LMFDB - Embedded newform 264.2.z.b.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(19,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	264.19
Dual form			264.2.z.b.139.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40421 - 0.167908i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.94361 + 0.471557i) q^{4} +(-1.03968 + 1.43099i) q^{5} +(0.274235 + 1.38737i) q^{6} +(-0.430909 + 1.32620i) q^{7} +(-2.65006 - 0.988513i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.70020 - 1.83484i) q^{10} +(-2.97889 - 1.45816i) q^{11} +(-0.152133 - 1.99421i) q^{12} +(-2.66400 + 1.93551i) q^{13} +(0.827766 - 1.78991i) q^{14} +(1.68223 + 0.546590i) q^{15} +(3.55527 + 1.83305i) q^{16} +(-2.21773 + 3.05245i) q^{17} +(1.23472 - 0.689534i) q^{18} +(-0.399566 + 0.129827i) q^{19} +(-2.69552 + 2.29103i) q^{20} +1.39445 q^{21} +(3.93815 + 2.54775i) q^{22} +1.44940i q^{23} +(-0.121217 + 2.82583i) q^{24} +(0.578275 + 1.77975i) q^{25} +(4.06581 - 2.27056i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.46290 + 2.37442i) q^{28} +(-2.45128 + 7.54427i) q^{29} +(-2.27043 - 1.04999i) q^{30} +(0.816325 + 1.12358i) q^{31} +(-4.68456 - 3.17094i) q^{32} +(-0.466268 + 3.28369i) q^{33} +(3.62669 - 3.91390i) q^{34} +(-1.44978 - 1.99544i) q^{35} +(-1.84959 + 0.760930i) q^{36} +(-8.91884 - 2.89791i) q^{37} +(0.582873 - 0.115214i) q^{38} +(2.66400 + 1.93551i) q^{39} +(4.16976 - 2.76449i) q^{40} +(3.29058 - 1.06918i) q^{41} +(-1.95810 - 0.234139i) q^{42} -3.60336i q^{43} +(-5.10220 - 4.23882i) q^{44} -1.76880i q^{45} +(0.243367 - 2.03527i) q^{46} +(-0.727433 + 0.236357i) q^{47} +(0.644694 - 3.94770i) q^{48} +(4.08999 + 2.97155i) q^{49} +(-0.513186 - 2.59624i) q^{50} +(3.58836 + 1.16593i) q^{51} +(-6.09050 + 2.50566i) q^{52} +(2.54374 + 3.50116i) q^{53} +(-1.03734 - 0.961215i) q^{54} +(5.18369 - 2.74674i) q^{55} +(2.45290 - 3.08856i) q^{56} +(0.246945 + 0.339891i) q^{57} +(4.70886 - 10.1821i) q^{58} +(3.69578 - 11.3745i) q^{59} +(3.01186 + 1.85563i) q^{60} +(-8.45451 - 6.14256i) q^{61} +(-0.957635 - 1.71480i) q^{62} +(-0.430909 - 1.32620i) q^{63} +(6.04568 + 5.23925i) q^{64} -5.82447i q^{65} +(1.20610 - 4.53270i) q^{66} +9.95011 q^{67} +(-5.74981 + 4.88699i) q^{68} +(1.37846 - 0.447890i) q^{69} +(1.70074 + 3.04545i) q^{70} +(7.57332 - 10.4238i) q^{71} +(2.72498 - 0.757945i) q^{72} +(-9.14630 - 2.97181i) q^{73} +(12.0373 + 5.56681i) q^{74} +(1.51394 - 1.09994i) q^{75} +(-0.837822 + 0.0639152i) q^{76} +(3.21744 - 3.32227i) q^{77} +(-3.41583 - 3.16518i) q^{78} +(-4.69761 + 3.41302i) q^{79} +(-6.31940 + 3.18178i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.80020 + 0.948832i) q^{82} +(-8.86730 + 12.2048i) q^{83} +(2.71027 + 0.657562i) q^{84} +(-2.06230 - 6.34711i) q^{85} +(-0.605033 + 5.05987i) q^{86} +7.93251 q^{87} +(6.45283 + 6.80889i) q^{88} +10.9210 q^{89} +(-0.296996 + 2.48377i) q^{90} +(-1.41893 - 4.36703i) q^{91} +(-0.683476 + 2.81708i) q^{92} +(0.816325 - 1.12358i) q^{93} +(1.06116 - 0.209753i) q^{94} +(0.229638 - 0.706752i) q^{95} +(-1.56814 + 5.43516i) q^{96} +(-11.2144 + 8.14771i) q^{97} +(-5.24426 - 4.85943i) q^{98} +(3.26706 - 0.571268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.40421	−	0.167908i	−0.992927	−	0.118729i
$2$	−1.40421	−	0.167908i	−0.992927	−	0.118729i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.94361	+	0.471557i	0.971807	+	0.235778i
$5$	−1.03968	+	1.43099i	−0.464957	+	0.639959i	−0.975528	−	0.219877i	$-0.929434\pi$
$5$	−1.03968	+	1.43099i	−0.464957	+	0.639959i	0.510570	+	0.859836i	$0.329434\pi$
$6$	0.274235	+	1.38737i	0.111956	+	0.566391i
$7$	−0.430909	+	1.32620i	−0.162868	+	0.501257i	−0.998873	−	0.0474657i	$-0.984886\pi$
$7$	−0.430909	+	1.32620i	−0.162868	+	0.501257i	0.836005	+	0.548722i	$0.184886\pi$
$8$	−2.65006	−	0.988513i	−0.936939	−	0.349492i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.70020	−	1.83484i	0.537650	−	0.580228i
$11$	−2.97889	−	1.45816i	−0.898168	−	0.439652i
$11$	−2.97889	−	1.45816i	−0.898168	−	0.439652i
$12$	−0.152133	−	1.99421i	−0.0439169	−	0.575678i
$13$	−2.66400	+	1.93551i	−0.738862	+	0.536815i	−0.892355	−	0.451335i	$-0.850948\pi$
$13$	−2.66400	+	1.93551i	−0.738862	+	0.536815i	0.153493	+	0.988150i	$0.450948\pi$
$14$	0.827766	−	1.78991i	0.221230	−	0.478374i
$15$	1.68223	+	0.546590i	0.434350	+	0.141129i
$16$	3.55527	+	1.83305i	0.888817	+	0.458262i
$17$	−2.21773	+	3.05245i	−0.537879	+	0.740327i	−0.988306	−	0.152487i	$-0.951272\pi$
$17$	−2.21773	+	3.05245i	−0.537879	+	0.740327i	0.450427	+	0.892813i	$0.351272\pi$
$18$	1.23472	−	0.689534i	0.291027	−	0.162525i
$19$	−0.399566	+	0.129827i	−0.0916666	+	0.0297843i	−0.354491	−	0.935059i	$-0.615346\pi$
$19$	−0.399566	+	0.129827i	−0.0916666	+	0.0297843i	0.262825	+	0.964844i	$0.415346\pi$
$20$	−2.69552	+	2.29103i	−0.602737	+	0.512289i
$21$	1.39445			0.304294
$22$	3.93815	+	2.54775i	0.839616	+	0.543181i
$23$			1.44940i			0.302222i	0.988517	+	0.151111i	$0.0482850\pi$
$23$			1.44940i			0.302222i	−0.988517	+	0.151111i	$0.951715\pi$
$24$	−0.121217	+	2.82583i	−0.0247433	+	0.576820i
$25$	0.578275	+	1.77975i	0.115655	+	0.355950i
$26$	4.06581	−	2.27056i	0.797371	−	0.445293i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.46290	+	2.37442i	−0.276462	+	0.448724i
$29$	−2.45128	+	7.54427i	−0.455191	+	1.40094i	0.415719	+	0.909493i	$0.363530\pi$
$29$	−2.45128	+	7.54427i	−0.455191	+	1.40094i	−0.870910	+	0.491442i	$0.836470\pi$
$30$	−2.27043	−	1.04999i	−0.414522	−	0.191701i
$31$	0.816325	+	1.12358i	0.146616	+	0.201800i	0.876008	−	0.482296i	$-0.160197\pi$
$31$	0.816325	+	1.12358i	0.146616	+	0.201800i	−0.729392	+	0.684096i	$0.760197\pi$
$32$	−4.68456	−	3.17094i	−0.828121	−	0.560549i
$33$	−0.466268	+	3.28369i	−0.0811668	+	0.571616i
$34$	3.62669	−	3.91390i	0.621972	−	0.671228i
$35$	−1.44978	−	1.99544i	−0.245057	−	0.337292i
$36$	−1.84959	+	0.760930i	−0.308265	+	0.126822i
$37$	−8.91884	−	2.89791i	−1.46625	−	0.476413i	−0.536276	−	0.844043i	$-0.680169\pi$
$37$	−8.91884	−	2.89791i	−1.46625	−	0.476413i	−0.929972	+	0.367630i	$0.880169\pi$
$38$	0.582873	−	0.115214i	0.0945545	−	0.0186901i
$39$	2.66400	+	1.93551i	0.426582	+	0.309930i
$40$	4.16976	−	2.76449i	0.659297	−	0.437104i
$41$	3.29058	−	1.06918i	0.513903	−	0.166977i	−0.0405736	−	0.999177i	$-0.512919\pi$
$41$	3.29058	−	1.06918i	0.513903	−	0.166977i	0.554476	+	0.832199i	$0.312919\pi$
$42$	−1.95810	−	0.234139i	−0.302141	−	0.0361285i
$43$		−	3.60336i		−	0.549507i	−0.961515	−	0.274753i	$-0.911404\pi$
$43$		−	3.60336i		−	0.549507i	0.961515	−	0.274753i	$-0.0885962\pi$
$44$	−5.10220	−	4.23882i	−0.769185	−	0.639026i
$45$		−	1.76880i		−	0.263678i
$46$	0.243367	−	2.03527i	0.0358824	−	0.300084i
$47$	−0.727433	+	0.236357i	−0.106107	+	0.0344763i	−0.361589	−	0.932337i	$-0.617766\pi$
$47$	−0.727433	+	0.236357i	−0.106107	+	0.0344763i	0.255482	+	0.966814i	$0.417766\pi$
$48$	0.644694	−	3.94770i	0.0930535	−	0.569802i
$49$	4.08999	+	2.97155i	0.584285	+	0.424508i
$50$	−0.513186	−	2.59624i	−0.0725754	−	0.367163i
$51$	3.58836	+	1.16593i	0.502472	+	0.163263i
$52$	−6.09050	+	2.50566i	−0.844600	+	0.347472i
$53$	2.54374	+	3.50116i	0.349410	+	0.480921i	0.947160	−	0.320761i	$-0.103939\pi$
$53$	2.54374	+	3.50116i	0.349410	+	0.480921i	−0.597751	+	0.801682i	$0.703939\pi$
$54$	−1.03734	−	0.961215i	−0.141164	−	0.130805i
$55$	5.18369	−	2.74674i	0.698969	−	0.370371i
$56$	2.45290	−	3.08856i	0.327783	−	0.412726i
$57$	0.246945	+	0.339891i	0.0327087	+	0.0450196i
$58$	4.70886	−	10.1821i	0.618303	−	1.33698i
$59$	3.69578	−	11.3745i	0.481150	−	1.48083i	−0.356330	−	0.934360i	$-0.615972\pi$
$59$	3.69578	−	11.3745i	0.481150	−	1.48083i	0.837480	−	0.546468i	$-0.184028\pi$
$60$	3.01186	+	1.85563i	0.388829	+	0.239560i
$61$	−8.45451	−	6.14256i	−1.08249	−	0.786474i	−0.104373	−	0.994538i	$-0.533284\pi$
$61$	−8.45451	−	6.14256i	−1.08249	−	0.786474i	−0.978115	+	0.208064i	$0.933284\pi$
$62$	−0.957635	−	1.71480i	−0.121620	−	0.217780i
$63$	−0.430909	−	1.32620i	−0.0542894	−	0.167086i
$64$	6.04568	+	5.23925i	0.755710	+	0.654906i
$65$		−	5.82447i		−	0.722437i
$66$	1.20610	−	4.53270i	0.148460	−	0.557936i
$67$	9.95011			1.21560			0.607800	−	0.794090i	$-0.292052\pi$
$67$	9.95011			1.21560			0.607800	+	0.794090i	$0.292052\pi$
$68$	−5.74981	+	4.88699i	−0.697267	+	0.592634i
$69$	1.37846	−	0.447890i	0.165948	−	0.0539197i
$70$	1.70074	+	3.04545i	0.203277	+	0.364001i
$71$	7.57332	−	10.4238i	0.898788	−	1.23708i	−0.0720652	−	0.997400i	$-0.522959\pi$
$71$	7.57332	−	10.4238i	0.898788	−	1.23708i	0.970853	−	0.239675i	$-0.0770410\pi$
$72$	2.72498	−	0.757945i	0.321142	−	0.0893246i
$73$	−9.14630	−	2.97181i	−1.07049	−	0.347824i	−0.279814	−	0.960054i	$-0.590273\pi$
$73$	−9.14630	−	2.97181i	−1.07049	−	0.347824i	−0.790680	+	0.612230i	$0.790273\pi$
$74$	12.0373	+	5.56681i	1.39931	+	0.647129i
$75$	1.51394	−	1.09994i	0.174815	−	0.127011i
$76$	−0.837822	+	0.0639152i	−0.0961047	+	0.00733157i
$77$	3.21744	−	3.32227i	0.366662	−	0.378607i
$78$	−3.41583	−	3.16518i	−0.386767	−	0.358385i
$79$	−4.69761	+	3.41302i	−0.528523	+	0.383994i	−0.819805	−	0.572643i	$-0.805918\pi$
$79$	−4.69761	+	3.41302i	−0.528523	+	0.383994i	0.291282	+	0.956637i	$0.405918\pi$
$80$	−6.31940	+	3.18178i	−0.706531	+	0.355734i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.80020	+	0.948832i	−0.530093	+	0.104781i
