LMFDB - Embedded newform 637.2.bb.a.423.4

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			423.4
Character	$\chi$	$=$	637.423
Dual form			637.2.bb.a.509.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347096 - 0.347096i) q^{2} +(2.11812 - 1.22290i) q^{3} -1.75905i q^{4} +(3.47544 + 0.931242i) q^{5} +(-1.15965 - 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 - 2.58241i) q^{9} +O(q^{10})$	\(q+(-0.347096 - 0.347096i) q^{2} +(2.11812 - 1.22290i) q^{3} -1.75905i q^{4} +(3.47544 + 0.931242i) q^{5} +(-1.15965 - 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 - 2.58241i) q^{9} +(-0.883082 - 1.52954i) q^{10} +(-2.04371 - 0.547609i) q^{11} +(-2.15114 - 3.72588i) q^{12} +(-0.582584 - 3.55817i) q^{13} +(8.50022 - 2.27763i) q^{15} -2.61235 q^{16} -1.14424 q^{17} +(-1.41385 + 0.378840i) q^{18} +(1.18001 + 4.40387i) q^{19} +(1.63810 - 6.11348i) q^{20} +(0.519289 + 0.899435i) q^{22} -1.48235i q^{23} +(-1.16804 + 4.35920i) q^{24} +(6.88137 + 3.97296i) q^{25} +(-1.03281 + 1.43724i) q^{26} +0.0442386i q^{27} +(2.75801 - 4.77701i) q^{29} +(-3.74095 - 2.15984i) q^{30} +(1.56920 + 5.85632i) q^{31} +(3.51624 + 3.51624i) q^{32} +(-4.99849 + 1.33934i) q^{33} +(0.397162 + 0.397162i) q^{34} +(-4.54259 - 2.62266i) q^{36} +(-1.91256 + 1.91256i) q^{37} +(1.11899 - 1.93814i) q^{38} +(-5.58526 - 6.82420i) q^{39} +(-5.74963 + 3.31955i) q^{40} +(1.21867 + 4.54813i) q^{41} +(-4.55704 + 2.63101i) q^{43} +(-0.963272 + 3.59498i) q^{44} +(7.58659 - 7.58659i) q^{45} +(-0.514518 + 0.514518i) q^{46} +(1.74658 - 6.51834i) q^{47} +(-5.53327 + 3.19464i) q^{48} +(-1.00950 - 3.76750i) q^{50} +(-2.42364 + 1.39929i) q^{51} +(-6.25900 + 1.02479i) q^{52} +(-1.74389 + 3.02051i) q^{53} +(0.0153550 - 0.0153550i) q^{54} +(-6.59283 - 3.80637i) q^{55} +(7.88489 + 7.88489i) q^{57} +(-2.61537 + 0.700787i) q^{58} +(8.08143 + 8.08143i) q^{59} +(-4.00646 - 14.9523i) q^{60} +(-8.20082 - 4.73474i) q^{61} +(1.48804 - 2.57737i) q^{62} +2.78376i q^{64} +(1.28878 - 12.9088i) q^{65} +(2.19983 + 1.27007i) q^{66} +(1.99321 - 7.43875i) q^{67} +2.01278i q^{68} +(-1.81276 - 3.13980i) q^{69} +(1.74779 - 6.52285i) q^{71} +(1.42408 + 5.31473i) q^{72} +(-5.46953 + 1.46556i) q^{73} +1.32768 q^{74} +19.4341 q^{75} +(7.74662 - 2.07570i) q^{76} +(-0.430029 + 4.30727i) q^{78} +(5.91160 + 10.2392i) q^{79} +(-9.07908 - 2.43273i) q^{80} +(4.52697 + 7.84094i) q^{81} +(1.15564 - 2.00163i) q^{82} +(-5.06789 + 5.06789i) q^{83} +(-3.97675 - 1.06557i) q^{85} +(2.49494 + 0.668517i) q^{86} -13.4910i q^{87} +(3.38102 - 1.95203i) q^{88} +(-7.05000 - 7.05000i) q^{89} -5.26655 q^{90} -2.60753 q^{92} +(10.4854 + 10.4854i) q^{93} +(-2.86872 + 1.65626i) q^{94} +16.4043i q^{95} +(11.7478 + 3.14782i) q^{96} +(13.1665 + 3.52795i) q^{97} +(-4.46123 + 4.46123i) 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 $

$2$	−0.347096	−	0.347096i	−0.245434	−	0.245434i	0.573660	−	0.819094i	$-0.305523\pi$
$2$	−0.347096	−	0.347096i	−0.245434	−	0.245434i	−0.819094	+	0.573660i	$0.805523\pi$
$3$	2.11812	−	1.22290i	1.22290	−	0.706040i	0.257363	−	0.966315i	$-0.417146\pi$
$3$	2.11812	−	1.22290i	1.22290	−	0.706040i	0.965535	+	0.260275i	$0.0838131\pi$
$4$		−	1.75905i		−	0.879524i
$5$	3.47544	+	0.931242i	1.55427	+	0.416464i	0.930843	−	0.365420i	$-0.119075\pi$
$5$	3.47544	+	0.931242i	1.55427	+	0.416464i	0.623423	+	0.781885i	$0.285741\pi$
$6$	−1.15965	−	0.310728i	−0.473427	−	0.126854i
$7$		0			0
$7$		0			0
$8$	−1.30475	+	1.30475i	−0.461299	+	0.461299i
$9$	1.49096	−	2.58241i	0.496985	−	0.860804i
$10$	−0.883082	−	1.52954i	−0.279255	−	0.483684i
$11$	−2.04371	−	0.547609i	−0.616201	−	0.165110i	−0.0628007	−	0.998026i	$-0.520003\pi$
$11$	−2.04371	−	0.547609i	−0.616201	−	0.165110i	−0.553400	+	0.832916i	$0.686670\pi$
$12$	−2.15114	−	3.72588i	−0.620980	−	1.07557i
$13$	−0.582584	−	3.55817i	−0.161580	−	0.986860i
$13$	−0.582584	−	3.55817i	−0.161580	−	0.986860i
$14$		0			0
$15$	8.50022	−	2.27763i	2.19475	−	0.588081i
$16$	−2.61235			−0.653088
$17$	−1.14424			−0.277519			−0.138760	−	0.990326i	$-0.544312\pi$
$17$	−1.14424			−0.277519			−0.138760	+	0.990326i	$0.544312\pi$
$18$	−1.41385	+	0.378840i	−0.333248	+	0.0892934i
$19$	1.18001	+	4.40387i	0.270713	+	1.01032i	0.958660	+	0.284555i	$0.0918457\pi$
$19$	1.18001	+	4.40387i	0.270713	+	1.01032i	−0.687946	+	0.725762i	$0.741488\pi$
$20$	1.63810	−	6.11348i	0.366291	−	1.36701i
$21$		0			0
$22$	0.519289	+	0.899435i	0.110713	+	0.191760i
$23$		−	1.48235i		−	0.309092i	−0.987986	−	0.154546i	$-0.950609\pi$
$23$		−	1.48235i		−	0.309092i	0.987986	−	0.154546i	$-0.0493914\pi$
$24$	−1.16804	+	4.35920i	−0.238426	+	0.889817i
$25$	6.88137	+	3.97296i	1.37627	+	0.794593i
$26$	−1.03281	+	1.43724i	−0.202552	+	0.281866i
$27$			0.0442386i			0.00851372i
$28$		0			0
$29$	2.75801	−	4.77701i	0.512149	−	0.887068i	−0.487752	−	0.872982i	$-0.662183\pi$
$29$	2.75801	−	4.77701i	0.512149	−	0.887068i	0.999901	−	0.0140858i	$-0.00448381\pi$
$30$	−3.74095	−	2.15984i	−0.683001	−	0.394331i
$31$	1.56920	+	5.85632i	0.281836	+	1.05183i	0.951121	+	0.308820i	$0.0999340\pi$
$31$	1.56920	+	5.85632i	0.281836	+	1.05183i	−0.669285	+	0.743006i	$0.733399\pi$
$32$	3.51624	+	3.51624i	0.621589	+	0.621589i
$33$	−4.99849	+	1.33934i	−0.870125	+	0.233149i
$34$	0.397162	+	0.397162i	0.0681127	+	0.0681127i
$35$		0			0
$36$	−4.54259	−	2.62266i	−0.757098	−	0.437111i
$37$	−1.91256	+	1.91256i	−0.314422	+	0.314422i	−0.846620	−	0.532198i	$-0.821366\pi$
$37$	−1.91256	+	1.91256i	−0.314422	+	0.314422i	0.532198	+	0.846620i	$0.321366\pi$
$38$	1.11899	−	1.93814i	0.181524	−	0.314408i
$39$	−5.58526	−	6.82420i	−0.894358	−	1.09275i
$40$	−5.74963	+	3.31955i	−0.909096	+	0.524867i
$41$	1.21867	+	4.54813i	0.190324	+	0.710299i	0.993428	+	0.114460i	$0.0365137\pi$
$41$	1.21867	+	4.54813i	0.190324	+	0.710299i	−0.803104	+	0.595839i	$0.796820\pi$
$42$		0			0
$43$	−4.55704	+	2.63101i	−0.694942	+	0.401225i	−0.805461	−	0.592649i	$-0.798082\pi$
$43$	−4.55704	+	2.63101i	−0.694942	+	0.401225i	0.110519	+	0.993874i	$0.464749\pi$
$44$	−0.963272	+	3.59498i	−0.145219	+	0.541964i
$45$	7.58659	−	7.58659i	1.13094	−	1.13094i
$46$	−0.514518	+	0.514518i	−0.0758615	+	0.0758615i
$47$	1.74658	−	6.51834i	0.254765	−	0.950797i	−0.713456	−	0.700700i	$-0.752871\pi$
$47$	1.74658	−	6.51834i	0.254765	−	0.950797i	0.968221	−	0.250097i	$-0.0804624\pi$
$48$	−5.53327	+	3.19464i	−0.798659	+	0.461106i
$49$		0			0
$50$	−1.00950	−	3.76750i	−0.142765	−	0.532804i
$51$	−2.42364	+	1.39929i	−0.339378	+	0.195940i
$52$	−6.25900	+	1.02479i	−0.867967	+	0.142113i
$53$	−1.74389	+	3.02051i	−0.239542	+	0.414899i	−0.960583	−	0.277994i	$-0.910331\pi$
$53$	−1.74389	+	3.02051i	−0.239542	+	0.414899i	0.721041	+	0.692892i	$0.243664\pi$
$54$	0.0153550	−	0.0153550i	0.00208955	−	0.00208955i
$55$	−6.59283	−	3.80637i	−0.888977	−	0.513251i
$56$		0			0
$57$	7.88489	+	7.88489i	1.04438	+	1.04438i
$58$	−2.61537	+	0.700787i	−0.343415	+	0.0920179i
$59$	8.08143	+	8.08143i	1.05211	+	1.05211i	0.998565	+	0.0535478i	$0.0170530\pi$
$59$	8.08143	+	8.08143i	1.05211	+	1.05211i	0.0535478	+	0.998565i	$0.482947\pi$
$60$	−4.00646	−	14.9523i	−0.517232	−	1.93033i
$61$	−8.20082	−	4.73474i	−1.05001	−	0.606222i	−0.127356	−	0.991857i	$-0.540649\pi$
$61$	−8.20082	−	4.73474i	−1.05001	−	0.606222i	−0.922651	+	0.385635i	$0.873982\pi$
$62$	1.48804	−	2.57737i	0.188982	−	0.327326i
$63$		0			0
$64$			2.78376i			0.347970i
$65$	1.28878	−	12.9088i	0.159854	−	1.60113i
$66$	2.19983	+	1.27007i	0.270781	+	0.156335i
$67$	1.99321	−	7.43875i	0.243509	−	0.908788i	−0.730618	−	0.682786i	$-0.760768\pi$
$67$	1.99321	−	7.43875i	0.243509	−	0.908788i	0.974127	−	0.226001i	$-0.0725654\pi$
$68$			2.01278i			0.244085i
$69$	−1.81276	−	3.13980i	−0.218231	−	0.377987i
$70$		0			0
$71$	1.74779	−	6.52285i	0.207425	−	0.774120i	−0.781272	−	0.624191i	$-0.785429\pi$
$71$	1.74779	−	6.52285i	0.207425	−	0.774120i	0.988697	−	0.149929i	$-0.0479045\pi$
$72$	1.42408	+	5.31473i	0.167829	+	0.626347i
$73$	−5.46953	+	1.46556i	−0.640161	+	0.171531i	−0.564276	−	0.825586i	$-0.690845\pi$
$73$	−5.46953	+	1.46556i	−0.640161	+	0.171531i	−0.0758844	+	0.997117i	$0.524178\pi$
$74$	1.32768			0.154340
$75$	19.4341			2.24406
$76$	7.74662	−	2.07570i	0.888598	−	0.238099i
$77$		0			0
$78$	−0.430029	+	4.30727i	−0.0486912	+	0.487703i
$79$	5.91160	+	10.2392i	0.665107	+	1.15200i	0.979256	+	0.202626i	$0.0649475\pi$
$79$	5.91160	+	10.2392i	0.665107	+	1.15200i	−0.314149	+	0.949374i	$0.601719\pi$
