LMFDB - Embedded newform 504.2.ca.a.101.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(5,504)]

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([0, 3, 5, 5]))

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

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

chi := DirichletCharacter("504.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ca (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			101.21
Character	$\chi$	$=$	504.101
Dual form			504.2.ca.a.5.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07099 - 0.923569i) q^{2} +(0.414791 + 1.68165i) q^{3} +(0.294039 + 1.97827i) q^{4} +(1.55193 + 0.896009i) q^{5} +(1.10888 - 2.18412i) q^{6} +(-0.676966 + 2.55768i) q^{7} +(1.51215 - 2.39027i) q^{8} +(-2.65590 + 1.39507i) q^{9} +O(q^{10})$	\(q+(-1.07099 - 0.923569i) q^{2} +(0.414791 + 1.68165i) q^{3} +(0.294039 + 1.97827i) q^{4} +(1.55193 + 0.896009i) q^{5} +(1.10888 - 2.18412i) q^{6} +(-0.676966 + 2.55768i) q^{7} +(1.51215 - 2.39027i) q^{8} +(-2.65590 + 1.39507i) q^{9} +(-0.834578 - 2.39293i) q^{10} +(2.69566 + 4.66903i) q^{11} +(-3.20479 + 1.31504i) q^{12} +(-1.44678 - 2.50590i) q^{13} +(3.08722 - 2.11402i) q^{14} +(-0.863046 + 2.98147i) q^{15} +(-3.82708 + 1.16338i) q^{16} +(1.11527 - 1.93170i) q^{17} +(4.13288 + 0.958801i) q^{18} +(-0.315657 - 0.546733i) q^{19} +(-1.31622 + 3.33360i) q^{20} +(-4.58192 - 0.0775184i) q^{21} +(1.42514 - 7.49011i) q^{22} +(-1.15392 - 0.666214i) q^{23} +(4.64683 + 1.55145i) q^{24} +(-0.894335 - 1.54903i) q^{25} +(-0.764883 + 4.01999i) q^{26} +(-3.44766 - 3.88763i) q^{27} +(-5.25882 - 0.587163i) q^{28} +(-2.96713 + 5.13923i) q^{29} +(3.67790 - 2.39604i) q^{30} -3.61626i q^{31} +(5.17323 + 2.28861i) q^{32} +(-6.73353 + 6.46984i) q^{33} +(-2.97851 + 1.03881i) q^{34} +(-3.34231 + 3.36278i) q^{35} +(-3.54075 - 4.84387i) q^{36} +(-4.92708 + 2.84465i) q^{37} +(-0.166881 + 0.877077i) q^{38} +(3.61393 - 3.47240i) q^{39} +(4.48847 - 2.35464i) q^{40} +(4.07147 + 7.05199i) q^{41} +(4.83560 + 4.31474i) q^{42} +(4.99769 + 2.88542i) q^{43} +(-8.44395 + 6.70562i) q^{44} +(-5.37177 - 0.214655i) q^{45} +(0.620538 + 1.77923i) q^{46} +4.89972 q^{47} +(-3.54383 - 5.95326i) q^{48} +(-6.08343 - 3.46292i) q^{49} +(-0.472816 + 2.48498i) q^{50} +(3.71105 + 1.07424i) q^{51} +(4.53193 - 3.59895i) q^{52} +(4.74975 - 8.22681i) q^{53} +(0.101916 + 7.34776i) q^{54} +9.66136i q^{55} +(5.08986 + 5.48574i) q^{56} +(0.788483 - 0.757604i) q^{57} +(7.92420 - 2.76371i) q^{58} +13.4612i q^{59} +(-6.15191 - 0.830667i) q^{60} +0.787671 q^{61} +(-3.33986 + 3.87298i) q^{62} +(-1.77018 - 7.73734i) q^{63} +(-3.42678 - 7.22891i) q^{64} -5.18532i q^{65} +(13.1869 - 0.710245i) q^{66} +6.61121i q^{67} +(4.14936 + 1.63830i) q^{68} +(0.641704 - 2.21682i) q^{69} +(6.68534 - 0.514646i) q^{70} -15.5448i q^{71} +(-0.681535 + 8.45787i) q^{72} +(9.92471 + 5.73004i) q^{73} +(7.90409 + 1.50391i) q^{74} +(2.23397 - 2.14649i) q^{75} +(0.988769 - 0.785214i) q^{76} +(-13.7667 + 3.73387i) q^{77} +(-7.07749 + 0.381193i) q^{78} -1.12006 q^{79} +(-6.98177 - 1.62362i) q^{80} +(5.10757 - 7.41031i) q^{81} +(2.15250 - 11.3129i) q^{82} +(10.6478 + 6.14753i) q^{83} +(-1.19391 - 9.08706i) q^{84} +(3.46165 - 1.99858i) q^{85} +(-2.68759 - 7.70597i) q^{86} +(-9.87312 - 2.85798i) q^{87} +(15.2365 + 0.616923i) q^{88} +(5.09915 + 8.83199i) q^{89} +(5.55486 + 5.19109i) q^{90} +(7.38870 - 2.00399i) q^{91} +(0.978652 - 2.47865i) q^{92} +(6.08128 - 1.49999i) q^{93} +(-5.24755 - 4.52523i) q^{94} -1.13132i q^{95} +(-1.70284 + 9.64885i) q^{96} +(-13.7295 - 7.92671i) q^{97} +(3.31704 + 9.32723i) q^{98} +(-13.6730 - 8.63982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} + 12 q^{12} - 18 q^{14} - 2 q^{15} - 2 q^{16} + 12 q^{18} - 6 q^{22} - 6 q^{23} - 12 q^{24} + 78 q^{25} - 6 q^{26} - 8 q^{28} + 7 q^{30} - 6 q^{33} + 6 q^{34} + 22 q^{36} - 33 q^{38} - 8 q^{39} - 18 q^{40} - 42 q^{42} - 9 q^{44} + 2 q^{46} - 12 q^{47} + 9 q^{48} - 2 q^{49} + 9 q^{50} + 21 q^{52} + 33 q^{54} + 18 q^{56} + 4 q^{57} - 3 q^{58} - 59 q^{60} + 12 q^{62} - 72 q^{63} - 8 q^{64} - 42 q^{66} - 18 q^{68} - 27 q^{70} + 12 q^{72} - 12 q^{73} - 57 q^{74} + 12 q^{76} + 19 q^{78} - 4 q^{79} - 57 q^{80} - 18 q^{81} + 69 q^{84} - 27 q^{86} - 6 q^{87} + 9 q^{88} - 24 q^{89} - 75 q^{90} - 36 q^{92} - 45 q^{96} - 45 q^{98}+O(q^{100}) $ 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 + 12 * q^12 - 18 * q^14 - 2 * q^15 - 2 * q^16 + 12 * q^18 - 6 * q^22 - 6 * q^23 - 12 * q^24 + 78 * q^25 - 6 * q^26 - 8 * q^28 + 7 * q^30 - 6 * q^33 + 6 * q^34 + 22 * q^36 - 33 * q^38 - 8 * q^39 - 18 * q^40 - 42 * q^42 - 9 * q^44 + 2 * q^46 - 12 * q^47 + 9 * q^48 - 2 * q^49 + 9 * q^50 + 21 * q^52 + 33 * q^54 + 18 * q^56 + 4 * q^57 - 3 * q^58 - 59 * q^60 + 12 * q^62 - 72 * q^63 - 8 * q^64 - 42 * q^66 - 18 * q^68 - 27 * q^70 + 12 * q^72 - 12 * q^73 - 57 * q^74 + 12 * q^76 + 19 * q^78 - 4 * q^79 - 57 * q^80 - 18 * q^81 + 69 * q^84 - 27 * q^86 - 6 * q^87 + 9 * q^88 - 24 * q^89 - 75 * q^90 - 36 * q^92 - 45 * q^96 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.07099	−	0.923569i	−0.757304	−	0.653062i
$2$	−1.07099	−	0.923569i	−0.757304	−	0.653062i
$3$	0.414791	+	1.68165i	0.239480	+	0.970901i
$3$	0.414791	+	1.68165i	0.239480	+	0.970901i
$4$	0.294039	+	1.97827i	0.147020	+	0.989134i
$5$	1.55193	+	0.896009i	0.694046	+	0.400707i	0.805126	−	0.593104i	$-0.202098\pi$
$5$	1.55193	+	0.896009i	0.694046	+	0.400707i	−0.111080	+	0.993811i	$0.535431\pi$
$6$	1.10888	−	2.18412i	0.452700	−	0.891663i
$7$	−0.676966	+	2.55768i	−0.255869	+	0.966711i
$7$	−0.676966	+	2.55768i	−0.255869	+	0.966711i
$8$	1.51215	−	2.39027i	0.534627	−	0.845088i
$9$	−2.65590	+	1.39507i	−0.885299	+	0.465023i
$10$	−0.834578	−	2.39293i	−0.263917	−	0.756712i
$11$	2.69566	+	4.66903i	0.812773	+	1.40776i	0.910916	+	0.412592i	$0.135377\pi$
$11$	2.69566	+	4.66903i	0.812773	+	1.40776i	−0.0981427	+	0.995172i	$0.531290\pi$
$12$	−3.20479	+	1.31504i	−0.925143	+	0.379619i
$13$	−1.44678	−	2.50590i	−0.401265	−	0.695011i	0.592614	−	0.805487i	$-0.298096\pi$
$13$	−1.44678	−	2.50590i	−0.401265	−	0.695011i	−0.993879	+	0.110475i	$0.964763\pi$
$14$	3.08722	−	2.11402i	0.825094	−	0.564996i
$15$	−0.863046	+	2.98147i	−0.222837	+	0.769811i
$16$	−3.82708	+	1.16338i	−0.956770	+	0.290844i
$17$	1.11527	−	1.93170i	0.270493	−	0.468507i	−0.698495	−	0.715615i	$-0.746147\pi$
$17$	1.11527	−	1.93170i	0.270493	−	0.468507i	0.968988	+	0.247108i	$0.0794801\pi$
$18$	4.13288	+	0.958801i	0.974129	+	0.225991i
$19$	−0.315657	−	0.546733i	−0.0724166	−	0.125429i	0.827543	−	0.561402i	$-0.189738\pi$
$19$	−0.315657	−	0.546733i	−0.0724166	−	0.125429i	−0.899960	+	0.435973i	$0.856404\pi$
$20$	−1.31622	+	3.33360i	−0.294315	+	0.745416i
$21$	−4.58192	−	0.0775184i	−0.999857	−	0.0169159i
$22$	1.42514	−	7.49011i	0.303841	−	1.59690i
$23$	−1.15392	−	0.666214i	−0.240608	−	0.138915i	0.374848	−	0.927086i	$-0.377695\pi$
$23$	−1.15392	−	0.666214i	−0.240608	−	0.138915i	−0.615456	+	0.788171i	$0.711028\pi$
$24$	4.64683	+	1.55145i	0.948530	+	0.316689i
$25$	−0.894335	−	1.54903i	−0.178867	−	0.309807i
$26$	−0.764883	+	4.01999i	−0.150006	+	0.788386i
$27$	−3.44766	−	3.88763i	−0.663502	−	0.748174i
$28$	−5.25882	−	0.587163i	−0.993824	−	0.110963i
$29$	−2.96713	+	5.13923i	−0.550983	+	0.954330i	0.447221	+	0.894423i	$0.352414\pi$
$29$	−2.96713	+	5.13923i	−0.550983	+	0.954330i	−0.998204	+	0.0599069i	$0.980920\pi$
$30$	3.67790	−	2.39604i	0.671490	−	0.437455i
$31$		−	3.61626i		−	0.649499i	−0.945800	−	0.324749i	$-0.894720\pi$
$31$		−	3.61626i		−	0.649499i	0.945800	−	0.324749i	$-0.105280\pi$
$32$	5.17323	+	2.28861i	0.914506	+	0.404573i
$33$	−6.73353	+	6.46984i	−1.17216	+	1.12625i
$34$	−2.97851	+	1.03881i	−0.510809	+	0.178154i
$35$	−3.34231	+	3.36278i	−0.564953	+	0.568413i
$36$	−3.54075	−	4.84387i	−0.590126	−	0.807311i
$37$	−4.92708	+	2.84465i	−0.810007	+	0.467658i	−0.846958	−	0.531659i	$-0.821569\pi$
$37$	−4.92708	+	2.84465i	−0.810007	+	0.467658i	0.0369510	+	0.999317i	$0.488235\pi$
$38$	−0.166881	+	0.877077i	−0.0270717	+	0.142281i
$39$	3.61393	−	3.47240i	0.578692	−	0.556030i
$40$	4.48847	−	2.35464i	0.709689	−	0.372301i
$41$	4.07147	+	7.05199i	0.635857	+	1.10134i	0.986333	+	0.164765i	$0.0526865\pi$
$41$	4.07147	+	7.05199i	0.635857	+	1.10134i	−0.350476	+	0.936572i	$0.613980\pi$
$42$	4.83560	+	4.31474i	0.746149	+	0.665779i
$43$	4.99769	+	2.88542i	0.762141	+	0.440022i	0.830064	−	0.557668i	$-0.188304\pi$
$43$	4.99769	+	2.88542i	0.762141	+	0.440022i	−0.0679231	+	0.997691i	$0.521637\pi$
$44$	−8.44395	+	6.70562i	−1.27297	+	1.01091i
$45$	−5.37177	−	0.214655i	−0.800776	−	0.0319988i
$46$	0.620538	+	1.77923i	0.0914933	+	0.262333i
$47$	4.89972			0.714697			0.357349	−	0.933971i	$-0.383681\pi$
$47$	4.89972			0.714697			0.357349	+	0.933971i	$0.383681\pi$
$48$	−3.54383	−	5.95326i	−0.511508	−	0.859278i
$49$	−6.08343	−	3.46292i	−0.869062	−	0.494704i
$50$	−0.472816	+	2.48498i	−0.0668663	+	0.351429i
$51$	3.71105	+	1.07424i	0.519652	+	0.150424i
$52$	4.53193	−	3.59895i	0.628465	−	0.499085i
$53$	4.74975	−	8.22681i	0.652429	−	1.13004i	−0.330103	−	0.943945i	$-0.607083\pi$
$53$	4.74975	−	8.22681i	0.652429	−	1.13004i	0.982532	−	0.186095i	$-0.0595832\pi$
$54$	0.101916	+	7.34776i	0.0138690	+	0.999904i
$55$			9.66136i			1.30274i
$56$	5.08986	+	5.48574i	0.680162	+	0.733062i
$57$	0.788483	−	0.757604i	0.104437	−	0.100347i
$58$	7.92420	−	2.76371i	1.04050	−	0.362892i
$59$			13.4612i			1.75250i	0.481856	+	0.876251i	$0.339963\pi$
