LMFDB - Embedded newform 234.2.z.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.66097 - 0.491112i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.174335 - 0.650628i) q^{5} +(0.904267 - 1.47726i) q^{6} +(1.26694 + 1.26694i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.51762 + 1.63144i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.66097 - 0.491112i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.174335 - 0.650628i) q^{5} +(0.904267 - 1.47726i) q^{6} +(1.26694 + 1.26694i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.51762 + 1.63144i) q^{9} +(0.583337 + 0.336790i) q^{10} +(0.952090 + 0.255112i) q^{11} +(1.19288 + 1.25580i) q^{12} +(2.90807 + 2.13146i) q^{13} +(-1.55168 + 0.895864i) q^{14} +(-0.609096 + 0.995053i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.20946 + 2.09485i) q^{17} +(-2.22746 + 2.00959i) q^{18} +(6.33213 + 1.69669i) q^{19} +(-0.476293 + 0.476293i) q^{20} +(-1.48214 - 2.72656i) q^{21} +(-0.492838 + 0.853620i) q^{22} -6.32605 q^{23} +(-1.52175 + 0.827212i) q^{24} +(3.93720 + 2.27315i) q^{25} +(-2.81150 + 2.25732i) q^{26} +(-3.38046 - 3.94620i) q^{27} +(-0.463733 - 1.73068i) q^{28} +(3.71748 - 2.14629i) q^{29} +(-0.803502 - 0.845880i) q^{30} +(-5.59289 - 1.49861i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.45610 - 0.891314i) q^{33} +(-2.33650 + 0.626062i) q^{34} +(1.04518 - 0.603436i) q^{35} +(-1.36460 - 2.67168i) q^{36} +(6.83094 - 1.83034i) q^{37} +(-3.27775 + 5.67724i) q^{38} +(-3.78342 - 4.96847i) q^{39} +(-0.336790 - 0.583337i) q^{40} +(-3.51849 - 3.51849i) q^{41} +(3.01726 - 0.725951i) q^{42} +0.892279i q^{43} +(-0.696978 - 0.696978i) q^{44} +(1.50037 - 1.35362i) q^{45} +(1.63730 - 6.11049i) q^{46} +(-0.981707 - 3.66378i) q^{47} +(-0.405168 - 1.68399i) q^{48} -3.78971i q^{49} +(-3.21471 + 3.21471i) q^{50} +(-0.980069 - 4.07345i) q^{51} +(-1.45273 - 3.29993i) q^{52} +9.00014i q^{53} +(4.68666 - 2.24392i) q^{54} +(0.331966 - 0.574981i) q^{55} +1.79173 q^{56} +(-9.68420 - 5.92793i) q^{57} +(1.11100 + 4.14631i) q^{58} +(1.22237 + 4.56196i) q^{59} +(1.02502 - 0.557194i) q^{60} +4.76398 q^{61} +(2.89509 - 5.01445i) q^{62} +(1.12274 + 5.25662i) q^{63} -1.00000i q^{64} +(1.89377 - 1.52048i) q^{65} +(1.23781 - 1.17580i) q^{66} +(-7.82927 + 7.82927i) q^{67} -2.41892i q^{68} +(10.5074 + 3.10679i) q^{69} +(0.312361 + 1.16575i) q^{70} +(1.70900 - 6.37808i) q^{71} +(2.93383 - 0.626624i) q^{72} +(-8.01788 - 8.01788i) q^{73} +7.07190i q^{74} +(-5.42319 - 5.70922i) q^{75} +(-4.63544 - 4.63544i) q^{76} +(0.883031 + 1.52946i) q^{77} +(5.77840 - 2.36857i) q^{78} +(-0.807117 + 1.39797i) q^{79} +(0.650628 - 0.174335i) q^{80} +(3.67681 + 8.21469i) q^{81} +(4.30925 - 2.48795i) q^{82} +(-7.31055 + 1.95885i) q^{83} +(-0.0797096 + 3.10234i) q^{84} +(1.57382 - 0.421703i) q^{85} +(-0.861875 - 0.230939i) q^{86} +(-7.22867 + 1.73921i) q^{87} +(0.853620 - 0.492838i) q^{88} +(0.440877 + 1.64537i) q^{89} +(0.919169 + 1.79959i) q^{90} +(0.983920 + 6.38480i) q^{91} +(5.47852 + 3.16302i) q^{92} +(8.55361 + 5.23587i) q^{93} +3.79302 q^{94} +(2.20783 - 3.82407i) q^{95} +(1.73148 + 0.0444876i) q^{96} +(-1.35833 + 1.35833i) q^{97} +(3.66058 + 0.980849i) q^{98} +(1.98080 + 2.19555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.66097	−	0.491112i	−0.958959	−	0.283543i
$3$	−1.66097	−	0.491112i	−0.958959	−	0.283543i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.174335	−	0.650628i	0.0779651	−	0.290970i	−0.915924	−	0.401351i	$-0.868541\pi$
$5$	0.174335	−	0.650628i	0.0779651	−	0.290970i	0.993889	+	0.110382i	$0.0352073\pi$
$6$	0.904267	−	1.47726i	0.369165	−	0.603089i
$7$	1.26694	+	1.26694i	0.478859	+	0.478859i	0.904767	−	0.425907i	$-0.140045\pi$
$7$	1.26694	+	1.26694i	0.478859	+	0.478859i	−0.425907	+	0.904767i	$0.640045\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.51762	+	1.63144i	0.839206	+	0.543813i
$10$	0.583337	+	0.336790i	0.184467	+	0.106502i
$11$	0.952090	+	0.255112i	0.287066	+	0.0769190i	0.399479	−	0.916743i	$-0.369191\pi$
$11$	0.952090	+	0.255112i	0.287066	+	0.0769190i	−0.112413	+	0.993662i	$0.535858\pi$
$12$	1.19288	+	1.25580i	0.344356	+	0.362518i
$13$	2.90807	+	2.13146i	0.806554	+	0.591161i
$13$	2.90807	+	2.13146i	0.806554	+	0.591161i
$14$	−1.55168	+	0.895864i	−0.414704	+	0.239430i
$15$	−0.609096	+	0.995053i	−0.157268	+	0.256922i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.20946	+	2.09485i	0.293337	+	0.508075i	0.974597	−	0.223967i	$-0.0719009\pi$
$17$	1.20946	+	2.09485i	0.293337	+	0.508075i	−0.681260	+	0.732042i	$0.738568\pi$
$18$	−2.22746	+	2.00959i	−0.525017	+	0.473664i
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.896959	−	0.442114i	$-0.145771\pi$
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.555732	+	0.831361i	$0.312438\pi$
$20$	−0.476293	+	0.476293i	−0.106502	+	0.106502i
$21$	−1.48214	−	2.72656i	−0.323429	−	0.594984i
$22$	−0.492838	+	0.853620i	−0.105073	+	0.181992i
$23$	−6.32605			−1.31907			−0.659536	−	0.751673i	$-0.729247\pi$
$23$	−6.32605			−1.31907			−0.659536	+	0.751673i	$0.729247\pi$
$24$	−1.52175	+	0.827212i	−0.310626	+	0.168854i
$25$	3.93720	+	2.27315i	0.787441	+	0.454629i
$26$	−2.81150	+	2.25732i	−0.551380	+	0.442696i
$27$	−3.38046	−	3.94620i	−0.650570	−	0.759446i
$28$	−0.463733	−	1.73068i	−0.0876374	−	0.327067i
$29$	3.71748	−	2.14629i	0.690318	−	0.398555i	−0.113413	−	0.993548i	$-0.536178\pi$
$29$	3.71748	−	2.14629i	0.690318	−	0.398555i	0.803731	+	0.594993i	$0.202845\pi$
$30$	−0.803502	−	0.845880i	−0.146699	−	0.154436i
$31$	−5.59289	−	1.49861i	−1.00451	−	0.269158i	−0.281178	−	0.959656i	$-0.590725\pi$
$31$	−5.59289	−	1.49861i	−1.00451	−	0.269158i	−0.723335	+	0.690498i	$0.757392\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.45610	−	0.891314i	−0.253475	−	0.155158i
$34$	−2.33650	+	0.626062i	−0.400706	+	0.107369i
$35$	1.04518	−	0.603436i	0.176668	−	0.101999i
$36$	−1.36460	−	2.67168i	−0.227434	−	0.445280i
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.350902	−	0.936412i	$-0.385875\pi$
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.772096	+	0.635505i	$0.219208\pi$
$38$	−3.27775	+	5.67724i	−0.531722	+	0.920969i
$39$	−3.78342	−	4.96847i	−0.605832	−	0.795592i
$40$	−0.336790	−	0.583337i	−0.0532512	−	0.0922337i
$41$	−3.51849	−	3.51849i	−0.549496	−	0.549496i	0.376799	−	0.926295i	$-0.377025\pi$
$41$	−3.51849	−	3.51849i	−0.549496	−	0.549496i	−0.926295	+	0.376799i	$0.877025\pi$
$42$	3.01726	−	0.725951i	0.465573	−	0.112017i
$43$			0.892279i			0.136071i	0.997683	+	0.0680356i	$0.0216731\pi$
$43$			0.892279i			0.136071i	−0.997683	+	0.0680356i	$0.978327\pi$
$44$	−0.696978	−	0.696978i	−0.105073	−	0.105073i
$45$	1.50037	−	1.35362i	0.223662	−	0.201785i
$46$	1.63730	−	6.11049i	0.241407	−	0.900943i
$47$	−0.981707	−	3.66378i	−0.143197	−	0.534417i	−0.999829	−	0.0184899i	$-0.994114\pi$
$47$	−0.981707	−	3.66378i	−0.143197	−	0.534417i	0.856632	−	0.515927i	$-0.172553\pi$
$48$	−0.405168	−	1.68399i	−0.0584810	−	0.243064i
$49$		−	3.78971i		−	0.541387i
$50$	−3.21471	+	3.21471i	−0.454629	+	0.454629i
$51$	−0.980069	−	4.07345i	−0.137237	−	0.570397i
$52$	−1.45273	−	3.29993i	−0.201458	−	0.457619i
$53$			9.00014i			1.23626i	0.786074	+	0.618132i	$0.212110\pi$
$53$			9.00014i			1.23626i	−0.786074	+	0.618132i	$0.787890\pi$
