LMFDB - Embedded newform 637.2.x.a.80.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (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			80.6
Character	$\chi$	$=$	637.80
Dual form			637.2.x.a.215.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.470172 + 1.75471i) q^{2} +3.06997i q^{3} +(-1.12588 + 0.650030i) q^{4} +(-0.288156 + 1.07541i) q^{5} +(-5.38690 + 1.44342i) q^{6} +(0.899098 + 0.899098i) q^{8} -6.42473 q^{9} +O(q^{10})$	\(q+(0.470172 + 1.75471i) q^{2} +3.06997i q^{3} +(-1.12588 + 0.650030i) q^{4} +(-0.288156 + 1.07541i) q^{5} +(-5.38690 + 1.44342i) q^{6} +(0.899098 + 0.899098i) q^{8} -6.42473 q^{9} -2.02252 q^{10} +(-0.0909069 - 0.0909069i) q^{11} +(-1.99557 - 3.45643i) q^{12} +(3.59376 + 0.291296i) q^{13} +(-3.30149 - 0.884632i) q^{15} +(-2.45498 + 4.25215i) q^{16} +(0.136785 + 0.236918i) q^{17} +(-3.02073 - 11.2735i) q^{18} +(-2.80666 - 2.80666i) q^{19} +(-0.374620 - 1.39810i) q^{20} +(0.116773 - 0.202257i) q^{22} +(-0.426046 - 0.245978i) q^{23} +(-2.76021 + 2.76021i) q^{24} +(3.25665 + 1.88023i) q^{25} +(1.17855 + 6.44296i) q^{26} -10.5138i q^{27} +(-4.62230 - 8.00606i) q^{29} -6.20908i q^{30} +(6.92046 - 1.85433i) q^{31} +(-6.15917 - 1.65034i) q^{32} +(0.279082 - 0.279082i) q^{33} +(-0.351410 + 0.351410i) q^{34} +(7.23351 - 4.17627i) q^{36} +(3.85295 - 1.03240i) q^{37} +(3.60526 - 6.24449i) q^{38} +(-0.894272 + 11.0328i) q^{39} +(-1.22598 + 0.707822i) q^{40} +(-2.31500 + 8.63969i) q^{41} +(8.44566 + 4.87610i) q^{43} +(0.161443 + 0.0432585i) q^{44} +(1.85133 - 6.90925i) q^{45} +(0.231304 - 0.863237i) q^{46} +(5.66021 + 1.51665i) q^{47} +(-13.0540 - 7.53673i) q^{48} +(-1.76806 + 6.59849i) q^{50} +(-0.727333 + 0.419926i) q^{51} +(-4.23552 + 2.00809i) q^{52} +(0.467445 - 0.809639i) q^{53} +(18.4487 - 4.94331i) q^{54} +(0.123958 - 0.0715671i) q^{55} +(8.61638 - 8.61638i) q^{57} +(11.8750 - 11.8750i) q^{58} +(-6.64843 - 1.78144i) q^{59} +(4.29214 - 1.15007i) q^{60} +7.78764i q^{61} +(6.50761 + 11.2715i) q^{62} -1.76356i q^{64} +(-1.34883 + 3.78085i) q^{65} +(0.620923 + 0.358490i) q^{66} +(-0.865162 + 0.865162i) q^{67} +(-0.308008 - 0.177829i) q^{68} +(0.755145 - 1.30795i) q^{69} +(-0.793943 - 2.96304i) q^{71} +(-5.77646 - 5.77646i) q^{72} +(-0.0318328 - 0.118802i) q^{73} +(3.62311 + 6.27540i) q^{74} +(-5.77224 + 9.99781i) q^{75} +(4.98439 + 1.33556i) q^{76} +(-19.7797 + 3.61811i) q^{78} +(-5.72736 - 9.92007i) q^{79} +(-3.86541 - 3.86541i) q^{80} +13.0030 q^{81} -16.2486 q^{82} +(-8.07011 - 8.07011i) q^{83} +(-0.294201 + 0.0788309i) q^{85} +(-4.58522 + 17.1123i) q^{86} +(24.5784 - 14.1903i) q^{87} -0.163468i q^{88} +(1.09599 + 4.09029i) q^{89} +12.9941 q^{90} +0.639571 q^{92} +(5.69274 + 21.2456i) q^{93} +10.6451i q^{94} +(3.82708 - 2.20957i) q^{95} +(5.06651 - 18.9085i) q^{96} +(2.39359 - 0.641359i) q^{97} +(0.584052 + 0.584052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.470172	+	1.75471i	0.332462	+	1.24077i	0.906594	+	0.422003i	$0.138673\pi$
$2$	0.470172	+	1.75471i	0.332462	+	1.24077i	−0.574132	+	0.818762i	$0.694661\pi$
$3$			3.06997i			1.77245i	0.463255	+	0.886225i	$0.346681\pi$
$3$			3.06997i			1.77245i	−0.463255	+	0.886225i	$0.653319\pi$
$4$	−1.12588	+	0.650030i	−0.562942	+	0.325015i
$5$	−0.288156	+	1.07541i	−0.128867	+	0.480940i	−0.999948	−	0.0102004i	$-0.996753\pi$
$5$	−0.288156	+	1.07541i	−0.128867	+	0.480940i	0.871081	+	0.491140i	$0.163420\pi$
$6$	−5.38690	+	1.44342i	−2.19919	+	0.589272i
$7$		0			0
$7$		0			0
$8$	0.899098	+	0.899098i	0.317879	+	0.317879i
$9$	−6.42473			−2.14158
$10$	−2.02252			−0.639577
$11$	−0.0909069	−	0.0909069i	−0.0274095	−	0.0274095i	0.693269	−	0.720679i	$-0.256170\pi$
$11$	−0.0909069	−	0.0909069i	−0.0274095	−	0.0274095i	−0.720679	+	0.693269i	$0.756170\pi$
$12$	−1.99557	−	3.45643i	−0.576072	−	0.997787i
$13$	3.59376	+	0.291296i	0.996731	+	0.0807911i
$13$	3.59376	+	0.291296i	0.996731	+	0.0807911i
$14$		0			0
$15$	−3.30149	−	0.884632i	−0.852441	−	0.228411i
$16$	−2.45498	+	4.25215i	−0.613746	+	1.06304i
$17$	0.136785	+	0.236918i	0.0331752	+	0.0574612i	0.882136	−	0.470994i	$-0.156105\pi$
$17$	0.136785	+	0.236918i	0.0331752	+	0.0574612i	−0.848961	+	0.528455i	$0.822771\pi$
$18$	−3.02073	−	11.2735i	−0.711993	−	2.65720i
$19$	−2.80666	−	2.80666i	−0.643893	−	0.643893i	0.307617	−	0.951510i	$-0.400468\pi$
$19$	−2.80666	−	2.80666i	−0.643893	−	0.643893i	−0.951510	+	0.307617i	$0.900468\pi$
$20$	−0.374620	−	1.39810i	−0.0837676	−	0.312625i
$21$		0			0
$22$	0.116773	−	0.202257i	0.0248961	−	0.0431213i
$23$	−0.426046	−	0.245978i	−0.0888367	−	0.0512899i	0.454924	−	0.890530i	$-0.349667\pi$
$23$	−0.426046	−	0.245978i	−0.0888367	−	0.0512899i	−0.543760	+	0.839241i	$0.683000\pi$
$24$	−2.76021	+	2.76021i	−0.563425	+	0.563425i
$25$	3.25665	+	1.88023i	0.651329	+	0.376045i
$26$	1.17855	+	6.44296i	0.231133	+	1.26357i
$27$		−	10.5138i		−	2.02339i
$28$		0			0
$29$	−4.62230	−	8.00606i	−0.858340	−	1.48669i	−0.873512	−	0.486803i	$-0.838163\pi$
$29$	−4.62230	−	8.00606i	−0.858340	−	1.48669i	0.0151718	−	0.999885i	$-0.495170\pi$
$30$		−	6.20908i		−	1.13362i
$31$	6.92046	−	1.85433i	1.24295	−	0.333048i	0.423341	−	0.905970i	$-0.360857\pi$
$31$	6.92046	−	1.85433i	1.24295	−	0.333048i	0.819609	+	0.572923i	$0.194190\pi$
$32$	−6.15917	−	1.65034i	−1.08880	−	0.291742i
$33$	0.279082	−	0.279082i	0.0485819	−	0.0485819i
$34$	−0.351410	+	0.351410i	−0.0602663	+	0.0602663i
$35$		0			0
$36$	7.23351	−	4.17627i	1.20558	−	0.696045i
$37$	3.85295	−	1.03240i	0.633422	−	0.169725i	0.0721998	−	0.997390i	$-0.476998\pi$
$37$	3.85295	−	1.03240i	0.633422	−	0.169725i	0.561222	+	0.827665i	$0.310331\pi$
$38$	3.60526	−	6.24449i	0.584850	−	1.01299i
$39$	−0.894272	+	11.0328i	−0.143198	+	1.76666i
$40$	−1.22598	+	0.707822i	−0.193845	+	0.111916i
$41$	−2.31500	+	8.63969i	−0.361542	+	1.34929i	0.510507	+	0.859874i	$0.329458\pi$
$41$	−2.31500	+	8.63969i	−0.361542	+	1.34929i	−0.872049	+	0.489419i	$0.837209\pi$
$42$		0			0
$43$	8.44566	+	4.87610i	1.28795	+	0.743599i	0.978288	−	0.207248i	$-0.0664506\pi$
$43$	8.44566	+	4.87610i	1.28795	+	0.743599i	0.309662	+	0.950847i	$0.399784\pi$
$44$	0.161443	+	0.0432585i	0.0243384	+	0.00652146i
$45$	1.85133	−	6.90925i	0.275980	−	1.02997i
$46$	0.231304	−	0.863237i	0.0341039	−	0.127277i
$47$	5.66021	+	1.51665i	0.825627	+	0.221226i	0.646805	−	0.762655i	$-0.276105\pi$
$47$	5.66021	+	1.51665i	0.825627	+	0.221226i	0.178822	+	0.983881i	$0.442771\pi$
$48$	−13.0540	−	7.53673i	−1.88418	−	1.08783i
$49$		0			0
$50$	−1.76806	+	6.59849i	−0.250041	+	0.933167i
$51$	−0.727333	+	0.419926i	−0.101847	+	0.0588014i
$52$	−4.23552	+	2.00809i	−0.587360	+	0.278472i
$53$	0.467445	−	0.809639i	0.0642086	−	0.111212i	−0.832134	−	0.554574i	$-0.812881\pi$
$53$	0.467445	−	0.809639i	0.0642086	−	0.111212i	0.896343	+	0.443362i	$0.146214\pi$
$54$	18.4487	−	4.94331i	2.51055	−	0.672700i
$55$	0.123958	−	0.0715671i	0.0167145	−	0.00965011i
$56$		0			0
$57$	8.61638	−	8.61638i	1.14127	−	1.14127i
$58$	11.8750	−	11.8750i	1.55927	−	1.55927i
$59$	−6.64843	−	1.78144i	−0.865552	−	0.231924i	−0.201389	−	0.979511i	$-0.564545\pi$
$59$	−6.64843	−	1.78144i	−0.865552	−	0.231924i	−0.664163	+	0.747587i	$0.731212\pi$
$60$	4.29214	−	1.15007i	0.554112	−	0.148474i
$61$			7.78764i			0.997105i	0.866860	+	0.498552i	$0.166135\pi$
$61$			7.78764i			0.997105i	−0.866860	+	0.498552i	$0.833865\pi$
$62$	6.50761	+	11.2715i	0.826468	+	1.43148i
$63$		0			0
$64$		−	1.76356i		−	0.220444i
$65$	−1.34883	+	3.78085i	−0.167302	+	0.468956i
$66$	0.620923	+	0.358490i	0.0764303	+	0.0441271i
$67$	−0.865162	+	0.865162i	−0.105696	+	0.105696i	−0.757977	−	0.652281i	$-0.773812\pi$
$67$	−0.865162	+	0.865162i	−0.105696	+	0.105696i	0.652281	+	0.757977i	$0.273812\pi$
$68$	−0.308008	−	0.177829i	−0.0373515	−	0.0215649i
$69$	0.755145	−	1.30795i	0.0909087	−	0.157459i
$70$		0			0
$71$	−0.793943	−	2.96304i	−0.0942237	−	0.351648i	0.902677	−	0.430319i	$-0.141599\pi$
$71$	−0.793943	−	2.96304i	−0.0942237	−	0.351648i	−0.996901	+	0.0786713i	$0.974932\pi$
$72$	−5.77646	−	5.77646i	−0.680763	−	0.680763i
$73$	−0.0318328	−	0.118802i	−0.00372575	−	0.0139047i	0.964038	−	0.265765i	$-0.0856244\pi$
$73$	−0.0318328	−	0.118802i	−0.00372575	−	0.0139047i	−0.967764	+	0.251860i	$0.918958\pi$
$74$	3.62311	+	6.27540i	0.421177	+	0.729501i
$75$	−5.77224	+	9.99781i	−0.666521	+	1.15445i
$76$	4.98439	+	1.33556i	0.571749	+	0.153200i
$77$		0			0
$78$	−19.7797	+	3.61811i	−2.23961	+	0.409671i
$79$	−5.72736	−	9.92007i	−0.644378	−	1.11610i	−0.984445	−	0.175694i	$-0.943783\pi$
$79$	−5.72736	−	9.92007i	−0.644378	−	1.11610i	0.340067	−	0.940401i	$-0.389550\pi$
