LMFDB - Embedded newform 504.2.be.a.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(139,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 2, 3]))

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

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

chi := DirichletCharacter("504.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.be (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			139.2
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41404 + 0.0218513i) q^{2} +(1.61755 + 0.619288i) q^{3} +(1.99905 - 0.0617973i) q^{4} +(-0.694615 + 1.20311i) q^{5} +(-2.30083 - 0.840355i) q^{6} +(2.06001 + 1.66022i) q^{7} +(-2.82539 + 0.131066i) q^{8} +(2.23297 + 2.00346i) q^{9} +O(q^{10})$	\(q+(-1.41404 + 0.0218513i) q^{2} +(1.61755 + 0.619288i) q^{3} +(1.99905 - 0.0617973i) q^{4} +(-0.694615 + 1.20311i) q^{5} +(-2.30083 - 0.840355i) q^{6} +(2.06001 + 1.66022i) q^{7} +(-2.82539 + 0.131066i) q^{8} +(2.23297 + 2.00346i) q^{9} +(0.955927 - 1.71643i) q^{10} +(-0.332753 - 0.576345i) q^{11} +(3.27183 + 1.13802i) q^{12} +(-2.27990 + 3.94891i) q^{13} +(-2.94923 - 2.30262i) q^{14} +(-1.86865 + 1.51593i) q^{15} +(3.99236 - 0.247071i) q^{16} -2.18303i q^{17} +(-3.20129 - 2.78419i) q^{18} +0.684648i q^{19} +(-1.31422 + 2.44799i) q^{20} +(2.30403 + 3.96124i) q^{21} +(0.483121 + 0.807706i) q^{22} +(-1.94657 - 1.12385i) q^{23} +(-4.65139 - 1.53772i) q^{24} +(1.53502 + 2.65873i) q^{25} +(3.13759 - 5.63375i) q^{26} +(2.37122 + 4.62356i) q^{27} +(4.22066 + 3.19156i) q^{28} +(-2.39216 + 1.38112i) q^{29} +(2.60923 - 2.18442i) q^{30} +(1.01501 - 1.75805i) q^{31} +(-5.63998 + 0.436608i) q^{32} +(-0.181323 - 1.13834i) q^{33} +(0.0477019 + 3.08690i) q^{34} +(-3.42835 + 1.32520i) q^{35} +(4.58761 + 3.86702i) q^{36} -10.7978i q^{37} +(-0.0149604 - 0.968123i) q^{38} +(-6.13337 + 4.97566i) q^{39} +(1.80487 - 3.49029i) q^{40} +(4.19523 + 2.42212i) q^{41} +(-3.34456 - 5.55103i) q^{42} +(-3.14828 - 5.45299i) q^{43} +(-0.700804 - 1.13158i) q^{44} +(-3.96144 + 1.29486i) q^{45} +(2.77709 + 1.54664i) q^{46} +(3.21524 + 5.56896i) q^{47} +(6.61087 + 2.07277i) q^{48} +(1.48732 + 6.84017i) q^{49} +(-2.22868 - 3.72602i) q^{50} +(1.35192 - 3.53116i) q^{51} +(-4.31359 + 8.03493i) q^{52} +0.320076i q^{53} +(-3.45405 - 6.48610i) q^{54} +0.924540 q^{55} +(-6.03794 - 4.42078i) q^{56} +(-0.423994 + 1.10746i) q^{57} +(3.35245 - 2.00523i) q^{58} +(12.2327 + 7.06256i) q^{59} +(-3.64183 + 3.14588i) q^{60} +(2.23796 + 3.87627i) q^{61} +(-1.39685 + 2.50814i) q^{62} +(1.27374 + 7.83438i) q^{63} +(7.96564 - 0.740624i) q^{64} +(-3.16731 - 5.48594i) q^{65} +(0.281272 + 1.60570i) q^{66} +(-7.10490 + 12.3061i) q^{67} +(-0.134905 - 4.36397i) q^{68} +(-2.45269 - 3.02337i) q^{69} +(4.81888 - 1.94881i) q^{70} +1.76784i q^{71} +(-6.57158 - 5.36790i) q^{72} -8.84044i q^{73} +(0.235945 + 15.2685i) q^{74} +(0.836458 + 5.25126i) q^{75} +(0.0423094 + 1.36864i) q^{76} +(0.271386 - 1.73972i) q^{77} +(8.56414 - 7.16982i) q^{78} +(11.0680 - 6.39012i) q^{79} +(-2.47590 + 4.97486i) q^{80} +(0.972271 + 8.94733i) q^{81} +(-5.98518 - 3.33331i) q^{82} +(-8.81951 + 5.09195i) q^{83} +(4.85065 + 7.77632i) q^{84} +(2.62642 + 1.51636i) q^{85} +(4.57097 + 7.64197i) q^{86} +(-4.72476 + 0.752593i) q^{87} +(1.01569 + 1.58479i) q^{88} -10.9341i q^{89} +(5.57335 - 1.91756i) q^{90} +(-11.2527 + 4.34966i) q^{91} +(-3.96073 - 2.12634i) q^{92} +(2.73057 - 2.21516i) q^{93} +(-4.66818 - 7.80450i) q^{94} +(-0.823706 - 0.475567i) q^{95} +(-9.39336 - 2.78653i) q^{96} +(-0.0581560 + 0.0335764i) q^{97} +(-2.25260 - 9.63980i) q^{98} +(0.411660 - 1.95362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41404	+	0.0218513i	−0.999881	+	0.0154512i
$2$	−1.41404	+	0.0218513i	−0.999881	+	0.0154512i
$3$	1.61755	+	0.619288i	0.933896	+	0.357546i
$3$	1.61755	+	0.619288i	0.933896	+	0.357546i
$4$	1.99905	−	0.0617973i	0.999523	−	0.0308986i
$5$	−0.694615	+	1.20311i	−0.310641	+	0.538047i	−0.978501	−	0.206240i	$-0.933877\pi$
$5$	−0.694615	+	1.20311i	−0.310641	+	0.538047i	0.667860	+	0.744287i	$0.267210\pi$
$6$	−2.30083	−	0.840355i	−0.939309	−	0.343073i
$7$	2.06001	+	1.66022i	0.778612	+	0.627505i
$7$	2.06001	+	1.66022i	0.778612	+	0.627505i
$8$	−2.82539	+	0.131066i	−0.998926	+	0.0463388i
$9$	2.23297	+	2.00346i	0.744322	+	0.667821i
$10$	0.955927	−	1.71643i	0.302291	−	0.542782i
$11$	−0.332753	−	0.576345i	−0.100329	−	0.173774i	0.811491	−	0.584364i	$-0.198656\pi$
$11$	−0.332753	−	0.576345i	−0.100329	−	0.173774i	−0.911820	+	0.410590i	$0.865323\pi$
$12$	3.27183	+	1.13802i	0.944497	+	0.328519i
$13$	−2.27990	+	3.94891i	−0.632331	+	1.09523i	0.354743	+	0.934964i	$0.384568\pi$
$13$	−2.27990	+	3.94891i	−0.632331	+	1.09523i	−0.987074	+	0.160265i	$0.948765\pi$
$14$	−2.94923	−	2.30262i	−0.788215	−	0.615400i
$15$	−1.86865	+	1.51593i	−0.482483	+	0.391411i
$16$	3.99236	−	0.247071i	0.998091	−	0.0617678i
$17$		−	2.18303i		−	0.529462i	−0.964322	−	0.264731i	$-0.914717\pi$
$17$		−	2.18303i		−	0.529462i	0.964322	−	0.264731i	$-0.0852831\pi$
$18$	−3.20129	−	2.78419i	−0.754552	−	0.656241i
$19$			0.684648i			0.157069i	0.996911	+	0.0785345i	$0.0250241\pi$
$19$			0.684648i			0.157069i	−0.996911	+	0.0785345i	$0.974976\pi$
$20$	−1.31422	+	2.44799i	−0.293868	+	0.547388i
$21$	2.30403	+	3.96124i	0.502780	+	0.864414i
$22$	0.483121	+	0.807706i	0.103002	+	0.172204i
$23$	−1.94657	−	1.12385i	−0.405887	−	0.234339i	0.283134	−	0.959080i	$-0.408626\pi$
$23$	−1.94657	−	1.12385i	−0.405887	−	0.234339i	−0.689021	+	0.724741i	$0.741959\pi$
$24$	−4.65139	−	1.53772i	−0.949461	−	0.313886i
$25$	1.53502	+	2.65873i	0.307004	+	0.531746i
$26$	3.13759	−	5.63375i	0.615333	−	1.10487i
$27$	2.37122	+	4.62356i	0.456342	+	0.889804i
$28$	4.22066	+	3.19156i	0.797629	+	0.603148i
$29$	−2.39216	+	1.38112i	−0.444213	+	0.256467i	−0.705383	−	0.708826i	$-0.749225\pi$
$29$	−2.39216	+	1.38112i	−0.444213	+	0.256467i	0.261170	+	0.965293i	$0.415892\pi$
$30$	2.60923	−	2.18442i	0.476377	−	0.398819i
$31$	1.01501	−	1.75805i	0.182301	−	0.315755i	−0.760363	−	0.649499i	$-0.774979\pi$
$31$	1.01501	−	1.75805i	0.182301	−	0.315755i	0.942664	+	0.333744i	$0.108312\pi$
$32$	−5.63998	+	0.436608i	−0.997017	+	0.0771821i
$33$	−0.181323	−	1.13834i	−0.0315642	−	0.198159i
$34$	0.0477019	+	3.08690i	0.00818080	+	0.529398i
$35$	−3.42835	+	1.32520i	−0.579496	+	0.224000i
$36$	4.58761	+	3.86702i	0.764601	+	0.644504i
$37$		−	10.7978i		−	1.77514i	−0.460668	−	0.887572i	$-0.652390\pi$
$37$		−	10.7978i		−	1.77514i	0.460668	−	0.887572i	$-0.347610\pi$
$38$	−0.0149604	−	0.968123i	−0.00242690	−	0.157050i
$39$	−6.13337	+	4.97566i	−0.982126	+	0.796743i
$40$	1.80487	−	3.49029i	0.285375	−	0.551863i
$41$	4.19523	+	2.42212i	0.655186	+	0.378272i	0.790440	−	0.612539i	$-0.209852\pi$
$41$	4.19523	+	2.42212i	0.655186	+	0.378272i	−0.135255	+	0.990811i	$0.543185\pi$
$42$	−3.34456	−	5.55103i	−0.516077	−	0.856542i
$43$	−3.14828	−	5.45299i	−0.480109	−	0.831573i	0.519631	−	0.854391i	$-0.326069\pi$
$43$	−3.14828	−	5.45299i	−0.480109	−	0.831573i	−0.999740	+	0.0228181i	$0.992736\pi$
$44$	−0.700804	−	1.13158i	−0.105650	−	0.170591i
$45$	−3.96144	+	1.29486i	−0.590536	+	0.193027i
$46$	2.77709	+	1.54664i	0.409460	+	0.228040i
$47$	3.21524	+	5.56896i	0.468991	+	0.812316i	0.999372	−	0.0354433i	$-0.0112843\pi$
$47$	3.21524	+	5.56896i	0.468991	+	0.812316i	−0.530381	+	0.847760i	$0.677951\pi$
$48$	6.61087	+	2.07277i	0.954197	+	0.299178i
$49$	1.48732	+	6.84017i	0.212474	+	0.977167i
$50$	−2.22868	−	3.72602i	−0.315183	−	0.526939i
$51$	1.35192	−	3.53116i	0.189307	−	0.494462i
$52$	−4.31359	+	8.03493i	−0.598188	+	1.11424i
$53$			0.320076i			0.0439659i	0.999758	+	0.0219829i	$0.00699795\pi$
$53$			0.320076i			0.0439659i	−0.999758	+	0.0219829i	$0.993002\pi$
$54$	−3.45405	−	6.48610i	−0.470036	−	0.882647i
$55$	0.924540			0.124665
$56$	−6.03794	−	4.42078i	−0.806854	−	0.590751i
$57$	−0.423994	+	1.10746i	−0.0561594	+	0.146686i
$58$	3.35245	−	2.00523i	0.440198	−	0.263300i
$59$	12.2327	+	7.06256i	1.59256	+	0.919467i	0.992865	+	0.119240i	$0.0380458\pi$
$59$	12.2327	+	7.06256i	1.59256	+	0.919467i	0.599698	+	0.800227i	$0.295288\pi$
$60$	−3.64183	+	3.14588i	−0.470158	+	0.406132i
$61$	2.23796	+	3.87627i	0.286542	+	0.496305i	0.972982	−	0.230881i	$-0.0741609\pi$
$61$	2.23796	+	3.87627i	0.286542	+	0.496305i	−0.686440	+	0.727186i	$0.740828\pi$
$62$	−1.39685	+	2.50814i	−0.177401	+	0.318534i
$63$	1.27374	+	7.83438i	0.160477	+	0.987040i
$64$	7.96564	−	0.740624i	0.995705	−	0.0925779i
$65$	−3.16731	−	5.48594i	−0.392856	−	0.680447i
$66$	0.281272	+	1.60570i	0.0346222	+	0.197648i
$67$	−7.10490	+	12.3061i	−0.868002	+	1.50342i	−0.00396741	+	0.999992i	$0.501263\pi$
$67$	−7.10490	+	12.3061i	−0.868002	+	1.50342i	−0.864035	+	0.503432i	$0.832070\pi$
$68$	−0.134905	−	4.36397i	−0.0163596	−	0.529209i
$69$	−2.45269	−	3.02337i	−0.295269	−	0.363972i
$70$	4.81888	−	1.94881i	0.575966	−	0.232928i
$71$			1.76784i			0.209804i	0.994483	+	0.104902i	$0.0334529\pi$
$71$			1.76784i			0.209804i	−0.994483	+	0.104902i	$0.966547\pi$
$72$	−6.57158	−	5.36790i	−0.774468	−	0.632613i
$73$		−	8.84044i		−	1.03470i	−0.855775	−	0.517348i	$-0.826919\pi$
$73$		−	8.84044i		−	1.03470i	0.855775	−	0.517348i	$-0.173081\pi$
