-0.784081\pi$
$317$	3.72880	−	13.9161i	0.209430	−	0.781605i	0.988053	−	0.154113i	$-0.0492519\pi$
$318$	16.0071	−	16.0071i	0.897633	−	0.897633i
$319$	11.2358	−	11.2358i	0.629085	−	0.629085i
$320$	7.20287	−	26.8815i	0.402653	−	1.50272i
$321$	−3.90173	+	2.25267i	−0.217773	+	0.125732i
$322$		0			0
$323$	0.120079	+	0.448141i	0.00668137	+	0.0249352i
$324$	−9.66448	+	5.57979i	−0.536916	+	0.309988i
$325$	−7.51894	−	19.3781i	−0.417076	−	1.07490i
$326$	−2.59156	+	4.48871i	−0.143533	+	0.248607i
$327$	9.69884	−	9.69884i	0.536347	−	0.536347i
$328$	0.308326	+	0.178012i	0.0170244	+	0.00982906i
$329$		0			0
$330$	40.1333	+	40.1333i	2.20926	+	2.20926i
$331$	−7.90514	+	2.11818i	−0.434506	+	0.116426i	−0.469441	−	0.882964i	$-0.655544\pi$
$331$	−7.90514	+	2.11818i	−0.434506	+	0.116426i	0.0349345	+	0.999390i	$0.488878\pi$
$332$	−7.40294	−	7.40294i	−0.406289	−	0.406289i
$333$	0.600024	+	2.23932i	0.0328811	+	0.122714i
$334$	5.93790	+	3.42825i	0.324908	+	0.187586i
$335$	8.85335	−	15.3345i	0.483710	−	0.837811i
$336$		0			0
$337$			1.63832i			0.0892447i	0.999004	+	0.0446224i	$0.0142085\pi$
$337$			1.63832i			0.0892447i	−0.999004	+	0.0446224i	$0.985792\pi$
$338$	14.1096	−	22.0741i	0.767459	−	1.20068i
$339$	−3.35273	−	1.93570i	−0.182095	−	0.105133i
$340$	1.10024	−	4.10615i	0.0596688	−	0.222687i
$341$		−	6.56879i		−	0.355720i
$342$	0.681080	+	1.17967i	0.0368286	+	0.0637890i
$343$		0			0
$344$	0.128812	−	0.480734i	0.00694510	−	0.0259194i
$345$	5.57399	+	20.8024i	0.300093	+	1.11996i
$346$	−27.3501	+	7.32845i	−1.47035	+	0.393980i
$347$	−9.63134			−0.517037			−0.258519	−	0.966006i	$-0.583234\pi$
$347$	−9.63134			−0.517037			−0.258519	+	0.966006i	$0.583234\pi$
$348$	7.95254			0.426301
$349$	28.4665	−	7.62758i	1.52378	−	0.408295i	0.602794	−	0.797897i	$-0.294054\pi$
$349$	28.4665	−	7.62758i	1.52378	−	0.408295i	0.920983	+	0.389602i	$0.127387\pi$
$350$		0			0
$351$	−12.7700	+	15.8865i	−0.681611	+	0.847961i
$352$	23.9422	+	41.4691i	1.27612	+	2.21031i
$353$	−15.4405	−	4.13727i	−0.821814	−	0.220205i	−0.176675	−	0.984269i	$-0.556534\pi$
$353$	−15.4405	−	4.13727i	−0.821814	−	0.220205i	−0.645140	+	0.764065i	$0.723201\pi$
$354$	−1.38539	−	2.39956i	−0.0736326	−	0.127535i
$355$	−3.73980	+	6.47752i	−0.198488	+	0.343791i
$356$	−5.95319	+	5.95319i	−0.315519	+	0.315519i
$357$		0			0
$358$	29.1255	+	7.80415i	1.53933	+	0.412462i
$359$	5.55095	+	1.48737i	0.292968	+	0.0785005i	0.402309	−	0.915504i	$-0.368208\pi$
$359$	5.55095	+	1.48737i	0.292968	+	0.0785005i	−0.109342	+	0.994004i	$0.534874\pi$
$360$		−	0.370758i		−	0.0195407i
$361$	15.9827	−	9.22761i	0.841194	−	0.485664i
$362$	−22.0033	−	22.0033i	−1.15647	−	1.15647i
$363$	−35.1580			−1.84531
$364$		0			0
$365$	−20.1941			−1.05701
$366$	2.24052	+	2.24052i	0.117114	+	0.117114i
$367$	−22.0499	+	12.7305i	−1.15099	+	0.664527i	−0.949129	−	0.314887i	$-0.898034\pi$
$367$	−22.0499	+	12.7305i	−1.15099	+	0.664527i	−0.201865	+	0.979413i	$0.564700\pi$
$368$			17.6128i			0.918129i
$369$	−2.55219	−	0.683858i	−0.132862	−	0.0356002i
$370$	16.1682	+	4.33226i	0.840546	+	0.225224i
$371$		0			0
$372$	2.32465	−	2.32465i	0.120527	−	0.120527i
$373$	−9.35778	+	16.2082i	−0.484528	+	0.839227i	−0.999842	−	0.0177746i	$-0.994342\pi$
$373$	−9.35778	+	16.2082i	−0.484528	+	0.839227i	0.515314	+	0.857001i	$0.327675\pi$
$374$	3.76592	+	6.52276i	0.194731	+	0.337284i
$375$	3.49974	+	0.937753i	0.180726	+	0.0484254i
$376$	−0.454017	−	0.786380i	−0.0234141	−	0.0405545i
$377$	8.98308	−	3.48554i	0.462652	−	0.179515i
$378$		0			0
$379$	−20.5112	+	5.49596i	−1.05359	+	0.282309i	−0.743735	−	0.668475i	$-0.766947\pi$
$379$	−20.5112	+	5.49596i	−1.05359	+	0.282309i	−0.309856	+	0.950784i	$0.600281\pi$
$380$	4.99164			0.256066
$381$	8.22207			0.421229
$382$	−33.3934	+	8.94774i	−1.70856	+	0.457806i
$383$	8.39979	+	31.3484i	0.429209	+	1.60183i	0.754556	+	0.656236i	$0.227852\pi$
$383$	8.39979	+	31.3484i	0.429209	+	1.60183i	−0.325347	+	0.945595i	$0.605481\pi$
$384$	−0.368682	+	1.37594i	−0.0188142	+	0.0702157i
$385$		0			0
$386$	−6.17941	−	10.7031i	−0.314524	−	0.544771i
$387$			3.69362i			0.187757i
$388$	4.64919	−	17.3510i	0.236027	−	0.880865i
$389$	6.03084	+	3.48191i	0.305776	+	0.176540i	0.645035	−	0.764153i	$-0.276843\pi$
$389$	6.03084	+	3.48191i	0.305776	+	0.176540i	−0.339259	+	0.940693i	$0.610176\pi$
$390$	12.4500	+	32.0867i	0.630431	+	1.62477i
$391$			2.85792i			0.144531i
$392$		0			0
$393$	12.6398	−	21.8927i	0.637591	−	1.10434i
$394$	−44.7923	−	25.8608i	−2.25660	−	1.30285i
$395$	10.3312	+	38.5564i	0.519817	+	1.93998i
$396$	7.93619	+	7.93619i	0.398809	+	0.398809i
$397$	14.4310	−	3.86677i	0.724270	−	0.194068i	0.122194	−	0.992506i	$-0.461007\pi$
$397$	14.4310	−	3.86677i	0.724270	−	0.194068i	0.602076	+	0.798439i	$0.294340\pi$
$398$	12.4365	+	12.4365i	0.623384	+	0.623384i
$399$		0			0
$400$	19.3401	+	11.1660i	0.967007	+	0.558302i
$401$	17.0943	−	17.0943i	0.853649	−	0.853649i	−0.136932	−	0.990581i	$-0.543724\pi$
$401$	17.0943	−	17.0943i	0.853649	−	0.853649i	0.990581	+	0.136932i	$0.0437241\pi$
$402$	−7.85061	+	13.5977i	−0.391553	+	0.678190i
$403$	1.60701	−	3.64476i	0.0800509	−	0.181559i
$404$	−30.6590	+	17.7010i	−1.52534	+	0.880657i
$405$	−4.59751	−	17.1582i	−0.228452	−	0.852595i
$406$		0			0
$407$	−13.0355	+	7.52605i	−0.646146	+	0.373052i
$408$	−0.0289818	+	0.108161i	−0.00143481	+	0.00535479i
$409$	26.5396	−	26.5396i	1.31230	−	1.31230i	0.392580	−	0.919718i	$-0.371583\pi$
$409$	26.5396	−	26.5396i	1.31230	−	1.31230i	0.919718	−	0.392580i	$-0.128417\pi$