$54$	4.68666	−	2.24392i	0.637774	−	0.305359i
$55$	0.331966	−	0.574981i	0.0447622	−	0.0775305i
$56$	1.79173			0.239430
$57$	−9.68420	−	5.92793i	−1.28270	−	0.785173i
$58$	1.11100	+	4.14631i	0.145881	+	0.544437i
$59$	1.22237	+	4.56196i	0.159139	+	0.593917i	0.998715	+	0.0506741i	$0.0161370\pi$
$59$	1.22237	+	4.56196i	0.159139	+	0.593917i	−0.839576	+	0.543243i	$0.817196\pi$
$60$	1.02502	−	0.557194i	0.132329	−	0.0719334i
$61$	4.76398			0.609965			0.304982	−	0.952358i	$-0.401349\pi$
$61$	4.76398			0.609965			0.304982	+	0.952358i	$0.401349\pi$
$62$	2.89509	−	5.01445i	0.367677	−	0.636835i
$63$	1.12274	+	5.25662i	0.141452	+	0.662272i
$64$		−	1.00000i		−	0.125000i
$65$	1.89377	−	1.52048i	0.234893	−	0.188593i
$66$	1.23781	−	1.17580i	0.152364	−	0.144730i
$67$	−7.82927	+	7.82927i	−0.956498	+	0.956498i	−0.999092	−	0.0425948i	$-0.986438\pi$
$67$	−7.82927	+	7.82927i	−0.956498	+	0.956498i	0.0425948	+	0.999092i	$0.486438\pi$
$68$		−	2.41892i		−	0.293337i
$69$	10.5074	+	3.10679i	1.26494	+	0.374014i
$70$	0.312361	+	1.16575i	0.0373343	+	0.139334i
$71$	1.70900	−	6.37808i	0.202821	−	0.756939i	−0.787281	−	0.616594i	$-0.788512\pi$
$71$	1.70900	−	6.37808i	0.202821	−	0.756939i	0.990103	−	0.140345i	$-0.0448212\pi$
$72$	2.93383	−	0.626624i	0.345755	−	0.0738483i
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	0.0597896	−	0.998211i	$-0.480957\pi$
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	−0.998211	+	0.0597896i	$0.980957\pi$
$74$			7.07190i			0.822092i
$75$	−5.42319	−	5.70922i	−0.626217	−	0.659244i
$76$	−4.63544	−	4.63544i	−0.531722	−	0.531722i
$77$	0.883031	+	1.52946i	0.100631	+	0.174298i
$78$	5.77840	−	2.36857i	0.654275	−	0.268188i
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	−0.907851	−	0.419292i	$-0.862278\pi$
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	0.817043	+	0.576576i	$0.195612\pi$
$80$	0.650628	−	0.174335i	0.0727424	−	0.0194913i
$81$	3.67681	+	8.21469i	0.408534	+	0.912743i
$82$	4.30925	−	2.48795i	0.475877	−	0.274748i
$83$	−7.31055	+	1.95885i	−0.802437	+	0.215012i	−0.636653	−	0.771150i	$-0.719682\pi$
$83$	−7.31055	+	1.95885i	−0.802437	+	0.215012i	−0.165783	+	0.986162i	$0.553015\pi$
$84$	−0.0797096	+	3.10234i	−0.00869703	+	0.338493i
$85$	1.57382	−	0.421703i	0.170704	−	0.0457401i
$86$	−0.861875	−	0.230939i	−0.0929384	−	0.0249028i
$87$	−7.22867	+	1.73921i	−0.774995	+	0.186463i
$88$	0.853620	−	0.492838i	0.0909962	−	0.0525367i
$89$	0.440877	+	1.64537i	0.0467329	+	0.174409i	0.985348	−	0.170557i	$-0.0545568\pi$
$89$	0.440877	+	1.64537i	0.0467329	+	0.174409i	−0.938615	+	0.344967i	$0.887890\pi$
$90$	0.919169	+	1.79959i	0.0968889	+	0.189693i
$91$	0.983920	+	6.38480i	0.103143	+	0.669309i
$92$	5.47852	+	3.16302i	0.571175	+	0.329768i
$93$	8.55361	+	5.23587i	0.886968	+	0.542935i
$94$	3.79302			0.391220
$95$	2.20783	−	3.82407i	0.226518	−	0.392341i
$96$	1.73148	+	0.0444876i	0.176718	+	0.00454049i
$97$	−1.35833	+	1.35833i	−0.137917	+	0.137917i	−0.772695	−	0.634778i	$-0.781092\pi$
$97$	−1.35833	+	1.35833i	−0.137917	+	0.137917i	0.634778	+	0.772695i	$0.281092\pi$
$98$	3.66058	+	0.980849i	0.369774	+	0.0990807i
$99$	1.98080	+	2.19555i	0.199078	+	0.220661i
$100$	−2.27315	−	3.93720i	−0.227315	−	0.393720i
$101$	−7.44597	−	12.8968i	−0.740902	−	1.28328i	−0.952085	−	0.305833i	$-0.901065\pi$
$101$	−7.44597	−	12.8968i	−0.740902	−	1.28328i	0.211183	−	0.977446i	$-0.432268\pi$
$102$	4.18831	+	0.107612i	0.414704	+	0.0106552i
$103$	−9.08751	+	5.24668i	−0.895419	+	0.516971i	−0.875711	−	0.482835i	$-0.839607\pi$
$103$	−9.08751	+	5.24668i	−0.895419	+	0.516971i	−0.0197081	+	0.999806i	$0.506274\pi$
$104$	3.56349	−	0.549146i	0.349429	−	0.0538482i
$105$	−2.03237	+	0.488986i	−0.198339	+	0.0477202i
$106$	−8.69347	−	2.32941i	−0.844384	−	0.226252i
$107$	1.87899	+	1.08484i	0.181649	+	0.104875i	0.588067	−	0.808812i	$-0.299889\pi$
$107$	1.87899	+	1.08484i	0.181649	+	0.104875i	−0.406418	+	0.913687i	$0.633222\pi$
$108$	0.954467	+	5.10774i	0.0918436	+	0.491492i
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	−0.982075	−	0.188489i	$-0.939641\pi$
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	0.188489	+	0.982075i	$0.439641\pi$
$110$	0.469470	+	0.469470i	0.0447622	+	0.0447622i
$111$	−12.2449	−	0.314612i	−1.16223	−	0.0298616i
$112$	−0.463733	+	1.73068i	−0.0438187	+	0.163534i
$113$	9.60049	+	5.54284i	0.903138	+	0.521427i	0.878217	−	0.478263i	$-0.158733\pi$
$113$	9.60049	+	5.54284i	0.903138	+	0.521427i	0.0249209	+	0.999689i	$0.492067\pi$
$114$	8.23240	−	7.81996i	0.771034	−	0.732406i
$115$	−1.10285	+	4.11590i	−0.102842	+	0.383810i
$116$	−4.29257			−0.398555
$117$	3.84406	+	10.1105i	0.355384	+	0.934720i
$118$	−4.72289			−0.434777
$119$	−1.12173	+	4.18637i	−0.102829	+	0.383764i
$120$	0.272913	+	1.13430i	0.0249134	+	0.103547i
$121$	−8.68489	−	5.01422i	−0.789535	−	0.455838i
$122$	−1.23301	+	4.60165i	−0.111631	+	0.416614i
$123$	4.11612	+	7.57206i	0.371138	+	0.682750i
$124$	4.09428	+	4.09428i	0.367677	+	0.367677i
$125$	4.54683	−	4.54683i	0.406681	−	0.406681i
$126$	−5.36809	−	0.276031i	−0.478228	−	0.0245908i
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	0.679731	−	0.733462i	$-0.262097\pi$
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	−0.295331	+	0.955395i	$0.595430\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	0.438208	−	1.48204i	0.0385821	−	0.130487i
$130$	0.978531	+	2.22277i	0.0858229	+	0.194950i
$131$	19.0361	−	10.9905i	1.66319	−	0.960242i	0.692010	−	0.721888i	$-0.256725\pi$
$131$	19.0361	−	10.9905i	1.66319	−	0.960242i	0.971178	−	0.238354i	$-0.0766080\pi$
$132$	0.815363	+	1.49995i	0.0709682	+	0.130554i
$133$	5.87284	+	10.1721i	0.509240	+	0.882030i
$134$	−5.53613	−	9.58886i	−0.478249	−	0.828351i
$135$	−3.15684	+	1.51146i	−0.271698	+	0.130086i
$136$	2.33650	+	0.626062i	0.200353	+	0.0536844i
$137$	−8.90180	+	8.90180i	−0.760532	+	0.760532i	−0.976419	−	0.215886i	$-0.930736\pi$
$137$	−8.90180	+	8.90180i	−0.760532	+	0.760532i	0.215886	+	0.976419i	$0.430736\pi$
$138$	−5.72044	+	9.34522i	−0.486956	+	0.795518i
$139$	9.84823	−	17.0576i	0.835316	−	1.44681i	−0.0584566	−	0.998290i	$-0.518618\pi$
$139$	9.84823	−	17.0576i	0.835316	−	1.44681i	0.893773	−	0.448520i	$-0.148049\pi$
$140$	−1.20687			−0.101999
$141$	−0.168742	+	6.56754i	−0.0142107	+	0.553087i
$142$	5.71843	+	3.30154i	0.479880	+	0.277059i
$143$	2.22498	+	2.77122i	0.186062	+	0.231741i
$144$	−0.154059	+	2.99604i	−0.0128382	+	0.249670i
$145$	−0.748347	−	2.79287i	−0.0621468	−	0.231935i
$146$	9.81985	−	5.66949i	0.812697	−	0.469211i
$147$	−1.86117	+	6.29458i	−0.153507	+	0.519168i
$148$	−6.83094	−	1.83034i	−0.561499	−	0.150453i
$149$	−9.34027	+	2.50272i	−0.765185	+	0.205031i	−0.620243	−	0.784410i	$-0.712966\pi$
$149$	−9.34027	+	2.50272i	−0.765185	+	0.205031i	−0.144942	+	0.989440i	$0.546299\pi$
$150$	6.91831	−	3.76075i	0.564878	−	0.307064i
$151$	4.80308	−	1.28698i	0.390869	−	0.104733i	−0.0580316	−	0.998315i	$-0.518482\pi$
$151$	4.80308	−	1.28698i	0.390869	−	0.104733i	0.448900	+	0.893582i	$0.351816\pi$
$152$	5.67724	−	3.27775i	0.460485	−	0.265861i
$153$	−0.372655	+	7.24718i	−0.0301274	+	0.585900i
$154$	−1.70589	+	0.457091i	−0.137464	+	0.0368334i
$155$	−1.95008	+	3.37763i	−0.156634	+	0.271298i
$156$	0.792304	+	6.19453i	0.0634351	+	0.495960i
