LMFDB - Embedded newform 840.2.cf.a.101.8

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			101.8
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.8

$q$-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} +(-1.72907 - 0.101633i) q^{3} +(1.84160 - 0.780068i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.42497 - 0.345745i) q^{6} +(-0.542825 - 2.58947i) q^{7} +(-2.33280 + 1.59939i) q^{8} +(2.97934 + 0.351460i) q^{9} +(1.05954 - 0.936685i) q^{10} +(-0.823745 + 1.42677i) q^{11} +(-3.26353 + 1.16162i) 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} +(-4.22807 + 0.351360i) q^{18} +(1.30047 + 2.25247i) q^{19} +(-1.20484 + 1.59636i) q^{20} +(0.675406 + 4.53253i) q^{21} +(0.740125 - 2.20922i) q^{22} +(-2.30643 + 1.33162i) q^{23} +(4.19611 - 2.52836i) 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} +(-1.92721 + 1.51191i) q^{30} +(-2.59210 - 1.49655i) q^{31} +(-3.04845 + 4.76518i) q^{32} +(1.56932 - 2.38326i) q^{33} +(-1.54150 + 4.60128i) q^{34} +(1.76483 + 1.97113i) q^{35} +(5.76092 - 1.67684i) q^{36} +(-2.72617 + 1.57395i) q^{37} +(-2.43625 - 2.75578i) q^{38} +(-2.38165 - 0.139991i) q^{39} +(1.22057 - 2.55151i) q^{40} +9.89169 q^{41} +(-2.21163 - 6.09169i) q^{42} +2.90434i q^{43} +(-0.404033 + 3.27011i) q^{44} +(-2.75592 + 1.18530i) q^{45} +(2.82181 - 2.49462i) q^{46} +(-4.47051 - 7.74314i) q^{47} +(-5.10398 + 4.68502i) q^{48} +(-6.41068 + 2.81126i) q^{49} +(-0.449244 + 1.34096i) q^{50} +(-3.26851 + 4.96375i) q^{51} +(2.53666 - 1.07448i) q^{52} +(1.68026 - 2.91030i) q^{53} +(7.34632 - 0.177815i) 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} +(2.24549 - 2.63776i) q^{60} +(-3.06938 - 5.31632i) q^{61} +(4.01363 + 1.34463i) q^{62} +(-0.707168 - 7.90569i) q^{63} +(2.88390 - 7.46211i) q^{64} +(-1.19288 + 0.688710i) q^{65} +(-1.50426 + 3.74467i) 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} +(-7.51233 + 3.94525i) q^{72} +(-14.6076 - 8.43373i) q^{73} +(3.33532 - 2.94860i) q^{74} +(-0.952550 + 1.44660i) q^{75} +(4.15202 + 3.13370i) q^{76} +(4.14172 + 1.35857i) q^{77} +(3.34020 - 0.476236i) q^{78} +(-2.67735 - 4.63731i) q^{79} +(-0.973564 + 3.87971i) q^{80} +(8.75295 + 2.09424i) q^{81} +(-13.7092 + 2.78376i) q^{82} -13.9725i q^{83} +(4.77951 + 7.82025i) q^{84} +3.43133i q^{85} +(-0.817351 - 4.02521i) q^{86} +(-0.341901 - 0.0200966i) q^{87} +(-0.360328 - 4.64585i) q^{88} +(-0.829066 - 1.43598i) q^{89} +(3.48593 - 2.41832i) q^{90} +(-0.747698 - 3.56678i) q^{91} +(-3.20878 + 4.25149i) q^{92} +(4.32981 + 2.85107i) q^{93} +(8.37492 + 9.47334i) q^{94} +(-2.25247 - 1.30047i) q^{95} +(5.75527 - 7.92949i) 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
$3$	−1.72907	−	0.101633i	−0.998277	−	0.0586777i
$3$	−1.72907	−	0.101633i	−0.998277	−	0.0586777i
$4$	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
$6$	2.42497	−	0.345745i	0.989988	−	0.141150i
$7$	−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
$9$	2.97934	+	0.351460i	0.993114	+	0.117153i
$10$	1.05954	−	0.936685i	0.335055	−	0.296206i
$11$	−0.823745	+	1.42677i	−0.248368	+	0.430187i	−0.963073	−	0.269239i	$-0.913228\pi$
$11$	−0.823745	+	1.42677i	−0.248368	+	0.430187i	0.714705	+	0.699426i	$0.246561\pi$
$12$	−3.26353	+	1.16162i	−0.942100	+	0.335332i
$13$	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	−0.579435	−	0.815019i	$-0.696727\pi$
$17$	1.71566	−	2.97162i	0.416110	−	0.720723i	0.995544	+	0.0942958i	$0.0300600\pi$
$18$	−4.22807	+	0.351360i	−0.996565	+	0.0828164i
$19$	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
$21$	0.675406	+	4.53253i	0.147386	+	0.989079i
$22$	0.740125	−	2.20922i	0.157795	−	0.471008i
$23$	−2.30643	+	1.33162i	−0.480925	+	0.277662i	−0.720802	−	0.693141i	$-0.756226\pi$
$23$	−2.30643	+	1.33162i	−0.480925	+	0.277662i	0.239877	+	0.970803i	$0.422893\pi$
$24$	4.19611	−	2.52836i	0.856528	−	0.516100i
$25$	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	$-0.494156\pi$
$29$	0.197737			0.0367189			0.0183594	+	0.999831i	$0.494156\pi$
$30$	−1.92721	+	1.51191i	−0.351859	+	0.276035i
$31$	−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
$33$	1.56932	−	2.38326i	0.273183	−	0.414872i
$34$	−1.54150	+	4.60128i	−0.264366	+	0.789113i
$35$	1.76483	+	1.97113i	0.298311	+	0.333182i
$36$	5.76092	−	1.67684i	0.960153	−	0.279473i
$37$	−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
$39$	−2.38165	−	0.139991i	−0.381369	−	0.0224165i
$40$	1.22057	−	2.55151i	0.192989	−	0.403429i
$41$	9.89169			1.54482			0.772411	−	0.635123i	$-0.219050\pi$
$41$	9.89169			1.54482			0.772411	+	0.635123i	$0.219050\pi$
$42$	−2.21163	−	6.09169i	−0.341262	−	0.939968i
$43$			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
$45$	−2.75592	+	1.18530i	−0.410828	+	0.176694i
$46$	2.82181	−	2.49462i	0.416052	−	0.367811i
$47$	−4.47051	−	7.74314i	−0.652090	−	1.12945i	−0.982615	−	0.185656i	$-0.940559\pi$
$47$	−4.47051	−	7.74314i	−0.652090	−	1.12945i	0.330524	−	0.943797i	$-0.392774\pi$
$48$	−5.10398	+	4.68502i	−0.736696	+	0.676225i
$49$	−6.41068	+	2.81126i	−0.915812	+	0.401608i
$50$	−0.449244	+	1.34096i	−0.0635327	+	0.189641i
$51$	−3.26851	+	4.96375i	−0.457683	+	0.695065i
$52$	2.53666	−	1.07448i	0.351771	−	0.149004i
$53$	1.68026	−	2.91030i	0.230802	−	0.399760i	−0.727243	−	0.686380i	$-0.759199\pi$
$53$	1.68026	−	2.91030i	0.230802	−	0.399760i	0.958044	+	0.286620i	$0.0925318\pi$
$54$	7.34632	−	0.177815i	0.999707	−	0.0241975i
$55$		−	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	$-0.979182\pi$
$59$	−11.9318	−	6.88885i	−1.55339	−	0.896851i	−0.555530	−	0.831497i	$-0.687485\pi$
$60$	2.24549	−	2.63776i	0.289891	−	0.340533i
$61$	−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
$63$	−0.707168	−	7.90569i	−0.0890948	−	0.996023i
$64$	2.88390	−	7.46211i	0.360488	−	0.932764i
$65$	−1.19288	+	0.688710i	−0.147959	+	0.0854239i
$66$	−1.50426	+	3.74467i	−0.185161	+	0.460937i
$67$	−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	$-0.996037\pi$
$71$		−	0.209796i		−	0.0248983i	0.999923	−	0.0124491i	$-0.00396278\pi$
$72$	−7.51233	+	3.94525i	−0.885336	+	0.464952i
$73$	−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
$75$	−0.952550	+	1.44660i	−0.109991	+	0.167039i
$76$	4.15202	+	3.13370i	0.476269	+	0.359460i
$77$	4.14172	+	1.35857i	0.471993	+	0.154824i
$78$	3.34020	−	0.476236i	0.378203	−	0.0539231i
$79$	−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
$81$	8.75295	+	2.09424i	0.972550	+	0.232693i
$82$	−13.7092	+	2.78376i	−1.51393	+	0.307415i
$83$		−	13.9725i		−	1.53368i	−0.641837	−	0.766841i	$-0.721827\pi$