$410$	−13.4897	+	13.4897i	−0.666207	+	0.666207i
$411$	−5.47756	+	20.4425i	−0.270188	+	1.00836i
$412$	−25.6866	+	14.8302i	−1.26549	+	0.730630i
$413$		0			0
$414$	2.17172	+	8.10499i	0.106734	+	0.398338i
$415$	14.4321	−	8.33236i	0.708443	−	0.409020i
$416$	3.13944	+	28.8669i	0.153924	+	1.41532i
$417$	2.58770	−	4.48203i	0.126720	−	0.219486i
$418$	−6.25371	+	6.25371i	−0.305879	+	0.305879i
$419$	−7.05130	−	4.07107i	−0.344478	−	0.198885i	0.317772	−	0.948167i	$-0.397065\pi$
$419$	−7.05130	−	4.07107i	−0.344478	−	0.198885i	−0.662251	+	0.749282i	$0.730399\pi$
$420$		0			0
$421$	2.46118	+	2.46118i	0.119951	+	0.119951i	0.764534	−	0.644583i	$-0.222969\pi$
$421$	2.46118	+	2.46118i	0.119951	+	0.119951i	−0.644583	+	0.764534i	$0.722969\pi$
$422$	21.0764	−	5.64740i	1.02598	−	0.274911i
$423$	4.76516	+	4.76516i	0.231690	+	0.231690i
$424$	−0.248496	−	0.927399i	−0.0120680	−	0.0450385i
$425$	3.13822	+	1.81185i	0.152226	+	0.0878876i
$426$	3.31623	−	5.74387i	0.160672	−	0.278292i
$427$		0			0
$428$			6.43252i			0.310927i
$429$	−28.3192	−	12.4862i	−1.36727	−	0.602841i
$430$	23.0956	+	13.3342i	1.11377	+	0.643034i
$431$	−3.96452	+	14.7958i	−0.190964	+	0.712688i	0.802310	+	0.596907i	$0.203604\pi$
$431$	−3.96452	+	14.7958i	−0.190964	+	0.712688i	−0.993275	+	0.115781i	$0.963063\pi$
$432$		−	21.8991i		−	1.05362i
$433$	6.16396	+	10.6763i	0.296221	+	0.513070i	0.975268	−	0.221025i	$-0.0709402\pi$
$433$	6.16396	+	10.6763i	0.296221	+	0.513070i	−0.679047	+	0.734095i	$0.737607\pi$
$434$		0			0
$435$	−3.27628	+	12.2272i	−0.157086	+	0.586251i
$436$	−5.06856	−	18.9161i	−0.242740	−	0.905919i
$437$	−3.24151	+	0.868559i	−0.155062	+	0.0415488i
$438$	17.9069			0.855625
$439$	7.77197			0.370936			0.185468	−	0.982650i	$-0.440620\pi$
$439$	7.77197			0.370936			0.185468	+	0.982650i	$0.440620\pi$
$440$	2.32519	−	0.623033i	0.110849	−	0.0297019i
$441$		0			0
$442$	0.493808	+	4.54053i	0.0234881	+	0.215971i
$443$	−3.14950	−	5.45509i	−0.149637	−	0.259179i	0.781456	−	0.623960i	$-0.214477\pi$
$443$	−3.14950	−	5.45509i	−0.149637	−	0.259179i	−0.931093	+	0.364781i	$0.881144\pi$
$444$	−7.27658	−	1.94975i	−0.345331	−	0.0925312i
$445$	−6.70060	−	11.6058i	−0.317639	−	0.550167i
$446$	−7.85462	+	13.6046i	−0.371927	+	0.644196i
$447$	14.6513	−	14.6513i	0.692982	−	0.692982i
$448$		0			0
$449$	14.6362	+	3.92175i	0.690723	+	0.185079i	0.587072	−	0.809535i	$-0.300281\pi$
$449$	14.6362	+	3.92175i	0.690723	+	0.185079i	0.103651	+	0.994614i	$0.466947\pi$
$450$	10.2767	+	2.75363i	0.484448	+	0.129808i
$451$		−	17.1552i		−	0.807805i
$452$	−4.78688	+	2.76370i	−0.225156	+	0.129994i
$453$	−24.2770	−	24.2770i	−1.14064	−	1.14064i
$454$	−28.7285			−1.34829
$455$		0			0
$456$	−0.131486			−0.00615742
$457$	10.9957	+	10.9957i	0.514356	+	0.514356i	0.915858	−	0.401502i	$-0.131512\pi$
$457$	10.9957	+	10.9957i	0.514356	+	0.514356i	−0.401502	+	0.915858i	$0.631512\pi$
$458$	19.9160	−	11.4985i	0.930613	−	0.537290i
$459$		−	3.55344i		−	0.165860i
$460$	29.7008	+	7.95829i	1.38480	+	0.371057i
$461$	29.6778	+	7.95214i	1.38223	+	0.370368i	0.871931	−	0.489628i	$-0.162867\pi$
$461$	29.6778	+	7.95214i	1.38223	+	0.370368i	0.510301	+	0.859996i	$0.329534\pi$
$462$		0			0
$463$	−4.11310	+	4.11310i	−0.191152	+	0.191152i	−0.796194	−	0.605042i	$-0.793156\pi$
$463$	−4.11310	+	4.11310i	−0.191152	+	0.191152i	0.605042	+	0.796194i	$0.293156\pi$
$464$	−5.17622	+	8.96548i	−0.240300	+	0.416212i
$465$	2.61650	+	4.53191i	0.121337	+	0.210162i
$466$	−42.6042	−	11.4158i	−1.97360	−	0.528825i
$467$	−4.08246	−	7.07102i	−0.188913	−	0.327208i	0.755975	−	0.654601i	$-0.227163\pi$
$467$	−4.08246	−	7.07102i	−0.188913	−	0.327208i	−0.944888	+	0.327393i	$0.893830\pi$
$468$	2.46194	+	6.34502i	0.113803	+	0.293299i
$469$		0			0
$470$	46.9984	−	12.5932i	2.16787	−	0.580880i
$471$	10.9845			0.506139
$472$	−0.117516			−0.00540911
$473$	−23.1644	+	6.20688i	−1.06510	+	0.285393i
$474$	−9.16104	−	34.1895i	−0.420781	−	1.57037i
$475$	−1.10129	+	4.11006i	−0.0505305	+	0.188583i
$476$		0			0
$477$	3.56274	+	6.17084i	0.163127	+	0.282544i
$478$		−	10.8027i		−	0.494105i
$479$	−9.46087	+	35.3085i	−0.432278	+	1.61328i	0.315218	+	0.949019i	$0.397922\pi$
$479$	−9.46087	+	35.3085i	−0.432278	+	1.61328i	−0.747497	+	0.664266i	$0.768744\pi$
$480$	−33.0362	−	19.0735i	−1.50789	−	0.870580i
$481$	−9.07408	+	0.986859i	−0.413743	+	0.0449969i
$482$		−	31.4616i		−	1.43304i
$483$		0			0
$484$	−25.0985	+	43.4719i	−1.14084	+	1.97599i
$485$	24.7623	+	14.2965i	1.12440	+	0.649171i
$486$	−4.76899	−	17.7981i	−0.216326	−	0.807339i
$487$	11.9118	+	11.9118i	0.539773	+	0.539773i	0.923462	−	0.383689i	$-0.125347\pi$
$487$	11.9118	+	11.9118i	0.539773	+	0.539773i	−0.383689	+	0.923462i	$0.625347\pi$
$488$	0.129809	−	0.0347821i	0.00587617	−	0.00157451i
$489$	2.62555	+	2.62555i	0.118731	+	0.118731i
$490$		0			0
$491$	8.48030	+	4.89611i	0.382711	+	0.220958i	0.678997	−	0.734141i	$-0.262415\pi$
$491$	8.48030	+	4.89611i	0.382711	+	0.220958i	−0.296286	+	0.955099i	$0.595748\pi$
$492$	6.07108	−	6.07108i	0.273705	−	0.273705i
$493$	−0.839916	+	1.45478i	−0.0378279	+	0.0655199i
$494$	−4.99987	+	1.94001i	−0.224955	+	0.0872851i
$495$	−15.4717	+	8.93256i	−0.695399	+	0.401489i
$496$	1.10766	+	4.13383i	0.0497352	+	0.185614i
$497$		0			0
$498$	−12.7975	+	7.38863i	−0.573469	+	0.331093i
$499$	−0.762677	+	2.84635i	−0.0341421	+	0.127420i	−0.980894	−	0.194545i	$-0.937677\pi$
$499$	−0.762677	+	2.84635i	−0.0341421	+	0.127420i	0.946751	+	0.321966i	$0.104344\pi$
