LMFDB - Embedded newform 798.2.bu.a.53.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.19
Character	$\chi$	$=$	798.53
Dual form			798.2.bu.a.527.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 + 0.984808i) q^{2} +(1.00105 - 1.41347i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.13790 - 3.12636i) q^{5} +(1.56582 + 0.740400i) q^{6} +(2.35336 - 1.20900i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.995780 - 2.82992i) q^{9} +(3.27646 + 0.577729i) q^{10} +0.301942i q^{11} +(-0.457249 + 1.67061i) q^{12} +(-4.16040 - 0.733591i) q^{13} +(1.59929 + 2.10767i) q^{14} +(-3.27991 - 4.73805i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.32954 + 3.96800i) q^{17} +(2.61401 - 1.47206i) q^{18} +(-3.80930 - 2.11878i) q^{19} +3.32701i q^{20} +(0.646957 - 4.53668i) q^{21} +(-0.297354 + 0.0524316i) q^{22} +(4.99086 + 0.880023i) q^{23} +(-1.72463 - 0.160205i) q^{24} +(-4.64911 - 3.90106i) q^{25} -4.22458i q^{26} +(-4.99682 - 1.42540i) q^{27} +(-1.79793 + 1.94099i) q^{28} +(-2.15076 + 0.782814i) q^{29} +(4.09652 - 4.05283i) q^{30} +(-5.45792 + 3.15113i) q^{31} +(0.766044 + 0.642788i) q^{32} +(0.426785 + 0.302260i) q^{33} +(-3.32954 + 3.96800i) q^{34} +(-1.10188 - 8.73319i) q^{35} +(1.90362 + 2.31867i) q^{36} +(-1.64763 + 0.951258i) q^{37} +(1.42511 - 4.11935i) q^{38} +(-5.20169 + 5.14623i) q^{39} +(-3.27646 + 0.577729i) q^{40} +(0.980048 + 5.55813i) q^{41} +(4.58010 - 0.150657i) q^{42} +(5.96069 - 5.00161i) q^{43} +(-0.103270 - 0.283732i) q^{44} +(-9.98045 - 0.107000i) q^{45} +5.06785i q^{46} +(2.54487 - 3.03286i) q^{47} +(-0.141707 - 1.72624i) q^{48} +(4.07662 - 5.69044i) q^{49} +(3.03449 - 5.25589i) q^{50} +(8.94169 - 0.734022i) q^{51} +(4.16040 - 0.733591i) q^{52} +(10.8725 - 3.95725i) q^{53} +(0.536053 - 5.16843i) q^{54} +(0.943979 + 0.343580i) q^{55} +(-2.22371 - 1.43357i) q^{56} +(-6.80814 + 3.26331i) q^{57} +(-1.14440 - 1.98215i) q^{58} +(-7.06308 + 5.92663i) q^{59} +(4.70262 + 3.33052i) q^{60} +(0.523848 - 2.97089i) q^{61} +(-4.05102 - 4.82781i) q^{62} +(-5.76481 - 5.45591i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-7.02761 + 12.1722i) q^{65} +(-0.223558 + 0.472788i) q^{66} +(12.4831 + 2.20110i) q^{67} +(-4.48588 - 2.58992i) q^{68} +(6.24001 - 6.17347i) q^{69} +(8.40918 - 2.60165i) q^{70} +(10.7378 - 9.01009i) q^{71} +(-1.95289 + 2.27733i) q^{72} +(2.96165 + 1.07795i) q^{73} +(-1.22291 - 1.45741i) q^{74} +(-10.1680 + 2.66618i) q^{75} +(4.30424 + 0.688141i) q^{76} +(0.365048 + 0.710578i) q^{77} +(-5.97131 - 4.22904i) q^{78} +(7.26233 + 8.65491i) q^{79} +(-1.13790 - 3.12636i) q^{80} +(-7.01684 + 5.63595i) q^{81} +(-5.30351 + 1.93032i) q^{82} +(5.22205 + 3.01495i) q^{83} +(0.943694 + 4.48436i) q^{84} +(16.1941 - 5.89417i) q^{85} +(5.96069 + 5.00161i) q^{86} +(-1.04655 + 3.82367i) q^{87} +(0.261489 - 0.150971i) q^{88} +(-2.06192 + 0.750477i) q^{89} +(-1.62771 - 9.84740i) q^{90} +(-10.6778 + 3.30353i) q^{91} +(-4.99086 + 0.880023i) q^{92} +(-1.00965 + 10.8690i) q^{93} +(3.42870 + 1.97956i) q^{94} +(-10.9587 + 9.49830i) q^{95} +(1.67541 - 0.439313i) q^{96} +(-0.366989 + 1.00830i) q^{97} +(6.31189 + 3.02656i) q^{98} +(0.854469 - 0.300667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.00105	−	1.41347i	0.577959	−	0.816066i
$3$	1.00105	−	1.41347i	0.577959	−	0.816066i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	1.13790	−	3.12636i	0.508886	−	1.39815i	−0.373502	−	0.927629i	$-0.621843\pi$
$5$	1.13790	−	3.12636i	0.508886	−	1.39815i	0.882388	−	0.470523i	$-0.155935\pi$
$6$	1.56582	+	0.740400i	0.639245	+	0.302267i
$7$	2.35336	−	1.20900i	0.889487	−	0.456960i
$7$	2.35336	−	1.20900i	0.889487	−	0.456960i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.995780	−	2.82992i	−0.331927	−	0.943305i
$10$	3.27646	+	0.577729i	1.03611	+	0.182694i
$11$			0.301942i			0.0910388i	0.998963	+	0.0455194i	$0.0144943\pi$
$11$			0.301942i			0.0910388i	−0.998963	+	0.0455194i	$0.985506\pi$
$12$	−0.457249	+	1.67061i	−0.131996	+	0.482262i
$13$	−4.16040	−	0.733591i	−1.15389	−	0.203461i	−0.436215	−	0.899842i	$-0.643681\pi$
$13$	−4.16040	−	0.733591i	−1.15389	−	0.203461i	−0.717672	+	0.696381i	$0.754792\pi$
$14$	1.59929	+	2.10767i	0.427429	+	0.563298i
$15$	−3.27991	−	4.73805i	−0.846869	−	1.22336i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	3.32954	+	3.96800i	0.807533	+	0.962380i	0.999820	−	0.0189585i	$-0.00603504\pi$
$17$	3.32954	+	3.96800i	0.807533	+	0.962380i	−0.192287	+	0.981339i	$0.561591\pi$
$18$	2.61401	−	1.47206i	0.616127	−	0.346968i
$19$	−3.80930	−	2.11878i	−0.873914	−	0.486081i
$19$	−3.80930	−	2.11878i	−0.873914	−	0.486081i
$20$			3.32701i			0.743941i
$21$	0.646957	−	4.53668i	0.141178	−	0.989984i
$22$	−0.297354	+	0.0524316i	−0.0633962	+	0.0111785i
$23$	4.99086	+	0.880023i	1.04067	+	0.183498i	0.667764	−	0.744373i	$-0.267252\pi$
$23$	4.99086	+	0.880023i	1.04067	+	0.183498i	0.372902	+	0.927871i	$0.378363\pi$
$24$	−1.72463	−	0.160205i	−0.352038	−	0.0327017i
$25$	−4.64911	−	3.90106i	−0.929821	−	0.780213i
$26$		−	4.22458i		−	0.828508i
$27$	−4.99682	−	1.42540i	−0.961639	−	0.274318i
$28$	−1.79793	+	1.94099i	−0.339777	+	0.366812i
$29$	−2.15076	+	0.782814i	−0.399387	+	0.145365i	−0.533901	−	0.845547i	$-0.679275\pi$
$29$	−2.15076	+	0.782814i	−0.399387	+	0.145365i	0.134515	+	0.990912i	$0.457052\pi$
$30$	4.09652	−	4.05283i	0.747918	−	0.739943i
$31$	−5.45792	+	3.15113i	−0.980271	+	0.565960i	−0.902352	−	0.431000i	$-0.858161\pi$
$31$	−5.45792	+	3.15113i	−0.980271	+	0.565960i	−0.0779191	+	0.996960i	$0.524828\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	0.426785	+	0.302260i	0.0742937	+	0.0526167i
$34$	−3.32954	+	3.96800i	−0.571012	+	0.680506i
$35$	−1.10188	−	8.73319i	−0.186252	−	1.47618i
$36$	1.90362	+	2.31867i	0.317269	+	0.386446i
$37$	−1.64763	+	0.951258i	−0.270868	+	0.156386i	−0.629282	−	0.777177i	$-0.716651\pi$
$37$	−1.64763	+	0.951258i	−0.270868	+	0.156386i	0.358414	+	0.933563i	$0.383318\pi$
$38$	1.42511	−	4.11935i	0.231183	−	0.668247i
$39$	−5.20169	+	5.14623i	−0.832938	+	0.824056i
$40$	−3.27646	+	0.577729i	−0.518054	+	0.0913469i
$41$	0.980048	+	5.55813i	0.153058	+	0.868034i	0.960540	+	0.278142i	$0.0897186\pi$
$41$	0.980048	+	5.55813i	0.153058	+	0.868034i	−0.807482	+	0.589892i	$0.799170\pi$
$42$	4.58010	−	0.150657i	0.706725	−	0.0232469i
$43$	5.96069	−	5.00161i	0.908997	−	0.762739i	−0.0629311	−	0.998018i	$-0.520045\pi$
$43$	5.96069	−	5.00161i	0.908997	−	0.762739i	0.971928	+	0.235279i	$0.0756004\pi$
$44$	−0.103270	−	0.283732i	−0.0155686	−	0.0427742i
$45$	−9.98045	−	0.107000i	−1.48780	−	0.0159506i
$46$			5.06785i			0.747214i
$47$	2.54487	−	3.03286i	0.371208	−	0.442388i	−0.547811	−	0.836602i	$-0.684539\pi$
$47$	2.54487	−	3.03286i	0.371208	−	0.442388i	0.919019	+	0.394214i	$0.128983\pi$
$48$	−0.141707	−	1.72624i	−0.0204537	−	0.249162i
$49$	4.07662	−	5.69044i	0.582375	−	0.812920i
$50$	3.03449	−	5.25589i	0.429141	−	0.743295i
$51$	8.94169	−	0.734022i	1.25209	−	0.102784i
$52$	4.16040	−	0.733591i	0.576944	−	0.101731i
$53$	10.8725	−	3.95725i	1.49345	−	0.543570i	0.539092	−	0.842247i	$-0.318767\pi$
$53$	10.8725	−	3.95725i	1.49345	−	0.543570i	0.954354	+	0.298677i	$0.0965453\pi$
$54$	0.536053	−	5.16843i	0.0729475	−	0.703334i
$55$	0.943979	+	0.343580i	0.127286	+	0.0463284i
$56$	−2.22371	−	1.43357i	−0.297155	−	0.191569i
$57$	−6.80814	+	3.26331i	−0.901760	+	0.432236i
$58$	−1.14440	−	1.98215i	−0.150267	−	0.260270i
$59$	−7.06308	+	5.92663i	−0.919535	+	0.771581i	−0.973909	−	0.226939i	$-0.927128\pi$
$59$	−7.06308	+	5.92663i	−0.919535	+	0.771581i	0.0543742	+	0.998521i	$0.482684\pi$
$60$	4.70262	+	3.33052i	0.607105	+	0.429968i
$61$	0.523848	−	2.97089i	0.0670719	−	0.380384i	−0.932732	−	0.360571i	$-0.882582\pi$
$61$	0.523848	−	2.97089i	0.0670719	−	0.380384i	0.999804	−	0.0198128i	$-0.00630702\pi$
$62$	−4.05102	−	4.82781i	−0.514479	−	0.613133i
$63$	−5.76481	−	5.45591i	−0.726297	−	0.687381i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−7.02761	+	12.1722i	−0.871667	+	1.50977i
$66$	−0.223558	+	0.472788i	−0.0275180	+	0.0581961i
$67$	12.4831	+	2.20110i	1.52505	+	0.268907i	0.872415	−	0.488765i	$-0.162553\pi$
$67$	12.4831	+	2.20110i	1.52505	+	0.268907i	0.652635	+	0.757673i	$0.273664\pi$
$68$	−4.48588	−	2.58992i	−0.543993	−	0.314075i
$69$	6.24001	−	6.17347i	0.751208	−	0.743198i
$70$	8.40918	−	2.60165i	1.00509	−	0.310956i
$71$	10.7378	−	9.01009i	1.27434	−	1.06930i	0.280346	−	0.959899i	$-0.409551\pi$
$71$	10.7378	−	9.01009i	1.27434	−	1.06930i	0.993998	−	0.109402i	$-0.0348937\pi$
$72$	−1.95289	+	2.27733i	−0.230150	+	0.268386i
$73$	2.96165	+	1.07795i	0.346635	+	0.126165i	0.509470	−	0.860489i	$-0.329842\pi$
$73$	2.96165	+	1.07795i	0.346635	+	0.126165i	−0.162835	+	0.986653i	$0.552064\pi$
$74$	−1.22291	−	1.45741i	−0.142161	−	0.169421i
$75$	−10.1680	+	2.66618i	−1.17410	+	0.307864i
$76$	4.30424	+	0.688141i	0.493730	+	0.0789352i
$77$	0.365048	+	0.710578i	0.0416011	+	0.0809779i
$78$	−5.97131	−	4.22904i	−0.676117	−	0.478844i
$79$	7.26233	+	8.65491i	0.817076	+	0.973753i	0.999956	−	0.00938202i	$-0.00298643\pi$
$79$	7.26233	+	8.65491i	0.817076	+	0.973753i	−0.182880	+	0.983135i	$0.558542\pi$
$80$	−1.13790	−	3.12636i	−0.127221	−	0.349538i
$81$	−7.01684	+	5.63595i	−0.779649	+	0.626216i