$83$		−	13.9725i		−	1.53368i	0.641837	−	0.766841i	$-0.278173\pi$
$84$	4.77951	+	7.82025i	0.521487	+	0.853259i
$85$			3.43133i			0.372180i
$86$	−0.817351	−	4.02521i	−0.0881373	−	0.434050i
$87$	−0.341901	−	0.0200966i	−0.0366556	−	0.00215458i
$88$	−0.360328	−	4.64585i	−0.0384111	−	0.495250i
$89$	−0.829066	−	1.43598i	−0.0878808	−	0.152214i	0.818734	−	0.574172i	$-0.194676\pi$
$89$	−0.829066	−	1.43598i	−0.0878808	−	0.152214i	−0.906615	+	0.421959i	$0.861343\pi$
$90$	3.48593	−	2.41832i	0.367450	−	0.254913i
$91$	−0.747698	−	3.56678i	−0.0783801	−	0.373900i
$92$	−3.20878	+	4.25149i	−0.334538	+	0.443248i
$93$	4.32981	+	2.85107i	0.448981	+	0.295643i
$94$	8.37492	+	9.47334i	0.863807	+	0.977101i
$95$	−2.25247	−	1.30047i	−0.231099	−	0.133425i
$96$	5.75527	−	7.92949i	0.587395	−	0.809300i
$97$			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	−0.329564	−	0.944133i	$-0.606902\pi$
$101$	−13.1853	−	7.61255i	−1.31199	−	0.757477i	−0.982425	+	0.186656i	$0.940235\pi$
$102$	3.13300	−	7.79925i	0.310214	−	0.772241i
$103$	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
$105$	−2.85118	−	3.58758i	−0.278247	−	0.350112i
$106$	−1.50969	+	4.50633i	−0.146635	+	0.437694i
$107$	0.944991	+	1.63677i	0.0913557	+	0.158233i	0.908082	−	0.418793i	$-0.137547\pi$
$107$	0.944991	+	1.63677i	0.0913557	+	0.158233i	−0.816726	+	0.577026i	$0.804213\pi$
$108$	−10.1314	+	2.31387i	−0.974898	+	0.222652i
$109$	−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	$0.392560\pi$
$113$			20.0607i			1.88715i	−0.331160	+	0.943575i	$0.607440\pi$
$114$	3.93237	+	5.01254i	0.368300	+	0.469467i
$115$	1.33162	−	2.30643i	0.124174	−	0.215076i
$116$	0.364153	−	0.154248i	0.0338108	−	0.0143216i
$117$	4.10380	+	0.484108i	0.379397	+	0.0447558i
$118$	18.4754	+	6.18955i	1.70080	+	0.569794i
$119$	−8.62621	−	2.82959i	−0.790763	−	0.259388i
$120$	−2.36976	+	4.28768i	−0.216329	+	0.391410i
$121$	4.14289	+	7.17569i	0.376626	+	0.652336i
$122$	5.75008	+	6.50425i	0.520588	+	0.588867i
$123$	−17.1034	−	1.00532i	−1.54216	−	0.0906467i
$124$	−5.94102	−	0.734032i	−0.533519	−	0.0659180i
$125$			1.00000i			0.0894427i
$126$	3.20494	+	10.7577i	0.285518	+	0.958373i
$127$	−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
$129$	0.295176	−	5.02180i	0.0259888	−	0.442145i
$130$	1.45943	−	1.29021i	0.128000	−	0.113159i
$131$	−0.590742	+	0.341065i	−0.0516134	+	0.0297990i	−0.525585	−	0.850741i	$-0.676153\pi$
$131$	−0.590742	+	0.341065i	−0.0516134	+	0.0297990i	0.473971	+	0.880540i	$0.342820\pi$
$132$	1.03095	−	5.61318i	0.0897328	−	0.488565i
$133$	5.12678	−	4.59021i	0.444548	−	0.398022i
$134$	9.44352	+	3.16373i	0.815796	+	0.273305i
$135$	4.88563	−	1.76937i	0.420488	−	0.152283i
$136$	0.750477	+	9.67620i	0.0643529	+	0.829727i
$137$	13.0282	+	7.52185i	1.11308	+	0.642635i	0.939624	−	0.342207i	$-0.111175\pi$
$137$	13.0282	+	7.52185i	1.11308	+	0.642635i	0.173452	+	0.984842i	$0.444508\pi$
$138$	−5.13262	+	4.02657i	−0.436918	+	0.342765i
$139$	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
$144$	9.30127	−	7.58198i	0.775106	−	0.631832i
$145$	−0.171245	+	0.0988686i	−0.0142212	+	0.00821059i
$146$	22.6186	+	7.57760i	1.87193	+	0.627127i
$147$	11.3702	−	4.20931i	0.937799	−	0.347178i
$148$	−3.79272	+	5.02519i	−0.311760	+	0.413068i
$149$	−7.24840	−	12.5546i	−0.593812	−	1.02851i	−0.993713	−	0.111955i	$-0.964289\pi$
$149$	−7.24840	−	12.5546i	−0.593812	−	1.02851i	0.399901	−	0.916558i	$-0.369044\pi$
$150$	0.913059	−	2.27295i	0.0745509	−	0.185586i
$151$	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
$156$	−4.49525	+	1.60004i	−0.359908	+	0.128106i
$157$	−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
$159$	−3.20106	+	4.86133i	−0.253861	+	0.385528i
$160$	0.257445	−	5.65099i	0.0203528	−	0.446750i
$161$	4.70018	+	5.24960i	0.370426	+	0.413726i
$162$	−12.7203	−	0.439174i	−0.999405	−	0.0345047i
$163$	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
$165$	−0.167439	+	2.84862i	−0.0130351	+	0.221765i
$166$	3.93220	+	19.3649i	0.305198	+	1.50301i
$167$	−5.30711			−0.410677			−0.205338	−	0.978691i	$-0.565829\pi$
$167$	−5.30711			−0.410677			−0.205338	+	0.978691i	$0.565829\pi$
$168$	−8.82487	−	9.49324i	−0.680854	−	0.732420i
$169$	−11.1027			−0.854055
$170$	−0.965658	−	4.75558i	−0.0740626	−	0.364736i
$171$	3.08288	+	7.16794i	0.235753	+	0.548146i
$172$	2.26558	+	5.34863i	0.172749	+	0.407830i
$173$	5.63839	−	3.25532i	0.428679	−	0.247498i	−0.270105	−	0.962831i	$-0.587058\pi$
$173$	5.63839	−	3.25532i	0.428679	−	0.247498i	0.698784	+	0.715333i	$0.253725\pi$
$174$	0.479506	−	0.0683667i	0.0363513	−	0.00518286i
$175$	−2.51396	−	0.824633i	−0.190037	−	0.0623364i
$176$	1.80684	+	6.33742i	0.136196	+	0.477701i
$177$	19.9308	+	13.1239i	1.49809	+	0.986456i
$178$	1.55315	+	1.75685i	0.116413	+	0.131682i
$179$	−5.52571	+	9.57082i	−0.413011	+	0.715356i	−0.995217	−	0.0976847i	$-0.968856\pi$
$179$	−5.52571	+	9.57082i	−0.413011	+	0.715356i	0.582206	+	0.813041i	$0.302190\pi$
$180$	−4.15068	+	4.33265i	−0.309374	+	0.322936i
$181$	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
$186$	−6.80317	−	2.73287i	−0.498833	−	0.200384i
$187$	2.82654	+	4.89571i	0.206697	+	0.358010i
$188$	−14.2731	−	10.7725i	−1.04097	−	0.785664i
$189$	0.419263	+	13.7413i	0.0304969	+	0.999535i
$190$	3.48775	+	1.16845i	0.253028	+	0.0847685i
$191$	−14.7228	+	8.50022i	−1.06531	+	0.615055i	−0.926895	−	0.375320i	$-0.877533\pi$
$191$	−14.7228	+	8.50022i	−1.06531	+	0.615055i	−0.138411	+	0.990375i	$0.544199\pi$
$192$	−5.74485	+	12.6094i	−0.414599	+	0.910004i
$193$	−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	$-0.240027\pi$
$197$	20.4615			1.45782			0.728910	+	0.684609i	$0.240027\pi$
$198$	2.98154	−	6.32190i	0.211889	−	0.449278i
$199$	−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
$201$	10.1875	+	6.70819i	0.718567	+	0.473159i
$202$	20.4163	+	6.83979i	1.43649	+	0.481246i
$203$	−0.107337	−	0.512034i	−0.00753356	−	0.0359377i
$204$	−2.14722	+	11.6909i	−0.150336	+	0.818528i
$205$	−8.56646	+	4.94585i	−0.598307	+	0.345433i
$206$	−3.92131	+	3.46664i	−0.273211	+	0.241532i
$207$	−7.33967	+	3.15673i	−0.510142	+	0.219408i
$208$	3.83334	−	3.95753i	0.265794	−	0.274405i
$209$	−4.28501			−0.296400
$210$	4.96117	+	4.16974i	0.342353	+	0.287740i
$211$			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
$213$	−0.0213222	+	0.362752i	−0.00146097	+	0.0248554i
$214$	−1.77032	−	2.00251i	−0.121016	−	0.136889i
$215$	−1.45217	−	2.51523i	−0.0990372	−	0.171537i
$216$	13.3903	−	6.05809i	0.911093	−	0.412201i
$217$	−2.46821	+	7.52452i	−0.167553	+	0.510798i
