LMFDB - Embedded newform 504.2.cs.a.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39778 - 0.214989i) q^{2} +(0.0497101 + 1.73134i) q^{3} +(1.90756 + 0.601014i) q^{4} +(0.261066 + 0.150726i) q^{5} +(0.302736 - 2.43071i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-2.53713 - 1.25019i) q^{8} +(-2.99506 + 0.172130i) q^{9} +O(q^{10})$	\(q+(-1.39778 - 0.214989i) q^{2} +(0.0497101 + 1.73134i) q^{3} +(1.90756 + 0.601014i) q^{4} +(0.261066 + 0.150726i) q^{5} +(0.302736 - 2.43071i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-2.53713 - 1.25019i) q^{8} +(-2.99506 + 0.172130i) q^{9} +(-0.332507 - 0.266808i) q^{10} +(4.82191 - 2.78393i) q^{11} +(-0.945733 + 3.33250i) q^{12} +(3.89009 + 2.24594i) q^{13} +(-0.512702 - 1.31800i) q^{14} +(-0.247981 + 0.459485i) q^{15} +(3.27756 + 2.29294i) q^{16} +1.83375 q^{17} +(4.22343 + 0.403307i) q^{18} +6.84330i q^{19} +(0.407409 + 0.444424i) q^{20} +(-1.47453 + 0.908719i) q^{21} +(-7.33847 + 2.85466i) q^{22} +(1.40037 - 2.42551i) q^{23} +(2.03838 - 4.45477i) q^{24} +(-2.45456 - 4.25143i) q^{25} +(-4.95462 - 3.97565i) q^{26} +(-0.446899 - 5.17690i) q^{27} +(0.433286 + 1.95250i) q^{28} +(-7.18043 + 4.14562i) q^{29} +(0.445406 - 0.588945i) q^{30} +(-0.798016 + 1.38220i) q^{31} +(-4.08834 - 3.90966i) q^{32} +(5.05962 + 8.20997i) q^{33} +(-2.56317 - 0.394237i) q^{34} +0.301453i q^{35} +(-5.81670 - 1.47172i) q^{36} +7.58101i q^{37} +(1.47124 - 9.56540i) q^{38} +(-3.69511 + 6.84670i) q^{39} +(-0.473921 - 0.708794i) q^{40} +(-2.15744 + 3.73679i) q^{41} +(2.25642 - 0.953178i) q^{42} +(9.40147 - 5.42794i) q^{43} +(10.8713 - 2.41248i) q^{44} +(-0.807851 - 0.406497i) q^{45} +(-2.47887 + 3.08926i) q^{46} +(1.32658 + 2.29770i) q^{47} +(-3.80693 + 5.78855i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.51692 + 6.47025i) q^{50} +(0.0911559 + 3.17484i) q^{51} +(6.07073 + 6.62226i) q^{52} +6.80500i q^{53} +(-0.488313 + 7.33223i) q^{54} +1.67845 q^{55} +(-0.185870 - 2.82231i) q^{56} +(-11.8481 + 0.340181i) q^{57} +(10.9279 - 4.25094i) q^{58} +(-6.43716 - 3.71650i) q^{59} +(-0.749195 + 0.727456i) q^{60} +(-12.0001 + 6.92824i) q^{61} +(1.41261 - 1.76045i) q^{62} +(-1.64660 - 2.50773i) q^{63} +(4.87406 + 6.34378i) q^{64} +(0.677045 + 1.17268i) q^{65} +(-5.30717 - 12.5635i) q^{66} +(5.39359 + 3.11399i) q^{67} +(3.49799 + 1.10211i) q^{68} +(4.26899 + 2.30394i) q^{69} +(0.0648091 - 0.421363i) q^{70} -1.62850 q^{71} +(7.81405 + 3.30767i) q^{72} +13.7111 q^{73} +(1.62984 - 10.5966i) q^{74} +(7.23864 - 4.46102i) q^{75} +(-4.11292 + 13.0540i) q^{76} +(4.82191 + 2.78393i) q^{77} +(6.63690 - 8.77574i) q^{78} +(-7.87368 - 13.6376i) q^{79} +(0.510053 + 1.09262i) q^{80} +(8.94074 - 1.03108i) q^{81} +(3.81898 - 4.75937i) q^{82} +(7.07454 - 4.08449i) q^{83} +(-3.35890 + 0.847223i) q^{84} +(0.478729 + 0.276395i) q^{85} +(-14.3081 + 5.56583i) q^{86} +(-7.53441 - 12.2257i) q^{87} +(-15.7143 + 1.03490i) q^{88} +3.57708 q^{89} +(1.04180 + 0.741871i) q^{90} +4.49188i q^{91} +(4.12906 - 3.78517i) q^{92} +(-2.43273 - 1.31292i) q^{93} +(-1.36028 - 3.49687i) q^{94} +(-1.03146 + 1.78655i) q^{95} +(6.56571 - 7.27265i) q^{96} +(-3.70357 - 6.41477i) q^{97} +(0.885075 - 1.10302i) q^{98} +(-13.9627 + 9.16803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.39778	−	0.214989i	−0.988377	−	0.152020i
$2$	−1.39778	−	0.214989i	−0.988377	−	0.152020i
$3$	0.0497101	+	1.73134i	0.0287001	+	0.999588i
$3$	0.0497101	+	1.73134i	0.0287001	+	0.999588i
$4$	1.90756	+	0.601014i	0.953780	+	0.300507i
$5$	0.261066	+	0.150726i	0.116752	+	0.0674069i	0.557239	−	0.830352i	$-0.311861\pi$
$5$	0.261066	+	0.150726i	0.116752	+	0.0674069i	−0.440487	+	0.897759i	$0.645194\pi$
$6$	0.302736	−	2.43071i	0.123591	−	0.992333i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−2.53713	−	1.25019i	−0.897011	−	0.442008i
$9$	−2.99506	+	0.172130i	−0.998353	+	0.0573766i
$10$	−0.332507	−	0.266808i	−0.105148	−	0.0843721i
$11$	4.82191	−	2.78393i	1.45386	−	0.839387i	0.455164	−	0.890408i	$-0.349581\pi$
$11$	4.82191	−	2.78393i	1.45386	−	0.839387i	0.998698	+	0.0510207i	$0.0162474\pi$
$12$	−0.945733	+	3.33250i	−0.273010	+	0.962011i
$13$	3.89009	+	2.24594i	1.07892	+	0.622912i	0.930604	−	0.366028i	$-0.119283\pi$
$13$	3.89009	+	2.24594i	1.07892	+	0.622912i	0.148312	+	0.988941i	$0.452616\pi$
$14$	−0.512702	−	1.31800i	−0.137025	−	0.352252i
$15$	−0.247981	+	0.459485i	−0.0640283	+	0.118639i
$16$	3.27756	+	2.29294i	0.819391	+	0.573235i
$17$	1.83375			0.444750			0.222375	−	0.974961i	$-0.428619\pi$
$17$	1.83375			0.444750			0.222375	+	0.974961i	$0.428619\pi$
$18$	4.22343	+	0.403307i	0.995472	+	0.0950603i
$19$			6.84330i			1.56996i	0.619521	+	0.784980i	$0.287327\pi$
$19$			6.84330i			1.56996i	−0.619521	+	0.784980i	$0.712673\pi$
$20$	0.407409	+	0.444424i	0.0910995	+	0.0993761i
$21$	−1.47453	+	0.908719i	−0.321768	+	0.198299i
$22$	−7.33847	+	2.85466i	−1.56457	+	0.608615i
$23$	1.40037	−	2.42551i	0.291998	−	0.505755i	−0.682284	−	0.731087i	$-0.739013\pi$
$23$	1.40037	−	2.42551i	0.291998	−	0.505755i	0.974282	+	0.225332i	$0.0723468\pi$
$24$	2.03838	−	4.45477i	0.416082	−	0.909327i
$25$	−2.45456	−	4.25143i	−0.490913	−	0.850286i
$26$	−4.95462	−	3.97565i	−0.971680	−	0.779690i
$27$	−0.446899	−	5.17690i	−0.0860058	−	0.996295i
$28$	0.433286	+	1.95250i	0.0818834	+	0.368988i
$29$	−7.18043	+	4.14562i	−1.33337	+	0.769823i	−0.985815	−	0.167836i	$-0.946322\pi$
$29$	−7.18043	+	4.14562i	−1.33337	+	0.769823i	−0.347557	+	0.937659i	$0.612989\pi$
$30$	0.445406	−	0.588945i	0.0813196	−	0.107526i
$31$	−0.798016	+	1.38220i	−0.143328	+	0.248251i	−0.928748	−	0.370712i	$-0.879114\pi$
$31$	−0.798016	+	1.38220i	−0.143328	+	0.248251i	0.785420	+	0.618963i	$0.212447\pi$
$32$	−4.08834	−	3.90966i	−0.722724	−	0.691137i
$33$	5.05962	+	8.20997i	0.880767	+	1.42917i
$34$	−2.56317	−	0.394237i	−0.439581	−	0.0676111i
$35$			0.301453i			0.0509548i
$36$	−5.81670	−	1.47172i	−0.969450	−	0.245287i
$37$			7.58101i			1.24631i	0.782098	+	0.623155i	$0.214149\pi$
$37$			7.58101i			1.24631i	−0.782098	+	0.623155i	$0.785851\pi$
$38$	1.47124	−	9.56540i	0.238666	−	1.55171i
$39$	−3.69511	+	6.84670i	−0.591691	+	1.09635i
$40$	−0.473921	−	0.708794i	−0.0749335	−	0.112070i
$41$	−2.15744	+	3.73679i	−0.336935	+	0.583588i	−0.983855	−	0.178970i	$-0.942724\pi$
$41$	−2.15744	+	3.73679i	−0.336935	+	0.583588i	0.646920	+	0.762558i	$0.276057\pi$
$42$	2.25642	−	0.953178i	0.348174	−	0.147079i
$43$	9.40147	−	5.42794i	1.43371	−	0.827753i	0.436309	−	0.899797i	$-0.356286\pi$
$43$	9.40147	−	5.42794i	1.43371	−	0.827753i	0.997401	+	0.0720442i	$0.0229523\pi$
$44$	10.8713	−	2.41248i	1.63890	−	0.363695i
$45$	−0.807851	−	0.406497i	−0.120427	−	0.0605970i
$46$	−2.47887	+	3.08926i	−0.365489	+	0.455487i
$47$	1.32658	+	2.29770i	0.193501	+	0.335154i	0.946408	−	0.322973i	$-0.104682\pi$
$47$	1.32658	+	2.29770i	0.193501	+	0.335154i	−0.752907	+	0.658127i	$0.771349\pi$
$48$	−3.80693	+	5.78855i	−0.549482	+	0.835505i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.51692	+	6.47025i	0.355946	+	0.915032i
$51$	0.0911559	+	3.17484i	0.0127644	+	0.444567i
$52$	6.07073	+	6.62226i	0.841858	+	0.918343i
$53$			6.80500i			0.934739i	0.884062	+	0.467370i	$0.154798\pi$
$53$			6.80500i			0.934739i	−0.884062	+	0.467370i	$0.845202\pi$
$54$	−0.488313	+	7.33223i	−0.0664510	+	0.997790i
$55$	1.67845			0.226322
$56$	−0.185870	−	2.82231i	−0.0248379	−	0.377147i
$57$	−11.8481	+	0.340181i	−1.56931	+	0.0450580i
$58$	10.9279	−	4.25094i	1.43490	−	0.558176i
$59$	−6.43716	−	3.71650i	−0.838047	−	0.483847i	0.0185527	−	0.999828i	$-0.494094\pi$
$59$	−6.43716	−	3.71650i	−0.838047	−	0.483847i	−0.856600	+	0.515981i	$0.827427\pi$
$60$	−0.749195	+	0.727456i	−0.0967206	+	0.0939141i
$61$	−12.0001	+	6.92824i	−1.53645	+	0.887070i	−0.537407	+	0.843323i	$0.680596\pi$
$61$	−12.0001	+	6.92824i	−1.53645	+	0.887070i	−0.999043	+	0.0437471i	$0.986070\pi$
$62$	1.41261	−	1.76045i	0.179401	−	0.223577i
$63$	−1.64660	−	2.50773i	−0.207452	−	0.315944i
$64$	4.87406	+	6.34378i	0.609257	+	0.792973i
$65$	0.677045	+	1.17268i	0.0839771	+	0.145453i
$66$	−5.30717	−	12.5635i	−0.653267	−	1.54646i
$67$	5.39359	+	3.11399i	0.658932	+	0.380435i	0.791870	−	0.610690i	$-0.209108\pi$
$67$	5.39359	+	3.11399i	0.658932	+	0.380435i	−0.132938	+	0.991124i	$0.542441\pi$
$68$	3.49799	+	1.10211i	0.424193	+	0.133651i
$69$	4.26899	+	2.30394i	0.513927	+	0.277362i
$70$	0.0648091	−	0.421363i	0.00774617	−	0.0503626i
$71$	−1.62850			−0.193268			−0.0966339	−	0.995320i	$-0.530808\pi$
$71$	−1.62850			−0.193268			−0.0966339	+	0.995320i	$0.530808\pi$
$72$	7.81405	+	3.30767i	0.920894	+	0.389813i
$73$	13.7111			1.60476			0.802380	−	0.596813i	$-0.203567\pi$
$73$	13.7111			1.60476			0.802380	+	0.596813i	$0.203567\pi$
$74$	1.62984	−	10.5966i	0.189465	−	1.23182i
$75$	7.23864	−	4.46102i	0.835846	−	0.515114i
$76$	−4.11292	+	13.0540i	−0.471784	+	1.49740i
$77$	4.82191	+	2.78393i	0.549508	+	0.317259i
$78$	6.63690	−	8.77574i	0.751481	−	0.993657i
$79$	−7.87368	−	13.6376i	−0.885858	−	1.53435i	−0.844727	−	0.535197i	$-0.820237\pi$