$82$	−5.30351	+	1.93032i	−0.585674	+	0.213168i
$83$	5.22205	+	3.01495i	0.573194	+	0.330934i	0.758424	−	0.651762i	$-0.225970\pi$
$83$	5.22205	+	3.01495i	0.573194	+	0.330934i	−0.185230	+	0.982695i	$0.559303\pi$
$84$	0.943694	+	4.48436i	0.102965	+	0.489283i
$85$	16.1941	−	5.89417i	1.75650	−	0.639312i
$86$	5.96069	+	5.00161i	0.642758	+	0.539338i
$87$	−1.04655	+	3.82367i	−0.112202	+	0.409941i
$88$	0.261489	−	0.150971i	0.0278748	−	0.0160935i
$89$	−2.06192	+	0.750477i	−0.218563	+	0.0795504i	−0.448981	−	0.893541i	$-0.648213\pi$
$89$	−2.06192	+	0.750477i	−0.218563	+	0.0795504i	0.230418	+	0.973092i	$0.425991\pi$
$90$	−1.62771	−	9.84740i	−0.171576	−	1.03801i
$91$	−10.6778	+	3.30353i	−1.11934	+	0.346304i
$92$	−4.99086	+	0.880023i	−0.520333	+	0.0917488i
$93$	−1.00965	+	10.8690i	−0.104696	+	1.12707i
$94$	3.42870	+	1.97956i	0.353643	+	0.204176i
$95$	−10.9587	+	9.49830i	−1.12434	+	0.974505i
$96$	1.67541	−	0.439313i	0.170996	−	0.0448372i
$97$	−0.366989	+	1.00830i	−0.0372621	+	0.102377i	−0.956928	−	0.290324i	$-0.906237\pi$
$97$	−0.366989	+	1.00830i	−0.0372621	+	0.102377i	0.919666	+	0.392701i	$0.128459\pi$
$98$	6.31189	+	3.02656i	0.637597	+	0.305728i
$99$	0.854469	−	0.300667i	0.0858774	−	0.0302182i
$100$	5.70297	+	2.07571i	0.570297	+	0.207571i
$101$	−1.20133	+	1.43169i	−0.119537	+	0.142458i	−0.822494	−	0.568774i	$-0.807418\pi$
$101$	−1.20133	+	1.43169i	−0.119537	+	0.142458i	0.702957	+	0.711232i	$0.251862\pi$
$102$	2.27558	+	8.67838i	0.225316	+	0.859288i
$103$	−13.8745	−	8.01045i	−1.36710	−	0.789294i	−0.376540	−	0.926400i	$-0.622886\pi$
$103$	−13.8745	−	8.01045i	−1.36710	−	0.789294i	−0.990556	+	0.137107i	$0.956220\pi$
$104$	1.44489	+	3.96981i	0.141683	+	0.389272i
$105$	−13.4471	−	7.18493i	−1.31231	−	0.701177i
$106$	5.78511	+	10.0201i	0.561900	+	0.973239i
$107$	−8.42357			−0.814337			−0.407169	−	0.913353i	$-0.633484\pi$
$107$	−8.42357			−0.814337			−0.407169	+	0.913353i	$0.633484\pi$
$108$	5.18299	−	0.369579i	0.498734	−	0.0355628i
$109$	4.25418	−	0.750127i	0.407477	−	0.0718491i	0.0338468	−	0.999427i	$-0.489224\pi$
$109$	4.25418	−	0.750127i	0.407477	−	0.0718491i	0.373630	+	0.927578i	$0.378113\pi$
$110$	−0.174440	+	0.989300i	−0.0166322	+	0.0943261i
$111$	−0.304792	+	3.28113i	−0.0289296	+	0.311431i
$112$	1.02565	−	2.43886i	0.0969146	−	0.230451i
$113$	10.8346			1.01924			0.509618	−	0.860401i	$-0.329787\pi$
$113$	10.8346			1.01924			0.509618	+	0.860401i	$0.329787\pi$
$114$	−4.39596	−	6.13804i	−0.411719	−	0.574880i
$115$	8.43039	−	14.6019i	0.786138	−	1.36163i
$116$	1.75332	−	1.47121i	0.162792	−	0.136598i
$117$	2.06684	+	12.5041i	0.191080	+	1.15600i
$118$	−7.06308	−	5.92663i	−0.650209	−	0.545590i
$119$	12.6329	+	5.31270i	1.15806	+	0.487015i
$120$	−2.46332	+	5.20951i	−0.224869	+	0.475561i
$121$	10.9088			0.991712
$122$	3.01672			0.273121
$123$	8.83732	+	4.17873i	0.796834	+	0.376783i
$124$	4.05102	−	4.82781i	0.363792	−	0.433550i
$125$	−3.08001	+	1.77825i	−0.275485	+	0.159051i
$126$	4.37198	−	6.62464i	0.389487	−	0.590169i
$127$	−19.1919	−	3.38404i	−1.70300	−	0.300285i	−0.764261	−	0.644908i	$-0.776896\pi$
$127$	−19.1919	−	3.38404i	−1.70300	−	0.300285i	−0.938741	+	0.344622i	$0.888007\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−1.10264	−	13.4321i	−0.0970821	−	1.18263i
$130$	−13.2076	−	4.80717i	−1.15838	−	0.421616i
$131$	−4.13220	+	0.728619i	−0.361032	+	0.0636597i	−0.351222	−	0.936292i	$-0.614234\pi$
$131$	−4.13220	+	0.728619i	−0.361032	+	0.0636597i	−0.00981012	+	0.999952i	$0.503123\pi$
$132$	−0.504425	−	0.138063i	−0.0439046	−	0.0120168i
$133$	−11.5263	−	0.380791i	−0.999455	−	0.0330188i
$134$			12.6756i			1.09501i
$135$	−10.1422	+	13.9999i	−0.872903	+	1.20492i
$136$	1.77161	−	4.86747i	0.151915	−	0.417382i
$137$	5.06975	+	13.9290i	0.433138	+	1.19004i	0.943876	+	0.330300i	$0.107150\pi$
$137$	5.06975	+	13.9290i	0.433138	+	1.19004i	−0.510738	+	0.859736i	$0.670628\pi$
$138$	7.16324	+	5.07319i	0.609776	+	0.431859i
$139$	−3.14718	+	17.8486i	−0.266941	+	1.51390i	0.496511	+	0.868030i	$0.334614\pi$
$139$	−3.14718	+	17.8486i	−0.266941	+	1.51390i	−0.763452	+	0.645865i	$0.776497\pi$
$140$	4.02236	+	7.82965i	0.339952	+	0.661726i
$141$	−1.73929	−	6.63315i	−0.146475	−	0.558612i
$142$	10.7378	+	9.01009i	0.901097	+	0.756110i
$143$	0.221502	−	1.25620i	0.0185229	−	0.105049i
$144$	−2.58185	−	1.52777i	−0.215154	−	0.127314i
$145$			7.61484i			0.632378i
$146$	−0.547291	+	3.10384i	−0.0452941	+	0.256876i
$147$	−3.96233	−	11.4586i	−0.326808	−	0.945091i
$148$	1.22291	−	1.45741i	0.100523	−	0.119799i
$149$	−1.39001	−	1.65655i	−0.113874	−	0.135710i	0.706096	−	0.708116i	$-0.250455\pi$
$149$	−1.39001	−	1.65655i	−0.113874	−	0.135710i	−0.819970	+	0.572406i	$0.806010\pi$
$150$	−4.39134	−	9.55058i	−0.358551	−	0.779802i
$151$	−4.10497	−	2.37000i	−0.334058	−	0.192868i	0.323584	−	0.946200i	$-0.395112\pi$
$151$	−4.10497	−	2.37000i	−0.334058	−	0.192868i	−0.657641	+	0.753331i	$0.728446\pi$
$152$	0.0697367	+	4.35834i	0.00565640	+	0.353508i
$153$	7.91360	−	13.3736i	0.639777	−	1.08119i
$154$	−0.636393	+	0.482893i	−0.0512820	+	0.0389126i
$155$	3.64100	+	20.6491i	0.292452	+	1.65858i
$156$	3.12788	−	6.61495i	0.250431	−	0.529620i
$157$	1.16854	+	6.62712i	0.0932597	+	0.528902i	0.995267	+	0.0971807i	$0.0309825\pi$
$157$	1.16854	+	6.62712i	0.0932597	+	0.528902i	−0.902007	+	0.431721i	$0.857906\pi$
$158$	−7.26233	+	8.65491i	−0.577760	+	0.688548i
$159$	5.29048	−	19.3293i	0.419562	−	1.53291i
$160$	2.88127	−	1.66350i	0.227785	−	0.131512i
$161$	12.8092	−	3.96295i	1.00951	−	0.312324i
$162$	−6.76879	−	5.93157i	−0.531806	−	0.466028i
$163$	5.99967	−	10.3917i	0.469930	−	0.813943i	−0.529479	−	0.848323i	$-0.677612\pi$
$163$	5.99967	−	10.3917i	0.469930	−	0.813943i	0.999409	+	0.0343803i	$0.0109457\pi$
$164$	−2.82194	−	4.88774i	−0.220356	−	0.381668i
$165$	1.43061	−	0.990341i	0.111373	−	0.0770980i
$166$	−2.06235	+	5.66625i	−0.160069	+	0.439786i
$167$	15.3629	+	12.8910i	1.18882	+	0.997539i	0.999879	+	0.0155504i	$0.00495006\pi$
$167$	15.3629	+	12.8910i	1.18882	+	0.997539i	0.188941	+	0.981988i	$0.439494\pi$
$168$	−4.25236	+	1.70806i	−0.328076	+	0.131779i
$169$	4.55477	+	1.65780i	0.350367	+	0.127523i
$170$	8.61670	+	14.9246i	0.660871	+	1.14466i
$171$	−2.20273	+	12.8898i	−0.168447	+	0.985711i
$172$	−3.89056	+	6.73865i	−0.296653	+	0.513818i
$173$	−0.213363	−	1.21004i	−0.0162217	−	0.0919977i	0.975622	−	0.219457i	$-0.0704287\pi$
$173$	−0.213363	−	1.21004i	−0.0162217	−	0.0919977i	−0.991844	+	0.127460i	$0.959318\pi$
$174$	−3.94731	−	0.366676i	−0.299245	−	0.0277976i
$175$	−15.6574	−	3.55983i	−1.18359	−	0.269098i
$176$	0.194084	+	0.231301i	0.0146297	+	0.0174349i
$177$	1.30657	+	15.9163i	0.0982076	+	1.19634i
$178$	−1.09712	−	1.90028i	−0.0822329	−	0.142432i
$179$	−21.8460			−1.63284			−0.816422	−	0.577456i	$-0.804046\pi$
$179$	−21.8460			−1.63284			−0.816422	+	0.577456i	$0.804046\pi$
$180$	9.41515	−	3.31297i	0.701764	−	0.246934i
$181$	−9.09388	−	24.9852i	−0.675943	−	1.85714i	−0.482129	−	0.876100i	$-0.660136\pi$
$181$	−9.09388	−	24.9852i	−0.675943	−	1.85714i	−0.193814	−	0.981038i	$-0.562086\pi$
$182$	−5.10753	−	9.94197i	−0.378595	−	0.736948i
$183$	−3.67486	−	3.71447i	−0.271653	−	0.274581i
$184$	−1.73331	−	4.76222i	−0.127781	−	0.351076i
$185$	1.09914	+	6.23352i	0.0808102	+	0.458298i
$186$	−10.8792	+	0.893075i	−0.797705	+	0.0654835i
$187$	−1.19810	+	1.00533i	−0.0876139	+	0.0735168i
$188$	−1.35410	+	3.72035i	−0.0987577	+	0.271335i
$189$	−13.4826	+	2.68670i	−0.980718	+	0.195429i
$190$	−11.2570	−	9.14284i	−0.816666	−	0.663291i
$191$	−10.9479	+	6.32075i	−0.792160	+	0.457354i	−0.840722	−	0.541466i	$-0.817869\pi$
$191$	−10.9479	+	6.32075i	−0.792160	+	0.457354i	0.0485625	+	0.998820i	$0.484536\pi$
$192$	0.723571	+	1.57367i	0.0522193	+	0.113570i
$193$	4.80479	−	13.2011i	0.345857	−	0.950233i	−0.637804	−	0.770199i	$-0.720157\pi$
$193$	4.80479	−	13.2011i	0.345857	−	0.950233i	0.983660	−	0.180034i	$-0.0576209\pi$
$194$	−1.05670	−	0.186325i	−0.0758669	−	0.0133774i
$195$	10.1699	+	22.1183i	0.728285	+	1.58392i
$196$	−1.88453	+	6.74155i	−0.134609	+	0.481540i
$197$	−5.87853	−	3.39397i	−0.418828	−	0.241811i	0.275748	−	0.961230i	$-0.411075\pi$
$197$	−5.87853	−	3.39397i	−0.418828	−	0.241811i	−0.694576	+	0.719419i	$0.744408\pi$
$198$	0.444477	+	0.789277i	0.0315876	+	0.0560915i
$199$	−2.15492	+	12.2212i	−0.152758	+	0.866336i	0.808048	+	0.589116i	$0.200524\pi$
$199$	−2.15492	+	12.2212i	−0.152758	+	0.866336i	−0.960807	+	0.277220i	$0.910587\pi$
$200$	−1.05387	+	5.97678i	−0.0745196	+	0.422622i
$201$	15.6074	−	15.4410i	1.10086	−	1.08912i
$202$	−1.61855	−	0.934468i	−0.113881	−	0.0657490i
$203$	−4.11510	+	4.44252i	−0.288823	+	0.311804i
$204$	−8.15139	+	3.74799i	−0.570711	+	0.262412i
$205$	18.4919	+	3.26063i	1.29153	+	0.227732i
$206$	5.47947	−	15.0547i	0.381773	−	1.04891i
$207$	−2.47941	−	15.0000i	−0.172331	−	1.04257i
$208$	−3.65859	+	2.11229i	−0.253678	+	0.146461i
$209$	0.639747	−	1.15019i	0.0442522	−	0.0795601i
$210$	4.74070	−	14.4905i	0.327139	−	0.999939i
$211$	0.930099	−	2.55543i	0.0640307	−	0.175923i	−0.903551	−	0.428480i	$-0.859049\pi$
$211$	0.930099	−	2.55543i	0.0640307	−	0.175923i	0.967582	+	0.252557i	$0.0812715\pi$
$212$	−8.86331	+	7.43720i	−0.608734	+	0.510789i
$213$	−1.98634	−	24.1971i	−0.136102	−	1.65796i