$218$	18.0461	+	6.04575i	1.22224	+	0.409470i
$219$	24.4004	+	16.0671i	1.64883	+	1.08571i
$220$	−1.28515	−	3.03402i	−0.0866451	−	0.204553i
$221$	2.36319	−	4.09316i	0.158965	−	0.275336i
$222$	−6.06667	+	4.75934i	−0.407168	+	0.319426i
$223$			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	0.940254	−	0.340472i	$-0.110587\pi$
$227$	16.8071	+	9.70356i	1.11552	+	0.644048i	0.175269	+	0.984521i	$0.443920\pi$
$228$	−6.86063	−	5.84036i	−0.454356	−	0.386787i
$229$	−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
$231$	−7.02323	−	2.77000i	−0.462095	−	0.182253i
$232$	−0.461281	+	0.316259i	−0.0302846	+	0.0207634i
$233$	−12.5257	+	7.23169i	−0.820583	+	0.473764i	−0.850618	−	0.525785i	$-0.823772\pi$
$233$	−12.5257	+	7.23169i	−0.820583	+	0.473764i	0.0300343	+	0.999549i	$0.490438\pi$
$234$	−5.82382	+	0.483970i	−0.380715	+	0.0316381i
$235$	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	$0.0230245\pi$
$239$			2.23455i			0.144541i	−0.997385	+	0.0722706i	$0.976975\pi$
$240$	2.07766	−	6.60934i	0.134113	−	0.426631i
$241$	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
$243$	−14.9216	−	4.51066i	−0.957221	−	0.289359i
$244$	−9.79966	−	7.39622i	−0.627359	−	0.473494i
$245$	4.14618	−	5.63996i	0.264890	−	0.360324i
$246$	23.9870	−	3.42000i	1.52936	−	0.218052i
$247$	1.79129	+	3.10260i	0.113977	+	0.197414i
$248$	8.44041	−	0.654630i	0.535966	−	0.0415691i
$249$	−1.42007	+	24.1594i	−0.0899931	+	1.53104i
$250$	−0.281424	−	1.38593i	−0.0177988	−	0.0876539i
$251$		−	2.36084i		−	0.149015i	−0.997220	−	0.0745074i	$-0.976262\pi$
$251$		−	2.36084i		−	0.149015i	0.997220	−	0.0745074i	$-0.0237384\pi$
$252$	−7.46930	−	14.0075i	−0.470521	−	0.882389i
$253$		−	4.38766i		−	0.275850i
$254$	12.5412	−	2.54660i	0.786908	−	0.159788i
$255$	0.348735	−	5.93299i	0.0218387	−	0.371538i
$256$	−0.509962	−	15.9919i	−0.0318726	−	0.999492i
$257$	−8.83359	−	15.3002i	−0.551024	−	0.954402i	−0.998201	−	0.0599566i	$-0.980904\pi$
$257$	−8.83359	−	15.3002i	−0.551024	−	0.954402i	0.447177	−	0.894446i	$-0.352430\pi$
$258$	1.00416	+	7.04293i	0.0625164	+	0.438473i
$259$	5.55553	+	6.20493i	0.345204	+	0.385556i
$260$	−1.65957	+	2.19886i	−0.102922	+	0.136367i
$261$	0.589127	+	0.0694967i	0.0364660	+	0.00430174i
$262$	0.722743	−	0.638941i	0.0446512	−	0.0394739i
$263$	−11.1459	−	6.43510i	−0.687287	−	0.396805i	0.115308	−	0.993330i	$-0.463214\pi$
$263$	−11.1459	−	6.43510i	−0.687287	−	0.396805i	−0.802595	+	0.596525i	$0.796548\pi$
$264$	0.150860	+	8.06961i	0.00928478	+	0.496650i
$265$			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	−0.143702	−	0.989621i	$-0.545901\pi$
$269$	−17.5918	−	10.1566i	−1.07259	−	0.619260i	−0.928888	+	0.370361i	$0.879234\pi$
$270$	−6.27319	+	3.82715i	−0.381774	+	0.232913i
$271$	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
$273$	0.930317	+	6.24319i	0.0563054	+	0.377855i
$274$	−20.1730	−	6.75830i	−1.21870	−	0.408284i
$275$	0.823745	+	1.42677i	0.0496737	+	0.0860374i
$276$	5.98028	−	7.02499i	0.359970	−	0.422855i
$277$	−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	$-0.656257\pi$
$281$		−	29.5670i		−	1.76382i	0.471416	−	0.881911i	$-0.343743\pi$
$282$	−13.5180	−	17.2312i	−0.804984	−	1.02610i
$283$	−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
$285$	3.76250	+	2.47752i	0.222871	+	0.146755i
$286$	1.01946	−	3.04302i	0.0602821	−	0.179938i
$287$	−5.36946	−	25.6142i	−0.316949	−	1.51196i
$288$	−10.7571	+	13.1257i	−0.633871	+	0.773439i
$289$	2.61300	+	4.52584i	0.153706	+	0.266226i
$290$	0.209510	−	0.185217i	0.0123029	−	0.0108763i
$291$	0.0850812	−	1.44748i	0.00498755	−	0.0848525i
$292$	−33.4803	−	4.13660i	−1.95929	−	0.242076i
$293$		−	8.00610i		−	0.467721i	−0.972270	−	0.233861i	$-0.924864\pi$
$293$		−	8.00610i		−	0.467721i	0.972270	−	0.233861i	$-0.0751360\pi$
$294$	−14.5737	+	9.03366i	−0.849956	+	0.526854i
$295$	13.7777			0.802168
$296$	3.84223	−	8.03192i	0.223325	−	0.466846i
$297$	5.51315	−	6.54899i	0.319905	−	0.380011i
$298$	13.5789	+	15.3599i	0.786607	+	0.889776i
$299$	−3.17693	+	1.83420i	−0.183726	+	0.106075i
$300$	−0.625771	+	3.40711i	−0.0361289	+	0.196710i
$301$	7.52069	−	1.57655i	0.433486	−	0.0908708i
$302$	−9.04815	+	27.0081i	−0.520663	+	1.55414i
$303$	22.0246	+	14.5027i	1.26528	+	0.833157i
$304$	10.0909	+	2.53217i	0.578751	+	0.145230i
$305$	5.31632	+	3.06938i	0.304412	+	0.175752i
$306$	−6.20983	+	13.1670i	−0.354992	+	0.752708i
$307$	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	$0.407652\pi$
$311$	−12.1119	+	20.9784i	−0.686801	+	1.18957i	−0.972867	+	0.231364i	$0.925681\pi$
$312$	5.77981	−	3.48262i	0.327217	−	0.197164i
$313$	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
$315$	4.56527	+	6.49294i	0.257224	+	0.365836i
$316$	−8.54803	−	6.45155i	−0.480864	−	0.362928i
$317$	−4.90985	−	8.50411i	−0.275765	−	0.477638i	0.694563	−	0.719432i	$-0.255598\pi$
$317$	−4.90985	−	8.50411i	−0.275765	−	0.477638i	−0.970328	+	0.241794i	$0.922264\pi$
$318$	3.06835	−	7.63831i	0.172065	−	0.428335i
$319$	−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
$324$	17.7531	−	2.97115i	0.986283	−	0.165064i
$325$	0.688710	−	1.19288i	0.0382027	−	0.0661691i
$326$	−11.3649	+	10.0471i	−0.629442	+	0.556458i
$327$	19.4678	+	12.8190i	1.07657	+	0.708894i
$328$	−23.0753	+	15.8207i	−1.27412	+	0.873551i
$329$	−17.6239	+	15.7794i	−0.971638	+	0.869947i
$330$	−0.569612	−	3.99511i	−0.0313561	−	0.219923i
$331$	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
$333$	−8.67536	+	3.73120i	−0.475407	+	0.204469i
$334$	7.35528	−	1.49355i	0.402463	−	0.0817234i
$335$	7.04235			0.384765
$336$	14.9023	+	10.6734i	0.812986	+	0.582283i
$337$	−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
$339$	2.03882	−	34.6862i	0.110734	−	1.88390i
$340$	2.67667	+	6.31913i	0.145163	+	0.342703i
$341$	4.27046	−	2.46555i	0.231258	−	0.133517i
$342$	−6.28988	−	9.06667i	−0.340118	−	0.490269i
$343$	10.7595	+	15.0742i	0.580960	+	0.813932i
$344$	−4.64517	−	6.77524i	−0.250451	−	0.365296i
$345$	−2.53687	+	3.85264i	−0.136580	+	0.207419i
$346$	−6.89828	+	6.09843i	−0.370854	+	0.327854i
$347$	1.17983	−	2.04352i	0.0633364	−	0.109702i	−0.832618	−	0.553847i	$-0.813159\pi$
$347$	1.17983	−	2.04352i	0.0633364	−	0.109702i	0.895955	+	0.444145i	$0.146493\pi$
$348$	−0.645321	+	0.229696i	−0.0345929	+	0.0123130i
$349$	−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	−0.760904	−	0.648865i	$-0.775244\pi$
$353$	3.40973	−	5.90583i	0.181482	−	0.314336i	0.942385	+	0.334529i	$0.108577\pi$
$354$	−31.3161	−	12.5798i	−1.66443	−	0.668611i