$74$	0.235945	+	15.2685i	0.0274281	+	1.77493i
$75$	0.836458	+	5.25126i	0.0965859	+	0.606364i
$76$	0.0423094	+	1.36864i	0.00485322	+	0.156994i
$77$	0.271386	−	1.73972i	0.0309273	−	0.198260i
$78$	8.56414	−	7.16982i	0.969698	−	0.811822i
$79$	11.0680	−	6.39012i	1.24525	−	0.718945i	0.275091	−	0.961418i	$-0.411292\pi$
$79$	11.0680	−	6.39012i	1.24525	−	0.718945i	0.970158	+	0.242473i	$0.0779587\pi$
$80$	−2.47590	+	4.97486i	−0.276814	+	0.556207i
$81$	0.972271	+	8.94733i	0.108030	+	0.994148i
$82$	−5.98518	−	3.33331i	−0.660952	−	0.368103i
$83$	−8.81951	+	5.09195i	−0.968067	+	0.558914i	−0.898646	−	0.438674i	$-0.855448\pi$
$83$	−8.81951	+	5.09195i	−0.968067	+	0.558914i	−0.0694207	+	0.997587i	$0.522115\pi$
$84$	4.85065	+	7.77632i	0.529250	+	0.848466i
$85$	2.62642	+	1.51636i	0.284875	+	0.164473i
$86$	4.57097	+	7.64197i	0.492900	+	0.824055i
$87$	−4.72476	+	0.752593i	−0.506548	+	0.0806865i
$88$	1.01569	+	1.58479i	0.108273	+	0.168939i
$89$		−	10.9341i		−	1.15901i	−0.814967	−	0.579507i	$-0.803245\pi$
$89$		−	10.9341i		−	1.15901i	0.814967	−	0.579507i	$-0.196755\pi$
$90$	5.57335	−	1.91756i	0.587483	−	0.202128i
$91$	−11.2527	+	4.34966i	−1.17960	+	0.455968i
$92$	−3.96073	−	2.12634i	−0.412934	−	0.221686i
$93$	2.73057	−	2.21516i	0.283147	−	0.229701i
$94$	−4.66818	−	7.80450i	−0.481486	−	0.804973i
$95$	−0.823706	−	0.475567i	−0.0845104	−	0.0487921i
$96$	−9.39336	−	2.78653i	−0.958706	−	0.284399i
$97$	−0.0581560	+	0.0335764i	−0.00590484	+	0.00340916i	−0.502950	−	0.864316i	$-0.667752\pi$
$97$	−0.0581560	+	0.0335764i	−0.00590484	+	0.00340916i	0.497045	+	0.867725i	$0.334419\pi$
$98$	−2.25260	−	9.63980i	−0.227547	−	0.973767i
$99$	0.411660	−	1.95362i	0.0413734	−	0.196346i
$100$	3.23288	+	5.22007i	0.323288	+	0.522007i
$101$	−5.02924	−	8.71091i	−0.500429	−	0.866768i	−1.00000		0.000494902i	$-0.999842\pi$
$101$	−5.02924	−	8.71091i	−0.500429	−	0.866768i	0.499571	−	0.866273i	$-0.333491\pi$
$102$	−1.83452	+	5.02276i	−0.181644	+	0.497328i
$103$	4.83465	−	8.37386i	0.476372	−	0.825101i	−0.523261	−	0.852172i	$-0.675285\pi$
$103$	4.83465	−	8.37386i	0.476372	−	0.825101i	0.999634	+	0.0270712i	$0.00861807\pi$
$104$	5.92404	−	11.4560i	0.580900	−	1.12335i
$105$	−6.36622	+	0.0204584i	−0.621279	+	0.00199654i
$106$	−0.00699407	−	0.452602i	−0.000679324	−	0.0439606i
$107$	13.7306			1.32739			0.663693	−	0.748005i	$-0.268988\pi$
$107$	13.7306			1.32739			0.663693	+	0.748005i	$0.268988\pi$
$108$	5.02591	+	9.09617i	0.483618	+	0.875279i
$109$		−	12.7853i		−	1.22461i	−0.790621	−	0.612306i	$-0.790242\pi$
$109$		−	12.7853i		−	1.22461i	0.790621	−	0.612306i	$-0.209758\pi$
$110$	−1.30734	+	0.0202024i	−0.124650	+	0.00192622i
$111$	6.68693	−	17.4660i	0.634696	−	1.65780i
$112$	8.63452	+	6.11924i	0.815885	+	0.578214i
$113$	9.06262	−	15.6969i	0.852540	−	1.47664i	−0.0263693	−	0.999652i	$-0.508395\pi$
$113$	9.06262	−	15.6969i	0.852540	−	1.47664i	0.878909	−	0.476990i	$-0.158272\pi$
$114$	0.575347	−	1.57526i	0.0538862	−	0.147536i
$115$	2.70423	−	1.56129i	0.252171	−	0.145591i
$116$	−4.69669	+	2.90874i	−0.436077	+	0.270070i
$117$	−13.0024	+	4.25007i	−1.20207	+	0.392919i
$118$	−17.4519	−	9.71947i	−1.60658	−	0.894750i
$119$	3.62431	−	4.49706i	0.332240	−	0.412245i
$120$	5.08097	−	4.52800i	0.463827	−	0.413348i
$121$	5.27855	−	9.14272i	0.479868	−	0.831156i
$122$	−3.24928	−	5.43231i	−0.294176	−	0.491818i
$123$	5.28603	+	6.51597i	0.476625	+	0.587525i
$124$	1.92041	−	3.57714i	0.172458	−	0.321237i
$125$	−11.2111			−1.00276
$126$	−1.97232	−	11.0503i	−0.175708	−	0.984442i
$127$			2.00605i			0.178008i	0.996031	+	0.0890041i	$0.0283684\pi$
$127$			2.00605i			0.178008i	−0.996031	+	0.0890041i	$0.971632\pi$
$128$	−11.2476	+	1.22133i	−0.994156	+	0.107952i
$129$	−1.71555	−	10.7702i	−0.151046	−	0.948263i
$130$	4.59859	+	7.68815i	0.403323	+	0.674296i
$131$	0.603178	+	0.348245i	0.0526999	+	0.0304263i	0.526118	−	0.850411i	$-0.323647\pi$
$131$	0.603178	+	0.348245i	0.0526999	+	0.0304263i	−0.473419	+	0.880838i	$0.656980\pi$
$132$	−0.432818	−	2.26438i	−0.0376720	−	0.197089i
$133$	−1.13667	+	1.41038i	−0.0985616	+	0.122296i
$134$	9.77775	−	17.5566i	0.844669	−	1.51666i
$135$	−7.20973	−	0.358754i	−0.620515	−	0.0308766i
$136$	0.286120	+	6.16790i	0.0245346	+	0.528893i
$137$	−6.40150	−	11.0877i	−0.546917	−	0.947289i	−0.998484	−	0.0550509i	$-0.982468\pi$
$137$	−6.40150	−	11.0877i	−0.546917	−	0.947289i	0.451566	−	0.892238i	$-0.350865\pi$
$138$	3.53428	+	4.22159i	0.300858	+	0.359366i
$139$	−8.15916	−	4.71069i	−0.692051	−	0.399556i	0.112329	−	0.993671i	$-0.464169\pi$
$139$	−8.15916	−	4.71069i	−0.692051	−	0.399556i	−0.804380	+	0.594115i	$0.797502\pi$
$140$	−6.77152	+	2.86101i	−0.572298	+	0.241799i
$141$	1.75204	+	10.9993i	0.147548	+	0.926304i
$142$	−0.0386295	−	2.49980i	−0.00324171	−	0.209779i
$143$	3.03457			0.253764
$144$	9.40981	+	7.44685i	0.784150	+	0.620571i
$145$		−	3.83737i		−	0.318677i
$146$	0.193175	+	12.5008i	0.0159872	+	1.03457i
$147$	−1.83022	+	11.9854i	−0.150954	+	0.988541i
$148$	−0.667274	−	21.5853i	−0.0548496	−	1.77430i
$149$	−2.70832	−	1.56365i	−0.221874	−	0.128099i	0.384943	−	0.922940i	$-0.374221\pi$
$149$	−2.70832	−	1.56365i	−0.221874	−	0.128099i	−0.606818	+	0.794841i	$0.707554\pi$
$150$	−1.29754	−	7.40724i	−0.105943	−	0.604799i
$151$	−12.8993	+	7.44743i	−1.04973	+	0.606063i	−0.922574	−	0.385819i	$-0.873919\pi$
$151$	−12.8993	+	7.44743i	−1.04973	+	0.606063i	−0.127158	+	0.991883i	$0.540585\pi$
$152$	−0.0897339	−	1.93440i	−0.00727838	−	0.156900i
$153$	4.37361	−	4.87462i	0.353586	−	0.394090i
$154$	−0.345736	+	2.46597i	−0.0278602	+	0.198714i
$155$	1.41008	+	2.44233i	0.113261	+	0.196173i
$156$	−11.9534	+	10.3256i	−0.957039	+	0.826708i
$157$	9.75119	−	16.8896i	0.778230	−	1.34793i	−0.154732	−	0.987957i	$-0.549451\pi$
$157$	9.75119	−	16.8896i	0.778230	−	1.34793i	0.932961	−	0.359977i	$-0.117215\pi$
$158$	−15.5110	+	9.27777i	−1.23399	+	0.738099i
$159$	−0.198219	+	0.517741i	−0.0157198	+	0.0410595i
$160$	3.39233	−	7.08878i	0.268187	−	0.560417i
$161$	−2.14411	−	5.54688i	−0.168980	−	0.437156i
$162$	−1.57035	−	12.6307i	−0.123378	−	0.992360i
$163$	−17.7311			−1.38881			−0.694403	−	0.719586i	$-0.744331\pi$
$163$	−17.7311			−1.38881			−0.694403	+	0.719586i	$0.744331\pi$
$164$	8.53614	+	4.58267i	0.666561	+	0.357847i
$165$	1.49549	+	0.572556i	0.116424	+	0.0445735i
$166$	12.3599	−	7.39296i	0.959316	−	0.573805i
$167$	2.31925	−	4.01706i	0.179469	−	0.310850i	−0.762230	−	0.647307i	$-0.775895\pi$
$167$	2.31925	−	4.01706i	0.179469	−	0.310850i	0.941699	+	0.336457i	$0.109229\pi$
$168$	−7.02896	−	10.8901i	−0.542296	−	0.840187i
$169$	−3.89590	−	6.74790i	−0.299685	−	0.519069i
$170$	−3.74701	−	2.08681i	−0.287382	−	0.160051i
$171$	−1.37167	+	1.52880i	−0.104894	+	0.116910i
$172$	−6.63054	−	10.7062i	−0.505574	−	0.816341i
$173$	3.62449	+	6.27781i	0.275565	+	0.477293i	0.970278	−	0.241995i	$-0.0778017\pi$
$173$	3.62449	+	6.27781i	0.275565	+	0.477293i	−0.694712	+	0.719288i	$0.744468\pi$
$174$	6.66458	−	1.16744i	0.505240	−	0.0885036i
$175$	−1.25193	+	8.02550i	−0.0946368	+	0.606671i
$176$	−1.47087	−	2.21876i	−0.110871	−	0.167246i
$177$	15.4133	+	18.9996i	1.15854	+	1.42810i
$178$	0.238924	+	15.4613i	0.0179081	+	1.15888i
$179$	18.4832			1.38150			0.690749	−	0.723095i	$-0.257281\pi$
$179$	18.4832			1.38150			0.690749	+	0.723095i	$0.257281\pi$
$180$	−7.83907	+	2.83330i	−0.584290	+	0.211182i
$181$	−5.94992			−0.442254			−0.221127	−	0.975245i	$-0.570973\pi$
$181$	−5.94992			−0.442254			−0.221127	+	0.975245i	$0.570973\pi$
$182$	15.8168	−	6.39649i	1.17242	−	0.474140i
$183$	1.21950	+	7.65601i	0.0901483	+	0.565949i
$184$	5.64711	+	2.92019i	0.416310	+	0.215279i
$185$	12.9909	+	7.50030i	0.955110	+	0.551433i
$186$	−3.81275	+	3.19200i	−0.279564	+	0.234049i
$187$	−1.25818	+	0.726408i	−0.0920069	+	0.0531202i
$188$	6.77156	+	10.9339i	0.493867	+	0.797437i
$189$	−2.79139	+	13.4614i	−0.203043	+	0.979170i
$190$	1.17515	+	0.654474i	0.0852542	+	0.0474805i
$191$	18.9353	−	10.9323i	1.37011	−	0.791034i	0.379169	−	0.925327i	$-0.376210\pi$
$191$	18.9353	−	10.9323i	1.37011	−	0.791034i	0.990942	+	0.134294i	$0.0428766\pi$
$192$	13.3435	+	3.73503i	0.962986	+	0.269552i
$193$	3.79089	−	6.56601i	0.272874	−	0.472632i	−0.696723	−	0.717341i	$-0.745359\pi$
$193$	3.79089	−	6.56601i	0.272874	−	0.472632i	0.969597	+	0.244709i	$0.0786924\pi$
$194$	0.0815014	−	0.0487493i	0.00585146	−	0.00349999i
$195$	−1.72592	−	10.8353i	−0.123596	−	0.775930i
$196$	3.39592	+	13.5819i	0.242565	+	0.970135i
$197$			1.99340i			0.142024i	0.997475	+	0.0710118i	$0.0226228\pi$
$197$			1.99340i			0.142024i	−0.997475	+	0.0710118i	$0.977377\pi$
$198$	−0.539416	+	2.77150i	−0.0383347	+	0.196962i
$199$	−6.99368			−0.495769			−0.247884	−	0.968790i	$-0.579735\pi$
$199$	−6.99368			−0.495769			−0.247884	+	0.968790i	$0.579735\pi$
$200$	−4.68550	−	7.31076i	−0.331315	−	0.516949i
$201$	−19.1136	+	15.5057i	−1.34817	+	1.09369i
$202$	7.30192	+	12.2077i	0.513761	+	0.858932i
$203$	−7.22085	−	1.12641i	−0.506804	−	0.0790582i
$204$	2.48433	−	7.14250i	0.173938	−	0.500075i
$205$	−5.82815	+	3.36488i	−0.407055	+	0.235014i
$206$	−6.65344	+	11.9467i	−0.463567	+	0.832363i
$207$	−2.09502	−	6.40939i	−0.145614	−	0.445484i
$208$	−8.12653	+	16.3288i	−0.563474	+	1.13220i
