LMFDB - Embedded newform 840.2.cf.a.101.121

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.121
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.121

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38593 - 0.281424i) q^{2} +(0.952550 + 1.44660i) q^{3} +(1.84160 - 0.780068i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.72727 + 1.73681i) q^{6} +(-0.542825 - 2.58947i) q^{7} +(2.33280 - 1.59939i) q^{8} +(-1.18530 + 2.75592i) q^{9} +(1.05954 - 0.936685i) q^{10} +(0.823745 - 1.42677i) q^{11} +(2.88266 + 1.92100i) q^{12} +1.37742 q^{13} +(-1.48106 - 3.43605i) q^{14} +(1.54823 + 0.776517i) q^{15} +(2.78299 - 2.87315i) q^{16} +(-1.71566 + 2.97162i) q^{17} +(-0.867158 + 4.15308i) q^{18} +(1.30047 + 2.25247i) q^{19} +(1.20484 - 1.59636i) q^{20} +(3.22885 - 3.25185i) q^{21} +(0.740125 - 2.20922i) q^{22} +(2.30643 - 1.33162i) q^{23} +(4.53578 + 1.85113i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.90901 - 0.387639i) q^{26} +(-5.11576 + 0.910496i) q^{27} +(-3.01963 - 4.34532i) q^{28} -0.197737 q^{29} +(2.36427 + 0.640487i) q^{30} +(-2.59210 - 1.49655i) q^{31} +(3.04845 - 4.76518i) q^{32} +(2.84862 - 0.167439i) q^{33} +(-1.54150 + 4.60128i) q^{34} +(-1.76483 - 1.97113i) q^{35} +(-0.0330433 + 5.99991i) q^{36} +(-2.72617 + 1.57395i) q^{37} +(2.43625 + 2.75578i) q^{38} +(1.31206 + 1.99257i) q^{39} +(1.22057 - 2.55151i) q^{40} -9.89169 q^{41} +(3.55981 - 5.41551i) q^{42} +2.90434i q^{43} +(0.404033 - 3.27011i) q^{44} +(0.351460 + 2.97934i) q^{45} +(2.82181 - 2.49462i) q^{46} +(4.47051 + 7.74314i) q^{47} +(6.80723 + 1.28905i) q^{48} +(-6.41068 + 2.81126i) q^{49} +(0.449244 - 1.34096i) q^{50} +(-5.93299 + 0.348735i) q^{51} +(2.53666 - 1.07448i) q^{52} +(-1.68026 + 2.91030i) q^{53} +(-6.83385 + 2.70158i) q^{54} -1.64749i q^{55} +(-5.40787 - 5.17252i) q^{56} +(-2.01967 + 4.02684i) q^{57} +(-0.274050 + 0.0556480i) q^{58} +(11.9318 + 6.88885i) q^{59} +(3.45696 + 0.222307i) q^{60} +(-3.06938 - 5.31632i) q^{61} +(-4.01363 - 1.34463i) q^{62} +(7.77976 + 1.57331i) q^{63} +(2.88390 - 7.46211i) q^{64} +(1.19288 - 0.688710i) q^{65} +(3.90086 - 1.03373i) q^{66} +(-6.09885 - 3.52117i) q^{67} +(-0.841504 + 6.81087i) q^{68} +(4.12331 + 2.06805i) q^{69} +(-3.00066 - 2.23518i) q^{70} +0.209796i q^{71} +(1.64272 + 8.32475i) q^{72} +(-14.6076 - 8.43373i) q^{73} +(-3.33532 + 2.94860i) q^{74} +(1.72907 - 0.101633i) q^{75} +(4.15202 + 3.13370i) q^{76} +(-4.14172 - 1.35857i) q^{77} +(2.37918 + 2.39232i) q^{78} +(-2.67735 - 4.63731i) q^{79} +(0.973564 - 3.87971i) q^{80} +(-6.19014 - 6.53316i) q^{81} +(-13.7092 + 2.78376i) q^{82} +13.9725i q^{83} +(3.40960 - 8.50733i) q^{84} +3.43133i q^{85} +(0.817351 + 4.02521i) q^{86} +(-0.188355 - 0.286046i) q^{87} +(-0.360328 - 4.64585i) q^{88} +(0.829066 + 1.43598i) q^{89} +(1.32556 + 4.03025i) q^{90} +(-0.747698 - 3.56678i) q^{91} +(3.20878 - 4.25149i) q^{92} +(-0.304197 - 5.17526i) q^{93} +(8.37492 + 9.47334i) q^{94} +(2.25247 + 1.30047i) q^{95} +(9.79711 - 0.129186i) q^{96} +0.837143i q^{97} +(-8.09360 + 5.70032i) q^{98} +(2.95567 + 3.96132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.38593	−	0.281424i	0.980000	−	0.198997i
$2$	1.38593	−	0.281424i	0.980000	−	0.198997i
$3$	0.952550	+	1.44660i	0.549955	+	0.835194i
$3$	0.952550	+	1.44660i	0.549955	+	0.835194i
$4$	1.84160	−	0.780068i	0.920800	−	0.390034i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.72727	+	1.73681i	0.705157	+	0.709051i
$7$	−0.542825	−	2.58947i	−0.205169	−	0.978727i
$7$	−0.542825	−	2.58947i	−0.205169	−	0.978727i
$8$	2.33280	−	1.59939i	0.824769	−	0.565470i
$9$	−1.18530	+	2.75592i	−0.395099	+	0.918638i
$10$	1.05954	−	0.936685i	0.335055	−	0.296206i
$11$	0.823745	−	1.42677i	0.248368	−	0.430187i	−0.714705	−	0.699426i	$-0.753439\pi$
$11$	0.823745	−	1.42677i	0.248368	−	0.430187i	0.963073	+	0.269239i	$0.0867723\pi$
$12$	2.88266	+	1.92100i	0.832153	+	0.554546i
$13$	1.37742			0.382027			0.191014	−	0.981587i	$-0.438823\pi$
$13$	1.37742			0.382027			0.191014	+	0.981587i	$0.438823\pi$
$14$	−1.48106	−	3.43605i	−0.395829	−	0.918324i
$15$	1.54823	+	0.776517i	0.399752	+	0.200496i
$16$	2.78299	−	2.87315i	0.695747	−	0.718287i
$17$	−1.71566	+	2.97162i	−0.416110	+	0.720723i	−0.995544	−	0.0942958i	$-0.969940\pi$
$17$	−1.71566	+	2.97162i	−0.416110	+	0.720723i	0.579435	+	0.815019i	$0.303273\pi$
$18$	−0.867158	+	4.15308i	−0.204391	+	0.978889i
$19$	1.30047	+	2.25247i	0.298347	+	0.516753i	0.975758	−	0.218852i	$-0.0702313\pi$
$19$	1.30047	+	2.25247i	0.298347	+	0.516753i	−0.677411	+	0.735605i	$0.736898\pi$
$20$	1.20484	−	1.59636i	0.269410	−	0.356957i
$21$	3.22885	−	3.25185i	0.704593	−	0.709611i
$22$	0.740125	−	2.20922i	0.157795	−	0.471008i
$23$	2.30643	−	1.33162i	0.480925	−	0.277662i	−0.239877	−	0.970803i	$-0.577107\pi$
$23$	2.30643	−	1.33162i	0.480925	−	0.277662i	0.720802	+	0.693141i	$0.243774\pi$
$24$	4.53578	+	1.85113i	0.925863	+	0.377859i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.90901	−	0.387639i	0.374387	−	0.0760223i
$27$	−5.11576	+	0.910496i	−0.984528	+	0.175225i
$28$	−3.01963	−	4.34532i	−0.570656	−	0.821189i
$29$	−0.197737			−0.0367189			−0.0183594	−	0.999831i	$-0.505844\pi$
$29$	−0.197737			−0.0367189			−0.0183594	+	0.999831i	$0.505844\pi$
$30$	2.36427	+	0.640487i	0.431655	+	0.116936i
$31$	−2.59210	−	1.49655i	−0.465555	−	0.268788i	0.248822	−	0.968549i	$-0.419956\pi$
$31$	−2.59210	−	1.49655i	−0.465555	−	0.268788i	−0.714377	+	0.699761i	$0.753290\pi$
$32$	3.04845	−	4.76518i	0.538895	−	0.842373i
$33$	2.84862	−	0.167439i	0.495881	−	0.0291474i
$34$	−1.54150	+	4.60128i	−0.264366	+	0.789113i
$35$	−1.76483	−	1.97113i	−0.298311	−	0.333182i
$36$	−0.0330433	+	5.99991i	−0.00550722	+	0.999985i
$37$	−2.72617	+	1.57395i	−0.448179	+	0.258756i	−0.707061	−	0.707153i	$-0.749979\pi$
$37$	−2.72617	+	1.57395i	−0.448179	+	0.258756i	0.258882	+	0.965909i	$0.416646\pi$
$38$	2.43625	+	2.75578i	0.395212	+	0.447047i
$39$	1.31206	+	1.99257i	0.210098	+	0.319067i
$40$	1.22057	−	2.55151i	0.192989	−	0.403429i
$41$	−9.89169			−1.54482			−0.772411	−	0.635123i	$-0.780950\pi$
$41$	−9.89169			−1.54482			−0.772411	+	0.635123i	$0.780950\pi$
$42$	3.55981	−	5.41551i	0.549291	−	0.835631i
$43$			2.90434i			0.442908i	0.975171	+	0.221454i	$0.0710802\pi$
$43$			2.90434i			0.442908i	−0.975171	+	0.221454i	$0.928920\pi$
$44$	0.404033	−	3.27011i	0.0609103	−	0.492988i
$45$	0.351460	+	2.97934i	0.0523925	+	0.444134i
$46$	2.82181	−	2.49462i	0.416052	−	0.367811i
$47$	4.47051	+	7.74314i	0.652090	+	1.12945i	0.982615	+	0.185656i	$0.0594411\pi$
$47$	4.47051	+	7.74314i	0.652090	+	1.12945i	−0.330524	+	0.943797i	$0.607226\pi$
$48$	6.80723	+	1.28905i	0.982539	+	0.186058i
$49$	−6.41068	+	2.81126i	−0.915812	+	0.401608i
$50$	0.449244	−	1.34096i	0.0635327	−	0.189641i
$51$	−5.93299	+	0.348735i	−0.830785	+	0.0488327i
$52$	2.53666	−	1.07448i	0.351771	−	0.149004i
$53$	−1.68026	+	2.91030i	−0.230802	+	0.399760i	−0.958044	−	0.286620i	$-0.907468\pi$
$53$	−1.68026	+	2.91030i	−0.230802	+	0.399760i	0.727243	+	0.686380i	$0.240801\pi$
$54$	−6.83385	+	2.70158i	−0.929969	+	0.367639i
$55$		−	1.64749i		−	0.222147i
$56$	−5.40787	−	5.17252i	−0.722657	−	0.691207i
$57$	−2.01967	+	4.02684i	−0.267511	+	0.533368i
$58$	−0.274050	+	0.0556480i	−0.0359845	+	0.00730694i
$59$	11.9318	+	6.88885i	1.55339	+	0.896851i	0.997862	+	0.0653547i	$0.0208179\pi$
$59$	11.9318	+	6.88885i	1.55339	+	0.896851i	0.555530	+	0.831497i	$0.312515\pi$
$60$	3.45696	+	0.222307i	0.446292	+	0.0286997i
$61$	−3.06938	−	5.31632i	−0.392994	−	0.680685i	0.599849	−	0.800113i	$-0.295227\pi$
$61$	−3.06938	−	5.31632i	−0.392994	−	0.680685i	−0.992843	+	0.119428i	$0.961894\pi$
$62$	−4.01363	−	1.34463i	−0.509731	−	0.170768i
$63$	7.77976	+	1.57331i	0.980158	+	0.198218i
$64$	2.88390	−	7.46211i	0.360488	−	0.932764i
$65$	1.19288	−	0.688710i	0.147959	−	0.0854239i
$66$	3.90086	−	1.03373i	0.480163	−	0.127243i
$67$	−6.09885	−	3.52117i	−0.745093	−	0.430180i	0.0788250	−	0.996888i	$-0.474883\pi$
$67$	−6.09885	−	3.52117i	−0.745093	−	0.430180i	−0.823918	+	0.566709i	$0.808217\pi$
$68$	−0.841504	+	6.81087i	−0.102047	+	0.825939i
$69$	4.12331	+	2.06805i	0.496389	+	0.248964i
$70$	−3.00066	−	2.23518i	−0.358647	−	0.267155i
$71$			0.209796i			0.0248983i	0.999923	+	0.0124491i	$0.00396278\pi$
$71$			0.209796i			0.0248983i	−0.999923	+	0.0124491i	$0.996037\pi$
$72$	1.64272	+	8.32475i	0.193597	+	0.981081i
$73$	−14.6076	−	8.43373i	−1.70970	−	0.987093i	−0.934922	−	0.354853i	$-0.884531\pi$
$73$	−14.6076	−	8.43373i	−1.70970	−	0.987093i	−0.774773	−	0.632239i	$-0.782136\pi$
$74$	−3.33532	+	2.94860i	−0.387724	+	0.342767i
$75$	1.72907	−	0.101633i	0.199655	−	0.0117355i
$76$	4.15202	+	3.13370i	0.476269	+	0.359460i
$77$	−4.14172	−	1.35857i	−0.471993	−	0.154824i
$78$	2.37918	+	2.39232i	0.269389	+	0.270877i
$79$	−2.67735	−	4.63731i	−0.301225	−	0.521738i	0.675188	−	0.737645i	$-0.264062\pi$
$79$	−2.67735	−	4.63731i	−0.301225	−	0.521738i	−0.976414	+	0.215908i	$0.930729\pi$
$80$	0.973564	−	3.87971i	0.108848	−	0.433765i
$81$	−6.19014	−	6.53316i	−0.687793	−	0.725907i
$82$	−13.7092	+	2.78376i	−1.51393	+	0.307415i
