LMFDB - Embedded newform 504.2.br.a.155.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(155,504)]

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, 1, 0]))

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

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

chi := DirichletCharacter("504.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.br (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:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.10
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29192 - 0.575281i) q^{2} +(0.410623 - 1.68267i) q^{3} +(1.33810 + 1.48643i) q^{4} +(1.67611 + 2.90312i) q^{5} +(-1.49850 + 1.93765i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.873604 - 2.69013i) q^{8} +(-2.66278 - 1.38189i) q^{9} +O(q^{10})$	\(q+(-1.29192 - 0.575281i) q^{2} +(0.410623 - 1.68267i) q^{3} +(1.33810 + 1.48643i) q^{4} +(1.67611 + 2.90312i) q^{5} +(-1.49850 + 1.93765i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.873604 - 2.69013i) q^{8} +(-2.66278 - 1.38189i) q^{9} +(-0.495295 - 4.71482i) q^{10} +(-0.931208 - 0.537633i) q^{11} +(3.05063 - 1.64123i) q^{12} +(1.24684 - 0.719865i) q^{13} +(-0.831193 - 1.14417i) q^{14} +(5.57324 - 1.62827i) q^{15} +(-0.418957 + 3.97800i) q^{16} +2.72213i q^{17} +(2.64512 + 3.31713i) q^{18} +6.49390 q^{19} +(-2.07247 + 6.37610i) q^{20} +(1.19695 - 1.25193i) q^{21} +(0.893754 + 1.23028i) q^{22} +(2.74636 + 4.75684i) q^{23} +(-4.88534 + 0.365361i) q^{24} +(-3.11872 + 5.40178i) q^{25} +(-2.02494 + 0.212722i) q^{26} +(-3.41866 + 3.91315i) q^{27} +(0.415616 + 1.95634i) q^{28} +(-0.590015 + 1.02194i) q^{29} +(-8.13689 - 1.10259i) q^{30} +(9.00497 - 5.19902i) q^{31} +(2.82973 - 4.89823i) q^{32} +(-1.28704 + 1.34615i) q^{33} +(1.56599 - 3.51677i) q^{34} +3.35223i q^{35} +(-1.50899 - 5.80715i) q^{36} +3.07642i q^{37} +(-8.38958 - 3.73582i) q^{38} +(-0.699316 - 2.39362i) q^{39} +(6.34551 - 7.04514i) q^{40} +(2.74938 - 1.58736i) q^{41} +(-2.26657 + 0.928806i) q^{42} +(2.28900 - 3.96466i) q^{43} +(-0.446898 - 2.10359i) q^{44} +(-0.451343 - 10.0466i) q^{45} +(-0.811555 - 7.72537i) q^{46} +(2.70286 - 4.68149i) q^{47} +(6.52164 + 2.33842i) q^{48} +(0.500000 + 0.866025i) q^{49} +(7.13667 - 5.18452i) q^{50} +(4.58046 + 1.11777i) q^{51} +(2.73844 + 0.890093i) q^{52} -12.5659 q^{53} +(6.66779 - 3.08878i) q^{54} -3.60454i q^{55} +(0.588503 - 2.76653i) q^{56} +(2.66654 - 10.9271i) q^{57} +(1.35015 - 0.980832i) q^{58} +(-11.1655 + 6.44638i) q^{59} +(9.87789 + 6.10545i) q^{60} +(1.14110 + 0.658814i) q^{61} +(-14.6246 + 1.53632i) q^{62} +(-1.61509 - 2.52814i) q^{63} +(-6.47363 + 4.70022i) q^{64} +(4.17970 + 2.41315i) q^{65} +(2.43716 - 0.998714i) q^{66} +(-2.57984 - 4.46841i) q^{67} +(-4.04626 + 3.64250i) q^{68} +(9.13192 - 2.66796i) q^{69} +(1.92847 - 4.33080i) q^{70} +14.0523 q^{71} +(-1.39125 + 8.37045i) q^{72} -3.81183 q^{73} +(1.76981 - 3.97448i) q^{74} +(7.80881 + 7.46588i) q^{75} +(8.68951 + 9.65273i) q^{76} +(-0.537633 - 0.931208i) q^{77} +(-0.473547 + 3.49467i) q^{78} +(1.96184 + 1.13267i) q^{79} +(-12.2508 + 5.45130i) q^{80} +(5.18078 + 7.35932i) q^{81} +(-4.46516 + 0.469067i) q^{82} +(-6.85242 - 3.95624i) q^{83} +(3.46254 + 0.103971i) q^{84} +(-7.90267 + 4.56261i) q^{85} +(-5.23799 + 3.80520i) q^{86} +(1.47731 + 1.41243i) q^{87} +(-0.632798 + 2.97475i) q^{88} -3.72610i q^{89} +(-5.19649 + 13.2390i) q^{90} +1.43973 q^{91} +(-3.39580 + 10.4474i) q^{92} +(-5.05061 - 17.2873i) q^{93} +(-6.18504 + 4.49319i) q^{94} +(10.8845 + 18.8525i) q^{95} +(-7.08017 - 6.77283i) q^{96} +(2.81825 - 4.88135i) q^{97} +(-0.147751 - 1.40647i) q^{98} +(1.73665 + 2.71842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{6}+O(q^{10}) $ 144 * q + 6 * q^6	$ 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.29192	−	0.575281i	−0.913524	−	0.406785i
$2$	−1.29192	−	0.575281i	−0.913524	−	0.406785i
$3$	0.410623	−	1.68267i	0.237073	−	0.971492i
$3$	0.410623	−	1.68267i	0.237073	−	0.971492i
$4$	1.33810	+	1.48643i	0.669052	+	0.743216i
$5$	1.67611	+	2.90312i	0.749581	+	1.29831i	0.948024	+	0.318200i	$0.103078\pi$
$5$	1.67611	+	2.90312i	0.749581	+	1.29831i	−0.198442	+	0.980113i	$0.563588\pi$
$6$	−1.49850	+	1.93765i	−0.611760	+	0.791043i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	−0.873604	−	2.69013i	−0.308866	−	0.951106i
$9$	−2.66278	−	1.38189i	−0.887593	−	0.460629i
$10$	−0.495295	−	4.71482i	−0.156626	−	1.49096i
$11$	−0.931208	−	0.537633i	−0.280770	−	0.162103i	0.353002	−	0.935623i	$-0.385161\pi$
$11$	−0.931208	−	0.537633i	−0.280770	−	0.162103i	−0.633772	+	0.773520i	$0.718494\pi$
$12$	3.05063	−	1.64123i	0.880642	−	0.473782i
$13$	1.24684	−	0.719865i	0.345812	−	0.199655i	−0.317027	−	0.948416i	$-0.602685\pi$
$13$	1.24684	−	0.719865i	0.345812	−	0.199655i	0.662839	+	0.748762i	$0.269351\pi$
$14$	−0.831193	−	1.14417i	−0.222146	−	0.305791i
$15$	5.57324	−	1.62827i	1.43901	−	0.420417i
$16$	−0.418957	+	3.97800i	−0.104739	+	0.994500i
$17$			2.72213i			0.660214i	0.943943	+	0.330107i	$0.107085\pi$
$17$			2.72213i			0.660214i	−0.943943	+	0.330107i	$0.892915\pi$
$18$	2.64512	+	3.31713i	0.623460	+	0.781855i
$19$	6.49390			1.48980			0.744901	−	0.667175i	$-0.232497\pi$
$19$	6.49390			1.48980			0.744901	+	0.667175i	$0.232497\pi$
$20$	−2.07247	+	6.37610i	−0.463418	+	1.42574i
$21$	1.19695	−	1.25193i	0.261195	−	0.273193i
$22$	0.893754	+	1.23028i	0.190549	+	0.262298i
$23$	2.74636	+	4.75684i	0.572656	+	0.991869i	0.996292	+	0.0860366i	$0.0274202\pi$
$23$	2.74636	+	4.75684i	0.572656	+	0.991869i	−0.423636	+	0.905832i	$0.639246\pi$
$24$	−4.88534	+	0.365361i	−0.997215	+	0.0745791i
$25$	−3.11872	+	5.40178i	−0.623744	+	1.08036i
$26$	−2.02494	+	0.212722i	−0.397124	+	0.0417181i
$27$	−3.41866	+	3.91315i	−0.657922	+	0.753086i
$28$	0.415616	+	1.95634i	0.0785440	+	0.369713i
$29$	−0.590015	+	1.02194i	−0.109563	+	0.189769i	−0.915593	−	0.402106i	$-0.868278\pi$
$29$	−0.590015	+	1.02194i	−0.109563	+	0.189769i	0.806030	+	0.591874i	$0.201612\pi$
$30$	−8.13689	−	1.10259i	−1.48559	−	0.201305i
$31$	9.00497	−	5.19902i	1.61734	−	0.933772i	0.629736	−	0.776809i	$-0.283163\pi$
$31$	9.00497	−	5.19902i	1.61734	−	0.933772i	0.987604	−	0.156963i	$-0.0501704\pi$
$32$	2.82973	−	4.89823i	0.500229	−	0.865893i
$33$	−1.28704	+	1.34615i	−0.224044	+	0.234335i
$34$	1.56599	−	3.51677i	0.268565	−	0.603122i
$35$			3.35223i			0.566630i
$36$	−1.50899	−	5.80715i	−0.251499	−	0.967858i
$37$			3.07642i			0.505760i	0.967498	+	0.252880i	$0.0813778\pi$
$37$			3.07642i			0.505760i	−0.967498	+	0.252880i	$0.918622\pi$
$38$	−8.38958	−	3.73582i	−1.36097	−	0.606029i
$39$	−0.699316	−	2.39362i	−0.111980	−	0.383286i
$40$	6.34551	−	7.04514i	1.00331	−	1.11394i
$41$	2.74938	−	1.58736i	0.429382	−	0.247904i	−0.269702	−	0.962944i	$-0.586925\pi$
$41$	2.74938	−	1.58736i	0.429382	−	0.247904i	0.699083	+	0.715040i	$0.253592\pi$
$42$	−2.26657	+	0.928806i	−0.349739	+	0.143318i
$43$	2.28900	−	3.96466i	0.349069	−	0.604605i	−0.637015	−	0.770851i	$-0.719831\pi$
$43$	2.28900	−	3.96466i	0.349069	−	0.604605i	0.986084	+	0.166246i	$0.0531645\pi$
$44$	−0.446898	−	2.10359i	−0.0673724	−	0.317128i
$45$	−0.451343	−	10.0466i	−0.0672823	−	1.49765i
$46$	−0.811555	−	7.72537i	−0.119657	−	1.13904i
$47$	2.70286	−	4.68149i	0.394252	−	0.682865i	−0.598753	−	0.800934i	$-0.704337\pi$
$47$	2.70286	−	4.68149i	0.394252	−	0.682865i	0.993005	+	0.118069i	$0.0376703\pi$
$48$	6.52164	+	2.33842i	0.941317	+	0.337522i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	7.13667	−	5.18452i	1.00928	−	0.733201i
$51$	4.58046	+	1.11777i	0.641393	+	0.156519i
$52$	2.73844	+	0.890093i	0.379753	+	0.123434i
$53$	−12.5659			−1.72607			−0.863033	−	0.505148i	$-0.831438\pi$
$53$	−12.5659			−1.72607			−0.863033	+	0.505148i	$0.831438\pi$
$54$	6.66779	−	3.08878i	0.907371	−	0.420330i
$55$		−	3.60454i		−	0.486036i
$56$	0.588503	−	2.76653i	0.0786420	−	0.369693i
$57$	2.66654	−	10.9271i	0.353192	−	1.44733i
$58$	1.35015	−	0.980832i	0.177283	−	0.128790i
$59$	−11.1655	+	6.44638i	−1.45362	+	0.839247i	−0.998684	−	0.0512782i	$-0.983670\pi$
$59$	−11.1655	+	6.44638i	−1.45362	+	0.839247i	−0.454934	+	0.890525i	$0.650337\pi$
$60$	9.87789	+	6.10545i	1.27523	+	0.788211i
$61$	1.14110	+	0.658814i	0.146103	+	0.0843525i	0.571269	−	0.820763i	$-0.306451\pi$
$61$	1.14110	+	0.658814i	0.146103	+	0.0843525i	−0.425167	+	0.905115i	$0.639784\pi$
$62$	−14.6246	+	1.53632i	−1.85732	+	0.195113i
$63$	−1.61509	−	2.52814i	−0.203482	−	0.318516i
$64$	−6.47363	+	4.70022i	−0.809204	+	0.587528i
$65$	4.17970	+	2.41315i	0.518428	+	0.299315i
$66$	2.43716	−	0.998714i	0.299994	−	0.122933i
$67$	−2.57984	−	4.46841i	−0.315177	−	0.545903i	0.664298	−	0.747468i	$-0.268731\pi$
$67$	−2.57984	−	4.46841i	−0.315177	−	0.545903i	−0.979475	+	0.201565i	$0.935397\pi$
$68$	−4.04626	+	3.64250i	−0.490682	+	0.441718i
$69$	9.13192	−	2.66796i	1.09935	−	0.321185i
$70$	1.92847	−	4.33080i	0.230497	−	0.517630i
$71$	14.0523			1.66770			0.833851	−	0.551990i	$-0.186131\pi$
$71$	14.0523			1.66770			0.833851	+	0.551990i	$0.186131\pi$
$72$	−1.39125	+	8.37045i	−0.163960	+	0.986467i