$80$	−9.07908	−	2.43273i	−1.01507	−	0.271988i
$81$	4.52697	+	7.84094i	0.502996	+	0.871215i
$82$	1.15564	−	2.00163i	0.127619	−	0.221043i
$83$	−5.06789	+	5.06789i	−0.556274	+	0.556274i	−0.928244	−	0.371971i	$-0.878682\pi$
$83$	−5.06789	+	5.06789i	−0.556274	+	0.556274i	0.371971	+	0.928244i	$0.378682\pi$
$84$		0			0
$85$	−3.97675	−	1.06557i	−0.431339	−	0.115577i
$86$	2.49494	+	0.668517i	0.269036	+	0.0720881i
$87$		−	13.4910i		−	1.44639i
$88$	3.38102	−	1.95203i	0.360418	−	0.208087i
$89$	−7.05000	−	7.05000i	−0.747299	−	0.747299i	0.226672	−	0.973971i	$-0.427215\pi$
$89$	−7.05000	−	7.05000i	−0.747299	−	0.747299i	−0.973971	+	0.226672i	$0.927215\pi$
$90$	−5.26655			−0.555143
$91$		0			0
$92$	−2.60753			−0.271854
$93$	10.4854	+	10.4854i	1.08729	+	1.08729i
$94$	−2.86872	+	1.65626i	−0.295886	+	0.170830i
$95$			16.4043i			1.68304i
$96$	11.7478	+	3.14782i	1.19901	+	0.321273i
$97$	13.1665	+	3.52795i	1.33685	+	0.358209i	0.855266	−	0.518190i	$-0.173394\pi$
$97$	13.1665	+	3.52795i	1.33685	+	0.358209i	0.481587	+	0.876398i	$0.340061\pi$
$98$		0			0
$99$	−4.46123	+	4.46123i	−0.448370	+	0.448370i
$100$	6.98864	−	12.1047i	0.698864	−	1.21047i
$101$	−4.87153	−	8.43773i	−0.484735	−	0.839586i	0.515111	−	0.857123i	$-0.327751\pi$
$101$	−4.87153	−	8.43773i	−0.484735	−	0.839586i	−0.999846	+	0.0175378i	$0.994417\pi$
$102$	1.32692	+	0.355548i	0.131385	+	0.0352045i
$103$	6.18363	+	10.7104i	0.609291	+	1.05532i	0.991357	+	0.131188i	$0.0418792\pi$
$103$	6.18363	+	10.7104i	0.609291	+	1.05532i	−0.382067	+	0.924135i	$0.624787\pi$
$104$	5.40266	+	3.88240i	0.529774	+	0.380701i
$105$		0			0
$106$	1.65370	−	0.443108i	0.160622	−	0.0430385i
$107$	−8.18718			−0.791484			−0.395742	−	0.918362i	$-0.629513\pi$
$107$	−8.18718			−0.791484			−0.395742	+	0.918362i	$0.629513\pi$
$108$	0.0778178			0.00748802
$109$	−2.87825	+	0.771224i	−0.275686	+	0.0738699i	−0.394013	−	0.919105i	$-0.628914\pi$
$109$	−2.87825	+	0.771224i	−0.275686	+	0.0738699i	0.118327	+	0.992975i	$0.462247\pi$
$110$	0.967168	+	3.60952i	0.0922159	+	0.344154i
$111$	−1.71217	+	6.38989i	−0.162512	+	0.606501i
$112$		0			0
$113$	−8.19898	−	14.2011i	−0.771295	−	1.33592i	−0.936853	−	0.349723i	$-0.886276\pi$
$113$	−8.19898	−	14.2011i	−0.771295	−	1.33592i	0.165558	−	0.986200i	$-0.447057\pi$
$114$		−	5.47362i		−	0.512652i
$115$	1.38043	−	5.15183i	0.128726	−	0.480410i
$116$	−8.40299	−	4.85147i	−0.780198	−	0.450448i
$117$	−10.0573	−	3.80061i	−0.929796	−	0.351366i
$118$		−	5.61007i		−	0.516448i
$119$		0			0
$120$	−8.11894	+	14.0624i	−0.741154	+	1.28372i
$121$	−5.64942	−	3.26169i	−0.513584	−	0.296518i
$122$	1.20306	+	4.48988i	0.108920	+	0.406495i
$123$	8.14318	+	8.14318i	0.734246	+	0.734246i
$124$	10.3016	−	2.76029i	0.925107	−	0.247882i
$125$	7.49503	+	7.49503i	0.670376	+	0.670376i
$126$		0			0
$127$	7.41767	+	4.28259i	0.658212	+	0.380019i	0.791595	−	0.611046i	$-0.209251\pi$
$127$	7.41767	+	4.28259i	0.658212	+	0.380019i	−0.133384	+	0.991064i	$0.542584\pi$
$128$	7.99871	−	7.99871i	0.706992	−	0.706992i
$129$	−6.43490	+	11.1456i	−0.566561	+	0.981313i
$130$	−4.92791	+	4.03325i	−0.432206	+	0.353739i
$131$	−12.7190	+	7.34330i	−1.11126	+	0.641587i	−0.939156	−	0.343491i	$-0.888390\pi$
$131$	−12.7190	+	7.34330i	−1.11126	+	0.641587i	−0.172106	+	0.985078i	$0.555057\pi$
$132$	2.35597	+	8.79258i	0.205060	+	0.765296i
$133$		0			0
$134$	−3.27379	+	1.89013i	−0.282813	+	0.163282i
$135$	−0.0411968	+	0.153749i	−0.00354566	+	0.0132326i
$136$	1.49295	−	1.49295i	0.128019	−	0.128019i
$137$	1.60893	−	1.60893i	0.137460	−	0.137460i	−0.635028	−	0.772489i	$-0.719012\pi$
$137$	1.60893	−	1.60893i	0.137460	−	0.137460i	0.772489	+	0.635028i	$0.219012\pi$
$138$	−0.460608	+	1.71901i	−0.0392096	+	0.146332i
$139$	4.23236	−	2.44355i	0.358984	−	0.207259i	−0.309651	−	0.950850i	$-0.600212\pi$
$139$	4.23236	−	2.44355i	0.358984	−	0.207259i	0.668635	+	0.743591i	$0.266879\pi$
$140$		0			0
$141$	−4.27178	−	15.9425i	−0.359749	−	1.34260i
$142$	−2.87071	+	1.65740i	−0.240904	+	0.139086i
$143$	−0.757858	+	7.59089i	−0.0633753	+	0.634782i
$144$	−3.89490	+	6.74616i	−0.324575	+	0.562180i
$145$	14.0339	−	14.0339i	1.16545	−	1.16545i
$146$	2.40714	+	1.38976i	0.199217	+	0.115018i
$147$		0			0
$148$	3.36428	+	3.36428i	0.276542	+	0.276542i
$149$	−2.67644	+	0.717149i	−0.219262	+	0.0587512i	−0.366778	−	0.930309i	$-0.619539\pi$
$149$	−2.67644	+	0.717149i	−0.219262	+	0.0587512i	0.147515	+	0.989060i	$0.452872\pi$
$150$	−6.74550	−	6.74550i	−0.550768	−	0.550768i
$151$	1.63414	+	6.09868i	0.132984	+	0.496304i	0.999998	−	0.00198027i	$-0.000630339\pi$
$151$	1.63414	+	6.09868i	0.132984	+	0.496304i	−0.867014	+	0.498284i	$0.833964\pi$
$152$	−7.28557	−	4.20633i	−0.590938	−	0.341178i
$153$	−1.70601	+	2.95490i	−0.137923	+	0.238890i
$154$		0			0
$155$			21.8146i			1.75219i
$156$	−12.0041	+	9.82475i	−0.961097	+	0.786610i
$157$	1.65313	+	0.954436i	0.131934	+	0.0761723i	0.564514	−	0.825423i	$-0.309063\pi$
$157$	1.65313	+	0.954436i	0.131934	+	0.0761723i	−0.432580	+	0.901595i	$0.642397\pi$
$158$	1.50209	−	5.60588i	0.119500	−	0.445980i
$159$			8.53040i			0.676505i
$160$	8.94602	+	15.4950i	0.707245	+	1.22498i
$161$		0			0
$162$	1.15027	−	4.29285i	0.0903734	−	0.337278i
$163$	1.59773	+	5.96280i	0.125144	+	0.467043i	0.999845	−	0.0176201i	$-0.00560895\pi$
$163$	1.59773	+	5.96280i	0.125144	+	0.467043i	−0.874701	+	0.484663i	$0.838942\pi$
$164$	8.00038	−	2.14370i	0.624725	−	0.167395i
$165$	−18.6192			−1.44950
$166$	3.51809			0.273057
$167$	−2.11863	+	0.567684i	−0.163944	+	0.0439287i	−0.339857	−	0.940477i	$-0.610379\pi$
$167$	−2.11863	+	0.567684i	−0.163944	+	0.0439287i	0.175913	+	0.984406i	$0.443712\pi$
$168$		0			0
$169$	−12.3212	+	4.14587i	−0.947784	+	0.318913i
$170$	1.01046	+	1.75017i	0.0774987	+	0.134232i
$171$	13.1319	+	3.51869i	1.00422	+	0.269081i
$172$	4.62807	+	8.01605i	0.352887	+	0.611218i
$173$	−9.47370	+	16.4089i	−0.720272	+	1.24755i	0.240618	+	0.970620i	$0.422650\pi$
$173$	−9.47370	+	16.4089i	−0.720272	+	1.24755i	−0.960891	+	0.276928i	$0.910684\pi$
$174$	−4.68269	+	4.68269i	−0.354993	+	0.354993i
$175$		0			0
$176$	5.33888	+	1.43055i	0.402433	+	0.107832i
$177$	27.0002	+	7.23469i	2.02946	+	0.543792i
$178$			4.89405i			0.366825i
$179$	10.2742	−	5.93179i	0.767926	−	0.443363i	−0.0642080	−	0.997937i	$-0.520452\pi$
$179$	10.2742	−	5.93179i	0.767926	−	0.443363i	0.832134	+	0.554574i	$0.187119\pi$
$180$	−13.3452	−	13.3452i	−0.994691	−	0.994691i
$181$	−10.2064			−0.758635			−0.379317	−	0.925267i	$-0.623841\pi$
$181$	−10.2064			−0.758635			−0.379317	+	0.925267i	$0.623841\pi$
$182$		0			0
$183$	−23.1604			−1.71207
$184$	1.93410	+	1.93410i	0.142584	+	0.142584i
$185$	−8.42804	+	4.86593i	−0.619642	+	0.357750i
$186$		−	7.27890i		−	0.533715i
$187$	2.33849	+	0.626598i	0.171008	+	0.0458213i
$188$	−11.4661	−	3.07232i	−0.836249	−	0.224072i
$189$		0			0
$190$	5.69386	−	5.69386i	0.413076	−	0.413076i
$191$	2.98574	−	5.17145i	0.216040	−	0.374193i	−0.737553	−	0.675289i	$-0.764019\pi$
$191$	2.98574	−	5.17145i	0.216040	−	0.374193i	0.953594	+	0.301096i	$0.0973524\pi$
$192$	3.40425	+	5.89633i	0.245681	+	0.425531i
$193$	0.969416	+	0.259754i	0.0697801	+	0.0186975i	0.293540	−	0.955947i	$-0.405167\pi$
$193$	0.969416	+	0.259754i	0.0697801	+	0.0186975i	−0.223760	+	0.974644i	$0.571833\pi$
$194$	−3.34549	−	5.79456i	−0.240192	−	0.416025i
$195$	−13.0563	−	28.9184i	−0.934981	−	2.07089i
$196$		0			0
$197$	−4.08621	+	1.09490i	−0.291130	+	0.0780081i	−0.401428	−	0.915890i	$-0.631486\pi$
$197$	−4.08621	+	1.09490i	−0.291130	+	0.0780081i	0.110298	+	0.993899i	$0.464819\pi$
$198$	3.09695			0.220091
$199$	15.0541			1.06716			0.533579	−	0.845750i	$-0.320847\pi$
$199$	15.0541			1.06716			0.533579	+	0.845750i	$0.320847\pi$
$200$	−14.1622	+	3.79475i	−1.00142	+	0.268329i
$201$	−4.87498	−	18.1937i	−0.343854	−	1.28328i
$202$	−1.23782	+	4.61959i	−0.0870924	+	0.325033i
$203$		0			0
$204$	2.46142	+	4.26330i	0.172334	+	0.298491i
$205$			16.9416i			1.18326i
$206$	1.57121	−	5.86383i	0.109471	−	0.408553i
$207$	−3.82804	−	2.21012i	−0.266067	−	0.153614i
$208$	1.52191	+	9.29519i	0.105526	+	0.644506i
$209$		−	9.64640i		−	0.667255i
$210$		0			0
$211$	12.3556	−	21.4005i	0.850592	−	1.47327i	−0.0300832	−	0.999547i	$-0.509577\pi$
$211$	12.3556	−	21.4005i	0.850592	−	1.47327i	0.880675	−	0.473721i	$-0.157089\pi$
$212$	5.31322	+	3.06759i	0.364913	+	0.210683i
$213$	−4.27474	−	15.9536i	−0.292900	−	1.09312i
$214$	2.84174	+	2.84174i	0.194257	+	0.194257i