$83$			13.9725i			1.53368i	0.641837	+	0.766841i	$0.278173\pi$
$83$			13.9725i			1.53368i	−0.641837	+	0.766841i	$0.721827\pi$
$84$	3.40960	−	8.50733i	0.372017	−	0.928226i
$85$			3.43133i			0.372180i
$86$	0.817351	+	4.02521i	0.0881373	+	0.434050i
$87$	−0.188355	−	0.286046i	−0.0201937	−	0.0306674i
$88$	−0.360328	−	4.64585i	−0.0384111	−	0.495250i
$89$	0.829066	+	1.43598i	0.0878808	+	0.152214i	0.906615	−	0.421959i	$-0.138657\pi$
$89$	0.829066	+	1.43598i	0.0878808	+	0.152214i	−0.818734	+	0.574172i	$0.805324\pi$
$90$	1.32556	+	4.03025i	0.139726	+	0.424825i
$91$	−0.747698	−	3.56678i	−0.0783801	−	0.373900i
$92$	3.20878	−	4.25149i	0.334538	−	0.443248i
$93$	−0.304197	−	5.17526i	−0.0315438	−	0.536650i
$94$	8.37492	+	9.47334i	0.863807	+	0.977101i
$95$	2.25247	+	1.30047i	0.231099	+	0.133425i
$96$	9.79711	−	0.129186i	0.999913	−	0.0131850i
$97$			0.837143i			0.0849990i	0.999096	+	0.0424995i	$0.0135321\pi$
$97$			0.837143i			0.0849990i	−0.999096	+	0.0424995i	$0.986468\pi$
$98$	−8.09360	+	5.70032i	−0.817577	+	0.575820i
$99$	2.95567	+	3.96132i	0.297056	+	0.398127i
$100$	0.245242	−	1.98491i	0.0245242	−	0.198491i
$101$	13.1853	+	7.61255i	1.31199	+	0.757477i	0.982425	−	0.186656i	$-0.0597650\pi$
$101$	13.1853	+	7.61255i	1.31199	+	0.757477i	0.329564	+	0.944133i	$0.393098\pi$
$102$	−8.12457	+	2.15301i	−0.804452	+	0.213180i
$103$	3.20513	−	1.85048i	0.315811	−	0.182334i	−0.333713	−	0.942675i	$-0.608302\pi$
$103$	3.20513	−	1.85048i	0.315811	−	0.182334i	0.649524	+	0.760341i	$0.274968\pi$
$104$	3.21324	−	2.20303i	0.315084	−	0.216025i
$105$	1.17034	−	4.43061i	0.114214	−	0.432383i
$106$	−1.50969	+	4.50633i	−0.146635	+	0.437694i
$107$	−0.944991	−	1.63677i	−0.0913557	−	0.158233i	0.816726	−	0.577026i	$-0.195787\pi$
$107$	−0.944991	−	1.63677i	−0.0913557	−	0.158233i	−0.908082	+	0.418793i	$0.862453\pi$
$108$	−8.71094	+	5.66741i	−0.838210	+	0.545347i
$109$	−11.6546	−	6.72880i	−1.11631	−	0.644502i	−0.175854	−	0.984416i	$-0.556269\pi$
$109$	−11.6546	−	6.72880i	−1.11631	−	0.644502i	−0.940457	+	0.339914i	$0.889602\pi$
$110$	−0.463643	−	2.28330i	−0.0442067	−	0.217705i
$111$	−4.87369	−	2.44440i	−0.462590	−	0.232012i
$112$	−8.95060	−	5.64684i	−0.845752	−	0.533576i
$113$		−	20.0607i		−	1.88715i	−0.331160	−	0.943575i	$-0.607440\pi$
$113$		−	20.0607i		−	1.88715i	0.331160	−	0.943575i	$-0.392560\pi$
$114$	−1.66586	+	6.14930i	−0.156022	+	0.575935i
$115$	1.33162	−	2.30643i	0.124174	−	0.215076i
$116$	−0.364153	+	0.154248i	−0.0338108	+	0.0143216i
$117$	−1.63265	+	3.79605i	−0.150939	+	0.350945i
$118$	18.4754	+	6.18955i	1.70080	+	0.569794i
$119$	8.62621	+	2.82959i	0.790763	+	0.259388i
$120$	4.85367	−	0.664770i	0.443077	−	0.0606849i
$121$	4.14289	+	7.17569i	0.376626	+	0.652336i
$122$	−5.75008	−	6.50425i	−0.520588	−	0.588867i
$123$	−9.42233	−	14.3093i	−0.849583	−	1.29023i
$124$	−5.94102	−	0.734032i	−0.533519	−	0.0659180i
$125$		−	1.00000i		−	0.0894427i
$126$	11.2250	−	0.00891817i	1.00000	−	0.000794494i
$127$	−9.04898			−0.802967			−0.401484	−	0.915866i	$-0.631505\pi$
$127$	−9.04898			−0.802967			−0.401484	+	0.915866i	$0.631505\pi$
$128$	1.89686	−	11.1536i	0.167661	−	0.985845i
$129$	−4.20142	+	2.76653i	−0.369914	+	0.243579i
$130$	1.45943	−	1.29021i	0.128000	−	0.113159i
$131$	0.590742	−	0.341065i	0.0516134	−	0.0297990i	−0.473971	−	0.880540i	$-0.657180\pi$
$131$	0.590742	−	0.341065i	0.0516134	−	0.0297990i	0.525585	+	0.850741i	$0.323847\pi$
$132$	5.11541	−	2.53047i	0.445239	−	0.220249i
$133$	5.12678	−	4.59021i	0.444548	−	0.398022i
$134$	−9.44352	−	3.16373i	−0.815796	−	0.273305i
$135$	−3.97513	+	3.34639i	−0.342125	+	0.288012i
$136$	0.750477	+	9.67620i	0.0643529	+	0.829727i
$137$	−13.0282	−	7.52185i	−1.11308	−	0.642635i	−0.173452	−	0.984842i	$-0.555492\pi$
$137$	−13.0282	−	7.52185i	−1.11308	−	0.642635i	−0.939624	+	0.342207i	$0.888825\pi$
$138$	6.29662	+	1.70577i	0.536004	+	0.145205i
$139$	2.81250			0.238553			0.119277	−	0.992861i	$-0.461942\pi$
$139$	2.81250			0.238553			0.119277	+	0.992861i	$0.461942\pi$
$140$	−4.78774	−	2.25335i	−0.404638	−	0.190443i
$141$	−6.94285	+	13.8428i	−0.584693	+	1.16577i
$142$	0.0590418	+	0.290763i	0.00495468	+	0.0244003i
$143$	1.13464	−	1.96526i	0.0948836	−	0.164343i
$144$	4.61949	+	11.0752i	0.384957	+	0.922934i
$145$	−0.171245	+	0.0988686i	−0.0142212	+	0.00821059i
$146$	−22.6186	−	7.57760i	−1.87193	−	0.627127i
$147$	−10.1733	−	6.59582i	−0.839076	−	0.544014i
$148$	−3.79272	+	5.02519i	−0.311760	+	0.413068i
$149$	7.24840	+	12.5546i	0.593812	+	1.02851i	0.993713	+	0.111955i	$0.0357111\pi$
$149$	7.24840	+	12.5546i	0.593812	+	1.02851i	−0.399901	+	0.916558i	$0.630956\pi$
$150$	2.36776	−	0.627457i	0.193327	−	0.0512317i
$151$	10.0704	−	17.4425i	0.819519	−	1.41945i	−0.0865186	−	0.996250i	$-0.527574\pi$
$151$	10.0704	−	17.4425i	0.819519	−	1.41945i	0.906037	−	0.423198i	$-0.139092\pi$
$152$	6.63631	+	3.17461i	0.538275	+	0.257495i
$153$	−6.15595	−	8.25047i	−0.497679	−	0.667011i
$154$	−6.12247	−	0.717309i	−0.493362	−	0.0578024i
$155$	−2.99310			−0.240411
$156$	3.97064	+	2.64603i	0.317905	+	0.211852i
$157$	−4.10091	+	7.10299i	−0.327288	+	0.566880i	−0.981973	−	0.189022i	$-0.939468\pi$
$157$	−4.10091	+	7.10299i	−0.327288	+	0.566880i	0.654684	+	0.755902i	$0.272802\pi$
$158$	−5.01567	−	5.67351i	−0.399025	−	0.451360i
$159$	−5.81056	+	0.341539i	−0.460808	+	0.0270858i
$160$	0.257445	−	5.65099i	0.0203528	−	0.446750i
$161$	−4.70018	−	5.24960i	−0.370426	−	0.413726i
$162$	−10.4177	−	7.31244i	−0.818491	−	0.574520i
$163$	9.28920	−	5.36312i	0.727586	−	0.420072i	−0.0899523	−	0.995946i	$-0.528671\pi$
$163$	9.28920	−	5.36312i	0.727586	−	0.420072i	0.817538	+	0.575874i	$0.195338\pi$
$164$	−18.2165	+	7.71619i	−1.42247	+	0.602533i
$165$	2.38326	−	1.56932i	0.185536	−	0.122171i
$166$	3.93220	+	19.3649i	0.305198	+	1.50301i
$167$	5.30711			0.410677			0.205338	−	0.978691i	$-0.434171\pi$
$167$	5.30711			0.410677			0.205338	+	0.978691i	$0.434171\pi$
$168$	2.33129	−	12.7501i	0.179863	−	0.983692i
$169$	−11.1027			−0.854055
$170$	0.965658	+	4.75558i	0.0740626	+	0.364736i
$171$	−7.74906	+	0.914123i	−0.592585	+	0.0699047i
$172$	2.26558	+	5.34863i	0.172749	+	0.407830i
$173$	−5.63839	+	3.25532i	−0.428679	+	0.247498i	−0.698784	−	0.715333i	$-0.746275\pi$
$173$	−5.63839	+	3.25532i	−0.428679	+	0.247498i	0.270105	+	0.962831i	$0.412942\pi$
$174$	−0.341546	−	0.343433i	−0.0258926	−	0.0260356i
$175$	−2.51396	−	0.824633i	−0.190037	−	0.0623364i
$176$	−1.80684	−	6.33742i	−0.136196	−	0.477701i
$177$	1.40027	+	23.8225i	0.105250	+	1.79061i
$178$	1.55315	+	1.75685i	0.116413	+	0.131682i
$179$	5.52571	−	9.57082i	0.413011	−	0.715356i	−0.582206	−	0.813041i	$-0.697810\pi$
$179$	5.52571	−	9.57082i	0.413011	−	0.715356i	0.995217	+	0.0976847i	$0.0311437\pi$
$180$	2.97134	+	5.21260i	0.221470	+	0.388524i
$181$	22.7305			1.68954			0.844772	−	0.535126i	$-0.179736\pi$
$181$	22.7305			1.68954			0.844772	+	0.535126i	$0.179736\pi$
$182$	−2.04004	−	4.73289i	−0.151218	−	0.350825i
$183$	4.76685	−	9.50422i	0.352376	−	0.702572i
$184$	3.25067	−	6.79529i	0.239642	−	0.500956i
$185$	−1.57395	+	2.72617i	−0.115719	+	0.200432i
$186$	−1.87804	−	7.08694i	−0.137705	−	0.519640i
$187$	2.82654	+	4.89571i	0.206697	+	0.358010i
$188$	14.2731	+	10.7725i	1.04097	+	0.785664i
$189$	5.13466	+	12.7529i	0.373492	+	0.927633i
$190$	3.48775	+	1.16845i	0.253028	+	0.0847685i
$191$	14.7228	−	8.50022i	1.06531	−	0.615055i	0.138411	−	0.990375i	$-0.455801\pi$
$191$	14.7228	−	8.50022i	1.06531	−	0.615055i	0.926895	+	0.375320i	$0.122467\pi$
$192$	13.5417	−	2.93619i	0.977291	−	0.211901i
$193$	−4.99640	+	8.65402i	−0.359649	+	0.622930i	−0.987902	−	0.155079i	$-0.950437\pi$
$193$	−4.99640	+	8.65402i	−0.359649	+	0.622930i	0.628253	+	0.778009i	$0.283770\pi$
$194$	0.235592	+	1.16022i	0.0169145	+	0.0832990i
$195$	2.13256	+	1.06959i	0.152716	+	0.0765949i
$196$	−9.61294	+	10.1780i	−0.686639	+	0.726999i
$197$	−20.4615			−1.45782			−0.728910	−	0.684609i	$-0.759973\pi$
$197$	−20.4615			−1.45782			−0.728910	+	0.684609i	$0.759973\pi$
$198$	5.21116	+	4.65831i	0.370341	+	0.331052i
$199$	−17.1607	−	9.90776i	−1.21649	−	0.702342i	−0.252327	−	0.967642i	$-0.581196\pi$
$199$	−17.1607	−	9.90776i	−1.21649	−	0.702342i	−0.964166	+	0.265300i	$0.914529\pi$
$200$	−0.218713	−	2.81996i	−0.0154654	−	0.199401i
$201$	−0.715734	−	12.1767i	−0.0504840	−	0.858877i
$202$	20.4163	+	6.83979i	1.43649	+	0.481246i
$203$	0.107337	+	0.512034i	0.00753356	+	0.0359377i
$204$	−10.6542	+	5.27037i	−0.745941	+	0.369000i
$205$	−8.56646	+	4.94585i	−0.598307	+	0.345433i
$206$	3.92131	−	3.46664i	0.273211	−	0.241532i
$207$	0.936022	+	7.93470i	0.0650580	+	0.551500i
$208$	3.83334	−	3.95753i	0.265794	−	0.274405i
$209$	4.28501			0.296400
$210$	0.375135	−	6.46987i	0.0258868	−	0.446464i
$211$			21.1942i			1.45907i	0.683945	+	0.729534i	$0.260263\pi$
$211$			21.1942i			1.45907i	−0.683945	+	0.729534i	$0.739737\pi$
$212$	−0.824140	+	6.67032i	−0.0566021	+	0.458120i
$213$	−0.303491	+	0.199842i	−0.0207949	+	0.0136929i
$214$	−1.77032	−	2.00251i	−0.121016	−	0.136889i
$215$	1.45217	+	2.51523i	0.0990372	+	0.171537i