$73$	−3.81183			−0.446141			−0.223070	−	0.974802i	$-0.571608\pi$
$73$	−3.81183			−0.446141			−0.223070	+	0.974802i	$0.571608\pi$
$74$	1.76981	−	3.97448i	0.205736	−	0.462024i
$75$	7.80881	+	7.46588i	0.901684	+	0.862085i
$76$	8.68951	+	9.65273i	0.996755	+	1.10724i
$77$	−0.537633	−	0.931208i	−0.0612690	−	0.106121i
$78$	−0.473547	+	3.49467i	−0.0536186	+	0.395693i
$79$	1.96184	+	1.13267i	0.220724	+	0.127435i	0.606286	−	0.795247i	$-0.292659\pi$
$79$	1.96184	+	1.13267i	0.220724	+	0.127435i	−0.385561	+	0.922682i	$0.625992\pi$
$80$	−12.2508	+	5.45130i	−1.36968	+	0.609474i
$81$	5.18078	+	7.35932i	0.575642	+	0.817702i
$82$	−4.46516	+	0.469067i	−0.493094	+	0.0517998i
$83$	−6.85242	−	3.95624i	−0.752150	−	0.434254i	0.0743200	−	0.997234i	$-0.476321\pi$
$83$	−6.85242	−	3.95624i	−0.752150	−	0.434254i	−0.826470	+	0.562980i	$0.809655\pi$
$84$	3.46254	+	0.103971i	0.377794	+	0.0113442i
$85$	−7.90267	+	4.56261i	−0.857165	+	0.494884i
$86$	−5.23799	+	3.80520i	−0.564827	+	0.410325i
$87$	1.47731	+	1.41243i	0.158384	+	0.151429i
$88$	−0.632798	+	2.97475i	−0.0674564	+	0.317110i
$89$		−	3.72610i		−	0.394965i	−0.980306	−	0.197483i	$-0.936723\pi$
$89$		−	3.72610i		−	0.394965i	0.980306	−	0.197483i	$-0.0632766\pi$
$90$	−5.19649	+	13.2390i	−0.547758	+	1.39551i
$91$	1.43973			0.150925
$92$	−3.39580	+	10.4474i	−0.354036	+	1.08922i
$93$	−5.05061	−	17.2873i	−0.523724	−	1.79261i
$94$	−6.18504	+	4.49319i	−0.637938	+	0.463437i
$95$	10.8845	+	18.8525i	1.11673	+	1.93423i
$96$	−7.08017	−	6.77283i	−0.722617	−	0.691249i
$97$	2.81825	−	4.88135i	0.286150	−	0.495626i	−0.686737	−	0.726906i	$-0.740958\pi$
$97$	2.81825	−	4.88135i	0.286150	−	0.495626i	0.972887	+	0.231279i	$0.0742911\pi$
$98$	−0.147751	−	1.40647i	−0.0149251	−	0.142075i
$99$	1.73665	+	2.71842i	0.174540	+	0.273212i
$100$	−12.2025	+	2.59238i	−1.22025	+	0.259238i
$101$	−3.94075	+	6.82557i	−0.392119	+	0.679170i	−0.992729	−	0.120372i	$-0.961591\pi$
$101$	−3.94075	+	6.82557i	−0.392119	+	0.679170i	0.600610	+	0.799542i	$0.294924\pi$
$102$	−5.27455	−	4.07912i	−0.522258	−	0.403893i
$103$	−16.1094	+	9.30074i	−1.58730	+	0.916429i	−0.593552	+	0.804796i	$0.702275\pi$
$103$	−16.1094	+	9.30074i	−1.58730	+	0.916429i	−0.993749	+	0.111633i	$0.964392\pi$
$104$	−3.02578	−	2.72530i	−0.296702	−	0.267237i
$105$	5.64071	+	1.37650i	0.550477	+	0.134333i
$106$	16.2342	+	7.22895i	1.57680	+	0.702138i
$107$		−	14.8456i		−	1.43518i	−0.696468	−	0.717588i	$-0.745246\pi$
$107$		−	14.8456i		−	1.43518i	0.696468	−	0.717588i	$-0.254754\pi$
$108$	−10.3912	+	0.154597i	−0.999889	+	0.0148761i
$109$			0.349221i			0.0334493i	0.999860	+	0.0167247i	$0.00532388\pi$
$109$			0.349221i			0.0334493i	−0.999860	+	0.0167247i	$0.994676\pi$
$110$	−2.07362	+	4.65677i	−0.197712	+	0.444006i
$111$	5.17661	+	1.26325i	0.491342	+	0.119902i
$112$	−2.35183	+	3.23557i	−0.222227	+	0.305733i
$113$	10.0408	−	5.79705i	0.944558	−	0.545341i	0.0531718	−	0.998585i	$-0.483067\pi$
$113$	10.0408	−	5.79705i	0.944558	−	0.545341i	0.891386	+	0.453245i	$0.149734\pi$
$114$	−9.73111	+	12.5829i	−0.911402	+	1.17850i
$115$	−9.20643	+	15.9460i	−0.858504	+	1.48697i
$116$	−2.30854	+	0.490439i	−0.214342	+	0.0455361i
$117$	−4.31484	+	0.193845i	−0.398907	+	0.0179210i
$118$	18.1333	−	1.90492i	1.66931	−	0.175362i
$119$	−1.36107	+	2.35744i	−0.124769	+	0.216106i
$120$	−9.24907	−	13.5703i	−0.844321	−	1.23879i
$121$	−4.92190	−	8.52498i	−0.447446	−	0.774998i
$122$	−1.09520	−	1.50759i	−0.0991551	−	0.136490i
$123$	−1.54205	−	5.27812i	−0.139042	−	0.475912i
$124$	19.7776	+	6.42844i	1.77608	+	0.577291i
$125$	−4.14818			−0.371024
$126$	0.632174	+	4.19528i	0.0563185	+	0.373745i
$127$			7.80026i			0.692162i	0.938205	+	0.346081i	$0.112488\pi$
$127$			7.80026i			0.692162i	−0.938205	+	0.346081i	$0.887512\pi$
$128$	11.0673	−	2.34815i	0.978225	−	0.207549i
$129$	−5.73132	−	5.47962i	−0.504614	−	0.482453i
$130$	−4.01159	−	5.52210i	−0.351840	−	0.484320i
$131$	−6.28673	+	3.62965i	−0.549274	+	0.317124i	−0.748829	−	0.662763i	$-0.769384\pi$
$131$	−6.28673	+	3.62965i	−0.549274	+	0.317124i	0.199555	+	0.979887i	$0.436050\pi$
$132$	−3.72315	−	0.111797i	−0.324059	−	0.00973065i
$133$	5.62388	+	3.24695i	0.487652	+	0.281546i
$134$	0.762347	+	7.25695i	0.0658568	+	0.626905i
$135$	−17.0904	−	3.36588i	−1.47091	−	0.289689i
$136$	7.32290	−	2.37807i	0.627934	−	0.203918i
$137$	−13.4222	−	7.74933i	−1.14674	−	0.662070i	−0.198648	−	0.980071i	$-0.563655\pi$
$137$	−13.4222	−	7.74933i	−1.14674	−	0.662070i	−0.948090	+	0.318001i	$0.896988\pi$
$138$	−13.3325	−	1.80663i	−1.13494	−	0.153791i
$139$	−6.00980	−	10.4093i	−0.509745	−	0.882904i	−0.999936	−	0.0112893i	$-0.996406\pi$
$139$	−6.00980	−	10.4093i	−0.509745	−	0.882904i	0.490191	−	0.871615i	$-0.336927\pi$
$140$	−4.98286	+	4.48563i	−0.421128	+	0.379105i
$141$	−6.76756	−	6.47035i	−0.569931	−	0.544902i
$142$	−18.1544	−	8.08402i	−1.52349	−	0.678396i
$143$	−1.54809			−0.129458
$144$	6.61274	−	10.0136i	0.551061	−	0.834465i
$145$	−3.95573			−0.328505
$146$	4.92457	+	2.19287i	0.407560	+	0.181483i
$147$	1.66255	−	0.485727i	0.137125	−	0.0400621i
$148$	−4.57289	+	4.11657i	−0.375889	+	0.338380i
$149$	4.56134	+	7.90047i	0.373679	+	0.647231i	0.990128	−	0.140163i	$-0.0447628\pi$
$149$	4.56134	+	7.90047i	0.373679	+	0.647231i	−0.616449	+	0.787395i	$0.711429\pi$
$150$	−5.79337	−	14.1376i	−0.473027	−	1.15433i
$151$	−5.72796	−	3.30704i	−0.466135	−	0.269123i	0.248485	−	0.968636i	$-0.420067\pi$
$151$	−5.72796	−	3.30704i	−0.466135	−	0.269123i	−0.714620	+	0.699512i	$0.753401\pi$
$152$	−5.67310	−	17.4694i	−0.460149	−	1.41696i
$153$	3.76168	−	7.24844i	0.304114	−	0.586001i
$154$	0.158872	+	1.51233i	0.0128023	+	0.121867i
$155$	30.1867	+	17.4283i	2.42466	+	1.39988i
$156$	2.62220	−	4.24240i	0.209944	−	0.339664i
$157$	−20.3621	+	11.7560i	−1.62507	+	0.938235i	−0.639535	+	0.768762i	$0.720873\pi$
$157$	−20.3621	+	11.7560i	−1.62507	+	0.938235i	−0.985535	+	0.169473i	$0.945794\pi$
$158$	−1.88293	−	2.59192i	−0.149798	−	0.206202i
$159$	−5.15986	+	21.1444i	−0.409204	+	1.67686i
$160$	18.9631	+	0.00502510i	1.49916	+	0.000397269i
$161$			5.49272i			0.432887i
$162$	−2.45946	−	12.4880i	−0.193234	−	0.981153i
$163$	−9.91376			−0.776506			−0.388253	−	0.921553i	$-0.626921\pi$
$163$	−9.91376			−0.776506			−0.388253	+	0.921553i	$0.626921\pi$
$164$	6.03846	+	1.96272i	0.471524	+	0.153263i
$165$	−6.06526	−	1.48011i	−0.472180	−	0.115226i
$166$	6.57681	+	9.05321i	0.510459	+	0.702665i
$167$	7.00366	+	12.1307i	0.541959	+	0.938701i	0.998792	+	0.0491480i	$0.0156506\pi$
$167$	7.00366	+	12.1307i	0.541959	+	0.938701i	−0.456832	+	0.889553i	$0.651016\pi$
$168$	−4.41351	−	2.12626i	−0.340509	−	0.164044i
$169$	−5.46359	+	9.46321i	−0.420276	+	0.727939i
$170$	12.8344	−	1.34826i	0.984352	−	0.103407i
$171$	−17.2918	−	8.97383i	−1.32234	−	0.686246i
$172$	8.95612	−	1.90269i	0.682897	−	0.145079i
$173$	12.1964	−	21.1247i	0.927273	−	1.60608i	0.139408	−	0.990235i	$-0.455480\pi$
$173$	12.1964	−	21.1247i	0.927273	−	1.60608i	0.787865	−	0.615848i	$-0.211187\pi$
$174$	−1.09602	−	2.67461i	−0.0830889	−	0.202762i
$175$	−5.40178	+	3.11872i	−0.408336	+	0.235753i
$176$	2.52884	−	3.47910i	0.190619	−	0.262247i
$177$	6.26236	+	21.4348i	0.470708	+	1.61114i
$178$	−2.14355	+	4.81381i	−0.160666	+	0.360810i
$179$		−	18.1295i		−	1.35506i	−0.735494	−	0.677531i	$-0.763050\pi$
$179$		−	18.1295i		−	1.35506i	0.735494	−	0.677531i	$-0.236950\pi$
$180$	14.3296	−	14.1142i	1.06806	−	1.05201i
$181$		−	0.593513i		−	0.0441154i	−0.999757	−	0.0220577i	$-0.992978\pi$
$181$		−	0.593513i		−	0.0441154i	0.999757	−	0.0220577i	$-0.00702176\pi$
$182$	−1.86001	−	0.828249i	−0.137873	−	0.0613939i
$183$	1.57713	−	1.64957i	0.116585	−	0.121940i
$184$	10.3973	−	11.5437i	0.766498	−	0.851011i
$185$	−8.93120	+	5.15643i	−0.656635	+	0.379108i
$186$	−3.42006	+	25.2392i	−0.250771	+	1.85063i
$187$	1.46351	−	2.53487i	0.107022	−	0.185368i
$188$	10.5754	−	2.24670i	0.771291	−	0.163858i
$189$	−4.91722	+	1.67956i	−0.357675	+	0.122170i
$190$	−3.21640	−	30.6176i	−0.233342	−	2.22123i
$191$	5.04588	−	8.73972i	0.365107	−	0.632384i	−0.623686	−	0.781675i	$-0.714366\pi$
$191$	5.04588	−	8.73972i	0.365107	−	0.632384i	0.988793	+	0.149291i	$0.0476991\pi$
$192$	5.25072	+	12.8230i	0.378938	+	0.925422i
$193$	9.33932	+	16.1762i	0.672259	+	1.16439i	0.977262	+	0.212036i	$0.0680093\pi$
$193$	9.33932	+	16.1762i	0.672259	+	1.16439i	−0.305003	+	0.952351i	$0.598657\pi$
$194$	−6.44910	+	4.68502i	−0.463018	+	0.336365i
$195$	5.77683	−	6.04218i	0.413687	−	0.432690i
$196$	−0.618236	+	1.90205i	−0.0441597	+	0.135861i
$197$	−16.9533			−1.20787			−0.603937	−	0.797032i	$-0.706402\pi$
$197$	−16.9533			−1.20787			−0.603937	+	0.797032i	$0.706402\pi$
$198$	−0.679755	−	4.51104i	−0.0483081	−	0.320586i
$199$		−	4.06295i		−	0.288015i	−0.989577	−	0.144007i	$-0.954001\pi$
$199$		−	4.06295i		−	0.288015i	0.989577	−	0.144007i	$-0.0459989\pi$
$200$	17.2560	+	3.67075i	1.22019	+	0.259561i
$201$	−8.57821	+	2.50619i	−0.605060	+	0.176773i
$202$	9.01774	−	6.55104i	0.634486	−	0.460930i
$203$	−1.02194	+	0.590015i	−0.0717258	+	0.0414109i
$204$	4.46764	+	8.30423i	0.312798	+	0.581413i
$205$	9.21657	+	5.32119i	0.643713	+	0.371648i
