LMFDB - Embedded newform 504.2.cy.a.347.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(347,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5, 4]))

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

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

chi := DirichletCharacter("504.347");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cy (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			347.8
Character	$\chi$	$=$	504.347
Dual form			504.2.cy.a.443.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36752 + 0.360384i) q^{2} +(-0.541502 + 1.64523i) q^{3} +(1.74025 - 0.985669i) q^{4} +0.493530 q^{5} +(0.147602 - 2.44504i) q^{6} +(1.32629 - 2.28931i) q^{7} +(-2.02461 + 1.97508i) q^{8} +(-2.41355 - 1.78179i) q^{9} +O(q^{10})$	\(q+(-1.36752 + 0.360384i) q^{2} +(-0.541502 + 1.64523i) q^{3} +(1.74025 - 0.985669i) q^{4} +0.493530 q^{5} +(0.147602 - 2.44504i) q^{6} +(1.32629 - 2.28931i) q^{7} +(-2.02461 + 1.97508i) q^{8} +(-2.41355 - 1.78179i) q^{9} +(-0.674914 + 0.177860i) q^{10} -2.81800i q^{11} +(0.679304 + 3.39684i) q^{12} +(-1.06812 - 0.616681i) q^{13} +(-0.988708 + 3.60866i) q^{14} +(-0.267247 + 0.811969i) q^{15} +(2.05691 - 3.43061i) q^{16} +(-6.60422 - 3.81295i) q^{17} +(3.94272 + 1.56683i) q^{18} +(-1.68224 - 2.91373i) q^{19} +(0.858863 - 0.486457i) q^{20} +(3.04825 + 3.42172i) q^{21} +(1.01556 + 3.85369i) q^{22} -8.30494 q^{23} +(-2.15313 - 4.40046i) q^{24} -4.75643 q^{25} +(1.68293 + 0.458391i) q^{26} +(4.23839 - 3.00600i) q^{27} +(0.0515758 - 5.29125i) q^{28} +(3.79280 + 6.56932i) q^{29} +(0.0728460 - 1.20670i) q^{30} +(3.59929 - 2.07805i) q^{31} +(-1.57654 + 5.43273i) q^{32} +(4.63626 + 1.52595i) q^{33} +(10.4056 + 2.83424i) q^{34} +(0.654565 - 1.12984i) q^{35} +(-5.95643 - 0.721785i) q^{36} +(2.93183 - 1.69269i) q^{37} +(3.35058 + 3.37835i) q^{38} +(1.59297 - 1.42337i) q^{39} +(-0.999205 + 0.974762i) q^{40} +(2.69756 + 1.55743i) q^{41} +(-5.40169 - 3.58075i) q^{42} +(-4.31794 - 7.47889i) q^{43} +(-2.77762 - 4.90402i) q^{44} +(-1.19116 - 0.879365i) q^{45} +(11.3572 - 2.99297i) q^{46} +(6.36527 - 11.0250i) q^{47} +(4.53032 + 5.24177i) q^{48} +(-3.48189 - 6.07260i) q^{49} +(6.50453 - 1.71414i) q^{50} +(9.84937 - 8.80074i) q^{51} +(-2.46664 - 0.0203613i) q^{52} +(-3.13823 + 5.43557i) q^{53} +(-4.71278 + 5.63823i) q^{54} -1.39077i q^{55} +(1.83635 + 7.25450i) q^{56} +(5.70470 - 1.18989i) q^{57} +(-7.55422 - 7.61683i) q^{58} +(0.986115 - 0.569333i) q^{59} +(0.335257 + 1.67644i) q^{60} +(6.06186 + 3.49981i) q^{61} +(-4.17322 + 4.13892i) q^{62} +(-7.28015 + 3.16220i) q^{63} +(0.198087 - 7.99755i) q^{64} +(-0.527150 - 0.304350i) q^{65} +(-6.89013 - 0.415943i) q^{66} +(3.37236 + 5.84110i) q^{67} +(-15.2513 - 0.125894i) q^{68} +(4.49714 - 13.6635i) q^{69} +(-0.487956 + 1.78098i) q^{70} -3.35435 q^{71} +(8.40568 - 1.15954i) q^{72} +(-5.90713 + 10.2315i) q^{73} +(-3.39933 + 3.37138i) q^{74} +(2.57561 - 7.82541i) q^{75} +(-5.79950 - 3.41248i) q^{76} +(-6.45129 - 3.73750i) q^{77} +(-1.66546 + 2.52058i) q^{78} +(4.20661 + 2.42869i) q^{79} +(1.01515 - 1.69311i) q^{80} +(2.65047 + 8.60087i) q^{81} +(-4.25025 - 1.15767i) q^{82} +(13.4493 - 7.76493i) q^{83} +(8.67739 + 2.95007i) q^{84} +(-3.25938 - 1.88180i) q^{85} +(8.60016 + 8.67145i) q^{86} +(-12.8618 + 2.68272i) q^{87} +(5.56579 + 5.70536i) q^{88} +(-2.03346 + 1.17402i) q^{89} +(1.94585 + 0.773277i) q^{90} +(-2.82842 + 1.62736i) q^{91} +(-14.4526 + 8.18592i) q^{92} +(1.46985 + 7.04693i) q^{93} +(-4.73144 + 17.3709i) q^{94} +(-0.830237 - 1.43801i) q^{95} +(-8.08438 - 5.53560i) q^{96} +(0.673775 + 1.16701i) q^{97} +(6.95004 + 7.04961i) q^{98} +(-5.02108 + 6.80140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9	$ 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 5 q^{12} - 3 q^{14} + q^{16} + 5 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} + 148 q^{25} + 6 q^{26} - 8 q^{27} + 24 q^{30} - 33 q^{32} + 22 q^{33} - 4 q^{34} - 30 q^{35} - 38 q^{36} - 12 q^{40} - 12 q^{41} + 7 q^{42} - 4 q^{43} - 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} + 26 q^{51} - 18 q^{52} - 40 q^{54} + 18 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{60} - 8 q^{64} - 6 q^{65} + 43 q^{66} + 2 q^{67} - 18 q^{70} - 11 q^{72} - 4 q^{73} - 36 q^{75} + 2 q^{76} - 29 q^{78} - 87 q^{80} - 10 q^{81} - 4 q^{82} - 72 q^{83} - 65 q^{84} + 14 q^{88} + 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} + 9 q^{94} - 88 q^{96} - 4 q^{97} - 57 q^{98} + 10 q^{99}+O(q^{100}) $ 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 5 * q^12 - 3 * q^14 + q^16 + 5 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 + 148 * q^25 + 6 * q^26 - 8 * q^27 + 24 * q^30 - 33 * q^32 + 22 * q^33 - 4 * q^34 - 30 * q^35 - 38 * q^36 - 12 * q^40 - 12 * q^41 + 7 * q^42 - 4 * q^43 - 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 + 26 * q^51 - 18 * q^52 - 40 * q^54 + 18 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^60 - 8 * q^64 - 6 * q^65 + 43 * q^66 + 2 * q^67 - 18 * q^70 - 11 * q^72 - 4 * q^73 - 36 * q^75 + 2 * q^76 - 29 * q^78 - 87 * q^80 - 10 * q^81 - 4 * q^82 - 72 * q^83 - 65 * q^84 + 14 * q^88 + 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 + 9 * q^94 - 88 * q^96 - 4 * q^97 - 57 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.36752	+	0.360384i	−0.966986	+	0.254830i
$2$	−1.36752	+	0.360384i	−0.966986	+	0.254830i
$3$	−0.541502	+	1.64523i	−0.312636	+	0.949873i
$3$	−0.541502	+	1.64523i	−0.312636	+	0.949873i
$4$	1.74025	−	0.985669i	0.870123	−	0.492834i
$5$	0.493530			0.220713			0.110357	−	0.993892i	$-0.464801\pi$
$5$	0.493530			0.220713			0.110357	+	0.993892i	$0.464801\pi$
$6$	0.147602	−	2.44504i	0.0602583	−	0.998183i
$7$	1.32629	−	2.28931i	0.501292	−	0.865278i
$7$	1.32629	−	2.28931i	0.501292	−	0.865278i
$8$	−2.02461	+	1.97508i	−0.715808	+	0.698298i
$9$	−2.41355	−	1.78179i	−0.804517	−	0.593929i
$10$	−0.674914	+	0.177860i	−0.213426	+	0.0562444i
$11$		−	2.81800i		−	0.849660i	−0.905273	−	0.424830i	$-0.860334\pi$
$11$		−	2.81800i		−	0.849660i	0.905273	−	0.424830i	$-0.139666\pi$
$12$	0.679304	+	3.39684i	0.196098	+	0.980584i
$13$	−1.06812	−	0.616681i	−0.296244	−	0.171036i	0.344510	−	0.938782i	$-0.388045\pi$
$13$	−1.06812	−	0.616681i	−0.296244	−	0.171036i	−0.640754	+	0.767746i	$0.721378\pi$
$14$	−0.988708	+	3.60866i	−0.264243	+	0.964456i
$15$	−0.267247	+	0.811969i	−0.0690029	+	0.209649i
$16$	2.05691	−	3.43061i	0.514228	−	0.857653i
$17$	−6.60422	−	3.81295i	−1.60176	−	0.924776i	−0.991135	−	0.132855i	$-0.957585\pi$
$17$	−6.60422	−	3.81295i	−1.60176	−	0.924776i	−0.610624	−	0.791921i	$-0.709081\pi$
$18$	3.94272	+	1.56683i	0.929308	+	0.369306i
$19$	−1.68224	−	2.91373i	−0.385933	−	0.668456i	0.605965	−	0.795491i	$-0.292787\pi$
$19$	−1.68224	−	2.91373i	−0.385933	−	0.668456i	−0.991898	+	0.127035i	$0.959454\pi$
$20$	0.858863	−	0.486457i	0.192048	−	0.108775i
$21$	3.04825	+	3.42172i	0.665182	+	0.746681i
$22$	1.01556	+	3.85369i	0.216519	+	0.821609i
$23$	−8.30494			−1.73170			−0.865850	−	0.500303i	$-0.833222\pi$
$23$	−8.30494			−1.73170			−0.865850	+	0.500303i	$0.833222\pi$
$24$	−2.15313	−	4.40046i	−0.439507	−	0.898239i
$25$	−4.75643			−0.951286
$26$	1.68293	+	0.458391i	0.330049	+	0.0898979i
$27$	4.23839	−	3.00600i	0.815678	−	0.578506i
$28$	0.0515758	−	5.29125i	0.00974691	−	0.999952i
$29$	3.79280	+	6.56932i	0.704305	+	1.21989i	0.966942	+	0.254997i	$0.0820744\pi$
$29$	3.79280	+	6.56932i	0.704305	+	1.21989i	−0.262637	+	0.964895i	$0.584592\pi$
$30$	0.0728460	−	1.20670i	0.0132998	−	0.220312i
$31$	3.59929	−	2.07805i	0.646452	−	0.373229i	−0.140643	−	0.990060i	$-0.544917\pi$
$31$	3.59929	−	2.07805i	0.646452	−	0.373229i	0.787096	+	0.616831i	$0.211584\pi$
$32$	−1.57654	+	5.43273i	−0.278696	+	0.960379i
$33$	4.63626	+	1.52595i	0.807069	+	0.265634i
$34$	10.4056	+	2.83424i	1.78454	+	0.486069i
$35$	0.654565	−	1.12984i	0.110642	−	0.190978i
$36$	−5.95643	−	0.721785i	−0.992738	−	0.120298i
$37$	2.93183	−	1.69269i	0.481990	−	0.278277i	−0.239256	−	0.970957i	$-0.576903\pi$
$37$	2.93183	−	1.69269i	0.481990	−	0.278277i	0.721245	+	0.692680i	$0.243570\pi$
$38$	3.35058	+	3.37835i	0.543535	+	0.548040i
$39$	1.59297	−	1.42337i	0.255079	−	0.227922i
$40$	−0.999205	+	0.974762i	−0.157988	+	0.154123i
$41$	2.69756	+	1.55743i	0.421288	+	0.243230i	0.695628	−	0.718402i	$-0.255126\pi$
$41$	2.69756	+	1.55743i	0.421288	+	0.243230i	−0.274341	+	0.961633i	$0.588460\pi$
$42$	−5.40169	−	3.58075i	−0.833499	−	0.552521i
$43$	−4.31794	−	7.47889i	−0.658480	−	1.14052i	−0.981009	−	0.193961i	$-0.937867\pi$
$43$	−4.31794	−	7.47889i	−0.658480	−	1.14052i	0.322530	−	0.946559i	$-0.395467\pi$
$44$	−2.77762	−	4.90402i	−0.418742	−	0.739309i
$45$	−1.19116	−	0.879365i	−0.177568	−	0.131088i
$46$	11.3572	−	2.99297i	1.67453	−	0.441290i
$47$	6.36527	−	11.0250i	0.928471	−	1.60816i	0.142589	−	0.989782i	$-0.454457\pi$
$47$	6.36527	−	11.0250i	0.928471	−	1.60816i	0.785882	−	0.618376i	$-0.212209\pi$
$48$	4.53032	+	5.24177i	0.653895	+	0.756585i
$49$	−3.48189	−	6.07260i	−0.497413	−	0.867514i
$50$	6.50453	−	1.71414i	0.919880	−	0.242416i
$51$	9.84937	−	8.80074i	1.37919	−	1.23235i
$52$	−2.46664	−	0.0203613i	−0.342061	−	0.00282360i
$53$	−3.13823	+	5.43557i	−0.431069	+	0.746633i	−0.996966	−	0.0778433i	$-0.975197\pi$
$53$	−3.13823	+	5.43557i	−0.431069	+	0.746633i	0.565897	+	0.824476i	$0.308530\pi$
$54$	−4.71278	+	5.63823i	−0.641329	+	0.767266i
$55$		−	1.39077i		−	0.187531i
$56$	1.83635	+	7.25450i	0.245393	+	0.969424i
$57$	5.70470	−	1.18989i	0.755605	−	0.157604i
$58$	−7.55422	−	7.61683i	−0.991918	−	1.00014i