$216$	−10.4778	+	10.3061i	−0.712924	+	0.701241i
$217$	−2.46821	+	7.52452i	−0.167553	+	0.510798i
$218$	−18.0461	−	6.04575i	−1.22224	−	0.409470i
$219$	−1.71429	−	29.1649i	−0.115841	−	1.97078i
$220$	−1.28515	−	3.03402i	−0.0866451	−	0.204553i
$221$	−2.36319	+	4.09316i	−0.158965	+	0.275336i
$222$	−7.44250	−	2.01619i	−0.499508	−	0.135318i
$223$			13.7501i			0.920776i	0.887718	+	0.460388i	$0.152290\pi$
$223$			13.7501i			0.920776i	−0.887718	+	0.460388i	$0.847710\pi$
$224$	−13.9941	−	5.30720i	−0.935017	−	0.354602i
$225$	1.79404	+	2.40446i	0.119603	+	0.160297i
$226$	−5.64556	−	27.8027i	−0.375537	−	1.84941i
$227$	−16.8071	−	9.70356i	−1.11552	−	0.644048i	−0.175269	−	0.984521i	$-0.556080\pi$
$227$	−16.8071	−	9.70356i	−1.11552	−	0.644048i	−0.940254	+	0.340472i	$0.889413\pi$
$228$	−0.578206	+	8.99132i	−0.0382926	+	0.595464i
$229$	−11.4014	−	19.7478i	−0.753427	−	1.30497i	−0.946153	−	0.323721i	$-0.895066\pi$
$229$	−11.4014	−	19.7478i	−0.753427	−	1.30497i	0.192726	−	0.981253i	$-0.438267\pi$
$230$	1.19645	−	3.57131i	0.0788913	−	0.235485i
$231$	−1.97988	−	7.28552i	−0.130267	−	0.479352i
$232$	−0.461281	+	0.316259i	−0.0302846	+	0.0207634i
$233$	12.5257	−	7.23169i	0.820583	−	0.473764i	−0.0300343	−	0.999549i	$-0.509562\pi$
$233$	12.5257	−	7.23169i	0.820583	−	0.473764i	0.850618	+	0.525785i	$0.176228\pi$
$234$	−1.19444	+	5.72053i	−0.0780830	+	0.373963i
$235$	7.74314	+	4.47051i	0.505107	+	0.291624i
$236$	27.3474	+	3.37886i	1.78017	+	0.219945i
$237$	4.15801	−	8.29032i	0.270092	−	0.538514i
$238$	12.7516	+	1.49398i	0.826565	+	0.0968405i
$239$		−	2.23455i		−	0.144541i	−0.997385	−	0.0722706i	$-0.976975\pi$
$239$		−	2.23455i		−	0.144541i	0.997385	−	0.0722706i	$-0.0230245\pi$
$240$	6.53976	−	2.28726i	0.422140	−	0.147642i
$241$	17.8687	+	10.3165i	1.15103	+	0.664545i	0.949137	−	0.314864i	$-0.101959\pi$
$241$	17.8687	+	10.3165i	1.15103	+	0.664545i	0.201888	+	0.979409i	$0.435292\pi$
$242$	7.76117	+	8.77910i	0.498907	+	0.564342i
$243$	3.55445	−	15.1778i	0.228018	−	0.973657i
$244$	−9.79966	−	7.39622i	−0.627359	−	0.473494i
$245$	−4.14618	+	5.63996i	−0.264890	+	0.360324i
$246$	−17.0857	−	17.1800i	−1.08934	−	1.09536i
$247$	1.79129	+	3.10260i	0.113977	+	0.197414i
$248$	−8.44041	+	0.654630i	−0.535966	+	0.0415691i
$249$	−20.2126	+	13.3095i	−1.28092	+	0.843456i
$250$	−0.281424	−	1.38593i	−0.0177988	−	0.0876539i
$251$			2.36084i			0.149015i	0.997220	+	0.0745074i	$0.0237384\pi$
$251$			2.36084i			0.149015i	−0.997220	+	0.0745074i	$0.976262\pi$
$252$	15.5545	−	3.17134i	0.979842	−	0.199775i
$253$		−	4.38766i		−	0.275850i
$254$	−12.5412	+	2.54660i	−0.786908	+	0.159788i
$255$	−4.96375	+	3.26851i	−0.310842	+	0.204682i
$256$	−0.509962	−	15.9919i	−0.0318726	−	0.999492i
$257$	8.83359	+	15.3002i	0.551024	+	0.954402i	0.998201	+	0.0599566i	$0.0190962\pi$
$257$	8.83359	+	15.3002i	0.551024	+	0.954402i	−0.447177	+	0.894446i	$0.647570\pi$
$258$	−5.04430	+	5.01659i	−0.314044	+	0.312319i
$259$	5.55553	+	6.20493i	0.345204	+	0.385556i
$260$	1.65957	−	2.19886i	0.102922	−	0.136367i
$261$	0.234377	−	0.544947i	0.0145076	−	0.0337314i
$262$	0.722743	−	0.638941i	0.0446512	−	0.0394739i
$263$	11.1459	+	6.43510i	0.687287	+	0.396805i	0.802595	−	0.596525i	$-0.203452\pi$
$263$	11.1459	+	6.43510i	0.687287	+	0.396805i	−0.115308	+	0.993330i	$0.536786\pi$
$264$	6.37746	−	4.94666i	0.392505	−	0.304446i
$265$			3.36052i			0.206435i
$266$	5.81355	−	7.80451i	0.356452	−	0.478525i
$267$	−1.28757	+	2.56717i	−0.0787978	+	0.157108i
$268$	−13.9784	−	1.72708i	−0.853867	−	0.105498i
$269$	17.5918	+	10.1566i	1.07259	+	0.619260i	0.928888	−	0.370361i	$-0.120766\pi$
$269$	17.5918	+	10.1566i	1.07259	+	0.619260i	0.143702	+	0.989621i	$0.454099\pi$
$270$	−4.56749	+	5.75656i	−0.277969	+	0.350333i
$271$	15.8628	−	9.15838i	0.963595	−	0.556332i	0.0663173	−	0.997799i	$-0.478875\pi$
$271$	15.8628	−	9.15838i	0.963595	−	0.556332i	0.897278	+	0.441467i	$0.145542\pi$
$272$	3.76322	+	13.1993i	0.228179	+	0.800327i
$273$	4.44748	−	4.47916i	0.269174	−	0.271091i
$274$	−20.1730	−	6.75830i	−1.21870	−	0.408284i
$275$	−0.823745	−	1.42677i	−0.0496737	−	0.0860374i
$276$	9.20672	+	0.592058i	0.554179	+	0.0356377i
$277$	−2.59877	−	1.50040i	−0.156145	−	0.0901505i	0.419891	−	0.907574i	$-0.362068\pi$
$277$	−2.59877	−	1.50040i	−0.156145	−	0.0901505i	−0.576037	+	0.817424i	$0.695401\pi$
$278$	3.89793	−	0.791506i	0.233782	−	0.0474713i
$279$	7.19677	−	5.36975i	0.430859	−	0.321478i
$280$	−7.26961	−	1.77560i	−0.434442	−	0.106112i
$281$			29.5670i			1.76382i	0.471416	+	0.881911i	$0.343743\pi$
$281$			29.5670i			1.76382i	−0.471416	+	0.881911i	$0.656257\pi$
$282$	−5.72661	+	21.1390i	−0.341014	+	1.25881i
$283$	−9.56503	+	16.5671i	−0.568582	+	0.984813i	0.428124	+	0.903720i	$0.359174\pi$
$283$	−9.56503	+	16.5671i	−0.568582	+	0.984813i	−0.996707	+	0.0810932i	$0.974159\pi$
$284$	0.163656	+	0.386361i	0.00971117	+	0.0229263i
$285$	0.264340	+	4.49718i	0.0156581	+	0.266390i
$286$	1.01946	−	3.04302i	0.0602821	−	0.179938i
$287$	5.36946	+	25.6142i	0.316949	+	1.51196i
$288$	9.51911	+	14.0494i	0.560919	+	0.827871i
$289$	2.61300	+	4.52584i	0.153706	+	0.266226i
$290$	−0.209510	+	0.185217i	−0.0123029	+	0.0108763i
$291$	−1.21101	+	0.797421i	−0.0709907	+	0.0467456i
$292$	−33.4803	−	4.13660i	−1.95929	−	0.242076i
$293$			8.00610i			0.467721i	0.972270	+	0.233861i	$0.0751360\pi$
$293$			8.00610i			0.467721i	−0.972270	+	0.233861i	$0.924864\pi$
$294$	−15.9556	−	6.27835i	−0.930552	−	0.366161i
$295$	13.7777			0.802168
$296$	−3.84223	+	8.03192i	−0.223325	+	0.466846i
$297$	−2.91501	+	8.04902i	−0.169146	+	0.467051i
$298$	13.5789	+	15.3599i	0.786607	+	0.889776i
$299$	3.17693	−	1.83420i	0.183726	−	0.106075i
$300$	3.10497	−	1.53596i	0.179266	−	0.0886785i
$301$	7.52069	−	1.57655i	0.433486	−	0.0908708i
$302$	9.04815	−	27.0081i	0.520663	−	1.55414i
$303$	1.54737	+	26.3252i	0.0888941	+	1.51234i
$304$	10.0909	+	2.53217i	0.578751	+	0.145230i
$305$	−5.31632	−	3.06938i	−0.304412	−	0.175752i
$306$	−10.8536	−	9.70214i	−0.620459	−	0.554634i
$307$	2.52743			0.144248			0.0721240	−	0.997396i	$-0.477022\pi$
$307$	2.52743			0.144248			0.0721240	+	0.997396i	$0.477022\pi$
$308$	−8.68717	+	0.728870i	−0.494998	+	0.0415312i
$309$	5.72995	+	2.87386i	0.325966	+	0.163488i
$310$	−4.14822	+	0.842330i	−0.235603	+	0.0478411i
$311$	12.1119	−	20.9784i	0.686801	−	1.18957i	−0.286066	−	0.958210i	$-0.592348\pi$
$311$	12.1119	−	20.9784i	0.686801	−	1.18957i	0.972867	−	0.231364i	$-0.0743189\pi$
$312$	6.24768	+	2.54978i	0.353705	+	0.144353i
$313$	6.79503	−	3.92311i	0.384078	−	0.221747i	−0.295513	−	0.955339i	$-0.595491\pi$
$313$	6.79503	−	3.92311i	0.384078	−	0.221747i	0.679591	+	0.733591i	$0.262157\pi$
$314$	−3.68462	+	10.9983i	−0.207935	+	0.620672i
$315$	7.52413	−	2.52736i	0.423936	−	0.142400i
$316$	−8.54803	−	6.45155i	−0.480864	−	0.362928i
$317$	4.90985	+	8.50411i	0.275765	+	0.477638i	0.970328	−	0.241794i	$-0.0777357\pi$
$317$	4.90985	+	8.50411i	0.275765	+	0.477638i	−0.694563	+	0.719432i	$0.744402\pi$
$318$	−7.95692	+	2.10858i	−0.446202	+	0.118243i
$319$	−0.162885	+	0.282125i	−0.00911981	+	0.0157960i
$320$	−1.23352	−	7.90433i	−0.0689561	−	0.441865i
$321$	1.46760	−	2.92613i	0.0819135	−	0.163321i
$322$	−7.99148	−	5.95283i	−0.445348	−	0.331738i
$323$	−8.92464			−0.496580
$324$	−16.4961	−	7.20274i	−0.916449	−	0.400152i
$325$	0.688710	−	1.19288i	0.0382027	−	0.0661691i
$326$	11.3649	−	10.0471i	0.629442	−	0.556458i
$327$	−1.36773	−	23.2691i	−0.0756359	−	1.28678i
$328$	−23.0753	+	15.8207i	−1.27412	+	0.873551i
$329$	17.6239	−	15.7794i	0.971638	−	0.869947i
$330$	2.86138	−	2.84567i	0.157514	−	0.156649i
$331$	22.1388	−	12.7819i	1.21686	−	0.702554i	0.252615	−	0.967567i	$-0.418710\pi$
$331$	22.1388	−	12.7819i	1.21686	−	0.702554i	0.964245	+	0.265013i	$0.0853762\pi$
$332$	10.8995	+	25.7318i	0.598189	+	1.41222i
$333$	−1.10636	−	9.37868i	−0.0606283	−	0.513949i
$334$	7.35528	−	1.49355i	0.402463	−	0.0817234i
$335$	−7.04235			−0.384765
$336$	−0.357182	−	18.3268i	−0.0194859	−	0.999810i
$337$	−8.35161			−0.454941			−0.227471	−	0.973785i	$-0.573046\pi$
$337$	−8.35161			−0.454941			−0.227471	+	0.973785i	$0.573046\pi$
$338$	−15.3876	+	3.12457i	−0.836974	+	0.169954i
$339$	29.0197	−	19.1088i	1.57614	−	1.03785i
$340$	2.67667	+	6.31913i	0.145163	+	0.342703i
$341$	−4.27046	+	2.46555i	−0.231258	+	0.133517i
$342$	−10.4824	+	3.44768i	−0.566823	+	0.186429i
$343$	10.7595	+	15.0742i	0.580960	+	0.813932i
$344$	4.64517	+	6.77524i	0.250451	+	0.365296i
$345$	4.60492	−	0.270673i	0.247921	−	0.0145725i
$346$	−6.89828	+	6.09843i	−0.370854	+	0.327854i
$347$	−1.17983	+	2.04352i	−0.0633364	+	0.109702i	−0.895955	−	0.444145i	$-0.853507\pi$
$347$	−1.17983	+	2.04352i	−0.0633364	+	0.109702i	0.832618	+	0.553847i	$0.186841\pi$
$348$	−0.570010	−	0.379854i	−0.0305557	−	0.0203623i
$349$	−34.8574			−1.86587			−0.932937	−	0.360040i	$-0.882763\pi$
$349$	−34.8574			−1.86587			−0.932937	+	0.360040i	$0.882763\pi$
$350$	−3.71624	−	0.435395i	−0.198641	−	0.0232728i
$351$	−7.04655	+	1.25414i	−0.376117	+	0.0669408i
$352$	−4.28766	−	8.27473i	−0.228533	−	0.441044i
