LMFDB - Embedded newform 840.2.cf.a.341.8

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			341.8
Character	$\chi$	$=$	840.341
Dual form			840.2.cf.a.101.8

$q$-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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$	$1$

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	0.714705	−	0.699426i	$-0.246561\pi$
$11$	−0.823745	−	1.42677i	−0.248368	−	0.430187i	−0.963073	+	0.269239i	$0.913228\pi$
$12$	−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	0.995544	−	0.0942958i	$-0.0300600\pi$
$17$	1.71566	+	2.97162i	0.416110	+	0.720723i	−0.579435	+	0.815019i	$0.696727\pi$
$18$	−4.22807	−	0.351360i	−0.996565	−	0.0828164i
$19$	1.30047	−	2.25247i	0.298347	−	0.516753i	−0.677411	−	0.735605i	$-0.736898\pi$
$19$	1.30047	−	2.25247i	0.298347	−	0.516753i	0.975758	+	0.218852i	$0.0702313\pi$
$20$	−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	0.239877	−	0.970803i	$-0.422893\pi$
$23$	−2.30643	−	1.33162i	−0.480925	−	0.277662i	−0.720802	+	0.693141i	$0.756226\pi$
$24$	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	−0.714377	−	0.699761i	$-0.753290\pi$
$31$	−2.59210	+	1.49655i	−0.465555	+	0.268788i	0.248822	+	0.968549i	$0.419956\pi$
$32$	−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	0.258882	−	0.965909i	$-0.416646\pi$
$37$	−2.72617	−	1.57395i	−0.448179	−	0.258756i	−0.707061	+	0.707153i	$0.749979\pi$
$38$	−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	$-0.928920\pi$
$43$		−	2.90434i		−	0.442908i	0.975171	−	0.221454i	$-0.0710802\pi$
$44$	−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	0.330524	+	0.943797i	$0.392774\pi$
$47$	−4.47051	+	7.74314i	−0.652090	+	1.12945i	−0.982615	+	0.185656i	$0.940559\pi$
$48$	−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	0.958044	−	0.286620i	$-0.0925318\pi$
$53$	1.68026	+	2.91030i	0.230802	+	0.399760i	−0.727243	+	0.686380i	$0.759199\pi$
$54$	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	−0.555530	+	0.831497i	$0.687485\pi$
$59$	−11.9318	+	6.88885i	−1.55339	+	0.896851i	−0.997862	+	0.0653547i	$0.979182\pi$
$60$	2.24549	+	2.63776i	0.289891	+	0.340533i
$61$	−3.06938	+	5.31632i	−0.392994	+	0.680685i	−0.992843	−	0.119428i	$-0.961894\pi$
$61$	−3.06938	+	5.31632i	−0.392994	+	0.680685i	0.599849	+	0.800113i	$0.295227\pi$
$62$	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	−0.823918	−	0.566709i	$-0.808217\pi$
$67$	−6.09885	+	3.52117i	−0.745093	+	0.430180i	0.0788250	+	0.996888i	$0.474883\pi$
$68$	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	$0.996037\pi$
$72$	−7.51233	−	3.94525i	−0.885336	−	0.464952i
$73$	−14.6076	+	8.43373i	−1.70970	+	0.987093i	−0.774773	+	0.632239i	$0.782136\pi$
$73$	−14.6076	+	8.43373i	−1.70970	+	0.987093i	−0.934922	+	0.354853i	$0.884531\pi$
$74$	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	−0.976414	−	0.215908i	$-0.930729\pi$
$79$	−2.67735	+	4.63731i	−0.301225	+	0.521738i	0.675188	+	0.737645i	$0.264062\pi$
$80$	−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	$0.278173\pi$
$83$			13.9725i			1.53368i	−0.641837	+	0.766841i	$0.721827\pi$
$84$	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	−0.906615	−	0.421959i	$-0.861343\pi$
$89$	−0.829066	+	1.43598i	−0.0878808	+	0.152214i	0.818734	+	0.574172i	$0.194676\pi$
$90$	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	$-0.986468\pi$
$97$		−	0.837143i		−	0.0849990i	0.999096	−	0.0424995i	$-0.0135321\pi$
$98$	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	$-0.940235\pi$
$101$	−13.1853	+	7.61255i	−1.31199	+	0.757477i	−0.329564	+	0.944133i	$0.606902\pi$
$102$	3.13300	+	7.79925i	0.310214	+	0.772241i
$103$	3.20513	+	1.85048i	0.315811	+	0.182334i	0.649524	−	0.760341i	$-0.274968\pi$
$103$	3.20513	+	1.85048i	0.315811	+	0.182334i	−0.333713	+	0.942675i	$0.608302\pi$
$104$	−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	−0.816726	−	0.577026i	$-0.804213\pi$
$107$	0.944991	−	1.63677i	0.0913557	−	0.158233i	0.908082	+	0.418793i	$0.137547\pi$
$108$	−10.1314	−	2.31387i	−0.974898	−	0.222652i
$109$	−11.6546	+	6.72880i	−1.11631	+	0.644502i	−0.940457	−	0.339914i	$-0.889602\pi$
$109$	−11.6546	+	6.72880i	−1.11631	+	0.644502i	−0.175854	+	0.984416i	$0.556269\pi$