$80$	−3.86541	−	3.86541i	−0.432166	−	0.432166i
$81$	13.0030			1.44478
$82$	−16.2486			−1.79436
$83$	−8.07011	−	8.07011i	−0.885810	−	0.885810i	0.108308	−	0.994117i	$-0.465457\pi$
$83$	−8.07011	−	8.07011i	−0.885810	−	0.885810i	−0.994117	+	0.108308i	$0.965457\pi$
$84$		0			0
$85$	−0.294201	+	0.0788309i	−0.0319106	+	0.00855041i
$86$	−4.58522	+	17.1123i	−0.494437	+	1.84526i
$87$	24.5784	−	14.1903i	2.63508	−	1.52136i
$88$		−	0.163468i		−	0.0174258i
$89$	1.09599	+	4.09029i	0.116175	+	0.433570i	0.999372	−	0.0354314i	$-0.0112805\pi$
$89$	1.09599	+	4.09029i	0.116175	+	0.433570i	−0.883197	+	0.469002i	$0.844614\pi$
$90$	12.9941			1.36970
$91$		0			0
$92$	0.639571			0.0666799
$93$	5.69274	+	21.2456i	0.590310	+	2.20307i
$94$			10.6451i			1.09796i
$95$	3.82708	−	2.20957i	0.392650	−	0.226697i
$96$	5.06651	−	18.9085i	0.517099	−	1.92984i
$97$	2.39359	−	0.641359i	0.243032	−	0.0651202i	−0.135247	−	0.990812i	$-0.543183\pi$
$97$	2.39359	−	0.641359i	0.243032	−	0.0651202i	0.378279	+	0.925692i	$0.376516\pi$
$98$		0			0
$99$	0.584052	+	0.584052i	0.0586995	+	0.0586995i
$100$	−4.88881			−0.488881
$101$	−1.68844			−0.168006			−0.0840029	−	0.996466i	$-0.526771\pi$
$101$	−1.68844			−0.168006			−0.0840029	+	0.996466i	$0.526771\pi$
$102$	−1.07882	−	1.07882i	−0.106819	−	0.106819i
$103$	−4.38460	−	7.59435i	−0.432027	−	0.748293i	0.565021	−	0.825077i	$-0.308868\pi$
$103$	−4.38460	−	7.59435i	−0.432027	−	0.748293i	−0.997048	+	0.0767837i	$0.975535\pi$
$104$	2.96924	+	3.49305i	0.291158	+	0.342522i
$105$		0			0
$106$	1.64046	+	0.439560i	0.159336	+	0.0426938i
$107$	1.34893	−	2.33642i	0.130406	−	0.225870i	−0.793427	−	0.608665i	$-0.791705\pi$
$107$	1.34893	−	2.33642i	0.130406	−	0.225870i	0.923833	+	0.382795i	$0.125039\pi$
$108$	6.83431	+	11.8374i	0.657631	+	1.13905i
$109$	2.40526	+	8.97655i	0.230382	+	0.859798i	0.980176	+	0.198127i	$0.0634857\pi$
$109$	2.40526	+	8.97655i	0.230382	+	0.859798i	−0.749794	+	0.661671i	$0.769848\pi$
$110$	0.183861	+	0.183861i	0.0175305	+	0.0175305i
$111$	3.16943	+	11.8285i	0.300829	+	1.12271i
$112$		0			0
$113$	−1.73470	+	3.00459i	−0.163187	+	0.282648i	−0.936010	−	0.351973i	$-0.885511\pi$
$113$	−1.73470	+	3.00459i	−0.163187	+	0.282648i	0.772823	+	0.634622i	$0.218844\pi$
$114$	19.1704	+	11.0680i	1.79547	+	1.03662i
$115$	0.387295	−	0.387295i	0.0361155	−	0.0361155i
$116$	10.4084	+	6.00927i	0.966392	+	0.557946i
$117$	−23.0890	−	1.87150i	−2.13458	−	0.173020i
$118$		−	12.5036i		−	1.15105i
$119$		0			0
$120$	−2.17299	−	3.76373i	−0.198366	−	0.343580i
$121$		−	10.9835i		−	0.998497i
$122$	−13.6650	+	3.66153i	−1.23717	+	0.331499i
$123$	−26.5236	−	7.10698i	−2.39155	−	0.640815i
$124$	−6.58626	+	6.58626i	−0.591464	+	0.591464i
$125$	−6.89673	+	6.89673i	−0.616862	+	0.616862i
$126$		0			0
$127$	−1.51307	+	0.873573i	−0.134264	+	0.0775171i	−0.565627	−	0.824661i	$-0.691366\pi$
$127$	−1.51307	+	0.873573i	−0.134264	+	0.0775171i	0.431364	+	0.902178i	$0.358033\pi$
$128$	−9.22381	+	2.47151i	−0.815278	+	0.218453i
$129$	−14.9695	+	25.9279i	−1.31799	+	2.28283i
$130$	−7.26846	−	0.589153i	−0.637486	−	0.0516721i
$131$	5.14945	−	2.97304i	0.449909	−	0.259755i	−0.257882	−	0.966176i	$-0.583025\pi$
$131$	5.14945	−	2.97304i	0.449909	−	0.259755i	0.707792	+	0.706421i	$0.249691\pi$
$132$	−0.132802	+	0.495625i	−0.0115590	+	0.0431386i
$133$		0			0
$134$	−1.92488	−	1.11133i	−0.166284	−	0.0960043i
$135$	11.3067	+	3.02963i	0.973128	+	0.260749i
$136$	−0.0900298	+	0.335996i	−0.00771999	+	0.0288114i
$137$	−5.08379	+	18.9730i	−0.434337	+	1.62097i	0.308309	+	0.951286i	$0.400237\pi$
$137$	−5.08379	+	18.9730i	−0.434337	+	1.62097i	−0.742647	+	0.669683i	$0.766430\pi$
$138$	2.65012	+	0.710096i	0.225593	+	0.0604474i
$139$	4.80542	+	2.77441i	0.407590	+	0.235322i	0.689754	−	0.724044i	$-0.257719\pi$
$139$	4.80542	+	2.77441i	0.407590	+	0.235322i	−0.282164	+	0.959366i	$0.591052\pi$
$140$		0			0
$141$	−4.65607	+	17.3767i	−0.392112	+	1.46338i
$142$	4.82597	−	2.78627i	0.404986	−	0.233819i
$143$	−0.300217	−	0.353179i	−0.0251054	−	0.0295343i
$144$	15.7726	−	27.3189i	1.31438	−	2.27658i
$145$	9.94177	−	2.66389i	0.825619	−	0.221224i
$146$	0.193495	−	0.111715i	0.0160138	−	0.00924556i
$147$		0			0
$148$	−3.66689	+	3.66689i	−0.301417	+	0.301417i
$149$	−0.304723	+	0.304723i	−0.0249638	+	0.0249638i	−0.719479	−	0.694515i	$-0.755619\pi$
$149$	−0.304723	+	0.304723i	−0.0249638	+	0.0249638i	0.694515	+	0.719479i	$0.255619\pi$
$150$	−20.2572	−	5.42790i	−1.65399	−	0.443186i
$151$	−3.42678	+	0.918204i	−0.278868	+	0.0747224i	−0.395542	−	0.918448i	$-0.629443\pi$
$151$	−3.42678	+	0.918204i	−0.278868	+	0.0747224i	0.116674	+	0.993170i	$0.462777\pi$
$152$		−	5.04693i		−	0.409360i
$153$	−0.878806	−	1.52214i	−0.0710473	−	0.123058i
$154$		0			0
$155$			7.97669i			0.640703i
$156$	−6.16478	−	13.0029i	−0.493577	−	1.04107i
$157$	−3.24916	−	1.87590i	−0.259311	−	0.149713i	0.364709	−	0.931122i	$-0.381168\pi$
$157$	−3.24916	−	1.87590i	−0.259311	−	0.149713i	−0.624020	+	0.781408i	$0.714502\pi$
$158$	14.7140	−	14.7140i	1.17058	−	1.17058i
$159$	2.48557	+	1.43504i	0.197119	+	0.113806i
$160$	3.54961	−	6.14810i	0.280621	−	0.486050i
$161$		0			0
$162$	6.11365	+	22.8164i	0.480333	+	1.79263i
$163$	4.76102	+	4.76102i	0.372912	+	0.372912i	0.868537	−	0.495625i	$-0.165061\pi$
$163$	4.76102	+	4.76102i	0.372912	+	0.372912i	−0.495625	+	0.868537i	$0.665061\pi$
$164$	−3.00964	−	11.2321i	−0.235013	−	0.877081i
$165$	0.219709	+	0.380547i	0.0171043	+	0.0296256i
$166$	10.3663	−	17.9550i	0.804584	−	1.39358i
$167$	−11.3562	−	3.04289i	−0.878770	−	0.235466i	−0.208894	−	0.977938i	$-0.566986\pi$
$167$	−11.3562	−	3.04289i	−0.878770	−	0.235466i	−0.669876	+	0.742473i	$0.733653\pi$
$168$		0			0
$169$	12.8303	+	2.09370i	0.986946	+	0.161054i
$170$	−0.276650	−	0.479172i	−0.0212181	−	0.0367508i
$171$	18.0321	+	18.0321i	1.37895	+	1.37895i
$172$	−12.6784			−0.966723
$173$	16.1407			1.22715			0.613576	−	0.789636i	$-0.289730\pi$
$173$	16.1407			1.22715			0.613576	+	0.789636i	$0.289730\pi$
$174$	36.4560	+	36.4560i	2.76372	+	2.76372i
$175$		0			0
$176$	0.609725	−	0.163375i	0.0459597	−	0.0123149i
$177$	5.46898	−	20.4105i	0.411074	−	1.53415i
$178$	−6.66196	+	3.84629i	−0.499335	+	0.288291i
$179$		−	9.19578i		−	0.687325i	−0.939093	−	0.343663i	$-0.888332\pi$
$179$		−	9.19578i		−	0.687325i	0.939093	−	0.343663i	$-0.111668\pi$
$180$	2.40684	+	8.98243i	0.179395	+	0.669511i
$181$	14.6492			1.08887			0.544433	−	0.838804i	$-0.316745\pi$
$181$	14.6492			1.08887			0.544433	+	0.838804i	$0.316745\pi$
$182$		0			0
$183$	−23.9078			−1.76732
$184$	−0.161899	−	0.604215i	−0.0119353	−	0.0445433i
$185$			4.44101i			0.326510i
$186$	−34.6033	+	19.9782i	−2.53723	+	1.46487i
$187$	0.00910282	−	0.0339722i	0.000665664	−	0.00248429i
$188$	−7.35861	+	1.97173i	−0.536682	+	0.143804i
$189$		0			0
$190$	5.67653	+	5.67653i	0.411819	+	0.411819i
$191$	6.03264			0.436507			0.218253	−	0.975892i	$-0.429964\pi$
$191$	6.03264			0.436507			0.218253	+	0.975892i	$0.429964\pi$
$192$	5.41407			0.390727
$193$	0.290670	+	0.290670i	0.0209229	+	0.0209229i	0.717491	−	0.696568i	$-0.245291\pi$
$193$	0.290670	+	0.290670i	0.0209229	+	0.0209229i	−0.696568	+	0.717491i	$0.745291\pi$
$194$	2.25080	+	3.89849i	0.161598	+	0.279895i
$195$	−11.6071	−	4.14087i	−0.831201	−	0.296534i
$196$		0			0
$197$	18.9784	+	5.08526i	1.35216	+	0.362309i	0.860931	−	0.508722i	$-0.169882\pi$
$197$	18.9784	+	5.08526i	1.35216	+	0.362309i	0.491227	+	0.871032i	$0.336549\pi$
$198$	−0.750235	+	1.29945i	−0.0533169	+	0.0923476i
$199$	−8.71102	−	15.0879i	−0.617508	−	1.06956i	−0.989939	−	0.141495i	$-0.954809\pi$
$199$	−8.71102	−	15.0879i	−0.617508	−	1.06956i	0.372431	−	0.928060i	$-0.378524\pi$
$200$	1.23754	+	4.61855i	0.0875071	+	0.326581i
$201$	−2.65602	−	2.65602i	−0.187341	−	0.187341i
$202$	−0.793857	−	2.96271i	−0.0558556	−	0.208456i
$203$		0			0
$204$	0.545929	−	0.945576i	0.0382227	−	0.0662036i
$205$	−8.62416	−	4.97916i	−0.602338	−	0.347760i
$206$	11.2643	−	11.2643i	0.784824	−	0.784824i
$207$	2.73723	+	1.58034i	0.190251	+	0.109841i
$208$	−10.0613	+	14.5661i	−0.697623	+	1.00998i
$209$			0.510290i			0.0352975i
$210$		0			0
$211$	7.69760	+	13.3326i	0.529925	+	0.917856i	0.999391	+	0.0349058i	$0.0111131\pi$
$211$	7.69760	+	13.3326i	0.529925	+	0.917856i	−0.469466	+	0.882951i	$0.655554\pi$
$212$			1.21541i			0.0834749i
$213$	9.09644	−	2.43738i	0.623278	−	0.167007i
$214$	4.73396	+	1.26846i	0.323607	+	0.0867102i
$215$	−7.67750	+	7.67750i	−0.523601	+	0.523601i
$216$	9.45297	−	9.45297i	0.643193	−	0.643193i
$217$		0			0
$218$	−14.6203	+	8.44105i	−0.990214	+	0.571700i