$353$	−3.40973	+	5.90583i	−0.181482	+	0.314336i	−0.942385	−	0.334529i	$-0.891423\pi$
$353$	−3.40973	+	5.90583i	−0.181482	+	0.314336i	0.760904	+	0.648865i	$0.224756\pi$
$354$	8.64491	+	32.6223i	0.459472	+	1.73386i
$355$	0.104898	+	0.181689i	0.00556742	+	0.00964305i
$356$	2.64697	+	1.99778i	0.140289	+	0.105882i
$357$	4.12362	+	15.1740i	0.218245	+	0.803093i
$358$	4.96479	−	14.8195i	0.262397	−	0.783237i
$359$	−9.68369	+	5.59088i	−0.511086	+	0.295076i	−0.733280	−	0.679927i	$-0.762011\pi$
$359$	−9.68369	+	5.59088i	−0.511086	+	0.295076i	0.222194	+	0.975002i	$0.428678\pi$
$360$	5.58502	+	6.38808i	0.294356	+	0.336682i
$361$	6.11758	−	10.5960i	0.321978	−	0.557682i
$362$	31.5029	−	6.39691i	1.65575	−	0.336214i
$363$	−6.43404	+	12.8283i	−0.337700	+	0.673311i
$364$	−4.15929	−	5.98533i	−0.218006	−	0.313717i
$365$	−16.8675			−0.882883
$366$	3.93180	−	14.5137i	0.205518	−	0.758643i
$367$	8.79576	+	5.07823i	0.459135	+	0.265082i	0.711680	−	0.702503i	$-0.247934\pi$
$367$	8.79576	+	5.07823i	0.459135	+	0.265082i	−0.252546	+	0.967585i	$0.581268\pi$
$368$	2.59283	−	10.3326i	0.135161	−	0.538625i
$369$	11.7246	−	27.2607i	0.610358	−	1.41913i
$370$	−1.41418	+	4.22122i	−0.0735196	+	0.219451i
$371$	8.44821	+	2.77120i	0.438609	+	0.143873i
$372$	−4.59727	−	9.29348i	−0.238357	−	0.481844i
$373$	19.3875	−	11.1934i	1.00384	−	0.579570i	0.0944613	−	0.995529i	$-0.469887\pi$
$373$	19.3875	−	11.1934i	1.00384	−	0.579570i	0.909384	+	0.415958i	$0.136554\pi$
$374$	5.29515	+	5.98965i	0.273806	+	0.309717i
$375$	1.44660	−	0.952550i	0.0747021	−	0.0491895i
$376$	22.8131	+	10.9131i	1.17650	+	0.562801i
$377$	−0.272367			−0.0140276
$378$	10.7052	+	16.2295i	0.550618	+	0.834757i
$379$		−	14.3447i		−	0.736837i	−0.929660	−	0.368418i	$-0.879899\pi$
$379$		−	14.3447i		−	0.736837i	0.929660	−	0.368418i	$-0.120101\pi$
$380$	5.16261	+	0.637856i	0.264836	+	0.0327213i
$381$	−8.61961	−	13.0902i	−0.441596	−	0.670634i
$382$	18.0126	−	15.9241i	0.921606	−	0.814746i
$383$	−7.85212	−	13.6003i	−0.401225	−	0.694941i	0.592649	−	0.805460i	$-0.298082\pi$
$383$	−7.85212	−	13.6003i	−0.401225	−	0.694941i	−0.993874	+	0.110519i	$0.964749\pi$
$384$	17.9416	−	7.88032i	0.915578	−	0.402141i
$385$	−4.26612	+	0.894299i	−0.217422	+	0.0455777i
$386$	−4.48921	+	13.4000i	−0.228495	+	0.682040i
$387$	−8.00411	−	3.44251i	−0.406872	−	0.174992i
$388$	0.653029	+	1.54168i	0.0331525	+	0.0782671i
$389$	−10.8259	+	18.7510i	−0.548896	+	0.950715i	0.449455	+	0.893303i	$0.351618\pi$
$389$	−10.8259	+	18.7510i	−0.548896	+	0.950715i	−0.998351	+	0.0574120i	$0.981715\pi$
$390$	3.25659	+	0.882220i	0.164904	+	0.0446729i
$391$			9.13845i			0.462151i
$392$	−10.4585	+	16.8113i	−0.528236	+	0.849098i
$393$	1.05610	+	0.529686i	0.0532730	+	0.0267191i
$394$	−28.3582	+	5.75836i	−1.42866	+	0.290102i
$395$	−4.63731	−	2.67735i	−0.233328	−	0.134712i
$396$	8.53326	+	4.98954i	0.428812	+	0.250734i
$397$	−10.7506	−	18.6206i	−0.539557	−	0.934539i	−0.998928	−	0.0462950i	$-0.985259\pi$
$397$	−10.7506	−	18.6206i	−0.539557	−	0.934539i	0.459371	−	0.888244i	$-0.348075\pi$
$398$	−26.5719	−	8.90201i	−1.33193	−	0.446217i
$399$	11.5237	+	3.04399i	0.576907	+	0.152390i
$400$	−1.09673	−	3.84671i	−0.0548363	−	0.192336i
$401$	16.7450	−	9.66771i	0.836204	−	0.482783i	−0.0197682	−	0.999805i	$-0.506293\pi$
$401$	16.7450	−	9.66771i	0.836204	−	0.482783i	0.855972	+	0.517022i	$0.172959\pi$
$402$	−4.41877	−	16.6746i	−0.220388	−	0.831654i
$403$	−3.57041	−	2.06137i	−0.177855	−	0.102684i
$404$	30.2204	+	3.73383i	1.50352	+	0.185765i
$405$	−8.62740	−	2.56281i	−0.428699	−	0.127347i
$406$	0.292860	+	0.679436i	0.0145344	+	0.0337198i
$407$			5.18614i			0.257067i
$408$	−13.2827	+	10.3027i	−0.657592	+	0.510060i
$409$	9.89529	+	5.71305i	0.489290	+	0.282492i	0.724280	−	0.689506i	$-0.242172\pi$
$409$	9.89529	+	5.71305i	0.489290	+	0.282492i	−0.234990	+	0.971998i	$0.575506\pi$
$410$	−10.4806	+	9.26540i	−0.517601	+	0.457586i
$411$	−1.52893	−	26.0116i	−0.0754168	−	1.28306i
$412$	4.45907	−	5.90807i	0.219683	−	0.291070i
$413$	11.3615	−	34.6365i	0.559065	−	1.70435i
$414$	3.53028	+	10.7335i	0.173504	+	0.527524i
$415$	6.98626	+	12.1006i	0.342942	+	0.593993i
$416$	4.19900	−	6.56365i	0.205873	−	0.321810i
$417$	2.67905	+	4.06856i	0.131193	+	0.199238i
$418$	5.93872	−	1.20590i	0.290472	−	0.0589827i
$419$			2.66588i			0.130237i	0.997878	+	0.0651184i	$0.0207425\pi$
$419$			2.66588i			0.130237i	−0.997878	+	0.0651184i	$0.979257\pi$
$420$	−1.30087	−	9.07236i	−0.0634759	−	0.442686i
$421$		−	25.0185i		−	1.21933i	−0.792661	−	0.609663i	$-0.791305\pi$
$421$		−	25.0185i		−	1.21933i	0.792661	−	0.609663i	$-0.208695\pi$
$422$	5.96456	+	29.3736i	0.290350	+	1.42989i
$423$	−26.6383	+	3.14241i	−1.29520	+	0.152789i
$424$	0.734991	+	9.47653i	0.0356943	+	0.460221i
$425$	1.71566	+	2.97162i	0.0832219	+	0.144145i
$426$	−0.364377	+	0.362376i	−0.0176541	+	0.0175572i
$427$	−12.1003	+	10.8339i	−0.585575	+	0.524289i
$428$	−3.01709	−	2.27712i	−0.145836	−	0.110069i
$429$	3.92374	−	0.230634i	0.189440	−	0.0111351i
$430$	2.72045	+	3.07726i	0.131192	+	0.148399i
$431$	13.8312	+	7.98542i	0.666223	+	0.384644i	0.794644	−	0.607076i	$-0.207657\pi$
$431$	13.8312	+	7.98542i	0.666223	+	0.384644i	−0.128421	+	0.991720i	$0.540991\pi$
$432$	−11.6211	+	17.2322i	−0.559121	+	0.829086i
$433$		−	20.6616i		−	0.992932i	−0.868056	−	0.496466i	$-0.834631\pi$
$433$		−	20.6616i		−	0.992932i	0.868056	−	0.496466i	$-0.165369\pi$
$434$	−1.30318	+	11.1231i	−0.0625546	+	0.533924i
$435$	−0.306143	−	0.153546i	−0.0146784	−	0.00736198i
$436$	−26.7121	−	3.30036i	−1.27928	−	0.158059i
$437$	5.99888	+	3.46345i	0.286965	+	0.165679i
$438$	−10.5836	−	39.9381i	−0.505704	−	1.90832i
$439$	31.4205	−	18.1406i	1.49962	−	0.865805i	0.499619	−	0.866245i	$-0.333473\pi$
$439$	31.4205	−	18.1406i	1.49962	−	0.865805i	1.00000		0.000439669i	$0.000139951\pi$
$440$	−2.63498	−	3.84326i	−0.125618	−	0.183220i
$441$	−0.149020	−	20.9995i	−0.00709617	−	0.999975i
$442$	−2.12330	+	6.33789i	−0.100995	+	0.301463i
$443$	5.63538	+	9.76076i	0.267745	+	0.463748i	0.968279	−	0.249871i	$-0.0803883\pi$
$443$	5.63538	+	9.76076i	0.267745	+	0.463748i	−0.700534	+	0.713619i	$0.747055\pi$
$444$	−10.8822	−	0.699802i	−0.516446	−	0.0332111i
$445$	1.43598	+	0.829066i	0.0680722	+	0.0393015i
$446$	3.86962	+	19.0567i	0.183232	+	0.902361i
$447$	−11.2570	+	22.4444i	−0.532438	+	1.06158i
$448$	−20.8883	−	3.41714i	−0.986882	−	0.161445i
$449$		−	0.736265i		−	0.0347465i	−0.999849	−	0.0173732i	$-0.994470\pi$
$449$		−	0.736265i		−	0.0347465i	0.999849	−	0.0173732i	$-0.00553035\pi$
$450$	3.16309	+	2.82752i	0.149110	+	0.133290i
$451$	−8.14823	+	14.1131i	−0.383685	+	0.664562i
$452$	−15.6487	−	36.9437i	−0.736052	−	1.73769i
$453$	34.8248	−	2.04697i	1.63621	−	0.0961750i
$454$	−26.0242	−	8.71854i	−1.22138	−	0.409181i
$455$	−2.43092	−	2.71508i	−0.113963	−	0.127285i
$456$	1.72902	+	12.6241i	0.0809688	+	0.591175i
$457$	4.63877	+	8.03459i	0.216993	+	0.375842i	0.953887	−	0.300166i	$-0.0970419\pi$
$457$	4.63877	+	8.03459i	0.216993	+	0.375842i	−0.736895	+	0.676008i	$0.763709\pi$
$458$	−21.3591	−	24.1605i	−0.998044	−	1.12894i
$459$	6.07128	−	16.7642i	0.283383	−	0.782485i
$460$	0.653137	−	5.28629i	0.0304527	−	0.246474i
$461$		−	30.1167i		−	1.40267i	−0.712829	−	0.701337i	$-0.752587\pi$
$461$		−	30.1167i		−	1.40267i	0.712829	−	0.701337i	$-0.247413\pi$
$462$	−4.79430	−	9.54003i	−0.223051	−	0.443842i
$463$	−3.82318			−0.177678			−0.0888391	−	0.996046i	$-0.528316\pi$
$463$	−3.82318			−0.177678			−0.0888391	+	0.996046i	$0.528316\pi$
$464$	−0.550300	+	0.568128i	−0.0255470	+	0.0263747i
$465$	−2.85107	−	4.32981i	−0.132215	−	0.200790i
$466$	15.3245	−	13.5476i	0.709894	−	0.627582i
$467$	−4.61267	+	2.66313i	−0.213449	+	0.123235i	−0.602913	−	0.797807i	$-0.705993\pi$
$467$	−4.61267	+	2.66313i	−0.213449	+	0.123235i	0.389464	+	0.921042i	$0.372660\pi$
$468$	−0.0455145	+	8.26439i	−0.00210391	+	0.382022i
$469$	−5.80735	+	17.7042i	−0.268159	+	0.817502i
$470$	11.9896	+	4.01670i	0.553037	+	0.185276i
$471$	−14.1815	+	0.833575i	−0.653449	+	0.0384091i
$472$	38.8525	−	3.01336i	1.78833	−	0.138701i
$473$	4.14382	+	2.39244i	0.190533	+	0.110004i
$474$	3.42962	−	12.6600i	0.157528	−	0.581491i
$475$	2.60093			0.119339
$476$	18.0933	−	1.51806i	0.829305	−	0.0695803i
$477$	−6.02892	−	8.08022i	−0.276045	−	0.369968i
$478$	−0.628857	−	3.09693i	−0.0287632	−	0.141650i
$479$	11.0967	−	19.2200i	0.507019	−	0.878183i	−0.492948	−	0.870059i	$-0.664081\pi$
$479$	11.0967	−	19.2200i	0.507019	−	0.878183i	0.999967	−	0.00812429i	$-0.00258607\pi$
$480$	8.41995	−	5.01043i	0.384316	−	0.228694i
$481$	−3.75507	+	2.16799i	−0.171217	+	0.0988519i
$482$	27.6681	+	9.26926i	1.26025	+	0.422203i
$483$	3.11691	−	11.7998i	0.141824	−	0.536908i
$484$	13.2271	+	9.98303i	0.601231	+	0.453774i
$485$	0.418572	+	0.724987i	0.0190064	+	0.0329200i
$486$	0.654810	−	22.0357i	0.0297028	−	0.999559i
$487$	13.8845	−	24.0487i	0.629168	−	1.08975i	−0.358551	−	0.933510i	$-0.616729\pi$
$487$	13.8845	−	24.0487i	0.629168	−	1.08975i	0.987719	−	0.156240i	$-0.0499374\pi$
$488$	−15.6631	−	7.49277i	−0.709036	−	0.339182i
$489$	16.6067	+	8.32911i	0.750981	+	0.376655i