$355$	0.104898	+	0.181689i	0.00556742	+	0.00964305i
$356$	−2.64697	−	1.99778i	−0.140289	−	0.105882i
$357$	14.6277	+	5.76925i	0.774180	+	0.305341i
$358$	4.96479	−	14.8195i	0.262397	−	0.783237i
$359$	9.68369	−	5.59088i	0.511086	−	0.295076i	−0.222194	−	0.975002i	$-0.571322\pi$
$359$	9.68369	−	5.59088i	0.511086	−	0.295076i	0.733280	+	0.679927i	$0.237989\pi$
$360$	4.53324	−	7.17285i	0.238923	−	0.378042i
$361$	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
$366$	−9.28123	−	11.8307i	−0.485138	−	0.618399i
$367$	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
$369$	29.4707	+	3.47653i	1.53418	+	0.180981i
$370$	−1.41418	+	4.22122i	−0.0735196	+	0.219451i
$371$	−8.44821	−	2.77120i	−0.438609	−	0.143873i
$372$	10.1978	+	1.87299i	0.528732	+	0.0971101i
$373$	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
$375$	0.101633	−	1.72907i	0.00524830	−	0.0892886i
$376$	22.8131	+	10.9131i	1.17650	+	0.562801i
$377$	0.272367			0.0140276
$378$	−4.44821	−	18.9265i	−0.228791	−	0.973475i
$379$		−	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
$381$	15.6463	+	0.919674i	0.801584	+	0.0471163i
$382$	18.0126	−	15.9241i	0.921606	−	0.814746i
$383$	7.85212	+	13.6003i	0.401225	+	0.694941i	0.993874	−	0.110519i	$-0.0352514\pi$
$383$	7.85212	+	13.6003i	0.401225	+	0.694941i	−0.592649	+	0.805460i	$0.701918\pi$
$384$	4.41337	−	19.0925i	0.225219	−	0.974308i
$385$	−4.26612	+	0.894299i	−0.217422	+	0.0455777i
$386$	4.48921	−	13.4000i	0.228495	−	0.682040i
$387$	−1.02076	+	8.65302i	−0.0518881	+	0.439858i
$388$	0.653029	+	1.54168i	0.0331525	+	0.0782671i
$389$	10.8259	−	18.7510i	0.548896	−	0.950715i	−0.449455	−	0.893303i	$-0.648382\pi$
$389$	10.8259	−	18.7510i	0.548896	−	0.950715i	0.998351	−	0.0574120i	$-0.0182849\pi$
$390$	−2.65458	+	2.08253i	−0.134420	+	0.105453i
$391$			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
$396$	−2.35307	+	9.60079i	−0.118246	+	0.482458i
$397$	−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
$399$	−9.33105	+	7.41573i	−0.467137	+	0.371251i
$400$	−1.09673	−	3.84671i	−0.0548363	−	0.192336i
$401$	−16.7450	+	9.66771i	−0.836204	+	0.482783i	−0.855972	−	0.517022i	$-0.827041\pi$
$401$	−16.7450	+	9.66771i	−0.836204	+	0.482783i	0.0197682	+	0.999805i	$0.493707\pi$
$402$	−16.0069	−	6.43008i	−0.798353	−	0.320703i
$403$	−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
$408$	−0.314205	−	16.8071i	−0.0155555	−	0.832074i
$409$	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
$411$	−21.7622	−	14.3299i	−1.07345	−	0.706841i
$412$	4.45907	−	5.90807i	0.219683	−	0.291070i
$413$	−11.3615	+	34.6365i	−0.559065	+	1.70435i
$414$	9.28388	−	6.44057i	0.456278	−	0.316537i
$415$	6.98626	+	12.1006i	0.342942	+	0.593993i
$416$	−4.19900	+	6.56365i	−0.205873	+	0.321810i
$417$	−4.86300	−	0.285842i	−0.238142	−	0.0139978i
$418$	5.93872	−	1.20590i	0.290472	−	0.0589827i
$419$		−	2.66588i		−	0.130237i	−0.997878	−	0.0651184i	$-0.979257\pi$
$419$		−	2.66588i		−	0.130237i	0.997878	−	0.0651184i	$-0.0207425\pi$
$420$	−8.04930	−	4.38278i	−0.392766	−	0.213858i
$421$		−	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
$423$	−10.5978	−	24.6407i	−0.515281	−	1.19807i
$424$	0.734991	+	9.47653i	0.0356943	+	0.460221i
$425$	−1.71566	−	2.97162i	−0.0832219	−	0.144145i
$426$	−0.0725361	−	0.508749i	−0.00351439	−	0.0246490i
$427$	−12.1003	+	10.8339i	−0.585575	+	0.524289i
$428$	3.01709	+	2.27712i	0.145836	+	0.110069i
$429$	2.16161	−	3.28274i	0.104363	−	0.158492i
$430$	2.72045	+	3.07726i	0.131192	+	0.148399i
$431$	−13.8312	−	7.98542i	−0.666223	−	0.384644i	0.128421	−	0.991720i	$-0.459009\pi$
$431$	−13.8312	−	7.98542i	−0.666223	−	0.384644i	−0.794644	+	0.607076i	$0.792343\pi$
$432$	−16.8531	+	12.1644i	−0.810844	+	0.585262i
$433$		−	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
$438$	−38.3390	−	15.4010i	−1.83191	−	0.735887i
$439$	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
$441$	−20.0877	+	6.12260i	−0.956555	+	0.291552i
$442$	−2.12330	+	6.33789i	−0.100995	+	0.301463i
$443$	−5.63538	−	9.76076i	−0.267745	−	0.463748i	0.700534	−	0.713619i	$-0.252945\pi$
$443$	−5.63538	−	9.76076i	−0.267745	−	0.463748i	−0.968279	+	0.249871i	$0.919612\pi$
$444$	7.06859	−	8.30342i	0.335460	−	0.394063i
$445$	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	$0.00553035\pi$
$449$			0.736265i			0.0347465i	−0.999849	+	0.0173732i	$0.994470\pi$
$450$	−1.80975	+	3.83729i	−0.0853123	+	0.180892i
$451$	−8.14823	+	14.1131i	−0.383685	+	0.664562i
$452$	15.6487	+	36.9437i	0.736052	+	1.73769i
$453$	−19.1851	+	29.1357i	−0.901397	+	1.36891i
$454$	−26.0242	−	8.71854i	−1.22138	−	0.409181i
$455$	2.43092	+	2.71508i	0.113963	+	0.127285i
$456$	11.1520	+	6.16358i	0.522239	+	0.288636i
$457$	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
$459$	−11.4826	+	13.6400i	−0.535960	+	0.636659i
$460$	0.653137	−	5.28629i	0.0304527	−	0.246474i
$461$			30.1167i			1.40267i	0.712829	+	0.701337i	$0.247413\pi$
$461$			30.1167i			1.40267i	−0.712829	+	0.701337i	$0.752587\pi$
$462$	10.5132	+	1.86252i	0.489121	+	0.0866522i
$463$	−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
$465$	−5.17526	−	0.304197i	−0.239997	−	0.0141068i
$466$	15.3245	−	13.5476i	0.709894	−	0.627582i
$467$	4.61267	−	2.66313i	0.213449	−	0.123235i	−0.389464	−	0.921042i	$-0.627340\pi$
$467$	4.61267	−	2.66313i	0.213449	−	0.123235i	0.602913	+	0.797807i	$0.294007\pi$
$468$	7.93520	−	2.30971i	0.366805	−	0.106767i
$469$	−5.80735	+	17.7042i	−0.268159	+	0.817502i
$470$	−11.9896	−	4.01670i	−0.553037	−	0.185276i
$471$	7.81265	−	11.8648i	0.359988	−	0.546699i
$472$	38.8525	−	3.01336i	1.78833	−	0.138701i
$473$	−4.14382	−	2.39244i	−0.190533	−	0.110004i
$474$	−8.09581	−	10.3196i	−0.371853	−	0.473996i
$475$	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	$0.335919\pi$
$479$	−11.0967	+	19.2200i	−0.507019	+	0.878183i	−0.999967	+	0.00812429i	$0.997414\pi$
$480$	−1.01947	+	9.74478i	−0.0465321	+	0.444786i
$481$	−3.75507	+	2.16799i	−0.171217	+	0.0988519i
$482$	−27.6681	−	9.26926i	−1.26025	−	0.422203i
$483$	−7.59339	−	9.55460i	−0.345511	−	0.434749i
$484$	13.2271	+	9.98303i	0.601231	+	0.453774i
$485$	−0.418572	−	0.724987i	−0.0190064	−	0.0329200i
$486$	21.9497	+	2.05216i	0.995658	+	0.0930881i
$487$	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	$-0.671247\pi$
$491$	−22.7085			−1.02482			−0.512410	+	0.858741i	$0.671247\pi$
$492$	−32.2818	+	11.4904i	−1.45538	+	0.518028i
$493$	0.339250	−	0.587599i	0.0152791	−	0.0264641i
$494$	−3.35574	−	3.79587i	−0.150982	−	0.170784i
$495$	0.579027	−	4.90843i	0.0260253	−	0.220618i