$59$			13.4612i			1.75250i	−0.481856	+	0.876251i	$0.660037\pi$
$60$	−6.15191	−	0.830667i	−0.794208	−	0.107239i
$61$	0.787671			0.100851			0.0504255	−	0.998728i	$-0.483942\pi$
$61$	0.787671			0.100851			0.0504255	+	0.998728i	$0.483942\pi$
$62$	−3.33986	+	3.87298i	−0.424163	+	0.491868i
$63$	−1.77018	−	7.73734i	−0.223022	−	0.974813i
$64$	−3.42678	−	7.22891i	−0.428348	−	0.903614i
$65$		−	5.18532i		−	0.643159i
$66$	13.1869	−	0.710245i	1.62319	−	0.0874251i
$67$			6.61121i			0.807688i	0.914828	+	0.403844i	$0.132326\pi$
$67$			6.61121i			0.807688i	−0.914828	+	0.403844i	$0.867674\pi$
$68$	4.14936	+	1.63830i	0.503184	+	0.198674i
$69$	0.641704	−	2.21682i	0.0772521	−	0.266874i
$70$	6.68534	−	0.514646i	0.799051	−	0.0615120i
$71$		−	15.5448i		−	1.84483i	−0.386204	−	0.922414i	$-0.626214\pi$
$71$		−	15.5448i		−	1.84483i	0.386204	−	0.922414i	$-0.373786\pi$
$72$	−0.681535	+	8.45787i	−0.0803197	+	0.996769i
$73$	9.92471	+	5.73004i	1.16160	+	0.670650i	0.951687	−	0.307070i	$-0.0993486\pi$
$73$	9.92471	+	5.73004i	1.16160	+	0.670650i	0.209913	+	0.977720i	$0.432682\pi$
$74$	7.90409	+	1.50391i	0.918832	+	0.174826i
$75$	2.23397	−	2.14649i	0.257957	−	0.247855i
$76$	0.988769	−	0.785214i	0.113420	−	0.0900702i
$77$	−13.7667	+	3.73387i	−1.56887	+	0.425513i
$78$	−7.07749	+	0.381193i	−0.801368	+	0.0431616i
$79$	−1.12006			−0.126017			−0.0630084	−	0.998013i	$-0.520069\pi$
$79$	−1.12006			−0.126017			−0.0630084	+	0.998013i	$0.520069\pi$
$80$	−6.98177	−	1.62362i	−0.780586	−	0.181526i
$81$	5.10757	−	7.41031i	0.567508	−	0.823368i
$82$	2.15250	−	11.3129i	0.237704	−	1.24930i
$83$	10.6478	+	6.14753i	1.16875	+	0.674779i	0.953386	−	0.301754i	$-0.0975722\pi$
$83$	10.6478	+	6.14753i	1.16875	+	0.674779i	0.215366	+	0.976533i	$0.430905\pi$
$84$	−1.19391	−	9.08706i	−0.130266	−	0.991479i
$85$	3.46165	−	1.99858i	0.375468	−	0.216777i
$86$	−2.68759	−	7.70597i	−0.289811	−	0.830956i
$87$	−9.87312	−	2.85798i	−1.05851	−	0.306407i
$88$	15.2365	+	0.616923i	1.62422	+	0.0657642i
$89$	5.09915	+	8.83199i	0.540509	+	0.936189i	0.998875	+	0.0474251i	$0.0151015\pi$
$89$	5.09915	+	8.83199i	0.540509	+	0.936189i	−0.458366	+	0.888764i	$0.651565\pi$
$90$	5.55486	+	5.19109i	0.585534	+	0.547189i
$91$	7.38870	−	2.00399i	0.774547	−	0.210075i
$92$	0.978652	−	2.47865i	0.102032	−	0.258417i
$93$	6.08128	−	1.49999i	0.630599	−	0.155542i
$94$	−5.24755	−	4.52523i	−0.541243	−	0.466742i
$95$		−	1.13132i		−	0.116071i
$96$	−1.70284	+	9.64885i	−0.173795	+	0.984782i
$97$	−13.7295	−	7.92671i	−1.39402	−	0.804835i	−0.400259	−	0.916402i	$-0.631080\pi$
$97$	−13.7295	−	7.92671i	−1.39402	−	0.804835i	−0.993757	+	0.111567i	$0.964413\pi$
$98$	3.31704	+	9.32723i	0.335072	+	0.942192i
$99$	−13.6730	−	8.63982i	−1.37419	−	0.868334i
$100$	2.80143	−	2.22471i	0.280143	−	0.222471i
$101$	−3.65020	+	2.10745i	−0.363209	+	0.209699i	−0.670487	−	0.741921i	$-0.733915\pi$
$101$	−3.65020	+	2.10745i	−0.363209	+	0.209699i	0.307279	+	0.951620i	$0.400582\pi$
$102$	−2.98237	−	4.57792i	−0.295298	−	0.453281i
$103$	7.08880	+	4.09272i	0.698480	+	0.403268i	0.806781	−	0.590850i	$-0.201208\pi$
$103$	7.08880	+	4.09272i	0.698480	+	0.403268i	−0.108301	+	0.994118i	$0.534541\pi$
$104$	−8.17753	−	0.331107i	−0.801873	−	0.0324677i
$105$	−7.04138	−	4.22575i	−0.687168	−	0.412391i
$106$	−12.6850	+	4.42411i	−1.23207	+	0.429707i
$107$	−2.93729	−	5.08754i	−0.283959	−	0.491831i	0.688397	−	0.725334i	$-0.258315\pi$
$107$	−2.93729	−	5.08754i	−0.283959	−	0.491831i	−0.972356	+	0.233503i	$0.924981\pi$
$108$	6.67702	−	7.96351i	0.642496	−	0.766289i
$109$	−16.1673	−	9.33417i	−1.54854	−	0.894051i	−0.998253	−	0.0590765i	$-0.981184\pi$
$109$	−16.1673	−	9.33417i	−1.54854	−	0.894051i	−0.550288	−	0.834975i	$-0.685482\pi$
$110$	8.92293	−	10.3472i	0.850768	−	0.986568i
$111$	−6.82742	−	7.10569i	−0.648030	−	0.674443i
$112$	−0.384735	−	10.5760i	−0.0363541	−	0.999339i
$113$	11.5918	−	6.69253i	1.09046	−	0.629580i	0.156765	−	0.987636i	$-0.449894\pi$
$113$	11.5918	−	6.69253i	1.09046	−	0.629580i	0.933700	+	0.358056i	$0.116560\pi$
$114$	−1.54416	+	0.0831682i	−0.144624	+	0.00778942i
$115$	−1.19387	−	2.06784i	−0.111329	−	0.192827i
$116$	−11.0392	−	4.35865i	−1.02497	−	0.404690i
$117$	7.33840	+	4.63705i	0.678435	+	0.428695i
$118$	12.4324	−	14.4168i	1.14449	−	1.32718i
$119$	4.18568	+	4.16020i	0.383700	+	0.381365i
$120$	5.82145	+	6.57135i	0.531423	+	0.599879i
$121$	−9.03321	+	15.6460i	−0.821201	+	1.42236i
$122$	−0.843588	−	0.727469i	−0.0763748	−	0.0658619i
$123$	−10.1702	+	9.77190i	−0.917014	+	0.881102i
$124$	7.15392	−	1.06332i	0.642441	−	0.0954891i
$125$		−	12.1654i		−	1.08811i
$126$	−5.25012	+	9.92150i	−0.467718	+	0.883878i
$127$	8.25424			0.732446			0.366223	−	0.930527i	$-0.380651\pi$
$127$	8.25424			0.732446			0.366223	+	0.930527i	$0.380651\pi$
$128$	−3.00635	+	10.9070i	−0.265727	+	0.964048i
$129$	−2.77927	+	9.60121i	−0.244701	+	0.845340i
$130$	−4.78900	+	5.55342i	−0.420023	+	0.487067i
$131$	2.63223	+	1.51972i	0.229979	+	0.132779i	0.610563	−	0.791968i	$-0.290943\pi$
$131$	2.63223	+	1.51972i	0.229979	+	0.132779i	−0.380583	+	0.924747i	$0.624277\pi$
$132$	−14.7790	−	11.4183i	−1.28635	−	0.993839i
$133$	1.61206	−	0.437228i	0.139783	−	0.0379125i
$134$	6.10591	−	7.08054i	0.527470	−	0.611665i
$135$	−1.86719	−	9.12247i	−0.160702	−	0.785137i
$136$	−2.93083	−	5.58683i	−0.251317	−	0.479067i
$137$	5.41090	−	3.12398i	0.462284	−	0.266900i	−0.250720	−	0.968060i	$-0.580667\pi$
$137$	5.41090	−	3.12398i	0.462284	−	0.266900i	0.713004	+	0.701160i	$0.247334\pi$
$138$	−2.73465	+	1.78154i	−0.232789	+	0.151655i
$139$	−5.45318	−	9.44519i	−0.462533	−	0.801131i	0.536553	−	0.843866i	$-0.319726\pi$
$139$	−5.45318	−	9.44519i	−0.462533	−	0.801131i	−0.999086	+	0.0427357i	$0.986393\pi$
$140$	−7.63524	−	5.62319i	−0.645296	−	0.475247i
$141$	2.03236	+	8.23961i	0.171156	+	0.693901i
$142$	−14.3567	+	16.6483i	−1.20479	+	1.39710i
$143$	7.80007	−	13.5101i	0.652275	−	1.12977i
$144$	8.54134	−	8.42885i	0.711779	−	0.702404i
$145$	−9.20959	+	5.31716i	−0.764815	+	0.441566i
$146$	−5.33718	−	15.3030i	−0.441708	−	1.26648i
$147$	3.30007	−	11.6666i	0.272185	−	0.962245i
$148$	−7.07624	−	8.91065i	−0.581663	−	0.732451i
$149$	3.24552	−	5.62141i	0.265883	−	0.460524i	−0.701911	−	0.712264i	$-0.747670\pi$
$149$	3.24552	−	5.62141i	0.265883	−	0.460524i	0.967795	+	0.251741i	$0.0810030\pi$
$150$	−4.37499	+	0.235637i	−0.357216	+	0.0192397i
$151$	2.78574	+	4.82505i	0.226701	+	0.392657i	0.956828	−	0.290654i	$-0.0938728\pi$
$151$	2.78574	+	4.82505i	0.226701	+	0.392657i	−0.730128	+	0.683311i	$0.760539\pi$
$152$	−1.78416	−	0.0722404i	−0.144715	−	0.00585947i
$153$	−0.267182	+	6.68628i	−0.0216004	+	0.540554i
$154$	18.1925	+	8.71561i	1.46600	+	0.702324i
$155$	3.24020	−	5.61219i	0.260259	−	0.450782i
$156$	7.93198	+	6.12830i	0.635067	+	0.490657i
$157$	0.318833			0.0254457			0.0127228	−	0.999919i	$-0.495950\pi$
$157$	0.318833			0.0254457			0.0127228	+	0.999919i	$0.495950\pi$
$158$	1.19958	+	1.03446i	0.0954331	+	0.0822968i
$159$	15.8048	+	4.57501i	1.25340	+	0.362822i
$160$	5.97788	+	8.18703i	0.472593	+	0.647241i
$161$	2.48512	−	2.50034i	0.195855	−	0.197054i
$162$	−12.3141	+	3.21917i	−0.967487	+	0.252922i
$163$	0.883375	−	0.510017i	0.0691913	−	0.0399476i	−0.465005	−	0.885308i	$-0.653948\pi$
$163$	0.883375	−	0.510017i	0.0691913	−	0.0399476i	0.534197	+	0.845360i	$0.320614\pi$
$164$	−12.7536	+	10.1280i	−0.995885	+	0.790865i
$165$	−16.2470	+	4.00745i	−1.26483	+	0.311979i
$166$	−5.72606	−	16.4180i	−0.444428	−	1.27428i
$167$	6.69476	+	11.5957i	0.518056	+	0.897300i	0.999780	+	0.0209764i	$0.00667750\pi$
$167$	6.69476	+	11.5957i	0.518056	+	0.897300i	−0.481724	+	0.876323i	$0.659989\pi$
$168$	−7.11386	+	10.8348i	−0.548846	+	0.835923i
$169$	2.31365	−	4.00736i	0.177973	−	0.308258i
$170$	−5.55322	−	1.05661i	−0.425913	−	0.0810382i
$171$	1.60108	+	1.01170i	0.122438	+	0.0773670i
$172$	−4.23861	+	10.7352i	−0.323191	+	0.818551i
$173$		−	9.97934i		−	0.758715i	−0.925250	−	0.379358i	$-0.876145\pi$
$173$		−	9.97934i		−	0.758715i	0.925250	−	0.379358i	$-0.123855\pi$
$174$	7.93448	+	12.1794i	0.601511	+	0.923316i
$175$	4.56737	−	1.23878i	0.345260	−	0.0936428i
$176$	−15.7484	−	14.7327i	−1.18708	−	1.11052i
$177$	−22.6371	+	5.58360i	−1.70151	+	0.419689i
$178$	2.69581	−	14.1684i	0.202060	−	1.06197i
$179$	0.106425	−	0.184334i	0.00795460	−	0.0137778i	−0.862021	−	0.506873i	$-0.830801\pi$
$179$	0.106425	−	0.184334i	0.00795460	−	0.0137778i	0.869975	+	0.493095i	$0.164135\pi$
$180$	−1.15487	−	10.6899i	−0.0860786	−	0.796779i
$181$	22.4982			1.67228			0.836139	−	0.548518i	$-0.184808\pi$
$181$	22.4982			1.67228			0.836139	+	0.548518i	$0.184808\pi$
$182$	−9.76405	−	4.67773i	−0.723760	−	0.346736i
$183$	0.326719	+	1.32459i	0.0241518	+	0.0979163i
$184$	−3.33733	+	1.75075i	−0.246031	+	0.129067i
$185$	−10.1953			−0.749576
$186$	−7.89834	−	4.01001i	−0.579134	−	0.294028i
$187$	12.0256			0.879397
$188$	1.44071	+	9.69295i	0.105075	+	0.706931i
$189$	12.2772	−	6.18621i	0.893038	−	0.449981i
$190$	−1.04486	+	1.21164i	−0.0758019	+	0.0879014i
$191$		−	11.9511i		−	0.864751i	−0.901694	−	0.432376i	$-0.857675\pi$
$191$		−	11.9511i		−	0.864751i	0.901694	−	0.432376i	$-0.142325\pi$
$192$	10.7351	−	8.76114i	0.774739	−	0.632281i
$193$	1.19187			0.0857923			0.0428962	−	0.999080i	$-0.486342\pi$
$193$	1.19187			0.0857923			0.0428962	+	0.999080i	$0.486342\pi$
$194$	7.38325	+	21.1695i	0.530087	+	1.51988i
$195$	8.71989	−	2.15082i	0.624444	−	0.154024i
$196$	5.06182	−	13.0529i	0.361559	−	0.932349i
$197$	5.44225			0.387744			0.193872	−	0.981027i	$-0.437895\pi$