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	0.604168	−	0.796857i	$-0.293506\pi$
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	−0.992182	+	0.124796i	$0.960172\pi$
$158$	−1.14144	−	1.14144i	−0.0908078	−	0.0908078i
$159$	4.42007	−	14.9489i	0.350535	−	1.18553i
$160$			0.673580i			0.0532512i
$161$	−8.01474	−	8.01474i	−0.631650	−	0.631650i
$162$	−8.88641	+	1.42541i	−0.698182	+	0.111991i
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	−0.899727	−	0.436453i	$-0.856234\pi$
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	0.997413	+	0.0718838i	$0.0229011\pi$
$164$	1.28786	+	4.80634i	0.100565	+	0.375312i
$165$	−0.833764	+	0.791992i	−0.0649084	+	0.0616565i
$166$		−	7.56843i		−	0.587424i
$167$	10.0054	−	10.0054i	0.774242	−	0.774242i	−0.204603	−	0.978845i	$-0.565590\pi$
$167$	10.0054	−	10.0054i	0.774242	−	0.774242i	0.978845	+	0.204603i	$0.0655903\pi$
$168$	−2.97600	−	0.879938i	−0.229603	−	0.0678887i
$169$	3.91375	+	12.3969i	0.301058	+	0.953606i
$170$			1.62934i			0.124964i
$171$	13.1739	+	14.6021i	1.00743	+	1.11665i
$172$	0.446139	−	0.772736i	0.0340178	−	0.0589206i
$173$	23.1979			1.76370			0.881852	−	0.471527i	$-0.156297\pi$
$173$	23.1979			1.76370			0.881852	+	0.471527i	$0.156297\pi$
$174$	0.190966	−	7.43250i	0.0144771	−	0.563456i
$175$	2.10827	+	7.86816i	0.159370	+	0.594777i
$176$	0.255112	+	0.952090i	0.0192298	+	0.0717664i
$177$	0.210110	−	8.17759i	0.0157928	−	0.614665i
$178$	−1.70342			−0.127677
$179$	2.78545	−	4.82455i	0.208194	−	0.360603i	−0.742951	−	0.669345i	$-0.766575\pi$
$179$	2.78545	−	4.82455i	0.208194	−	0.360603i	0.951146	+	0.308742i	$0.0999080\pi$
$180$	−1.97617	+	0.422081i	−0.147295	+	0.0314601i
$181$		−	20.8410i		−	1.54910i	−0.632514	−	0.774549i	$-0.717977\pi$
$181$		−	20.8410i		−	1.54910i	0.632514	−	0.774549i	$-0.282023\pi$
$182$	−6.42190	−	0.702114i	−0.476023	−	0.0520441i
$183$	−7.91281	−	2.33964i	−0.584931	−	0.172951i
$184$	−4.47319	+	4.47319i	−0.329768	+	0.329768i
$185$		−	4.76349i		−	0.350219i
$186$	−7.27130	+	6.90701i	−0.533158	+	0.506447i
$187$	0.617094	+	2.30303i	0.0451264	+	0.168414i
$188$	−0.981707	+	3.66378i	−0.0715983	+	0.267209i
$189$	0.716755	−	9.28246i	0.0521363	−	0.675200i
$190$	3.12234	+	3.12234i	0.226518	+	0.226518i
$191$		−	18.0727i		−	1.30769i	−0.756626	−	0.653847i	$-0.773154\pi$
$191$		−	18.0727i		−	1.30769i	0.756626	−	0.653847i	$-0.226846\pi$
$192$	−0.491112	+	1.66097i	−0.0354429	+	0.119870i
$193$	5.20610	+	5.20610i	0.374743	+	0.374743i	0.869201	−	0.494458i	$-0.164634\pi$
$193$	5.20610	+	5.20610i	0.374743	+	0.374743i	−0.494458	+	0.869201i	$0.664634\pi$
$194$	−0.960483	−	1.66361i	−0.0689587	−	0.119440i
$195$	−3.89221	+	1.59542i	−0.278727	+	0.114250i
$196$	−1.89486	+	3.28199i	−0.135347	+	0.234428i
$197$	−23.6473	+	6.33628i	−1.68480	+	0.451441i	−0.969040	−	0.246904i	$-0.920587\pi$
$197$	−23.6473	+	6.33628i	−1.68480	+	0.451441i	−0.715761	+	0.698345i	$0.753920\pi$
$198$	−2.63341	+	1.34506i	−0.187148	+	0.0955889i
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	−0.726503	−	0.687164i	$-0.758856\pi$
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	0.231850	+	0.972752i	$0.425522\pi$
$200$	4.39138	−	1.17667i	0.310517	−	0.0832029i
$201$	16.8492	−	9.15911i	1.18845	−	0.646034i
$202$	14.3845	−	3.85432i	1.01209	−	0.271189i
$203$	7.42905	+	1.99061i	0.521417	+	0.139713i
$204$	−1.18796	+	4.01774i	−0.0831738	+	0.281298i
$205$	−2.90262	+	1.67583i	−0.202728	+	0.117045i
$206$	−2.71588	−	10.1358i	−0.189224	−	0.706195i
$207$	−15.9266	−	10.3206i	−1.10697	−	0.717329i
$208$	−0.391864	+	3.58419i	−0.0271709	+	0.248519i
$209$	5.59591	+	3.23080i	0.387077	+	0.223479i
$210$	0.0536908	−	2.08967i	0.00370502	−	0.144201i
$211$	−14.0818			−0.969432			−0.484716	−	0.874672i	$-0.661077\pi$
$211$	−14.0818			−0.969432			−0.484716	+	0.874672i	$0.661077\pi$
$212$	4.50007	−	7.79435i	0.309066	−	0.535318i
$213$	−5.97094	+	9.75447i	−0.409122	+	0.668365i
$214$	−1.53419	+	1.53419i	−0.104875	+	0.104875i
$215$	0.580542	+	0.155556i	0.0395926	+	0.0106088i
$216$	−5.18073	−	0.400036i	−0.352504	−	0.0272190i
$217$	−5.18722	−	8.98452i	−0.352131	−	0.609909i
$218$	−5.85858	−	10.1474i	−0.396793	−	0.687265i
$219$	9.37975	+	17.2551i	0.633825	+	1.16599i
$220$	−0.574981	+	0.331966i	−0.0387652	+	0.0223811i
$221$	−0.947887	+	8.66987i	−0.0637618	+	0.583199i
$222$	3.47309	−	11.7462i	0.233099	−	0.788353i
$223$	−22.9327	−	6.14479i	−1.53568	−	0.411485i	−0.610816	−	0.791773i	$-0.709158\pi$
$223$	−22.9327	−	6.14479i	−1.53568	−	0.411485i	−0.924868	+	0.380287i	$0.875825\pi$
$224$	−1.55168	−	0.895864i	−0.103676	−	0.0598574i
$225$	6.20388	+	12.1462i	0.413592	+	0.809748i
$226$	−7.83876	+	7.83876i	−0.521427	+	0.521427i
$227$	−16.9292	−	16.9292i	−1.12363	−	1.12363i	−0.991191	−	0.132438i	$-0.957719\pi$
$227$	−16.9292	−	16.9292i	−1.12363	−	1.12363i	−0.132438	−	0.991191i	$-0.542281\pi$
$228$	5.42280	+	9.97584i	0.359134	+	0.660666i
$229$	5.31509	−	19.8362i	0.351231	−	1.31081i	−0.533930	−	0.845529i	$-0.679286\pi$
$229$	5.31509	−	19.8362i	0.351231	−	1.31081i	0.885161	−	0.465284i	$-0.154048\pi$
$230$	−3.69022	−	2.13055i	−0.243326	−	0.140484i
$231$	−0.715552	−	2.97404i	−0.0470799	−	0.195677i
$232$	1.11100	−	4.14631i	0.0729407	−	0.272218i
$233$	−2.79071			−0.182825			−0.0914126	−	0.995813i	$-0.529138\pi$
$233$	−2.79071			−0.182825			−0.0914126	+	0.995813i	$0.529138\pi$
$234$	−10.7610	+	1.09628i	−0.703466	+	0.0716660i
$235$	−2.55490			−0.166664
$236$	1.22237	−	4.56196i	0.0795697	−	0.296958i
$237$	2.02715	−	1.92559i	0.131678	−	0.125081i
$238$	−3.75339	−	2.16702i	−0.243296	−	0.140467i
$239$	2.03334	−	7.58852i	0.131526	−	0.490861i	−0.868462	−	0.495755i	$-0.834891\pi$
$239$	2.03334	−	7.58852i	0.131526	−	0.490861i	0.999988	+	0.00489453i	$0.00155798\pi$
$240$	−1.16629	−	0.0299659i	−0.0752837	−	0.00193429i
$241$	−16.4615	−	16.4615i	−1.06038	−	1.06038i	−0.998056	−	0.0623240i	$-0.980149\pi$
$241$	−16.4615	−	16.4615i	−1.06038	−	1.06038i	−0.0623240	−	0.998056i	$-0.519851\pi$
$242$	7.09118	−	7.09118i	0.455838	−	0.455838i
$243$	−2.07273	−	15.4500i	−0.132966	−	0.991121i
$244$	−4.12572	−	2.38199i	−0.264122	−	0.152491i
$245$	−2.46569	−	0.660680i	−0.157527	−	0.0422093i
$246$	−8.37938	+	2.01607i	−0.534250	+	0.128540i
$247$	14.7979	+	18.4308i	0.941566	+	1.17272i
$248$	−5.01445	+	2.89509i	−0.318418	+	0.183839i
$249$	13.1046	+	0.336701i	0.830469	+	0.0213376i
$250$	3.21509	+	5.56871i	0.203340	+	0.352196i
$251$	13.0241	+	22.5583i	0.822071	+	1.42387i	0.904138	+	0.427241i	$0.140515\pi$
$251$	13.0241	+	22.5583i	0.822071	+	1.42387i	−0.0820668	+	0.996627i	$0.526152\pi$
$252$	1.65599	−	5.11374i	0.104318	−	0.322135i
$253$	−6.02296	−	1.61385i	−0.378660	−	0.101462i
$254$	−3.53704	+	3.53704i	−0.221933	+	0.221933i
$255$	−2.82116	−	0.0724851i	−0.176668	−	0.00453920i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.20155			−0.449220			−0.224610	−	0.974449i	$-0.572111\pi$
$257$	−7.20155			−0.449220			−0.224610	+	0.974449i	$0.572111\pi$
$258$	1.31813	+	0.806858i	0.0820631	+	0.0502328i
$259$	10.9733	+	6.33546i	0.681851	+	0.393667i
$260$	−2.40029	+	0.369894i	−0.148860	+	0.0229398i
$261$	12.8607	+	0.661308i	0.796059	+	0.0409339i
$262$	5.68909	+	21.2320i	0.351473	+	1.31172i
$263$	9.92027	−	5.72747i	0.611710	−	0.353171i	−0.161924	−	0.986803i	$-0.551770\pi$
$263$	9.92027	−	5.72747i	0.611710	−	0.353171i	0.773634	+	0.633632i	$0.218437\pi$
