LMFDB - Embedded newform 234.2.y.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (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			11.3
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.04058 + 1.38462i) q^{3} -1.00000i q^{4} +(1.51706 + 0.406496i) q^{5} +(-0.243274 - 1.71488i) q^{6} +(4.52587 + 1.21270i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.834373 - 2.88164i) q^{9} +(-1.36016 + 0.785290i) q^{10} +(-1.08184 - 1.08184i) q^{11} +(1.38462 + 1.04058i) q^{12} +(-1.01269 + 3.46041i) q^{13} +(-4.05778 + 2.34276i) q^{14} +(-2.14148 + 1.67757i) q^{15} -1.00000 q^{16} +(-2.99188 + 5.18209i) q^{17} +(2.62761 + 1.44763i) q^{18} +(5.70943 - 1.52984i) q^{19} +(0.406496 - 1.51706i) q^{20} +(-6.38869 + 5.00471i) q^{21} +1.52995 q^{22} +(-2.48702 + 4.30764i) q^{23} +(-1.71488 + 0.243274i) q^{24} +(-2.19388 - 1.26664i) q^{25} +(-1.73080 - 3.16296i) q^{26} +(4.85822 + 1.84329i) q^{27} +(1.21270 - 4.52587i) q^{28} -6.86939i q^{29} +(0.328030 - 2.70047i) q^{30} +(-0.271305 + 1.01253i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.62369 - 0.372198i) q^{33} +(-1.54871 - 5.77988i) q^{34} +(6.37308 + 3.67950i) q^{35} +(-2.88164 + 0.834373i) q^{36} +(-6.94881 - 1.86193i) q^{37} +(-2.95542 + 5.11893i) q^{38} +(-3.73759 - 5.00304i) q^{39} +(0.785290 + 1.36016i) q^{40} +(1.34176 + 5.00750i) q^{41} +(0.978615 - 8.05635i) q^{42} +(10.6164 - 6.12935i) q^{43} +(-1.08184 + 1.08184i) q^{44} +(-0.0944233 - 4.71079i) q^{45} +(-1.28737 - 4.80455i) q^{46} +(6.14146 - 1.64560i) q^{47} +(1.04058 - 1.38462i) q^{48} +(12.9507 + 7.47708i) q^{49} +(2.44696 - 0.655661i) q^{50} +(-4.06195 - 9.53504i) q^{51} +(3.46041 + 1.01269i) q^{52} -2.78130i q^{53} +(-4.73868 + 2.13188i) q^{54} +(-1.20146 - 2.08099i) q^{55} +(2.34276 + 4.05778i) q^{56} +(-3.82288 + 9.49734i) q^{57} +(4.85740 + 4.85740i) q^{58} +(-4.22367 - 4.22367i) q^{59} +(1.67757 + 2.14148i) q^{60} +(-2.18623 - 3.78666i) q^{61} +(-0.524122 - 0.907805i) q^{62} +(-0.281694 - 14.0538i) q^{63} +1.00000i q^{64} +(-2.94296 + 4.83801i) q^{65} +(-1.59205 + 2.11841i) q^{66} +(-5.41695 + 1.45147i) q^{67} +(5.18209 + 2.99188i) q^{68} +(-3.37652 - 7.92604i) q^{69} +(-7.10824 + 1.90465i) q^{70} +(0.0745019 + 0.278045i) q^{71} +(1.44763 - 2.62761i) q^{72} +(0.964880 - 0.964880i) q^{73} +(6.23013 - 3.59697i) q^{74} +(4.03674 - 1.71966i) q^{75} +(-1.52984 - 5.70943i) q^{76} +(-3.58432 - 6.20823i) q^{77} +(6.18056 + 0.894812i) q^{78} +(-0.0673941 + 0.116730i) q^{79} +(-1.51706 - 0.406496i) q^{80} +(-7.60764 + 4.80872i) q^{81} +(-4.48960 - 2.59207i) q^{82} +(-3.00217 - 11.2043i) q^{83} +(5.00471 + 6.38869i) q^{84} +(-6.64538 + 6.64538i) q^{85} +(-3.17279 + 11.8410i) q^{86} +(9.51153 + 7.14818i) q^{87} -1.52995i q^{88} +(1.46167 - 5.45501i) q^{89} +(3.39780 + 3.26427i) q^{90} +(-8.77976 + 14.4333i) q^{91} +(4.30764 + 2.48702i) q^{92} +(-1.11965 - 1.42927i) q^{93} +(-3.17905 + 5.50628i) q^{94} +9.28344 q^{95} +(0.243274 + 1.71488i) q^{96} +(-1.72699 + 6.44523i) q^{97} +(-14.4446 + 3.87042i) q^{98} +(-2.21481 + 4.02013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.04058	+	1.38462i	−0.600781	+	0.799414i
$3$	−1.04058	+	1.38462i	−0.600781	+	0.799414i
$4$		−	1.00000i		−	0.500000i
$5$	1.51706	+	0.406496i	0.678452	+	0.181791i	0.581559	−	0.813504i	$-0.302443\pi$
$5$	1.51706	+	0.406496i	0.678452	+	0.181791i	0.0968927	+	0.995295i	$0.469110\pi$
$6$	−0.243274	−	1.71488i	−0.0993163	−	0.700097i
$7$	4.52587	+	1.21270i	1.71062	+	0.458359i	0.975576	−	0.219662i	$-0.0704955\pi$
$7$	4.52587	+	1.21270i	1.71062	+	0.458359i	0.735042	+	0.678021i	$0.237162\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.834373	−	2.88164i	−0.278124	−	0.960545i
$10$	−1.36016	+	0.785290i	−0.430121	+	0.248331i
$11$	−1.08184	−	1.08184i	−0.326187	−	0.326187i	0.524947	−	0.851135i	$-0.324085\pi$
$11$	−1.08184	−	1.08184i	−0.326187	−	0.326187i	−0.851135	+	0.524947i	$0.824085\pi$
$12$	1.38462	+	1.04058i	0.399707	+	0.300391i
$13$	−1.01269	+	3.46041i	−0.280869	+	0.959746i
$13$	−1.01269	+	3.46041i	−0.280869	+	0.959746i
$14$	−4.05778	+	2.34276i	−1.08449	+	0.626130i
$15$	−2.14148	+	1.67757i	−0.552927	+	0.433147i
$16$	−1.00000			−0.250000
$17$	−2.99188	+	5.18209i	−0.725638	+	1.25684i	0.233072	+	0.972459i	$0.425122\pi$
$17$	−2.99188	+	5.18209i	−0.725638	+	1.25684i	−0.958711	+	0.284383i	$0.908211\pi$
$18$	2.62761	+	1.44763i	0.619335	+	0.341210i
$19$	5.70943	−	1.52984i	1.30983	−	0.350968i	0.464673	−	0.885483i	$-0.346172\pi$
$19$	5.70943	−	1.52984i	1.30983	−	0.350968i	0.845160	+	0.534514i	$0.179505\pi$
$20$	0.406496	−	1.51706i	0.0908953	−	0.339226i
$21$	−6.38869	+	5.00471i	−1.39413	+	1.09212i
$22$	1.52995			0.326187
$23$	−2.48702	+	4.30764i	−0.518579	+	0.898204i	0.481188	+	0.876617i	$0.340205\pi$
$23$	−2.48702	+	4.30764i	−0.518579	+	0.898204i	−0.999767	+	0.0215873i	$0.993128\pi$
$24$	−1.71488	+	0.243274i	−0.350049	+	0.0496581i
$25$	−2.19388	−	1.26664i	−0.438777	−	0.253328i
$26$	−1.73080	−	3.16296i	−0.339438	−	0.620308i
$27$	4.85822	+	1.84329i	0.934965	+	0.354741i
$28$	1.21270	−	4.52587i	0.229179	−	0.855309i
$29$		−	6.86939i		−	1.27561i	−0.770196	−	0.637807i	$-0.779842\pi$
$29$		−	6.86939i		−	1.27561i	0.770196	−	0.637807i	$-0.220158\pi$
$30$	0.328030	−	2.70047i	0.0598898	−	0.493037i
$31$	−0.271305	+	1.01253i	−0.0487279	+	0.181855i	−0.986001	−	0.166742i	$-0.946675\pi$
$31$	−0.271305	+	1.01253i	−0.0487279	+	0.181855i	0.937273	+	0.348597i	$0.113342\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.62369	−	0.372198i	0.456726	−	0.0647914i
$34$	−1.54871	−	5.77988i	−0.265602	−	0.991240i
$35$	6.37308	+	3.67950i	1.07725	+	0.621949i
$36$	−2.88164	+	0.834373i	−0.480273	+	0.139062i
$37$	−6.94881	−	1.86193i	−1.14238	−	0.306099i	−0.362471	−	0.931995i	$-0.618067\pi$
$37$	−6.94881	−	1.86193i	−1.14238	−	0.306099i	−0.779906	+	0.625896i	$0.784733\pi$
$38$	−2.95542	+	5.11893i	−0.479432	+	0.830400i
$39$	−3.73759	−	5.00304i	−0.598493	−	0.801128i
$40$	0.785290	+	1.36016i	0.124165	+	0.215061i
$41$	1.34176	+	5.00750i	0.209547	+	0.782040i	0.988015	+	0.154356i	$0.0493303\pi$
$41$	1.34176	+	5.00750i	0.209547	+	0.782040i	−0.778468	+	0.627684i	$0.784003\pi$
$42$	0.978615	−	8.05635i	0.151004	−	1.24312i
$43$	10.6164	−	6.12935i	1.61898	−	0.934718i	0.631794	−	0.775137i	$-0.282319\pi$
$43$	10.6164	−	6.12935i	1.61898	−	0.934718i	0.987185	−	0.159581i	$-0.0510143\pi$
$44$	−1.08184	+	1.08184i	−0.163094	+	0.163094i
$45$	−0.0944233	−	4.71079i	−0.0140758	−	0.702244i
$46$	−1.28737	−	4.80455i	−0.189813	−	0.708392i
$47$	6.14146	−	1.64560i	0.895823	−	0.240035i	0.218602	−	0.975814i	$-0.429850\pi$
$47$	6.14146	−	1.64560i	0.895823	−	0.240035i	0.677222	+	0.735779i	$0.263184\pi$
$48$	1.04058	−	1.38462i	0.150195	−	0.199853i
$49$	12.9507	+	7.47708i	1.85010	+	1.06815i
$50$	2.44696	−	0.655661i	0.346052	−	0.0927244i
$51$	−4.06195	−	9.53504i	−0.568787	−	1.33517i
$52$	3.46041	+	1.01269i	0.479873	+	0.140435i
$53$		−	2.78130i		−	0.382041i	−0.981586	−	0.191021i	$-0.938820\pi$
$53$		−	2.78130i		−	0.382041i	0.981586	−	0.191021i	$-0.0611798\pi$
$54$	−4.73868	+	2.13188i	−0.644853	+	0.290112i
$55$	−1.20146	−	2.08099i	−0.162005	−	0.280600i
$56$	2.34276	+	4.05778i	0.313065	+	0.542244i
$57$	−3.82288	+	9.49734i	−0.506353	+	1.25795i
$58$	4.85740	+	4.85740i	0.637807	+	0.637807i
$59$	−4.22367	−	4.22367i	−0.549875	−	0.549875i	0.376529	−	0.926405i	$-0.377117\pi$
$59$	−4.22367	−	4.22367i	−0.549875	−	0.549875i	−0.926405	+	0.376529i	$0.877117\pi$
$60$	1.67757	+	2.14148i	0.216574	+	0.276463i
$61$	−2.18623	−	3.78666i	−0.279918	−	0.484833i	0.691446	−	0.722428i	$-0.256974\pi$
$61$	−2.18623	−	3.78666i	−0.279918	−	0.484833i	−0.971364	+	0.237596i	$0.923641\pi$
$62$	−0.524122	−	0.907805i	−0.0665635	−	0.115291i
$63$	−0.281694	−	14.0538i	−0.0354901	−	1.77061i
$64$			1.00000i			0.125000i
$65$	−2.94296	+	4.83801i	−0.365029	+	0.600082i
$66$	−1.59205	+	2.11841i	−0.195967	+	0.260759i
$67$	−5.41695	+	1.45147i	−0.661785	+	0.177325i	−0.574052	−	0.818819i	$-0.694629\pi$
$67$	−5.41695	+	1.45147i	−0.661785	+	0.177325i	−0.0877337	+	0.996144i	$0.527962\pi$
$68$	5.18209	+	2.99188i	0.628421	+	0.362819i
$69$	−3.37652	−	7.92604i	−0.406485	−	0.954183i
$70$	−7.10824	+	1.90465i	−0.849598	+	0.227649i
$71$	0.0745019	+	0.278045i	0.00884175	+	0.0329979i	0.970206	−	0.242282i	$-0.0778960\pi$
$71$	0.0745019	+	0.278045i	0.00884175	+	0.0329979i	−0.961364	+	0.275280i	$0.911229\pi$
$72$	1.44763	−	2.62761i	0.170605	−	0.309667i
$73$	0.964880	−	0.964880i	0.112931	−	0.112931i	−0.648383	−	0.761314i	$-0.724555\pi$
$73$	0.964880	−	0.964880i	0.112931	−	0.112931i	0.761314	+	0.648383i	$0.224555\pi$
$74$	6.23013	−	3.59697i	0.724238	−	0.418139i
$75$	4.03674	−	1.71966i	0.466122	−	0.198569i
$76$	−1.52984	−	5.70943i	−0.175484	−	0.654916i
$77$	−3.58432	−	6.20823i	−0.408471	−	0.707493i
$78$	6.18056	+	0.894812i	0.699811	+	0.101318i
$79$	−0.0673941	+	0.116730i	−0.00758243	+	0.0131331i	−0.869792	−	0.493419i	$-0.835747\pi$
$79$	−0.0673941	+	0.116730i	−0.00758243	+	0.0131331i	0.862209	+	0.506552i	$0.169080\pi$
$80$	−1.51706	−	0.406496i	−0.169613	−	0.0454476i
$81$	−7.60764	+	4.80872i	−0.845294	+	0.534302i