$215$	−18.2878	+	4.90021i	−1.24722	+	0.334192i
$216$	−0.0577203	−	0.0577203i	−0.00392737	−	0.00392737i
$217$		0			0
$218$	1.26672	+	0.731339i	0.0857929	+	0.0495325i
$219$	−9.79291	+	9.79291i	−0.661743	+	0.661743i
$220$	−6.69560	+	11.5971i	−0.451417	+	0.781877i
$221$	0.666617	+	4.07141i	0.0448415	+	0.273873i
$222$	2.81219	−	1.62362i	0.188742	−	0.108970i
$223$	−0.193376	−	0.721689i	−0.0129494	−	0.0483279i	0.959149	−	0.282902i	$-0.0912971\pi$
$223$	−0.193376	−	0.721689i	−0.0129494	−	0.0483279i	−0.972098	+	0.234574i	$0.924630\pi$
$224$		0			0
$225$	20.5197	−	11.8470i	1.36798	−	0.789802i
$226$	−2.08329	+	7.77496i	−0.138579	+	0.517183i
$227$	7.33399	−	7.33399i	0.486774	−	0.486774i	−0.420513	−	0.907287i	$-0.638150\pi$
$227$	7.33399	−	7.33399i	0.486774	−	0.486774i	0.907287	+	0.420513i	$0.138150\pi$
$228$	13.8699	−	13.8699i	0.918556	−	0.918556i
$229$	−0.444567	+	1.65915i	−0.0293778	+	0.109639i	−0.979058	−	0.203582i	$-0.934742\pi$
$229$	−0.444567	+	1.65915i	−0.0293778	+	0.109639i	0.949680	+	0.313222i	$0.101408\pi$
$230$	−2.26732	+	1.30904i	−0.149503	+	0.0863154i
$231$		0			0
$232$	2.63429	+	9.83132i	0.172950	+	0.645458i
$233$	7.19720	−	4.15531i	0.471504	−	0.272223i	−0.245365	−	0.969431i	$-0.578908\pi$
$233$	7.19720	−	4.15531i	0.471504	−	0.272223i	0.716869	+	0.697208i	$0.245574\pi$
$234$	2.17166	+	4.81002i	0.141966	+	0.314441i
$235$	12.1403	−	21.0276i	0.791946	−	1.37169i
$236$	14.2156	−	14.2156i	0.925359	−	0.925359i
$237$	25.0430	+	14.4586i	1.62672	+	0.939185i
$238$		0			0
$239$	5.13978	+	5.13978i	0.332465	+	0.332465i	0.853522	−	0.521057i	$-0.174462\pi$
$239$	5.13978	+	5.13978i	0.332465	+	0.332465i	−0.521057	+	0.853522i	$0.674462\pi$
$240$	−22.2056	+	5.94996i	−1.43336	+	0.384068i
$241$	−5.48024	−	5.48024i	−0.353013	−	0.353013i	0.508216	−	0.861229i	$-0.330305\pi$
$241$	−5.48024	−	5.48024i	−0.353013	−	0.353013i	−0.861229	+	0.508216i	$0.830305\pi$
$242$	0.828770	+	3.09301i	0.0532753	+	0.198826i
$243$	19.0624	+	11.0057i	1.22285	+	0.706014i
$244$	−8.32864	+	14.4256i	−0.533187	+	0.923507i
$245$		0			0
$246$		−	5.65293i		−	0.360418i
$247$	14.9823	−	6.76431i	0.953299	−	0.430403i
$248$	−9.68845	−	5.59363i	−0.615217	−	0.355196i
$249$	−4.53689	+	16.9319i	−0.287514	+	1.07302i
$250$		−	5.20299i		−	0.329066i
$251$	1.76122	+	3.05052i	0.111167	+	0.192547i	0.916241	−	0.400627i	$-0.131208\pi$
$251$	1.76122	+	3.05052i	0.111167	+	0.192547i	−0.805074	+	0.593174i	$0.797874\pi$
$252$		0			0
$253$	−0.811749	+	3.02949i	−0.0510343	+	0.190462i
$254$	−1.08817	−	4.06111i	−0.0682780	−	0.254817i
$255$	−9.72631	+	2.60616i	−0.609085	+	0.163204i
$256$	0.0148769			0.000929806
$257$	−10.8515			−0.676896			−0.338448	−	0.940985i	$-0.609902\pi$
$257$	−10.8515			−0.676896			−0.338448	+	0.940985i	$0.609902\pi$
$258$	6.10211	−	1.63506i	0.379901	−	0.101794i
$259$		0			0
$260$	−22.7071	−	2.26703i	−1.40824	−	0.140595i
$261$	−8.22414	−	14.2446i	−0.509061	−	0.881720i
$262$	6.96354	+	1.86587i	0.430209	+	0.115274i
$263$	2.34957	+	4.06957i	0.144881	+	0.250940i	0.929328	−	0.369254i	$-0.120387\pi$
$263$	2.34957	+	4.06957i	0.144881	+	0.250940i	−0.784448	+	0.620195i	$0.787054\pi$
$264$	4.77427	−	8.26928i	0.293836	−	0.508939i
$265$	−8.87362	+	8.87362i	−0.545102	+	0.545102i
$266$		0			0
$267$	−23.5542	−	6.31132i	−1.44149	−	0.386247i
$268$	−13.0851	−	3.50615i	−0.799301	−	0.214172i
$269$			25.7108i			1.56762i	0.621002	+	0.783809i	$0.286726\pi$
$269$			25.7108i			1.56762i	−0.621002	+	0.783809i	$0.713274\pi$
$270$	0.0676648	−	0.0390663i	0.00411795	−	0.00237750i
$271$	−0.937761	−	0.937761i	−0.0569650	−	0.0569650i	0.678050	−	0.735015i	$-0.262825\pi$
$271$	−0.937761	−	0.937761i	−0.0569650	−	0.0569650i	−0.735015	+	0.678050i	$0.762825\pi$
$272$	2.98916			0.181244
$273$		0			0
$274$	−1.11691			−0.0674749
$275$	−11.8879	−	11.8879i	−0.716866	−	0.716866i
$276$	−5.52306	+	3.18874i	−0.332449	+	0.191940i
$277$			0.181365i			0.0108972i	0.999985	+	0.00544859i	$0.00173435\pi$
$277$			0.181365i			0.0108972i	−0.999985	+	0.00544859i	$0.998266\pi$
$278$	−2.31718	−	0.620887i	−0.138975	−	0.0372383i
$279$	17.4630	+	4.67921i	1.04548	+	0.280137i
$280$		0			0
$281$	5.50563	−	5.50563i	0.328439	−	0.328439i	−0.523554	−	0.851993i	$-0.675394\pi$
$281$	5.50563	−	5.50563i	0.328439	−	0.328439i	0.851993	+	0.523554i	$0.175394\pi$
$282$	−4.05086	+	7.01630i	−0.241225	+	0.417815i
$283$	3.65425	+	6.32935i	0.217223	+	0.376241i	0.953958	−	0.299941i	$-0.0969669\pi$
$283$	3.65425	+	6.32935i	0.217223	+	0.376241i	−0.736735	+	0.676181i	$0.763634\pi$
$284$	−11.4740	−	3.07445i	−0.680857	−	0.182435i
$285$	20.0607	+	34.7462i	1.18830	+	2.05819i
$286$	2.89782	−	2.37172i	0.171351	−	0.140243i
$287$		0			0
$288$	14.3229	−	3.83782i	0.843987	−	0.226146i
$289$	−15.6907			−0.922983
$290$	−9.74219			−0.572081
$291$	32.2025	−	8.62863i	1.88774	−	0.505819i
$292$	2.57799	+	9.62118i	0.150865	+	0.563037i
$293$	8.30804	−	31.0060i	0.485361	−	1.81139i	−0.0930708	−	0.995659i	$-0.529668\pi$
$293$	8.30804	−	31.0060i	0.485361	−	1.81139i	0.578431	−	0.815731i	$-0.303665\pi$
$294$		0			0
$295$	20.5608	+	35.6123i	1.19710	+	2.07343i
$296$		−	4.99082i		−	0.290086i
$297$	0.0242255	−	0.0904107i	0.00140570	−	0.00524616i
$298$	1.17790	+	0.680061i	0.0682339	+	0.0393949i
$299$	−5.27446	+	0.863594i	−0.305030	+	0.0499430i
$300$		−	34.1855i		−	1.97370i
$301$		0			0
$302$	1.54963	−	2.68403i	0.0891709	−	0.154449i
$303$	−20.6370	−	11.9148i	−1.18556	−	0.684485i
$304$	−3.08261	−	11.5044i	−0.176800	−	0.659825i
$305$	−24.0923	−	24.0923i	−1.37952	−	1.37952i
$306$	1.61779	−	0.433484i	0.0924826	−	0.0247806i
$307$	−9.65602	−	9.65602i	−0.551098	−	0.551098i	0.375659	−	0.926758i	$-0.377416\pi$
$307$	−9.65602	−	9.65602i	−0.551098	−	0.551098i	−0.926758	+	0.375659i	$0.877416\pi$
$308$		0			0
$309$	26.1953	+	15.1239i	1.49020	+	0.860368i
$310$	7.57176	−	7.57176i	0.430047	−	0.430047i
$311$	8.29369	−	14.3651i	0.470292	−	0.814570i	−0.529131	−	0.848540i	$-0.677482\pi$
$311$	8.29369	−	14.3651i	0.470292	−	0.814570i	0.999423	+	0.0339706i	$0.0108153\pi$
$312$	16.1913	+	1.61650i	0.916649	+	0.0915163i
$313$	8.06261	−	4.65495i	0.455725	−	0.263113i	−0.254520	−	0.967068i	$-0.581917\pi$
$313$	8.06261	−	4.65495i	0.455725	−	0.263113i	0.710245	+	0.703954i	$0.248584\pi$
$314$	−0.242514	−	0.905076i	−0.0136859	−	0.0510764i
$315$		0			0
$316$	18.0112	−	10.3988i	1.01321	−	0.584978i
$317$	8.57788	−	32.0131i	0.481782	−	1.79803i	−0.112353	−	0.993668i	$-0.535839\pi$
$317$	8.57788	−	32.0131i	0.481782	−	1.79803i	0.594135	−	0.804365i	$-0.297495\pi$
$318$	2.96087	−	2.96087i	0.166037	−	0.166037i
$319$	−8.25249	+	8.25249i	−0.462051	+	0.462051i
$320$	−2.59235	+	9.67479i	−0.144917	+	0.540837i
$321$	−17.3414	+	10.0121i	−0.967904	+	0.558820i
$322$		0			0
$323$	−1.35022	−	5.03909i	−0.0751282	−	0.280382i
$324$	13.7926	−	7.96316i	0.766255	−	0.442398i
$325$	10.1275	−	26.7997i	0.561773	−	1.48658i
$326$	1.51510	−	2.62423i	0.0839136	−	0.145343i
$327$	−5.15335	+	5.15335i	−0.284981	+	0.284981i
$328$	−7.52423	−	4.34412i	−0.415456	−	0.239864i
$329$		0			0
$330$	6.46265	+	6.46265i	0.355757	+	0.355757i
$331$	22.7451	−	6.09453i	1.25018	−	0.334985i	0.427776	−	0.903885i	$-0.359297\pi$
$331$	22.7451	−	6.09453i	1.25018	−	0.334985i	0.822407	+	0.568900i	$0.192631\pi$
$332$	8.91467	+	8.91467i	0.489256	+	0.489256i
$333$	2.08747	+	7.79055i	0.114393	+	0.426920i
$334$	0.932407	+	0.538326i	0.0510191	+	0.0294559i
$335$	13.8546	−	23.9968i	0.756955	−	1.31109i
$336$		0			0
$337$		−	24.5958i		−	1.33982i	−0.742442	−	0.669911i	$-0.766332\pi$
$337$		−	24.5958i		−	1.33982i	0.742442	−	0.669911i	$-0.233668\pi$
$338$	5.71565	+	2.83762i	0.310890	+	0.154346i
$339$	−34.7329	−	20.0530i	−1.88643	−	1.08913i
$340$	−1.87438	+	6.99529i	−0.101653	+	0.379373i
$341$		−	12.8279i		−	0.694670i
$342$	−3.33672	−	5.77937i	−0.180429	−	0.312512i
$343$		0			0
$344$	2.51299	−	9.37860i	0.135491	−	0.505660i
$345$	−3.37624	−	12.6003i	−0.181771	−	0.678378i
$346$	8.98376	−	2.40719i	0.482970	−	0.129411i
$347$	−33.3591			−1.79081			−0.895406	−	0.445251i	$-0.853115\pi$
$347$	−33.3591			−1.79081			−0.895406	+	0.445251i	$0.853115\pi$
$348$	−23.7314			−1.27214
$349$	−5.28189	+	1.41528i	−0.282733	+	0.0757580i	−0.397399	−	0.917646i	$-0.630087\pi$
$349$	−5.28189	+	1.41528i	−0.282733	+	0.0757580i	0.114666	+	0.993404i	$0.463420\pi$
$350$		0			0
$351$	0.157409	−	0.0257727i	0.00840184	−	0.00137564i
$352$	−5.26063	−	9.11168i	−0.280393	−	0.485654i