$59$	0.986115	−	0.569333i	0.128381	−	0.0741209i	−0.434434	−	0.900704i	$-0.643052\pi$
$59$	0.986115	−	0.569333i	0.128381	−	0.0741209i	0.562815	+	0.826583i	$0.309718\pi$
$60$	0.335257	+	1.67644i	0.0432815	+	0.216428i
$61$	6.06186	+	3.49981i	0.776141	+	0.448105i	0.835061	−	0.550157i	$-0.185432\pi$
$61$	6.06186	+	3.49981i	0.776141	+	0.448105i	−0.0589197	+	0.998263i	$0.518766\pi$
$62$	−4.17322	+	4.13892i	−0.530000	+	0.525643i
$63$	−7.28015	+	3.16220i	−0.917212	+	0.398399i
$64$	0.198087	−	7.99755i	0.0247609	−	0.999693i
$65$	−0.527150	−	0.304350i	−0.0653849	−	0.0377500i
$66$	−6.89013	−	0.415943i	−0.848116	−	0.0511991i
$67$	3.37236	+	5.84110i	0.411999	+	0.713604i	0.995108	−	0.0987902i	$-0.0314973\pi$
$67$	3.37236	+	5.84110i	0.411999	+	0.713604i	−0.583109	+	0.812394i	$0.698164\pi$
$68$	−15.2513	−	0.125894i	−1.84949	−	0.0152669i
$69$	4.49714	−	13.6635i	0.541392	−	1.64490i
$70$	−0.487956	+	1.78098i	−0.0583220	+	0.212868i
$71$	−3.35435			−0.398089			−0.199044	−	0.979990i	$-0.563784\pi$
$71$	−3.35435			−0.398089			−0.199044	+	0.979990i	$0.563784\pi$
$72$	8.40568	−	1.15954i	0.990619	−	0.136654i
$73$	−5.90713	+	10.2315i	−0.691377	+	1.19750i	0.280009	+	0.959997i	$0.409662\pi$
$73$	−5.90713	+	10.2315i	−0.691377	+	1.19750i	−0.971387	+	0.237503i	$0.923671\pi$
$74$	−3.39933	+	3.37138i	−0.395164	+	0.391915i
$75$	2.57561	−	7.82541i	0.297406	−	0.903601i
$76$	−5.79950	−	3.41248i	−0.665248	−	0.391438i
$77$	−6.45129	−	3.73750i	−0.735192	−	0.425928i
$78$	−1.66546	+	2.52058i	−0.188577	+	0.285399i
$79$	4.20661	+	2.42869i	0.473281	+	0.273249i	0.717612	−	0.696443i	$-0.245235\pi$
$79$	4.20661	+	2.42869i	0.473281	+	0.273249i	−0.244331	+	0.969692i	$0.578568\pi$
$80$	1.01515	−	1.69311i	0.113497	−	0.189295i
$81$	2.65047	+	8.60087i	0.294496	+	0.955653i
$82$	−4.25025	−	1.15767i	−0.469362	−	0.127844i
$83$	13.4493	−	7.76493i	1.47625	−	0.852312i	0.476607	−	0.879117i	$-0.341867\pi$
$83$	13.4493	−	7.76493i	1.47625	−	0.852312i	0.999641	+	0.0268048i	$0.00853324\pi$
$84$	8.67739	+	2.95007i	0.946781	+	0.321880i
$85$	−3.25938	−	1.88180i	−0.353529	−	0.204110i
$86$	8.60016	+	8.67145i	0.927380	+	0.935066i
$87$	−12.8618	+	2.68272i	−1.37893	+	0.287618i
$88$	5.56579	+	5.70536i	0.593316	+	0.608193i
$89$	−2.03346	+	1.17402i	−0.215547	+	0.124446i	−0.603887	−	0.797070i	$-0.706382\pi$
$89$	−2.03346	+	1.17402i	−0.215547	+	0.124446i	0.388340	+	0.921516i	$0.373049\pi$
$90$	1.94585	+	0.773277i	0.205110	+	0.0815106i
$91$	−2.82842	+	1.62736i	−0.296499	+	0.170594i
$92$	−14.4526	+	8.18592i	−1.50679	+	0.853442i
$93$	1.46985	+	7.04693i	0.152416	+	0.730733i
$94$	−4.73144	+	17.3709i	−0.488011	+	1.79167i
$95$	−0.830237	−	1.43801i	−0.0851806	−	0.147537i
$96$	−8.08438	−	5.53560i	−0.825108	−	0.564975i
$97$	0.673775	+	1.16701i	0.0684114	+	0.118492i	0.898202	−	0.439583i	$-0.144874\pi$
$97$	0.673775	+	1.16701i	0.0684114	+	0.118492i	−0.829791	+	0.558075i	$0.811540\pi$
$98$	6.95004	+	7.04961i	0.702060	+	0.712118i
$99$	−5.02108	+	6.80140i	−0.504638	+	0.683566i
$100$	−8.27736	+	4.68826i	−0.827736	+	0.468826i
$101$	6.68371			0.665054			0.332527	−	0.943094i	$-0.392099\pi$
$101$	6.68371			0.665054			0.332527	+	0.943094i	$0.392099\pi$
$102$	−10.2976	+	15.5848i	−1.01961	+	1.54312i
$103$		−	8.52804i		−	0.840293i	−0.907456	−	0.420146i	$-0.861979\pi$
$103$		−	8.52804i		−	0.840293i	0.907456	−	0.420146i	$-0.138021\pi$
$104$	3.38053	−	0.861093i	0.331488	−	0.0844371i
$105$	1.50440	+	1.68872i	0.146814	+	0.164802i
$106$	2.33271	−	8.56424i	0.226573	−	0.831832i
$107$	−9.45941	+	5.46139i	−0.914476	+	0.527973i	−0.881869	−	0.471495i	$-0.843714\pi$
$107$	−9.45941	+	5.46139i	−0.914476	+	0.527973i	−0.0326073	+	0.999468i	$0.510381\pi$
$108$	4.41292	−	9.40883i	0.424633	−	0.905366i
$109$	1.48784	+	0.859005i	0.142509	+	0.0822778i	0.569559	−	0.821950i	$-0.307114\pi$
$109$	1.48784	+	0.859005i	0.142509	+	0.0822778i	−0.427050	+	0.904228i	$0.640447\pi$
$110$	0.501211	+	1.90191i	0.0477886	+	0.181340i
$111$	1.19727	+	5.74012i	0.113640	+	0.544828i
$112$	−5.12567	−	9.25892i	−0.484330	−	0.874885i
$113$	−7.38337	−	4.26279i	−0.694569	−	0.401009i	0.110753	−	0.993848i	$-0.464674\pi$
$113$	−7.38337	−	4.26279i	−0.694569	−	0.401009i	−0.805321	+	0.592839i	$0.798007\pi$
$114$	−7.37249	+	3.68308i	−0.690497	+	0.344952i
$115$	−4.09873			−0.382209
$116$	13.0756	+	7.69378i	1.21404	+	0.714350i
$117$	1.47917	+	3.39156i	0.136750	+	0.313550i
$118$	−1.14336	+	1.13396i	−0.105255	+	0.104389i
$119$	−17.4882	+	10.0620i	−1.60314	+	0.922384i
$120$	−1.06264	−	2.17175i	−0.0970049	−	0.198253i
$121$	3.05886			0.278078
$122$	−9.55102	−	2.60148i	−0.864708	−	0.235527i
$123$	−4.02307	+	3.59474i	−0.362748	+	0.324127i
$124$	4.21539	−	7.16404i	0.378553	−	0.643350i
$125$	−4.81509			−0.430674
$126$	8.81617	−	6.94803i	0.785407	−	0.618980i
$127$			17.2993i			1.53507i	0.641010	+	0.767533i	$0.278516\pi$
$127$			17.2993i			1.53507i	−0.641010	+	0.767533i	$0.721484\pi$
$128$	2.61130	+	11.0082i	0.230809	+	0.972999i
$129$	14.6427	−	3.05417i	1.28921	−	0.268904i
$130$	0.830573	+	0.226230i	0.0728461	+	0.0198416i
$131$		−	12.9009i		−	1.12715i	−0.826063	−	0.563577i	$-0.809425\pi$
$131$		−	12.9009i		−	1.12715i	0.826063	−	0.563577i	$-0.190575\pi$
$132$	9.57232	−	1.91428i	0.833163	−	0.166617i
$133$	−8.90159	−	0.0132864i	−0.771866	−	0.00115207i
$134$	−6.71682	−	6.77250i	−0.580245	−	0.585055i
$135$	2.09177	−	1.48355i	0.180031	−	0.127684i
$136$	20.9019	−	5.32416i	1.79232	−	0.456543i
$137$		−	5.10488i		−	0.436140i	−0.975933	−	0.218070i	$-0.930024\pi$
$137$		−	5.10488i		−	0.436140i	0.975933	−	0.218070i	$-0.0699760\pi$
$138$	−1.22583	+	20.3059i	−0.104349	+	1.72855i
$139$	−5.63690	+	9.76340i	−0.478116	+	0.828121i	−0.999685	−	0.0250882i	$-0.992013\pi$
$139$	−5.63690	+	9.76340i	−0.478116	+	0.828121i	0.521570	+	0.853209i	$0.325347\pi$
$140$	0.0254542	−	2.61139i	0.00215127	−	0.220703i
$141$	14.6918	+	16.4424i	1.23727	+	1.38470i
$142$	4.58716	−	1.20886i	0.384946	−	0.101445i
$143$	−1.73781	+	3.00997i	−0.145323	+	0.251706i
$144$	−11.0771	+	4.61498i	−0.923091	+	0.384582i
$145$	1.87186	+	3.24215i	0.155449	+	0.269246i
$146$	4.39089	−	16.1206i	0.363393	−	1.33415i
$147$	11.8763	−	2.44018i	0.979537	−	0.201263i
$148$	3.43367	−	5.83551i	0.282246	−	0.479676i
$149$	3.89774			0.319315			0.159658	−	0.987172i	$-0.448961\pi$
$149$	3.89774			0.319315			0.159658	+	0.987172i	$0.448961\pi$
$150$	−0.702059	+	11.6297i	−0.0573228	+	0.949557i
$151$		−	6.44147i		−	0.524200i	−0.965041	−	0.262100i	$-0.915585\pi$
$151$		−	6.44147i		−	0.524200i	0.965041	−	0.262100i	$-0.0844150\pi$
$152$	9.16076	+	2.57660i	0.743036	+	0.208990i
$153$	9.14577	+	20.9701i	0.739392	+	1.69533i
$154$	10.1692	+	2.78618i	0.819460	+	0.224517i
$155$	1.77636	−	1.02558i	0.142681	−	0.0823766i
$156$	1.36919	−	4.04716i	0.109623	−	0.324032i
$157$	−12.6639	+	7.31148i	−1.01069	+	0.583520i	−0.911392	−	0.411538i	$-0.864992\pi$
$157$	−12.6639	+	7.31148i	−1.01069	+	0.583520i	−0.0992936	+	0.995058i	$0.531658\pi$
$158$	−6.62791	−	1.80529i	−0.527288	−	0.143622i
$159$	−7.24339	−	8.10647i	−0.574439	−	0.642885i
$160$	−0.778069	+	2.68121i	−0.0615118	+	0.211968i
$161$	−11.0148	+	19.0126i	−0.868088	+	1.49840i
$162$	−6.72420	−	10.8067i	−0.528303	−	0.849056i
$163$	4.48262	+	7.76412i	0.351106	+	0.608133i	0.986443	−	0.164101i	$-0.0524724\pi$
$163$	4.48262	+	7.76412i	0.351106	+	0.608133i	−0.635338	+	0.772234i	$0.719139\pi$
$164$	6.22953	+	0.0514227i	0.486444	+	0.00401544i
$165$	2.28813	+	0.753103i	0.178131	+	0.0586290i
$166$	−15.5938	+	15.4656i	−1.21032	+	1.20037i
$167$	6.23995	−	10.8079i	0.482862	−	0.836342i	−0.516944	−	0.856019i	$-0.672931\pi$
$167$	6.23995	−	10.8079i	0.482862	−	0.836342i	0.999806	+	0.0196773i	$0.00626387\pi$
$168$	−12.9297	−	0.907104i	−0.997548	−	0.0699846i
$169$	−5.73941	−	9.94095i	−0.441493	−	0.764688i
$170$	5.13545	+	1.39878i	0.393871	+	0.107282i
$171$	−1.13147	+	10.0299i	−0.0865255	+	0.767002i
$172$	−14.8860	−	8.75905i	−1.13505	−	0.667872i
$173$	2.24448	−	3.88755i	0.170645	−	0.295565i	−0.768001	−	0.640449i	$-0.778748\pi$
$173$	2.24448	−	3.88755i	0.170645	−	0.295565i	0.938645	+	0.344884i	$0.112082\pi$
$174$	16.6221	−	8.30389i	1.26011	−	0.629516i
$175$	−6.30842	+	10.8889i	−0.476872	+	0.823127i
$176$	−9.66748	−	5.79639i	−0.728714	−	0.436919i
$177$	0.402701	+	1.93068i	0.0302689	+	0.145119i
$178$	2.35771	−	2.33833i	0.176718	−	0.175265i
$179$	−7.27282	−	4.19897i	−0.543596	−	0.313846i	0.202939	−	0.979191i	$-0.434951\pi$
$179$	−7.27282	−	4.19897i	−0.543596	−	0.313846i	−0.746535	+	0.665346i	$0.768284\pi$
$180$	−2.93967	−	0.356222i	−0.219110	−	0.0265513i
$181$		−	14.1954i		−	1.05514i	−0.849512	−	0.527569i	$-0.823104\pi$
$181$		−	14.1954i		−	1.05514i	0.849512	−	0.527569i	$-0.176896\pi$
$182$	3.28145	−	3.24478i	0.243238	−	0.240519i
$183$	−9.04050	+	8.07798i	−0.668293	+	0.597142i
$184$	16.8143	−	16.4030i	1.23956	−	1.20924i
$185$	1.44694	−	0.835393i	0.106381	−	0.0614193i
$186$	−4.54966	−	9.10714i	−0.333597	−	0.667768i
$187$	−10.7449	+	18.6107i	−0.785745	+	1.36095i
$188$	0.210166	−	25.4602i	0.0153279	−	1.85688i
$189$	−1.26033	−	13.6898i	−0.0916752	−	0.995789i
$190$	1.65361	+	1.66731i	0.119965	+	0.120960i
$191$	6.60209	−	11.4352i	0.477711	−	0.827419i	−0.521963	−	0.852968i	$-0.674800\pi$
$191$	6.60209	−	11.4352i	0.477711	−	0.827419i	0.999674	+	0.0255491i	$0.00813343\pi$
$192$	13.0505	+	4.65658i	0.941841	+	0.336060i
$193$	−1.80182	−	3.12085i	−0.129698	−	0.224643i	0.793862	−	0.608098i	$-0.208067\pi$
$193$	−1.80182	−	3.12085i	−0.129698	−	0.224643i	−0.923560	+	0.383455i	$0.874734\pi$
$194$	−1.34198	−	1.35310i	−0.0963483	−	0.0971469i