$219$	0.364718	−	0.0977259i	0.0246454	−	0.00660370i
$220$	−0.0930415	+	0.161153i	−0.00627286	+	0.0108649i
$221$	0.422559	+	0.891274i	0.0284244	+	0.0599536i
$222$	−19.2653	+	11.1228i	−1.29300	+	0.746516i
$223$	3.59157	−	13.4039i	0.240509	−	0.897592i	−0.735079	−	0.677982i	$-0.762855\pi$
$223$	3.59157	−	13.4039i	0.240509	−	0.897592i	0.975588	−	0.219610i	$-0.0704786\pi$
$224$		0			0
$225$	−20.9231	−	12.0799i	−1.39487	−	0.805330i
$226$	−6.08779	−	1.63122i	−0.404954	−	0.108507i
$227$	−3.09161	+	11.5380i	−0.205197	+	0.765807i	0.784192	+	0.620518i	$0.213078\pi$
$227$	−3.09161	+	11.5380i	−0.205197	+	0.765807i	−0.989389	+	0.145289i	$0.953589\pi$
$228$	−4.10015	+	15.3020i	−0.271539	+	1.01340i
$229$	23.7322	+	6.35901i	1.56826	+	0.420215i	0.935268	−	0.353939i	$-0.115158\pi$
$229$	23.7322	+	6.35901i	1.56826	+	0.420215i	0.632997	+	0.774155i	$0.281825\pi$
$230$	0.861686	+	0.497495i	0.0568179	+	0.0328038i
$231$		0			0
$232$	3.04233	−	11.3541i	0.199739	−	0.745435i
$233$	−15.3919	+	8.88654i	−1.00836	+	0.582177i	−0.910711	−	0.413044i	$-0.864465\pi$
$233$	−15.3919	+	8.88654i	−1.00836	+	0.582177i	−0.0976486	+	0.995221i	$0.531132\pi$
$234$	−7.57186	−	41.3943i	−0.494988	−	2.70603i
$235$	−3.26205	+	5.65004i	−0.212793	+	0.368568i
$236$	8.64336	−	2.31598i	0.562635	−	0.150757i
$237$	30.4544	−	17.5828i	1.97822	−	1.14213i
$238$		0			0
$239$	17.0580	−	17.0580i	1.10339	−	1.10339i	0.109392	−	0.993999i	$-0.465110\pi$
$239$	17.0580	−	17.0580i	1.10339	−	1.10339i	0.993999	−	0.109392i	$-0.0348902\pi$
$240$	11.8667	−	11.8667i	0.765992	−	0.765992i
$241$	−10.0223	−	2.68547i	−0.645594	−	0.172986i	−0.0788579	−	0.996886i	$-0.525127\pi$
$241$	−10.0223	−	2.68547i	−0.645594	−	0.172986i	−0.566736	+	0.823900i	$0.691794\pi$
$242$	19.2728	−	5.16413i	1.23890	−	0.331963i
$243$			8.37731i			0.537405i
$244$	−5.06220	−	8.76798i	−0.324074	−	0.561312i
$245$		0			0
$246$		−	49.8827i		−	3.18040i
$247$	−9.26892	−	10.9041i	−0.589767	−	0.693809i
$248$	7.88939	+	4.55494i	0.500977	+	0.289239i
$249$	24.7750	−	24.7750i	1.57005	−	1.57005i
$250$	−15.3444	−	8.85909i	−0.970465	−	0.560298i
$251$	−4.56198	+	7.90158i	−0.287950	+	0.498743i	−0.973320	−	0.229451i	$-0.926307\pi$
$251$	−4.56198	+	7.90158i	−0.287950	+	0.498743i	0.685371	+	0.728194i	$0.259640\pi$
$252$		0			0
$253$	0.0163694	+	0.0610915i	0.00102914	+	0.00384079i
$254$	−2.24427	−	2.24427i	−0.140818	−	0.140818i
$255$	−0.242009	−	0.903188i	−0.0151552	−	0.0565599i
$256$	−10.4371	−	18.0776i	−0.652320	−	1.12985i
$257$	15.3580	−	26.6008i	0.958003	−	1.65931i	0.230661	−	0.973034i	$-0.425911\pi$
$257$	15.3580	−	26.6008i	0.958003	−	1.65931i	0.727342	−	0.686276i	$-0.240756\pi$
$258$	−52.5342	−	14.0765i	−3.27064	−	0.876364i
$259$		0			0
$260$	−0.939035	−	5.13358i	−0.0582365	−	0.318371i
$261$	29.6970	+	51.4368i	1.83820	+	3.18386i
$262$	7.63794	+	7.63794i	0.471873	+	0.471873i
$263$	5.54678			0.342029			0.171015	−	0.985268i	$-0.445295\pi$
$263$	5.54678			0.342029			0.171015	+	0.985268i	$0.445295\pi$
$264$	0.501843			0.0308863
$265$	0.736000	+	0.736000i	0.0452121	+	0.0452121i
$266$		0			0
$267$	−12.5571	+	3.36466i	−0.768481	+	0.205914i
$268$	0.411691	−	1.53645i	0.0251481	−	0.0938538i
$269$	−4.72057	+	2.72542i	−0.287818	+	0.166172i	−0.636958	−	0.770899i	$-0.719807\pi$
$269$	−4.72057	+	2.72542i	−0.287818	+	0.166172i	0.349139	+	0.937071i	$0.386474\pi$
$270$			21.2644i			1.29411i
$271$	−2.76799	−	10.3303i	−0.168144	−	0.627521i	−0.997618	−	0.0689762i	$-0.978027\pi$
$271$	−2.76799	−	10.3303i	−0.168144	−	0.627521i	0.829475	−	0.558544i	$-0.188640\pi$
$272$	−1.34322			−0.0814446
$273$		0			0
$274$	−35.6823			−2.15564
$275$	−0.125126	−	0.466977i	−0.00754539	−	0.0281598i
$276$			1.96347i			0.118187i
$277$	21.2619	−	12.2755i	1.27750	−	0.737566i	0.301113	−	0.953588i	$-0.402642\pi$
$277$	21.2619	−	12.2755i	1.27750	−	0.737566i	0.976388	+	0.216023i	$0.0693086\pi$
$278$	−2.60890	+	9.73655i	−0.156472	+	0.583960i
$279$	−44.4621	+	11.9136i	−2.66187	+	0.713247i
$280$		0			0
$281$	8.66937	+	8.66937i	0.517172	+	0.517172i	0.916714	−	0.399543i	$-0.130831\pi$
$281$	8.66937	+	8.66937i	0.517172	+	0.517172i	−0.399543	+	0.916714i	$0.630831\pi$
$282$	−32.6802			−1.94608
$283$	−2.83541			−0.168548			−0.0842738	−	0.996443i	$-0.526857\pi$
$283$	−2.83541			−0.168548			−0.0842738	+	0.996443i	$0.526857\pi$
$284$	2.81995	+	2.81995i	0.167333	+	0.167333i
$285$	6.78331	+	11.7490i	0.401809	+	0.695953i
$286$	0.478571	−	0.692848i	0.0282985	−	0.0409690i
$287$		0			0
$288$	39.5710	+	10.6030i	2.33174	+	0.624789i
$289$	8.46258	−	14.6576i	0.497799	−	0.862213i
$290$	9.34870	+	16.1924i	0.548974	+	0.950851i
$291$	1.96896	+	7.34824i	0.115422	+	0.430762i
$292$	0.113065	+	0.113065i	0.00661661	+	0.00661661i
$293$	5.11331	+	19.0831i	0.298723	+	1.11485i	0.938215	+	0.346052i	$0.112478\pi$
$293$	5.11331	+	19.0831i	0.298723	+	1.11485i	−0.639493	+	0.768797i	$0.720856\pi$
$294$		0			0
$295$	3.83157	−	6.63648i	0.223083	−	0.386391i
$296$	4.39241	+	2.53596i	0.255304	+	0.147400i
$297$	−0.955780	+	0.955780i	−0.0554600	+	0.0554600i
$298$	−0.677971	−	0.391427i	−0.0392738	−	0.0226747i
$299$	−1.45946	−	1.00809i	−0.0844025	−	0.0582994i
$300$		−	15.0085i		−	0.866517i
$301$		0			0
$302$	−3.22236	−	5.58129i	−0.185426	−	0.321167i
$303$		−	5.18346i		−	0.297782i
$304$	18.8247	−	5.04406i	1.07967	−	0.289296i
$305$	−8.37493	−	2.24406i	−0.479547	−	0.128494i
$306$	2.25772	−	2.25772i	0.129065	−	0.129065i
$307$	−6.98294	+	6.98294i	−0.398537	+	0.398537i	−0.877717	−	0.479180i	$-0.840934\pi$
$307$	−6.98294	+	6.98294i	−0.398537	+	0.398537i	0.479180	+	0.877717i	$0.340934\pi$
$308$		0			0
$309$	23.3144	−	13.4606i	1.32631	−	0.765746i
$310$	−13.9968	+	3.75042i	−0.794962	+	0.213010i
$311$	13.2286	−	22.9126i	0.750126	−	1.29926i	−0.197636	−	0.980276i	$-0.563326\pi$
$311$	13.2286	−	22.9126i	0.750126	−	1.29926i	0.947761	−	0.318980i	$-0.103340\pi$
$312$	−10.7236	+	9.11549i	−0.607103	+	0.516063i
$313$	−10.2371	+	5.91040i	−0.578636	+	0.334076i	−0.760591	−	0.649231i	$-0.775091\pi$
$313$	−10.2371	+	5.91040i	−0.578636	+	0.334076i	0.181955	+	0.983307i	$0.441757\pi$
$314$	1.76400	−	6.58332i	0.0995480	−	0.371518i
$315$		0			0
$316$	12.8967	+	7.44590i	0.725495	+	0.418865i
$317$	−3.52831	−	0.945407i	−0.198170	−	0.0530994i	0.158369	−	0.987380i	$-0.449376\pi$
$317$	−3.52831	−	0.945407i	−0.198170	−	0.0530994i	−0.356538	+	0.934281i	$0.616043\pi$
$318$	−1.34944	+	5.03617i	−0.0756726	+	0.282414i
$319$	−0.307607	+	1.14800i	−0.0172227	+	0.0642759i
$320$	1.89655	+	0.508180i	0.106020	+	0.0284081i
$321$	7.17274	+	4.14118i	0.400343	+	0.231138i
$322$		0			0
$323$	0.281041	−	1.04886i	0.0156375	−	0.0583601i
$324$	−14.6399	+	8.45233i	−0.813326	+	0.469574i
$325$	11.1559	+	7.70574i	0.618819	+	0.427437i
$326$	−6.11569	+	10.5927i	−0.338717	+	0.586675i
$327$	−27.5578	+	7.38408i	−1.52395	+	0.408341i
$328$	−9.84934	+	5.68652i	−0.543839	+	0.313985i
$329$		0			0
$330$	−0.564448	+	0.564448i	−0.0310718	+	0.0310718i
$331$	6.09024	−	6.09024i	0.334750	−	0.334750i	−0.519637	−	0.854387i	$-0.673933\pi$
$331$	6.09024	−	6.09024i	0.334750	−	0.334750i	0.854387	+	0.519637i	$0.173933\pi$
$332$	14.3318	+	3.84020i	0.786561	+	0.210758i
$333$	−24.7542	+	6.63287i	−1.35652	+	0.363479i
$334$		−	21.3575i		−	1.16863i
$335$	−0.681105	−	1.17971i	−0.0372128	−	0.0644544i
$336$		0			0
$337$		−	26.3426i		−	1.43497i	−0.696572	−	0.717487i	$-0.745292\pi$
$337$		−	26.3426i		−	1.43497i	0.696572	−	0.717487i	$-0.254708\pi$
$338$	2.35862	+	23.4978i	0.128292	+	1.27811i
$339$	−9.22402	−	5.32549i	−0.500980	−	0.289241i
$340$	0.279994	−	0.279994i	0.0151848	−	0.0151848i
$341$	−0.797688	−	0.460546i	−0.0431972	−	0.0249399i
$342$	−23.1628	+	40.1192i	−1.25250	+	2.16940i
$343$		0			0
$344$	3.20938	+	11.9776i	0.173038	+	0.645787i
$345$	1.18899	+	1.18899i	0.0640129	+	0.0640129i
$346$	7.58889	+	28.3221i	0.407981	+	1.52261i
$347$	−2.61338	−	4.52651i	−0.140294	−	0.242996i	0.787314	−	0.616553i	$-0.211471\pi$
$347$	−2.61338	−	4.52651i	−0.140294	−	0.242996i	−0.927607	+	0.373557i	$0.878138\pi$
$348$	−18.4483	+	31.9534i	−0.988932	+	1.71288i
$349$	−11.2071	−	3.00292i	−0.599900	−	0.160743i	−0.0539262	−	0.998545i	$-0.517174\pi$
$349$	−11.2071	−	3.00292i	−0.599900	−	0.160743i	−0.545974	+	0.837802i	$0.683840\pi$
$350$		0			0
$351$	3.06264	−	37.7842i	0.163472	−	2.01677i
$352$	0.409883	+	0.709938i	0.0218468	+	0.0378398i
$353$	−6.10423	−	6.10423i	−0.324895	−	0.324895i	0.525746	−	0.850641i	$-0.323786\pi$
$353$	−6.10423	−	6.10423i	−0.324895	−	0.324895i	−0.850641	+	0.525746i	$0.823786\pi$
$354$	38.3858			2.04018
$355$	3.41527			0.181264