$206$	26.1625	−	2.74839i	1.82283	−	0.191489i
$207$	−0.739539	−	16.4616i	−0.0514015	−	1.14416i
$208$	2.34125	+	5.26153i	0.162336	+	0.364822i
$209$	−6.04717	−	3.49134i	−0.418292	−	0.241501i
$210$	−6.49545	−	5.02332i	−0.448229	−	0.346642i
$211$	5.98684	+	10.3695i	0.412151	+	0.713866i	0.995125	−	0.0986247i	$-0.0314443\pi$
$211$	5.98684	+	10.3695i	0.412151	+	0.713866i	−0.582974	+	0.812491i	$0.698111\pi$
$212$	−16.8145	−	18.6784i	−1.15483	−	1.28284i
$213$	5.77019	−	23.6454i	0.395367	−	1.62016i
$214$	−8.54038	+	19.1793i	−0.583808	+	1.31107i
$215$	15.3465			1.04662
$216$	13.5135	+	5.77811i	0.919474	+	0.393150i
$217$	10.3980			0.705865
$218$	0.200900	−	0.451165i	0.0136067	−	0.0305568i
$219$	−1.56522	+	6.41406i	−0.105768	+	0.433422i
$220$	5.35790	−	4.82325i	0.361230	−	0.325183i
$221$	1.95957	+	3.39407i	0.131815	+	0.228310i
$222$	−5.96103	−	4.61002i	−0.400078	−	0.309404i
$223$	−12.1191	−	6.99697i	−0.811556	−	0.468552i	0.0359402	−	0.999354i	$-0.488557\pi$
$223$	−12.1191	−	6.99697i	−0.811556	−	0.468552i	−0.847496	+	0.530802i	$0.821891\pi$
$224$	4.89973	−	2.82713i	0.327377	−	0.188895i
$225$	15.7691	−	10.0740i	1.05127	−	0.671602i
$226$	−16.3068	+	1.71304i	−1.08471	+	0.113950i
$227$	5.60231	+	3.23450i	0.371838	+	0.214681i	0.674261	−	0.738493i	$-0.264462\pi$
$227$	5.60231	+	3.23450i	0.371838	+	0.214681i	−0.302423	+	0.953174i	$0.597795\pi$
$228$	19.8105	−	10.6580i	1.31198	−	0.705841i
$229$	−23.5577	+	13.6010i	−1.55673	+	0.898781i	−0.559168	+	0.829054i	$0.688879\pi$
$229$	−23.5577	+	13.6010i	−1.55673	+	0.898781i	−0.997566	+	0.0697269i	$0.977787\pi$
$230$	21.0674	−	15.3046i	1.38914	−	1.00916i
$231$	−1.78768	+	0.522286i	−0.117621	+	0.0343639i
$232$	3.26458	+	0.694451i	0.214330	+	0.0455929i
$233$			4.75217i			0.311325i	0.987810	+	0.155662i	$0.0497512\pi$
$233$			4.75217i			0.311325i	−0.987810	+	0.155662i	$0.950249\pi$
$234$	5.68593	+	2.23181i	0.371701	+	0.145898i
$235$	18.1212			1.18210
$236$	−24.5226	−	7.97076i	−1.59629	−	0.518852i
$237$	2.71149	−	2.83604i	0.176130	−	0.184220i
$238$	3.11457	−	2.26262i	0.201888	−	0.146664i
$239$	11.1798	+	19.3640i	0.723162	+	1.25255i	0.959726	+	0.280938i	$0.0906455\pi$
$239$	11.1798	+	19.3640i	0.723162	+	1.25255i	−0.236564	+	0.971616i	$0.576021\pi$
$240$	4.14230	+	22.8525i	0.267384	+	1.47512i
$241$	−0.930351	+	1.61141i	−0.0599292	+	0.103800i	−0.894433	−	0.447201i	$-0.852421\pi$
$241$	−0.930351	+	1.61141i	−0.0599292	+	0.103800i	0.834504	+	0.551001i	$0.185754\pi$
$242$	1.45443	+	13.8451i	0.0934944	+	0.889994i
$243$	14.5107	−	5.69565i	0.930860	−	0.365376i
$244$	0.547627	+	2.57773i	0.0350582	+	0.165022i
$245$	−1.67611	+	2.90312i	−0.107083	+	0.185473i
$246$	−1.04421	+	7.70601i	−0.0665762	+	0.491317i
$247$	8.09687	−	4.67473i	0.515192	−	0.297446i
$248$	−21.8528	−	19.6827i	−1.38766	−	1.24985i
$249$	−9.47082	+	9.90585i	−0.600189	+	0.627758i
$250$	5.35910	+	2.38637i	0.338939	+	0.150927i
$251$			14.9214i			0.941831i	0.882178	+	0.470915i	$0.156076\pi$
$251$			14.9214i			0.941831i	−0.882178	+	0.470915i	$0.843924\pi$
$252$	1.59675	−	5.78363i	0.100586	−	0.364335i
$253$		−	5.90614i		−	0.371316i
$254$	4.48734	−	10.0773i	0.281561	−	0.632306i
$255$	4.43236	+	15.1711i	0.277565	+	0.950052i
$256$	−15.6489	−	3.33322i	−0.978059	−	0.208326i
$257$	−16.4430	+	9.49337i	−1.02569	+	0.592180i	−0.915746	−	0.401758i	$-0.868399\pi$
$257$	−16.4430	+	9.49337i	−1.02569	+	0.592180i	−0.109940	+	0.993938i	$0.535066\pi$
$258$	4.25207	+	10.3763i	0.264722	+	0.646002i
$259$	−1.53821	+	2.66426i	−0.0955797	+	0.165549i
$260$	2.00589	+	9.44189i	0.124400	+	0.585561i
$261$	2.98328	−	1.90585i	0.184660	−	0.117969i
$262$	10.2100	−	1.07257i	0.630777	−	0.0662635i
$263$	9.10839	−	15.7762i	0.561647	−	0.972802i	−0.435706	−	0.900089i	$-0.643501\pi$
$263$	9.10839	−	15.7762i	0.561647	−	0.972802i	0.997353	−	0.0727125i	$-0.0231656\pi$
$264$	4.74570	+	2.28629i	0.292077	+	0.140712i
$265$	−21.0620	−	36.4804i	−1.29383	−	2.24097i
$266$	−5.39768	−	7.43010i	−0.330953	−	0.455569i
$267$	−6.26980	−	1.53002i	−0.383706	−	0.0936356i
$268$	3.18989	−	9.81394i	0.194854	−	0.599482i
$269$	1.80995			0.110355			0.0551773	−	0.998477i	$-0.482428\pi$
$269$	1.80995			0.110355			0.0551773	+	0.998477i	$0.482428\pi$
$270$	20.1431	+	14.1802i	1.22587	+	0.862981i
$271$		−	24.6211i		−	1.49563i	−0.663910	−	0.747813i	$-0.731104\pi$
$271$		−	24.6211i		−	1.49563i	0.663910	−	0.747813i	$-0.268896\pi$
$272$	−10.8286	−	1.14046i	−0.656583	−	0.0691504i
$273$	0.591186	−	2.42260i	0.0357802	−	0.146622i
$274$	12.8824	+	17.7330i	0.778253	+	1.07129i
$275$	5.80835	−	3.35345i	0.350257	−	0.202221i
$276$	16.1852	+	10.0040i	0.974235	+	0.602168i
$277$	15.8462	+	9.14883i	0.952108	+	0.549700i	0.893735	−	0.448595i	$-0.148075\pi$
$277$	15.8462	+	9.14883i	0.952108	+	0.549700i	0.0583728	+	0.998295i	$0.481409\pi$
$278$	1.77591	+	16.9053i	0.106512	+	1.01391i
$279$	−31.1627	+	1.39999i	−1.86566	+	0.0838153i
$280$	9.01794	−	2.92852i	0.538925	−	0.175013i
$281$	3.94424	+	2.27721i	0.235294	+	0.135847i	0.613012	−	0.790074i	$-0.289958\pi$
$281$	3.94424	+	2.27721i	0.235294	+	0.135847i	−0.377718	+	0.925921i	$0.623291\pi$
$282$	5.02086	+	12.2524i	0.298988	+	0.729620i
$283$	−9.97260	−	17.2730i	−0.592809	−	1.02678i	−0.993852	−	0.110717i	$-0.964685\pi$
$283$	−9.97260	−	17.2730i	−0.592809	−	1.02678i	0.401043	−	0.916059i	$-0.368648\pi$
$284$	18.8034	+	20.8878i	1.11578	+	1.23946i
$285$	36.1921	−	10.5738i	2.14383	−	0.626338i
$286$	2.00001	+	0.890589i	0.118263	+	0.0526616i
$287$	3.17472			0.187398
$288$	−14.3037	+	9.13254i	−0.842855	+	0.538140i
$289$	9.58999			0.564117
$290$	5.11048	+	2.27566i	0.300098	+	0.133631i
$291$	−7.05648	−	6.74659i	−0.413658	−	0.395492i
$292$	−5.10062	−	5.66602i	−0.298491	−	0.331579i
$293$	−8.23125	−	14.2569i	−0.480874	−	0.832899i	0.518885	−	0.854844i	$-0.326347\pi$
$293$	−8.23125	−	14.2569i	−0.480874	−	0.832899i	−0.999759	+	0.0219452i	$0.993014\pi$
$294$	−2.42731	−	0.328913i	−0.141563	−	0.0191826i
$295$	−37.4292	−	21.6097i	−2.17921	−	1.25817i
$296$	8.27598	−	2.68757i	0.481031	−	0.156212i
$297$	5.28733	−	1.80597i	0.306802	−	0.104793i
$298$	−1.34788	−	12.8308i	−0.0780808	−	0.743268i
$299$	6.84856	+	3.95402i	0.396063	+	0.228667i
$300$	−0.648513	+	21.5974i	−0.0374419	+	1.24693i
$301$	3.96466	−	2.28900i	0.228519	−	0.131936i
$302$	5.49758	+	7.56762i	0.316350	+	0.435467i
$303$	9.86705	+	9.43372i	0.566847	+	0.541953i
$304$	−2.72067	+	25.8327i	−0.156041	+	1.48161i
$305$			4.41699i			0.252916i
$306$	−9.02967	+	7.20036i	−0.516192	+	0.411617i
$307$	−12.6639			−0.722766			−0.361383	−	0.932418i	$-0.617695\pi$
$307$	−12.6639			−0.722766			−0.361383	+	0.932418i	$0.617695\pi$
$308$	0.664768	−	2.04521i	0.0378787	−	0.116537i
$309$	9.03524	+	30.9259i	0.513997	+	1.75931i
$310$	−28.9726	−	39.8818i	−1.64553	−	2.26513i
$311$	−13.2369	−	22.9269i	−0.750593	−	1.30007i	−0.947535	−	0.319651i	$-0.896434\pi$
$311$	−13.2369	−	22.9269i	−0.750593	−	1.30007i	0.196942	−	0.980415i	$-0.436899\pi$
$312$	−5.82824	+	3.97233i	−0.329959	+	0.224889i
$313$	16.8999	−	29.2715i	0.955239	−	1.65452i	0.221419	−	0.975179i	$-0.428931\pi$
$313$	16.8999	−	29.2715i	0.955239	−	1.65452i	0.733820	−	0.679344i	$-0.237736\pi$
$314$	33.0691	−	3.47394i	1.86620	−	0.196046i
$315$	4.63240	−	8.92624i	0.261006	−	0.502937i
$316$	0.941511	+	4.43177i	0.0529641	+	0.249307i
$317$	−9.91654	+	17.1759i	−0.556968	+	0.964697i	0.440779	+	0.897615i	$0.354702\pi$
$317$	−9.91654	+	17.1759i	−0.556968	+	0.964697i	−0.997747	+	0.0670816i	$0.978631\pi$
$318$	18.8301	−	24.3484i	1.05594	−	1.36539i
$319$	1.09885	−	0.634423i	0.0615240	−	0.0355209i
$320$	−24.4958	−	10.9156i	−1.36936	−	0.610200i
$321$	−24.9803	−	6.09593i	−1.39426	−	0.340242i
$322$	3.15986	−	7.09615i	0.176092	−	0.395453i
$323$			17.6773i			0.983589i
$324$	−4.00671	+	17.5484i	−0.222595	+	0.974911i
$325$			8.98023i			0.498134i
$326$	12.8078	+	5.70320i	0.709356	+	0.315871i
$327$	0.587625	+	0.143398i	0.0324958	+	0.00792994i
$328$	−6.67208	−	6.00949i	−0.368404	−	0.331818i
$329$	4.68149	−	2.70286i	0.258099	−	0.149013i
$330$	6.98434	+	5.40140i	0.384476	+	0.297338i
$331$	14.0341	−	24.3078i	0.771385	−	1.33608i	−0.165420	−	0.986223i	$-0.552898\pi$
$331$	14.0341	−	24.3078i	0.771385	−	1.33608i	0.936804	−	0.349854i	$-0.113769\pi$
$332$	−3.28856	−	15.4795i	−0.180483	−	0.849549i
$333$	4.25126	−	8.19182i	0.232968	−	0.448909i
$334$	−2.06959	−	19.7009i	−0.113243	−	1.07799i
$335$	8.64820	−	14.9791i	0.472502	−	0.818397i
$336$	4.47869	+	5.28595i	0.244333	+	0.288372i
$337$	0.907991	+	1.57269i	0.0494614	+	0.0856697i	0.889696	−	0.456553i	$-0.150916\pi$
$337$	0.907991	+	1.57269i	0.0494614	+	0.0856697i	−0.840235	+	0.542223i	$0.817583\pi$
$338$	12.5025	−	9.08260i	0.680047	−	0.494028i
$339$	−5.63157	−	19.2758i	−0.305865	−	1.04692i
$340$	−17.3566	−	5.64153i	−0.941293	−	0.305955i
$341$	−11.1807			−0.605467
$342$	17.1771	+	21.5411i	0.928832	+	1.16481i
$343$			1.00000i			0.0539949i
$344$	−12.6651	−	2.69416i	−0.682859	−	0.145260i
$345$	23.0515	+	22.0392i	1.24105	+	1.18655i
$346$	−27.9094	+	20.2751i	−1.50042	+	1.08999i
$347$	7.11392	−	4.10722i	0.381895	−	0.220487i	−0.296747	−	0.954956i	$-0.595902\pi$