$195$	0.786178	−	0.702476i	0.0562994	−	0.0503053i
$196$	−12.0449	−	7.13583i	−0.860351	−	0.509702i
$197$	18.1668			1.29433			0.647166	−	0.762349i	$-0.275954\pi$
$197$	18.1668			1.29433			0.647166	+	0.762349i	$0.275954\pi$
$198$	4.41534	−	11.1106i	0.313784	−	0.789596i
$199$	−2.55436	−	1.47476i	−0.181074	−	0.104543i	0.406723	−	0.913551i	$-0.366671\pi$
$199$	−2.55436	−	1.47476i	−0.181074	−	0.104543i	−0.587797	+	0.809008i	$0.700005\pi$
$200$	9.62991	−	9.39435i	0.680938	−	0.664281i
$201$	−11.4361	+	2.38534i	−0.806639	+	0.168249i
$202$	−9.14014	+	2.40870i	−0.643098	+	0.169476i
$203$	20.0696	+	0.0299555i	1.40861	+	0.00210246i
$204$	8.46572	−	25.0237i	0.592719	−	1.75201i
$205$	1.33132	+	0.768640i	0.0929837	+	0.0536841i
$206$	3.07337	+	11.6623i	0.214132	+	0.812551i
$207$	20.0444	+	14.7976i	1.39318	+	1.02851i
$208$	−4.31263	+	2.39585i	−0.299027	+	0.166123i
$209$	−8.21091	+	4.74057i	−0.567961	+	0.327912i
$210$	−2.66589	−	1.76720i	−0.183964	−	0.121949i
$211$	−12.2213	+	21.1680i	−0.841351	+	1.45726i	0.0474015	+	0.998876i	$0.484906\pi$
$211$	−12.2213	+	21.1680i	−0.841351	+	1.45726i	−0.888753	+	0.458387i	$0.848427\pi$
$212$	−0.103617	+	12.5525i	−0.00711642	+	0.862108i
$213$	1.81639	−	5.51868i	0.124457	−	0.378134i
$214$	10.9678	−	10.8776i	0.749742	−	0.743578i
$215$	−2.13103	−	3.69105i	−0.145335	−	0.251728i
$216$	−2.64397	+	14.4572i	−0.179900	+	0.983685i
$217$	0.0164125	−	10.9960i	0.00111415	−	0.746458i
$218$	−2.34423	−	0.638516i	−0.158771	−	0.0432458i
$219$	−13.6344	−	15.2589i	−0.921324	−	1.03110i
$220$	−1.37084	−	2.42028i	−0.0924218	−	0.163175i
$221$	4.70274	+	8.14539i	0.316341	+	0.547918i
$222$	−3.70595	−	7.41828i	−0.248727	−	0.497882i
$223$	2.78186	−	1.60611i	0.186287	−	0.107553i	−0.403956	−	0.914778i	$-0.632365\pi$
$223$	2.78186	−	1.60611i	0.186287	−	0.107553i	0.590243	+	0.807226i	$0.299032\pi$
$224$	10.3462	+	10.8146i	0.691288	+	0.722580i
$225$	11.4799	+	8.47494i	0.765326	+	0.564996i
$226$	11.6332	+	3.16862i	0.773827	+	0.210773i
$227$		−	10.3578i		−	0.687470i	−0.939067	−	0.343735i	$-0.888308\pi$
$227$		−	10.3578i		−	0.687470i	0.939067	−	0.343735i	$-0.111692\pi$
$228$	8.75474	−	7.69363i	0.579797	−	0.509523i
$229$		−	21.0384i		−	1.39025i	−0.718887	−	0.695127i	$-0.755348\pi$
$229$		−	21.0384i		−	1.39025i	0.718887	−	0.695127i	$-0.244652\pi$
$230$	5.60512	−	1.47712i	0.369591	−	0.0973984i
$231$	9.64242	−	8.58997i	0.634425	−	0.565179i
$232$	−20.6539	−	5.80921i	−1.35599	−	0.381393i
$233$	−2.23891	+	1.29264i	−0.146676	+	0.0846835i	−0.571542	−	0.820573i	$-0.693655\pi$
$233$	−2.23891	+	1.29264i	−0.146676	+	0.0846835i	0.424866	+	0.905256i	$0.360321\pi$
$234$	−3.24507	−	4.10497i	−0.212137	−	0.268350i
$235$	3.14145	−	5.44115i	0.204926	−	0.354942i
$236$	1.15491	−	1.96276i	0.0751781	−	0.127765i
$237$	−6.27364	+	5.60570i	−0.407516	+	0.364129i
$238$	20.2893	−	20.0625i	1.31516	−	1.30046i
$239$	9.86857	−	17.0929i	0.638345	−	1.10565i	−0.347451	−	0.937698i	$-0.612953\pi$
$239$	9.86857	−	17.0929i	0.638345	−	1.10565i	0.985796	−	0.167948i	$-0.0537140\pi$
$240$	2.23585	+	2.58697i	0.144323	+	0.166988i
$241$	−3.73096			−0.240332			−0.120166	−	0.992754i	$-0.538343\pi$
$241$	−3.73096			−0.240332			−0.120166	+	0.992754i	$0.538343\pi$
$242$	−4.18306	+	1.10236i	−0.268897	+	0.0708627i
$243$	−15.5856	−	0.296762i	−0.999819	−	0.0190373i
$244$	13.9988	+	0.115555i	0.896180	+	0.00739767i
$245$	−1.71841	−	2.99701i	−0.109785	−	0.191472i
$246$	4.20615	−	6.36575i	0.268175	−	0.405865i
$247$			4.14963i			0.264035i
$248$	−3.18284	+	11.3162i	−0.202110	+	0.718577i
$249$	5.49229	+	26.3318i	0.348060	+	1.66871i
$250$	6.58475	−	1.73528i	0.416456	−	0.109749i
$251$		−	20.0259i		−	1.26402i	−0.774959	−	0.632012i	$-0.782229\pi$
$251$		−	20.0259i		−	1.26402i	0.774959	−	0.632012i	$-0.217771\pi$
$252$	−9.55237	+	12.6788i	−0.601742	+	0.798690i
$253$			23.4034i			1.47136i
$254$	−6.23440	−	23.6572i	−0.391181	−	1.48439i
$255$	4.86095	−	4.34342i	0.304405	−	0.271996i
$256$	−7.53821	−	14.1129i	−0.471138	−	0.882059i
$257$		−	15.5911i		−	0.972543i	−0.873808	−	0.486272i	$-0.838357\pi$
$257$		−	15.5911i		−	0.972543i	0.873808	−	0.486272i	$-0.161643\pi$
$258$	−18.9235	+	9.45363i	−1.17813	+	0.588557i
$259$	0.0133689	−	8.95687i	0.000830702	−	0.556553i
$260$	−1.21736	−	0.0100489i	−0.0754974	−	0.000623206i
$261$	2.55101	−	22.6133i	0.157904	−	1.39973i
$262$	4.64927	+	17.6423i	0.287233	+	1.08994i
$263$	3.31077			0.204151			0.102075	−	0.994777i	$-0.467452\pi$
$263$	3.31077			0.204151			0.102075	+	0.994777i	$0.467452\pi$
$264$	−12.4005	+	6.06754i	−0.763198	+	0.373431i
$265$	−1.54881	+	2.68261i	−0.0951425	+	0.164792i
$266$	12.1779	−	3.18983i	0.746677	−	0.195581i
$267$	−0.830408	−	3.98124i	−0.0508201	−	0.243648i
$268$	11.6261	+	6.84092i	0.710179	+	0.417876i
$269$	1.06771	−	1.84932i	0.0650992	−	0.112755i	−0.831639	−	0.555317i	$-0.812597\pi$
$269$	1.06771	−	1.84932i	0.0650992	−	0.112755i	0.896738	+	0.442562i	$0.145930\pi$
$270$	−2.32590	+	2.78263i	−0.141550	+	0.169346i
$271$	1.02266	−	0.590432i	0.0621221	−	0.0358662i	−0.468617	−	0.883401i	$-0.655248\pi$
$271$	1.02266	−	0.590432i	0.0621221	−	0.0358662i	0.530739	+	0.847535i	$0.321914\pi$
$272$	−26.6651	+	14.8136i	−1.61681	+	0.898208i
$273$	−1.14579	−	5.53461i	−0.0693465	−	0.334970i
$274$	1.83972	+	6.98105i	0.111142	+	0.421741i
$275$			13.4036i			0.808269i
$276$	−5.64158	−	28.2106i	−0.339583	−	1.69808i
$277$		−	13.5241i		−	0.812587i	−0.913743	−	0.406294i	$-0.866821\pi$
$277$		−	13.5241i		−	0.812587i	0.913743	−	0.406294i	$-0.133179\pi$
$278$	4.19002	−	15.3831i	0.251301	−	0.922619i
$279$	−12.3897	−	1.39769i	−0.741754	−	0.0836773i
$280$	0.906294	+	3.58031i	0.0541615	+	0.213965i
$281$	0.117926	−	0.0680848i	0.00703489	−	0.00406160i	−0.496478	−	0.868049i	$-0.665374\pi$
$281$	0.117926	−	0.0680848i	0.00703489	−	0.00406160i	0.503513	+	0.863987i	$0.332040\pi$
$282$	−26.0170	−	17.1907i	−1.54929	−	1.02369i
$283$	10.6888	+	18.5135i	0.635382	+	1.10051i	0.986434	+	0.164158i	$0.0524905\pi$
$283$	10.6888	+	18.5135i	0.635382	+	1.10051i	−0.351052	+	0.936356i	$0.614176\pi$
$284$	−5.83740	+	3.30628i	−0.346386	+	0.196192i
$285$	2.81544	−	0.587244i	0.166772	−	0.0347853i
$286$	1.29175	−	4.74249i	0.0763827	−	0.280429i
$287$	7.14321	−	4.10993i	0.421650	−	0.242601i
$288$	13.4850	−	10.3031i	0.794613	−	0.607117i
$289$	20.5772	+	35.6407i	1.21042	+	2.09651i
$290$	−3.72823	−	3.75913i	−0.218929	−	0.220744i
$291$	−2.28485	+	0.476574i	−0.133940	+	0.0279373i
$292$	−0.195039	+	23.6277i	−0.0114138	+	1.38271i
$293$	−11.0585	+	19.1538i	−0.646043	+	1.11898i	0.338016	+	0.941140i	$0.390244\pi$
$293$	−11.0585	+	19.1538i	−0.646043	+	1.11898i	−0.984059	+	0.177840i	$0.943089\pi$
$294$	−15.3617	+	7.61702i	−0.895911	+	0.444234i
$295$	0.486677	−	0.280983i	0.0283354	−	0.0163595i
$296$	−2.59260	+	9.21765i	−0.150692	+	0.535765i
$297$	−8.47093	−	11.9438i	−0.491533	−	0.693049i
$298$	−5.33025	+	1.40468i	−0.308773	+	0.0813712i
$299$	8.87069	+	5.12150i	0.513005	+	0.296184i
$300$	−3.23106	−	16.1568i	−0.186545	−	0.932816i
$301$	−22.8484	−	0.0341031i	−1.31696	−	0.00196567i
$302$	2.32141	+	8.80887i	0.133582	+	0.506894i
$303$	−3.61924	+	10.9962i	−0.207920	+	0.631717i
$304$	−13.4561	−	0.222167i	−0.771762	−	0.0127421i
$305$	2.99171	+	1.72726i	0.171305	+	0.0989027i
$306$	−20.0644	−	25.3811i	−1.14700	−	1.45094i
$307$	5.51511			0.314764			0.157382	−	0.987538i	$-0.449695\pi$
$307$	5.51511			0.314764			0.157382	+	0.987538i	$0.449695\pi$
$308$	−14.9108	−	0.145341i	−0.849620	−	0.00828156i
$309$	14.0306	+	4.61795i	0.798171	+	0.262706i
$310$	−2.05961	+	2.04268i	−0.116978	+	0.116016i
$311$	6.14346	+	10.6408i	0.348364	+	0.603384i	0.985959	−	0.166988i	$-0.0534040\pi$
$311$	6.14346	+	10.6408i	0.348364	+	0.603384i	−0.637595	+	0.770372i	$0.720071\pi$
$312$	−0.413865	+	6.02802i	−0.0234305	+	0.341269i
$313$	3.58969	−	6.21753i	0.202902	−	0.351436i	−0.746561	−	0.665317i	$-0.768296\pi$
$313$	3.58969	−	6.21753i	0.202902	−	0.351436i	0.949462	+	0.313882i	$0.101630\pi$
$314$	14.6832	−	14.5625i	0.828621	−	0.821809i
$315$	−3.59297	+	1.56064i	−0.202441	+	0.0879320i
$316$	9.71443	+	0.0801894i	0.546479	+	0.00451101i
$317$	−15.8964	+	27.5333i	−0.892829	+	1.54643i	−0.0563612	+	0.998410i	$0.517950\pi$
$317$	−15.8964	+	27.5333i	−0.892829	+	1.54643i	−0.836468	+	0.548015i	$0.815383\pi$
$318$	12.8270	+	8.47538i	0.719300	+	0.475276i
$319$	18.5124	−	10.6881i	1.03649	−	0.598419i
$320$	0.0977620	−	3.94703i	0.00546506	−	0.220645i
$321$	−3.86295	−	18.5202i	−0.215609	−	1.03370i
$322$	8.21116	−	29.9698i	0.457590	−	1.67015i
$323$			25.6573i			1.42761i
$324$	13.0901	+	12.3552i	0.727227	+	0.686397i
$325$	5.08045	+	2.93320i	0.281812	+	0.162704i
$326$	−8.92816	−	9.00216i	−0.494485	−	0.498584i
$327$	−2.21893	+	1.98268i	−0.122707	+	0.109643i
$328$	−8.53756	+	2.17470i	−0.471408	+	0.120078i
$329$	−16.7974	−	29.1945i	−0.926069	−	1.60954i
$330$	−3.40048	−	0.205280i	−0.187190	−	0.0113003i
$331$	−0.872258	+	1.51080i	−0.0479437	+	0.0830409i	−0.889001	−	0.457905i	$-0.848600\pi$
$331$	−0.872258	+	1.51080i	−0.0479437	+	0.0830409i	0.841058	+	0.540945i	$0.181933\pi$
$332$	15.7514	−	26.7694i	0.864468	−	1.46916i
$333$	−10.0921	−	1.13849i	−0.553046	−	0.0623891i
$334$	−4.63829	+	17.0289i	−0.253796	+	0.931779i
$335$	1.66436	+	2.88275i	0.0909336	+	0.157502i
$336$	18.0086	−	3.41917i	0.982449	−	0.186531i
$337$	10.6876	−	18.5114i	0.582188	−	1.00838i	−0.413031	−	0.910717i	$-0.635530\pi$
$337$	10.6876	−	18.5114i	0.582188	−	1.00838i	0.995220	−	0.0976629i	$-0.0311367\pi$
$338$	11.4313	+	11.5261i	0.621783	+	0.626937i
$339$	11.0114	−	9.83902i	0.598055	−	0.534382i