$356$	−3.89277	−	3.89277i	−0.206316	−	0.206316i
$357$		0			0
$358$	16.1359	−	4.32360i	0.852809	−	0.228510i
$359$	−8.03606	+	29.9910i	−0.424127	+	1.58286i	0.341695	+	0.939811i	$0.388999\pi$
$359$	−8.03606	+	29.9910i	−0.424127	+	1.58286i	−0.765822	+	0.643053i	$0.777668\pi$
$360$	7.87661	−	4.54756i	0.415134	−	0.239678i
$361$		−	3.24528i		−	0.170804i
$362$	6.88765	+	25.7051i	0.362007	+	1.35103i
$363$	33.7190			1.76979
$364$		0			0
$365$	0.136934			0.00716744
$366$	−11.2408	−	41.9512i	−0.587566	−	2.19283i
$367$			2.61926i			0.136724i	0.997661	+	0.0683622i	$0.0217773\pi$
$367$			2.61926i			0.136724i	−0.997661	+	0.0683622i	$0.978223\pi$
$368$	2.09187	−	1.20774i	0.109046	−	0.0629579i
$369$	14.8732	−	55.5077i	0.774270	−	2.88962i
$370$	−7.79268	+	2.08804i	−0.405122	+	0.108552i
$371$		0			0
$372$	−20.2197	−	20.2197i	−1.04834	−	1.04834i
$373$	35.8363			1.85553			0.927767	−	0.373161i	$-0.121726\pi$
$373$	35.8363			1.85553			0.927767	+	0.373161i	$0.121726\pi$
$374$	0.0638912			0.00330373
$375$	−21.1728	−	21.1728i	−1.09336	−	1.09336i
$376$	3.72547	+	6.45270i	0.192126	+	0.332773i
$377$	−14.2793	−	30.1184i	−0.735423	−	1.55117i
$378$		0			0
$379$	−22.2660	−	5.96617i	−1.14373	−	0.306461i	−0.363280	−	0.931680i	$-0.618343\pi$
$379$	−22.2660	−	5.96617i	−1.14373	−	0.306461i	−0.780450	+	0.625219i	$0.785010\pi$
$380$	−2.87257	+	4.97544i	−0.147360	+	0.255234i
$381$	−2.68185	−	4.64509i	−0.137395	−	0.237975i
$382$	2.83638	+	10.5855i	0.145122	+	0.541602i
$383$	9.22669	+	9.22669i	0.471462	+	0.471462i	0.902387	−	0.430926i	$-0.141813\pi$
$383$	9.22669	+	9.22669i	0.471462	+	0.471462i	−0.430926	+	0.902387i	$0.641813\pi$
$384$	−7.58748	−	28.3169i	−0.387197	−	1.44504i
$385$		0			0
$386$	−0.373376	+	0.646707i	−0.0190044	+	0.0329165i
$387$	−54.2611	−	31.3277i	−2.75825	−	1.59247i
$388$	−2.27800	+	2.27800i	−0.115648	+	0.115648i
$389$	−21.4938	−	12.4094i	−1.08978	−	0.629183i	−0.156260	−	0.987716i	$-0.549944\pi$
$389$	−21.4938	−	12.4094i	−1.08978	−	0.629183i	−0.933517	+	0.358533i	$0.883277\pi$
$390$	1.80868	−	22.3140i	0.0915862	−	1.12991i
$391$		−	0.134584i		−	0.00680621i
$392$		0			0
$393$	9.12714	+	15.8087i	0.460403	+	0.797442i
$394$			35.6925i			1.79816i
$395$	12.3186	−	3.30075i	0.619814	−	0.166079i
$396$	−1.03723	−	0.277924i	−0.0521226	−	0.0139662i
$397$	−6.84066	+	6.84066i	−0.343323	+	0.343323i	−0.857615	−	0.514292i	$-0.828055\pi$
$397$	−6.84066	+	6.84066i	−0.343323	+	0.343323i	0.514292	+	0.857615i	$0.328055\pi$
$398$	22.3792	−	22.3792i	1.12177	−	1.12177i
$399$		0			0
$400$	−15.9900	+	9.23184i	−0.799501	+	0.461592i
$401$	6.76490	−	1.81265i	0.337823	−	0.0905194i	−0.0859195	−	0.996302i	$-0.527383\pi$
$401$	6.76490	−	1.81265i	0.337823	−	0.0905194i	0.423743	+	0.905783i	$0.360716\pi$
$402$	3.41175	−	5.90933i	0.170163	−	0.294731i
$403$	25.4107	−	4.64813i	1.26579	−	0.231540i
$404$	1.90099	−	1.09754i	0.0945776	−	0.0546044i
$405$	−3.74689	+	13.9836i	−0.186185	+	0.694850i
$406$		0			0
$407$	−0.444112	−	0.256408i	−0.0220138	−	0.0127097i
$408$	−1.03150	−	0.276389i	−0.0510668	−	0.0136833i
$409$	3.93505	−	14.6858i	0.194576	−	0.726166i	−0.797801	−	0.602921i	$-0.794003\pi$
$409$	3.93505	−	14.6858i	0.194576	−	0.726166i	0.992376	−	0.123245i	$-0.0393300\pi$
$410$	4.68213	−	17.4739i	0.231234	−	0.862977i
$411$	−58.2465	−	15.6071i	−2.87309	−	0.769841i
$412$	9.87310	+	5.70024i	0.486413	+	0.280831i
$413$		0			0
$414$	−1.48606	+	5.54607i	−0.0730361	+	0.272574i
$415$	11.0042	−	6.35326i	0.540173	−	0.311869i
$416$	−21.6539	−	7.72509i	−1.06167	−	0.378754i
$417$	−8.51736	+	14.7525i	−0.417097	+	0.722433i
$418$	−0.895410	+	0.239924i	−0.0437959	+	0.0117351i
$419$	21.4435	−	12.3804i	1.04758	−	0.604823i	0.125612	−	0.992079i	$-0.459911\pi$
$419$	21.4435	−	12.3804i	1.04758	−	0.604823i	0.921972	+	0.387257i	$0.126577\pi$
$420$		0			0
$421$	−4.11077	+	4.11077i	−0.200347	+	0.200347i	−0.800149	−	0.599802i	$-0.795246\pi$
$421$	−4.11077	+	4.11077i	−0.200347	+	0.200347i	0.599802	+	0.800149i	$0.295246\pi$
$422$	−19.7757	+	19.7757i	−0.962665	+	0.962665i
$423$	−36.3653	−	9.74407i	−1.76814	−	0.473773i
$424$	1.14822	−	0.307666i	0.0557627	−	0.0149416i
$425$			1.02875i			0.0499015i
$426$	8.55379	+	14.8156i	0.414432	+	0.717818i
$427$		0			0
$428$			3.50738i			0.169536i
$429$	1.08425	−	0.921658i	0.0523480	−	0.0444981i
$430$	−17.0815	−	9.86201i	−0.823744	−	0.475589i
$431$	−13.6699	+	13.6699i	−0.658458	+	0.658458i	−0.955015	−	0.296557i	$-0.904161\pi$
$431$	−13.6699	+	13.6699i	−0.658458	+	0.658458i	0.296557	+	0.955015i	$0.404161\pi$
$432$	44.7064	+	25.8113i	2.15094	+	1.24185i
$433$	1.10640	−	1.91634i	0.0531702	−	0.0920934i	−0.838215	−	0.545339i	$-0.816401\pi$
$433$	1.10640	−	1.91634i	0.0531702	−	0.0920934i	0.891385	+	0.453246i	$0.149734\pi$
$434$		0			0
$435$	8.17807	+	30.5210i	0.392108	+	1.46337i
$436$	−8.54307	−	8.54307i	−0.409139	−	0.409139i
$437$	0.505391	+	1.88614i	0.0241761	+	0.0902265i
$438$	0.342961	+	0.594025i	0.0163873	+	0.0283836i
$439$	−3.67134	+	6.35896i	−0.175224	+	0.303496i	−0.940239	−	0.340516i	$-0.889398\pi$
$439$	−3.67134	+	6.35896i	−0.175224	+	0.303496i	0.765015	+	0.644013i	$0.222732\pi$
$440$	0.175796	+	0.0471044i	0.00838075	+	0.00224562i
$441$		0			0
$442$	−1.36525	+	1.16052i	−0.0649383	+	0.0552003i
$443$	−13.2926	−	23.0235i	−0.631552	−	1.09388i	−0.987235	−	0.159273i	$-0.949085\pi$
$443$	−13.2926	−	23.0235i	−0.631552	−	1.09388i	0.355683	−	0.934607i	$-0.384248\pi$
$444$	−11.2573	−	11.2573i	−0.534246	−	0.534246i
$445$	−4.71457			−0.223492
$446$	25.2086			1.19366
$447$	−0.935490	−	0.935490i	−0.0442472	−	0.0442472i
$448$		0			0
$449$	−21.6019	+	5.78821i	−1.01946	+	0.273163i	−0.729576	−	0.683900i	$-0.760282\pi$
$449$	−21.6019	+	5.78821i	−1.01946	+	0.273163i	−0.289881	+	0.957063i	$0.593616\pi$
$450$	11.3593	−	42.3935i	0.535483	−	1.99845i
$451$	0.995856	−	0.574958i	0.0468930	−	0.0270737i
$452$		−	4.51043i		−	0.212153i
$453$	−2.81886	−	10.5201i	−0.132442	−	0.494279i
$454$	−21.6995			−1.01841
$455$		0			0
$456$	15.4939			0.725570
$457$	0.585332	+	2.18449i	0.0273807	+	0.102186i	0.978264	−	0.207364i	$-0.0664883\pi$
$457$	0.585332	+	2.18449i	0.0273807	+	0.102186i	−0.950883	+	0.309550i	$0.899822\pi$
$458$			44.6328i			2.08555i
$459$	2.49092	−	1.43813i	0.116266	−	0.0671263i
$460$	−0.184296	+	0.687804i	−0.00859287	+	0.0320690i
$461$	−3.60574	+	0.966154i	−0.167936	+	0.0449983i	−0.341807	−	0.939770i	$-0.611039\pi$
$461$	−3.60574	+	0.966154i	−0.167936	+	0.0449983i	0.173871	+	0.984768i	$0.444372\pi$
$462$		0			0
$463$	−15.5412	−	15.5412i	−0.722262	−	0.722262i	0.246804	−	0.969066i	$-0.420620\pi$
$463$	−15.5412	−	15.5412i	−0.722262	−	0.722262i	−0.969066	+	0.246804i	$0.920620\pi$
$464$	45.3907			2.10721
$465$	−24.4882			−1.13561
$466$	−22.8301	−	22.8301i	−1.05759	−	1.05759i
$467$	−2.73553	−	4.73808i	−0.126585	−	0.219252i	0.795766	−	0.605604i	$-0.207068\pi$
$467$	−2.73553	−	4.73808i	−0.126585	−	0.219252i	−0.922351	+	0.386352i	$0.873735\pi$
$468$	27.2121	−	12.9014i	1.25788	−	0.596369i
$469$		0			0
$470$	−11.4479	−	3.06745i	−0.528052	−	0.141491i
$471$	5.75897	−	9.97483i	0.265359	−	0.459616i
$472$	−4.37590	−	7.57928i	−0.201417	−	0.348865i
$473$	−0.324497	−	1.21104i	−0.0149204	−	0.0556837i
$474$	45.1715	+	45.1715i	2.07480	+	2.07480i
$475$	−3.86315	−	14.4175i	−0.177253	−	0.661519i
$476$		0			0
$477$	−3.00321	+	5.20171i	−0.137508	+	0.238170i
$478$	37.9520	+	21.9116i	1.73588	+	1.00221i
$479$	1.12124	−	1.12124i	0.0512305	−	0.0512305i	−0.681027	−	0.732258i	$-0.738467\pi$
$479$	1.12124	−	1.12124i	0.0512305	−	0.0512305i	0.732258	+	0.681027i	$0.238467\pi$
$480$	18.8745	+	10.8972i	0.861499	+	0.497387i
$481$	14.1473	−	2.58784i	0.645063	−	0.117995i
$482$		−	18.8489i		−	0.858542i
$483$		0			0
$484$	7.13958	+	12.3661i	0.324527	+	0.562096i
$485$			2.75891i			0.125276i
$486$	−14.6997	+	3.93878i	−0.666793	+	0.178667i
$487$	−7.61733	−	2.04106i	−0.345174	−	0.0924891i	0.0820672	−	0.996627i	$-0.473848\pi$
$487$	−7.61733	−	2.04106i	−0.345174	−	0.0924891i	−0.427241	+	0.904138i	$0.640514\pi$
$488$	−7.00185	+	7.00185i	−0.316959	+	0.316959i
$489$	−14.6162	+	14.6162i	−0.660967	+	0.660967i
$490$		0			0
$491$	7.46842	−	4.31189i	0.337045	−	0.194593i	−0.321919	−	0.946767i	$-0.604328\pi$
$491$	7.46842	−	4.31189i	0.337045	−	0.194593i	0.658965	+	0.752174i	$0.270995\pi$
$492$	34.4823	−	9.23950i	1.55458	−	0.416549i
$493$	1.26452	−	2.19022i	0.0569512	−	0.0986424i
$494$	14.7754	−	21.3910i	0.664779	−	0.962428i
$495$	−0.796396	+	0.459800i	−0.0357953	+	0.0206665i
$496$	−9.10470	+	33.9792i	−0.408813	+	1.52571i
$497$		0			0