$347$	7.11392	−	4.10722i	0.381895	−	0.220487i	0.678643	+	0.734469i	$0.262569\pi$
$348$	−0.122689	+	4.08590i	−0.00657682	+	0.219027i
$349$	23.8217	+	13.7535i	1.27515	+	0.736207i	0.975952	−	0.217985i	$-0.0699485\pi$
$349$	23.8217	+	13.7535i	1.27515	+	0.736207i	0.299195	+	0.954192i	$0.403282\pi$
$350$	8.77280	−	0.921588i	0.468926	−	0.0492609i
$351$	−1.44559	+	7.34006i	−0.0771600	+	0.391784i
$352$	−5.26851	+	3.03992i	−0.280813	+	0.162028i
$353$	−0.891222	−	0.514547i	−0.0474349	−	0.0273866i	0.476095	−	0.879394i	$-0.342052\pi$
$353$	−0.891222	−	0.514547i	−0.0474349	−	0.0273866i	−0.523530	+	0.852007i	$0.675385\pi$
$354$	4.24060	−	31.2947i	0.225385	−	1.66329i
$355$	23.5533	+	40.7955i	1.25008	+	2.16520i
$356$	5.53859	−	4.98590i	0.293545	−	0.264252i
$357$	3.40791	+	3.25825i	0.180366	+	0.172445i
$358$	−10.4296	+	23.4218i	−0.551219	+	1.23788i
$359$	−27.0391			−1.42707			−0.713536	−	0.700619i	$-0.752907\pi$
$359$	−27.0391			−1.42707			−0.713536	+	0.700619i	$0.752907\pi$
$360$	−26.6323	+	9.99089i	−1.40364	+	0.526566i
$361$	23.1707			1.21951
$362$	−0.341436	+	0.766769i	−0.0179455	+	0.0403005i
$363$	−16.3658	+	4.78140i	−0.858982	+	0.250958i
$364$	1.92651	+	2.14006i	0.100976	+	0.112170i
$365$	−6.38906	−	11.0662i	−0.334419	−	0.579230i
$366$	−2.98649	+	1.22382i	−0.156106	+	0.0639701i
$367$	−10.7007	−	6.17807i	−0.558574	−	0.322493i	0.193999	−	0.981002i	$-0.437854\pi$
$367$	−10.7007	−	6.17807i	−0.558574	−	0.322493i	−0.752573	+	0.658509i	$0.771187\pi$
$368$	−20.0733	+	8.93211i	−1.04639	+	0.465618i
$369$	−9.51455	+	0.427443i	−0.495308	+	0.0222518i
$370$	14.5048	−	1.52374i	0.754067	−	0.0792152i
$371$	−10.8824	−	6.28297i	−0.564988	−	0.326196i
$372$	18.9381	−	30.6395i	0.981894	−	1.58859i
$373$	−11.3267	+	6.53946i	−0.586473	+	0.338600i	−0.763702	−	0.645569i	$-0.776620\pi$
$373$	−11.3267	+	6.53946i	−0.586473	+	0.338600i	0.177229	+	0.984170i	$0.443287\pi$
$374$	−3.34900	+	2.43292i	−0.173173	+	0.125803i
$375$	−1.70333	+	6.98003i	−0.0879598	+	0.360447i
$376$	−14.9550	−	3.18128i	−0.771248	−	0.164062i
$377$			1.69892i			0.0874990i
$378$	7.31887	+	0.658934i	0.376442	+	0.0338919i
$379$	−26.2714			−1.34947			−0.674735	−	0.738060i	$-0.735742\pi$
$379$	−26.2714			−1.34947			−0.674735	+	0.738060i	$0.735742\pi$
$380$	−13.4584	+	41.4057i	−0.690401	+	2.12407i
$381$	13.1253	+	3.20296i	0.672429	+	0.164093i
$382$	−11.5467	+	8.38820i	−0.590778	+	0.429178i
$383$	−12.5259	−	21.6956i	−0.640046	−	1.10859i	−0.985422	−	0.170127i	$-0.945582\pi$
$383$	−12.5259	−	21.6956i	−0.640046	−	1.10859i	0.345376	−	0.938464i	$-0.387751\pi$
$384$	0.593340	−	19.5869i	0.0302787	−	0.999541i
$385$	1.80227	−	3.12162i	0.0918522	−	0.159093i
$386$	−2.75979	−	26.2710i	−0.140470	−	1.33716i
$387$	−11.5738	+	7.39388i	−0.588330	+	0.375852i
$388$	11.0269	−	2.34262i	0.559806	−	0.118928i
$389$	8.99052	−	15.5720i	0.455838	−	0.789534i	−0.542898	−	0.839798i	$-0.682673\pi$
$389$	8.99052	−	15.5720i	0.455838	−	0.789534i	0.998736	+	0.0502645i	$0.0160064\pi$
$390$	−10.9391	+	4.48270i	−0.553925	+	0.226990i
$391$	−12.9487	+	7.47596i	−0.654846	+	0.378076i
$392$	1.89292	−	2.10163i	0.0956070	−	0.106148i
$393$	3.52604	+	12.0689i	0.177865	+	0.608797i
$394$	21.9023	+	9.75292i	1.10342	+	0.491345i
$395$			7.59393i			0.382092i
$396$	−1.71693	+	6.21895i	−0.0862789	+	0.312514i
$397$		−	3.71198i		−	0.186299i	−0.995652	−	0.0931494i	$-0.970307\pi$
$397$		−	3.71198i		−	0.186299i	0.995652	−	0.0931494i	$-0.0296934\pi$
$398$	−2.33734	+	5.24900i	−0.117160	+	0.263109i
$399$	7.77285	−	8.12988i	0.389129	−	0.407003i
$400$	−20.1817	−	14.6694i	−1.00908	−	0.733469i
$401$	25.7821	−	14.8853i	1.28750	−	0.743338i	0.309291	−	0.950967i	$-0.399908\pi$
$401$	25.7821	−	14.8853i	1.28750	−	0.743338i	0.978208	+	0.207629i	$0.0665748\pi$
$402$	12.5241	+	1.69709i	0.624646	+	0.0846429i
$403$	7.48519	−	12.9647i	0.372864	−	0.645819i
$404$	−15.4189	+	3.27567i	−0.767118	+	0.162971i
$405$	−12.6814	+	27.3754i	−0.630143	+	1.36030i
$406$	1.65968	−	0.174351i	0.0823686	−	0.00865287i
$407$	1.65399	−	2.86479i	0.0819850	−	0.142002i
$408$	−0.994562	−	13.2985i	−0.0492382	−	0.658376i
$409$	14.6627	+	25.3965i	0.725022	+	1.25577i	0.958965	+	0.283524i	$0.0915037\pi$
$409$	14.6627	+	25.3965i	0.725022	+	1.25577i	−0.233943	+	0.972250i	$0.575163\pi$
$410$	−8.84587	−	12.1767i	−0.436866	−	0.601362i
$411$	−18.5511	+	19.4032i	−0.915056	+	0.957088i
$412$	−35.3809	−	11.5001i	−1.74309	−	0.566569i
$413$	−12.8928			−0.634411
$414$	−8.51460	+	21.6924i	−0.418470	+	1.06612i
$415$		−	26.5245i		−	1.30204i
$416$	0.00215820	−	8.14434i	0.000105815	−	0.399309i
$417$	−19.9832	+	5.83825i	−0.978581	+	0.285900i
$418$	5.80395	+	7.98934i	0.283880	+	0.390771i
$419$	−8.38915	+	4.84348i	−0.409837	+	0.236620i	−0.690720	−	0.723123i	$-0.742706\pi$
$419$	−8.38915	+	4.84348i	−0.409837	+	0.236620i	0.280883	+	0.959742i	$0.409373\pi$
$420$	5.50177	+	10.2264i	0.268459	+	0.498998i
$421$	11.4422	+	6.60613i	0.557657	+	0.321963i	0.752204	−	0.658930i	$-0.228991\pi$
$421$	11.4422	+	6.60613i	0.557657	+	0.321963i	−0.194548	+	0.980893i	$0.562324\pi$
$422$	−1.76912	−	16.8407i	−0.0861195	−	0.819791i
$423$	−13.6664	+	8.73072i	−0.664483	+	0.424502i
$424$	10.9777	+	33.8041i	0.533123	+	1.64167i
$425$	−14.7044	−	8.48957i	−0.713267	−	0.411805i
$426$	−21.0574	+	27.2285i	−1.02023	+	1.31922i
$427$	0.658814	+	1.14110i	0.0318822	+	0.0552217i
$428$	22.0669	−	19.8649i	1.06665	−	0.960207i
$429$	−0.635682	+	2.60494i	−0.0306910	+	0.125768i
$430$	−19.8264	−	8.82855i	−0.956114	−	0.425750i
$431$	7.56489			0.364388			0.182194	−	0.983263i	$-0.441680\pi$
$431$	7.56489			0.364388			0.182194	+	0.983263i	$0.441680\pi$
$432$	−14.1342	−	15.2389i	−0.680034	−	0.733181i
$433$	−27.4459			−1.31897			−0.659484	−	0.751719i	$-0.729225\pi$
$433$	−27.4459			−1.31897			−0.659484	+	0.751719i	$0.729225\pi$
$434$	−13.4334	−	5.98180i	−0.644825	−	0.287135i
$435$	−1.62431	+	6.65620i	−0.0778798	+	0.319140i
$436$	−0.519094	+	0.467294i	−0.0248601	+	0.0223793i
$437$	17.8346	+	30.8904i	0.853144	+	1.47769i
$438$	5.71203	−	7.38600i	0.272931	−	0.352917i
$439$	3.41133	+	1.96953i	0.162814	+	0.0940006i	0.579193	−	0.815190i	$-0.303368\pi$
$439$	3.41133	+	1.96953i	0.162814	+	0.0940006i	−0.416379	+	0.909191i	$0.636701\pi$
$440$	−9.69669	+	3.14894i	−0.462272	+	0.150120i
$441$	−0.134640	−	2.99698i	−0.00641142	−	0.142713i
$442$	−0.579057	−	5.51217i	−0.0275429	−	0.262187i
$443$	2.58753	+	1.49391i	0.122937	+	0.0709779i	0.560208	−	0.828352i	$-0.310721\pi$
$443$	2.58753	+	1.49391i	0.122937	+	0.0709779i	−0.437270	+	0.899330i	$0.644055\pi$
$444$	5.04911	+	9.38503i	0.239620	+	0.445394i
$445$	10.8173	−	6.24536i	0.512789	−	0.296059i
$446$	11.6317	+	16.0114i	0.550776	+	0.758162i
$447$	15.1669	−	4.43113i	0.717369	−	0.209585i
$448$	−7.95644	+	0.833698i	−0.375906	+	0.0393885i
$449$		−	9.27240i		−	0.437592i	−0.975771	−	0.218796i	$-0.929787\pi$
$449$		−	9.27240i		−	0.437592i	0.975771	−	0.218796i	$-0.0702129\pi$
$450$	−26.1678	+	3.94315i	−1.23356	+	0.185882i
$451$	−3.41367			−0.160743
$452$	22.0525	+	7.16789i	1.03726	+	0.337149i
$453$	−7.91670	+	8.28035i	−0.371959	+	0.389045i
$454$	−5.37698	−	7.40161i	−0.252354	−	0.347375i
$455$	2.41315	+	4.17970i	0.113130	+	0.195948i
$456$	−31.7249	+	2.37262i	−1.48565	+	0.111108i
$457$	−6.20225	+	10.7426i	−0.290129	+	0.502518i	−0.973840	−	0.227235i	$-0.927032\pi$
$457$	−6.20225	+	10.7426i	−0.290129	+	0.502518i	0.683711	+	0.729753i	$0.260365\pi$
$458$	38.2590	−	4.01913i	1.78772	−	0.187802i
$459$	−10.6521	−	9.30605i	−0.497198	−	0.434369i
$460$	−36.0218	+	7.65268i	−1.67953	+	0.356808i
$461$	2.38055	−	4.12323i	0.110873	−	0.192038i	−0.805249	−	0.592936i	$-0.797969\pi$
$461$	2.38055	−	4.12323i	0.110873	−	0.192038i	0.916123	+	0.400898i	$0.131302\pi$
$462$	2.61000	+	0.353669i	0.121428	+	0.0164542i
$463$	1.92261	−	1.11002i	0.0893511	−	0.0515869i	−0.454659	−	0.890666i	$-0.650239\pi$
$463$	1.92261	−	1.11002i	0.0893511	−	0.0515869i	0.544010	+	0.839079i	$0.316905\pi$
$464$	−3.81807	−	2.77522i	−0.177249	−	0.128837i
$465$	41.7215	−	43.6379i	1.93479	−	2.02366i
$466$	2.73383	−	6.13941i	0.126642	−	0.284403i
$467$		−	9.60275i		−	0.444362i	−0.975005	−	0.222181i	$-0.928682\pi$
$467$		−	9.60275i		−	0.444362i	0.975005	−	0.222181i	$-0.0713177\pi$
$468$	−6.06184	−	6.15433i	−0.280209	−	0.284484i
$469$		−	5.15967i		−	0.238252i
$470$	−23.4111	−	10.4248i	−1.07987	−	0.480859i
$471$	11.4205	+	39.0900i	0.526227	+	1.80117i
$472$	27.0958	+	24.4050i	1.24719	+	1.12333i
$473$	−4.26307	+	2.46128i	−0.196016	+	0.113170i
$474$	−5.13454	+	2.10406i	−0.235837	+	0.0966426i
$475$	−20.2526	+	35.0786i	−0.929255	+	1.60952i
$476$	−5.32542	+	1.13136i	−0.244090	+	0.0518559i
$477$	33.4603	+	17.3647i	1.53204	+	0.795076i
$478$	−3.30366	−	31.4483i	−0.151106	−	1.43841i
$479$	−8.76143	+	15.1752i	−0.400320	+	0.693374i	−0.993764	−	0.111501i	$-0.964434\pi$
$479$	−8.76143	+	15.1752i	−0.400320	+	0.693374i	0.593445	+	0.804875i	$0.297768\pi$
$480$	7.79512	−	31.9066i	0.355797	−	1.45633i
$481$	2.21461	+	3.83581i	0.100977	+	0.174898i
$482$	2.12895	−	1.54660i	0.0969712	−	0.0704458i
