LMFDB - Embedded newform 234.2.z.a.167.1

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			167.1
Character	$\chi$	$=$	234.167
Dual form			234.2.z.a.227.1

$q$-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} +(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} - 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}+ \cdots + 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

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	0.993889	−	0.110382i	$-0.0352073\pi$
$5$	0.174335	+	0.650628i	0.0779651	+	0.290970i	−0.915924	+	0.401351i	$0.868541\pi$
$6$	0.904267	+	1.47726i	0.369165	+	0.603089i
$7$	1.26694	−	1.26694i	0.478859	−	0.478859i	−0.425907	−	0.904767i	$-0.640045\pi$
$7$	1.26694	−	1.26694i	0.478859	−	0.478859i	0.904767	+	0.425907i	$0.140045\pi$
$8$	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	−0.112413	−	0.993662i	$-0.535858\pi$
$11$	0.952090	−	0.255112i	0.287066	−	0.0769190i	0.399479	+	0.916743i	$0.369191\pi$
$12$	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	−0.681260	−	0.732042i	$-0.738568\pi$
$17$	1.20946	−	2.09485i	0.293337	−	0.508075i	0.974597	+	0.223967i	$0.0719009\pi$
$18$	−2.22746	−	2.00959i	−0.525017	−	0.473664i
$19$	6.33213	−	1.69669i	1.45269	−	0.389247i	0.555732	−	0.831361i	$-0.312438\pi$
$19$	6.33213	−	1.69669i	1.45269	−	0.389247i	0.896959	+	0.442114i	$0.145771\pi$
$20$	−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	0.803731	−	0.594993i	$-0.202845\pi$
$29$	3.71748	+	2.14629i	0.690318	+	0.398555i	−0.113413	+	0.993548i	$0.536178\pi$
$30$	−0.803502	+	0.845880i	−0.146699	+	0.154436i
$31$	−5.59289	+	1.49861i	−1.00451	+	0.269158i	−0.723335	−	0.690498i	$-0.757392\pi$
$31$	−5.59289	+	1.49861i	−1.00451	+	0.269158i	−0.281178	+	0.959656i	$0.590725\pi$
$32$	−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	0.772096	−	0.635505i	$-0.219208\pi$
$37$	6.83094	+	1.83034i	1.12300	+	0.300907i	0.350902	+	0.936412i	$0.385875\pi$
$38$	−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	−0.926295	−	0.376799i	$-0.877025\pi$
$41$	−3.51849	+	3.51849i	−0.549496	+	0.549496i	0.376799	+	0.926295i	$0.377025\pi$
$42$	3.01726	+	0.725951i	0.465573	+	0.112017i
$43$		−	0.892279i		−	0.136071i	−0.997683	−	0.0680356i	$-0.978327\pi$
$43$		−	0.892279i		−	0.136071i	0.997683	−	0.0680356i	$-0.0216731\pi$
$44$	−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	0.856632	+	0.515927i	$0.172553\pi$
$47$	−0.981707	+	3.66378i	−0.143197	+	0.534417i	−0.999829	+	0.0184899i	$0.994114\pi$
$48$	−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	$-0.787890\pi$
$53$		−	9.00014i		−	1.23626i	0.786074	−	0.618132i	$-0.212110\pi$
$54$	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	−0.839576	−	0.543243i	$-0.817196\pi$
$59$	1.22237	−	4.56196i	0.159139	−	0.593917i	0.998715	−	0.0506741i	$-0.0161370\pi$
$60$	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	0.0425948	−	0.999092i	$-0.486438\pi$
$67$	−7.82927	−	7.82927i	−0.956498	−	0.956498i	−0.999092	+	0.0425948i	$0.986438\pi$
$68$			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	0.990103	+	0.140345i	$0.0448212\pi$
$71$	1.70900	+	6.37808i	0.202821	+	0.756939i	−0.787281	+	0.616594i	$0.788512\pi$
$72$	2.93383	+	0.626624i	0.345755	+	0.0738483i
$73$	−8.01788	+	8.01788i	−0.938421	+	0.938421i	−0.998211	−	0.0597896i	$-0.980957\pi$
$73$	−8.01788	+	8.01788i	−0.938421	+	0.938421i	0.0597896	+	0.998211i	$0.480957\pi$
$74$		−	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	0.817043	−	0.576576i	$-0.195612\pi$
$79$	−0.807117	−	1.39797i	−0.0908078	−	0.157284i	−0.907851	+	0.419292i	$0.862278\pi$
$80$	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	−0.165783	−	0.986162i	$-0.553015\pi$
$83$	−7.31055	−	1.95885i	−0.802437	−	0.215012i	−0.636653	+	0.771150i	$0.719682\pi$
$84$	−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	−0.938615	−	0.344967i	$-0.887890\pi$
$89$	0.440877	−	1.64537i	0.0467329	−	0.174409i	0.985348	+	0.170557i	$0.0545568\pi$
$90$	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	0.634778	−	0.772695i	$-0.281092\pi$
$97$	−1.35833	−	1.35833i	−0.137917	−	0.137917i	−0.772695	+	0.634778i	$0.781092\pi$
$98$	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	0.211183	+	0.977446i	$0.432268\pi$
$101$	−7.44597	+	12.8968i	−0.740902	+	1.28328i	−0.952085	+	0.305833i	$0.901065\pi$
$102$	4.18831	−	0.107612i	0.414704	−	0.0106552i
$103$	−9.08751	−	5.24668i	−0.895419	−	0.516971i	−0.0197081	−	0.999806i	$-0.506274\pi$
$103$	−9.08751	−	5.24668i	−0.895419	−	0.516971i	−0.875711	+	0.482835i	$0.839607\pi$
$104$	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	−0.406418	−	0.913687i	$-0.633222\pi$
$107$	1.87899	−	1.08484i	0.181649	−	0.104875i	0.588067	+	0.808812i	$0.299889\pi$
$108$	0.954467	−	5.10774i	0.0918436	−	0.491492i
$109$	−8.28528	−	8.28528i	−0.793586	−	0.793586i	0.188489	−	0.982075i	$-0.439641\pi$