$340$	−7.52696	−	0.0621326i	−0.408207	−	0.00336961i
$341$	−5.85596	−	10.1428i	−0.317118	−	0.549265i
$342$	−2.06729	−	14.1238i	−0.111786	−	0.763729i
$343$	−18.5201	−	0.0829287i	−0.999990	−	0.00447773i
$344$	23.5136	+	6.61354i	1.26777	+	0.356578i
$345$	2.21947	−	6.74335i	0.119492	−	0.363050i
$346$	−1.66837	+	6.12520i	−0.0896919	+	0.329293i
$347$	16.4114	−	9.47511i	0.881009	−	0.508651i	0.0100177	−	0.999950i	$-0.496811\pi$
$347$	16.4114	−	9.47511i	0.881009	−	0.508651i	0.870991	+	0.491299i	$0.163478\pi$
$348$	−19.7385	+	17.3461i	−1.05809	+	0.929848i
$349$	6.12272	−	3.53495i	0.327742	−	0.189222i	−0.327096	−	0.944991i	$-0.606070\pi$
$349$	6.12272	−	3.53495i	0.327742	−	0.189222i	0.654838	+	0.755769i	$0.272737\pi$
$350$	4.70272	−	17.1644i	0.251371	−	0.917473i
$351$	−6.38086	+	0.597046i	−0.340585	+	0.0318680i
$352$	15.3094	+	4.44270i	0.815996	+	0.236796i
$353$			8.69062i			0.462555i	0.972888	+	0.231278i	$0.0742906\pi$
$353$			8.69062i			0.462555i	−0.972888	+	0.231278i	$0.925709\pi$
$354$	−1.24649	−	2.49512i	−0.0662502	−	0.132614i
$355$	−1.65547			−0.0878634
$356$	−2.38153	+	4.04741i	−0.126221	+	0.214512i
$357$	−7.08446	−	34.2206i	−0.374949	−	1.81115i
$358$	11.4590	+	3.12118i	0.605627	+	0.164959i
$359$	2.04030	+	3.53390i	0.107683	+	0.186512i	0.914831	−	0.403836i	$-0.132324\pi$
$359$	2.04030	+	3.53390i	0.107683	+	0.186512i	−0.807148	+	0.590349i	$0.798990\pi$
$360$	4.14845	−	0.572269i	0.218643	−	0.0301612i
$361$	3.84010	−	6.65126i	0.202111	−	0.350066i
$362$	5.11581	+	19.4126i	0.268881	+	1.02030i
$363$	−1.65638	+	5.03252i	−0.0869372	+	0.264139i
$364$	−3.31810	+	5.61990i	−0.173916	+	0.294563i
$365$	−2.91534	+	5.04952i	−0.152596	+	0.264304i
$366$	9.45193	−	14.3049i	0.494060	−	0.747729i
$367$		−	4.92080i		−	0.256864i	−0.991718	−	0.128432i	$-0.959006\pi$
$367$		−	4.92080i		−	0.256864i	0.991718	−	0.128432i	$-0.0409944\pi$
$368$	−17.0826	+	28.4910i	−0.890490	+	1.48520i
$369$	−3.73567	−	8.56542i	−0.194471	−	0.445898i
$370$	−1.67767	+	1.66388i	−0.0872178	+	0.0865008i
$371$	8.28149	+	14.3935i	0.429954	+	0.747275i
$372$	9.50384	+	10.8146i	0.492751	+	0.560711i
$373$			28.0489i			1.45231i	0.687528	+	0.726157i	$0.258696\pi$
$373$			28.0489i			1.45231i	−0.687528	+	0.726157i	$0.741304\pi$
$374$	7.98691	−	29.3229i	0.412993	−	1.51625i
$375$	2.60738	−	7.92191i	0.134644	−	0.409086i
$376$	8.88806	+	34.8932i	0.458367	+	1.79948i
$377$		−	9.35577i		−	0.481847i
$378$	6.65713	+	18.2670i	0.342406	+	0.939552i
$379$	4.59576			0.236068			0.118034	−	0.993010i	$-0.462341\pi$
$379$	4.59576			0.236068			0.118034	+	0.993010i	$0.462341\pi$
$380$	−2.86222	−	1.68416i	−0.146829	−	0.0863955i
$381$	−28.4613	−	9.36760i	−1.45812	−	0.479917i
$382$	−4.90747	+	18.0171i	−0.251088	+	0.921838i
$383$	21.4031			1.09365			0.546825	−	0.837247i	$-0.315836\pi$
$383$	21.4031			1.09365			0.546825	+	0.837247i	$0.315836\pi$
$384$	−19.5251	−	1.66479i	−0.996385	−	0.0849557i
$385$	−3.18390	−	1.84457i	−0.162267	−	0.0940078i
$386$	3.58874	+	3.61848i	0.182662	+	0.184176i
$387$	−2.90422	+	25.7443i	−0.147630	+	1.30866i
$388$	2.32282	+	1.36677i	0.117923	+	0.0693872i
$389$	8.40999			0.426403			0.213202	−	0.977008i	$-0.431611\pi$
$389$	8.40999			0.426403			0.213202	+	0.977008i	$0.431611\pi$
$390$	−0.821956	+	1.24398i	−0.0416214	+	0.0629913i
$391$	54.8477	+	31.6663i	2.77377	+	1.60144i
$392$	19.0434	+	5.41762i	0.961835	+	0.273631i
$393$	21.2249	+	6.98584i	1.07065	+	0.352389i
$394$	−24.8436	+	6.54704i	−1.25160	+	0.329835i
$395$	2.07609	+	1.19863i	0.104459	+	0.0603096i
$396$	−2.03399	+	16.7852i	−0.102212	+	0.843490i
$397$	0.699141	−	0.403649i	0.0350889	−	0.0202586i	−0.482353	−	0.875977i	$-0.660218\pi$
$397$	0.699141	−	0.403649i	0.0350889	−	0.0202586i	0.517442	+	0.855718i	$0.326884\pi$
$398$	4.02464	+	1.09622i	0.201737	+	0.0549486i
$399$	4.84209	−	14.6380i	0.242407	−	0.732815i
$400$	−9.78356	+	16.3175i	−0.489178	+	0.815873i
$401$		−	22.4408i		−	1.12064i	−0.828276	−	0.560320i	$-0.810678\pi$
$401$		−	22.4408i		−	1.12064i	0.828276	−	0.560320i	$-0.189322\pi$
$402$	14.7795	−	7.38339i	0.737133	−	0.368250i
$403$	−5.12598			−0.255343
$404$	11.6313	−	6.58792i	0.578679	−	0.327761i
$405$	1.30808	+	4.24478i	0.0649992	+	0.210925i
$406$	−27.4564	+	7.19179i	−1.36264	+	0.356923i
$407$	−4.77001	−	8.26190i	−0.236441	−	0.409527i
$408$	−2.55894	+	37.2714i	−0.126686	+	1.84521i
$409$	−10.3667	−	17.9556i	−0.512598	−	0.887847i	−0.999893	−	0.0146091i	$-0.995350\pi$
$409$	−10.3667	−	17.9556i	−0.512598	−	0.887847i	0.487295	−	0.873238i	$-0.337984\pi$
$410$	−2.09762	−	0.571346i	−0.103594	−	0.0282168i
$411$	8.39870	+	2.76430i	0.414277	+	0.136353i
$412$	−8.40582	−	14.8409i	−0.414125	−	0.731158i
$413$	0.00449659	−	3.01263i	0.000221263	−	0.148242i
$414$	−32.7441	−	13.0124i	−1.60928	−	0.639527i
$415$	6.63760	−	3.83222i	0.325827	−	0.188116i
$416$	5.03419	−	4.83059i	0.246822	−	0.236839i
$417$	−13.0106	−	14.5609i	−0.637133	−	0.713049i
$418$	9.52019	−	9.44193i	0.465648	−	0.461820i
$419$	−8.66133	−	5.00062i	−0.423133	−	0.244296i	0.273284	−	0.961934i	$-0.411890\pi$
$419$	−8.66133	−	5.00062i	−0.423133	−	0.244296i	−0.696417	+	0.717637i	$0.745224\pi$
$420$	4.28255	+	1.45595i	0.208967	+	0.0710430i
$421$	−32.0923	+	18.5285i	−1.56408	+	0.903023i	−0.567244	+	0.823550i	$0.691990\pi$
$421$	−32.0923	+	18.5285i	−1.56408	+	0.903023i	−0.996837	+	0.0794731i	$0.974676\pi$
$422$	9.08436	−	33.3521i	0.442220	−	1.62355i
$423$	−35.0071	+	15.2678i	−1.70210	+	0.742346i
$424$	−4.38202	−	17.2032i	−0.212810	−	0.835459i
$425$	31.4125	+	18.1360i	1.52373	+	0.879726i
$426$	−0.495109	+	8.20152i	−0.0239881	+	0.397365i
$427$	16.0520	−	9.23569i	0.776809	−	0.446946i
$428$	−11.0786	+	18.8280i	−0.535503	+	0.910087i
$429$	−4.01106	−	4.48899i	−0.193656	−	0.216731i
$430$	4.24443	+	4.27962i	0.204685	+	0.206381i
$431$	−8.52826	+	14.7714i	−0.410792	+	0.711513i	−0.994977	−	0.100108i	$-0.968081\pi$
$431$	−8.52826	+	14.7714i	−0.410792	+	0.711513i	0.584185	+	0.811621i	$0.301414\pi$
$432$	−1.59443	−	20.7234i	−0.0767123	−	0.997053i
$433$	−20.4041			−0.980558			−0.490279	−	0.871565i	$-0.663105\pi$
$433$	−20.4041			−0.980558			−0.490279	+	0.871565i	$0.663105\pi$
$434$	3.94035	+	15.0432i	0.189143	+	0.722098i
$435$	−6.34769	+	1.32400i	−0.304349	+	0.0634810i
$436$	3.43590	+	0.0283623i	0.164550	+	0.00135831i
$437$	13.9709	+	24.1984i	0.668321	+	1.15757i
$438$	24.1444	+	15.9533i	1.15366	+	0.762280i
$439$	24.8140	+	14.3264i	1.18431	+	0.683761i	0.957007	−	0.290064i	$-0.0936765\pi$
$439$	24.8140	+	14.3264i	1.18431	+	0.683761i	0.227301	+	0.973825i	$0.427010\pi$
$440$	2.74688	+	2.81576i	0.130953	+	0.134236i
$441$	−2.41636	+	20.8605i	−0.115065	+	0.993358i
$442$	−9.36659	−	9.44423i	−0.445523	−	0.449216i
$443$	8.71486	+	5.03152i	0.414055	+	0.239055i	0.692531	−	0.721388i	$-0.256496\pi$
$443$	8.71486	+	5.03152i	0.414055	+	0.239055i	−0.278475	+	0.960443i	$0.589829\pi$
$444$	7.74141	+	8.80911i	0.367391	+	0.418062i
$445$	−1.00357	+	0.579414i	−0.0475740	+	0.0274668i
$446$	−3.22544	+	3.19893i	−0.152729	+	0.151474i
$447$	−2.11063	+	6.41267i	−0.0998295	+	0.303309i
$448$	−18.0461	−	11.0606i	−0.852600	−	0.522563i
$449$		−	4.10707i		−	0.193825i	−0.995293	−	0.0969123i	$-0.969103\pi$
$449$		−	4.10707i		−	0.193825i	0.995293	−	0.0969123i	$-0.0308966\pi$
$450$	−18.7533	−	7.45252i	−0.884037	−	0.351315i
$451$	4.38886	−	7.60172i	0.206663	−	0.357951i
$452$	−17.0506	−	0.140747i	−0.801992	−	0.00662018i
$453$	10.5977	+	3.48807i	0.497923	+	0.163884i
$454$	3.73278	+	14.1645i	0.175188	+	0.664774i
$455$	−1.39591	+	0.803152i	−0.0654411	+	0.0376523i
$456$	−9.19966	+	13.6763i	−0.430813	+	0.640452i
$457$	12.4908	−	21.6348i	0.584296	−	1.01203i	−0.410666	−	0.911786i	$-0.634704\pi$
$457$	12.4908	−	21.6348i	0.584296	−	1.01203i	0.994963	−	0.100245i	$-0.0319628\pi$
$458$	7.58190	+	28.7705i	0.354279	+	1.34436i
$459$	−39.4530	+	3.69155i	−1.84151	+	0.172307i
$460$	−7.13281	+	4.04000i	−0.332569	+	0.188366i
$461$	2.91281	+	5.04513i	0.135663	+	0.234975i	0.925851	−	0.377890i	$-0.123350\pi$
$461$	2.91281	+	5.04513i	0.135663	+	0.234975i	−0.790188	+	0.612865i	$0.790017\pi$
$462$	−10.0906	+	15.2220i	−0.469455	+	0.708191i
$463$	−23.9525	−	13.8290i	−1.11317	−	0.642686i	−0.173518	−	0.984831i	$-0.555513\pi$
$463$	−23.9525	−	13.8290i	−1.11317	−	0.642686i	−0.939647	+	0.342145i	$0.888847\pi$
$464$	30.3382	+	0.500898i	1.40842	+	0.0232536i
$465$	0.725414	+	3.47787i	0.0336403	+	0.161282i
$466$	2.59592	−	2.57458i	0.120254	−	0.119265i
$467$	−2.05655	+	1.18735i	−0.0951660	+	0.0549441i	−0.546828	−	0.837245i	$-0.684165\pi$
$467$	−2.05655	+	1.18735i	−0.0951660	+	0.0549441i	0.451662	+	0.892189i	$0.350831\pi$
$468$	5.91708	+	4.44417i	0.273517	+	0.205432i
$469$	17.8448	+	0.0266349i	0.823998	+	0.00122988i
$470$	−2.33510	+	8.57304i	−0.107710	+	0.395445i
$471$	−5.17156	−	24.7941i	−0.238293	−	1.14245i
$472$	−0.872015	+	3.10034i	−0.0401378	+	0.142705i
$473$	−21.0755	+	12.1680i	−0.969054	+	0.559484i
$474$	6.55914	−	9.92685i	0.301271	−	0.455955i
$475$	8.00148	+	13.8590i	0.367133	+	0.635893i
$476$	−20.5159	+	34.7479i	−0.940344	+	1.59267i
$477$	17.2593	−	7.52737i	0.790249	−	0.344655i
$478$	−7.33551	+	26.9314i	−0.335518	+	1.23181i
$479$	−36.0772			−1.64841			−0.824204	−	0.566293i	$-0.808377\pi$
$479$	−36.0772			−1.64841			−0.824204	+	0.566293i	$0.808377\pi$
$480$	−3.98988	−	2.73198i	−0.182112	−	0.124697i
$481$	−4.17540			−0.190382
$482$	5.10218	−	1.34458i	0.232398	−	0.0612439i
$483$	−25.3155	−	28.4172i	−1.15190	−	1.29303i
$484$	5.32317	−	3.01502i	0.241962	−	0.137046i
$485$	0.332528	+	0.575955i	0.0150993	+	0.0261528i
$486$	21.4207	−	5.21099i	0.971662	−	0.236375i