$483$	9.24246	+	2.25544i	0.420546	+	0.102626i
$484$	6.08579	−	18.7234i	0.276627	−	0.851063i
$485$	18.8948			0.857970
$486$	−22.0232	−	0.989399i	−0.998992	−	0.0448800i
$487$			23.4680i			1.06344i	0.846922	+	0.531718i	$0.178453\pi$
$487$			23.4680i			1.06344i	−0.846922	+	0.531718i	$0.821547\pi$
$488$	0.775428	−	3.64525i	0.0351020	−	0.165013i
$489$	−4.07081	+	16.6816i	−0.184089	+	0.754369i
$490$	3.83551	−	2.78635i	0.173271	−	0.125874i
$491$	17.5277	−	10.1196i	0.791015	−	0.456692i	−0.0493050	−	0.998784i	$-0.515701\pi$
$491$	17.5277	−	10.1196i	0.791015	−	0.456692i	0.840320	+	0.542091i	$0.182367\pi$
$492$	5.78215	−	9.35482i	0.260679	−	0.421748i
$493$	−2.78184	−	1.60610i	−0.125288	−	0.0723350i
$494$	−13.1498	+	1.38139i	−0.591636	+	0.0621518i
$495$	−4.98107	+	9.59809i	−0.223882	+	0.431402i
$496$	16.9090	+	37.9999i	0.759237	+	1.70625i
$497$	12.1697	+	7.02615i	0.545883	+	0.315166i
$498$	17.9342	−	7.34917i	0.803649	−	0.329324i
$499$	2.29968	+	3.98316i	0.102948	+	0.178311i	0.912898	−	0.408188i	$-0.133839\pi$
$499$	2.29968	+	3.98316i	0.102948	+	0.178311i	−0.809950	+	0.586499i	$0.800506\pi$
$500$	−5.55069	−	6.16598i	−0.248234	−	0.275751i
$501$	23.2878	−	6.80373i	1.04042	−	0.303968i
$502$	8.58400	−	19.2772i	0.383123	−	0.860385i
$503$	20.4383			0.911300			0.455650	−	0.890159i	$-0.349407\pi$
$503$	20.4383			0.911300			0.455650	+	0.890159i	$0.349407\pi$
$504$	−5.39008	+	6.55340i	−0.240093	+	0.291912i
$505$	−26.4206			−1.17570
$506$	−3.39769	+	7.63025i	−0.151046	+	0.339206i
$507$	13.6800	+	13.0792i	0.607551	+	0.580870i
$508$	−11.5946	+	10.4376i	−0.514425	+	0.463092i
$509$	6.27224	+	10.8638i	0.278012	+	0.481531i	0.970891	−	0.239523i	$-0.0769911\pi$
$509$	6.27224	+	10.8638i	0.278012	+	0.481531i	−0.692878	+	0.721054i	$0.743658\pi$
$510$	3.00140	−	22.1497i	0.132904	−	0.980805i
$511$	−3.30114	−	1.90591i	−0.146034	−	0.0843127i
$512$	18.2996	+	13.3088i	0.808737	+	0.588171i
$513$	−22.2004	+	25.4116i	−0.980173	+	1.12195i
$514$	26.7043	−	2.80531i	1.17788	−	0.123737i
$515$	−54.0022	−	31.1782i	−2.37962	−	1.37388i
$516$	0.475979	−	15.8515i	0.0209538	−	0.697824i
$517$	−5.03385	+	2.90629i	−0.221388	+	0.127819i
$518$	3.51994	−	2.55710i	0.154657	−	0.112352i
$519$	−30.5379	−	29.1968i	−1.34047	−	1.28160i
$520$	2.84030	−	13.3521i	0.124555	−	0.585528i
$521$		−	0.336158i		−	0.0147273i	−0.999973	−	0.00736367i	$-0.997656\pi$
$521$		−	0.336158i		−	0.0147273i	0.999973	−	0.00736367i	$-0.00234395\pi$
$522$	−4.95055	+	0.745984i	−0.216680	+	0.0326508i
$523$	37.8262			1.65402			0.827012	−	0.562184i	$-0.190039\pi$
$523$	37.8262			1.65402			0.827012	+	0.562184i	$0.190039\pi$
$524$	−13.8075	−	4.48795i	−0.603184	−	0.196057i
$525$	3.02969	+	10.3700i	0.132227	+	0.452586i
$526$	−20.8430	+	15.1417i	−0.908799	+	0.660208i
$527$	14.1524	+	24.5127i	0.616490	+	1.06779i
$528$	−4.81579	−	5.68381i	−0.209580	−	0.247356i
$529$	−3.58500	+	6.20940i	−0.155869	+	0.269974i
$530$	6.22386	+	59.2462i	0.270347	+	2.57349i
$531$	38.6393	−	1.73588i	1.67680	−	0.0753307i
$532$	2.69897	+	12.7043i	0.117015	+	0.550800i
$533$	2.28537	−	3.95837i	0.0989902	−	0.171456i
$534$	7.21988	+	5.58356i	0.312435	+	0.241624i
$535$	43.0984	−	24.8829i	1.86331	−	1.07578i
$536$	−9.76686	+	10.8437i	−0.421864	+	0.468378i
$537$	−30.5060	−	7.44438i	−1.31643	−	0.321249i
$538$	−2.33831	−	1.04123i	−0.100812	−	0.0448906i
$539$		−	1.07527i		−	0.0463150i
$540$	−17.8656	−	29.9076i	−0.768812	−	1.28702i
$541$		−	12.7169i		−	0.546743i	−0.961909	−	0.273372i	$-0.911861\pi$
$541$		−	12.7169i		−	0.546743i	0.961909	−	0.273372i	$-0.0881388\pi$
$542$	−14.1641	+	31.8084i	−0.608398	+	1.36629i
$543$	−0.998688	−	0.243710i	−0.0428578	−	0.0104586i
$544$	13.3336	+	7.70289i	0.571675	+	0.330259i
$545$	−1.01383	+	0.585335i	−0.0434277	+	0.0250730i
$546$	−2.15744	+	2.78970i	−0.0923298	+	0.119388i
$547$	14.0769	−	24.3820i	0.601886	−	1.04250i	−0.390649	−	0.920540i	$-0.627749\pi$
$547$	14.0769	−	24.3820i	0.601886	−	1.04250i	0.992535	−	0.121958i	$-0.0389173\pi$
$548$	−6.44149	−	30.3206i	−0.275167	−	1.29523i
$549$	−2.12809	−	3.33115i	−0.0908246	−	0.142170i
$550$	−9.43309	+	0.990953i	−0.402229	+	0.0422544i
$551$	−3.83150	+	6.63634i	−0.163227	+	0.282718i
$552$	−15.1549	−	22.2353i	−0.645034	−	0.946399i
$553$	1.13267	+	1.96184i	0.0481660	+	0.0834259i
$554$	−15.2089	−	20.9356i	−0.646164	−	0.889467i
$555$	5.00924	+	17.1456i	0.212630	+	0.727792i
$556$	7.43095	−	22.8619i	0.315143	−	0.969559i
$557$	−23.0968			−0.978641			−0.489320	−	0.872104i	$-0.662755\pi$
$557$	−23.0968			−0.978641			−0.489320	+	0.872104i	$0.662755\pi$
$558$	41.0650	+	16.1186i	1.73842	+	0.682356i
$559$		−	6.59108i		−	0.278773i
$560$	−13.3352	−	1.40444i	−0.563513	−	0.0593484i
$561$	−3.66441	−	3.50348i	−0.154712	−	0.147917i
$562$	−3.78560	−	5.21102i	−0.159686	−	0.219814i
$563$	11.5879	−	6.69027i	0.488371	−	0.281961i	−0.235527	−	0.971868i	$-0.575682\pi$
$563$	11.5879	−	6.69027i	0.488371	−	0.281961i	0.723898	+	0.689907i	$0.242348\pi$
$564$	0.562038	−	18.7175i	0.0236661	−	0.788149i
$565$	33.6590	+	19.4330i	1.41605	+	0.817554i
$566$	2.94692	+	28.0524i	0.123868	+	1.17913i
$567$	0.807025	+	8.96374i	0.0338919	+	0.376442i
$568$	−12.2762	−	37.8026i	−0.515096	−	1.58616i
$569$	33.4731	+	19.3257i	1.40326	+	0.810175i	0.994726	−	0.102566i	$-0.0327054\pi$
$569$	33.4731	+	19.3257i	1.40326	+	0.810175i	0.408538	+	0.912741i	$0.366039\pi$
$570$	−52.8401	−	7.16012i	−2.21323	−	0.299905i
$571$	−6.19419	−	10.7286i	−0.259219	−	0.448980i	0.706814	−	0.707399i	$-0.250132\pi$
$571$	−6.19419	−	10.7286i	−0.259219	−	0.448980i	−0.966033	+	0.258419i	$0.916798\pi$
$572$	−2.07151	−	2.30114i	−0.0866142	−	0.0962153i
$573$	−12.6341	−	12.0793i	−0.527799	−	0.504619i
$574$	−4.10147	−	1.82635i	−0.171192	−	0.0762305i
$575$	−34.2605			−1.42876
$576$	23.7330	−	3.56983i	0.988876	−	0.148743i
$577$	−21.8101			−0.907968			−0.453984	−	0.891010i	$-0.649998\pi$
$577$	−21.8101			−0.907968			−0.453984	+	0.891010i	$0.649998\pi$
$578$	−12.3895	−	5.51694i	−0.515334	−	0.229474i
$579$	31.0542	−	9.07272i	1.29057	−	0.377050i
$580$	−5.29317	−	5.87992i	−0.219787	−	0.244150i
$581$	−3.95624	−	6.85242i	−0.164133	−	0.284286i
$582$	5.23521	+	12.7755i	0.217007	+	0.529561i
$583$	11.7015	+	6.75587i	0.484627	+	0.279800i
$584$	3.33003	+	10.2543i	0.137798	+	0.424327i
$585$	−7.79492	−	12.2016i	−0.322280	−	0.504473i
$586$	2.43235	+	23.1541i	0.100479	+	0.956486i
$587$	−2.92755	−	1.69022i	−0.120833	−	0.0697628i	0.438365	−	0.898797i	$-0.355558\pi$
$587$	−2.92755	−	1.69022i	−0.120833	−	0.0697628i	−0.559198	+	0.829034i	$0.688891\pi$
$588$	2.94666	+	1.82131i	0.121518	+	0.0751096i
$589$	58.4774	−	33.7619i	2.40952	−	1.39114i
$590$	35.9237	+	49.4503i	1.47896	+	2.03584i
$591$	−6.96141	+	28.5269i	−0.286354	+	1.17344i
$592$	−12.2380	−	1.28889i	−0.502978	−	0.0529730i
$593$		−	41.8323i		−	1.71785i	−0.512104	−	0.858924i	$-0.671134\pi$
$593$		−	41.8323i		−	1.71785i	0.512104	−	0.858924i	$-0.328866\pi$
$594$	−7.86973	−	0.708529i	−0.322899	−	0.0290713i
$595$	−9.12521			−0.374097
$596$	−5.63996	+	17.3518i	−0.231022	+	0.710756i
$597$	−6.83662	−	1.66834i	−0.279804	−	0.0682806i
$598$	−6.57311	−	9.04812i	−0.268794	−	0.370005i
$599$	−8.68144	−	15.0367i	−0.354714	−	0.614383i	0.632355	−	0.774679i	$-0.282088\pi$
$599$	−8.68144	−	15.0367i	−0.354714	−	0.614383i	−0.987069	+	0.160296i	$0.948755\pi$
$600$	13.2624	−	27.5290i	0.541435	−	1.12387i
$601$	−14.3839	+	24.9137i	−0.586732	+	1.01625i	0.407925	+	0.913015i	$0.366252\pi$
$601$	−14.3839	+	24.9137i	−0.586732	+	1.01625i	−0.994657	+	0.103234i	$0.967081\pi$
$602$	−6.43883	+	0.676404i	−0.262427	+	0.0275682i
$603$	0.694697	+	15.4634i	0.0282903	+	0.629719i
$604$	−2.74892	−	12.9394i	−0.111852	−	0.526496i
$605$	16.4993	−	28.5777i	0.670793	−	1.16185i
$606$	−7.32038	−	17.8639i	−0.297370	−	0.725672i
$607$	28.0022	−	16.1671i	1.13658	−	0.656202i	0.190995	−	0.981591i	$-0.438829\pi$
$607$	28.0022	−	16.1671i	1.13658	−	0.656202i	0.945580	+	0.325389i	$0.105495\pi$
$608$	18.3759	−	31.8086i	0.745243	−	1.29001i
$609$	0.573172	+	1.96186i	0.0232261	+	0.0794984i
$610$	2.54101	−	5.70639i	0.102882	−	0.231045i
$611$		−	7.78277i		−	0.314857i
$612$	15.8078	−	4.10768i	0.638993	−	0.166043i
$613$			24.8458i			1.00351i	0.865009	+	0.501757i	$0.167313\pi$
$613$			24.8458i			1.00351i	−0.865009	+	0.501757i	$0.832687\pi$
$614$	16.3607	+	7.28529i	0.660264	+	0.294010i
$615$	12.7383	−	13.3235i	0.513660	−	0.537254i
$616$	−2.03540	+	2.25981i	−0.0820084	+	0.0910504i
$617$	1.42687	−	0.823801i	0.0574435	−	0.0331650i	−0.471003	−	0.882131i	$-0.656108\pi$
$617$	1.42687	−	0.823801i	0.0574435	−	0.0331650i	0.528447	+	0.848966i	$0.322775\pi$
$618$	6.11827	−	45.1515i	0.246113	−	1.81626i
$619$	18.2920	−	31.6827i	0.735218	−	1.27343i	−0.219410	−	0.975633i	$-0.570413\pi$
$619$	18.2920	−	31.6827i	0.735218	−	1.27343i	0.954628	−	0.297802i	$-0.0962535\pi$
$620$	14.4870	+	68.1914i	0.581811	+	2.73863i
$621$	−28.0031	−	5.51509i	−1.12373	−	0.221313i
$622$	3.91152	+	37.2346i	0.156838	+	1.49297i
$623$	1.86305	−	3.22689i	0.0746414	−	0.129283i
$624$	9.81481	−	1.77905i	0.392907	−	0.0712191i
$625$	8.64078	+	14.9663i	0.345631	+	0.598651i