$79$	−7.87368	−	13.6376i	−0.885858	−	1.53435i	−0.0411308	−	0.999154i	$-0.513096\pi$
$80$	0.510053	+	1.09262i	0.0570256	+	0.122159i
$81$	8.94074	−	1.03108i	0.993416	−	0.114564i
$82$	3.81898	−	4.75937i	0.421736	−	0.525584i
$83$	7.07454	−	4.08449i	0.776532	−	0.448331i	−0.0586680	−	0.998278i	$-0.518685\pi$
$83$	7.07454	−	4.08449i	0.776532	−	0.448331i	0.835200	+	0.549947i	$0.185352\pi$
$84$	−3.35890	+	0.847223i	−0.366486	+	0.0924396i
$85$	0.478729	+	0.276395i	0.0519255	+	0.0299792i
$86$	−14.3081	+	5.56583i	−1.54288	+	0.600179i
$87$	−7.53441	−	12.2257i	−0.807774	−	1.31073i
$88$	−15.7143	+	1.03490i	−1.67515	+	0.110321i
$89$	3.57708			0.379170			0.189585	−	0.981864i	$-0.439286\pi$
$89$	3.57708			0.379170			0.189585	+	0.981864i	$0.439286\pi$
$90$	1.04180	+	0.741871i	0.109816	+	0.0782001i
$91$			4.49188i			0.470877i
$92$	4.12906	−	3.78517i	0.430484	−	0.394631i
$93$	−2.43273	−	1.31292i	−0.252262	−	0.136144i
$94$	−1.36028	−	3.49687i	−0.140302	−	0.360675i
$95$	−1.03146	+	1.78655i	−0.105826	+	0.183296i
$96$	6.56571	−	7.27265i	0.670110	−	0.742262i
$97$	−3.70357	−	6.41477i	−0.376041	−	0.651322i	0.614441	−	0.788962i	$-0.289381\pi$
$97$	−3.70357	−	6.41477i	−0.376041	−	0.651322i	−0.990482	+	0.137641i	$0.956048\pi$
$98$	0.885075	−	1.10302i	0.0894060	−	0.111421i
$99$	−13.9627	+	9.16803i	−1.40330	+	0.921422i
$100$	−2.12706	−	9.58508i	−0.212706	−	0.958508i
$101$	11.7971	−	6.81107i	1.17386	−	0.677727i	0.219272	−	0.975664i	$-0.429632\pi$
$101$	11.7971	−	6.81107i	1.17386	−	0.677727i	0.954586	+	0.297937i	$0.0962984\pi$
$102$	0.555142	−	4.45732i	0.0549672	−	0.441340i
$103$	1.52924	−	2.64872i	0.150681	−	0.260986i	−0.780797	−	0.624784i	$-0.785187\pi$
$103$	1.52924	−	2.64872i	0.150681	−	0.260986i	0.931478	+	0.363798i	$0.118520\pi$
$104$	−7.06180	−	10.5616i	−0.692467	−	1.03565i
$105$	−0.521916	+	0.0149852i	−0.0509338	+	0.00146241i
$106$	1.46300	−	9.51188i	0.142099	−	0.923875i
$107$			0.637063i			0.0615872i	0.999526	+	0.0307936i	$0.00980346\pi$
$107$			0.637063i			0.0615872i	−0.999526	+	0.0307936i	$0.990197\pi$
$108$	2.25890	−	10.1438i	0.217363	−	0.976091i
$109$		−	9.32631i		−	0.893299i	−0.894709	−	0.446649i	$-0.852617\pi$
$109$		−	9.32631i		−	0.893299i	0.894709	−	0.446649i	$-0.147383\pi$
$110$	−2.34609	−	0.360848i	−0.223691	−	0.0344055i
$111$	−13.1253	+	0.376852i	−1.24580	+	0.0357692i
$112$	−0.346963	+	3.98492i	−0.0327849	+	0.376540i
$113$	−7.29542	+	12.6360i	−0.686296	+	1.18870i	0.286732	+	0.958011i	$0.407431\pi$
$113$	−7.29542	+	12.6360i	−0.686296	+	1.18870i	−0.973028	+	0.230688i	$0.925902\pi$
$114$	16.6341	+	2.07171i	1.55792	+	0.194033i
$115$	0.731177	−	0.422145i	0.0681826	−	0.0393653i
$116$	−16.1887	+	3.59248i	−1.50308	+	0.333553i
$117$	−12.0376	−	6.05713i	−1.11288	−	0.559982i
$118$	8.19871	+	6.57876i	0.754752	+	0.605624i
$119$	0.916875	+	1.58807i	0.0840498	+	0.145579i
$120$	1.20360	−	0.855752i	0.109873	−	0.0781191i
$121$	10.0006	−	17.3215i	0.909142	−	1.57468i
$122$	18.2629	−	7.10424i	1.65345	−	0.643188i
$123$	−6.57689	−	3.54949i	−0.593018	−	0.320047i
$124$	−2.35299	+	2.15702i	−0.211304	+	0.193706i
$125$		−	2.98713i		−	0.267177i
$126$	1.76244	+	3.85925i	0.157011	+	0.343809i
$127$	−4.70199			−0.417234			−0.208617	−	0.977997i	$-0.566896\pi$
$127$	−4.70199			−0.417234			−0.208617	+	0.977997i	$0.566896\pi$
$128$	−5.44900	−	9.91506i	−0.481628	−	0.876376i
$129$	9.86494	+	16.0073i	0.868560	+	1.40936i
$130$	−0.694245	−	1.78470i	−0.0608893	−	0.156528i
$131$	−1.21619	−	0.702166i	−0.106259	−	0.0613485i	0.445929	−	0.895068i	$-0.352873\pi$
$131$	−1.21619	−	0.702166i	−0.106259	−	0.0613485i	−0.552188	+	0.833720i	$0.686207\pi$
$132$	4.71722	+	18.7019i	0.410582	+	1.62779i
$133$	−5.92647	+	3.42165i	−0.513890	+	0.296694i
$134$	−6.86956	−	5.51223i	−0.593440	−	0.476184i
$135$	0.663625	−	1.41887i	0.0571157	−	0.122117i
$136$	−4.65246	−	2.29253i	−0.398946	−	0.196583i
$137$	−5.36384	−	9.29045i	−0.458264	−	0.793737i	0.540605	−	0.841276i	$-0.318195\pi$
$137$	−5.36384	−	9.29045i	−0.458264	−	0.793737i	−0.998869	+	0.0475396i	$0.984862\pi$
$138$	−5.47178	−	4.13818i	−0.465789	−	0.352266i
$139$	3.58101	+	2.06749i	0.303737	+	0.175363i	0.644120	−	0.764924i	$-0.277224\pi$
$139$	3.58101	+	2.06749i	0.303737	+	0.175363i	−0.340383	+	0.940287i	$0.610557\pi$
$140$	−0.181177	+	0.575039i	−0.0153123	+	0.0485996i
$141$	−3.91215	+	2.41097i	−0.329463	+	0.203041i
$142$	2.27628	+	0.350111i	0.191022	+	0.0293807i
$143$	25.0102			2.09146
$144$	−10.2112	−	6.30332i	−0.850931	−	0.525277i
$145$	−2.49942			−0.207565
$146$	−19.1650	−	2.94774i	−1.58611	−	0.243956i
$147$	−1.52424	−	0.822618i	−0.125717	−	0.0678484i
$148$	−4.55629	+	14.4612i	−0.374525	+	1.18870i
$149$	−7.74341	−	4.47066i	−0.634365	−	0.366251i	0.148076	−	0.988976i	$-0.452692\pi$
$149$	−7.74341	−	4.47066i	−0.634365	−	0.366251i	−0.782441	+	0.622725i	$0.786025\pi$
$150$	−11.0771	+	4.67927i	−0.904439	+	0.382061i
$151$	1.46609	+	2.53934i	0.119309	+	0.206649i	0.919494	−	0.393104i	$-0.128599\pi$
$151$	1.46609	+	2.53934i	0.119309	+	0.206649i	−0.800185	+	0.599753i	$0.795266\pi$
$152$	8.55541	−	17.3623i	0.693935	−	1.40827i
$153$	−5.49219	+	0.315643i	−0.444017	+	0.0255182i
$154$	−6.14144	−	4.92798i	−0.494891	−	0.397108i
$155$	−0.416669	+	0.240564i	−0.0334677	+	0.0193226i
$156$	−11.1636	+	10.8397i	−0.893803	+	0.867868i
$157$	1.52675	+	0.881468i	0.121848	+	0.0703488i	0.559685	−	0.828705i	$-0.310922\pi$
$157$	1.52675	+	0.881468i	0.121848	+	0.0703488i	−0.437837	+	0.899054i	$0.644255\pi$
$158$	8.07370	+	20.7551i	0.642309	+	1.65119i
$159$	−11.7818	+	0.338277i	−0.934354	+	0.0268271i
$160$	−0.478038	−	1.63690i	−0.0377922	−	0.129408i
$161$	2.80074			0.220729
$162$	−12.7188	−	0.480949i	−0.999286	−	0.0377869i
$163$		−	17.2121i		−	1.34815i	−0.738662	−	0.674076i	$-0.764542\pi$
$163$		−	17.2121i		−	1.34815i	0.738662	−	0.674076i	$-0.235458\pi$
$164$	−6.36130	+	5.83150i	−0.496734	+	0.455363i
$165$	0.0834357	+	2.90596i	0.00649546	+	0.226229i
$166$	−10.7667	+	4.18825i	−0.835662	+	0.325071i
$167$	6.09746	−	10.5611i	0.471835	−	0.817243i	−0.527645	−	0.849465i	$-0.676925\pi$
$167$	6.09746	−	10.5611i	0.471835	−	0.817243i	0.999481	+	0.0322219i	$0.0102583\pi$
$168$	4.87714	−	0.462101i	0.376279	−	0.0356519i
$169$	3.58851	+	6.21549i	0.276039	+	0.478114i
$170$	−0.609735	−	0.489260i	−0.0467645	−	0.0375245i
$171$	−1.17793	−	20.4961i	−0.0900789	−	1.56737i
$172$	21.1961	−	4.70370i	1.61619	−	0.358654i
$173$	2.95115	−	1.70385i	0.224372	−	0.129541i	−0.383601	−	0.923499i	$-0.625316\pi$
$173$	2.95115	−	1.70385i	0.224372	−	0.129541i	0.607973	+	0.793958i	$0.291983\pi$
$174$	7.90304	+	18.7086i	0.599128	+	1.41829i
$175$	2.45456	−	4.25143i	0.185548	−	0.321378i
$176$	22.1875	+	1.93184i	1.67245	+	0.145618i
$177$	6.11452	−	11.3296i	0.459595	−	0.851589i
$178$	−4.99996	−	0.769034i	−0.374763	−	0.0576415i
$179$		−	0.675455i		−	0.0504859i	−0.999681	−	0.0252430i	$-0.991964\pi$
$179$		−	0.675455i		−	0.0504859i	0.999681	−	0.0252430i	$-0.00803593\pi$
$180$	−1.29671	−	1.26095i	−0.0966513	−	0.0939854i
$181$		−	8.62514i		−	0.641101i	−0.947231	−	0.320551i	$-0.896132\pi$
$181$		−	8.62514i		−	0.641101i	0.947231	−	0.320551i	$-0.103868\pi$
$182$	0.965707	−	6.27865i	0.0715830	−	0.465405i
$183$	−12.5916	−	20.4317i	−0.930801	−	1.51036i
$184$	−6.58527	+	4.40312i	−0.485473	+	0.324602i
$185$	−1.14266	+	1.97914i	−0.0840098	+	0.145509i
$186$	3.11815	+	2.35819i	0.228634	+	0.172911i
$187$	8.84219	−	5.10504i	0.646605	−	0.373317i
$188$	1.14958	+	5.18029i	0.0838414	+	0.377812i
$189$	4.25988	−	2.97548i	0.309860	−	0.216434i
$190$	1.82585	−	2.27544i	0.132461	−	0.165078i
$191$	2.31301	+	4.00624i	0.167363	+	0.289882i	0.937492	−	0.348007i	$-0.113141\pi$
$191$	2.31301	+	4.00624i	0.167363	+	0.289882i	−0.770129	+	0.637888i	$0.779808\pi$
$192$	−10.7409	+	8.75399i	−0.775160	+	0.631765i
$193$	6.71513	−	11.6310i	0.483366	−	0.837214i	−0.516452	−	0.856316i	$-0.672747\pi$
$193$	6.71513	−	11.6310i	0.483366	−	0.837214i	0.999818	+	0.0191020i	$0.00608072\pi$
$194$	3.79766	+	9.76265i	0.272656	+	0.700917i
$195$	−1.99664	+	1.23049i	−0.142983	+	0.0881170i
$196$	−1.47427	+	1.35149i	−0.105305	+	0.0965348i
$197$			19.5821i			1.39517i	0.716504	+	0.697583i	$0.245741\pi$
$197$			19.5821i			1.39517i	−0.716504	+	0.697583i	$0.754259\pi$
$198$	21.4878	−	9.81303i	1.52707	−	0.697382i
$199$	21.9144			1.55347			0.776734	−	0.629829i	$-0.216875\pi$
$199$	21.9144			1.55347			0.776734	+	0.629829i	$0.216875\pi$
$200$	0.912459	+	13.8551i	0.0645206	+	0.979703i
$201$	−5.12325	+	9.49292i	−0.361366	+	0.669579i
$202$	−17.9541	+	6.98410i	−1.26324	+	0.491400i
$203$	−7.18043	−	4.14562i	−0.503967	−	0.290966i
$204$	−1.73424	+	6.11098i	−0.121421	+	0.427854i
$205$	−1.12646	+	0.650365i	−0.0786757	+	0.0454234i
$206$	−2.70698	+	3.37355i	−0.188605	+	0.235046i
$207$	−3.77669	+	7.50560i	−0.262498	+	0.521675i
$208$	7.60019	+	16.2810i	0.526979	+	1.12888i
$209$	19.0513	+	32.9978i	1.31780	+	2.28250i
$210$	0.732744	+	0.0912604i	0.0505641	+	0.00629757i
$211$	0.992808	+	0.573198i	0.0683477	+	0.0394606i	0.533784	−	0.845621i	$-0.320769\pi$
$211$	0.992808	+	0.573198i	0.0683477	+	0.0394606i	−0.465437	+	0.885081i	$0.654103\pi$