$500$	3.65790	−	3.65790i	0.163586	−	0.163586i
$501$	3.47321	−	3.47321i	0.155172	−	0.155172i
$502$	2.40653	−	8.98127i	0.107408	−	0.400854i
$503$	24.6898	−	14.2547i	1.10086	−	0.635584i	0.164416	−	0.986391i	$-0.447426\pi$
$503$	24.6898	−	14.2547i	1.10086	−	0.635584i	0.936448	+	0.350807i	$0.114093\pi$
$504$		0			0
$505$	−14.5849	−	54.4314i	−0.649018	−	2.42217i
$506$	−47.1807	+	27.2398i	−2.09744	+	1.21096i
$507$	−12.6586	−	13.8562i	−0.562186	−	0.615377i
$508$	5.86956	−	10.1664i	0.260419	−	0.451060i
$509$	13.6285	−	13.6285i	0.604072	−	0.604072i	−0.337319	−	0.941390i	$-0.609520\pi$
$509$	13.6285	−	13.6285i	0.604072	−	0.604072i	0.941390	+	0.337319i	$0.109520\pi$
$510$	−5.19632	−	3.00010i	−0.230097	−	0.132847i
$511$		0			0
$512$	−22.7359	−	22.7359i	−1.00479	−	1.00479i
$513$	4.03037	−	1.07994i	0.177945	−	0.0476803i
$514$	22.3234	+	22.3234i	0.984642	+	0.984642i
$515$	−12.2194	−	45.6035i	−0.538452	−	2.00953i
$516$	−10.3943	−	6.00113i	−0.457582	−	0.264185i
$517$	−21.8770	+	37.8921i	−0.962149	+	1.66649i
$518$		0			0
$519$			20.2843i			0.890381i
$520$	1.44258	+	0.223146i	0.0632612	+	0.00978561i
$521$	−9.05428	−	5.22749i	−0.396675	−	0.229020i	0.288373	−	0.957518i	$-0.406886\pi$
$521$	−9.05428	−	5.22749i	−0.396675	−	0.229020i	−0.685048	+	0.728498i	$0.740219\pi$
$522$	−1.27650	+	4.76395i	−0.0558708	+	0.208513i
$523$			18.4333i			0.806033i	0.915193	+	0.403016i	$0.132038\pi$
$523$			18.4333i			0.806033i	−0.915193	+	0.403016i	$0.867962\pi$
$524$	−18.0465	−	31.2574i	−0.788365	−	1.36549i
$525$		0			0
$526$	12.4715	−	46.5444i	0.543785	−	2.02943i
$527$	0.179733	+	0.670773i	0.00782929	+	0.0292193i
$528$	32.1192	−	8.60632i	1.39781	−	0.374542i
$529$	2.32795			0.101215
$530$	51.4470			2.23472
$531$	0.842426	−	0.225727i	0.0365582	−	0.00979574i
$532$		0			0
$533$	4.19689	−	9.51872i	0.181788	−	0.412301i
$534$	5.94169	+	10.2913i	0.257122	+	0.445348i
$535$	−9.89016	−	2.65006i	−0.427589	−	0.114572i
$536$	0.332965	+	0.576713i	0.0143819	+	0.0249102i
$537$	10.8005	−	18.7070i	0.466075	−	0.807266i
$538$	−19.2858	+	19.2858i	−0.831469	+	0.831469i
$539$		0			0
$540$	−36.9288	−	9.89505i	−1.58916	−	0.425815i
$541$	40.4921	+	10.8498i	1.74089	+	0.466470i	0.982644	−	0.185499i	$-0.0593901\pi$
$541$	40.4921	+	10.8498i	1.74089	+	0.466470i	0.758246	+	0.651969i	$0.226057\pi$
$542$			43.6387i			1.87444i
$543$	−19.3053	+	11.1459i	−0.828470	+	0.478317i
$544$	−3.57953	−	3.57953i	−0.153471	−	0.153471i
$545$	31.1722			1.33527
$546$		0			0
$547$	39.3151			1.68099			0.840496	−	0.541818i	$-0.182264\pi$
$547$	39.3151			1.68099			0.840496	+	0.541818i	$0.182264\pi$
$548$	21.3663	+	21.3663i	0.912724	+	0.912724i
$549$	−0.863737	+	0.498679i	−0.0368634	+	0.0212831i
$550$			69.0772i			2.94546i
$551$	−1.90529	−	0.510522i	−0.0811683	−	0.0217490i
$552$	−0.782357	−	0.209632i	−0.0332993	−	0.00892253i
$553$		0			0
$554$	−30.5185	+	30.5185i	−1.29661	+	1.29661i
$555$	5.99559	−	10.3847i	0.254499	−	0.440805i
$556$	−3.69460	−	6.39924i	−0.156686	−	0.271388i
$557$	41.1681	+	11.0310i	1.74435	+	0.467397i	0.983405	−	0.181421i	$-0.0580697\pi$
$557$	41.1681	+	11.0310i	1.74435	+	0.467397i	0.760944	+	0.648818i	$0.224736\pi$
$558$	1.01943	+	1.76571i	0.0431561	+	0.0747486i
$559$	−14.3715	−	2.22306i	−0.607848	−	0.0940255i
$560$		0			0
$561$	5.21180	−	1.39650i	0.220042	−	0.0589602i
$562$	−2.49307			−0.105164
$563$	37.3926			1.57591			0.787955	−	0.615733i	$-0.211140\pi$
$563$	37.3926			1.57591			0.787955	+	0.615733i	$0.211140\pi$
$564$	−21.1518	+	5.66761i	−0.890652	+	0.238650i
$565$	−2.27718	−	8.49854i	−0.0958015	−	0.357536i
$566$	−9.62909	+	35.9363i	−0.404741	+	1.51051i
$567$		0			0
$568$	−0.140650	−	0.243613i	−0.00590155	−	0.0102218i
$569$			31.1625i			1.30640i	0.757186	+	0.653199i	$0.226574\pi$
$569$			31.1625i			1.30640i	−0.757186	+	0.653199i	$0.773426\pi$
$570$	1.82354	−	6.80553i	0.0763795	−	0.285052i
$571$	−16.5495	−	9.55483i	−0.692573	−	0.399857i	0.112002	−	0.993708i	$-0.464274\pi$
$571$	−16.5495	−	9.55483i	−0.692573	−	0.399857i	−0.804575	+	0.593851i	$0.797607\pi$
$572$	−35.6554	+	26.1023i	−1.49083	+	1.09139i
$573$			24.7663i			1.03463i
$574$		0			0
$575$	−13.1055	+	22.6995i	−0.546539	+	0.946633i
$576$	−6.72702	−	3.88385i	−0.280293	−	0.161827i
$577$	−5.15872	−	19.2526i	−0.214760	−	0.801497i	−0.986251	−	0.165256i	$-0.947155\pi$
$577$	−5.15872	−	19.2526i	−0.214760	−	0.801497i	0.771490	−	0.636241i	$-0.219512\pi$
$578$	23.6619	+	23.6619i	0.984206	+	0.984206i
$579$	−8.55194	+	2.29149i	−0.355406	+	0.0952309i
$580$	12.7798	+	12.7798i	0.530652	+	0.530652i
$581$		0			0
$582$	−21.9577	−	12.6773i	−0.910176	−	0.525490i
$583$	−32.7132	+	32.7132i	−1.35484	+	1.35484i
$584$	0.379740	−	0.657728i	0.0157137	−	0.0272170i
$585$	−10.7699	+	1.17129i	−0.445281	+	0.0484268i
$586$	−21.6861	+	12.5205i	−0.895847	+	0.517217i
$587$	10.4047	+	38.8308i	0.429447	+	1.60272i	0.754016	+	0.656856i	$0.228114\pi$
$587$	10.4047	+	38.8308i	0.429447	+	1.60272i	−0.324569	+	0.945862i	$0.605219\pi$
$588$		0			0
$589$	−0.706179	+	0.407713i	−0.0290976	+	0.0167995i
$590$	1.62979	−	6.08244i	0.0670972	−	0.250410i
$591$	−26.2000	+	26.2000i	−1.07772	+	1.07772i
$592$	6.93434	−	6.93434i	0.285000	−	0.285000i
$593$	1.86107	−	6.94560i	0.0764249	−	0.285222i	−0.917128	−	0.398594i	$-0.869498\pi$
$593$	1.86107	−	6.94560i	0.0764249	−	0.285222i	0.993553	+	0.113372i	$0.0361651\pi$
$594$	58.6627	−	33.8689i	2.40696	−	1.38966i
$595$		0			0
$596$	−7.65669	−	28.5752i	−0.313630	−	1.17048i
$597$	10.9116	−	6.29979i	0.446580	−	0.257833i