$264$	−1.65987	+	0.399364i	−0.102158	+	0.0245792i
$265$	5.85574	+	1.56904i	0.359715	+	0.0963855i
$266$	−11.3455	+	3.04001i	−0.695635	+	0.186395i
$267$	0.0757809	−	2.94943i	0.00463771	−	0.180502i
$268$	10.6950	−	2.86571i	0.653300	−	0.175051i
$269$	−21.7795	+	12.5744i	−1.32792	+	0.766674i	−0.984977	−	0.172683i	$-0.944756\pi$
$269$	−21.7795	+	12.5744i	−1.32792	+	0.766674i	−0.342941	+	0.939357i	$0.611423\pi$
$270$	−0.642910	−	3.44047i	−0.0391262	−	0.209380i
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	−0.0664215	−	0.997792i	$-0.521158\pi$
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	0.441373	+	0.897324i	$0.354492\pi$
$272$	−1.20946	+	2.09485i	−0.0733343	+	0.127019i
$273$	1.50139	−	11.0882i	0.0908683	−	0.671085i
$274$	−6.29452	−	10.9024i	−0.380266	−	0.658640i
$275$	3.16866	+	3.16866i	0.191078	+	0.191078i
$276$	−7.54624	−	7.94424i	−0.454230	−	0.478187i
$277$		−	19.4429i		−	1.16821i	−0.811679	−	0.584104i	$-0.801446\pi$
$277$		−	19.4429i		−	1.16821i	0.811679	−	0.584104i	$-0.198554\pi$
$278$	13.9275	+	13.9275i	0.835316	+	0.835316i
$279$	−11.6359	−	12.8974i	−0.696621	−	0.772146i
$280$	0.312361	−	1.16575i	0.0186672	−	0.0696668i
$281$	7.71478	+	28.7919i	0.460225	+	1.71758i	0.672255	+	0.740320i	$0.265326\pi$
$281$	7.71478	+	28.7919i	0.460225	+	1.71758i	−0.212030	+	0.977263i	$0.568007\pi$
$282$	−6.30008	−	1.86280i	−0.375165	−	0.110928i
$283$			22.0759i			1.31228i	0.754640	+	0.656139i	$0.227812\pi$
$283$			22.0759i			1.31228i	−0.754640	+	0.656139i	$0.772188\pi$
$284$	−4.66908	+	4.66908i	−0.277059	+	0.277059i
$285$	−5.54518	+	5.26736i	−0.328468	+	0.312012i
$286$	−3.25267	+	1.43192i	−0.192334	+	0.0846714i
$287$		−	8.91545i		−	0.526262i
$288$	−2.85408	−	0.924242i	−0.168178	−	0.0544615i
$289$	5.57442	−	9.65517i	0.327907	−	0.567951i
$290$	2.89139			0.169788
$291$	2.92323	−	1.58905i	0.171363	−	0.0931516i
$292$	2.93475	+	10.9526i	0.171743	+	0.640954i
$293$	2.45563	+	9.16452i	0.143459	+	0.535397i	0.999819	+	0.0190176i	$0.00605386\pi$
$293$	2.45563	+	9.16452i	0.143459	+	0.535397i	−0.856360	+	0.516379i	$0.827279\pi$
$294$	−5.59839	−	3.42691i	−0.326505	−	0.199861i
$295$	3.18124			0.185219
$296$	3.53595	−	6.12445i	0.205523	−	0.355976i
$297$	−2.21178	−	4.61953i	−0.128341	−	0.268052i
$298$		−	9.66976i		−	0.560154i
$299$	−18.3966	−	13.4837i	−1.06390	−	0.779784i
$300$	1.84201	+	7.65593i	0.106349	+	0.442015i
$301$	−1.13047	+	1.13047i	−0.0651590	+	0.0651590i
$302$			4.97251i			0.286136i
$303$	6.03374	+	25.0780i	0.346629	+	1.44069i
$304$	1.69669	+	6.33213i	0.0973119	+	0.363173i
$305$	0.830529	−	3.09958i	0.0475560	−	0.177481i
$306$	−6.90379	−	2.23567i	−0.394663	−	0.127805i
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	0.796385	−	0.604790i	$-0.206743\pi$
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	−0.604790	+	0.796385i	$0.706743\pi$
$308$		−	1.76606i		−	0.100631i
$309$	17.6708	−	4.25157i	1.00525	−	0.241864i
$310$	−2.75782	−	2.75782i	−0.156634	−	0.156634i
$311$	10.5634	+	18.2964i	0.598996	+	1.03749i	0.992970	+	0.118370i	$0.0377669\pi$
$311$	10.5634	+	18.2964i	0.598996	+	1.03749i	−0.393973	+	0.919122i	$0.628900\pi$
$312$	−6.18852	−	0.837956i	−0.350356	−	0.0474399i
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	−0.974281	−	0.225336i	$-0.927652\pi$
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	0.682287	+	0.731084i	$0.260985\pi$
$314$	9.39229	−	2.51666i	0.530038	−	0.142023i
$315$	3.61584	+	0.185929i	0.203729	+	0.0104759i
$316$	1.39797	−	0.807117i	0.0786419	−	0.0454039i
$317$	−16.1862	+	4.33708i	−0.909108	+	0.243595i	−0.682924	−	0.730490i	$-0.739292\pi$
$317$	−16.1862	+	4.33708i	−0.909108	+	0.243595i	−0.226185	+	0.974084i	$0.572625\pi$
$318$	13.2956	+	8.13853i	0.745578	+	0.456386i
$319$	4.08691	−	1.09509i	0.228823	−	0.0613130i
$320$	−0.650628	−	0.174335i	−0.0363712	−	0.00974564i
$321$	−2.58817	−	2.72467i	−0.144457	−	0.152076i
$322$	9.81601	−	5.66728i	0.547025	−	0.315825i
$323$	4.10416	+	15.3169i	0.228361	+	0.852256i
$324$	0.923132	−	8.95253i	0.0512851	−	0.497363i
$325$	6.60454	+	15.0025i	0.366354	+	0.832187i
$326$	4.17312	+	2.40935i	0.231128	+	0.133442i
$327$	17.8306	−	9.69257i	0.986033	−	0.536001i
$328$	−4.97589			−0.274748
$329$	3.39803	−	5.88557i	0.187340	−	0.324482i
$330$	−0.549212	−	1.01034i	−0.0302331	−	0.0556172i
$331$	10.4331	−	10.4331i	0.573455	−	0.573455i	−0.359637	−	0.933092i	$-0.617100\pi$
$331$	10.4331	−	10.4331i	0.573455	−	0.573455i	0.933092	+	0.359637i	$0.117100\pi$
$332$	7.31055	+	1.95885i	0.401218	+	0.107506i
$333$	20.1838	+	6.53615i	1.10606	+	0.358179i
$334$	7.07490	+	12.2541i	0.387121	+	0.670513i
$335$	3.72903	+	6.45886i	0.203738	+	0.352885i
$336$	1.62020	−	2.64685i	0.0883892	−	0.144398i
$337$	−3.36489	+	1.94272i	−0.183297	+	0.105827i	−0.588841	−	0.808249i	$-0.700416\pi$
$337$	−3.36489	+	1.94272i	−0.183297	+	0.105827i	0.405544	+	0.914076i	$0.367082\pi$
$338$	−12.9874	+	0.571843i	−0.706422	+	0.0311042i
$339$	−13.2239	−	13.9214i	−0.718225	−	0.756106i
$340$	−1.57382	−	0.421703i	−0.0853522	−	0.0228701i
$341$	−4.94262	−	2.85362i	−0.267658	−	0.154532i
$342$	−17.5142	+	8.94566i	−0.947060	+	0.483726i
$343$	13.6699	−	13.6699i	0.738108	−	0.738108i
$344$	0.630936	+	0.630936i	0.0340178	+	0.0340178i
$345$	3.85317	−	6.29475i	0.207448	−	0.338898i
$346$	−6.00406	+	22.4074i	−0.322780	+	1.20463i
$347$	27.9881	+	16.1590i	1.50248	+	0.867459i	0.999996	+	0.00287338i	$0.000914625\pi$
$347$	27.9881	+	16.1590i	1.50248	+	0.867459i	0.502486	+	0.864585i	$0.332419\pi$
$348$	7.12982	+	2.10813i	0.382198	+	0.113008i
$349$	4.90845	−	18.3186i	0.262743	−	0.980571i	−0.700874	−	0.713285i	$-0.747207\pi$
$349$	4.90845	−	18.3186i	0.262743	−	0.980571i	0.963617	−	0.267286i	$-0.0861268\pi$
$350$	−8.14572			−0.435407
$351$	−1.41946	−	18.6811i	−0.0757649	−	0.997126i
$352$	−0.985676			−0.0525367
$353$	5.07215	−	18.9295i	0.269963	−	1.00752i	−0.689178	−	0.724592i	$-0.742028\pi$
$353$	5.07215	−	18.9295i	0.269963	−	1.00752i	0.959142	−	0.282926i	$-0.0913050\pi$
$354$	7.84456	+	2.31947i	0.416934	+	0.123278i
$355$	−3.85182	−	2.22385i	−0.204433	−	0.118030i
$356$	0.440877	−	1.64537i	0.0233664	−	0.0872047i
$357$	3.91913	−	6.40252i	0.207423	−	0.338857i
$358$	3.93922	+	3.93922i	0.208194	+	0.208194i
$359$	−19.2085	+	19.2085i	−1.01379	+	1.01379i	−0.0138835	+	0.999904i	$0.504419\pi$
$359$	−19.2085	+	19.2085i	−1.01379	+	1.01379i	−0.999904	+	0.0138835i	$0.995581\pi$
$360$	0.103771	−	2.01807i	0.00546920	−	0.106362i
$361$	20.7627	+	11.9873i	1.09277	+	0.630913i
$362$	20.1308	+	5.39404i	1.05805	+	0.283504i
$363$	11.9628	+	12.5937i	0.627882	+	0.660998i
$364$	2.34030	−	6.02136i	0.122665	−	0.315605i
$365$	−6.61445	+	3.81886i	−0.346216	+	0.199888i
$366$	4.30791	−	7.03764i	0.225178	−	0.367863i
$367$	−3.84715	−	6.66345i	−0.200819	−	0.347829i	0.747973	−	0.663729i	$-0.231027\pi$
$367$	−3.84715	−	6.66345i	−0.200819	−	0.347829i	−0.948793	+	0.315899i	$0.897694\pi$
$368$	−3.16302	−	5.47852i	−0.164884	−	0.285587i
$369$	−3.11801	−	14.5984i	−0.162317	−	0.759963i
$370$	4.60118	+	1.23288i	0.239204	+	0.0640945i
$371$	−11.4027	+	11.4027i	−0.591997	+	0.591997i
$372$	−4.78971	−	8.81121i	−0.248335	−	0.456840i
$373$	8.04898	−	13.9412i	0.416760	−	0.721850i	−0.578851	−	0.815433i	$-0.696499\pi$