$214$	−1.46274	−	8.29559i	−0.0999907	−	0.567075i
$215$	−8.85417	−	24.3266i	−0.603850	−	1.65906i
$216$	1.26398	+	5.04007i	0.0860031	+	0.342934i
$217$	−9.03473	+	14.0144i	−0.613318	+	0.951359i
$218$	1.47746	+	4.05929i	0.100066	+	0.274930i
$219$	4.48842	−	3.10711i	0.303300	−	0.209959i
$220$	−1.00456			−0.0677275
$221$	−10.9413	−	18.9510i	−0.735995	−	1.27478i
$222$	−3.28421	+	0.269600i	−0.220422	+	0.0180944i
$223$	7.05212	+	8.40439i	0.472245	+	0.562800i	0.948610	−	0.316448i	$-0.102490\pi$
$223$	7.05212	+	8.40439i	0.472245	+	0.562800i	−0.476365	+	0.879248i	$0.658046\pi$
$224$	2.57991	+	0.586562i	0.172378	+	0.0391913i
$225$	−6.41019	+	17.0412i	−0.427346	+	1.13608i
$226$	1.88141	+	10.6700i	0.125150	+	0.709759i
$227$	−8.62493	+	14.9388i	−0.572457	+	0.991525i	0.423856	+	0.905730i	$0.360676\pi$
$227$	−8.62493	+	14.9388i	−0.572457	+	0.991525i	−0.996313	+	0.0857950i	$0.972657\pi$
$228$	5.28144	−	5.39503i	0.349772	−	0.357295i
$229$	8.01844	+	13.8883i	0.529873	+	0.917767i	0.999393	+	0.0348453i	$0.0110938\pi$
$229$	8.01844	+	13.8883i	0.529873	+	0.917767i	−0.469519	+	0.882922i	$0.655573\pi$
$230$	15.8439	+	5.76673i	1.04472	+	0.380247i
$231$	1.36981	+	0.195343i	0.0901270	+	0.0128526i
$232$	1.75332	+	1.47121i	0.115111	+	0.0965896i
$233$	4.87332	−	13.3893i	0.319262	−	0.877164i	−0.671434	−	0.741065i	$-0.734321\pi$
$233$	4.87332	−	13.3893i	0.319262	−	0.877164i	0.990695	−	0.136099i	$-0.0434566\pi$
$234$	−11.9552	+	4.20675i	−0.781536	+	0.275004i
$235$	−6.58601	−	11.4073i	−0.429624	−	0.744130i
$236$	4.61010	−	7.98492i	0.300092	−	0.519774i
$237$	19.5034	−	1.60103i	1.26688	−	0.103998i
$238$	−3.03830	+	13.3636i	−0.196944	+	0.866231i
$239$	−21.4895	+	12.4070i	−1.39004	+	0.802541i	−0.993319	−	0.115398i	$-0.963186\pi$
$239$	−21.4895	+	12.4070i	−1.39004	+	0.802541i	−0.396723	+	0.917939i	$0.629852\pi$
$240$	−5.55812	−	1.52127i	−0.358775	−	0.0981976i
$241$	−11.5262	+	13.7363i	−0.742465	+	0.884836i	−0.996605	−	0.0823317i	$-0.973763\pi$
$241$	−11.5262	+	13.7363i	−0.742465	+	0.884836i	0.254140	+	0.967168i	$0.418208\pi$
$242$	1.89430	+	10.7431i	0.121770	+	0.690593i
$243$	0.941983	+	15.5600i	0.0604283	+	0.998173i
$244$	0.523848	+	2.97089i	0.0335360	+	0.190192i
$245$	−13.1516	−	19.2202i	−0.840224	−	1.22793i
$246$	−2.58066	+	9.42869i	−0.164537	+	0.601151i
$247$	14.2939	+	11.6094i	0.909500	+	0.738690i
$248$	5.45792	+	3.15113i	0.346578	+	0.200097i
$249$	9.48908	−	4.36306i	0.601346	−	0.276498i
$250$	−2.28607	−	2.72443i	−0.144584	−	0.172308i
$251$	6.14448	−	7.32271i	0.387836	−	0.462205i	−0.536435	−	0.843942i	$-0.680229\pi$
$251$	6.14448	−	7.32271i	0.387836	−	0.462205i	0.924271	+	0.381736i	$0.124674\pi$
$252$	7.28318	+	3.15520i	0.458797	+	0.198759i
$253$	−0.265716	+	1.50695i	−0.0167054	+	0.0947410i
$254$		−	19.4879i		−	1.22278i
$255$	7.87996	−	28.7902i	0.493462	−	1.80291i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	5.60072	+	4.69956i	0.349363	+	0.293150i	0.800534	−	0.599287i	$-0.204549\pi$
$257$	5.60072	+	4.69956i	0.349363	+	0.293150i	−0.451171	+	0.892437i	$0.648994\pi$
$258$	13.0366	−	3.41835i	0.811623	−	0.212817i
$259$	−2.72739	+	4.23064i	−0.169472	+	0.262879i
$260$	2.44066	−	13.8417i	0.151363	−	0.858425i
$261$	4.35698	+	5.30697i	0.269691	+	0.328493i
$262$	−1.43510	−	3.94290i	−0.0886607	−	0.243593i
$263$	−10.0400	+	27.5846i	−0.619091	+	1.70094i	0.0901089	+	0.995932i	$0.471278\pi$
$263$	−10.0400	+	27.5846i	−0.619091	+	1.70094i	−0.709200	+	0.705007i	$0.750944\pi$
$264$	0.0483725	−	0.520736i	0.00297712	−	0.0320491i
$265$		−	38.4942i		−	2.36468i
$266$	−1.62651	−	11.4173i	−0.0997278	−	0.700039i
$267$	−1.00332	+	3.66572i	−0.0614021	+	0.224339i
$268$	−12.4831	+	2.20110i	−0.762525	+	0.134454i
$269$	−0.0610317	−	0.0222137i	−0.00372117	−	0.00135439i	0.340159	−	0.940368i	$-0.389519\pi$
$269$	−0.0610317	−	0.0222137i	−0.00372117	−	0.00135439i	−0.343880	+	0.939014i	$0.611741\pi$
$270$	−15.5484	−	7.55707i	−0.946246	−	0.459909i
$271$	12.6672	+	4.61049i	0.769479	+	0.280068i	0.696779	−	0.717286i	$-0.254616\pi$
$271$	12.6672	+	4.61049i	0.769479	+	0.280068i	0.0727007	+	0.997354i	$0.476838\pi$
$272$	5.10116	+	0.899471i	0.309303	+	0.0545385i
$273$	−6.01967	+	18.3998i	−0.364327	+	1.11361i
$274$	−12.8370	+	7.41147i	−0.775515	+	0.447744i
$275$	1.17789	−	1.40376i	0.0710296	−	0.0846498i
$276$	−3.75224	+	7.93537i	−0.225858	+	0.477653i
$277$	23.1951			1.39366			0.696829	−	0.717237i	$-0.254594\pi$
$277$	23.1951			1.39366			0.696829	+	0.717237i	$0.254594\pi$
$278$	−18.1239			−1.08700
$279$	14.3523	+	12.3076i	0.859251	+	0.736838i
$280$	−7.01223	+	5.32086i	−0.419061	+	0.317982i
$281$	−4.66672	−	3.91584i	−0.278393	−	0.233600i	0.492890	−	0.870092i	$-0.335940\pi$
$281$	−4.66672	−	3.91584i	−0.278393	−	0.233600i	−0.771283	+	0.636492i	$0.780385\pi$
$282$	6.23035	−	2.86470i	0.371012	−	0.170591i
$283$	−12.2181	+	10.2522i	−0.726289	+	0.609429i	−0.929117	−	0.369785i	$-0.879431\pi$
$283$	−12.2181	+	10.2522i	−0.726289	+	0.609429i	0.202828	+	0.979214i	$0.434987\pi$
$284$	−7.00861	+	12.1393i	−0.415884	+	0.720333i
$285$	2.45530	+	24.9981i	0.145439	+	1.48076i
$286$	1.27558			0.0754264
$287$	9.02620	+	11.8954i	0.532800	+	0.702164i
$288$	1.05622	−	2.80792i	0.0622385	−	0.165458i
$289$	−1.70711	+	9.68149i	−0.100418	+	0.569499i
$290$	−7.49915	+	1.32230i	−0.440365	+	0.0776483i
$291$	1.05782	+	1.52809i	0.0620103	+	0.0895780i
$292$	−3.15172			−0.184441
$293$	3.55344	+	6.15474i	0.207594	+	0.359564i	0.950956	−	0.309326i	$-0.100103\pi$
$293$	3.55344	+	6.15474i	0.207594	+	0.359564i	−0.743362	+	0.668889i	$0.766770\pi$
$294$	10.5965	−	5.89190i	0.618000	−	0.343623i
$295$	10.4917	+	28.8257i	0.610850	+	1.67830i
$296$	1.64763	+	0.951258i	0.0957664	+	0.0552908i
$297$	0.430387	−	1.50875i	0.0249736	−	0.0875465i
$298$	1.39001	−	1.65655i	0.0805212	−	0.0959615i
$299$	−20.1184	−	7.32250i	−1.16348	−	0.423471i
$300$	8.64294	−	5.98306i	0.499000	−	0.345432i
$301$	7.98070	−	18.9771i	0.460000	−	1.09382i
$302$	1.62118	−	4.45415i	0.0932883	−	0.256308i
$303$	0.821049	+	3.13124i	0.0471680	+	0.179885i
$304$	−4.28002	+	0.825495i	−0.245476	+	0.0473454i
$305$	−8.69200	−	5.01833i	−0.497703	−	0.287349i
$306$	14.5446	+	5.47108i	0.831458	+	0.312761i
$307$	−15.1712	+	2.67510i	−0.865867	+	0.152676i	−0.588902	−	0.808204i	$-0.700440\pi$
$307$	−15.1712	+	2.67510i	−0.865867	+	0.152676i	−0.276965	+	0.960880i	$0.589329\pi$
$308$	−0.586065	−	0.542871i	−0.0333942	−	0.0309329i
$309$	−25.2117	+	11.5923i	−1.43424	+	0.659461i
$310$	−19.7032	+	7.17137i	−1.11906	+	0.407306i
$311$	11.2917	−	6.51928i	0.640295	−	0.369674i	−0.144433	−	0.989515i	$-0.546136\pi$
$311$	11.2917	−	6.51928i	0.640295	−	0.369674i	0.784728	+	0.619840i	$0.212803\pi$
$312$	7.05761	+	1.93169i	0.399558	+	0.109360i
$313$	4.52176	+	3.79420i	0.255585	+	0.214461i	0.761573	−	0.648079i	$-0.224428\pi$
$313$	4.52176	+	3.79420i	0.255585	+	0.214461i	−0.505988	+	0.862541i	$0.668872\pi$
$314$	−6.32353	+	2.30158i	−0.356857	+	0.129885i
$315$	−23.6170	+	11.8146i	−1.33067	+	0.665676i
$316$	−9.78451	−	5.64909i	−0.550422	−	0.317786i
$317$	17.1109	−	6.22787i	0.961045	−	0.349792i	0.186602	−	0.982436i	$-0.440252\pi$
$317$	17.1109	−	6.22787i	0.961045	−	0.349792i	0.774443	+	0.632644i	$0.218030\pi$
$318$	19.9543	+	1.85361i	1.11898	+	0.103945i
$319$	−0.236364	−	0.649405i	−0.0132338	−	0.0363597i
$320$	2.13856	+	2.54864i	0.119549	+	0.142473i
$321$	−8.43245	+	11.9064i	−0.470653	+	0.664553i
$322$	6.12705	+	11.9265i	0.341447	+	0.664637i
$323$	−4.27594	−	22.1699i	−0.237920	−	1.23356i
$324$	4.66607	−	7.69596i	0.259226	−	0.427553i
$325$	16.4804	+	19.6405i	0.914166	+	1.08946i
$326$	11.2757	+	4.10401i	0.624502	+	0.227300i
$327$	3.19839	−	6.76406i	0.176871	−	0.374054i
$328$	4.32346	−	3.62781i	0.238723	−	0.200312i
$329$	2.32227	−	10.2142i	0.128031	−	0.563126i
$330$	1.22372	+	1.23691i	0.0673635	+	0.0680896i
$331$	−23.9754	−	13.8422i	−1.31780	−	0.760835i	−0.334429	−	0.942421i	$-0.608544\pi$
$331$	−23.9754	−	13.8422i	−1.31780	−	0.760835i	−0.983375	+	0.181586i	$0.941877\pi$
$332$	−5.93829	−	1.04708i	−0.325906	−	0.0574660i
$333$	4.33265	+	3.71540i	0.237428	+	0.203603i
$334$	−10.0275	+	17.3681i	−0.548678	+	0.950338i
$335$	21.0860	−	36.5220i	1.15205	−	1.99541i
$336$	−2.42052	−	3.89115i	−0.132050	−	0.212280i
$337$	−1.66029	−	1.97865i	−0.0904416	−	0.107784i	0.718926	−	0.695087i	$-0.244634\pi$
$337$	−1.66029	−	1.97865i	−0.0904416	−	0.107784i	−0.809367	+	0.587303i	$0.800190\pi$
$338$	−0.841687	+	4.77345i	−0.0457817	+	0.259641i
$339$	10.8460	−	15.3144i	0.589076	−	0.831763i
$340$	−13.2015	+	11.0774i	−0.715954	+	0.600757i
$341$	−0.951457	−	1.64797i	−0.0515243	−	0.0892427i
$342$	−13.0765	+	0.0690295i	−0.707097	+	0.00373269i
$343$	2.71401	−	18.3203i	0.146543	−	0.989204i
$344$	−7.31187	−	2.66130i	−0.394230	−	0.143488i
$345$	−12.2000	−	26.5333i	−0.656825	−	1.42851i
$346$	1.15461	−	0.420243i	0.0620721	−	0.0225924i
$347$	−19.3774	+	3.41675i	−1.04023	+	0.183421i	−0.667570	−	0.744547i	$-0.732666\pi$
$347$	−19.3774	+	3.41675i	−1.04023	+	0.183421i	−0.372661	+	0.927968i	$0.621555\pi$
$348$	−0.324338	−	3.95102i	−0.0173864	−	0.211797i
$349$	9.59031	−	16.6109i	0.513357	−	0.889161i	−0.486523	−	0.873668i	$-0.661735\pi$
$349$	9.59031	−	16.6109i	0.513357	−	0.889161i	0.999880	−	0.0154930i	$-0.00493177\pi$