$109$	−8.28528	−	8.28528i	−0.793586	−	0.793586i	−0.982075	+	0.188489i	$0.939641\pi$
$110$	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	0.0249209	−	0.999689i	$-0.492067\pi$
$113$	9.60049	−	5.54284i	0.903138	−	0.521427i	0.878217	+	0.478263i	$0.158733\pi$
$114$	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	−0.295331	−	0.955395i	$-0.595430\pi$
$127$	4.33197	−	2.50106i	0.384400	−	0.221933i	0.679731	+	0.733462i	$0.262097\pi$
$128$	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	0.971178	+	0.238354i	$0.0766080\pi$
$131$	19.0361	+	10.9905i	1.66319	+	0.960242i	0.692010	+	0.721888i	$0.256725\pi$
$132$	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	0.215886	−	0.976419i	$-0.430736\pi$
$137$	−8.90180	−	8.90180i	−0.760532	−	0.760532i	−0.976419	+	0.215886i	$0.930736\pi$
$138$	−5.72044	−	9.34522i	−0.486956	−	0.795518i
$139$	9.84823	+	17.0576i	0.835316	+	1.44681i	0.893773	+	0.448520i	$0.148049\pi$
$139$	9.84823	+	17.0576i	0.835316	+	1.44681i	−0.0584566	+	0.998290i	$0.518618\pi$
$140$	−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	−0.144942	−	0.989440i	$-0.546299\pi$
$149$	−9.34027	−	2.50272i	−0.765185	−	0.205031i	−0.620243	+	0.784410i	$0.712966\pi$
$150$	6.91831	+	3.76075i	0.564878	+	0.307064i
$151$	4.80308	+	1.28698i	0.390869	+	0.104733i	0.448900	−	0.893582i	$-0.351816\pi$
$151$	4.80308	+	1.28698i	0.390869	+	0.104733i	−0.0580316	+	0.998315i	$0.518482\pi$
$152$	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	−0.992182	−	0.124796i	$-0.960172\pi$
$157$	−4.86181	+	8.42090i	−0.388015	+	0.672061i	0.604168	+	0.796857i	$0.293506\pi$
$158$	−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	0.997413	−	0.0718838i	$-0.0229011\pi$
$163$	1.24717	+	4.65451i	0.0976861	+	0.364570i	−0.899727	+	0.436453i	$0.856234\pi$
$164$	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	0.978845	−	0.204603i	$-0.0655903\pi$
$167$	10.0054	+	10.0054i	0.774242	+	0.774242i	−0.204603	+	0.978845i	$0.565590\pi$
$168$	−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	0.951146	−	0.308742i	$-0.0999080\pi$
$179$	2.78545	+	4.82455i	0.208194	+	0.360603i	−0.742951	+	0.669345i	$0.766575\pi$
$180$	−1.97617	−	0.422081i	−0.147295	−	0.0314601i
$181$			20.8410i			1.54910i	0.632514	+	0.774549i	$0.282023\pi$
$181$			20.8410i			1.54910i	−0.632514	+	0.774549i	$0.717977\pi$
$182$	−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	$0.226846\pi$
$191$			18.0727i			1.30769i	−0.756626	+	0.653847i	$0.773154\pi$
$192$	−0.491112	−	1.66097i	−0.0354429	−	0.119870i
$193$	5.20610	−	5.20610i	0.374743	−	0.374743i	−0.494458	−	0.869201i	$-0.664634\pi$
$193$	5.20610	−	5.20610i	0.374743	−	0.374743i	0.869201	+	0.494458i	$0.164634\pi$
$194$	−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	−0.715761	−	0.698345i	$-0.753920\pi$
$197$	−23.6473	−	6.33628i	−1.68480	−	0.451441i	−0.969040	+	0.246904i	$0.920587\pi$
$198$	−2.63341	−	1.34506i	−0.187148	−	0.0955889i
$199$	−6.97794	−	4.02871i	−0.494653	−	0.285588i	0.231850	−	0.972752i	$-0.425522\pi$
$199$	−6.97794	−	4.02871i	−0.494653	−	0.285588i	−0.726503	+	0.687164i	$0.758856\pi$
$200$	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	−0.924868	−	0.380287i	$-0.875825\pi$
$223$	−22.9327	+	6.14479i	−1.53568	+	0.411485i	−0.610816	+	0.791773i	$0.709158\pi$
$224$	−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	−0.132438	+	0.991191i	$0.542281\pi$
$227$	−16.9292	+	16.9292i	−1.12363	+	1.12363i	−0.991191	+	0.132438i	$0.957719\pi$
$228$	5.42280	−	9.97584i	0.359134	−	0.660666i
$229$	5.31509	+	19.8362i	0.351231	+	1.31081i	0.885161	+	0.465284i	$0.154048\pi$
$229$	5.31509	+	19.8362i	0.351231	+	1.31081i	−0.533930	+	0.845529i	$0.679286\pi$
$230$	−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	0.999988	−	0.00489453i	$-0.00155798\pi$
$239$	2.03334	+	7.58852i	0.131526	+	0.490861i	−0.868462	+	0.495755i	$0.834891\pi$
$240$	−1.16629	+	0.0299659i	−0.0752837	+	0.00193429i
$241$	−16.4615	+	16.4615i	−1.06038	+	1.06038i	−0.0623240	+	0.998056i	$0.519851\pi$
$241$	−16.4615	+	16.4615i	−1.06038	+	1.06038i	−0.998056	+	0.0623240i	$0.980149\pi$
$242$	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	−0.0820668	−	0.996627i	$-0.526152\pi$
$251$	13.0241	−	22.5583i	0.822071	−	1.42387i	0.904138	−	0.427241i	$-0.140515\pi$
$252$	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	0.773634	−	0.633632i	$-0.218437\pi$
$263$	9.92027	+	5.72747i	0.611710	+	0.353171i	−0.161924	+	0.986803i	$0.551770\pi$
$264$	−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	−0.342941	−	0.939357i	$-0.611423\pi$
$269$	−21.7795	−	12.5744i	−1.32792	−	0.766674i	−0.984977	+	0.172683i	$0.944756\pi$
$270$	−0.642910	+	3.44047i	−0.0391262	+	0.209380i
$271$	6.17248	+	1.65391i	0.374952	+	0.100468i	0.441373	−	0.897324i	$-0.354492\pi$
$271$	6.17248	+	1.65391i	0.374952	+	0.100468i	−0.0664215	+	0.997792i	$0.521158\pi$