$82$	−4.48960	−	2.59207i	−0.495794	−	0.286247i
$83$	−3.00217	−	11.2043i	−0.329531	−	1.22983i	−0.909678	−	0.415314i	$-0.863672\pi$
$83$	−3.00217	−	11.2043i	−0.329531	−	1.22983i	0.580147	−	0.814512i	$-0.302995\pi$
$84$	5.00471	+	6.38869i	0.546059	+	0.697063i
$85$	−6.64538	+	6.64538i	−0.720793	+	0.720793i
$86$	−3.17279	+	11.8410i	−0.342130	+	1.27685i
$87$	9.51153	+	7.14818i	1.01974	+	0.766365i
$88$		−	1.52995i		−	0.163094i
$89$	1.46167	−	5.45501i	0.154936	−	0.578230i	−0.844175	−	0.536068i	$-0.819909\pi$
$89$	1.46167	−	5.45501i	0.154936	−	0.578230i	0.999111	−	0.0421616i	$-0.0134244\pi$
$90$	3.39780	+	3.26427i	0.358160	+	0.344084i
$91$	−8.77976	+	14.4333i	−0.920368	+	1.51302i
$92$	4.30764	+	2.48702i	0.449102	+	0.259289i
$93$	−1.11965	−	1.42927i	−0.116103	−	0.148209i
$94$	−3.17905	+	5.50628i	−0.327894	+	0.567929i
$95$	9.28344			0.952461
$96$	0.243274	+	1.71488i	0.0248291	+	0.175024i
$97$	−1.72699	+	6.44523i	−0.175350	+	0.654414i	0.821142	+	0.570724i	$0.193337\pi$
$97$	−1.72699	+	6.44523i	−0.175350	+	0.654414i	−0.996492	+	0.0836903i	$0.973329\pi$
$98$	−14.4446	+	3.87042i	−1.45913	+	0.390972i
$99$	−2.21481	+	4.02013i	−0.222597	+	0.404038i
$100$	−1.26664	+	2.19388i	−0.126664	+	0.219388i
$101$	7.65990			0.762188			0.381094	−	0.924536i	$-0.375547\pi$
$101$	7.65990			0.762188			0.381094	+	0.924536i	$0.375547\pi$
$102$	9.61452	+	3.87006i	0.951980	+	0.383193i
$103$	−2.46359	+	1.42235i	−0.242744	+	0.140149i	−0.616437	−	0.787404i	$-0.711425\pi$
$103$	−2.46359	+	1.42235i	−0.242744	+	0.140149i	0.373693	+	0.927552i	$0.378091\pi$
$104$	−3.16296	+	1.73080i	−0.310154	+	0.169719i
$105$	−11.7264	+	4.99550i	−1.14438	+	0.487511i
$106$	1.96668	+	1.96668i	0.191021	+	0.191021i
$107$	14.7551	−	8.51888i	1.42643	−	0.823551i	0.429595	−	0.903022i	$-0.358656\pi$
$107$	14.7551	−	8.51888i	1.42643	−	0.823551i	0.996837	+	0.0794704i	$0.0253229\pi$
$108$	1.84329	−	4.85822i	0.177371	−	0.467482i
$109$	−1.44362	−	1.44362i	−0.138274	−	0.138274i	0.634582	−	0.772856i	$-0.281172\pi$
$109$	−1.44362	−	1.44362i	−0.138274	−	0.138274i	−0.772856	+	0.634582i	$0.781172\pi$
$110$	2.32104	+	0.621920i	0.221302	+	0.0592978i
$111$	9.80888	−	7.68400i	0.931018	−	0.729333i
$112$	−4.52587	−	1.21270i	−0.427655	−	0.114590i
$113$		−	8.31066i		−	0.781802i	−0.920433	−	0.390901i	$-0.872164\pi$
$113$		−	8.31066i		−	0.781802i	0.920433	−	0.390901i	$-0.127836\pi$
$114$	−4.01244	−	9.41882i	−0.375800	−	0.882153i
$115$	−5.52400	+	5.52400i	−0.515116	+	0.515116i
$116$	−6.86939			−0.637807
$117$	10.8166	+	0.0309261i	0.999996	+	0.00285912i
$118$	5.97318			0.549875
$119$	−19.8252	+	19.8252i	−1.81738	+	1.81738i
$120$	−2.70047	−	0.328030i	−0.246518	−	0.0299449i
$121$		−	8.65924i		−	0.787204i
$122$	4.22347	+	1.13168i	0.382375	+	0.102457i
$123$	−8.32972	−	3.35289i	−0.751065	−	0.302320i
$124$	1.01253	+	0.271305i	0.0909275	+	0.0243639i
$125$	−8.36622	−	8.36622i	−0.748297	−	0.748297i
$126$	10.1367	+	9.73832i	0.903048	+	0.867558i
$127$	−10.0790	+	5.81914i	−0.894371	+	0.516365i	−0.875370	−	0.483454i	$-0.839382\pi$
$127$	−10.0790	+	5.81914i	−0.894371	+	0.516365i	−0.0190013	+	0.999819i	$0.506049\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−2.56034	+	21.0778i	−0.225426	+	1.85579i
$130$	−1.34001	−	5.50198i	−0.117526	−	0.482555i
$131$	4.72499	−	2.72798i	0.412825	−	0.238344i	−0.279178	−	0.960239i	$-0.590062\pi$
$131$	4.72499	−	2.72798i	0.412825	−	0.238344i	0.692003	+	0.721895i	$0.256729\pi$
$132$	−0.372198	−	2.62369i	−0.0323957	−	0.228363i
$133$	27.6954			2.40149
$134$	2.80402	−	4.85670i	0.242230	−	0.419555i
$135$	6.62094	+	4.77123i	0.569840	+	0.410642i
$136$	−5.77988	+	1.54871i	−0.495620	+	0.132801i
$137$	0.379002	−	1.41446i	0.0323803	−	0.120845i	−0.947844	−	0.318735i	$-0.896742\pi$
$137$	0.379002	−	1.41446i	0.0323803	−	0.120845i	0.980224	+	0.197890i	$0.0634088\pi$
$138$	7.99211	+	3.21700i	0.680334	+	0.273849i
$139$	−7.49403			−0.635636			−0.317818	−	0.948152i	$-0.602950\pi$
$139$	−7.49403			−0.635636			−0.317818	+	0.948152i	$0.602950\pi$
$140$	3.67950	−	6.37308i	0.310974	−	0.538623i
$141$	−4.11216	+	10.2160i	−0.346306	+	0.860342i
$142$	−0.249288	−	0.143927i	−0.0209198	−	0.0120781i
$143$	4.83919	−	2.64805i	0.404673	−	0.221441i
$144$	0.834373	+	2.88164i	0.0695311	+	0.240136i
$145$	2.79238	−	10.4213i	0.231895	−	0.865443i
$146$			1.36455i			0.112931i
$147$	−23.8292	+	10.1513i	−1.96540	+	0.837266i
$148$	−1.86193	+	6.94881i	−0.153049	+	0.571188i
$149$	−0.424349	+	0.424349i	−0.0347641	+	0.0347641i	−0.724275	−	0.689511i	$-0.757825\pi$
$149$	−0.424349	+	0.424349i	−0.0347641	+	0.0347641i	0.689511	+	0.724275i	$0.257825\pi$
$150$	−1.63842	+	4.07039i	−0.133776	+	0.332346i
$151$	0.470936	+	1.75756i	0.0383242	+	0.143028i	0.982437	−	0.186595i	$-0.0597451\pi$
$151$	0.470936	+	1.75756i	0.0383242	+	0.143028i	−0.944113	+	0.329623i	$0.893078\pi$
$152$	5.11893	+	2.95542i	0.415200	+	0.239716i
$153$	17.4293	+	4.29772i	1.40907	+	0.347450i
$154$	6.92438	+	1.85538i	0.557982	+	0.149511i
$155$	−0.823175	+	1.42578i	−0.0661190	+	0.114521i
$156$	−5.00304	+	3.73759i	−0.400564	+	0.299246i
$157$	−1.01577	−	1.75937i	−0.0810676	−	0.140413i	0.822641	−	0.568561i	$-0.192500\pi$
$157$	−1.01577	−	1.75937i	−0.0810676	−	0.140413i	−0.903709	+	0.428148i	$0.859166\pi$
$158$	−0.0348857	−	0.130195i	−0.00277536	−	0.0103578i
$159$	3.85106	+	2.89418i	0.305409	+	0.229523i
$160$	1.36016	−	0.785290i	0.107530	−	0.0620826i
$161$	−16.4798	+	16.4798i	−1.29879	+	1.29879i
$162$	1.97914	−	8.77969i	0.155496	−	0.689798i
$163$	−2.35591	−	8.79238i	−0.184529	−	0.688672i	−0.994731	−	0.102521i	$-0.967309\pi$
$163$	−2.35591	−	8.79238i	−0.184529	−	0.688672i	0.810202	−	0.586151i	$-0.199358\pi$
$164$	5.00750	−	1.34176i	0.391020	−	0.104774i
$165$	4.13160	+	0.501871i	0.321645	+	0.0390706i
$166$	10.0455	+	5.79975i	0.779679	+	0.450148i
$167$	3.61344	−	0.968219i	0.279617	−	0.0749231i	−0.116285	−	0.993216i	$-0.537099\pi$
$167$	3.61344	−	0.968219i	0.279617	−	0.0749231i	0.395902	+	0.918293i	$0.370432\pi$
$168$	−8.05635	−	0.978615i	−0.621561	−	0.0755018i
$169$	−10.9489	−	7.00865i	−0.842225	−	0.539127i
$170$		−	9.39799i		−	0.720793i
$171$	−9.17222	−	15.1760i	−0.701417	−	1.16054i
$172$	−6.12935	−	10.6164i	−0.467359	−	0.809489i
$173$	0.507126	+	0.878368i	0.0385561	+	0.0667811i	0.884659	−	0.466238i	$-0.154391\pi$
$173$	0.507126	+	0.878368i	0.0385561	+	0.0667811i	−0.846103	+	0.533019i	$0.821058\pi$
$174$	−11.7802	+	1.67115i	−0.893054	+	0.126689i
$175$	−8.39317	−	8.39317i	−0.634464	−	0.634464i
$176$	1.08184	+	1.08184i	0.0815468	+	0.0815468i
$177$	10.2433	−	1.45312i	0.769933	−	0.109223i
$178$	2.82372	+	4.89083i	0.211647	+	0.366583i
$179$	11.6793	+	20.2291i	0.872951	+	1.51200i	0.858930	+	0.512094i	$0.171130\pi$
$179$	11.6793	+	20.2291i	0.872951	+	1.51200i	0.0140213	+	0.999902i	$0.495537\pi$
$180$	−4.71079	+	0.0944233i	−0.351122	+	0.00703790i
$181$			8.51778i			0.633122i	0.948572	+	0.316561i	$0.102528\pi$
$181$			8.51778i			0.633122i	−0.948572	+	0.316561i	$0.897472\pi$
$182$	−3.99765	−	16.4141i	−0.296326	−	1.21669i
$183$	7.51806	+	0.913228i	0.555751	+	0.0675078i
$184$	−4.80455	+	1.28737i	−0.354196	+	0.0949065i
$185$	−9.78492	−	5.64933i	−0.719401	−	0.415347i
$186$	1.80236	+	0.218935i	0.132156	+	0.0160531i
$187$	8.84295	−	2.36946i	0.646660	−	0.173272i
$188$	−1.64560	−	6.14146i	−0.120018	−	0.447912i
$189$	19.7523	+	14.2341i	1.43677	+	1.03538i
$190$	−6.56438	+	6.56438i	−0.476230	+	0.476230i
$191$	13.5364	−	7.81525i	0.979461	−	0.565492i	0.0773534	−	0.997004i	$-0.475353\pi$
$191$	13.5364	−	7.81525i	0.979461	−	0.565492i	0.902107	+	0.431512i	$0.142020\pi$
$192$	−1.38462	−	1.04058i	−0.0999267	−	0.0750976i
$193$	−4.09187	−	15.2711i	−0.294540	−	1.09924i	−0.941582	−	0.336783i	$-0.890661\pi$
$193$	−4.09187	−	15.2711i	−0.294540	−	1.09924i	0.647043	−	0.762454i	$-0.276005\pi$
$194$	−3.33630	−	5.77864i	−0.239532	−	0.414882i
$195$	−3.63644	−	9.10925i	−0.260411	−	0.652327i
$196$	7.47708	−	12.9507i	0.534077	−	0.925049i
$197$	−13.3907	−	3.58802i	−0.954045	−	0.255635i	−0.251967	−	0.967736i	$-0.581077\pi$
$197$	−13.3907	−	3.58802i	−0.954045	−	0.255635i	−0.702078	+	0.712100i	$0.747744\pi$
$198$	−1.27655	−	4.40877i	−0.0907206	−	0.313318i
$199$	−10.8199	−	6.24687i	−0.767002	−	0.442829i	0.0648021	−	0.997898i	$-0.479358\pi$
$199$	−10.8199	−	6.24687i	−0.767002	−	0.442829i	−0.831804	+	0.555069i	$0.812692\pi$
$200$	−0.655661	−	2.44696i	−0.0463622	−	0.173026i
$201$	3.62705	−	9.01081i	0.255832	−	0.635574i
$202$	−5.41637	+	5.41637i	−0.381094	+	0.381094i
$203$	8.33054	−	31.0900i	0.584689	−	2.18209i
$204$	−9.53504	+	4.06195i	−0.667586	+	0.284394i
$205$			8.14212i			0.568670i
$206$	0.736264	−	2.74777i	0.0512979	−	0.191446i
$207$	14.4881	+	3.57250i	1.00700	+	0.248306i
$208$	1.01269	−	3.46041i	0.0702174	−	0.239936i
$209$	−7.83173	−	4.52165i	−0.541732	−	0.312769i
$210$	4.75950	−	11.8242i	0.328436	−	0.815947i
$211$	−3.90948	+	6.77143i	−0.269140	+	0.466164i	−0.968640	−	0.248468i	$-0.920073\pi$
$211$	−3.90948	+	6.77143i	−0.269140	+	0.466164i	0.699500	+	0.714633i	$0.253406\pi$
$212$	−2.78130			−0.191021
$213$	−0.462513	−	0.186172i	−0.0316909	−	0.0127563i