$350$	0.786866	−	16.0377i	0.0420597	−	0.857252i
$351$	19.7431	+	9.59585i	1.05381	+	0.512188i
$352$	−0.194084	+	0.231301i	−0.0103447	+	0.0123284i
$353$			33.4628i			1.78104i	0.454941	+	0.890522i	$0.349660\pi$
$353$			33.4628i			1.78104i	−0.454941	+	0.890522i	$0.650340\pi$
$354$	−15.4476	+	4.05056i	−0.821032	+	0.215285i
$355$	−15.9502	−	43.8229i	−0.846551	−	2.32588i
$356$	1.68089	−	1.41044i	0.0890871	−	0.0747530i
$357$	20.1556	−	12.5379i	1.06675	−	0.663578i
$358$	−3.79351	−	21.5141i	−0.200493	−	1.13705i
$359$	10.8355	−	1.91059i	0.571876	−	0.100837i	0.119771	−	0.992802i	$-0.461784\pi$
$359$	10.8355	−	1.91059i	0.571876	−	0.100837i	0.452106	+	0.891964i	$0.350673\pi$
$360$	4.89756	+	8.69682i	0.258124	+	0.458363i
$361$	10.0216	+	16.1421i	0.527451	+	0.849585i
$362$	23.0265	−	13.2944i	1.21025	−	0.698737i
$363$	10.9203	−	15.4193i	0.573169	−	0.809302i
$364$	8.90401	−	6.75634i	0.466697	−	0.354128i
$365$	6.74014	−	8.03259i	0.352795	−	0.420445i
$366$	3.01990	−	4.26404i	0.157853	−	0.222885i
$367$	−11.0145	−	9.24227i	−0.574952	−	0.482442i	0.308333	−	0.951279i	$-0.400229\pi$
$367$	−11.0145	−	9.24227i	−0.574952	−	0.482442i	−0.883285	+	0.468836i	$0.844673\pi$
$368$	4.38889	−	2.53393i	0.228787	−	0.132090i
$369$	14.7531	−	8.30813i	0.768017	−	0.432504i
$370$	−5.94796	+	2.16488i	−0.309220	+	0.112547i
$371$	20.8025	−	22.4577i	1.08001	−	1.16594i
$372$	−2.76867	−	10.5589i	−0.143549	−	0.547452i
$373$			19.4666i			1.00794i	0.863720	+	0.503972i	$0.168129\pi$
$373$			19.4666i			1.00794i	−0.863720	+	0.503972i	$0.831871\pi$
$374$	−1.19810	−	1.00533i	−0.0619524	−	0.0519842i
$375$	−0.569768	+	6.13362i	−0.0294227	+	0.316739i
$376$	−3.89897	−	0.687494i	−0.201074	−	0.0354548i
$377$	9.52230	−	1.67904i	0.490423	−	0.0864749i
$378$	−4.98712	−	12.8113i	−0.256510	−	0.658941i
$379$			3.01169i			0.154700i	0.997004	+	0.0773502i	$0.0246459\pi$
$379$			3.01169i			0.154700i	−0.997004	+	0.0773502i	$0.975354\pi$
$380$	7.04919	−	12.6736i	0.361616	−	0.650141i
$381$	−23.9953	+	23.7395i	−1.22932	+	1.21621i
$382$	−8.12580	−	9.68396i	−0.415752	−	0.495474i
$383$	13.9090	−	11.6710i	0.710714	−	0.596360i	−0.214085	−	0.976815i	$-0.568677\pi$
$383$	13.9090	−	11.6710i	0.710714	−	0.596360i	0.924799	+	0.380455i	$0.124233\pi$
$384$	−1.42412	+	0.985844i	−0.0726742	+	0.0503086i
$385$	2.63691	−	0.332705i	0.134390	−	0.0169562i
$386$	13.8349	+	2.43946i	0.704175	+	0.124165i
$387$	−20.0897	−	11.8877i	−1.02122	−	0.604288i
$388$		−	1.07301i		−	0.0544736i
$389$	3.07898	+	0.542907i	0.156110	+	0.0275265i	0.251157	−	0.967946i	$-0.419189\pi$
$389$	3.07898	+	0.542907i	0.156110	+	0.0275265i	−0.0950467	+	0.995473i	$0.530300\pi$
$390$	−20.0163	+	13.8562i	−1.01356	+	0.701638i
$391$	13.1254	+	22.7338i	0.663778	+	1.14970i
$392$	−6.96638	−	0.685239i	−0.351855	−	0.0346098i
$393$	−3.10668	+	6.57012i	−0.156711	+	0.331419i
$394$	2.32161	−	6.37858i	0.116961	−	0.321348i
$395$	35.3222	−	12.8562i	1.77725	−	0.646868i
$396$	−0.700104	+	0.574781i	−0.0351816	+	0.0288838i
$397$	−4.99822	−	28.3463i	−0.250853	−	1.42266i	−0.806497	−	0.591239i	$-0.798639\pi$
$397$	−4.99822	−	28.3463i	−0.250853	−	1.42266i	0.555643	−	0.831421i	$-0.312472\pi$
$398$	−12.4097			−0.622042
$399$	−12.0767	+	15.9108i	−0.604589	+	0.796537i
$400$	−6.06898			−0.303449
$401$	−2.95345	−	16.7498i	−0.147488	−	0.836447i	−0.965336	−	0.261012i	$-0.915944\pi$
$401$	−2.95345	−	16.7498i	−0.147488	−	0.836447i	0.817847	−	0.575435i	$-0.195167\pi$
$402$	17.9166	+	12.6890i	0.893599	+	0.632870i
$403$	25.0188	−	9.10609i	1.24627	−	0.453606i
$404$	0.639214	−	1.75623i	0.0318021	−	0.0873755i
$405$	9.63553	+	28.3504i	0.478793	+	1.40874i
$406$	−5.08961	−	3.28115i	−0.252593	−	0.162841i
$407$	−0.287224	−	0.497487i	−0.0142372	−	0.0246595i
$408$	−5.10652	−	7.37672i	−0.252811	−	0.365202i
$409$	−1.86037	−	0.328034i	−0.0919896	−	0.0162202i	0.127464	−	0.991843i	$-0.459316\pi$
$409$	−1.86037	−	0.328034i	−0.0919896	−	0.0162202i	−0.219453	+	0.975623i	$0.570427\pi$
$410$			18.7772i			0.927340i
$411$	24.7633	+	6.77778i	1.22148	+	0.334323i
$412$	15.7775	+	2.78200i	0.777302	+	0.137059i
$413$	−9.45667	+	22.4868i	−0.465332	+	1.10650i
$414$	14.3416	−	5.04646i	0.704851	−	0.248020i
$415$	15.3680	−	12.8953i	0.754386	−	0.633005i
$416$	−2.71551	−	3.23622i	−0.133139	−	0.158669i
$417$	22.0779	+	22.3158i	1.08116	+	1.09281i
$418$	1.24380	+	0.430300i	0.0608364	+	0.0210466i
$419$			8.51566i			0.416017i	0.978127	+	0.208009i	$0.0666982\pi$
$419$			8.51566i			0.416017i	−0.978127	+	0.208009i	$0.933302\pi$
$420$	15.0936	+	2.15243i	0.736490	+	0.105028i
$421$	31.7491	−	5.59822i	1.54736	−	0.272841i	0.666239	−	0.745738i	$-0.267903\pi$
$421$	31.7491	−	5.59822i	1.54736	−	0.272841i	0.881117	+	0.472898i	$0.156792\pi$
$422$	2.67811	+	0.472224i	0.130369	+	0.0229875i
$423$	−11.1169	−	4.18171i	−0.540521	−	0.203322i
$424$	−8.86331	−	7.43720i	−0.430440	−	0.361182i
$425$		−	31.4364i		−	1.52489i
$426$	23.4846	−	6.15795i	1.13783	−	0.298354i
$427$	−2.35901	−	7.62492i	−0.114161	−	0.368996i
$428$	7.91556	−	2.88103i	0.382613	−	0.139260i
$429$	−1.55386	−	1.57061i	−0.0750210	−	0.0758296i
$430$	22.4196	−	12.9439i	1.08117	−	0.624212i
$431$	25.9581	+	21.7814i	1.25036	+	1.04917i	0.996641	+	0.0818964i	$0.0260977\pi$
$431$	25.9581	+	21.7814i	1.25036	+	1.04917i	0.253717	+	0.967278i	$0.418347\pi$
$432$	−4.74402	+	2.11998i	−0.228247	+	0.101998i
$433$	−5.44953	+	6.49449i	−0.261888	+	0.312105i	−0.880925	−	0.473256i	$-0.843079\pi$
$433$	−5.44953	+	6.49449i	−0.261888	+	0.312105i	0.619037	+	0.785362i	$0.287523\pi$
$434$	−15.3703	−	6.46390i	−0.737800	−	0.310277i
$435$	10.7633	+	7.62287i	0.516062	+	0.365488i
$436$	−3.74106	+	2.15990i	−0.179164	+	0.103441i
$437$	−17.1471	−	13.9268i	−0.820258	−	0.666209i
$438$	3.83931	+	3.88069i	0.183449	+	0.185427i
$439$	6.35179	−	1.11999i	0.303154	−	0.0534543i	−0.0200018	−	0.999800i	$-0.506367\pi$
$439$	6.35179	−	1.11999i	0.303154	−	0.0534543i	0.323156	+	0.946346i	$0.395256\pi$
$440$	−0.174440	−	0.989300i	−0.00831612	−	0.0471630i
$441$	−20.1629	−	5.87007i	−0.960138	−	0.279527i
$442$	16.7631	−	14.0659i	0.797340	−	0.669048i
$443$	−13.1613	−	36.1605i	−0.625314	−	1.71804i	−0.693591	−	0.720369i	$-0.743973\pi$
$443$	−13.1613	−	36.1605i	−0.625314	−	1.71804i	0.0682778	−	0.997666i	$-0.478250\pi$
$444$	−0.835801	−	3.18750i	−0.0396654	−	0.151272i
$445$			7.30028i			0.346067i
$446$	−7.05212	+	8.40439i	−0.333928	+	0.397960i
$447$	−3.73296	+	0.306438i	−0.176563	+	0.0144940i
$448$	−0.129654	+	2.64257i	−0.00612556	+	0.124850i
$449$	−6.58960	+	11.4135i	−0.310982	+	0.538637i	−0.978575	−	0.205889i	$-0.933991\pi$
$449$	−6.58960	+	11.4135i	−0.310982	+	0.538637i	0.667593	+	0.744526i	$0.267325\pi$
$450$	−17.8954	−	3.35364i	−0.843597	−	0.158092i
$451$	−1.67823	+	0.295917i	−0.0790248	+	0.0139342i
$452$	−10.1812	+	3.70566i	−0.478884	+	0.174300i
$453$	−7.45922	+	3.42974i	−0.350465	+	0.161143i
$454$	−16.2096	−	5.89980i	−0.760753	−	0.276891i
$455$	−1.82231	+	37.1419i	−0.0854313	+	1.74124i
$456$	6.23018	+	4.26437i	0.291755	+	0.199697i
$457$	9.81034	+	16.9920i	0.458909	+	0.794853i	0.998904	−	0.0468153i	$-0.0149072\pi$
$457$	9.81034	+	16.9920i	0.458909	+	0.794853i	−0.539995	+	0.841668i	$0.681574\pi$
$458$	−12.2850	+	10.3083i	−0.574038	+	0.481675i
$459$	−10.9812	−	24.5733i	−0.512557	−	1.14698i
$460$	−2.92784	+	16.6046i	−0.136511	+	0.774195i
$461$	18.1867	+	21.6741i	0.847041	+	1.00946i	0.999775	+	0.0211969i	$0.00674768\pi$
$461$	18.1867	+	21.6741i	0.847041	+	1.00946i	−0.152734	+	0.988267i	$0.548808\pi$
$462$	0.0454897	+	1.38292i	0.00211637	+	0.0643394i
$463$	−11.4652	+	19.8582i	−0.532831	+	0.922890i	0.466434	+	0.884556i	$0.345538\pi$
$463$	−11.4652	+	19.8582i	−0.532831	+	0.922890i	−0.999265	+	0.0383342i	$0.987795\pi$
$464$	−1.14440	+	1.98215i	−0.0531273	+	0.0920192i
$465$	32.8317	+	15.5245i	1.52253	+	0.719930i
$466$	14.0322	+	2.47425i	0.650027	+	0.114617i
$467$	−3.82022	−	2.20560i	−0.176779	−	0.102063i	0.409000	−	0.912535i	$-0.365878\pi$
$467$	−3.82022	−	2.20560i	−0.176779	−	0.102063i	−0.585778	+	0.810471i	$0.699211\pi$
$468$	−6.21884	−	11.0431i	−0.287466	−	0.510467i
$469$	32.0383	−	9.91208i	1.47939	−	0.457697i
$470$	10.0903	−	8.46681i	0.465433	−	0.390545i
$471$	10.5370	+	4.98242i	0.485519	+	0.229578i
$472$	8.66415	+	3.15349i	0.398800	+	0.145151i
$473$	1.51019	+	1.79978i	0.0694388	+	0.0827540i
$474$	4.96344	+	18.9291i	0.227978	+	0.869442i
$475$	9.44437	+	24.7107i	0.433337	+	1.13381i
$476$	−13.6881	−	0.671587i	−0.627394	−	0.0307821i
$477$	−22.0253	−	26.8276i	−1.00847	−	1.22835i
$478$	−15.9501	−	19.0086i	−0.729541	−	0.869433i
$479$	−5.91173	−	16.2424i	−0.270114	−	0.742132i	−0.998383	−	0.0568410i	$-0.981897\pi$
$479$	−5.91173	−	16.2424i	−0.270114	−	0.742132i	0.728269	−	0.685291i	$-0.240325\pi$
$480$	0.533003	−	5.73784i	0.0243281	−	0.261895i
$481$	7.55262	−	2.74893i	0.344370	−	0.125340i
$482$	−15.5292	−	8.96576i	−0.707334	−	0.408379i
$483$	7.22125	−	22.0726i	0.328578	−	1.00434i
$484$	−10.2509	+	3.73104i	−0.465952	+	0.169593i
$485$	2.73470	+	2.29469i	0.124176	+	0.104196i
$486$	−15.1600	+	3.62963i	−0.687672	+	0.164643i
$487$	−8.73876	+	5.04532i	−0.395991	+	0.228625i	−0.684753	−	0.728776i	$-0.740090\pi$
$487$	−8.73876	+	5.04532i	−0.395991	+	0.228625i	0.288762	+	0.957401i	$0.406756\pi$