$373$	8.04898	−	13.9412i	0.416760	−	0.721850i	0.995611	+	0.0935830i	$0.0298321\pi$
$374$	−2.38427			−0.123288
$375$	−9.78513	+	5.31913i	−0.505302	+	0.274679i
$376$	−3.28485	−	1.89651i	−0.169403	−	0.0978051i
$377$	15.3854	+	1.68210i	0.792389	+	0.0866328i
$378$	8.78066	+	3.09481i	0.451628	+	0.159180i
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	0.892446	+	0.451153i	$0.148987\pi$
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	−0.547305	+	0.836933i	$0.684346\pi$
$380$	−3.82407	+	2.20783i	−0.196171	+	0.113259i
$381$	−5.96695	−	6.28166i	−0.305696	−	0.321819i
$382$	17.4569	+	4.67756i	0.893172	+	0.239325i
$383$	−30.3863	+	8.14198i	−1.55267	+	0.416036i	−0.930333	−	0.366716i	$-0.880482\pi$
$383$	−30.3863	+	8.14198i	−1.55267	+	0.416036i	−0.622334	+	0.782752i	$0.713815\pi$
$384$	−1.47726	−	0.904267i	−0.0753862	−	0.0461457i
$385$	1.14905	−	0.307887i	0.0585610	−	0.0156914i
$386$	−6.37614	+	3.68127i	−0.324537	+	0.187372i
$387$	−1.45570	+	2.24642i	−0.0739973	+	0.114192i
$388$	1.85551	−	0.497183i	0.0941993	−	0.0252406i
$389$	−12.6984	+	21.9943i	−0.643836	+	1.11516i	0.340733	+	0.940160i	$0.389325\pi$
$389$	−12.6984	+	21.9943i	−0.643836	+	1.11516i	−0.984569	+	0.174997i	$0.944009\pi$
$390$	−0.533680	−	4.17251i	−0.0270239	−	0.211283i
$391$	−7.65110	−	13.2521i	−0.386933	−	0.670187i
$392$	−2.67973	−	2.67973i	−0.135347	−	0.135347i
$393$	−37.0158	+	8.90598i	−1.86720	+	0.449247i
$394$		−	24.4815i		−	1.23336i
$395$	0.768848	+	0.768848i	0.0386850	+	0.0386850i
$396$	−0.617648	−	2.89180i	−0.0310380	−	0.145319i
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	−0.956950	−	0.290254i	$-0.906260\pi$
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	0.973870	+	0.227108i	$0.0729270\pi$
$398$	−2.08542	−	7.78288i	−0.104532	−	0.390120i
$399$	−4.75898	−	19.7797i	−0.238247	−	0.990222i
$400$			4.54629i			0.227315i
$401$	1.01652	−	1.01652i	0.0507627	−	0.0507627i	−0.681270	−	0.732032i	$-0.738572\pi$
$401$	1.01652	−	1.01652i	0.0507627	−	0.0507627i	0.732032	+	0.681270i	$0.238572\pi$
$402$	4.48613	+	18.6456i	0.223748	+	0.929960i
$403$	−13.0703	−	16.2791i	−0.651077	−	0.810919i
$404$			14.8919i			0.740902i
$405$	5.98570	−	0.960127i	0.297432	−	0.0477091i
$406$	−3.84556	+	6.66071i	−0.190852	+	0.330565i
$407$	6.97060			0.345520
$408$	−3.57338	−	2.18735i	−0.176908	−	0.108290i
$409$	5.94553	+	22.1890i	0.293987	+	1.09718i	0.942018	+	0.335562i	$0.108926\pi$
$409$	5.94553	+	22.1890i	0.293987	+	1.09718i	−0.648031	+	0.761614i	$0.724407\pi$
$410$	−0.867474	−	3.23746i	−0.0428415	−	0.159887i
$411$	19.1574	−	10.4138i	0.944963	−	0.513676i
$412$	10.4934			0.516971
$413$	−4.23107	+	7.32842i	−0.208197	+	0.360608i
$414$	14.0910	−	12.7127i	0.692535	−	0.624797i
$415$			5.09794i			0.250248i
$416$	−3.36064	−	1.30617i	−0.164769	−	0.0640402i
$417$	−24.7348	+	23.4956i	−1.21127	+	1.15058i
$418$	−4.56904	+	4.56904i	−0.223479	+	0.223479i
$419$			6.60549i			0.322699i	0.986897	+	0.161350i	$0.0515847\pi$
$419$			6.60549i			0.322699i	−0.986897	+	0.161350i	$0.948415\pi$
$420$	2.00457	+	0.592709i	0.0978132	+	0.0289212i
$421$	−2.43480	−	9.08681i	−0.118665	−	0.442864i	0.880870	−	0.473359i	$-0.156958\pi$
$421$	−2.43480	−	9.08681i	−0.118665	−	0.442864i	−0.999535	+	0.0304944i	$0.990292\pi$
$422$	3.64464	−	13.6020i	0.177418	−	0.662134i
$423$	3.50567	−	10.8256i	0.170452	−	0.526358i
$424$	6.36406	+	6.36406i	0.309066	+	0.309066i
$425$			10.9971i			0.533438i
$426$	−7.87670	−	8.29213i	−0.381627	−	0.401755i
$427$	6.03569	+	6.03569i	0.292087	+	0.292087i
$428$	−1.08484	−	1.87899i	−0.0524376	−	0.0908246i
$429$	−2.33464	−	5.69563i	−0.112718	−	0.274987i
$430$	−0.300510	+	0.520499i	−0.0144919	+	0.0251007i
$431$	1.92865	−	0.516780i	0.0928998	−	0.0248924i	−0.212070	−	0.977255i	$-0.568020\pi$
$431$	1.92865	−	0.516780i	0.0928998	−	0.0248924i	0.304970	+	0.952362i	$0.401354\pi$
$432$	1.72728	−	4.90066i	0.0831036	−	0.235783i
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.985936	−	0.167122i	$-0.946553\pi$
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.348236	+	0.937407i	$0.613219\pi$
$434$	10.0209	−	2.68510i	0.481020	−	0.128889i
$435$	−0.128631	+	5.00638i	−0.00616738	+	0.240038i
$436$	11.3179	−	3.03262i	0.542029	−	0.145236i
$437$	−40.0574	−	10.7333i	−1.91620	−	0.513445i
$438$	−19.0948	+	4.59420i	−0.912385	+	0.219519i
$439$	−22.6287	+	13.0647i	−1.08001	+	0.623542i	−0.930898	−	0.365278i	$-0.880974\pi$
$439$	−22.6287	+	13.0647i	−1.08001	+	0.623542i	−0.149109	+	0.988821i	$0.547640\pi$
$440$	−0.171838	−	0.641308i	−0.00819206	−	0.0305732i
$441$	6.18268	−	9.54105i	0.294414	−	0.454336i
$442$	−8.12912	−	3.15952i	−0.386663	−	0.150283i
$443$	9.85727	+	5.69110i	0.468333	+	0.270392i	0.715542	−	0.698570i	$-0.246180\pi$
$443$	9.85727	+	5.69110i	0.468333	+	0.270392i	−0.247209	+	0.968962i	$0.579513\pi$
$444$	10.4471	+	6.39489i	0.495795	+	0.303488i
$445$	1.14739			0.0543914
$446$	11.8708	−	20.5609i	0.562099	−	0.973585i
$447$	16.7430	+	0.430184i	0.791916	+	0.0203470i
$448$	1.26694	−	1.26694i	0.0598574	−	0.0598574i
$449$	−13.3760	−	3.58409i	−0.631253	−	0.169144i	−0.0710148	−	0.997475i	$-0.522624\pi$
$449$	−13.3760	−	3.58409i	−0.631253	−	0.169144i	−0.560238	+	0.828331i	$0.689290\pi$
$450$	−13.3380	+	2.84881i	−0.628761	+	0.134294i
$451$	−2.45231	−	4.24752i	−0.115475	−	0.200008i
$452$	−5.54284	−	9.60049i	−0.260713	−	0.451569i
$453$	−8.60980	−	0.221215i	−0.404524	−	0.0103936i
$454$	20.7339	−	11.9707i	0.973092	−	0.561815i
$455$	4.32566	+	0.472930i	0.202790	+	0.0221713i
$456$	−11.0394	+	2.65608i	−0.516969	+	0.124382i
$457$	−32.5303	−	8.71648i	−1.52171	−	0.407740i	−0.601402	−	0.798946i	$-0.705391\pi$
$457$	−32.5303	−	8.71648i	−1.52171	−	0.407740i	−0.920303	+	0.391207i	$0.872058\pi$
$458$	17.7846	+	10.2680i	0.831022	+	0.479791i
$459$	4.17814	−	11.8543i	0.195019	−	0.553312i
$460$	3.01305	−	3.01305i	0.140484	−	0.140484i
$461$	6.35961	+	6.35961i	0.296196	+	0.296196i	0.839522	−	0.543326i	$-0.182835\pi$
$461$	6.35961	+	6.35961i	0.296196	+	0.296196i	−0.543326	+	0.839522i	$0.682835\pi$
$462$	3.05790	+	0.0785678i	0.142266	+	0.00365531i
$463$	4.90786	−	18.3164i	0.228087	−	0.851234i	−0.753057	−	0.657956i	$-0.771421\pi$
$463$	4.90786	−	18.3164i	0.228087	−	0.851234i	0.981144	−	0.193278i	$-0.0619120\pi$
$464$	3.71748	+	2.14629i	0.172580	+	0.0996388i
$465$	4.89780	−	4.65242i	0.227130	−	0.215751i
$466$	0.722288	−	2.69562i	0.0334593	−	0.124872i
$467$	33.1417			1.53362			0.766808	−	0.641877i	$-0.221844\pi$
$467$	33.1417			1.53362			0.766808	+	0.641877i	$0.221844\pi$
$468$	1.72622	−	10.6780i	0.0797944	−	0.493592i
$469$	−19.8385			−0.916056
$470$	0.661258	−	2.46785i	0.0305015	−	0.113833i
$471$	3.93970	+	16.3745i	0.181532	+	0.754498i
$472$	4.09014	+	2.36144i	0.188264	+	0.108694i
$473$	−0.227631	+	0.849529i	−0.0104665	+	0.0390614i
$474$	1.33531	+	2.45646i	0.0613330	+	0.112829i
$475$	21.0741	+	21.0741i	0.966945	+	0.966945i
$476$	3.06463	−	3.06463i	0.140467	−	0.140467i
$477$	−14.6832	+	22.6589i	−0.672297	+	1.03748i
$478$	6.80368	+	3.92811i	0.311193	+	0.179667i
$479$	−29.7832	−	7.98038i	−1.36083	−	0.364633i	−0.496707	−	0.867918i	$-0.665458\pi$
$479$	−29.7832	−	7.98038i	−1.36083	−	0.364633i	−0.864120	+	0.503285i	$0.832124\pi$
$480$	0.330803	−	1.11879i	0.0150990	−	0.0510657i
$481$	23.7661	+	9.23710i	1.08364	+	0.421176i
$482$	20.1612	−	11.6401i	0.918316	−	0.530190i