$83$	−8.86730	+	12.2048i	−0.973313	+	1.33965i	−0.0329578	+	0.999457i	$0.510493\pi$
$83$	−8.86730	+	12.2048i	−0.973313	+	1.33965i	−0.940355	+	0.340194i	$0.889507\pi$
$84$	2.71027	+	0.657562i	0.295715	+	0.0717459i
$85$	−2.06230	−	6.34711i	−0.223688	−	0.688441i
$86$	−0.605033	+	5.05987i	−0.0652424	+	0.545620i
$87$	7.93251			0.850455
$88$	6.45283	+	6.80889i	0.687874	+	0.725830i
$89$	10.9210			1.15763			0.578814	−	0.815460i	$-0.303516\pi$
$89$	10.9210			1.15763			0.578814	+	0.815460i	$0.303516\pi$
$90$	−0.296996	+	2.48377i	−0.0313062	+	0.261812i
$91$	−1.41893	−	4.36703i	−0.148745	−	0.457789i
$92$	−0.683476	+	2.81708i	−0.0712573	+	0.293701i
$93$	0.816325	−	1.12358i	0.0846490	−	0.116509i
$94$	1.06116	−	0.209753i	0.109450	−	0.0216344i
$95$	0.229638	−	0.706752i	0.0235603	−	0.0725113i
$96$	−1.56814	+	5.43516i	−0.160047	+	0.554724i
$97$	−11.2144	+	8.14771i	−1.13865	+	0.827275i	−0.986930	−	0.161149i	$-0.948480\pi$
$97$	−11.2144	+	8.14771i	−1.13865	+	0.827275i	−0.151716	+	0.988424i	$0.548480\pi$
$98$	−5.24426	−	4.85943i	−0.529751	−	0.490877i
$99$	3.26706	−	0.571268i	0.328351	−	0.0574146i
$100$	0.284692	+	3.73183i	0.0284692	+	0.373183i
$101$	6.49406	−	4.71821i	0.646183	−	0.469480i	−0.215786	−	0.976441i	$-0.569231\pi$
$101$	6.49406	−	4.71821i	0.646183	−	0.469480i	0.861969	+	0.506961i	$0.169231\pi$
$102$	−4.84305	−	2.23973i	−0.479533	−	0.221766i
$103$	−11.7338	−	3.81254i	−1.15617	−	0.375661i	−0.332703	−	0.943032i	$-0.607961\pi$
$103$	−11.7338	−	3.81254i	−1.15617	−	0.375661i	−0.823463	+	0.567370i	$0.807961\pi$
$104$	8.97306	−	2.49583i	0.879881	−	0.244736i
$105$	−1.44978	+	1.99544i	−0.141484	+	0.194735i
$106$	−2.98407	−	5.34348i	−0.289839	−	0.519004i
$107$	−6.82340	+	2.21706i	−0.659643	+	0.214331i	−0.619661	−	0.784869i	$-0.712730\pi$
$107$	−6.82340	+	2.21706i	−0.659643	+	0.214331i	−0.0399817	+	0.999200i	$0.512730\pi$
$108$	1.29524	+	1.52392i	0.124635	+	0.146640i
$109$	9.38007			0.898448			0.449224	−	0.893419i	$-0.351700\pi$
$109$	9.38007			0.898448			0.449224	+	0.893419i	$0.351700\pi$
$110$	−7.74020	+	2.98662i	−0.737999	+	0.284763i
$111$			9.37782i			0.890103i
$112$	−3.96298	+	3.92512i	−0.374467	+	0.370889i
$113$	0.566005	+	1.74198i	0.0532452	+	0.163872i	0.974143	−	0.225932i	$-0.0725427\pi$
$113$	0.566005	+	1.74198i	0.0532452	+	0.163872i	−0.920898	+	0.389804i	$0.872543\pi$
$114$	−0.289692	−	0.518742i	−0.0271322	−	0.0485847i
$115$	−2.07408	−	1.50691i	−0.193409	−	0.140520i
$116$	−8.32189	+	13.5072i	−0.772668	+	1.25411i
$117$	1.01756	−	3.13173i	0.0940734	−	0.289528i
$118$	−7.09952	+	15.3516i	−0.653564	+	1.41323i
$119$	−3.09251	−	4.25648i	−0.283490	−	0.390191i
$120$	−3.91771	−	3.11141i	−0.357636	−	0.284031i
$121$	6.74753	+	8.68740i	0.613412	+	0.789763i
$122$	10.8405	+	10.0450i	0.981455	+	0.909434i
$123$	−2.03369	−	2.79914i	−0.183372	−	0.252390i
$124$	1.05679	+	2.56874i	0.0949027	+	0.230680i
$125$	−11.5592	−	3.75580i	−1.03388	−	0.335929i
$126$	0.382407	+	1.93462i	0.0340675	+	0.172349i
$127$	5.77997	+	4.19940i	0.512890	+	0.372636i	0.813919	−	0.580979i	$-0.197330\pi$
$127$	5.77997	+	4.19940i	0.512890	+	0.372636i	−0.301029	+	0.953615i	$0.597330\pi$
$128$	−7.60970	−	8.37213i	−0.672609	−	0.739998i
$129$	−3.42700	+	1.11350i	−0.301730	+	0.0980381i
$130$	−0.977976	+	8.17879i	−0.0857742	+	0.717327i
$131$			8.74918i			0.764420i	0.924076	+	0.382210i	$0.124837\pi$
$131$			8.74918i			0.764420i	−0.924076	+	0.382210i	$0.875163\pi$
$132$	−2.45469	+	6.16235i	−0.213653	+	0.536363i
$133$		−	0.585847i		−	0.0507994i
$134$	−13.9721	−	1.67070i	−1.20700	−	0.144327i
$135$	−1.68223	+	0.546590i	−0.144783	+	0.0470430i
$136$	8.89451	−	5.89692i	0.762698	−	0.505657i
$137$	6.84644	+	4.97423i	0.584930	+	0.424977i	0.840498	−	0.541814i	$-0.182262\pi$
$137$	6.84644	+	4.97423i	0.584930	+	0.424977i	−0.255568	+	0.966791i	$0.582262\pi$
$138$	−2.01086	+	0.397477i	−0.171176	+	0.0338355i
$139$	−5.45350	−	1.77195i	−0.462560	−	0.150295i	0.0684604	−	0.997654i	$-0.478191\pi$
$139$	−5.45350	−	1.77195i	−0.462560	−	0.150295i	−0.531021	+	0.847359i	$0.678191\pi$
$140$	−1.87684	−	4.56203i	−0.158622	−	0.385562i
$141$	0.449578	+	0.618791i	0.0378613	+	0.0521116i
$142$	−12.3848	+	13.3656i	−1.03931	+	1.12161i
$143$	10.7581	−	1.88112i	0.899634	−	0.157307i
$144$	−3.95371	+	0.606767i	−0.329476	+	0.0505640i
$145$	−8.24724	−	11.3514i	−0.684896	−	0.942679i
$146$	12.3443	+	5.70879i	1.02162	+	0.472463i
$147$	1.56224	−	4.80808i	0.128851	−	0.396563i
$148$	−15.9682	−	9.83815i	−1.31258	−	0.808691i
$149$	15.6781	+	11.3908i	1.28440	+	0.933168i	0.999676	−	0.0254423i	$-0.00809940\pi$
$149$	15.6781	+	11.3908i	1.28440	+	0.933168i	0.284720	+	0.958611i	$0.408099\pi$
$150$	−2.31059	+	1.29035i	−0.188659	+	0.105357i
$151$	−3.22214	−	9.91672i	−0.262214	−	0.807011i	−0.992322	−	0.123680i	$-0.960530\pi$
$151$	−3.22214	−	9.91672i	−0.262214	−	0.807011i	0.730108	−	0.683331i	$-0.239470\pi$
$152$	1.18721	+	0.0509267i	0.0962954	+	0.00413070i
$153$		−	3.77303i		−	0.305031i
$154$	−5.07580	+	4.12492i	−0.409020	+	0.332396i
$155$	−2.45654			−0.197314
$156$	4.26509	+	5.01812i	0.341481	+	0.401771i
$157$	16.9246	−	5.49914i	1.35073	−	0.438879i	0.457792	−	0.889059i	$-0.348640\pi$
$157$	16.9246	−	5.49914i	1.35073	−	0.438879i	0.892938	+	0.450180i	$0.148640\pi$
$158$	7.16951	−	4.00383i	0.570376	−	0.318527i
$159$	2.54374	−	3.50116i	0.201732	−	0.277660i
$160$	9.40802	−	3.40681i	0.743769	−	0.269332i
$161$	−1.92220	−	0.624560i	−0.151491	−	0.0492223i
$162$	−0.593615	+	1.28360i	−0.0466388	+	0.100849i
$163$	−4.84269	+	3.51842i	−0.379308	+	0.275584i	−0.761060	−	0.648681i	$-0.775321\pi$
$163$	−4.84269	+	3.51842i	−0.379308	+	0.275584i	0.381752	+	0.924265i	$0.375321\pi$
$164$	6.89980	−	0.526367i	0.538784	−	0.0411024i
$165$	−4.21416	−	4.08119i	−0.328072	−	0.317721i
$166$	14.5008	−	15.6492i	1.12548	−	1.21461i
$167$	4.20600	−	3.05584i	0.325470	−	0.236468i	−0.413036	−	0.910715i	$-0.635532\pi$
$167$	4.20600	−	3.05584i	0.325470	−	0.236468i	0.738506	+	0.674247i	$0.235532\pi$
$168$	−3.69538	−	1.37843i	−0.285105	−	0.106348i
$169$	−0.666510	+	2.05131i	−0.0512700	+	0.157793i
$170$	1.83017	+	9.25895i	0.140368	+	0.710129i
$171$	0.246945	−	0.339891i	0.0188844	−	0.0259921i
$172$	1.69919	−	7.00353i	0.129562	−	0.534014i
$173$	4.33891	+	13.3538i	0.329881	+	1.01527i	0.969189	+	0.246319i	$0.0792212\pi$
$173$	4.33891	+	13.3538i	0.329881	+	1.01527i	−0.639307	+	0.768951i	$0.720779\pi$
$174$	−11.1389	−	1.33193i	−0.844439	−	0.100974i
$175$	−2.60949			−0.197259
$176$	−7.91786	−	10.6446i	−0.596831	−	0.802367i
$177$	−11.9598			−0.898954
$178$	−15.3354	−	1.83373i	−1.14944	−	0.137444i
$179$	7.11085	+	21.8849i	0.531490	+	1.63576i	0.751114	+	0.660173i	$0.229517\pi$
$179$	7.11085	+	21.8849i	0.531490	+	1.63576i	−0.219624	+	0.975585i	$0.570483\pi$
$180$	0.834091	−	3.43787i	0.0621694	−	0.256244i
$181$	−11.4700	+	15.7871i	−0.852559	+	1.17345i	0.130734	+	0.991418i	$0.458267\pi$
$181$	−11.4700	+	15.7871i	−0.852559	+	1.17345i	−0.983293	+	0.182030i	$0.941733\pi$
$182$	1.25922	+	6.37048i	0.0933398	+	0.472212i
$183$	−3.22933	+	9.93887i	−0.238719	+	0.734702i
$184$	1.43275	−	3.84101i	0.105624	−	0.283163i
$185$	13.4196	−	9.74989i	0.986627	−	0.716827i
$186$	−1.33495	+	1.44067i	−0.0978833	+	0.105635i
$187$	11.0573	−	5.85908i	0.808592	−	0.428458i
$188$	−1.52530	+	0.116361i	−0.111244	+	0.00848653i
$189$	−1.12813	+	0.819637i	−0.0820596	+	0.0596198i
$190$	−0.441129	+	0.953871i	−0.0320029	+	0.0692011i
$191$	−24.3481	−	7.91117i	−1.76177	−	0.572432i	−0.764385	−	0.644760i	$-0.776957\pi$
$191$	−24.3481	−	7.91117i	−1.76177	−	0.572432i	−0.997381	+	0.0723280i	$0.976957\pi$
$192$	3.11460	−	7.36880i	0.224777	−	0.531798i
$193$	12.9917	−	17.8816i	0.935166	−	1.28715i	−0.0226438	−	0.999744i	$-0.507208\pi$
$193$	12.9917	−	17.8816i	0.935166	−	1.28715i	0.957810	−	0.287402i	$-0.0927917\pi$
$194$	17.1154	−	9.55812i	1.22881	−	0.686233i
$195$	−5.53940	+	1.79986i	−0.396685	+	0.128891i
$196$	6.54811	+	7.70422i	0.467722	+	0.550301i
$197$	18.2227			1.29832			0.649158	−	0.760653i	$-0.275121\pi$
$197$	18.2227			1.29832			0.649158	+	0.760653i	$0.275121\pi$
$198$	−4.68355	+	0.253615i	−0.332846	+	0.0180236i
$199$			13.2643i			0.940284i	0.882591	+	0.470142i	$0.155797\pi$
$199$			13.2643i			0.940284i	−0.882591	+	0.470142i	$0.844203\pi$
$200$	0.226838	−	5.28808i	0.0160399	−	0.373924i
$201$	−3.07475	−	9.46312i	−0.216876	−	0.667477i
$202$	−9.91125	+	5.53496i	−0.697353	+	0.389438i
$203$	−8.94893	−	6.50178i	−0.628092	−	0.456335i
$204$	6.42459	+	3.95824i	0.449811	+	0.277132i
$205$	−1.89116	+	5.82039i	−0.132084	+	0.406514i
$206$	15.8366	+	7.32381i	1.10339	+	0.510274i
$207$	−0.851938	−	1.17259i	−0.0592138	−	0.0815008i
$208$	−13.0191	+	1.99802i	−0.902715	+	0.138538i
$209$	1.37957	+	0.195892i	0.0954268	+	0.0135501i
$210$	2.37084	−	2.55860i	0.163604	−	0.176560i
$211$	11.2460	+	15.4787i	0.774204	+	1.06560i	0.995898	+	0.0904841i	$0.0288414\pi$
$211$	11.2460	+	15.4787i	0.774204	+	1.06560i	−0.221694	+	0.975116i	$0.571159\pi$
$212$	3.29305	+	8.00442i	0.226168	+	0.549746i
$213$	−12.2539	−	3.98153i	−0.839623	−	0.272810i
$214$	9.95375	−	1.96751i	0.680424	−	0.134496i
$215$	5.15637	+	3.74632i	0.351662	+	0.255497i
$216$	−1.56291	−	2.35739i	−0.106343	−	0.160400i
$217$	−1.84185	+	0.598452i	−0.125033	+	0.0406256i
$218$	−13.1716	−	1.57499i	−0.892093	−	0.106672i