$212$	−4.08990	+	12.9809i	−0.280896	+	0.891535i
$213$	−0.0809530	−	2.81949i	−0.00554681	−	0.193188i
$214$	0.136962	−	0.890472i	0.00936251	−	0.0608714i
$215$	3.27253			0.223185
$216$	−5.33826	+	13.6932i	−0.363222	+	0.931702i
$217$	−1.59603			−0.108346
$218$	−2.00506	+	13.0361i	−0.135800	+	0.882916i
$219$	0.681579	+	23.7385i	0.0460568	+	1.60410i
$220$	3.20174	+	1.00877i	0.215861	+	0.0680113i
$221$	7.13345	+	4.11850i	0.479848	+	0.277040i
$222$	18.4272	+	2.29504i	1.23675	+	0.154033i
$223$	−0.741020	−	1.28348i	−0.0496224	−	0.0859485i	0.840147	−	0.542358i	$-0.182468\pi$
$223$	−0.741020	−	1.28348i	−0.0496224	−	0.0859485i	−0.889770	+	0.456410i	$0.849135\pi$
$224$	1.34169	−	5.49544i	0.0896456	−	0.367180i
$225$	8.08336	+	12.3108i	0.538890	+	0.820718i
$226$	12.9140	−	16.0939i	0.859026	−	1.07055i
$227$	3.11533	−	1.79864i	0.206772	−	0.119380i	−0.393038	−	0.919522i	$-0.628576\pi$
$227$	3.11533	−	1.79864i	0.206772	−	0.119380i	0.599810	+	0.800142i	$0.295243\pi$
$228$	−22.8053	−	6.47193i	−1.51032	−	0.428614i
$229$	−19.3194	−	11.1540i	−1.27666	−	0.737079i	−0.300426	−	0.953805i	$-0.597129\pi$
$229$	−19.3194	−	11.1540i	−1.27666	−	0.737079i	−0.976233	+	0.216726i	$0.930462\pi$
$230$	−1.11278	+	0.432870i	−0.0733745	+	0.0285426i
$231$	−4.58023	+	8.48675i	−0.301357	+	0.558387i
$232$	23.4005	−	1.54109i	1.53632	−	0.101178i
$233$	−3.29024			−0.215551			−0.107775	−	0.994175i	$-0.534373\pi$
$233$	−3.29024			−0.215551			−0.107775	+	0.994175i	$0.534373\pi$
$234$	15.5237	+	11.0545i	1.01482	+	0.722653i
$235$			0.799801i			0.0521733i
$236$	−10.0456	−	10.9583i	−0.653913	−	0.713322i
$237$	23.2199	−	14.3099i	1.50829	−	0.929529i
$238$	−0.940168	−	2.41689i	−0.0609420	−	0.156664i
$239$	3.84345	−	6.65705i	0.248612	−	0.430609i	−0.714529	−	0.699606i	$-0.753359\pi$
$239$	3.84345	−	6.65705i	0.248612	−	0.430609i	0.963141	+	0.268997i	$0.0866922\pi$
$240$	−1.86634	+	0.937388i	−0.120472	+	0.0605081i
$241$	−5.84868	−	10.1302i	−0.376746	−	0.652544i	0.613840	−	0.789430i	$-0.289624\pi$
$241$	−5.84868	−	10.1302i	−0.376746	−	0.652544i	−0.990587	+	0.136886i	$0.956290\pi$
$242$	−17.7025	+	22.0615i	−1.13796	+	1.41817i
$243$	2.22959	+	15.4282i	0.143028	+	0.989719i
$244$	−27.0548	+	6.00382i	−1.73201	+	0.384355i
$245$	−0.261066	+	0.150726i	−0.0166789	+	0.00962955i
$246$	8.42992	+	6.37536i	0.537472	+	0.406478i
$247$	−15.3696	+	26.6210i	−0.977947	+	1.69385i
$248$	3.75268	−	2.50916i	0.238296	−	0.159332i
$249$	7.42330	+	12.0454i	0.470433	+	0.763345i
$250$	−0.642202	+	4.17534i	−0.0406164	+	0.264072i
$251$		−	14.4730i		−	0.913529i	−0.889588	−	0.456764i	$-0.849008\pi$
$251$		−	14.4730i		−	0.913529i	0.889588	−	0.456764i	$-0.150992\pi$
$252$	−1.63380	−	5.77327i	−0.102920	−	0.363682i
$253$		−	15.5942i		−	0.980396i
$254$	6.57233	+	1.01088i	0.412385	+	0.0634281i
$255$	−0.454734	+	0.842582i	−0.0284766	+	0.0527645i
$256$	5.48485	+	15.0305i	0.342803	+	0.939407i
$257$	0.876856	−	1.51876i	0.0546968	−	0.0947376i	−0.837381	−	0.546620i	$-0.815914\pi$
$257$	0.876856	−	1.51876i	0.0546968	−	0.0947376i	0.892077	+	0.451883i	$0.149247\pi$
$258$	−10.3476	−	24.4955i	−0.644213	−	1.52502i
$259$	−6.56534	+	3.79050i	−0.407951	+	0.235530i
$260$	0.586708	+	2.64386i	0.0363861	+	0.163965i
$261$	20.7922	−	13.6523i	1.28701	−	0.845059i
$262$	1.54900	+	1.24294i	0.0956975	+	0.0767890i
$263$	1.65069	+	2.85908i	0.101786	+	0.176298i	0.912420	−	0.409254i	$-0.134211\pi$
$263$	1.65069	+	2.85908i	0.101786	+	0.176298i	−0.810635	+	0.585552i	$0.800878\pi$
$264$	−2.57292	−	27.1552i	−0.158352	−	1.67129i
$265$	−1.02569	+	1.77655i	−0.0630078	+	0.109133i
$266$	9.01950	−	3.50857i	0.553021	−	0.215124i
$267$	0.177817	+	6.19313i	0.0108822	+	0.379013i
$268$	8.41704	+	9.18175i	0.514153	+	0.560864i
$269$			26.8939i			1.63975i	0.572543	+	0.819875i	$0.305957\pi$
$269$			26.8939i			1.63975i	−0.572543	+	0.819875i	$0.694043\pi$
$270$	−1.23264	+	1.84059i	−0.0750162	+	0.112015i
$271$	8.60539			0.522740			0.261370	−	0.965239i	$-0.415826\pi$
$271$	8.60539			0.522740			0.261370	+	0.965239i	$0.415826\pi$
$272$	6.01024	+	4.20468i	0.364424	+	0.254946i
$273$	−7.77697	+	0.223292i	−0.470683	+	0.0135142i
$274$	5.50011	+	14.1391i	0.332274	+	0.854177i
$275$	−23.6714	−	13.6667i	−1.42744	−	0.824132i
$276$	6.75866	+	6.96063i	0.406823	+	0.418981i
$277$	−2.02233	+	1.16759i	−0.121510	+	0.0701537i	−0.559523	−	0.828815i	$-0.689016\pi$
$277$	−2.02233	+	1.16759i	−0.121510	+	0.0701537i	0.438013	+	0.898969i	$0.355682\pi$
$278$	−4.56096	−	3.65977i	−0.273548	−	0.219499i
$279$	2.15218	−	4.27714i	0.128848	−	0.256066i
$280$	0.376873	−	0.764825i	0.0225224	−	0.0457070i
$281$	−4.04059	−	6.99851i	−0.241041	−	0.417496i	0.719970	−	0.694005i	$-0.244156\pi$
$281$	−4.04059	−	6.99851i	−0.241041	−	0.417496i	−0.961011	+	0.276509i	$0.910822\pi$
$282$	5.98665	−	2.52893i	0.356500	−	0.150596i
$283$	4.02275	+	2.32254i	0.239128	+	0.138061i	0.614776	−	0.788702i	$-0.289246\pi$
$283$	4.02275	+	2.32254i	0.239128	+	0.138061i	−0.375648	+	0.926762i	$0.622580\pi$
$284$	−3.10647	−	0.978754i	−0.184335	−	0.0580784i
$285$	−3.14439	−	1.69700i	−0.186258	−	0.100522i
$286$	−34.9587	−	5.37693i	−2.06715	−	0.317944i
$287$	−4.31487			−0.254699
$288$	12.9178	+	11.0059i	0.761188	+	0.648531i
$289$	−13.6374			−0.802198
$290$	3.49363	+	0.537348i	0.205153	+	0.0315542i
$291$	10.9220	−	6.73101i	0.640261	−	0.394579i
$292$	26.1547	+	8.24055i	1.53059	+	0.482242i
$293$	−23.3105	−	13.4583i	−1.36181	−	0.786244i	−0.371949	−	0.928253i	$-0.621311\pi$
$293$	−23.3105	−	13.4583i	−1.36181	−	0.786244i	−0.989865	+	0.142009i	$0.954644\pi$
$294$	1.95369	+	1.47753i	0.113941	+	0.0861714i
$295$	−1.12035	−	1.94050i	−0.0652292	−	0.112980i
$296$	9.47769	−	19.2340i	0.550879	−	1.11795i
$297$	−16.5670	−	23.7184i	−0.961317	−	1.37628i
$298$	9.86241	+	7.91374i	0.571314	+	0.458430i
$299$	10.8951	−	6.29030i	0.630081	−	0.363778i
$300$	16.4893	−	4.15913i	0.952008	−	0.240127i
$301$	9.40147	+	5.42794i	0.541891	+	0.312861i
$302$	−1.50333	−	3.86462i	−0.0865071	−	0.222384i
$303$	12.3787	+	20.0862i	0.711138	+	1.15392i
$304$	−15.6913	+	22.4293i	−0.899956	+	1.28641i
$305$	−4.17707			−0.239178
$306$	7.74471	+	0.739564i	0.442736	+	0.0422780i
$307$		−	17.7274i		−	1.01175i	−0.862606	−	0.505877i	$-0.831169\pi$
$307$		−	17.7274i		−	1.01175i	0.862606	−	0.505877i	$-0.168831\pi$
$308$	7.52490	+	8.20855i	0.428771	+	0.467726i
$309$	4.66185	+	2.51596i	0.265203	+	0.143128i
$310$	0.634129	−	0.246675i	0.0360161	−	0.0140102i
$311$	−12.6009	+	21.8255i	−0.714534	+	1.23761i	0.248605	+	0.968605i	$0.420028\pi$
$311$	−12.6009	+	21.8255i	−0.714534	+	1.23761i	−0.963139	+	0.269004i	$0.913306\pi$
$312$	17.9346	−	12.7514i	1.01535	−	0.721905i
$313$	−6.01497	−	10.4182i	−0.339986	−	0.588873i	0.644444	−	0.764652i	$-0.277089\pi$
$313$	−6.01497	−	10.4182i	−0.339986	−	0.588873i	−0.984430	+	0.175779i	$0.943756\pi$
$314$	−1.94455	−	1.56033i	−0.109737	−	0.0880545i
$315$	−0.0518890	−	0.902868i	−0.00292361	−	0.0508709i
$316$	−6.82311	−	30.7467i	−0.383830	−	1.72964i
$317$	−18.3142	+	10.5737i	−1.02863	+	0.593880i	−0.916592	−	0.399824i	$-0.869071\pi$
$317$	−18.3142	+	10.5737i	−1.02863	+	0.593880i	−0.112038	+	0.993704i	$0.535738\pi$
$318$	16.5410	+	2.06012i	0.927573	+	0.115526i
$319$	−23.0823	+	39.9797i	−1.29236	+	2.23843i
$320$	0.316274	+	2.39079i	0.0176803	+	0.133649i
$321$	−1.10297	+	0.0316684i	−0.0615618	+	0.00176756i
$322$	−3.91481	−	0.602130i	−0.218164	−	0.0335554i
$323$			12.5489i			0.698239i
$324$	17.6747	+	3.40667i	0.981927	+	0.189260i
$325$		−	22.0512i		−	1.22318i
$326$	−3.70041	+	24.0586i	−0.204947	+	1.33248i
$327$	16.1470	−	0.463612i	0.892931	−	0.0256378i
$328$	10.1454	−	6.78352i	0.560185	−	0.374557i
$329$	−1.32658	+	2.29770i	−0.0731366	+	0.126676i
$330$	0.508126	−	4.07982i	0.0279714	−	0.224587i
$331$	2.66939	−	1.54117i	0.146723	−	0.0847105i	−0.424841	−	0.905268i	$-0.639670\pi$
$331$	2.66939	−	1.54117i	0.146723	−	0.0847105i	0.571564	+	0.820557i	$0.306337\pi$
$332$	15.9499	−	3.53950i	0.875367	−	0.194255i
$333$	−1.30492	−	22.7056i	−0.0715090	−	1.24426i
$334$	−10.7934	+	13.4512i	−0.590589	+	0.736016i
$335$	0.938721	+	1.62591i	0.0512878	+	0.0888331i
$336$	−6.91649	−	0.402619i	−0.377326	−	0.0219646i
$337$	14.1875	−	24.5735i	0.772845	−	1.33861i	−0.163153	−	0.986601i	$-0.552166\pi$
$337$	14.1875	−	24.5735i	0.772845	−	1.33861i	0.935998	−	0.352006i	$-0.114500\pi$
$338$	−3.67968	−	9.45935i	−0.200148	−	0.514521i
$339$	−22.2399	−	12.0027i	−1.20791	−	0.651897i
$340$	0.747088	+	0.814962i	0.0405165	+	0.0441975i
$341$			8.88648i			0.481230i
$342$	−2.75995	+	28.9022i	−0.149241	+	1.56285i
$343$	−1.00000			−0.0539949
$344$	−30.6387	+	2.01778i	−1.65193	+	0.108791i
$345$	0.767223	+	1.24493i	0.0413059	+	0.0670248i
$346$	−4.49136	+	1.74713i	−0.241457	+	0.0939265i
$347$	3.91981	+	2.26310i	0.210426	+	0.121490i	0.601509	−	0.798866i	$-0.294566\pi$
$347$	3.91981	+	2.26310i	0.210426	+	0.121490i	−0.391083	+	0.920355i	$0.627900\pi$
$348$	−7.02454	−	27.8495i	−0.376555	−	1.49289i
$349$	7.68619	−	4.43762i	0.411432	−	0.237540i	−0.279973	−	0.960008i	$-0.590325\pi$