$487$	−14.1797	−	8.18667i	−0.642545	−	0.370973i	0.143049	−	0.989716i	$-0.454309\pi$
$487$	−14.1797	−	8.18667i	−0.642545	−	0.370973i	−0.785594	+	0.618742i	$0.787643\pi$
$488$	−19.1853	+	4.88692i	−0.868479	+	0.221220i
$489$	−15.2011	+	3.17065i	−0.687418	+	0.143382i
$490$	3.43005	+	3.47919i	0.154954	+	0.157174i
$491$	−15.9995	−	9.23733i	−0.722049	−	0.416875i	0.0934576	−	0.995623i	$-0.470208\pi$
$491$	−15.9995	−	9.23733i	−0.722049	−	0.416875i	−0.815506	+	0.578748i	$0.803541\pi$
$492$	−3.45790	+	10.2211i	−0.155894	+	0.460805i
$493$		−	57.8470i		−	2.60530i
$494$	−1.49546	−	5.67472i	−0.0672840	−	0.255318i
$495$	−2.47805	+	3.35669i	−0.111380	+	0.150872i
$496$	0.274440	−	16.6222i	0.0123227	−	0.746357i
$497$	−4.44886	+	7.67916i	−0.199559	+	0.344457i
$498$	−17.0004	−	34.0301i	−0.761807	−	1.52492i
$499$	−28.1940			−1.26213			−0.631067	−	0.775728i	$-0.717383\pi$
$499$	−28.1940			−1.26213			−0.631067	+	0.775728i	$0.717383\pi$
$500$	−8.37943	+	4.74608i	−0.374740	+	0.212251i
$501$	14.4025	+	16.1187i	0.643458	+	0.720128i
$502$	7.21702	+	27.3859i	0.322111	+	1.22229i
$503$	−14.8487			−0.662072			−0.331036	−	0.943618i	$-0.607398\pi$
$503$	−14.8487			−0.662072			−0.331036	+	0.943618i	$0.607398\pi$
$504$	8.49385	−	20.7811i	0.378346	−	0.925664i
$505$	3.29861			0.146786
$506$	−8.43421	−	32.0047i	−0.374946	−	1.42278i
$507$	19.4630	−	4.05960i	0.864384	−	0.180293i
$508$	17.0514	+	30.1051i	0.756533	+	1.33570i
$509$	0.362558			0.0160701			0.00803505	−	0.999968i	$-0.497442\pi$
$509$	0.362558			0.0160701			0.00803505	+	0.999968i	$0.497442\pi$
$510$	−5.08217	+	7.69155i	−0.225042	+	0.340588i
$511$	15.5884	+	27.0932i	0.689589	+	1.19853i
$512$	15.3948	+	16.5831i	0.680359	+	0.732879i
$513$	−15.8887	−	7.29270i	−0.701503	−	0.321981i
$514$	5.61877	+	21.3211i	0.247833	+	0.940435i
$515$		−	4.20884i		−	0.185464i
$516$	22.4714	−	19.7478i	0.989249	−	0.869349i
$517$	−31.0684	−	17.9374i	−1.36639	−	0.788884i
$518$	3.20963	+	12.2536i	0.141023	+	0.538391i
$519$	5.18052	+	5.79779i	0.227400	+	0.254495i
$520$	1.66839	−	0.424975i	0.0731637	−	0.0186364i
$521$	13.1642	+	7.60033i	0.576732	+	0.332976i	0.759834	−	0.650118i	$-0.225280\pi$
$521$	13.1642	+	7.60033i	0.576732	+	0.332976i	−0.183102	+	0.983094i	$0.558614\pi$
$522$	4.66092	+	31.8436i	0.204003	+	1.39376i
$523$	0.380494	+	0.659035i	0.0166378	+	0.0288176i	0.874224	−	0.485522i	$-0.161370\pi$
$523$	0.380494	+	0.659035i	0.0166378	+	0.0288176i	−0.857587	+	0.514340i	$0.828037\pi$
$524$	−12.7160	−	22.4507i	−0.555500	−	0.980763i
$525$	−14.4988	−	16.2752i	−0.632778	−	0.710307i
$526$	−4.52756	+	1.19315i	−0.197411	+	0.0520238i
$527$	−31.6941			−1.38061
$528$	14.7713	−	12.7665i	0.642840	−	0.555589i
$529$	45.9721			1.99879
$530$	1.15126	−	4.22670i	0.0500075	−	0.183596i
$531$	−3.39447	−	0.382930i	−0.147307	−	0.0166178i
$532$	−15.5041	+	8.75090i	−0.672186	+	0.379400i
$533$	−1.92088	−	3.32706i	−0.0832025	−	0.144111i
$534$	2.57038	+	5.14518i	0.111231	+	0.222654i
$535$	−4.66850	+	2.69536i	−0.201837	+	0.116531i
$536$	−18.3644	−	5.16525i	−0.793220	−	0.223105i
$537$	10.8465	−	9.69171i	0.468061	−	0.418228i
$538$	−0.793647	+	2.91378i	−0.0342166	+	0.125622i
$539$	−17.1126	+	9.81197i	−0.737092	+	0.422632i
$540$	2.17790	−	4.64354i	0.0937221	−	0.199826i
$541$	−28.7983	+	16.6267i	−1.23814	+	0.714838i	−0.968713	−	0.248183i	$-0.920166\pi$
$541$	−28.7983	+	16.6267i	−1.23814	+	0.714838i	−0.269423	+	0.963022i	$0.586833\pi$
$542$	−1.18573	+	1.17598i	−0.0509314	+	0.0505127i
$543$	23.3547	+	7.68684i	1.00225	+	0.329874i
$544$	31.1265	−	29.8677i	1.33454	−	1.28057i
$545$	0.734293	+	0.423944i	0.0314537	+	0.0181598i
$546$	3.56149	+	7.15579i	0.152418	+	0.306240i
$547$	5.99130	+	10.3772i	0.256169	+	0.443698i	0.965212	−	0.261467i	$-0.0842062\pi$
$547$	5.99130	+	10.3772i	0.256169	+	0.443698i	−0.709043	+	0.705165i	$0.750873\pi$
$548$	−5.03172	−	8.88375i	−0.214945	−	0.379495i
$549$	−8.39468	−	19.2479i	−0.358276	−	0.821481i
$550$	−4.83046	−	18.3298i	−0.205971	−	0.781585i
$551$	12.7608	−	22.1024i	0.543629	−	0.941594i
$552$	17.8817	+	36.5455i	0.761094	+	1.55548i
$553$	11.1392	−	6.40909i	0.473688	−	0.272542i
$554$	4.87389	+	18.4946i	0.207072	+	0.785760i
$555$	0.590890	+	2.83292i	0.0250819	+	0.120251i
$556$	−0.186117	+	22.5468i	−0.00789311	+	0.956199i
$557$	1.86487	−	3.23005i	0.0790171	−	0.136862i	−0.823809	−	0.566867i	$-0.808155\pi$
$557$	1.86487	−	3.23005i	0.0790171	−	0.136862i	0.902826	+	0.430006i	$0.141488\pi$
$558$	17.4470	−	2.55370i	0.738589	−	0.108107i
$559$			10.6512i			0.450496i
$560$	−2.52967	−	4.56955i	−0.106898	−	0.193099i
$561$	−24.8005	−	27.7556i	−1.04708	−	1.17184i
$562$	−0.136730	+	0.135606i	−0.00576762	+	0.00572021i
$563$	−14.2704	+	8.23903i	−0.601427	+	0.347234i	−0.769603	−	0.638523i	$-0.779546\pi$
$563$	−14.2704	+	8.23903i	−0.601427	+	0.347234i	0.168176	+	0.985757i	$0.446212\pi$
$564$	41.7741	+	14.1325i	1.75901	+	0.595087i
$565$	−3.64391	−	2.10381i	−0.153300	−	0.0885080i
$566$	−21.2891	−	21.4656i	−0.894849	−	0.902266i
$567$	23.2054	+	5.33954i	0.974534	+	0.224240i
$568$	6.79126	−	6.62513i	0.284955	−	0.277984i
$569$	13.6150	+	7.86063i	0.570771	+	0.329535i	0.757457	−	0.652885i	$-0.226441\pi$
$569$	13.6150	+	7.86063i	0.570771	+	0.329535i	−0.186686	+	0.982420i	$0.559775\pi$
$570$	−3.63854	+	1.81771i	−0.152402	+	0.0761354i
$571$	5.40685	+	9.36495i	0.226270	+	0.391911i	0.956700	−	0.291077i	$-0.0940136\pi$
$571$	5.40685	+	9.36495i	0.226270	+	0.391911i	−0.730430	+	0.682988i	$0.760680\pi$
$572$	−0.0573782	+	6.95099i	−0.00239910	+	0.290636i
$573$	15.2384	+	17.0541i	0.636593	+	0.712445i
$574$	−8.28735	+	8.19473i	−0.345907	+	0.342041i
$575$	39.5019			1.64734
$576$	−14.7280	+	18.9495i	−0.613668	+	0.789564i
$577$	15.7562	−	27.2905i	0.655938	−	1.13612i	−0.325720	−	0.945466i	$-0.605607\pi$
$577$	15.7562	−	27.2905i	0.655938	−	1.13612i	0.981658	−	0.190652i	$-0.0610601\pi$
$578$	−40.9841	−	41.3238i	−1.70472	−	1.71885i
$579$	6.11019	−	1.27446i	0.253931	−	0.0529649i
$580$	6.45318	+	3.79711i	0.267954	+	0.157666i
$581$	0.0613274	−	41.0881i	0.00254429	−	1.70462i
$582$	2.95284	−	1.47515i	0.122399	−	0.0611470i
$583$	15.3174	+	8.84353i	0.634384	+	0.366262i
$584$	−8.24834	−	32.3818i	−0.341319	−	1.33997i
$585$	0.730016	+	1.67383i	0.0301825	+	0.0692045i
$586$	8.21999	−	30.1787i	0.339565	−	1.24667i
$587$	4.75383	−	2.74463i	0.196212	−	0.113283i	−0.398676	−	0.917092i	$-0.630530\pi$
$587$	4.75383	−	2.74463i	0.196212	−	0.113283i	0.594887	+	0.803809i	$0.297197\pi$
$588$	18.2624	−	15.9526i	0.753129	−	0.657873i
$589$	−12.1098	−	6.99159i	−0.498975	−	0.288083i
$590$	−0.564280	+	0.559642i	−0.0232311	+	0.0230401i
$591$	−9.83736	+	29.8886i	−0.404655	+	1.22945i
$592$	0.223547	−	13.5397i	0.00918771	−	0.556478i
$593$	0.216566	−	0.125034i	0.00889329	−	0.00513454i	−0.495547	−	0.868581i	$-0.665032\pi$
$593$	0.216566	−	0.125034i	0.00889329	−	0.00513454i	0.504440	+	0.863447i	$0.331699\pi$
$594$	15.8886	+	13.2806i	0.651915	+	0.544911i
$595$	−8.63093	+	4.96591i	−0.353834	+	0.203582i
$596$	6.78303	−	3.84188i	0.277844	−	0.157370i
$597$	3.80951	−	3.40393i	0.155913	−	0.139313i
$598$	−13.9766	−	3.80691i	−0.571546	−	0.155676i
$599$	16.3224	+	28.2711i	0.666913	+	1.15513i	0.978763	+	0.204996i	$0.0657182\pi$
$599$	16.3224	+	28.2711i	0.666913	+	1.15513i	−0.311849	+	0.950132i	$0.600948\pi$
$600$	10.2412	+	20.9305i	0.418097	+	0.854482i
$601$	0.781275	+	1.35321i	0.0318689	+	0.0551985i	0.881520	−	0.472147i	$-0.156521\pi$
$601$	0.781275	+	1.35321i	0.0318689	+	0.0551985i	−0.849651	+	0.527345i	$0.823187\pi$
$602$	31.2580	−	8.18756i	1.27398	−	0.333700i
$603$	2.26823	−	20.1066i	0.0923694	−	0.818805i
$604$	−6.34916	−	11.2098i	−0.258344	−	0.456118i
$605$	1.50964			0.0613755
$606$	0.986529	−	16.3419i	0.0400750	−	0.663845i
$607$		−	26.1106i		−	1.05980i	−0.848061	−	0.529898i	$-0.822230\pi$
$607$		−	26.1106i		−	1.05980i	0.848061	−	0.529898i	$-0.177770\pi$
$608$	18.4816	−	4.54556i	0.749530	−	0.184347i
$609$	−10.9170	+	33.0028i	−0.442379	+	1.33734i
$610$	−4.71371	−	1.28391i	−0.190852	−	0.0519840i
$611$	−13.5978	+	7.85068i	−0.550107	+	0.317605i
$612$	36.5854	+	27.4784i	1.47888	+	1.11075i
$613$	20.2461	+	11.6891i	0.817734	+	0.472119i	0.849634	−	0.527372i	$-0.176823\pi$
$613$	20.2461	+	11.6891i	0.817734	+	0.472119i	−0.0319003	+	0.999491i	$0.510156\pi$
$614$	−7.54204	+	1.98756i	−0.304372	+	0.0802113i
$615$	−1.98550	+	1.77411i	−0.0800632	+	0.0715391i
$616$	20.4432	−	5.17485i	0.823680	−	0.208501i
$617$	16.2588	+	9.38702i	0.654555	+	0.377907i	0.790199	−	0.612850i	$-0.209977\pi$
$617$	16.2588	+	9.38702i	0.654555	+	0.377907i	−0.135644	+	0.990758i	$0.543310\pi$
$618$	−20.8514	−	1.25876i	−0.838766	−	0.0506346i
$619$	−5.30134			−0.213079			−0.106539	−	0.994308i	$-0.533977\pi$
$619$	−5.30134			−0.213079			−0.106539	+	0.994308i	$0.533977\pi$
$620$	2.08042	−	3.53566i	0.0835516	−	0.141996i
$621$	−35.1996	+	24.9647i	−1.41251	+	1.00180i
$622$	−12.2361	−	12.3375i	−0.490623	−	0.494690i
$623$	−0.00927241	+	6.21232i	−0.000371491	+	0.248892i
$624$	−1.60643	−	8.39262i	−0.0643088	−	0.335973i
$625$	21.4058			0.856230
$626$	−2.66829	+	9.79630i	−0.106646	+	0.391539i
$627$	−3.35310	−	16.0758i	−0.133910	−	0.642008i
$628$	−14.8315	+	25.2062i	−0.591843	+	1.00584i
$629$	−25.8166			−1.02938
$630$	4.35104	−	3.42906i	0.173350	−	0.136617i
$631$		−	25.1464i		−	1.00106i	−0.865718	−	0.500532i	$-0.833138\pi$
$631$		−	25.1464i		−	1.00106i	0.865718	−	0.500532i	$-0.166862\pi$
$632$	−13.3136	+	3.39127i	−0.529587	+	0.134897i
$633$	−28.2083	−	31.5694i	−1.12118	−	1.25477i
$634$	11.8161	−	43.3813i	0.469277	−	1.72289i
$635$			8.53772i			0.338809i