$496$	−11.5136	+	3.28261i	−0.516975	+	0.147393i
$497$	−0.543261	+	0.113883i	−0.0243686	+	0.00510834i
$498$	−4.83093	−	33.8829i	−0.216479	−	1.51833i
$499$	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
$501$	9.17635	+	0.539377i	0.409969	+	0.0240976i
$502$	0.664397	+	3.27195i	0.0296535	+	0.146034i
$503$	40.5042			1.80599			0.902996	−	0.429650i	$-0.141363\pi$
$503$	40.5042			1.80599			0.902996	+	0.429650i	$0.141363\pi$
$504$	14.2940	+	17.3113i	0.636704	+	0.771109i
$505$	15.2251			0.677508
$506$	1.23479	+	6.08099i	0.0548933	+	0.270333i
$507$	19.1973	+	1.12840i	0.852583	+	0.0501140i
$508$	−16.6646	+	7.05882i	−0.739373	+	0.313185i
$509$	−22.3633	+	12.9115i	−0.991238	+	0.572292i	−0.905644	−	0.424039i	$-0.860612\pi$
$509$	−22.3633	+	12.9115i	−0.991238	+	0.572292i	−0.0855938	+	0.996330i	$0.527279\pi$
$510$	1.18636	+	8.32085i	0.0525331	+	0.368453i
$511$	−13.9095	+	42.4040i	−0.615318	+	1.87584i
$512$	5.20727	+	22.0201i	0.230131	+	0.973160i
$513$	−4.60200	−	12.7072i	−0.203183	−	0.561035i
$514$	16.5486	+	18.7191i	0.729927	+	0.825662i
$515$	−1.85048	+	3.20513i	−0.0815420	+	0.141235i
$516$	−3.37375	−	9.47840i	−0.148521	−	0.417263i
$517$	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	$-0.622712\pi$
$521$	14.0250	−	24.2921i	0.614448	−	1.06426i	0.990481	−	0.137649i	$-0.0439546\pi$
$522$	−0.836046	+	0.0694770i	−0.0365927	+	0.00304092i
$523$	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
$525$	4.26299	+	1.68135i	0.186052	+	0.0733800i
$526$	17.2584	+	5.78186i	0.752504	+	0.252101i
$527$	−8.89434	+	5.13515i	−0.387443	+	0.223691i
$528$	−2.48006	−	11.1415i	−0.107931	−	0.484870i
$529$	−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
$534$	−2.50694	−	3.19557i	−0.108486	−	0.138286i
$535$	−1.63677	−	0.944991i	−0.0707638	−	0.0408555i
$536$	19.8591	−	1.54026i	0.857783	−	0.0665289i
$537$	10.5270	−	15.9870i	0.454275	−	0.689889i
$538$	27.2393	+	9.12560i	1.17437	+	0.393433i
$539$	1.26976	−	11.4623i	0.0546922	−	0.493717i
$540$	7.61715	−	7.06959i	0.327790	−	0.304227i
$541$	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
$543$	−39.3025	−	2.31016i	−1.68663	−	0.0991387i
$544$	8.93017	+	17.2343i	0.382878	+	0.738913i
$545$	13.4576			0.576460
$546$	−3.04634	−	8.39081i	−0.130371	−	0.359094i
$547$			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
$549$	−7.27626	−	16.9179i	−0.310543	−	0.722038i
$550$	−1.54318	−	1.74558i	−0.0658014	−	0.0744317i
$551$	0.257150	+	0.445397i	0.0109550	+	0.0189746i
$552$	−6.31124	+	11.4191i	−0.268624	+	0.486031i
$553$	−10.5548	+	9.45016i	−0.448837	+	0.401862i
$554$	4.02397	+	1.34809i	0.170962	+	0.0572751i
$555$	−2.99854	+	4.55376i	−0.127281	+	0.193296i
$556$	5.17950	−	2.19394i	0.219660	−	0.0930439i
$557$	−9.38926	+	16.2627i	−0.397836	+	0.689072i	−0.993459	−	0.114192i	$-0.963572\pi$
$557$	−9.38926	+	16.2627i	−0.397836	+	0.689072i	0.595623	+	0.803264i	$0.296905\pi$
$558$	11.4854	+	5.41675i	0.486215	+	0.229309i
$559$			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	0.210010	−	0.977699i	$-0.432650\pi$
$563$	−12.6159	−	7.28380i	−0.531697	−	0.306975i	−0.741707	+	0.670724i	$0.765984\pi$
$564$	23.5842	+	20.0770i	0.993076	+	0.845392i
$565$	−10.0303	−	17.3731i	−0.421979	−	0.730890i
$566$	8.59407	−	25.6527i	0.361236	−	1.07826i
$567$	0.671637	−	23.8023i	0.0282061	−	0.999602i
$568$	0.335546	+	0.489413i	0.0140792	+	0.0205353i
$569$	−31.0916	+	17.9508i	−1.30343	+	0.752535i	−0.980991	−	0.194055i	$-0.937836\pi$
$569$	−31.0916	+	17.9508i	−1.30343	+	0.752535i	−0.322439	+	0.946590i	$0.604503\pi$
$570$	−5.91180	−	2.37480i	−0.247618	−	0.0994695i
$571$	−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
$576$	11.2148	−	21.2186i	0.467282	−	0.884109i
$577$	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
$579$	9.51864	−	14.4556i	0.395581	−	0.600753i
$580$	−0.238241	+	0.315660i	−0.00989244	+	0.0131071i
$581$	−36.1814	+	7.58464i	−1.50106	+	0.314664i
$582$	0.289438	+	2.03004i	0.0119976	+	0.0841480i
$583$	2.76821	+	4.79468i	0.114648	+	0.198576i
$584$	47.5655	−	3.68914i	1.96827	−	0.152658i
$585$	−3.79605	+	1.63265i	−0.156947	+	0.0675019i
$586$	2.25311	+	11.0959i	0.0930751	+	0.458367i
$587$		−	30.9360i		−	1.27687i	−0.769677	−	0.638434i	$-0.779583\pi$
$587$		−	30.9360i		−	1.27687i	0.769677	−	0.638434i	$-0.220417\pi$
$588$	17.6558	−	16.6214i	0.728114	−	0.685456i
$589$		−	7.78484i		−	0.320769i
$590$	−19.0949	+	3.87738i	−0.786125	+	0.159629i
$591$	−35.3793	−	2.07956i	−1.45531	−	0.0855416i
$592$	−3.06469	+	12.2130i	−0.125958	+	0.501950i
$593$	−7.77983	−	13.4751i	−0.319479	−	0.553355i	0.660900	−	0.750474i	$-0.270175\pi$
$593$	−7.77983	−	13.4751i	−0.319479	−	0.553355i	−0.980379	+	0.197119i	$0.936841\pi$
$594$	−5.79779	+	10.6280i	−0.237886	+	0.436071i
$595$	8.88531	−	1.86261i	0.364262	−	0.0763596i
$596$	−23.1421	−	17.4663i	−0.947938	−	0.715448i
$597$	28.6651	+	18.8753i	1.17318	+	0.772513i
$598$	3.88681	−	3.43614i	0.158943	−	0.140514i
$599$	27.4909	+	15.8719i	1.12325	+	0.648508i	0.942228	−	0.334972i	$-0.108727\pi$
$599$	27.4909	+	15.8719i	1.12325	+	0.648508i	0.181020	+	0.983479i	$0.442060\pi$
$600$	−0.0915695	−	4.89812i	−0.00373831	−	0.199965i
$601$			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
$606$	−34.6060	−	13.9014i	−1.40577	−	0.564707i
$607$	−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
$609$	0.133553	+	0.896250i	0.00541184	+	0.0363179i
$610$	−8.23184	−	2.75780i	−0.333298	−	0.111660i
$611$	−6.15776	−	10.6656i	−0.249116	−	0.431482i
$612$	4.90087	−	19.9961i	0.198106	−	0.808296i
$613$	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	$0.0186870\pi$
$617$			2.91483i			0.117347i	−0.998277	+	0.0586733i	$0.981313\pi$
$618$	7.13254	−	5.59552i	0.286913	−	0.225085i
$619$	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
$621$	13.0116	−	4.71225i	0.522137	−	0.189096i
$622$	10.8824	−	32.4831i	0.436343	−	1.30245i
$623$	−3.26840	+	2.92633i	−0.130946	+	0.117241i
$624$	−7.03032	+	6.45324i	−0.281438	+	0.258336i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.31337	+	7.34944i	−0.332269	+	0.293743i
$627$	7.40906	+	0.435497i	0.295889	+	0.0173921i
$628$	−2.01143	+	16.2799i	−0.0802647	+	0.649637i
$629$			10.8015i			0.430684i
$630$	−8.15441	−	7.71398i	−0.324880	−	0.307332i
$631$	−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
$633$	2.15402	−	36.6461i	0.0856148	−	1.45655i
$634$	9.19796	+	10.4043i	0.365298	+	0.413209i
$635$	7.83665	−	4.52449i	0.310988	−	0.179549i
$636$	−2.10292	+	11.4497i	−0.0833860	+	0.454009i
$637$	−8.83020	+	3.87228i	−0.349865	+	0.153425i