$349$	7.68619	−	4.43762i	0.411432	−	0.237540i	0.691405	+	0.722468i	$0.256992\pi$
$350$	−4.34494	+	5.41484i	−0.232247	+	0.289435i
$351$	9.88854	−	21.1423i	0.527811	−	1.12849i
$352$	−30.5979	−	7.47036i	−1.63087	−	0.398172i
$353$	−4.39741	−	7.61654i	−0.234051	−	0.405388i	0.724946	−	0.688806i	$-0.241865\pi$
$353$	−4.39741	−	7.61654i	−0.234051	−	0.405388i	−0.958996	+	0.283418i	$0.908531\pi$
$354$	−10.9825	+	14.5218i	−0.583713	+	0.771823i
$355$	−0.425146	−	0.245458i	−0.0225644	−	0.0130276i
$356$	6.82349	+	2.14987i	0.361644	+	0.113943i
$357$	−2.70392	+	1.66636i	−0.143106	+	0.0881933i
$358$	−0.145216	+	0.944136i	−0.00767489	+	0.0498991i
$359$	4.62054			0.243863			0.121931	−	0.992539i	$-0.461091\pi$
$359$	4.62054			0.243863			0.121931	+	0.992539i	$0.461091\pi$
$360$	1.54143	+	2.04130i	0.0812403	+	0.107586i
$361$	−27.8307			−1.46477
$362$	−1.85431	+	12.0560i	−0.0974605	+	0.633650i
$363$	30.4864	+	16.4533i	1.60012	+	0.863574i
$364$	−2.69969	+	8.56854i	−0.141502	+	0.449113i
$365$	3.57949	+	2.06662i	0.187359	+	0.108172i
$366$	13.2077	+	31.2661i	0.690377	+	1.63430i
$367$	3.91770	+	6.78566i	0.204502	+	0.354209i	0.949974	−	0.312329i	$-0.101109\pi$
$367$	3.91770	+	6.78566i	0.204502	+	0.354209i	−0.745472	+	0.666537i	$0.767776\pi$
$368$	10.1514	−	4.73881i	0.529176	−	0.247027i
$369$	5.81843	−	11.5633i	0.302895	−	0.601959i
$370$	2.02267	−	2.52074i	0.105154	−	0.131047i
$371$	−5.89331	+	3.40250i	−0.305965	+	0.176649i
$372$	−3.85149	−	3.96659i	−0.199690	−	0.205658i
$373$	5.41449	+	3.12605i	0.280351	+	0.161861i	0.633582	−	0.773675i	$-0.281584\pi$
$373$	5.41449	+	3.12605i	0.280351	+	0.161861i	−0.353231	+	0.935536i	$0.614917\pi$
$374$	−13.4569	+	5.23473i	−0.695841	+	0.270681i
$375$	5.17173	−	0.148491i	0.267067	−	0.00766802i
$376$	−0.493142	−	7.48804i	−0.0254319	−	0.386166i
$377$	−37.2433			−1.91813
$378$	−6.59405	+	3.24322i	−0.339161	+	0.166813i
$379$			29.1386i			1.49675i	0.663276	+	0.748375i	$0.269166\pi$
$379$			29.1386i			1.49675i	−0.663276	+	0.748375i	$0.730834\pi$
$380$	−3.04132	+	2.78802i	−0.156016	+	0.143023i
$381$	−0.233736	−	8.14073i	−0.0119747	−	0.417062i
$382$	−2.37177	−	6.09711i	−0.121350	−	0.311955i
$383$	19.2344	−	33.3150i	0.982833	−	1.70232i	0.331638	−	0.943407i	$-0.392399\pi$
$383$	19.2344	−	33.3150i	0.982833	−	1.70232i	0.651195	−	0.758911i	$-0.274268\pi$
$384$	16.8954	−	9.92693i	0.862192	−	0.506582i
$385$	0.839224	+	1.45358i	0.0427708	+	0.0740812i
$386$	−11.8868	+	14.8138i	−0.605022	+	0.754002i
$387$	−27.2236	+	17.8753i	−1.38385	+	0.908651i
$388$	−3.20941	−	14.4625i	−0.162933	−	0.734220i
$389$	21.3421	−	12.3219i	1.08209	−	0.624744i	0.150629	−	0.988590i	$-0.451870\pi$
$389$	21.3421	−	12.3219i	1.08209	−	0.624744i	0.931459	+	0.363847i	$0.118537\pi$
$390$	3.05540	−	1.29069i	0.154716	−	0.0653566i
$391$	2.56793	−	4.44779i	0.129866	−	0.224934i
$392$	2.35126	−	1.57212i	0.118757	−	0.0794043i
$393$	1.15523	−	2.14054i	0.0582736	−	0.107976i
$394$	4.20994	−	27.3714i	0.212094	−	1.37895i
$395$		−	4.74708i		−	0.238852i
$396$	−32.1448	+	9.09678i	−1.61534	+	0.457130i
$397$			15.8732i			0.796651i	0.917244	+	0.398326i	$0.130409\pi$
$397$			15.8732i			0.796651i	−0.917244	+	0.398326i	$0.869591\pi$
$398$	−30.6314	−	4.71135i	−1.53541	−	0.236159i
$399$	−6.21863	−	10.0906i	−0.311321	−	0.505163i
$400$	1.70328	−	19.5625i	0.0851642	−	0.978125i
$401$	−3.53681	+	6.12594i	−0.176620	+	0.305915i	−0.940721	−	0.339182i	$-0.889850\pi$
$401$	−3.53681	+	6.12594i	−0.176620	+	0.305915i	0.764101	+	0.645097i	$0.223183\pi$
$402$	9.20204	−	12.1675i	0.458956	−	0.606862i
$403$	−6.20870	+	3.58459i	−0.309277	+	0.178561i
$404$	26.5973	−	5.90228i	1.32326	−	0.293650i
$405$	2.48953	+	1.07843i	0.123706	+	0.0535874i
$406$	9.14537	+	7.33837i	0.453877	+	0.364197i
$407$	21.1050	+	36.5549i	1.04614	+	1.81196i
$408$	3.73788	−	8.16895i	0.185052	−	0.404423i
$409$	−4.14474	+	7.17890i	−0.204944	+	0.354974i	−0.950115	−	0.311900i	$-0.899035\pi$
$409$	−4.14474	+	7.17890i	−0.204944	+	0.354974i	0.745171	+	0.666874i	$0.232368\pi$
$410$	1.71437	−	0.666887i	0.0846666	−	0.0329352i
$411$	15.8183	−	9.74845i	0.780258	−	0.480856i
$412$	4.50904	−	4.13350i	0.222144	−	0.203643i
$413$		−	7.43300i		−	0.365754i
$414$	6.89259	−	9.67920i	0.338752	−	0.475707i
$415$	2.46256			0.120882
$416$	−7.12314	−	24.3911i	−0.349241	−	1.19587i
$417$	−3.40152	+	6.30270i	−0.166573	+	0.308645i
$418$	−19.5353	−	50.2193i	−0.955500	−	2.45631i
$419$	−8.25828	−	4.76792i	−0.403443	−	0.232928i	0.284525	−	0.958669i	$-0.408164\pi$
$419$	−8.25828	−	4.76792i	−0.403443	−	0.232928i	−0.687969	+	0.725740i	$0.741497\pi$
$420$	−1.00459	−	0.285094i	−0.0490191	−	0.0139112i
$421$	−18.1336	+	10.4694i	−0.883778	+	0.510250i	−0.871902	−	0.489680i	$-0.837114\pi$
$421$	−18.1336	+	10.4694i	−0.883778	+	0.510250i	−0.0118758	+	0.999929i	$0.503780\pi$
$422$	−1.26449	−	1.01465i	−0.0615545	−	0.0493922i
$423$	−4.36868	−	6.65340i	−0.212413	−	0.323500i
$424$	8.50754	−	17.2652i	0.413163	−	0.838471i
$425$	−4.50106	−	7.79606i	−0.218333	−	0.378164i
$426$	−0.493006	+	3.95842i	−0.0238862	+	0.191786i
$427$	−12.0001	−	6.92824i	−0.580724	−	0.335281i
$428$	−0.382884	+	1.21524i	−0.0185074	+	0.0587406i
$429$	1.24326	+	43.3011i	0.0600251	+	2.09060i
$430$	−4.57427	−	0.703560i	−0.220591	−	0.0339287i
$431$	13.0695			0.629538			0.314769	−	0.949168i	$-0.398073\pi$
$431$	13.0695			0.629538			0.314769	+	0.949168i	$0.398073\pi$
$432$	10.4056	−	17.9923i	0.500639	−	0.865656i
$433$	16.1917			0.778122			0.389061	−	0.921212i	$-0.372799\pi$
$433$	16.1917			0.778122			0.389061	+	0.921212i	$0.372799\pi$
$434$	2.23090	+	0.343130i	0.107086	+	0.0164708i
$435$	−0.124246	−	4.32734i	−0.00595715	−	0.207480i
$436$	5.60525	−	17.7905i	0.268443	−	0.852010i
$437$	16.5985	+	9.58315i	0.794014	+	0.458424i
$438$	4.15083	−	33.3277i	0.198334	−	1.59246i
$439$	−8.37236	−	14.5014i	−0.399591	−	0.692112i	0.594084	−	0.804403i	$-0.297515\pi$
$439$	−8.37236	−	14.5014i	−0.399591	−	0.692112i	−0.993675	+	0.112291i	$0.964181\pi$
$440$	−4.25844	−	2.09838i	−0.203013	−	0.100036i
$441$	1.34846	−	2.67986i	0.0642124	−	0.127612i
$442$	−9.08553	−	7.29036i	−0.432155	−	0.346767i
$443$	−23.2988	+	13.4516i	−1.10696	+	0.639104i	−0.938040	−	0.346526i	$-0.887361\pi$
$443$	−23.2988	+	13.4516i	−1.10696	+	0.639104i	−0.168920	+	0.985630i	$0.554028\pi$
$444$	−25.2637	−	7.16961i	−1.19896	−	0.340255i
$445$	0.933852	+	0.539160i	0.0442688	+	0.0255586i
$446$	0.759845	+	1.95334i	0.0359797	+	0.0924932i
$447$	7.35530	−	13.6287i	0.347894	−	0.644615i
$448$	−3.05685	+	7.39295i	−0.144422	+	0.349284i
$449$	−33.1778			−1.56576			−0.782878	−	0.622175i	$-0.786249\pi$
$449$	−33.1778			−1.56576			−0.782878	+	0.622175i	$0.786249\pi$
$450$	−8.65204	−	18.9455i	−0.407861	−	0.893101i
$451$			24.0246i			1.13128i
$452$	−21.5109	+	19.7194i	−1.01179	+	0.927520i
$453$	−4.32357	+	2.66452i	−0.203139	+	0.125190i
$454$	−4.74123	+	1.84433i	−0.222517	+	0.0865588i
$455$	−0.677045	+	1.17268i	−0.0317404	+	0.0549759i
$456$	30.4853	+	13.9492i	1.42761	+	0.653232i
$457$	−7.13823	−	12.3638i	−0.333912	−	0.578353i	0.649363	−	0.760478i	$-0.275036\pi$
$457$	−7.13823	−	12.3638i	−0.333912	−	0.578353i	−0.983275	+	0.182126i	$0.941702\pi$
$458$	24.6061	+	19.7443i	1.14977	+	0.922591i
$459$	−0.819502	−	9.49314i	−0.0382511	−	0.443102i
$460$	1.64848	−	0.365819i	0.0768608	−	0.0170564i
$461$	29.3672	−	16.9552i	1.36777	−	0.789682i	0.377126	−	0.926162i	$-0.376912\pi$
$461$	29.3672	−	16.9552i	1.36777	−	0.789682i	0.990643	+	0.136480i	$0.0435790\pi$
$462$	8.22670	−	10.8779i	0.382741	−	0.506085i
$463$	−2.62977	+	4.55490i	−0.122216	+	0.211684i	−0.920641	−	0.390410i	$-0.872333\pi$
$463$	−2.62977	+	4.55490i	−0.122216	+	0.211684i	0.798425	+	0.602094i	$0.205667\pi$
$464$	−33.0400	−	2.87675i	−1.53384	−	0.133550i
$465$	−0.437210	−	0.709436i	−0.0202751	−	0.0328993i
$466$	4.59902	+	0.707366i	0.213045	+	0.0327681i
$467$			33.6669i			1.55792i	0.627074	+	0.778960i	$0.284252\pi$
$467$			33.6669i			1.55792i	−0.627074	+	0.778960i	$0.715748\pi$
$468$	−19.3221	−	18.7891i	−0.893163	−	0.868527i
$469$			6.22798i			0.287581i
$470$	0.171949	−	1.11794i	0.00793140	−	0.0515669i
$471$	−1.45022	+	2.68713i	−0.0668228	+	0.123817i
$472$	11.6856	+	17.4769i	0.537873	+	0.804440i
$473$	30.2220	−	52.3461i	1.38961	−	2.40688i
$474$	−35.5327	+	15.0100i	−1.63207	+	0.689434i
$475$	29.0938	−	16.7973i	1.33491	−	0.770713i
$476$	0.794539	+	3.58040i	0.0364176	+	0.164107i
$477$	−1.17134	−	20.3814i	−0.0536321	−	0.933199i
$478$	−6.80348	+	8.47877i	−0.311184	+	0.387810i
$479$	−1.80943	−	3.13403i	−0.0826751	−	0.143197i	0.821723	−	0.569887i	$-0.193013\pi$
$479$	−1.80943	−	3.13403i	−0.0826751	−	0.143197i	−0.904398	+	0.426690i	$0.859680\pi$
$480$	2.81026	−	0.909015i	0.128270	−	0.0414907i
$481$	−17.0265	+	29.4908i	−0.776342	+	1.34466i
$482$	5.99726	+	15.4172i	0.273168	+	0.702233i
$483$	0.139225	+	4.84903i	0.00633496	+	0.220638i
$484$	29.4871	−	27.0313i	1.34032	−	1.22869i
$485$		−	2.23290i		−	0.101391i
$486$	0.200431	−	22.0445i	0.00909173	−	0.999959i
$487$	−21.0550			−0.954094			−0.477047	−	0.878878i	$-0.658293\pi$