$353$	−4.26881	−	1.14383i	−0.227206	−	0.0608797i	0.143420	−	0.989662i	$-0.454190\pi$
$353$	−4.26881	−	1.14383i	−0.227206	−	0.0608797i	−0.370626	+	0.928782i	$0.620857\pi$
$354$	−6.86054	−	11.8828i	−0.364633	−	0.631563i
$355$	12.1487	−	21.0422i	0.644787	−	1.11680i
$356$	−12.4013	+	12.4013i	−0.657267	+	0.657267i
$357$		0			0
$358$	−5.62502	−	1.50722i	−0.297291	−	0.0796590i
$359$	−26.8237	−	7.18738i	−1.41570	−	0.379335i	−0.531743	−	0.846906i	$-0.678463\pi$
$359$	−26.8237	−	7.18738i	−1.41570	−	0.379335i	−0.883956	+	0.467570i	$0.845129\pi$
$360$			19.7972i			1.04340i
$361$	−1.54713	+	0.893234i	−0.0814278	+	0.0470123i
$362$	3.54260	+	3.54260i	0.186195	+	0.186195i
$363$	−15.9549			−0.837413
$364$		0			0
$365$	−20.3739			−1.06642
$366$	8.03889	+	8.03889i	0.420199	+	0.420199i
$367$	14.5923	−	8.42486i	0.761711	−	0.439774i	−0.0681985	−	0.997672i	$-0.521725\pi$
$367$	14.5923	−	8.42486i	0.761711	−	0.439774i	0.829910	+	0.557898i	$0.188392\pi$
$368$			3.87242i			0.201864i
$369$	13.5621	+	3.63396i	0.706016	+	0.189176i
$370$	4.61428	+	1.23639i	0.239885	+	0.0642770i
$371$		0			0
$372$	18.4444	−	18.4444i	0.956296	−	0.956296i
$373$	−1.39145	+	2.41007i	−0.0720466	+	0.124788i	−0.899798	−	0.436306i	$-0.856286\pi$
$373$	−1.39145	+	2.41007i	−0.0720466	+	0.124788i	0.827752	+	0.561095i	$0.189620\pi$
$374$	−0.594192	−	1.02917i	−0.0307250	−	0.0532172i
$375$	25.0410	+	6.70972i	1.29311	+	0.346489i
$376$	6.22595	+	10.7837i	0.321079	+	0.556125i
$377$	−18.6042	−	7.03046i	−0.958165	−	0.362087i
$378$		0			0
$379$	0.734071	−	0.196694i	0.0377067	−	0.0101035i	−0.239916	−	0.970794i	$-0.577120\pi$
$379$	0.734071	−	0.196694i	0.0377067	−	0.0101035i	0.277623	+	0.960690i	$0.410453\pi$
$380$	28.8559			1.48028
$381$	20.9487			1.07323
$382$	−2.83133	+	0.758652i	−0.144863	+	0.0388160i
$383$	−8.14389	−	30.3934i	−0.416134	−	1.55303i	−0.782554	−	0.622582i	$-0.786084\pi$
$383$	−8.14389	−	30.3934i	−0.416134	−	1.55303i	0.366421	−	0.930449i	$-0.380583\pi$
$384$	7.16063	−	26.7238i	0.365414	−	1.36374i
$385$		0			0
$386$	−0.246321	−	0.426640i	−0.0125374	−	0.0217154i
$387$			15.6909i			0.797611i
$388$	6.20583	−	23.1605i	0.315053	−	1.17579i
$389$	−23.4348	−	13.5301i	−1.18819	−	0.686003i	−0.230297	−	0.973120i	$-0.573970\pi$
$389$	−23.4348	−	13.5301i	−1.18819	−	0.686003i	−0.957895	+	0.287118i	$0.907303\pi$
$390$	−5.50566	+	14.5692i	−0.278790	+	0.737742i
$391$			1.69617i			0.0857789i
$392$		0			0
$393$	−17.9602	+	31.1080i	−0.905973	+	1.56919i
$394$	1.79834	+	1.03827i	0.0905991	+	0.0523074i
$395$	11.0103	+	41.0909i	0.553987	+	2.06751i
$396$	7.84752	+	7.84752i	0.394353	+	0.394353i
$397$	−0.220507	+	0.0590847i	−0.0110669	+	0.00296537i	−0.264348	−	0.964427i	$-0.585157\pi$
$397$	−0.220507	+	0.0590847i	−0.0110669	+	0.00296537i	0.253281	+	0.967393i	$0.418490\pi$
$398$	−5.22522	−	5.22522i	−0.261917	−	0.261917i
$399$		0			0
$400$	−17.9766	−	10.3788i	−0.898828	−	0.518939i
$401$	−18.1702	+	18.1702i	−0.907379	+	0.907379i	−0.996060	−	0.0886812i	$-0.971735\pi$
$401$	−18.1702	+	18.1702i	−0.907379	+	0.907379i	0.0886812	+	0.996060i	$0.471735\pi$
$402$	−4.62286	+	8.00703i	−0.230567	+	0.399354i
$403$	19.9236	−	8.99527i	0.992466	−	0.448086i
$404$	−14.8424	+	8.56925i	−0.738436	+	0.426336i
$405$	8.43141	+	31.4664i	0.418960	+	1.56358i
$406$		0			0
$407$	4.95604	−	2.86137i	0.245662	−	0.141833i
$408$	1.33652	−	4.98797i	0.0661678	−	0.246941i
$409$	−21.1061	+	21.1061i	−1.04363	+	1.04363i	−0.0446236	+	0.999004i	$0.514209\pi$
$409$	−21.1061	+	21.1061i	−1.04363	+	1.04363i	−0.999004	+	0.0446236i	$0.985791\pi$
$410$	5.88038	−	5.88038i	0.290411	−	0.290411i
$411$	1.44035	−	5.37547i	0.0710474	−	0.265153i
$412$	18.8400	−	10.8773i	0.928182	−	0.535886i
$413$		0			0
$414$	0.561574	+	2.09582i	0.0275998	+	0.103004i
$415$	−22.3326	+	12.8937i	−1.09627	+	0.632929i
$416$	10.4629	−	14.5599i	0.512985	−	0.713857i
$417$	5.97643	−	10.3515i	0.292667	−	0.506914i
$418$	−3.34823	+	3.34823i	−0.163767	+	0.163767i
$419$	−7.72615	−	4.46069i	−0.377447	−	0.217919i	0.299260	−	0.954172i	$-0.403260\pi$
$419$	−7.72615	−	4.46069i	−0.377447	−	0.217919i	−0.676707	+	0.736253i	$0.736594\pi$
$420$		0			0
$421$	18.1408	+	18.1408i	0.884130	+	0.884130i	0.993951	−	0.109821i	$-0.0350278\pi$
$421$	18.1408	+	18.1408i	0.884130	+	0.884130i	−0.109821	+	0.993951i	$0.535028\pi$
$422$	−11.7166	+	3.13945i	−0.570354	+	0.152826i
$423$	−14.2290	−	14.2290i	−0.691835	−	0.691835i
$424$	−1.66567	−	6.21635i	−0.0808919	−	0.301893i
$425$	−7.87395	−	4.54603i	−0.381943	−	0.220515i
$426$	−4.05367	+	7.02116i	−0.196401	+	0.340176i
$427$		0			0
$428$			14.4016i			0.696130i
$429$	7.67765	+	17.0052i	0.370680	+	0.821019i
$430$	8.04848	+	4.64679i	0.388132	+	0.224088i
$431$	−3.04559	+	11.3663i	−0.146701	+	0.547496i	0.852973	+	0.521955i	$0.174797\pi$
$431$	−3.04559	+	11.3663i	−0.146701	+	0.547496i	−0.999674	+	0.0255403i	$0.991869\pi$
$432$		−	0.115567i		−	0.00556020i
$433$	−6.26407	−	10.8497i	−0.301032	−	0.521403i	0.675338	−	0.737508i	$-0.263998\pi$
$433$	−6.26407	−	10.8497i	−0.301032	−	0.521403i	−0.976370	+	0.216106i	$0.930664\pi$
$434$		0			0
$435$	12.5634	−	46.8874i	0.602370	−	2.24808i
$436$	1.35662	+	5.06298i	0.0649703	+	0.242473i
$437$	6.52808	−	1.74919i	0.312280	−	0.0836752i
$438$	6.79816			0.324828
$439$	−17.7638			−0.847819			−0.423910	−	0.905705i	$-0.639343\pi$
$439$	−17.7638			−0.847819			−0.423910	+	0.905705i	$0.639343\pi$
$440$	13.5684	−	3.63563i	0.646847	−	0.173322i
$441$		0			0
$442$	1.18179	−	1.64455i	0.0562120	−	0.0782233i
$443$	3.34945	+	5.80142i	0.159137	+	0.275634i	0.934558	−	0.355811i	$-0.115795\pi$
$443$	3.34945	+	5.80142i	0.159137	+	0.275634i	−0.775421	+	0.631445i	$0.782462\pi$
$444$	11.2401	+	3.01178i	0.533433	+	0.142933i
$445$	−17.9366	−	31.0671i	−0.850278	−	1.47272i
$446$	−0.183375	+	0.317615i	−0.00868307	+	0.0150395i
$447$	−4.79202	+	4.79202i	−0.226655	+	0.226655i
$448$		0			0
$449$	22.8700	+	6.12801i	1.07930	+	0.289199i	0.754311	−	0.656518i	$-0.227971\pi$
$449$	22.8700	+	6.12801i	1.07930	+	0.289199i	0.324993	+	0.945716i	$0.394638\pi$
$450$	−11.2343	−	3.01023i	−0.529592	−	0.141904i
$451$		−	9.96240i		−	0.469111i
$452$	−24.9803	+	14.4224i	−1.17498	+	0.678373i
$453$	10.9194	+	10.9194i	0.513036	+	0.513036i
$454$	−5.09120			−0.238942
$455$		0			0
$456$	−20.5756			−0.963542
$457$	−22.5829	−	22.5829i	−1.05638	−	1.05638i	−0.998312	−	0.0580710i	$-0.981505\pi$
$457$	−22.5829	−	22.5829i	−1.05638	−	1.05638i	−0.0580710	−	0.998312i	$-0.518495\pi$
$458$	0.730190	−	0.421575i	0.0341195	−	0.0196989i
$459$		−	0.0506196i		−	0.00236272i
$460$	−9.06232	−	2.42824i	−0.422533	−	0.113217i
$461$	36.7537	+	9.84812i	1.71179	+	0.458673i	0.975862	−	0.218388i	$-0.0700798\pi$
$461$	36.7537	+	9.84812i	1.71179	+	0.458673i	0.735927	+	0.677060i	$0.236746\pi$
$462$		0			0
$463$	−9.11397	+	9.11397i	−0.423562	+	0.423562i	−0.886428	−	0.462866i	$-0.846821\pi$
$463$	−9.11397	+	9.11397i	−0.423562	+	0.423562i	0.462866	+	0.886428i	$0.346821\pi$
$464$	−7.20488	+	12.4792i	−0.334478	+	0.579333i
$465$	26.6770	+	46.2060i	1.23712	+	2.14275i
$466$	−3.94041	−	1.05583i	−0.182536	−	0.0489104i
$467$	−8.92031	−	15.4504i	−0.412783	−	0.714960i	0.582410	−	0.812895i	$-0.302110\pi$
$467$	−8.92031	−	15.4504i	−0.412783	−	0.714960i	−0.995193	+	0.0979345i	$0.968776\pi$
$468$	−6.68545	+	17.6912i	−0.309035	+	0.817778i
$469$		0			0
$470$	−11.5125	+	3.08475i	−0.531030	+	0.142289i
$471$	4.66871			0.215123
$472$	−21.0885			−0.970677
$473$	10.7540	−	2.88153i	0.494470	−	0.132493i
$474$	−3.67380	−	13.7108i	−0.168743	−	0.629759i
$475$	−9.37629	+	34.9928i	−0.430214	+	1.60558i
$476$		0			0
$477$	5.20013	+	9.00689i	0.238098	+	0.412397i
$478$		−	3.56799i		−	0.163196i
$479$	−2.37889	+	8.87813i	−0.108694	+	0.405652i	−0.998738	−	0.0502226i	$-0.984007\pi$
$479$	−2.37889	+	8.87813i	−0.108694	+	0.405652i	0.890044	+	0.455875i	$0.150674\pi$
$480$	37.8975	+	21.8801i	1.72978	+	0.998686i
$481$	7.91944	+	5.69098i	0.361095	+	0.259487i
$482$			3.80434i			0.173283i
$483$		0			0
$484$	−5.73748	+	9.93760i	−0.260794	+	0.451709i
$485$	42.4740	+	24.5224i	1.92864	+	1.11350i
$486$	−2.79645	−	10.4365i	−0.126850	−	0.473409i
$487$	7.82334	+	7.82334i	0.354509	+	0.354509i	0.861784	−	0.507275i	$-0.169347\pi$
$487$	7.82334	+	7.82334i	0.354509	+	0.354509i	−0.507275	+	0.861784i	$0.669347\pi$
$488$	16.8777	−	4.52236i	0.764017	−	0.204718i
$489$	10.6761	+	10.6761i	0.482789	+	0.482789i
$490$		0			0