$488$	−2.83479	+	1.03178i	−0.128325	+	0.0467065i
$489$	−8.68238	−	18.8830i	−0.392631	−	0.853920i
$490$	16.6444	−	16.2893i	0.751919	−	0.735877i
$491$	23.0604	−	4.06616i	1.04070	−	0.183503i	0.372921	−	0.927863i	$-0.378356\pi$
$491$	23.0604	−	4.06616i	1.04070	−	0.183503i	0.667779	+	0.744360i	$0.267245\pi$
$492$	−9.73357	−	0.904176i	−0.438823	−	0.0407634i
$493$	−10.2673	−	5.92781i	−0.462414	−	0.266975i
$494$	−8.95094	+	16.0927i	−0.402722	+	0.724045i
$495$	0.0323077	−	3.01351i	0.00145212	−	0.135447i
$496$	−2.15550	+	5.92219i	−0.0967848	+	0.265914i
$497$	14.3767	−	34.1861i	0.644884	−	1.53345i
$498$	5.94454	+	8.58729i	0.266381	+	0.384805i
$499$	−32.3681	−	11.7810i	−1.44899	−	0.527390i	−0.506683	−	0.862132i	$-0.669129\pi$
$499$	−32.3681	−	11.7810i	−1.44899	−	0.527390i	−0.942310	+	0.334742i	$0.891351\pi$
$500$	2.28607	−	2.72443i	0.102236	−	0.121840i
$501$	33.6002	−	8.81039i	1.50115	−	0.393619i
$502$	8.27844	+	4.77956i	0.369485	+	0.213322i
$503$	−11.0359	−	30.3209i	−0.492066	−	1.35194i	−0.898786	−	0.438387i	$-0.855550\pi$
$503$	−11.0359	−	30.3209i	−0.492066	−	1.35194i	0.406720	−	0.913553i	$-0.366672\pi$
$504$	−1.84256	+	7.72043i	−0.0820740	+	0.343895i
$505$	3.10898	+	5.38492i	0.138348	+	0.239626i
$506$	−1.53019			−0.0680255
$507$	6.90282	−	4.77847i	0.306565	−	0.212219i
$508$	19.1919	−	3.38404i	0.851501	−	0.150143i
$509$	4.29749	−	24.3723i	0.190483	−	1.08028i	−0.728224	−	0.685340i	$-0.759654\pi$
$509$	4.29749	−	24.3723i	0.190483	−	1.08028i	0.918706	−	0.394941i	$-0.129235\pi$
$510$	29.7212	+	2.76087i	1.31608	+	0.122254i
$511$	8.27308	−	1.04383i	0.365980	−	0.0461764i
$512$	1.00000			0.0441942
$513$	16.0143	+	16.0169i	0.707049	+	0.707164i
$514$	−3.65561	+	6.33170i	−0.161242	+	0.279279i
$515$	−40.8315	+	34.2617i	−1.79925	+	1.50975i
$516$	5.63020	+	12.2449i	0.247856	+	0.539054i
$517$	0.915746	+	0.768403i	0.0402745	+	0.0337943i
$518$	−4.63997	−	1.95131i	−0.203869	−	0.0857357i
$519$	−1.92394	−	0.909735i	−0.0844516	−	0.0399329i
$520$	14.0552			0.616362
$521$	19.7917			0.867089			0.433544	−	0.901132i	$-0.357263\pi$
$521$	19.7917			0.867089			0.433544	+	0.901132i	$0.357263\pi$
$522$	−4.46976	+	5.21234i	−0.195636	+	0.228138i
$523$	−13.7481	+	16.3844i	−0.601164	+	0.716439i	−0.977710	−	0.209959i	$-0.932667\pi$
$523$	−13.7481	+	16.3844i	−0.601164	+	0.716439i	0.376547	+	0.926398i	$0.377111\pi$
$524$	3.63380	−	2.09797i	0.158743	−	0.0916505i
$525$	−20.7056	+	18.5677i	−0.903668	+	0.810360i
$526$	−28.9089	−	5.09743i	−1.26049	−	0.222258i
$527$	−30.6760	−	11.1652i	−1.33627	−	0.486362i
$528$	0.521225	−	0.0427873i	0.0226834	−	0.00186208i
$529$	2.52130	+	0.917679i	0.109622	+	0.0398991i
$530$	37.9094	−	6.68445i	1.64668	−	0.290354i
$531$	23.8051	+	14.0863i	1.03305	+	0.611293i
$532$	10.9614	−	3.58439i	0.475237	−	0.155403i
$533$		−	23.8430i		−	1.03276i
$534$	−3.78426	−	0.351529i	−0.163761	−	0.0152122i
$535$	−9.58521	+	26.3351i	−0.414405	+	1.13857i
$536$	−4.33533	−	11.9112i	−0.187258	−	0.514486i
$537$	−21.8690	+	30.8786i	−0.943717	+	1.33251i
$538$	0.0112782	−	0.0639619i	0.000486238	−	0.00275759i
$539$	1.71818	+	1.23090i	0.0740073	+	0.0530187i
$540$	4.74231	−	16.6245i	0.204076	−	0.715403i
$541$	−21.9770	−	18.4409i	−0.944863	−	0.792835i	0.0335616	−	0.999437i	$-0.489315\pi$
$541$	−21.9770	−	18.4409i	−0.944863	−	0.792835i	−0.978425	+	0.206602i	$0.933759\pi$
$542$	−2.34081	+	13.2754i	−0.100546	+	0.570227i
$543$	−44.4193	−	12.1577i	−1.90621	−	0.521736i
$544$			5.17985i			0.222084i
$545$	2.49568	−	14.1537i	0.106903	−	0.606277i
$546$	−19.1656	−	2.73312i	−0.820210	−	0.116967i
$547$	3.89418	−	4.64090i	0.166503	−	0.198430i	−0.676341	−	0.736589i	$-0.736435\pi$
$547$	3.89418	−	4.64090i	0.166503	−	0.198430i	0.842844	+	0.538158i	$0.180880\pi$
$548$	−9.52801	−	11.3550i	−0.407016	−	0.485063i
$549$	−8.92901	+	1.47591i	−0.381081	+	0.0629902i
$550$	1.58697	+	0.916238i	0.0676687	+	0.0390685i
$551$	9.85152	+	1.57501i	0.419689	+	0.0670978i
$552$	−8.46638	−	2.31727i	−0.360353	−	0.0986296i
$553$	27.5547	+	11.5880i	1.17174	+	0.492770i
$554$	4.02779	+	22.8427i	0.171124	+	0.970494i
$555$	9.91118	+	4.68650i	0.420706	+	0.198931i
$556$	−3.14718	−	17.8486i	−0.133470	−	0.756948i
$557$	−7.96281	+	9.48970i	−0.337395	+	0.402092i	−0.907889	−	0.419210i	$-0.862307\pi$
$557$	−7.96281	+	9.48970i	−0.337395	+	0.402092i	0.570494	+	0.821301i	$0.306752\pi$
$558$	−9.62838	+	16.2715i	−0.407602	+	0.688826i
$559$	−28.4680	+	16.4360i	−1.20407	+	0.695169i
$560$	−6.45768	−	5.98174i	−0.272887	−	0.252775i
$561$	0.221632	+	2.69987i	0.00935729	+	0.113988i
$562$	3.04598	−	5.27580i	0.128487	−	0.222546i
$563$	−1.86222	−	3.22546i	−0.0784831	−	0.135937i	0.824113	−	0.566426i	$-0.191674\pi$
$563$	−1.86222	−	3.22546i	−0.0784831	−	0.135937i	−0.902596	+	0.430489i	$0.858341\pi$
$564$	3.90307	+	5.63825i	0.164349	+	0.237413i
$565$	12.3288	−	33.8730i	0.518675	−	1.42505i
$566$	−12.2181	−	10.2522i	−0.513564	−	0.430931i
$567$	−9.69930	+	21.7468i	−0.407332	+	0.913280i
$568$	−13.1719	−	4.79417i	−0.552680	−	0.201159i
$569$	21.2080	+	36.7333i	0.889084	+	1.53994i	0.840960	+	0.541097i	$0.181991\pi$
$569$	21.2080	+	36.7333i	0.889084	+	1.53994i	0.0481239	+	0.998841i	$0.484676\pi$
$570$	−24.1919	+	6.75887i	−1.01329	+	0.283098i
$571$	−19.4001	+	33.6020i	−0.811870	+	1.40620i	0.0996832	+	0.995019i	$0.468217\pi$
$571$	−19.4001	+	33.6020i	−0.811870	+	1.40620i	−0.911554	+	0.411181i	$0.865116\pi$
$572$	0.221502	+	1.25620i	0.00926144	+	0.0525243i
$573$	−2.02523	+	21.8019i	−0.0846053	+	0.910786i
$574$	−10.1473	+	10.9547i	−0.423541	+	0.457240i
$575$	−19.7700	−	23.5610i	−0.824466	−	0.982561i
$576$	2.94867	+	0.552587i	0.122861	+	0.0230245i
$577$	−8.19513	−	14.1944i	−0.341168	−	0.590920i	0.643482	−	0.765461i	$-0.277489\pi$
$577$	−8.19513	−	14.1944i	−0.341168	−	0.590920i	−0.984650	+	0.174541i	$0.944156\pi$
$578$	−9.83084			−0.408909
$579$	−13.8494	−	20.0064i	−0.575562	−	0.831438i
$580$	−2.60443	−	7.15561i	−0.108143	−	0.297120i
$581$	15.9344	+	0.781799i	0.661072	+	0.0324345i
$582$	−1.32118	+	1.30709i	−0.0547648	+	0.0541808i
$583$	1.19486	+	3.28285i	0.0494860	+	0.135962i
$584$	−0.547291	−	3.10384i	−0.0226471	−	0.128438i
$585$	41.4442	+	7.76673i	1.71351	+	0.321115i
$586$	−5.44419	+	4.56821i	−0.224897	+	0.188711i
$587$	−0.879758	+	2.41712i	−0.0363115	+	0.0997650i	−0.956523	−	0.291655i	$-0.905794\pi$
$587$	−0.879758	+	2.41712i	−0.0363115	+	0.0997650i	0.920212	+	0.391420i	$0.128016\pi$
$588$	7.64245	+	9.41238i	0.315169	+	0.388160i
$589$	27.4674	−	0.439499i	1.13177	−	0.0181092i
$590$	−26.5659	+	15.3378i	−1.09370	+	0.631448i
$591$	−10.6820	+	4.91156i	−0.439399	+	0.202035i
$592$	−0.650699	+	1.78778i	−0.0267436	+	0.0734773i
$593$	−39.4651	−	6.95876i	−1.62064	−	0.285762i	−0.711634	−	0.702551i	$-0.752044\pi$
$593$	−39.4651	−	6.95876i	−1.62064	−	0.285762i	−0.909003	+	0.416789i	$0.863156\pi$
$594$	1.56056	+	0.161857i	0.0640307	+	0.00664106i
$595$	30.9845	−	33.4498i	1.27024	−	1.37131i
$596$	1.87276	+	1.08124i	0.0767112	+	0.0442892i
$597$	15.1170	+	15.2800i	0.618699	+	0.625368i
$598$	3.71773	−	21.0843i	0.152029	−	0.862201i
$599$	−0.120064	+	0.680919i	−0.00490570	+	0.0278216i	−0.987162	−	0.159720i	$-0.948941\pi$
$599$	−0.120064	+	0.680919i	−0.00490570	+	0.0278216i	0.982257	+	0.187542i	$0.0600520\pi$
$600$	7.39300	+	7.47268i	0.301818	+	0.305071i
$601$	−33.5491	−	19.3696i	−1.36850	−	0.790103i	−0.377762	−	0.925903i	$-0.623306\pi$
$601$	−33.5491	−	19.3696i	−1.36850	−	0.790103i	−0.990736	+	0.135800i	$0.956640\pi$
$602$	20.0746	+	4.56411i	0.818181	+	0.186019i
$603$	−6.20146	−	37.5179i	−0.252543	−	1.52785i
$604$	4.66800	+	0.823094i	0.189938	+	0.0334912i
$605$	12.4132	−	34.1050i	0.504668	−	1.38656i
$606$	−2.94109	+	1.35231i	−0.119474	+	0.0549338i
$607$	8.95263	−	5.16880i	0.363376	−	0.209795i	−0.307185	−	0.951650i	$-0.599387\pi$
$607$	8.95263	−	5.16880i	0.363376	−	0.209795i	0.670561	+	0.741855i	$0.266054\pi$
$608$	−1.55617	−	4.07165i	−0.0631111	−	0.165127i
$609$	2.15992	+	10.2638i	0.0875245	+	0.415909i
$610$	3.43274	−	9.43137i	0.138988	−	0.381865i
$611$	−12.8126	+	10.7510i	−0.518341	+	0.434940i
$612$	−2.86232	+	15.2737i	−0.115702	+	0.617401i
$613$	−3.31033	−	18.7738i	−0.133703	−	0.758267i	−0.975754	−	0.218869i	$-0.929763\pi$
$613$	−3.31033	−	18.7738i	−0.133703	−	0.758267i	0.842051	−	0.539397i	$-0.181348\pi$
$614$	−5.26891	−	14.4762i	−0.212636	−	0.584212i
$615$	23.1202	−	22.8737i	0.932298	−	0.922356i
$616$	0.432854	−	0.671430i	0.0174402	−	0.0270527i
$617$	7.86913	+	21.6202i	0.316799	+	0.870398i	0.991240	+	0.132070i	$0.0421623\pi$
$617$	7.86913	+	21.6202i	0.316799	+	0.870398i	−0.674441	+	0.738328i	$0.735615\pi$
$618$	−15.7941	−	22.8157i	−0.635333	−	0.917780i
$619$	−37.4410			−1.50488			−0.752440	−	0.658661i	$-0.771123\pi$
$619$	−37.4410			−1.50488			−0.752440	+	0.658661i	$0.771123\pi$
$620$	−10.4838	−	18.1585i	−0.421041	−	0.729264i
$621$	−23.6841	−	11.5113i	−0.950409	−	0.461932i
$622$	8.38102	+	9.98811i	0.336048	+	0.400487i
$623$	−3.94511	+	4.25901i	−0.158058	+	0.170634i
$624$	−0.676799	+	7.28582i	−0.0270936	+	0.291666i
$625$	−3.21465	−	18.2312i	−0.128586	−	0.729246i
$626$	−2.95137	+	5.11192i	−0.117960	+	0.204313i
$627$	−0.985330	−	2.05566i	−0.0393503	−	0.0820952i
$628$	−3.36468	−	5.82779i	−0.134265	−	0.232554i
$629$	−9.26043	−	3.37052i	−0.369238	−	0.134392i