$498$	55.1214	+	31.8244i	2.47005	+	1.42608i
$499$	−15.3177	−	4.10435i	−0.685712	−	0.183736i	−0.100890	−	0.994898i	$-0.532169\pi$
$499$	−15.3177	−	4.10435i	−0.685712	−	0.183736i	−0.584822	+	0.811161i	$0.698836\pi$
$500$	3.28184	−	12.2480i	0.146768	−	0.547747i
$501$	9.34158	−	34.8633i	0.417351	−	1.55758i
$502$	−16.0099	−	4.28983i	−0.714556	−	0.191465i
$503$	21.6152	+	12.4795i	0.963773	+	0.556435i	0.897332	−	0.441356i	$-0.145502\pi$
$503$	21.6152	+	12.4795i	0.963773	+	0.556435i	0.0664408	+	0.997790i	$0.478836\pi$
$504$		0			0
$505$	0.486534	−	1.81577i	0.0216505	−	0.0808007i
$506$	−0.0995013	+	0.0574471i	−0.00442337	+	0.00255384i
$507$	−6.42760	+	39.3886i	−0.285460	+	1.74931i
$508$	1.13570	−	1.96709i	0.0503884	−	0.0872753i
$509$	5.00875	−	1.34209i	0.222009	−	0.0594872i	−0.146100	−	0.989270i	$-0.546672\pi$
$509$	5.00875	−	1.34209i	0.222009	−	0.0594872i	0.368109	+	0.929783i	$0.380005\pi$
$510$	1.47105	−	0.849308i	0.0651390	−	0.0376080i
$511$		0			0
$512$	13.3091	−	13.3091i	0.588184	−	0.588184i
$513$	−29.5088	+	29.5088i	−1.30285	+	1.30285i
$514$	53.8974	+	14.4418i	2.37731	+	0.636999i
$515$	9.43051	−	2.52690i	0.415558	−	0.111348i
$516$		−	38.9225i		−	1.71347i
$517$	−0.376678	−	0.652426i	−0.0165663	−	0.0286937i
$518$		0			0
$519$			49.5514i			2.17506i
$520$	−4.61208	+	2.18662i	−0.202253	+	0.0958896i
$521$	12.8926	+	7.44352i	0.564833	+	0.326107i	0.755083	−	0.655629i	$-0.227596\pi$
$521$	12.8926	+	7.44352i	0.564833	+	0.326107i	−0.190250	+	0.981736i	$0.560930\pi$
$522$	−76.2938	+	76.2938i	−3.33929	+	3.33929i
$523$	15.9255	+	9.19458i	0.696372	+	0.402051i	0.805995	−	0.591923i	$-0.201631\pi$
$523$	15.9255	+	9.19458i	0.696372	+	0.402051i	−0.109623	+	0.993973i	$0.534964\pi$
$524$	−3.86512	+	6.69459i	−0.168849	+	0.292455i
$525$		0			0
$526$	2.60794	+	9.73298i	0.113712	+	0.424378i
$527$	1.38594	+	1.38594i	0.0603725	+	0.0603725i
$528$	0.501558	+	1.87184i	0.0218275	+	0.0814613i
$529$	−11.3790	−	19.7090i	−0.494739	−	0.856913i
$530$	−0.945417	+	1.63751i	−0.0410663	+	0.0711289i
$531$	42.7144	+	11.4453i	1.85365	+	0.496683i
$532$		0			0
$533$	−10.8363	+	30.3747i	−0.469371	+	1.31567i
$534$	−11.8080	−	20.4520i	−0.510982	−	0.885046i
$535$	2.12391	+	2.12391i	0.0918248	+	0.0918248i
$536$	−1.55573			−0.0671973
$537$	28.2308			1.21825
$538$	−7.00181	−	7.00181i	−0.301869	−	0.301869i
$539$		0			0
$540$	−14.6994	+	3.93870i	−0.632562	+	0.169494i
$541$	−6.71321	+	25.0540i	−0.288623	+	1.07716i	0.657527	+	0.753431i	$0.271602\pi$
$541$	−6.71321	+	25.0540i	−0.288623	+	1.07716i	−0.946151	+	0.323726i	$0.895064\pi$
$542$	16.8252	−	9.71404i	0.722704	−	0.417254i
$543$			44.9727i			1.92996i
$544$	−0.451484	−	1.68496i	−0.0193572	−	0.0722422i
$545$	−10.3466			−0.443200
$546$		0			0
$547$	−32.7020			−1.39824			−0.699119	−	0.715006i	$-0.746424\pi$
$547$	−32.7020			−1.39824			−0.699119	+	0.715006i	$0.746424\pi$
$548$	−6.60923	−	24.6660i	−0.282332	−	1.05368i
$549$		−	50.0335i		−	2.13538i
$550$	0.760577	−	0.439119i	0.0324311	−	0.0187241i
$551$	−9.49708	+	35.4436i	−0.404589	+	1.50995i
$552$	1.85492	−	0.497025i	0.0789508	−	0.0211548i
$553$		0			0
$554$	31.5367	+	31.5367i	1.33987	+	1.33987i
$555$	−13.6338			−0.578722
$556$	−7.21380			−0.305933
$557$	6.56455	+	6.56455i	0.278149	+	0.278149i	0.832370	−	0.554221i	$-0.186984\pi$
$557$	6.56455	+	6.56455i	0.278149	+	0.278149i	−0.554221	+	0.832370i	$0.686984\pi$
$558$	−41.8097	−	72.4165i	−1.76994	−	3.06563i
$559$	28.9313	+	19.9838i	1.22366	+	0.845223i
$560$		0			0
$561$	0.104294	+	0.0279454i	0.00440328	+	0.00117986i
$562$	−11.1361	+	19.2883i	−0.469749	+	0.813628i
$563$	17.3494	+	30.0500i	0.731189	+	1.26646i	0.956375	+	0.292141i	$0.0943678\pi$
$563$	17.3494	+	30.0500i	0.731189	+	1.26646i	−0.225186	+	0.974316i	$0.572299\pi$
$564$	−6.05317	−	22.5907i	−0.254884	−	0.951242i
$565$	−2.73132	−	2.73132i	−0.114907	−	0.114907i
$566$	−1.33313	−	4.97531i	−0.0560357	−	0.209128i
$567$		0			0
$568$	1.95023	−	3.37789i	0.0818297	−	0.141733i
$569$	−24.9820	−	14.4234i	−1.04730	−	0.604659i	−0.125408	−	0.992105i	$-0.540024\pi$
$569$	−24.9820	−	14.4234i	−1.04730	−	0.604659i	−0.921892	+	0.387446i	$0.873357\pi$
$570$	−17.4268	+	17.4268i	−0.729928	+	0.729928i
$571$	21.3819	+	12.3448i	0.894804	+	0.516615i	0.875511	−	0.483199i	$-0.160525\pi$
$571$	21.3819	+	12.3448i	0.894804	+	0.516615i	0.0192930	+	0.999814i	$0.493858\pi$
$572$	0.567586	+	0.202488i	0.0237320	+	0.00846647i
$573$			18.5200i			0.773686i
$574$		0			0
$575$	−0.924987	−	1.60212i	−0.0385746	−	0.0668132i
$576$			11.3304i			0.472099i
$577$	3.59432	−	0.963094i	0.149633	−	0.0400941i	−0.183225	−	0.983071i	$-0.558654\pi$
$577$	3.59432	−	0.963094i	0.149633	−	0.0400941i	0.332858	+	0.942977i	$0.391987\pi$
$578$	29.6987	+	7.95774i	1.23530	+	0.330998i
$579$	−0.892350	+	0.892350i	−0.0370848	+	0.0370848i
$580$	−9.46168	+	9.46168i	−0.392875	+	0.392875i
$581$		0			0
$582$	−11.9683	+	6.90988i	−0.496101	+	0.286424i
$583$	−0.116096	+	0.0311078i	−0.00480819	+	0.00128835i
$584$	0.0781935	−	0.135435i	0.00323567	−	0.00560435i
$585$	8.66587	−	24.2909i	0.358290	−	1.00431i
$586$	−31.0812	+	17.9447i	−1.28395	+	0.741290i
$587$	4.43305	−	16.5444i	0.182972	−	0.682859i	−0.812084	−	0.583540i	$-0.801667\pi$
$587$	4.43305	−	16.5444i	0.182972	−	0.682859i	0.995056	−	0.0993189i	$-0.0316664\pi$
$588$		0			0
$589$	−24.6279	−	14.2189i	−1.01477	−	0.585880i
$590$	13.4466	+	3.60300i	0.553587	+	0.148333i
$591$	−15.6116	+	58.2633i	−0.642175	+	2.39663i
$592$	−5.06903	+	18.9179i	−0.208336	+	0.777520i
$593$	19.7983	+	5.30494i	0.813019	+	0.217848i	0.641292	−	0.767297i	$-0.278399\pi$
$593$	19.7983	+	5.30494i	0.813019	+	0.217848i	0.171727	+	0.985145i	$0.445065\pi$
$594$	−2.12649	−	1.22773i	−0.0872511	−	0.0503745i
$595$		0			0
$596$	0.145004	−	0.541161i	0.00593958	−	0.0221668i
$597$	46.3195	−	26.7426i	1.89573	−	1.09450i
$598$	1.08271	−	3.03489i	0.0442753	−	0.124106i
$599$	19.5672	−	33.8914i	0.799494	−	1.38476i	−0.120452	−	0.992719i	$-0.538434\pi$
$599$	19.5672	−	33.8914i	0.799494	−	1.38476i	0.919946	−	0.392045i	$-0.128232\pi$
$600$	−14.1788	+	3.79920i	−0.578848	+	0.155102i
$601$	−29.2750	+	16.9020i	−1.19415	+	0.689445i	−0.959246	−	0.282573i	$-0.908812\pi$
$601$	−29.2750	+	16.9020i	−1.19415	+	0.689445i	−0.234908	+	0.972018i	$0.575479\pi$
$602$		0			0
$603$	5.55843	−	5.55843i	0.226357	−	0.226357i
$604$	3.26130	−	3.26130i	0.132701	−	0.132701i
$605$	11.8118	+	3.16496i	0.480217	+	0.128674i
$606$	9.09545	−	2.43712i	0.369478	−	0.0990012i
$607$		−	28.9227i		−	1.17394i	−0.809610	−	0.586968i	$-0.800322\pi$
$607$		−	28.9227i		−	1.17394i	0.809610	−	0.586968i	$-0.199678\pi$
$608$	12.6548	+	21.9187i	0.513218	+	0.888920i
$609$		0			0
$610$		−	15.7506i		−	0.637725i
$611$	19.8997	+	7.09928i	0.805055	+	0.287206i
$612$	1.97887	+	1.14250i	0.0799910	+	0.0461829i
$613$	−12.9884	+	12.9884i	−0.524598	+	0.524598i	−0.918957	−	0.394359i	$-0.870967\pi$
$613$	−12.9884	+	12.9884i	−0.524598	+	0.524598i	0.394359	+	0.918957i	$0.370967\pi$
$614$	−15.5362	−	8.96983i	−0.626990	−	0.361993i
$615$	15.2859	−	26.4759i	0.616387	−	1.06761i
$616$		0			0
$617$	−3.13670	−	11.7063i	−0.126279	−	0.471279i	0.873603	−	0.486639i	$-0.161777\pi$
$617$	−3.13670	−	11.7063i	−0.126279	−	0.471279i	−0.999882	+	0.0153601i	$0.995111\pi$
$618$	34.5812	+	34.5812i	1.39106	+	1.39106i
$619$	−6.26859	−	23.3947i	−0.251956	−	0.940312i	−0.969759	−	0.244065i	$-0.921519\pi$
$619$	−6.26859	−	23.3947i	−0.251956	−	0.940312i	0.717803	−	0.696246i	$-0.245148\pi$
$620$	−5.18509	−	8.98083i	−0.208238	−	0.360679i
$621$	−2.58617	+	4.47937i	−0.103779	+	0.179751i
$622$	46.4247	+	12.4395i	1.86146	+	0.498777i
$623$		0			0
$624$	−44.7176	−	30.8878i	−1.79014	−	1.23650i
$625$	3.97162	+	6.87905i	0.158865	+	0.275162i
$626$	−15.1842	−	15.1842i	−0.606884	−	0.606884i
$627$	−1.56658			−0.0625630
$628$	4.87757			0.194636
$629$	0.771620	+	0.771620i	0.0307665	+	0.0307665i
$630$		0			0
$631$	−7.36652	+	1.97385i	−0.293256	+	0.0785778i	−0.402448	−	0.915443i	$-0.631841\pi$
$631$	−7.36652	+	1.97385i	−0.293256	+	0.0785778i	0.109191	+	0.994021i	$0.465174\pi$
$632$	3.76966	−	14.0686i	0.149949	−	0.559618i
$633$	−40.9308	+	23.6314i	−1.62685	+	0.939265i
$634$		−	6.63565i		−	0.263535i
$635$	−0.503451	−	1.87891i	−0.0199789	−	0.0745621i
$636$	−3.73129			−0.147955
$637$		0			0
$638$	−2.15904			−0.0854772
$639$	5.10087	+	19.0367i	0.201787	+	0.753081i
$640$		−	10.6316i		−	0.420251i
$641$	22.9611	−	13.2566i	0.906908	−	0.523603i	0.0274727	−	0.999623i	$-0.491254\pi$
$641$	22.9611	−	13.2566i	0.906908	−	0.523603i	0.879435	+	0.476019i	$0.157921\pi$
$642$	−3.89414	+	14.5331i	−0.153689	+	0.573577i