$272$	−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	$0.198554\pi$
$277$			19.4429i			1.16821i	−0.811679	+	0.584104i	$0.801446\pi$
$278$	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	−0.212030	−	0.977263i	$-0.568007\pi$
$281$	7.71478	−	28.7919i	0.460225	−	1.71758i	0.672255	−	0.740320i	$-0.265326\pi$
$282$	−6.30008	+	1.86280i	−0.375165	+	0.110928i
$283$		−	22.0759i		−	1.31228i	−0.754640	−	0.656139i	$-0.772188\pi$
$283$		−	22.0759i		−	1.31228i	0.754640	−	0.656139i	$-0.227812\pi$
$284$	−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	−0.856360	−	0.516379i	$-0.827279\pi$
$293$	2.45563	−	9.16452i	0.143459	−	0.535397i	0.999819	−	0.0190176i	$-0.00605386\pi$
$294$	−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	−0.604790	−	0.796385i	$-0.706743\pi$
$307$	3.35703	−	3.35703i	0.191596	−	0.191596i	0.796385	+	0.604790i	$0.206743\pi$
$308$			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	−0.393973	−	0.919122i	$-0.628900\pi$
$311$	10.5634	−	18.2964i	0.598996	−	1.03749i	0.992970	−	0.118370i	$-0.0377669\pi$
$312$	−6.18852	+	0.837956i	−0.350356	+	0.0474399i
$313$	−5.16590	−	8.94760i	−0.291994	−	0.505748i	0.682287	−	0.731084i	$-0.260985\pi$
$313$	−5.16590	−	8.94760i	−0.291994	−	0.505748i	−0.974281	+	0.225336i	$0.927652\pi$
$314$	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	−0.226185	−	0.974084i	$-0.572625\pi$
$317$	−16.1862	−	4.33708i	−0.909108	−	0.243595i	−0.682924	+	0.730490i	$0.739292\pi$
$318$	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	0.933092	−	0.359637i	$-0.117100\pi$
$331$	10.4331	+	10.4331i	0.573455	+	0.573455i	−0.359637	+	0.933092i	$0.617100\pi$
$332$	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	0.405544	−	0.914076i	$-0.367082\pi$
$337$	−3.36489	−	1.94272i	−0.183297	−	0.105827i	−0.588841	+	0.808249i	$0.700416\pi$
$338$	−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	0.502486	−	0.864585i	$-0.332419\pi$
$347$	27.9881	−	16.1590i	1.50248	−	0.867459i	0.999996	−	0.00287338i	$-0.000914625\pi$
$348$	7.12982	−	2.10813i	0.382198	−	0.113008i
$349$	4.90845	+	18.3186i	0.262743	+	0.980571i	0.963617	+	0.267286i	$0.0861268\pi$
$349$	4.90845	+	18.3186i	0.262743	+	0.980571i	−0.700874	+	0.713285i	$0.747207\pi$
$350$	−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	0.959142	+	0.282926i	$0.0913050\pi$
$353$	5.07215	+	18.9295i	0.269963	+	1.00752i	−0.689178	+	0.724592i	$0.742028\pi$
$354$	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	−0.999904	−	0.0138835i	$-0.995581\pi$
$359$	−19.2085	−	19.2085i	−1.01379	−	1.01379i	−0.0138835	−	0.999904i	$-0.504419\pi$
$360$	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	−0.948793	−	0.315899i	$-0.897694\pi$
$367$	−3.84715	+	6.66345i	−0.200819	+	0.347829i	0.747973	+	0.663729i	$0.231027\pi$
$368$	−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	0.995611	−	0.0935830i	$-0.0298321\pi$
$373$	8.04898	+	13.9412i	0.416760	+	0.721850i	−0.578851	+	0.815433i	$0.696499\pi$
$374$	−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	−0.547305	−	0.836933i	$-0.684346\pi$
$379$	6.71919	−	25.0764i	0.345142	−	1.28809i	0.892446	−	0.451153i	$-0.148987\pi$
$380$	−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	−0.622334	−	0.782752i	$-0.713815\pi$
$383$	−30.3863	−	8.14198i	−1.55267	−	0.416036i	−0.930333	+	0.366716i	$0.880482\pi$
$384$	−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	−0.984569	−	0.174997i	$-0.944009\pi$
$389$	−12.6984	−	21.9943i	−0.643836	−	1.11516i	0.340733	−	0.940160i	$-0.389325\pi$
$390$	−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	0.973870	−	0.227108i	$-0.0729270\pi$
$397$	0.337126	+	1.25817i	0.0169199	+	0.0631458i	−0.956950	+	0.290254i	$0.906260\pi$
$398$	−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	0.732032	−	0.681270i	$-0.238572\pi$
$401$	1.01652	+	1.01652i	0.0507627	+	0.0507627i	−0.681270	+	0.732032i	$0.738572\pi$
$402$	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	−0.648031	−	0.761614i	$-0.724407\pi$
$409$	5.94553	−	22.1890i	0.293987	−	1.09718i	0.942018	−	0.335562i	$-0.108926\pi$
$410$	−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	$-0.948415\pi$
$419$		−	6.60549i		−	0.322699i	0.986897	−	0.161350i	$-0.0515847\pi$
$420$	2.00457	−	0.592709i	0.0978132	−	0.0289212i
$421$	−2.43480	+	9.08681i	−0.118665	+	0.442864i	−0.999535	−	0.0304944i	$-0.990292\pi$
$421$	−2.43480	+	9.08681i	−0.118665	+	0.442864i	0.880870	+	0.473359i	$0.156958\pi$
$422$	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	0.304970	−	0.952362i	$-0.401354\pi$
$431$	1.92865	+	0.516780i	0.0928998	+	0.0248924i	−0.212070	+	0.977255i	$0.568020\pi$
$432$	1.72728	+	4.90066i	0.0831036	+	0.235783i
$433$	−27.7623	−	16.0286i	−1.33417	−	0.770285i	−0.348236	−	0.937407i	$-0.613219\pi$