$209$	0.394593	−	0.227818i	0.0272946	−	0.0157585i
$210$	9.00167	−	0.168039i	0.621174	−	0.0115958i
$211$	−0.905844	+	1.56897i	−0.0623609	+	0.108012i	−0.895520	−	0.445021i	$-0.853196\pi$
$211$	−0.905844	+	1.56897i	−0.0623609	+	0.108012i	0.833159	+	0.553033i	$0.186530\pi$
$212$	0.0197799	+	0.639847i	0.00135849	+	0.0439449i
$213$	−1.09480	+	2.85958i	−0.0750145	+	0.195935i
$214$	−19.4157	+	0.300031i	−1.32723	+	0.0205097i
$215$	8.74738			0.596566
$216$	−7.30562	−	12.7526i	−0.497084	−	0.867702i
$217$	5.00969	−	1.93646i	0.340080	−	0.131456i
$218$	0.279375	+	18.0790i	0.0189217	+	1.22447i
$219$	5.47477	−	14.2999i	0.369951	−	0.966297i
$220$	1.84820	−	0.0571341i	0.124605	−	0.00385198i
$221$	8.62056	+	4.97708i	0.579882	+	0.334795i
$222$	−9.07397	+	24.8438i	−0.609005	+	1.66741i
$223$	10.2150	+	17.6928i	0.684045	+	1.18480i	0.973736	+	0.227680i	$0.0731141\pi$
$223$	10.2150	+	17.6928i	0.684045	+	1.18480i	−0.289691	+	0.957120i	$0.593553\pi$
$224$	−12.3433	−	8.46421i	−0.824722	−	0.565539i
$225$	−1.89903	+	9.01221i	−0.126602	+	0.600814i
$226$	−12.4720	+	22.3942i	−0.829622	+	1.48964i
$227$	−16.8114	+	9.70609i	−1.11581	+	0.644216i	−0.940329	−	0.340266i	$-0.889483\pi$
$227$	−16.8114	+	9.70609i	−1.11581	+	0.644216i	−0.175486	+	0.984482i	$0.556150\pi$
$228$	−0.779145	+	2.24005i	−0.0516002	+	0.148351i
$229$	2.76630	−	4.79137i	0.182802	−	0.316623i	−0.760031	−	0.649886i	$-0.774817\pi$
$229$	2.76630	−	4.79137i	0.182802	−	0.316623i	0.942834	+	0.333263i	$0.108150\pi$
$230$	−3.78978	+	2.26682i	−0.249891	+	0.149470i
$231$	1.51637	−	2.64603i	0.0997698	−	0.174096i
$232$	6.57777	−	4.21572i	0.431852	−	0.276776i
$233$	1.31945			0.0864404			0.0432202	−	0.999066i	$-0.486238\pi$
$233$	1.31945			0.0864404			0.0432202	+	0.999066i	$0.486238\pi$
$234$	18.2931	−	6.29391i	1.19586	−	0.411446i
$235$	−8.93342			−0.582752
$236$	24.8902	+	13.3624i	1.62021	+	0.869820i
$237$	21.8604	−	3.48209i	1.41999	−	0.226186i
$238$	−5.02667	+	6.43825i	−0.325831	+	0.417329i
$239$	17.2369	+	9.95175i	1.11496	+	0.643725i	0.940111	−	0.340869i	$-0.110721\pi$
$239$	17.2369	+	9.95175i	1.11496	+	0.643725i	0.174854	+	0.984594i	$0.444055\pi$
$240$	−7.08578	+	6.51382i	−0.457385	+	0.420465i
$241$	−18.6956	+	10.7939i	−1.20429	+	0.695299i	−0.961507	−	0.274781i	$-0.911395\pi$
$241$	−18.6956	+	10.7939i	−1.20429	+	0.695299i	−0.242786	+	0.970080i	$0.578061\pi$
$242$	−7.26433	+	13.0436i	−0.466969	+	0.838472i
$243$	−3.96827	+	15.0749i	−0.254564	+	0.967056i
$244$	4.71333	+	7.61053i	0.301740	+	0.487214i
$245$	−9.26258	−	2.96188i	−0.591764	−	0.189228i
$246$	−7.61707	−	9.09836i	−0.485647	−	0.580091i
$247$	−2.70361	−	1.56093i	−0.172027	−	0.0993196i
$248$	−2.63738	+	5.10020i	−0.167474	+	0.323863i
$249$	−17.4194	+	2.77469i	−1.10391	+	0.175839i
$250$	15.8531	−	0.244978i	1.00264	−	0.0154937i
$251$		−	10.0882i		−	0.636764i	−0.947963	−	0.318382i	$-0.896861\pi$
$251$		−	10.0882i		−	0.636764i	0.947963	−	0.318382i	$-0.103139\pi$
$252$	3.03042	+	15.5826i	0.190898	+	0.981610i
$253$			1.49586i			0.0940438i
$254$	−0.0438347	−	2.83665i	−0.00275044	−	0.177987i
$255$	3.30931	+	4.07931i	0.207237	+	0.255456i
$256$	15.8779	−	1.97280i	0.992369	−	0.123300i
$257$	−3.44928	−	1.99144i	−0.215160	−	0.124223i	0.388547	−	0.921429i	$-0.372977\pi$
$257$	−3.44928	−	1.99144i	−0.215160	−	0.124223i	−0.603707	+	0.797206i	$0.706310\pi$
$258$	2.66121	+	15.1921i	0.165680	+	0.945816i
$259$	17.9267	−	22.2436i	1.11391	−	1.38215i
$260$	−6.67061	−	10.7709i	−0.413694	−	0.667983i
$261$	−8.10863	−	1.70863i	−0.501912	−	0.105761i
$262$	−0.860530	−	0.479254i	−0.0531637	−	0.0296084i
$263$	1.35137	−	0.780215i	0.0833292	−	0.0481101i	−0.457756	−	0.889078i	$-0.651347\pi$
$263$	1.35137	−	0.780215i	0.0833292	−	0.0481101i	0.541086	+	0.840968i	$0.318013\pi$
$264$	0.661504	+	3.19248i	0.0407128	+	0.196484i
$265$	−0.385087	−	0.222330i	−0.0236557	−	0.0136576i
$266$	1.57648	−	2.01918i	0.0966603	−	0.123804i
$267$	6.77136	−	17.6865i	0.414401	−	1.08240i
$268$	−13.4425	+	25.0394i	−0.821134	+	1.52953i
$269$	27.4039			1.67085			0.835423	−	0.549607i	$-0.185223\pi$
$269$	27.4039			1.67085			0.835423	+	0.549607i	$0.185223\pi$
$270$	10.2027	+	0.349752i	0.620918	+	0.0212852i
$271$	−4.73196			−0.287446			−0.143723	−	0.989618i	$-0.545907\pi$
$271$	−4.73196			−0.287446			−0.143723	+	0.989618i	$0.545907\pi$
$272$	−0.539363	−	8.71543i	−0.0327037	−	0.528451i
$273$	−20.8955	+	0.0671497i	−1.26466	+	0.00406408i
$274$	9.29429	+	15.5387i	0.561489	+	0.938725i
$275$	1.02156	−	1.76940i	0.0616026	−	0.106699i
$276$	−5.08988	−	5.89229i	−0.306375	−	0.354674i
$277$	6.98595	−	4.03334i	0.419745	−	0.242340i	−0.275223	−	0.961380i	$-0.588752\pi$
$277$	6.98595	−	4.03334i	0.419745	−	0.242340i	0.694968	+	0.719040i	$0.255418\pi$
$278$	11.6403	+	6.48284i	0.698142	+	0.388815i
$279$	5.78867	−	1.89213i	0.346558	−	0.113279i
$280$	9.51272	−	4.19356i	0.568494	−	0.250613i
$281$	−11.5676	−	20.0358i	−0.690068	−	1.19523i	−0.971815	−	0.235744i	$-0.924247\pi$
$281$	−11.5676	−	20.0358i	−0.690068	−	1.19523i	0.281747	−	0.959489i	$-0.409086\pi$
$282$	−2.71781	−	15.5152i	−0.161843	−	0.923914i
$283$	−21.3691	−	12.3375i	−1.27026	−	0.733385i	−0.295224	−	0.955428i	$-0.595394\pi$
$283$	−21.3691	−	12.3375i	−1.27026	−	0.733385i	−0.975037	+	0.222043i	$0.928728\pi$
$284$	0.109248	+	3.53399i	0.00648265	+	0.209704i
$285$	−1.03788	−	1.27937i	−0.0614785	−	0.0757831i
$286$	−4.29102	+	0.0663092i	−0.253734	+	0.00392095i
$287$	4.62098	+	11.9546i	0.272768	+	0.705659i
$288$	−13.4686	−	10.3246i	−0.793645	−	0.608381i
$289$	12.2344			0.719670
$290$	0.0838514	+	5.42622i	0.00492393	+	0.318639i
$291$	−0.114864	+	0.0182963i	−0.00673344	+	0.00107255i
$292$	−0.546315	−	17.6724i	−0.0319707	−	1.03420i
$293$	−14.6074	+	25.3008i	−0.853375	+	1.47809i	0.0247690	+	0.999693i	$0.492115\pi$
$293$	−14.6074	+	25.3008i	−0.853375	+	1.47809i	−0.878144	+	0.478396i	$0.841218\pi$
$294$	2.32611	−	16.9879i	0.135662	−	0.990755i
$295$	−16.9940	+	9.81152i	−0.989432	+	0.571249i
$296$	1.41522	+	30.5079i	0.0822580	+	1.77324i
$297$	1.87573	−	2.90514i	0.108841	−	0.168574i
$298$	3.86386	+	2.15189i	0.223827	+	0.124656i
$299$	8.87596	−	5.12454i	0.513310	−	0.296360i
$300$	1.99663	+	10.4458i	0.115276	+	0.603090i
$301$	2.56767	−	16.4601i	0.147998	−	0.948744i
$302$	18.0775	−	10.8129i	1.04024	−	0.622210i
$303$	−2.74052	−	17.2049i	−0.157439	−	0.988397i
$304$	0.169157	+	2.73336i	0.00970180	+	0.156769i
$305$	−6.21809			−0.356047
$306$	−6.07797	+	6.98850i	−0.347454	+	0.399506i
$307$		−	7.32417i		−	0.418012i	−0.977914	−	0.209006i	$-0.932977\pi$
$307$		−	7.32417i		−	0.418012i	0.977914	−	0.209006i	$-0.0670229\pi$
$308$	0.435002	−	3.49455i	0.0247865	−	0.199121i
$309$	13.0061	−	10.5511i	0.739894	−	0.600233i
$310$	−2.04729	−	3.42276i	−0.116278	−	0.194400i
$311$	−7.08846	+	12.2776i	−0.401950	+	0.696198i	−0.993961	−	0.109732i	$-0.965001\pi$
$311$	−7.08846	+	12.2776i	−0.401950	+	0.696198i	0.592011	+	0.805930i	$0.298334\pi$
$312$	16.6770	−	14.8620i	0.944151	−	0.841397i
$313$	−1.08144	+	0.624371i	−0.0611267	+	0.0352915i	−0.530252	−	0.847840i	$-0.677903\pi$
$313$	−1.08144	+	0.624371i	−0.0611267	+	0.0352915i	0.469125	+	0.883132i	$0.344569\pi$
$314$	−13.4196	+	24.0957i	−0.757310	+	1.35980i
$315$	−10.3104	−	3.90943i	−0.580924	−	0.220271i
$316$	21.7306	−	13.4581i	1.22244	−	0.757078i
$317$	−14.1656	+	8.17850i	−0.795618	+	0.459350i	−0.841937	−	0.539576i	$-0.818584\pi$
$317$	−14.1656	+	8.17850i	−0.795618	+	0.459350i	0.0463185	+	0.998927i	$0.485251\pi$
$318$	0.268978	−	0.736440i	0.0150835	−	0.0412975i
$319$	1.59200	+	0.919140i	0.0891347	+	0.0514620i
$320$	−4.64201	+	10.0980i	−0.259496	+	0.564494i
$321$	22.2100	+	8.50319i	1.23964	+	0.474602i
$322$	3.15308	+	7.79669i	0.175714	+	0.434493i
$323$	1.49460			0.0831620
$324$	2.49654	+	17.8260i	0.138696	+	0.990335i
$325$	−13.9988			−0.776512
$326$	25.0725	−	0.387446i	1.38864	−	0.0214587i
$327$	7.91779	−	20.6810i	0.437855	−	1.14366i
$328$	−12.1706	−	6.29358i	−0.672010	−	0.347505i
$329$	−2.62228	+	16.8102i	−0.144571	+	0.926774i
$330$	−2.12721	−	0.776942i	−0.117099	−	0.0427692i
$331$	5.37189	+	9.30438i	0.295266	+	0.511415i	0.975047	−	0.222000i	$-0.0712585\pi$
$331$	5.37189	+	9.30438i	0.295266	+	0.511415i	−0.679781	+	0.733415i	$0.737925\pi$
$332$	−17.3159	+	10.7241i	−0.950335	+	0.588559i
$333$	21.6330	−	24.1111i	1.18548	−	1.32128i
$334$	−3.19175	+	5.73099i	−0.174645	+	0.313586i
$335$	−9.87035	−	17.0959i	−0.539275	−	0.934051i
$336$	10.1772	+	15.2455i	0.555213	+	0.831708i
$337$	−7.69707	+	13.3317i	−0.419286	+	0.726225i	−0.995868	−	0.0908145i	$-0.971053\pi$
$337$	−7.69707	+	13.3317i	−0.419286	+	0.726225i	0.576582	+	0.817040i	$0.304386\pi$
$338$	5.65643	+	9.45671i	0.307669	+	0.514377i
$339$	24.3802	−	19.7783i	1.32415	−	1.07421i
$340$	5.34403	+	2.86897i	0.289821	+	0.155592i
$341$	−1.35099			−0.0731602
$342$	1.90619	−	2.19176i	0.103075	−	0.118517i
$343$	−8.29231	+	16.5601i	−0.447743	+	0.894162i
$344$	9.60983	+	14.9942i	0.518127	+	0.808432i
$345$	5.34112	−	0.850772i	0.287556	−	0.0458040i
$346$	−5.26237	−	8.79790i	−0.282907	−	0.472978i
$347$	−5.31547	+	9.20666i	−0.285349	+	0.494240i	−0.972694	−	0.232092i	$-0.925443\pi$
$347$	−5.31547	+	9.20666i	−0.285349	+	0.494240i	0.687344	+	0.726332i	$0.258776\pi$