$638$	0.146350	−	0.436845i	0.00579406	−	0.0172949i
$639$	0.0737350	−	0.625055i	0.00291691	−	0.0247268i
$640$	−3.93405	−	10.6077i	−0.155507	−	0.419306i
$641$	−11.2806	−	6.51286i	−0.445557	−	0.257242i	0.260395	−	0.965502i	$-0.416147\pi$
$641$	−11.2806	−	6.51286i	−0.445557	−	0.257242i	−0.705952	+	0.708260i	$0.749481\pi$
$642$	2.85748	+	3.64239i	0.112776	+	0.143754i
$643$	−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	−0.685537	−	0.728038i	$-0.740433\pi$
$647$	7.31878	−	12.6765i	0.287731	−	0.498364i	0.973268	+	0.229674i	$0.0737658\pi$
$648$	−23.7684	+	9.11395i	−0.933710	+	0.358030i
$649$	19.6576	−	11.3493i	0.771627	−	0.445499i
$650$	−0.618798	+	1.84707i	−0.0242712	+	0.0724479i
$651$	5.03243	−	12.7595i	0.197237	−	0.500086i
$652$	12.9234	−	17.1229i	0.506119	−	0.670586i
$653$	5.80499	+	10.0545i	0.227167	+	0.393465i	0.956967	−	0.290196i	$-0.0937204\pi$
$653$	5.80499	+	10.0545i	0.227167	+	0.393465i	−0.729800	+	0.683660i	$0.760387\pi$
$654$	−30.5885	−	12.2876i	−1.19611	−	0.480483i
$655$	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	$-0.314622\pi$
$659$	28.2389			1.10003			0.550015	+	0.835155i	$0.314622\pi$
$660$	1.91376	+	5.37663i	0.0744931	+	0.209285i
$661$	−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
$663$	−4.50211	+	6.83717i	−0.174847	+	0.265534i
$664$	22.3475	+	32.5951i	0.867252	+	1.26493i
$665$	−2.14481	+	6.53863i	−0.0831723	+	0.253557i
$666$	10.9734	−	7.61264i	0.425210	−	0.294984i
$667$	−0.456068	+	0.263311i	−0.0176590	+	0.0101954i
$668$	−9.77358	+	4.13991i	−0.378151	+	0.160178i
$669$	1.39746	−	23.7749i	0.0540291	−	0.919190i
$670$	−9.76020	+	1.98189i	−0.377069	+	0.0765670i
$671$	10.1135			0.390429
$672$	−23.6573	−	10.5988i	−0.912599	−	0.408856i
$673$	−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
$675$	−3.34639	+	3.97513i	−0.128803	+	0.153003i
$676$	−20.4468	+	8.66087i	−0.786414	+	0.333111i
$677$	27.4706	−	15.8601i	1.05578	−	0.609554i	0.131517	−	0.991314i	$-0.458015\pi$
$677$	27.4706	−	15.8601i	1.05578	−	0.609554i	0.924262	+	0.381759i	$0.124682\pi$
$678$	6.93588	+	48.6464i	0.266371	+	1.86826i
$679$	2.16775	−	0.454422i	0.0831908	−	0.0174391i
$680$	−5.48803	−	8.00460i	−0.210456	−	0.306962i
$681$	−28.0743	−	18.4863i	−1.07581	−	0.708395i
$682$	−5.22468	+	4.61889i	−0.200064	+	0.176866i
$683$	8.35024	−	14.4630i	0.319513	−	0.553413i	−0.660873	−	0.750497i	$-0.729814\pi$
$683$	8.35024	−	14.4630i	0.319513	−	0.553413i	0.980386	+	0.197085i	$0.0631473\pi$
$684$	11.2689	+	10.7956i	0.430878	+	0.412782i
$685$	−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
$690$	2.43170	−	6.05343i	0.0925731	−	0.230450i
$691$	−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
$693$	11.8621	+	5.50331i	0.450604	+	0.209053i
$694$	−1.06006	+	3.16421i	−0.0402394	+	0.120112i
$695$	−2.43570	+	1.40625i	−0.0923912	+	0.0533421i
$696$	0.829728	−	0.499951i	0.0314508	−	0.0189506i
$697$	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	$-0.571455\pi$
$701$	−11.7874			−0.445203			−0.222601	+	0.974910i	$0.571455\pi$
$702$	10.1190	−	0.244926i	0.381916	−	0.00924412i
$703$	−7.09057	−	4.09374i	−0.267426	−	0.154398i
$704$	8.27110	+	10.2615i	0.311729	+	0.386746i
$705$	−12.9341	−	8.51676i	−0.487125	−	0.320760i
$706$	−3.06361	+	9.14464i	−0.115300	+	0.344163i
$707$	−12.5551	+	38.2753i	−0.472184	+	1.43949i
$708$	46.9421	+	8.62168i	1.76419	+	0.324022i
$709$	−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
$711$	−6.34691	−	14.7571i	−0.238028	−	0.553435i
$712$	4.23074	+	2.02386i	0.158554	+	0.0758474i
$713$	7.97134			0.298529
$714$	−21.8966	−	3.87918i	−0.819459	−	0.145175i
$715$		−	2.26928i		−	0.0848664i
$716$	−2.71027	+	21.9361i	−0.101288	+	0.819789i
$717$	0.227104	−	3.86369i	0.00848135	−	0.144292i
$718$	−11.8475	+	10.4738i	−0.442145	+	0.390879i
$719$	20.9182	+	36.2313i	0.780116	+	1.35120i	0.931874	+	0.362783i	$0.118173\pi$
$719$	20.9182	+	36.2313i	0.780116	+	1.35120i	−0.151758	+	0.988418i	$0.548493\pi$
$720$	−4.26414	+	11.2168i	−0.158915	+	0.418026i
$721$	−6.53159	−	7.29509i	−0.243249	−	0.271683i
$722$	−5.49658	+	16.4069i	−0.204561	+	0.610601i
$723$	−29.8477	−	19.6540i	−1.11005	−	0.730939i
$724$	41.8605	−	17.7313i	1.55573	−	0.658980i
$725$	0.0988686	−	0.171245i	0.00367189	−	0.00635990i
$726$	12.5273	+	15.9684i	0.464933	+	0.592644i
$727$		−	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
$732$	16.1926	+	13.7845i	0.598495	+	0.509490i
$733$	−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
$735$	−7.74223	+	9.33048i	−0.285577	+	0.344160i
$736$	0.685639	−	15.0500i	0.0252730	−	0.554749i
$737$	10.0478	−	5.80110i	0.370115	−	0.213686i
$738$	−41.8227	+	3.47555i	−1.53952	+	0.127937i
$739$	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	$0.152658\pi$
$743$			25.1546i			0.922832i	−0.887184	+	0.461416i	$0.847342\pi$
$744$	−14.6606	+	0.274076i	−0.537482	+	0.0100481i
$745$	12.5546	+	7.24840i	0.459965	+	0.265561i
$746$	−23.7196	+	20.9693i	−0.868435	+	0.767741i
$747$	4.91078	−	41.6289i	0.179676	−	1.52312i
$748$	9.02434	+	6.81105i	0.329963	+	0.249037i
$749$	3.72540	−	3.33550i	0.136123	−	0.121877i
$750$	0.345745	+	2.42497i	0.0126248	+	0.0885472i
$751$	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
$753$	−0.239939	+	4.08205i	−0.00874385	+	0.148758i
$754$	−0.377481	+	0.0766507i	−0.0137471	+	0.00279145i
$755$			20.1408i			0.733000i
$756$	11.4913	+	24.9790i	0.417934	+	0.908477i
$757$			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
$759$	−0.445931	+	7.58656i	−0.0161863	+	0.275375i
$760$	7.33452	−	0.568858i	0.266051	−	0.0206347i
$761$	9.26978	+	16.0557i	0.336029	+	0.582019i	0.983682	−	0.179916i	$-0.0575826\pi$
$761$	9.26978	+	16.0557i	0.336029	+	0.582019i	−0.647653	+	0.761936i	$0.724249\pi$
$762$	−21.9435	+	3.12864i	−0.794928	+	0.113339i
$763$	−11.0976	+	33.8318i	−0.401760	+	1.22479i
$764$	−20.4828	+	27.1388i	−0.741042	+	0.981848i
$765$	−1.20597	+	10.2231i	−0.0436021	+	0.369617i
$766$	−14.7099	−	16.6392i	−0.531491	−	0.601200i
$767$	−16.4351	−	9.48883i	−0.593438	−	0.342622i
$768$	−0.743541	+	27.7028i	−0.0268302	+	0.999640i
$769$		−	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	0.812694	−	0.582691i	$-0.198000\pi$
$773$	19.8628	+	11.4678i	0.714415	+	0.412468i	−0.0982785	+	0.995159i	$0.531334\pi$
$774$	−1.02047	−	12.2797i	−0.0366800	−	0.441386i
$775$	−2.59210	+	1.49655i	−0.0931109	+	0.0537576i
$776$	−1.33892	−	1.95289i	−0.0480644	−	0.0701045i
$777$	−8.97525	−	11.2934i	−0.321985	−	0.405147i
$778$	−9.72696	+	29.0343i	−0.348728	+	1.04093i
$779$	12.8638	+	22.2808i	0.460893	+	0.798291i