$433$	−27.7623	−	16.0286i	−1.33417	−	0.770285i	−0.985936	+	0.167122i	$0.946553\pi$
$434$	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	−0.149109	−	0.988821i	$-0.547640\pi$
$439$	−22.6287	−	13.0647i	−1.08001	−	0.623542i	−0.930898	+	0.365278i	$0.880974\pi$
$440$	−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	−0.247209	−	0.968962i	$-0.579513\pi$
$443$	9.85727	−	5.69110i	0.468333	−	0.270392i	0.715542	+	0.698570i	$0.246180\pi$
$444$	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	−0.560238	−	0.828331i	$-0.689290\pi$
$449$	−13.3760	+	3.58409i	−0.631253	+	0.169144i	−0.0710148	+	0.997475i	$0.522624\pi$
$450$	−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	−0.920303	−	0.391207i	$-0.872058\pi$
$457$	−32.5303	+	8.71648i	−1.52171	+	0.407740i	−0.601402	+	0.798946i	$0.705391\pi$
$458$	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	−0.543326	−	0.839522i	$-0.682835\pi$
$461$	6.35961	−	6.35961i	0.296196	−	0.296196i	0.839522	+	0.543326i	$0.182835\pi$
$462$	3.05790	−	0.0785678i	0.142266	−	0.00365531i
$463$	4.90786	+	18.3164i	0.228087	+	0.851234i	0.981144	+	0.193278i	$0.0619120\pi$
$463$	4.90786	+	18.3164i	0.228087	+	0.851234i	−0.753057	+	0.657956i	$0.771421\pi$
$464$	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	−0.864120	−	0.503285i	$-0.832124\pi$
$479$	−29.7832	+	7.98038i	−1.36083	+	0.364633i	−0.496707	+	0.867918i	$0.665458\pi$
$480$	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	−0.672787	−	0.739836i	$-0.734903\pi$
$487$	−19.5417	+	5.23619i	−0.885520	+	0.237274i	−0.212733	+	0.977110i	$0.568236\pi$
$488$	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	0.816645	−	0.577140i	$-0.195831\pi$
$499$	40.4871	−	10.8485i	1.81245	−	0.485645i	0.995805	+	0.0914956i	$0.0291647\pi$
$500$	−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	0.722963	−	0.690886i	$-0.242780\pi$
$503$	10.9025	+	6.29458i	0.486120	+	0.280661i	−0.236843	+	0.971548i	$0.576113\pi$
$504$	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	−0.0419113	+	0.999121i	$0.513345\pi$
$509$	−23.4868	+	23.4868i	−1.04103	+	1.04103i	−0.999121	+	0.0419113i	$0.986655\pi$
$510$	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	$0.125642\pi$
$521$			17.5549i			0.769094i	−0.923105	+	0.384547i	$0.874358\pi$
$522$	−3.96738	−	12.2514i	−0.173647	−	0.536227i
$523$	−4.19432	−	7.26477i	−0.183405	−	0.317666i	0.759633	−	0.650352i	$-0.225379\pi$
$523$	−4.19432	−	7.26477i	−0.183405	−	0.317666i	−0.943038	+	0.332686i	$0.892045\pi$
$524$	−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	−0.675531	−	0.737332i	$-0.736086\pi$
$541$	1.43745	−	1.43745i	0.0618007	−	0.0618007i	0.737332	+	0.675531i	$0.236086\pi$
$542$		−	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	0.964539	−	0.263940i	$-0.0850222\pi$
$547$	5.93332	+	10.2768i	0.253691	+	0.439405i	−0.710848	+	0.703345i	$0.751689\pi$
$548$	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	0.442470	+	0.896783i	$0.354102\pi$
$557$	−9.18337	+	34.2728i	−0.389112	+	1.45219i	−0.831582	+	0.555402i	$0.812564\pi$
$558$	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	0.932427	+	0.361358i	$0.117687\pi$
$563$	18.4876	+	32.0214i	0.779159	+	1.34954i	−0.153268	+	0.988185i	$0.548980\pi$
$564$	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	−0.485667	−	0.874144i	$-0.661423\pi$
$569$	12.2655	−	21.2445i	0.514198	−	0.890616i	0.999864	−	0.0164722i	$-0.00524351\pi$
$570$	−3.65269	+	6.71952i	−0.152994	+	0.281450i
$571$	7.42838	+	4.28878i	0.310868	+	0.179480i	0.647315	−	0.762223i	$-0.275892\pi$
$571$	7.42838	+	4.28878i	0.310868	+	0.179480i	−0.336447	+	0.941702i	$0.609225\pi$
$572$	−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	0.686174	−	0.727437i	$-0.259289\pi$
$577$	−0.991168	−	0.991168i	−0.0412629	−	0.0412629i	−0.727437	+	0.686174i	$0.759289\pi$
$578$	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	0.799318	+	0.600908i	$0.205194\pi$
$587$	9.87397	+	36.8502i	0.407543	+	1.52097i	−0.391775	+	0.920061i	$0.628139\pi$
$588$	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	0.997139	−	0.0755923i	$-0.0240847\pi$
$593$	22.4411	+	22.4411i	0.921547	+	0.921547i	−0.0755923	+	0.997139i	$0.524085\pi$
$594$	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	0.740464	−	0.672096i	$-0.234606\pi$
$599$	12.9383	+	7.46992i	0.528644	+	0.305213i	−0.211820	+	0.977309i	$0.567939\pi$
$600$	−7.87181	+	0.202253i	−0.321365	+	0.00825696i
$601$	4.71759	−	8.17110i	0.192434	−	0.333306i	−0.753622	−	0.657308i	$-0.771695\pi$
$601$	4.71759	−	8.17110i	0.192434	−	0.333306i	0.946056	+	0.324002i	$0.105028\pi$
$602$	−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	0.770358	−	0.637611i	$-0.220077\pi$
$607$	−4.11465	−	7.12678i	−0.167008	−	0.289267i	−0.937367	+	0.348344i	$0.886744\pi$
$608$	−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	0.774280	+	0.632843i	$0.218112\pi$