$491$	2.45531	+	1.41757i	0.110807	+	0.0639743i	0.554379	−	0.832264i	$-0.312956\pi$
$491$	2.45531	+	1.41757i	0.110807	+	0.0639743i	−0.443572	+	0.896239i	$0.646289\pi$
$492$	14.3243	−	14.3243i	0.645787	−	0.645787i
$493$	−3.15583	+	5.46605i	−0.142131	+	0.246179i
$494$	−7.54815	−	2.85242i	−0.339607	−	0.128336i
$495$	−19.6592	+	11.3503i	−0.883617	+	0.510157i
$496$	−4.09929	−	15.2988i	−0.184064	−	0.686935i
$497$		0			0
$498$	7.45174	−	4.30226i	0.333920	−	0.192789i
$499$	−9.92738	+	37.0495i	−0.444411	+	1.65856i	0.273077	+	0.961992i	$0.411959\pi$
$499$	−9.92738	+	37.0495i	−0.444411	+	1.65856i	−0.717488	+	0.696571i	$0.754708\pi$
$500$	13.1841	−	13.1841i	0.589612	−	0.589612i
$501$	−3.79328	+	3.79328i	−0.169471	+	0.169471i
$502$	0.447511	−	1.67014i	0.0199734	−	0.0745418i
$503$	−25.0453	+	14.4599i	−1.11672	+	0.644736i	−0.940561	−	0.339626i	$-0.889699\pi$
$503$	−25.0453	+	14.4599i	−1.11672	+	0.644736i	−0.176155	+	0.984362i	$0.556366\pi$
$504$		0			0
$505$	−9.07314	−	33.8614i	−0.403750	−	1.50681i
$506$	1.33328	−	0.769769i	0.0592715	−	0.0342204i
$507$	−21.0278	+	23.8490i	−0.933877	+	1.05917i
$508$	7.53329	−	13.0480i	0.334236	−	0.578913i
$509$	−9.05020	+	9.05020i	−0.401143	+	0.401143i	−0.878636	−	0.477493i	$-0.841546\pi$
$509$	−9.05020	+	9.05020i	−0.401143	+	0.401143i	0.477493	+	0.878636i	$0.341546\pi$
$510$	4.28055	+	2.47138i	0.189546	+	0.109434i
$511$		0			0
$512$	−16.0026	−	16.0026i	−0.707221	−	0.707221i
$513$	−0.194821	+	0.0522021i	−0.00860155	+	0.00230478i
$514$	3.76650	+	3.76650i	0.166133	+	0.166133i
$515$	11.5169	+	42.9817i	0.507496	+	1.89400i
$516$	19.6056	+	11.3193i	0.863089	+	0.498305i
$517$	−7.13901	+	12.3651i	−0.313973	+	0.543817i
$518$		0			0
$519$			46.3415i			2.03416i
$520$	15.1612	+	18.5243i	0.664861	+	0.812342i
$521$	−13.9866	−	8.07515i	−0.612763	−	0.353779i	0.161283	−	0.986908i	$-0.448437\pi$
$521$	−13.9866	−	8.07515i	−0.612763	−	0.353779i	−0.774046	+	0.633129i	$0.781770\pi$
$522$	−2.08969	+	7.79881i	−0.0914631	+	0.341345i
$523$			36.1273i			1.57974i	0.613277	+	0.789868i	$0.289851\pi$
$523$			36.1273i			1.57974i	−0.613277	+	0.789868i	$0.710149\pi$
$524$	12.9172	+	22.3733i	0.564292	+	0.977382i
$525$		0			0
$526$	0.597006	−	2.22806i	0.0260307	−	0.0971479i
$527$	−1.79554	−	6.70104i	−0.0782149	−	0.291902i
$528$	13.0578	−	3.49883i	0.568268	−	0.152267i
$529$	20.8026			0.904462
$530$	6.15999			0.267573
$531$	32.9187	−	8.82053i	1.42855	−	0.382778i
$532$		0			0
$533$	15.4731	−	6.98590i	0.670212	−	0.302593i
$534$	5.98493	+	10.3662i	0.258993	+	0.448589i
$535$	−28.4541	−	7.62425i	−1.23018	−	0.329625i
$536$	7.10508	+	12.3064i	0.306893	+	0.531553i
$537$	14.5079	−	25.1285i	0.626063	−	1.08437i
$538$	8.92413	−	8.92413i	0.384747	−	0.384747i
$539$		0			0
$540$	0.270451	+	0.0724673i	0.0116384	+	0.00311849i
$541$	25.1563	+	6.74062i	1.08155	+	0.289802i	0.755233	−	0.655457i	$-0.227524\pi$
$541$	25.1563	+	6.74062i	1.08155	+	0.289802i	0.326322	+	0.945259i	$0.394191\pi$
$542$			0.650986i			0.0279623i
$543$	−21.6184	+	12.4814i	−0.927732	+	0.535627i
$544$	−4.02342	−	4.02342i	−0.172503	−	0.172503i
$545$	−10.7214			−0.459254
$546$		0			0
$547$	−21.3472			−0.912739			−0.456369	−	0.889790i	$-0.650850\pi$
$547$	−21.3472			−0.912739			−0.456369	+	0.889790i	$0.650850\pi$
$548$	−2.83019	−	2.83019i	−0.120900	−	0.120900i
$549$	−24.4541	+	14.1186i	−1.04368	+	0.602567i
$550$			8.25247i			0.351886i
$551$	24.2918	+	6.50897i	1.03487	+	0.277291i
$552$	6.46186	+	1.73145i	0.275035	+	0.0736954i
$553$		0			0
$554$	0.0629511	−	0.0629511i	0.00267454	−	0.00267454i
$555$	−11.9011	+	20.6133i	−0.505172	+	0.874984i
$556$	−4.29833	−	7.44492i	−0.182290	−	0.315735i
$557$	6.33615	+	1.69776i	0.268471	+	0.0719366i	0.390543	−	0.920585i	$-0.372287\pi$
$557$	6.33615	+	1.69776i	0.268471	+	0.0719366i	−0.122072	+	0.992521i	$0.538954\pi$
$558$	−4.43721	−	7.68548i	−0.187842	−	0.325352i
$559$	12.0164	+	14.6819i	0.508241	+	0.620980i
$560$		0			0
$561$	5.71948	−	1.53253i	0.241476	−	0.0647034i
$562$	−3.82197			−0.161220
$563$	10.0916			0.425310			0.212655	−	0.977127i	$-0.431789\pi$
$563$	10.0916			0.425310			0.212655	+	0.977127i	$0.431789\pi$
$564$	−28.0437	+	7.51428i	−1.18085	+	0.316408i
$565$	−15.2705	−	56.9902i	−0.642434	−	2.39760i
$566$	0.928516	−	3.46527i	0.0390284	−	0.145656i
$567$		0			0
$568$	6.23026	+	10.7911i	0.261416	+	0.452786i
$569$		−	31.3060i		−	1.31241i	−0.754581	−	0.656207i	$-0.772160\pi$
$569$		−	31.3060i		−	1.31241i	0.754581	−	0.656207i	$-0.227840\pi$
$570$	5.09727	−	19.0233i	0.213501	−	0.796797i
$571$	−8.05884	−	4.65277i	−0.337252	−	0.194713i	0.321804	−	0.946806i	$-0.395711\pi$
$571$	−8.05884	−	4.65277i	−0.337252	−	0.194713i	−0.659056	+	0.752094i	$0.729044\pi$
$572$	13.3527	+	1.33311i	0.558306	+	0.0557401i
$573$		−	14.6050i		−	0.610133i
$574$		0			0
$575$	5.88933	−	10.2006i	0.245602	−	0.425395i
$576$	7.18881	+	4.15046i	0.299534	+	0.172936i
$577$	4.44854	+	16.6022i	0.185195	+	0.691158i	0.994589	+	0.103891i	$0.0331294\pi$
$577$	4.44854	+	16.6022i	0.185195	+	0.691158i	−0.809393	+	0.587267i	$0.800204\pi$
$578$	5.44618	+	5.44618i	0.226531	+	0.226531i
$579$	2.37099	−	0.635306i	0.0985351	−	0.0264024i
$580$	−24.6862	−	24.6862i	−1.02504	−	1.02504i
$581$		0			0
$582$	−14.1723	−	8.18239i	−0.587461	−	0.339171i
$583$	5.21806	−	5.21806i	0.216110	−	0.216110i
$584$	5.22419	−	9.04857i	0.216179	−	0.374432i
$585$	−31.4142	−	22.5746i	−1.29882	−	0.933343i
$586$	−13.6457	+	7.87838i	−0.563701	+	0.325453i
$587$	−5.01190	−	18.7047i	−0.206863	−	0.772025i	−0.988873	−	0.148759i	$-0.952472\pi$
$587$	−5.01190	−	18.7047i	−0.206863	−	0.772025i	0.782010	−	0.623266i	$-0.214195\pi$
$588$		0			0
$589$	−23.9388	+	13.8211i	−0.986380	+	0.569487i
$590$	5.22433	−	19.4975i	0.215082	−	0.802698i
$591$	−7.31614	+	7.31614i	−0.300946	+	0.300946i
$592$	4.99627	−	4.99627i	0.205345	−	0.205345i
$593$	2.62077	−	9.78085i	0.107622	−	0.401651i	−0.891007	−	0.453989i	$-0.850001\pi$
$593$	2.62077	−	9.78085i	0.107622	−	0.401651i	0.998629	+	0.0523376i	$0.0166672\pi$
$594$	−0.0397897	+	0.0229726i	−0.00163259	+	0.000942578i
$595$		0			0
$596$	1.26150	+	4.70799i	0.0516731	+	0.192847i
$597$	31.8864	−	18.4096i	1.30502	−	0.753456i
$598$	2.13049	+	1.53099i	0.0871224	+	0.0626070i
$599$	−8.96728	+	15.5318i	−0.366393	+	0.634611i	−0.988999	−	0.147924i	$-0.952741\pi$
$599$	−8.96728	+	15.5318i	−0.366393	+	0.634611i	0.622606	+	0.782536i	$0.286074\pi$
$600$	−25.3567	+	25.3567i	−1.03518	+	1.03518i
$601$	−29.5092	−	17.0372i	−1.20371	−	0.694960i	−0.242329	−	0.970194i	$-0.577911\pi$
$601$	−29.5092	−	17.0372i	−1.20371	−	0.694960i	−0.961377	+	0.275234i	$0.911245\pi$
$602$		0			0
$603$	−16.2381	−	16.2381i	−0.661268	−	0.661268i
$604$	10.7279	−	2.87453i	0.436511	−	0.116963i
$605$	−16.5968	−	16.5968i	−0.674756	−	0.674756i
$606$	3.02744	+	11.2986i	0.122981	+	0.458973i
$607$	27.7235	+	16.0061i	1.12526	+	0.649669i	0.942739	−	0.333533i	$-0.108241\pi$
$607$	27.7235	+	16.0061i	1.12526	+	0.649669i	0.182522	+	0.983202i	$0.441574\pi$
$608$	−11.3358	+	19.6342i	−0.459729	+	0.796274i
$609$		0			0
$610$			16.7247i			0.677162i
$611$	−24.2109	−	2.41716i	−0.979468	−	0.0977880i
$612$	5.19782	+	3.00096i	0.210109	+	0.121307i
$613$	4.48824	−	16.7504i	0.181279	−	0.676541i	−0.814118	−	0.580699i	$-0.802779\pi$
$613$	4.48824	−	16.7504i	0.181279	−	0.676541i	0.995397	−	0.0958413i	$-0.0305541\pi$
$614$			6.70313i			0.270516i
$615$	20.7179	+	35.8845i	0.835426	+	1.44700i
$616$		0			0
$617$	−4.46908	+	16.6788i	−0.179918	+	0.671464i	0.815743	+	0.578414i	$0.196328\pi$
$617$	−4.46908	+	16.6788i	−0.179918	+	0.671464i	−0.995661	+	0.0930497i	$0.970338\pi$
$618$	−3.84286	−	14.3417i	−0.154582	−	0.576909i
$619$	2.93095	−	0.785345i	0.117805	−	0.0315657i	−0.199435	−	0.979911i	$-0.563911\pi$
$619$	2.93095	−	0.785345i	0.117805	−	0.0315657i	0.317240	+	0.948345i	$0.397244\pi$
$620$	38.3730			1.54110
$621$	0.0655771			0.00263152
$622$	−7.86477	+	2.10736i	−0.315349	+	0.0844974i
$623$		0			0
$624$	14.5907	+	17.8272i	0.584094	+	0.713659i
$625$	−0.795947	−	1.37862i	−0.0318379	−	0.0551448i
$626$	−4.41421	−	1.18278i	−0.176427	−	0.0472736i
$627$	−11.7966	−	20.4322i	−0.471109	−	0.815985i
$628$	1.67890	−	2.90794i	0.0669954	−	0.116039i
$629$	2.18843	−	2.18843i	0.0872583	−	0.0872583i
$630$		0			0
$631$	−46.4748	−	12.4529i	−1.85013	−	0.495742i	−0.850587	−	0.525834i	$-0.823753\pi$
$631$	−46.4748	−	12.4529i	−1.85013	−	0.495742i	−0.999547	+	0.0300916i	$0.990420\pi$
$632$	−21.0728	−	5.64643i	−0.838229	−	0.224603i