$490$	−4.15910	+	8.98342i	−0.187889	+	0.405830i
$491$	22.7085			1.02482			0.512410	−	0.858741i	$-0.328753\pi$
$491$	22.7085			1.02482			0.512410	+	0.858741i	$0.328753\pi$
$492$	−28.5144	−	19.0020i	−1.28553	−	0.856675i
$493$	0.339250	−	0.587599i	0.0152791	−	0.0264641i
$494$	3.35574	+	3.79587i	0.150982	+	0.170784i
$495$	4.54034	+	1.95277i	0.204073	+	0.0877703i
$496$	−11.5136	+	3.28261i	−0.516975	+	0.147393i
$497$	0.543261	−	0.113883i	0.0243686	−	0.00510834i
$498$	−24.2677	+	24.1344i	−1.08746	+	1.08149i
$499$	37.0682	−	21.4013i	1.65940	−	0.958056i	0.686410	−	0.727215i	$-0.259186\pi$
$499$	37.0682	−	21.4013i	1.65940	−	0.958056i	0.972992	−	0.230841i	$-0.0741476\pi$
$500$	−0.780068	−	1.84160i	−0.0348857	−	0.0823589i
$501$	5.05529	+	7.67726i	0.225854	+	0.342995i
$502$	0.664397	+	3.27195i	0.0296535	+	0.146034i
$503$	−40.5042			−1.80599			−0.902996	−	0.429650i	$-0.858637\pi$
$503$	−40.5042			−1.80599			−0.902996	+	0.429650i	$0.858637\pi$
$504$	20.6650	−	8.77266i	0.920490	−	0.390766i
$505$	15.2251			0.677508
$506$	−1.23479	−	6.08099i	−0.0548933	−	0.270333i
$507$	−10.5759	−	16.0612i	−0.469692	−	0.713302i
$508$	−16.6646	+	7.05882i	−0.739373	+	0.313185i
$509$	22.3633	−	12.9115i	0.991238	−	0.572292i	0.0855938	−	0.996330i	$-0.472721\pi$
$509$	22.3633	−	12.9115i	0.991238	−	0.572292i	0.905644	+	0.424039i	$0.139388\pi$
$510$	−5.95958	+	5.92684i	−0.263894	+	0.262445i
$511$	−13.9095	+	42.4040i	−0.615318	+	1.87584i
$512$	−5.20727	−	22.0201i	−0.230131	−	0.973160i
$513$	−8.70374	−	10.3390i	−0.384279	−	0.456480i
$514$	16.5486	+	18.7191i	0.729927	+	0.825662i
$515$	1.85048	−	3.20513i	0.0815420	−	0.141235i
$516$	−5.57925	+	8.37223i	−0.245613	+	0.368567i
$517$	14.7302			0.647835
$518$	9.44579	+	7.03614i	0.415024	+	0.309150i
$519$	−10.0800	−	5.05563i	−0.442463	−	0.221917i
$520$	1.68123	−	3.51450i	0.0737270	−	0.154121i
$521$	−14.0250	+	24.2921i	−0.614448	+	1.06426i	0.376033	+	0.926606i	$0.377288\pi$
$521$	−14.0250	+	24.2921i	−0.614448	+	1.06426i	−0.990481	+	0.137649i	$0.956045\pi$
$522$	0.171469	−	0.821217i	0.00750501	−	0.0359437i
$523$	4.17316	+	7.22812i	0.182479	+	0.316064i	0.942724	−	0.333573i	$-0.108254\pi$
$523$	4.17316	+	7.22812i	0.182479	+	0.316064i	−0.760245	+	0.649637i	$0.774921\pi$
$524$	0.821857	−	1.08893i	0.0359030	−	0.0475699i
$525$	−1.20176	−	4.42219i	−0.0524489	−	0.193000i
$526$	17.2584	+	5.78186i	0.752504	+	0.252101i
$527$	8.89434	−	5.13515i	0.387443	−	0.223691i
$528$	7.44659	−	8.65049i	0.324071	−	0.376464i
$529$	−7.95357	+	13.7760i	−0.345808	+	0.598956i
$530$	0.945732	+	4.65745i	0.0410800	+	0.202307i
$531$	−33.1278	+	24.7178i	−1.43763	+	1.07266i
$532$	5.86080	−	12.4526i	0.254098	−	0.539887i
$533$	−13.6250			−0.590165
$534$	−1.06201	+	3.92027i	−0.0459578	+	0.169647i
$535$	−1.63677	−	0.944991i	−0.0707638	−	0.0408555i
$536$	−19.8591	+	1.54026i	−0.857783	+	0.0665289i
$537$	19.1087	−	1.12319i	0.824599	−	0.0484691i
$538$	27.2393	+	9.12560i	1.17437	+	0.393433i
$539$	−1.26976	+	11.4623i	−0.0546922	+	0.493717i
$540$	−4.71019	+	9.26359i	−0.202694	+	0.398642i
$541$	1.09988	−	0.635014i	0.0472874	−	0.0273014i	−0.476170	−	0.879353i	$-0.657975\pi$
$541$	1.09988	−	0.635014i	0.0472874	−	0.0273014i	0.523457	+	0.852052i	$0.324642\pi$
$542$	19.4073	−	17.1570i	0.833615	−	0.736958i
$543$	21.6519	+	32.8819i	0.929173	+	1.41110i
$544$	8.93017	+	17.2343i	0.382878	+	0.738913i
$545$	−13.4576			−0.576460
$546$	4.90336	−	7.45943i	0.209844	−	0.319234i
$547$			45.2183i			1.93339i	0.255924	+	0.966697i	$0.417620\pi$
$547$			45.2183i			1.93339i	−0.255924	+	0.966697i	$0.582380\pi$
$548$	−29.8603	−	3.68934i	−1.27557	−	0.157601i
$549$	18.2895	−	2.15753i	0.780575	−	0.0920810i
$550$	−1.54318	−	1.74558i	−0.0658014	−	0.0744317i
$551$	−0.257150	−	0.445397i	−0.0109550	−	0.0189746i
$552$	12.9265	−	1.77044i	0.550188	−	0.0753551i
$553$	−10.5548	+	9.45016i	−0.448837	+	0.401862i
$554$	−4.02397	−	1.34809i	−0.170962	−	0.0572751i
$555$	−5.44294	+	0.319930i	−0.231040	+	0.0135803i
$556$	5.17950	−	2.19394i	0.219660	−	0.0930439i
$557$	9.38926	−	16.2627i	0.397836	−	0.689072i	−0.595623	−	0.803264i	$-0.703095\pi$
$557$	9.38926	−	16.2627i	0.397836	−	0.689072i	0.993459	+	0.114192i	$0.0364281\pi$
$558$	8.46304	−	9.46744i	0.358269	−	0.400789i
$559$			4.00049i			0.169203i
$560$	−10.5749	−	0.415005i	−0.446870	−	0.0175372i
$561$	−4.38971	+	8.75227i	−0.185334	+	0.369521i
$562$	8.32088	+	40.9778i	0.350995	+	1.72855i
$563$	12.6159	+	7.28380i	0.531697	+	0.306975i	0.741707	−	0.670724i	$-0.234016\pi$
$563$	12.6159	+	7.28380i	0.531697	+	0.306975i	−0.210010	+	0.977699i	$0.567350\pi$
$564$	−1.98765	+	30.9087i	−0.0836953	+	1.30149i
$565$	−10.0303	−	17.3731i	−0.421979	−	0.730890i
$566$	−8.59407	+	25.6527i	−0.361236	+	1.07826i
$567$	−13.5572	+	19.5755i	−0.569351	+	0.822095i
$568$	0.335546	+	0.489413i	0.0140792	+	0.0205353i
$569$	31.0916	−	17.9508i	1.30343	−	0.752535i	0.322439	−	0.946590i	$-0.395497\pi$
$569$	31.0916	−	17.9508i	1.30343	−	0.752535i	0.980991	+	0.194055i	$0.0621640\pi$
$570$	1.63197	+	6.15838i	0.0683558	+	0.257946i
$571$	−1.12979	−	0.652286i	−0.0472804	−	0.0272973i	0.476174	−	0.879351i	$-0.342023\pi$
$571$	−1.12979	−	0.652286i	−0.0472804	−	0.0272973i	−0.523454	+	0.852054i	$0.675357\pi$
$572$	0.556523	−	4.50432i	0.0232694	−	0.188335i
$573$	26.3206	+	13.2011i	1.09956	+	0.551485i
$574$	14.6501	+	33.9884i	0.611485	+	1.41865i
$575$		−	2.66324i		−	0.111065i
$576$	17.1467	+	16.7926i	0.714445	+	0.699692i
$577$	1.79607	+	1.03696i	0.0747714	+	0.0431693i	0.536920	−	0.843633i	$-0.319588\pi$
$577$	1.79607	+	1.03696i	0.0747714	+	0.0431693i	−0.462148	+	0.886803i	$0.652921\pi$
$578$	4.89511	+	5.53714i	0.203610	+	0.230315i
$579$	−17.2782	+	1.01560i	−0.718058	+	0.0422068i
$580$	−0.238241	+	0.315660i	−0.00989244	+	0.0131071i
$581$	36.1814	−	7.58464i	1.50106	−	0.314664i
$582$	−1.45396	+	1.44598i	−0.0602686	+	0.0599376i
$583$	2.76821	+	4.79468i	0.114648	+	0.198576i
$584$	−47.5655	+	3.68914i	−1.96827	+	0.152658i
$585$	0.484108	+	4.10380i	0.0200154	+	0.169671i
$586$	2.25311	+	11.0959i	0.0930751	+	0.458367i
$587$			30.9360i			1.27687i	0.769677	+	0.638434i	$0.220417\pi$
$587$			30.9360i			1.27687i	−0.769677	+	0.638434i	$0.779583\pi$
$588$	−23.8803	−	4.21104i	−0.984806	−	0.173660i
$589$		−	7.78484i		−	0.320769i
$590$	19.0949	−	3.87738i	0.786125	−	0.159629i
$591$	−19.4906	−	29.5996i	−0.801736	−	1.21756i
$592$	−3.06469	+	12.2130i	−0.125958	+	0.501950i
$593$	7.77983	+	13.4751i	0.319479	+	0.553355i	0.980379	−	0.197119i	$-0.0631586\pi$
$593$	7.77983	+	13.4751i	0.319479	+	0.553355i	−0.660900	+	0.750474i	$0.729825\pi$
$594$	−1.77481	+	11.9757i	−0.0728215	+	0.491370i
$595$	8.88531	−	1.86261i	0.364262	−	0.0763596i
$596$	23.1421	+	17.4663i	0.947938	+	0.715448i
$597$	−2.01391	−	34.2623i	−0.0824237	−	1.40226i
$598$	3.88681	−	3.43614i	0.158943	−	0.140514i
$599$	−27.4909	−	15.8719i	−1.12325	−	0.648508i	−0.181020	−	0.983479i	$-0.557940\pi$
$599$	−27.4909	−	15.8719i	−1.12325	−	0.648508i	−0.942228	+	0.334972i	$0.891273\pi$
$600$	3.87101	−	3.00254i	0.158033	−	0.122578i
$601$			25.8424i			1.05413i	0.849824	+	0.527067i	$0.176708\pi$
$601$			25.8424i			1.05413i	−0.849824	+	0.527067i	$0.823292\pi$
$602$	9.97947	−	4.30149i	0.406733	−	0.175316i
$603$	16.9330	−	12.6343i	0.689565	−	0.514508i
$604$	4.93937	−	39.9777i	0.200980	−	1.62667i
$605$	7.17569	+	4.14289i	0.291733	+	0.168432i
$606$	9.55310	+	36.0494i	0.388068	+	1.46441i
$607$	−25.1523	+	14.5217i	−1.02090	+	0.589418i	−0.914365	−	0.404891i	$-0.867310\pi$
$607$	−25.1523	+	14.5217i	−1.02090	+	0.589418i	−0.106537	+	0.994309i	$0.533976\pi$
$608$	14.6978	+	0.669598i	0.596076	+	0.0271558i
$609$	−0.638464	+	0.643011i	−0.0258719	+	0.0260561i
$610$	−8.23184	−	2.75780i	−0.333298	−	0.111660i
$611$	6.15776	+	10.6656i	0.249116	+	0.431482i
$612$	−17.7727	−	10.3920i	−0.718420	−	0.420072i
$613$	35.9432	+	20.7518i	1.45173	+	0.838158i	0.998580	−	0.0532757i	$-0.0169662\pi$
$613$	35.9432	+	20.7518i	1.45173	+	0.838158i	0.453152	+	0.891433i	$0.350300\pi$
$614$	3.50284	−	0.711280i	0.141363	−	0.0287049i
$615$	−15.3146	−	7.68106i	−0.617546	−	0.309730i
$616$	−11.8347	+	3.45494i	−0.476833	+	0.139204i
$617$		−	2.91483i		−	0.117347i	−0.998277	−	0.0586733i	$-0.981313\pi$
$617$		−	2.91483i		−	0.117347i	0.998277	−	0.0586733i	$-0.0186870\pi$
$618$	8.75009	+	2.37042i	0.351980	+	0.0953524i
$619$	5.02146	−	8.69742i	0.201829	−	0.349579i	−0.747289	−	0.664500i	$-0.768645\pi$
$619$	5.02146	−	8.69742i	0.201829	−	0.349579i	0.949118	+	0.314921i	$0.101978\pi$
$620$	−5.51209	+	2.33482i	−0.221371	+	0.0937686i
$621$	−10.5867	+	8.91225i	−0.424831	+	0.357636i
$622$	10.8824	−	32.4831i	0.436343	−	1.30245i
$623$	3.26840	−	2.92633i	0.130946	−	0.117241i
$624$	9.37641	+	1.77556i	0.375357	+	0.0710794i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.31337	−	7.34944i	0.332269	−	0.293743i
$627$	4.08168	+	6.19869i	0.163007	+	0.247552i
$628$	−2.01143	+	16.2799i	−0.0802647	+	0.649637i
$629$		−	10.8015i		−	0.430684i
$630$	9.71665	−	5.62021i	0.387121	−	0.223914i
$631$	−16.4909			−0.656494			−0.328247	−	0.944592i	$-0.606458\pi$