$626$	−38.6726	+	28.0942i	−1.54567	+	1.12287i
$627$	−8.35788	+	8.74179i	−0.333782	+	0.349114i
$628$	−44.7211	−	14.5360i	−1.78457	−	0.580050i
$629$	−8.37442			−0.333910
$630$	−11.1198	+	8.86704i	−0.443023	+	0.353271i
$631$			13.1680i			0.524210i	0.965039	+	0.262105i	$0.0844167\pi$
$631$			13.1680i			0.524210i	−0.965039	+	0.262105i	$0.915583\pi$
$632$	1.33316	−	6.26712i	0.0530302	−	0.249292i
$633$	19.9068	−	5.81594i	0.791225	−	0.231163i
$634$	22.6923	−	16.4851i	0.901228	−	0.654708i
$635$	−22.6451	+	13.0741i	−0.898642	+	0.518831i
$636$	−38.3341	+	20.6236i	−1.52005	+	0.817779i
$637$	1.24684	+	0.719865i	0.0494017	+	0.0285221i
$638$	−1.78460	+	0.187473i	−0.0706530	+	0.00742214i
$639$	−37.4182	−	19.4187i	−1.48024	−	0.768192i
$640$	25.3671	+	28.1940i	1.00272	+	1.11447i
$641$	0.907008	+	0.523661i	0.0358247	+	0.0206834i	0.517805	−	0.855498i	$-0.326749\pi$
$641$	0.907008	+	0.523661i	0.0358247	+	0.0206834i	−0.481981	+	0.876182i	$0.660082\pi$
$642$	28.7656	+	22.2461i	1.13529	+	0.877984i
$643$	−5.30528	−	9.18901i	−0.209220	−	0.362379i	0.742249	−	0.670124i	$-0.233759\pi$
$643$	−5.30528	−	9.18901i	−0.209220	−	0.362379i	−0.951469	+	0.307745i	$0.900426\pi$
$644$	−8.16455	+	7.34983i	−0.321729	+	0.289624i
$645$	6.30162	−	25.8231i	0.248126	−	1.01678i
$646$	10.1694	−	22.8376i	0.400109	−	0.898532i
$647$	−6.74943			−0.265347			−0.132674	−	0.991160i	$-0.542356\pi$
$647$	−6.74943			−0.265347			−0.132674	+	0.991160i	$0.542356\pi$
$648$	15.2716	−	20.3661i	0.599925	−	0.800056i
$649$	13.8632			0.544176
$650$	5.16616	−	11.6017i	0.202633	−	0.455057i
$651$	4.26967	−	17.4965i	0.167342	−	0.685742i
$652$	−13.2656	−	14.7361i	−0.519523	−	0.577111i
$653$	−17.1633	−	29.7277i	−0.671653	−	1.16334i	−0.977435	−	0.211235i	$-0.932251\pi$
$653$	−17.1633	−	29.7277i	−0.671653	−	1.16334i	0.305782	−	0.952101i	$-0.401082\pi$
$654$	−0.676670	−	0.523308i	−0.0264599	−	0.0204630i
$655$	−21.0746	−	12.1674i	−0.823452	−	0.475420i
$656$	5.16263	+	11.6021i	0.201567	+	0.452985i
$657$	10.1501	+	5.26752i	0.395991	+	0.205505i
$658$	−7.60300	+	0.798700i	−0.296396	+	0.0311366i
$659$	15.9041	+	9.18223i	0.619535	+	0.357689i	0.776688	−	0.629885i	$-0.216898\pi$
$659$	15.9041	+	9.18223i	0.619535	+	0.357689i	−0.157153	+	0.987574i	$0.550231\pi$
$660$	−5.91587	−	10.9961i	−0.230275	−	0.428024i
$661$	10.2306	−	5.90662i	0.397923	−	0.229741i	−0.287664	−	0.957731i	$-0.592879\pi$
$661$	10.2306	−	5.90662i	0.397923	−	0.229741i	0.685587	+	0.727990i	$0.259545\pi$
$662$	−32.1147	+	23.3301i	−1.24817	+	0.906751i
$663$	6.51576	−	1.90363i	0.253051	−	0.0739309i
$664$	−4.65652	+	21.8901i	−0.180708	+	0.849501i
$665$			21.7690i			0.844167i
$666$	−10.2049	+	8.13749i	−0.395431	+	0.315321i
$667$	−6.48157			−0.250968
$668$	−8.65982	+	26.6426i	−0.335058	+	1.03083i
$669$	−16.7500	+	17.5194i	−0.647592	+	0.677339i
$670$	−19.7900	+	14.3767i	−0.764553	+	0.555419i
$671$	−0.708401	−	1.22699i	−0.0273475	−	0.0473673i
$672$	−2.74519	−	9.40553i	−0.105898	−	0.362826i
$673$	−9.35650	+	16.2059i	−0.360667	+	0.624693i	−0.988071	−	0.154001i	$-0.950784\pi$
$673$	−9.35650	+	16.2059i	−0.360667	+	0.624693i	0.627404	+	0.778694i	$0.284117\pi$
$674$	−0.268313	−	2.55413i	−0.0103350	−	0.0983815i
$675$	−10.4761	−	30.6709i	−0.403227	−	1.18052i
$676$	−21.3773	+	4.54151i	−0.822202	+	0.174673i
$677$	−13.8978	+	24.0716i	−0.534134	+	0.925148i	0.465070	+	0.885274i	$0.346029\pi$
$677$	−13.8978	+	24.0716i	−0.534134	+	0.925148i	−0.999205	+	0.0398741i	$0.987304\pi$
$678$	−3.81346	+	28.1424i	−0.146455	+	1.08080i
$679$	4.88135	−	2.81825i	0.187329	−	0.108155i
$680$	19.1778	+	17.2733i	0.735436	+	0.662401i
$681$	7.74303	−	8.09870i	0.296714	−	0.310343i
$682$	14.4445	+	6.43203i	0.553109	+	0.246295i
$683$			5.07114i			0.194042i	0.995282	+	0.0970209i	$0.0309314\pi$
$683$			5.07114i			0.194042i	−0.995282	+	0.0970209i	$0.969069\pi$
$684$	−9.79924	−	37.7110i	−0.374683	−	1.44192i
$685$		−	51.9550i		−	1.98510i
$686$	0.575281	−	1.29192i	0.0219643	−	0.0493257i
$687$	13.2128	+	45.2247i	0.504099	+	1.72543i
$688$	14.8124	+	10.7667i	0.564719	+	0.410475i
$689$	−15.6678	+	9.04579i	−0.596894	+	0.344617i
$690$	−17.1020	−	41.7340i	−0.651061	−	1.58878i
$691$	−9.12328	+	15.8020i	−0.347066	+	0.601136i	−0.985727	−	0.168352i	$-0.946155\pi$
$691$	−9.12328	+	15.8020i	−0.347066	+	0.601136i	0.638661	+	0.769488i	$0.279489\pi$
$692$	47.7205	−	10.1380i	1.81406	−	0.385389i
$693$	0.144774	+	3.22255i	0.00549950	+	0.122415i
$694$	−11.5534	+	1.21369i	−0.438561	+	0.0460712i
$695$	20.1462	−	34.8943i	0.764190	−	1.32362i
$696$	2.50904	−	5.20807i	0.0951051	−	0.197411i
$697$	4.32100	+	7.48419i	0.163670	+	0.283484i
$698$	−22.8636	−	31.4725i	−0.865400	−	1.19125i
$699$	7.99634	+	1.95135i	0.302449	+	0.0738067i
$700$	−11.8639	−	3.85621i	−0.448413	−	0.145751i
$701$	15.7083			0.593296			0.296648	−	0.954987i	$-0.404131\pi$
$701$	15.7083			0.593296			0.296648	+	0.954987i	$0.404131\pi$
$702$	6.09018	−	8.65113i	0.229859	−	0.326516i
$703$			19.9779i			0.753483i
$704$	8.55529	−	0.896447i	0.322440	−	0.0337861i
$705$	7.44097	−	30.4920i	0.280243	−	1.14840i
$706$	0.855376	+	1.17746i	0.0321925	+	0.0443141i
$707$	−6.82557	+	3.94075i	−0.256702	+	0.148207i
$708$	−23.4817	+	37.9906i	−0.882498	+	1.42777i
$709$	4.54193	+	2.62229i	0.170576	+	0.0984821i	0.582857	−	0.812574i	$-0.301935\pi$
$709$	4.54193	+	2.62229i	0.170576	+	0.0984821i	−0.412281	+	0.911057i	$0.635268\pi$
$710$	−6.96004	−	66.2541i	−0.261206	−	2.48647i
$711$	−3.65873	−	5.72709i	−0.137213	−	0.214783i
$712$	−10.0237	+	3.25513i	−0.375654	+	0.121991i
$713$	49.4618	+	28.5568i	1.85236	+	1.06946i
$714$	−2.52833	−	6.16989i	−0.0946205	−	0.230902i
$715$	−2.59478	−	4.49430i	−0.0970394	−	0.168077i
$716$	26.9483	−	24.2591i	1.00710	−	0.906607i
$717$	37.1740	−	10.8607i	1.38829	−	0.405600i
$718$	34.9324	+	15.5551i	1.30366	+	0.580511i
$719$	−25.0085			−0.932659			−0.466330	−	0.884611i	$-0.654424\pi$
$719$	−25.0085			−0.932659			−0.466330	+	0.884611i	$0.654424\pi$
$720$	40.1543	+	2.41363i	1.49646	+	0.0899508i
$721$	−18.6015			−0.692755
$722$	−29.9347	−	13.3297i	−1.11405	−	0.496079i
$723$	2.32946	+	2.22716i	0.0866336	+	0.0828290i
$724$	0.882216	−	0.794181i	0.0327873	−	0.0295155i
$725$	−3.68018	−	6.37426i	−0.136678	−	0.236734i
$726$	23.8939	+	3.23776i	0.886787	+	0.120164i
$727$	16.4229	+	9.48179i	0.609093	+	0.351660i	0.772610	−	0.634880i	$-0.218951\pi$
$727$	16.4229	+	9.48179i	0.609093	+	0.351660i	−0.163517	+	0.986540i	$0.552284\pi$
$728$	−1.25775	−	3.87307i	−0.0466155	−	0.143545i
$729$	−3.62551	−	26.7555i	−0.134278	−	0.990944i
$730$	1.88798	+	17.9721i	0.0698773	+	0.665177i
$731$	10.7923	+	6.23096i	0.399169	+	0.230460i
$732$	4.56234	+	0.136995i	0.168629	+	0.00506349i
$733$	3.53815	−	2.04275i	0.130685	−	0.0754508i	−0.433232	−	0.901282i	$-0.642627\pi$
$733$	3.53815	−	2.04275i	0.130685	−	0.0754508i	0.563917	+	0.825831i	$0.309294\pi$
$734$	10.2703	+	14.1375i	0.379085	+	0.521824i
$735$	4.19674	+	4.01244i	0.154799	+	0.148001i
$736$	31.0715	+	0.00823377i	1.14531	+	0.000303501i
$737$			5.54802i			0.204364i
$738$	12.5379	+	4.92132i	0.461527	+	0.181156i
$739$	21.9747			0.808353			0.404176	−	0.914681i	$-0.367558\pi$
$739$	21.9747			0.808353			0.404176	+	0.914681i	$0.367558\pi$
$740$	−19.6156	−	6.37578i	−0.721082	−	0.234378i
$741$	−4.54129	−	15.5439i	−0.166828	−	0.571021i
$742$	10.4447	+	14.3775i	0.383438	+	0.527816i
$743$	1.01423	+	1.75670i	0.0372084	+	0.0644469i	0.884030	−	0.467430i	$-0.154820\pi$
$743$	1.01423	+	1.75670i	0.0372084	+	0.0644469i	−0.846821	+	0.531877i	$0.821487\pi$
$744$	−42.0928	+	28.6890i	−1.54320	+	1.05179i
$745$	−15.2906	+	26.4842i	−0.560206	+	0.970305i
$746$	18.3952	−	1.93242i	0.673495	−	0.0707511i
$747$	12.7794	+	20.0039i	0.467573	+	0.731903i
$748$	5.72624	−	1.21652i	0.209372	−	0.0444802i
$749$	7.42279	−	12.8566i	0.271223	−	0.469772i
$750$	6.21604	−	8.03772i	0.226978	−	0.293496i
$751$	21.1821	−	12.2295i	0.772945	−	0.446260i	−0.0609790	−	0.998139i	$-0.519422\pi$
$751$	21.1821	−	12.2295i	0.772945	−	0.446260i	0.833924	+	0.551879i	$0.186089\pi$
$752$	17.4906	+	12.7133i	0.637815	+	0.463607i
$753$	25.1079	+	6.12707i	0.914981	+	0.223283i
$754$	0.977359	−	2.19487i	0.0355933	−	0.0799325i
$755$		−	22.1719i		−	0.806919i
$756$	−9.07630	−	5.06169i	−0.330102	−	0.184092i
$757$			10.6871i			0.388430i	0.980959	+	0.194215i	$0.0622159\pi$
$757$			10.6871i			0.388430i	−0.980959	+	0.194215i	$0.937784\pi$
$758$	33.9405	+	15.1134i	1.23277	+	0.548945i
$759$	−9.93810	−	2.42519i	−0.360730	−	0.0880290i
$760$	41.2071	−	45.7505i	1.49474	−	1.65954i
$761$	−12.7771	+	7.37685i	−0.463169	+	0.267411i	−0.713376	−	0.700782i	$-0.752835\pi$
$761$	−12.7771	+	7.37685i	−0.463169	+	0.267411i	0.250207	+	0.968192i	$0.419501\pi$
$762$	−15.1142	−	11.6887i	−0.547530	−	0.423437i
$763$	−0.174611	+	0.302435i	−0.00632133	+	0.0109489i
$764$	19.7429	−	4.19429i	0.714273	−	0.151744i
$765$	27.3481	−	1.22862i	0.988771	−	0.0444207i
$766$	3.70144	+	35.2348i	0.133739	+	1.27309i
$767$	−9.28105	+	16.0752i	−0.335119	+	0.580443i
$768$	−12.0345	+	24.9634i	−0.434259	+	0.900788i
$769$	−19.3307	−	33.4817i	−0.697082	−	1.20738i	−0.969474	−	0.245195i	$-0.921148\pi$