$636$	−20.5956	−	6.96766i	−0.816668	−	0.276286i
$637$	−0.0257725	+	8.63349i	−0.00102114	+	0.342071i
$638$	−21.4643	+	21.2878i	−0.849778	+	0.842793i
$639$	8.09591	+	5.97674i	0.320269	+	0.236436i
$640$	1.28875	+	5.43289i	0.0509425	+	0.214754i
$641$			6.75758i			0.266908i	0.991055	+	0.133454i	$0.0426069\pi$
$641$			6.75758i			0.266908i	−0.991055	+	0.133454i	$0.957393\pi$
$642$	11.9571	+	23.9347i	0.471909	+	0.944629i
$643$	25.0129	−	43.3236i	0.986412	−	1.70852i	0.350925	−	0.936404i	$-0.385867\pi$
$643$	25.0129	−	43.3236i	0.986412	−	1.70852i	0.635487	−	0.772111i	$-0.280799\pi$
$644$	−0.428334	+	43.9435i	−0.0168787	+	1.73162i
$645$	7.22658	−	1.50732i	0.284546	−	0.0593507i
$646$	−9.24648	−	35.0869i	−0.363798	−	1.38048i
$647$	10.2261	−	17.7121i	0.402029	−	0.696334i	−0.591942	−	0.805981i	$-0.701639\pi$
$647$	10.2261	−	17.7121i	0.402029	−	0.696334i	0.993971	+	0.109646i	$0.0349719\pi$
$648$	−22.3536	−	12.1785i	−0.878133	−	0.478417i
$649$	−1.60438	−	2.77887i	−0.0629776	−	0.109080i
$650$	−8.00471	−	2.18031i	−0.313971	−	0.0855186i
$651$	18.0821	+	5.98136i	0.708692	+	0.234428i
$652$	15.4537	+	9.09311i	0.605214	+	0.356114i
$653$	−22.3875			−0.876092			−0.438046	−	0.898953i	$-0.644329\pi$
$653$	−22.3875			−0.876092			−0.438046	+	0.898953i	$0.644329\pi$
$654$	2.31991	−	3.51104i	0.0907156	−	0.137292i
$655$		−	6.36696i		−	0.248778i
$656$	10.8916	−	6.05076i	0.425245	−	0.236243i
$657$	32.4874	−	14.1689i	1.26746	−	0.552781i
$658$	33.4921	+	33.8706i	1.30566	+	1.32041i
$659$	16.6000	−	9.58399i	0.646643	−	0.373339i	−0.140526	−	0.990077i	$-0.544879\pi$
$659$	16.6000	−	9.58399i	0.646643	−	0.373339i	0.787169	+	0.616738i	$0.211546\pi$
$660$	4.72422	−	0.944755i	0.183890	−	0.0367745i
$661$	22.8269	−	13.1791i	0.887862	−	0.512607i	0.0146196	−	0.999893i	$-0.495346\pi$
$661$	22.8269	−	13.1791i	0.887862	−	0.512607i	0.873243	+	0.487286i	$0.162013\pi$
$662$	0.648367	−	2.38040i	0.0251995	−	0.0925168i
$663$	−15.9476	+	3.32634i	−0.619352	+	0.129185i
$664$	−11.8931	+	42.2844i	−0.461542	+	1.64095i
$665$	−4.39320	−	0.00655721i	−0.170361	−	0.000254278i
$666$	14.2115	−	2.08013i	0.550686	−	0.0806034i
$667$	−31.4990	−	54.5578i	−1.21964	−	2.11249i
$668$	0.206028	−	24.9590i	0.00797147	−	0.965691i
$669$	1.13603	+	5.44650i	0.0439215	+	0.210574i
$670$	−3.31495	−	3.34243i	−0.128068	−	0.129129i
$671$	9.86249	−	17.0823i	0.380737	−	0.659456i
$672$	−23.3950	+	11.1658i	−0.902480	+	0.430731i
$673$	−4.23588	−	7.33676i	−0.163281	−	0.282811i	0.772762	−	0.634695i	$-0.218874\pi$
$673$	−4.23588	−	7.33676i	−0.163281	−	0.282811i	−0.936044	+	0.351884i	$0.885541\pi$
$674$	−7.94428	+	29.1664i	−0.306002	+	1.12345i
$675$	−20.1596	+	14.2978i	−0.775943	+	0.550324i
$676$	−19.7865	−	11.6425i	−0.761018	−	0.447790i
$677$	17.0372	−	29.5092i	0.654791	−	1.13413i	−0.327155	−	0.944971i	$-0.606090\pi$
$677$	17.0372	−	29.5092i	0.654791	−	1.13413i	0.981946	−	0.189161i	$-0.0605768\pi$
$678$	−11.5125	+	17.4234i	−0.442134	+	0.669142i
$679$	3.56528	+	0.00532147i	0.136823	+	0.000204219i
$680$	10.3157	−	2.62763i	0.395589	−	0.100765i
$681$	17.0409	+	5.60876i	0.653010	+	0.214928i
$682$	11.6635	+	11.7602i	0.446618	+	0.450320i
$683$	11.1403	+	6.43186i	0.426272	+	0.246108i	0.697757	−	0.716334i	$-0.254181\pi$
$683$	11.1403	+	6.43186i	0.426272	+	0.246108i	−0.271485	+	0.962443i	$0.587515\pi$
$684$	7.91708	+	18.5697i	0.302717	+	0.710029i
$685$		−	2.51941i		−	0.0962617i
$686$	25.3565	−	6.56094i	0.968117	−	0.250498i
$687$	34.6129	+	11.3923i	1.32056	+	0.434644i
$688$	−34.5388	−	0.570252i	−1.31678	−	0.0217407i
$689$	6.70402	−	3.87057i	0.255403	−	0.147457i
$690$	−0.604982	+	10.0216i	−0.0230313	+	0.381514i
$691$	−1.07534	+	1.86254i	−0.0409078	+	0.0708545i	−0.885754	−	0.464154i	$-0.846358\pi$
$691$	−1.07534	+	1.86254i	−0.0409078	+	0.0708545i	0.844847	+	0.535009i	$0.179692\pi$
$692$	0.0741072	−	8.97761i	0.00281713	−	0.341277i
$693$	8.91108	+	20.5155i	0.338504	+	0.779318i
$694$	−19.0283	+	18.8718i	−0.722303	+	0.716365i
$695$	−2.78198	+	4.81852i	−0.105526	+	0.182777i
$696$	20.7416	−	30.8347i	0.786208	−	1.16878i
$697$	−11.8768	−	20.5713i	−0.449867	−	0.779193i
$698$	−7.09902	+	7.04066i	−0.268702	+	0.266493i
$699$	−0.914309	−	4.38349i	−0.0345823	−	0.165799i
$700$	−0.245317	+	25.1675i	−0.00927210	+	0.951241i
$701$	25.8425			0.976056			0.488028	−	0.872828i	$-0.337716\pi$
$701$	25.8425			0.976056			0.488028	+	0.872828i	$0.337716\pi$
$702$	8.51082	−	3.11604i	0.321220	−	0.117607i
$703$	−9.86411	−	5.69504i	−0.372032	−	0.214793i
$704$	−22.5371	−	0.558211i	−0.849399	−	0.0210384i
$705$	7.25084	+	8.11480i	0.273082	+	0.305621i
$706$	−3.13197	−	11.8846i	−0.117873	−	0.447284i
$707$	8.86456	−	15.3011i	0.333386	−	0.575457i
$708$	2.60381	+	2.96293i	0.0978571	+	0.111354i
$709$	16.0923	+	9.29087i	0.604357	+	0.348926i	0.770754	−	0.637133i	$-0.219880\pi$
$709$	16.0923	+	9.29087i	0.604357	+	0.348926i	−0.166397	+	0.986059i	$0.553213\pi$
$710$	2.26390	−	0.596606i	0.0849626	−	0.0223902i
$711$	−5.82547	−	13.3571i	−0.218472	−	0.500929i
$712$	1.79818	−	6.39319i	0.0673896	−	0.239595i
$713$	−29.8919	+	17.2581i	−1.11946	+	0.646322i
$714$	22.0208	+	44.2444i	0.824106	+	1.65581i
$715$	−0.857659	+	1.48551i	−0.0320746	+	0.0555549i
$716$	−16.7953	−	0.138640i	−0.627670	−	0.00518121i
$717$	22.7778	+	25.4919i	0.850653	+	0.952011i
$718$	−4.06372	−	4.09741i	−0.151657	−	0.152914i
$719$	3.05461	+	5.29075i	0.113918	+	0.197312i	0.917347	−	0.398089i	$-0.130327\pi$
$719$	3.05461	+	5.29075i	0.113918	+	0.197312i	−0.803429	+	0.595401i	$0.796993\pi$
$720$	−5.46687	+	2.27763i	−0.203738	+	0.0848822i
$721$	−19.5233	−	11.3107i	−0.727087	−	0.421232i
$722$	−2.85443	+	10.4797i	−0.106231	+	0.390013i
$723$	2.02032	−	6.13828i	0.0751366	−	0.228285i
$724$	−13.9920	−	24.7035i	−0.520008	−	0.918099i
$725$	−18.0402	−	31.2465i	−0.669995	−	1.16047i
$726$	0.451494	−	7.47903i	0.0167565	−	0.277573i
$727$	−15.5425	+	8.97348i	−0.576441	+	0.332808i	−0.759718	−	0.650253i	$-0.774663\pi$
$727$	−15.5425	+	8.97348i	−0.576441	+	0.332808i	0.183277	+	0.983061i	$0.441329\pi$
$728$	2.51226	−	8.88114i	0.0931106	−	0.329157i
$729$	8.92789	−	25.4812i	0.330662	−	0.943749i
$730$	2.16703	−	7.95599i	0.0802055	−	0.294464i
$731$			65.8564i			2.43579i
$732$	−7.77048	+	22.9686i	−0.287205	+	0.848945i
$733$			19.0105i			0.702169i	0.936344	+	0.351084i	$0.114187\pi$
$733$			19.0105i			0.702169i	−0.936344	+	0.351084i	$0.885813\pi$
$734$	1.77338	+	6.72932i	0.0654567	+	0.248384i
$735$	5.86128	−	1.20430i	0.216197	−	0.0444213i
$736$	13.0931	−	45.1185i	0.482617	−	1.66309i
$737$	16.4602	−	9.50332i	0.606321	−	0.350059i
$738$	8.19547	+	10.3671i	0.301679	+	0.381620i
$739$	20.6435	−	35.7556i	0.759383	−	1.31529i	−0.183783	−	0.982967i	$-0.558834\pi$
$739$	20.6435	−	35.7556i	0.759383	−	1.31529i	0.943166	−	0.332323i	$-0.107832\pi$
$740$	1.69462	−	2.88000i	0.0622954	−	0.105871i
$741$	−6.82709	−	2.24703i	−0.250799	−	0.0825468i
$742$	−16.5123	−	16.6990i	−0.606187	−	0.613039i
$743$	0.661505	−	1.14576i	0.0242683	−	0.0420339i	−0.853636	−	0.520870i	$-0.825608\pi$
$743$	0.661505	−	1.14576i	0.0242683	−	0.0420339i	0.877904	+	0.478836i	$0.158941\pi$
$744$	−16.8941	−	11.3642i	−0.619370	−	0.416632i
$745$	1.92365			0.0704771
$746$	−10.1084	−	38.3575i	−0.370094	−	1.40437i
$747$	−46.2959	−	5.22265i	−1.69388	−	0.191087i
$748$	−0.354771	+	42.9782i	−0.0129717	+	1.57144i
$749$	−0.0431341	+	28.8989i	−0.00157608	+	1.05594i
$750$	−0.710716	+	11.7731i	−0.0259517	+	0.429892i
$751$		−	22.6381i		−	0.826075i	−0.910714	−	0.413037i	$-0.864468\pi$
$751$		−	22.6381i		−	0.826075i	0.910714	−	0.413037i	$-0.135532\pi$
$752$	−24.7296	−	44.5142i	−0.901796	−	1.62327i
$753$	32.9472	+	10.8441i	1.20066	+	0.395179i
$754$	3.37167	+	12.7942i	0.122789	+	0.465939i
$755$		−	3.17906i		−	0.115698i
$756$	−15.6869	−	22.5814i	−0.570528	−	0.821278i
$757$		−	45.9622i		−	1.67052i	−0.549852	−	0.835262i	$-0.685316\pi$
$757$		−	45.9622i		−	1.67052i	0.549852	−	0.835262i	$-0.314684\pi$
$758$	−6.28482	+	1.65624i	−0.228275	+	0.0601574i
$759$	−38.5039	−	12.6730i	−1.39760	−	0.459999i
$760$	4.52110	+	1.27163i	0.163998	+	0.0461268i
$761$			3.22936i			0.117064i	0.998286	+	0.0585321i	$0.0186420\pi$
$761$			3.22936i			0.117064i	−0.998286	+	0.0585321i	$0.981358\pi$
$762$	42.2975	+	2.55341i	1.53228	+	0.0925004i
$763$	3.93984	−	2.26684i	0.142632	−	0.0820650i
$764$	0.217985	−	26.4075i	0.00788642	−	0.955389i
$765$	4.51371	+	10.3494i	0.163193	+	0.374182i
$766$	−29.2693	+	7.71336i	−1.05754	+	0.278695i
$767$	−1.40439			−0.0507095
$768$	27.3010	−	4.75990i	0.985139	−	0.171758i
$769$	−19.8117	+	34.3148i	−0.714427	+	1.23742i	0.248753	+	0.968567i	$0.419979\pi$
$769$	−19.8117	+	34.3148i	−0.714427	+	1.23742i	−0.963180	+	0.268857i	$0.913354\pi$
$770$	5.01881	+	1.37506i	0.180865	+	0.0495538i
$771$	25.6508	+	8.44258i	0.923793	+	0.304052i
$772$	−6.21173	−	3.65504i	−0.223565	−	0.131548i
$773$	4.06730	−	7.04478i	0.146291	−	0.253383i	−0.783563	−	0.621312i	$-0.786600\pi$
$773$	4.06730	−	7.04478i	0.146291	−	0.253383i	0.929854	+	0.367929i	$0.119933\pi$
$774$	−5.30627	−	36.2527i	−0.190730	−	1.30307i
$775$	−17.1198	+	9.88411i	−0.614961	+	0.355048i
$776$	−3.66908	−	1.03198i	−0.131712	−	0.0370460i
$777$	14.7289	+	4.87216i	0.528395	+	0.174788i
$778$	−11.5009	+	3.03083i	−0.412326	+	0.108661i
$779$		−	10.4799i		−	0.375483i
$780$	0.675734	−	1.99739i	0.0241952	−	0.0715181i
$781$			9.45258i			0.338240i
$782$	−86.4176	−	23.5382i	−3.09029	−	0.841725i
$783$	35.8227	+	16.4422i	1.28020	+	0.587595i
$784$	−27.9947	−	0.545801i	−0.999810	−	0.0194929i
$785$	−6.24999	+	3.60843i	−0.223072	+	0.128790i