$348$	−9.39850	+	1.79645i	−0.503813	+	0.0962996i
$349$	12.5393	+	21.7187i	0.671214	+	1.16258i	0.977560	+	0.210657i	$0.0675602\pi$
$349$	12.5393	+	21.7187i	0.671214	+	1.16258i	−0.306346	+	0.951920i	$0.599107\pi$
$350$	1.59491	−	11.3758i	0.0852517	−	0.608061i
$351$	−23.6642	−	1.17752i	−1.26310	−	0.0628514i
$352$	2.12836	+	3.10529i	0.113442	+	0.165513i
$353$	−12.9073	+	7.45205i	−0.686987	+	0.396632i	−0.802482	−	0.596676i	$-0.796488\pi$
$353$	−12.9073	+	7.45205i	−0.686987	+	0.396632i	0.115495	+	0.993308i	$0.463155\pi$
$354$	−22.2103	−	26.5295i	−1.18046	−	1.41003i
$355$	−2.12690	−	1.22797i	−0.112884	−	0.0651737i
$356$	−0.675699	−	21.8578i	−0.0358120	−	1.15846i
$357$	8.64750	−	5.02976i	0.457674	−	0.266203i
$358$	−26.1360	+	0.403881i	−1.38133	+	0.0213457i
$359$		−	26.4328i		−	1.39507i	−0.716550	−	0.697536i	$-0.754280\pi$
$359$		−	26.4328i		−	1.39507i	0.716550	−	0.697536i	$-0.245720\pi$
$360$	11.0229	−	4.17770i	0.580957	−	0.220184i
$361$	18.5313			0.975329
$362$	8.41345	−	0.130013i	0.442201	−	0.00683334i
$363$	14.2003	−	11.5199i	0.745323	−	0.604638i
$364$	−22.2258	+	9.39054i	−1.16495	+	0.492198i
$365$	10.6360	+	6.14070i	0.556714	+	0.321419i
$366$	−1.89173	−	10.7993i	−0.0988821	−	0.564488i
$367$	−10.2874	−	17.8183i	−0.536997	−	0.930106i	−0.999064	−	0.0432607i	$-0.986225\pi$
$367$	−10.2874	−	17.8183i	−0.536997	−	0.930106i	0.462067	−	0.886845i	$-0.347108\pi$
$368$	−8.04907	−	4.00588i	−0.419587	−	0.208821i
$369$	4.51519	+	13.8135i	0.235051	+	0.719103i
$370$	−18.5336	−	10.3219i	−0.963517	−	0.536610i
$371$	−0.531398	+	0.659362i	−0.0275888	+	0.0342324i
$372$	5.32164	−	4.59694i	0.275914	−	0.238340i
$373$	−20.7983	−	12.0079i	−1.07689	−	0.621745i	−0.146837	−	0.989161i	$-0.546909\pi$
$373$	−20.7983	−	12.0079i	−1.07689	−	0.621745i	−0.930057	+	0.367416i	$0.880243\pi$
$374$	1.76324	−	1.05467i	0.0911751	−	0.0545355i
$375$	−18.1346	−	6.94292i	−0.936468	−	0.358531i
$376$	−9.81421	−	15.3131i	−0.506129	−	0.789711i
$377$		−	12.5952i		−	0.648687i
$378$	3.65300	−	19.0960i	0.187890	−	0.982190i
$379$	−4.82465			−0.247826			−0.123913	−	0.992293i	$-0.539544\pi$
$379$	−4.82465			−0.247826			−0.123913	+	0.992293i	$0.539544\pi$
$380$	−1.67601	−	0.899776i	−0.0859777	−	0.0461576i
$381$	−1.24232	+	3.24490i	−0.0636461	+	0.166241i
$382$	−26.5365	+	15.8725i	−1.35772	+	0.812109i
$383$	−17.7772	+	30.7910i	−0.908371	+	1.57335i	−0.0920443	+	0.995755i	$0.529340\pi$
$383$	−17.7772	+	30.7910i	−0.908371	+	1.57335i	−0.816327	+	0.577590i	$0.803993\pi$
$384$	−18.9500	−	4.98992i	−0.967036	−	0.254641i
$385$	1.90457	+	1.53494i	0.0970657	+	0.0782280i
$386$	−5.21701	+	9.36747i	−0.265539	+	0.476792i
$387$	3.89485	−	18.4838i	0.197986	−	0.939585i
$388$	−0.114181	+	0.0707145i	−0.00579669	+	0.00358999i
$389$	22.2736	−	12.8597i	1.12932	−	0.652011i	0.185553	−	0.982634i	$-0.440592\pi$
$389$	22.2736	−	12.8597i	1.12932	−	0.652011i	0.943763	+	0.330624i	$0.107259\pi$
$390$	2.67729	+	15.2839i	0.135570	+	0.773928i
$391$	−2.45340	+	4.24941i	−0.124074	+	0.214902i
$392$	−5.09876	−	19.1312i	−0.257526	−	0.966271i
$393$	0.760009	+	0.936846i	0.0383374	+	0.0472576i
$394$	−0.0435582	−	2.81875i	−0.00219443	−	0.142007i
$395$			17.7547i			0.893336i
$396$	0.702198	−	3.93081i	0.0352868	−	0.197530i
$397$	22.0344			1.10588			0.552938	−	0.833222i	$-0.313507\pi$
$397$	22.0344			1.10588			0.552938	+	0.833222i	$0.313507\pi$
$398$	9.88937	−	0.152821i	0.495710	−	0.00766021i
$399$	−2.71206	+	1.57745i	−0.135773	+	0.0789712i
$400$	6.78525	+	10.2354i	0.339263	+	0.511768i
$401$	2.28424	−	3.95642i	0.114069	−	0.197574i	−0.803338	−	0.595523i	$-0.796945\pi$
$401$	2.28424	−	3.95642i	0.114069	−	0.197574i	0.917407	+	0.397949i	$0.130278\pi$
$402$	26.6886	−	22.3435i	1.33111	−	1.11439i
$403$	4.62825	+	8.01636i	0.230549	+	0.399323i
$404$	−10.5920	−	17.1027i	−0.526972	−	0.850891i
$405$	−11.4400	−	5.04520i	−0.568456	−	0.250698i
$406$	10.2352	+	1.43500i	0.507965	+	0.0712181i
$407$	−6.22324	+	3.59299i	−0.308475	+	0.178098i
$408$	−3.35689	+	10.1541i	−0.166191	+	0.502703i
$409$	1.68001	+	0.969956i	0.0830713	+	0.0479612i	0.540960	−	0.841048i	$-0.318061\pi$
$409$	1.68001	+	0.969956i	0.0830713	+	0.0479612i	−0.457889	+	0.889009i	$0.651394\pi$
$410$	8.16773	−	4.88545i	0.403376	−	0.241275i
$411$	−3.48829	−	21.8994i	−0.172065	−	1.08022i
$412$	9.14721	−	17.0385i	0.450650	−	0.839427i
$413$	13.4741	+	34.8580i	0.663019	+	1.71525i
$414$	3.10251	+	9.01739i	0.152480	+	0.443181i
$415$		−	14.1478i		−	0.694487i
$416$	11.1345	−	23.2672i	0.545913	−	1.14077i
$417$	−10.2806	−	12.6727i	−0.503444	−	0.620583i
$418$	−0.552994	+	0.330768i	−0.0270478	+	0.0161784i
$419$	−8.92695	−	5.15398i	−0.436110	−	0.251788i	0.265836	−	0.964018i	$-0.414352\pi$
$419$	−8.92695	−	5.15398i	−0.436110	−	0.251788i	−0.701946	+	0.712230i	$0.747685\pi$
$420$	−12.7251	+	0.434312i	−0.620921	+	0.0211923i
$421$	−0.205252	+	0.118502i	−0.0100034	+	0.00577544i	−0.504993	−	0.863123i	$-0.668505\pi$
$421$	−0.205252	+	0.118502i	−0.0100034	+	0.00577544i	0.494990	+	0.868899i	$0.335172\pi$
$422$	1.24662	−	2.23838i	0.0606845	−	0.108963i
$423$	−3.97768	+	18.8769i	−0.193402	+	0.917827i
$424$	−0.0419511	−	0.904340i	−0.00203732	−	0.0439186i
$425$	5.80408	−	3.35099i	0.281539	−	0.162547i
$426$	1.48561	−	4.06749i	0.0719781	−	0.197071i
$427$	−1.82523	+	11.7007i	−0.0883291	+	0.566236i
$428$	27.4481	−	0.848514i	1.32675	−	0.0410145i
$429$	4.90859	+	1.87927i	0.236989	+	0.0907322i
$430$	−12.3692	+	0.191141i	−0.596495	+	0.00921765i
$431$			7.02144i			0.338211i	0.985598	+	0.169105i	$0.0540878\pi$
$431$			7.02144i			0.338211i	−0.985598	+	0.169105i	$0.945912\pi$
$432$	10.6091	+	17.8731i	0.510432	+	0.859918i
$433$			38.2507i			1.83821i	0.394012	+	0.919105i	$0.371087\pi$
$433$			38.2507i			1.83821i	−0.394012	+	0.919105i	$0.628913\pi$
$434$	−7.04161	+	2.84771i	−0.338008	+	0.136695i
$435$	2.37644	−	6.20716i	0.113942	−	0.297611i
$436$	−0.790098	−	25.5584i	−0.0378388	−	1.22403i
$437$	0.769442	−	1.33271i	0.0368074	−	0.0637523i
$438$	−7.42911	+	20.3403i	−0.354976	+	0.971898i
$439$	−17.3436	−	30.0400i	−0.827764	−	1.43373i	−0.899788	−	0.436327i	$-0.856279\pi$
$439$	−17.3436	−	30.0400i	−0.827764	−	1.43373i	0.0720239	−	0.997403i	$-0.477054\pi$
$440$	−2.61219	+	0.121176i	−0.124531	+	0.00577682i
$441$	−10.3829	+	18.2536i	−0.494424	+	0.869221i
$442$	−12.2986	−	6.84945i	−0.584986	−	0.325795i
$443$	8.53973	+	14.7912i	0.405735	+	0.702753i	0.994407	−	0.105619i	$-0.0336823\pi$
$443$	8.53973	+	14.7912i	0.405735	+	0.702753i	−0.588672	+	0.808372i	$0.700349\pi$
$444$	12.2881	−	35.3286i	0.583169	−	1.67662i
$445$	13.1549	+	7.59500i	0.623604	+	0.360038i
$446$	−14.8310	−	24.7953i	−0.702270	−	1.17409i
$447$	−3.41251	−	4.20652i	−0.161406	−	0.198962i
$448$	17.6389	+	11.6991i	0.833362	+	0.552728i
$449$	−22.2778			−1.05136			−0.525678	−	0.850684i	$-0.676188\pi$
$449$	−22.2778			−1.05136			−0.525678	+	0.850684i	$0.676188\pi$
$450$	2.48838	−	12.7852i	0.117303	−	0.602699i
$451$		−	3.22387i		−	0.151806i
$452$	17.1466	−	31.9389i	0.806506	−	1.50228i
$453$	−25.4775	+	4.05823i	−1.19704	+	0.190672i
$454$	23.5600	−	14.0922i	1.10573	−	0.661380i
$455$	2.58318	−	16.5595i	0.121102	−	0.776324i
$456$	1.05280	−	3.18456i	0.0493018	−	0.149131i
$457$	13.6607	+	23.6610i	0.639019	+	1.10681i	0.985648	+	0.168811i	$0.0539929\pi$
$457$	13.6607	+	23.6610i	0.639019	+	1.10681i	−0.346629	+	0.938002i	$0.612674\pi$
$458$	−3.80697	+	6.83566i	−0.177888	+	0.319410i
$459$	10.0933	−	5.17644i	0.471117	−	0.241616i
$460$	5.30939	−	3.28820i	0.247552	−	0.153313i
$461$	−7.67896	−	13.3003i	−0.357645	−	0.619459i	0.629922	−	0.776658i	$-0.283087\pi$
$461$	−7.67896	−	13.3003i	−0.357645	−	0.619459i	−0.987567	+	0.157200i	$0.949753\pi$
$462$	−2.08639	+	3.77474i	−0.0970679	+	0.175617i
$463$	14.3316	+	8.27434i	0.666045	+	0.384541i	0.794576	−	0.607164i	$-0.207693\pi$
$463$	14.3316	+	8.27434i	0.666045	+	0.384541i	−0.128531	+	0.991705i	$0.541026\pi$
$464$	−9.20914	+	6.10495i	−0.427524	+	0.283415i
$465$	0.768378	+	4.82385i	0.0356327	+	0.223701i
$466$	−1.86577	+	0.0288317i	−0.0864300	+	0.00133560i
$467$		−	32.4101i		−	1.49976i	−0.661574	−	0.749880i	$-0.730111\pi$
$467$		−	32.4101i		−	1.49976i	0.661574	−	0.749880i	$-0.269889\pi$
$468$	−25.7298	+	9.29960i	−1.18936	+	0.429874i
$469$	−35.0670	+	13.5549i	−1.61924	+	0.625908i
$470$	12.6323	−	0.195206i	0.582682	−	0.00900420i
$471$	26.2326	−	21.2810i	1.20873	−	0.980576i
$472$	−35.4878	−	18.3512i	−1.63346	−	0.844682i
$473$	−2.09520	+	3.62899i	−0.0963374	+	0.166861i
$474$	−30.8356	+	5.40150i	−1.41632	+	0.248099i
$475$	−1.82030	+	1.05095i	−0.0835209	+	0.0482208i
$476$	6.96725	−	9.21381i	0.319344	−	0.422314i
$477$	−0.641261	+	0.714719i	−0.0293613	+	0.0327248i
$478$	−24.5913	−	13.6956i	−1.12478	−	0.626421i
$479$	4.70436	+	8.14819i	0.214948	+	0.372300i	0.953256	−	0.302163i	$-0.0977086\pi$
$479$	4.70436	+	8.14819i	0.214948	+	0.372300i	−0.738309	+	0.674463i	$0.764375\pi$
$480$	9.87727	−	9.36567i	0.450834	−	0.427482i
$481$	42.6394	+	24.6179i	1.94419	+	1.12248i
$482$	26.2006	−	15.6716i	1.19341	−	0.713823i
$483$	−0.0331006	−	10.3002i	−0.00150613	−	0.468676i
$484$	9.98707	−	18.6029i	0.453958	−	0.845587i
$485$		−	0.0932906i		−	0.00423611i
$486$	5.28190	−	21.4033i	0.239592	−	0.970874i