$633$		−	60.4383i		−	2.40221i
$634$	−14.0890	+	8.13426i	−0.559544	+	0.323053i
$635$	21.7916	+	21.7916i	0.864772	+	0.864772i
$636$	15.0054			0.595002
$637$		0			0
$638$	5.72881			0.226806
$639$	−14.2388	−	14.2388i	−0.563278	−	0.563278i
$640$	35.2478	−	20.3503i	1.39329	−	0.804417i
$641$		−	50.4462i		−	1.99251i	−0.0864867	−	0.996253i	$-0.527564\pi$
$641$		−	50.4462i		−	1.99251i	0.0864867	−	0.996253i	$-0.472436\pi$
$642$	9.49429	+	2.54399i	0.374710	+	0.100403i
$643$	23.5329	+	6.30561i	0.928046	+	0.248669i	0.691021	−	0.722834i	$-0.257161\pi$
$643$	23.5329	+	6.30561i	0.928046	+	0.248669i	0.237025	+	0.971504i	$0.423828\pi$
$644$		0			0
$645$	−32.7434	+	32.7434i	−1.28927	+	1.28927i
$646$	−1.28039	+	2.21770i	−0.0503763	+	0.0872543i
$647$	−21.8129	−	37.7811i	−0.857554	−	1.48533i	−0.874255	−	0.485467i	$-0.838650\pi$
$647$	−21.8129	−	37.7811i	−0.857554	−	1.48533i	0.0167008	−	0.999861i	$-0.494684\pi$
$648$	−16.1370	−	4.32391i	−0.633923	−	0.169859i
$649$	−12.0906	−	20.9415i	−0.474598	−	0.822028i
$650$	−12.8173	+	5.78685i	−0.502735	+	0.226979i
$651$		0			0
$652$	10.4889	−	2.81048i	0.410776	−	0.110067i
$653$	48.0114			1.87883			0.939416	−	0.342780i	$-0.111368\pi$
$653$	48.0114			1.87883			0.939416	+	0.342780i	$0.111368\pi$
$654$	3.57741			0.139888
$655$	−51.0425	+	13.6768i	−1.99439	+	0.534396i
$656$	−3.18359	−	11.8813i	−0.124298	−	0.463887i
$657$	−4.37016	+	16.3097i	−0.170496	+	0.636301i
$658$		0			0
$659$	2.00241	+	3.46828i	0.0780030	+	0.135105i	0.902388	−	0.430924i	$-0.141812\pi$
$659$	2.00241	+	3.46828i	0.0780030	+	0.135105i	−0.824385	+	0.566029i	$0.808479\pi$
$660$			32.7521i			1.27487i
$661$	−5.45564	+	20.3607i	−0.212200	+	0.791941i	0.774934	+	0.632043i	$0.217783\pi$
$661$	−5.45564	+	20.3607i	−0.212200	+	0.791941i	−0.987134	+	0.159898i	$0.948883\pi$
$662$	−10.0101	−	5.77934i	−0.389054	−	0.224620i
$663$	6.39089	+	7.80853i	0.248202	+	0.303258i
$664$		−	13.2247i		−	0.513217i
$665$		0			0
$666$	1.97952	−	3.42862i	0.0767047	−	0.132856i
$667$	−7.08120	−	4.08833i	−0.274185	−	0.158301i
$668$	0.998584	+	3.72677i	0.0386364	+	0.144193i
$669$	−1.29214	−	1.29214i	−0.0499572	−	0.0499572i
$670$	−13.1381	+	3.52033i	−0.507567	+	0.136002i
$671$	14.1673	+	14.1673i	0.546921	+	0.546921i
$672$		0			0
$673$	−39.2951	−	22.6870i	−1.51471	−	0.874521i	−0.999851	−	0.0172480i	$-0.994510\pi$
$673$	−39.2951	−	22.6870i	−1.51471	−	0.874521i	−0.514863	−	0.857273i	$-0.672157\pi$
$674$	−8.53712	+	8.53712i	−0.328838	+	0.328838i
$675$	−0.175758	+	0.304422i	−0.00676494	+	0.0117172i
$676$	7.29279	+	21.6736i	0.280492	+	0.833599i
$677$	12.2354	−	7.06412i	0.470245	−	0.271496i	−0.246097	−	0.969245i	$-0.579148\pi$
$677$	12.2354	−	7.06412i	0.470245	−	0.271496i	0.716342	+	0.697749i	$0.245815\pi$
$678$	5.09531	+	19.0160i	0.195684	+	0.730304i
$679$		0			0
$680$	6.57896	−	3.79837i	0.252292	−	0.145661i
$681$	6.56556	−	24.5030i	0.251593	−	0.938957i
$682$	−4.45251	+	4.45251i	−0.170496	+	0.170496i
$683$	−0.171916	+	0.171916i	−0.00657818	+	0.00657818i	−0.710388	−	0.703810i	$-0.751481\pi$
$683$	−0.171916	+	0.171916i	−0.00657818	+	0.00657818i	0.703810	+	0.710388i	$0.251481\pi$
$684$	6.18955	−	23.0997i	0.236664	−	0.883240i
$685$	7.09006	−	4.09345i	0.270897	−	0.156403i
$686$		0			0
$687$	1.08732	+	4.05793i	0.0414838	+	0.154820i
$688$	11.9046	−	6.87311i	0.453858	−	0.262035i
$689$	11.7635	+	4.44536i	0.448152	+	0.169355i
$690$	−3.20164	+	5.54540i	−0.121884	+	0.211110i
$691$	−25.5418	+	25.5418i	−0.971656	+	0.971656i	−0.999609	−	0.0279531i	$-0.991101\pi$
$691$	−25.5418	+	25.5418i	−0.971656	+	0.971656i	0.0279531	+	0.999609i	$0.491101\pi$
$692$	28.8641	+	16.6647i	1.09725	+	0.633497i
$693$		0			0
$694$	11.5788	+	11.5788i	0.439526	+	0.439526i
$695$	16.9849	−	4.55108i	0.644273	−	0.172632i
$696$	17.6024	+	17.6024i	0.667219	+	0.667219i
$697$	−1.39445	−	5.20416i	−0.0528186	−	0.197122i
$698$	2.32456	+	1.34208i	0.0879858	+	0.0507986i
$699$	10.1630	−	17.6029i	0.384401	−	0.665802i
$700$		0			0
$701$			26.1953i			0.989383i	0.869069	+	0.494691i	$0.164719\pi$
$701$			26.1953i			0.989383i	−0.869069	+	0.494691i	$0.835281\pi$
$702$	−0.0635815	−	0.0456903i	−0.00239973	−	0.00172447i
$703$	−10.6795	−	6.16581i	−0.402785	−	0.232548i
$704$	1.52441	−	5.68918i	0.0574534	−	0.214419i
$705$		−	59.3854i		−	2.23658i
$706$	1.08467	+	1.87871i	0.0408221	+	0.0707060i
$707$		0			0
$708$	12.7262	−	47.4947i	0.478279	−	1.78496i
$709$	4.04305	+	15.0889i	0.151840	+	0.566674i	0.999355	+	0.0359035i	$0.0114309\pi$
$709$	4.04305	+	15.0889i	0.151840	+	0.566674i	−0.847515	+	0.530771i	$0.821902\pi$
$710$	−11.5204	+	3.08689i	−0.432354	+	0.115849i
$711$	35.2558			1.32219
$712$	18.3970			0.689456
$713$	8.68112	−	2.32610i	0.325111	−	0.0871131i
$714$		0			0
$715$	−9.70285	+	25.6760i	−0.362866	+	0.960227i
$716$	−10.4343	−	18.0727i	−0.389948	−	0.675410i
$717$	17.1721	+	4.60125i	0.641304	+	0.171837i
$718$	6.81568	+	11.8051i	0.254359	+	0.440562i
$719$	0.698769	−	1.21030i	0.0260597	−	0.0451367i	−0.852701	−	0.522399i	$-0.825037\pi$
$719$	0.698769	−	1.21030i	0.0260597	−	0.0451367i	0.878761	+	0.477262i	$0.158371\pi$
$720$	−19.8188	+	19.8188i	−0.738604	+	0.738604i
$721$		0			0
$722$	0.847040	+	0.226964i	0.0315236	+	0.00844671i
$723$	−18.3096	−	4.90603i	−0.680940	−	0.182457i
$724$			17.9535i			0.667238i
$725$	37.9578	−	21.9149i	1.40972	−	0.813900i
$726$	5.53787	+	5.53787i	0.205530	+	0.205530i
$727$	−8.63150			−0.320124			−0.160062	−	0.987107i	$-0.551169\pi$
$727$	−8.63150			−0.320124			−0.160062	+	0.987107i	$0.551169\pi$
$728$		0			0
$729$	26.6734			0.987905
$730$	7.07168	+	7.07168i	0.261735	+	0.261735i
$731$	5.21435	−	3.01051i	0.192860	−	0.111348i
$732$			40.7403i			1.50581i
$733$	−0.784228	−	0.210133i	−0.0289661	−	0.00776145i	0.244307	−	0.969698i	$-0.421440\pi$
$733$	−0.784228	−	0.210133i	−0.0289661	−	0.00776145i	−0.273273	+	0.961937i	$0.588106\pi$
$734$	−7.98916	−	2.14069i	−0.294885	−	0.0790143i
$735$		0			0
$736$	5.21230	−	5.21230i	0.192128	−	0.192128i
$737$	−8.14706	+	14.1111i	−0.300101	+	0.519790i
$738$	−3.44603	−	5.96869i	−0.126850	−	0.219711i
$739$	21.6112	+	5.79070i	0.794981	+	0.213014i	0.633379	−	0.773842i	$-0.281667\pi$
$739$	21.6112	+	5.79070i	0.794981	+	0.213014i	0.161601	+	0.986856i	$0.448334\pi$
$740$	8.55941	+	14.8253i	0.314650	+	0.544990i
$741$	23.4622	−	32.6494i	0.861905	−	1.19941i
$742$		0			0
$743$	21.2232	−	5.68675i	0.778605	−	0.208627i	0.152436	−	0.988313i	$-0.451288\pi$
$743$	21.2232	−	5.68675i	0.778605	−	0.208627i	0.626170	+	0.779687i	$0.284622\pi$
$744$	−27.3617			−1.00313
$745$	−9.96965			−0.365260
$746$	1.31949	−	0.353557i	0.0483100	−	0.0129446i
$747$	5.53138	+	20.6434i	0.202383	+	0.755302i
$748$	1.10222	−	4.11352i	0.0403010	−	0.150405i
$749$		0			0
$750$	−6.36272	−	11.0206i	−0.232334	−	0.402414i
$751$		−	25.4210i		−	0.927626i	−0.885933	−	0.463813i	$-0.846481\pi$
$751$		−	25.4210i		−	0.927626i	0.885933	−	0.463813i	$-0.153519\pi$
$752$	−4.56269	+	17.0282i	−0.166384	+	0.620954i
$753$	7.46095	+	4.30758i	0.271892	+	0.156977i
$754$	4.01720	+	8.89768i	0.146298	+	0.324035i
$755$			22.7174i			0.826771i
$756$		0			0
$757$	19.9731	−	34.5945i	0.725936	−	1.25736i	−0.232651	−	0.972560i	$-0.574740\pi$
$757$	19.9731	−	34.5945i	0.725936	−	1.25736i	0.958587	−	0.284799i	$-0.0919267\pi$
$758$	−0.323065	−	0.186521i	−0.0117342	−	0.00677476i
$759$	1.98537	+	7.40951i	0.0720645	+	0.268948i
$760$	−21.4035	−	21.4035i	−0.776386	−	0.776386i
$761$	−16.8436	+	4.51324i	−0.610581	+	0.163605i	−0.550842	−	0.834609i	$-0.685693\pi$
$761$	−16.8436	+	4.51324i	−0.610581	+	0.163605i	−0.0597387	+	0.998214i	$0.519027\pi$
$762$	−7.27120	−	7.27120i	−0.263408	−	0.263408i
$763$		0			0
$764$	−9.09684	−	5.25206i	−0.329112	−	0.190013i
$765$	−8.68089	+	8.68089i	−0.313858	+	0.313858i
$766$	−7.72272	+	13.3761i	−0.279033	+	0.483300i
$767$	24.0470	−	33.4633i	0.868288	−	1.20829i
$768$	0.0315111	−	0.0181929i	0.00113706	−	0.000656480i
$769$	−0.710240	−	2.65065i	−0.0256119	−	0.0955849i	0.951937	−	0.306295i	$-0.0990892\pi$
$769$	−0.710240	−	2.65065i	−0.0256119	−	0.0955849i	−0.977549	+	0.210710i	$0.932423\pi$
$770$		0			0
$771$	−22.9847	+	13.2702i	−0.827774	+	0.477915i
$772$	0.456920	−	1.70525i	0.0164449	−	0.0613733i
$773$	9.40098	−	9.40098i	0.338130	−	0.338130i	−0.517533	−	0.855663i	$-0.673150\pi$
$773$	9.40098	−	9.40098i	0.338130	−	0.338130i	0.855663	+	0.517533i	$0.173150\pi$
$774$	5.44623	−	5.44623i	0.195761	−	0.195761i