$197$	5.44225			0.387744			0.193872	+	0.981027i	$0.437895\pi$
$198$	6.66419	+	21.8811i	0.473603	+	1.55502i
$199$	8.07803	+	4.66385i	0.572636	+	0.330612i	0.758202	−	0.652020i	$-0.226078\pi$
$199$	8.07803	+	4.66385i	0.572636	+	0.330612i	−0.185565	+	0.982632i	$0.559412\pi$
$200$	−5.05498	−	0.204675i	−0.357441	−	0.0144727i
$201$	−11.1177	+	2.74227i	−0.784185	+	0.193425i
$202$	5.85570	+	1.11416i	0.412006	+	0.0783922i
$203$	−11.1358	−	11.0681i	−0.781582	−	0.776825i
$204$	−1.03394	+	7.65733i	−0.0723901	+	0.536120i
$205$			14.5923i			1.01917i
$206$	−3.81212	−	10.9303i	−0.265603	−	0.761547i
$207$	3.99409	+	0.159603i	0.277609	+	0.0110932i
$208$	8.45225	+	7.90713i	0.586058	+	0.548261i
$209$	1.70181	−	2.94762i	0.117717	−	0.203891i
$210$	3.63848	+	11.0289i	0.251079	+	0.761069i
$211$	16.6090	−	9.58924i	1.14341	−	0.660150i	0.196140	−	0.980576i	$-0.437159\pi$
$211$	16.6090	−	9.58924i	1.14341	−	0.660150i	0.947274	+	0.320426i	$0.103826\pi$
$212$	17.6715	+	6.97728i	1.21368	+	0.479201i
$213$	26.1409	−	6.44784i	1.79115	−	0.441799i
$214$	−1.55288	+	8.16150i	−0.106153	+	0.557908i
$215$	5.17072	+	8.95595i	0.352640	+	0.610791i
$216$	−14.5059	+	2.36215i	−0.986999	+	0.160724i
$217$	9.24922	+	2.44808i	0.627878	+	0.166187i
$218$	8.69421	+	24.9284i	0.588846	+	1.68836i
$219$	−5.51923	+	19.0667i	−0.372955	+	1.28841i
$220$	−19.1127	+	2.84082i	−1.28858	+	0.191528i
$221$	−6.45420			−0.434157
$222$	0.749500	+	13.9157i	0.0503032	+	0.933962i
$223$	14.7938	+	8.54118i	0.990664	+	0.571960i	0.905473	−	0.424405i	$-0.139517\pi$
$223$	14.7938	+	8.54118i	0.990664	+	0.571960i	0.0851910	+	0.996365i	$0.472850\pi$
$224$	−9.35563	+	11.6821i	−0.625099	+	0.780545i
$225$	4.53627	+	2.86642i	0.302418	+	0.191094i
$226$	−18.5957	−	3.53820i	−1.23697	−	0.235358i
$227$	8.22434	−	4.74832i	0.545868	−	0.315157i	−0.201586	−	0.979471i	$-0.564609\pi$
$227$	8.22434	−	4.74832i	0.545868	−	0.315157i	0.747454	+	0.664314i	$0.231276\pi$
$228$	1.73059	+	1.33706i	0.114611	+	0.0885492i
$229$	−12.2675	+	21.2480i	−0.810660	+	1.40410i	0.101743	+	0.994811i	$0.467558\pi$
$229$	−12.2675	+	21.2480i	−0.810660	+	1.40410i	−0.912403	+	0.409293i	$0.865775\pi$
$230$	−0.631173	+	3.31725i	−0.0416183	+	0.218733i
$231$	−11.9894	−	21.6021i	−0.788843	−	1.42131i
$232$	7.79738	+	14.8636i	0.511923	+	0.975840i
$233$	19.2901	−	11.1371i	1.26374	−	0.729618i	0.289941	−	0.957045i	$-0.406364\pi$
$233$	19.2901	−	11.1371i	1.26374	−	0.729618i	0.973795	+	0.227426i	$0.0730310\pi$
$234$	−3.57672	−	11.7438i	−0.233817	−	0.767713i
$235$	7.60404	+	4.39019i	0.496033	+	0.286385i
$236$	−26.6299	+	3.95813i	−1.73346	+	0.257652i
$237$	−0.464592	−	1.88355i	−0.0301785	−	0.122350i
$238$	−0.640584	−	8.32129i	−0.0415229	−	0.539389i
$239$	−12.4677	+	7.19824i	−0.806470	+	0.465616i	−0.845729	−	0.533613i	$-0.820834\pi$
$239$	−12.4677	+	7.19824i	−0.806470	+	0.465616i	0.0392585	+	0.999229i	$0.487500\pi$
$240$	−0.165620	−	12.4144i	−0.0106907	−	0.801344i
$241$	−9.55425	+	5.51615i	−0.615444	+	0.355327i	−0.775093	−	0.631847i	$-0.782297\pi$
$241$	−9.55425	+	5.51615i	−0.615444	+	0.355327i	0.159649	+	0.987174i	$0.448964\pi$
$242$	24.1246	−	8.41389i	1.55079	−	0.540865i
$243$	14.5801	+	5.51541i	0.935316	+	0.353814i
$244$	0.231606	+	1.55822i	0.0148271	+	0.0997550i
$245$	−6.33827	−	10.8250i	−0.404937	−	0.691586i
$246$	19.9172	−	1.07274i	1.26987	−	0.0683953i
$247$	−0.913372	+	1.58201i	−0.0581165	+	0.100661i
$248$	−8.64383	−	5.46834i	−0.548884	−	0.347240i
$249$	−5.92137	+	20.4559i	−0.375251	+	1.29634i
$250$	−11.2356	+	13.0290i	−0.710602	+	0.824029i
$251$			12.8663i			0.812115i	0.913848	+	0.406057i	$0.133097\pi$
$251$			12.8663i			0.812115i	−0.913848	+	0.406057i	$0.866903\pi$
$252$	14.7860	−	5.77697i	0.931432	−	0.363915i
$253$		−	7.18355i		−	0.451626i
$254$	−8.84021	−	7.62337i	−0.554684	−	0.478333i
$255$	4.79678	+	4.99229i	0.300386	+	0.312629i
$256$	13.2931	−	8.90467i	0.830819	−	0.556542i
$257$	6.25131	−	10.8276i	0.389946	−	0.675406i	−0.602496	−	0.798122i	$-0.705827\pi$
$257$	6.25131	−	10.8276i	0.389946	−	0.675406i	0.992442	+	0.122716i	$0.0391604\pi$
$258$	11.8440	−	7.71596i	0.737372	−	0.480375i
$259$	−3.94024	−	14.5276i	−0.244834	−	0.902703i
$260$	10.2579	−	1.52469i	0.636170	−	0.0945570i
$261$	0.710829	−	17.7886i	0.0439992	−	1.10109i
$262$	−1.41553	−	4.05866i	−0.0874516	−	0.250745i
$263$	−25.7850	+	14.8870i	−1.58997	+	0.917969i	−0.596658	+	0.802496i	$0.703505\pi$
$263$	−25.7850	+	14.8870i	−1.58997	+	0.917969i	−0.993311	+	0.115473i	$0.963162\pi$
$264$	5.28252	+	25.8783i	0.325116	+	1.59270i
$265$	14.7426	−	8.51165i	0.905631	−	0.522866i
$266$	−2.13031	−	1.02058i	−0.130617	−	0.0625757i
$267$	−12.7372	+	12.2384i	−0.779506	+	0.748979i
$268$	−13.0787	+	1.94395i	−0.798911	+	0.118746i
$269$	4.58636	+	2.64794i	0.279635	+	0.161448i	0.633258	−	0.773940i	$-0.281717\pi$
$269$	4.58636	+	2.64794i	0.279635	+	0.161448i	−0.353623	+	0.935388i	$0.615050\pi$
$270$	−6.42550	+	11.4946i	−0.391043	+	0.699536i
$271$	−13.1755	+	7.60690i	−0.800357	+	0.462086i	−0.843596	−	0.536978i	$-0.819566\pi$
$271$	−13.1755	+	7.60690i	−0.800357	+	0.462086i	0.0432388	+	0.999065i	$0.486232\pi$
$272$	−2.02093	+	8.69027i	−0.122537	+	0.526925i
$273$	6.43478	+	11.5940i	0.389451	+	0.701699i
$274$	−8.68023	−	1.65158i	−0.524392	−	0.0997758i
$275$	4.82165	−	8.35135i	0.290757	−	0.503605i
$276$	4.57415	+	0.617630i	0.275332	+	0.0371769i
$277$	−21.9588	+	12.6779i	−1.31938	+	0.761743i	−0.983628	−	0.180208i	$-0.942323\pi$
$277$	−21.9588	+	12.6779i	−1.31938	+	0.761743i	−0.335749	+	0.941951i	$0.608989\pi$
$278$	−2.88298	+	15.1521i	−0.172910	+	0.908763i
$279$	5.04492	+	9.60440i	0.302032	+	0.575001i
$280$	2.98386	+	13.0741i	0.178320	+	0.781324i
$281$	7.67421	+	4.43071i	0.457805	+	0.264314i	0.711121	−	0.703070i	$-0.248188\pi$
$281$	7.67421	+	4.43071i	0.457805	+	0.264314i	−0.253316	+	0.967384i	$0.581521\pi$
$282$	5.43322	−	10.7016i	0.323543	−	0.637269i
$283$	−29.3778			−1.74633			−0.873164	−	0.487426i	$-0.837936\pi$
$283$	−29.3778			−1.74633			−0.873164	+	0.487426i	$0.837936\pi$
$284$	30.7517	−	4.57078i	1.82478	−	0.271226i
$285$	1.90249	−	0.469264i	0.112694	−	0.0277968i
$286$	−20.8313	+	7.26530i	−1.23178	+	0.429606i
$287$	−20.7930	+	5.63955i	−1.22737	+	0.332892i
$288$	−16.9323	+	1.13869i	−0.997746	+	0.0670977i
$289$	6.01235	+	10.4137i	0.353667	+	0.612570i
$290$	14.7741	+	2.81107i	0.867567	+	0.165072i
$291$	7.63509	−	26.3761i	0.447577	−	1.54619i
$292$	−8.41729	+	21.3186i	−0.492584	+	1.24758i
$293$	3.87316	−	2.23617i	0.226273	−	0.130639i	−0.382579	−	0.923923i	$-0.624964\pi$
$293$	3.87316	−	2.23617i	0.226273	−	0.130639i	0.608851	+	0.793284i	$0.291631\pi$
$294$	−14.3093	+	9.44696i	−0.834533	+	0.550958i
$295$	−12.0614	+	20.8909i	−0.702240	+	1.21632i
$296$	−0.651020	+	16.0786i	−0.0378398	+	0.934550i
$297$	8.85770	−	26.5769i	0.513976	−	1.54215i
$298$	−8.66768	+	3.02301i	−0.502105	+	0.175118i
$299$			3.85546i			0.222967i
$300$	4.90320	+	3.78824i	0.283086	+	0.218714i
$301$	−10.7632	+	10.8292i	−0.620383	+	0.624182i
$302$	1.47276	−	7.74041i	0.0847481	−	0.445410i
$303$	−5.05806	−	5.26422i	−0.290578	−	0.302421i
$304$	1.84410	+	1.72517i	0.105766	+	0.0989450i
$305$	1.22241	+	0.705760i	0.0699951	+	0.0404117i
$306$	6.46139	−	6.91418i	0.369373	−	0.395257i
$307$	14.9616			0.853906			0.426953	−	0.904274i	$-0.359587\pi$
$307$	14.9616			0.853906			0.426953	+	0.904274i	$0.359587\pi$
$308$	−11.4345	−	26.1364i	−0.651544	−	1.48926i
$309$	−3.94215	+	13.6185i	−0.224261	+	0.774730i
$310$	−8.65347	+	3.01805i	−0.491484	+	0.171414i
$311$	−4.54064			−0.257476			−0.128738	−	0.991679i	$-0.541093\pi$
$311$	−4.54064			−0.257476			−0.128738	+	0.991679i	$0.541093\pi$
$312$	−2.83516	−	13.8891i	−0.160509	−	0.786315i
$313$		−	3.91281i		−	0.221165i	−0.993867	−	0.110583i	$-0.964728\pi$
$313$		−	3.91281i		−	0.221165i	0.993867	−	0.110583i	$-0.0352717\pi$
$314$	−0.341467	−	0.294465i	−0.0192701	−	0.0166176i
$315$	4.18552	−	13.5939i	0.235828	−	0.765932i
$316$	−0.329342	−	2.21578i	−0.0185269	−	0.124648i
$317$	34.2695			1.92477			0.962383	−	0.271698i	$-0.0875852\pi$
$317$	34.2695			1.92477			0.962383	+	0.271698i	$0.0875852\pi$
$318$	−12.7014	−	19.4966i	−0.712260	−	1.09332i
$319$	−31.9936			−1.79130
$320$	1.15904	−	14.2892i	0.0647921	−	0.798791i
$321$	7.33710	−	7.04976i	0.409517	−	0.393479i
$322$	−4.97078	+	0.382657i	−0.277011	+	0.0213247i
$323$	−1.40817			−0.0783526
$324$	16.1614	+	7.92522i	0.897856	+	0.440290i
$325$	−2.58782	+	4.48223i	−0.143546	+	0.248629i
$326$	−1.41712	−	0.269635i	−0.0784871	−	0.0149337i
$327$	8.99077	−	31.0594i	0.497191	−	1.71759i
$328$	23.0129	+	0.931787i	1.27067	+	0.0514493i
$329$	−3.31695	+	12.5319i	−0.182869	+	0.690906i
$330$	21.1016	+	10.7133i	1.16160	+	0.589749i
$331$			4.94709i			0.271917i	0.990715	+	0.135958i	$0.0434113\pi$
$331$			4.94709i			0.271917i	−0.990715	+	0.135958i	$0.956589\pi$
$332$	−9.03058	+	22.8719i	−0.495617	+	1.25526i
$333$	9.11734	−	14.4287i	0.499627	−	0.790689i
$334$	3.53938	−	18.6019i	0.193666	−	1.01785i
$335$	−5.92370	+	10.2602i	−0.323646	+	0.560572i
$336$	17.6256	−	5.03383i	0.961553	−	0.274618i
$337$	−0.458607	−	0.794331i	−0.0249819	−	0.0432700i	0.853264	−	0.521479i	$-0.174619\pi$
$337$	−0.458607	−	0.794331i	−0.0249819	−	0.0432700i	−0.878246	+	0.478209i	$0.841286\pi$
$338$	−6.17897	+	2.15502i	−0.336092	+	0.117218i
$339$	16.0627	+	16.7174i	0.872405	+	0.907962i
$340$	4.97159	+	6.26040i	0.269622	+	0.339518i
$341$	16.8844	−	9.74821i	0.914342	−	0.527895i
$342$	−0.780363	−	2.56224i	−0.0421972	−	0.138550i