$786$	−31.5431	−	1.90419i	−1.12511	−	0.0679204i
$787$	6.90036	+	11.9518i	0.245971	+	0.426035i	0.962404	−	0.271621i	$-0.0875598\pi$
$787$	6.90036	+	11.9518i	0.245971	+	0.426035i	−0.716433	+	0.697656i	$0.754226\pi$
$788$	31.6147	−	17.9065i	1.12623	−	0.637892i
$789$	−1.79279	+	5.44697i	−0.0638249	+	0.193917i
$790$	−3.27107	−	0.890966i	−0.116379	−	0.0316991i
$791$	−19.5514	+	11.2491i	−0.695167	+	0.399972i
$792$	−3.26760	−	23.6872i	−0.116109	−	0.841689i
$793$	−4.31654	−	7.47646i	−0.153285	−	0.265497i
$794$	−0.810623	+	0.803959i	−0.0287679	+	0.0285314i
$795$	−3.57483	−	4.00078i	−0.126786	−	0.141893i
$796$	−5.89885	−	0.0486931i	−0.209079	−	0.00172588i
$797$	−8.53278	+	14.7792i	−0.302247	+	0.523506i	−0.976644	−	0.214862i	$-0.931070\pi$
$797$	−8.53278	+	14.7792i	−0.302247	+	0.523506i	0.674398	+	0.738368i	$0.264403\pi$
$798$	−1.34638	+	21.7628i	−0.0476613	+	0.770394i
$799$	−84.0754	+	48.5409i	−2.97437	+	1.71726i
$800$	7.49870	−	25.8404i	0.265119	−	0.913595i
$801$	6.99972	+	0.789639i	0.247323	+	0.0279005i
$802$	8.08731	+	30.6883i	0.285573	+	1.08364i
$803$	28.8323	+	16.6463i	1.01747	+	0.587436i
$804$	−17.5504	+	15.4233i	−0.618956	+	0.543936i
$805$	−5.43613	+	9.38328i	−0.191598	+	0.330717i
$806$	7.00990	−	1.84732i	0.246913	−	0.0650692i
$807$	2.46439	+	2.75803i	0.0867506	+	0.0970872i
$808$	−13.5319	+	13.2009i	−0.476051	+	0.464406i
$809$	−23.4724	−	13.5518i	−0.825244	−	0.476455i	0.0269775	−	0.999636i	$-0.491412\pi$
$809$	−23.4724	−	13.5518i	−0.825244	−	0.476455i	−0.852221	+	0.523181i	$0.824745\pi$
$810$	−3.31859	−	5.33343i	−0.116603	−	0.187398i
$811$	19.9662			0.701107			0.350553	−	0.936543i	$-0.385994\pi$
$811$	19.9662			0.701107			0.350553	+	0.936543i	$0.385994\pi$
$812$	34.9555	−	19.7298i	1.22670	−	0.692381i
$813$	0.417624	+	2.00223i	0.0146467	+	0.0702211i
$814$	9.50057	+	9.57931i	0.332995	+	0.335755i
$815$	2.21230	+	3.83182i	0.0774937	+	0.134223i
$816$	−9.93262	−	51.8917i	−0.347711	−	1.81657i
$817$	−14.5277	+	25.1627i	−0.508259	+	0.880330i
$818$	20.6476	+	20.8187i	0.721926	+	0.727909i
$819$	9.72615	+	1.11191i	0.339859	+	0.0388533i
$820$	3.07446	+	0.0253786i	0.107365	+	0.000886260i
$821$	15.5056	−	26.8564i	0.541148	−	0.937296i	−0.457690	−	0.889112i	$-0.651323\pi$
$821$	15.5056	−	26.8564i	0.541148	−	0.937296i	0.998838	−	0.0481844i	$-0.0153435\pi$
$822$	−12.4816	−	0.753491i	−0.435347	−	0.0262810i
$823$	20.2851	−	11.7116i	0.707095	−	0.408241i	−0.102890	−	0.994693i	$-0.532809\pi$
$823$	20.2851	−	11.7116i	0.707095	−	0.408241i	0.809984	+	0.586452i	$0.199476\pi$
$824$	16.8436	+	17.2660i	0.586774	+	0.601488i
$825$	−22.0520	−	7.25809i	−0.767753	−	0.252694i
$826$	1.07955	+	4.12146i	0.0375625	+	0.143404i
$827$			2.50883i			0.0872407i	0.999048	+	0.0436204i	$0.0138892\pi$
$827$			2.50883i			0.0872407i	−0.999048	+	0.0436204i	$0.986111\pi$
$828$	49.4678	+	5.99439i	1.71912	+	0.208319i
$829$	35.7204	+	20.6232i	1.24062	+	0.716272i	0.969220	−	0.246194i	$-0.0791802\pi$
$829$	35.7204	+	20.6232i	1.24062	+	0.716272i	0.271400	+	0.962467i	$0.412513\pi$
$830$	−7.69601	+	7.63275i	−0.267132	+	0.264936i
$831$	22.2503	+	7.32335i	0.771855	+	0.254044i
$832$	−5.14351	+	8.42020i	−0.178319	+	0.291918i
$833$	−0.159352	+	53.3811i	−0.00552121	+	1.84954i
$834$	23.0399	+	15.2235i	0.797805	+	0.527148i
$835$	3.07960	−	5.33403i	0.106574	−	0.184592i
$836$	−9.61637	+	16.3430i	−0.332589	+	0.565235i
$837$	9.00857	−	19.6271i	0.311382	−	0.678412i
$838$	13.6467	+	3.71706i	0.471418	+	0.128404i
$839$	25.2391	+	43.7153i	0.871349	+	1.50922i	0.860602	+	0.509279i	$0.170088\pi$
$839$	25.2391	+	43.7153i	0.871349	+	1.50922i	0.0107475	+	0.999942i	$0.496579\pi$
$840$	−6.38119	−	0.447683i	−0.220172	−	0.0154465i
$841$	−14.2706	+	24.7174i	−0.492090	+	0.852324i
$842$	37.2096	−	36.9037i	1.28233	−	1.27179i
$843$	0.0481577	+	0.230884i	0.00165864	+	0.00795206i
$844$	−0.403519	+	48.8837i	−0.0138897	+	1.68264i
$845$	−2.83257	−	4.90615i	−0.0974433	−	0.168777i
$846$	42.3708	−	33.4951i	1.45674	−	1.15158i
$847$	4.05694	−	7.00268i	0.139398	−	0.240615i
$848$	12.1923	+	21.9465i	0.418684	+	0.753647i
$849$	−36.2469	+	7.56038i	−1.24399	+	0.259472i
$850$	−49.4933	−	13.4809i	−1.69761	−	0.462390i
$851$	−24.3487	+	14.0577i	−0.834662	+	0.481892i
$852$	−2.27863	−	11.3942i	−0.0780645	−	0.390359i
$853$	36.3516	−	20.9876i	1.24466	−	0.718602i	0.274617	−	0.961554i	$-0.411449\pi$
$853$	36.3516	−	20.9876i	1.24466	−	0.718602i	0.970038	+	0.242952i	$0.0781156\pi$
$854$	−18.6231	+	18.4149i	−0.637268	+	0.630145i
$855$	−0.558413	+	4.95003i	−0.0190973	+	0.169287i
$856$	8.36490	−	29.7403i	0.285907	−	1.01650i
$857$		−	29.9522i		−	1.02315i	−0.859240	−	0.511573i	$-0.829063\pi$
$857$		−	29.9522i		−	1.02315i	0.859240	−	0.511573i	$-0.170937\pi$
$858$	7.10299	+	4.69328i	0.242492	+	0.160226i
$859$	6.79785			0.231940			0.115970	−	0.993253i	$-0.463002\pi$
$859$	6.79785			0.231940			0.115970	+	0.993253i	$0.463002\pi$
$860$	−7.34668	−	4.32285i	−0.250520	−	0.147408i
$861$	2.89371	+	13.9777i	0.0986175	+	0.476360i
$862$	6.33923	−	23.2737i	0.215915	−	0.792705i
$863$	−27.0742	−	46.8939i	−0.921617	−	1.59629i	−0.796913	−	0.604094i	$-0.793535\pi$
$863$	−27.0742	−	46.8939i	−0.921617	−	1.59629i	−0.124704	−	0.992194i	$-0.539798\pi$
$864$	9.64880	+	27.7651i	0.328259	+	0.944588i
$865$	1.10772	−	1.91862i	0.0376635	−	0.0652351i
$866$	27.9031	−	7.35332i	0.948186	−	0.249876i
$867$	−69.7797	+	14.5546i	−2.36984	+	0.494302i
$868$	−10.8099	−	19.1519i	−0.366911	−	0.650059i
$869$	6.84405	−	11.8543i	0.232169	−	0.402128i
$870$	8.20347	−	4.09821i	0.278124	−	0.138942i
$871$		−	8.31867i		−	0.281868i
$872$	−4.70890	+	1.19946i	−0.159464	+	0.0406188i
$873$	0.453177	−	4.01717i	0.0153377	−	0.135960i
$874$	−27.8263	−	28.0570i	−0.941240	−	0.949042i
$875$	−6.38622	+	11.0232i	−0.215894	+	0.372653i
$876$	−38.7674	−	13.1153i	−1.30983	−	0.443126i
$877$			39.1750i			1.32285i	0.750013	+	0.661423i	$0.230047\pi$
$877$			39.1750i			1.32285i	−0.750013	+	0.661423i	$0.769953\pi$
$878$	−39.0968	−	10.6491i	−1.31945	−	0.359389i
$879$	−25.5243	−	28.5656i	−0.860912	−	0.963493i
$880$	−4.77119	−	2.86069i	−0.160837	−	0.0964338i
$881$			37.8658i			1.27573i	0.770148	+	0.637866i	$0.220182\pi$
$881$			37.8658i			1.27573i	−0.770148	+	0.637866i	$0.779818\pi$
$882$	−4.21337	−	29.3981i	−0.141872	−	0.989885i
$883$	7.40423			0.249172			0.124586	−	0.992209i	$-0.460240\pi$
$883$	7.40423			0.249172			0.124586	+	0.992209i	$0.460240\pi$
$884$	16.2126	+	9.53964i	0.545288	+	0.320853i
$885$	0.198745	+	0.952847i	0.00668073	+	0.0320296i
$886$	−13.7311	−	3.74003i	−0.461304	−	0.125649i
$887$	−20.5216			−0.689049			−0.344524	−	0.938777i	$-0.611960\pi$
$887$	−20.5216			−0.689049			−0.344524	+	0.938777i	$0.611960\pi$
$888$	−13.7612	−	9.25679i	−0.461797	−	0.310637i
$889$	39.6035	+	22.9440i	1.32826	+	0.769516i
$890$	1.16360	−	1.15403i	0.0390040	−	0.0386833i
$891$	24.2373	−	7.46903i	0.811980	−	0.250222i
$892$	3.25803	−	5.53701i	0.109087	−	0.185393i
$893$	−42.8318			−1.43331
$894$	0.575314	−	9.53012i	0.0192414	−	0.318735i
$895$	−3.58935	−	2.07231i	−0.119979	−	0.0692698i
$896$	28.6646	+	8.62207i	0.957617	+	0.288043i
$897$	−13.2295	+	11.8210i	−0.441721	+	0.394692i
$898$	1.48012	+	5.61652i	0.0493924	+	0.187426i
$899$	27.3028	+	15.7633i	0.910599	+	0.525734i
$900$	28.3313	+	3.43312i	0.944377	+	0.114437i
$901$	41.4511	−	23.9318i	1.38094	−	0.797284i
$902$	−3.26233	+	11.9772i	−0.108624	+	0.398798i
$903$	12.4285	−	37.5723i	0.413596	−	1.25033i
$904$	23.3678	−	5.95229i	0.777202	−	0.197970i
$905$		−	7.00586i		−	0.232883i
$906$	−15.7497	−	0.950775i	−0.523247	−	0.0315874i
$907$	0.0175841			0.000583872			0.000291936	−	1.00000i	$-0.499907\pi$
$907$	0.0175841			0.000583872			0.000291936		1.00000i	$0.499907\pi$
$908$	−10.2093	−	18.0251i	−0.338809	−	0.598184i
$909$	−16.1315	−	11.9089i	−0.535047	−	0.394995i
$910$	1.61949	−	1.60139i	0.0536857	−	0.0530857i
$911$	−12.9340	−	22.4023i	−0.428521	−	0.742221i	0.568221	−	0.822876i	$-0.307632\pi$
$911$	−12.9340	−	22.4023i	−0.428521	−	0.742221i	−0.996742	+	0.0806555i	$0.974299\pi$
$912$	7.65203	−	22.0181i	0.253384	−	0.729092i
$913$	−21.8816	−	37.9000i	−0.724175	−	1.25431i
$914$	−9.28469	+	34.0876i	−0.307110	+	1.12752i
$915$	−4.46175	+	3.98672i	−0.147501	+	0.131797i
$916$	−20.7369	−	36.6119i	−0.685165	−	1.20969i
$917$	−29.5341	−	17.1103i	−0.975302	−	0.565033i
$918$	52.6226	−	19.2665i	1.73680	−	0.635890i
$919$	42.2718	−	24.4056i	1.39442	−	0.805068i	0.400618	−	0.916245i	$-0.368796\pi$
$919$	42.2718	−	24.4056i	1.39442	−	0.805068i	0.993801	+	0.111178i	$0.0354622\pi$
$920$	8.29834	−	8.09535i	0.273588	−	0.266896i
$921$	−2.98644	+	9.07361i	−0.0984065	+	0.298986i
$922$	−5.80152	−	5.84961i	−0.191063	−	0.192647i
$923$	3.58286	+	2.06856i	0.117931	+	0.0680876i
$924$	8.31332	−	24.4529i	0.273488	−	0.804442i
$925$	−13.9450	+	8.05117i	−0.458510	+	0.264721i
$926$	37.7393	+	10.2793i	1.24019	+	0.337800i
$927$	−15.1952	+	20.5829i	−0.499074	+	0.676030i
$928$	−41.6688	+	10.2484i	−1.36785	+	0.336421i
$929$	5.77430	+	3.33379i	0.189448	+	0.109378i	0.591724	−	0.806140i	$-0.298447\pi$
$929$	5.77430	+	3.33379i	0.189448	+	0.109378i	−0.402276	+	0.915519i	$0.631781\pi$
$930$	−2.24539	−	4.49464i	−0.0736293	−	0.147385i
$931$	−11.8365	+	20.3609i	−0.387927	+	0.667301i
$932$	−2.62215	+	4.45634i	−0.0858914	+	0.145972i
$933$	−20.8332	+	4.34539i	−0.682049	+	0.142262i
$934$	2.38449	−	2.36488i	0.0780227	−	0.0773813i
$935$	−5.30293	+	9.18494i	−0.173424	+	0.300380i
$936$	−9.69336	−	3.94508i	−0.316837	−	0.128949i
$937$	12.6512			0.413295			0.206648	−	0.978415i	$-0.433745\pi$
$937$	12.6512			0.413295			0.206648	+	0.978415i	$0.433745\pi$