$769$	−19.3307	−	33.4817i	−0.697082	−	1.20738i	0.272392	−	0.962186i	$-0.412185\pi$
$770$	−4.12419	+	2.99607i	−0.148626	+	0.107971i
$771$	9.22237	+	31.5664i	0.332135	+	1.13684i
$772$	−11.5478	+	35.5277i	−0.415615	+	1.27867i
$773$	2.27336			0.0817672			0.0408836	−	0.999164i	$-0.486983\pi$
$773$	2.27336			0.0817672			0.0408836	+	0.999164i	$0.486983\pi$
$774$	19.2060	−	2.89409i	0.690344	−	0.104026i
$775$			64.8572i			2.32974i
$776$	−15.5935	−	3.31710i	−0.559775	−	0.119077i
$777$	3.85145	+	3.68231i	0.138170	+	0.132102i
$778$	−20.5733	+	14.9457i	−0.737589	+	0.535830i
$779$	17.8542	−	10.3081i	0.639694	−	0.369327i
$780$	16.7113	+	0.501796i	0.598360	+	0.0179672i
$781$	−13.0856	−	7.55499i	−0.468240	−	0.270339i
$782$	21.0295	−	2.20916i	0.752013	−	0.0789995i
$783$	−1.98193	−	5.80247i	−0.0708283	−	0.207363i
$784$	−3.65453	+	1.62617i	−0.130519	+	0.0580776i
$785$	−68.2583	−	39.4090i	−2.43624	−	1.40657i
$786$	2.38768	−	17.6205i	0.0851657	−	0.628504i
$787$	−11.3863	−	19.7216i	−0.405877	−	0.702999i	0.588546	−	0.808464i	$-0.299700\pi$
$787$	−11.3863	−	19.7216i	−0.405877	−	0.702999i	−0.994423	+	0.105464i	$0.966367\pi$
$788$	−22.6853	−	25.1999i	−0.808130	−	0.897710i
$789$	−22.8061	−	21.8045i	−0.811917	−	0.776261i
$790$	4.36864	−	9.81074i	0.155429	−	0.349050i
$791$	11.5941			0.412239
$792$	5.79577	−	7.04665i	0.205944	−	0.250392i
$793$	1.89703			0.0673655
$794$	−2.13543	+	4.79557i	−0.0757835	+	0.170188i
$795$	−70.0331	+	20.4607i	−2.48382	+	0.725668i
$796$	6.03930	−	5.43665i	0.214057	−	0.192697i
$797$	5.84445	+	10.1229i	0.207021	+	0.358571i	0.950775	−	0.309883i	$-0.100290\pi$
$797$	5.84445	+	10.1229i	0.207021	+	0.358571i	−0.743754	+	0.668454i	$0.766957\pi$
$798$	−14.7188	+	6.03157i	−0.521041	+	0.213515i
$799$	12.7436	+	7.35754i	0.450837	+	0.260291i
$800$	17.6340	+	30.5618i	0.623458	+	1.08052i
$801$	−5.14904	+	9.92177i	−0.181933	+	0.350568i
$802$	−41.8717	+	4.39865i	−1.47854	+	0.155322i
$803$	3.54961	+	2.04937i	0.125263	+	0.0723205i
$804$	−15.2038	−	9.39738i	−0.536197	−	0.331420i
$805$	−15.9460	+	9.20643i	−0.562023	+	0.324484i
$806$	−17.1286	+	12.4433i	−0.603330	+	0.438296i
$807$	0.743207	−	3.04556i	0.0261621	−	0.107209i
$808$	21.8044	+	4.63828i	0.767074	+	0.163174i
$809$		−	37.2212i		−	1.30863i	−0.756223	−	0.654314i	$-0.772957\pi$
$809$		−	37.2212i		−	1.30863i	0.756223	−	0.654314i	$-0.227043\pi$
$810$	32.1319	−	28.0715i	1.12900	−	0.986331i
$811$	−38.4333			−1.34957			−0.674787	−	0.738012i	$-0.735765\pi$
$811$	−38.4333			−1.34957			−0.674787	+	0.738012i	$0.735765\pi$
$812$	−2.24447	−	0.729536i	−0.0787655	−	0.0256017i
$813$	−41.4293	−	10.1100i	−1.45299	−	0.354572i
$814$	−3.78487	+	2.74956i	−0.132660	+	0.0963721i
$815$	−16.6166	−	28.7808i	−0.582054	−	1.00815i
$816$	−6.36550	+	17.7528i	−0.222837	+	0.621471i
$817$	14.8645	−	25.7461i	0.520044	−	0.900742i
$818$	−4.33285	−	41.2453i	−0.151494	−	1.44211i
$819$	−3.83368	−	1.98954i	−0.133960	−	0.0695203i
$820$	4.42314	+	20.8201i	0.154463	+	0.727069i
$821$	−17.3546	+	30.0590i	−0.605679	+	1.04907i	0.386264	+	0.922388i	$0.373765\pi$
$821$	−17.3546	+	30.0590i	−0.605679	+	1.04907i	−0.991944	+	0.126679i	$0.959568\pi$
$822$	35.1287	−	14.3952i	1.22525	−	0.502092i
$823$	−7.47588	+	4.31620i	−0.260593	+	0.150453i	−0.624605	−	0.780941i	$-0.714740\pi$
$823$	−7.47588	+	4.31620i	−0.260593	+	0.150453i	0.364012	+	0.931394i	$0.381407\pi$
$824$	39.0934	+	35.2111i	1.36188	+	1.22664i
$825$	−3.25773	−	11.1506i	−0.113420	−	0.388213i
$826$	16.6564	+	7.41696i	0.579550	+	0.258069i
$827$			41.1817i			1.43203i	0.698086	+	0.716014i	$0.254035\pi$
$827$			41.1817i			1.43203i	−0.698086	+	0.716014i	$0.745965\pi$
$828$	23.4794	−	23.1266i	0.815966	−	0.803703i
$829$			8.92391i			0.309940i	0.987919	+	0.154970i	$0.0495281\pi$
$829$			8.92391i			0.309940i	−0.987919	+	0.154970i	$0.950472\pi$
$830$	−15.2590	+	34.2674i	−0.529648	+	1.18944i
$831$	21.9013	−	22.9073i	0.759748	−	0.794646i
$832$	−4.68807	+	10.5206i	−0.162530	+	0.364736i
$833$	−2.35744	+	1.36107i	−0.0816803	+	0.0471582i
$834$	29.1753	+	3.95341i	1.01026	+	0.136895i
$835$	−23.4779	+	40.6648i	−0.812485	+	1.40726i
$836$	−2.90211	−	13.6605i	−0.100372	−	0.472457i
$837$	−10.4404	+	53.0115i	−0.360872	+	1.83235i
$838$	13.6245	−	1.43126i	0.470649	−	0.0494420i
$839$	−3.31234	+	5.73713i	−0.114355	+	0.198068i	−0.917522	−	0.397686i	$-0.869813\pi$
$839$	−3.31234	+	5.73713i	−0.114355	+	0.198068i	0.803167	+	0.595754i	$0.203147\pi$
$840$	−1.22477	−	16.3768i	−0.0422587	−	0.565052i
$841$	13.8038	+	23.9088i	0.475992	+	0.824442i
$842$	−10.9819	−	15.1170i	−0.378463	−	0.520967i
$843$	5.45140	−	5.70180i	0.187756	−	0.196380i
$844$	−7.40255	+	22.7745i	−0.254806	+	0.783930i
$845$	−36.6304			−1.26012
$846$	22.6785	−	3.41735i	0.779702	−	0.117491i
$847$		−	9.84380i		−	0.338237i
$848$	5.26459	−	49.9873i	0.180787	−	1.71657i
$849$	−33.1599	+	9.68792i	−1.13804	+	0.332489i
$850$	14.1129	+	19.4270i	0.484070	+	0.666340i
$851$	−14.6340	+	8.44896i	−0.501648	+	0.289627i
$852$	42.8684	−	23.0630i	1.46865	−	0.790127i
$853$	10.8969	+	6.29131i	0.373102	+	0.215410i	0.674813	−	0.737989i	$-0.264224\pi$
$853$	10.8969	+	6.29131i	0.373102	+	0.215410i	−0.301711	+	0.953399i	$0.597558\pi$
$854$	−0.194681	−	1.85321i	−0.00666184	−	0.0634155i
$855$	−2.93098	−	65.2413i	−0.100237	−	2.23121i
$856$	−39.9366	+	12.9692i	−1.36500	+	0.443277i
$857$	21.3346	+	12.3175i	0.728777	+	0.420759i	0.817974	−	0.575255i	$-0.195097\pi$
$857$	21.3346	+	12.3175i	0.728777	+	0.420759i	−0.0891979	+	0.996014i	$0.528430\pi$
$858$	2.31982	−	2.99967i	0.0791973	−	0.102407i
$859$	26.2504	+	45.4670i	0.895651	+	1.55131i	0.832997	+	0.553278i	$0.186623\pi$
$859$	26.2504	+	45.4670i	0.895651	+	1.55131i	0.0626545	+	0.998035i	$0.480043\pi$
$860$	20.5352	+	22.8115i	0.700245	+	0.777866i
$861$	1.30361	−	5.34201i	0.0444269	−	0.182055i
$862$	−9.77322	−	4.35194i	−0.332877	−	0.148228i
$863$	−21.9563			−0.747402			−0.373701	−	0.927549i	$-0.621911\pi$
$863$	−21.9563			−0.747402			−0.373701	+	0.927549i	$0.621911\pi$
$864$	9.49364	+	27.8185i	0.322980	+	0.946406i
$865$	81.7700			2.78026
$866$	35.4579	+	15.7891i	1.20491	+	0.536536i
$867$	3.93787	−	16.1368i	0.133737	−	0.548035i
$868$	13.9137	+	15.4560i	0.472261	+	0.524610i
$869$	−1.21792	−	2.10950i	−0.0413151	−	0.0715599i
$870$	5.92766	−	7.66483i	0.200967	−	0.259862i
$871$	−6.43330	−	3.71427i	−0.217984	−	0.125853i
$872$	0.939452	−	0.305081i	0.0318139	−	0.0103314i
$873$	−14.2499	+	9.10345i	−0.482284	+	0.308105i
$874$	−5.27016	−	50.1678i	−0.178266	−	1.69695i
$875$	−3.59243	−	2.07409i	−0.121446	−	0.0701170i
$876$	−11.6285	+	6.25608i	−0.392890	+	0.211373i
$877$	−38.8392	+	22.4238i	−1.31151	+	0.757199i	−0.982346	−	0.187074i	$-0.940100\pi$
$877$	−38.8392	+	22.4238i	−1.31151	+	0.757199i	−0.329162	+	0.944273i	$0.606766\pi$
$878$	−3.27412	−	4.50694i	−0.110496	−	0.152102i
$879$	−27.3697	+	7.99628i	−0.923157	+	0.269708i
$880$	14.3389	+	1.51015i	0.483363	+	0.0509071i
$881$			2.97222i			0.100137i	0.998746	+	0.0500684i	$0.0159439\pi$
$881$			2.97222i			0.100137i	−0.998746	+	0.0500684i	$0.984056\pi$
$882$	−1.55016	+	3.94930i	−0.0521966	+	0.132980i
$883$	0.602481			0.0202751			0.0101376	−	0.999949i	$-0.496773\pi$
$883$	0.602481			0.0202751			0.0101376	+	0.999949i	$0.496773\pi$
$884$	−2.42295	+	7.45439i	−0.0814927	+	0.250718i
$885$	−51.7314	+	54.1076i	−1.73893	+	1.81881i
$886$	−2.48346	−	3.41857i	−0.0834334	−	0.114849i
$887$	12.3875	+	21.4558i	0.415932	+	0.720415i	0.995526	−	0.0944902i	$-0.0301221\pi$
$887$	12.3875	+	21.4558i	0.415932	+	0.720415i	−0.579594	+	0.814906i	$0.696789\pi$
$888$	−1.12400	−	15.0293i	−0.0377191	−	0.504352i
$889$	−3.90013	+	6.75523i	−0.130806	+	0.226563i
$890$	−17.5679	+	1.84552i	−0.588877	+	0.0618619i
$891$	−0.867767	−	9.63841i	−0.0290713	−	0.322899i
$892$	−5.81611	−	27.3769i	−0.194738	−	0.916646i
$893$	17.5521	−	30.4011i	0.587358	−	1.01733i
$894$	−22.1435	−	3.00057i	−0.740590	−	0.100354i
$895$	52.6320	−	30.3871i	1.75929	−	1.01573i
$896$	10.7587	+	3.50012i	0.359422	+	0.116931i
$897$	9.46550	−	9.90028i	0.316044	−	0.330561i
$898$	−5.33424	+	11.9792i	−0.178006	+	0.399751i
$899$			12.2700i			0.409227i
$900$	36.0750	+	9.95961i	1.20250	+	0.331987i
$901$		−	34.2062i		−	1.13957i
$902$	4.41018	+	1.96382i	0.146843	+	0.0653879i
$903$	−2.22366	−	7.61114i	−0.0739987	−	0.253283i
$904$	−24.3665	−	21.9467i	−0.810418	−	0.729937i
$905$	1.72304	−	0.994795i	0.0572756	−	0.0330681i
$906$	14.9913	−	6.14320i	0.498051	−	0.204094i
$907$	6.01412	−	10.4168i	0.199696	−	0.345883i	−0.748734	−	0.662870i	$-0.769338\pi$
$907$	6.01412	−	10.4168i	0.199696	−	0.345883i	0.948430	+	0.316987i	$0.102671\pi$
$908$	2.68862	+	12.6555i	0.0892249	+	0.419989i
$909$	19.9255	−	12.7293i	0.660887	−	0.422205i
$910$	−0.713092	−	6.78807i	−0.0236388	−	0.225022i
$911$	−11.2709	+	19.5219i	−0.373423	+	0.646788i	−0.990090	−	0.140437i	$-0.955149\pi$
$911$	−11.2709	+	19.5219i	−0.373423	+	0.646788i	0.616667	+	0.787224i	$0.288483\pi$
$912$	42.3509	+	15.1855i	1.40238	+	0.502842i
$913$	4.25402	+	7.36817i	0.140787	+	0.243851i
$914$	14.1928	−	10.3105i	0.469457	−	0.341042i