$343$	12.9753	−	13.2152i	0.700602	−	0.713553i
$344$	14.4542	−	7.58263i	0.779319	−	0.408828i
$345$	2.98218	−	2.86539i	0.160555	−	0.154267i
$346$	−9.21661	+	10.6878i	−0.495488	+	0.574578i
$347$	−26.9748			−1.44808			−0.724041	−	0.689757i	$-0.757718\pi$
$347$	−26.9748			−1.44808			−0.724041	+	0.689757i	$0.757718\pi$
$348$	2.75075	−	20.3720i	0.147456	−	1.09206i
$349$	8.18283	−	14.1731i	0.438017	−	0.758667i	−0.559520	−	0.828817i	$-0.689014\pi$
$349$	8.18283	−	14.1731i	0.438017	−	0.758667i	0.997536	+	0.0701498i	$0.0223477\pi$
$350$	−6.03570	−	2.89156i	−0.322622	−	0.154560i
$351$	−4.75399	+	14.2640i	−0.253749	+	0.761358i
$352$	3.25969	+	30.3233i	0.173742	+	1.61623i
$353$	−10.6124	−	18.3812i	−0.564842	−	0.978334i	−0.997064	−	0.0765675i	$-0.975604\pi$
$353$	−10.6124	−	18.3812i	−0.564842	−	0.978334i	0.432223	−	0.901767i	$-0.357729\pi$
$354$	29.4009	+	14.9269i	1.56264	+	0.793357i
$355$	13.9283	−	24.1245i	0.739236	−	1.28039i
$356$	−15.9727	+	12.6844i	−0.846550	+	0.672273i
$357$	−5.25982	+	8.76446i	−0.278379	+	0.463864i
$358$	−0.284226	+	0.0991288i	−0.0150218	+	0.00523912i
$359$	−21.1858	+	12.2316i	−1.11814	+	0.645560i	−0.940926	−	0.338611i	$-0.890043\pi$
$359$	−21.1858	+	12.2316i	−1.11814	+	0.645560i	−0.177217	+	0.984172i	$0.556709\pi$
$360$	−8.63602	+	12.5154i	−0.455158	+	0.659619i
$361$	9.30072	−	16.1093i	0.489512	−	0.847859i
$362$	−24.0953	−	20.7786i	−1.26642	−	1.09210i
$363$	−30.0580	−	8.70088i	−1.57763	−	0.456678i
$364$	6.13700	+	14.0276i	0.321666	+	0.735245i
$365$	10.2683	+	17.7853i	0.537469	+	0.930923i
$366$	0.873435	−	1.72037i	0.0456552	−	0.0899250i
$367$	6.69167	−	3.86344i	0.349302	−	0.201670i	−0.315076	−	0.949067i	$-0.602030\pi$
$367$	6.69167	−	3.86344i	0.349302	−	0.201670i	0.664378	+	0.747397i	$0.268697\pi$
$368$	5.19119	+	1.20722i	0.270609	+	0.0629305i
$369$	−20.6514	−	13.0494i	−1.07507	−	0.679324i
$370$	10.9191	+	9.41610i	0.567657	+	0.489520i
$371$	17.8261	+	17.7176i	0.925486	+	0.919853i
$372$	4.75552	+	11.5893i	0.246562	+	0.600879i
$373$	−10.1146	−	5.83969i	−0.523716	−	0.302367i	0.214738	−	0.976672i	$-0.431110\pi$
$373$	−10.1146	−	5.83969i	−0.523716	−	0.302367i	−0.738454	+	0.674304i	$0.764444\pi$
$374$	−12.8793	−	11.1064i	−0.665971	−	0.574301i
$375$	20.4580	−	5.04611i	1.05645	−	0.260580i
$376$	7.40913	−	11.7117i	0.382097	−	0.603982i
$377$	17.1712			0.884360
$378$	−18.8622	−	4.71352i	−0.970167	−	0.242437i
$379$		−	9.48623i		−	0.487275i	−0.969866	−	0.243637i	$-0.921659\pi$
$379$		−	9.48623i		−	0.487275i	0.969866	−	0.243637i	$-0.0783407\pi$
$380$	2.23806	−	0.332654i	0.114810	−	0.0170648i
$381$	3.42379	+	13.8808i	0.175406	+	0.711132i
$382$	−11.0377	+	12.7995i	−0.564736	+	0.654880i
$383$	11.5739	−	20.0465i	0.591397	−	1.02433i	−0.402647	−	0.915355i	$-0.631910\pi$
$383$	11.5739	−	20.0465i	0.591397	−	1.02433i	0.994045	−	0.108975i	$-0.0347568\pi$
$384$	−19.5887	−	0.531523i	−0.999632	−	0.0271242i
$385$	−24.7106	−	6.54042i	−1.25937	−	0.333330i
$386$	−1.27648	−	1.10077i	−0.0649709	−	0.0560277i
$387$	−17.2987	−	0.691253i	−0.879342	−	0.0351383i
$388$	11.6441	−	29.4913i	0.591142	−	1.49719i
$389$	3.30279	+	5.72061i	0.167458	+	0.290046i	0.937526	−	0.347916i	$-0.113111\pi$
$389$	3.30279	+	5.72061i	0.167458	+	0.290046i	−0.770067	+	0.637963i	$0.779777\pi$
$390$	−11.3253	−	5.74991i	−0.573481	−	0.291158i
$391$	−2.57386	+	1.48602i	−0.130165	+	0.0751511i
$392$	−17.4764	+	9.30457i	−0.882692	+	0.469952i
$393$	−1.46381	+	5.05686i	−0.0738395	+	0.255085i
$394$	−5.82859	−	5.02629i	−0.293640	−	0.253221i
$395$	−1.73826	−	1.00359i	−0.0874615	−	0.0504959i
$396$	13.0715	−	29.5893i	0.656866	−	1.48692i
$397$	−15.3979	−	26.6699i	−0.772796	−	1.33852i	−0.936025	−	0.351934i	$-0.885524\pi$
$397$	−15.3979	−	26.6699i	−0.772796	−	1.33852i	0.163229	−	0.986588i	$-0.447809\pi$
$398$	−4.34410	−	12.4556i	−0.217750	−	0.624341i
$399$	1.40393	+	2.52956i	0.0702845	+	0.126636i
$400$	5.22480	+	4.88783i	0.261240	+	0.244392i
$401$	−16.0971	−	9.29369i	−0.803853	−	0.464105i	0.0409638	−	0.999161i	$-0.486957\pi$
$401$	−16.0971	−	9.29369i	−0.803853	−	0.464105i	−0.844817	+	0.535056i	$0.820290\pi$
$402$	14.4397	+	7.33106i	0.720185	+	0.365640i
$403$	−9.06197	+	5.23193i	−0.451409	+	0.260621i
$404$	−5.24239	−	6.60141i	−0.260819	−	0.328432i
$405$	14.5663	−	6.92388i	0.723806	−	0.344050i
$406$	1.70425	+	22.1385i	0.0845805	+	1.09872i
$407$	−26.5635	−	15.3365i	−1.31670	−	0.760200i
$408$	8.17941	−	7.24601i	0.404941	−	0.358731i
$409$		−	9.42998i		−	0.466283i	−0.972443	−	0.233141i	$-0.925100\pi$
$409$		−	9.42998i		−	0.466283i	0.972443	−	0.233141i	$-0.0749005\pi$
$410$	13.4770	−	15.6282i	0.665582	−	0.771822i
$411$	7.49784	+	7.80343i	0.369841	+	0.384915i
$412$	−6.01211	+	15.2270i	−0.296195	+	0.750178i
$413$	−34.4295	−	9.11279i	−1.69416	−	0.448411i
$414$	−4.13023	−	3.85976i	−0.202990	−	0.189697i
$415$	11.0165	+	19.0811i	0.540778	+	0.936655i
$416$	−1.74950	−	16.2747i	−0.0857761	−	0.797933i
$417$	13.6216	−	13.0881i	0.667052	−	0.640929i
$418$	−4.54495	+	1.58513i	−0.222301	+	0.0775313i
$419$	−11.7367	+	6.77620i	−0.573376	+	0.331039i	−0.758497	−	0.651677i	$-0.774066\pi$
$419$	−11.7367	+	6.77620i	−0.573376	+	0.331039i	0.185120	+	0.982716i	$0.440733\pi$
$420$	6.28921	−	15.1723i	0.306882	−	0.740330i
$421$	1.39692	+	0.806512i	0.0680817	+	0.0393070i	0.533654	−	0.845703i	$-0.320818\pi$
$421$	1.39692	+	0.806512i	0.0680817	+	0.0393070i	−0.465573	+	0.885010i	$0.654152\pi$
$422$	−26.6444	−	5.06963i	−1.29703	−	0.246786i
$423$	−13.0131	+	6.83544i	−0.632721	+	0.332351i
$424$	−12.4819	−	23.7934i	−0.606177	−	1.15551i
$425$	−3.98970			−0.193529
$426$	−33.9517	−	17.2374i	−1.64496	−	0.835153i
$427$	−0.533227	+	2.01461i	−0.0258047	+	0.0974937i
$428$	9.20083	−	7.30668i	0.444739	−	0.353182i
$429$	25.9547	+	7.51311i	1.25310	+	0.362736i
$430$	2.73365	−	14.3673i	0.131828	−	0.692851i
$431$	−11.0523	−	6.38102i	−0.532368	−	0.307363i	0.209612	−	0.977785i	$-0.432780\pi$
$431$	−11.0523	−	6.38102i	−0.532368	−	0.307363i	−0.741980	+	0.670422i	$0.766113\pi$
$432$	17.7172	+	10.8673i	0.852421	+	0.522855i
$433$		−	38.1875i		−	1.83517i	−0.397535	−	0.917587i	$-0.630134\pi$
$433$		−	38.1875i		−	1.83517i	0.397535	−	0.917587i	$-0.369866\pi$
$434$	−7.64485	−	11.1642i	−0.366964	−	0.535897i
$435$	−12.7617	−	13.2818i	−0.611875	−	0.636813i
$436$	13.7117	−	34.7278i	0.656670	−	1.66316i
$437$			0.841179i			0.0402391i
$438$	23.5204	−	15.3228i	1.12385	−	0.732152i
$439$			26.8584i			1.28188i	0.767591	+	0.640940i	$0.221455\pi$
$439$			26.8584i			1.28188i	−0.767591	+	0.640940i	$0.778545\pi$
$440$	23.0933	+	14.6095i	1.10093	+	0.696479i
$441$	20.9880	+	0.710366i	0.999428	+	0.0338269i
$442$	6.91239	+	5.96091i	0.328789	+	0.283531i
$443$	−11.1757			−0.530975			−0.265487	−	0.964114i	$-0.585533\pi$
$443$	−11.1757			−0.530975			−0.265487	+	0.964114i	$0.585533\pi$
$444$	12.0494	−	15.5958i	0.571841	−	0.740145i
$445$			18.2755i			0.866344i
$446$	−7.95560	−	22.8106i	−0.376708	−	1.08011i
$447$	10.7995	+	3.12612i	0.510797	+	0.147860i
$448$	20.8090	−	3.87087i	0.983135	−	0.182881i
$449$			8.36475i			0.394757i	0.980327	+	0.197378i	$0.0632428\pi$
$449$			8.36475i			0.394757i	−0.980327	+	0.197378i	$0.936757\pi$
$450$	−2.21097	−	7.25946i	−0.104226	−	0.342214i
$451$	−21.9506	+	38.0196i	−1.03361	+	1.79027i
$452$	16.6481	+	20.9638i	0.783059	+	0.986055i
$453$	−6.95855	+	6.68604i	−0.326941	+	0.314137i
$454$	−13.1936	−	2.51034i	−0.619206	−	0.117816i
$455$	13.2624	+	3.51029i	0.621749	+	0.164565i
$456$	−0.618572	−	3.03030i	−0.0289673	−	0.141907i
$457$	33.9577			1.58848			0.794238	−	0.607607i	$-0.207870\pi$
$457$	33.9577			1.58848			0.794238	+	0.607607i	$0.207870\pi$
$458$	32.7623	−	11.4264i	1.53088	−	0.533923i
$459$	−11.3548	+	2.32410i	−0.529997	+	0.108480i
$460$	3.73969	−	2.96981i	0.174364	−	0.138468i
$461$	9.28437	+	5.36033i	0.432416	+	0.249656i	0.700375	−	0.713775i	$-0.253016\pi$
$461$	9.28437	+	5.36033i	0.432416	+	0.249656i	−0.267959	+	0.963430i	$0.586349\pi$
$462$	−7.11050	+	34.2086i	−0.330811	+	1.59153i
$463$	−4.98196	−	8.62901i	−0.231531	−	0.401024i	0.726728	−	0.686926i	$-0.241040\pi$
$463$	−4.98196	−	8.62901i	−0.231531	−	0.401024i	−0.958259	+	0.285902i	$0.907707\pi$
$464$	5.37661	−	23.1201i	0.249603	−	1.07333i
$465$	10.7817	+	3.12099i	0.499992	+	0.144733i
$466$	−30.9454	−	5.88797i	−1.43352	−	0.272755i
$467$	−9.31122	+	5.37584i	−0.430872	+	0.248764i	−0.699718	−	0.714419i	$-0.746691\pi$
$467$	−9.31122	+	5.37584i	−0.430872	+	0.248764i	0.268846	+	0.963183i	$0.413358\pi$
$468$	−7.01554	+	15.8808i	−0.324294	+	0.734090i
$469$	−16.9093	−	4.47557i	−0.780801	−	0.206662i
$470$	−4.08920	−	11.7247i	−0.188621	−	0.540820i
$471$	0.132249	+	0.536166i	0.00609373	+	0.0247052i
$472$	32.1759	+	20.3554i	1.48102	+	0.936935i
$473$			31.1125i			1.43055i
$474$	−1.24202	+	2.44635i	−0.0570478	+	0.112365i
$475$	−0.564606	+	0.977926i	−0.0259059	+	0.0448703i
$476$	−6.99923	+	9.50365i	−0.320809	+	0.435599i
$477$	−1.13789	+	28.4758i	−0.0521003	+	1.30382i
$478$	20.0009	+	3.80556i	0.914819	+	0.174062i
$479$	19.9848	+	34.6147i	0.913130	+	1.58159i	0.809616	+	0.586960i	$0.199676\pi$
$479$	19.9848	+	34.6147i	0.913130	+	1.58159i	0.103515	+	0.994628i	$0.466991\pi$
$480$	−11.2881	+	13.4486i	−0.515231	+	0.613843i
$481$	14.2568	+	8.23118i	0.650055	+	0.375309i
$482$	15.3271	+	2.91627i	0.698128	+	0.132833i
$483$	5.23551	+	3.14199i	0.238224	+	0.142965i
$484$	−33.6080	−	13.2696i	−1.52764	−	0.603162i
$485$	−14.2048	−	24.6034i	−0.645007	−	1.11718i
$486$	−10.5213	−	19.3727i	−0.477256	−	0.878764i