$643$	11.1885	−	2.99795i	0.441231	−	0.118228i	−0.0313623	−	0.999508i	$-0.509985\pi$
$643$	11.1885	−	2.99795i	0.441231	−	0.118228i	0.472593	+	0.881281i	$0.343318\pi$
$644$		0			0
$645$	−23.5697	−	23.5697i	−0.928057	−	0.928057i
$646$	1.97258			0.0776101
$647$	−38.5934			−1.51726			−0.758631	−	0.651521i	$-0.774131\pi$
$647$	−38.5934			−1.51726			−0.758631	+	0.651521i	$0.774131\pi$
$648$	11.6910	+	11.6910i	0.459264	+	0.459264i
$649$	0.442443	+	0.766333i	0.0173674	+	0.0300812i
$650$	−8.27611	+	23.1984i	−0.324616	+	0.909916i
$651$		0			0
$652$	−8.45516	−	2.26555i	−0.331129	−	0.0887259i
$653$	−13.0162	+	22.5446i	−0.509361	+	0.882240i	0.490580	+	0.871396i	$0.336785\pi$
$653$	−13.0162	+	22.5446i	−0.509361	+	0.882240i	−0.999941	+	0.0108435i	$0.996548\pi$
$654$	−25.9138	−	44.8840i	−1.01331	−	1.75510i
$655$	1.71340	+	6.39449i	0.0669480	+	0.249853i
$656$	−31.0540	−	31.0540i	−1.21246	−	1.21246i
$657$	0.204517	+	0.763269i	0.00797898	+	0.0297780i
$658$		0			0
$659$	24.8221	−	42.9932i	0.966933	−	1.67478i	0.262605	−	0.964903i	$-0.415418\pi$
$659$	24.8221	−	42.9932i	0.966933	−	1.67478i	0.704328	−	0.709874i	$-0.251248\pi$
$660$	−0.494734	−	0.285635i	−0.0192575	−	0.0111183i
$661$	8.57180	−	8.57180i	0.333404	−	0.333404i	−0.520474	−	0.853878i	$-0.674245\pi$
$661$	8.57180	−	8.57180i	0.333404	−	0.333404i	0.853878	+	0.520474i	$0.174245\pi$
$662$	13.5501	+	7.82313i	0.526638	+	0.304055i
$663$	−2.73619	+	1.29725i	−0.106265	+	0.0503808i
$664$		−	14.5116i		−	0.563161i
$665$		0			0
$666$	−23.2775	−	40.3178i	−0.901984	−	1.56228i
$667$			4.54793i			0.176097i
$668$	14.7638	−	3.95594i	0.571227	−	0.153060i
$669$	41.1496	+	11.0260i	1.59094	+	0.426290i
$670$	1.74981	−	1.74981i	0.0676009	−	0.0676009i
$671$	0.707950	−	0.707950i	0.0273301	−	0.0273301i
$672$		0			0
$673$	34.6870	−	20.0265i	1.33708	−	0.771966i	0.350710	−	0.936484i	$-0.385940\pi$
$673$	34.6870	−	20.0265i	1.33708	−	0.771966i	0.986374	+	0.164519i	$0.0526070\pi$
$674$	46.2236	−	12.3856i	1.78047	−	0.477075i
$675$	19.7684	−	34.2398i	0.760885	−	1.31789i
$676$	−15.8064	+	5.98281i	−0.607938	+	0.230108i
$677$	−33.3532	+	19.2565i	−1.28187	+	0.740086i	−0.977190	−	0.212369i	$-0.931882\pi$
$677$	−33.3532	+	19.2565i	−1.28187	+	0.740086i	−0.304678	+	0.952455i	$0.598549\pi$
$678$	5.00780	−	18.6894i	0.192323	−	0.717760i
$679$		0			0
$680$	−0.335392	−	0.193639i	−0.0128617	−	0.00742570i
$681$	−35.4215	−	9.49116i	−1.35735	−	0.363702i
$682$	0.433072	−	1.61625i	0.0165832	−	0.0618892i
$683$	−9.87146	+	36.8408i	−0.377721	+	1.40967i	0.471607	+	0.881809i	$0.343674\pi$
$683$	−9.87146	+	36.8408i	−0.377721	+	1.40967i	−0.849328	+	0.527865i	$0.822993\pi$
$684$	−32.0234	−	8.58064i	−1.22445	−	0.328089i
$685$	−18.9389	−	10.9344i	−0.723617	−	0.417780i
$686$		0			0
$687$	−19.5220	+	72.8571i	−0.744810	+	2.77967i
$688$	−41.4679	+	23.9415i	−1.58095	+	0.912761i
$689$	1.91573	−	2.77349i	0.0729836	−	0.105661i
$690$	−1.52729	+	2.64535i	−0.0581431	+	0.100707i
$691$	−5.69382	+	1.52565i	−0.216603	+	0.0580386i	−0.365489	−	0.930816i	$-0.619098\pi$
$691$	−5.69382	+	1.52565i	−0.216603	+	0.0580386i	0.148886	+	0.988854i	$0.452431\pi$
$692$	−18.1725	+	10.4919i	−0.690816	+	0.398843i
$693$		0			0
$694$	6.71396	−	6.71396i	0.254858	−	0.254858i
$695$	−4.36835	+	4.36835i	−0.165701	+	0.165701i
$696$	34.8569	+	9.33987i	1.32125	+	0.354027i
$697$	−2.36356	+	0.633314i	−0.0895262	+	0.0239885i
$698$		−	21.0770i		−	0.797776i
$699$	−27.2814	−	47.2528i	−1.03188	−	1.78727i
$700$		0			0
$701$			39.7256i			1.50041i	0.661203	+	0.750207i	$0.270046\pi$
$701$			39.7256i			1.50041i	−0.661203	+	0.750207i	$0.729954\pi$
$702$	67.7403	−	12.3911i	2.55669	−	0.467671i
$703$	−13.7115	−	7.91636i	−0.517140	−	0.298571i
$704$	−0.160319	+	0.160319i	−0.00604226	+	0.00604226i
$705$	−17.3455	−	10.0144i	−0.653268	−	0.377164i
$706$	7.84109	−	13.5812i	0.295103	−	0.511134i
$707$		0			0
$708$	7.11000	+	26.5349i	0.267210	+	0.997241i
$709$	0.300391	+	0.300391i	0.0112814	+	0.0112814i	0.712725	−	0.701444i	$-0.247461\pi$
$709$	0.300391	+	0.300391i	0.0112814	+	0.0112814i	−0.701444	+	0.712725i	$0.747461\pi$
$710$	1.60577	+	5.99280i	0.0602633	+	0.224906i
$711$	36.7967	+	63.7338i	1.37999	+	2.39020i
$712$	−2.69217	+	4.66298i	−0.100893	+	0.174752i
$713$	−3.40455	−	0.912248i	−0.127502	−	0.0341639i
$714$		0			0
$715$	0.466323	−	0.221087i	0.0174395	−	0.00826818i
$716$	5.97753	+	10.3534i	0.223391	+	0.386924i
$717$	52.3676	+	52.3676i	1.95570	+	1.95570i
$718$	−56.4037			−2.10497
$719$	5.50107			0.205155			0.102578	−	0.994725i	$-0.467291\pi$
$719$	5.50107			0.205155			0.102578	+	0.994725i	$0.467291\pi$
$720$	24.8342	+	24.8342i	0.925516	+	0.925516i
$721$		0			0
$722$	5.69451	−	1.52584i	0.211928	−	0.0567859i
$723$	8.24432	−	30.7682i	0.306610	−	1.14428i
$724$	−16.4933	+	9.52242i	−0.612969	+	0.353898i
$725$		−	34.7639i		−	1.29110i
$726$	15.8537	+	59.1669i	0.588387	+	2.19589i
$727$	10.8373			0.401935			0.200967	−	0.979598i	$-0.435591\pi$
$727$	10.8373			0.401935			0.200967	+	0.979598i	$0.435591\pi$
$728$		0			0
$729$	13.2908			0.492253
$730$	0.0643825	+	0.240279i	0.00238290	+	0.00889312i
$731$			2.66791i			0.0986762i
$732$	26.9175	−	15.5408i	0.994898	−	0.574405i
$733$	−7.78294	+	29.0463i	−0.287469	+	1.07285i	0.659547	+	0.751664i	$0.270748\pi$
$733$	−7.78294	+	29.0463i	−0.287469	+	1.07285i	−0.947016	+	0.321187i	$0.895918\pi$
$734$	−4.59604	+	1.23150i	−0.169643	+	0.0454557i
$735$		0			0
$736$	2.21814	+	2.21814i	0.0817617	+	0.0817617i
$737$	0.157298			0.00579416
$738$	104.393			3.84275
$739$	32.1610	+	32.1610i	1.18306	+	1.18306i	0.978947	+	0.204113i	$0.0654310\pi$
$739$	32.1610	+	32.1610i	1.18306	+	1.18306i	0.204113	+	0.978947i	$0.434569\pi$
$740$	−2.88679	−	5.00007i	−0.106121	−	0.183806i
$741$	33.4752	−	28.4553i	1.22974	−	1.04533i
$742$		0			0
$743$	−43.4013	−	11.6293i	−1.59224	−	0.426639i	−0.649552	−	0.760317i	$-0.725044\pi$
$743$	−43.4013	−	11.6293i	−1.59224	−	0.426639i	−0.942687	+	0.333678i	$0.891710\pi$
$744$	−13.9836	+	24.2202i	−0.512662	+	0.887956i
$745$	−0.239895	−	0.415511i	−0.00878908	−	0.0152231i
$746$	16.8492	+	62.8822i	0.616894	+	2.30228i
$747$	51.8483	+	51.8483i	1.89703	+	1.89703i
$748$	0.0118342	+	0.0441659i	0.000432702	+	0.00161486i
$749$		0			0
$750$	27.1972	−	47.1069i	0.993100	−	1.72010i
$751$	−14.5396	−	8.39446i	−0.530559	−	0.306318i	0.210685	−	0.977554i	$-0.432430\pi$
$751$	−14.5396	−	8.39446i	−0.530559	−	0.306318i	−0.741244	+	0.671236i	$0.765764\pi$
$752$	−20.3447	+	20.3447i	−0.741897	+	0.741897i
$753$	−24.2576	−	14.0052i	−0.883997	−	0.510376i
$754$	46.1352	−	39.2169i	1.68014	−	1.42819i
$755$		−	3.94980i		−	0.143748i
$756$		0			0
$757$	7.76400	+	13.4476i	0.282187	+	0.488763i	0.971923	−	0.235298i	$-0.0756067\pi$
$757$	7.76400	+	13.4476i	0.282187	+	0.488763i	−0.689736	+	0.724061i	$0.742273\pi$
$758$		−	41.8755i		−	1.52099i
$759$	−0.187549	+	0.0502537i	−0.00680761	+	0.00182409i
$760$	5.42754	+	1.45431i	0.196878	+	0.0527532i
$761$	28.3360	−	28.3360i	1.02718	−	1.02718i	0.0275603	−	0.999620i	$-0.491226\pi$
$761$	28.3360	−	28.3360i	1.02718	−	1.02718i	0.999620	−	0.0275603i	$-0.00877384\pi$
$762$	6.88985	−	6.88985i	0.249593	−	0.249593i
$763$		0			0
$764$	−6.79206	+	3.92140i	−0.245728	+	0.141871i
$765$	1.89016	−	0.506467i	0.0683389	−	0.0183114i
$766$	−11.8520	+	20.5283i	−0.428230	+	0.741716i
$767$	−23.3740	−	8.33875i	−0.843985	−	0.301095i
$768$	55.4978	−	32.0417i	2.00260	−	1.15620i
$769$	−12.5630	+	46.8857i	−0.453033	+	1.69074i	0.240774	+	0.970581i	$0.422599\pi$
$769$	−12.5630	+	46.8857i	−0.453033	+	1.69074i	−0.693807	+	0.720161i	$0.744068\pi$
$770$		0			0
$771$	81.6636	+	47.1485i	2.94104	+	1.69801i
$772$	−0.516206	−	0.138317i	−0.0185786	−	0.00497813i
$773$	12.1817	−	45.4628i	0.438146	−	1.63518i	−0.295278	−	0.955411i	$-0.595412\pi$
$773$	12.1817	−	45.4628i	0.438146	−	1.63518i	0.733424	−	0.679772i	$-0.237921\pi$
$774$	29.4588	−	109.942i	1.05887	−	3.95177i
$775$	26.0240	+	6.97312i	0.934811	+	0.250482i
$776$	2.72871	+	1.57542i	0.0979551	+	0.0565544i
$777$		0			0
$778$	11.6691	−	43.5498i	0.418359	−	1.56134i
$779$	30.7461	−	17.7513i	1.10159	−	0.636006i
$780$	15.7599	−	2.88281i	0.564296	−	0.103221i
$781$	−0.197185	+	0.341535i	−0.00705585	+	0.0122211i
$782$	0.236156	−	0.0632777i	0.00844491	−	0.00226281i
$783$	−84.1744	+	48.5981i	−3.00815	+	1.73675i
$784$		0			0
$785$	2.95364	−	2.95364i	0.105420	−	0.105420i
$786$	−23.4483	+	23.4483i	−0.836372	+	0.836372i
$787$	−26.8138	−	7.18474i	−0.955810	−	0.256108i	−0.252984	−	0.967470i	$-0.581412\pi$
$787$	−26.8138	−	7.18474i	−0.955810	−	0.256108i	−0.702826	+	0.711362i	$0.748079\pi$