$915$	7.43235	+	1.81372i	0.245706	+	0.0599596i
$916$	−51.7396	−	16.8173i	−1.70952	−	0.555658i
$917$	−7.25929			−0.239723
$918$	8.40807	+	18.1506i	0.277508	+	0.599060i
$919$			36.9071i			1.21745i	0.793380	+	0.608726i	$0.208319\pi$
$919$			36.9071i			1.21745i	−0.793380	+	0.608726i	$0.791681\pi$
$920$	50.9397	+	10.8360i	1.67943	+	0.357253i
$921$	−5.20007	+	21.3092i	−0.171348	+	0.702161i
$922$	−5.44749	+	3.95739i	−0.179403	+	0.130330i
$923$	17.5210	−	10.1158i	0.576711	−	0.332964i
$924$	−3.16845	−	1.95840i	−0.104234	−	0.0644265i
$925$	−16.6181	−	9.59449i	−0.546401	−	0.315465i
$926$	−3.12242	+	0.328012i	−0.102609	+	0.0107792i
$927$	55.7482	−	2.50450i	1.83101	−	0.0822585i
$928$	3.33610	+	5.78182i	0.109513	+	0.189798i
$929$	42.0350	+	24.2689i	1.37912	+	0.796237i	0.992054	−	0.125814i	$-0.0401543\pi$
$929$	42.0350	+	24.2689i	1.37912	+	0.796237i	0.387069	+	0.922051i	$0.373488\pi$
$930$	−79.0048	+	32.3750i	−2.59067	+	1.06162i
$931$	3.24695	+	5.62388i	0.106414	+	0.184315i
$932$	−7.06377	+	6.35889i	−0.231381	+	0.208292i
$933$	−44.0138	+	12.8590i	−1.44095	+	0.420985i
$934$	−5.52428	+	12.4060i	−0.180760	+	0.405936i
$935$	9.81204			0.320888
$936$	4.29093	+	11.4381i	0.140253	+	0.373868i
$937$	38.6810			1.26365			0.631827	−	0.775109i	$-0.282305\pi$
$937$	38.6810			1.26365			0.631827	+	0.775109i	$0.282305\pi$
$938$	−2.96826	+	6.66587i	−0.0969172	+	0.217649i
$939$	−42.3149	−	40.4566i	−1.38089	−	1.32025i
$940$	24.2480	+	26.9359i	0.790884	+	0.878552i
$941$	−13.1697	−	22.8105i	−0.429319	−	0.743602i	0.567494	−	0.823378i	$-0.307913\pi$
$941$	−13.1697	−	22.8105i	−0.429319	−	0.743602i	−0.996813	+	0.0797753i	$0.974580\pi$
$942$	7.73344	−	57.0710i	0.251969	−	1.85948i
$943$	15.1016	+	8.71891i	0.491776	+	0.283927i
$944$	−20.9658	−	47.1169i	−0.682380	−	1.53353i
$945$	−13.1178	−	11.4601i	−0.426721	−	0.372798i
$946$	6.92346	−	0.727314i	0.225101	−	0.0236470i
$947$	−28.0647	−	16.2031i	−0.911979	−	0.526532i	−0.0309119	−	0.999522i	$-0.509841\pi$
$947$	−28.0647	−	16.2031i	−0.911979	−	0.526532i	−0.881068	+	0.472991i	$0.843174\pi$
$948$	7.84383	+	0.235530i	0.254756	+	0.00764965i
$949$	−4.75275	+	2.74400i	−0.154281	+	0.0890741i
$950$	46.3448	−	33.6677i	1.50362	−	1.09233i
$951$	24.8295	+	23.7391i	0.805153	+	0.769794i
$952$	7.53085	+	1.60198i	0.244076	+	0.0519206i
$953$		−	4.88435i		−	0.158220i	−0.996866	−	0.0791098i	$-0.974792\pi$
$953$		−	4.88435i		−	0.158220i	0.996866	−	0.0791098i	$-0.0252078\pi$
$954$	−33.2384	−	41.6829i	−1.07613	−	1.34953i
$955$	33.8299			1.09471
$956$	−13.8235	+	42.5291i	−0.447085	+	1.37549i
$957$	−0.616313	−	2.10952i	−0.0199226	−	0.0681911i
$958$	20.0491	−	14.5649i	0.647756	−	0.470570i
$959$	−7.74933	−	13.4222i	−0.250239	−	0.433426i
$960$	−28.4259	+	36.7363i	−0.917442	+	1.18566i
$961$	38.5597	−	66.7873i	1.24386	−	2.15443i
$962$	−0.654421	−	6.22958i	−0.0210994	−	0.200850i
$963$	−20.5149	+	39.5305i	−0.661084	+	1.27385i
$964$	−3.64016	+	0.773337i	−0.117242	+	0.0249075i
$965$	−31.3076	+	54.2263i	−1.00783	+	1.74561i
$966$	−10.6430	−	8.23085i	−0.342432	−	0.264823i
$967$	38.9608	−	22.4940i	1.25289	−	0.723358i	0.281210	−	0.959646i	$-0.409264\pi$
$967$	38.9608	−	22.4940i	1.25289	−	0.723358i	0.971683	+	0.236288i	$0.0759308\pi$
$968$	−18.6335	+	20.6880i	−0.598905	+	0.664938i
$969$	29.7450	+	7.25868i	0.955548	+	0.233182i
$970$	−24.4106	−	10.8698i	−0.783776	−	0.349010i
$971$		−	9.38126i		−	0.301059i	−0.988606	−	0.150530i	$-0.951902\pi$
$971$		−	9.38126i		−	0.301059i	0.988606	−	0.150530i	$-0.0480979\pi$
$972$	27.8830	+	13.9477i	0.894347	+	0.447374i
$973$		−	12.0196i		−	0.385331i
$974$	13.5007	−	30.3187i	0.432590	−	0.971474i
$975$	15.1108	+	3.68748i	0.483933	+	0.118094i
$976$	−3.09883	+	4.26328i	−0.0991912	+	0.136464i
$977$	12.1699	−	7.02630i	0.389350	−	0.224791i	−0.292529	−	0.956257i	$-0.594497\pi$
$977$	12.1699	−	7.02630i	0.389350	−	0.224791i	0.681878	+	0.731466i	$0.261163\pi$
$978$	14.8558	−	19.2094i	0.475035	−	0.614250i
$979$	−2.00327	+	3.46977i	−0.0640249	+	0.110894i
$980$	−6.55810	+	1.39324i	−0.209491	+	0.0445054i
$981$	0.482585	−	0.929899i	0.0154077	−	0.0296894i
$982$	−28.4660	+	2.99037i	−0.908386	+	0.0954266i
$983$	6.77559	−	11.7357i	0.216108	−	0.374310i	−0.737507	−	0.675340i	$-0.763997\pi$
$983$	6.77559	−	11.7357i	0.216108	−	0.374310i	0.953615	+	0.301030i	$0.0973304\pi$
$984$	−12.8517	+	8.75930i	−0.409697	+	0.279236i
$985$	−28.4157	−	49.2174i	−0.905399	−	1.56820i
$986$	2.66996	+	3.67529i	0.0850287	+	0.117045i
$987$	−2.62570	−	8.98726i	−0.0835770	−	0.286068i
$988$	17.7831	+	5.78017i	0.565756	+	0.183892i
$989$	25.1457			0.799586
$990$	11.9567	−	9.53443i	0.380010	−	0.303024i
$991$			9.75000i			0.309719i	0.987936	+	0.154860i	$0.0494925\pi$
$991$			9.75000i			0.309719i	−0.987936	+	0.154860i	$0.950507\pi$
$992$	0.0155870	−	58.8202i	0.000494888	−	1.86754i
$993$	−35.1394	−	33.5962i	−1.11511	−	1.06614i
$994$	−11.6802	−	16.0782i	−0.370473	−	0.509969i
$995$	11.7952	−	6.80997i	0.373934	−	0.215891i
$996$	−27.3973	−	0.822670i	−0.868117	−	0.0260673i
$997$	−28.7202	−	16.5816i	−0.909577	−	0.525144i	−0.0292817	−	0.999571i	$-0.509322\pi$
$997$	−28.7202	−	16.5816i	−0.909577	−	0.525144i	−0.880295	+	0.474427i	$0.842655\pi$
$998$	−0.679559	−	6.46887i	−0.0215111	−	0.204769i
$999$	−12.0385	−	10.5172i	−0.380881	−	0.332751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.10	✓	144
8.3	odd	2	inner	504.2.br.a.155.15	yes	144
9.5	odd	6	inner	504.2.br.a.491.15	yes	144
72.59	even	6	inner	504.2.br.a.491.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.10	✓	144	1.1	even	1	trivial
504.2.br.a.155.15	yes	144	8.3	odd	2	inner
504.2.br.a.491.10	yes	144	72.59	even	6	inner
504.2.br.a.491.15	yes	144	9.5	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.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29192 - 0.575281i) q^{2} +(0.410623 - 1.68267i) q^{3} +(1.33810 + 1.48643i) q^{4} +(1.67611 + 2.90312i) q^{5} +(-1.49850 + 1.93765i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.873604 - 2.69013i) q^{8} +(-2.66278 - 1.38189i) q^{9} +O(q^{10})\)	\(q+(-1.29192 - 0.575281i) q^{2} +(0.410623 - 1.68267i) q^{3} +(1.33810 + 1.48643i) q^{4} +(1.67611 + 2.90312i) q^{5} +(-1.49850 + 1.93765i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.873604 - 2.69013i) q^{8} +(-2.66278 - 1.38189i) q^{9} +(-0.495295 - 4.71482i) q^{10} +(-0.931208 - 0.537633i) q^{11} +(3.05063 - 1.64123i) q^{12} +(1.24684 - 0.719865i) q^{13} +(-0.831193 - 1.14417i) q^{14} +(5.57324 - 1.62827i) q^{15} +(-0.418957 + 3.97800i) q^{16} +2.72213i q^{17} +(2.64512 + 3.31713i) q^{18} +6.49390 q^{19} +(-2.07247 + 6.37610i) q^{20} +(1.19695 - 1.25193i) q^{21} +(0.893754 + 1.23028i) q^{22} +(2.74636 + 4.75684i) q^{23} +(-4.88534 + 0.365361i) q^{24} +(-3.11872 + 5.40178i) q^{25} +(-2.02494 + 0.212722i) q^{26} +(-3.41866 + 3.91315i) q^{27} +(0.415616 + 1.95634i) q^{28} +(-0.590015 + 1.02194i) q^{29} +(-8.13689 - 1.10259i) q^{30} +(9.00497 - 5.19902i) q^{31} +(2.82973 - 4.89823i) q^{32} +(-1.28704 + 1.34615i) q^{33} +(1.56599 - 3.51677i) q^{34} +3.35223i q^{35} +(-1.50899 - 5.80715i) q^{36} +3.07642i q^{37} +(-8.38958 - 3.73582i) q^{38} +(-0.699316 - 2.39362i) q^{39} +(6.34551 - 7.04514i) q^{40} +(2.74938 - 1.58736i) q^{41} +(-2.26657 + 0.928806i) q^{42} +(2.28900 - 3.96466i) q^{43} +(-0.446898 - 2.10359i) q^{44} +(-0.451343 - 10.0466i) q^{45} +(-0.811555 - 7.72537i) q^{46} +(2.70286 - 4.68149i) q^{47} +(6.52164 + 2.33842i) q^{48} +(0.500000 + 0.866025i) q^{49} +(7.13667 - 5.18452i) q^{50} +(4.58046 + 1.11777i) q^{51} +(2.73844 + 0.890093i) q^{52} -12.5659 q^{53} +(6.66779 - 3.08878i) q^{54} -3.60454i q^{55} +(0.588503 - 2.76653i) q^{56} +(2.66654 - 10.9271i) q^{57} +(1.35015 - 0.980832i) q^{58} +(-11.1655 + 6.44638i) q^{59} +(9.87789 + 6.10545i) q^{60} +(1.14110 + 0.658814i) q^{61} +(-14.6246 + 1.53632i) q^{62} +(-1.61509 - 2.52814i) q^{63} +(-6.47363 + 4.70022i) q^{64} +(4.17970 + 2.41315i) q^{65} +(2.43716 - 0.998714i) q^{66} +(-2.57984 - 4.46841i) q^{67} +(-4.04626 + 3.64250i) q^{68} +(9.13192 - 2.66796i) q^{69} +(1.92847 - 4.33080i) q^{70} +14.0523 q^{71} +(-1.39125 + 8.37045i) q^{72} -3.81183 q^{73} +(1.76981 - 3.97448i) q^{74} +(7.80881 + 7.46588i) q^{75} +(8.68951 + 9.65273i) q^{76} +(-0.537633 - 0.931208i) q^{77} +(-0.473547 + 3.49467i) q^{78} +(1.96184 + 1.13267i) q^{79} +(-12.2508 + 5.45130i) q^{80} +(5.18078 + 7.35932i) q^{81} +(-4.46516 + 0.469067i) q^{82} +(-6.85242 - 3.95624i) q^{83} +(3.46254 + 0.103971i) q^{84} +(-7.90267 + 4.56261i) q^{85} +(-5.23799 + 3.80520i) q^{86} +(1.47731 + 1.41243i) q^{87} +(-0.632798 + 2.97475i) q^{88} -3.72610i q^{89} +(-5.19649 + 13.2390i) q^{90} +1.43973 q^{91} +(-3.39580 + 10.4474i) q^{92} +(-5.05061 - 17.2873i) q^{93} +(-6.18504 + 4.49319i) q^{94} +(10.8845 + 18.8525i) q^{95} +(-7.08017 - 6.77283i) q^{96} +(2.81825 - 4.88135i) q^{97} +(-0.147751 - 1.40647i) q^{98} +(1.73665 + 2.71842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{6}+O(q^{10}) \) 144 * q + 6 * q^6	\( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

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