$219$			9.61699i			0.649856i
$220$	11.3703	−	2.89421i	0.766588	−	0.195127i
$221$		−	12.4242i		−	0.835740i
$222$	1.57461	−	13.1684i	0.105681	−	0.883807i
$223$	−1.64768	+	0.535364i	−0.110337	+	0.0358507i	−0.363665	−	0.931530i	$-0.618475\pi$
$223$	−1.64768	+	0.535364i	−0.110337	+	0.0358507i	0.253328	+	0.967380i	$0.418475\pi$
$224$	6.22392	−	4.84628i	0.415853	−	0.323806i
$225$	−1.51394	−	1.09994i	−0.100930	−	0.0733296i
$226$	−0.502296	−	2.54115i	−0.0334123	−	0.169035i
$227$	5.99045	+	1.94642i	0.397600	+	0.129188i	0.500991	−	0.865453i	$-0.332969\pi$
$227$	5.99045	+	1.94642i	0.397600	+	0.129188i	−0.103390	+	0.994641i	$0.532969\pi$
$228$	0.319688	+	0.777065i	0.0211719	+	0.0514624i
$229$	−2.03611	−	2.80246i	−0.134550	−	0.185192i	0.736426	−	0.676519i	$-0.236512\pi$
$229$	−2.03611	−	2.80246i	−0.134550	−	0.185192i	−0.870975	+	0.491327i	$0.836512\pi$
$230$	2.65943	+	2.46427i	0.175357	+	0.162489i
$231$	−4.15391	−	2.03333i	−0.273307	−	0.133783i
$232$	13.9537	−	17.5697i	0.916103	−	1.15351i
$233$	−8.63879	−	11.8903i	−0.565946	−	0.778958i	0.426121	−	0.904666i	$-0.359880\pi$
$233$	−8.63879	−	11.8903i	−0.565946	−	0.778958i	−0.992067	+	0.125708i	$0.959880\pi$
$234$	−1.95471	+	4.22674i	−0.127783	+	0.276311i
$235$	0.418069	−	1.28669i	0.0272718	−	0.0839341i
$236$	12.5469	−	20.3648i	0.816732	−	1.32563i
$237$	4.69761	+	3.41302i	0.305143	+	0.221699i
$238$	3.62784	+	6.49625i	0.235158	+	0.421089i
$239$	−6.25422	−	19.2485i	−0.404552	−	1.24508i	−0.921269	−	0.388927i	$-0.872846\pi$
$239$	−6.25422	−	19.2485i	−0.404552	−	1.24508i	0.516717	−	0.856156i	$-0.327154\pi$
$240$	4.97886	+	5.02688i	0.321384	+	0.324484i
$241$		−	8.76302i		−	0.564476i	−0.959344	−	0.282238i	$-0.908923\pi$
$241$		−	8.76302i		−	0.564476i	0.959344	−	0.282238i	$-0.0910768\pi$
$242$	−8.01626	−	13.3319i	−0.515305	−	0.857007i
$243$	−1.00000			−0.0641500
$244$	−13.5357	−	15.9255i	−0.866536	−	1.01953i
$245$	−8.50454	+	2.76329i	−0.543335	+	0.176540i
$246$	2.38573	+	4.27205i	0.152109	+	0.272376i
$247$	0.813163	−	1.11922i	0.0517403	−	0.0712145i
$248$	−1.05265	−	3.78450i	−0.0668430	−	0.240316i
$249$	14.3476	+	4.66182i	0.909242	+	0.295431i
$250$	15.6009	+	7.21482i	0.986687	+	0.456305i
$251$	−4.24381	+	3.08331i	−0.267867	+	0.194617i	−0.713608	−	0.700545i	$-0.752940\pi$
$251$	−4.24381	+	3.08331i	−0.267867	+	0.194617i	0.445741	+	0.895162i	$0.352940\pi$
$252$	−0.212141	−	2.78082i	−0.0133636	−	0.175175i
$253$	2.11346	−	4.31761i	0.132872	−	0.271446i
$254$	−7.41118	−	6.86734i	−0.465019	−	0.430895i
$255$	−5.39917	+	3.92273i	−0.338109	+	0.245651i
$256$	9.27987	+	13.0340i	0.579992	+	0.814622i
$257$	−1.45063	+	4.46459i	−0.0904879	+	0.278493i	−0.986052	−	0.166440i	$-0.946773\pi$
$257$	−1.45063	+	4.46459i	−0.0904879	+	0.278493i	0.895564	+	0.444933i	$0.146773\pi$
$258$	4.99919	−	0.988166i	0.311236	−	0.0615205i
$259$	7.68641	−	10.5794i	0.477610	−	0.657374i
$260$	2.74657	−	11.3205i	0.170335	−	0.702069i
$261$	−2.45128	−	7.54427i	−0.151730	−	0.466978i
$262$	1.46906	−	12.2857i	0.0907588	−	0.759013i
$263$	−23.0463			−1.42110			−0.710548	−	0.703648i	$-0.751553\pi$
$263$	−23.0463			−1.42110			−0.710548	+	0.703648i	$0.751553\pi$
$264$	4.48161	−	8.24107i	0.275824	−	0.507203i
$265$	−7.65479			−0.470230
$266$	−0.0983685	+	0.822653i	−0.00603136	+	0.0504401i
$267$	−3.37479	−	10.3865i	−0.206534	−	0.635645i
$268$	19.3392	+	4.69204i	1.18133	+	0.286612i
$269$	−5.66339	+	7.79498i	−0.345303	+	0.475268i	−0.945981	−	0.324223i	$-0.894897\pi$
$269$	−5.66339	+	7.79498i	−0.345303	+	0.475268i	0.600678	+	0.799491i	$0.294897\pi$
$270$	2.45398	−	0.485067i	0.149345	−	0.0295202i
$271$	−7.25330	+	22.3234i	−0.440607	+	1.35605i	0.446624	+	0.894722i	$0.352626\pi$
$271$	−7.25330	+	22.3234i	−0.440607	+	1.35605i	−0.887230	+	0.461326i	$0.847374\pi$
$272$	−13.4799	+	6.78705i	−0.817340	+	0.411526i
$273$	−3.71482	+	2.69897i	−0.224831	+	0.163349i
$274$	−8.77862	−	8.13443i	−0.530336	−	0.491419i
$275$	0.872544	−	6.14489i	0.0526164	−	0.370551i
$276$	2.89041	−	0.220502i	0.173982	−	0.0132726i
$277$	16.1312	−	11.7200i	0.969227	−	0.704185i	0.0139521	−	0.999903i	$-0.495559\pi$
$277$	16.1312	−	11.7200i	0.969227	−	0.704185i	0.955275	+	0.295718i	$0.0955588\pi$
$278$	7.36034	+	3.40388i	0.441444	+	0.204151i
$279$	−1.32084	−	0.429168i	−0.0790767	−	0.0256936i
$280$	1.86947	+	6.72118i	0.111722	+	0.401667i
$281$	−3.73754	+	5.14428i	−0.222963	+	0.306882i	−0.905814	−	0.423675i	$-0.860740\pi$
$281$	−3.73754	+	5.14428i	−0.222963	+	0.306882i	0.682851	+	0.730557i	$0.260740\pi$
$282$	−0.527402	−	0.944401i	−0.0314064	−	0.0562383i
$283$	−8.30006	+	2.69685i	−0.493387	+	0.160311i	−0.545134	−	0.838349i	$-0.683521\pi$
$283$	−8.30006	+	2.69685i	−0.493387	+	0.160311i	0.0517465	+	0.998660i	$0.483521\pi$
$284$	19.6350	−	16.6886i	1.16512	−	0.990284i
$285$	−0.743124			−0.0440188
$286$	−15.4224	+	0.835126i	−0.911948	+	0.0493821i
$287$			4.82469i			0.284792i
$288$	5.65372	−	0.188169i	0.333149	−	0.0110880i
$289$	0.854199	+	2.62895i	0.0502470	+	0.154644i
$290$	9.67488	+	17.3245i	0.568128	+	1.01733i
$291$	11.2144	+	8.14771i	0.657398	+	0.477627i
$292$	−16.3755	−	10.0891i	−0.958303	−	0.590417i
$293$	−6.37463	+	19.6191i	−0.372410	+	1.14616i	0.572799	+	0.819696i	$0.305857\pi$
$293$	−6.37463	+	19.6191i	−0.372410	+	1.14616i	−0.945209	+	0.326465i	$0.894143\pi$
$294$	−3.00103	+	6.48924i	−0.175023	+	0.378460i
$295$	12.4343	+	17.1144i	0.723955	+	0.996438i
$296$	20.7709	+	16.4960i	1.20728	+	0.958812i
$297$	−1.55288	−	2.93062i	−0.0901075	−	0.170052i
$298$	−20.1027	−	18.6275i	−1.16452	−	1.07906i
$299$	−2.80534	−	3.86122i	−0.162237	−	0.223300i
$300$	3.46121	−	1.42396i	0.199833	−	0.0822122i
$301$	4.77877	+	1.55272i	0.275444	+	0.0894971i
$302$	2.85946	+	14.4662i	0.164543	+	0.832435i
$303$	−6.49406	−	4.71821i	−0.373074	−	0.271054i
$304$	−1.65854	−	0.270854i	−0.0951239	−	0.0155345i
$305$	17.5799	−	5.71205i	1.00662	−	0.327071i
$306$	−0.633522	+	5.29813i	−0.0362161	+	0.302874i
$307$			24.6574i			1.40727i	0.710560	+	0.703637i	$0.248442\pi$
$307$			24.6574i			1.40727i	−0.710560	+	0.703637i	$0.751558\pi$
$308$	7.82010	−	4.93999i	0.445592	−	0.281482i
$309$			12.3377i			0.701864i
$310$	3.44950	+	0.412473i	0.195918	+	0.0234269i
$311$	−24.3504	+	7.91194i	−1.38079	+	0.448645i	−0.902928	−	0.429792i	$-0.858587\pi$
$311$	−24.3504	+	7.91194i	−1.38079	+	0.448645i	−0.477859	+	0.878437i	$0.658587\pi$
$312$	−5.14650	−	7.76264i	−0.291363	−	0.439473i
$313$	3.15731	+	2.29392i	0.178462	+	0.129660i	0.673430	−	0.739251i	$-0.264820\pi$
$313$	3.15731	+	2.29392i	0.178462	+	0.129660i	−0.494968	+	0.868911i	$0.664820\pi$
$314$	−24.6890	+	4.88017i	−1.39328	+	0.275404i
$315$	2.34579	+	0.762192i	0.132170	+	0.0429447i
$316$	−10.7398	+	4.41839i	−0.604160	+	0.248554i
$317$	−3.74958	−	5.16085i	−0.210597	−	0.289862i	0.690631	−	0.723208i	$-0.257333\pi$
$317$	−3.74958	−	5.16085i	−0.210597	−	0.289862i	−0.901228	+	0.433345i	$0.857333\pi$
$318$	−4.15982	+	4.48925i	−0.233271	+	0.251745i
$319$	18.3028	−	18.8991i	1.02476	−	1.05815i
$320$	−13.7829	+	3.20420i	−0.770486	+	0.179120i
$321$	4.21709	+	5.80433i	0.235375	+	0.323966i
$322$	2.59430	+	1.19977i	0.144575	+	0.0668604i
$323$	0.489840	−	1.50757i	0.0272554	−	0.0838836i
$324$	1.04909	−	1.70277i	0.0582826	−	0.0945982i
$325$	−4.98525	−	3.62200i	−0.276532	−	0.200912i
$326$	7.39092	−	4.12747i	0.409345	−	0.228600i
$327$	−2.89860	−	8.92098i	−0.160293	−	0.493331i
$328$	−9.77715	−	0.419402i	−0.539853	−	0.0231576i
$329$		−	1.06657i		−	0.0588019i
$330$	5.23230	+	6.43845i	0.288029	+	0.354425i
$331$	−4.34773			−0.238973			−0.119486	−	0.992836i	$-0.538125\pi$
$331$	−4.34773			−0.238973			−0.119486	+	0.992836i	$0.538125\pi$
$332$	−22.9899	+	19.5400i	−1.26173	+	1.07240i
$333$	8.91884	−	2.89791i	0.488749	−	0.158804i
$334$	−6.41922	+	3.58482i	−0.351244	+	0.196153i
$335$	−10.3449	+	14.2385i	−0.565202	+	0.777934i
$336$	4.95764	+	2.55609i	0.270462	+	0.139446i
$337$	9.71778	+	3.15750i	0.529361	+	0.172000i	0.561490	−	0.827484i	$-0.310229\pi$
$337$	9.71778	+	3.15750i	0.529361	+	0.172000i	−0.0321283	+	0.999484i	$0.510229\pi$
$338$	1.28035	−	2.76855i	0.0696419	−	0.150589i
$339$	1.48182	−	1.07660i	0.0804814	−	0.0584731i
$340$	−1.01529	−	13.3088i	−0.0550621	−	0.721772i
$341$	−0.793386	−	4.53734i	−0.0429642	−	0.245711i
$342$	−0.403833	+	0.435814i	−0.0218368	+	0.0235661i
$343$	−13.6002	+	9.88114i	−0.734343	+	0.533531i
$344$	−3.56197	+	9.54913i	−0.192048	+	0.514854i
$345$	−0.792229	+	2.43823i	−0.0426522	+	0.131270i
$346$	−3.85054	−	19.4801i	−0.207006	−	1.04726i
$347$	4.37155	−	6.01692i	0.234677	−	0.323005i	−0.675394	−	0.737457i	$-0.736027\pi$
$347$	4.37155	−	6.01692i	0.234677	−	0.323005i	0.910071	+	0.414452i	$0.136027\pi$
$348$	15.4177	+	3.74063i	0.826478	+	0.200519i
$349$	1.81469	+	5.58504i	0.0971382	+	0.298961i	0.987805	−	0.155696i	$-0.0497620\pi$
$349$	1.81469	+	5.58504i	0.0971382	+	0.298961i	−0.890667	+	0.454657i	$0.849762\pi$
$350$	3.66427	+	0.438154i	0.195863	+	0.0234203i
$351$	−3.29289			−0.175762
$352$	9.33103	+	16.2767i	0.497345	+	0.867553i
$353$	−26.3624			−1.40313			−0.701565	−	0.712605i	$-0.747515\pi$
$353$	−26.3624			−1.40313			−0.701565	+	0.712605i	$0.747515\pi$
$354$	16.7941	+	2.00815i	0.892596	+	0.106732i
$355$	7.04254	+	21.6747i	0.373779	+	1.15037i
$356$	21.2263	+	5.14989i	1.12499	+	0.272944i
$357$	−3.09251	+	4.25648i	−0.163673	+	0.225277i