$214$	−4.40970	+	16.4572i	−0.301441	+	1.12499i
$215$	18.5972	−	4.98312i	1.26832	−	0.339846i
$216$	2.13188	+	4.73868i	0.145056	+	0.322426i
$217$	−2.45579	+	4.25355i	−0.166710	+	0.288750i
$218$	2.04159			0.138274
$219$	0.331959	+	2.34004i	0.0224317	+	0.158125i
$220$	−2.08099	+	1.20146i	−0.140300	+	0.0810023i
$221$	−14.9023	−	15.6010i	−1.00244	−	1.04944i
$222$	−1.50252	+	12.3693i	−0.100842	+	0.830176i
$223$	−1.50200	−	1.50200i	−0.100581	−	0.100581i	0.655026	−	0.755607i	$-0.272658\pi$
$223$	−1.50200	−	1.50200i	−0.100581	−	0.100581i	−0.755607	+	0.655026i	$0.772658\pi$
$224$	4.05778	−	2.34276i	0.271122	−	0.156532i
$225$	−1.81948	+	7.37882i	−0.121298	+	0.491921i
$226$	5.87653	+	5.87653i	0.390901	+	0.390901i
$227$	−18.1107	−	4.85274i	−1.20205	−	0.322088i	−0.398411	−	0.917207i	$-0.630438\pi$
$227$	−18.1107	−	4.85274i	−1.20205	−	0.322088i	−0.803637	+	0.595119i	$0.797105\pi$
$228$	9.49734	+	3.82288i	0.628976	+	0.253177i
$229$	21.4410	+	5.74509i	1.41686	+	0.379646i	0.884369	−	0.466789i	$-0.154589\pi$
$229$	21.4410	+	5.74509i	1.41686	+	0.379646i	0.532491	+	0.846436i	$0.321256\pi$
$230$		−	7.81211i		−	0.515116i
$231$	12.3258	+	1.49724i	0.810981	+	0.0985109i
$232$	4.85740	−	4.85740i	0.318904	−	0.318904i
$233$	18.3697			1.20344			0.601721	−	0.798707i	$-0.294482\pi$
$233$	18.3697			1.20344			0.601721	+	0.798707i	$0.294482\pi$
$234$	−7.67037	+	7.62663i	−0.501428	+	0.498568i
$235$	9.98591			0.651409
$236$	−4.22367	+	4.22367i	−0.274938	+	0.274938i
$237$	−0.0914981	−	0.214783i	−0.00594344	−	0.0139516i
$238$		−	28.0371i		−	1.81738i
$239$	8.67535	+	2.32455i	0.561161	+	0.150363i	0.528240	−	0.849095i	$-0.322852\pi$
$239$	8.67535	+	2.32455i	0.561161	+	0.150363i	0.0329216	+	0.999458i	$0.489519\pi$
$240$	2.14148	−	1.67757i	0.138232	−	0.108287i
$241$	−4.08094	−	1.09348i	−0.262876	−	0.0704375i	0.124974	−	0.992160i	$-0.460115\pi$
$241$	−4.08094	−	1.09348i	−0.262876	−	0.0704375i	−0.387850	+	0.921723i	$0.626782\pi$
$242$	6.12301	+	6.12301i	0.393602	+	0.393602i
$243$	1.25812	−	15.5376i	0.0807085	−	0.996738i
$244$	−3.78666	+	2.18623i	−0.242416	+	0.139959i
$245$	16.6076	+	16.6076i	1.06102	+	1.06102i
$246$	8.26085	−	3.51915i	0.526693	−	0.224373i
$247$	−0.488008	+	21.3062i	−0.0310512	+	1.35568i
$248$	−0.907805	+	0.524122i	−0.0576457	+	0.0332818i
$249$	18.6377	+	7.50208i	1.18112	+	0.475425i
$250$	11.8316			0.748297
$251$	0.0344162	−	0.0596107i	0.00217233	−	0.00376259i	−0.864937	−	0.501880i	$-0.832642\pi$
$251$	0.0344162	−	0.0596107i	0.00217233	−	0.00376259i	0.867110	+	0.498118i	$0.165975\pi$
$252$	−14.0538	+	0.281694i	−0.885303	+	0.0177450i
$253$	7.35074	−	1.96962i	0.462137	−	0.123829i
$254$	3.01221	−	11.2417i	0.189003	−	0.705368i
$255$	−2.28629	−	16.1164i	−0.143173	−	1.00925i
$256$	1.00000			0.0625000
$257$	−6.98389	+	12.0965i	−0.435643	+	0.754556i	−0.997348	−	0.0727815i	$-0.976812\pi$
$257$	−6.98389	+	12.0965i	−0.435643	+	0.754556i	0.561705	+	0.827338i	$0.310146\pi$
$258$	−13.0938	−	16.7147i	−0.815184	−	1.04061i
$259$	−29.1914	−	16.8537i	−1.81387	−	1.04724i
$260$	4.83801	+	2.94296i	0.300041	+	0.182515i
$261$	−19.7951	+	5.73163i	−1.22529	+	0.354779i
$262$	−1.41210	+	5.27005i	−0.0872401	+	0.325584i
$263$			23.9692i			1.47800i	0.673705	+	0.739001i	$0.264702\pi$
$263$			23.9692i			1.47800i	−0.673705	+	0.739001i	$0.735298\pi$
$264$	2.11841	+	1.59205i	0.130379	+	0.0979836i
$265$	1.13059	−	4.21942i	0.0694515	−	0.259197i
$266$	−19.5836	+	19.5836i	−1.20075	+	1.20075i
$267$	6.03216	+	7.70025i	0.369162	+	0.471248i
$268$	1.45147	+	5.41695i	0.0886624	+	0.330893i
$269$	−22.7826	−	13.1536i	−1.38908	−	0.801987i	−0.395870	−	0.918307i	$-0.629557\pi$
$269$	−22.7826	−	13.1536i	−1.38908	−	0.801987i	−0.993212	+	0.116320i	$0.962890\pi$
$270$	−8.05548	+	1.30794i	−0.490241	+	0.0795987i
$271$	4.66870	+	1.25097i	0.283603	+	0.0759913i	0.397817	−	0.917465i	$-0.369768\pi$
$271$	4.66870	+	1.25097i	0.283603	+	0.0759913i	−0.114213	+	0.993456i	$0.536435\pi$
$272$	2.99188	−	5.18209i	0.181410	−	0.314211i
$273$	−10.8486	−	27.1757i	−0.656589	−	1.64475i
$274$	0.732176	+	1.26817i	0.0442324	+	0.0766127i
$275$	1.00313	+	3.74374i	0.0604911	+	0.225756i
$276$	−7.92604	+	3.37652i	−0.477092	+	0.203242i
$277$	−12.6229	+	7.28781i	−0.758434	+	0.437882i	−0.828733	−	0.559644i	$-0.810938\pi$
$277$	−12.6229	+	7.28781i	−0.758434	+	0.437882i	0.0702994	+	0.997526i	$0.477605\pi$
$278$	5.29908	−	5.29908i	0.317818	−	0.317818i
$279$	3.14410	−	0.0630204i	0.188232	−	0.00377293i
$280$	1.90465	+	7.10824i	0.113824	+	0.424799i
$281$	−22.2228	+	5.95459i	−1.32570	+	0.355221i	−0.851112	−	0.524985i	$-0.824071\pi$
$281$	−22.2228	+	5.95459i	−1.32570	+	0.355221i	−0.474592	+	0.880206i	$0.657404\pi$
$282$	−4.31606	−	10.1315i	−0.257018	−	0.603324i
$283$	12.4400	+	7.18223i	0.739480	+	0.426939i	0.821880	−	0.569660i	$-0.192925\pi$
$283$	12.4400	+	7.18223i	0.739480	+	0.426939i	−0.0824000	+	0.996599i	$0.526258\pi$
$284$	0.278045	−	0.0745019i	0.0164989	−	0.00442087i
$285$	−9.66019	+	12.8541i	−0.572220	+	0.761410i
$286$	−1.54937	+	5.29427i	−0.0916161	+	0.313057i
$287$			24.2905i			1.43382i
$288$	−2.62761	−	1.44763i	−0.154834	−	0.0853026i
$289$	−9.40274	−	16.2860i	−0.553102	−	0.958001i
$290$	5.39447	+	9.34349i	0.316774	+	0.548669i
$291$	−7.12715	−	9.09804i	−0.417801	−	0.533337i
$292$	−0.964880	−	0.964880i	−0.0564653	−	0.0564653i
$293$	8.61260	+	8.61260i	0.503153	+	0.503153i	0.912416	−	0.409263i	$-0.134214\pi$
$293$	8.61260	+	8.61260i	0.503153	+	0.503153i	−0.409263	+	0.912416i	$0.634214\pi$
$294$	9.67174	−	24.0279i	0.564067	−	1.40133i
$295$	−4.69068	−	8.12449i	−0.273102	−	0.473026i
$296$	−3.59697	−	6.23013i	−0.209069	−	0.362119i
$297$	−3.26168	−	7.24997i	−0.189262	−	0.420686i
$298$		−	0.600121i		−	0.0347641i
$299$	−12.3876	−	12.9684i	−0.716395	−	0.749982i
$300$	−1.71966	−	4.03674i	−0.0992847	−	0.233061i
$301$	55.4813	−	14.8662i	3.19789	−	0.856872i
$302$	−1.57578	−	0.909778i	−0.0906761	−	0.0523519i
$303$	−7.97076	+	10.6061i	−0.457908	+	0.609304i
$304$	−5.70943	+	1.52984i	−0.327458	+	0.0877421i
$305$	−1.77739	−	6.63330i	−0.101773	−	0.379822i
$306$	−15.3633	+	9.28540i	−0.878261	+	0.530811i
$307$	−6.82241	+	6.82241i	−0.389375	+	0.389375i	−0.874465	−	0.485089i	$-0.838787\pi$
$307$	−6.82241	+	6.82241i	−0.389375	+	0.389375i	0.485089	+	0.874465i	$0.338787\pi$
$308$	−6.20823	+	3.58432i	−0.353747	+	0.204236i
$309$	0.594142	−	4.89122i	0.0337996	−	0.278252i
$310$	−0.426107	−	1.59025i	−0.0242012	−	0.0903203i
$311$	7.73754	+	13.4018i	0.438756	+	0.759947i	0.997594	−	0.0693297i	$-0.0220860\pi$
$311$	7.73754	+	13.4018i	0.438756	+	0.759947i	−0.558838	+	0.829277i	$0.688753\pi$
$312$	0.894812	−	6.18056i	0.0506588	−	0.349905i
$313$	13.3960	−	23.2026i	0.757189	−	1.31149i	−0.187090	−	0.982343i	$-0.559906\pi$
$313$	13.3960	−	23.2026i	0.757189	−	1.31149i	0.944279	−	0.329146i	$-0.106761\pi$
$314$	1.96232	+	0.525803i	0.110740	+	0.0296728i
$315$	5.28545	−	21.4350i	0.297801	−	1.20772i
$316$	0.116730	+	0.0673941i	0.00656657	+	0.00379121i
$317$	3.72829	+	13.9142i	0.209402	+	0.781498i	0.988063	+	0.154053i	$0.0492326\pi$
$317$	3.72829	+	13.9142i	0.209402	+	0.781498i	−0.778661	+	0.627445i	$0.784101\pi$
$318$	−4.76961	+	0.676619i	−0.267466	+	0.0379429i
$319$	−7.43159	+	7.43159i	−0.416089	+	0.416089i
$320$	−0.406496	+	1.51706i	−0.0227238	+	0.0848065i
$321$	−3.55849	+	29.2949i	−0.198616	+	1.63508i
$322$		−	23.3060i		−	1.29879i
$323$	−9.15418	+	34.1639i	−0.509352	+	1.90093i
$324$	4.80872	+	7.60764i	0.267151	+	0.422647i
$325$	6.60482	−	6.30903i	0.366369	−	0.349962i
$326$	7.88303	+	4.55127i	0.436601	+	0.252072i
$327$	3.50108	−	0.496666i	0.193610	−	0.0274657i
$328$	−2.59207	+	4.48960i	−0.143123	+	0.247897i
$329$	29.7911			1.64243
$330$	−3.27636	+	2.56661i	−0.180358	+	0.141287i
$331$	−7.95647	+	29.6940i	−0.437327	+	1.63213i	0.298107	+	0.954532i	$0.403645\pi$
$331$	−7.95647	+	29.6940i	−0.437327	+	1.63213i	−0.735435	+	0.677596i	$0.763022\pi$
$332$	−11.2043	+	3.00217i	−0.614913	+	0.164765i
$333$	0.432499	+	21.5775i	0.0237008	+	1.18244i
$334$	−1.87046	+	3.23973i	−0.102347	+	0.177270i
$335$	−8.80787			−0.481225
$336$	6.38869	−	5.00471i	0.348531	−	0.273030i
$337$	−26.0523	+	15.0413i	−1.41916	+	0.819353i	−0.996225	−	0.0868060i	$-0.972334\pi$
$337$	−26.0523	+	15.0413i	−1.41916	+	0.819353i	−0.422936	+	0.906159i	$0.639001\pi$
$338$	12.6979	−	2.78620i	0.690676	−	0.151549i
$339$	11.5072	+	8.64794i	0.624983	+	0.469692i
$340$	6.64538	+	6.64538i	0.360396	+	0.360396i
$341$	1.38890	−	0.801882i	0.0752132	−	0.0434244i
$342$	17.2168	+	4.24534i	0.930979	+	0.229561i
$343$	26.3535	+	26.3535i	1.42295	+	1.42295i
$344$	11.8410	+	3.17279i	0.638424	+	0.171065i
$345$	−1.90049	−	13.3968i	−0.102319	−	0.721262i
$346$	−0.979692	−	0.262508i	−0.0526686	−	0.0141125i
$347$			17.1041i			0.918194i	0.888386	+	0.459097i	$0.151827\pi$
$347$			17.1041i			0.918194i	−0.888386	+	0.459097i	$0.848173\pi$
$348$	7.14818	−	9.51153i	0.383183	−	0.509872i
$349$	−1.97713	+	1.97713i	−0.105833	+	0.105833i	−0.758041	−	0.652207i	$-0.773843\pi$
$349$	−1.97713	+	1.97713i	−0.105833	+	0.105833i	0.652207	+	0.758041i	$0.273843\pi$
$350$	11.8697			0.634464
$351$	−11.2984	+	14.9448i	−0.603064	+	0.797693i