$630$	−15.7361	−	21.2066i	−0.626943	−	0.844891i
$631$	8.72541	+	7.32149i	0.347353	+	0.291464i	0.799726	−	0.600365i	$-0.204978\pi$
$631$	8.72541	+	7.32149i	0.347353	+	0.291464i	−0.452373	+	0.891829i	$0.649422\pi$
$632$	3.86421	−	10.6168i	0.153710	−	0.422314i
$633$	−2.68093	−	3.87279i	−0.106557	−	0.153929i
$634$	9.10453	+	15.7695i	0.361587	+	0.626287i
$635$	−32.4182	+	56.1500i	−1.28648	+	2.22825i
$636$	1.63958	+	19.9730i	0.0650137	+	0.791982i
$637$	−21.1348	+	20.6839i	−0.837393	+	0.819528i
$638$	0.598495	−	0.345541i	0.0236946	−	0.0136801i
$639$	−36.1903	−	21.4150i	−1.43167	−	0.847165i
$640$	−2.13856	+	2.54864i	−0.0845340	+	0.100744i
$641$	−3.53388	−	20.0416i	−0.139580	−	0.791596i	−0.971560	−	0.236792i	$-0.923904\pi$
$641$	−3.53388	−	20.0416i	−0.139580	−	0.791596i	0.831981	−	0.554805i	$-0.187207\pi$
$642$	−13.1898	−	6.23681i	−0.520561	−	0.246147i
$643$	−2.76062	−	15.6562i	−0.108868	−	0.617421i	−0.989605	−	0.143815i	$-0.954063\pi$
$643$	−2.76062	−	15.6562i	−0.108868	−	0.617421i	0.880737	−	0.473606i	$-0.157048\pi$
$644$	−10.6813	+	8.10498i	−0.420904	+	0.319381i
$645$	−43.2484	−	11.8372i	−1.70290	−	0.466090i
$646$	21.0905	−	8.06073i	0.829796	−	0.317145i
$647$	−10.3031	−	5.94848i	−0.405056	−	0.233859i	0.283607	−	0.958940i	$-0.408469\pi$
$647$	−10.3031	−	5.94848i	−0.405056	−	0.233859i	−0.688663	+	0.725081i	$0.741802\pi$
$648$	8.38930	+	3.25879i	0.329563	+	0.128017i
$649$	−1.78950	−	2.13264i	−0.0702438	−	0.0837133i
$650$	−16.4804	+	19.6405i	−0.646413	+	0.770365i
$651$	10.7646	+	26.7995i	0.421899	+	1.05035i
$652$	−2.08366	+	11.8170i	−0.0816025	+	0.462791i
$653$			45.4998i			1.78054i	0.455430	+	0.890271i	$0.349485\pi$
$653$			45.4998i			1.78054i	−0.455430	+	0.890271i	$0.650515\pi$
$654$	7.21670	+	1.97523i	0.282195	+	0.0772375i
$655$	−2.42412	+	13.7479i	−0.0947182	+	0.537174i
$656$	4.32346	+	3.62781i	0.168803	+	0.141642i
$657$	0.101363	−	9.45462i	0.00395453	−	0.368860i
$658$	10.4623	+	0.513314i	0.407861	+	0.0200111i
$659$	−1.57338	+	8.92306i	−0.0612901	+	0.347593i	0.938706	+	0.344719i	$0.112026\pi$
$659$	−1.57338	+	8.92306i	−0.0612901	+	0.347593i	−0.999996	+	0.00287390i	$0.999085\pi$
$660$	−1.00562	+	1.41992i	−0.0391437	+	0.0552701i
$661$	0.266614	+	0.732516i	0.0103701	+	0.0284916i	0.944770	−	0.327735i	$-0.106285\pi$
$661$	0.266614	+	0.732516i	0.0103701	+	0.0284916i	−0.934400	+	0.356227i	$0.884063\pi$
$662$	9.46861	−	26.0148i	0.368008	−	1.01109i
$663$	−37.7395	−	3.50571i	−1.46568	−	0.136151i
$664$		−	6.02990i		−	0.234005i
$665$	−14.3063	+	35.6020i	−0.554774	+	1.38059i
$666$	−2.90660	+	4.91200i	−0.112628	+	0.190336i
$667$	−11.4231	+	2.01419i	−0.442302	+	0.0779898i
$668$	−18.8454	−	6.85918i	−0.729152	−	0.265390i
$669$	18.9389	−	1.55469i	0.732220	−	0.0601078i
$670$	39.6287	+	14.4237i	1.53099	+	0.557235i
$671$	0.897036	+	0.158172i	0.0346297	+	0.00610615i
$672$	3.41172	−	3.05944i	0.131610	−	0.118020i
$673$	−23.0204	+	13.2908i	−0.887372	+	0.512324i	−0.873082	−	0.487574i	$-0.837882\pi$
$673$	−23.0204	+	13.2908i	−0.887372	+	0.512324i	−0.0142897	+	0.999898i	$0.504549\pi$
$674$	1.66029	−	1.97865i	0.0639518	−	0.0762148i
$675$	17.6702	+	26.1197i	0.680126	+	1.00535i
$676$	−4.84708			−0.186426
$677$	−26.1954			−1.00677			−0.503385	−	0.864062i	$-0.667912\pi$
$677$	−26.1954			−1.00677			−0.503385	+	0.864062i	$0.667912\pi$
$678$	16.9651	+	8.02196i	0.651542	+	0.308081i
$679$	0.355373	+	2.81658i	0.0136380	+	0.108090i
$680$	−13.2015	−	11.0774i	−0.506256	−	0.424799i
$681$	12.4815	+	27.1456i	0.478293	+	1.04022i
$682$	1.45772	−	1.22317i	0.0558189	−	0.0468376i
$683$	−10.6073	+	18.3723i	−0.405876	+	0.702997i	−0.994423	−	0.105465i	$-0.966367\pi$
$683$	−10.6073	+	18.3723i	−0.405876	+	0.702997i	0.588547	+	0.808463i	$0.299700\pi$
$684$	−2.33869	−	12.8659i	−0.0894222	−	0.491939i
$685$	49.3161			1.88427
$686$	18.5133	−	0.508511i	0.706840	−	0.0194150i
$687$	27.6576	+	2.56919i	1.05520	+	0.0980206i
$688$	1.35118	−	7.66292i	0.0515132	−	0.292146i
$689$	−48.1368	+	8.48781i	−1.83386	+	0.323360i
$690$	24.0117	−	16.6221i	0.914111	−	0.632792i
$691$	−26.3558			−1.00262			−0.501312	−	0.865267i	$-0.667149\pi$
$691$	−26.3558			−1.00262			−0.501312	+	0.865267i	$0.667149\pi$
$692$	0.614354	+	1.06409i	0.0233542	+	0.0404507i
$693$	1.64737	−	1.74063i	0.0625783	−	0.0661212i
$694$	−6.72969	−	18.4897i	−0.255455	−	0.701858i
$695$	52.2199	+	30.1492i	1.98081	+	1.14362i
$696$	3.83467	−	1.00550i	0.145353	−	0.0381133i
$697$	−18.7915	+	22.3949i	−0.711780	+	0.848266i
$698$	18.0239	+	6.56016i	0.682214	+	0.248306i
$699$	−14.0469	−	20.2917i	−0.531303	−	0.767503i
$700$	15.9307	−	2.01001i	0.602124	−	0.0759712i
$701$	4.17196	−	11.4624i	0.157573	−	0.432927i	−0.835635	−	0.549286i	$-0.814900\pi$
$701$	4.17196	−	11.4624i	0.157573	−	0.432927i	0.993207	+	0.116358i	$0.0371221\pi$
$702$	−6.02171	+	21.1095i	−0.227275	+	0.796726i
$703$	8.29181	−	0.132675i	0.312732	−	0.00500394i
$704$	−0.261489	−	0.150971i	−0.00985524	−	0.00568993i
$705$	−22.7168	−	2.11022i	−0.855564	−	0.0794755i
$706$	−32.9544	+	5.81075i	−1.24025	+	0.218690i
$707$	−1.09625	+	4.82169i	−0.0412286	+	0.181338i
$708$	−6.67147	−	14.5096i	−0.250729	−	0.545303i
$709$	6.10527	−	2.22214i	0.229288	−	0.0834541i	−0.224821	−	0.974400i	$-0.572180\pi$
$709$	6.10527	−	2.22214i	0.229288	−	0.0834541i	0.454109	+	0.890946i	$0.349958\pi$
$710$	40.3874	−	23.3177i	1.51571	−	0.875097i
$711$	17.2610	−	29.1702i	0.647337	−	1.09397i
$712$	1.68089	+	1.41044i	0.0629941	+	0.0528583i
$713$	−30.0128	+	10.9238i	−1.12399	+	0.409098i
$714$	15.8474	+	17.6722i	0.593076	+	0.661365i
$715$	−3.67528	−	2.12193i	−0.137448	−	0.0793555i
$716$	20.5285	−	7.47176i	0.767186	−	0.279233i
$717$	−3.97532	+	42.7948i	−0.148461	+	1.59820i
$718$	3.76313	+	10.3391i	0.140439	+	0.385853i
$719$	−19.7679	−	23.5584i	−0.737216	−	0.878580i	0.258965	−	0.965887i	$-0.416619\pi$
$719$	−19.7679	−	23.5584i	−0.737216	−	0.878580i	−0.996182	+	0.0873063i	$0.972174\pi$
$720$	−7.71425	+	6.33334i	−0.287493	+	0.236030i
$721$	−42.3364	−	2.07717i	−1.57669	−	0.0773579i
$722$	−14.1567	+	12.6724i	−0.526856	+	0.471617i
$723$	7.87756	+	30.0427i	0.292970	+	1.11730i
$724$	17.0909	+	20.3682i	0.635179	+	0.756977i
$725$	13.0529	+	4.75088i	0.484774	+	0.176443i
$726$	17.0813	+	8.07690i	0.633947	+	0.299762i
$727$	−23.7861	+	19.9589i	−0.882178	+	0.740235i	−0.966626	−	0.256193i	$-0.917532\pi$
$727$	−23.7861	+	19.9589i	−0.882178	+	0.740235i	0.0844481	+	0.996428i	$0.473087\pi$
$728$	8.19986	+	7.59552i	0.303907	+	0.281509i
$729$	22.9365	+	14.2449i	0.849500	+	0.527589i
$730$	9.08097	+	5.24290i	0.336102	+	0.194048i
$731$	39.6927	+	6.99890i	1.46809	+	0.258864i
$732$	4.72366	+	2.23358i	0.174591	+	0.0825556i
$733$	1.46464	−	2.53683i	0.0540978	−	0.0937001i	−0.837708	−	0.546118i	$-0.816105\pi$
$733$	1.46464	−	2.53683i	0.0540978	−	0.0937001i	0.891806	+	0.452418i	$0.149438\pi$
$734$	7.18921	−	12.4521i	0.265358	−	0.459614i
$735$	−40.3326	−	0.651109i	−1.48769	−	0.0240165i
$736$	3.25755	+	3.88220i	0.120075	+	0.143100i
$737$	−0.664604	+	3.76916i	−0.0244810	+	0.138839i
$738$	10.7438	+	13.0863i	0.395483	+	0.481714i
$739$	12.4934	−	10.4832i	0.459576	−	0.385630i	−0.383399	−	0.923583i	$-0.625247\pi$
$739$	12.4934	−	10.4832i	0.459576	−	0.385630i	0.842975	+	0.537953i	$0.180802\pi$
$740$	−3.16484	−	5.48167i	−0.116342	−	0.201510i
$741$	30.7185	−	8.58230i	1.12847	−	0.315279i
$742$	25.7288	+	16.5867i	0.944534	+	0.608918i
$743$	46.6700	+	16.9865i	1.71216	+	0.623175i	0.997115	−	0.0759059i	$-0.0241849\pi$
$743$	46.6700	+	16.9865i	1.71216	+	0.623175i	0.715043	+	0.699080i	$0.246407\pi$
$744$	9.91769	−	4.56014i	0.363600	−	0.167183i
$745$	−6.76068	+	2.46069i	−0.247692	+	0.0901526i
$746$	−19.1709	+	3.38035i	−0.701896	+	0.123763i
$747$	3.33204	−	17.7802i	0.121913	−	0.650543i
$748$	0.782006	−	1.35447i	0.0285930	−	0.0495245i
$749$	−19.8237	+	10.1841i	−0.724342	+	0.372120i
$750$	−6.13938	+	0.503981i	−0.224178	+	0.0184028i
$751$	−26.1778	+	31.1975i	−0.955241	+	1.13841i	0.0350478	+	0.999386i	$0.488842\pi$
$751$	−26.1778	+	31.1975i	−0.955241	+	1.13841i	−0.990289	+	0.139026i	$0.955603\pi$
$752$		−	3.95912i		−	0.144374i
$753$	−4.19945	−	16.0155i	−0.153036	−	0.583636i
$754$	3.30706	+	9.08607i	0.120436	+	0.330895i
$755$	−12.0806	+	10.1368i	−0.439656	+	0.368916i
$756$	11.7506	−	7.13601i	0.427366	−	0.259534i
$757$	1.83818	+	10.4248i	0.0668098	+	0.378897i	0.999819	+	0.0190439i	$0.00606223\pi$
$757$	1.83818	+	10.4248i	0.0668098	+	0.378897i	−0.933009	+	0.359854i	$0.882827\pi$
$758$	−2.96594	+	0.522975i	−0.107728	+	0.0189953i
$759$	1.86403	+	1.88412i	0.0676598	+	0.0683891i
$760$	13.7051	+	4.74135i	0.497137	+	0.171987i
$761$	−20.4787	+	11.8234i	−0.742352	+	0.428597i	−0.822924	−	0.568152i	$-0.807659\pi$
$761$	−20.4787	+	11.8234i	−0.742352	+	0.428597i	0.0805718	+	0.996749i	$0.474325\pi$
$762$	−27.5455	−	19.5085i	−0.997870	−	0.706717i
$763$	9.10472	−	6.90864i	0.329613	−	0.250109i
$764$	8.12580	−	9.68396i	0.293981	−	0.350353i
$765$	−32.8058	−	39.9586i	−1.18609	−	1.44471i
$766$	13.9090	+	11.6710i	0.502551	+	0.421690i
$767$	33.7330	−	19.4757i	1.21803	−	0.703228i
$768$	−1.21816	−	1.23129i	−0.0439566	−	0.0444304i
$769$	35.8002	−	13.0302i	1.29099	−	0.469881i	0.396936	−	0.917846i	$-0.370074\pi$
$769$	35.8002	−	13.0302i	1.29099	−	0.469881i	0.894051	+	0.447966i	$0.147851\pi$