$358$	−6.31047	−	31.9250i	−0.333519	−	1.68729i
$359$	−1.23260	+	3.79354i	−0.0650539	+	0.200215i	−0.978300	−	0.207193i	$-0.933567\pi$
$359$	−1.23260	+	3.79354i	−0.0650539	+	0.200215i	0.913246	+	0.407408i	$0.133567\pi$
$360$	−1.74848	+	4.68744i	−0.0921532	+	0.247050i
$361$	−15.2285	+	11.0642i	−0.801501	+	0.582325i
$362$	18.7571	−	20.2425i	0.985851	−	1.06392i
$363$	6.17710	−	9.10183i	0.324214	−	0.477722i
$364$	−0.698558	−	9.15693i	−0.0366144	−	0.479954i
$365$	13.7618	−	9.99855i	0.720327	−	0.523348i
$366$	6.20348	−	13.4140i	0.324261	−	0.701163i
$367$	31.5697	+	10.2576i	1.64792	+	0.535443i	0.978288	−	0.207248i	$-0.0664509\pi$
$367$	31.5697	+	10.2576i	1.64792	+	0.535443i	0.669634	+	0.742691i	$0.266451\pi$
$368$	−2.65683	+	5.15302i	−0.138497	+	0.268620i
$369$	−2.03369	+	2.79914i	−0.105870	+	0.145717i
$370$	−20.4810	+	11.4376i	−1.06476	+	0.594615i
$371$	−5.73936	+	1.86483i	−0.297973	+	0.0968171i
$372$	2.11645	−	1.79885i	0.109733	−	0.0932662i
$373$	30.7237			1.59081			0.795407	−	0.606075i	$-0.207257\pi$
$373$	30.7237			1.59081			0.795407	+	0.606075i	$0.207257\pi$
$374$	−16.5106	+	6.37076i	−0.853743	+	0.329424i
$375$			12.1540i			0.627632i
$376$	2.16139	+	0.0927151i	0.111465	+	0.00478142i
$377$	−8.07180	−	24.8424i	−0.415719	−	1.27945i
$378$	1.72176	−	0.961520i	0.0885578	−	0.0494552i
$379$	−29.7001	−	21.5784i	−1.52559	−	1.10841i	−0.958626	−	0.284667i	$-0.908117\pi$
$379$	−29.7001	−	21.5784i	−1.52559	−	1.10841i	−0.566967	−	0.823741i	$-0.691883\pi$
$380$	0.779601	−	1.26537i	0.0399927	−	0.0649119i
$381$	2.20775	−	6.79476i	0.113107	−	0.348106i
$382$	32.8615	+	15.1972i	1.68134	+	0.777556i
$383$	7.33813	+	10.1001i	0.374961	+	0.516090i	0.954241	−	0.299039i	$-0.0966661\pi$
$383$	7.33813	+	10.1001i	0.374961	+	0.516090i	−0.579280	+	0.815129i	$0.696666\pi$
$384$	−5.61084	+	9.82438i	−0.286327	+	0.501348i
$385$	1.40904	+	8.05821i	0.0718111	+	0.410684i
$386$	−21.2456	+	22.9281i	−1.08137	+	1.16701i
$387$	2.11800	+	2.91518i	0.107664	+	0.148187i
$388$	−25.6385	+	10.5478i	−1.30160	+	0.535483i
$389$	−31.6936	−	10.2979i	−1.60693	−	0.522122i	−0.638120	−	0.769937i	$-0.720288\pi$
$389$	−31.6936	−	10.2979i	−1.60693	−	0.522122i	−0.968807	+	0.247815i	$0.920288\pi$
$390$	8.08070	−	1.59727i	0.409182	−	0.0808811i
$391$	−4.42422	−	3.21439i	−0.223743	−	0.162559i
$392$	−7.90133	−	11.9178i	−0.399077	−	0.601941i
$393$	8.32097	−	2.70365i	0.419737	−	0.136381i
$394$	−25.5886	−	3.05975i	−1.28913	−	0.154148i
$395$		−	10.2707i		−	0.516774i
$396$	6.61928	+	0.430278i	0.332631	+	0.0216223i
$397$			14.1022i			0.707767i	0.935289	+	0.353884i	$0.115139\pi$
$397$			14.1022i			0.707767i	−0.935289	+	0.353884i	$0.884861\pi$
$398$	2.22719	−	18.6259i	0.111639	−	0.933633i
$399$	−0.557174	+	0.181037i	−0.0278936	+	0.00906317i
$400$	−1.20644	+	7.38749i	−0.0603220	+	0.369374i
$401$	9.67496	+	7.02927i	0.483145	+	0.351025i	0.802542	−	0.596596i	$-0.203480\pi$
$401$	9.67496	+	7.02927i	0.483145	+	0.351025i	−0.319397	+	0.947621i	$0.603480\pi$
$402$	2.72867	+	13.8045i	0.136094	+	0.688505i
$403$	−4.34939	−	1.41320i	−0.216658	−	0.0703966i
$404$	14.8469	−	6.10806i	0.738658	−	0.303887i
$405$	1.03968	+	1.43099i	0.0516619	+	0.0711065i
$406$	11.4745	+	10.6325i	0.569469	+	0.527680i
$407$	22.3426	+	21.6376i	1.10748	+	1.07254i
$408$	−8.35686	−	6.63694i	−0.413726	−	0.328577i
$409$	−9.59791	−	13.2104i	−0.474586	−	0.653212i	0.502867	−	0.864364i	$-0.332279\pi$
$409$	−9.59791	−	13.2104i	−0.474586	−	0.653212i	−0.977453	+	0.211152i	$0.932279\pi$
$410$	3.63288	−	7.85552i	0.179415	−	0.387956i
$411$	2.61511	−	8.04847i	0.128994	−	0.397002i
$412$	−21.0082	−	12.9433i	−1.03500	−	0.637669i
$413$	13.4923	+	9.80270i	0.663911	+	0.482359i
$414$	0.999412	+	1.78961i	0.0491184	+	0.0879547i
$415$	−8.24584	−	25.3781i	−0.404772	−	1.24576i
$416$	18.6171	−	0.619620i	0.912778	−	0.0303794i
$417$			5.73415i			0.280803i
$418$	−1.90431	−	0.506715i	−0.0931430	−	0.0247842i
$419$	5.36954			0.262319			0.131159	−	0.991361i	$-0.458130\pi$
$419$	5.36954			0.262319			0.131159	+	0.991361i	$0.458130\pi$
$420$	−3.75877	+	3.19472i	−0.183409	+	0.155887i
$421$	8.90313	−	2.89280i	0.433912	−	0.140987i	−0.0839132	−	0.996473i	$-0.526742\pi$
$421$	8.90313	−	2.89280i	0.433912	−	0.140987i	0.517825	+	0.855487i	$0.326742\pi$
$422$	−13.1927	−	23.6237i	−0.642210	−	1.14998i
$423$	0.449578	−	0.618791i	0.0218592	−	0.0300867i
$424$	−3.28013	−	11.7928i	−0.159297	−	0.572710i
$425$	−6.71504	−	2.18185i	−0.325727	−	0.105835i
$426$	16.5385	+	7.64843i	0.801293	+	0.370568i
$427$	11.7894	−	8.56549i	0.570528	−	0.414513i
$428$	−14.3075	+	1.09148i	−0.691580	+	0.0527588i
$429$	−5.11348	−	9.65022i	−0.246881	−	0.465917i
$430$	−6.61159	−	6.12642i	−0.318839	−	0.295442i
$431$	30.9429	−	22.4813i	1.49047	−	1.08289i	0.516477	−	0.856301i	$-0.327243\pi$
$431$	30.9429	−	22.4813i	1.49047	−	1.08289i	0.973991	−	0.226587i	$-0.0727567\pi$
$432$	1.79883	+	3.57270i	0.0865464	+	0.171892i
$433$	3.07438	−	9.46196i	0.147745	−	0.454713i	−0.849609	−	0.527414i	$-0.823162\pi$
$433$	3.07438	−	9.46196i	0.147745	−	0.454713i	0.997354	+	0.0727008i	$0.0231618\pi$
$434$	2.68683	−	0.531092i	0.128972	−	0.0254932i
$435$	−8.24724	+	11.3514i	−0.395425	+	0.544256i
$436$	18.2312	+	4.42324i	0.873118	+	0.211835i
$437$	−0.188171	−	0.579132i	−0.00900145	−	0.0277036i
$438$	1.61477	−	13.5043i	0.0771567	−	0.645259i
$439$	15.8844			0.758122			0.379061	−	0.925372i	$-0.376247\pi$
$439$	15.8844			0.758122			0.379061	+	0.925372i	$0.376247\pi$
$440$	−16.4523	+	2.15490i	−0.784333	+	0.102731i
$441$	−5.05551			−0.240739
$442$	−2.08612	+	17.4462i	−0.0992266	+	0.829829i
$443$	−1.67612	−	5.15857i	−0.0796349	−	0.245091i	0.903311	−	0.428986i	$-0.141129\pi$
$443$	−1.67612	−	5.15857i	−0.0796349	−	0.245091i	−0.982946	+	0.183895i	$0.941129\pi$
$444$	−4.42217	+	18.2269i	−0.209867	+	0.865008i
$445$	−11.3543	+	15.6279i	−0.538247	+	0.740834i
$446$	2.40358	−	0.475105i	0.113813	−	0.0224969i
$447$	5.98848	−	18.4307i	0.283246	−	0.871740i
$448$	−9.55343	+	5.76015i	−0.451357	+	0.272141i
$449$	−8.05234	+	5.85037i	−0.380013	+	0.276096i	−0.761351	−	0.648340i	$-0.775464\pi$
$449$	−8.05234	+	5.85037i	−0.380013	+	0.276096i	0.381338	+	0.924436i	$0.375464\pi$
$450$	1.94121	+	1.79876i	0.0915093	+	0.0847942i
$451$	−11.3613	−	1.61325i	−0.534983	−	0.0759650i
$452$	0.278651	+	3.65264i	0.0131066	+	0.171806i
$453$	−8.43566	+	6.12887i	−0.396342	+	0.287959i
$454$	−8.08504	−	3.73902i	−0.379450	−	0.175481i
$455$	7.72442	+	2.50982i	0.362126	+	0.117662i
$456$	−0.318434	−	1.14484i	−0.0149120	−	0.0536121i
$457$	−14.7492	+	20.3005i	−0.689939	+	0.949619i	−0.999999	−	0.00109777i	$-0.999651\pi$
$457$	−14.7492	+	20.3005i	−0.689939	+	0.949619i	0.310061	+	0.950717i	$0.399651\pi$
$458$	2.38857	+	4.27713i	0.111611	+	0.199857i
$459$	−3.58836	+	1.16593i	−0.167491	+	0.0544210i
$460$	−3.32062	−	3.90690i	−0.154825	−	0.182160i
$461$	−34.5074			−1.60717			−0.803585	−	0.595190i	$-0.797077\pi$
$461$	−34.5074			−1.60717			−0.803585	+	0.595190i	$0.797077\pi$
$462$	5.49155	+	3.55270i	0.255490	+	0.165287i
$463$		−	22.7879i		−	1.05905i	−0.848296	−	0.529523i	$-0.822371\pi$
$463$		−	22.7879i		−	1.05905i	0.848296	−	0.529523i	$-0.177629\pi$
$464$	−22.5440	+	22.3286i	−1.04658	+	1.03658i
$465$	0.759113	+	2.33631i	0.0352030	+	0.108344i
$466$	10.1342	+	18.1470i	0.469458	+	0.840642i
$467$	4.94788	+	3.59484i	0.228960	+	0.166349i	0.696351	−	0.717702i	$-0.254806\pi$
$467$	4.94788	+	3.59484i	0.228960	+	0.166349i	−0.467390	+	0.884051i	$0.654806\pi$
$468$	3.45453	−	5.60703i	0.159686	−	0.259185i
$469$	−4.28759	+	13.1958i	−0.197982	+	0.609327i
$470$	−0.803102	+	1.73658i	−0.0370443	+	0.0801024i
$471$	−10.4600	−	14.3969i	−0.481970	−	0.663375i
$472$	−21.0379	+	26.4897i	−0.968346	+	1.21929i
$473$	−5.25428	+	10.7340i	−0.241592	+	0.493549i
$474$	−6.02336	−	5.58136i	−0.276662	−	0.256360i
$475$	−0.462118	−	0.636050i	−0.0212034	−	0.0291840i
$476$	−4.00348	−	9.73125i	−0.183499	−	0.446031i
$477$	−4.11586	−	1.33732i	−0.188452	−	0.0612318i
$478$	5.55026	+	28.0791i	0.253863	+	1.28431i
$479$	2.50936	+	1.82316i	0.114656	+	0.0833022i	0.643635	−	0.765332i	$-0.277425\pi$
$479$	2.50936	+	1.82316i	0.114656	+	0.0833022i	−0.528980	+	0.848634i	$0.677425\pi$
$480$	−6.14731	−	7.89479i	−0.280585	−	0.360346i
$481$	29.3688	−	9.54249i	1.33910	−	0.435100i
$482$	−1.47138	+	12.3051i	−0.0670197	+	0.560483i
$483$			2.02112i			0.0919641i
$484$	9.01799	+	20.0668i	0.409909	+	0.912127i
$485$		−	24.5186i		−	1.11333i
$486$	1.40421	+	0.167908i	0.0636963	+	0.00761647i
$487$	20.1262	−	6.53939i	0.912003	−	0.296328i	0.184821	−	0.982772i	$-0.440829\pi$
$487$	20.1262	−	6.53939i	0.912003	−	0.296328i	0.727182	+	0.686444i	$0.240829\pi$
$488$	16.3330	+	24.6356i	0.739360	+	1.11520i
$489$	4.84269	+	3.51842i	0.218994	+	0.159108i
$490$	12.4061	−	2.45226i	0.560452	−	0.110782i
$491$	−4.96607	−	1.61357i	−0.224116	−	0.0728195i	0.194807	−	0.980842i	$-0.437592\pi$
$491$	−4.96607	−	1.61357i	−0.224116	−	0.0728195i	−0.418922	+	0.908022i	$0.637592\pi$
$492$	−2.63276	−	6.39944i	−0.118694	−	0.288509i
$493$	−17.5922	−	24.2136i	−0.792312	−	1.09052i
$494$	−1.32978	+	1.43509i	−0.0598296	+	0.0645677i
$495$	−2.57920	+	5.26906i	−0.115926	+	0.236827i
$496$	0.842688	+	5.49098i	0.0378378	+	0.246552i
$497$	10.5606	+	14.5354i	0.473708	+	0.652003i
$498$	−19.3643	−	8.95525i	−0.867735	−	0.401294i