$487$	−21.0550			−0.954094			−0.477047	+	0.878878i	$0.658293\pi$
$488$	39.1073	−	2.57550i	1.77030	−	0.116587i
$489$	29.7999	−	0.855612i	1.34760	−	0.0386921i
$490$	0.397316	−	0.154555i	0.0179489	−	0.00698210i
$491$	−7.65527	−	4.41977i	−0.345478	−	0.199462i	0.317214	−	0.948354i	$-0.397253\pi$
$491$	−7.65527	−	4.41977i	−0.345478	−	0.199462i	−0.662692	+	0.748892i	$0.730586\pi$
$492$	−10.4125	−	10.7237i	−0.469432	−	0.483460i
$493$	−13.1671	+	7.60204i	−0.593017	+	0.342379i
$494$	27.2066	−	33.9059i	1.22408	−	1.52550i
$495$	−5.02705	+	0.288911i	−0.225949	+	0.0129856i
$496$	−5.78486	+	2.70046i	−0.259748	+	0.121254i
$497$	−0.814252	−	1.41033i	−0.0365242	−	0.0632618i
$498$	−7.78649	−	18.4327i	−0.348921	−	0.825988i
$499$	−5.50168	−	3.17639i	−0.246289	−	0.142195i	0.371775	−	0.928323i	$-0.378749\pi$
$499$	−5.50168	−	3.17639i	−0.246289	−	0.142195i	−0.618064	+	0.786128i	$0.712083\pi$
$500$	1.79531	−	5.69813i	0.0802887	−	0.254828i
$501$	18.5879	+	10.0318i	0.830448	+	0.448186i
$502$	−3.11154	+	20.2300i	−0.138875	+	0.902911i
$503$	15.9155			0.709636			0.354818	−	0.934935i	$-0.384543\pi$
$503$	15.9155			0.709636			0.354818	+	0.934935i	$0.384543\pi$
$504$	1.04250	+	8.42100i	0.0464364	+	0.375101i
$505$	4.10643			0.182734
$506$	−3.35258	+	21.7971i	−0.149040	+	0.969001i
$507$	−10.5827	+	6.52190i	−0.469995	+	0.289648i
$508$	−8.96933	−	2.82596i	−0.397949	−	0.125382i
$509$	−29.4112	−	16.9806i	−1.30363	−	0.752651i	−0.322605	−	0.946534i	$-0.604559\pi$
$509$	−29.4112	−	16.9806i	−1.30363	−	0.752651i	−0.981025	+	0.193883i	$0.937892\pi$
$510$	0.816763	−	1.07998i	0.0361669	−	0.0478222i
$511$	6.85554	+	11.8741i	0.303271	+	0.525281i
$512$	−4.43519	−	22.1885i	−0.196010	−	0.980602i
$513$	35.4270	−	3.05826i	1.56414	−	0.135026i
$514$	−1.55217	+	1.93437i	−0.0684631	+	0.0853214i
$515$	0.798464	−	0.460994i	0.0351845	−	0.0203138i
$516$	9.19735	+	36.4638i	0.404891	+	1.60523i
$517$	12.7933	+	7.38621i	0.562648	+	0.324845i
$518$	9.99180	−	3.88680i	0.439015	−	0.170776i
$519$	3.09664	+	5.02474i	0.135927	+	0.220562i
$520$	−0.251685	−	3.82167i	−0.0110371	−	0.167591i
$521$	−18.6090			−0.815277			−0.407638	−	0.913143i	$-0.633648\pi$
$521$	−18.6090			−0.815277			−0.407638	+	0.913143i	$0.633648\pi$
$522$	−31.9980	+	14.6128i	−1.40051	+	0.639586i
$523$			30.0715i			1.31494i	0.753482	+	0.657468i	$0.228373\pi$
$523$			30.0715i			1.31494i	−0.753482	+	0.657468i	$0.771627\pi$
$524$	−1.89794	−	2.07037i	−0.0829118	−	0.0904445i
$525$	7.48267	+	4.03834i	0.326571	+	0.176248i
$526$	−1.69262	−	4.35123i	−0.0738018	−	0.189723i
$527$	−1.46336	+	2.53462i	−0.0637450	+	0.110410i
$528$	−2.24173	+	38.5101i	−0.0975586	+	1.67594i
$529$	7.57792	+	13.1253i	0.329475	+	0.570667i
$530$	1.81563	−	2.26271i	0.0788659	−	0.0982859i
$531$	19.9194	+	10.0231i	0.864428	+	0.434965i
$532$	−13.3615	+	2.96510i	−0.579296	+	0.128554i
$533$	−16.7852	+	9.69095i	−0.727049	+	0.419762i
$534$	1.08291	−	8.69484i	0.0468620	−	0.376262i
$535$	−0.0960221	+	0.166315i	−0.00415140	+	0.00719043i
$536$	−9.79116	−	14.6436i	−0.422914	−	0.632507i
$537$	1.16944	−	0.0335769i	0.0504651	−	0.00144895i
$538$	5.78190	−	37.5917i	0.249275	−	1.62069i
$539$			5.56786i			0.239825i
$540$	2.11866	−	2.30773i	0.0911728	−	0.0993089i
$541$		−	22.5393i		−	0.969041i	−0.874780	−	0.484521i	$-0.838994\pi$
$541$		−	22.5393i		−	0.969041i	0.874780	−	0.484521i	$-0.161006\pi$
$542$	−12.0284	−	1.85007i	−0.516665	−	0.0794672i
$543$	14.9330	−	0.428756i	0.640837	−	0.0183997i
$544$	−7.49701	−	7.16934i	−0.321431	−	0.307383i
$545$	1.40572	−	2.43478i	0.0602145	−	0.104295i
$546$	10.9185	+	1.35985i	0.467267	+	0.0581963i
$547$	2.88604	−	1.66625i	0.123398	−	0.0712439i	−0.437030	−	0.899447i	$-0.643970\pi$
$547$	2.88604	−	1.66625i	0.123398	−	0.0712439i	0.560429	+	0.828203i	$0.310636\pi$
$548$	−4.64816	−	20.9458i	−0.198559	−	0.894762i
$549$	34.7483	−	22.8160i	1.48302	−	0.973765i
$550$	30.1491	+	24.1921i	1.28556	+	1.03155i
$551$	−28.3697	−	49.1378i	−1.20859	−	2.09334i
$552$	−7.95063	−	11.1824i	−0.338401	−	0.475957i
$553$	7.87368	−	13.6376i	0.334823	−	0.579930i
$554$	3.07778	−	1.19725i	0.130762	−	0.0508664i
$555$	−3.48336	−	1.87994i	−0.147860	−	0.0797991i
$556$	5.58839	+	6.09610i	0.237000	+	0.258532i
$557$		−	6.63436i		−	0.281107i	−0.990073	−	0.140553i	$-0.955112\pi$
$557$		−	6.63436i		−	0.281107i	0.990073	−	0.140553i	$-0.0448882\pi$
$558$	−3.92781	+	5.51579i	−0.166278	+	0.233502i
$559$	48.7633			2.06247
$560$	−0.691213	+	0.988030i	−0.0292091	+	0.0417519i
$561$	9.27809	+	15.0550i	0.391721	+	0.635624i
$562$	4.14324	+	10.6510i	0.174772	+	0.449287i
$563$	22.3039	+	12.8771i	0.939995	+	0.542707i	0.889959	−	0.456041i	$-0.150733\pi$
$563$	22.3039	+	12.8771i	0.939995	+	0.542707i	0.0500365	+	0.998747i	$0.484066\pi$
$564$	−8.91169	+	2.24782i	−0.375250	+	0.0946501i
$565$	−3.80917	+	2.19922i	−0.160253	+	0.0925221i
$566$	−5.12359	−	4.11124i	−0.215361	−	0.172808i
$567$	5.36331	+	7.22737i	0.225238	+	0.303521i
$568$	4.13173	+	2.03594i	0.173363	+	0.0854260i
$569$	−1.80269	−	3.12235i	−0.0755727	−	0.130896i	0.825763	−	0.564018i	$-0.190745\pi$
$569$	−1.80269	−	3.12235i	−0.0755727	−	0.130896i	−0.901335	+	0.433122i	$0.857412\pi$
$570$	4.03032	+	3.04804i	0.168812	+	0.127668i
$571$	−10.0790	−	5.81912i	−0.421793	−	0.243522i	0.274051	−	0.961715i	$-0.411636\pi$
$571$	−10.0790	−	5.81912i	−0.421793	−	0.243522i	−0.695844	+	0.718193i	$0.744970\pi$
$572$	47.7084	+	15.0315i	1.99479	+	0.628498i
$573$	−6.82118	+	4.20375i	−0.284959	+	0.175614i
$574$	6.03123	+	0.927651i	0.251739	+	0.0387194i
$575$	−13.7492			−0.573381
$576$	−15.6900	−	18.1610i	−0.653752	−	0.756709i
$577$	38.5835			1.60625			0.803126	−	0.595810i	$-0.203169\pi$
$577$	38.5835			1.60625			0.803126	+	0.595810i	$0.203169\pi$
$578$	19.0620	+	2.93189i	0.792874	+	0.121950i
$579$	20.4709	+	11.0480i	0.850742	+	0.459139i
$580$	−4.76779	−	1.50219i	−0.197972	−	0.0623749i
$581$	7.07454	+	4.08449i	0.293501	+	0.169453i
$582$	−16.7137	+	7.06033i	−0.692803	+	0.292660i
$583$	18.9447	+	32.8131i	0.784608	+	1.35898i
$584$	−34.7868	−	17.1414i	−1.43949	−	0.709318i
$585$	−2.22964	−	3.39569i	−0.0921844	−	0.140395i
$586$	29.6895	+	23.8233i	1.22646	+	0.984130i
$587$	−28.5529	+	16.4850i	−1.17850	+	0.680409i	−0.955668	−	0.294447i	$-0.904864\pi$
$587$	−28.5529	+	16.4850i	−1.17850	+	0.680409i	−0.222835	+	0.974856i	$0.571531\pi$
$588$	−2.41317	−	2.48528i	−0.0995173	−	0.102491i
$589$	−9.45883	−	5.46106i	−0.389744	−	0.225019i
$590$	1.14881	+	2.95325i	0.0472957	+	0.121583i
$591$	−33.9032	+	0.973427i	−1.39459	+	0.0400414i
$592$	−17.3828	+	24.8472i	−0.714428	+	1.02121i
$593$	9.58622			0.393659			0.196829	−	0.980438i	$-0.436935\pi$
$593$	9.58622			0.393659			0.196829	+	0.980438i	$0.436935\pi$
$594$	18.0578	+	36.7148i	0.740921	+	1.50643i
$595$			0.552789i			0.0226621i
$596$	−12.0841	−	13.1819i	−0.494983	−	0.539954i
$597$	1.08936	+	37.9411i	0.0445847	+	1.55283i
$598$	−16.5813	+	6.45010i	−0.678060	+	0.263764i
$599$	17.1588	−	29.7199i	0.701090	−	1.21432i	−0.266994	−	0.963698i	$-0.586030\pi$
$599$	17.1588	−	29.7199i	0.701090	−	1.21432i	0.968084	−	0.250625i	$-0.0806363\pi$
$600$	−23.9425	+	2.26851i	−0.977448	+	0.0926116i
$601$	2.34179	+	4.05609i	0.0955235	+	0.165451i	0.909827	−	0.414988i	$-0.136214\pi$
$601$	2.34179	+	4.05609i	0.0955235	+	0.165451i	−0.814303	+	0.580439i	$0.802881\pi$
$602$	−11.9742	−	9.60826i	−0.488032	−	0.391603i
$603$	−16.6901	−	8.39818i	−0.679674	−	0.342001i
$604$	1.27047	+	5.72508i	0.0516947	+	0.232950i
$605$	5.22160	−	3.01469i	0.212288	−	0.122565i
$606$	−12.9843	−	30.7373i	−0.527453	−	1.24862i
$607$	−9.91054	+	17.1656i	−0.402256	+	0.696728i	−0.993998	−	0.109399i	$-0.965107\pi$
$607$	−9.91054	+	17.1656i	−0.402256	+	0.696728i	0.591742	+	0.806128i	$0.298441\pi$
$608$	26.7550	−	27.9777i	1.08506	−	1.13465i
$609$	6.82053	−	12.6378i	0.276382	−	0.512111i
$610$	5.83861	+	0.898026i	0.236398	+	0.0363600i
$611$			11.9177i			0.482137i
$612$	−10.6664	−	2.69878i	−0.431163	−	0.109092i
$613$		−	6.43092i		−	0.259742i	−0.991531	−	0.129871i	$-0.958544\pi$
$613$		−	6.43092i		−	0.259742i	0.991531	−	0.129871i	$-0.0414564\pi$
$614$	−3.81120	+	24.7789i	−0.153807	+	0.999995i
$615$	−1.18200	−	1.91796i	−0.0476627	−	0.0773396i
$616$	−8.75338	−	13.0915i	−0.352684	−	0.527471i
$617$	−3.25288	+	5.63416i	−0.130956	+	0.226823i	−0.924045	−	0.382283i	$-0.875138\pi$
$617$	−3.25288	+	5.63416i	−0.130956	+	0.226823i	0.793089	+	0.609105i	$0.208471\pi$
$618$	−5.97532	−	4.51900i	−0.240363	−	0.181781i
$619$	−12.6662	+	7.31285i	−0.509098	+	0.293928i	−0.732463	−	0.680807i	$-0.761629\pi$
$619$	−12.6662	+	7.31285i	−0.509098	+	0.293928i	0.223365	+	0.974735i	$0.428296\pi$
$620$	−0.939403	+	0.208466i	−0.0377273	+	0.00837219i
$621$	−13.1825	−	6.16562i	−0.528994	−	0.247418i
$622$	22.3055	−	27.7981i	0.894371	−	1.11460i
$623$	1.78854	+	3.09784i	0.0716563	+	0.124112i
$624$	−27.8100	+	13.9678i	−1.11329	+	0.559161i
$625$	−11.8226	+	20.4773i	−0.472903	+	0.819092i
$626$	6.16777	+	15.8555i	0.246514	+	0.633714i
$627$	−56.1832	+	34.6245i	−2.24374	+	1.38277i
$628$	2.38259	+	2.59905i	0.0950756	+	0.103713i