$483$	9.37608	+	17.2483i	0.426627	+	0.784827i
$484$	5.01422	+	8.68489i	0.227919	+	0.394768i
$485$	0.646962	+	1.12057i	0.0293770	+	0.0508825i
$486$	15.4601	+	1.99666i	0.701282	+	0.0905703i
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.212733	−	0.977110i	$-0.568236\pi$
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.672787	+	0.739836i	$0.734903\pi$
$488$	3.36864	−	3.36864i	0.152491	−	0.152491i
$489$	−4.35740	+	7.11849i	−0.197048	+	0.321909i
$490$	1.27634	−	2.21068i	0.0576590	−	0.0998683i
$491$	−15.1024			−0.681562			−0.340781	−	0.940143i	$-0.610691\pi$
$491$	−15.1024			−0.681562			−0.340781	+	0.940143i	$0.610691\pi$
$492$	0.221365	−	8.61566i	0.00997992	−	0.388424i
$493$	8.99228	+	5.19169i	0.404992	+	0.233822i
$494$	−21.6327	+	9.52340i	−0.973303	+	0.428478i
$495$	1.77381	−	0.906002i	0.0797268	−	0.0407218i
$496$	−1.49861	−	5.59289i	−0.0672896	−	0.251128i
$497$	10.2459	−	5.91546i	0.459590	−	0.265345i
$498$	−3.71694	+	12.5709i	−0.166560	+	0.563316i
$499$	40.4871	+	10.8485i	1.81245	+	0.485645i	0.995805	−	0.0914956i	$-0.0291647\pi$
$499$	40.4871	+	10.8485i	1.81245	+	0.485645i	0.816645	+	0.577140i	$0.195831\pi$
$500$	−6.21109	+	1.66426i	−0.277768	+	0.0744278i
$501$	−21.5324	+	11.7049i	−0.961998	+	0.522936i
$502$	−25.1605	+	6.74174i	−1.12297	+	0.300899i
$503$	10.9025	−	6.29458i	0.486120	−	0.280661i	−0.236843	−	0.971548i	$-0.576113\pi$
$503$	10.9025	−	6.29458i	0.486120	−	0.280661i	0.722963	+	0.690886i	$0.242780\pi$
$504$	4.51089	+	2.92310i	0.200931	+	0.130205i
$505$	−9.68912	+	2.59619i	−0.431160	+	0.115529i
$506$	3.11771	−	5.40004i	0.138599	−	0.240061i
$507$	−0.412356	−	22.5129i	−0.0183134	−	0.999832i
$508$	−2.50106	−	4.33197i	−0.110967	−	0.192200i
$509$	−23.4868	−	23.4868i	−1.04103	−	1.04103i	−0.999121	−	0.0419113i	$-0.986655\pi$
$509$	−23.4868	−	23.4868i	−1.04103	−	1.04103i	−0.0419113	−	0.999121i	$-0.513345\pi$
$510$	0.800185	−	2.70627i	0.0354328	−	0.119836i
$511$		−	20.3164i		−	0.898744i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−14.7101	−	30.7235i	−0.649465	−	1.35647i
$514$	1.86390	−	6.95616i	0.0822130	−	0.306823i
$515$	1.82936	+	6.82727i	0.0806113	+	0.300846i
$516$	−1.12052	+	1.06438i	−0.0493282	+	0.0468569i
$517$		−	3.73869i		−	0.164427i
$518$	−8.95970	+	8.95970i	−0.393667	+	0.393667i
$519$	−38.5309	−	11.3928i	−1.69132	−	0.500086i
$520$	0.263952	−	2.41424i	0.0115750	−	0.105871i
$521$		−	17.5549i		−	0.769094i	−0.923105	−	0.384547i	$-0.874358\pi$
$521$		−	17.5549i		−	0.769094i	0.923105	−	0.384547i	$-0.125642\pi$
$522$	−3.96738	+	12.2514i	−0.173647	+	0.536227i
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	−0.943038	−	0.332686i	$-0.892045\pi$
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	0.759633	+	0.650352i	$0.225379\pi$
$524$	−21.9809			−0.960242
$525$	0.362383	−	14.1041i	0.0158157	−	0.615555i
$526$	2.96476	+	11.0646i	0.129270	+	0.482440i
$527$	−3.62502	−	13.5287i	−0.157908	−	0.589321i
$528$	0.0438503	−	1.70668i	0.00190834	−	0.0742736i
$529$	17.0189			0.739951
$530$	−3.03116	+	5.25012i	−0.131665	+	0.228050i
$531$	−4.36509	+	13.4795i	−0.189429	+	0.584961i
$532$		−	11.7457i		−	0.509240i
$533$	−2.73249	−	17.7315i	−0.118357	−	0.768038i
$534$	2.82932	+	0.836568i	0.122437	+	0.0362018i
$535$	1.03340	−	1.03340i	0.0446778	−	0.0446778i
$536$			11.0723i			0.478249i
$537$	−6.99593	+	6.64544i	−0.301897	+	0.286772i
$538$	−6.50898	−	24.2918i	−0.280622	−	1.04730i
$539$	0.966799	−	3.60814i	0.0416430	−	0.155414i
$540$	3.48964	+	0.269456i	0.150170	+	0.0115955i
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	0.737332	−	0.675531i	$-0.236086\pi$
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	−0.675531	+	0.737332i	$0.736086\pi$
$542$			6.39022i			0.274484i
$543$	−10.2352	+	34.6162i	−0.439236	+	1.48552i
$544$	−1.71043	−	1.71043i	−0.0733343	−	0.0733343i
$545$	3.94622	+	6.83505i	0.169037	+	0.292781i
$546$	10.3217	+	4.32006i	0.441730	+	0.184881i
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	−0.710848	−	0.703345i	$-0.751689\pi$
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	0.964539	+	0.263940i	$0.0850222\pi$
$548$	12.1601	−	3.25829i	0.519453	−	0.139187i
$549$	11.9939	+	7.77214i	0.511886	+	0.331707i
$550$	−3.88080	+	2.24058i	−0.165478	+	0.0955388i
$551$	27.1811	−	7.28317i	1.15796	−	0.310273i
$552$	9.62665	−	5.23298i	0.409738	−	0.222731i
$553$	−2.79372	+	0.748574i	−0.118801	+	0.0318326i
$554$	18.7804	+	5.03218i	0.797901	+	0.213797i
$555$	−2.33941	+	7.91200i	−0.0993022	+	0.335846i
$556$	−17.0576	+	9.84823i	−0.723405	+	0.417658i
$557$	−9.18337	−	34.2728i	−0.389112	−	1.45219i	−0.831582	−	0.555402i	$-0.812564\pi$
$557$	−9.18337	−	34.2728i	−0.389112	−	1.45219i	0.442470	−	0.896783i	$-0.354102\pi$
$558$	15.4695	−	7.90130i	0.654876	−	0.334489i
$559$	−1.90186	+	2.59481i	−0.0804400	+	0.109749i
$560$	1.04518	+	0.603436i	0.0441670	+	0.0254998i
$561$	0.106070	−	4.12831i	0.00447829	−	0.174298i
$562$	−29.8076			−1.25736
$563$	18.4876	−	32.0214i	0.779159	−	1.34954i	−0.153268	−	0.988185i	$-0.548980\pi$
$563$	18.4876	−	32.0214i	0.779159	−	1.34954i	0.932427	−	0.361358i	$-0.117687\pi$
$564$	3.42991	−	5.60329i	0.144425	−	0.235941i
$565$	5.28003	−	5.28003i	0.222133	−	0.222133i
$566$	−21.3237	−	5.71368i	−0.896303	−	0.240164i
$567$	−5.74923	+	15.0658i	−0.241445	+	0.632706i
$568$	−3.30154	−	5.71843i	−0.138529	−	0.239940i
$569$	12.2655	+	21.2445i	0.514198	+	0.890616i	0.999864	+	0.0164722i	$0.00524351\pi$
$569$	12.2655	+	21.2445i	0.514198	+	0.890616i	−0.485667	+	0.874144i	$0.661423\pi$
$570$	−3.65269	−	6.71952i	−0.152994	−	0.281450i
$571$	7.42838	−	4.28878i	0.310868	−	0.179480i	−0.336447	−	0.941702i	$-0.609225\pi$
$571$	7.42838	−	4.28878i	0.310868	−	0.179480i	0.647315	+	0.762223i	$0.275892\pi$
$572$	−0.541280	−	3.51244i	−0.0226320	−	0.146863i
$573$	−8.87571	+	30.0181i	−0.370788	+	1.25403i
$574$	8.61166	+	2.30749i	0.359444	+	0.0963127i
$575$	−24.9069	−	14.3800i	−1.03869	−	0.599688i
$576$	1.63144	−	2.51762i	0.0679766	−	0.104901i
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	−0.727437	−	0.686174i	$-0.759289\pi$
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	0.686174	+	0.727437i	$0.259289\pi$
$578$	7.88341	+	7.88341i	0.327907	+	0.327907i
$579$	−6.09038	−	11.2039i	−0.253107	−	0.465619i
$580$	−0.748347	+	2.79287i	−0.0310734	+	0.115968i
$581$	−11.7438	−	6.78029i	−0.487215	−	0.281294i
$582$	0.778314	+	3.23490i	0.0322622	+	0.134091i
$583$	−2.29604	+	8.56894i	−0.0950923	+	0.354889i
$584$	−11.3390			−0.469211
$585$	7.24836	−	0.738431i	0.299683	−	0.0305304i
$586$	−9.48781			−0.391938
$587$	9.87397	−	36.8502i	0.407543	−	1.52097i	−0.391775	−	0.920061i	$-0.628139\pi$
$587$	9.87397	−	36.8502i	0.407543	−	1.52097i	0.799318	−	0.600908i	$-0.205194\pi$
$588$	4.75911	−	4.52068i	0.196262	−	0.186430i
$589$	−32.8722	−	18.9788i	−1.35448	−	0.782008i
$590$	−0.823366	+	3.07284i	−0.0338975	+	0.126507i
$591$	42.3892	+	1.08912i	1.74366	+	0.0448005i
$592$	5.00059	+	5.00059i	0.205523	+	0.205523i
$593$	22.4411	−	22.4411i	0.921547	−	0.921547i	−0.0755923	−	0.997139i	$-0.524085\pi$
$593$	22.4411	−	22.4411i	0.921547	−	0.921547i	0.997139	+	0.0755923i	$0.0240847\pi$
$594$	5.03457	−	0.940795i	0.206571	−	0.0386013i
$595$	2.52821	+	1.45966i	0.103647	+	0.0598403i
$596$	9.34027	+	2.50272i	0.382592	+	0.102515i