$499$	−9.84802	+	30.3091i	−0.440858	+	1.35682i	0.446105	+	0.894980i	$0.352811\pi$
$499$	−9.84802	+	30.3091i	−0.440858	+	1.35682i	−0.886963	+	0.461840i	$0.847189\pi$
$500$	−20.6955	−	12.7506i	−0.925531	−	0.570226i
$501$	−4.20600	−	3.05584i	−0.187910	−	0.136525i
$502$	6.47691	−	3.61704i	0.289079	−	0.161437i
$503$	−4.38495	−	13.4955i	−0.195515	−	0.601734i	−0.999970	−	0.00772063i	$-0.997542\pi$
$503$	−4.38495	−	13.4955i	−0.195515	−	0.601734i	0.804455	−	0.594014i	$-0.202458\pi$
$504$	−0.169031	+	3.94047i	−0.00752924	+	0.175523i
$505$			14.1984i			0.631819i
$506$	−3.69271	+	5.70796i	−0.164161	+	0.253750i
$507$	2.15687			0.0957900
$508$	9.25378	+	10.8876i	0.410570	+	0.483059i
$509$	−8.45834	+	2.74828i	−0.374909	+	0.121815i	−0.490410	−	0.871492i	$-0.663153\pi$
$509$	−8.45834	+	2.74828i	−0.374909	+	0.121815i	0.115500	+	0.993307i	$0.463153\pi$
$510$	8.24023	−	4.60177i	0.364884	−	0.203770i
$511$	7.88244	−	10.8492i	0.348699	−	0.479942i
$512$	−10.8424	−	19.8606i	−0.479170	−	0.877722i
$513$	−0.399566	−	0.129827i	−0.0176412	−	0.00573199i
$514$	2.78663	−	6.02564i	0.122913	−	0.265780i
$515$	17.6551	−	12.8272i	0.777975	−	0.565232i
$516$	−7.18583	+	0.548188i	−0.316339	+	0.0241326i
$517$	2.51159	+	0.356633i	0.110459	+	0.0156847i
$518$	−12.5697	+	13.5651i	−0.552281	+	0.596018i
$519$	11.3594	−	8.25310i	0.498623	−	0.362271i
$520$	−5.75757	+	15.4352i	−0.252486	+	0.676880i
$521$	−8.34024	+	25.6686i	−0.365393	+	1.12456i	0.584342	+	0.811507i	$0.301353\pi$
$521$	−8.34024	+	25.6686i	−0.365393	+	1.12456i	−0.949735	+	0.313056i	$0.898647\pi$
$522$	2.17537	+	11.0053i	0.0952134	+	0.481690i
$523$	25.2868	−	34.8043i	1.10571	−	1.52188i	0.278129	−	0.960544i	$-0.410286\pi$
$523$	25.2868	−	34.8043i	1.10571	−	1.52188i	0.827585	−	0.561341i	$-0.189714\pi$
$524$	−4.12574	+	17.0050i	−0.180234	+	0.742868i
$525$	0.806375	+	2.48177i	0.0351931	+	0.108313i
$526$	32.3619	+	3.86966i	1.41105	+	0.168725i
$527$	−5.24004			−0.228260
$528$	−7.67686	+	10.8197i	−0.334093	+	0.470867i
$529$	20.8992			0.908662
$530$	10.7489	+	1.28530i	0.466904	+	0.0558299i
$531$	3.69578	+	11.3745i	0.160383	+	0.493609i
$532$	0.276260	−	1.13866i	0.0119774	−	0.0493672i
$533$	−6.69673	+	9.21726i	−0.290067	+	0.399244i
$534$	2.99493	+	15.1515i	0.129603	+	0.655670i
$535$	3.92154	−	12.0692i	0.169543	−	0.521799i
$536$	−26.3684	−	9.83582i	−1.13894	−	0.424843i
$537$	18.6164	−	13.5256i	0.803359	−	0.583674i
$538$	9.26143	−	9.99487i	0.399288	−	0.430909i
$539$	−7.85062	−	14.8158i	−0.338150	−	0.638162i
$540$	−3.52736	+	0.269093i	−0.151793	+	0.0115799i
$541$	16.3673	−	11.8916i	0.703686	−	0.511258i	−0.177444	−	0.984131i	$-0.556783\pi$
$541$	16.3673	−	11.8916i	0.703686	−	0.511258i	0.881131	+	0.472873i	$0.156783\pi$
$542$	13.9334	−	30.1288i	0.598493	−	1.29414i
$543$	18.5589	+	6.03014i	0.796437	+	0.258778i
$544$	20.0682	−	7.26707i	0.860418	−	0.311573i
$545$	−9.75224	+	13.4228i	−0.417740	+	0.574970i
$546$	5.66957	−	3.16618i	0.242635	−	0.135500i
$547$	13.6380	−	4.43124i	0.583117	−	0.189466i	−0.00257925	−	0.999997i	$-0.500821\pi$
$547$	13.6380	−	4.43124i	0.583117	−	0.189466i	0.585697	+	0.810530i	$0.300821\pi$
$548$	10.9612	+	12.8965i	0.468239	+	0.550909i
$549$	10.4503			0.446010
$550$	−2.25701	+	8.48220i	−0.0962393	+	0.361682i
$551$		−	3.33267i		−	0.141977i
$552$	−4.09577	−	0.175692i	−0.174327	−	0.00747797i
$553$	−2.50210	−	7.70067i	−0.106400	−	0.327466i
$554$	−24.6194	+	13.7488i	−1.04598	+	0.584129i
$555$	−13.4196	−	9.74989i	−0.569629	−	0.413860i
$556$	−9.76393	−	6.01562i	−0.414083	−	0.255119i
$557$	9.72693	−	29.9364i	0.412143	−	1.26845i	−0.502638	−	0.864497i	$-0.667637\pi$
$557$	9.72693	−	29.9364i	0.412143	−	1.26845i	0.914781	−	0.403949i	$-0.132363\pi$
$558$	1.78268	+	0.824422i	0.0754668	+	0.0349006i
$559$	6.97434	+	9.59936i	0.294983	+	0.406010i
$560$	−1.49660	−	9.75185i	−0.0632427	−	0.412091i
$561$	−8.98922	−	8.70559i	−0.379525	−	0.367550i
$562$	6.11206	−	6.59609i	0.257822	−	0.278239i
$563$	11.5320	+	15.8725i	0.486017	+	0.668946i	0.979647	−	0.200726i	$-0.0643302\pi$
$563$	11.5320	+	15.8725i	0.486017	+	0.668946i	−0.493630	+	0.869672i	$0.664330\pi$
$564$	0.582011	+	1.41469i	0.0245071	+	0.0595693i
$565$	−3.08122	−	1.00115i	−0.129628	−	0.0421187i
$566$	12.1079	−	2.39330i	0.508931	−	0.100598i
$567$	1.12813	+	0.819637i	0.0473771	+	0.0344215i
$568$	−30.3738	+	20.1374i	−1.27446	+	0.844945i
$569$	25.2020	−	8.18862i	1.05652	−	0.343285i	0.271297	−	0.962496i	$-0.412547\pi$
$569$	25.2020	−	8.18862i	1.05652	−	0.343285i	0.785225	+	0.619211i	$0.212547\pi$
$570$	1.04350	+	0.124776i	0.0437075	+	0.00522631i
$571$		−	15.2004i		−	0.636116i	−0.948071	−	0.318058i	$-0.896969\pi$
$571$		−	15.2004i		−	0.636116i	0.948071	−	0.318058i	$-0.103031\pi$
$572$	21.7966	+	1.41686i	0.911360	+	0.0592418i
$573$			25.6011i			1.06950i
$574$	0.810105	−	6.77488i	0.0338131	−	0.282778i
$575$	−2.57957	+	0.838154i	−0.107576	+	0.0349534i
$576$	−7.97061	−	0.685077i	−0.332109	−	0.0285449i
$577$	17.6624	+	12.8325i	0.735296	+	0.534224i	0.891234	−	0.453543i	$-0.149840\pi$
$577$	17.6624	+	12.8325i	0.735296	+	0.534224i	−0.155939	+	0.987767i	$0.549840\pi$
$578$	−0.758053	−	3.83503i	−0.0315308	−	0.159516i
$579$	−21.0211	−	6.83016i	−0.873606	−	0.283852i
$580$	−10.6766	−	25.9517i	−0.443324	−	1.07759i
$581$	−12.3650	−	17.0190i	−0.512987	−	0.706066i
$582$	−14.3793	−	13.3241i	−0.596040	−	0.552301i
$583$	−2.47226	−	14.1387i	−0.102390	−	0.585567i
$584$	21.3006	+	16.9167i	0.881425	+	0.700019i
$585$	3.42354	+	4.71210i	0.141546	+	0.194821i
$586$	12.2455	−	26.4790i	0.505858	−	1.09384i
$587$	7.06883	−	21.7556i	0.291762	−	0.897951i	−0.692528	−	0.721391i	$-0.743503\pi$
$587$	7.06883	−	21.7556i	0.291762	−	0.897951i	0.984290	−	0.176560i	$-0.0564969\pi$
$588$	5.30367	−	8.60836i	0.218720	−	0.355003i
$589$	−0.472045	−	0.342961i	−0.0194503	−	0.0141315i
$590$	−14.5868	−	26.1200i	−0.600528	−	1.07534i
$591$	−5.63114	−	17.3309i	−0.231634	−	0.712896i
$592$	−26.3969	−	26.6515i	−1.08490	−	1.09537i
$593$			13.3772i			0.549336i	0.961539	+	0.274668i	$0.0885679\pi$
$593$			13.3772i			0.549336i	−0.961539	+	0.274668i	$0.911432\pi$
$594$	1.68850	+	4.37595i	0.0692800	+	0.179548i
$595$	9.30620			0.381517
$596$	25.1007	+	29.5324i	1.02816	+	1.20969i
$597$	12.6151	−	4.09891i	0.516303	−	0.167757i
$598$	3.29096	+	5.89300i	0.134577	+	0.240983i
$599$	13.8109	−	19.0091i	0.564300	−	0.776692i	−0.427565	−	0.903984i	$-0.640629\pi$
$599$	13.8109	−	19.0091i	0.564300	−	0.776692i	0.991865	+	0.127292i	$0.0406287\pi$
$600$	−5.09936	+	1.41837i	−0.208180	+	0.0579047i
$601$	11.5910	+	3.76616i	0.472809	+	0.153625i	0.535722	−	0.844394i	$-0.320039\pi$
$601$	11.5910	+	3.76616i	0.472809	+	0.153625i	−0.0629138	+	0.998019i	$0.520039\pi$
$602$	−6.44969	−	2.98274i	−0.262870	−	0.121567i
$603$	−8.04981	+	5.84853i	−0.327814	+	0.238171i
$604$	−1.58630	−	20.7937i	−0.0645454	−	0.846083i
$605$	−19.4468	+	0.623576i	−0.790626	+	0.0253520i
$606$	8.32680	+	7.71577i	0.338253	+	0.313432i
$607$	−33.2882	+	24.1853i	−1.35113	+	0.981652i	−0.352173	+	0.935935i	$0.614557\pi$
$607$	−33.2882	+	24.1853i	−1.35113	+	0.981652i	−0.998954	+	0.0457169i	$0.985443\pi$
$608$	2.28346	+	0.658819i	0.0926066	+	0.0267186i
$609$	−3.41819	+	10.5201i	−0.138512	+	0.426296i
$610$	−25.6450	+	5.06912i	−1.03833	+	0.205243i
$611$	1.48041	−	2.03761i	0.0598911	−	0.0824330i
$612$	1.77920	−	7.33331i	0.0719198	−	0.296432i
$613$	−3.01493	−	9.27900i	−0.121772	−	0.374775i	0.871527	−	0.490347i	$-0.163130\pi$
$613$	−3.01493	−	9.27900i	−0.121772	−	0.374775i	−0.993299	+	0.115572i	$0.963130\pi$
$614$	4.14018	−	34.6242i	0.167084	−	1.39732i
$615$	6.11992			0.246779
$616$	−11.8105	+	5.62373i	−0.475860	+	0.226587i
$617$	−19.8476			−0.799035			−0.399518	−	0.916725i	$-0.630822\pi$
$617$	−19.8476			−0.799035			−0.399518	+	0.916725i	$0.630822\pi$
$618$	2.07159	−	17.3247i	0.0833316	−	0.696900i
$619$	0.849909	+	2.61575i	0.0341607	+	0.105136i	0.966683	−	0.255977i	$-0.0823970\pi$
$619$	0.849909	+	2.61575i	0.0341607	+	0.105136i	−0.932522	+	0.361113i	$0.882397\pi$
$620$	−4.77457	−	1.15840i	−0.191751	−	0.0465224i
$621$	−0.851938	+	1.17259i	−0.0341871	+	0.0470545i
$622$	35.5216	−	7.02139i	1.42429	−	0.281532i
$623$	−4.70597	+	14.4835i	−0.188541	+	0.580269i
$624$	5.92336	+	11.7645i	0.237124	+	0.470958i
$625$	9.82260	−	7.13654i	0.392904	−	0.285462i
$626$	−4.04837	−	3.75129i	−0.161805	−	0.149932i
$627$	−0.240006	−	1.37258i	−0.00958490	−	0.0548156i
$628$	35.4880	−	2.70729i	1.41613	−	0.108033i
$629$	28.6253	−	20.7975i	1.14136	−	0.829250i
$630$	−3.16600	−	1.46415i	−0.126136	−	0.0583333i
$631$	−5.16849	−	1.67934i	−0.205754	−	0.0668536i	0.204327	−	0.978903i	$-0.434500\pi$
$631$	−5.16849	−	1.67934i	−0.205754	−	0.0668536i	−0.410081	+	0.912049i	$0.634500\pi$
$632$	15.8228	−	4.40106i	0.629397	−	0.175065i
$633$	11.2460	−	15.4787i	0.446987	−	0.615225i
$634$	4.39865	+	7.87651i	0.174693	+	0.312816i
$635$	−12.0186	+	3.90508i	−0.476943	+	0.154968i
$636$	6.59504	−	5.60538i	0.261510	−	0.222268i
$637$	−16.6472			−0.659588
$638$	−28.8744	+	23.4652i	−1.14315	+	0.928996i
$639$			12.8845i			0.509703i
$640$	19.8921	−	2.18511i	0.786303	−	0.0863742i
$641$	−5.69933	−	17.5407i	−0.225110	−	0.692817i	−0.998280	−	0.0586191i	$-0.981330\pi$
$641$	−5.69933	−	17.5407i	−0.225110	−	0.692817i	0.773170	−	0.634198i	$-0.218670\pi$