$629$			13.9017i			0.554296i
$630$	−0.121578	+	1.27316i	−0.00484378	+	0.0507240i
$631$	−10.0303			−0.399302			−0.199651	−	0.979867i	$-0.563981\pi$
$631$	−10.0303			−0.399302			−0.199651	+	0.979867i	$0.563981\pi$
$632$	2.92696	+	44.4440i	0.116428	+	1.76789i
$633$	−0.943047	+	1.74738i	−0.0374827	+	0.0694521i
$634$	27.8724	−	10.8423i	1.10696	−	0.430605i
$635$	−1.22753	−	0.708714i	−0.0487130	−	0.0281244i
$636$	−22.6777	−	6.43572i	−0.899230	−	0.255193i
$637$	−3.89009	+	2.24594i	−0.154131	+	0.0889875i
$638$	40.8591	−	50.9202i	1.61763	−	2.01595i
$639$	4.87746	−	0.280314i	0.192949	−	0.0110891i
$640$	0.0719145	−	3.40979i	0.00284267	−	0.134784i
$641$	−8.90354	−	15.4214i	−0.351669	−	0.609108i	0.634873	−	0.772616i	$-0.281052\pi$
$641$	−8.90354	−	15.4214i	−0.351669	−	0.609108i	−0.986542	+	0.163508i	$0.947719\pi$
$642$	1.54852	+	0.192862i	0.0611150	+	0.00761164i
$643$	−7.83524	−	4.52368i	−0.308992	−	0.178396i	0.337484	−	0.941331i	$-0.390424\pi$
$643$	−7.83524	−	4.52368i	−0.308992	−	0.178396i	−0.646475	+	0.762935i	$0.723758\pi$
$644$	5.34258	+	1.68329i	0.210527	+	0.0663307i
$645$	0.162678	+	5.66586i	0.00640543	+	0.223093i
$646$	2.69788	−	17.5406i	0.106147	−	0.690124i
$647$	−41.0889			−1.61537			−0.807685	−	0.589615i	$-0.799280\pi$
$647$	−41.0889			−1.61537			−0.807685	+	0.589615i	$0.799280\pi$
$648$	−23.9729	−	8.56164i	−0.941743	−	0.336333i
$649$	−41.3859			−1.62454
$650$	−4.74078	+	30.8227i	−0.185949	+	1.20897i
$651$	−0.0793388	−	2.76327i	−0.00310953	−	0.108301i
$652$	10.3447	−	32.8330i	0.405129	−	1.28584i
$653$	19.3213	+	11.1552i	0.756101	+	0.436535i	0.827894	−	0.560884i	$-0.189539\pi$
$653$	19.3213	+	11.1552i	0.756101	+	0.436535i	−0.0717930	+	0.997420i	$0.522872\pi$
$654$	−22.6696	−	2.82341i	−0.886450	−	0.110404i
$655$	−0.211670	−	0.366623i	−0.00827062	−	0.0143251i
$656$	−15.6394	+	7.30069i	−0.610615	+	0.285044i
$657$	−41.0655	+	2.36008i	−1.60212	+	0.0920757i
$658$	2.34824	−	2.92647i	0.0915440	−	0.114086i
$659$	40.9034	−	23.6156i	1.59337	−	0.919932i	0.600645	−	0.799516i	$-0.294910\pi$
$659$	40.9034	−	23.6156i	1.59337	−	0.919932i	0.992723	−	0.120416i	$-0.0384230\pi$
$660$	−1.58736	+	5.59343i	−0.0617881	+	0.217724i
$661$	9.98742	+	5.76624i	0.388466	+	0.224281i	0.681495	−	0.731823i	$-0.261330\pi$
$661$	9.98742	+	5.76624i	0.388466	+	0.224281i	−0.293029	+	0.956103i	$0.594663\pi$
$662$	−4.06254	+	1.58032i	−0.157895	+	0.0614211i
$663$	−6.77591	+	12.5551i	−0.263154	+	0.487601i
$664$	−23.0554	+	1.51837i	−0.894723	+	0.0589241i
$665$	−2.06293			−0.0799970
$666$	−3.05747	+	32.0178i	−0.118475	+	1.24067i
$667$			23.2216i			0.899146i
$668$	17.9786	−	16.4813i	0.695614	−	0.637680i
$669$	2.18531	−	1.34676i	0.0844889	−	0.0520687i
$670$	−0.962568	−	2.47448i	−0.0371873	−	0.0955974i
$671$	−38.5755	+	66.8147i	−1.48919	+	2.57935i
$672$	9.58116	+	2.04974i	0.369601	+	0.0790706i
$673$	17.0055	+	29.4544i	0.655515	+	1.13538i	0.981765	+	0.190101i	$0.0608816\pi$
$673$	17.0055	+	29.4544i	0.655515	+	1.13538i	−0.326250	+	0.945284i	$0.605785\pi$
$674$	−25.1141	+	31.2982i	−0.967358	+	1.20556i
$675$	−20.9123	+	14.6070i	−0.804914	+	0.562223i
$676$	3.10970	+	14.0132i	0.119604	+	0.538968i
$677$	17.6253	−	10.1760i	0.677396	−	0.391095i	−0.121477	−	0.992594i	$-0.538763\pi$
$677$	17.6253	−	10.1760i	0.677396	−	0.391095i	0.798873	+	0.601499i	$0.205430\pi$
$678$	28.5060	+	21.5584i	1.09477	+	0.827947i
$679$	3.70357	−	6.41477i	0.142130	−	0.246176i
$680$	−0.869053	−	1.29975i	−0.0333267	−	0.0498432i
$681$	3.26891	+	5.30428i	0.125265	+	0.203261i
$682$	1.91050	−	12.4213i	0.0731568	−	0.475637i
$683$		−	33.2209i		−	1.27116i	−0.772034	−	0.635582i	$-0.780760\pi$
$683$		−	33.2209i		−	1.27116i	0.772034	−	0.635582i	$-0.219240\pi$
$684$	10.0714	−	39.8054i	0.385091	−	1.52200i
$685$		−	3.23389i		−	0.123561i
$686$	1.39778	+	0.214989i	0.0533674	+	0.00820833i
$687$	18.3510	−	34.0028i	0.700135	−	1.29729i
$688$	43.2598	+	3.76658i	1.64927	+	0.143600i
$689$	−15.2836	+	26.4721i	−0.582261	+	1.00850i
$690$	−0.804760	−	1.90508i	−0.0306367	−	0.0725251i
$691$	8.74120	−	5.04673i	0.332531	−	0.191987i	−0.324433	−	0.945909i	$-0.605174\pi$
$691$	8.74120	−	5.04673i	0.332531	−	0.191987i	0.656964	+	0.753922i	$0.271840\pi$
$692$	6.65354	−	1.47651i	0.252929	−	0.0561284i
$693$	−14.9211	−	7.50804i	−0.566806	−	0.285207i
$694$	−4.99247	−	4.00603i	−0.189512	−	0.152067i
$695$	0.623252	+	1.07950i	0.0236413	+	0.0409479i
$696$	3.83139	+	40.4375i	0.145229	+	1.53278i
$697$	−3.95620	+	6.85234i	−0.149852	+	0.259551i
$698$	−11.6976	+	4.55036i	−0.442761	+	0.172234i
$699$	−0.163558	−	5.69651i	−0.00618633	−	0.215462i
$700$	7.23739	−	6.63462i	0.273548	−	0.250765i
$701$			0.148992i			0.00562734i	0.999996	+	0.00281367i	$0.000895621\pi$
$701$			0.148992i			0.00562734i	−0.999996	+	0.00281367i	$0.999104\pi$
$702$	−18.3673	+	27.4263i	−0.693230	+	1.03514i
$703$	−51.8791			−1.95666
$704$	41.1629	+	17.0201i	1.55139	+	0.641470i
$705$	−1.38473	+	0.0397582i	−0.0521518	+	0.00149738i
$706$	4.50912	+	11.5916i	0.169703	+	0.436256i
$707$	11.7971	+	6.81107i	0.443677	+	0.256157i
$708$	18.4731	−	17.9371i	0.694261	−	0.674116i
$709$	33.3995	−	19.2832i	1.25435	−	0.724197i	0.282377	−	0.959304i	$-0.408877\pi$
$709$	33.3995	−	19.2832i	1.25435	−	0.724197i	0.971970	+	0.235107i	$0.0755439\pi$
$710$	0.541489	+	0.434498i	0.0203217	+	0.0163064i
$711$	25.9296	+	39.4901i	0.972434	+	1.48100i
$712$	−9.07551	−	4.47202i	−0.340119	−	0.167596i
$713$	2.23504	+	3.87120i	0.0837027	+	0.144977i
$714$	4.13772	−	1.74789i	0.154850	−	0.0654132i
$715$	6.52930	+	3.76970i	0.244182	+	0.140979i
$716$	0.405958	−	1.28847i	0.0151714	−	0.0481524i
$717$	11.7167	+	6.32338i	0.437567	+	0.236151i
$718$	−6.45849	−	0.993368i	−0.241029	−	0.0370721i
$719$	−6.26103			−0.233497			−0.116749	−	0.993162i	$-0.537247\pi$
$719$	−6.26103			−0.233497			−0.116749	+	0.993162i	$0.537247\pi$
$720$	−1.71571	−	3.18467i	−0.0639408	−	0.118686i
$721$	3.05848			0.113904
$722$	38.9011	+	5.98330i	1.44775	+	0.222675i
$723$	17.2481	−	10.6296i	0.641462	−	0.395319i
$724$	5.18383	−	16.4530i	0.192656	−	0.611470i
$725$	35.2496	+	20.3514i	1.30914	+	0.755832i
$726$	−39.0760	−	29.5523i	−1.45024	−	1.09679i
$727$	−13.5643	−	23.4941i	−0.503073	−	0.871347i	−0.999994	−	0.00355153i	$-0.998870\pi$
$727$	−13.5643	−	23.4941i	−0.503073	−	0.871347i	0.496921	−	0.867796i	$-0.334464\pi$
$728$	5.61570	−	11.3965i	0.208132	−	0.422382i
$729$	−26.6006	+	4.62710i	−0.985206	+	0.171374i
$730$	−4.55903	−	3.65823i	−0.168737	−	0.135397i
$731$	17.2399	−	9.95349i	0.637642	−	0.368143i
$732$	−11.7395	−	46.5425i	−0.433905	−	1.72026i
$733$	−2.47212	−	1.42728i	−0.0913100	−	0.0527179i	0.453650	−	0.891180i	$-0.350122\pi$
$733$	−2.47212	−	1.42728i	−0.0913100	−	0.0527179i	−0.544960	+	0.838462i	$0.683455\pi$
$734$	−4.01723	−	10.3271i	−0.148279	−	0.381180i
$735$	−0.273936	−	0.444500i	−0.0101043	−	0.0163956i
$736$	−15.2081	+	4.44136i	−0.560579	+	0.163711i
$737$	34.6766			1.27733
$738$	−10.6188	+	14.9119i	−0.390885	+	0.548916i
$739$		−	36.6549i		−	1.34837i	−0.738561	−	0.674186i	$-0.764494\pi$
$739$		−	36.6549i		−	1.34837i	0.738561	−	0.674186i	$-0.235506\pi$
$740$	−3.36918	+	3.08857i	−0.123853	+	0.113538i
$741$	−46.8540	−	25.2867i	−1.72122	−	0.928930i
$742$	8.96903	−	3.48894i	0.329263	−	0.128083i
$743$	15.9243	−	27.5817i	0.584205	−	1.01187i	−0.410768	−	0.911740i	$-0.634740\pi$
$743$	15.9243	−	27.5817i	0.584205	−	1.01187i	0.994974	−	0.100134i	$-0.0319271\pi$
$744$	4.53075	+	6.37243i	0.166105	+	0.233625i
$745$	−1.34769	−	2.33427i	−0.0493756	−	0.0855211i
$746$	−6.89617	−	5.53358i	−0.252487	−	0.202599i
$747$	−20.4856	+	13.4510i	−0.749529	+	0.492147i
$748$	19.9352	−	4.42388i	0.728903	−	0.161753i
$749$	−0.551713	+	0.318531i	−0.0201591	+	0.0116389i
$750$	−7.26085	−	0.904311i	−0.265129	−	0.0330208i
$751$	26.0911	−	45.1910i	0.952076	−	1.64904i	0.211154	−	0.977453i	$-0.432278\pi$
$751$	26.0911	−	45.1910i	0.952076	−	1.64904i	0.740922	−	0.671591i	$-0.234389\pi$
$752$	−0.920546	+	10.5726i	−0.0335689	+	0.385544i
$753$	25.0577	−	0.719454i	0.913152	−	0.0262184i
$754$	52.0578	+	8.00692i	1.89583	+	0.291595i
$755$			0.883912i			0.0321689i
$756$	9.91427	−	3.11565i	0.360578	−	0.113315i
$757$		−	19.8648i		−	0.721999i	−0.932566	−	0.361000i	$-0.882436\pi$
$757$		−	19.8648i		−	0.721999i	0.932566	−	0.361000i	$-0.117564\pi$
$758$	6.26449	−	40.7293i	0.227537	−	1.47935i
$759$	26.9987	−	0.775186i	0.979992	−	0.0281375i
$760$	4.85048	−	3.24318i	0.175946	−	0.117643i
$761$	−14.9359	+	25.8697i	−0.541426	+	0.937778i	0.457396	+	0.889263i	$0.348782\pi$
$761$	−14.9359	+	25.8697i	−0.541426	+	0.937778i	−0.998822	+	0.0485146i	$0.984551\pi$
$762$	−1.42346	+	11.4292i	−0.0515665	+	0.414035i
$763$	8.07683	−	4.66316i	0.292401	−	0.168818i
$764$	2.00439	+	9.03230i	0.0725162	+	0.326777i
$765$	−1.48140	−	0.745414i	−0.0535601	−	0.0269505i
$766$	−34.0478	+	42.4317i	−1.23020	+	1.53312i
$767$	−16.6941	−	28.9150i	−0.602788	−	1.04406i
$768$	−25.7502	+	10.2433i	−0.929182	+	0.369623i
$769$	0.274706	−	0.475805i	0.00990615	−	0.0171580i	−0.861030	−	0.508554i	$-0.830180\pi$