$631$	−16.4909			−0.656494			−0.328247	+	0.944592i	$0.606458\pi$
$632$	−13.6626	−	6.53578i	−0.543468	−	0.259979i
$633$	−30.6595	+	20.1885i	−1.21860	+	0.802421i
$634$	9.19796	+	10.4043i	0.365298	+	0.413209i
$635$	−7.83665	+	4.52449i	−0.310988	+	0.179549i
$636$	−10.4343	+	5.16162i	−0.413748	+	0.204671i
$637$	−8.83020	+	3.87228i	−0.349865	+	0.153425i
$638$	−0.146350	+	0.436845i	−0.00579406	+	0.0172949i
$639$	−0.578181	−	0.248671i	−0.0228725	−	0.00983728i
$640$	−3.93405	−	10.6077i	−0.155507	−	0.419306i
$641$	11.2806	+	6.51286i	0.445557	+	0.257242i	0.705952	−	0.708260i	$-0.250519\pi$
$641$	11.2806	+	6.51286i	0.445557	+	0.257242i	−0.260395	+	0.965502i	$0.583853\pi$
$642$	1.21051	−	4.46843i	0.0477750	−	0.176355i
$643$	−22.4699			−0.886125			−0.443062	−	0.896491i	$-0.646108\pi$
$643$	−22.4699			−0.886125			−0.443062	+	0.896491i	$0.646108\pi$
$644$	−12.7509	−	6.00121i	−0.502456	−	0.236481i
$645$	−2.25527	+	4.49659i	−0.0888011	+	0.177053i
$646$	−12.3689	+	2.51161i	−0.486649	+	0.0988180i
$647$	−7.31878	+	12.6765i	−0.287731	+	0.498364i	−0.973268	−	0.229674i	$-0.926234\pi$
$647$	−7.31878	+	12.6765i	−0.287731	+	0.498364i	0.685537	+	0.728038i	$0.259567\pi$
$648$	−24.8894	−	5.34010i	−0.977749	−	0.209779i
$649$	19.6576	−	11.3493i	0.771627	−	0.445499i
$650$	0.618798	−	1.84707i	0.0242712	−	0.0724479i
$651$	−13.2360	+	3.59697i	−0.518762	+	0.140976i
$652$	12.9234	−	17.1229i	0.506119	−	0.670586i
$653$	−5.80499	−	10.0545i	−0.227167	−	0.393465i	0.729800	−	0.683660i	$-0.239613\pi$
$653$	−5.80499	−	10.0545i	−0.227167	−	0.393465i	−0.956967	+	0.290196i	$0.906280\pi$
$654$	−8.44407	−	31.8644i	−0.330189	−	1.24600i
$655$	0.341065	−	0.590742i	0.0133265	−	0.0230822i
$656$	−27.5285	+	28.4203i	−1.07481	+	1.10963i
$657$	40.5570	−	30.2609i	1.58228	−	1.18059i
$658$	19.9848	−	26.8289i	0.779089	−	1.04590i
$659$	−28.2389			−1.10003			−0.550015	−	0.835155i	$-0.685378\pi$
$659$	−28.2389			−1.10003			−0.550015	+	0.835155i	$0.685378\pi$
$660$	3.16483	−	4.74916i	0.123191	−	0.184861i
$661$	−1.24831	+	2.16213i	−0.0485535	+	0.0840971i	−0.889281	−	0.457362i	$-0.848794\pi$
$661$	−1.24831	+	2.16213i	−0.0485535	+	0.0840971i	0.840727	+	0.541459i	$0.182128\pi$
$662$	27.0857	−	23.9451i	1.05272	−	0.930654i
$663$	−8.17222	+	0.480355i	−0.317383	+	0.0186554i
$664$	22.3475	+	32.5951i	0.867252	+	1.26493i
$665$	2.14481	−	6.53863i	0.0831723	−	0.253557i
$666$	−4.17273	−	12.6868i	−0.161690	−	0.491605i
$667$	−0.456068	+	0.263311i	−0.0176590	+	0.0101954i
$668$	9.77358	−	4.13991i	0.378151	−	0.160178i
$669$	−19.8909	+	13.0977i	−0.769027	+	0.506385i
$670$	−9.76020	+	1.98189i	−0.377069	+	0.0765670i
$671$	−10.1135			−0.390429
$672$	−5.65264	−	25.2992i	−0.218055	−	0.975936i
$673$	−7.13852			−0.275170			−0.137585	−	0.990490i	$-0.543934\pi$
$673$	−7.13852			−0.275170			−0.137585	+	0.990490i	$0.543934\pi$
$674$	−11.5747	+	2.35035i	−0.445843	+	0.0905319i
$675$	−1.76937	+	4.88563i	−0.0681030	+	0.188048i
$676$	−20.4468	+	8.66087i	−0.786414	+	0.333111i
$677$	−27.4706	+	15.8601i	−1.05578	+	0.609554i	−0.924262	−	0.381759i	$-0.875318\pi$
$677$	−27.4706	+	15.8601i	−1.05578	+	0.609554i	−0.131517	+	0.991314i	$0.541985\pi$
$678$	34.8416	−	34.6503i	1.33809	−	1.33074i
$679$	2.16775	−	0.454422i	0.0831908	−	0.0174391i
$680$	5.48803	+	8.00460i	0.210456	+	0.306962i
$681$	−1.97240	−	33.5562i	−0.0755826	−	1.28588i
$682$	−5.22468	+	4.61889i	−0.200064	+	0.176866i
$683$	−8.35024	+	14.4630i	−0.319513	+	0.553413i	−0.980386	−	0.197085i	$-0.936853\pi$
$683$	−8.35024	+	14.4630i	−0.319513	+	0.553413i	0.660873	+	0.750497i	$0.270186\pi$
$684$	−13.5576	+	7.72824i	−0.518388	+	0.295497i
$685$	−15.0437			−0.574790
$686$	19.1542	+	17.8638i	0.731311	+	0.682044i
$687$	17.7068	−	35.3041i	0.675556	−	1.34693i
$688$	8.34460	+	8.08274i	0.318135	+	0.308152i
$689$	−2.31442	+	4.00870i	−0.0881725	+	0.152719i
$690$	6.30592	−	1.67107i	0.240062	−	0.0636165i
$691$	−1.70899	−	2.96006i	−0.0650131	−	0.112606i	0.831687	−	0.555245i	$-0.187376\pi$
$691$	−1.70899	−	2.96006i	−0.0650131	−	0.112606i	−0.896700	+	0.442639i	$0.854042\pi$
$692$	−7.84428	+	10.3933i	−0.298195	+	0.395095i
$693$	8.65329	−	9.80391i	0.328711	−	0.372420i
$694$	−1.06006	+	3.16421i	−0.0402394	+	0.120112i
$695$	2.43570	−	1.40625i	0.0923912	−	0.0533421i
$696$	−0.896893	−	0.366036i	−0.0339966	−	0.0138746i
$697$	16.9708	−	29.3943i	0.642815	−	1.11339i
$698$	−48.3099	+	9.80971i	−1.82856	+	0.371303i
$699$	22.3927	+	11.2311i	0.846969	+	0.424798i
$700$	−5.27298	+	0.442413i	−0.199300	+	0.0167216i
$701$	11.7874			0.445203			0.222601	−	0.974910i	$-0.428545\pi$
$701$	11.7874			0.445203			0.222601	+	0.974910i	$0.428545\pi$
$702$	−9.41307	+	3.72121i	−0.355274	+	0.140448i
$703$	−7.09057	−	4.09374i	−0.267426	−	0.154398i
$704$	−8.27110	−	10.2615i	−0.311729	−	0.386746i
$705$	0.908701	+	15.4596i	0.0342236	+	0.582242i
$706$	−3.06361	+	9.14464i	−0.115300	+	0.344163i
$707$	12.5551	−	38.2753i	0.472184	−	1.43949i
$708$	21.1619	+	42.7793i	0.795314	+	1.60775i
$709$	−29.0282	+	16.7594i	−1.09018	+	0.629414i	−0.933624	−	0.358256i	$-0.883372\pi$
$709$	−29.0282	+	16.7594i	−1.09018	+	0.629414i	−0.156553	+	0.987670i	$0.550038\pi$
$710$	0.196513	+	0.222287i	0.00737501	+	0.00834229i
$711$	15.9535	−	1.88196i	0.598302	−	0.0705791i
$712$	4.23074	+	2.02386i	0.158554	+	0.0758474i
$713$	−7.97134			−0.298529
$714$	9.98537	+	19.8696i	0.373693	+	0.743601i
$715$		−	2.26928i		−	0.0848664i
$716$	2.71027	−	21.9361i	0.101288	−	0.819789i
$717$	3.23250	−	2.12852i	0.120720	−	0.0794911i
$718$	−11.8475	+	10.4738i	−0.442145	+	0.390879i
$719$	−20.9182	−	36.2313i	−0.780116	−	1.35120i	−0.931874	−	0.362783i	$-0.881827\pi$
$719$	−20.9182	−	36.2313i	−0.780116	−	1.35120i	0.151758	−	0.988418i	$-0.451507\pi$
$720$	9.53820	+	7.28167i	0.355468	+	0.271372i
$721$	−6.53159	−	7.29509i	−0.243249	−	0.271683i
$722$	5.49658	−	16.4069i	0.204561	−	0.610601i
$723$	2.09699	+	35.6759i	0.0779880	+	1.32680i
$724$	41.8605	−	17.7313i	1.55573	−	0.658980i
$725$	−0.0988686	+	0.171245i	−0.00367189	+	0.00635990i
$726$	−5.30694	+	19.5898i	−0.196959	+	0.727046i
$727$		−	27.6114i		−	1.02405i	−0.858971	−	0.512025i	$-0.828896\pi$
$727$		−	27.6114i		−	1.02405i	0.858971	−	0.512025i	$-0.171104\pi$
$728$	−7.44891	−	7.12473i	−0.276075	−	0.264060i
$729$	25.3420	−	9.31576i	0.938592	−	0.345028i
$730$	−23.3771	+	4.74691i	−0.865225	+	0.175691i
$731$	−8.63058	−	4.98287i	−0.319214	−	0.184298i
$732$	1.36469	−	21.2214i	0.0504404	−	0.784367i
$733$	−4.69685	−	8.13519i	−0.173482	−	0.300480i	0.766153	−	0.642658i	$-0.222169\pi$
$733$	−4.69685	−	8.13519i	−0.173482	−	0.300480i	−0.939635	+	0.342179i	$0.888835\pi$
$734$	13.6194	+	4.56273i	0.502703	+	0.168414i
$735$	−12.1082	−	0.625524i	−0.446618	−	0.0230728i
$736$	0.685639	−	15.0500i	0.0252730	−	0.554749i
$737$	−10.0478	+	5.80110i	−0.370115	+	0.213686i
$738$	8.57765	−	41.0809i	0.315748	−	1.51221i
$739$	29.0910	+	16.7957i	1.07013	+	0.617841i	0.928217	−	0.372038i	$-0.121341\pi$
$739$	29.0910	+	16.7957i	1.07013	+	0.617841i	0.141914	+	0.989879i	$0.454674\pi$
$740$	−0.771997	+	6.24830i	−0.0283792	+	0.229692i
$741$	−2.78193	+	5.54665i	−0.102197	+	0.203761i
$742$	12.4885	+	1.46315i	0.458467	+	0.0537141i
$743$		−	25.1546i		−	0.922832i	−0.887184	−	0.461416i	$-0.847342\pi$
$743$		−	25.1546i		−	0.922832i	0.887184	−	0.461416i	$-0.152658\pi$
$744$	−8.98690	−	11.5863i	−0.329476	−	0.424775i
$745$	12.5546	+	7.24840i	0.459965	+	0.265561i
$746$	23.7196	−	20.9693i	0.868435	−	0.767741i
$747$	−38.5071	−	16.5616i	−1.40890	−	0.605957i
$748$	9.02434	+	6.81105i	0.329963	+	0.249037i
$749$	−3.72540	+	3.33550i	−0.136123	+	0.121877i
$750$	1.73681	−	1.72727i	0.0634195	−	0.0630712i
$751$	25.3743	+	43.9496i	0.925922	+	1.60374i	0.790071	+	0.613016i	$0.210044\pi$
$751$	25.3743	+	43.9496i	0.925922	+	1.60374i	0.135852	+	0.990729i	$0.456623\pi$
$752$	34.6886	+	8.70465i	1.26496	+	0.317426i
$753$	−3.41519	+	2.24882i	−0.124456	+	0.0819514i
$754$	−0.377481	+	0.0766507i	−0.0137471	+	0.00279145i
$755$		−	20.1408i		−	0.733000i
$756$	19.4041	+	19.4803i	0.705720	+	0.708491i
$757$			9.38564i			0.341127i	0.985347	+	0.170563i	$0.0545588\pi$
$757$			9.38564i			0.341127i	−0.985347	+	0.170563i	$0.945441\pi$
$758$	−4.03694	−	19.8807i	−0.146628	−	0.722100i
$759$	6.34719	−	4.17947i	0.230388	−	0.151705i
$760$	7.33452	−	0.568858i	0.266051	−	0.0206347i
$761$	−9.26978	−	16.0557i	−0.336029	−	0.582019i	0.647653	−	0.761936i	$-0.275751\pi$
$761$	−9.26978	−	16.0557i	−0.336029	−	0.582019i	−0.983682	+	0.179916i	$0.942417\pi$
$762$	−15.6301	−	15.7164i	−0.566218	−	0.569345i
$763$	−11.0976	+	33.8318i	−0.401760	+	1.22479i
$764$	20.4828	−	27.1388i	0.741042	−	0.981848i
$765$	−9.45645	−	4.06714i	−0.341899	−	0.147048i
$766$	−14.7099	−	16.6392i	−0.531491	−	0.601200i
$767$	16.4351	+	9.48883i	0.593438	+	0.342622i
$768$	22.6481	−	15.9708i	0.817242	−	0.576295i
$769$		−	43.3998i		−	1.56504i	−0.622628	−	0.782518i	$-0.713935\pi$
$769$		−	43.3998i		−	1.56504i	0.622628	−	0.782518i	$-0.286065\pi$
$770$	−5.66087	+	2.44003i	−0.204003	+	0.0879324i
$771$	−13.7189	+	27.3529i	−0.494073	+	0.985091i
$772$	−2.45065	+	19.8348i	−0.0882008	+	0.713869i