$487$	17.6666	−	30.5995i	0.800552	−	1.38660i	−0.118701	−	0.992930i	$-0.537873\pi$
$487$	17.6666	−	30.5995i	0.800552	−	1.38660i	0.919253	−	0.393667i	$-0.128794\pi$
$488$	1.19108	−	1.88275i	0.0539176	−	0.0852279i
$489$	1.22409	+	1.27398i	0.0553551	+	0.0576113i
$490$	−3.20945	+	17.4473i	−0.144988	+	0.788191i
$491$	13.0858	+	22.6653i	0.590554	+	1.02287i	0.994158	+	0.107936i	$0.0344240\pi$
$491$	13.0858	+	22.6653i	0.590554	+	1.02287i	−0.403604	+	0.914934i	$0.632243\pi$
$492$	−22.3219	−	17.2460i	−1.00635	−	0.777510i
$493$	6.61831	+	11.4632i	0.298074	+	0.516279i
$494$	2.43931	−	0.850751i	0.109750	−	0.0382771i
$495$	−13.4783	−	25.6596i	−0.605802	−	1.15331i
$496$	4.20707	+	13.8397i	0.188903	+	0.621421i
$497$	39.7586	+	10.5233i	1.78342	+	0.472035i
$498$	25.2342	−	16.4393i	1.13077	−	0.736660i
$499$	−8.11771	−	4.68676i	−0.363398	−	0.209808i	0.307172	−	0.951654i	$-0.400617\pi$
$499$	−8.11771	−	4.68676i	−0.363398	−	0.209808i	−0.670571	+	0.741846i	$0.733951\pi$
$500$	24.0665	−	3.57711i	1.07628	−	0.159973i
$501$	−16.7229	+	16.0680i	−0.747125	+	0.717867i
$502$	11.8829	−	13.7797i	0.530361	−	0.615018i
$503$	6.00123			0.267582			0.133791	−	0.991010i	$-0.457285\pi$
$503$	6.00123			0.267582			0.133791	+	0.991010i	$0.457285\pi$
$504$	−21.1711	−	7.46884i	−0.943037	−	0.332689i
$505$	−7.55316			−0.336111
$506$	−6.63451	+	7.69351i	−0.294940	+	0.342018i
$507$	7.69866	+	2.22853i	0.341909	+	0.0989726i
$508$	2.42707	+	16.3291i	0.107684	+	0.724487i
$509$	−15.6244	−	9.02075i	−0.692539	−	0.399838i	0.112023	−	0.993706i	$-0.464267\pi$
$509$	−15.6244	−	9.02075i	−0.692539	−	0.399838i	−0.804563	+	0.593868i	$0.797600\pi$
$510$	−0.526580	−	9.77685i	−0.0233174	−	0.432926i
$511$	−21.3743	+	21.5052i	−0.945543	+	0.951333i
$512$	−22.4609	−	2.74030i	−0.992640	−	0.121105i
$513$	−1.03722	+	3.11211i	−0.0457943	+	0.137403i
$514$	−16.6951	+	5.82272i	−0.736390	+	0.256829i
$515$	7.33423	+	12.7033i	0.323185	+	0.559772i
$516$	−19.8110	−	2.67500i	−0.872130	−	0.117760i
$517$	13.2080	+	22.8769i	0.580887	+	1.00613i
$518$	−9.19732	+	19.1980i	−0.404107	+	0.843513i
$519$	16.7818	−	4.13934i	0.736638	−	0.181697i
$520$	−12.3943	−	7.84100i	−0.543526	−	0.343850i
$521$	−9.18360	+	15.9065i	−0.402341	+	0.696875i	−0.994008	−	0.109308i	$-0.965137\pi$
$521$	−9.18360	+	15.9065i	−0.402341	+	0.696875i	0.591667	+	0.806182i	$0.298470\pi$
$522$	−17.1903	+	18.3949i	−0.752399	+	0.805124i
$523$	15.8603	+	27.4708i	0.693521	+	1.20121i	0.970677	+	0.240388i	$0.0772747\pi$
$523$	15.8603	+	27.4708i	0.693521	+	1.20121i	−0.277156	+	0.960825i	$0.589392\pi$
$524$	−2.23243	+	5.65412i	−0.0975243	+	0.247001i
$525$	3.97769	+	7.16688i	0.173601	+	0.312788i
$526$	41.3646	+	7.87042i	1.80358	+	0.343167i
$527$	−6.98554	−	4.03310i	−0.304295	−	0.175685i
$528$	18.2429	−	32.5942i	0.793922	−	1.41848i
$529$	−10.6123	−	18.3811i	−0.461405	−	0.799177i
$530$	−23.6503	−	4.49993i	−1.02730	−	0.195464i
$531$	−18.7793	−	35.7516i	−0.814953	−	1.55149i
$532$	1.33896	+	3.06052i	0.0580513	+	0.132690i
$533$	11.7811	−	20.4054i	0.510294	−	0.883855i
$534$	24.9445	−	1.34351i	1.07945	−	0.0581393i
$535$		−	10.5274i		−	0.455137i
$536$	15.8026	+	9.99716i	0.682567	+	0.431812i
$537$	0.354130	+	0.102510i	0.0152818	+	0.00442363i
$538$	−2.46639	−	7.07174i	−0.106334	−	0.304884i
$539$	−0.230402	−	37.7386i	−0.00992413	−	1.62552i
$540$	17.4977	−	6.37616i	0.752979	−	0.274386i
$541$	−4.09032	+	2.36155i	−0.175857	+	0.101531i	−0.585344	−	0.810785i	$-0.699041\pi$
$541$	−4.09032	+	2.36155i	−0.175857	+	0.101531i	0.409488	+	0.912316i	$0.365707\pi$
$542$	21.1364	+	4.02161i	0.907885	+	0.172743i
$543$	9.33205	+	37.8341i	0.400477	+	1.62362i
$544$	10.1905	−	7.44072i	0.436912	−	0.319018i
$545$	−16.7270	−	28.9720i	−0.716506	−	1.24102i
$546$	3.81626	−	18.3600i	0.163321	−	0.785736i
$547$	−29.4087	−	16.9791i	−1.25743	−	0.725976i	−0.284854	−	0.958571i	$-0.591945\pi$
$547$	−29.4087	−	16.9791i	−1.25743	−	0.725976i	−0.972574	+	0.232595i	$0.925278\pi$
$548$	7.77109	+	9.78562i	0.331964	+	0.418021i
$549$	−2.09197	+	1.09885i	−0.0892832	+	0.0468980i
$550$	−12.8770	+	4.49108i	−0.549077	+	0.191500i
$551$	3.74638			0.159601
$552$	−4.32845	−	4.88602i	−0.184231	−	0.207963i
$553$	0.758245	−	2.86476i	0.0322438	−	0.121822i
$554$	35.2266	+	6.70256i	1.49664	+	0.284764i
$555$	−4.22894	−	17.1450i	−0.179508	−	0.727765i
$556$	17.0817	−	13.5651i	0.724424	−	0.575289i
$557$	1.67195	−	2.89591i	0.0708429	−	0.122704i	−0.828428	−	0.560095i	$-0.810764\pi$
$557$	1.67195	−	2.89591i	0.0708429	−	0.122704i	0.899271	+	0.437392i	$0.144098\pi$
$558$	3.46727	−	14.9456i	0.146781	−	0.632696i
$559$		−	16.6983i		−	0.706262i
$560$	8.87912	−	16.7580i	0.375211	−	0.708154i
$561$	4.98810	+	20.2228i	0.210598	+	0.853807i
$562$	−4.12694	−	11.8329i	−0.174084	−	0.499141i
$563$			6.42986i			0.270986i	0.990778	+	0.135493i	$0.0432619\pi$
$563$			6.42986i			0.270986i	−0.990778	+	0.135493i	$0.956738\pi$
$564$	−15.7026	+	6.44332i	−0.661197	+	0.271313i
$565$	23.9863			1.00911
$566$	31.4633	+	27.1324i	1.32250	+	1.14046i
$567$	15.4955	+	18.0801i	0.650751	+	0.759291i
$568$	−37.1562	−	23.5061i	−1.55904	−	0.986295i
$569$		−	8.05324i		−	0.337609i	−0.985650	−	0.168805i	$-0.946009\pi$
$569$		−	8.05324i		−	0.337609i	0.985650	−	0.168805i	$-0.0539907\pi$
$570$	−2.47095	−	1.25451i	−0.103497	−	0.0525455i
$571$			0.311840i			0.0130501i	0.999979	+	0.00652504i	$0.00207700\pi$
$571$			0.311840i			0.0130501i	−0.999979	+	0.00652504i	$0.997923\pi$
$572$	29.0202	+	11.4581i	1.21339	+	0.479088i
$573$	20.0976	−	4.95721i	0.839588	−	0.207091i
$574$	27.4776	+	13.1639i	1.14689	+	0.549449i
$575$			2.38327i			0.0993894i
$576$	19.1860	+	14.4186i	0.799417	+	0.600777i
$577$	−23.4397	−	13.5329i	−0.975806	−	0.563382i	−0.0748046	−	0.997198i	$-0.523833\pi$
$577$	−23.4397	−	13.5329i	−0.975806	−	0.563382i	−0.901001	+	0.433816i	$0.857167\pi$
$578$	3.17860	−	16.7058i	0.132212	−	0.694869i
$579$	0.494375	+	2.00430i	0.0205455	+	0.0832959i
$580$	−13.2267	−	16.6556i	−0.549210	−	0.691585i
$581$	−22.9316	+	23.0721i	−0.951365	+	0.957191i
$582$	−32.5373	+	21.1970i	−1.34871	+	0.878643i
$583$	51.2150			2.12111
$584$	28.7040	−	15.0580i	1.18778	−	0.623106i
$585$	7.23387	+	13.7717i	0.299084	+	0.569388i
$586$	−6.21338	−	1.18222i	−0.256672	−	0.0488369i
$587$	−32.1618	−	18.5686i	−1.32746	−	0.766409i	−0.342553	−	0.939499i	$-0.611292\pi$
$587$	−32.1618	−	18.5686i	−1.32746	−	0.766409i	−0.984906	+	0.173090i	$0.944625\pi$
$588$	24.0500	+	3.09799i	0.991805	+	0.127759i
$589$	−1.97713	+	1.14150i	−0.0814661	+	0.0470345i
$590$	32.2118	−	11.2344i	1.32614	−	0.462515i
$591$	2.25740	+	9.15196i	0.0928569	+	0.376461i
$592$	15.5469	−	16.6188i	0.638976	−	0.683027i
$593$	10.5332	+	18.2440i	0.432545	+	0.749189i	0.997092	−	0.0762115i	$-0.0242824\pi$
$593$	10.5332	+	18.2440i	0.432545	+	0.749189i	−0.564547	+	0.825401i	$0.690949\pi$
$594$	−34.0322	+	20.2829i	−1.39636	+	0.832219i
$595$	2.76831	+	10.2068i	0.113490	+	0.418436i
$596$	12.0750	+	4.76759i	0.494609	+	0.195288i
$597$	−4.49227	+	15.5189i	−0.183856	+	0.635148i
$598$	3.56079	−	4.12916i	0.145611	−	0.168854i
$599$		−	45.1813i		−	1.84606i	−0.384729	−	0.923030i	$-0.625705\pi$
$599$		−	45.1813i		−	1.84606i	0.384729	−	0.923030i	$-0.374295\pi$
$600$	−1.75257	−	8.58561i	−0.0715484	−	0.350506i
$601$	−14.9532	−	8.63326i	−0.609956	−	0.352158i	0.162992	−	0.986627i	$-0.447885\pi$
$601$	−14.9532	−	8.63326i	−0.609956	−	0.352158i	−0.772948	+	0.634469i	$0.781219\pi$
$602$	21.5288	−	1.65732i	0.877448	−	0.0675471i
$603$	−9.22308	−	17.5587i	−0.375593	−	0.715045i
$604$	−8.72612	+	6.92970i	−0.355061	+	0.281965i
$605$	−28.0379	+	16.1877i	−1.13990	+	0.658122i
$606$	0.555263	+	10.3094i	0.0225560	+	0.418790i
$607$	−8.31247	−	4.79921i	−0.337393	−	0.194794i	0.321726	−	0.946833i	$-0.395737\pi$
$607$	−8.31247	−	4.79921i	−0.337393	−	0.194794i	−0.659118	+	0.752039i	$0.729070\pi$
$608$	−0.381703	−	3.55079i	−0.0154801	−	0.144004i
$609$	13.9936	−	23.3175i	0.567047	−	0.944873i
$610$	−0.657373	−	1.88485i	−0.0266163	−	0.0763151i
$611$	−7.08882	−	12.2782i	−0.286783	−	0.496723i
$612$	−13.3058	+	1.43747i	−0.537856	+	0.0581063i
$613$	−10.8395	−	6.25819i	−0.437803	−	0.252766i	0.264862	−	0.964286i	$-0.414674\pi$
$613$	−10.8395	−	6.25819i	−0.437803	−	0.252766i	−0.702665	+	0.711520i	$0.748007\pi$
$614$	−16.0238	−	13.8181i	−0.646667	−	0.557654i
$615$	−24.5391	+	6.05276i	−0.989514	+	0.244071i
$616$	−11.8925	+	38.5524i	−0.479162	+	1.55332i
$617$	17.6047	−	10.1641i	0.708737	−	0.409189i	−0.101856	−	0.994799i	$-0.532478\pi$
$617$	17.6047	−	10.1641i	0.708737	−	0.409189i	0.810593	+	0.585610i	$0.199145\pi$
$618$	16.7996	−	10.9444i	0.675781	−	0.440250i
$619$	5.73698	+	9.93673i	0.230588	+	0.399391i	0.957981	−	0.286830i	$-0.0926015\pi$
$619$	5.73698	+	9.93673i	0.230588	+	0.399391i	−0.727393	+	0.686221i	$0.759268\pi$
$620$	12.0552	+	4.75978i	0.484147	+	0.191157i
$621$	1.38832	+	6.78287i	0.0557113	+	0.272187i
$622$	4.86298	+	4.19360i	0.194988	+	0.168148i
$623$	−26.0413	+	7.06302i	−1.04332	+	0.282974i
$624$	−9.79110	+	17.4935i	−0.391958	+	0.700302i
$625$	6.42865	−	11.1348i	0.257146	−	0.445390i
$626$	−3.61375	+	4.19058i	−0.144435	+	0.167489i
$627$	5.66276	+	1.63920i	0.226149	+	0.0654633i
$628$	0.0937495	+	0.630738i	0.00374101	+	0.0251692i
$629$			12.6902i			0.505992i
$630$	−17.0376	+	10.6933i	−0.678794	+	0.426033i
$631$	−30.9292			−1.23127			−0.615635	−	0.788031i	$-0.711100\pi$
$631$	−30.9292			−1.23127			−0.615635	+	0.788031i	$0.711100\pi$
$632$	−1.69371	+	2.67725i	−0.0673720	+	0.106495i
$633$	23.0150	+	23.9531i	0.914765	+	0.952049i