$597$	13.5687	−	3.26461i	0.555329	−	0.133612i
$598$	17.7857	−	14.2799i	0.727310	−	0.583948i
$599$	12.9383	−	7.46992i	0.528644	−	0.305213i	−0.211820	−	0.977309i	$-0.567939\pi$
$599$	12.9383	−	7.46992i	0.528644	−	0.305213i	0.740464	+	0.672096i	$0.234606\pi$
$600$	−7.87181	−	0.202253i	−0.321365	−	0.00825696i
$601$	4.71759	+	8.17110i	0.192434	+	0.333306i	0.946056	−	0.324002i	$-0.105028\pi$
$601$	4.71759	+	8.17110i	0.192434	+	0.333306i	−0.753622	+	0.657308i	$0.771695\pi$
$602$	−0.799360	−	1.38453i	−0.0325795	−	0.0564293i
$603$	−32.4841	+	6.93814i	−1.32285	+	0.282543i
$604$	−4.80308	−	1.28698i	−0.195434	−	0.0523665i
$605$	−4.77648	+	4.77648i	−0.194191	+	0.194191i
$606$	−25.7851	−	0.662506i	−1.04745	−	0.0269125i
$607$	−4.11465	+	7.12678i	−0.167008	+	0.289267i	−0.937367	−	0.348344i	$-0.886744\pi$
$607$	−4.11465	+	7.12678i	−0.167008	+	0.289267i	0.770358	+	0.637611i	$0.220077\pi$
$608$	−6.55551			−0.265861
$609$	−11.3618	−	6.95483i	−0.460403	−	0.281824i
$610$	2.77901	+	1.60446i	0.112519	+	0.0649627i
$611$	4.95433	−	12.7470i	0.200431	−	0.515688i
$612$	3.94632	−	6.08992i	0.159521	−	0.246170i
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	−0.986968	−	0.160918i	$-0.948555\pi$
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	0.774280	−	0.632843i	$-0.218112\pi$
$614$	−4.11150	+	2.37378i	−0.165927	+	0.0957979i
$615$	5.64418	−	1.35799i	0.227595	−	0.0547593i
$616$	1.70589	+	0.457091i	0.0687321	+	0.0184167i
$617$	31.6362	−	8.47690i	1.27363	−	0.341267i	0.442207	−	0.896913i	$-0.354195\pi$
$617$	31.6362	−	8.47690i	1.27363	−	0.341267i	0.831419	+	0.555646i	$0.187529\pi$
$618$	−0.466824	+	18.1690i	−0.0187784	+	0.730866i
$619$	−9.36687	+	2.50985i	−0.376486	+	0.100879i	−0.442100	−	0.896966i	$-0.645766\pi$
$619$	−9.36687	+	2.50985i	−0.376486	+	0.100879i	0.0656133	+	0.997845i	$0.479100\pi$
$620$	3.37763	−	1.95008i	0.135649	−	0.0783169i
$621$	21.3850	+	24.9638i	0.858149	+	1.00176i
$622$	−20.4069	+	5.46802i	−0.818244	+	0.219248i
$623$	−1.52603	+	2.64316i	−0.0611391	+	0.105896i
$624$	2.41111	−	5.76078i	0.0965217	−	0.230616i
$625$	9.20010	+	15.9350i	0.368004	+	0.637402i
$626$	−7.30568	−	7.30568i	−0.291994	−	0.291994i
$627$	−7.70794	−	8.11447i	−0.307825	−	0.324061i
$628$			9.72362i			0.388015i
$629$	12.0960	+	12.0960i	0.482300	+	0.482300i
$630$	−1.11544	+	3.44451i	−0.0444402	+	0.137233i
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	0.745878	+	0.666083i	$0.232030\pi$
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	−0.978991	+	0.203906i	$0.934636\pi$
$632$	0.417795	+	1.55923i	0.0166190	+	0.0620229i
$633$	23.3894	+	6.91574i	0.929646	+	0.274876i
$634$		−	16.7572i		−	0.665514i
$635$	2.38248	−	2.38248i	0.0945457	−	0.0945457i
$636$	−11.3024	+	10.7361i	−0.448168	+	0.425715i
$637$	8.07762	−	11.0207i	0.320047	−	0.436658i
$638$			4.23108i			0.167510i
$639$	14.7081	−	13.2694i	0.581842	−	0.524931i
$640$	0.336790	−	0.583337i	0.0133128	−	0.0230584i
$641$	10.7880			0.426100			0.213050	−	0.977041i	$-0.431660\pi$
$641$	10.7880			0.426100			0.213050	+	0.977041i	$0.431660\pi$
$642$	3.30170	−	1.79478i	0.130308	−	0.0708344i
$643$	2.77540	+	10.3579i	0.109451	+	0.408477i	0.998812	−	0.0487289i	$-0.0155170\pi$
$643$	2.77540	+	10.3579i	0.109451	+	0.408477i	−0.889361	+	0.457206i	$0.848850\pi$
$644$	2.93360	+	10.9483i	0.115600	+	0.431425i
$645$	−0.887865	−	0.543483i	−0.0349596	−	0.0213996i
$646$	−15.8572			−0.623895
$647$	−2.44136	+	4.22856i	−0.0959799	+	0.166242i	−0.910017	−	0.414571i	$-0.863932\pi$
$647$	−2.44136	+	4.22856i	−0.0959799	+	0.166242i	0.814037	+	0.580813i	$0.197265\pi$
$648$	8.40856	+	3.20876i	0.330319	+	0.126052i
$649$			4.65524i			0.182734i
$650$	−16.2006	+	2.49658i	−0.635442	+	0.0979238i
$651$	4.20339	+	17.4705i	0.164744	+	0.684723i
$652$	−3.40734	+	3.40734i	−0.133442	+	0.133442i
$653$			21.9436i			0.858719i	0.903134	+	0.429360i	$0.141261\pi$
$653$			21.9436i			0.858719i	−0.903134	+	0.429360i	$0.858739\pi$
$654$	4.74742	+	19.7316i	0.185639	+	0.771568i
$655$	−3.83206	−	14.3014i	−0.149731	−	0.558803i
$656$	1.28786	−	4.80634i	0.0502823	−	0.187656i
$657$	−7.10528	−	33.2666i	−0.277203	−	1.29786i
$658$	4.80554	+	4.80554i	0.187340	+	0.187340i
$659$			42.3078i			1.64808i	0.566534	+	0.824038i	$0.308284\pi$
$659$			42.3078i			1.64808i	−0.566534	+	0.824038i	$0.691716\pi$
$660$	1.11806	−	0.269004i	0.0435203	−	0.0104710i
$661$	−22.1456	−	22.1456i	−0.861363	−	0.861363i	0.130133	−	0.991497i	$-0.458460\pi$
$661$	−22.1456	−	22.1456i	−0.861363	−	0.861363i	−0.991497	+	0.130133i	$0.958460\pi$
$662$	7.37732	+	12.7779i	0.286728	+	0.496627i
$663$	5.83228	−	13.9349i	0.226507	−	0.541185i
$664$	−3.78422	+	6.55446i	−0.146856	+	0.254362i
$665$	7.64207	−	2.04769i	0.296347	−	0.0794059i
$666$	−11.5374	+	17.8044i	−0.447065	+	0.689905i
$667$	−23.5169	+	13.5775i	−0.910579	+	0.525723i
$668$	−13.6676	+	3.66224i	−0.528817	+	0.141696i
$669$	35.0726	+	21.4688i	1.35599	+	0.830031i
$670$	−7.20392	+	1.93029i	−0.278312	+	0.0745734i
$671$	4.53573	+	1.21535i	0.175100	+	0.0469179i
$672$	2.13732	+	2.25005i	0.0824490	+	0.0867975i
$673$	−32.9394	+	19.0176i	−1.26972	+	0.733075i	−0.974935	−	0.222488i	$-0.928582\pi$
$673$	−32.9394	+	19.0176i	−1.26972	+	0.733075i	−0.294787	+	0.955563i	$0.595249\pi$
$674$	−1.00563	−	3.75304i	−0.0387352	−	0.144562i
$675$	−4.33928	−	23.2213i	−0.167019	−	0.893787i
$676$	2.80903	−	12.6929i	0.108040	−	0.488188i
$677$	−4.73877	−	2.73593i	−0.182126	−	0.105150i	0.406165	−	0.913800i	$-0.366866\pi$
$677$	−4.73877	−	2.73593i	−0.182126	−	0.105150i	−0.588291	+	0.808649i	$0.700199\pi$
$678$	16.8696	−	9.17022i	0.647874	−	0.352180i
$679$	−3.44185			−0.132086
$680$	0.814668	−	1.41105i	0.0312411	−	0.0541111i
$681$	19.8047	+	36.4329i	0.758917	+	1.39611i
$682$	4.03563	−	4.03563i	0.154532	−	0.154532i
$683$	24.9699	+	6.69067i	0.955447	+	0.256011i	0.702672	−	0.711514i	$-0.251990\pi$
$683$	24.9699	+	6.69067i	0.955447	+	0.256011i	0.252775	+	0.967525i	$0.418657\pi$
$684$	−4.10784	−	19.2327i	−0.157067	−	0.735382i
$685$	4.23986	+	7.34366i	0.161997	+	0.280587i
$686$	9.66611	+	16.7422i	0.369054	+	0.639220i
$687$	−18.5700	+	30.3370i	−0.708489	+	1.15743i
$688$	−0.772736	+	0.446139i	−0.0294603	+	0.0170089i
$689$	−19.1834	+	26.1730i	−0.730831	+	0.997113i
$690$	5.08299	+	5.35108i	0.193506	+	0.203712i
$691$	32.7059	+	8.76352i	1.24419	+	0.333380i	0.820090	−	0.572235i	$-0.193923\pi$
$691$	32.7059	+	8.76352i	1.24419	+	0.333380i	0.424101	+	0.905615i	$0.360590\pi$
$692$	−20.0900	−	11.5989i	−0.763706	−	0.440926i
$693$	−0.272077	+	5.29120i	−0.0103354	+	0.200996i
$694$	−22.8522	+	22.8522i	−0.867459	+	0.867459i
$695$	−9.38129	−	9.38129i	−0.355852	−	0.355852i
$696$	−3.88163	+	6.34125i	−0.147133	+	0.240365i
$697$	3.11522	−	11.6262i	0.117997	−	0.440372i
$698$	16.4240	+	9.48239i	0.621657	+	0.358914i
$699$	4.63527	+	1.37055i	0.175322	+	0.0518389i
$700$	2.10827	−	7.86816i	0.0796850	−	0.297388i
$701$	29.4689			1.11303			0.556513	−	0.830839i	$-0.312139\pi$
$701$	29.4689			1.11303			0.556513	+	0.830839i	$0.312139\pi$
$702$	18.4120	+	3.46395i	0.694915	+	0.130738i
$703$	46.3599			1.74850
$704$	0.255112	−	0.952090i	0.00961488	−	0.0358832i
$705$	4.24361	+	1.25474i	0.159824	+	0.0472563i
$706$	16.9718	+	9.79865i	0.638740	+	0.368777i
$707$	6.90589	−	25.7731i	0.259723	−	0.969298i