$770$	0.785546	+	2.53908i	0.0283091	+	0.0915021i
$771$	12.2493	−	3.21192i	0.441148	−	0.115674i
$772$			14.0483i			0.505608i
$773$	5.84234	+	4.90230i	0.210134	+	0.176324i	0.741780	−	0.670643i	$-0.233982\pi$
$773$	5.84234	+	4.90230i	0.210134	+	0.176324i	−0.531646	+	0.846967i	$0.678426\pi$
$774$	8.21861	−	21.8488i	0.295412	−	0.785337i
$775$	37.6672	+	6.64174i	1.35305	+	0.238578i
$776$	1.05670	−	0.186325i	0.0379335	−	0.00668869i
$777$	3.24961	+	8.09018i	0.116579	+	0.290234i
$778$			3.12648i			0.112090i
$779$	8.04314	−	23.2491i	0.288175	−	0.832986i
$780$	−17.1215	−	17.3061i	−0.613049	−	0.619657i
$781$	2.72052	+	3.24219i	0.0973479	+	0.116015i
$782$	−20.1092	+	16.8736i	−0.719104	+	0.603400i
$783$	11.8628	−	0.845891i	0.423942	−	0.0302297i
$784$	−0.534871	−	6.97954i	−0.0191025	−	0.249269i
$785$	22.0485	+	3.88774i	0.786944	+	0.138759i
$786$	−7.00978	−	1.91859i	−0.250030	−	0.0684340i
$787$			1.94270i			0.0692498i	0.999400	+	0.0346249i	$0.0110237\pi$
$787$			1.94270i			0.0692498i	−0.999400	+	0.0346249i	$0.988976\pi$
$788$	6.68482	+	1.17871i	0.238137	+	0.0419900i
$789$	28.9394	+	41.8049i	1.03027	+	1.48829i
$790$	18.7946	+	32.5531i	0.668681	+	1.15819i
$791$	25.4978	−	13.0991i	0.906597	−	0.465750i
$792$	−0.687620	−	0.589658i	−0.0244335	−	0.0209526i
$793$	−4.35884	+	11.9758i	−0.154787	+	0.425273i
$794$	27.0477	−	9.84456i	0.959887	−	0.349370i
$795$	−54.4103	−	38.5348i	−1.92974	−	1.36669i
$796$	−2.15492	−	12.2212i	−0.0763792	−	0.433168i
$797$	−45.2165			−1.60165			−0.800826	−	0.598898i	$-0.795606\pi$
$797$	−45.2165			−1.60165			−0.800826	+	0.598898i	$0.795606\pi$
$798$	−17.7662	−	9.13031i	−0.628916	−	0.323209i
$799$	20.5076			0.725508
$800$	−1.05387	−	5.97678i	−0.0372598	−	0.211311i
$801$	4.17701	+	5.08775i	0.147587	+	0.179767i
$802$	15.9825	−	5.81716i	0.564362	−	0.205411i
$803$	−0.325479	+	0.894245i	−0.0114859	+	0.0315572i
$804$	−9.38505	+	19.8478i	−0.330985	+	0.699979i
$805$	2.18606	−	44.5558i	0.0770486	−	1.57039i
$806$	13.3122	+	23.0574i	0.468902	+	0.812163i
$807$	−0.0924944	+	0.0640292i	−0.00325596	+	0.00225393i
$808$	1.84054	+	0.324537i	0.0647501	+	0.0114172i
$809$		−	30.6021i		−	1.07591i	−0.842973	−	0.537956i	$-0.819197\pi$
$809$		−	30.6021i		−	1.07591i	0.842973	−	0.537956i	$-0.180803\pi$
$810$	−26.2465	+	14.4121i	−0.922207	+	0.506391i
$811$	30.9393	+	5.45543i	1.08643	+	0.191566i	0.688055	−	0.725659i	$-0.258465\pi$
$811$	30.9393	+	5.45543i	1.08643	+	0.191566i	0.398370	+	0.917225i	$0.369576\pi$
$812$	2.34750	−	5.58205i	0.0823810	−	0.195892i
$813$	19.1974	−	13.2894i	0.673281	−	0.466078i
$814$	0.440053	−	0.369248i	0.0154239	−	0.0129422i
$815$	−25.6613	−	30.5819i	−0.898876	−	1.07124i
$816$	6.37791	−	6.30990i	0.223271	−	0.220891i
$817$	−33.3034	+	6.42328i	−1.16514	+	0.224722i
$818$		−	1.88907i		−	0.0660499i
$819$	19.9815	+	26.9278i	0.698210	+	0.940933i
$820$	−18.4919	+	3.26063i	−0.645767	+	0.113866i
$821$	6.50342	+	1.14673i	0.226971	+	0.0400211i	0.285977	−	0.958237i	$-0.407682\pi$
$821$	6.50342	+	1.14673i	0.226971	+	0.0400211i	−0.0590059	+	0.998258i	$0.518793\pi$
$822$	−2.37471	+	25.5640i	−0.0828275	+	0.891648i
$823$	−33.2123	−	27.8684i	−1.15771	−	0.971433i	−0.157837	−	0.987465i	$-0.550452\pi$
$823$	−33.2123	−	27.8684i	−1.15771	−	0.971433i	−0.999871	+	0.0160321i	$0.994897\pi$
$824$			16.0209i			0.558115i
$825$	−0.805031	−	3.07015i	−0.0280276	−	0.106889i
$826$	−23.7873	−	5.40822i	−0.827666	−	0.188176i
$827$	−25.6786	+	9.34624i	−0.892932	+	0.325001i	−0.747417	−	0.664355i	$-0.768706\pi$
$827$	−25.6786	+	9.34624i	−0.892932	+	0.325001i	−0.145515	+	0.989356i	$0.546484\pi$
$828$	7.46019	+	13.2474i	0.259259	+	0.460379i
$829$	7.63483	−	4.40797i	0.265169	−	0.153095i	−0.361521	−	0.932364i	$-0.617743\pi$
$829$	7.63483	−	4.40797i	0.265169	−	0.153095i	0.626690	+	0.779269i	$0.284409\pi$
$830$	15.3680	+	12.8953i	0.533431	+	0.447602i
$831$	23.2196	−	32.7855i	0.805477	−	1.13732i
$832$	2.71551	−	3.23622i	0.0941433	−	0.112196i
$833$	36.1529	−	2.77055i	1.25263	−	0.0959938i
$834$	−18.1430	+	25.6175i	−0.628241	+	0.887063i
$835$	57.7836	−	33.3614i	1.99969	−	1.15452i
$836$	−0.207778	+	1.29963i	−0.00718616	+	0.0449486i
$837$	31.7639	−	7.96594i	1.09792	−	0.275343i
$838$	−8.38629	+	1.47873i	−0.289700	+	0.0510818i
$839$	−6.93362	−	39.3225i	−0.239375	−	1.35756i	−0.833201	−	0.552970i	$-0.813494\pi$
$839$	−6.93362	−	39.3225i	−0.239375	−	1.35756i	0.593826	−	0.804593i	$-0.297617\pi$
$840$	0.501238	+	15.2380i	0.0172943	+	0.525762i
$841$	−18.2023	+	15.2735i	−0.627666	+	0.526674i
$842$	11.0263	+	30.2946i	0.379993	+	1.04402i
$843$	−10.2066	+	2.67628i	−0.351532	+	0.0921761i
$844$			2.71943i			0.0936066i
$845$	10.3658	−	12.3534i	0.356593	−	0.424972i
$846$	2.18776	−	11.6741i	0.0752166	−	0.401365i
$847$	25.6724	−	13.1888i	0.882115	−	0.453173i
$848$	5.78511	−	10.0201i	0.198662	−	0.344092i
$849$	2.26017	+	27.5328i	0.0775687	+	0.944925i
$850$	30.9588	−	5.45887i	1.06188	−	0.187238i
$851$	−9.06020	+	3.29764i	−0.310580	+	0.113042i
$852$	10.1425	+	22.0585i	0.347475	+	0.755712i
$853$	17.4252	+	6.34226i	0.596628	+	0.217155i	0.622642	−	0.782507i	$-0.286059\pi$
$853$	17.4252	+	6.34226i	0.596628	+	0.217155i	−0.0260144	+	0.999662i	$0.508282\pi$
$854$	7.09944	−	3.64723i	0.242938	−	0.124806i
$855$	37.7918	+	21.5539i	1.29245	+	0.737129i
$856$	4.21178	+	7.29502i	0.143956	+	0.249339i
$857$	−16.0840	+	13.4961i	−0.549419	+	0.461017i	−0.874744	−	0.484585i	$-0.838971\pi$
$857$	−16.0840	+	13.4961i	−0.549419	+	0.461017i	0.325325	+	0.945602i	$0.394526\pi$
$858$	1.27692	−	1.80299i	0.0435934	−	0.0615529i
$859$	2.79218	−	15.8353i	0.0952680	−	0.540292i	−0.899397	−	0.437133i	$-0.855994\pi$
$859$	2.79218	−	15.8353i	0.0952680	−	0.540292i	0.994665	−	0.103159i	$-0.0328950\pi$
$860$	16.6404	+	19.8313i	0.567433	+	0.676240i
$861$	25.8495	−	0.850291i	0.880949	−	0.0289778i
$862$	−16.9429	+	29.3460i	−0.577079	+	0.999530i
$863$	15.5190	−	26.8798i	0.528274	−	0.914998i	−0.471182	−	0.882036i	$-0.656173\pi$
$863$	15.5190	−	26.8798i	0.528274	−	0.914998i	0.999457	−	0.0329620i	$-0.0104940\pi$
$864$	−2.91156	−	4.30381i	−0.0990533	−	0.146419i
$865$	−4.02581	−	0.709859i	−0.136882	−	0.0241359i
$866$	−7.34213	−	4.23898i	−0.249496	−	0.144046i
$867$	11.9756	+	12.1046i	0.406711	+	0.411095i
$868$	3.69667	−	16.2593i	0.125473	−	0.551876i
$869$	−2.61328	+	2.19280i	−0.0886493	+	0.0743856i
$870$	−5.63803	+	11.9235i	−0.191147	+	0.404244i
$871$	−50.3199	−	18.3149i	−1.70502	−	0.620578i
$872$	−2.77672	−	3.30916i	−0.0940316	−	0.112062i
$873$	3.21883	+	0.0345090i	0.108941	+	0.00116795i
$874$	10.7376	−	19.3050i	0.363206	−	0.653001i
$875$	−5.09848	+	7.90860i	−0.172360	+	0.267360i
$876$	−3.15505	+	4.45486i	−0.106599	+	0.150516i
$877$	−12.9151	−	15.3916i	−0.436111	−	0.519737i	0.502564	−	0.864540i	$-0.332390\pi$
$877$	−12.9151	−	15.3916i	−0.436111	−	0.519737i	−0.938675	+	0.344803i	$0.887946\pi$
$878$	2.20595	+	6.06081i	0.0744473	+	0.204542i
$879$	12.2567	+	1.13856i	0.413408	+	0.0384026i
$880$	0.943979	−	0.343580i	0.0318215	−	0.0115821i
$881$	23.6938	+	13.6796i	0.798265	+	0.460878i	0.842864	−	0.538126i	$-0.180868\pi$
$881$	23.6938	+	13.6796i	0.798265	+	0.460878i	−0.0445991	+	0.999005i	$0.514201\pi$
$882$	2.27964	−	20.8759i	0.0767596	−	0.702928i
$883$	−9.36632	+	3.40906i	−0.315202	+	0.114724i	−0.494776	−	0.869020i	$-0.664750\pi$
$883$	−9.36632	+	3.40906i	−0.315202	+	0.114724i	0.179575	+	0.983744i	$0.442528\pi$
$884$	16.7631	+	14.0659i	0.563805	+	0.473088i
$885$	51.2469	+	14.0264i	1.72265	+	0.471493i
$886$	33.3257	−	19.2406i	1.11960	−	0.646400i
$887$	44.0383	−	16.0286i	1.47866	−	0.538189i	0.528225	−	0.849105i	$-0.322858\pi$
$887$	44.0383	−	16.0286i	1.47866	−	0.538189i	0.950438	+	0.310915i	$0.100636\pi$
$888$	2.99394	−	1.37661i	0.100470	−	0.0461959i
$889$	−49.2567	+	15.2391i	−1.65202	+	0.511104i
$890$	−7.18937	+	1.26768i	−0.240988	+	0.0424927i
$891$	−1.70173	−	2.11868i	−0.0570100	−	0.0709783i
$892$	−9.50130	−	5.48558i	−0.318127	−	0.183671i
$893$	−16.1201	+	6.16107i	−0.539440	+	0.206172i
$894$	−0.950004	−	3.62304i	−0.0317729	−	0.121172i
$895$	−24.8586	+	68.2984i	−0.830931	+	2.28296i
$896$	−2.62494	+	0.331194i	−0.0876931	+	0.0110644i
$897$	−30.4897	+	21.1065i	−1.01802	+	0.704725i
$898$	−12.3844	−	4.50755i	−0.413273	−	0.150419i
$899$	9.27194	−	11.0499i	0.309237	−	0.368534i
$900$	0.195184	−	18.2059i	0.00650615	−	0.606863i
$901$	51.9027	+	29.9660i	1.72913	+	0.998313i
$902$	−0.582843	−	1.60135i	−0.0194066	−	0.0533191i
$903$	−18.8344	−	30.2776i	−0.626769	−	1.00757i
$904$	−5.41731	−	9.38306i	−0.180177	−	0.312076i
$905$	−88.4609			−2.94054
$906$	−4.67291	−	6.75033i	−0.155247	−	0.224265i
$907$	1.87989	−	0.331476i	0.0624208	−	0.0110065i	−0.142351	−	0.989816i	$-0.545466\pi$
$907$	1.87989	−	0.331476i	0.0624208	−	0.0110065i	0.204771	+	0.978810i	$0.434355\pi$
$908$	2.99541	−	16.9878i	0.0994061	−	0.563760i
$909$	5.24782	+	1.97401i	0.174059	+	0.0654739i
$910$	−36.8941	+	4.65500i	−1.22303	+	0.154312i
$911$	3.15220			0.104437			0.0522185	−	0.998636i	$-0.483371\pi$
$911$	3.15220			0.104437			0.0522185	+	0.998636i	$0.483371\pi$
$912$	−3.11772	+	6.87603i	−0.103238	+	0.227688i
$913$	−0.910338	+	1.57675i	−0.0301278	+	0.0521829i
$914$	−15.0303	+	12.6119i	−0.497159	+	0.417166i