$613$	−5.26589	+	19.6526i	−0.212687	+	0.793760i	−0.986968	+	0.160918i	$0.948555\pi$
$614$	−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	0.831419	−	0.555646i	$-0.187529\pi$
$617$	31.6362	+	8.47690i	1.27363	+	0.341267i	0.442207	+	0.896913i	$0.354195\pi$
$618$	−0.466824	−	18.1690i	−0.0187784	−	0.730866i
$619$	−9.36687	−	2.50985i	−0.376486	−	0.100879i	0.0656133	−	0.997845i	$-0.479100\pi$
$619$	−9.36687	−	2.50985i	−0.376486	−	0.100879i	−0.442100	+	0.896966i	$0.645766\pi$
$620$	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	−0.978991	−	0.203906i	$-0.934636\pi$
$631$	−5.85572	−	21.8539i	−0.233113	−	0.869988i	0.745878	−	0.666083i	$-0.232030\pi$
$632$	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	−0.889361	−	0.457206i	$-0.848850\pi$
$643$	2.77540	−	10.3579i	0.109451	−	0.408477i	0.998812	+	0.0487289i	$0.0155170\pi$
$644$	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	0.814037	−	0.580813i	$-0.197265\pi$
$647$	−2.44136	−	4.22856i	−0.0959799	−	0.166242i	−0.910017	+	0.414571i	$0.863932\pi$
$648$	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	$-0.858739\pi$
$653$		−	21.9436i		−	0.858719i	0.903134	−	0.429360i	$-0.141261\pi$
$654$	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	$-0.691716\pi$
$659$		−	42.3078i		−	1.64808i	0.566534	−	0.824038i	$-0.308284\pi$
$660$	1.11806	+	0.269004i	0.0435203	+	0.0104710i
$661$	−22.1456	+	22.1456i	−0.861363	+	0.861363i	−0.991497	−	0.130133i	$-0.958460\pi$
$661$	−22.1456	+	22.1456i	−0.861363	+	0.861363i	0.130133	+	0.991497i	$0.458460\pi$
$662$	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	−0.294787	−	0.955563i	$-0.595249\pi$
$673$	−32.9394	−	19.0176i	−1.26972	−	0.733075i	−0.974935	+	0.222488i	$0.928582\pi$
$674$	−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	−0.588291	−	0.808649i	$-0.700199\pi$
$677$	−4.73877	+	2.73593i	−0.182126	+	0.105150i	0.406165	+	0.913800i	$0.366866\pi$
$678$	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	0.252775	−	0.967525i	$-0.418657\pi$
$683$	24.9699	−	6.69067i	0.955447	−	0.256011i	0.702672	+	0.711514i	$0.251990\pi$
$684$	−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	0.424101	−	0.905615i	$-0.360590\pi$
$691$	32.7059	−	8.76352i	1.24419	−	0.333380i	0.820090	+	0.572235i	$0.193923\pi$
$692$	−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	−0.513464	−	0.858111i	$-0.671638\pi$
$709$	9.17695	−	9.17695i	0.344648	−	0.344648i	0.858111	+	0.513464i	$0.171638\pi$
$710$	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	−0.892101	−	0.451837i	$-0.850769\pi$
$719$	−1.46802	+	2.54269i	−0.0547480	+	0.0948263i	0.837353	+	0.546663i	$0.184102\pi$
$720$	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	0.311569	−	0.950224i	$-0.399146\pi$
$727$	34.7895	−	20.0857i	1.29027	−	0.744938i	0.978702	+	0.205285i	$0.0658122\pi$
$728$	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	−0.0173384	−	0.999850i	$-0.505519\pi$
$733$	12.6590	−	3.39197i	0.467571	−	0.125285i	0.484909	+	0.874564i	$0.338853\pi$
$734$	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	−0.132990	−	0.991117i	$-0.542458\pi$
$739$	−20.2177	−	5.41732i	−0.743721	−	0.199279i	−0.610731	+	0.791838i	$0.709124\pi$
$740$	−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	−0.455655	−	0.890157i	$-0.650595\pi$
$743$	11.8437	−	11.8437i	0.434502	−	0.434502i	0.890157	+	0.455655i	$0.150595\pi$
$744$	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	$0.0546796\pi$
$751$			9.36886i			0.341875i	−0.985282	+	0.170937i	$0.945320\pi$
$752$	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	0.891490	−	0.453041i	$-0.149661\pi$
$757$	1.46922	+	2.54477i	0.0533999	+	0.0924913i	−0.838090	+	0.545532i	$0.816328\pi$
$758$	−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	−0.900299	−	0.435273i	$-0.856652\pi$
$761$	2.67639	−	9.98843i	0.0970191	−	0.362080i	0.997318	+	0.0731923i	$0.0233187\pi$
$762$	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	0.707997	−	0.706215i	$-0.249599\pi$
$769$	0.0494190	+	0.0494190i	0.00178210	+	0.00178210i	−0.706215	+	0.707997i	$0.749599\pi$
$770$		−	1.18958i		−	0.0428696i
$771$	11.9615	−	3.53676i	0.430784	−	0.127373i
$772$	−1.90556	+	7.11166i	−0.0685827	+	0.255954i
$773$	6.52883	+	24.3659i	0.234826	+	0.876382i	0.978227	+	0.207536i	$0.0665445\pi$
$773$	6.52883	+	24.3659i	0.234826	+	0.876382i	−0.743402	+	0.668845i	$0.766789\pi$
$774$	−1.79311	+	1.98751i	−0.0644520	+	0.0714397i
$775$	−18.6138	+	18.6138i	−0.668627	+	0.668627i
$776$		−	1.92097i		−	0.0689587i
$777$	−15.1149	+	15.9121i	−0.542245	+	0.570845i
$778$	−17.9583	+	17.9583i	−0.643836	+	0.643836i
$779$	−16.3098	+	28.2493i	−0.584358	+	1.01214i
$780$	4.16846	−	0.564431i	0.149255	−	0.0202099i
$781$	3.25425	+	5.63652i	0.116446	+	0.201691i
$782$	14.7808	+	3.96050i	0.528560	+	0.141627i
$783$	−21.0365	+	7.41446i	−0.751782	+	0.264971i