$642$	−4.94709	−	8.85858i	−0.195246	−	0.349620i
$643$	−36.3473	−	26.4078i	−1.43340	−	1.04142i	−0.989372	−	0.145408i	$-0.953551\pi$
$643$	−36.3473	−	26.4078i	−1.43340	−	1.04142i	−0.444024	−	0.896015i	$-0.646449\pi$
$644$	−3.44150	−	2.12033i	−0.135614	−	0.0835527i
$645$	1.96956	−	6.06168i	0.0775513	−	0.238678i
$646$	−0.940972	+	2.03470i	−0.0370221	+	0.0800542i
$647$	12.0677	+	16.6098i	0.474430	+	0.652997i	0.977423	−	0.211294i	$-0.0677677\pi$
$647$	12.0677	+	16.6098i	0.474430	+	0.652997i	−0.502993	+	0.864291i	$0.667768\pi$
$648$	−1.75905	+	2.21489i	−0.0691019	+	0.0870092i
$649$	−27.5951	+	28.4942i	−1.08320	+	1.11849i
$650$	6.39218	+	5.92311i	0.250722	+	0.232324i
$651$	1.13832	+	1.56677i	0.0446144	+	0.0614065i
$652$	−11.0714	+	4.55484i	−0.433591	+	0.178381i
$653$	4.82108	+	1.56646i	0.188664	+	0.0613005i	0.401825	−	0.915717i	$-0.368376\pi$
$653$	4.82108	+	1.56646i	0.188664	+	0.0613005i	−0.213161	+	0.977017i	$0.568376\pi$
$654$	2.57234	+	13.0136i	0.100587	+	0.508873i
$655$	−12.5200	−	9.09632i	−0.489197	−	0.355423i
$656$	13.6588	+	2.23059i	0.533285	+	0.0870900i
$657$	9.14630	−	2.97181i	0.356831	−	0.115941i
$658$	−0.179086	+	1.49769i	−0.00698149	+	0.0583860i
$659$		−	24.6770i		−	0.961279i	−0.876918	−	0.480640i	$-0.840405\pi$
$659$		−	24.6770i		−	0.961279i	0.876918	−	0.480640i	$-0.159595\pi$
$660$	−6.26618	−	9.91948i	−0.243911	−	0.386115i
$661$			29.9755i			1.16591i	0.812504	+	0.582956i	$0.198104\pi$
$661$			29.9755i			1.16591i	−0.812504	+	0.582956i	$0.801896\pi$
$662$	6.10513	+	0.730019i	0.237282	+	0.0283730i
$663$	−11.8161	+	3.83928i	−0.458899	+	0.149105i
$664$	35.5635	−	23.5781i	1.38013	−	0.915006i
$665$	0.838342	+	0.609091i	0.0325095	+	0.0236196i
$666$	−13.0105	+	2.57172i	−0.504147	+	0.0996523i
$667$	−10.9347	−	3.55289i	−0.423393	−	0.137569i
$668$	9.61585	−	3.95601i	0.372048	−	0.153062i
$669$	1.01832	+	1.40160i	0.0393707	+	0.0541891i
$670$	16.9172	−	18.2569i	0.653567	−	0.705325i
$671$	16.2282	+	30.6260i	0.626482	+	1.18230i
$672$	−6.53238	−	4.42172i	−0.251992	−	0.170572i
$673$	−0.00676354	−	0.00930921i	−0.000260715	−	0.000358844i	0.808887	−	0.587965i	$-0.200071\pi$
$673$	−0.00676354	−	0.00930921i	−0.000260715	−	0.000358844i	−0.809147	+	0.587606i	$0.800071\pi$
$674$	−13.1156	−	6.06549i	−0.505196	−	0.233634i
$675$	−0.578275	+	1.77975i	−0.0222578	+	0.0685025i
$676$	−2.26274	+	3.67265i	−0.0870286	+	0.141256i
$677$	0.292248	+	0.212331i	0.0112320	+	0.00816054i	0.593387	−	0.804917i	$-0.297790\pi$
$677$	0.292248	+	0.212331i	0.0112320	+	0.00816054i	−0.582155	+	0.813078i	$0.697790\pi$
$678$	−2.26156	+	1.26297i	−0.0868546	+	0.0485041i
$679$	−5.97313	−	18.3834i	−0.229228	−	0.705491i
$680$	−0.808972	+	18.8589i	−0.0310227	+	0.723204i
$681$		−	6.29873i		−	0.241368i
$682$	0.352224	+	6.50459i	0.0134874	+	0.249074i
$683$	16.8584			0.645070			0.322535	−	0.946557i	$-0.395465\pi$
$683$	16.8584			0.645070			0.322535	+	0.946557i	$0.395465\pi$
$684$	0.640244	−	0.544168i	0.0244803	−	0.0208068i
$685$	−14.2362	+	4.62561i	−0.543935	+	0.176735i
$686$	20.7567	−	11.5916i	0.792494	−	0.442570i
$687$	−2.03611	+	2.80246i	−0.0776824	+	0.106921i
$688$	6.60513	−	12.8109i	0.251818	−	0.488411i
$689$	−13.5531	−	4.40366i	−0.516331	−	0.167766i
$690$	1.52186	−	3.29077i	0.0579361	−	0.125277i
$691$	33.4931	−	24.3341i	1.27414	−	0.925714i	0.274777	−	0.961508i	$-0.411396\pi$
$691$	33.4931	−	24.3341i	1.27414	−	0.925714i	0.999359	+	0.0357938i	$0.0113959\pi$
$692$	2.13610	+	28.0007i	0.0812022	+	1.06443i
$693$	−0.650187	+	4.57893i	−0.0246986	+	0.173939i
$694$	−7.14886	+	7.71500i	−0.271367	+	0.292857i
$695$	8.20552	−	5.96166i	0.311253	−	0.226139i
$696$	−21.0217	−	7.84139i	−0.796824	−	0.297227i
$697$	−4.03403	+	12.4155i	−0.152800	+	0.470269i
$698$	−1.61043	−	8.14728i	−0.0609558	−	0.308379i
$699$	−8.63879	+	11.8903i	−0.326749	+	0.449732i
$700$	−5.07183	−	1.23052i	−0.191697	−	0.0465093i
$701$	9.88537	+	30.4240i	0.373365	+	1.14910i	0.944575	+	0.328296i	$0.106474\pi$
$701$	9.88537	+	30.4240i	0.373365	+	1.14910i	−0.571210	+	0.820804i	$0.693526\pi$
$702$	4.62391	+	0.552903i	0.174518	+	0.0208680i
$703$	3.93989			0.148596
$704$	−10.3697	−	24.4227i	−0.390824	−	0.920465i
$705$	−1.35290			−0.0509532
$706$	37.0184	+	4.42647i	1.39321	+	0.166592i
$707$	3.45895	+	10.6455i	0.130087	+	0.400367i
$708$	−23.2453	−	5.63973i	−0.873610	−	0.211954i
$709$	−20.2031	+	27.8072i	−0.758743	+	1.04432i	0.238574	+	0.971124i	$0.423320\pi$
$709$	−20.2031	+	27.8072i	−0.758743	+	1.04432i	−0.997318	+	0.0731963i	$0.976680\pi$
$710$	−6.24985	−	31.6184i	−0.234553	−	1.18662i
$711$	1.79433	−	5.52238i	0.0672926	−	0.207105i
$712$	−28.9415	−	10.7956i	−1.08463	−	0.404582i
$713$	−1.62851	+	1.18318i	−0.0609883	+	0.0443106i
$714$	5.05724	−	5.45774i	0.189262	−	0.204251i
$715$	−8.49302	+	17.3504i	−0.317621	+	0.648870i
$716$	3.50075	+	45.8890i	0.130829	+	1.71495i
$717$	−16.3738	+	11.8962i	−0.611489	+	0.444273i
$718$	2.36779	−	5.11997i	0.0883652	−	0.191075i
$719$	25.4856	+	8.28077i	0.950452	+	0.308821i	0.742899	−	0.669403i	$-0.233450\pi$
$719$	25.4856	+	8.28077i	0.950452	+	0.308821i	0.207553	+	0.978224i	$0.433450\pi$
$720$	3.24230	−	6.28857i	0.120833	−	0.234361i
$721$	10.1124	−	13.9185i	0.376605	−	0.518353i
$722$	23.2418	−	12.9794i	0.864971	−	0.483044i
$723$	−8.33413	+	2.70792i	−0.309950	+	0.100709i
$724$	−29.7378	+	25.2753i	−1.10520	+	0.939349i
$725$	−14.8444			−0.551307
$726$	−10.2022	+	11.7437i	−0.378640	+	0.435850i
$727$			26.4551i			0.981165i	0.871395	+	0.490583i	$0.163216\pi$
$727$			26.4551i			0.981165i	−0.871395	+	0.490583i	$0.836784\pi$
$728$	−0.556601	+	12.9756i	−0.0206290	+	0.480906i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−21.0033	+	11.7293i	−0.777368	+	0.434123i
$731$	10.9990	+	7.99128i	0.406814	+	0.295568i
$732$	−10.9633	+	17.7945i	−0.405216	+	0.657704i
$733$	0.587267	−	1.80742i	0.0216912	−	0.0667586i	−0.939625	−	0.342206i	$-0.888826\pi$
$733$	0.587267	−	1.80742i	0.0216912	−	0.0667586i	0.961316	+	0.275447i	$0.0888260\pi$
$734$	−42.6081	−	19.7046i	−1.57269	−	0.727311i
$735$	5.25609	+	7.23439i	0.193874	+	0.266845i
$736$	4.59598	−	6.78982i	0.169410	−	0.250276i
$737$	−29.6403	−	14.5089i	−1.09181	−	0.534441i
$738$	3.32573	−	3.58911i	0.122422	−	0.132117i
$739$	8.35357	+	11.4977i	0.307291	+	0.422950i	0.934534	−	0.355874i	$-0.115817\pi$
$739$	8.35357	+	11.4977i	0.307291	+	0.422950i	−0.627243	+	0.778824i	$0.715817\pi$
$740$	30.6801	−	12.6219i	1.12782	−	0.463992i
$741$	−1.31573	−	0.427505i	−0.0483344	−	0.0157048i
$742$	8.37238	−	1.65493i	0.307360	−	0.0607544i
$743$	19.8113	+	14.3937i	0.726806	+	0.528055i	0.888551	−	0.458777i	$-0.151712\pi$
$743$	19.8113	+	14.3937i	0.726806	+	0.528055i	−0.161746	+	0.986832i	$0.551712\pi$
$744$	−3.27398	+	2.17060i	−0.120030	+	0.0795780i
$745$	−32.6002	+	10.5924i	−1.19438	+	0.388077i
$746$	−43.1426	−	5.15876i	−1.57956	−	0.188876i
$747$		−	15.0860i		−	0.551966i
$748$	24.2541	−	6.17362i	0.886816	−	0.225730i
$749$		−	10.0045i		−	0.365558i
$750$	2.04076	−	17.0668i	0.0745181	−	0.623192i
$751$	−38.6132	+	12.5462i	−1.40901	+	0.457817i	−0.912095	−	0.409980i	$-0.865536\pi$
$751$	−38.6132	+	12.5462i	−1.40901	+	0.457817i	−0.496920	+	0.867796i	$0.665536\pi$
$752$	−3.01947	−	0.493106i	−0.110109	−	0.0179817i
$753$	4.24381	+	3.08331i	0.154653	+	0.112362i
$754$	7.16326	+	36.2393i	0.260870	+	1.31976i
$755$	17.5407	+	5.69932i	0.638372	+	0.207420i
$756$	−2.57916	+	1.06108i	−0.0938032	+	0.0385911i
$757$	−7.32712	−	10.0849i	−0.266309	−	0.366542i	0.654831	−	0.755776i	$-0.272740\pi$
$757$	−7.32712	−	10.0849i	−0.266309	−	0.366542i	−0.921139	+	0.389233i	$0.872740\pi$
$758$	38.0820	+	35.2875i	1.38320	+	1.28170i
$759$	−4.75939	−	0.675810i	−0.172755	−	0.0245304i
$760$	−1.30719	+	1.64594i	−0.0474167	+	0.0597045i
$761$	19.4146	+	26.7219i	0.703779	+	0.968668i	0.999909	+	0.0135207i	$0.00430390\pi$
$761$	19.4146	+	26.7219i	0.703779	+	0.968668i	−0.296130	+	0.955148i	$0.595696\pi$
$762$	−4.24105	+	9.17058i	−0.153637	+	0.332215i
$763$	−4.04195	+	12.4399i	−0.146329	+	0.450353i
$764$	−43.5927	−	26.8578i	−1.57713	−	0.971680i
$765$	5.39917	+	3.92273i	0.195207	+	0.141827i
$766$	−8.60840	−	15.4148i	−0.311034	−	0.556958i
$767$	12.1698	+	37.4548i	0.439427	+	1.35242i
$768$	9.52839	−	12.8534i	0.343826	−	0.463807i
$769$		−	45.9291i		−	1.65625i	−0.560546	−	0.828123i	$-0.689409\pi$
$769$		−	45.9291i		−	1.65625i	0.560546	−	0.828123i	$-0.310591\pi$
$770$	−0.625543	−	11.5520i	−0.0225430	−	0.416306i
$771$	4.69434			0.169063
$772$	33.6831	−	28.6286i	1.21228	−	1.03037i
$773$	13.4151	−	4.35884i	0.482509	−	0.156777i	−0.0576547	−	0.998337i	$-0.518362\pi$
$773$	13.4151	−	4.35884i	0.482509	−	0.156777i	0.540164	+	0.841560i	$0.318362\pi$
$774$	−2.48464	−	4.44915i	−0.0893084	−	0.159921i
$775$	−1.52762	+	2.10259i	−0.0548737	+	0.0755272i
$776$	37.7729	−	10.5064i	1.35597	−	0.377158i
$777$	−12.4369	−	4.04098i	−0.446170	−	0.144969i
$778$	42.7753	+	19.7820i	1.53357	+	0.709218i
$779$	−1.17600	+	0.854411i	−0.0421344	+	0.0306125i
$780$	−11.6152	+	0.886092i	−0.415891	+	0.0317272i
$781$	−37.7596	+	20.0081i	−1.35115	+	0.715947i
$782$	5.67282	+	5.25654i	0.202860	+	0.187973i
$783$	−6.41754	+	4.66261i	−0.229344	+	0.166628i
$784$	9.09403	+	18.0618i	0.324787	+	0.645065i
$785$	−9.72688	+	29.9363i	−0.347167	+	1.06847i
$786$	−12.1384	+	2.39933i	−0.432961	+	0.0855813i