$788$	−24.6731	+	6.61113i	−0.878942	+	0.235512i
$789$			17.0285i			0.606229i
$790$	11.5837	+	20.0635i	0.412129	+	0.713829i
$791$		0			0
$792$			1.05024i			0.0373187i
$793$	−2.26851	+	27.9869i	−0.0805571	+	0.993845i
$794$	−15.2196	−	8.78706i	−0.540125	−	0.311841i
$795$	−2.25950	+	2.25950i	−0.0801362	+	0.0801362i
$796$	19.6152	+	11.3248i	0.695243	+	0.401399i
$797$	−12.9913	+	22.5016i	−0.460177	+	0.797049i	−0.998969	−	0.0453891i	$-0.985547\pi$
$797$	−12.9913	+	22.5016i	−0.460177	+	0.797049i	0.538793	+	0.842438i	$0.318881\pi$
$798$		0			0
$799$	0.414909	+	1.54846i	0.0146784	+	0.0547807i
$800$	−16.9552	−	16.9552i	−0.599457	−	0.599457i
$801$	−7.04145	−	26.2790i	−0.248797	−	0.928524i
$802$	6.36134	+	11.0182i	0.224627	+	0.389065i
$803$	−0.00790607	+	0.0136937i	−0.000278999	+	0.000483241i
$804$	4.71687	+	1.26388i	0.166351	+	0.0445737i
$805$		0			0
$806$	20.1035	+	42.4028i	0.708115	+	1.49358i
$807$	−8.36698	−	14.4920i	−0.294532	−	0.510144i
$808$	−1.51807	−	1.51807i	−0.0534056	−	0.0534056i
$809$	−30.0960			−1.05812			−0.529060	−	0.848584i	$-0.677455\pi$
$809$	−30.0960			−1.05812			−0.529060	+	0.848584i	$0.677455\pi$
$810$	−26.2988			−0.924046
$811$	−25.5228	−	25.5228i	−0.896227	−	0.896227i	0.0988731	−	0.995100i	$-0.468476\pi$
$811$	−25.5228	−	25.5228i	−0.896227	−	0.896227i	−0.995100	+	0.0988731i	$0.968476\pi$
$812$		0			0
$813$	31.7137	−	8.49766i	1.11225	−	0.298026i
$814$	0.241112	−	0.899842i	0.00845097	−	0.0315395i
$815$	−6.49198	+	3.74815i	−0.227404	+	0.131292i
$816$		−	4.12364i		−	0.144356i
$817$	−10.0185	−	37.3897i	−0.350504	−	1.30810i
$818$	27.6194			0.965691
$819$		0			0
$820$	12.9464			0.452108
$821$	−12.5021	−	46.6583i	−0.436325	−	1.62839i	−0.737876	−	0.674936i	$-0.764171\pi$
$821$	−12.5021	−	46.6583i	−0.436325	−	1.62839i	0.301552	−	0.953450i	$-0.402495\pi$
$822$		−	109.544i		−	3.82077i
$823$	−18.6307	+	10.7564i	−0.649424	+	0.374945i	−0.788235	−	0.615374i	$-0.789005\pi$
$823$	−18.6307	+	10.7564i	−0.649424	+	0.374945i	0.138812	+	0.990319i	$0.455672\pi$
$824$	2.88588	−	10.7702i	0.100534	−	0.375199i
$825$	1.43361	−	0.384134i	0.0499118	−	0.0133738i
$826$		0			0
$827$	−19.3309	−	19.3309i	−0.672200	−	0.672200i	0.286023	−	0.958223i	$-0.407667\pi$
$827$	−19.3309	−	19.3309i	−0.672200	−	0.672200i	−0.958223	+	0.286023i	$0.907667\pi$
$828$	−4.10907			−0.142800
$829$	1.60123			0.0556130			0.0278065	−	0.999613i	$-0.491148\pi$
$829$	1.60123			0.0556130			0.0278065	+	0.999613i	$0.491148\pi$
$830$	16.3220	+	16.3220i	0.566543	+	0.566543i
$831$	37.6856	+	65.2733i	1.30730	+	2.26431i
$832$	0.513717	−	6.33780i	0.0178099	−	0.219724i
$833$		0			0
$834$	−29.8910	−	8.00926i	−1.03504	−	0.277338i
$835$	6.54473	−	11.3358i	0.226490	−	0.392292i
$836$	−0.331704	−	0.574528i	−0.0114722	−	0.0198705i
$837$	−19.4961	−	72.7605i	−0.673885	−	2.51497i
$838$	31.8061	+	31.8061i	1.09872	+	1.09872i
$839$	−0.167923	−	0.626698i	−0.00579736	−	0.0216360i	0.962967	−	0.269621i	$-0.0868984\pi$
$839$	−0.167923	−	0.626698i	−0.00579736	−	0.0216360i	−0.968764	+	0.247985i	$0.920232\pi$
$840$		0			0
$841$	−28.2313	+	48.8981i	−0.973495	+	1.68614i
$842$	−9.14596	−	5.28042i	−0.315191	−	0.181975i
$843$	−26.6147	+	26.6147i	−0.916660	+	0.916660i
$844$	−17.3332	−	10.0073i	−0.596634	−	0.344467i
$845$	−5.94872	+	13.1946i	−0.204642	+	0.453907i
$846$		−	68.3919i		−	2.35136i
$847$		0			0
$848$	2.29514	+	3.97530i	0.0788154	+	0.136512i
$849$		−	8.70463i		−	0.298742i
$850$	−1.80515	+	0.483688i	−0.0619161	+	0.0165904i
$851$	−1.89548	−	0.507893i	−0.0649762	−	0.0174103i
$852$	−8.65717	+	8.65717i	−0.296590	+	0.296590i
$853$	−19.5375	+	19.5375i	−0.668953	+	0.668953i	−0.957474	−	0.288521i	$-0.906837\pi$
$853$	−19.5375	+	19.5375i	−0.668953	+	0.668953i	0.288521	+	0.957474i	$0.406837\pi$
$854$		0			0
$855$	−24.5880	+	14.1959i	−0.840891	+	0.485489i
$856$	3.31349	−	0.887847i	0.113253	−	0.0303460i
$857$	16.1513	−	27.9748i	0.551717	−	0.955602i	−0.446434	−	0.894817i	$-0.647306\pi$
$857$	16.1513	−	27.9748i	0.551717	−	0.955602i	0.998151	−	0.0607851i	$-0.0193604\pi$
$858$	2.12702	+	1.46920i	0.0726154	+	0.0501577i
$859$	−25.7564	+	14.8704i	−0.878796	+	0.507373i	−0.870261	−	0.492591i	$-0.836050\pi$
$859$	−25.7564	+	14.8704i	−0.878796	+	0.507373i	−0.00853452	+	0.999964i	$0.502717\pi$
$860$	3.65337	−	13.6346i	0.124579	−	0.464935i
$861$		0			0
$862$	−30.4140	−	17.5595i	−1.03590	−	0.598079i
$863$	−30.6982	−	8.22555i	−1.04498	−	0.280001i	−0.304803	−	0.952415i	$-0.598591\pi$
$863$	−30.6982	−	8.22555i	−1.04498	−	0.280001i	−0.740175	+	0.672414i	$0.765257\pi$
$864$	−17.3514	+	64.7565i	−0.590308	+	2.20306i
$865$	−4.65103	+	17.3579i	−0.158140	+	0.590186i
$866$	3.88281	+	1.04040i	0.131943	+	0.0353541i
$867$	44.9985	+	25.9799i	1.52823	+	0.882323i
$868$		0			0
$869$	−0.381147	+	1.42246i	−0.0129295	+	0.0482536i
$870$	−49.7103	+	28.7002i	−1.68534	+	0.973029i
$871$	−3.36121	+	2.85717i	−0.113890	+	0.0968115i
$872$	−5.90823	+	10.2334i	−0.200078	+	0.346545i
$873$	−15.3781	+	4.12056i	−0.520471	+	0.139460i
$874$	−3.07201	+	1.77363i	−0.103912	+	0.0599938i
$875$		0			0
$876$	−0.347106	+	0.347106i	−0.0117276	+	0.0117276i
$877$	11.5269	−	11.5269i	0.389236	−	0.389236i	−0.485179	−	0.874415i	$-0.661246\pi$
$877$	11.5269	−	11.5269i	0.389236	−	0.389236i	0.874415	+	0.485179i	$0.161246\pi$
$878$	−12.8843	−	3.45233i	−0.434823	−	0.116510i
$879$	−58.5847	+	15.6977i	−1.97601	+	0.529471i
$880$			0.702784i			0.0236908i
$881$	−24.6284	−	42.6577i	−0.829752	−	1.43717i	−0.898232	−	0.439521i	$-0.855148\pi$
$881$	−24.6284	−	42.6577i	−0.829752	−	1.43717i	0.0684801	−	0.997652i	$-0.478185\pi$
$882$		0			0
$883$		−	40.1403i		−	1.35083i	−0.737439	−	0.675414i	$-0.763965\pi$
$883$		−	40.1403i		−	1.35083i	0.737439	−	0.675414i	$-0.236035\pi$
$884$	−1.05511	−	0.728796i	−0.0354871	−	0.0245120i
$885$	20.3738	+	11.7628i	0.684858	+	0.395403i
$886$	34.1497	−	34.1497i	1.14728	−	1.14728i
$887$	−38.3787	−	22.1580i	−1.28863	−	0.743992i	−0.310221	−	0.950664i	$-0.600403\pi$
$887$	−38.3787	−	22.1580i	−1.28863	−	0.743992i	−0.978410	+	0.206673i	$0.933737\pi$
$888$	−7.78532	+	13.4846i	−0.261258	+	0.452513i
$889$		0			0
$890$	−2.21666	−	8.27270i	−0.0743027	−	0.277301i
$891$	−1.18206	−	1.18206i	−0.0396005	−	0.0396005i
$892$	4.66925	+	17.4259i	0.156338	+	0.583462i
$893$	−11.6296	−	20.1430i	−0.389169	−	0.674061i
$894$	1.20167	−	2.08135i	0.0401898	−	0.0696108i
$895$	9.88927	+	2.64982i	0.330562	+	0.0885738i
$896$		0			0
$897$	3.09481	−	4.48049i	0.103333	−	0.149599i
$898$	−20.3132	−	35.1836i	−0.677862	−	1.17409i
$899$	−46.8343	−	46.8343i	−1.56201	−	1.56201i
$900$	31.4093			1.04698
$901$	0.255758			0.00852053
$902$	1.47711	+	1.47711i	0.0491823	+	0.0491823i
$903$		0			0
$904$	−4.26109	+	1.14176i	−0.141722	+	0.0379742i
$905$	−4.22126	+	15.7540i	−0.140319	+	0.523679i
$906$	17.1344	−	9.89255i	0.569253	−	0.328658i
$907$		−	54.1580i		−	1.79829i	−0.437654	−	0.899143i	$-0.644191\pi$
$907$		−	54.1580i		−	1.79829i	0.437654	−	0.899143i	$-0.355809\pi$
$908$	−4.01928	−	15.0001i	−0.133384	−	0.497797i
$909$	10.8478			0.359798
$910$		0			0
$911$	5.80658			0.192381			0.0961903	−	0.995363i	$-0.469334\pi$
$911$	5.80658			0.192381			0.0961903	+	0.995363i	$0.469334\pi$
$912$	15.4851	+	57.7912i	0.512763	+	1.91366i
$913$			1.46726i			0.0485591i
$914$	−3.55793	+	2.05417i	−0.117686	+	0.0679460i
$915$	6.88919	−	25.7108i	0.227750	−	0.849973i
$916$	−30.8532	+	8.26709i	−1.01942	+	0.273152i
$917$		0			0
$918$	3.69467	+	3.69467i	0.121942	+	0.121942i
$919$	−18.8392			−0.621447			−0.310724	−	0.950500i	$-0.600571\pi$
$919$	−18.8392			−0.621447			−0.310724	+	0.950500i	$0.600571\pi$
$920$	0.696433			0.0229607
$921$	−21.4374	−	21.4374i	−0.706387	−	0.706387i
$922$	−3.39063	−	5.87275i	−0.111665	−	0.193409i
$923$	−1.99012	−	10.8797i	−0.0655057	−	0.358111i
$924$		0			0
$925$	14.4888	+	3.88227i	0.476390	+	0.127648i
$926$	19.9632	−	34.5774i	0.656033	−	1.13628i
$927$	28.1699	+	48.7916i	0.925220	+	1.60253i
$928$	15.2568	+	56.9391i	0.500828	+	1.86912i
$929$	−21.3734	−	21.3734i	−0.701239	−	0.701239i	0.263437	−	0.964677i	$-0.415144\pi$
$929$	−21.3734	−	21.3734i	−0.701239	−	0.701239i	−0.964677	+	0.263437i	$0.915144\pi$
$930$	−11.5137	−	42.9697i	−0.377549	−	1.40903i
$931$		0			0
$932$	11.5530	−	20.0104i	0.378432	−	0.655464i
$933$	70.3411	+	40.6115i	2.30287	+	1.32956i
$934$	7.02777	−	7.02777i	0.229956	−	0.229956i
$935$	0.0339111	+	0.0195786i	0.00110901	+	0.000640289i
$936$	−19.0766	−	22.4419i	−0.623538	−	0.733537i
$937$		−	29.0475i		−	0.948939i	−0.880272	−	0.474470i	$-0.842640\pi$