$634$	−36.7023	−	31.6502i	−1.45763	−	1.25699i
$635$	12.8100	+	7.39588i	0.508351	+	0.293496i
$636$	−4.40337	+	32.6113i	−0.174605	+	1.29312i
$637$	0.123659	+	20.2546i	0.00489953	+	0.802515i
$638$	34.2648	+	29.5483i	1.35656	+	1.16983i
$639$	21.6860	+	41.2853i	0.857886	+	1.63322i
$640$	−14.4384	+	14.2332i	−0.570728	+	0.562615i
$641$	−43.4635	+	25.0937i	−1.71670	+	0.991140i	−0.791940	+	0.610599i	$0.790929\pi$
$641$	−43.4635	+	25.0937i	−1.71670	+	0.991140i	−0.924764	+	0.380541i	$0.875738\pi$
$642$	−14.3689	+	0.773908i	−0.567095	+	0.0305437i
$643$	−4.88154	−	8.45507i	−0.192509	−	0.333436i	0.753572	−	0.657365i	$-0.228329\pi$
$643$	−4.88154	−	8.45507i	−0.192509	−	0.333436i	−0.946081	+	0.323930i	$0.894996\pi$
$644$	5.67707	+	4.18104i	0.223708	+	0.164756i
$645$	−12.9160	+	12.4102i	−0.508567	+	0.488651i
$646$	1.50813	+	1.30054i	0.0593368	+	0.0511691i
$647$	−7.75955	+	13.4399i	−0.305059	+	0.528378i	−0.977275	−	0.211978i	$-0.932010\pi$
$647$	−7.75955	+	13.4399i	−0.305059	+	0.528378i	0.672215	+	0.740356i	$0.265343\pi$
$648$	−9.98921	−	23.4140i	−0.392413	−	0.919789i
$649$	−62.8508	+	36.2869i	−2.46711	+	1.42439i
$650$	6.91117	−	2.41039i	0.271078	−	0.0945434i
$651$	−0.280326	+	16.5694i	−0.0109869	+	0.649406i
$652$	1.26870	+	1.59759i	0.0496860	+	0.0625663i
$653$	−9.36773	+	16.2254i	−0.366588	+	0.634948i	−0.989030	−	0.147718i	$-0.952807\pi$
$653$	−9.36773	+	16.2254i	−0.366588	+	0.634948i	0.622442	+	0.782666i	$0.286141\pi$
$654$	−38.3145	+	24.9607i	−1.49822	+	0.976041i
$655$	2.72337	+	4.71701i	0.106411	+	0.184309i
$656$	−23.7860	−	22.2519i	−0.928686	−	0.868791i
$657$	−34.3528	−	1.37273i	−1.34023	−	0.0535553i
$658$	15.1265	−	10.3581i	0.589692	−	0.403801i
$659$	3.39565	−	5.88144i	0.132276	−	0.229109i	−0.792278	−	0.610161i	$-0.791105\pi$
$659$	3.39565	−	5.88144i	0.132276	−	0.229109i	0.924554	+	0.381052i	$0.124438\pi$
$660$	−12.7051	−	30.9626i	−0.494544	−	1.20522i
$661$	39.1874			1.52421			0.762106	−	0.647452i	$-0.224165\pi$
$661$	39.1874			1.52421			0.762106	+	0.647452i	$0.224165\pi$
$662$	4.56898	−	5.29828i	0.177578	−	0.205924i
$663$	−2.67715	−	10.8537i	−0.103972	−	0.421523i
$664$	30.7954	−	16.1552i	1.19509	−	0.626943i
$665$	2.89356	+	0.765869i	0.112208	+	0.0296991i
$666$	−23.0905	+	7.03252i	−0.894739	+	0.272505i
$667$	6.84765	−	3.95349i	0.265142	−	0.153080i
$668$	−20.9708	+	16.6536i	−0.811385	+	0.644347i
$669$	−8.22696	+	28.4207i	−0.318073	+	1.09881i
$670$	15.8202	−	5.51757i	0.611187	−	0.213162i
$671$	2.12330	+	3.67766i	0.0819689	+	0.141974i
$672$	−23.5259	−	10.8873i	−0.907531	−	0.419985i
$673$	25.5089	−	44.1826i	0.983294	−	1.70312i	0.334009	−	0.942570i	$-0.391598\pi$
$673$	25.5089	−	44.1826i	0.983294	−	1.70312i	0.649285	−	0.760545i	$-0.275068\pi$
$674$	−0.242456	+	1.27428i	−0.00933906	+	0.0490833i
$675$	−2.93870	+	8.81739i	−0.113111	+	0.339381i
$676$	8.60793	+	3.39870i	0.331074	+	0.130719i
$677$			22.0832i			0.848728i	0.905492	+	0.424364i	$0.139502\pi$
$677$			22.0832i			0.848728i	−0.905492	+	0.424364i	$0.860498\pi$
$678$	−1.76333	−	32.7391i	−0.0677202	−	1.25734i
$679$	29.5684	−	29.7494i	1.13473	−	1.14168i
$680$	0.457391	−	11.2964i	0.0175401	−	0.433199i
$681$	11.3964	+	11.8609i	0.436711	+	0.454510i
$682$	−27.0862	−	5.15368i	−1.03718	−	0.197344i
$683$	15.2032	−	26.3326i	0.581733	−	1.00759i	−0.413541	−	0.910485i	$-0.635708\pi$
$683$	15.2032	−	26.3326i	0.581733	−	1.00759i	0.995274	−	0.0971054i	$-0.0309584\pi$
$684$	−1.53064	+	3.46485i	−0.0585255	+	0.132482i
$685$	11.1965			0.427795
$686$	−26.1016	+	2.16971i	−0.996563	+	0.0828399i
$687$	−40.8201	−	11.8162i	−1.55738	−	0.450816i
$688$	−22.4834	−	5.22854i	−0.857171	−	0.199336i
$689$	−27.4874			−1.04719
$690$	−5.84027	+	0.314556i	−0.222335	+	0.0119750i
$691$	−37.0713			−1.41026			−0.705130	−	0.709078i	$-0.749111\pi$
$691$	−37.0713			−1.41026			−0.705130	+	0.709078i	$0.749111\pi$
$692$	19.7418	−	2.93432i	0.750471	−	0.111546i
$693$	31.3540	−	29.1223i	1.19104	−	1.10626i
$694$	28.8897	+	24.9131i	1.09664	+	0.945688i
$695$		−	19.5444i		−	0.741362i
$696$	−21.7610	+	19.2777i	−0.824849	+	0.730721i
$697$	18.1632			0.687978
$698$	−21.8535	+	7.62181i	−0.827169	+	0.288490i
$699$	26.7301	+	27.8196i	1.01103	+	1.05223i
$700$	3.79362	+	8.67122i	0.143385	+	0.327741i
$701$	12.8133			0.483952			0.241976	−	0.970282i	$-0.422204\pi$
$701$	12.8133			0.483952			0.241976	+	0.970282i	$0.422204\pi$
$702$	18.2653	−	10.8860i	0.689379	−	0.410865i
$703$	3.11053	+	1.79587i	0.117316	+	0.0677324i
$704$	24.5145	−	35.4864i	0.923926	−	1.33745i
$705$	−4.22868	+	14.6083i	−0.159261	+	0.550182i
$706$	−5.61056	+	29.4874i	−0.211156	+	1.10977i
$707$	−2.91910	−	10.7627i	−0.109784	−	0.404774i
$708$	−17.7020	−	43.1404i	−0.665283	−	1.62131i
$709$		−	25.2836i		−	0.949544i	−0.880109	−	0.474772i	$-0.842530\pi$
$709$		−	25.2836i		−	0.949544i	0.880109	−	0.474772i	$-0.157470\pi$
$710$	−37.1977	+	12.9733i	−1.39600	+	0.486881i
$711$	2.97477	−	1.56256i	0.111563	−	0.0586007i
$712$	28.8215	+	1.16698i	1.08013	+	0.0437344i
$713$	−2.40920	+	4.17286i	−0.0902253	+	0.156275i
$714$	13.7278	−	4.52884i	0.513750	−	0.169488i
$715$	24.2104	−	13.9779i	0.905417	−	0.522743i
$716$	0.395955	+	0.156336i	0.0147975	+	0.00584256i
$717$	−17.2764	−	17.9806i	−0.645200	−	0.671497i
$718$	33.9865	+	6.46660i	1.26837	+	0.241332i
$719$	3.56334	+	6.17189i	0.132890	+	0.230173i	0.924790	−	0.380479i	$-0.124241\pi$
$719$	3.56334	+	6.17189i	0.132890	+	0.230173i	−0.791899	+	0.610652i	$0.790908\pi$
$720$	20.8079	−	5.42788i	0.775465	−	0.202285i
$721$	−15.2667	+	15.3602i	−0.568563	+	0.572045i
$722$	−24.8391	+	8.66306i	−0.924414	+	0.322406i
$723$	−13.2393	−	13.7789i	−0.492373	−	0.512441i
$724$	6.61535	+	44.5074i	0.245858	+	1.65411i
$725$	10.6145			0.394211
$726$	24.1559	+	37.0792i	0.896509	+	1.37614i
$727$	−36.1143	−	20.8506i	−1.33941	−	0.773307i	−0.352688	−	0.935741i	$-0.614732\pi$
$727$	−36.1143	−	20.8506i	−1.33941	−	0.773307i	−0.986719	+	0.162434i	$0.948065\pi$
$728$	6.38278	−	20.6913i	0.236561	−	0.766872i
$729$	−3.22729	+	26.8064i	−0.119529	+	0.992831i
$730$	5.42865	−	28.5314i	0.200923	−	1.05599i
$731$	11.1475	−	6.43604i	0.412307	−	0.238045i
$732$	−2.52432	+	1.03582i	−0.0933015	+	0.0382849i
$733$	−7.16004	+	12.4016i	−0.264462	+	0.458062i	−0.967423	−	0.253167i	$-0.918528\pi$
$733$	−7.16004	+	12.4016i	−0.264462	+	0.458062i	0.702960	+	0.711229i	$0.251861\pi$
$734$	−10.7349	−	2.04252i	−0.396231	−	0.0753908i
$735$	15.5749	−	15.1489i	0.574488	−	0.558775i
$736$	−4.44476	−	6.08734i	−0.163836	−	0.224382i
$737$	−30.8679	+	17.8216i	−1.13703	+	0.656467i
$738$	10.0654	+	33.0488i	0.370514	+	1.21654i
$739$	−22.7633	−	13.1424i	−0.837361	−	0.483451i	0.0190053	−	0.999819i	$-0.493950\pi$
$739$	−22.7633	−	13.1424i	−0.837361	−	0.483451i	−0.856366	+	0.516369i	$0.827283\pi$
$740$	−2.99783	−	20.1691i	−0.110202	−	0.741431i
$741$	−3.03924	−	0.879770i	−0.111649	−	0.0323192i
$742$	−2.72814	−	35.4390i	−0.100153	−	1.30101i
$743$	−30.0581	+	17.3541i	−1.10273	+	0.636659i	−0.936936	−	0.349502i	$-0.886351\pi$
$743$	−30.0581	+	17.3541i	−1.10273	+	0.636659i	−0.165790	+	0.986161i	$0.553017\pi$
$744$	5.61045	−	16.8041i	0.205689	−	0.616069i
$745$	10.0737	−	5.81603i	0.369071	−	0.213083i
$746$	5.43932	+	15.5958i	0.199147	+	0.571003i
$747$	−36.8558	−	1.47275i	−1.34848	−	0.0538851i
$748$	3.53599	+	23.7898i	0.129289	+	0.869841i
$749$	15.0007	−	4.06855i	0.548115	−	0.148662i
$750$	−26.5707	−	13.4900i	−0.970226	−	0.492586i
$751$	6.05397	−	10.4858i	0.220912	−	0.382631i	−0.734173	−	0.678963i	$-0.762430\pi$
$751$	6.05397	−	10.4858i	0.220912	−	0.382631i	0.955085	+	0.296331i	$0.0957632\pi$
$752$	−18.7516	+	5.70022i	−0.683801	+	0.207865i
$753$	−21.6366	+	5.33684i	−0.788483	+	0.194485i
$754$	−18.3902	−	15.8588i	−0.669730	−	0.577542i
$755$			9.98421i			0.363363i
$756$	15.8480	+	22.4687i	0.576385	+	0.817178i
$757$			21.4770i			0.780594i	0.920689	+	0.390297i	$0.127628\pi$
$757$			21.4770i			0.780594i	−0.920689	+	0.390297i	$0.872372\pi$
$758$	−8.76119	+	10.1597i	−0.318221	+	0.369015i
$759$	12.0802	−	2.97968i	0.438484	−	0.108155i
$760$	−2.70417	−	1.71074i	−0.0980906	−	0.0620550i
$761$	14.1404	−	24.4919i	0.512589	−	0.887830i	−0.487305	−	0.873232i	$-0.662020\pi$
$761$	14.1404	−	24.4919i	0.512589	−	0.887830i	0.999893	−	0.0145978i	$-0.00464679\pi$
$762$	9.15299	−	18.0283i	0.331578	−	0.653095i
$763$	34.8185	−	35.0317i	1.26051	−	1.26823i
$764$	23.6425	−	3.51409i	0.855354	−	0.127135i
$765$	−6.40562	+	10.1373i	−0.231596	+	0.366514i
$766$	−30.9099	+	10.7804i	−1.11682	+	0.389510i
$767$	33.7324	−	19.4754i	1.21801	−	0.703217i
$768$	20.4884	+	18.6608i	0.739312	+	0.673363i
$769$	18.5576	−	10.7142i	0.669202	−	0.386364i	−0.126572	−	0.991957i	$-0.540397\pi$
$769$	18.5576	−	10.7142i	0.669202	−	0.386364i	0.795774	+	0.605593i	$0.207064\pi$
$770$	20.4243	+	29.8267i	0.736041	+	1.07488i
$771$	20.8012	+	6.02133i	0.749137	+	0.216853i
$772$	0.350455	+	2.35783i	0.0126132	+	0.0848601i
$773$	4.02683	+	2.32489i	0.144835	+	0.0836205i	0.570666	−	0.821182i	$-0.306685\pi$
$773$	4.02683	+	2.32489i	0.144835	+	0.0836205i	−0.425831	+	0.904803i	$0.640018\pi$
$774$	17.8883	+	16.7169i	0.642982	+	0.600876i
$775$	−5.60171	+	3.23415i	−0.201219	+	0.116174i
$776$	−39.7080	+	20.8307i	−1.42544	+	0.747779i
$777$	22.7960	−	12.6520i	0.817802	−	0.453889i
$778$	1.74612	−	9.17707i	0.0626014	−	0.329014i
$779$	2.57037	−	4.45202i	0.0920932	−	0.159510i
$780$	6.81889	+	16.6178i	0.244156	+	0.595014i
$781$	72.5790	−	41.9035i	2.59708	−	1.49943i
$782$	4.12901	+	0.785626i	0.147653	+	0.0280939i