$938$	−24.4128	+	6.39457i	−0.797107	+	0.208790i
$939$	8.28544	+	9.27267i	0.270385	+	0.302602i
$940$	0.103723	−	12.5654i	0.00338307	−	0.409837i
$941$	22.0678	+	38.2226i	0.719390	+	1.24602i	0.961242	+	0.275707i	$0.0889119\pi$
$941$	22.0678	+	38.2226i	0.719390	+	1.24602i	−0.241852	+	0.970313i	$0.577755\pi$
$942$	16.0076	+	32.0428i	0.521557	+	1.04401i
$943$	−22.4031	−	12.9344i	−0.729544	−	0.421202i
$944$	0.0751895	−	4.55405i	0.00244721	−	0.148222i
$945$	−0.622008	−	6.75634i	−0.0202339	−	0.219784i
$946$	24.4362	−	24.2353i	0.794488	−	0.787957i
$947$	−28.6425	−	16.5367i	−0.930756	−	0.537372i	−0.0437051	−	0.999044i	$-0.513916\pi$
$947$	−28.6425	−	16.5367i	−0.930756	−	0.537372i	−0.887050	+	0.461673i	$0.847250\pi$
$948$	−5.39231	+	15.9390i	−0.175134	+	0.517676i
$949$	12.6191	−	7.28562i	0.409632	−	0.236501i
$950$	−15.9368	−	16.0689i	−0.517057	−	0.521343i
$951$	−36.6907	−	41.0625i	−1.18978	−	1.33154i
$952$	15.5334	−	54.9123i	0.503439	−	1.77972i
$953$			50.5097i			1.63617i	0.575097	+	0.818085i	$0.304964\pi$
$953$			50.5097i			1.63617i	−0.575097	+	0.818085i	$0.695036\pi$
$954$	−20.8898	+	16.5138i	−0.676331	+	0.534656i
$955$	3.25833	−	5.64359i	0.105437	−	0.182622i
$956$	0.325836	−	39.4729i	0.0105383	−	1.27665i
$957$	7.55992	+	36.2447i	0.244377	+	1.17162i
$958$	49.3364	−	13.0016i	1.59399	−	0.420064i
$959$	−11.6867	−	6.77058i	−0.377382	−	0.218633i
$960$	6.44082	+	2.29816i	0.207877	+	0.0741728i
$961$	−6.86339	+	11.8877i	−0.221400	+	0.383475i
$962$	5.70996	−	1.50475i	0.184097	−	0.0485151i
$963$	32.5618	+	3.67330i	1.04929	+	0.118370i
$964$	−6.49279	+	3.67749i	−0.209119	+	0.118444i
$965$	−0.889252	−	1.54023i	−0.0286260	−	0.0495817i
$966$	44.8607	+	29.7379i	1.44337	+	0.956801i
$967$	36.1364	+	20.8633i	1.16207	+	0.670920i	0.951799	−	0.306724i	$-0.0992328\pi$
$967$	36.1364	+	20.8633i	1.16207	+	0.670920i	0.210269	+	0.977644i	$0.432566\pi$
$968$	−6.19299	+	6.04150i	−0.199050	+	0.194181i
$969$	−42.2121	−	13.8934i	−1.35605	−	0.446322i
$970$	−0.662305	−	0.667794i	−0.0212653	−	0.0214416i
$971$	−3.38167	+	1.95241i	−0.108523	+	0.0626557i	−0.553279	−	0.832996i	$-0.686624\pi$
$971$	−3.38167	+	1.95241i	−0.108523	+	0.0626557i	0.444756	+	0.895652i	$0.353290\pi$
$972$	−27.4153	+	14.8458i	−0.879348	+	0.476180i
$973$	14.8753	+	25.8538i	0.476879	+	0.828833i
$974$	22.3415	+	6.08532i	0.715867	+	0.194986i
$975$	−7.57685	+	6.77016i	−0.242653	+	0.216819i
$976$	24.4752	−	13.5971i	0.783433	−	0.435232i
$977$	−3.67662	+	2.12270i	−0.117626	+	0.0679112i	−0.557658	−	0.830070i	$-0.688300\pi$
$977$	−3.67662	+	2.12270i	−0.117626	+	0.0679112i	0.440033	+	0.897982i	$0.354967\pi$
$978$	19.6452	−	9.81418i	0.628185	−	0.313823i
$979$	3.30839	+	5.73030i	0.105737	+	0.183141i
$980$	−5.94452	−	3.52174i	−0.189891	−	0.112498i
$981$	−2.06042	−	4.72427i	−0.0657840	−	0.150834i
$982$	25.2087	+	6.86630i	0.804443	+	0.219112i
$983$	30.3382			0.967637			0.483819	−	0.875168i	$-0.339249\pi$
$983$	30.3382			0.967637			0.483819	+	0.875168i	$0.339249\pi$
$984$	1.04522	−	15.2238i	0.0333204	−	0.485318i
$985$	8.96586			0.285676
$986$	20.8471	+	79.1071i	0.663908	+	2.51928i
$987$	57.1274	−	11.8267i	1.81838	−	0.376447i
$988$	4.09016	+	7.22138i	0.130125	+	0.229743i
$989$	35.8602	+	62.1118i	1.14029	+	1.97504i
$990$	2.17910	−	5.48341i	0.0692563	−	0.174274i
$991$	−52.1229	−	30.0932i	−1.65574	−	0.955941i	−0.974649	−	0.223741i	$-0.928173\pi$
$991$	−52.1229	−	30.0932i	−1.65574	−	0.955941i	−0.681090	−	0.732200i	$-0.738494\pi$
$992$	5.61506	+	22.8301i	0.178278	+	0.724857i
$993$	−2.01327	−	2.25316i	−0.0638893	−	0.0715020i
$994$	3.31648	−	12.1047i	0.105192	−	0.383939i
$995$	−1.26065	−	0.727839i	−0.0399654	−	0.0230741i
$996$	35.5124	+	40.4103i	1.12525	+	1.28045i
$997$		−	8.42083i		−	0.266690i	−0.991070	−	0.133345i	$-0.957428\pi$
$997$		−	8.42083i		−	0.266690i	0.991070	−	0.133345i	$-0.0425719\pi$
$998$	38.5559	−	10.1607i	1.22047	−	0.321630i
$999$	7.33799	−	15.9874i	0.232164	−	0.505818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cy.a.347.8	yes	184
7.2	even	3		504.2.bt.a.275.68	yes	184
8.3	odd	2	inner	504.2.cy.a.347.39	yes	184
9.2	odd	6		504.2.bt.a.11.25	✓	184
56.51	odd	6		504.2.bt.a.275.25	yes	184
63.2	odd	6	inner	504.2.cy.a.443.39	yes	184
72.11	even	6		504.2.bt.a.11.68	yes	184
504.443	even	6	inner	504.2.cy.a.443.8	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.25	✓	184	9.2	odd	6
504.2.bt.a.11.68	yes	184	72.11	even	6
504.2.bt.a.275.25	yes	184	56.51	odd	6
504.2.bt.a.275.68	yes	184	7.2	even	3
504.2.cy.a.347.8	yes	184	1.1	even	1	trivial
504.2.cy.a.347.39	yes	184	8.3	odd	2	inner
504.2.cy.a.443.8	yes	184	504.443	even	6	inner
504.2.cy.a.443.39	yes	184	63.2	odd	6	inner

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cy (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36752 + 0.360384i) q^{2} +(-0.541502 + 1.64523i) q^{3} +(1.74025 - 0.985669i) q^{4} +0.493530 q^{5} +(0.147602 - 2.44504i) q^{6} +(1.32629 - 2.28931i) q^{7} +(-2.02461 + 1.97508i) q^{8} +(-2.41355 - 1.78179i) q^{9} +O(q^{10})\)	\(q+(-1.36752 + 0.360384i) q^{2} +(-0.541502 + 1.64523i) q^{3} +(1.74025 - 0.985669i) q^{4} +0.493530 q^{5} +(0.147602 - 2.44504i) q^{6} +(1.32629 - 2.28931i) q^{7} +(-2.02461 + 1.97508i) q^{8} +(-2.41355 - 1.78179i) q^{9} +(-0.674914 + 0.177860i) q^{10} -2.81800i q^{11} +(0.679304 + 3.39684i) q^{12} +(-1.06812 - 0.616681i) q^{13} +(-0.988708 + 3.60866i) q^{14} +(-0.267247 + 0.811969i) q^{15} +(2.05691 - 3.43061i) q^{16} +(-6.60422 - 3.81295i) q^{17} +(3.94272 + 1.56683i) q^{18} +(-1.68224 - 2.91373i) q^{19} +(0.858863 - 0.486457i) q^{20} +(3.04825 + 3.42172i) q^{21} +(1.01556 + 3.85369i) q^{22} -8.30494 q^{23} +(-2.15313 - 4.40046i) q^{24} -4.75643 q^{25} +(1.68293 + 0.458391i) q^{26} +(4.23839 - 3.00600i) q^{27} +(0.0515758 - 5.29125i) q^{28} +(3.79280 + 6.56932i) q^{29} +(0.0728460 - 1.20670i) q^{30} +(3.59929 - 2.07805i) q^{31} +(-1.57654 + 5.43273i) q^{32} +(4.63626 + 1.52595i) q^{33} +(10.4056 + 2.83424i) q^{34} +(0.654565 - 1.12984i) q^{35} +(-5.95643 - 0.721785i) q^{36} +(2.93183 - 1.69269i) q^{37} +(3.35058 + 3.37835i) q^{38} +(1.59297 - 1.42337i) q^{39} +(-0.999205 + 0.974762i) q^{40} +(2.69756 + 1.55743i) q^{41} +(-5.40169 - 3.58075i) q^{42} +(-4.31794 - 7.47889i) q^{43} +(-2.77762 - 4.90402i) q^{44} +(-1.19116 - 0.879365i) q^{45} +(11.3572 - 2.99297i) q^{46} +(6.36527 - 11.0250i) q^{47} +(4.53032 + 5.24177i) q^{48} +(-3.48189 - 6.07260i) q^{49} +(6.50453 - 1.71414i) q^{50} +(9.84937 - 8.80074i) q^{51} +(-2.46664 - 0.0203613i) q^{52} +(-3.13823 + 5.43557i) q^{53} +(-4.71278 + 5.63823i) q^{54} -1.39077i q^{55} +(1.83635 + 7.25450i) q^{56} +(5.70470 - 1.18989i) q^{57} +(-7.55422 - 7.61683i) q^{58} +(0.986115 - 0.569333i) q^{59} +(0.335257 + 1.67644i) q^{60} +(6.06186 + 3.49981i) q^{61} +(-4.17322 + 4.13892i) q^{62} +(-7.28015 + 3.16220i) q^{63} +(0.198087 - 7.99755i) q^{64} +(-0.527150 - 0.304350i) q^{65} +(-6.89013 - 0.415943i) q^{66} +(3.37236 + 5.84110i) q^{67} +(-15.2513 - 0.125894i) q^{68} +(4.49714 - 13.6635i) q^{69} +(-0.487956 + 1.78098i) q^{70} -3.35435 q^{71} +(8.40568 - 1.15954i) q^{72} +(-5.90713 + 10.2315i) q^{73} +(-3.39933 + 3.37138i) q^{74} +(2.57561 - 7.82541i) q^{75} +(-5.79950 - 3.41248i) q^{76} +(-6.45129 - 3.73750i) q^{77} +(-1.66546 + 2.52058i) q^{78} +(4.20661 + 2.42869i) q^{79} +(1.01515 - 1.69311i) q^{80} +(2.65047 + 8.60087i) q^{81} +(-4.25025 - 1.15767i) q^{82} +(13.4493 - 7.76493i) q^{83} +(8.67739 + 2.95007i) q^{84} +(-3.25938 - 1.88180i) q^{85} +(8.60016 + 8.67145i) q^{86} +(-12.8618 + 2.68272i) q^{87} +(5.56579 + 5.70536i) q^{88} +(-2.03346 + 1.17402i) q^{89} +(1.94585 + 0.773277i) q^{90} +(-2.82842 + 1.62736i) q^{91} +(-14.4526 + 8.18592i) q^{92} +(1.46985 + 7.04693i) q^{93} +(-4.73144 + 17.3709i) q^{94} +(-0.830237 - 1.43801i) q^{95} +(-8.08438 - 5.53560i) q^{96} +(0.673775 + 1.16701i) q^{97} +(6.95004 + 7.04961i) q^{98} +(-5.02108 + 6.80140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9	\( 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 5 q^{12} - 3 q^{14} + q^{16} + 5 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} + 148 q^{25} + 6 q^{26} - 8 q^{27} + 24 q^{30} - 33 q^{32} + 22 q^{33} - 4 q^{34} - 30 q^{35} - 38 q^{36} - 12 q^{40} - 12 q^{41} + 7 q^{42} - 4 q^{43} - 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} + 26 q^{51} - 18 q^{52} - 40 q^{54} + 18 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{60} - 8 q^{64} - 6 q^{65} + 43 q^{66} + 2 q^{67} - 18 q^{70} - 11 q^{72} - 4 q^{73} - 36 q^{75} + 2 q^{76} - 29 q^{78} - 87 q^{80} - 10 q^{81} - 4 q^{82} - 72 q^{83} - 65 q^{84} + 14 q^{88} + 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} + 9 q^{94} - 88 q^{96} - 4 q^{97} - 57 q^{98} + 10 q^{99}+O(q^{100}) \) 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 5 * q^12 - 3 * q^14 + q^16 + 5 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 + 148 * q^25 + 6 * q^26 - 8 * q^27 + 24 * q^30 - 33 * q^32 + 22 * q^33 - 4 * q^34 - 30 * q^35 - 38 * q^36 - 12 * q^40 - 12 * q^41 + 7 * q^42 - 4 * q^43 - 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 + 26 * q^51 - 18 * q^52 - 40 * q^54 + 18 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^60 - 8 * q^64 - 6 * q^65 + 43 * q^66 + 2 * q^67 - 18 * q^70 - 11 * q^72 - 4 * q^73 - 36 * q^75 + 2 * q^76 - 29 * q^78 - 87 * q^80 - 10 * q^81 - 4 * q^82 - 72 * q^83 - 65 * q^84 + 14 * q^88 + 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 + 9 * q^94 - 88 * q^96 - 4 * q^97 - 57 * q^98 + 10 * q^99

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