$784$	3.28199	+	1.89486i	0.117214	+	0.0676734i
$785$	−6.32646	−	1.69517i	−0.225801	−	0.0605032i
$786$	0.977879	+	38.0596i	0.0348798	+	1.35754i
$787$	−29.0692	−	7.78906i	−1.03620	−	0.277650i	−0.299664	−	0.954045i	$-0.596875\pi$
$787$	−29.0692	−	7.78906i	−1.03620	−	0.277650i	−0.736539	+	0.676395i	$0.763541\pi$
$788$	23.6473	−	6.33628i	0.842401	−	0.225721i
$789$	−19.2901	−	4.64118i	−0.686744	−	0.165230i
$790$	−0.941643	−	0.543658i	−0.0335022	−	0.0193425i
$791$	5.14080	−	19.1857i	0.182786	−	0.682166i
$792$	2.95313	−	0.151852i	0.104935	−	0.00539582i
$793$	13.8540	−	10.1542i	0.491969	−	0.360587i
$794$	1.12805	−	0.651278i	0.0400329	−	0.0231130i
$795$	−8.95562	+	5.48195i	−0.317623	+	0.194425i
$796$	8.05743			0.285588
$797$	−13.7961	−	23.8955i	−0.488682	−	0.846422i	0.511233	−	0.859442i	$-0.329189\pi$
$797$	−13.7961	−	23.8955i	−0.488682	−	0.846422i	−0.999915	+	0.0130203i	$0.995855\pi$
$798$	20.3374	−	0.522537i	0.719937	−	0.0184976i
$799$	6.48772	+	6.48772i	0.229519	+	0.229519i
$800$	−4.39138	+	1.17667i	−0.155259	+	0.0416014i
$801$	−1.57437	−	4.86169i	−0.0556276	−	0.171779i
$802$	0.718789	−	1.24498i	0.0253813	−	0.0439618i
$803$	−5.58828	+	9.67919i	−0.197206	+	0.341571i
$804$	−19.1714	+	0.492578i	−0.676123	+	0.0173719i
$805$	−6.61187	−	3.81736i	−0.233038	−	0.134544i
$806$	19.1072	+	8.41159i	0.673023	+	0.296286i
$807$	42.3504	+	10.1895i	1.49080	+	0.358687i
$808$	−14.3845	+	3.85432i	−0.506045	+	0.135594i
$809$	−31.3309	+	18.0889i	−1.10154	+	0.635972i	−0.936624	−	0.350336i	$-0.886067\pi$
$809$	−31.3309	+	18.0889i	−1.10154	+	0.635972i	−0.164912	+	0.986308i	$0.552734\pi$
$810$	−0.621803	−	6.03024i	−0.0218479	−	0.211881i
$811$	0.803239	+	0.803239i	0.0282055	+	0.0282055i	0.721069	−	0.692863i	$-0.243651\pi$
$811$	0.803239	+	0.803239i	0.0282055	+	0.0282055i	−0.692863	+	0.721069i	$0.743651\pi$
$812$	−5.43845	+	5.43845i	−0.190852	+	0.190852i
$813$	−11.0645	+	0.284285i	−0.388050	+	0.00997032i
$814$	−1.80412	−	6.73309i	−0.0632345	−	0.235995i
$815$	−2.81093	+	1.62289i	−0.0984626	+	0.0568474i
$816$	3.03767	+	2.88549i	0.106340	+	0.101012i
$817$	−1.51392	−	5.65003i	−0.0529654	−	0.197669i
$818$	−22.9718			−0.803189
$819$	−7.93928	−	17.6797i	−0.277421	−	0.617779i
$820$	3.35166			0.117045
$821$	12.5434	+	46.8128i	0.437769	+	1.63378i	0.734351	+	0.678770i	$0.237486\pi$
$821$	12.5434	+	46.8128i	0.437769	+	1.63378i	−0.296582	+	0.955007i	$0.595847\pi$
$822$	5.10068	−	21.1999i	0.177907	−	0.739431i
$823$	−24.4935	+	14.1414i	−0.853791	+	0.492937i	−0.861928	−	0.507030i	$-0.830743\pi$
$823$	−24.4935	+	14.1414i	−0.853791	+	0.492937i	0.00813687	+	0.999967i	$0.497410\pi$
$824$	−2.71588	−	10.1358i	−0.0946122	−	0.353098i
$825$	−3.70688	+	6.81921i	−0.129057	+	0.237414i
$826$	−5.98363	+	5.98363i	−0.208197	+	0.208197i
$827$	−13.1080	−	13.1080i	−0.455810	−	0.455810i	0.441467	−	0.897277i	$-0.354458\pi$
$827$	−13.1080	−	13.1080i	−0.455810	−	0.455810i	−0.897277	+	0.441467i	$0.854458\pi$
$828$	8.63254	−	16.9012i	0.300001	−	0.587356i
$829$	46.5863	−	26.8966i	1.61801	−	0.934159i	0.630577	−	0.776127i	$-0.282818\pi$
$829$	46.5863	−	26.8966i	1.61801	−	0.934159i	0.987434	−	0.158032i	$-0.0505148\pi$
$830$	−4.92424	+	1.31945i	−0.170923	+	0.0457986i
$831$	−9.54861	−	32.2939i	−0.331238	−	1.12026i
$832$	2.13146	+	2.90807i	0.0738951	+	0.100819i
$833$	7.93886	+	4.58350i	0.275065	+	0.158809i
$834$	−16.2932	+	29.9731i	−0.564186	+	1.03788i
$835$	−4.76551	+	8.25410i	−0.164917	+	0.285645i
$836$	−3.23080	+	5.59591i	−0.111740	+	0.193539i
$837$	12.9927	−	27.1366i	0.449095	−	0.937979i
$838$	−6.38041	+	1.70963i	−0.220408	+	0.0590581i
$839$	3.08099	+	3.08099i	0.106368	+	0.106368i	0.758288	−	0.651920i	$-0.226036\pi$
$839$	3.08099	+	3.08099i	0.106368	+	0.106368i	−0.651920	+	0.758288i	$0.726036\pi$
$840$	−1.09133	−	1.78287i	−0.0376546	−	0.0615147i
$841$	−5.28691	−	9.15719i	−0.182307	−	0.315765i
$842$	9.40736			0.324199
$843$	1.32607	+	51.6113i	0.0456722	+	1.77759i
$844$	12.1952	−	7.04091i	0.419776	−	0.242358i
$845$	8.74806	+	0.385182i	0.300942	+	0.0132507i
$846$	9.54939	−	6.18809i	0.328315	−	0.212751i
$847$	−4.65052	+	17.3560i	−0.159794	+	0.596359i
$848$	−7.79435	−	4.50007i	−0.267659	−	0.154533i
$849$	10.8418	+	36.6674i	0.372088	+	1.25842i
$850$	−10.6224	+	2.84626i	−0.364345	+	0.0976260i
$851$	−43.2128	−	11.5788i	−1.48132	−	0.396917i
$852$	10.0482	+	5.46215i	0.344246	+	0.187130i
$853$	−10.9121	−	2.92390i	−0.373625	−	0.100112i	0.0671200	−	0.997745i	$-0.478619\pi$
$853$	−10.9121	−	2.92390i	−0.373625	−	0.100112i	−0.440745	+	0.897632i	$0.645286\pi$
$854$	−7.39218	−	4.26788i	−0.252955	−	0.146044i
$855$	11.7972	+	6.02562i	0.403456	+	0.206072i
$856$	2.09574	+	0.561553i	0.0716311	+	0.0191935i
$857$	8.91122	+	15.4347i	0.304401	+	0.527239i	0.977128	−	0.212653i	$-0.0682103\pi$
$857$	8.91122	+	15.4347i	0.304401	+	0.527239i	−0.672726	+	0.739891i	$0.734877\pi$