$783$	30.2091	−	6.18319i	1.07958	−	0.220969i
$784$	27.3105	+	6.17558i	0.975374	+	0.220556i
$785$	0.494808	+	0.285678i	0.0176605	+	0.0101963i
$786$	6.23809	−	4.06392i	0.222505	−	0.144955i
$787$	37.9508			1.35280			0.676399	−	0.736535i	$-0.263539\pi$
$787$	37.9508			1.35280			0.676399	+	0.736535i	$0.263539\pi$
$788$	1.60023	+	10.7662i	0.0570060	+	0.383531i
$789$	−35.7300	−	37.1863i	−1.27202	−	1.32387i
$790$	0.934780	+	2.68024i	0.0332580	+	0.0953585i
$791$	9.27007	+	34.1787i	0.329606	+	1.21526i
$792$	−41.3272	+	19.6175i	−1.46850	+	0.697076i
$793$	−1.13959	−	1.97382i	−0.0404679	−	0.0700925i
$794$	−8.14052	+	42.7841i	−0.288896	+	1.51835i
$795$	20.4287	+	21.2613i	0.724532	+	0.754062i
$796$	−6.85109	+	17.3519i	−0.242830	+	0.615020i
$797$	20.1513	−	11.6344i	0.713797	−	0.412111i	−0.0986686	−	0.995120i	$-0.531458\pi$
$797$	20.1513	−	11.6344i	0.713797	−	0.412111i	0.812465	+	0.583010i	$0.198125\pi$
$798$	0.832625	−	4.00576i	0.0294746	−	0.141802i
$799$	5.46451	−	9.46480i	0.193320	−	0.334841i
$800$	−1.08146	−	10.0603i	−0.0382354	−	0.355685i
$801$	−25.8640	−	16.3432i	−0.913861	−	0.577458i
$802$	8.65651	+	24.8203i	0.305672	+	0.876434i
$803$			61.7850i			2.18035i
$804$	−8.69400	−	21.1875i	−0.306614	−	0.747226i
$805$	6.09707	−	1.65367i	0.214894	−	0.0582842i
$806$	14.5373	+	2.76601i	0.512056	+	0.0974287i
$807$	−2.55052	+	8.81100i	−0.0897826	+	0.310162i
$808$	−0.482305	+	11.9118i	−0.0169674	+	0.419054i
$809$	−41.6827	−	24.0655i	−1.46549	−	0.846098i	−0.466229	−	0.884664i	$-0.654388\pi$
$809$	−41.6827	−	24.0655i	−1.46549	−	0.846098i	−0.999256	+	0.0385655i	$0.987721\pi$
$810$	−21.9951	−	6.03760i	−0.772828	−	0.212140i
$811$	38.8536			1.36434			0.682168	−	0.731196i	$-0.261037\pi$
$811$	38.8536			1.36434			0.682168	+	0.731196i	$0.261037\pi$
$812$	18.6212	−	25.2841i	0.653476	−	0.887298i
$813$	−18.2573	−	19.0014i	−0.640310	−	0.666408i
$814$	14.2850	+	40.9584i	0.500688	+	1.43559i
$815$	1.82792			0.0640292
$816$	−15.4523	+	0.206149i	−0.540937	+	0.00721665i
$817$		−	3.64321i		−	0.127460i
$818$	−8.70924	+	10.0994i	−0.304511	+	0.353118i
$819$	−16.8279	+	15.6301i	−0.588015	+	0.546161i
$820$	−28.8675	+	4.29071i	−1.00810	+	0.149838i
$821$	−8.74845			−0.305323			−0.152661	−	0.988279i	$-0.548784\pi$
$821$	−8.74845			−0.305323			−0.152661	+	0.988279i	$0.548784\pi$
$822$	−0.823097	−	15.2822i	−0.0287088	−	0.533027i
$823$	−31.4495			−1.09626			−0.548131	−	0.836392i	$-0.684661\pi$
$823$	−31.4495			−1.09626			−0.548131	+	0.836392i	$0.684661\pi$
$824$	20.5021	−	10.7553i	0.714223	−	0.374679i
$825$	16.0440	+	4.64427i	0.558582	+	0.161693i
$826$	28.4573	+	41.5577i	0.990156	+	1.44598i
$827$	−14.0862			−0.489824			−0.244912	−	0.969545i	$-0.578759\pi$
$827$	−14.0862			−0.489824			−0.244912	+	0.969545i	$0.578759\pi$
$828$	0.858683	+	7.94832i	0.0298413	+	0.276223i
$829$	7.61791	−	13.1946i	0.264581	−	0.458268i	−0.702873	−	0.711316i	$-0.748100\pi$
$829$	7.61791	−	13.1946i	0.264581	−	0.458268i	0.967454	+	0.253048i	$0.0814330\pi$
$830$	5.82419	−	30.6102i	0.202160	−	1.06249i
$831$	−30.4282	−	31.6684i	−1.05554	−	1.09856i
$832$	−13.1571	+	19.0458i	−0.456141	+	0.660295i
$833$	−13.4740	+	7.88929i	−0.466847	+	0.273348i
$834$	−26.6764	+	1.43679i	−0.923727	+	0.0497519i
$835$			23.9943i			0.830356i
$836$	6.33157	+	2.49992i	0.218982	+	0.0864614i
$837$	−14.0587	+	12.4676i	−0.485938	+	0.430944i
$838$	18.8282	+	3.58244i	0.650409	+	0.123753i
$839$	−13.1004	+	22.6905i	−0.452276	+	0.783364i	−0.998527	−	0.0542569i	$-0.982721\pi$
$839$	−13.1004	+	22.6905i	−0.452276	+	0.783364i	0.546251	+	0.837621i	$0.316054\pi$
$840$	−20.7483	+	10.4408i	−0.715885	+	0.360242i
$841$	−3.10776	−	5.38281i	−0.107164	−	0.185614i
$842$	−0.751217	−	2.15392i	−0.0258886	−	0.0742289i
$843$	−4.26770	+	14.7432i	−0.146988	+	0.507781i
$844$	23.8538	+	30.0375i	0.821081	+	1.03393i
$845$	7.18126	−	4.14610i	0.247043	−	0.142630i
$846$	20.2500	+	4.69785i	0.696208	+	0.161516i
$847$	−33.9022	−	33.6958i	−1.16489	−	1.15780i
$848$	−8.60682	+	37.0104i	−0.295559	+	1.27094i
$849$	−12.1857	−	49.4032i	−0.418211	−	1.69551i
$850$	4.27293	+	3.68477i	0.146560	+	0.126386i
$851$	7.58059			0.259859
$852$	20.4420	+	49.8178i	0.700332	+	1.70673i
$853$	1.77756	−	3.07882i	0.0608625	−	0.105417i	−0.833989	−	0.551782i	$-0.813948\pi$
$853$	1.77756	−	3.07882i	0.0608625	−	0.105417i	0.894851	+	0.446365i	$0.147282\pi$
$854$	2.43171	−	1.66515i	0.0832114	−	0.0569804i
$855$	1.57828	+	3.00468i	0.0539759	+	0.102758i
$856$	−16.6022	−	0.672221i	−0.567452	−	0.0229760i
$857$	4.45746	+	7.72055i	0.152264	+	0.263729i	0.932059	−	0.362305i	$-0.118010\pi$
$857$	4.45746	+	7.72055i	0.152264	+	0.263729i	−0.779795	+	0.626034i	$0.784677\pi$
$858$	−20.8583	−	32.0174i	−0.712092	−	1.09306i
$859$	12.5249	−	21.6938i	0.427344	−	0.740182i	−0.569292	−	0.822136i	$-0.692783\pi$
$859$	12.5249	−	21.6938i	0.427344	−	0.740182i	0.996636	+	0.0819535i	$0.0261159\pi$
$860$	−16.1969	+	12.8625i	−0.552309	+	0.438607i
$861$	−18.1085	−	32.6273i	−0.617136	−	1.11193i
$862$	5.94354	+	17.0415i	0.202438	+	0.580437i
$863$	18.3314	−	10.5836i	0.624007	−	0.360270i	−0.154421	−	0.988005i	$-0.549351\pi$
$863$	18.3314	−	10.5836i	0.624007	−	0.360270i	0.778427	+	0.627735i	$0.216018\pi$
$864$	−8.93825	−	28.0019i	−0.304085	−	0.952645i
$865$	8.94158	−	15.4873i	0.304023	−	0.526583i
$866$	−35.2688	+	40.8984i	−1.19848	+	1.38979i
$867$	−15.0183	+	14.4302i	−0.510049	+	0.490074i
$868$	−2.12333	+	19.0173i	−0.0720706	+	0.645488i
$869$	−3.01931	−	5.22960i	−0.102423	−	0.177402i
$870$	1.40095	+	26.0109i	0.0474966	+	0.881854i
$871$	16.5670	−	9.56497i	0.561352	−	0.324097i
$872$	−46.7586	+	24.5294i	−1.58344	+	0.830670i
$873$	47.5223	+	1.89898i	1.60839	+	0.0642708i
$874$	0.776887	−	0.900894i	0.0262786	−	0.0304732i
$875$	31.1152	+	8.23558i	1.05189	+	0.278414i
$876$	−39.3418	−	5.31217i	−1.32924	−	0.179482i
$877$	−25.7492	−	14.8663i	−0.869490	−	0.502000i	−0.00231147	−	0.999997i	$-0.500736\pi$
$877$	−25.7492	−	14.8663i	−0.869490	−	0.502000i	−0.867179	+	0.497997i	$0.834069\pi$
$878$	24.8056	−	28.7651i	0.837148	−	0.970774i
$879$	5.36701	+	5.58576i	0.181025	+	0.188403i
$880$	−11.2398	−	36.9748i	−0.378893	−	1.24642i
$881$	−22.5816			−0.760794			−0.380397	−	0.924823i	$-0.624213\pi$
$881$	−22.5816			−0.760794			−0.380397	+	0.924823i	$0.624213\pi$
$882$	−21.8218	−	20.1447i	−0.734780	−	0.678306i
$883$		−	19.6946i		−	0.662776i	−0.943495	−	0.331388i	$-0.892483\pi$
$883$		−	19.6946i		−	0.662776i	0.943495	−	0.331388i	$-0.107517\pi$
$884$	−1.89779	−	12.7681i	−0.0638295	−	0.429439i
$885$	−40.1342	−	11.6176i	−1.34909	−	0.390523i
$886$	11.9691	+	10.3216i	0.402110	+	0.346760i
$887$	2.16405	−	3.74825i	0.0726618	−	0.125854i	−0.827405	−	0.561605i	$-0.810184\pi$
$887$	2.16405	−	3.74825i	0.0726618	−	0.125854i	0.900067	+	0.435751i	$0.143517\pi$
$888$	−27.3086	+	5.57448i	−0.916418	+	0.187067i
$889$	−5.58785	+	21.1117i	−0.187410	+	0.708064i
$890$	16.8787	−	19.5729i	0.565776	−	0.656086i
$891$	48.3672	+	3.87167i	1.62036	+	0.129706i
$892$	−12.5468	+	31.7775i	−0.420098	+	1.06399i
$893$	−1.54663	−	2.67884i	−0.0517560	−	0.0896439i
$894$	−8.67892	−	13.3221i	−0.290267	−	0.445557i
$895$	0.330330	−	0.190716i	0.0110417	−	0.00637494i
$896$	−25.8613	−	15.0729i	−0.863965	−	0.503551i
$897$	−6.48354	+	1.59921i	−0.216479	+	0.0533961i
$898$	7.72542	−	8.95856i	0.257801	−	0.298951i
$899$	18.5848	+	10.7299i	0.619837	+	0.357863i
$900$	−4.33670	+	9.81679i	−0.144557	+	0.327226i
$901$	−10.5945	−	18.3502i	−0.352954	−	0.611335i
$902$	58.6227	−	20.4457i	1.95192	−	0.680767i
$903$	−22.6753	−	13.6082i	−0.754588	−	0.452851i
$904$	1.53164	−	37.8277i	0.0509414	−	1.25813i
$905$	34.9157	+	20.1586i	1.16064	+	0.670094i
$906$	13.6276	−	0.733979i	0.452745	−	0.0243848i
$907$	−21.9875	+	12.6945i	−0.730083	+	0.421514i	−0.818453	−	0.574574i	$-0.805168\pi$
$907$	−21.9875	+	12.6945i	−0.730083	+	0.421514i	0.0883695	+	0.996088i	$0.471834\pi$
$908$	11.8117	+	14.8737i	0.391986	+	0.493602i
$909$	6.75453	−	10.6894i	0.224034	−	0.354546i
$910$	−10.9619	−	16.0082i	−0.363383	−	0.530667i
$911$	33.4684	+	19.3230i	1.10886	+	0.640199i	0.938533	−	0.345189i	$-0.112185\pi$
$911$	33.4684	+	19.3230i	1.10886	+	0.640199i	0.170324	+	0.985388i	$0.445519\pi$
$912$	−2.13621	+	3.81672i	−0.0707369	+	0.126384i
$913$			66.2867i			2.19377i
$914$	−36.3684	−	31.3623i	−1.20296	−	1.03737i
$915$	−0.679796	+	2.34841i	−0.0224734	+	0.0776362i
$916$	−45.6413	−	18.0207i	−1.50803	−	0.595420i
$917$	−5.66889	+	5.70361i	−0.187203	+	0.188350i
$918$	14.3074	+	7.99787i	0.472213	+	0.263969i
$919$	21.2061	+	36.7300i	0.699525	+	1.21161i	0.968631	+	0.248502i	$0.0799382\pi$
$919$	21.2061	+	36.7300i	0.699525	+	1.21161i	−0.269107	+	0.963110i	$0.586728\pi$
$920$	−6.74800	−	0.273225i	−0.222475	−	0.00900798i
$921$	6.20596	+	25.1602i	0.204493	+	0.829058i
$922$	−4.99283	−	14.3156i	−0.164430	−	0.471460i
$923$	−38.9537	+	22.4899i	−1.28218	+	0.740264i
$924$	39.2093	−	30.0701i	1.28989	−	0.989232i
$925$	8.81293	+	5.08815i	0.289767	+	0.167297i
$926$	−2.63386	+	13.8428i	−0.0865540	+	0.454902i
$927$	−24.5367	−	0.980483i	−0.805892	−	0.0322033i
$928$	−27.1113	+	19.7958i	−0.889973	+	0.649828i
$929$	15.4062			0.505460			0.252730	−	0.967537i	$-0.418672\pi$
$929$	15.4062			0.505460			0.252730	+	0.967537i	$0.418672\pi$
$930$	−8.66469	−	13.3002i	−0.284126	−	0.436132i
$931$	0.0269796	+	4.41911i	0.000884222	+	0.144830i
$932$	27.7043	+	34.8862i	0.907484	+	1.14274i
$933$	−1.88342	−	7.63577i	−0.0616603	−	0.249984i
$934$	14.9372	+	2.84209i	0.488760	+	0.0929961i