$769$	0.274706	−	0.475805i	0.00990615	−	0.0171580i	0.870936	+	0.491396i	$0.163513\pi$
$770$	−0.860543	−	2.21220i	−0.0310118	−	0.0797222i
$771$	2.67307	+	1.44264i	0.0962683	+	0.0519553i
$772$	19.7999	−	18.1508i	0.712613	−	0.653263i
$773$		−	32.9181i		−	1.18398i	−0.805945	−	0.591991i	$-0.798342\pi$
$773$		−	32.9181i		−	1.18398i	0.805945	−	0.591991i	$-0.201658\pi$
$774$	41.8955	−	19.1328i	1.50590	−	0.687716i
$775$	7.83512			0.281446
$776$	1.37677	+	20.9053i	0.0494230	+	0.750456i
$777$	−6.88900	−	11.1784i	−0.247142	−	0.401023i
$778$	−32.4806	+	12.6349i	−1.16448	+	0.452983i
$779$	−25.5719	−	14.7640i	−0.916210	−	0.528974i
$780$	−4.54826	+	1.14722i	−0.162854	+	0.0410770i
$781$	−7.85250	+	4.53364i	−0.280985	+	0.162227i
$782$	−4.54562	+	5.66494i	−0.162551	+	0.202578i
$783$	24.6704	+	35.3197i	0.881648	+	1.26222i
$784$	−3.62453	+	1.69198i	−0.129447	+	0.0604280i
$785$	0.265721	+	0.460242i	0.00948399	+	0.0164267i
$786$	−2.07495	+	2.74363i	−0.0740108	+	0.0978620i
$787$	−15.9085	−	9.18476i	−0.567076	−	0.327402i	0.188905	−	0.981995i	$-0.439506\pi$
$787$	−15.9085	−	9.18476i	−0.567076	−	0.327402i	−0.755981	+	0.654594i	$0.772840\pi$
$788$	−11.7691	+	37.3540i	−0.419257	+	1.33068i
$789$	−4.86797	+	3.00002i	−0.173304	+	0.106804i
$790$	−1.02057	+	6.63536i	−0.0363103	+	0.236076i
$791$	−14.5908			−0.518791
$792$	46.8870	−	5.80447i	1.66606	−	0.206253i
$793$	−62.2417			−2.21027
$794$	3.41256	−	22.1871i	0.121107	−	0.787392i
$795$	−3.12680	−	1.68751i	−0.110896	−	0.0598498i
$796$	41.8029	+	13.1708i	1.48167	+	0.466828i
$797$	11.9227	+	6.88359i	0.422325	+	0.243829i	0.696071	−	0.717973i	$-0.254930\pi$
$797$	11.9227	+	6.88359i	0.422325	+	0.243829i	−0.273747	+	0.961802i	$0.588263\pi$
$798$	6.52288	+	15.4414i	0.230907	+	0.546619i
$799$	2.43261	+	4.21341i	0.0860597	+	0.149060i
$800$	−6.58654	+	26.9778i	−0.232869	+	0.953810i
$801$	−10.7136	+	0.615722i	−0.378545	+	0.0217555i
$802$	6.26069	−	7.80232i	0.221073	−	0.275510i
$803$	66.1136	−	38.1707i	2.33310	−	1.34702i
$804$	−15.4783	+	15.0292i	−0.545877	+	0.530038i
$805$	0.731177	+	0.422145i	0.0257706	+	0.0148787i
$806$	9.44902	−	3.67566i	0.332828	−	0.129470i
$807$	−46.5624	+	1.33690i	−1.63907	+	0.0470610i
$808$	−38.4460	+	2.53195i	−1.35252	+	0.0890736i
$809$	−24.5122			−0.861802			−0.430901	−	0.902399i	$-0.641804\pi$
$809$	−24.5122			−0.861802			−0.430901	+	0.902399i	$0.641804\pi$
$810$	−3.24796	−	2.04262i	−0.114122	−	0.0717704i
$811$			22.0933i			0.775801i	0.921701	+	0.387901i	$0.126800\pi$
$811$			22.0933i			0.775801i	−0.921701	+	0.387901i	$0.873200\pi$
$812$	−11.2055	−	12.2236i	−0.393237	−	0.428963i
$813$	0.427775	+	14.8988i	0.0150027	+	0.522525i
$814$	−21.6412	−	55.6330i	−0.758522	−	1.94994i
$815$	2.59431	−	4.49348i	0.0908747	−	0.157400i
$816$	−6.98095	+	10.6148i	−0.244382	+	0.371591i
$817$	37.1450	+	64.3370i	1.29954	+	2.25087i
$818$	7.33681	−	9.14343i	0.256526	−	0.319693i
$819$	−0.773187	−	13.4535i	−0.0270173	−	0.470102i
$820$	−2.53968	+	0.563588i	−0.0886894	+	0.0196813i
$821$	21.6475	−	12.4982i	0.755503	−	0.436190i	−0.0721761	−	0.997392i	$-0.522994\pi$
$821$	21.6475	−	12.4982i	0.755503	−	0.436190i	0.827679	+	0.561202i	$0.189661\pi$
$822$	−24.2062	+	10.2254i	−0.844289	+	0.356652i
$823$	−18.8687	+	32.6816i	−0.657723	+	1.13921i	0.323481	+	0.946235i	$0.395147\pi$
$823$	−18.8687	+	32.6816i	−0.657723	+	1.13921i	−0.981204	+	0.192975i	$0.938186\pi$
$824$	−7.19128	+	4.80831i	−0.250520	+	0.167506i
$825$	22.4849	−	41.6625i	0.782824	−	1.45050i
$826$	−1.59802	+	10.3897i	−0.0556021	+	0.361503i
$827$		−	19.8453i		−	0.690088i	−0.938586	−	0.345044i	$-0.887864\pi$
$827$		−	19.8453i		−	0.690088i	0.938586	−	0.345044i	$-0.112136\pi$
$828$	−11.7152	+	12.0475i	−0.407132	+	0.418681i
$829$			41.8793i			1.45453i	0.686357	+	0.727265i	$0.259209\pi$
$829$			41.8793i			1.45453i	−0.686357	+	0.727265i	$0.740791\pi$
$830$	−3.44211	−	0.529424i	−0.119477	−	0.0183766i
$831$	−2.12202	−	3.44329i	−0.0736122	−	0.119446i
$832$	4.71273	+	35.6247i	0.163385	+	1.23506i
$833$	−0.916875	+	1.58807i	−0.0317679	+	0.0550235i
$834$	6.10958	−	8.07848i	0.211557	−	0.279735i
$835$	3.18367	−	1.83809i	0.110176	−	0.0636099i
$836$	16.5093	+	74.3953i	0.570986	+	2.57301i
$837$	7.51216	+	3.51354i	0.259658	+	0.121446i
$838$	10.5182	+	8.43993i	0.363344	+	0.291553i
$839$	−7.51813	−	13.0218i	−0.259555	−	0.449562i	0.706568	−	0.707645i	$-0.250242\pi$
$839$	−7.51813	−	13.0218i	−0.259555	−	0.449562i	−0.966123	+	0.258083i	$0.916909\pi$
$840$	1.34290	+	0.614474i	0.0463346	+	0.0212014i
$841$	19.8724	−	34.4200i	0.685255	−	1.18690i
$842$	27.5976	−	10.7354i	0.951075	−	0.369967i
$843$	11.9159	−	7.34352i	0.410406	−	0.252924i
$844$	1.54934	+	1.69010i	0.0533305	+	0.0581757i
$845$			2.16353i			0.0744278i
$846$	4.67603	+	10.2392i	0.160765	+	0.352031i
$847$	20.0011			0.687246
$848$	−15.6035	+	22.3038i	−0.535825	+	0.765917i
$849$	−3.82113	+	7.08020i	−0.131141	+	0.242992i
$850$	4.61540	+	11.8648i	0.158307	+	0.406960i
$851$	18.3878	+	10.6162i	0.630327	+	0.363919i
$852$	1.54013	−	5.42700i	0.0527640	−	0.185926i
$853$	−43.7923	+	25.2835i	−1.49942	+	0.865689i	−1.00000		0.000671483i	$-0.999786\pi$
$853$	−43.7923	+	25.2835i	−1.49942	+	0.865689i	−0.499418	+	0.866361i	$0.666453\pi$
$854$	15.2839	+	12.2640i	0.523004	+	0.419666i
$855$	2.78178	−	5.52836i	0.0951348	−	0.189066i
$856$	0.796449	−	1.61631i	0.0272221	−	0.0552444i
$857$	−17.0111	−	29.4640i	−0.581087	−	1.00647i	−0.995351	−	0.0963156i	$-0.969294\pi$
$857$	−17.0111	−	29.4640i	−0.581087	−	1.00647i	0.414264	−	0.910157i	$-0.364039\pi$
$858$	7.57148	−	60.7926i	0.258486	−	2.07542i
$859$	−9.88151	−	5.70509i	−0.337153	−	0.194655i	0.321860	−	0.946787i	$-0.395692\pi$
$859$	−9.88151	−	5.70509i	−0.337153	−	0.194655i	−0.659012	+	0.752132i	$0.729025\pi$
$860$	6.24255	+	1.96684i	0.212869	+	0.0670686i
$861$	−0.214493	−	7.47050i	−0.00730989	−	0.254594i
$862$	−18.2683	−	2.80981i	−0.622221	−	0.0957026i
$863$	−46.0175			−1.56646			−0.783228	−	0.621735i	$-0.786428\pi$
$863$	−46.0175			−1.56646			−0.783228	+	0.621735i	$0.786428\pi$
$864$	−18.4128	+	22.9122i	−0.626417	+	0.779488i
$865$	1.02726			0.0349279
$866$	−22.6324	−	3.48104i	−0.769079	−	0.118291i
$867$	−0.677914	−	23.6109i	−0.0230232	−	0.801867i
$868$	−3.04452	−	0.959237i	−0.103338	−	0.0325586i
$869$	−75.9324	−	43.8396i	−2.57583	−	1.48716i
$870$	−0.756663	+	6.07536i	−0.0256533	+	0.205974i
$871$	13.9877	+	24.2274i	0.473955	+	0.820914i
$872$	−11.6597	+	23.6621i	−0.394846	+	0.801299i
$873$	12.1966	+	18.5751i	0.412792	+	0.628673i
$874$	−21.1407	−	16.9636i	−0.715096	−	0.573803i
$875$	2.58693	−	1.49357i	0.0874543	−	0.0504918i
$876$	−12.9670	+	45.6922i	−0.438115	+	1.54380i
$877$	6.62795	+	3.82665i	0.223810	+	0.129217i	0.607713	−	0.794157i	$-0.292087\pi$
$877$	6.62795	+	3.82665i	0.223810	+	0.129217i	−0.383903	+	0.923373i	$0.625420\pi$
$878$	8.58505	+	22.0696i	0.289732	+	0.744814i
$879$	22.1421	−	41.0274i	0.746836	−	1.38382i
$880$	5.50122	+	3.84858i	0.185446	+	0.129736i
$881$	50.9760			1.71742			0.858712	−	0.512459i	$-0.171265\pi$
$881$	50.9760			1.71742			0.858712	+	0.512459i	$0.171265\pi$
$882$	−2.46099	+	3.45594i	−0.0828658	+	0.116368i
$883$			21.1002i			0.710078i	0.934852	+	0.355039i	$0.115532\pi$
$883$			21.1002i			0.710078i	−0.934852	+	0.355039i	$0.884468\pi$
$884$	11.1322	+	12.1436i	0.374416	+	0.408433i
$885$	3.30397	−	2.03616i	0.111062	−	0.0684449i
$886$	35.4585	−	13.7933i	1.19125	−	0.463395i
$887$	13.9855	−	24.2236i	0.469588	−	0.813350i	−0.529808	−	0.848118i	$-0.677736\pi$
$887$	13.9855	−	24.2236i	0.469588	−	0.813350i	0.999395	+	0.0347680i	$0.0110692\pi$
$888$	33.7717	+	15.4529i	1.13330	+	0.518567i
$889$	−2.35100	−	4.07204i	−0.0788499	−	0.136572i
$890$	−1.18940	−	0.954393i	−0.0398689	−	0.0319913i
$891$	40.2410	−	29.8622i	1.34813	−	1.00042i
$892$	−0.642147	−	2.89369i	−0.0215007	−	0.0968878i
$893$	−15.7238	+	9.07817i	−0.526178	+	0.303789i
$894$	−13.2111	+	17.4686i	−0.441845	+	0.584236i
$895$	0.101809	−	0.176338i	0.00340310	−	0.00589434i
$896$	5.86220	−	9.67650i	0.195842	−	0.323269i
$897$	11.4322	+	18.5504i	0.381711	+	0.619381i
$898$	46.3751	+	7.13287i	1.54756	+	0.238027i
$899$		−	13.2331i		−	0.441348i
$900$	8.02053	+	28.3417i	0.267351	+	0.944724i
$901$			12.4787i			0.415725i
$902$	5.16504	−	33.5811i	0.171977	−	1.11813i
$903$	−8.93025	+	16.5469i	−0.297180	+	0.550647i
$904$	34.3069	−	22.9386i	1.14103	−	0.762928i
$905$	1.30004	−	2.25173i	0.0432146	−	0.0748499i
$906$	6.61624	−	2.79489i	0.219810	−	0.0928539i
$907$	−8.88873	+	5.13191i	−0.295145	+	0.170402i	−0.640260	−	0.768158i	$-0.721173\pi$
$907$	−8.88873	+	5.13191i	−0.295145	+	0.170402i	0.345115	+	0.938561i	$0.387840\pi$
$908$	7.02369	−	1.55865i	0.233089	−	0.0517256i
$909$	−34.1607	+	22.4302i	−1.13304	+	0.743963i
$910$	1.19847	−	1.49358i	0.0397289	−	0.0495118i
$911$	11.8894	+	20.5930i	0.393913	+	0.682277i	0.992962	−	0.118435i	$-0.0377878\pi$
$911$	11.8894	+	20.5930i	0.393913	+	0.682277i	−0.599049	+	0.800713i	$0.704454\pi$
$912$	−39.6128	−	26.0519i	−1.31171	−	0.862665i
$913$	22.7419	−	39.3901i	0.752646	−	1.30362i
$914$	7.31957	+	18.8164i	0.242110	+	0.622392i