$598$	−32.8427	+	3.57183i	−1.34304	+	0.146063i
$599$	14.6877	−	25.4398i	0.600123	−	1.03944i	−0.392679	−	0.919676i	$-0.628452\pi$
$599$	14.6877	−	25.4398i	0.600123	−	1.03944i	0.992802	−	0.119768i	$-0.0382150\pi$
$600$	−0.726185	+	0.726185i	−0.0296464	+	0.0296464i
$601$	−40.3495	−	23.2958i	−1.64589	−	0.950255i	−0.978682	−	0.205384i	$-0.934156\pi$
$601$	−40.3495	−	23.2958i	−1.64589	−	0.950255i	−0.667208	−	0.744871i	$-0.732511\pi$
$602$		0			0
$603$	−3.49466	−	3.49466i	−0.142314	−	0.142314i
$604$	−47.3488	+	12.6871i	−1.92659	+	0.516229i
$605$	−56.4991	−	56.4991i	−2.29702	−	2.29702i
$606$	12.9330	+	48.2665i	0.525366	+	1.96069i
$607$	18.6085	+	10.7436i	0.755295	+	0.436070i	0.827604	−	0.561312i	$-0.189703\pi$
$607$	18.6085	+	10.7436i	0.755295	+	0.436070i	−0.0723088	+	0.997382i	$0.523037\pi$
$608$	2.97210	−	5.14782i	0.120534	−	0.208772i
$609$		0			0
$610$			7.20107i			0.291563i
$611$	−21.4087	+	15.6727i	−0.866104	+	0.634052i
$612$	−1.02755	−	0.593258i	−0.0415364	−	0.0239810i
$613$	7.39841	−	27.6112i	0.298819	−	1.11521i	−0.639318	−	0.768943i	$-0.720783\pi$
$613$	7.39841	−	27.6112i	0.298819	−	1.11521i	0.938137	−	0.346265i	$-0.112550\pi$
$614$			10.0146i			0.404156i
$615$	6.83329	+	11.8356i	0.275545	+	0.477257i
$616$		0			0
$617$	−5.40928	+	20.1877i	−0.217769	+	0.812726i	0.767404	+	0.641164i	$0.221548\pi$
$617$	−5.40928	+	20.1877i	−0.217769	+	0.812726i	−0.985173	+	0.171562i	$0.945119\pi$
$618$	10.8354	+	40.4384i	0.435866	+	1.62667i
$619$	4.33146	−	1.16061i	0.174096	−	0.0466489i	−0.170718	−	0.985320i	$-0.554609\pi$
$619$	4.33146	−	1.16061i	0.174096	−	0.0466489i	0.344814	+	0.938671i	$0.387942\pi$
$620$	7.47144			0.300060
$621$	25.7029			1.03142
$622$	−35.7510	+	9.57946i	−1.43349	+	0.384101i
$623$		0			0
$624$	19.9272	+	3.08245i	0.797725	+	0.123397i
$625$	−10.2952	−	17.8317i	−0.411806	−	0.713269i
$626$	17.5009	+	4.68935i	0.699476	+	0.187424i
$627$	3.16787	+	5.48690i	0.126512	+	0.219126i
$628$	7.84159	−	13.5820i	0.312914	−	0.541982i
$629$	1.12520	−	1.12520i	0.0448645	−	0.0448645i
$630$		0			0
$631$	−9.89598	−	2.65162i	−0.393953	−	0.105559i	0.0564039	−	0.998408i	$-0.482037\pi$
$631$	−9.89598	−	2.65162i	−0.393953	−	0.105559i	−0.450357	+	0.892849i	$0.648703\pi$
$632$	−1.45007	−	0.388544i	−0.0576806	−	0.0154555i
$633$		−	15.6313i		−	0.621290i
$634$	−25.1439	+	14.5168i	−0.998592	+	0.576537i
$635$	13.2129	+	13.2129i	0.524339	+	0.524339i
$636$	−23.1539			−0.918114
$637$		0			0
$638$	−32.0220			−1.26776
$639$	1.47620	+	1.47620i	0.0583977	+	0.0583977i
$640$	−2.80362	+	1.61867i	−0.110823	+	0.0639836i
$641$		−	32.0455i		−	1.26572i	−0.774266	−	0.632860i	$-0.781881\pi$
$641$		−	32.0455i		−	1.26572i	0.774266	−	0.632860i	$-0.218119\pi$
$642$	8.77000	+	2.34991i	0.346124	+	0.0927437i
$643$	−44.5502	−	11.9372i	−1.75689	−	0.470757i	−0.770815	−	0.637059i	$-0.780151\pi$
$643$	−44.5502	−	11.9372i	−1.75689	−	0.470757i	−0.986075	+	0.166302i	$0.946817\pi$
$644$		0			0
$645$	13.5091	−	13.5091i	0.531921	−	0.531921i
$646$	0.467487	−	0.809711i	0.0183930	−	0.0318576i
$647$	−15.3506	−	26.5881i	−0.603496	−	1.04529i	−0.992287	−	0.123959i	$-0.960441\pi$
$647$	−15.3506	−	26.5881i	−0.603496	−	1.04529i	0.388792	−	0.921326i	$-0.372893\pi$
$648$	0.645301	+	0.172908i	0.0253498	+	0.00679246i
$649$	2.83128	+	4.90392i	0.111137	+	0.192496i
$650$	−16.8993	+	38.3282i	−0.662844	+	1.50336i
$651$		0			0
$652$	5.12074	−	1.37210i	0.200544	−	0.0537355i
$653$	−15.3539			−0.600844			−0.300422	−	0.953806i	$-0.597127\pi$
$653$	−15.3539			−0.600844			−0.300422	+	0.953806i	$0.597127\pi$
$654$	−27.6416			−1.08087
$655$	55.4939	−	14.8696i	2.16833	−	0.581001i
$656$	2.89277	+	10.7960i	0.112944	+	0.421512i
$657$	−1.45883	+	5.44441i	−0.0569142	+	0.212407i
$658$		0			0
$659$	4.71985	+	8.17502i	0.183859	+	0.318454i	0.943192	−	0.332250i	$-0.107808\pi$
$659$	4.71985	+	8.17502i	0.183859	+	0.318454i	−0.759332	+	0.650703i	$0.774474\pi$
$660$		−	58.0520i		−	2.25967i
$661$	−2.13827	+	7.98013i	−0.0831691	+	0.310391i	−0.994961	−	0.100261i	$-0.968032\pi$
$661$	−2.13827	+	7.98013i	−0.0831691	+	0.310391i	0.911792	+	0.410652i	$0.134699\pi$
$662$	14.2832	+	8.24641i	0.555132	+	0.320506i
$663$	3.23347	+	0.500171i	0.125577	+	0.0194250i
$664$			0.626743i			0.0243224i
$665$		0			0
$666$	2.33599	−	4.04605i	0.0905178	−	0.156781i
$667$	−10.5227	−	6.07531i	−0.407442	−	0.235237i
$668$	−1.81508	−	6.77398i	−0.0702277	−	0.262093i
$669$	7.95763	+	7.95763i	0.307660	+	0.307660i
$670$	−34.4675	+	9.23555i	−1.33160	+	0.356800i
$671$	−4.57890	−	4.57890i	−0.176766	−	0.176766i
$672$		0			0
$673$	−27.2566	−	15.7366i	−1.05067	−	0.606602i	−0.127830	−	0.991796i	$-0.540801\pi$
$673$	−27.2566	−	15.7366i	−1.05067	−	0.606602i	−0.922836	+	0.385194i	$0.874134\pi$
$674$	2.33459	−	2.33459i	0.0899252	−	0.0899252i
$675$	16.2950	−	28.2237i	0.627193	−	1.08633i
$676$	−26.1695	+	5.76031i	−1.00652	+	0.221550i
$677$	40.8799	−	23.6020i	1.57114	−	0.907099i	0.575112	−	0.818074i	$-0.304958\pi$
$677$	40.8799	−	23.6020i	1.57114	−	0.907099i	0.996029	−	0.0890246i	$-0.0283750\pi$
$678$	2.01926	+	7.53599i	0.0775493	+	0.289418i
$679$		0			0
$680$	−0.220390	+	0.127242i	−0.00845157	+	0.00487952i
$681$	−5.32663	+	19.8792i	−0.204117	+	0.761774i
$682$	−9.36050	+	9.36050i	−0.358432	+	0.358432i
$683$	−32.1357	+	32.1357i	−1.22964	+	1.22964i	−0.265538	+	0.964100i	$0.585550\pi$
$683$	−32.1357	+	32.1357i	−1.22964	+	1.22964i	−0.964100	+	0.265538i	$0.914450\pi$
$684$	0.360597	−	1.34577i	0.0137878	−	0.0514567i