$787$	−18.5090	+	25.4755i	−0.659776	+	0.908104i	−0.999474	−	0.0324309i	$-0.989675\pi$
$787$	−18.5090	+	25.4755i	−0.659776	+	0.908104i	0.339698	+	0.940535i	$0.389675\pi$
$788$	35.4180	+	8.59306i	1.26171	+	0.306115i
$789$	7.12170	+	21.9184i	0.253539	+	0.780314i
$790$	−1.72453	+	14.4222i	−0.0613560	+	0.513118i
$791$	−2.55411			−0.0908138
$792$	−9.22261	−	1.71563i	−0.327711	−	0.0609623i
$793$	34.4118			1.22200
$794$	2.36787	−	19.8024i	0.0840325	−	0.702761i
$795$	2.36546	+	7.28014i	0.0838943	+	0.258200i
$796$	−6.25489	+	25.7808i	−0.221699	+	0.913775i
$797$	19.3111	−	26.5794i	0.684033	−	0.941490i	−0.315941	−	0.948779i	$-0.602320\pi$
$797$	19.3111	−	26.5794i	0.684033	−	0.941490i	0.999973	+	0.00728889i	$0.00232015\pi$
$798$	0.812787	−	0.160660i	0.0287723	−	0.00568729i
$799$	0.891783	−	2.74463i	0.0315490	−	0.0970979i
$800$	2.93451	−	10.1710i	0.103751	−	0.359600i
$801$	−8.83531	+	6.41923i	−0.312180	+	0.226812i
$802$	−12.4054	−	11.4951i	−0.438050	−	0.405906i
$803$	22.9124	+	22.1895i	0.808561	+	0.783050i
$804$	−1.51374	−	19.8426i	−0.0533854	−	0.699794i
$805$	2.89220	−	2.10131i	0.101937	−	0.0740614i
$806$	5.87017	+	2.71473i	0.206768	+	0.0956223i
$807$	9.16355	+	2.97742i	0.322572	+	0.104810i
$808$	−21.8737	+	6.08410i	−0.769514	+	0.214038i
$809$	3.52470	−	4.85134i	0.123922	−	0.170564i	−0.742549	−	0.669792i	$-0.766383\pi$
$809$	3.52470	−	4.85134i	0.123922	−	0.170564i	0.866470	+	0.499228i	$0.166383\pi$
$810$	−1.21965	−	2.18398i	−0.0428541	−	0.0767373i
$811$	−39.0150	+	12.6767i	−1.37000	+	0.445140i	−0.899369	−	0.437189i	$-0.855974\pi$
$811$	−39.0150	+	12.6767i	−1.37000	+	0.445140i	−0.470632	+	0.882330i	$0.655974\pi$
$812$	−14.3273	−	16.8569i	−0.502790	−	0.591560i
$813$	23.4722			0.823205
$814$	−27.7406	−	34.1353i	−0.972306	−	1.19644i
$815$		−	10.5879i		−	0.370876i
$816$	10.6204	+	10.7228i	0.371788	+	0.375374i
$817$	0.467812	+	1.43978i	0.0163667	+	0.0503714i
$818$	11.2594	+	20.1617i	0.393674	+	0.704939i
$819$	3.71482	+	2.69897i	0.129806	+	0.0943098i
$820$	−6.42033	+	10.4208i	−0.224208	+	0.363910i
$821$	−7.86487	+	24.2056i	−0.274486	+	0.844781i	0.714869	+	0.699258i	$0.246486\pi$
$821$	−7.86487	+	24.2056i	−0.274486	+	0.844781i	−0.989355	+	0.145523i	$0.953514\pi$
$822$	−5.02356	+	10.8626i	−0.175217	+	0.378878i
$823$	−8.33462	−	11.4716i	−0.290526	−	0.399875i	0.638659	−	0.769490i	$-0.279490\pi$
$823$	−8.33462	−	11.4716i	−0.290526	−	0.399875i	−0.929185	+	0.369615i	$0.879490\pi$
$824$	27.3266	+	21.7025i	0.951967	+	0.756043i
$825$	−6.11376	+	1.06903i	−0.212854	+	0.0372190i
$826$	−17.3000	−	16.0305i	−0.601945	−	0.557773i
$827$	16.3323	+	22.4795i	0.567931	+	0.781690i	0.992308	−	0.123796i	$-0.0395068\pi$
$827$	16.3323	+	22.4795i	0.567931	+	0.781690i	−0.424377	+	0.905486i	$0.639507\pi$
$828$	−1.10289	−	2.68080i	−0.0383282	−	0.0931643i
$829$	47.9834	+	15.5908i	1.66653	+	0.541490i	0.982226	−	0.187703i	$-0.0601044\pi$
$829$	47.9834	+	15.5908i	1.66653	+	0.541490i	0.684308	+	0.729193i	$0.260104\pi$
$830$	7.31770	+	37.0207i	0.254001	+	1.28501i
$831$	−16.1312	−	11.7200i	−0.559584	−	0.406561i
$832$	−26.2464	−	2.25589i	−0.909929	−	0.0782087i
$833$	−18.1410	+	5.89437i	−0.628549	+	0.204228i
$834$	0.962811	−	8.05196i	0.0333394	−	0.278816i
$835$			9.19584i			0.318235i
$836$	2.58897	+	1.03128i	0.0895415	+	0.0356677i
$837$			1.38882i			0.0480045i
$838$	−7.53996	−	0.901589i	−0.260464	−	0.0311449i
$839$	−44.3548	+	14.4117i	−1.53130	+	0.497548i	−0.948959	−	0.315399i	$-0.897862\pi$
$839$	−44.3548	+	14.4117i	−1.53130	+	0.497548i	−0.582337	+	0.812947i	$0.697862\pi$
$840$	5.81452	−	3.85494i	0.200620	−	0.133008i
$841$	−27.4457	−	19.9405i	−0.946403	−	0.687602i
$842$	−12.9876	+	2.56719i	−0.447582	+	0.0884714i
$843$	6.04746	+	1.96494i	0.208286	+	0.0676761i
$844$	14.5587	+	35.3878i	0.501131	+	1.21810i
$845$	−2.24245	−	3.08646i	−0.0771425	−	0.106178i
$846$	−0.735203	+	0.793425i	−0.0252768	+	0.0272785i
$847$	−14.4288	+	5.20510i	−0.495779	+	0.178849i
$848$	2.62589	+	17.1104i	0.0901734	+	0.587572i
$849$	5.12972	+	7.06045i	0.176052	+	0.242314i
$850$	9.06298	+	4.19129i	0.310858	+	0.143760i
$851$	4.20023	−	12.9270i	0.143982	−	0.443132i
$852$	−21.9393	−	13.5170i	−0.751629	−	0.463083i
$853$	−41.5877	−	30.2152i	−1.42394	−	1.03455i	−0.991106	−	0.133073i	$-0.957515\pi$
$853$	−41.5877	−	30.2152i	−1.42394	−	1.03455i	−0.432829	−	0.901476i	$-0.642485\pi$
$854$	−17.9930	+	10.0482i	−0.615707	+	0.343843i
$855$	0.229638	+	0.706752i	0.00785345	+	0.0241704i
$856$	20.2740	+	0.869678i	0.692952	+	0.0297250i
$857$		−	17.4541i		−	0.596221i	−0.954531	−	0.298111i	$-0.903644\pi$
$857$		−	17.4541i		−	0.596221i	0.954531	−	0.298111i	$-0.0963565\pi$
$858$	5.56005	+	14.4095i	0.189817	+	0.491933i
$859$	−35.3164			−1.20498			−0.602489	−	0.798127i	$-0.705824\pi$
$859$	−35.3164			−1.20498			−0.602489	+	0.798127i	$0.705824\pi$
$860$	8.25539	+	9.71293i	0.281506	+	0.331208i
$861$	4.58855	−	1.49091i	0.156377	−	0.0508101i
$862$	−47.2252	+	26.3730i	−1.60850	+	0.898267i
$863$	−3.84304	+	5.28949i	−0.130819	+	0.180056i	−0.869401	−	0.494106i	$-0.835495\pi$
$863$	−3.84304	+	5.28949i	−0.130819	+	0.180056i	0.738583	+	0.674163i	$0.235495\pi$
$864$	−1.92606	−	5.31886i	−0.0655258	−	0.180951i
$865$	−23.6202	−	7.67468i	−0.803112	−	0.260947i
$866$	−5.90581	+	12.7704i	−0.200688	+	0.433955i
$867$	2.23632	−	1.62478i	0.0759495	−	0.0551805i
$868$	−3.86204	+	0.294625i	−0.131086	+	0.0100002i
$869$	18.9704	−	3.31711i	0.643526	−	0.112525i
$870$	13.4868	−	14.5549i	0.457247	−	0.493458i
$871$	−26.5071	+	19.2586i	−0.898160	+	0.652552i
$872$	−24.8578	−	9.27233i	−0.841791	−	0.314001i
$873$	4.28351	−	13.1833i	0.144975	−	0.446186i
$874$	0.166991	+	0.844818i	0.00564856	+	0.0285764i
$875$	9.96190	−	13.7114i	0.336774	−	0.463529i
$876$	−4.53496	+	18.6917i	−0.153222	+	0.631534i
$877$	9.06904	+	27.9116i	0.306240	+	0.942509i	0.979212	+	0.202841i	$0.0650175\pi$
$877$	9.06904	+	27.9116i	0.306240	+	0.942509i	−0.672972	+	0.739668i	$0.734982\pi$
$878$	−22.3051	−	2.66712i	−0.752759	−	0.0900110i
$879$	20.6288			0.695790
$880$	23.4643	−	0.263455i	0.790983	−	0.00888108i
$881$	1.12915			0.0380420			0.0190210	−	0.999819i	$-0.493945\pi$
$881$	1.12915			0.0380420			0.0190210	+	0.999819i	$0.493945\pi$
$882$	7.09900	+	0.848861i	0.239036	+	0.0285826i
$883$	4.24530	+	13.0657i	0.142866	+	0.439695i	0.996730	−	0.0807999i	$-0.0257475\pi$
$883$	4.24530	+	13.0657i	0.142866	+	0.439695i	−0.853865	+	0.520495i	$0.825747\pi$
$884$	5.85870	−	24.1478i	0.197049	−	0.812178i
$885$	12.4343	−	17.1144i	0.417975	−	0.575294i
$886$	1.48746	+	7.52515i	0.0499722	+	0.252812i
$887$	1.98190	−	6.09967i	0.0665458	−	0.204807i	−0.912254	−	0.409624i	$-0.865660\pi$
$887$	1.98190	−	6.09967i	0.0665458	−	0.204807i	0.978800	+	0.204817i	$0.0656599\pi$
$888$	9.27010	−	24.8518i	0.311084	−	0.833973i
$889$	−8.05988	+	5.85584i	−0.270320	+	0.196399i
$890$	18.5679	−	20.0384i	0.622399	−	0.671688i
$891$	−2.30732	+	2.38249i	−0.0772982	+	0.0798165i
$892$	−3.45491	+	0.263566i	−0.115679	+	0.00882485i
$893$	0.259972	−	0.188880i	0.00869962	−	0.00632064i
$894$	−11.5037	+	24.8750i	−0.384743	+	0.831945i
$895$	−38.7101	−	12.5777i	−1.29394	−	0.420426i
$896$	14.3822	−	6.48436i	0.480476	−	0.216627i
$897$	−2.80534	+	3.86122i	−0.0936675	+	0.128922i
$898$	12.2895	−	6.86309i	0.410106	−	0.229024i
$899$	−10.4776	+	3.40438i	−0.349447	+	0.113542i
$900$	−2.42384	−	2.85178i	−0.0807945	−	0.0950593i
$901$	−16.3284			−0.543979
$902$	15.6828	+	4.17300i	0.522180	+	0.138946i
$903$		−	5.02470i		−	0.167211i
$904$	0.222025	−	5.17587i	0.00738443	−	0.172147i
$905$	−10.6661	−	32.8270i	−0.354554	−	1.09121i
$906$	12.8745	−	7.18981i	0.427728	−	0.238865i
$907$	9.91808	+	7.20591i	0.329325	+	0.239268i	0.740144	−	0.672448i	$-0.234757\pi$
$907$	9.91808	+	7.20591i	0.329325	+	0.239268i	−0.410819	+	0.911717i	$0.634757\pi$
$908$	10.7253	+	6.60792i	0.355931	+	0.219291i
$909$	−2.48051	+	7.63423i	−0.0822733	+	0.253211i
$910$	−10.4253	−	4.82130i	−0.345595	−	0.159825i
$911$	−21.4231	−	29.4864i	−0.709779	−	0.976927i	−0.999802	−	0.0199074i	$-0.993663\pi$
$911$	−21.4231	−	29.4864i	−0.709779	−	0.976927i	0.290023	−	0.957020i	$-0.406337\pi$
$912$	0.254920	+	1.66106i	0.00844125	+	0.0550034i
$913$	44.2113	−	23.4267i	1.46318	−	0.775312i
$914$	24.1196	−	26.0297i	0.797806	−	0.860986i
$915$	−10.8650	−	14.9544i	−0.359185	−	0.494376i
$916$	−2.63589	−	6.40705i	−0.0870923	−	0.211695i
$917$	−11.6032	−	3.77010i	−0.383170	−	0.124500i
$918$	5.23459	−	1.03470i	0.172767	−	0.0341501i
$919$	−10.4315	−	7.57891i	−0.344103	−	0.250005i	0.402288	−	0.915513i	$-0.368215\pi$
$919$	−10.4315	−	7.57891i	−0.344103	−	0.250005i	−0.746391	+	0.665508i	$0.768215\pi$
$920$	4.00685	+	6.04367i	0.132102	+	0.199254i
$921$	23.4506	−	7.61956i	0.772724	−	0.251073i
$922$	48.4557	+	5.79407i	1.59580	+	0.190818i
$923$			42.4273i			1.39651i
$924$	−7.11476	−	5.91082i	−0.234058	−	0.194452i
$925$		−	17.5491i		−	0.577010i
$926$	−3.82628	+	31.9991i	−0.125739	+	1.05155i
$927$	11.7338	−	3.81254i	0.385389	−	0.125220i
$928$	35.4056	−	27.5687i	1.16225	−	0.904987i
$929$	11.5280	+	8.37561i	0.378223	+	0.274795i	0.760612	−	0.649206i	$-0.224899\pi$
$929$	11.5280	+	8.37561i	0.378223	+	0.274795i	−0.382390	+	0.924001i	$0.624899\pi$
$930$	−0.673669	−	3.40813i	−0.0220905	−	0.111757i
$931$	−2.02001	−	0.656340i	−0.0662031	−	0.0215107i
$932$	−11.1835	−	27.1838i	−0.366329	−	0.890435i