$352$	−1.52995			−0.0815468
$353$	−23.6505	+	23.6505i	−1.25879	+	1.25879i	−0.307119	+	0.951671i	$0.599365\pi$
$353$	−23.6505	+	23.6505i	−1.25879	+	1.25879i	−0.951671	+	0.307119i	$0.900635\pi$
$354$	−6.21559	+	8.27061i	−0.330355	+	0.439578i
$355$			0.452097i			0.0239948i
$356$	−5.45501	−	1.46167i	−0.289115	−	0.0774681i
$357$	−6.82070	−	48.0803i	−0.360990	−	2.54468i
$358$	−22.5626	−	6.04564i	−1.19247	−	0.319522i
$359$	4.06738	+	4.06738i	0.214668	+	0.214668i	0.806247	−	0.591579i	$-0.201495\pi$
$359$	4.06738	+	4.06738i	0.214668	+	0.214668i	−0.591579	+	0.806247i	$0.701495\pi$
$360$	3.26427	−	3.39780i	0.172042	−	0.179080i
$361$	13.8027	−	7.96897i	0.726456	−	0.419420i
$362$	−6.02298	−	6.02298i	−0.316561	−	0.316561i
$363$	11.9898	+	9.01066i	0.629301	+	0.472937i
$364$	14.4333	+	8.77976i	0.756510	+	0.460184i
$365$	1.85601	−	1.07157i	0.0971477	−	0.0560883i
$366$	−5.96182	+	4.67032i	−0.311630	+	0.244122i
$367$	2.87993			0.150331			0.0751656	−	0.997171i	$-0.476051\pi$
$367$	2.87993			0.150331			0.0751656	+	0.997171i	$0.476051\pi$
$368$	2.48702	−	4.30764i	0.129645	−	0.224551i
$369$	13.3103	−	8.04457i	0.692905	−	0.418784i
$370$	10.9137	−	2.92431i	0.567374	−	0.152027i
$371$	3.37290	−	12.5878i	0.175112	−	0.653527i
$372$	−1.42927	+	1.11965i	−0.0741044	+	0.0580513i
$373$	−17.0979			−0.885297			−0.442648	−	0.896695i	$-0.645961\pi$
$373$	−17.0979			−0.885297			−0.442648	+	0.896695i	$0.645961\pi$
$374$	−4.57745	+	7.92837i	−0.236694	+	0.409966i
$375$	20.2898	−	2.87833i	1.04776	−	0.148636i
$376$	5.50628	+	3.17905i	0.283965	+	0.163947i
$377$	23.7709	+	6.95656i	1.22427	+	0.358281i
$378$	−24.0320	+	3.90199i	−1.23607	+	0.200697i
$379$	5.27326	−	19.6801i	0.270869	−	1.01090i	−0.687690	−	0.726004i	$-0.741375\pi$
$379$	5.27326	−	19.6801i	0.270869	−	1.01090i	0.958559	−	0.284893i	$-0.0919581\pi$
$380$		−	9.28344i		−	0.476230i
$381$	2.43076	−	20.0110i	0.124532	−	1.02519i
$382$	−4.04547	+	15.0979i	−0.206984	+	0.772476i
$383$	−11.4042	+	11.4042i	−0.582726	+	0.582726i	−0.935651	−	0.352925i	$-0.885187\pi$
$383$	−11.4042	+	11.4042i	−0.582726	+	0.582726i	0.352925	+	0.935651i	$0.385187\pi$
$384$	1.71488	−	0.243274i	0.0875122	−	0.0124145i
$385$	−2.91402	−	10.8753i	−0.148512	−	0.554256i
$386$	13.6917	+	7.90489i	0.696888	+	0.402348i
$387$	−26.5206	−	25.4783i	−1.34812	−	1.29513i
$388$	6.44523	+	1.72699i	0.327207	+	0.0876749i
$389$	18.1024	−	31.3543i	0.917828	−	1.58972i	0.115121	−	0.993351i	$-0.463274\pi$
$389$	18.1024	−	31.3543i	0.917828	−	1.58972i	0.802707	−	0.596373i	$-0.203392\pi$
$390$	9.01257	+	3.86986i	0.456369	+	0.195958i
$391$	−14.8817	−	25.7759i	−0.752601	−	1.30354i
$392$	3.87042	+	14.4446i	0.195486	+	0.729563i
$393$	−1.13953	+	9.38103i	−0.0574814	+	0.473210i
$394$	12.0057	−	6.93151i	0.604840	−	0.349205i
$395$	−0.149691	+	0.149691i	−0.00753179	+	0.00753179i
$396$	4.02013	+	2.21481i	0.202019	+	0.111299i
$397$	−0.170003	−	0.634461i	−0.00853223	−	0.0318427i	0.961528	−	0.274705i	$-0.0885803\pi$
$397$	−0.170003	−	0.634461i	−0.00853223	−	0.0318427i	−0.970061	+	0.242863i	$0.921914\pi$
$398$	12.0680	−	3.23362i	0.604915	−	0.162087i
$399$	−28.8193	+	38.3477i	−1.44277	+	1.91979i
$400$	2.19388	+	1.26664i	0.109694	+	0.0633319i
$401$	−2.91390	+	0.780777i	−0.145513	+	0.0389902i	−0.330840	−	0.943687i	$-0.607332\pi$
$401$	−2.91390	+	0.780777i	−0.145513	+	0.0389902i	0.185327	+	0.982677i	$0.440666\pi$
$402$	3.80690	+	8.93631i	0.189871	+	0.445703i
$403$	−3.22901	−	1.96420i	−0.160848	−	0.0978439i
$404$		−	7.65990i		−	0.381094i
$405$	−13.4960	+	4.20265i	−0.670622	+	0.208831i
$406$	16.0934	+	27.8745i	0.798700	+	1.38339i
$407$	5.50320	+	9.53181i	0.272783	+	0.472475i
$408$	3.87006	−	9.61452i	0.191596	−	0.475990i
$409$	1.66863	+	1.66863i	0.0825083	+	0.0825083i	0.747156	−	0.664648i	$-0.231419\pi$
$409$	1.66863	+	1.66863i	0.0825083	+	0.0825083i	−0.664648	+	0.747156i	$0.731419\pi$
$410$	−5.75735	−	5.75735i	−0.284335	−	0.284335i
$411$	1.56411	+	1.99663i	0.0771517	+	0.0984867i
$412$	1.42235	+	2.46359i	0.0700743	+	0.121372i
$413$	−13.9937	−	24.2379i	−0.688587	−	1.19267i
$414$	−12.7708	+	7.71852i	−0.627650	+	0.379345i
$415$		−	18.2179i		−	0.894283i
$416$	1.73080	+	3.16296i	0.0848596	+	0.155077i
$417$	7.79817	−	10.3764i	0.381878	−	0.508136i
$418$	8.73516	−	2.34058i	0.427251	−	0.114481i
$419$	−19.7189	−	11.3847i	−0.963333	−	0.556181i	−0.0661358	−	0.997811i	$-0.521067\pi$
$419$	−19.7189	−	11.3847i	−0.963333	−	0.556181i	−0.897197	+	0.441630i	$0.854400\pi$
$420$	4.99550	+	11.7264i	0.243755	+	0.572192i
$421$	−32.9974	+	8.84164i	−1.60820	+	0.430915i	−0.947505	−	0.319742i	$-0.896404\pi$
$421$	−32.9974	+	8.84164i	−1.60820	+	0.430915i	−0.660692	+	0.750657i	$0.729737\pi$
$422$	−2.02370	−	7.55254i	−0.0985121	−	0.367652i
$423$	−9.86628	−	16.3244i	−0.479715	−	0.793719i
$424$	1.96668	−	1.96668i	0.0955104	−	0.0955104i
$425$	13.1277	−	7.57927i	0.636786	−	0.367649i
$426$	0.458690	−	0.195403i	0.0222236	−	0.00946731i
$427$	−5.30250	−	19.7892i	−0.256606	−	0.957666i
$428$	−8.51888	−	14.7551i	−0.411776	−	0.713216i
$429$	−1.36902	+	9.45597i	−0.0660970	+	0.456539i
$430$	−9.62664	+	16.6738i	−0.464238	+	0.804084i
$431$	−6.97762	−	1.86965i	−0.336100	−	0.0900578i	0.0868218	−	0.996224i	$-0.472329\pi$
$431$	−6.97762	−	1.86965i	−0.336100	−	0.0900578i	−0.422922	+	0.906166i	$0.638996\pi$
$432$	−4.85822	−	1.84329i	−0.233741	−	0.0886853i
$433$	16.0208	+	9.24961i	0.769910	+	0.444508i	0.832842	−	0.553510i	$-0.186712\pi$
$433$	16.0208	+	9.24961i	0.769910	+	0.444508i	−0.0629325	+	0.998018i	$0.520045\pi$
$434$	−1.27121	−	4.74421i	−0.0610200	−	0.227730i
$435$	11.5239	+	14.7106i	0.552529	+	0.705321i
$436$	−1.44362	+	1.44362i	−0.0691369	+	0.0691369i
$437$	−7.60945	+	28.3989i	−0.364010	+	1.35850i
$438$	−1.88939	−	1.41992i	−0.0902783	−	0.0678466i
$439$			20.3207i			0.969855i	0.874554	+	0.484927i	$0.161154\pi$
$439$			20.3207i			0.969855i	−0.874554	+	0.484927i	$0.838846\pi$
$440$	0.621920	−	2.32104i	0.0296489	−	0.110651i
$441$	10.7405	−	43.5578i	0.511453	−	2.07418i
$442$	21.5691	+	0.494029i	1.02594	+	0.0234986i
$443$	8.71411	+	5.03109i	0.414020	+	0.239034i	0.692515	−	0.721403i	$-0.256502\pi$
$443$	8.71411	+	5.03109i	0.414020	+	0.239034i	−0.278496	+	0.960437i	$0.589836\pi$
$444$	−7.68400	−	9.80888i	−0.364667	−	0.465509i
$445$	4.43488	−	7.68144i	0.210234	−	0.364135i
$446$	2.12414			0.100581
$447$	−0.145994	−	1.02914i	−0.00690527	−	0.0486764i
$448$	−1.21270	+	4.52587i	−0.0572949	+	0.213827i
$449$	22.3408	−	5.98619i	1.05433	−	0.282506i	0.310288	−	0.950643i	$-0.399574\pi$
$449$	22.3408	−	5.98619i	1.05433	−	0.282506i	0.744039	+	0.668137i	$0.232908\pi$
$450$	−3.93105	−	6.50418i	−0.185311	−	0.306610i
$451$	3.96575	−	6.86889i	0.186740	−	0.323443i
$452$	−8.31066			−0.390901
$453$	−2.92360	−	1.17681i	−0.137363	−	0.0552916i
$454$	16.2376	−	9.37478i	0.762068	−	0.439980i
$455$	−19.1865	+	18.3273i	−0.899478	+	0.859197i
$456$	−9.41882	+	4.01244i	−0.441077	+	0.187900i
$457$	15.7054	+	15.7054i	0.734667	+	0.734667i	0.971540	−	0.236874i	$-0.0761228\pi$
$457$	15.7054	+	15.7054i	0.734667	+	0.734667i	−0.236874	+	0.971540i	$0.576123\pi$
$458$	−19.2235	+	11.0987i	−0.898253	+	0.518607i
$459$	−24.0873	+	19.6608i	−1.12430	+	0.917690i
$460$	5.52400	+	5.52400i	0.257558	+	0.257558i
$461$	23.0977	+	6.18902i	1.07577	+	0.288251i	0.752861	−	0.658180i	$-0.228673\pi$
$461$	23.0977	+	6.18902i	1.07577	+	0.288251i	0.322907	+	0.946431i	$0.395340\pi$
$462$	−9.77440	+	7.65699i	−0.454746	+	0.356235i
$463$	−14.9267	−	3.99959i	−0.693702	−	0.185877i	−0.105294	−	0.994441i	$-0.533578\pi$
$463$	−14.9267	−	3.99959i	−0.693702	−	0.185877i	−0.588408	+	0.808564i	$0.700245\pi$
$464$			6.86939i			0.318904i
$465$	−1.11759	−	2.62343i	−0.0518270	−	0.121659i
$466$	−12.9894	+	12.9894i	−0.601721	+	0.601721i
$467$	−30.0205			−1.38918			−0.694591	−	0.719405i	$-0.744415\pi$
$467$	−30.0205			−1.38918			−0.694591	+	0.719405i	$0.744415\pi$
$468$	0.0309261	−	10.8166i	0.00142956	−	0.499998i
$469$	−26.2766			−1.21334
$470$	−7.06111	+	7.06111i	−0.325705	+	0.325705i
$471$	3.49307	+	0.424307i	0.160952	+	0.0195510i
$472$		−	5.97318i		−	0.274938i
$473$	−18.1162	−	4.85422i	−0.832983	−	0.223197i
$474$	0.216573	+	0.0871755i	0.00994754	+	0.00400410i
$475$	−14.4636	−	3.87550i	−0.663634	−	0.177820i
$476$	19.8252	+	19.8252i	0.908688	+	0.908688i
$477$	−8.01470	+	2.32064i	−0.366968	+	0.106255i
$478$	−7.77810	+	4.49069i	−0.355762	+	0.205399i
$479$	−0.352246	−	0.352246i	−0.0160945	−	0.0160945i	0.699014	−	0.715108i	$-0.253623\pi$
$479$	−0.352246	−	0.352246i	−0.0160945	−	0.0160945i	−0.715108	+	0.699014i	$0.753623\pi$
$480$	−0.328030	+	2.70047i	−0.0149725	+	0.123259i
$481$	13.4800	−	22.1602i	0.614636	−	1.01042i
$482$	3.65887	−	2.11245i	0.166657	−	0.0962194i
$483$	−5.66974	−	39.9669i	−0.257982	−	1.81856i
$484$	−8.65924			−0.393602
$485$	−5.23992	+	9.07581i	−0.237933	+	0.412111i
$486$	10.0971	+	11.8764i	0.458015	+	0.538723i
$487$	22.2998	−	5.97522i	1.01050	−	0.270763i	0.284663	−	0.958628i	$-0.408118\pi$
$487$	22.2998	−	5.97522i	1.01050	−	0.270763i	0.725839	+	0.687865i	$0.241452\pi$
$488$	1.13168	−	4.22347i	0.0512286	−	0.191188i