$773$	−19.8628	−	11.4678i	−0.714415	−	0.412468i	0.0982785	−	0.995159i	$-0.468666\pi$
$773$	−19.8628	−	11.4678i	−0.714415	−	0.412468i	−0.812694	+	0.582691i	$0.802000\pi$
$774$	−12.0619	−	2.51852i	−0.433558	−	0.0905263i
$775$	−2.59210	+	1.49655i	−0.0931109	+	0.0537576i
$776$	1.33892	+	1.95289i	0.0480644	+	0.0701045i
$777$	−3.68413	+	13.9471i	−0.132168	+	0.500351i
$778$	−9.72696	+	29.0343i	−0.348728	+	1.04093i
$779$	−12.8638	−	22.2808i	−0.460893	−	0.798291i
$780$	4.76169	+	0.306210i	0.170496	+	0.0109641i
$781$	0.299331	+	0.172819i	0.0107109	+	0.00618394i
$782$	2.57178	+	12.6652i	0.0919667	+	0.452908i
$783$	1.01158	−	0.180039i	0.0361508	−	0.00643407i
$784$	−9.76369	+	26.2425i	−0.348703	+	0.937233i
$785$			8.20182i			0.292736i
$786$	1.61274	+	0.436896i	0.0575246	+	0.0155836i
$787$	−17.1870	+	29.7687i	−0.612650	+	1.06114i	0.378142	+	0.925748i	$0.376563\pi$
$787$	−17.1870	+	29.7687i	−0.612650	+	1.06114i	−0.990792	+	0.135393i	$0.956770\pi$
$788$	−37.6819	+	15.9614i	−1.34236	+	0.568600i
$789$	1.30803	+	22.2534i	0.0465673	+	0.792243i
$790$	−7.18045	−	2.40557i	−0.255469	−	0.0855863i
$791$	−51.9464	+	10.8894i	−1.84700	+	0.387184i
$792$	13.2307	+	4.51368i	0.470131	+	0.160387i
$793$	−4.22782	−	7.32280i	−0.150134	−	0.260040i
$794$	−20.1398	−	22.7813i	−0.714736	−	0.808479i
$795$	−4.86133	+	3.20106i	−0.172414	+	0.113530i
$796$	−39.3320	−	4.85959i	−1.39408	−	0.172244i
$797$		−	26.8539i		−	0.951216i	−0.879657	−	0.475608i	$-0.842228\pi$
$797$		−	26.8539i		−	0.951216i	0.879657	−	0.475608i	$-0.157772\pi$
$798$	16.8277	+	0.975700i	0.595694	+	0.0345394i
$799$	−30.6795			−1.08536
$800$	−2.60254	−	5.02263i	−0.0920138	−	0.177577i
$801$	−4.94014	+	0.582767i	−0.174551	+	0.0205910i
$802$	20.4866	−	18.1112i	0.723408	−	0.639529i
$803$	−24.0659	+	13.8945i	−0.849269	+	0.490325i
$804$	−10.8167	−	21.8663i	−0.381477	−	0.771164i
$805$	−6.69527	−	2.19620i	−0.235977	−	0.0774058i
$806$	−5.52845	−	1.85212i	−0.194731	−	0.0652382i
$807$	2.06449	+	35.1229i	0.0726735	+	1.23639i
$808$	42.9342	−	3.32993i	1.51042	−	0.117147i
$809$	−12.4937	−	7.21326i	−0.439256	−	0.253605i	0.264026	−	0.964516i	$-0.414950\pi$
$809$	−12.4937	−	7.21326i	−0.439256	−	0.253605i	−0.703282	+	0.710911i	$0.748283\pi$
$810$	−12.6782	−	1.12392i	−0.445467	−	0.0394905i
$811$	−1.12930			−0.0396551			−0.0198276	−	0.999803i	$-0.506312\pi$
$811$	−1.12930			−0.0396551			−0.0198276	+	0.999803i	$0.506312\pi$
$812$	0.597093	+	0.859232i	0.0209538	+	0.0301531i
$813$	28.3586	+	14.2233i	0.994579	+	0.498832i
$814$	1.45951	+	7.18762i	0.0511556	+	0.251926i
$815$	5.36312	−	9.28920i	0.187862	−	0.325386i
$816$	−15.5095	+	18.0169i	−0.542940	+	0.630717i
$817$	−6.54194	+	3.77699i	−0.228874	+	0.132140i
$818$	15.3220	+	5.13311i	0.535720	+	0.179475i
$819$	10.7160	+	2.16711i	0.374447	+	0.0757248i
$820$	−11.9179	+	15.7907i	−0.416191	+	0.551435i
$821$	−1.10924	−	1.92127i	−0.0387128	−	0.0670526i	0.846020	−	0.533151i	$-0.178992\pi$
$821$	−1.10924	−	1.92127i	−0.0387128	−	0.0670526i	−0.884733	+	0.466099i	$0.845659\pi$
$822$	−9.43928	−	35.6199i	−0.329233	−	1.24239i
$823$	9.77481	−	16.9305i	0.340728	−	0.590159i	−0.643840	−	0.765160i	$-0.722660\pi$
$823$	9.77481	−	16.9305i	0.340728	−	0.590159i	0.984568	+	0.175001i	$0.0559930\pi$
$824$	4.51728	−	9.44306i	0.157367	−	0.328965i
$825$	1.27930	−	2.55070i	0.0445396	−	0.0888038i
$826$	5.99874	−	51.2012i	0.208723	−	1.78152i
$827$	41.4110			1.44000			0.720000	−	0.693974i	$-0.244142\pi$
$827$	41.4110			1.44000			0.720000	+	0.693974i	$0.244142\pi$
$828$	7.91339	+	13.8824i	0.275009	+	0.482447i
$829$	−11.1590	+	19.3279i	−0.387567	+	0.671286i	−0.992122	−	0.125278i	$-0.960018\pi$
$829$	−11.1590	+	19.3279i	−0.387567	+	0.671286i	0.604555	+	0.796564i	$0.293351\pi$
$830$	13.0878	+	14.8044i	0.454286	+	0.513869i
$831$	−0.304980	−	5.18859i	−0.0105797	−	0.179990i
$832$	3.97234	−	10.2785i	0.137716	−	0.356341i
$833$	2.64460	−	23.8733i	0.0916298	−	0.827159i
$834$	4.85796	+	4.88479i	0.168217	+	0.169146i
$835$	4.59609	−	2.65356i	0.159054	−	0.0918301i
$836$	7.89127	−	3.34260i	0.272925	−	0.115606i
$837$	14.6232	+	5.29589i	0.505450	+	0.183053i
$838$	0.750243	+	3.69472i	0.0259167	+	0.127632i
$839$	−55.2304			−1.90676			−0.953382	−	0.301765i	$-0.902424\pi$
$839$	−55.2304			−1.90676			−0.953382	+	0.301765i	$0.902424\pi$
$840$	−4.35609	−	12.2076i	−0.150300	−	0.421201i
$841$	−28.9609			−0.998652
$842$	−7.04080	−	34.6738i	−0.242642	−	1.19494i
$843$	−42.7717	+	28.1641i	−1.47313	+	0.970023i
$844$	16.5329	+	39.0312i	0.569086	+	1.34351i
$845$	−9.61523	+	5.55136i	−0.330774	+	0.190973i
$846$	−36.0345	+	11.8518i	−1.23889	+	0.407474i
$847$	16.3324	−	14.6230i	0.561186	−	0.502453i
$848$	3.68557	+	12.9270i	0.126563	+	0.443914i
$849$	−33.0771	+	1.94424i	−1.13520	+	0.0667262i
$850$	3.21407	+	3.63562i	0.110242	+	0.124701i
$851$	−4.19181	+	7.26043i	−0.143694	+	0.248884i
$852$	−0.403020	+	0.604772i	−0.0138072	+	0.0207192i
$853$	−37.1831			−1.27312			−0.636562	−	0.771226i	$-0.719644\pi$
$853$	−37.1831			−1.27312			−0.636562	+	0.771226i	$0.719644\pi$
$854$	−13.7212	+	18.4203i	−0.469531	+	0.630331i
$855$	−6.25382	+	4.66618i	−0.213876	+	0.159580i
$856$	−4.82231	−	2.30685i	−0.164823	−	0.0788465i
$857$	−12.0282	+	20.8335i	−0.410877	+	0.711659i	−0.994986	−	0.100016i	$-0.968111\pi$
$857$	−12.0282	+	20.8335i	−0.410877	+	0.711659i	0.584109	+	0.811675i	$0.301444\pi$
$858$	5.37313	−	1.42388i	0.183436	−	0.0486104i
$859$	16.8953	+	29.2636i	0.576461	+	0.998460i	0.995881	+	0.0906678i	$0.0289001\pi$
$859$	16.8953	+	29.2636i	0.576461	+	0.998460i	−0.419420	+	0.907792i	$0.637767\pi$
$860$	4.63637	+	3.49926i	0.158099	+	0.119324i
$861$	−31.9388	+	32.1663i	−1.08847	+	1.09622i
$862$	21.4163	+	7.17481i	0.729442	+	0.244375i
$863$	1.17157	−	0.676409i	0.0398808	−	0.0230252i	−0.479927	−	0.877308i	$-0.659337\pi$
$863$	1.17157	−	0.676409i	0.0398808	−	0.0230252i	0.519808	+	0.854283i	$0.326004\pi$
$864$	−11.2565	+	27.1531i	−0.382953	+	0.923768i
$865$	−3.25532	+	5.63839i	−0.110684	+	0.191711i
$866$	−5.81467	−	28.6355i	−0.197590	−	0.973074i
$867$	−4.05807	+	8.09105i	−0.137819	+	0.274787i
$868$	1.32418	+	15.7825i	0.0449457	+	0.535694i
$869$	−8.82182			−0.299260
$870$	−0.467504	−	0.126648i	−0.0158499	−	0.00429377i
$871$	−8.40068	−	4.85013i	−0.284646	−	0.164340i
$872$	−37.9499	+	2.94336i	−1.28515	+	0.0996747i
$873$	−2.30710	−	0.992264i	−0.0780834	−	0.0335830i
$874$	9.28872	+	3.11187i	0.314196	+	0.105261i
$875$	−2.58947	+	0.542825i	−0.0875400	+	0.0183508i
$876$	−25.9077	−	52.3729i	−0.875339	−	1.76952i
$877$	−27.4895	+	15.8711i	−0.928255	+	0.535928i	−0.886259	−	0.463189i	$-0.846705\pi$
$877$	−27.4895	+	15.8711i	−0.928255	+	0.535928i	−0.0419959	+	0.999118i	$0.513372\pi$
$878$	38.4414	−	33.9841i	1.29733	−	1.14691i
$879$	−11.5816	+	7.62621i	−0.390638	+	0.257226i
$880$	−4.73348	−	4.58494i	−0.159566	−	0.154558i
$881$	29.3158			0.987676			0.493838	−	0.869554i	$-0.335594\pi$
$881$	29.3158			0.987676			0.493838	+	0.869554i	$0.335594\pi$
$882$	−6.11629	−	29.0618i	−0.205946	−	0.978563i
$883$		−	52.2974i		−	1.75995i	−0.475023	−	0.879974i	$-0.657560\pi$
$883$		−	52.2974i		−	1.75995i	0.475023	−	0.879974i	$-0.342440\pi$
$884$	−1.15910	+	9.38142i	−0.0389849	+	0.315531i
$885$	13.1239	+	19.9308i	0.441156	+	0.669966i
$886$	10.5571	+	11.9418i	0.354674	+	0.401192i
$887$	−10.8095	−	18.7226i	−0.362947	−	0.628642i	0.625498	−	0.780226i	$-0.284896\pi$
$887$	−10.8095	−	18.7226i	−0.362947	−	0.628642i	−0.988444	+	0.151584i	$0.951563\pi$
$888$	−15.2789	+	2.09263i	−0.512726	+	0.0702242i
$889$	4.91202	+	23.4320i	0.164744	+	0.785885i
$890$	2.22349	+	0.744906i	0.0745316	+	0.0249693i
$891$	−14.4204	+	3.45024i	−0.483102	+	0.115587i
$892$	10.7260	+	25.3222i	0.359134	+	0.847851i
$893$	−11.6275	+	20.1394i	−0.389099	+	0.673939i
$894$	−9.28502	+	34.2744i	−0.310537	+	1.14631i
$895$		−	11.0514i		−	0.369408i
$896$	−29.9114	+	1.14257i	−0.999271	+	0.0381705i
$897$	5.67953	+	2.84857i	0.189634	+	0.0951111i
$898$	−0.207203	−	1.02041i	−0.00691444	−	0.0340515i
$899$	0.512554	+	0.295923i	0.0170946	+	0.00986959i
$900$	5.17955	+	3.02857i	0.172652	+	0.100952i
$901$	−5.76552	−	9.98618i	−0.192077	−	0.332688i
$902$	−7.32109	+	21.8529i	−0.243766	+	0.727623i
$903$	9.44447	+	9.37769i	0.314292	+	0.312070i
$904$	−32.0848	−	46.7975i	−1.06713	−	1.55646i
$905$	19.6852	−	11.3652i	0.654358	−	0.377794i
$906$	47.6887	−	12.6375i	1.58435	−	0.419853i
$907$	24.1500	+	13.9430i	0.801889	+	0.462971i	0.844131	−	0.536137i	$-0.180117\pi$
$907$	24.1500	+	13.9430i	0.801889	+	0.462971i	−0.0422424	+	0.999107i	$0.513450\pi$
$908$	−38.5213	−	4.75943i	−1.27838	−	0.157947i
$909$	−36.6081	+	27.3145i	−1.21421	+	0.905965i
$910$	−4.13317	−	3.07878i	−0.137013	−	0.102061i
$911$			42.9016i			1.42139i	0.703499	+	0.710697i	$0.251620\pi$
$911$			42.9016i			1.42139i	−0.703499	+	0.710697i	$0.748380\pi$
$912$	5.94901	+	17.0095i	0.196992	+	0.563239i
$913$	19.9355	+	11.5098i	0.659770	+	0.380918i
$914$	8.69014	+	9.82991i	0.287444	+	0.325144i
$915$	−0.623899	−	10.6143i	−0.0206255	−	0.350899i
$916$	−36.4015	−	27.4737i	−1.20274	−	0.907758i