$775$	−12.4687	+	46.5339i	−0.447890	+	1.67155i
$776$	−21.7820	+	12.5759i	−0.781930	+	0.451448i
$777$		0			0
$778$	3.43789	+	12.8304i	0.123254	+	0.459991i
$779$	−18.5913	+	10.7337i	−0.666103	+	0.384575i
$780$	−50.8688	+	22.9667i	−1.82140	+	0.822338i
$781$	−7.14395	+	12.3737i	−0.255631	+	0.442765i
$782$	0.588733	−	0.588733i	0.0210530	−	0.0210530i
$783$	0.211328	+	0.122010i	0.00755225	+	0.00436029i
$784$		0			0
$785$	4.85655	+	4.85655i	0.173338	+	0.173338i
$786$	17.0314	−	4.56354i	0.607489	−	0.162776i
$787$	−15.5115	−	15.5115i	−0.552925	−	0.552925i	0.374359	−	0.927284i	$-0.377863\pi$
$787$	−15.5115	−	15.5115i	−0.552925	−	0.552925i	−0.927284	+	0.374359i	$0.877863\pi$
$788$	1.92598	+	7.18784i	0.0686101	+	0.256056i
$789$	9.95333	+	5.74656i	0.354348	+	0.204583i
$790$	10.4409	−	18.0841i	0.371469	−	0.643403i
$791$		0			0
$792$		−	11.6416i		−	0.413666i
$793$	−12.0694	+	31.9383i	−0.428596	+	1.13416i
$794$	0.0970451	+	0.0560290i	0.00344400	+	0.00198840i
$795$	−7.94387	+	29.6469i	−0.281740	+	1.05147i
$796$		−	26.4809i		−	0.938591i
$797$	−23.0740	−	39.9654i	−0.817324	−	1.41565i	−0.907647	−	0.419735i	$-0.862123\pi$
$797$	−23.0740	−	39.9654i	−0.817324	−	1.41565i	0.0903225	−	0.995913i	$-0.471210\pi$
$798$		0			0
$799$	−1.99851	+	7.45855i	−0.0707023	+	0.263865i
$800$	10.2267	+	38.1664i	0.361567	+	1.34939i
$801$	−28.7172	+	7.69476i	−1.01467	+	0.271881i
$802$	12.6136			0.445403
$803$	11.9807			0.422789
$804$	−32.0035	+	8.57532i	−1.12868	+	0.302428i
$805$		0			0
$806$	−10.0376	−	3.79318i	−0.353560	−	0.133609i
$807$	31.4417	+	54.4587i	1.10680	+	1.91704i
$808$	17.3653	+	4.65301i	0.610908	+	0.163692i
$809$	18.6015	+	32.2188i	0.653994	+	1.13275i	0.982145	+	0.188126i	$0.0602413\pi$
$809$	18.6015	+	32.2188i	0.653994	+	1.13275i	−0.328151	+	0.944625i	$0.606425\pi$
$810$	7.99537	−	13.8484i	0.280929	−	0.486583i
$811$	−5.71666	+	5.71666i	−0.200739	+	0.200739i	−0.800317	−	0.599578i	$-0.795335\pi$
$811$	−5.71666	+	5.71666i	−0.200739	+	0.200739i	0.599578	+	0.800317i	$0.295335\pi$
$812$		0			0
$813$	−3.13308	−	0.839506i	−0.109882	−	0.0294427i
$814$	−2.71339	−	0.727051i	−0.0951043	−	0.0254831i
$815$			22.2113i			0.778027i
$816$	6.33140	−	3.65544i	0.221643	−	0.127966i
$817$	−16.9640	−	16.9640i	−0.593494	−	0.593494i
$818$	14.6517			0.512283
$819$		0			0
$820$	29.8012			1.04070
$821$	4.54301	+	4.54301i	0.158552	+	0.158552i	0.781925	−	0.623373i	$-0.214238\pi$
$821$	4.54301	+	4.54301i	0.158552	+	0.158552i	−0.623373	+	0.781925i	$0.714238\pi$
$822$	−2.36575	+	1.36586i	−0.0825149	+	0.0476400i
$823$		−	8.90568i		−	0.310433i	−0.987881	−	0.155216i	$-0.950393\pi$
$823$		−	8.90568i		−	0.310433i	0.987881	−	0.155216i	$-0.0496075\pi$
$824$	−22.0424	−	5.90625i	−0.767885	−	0.205754i
$825$	−39.7176	−	10.6423i	−1.38279	−	0.370517i
$826$		0			0
$827$	−0.00569088	+	0.00569088i	−0.000197891	+	0.000197891i	−0.707206	−	0.707008i	$-0.750045\pi$
$827$	−0.00569088	+	0.00569088i	−0.000197891	+	0.000197891i	0.707008	+	0.707206i	$0.250045\pi$
$828$	−3.88771	+	6.73371i	−0.135107	+	0.234013i
$829$	8.36149	+	14.4825i	0.290407	+	0.502999i	0.973906	−	0.226952i	$-0.0728761\pi$
$829$	8.36149	+	14.4825i	0.290407	+	0.502999i	−0.683499	+	0.729951i	$0.739543\pi$
$830$	12.2269	+	3.27620i	0.424403	+	0.113718i
$831$	0.221791	+	0.384153i	0.00769384	+	0.0133261i
$832$	9.90509	−	1.62177i	0.343397	−	0.0562249i
$833$		0			0
$834$	−5.66735	+	1.51856i	−0.196244	+	0.0525835i
$835$	−7.89182			−0.273108
$836$	−16.9685			−0.586867
$837$	−0.259075	+	0.0694190i	−0.00895495	+	0.00239947i
$838$	1.13343	+	4.23000i	0.0391535	+	0.146123i
$839$	5.65746	−	21.1139i	0.195317	−	0.728934i	−0.796867	−	0.604154i	$-0.793511\pi$
$839$	5.65746	−	21.1139i	0.195317	−	0.728934i	0.992185	−	0.124779i	$-0.0398223\pi$
$840$		0			0
$841$	−0.713208	−	1.23531i	−0.0245934	−	0.0425970i
$842$		−	12.5932i		−	0.433991i
$843$	4.92877	−	18.3944i	0.169756	−	0.633538i
$844$	−37.6444	−	21.7340i	−1.29578	−	0.748116i
$845$	−46.6824	+	2.93473i	−1.60592	+	0.100958i
$846$			9.87762i			0.339600i
$847$		0			0
$848$	4.55565	−	7.89062i	0.156442	−	0.270965i
$849$	15.4803	+	8.93755i	0.531282	+	0.306736i
$850$	1.15511	+	4.31093i	0.0396199	+	0.147864i
$851$	2.83508	+	2.83508i	0.0971853	+	0.0971853i
$852$	−28.0631	+	7.51948i	−0.961425	+	0.257613i
$853$	34.9450	+	34.9450i	1.19649	+	1.19649i	0.975209	+	0.221284i	$0.0710248\pi$
$853$	34.9450	+	34.9450i	1.19649	+	1.19649i	0.221284	+	0.975209i	$0.428975\pi$
$854$		0			0
$855$	42.3626	+	24.4580i	1.44877	+	0.836448i
$856$	10.6822	−	10.6822i	0.365111	−	0.365111i
$857$	12.4193	−	21.5108i	0.424235	−	0.734796i	−0.572114	−	0.820174i	$-0.693876\pi$
$857$	12.4193	−	21.5108i	0.424235	−	0.734796i	0.996349	+	0.0853781i	$0.0272098\pi$
$858$	3.23756	−	8.56732i	0.110528	−	0.292483i
$859$	17.8657	−	10.3147i	0.609569	−	0.351935i	−0.163228	−	0.986588i	$-0.552191\pi$
$859$	17.8657	−	10.3147i	0.609569	−	0.351935i	0.772797	+	0.634654i	$0.218857\pi$
$860$	8.61971	+	32.1692i	0.293930	+	1.09696i
$861$		0			0
$862$	5.00231	−	2.88809i	0.170379	−	0.0983686i
$863$	−5.83745	+	21.7857i	−0.198709	+	0.741593i	0.792566	+	0.609786i	$0.208745\pi$
$863$	−5.83745	+	21.7857i	−0.198709	+	0.741593i	−0.991275	+	0.131807i	$0.957922\pi$
$864$	−0.155553	+	0.155553i	−0.00529203	+	0.00529203i
$865$	−48.2060	+	48.2060i	−1.63905	+	1.63905i
$866$	−1.59165	+	5.94012i	−0.0540864	+	0.201853i
$867$	−33.2348	+	19.1881i	−1.12871	+	0.651663i
$868$		0			0
$869$	−6.47450	−	24.1632i	−0.219632	−	0.819679i
$870$	−20.6351	+	11.9137i	−0.699596	+	0.403912i
$871$	−27.6296	−	2.75848i	−0.936192	−	0.0934674i
$872$	2.74914	−	4.76165i	0.0930976	−	0.161250i
$873$	28.7412	−	28.7412i	0.972744	−	0.972744i
$874$	−2.87301	−	1.65873i	−0.0971809	−	0.0561074i
$875$		0			0
$876$	17.2262	+	17.2262i	0.582019	+	0.582019i
$877$	−12.4394	+	3.33311i	−0.420047	+	0.112551i	−0.462650	−	0.886541i	$-0.653101\pi$
$877$	−12.4394	+	3.33311i	−0.420047	+	0.112551i	0.0426034	+	0.999092i	$0.486435\pi$
$878$	6.16574	+	6.16574i	0.208084	+	0.208084i
$879$	−20.3198	−	75.8343i	−0.685368	−	2.55783i
$880$	17.2228	+	9.94358i	0.580580	+	0.335198i
$881$	3.52615	−	6.10747i	0.118799	−	0.205766i	−0.800493	−	0.599342i	$-0.795429\pi$
$881$	3.52615	−	6.10747i	0.118799	−	0.205766i	0.919292	+	0.393576i	$0.128762\pi$
$882$		0			0
$883$		−	55.6508i		−	1.87280i	−0.350938	−	0.936399i	$-0.614137\pi$
$883$		−	55.6508i		−	1.87280i	0.350938	−	0.936399i	$-0.385863\pi$
$884$	7.16181	−	1.17261i	0.240878	−	0.0394392i
$885$	87.1005	+	50.2875i	2.92785	+	1.69040i
$886$	0.851068	−	3.17623i	0.0285922	−	0.106708i
$887$			14.9081i			0.500565i	0.968173	+	0.250282i	$0.0805235\pi$
$887$			14.9081i			0.500565i	−0.968173	+	0.250282i	$0.919477\pi$
$888$	−6.10326	−	10.5712i	−0.204812	−	0.354745i
$889$		0			0
$890$	−4.55755	+	17.0090i	−0.152769	+	0.570143i
$891$	−4.95802	−	18.5036i	−0.166100	−	0.619893i
$892$	−1.26949	+	0.340158i	−0.0425055	+	0.0113893i
$893$	30.7669			1.02957
$894$	3.32658			0.111257
$895$	41.2312	−	11.0479i	1.37821	−	0.369289i
$896$		0			0
$897$	−10.1159	+	8.27932i	−0.337759	+	0.276439i
$898$	−5.81109	−	10.0651i	−0.193919	−	0.335877i
$899$	32.3035	+	8.65571i	1.07738	+	0.288684i
$900$	−20.8395	−	36.0951i	−0.694650	−	1.20317i
$901$	1.99543	−	3.45619i	0.0664775	−	0.115142i
$902$	−3.45791	+	3.45791i	−0.115136	+	0.115136i
$903$		0			0
$904$	29.2265	+	7.83121i	0.972058	+	0.260462i
$905$	−35.4717	−	9.50462i	−1.17912	−	0.315944i
$906$		−	7.58013i		−	0.251833i
$907$	−1.94216	+	1.12131i	−0.0644883	+	0.0372324i	−0.531897	−	0.846809i	$-0.678521\pi$
$907$	−1.94216	+	1.12131i	−0.0644883	+	0.0372324i	0.467409	+	0.884041i	$0.345187\pi$
$908$	−12.9008	−	12.9008i	−0.428130	−	0.428130i
$909$	−29.0529			−0.963625
$910$		0			0
$911$	−22.3252			−0.739667			−0.369834	−	0.929098i	$-0.620585\pi$
$911$	−22.3252			−0.739667			−0.369834	+	0.929098i	$0.620585\pi$
$912$	−20.5981	−	20.5981i	−0.682071	−	0.682071i
$913$	13.1325	−	7.58206i	0.434623	−	0.250930i
$914$			15.6769i			0.518545i
$915$	−80.4928	−	21.5680i	−2.66101	−	0.713015i
$916$	2.91852	+	0.782015i	0.0964305	+	0.0258385i
$917$		0			0
$918$	−0.0175699	+	0.0175699i	−0.000579892	+	0.000579892i
$919$	20.7445	−	35.9305i	0.684297	−	1.18524i	−0.289361	−	0.957220i	$-0.593443\pi$
$919$	20.7445	−	35.9305i	0.684297	−	1.18524i	0.973657	−	0.228017i	$-0.0732240\pi$
$920$	4.92074	+	8.52297i	0.162232	+	0.280994i
$921$	−32.2609	−	8.64429i	−1.06303	−	0.284839i