$780$	3.09298	−	3.63330i	0.110746	−	0.130093i
$781$	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
$786$	−1.31461	+	1.03132i	−0.0468905	+	0.0367859i
$787$	−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
$789$	18.6180	+	12.2595i	0.662819	+	0.436450i
$790$	−7.18045	−	2.40557i	−0.255469	−	0.0855863i
$791$	51.9464	−	10.8894i	1.84700	−	0.387184i
$792$	0.559291	−	13.9682i	0.0198735	−	0.496339i
$793$	−4.22782	−	7.32280i	−0.150134	−	0.260040i
$794$	20.1398	+	22.7813i	0.714736	+	0.808479i
$795$	0.341539	−	5.81056i	0.0121132	−	0.206079i
$796$	−39.3320	−	4.85959i	−1.39408	−	0.172244i
$797$			26.8539i			0.951216i	0.879657	+	0.475608i	$0.157772\pi$
$797$			26.8539i			0.951216i	−0.879657	+	0.475608i	$0.842228\pi$
$798$	10.8452	−	12.9037i	0.383917	−	0.456785i
$799$	−30.6795			−1.08536
$800$	2.60254	+	5.02263i	0.0920138	+	0.177577i
$801$	−1.96538	−	4.56967i	−0.0694433	−	0.161461i
$802$	20.4866	−	18.1112i	0.723408	−	0.639529i
$803$	24.0659	−	13.8945i	0.849269	−	0.490325i
$804$	23.9941	+	4.40689i	0.846205	+	0.155419i
$805$	−6.69527	−	2.19620i	−0.235977	−	0.0774058i
$806$	5.52845	+	1.85212i	0.194731	+	0.0652382i
$807$	29.3851	+	19.3494i	1.03440	+	0.681130i
$808$	42.9342	−	3.32993i	1.51042	−	0.117147i
$809$	12.4937	+	7.21326i	0.439256	+	0.253605i	0.703282	−	0.710911i	$-0.251717\pi$
$809$	12.4937	+	7.21326i	0.439256	+	0.253605i	−0.264026	+	0.964516i	$0.585050\pi$
$810$	11.2357	−	5.97984i	0.394783	−	0.210110i
$811$	−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
$816$	5.16538	+	23.2050i	0.180824	+	0.812337i
$817$	−6.54194	+	3.77699i	−0.228874	+	0.132140i
$818$	−15.3220	−	5.13311i	−0.535720	−	0.179475i
$819$	−0.974067	−	10.8894i	−0.0340367	−	0.380508i
$820$	−11.9179	+	15.7907i	−0.416191	+	0.551435i
$821$	1.10924	+	1.92127i	0.0387128	+	0.0670526i	0.884733	−	0.466099i	$-0.154341\pi$
$821$	1.10924	+	1.92127i	0.0387128	+	0.0670526i	−0.846020	+	0.533151i	$0.821008\pi$
$822$	34.1937	+	13.7358i	1.19264	+	0.479091i
$823$	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	$-0.755858\pi$
$827$	−41.4110			−1.44000			−0.720000	+	0.693974i	$0.755858\pi$
$828$	−11.0543	+	11.5389i	−0.384162	+	0.401004i
$829$	−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
$831$	4.34096	+	2.85842i	0.150586	+	0.0991574i
$832$	3.97234	−	10.2785i	0.137716	−	0.356341i
$833$	−2.64460	+	23.8733i	−0.0916298	+	0.827159i
$834$	6.82022	−	0.972408i	0.236165	−	0.0336717i
$835$	4.59609	−	2.65356i	0.159054	−	0.0918301i
$836$	−7.89127	+	3.34260i	−0.272925	+	0.115606i
$837$	11.8979	+	10.0161i	0.411253	+	0.346206i
$838$	0.750243	+	3.69472i	0.0259167	+	0.127632i
$839$	55.2304			1.90676			0.953382	−	0.301765i	$-0.0975759\pi$
$839$	55.2304			1.90676			0.953382	+	0.301765i	$0.0975759\pi$
$840$	12.3892	+	3.80895i	0.427467	+	0.131421i
$841$	−28.9609			−0.998652
$842$	7.04080	+	34.6738i	0.242642	+	1.19494i
$843$	−3.00498	+	51.1234i	−0.103497	+	1.76078i
$844$	16.5329	+	39.0312i	0.569086	+	1.34351i
$845$	9.61523	−	5.55136i	0.330774	−	0.190973i
$846$	21.6222	+	31.1678i	0.743388	+	1.07157i
$847$	16.3324	−	14.6230i	0.561186	−	0.502453i
$848$	−3.68557	−	12.9270i	−0.126563	−	0.443914i
$849$	18.2223	−	27.6735i	0.625389	−	0.949753i
$850$	3.21407	+	3.63562i	0.110242	+	0.124701i
$851$	4.19181	−	7.26043i	0.143694	−	0.248884i
$852$	0.243704	+	0.684677i	0.00834917	+	0.0234567i
$853$	−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	−0.584109	−	0.811675i	$-0.698556\pi$
$857$	12.0282	−	20.8335i	0.410877	−	0.711659i	0.994986	+	0.100016i	$0.0318893\pi$
$858$	−2.07199	+	5.15798i	−0.0707366	+	0.176091i
$859$	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
$861$	6.68091	+	44.8344i	0.227685	+	1.52795i
$862$	21.4163	+	7.17481i	0.729442	+	0.244375i
$863$	−1.17157	+	0.676409i	−0.0398808	+	0.0230252i	−0.519808	−	0.854283i	$-0.673996\pi$
$863$	−1.17157	+	0.676409i	−0.0398808	+	0.0230252i	0.479927	+	0.877308i	$0.340663\pi$
$864$	19.9338	−	21.6019i	0.678162	−	0.734912i
$865$	−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
$870$	−0.381081	+	0.298960i	−0.0129199	+	0.0101357i
$871$	−8.40068	−	4.85013i	−0.284646	−	0.164340i
$872$	37.9499	−	2.94336i	1.28515	−	0.0996747i
$873$	−0.294222	+	2.49414i	−0.00995791	+	0.0844137i
$874$	9.28872	+	3.11187i	0.314196	+	0.105261i
$875$	2.58947	−	0.542825i	0.0875400	−	0.0183508i
$876$	57.4693	+	10.5552i	1.94171	+	0.356626i
$877$	−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
$879$	−0.813683	+	13.8431i	−0.0274448	+	0.466915i
$880$	−4.73348	−	4.58494i	−0.159566	−	0.154558i
$881$	−29.3158			−0.987676			−0.493838	−	0.869554i	$-0.664406\pi$
$881$	−29.3158			−0.987676			−0.493838	+	0.869554i	$0.664406\pi$
$882$	26.1170	−	14.1386i	0.879406	−	0.476073i
$883$		−	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
$885$	−23.8225	−	1.40027i	−0.800786	−	0.0470694i
$886$	10.5571	+	11.9418i	0.354674	+	0.401192i
$887$	10.8095	+	18.7226i	0.362947	+	0.628642i	0.988444	−	0.151584i	$-0.0484374\pi$
$887$	10.8095	+	18.7226i	0.362947	+	0.628642i	−0.625498	+	0.780226i	$0.715104\pi$
$888$	−7.45978	+	13.4972i	−0.250334	+	0.452937i
$889$	4.91202	+	23.4320i	0.164744	+	0.785885i
$890$	−2.22349	−	0.744906i	−0.0745316	−	0.0249693i
$891$	−10.1982	+	10.7633i	−0.341652	+	0.360585i
$892$	10.7260	+	25.3222i	0.359134	+	0.847851i
$893$	11.6275	−	20.1394i	0.389099	−	0.673939i
$894$	−21.9178	−	27.9384i	−0.733042	−	0.934399i
$895$		−	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
$900$	1.42827	−	5.82752i	0.0476091	−	0.194251i
$901$	−5.76552	−	9.98618i	−0.192077	−	0.332688i
$902$	7.32109	−	21.8529i	0.243766	−	0.727623i
$903$	−13.1640	+	1.96161i	−0.438071	+	0.0652782i
$904$	−32.0848	−	46.7975i	−1.06713	−	1.55646i
$905$	−19.6852	+	11.3652i	−0.654358	+	0.377794i
$906$	18.3898	−	45.7792i	0.610959	−	1.52091i
$907$	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	$-0.748380\pi$
$911$		−	42.9016i		−	1.42139i	0.703499	−	0.710697i	$-0.251620\pi$
$912$	−17.1904	−	5.40386i	−0.569232	−	0.178940i
$913$	19.9355	+	11.5098i	0.659770	+	0.380918i
$914$	−8.69014	−	9.82991i	−0.287444	−	0.325144i
$915$	−8.88032	−	5.84747i	−0.293574	−	0.193312i
$916$	−36.4015	−	27.4737i	−1.20274	−	0.907758i
$917$	1.20385	+	1.34457i	0.0397545	+	0.0444016i
$918$	12.0754	−	22.1355i	0.398548	−	0.730581i
$919$	−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
$921$	−4.37009	−	0.256870i	−0.143999	−	0.00846415i
$922$	−8.47557	−	41.7396i	−0.279128	−	1.37462i
$923$		−	0.288978i		−	0.00951182i
$924$	−15.0948	+	0.377363i	−0.496582	+	0.0124143i
$925$			3.14790i			0.103502i