$708$	−4.27075	+	6.97694i	−0.160505	+	0.262210i
$709$	9.17695	+	9.17695i	0.344648	+	0.344648i	0.858111	−	0.513464i	$-0.171638\pi$
$709$	9.17695	+	9.17695i	0.344648	+	0.344648i	−0.513464	+	0.858111i	$0.671638\pi$
$710$	3.14500	−	3.14500i	0.118030	−	0.118030i
$711$	−4.31271	+	2.20279i	−0.161739	+	0.0826110i
$712$	1.47520	+	0.851709i	0.0552856	+	0.0319191i
$713$	35.3809	+	9.48027i	1.32502	+	0.355039i
$714$	5.17001	+	5.44269i	0.193483	+	0.203687i
$715$	2.19093	−	0.964514i	0.0819361	−	0.0360708i
$716$	−4.82455	+	2.78545i	−0.180302	+	0.104097i
$717$	−7.10412	+	11.6057i	−0.265308	+	0.433422i
$718$	−13.5825	−	23.5255i	−0.506894	−	0.877965i
$719$	−1.46802	−	2.54269i	−0.0547480	−	0.0948263i	0.837353	−	0.546663i	$-0.184102\pi$
$719$	−1.46802	−	2.54269i	−0.0547480	−	0.0948263i	−0.892101	+	0.451837i	$0.850769\pi$
$720$	1.92245	+	0.622551i	0.0716455	+	0.0232011i
$721$	−18.1606	−	4.86612i	−0.676336	−	0.181224i
$722$	−16.9527	+	16.9527i	−0.630913	+	0.630913i
$723$	19.2576	+	35.4265i	0.716198	+	1.31753i
$724$	−10.4205	+	18.0488i	−0.387274	+	0.670779i
$725$	19.5153			0.724779
$726$	−15.2608	+	8.29565i	−0.566380	+	0.307881i
$727$	34.7895	+	20.0857i	1.29027	+	0.744938i	0.978702	−	0.205285i	$-0.0658122\pi$
$727$	34.7895	+	20.0857i	1.29027	+	0.744938i	0.311569	+	0.950224i	$0.399146\pi$
$728$	5.21047	+	3.81900i	0.193113	+	0.141541i
$729$	−4.14496	+	26.6799i	−0.153517	+	0.988146i
$730$	−1.97679	−	7.37746i	−0.0731641	−	0.273052i
$731$	−1.86919	+	1.07917i	−0.0691343	+	0.0399147i
$732$	5.68287	+	5.98259i	0.210045	+	0.221123i
$733$	12.6590	+	3.39197i	0.467571	+	0.125285i	0.484909	−	0.874564i	$-0.338853\pi$
$733$	12.6590	+	3.39197i	0.467571	+	0.125285i	−0.0173384	+	0.999850i	$0.505519\pi$
$734$	7.43211	−	1.99143i	0.274324	−	0.0735050i
$735$	3.77096	+	2.30830i	0.139094	+	0.0851428i
$736$	6.11049	−	1.63730i	0.225236	−	0.0603517i
$737$	−9.45150	+	5.45683i	−0.348151	+	0.201005i
$738$	14.9080	+	0.766579i	0.548770	+	0.0282182i
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.610731	−	0.791838i	$-0.709124\pi$
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.132990	+	0.991117i	$0.542458\pi$
$740$	−2.38175	+	4.12531i	−0.0875547	+	0.151649i
$741$	−15.5272	−	37.8803i	−0.570405	−	1.39157i
$742$	−8.06290	−	13.9654i	−0.295998	−	0.512684i
$743$	11.8437	+	11.8437i	0.434502	+	0.434502i	0.890157	−	0.455655i	$-0.150595\pi$
$743$	11.8437	+	11.8437i	0.434502	+	0.434502i	−0.455655	+	0.890157i	$0.650595\pi$
$744$	9.75064	−	2.34600i	0.357476	−	0.0860085i
$745$			6.51335i			0.238631i
$746$	11.3830	+	11.3830i	0.416760	+	0.416760i
$747$	−21.6009	−	6.99506i	−0.790336	−	0.255936i
$748$	0.617094	−	2.30303i	0.0225632	−	0.0842070i
$749$	1.00615	+	3.75500i	0.0367639	+	0.137205i
$750$	−2.60531	−	10.8284i	−0.0951324	−	0.395397i
$751$		−	9.36886i		−	0.341875i	−0.985282	−	0.170937i	$-0.945320\pi$
$751$		−	9.36886i		−	0.341875i	0.985282	−	0.170937i	$-0.0546796\pi$
$752$	2.68207	−	2.68207i	0.0978051	−	0.0978051i
$753$	−10.5539	−	43.8649i	−0.384604	−	1.59852i
$754$	−5.60683	+	14.4258i	−0.204189	+	0.525357i
$755$		−	3.34938i		−	0.121897i
$756$	−5.26196	+	7.68047i	−0.191376	+	0.279336i
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	−0.838090	−	0.545532i	$-0.816328\pi$
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	0.891490	+	0.453041i	$0.149661\pi$
$758$	−25.9610			−0.942945
$759$	9.21136	+	5.63849i	0.334351	+	0.204664i
$760$	−1.14286	−	4.26520i	−0.0414558	−	0.154715i
$761$	2.67639	+	9.98843i	0.0970191	+	0.362080i	0.997318	−	0.0731923i	$-0.0233187\pi$
$761$	2.67639	+	9.98843i	0.0970191	+	0.362080i	−0.900299	+	0.435273i	$0.856652\pi$
$762$	7.61198	−	4.13782i	0.275753	−	0.149897i
$763$	−20.9940			−0.760032
$764$	−9.03635	+	15.6514i	−0.326924	+	0.566248i
$765$	4.65025	+	1.50590i	0.168130	+	0.0544459i
$766$		−	31.4582i		−	1.13663i
$767$	−6.16889	+	15.8719i	−0.222746	+	0.573103i
$768$	1.25580	−	1.19288i	0.0453147	−	0.0430445i
$769$	0.0494190	−	0.0494190i	0.00178210	−	0.00178210i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.66097 - 0.491112i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.174335 - 0.650628i) q^{5} +(0.904267 - 1.47726i) q^{6} +(1.26694 + 1.26694i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.51762 + 1.63144i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.66097 - 0.491112i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.174335 - 0.650628i) q^{5} +(0.904267 - 1.47726i) q^{6} +(1.26694 + 1.26694i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.51762 + 1.63144i) q^{9} +(0.583337 + 0.336790i) q^{10} +(0.952090 + 0.255112i) q^{11} +(1.19288 + 1.25580i) q^{12} +(2.90807 + 2.13146i) q^{13} +(-1.55168 + 0.895864i) q^{14} +(-0.609096 + 0.995053i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.20946 + 2.09485i) q^{17} +(-2.22746 + 2.00959i) q^{18} +(6.33213 + 1.69669i) q^{19} +(-0.476293 + 0.476293i) q^{20} +(-1.48214 - 2.72656i) q^{21} +(-0.492838 + 0.853620i) q^{22} -6.32605 q^{23} +(-1.52175 + 0.827212i) q^{24} +(3.93720 + 2.27315i) q^{25} +(-2.81150 + 2.25732i) q^{26} +(-3.38046 - 3.94620i) q^{27} +(-0.463733 - 1.73068i) q^{28} +(3.71748 - 2.14629i) q^{29} +(-0.803502 - 0.845880i) q^{30} +(-5.59289 - 1.49861i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.45610 - 0.891314i) q^{33} +(-2.33650 + 0.626062i) q^{34} +(1.04518 - 0.603436i) q^{35} +(-1.36460 - 2.67168i) q^{36} +(6.83094 - 1.83034i) q^{37} +(-3.27775 + 5.67724i) q^{38} +(-3.78342 - 4.96847i) q^{39} +(-0.336790 - 0.583337i) q^{40} +(-3.51849 - 3.51849i) q^{41} +(3.01726 - 0.725951i) q^{42} +0.892279i q^{43} +(-0.696978 - 0.696978i) q^{44} +(1.50037 - 1.35362i) q^{45} +(1.63730 - 6.11049i) q^{46} +(-0.981707 - 3.66378i) q^{47} +(-0.405168 - 1.68399i) q^{48} -3.78971i q^{49} +(-3.21471 + 3.21471i) q^{50} +(-0.980069 - 4.07345i) q^{51} +(-1.45273 - 3.29993i) q^{52} +9.00014i q^{53} +(4.68666 - 2.24392i) q^{54} +(0.331966 - 0.574981i) q^{55} +1.79173 q^{56} +(-9.68420 - 5.92793i) q^{57} +(1.11100 + 4.14631i) q^{58} +(1.22237 + 4.56196i) q^{59} +(1.02502 - 0.557194i) q^{60} +4.76398 q^{61} +(2.89509 - 5.01445i) q^{62} +(1.12274 + 5.25662i) q^{63} -1.00000i q^{64} +(1.89377 - 1.52048i) q^{65} +(1.23781 - 1.17580i) q^{66} +(-7.82927 + 7.82927i) q^{67} -2.41892i q^{68} +(10.5074 + 3.10679i) q^{69} +(0.312361 + 1.16575i) q^{70} +(1.70900 - 6.37808i) q^{71} +(2.93383 - 0.626624i) q^{72} +(-8.01788 - 8.01788i) q^{73} +7.07190i q^{74} +(-5.42319 - 5.70922i) q^{75} +(-4.63544 - 4.63544i) q^{76} +(0.883031 + 1.52946i) q^{77} +(5.77840 - 2.36857i) q^{78} +(-0.807117 + 1.39797i) q^{79} +(0.650628 - 0.174335i) q^{80} +(3.67681 + 8.21469i) q^{81} +(4.30925 - 2.48795i) q^{82} +(-7.31055 + 1.95885i) q^{83} +(-0.0797096 + 3.10234i) q^{84} +(1.57382 - 0.421703i) q^{85} +(-0.861875 - 0.230939i) q^{86} +(-7.22867 + 1.73921i) q^{87} +(0.853620 - 0.492838i) q^{88} +(0.440877 + 1.64537i) q^{89} +(0.919169 + 1.79959i) q^{90} +(0.983920 + 6.38480i) q^{91} +(5.47852 + 3.16302i) q^{92} +(8.55361 + 5.23587i) q^{93} +3.79302 q^{94} +(2.20783 - 3.82407i) q^{95} +(1.73148 + 0.0444876i) q^{96} +(-1.35833 + 1.35833i) q^{97} +(3.66058 + 0.980849i) q^{98} +(1.98080 + 2.19555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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