$489$	14.6257	+	5.88715i	0.661396	+	0.266226i
$490$	−23.4867			−1.06102
$491$	1.59861	−	2.76887i	0.0721442	−	0.124957i	−0.827697	−	0.561176i	$-0.810349\pi$
$491$	1.59861	−	2.76887i	0.0721442	−	0.124957i	0.899841	+	0.436218i	$0.143682\pi$
$492$	−3.35289	+	8.32972i	−0.151160	+	0.375533i
$493$	35.5978	+	20.5524i	1.60325	+	0.925635i
$494$	−14.7207	−	15.4108i	−0.662316	−	0.693367i
$495$	−4.99418	+	5.19848i	−0.224472	+	0.233654i
$496$	0.271305	−	1.01253i	0.0121820	−	0.0454637i
$497$			1.34874i			0.0604994i
$498$	−18.4836	+	7.87407i	−0.828270	+	0.352846i
$499$	8.82459	−	32.9338i	0.395043	−	1.47432i	−0.426664	−	0.904410i	$-0.640311\pi$
$499$	8.82459	−	32.9338i	0.395043	−	1.47432i	0.821707	−	0.569910i	$-0.193022\pi$
$500$	−8.36622	+	8.36622i	−0.374149	+	0.374149i
$501$	−2.41947	+	6.01078i	−0.108094	+	0.268542i
$502$	0.0178152	+	0.0664871i	0.000795129	+	0.00296746i
$503$	−0.778425	−	0.449424i	−0.0347083	−	0.0200388i	0.482545	−	0.875871i	$-0.339712\pi$
$503$	−0.778425	−	0.449424i	−0.0347083	−	0.0200388i	−0.517254	+	0.855832i	$0.673046\pi$
$504$	9.73832	−	10.1367i	0.433779	−	0.451524i
$505$	11.6206	+	3.11372i	0.517108	+	0.138559i
$506$	−3.80502	+	6.59049i	−0.169154	+	0.292983i
$507$	21.0976	−	7.86707i	0.936978	−	0.349389i
$508$	5.81914	+	10.0790i	0.258183	+	0.447185i
$509$	−1.25690	−	4.69081i	−0.0557111	−	0.207917i	0.932460	−	0.361274i	$-0.117658\pi$
$509$	−1.25690	−	4.69081i	−0.0557111	−	0.207917i	−0.988171	+	0.153357i	$0.950991\pi$
$510$	13.0127	+	9.77939i	0.576211	+	0.433039i
$511$	5.53704	−	3.19681i	0.244944	−	0.141419i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	30.5576	+	3.09184i	1.34915	+	0.136508i
$514$	−3.61513	−	13.4918i	−0.159457	−	0.595100i
$515$	−4.31560	+	1.15636i	−0.190168	+	0.0509554i
$516$	21.0778	+	2.56034i	0.927897	+	0.112713i
$517$	−8.42436	−	4.86380i	−0.370503	−	0.213910i
$518$	32.5588	−	8.72411i	1.43055	−	0.383315i
$519$	−1.74392	−	0.211836i	−0.0765495	−	0.00929856i
$520$	−5.50198	+	1.34001i	−0.241278	+	0.0587632i
$521$		−	14.7602i		−	0.646655i	−0.946287	−	0.323327i	$-0.895198\pi$
$521$		−	14.7602i		−	0.646655i	0.946287	−	0.323327i	$-0.104802\pi$
$522$	9.94436	−	18.0501i	0.435253	−	0.790032i
$523$	−7.04052	−	12.1945i	−0.307860	−	0.533230i	0.670034	−	0.742331i	$-0.266280\pi$
$523$	−7.04052	−	12.1945i	−0.307860	−	0.533230i	−0.977894	+	0.209101i	$0.932946\pi$
$524$	−2.72798	−	4.72499i	−0.119172	−	0.206412i
$525$	20.3552	−	2.88760i	0.888374	−	0.126025i
$526$	−16.9488	−	16.9488i	−0.739001	−	0.739001i
$527$	−4.43529	−	4.43529i	−0.193204	−	0.193204i
$528$	−2.62369	+	0.372198i	−0.114181	+	0.0161979i
$529$	−0.870493	−	1.50774i	−0.0378475	−	0.0655538i
$530$	2.18413	+	3.78302i	0.0948726	+	0.164324i
$531$	−8.64697	+	15.6952i	−0.375247	+	0.681114i
$532$		−	27.6954i		−	1.20075i
$533$	−18.6868	−	0.428011i	−0.809415	−	0.0185392i
$534$	−9.71028	−	1.17952i	−0.420205	−	0.0510428i
$535$	25.8474	−	6.92578i	1.11748	−	0.299428i
$536$	−4.85670	−	2.80402i	−0.209778	−	0.121115i
$537$	−40.1630	−	4.87865i	−1.73316	−	0.210529i
$538$	25.4107	−	6.80878i	1.09553	−	0.293547i
$539$	−5.92157	−	22.0996i	−0.255060	−	0.951897i
$540$	4.77123	−	6.62094i	0.205321	−	0.284920i
$541$	22.4390	−	22.4390i	0.964730	−	0.964730i	−0.0346688	−	0.999399i	$-0.511038\pi$
$541$	22.4390	−	22.4390i	0.964730	−	0.964730i	0.999399	+	0.0346688i	$0.0110376\pi$
$542$	−4.18584	+	2.41670i	−0.179797	+	0.103806i
$543$	−11.7939	−	8.86346i	−0.506126	−	0.380368i
$544$	1.54871	+	5.77988i	0.0664005	+	0.247810i
$545$	−1.60324	−	2.77689i	−0.0686752	−	0.118949i
$546$	26.8873	+	11.5450i	1.15067	+	0.494080i
$547$	1.46832	−	2.54321i	0.0627810	−	0.108740i	−0.832927	−	0.553384i	$-0.813336\pi$
$547$	1.46832	−	2.54321i	0.0627810	−	0.108740i	0.895708	+	0.444644i	$0.146670\pi$
$548$	−1.41446	−	0.379002i	−0.0604225	−	0.0161902i
$549$	−9.08765	+	9.45941i	−0.387851	+	0.403718i
$550$	−3.35654	−	1.93790i	−0.143123	−	0.0826323i
$551$	−10.5090	−	39.2203i	−0.447700	−	1.67084i
$552$	3.21700	−	7.99211i	0.136925	−	0.340167i
$553$	−0.446576	+	0.446576i	−0.0189903	+	0.0189903i
$554$	3.77245	−	14.0790i	0.160276	−	0.598158i
$555$	18.0042	−	7.66985i	0.764237	−	0.325567i
$556$			7.49403i			0.317818i
$557$	−3.80383	+	14.1961i	−0.161173	+	0.601507i	0.837324	+	0.546707i	$0.184119\pi$
$557$	−3.80383	+	14.1961i	−0.161173	+	0.601507i	−0.998497	+	0.0548002i	$0.982548\pi$
$558$	−2.17865	+	2.26778i	−0.0922297	+	0.0960026i
$559$	10.4590	+	42.9441i	0.442370	+	1.81634i
$560$	−6.37308	−	3.67950i	−0.269312	−	0.155487i
$561$	−5.92101	+	14.7098i	−0.249985	+	0.621048i
$562$	11.5034	−	19.9245i	0.485241	−	0.840462i
$563$	28.7217			1.21047			0.605237	−	0.796045i	$-0.293078\pi$
$563$	28.7217			1.21047			0.605237	+	0.796045i	$0.293078\pi$
$564$	10.2160	+	4.11216i	0.430171	+	0.173153i
$565$	3.37825	−	12.6078i	0.142124	−	0.530415i
$566$	−13.8750	+	3.71780i	−0.583210	+	0.156271i
$567$	−40.2628	+	12.5378i	−1.69088	+	0.526538i
$568$	−0.143927	+	0.249288i	−0.00603903	+	0.0104599i
$569$	−11.2305			−0.470807			−0.235403	−	0.971898i	$-0.575641\pi$
$569$	−11.2305			−0.470807			−0.235403	+	0.971898i	$0.575641\pi$
$570$	−2.25842	−	15.9200i	−0.0945948	−	0.666815i
$571$	−35.2056	+	20.3260i	−1.47331	+	0.850615i	−0.999549	−	0.0300392i	$-0.990437\pi$
$571$	−35.2056	+	20.3260i	−1.47331	+	0.850615i	−0.473760	+	0.880654i	$0.657103\pi$
$572$	−2.64805	−	4.83919i	−0.110720	−	0.202337i
$573$	−3.26457	+	26.8753i	−0.136380	+	1.12273i
$574$	−17.1759	−	17.1759i	−0.716910	−	0.716910i
$575$	10.9124	−	6.30030i	0.455080	−	0.262741i
$576$	2.88164	−	0.834373i	0.120068	−	0.0347655i
$577$	−9.12182	−	9.12182i	−0.379746	−	0.379746i	0.491264	−	0.871011i	$-0.336535\pi$
$577$	−9.12182	−	9.12182i	−0.379746	−	0.379746i	−0.871011	+	0.491264i	$0.836535\pi$
$578$	18.1647	+	4.86721i	0.755552	+	0.202449i
$579$	25.4027	+	10.2251i	1.05570	+	0.424942i
$580$	−10.4213	−	2.79238i	−0.432721	−	0.115947i
$581$		−	54.3497i		−	2.25481i
$582$	11.4729	+	1.39363i	0.475569	+	0.0577679i
$583$	−3.00893	+	3.00893i	−0.124617	+	0.124617i
$584$	1.36455			0.0564653
$585$	16.3969	+	4.44383i	0.677929	+	0.183730i
$586$	−12.1801			−0.503153
$587$	25.9757	−	25.9757i	1.07213	−	1.07213i	0.0749440	−	0.997188i	$-0.476122\pi$
$587$	25.9757	−	25.9757i	1.07213	−	1.07213i	0.997188	−	0.0749440i	$-0.0238778\pi$
$588$	10.1513	+	23.8292i	0.418633	+	0.982700i
$589$			6.19599i			0.255301i
$590$	9.06169	+	2.42807i	0.373064	+	0.0999622i
$591$	18.9021	−	14.8074i	0.777530	−	0.609095i
$592$	6.94881	+	1.86193i	0.285594	+	0.0765247i
$593$	−27.5996	−	27.5996i	−1.13338	−	1.13338i	−0.989611	−	0.143768i	$-0.954078\pi$
$593$	−27.5996	−	27.5996i	−1.13338	−	1.13338i	−0.143768	−	0.989611i	$-0.545922\pi$
$594$	7.43285	+	2.82015i	0.304974	+	0.115712i
$595$	−38.1350	+	22.0173i	−1.56338	+	0.902619i
$596$	0.424349	+	0.424349i	0.0173820	+	0.0173820i
$597$	19.9086	−	8.48111i	0.814804	−	0.347109i
$598$	17.9294	+	0.410664i	0.733189	+	0.0167933i
$599$	40.1298	−	23.1689i	1.63966	−	0.946657i	0.658708	−	0.752399i	$-0.271103\pi$
$599$	40.1298	−	23.1689i	1.63966	−	0.946657i	0.980950	−	0.194259i	$-0.0622301\pi$
$600$	4.07039	+	1.63842i	0.166173	+	0.0668882i
$601$	−21.0902			−0.860289			−0.430145	−	0.902760i	$-0.641537\pi$
$601$	−21.0902			−0.860289			−0.430145	+	0.902760i	$0.641537\pi$
$602$	−28.7192	+	49.7432i	−1.17051	+	2.02738i
$603$	8.70235	+	14.3986i	0.354387	+	0.586356i
$604$	1.75756	−	0.470936i	0.0715140	−	0.0191621i
$605$	3.51995	−	13.1366i	0.143106	−	0.534080i
$606$	−1.86346	−	13.1358i	−0.0756977	−	0.533606i
$607$	10.2282			0.415151			0.207576	−	0.978219i	$-0.433443\pi$
$607$	10.2282			0.415151			0.207576	+	0.978219i	$0.433443\pi$
$608$	2.95542	−	5.11893i	0.119858	−	0.207600i
$609$	34.3794	+	43.8864i	1.39312	+	1.77837i
$610$	5.94726	+	3.43365i	0.240797	+	0.139024i
$611$	−0.524935	+	22.9185i	−0.0212366	+	0.927182i
$612$	4.29772	−	17.4293i	0.173725	−	0.704536i
$613$	−12.0361	+	44.9194i	−0.486134	+	1.81428i	0.0887657	+	0.996053i	$0.471708\pi$
$613$	−12.0361	+	44.9194i	−0.486134	+	1.81428i	−0.574900	+	0.818224i	$0.694959\pi$
$614$		−	9.64834i		−	0.389375i
$615$	−11.2738	−	8.47255i	−0.454603	−	0.341646i
$616$	1.85538	−	6.92438i	0.0747554	−	0.278991i
$617$	−16.1123	+	16.1123i	−0.648657	+	0.648657i	−0.952668	−	0.304012i	$-0.901674\pi$
$617$	−16.1123	+	16.1123i	−0.648657	+	0.648657i	0.304012	+	0.952668i	$0.401674\pi$
$618$	3.03849	+	3.87874i	0.122226	+	0.156026i
$619$	−7.63393	−	28.4902i	−0.306834	−	1.14512i	−0.931355	−	0.364111i	$-0.881373\pi$
$619$	−7.63393	−	28.4902i	−0.306834	−	1.14512i	0.624522	−	0.781007i	$-0.285294\pi$
$620$	1.42578	+	0.823175i	0.0572607	+	0.0330595i
$621$	−20.0227	+	16.3432i	−0.803483	+	0.655828i
$622$	−14.9478	−	4.00525i	−0.599351	−	0.160596i
$623$	13.2306	−	22.9161i	0.530074	−	0.918115i
$624$	3.73759	+	5.00304i	0.149623	+	0.200282i
$625$	−2.95806	−	5.12350i	−0.118322	−	0.204940i
$626$	6.93430	+	25.8792i	0.277150	+	1.03434i
$627$	14.4104	−	6.13886i	0.575494	−	0.245162i
$628$	−1.75937	+	1.01577i	−0.0702066	+	0.0405338i
$629$	30.4387	−	30.4387i	1.21367	−	1.21367i
$630$	11.4194	+	18.8942i	0.454961	+	0.752762i
$631$	11.3620	+	42.4037i	0.452315	+	1.68806i	0.695863	+	0.718174i	$0.255022\pi$