$922$	−9.33881	−	16.1753i	−0.307557	−	0.532705i
$923$	−24.2277	−	2.41884i	−0.797463	−	0.0796170i
$924$		0			0
$925$	−20.7595	+	5.56250i	−0.682569	+	0.182894i
$926$	6.32684			0.207913
$927$	36.8781			1.21123
$928$	26.4949	−	7.09929i	0.869738	−	0.233046i
$929$	12.8455	+	47.9399i	0.421446	+	1.57286i	0.771563	+	0.636152i	$0.219475\pi$
$929$	12.8455	+	47.9399i	0.421446	+	1.57286i	−0.350117	+	0.936706i	$0.613858\pi$
$930$	6.77842	−	25.2974i	0.222273	−	0.829534i
$931$		0			0
$932$	−7.30938	−	12.6602i	−0.239427	−	0.414699i
$933$		−	40.5693i		−	1.32818i
$934$	−2.26658	+	8.45898i	−0.0741647	+	0.276786i
$935$	7.54379	+	4.35541i	0.246708	+	0.142437i
$936$	18.0811	−	8.16339i	0.590999	−	0.266829i
$937$		−	47.8712i		−	1.56388i	−0.623352	−	0.781942i	$-0.714229\pi$
$937$		−	47.8712i		−	1.56388i	0.623352	−	0.781942i	$-0.285771\pi$
$938$		0			0
$939$	11.3850	−	19.7195i	0.371537	−	0.643521i
$940$	−36.9886	−	21.3554i	−1.20644	−	0.696536i
$941$	−1.97050	−	7.35402i	−0.0642366	−	0.239734i	0.926341	−	0.376686i	$-0.122936\pi$
$941$	−1.97050	−	7.35402i	−0.0642366	−	0.239734i	−0.990578	+	0.136951i	$0.956270\pi$
$942$	−1.62049	−	1.62049i	−0.0527984	−	0.0527984i
$943$	6.74192	−	1.80649i	0.219547	−	0.0588275i
$944$	−21.1115	−	21.1115i	−0.687122	−	0.687122i
$945$		0			0
$946$	−4.73284	−	2.73251i	−0.153878	−	0.0888414i
$947$	−5.00535	+	5.00535i	−0.162652	+	0.162652i	−0.783740	−	0.621088i	$-0.786691\pi$
$947$	−5.00535	+	5.00535i	−0.162652	+	0.162652i	0.621088	+	0.783740i	$0.286691\pi$
$948$	25.4333	−	44.0518i	0.826036	−	1.43074i
$949$	8.40117	+	18.6077i	0.272714	+	0.604033i
$950$	15.4003	−	8.89138i	0.499653	−	0.288475i
$951$	−20.9797	−	78.2974i	−0.680314	−	2.53897i
$952$		0			0
$953$	41.2624	−	23.8229i	1.33662	−	0.771698i	0.350316	−	0.936632i	$-0.386074\pi$
$953$	41.2624	−	23.8229i	1.33662	−	0.771698i	0.986305	+	0.164933i	$0.0527408\pi$
$954$	1.32131	−	4.93120i	0.0427790	−	0.159653i
$955$	15.1926	−	15.1926i	0.491622	−	0.491622i
$956$	9.04113	−	9.04113i	0.292411	−	0.292411i
$957$	−7.38782	+	27.5717i	−0.238814	+	0.891267i
$958$	3.90727	−	2.25586i	0.126238	−	0.0728836i
$959$		0			0
$960$	6.34036	+	23.6626i	0.204634	+	0.763706i
$961$	−4.98732	+	2.87943i	−0.160881	+	0.0928848i
$962$	−0.773487	−	4.72412i	−0.0249382	−	0.152312i
$963$	−12.2067	+	21.1427i	−0.393356	+	0.681313i
$964$	−9.64000	+	9.64000i	−0.310484	+	0.310484i
$965$	3.12726	+	1.80552i	0.100670	+	0.0581218i
$966$		0			0
$967$	31.2419	+	31.2419i	1.00467	+	1.00467i	0.999989	+	0.00468303i	$0.00149066\pi$
$967$	31.2419	+	31.2419i	1.00467	+	1.00467i	0.00468303	+	0.999989i	$0.498509\pi$
$968$	11.6268	−	3.11539i	0.373699	−	0.100132i
$969$	−9.02221	−	9.02221i	−0.289835	−	0.289835i
$970$	−6.23093	−	23.2542i	−0.200063	−	0.746646i
$971$	6.43644	+	3.71608i	0.206555	+	0.119255i	0.599709	−	0.800218i	$-0.295283\pi$
$971$	6.43644	+	3.71608i	0.206555	+	0.119255i	−0.393154	+	0.919473i	$0.628616\pi$
$972$	19.3595	−	33.5317i	0.620957	−	1.07553i
$973$		0			0
$974$		−	5.43090i		−	0.174017i
$975$	−11.3220	−	69.1499i	−0.362594	−	2.21457i
$976$	21.4234	+	12.3688i	0.685746	+	0.395916i
$977$	9.90514	−	36.9665i	0.316893	−	1.18266i	−0.605320	−	0.795982i	$-0.706955\pi$
$977$	9.90514	−	36.9665i	0.316893	−	1.18266i	0.922214	−	0.386680i	$-0.126378\pi$
$978$		−	7.41125i		−	0.236986i
$979$	10.5475	+	18.2688i	0.337099	+	0.583873i
$980$		0			0
$981$	−2.29972	+	8.58268i	−0.0734245	+	0.274024i
$982$	−0.360194	−	1.34426i	−0.0114943	−	0.0428972i
$983$	−24.8597	+	6.66114i	−0.792902	+	0.212458i	−0.632465	−	0.774589i	$-0.717957\pi$
$983$	−24.8597	+	6.66114i	−0.792902	+	0.212458i	−0.160437	+	0.987046i	$0.551290\pi$
$984$	−21.2496			−0.677414
$985$	−15.2210			−0.484982
$986$	2.99262	−	0.801870i	0.0953044	−	0.0255367i
$987$		0			0
$988$	−11.8988	−	26.3545i	−0.378550	−	0.838449i
$989$	3.90007	+	6.75513i	0.124015	+	0.214801i
$990$	10.7633	+	2.88401i	0.342079	+	0.0916599i
$991$	23.4047	+	40.5381i	0.743474	+	1.28774i	0.950904	+	0.309485i	$0.100157\pi$
$991$	23.4047	+	40.5381i	0.743474	+	1.28774i	−0.207430	+	0.978250i	$0.566510\pi$
$992$	−15.0745	+	26.1099i	−0.478617	+	0.828989i
$993$	40.7238	−	40.7238i	1.29233	−	1.29233i
$994$		0			0
$995$	52.3197	+	14.0190i	1.65865	+	0.444433i
$996$	29.7841	+	7.98062i	0.943745	+	0.252876i
$997$		−	28.2264i		−	0.893939i	−0.894549	−	0.446969i	$-0.852503\pi$
$997$		−	28.2264i		−	0.893939i	0.894549	−	0.446969i	$-0.147497\pi$
$998$	16.3055	−	9.41398i	0.516141	−	0.297994i
$999$	−0.0846088	−	0.0846088i	−0.00267690	−	0.00267690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.423.4		28
7.2	even	3		91.2.w.a.33.4	✓	28
7.3	odd	6		637.2.bd.b.293.4		28
7.4	even	3		637.2.bd.a.293.4		28
7.5	odd	6		637.2.x.a.215.4		28
7.6	odd	2		91.2.ba.a.59.4	yes	28
13.2	odd	12		637.2.x.a.80.4		28
21.2	odd	6		819.2.gh.b.397.4		28
21.20	even	2		819.2.et.b.514.4		28
91.2	odd	12		91.2.ba.a.54.4	yes	28
91.41	even	12		91.2.w.a.80.4	yes	28
91.54	even	12	inner	637.2.bb.a.509.4		28
91.67	odd	12		637.2.bd.b.587.4		28
91.80	even	12		637.2.bd.a.587.4		28
273.2	even	12		819.2.et.b.145.4		28
273.41	odd	12		819.2.gh.b.262.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.4	✓	28	7.2	even	3
91.2.w.a.80.4	yes	28	91.41	even	12
91.2.ba.a.54.4	yes	28	91.2	odd	12
91.2.ba.a.59.4	yes	28	7.6	odd	2
637.2.x.a.80.4		28	13.2	odd	12
637.2.x.a.215.4		28	7.5	odd	6
637.2.bb.a.423.4		28	1.1	even	1	trivial
637.2.bb.a.509.4		28	91.54	even	12	inner
637.2.bd.a.293.4		28	7.4	even	3
637.2.bd.a.587.4		28	91.80	even	12
637.2.bd.b.293.4		28	7.3	odd	6
637.2.bd.b.587.4		28	91.67	odd	12
819.2.et.b.145.4		28	273.2	even	12
819.2.et.b.514.4		28	21.20	even	2
819.2.gh.b.262.4		28	273.41	odd	12
819.2.gh.b.397.4		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)

\(f(q)\)	\(=\)	\(q+(-0.347096 - 0.347096i) q^{2} +(2.11812 - 1.22290i) q^{3} -1.75905i q^{4} +(3.47544 + 0.931242i) q^{5} +(-1.15965 - 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 - 2.58241i) q^{9} +O(q^{10})\)	\(q+(-0.347096 - 0.347096i) q^{2} +(2.11812 - 1.22290i) q^{3} -1.75905i q^{4} +(3.47544 + 0.931242i) q^{5} +(-1.15965 - 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 - 2.58241i) q^{9} +(-0.883082 - 1.52954i) q^{10} +(-2.04371 - 0.547609i) q^{11} +(-2.15114 - 3.72588i) q^{12} +(-0.582584 - 3.55817i) q^{13} +(8.50022 - 2.27763i) q^{15} -2.61235 q^{16} -1.14424 q^{17} +(-1.41385 + 0.378840i) q^{18} +(1.18001 + 4.40387i) q^{19} +(1.63810 - 6.11348i) q^{20} +(0.519289 + 0.899435i) q^{22} -1.48235i q^{23} +(-1.16804 + 4.35920i) q^{24} +(6.88137 + 3.97296i) q^{25} +(-1.03281 + 1.43724i) q^{26} +0.0442386i q^{27} +(2.75801 - 4.77701i) q^{29} +(-3.74095 - 2.15984i) q^{30} +(1.56920 + 5.85632i) q^{31} +(3.51624 + 3.51624i) q^{32} +(-4.99849 + 1.33934i) q^{33} +(0.397162 + 0.397162i) q^{34} +(-4.54259 - 2.62266i) q^{36} +(-1.91256 + 1.91256i) q^{37} +(1.11899 - 1.93814i) q^{38} +(-5.58526 - 6.82420i) q^{39} +(-5.74963 + 3.31955i) q^{40} +(1.21867 + 4.54813i) q^{41} +(-4.55704 + 2.63101i) q^{43} +(-0.963272 + 3.59498i) q^{44} +(7.58659 - 7.58659i) q^{45} +(-0.514518 + 0.514518i) q^{46} +(1.74658 - 6.51834i) q^{47} +(-5.53327 + 3.19464i) q^{48} +(-1.00950 - 3.76750i) q^{50} +(-2.42364 + 1.39929i) q^{51} +(-6.25900 + 1.02479i) q^{52} +(-1.74389 + 3.02051i) q^{53} +(0.0153550 - 0.0153550i) q^{54} +(-6.59283 - 3.80637i) q^{55} +(7.88489 + 7.88489i) q^{57} +(-2.61537 + 0.700787i) q^{58} +(8.08143 + 8.08143i) q^{59} +(-4.00646 - 14.9523i) q^{60} +(-8.20082 - 4.73474i) q^{61} +(1.48804 - 2.57737i) q^{62} +2.78376i q^{64} +(1.28878 - 12.9088i) q^{65} +(2.19983 + 1.27007i) q^{66} +(1.99321 - 7.43875i) q^{67} +2.01278i q^{68} +(-1.81276 - 3.13980i) q^{69} +(1.74779 - 6.52285i) q^{71} +(1.42408 + 5.31473i) q^{72} +(-5.46953 + 1.46556i) q^{73} +1.32768 q^{74} +19.4341 q^{75} +(7.74662 - 2.07570i) q^{76} +(-0.430029 + 4.30727i) q^{78} +(5.91160 + 10.2392i) q^{79} +(-9.07908 - 2.43273i) q^{80} +(4.52697 + 7.84094i) q^{81} +(1.15564 - 2.00163i) q^{82} +(-5.06789 + 5.06789i) q^{83} +(-3.97675 - 1.06557i) q^{85} +(2.49494 + 0.668517i) q^{86} -13.4910i q^{87} +(3.38102 - 1.95203i) q^{88} +(-7.05000 - 7.05000i) q^{89} -5.26655 q^{90} -2.60753 q^{92} +(10.4854 + 10.4854i) q^{93} +(-2.86872 + 1.65626i) q^{94} +16.4043i q^{95} +(11.7478 + 3.14782i) q^{96} +(13.1665 + 3.52795i) q^{97} +(-4.46123 + 4.46123i) 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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