$917$	−1.20385	−	1.34457i	−0.0397545	−	0.0444016i
$918$	3.69651	−	24.9426i	0.122003	−	0.823228i
$919$	−20.7984	−	36.0240i	−0.686077	−	1.18832i	−0.973097	−	0.230396i	$-0.925998\pi$
$919$	−20.7984	−	36.0240i	−0.686077	−	1.18832i	0.287020	−	0.957925i	$-0.407335\pi$
$920$	−0.582486	−	7.51023i	−0.0192040	−	0.247605i
$921$	2.40750	+	3.65618i	0.0793299	+	0.120475i
$922$	−8.47557	−	41.7396i	−0.279128	−	1.37462i
$923$			0.288978i			0.00951182i
$924$	−9.32935	−	11.8726i	−0.306913	−	0.390579i
$925$			3.14790i			0.103502i
$926$	−5.29865	+	1.07593i	−0.174125	+	0.0353574i
$927$	1.30074	+	11.0264i	0.0427219	+	0.362156i
$928$	−0.602792	+	0.942253i	−0.0197876	+	0.0309310i
$929$	23.7400	+	41.1188i	0.778883	+	1.34907i	0.932586	+	0.360948i	$0.117547\pi$
$929$	23.7400	+	41.1188i	0.778883	+	1.34907i	−0.153702	+	0.988117i	$0.549120\pi$
$930$	−5.16990	−	5.19845i	−0.169528	−	0.170464i
$931$	−14.6691	−	10.7839i	−0.480762	−	0.353429i
$932$	17.4261	−	23.0888i	0.570809	−	0.756297i
$933$	41.8844	−	2.46193i	1.37123	−	0.0805999i
$934$	−5.64337	+	4.98902i	−0.184657	+	0.163246i
$935$	4.89571	+	2.82654i	0.160107	+	0.0924377i
$936$	2.26272	+	11.4667i	0.0739593	+	0.374800i
$937$		−	56.9775i		−	1.86137i	−0.365815	−	0.930687i	$-0.619210\pi$
$937$		−	56.9775i		−	1.86137i	0.365815	−	0.930687i	$-0.380790\pi$
$938$	−3.06620	+	26.1710i	−0.100115	+	0.854515i
$939$	12.1478	+	6.09272i	0.396427	+	0.198828i
$940$	17.7471	+	2.19271i	0.578846	+	0.0715183i
$941$	−16.4078	−	9.47305i	−0.534879	−	0.308812i	0.208122	−	0.978103i	$-0.433265\pi$
$941$	−16.4078	−	9.47305i	−0.534879	−	0.308812i	−0.743001	+	0.669290i	$0.766598\pi$
$942$	−19.4200	+	5.14629i	−0.632737	+	0.167675i
$943$	−22.8145	+	13.1720i	−0.742943	+	0.428939i
$944$	52.9988	−	15.1103i	1.72496	−	0.491800i
$945$	10.8232	+	8.47696i	0.352078	+	0.275756i
$946$	6.41633	+	2.14958i	0.208613	+	0.0698887i
$947$	−2.81753	−	4.88010i	−0.0915573	−	0.158582i	0.816609	−	0.577191i	$-0.195851\pi$
$947$	−2.81753	−	4.88010i	−0.0915573	−	0.158582i	−0.908167	+	0.418609i	$0.862518\pi$
$948$	1.19039	−	18.5110i	0.0386620	−	0.601209i
$949$	−20.1208	−	11.6168i	−0.653150	−	0.377097i
$950$	3.60471	−	0.731965i	0.116952	−	0.0237481i
$951$	−7.62516	+	15.2032i	−0.247263	+	0.492996i
$952$	24.6488	−	7.19582i	0.798873	−	0.233218i
$953$			0.326501i			0.0105764i	0.999986	+	0.00528821i	$0.00168330\pi$
$953$			0.326501i			0.0105764i	−0.999986	+	0.00528821i	$0.998317\pi$
$954$	−10.6296	−	9.50194i	−0.344147	−	0.307637i
$955$	8.50022	−	14.7228i	0.275061	−	0.476419i
$956$	−1.74310	−	4.11515i	−0.0563760	−	0.133094i
$957$	−0.563278	+	0.0331089i	−0.0182082	+	0.00107026i
$958$	9.97022	−	29.7604i	0.322123	−	0.961515i
$959$	−12.4055	+	37.8192i	−0.400596	+	1.22125i
$960$	10.2594	−	9.31368i	0.331121	−	0.300598i
$961$	−11.0207	−	19.0884i	−0.355506	−	0.615754i
$962$	−4.59414	+	4.06145i	−0.148121	+	0.130946i
$963$	5.63090	−	0.664252i	0.181453	−	0.0214052i
$964$	40.9546	+	5.06007i	1.31906	+	0.162974i
$965$			9.99280i			0.321680i
$966$	0.999075	−	17.2308i	0.0321447	−	0.554393i
$967$	−6.95986			−0.223814			−0.111907	−	0.993719i	$-0.535696\pi$
$967$	−6.95986			−0.223814			−0.111907	+	0.993719i	$0.535696\pi$
$968$	21.1413	+	10.1134i	0.679506	+	0.325055i
$969$	−8.50117	−	12.9104i	−0.273097	−	0.414741i
$970$	0.784140	+	0.886985i	0.0251772	+	0.0284794i
$971$	−33.1705	+	19.1510i	−1.06449	+	0.614585i	−0.926672	−	0.375872i	$-0.877343\pi$
$971$	−33.1705	+	19.1510i	−1.06449	+	0.614585i	−0.137821	+	0.990457i	$0.544010\pi$
$972$	−5.29385	−	30.7242i	−0.169800	−	0.985478i
$973$	−1.52670	−	7.28288i	−0.0489436	−	0.233478i
$974$	12.4751	−	37.2372i	0.399727	−	1.19316i
$975$	2.38165	−	0.139991i	0.0762738	−	0.00448330i
$976$	−23.8166	−	5.97647i	−0.762351	−	0.191302i
$977$	−46.5776	−	26.8916i	−1.49015	−	0.860339i	−0.490214	−	0.871602i	$-0.663081\pi$
$977$	−46.5776	−	26.8916i	−1.49015	−	0.860339i	−0.999937	+	0.0112636i	$0.996415\pi$
$978$	25.3597	+	6.87002i	0.810915	+	0.219679i
$979$	2.73175			0.0873073
$980$	−3.23606	+	13.6209i	−0.103372	+	0.435102i
$981$	32.3582	−	24.1435i	1.03312	−	0.770844i
$982$	31.4724	−	6.39072i	1.00432	−	0.203936i
$983$	3.63683	−	6.29918i	0.115997	−	0.200913i	−0.802181	−	0.597081i	$-0.796327\pi$
$983$	3.63683	−	6.29918i	0.115997	−	0.200913i	0.918178	+	0.396168i	$0.129660\pi$
$984$	−44.8666	−	18.3108i	−1.43029	−	0.583726i
$985$	−17.7202	+	10.2307i	−0.564611	+	0.325979i
$986$	0.304813	−	0.909844i	0.00970721	−	0.0289753i
$987$	39.6141	+	10.4641i	1.26093	+	0.333075i
$988$	5.71907	+	4.31642i	0.181948	+	0.137324i
$989$	3.86748	+	6.69867i	0.122979	+	0.213005i
$990$	6.84215	+	1.42863i	0.217458	+	0.0454049i
$991$	−3.83543	+	6.64316i	−0.121837	+	0.211027i	−0.920492	−	0.390762i	$-0.872212\pi$
$991$	−3.83543	+	6.64316i	−0.121837	+	0.211027i	0.798655	+	0.601789i	$0.205545\pi$
$992$	−15.0332	+	7.78966i	−0.477305	+	0.247322i
$993$	39.5785	+	19.8506i	1.25599	+	0.629941i
$994$	0.720872	−	0.310720i	0.0228647	−	0.00985545i
$995$	−19.8155			−0.628194
$996$	−26.8413	+	40.2780i	−0.850498	+	1.27626i
$997$	−20.2837	+	35.1324i	−0.642391	+	1.11265i	0.342506	+	0.939516i	$0.388724\pi$
$997$	−20.2837	+	35.1324i	−0.642391	+	1.11265i	−0.984897	+	0.173139i	$0.944609\pi$
$998$	45.3511	−	40.0926i	1.43556	−	1.26911i
$999$	12.5133	−	10.5341i	0.395904	−	0.333285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.101.121	yes	256
3.2	odd	2	inner	840.2.cf.a.101.8	✓	256
7.5	odd	6	inner	840.2.cf.a.341.37	yes	256
8.5	even	2	inner	840.2.cf.a.101.92	yes	256
21.5	even	6	inner	840.2.cf.a.341.92	yes	256
24.5	odd	2	inner	840.2.cf.a.101.37	yes	256
56.5	odd	6	inner	840.2.cf.a.341.8	yes	256
168.5	even	6	inner	840.2.cf.a.341.121	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.8	✓	256	3.2	odd	2	inner
840.2.cf.a.101.37	yes	256	24.5	odd	2	inner
840.2.cf.a.101.92	yes	256	8.5	even	2	inner
840.2.cf.a.101.121	yes	256	1.1	even	1	trivial
840.2.cf.a.341.8	yes	256	56.5	odd	6	inner
840.2.cf.a.341.37	yes	256	7.5	odd	6	inner
840.2.cf.a.341.92	yes	256	21.5	even	6	inner
840.2.cf.a.341.121	yes	256	168.5	even	6	inner

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38593 - 0.281424i) q^{2} +(0.952550 + 1.44660i) q^{3} +(1.84160 - 0.780068i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.72727 + 1.73681i) q^{6} +(-0.542825 - 2.58947i) q^{7} +(2.33280 - 1.59939i) q^{8} +(-1.18530 + 2.75592i) q^{9} +(1.05954 - 0.936685i) q^{10} +(0.823745 - 1.42677i) q^{11} +(2.88266 + 1.92100i) q^{12} +1.37742 q^{13} +(-1.48106 - 3.43605i) q^{14} +(1.54823 + 0.776517i) q^{15} +(2.78299 - 2.87315i) q^{16} +(-1.71566 + 2.97162i) q^{17} +(-0.867158 + 4.15308i) q^{18} +(1.30047 + 2.25247i) q^{19} +(1.20484 - 1.59636i) q^{20} +(3.22885 - 3.25185i) q^{21} +(0.740125 - 2.20922i) q^{22} +(2.30643 - 1.33162i) q^{23} +(4.53578 + 1.85113i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.90901 - 0.387639i) q^{26} +(-5.11576 + 0.910496i) q^{27} +(-3.01963 - 4.34532i) q^{28} -0.197737 q^{29} +(2.36427 + 0.640487i) q^{30} +(-2.59210 - 1.49655i) q^{31} +(3.04845 - 4.76518i) q^{32} +(2.84862 - 0.167439i) q^{33} +(-1.54150 + 4.60128i) q^{34} +(-1.76483 - 1.97113i) q^{35} +(-0.0330433 + 5.99991i) q^{36} +(-2.72617 + 1.57395i) q^{37} +(2.43625 + 2.75578i) q^{38} +(1.31206 + 1.99257i) q^{39} +(1.22057 - 2.55151i) q^{40} -9.89169 q^{41} +(3.55981 - 5.41551i) q^{42} +2.90434i q^{43} +(0.404033 - 3.27011i) q^{44} +(0.351460 + 2.97934i) q^{45} +(2.82181 - 2.49462i) q^{46} +(4.47051 + 7.74314i) q^{47} +(6.80723 + 1.28905i) q^{48} +(-6.41068 + 2.81126i) q^{49} +(0.449244 - 1.34096i) q^{50} +(-5.93299 + 0.348735i) q^{51} +(2.53666 - 1.07448i) q^{52} +(-1.68026 + 2.91030i) q^{53} +(-6.83385 + 2.70158i) q^{54} -1.64749i q^{55} +(-5.40787 - 5.17252i) q^{56} +(-2.01967 + 4.02684i) q^{57} +(-0.274050 + 0.0556480i) q^{58} +(11.9318 + 6.88885i) q^{59} +(3.45696 + 0.222307i) q^{60} +(-3.06938 - 5.31632i) q^{61} +(-4.01363 - 1.34463i) q^{62} +(7.77976 + 1.57331i) q^{63} +(2.88390 - 7.46211i) q^{64} +(1.19288 - 0.688710i) q^{65} +(3.90086 - 1.03373i) q^{66} +(-6.09885 - 3.52117i) q^{67} +(-0.841504 + 6.81087i) q^{68} +(4.12331 + 2.06805i) q^{69} +(-3.00066 - 2.23518i) q^{70} +0.209796i q^{71} +(1.64272 + 8.32475i) q^{72} +(-14.6076 - 8.43373i) q^{73} +(-3.33532 + 2.94860i) q^{74} +(1.72907 - 0.101633i) q^{75} +(4.15202 + 3.13370i) q^{76} +(-4.14172 - 1.35857i) q^{77} +(2.37918 + 2.39232i) q^{78} +(-2.67735 - 4.63731i) q^{79} +(0.973564 - 3.87971i) q^{80} +(-6.19014 - 6.53316i) q^{81} +(-13.7092 + 2.78376i) q^{82} +13.9725i q^{83} +(3.40960 - 8.50733i) q^{84} +3.43133i q^{85} +(0.817351 + 4.02521i) q^{86} +(-0.188355 - 0.286046i) q^{87} +(-0.360328 - 4.64585i) q^{88} +(0.829066 + 1.43598i) q^{89} +(1.32556 + 4.03025i) q^{90} +(-0.747698 - 3.56678i) q^{91} +(3.20878 - 4.25149i) q^{92} +(-0.304197 - 5.17526i) q^{93} +(8.37492 + 9.47334i) q^{94} +(2.25247 + 1.30047i) q^{95} +(9.79711 - 0.129186i) q^{96} +0.837143i q^{97} +(-8.09360 + 5.70032i) q^{98} +(2.95567 + 3.96132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

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