$915$	−0.207642	−	7.23192i	−0.00686445	−	0.239080i
$916$	−30.1491	−	32.8882i	−0.996153	−	1.08666i
$917$		−	1.40433i		−	0.0463751i
$918$	−0.895444	+	13.4455i	−0.0295541	+	0.443767i
$919$	−19.2829			−0.636085			−0.318042	−	0.948076i	$-0.603025\pi$
$919$	−19.2829			−0.636085			−0.318042	+	0.948076i	$0.603025\pi$
$920$	−2.38285	+	0.156928i	−0.0785604	+	0.00517377i
$921$	30.6921	−	0.881229i	1.01134	−	0.0290375i
$922$	−44.6940	+	17.3859i	−1.47192	+	0.572575i
$923$	−6.33502	−	3.65753i	−0.208520	−	0.120389i
$924$	−13.8377	+	13.4362i	−0.455227	+	0.442018i
$925$	32.2301	−	18.6081i	1.05972	−	0.611829i
$926$	4.65509	−	5.80136i	0.152976	−	0.190645i
$927$	−4.12424	+	8.19630i	−0.135458	+	0.269202i
$928$	45.5640	+	11.1243i	1.49571	+	0.365173i
$929$	13.1023	+	22.6938i	0.429873	+	0.744561i	0.996862	−	0.0791643i	$-0.0252252\pi$
$929$	13.1023	+	22.6938i	0.429873	+	0.744561i	−0.566989	+	0.823725i	$0.691892\pi$
$930$	0.458601	+	1.08563i	0.0150381	+	0.0355992i
$931$	−5.92647	−	3.42165i	−0.194232	−	0.112140i
$932$	−6.27633	−	1.97748i	−0.205588	−	0.0647745i
$933$	−38.4136	−	20.7315i	−1.25761	−	0.678720i
$934$	7.23803	−	47.0588i	0.236836	−	1.53981i
$935$	3.07785			0.100657
$936$	22.9685	+	30.4170i	0.750748	+	0.994211i
$937$	−3.04363			−0.0994310			−0.0497155	−	0.998763i	$-0.515831\pi$
$937$	−3.04363			−0.0994310			−0.0497155	+	0.998763i	$0.515831\pi$
$938$	1.33895	−	8.70533i	0.0437183	−	0.284239i
$939$	17.7385	−	10.9318i	0.578873	−	0.356747i
$940$	−0.480692	+	1.52567i	−0.0156784	+	0.0497618i
$941$	−26.2823	−	15.1741i	−0.856779	−	0.494661i	0.00615357	−	0.999981i	$-0.498041\pi$
$941$	−26.2823	−	15.1741i	−0.856779	−	0.494661i	−0.862932	+	0.505320i	$0.831375\pi$
$942$	2.60480	−	3.44423i	0.0848688	−	0.112219i
$943$	6.04242	+	10.4658i	0.196768	+	0.340813i
$944$	−12.5765	−	26.9411i	−0.409330	−	0.876858i
$945$	1.56059	−	0.134719i	0.0507660	−	0.00438241i
$946$	−53.4975	+	66.6707i	−1.73935	+	2.16765i
$947$	−1.86205	+	1.07505i	−0.0605083	+	0.0349345i	−0.529949	−	0.848030i	$-0.677789\pi$
$947$	−1.86205	+	1.07505i	−0.0605083	+	0.0349345i	0.469441	+	0.882964i	$0.344456\pi$
$948$	52.8938	−	13.3415i	1.71791	−	0.433313i
$949$	53.3373	+	30.7943i	1.73140	+	0.999625i
$950$	−44.2778	+	17.2240i	−1.43656	+	0.558821i
$951$	−19.2171	−	31.1825i	−0.623157	−	1.01116i
$952$	−0.340839	−	5.17542i	−0.0110467	−	0.167736i
$953$	−5.38269			−0.174362			−0.0871812	−	0.996192i	$-0.527786\pi$
$953$	−5.38269			−0.174362			−0.0871812	+	0.996192i	$0.527786\pi$
$954$	−2.74450	+	28.7404i	−0.0888566	+	0.930506i
$955$			1.39452i			0.0451257i
$956$	11.3326	−	10.3887i	0.366522	−	0.335996i
$957$	−70.3657	−	37.9758i	−2.27460	−	1.22758i
$958$	1.85540	+	4.76968i	0.0599452	+	0.154101i
$959$	5.36384	−	9.29045i	0.173208	−	0.300004i
$960$	−4.12355	+	0.666423i	−0.133087	+	0.0215087i
$961$	14.2263	+	24.6407i	0.458914	+	0.794863i
$962$	30.1394	−	37.5610i	0.971735	−	1.21101i
$963$	−0.109657	−	1.90804i	−0.00353366	−	0.0614857i
$964$	−5.06830	−	22.8391i	−0.163239	−	0.735598i
$965$	3.50618	−	2.02430i	0.112868	−	0.0651644i
$966$	0.847884	−	6.80779i	0.0272802	−	0.219037i
$967$	−2.32271	+	4.02305i	−0.0746933	+	0.129373i	−0.900953	−	0.433917i	$-0.857131\pi$
$967$	−2.32271	+	4.02305i	−0.0746933	+	0.129373i	0.826260	+	0.563290i	$0.190464\pi$
$968$	−47.0278	+	31.4442i	−1.51153	+	1.01066i
$969$	−21.7264	+	0.623807i	−0.697952	+	0.0200396i
$970$	−0.480050	+	3.12110i	−0.0154135	+	0.100212i
$971$			48.3913i			1.55295i	0.630147	+	0.776476i	$0.282995\pi$
$971$			48.3913i			1.55295i	−0.630147	+	0.776476i	$0.717005\pi$
$972$	−5.01949	+	30.7702i	−0.161000	+	0.986954i
$973$			4.13499i			0.132562i
$974$	29.4302	+	4.52660i	0.943005	+	0.145042i
$975$	38.1781	−	1.09617i	1.22268	−	0.0351055i
$976$	−55.2170	−	4.80768i	−1.76745	−	0.153890i
$977$	14.4221	−	24.9797i	0.461402	−	0.799172i	−0.537629	−	0.843182i	$-0.680680\pi$
$977$	14.4221	−	24.9797i	0.461402	−	0.799172i	0.999031	+	0.0440094i	$0.0140131\pi$
$978$	−41.8375	−	5.21070i	−1.33782	−	0.166620i
$979$	17.2484	−	9.95834i	0.551260	−	0.318270i
$980$	−0.588587	+	0.130615i	−0.0188017	+	0.00417235i
$981$	1.60534	+	27.9329i	0.0512544	+	0.891827i
$982$	9.75016	+	7.82366i	0.311140	+	0.249663i
$983$	17.0109	+	29.4638i	0.542564	+	0.939748i	0.998756	+	0.0498669i	$0.0158797\pi$
$983$	17.0109	+	29.4638i	0.542564	+	0.939748i	−0.456192	+	0.889881i	$0.650787\pi$
$984$	12.2489	+	17.2279i	0.390480	+	0.549205i
$985$	−2.95154	+	5.11221i	−0.0940438	+	0.162889i
$986$	20.0391	−	7.79516i	0.638173	−	0.248249i
$987$	−4.04404	−	2.18254i	−0.128723	−	0.0694709i
$988$	−45.3181	+	41.5438i	−1.44176	+	1.32168i
$989$		−	30.4045i		−	0.966807i
$990$	7.08880	+	0.676929i	0.225297	+	0.0215142i
$991$	3.93755			0.125080			0.0625402	−	0.998042i	$-0.480080\pi$
$991$	3.93755			0.125080			0.0625402	+	0.998042i	$0.480080\pi$
$992$	8.66651	−	2.53095i	0.275162	−	0.0803579i
$993$	2.80098	+	4.54500i	0.0888866	+	0.144231i
$994$	0.834937	+	2.14638i	0.0264826	+	0.0680789i
$995$	5.72108	+	3.30307i	0.181371	+	0.104714i
$996$	6.92095	+	27.4388i	0.219299	+	0.869431i
$997$	−20.4948	+	11.8327i	−0.649077	+	0.374745i	−0.788102	−	0.615544i	$-0.788936\pi$
$997$	−20.4948	+	11.8327i	−0.649077	+	0.374745i	0.139026	+	0.990289i	$0.455603\pi$
$998$	7.00722	+	5.62269i	0.221810	+	0.177983i
$999$	39.2461	−	3.38795i	1.24169	−	0.107190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.2	✓	72
8.5	even	2	inner	504.2.cs.a.85.23	yes	72
9.7	even	3	inner	504.2.cs.a.421.23	yes	72
72.61	even	6	inner	504.2.cs.a.421.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.2	✓	72	1.1	even	1	trivial
504.2.cs.a.85.23	yes	72	8.5	even	2	inner
504.2.cs.a.421.2	yes	72	72.61	even	6	inner
504.2.cs.a.421.23	yes	72	9.7	even	3	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.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39778 - 0.214989i) q^{2} +(0.0497101 + 1.73134i) q^{3} +(1.90756 + 0.601014i) q^{4} +(0.261066 + 0.150726i) q^{5} +(0.302736 - 2.43071i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-2.53713 - 1.25019i) q^{8} +(-2.99506 + 0.172130i) q^{9} +O(q^{10})\)	\(q+(-1.39778 - 0.214989i) q^{2} +(0.0497101 + 1.73134i) q^{3} +(1.90756 + 0.601014i) q^{4} +(0.261066 + 0.150726i) q^{5} +(0.302736 - 2.43071i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-2.53713 - 1.25019i) q^{8} +(-2.99506 + 0.172130i) q^{9} +(-0.332507 - 0.266808i) q^{10} +(4.82191 - 2.78393i) q^{11} +(-0.945733 + 3.33250i) q^{12} +(3.89009 + 2.24594i) q^{13} +(-0.512702 - 1.31800i) q^{14} +(-0.247981 + 0.459485i) q^{15} +(3.27756 + 2.29294i) q^{16} +1.83375 q^{17} +(4.22343 + 0.403307i) q^{18} +6.84330i q^{19} +(0.407409 + 0.444424i) q^{20} +(-1.47453 + 0.908719i) q^{21} +(-7.33847 + 2.85466i) q^{22} +(1.40037 - 2.42551i) q^{23} +(2.03838 - 4.45477i) q^{24} +(-2.45456 - 4.25143i) q^{25} +(-4.95462 - 3.97565i) q^{26} +(-0.446899 - 5.17690i) q^{27} +(0.433286 + 1.95250i) q^{28} +(-7.18043 + 4.14562i) q^{29} +(0.445406 - 0.588945i) q^{30} +(-0.798016 + 1.38220i) q^{31} +(-4.08834 - 3.90966i) q^{32} +(5.05962 + 8.20997i) q^{33} +(-2.56317 - 0.394237i) q^{34} +0.301453i q^{35} +(-5.81670 - 1.47172i) q^{36} +7.58101i q^{37} +(1.47124 - 9.56540i) q^{38} +(-3.69511 + 6.84670i) q^{39} +(-0.473921 - 0.708794i) q^{40} +(-2.15744 + 3.73679i) q^{41} +(2.25642 - 0.953178i) q^{42} +(9.40147 - 5.42794i) q^{43} +(10.8713 - 2.41248i) q^{44} +(-0.807851 - 0.406497i) q^{45} +(-2.47887 + 3.08926i) q^{46} +(1.32658 + 2.29770i) q^{47} +(-3.80693 + 5.78855i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.51692 + 6.47025i) q^{50} +(0.0911559 + 3.17484i) q^{51} +(6.07073 + 6.62226i) q^{52} +6.80500i q^{53} +(-0.488313 + 7.33223i) q^{54} +1.67845 q^{55} +(-0.185870 - 2.82231i) q^{56} +(-11.8481 + 0.340181i) q^{57} +(10.9279 - 4.25094i) q^{58} +(-6.43716 - 3.71650i) q^{59} +(-0.749195 + 0.727456i) q^{60} +(-12.0001 + 6.92824i) q^{61} +(1.41261 - 1.76045i) q^{62} +(-1.64660 - 2.50773i) q^{63} +(4.87406 + 6.34378i) q^{64} +(0.677045 + 1.17268i) q^{65} +(-5.30717 - 12.5635i) q^{66} +(5.39359 + 3.11399i) q^{67} +(3.49799 + 1.10211i) q^{68} +(4.26899 + 2.30394i) q^{69} +(0.0648091 - 0.421363i) q^{70} -1.62850 q^{71} +(7.81405 + 3.30767i) q^{72} +13.7111 q^{73} +(1.62984 - 10.5966i) q^{74} +(7.23864 - 4.46102i) q^{75} +(-4.11292 + 13.0540i) q^{76} +(4.82191 + 2.78393i) q^{77} +(6.63690 - 8.77574i) q^{78} +(-7.87368 - 13.6376i) q^{79} +(0.510053 + 1.09262i) q^{80} +(8.94074 - 1.03108i) q^{81} +(3.81898 - 4.75937i) q^{82} +(7.07454 - 4.08449i) q^{83} +(-3.35890 + 0.847223i) q^{84} +(0.478729 + 0.276395i) q^{85} +(-14.3081 + 5.56583i) q^{86} +(-7.53441 - 12.2257i) q^{87} +(-15.7143 + 1.03490i) q^{88} +3.57708 q^{89} +(1.04180 + 0.741871i) q^{90} +4.49188i q^{91} +(4.12906 - 3.78517i) q^{92} +(-2.43273 - 1.31292i) q^{93} +(-1.36028 - 3.49687i) q^{94} +(-1.03146 + 1.78655i) q^{95} +(6.56571 - 7.27265i) q^{96} +(-3.70357 - 6.41477i) q^{97} +(0.885075 - 1.10302i) q^{98} +(-13.9627 + 9.16803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

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