$935$	18.6629	+	10.7750i	0.610341	+	0.352381i
$936$	22.1806	−	10.5288i	0.724995	−	0.344145i
$937$			49.3800i			1.61318i	0.591114	+	0.806588i	$0.298688\pi$
$937$			49.3800i			1.61318i	−0.591114	+	0.806588i	$0.701312\pi$
$938$	13.9762	+	20.4102i	0.456340	+	0.666418i
$939$	6.57998	−	1.62300i	0.214730	−	0.0529646i
$940$	−6.44909	+	16.3337i	−0.210346	+	0.532747i
$941$		−	7.54099i		−	0.245829i	−0.992417	−	0.122915i	$-0.960776\pi$
$941$		−	7.54099i		−	0.245829i	0.992417	−	0.122915i	$-0.0392241\pi$
$942$	0.353549	−	0.696370i	0.0115193	−	0.0226890i
$943$		−	10.8499i		−	0.353321i
$944$	−15.6605	−	51.5172i	−0.509704	−	1.67674i
$945$	24.5964	+	1.39994i	0.800120	+	0.0455401i
$946$	28.7345	−	33.3211i	0.934240	−	1.08336i
$947$	23.6860			0.769691			0.384846	−	0.922981i	$-0.374255\pi$
$947$	23.6860			0.769691			0.384846	+	0.922981i	$0.374255\pi$
$948$	3.58956	−	1.47293i	0.116584	−	0.0478384i
$949$		−	33.1604i		−	1.07643i
$950$	1.50787	−	0.525896i	0.0489217	−	0.0170623i
$951$	14.2147	+	57.6293i	0.460943	+	1.86876i
$952$	16.2734	−	3.71403i	0.527423	−	0.120373i
$953$		−	36.2755i		−	1.17508i	−0.809196	−	0.587539i	$-0.800097\pi$
$953$		−	36.2755i		−	1.17508i	0.809196	−	0.587539i	$-0.199903\pi$
$954$	27.5180	−	29.4464i	0.890929	−	0.953362i
$955$	10.7083	−	18.5473i	0.346512	−	0.600177i
$956$	−17.9060	−	22.5479i	−0.579123	−	0.729252i
$957$	−13.2707	−	53.8020i	−0.428979	−	1.73917i
$958$	10.5656	−	55.5294i	0.341358	−	1.79407i
$959$	4.32714	+	15.9542i	0.139731	+	0.515187i
$960$	24.5102	−	3.97795i	0.791064	−	0.128388i
$961$	17.9227			0.578151
$962$	−7.66685	−	21.9827i	−0.247189	−	0.708750i
$963$	14.8986	+	9.41425i	0.480101	+	0.303370i
$964$	−13.7217	−	17.2789i	−0.441948	−	0.556516i
$965$	1.84970	+	1.06792i	0.0595438	+	0.0343776i
$966$	−2.70533	−	8.20039i	−0.0870426	−	0.263843i
$967$	15.4745	+	26.8025i	0.497625	+	0.861912i	0.999996	−	0.00274026i	$-0.000872254\pi$
$967$	15.4745	+	26.8025i	0.497625	+	0.861912i	−0.502371	+	0.864652i	$0.667539\pi$
$968$	23.7385	+	45.2509i	0.762984	+	1.45442i
$969$	−0.584096	−	2.36805i	−0.0187639	−	0.0760727i
$970$	−7.50978	+	39.4692i	−0.241125	+	1.26728i
$971$	11.7614	−	6.79042i	0.377440	−	0.217915i	−0.299264	−	0.954170i	$-0.596741\pi$
$971$	11.7614	−	6.79042i	0.377440	−	0.217915i	0.676704	+	0.736255i	$0.263408\pi$
$972$	−6.62383	+	30.4651i	−0.212460	+	0.977170i
$973$	27.8494	−	7.55341i	0.892810	−	0.242151i
$974$	−47.1816	+	16.4554i	−1.51180	+	0.527265i
$975$	−8.61094	−	2.49261i	−0.275771	−	0.0798274i
$976$	−3.01448	+	0.916357i	−0.0964912	+	0.0293319i
$977$			9.80992i			0.313847i	0.987611	+	0.156923i	$0.0501576\pi$
$977$			9.80992i			0.313847i	−0.987611	+	0.156923i	$0.949842\pi$
$978$	−0.134378	−	2.49495i	−0.00429692	−	0.0797796i
$979$	−27.4912	+	47.6161i	−0.878622	+	1.52182i
$980$	19.5511	−	15.7218i	0.624538	−	0.502214i
$981$	55.9603	+	2.23616i	1.78668	+	0.0713952i
$982$	6.91819	−	36.3599i	0.220768	−	1.16029i
$983$	0.212781	+	0.368547i	0.00678666	+	0.0117548i	0.869399	−	0.494111i	$-0.164506\pi$
$983$	0.212781	+	0.368547i	0.00678666	+	0.0117548i	−0.862612	+	0.505866i	$0.831173\pi$
$984$	7.97860	+	39.0861i	0.254348	+	1.24602i
$985$	8.44601	+	4.87630i	0.269112	+	0.155372i
$986$	3.49896	−	18.3895i	0.111430	−	0.585641i
$987$	−22.4501	−	0.379818i	−0.714595	−	0.0120897i
$988$	−3.39820	−	1.34172i	−0.108111	−	0.0426859i
$989$	−3.84461	−	6.65906i	−0.122251	−	0.211746i
$990$	−9.26331	+	39.9292i	−0.294407	+	1.26903i
$991$	21.9251	−	37.9753i	0.696473	−	1.20633i	−0.273209	−	0.961955i	$-0.588085\pi$
$991$	21.9251	−	37.9753i	0.696473	−	1.20633i	0.969682	−	0.244371i	$-0.0785816\pi$
$992$	8.27621	−	18.7077i	0.262770	−	0.593970i
$993$	−8.31928	+	2.05201i	−0.264004	+	0.0651186i
$994$	−32.8620	−	47.9901i	−1.04232	−	1.52215i
$995$	8.35771	+	14.4760i	0.264957	+	0.458919i
$996$	−42.2083	−	5.69922i	−1.33742	−	0.180587i
$997$	−9.11260	−	15.7835i	−0.288599	−	0.499868i	0.684877	−	0.728659i	$-0.259856\pi$
$997$	−9.11260	−	15.7835i	−0.288599	−	0.499868i	−0.973476	+	0.228791i	$0.926523\pi$
$998$	4.36543	+	12.5167i	0.138185	+	0.396210i
$999$	28.0459	+	9.34727i	0.887331	+	0.295734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ca.a.101.21	yes	184
7.5	odd	6		504.2.y.a.173.43	yes	184
8.5	even	2	inner	504.2.ca.a.101.72	yes	184
9.5	odd	6		504.2.y.a.437.11	yes	184
56.5	odd	6		504.2.y.a.173.11	✓	184
63.5	even	6	inner	504.2.ca.a.5.72	yes	184
72.5	odd	6		504.2.y.a.437.43	yes	184
504.5	even	6	inner	504.2.ca.a.5.21	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.11	✓	184	56.5	odd	6
504.2.y.a.173.43	yes	184	7.5	odd	6
504.2.y.a.437.11	yes	184	9.5	odd	6
504.2.y.a.437.43	yes	184	72.5	odd	6
504.2.ca.a.5.21	yes	184	504.5	even	6	inner
504.2.ca.a.5.72	yes	184	63.5	even	6	inner
504.2.ca.a.101.21	yes	184	1.1	even	1	trivial
504.2.ca.a.101.72	yes	184	8.5	even	2	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.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07099 - 0.923569i) q^{2} +(0.414791 + 1.68165i) q^{3} +(0.294039 + 1.97827i) q^{4} +(1.55193 + 0.896009i) q^{5} +(1.10888 - 2.18412i) q^{6} +(-0.676966 + 2.55768i) q^{7} +(1.51215 - 2.39027i) q^{8} +(-2.65590 + 1.39507i) q^{9} +O(q^{10})\)	\(q+(-1.07099 - 0.923569i) q^{2} +(0.414791 + 1.68165i) q^{3} +(0.294039 + 1.97827i) q^{4} +(1.55193 + 0.896009i) q^{5} +(1.10888 - 2.18412i) q^{6} +(-0.676966 + 2.55768i) q^{7} +(1.51215 - 2.39027i) q^{8} +(-2.65590 + 1.39507i) q^{9} +(-0.834578 - 2.39293i) q^{10} +(2.69566 + 4.66903i) q^{11} +(-3.20479 + 1.31504i) q^{12} +(-1.44678 - 2.50590i) q^{13} +(3.08722 - 2.11402i) q^{14} +(-0.863046 + 2.98147i) q^{15} +(-3.82708 + 1.16338i) q^{16} +(1.11527 - 1.93170i) q^{17} +(4.13288 + 0.958801i) q^{18} +(-0.315657 - 0.546733i) q^{19} +(-1.31622 + 3.33360i) q^{20} +(-4.58192 - 0.0775184i) q^{21} +(1.42514 - 7.49011i) q^{22} +(-1.15392 - 0.666214i) q^{23} +(4.64683 + 1.55145i) q^{24} +(-0.894335 - 1.54903i) q^{25} +(-0.764883 + 4.01999i) q^{26} +(-3.44766 - 3.88763i) q^{27} +(-5.25882 - 0.587163i) q^{28} +(-2.96713 + 5.13923i) q^{29} +(3.67790 - 2.39604i) q^{30} -3.61626i q^{31} +(5.17323 + 2.28861i) q^{32} +(-6.73353 + 6.46984i) q^{33} +(-2.97851 + 1.03881i) q^{34} +(-3.34231 + 3.36278i) q^{35} +(-3.54075 - 4.84387i) q^{36} +(-4.92708 + 2.84465i) q^{37} +(-0.166881 + 0.877077i) q^{38} +(3.61393 - 3.47240i) q^{39} +(4.48847 - 2.35464i) q^{40} +(4.07147 + 7.05199i) q^{41} +(4.83560 + 4.31474i) q^{42} +(4.99769 + 2.88542i) q^{43} +(-8.44395 + 6.70562i) q^{44} +(-5.37177 - 0.214655i) q^{45} +(0.620538 + 1.77923i) q^{46} +4.89972 q^{47} +(-3.54383 - 5.95326i) q^{48} +(-6.08343 - 3.46292i) q^{49} +(-0.472816 + 2.48498i) q^{50} +(3.71105 + 1.07424i) q^{51} +(4.53193 - 3.59895i) q^{52} +(4.74975 - 8.22681i) q^{53} +(0.101916 + 7.34776i) q^{54} +9.66136i q^{55} +(5.08986 + 5.48574i) q^{56} +(0.788483 - 0.757604i) q^{57} +(7.92420 - 2.76371i) q^{58} +13.4612i q^{59} +(-6.15191 - 0.830667i) q^{60} +0.787671 q^{61} +(-3.33986 + 3.87298i) q^{62} +(-1.77018 - 7.73734i) q^{63} +(-3.42678 - 7.22891i) q^{64} -5.18532i q^{65} +(13.1869 - 0.710245i) q^{66} +6.61121i q^{67} +(4.14936 + 1.63830i) q^{68} +(0.641704 - 2.21682i) q^{69} +(6.68534 - 0.514646i) q^{70} -15.5448i q^{71} +(-0.681535 + 8.45787i) q^{72} +(9.92471 + 5.73004i) q^{73} +(7.90409 + 1.50391i) q^{74} +(2.23397 - 2.14649i) q^{75} +(0.988769 - 0.785214i) q^{76} +(-13.7667 + 3.73387i) q^{77} +(-7.07749 + 0.381193i) q^{78} -1.12006 q^{79} +(-6.98177 - 1.62362i) q^{80} +(5.10757 - 7.41031i) q^{81} +(2.15250 - 11.3129i) q^{82} +(10.6478 + 6.14753i) q^{83} +(-1.19391 - 9.08706i) q^{84} +(3.46165 - 1.99858i) q^{85} +(-2.68759 - 7.70597i) q^{86} +(-9.87312 - 2.85798i) q^{87} +(15.2365 + 0.616923i) q^{88} +(5.09915 + 8.83199i) q^{89} +(5.55486 + 5.19109i) q^{90} +(7.38870 - 2.00399i) q^{91} +(0.978652 - 2.47865i) q^{92} +(6.08128 - 1.49999i) q^{93} +(-5.24755 - 4.52523i) q^{94} -1.13132i q^{95} +(-1.70284 + 9.64885i) q^{96} +(-13.7295 - 7.92671i) q^{97} +(3.31704 + 9.32723i) q^{98} +(-13.6730 - 8.63982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} + 12 q^{12} - 18 q^{14} - 2 q^{15} - 2 q^{16} + 12 q^{18} - 6 q^{22} - 6 q^{23} - 12 q^{24} + 78 q^{25} - 6 q^{26} - 8 q^{28} + 7 q^{30} - 6 q^{33} + 6 q^{34} + 22 q^{36} - 33 q^{38} - 8 q^{39} - 18 q^{40} - 42 q^{42} - 9 q^{44} + 2 q^{46} - 12 q^{47} + 9 q^{48} - 2 q^{49} + 9 q^{50} + 21 q^{52} + 33 q^{54} + 18 q^{56} + 4 q^{57} - 3 q^{58} - 59 q^{60} + 12 q^{62} - 72 q^{63} - 8 q^{64} - 42 q^{66} - 18 q^{68} - 27 q^{70} + 12 q^{72} - 12 q^{73} - 57 q^{74} + 12 q^{76} + 19 q^{78} - 4 q^{79} - 57 q^{80} - 18 q^{81} + 69 q^{84} - 27 q^{86} - 6 q^{87} + 9 q^{88} - 24 q^{89} - 75 q^{90} - 36 q^{92} - 45 q^{96} - 45 q^{98}+O(q^{100}) \) 184 * q - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 + 12 * q^12 - 18 * q^14 - 2 * q^15 - 2 * q^16 + 12 * q^18 - 6 * q^22 - 6 * q^23 - 12 * q^24 + 78 * q^25 - 6 * q^26 - 8 * q^28 + 7 * q^30 - 6 * q^33 + 6 * q^34 + 22 * q^36 - 33 * q^38 - 8 * q^39 - 18 * q^40 - 42 * q^42 - 9 * q^44 + 2 * q^46 - 12 * q^47 + 9 * q^48 - 2 * q^49 + 9 * q^50 + 21 * q^52 + 33 * q^54 + 18 * q^56 + 4 * q^57 - 3 * q^58 - 59 * q^60 + 12 * q^62 - 72 * q^63 - 8 * q^64 - 42 * q^66 - 18 * q^68 - 27 * q^70 + 12 * q^72 - 12 * q^73 - 57 * q^74 + 12 * q^76 + 19 * q^78 - 4 * q^79 - 57 * q^80 - 18 * q^81 + 69 * q^84 - 27 * q^86 - 6 * q^87 + 9 * q^88 - 24 * q^89 - 75 * q^90 - 36 * q^92 - 45 * q^96 - 45 * q^98

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