$926$	5.29865	−	1.07593i	0.174125	−	0.0353574i
$927$	10.1996	−	4.38675i	0.334997	−	0.144080i
$928$	−0.602792	+	0.942253i	−0.0197876	+	0.0309310i
$929$	−23.7400	−	41.1188i	−0.778883	−	1.34907i	−0.932586	−	0.360948i	$-0.882453\pi$
$929$	−23.7400	−	41.1188i	−0.778883	−	1.34907i	0.153702	−	0.988117i	$-0.450880\pi$
$930$	7.25816	−	1.03485i	0.238004	−	0.0339340i
$931$	−14.6691	−	10.7839i	−0.480762	−	0.353429i
$932$	−17.4261	+	23.0888i	−0.570809	+	0.756297i
$933$	23.0743	−	35.0420i	0.755419	−	1.14722i
$934$	−5.64337	+	4.98902i	−0.184657	+	0.163246i
$935$	−4.89571	−	2.82654i	−0.160107	−	0.0924377i
$936$	−10.3476	+	5.43426i	−0.338223	+	0.177624i
$937$		−	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	0.743001	−	0.669290i	$-0.233402\pi$
$941$	16.4078	+	9.47305i	0.534879	+	0.308812i	−0.208122	+	0.978103i	$0.566735\pi$
$942$	−7.48875	+	18.6424i	−0.243997	+	0.607401i
$943$	−22.8145	+	13.1720i	−0.742943	+	0.428939i
$944$	−52.9988	+	15.1103i	−1.72496	+	0.491800i
$945$	−7.23376	−	11.6907i	−0.235314	−	0.380299i
$946$	6.41633	+	2.14958i	0.208613	+	0.0698887i
$947$	2.81753	+	4.88010i	0.0915573	+	0.158582i	0.908167	−	0.418609i	$-0.137482\pi$
$947$	2.81753	+	4.88010i	0.0915573	+	0.158582i	−0.816609	+	0.577191i	$0.804149\pi$
$948$	14.1244	+	12.0239i	0.458740	+	0.390519i
$949$	−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	$-0.998317\pi$
$953$		−	0.326501i		−	0.0105764i	0.999986	−	0.00528821i	$-0.00168330\pi$
$954$	−6.08169	+	12.8953i	−0.196902	+	0.417501i
$955$	8.50022	−	14.7228i	0.275061	−	0.476419i
$956$	1.74310	+	4.11515i	0.0563760	+	0.133094i
$957$	0.310312	−	0.471259i	0.0100310	−	0.0152336i
$958$	9.97022	−	29.7604i	0.322123	−	0.961515i
$959$	12.4055	−	37.8192i	0.400596	−	1.22125i
$960$	−1.32951	−	13.7925i	−0.0429097	−	0.445150i
$961$	−11.0207	−	19.0884i	−0.355506	−	0.615754i
$962$	4.59414	−	4.06145i	0.148121	−	0.130946i
$963$	2.24019	+	5.20863i	0.0721891	+	0.167846i
$964$	40.9546	+	5.06007i	1.31906	+	0.162974i
$965$		−	9.99280i		−	0.321680i
$966$	13.2128	+	11.1050i	0.425115	+	0.357299i
$967$	−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
$969$	−15.4313	−	0.907037i	−0.495725	−	0.0291382i
$970$	0.784140	+	0.886985i	0.0251772	+	0.0284794i
$971$	33.1705	−	19.1510i	1.06449	−	0.614585i	0.137821	−	0.990457i	$-0.455990\pi$
$971$	33.1705	−	19.1510i	1.06449	−	0.614585i	0.926672	+	0.375872i	$0.122657\pi$
$972$	−30.9982	+	3.33302i	−0.994269	+	0.106907i
$973$	−1.52670	−	7.28288i	−0.0489436	−	0.233478i
$974$	−12.4751	+	37.2372i	−0.399727	+	1.19316i
$975$	−1.31206	+	1.99257i	−0.0420196	+	0.0638134i
$976$	−23.8166	−	5.97647i	−0.762351	−	0.191302i
$977$	46.5776	+	26.8916i	1.49015	+	0.860339i	0.999937	−	0.0112636i	$-0.00358538\pi$
$977$	46.5776	+	26.8916i	1.49015	+	0.860339i	0.490214	+	0.871602i	$0.336919\pi$
$978$	20.6717	−	16.2171i	0.661009	−	0.518565i
$979$	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	−0.918178	−	0.396168i	$-0.870340\pi$
$983$	−3.63683	+	6.29918i	−0.115997	+	0.200913i	0.802181	+	0.597081i	$0.203673\pi$
$984$	41.5067	−	25.0098i	1.32318	−	0.797283i
$985$	−17.7202	+	10.2307i	−0.564611	+	0.325979i
$986$	−0.304813	+	0.909844i	−0.00970721	+	0.0289753i
$987$	32.0766	−	25.4925i	1.02101	−	0.811434i
$988$	5.71907	+	4.31642i	0.181948	+	0.137324i
$989$	−3.86748	−	6.69867i	−0.122979	−	0.213005i
$990$	0.578862	+	6.96570i	0.0183975	+	0.221384i
$991$	−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
$996$	16.2308	+	45.5997i	0.514292	+	1.44488i
$997$	−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
$999$	15.3795	−	5.56980i	0.486585	−	0.176221i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.8	✓	256	1.1	even	1	trivial
840.2.cf.a.101.37	yes	256	8.5	even	2	inner
840.2.cf.a.101.92	yes	256	24.5	odd	2	inner
840.2.cf.a.101.121	yes	256	3.2	odd	2	inner
840.2.cf.a.341.8	yes	256	168.5	even	6	inner
840.2.cf.a.341.37	yes	256	21.5	even	6	inner
840.2.cf.a.341.92	yes	256	7.5	odd	6	inner
840.2.cf.a.341.121	yes	256	56.5	odd	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} +(-1.72907 - 0.101633i) q^{3} +(1.84160 - 0.780068i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.42497 - 0.345745i) q^{6} +(-0.542825 - 2.58947i) q^{7} +(-2.33280 + 1.59939i) q^{8} +(2.97934 + 0.351460i) q^{9} +(1.05954 - 0.936685i) q^{10} +(-0.823745 + 1.42677i) q^{11} +(-3.26353 + 1.16162i) 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} +(-4.22807 + 0.351360i) q^{18} +(1.30047 + 2.25247i) q^{19} +(-1.20484 + 1.59636i) q^{20} +(0.675406 + 4.53253i) q^{21} +(0.740125 - 2.20922i) q^{22} +(-2.30643 + 1.33162i) q^{23} +(4.19611 - 2.52836i) 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} +(-1.92721 + 1.51191i) q^{30} +(-2.59210 - 1.49655i) q^{31} +(-3.04845 + 4.76518i) q^{32} +(1.56932 - 2.38326i) q^{33} +(-1.54150 + 4.60128i) q^{34} +(1.76483 + 1.97113i) q^{35} +(5.76092 - 1.67684i) q^{36} +(-2.72617 + 1.57395i) q^{37} +(-2.43625 - 2.75578i) q^{38} +(-2.38165 - 0.139991i) q^{39} +(1.22057 - 2.55151i) q^{40} +9.89169 q^{41} +(-2.21163 - 6.09169i) q^{42} +2.90434i q^{43} +(-0.404033 + 3.27011i) q^{44} +(-2.75592 + 1.18530i) q^{45} +(2.82181 - 2.49462i) q^{46} +(-4.47051 - 7.74314i) q^{47} +(-5.10398 + 4.68502i) q^{48} +(-6.41068 + 2.81126i) q^{49} +(-0.449244 + 1.34096i) q^{50} +(-3.26851 + 4.96375i) q^{51} +(2.53666 - 1.07448i) q^{52} +(1.68026 - 2.91030i) q^{53} +(7.34632 - 0.177815i) 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} +(2.24549 - 2.63776i) q^{60} +(-3.06938 - 5.31632i) q^{61} +(4.01363 + 1.34463i) q^{62} +(-0.707168 - 7.90569i) q^{63} +(2.88390 - 7.46211i) q^{64} +(-1.19288 + 0.688710i) q^{65} +(-1.50426 + 3.74467i) 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} +(-7.51233 + 3.94525i) q^{72} +(-14.6076 - 8.43373i) q^{73} +(3.33532 - 2.94860i) q^{74} +(-0.952550 + 1.44660i) q^{75} +(4.15202 + 3.13370i) q^{76} +(4.14172 + 1.35857i) q^{77} +(3.34020 - 0.476236i) q^{78} +(-2.67735 - 4.63731i) q^{79} +(-0.973564 + 3.87971i) q^{80} +(8.75295 + 2.09424i) q^{81} +(-13.7092 + 2.78376i) q^{82} -13.9725i q^{83} +(4.77951 + 7.82025i) q^{84} +3.43133i q^{85} +(-0.817351 - 4.02521i) q^{86} +(-0.341901 - 0.0200966i) q^{87} +(-0.360328 - 4.64585i) q^{88} +(-0.829066 - 1.43598i) q^{89} +(3.48593 - 2.41832i) q^{90} +(-0.747698 - 3.56678i) q^{91} +(-3.20878 + 4.25149i) q^{92} +(4.32981 + 2.85107i) q^{93} +(8.37492 + 9.47334i) q^{94} +(-2.25247 - 1.30047i) q^{95} +(5.75527 - 7.92949i) 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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