$487$			26.4564i			1.19885i	0.800429	+	0.599427i	$0.204605\pi$
$487$			26.4564i			1.19885i	−0.800429	+	0.599427i	$0.795395\pi$
$488$	−6.83116	−	10.6586i	−0.309232	−	0.482494i
$489$	−28.6810	−	10.9806i	−1.29700	−	0.496562i
$490$	13.1624	+	3.98583i	0.594617	+	0.180062i
$491$	−11.7327	+	20.3217i	−0.529491	+	0.917106i	0.469917	+	0.882711i	$0.344284\pi$
$491$	−11.7327	+	20.3217i	−0.529491	+	0.917106i	−0.999408	+	0.0343951i	$0.989050\pi$
$492$	10.9697	+	12.6991i	0.494552	+	0.572517i
$493$	3.01501	+	5.22215i	0.135789	+	0.235194i
$494$	3.85713	+	2.14815i	0.173541	+	0.0966497i
$495$	2.06447	+	1.85228i	0.0927909	+	0.0832539i
$496$	3.61792	−	7.26955i	0.162450	−	0.326412i
$497$	−2.93501	+	3.64177i	−0.131653	+	0.163356i
$498$	24.5712	−	4.30417i	1.10106	−	0.192874i
$499$	16.5032	−	28.5844i	0.738786	−	1.27962i	−0.214256	−	0.976778i	$-0.568733\pi$
$499$	16.5032	−	28.5844i	0.738786	−	1.27962i	0.953042	−	0.302838i	$-0.0979340\pi$
$500$	−22.4116	+	0.692818i	−1.00228	+	0.0309838i
$501$	6.23924	−	5.06154i	0.278749	−	0.226133i
$502$	0.220441	+	14.2652i	0.00983874	+	0.636688i
$503$	−29.6875			−1.32370			−0.661849	−	0.749637i	$-0.730228\pi$
$503$	−29.6875			−1.32370			−0.661849	+	0.749637i	$0.730228\pi$
$504$	−4.62564	−	21.9682i	−0.206043	−	0.978543i
$505$	13.9736			0.621815
$506$	−0.0326864	−	2.11521i	−0.00145309	−	0.0940325i
$507$	−2.12294	−	13.3278i	−0.0942832	−	0.591908i
$508$	0.123969	+	4.01019i	0.00550022	+	0.177923i
$509$	17.1429	−	29.6924i	0.759846	−	1.31609i	−0.183083	−	0.983097i	$-0.558608\pi$
$509$	17.1429	−	29.6924i	0.759846	−	1.31609i	0.942929	−	0.332994i	$-0.108059\pi$
$510$	−4.76865	−	5.69601i	−0.211159	−	0.252224i
$511$	14.6771	−	18.2114i	0.649277	−	0.805626i
$512$	−22.4090	+	3.13657i	−0.990346	+	0.138618i
$513$	−3.16551	+	1.62345i	−0.139761	+	0.0716772i
$514$	4.92095	+	2.74062i	0.217054	+	0.120883i
$515$	6.71644	+	11.6332i	0.295962	+	0.512621i
$516$	−4.09504	−	21.4241i	−0.180274	−	0.943143i
$517$	2.13976	−	3.70617i	0.0941066	−	0.162997i
$518$	−24.8632	+	31.8451i	−1.09242	+	1.39920i
$519$	1.97505	+	12.3993i	0.0866950	+	0.544269i
$520$	9.66790	+	15.0848i	0.423965	+	0.661512i
$521$			41.9787i			1.83912i	0.392947	+	0.919561i	$0.371455\pi$
$521$			41.9787i			1.83912i	−0.392947	+	0.919561i	$0.628545\pi$
$522$	11.5033	+	2.23889i	0.503486	+	0.0979935i
$523$			8.05478i			0.352211i	0.984371	+	0.176106i	$0.0563500\pi$
$523$			8.05478i			0.352211i	−0.984371	+	0.176106i	$0.943650\pi$
$524$	1.22730	+	0.658882i	0.0536149	+	0.0287834i
$525$	−6.99515	+	12.2064i	−0.305294	+	0.532730i
$526$	−1.89385	+	1.13279i	−0.0825759	+	0.0493919i
$527$	−3.83787	−	2.21579i	−0.167180	−	0.0965214i
$528$	−1.00516	−	4.49986i	−0.0437438	−	0.195831i
$529$	−8.97392	−	15.5433i	−0.390170	−	0.675795i
$530$	0.549388	+	0.305970i	0.0238639	+	0.0132905i
$531$	13.1656	+	40.2782i	0.571340	+	1.74793i
$532$	−2.18509	+	2.88966i	−0.0947358	+	0.125283i
$533$	−19.1294	+	11.0444i	−0.828588	+	0.478386i
$534$	−9.18854	+	25.1575i	−0.397627	+	1.08867i
$535$	−9.53748	+	16.5194i	−0.412341	+	0.714196i
$536$	18.4612	−	35.7006i	0.797403	−	1.54203i
$537$	29.8975	+	11.4464i	1.29017	+	0.493949i
$538$	−38.7504	+	0.598810i	−1.67065	+	0.0258165i
$539$	3.44739	−	3.13329i	0.148489	−	0.134960i
$540$	−14.4347	−	0.271623i	−0.621173	−	0.0116888i
$541$			23.6939i			1.01868i	0.860565	+	0.509340i	$0.170111\pi$
$541$			23.6939i			1.01868i	−0.860565	+	0.509340i	$0.829889\pi$
$542$	6.69120	−	0.103399i	0.287412	−	0.00444138i
$543$	−9.62431	−	3.68471i	−0.413019	−	0.158126i
$544$	0.953126	+	12.3122i	0.0408649	+	0.527882i
$545$	15.3821	+	8.88087i	0.658898	+	0.380415i
$546$	29.5458	−	0.551546i	1.26444	−	0.0236040i
$547$	10.3565	+	17.9380i	0.442811	+	0.766972i	0.997897	−	0.0648216i	$-0.0206478\pi$
$547$	10.3565	+	17.9380i	0.442811	+	0.766972i	−0.555086	+	0.831793i	$0.687315\pi$
$548$	−13.4821	−	21.7693i	−0.575926	−	0.929937i
$549$	−2.76866	+	13.1392i	−0.118164	+	0.560769i
$550$	−1.40587	+	2.52433i	−0.0599467	+	0.107638i
$551$	−0.945578	−	1.63779i	−0.0402830	−	0.0697721i
$552$	7.32607	+	8.22074i	0.311818	+	0.349898i
$553$	33.4093	+	5.21164i	1.42071	+	0.221621i
$554$	−9.79032	+	5.85598i	−0.415951	+	0.248797i
$555$	16.3687	+	20.1773i	0.694811	+	0.856477i
$556$	−16.6016	−	8.91267i	−0.704066	−	0.377981i
$557$		−	14.6654i		−	0.621391i	−0.950509	−	0.310696i	$-0.899438\pi$
$557$		−	14.6654i		−	0.621391i	0.950509	−	0.310696i	$-0.100562\pi$
$558$	−8.14409	+	2.80204i	−0.344767	+	0.118620i
$559$	28.7111			1.21435
$560$	−13.3598	+	6.13774i	−0.564554	+	0.259367i
$561$	−2.48502	+	0.395832i	−0.104918	+	0.0167120i
$562$	16.7950	+	28.0787i	0.708453	+	1.18443i
$563$	25.8457	+	14.9220i	1.08927	+	0.628888i	0.933381	−	0.358887i	$-0.116844\pi$
$563$	25.8457	+	14.9220i	1.08927	+	0.628888i	0.155885	+	0.987775i	$0.450177\pi$
$564$	4.18213	+	21.8797i	0.176099	+	0.921303i
$565$	12.5901	+	21.8066i	0.529668	+	0.917412i
$566$	30.4864	+	16.9788i	1.28144	+	0.713671i
$567$	−12.8517	+	20.0458i	−0.539719	+	0.841845i
$568$	−0.231703	−	4.99483i	−0.00972205	−	0.209578i
$569$	11.6535	+	20.1845i	0.488542	+	0.846179i	0.999913	−	0.0131809i	$-0.00419574\pi$
$569$	11.6535	+	20.1845i	0.488542	+	0.846179i	−0.511372	+	0.859360i	$0.670862\pi$
$570$	1.49556	+	1.78640i	0.0626421	+	0.0748241i
$571$	7.63178	−	13.2186i	0.319380	−	0.553182i	−0.660979	−	0.750404i	$-0.729859\pi$
$571$	7.63178	−	13.2186i	0.319380	−	0.553182i	0.980359	+	0.197222i	$0.0631921\pi$
$572$	6.06625	−	0.187528i	0.253643	−	0.00784096i
$573$	37.3991	−	5.95720i	1.56237	−	0.248865i
$574$	−6.79550	−	16.8034i	−0.283639	−	0.701361i
$575$		−	6.90053i		−	0.287772i
$576$	19.2708	+	14.3051i	0.802951	+	0.596045i
$577$		−	31.4769i		−	1.31040i	−0.755456	−	0.655199i	$-0.772585\pi$
$577$		−	31.4769i		−	1.31040i	0.755456	−	0.655199i	$-0.227415\pi$
$578$	−17.3000	+	0.267337i	−0.719585	+	0.0111197i
$579$	10.1982	−	8.27323i	0.423823	−	0.343824i
$580$	−0.237139	−	7.67108i	−0.00984668	−	0.318524i
$581$	−26.6221	−	4.15288i	−1.10447	−	0.172290i
$582$	0.162023	−	0.0283817i	0.00671606	−	0.00117646i
$583$	0.184474	−	0.106506i	0.00764014	−	0.00441104i
$584$	1.15868	+	24.9777i	0.0479465	+	1.03358i
$585$	3.91838	−	18.5955i	0.162005	−	0.768829i
$586$	20.1027	−	36.0957i	0.830435	−	1.49110i
$587$	−1.05732	+	0.610444i	−0.0436403	+	0.0251957i	−0.521661	−	0.853153i	$-0.674688\pi$
$587$	−1.05732	+	0.610444i	−0.0436403	+	0.0251957i	0.478021	+	0.878348i	$0.341354\pi$
$588$	−2.91802	+	24.0725i	−0.120337	+	0.992733i
$589$	1.20364	+	0.694924i	0.0495953	+	0.0286339i
$590$	23.8160	−	14.2453i	0.980487	−	0.586468i
$591$	−1.23449	+	3.22443i	−0.0507800	+	0.132635i
$592$	−2.66782	−	43.1087i	−0.109647	−	1.77176i
$593$		−	24.8132i		−	1.01896i	−0.860484	−	0.509478i	$-0.829839\pi$
$593$		−	24.8132i		−	1.01896i	0.860484	−	0.509478i	$-0.170161\pi$
$594$	−2.58889	+	4.14899i	−0.106223	+	0.170235i
$595$	2.89296	+	7.48417i	0.118600	+	0.306821i
$596$	−5.51069	−	2.95844i	−0.225727	−	0.121183i
$597$	−11.3127	−	4.33110i	−0.462996	−	0.177260i
$598$	−12.4390	+	7.44028i	−0.508670	+	0.304256i
$599$	−28.4335	−	16.4161i	−1.16176	−	0.670743i	−0.210036	−	0.977694i	$-0.567358\pi$
$599$	−28.4335	−	16.4161i	−1.16176	−	0.670743i	−0.951726	+	0.306950i	$0.900692\pi$
$600$	−3.05158	−	14.7272i	−0.124580	−	0.601237i
$601$	−36.5155	+	21.0822i	−1.48950	+	0.859962i	−0.999928	−	0.0120030i	$-0.996179\pi$
$601$	−36.5155	+	21.0822i	−1.48950	+	0.859962i	−0.489569	+	0.871965i	$0.662846\pi$
$602$	−3.27112	+	23.3314i	−0.133321	+	0.950917i
$603$	−40.5197	+	13.2446i	−1.65009	+	0.539361i
$604$	−25.3261	+	15.6849i	−1.03050	+	0.638209i
$605$	7.33312	+	12.7013i	0.298134	+	0.516383i
$606$	4.25117	+	24.2686i	0.172692	+	0.985846i
$607$	−11.7519	+	20.3550i	−0.476997	+	0.826183i	−0.999652	−	0.0263611i	$-0.991608\pi$
$607$	−11.7519	+	20.3550i	−0.476997	+	0.826183i	0.522656	+	0.852544i	$0.324941\pi$
$608$	−0.298923	−	3.86140i	−0.0121229	−	0.156600i
$609$	−10.9825	−	6.29381i	−0.445035	−	0.255038i
$610$	8.79266	−	0.135873i	0.356004	−	0.00550134i
$611$	−29.3217			−1.18623
$612$	8.44181	−	10.0149i	0.341240	−	0.404827i
$613$		−	37.4425i		−	1.51229i	−0.654405	−	0.756144i	$-0.727081\pi$
$613$		−	37.4425i		−	1.51229i	0.654405	−	0.756144i	$-0.272919\pi$
$614$	0.160042	+	10.3567i	0.00645878	+	0.417962i
$615$	−11.5112	+	1.83358i	−0.464175	+	0.0739371i
$616$	−0.538752	+	4.95096i	−0.0217069	+	0.199480i
$617$	−15.4423	+	26.7468i	−0.621682	+	1.07678i	0.367490	+	0.930027i	$0.380217\pi$
$617$	−15.4423	+	26.7468i	−0.621682	+	1.07678i	−0.989172	+	0.146758i	$0.953116\pi$
$618$	−18.1607	+	15.2040i	−0.730531	+	0.611594i
$619$	7.68931	−	4.43943i	0.309060	−	0.178436i	−0.337446	−	0.941345i	$-0.609563\pi$
$619$	7.68931	−	4.43943i	0.309060	−	0.178436i	0.646506	+	0.762909i	$0.276230\pi$
$620$	2.96975	+	4.79520i	0.119268	+	0.192580i
$621$	0.580445	−	11.6650i	0.0232924	−	0.468099i
$622$	9.75512	−	17.5159i	0.391145	−	0.702325i
$623$	18.1531	−	22.5244i	0.727288	−	0.902423i
$624$	−23.2573	+	21.3800i	−0.931037	+	0.855885i
$625$	0.112329	−	0.194560i	0.00449316	−	0.00778238i
$626$	1.51556	−	0.906519i	0.0605741	−	0.0362318i
$627$	0.779361	−	0.124142i	0.0311247	−	0.00495776i
$628$	18.4493	−	34.3656i	0.736209	−	1.37134i
$629$	−23.5718			−0.939871