$858$	6.10580	+	0.780955i	0.208449	+	0.0266614i
$859$	−12.6436	+	21.8993i	−0.431393	+	0.747194i	−0.996994	−	0.0774851i	$-0.975311\pi$
$859$	−12.6436	+	21.8993i	−0.431393	+	0.747194i	0.565601	+	0.824679i	$0.308644\pi$
$860$	−0.424986	+	0.424986i	−0.0144919	+	0.0144919i
$861$	−4.37848	−	14.8083i	−0.149218	−	0.504664i
$862$		−	1.99669i		−	0.0680074i
$863$	−9.09474	+	9.09474i	−0.309589	+	0.309589i	−0.844750	−	0.535161i	$-0.820251\pi$
$863$	−9.09474	+	9.09474i	−0.309589	+	0.309589i	0.535161	+	0.844750i	$0.320251\pi$
$864$	4.28663	−	2.93681i	0.145834	−	0.0999122i
$865$	4.04421	+	15.0932i	0.137507	+	0.513184i
$866$	−8.29701	+	30.9649i	−0.281944	+	1.05223i
$867$	−14.0007	−	13.2993i	−0.475488	−	0.451666i
$868$		−	10.3744i		−	0.352131i
$869$	−1.12509	−	1.12509i	−0.0381659	−	0.0381659i
$870$	−4.80250	+	1.42000i	−0.162820	+	0.0481423i
$871$	−39.4559	−	6.08029i	−1.33691	−	0.206023i
$872$		−	11.7172i		−	0.396793i
$873$	−5.63578	−	1.20372i	−0.190742	−	0.0407398i
$874$	20.7352	+	35.9145i	0.701379	+	1.21482i
$875$	11.5211			0.389486
$876$	0.504444	+	19.6332i	0.0170436	+	0.663345i
$877$	13.3656	−	49.8810i	0.451323	−	1.68436i	−0.247355	−	0.968925i	$-0.579561\pi$
$877$	13.3656	−	49.8810i	0.451323	−	1.68436i	0.698678	−	0.715436i	$-0.253772\pi$
$878$	−6.76277	+	25.2390i	−0.228232	+	0.851775i
$879$	0.422089	+	16.4279i	0.0142367	+	0.554101i
$880$	0.663931			0.0223811
$881$	21.3121	+	36.9136i	0.718023	+	1.24365i	0.961782	+	0.273816i	$0.0882860\pi$
$881$	21.3121	+	36.9136i	0.718023	+	1.24365i	−0.243759	+	0.969836i	$0.578381\pi$
$882$	7.61575	−	8.44142i	0.256436	−	0.284237i
$883$			33.4740i			1.12649i	0.826290	+	0.563245i	$0.190447\pi$
$883$			33.4740i			1.12649i	−0.826290	+	0.563245i	$0.809553\pi$
$884$	5.15583	+	7.03439i	0.173409	+	0.236592i
$885$	−5.28394	+	1.56235i	−0.177618	+	0.0525177i
$886$	−8.04843	−	8.04843i	−0.270392	−	0.270392i
$887$		−	4.71119i		−	0.158186i	−0.996867	−	0.0790931i	$-0.974798\pi$
$887$		−	4.71119i		−	0.158186i	0.996867	−	0.0790931i	$-0.0252024\pi$
$888$	−8.88089	−	8.43596i	−0.298023	−	0.283092i
$889$	2.31965	−	8.65706i	0.0777987	−	0.290349i
$890$	−0.296966	−	1.10829i	−0.00995431	−	0.0371500i
$891$	1.40499	−	8.75911i	0.0470690	−	0.293441i
$892$	16.7879	−	16.7879i	0.562099	−	0.562099i
$893$			24.8652i			0.832082i
$894$	−4.74893	−	16.0611i	−0.158828	−	0.537165i
$895$	−2.65338	+	2.65338i	−0.0886928	+	0.0886928i
$896$	0.895864	−	1.55168i	0.0299287	−	0.0518381i
$897$	23.9341	−	31.4308i	0.799137	−	1.04944i
$898$	6.92393	+	11.9926i	0.231055	+	0.400198i
$899$	−24.0079	−	6.43289i	−0.800708	−	0.214549i
$900$	0.700395	+	13.6209i	0.0233465	+	0.454029i
$901$	−18.8539	−	10.8853i	−0.628115	−	0.362642i
$902$	4.73750	+	1.26941i	0.157741	+	0.0422667i
$903$	2.43285	+	1.32248i	0.0809602	+	0.0440094i
$904$	10.7080	+	2.86919i	0.356141	+	0.0954277i
$905$	−13.5597	+	3.63332i	−0.450740	+	0.120776i
$906$	2.44206	+	8.25917i	0.0811319	+	0.274393i
$907$	1.92854	+	1.11344i	0.0640360	+	0.0369712i	0.531676	−	0.846948i	$-0.321562\pi$
$907$	1.92854	+	1.11344i	0.0640360	+	0.0369712i	−0.467640	+	0.883919i	$0.654896\pi$
$908$	6.19651	−	23.1257i	0.205638	−	0.767453i
$909$	2.29423	+	44.6169i	0.0760948	+	1.47985i
$910$	−1.57638	−	4.05587i	−0.0522564	−	0.134451i
$911$	−10.3509	+	5.97609i	−0.342940	+	0.197997i	−0.661571	−	0.749882i	$-0.730110\pi$
$911$	−10.3509	+	5.97609i	−0.342940	+	0.197997i	0.318631	+	0.947879i	$0.396777\pi$
$912$	0.291639	+	11.3507i	0.00965712	+	0.375860i
$913$	−7.46002			−0.246891
$914$	16.8389	+	29.1659i	0.556983	+	0.964722i
$915$	−2.90172	−	4.74041i	−0.0959279	−	0.156713i
$916$	−14.5211	−	14.5211i	−0.479791	−	0.479791i
$917$	38.0419	−	10.1933i	1.25625	−	0.336612i
$918$	10.3690	−	7.10390i	0.342228	−	0.234464i
$919$	2.28777	−	3.96254i	0.0754667	−	0.130712i	−0.825822	−	0.563930i	$-0.809289\pi$
$919$	2.28777	−	3.96254i	0.0754667	−	0.130712i	0.901289	+	0.433218i	$0.142622\pi$
$920$	2.13055	−	3.69022i	0.0702421	−	0.121663i
$921$	−3.92724	+	7.22459i	−0.129407	+	0.238058i
$922$	−7.78890	−	4.49692i	−0.256514	−	0.148098i
$923$	18.5645	+	14.9052i	0.611059	+	0.490612i
$924$	−0.867334	−	2.93337i	−0.0285332	−	0.0965008i
$925$	31.0554	−	8.32127i	1.02110	−	0.273602i
$926$	16.4220	−	9.48125i	0.539661	−	0.311573i
$927$	−31.4385	+	1.61659i	−1.03258	+	0.0530958i
$928$	−3.03531	−	3.03531i	−0.0996388	−	0.0996388i
$929$	33.3985	−	33.3985i	1.09577	−	1.09577i	0.100868	−	0.994900i	$-0.467838\pi$
$929$	33.3985	−	33.3985i	1.09577	−	1.09577i	0.994900	−	0.100868i	$-0.0321621\pi$
$930$	3.22625	−	5.93505i	0.105793	−	0.194618i
$931$	6.42997	+	23.9970i	0.210734	+	0.786469i
$932$	2.41682	−	1.39535i	0.0791657	−	0.0457063i
$933$	−8.55992	+	35.5775i	−0.280239	+	1.16475i
$934$	−8.57771	−	32.0124i	−0.280671	−	1.04748i
$935$	1.60600			0.0525217
$936$	9.86740	−	4.43107i	0.322526	−	0.144834i