$685$	−41.6538	+	24.0488i	−1.59151	+	0.918858i
$686$		0			0
$687$	−4.26394	−	15.9132i	−0.162680	−	0.607128i
$688$	13.5310	−	7.81214i	0.515866	−	0.297835i
$689$	−26.1544	+	10.1482i	−0.996402	+	0.386616i
$690$	21.7004	−	37.5863i	0.826121	−	1.43088i
$691$	13.3618	−	13.3618i	0.508308	−	0.508308i	−0.405699	−	0.914007i	$-0.632972\pi$
$691$	13.3618	−	13.3618i	0.508308	−	0.508308i	0.914007	+	0.405699i	$0.132972\pi$
$692$	25.0810	+	14.4805i	0.953435	+	0.550466i
$693$		0			0
$694$	13.7246	+	13.7246i	0.520980	+	0.520980i
$695$	11.3611	−	3.04420i	0.430951	−	0.115473i
$696$	−0.336637	−	0.336637i	−0.0127602	−	0.0127602i
$697$	0.469393	+	1.75180i	0.0177795	+	0.0663542i
$698$	−51.4340	−	29.6954i	−1.94680	−	1.12399i
$699$	−15.7987	+	27.3642i	−0.597563	+	1.03501i
$700$		0			0
$701$			31.6032i			1.19364i	0.802377	+	0.596818i	$0.203569\pi$
$701$			31.6032i			1.19364i	−0.802377	+	0.596818i	$0.796431\pi$
$702$	40.8354	−	4.44109i	1.54123	−	0.167618i
$703$	1.61818	+	0.934256i	0.0610308	+	0.0352361i
$704$	13.0531	−	48.7148i	0.491957	−	1.83601i
$705$		−	34.8564i		−	1.31277i
$706$	16.1071	+	27.8982i	0.606197	+	1.04996i
$707$		0			0
$708$	−0.733492	+	2.73743i	−0.0275663	+	0.102879i
$709$	−5.02350	−	18.7480i	−0.188661	−	0.704094i	−0.993817	−	0.111030i	$-0.964585\pi$
$709$	−5.02350	−	18.7480i	−0.188661	−	0.704094i	0.805156	−	0.593064i	$-0.202082\pi$
$710$	14.5597	−	3.90125i	0.546414	−	0.146411i
$711$	11.1413			0.417831
$712$	0.504006			0.0188884
$713$	−4.85186	+	1.30005i	−0.181704	+	0.0486873i
$714$		0			0
$715$	−25.4438	−	65.5747i	−0.951543	−	2.45236i
$716$	−15.4205	−	26.7090i	−0.576290	−	0.998163i
$717$	−7.47517	−	2.00296i	−0.279165	−	0.0748021i
$718$	−5.79058	−	10.0296i	−0.216103	−	0.374301i
$719$	−2.23540	+	3.87183i	−0.0833665	+	0.144395i	−0.904694	−	0.426062i	$-0.859901\pi$
$719$	−2.23540	+	3.87183i	−0.0833665	+	0.144395i	0.821327	+	0.570457i	$0.193234\pi$
$720$	8.23028	−	8.23028i	0.306724	−	0.306724i
$721$		0			0
$722$	−35.9246	−	9.62596i	−1.33697	−	0.358241i
$723$	−21.7705	−	5.83339i	−0.809654	−	0.216946i
$724$			31.8273i			1.18285i
$725$	−13.3423	+	7.70318i	−0.495520	+	0.286089i
$726$	50.1000	+	50.1000i	1.85938	+	1.85938i
$727$	25.9080			0.960874			0.480437	−	0.877029i	$-0.340478\pi$
$727$	25.9080			0.960874			0.480437	+	0.877029i	$0.340478\pi$
$728$		0			0
$729$	−29.4421			−1.09045
$730$	28.7765	+	28.7765i	1.06507	+	1.06507i
$731$	2.19560	−	1.26763i	0.0812073	−	0.0468851i
$732$		−	3.24087i		−	0.119786i
$733$	46.3272	+	12.4133i	1.71114	+	0.458497i	0.975703	−	0.219100i	$-0.0703119\pi$
$733$	46.3272	+	12.4133i	1.71114	+	0.458497i	0.735433	+	0.677597i	$0.236979\pi$
$734$	49.5619	+	13.2801i	1.82936	+	0.490177i
$735$		0			0
$736$	25.8916	−	25.8916i	0.954376	−	0.954376i
$737$	16.0441	−	27.7892i	0.590991	−	1.02363i
$738$	2.66237	+	4.61136i	0.0980033	+	0.169747i
$739$	16.8688	+	4.51998i	0.620529	+	0.166270i	0.555368	−	0.831605i	$-0.312577\pi$
$739$	16.8688	+	4.51998i	0.620529	+	0.166270i	0.0651605	+	0.997875i	$0.479244\pi$
$740$	−8.56025	−	14.8268i	−0.314681	−	0.545043i
$741$	0.415389	+	3.81946i	0.0152597	+	0.140311i
$742$		0			0
$743$	−33.0523	+	8.85634i	−1.21257	+	0.324908i	−0.807770	−	0.589497i	$-0.799326\pi$
$743$	−33.0523	+	8.85634i	−1.21257	+	0.324908i	−0.404801	+	0.914405i	$0.632659\pi$
$744$	−0.196808			−0.00721532
$745$	47.0894			1.72522
$746$	36.4314	−	9.76176i	1.33385	−	0.357403i
$747$	−1.20386	−	4.49288i	−0.0440470	−	0.164386i
$748$	1.99386	−	7.44118i	0.0729027	−	0.272077i
$749$		0			0
$750$	−3.65083	−	6.32342i	−0.133309	−	0.230899i
$751$			5.56485i			0.203064i	0.994832	+	0.101532i	$0.0323745\pi$
$751$			5.56485i			0.203064i	−0.994832	+	0.101532i	$0.967626\pi$
$752$	7.37798	−	27.5350i	0.269047	−	1.00410i
$753$	−5.76857	−	3.33049i	−0.210219	−	0.121370i
$754$	−17.7677	−	7.83397i	−0.647063	−	0.285296i
$755$		−	78.0268i		−	2.83969i
$756$		0			0
$757$	−9.89589	+	17.1402i	−0.359672	+	0.622971i	−0.987906	−	0.155054i	$-0.950445\pi$
$757$	−9.89589	+	17.1402i	−0.359672	+	0.622971i	0.628234	+	0.778025i	$0.283778\pi$
$758$	37.0601	+	21.3967i	1.34609	+	0.777163i
$759$	10.1012	+	37.6982i	0.366651	+	1.36836i
$760$	−0.211300	−	0.211300i	−0.00766464	−	0.00766464i
$761$	−32.7829	+	8.78414i	−1.18838	+	0.318425i	−0.798245	−	0.602334i	$-0.794238\pi$
$761$	−32.7829	+	8.78414i	−1.18838	+	0.318425i	−0.390133	+	0.920758i	$0.627571\pi$
$762$	−11.7164	−	11.7164i	−0.424441	−	0.424441i
$763$		0			0
$764$	30.6229	+	17.6801i	1.10790	+	0.639644i
$765$	1.33548	−	1.33548i	0.0482844	−	0.0482844i
$766$	32.7018	−	56.6411i	1.18156	−	2.04653i
$767$	0.371254	+	3.41365i	0.0134052	+	0.123260i
$768$	−18.7238	+	10.8102i	−0.675635	+	0.390078i
$769$	−4.79803	−	17.9065i	−0.173021	−	0.645725i	−0.996880	−	0.0789297i	$-0.974850\pi$
$769$	−4.79803	−	17.9065i	−0.173021	−	0.645725i	0.823859	−	0.566795i	$-0.191817\pi$
$770$		0			0
$771$	19.5862	−	11.3081i	0.705378	−	0.407250i
$772$	−3.27168	+	12.2101i	−0.117750	+	0.439451i
$773$	−16.3963	+	16.3963i	−0.589735	+	0.589735i	−0.937560	−	0.347824i	$-0.886921\pi$
$773$	−16.3963	+	16.3963i	−0.589735	+	0.589735i	0.347824	+	0.937560i	$0.386921\pi$
$774$	5.26340	−	5.26340i	0.189189	−	0.189189i
$775$	−1.64840	+	6.15190i	−0.0592122	+	0.220983i
$776$	−0.931285	+	0.537678i	−0.0334312	+	0.0193015i
$777$		0			0
$778$	−3.63222	−	13.5556i	−0.130221	−	0.485993i
$779$	−1.84427	+	1.06479i	−0.0660778	+	0.0381500i
$780$	14.2020	−	32.2108i	0.508514	−	1.15333i
$781$	−6.77729	+	11.7386i	−0.242510	+	0.420040i