$630$	14.6648	+	5.30281i	0.584258	+	0.211269i
$631$		−	0.336315i		−	0.0133885i	−0.999978	−	0.00669425i	$-0.997869\pi$
$631$		−	0.336315i		−	0.0133885i	0.999978	−	0.00669425i	$-0.00213086\pi$
$632$	−30.4339	+	19.5052i	−1.21060	+	0.775876i
$633$	−2.43689	+	1.97691i	−0.0968578	+	0.0785752i
$634$	19.8521	−	11.8743i	0.788426	−	0.471589i
$635$	−2.41350	−	1.39343i	−0.0957767	−	0.0552967i
$636$	−0.364254	+	1.04724i	−0.0144436	+	0.0415256i
$637$	−30.4021	−	9.72164i	−1.20458	−	0.385185i
$638$	−2.27124	−	1.26492i	−0.0899192	−	0.0500786i
$639$	−3.54180	+	3.94752i	−0.140111	+	0.156162i
$640$	6.34335	−	14.3804i	0.250743	−	0.568437i
$641$	−10.7527	−	18.6243i	−0.424708	−	0.735616i	0.571685	−	0.820473i	$-0.306290\pi$
$641$	−10.7527	−	18.6243i	−0.424708	−	0.735616i	−0.996393	+	0.0848574i	$0.972957\pi$
$642$	−31.5917	−	11.5386i	−1.24683	−	0.455391i
$643$	2.51035	+	1.44935i	0.0989986	+	0.0571568i	0.548682	−	0.836031i	$-0.315130\pi$
$643$	2.51035	+	1.44935i	0.0989986	+	0.0571568i	−0.449683	+	0.893188i	$0.648463\pi$
$644$	−4.62896	−	10.9560i	−0.182406	−	0.431726i
$645$	14.1494	+	5.41714i	0.557131	+	0.213300i
$646$	−2.11344	+	0.0326590i	−0.0831521	+	0.00128495i
$647$	43.4621			1.70867			0.854336	−	0.519722i	$-0.173964\pi$
$647$	43.4621			1.70867			0.854336	+	0.519722i	$0.173964\pi$
$648$	−3.91973	−	25.1523i	−0.153982	−	0.988074i
$649$		−	9.40034i		−	0.368996i
$650$	19.7949	−	0.305891i	0.776420	−	0.0119980i
$651$	9.30267	−	0.0298950i	0.364600	−	0.00117168i
$652$	−35.4452	+	1.09573i	−1.38814	+	0.0429122i
$653$	−39.0856	−	22.5661i	−1.52954	−	0.883078i	−0.999381	−	0.0351771i	$-0.988800\pi$
$653$	−39.0856	−	22.5661i	−1.52954	−	0.883078i	−0.530155	−	0.847901i	$-0.677866\pi$
$654$	−10.7442	+	29.4168i	−0.420132	+	1.15029i
$655$	−0.837953	+	0.483792i	−0.0327415	+	0.0189033i
$656$	17.3473	+	8.63346i	0.677300	+	0.337080i
$657$	17.7115	−	19.7404i	0.690991	−	0.770146i
$658$	3.34069	−	23.8276i	0.130234	−	0.928897i
$659$	17.7441	+	30.7337i	0.691213	+	1.19722i	0.971441	+	0.237283i	$0.0762569\pi$
$659$	17.7441	+	30.7337i	0.691213	+	1.19722i	−0.280227	+	0.959934i	$0.590410\pi$
$660$	3.02494	+	1.05215i	0.117746	+	0.0409548i
$661$	−7.08827	+	12.2772i	−0.275702	+	0.477530i	−0.970312	−	0.241857i	$-0.922244\pi$
$661$	−7.08827	+	12.2772i	−0.275702	+	0.477530i	0.694610	+	0.719386i	$0.255577\pi$
$662$	−7.79940	−	13.0394i	−0.303132	−	0.506792i
$663$	10.8620	+	13.3893i	0.421845	+	0.519998i
$664$	24.2512	−	15.5427i	0.941128	−	0.603172i
$665$	−0.907298	−	2.34721i	−0.0351835	−	0.0910209i
$666$	−30.0631	+	34.5669i	−1.16492	+	1.33944i
$667$	6.20867			0.240401
$668$	4.38805	−	8.17362i	0.169779	−	0.316247i
$669$	5.56631	+	34.9451i	0.215206	+	1.35106i
$670$	14.3307	+	23.9588i	0.553643	+	0.925607i
$671$	1.48938	−	2.57968i	0.0574967	−	0.0995873i
$672$	−14.7242	−	21.3354i	−0.567998	−	0.823030i
$673$	−17.5118	−	30.3313i	−0.675029	−	1.16918i	−0.976460	−	0.215697i	$-0.930798\pi$
$673$	−17.5118	−	30.3313i	−0.675029	−	1.16918i	0.301431	−	0.953488i	$-0.402536\pi$
$674$	10.5927	−	19.0198i	0.408015	−	0.732617i
$675$	−8.65293	+	13.4017i	−0.333051	+	0.515832i
$676$	−8.20509	−	13.2486i	−0.315580	−	0.509562i
$677$	−23.4003	−	40.5305i	−0.899346	−	1.55771i	−0.828332	−	0.560237i	$-0.810710\pi$
$677$	−23.4003	−	40.5305i	−0.899346	−	1.55771i	−0.0710138	−	0.997475i	$-0.522623\pi$
$678$	−34.0425	+	28.5001i	−1.30739	+	1.09454i
$679$	−0.175546	−	0.0273841i	−0.00673685	−	0.00105091i
$680$	−7.61939	−	3.94008i	−0.292190	−	0.151095i
$681$	−33.2043	+	5.28901i	−1.27239	+	0.202675i
$682$	1.91036	−	0.0295208i	0.0731514	−	0.00113041i
$683$	18.5046			0.708057			0.354028	−	0.935235i	$-0.384812\pi$
$683$	18.5046			0.708057			0.354028	+	0.935235i	$0.384812\pi$
$684$	−2.64755	+	3.14090i	−0.101232	+	0.120095i
$685$	17.7863			0.679580
$686$	11.3638	−	23.5979i	0.433874	−	0.900974i
$687$	7.44188	−	6.03717i	0.283925	−	0.230332i
$688$	−13.9164	−	20.9924i	−0.530556	−	0.800330i
$689$	−1.26395	−	0.729743i	−0.0481527	−	0.0278010i
$690$	−7.53400	+	1.31974i	−0.286814	+	0.0502416i
$691$	−1.57121	+	0.907139i	−0.0597717	+	0.0345092i	−0.529588	−	0.848255i	$-0.677653\pi$
$691$	−1.57121	+	0.907139i	−0.0597717	+	0.0345092i	0.469816	+	0.882764i	$0.344320\pi$
$692$	7.63348	+	12.3256i	0.290181	+	0.468550i
$693$	4.09146	−	3.34103i	0.155422	−	0.126915i
$694$	7.31514	−	13.1348i	0.277679	−	0.498590i
$695$	11.3349	−	6.54423i	0.429959	−	0.248237i
$696$	13.2506	−	2.74562i	0.502264	−	0.104073i
$697$	5.28755	−	9.15831i	0.200280	−	0.346896i
$698$	−18.2057	−	30.4372i	−0.689097	−	1.15207i
$699$	2.13429	+	0.817122i	0.0807263	+	0.0309064i
$700$	−2.00670	+	16.1207i	−0.0758463	+	0.609305i
$701$		−	13.2082i		−	0.498865i	−0.968392	−	0.249433i	$-0.919756\pi$
$701$		−	13.2082i		−	0.498865i	0.968392	−	0.249433i	$-0.0802441\pi$
$702$	33.4879	+	1.14797i	1.26392	+	0.0433275i
$703$	7.39268			0.278820
$704$	−3.07744	−	4.34451i	−0.115986	−	0.163740i
$705$	−14.4503	−	5.53236i	−0.544229	−	0.208361i
$706$	18.0887	−	10.8196i	0.680777	−	0.407200i
$707$	4.10174	−	26.2943i	0.154262	−	0.988897i
$708$	31.9860	+	37.0286i	1.20211	+	1.39162i
$709$	9.76964	−	5.64050i	0.366906	−	0.211834i	−0.305200	−	0.952288i	$-0.598723\pi$
$709$	9.76964	−	5.64050i	0.366906	−	0.211834i	0.672106	+	0.740455i	$0.265390\pi$
$710$	3.03437	+	1.68993i	0.113878	+	0.0634218i
$711$	37.5169	+	7.90544i	1.40699	+	0.296477i
$712$	1.43309	+	30.8931i	0.0537073	+	1.15777i
$713$	−3.95157	+	2.28144i	−0.147987	+	0.0854406i
$714$	−12.1180	+	7.30126i	−0.453506	+	0.273243i
$715$	−2.10786	+	3.65092i	−0.0788295	+	0.136537i
$716$	36.9487	−	1.14221i	1.38084	−	0.0426864i
$717$	21.7187	+	26.7721i	0.811099	+	0.999823i
$718$	0.577591	+	37.3772i	0.0215555	+	1.39491i
$719$	−19.2468			−0.717786			−0.358893	−	0.933379i	$-0.616846\pi$
$719$	−19.2468			−0.717786			−0.358893	+	0.933379i	$0.616846\pi$
$720$	−15.4956	+	6.14832i	−0.577485	+	0.229135i
$721$	23.8619	−	9.22367i	0.888665	−	0.343508i
$722$	−26.2040	+	0.404931i	−0.975213	+	0.0150700i
$723$	−36.9258	+	5.88180i	−1.37328	+	0.218746i
$724$	−11.8942	+	0.367689i	−0.442043	+	0.0136650i
$725$	−7.34403	−	4.24008i	−0.272751	−	0.157473i
$726$	−19.8282	+	16.6000i	−0.735892	+	0.616082i
$727$	21.9867	+	38.0821i	0.815441	+	1.41239i	0.909011	+	0.416773i	$0.136839\pi$
$727$	21.9867	+	38.0821i	0.815441	+	1.41239i	−0.0935694	+	0.995613i	$0.529828\pi$
$728$	31.2231	−	13.7643i	1.15721	−	0.510139i
$729$	−15.7546	+	21.9270i	−0.583503	+	0.812111i
$730$	−15.1740	−	8.45082i	−0.561614	−	0.312779i
$731$	−11.9040	+	6.87278i	−0.440286	+	0.254199i
$732$	2.91096	+	15.2294i	0.107592	+	0.562893i
$733$	−8.41971	+	14.5834i	−0.310989	+	0.538649i	−0.978577	−	0.205882i	$-0.933994\pi$
$733$	−8.41971	+	14.5834i	−0.310989	+	0.538649i	0.667588	+	0.744531i	$0.267327\pi$
$734$	14.9362	+	24.9710i	0.551304	+	0.921697i
$735$	−13.1485	−	10.5272i	−0.484989	−	0.388302i
$736$	11.4693	+	5.48861i	0.422763	+	0.202313i
$737$	9.45671			0.348342
$738$	−6.68652	−	19.4343i	−0.246134	−	0.715385i
$739$	17.2419			0.634252			0.317126	−	0.948383i	$-0.397282\pi$
$739$	17.2419			0.634252			0.317126	+	0.948383i	$0.397282\pi$
$740$	26.4329	+	14.1906i	0.971693	+	0.521658i
$741$	−3.40657	−	4.19920i	−0.125144	−	0.154262i
$742$	0.737013	−	0.943979i	0.0270566	−	0.0346545i
$743$	−7.81374	−	4.51126i	−0.286658	−	0.165502i	0.349776	−	0.936834i	$-0.386258\pi$
$743$	−7.81374	−	4.51126i	−0.286658	−	0.165502i	−0.636434	+	0.771331i	$0.719591\pi$
$744$	−7.42459	+	6.61656i	−0.272199	+	0.242575i
$745$	3.76248	−	2.17227i	0.137847	−	0.0795859i
$746$	29.6721	+	16.5252i	1.08637	+	0.605031i
$747$	−29.8952	−	6.29942i	−1.09381	−	0.230484i
$748$	−2.47026	+	1.52987i	−0.0903216	+	0.0559377i
$749$	28.2852	+	22.7959i	1.03352	+	0.832942i
$750$	25.7949	+	9.42134i	0.941896	+	0.344019i
$751$	4.73922	+	2.73619i	0.172937	+	0.0998450i	0.583970	−	0.811775i	$-0.301499\pi$
$751$	4.73922	+	2.73619i	0.172937	+	0.0998450i	−0.411033	+	0.911620i	$0.634832\pi$
$752$	14.2123	+	21.4389i	0.518271	+	0.781797i
$753$	6.24752	−	16.3183i	0.227672	−	0.594671i
$754$	0.275222	+	17.8102i	0.0100230	+	0.648610i
$755$		−	20.6924i		−	0.753073i
$756$	−4.74823	+	27.0824i	−0.172691	+	0.984976i
$757$			23.5580i			0.856230i	0.903724	+	0.428115i	$0.140822\pi$
$757$			23.5580i			0.856230i	−0.903724	+	0.428115i	$0.859178\pi$
$758$	6.82228	−	0.105425i	0.247796	−	0.00382920i
$759$	−0.926366	+	2.41963i	−0.0336250	+	0.0878271i
$760$	2.38962	+	1.23570i	0.0866806	+	0.0448236i
$761$	−20.7406	−	11.9746i	−0.751845	−	0.434078i	0.0745151	−	0.997220i	$-0.476259\pi$
$761$	−20.7406	−	11.9746i	−0.751845	−	0.434078i	−0.826360	+	0.563142i	$0.809592\pi$
$762$	1.68579	−	4.61558i	0.0610699	−	0.167205i
$763$	21.2265	−	26.3379i	0.768450	−	0.953497i
$764$	37.1769	−	23.0243i	1.34501	−	0.832990i
$765$	2.82672	+	8.64792i	0.102200	+	0.312666i
$766$	24.4649	−	43.9283i	0.883953	−	1.58719i
$767$	−55.7787	+	32.2039i	−2.01405	+	1.16281i
$768$	26.9051	+	6.64189i	0.970855	+	0.239669i
$769$	−23.2734	−	13.4369i	−0.839260	−	0.484547i	0.0177529	−	0.999842i	$-0.494349\pi$
$769$	−23.2734	−	13.4369i	−0.839260	−	0.484547i	−0.857012	+	0.515296i	$0.827682\pi$
$770$	−2.72668	−	2.12886i	−0.0982628	−	0.0767188i
$771$	−4.34612	−	5.35736i	−0.156522	−	0.192941i