$915$	−15.7944	+	7.26224i	−0.522147	+	0.240082i
$916$	−12.2850	−	10.3083i	−0.405906	−	0.340596i
$917$	−8.84367	+	6.71055i	−0.292044	+	0.221602i
$918$	22.2931	−	15.0814i	0.735782	−	0.497762i
$919$	20.7179			0.683421			0.341711	−	0.939805i	$-0.388994\pi$
$919$	20.7179			0.683421			0.341711	+	0.939805i	$0.388994\pi$
$920$	−16.8608			−0.555883
$921$	−11.4061	+	24.1219i	−0.375842	+	0.794845i
$922$	−18.1867	+	21.6741i	−0.598948	+	0.713799i
$923$	−51.2833	+	29.6084i	−1.68801	+	0.974574i
$924$	−1.35401	+	0.284941i	−0.0445438	+	0.00937385i
$925$	11.3709	+	2.00500i	0.373873	+	0.0659239i
$926$	−21.5474	−	7.84263i	−0.708093	−	0.257725i
$927$	−8.85295	+	47.2404i	−0.290769	+	1.55158i
$928$	−2.15076	−	0.782814i	−0.0706023	−	0.0256971i
$929$	18.8752	−	3.32820i	0.619274	−	0.109195i	0.144795	−	0.989462i	$-0.453748\pi$
$929$	18.8752	−	3.32820i	0.619274	−	0.109195i	0.474479	+	0.880267i	$0.342637\pi$
$930$	−9.58745	+	35.0287i	−0.314385	+	1.14864i
$931$	−27.5859	+	13.0392i	−0.904090	+	0.427341i
$932$			14.2486i			0.466729i
$933$	2.08884	−	22.4866i	0.0683856	−	0.736179i
$934$	1.50872	−	4.14518i	0.0493669	−	0.135634i
$935$	1.77969	+	4.88967i	0.0582022	+	0.159909i
$936$	9.79543	−	8.04198i	0.320174	−	0.262860i
$937$	6.09215	−	34.5503i	0.199022	−	1.12871i	−0.707552	−	0.706661i	$-0.750201\pi$
$937$	6.09215	−	34.5503i	0.199022	−	1.12871i	0.906574	−	0.422047i	$-0.138688\pi$
$938$	15.3249	+	29.8304i	0.500375	+	0.973996i
$939$	9.88951	−	2.59315i	0.322732	−	0.0846242i
$940$	10.0903	+	8.46681i	0.329111	+	0.276157i
$941$	−3.65035	+	20.7022i	−0.118998	+	0.674871i	0.865695	+	0.500572i	$0.166877\pi$
$941$	−3.65035	+	20.7022i	−0.118998	+	0.674871i	−0.984693	+	0.174299i	$0.944234\pi$
$942$	−3.07699	+	11.2421i	−0.100254	+	0.366287i
$943$			28.6023i			0.931419i
$944$	−1.60107	+	9.08012i	−0.0521104	+	0.295533i
$945$	−6.94235	+	45.2089i	−0.225835	+	1.47064i
$946$	−1.51019	+	1.79978i	−0.0491007	+	0.0585159i
$947$	−33.9648	−	40.4776i	−1.10371	−	1.31535i	−0.944651	−	0.328076i	$-0.893600\pi$
$947$	−33.9648	−	40.4776i	−1.10371	−	1.31535i	−0.159055	−	0.987270i	$-0.550845\pi$
$948$	−17.7796	+	8.17504i	−0.577456	+	0.265513i
$949$	−11.5309	−	6.65735i	−0.374308	−	0.216107i
$950$	−22.6953	+	13.5919i	−0.736334	+	0.440978i
$951$	8.32608	−	30.4202i	0.269992	−	0.986441i
$952$	−1.71553	−	13.5968i	−0.0556008	−	0.440675i
$953$	−4.20235	−	23.8327i	−0.136127	−	0.772017i	−0.974068	−	0.226256i	$-0.927352\pi$
$953$	−4.20235	−	23.8327i	−0.136127	−	0.772017i	0.837940	−	0.545762i	$-0.183760\pi$
$954$	22.5954	−	26.3492i	0.731552	−	0.853087i
$955$	7.30336	+	41.4194i	0.236331	+	1.34030i
$956$	15.9501	−	19.0086i	0.515863	−	0.614782i
$957$	−1.15453	−	0.315997i	−0.0373205	−	0.0102147i
$958$	14.9690	−	8.64238i	0.483628	−	0.279222i
$959$	28.7712	+	26.6507i	0.929069	+	0.860595i
$960$	5.74323	−	0.471461i	0.185362	−	0.0152163i
$961$	4.35925	−	7.55044i	0.140621	−	0.243563i
$962$	4.01867	+	6.96053i	0.129567	+	0.224417i
$963$	8.38802	+	23.8380i	0.270300	+	0.768168i
$964$	6.13294	−	16.8501i	0.197529	−	0.542706i
$965$	−35.8039	−	30.0431i	−1.15257	−	0.967121i
$966$	22.9912	+	3.27868i	0.739730	+	0.105490i
$967$	−27.1361	−	9.87674i	−0.872639	−	0.317614i	−0.133403	−	0.991062i	$-0.542591\pi$
$967$	−27.1361	−	9.87674i	−0.872639	−	0.317614i	−0.739235	+	0.673447i	$0.764813\pi$
$968$	−5.45442	−	9.44733i	−0.175312	−	0.303649i
$969$	−35.6168	−	16.1493i	−1.14418	−	0.518791i
$970$	−1.78495	+	3.09162i	−0.0573112	+	0.0992660i
$971$	−5.38437	−	30.5363i	−0.172793	−	0.979957i	−0.940661	−	0.339348i	$-0.889793\pi$
$971$	−5.38437	−	30.5363i	−0.172793	−	0.979957i	0.767868	−	0.640608i	$-0.221318\pi$
$972$	−6.20700	−	14.2994i	−0.199090	−	0.458654i
$973$	14.1725	+	45.8091i	0.454350	+	1.46857i
$974$	−6.48614	−	7.72988i	−0.207829	−	0.247681i
$975$	44.2590	−	3.63321i	1.41742	−	0.116356i
$976$	−1.50836	−	2.61256i	−0.0482815	−	0.0836260i
$977$	−26.1351			−0.836137			−0.418069	−	0.908415i	$-0.637293\pi$
$977$	−26.1351			−0.836137			−0.418069	+	0.908415i	$0.637293\pi$
$978$	17.0885	−	11.8295i	0.546429	−	0.378265i
$979$	−0.226600	−	0.622579i	−0.00724218	−	0.0198977i
$980$	18.9321	+	13.5630i	0.604765	+	0.433253i
$981$	−6.35902	−	11.2920i	−0.203028	−	0.360526i
$982$	8.00878	+	22.0039i	0.255570	+	0.702174i
$983$	8.08373	+	45.8451i	0.257831	+	1.46223i	0.788700	+	0.614779i	$0.210755\pi$
$983$	8.08373	+	45.8451i	0.257831	+	1.46223i	−0.530869	+	0.847454i	$0.678134\pi$
$984$	−0.799777	−	9.74271i	−0.0254960	−	0.310586i
$985$	−17.3000	+	14.5164i	−0.551224	+	0.462532i
$986$	4.05486	−	11.1406i	0.129133	−	0.354790i
$987$	−12.1127	−	13.5074i	−0.385551	−	0.429945i
$988$	−17.4025	−	6.02049i	−0.553648	−	0.191537i
$989$	34.1505	−	19.7168i	1.08592	−	0.626958i
$990$	2.97334	−	0.491474i	0.0944990	−	0.0156201i
$991$	14.5288	−	39.9177i	0.461524	−	1.26803i	−0.462815	−	0.886455i	$-0.653161\pi$
$991$	14.5288	−	39.9177i	0.461524	−	1.26803i	0.924339	−	0.381572i	$-0.124617\pi$
$992$	−6.20652	−	1.09438i	−0.197057	−	0.0347465i
$993$	−43.5661	+	20.0316i	−1.38253	+	0.635684i
$994$	36.1632	+	8.22197i	1.14703	+	0.260785i
$995$	35.7557	+	20.6436i	1.13353	+	0.654446i
$996$	−7.42457	+	7.34540i	−0.235256	+	0.232748i
$997$	6.57737	−	37.3021i	0.208307	−	1.18137i	−0.683842	−	0.729630i	$-0.739692\pi$
$997$	6.57737	−	37.3021i	0.208307	−	1.18137i	0.892150	−	0.451740i	$-0.149196\pi$
$998$	5.98137	−	33.9221i	0.189337	−	1.07378i
$999$	9.58882	−	2.40475i	0.303377	−	0.0760828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.53.19	✓	162
3.2	odd	2		798.2.bu.b.53.15	yes	162
7.2	even	3		798.2.cc.a.737.19	yes	162
19.14	odd	18		798.2.cc.b.641.22	yes	162
21.2	odd	6		798.2.cc.b.737.22	yes	162
57.14	even	18		798.2.cc.a.641.19	yes	162
133.128	odd	18		798.2.bu.b.527.15	yes	162
399.128	even	18	inner	798.2.bu.a.527.19	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.19	✓	162	1.1	even	1	trivial
798.2.bu.a.527.19	yes	162	399.128	even	18	inner
798.2.bu.b.53.15	yes	162	3.2	odd	2
798.2.bu.b.527.15	yes	162	133.128	odd	18
798.2.cc.a.641.19	yes	162	57.14	even	18
798.2.cc.a.737.19	yes	162	7.2	even	3
798.2.cc.b.641.22	yes	162	19.14	odd	18
798.2.cc.b.737.22	yes	162	21.2	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.00105 - 1.41347i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.13790 - 3.12636i) q^{5} +(1.56582 + 0.740400i) q^{6} +(2.35336 - 1.20900i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.995780 - 2.82992i) q^{9} +(3.27646 + 0.577729i) q^{10} +0.301942i q^{11} +(-0.457249 + 1.67061i) q^{12} +(-4.16040 - 0.733591i) q^{13} +(1.59929 + 2.10767i) q^{14} +(-3.27991 - 4.73805i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.32954 + 3.96800i) q^{17} +(2.61401 - 1.47206i) q^{18} +(-3.80930 - 2.11878i) q^{19} +3.32701i q^{20} +(0.646957 - 4.53668i) q^{21} +(-0.297354 + 0.0524316i) q^{22} +(4.99086 + 0.880023i) q^{23} +(-1.72463 - 0.160205i) q^{24} +(-4.64911 - 3.90106i) q^{25} -4.22458i q^{26} +(-4.99682 - 1.42540i) q^{27} +(-1.79793 + 1.94099i) q^{28} +(-2.15076 + 0.782814i) q^{29} +(4.09652 - 4.05283i) q^{30} +(-5.45792 + 3.15113i) q^{31} +(0.766044 + 0.642788i) q^{32} +(0.426785 + 0.302260i) q^{33} +(-3.32954 + 3.96800i) q^{34} +(-1.10188 - 8.73319i) q^{35} +(1.90362 + 2.31867i) q^{36} +(-1.64763 + 0.951258i) q^{37} +(1.42511 - 4.11935i) q^{38} +(-5.20169 + 5.14623i) q^{39} +(-3.27646 + 0.577729i) q^{40} +(0.980048 + 5.55813i) q^{41} +(4.58010 - 0.150657i) q^{42} +(5.96069 - 5.00161i) q^{43} +(-0.103270 - 0.283732i) q^{44} +(-9.98045 - 0.107000i) q^{45} +5.06785i q^{46} +(2.54487 - 3.03286i) q^{47} +(-0.141707 - 1.72624i) q^{48} +(4.07662 - 5.69044i) q^{49} +(3.03449 - 5.25589i) q^{50} +(8.94169 - 0.734022i) q^{51} +(4.16040 - 0.733591i) q^{52} +(10.8725 - 3.95725i) q^{53} +(0.536053 - 5.16843i) q^{54} +(0.943979 + 0.343580i) q^{55} +(-2.22371 - 1.43357i) q^{56} +(-6.80814 + 3.26331i) q^{57} +(-1.14440 - 1.98215i) q^{58} +(-7.06308 + 5.92663i) q^{59} +(4.70262 + 3.33052i) q^{60} +(0.523848 - 2.97089i) q^{61} +(-4.05102 - 4.82781i) q^{62} +(-5.76481 - 5.45591i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-7.02761 + 12.1722i) q^{65} +(-0.223558 + 0.472788i) q^{66} +(12.4831 + 2.20110i) q^{67} +(-4.48588 - 2.58992i) q^{68} +(6.24001 - 6.17347i) q^{69} +(8.40918 - 2.60165i) q^{70} +(10.7378 - 9.01009i) q^{71} +(-1.95289 + 2.27733i) q^{72} +(2.96165 + 1.07795i) q^{73} +(-1.22291 - 1.45741i) q^{74} +(-10.1680 + 2.66618i) q^{75} +(4.30424 + 0.688141i) q^{76} +(0.365048 + 0.710578i) q^{77} +(-5.97131 - 4.22904i) q^{78} +(7.26233 + 8.65491i) q^{79} +(-1.13790 - 3.12636i) q^{80} +(-7.01684 + 5.63595i) q^{81} +(-5.30351 + 1.93032i) q^{82} +(5.22205 + 3.01495i) q^{83} +(0.943694 + 4.48436i) q^{84} +(16.1941 - 5.89417i) q^{85} +(5.96069 + 5.00161i) q^{86} +(-1.04655 + 3.82367i) q^{87} +(0.261489 - 0.150971i) q^{88} +(-2.06192 + 0.750477i) q^{89} +(-1.62771 - 9.84740i) q^{90} +(-10.6778 + 3.30353i) q^{91} +(-4.99086 + 0.880023i) q^{92} +(-1.00965 + 10.8690i) q^{93} +(3.42870 + 1.97956i) q^{94} +(-10.9587 + 9.49830i) q^{95} +(1.67541 - 0.439313i) q^{96} +(-0.366989 + 1.00830i) q^{97} +(6.31189 + 3.02656i) q^{98} +(0.854469 - 0.300667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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