$631$	11.3620	+	42.4037i	0.452315	+	1.68806i	−0.243548	+	0.969889i	$0.578311\pi$
$632$	−0.130195	+	0.0348857i	−0.00517889	+	0.00138768i
$633$	−5.30774	−	12.4594i	−0.210964	−	0.495217i
$634$	−12.4751	−	7.20250i	−0.495450	−	0.286048i
$635$	−17.6560	+	4.73092i	−0.700658	+	0.187741i
$636$	2.89418	−	3.85106i	0.114762	−	0.152705i
$637$	−38.9888	+	37.2428i	−1.54479	+	1.47561i
$638$		−	10.5099i		−	0.416089i
$639$	0.739062	−	0.446680i	0.0292368	−	0.0176704i
$640$	−0.785290	−	1.36016i	−0.0310413	−	0.0537651i
$641$	22.6855	+	39.2924i	0.896022	+	1.55196i	0.832534	+	0.553973i	$0.186889\pi$
$641$	22.6855	+	39.2924i	0.896022	+	1.55196i	0.0634878	+	0.997983i	$0.479778\pi$
$642$	−18.1984	−	23.2309i	−0.718234	−	0.916850i
$643$	19.4333	+	19.4333i	0.766375	+	0.766375i	0.977466	−	0.211091i	$-0.0677017\pi$
$643$	19.4333	+	19.4333i	0.766375	+	0.766375i	−0.211091	+	0.977466i	$0.567702\pi$
$644$	16.4798	+	16.4798i	0.649395	+	0.649395i
$645$	−12.4522	+	30.9356i	−0.490306	+	1.21809i
$646$	−17.6845	−	30.6305i	−0.695788	−	1.20514i
$647$	−1.29346	−	2.24034i	−0.0508513	−	0.0880770i	0.839479	−	0.543392i	$-0.182860\pi$
$647$	−1.29346	−	2.24034i	−0.0508513	−	0.0880770i	−0.890331	+	0.455315i	$0.849527\pi$
$648$	−8.77969	−	1.97914i	−0.344899	−	0.0777480i
$649$			9.13869i			0.358725i
$650$	−0.209151	+	9.13147i	−0.00820360	+	0.358166i
$651$	−3.33412	−	7.82651i	−0.130674	−	0.306745i
$652$	−8.79238	+	2.35591i	−0.344336	+	0.0922646i
$653$	1.89876	+	1.09625i	0.0743042	+	0.0428995i	0.536692	−	0.843778i	$-0.319674\pi$
$653$	1.89876	+	1.09625i	0.0743042	+	0.0428995i	−0.462388	+	0.886678i	$0.653007\pi$
$654$	−2.12444	+	2.82684i	−0.0830723	+	0.110538i
$655$	8.27703	−	2.21782i	0.323410	−	0.0866575i
$656$	−1.34176	−	5.00750i	−0.0523868	−	0.195510i
$657$	−3.58550	−	1.97536i	−0.139884	−	0.0770663i
$658$	−21.0655	+	21.0655i	−0.821217	+	0.821217i
$659$	−19.3027	+	11.1444i	−0.751925	+	0.434124i	−0.826389	−	0.563099i	$-0.809609\pi$
$659$	−19.3027	+	11.1444i	−0.751925	+	0.434124i	0.0744639	+	0.997224i	$0.476275\pi$
$660$	0.501871	−	4.13160i	0.0195353	−	0.160822i
$661$	6.60372	+	24.6454i	0.256855	+	0.958596i	0.967049	+	0.254590i	$0.0819406\pi$
$661$	6.60372	+	24.6454i	0.256855	+	0.958596i	−0.710194	+	0.704006i	$0.751393\pi$
$662$	−15.3707	−	26.6229i	−0.597400	−	1.03473i
$663$	37.1087	−	4.40001i	1.44118	−	0.170882i
$664$	5.79975	−	10.0455i	0.225074	−	0.389839i
$665$	42.0156	+	11.2581i	1.62930	+	0.436569i
$666$	−15.5634	−	14.9518i	−0.603069	−	0.579369i
$667$	29.5909	+	17.0843i	1.14576	+	0.661506i
$668$	−0.968219	−	3.61344i	−0.0374615	−	0.139808i
$669$	3.64266	−	0.516750i	0.140833	−	0.0199787i
$670$	6.22810	−	6.22810i	0.240613	−	0.240613i
$671$	−1.73141	+	6.46172i	−0.0668405	+	0.249452i
$672$	−0.978615	+	8.05635i	−0.0377509	+	0.310780i
$673$		−	17.3697i		−	0.669552i	−0.942298	−	0.334776i	$-0.891339\pi$
$673$		−	17.3697i		−	0.669552i	0.942298	−	0.334776i	$-0.108661\pi$
$674$	7.78596	−	29.0576i	0.299904	−	1.11926i
$675$	−8.32358	−	10.1976i	−0.320375	−	0.392505i
$676$	−7.00865	+	10.9489i	−0.269563	+	0.421112i
$677$	−1.50598	−	0.869476i	−0.0578794	−	0.0334167i	0.470781	−	0.882250i	$-0.343972\pi$
$677$	−1.50598	−	0.869476i	−0.0578794	−	0.0334167i	−0.528660	+	0.848833i	$0.677306\pi$
$678$	−14.2518	+	2.02177i	−0.547337	+	0.0776456i
$679$	−15.6323	+	27.0760i	−0.599913	+	1.03908i
$680$	−9.39799			−0.360396
$681$	25.5649	−	20.0268i	0.979649	−	0.767429i
$682$	−0.415085	+	1.54912i	−0.0158944	+	0.0593188i
$683$	−40.4081	+	10.8273i	−1.54617	+	0.414296i	−0.928254	−	0.371947i	$-0.878690\pi$
$683$	−40.4081	+	10.8273i	−1.54617	+	0.414296i	−0.617918	+	0.786243i	$0.712024\pi$
$684$	−15.1760	+	9.17222i	−0.580270	+	0.350709i
$685$	1.14994	−	1.99176i	0.0439370	−	0.0761011i
$686$	−37.2694			−1.42295
$687$	−30.2659	+	23.7095i	−1.15472	+	0.904572i
$688$	−10.6164	+	6.12935i	−0.404745	+	0.233679i
$689$	9.62446	+	2.81660i	0.366663	+	0.107304i
$690$	10.8168	+	8.12916i	0.411790	+	0.309472i
$691$	6.97222	+	6.97222i	0.265236	+	0.265236i	0.827177	−	0.561941i	$-0.189945\pi$
$691$	6.97222	+	6.97222i	0.265236	+	0.265236i	−0.561941	+	0.827177i	$0.689945\pi$
$692$	0.878368	−	0.507126i	0.0333905	−	0.0192780i
$693$	−14.8992	+	15.5087i	−0.565973	+	0.589126i
$694$	−12.0944	−	12.0944i	−0.459097	−	0.459097i
$695$	−11.3689	−	3.04629i	−0.431248	−	0.115553i
$696$	1.67115	+	11.7802i	0.0633446	+	0.446527i
$697$	−29.9637	−	8.02875i	−1.13496	−	0.304111i
$698$		−	2.79608i		−	0.105833i
$699$	−19.1152	+	25.4352i	−0.723005	+	0.962047i
$700$	−8.39317	+	8.39317i	−0.317232	+	0.317232i
$701$	−9.99927			−0.377667			−0.188834	−	0.982009i	$-0.560471\pi$
$701$	−9.99927			−0.377667			−0.188834	+	0.982009i	$0.560471\pi$
$702$	−2.57837	−	18.5567i	−0.0973142	−	0.700378i
$703$	−42.5221			−1.60375
$704$	1.08184	−	1.08184i	0.0407734	−	0.0407734i
$705$	−10.3912	+	13.8267i	−0.391354	+	0.520745i
$706$		−	33.4469i		−	1.25879i
$707$	34.6677	+	9.28919i	1.30381	+	0.349356i
$708$	−1.45312	−	10.2433i	−0.0546116	−	0.384966i
$709$	19.6851	+	5.27462i	0.739291	+	0.198092i	0.608763	−	0.793352i	$-0.291666\pi$
$709$	19.6851	+	5.27462i	0.739291	+	0.198092i	0.130528	+	0.991445i	$0.458333\pi$
$710$	−0.319681	−	0.319681i	−0.0119974	−	0.0119974i
$711$	0.392605	+	0.0968089i	0.0147238	+	0.00363062i
$712$	4.89083	−	2.82372i	0.183292	−	0.105823i
$713$	−3.68685	−	3.68685i	−0.138074	−	0.138074i
$714$	38.8209	+	29.1749i	1.45283	+	1.09184i
$715$	8.41778	−	2.05015i	0.314807	−	0.0766712i
$716$	20.2291	−	11.6793i	0.755998	−	0.436475i
$717$	−12.2461	+	9.59321i	−0.457337	+	0.358265i
$718$	−5.75214			−0.214668
$719$	9.70859	−	16.8158i	0.362069	−	0.627123i	−0.626232	−	0.779637i	$-0.715404\pi$
$719$	9.70859	−	16.8158i	0.362069	−	0.627123i	0.988301	+	0.152514i	$0.0487370\pi$
$720$	0.0944233	+	4.71079i	0.00351895	+	0.175561i
$721$	−12.8748	+	3.44978i	−0.479481	+	0.128477i
$722$	−4.12504	+	15.3949i	−0.153518	+	0.572938i
$723$	5.76062	−	4.51271i	0.214240	−	0.167829i
$724$	8.51778			0.316561
$725$	−8.70104	+	15.0706i	−0.323149	+	0.559710i
$726$	−14.8496	+	2.10657i	−0.551119	+	0.0781821i
$727$	38.1818	+	22.0442i	1.41608	+	0.817576i	0.995952	−	0.0898878i	$-0.0286508\pi$
$727$	38.1818	+	22.0442i	1.41608	+	0.817576i	0.420131	+	0.907464i	$0.361984\pi$
$728$	−16.4141	+	3.99765i	−0.608347	+	0.148163i
$729$	20.2046	+	17.9102i	0.748318	+	0.663341i
$730$	−0.554683	+	2.07010i	−0.0205297	+	0.0766180i
$731$			73.3533i			2.71307i
$732$	0.913228	−	7.51806i	0.0337539	−	0.277876i
$733$	9.30736	−	34.7355i	0.343775	−	1.28299i	−0.550261	−	0.834992i	$-0.685472\pi$
$733$	9.30736	−	34.7355i	0.343775	−	1.28299i	0.894037	−	0.447994i	$-0.147861\pi$
$734$	−2.03642	+	2.03642i	−0.0751656	+	0.0751656i
$735$	−40.2769	+	5.71371i	−1.48564	+	0.210753i
$736$	1.28737	+	4.80455i	0.0474532	+	0.177098i
$737$	7.43053	+	4.29002i	0.273707	+	0.158025i
$738$	−3.72341	+	15.1001i	−0.137061	+	0.555844i
$739$	−40.1431	−	10.7563i	−1.47669	−	0.395677i	−0.571470	−	0.820623i	$-0.693627\pi$
$739$	−40.1431	−	10.7563i	−1.47669	−	0.395677i	−0.905219	+	0.424946i	$0.860293\pi$
$740$	−5.64933	+	9.78492i	−0.207673	+	0.359701i
$741$	−28.9933	−	22.8466i	−1.06510	−	0.839291i
$742$	6.51594	+	11.2859i	0.239208	+	0.414320i
$743$	−6.90641	−	25.7751i	−0.253372	−	0.945596i	−0.968989	−	0.247103i	$-0.920521\pi$
$743$	−6.90641	−	25.7751i	−0.253372	−	0.945596i	0.715617	−	0.698492i	$-0.246145\pi$
$744$	0.218935	−	1.80236i	0.00802655	−	0.0660778i
$745$	−0.816261	+	0.471269i	−0.0299055	+	0.0172660i
$746$	12.0901	−	12.0901i	0.442648	−	0.442648i
$747$	−29.7816	+	17.9997i	−1.08965	+	0.658574i
$748$	−2.36946	−	8.84295i	−0.0866360	−	0.323330i
$749$	77.1107	−	20.6617i	2.81756	−	0.754964i
$750$	−12.3118	+	16.3824i	−0.449563	+	0.598199i
$751$	3.69581	+	2.13378i	0.134862	+	0.0778626i	0.565913	−	0.824465i	$-0.308524\pi$
$751$	3.69581	+	2.13378i	0.134862	+	0.0778626i	−0.431051	+	0.902328i	$0.641857\pi$
$752$	−6.14146	+	1.64560i	−0.223956	+	0.0600088i
$753$	0.0467255	+	0.109683i	0.00170277	+	0.00399709i
$754$	−21.7276	+	11.8896i	−0.791273	+	0.432992i
$755$			2.85776i			0.104005i
$756$	14.2341	−	19.7523i	0.517688	−	0.718384i
$757$	8.81337	+	15.2652i	0.320327	+	0.554823i	0.980556	−	0.196242i	$-0.0628738\pi$
$757$	8.81337	+	15.2652i	0.320327	+	0.554823i	−0.660228	+	0.751065i	$0.729540\pi$
$758$	10.1872	+	17.6447i	0.370014	+	0.640883i
$759$	−4.92186	+	12.2276i	−0.178652	+	0.443833i
$760$	6.56438	+	6.56438i	0.238115	+	0.238115i
$761$	−5.20787	−	5.20787i	−0.188785	−	0.188785i	0.606386	−	0.795171i	$-0.292619\pi$
$761$	−5.20787	−	5.20787i	−0.188785	−	0.188785i	−0.795171	+	0.606386i	$0.792619\pi$
$762$	12.4311	+	15.8687i	0.450332	+	0.574863i
$763$	−4.78296	−	8.28433i	−0.173155	−	0.299913i
$764$	−7.81525	−	13.5364i	−0.282746	−	0.489730i
$765$	24.6943	+	13.6048i	0.892824	+	0.491884i
$766$		−	16.1279i		−	0.582726i
$767$	18.8929	−	10.3384i	0.682184	−	0.373298i
$768$	−1.04058	+	1.38462i	−0.0375488	+	0.0499634i
$769$	−11.3565	+	3.04296i	−0.409525	+	0.109732i	−0.457699	−	0.889107i	$-0.651326\pi$
$769$	−11.3565	+	3.04296i	−0.409525	+	0.109732i	0.0481743	+	0.998839i	$0.484660\pi$