$937$		−	29.0475i		−	0.948939i	0.880272	−	0.474470i	$-0.157360\pi$
$938$		0			0
$939$	−18.1448	−	31.4277i	−0.592132	−	1.02560i
$940$		−	8.48172i		−	0.276643i
$941$	−51.2078	+	13.7211i	−1.66933	+	0.447295i	−0.964929	−	0.262510i	$-0.915450\pi$
$941$	−51.2078	+	13.7211i	−1.66933	+	0.447295i	−0.704398	+	0.709805i	$0.748783\pi$
$942$	20.2106	+	5.41542i	0.658498	+	0.176444i
$943$	3.11147	−	3.11147i	0.101323	−	0.101323i
$944$	23.8967	−	23.8967i	0.777773	−	0.777773i
$945$		0			0
$946$	1.97245	−	1.13879i	0.0641299	−	0.0370254i
$947$	−37.6168	+	10.0794i	−1.22238	+	0.327536i	−0.811609	−	0.584201i	$-0.801408\pi$
$947$	−37.6168	+	10.0794i	−1.22238	+	0.327536i	−0.410774	+	0.911737i	$0.634741\pi$
$948$	−22.8587	+	39.5925i	−0.742417	+	1.28590i
$949$	−0.0797932	−	0.436218i	−0.00259020	−	0.0141602i
$950$	23.4821	−	13.5574i	0.761860	−	0.439860i
$951$	2.90237	−	10.8318i	0.0941160	−	0.351246i
$952$		0			0
$953$	−2.01127	−	1.16121i	−0.0651515	−	0.0376153i	0.467070	−	0.884220i	$-0.345309\pi$
$953$	−2.01127	−	1.16121i	−0.0651515	−	0.0376153i	−0.532222	+	0.846605i	$0.678643\pi$
$954$	−10.5395	−	2.82405i	−0.341229	−	0.0914321i
$955$	−1.73834	+	6.48759i	−0.0562515	+	0.209933i
$956$	−8.11713	+	30.2935i	−0.262527	+	0.979763i
$957$	−3.52434	−	0.944345i	−0.113926	−	0.0305263i
$958$	2.49461	+	1.44027i	0.0805973	+	0.0465329i
$959$		0			0
$960$	−1.56010	+	5.82236i	−0.0503519	+	0.187916i
$961$	17.6074	−	10.1656i	0.567980	−	0.327923i
$962$	11.1926	+	23.6077i	0.360863	+	0.761143i
$963$	−8.66653	+	15.0109i	−0.279275	+	0.483718i
$964$	13.0296	−	3.49127i	0.419655	−	0.112446i
$965$	−0.396349	+	0.228832i	−0.0127589	+	0.00736638i
$966$		0			0
$967$	−20.9764	+	20.9764i	−0.674557	+	0.674557i	−0.958763	−	0.284206i	$-0.908270\pi$
$967$	−20.9764	+	20.9764i	−0.674557	+	0.674557i	0.284206	+	0.958763i	$0.408270\pi$
$968$	9.87522	−	9.87522i	0.317401	−	0.317401i
$969$	3.21997	+	0.862788i	0.103440	+	0.0277168i
$970$	−4.84107	+	1.29716i	−0.155438	+	0.0416494i
$971$			41.7496i			1.33981i	0.742448	+	0.669904i	$0.233665\pi$
$971$			41.7496i			1.33981i	−0.742448	+	0.669904i	$0.766335\pi$
$972$	−5.44550	−	9.43189i	−0.174665	−	0.302528i
$973$		0			0
$974$		−	14.3258i		−	0.459029i
$975$	−23.6564	+	34.2484i	−0.757611	+	1.09683i
$976$	−33.1142	−	19.1185i	−1.05996	−	0.611969i
$977$	3.42899	−	3.42899i	0.109703	−	0.109703i	−0.650124	−	0.759828i	$-0.725283\pi$
$977$	3.42899	−	3.42899i	0.109703	−	0.109703i	0.759828	+	0.650124i	$0.225283\pi$
$978$	−32.5193	−	18.7750i	−1.03985	−	0.600358i
$979$	0.272203	−	0.471469i	0.00869963	−	0.0150682i
$980$		0			0
$981$	−15.4531	−	57.6719i	−0.493381	−	1.84132i
$982$	11.0776	+	11.0776i	0.353499	+	0.353499i
$983$	1.10131	+	4.11013i	0.0351262	+	0.131093i	0.981262	−	0.192676i	$-0.0617167\pi$
$983$	1.10131	+	4.11013i	0.0351262	+	0.131093i	−0.946136	+	0.323769i	$0.895050\pi$
$984$	−17.4575	−	30.2372i	−0.556523	−	0.963927i
$985$	−10.9375	+	18.9443i	−0.348498	+	0.603616i
$986$	4.43773	+	1.18909i	0.141326	+	0.0378682i
$987$		0			0
$988$	17.5237	+	6.25164i	0.557503	+	0.198891i
$989$	−2.39882	−	4.15489i	−0.0762782	−	0.132118i
$990$	−1.18126	−	1.18126i	−0.0375428	−	0.0375428i
$991$	−46.8913			−1.48955			−0.744776	−	0.667315i	$-0.767444\pi$
$991$	−46.8913			−1.48955			−0.744776	+	0.667315i	$0.767444\pi$
$992$	−45.6845			−1.45049
$993$	18.6969	+	18.6969i	0.593328	+	0.593328i
$994$		0			0
$995$	18.7359	−	5.02027i	0.593968	−	0.159153i
$996$	−11.7893	+	43.9983i	−0.373559	+	1.39414i
$997$	−8.37363	+	4.83452i	−0.265195	+	0.153111i	−0.626702	−	0.779259i	$-0.715596\pi$
$997$	−8.37363	+	4.83452i	−0.265195	+	0.153111i	0.361507	+	0.932369i	$0.382262\pi$
$998$		−	28.8078i		−	0.911893i
$999$	−10.8544	−	40.5093i	−0.343419	−	1.28166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.a.80.6		28
7.2	even	3		91.2.ba.a.54.6	yes	28
7.3	odd	6		637.2.bd.a.587.2		28
7.4	even	3		637.2.bd.b.587.2		28
7.5	odd	6		637.2.bb.a.509.6		28
7.6	odd	2		91.2.w.a.80.6	yes	28
13.7	odd	12		637.2.bb.a.423.6		28
21.2	odd	6		819.2.et.b.145.2		28
21.20	even	2		819.2.gh.b.262.2		28
91.20	even	12		91.2.ba.a.59.6	yes	28
91.33	even	12	inner	637.2.x.a.215.6		28
91.46	odd	12		637.2.bd.a.293.2		28
91.59	even	12		637.2.bd.b.293.2		28
91.72	odd	12		91.2.w.a.33.6	✓	28
273.20	odd	12		819.2.et.b.514.2		28
273.254	even	12		819.2.gh.b.397.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.6	✓	28	91.72	odd	12
91.2.w.a.80.6	yes	28	7.6	odd	2
91.2.ba.a.54.6	yes	28	7.2	even	3
91.2.ba.a.59.6	yes	28	91.20	even	12
637.2.x.a.80.6		28	1.1	even	1	trivial
637.2.x.a.215.6		28	91.33	even	12	inner
637.2.bb.a.423.6		28	13.7	odd	12
637.2.bb.a.509.6		28	7.5	odd	6
637.2.bd.a.293.2		28	91.46	odd	12
637.2.bd.a.587.2		28	7.3	odd	6
637.2.bd.b.293.2		28	91.59	even	12
637.2.bd.b.587.2		28	7.4	even	3
819.2.et.b.145.2		28	21.2	odd	6
819.2.et.b.514.2		28	273.20	odd	12
819.2.gh.b.262.2		28	21.20	even	2
819.2.gh.b.397.2		28	273.254	even	12

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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.470172 + 1.75471i) q^{2} +3.06997i q^{3} +(-1.12588 + 0.650030i) q^{4} +(-0.288156 + 1.07541i) q^{5} +(-5.38690 + 1.44342i) q^{6} +(0.899098 + 0.899098i) q^{8} -6.42473 q^{9} +O(q^{10})\)	\(q+(0.470172 + 1.75471i) q^{2} +3.06997i q^{3} +(-1.12588 + 0.650030i) q^{4} +(-0.288156 + 1.07541i) q^{5} +(-5.38690 + 1.44342i) q^{6} +(0.899098 + 0.899098i) q^{8} -6.42473 q^{9} -2.02252 q^{10} +(-0.0909069 - 0.0909069i) q^{11} +(-1.99557 - 3.45643i) q^{12} +(3.59376 + 0.291296i) q^{13} +(-3.30149 - 0.884632i) q^{15} +(-2.45498 + 4.25215i) q^{16} +(0.136785 + 0.236918i) q^{17} +(-3.02073 - 11.2735i) q^{18} +(-2.80666 - 2.80666i) q^{19} +(-0.374620 - 1.39810i) q^{20} +(0.116773 - 0.202257i) q^{22} +(-0.426046 - 0.245978i) q^{23} +(-2.76021 + 2.76021i) q^{24} +(3.25665 + 1.88023i) q^{25} +(1.17855 + 6.44296i) q^{26} -10.5138i q^{27} +(-4.62230 - 8.00606i) q^{29} -6.20908i q^{30} +(6.92046 - 1.85433i) q^{31} +(-6.15917 - 1.65034i) q^{32} +(0.279082 - 0.279082i) q^{33} +(-0.351410 + 0.351410i) q^{34} +(7.23351 - 4.17627i) q^{36} +(3.85295 - 1.03240i) q^{37} +(3.60526 - 6.24449i) q^{38} +(-0.894272 + 11.0328i) q^{39} +(-1.22598 + 0.707822i) q^{40} +(-2.31500 + 8.63969i) q^{41} +(8.44566 + 4.87610i) q^{43} +(0.161443 + 0.0432585i) q^{44} +(1.85133 - 6.90925i) q^{45} +(0.231304 - 0.863237i) q^{46} +(5.66021 + 1.51665i) q^{47} +(-13.0540 - 7.53673i) q^{48} +(-1.76806 + 6.59849i) q^{50} +(-0.727333 + 0.419926i) q^{51} +(-4.23552 + 2.00809i) q^{52} +(0.467445 - 0.809639i) q^{53} +(18.4487 - 4.94331i) q^{54} +(0.123958 - 0.0715671i) q^{55} +(8.61638 - 8.61638i) q^{57} +(11.8750 - 11.8750i) q^{58} +(-6.64843 - 1.78144i) q^{59} +(4.29214 - 1.15007i) q^{60} +7.78764i q^{61} +(6.50761 + 11.2715i) q^{62} -1.76356i q^{64} +(-1.34883 + 3.78085i) q^{65} +(0.620923 + 0.358490i) q^{66} +(-0.865162 + 0.865162i) q^{67} +(-0.308008 - 0.177829i) q^{68} +(0.755145 - 1.30795i) q^{69} +(-0.793943 - 2.96304i) q^{71} +(-5.77646 - 5.77646i) q^{72} +(-0.0318328 - 0.118802i) q^{73} +(3.62311 + 6.27540i) q^{74} +(-5.77224 + 9.99781i) q^{75} +(4.98439 + 1.33556i) q^{76} +(-19.7797 + 3.61811i) q^{78} +(-5.72736 - 9.92007i) q^{79} +(-3.86541 - 3.86541i) q^{80} +13.0030 q^{81} -16.2486 q^{82} +(-8.07011 - 8.07011i) q^{83} +(-0.294201 + 0.0788309i) q^{85} +(-4.58522 + 17.1123i) q^{86} +(24.5784 - 14.1903i) q^{87} -0.163468i q^{88} +(1.09599 + 4.09029i) q^{89} +12.9941 q^{90} +0.639571 q^{92} +(5.69274 + 21.2456i) q^{93} +10.6451i q^{94} +(3.82708 - 2.20957i) q^{95} +(5.06651 - 18.9085i) q^{96} +(2.39359 - 0.641359i) q^{97} +(0.584052 + 0.584052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 + 6 * q^5 - 12 * q^6 - 4 * q^8 - 12 * q^9 + 12 * q^10 + 2 * q^11 - 8 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 8 * q^19 + 36 * q^20 - 8 * q^22 - 6 * q^23 - 12 * q^24 - 24 * q^26 - 8 * q^29 + 38 * q^31 - 20 * q^32 - 18 * q^33 - 12 * q^34 + 54 * q^36 - 16 * q^37 + 28 * q^39 - 48 * q^40 - 18 * q^41 + 48 * q^43 - 6 * q^44 - 12 * q^45 + 18 * q^46 + 42 * q^47 - 12 * q^48 + 10 * q^50 + 12 * q^51 + 28 * q^52 + 12 * q^53 + 30 * q^54 + 6 * q^55 + 12 * q^57 + 62 * q^58 + 6 * q^59 + 16 * q^60 + 36 * q^62 - 2 * q^65 - 66 * q^66 - 4 * q^67 - 30 * q^68 - 42 * q^69 - 42 * q^71 - 38 * q^72 - 14 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 - 12 * q^80 + 12 * q^81 + 108 * q^82 + 66 * q^83 - 54 * q^85 - 30 * q^86 - 42 * q^87 + 30 * q^89 + 72 * q^90 - 156 * q^92 + 14 * q^93 - 6 * q^95 - 18 * q^96 - 62 * q^97 - 36 * q^99

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