$933$	15.0494	+	20.7137i	0.492695	+	0.678137i
$934$	−6.34426	−	5.87870i	−0.207590	−	0.192357i
$935$	−3.11175	+	21.9145i	−0.101765	+	0.716680i
$936$	−5.79235	+	7.29340i	−0.189329	+	0.238392i
$937$	−29.3763	−	40.4330i	−0.959681	−	1.32089i	−0.947090	−	0.320967i	$-0.895992\pi$
$937$	−29.3763	−	40.4330i	−0.959681	−	1.32089i	−0.0125913	−	0.999921i	$-0.504008\pi$
$938$	8.23637	−	17.8098i	0.268927	−	0.581511i
$939$	1.20599	−	3.71165i	0.0393559	−	0.121125i
$940$	1.41931	−	2.30368i	0.0462928	−	0.0751376i
$941$	−3.47674	−	2.52600i	−0.113338	−	0.0823452i	0.529672	−	0.848202i	$-0.322315\pi$
$941$	−3.47674	−	2.52600i	−0.113338	−	0.0823452i	−0.643011	+	0.765857i	$0.722315\pi$
$942$	12.2706	+	21.9726i	0.399799	+	0.715907i
$943$	1.54967	+	4.76938i	0.0504641	+	0.155312i
$944$	33.9894	−	33.6647i	1.10626	−	1.09569i
$945$		−	2.46651i		−	0.0802354i
$946$	9.18043	−	14.1905i	0.298482	−	0.461374i
$947$	0.231238			0.00751424			0.00375712	−	0.999993i	$-0.498804\pi$
$947$	0.231238			0.00751424			0.00375712	+	0.999993i	$0.498804\pi$
$948$	7.52092	+	8.84878i	0.244268	+	0.287395i
$949$	30.1178	−	9.78586i	0.977664	−	0.317662i
$950$	0.542112	+	0.970742i	0.0175884	+	0.0314950i
$951$	−3.74958	+	5.16085i	−0.121588	+	0.167352i
$952$	3.98777	+	14.3369i	0.129244	+	0.464663i
$953$	50.8341	+	16.5170i	1.64668	+	0.535039i	0.978017	−	0.208527i	$-0.0668670\pi$
$953$	50.8341	+	16.5170i	1.64668	+	0.535039i	0.668663	+	0.743566i	$0.266867\pi$
$954$	5.55498	+	2.56897i	0.179849	+	0.0831735i
$955$	36.6349	−	26.6168i	1.18548	−	0.861301i
$956$	−3.07903	−	40.3609i	−0.0995828	−	1.30536i
$957$	−23.6301	−	11.5669i	−0.763851	−	0.373904i
$958$	−3.21755	−	2.98144i	−0.103954	−	0.0963259i
$959$	−9.54701	+	6.93631i	−0.308289	+	0.223985i
$960$	7.30652	+	12.1181i	0.235817	+	0.391111i
$961$	8.98349	−	27.6483i	0.289790	−	0.891882i
$962$	−42.8422	+	8.46841i	−1.38129	+	0.273032i
$963$	4.21709	−	5.80433i	0.135894	−	0.187042i
$964$	4.13226	−	17.0319i	0.133091	−	0.548562i
$965$	12.0812	+	37.1821i	0.388908	+	1.19694i
$966$	0.339362	−	2.83808i	0.0109188	−	0.0913136i
$967$	1.08508			0.0348938			0.0174469	−	0.999848i	$-0.494446\pi$
$967$	1.08508			0.0348938			0.0174469	+	0.999848i	$0.494446\pi$
$968$	−9.29378	−	29.6922i	−0.298713	−	0.954343i
$969$	−1.58516			−0.0509225
$970$	−4.11688	+	34.4293i	−0.132185	+	1.10546i
$971$	−10.1034	−	31.0950i	−0.324233	−	0.997887i	−0.971786	−	0.235866i	$-0.924207\pi$
$971$	−10.1034	−	31.0950i	−0.324233	−	0.997887i	0.647552	−	0.762021i	$-0.275793\pi$
$972$	−1.94361	−	0.471557i	−0.0623414	−	0.0151252i
$973$	4.69992	−	6.46889i	0.150673	−	0.207383i
$974$	−29.3594	+	5.80333i	−0.940735	+	0.185951i
$975$	−1.90420	+	5.86052i	−0.0609831	+	0.187687i
$976$	−18.7984	−	37.3360i	−0.601723	−	1.19510i
$977$	−40.9534	+	29.7544i	−1.31021	+	0.951926i	−0.310215	+	0.950667i	$0.600401\pi$
$977$	−40.9534	+	29.7544i	−1.31021	+	0.951926i	−0.999999	+	0.00125964i	$0.999599\pi$
$978$	−6.20938	−	5.75373i	−0.198554	−	0.183984i
$979$	−32.5325	−	15.9246i	−1.03974	−	0.508954i
$980$	−17.8326	+	1.36040i	−0.569641	+	0.0434564i
$981$	−7.58864	+	5.51347i	−0.242287	+	0.176032i
$982$	6.70247	+	3.09964i	0.213884	+	0.0989135i
$983$	23.1688	+	7.52801i	0.738971	+	0.240106i	0.654229	−	0.756297i	$-0.272993\pi$
$983$	23.1688	+	7.52801i	0.738971	+	0.240106i	0.0847421	+	0.996403i	$0.472993\pi$
$984$	2.62243	+	9.42823i	0.0836001	+	0.300561i
$985$	−18.9457	+	26.0766i	−0.603662	+	0.830869i
$986$	20.6375	+	36.9548i	0.657231	+	1.17688i
$987$	−1.01437	+	0.329588i	−0.0322877	+	0.0104909i
$988$	2.10825	−	1.79188i	0.0670724	−	0.0570074i
$989$	5.22272			0.166073
$990$	4.50646	−	6.96580i	0.143225	−	0.221388i
$991$		−	27.0358i		−	0.858821i	−0.903110	−	0.429410i	$-0.858721\pi$
$991$		−	27.0358i		−	0.858821i	0.903110	−	0.429410i	$-0.141279\pi$
$992$	−0.261332	−	7.85198i	−0.00829730	−	0.249301i
$993$	1.34352	+	4.13494i	0.0426354	+	0.131218i
$994$	−12.3887	−	22.1840i	−0.392946	−	0.703635i
$995$	−18.9812	−	13.7906i	−0.601743	−	0.437192i
$996$	25.6879	+	15.8265i	0.813952	+	0.501481i
$997$	4.82347	−	14.8451i	0.152761	−	0.470149i	−0.845166	−	0.534503i	$-0.820499\pi$
$997$	4.82347	−	14.8451i	0.152761	−	0.470149i	0.997927	+	0.0643542i	$0.0204987\pi$
$998$	18.9178	−	40.9068i	0.598833	−	1.29488i
$999$	−5.51214	−	7.58682i	−0.174397	−	0.240036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.z.b.19.1	✓	48
3.2	odd	2		792.2.bp.d.19.12		48
4.3	odd	2		1056.2.bp.a.943.4		48
8.3	odd	2	inner	264.2.z.b.19.7	yes	48
8.5	even	2		1056.2.bp.a.943.9		48
11.7	odd	10	inner	264.2.z.b.139.7	yes	48
24.11	even	2		792.2.bp.d.19.6		48
33.29	even	10		792.2.bp.d.667.6		48
44.7	even	10		1056.2.bp.a.271.9		48
88.29	odd	10		1056.2.bp.a.271.4		48
88.51	even	10	inner	264.2.z.b.139.1	yes	48
264.227	odd	10		792.2.bp.d.667.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.1	✓	48	1.1	even	1	trivial
264.2.z.b.19.7	yes	48	8.3	odd	2	inner
264.2.z.b.139.1	yes	48	88.51	even	10	inner
264.2.z.b.139.7	yes	48	11.7	odd	10	inner
792.2.bp.d.19.6		48	24.11	even	2
792.2.bp.d.19.12		48	3.2	odd	2
792.2.bp.d.667.6		48	33.29	even	10
792.2.bp.d.667.12		48	264.227	odd	10
1056.2.bp.a.271.4		48	88.29	odd	10
1056.2.bp.a.271.9		48	44.7	even	10
1056.2.bp.a.943.4		48	4.3	odd	2
1056.2.bp.a.943.9		48	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40421 - 0.167908i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.94361 + 0.471557i) q^{4} +(-1.03968 + 1.43099i) q^{5} +(0.274235 + 1.38737i) q^{6} +(-0.430909 + 1.32620i) q^{7} +(-2.65006 - 0.988513i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.70020 - 1.83484i) q^{10} +(-2.97889 - 1.45816i) q^{11} +(-0.152133 - 1.99421i) q^{12} +(-2.66400 + 1.93551i) q^{13} +(0.827766 - 1.78991i) q^{14} +(1.68223 + 0.546590i) q^{15} +(3.55527 + 1.83305i) q^{16} +(-2.21773 + 3.05245i) q^{17} +(1.23472 - 0.689534i) q^{18} +(-0.399566 + 0.129827i) q^{19} +(-2.69552 + 2.29103i) q^{20} +1.39445 q^{21} +(3.93815 + 2.54775i) q^{22} +1.44940i q^{23} +(-0.121217 + 2.82583i) q^{24} +(0.578275 + 1.77975i) q^{25} +(4.06581 - 2.27056i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.46290 + 2.37442i) q^{28} +(-2.45128 + 7.54427i) q^{29} +(-2.27043 - 1.04999i) q^{30} +(0.816325 + 1.12358i) q^{31} +(-4.68456 - 3.17094i) q^{32} +(-0.466268 + 3.28369i) q^{33} +(3.62669 - 3.91390i) q^{34} +(-1.44978 - 1.99544i) q^{35} +(-1.84959 + 0.760930i) q^{36} +(-8.91884 - 2.89791i) q^{37} +(0.582873 - 0.115214i) q^{38} +(2.66400 + 1.93551i) q^{39} +(4.16976 - 2.76449i) q^{40} +(3.29058 - 1.06918i) q^{41} +(-1.95810 - 0.234139i) q^{42} -3.60336i q^{43} +(-5.10220 - 4.23882i) q^{44} -1.76880i q^{45} +(0.243367 - 2.03527i) q^{46} +(-0.727433 + 0.236357i) q^{47} +(0.644694 - 3.94770i) q^{48} +(4.08999 + 2.97155i) q^{49} +(-0.513186 - 2.59624i) q^{50} +(3.58836 + 1.16593i) q^{51} +(-6.09050 + 2.50566i) q^{52} +(2.54374 + 3.50116i) q^{53} +(-1.03734 - 0.961215i) q^{54} +(5.18369 - 2.74674i) q^{55} +(2.45290 - 3.08856i) q^{56} +(0.246945 + 0.339891i) q^{57} +(4.70886 - 10.1821i) q^{58} +(3.69578 - 11.3745i) q^{59} +(3.01186 + 1.85563i) q^{60} +(-8.45451 - 6.14256i) q^{61} +(-0.957635 - 1.71480i) q^{62} +(-0.430909 - 1.32620i) q^{63} +(6.04568 + 5.23925i) q^{64} -5.82447i q^{65} +(1.20610 - 4.53270i) q^{66} +9.95011 q^{67} +(-5.74981 + 4.88699i) q^{68} +(1.37846 - 0.447890i) q^{69} +(1.70074 + 3.04545i) q^{70} +(7.57332 - 10.4238i) q^{71} +(2.72498 - 0.757945i) q^{72} +(-9.14630 - 2.97181i) q^{73} +(12.0373 + 5.56681i) q^{74} +(1.51394 - 1.09994i) q^{75} +(-0.837822 + 0.0639152i) q^{76} +(3.21744 - 3.32227i) q^{77} +(-3.41583 - 3.16518i) q^{78} +(-4.69761 + 3.41302i) q^{79} +(-6.31940 + 3.18178i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.80020 + 0.948832i) q^{82} +(-8.86730 + 12.2048i) q^{83} +(2.71027 + 0.657562i) q^{84} +(-2.06230 - 6.34711i) q^{85} +(-0.605033 + 5.05987i) q^{86} +7.93251 q^{87} +(6.45283 + 6.80889i) q^{88} +10.9210 q^{89} +(-0.296996 + 2.48377i) q^{90} +(-1.41893 - 4.36703i) q^{91} +(-0.683476 + 2.81708i) q^{92} +(0.816325 - 1.12358i) q^{93} +(1.06116 - 0.209753i) q^{94} +(0.229638 - 0.706752i) q^{95} +(-1.56814 + 5.43516i) q^{96} +(-11.2144 + 8.14771i) q^{97} +(-5.24426 - 4.85943i) q^{98} +(3.26706 - 0.571268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{3} + 4 q^{4} - 12 q^{9} + 4 q^{11} + 6 q^{12} - 16 q^{14} + 20 q^{16} - 5 q^{18} + 25 q^{20} + 3 q^{22} + 20 q^{24} - 4 q^{25} + 4 q^{26} + 12 q^{27} - 25 q^{28} - 10 q^{30} - 4 q^{33} + 4 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 48 * q + 12 * q^3 + 4 * q^4 - 12 * q^9 + 4 * q^11 + 6 * q^12 - 16 * q^14 + 20 * q^16 - 5 * q^18 + 25 * q^20 + 3 * q^22 + 20 * q^24 - 4 * q^25 + 4 * q^26 + 12 * q^27 - 25 * q^28 - 10 * q^30 - 4 * q^33 + 4 * q^36 + 26 * q^38 - 65 * q^40 - 60 * q^41 - 4 * q^42 - 43 * q^44 - 5 * q^46 + 5 * q^48 - 12 * q^49 - 80 * q^50 - 15 * q^52 - 14 * q^56 + 73 * q^58 - 8 * q^59 - 25 * q^60 - 45 * q^62 - 38 * q^64 - 13 * q^66 + 8 * q^67 - 55 * q^68 - 40 * q^70 + 20 * q^72 + 60 * q^74 - 36 * q^75 + 46 * q^78 - 12 * q^81 - 35 * q^82 - 100 * q^83 + 45 * q^84 + 81 * q^86 - 18 * q^88 + 96 * q^89 + 10 * q^90 - 20 * q^91 + 59 * q^92 + 35 * q^94 - 40 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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