$770$	9.75052	+	5.62946i	0.351384	+	0.202872i
$771$	−9.48174	−	22.2574i	−0.341476	−	0.801582i
$772$	−15.2711	+	4.09187i	−0.549618	+	0.147270i
$773$	1.81323	+	6.76707i	0.0652173	+	0.243394i	0.990838	−	0.135059i	$-0.0431225\pi$
$773$	1.81323	+	6.76707i	0.0652173	+	0.243394i	−0.925620	+	0.378454i	$0.876456\pi$
$774$	36.7687	−	0.736994i	1.32162	−	0.0264907i
$775$	1.87772	−	1.87772i	0.0674496	−	0.0674496i
$776$	−5.77864	+	3.33630i	−0.207441	+	0.119766i
$777$	53.7122	−	22.8815i	1.92691	−	0.820870i
$778$	9.37049	+	34.9712i	0.335948	+	1.25378i
$779$	15.3213	+	26.5373i	0.548943	+	0.950797i
$780$	−9.10925	+	3.63644i	−0.326163	+	0.130206i
$781$	0.220201	−	0.381400i	0.00787942	−	0.0136476i
$782$	28.7493	+	7.70335i	1.02807	+	0.275471i
$783$	12.6623	−	33.3730i	0.452513	−	1.19265i
$784$	−12.9507	−	7.47708i	−0.462524	−	0.267039i
$785$	−0.825816	−	3.08199i	−0.0294746	−	0.110001i
$786$	−5.82762	−	7.43916i	−0.207864	−	0.265346i
$787$	−3.09713	+	3.09713i	−0.110401	+	0.110401i	−0.760149	−	0.649749i	$-0.774874\pi$
$787$	−3.09713	+	3.09713i	−0.110401	+	0.110401i	0.649749	+	0.760149i	$0.274874\pi$
$788$	−3.58802	+	13.3907i	−0.127818	+	0.477022i
$789$	−33.1883	−	24.9419i	−1.18153	−	0.887955i
$790$		−	0.211696i		−	0.00753179i
$791$	10.0784	−	37.6130i	0.358346	−	1.33736i
$792$	−4.40877	+	1.27655i	−0.156659	+	0.0453603i
$793$	15.3174	−	3.73055i	0.543937	−	0.132476i
$794$	0.568843	+	0.328421i	0.0201875	+	0.0116552i
$795$	4.66584	+	5.95610i	0.165480	+	0.211241i
$796$	−6.24687	+	10.8199i	−0.221414	+	0.383501i
$797$	29.1084			1.03107			0.515536	−	0.856868i	$-0.327593\pi$
$797$	29.1084			1.03107			0.515536	+	0.856868i	$0.327593\pi$
$798$	−6.73757	−	47.4943i	−0.238507	−	1.68128i
$799$	−9.84688	+	36.7490i	−0.348357	+	1.30009i
$800$	−2.44696	+	0.655661i	−0.0865131	+	0.0231811i
$801$	−16.9389	+	0.339524i	−0.598508	+	0.0119965i
$802$	1.50835	−	2.61253i	0.0532615	−	0.0922517i
$803$	−2.08769			−0.0736731
$804$	−9.01081	−	3.62705i	−0.317787	−	0.127916i
$805$	−31.6999	+	18.3019i	−1.11727	+	0.645058i
$806$	3.67215	−	0.894353i	0.129346	−	0.0315022i
$807$	41.9200	−	17.8580i	1.47565	−	0.628632i
$808$	5.41637	+	5.41637i	0.190547	+	0.190547i
$809$	−11.8364	+	6.83376i	−0.416146	+	0.240262i	−0.693427	−	0.720527i	$-0.743900\pi$
$809$	−11.8364	+	6.83376i	−0.416146	+	0.240262i	0.277281	+	0.960789i	$0.410567\pi$
$810$	6.57139	−	12.5148i	0.230895	−	0.439727i
$811$	−14.3128	−	14.3128i	−0.502590	−	0.502590i	0.409652	−	0.912242i	$-0.365650\pi$
$811$	−14.3128	−	14.3128i	−0.502590	−	0.502590i	−0.912242	+	0.409652i	$0.865650\pi$
$812$	−31.0900	−	8.33054i	−1.09104	−	0.292345i
$813$	−6.59030	+	5.16266i	−0.231132	+	0.181062i
$814$	−10.6314	−	2.84866i	−0.372629	−	0.0998456i
$815$		−	14.2963i		−	0.500776i
$816$	4.06195	+	9.53504i	0.142197	+	0.333793i
$817$	51.2364	−	51.2364i	1.79253	−	1.79253i
$818$	−2.35979			−0.0825083
$819$	48.9171	+	13.2573i	1.70930	+	0.463248i
$820$	8.14212			0.284335
$821$	−22.0358	+	22.0358i	−0.769055	+	0.769055i	−0.977940	−	0.208885i	$-0.933017\pi$
$821$	−22.0358	+	22.0358i	−0.769055	+	0.769055i	0.208885	+	0.977940i	$0.433017\pi$
$822$	−2.51782	−	0.305843i	−0.0878192	−	0.0106675i
$823$		−	25.0387i		−	0.872793i	−0.899754	−	0.436397i	$-0.856254\pi$
$823$		−	25.0387i		−	0.872793i	0.899754	−	0.436397i	$-0.143746\pi$
$824$	−2.74777	−	0.736264i	−0.0957232	−	0.0256490i
$825$	−6.22751	−	2.50671i	−0.216814	−	0.0872724i
$826$	27.0338	+	7.24369i	0.940627	+	0.252040i
$827$	−0.771368	−	0.771368i	−0.0268231	−	0.0268231i	0.693568	−	0.720391i	$-0.256038\pi$
$827$	−0.771368	−	0.771368i	−0.0268231	−	0.0268231i	−0.720391	+	0.693568i	$0.756038\pi$
$828$	3.57250	−	14.4881i	0.124153	−	0.503498i
$829$	9.17897	−	5.29948i	0.318799	−	0.184058i	−0.332058	−	0.943259i	$-0.607743\pi$
$829$	9.17897	−	5.29948i	0.318799	−	0.184058i	0.650857	+	0.759200i	$0.274410\pi$
$830$	12.8820	+	12.8820i	0.447142	+	0.447142i
$831$	3.04425	−	25.0615i	0.105604	−	0.869373i
$832$	−3.46041	−	1.01269i	−0.119968	−	0.0351087i
$833$	−77.4939	+	44.7411i	−2.68500	+	1.55019i
$834$	1.82310	+	12.8514i	0.0631290	+	0.445007i
$835$	5.87540			0.203327
$836$	−4.52165	+	7.83173i	−0.156385	+	0.270866i
$837$	−3.18444	+	4.41898i	−0.110070	+	0.152742i
$838$	21.9936	−	5.89317i	0.759757	−	0.203576i
$839$	7.27925	−	27.1665i	0.251308	−	0.937893i	−0.718800	−	0.695217i	$-0.755308\pi$
$839$	7.27925	−	27.1665i	0.251308	−	0.937893i	0.970108	−	0.242676i	$-0.0780250\pi$
$840$	−11.8242	−	4.75950i	−0.407974	−	0.164218i
$841$	−18.1886			−0.627192
$842$	17.0807	−	29.5847i	0.588641	−	1.01956i
$843$	14.8798	−	36.9666i	0.512489	−	1.27320i
$844$	6.77143	+	3.90948i	0.233082	+	0.134570i
$845$	−13.7612	−	15.0833i	−0.473401	−	0.518880i
$846$	18.5196	+	4.56658i	0.636717	+	0.157002i
$847$	10.5011	−	39.1906i	0.360822	−	1.34660i
$848$			2.78130i			0.0955104i
$849$	−22.8895	+	9.75101i	−0.785567	+	0.334654i
$850$	−3.92332	+	14.6420i	−0.134569	+	0.502218i
$851$	25.3023	−	25.3023i	0.867352	−	0.867352i
$852$	−0.186172	+	0.462513i	−0.00637814	+	0.0158454i
$853$	−1.03388	−	3.85850i	−0.0353994	−	0.132112i	0.945965	−	0.324269i	$-0.105118\pi$
$853$	−1.03388	−	3.85850i	−0.0353994	−	0.132112i	−0.981364	+	0.192157i	$0.938452\pi$
$854$	17.7425	+	10.2436i	0.607136	+	0.350530i
$855$	−7.74585	−	26.7515i	−0.264902	−	0.914881i
$856$	16.4572	+	4.40970i	0.562496	+	0.150720i
$857$	6.21869	−	10.7711i	0.212426	−	0.367933i	−0.740047	−	0.672555i	$-0.765197\pi$
$857$	6.21869	−	10.7711i	0.212426	−	0.367933i	0.952473	+	0.304622i	$0.0985301\pi$
$858$	−5.71834	−	7.65443i	−0.195221	−	0.261318i
$859$	5.87753	+	10.1802i	0.200539	+	0.347343i	0.948702	−	0.316171i	$-0.102397\pi$
$859$	5.87753	+	10.1802i	0.200539	+	0.347343i	−0.748163	+	0.663514i	$0.769064\pi$
$860$	−4.98312	−	18.5972i	−0.169923	−	0.634161i
$861$	−33.6332	−	25.2762i	−1.14622	−	0.861412i
$862$	6.25597	−	3.61188i	0.213079	−	0.123021i
$863$	−34.3113	+	34.3113i	−1.16797	+	1.16797i	−0.185284	+	0.982685i	$0.559321\pi$
$863$	−34.3113	+	34.3113i	−1.16797	+	1.16797i	−0.982685	+	0.185284i	$0.940679\pi$
$864$	4.73868	−	2.13188i	0.161213	−	0.0725279i
$865$	0.412289	+	1.53869i	0.0140183	+	0.0523169i
$866$	−17.8689	+	4.78795i	−0.607209	+	0.162701i
$867$	32.3344	+	3.92769i	1.09813	+	0.133391i
$868$	4.25355	+	2.45579i	0.144375	+	0.0833548i
$869$	0.199193	−	0.0533736i	0.00675716	−	0.00181058i
$870$	−18.5506	−	2.25337i	−0.628925	−	0.0763963i
$871$	0.463008	−	20.2148i	0.0156884	−	0.684951i
$872$		−	2.04159i		−	0.0691369i
$873$	20.0138	−	0.401156i	0.677363	−	0.0135771i
$874$	−14.7003	−	25.4617i	−0.497246	−	0.861256i
$875$	−27.7187	−	48.0102i	−0.937062	−	1.62304i
$876$	2.34004	−	0.331959i	0.0790625	−	0.0112159i
$877$	2.92318	+	2.92318i	0.0987089	+	0.0987089i	0.754737	−	0.656028i	$-0.227765\pi$
$877$	2.92318	+	2.92318i	0.0987089	+	0.0987089i	−0.656028	+	0.754737i	$0.727765\pi$
$878$	−14.3689	−	14.3689i	−0.484927	−	0.484927i
$879$	−20.8873	+	2.96309i	−0.704513	+	0.0999426i
$880$	1.20146	+	2.08099i	0.0405011	+	0.0701500i
$881$	−23.7044	−	41.0573i	−0.798622	−	1.38325i	−0.920513	−	0.390711i	$-0.872229\pi$
$881$	−23.7044	−	41.0573i	−0.798622	−	1.38325i	0.121891	−	0.992543i	$-0.461104\pi$
$882$	23.2053	+	38.3947i	0.781364	+	1.29282i
$883$		−	10.8472i		−	0.365036i	−0.983202	−	0.182518i	$-0.941575\pi$
$883$		−	10.8472i		−	0.365036i	0.983202	−	0.182518i	$-0.0584248\pi$
$884$	−15.6010	+	14.9023i	−0.524719	+	0.501220i
$885$	16.1304	+	1.95938i	0.542218	+	0.0658639i
$886$	−9.71932	+	2.60429i	−0.326527	+	0.0874927i
$887$	19.7335	+	11.3932i	0.662587	+	0.382545i	0.793262	−	0.608880i	$-0.208381\pi$
$887$	19.7335	+	11.3932i	0.662587	+	0.382545i	−0.130675	+	0.991425i	$0.541714\pi$
$888$	12.3693	+	1.50252i	0.415088	+	0.0504212i
$889$	−52.6734	+	14.1138i	−1.76661	+	0.473361i
$890$	2.29566	+	8.56753i	0.0769508	+	0.287184i
$891$	13.4325	+	3.02800i	0.450007	+	0.101442i
$892$	−1.50200	+	1.50200i	−0.0502906	+	0.0502906i
$893$	32.5467	−	18.7908i	1.08913	−	0.628812i
$894$	0.830942	+	0.624476i	0.0277909	+	0.0208856i
$895$	9.49517	+	35.4365i	0.317388	+	1.18451i
$896$	−2.34276	−	4.05778i	−0.0782662	−	0.135561i
$897$	30.8467	−	3.65753i	1.02994	−	0.122121i
$898$	−11.5644	+	20.0302i	−0.385910	+	0.668416i
$899$	6.95544	+	1.86370i	0.231977	+	0.0621580i
$900$	7.37882	+	1.81948i	0.245961	+	0.0606492i
$901$	14.4130	+	8.32134i	0.480166	+	0.277224i
$902$	2.05283	+	7.66125i	0.0683516	+	0.255092i
$903$	−37.1489	+	92.2903i	−1.23624	+	3.07123i
$904$	5.87653	−	5.87653i	0.195450	−	0.195450i
$905$	−3.46244	+	12.9220i	−0.115096	+	0.429542i
$906$	2.89943	−	1.23517i	0.0963272	−	0.0410357i
$907$		−	30.6280i		−	1.01699i	−0.861066	−	0.508493i	$-0.830203\pi$
$907$		−	30.6280i		−	1.01699i	0.861066	−	0.508493i	$-0.169797\pi$
$908$	−4.85274	+	18.1107i	−0.161044	+	0.601024i
$909$	−6.39121	−	22.0730i	−0.211983	−	0.732116i
$910$	0.607570	−	26.5263i	0.0201408	−	0.879337i
$911$	44.3084	+	25.5815i	1.46800	+	0.847552i	0.999358	−	0.0358341i	$-0.0114088\pi$
$911$	44.3084	+	25.5815i	1.46800	+	0.847552i	0.468646	+	0.883386i	$0.344742\pi$
$912$	3.82288	−	9.49734i	0.126588	−	0.314488i
$913$	−8.87335	+	15.3691i	−0.293665	+	0.508643i
$914$	−22.2108			−0.734667