$772$	7.17239	−	13.3600i	0.258140	−	0.480838i
$773$	0.543383			0.0195441			0.00977207	−	0.999952i	$-0.496889\pi$
$773$	0.543383			0.0195441			0.00977207	+	0.999952i	$0.496889\pi$
$774$	−5.10360	+	26.2220i	−0.183445	+	0.942531i
$775$	6.23224			0.223869
$776$	0.159912	−	0.102489i	0.00574052	−	0.00367912i
$777$	42.7726	−	24.8784i	1.53446	−	0.892508i
$778$	−31.2149	+	18.6708i	−1.11911	+	0.669382i
$779$	−1.65830	+	2.87226i	−0.0594147	+	0.102909i
$780$	−4.11978	−	21.5536i	−0.147512	−	0.771741i
$781$	1.01888	−	0.588253i	0.0364585	−	0.0210494i
$782$	3.37636	−	6.06246i	0.120738	−	0.216793i
$783$	−12.0580	−	7.78537i	−0.430919	−	0.278226i
$784$	7.62791	+	26.9410i	0.272425	+	0.962177i
$785$	13.5466	+	23.4635i	0.483500	+	0.837447i
$786$	−1.09516	−	1.30813i	−0.0390630	−	0.0466596i
$787$	−36.8479	−	21.2741i	−1.31349	−	0.758341i	−0.330814	−	0.943696i	$-0.607323\pi$
$787$	−36.8479	−	21.2741i	−1.31349	−	0.758341i	−0.982672	+	0.185354i	$0.940657\pi$
$788$	0.123187	+	3.98489i	0.00438834	+	0.141956i
$789$	2.66910	−	0.425153i	0.0950224	−	0.0151358i
$790$	−0.387962	−	25.1059i	−0.0138031	−	0.893229i
$791$	44.7295	−	17.2899i	1.59040	−	0.614758i
$792$	−0.907047	+	5.57368i	−0.0322305	+	0.198052i
$793$	−20.4093			−0.724757
$794$	−31.1577	+	0.481480i	−1.10574	+	0.0170871i
$795$	−0.485212	−	0.598110i	−0.0172087	−	0.0212128i
$796$	−13.9807	+	0.432190i	−0.495532	+	0.0153186i
$797$	−10.0297	+	17.3719i	−0.355269	+	0.615345i	−0.987164	−	0.159710i	$-0.948944\pi$
$797$	−10.0297	+	17.3719i	−0.355269	+	0.615345i	0.631895	+	0.775054i	$0.282278\pi$
$798$	3.80050	−	2.28984i	0.134536	−	0.0810596i
$799$	12.1572	−	7.01895i	0.430090	−	0.248313i
$800$	−9.81830	−	14.3250i	−0.347129	−	0.506465i
$801$	21.9061	−	24.4155i	0.774014	−	0.862680i
$802$	−3.14356	+	5.64446i	−0.111003	+	0.199313i
$803$	−5.09514	+	2.94168i	−0.179804	+	0.103810i
$804$	−37.2507	+	32.1778i	−1.31373	+	1.13482i
$805$	8.16284	+	1.27335i	0.287702	+	0.0448797i
$806$	−6.71971	−	11.2344i	−0.236692	−	0.395713i
$807$	44.3273	+	16.9709i	1.56040	+	0.597404i
$808$	15.3513	+	23.9525i	0.540056	+	0.842647i
$809$	15.5846			0.547925			0.273963	−	0.961740i	$-0.411666\pi$
$809$	15.5846			0.547925			0.273963	+	0.961740i	$0.411666\pi$
$810$	16.2869	+	6.88416i	0.572262	+	0.241885i
$811$			44.1901i			1.55172i	0.630902	+	0.775862i	$0.282685\pi$
$811$			44.1901i			1.55172i	−0.630902	+	0.775862i	$0.717315\pi$
$812$	−14.5044	−	1.80551i	−0.509005	−	0.0633609i
$813$	−7.65420	−	2.93044i	−0.268444	−	0.102775i
$814$	8.72144	−	5.21664i	0.305686	−	0.182843i
$815$	12.3163	−	21.3324i	0.431420	−	0.747242i
$816$	4.52491	−	14.4317i	0.158404	−	0.505211i
$817$	3.73338	−	2.15547i	0.130614	−	0.0754102i
$818$	−2.39681	−	1.33485i	−0.0838024	−	0.0466719i
$819$	−33.8413	−	12.8317i	−1.18251	−	0.448377i
$820$	−11.4428	+	7.08671i	−0.399599	+	0.247479i
$821$	13.3608	−	7.71385i	0.466294	−	0.269215i	−0.248393	−	0.968659i	$-0.579902\pi$
$821$	13.3608	−	7.71385i	0.466294	−	0.269215i	0.714687	+	0.699444i	$0.246569\pi$
$822$	5.41112	+	30.8905i	0.188735	+	1.07743i
$823$	−29.3935	−	16.9703i	−1.02459	−	0.591549i	−0.109162	−	0.994024i	$-0.534817\pi$
$823$	−29.3935	−	16.9703i	−1.02459	−	0.591549i	−0.915431	+	0.402475i	$0.868150\pi$
$824$	−12.5622	+	24.2931i	−0.437627	+	0.846289i
$825$	2.74820	−	2.22946i	0.0956802	−	0.0776199i
$826$	−19.8147	−	48.9963i	−0.689442	−	1.70480i
$827$	−9.17132			−0.318918			−0.159459	−	0.987205i	$-0.550975\pi$
$827$	−9.17132			−0.318918			−0.159459	+	0.987205i	$0.550975\pi$
$828$	−4.58413	−	12.6832i	−0.159309	−	0.440772i
$829$	−5.43073			−0.188617			−0.0943085	−	0.995543i	$-0.530064\pi$
$829$	−5.43073			−0.188617			−0.0943085	+	0.995543i	$0.530064\pi$
$830$	0.309147	+	20.0056i	0.0107306	+	0.694404i
$831$	13.7980	−	2.19784i	0.478646	−	0.0762421i
$832$	−15.2362	+	33.1441i	−0.528221	+	1.14907i
$833$	14.9323	−	3.24685i	0.517372	−	0.112497i
$834$	14.8142	+	17.6951i	0.512972	+	0.612730i
$835$	3.22198	+	5.58063i	0.111501	+	0.193126i
$836$	0.774731	−	0.479804i	0.0267946	−	0.0165944i
$837$	10.5353	+	0.524231i	0.364152	+	0.0181201i
$838$	12.7357	+	7.09289i	0.439949	+	0.245020i
$839$	−1.59887	−	2.76932i	−0.0551991	−	0.0956076i	0.837105	−	0.547042i	$-0.184246\pi$
$839$	−1.59887	−	2.76932i	−0.0551991	−	0.0956076i	−0.892305	+	0.451434i	$0.850913\pi$
$840$	17.9844	−	0.892196i	0.620519	−	0.0307837i
$841$	−10.6850	+	18.5070i	−0.368450	+	0.638174i
$842$	0.287646	−	0.172052i	0.00991292	−	0.00592931i
$843$	−6.30341	−	39.5726i	−0.217101	−	1.36295i
$844$	−1.71386	+	3.19242i	−0.0589937	+	0.109887i
$845$	10.8246			0.372378
$846$	5.21214	−	26.7797i	0.179197	−	0.920706i
$847$	26.0528	−	10.0706i	0.895186	−	0.346028i
$848$	0.0790816	+	1.27786i	0.00271567	+	0.0438819i
$849$	−26.9252	−	33.1901i	−0.924072	−	1.13908i
$850$	−8.13401	+	4.86527i	−0.278994	+	0.166878i
$851$	−12.1351	+	21.0186i	−0.415986	+	0.720508i
$852$	−2.01184	+	5.78408i	−0.0689246	+	0.198159i
$853$	−9.28513	−	16.0823i	−0.317917	−	0.550648i	0.662136	−	0.749383i	$-0.269650\pi$
$853$	−9.28513	−	16.0823i	−0.317917	−	0.550648i	−0.980053	+	0.198735i	$0.936317\pi$
$854$	2.32528	−	16.5852i	0.0795696	−	0.567533i
$855$	−0.886526	−	2.71219i	−0.0303186	−	0.0927549i
$856$	−38.7943	+	1.79961i	−1.32596	+	0.0615094i
$857$	6.36981	−	3.67761i	0.217589	−	0.125625i	−0.387245	−	0.921977i	$-0.626573\pi$
$857$	6.36981	−	3.67761i	0.217589	−	0.125625i	0.604833	+	0.796352i	$0.293240\pi$
$858$	−6.98203	−	2.55012i	−0.238363	−	0.0870596i
$859$	10.1767	+	5.87555i	0.347226	+	0.200471i	0.663463	−	0.748209i	$-0.269086\pi$
$859$	10.1767	+	5.87555i	0.347226	+	0.200471i	−0.316237	+	0.948680i	$0.602419\pi$
$860$	17.4864	−	0.540565i	0.596282	−	0.0184331i
$861$	0.0713384	+	22.1990i	0.00243121	+	0.756539i
$862$	−0.153427	−	9.92863i	−0.00522575	−	0.338170i
$863$			50.2847i			1.71171i	0.517215	+	0.855855i	$0.326969\pi$
$863$			50.2847i			1.71171i	−0.517215	+	0.855855i	$0.673031\pi$
$864$	−15.3923	−	25.0415i	−0.523658	−	0.851929i
$865$	−10.0705			−0.342408
$866$	−0.835825	−	54.0882i	−0.0284025	−	1.83799i
$867$	19.7898	+	7.57661i	0.672097	+	0.257315i
$868$	9.89492	−	4.18066i	0.335856	−	0.141901i
$869$	−7.36582	−	4.25266i	−0.249868	−	0.144262i
$870$	−3.22476	+	8.82913i	−0.109329	+	0.299336i
$871$	−32.3970	−	56.1132i	−1.09773	−	1.90132i
$872$	1.67572	+	36.1235i	0.0567470	+	1.22330i
$873$	−0.197129	−	0.0415385i	−0.00667181	−	0.00140586i
$874$	−1.05890	+	1.90133i	−0.0358180	+	0.0643134i
$875$	−23.0951	−	18.6130i	−0.780757	−	0.629234i
$876$	10.0606	−	28.9245i	0.339917	−	0.977267i
$877$	26.4207	+	15.2540i	0.892164	+	0.515091i	0.874650	−	0.484755i	$-0.161091\pi$
$877$	26.4207	+	15.2540i	0.892164	+	0.515091i	0.0175143	+	0.999847i	$0.494425\pi$
$878$	25.1810	+	42.0989i	0.849818	+	1.42077i
$879$	−39.2968	+	31.8792i	−1.32545	+	1.07526i
$880$	3.69110	−	0.228427i	0.124427	−	0.00770028i
$881$		−	15.6227i		−	0.526342i	−0.964749	−	0.263171i	$-0.915232\pi$
$881$		−	15.6227i		−	0.526342i	0.964749	−	0.263171i	$-0.0847684\pi$
$882$	14.2830	−	26.0383i	0.480934	−	0.876757i
$883$	16.8043			0.565510			0.282755	−	0.959192i	$-0.408752\pi$
$883$	16.8043			0.565510			0.282755	+	0.959192i	$0.408752\pi$
$884$	17.5405	+	9.41669i	0.589950	+	0.316718i
$885$	−33.5650	+	5.34646i	−1.12827	+	0.179719i
$886$	−12.3988	−	20.7289i	−0.416545	−	0.696400i
$887$	−8.81776	+	15.2728i	−0.296071	+	0.512811i	−0.975234	−	0.221178i	$-0.929010\pi$
$887$	−8.81776	+	15.2728i	−0.296071	+	0.512811i	0.679162	+	0.733988i	$0.262343\pi$
$888$	−16.6040	+	50.2247i	−0.557193	+	1.68543i
$889$	−3.33049	+	4.13249i	−0.111701	+	0.138599i
$890$	−18.7676	−	10.4522i	−0.629092	−	0.350359i
$891$	4.83322	−	3.53761i	0.161919	−	0.118514i
$892$	21.5136	+	34.7375i	0.720327	+	1.16310i
$893$	−3.81278	+	2.20131i	−0.127590	+	0.0736640i
$894$	4.91736	+	5.87364i	0.164461	+	0.196444i
$895$	−12.8387	+	22.2373i	−0.429150	+	0.743310i
$896$	−25.1979	−	16.1576i	−0.841802	−	0.539786i
$897$	17.5309	−	2.79245i	0.585340	−	0.0932371i
$898$	31.5018	−	0.486798i	1.05123	−	0.0162447i
$899$			5.60738i			0.187017i
$900$	−3.23931	+	18.1332i	−0.107977	+	0.604439i
$901$	0.698735			0.0232782
$902$	0.0704456	+	4.55869i	0.00234558	+	0.151788i
$903$	14.3469	−	25.0350i	0.477434	−	0.833111i
$904$	−23.5481	+	45.5377i	−0.783198	+	1.51456i
$905$	4.13290	−	7.15840i	0.137382	−	0.237953i
$906$	35.9376	−	6.29523i	1.19395	−	0.209145i
$907$	5.18499	+	8.98067i	0.172165	+	0.298198i	0.939176	−	0.343435i	$-0.111590\pi$
$907$	5.18499	+	8.98067i	0.172165	+	0.298198i	−0.767012	+	0.641633i	$0.778257\pi$
$908$	−33.0070	+	20.4418i	−1.09538	+	0.678386i
$909$	6.22185	−	29.5271i	0.206366	−	0.979351i
$910$	−3.29089	+	23.4724i	−0.109092	+	0.778102i
$911$	−44.4979	+	25.6909i	−1.47428	+	0.851177i	−0.999580	−	0.0289691i	$-0.990778\pi$
$911$	−44.4979	+	25.6909i	−1.47428	+	0.851177i	−0.474702	+	0.880146i	$0.657444\pi$
$912$	−1.41912	+	4.52612i	−0.0469917	+	0.149875i
$913$	5.86943	+	3.38872i	0.194250	+	0.112150i
$914$	−19.8338	−	33.1592i	−0.656044	−	1.09681i
$915$	−10.0581	−	3.85079i	−0.332511	−	0.127303i
$916$	5.23387	−	9.74912i	0.172932	−	0.322120i
$917$	0.664391	+	1.71880i	0.0219401	+	0.0567598i
$918$	−14.1593	+	7.54028i	−0.467328	+	0.248866i