$937$	34.1939			1.11707			0.558533	−	0.829482i	$-0.311365\pi$
$937$	34.1939			1.11707			0.558533	+	0.829482i	$0.311365\pi$
$938$	5.13458	+	19.1625i	0.167650	+	0.625678i
$939$	12.9747	+	12.3246i	0.423412	+	0.402199i
$940$	2.21261	−	1.27745i	0.0721674	−	0.0416659i
$941$	−7.56472	−	28.2319i	−0.246603	−	0.920334i	−0.972571	−	0.232606i	$-0.925275\pi$
$941$	−7.56472	−	28.2319i	−0.246603	−	0.920334i	0.725968	−	0.687728i	$-0.241392\pi$
$942$	−16.8362	+	0.432580i	−0.548554	+	0.0140942i
$943$	22.2581	−	22.2581i	0.724824	−	0.724824i
$944$	−3.33959	−	3.33959i	−0.108694	−	0.108694i
$945$	−5.91447	+	2.08460i	−0.192398	+	0.0678121i
$946$	−0.761667	+	0.439749i	−0.0247639	+	0.0142975i
$947$	−26.6581	+	7.14301i	−0.866271	+	0.232117i	−0.664474	−	0.747311i	$-0.731345\pi$
$947$	−26.6581	+	7.14301i	−0.866271	+	0.232117i	−0.201796	+	0.979428i	$0.564678\pi$
$948$	−2.71836	−	0.654036i	−0.0882883	−	0.0212421i
$949$	−6.22676	+	40.4063i	−0.202129	+	1.31165i
$950$	−25.8104	−	14.9016i	−0.837399	−	0.483472i
$951$	29.0148	−	0.745487i	0.940868	−	0.0241741i
$952$	2.16702	−	3.75339i	0.0702336	−	0.121648i
$953$	8.06765	−	13.9736i	0.261337	−	0.452649i	−0.705261	−	0.708948i	$-0.749170\pi$
$953$	8.06765	−	13.9736i	0.261337	−	0.452649i	0.966597	+	0.256299i	$0.0825033\pi$
$954$	−18.0866	+	20.0474i	−0.585574	+	0.649059i
$955$	−11.7586	+	3.15071i	−0.380500	+	0.101955i
$956$	−5.55518	−	5.55518i	−0.179667	−	0.179667i
$957$	−7.32604	+	0.188231i	−0.236817	+	0.00608463i
$958$	15.4169	+	26.7029i	0.498097	+	0.862730i
$959$	−22.5561			−0.728376
$960$	0.995053	−	0.609096i	0.0321152	−	0.0196585i
$961$	2.18777	−	1.26311i	0.0705733	−	0.0407455i
$962$	−15.0735	−	20.5656i	−0.485989	−	0.663061i
$963$	2.96074	−	5.79667i	0.0954086	−	0.186795i
$964$	6.02534	−	22.4869i	0.194063	−	0.724253i
$965$	4.29484	+	2.47963i	0.138256	+	0.0798220i
$966$	−19.0873	−	4.59240i	−0.614125	−	0.147758i
$967$	31.3117	−	8.38995i	1.00692	−	0.269803i	0.282576	−	0.959245i	$-0.408811\pi$
$967$	31.3117	−	8.38995i	1.00692	−	0.269803i	0.724341	+	0.689442i	$0.242144\pi$
$968$	−9.68673	−	2.59555i	−0.311343	−	0.0834242i
$969$	0.705450	+	27.4565i	0.0226623	+	0.882030i
$970$	−1.24983	−	0.334892i	−0.0401298	−	0.0107527i
$971$	−23.3310	−	13.4701i	−0.748727	−	0.432278i	0.0765068	−	0.997069i	$-0.475623\pi$
$971$	−23.3310	−	13.4701i	−0.748727	−	0.432278i	−0.825234	+	0.564791i	$0.808957\pi$
$972$	−5.92998	−	14.4165i	−0.190204	−	0.462409i
$973$	34.0882	+	9.13391i	1.09282	+	0.292820i
$974$	10.1155	+	17.5206i	0.324123	+	0.561397i
$975$	−3.60204	+	28.1622i	−0.115358	+	0.901911i
$976$	2.38199	−	4.12572i	0.0762456	−	0.132061i
$977$	−10.8073	+	10.8073i	−0.345755	+	0.345755i	−0.858526	−	0.512771i	$-0.828619\pi$
$977$	−10.8073	+	10.8073i	−0.345755	+	0.345755i	0.512771	+	0.858526i	$0.328619\pi$
$978$	−5.74815	+	6.05132i	−0.183806	+	0.193500i
$979$		−	1.67902i		−	0.0536616i
$980$	1.80501	−	1.80501i	0.0576590	−	0.0576590i
$981$	−34.3761	−	7.34224i	−1.09754	−	0.234420i
$982$	3.90879	+	14.5878i	0.124735	+	0.465516i
$983$	−0.756578	+	2.82359i	−0.0241311	+	0.0900584i	−0.976941	−	0.213508i	$-0.931511\pi$
$983$	−0.756578	+	2.82359i	−0.0241311	+	0.0900584i	0.952810	+	0.303567i	$0.0981776\pi$
$984$	8.26479	−	2.44372i	0.263472	−	0.0779029i
$985$		−	16.4902i		−	0.525423i
$986$	−7.34216	−	7.34216i	−0.233822	−	0.233822i
$987$	−8.53449	−	8.10691i	−0.271656	−	0.258046i
$988$	−3.59993	+	23.3605i	−0.114529	+	0.743195i
$989$			5.64460i			0.179488i
$990$	0.416035	−	1.94786i	0.0132225	−	0.0619070i
$991$	20.0775	+	34.7753i	0.637784	+	1.10467i	0.985918	+	0.167229i	$0.0534821\pi$
$991$	20.0775	+	34.7753i	0.637784	+	1.10467i	−0.348134	+	0.937445i	$0.613185\pi$
$992$	5.79018			0.183839
$993$	−22.4528	−	12.2052i	−0.712520	−	0.387321i
$994$	3.06207	−	11.4278i	0.0971229	−	0.362467i
$995$	1.40469	−	5.24239i	0.0445318	−	0.166195i
$996$	−11.1806	+	6.84388i	−0.354269	+	0.216857i
$997$	15.6393			0.495303			0.247651	−	0.968849i	$-0.420341\pi$
$997$	15.6393			0.495303			0.247651	+	0.968849i	$0.420341\pi$
$998$	−20.9577	−	36.2997i	−0.663403	−	1.14905i
$999$	−30.3146	+	20.7688i	−0.959112	+	0.657096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.167.1	yes	56
3.2	odd	2		702.2.bc.a.557.11		56
9.2	odd	6		234.2.y.a.11.13	✓	56
9.7	even	3		702.2.bb.a.89.4		56
13.6	odd	12		234.2.y.a.149.13	yes	56
39.32	even	12		702.2.bb.a.71.4		56
117.97	odd	12		702.2.bc.a.305.11		56
117.110	even	12	inner	234.2.z.a.227.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.13	✓	56	9.2	odd	6
234.2.y.a.149.13	yes	56	13.6	odd	12
234.2.z.a.167.1	yes	56	1.1	even	1	trivial
234.2.z.a.227.1	yes	56	117.110	even	12	inner
702.2.bb.a.71.4		56	39.32	even	12
702.2.bb.a.89.4		56	9.7	even	3
702.2.bc.a.305.11		56	117.97	odd	12
702.2.bc.a.557.11		56	3.2	odd	2

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

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