$915$	11.0342	+	4.44149i	0.364778	+	0.146831i
$916$	5.74509	−	21.4410i	0.189823	−	0.708430i
$917$	24.6929	−	6.61645i	0.815433	−	0.218494i
$918$	3.12999	−	30.9346i	0.103305	−	1.02099i
$919$	5.50249	−	9.53060i	0.181511	−	0.314385i	−0.760885	−	0.648887i	$-0.775235\pi$
$919$	5.50249	−	9.53060i	0.181511	−	0.314385i	0.942395	+	0.334502i	$0.108568\pi$
$920$	−7.81211			−0.257558
$921$	−2.34719	−	16.5458i	−0.0773426	−	0.545201i
$922$	−20.7088	+	11.9563i	−0.682010	+	0.393758i
$923$	−1.03760	−	0.0237656i	−0.0341529	−	0.000782255i
$924$	1.49724	−	12.3258i	0.0492555	−	0.405491i
$925$	12.8865	+	12.8865i	0.423705	+	0.423705i
$926$	13.3829	−	7.72662i	0.439789	−	0.253912i
$927$	6.15425	+	5.91239i	0.202132	+	0.194188i
$928$	−4.85740	−	4.85740i	−0.159452	−	0.159452i
$929$	−49.3987	−	13.2363i	−1.62072	−	0.434270i	−0.669506	−	0.742806i	$-0.733494\pi$
$929$	−49.3987	−	13.2363i	−1.62072	−	0.434270i	−0.951213	+	0.308536i	$0.900161\pi$
$930$	2.64530	+	1.06479i	0.0867429	+	0.0349159i
$931$	85.3797	+	22.8774i	2.79821	+	0.749777i
$932$		−	18.3697i		−	0.601721i
$933$	−26.6080	−	3.23211i	−0.871108	−	0.105815i
$934$	21.2277	−	21.2277i	0.694591	−	0.694591i
$935$	14.3785			0.470227
$936$	7.62663	+	7.67037i	0.249284	+	0.250714i
$937$	−12.0914			−0.395010			−0.197505	−	0.980302i	$-0.563284\pi$
$937$	−12.0914			−0.395010			−0.197505	+	0.980302i	$0.563284\pi$
$938$	18.5804	−	18.5804i	0.606670	−	0.606670i
$939$	18.1872	+	42.6927i	0.593518	+	1.39322i
$940$		−	9.98591i		−	0.325705i
$941$	−37.8303	−	10.1366i	−1.23323	−	0.330444i	−0.417395	−	0.908725i	$-0.637057\pi$
$941$	−37.8303	−	10.1366i	−1.23323	−	0.330444i	−0.815837	+	0.578281i	$0.803724\pi$
$942$	−2.77000	+	2.16994i	−0.0902516	+	0.0707005i
$943$	−24.9075	−	6.67393i	−0.811099	−	0.217333i
$944$	4.22367	+	4.22367i	0.137469	+	0.137469i
$945$	24.1794	+	29.6232i	0.786557	+	0.963643i
$946$	16.2425	−	9.37763i	0.528090	−	0.304893i
$947$	−8.90120	−	8.90120i	−0.289250	−	0.289250i	0.547534	−	0.836784i	$-0.315567\pi$
$947$	−8.90120	−	8.90120i	−0.289250	−	0.289250i	−0.836784	+	0.547534i	$0.815567\pi$
$948$	−0.214783	+	0.0914981i	−0.00697582	+	0.00297172i
$949$	2.36176	+	4.31601i	0.0766660	+	0.140104i
$950$	12.9677	−	7.48689i	0.420727	−	0.242907i
$951$	−23.1455	−	9.31657i	−0.750544	−	0.302110i
$952$	−28.0371			−0.908688
$953$	−8.10265	+	14.0342i	−0.262471	+	0.454612i	−0.966898	−	0.255164i	$-0.917871\pi$
$953$	−8.10265	+	14.0342i	−0.262471	+	0.454612i	0.704427	+	0.709776i	$0.251204\pi$
$954$	4.02631	−	7.30819i	0.130357	−	0.236612i
$955$	23.7125	−	6.35374i	0.767318	−	0.205602i
$956$	2.32455	−	8.67535i	0.0751814	−	0.280581i
$957$	−2.55678	−	18.0232i	−0.0826489	−	0.582606i
$958$	0.498151			0.0160945
$959$	3.43063	−	5.94203i	0.110781	−	0.191878i
$960$	−1.67757	−	2.14148i	−0.0541434	−	0.0691158i
$961$	25.8952	+	14.9506i	0.835329	+	0.482277i
$962$	6.13781	+	25.2014i	0.197891	+	0.812527i
$963$	−36.8596	−	35.4110i	−1.18778	−	1.14110i
$964$	−1.09348	+	4.08094i	−0.0352187	+	0.131438i
$965$		−	24.8305i		−	0.799323i
$966$	32.2700	+	24.2518i	1.03827	+	0.780288i
$967$	11.7831	−	43.9751i	0.378919	−	1.41414i	−0.468616	−	0.883402i	$-0.655247\pi$
$967$	11.7831	−	43.9751i	0.378919	−	1.41414i	0.847534	−	0.530741i	$-0.178086\pi$
$968$	6.12301	−	6.12301i	0.196801	−	0.196801i
$969$	−37.7785	−	48.2255i	−1.21362	−	1.54923i
$970$	−2.71238	−	10.1228i	−0.0870894	−	0.325022i
$971$	32.5825	+	18.8115i	1.04562	+	0.603690i	0.921421	−	0.388567i	$-0.127030\pi$
$971$	32.5825	+	18.8115i	1.04562	+	0.603690i	0.124202	+	0.992257i	$0.460363\pi$
$972$	−15.5376	−	1.25812i	−0.498369	−	0.0403542i
$973$	−33.9170	−	9.08804i	−1.08733	−	0.291349i
$974$	−11.5432	+	19.9935i	−0.369869	+	0.640632i
$975$	1.86278	+	15.7103i	0.0596567	+	0.503131i
$976$	2.18623	+	3.78666i	0.0699795	+	0.121208i
$977$	0.495778	+	1.85027i	0.0158614	+	0.0591954i	0.973403	−	0.229100i	$-0.0735782\pi$
$977$	0.495778	+	1.85027i	0.0158614	+	0.0591954i	−0.957542	+	0.288295i	$0.906912\pi$
$978$	−14.5048	+	6.17907i	−0.463811	+	0.197585i
$979$	−7.48275	+	4.32017i	−0.239150	+	0.138073i
$980$	16.6076	−	16.6076i	0.530511	−	0.530511i
$981$	−2.95547	+	5.36451i	−0.0943610	+	0.171276i
$982$	0.827501	+	3.08827i	0.0264066	+	0.0985508i
$983$	−45.6118	+	12.2217i	−1.45479	+	0.389810i	−0.897687	−	0.440633i	$-0.854754\pi$
$983$	−45.6118	+	12.2217i	−1.45479	+	0.389810i	−0.557104	+	0.830443i	$0.688087\pi$
$984$	−3.51915	−	8.26085i	−0.112186	−	0.263346i
$985$	−18.8560	−	10.8865i	−0.600801	−	0.346873i
$986$	−39.7042	+	10.6387i	−1.26444	+	0.338806i
$987$	−31.0001	+	41.2494i	−0.986743	+	1.31298i
$988$	21.3062	+	0.488008i	0.677841	+	0.0155256i
$989$			60.9752i			1.93890i
$990$	−0.144463	−	7.20730i	−0.00459135	−	0.229063i
$991$	1.33681	+	2.31541i	0.0424650	+	0.0735516i	0.886477	−	0.462773i	$-0.153146\pi$
$991$	1.33681	+	2.31541i	0.0424650	+	0.0735516i	−0.844012	+	0.536325i	$0.819812\pi$
$992$	0.524122	+	0.907805i	0.0166409	+	0.0288228i
$993$	−32.8356	−	41.9158i	−1.04201	−	1.33016i
$994$	−0.953706	−	0.953706i	−0.0302497	−	0.0302497i
$995$	−13.8751	−	13.8751i	−0.439872	−	0.439872i
$996$	7.50208	−	18.6377i	0.237712	−	0.590558i
$997$	28.3561	+	49.1143i	0.898048	+	1.55546i	0.829987	+	0.557783i	$0.188348\pi$
$997$	28.3561	+	49.1143i	0.898048	+	1.55546i	0.0680612	+	0.997681i	$0.478319\pi$
$998$	17.0478	+	29.5276i	0.539639	+	0.934681i
$999$	−30.3268	−	21.8543i	−0.959496	−	0.691440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.11.3	✓	56
3.2	odd	2		702.2.bb.a.89.9		56
9.4	even	3		702.2.bc.a.557.2		56
9.5	odd	6		234.2.z.a.167.14	yes	56
13.6	odd	12		234.2.z.a.227.14	yes	56
39.32	even	12		702.2.bc.a.305.2		56
117.32	even	12	inner	234.2.y.a.149.3	yes	56
117.58	odd	12		702.2.bb.a.71.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.3	✓	56	1.1	even	1	trivial
234.2.y.a.149.3	yes	56	117.32	even	12	inner
234.2.z.a.167.14	yes	56	9.5	odd	6
234.2.z.a.227.14	yes	56	13.6	odd	12
702.2.bb.a.71.9		56	117.58	odd	12
702.2.bb.a.89.9		56	3.2	odd	2
702.2.bc.a.305.2		56	39.32	even	12
702.2.bc.a.557.2		56	9.4	even	3

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.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.04058 + 1.38462i) q^{3} -1.00000i q^{4} +(1.51706 + 0.406496i) q^{5} +(-0.243274 - 1.71488i) q^{6} +(4.52587 + 1.21270i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.834373 - 2.88164i) q^{9} +(-1.36016 + 0.785290i) q^{10} +(-1.08184 - 1.08184i) q^{11} +(1.38462 + 1.04058i) q^{12} +(-1.01269 + 3.46041i) q^{13} +(-4.05778 + 2.34276i) q^{14} +(-2.14148 + 1.67757i) q^{15} -1.00000 q^{16} +(-2.99188 + 5.18209i) q^{17} +(2.62761 + 1.44763i) q^{18} +(5.70943 - 1.52984i) q^{19} +(0.406496 - 1.51706i) q^{20} +(-6.38869 + 5.00471i) q^{21} +1.52995 q^{22} +(-2.48702 + 4.30764i) q^{23} +(-1.71488 + 0.243274i) q^{24} +(-2.19388 - 1.26664i) q^{25} +(-1.73080 - 3.16296i) q^{26} +(4.85822 + 1.84329i) q^{27} +(1.21270 - 4.52587i) q^{28} -6.86939i q^{29} +(0.328030 - 2.70047i) q^{30} +(-0.271305 + 1.01253i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.62369 - 0.372198i) q^{33} +(-1.54871 - 5.77988i) q^{34} +(6.37308 + 3.67950i) q^{35} +(-2.88164 + 0.834373i) q^{36} +(-6.94881 - 1.86193i) q^{37} +(-2.95542 + 5.11893i) q^{38} +(-3.73759 - 5.00304i) q^{39} +(0.785290 + 1.36016i) q^{40} +(1.34176 + 5.00750i) q^{41} +(0.978615 - 8.05635i) q^{42} +(10.6164 - 6.12935i) q^{43} +(-1.08184 + 1.08184i) q^{44} +(-0.0944233 - 4.71079i) q^{45} +(-1.28737 - 4.80455i) q^{46} +(6.14146 - 1.64560i) q^{47} +(1.04058 - 1.38462i) q^{48} +(12.9507 + 7.47708i) q^{49} +(2.44696 - 0.655661i) q^{50} +(-4.06195 - 9.53504i) q^{51} +(3.46041 + 1.01269i) q^{52} -2.78130i q^{53} +(-4.73868 + 2.13188i) q^{54} +(-1.20146 - 2.08099i) q^{55} +(2.34276 + 4.05778i) q^{56} +(-3.82288 + 9.49734i) q^{57} +(4.85740 + 4.85740i) q^{58} +(-4.22367 - 4.22367i) q^{59} +(1.67757 + 2.14148i) q^{60} +(-2.18623 - 3.78666i) q^{61} +(-0.524122 - 0.907805i) q^{62} +(-0.281694 - 14.0538i) q^{63} +1.00000i q^{64} +(-2.94296 + 4.83801i) q^{65} +(-1.59205 + 2.11841i) q^{66} +(-5.41695 + 1.45147i) q^{67} +(5.18209 + 2.99188i) q^{68} +(-3.37652 - 7.92604i) q^{69} +(-7.10824 + 1.90465i) q^{70} +(0.0745019 + 0.278045i) q^{71} +(1.44763 - 2.62761i) q^{72} +(0.964880 - 0.964880i) q^{73} +(6.23013 - 3.59697i) q^{74} +(4.03674 - 1.71966i) q^{75} +(-1.52984 - 5.70943i) q^{76} +(-3.58432 - 6.20823i) q^{77} +(6.18056 + 0.894812i) q^{78} +(-0.0673941 + 0.116730i) q^{79} +(-1.51706 - 0.406496i) q^{80} +(-7.60764 + 4.80872i) q^{81} +(-4.48960 - 2.59207i) q^{82} +(-3.00217 - 11.2043i) q^{83} +(5.00471 + 6.38869i) q^{84} +(-6.64538 + 6.64538i) q^{85} +(-3.17279 + 11.8410i) q^{86} +(9.51153 + 7.14818i) q^{87} -1.52995i q^{88} +(1.46167 - 5.45501i) q^{89} +(3.39780 + 3.26427i) q^{90} +(-8.77976 + 14.4333i) q^{91} +(4.30764 + 2.48702i) q^{92} +(-1.11965 - 1.42927i) q^{93} +(-3.17905 + 5.50628i) q^{94} +9.28344 q^{95} +(0.243274 + 1.71488i) q^{96} +(-1.72699 + 6.44523i) q^{97} +(-14.4446 + 3.87042i) q^{98} +(-2.21481 + 4.02013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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