$782$	4.07253	−	4.07253i	0.145633	−	0.145633i
$783$	13.0836	+	7.55382i	0.467570	+	0.269952i
$784$		0			0
$785$	17.6522	+	17.6522i	0.630033	+	0.630033i
$786$	−49.2086	+	13.1854i	−1.75521	+	0.470308i
$787$	−11.1188	−	11.1188i	−0.396342	−	0.396342i	0.480598	−	0.876941i	$-0.340419\pi$
$787$	−11.1188	−	11.1188i	−0.396342	−	0.396342i	−0.876941	+	0.480598i	$0.840419\pi$
$788$	13.6920	+	51.0992i	0.487757	+	1.82033i
$789$	−29.8950	−	17.2599i	−1.06429	−	0.614468i
$790$	40.2209	−	69.6646i	1.43099	−	2.47856i
$791$		0			0
$792$		−	0.671889i		−	0.0238745i
$793$	−1.42045	−	3.66085i	−0.0504417	−	0.130000i
$794$	−26.0742	−	15.0540i	−0.925340	−	0.534245i
$795$	9.53894	−	35.5998i	0.338311	−	1.26259i
$796$		−	17.9891i		−	0.637608i
$797$	−10.8696	−	18.8267i	−0.385021	−	0.666876i	0.606751	−	0.794892i	$-0.292473\pi$
$797$	−10.8696	−	18.8267i	−0.385021	−	0.666876i	−0.991772	+	0.128016i	$0.959139\pi$
$798$		0			0
$799$	1.19718	−	4.46794i	0.0423533	−	0.158064i
$800$	−12.0163	−	44.8455i	−0.424840	−	1.58553i
$801$	−3.61302	+	0.968105i	−0.127660	+	0.0342063i
$802$	−48.7187			−1.72032
$803$	−36.5958			−1.29144
$804$	15.5123	−	4.15650i	0.547075	−	0.146588i
$805$		0			0
$806$	−7.48376	+	2.90379i	−0.263604	+	0.102282i
$807$	9.76935	+	16.9210i	0.343897	+	0.595648i
$808$	2.04711	+	0.548522i	0.0720171	+	0.0192969i
$809$	−17.8402	−	30.9002i	−0.627229	−	1.08639i	−0.988105	−	0.153779i	$-0.950856\pi$
$809$	−17.8402	−	30.9002i	−0.627229	−	1.08639i	0.360876	−	0.932614i	$-0.382478\pi$
$810$	−17.8989	+	31.0018i	−0.628902	+	1.08929i
$811$	−0.747882	+	0.747882i	−0.0262617	+	0.0262617i	−0.720116	−	0.693854i	$-0.755911\pi$
$811$	−0.747882	+	0.747882i	−0.0262617	+	0.0262617i	0.693854	+	0.720116i	$0.255911\pi$
$812$		0			0
$813$	30.1967	+	8.09117i	1.05904	+	0.283770i
$814$	29.3001	+	7.85095i	1.02697	+	0.275176i
$815$			8.43855i			0.295590i
$816$	−3.04437	+	1.75767i	−0.106574	+	0.0615308i
$817$	2.10504	+	2.10504i	0.0736461	+	0.0736461i
$818$	−75.6376			−2.64461
$819$		0			0
$820$	19.5125			0.681407
$821$	7.82100	+	7.82100i	0.272955	+	0.272955i	0.830289	−	0.557334i	$-0.188176\pi$
$821$	7.82100	+	7.82100i	0.272955	+	0.272955i	−0.557334	+	0.830289i	$0.688176\pi$
$822$	36.9360	−	21.3250i	1.28829	−	0.743796i
$823$		−	23.6095i		−	0.822977i	−0.911415	−	0.411488i	$-0.865009\pi$
$823$		−	23.6095i		−	0.822977i	0.911415	−	0.411488i	$-0.134991\pi$
$824$	1.71510	+	0.459560i	0.0597484	+	0.0160095i
$825$	47.7994	+	12.8078i	1.66416	+	0.445910i
$826$		0			0
$827$	−1.09240	+	1.09240i	−0.0379865	+	0.0379865i	−0.725845	−	0.687858i	$-0.758551\pi$
$827$	−1.09240	+	1.09240i	−0.0379865	+	0.0379865i	0.687858	+	0.725845i	$0.258551\pi$
$828$	4.29118	−	7.43253i	0.149129	−	0.258298i
$829$	19.1064	+	33.0932i	0.663591	+	1.14937i	0.979665	+	0.200639i	$0.0643020\pi$
$829$	19.1064	+	33.0932i	0.663591	+	1.14937i	−0.316074	+	0.948735i	$0.602365\pi$
$830$	−32.4392	−	8.69207i	−1.12598	−	0.301706i
$831$	15.4594	+	26.7765i	0.536280	+	0.928865i
$832$	19.1604	−	23.8366i	0.664267	−	0.826384i
$833$		0			0
$834$	−10.0743	+	2.69941i	−0.348846	+	0.0934729i
$835$	11.1630			0.386310
$836$	9.04588			0.312858
$837$	6.03263	−	1.61644i	0.208518	−	0.0558722i
$838$	4.24682	+	15.8493i	0.146704	+	0.547506i
$839$	−10.2082	+	38.0974i	−0.352425	+	1.31527i	0.531268	+	0.847204i	$0.321716\pi$
$839$	−10.2082	+	38.0974i	−0.352425	+	1.31527i	−0.883694	+	0.468066i	$0.844951\pi$
$840$		0			0
$841$	10.9291	+	18.9297i	0.376864	+	0.652747i
$842$		−	7.01435i		−	0.241730i
$843$	−0.462248	+	1.72513i	−0.0159207	+	0.0594167i
$844$	−19.3277	−	11.1589i	−0.665288	−	0.384104i
$845$	1.92467	−	42.6095i	0.0662108	−	1.46581i
$846$		−	13.5807i		−	0.466914i
$847$		0			0
$848$	15.0707	−	26.1031i	0.517528	−	0.896385i
$849$	23.0815	+	13.3261i	0.792154	+	0.457350i
$850$	−1.89007	−	7.05382i	−0.0648288	−	0.241944i
$851$	8.13881	+	8.13881i	0.278995	+	0.278995i
$852$	−6.55263	+	1.75577i	−0.224490	+	0.0601518i
$853$	−2.18217	−	2.18217i	−0.0747162	−	0.0747162i	0.668761	−	0.743477i	$-0.266825\pi$
$853$	−2.18217	−	2.18217i	−0.0747162	−	0.0747162i	−0.743477	+	0.668761i	$0.766825\pi$
$854$		0			0
$855$	1.92059	+	1.10886i	0.0656829	+	0.0379220i
$856$	0.272293	−	0.272293i	0.00930678	−	0.00930678i
$857$	−14.7330	+	25.5183i	−0.503270	+	0.871689i	0.496723	+	0.867909i	$0.334536\pi$
$857$	−14.7330	+	25.5183i	−0.503270	+	0.871689i	−0.999993	+	0.00377978i	$0.998797\pi$
$858$	22.5620	+	58.1477i	0.770254	+	1.98513i
$859$	44.5926	−	25.7455i	1.52148	−	0.878426i	0.521800	−	0.853068i	$-0.325261\pi$
$859$	44.5926	−	25.7455i	1.52148	−	0.878426i	0.999678	−	0.0253585i	$-0.00807272\pi$
$860$	−7.05980	−	26.3475i	−0.240737	−	0.898443i
$861$		0			0
$862$	26.7334	−	15.4345i	0.910543	−	0.525702i
$863$	8.33816	−	31.1185i	0.283834	−	1.05928i	−0.665852	−	0.746083i	$-0.731932\pi$
$863$	8.33816	−	31.1185i	0.283834	−	1.05928i	0.949687	−	0.313201i	$-0.101401\pi$
$864$	−32.1926	+	32.1926i	−1.09522	+	1.09522i
$865$	−32.5970	+	32.5970i	−1.10833	+	1.10833i
$866$	6.43005	−	23.9973i	0.218502	−	0.815461i
$867$	20.7606	−	11.9861i	0.705066	−	0.407070i
$868$		0			0
$869$	18.7222	+	69.8721i	0.635106	+	2.37025i
$870$	22.0925	−	12.7551i	0.749005	−	0.432438i
$871$	15.7007	−	11.4940i	0.531997	−	0.389460i
$872$	−0.586177	+	1.01529i	−0.0198505	+	0.0343820i
$873$	5.64323	−	5.64323i	0.190994	−	0.190994i
$874$	5.85683	+	3.38144i	0.198110	+	0.114379i
$875$		0			0
$876$	−12.9510	−	12.9510i	−0.437574	−	0.437574i
$877$	−23.9651	+	6.42144i	−0.809245	+	0.216837i	−0.639639	−	0.768675i	$-0.720916\pi$