$919$			6.66780i			0.219951i	0.993934	+	0.109975i	$0.0350772\pi$
$919$			6.66780i			0.219951i	−0.993934	+	0.109975i	$0.964923\pi$
$920$	−7.43587	+	4.76568i	−0.245153	+	0.157120i
$921$	4.53577	−	11.8472i	0.149459	−	0.390380i
$922$	11.1490	+	18.6395i	0.367173	+	0.613859i
$923$	−6.98103	−	4.03050i	−0.229783	−	0.132665i
$924$	2.86777	−	5.38324i	0.0943428	−	0.177096i
$925$	28.7084	−	16.5748i	0.943927	−	0.544976i
$926$	−20.4463	−	11.3871i	−0.671907	−	0.374204i
$927$	27.5723	−	9.01250i	0.905594	−	0.296009i
$928$	12.8887	−	8.83390i	0.423094	−	0.289987i
$929$	−45.2877	+	26.1468i	−1.48584	+	0.857850i	−0.999870	−	0.0161251i	$-0.994867\pi$
$929$	−45.2877	+	26.1468i	−1.48584	+	0.857850i	−0.485970	+	0.873975i	$0.661534\pi$
$930$	−1.19193	−	6.80436i	−0.0390848	−	0.223124i
$931$	−4.68311	+	1.01829i	−0.153483	+	0.0333730i
$932$	2.63765	−	0.0815388i	0.0863991	−	0.00267089i
$933$	−19.0693	+	15.4699i	−0.624302	+	0.506460i
$934$	0.708201	+	45.8293i	0.0231730	+	1.49958i
$935$		−	2.01830i		−	0.0660053i
$936$	36.1799	−	13.7123i	1.18258	−	0.448200i
$937$		−	39.8846i		−	1.30297i	−0.758660	−	0.651487i	$-0.774146\pi$
$937$		−	39.8846i		−	1.30297i	0.758660	−	0.651487i	$-0.225854\pi$
$938$	49.2901	−	19.9335i	1.60938	−	0.650853i
$939$	−2.13596	+	0.340230i	−0.0697043	+	0.0111030i
$940$	−17.8583	+	0.552061i	−0.582474	+	0.0180062i
$941$	15.4336	−	26.7317i	0.503120	−	0.871430i	−0.496873	−	0.867823i	$-0.665519\pi$
$941$	15.4336	−	26.7317i	0.503120	−	0.871430i	0.999993	−	0.00360673i	$-0.00114806\pi$
$942$	−36.6290	+	30.6655i	−1.19344	+	0.999135i
$943$	−5.44420	−	9.42964i	−0.177288	−	0.307071i
$944$	50.5824	+	25.1739i	1.64632	+	0.819342i
$945$	−14.2565	−	12.7088i	−0.463765	−	0.413417i
$946$	2.88341	−	5.17734i	0.0937477	−	0.168330i
$947$	−17.7086	−	30.6723i	−0.575453	−	0.996715i	−0.995992	−	0.0894401i	$-0.971492\pi$
$947$	−17.7086	−	30.6723i	−0.575453	−	0.996715i	0.420539	−	0.907275i	$-0.361841\pi$
$948$	43.4848	−	8.31176i	1.41232	−	0.269953i
$949$	34.9101	+	20.1553i	1.13323	+	0.654270i
$950$	2.55101	−	1.52586i	0.0827658	−	0.0495055i
$951$	−27.9784	+	4.45660i	−0.907263	+	0.144515i
$952$	−9.65068	+	13.1810i	−0.312780	+	0.427198i
$953$	32.1207			1.04049			0.520245	−	0.854017i	$-0.325840\pi$
$953$	32.1207			1.04049			0.520245	+	0.854017i	$0.325840\pi$
$954$	0.891154	−	1.02466i	0.0288522	−	0.0331745i
$955$			30.3750i			0.982911i
$956$	35.0724	+	18.8288i	1.13432	+	0.608967i
$957$	2.00593	+	2.47266i	0.0648425	+	0.0799299i
$958$	−6.83022	−	11.4191i	−0.220674	−	0.368935i
$959$	5.22092	−	33.4688i	0.168592	−	1.08076i
$960$	−13.7623	+	13.4593i	−0.444175	+	0.434397i
$961$	13.4395	+	23.2779i	0.433533	+	0.750900i
$962$	−60.8320	−	33.8791i	−1.96130	−	1.09230i
$963$	30.6599	+	27.5087i	0.988003	+	0.886457i
$964$	−36.7064	+	22.7329i	−1.18223	+	0.732178i
$965$	5.26642	+	9.12170i	0.169532	+	0.293638i
$966$	0.271878	+	14.5642i	0.00874754	+	0.468597i
$967$	−0.0738710	−	0.0426494i	−0.00237553	−	0.00137151i	0.498812	−	0.866710i	$-0.333770\pi$
$967$	−0.0738710	−	0.0426494i	−0.00237553	−	0.00137151i	−0.501187	+	0.865339i	$0.667103\pi$
$968$	−13.7157	+	26.5236i	−0.440838	+	0.852500i
$969$	2.41760	+	0.925590i	0.0776646	+	0.0297342i
$970$	0.00203852	+	0.131917i	6.54528e−5	+	0.00423560i
$971$			32.9976i			1.05894i	0.848328	+	0.529471i	$0.177610\pi$
$971$			32.9976i			1.05894i	−0.848328	+	0.529471i	$0.822390\pi$
$972$	−7.00116	+	30.3806i	−0.224562	+	0.974460i
$973$	−8.98718	−	23.2501i	−0.288116	−	0.745364i
$974$	−0.578106	−	37.4106i	−0.0185237	−	1.19871i
$975$	−22.6438	−	8.66927i	−0.725182	−	0.277639i
$976$	9.89247	+	14.9225i	0.316650	+	0.477658i
$977$	−17.9953	+	31.1688i	−0.575721	+	0.997178i	0.420242	+	0.907412i	$0.361945\pi$
$977$	−17.9953	+	31.1688i	−0.575721	+	0.997178i	−0.995963	+	0.0897657i	$0.971388\pi$
$978$	40.7962	+	14.9004i	1.30452	+	0.476462i
$979$	−6.30182	+	3.63836i	−0.201407	+	0.116282i
$980$	−18.6993	−	5.34853i	−0.597329	−	0.170853i
$981$	25.6149	−	28.5492i	0.817821	−	0.911505i
$982$	16.1466	−	28.9922i	0.515258	−	0.925177i
$983$	2.81174	+	4.87007i	0.0896805	+	0.155331i	0.907376	−	0.420320i	$-0.138082\pi$
$983$	2.81174	+	4.87007i	0.0896805	+	0.155331i	−0.817696	+	0.575651i	$0.804749\pi$
$984$	−15.7891	−	17.7173i	−0.503339	−	0.564808i
$985$	−2.39827	−	1.38464i	−0.0764153	−	0.0441184i
$986$	−4.37747	−	7.31848i	−0.139407	−	0.233068i
$987$	−14.6520	+	25.5674i	−0.466378	+	0.813819i
$988$	−5.50110	−	2.95329i	−0.175013	−	0.0939568i
$989$			14.1528i			0.450033i
$990$	−2.95972	−	2.57410i	−0.0940662	−	0.0818102i
$991$			7.65210i			0.243077i	0.992587	+	0.121539i	$0.0387828\pi$
$991$			7.65210i			0.243077i	−0.992587	+	0.121539i	$0.961217\pi$
$992$	−4.95706	+	10.3585i	−0.157387	+	0.328883i
$993$	2.92723	+	18.3771i	0.0928929	+	0.583179i
$994$	4.07065	−	5.21376i	0.129113	−	0.165370i
$995$	4.85791	−	8.41415i	0.154006	−	0.266747i
$996$	−34.6507	+	6.62320i	−1.09795	+	0.209864i
$997$	−12.2168	−	21.1601i	−0.386910	−	0.670148i	0.605122	−	0.796133i	$-0.293124\pi$
$997$	−12.2168	−	21.1601i	−0.386910	−	0.670148i	−0.992032	+	0.125985i	$0.959791\pi$
$998$	−22.7117	+	40.7803i	−0.718926	+	1.29088i
$999$	49.9242	−	25.6040i	1.57953	−	0.810074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.be.a.139.2	yes	184
7.6	odd	2	inner	504.2.be.a.139.1	✓	184
8.3	odd	2	inner	504.2.be.a.139.64	yes	184
9.7	even	3	inner	504.2.be.a.475.63	yes	184
56.27	even	2	inner	504.2.be.a.139.63	yes	184
63.34	odd	6	inner	504.2.be.a.475.64	yes	184
72.43	odd	6	inner	504.2.be.a.475.1	yes	184
504.475	even	6	inner	504.2.be.a.475.2	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.1	✓	184	7.6	odd	2	inner
504.2.be.a.139.2	yes	184	1.1	even	1	trivial
504.2.be.a.139.63	yes	184	56.27	even	2	inner
504.2.be.a.139.64	yes	184	8.3	odd	2	inner
504.2.be.a.475.1	yes	184	72.43	odd	6	inner
504.2.be.a.475.2	yes	184	504.475	even	6	inner
504.2.be.a.475.63	yes	184	9.7	even	3	inner
504.2.be.a.475.64	yes	184	63.34	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.41404 + 0.0218513i) q^{2} +(1.61755 + 0.619288i) q^{3} +(1.99905 - 0.0617973i) q^{4} +(-0.694615 + 1.20311i) q^{5} +(-2.30083 - 0.840355i) q^{6} +(2.06001 + 1.66022i) q^{7} +(-2.82539 + 0.131066i) q^{8} +(2.23297 + 2.00346i) q^{9} +O(q^{10})\)	\(q+(-1.41404 + 0.0218513i) q^{2} +(1.61755 + 0.619288i) q^{3} +(1.99905 - 0.0617973i) q^{4} +(-0.694615 + 1.20311i) q^{5} +(-2.30083 - 0.840355i) q^{6} +(2.06001 + 1.66022i) q^{7} +(-2.82539 + 0.131066i) q^{8} +(2.23297 + 2.00346i) q^{9} +(0.955927 - 1.71643i) q^{10} +(-0.332753 - 0.576345i) q^{11} +(3.27183 + 1.13802i) q^{12} +(-2.27990 + 3.94891i) q^{13} +(-2.94923 - 2.30262i) q^{14} +(-1.86865 + 1.51593i) q^{15} +(3.99236 - 0.247071i) q^{16} -2.18303i q^{17} +(-3.20129 - 2.78419i) q^{18} +0.684648i q^{19} +(-1.31422 + 2.44799i) q^{20} +(2.30403 + 3.96124i) q^{21} +(0.483121 + 0.807706i) q^{22} +(-1.94657 - 1.12385i) q^{23} +(-4.65139 - 1.53772i) q^{24} +(1.53502 + 2.65873i) q^{25} +(3.13759 - 5.63375i) q^{26} +(2.37122 + 4.62356i) q^{27} +(4.22066 + 3.19156i) q^{28} +(-2.39216 + 1.38112i) q^{29} +(2.60923 - 2.18442i) q^{30} +(1.01501 - 1.75805i) q^{31} +(-5.63998 + 0.436608i) q^{32} +(-0.181323 - 1.13834i) q^{33} +(0.0477019 + 3.08690i) q^{34} +(-3.42835 + 1.32520i) q^{35} +(4.58761 + 3.86702i) q^{36} -10.7978i q^{37} +(-0.0149604 - 0.968123i) q^{38} +(-6.13337 + 4.97566i) q^{39} +(1.80487 - 3.49029i) q^{40} +(4.19523 + 2.42212i) q^{41} +(-3.34456 - 5.55103i) q^{42} +(-3.14828 - 5.45299i) q^{43} +(-0.700804 - 1.13158i) q^{44} +(-3.96144 + 1.29486i) q^{45} +(2.77709 + 1.54664i) q^{46} +(3.21524 + 5.56896i) q^{47} +(6.61087 + 2.07277i) q^{48} +(1.48732 + 6.84017i) q^{49} +(-2.22868 - 3.72602i) q^{50} +(1.35192 - 3.53116i) q^{51} +(-4.31359 + 8.03493i) q^{52} +0.320076i q^{53} +(-3.45405 - 6.48610i) q^{54} +0.924540 q^{55} +(-6.03794 - 4.42078i) q^{56} +(-0.423994 + 1.10746i) q^{57} +(3.35245 - 2.00523i) q^{58} +(12.2327 + 7.06256i) q^{59} +(-3.64183 + 3.14588i) q^{60} +(2.23796 + 3.87627i) q^{61} +(-1.39685 + 2.50814i) q^{62} +(1.27374 + 7.83438i) q^{63} +(7.96564 - 0.740624i) q^{64} +(-3.16731 - 5.48594i) q^{65} +(0.281272 + 1.60570i) q^{66} +(-7.10490 + 12.3061i) q^{67} +(-0.134905 - 4.36397i) q^{68} +(-2.45269 - 3.02337i) q^{69} +(4.81888 - 1.94881i) q^{70} +1.76784i q^{71} +(-6.57158 - 5.36790i) q^{72} -8.84044i q^{73} +(0.235945 + 15.2685i) q^{74} +(0.836458 + 5.25126i) q^{75} +(0.0423094 + 1.36864i) q^{76} +(0.271386 - 1.73972i) q^{77} +(8.56414 - 7.16982i) q^{78} +(11.0680 - 6.39012i) q^{79} +(-2.47590 + 4.97486i) q^{80} +(0.972271 + 8.94733i) q^{81} +(-5.98518 - 3.33331i) q^{82} +(-8.81951 + 5.09195i) q^{83} +(4.85065 + 7.77632i) q^{84} +(2.62642 + 1.51636i) q^{85} +(4.57097 + 7.64197i) q^{86} +(-4.72476 + 0.752593i) q^{87} +(1.01569 + 1.58479i) q^{88} -10.9341i q^{89} +(5.57335 - 1.91756i) q^{90} +(-11.2527 + 4.34966i) q^{91} +(-3.96073 - 2.12634i) q^{92} +(2.73057 - 2.21516i) q^{93} +(-4.66818 - 7.80450i) q^{94} +(-0.823706 - 0.475567i) q^{95} +(-9.39336 - 2.78653i) q^{96} +(-0.0581560 + 0.0335764i) q^{97} +(-2.25260 - 9.63980i) q^{98} +(0.411660 - 1.95362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

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