$877$	−23.9651	+	6.42144i	−0.809245	+	0.216837i	−0.169606	+	0.985512i	$0.554250\pi$
$878$	−11.0750	−	11.0750i	−0.373764	−	0.373764i
$879$	4.64293	+	17.3276i	0.156602	+	0.584447i
$880$	65.4462	+	37.7854i	2.20619	+	1.27375i
$881$	−8.18440	+	14.1758i	−0.275740	+	0.477595i	−0.970321	−	0.241819i	$-0.922256\pi$
$881$	−8.18440	+	14.1758i	−0.275740	+	0.477595i	0.694582	+	0.719414i	$0.255589\pi$
$882$		0			0
$883$		−	13.3555i		−	0.449449i	−0.974422	−	0.224724i	$-0.927852\pi$
$883$		−	13.3555i		−	0.449449i	0.974422	−	0.224724i	$-0.0721482\pi$
$884$	2.92675	−	3.64103i	0.0984373	−	0.122461i
$885$	−3.90669	−	2.25553i	−0.131322	−	0.0758187i
$886$	−3.28546	+	12.2615i	−0.110377	+	0.411934i
$887$			16.4923i			0.553757i	0.960905	+	0.276878i	$0.0892999\pi$
$887$			16.4923i			0.553757i	−0.960905	+	0.276878i	$0.910700\pi$
$888$	0.225488	+	0.390557i	0.00756689	+	0.0131062i
$889$		0			0
$890$	−6.98987	+	26.0865i	−0.234301	+	0.874423i
$891$	−8.33164	−	31.0941i	−0.279120	−	1.04169i
$892$	15.5202	−	4.15862i	0.519654	−	0.139241i
$893$	5.43146			0.181757
$894$	−41.7561			−1.39653
$895$	47.4187	−	12.7058i	1.58503	−	0.424708i
$896$		0			0
$897$	−3.61786	+	23.3884i	−0.120797	+	0.780917i
$898$	−15.2680	−	26.4450i	−0.509500	−	0.882480i
$899$	−2.85183	−	0.764145i	−0.0951138	−	0.0254857i
$900$	−5.44099	−	9.42407i	−0.181366	−	0.314136i
$901$	2.44543	−	4.23561i	0.0814690	−	0.141108i
$902$	−24.4460	+	24.4460i	−0.813964	+	0.813964i
$903$		0			0
$904$	0.319621	+	0.0856423i	0.0106304	+	0.00284842i
$905$	−48.9354	−	13.1122i	−1.62667	−	0.435864i
$906$			69.1894i			2.29866i
$907$	11.2778	−	6.51123i	0.374473	−	0.216202i	−0.300938	−	0.953644i	$-0.597300\pi$
$907$	11.2778	−	6.51123i	0.374473	−	0.216202i	0.675411	+	0.737442i	$0.263966\pi$
$908$	20.7776	+	20.7776i	0.689528	+	0.689528i
$909$	−15.7285			−0.521683
$910$		0			0
$911$	29.0374			0.962053			0.481026	−	0.876706i	$-0.340264\pi$
$911$	29.0374			0.962053			0.481026	+	0.876706i	$0.340264\pi$
$912$	−2.91880	−	2.91880i	−0.0966513	−	0.0966513i
$913$	26.1539	−	15.1000i	0.865567	−	0.499735i
$914$		−	31.3376i		−	1.03656i
$915$	4.98293	+	1.33517i	0.164731	+	0.0441394i
$916$	−22.7202	−	6.08787i	−0.750698	−	0.201149i
$917$		0			0
$918$	−5.06364	+	5.06364i	−0.167125	+	0.167125i
$919$	7.73929	−	13.4048i	0.255296	−	0.442185i	−0.709680	−	0.704524i	$-0.751161\pi$
$919$	7.73929	−	13.4048i	0.255296	−	0.442185i	0.964976	+	0.262339i	$0.0844939\pi$
$920$	−0.920373	−	1.59413i	−0.0303438	−	0.0525570i
$921$	6.92979	+	1.85683i	0.228345	+	0.0611847i
$922$	−30.9590	−	53.6225i	−1.01958	−	1.76596i
$923$	−6.63222	+	4.85527i	−0.218302	+	0.159813i
$924$		0			0
$925$	14.0968	−	3.77723i	0.463501	−	0.124195i
$926$	11.7223			0.385219
$927$	−13.1776			−0.432810
$928$	20.7889	−	5.57038i	0.682430	−	0.182857i
$929$	11.7050	+	43.6835i	0.384028	+	1.43321i	0.839694	+	0.543060i	$0.182734\pi$
$929$	11.7050	+	43.6835i	0.384028	+	1.43321i	−0.455666	+	0.890151i	$0.650599\pi$
$930$	2.72945	−	10.1865i	0.0895023	−	0.334027i
$931$		0			0
$932$	22.5568	+	39.0695i	0.738871	+	1.27976i
$933$			26.5148i			0.868055i
$934$	−4.25869	+	15.8937i	−0.139349	+	0.520057i
$935$	10.6196	+	6.13122i	0.347298	+	0.200512i
$936$	0.164373	−	0.372805i	0.00537271	−	0.0121855i
$937$			26.8615i			0.877526i	0.898603	+	0.438763i	$0.144583\pi$
$937$			26.8615i			0.877526i	−0.898603	+	0.438763i	$0.855417\pi$
$938$		0			0
$939$	6.48978	−	11.2406i	0.211786	−	0.366824i
$940$	−43.0990	−	24.8832i	−1.40574	−	0.811602i
$941$	−0.376369	−	1.40463i	−0.0122693	−	0.0457896i	0.959520	−	0.281641i	$-0.0908788\pi$
$941$	−0.376369	−	1.40463i	−0.0122693	−	0.0457896i	−0.971789	+	0.235852i	$0.924212\pi$
$942$	−15.6529	−	15.6529i	−0.509998	−	0.509998i
$943$	−12.6712	+	3.39524i	−0.412631	+	0.110564i
$944$	−2.60868	−	2.60868i	−0.0849054	−	0.0849054i
$945$		0			0
$946$	41.8539	+	24.1644i	1.36079	+	0.785652i
$947$	−27.4153	+	27.4153i	−0.890878	+	0.890878i	−0.994606	−	0.103727i	$-0.966923\pi$
$947$	−27.4153	+	27.4153i	−0.890878	+	0.890878i	0.103727	+	0.994606i	$0.466923\pi$
$948$	−18.1016	+	31.3529i	−0.587912	+	1.01829i
$949$	−20.3056	−	8.95293i	−0.659147	−	0.290624i
$950$	7.42616	−	4.28749i	0.240936	−	0.139105i
$951$	5.38322	+	20.0904i	0.174563	+	0.651477i
$952$		0			0
$953$	20.6259	−	11.9084i	0.668138	−	0.385750i	−0.127233	−	0.991873i	$-0.540609\pi$
$953$	20.6259	−	11.9084i	0.668138	−	0.385750i	0.795371	+	0.606123i	$0.207276\pi$
$954$	3.71654	−	13.8703i	0.120327	−	0.449068i
$955$	−39.7996	+	39.7996i	−1.28789	+	1.28789i
$956$	−7.81297	+	7.81297i	−0.252690	+	0.252690i
$957$	−5.93729	+	22.1583i	−0.191925	+	0.716275i
$958$	63.7962	−	36.8327i	2.06116	−	1.19001i
$959$		0			0
$960$	10.3987	+	38.8084i	0.335616	+	1.25254i
$961$	25.7898	−	14.8897i	0.831929	−	0.480314i
$962$	14.3368	+	11.5243i	0.462237	+	0.371557i
$963$	−1.42893	+	2.47499i	−0.0460468	+	0.0797553i
$964$	−22.7543	+	22.7543i	−0.732868	+	0.732868i
$965$	−17.4255	−	10.0606i	−0.560946	−	0.323862i
$966$		0			0
$967$	5.04001	+	5.04001i	0.162076	+	0.162076i	0.783486	−	0.621410i	$-0.213440\pi$
$967$	5.04001	+	5.04001i	0.162076	+	0.162076i	−0.621410	+	0.783486i	$0.713440\pi$
$968$	2.90263	−	0.777758i	0.0932941	−	0.0249981i
$969$	−0.473618	−	0.473618i	−0.0152148	−	0.0152148i
$970$	−14.9137	−	55.6587i	−0.478850	−	1.78709i
$971$	−14.4726	−	8.35573i	−0.464446	−	0.268148i	0.249466	−	0.968384i	$-0.419745\pi$
$971$	−14.4726	−	8.35573i	−0.464446	−	0.268148i	−0.713912	+	0.700235i	$0.753078\pi$
$972$	−9.42319	+	16.3214i	−0.302249	+	0.523510i
$973$		0			0
$974$		−	33.9484i		−	1.08778i
$975$	23.3886	+	18.8003i	0.749036	+	0.602093i
$976$	3.65367	+	2.10945i	0.116951	+	0.0675218i
$977$	−12.7436	+	47.5599i	−0.407705	+	1.52157i	0.391308	+	0.920260i	$0.372023\pi$
$977$	−12.7436	+	47.5599i	−0.407705	+	1.52157i	−0.799012	+	0.601315i	$0.794644\pi$
$978$		−	7.48280i		−	0.239273i
$979$	−12.1429	−	21.0321i	−0.388088	−	0.672188i
$980$		0			0
$981$	2.25189	−	8.40415i	0.0718972	−	0.268324i
$982$	−5.10747	−	19.0613i	−0.162986	−	0.608272i
$983$	34.1190	−	9.14216i	1.08823	−	0.291590i	0.330265	−	0.943888i	$-0.392862\pi$
$983$	34.1190	−	9.14216i	1.08823	−	0.291590i	0.757962	+	0.652298i	$0.226195\pi$
$984$	−0.513986			−0.0163853
$985$	−84.2071			−2.68306
$986$	3.26993	−	0.876175i	0.104136	−	0.0279031i
$987$		0			0
$988$	5.01920	+	2.21301i	0.159682	+	0.0704054i
$989$	9.16909	+	15.8813i	0.291560	+	0.504997i
$990$	34.7759	+	9.31818i	1.10525	+	0.296151i
$991$	−3.41914	−	5.92212i	−0.108613	−	0.188122i	0.806596	−	0.591103i	$-0.201307\pi$
$991$	−3.41914	−	5.92212i	−0.108613	−	0.188122i	−0.915208	+	0.402981i	$0.867974\pi$
$992$	4.44861	−	7.70522i	0.141243	−	0.244641i
$993$	8.35456	−	8.35456i	0.265124	−	0.265124i
$994$		0			0
$995$	27.6588	+	7.41114i	0.876842	+	0.234949i
$996$	14.5994	+	3.91190i	0.462600	+	0.123953i
$997$			49.4814i			1.56709i	0.621335	+	0.783545i	$0.286591\pi$
$997$			49.4814i			1.56709i	−0.621335	+	0.783545i	$0.713409\pi$
$998$	5.14285	−	2.96923i	0.162794	−	0.0939892i
$999$	−10.1195	−	10.1195i	−0.320167	−	0.320167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.423.2		28
7.2	even	3		91.2.w.a.33.2	✓	28
7.3	odd	6		637.2.bd.b.293.6		28
7.4	even	3		637.2.bd.a.293.6		28
7.5	odd	6		637.2.x.a.215.2		28
7.6	odd	2		91.2.ba.a.59.2	yes	28
13.2	odd	12		637.2.x.a.80.2		28
21.2	odd	6		819.2.gh.b.397.6		28
21.20	even	2		819.2.et.b.514.6		28
91.2	odd	12		91.2.ba.a.54.2	yes	28
91.41	even	12		91.2.w.a.80.2	yes	28
91.54	even	12	inner	637.2.bb.a.509.2		28
91.67	odd	12		637.2.bd.b.587.6		28
91.80	even	12		637.2.bd.a.587.6		28
273.2	even	12		819.2.et.b.145.6		28
273.41	odd	12		819.2.gh.b.262.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.2	✓	28	7.2	even	3
91.2.w.a.80.2	yes	28	91.41	even	12
91.2.ba.a.54.2	yes	28	91.2	odd	12
91.2.ba.a.59.2	yes	28	7.6	odd	2
637.2.x.a.80.2		28	13.2	odd	12
637.2.x.a.215.2		28	7.5	odd	6
637.2.bb.a.423.2		28	1.1	even	1	trivial
637.2.bb.a.509.2		28	91.54	even	12	inner
637.2.bd.a.293.6		28	7.4	even	3
637.2.bd.a.587.6		28	91.80	even	12
637.2.bd.b.293.6		28	7.3	odd	6
637.2.bd.b.587.6		28	91.67	odd	12
819.2.et.b.145.6		28	273.2	even	12
819.2.et.b.514.6		28	21.20	even	2
819.2.gh.b.262.6		28	273.41	odd	12
819.2.gh.b.397.6		28	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42500 - 1.42500i) q^{2} +(-1.25027 + 0.721843i) q^{3} +2.06123i q^{4} +(-3.16920 - 0.849184i) q^{5} +(2.81025 + 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 + 0.793083i) q^{9} +O(q^{10})\)	\(q+(-1.42500 - 1.42500i) q^{2} +(-1.25027 + 0.721843i) q^{3} +2.06123i q^{4} +(-3.16920 - 0.849184i) q^{5} +(2.81025 + 0.753004i) q^{6} +(0.0872533 - 0.0872533i) q^{8} +(-0.457887 + 0.793083i) q^{9} +(3.30601 + 5.72618i) q^{10} +(-5.74323 - 1.53889i) q^{11} +(-1.48788 - 2.57709i) q^{12} +(-2.81021 - 2.25892i) q^{13} +(4.57532 - 1.22595i) q^{15} +3.87379 q^{16} +0.628578 q^{17} +(1.78263 - 0.477654i) q^{18} +(0.191033 + 0.712944i) q^{19} +(1.75036 - 6.53244i) q^{20} +(5.99117 + 10.3770i) q^{22} +4.54665i q^{23} +(-0.0461069 + 0.172073i) q^{24} +(4.99256 + 2.88246i) q^{25} +(0.785596 + 7.22349i) q^{26} -5.65314i q^{27} +(-1.33622 + 2.31439i) q^{29} +(-8.26680 - 4.77284i) q^{30} +(0.285936 + 1.06713i) q^{31} +(-5.69464 - 5.69464i) q^{32} +(8.29142 - 2.22168i) q^{33} +(-0.895721 - 0.895721i) q^{34} +(-1.63473 - 0.943810i) q^{36} +(1.79007 - 1.79007i) q^{37} +(0.743721 - 1.28816i) q^{38} +(5.14410 + 0.795719i) q^{39} +(-0.350617 + 0.202429i) q^{40} +(0.746755 + 2.78693i) q^{41} +(3.49297 - 2.01667i) q^{43} +(3.17202 - 11.8381i) q^{44} +(2.12461 - 2.12461i) q^{45} +(6.47896 - 6.47896i) q^{46} +(1.90459 - 7.10802i) q^{47} +(-4.84328 + 2.79627i) q^{48} +(-3.00689 - 11.2219i) q^{50} +(-0.785891 + 0.453734i) q^{51} +(4.65615 - 5.79250i) q^{52} +(3.89042 - 6.73840i) q^{53} +(-8.05571 + 8.05571i) q^{54} +(16.8946 + 9.75412i) q^{55} +(-0.753475 - 0.753475i) q^{57} +(5.20211 - 1.39390i) q^{58} +(-0.673419 - 0.673419i) q^{59} +(2.52697 + 9.43079i) q^{60} +(0.943178 + 0.544544i) q^{61} +(1.11320 - 1.92811i) q^{62} +8.48212i q^{64} +(6.98788 + 9.54534i) q^{65} +(-14.9811 - 8.64936i) q^{66} +(-1.39678 + 5.21286i) q^{67} +1.29564i q^{68} +(-3.28197 - 5.68453i) q^{69} +(0.590023 - 2.20200i) q^{71} +(0.0292470 + 0.109151i) q^{72} +(5.94515 - 1.59300i) q^{73} -5.10168 q^{74} -8.32273 q^{75} +(-1.46954 + 0.393762i) q^{76} +(-6.19643 - 8.46422i) q^{78} +(-6.08299 - 10.5361i) q^{79} +(-12.2768 - 3.28956i) q^{80} +(2.70702 + 4.68870i) q^{81} +(2.90724 - 5.03549i) q^{82} +(-3.59152 + 3.59152i) q^{83} +(-1.99209 - 0.533778i) q^{85} +(-7.85121 - 2.10373i) q^{86} -3.85815i q^{87} +(-0.635390 + 0.366843i) q^{88} +(2.88817 + 2.88817i) q^{89} -6.05511 q^{90} -9.37170 q^{92} +(-1.12779 - 1.12779i) q^{93} +(-12.8429 + 7.41487i) q^{94} -2.42168i q^{95} +(11.2305 + 3.00919i) q^{96} +(-8.41780 - 2.25554i) q^{97} +(3.85022 - 3.85022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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