$110$	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	$-0.392560\pi$
$114$	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	0.473971	−	0.880540i	$-0.342820\pi$
$131$	−0.590742	−	0.341065i	−0.0516134	−	0.0297990i	−0.525585	+	0.850741i	$0.676153\pi$
$132$	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	0.173452	−	0.984842i	$-0.444508\pi$
$137$	13.0282	−	7.52185i	1.11308	−	0.642635i	0.939624	+	0.342207i	$0.111175\pi$
$138$	−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	0.399901	+	0.916558i	$0.369044\pi$
$149$	−7.24840	+	12.5546i	−0.593812	+	1.02851i	−0.993713	+	0.111955i	$0.964289\pi$
$150$	0.913059	+	2.27295i	0.0745509	+	0.185586i
$151$	10.0704	+	17.4425i	0.819519	+	1.41945i	0.906037	+	0.423198i	$0.139092\pi$
$151$	10.0704	+	17.4425i	0.819519	+	1.41945i	−0.0865186	+	0.996250i	$0.527574\pi$
$152$	−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	0.654684	−	0.755902i	$-0.272802\pi$
$157$	−4.10091	−	7.10299i	−0.327288	−	0.566880i	−0.981973	+	0.189022i	$0.939468\pi$
$158$	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	0.817538	−	0.575874i	$-0.195338\pi$
$163$	9.28920	+	5.36312i	0.727586	+	0.420072i	−0.0899523	+	0.995946i	$0.528671\pi$
$164$	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	0.698784	−	0.715333i	$-0.253725\pi$
$173$	5.63839	+	3.25532i	0.428679	+	0.247498i	−0.270105	+	0.962831i	$0.587058\pi$
$174$	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	0.582206	−	0.813041i	$-0.302190\pi$
$179$	−5.52571	−	9.57082i	−0.413011	−	0.715356i	−0.995217	+	0.0976847i	$0.968856\pi$
$180$	−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	−0.138411	−	0.990375i	$-0.544199\pi$
$191$	−14.7228	−	8.50022i	−1.06531	−	0.615055i	−0.926895	+	0.375320i	$0.877533\pi$
$192$	−5.74485	−	12.6094i	−0.414599	−	0.910004i
$193$	−4.99640	−	8.65402i	−0.359649	−	0.622930i	0.628253	−	0.778009i	$-0.283770\pi$
$193$	−4.99640	−	8.65402i	−0.359649	−	0.622930i	−0.987902	+	0.155079i	$0.950437\pi$
$194$	−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	−0.964166	−	0.265300i	$-0.914529\pi$
$199$	−17.1607	+	9.90776i	−1.21649	+	0.702342i	−0.252327	+	0.967642i	$0.581196\pi$
$200$	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	$-0.739737\pi$
$211$		−	21.1942i		−	1.45907i	0.683945	−	0.729534i	$-0.260263\pi$
$212$	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	$-0.847710\pi$
$223$		−	13.7501i		−	0.920776i	0.887718	−	0.460388i	$-0.152290\pi$
$224$	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	$-0.443920\pi$
$227$	16.8071	−	9.70356i	1.11552	−	0.644048i	0.940254	+	0.340472i	$0.110587\pi$
$228$	−6.86063	+	5.84036i	−0.454356	+	0.386787i
$229$	−11.4014	+	19.7478i	−0.753427	+	1.30497i	0.192726	+	0.981253i	$0.438267\pi$
$229$	−11.4014	+	19.7478i	−0.753427	+	1.30497i	−0.946153	+	0.323721i	$0.895066\pi$
$230$	−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	0.0300343	−	0.999549i	$-0.490438\pi$
$233$	−12.5257	−	7.23169i	−0.820583	−	0.473764i	−0.850618	+	0.525785i	$0.823772\pi$
$234$	−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	$-0.976975\pi$
$239$		−	2.23455i		−	0.144541i	0.997385	−	0.0722706i	$-0.0230245\pi$
$240$	2.07766	+	6.60934i	0.134113	+	0.426631i
$241$	17.8687	−	10.3165i	1.15103	−	0.664545i	0.201888	−	0.979409i	$-0.435292\pi$
$241$	17.8687	−	10.3165i	1.15103	−	0.664545i	0.949137	+	0.314864i	$0.101959\pi$
$242$	−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	$0.0237384\pi$
$251$			2.36084i			0.149015i	−0.997220	+	0.0745074i	$0.976262\pi$
$252$	−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	0.447177	+	0.894446i	$0.352430\pi$
$257$	−8.83359	+	15.3002i	−0.551024	+	0.954402i	−0.998201	+	0.0599566i	$0.980904\pi$
$258$	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	−0.802595	−	0.596525i	$-0.796548\pi$
$263$	−11.1459	+	6.43510i	−0.687287	+	0.396805i	0.115308	+	0.993330i	$0.463214\pi$
$264$	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	−0.928888	−	0.370361i	$-0.879234\pi$
$269$	−17.5918	+	10.1566i	−1.07259	+	0.619260i	−0.143702	+	0.989621i	$0.545901\pi$
$270$	−6.27319	−	3.82715i	−0.381774	−	0.232913i
$271$	15.8628	+	9.15838i	0.963595	+	0.556332i	0.897278	−	0.441467i	$-0.145542\pi$
$271$	15.8628	+	9.15838i	0.963595	+	0.556332i	0.0663173	+	0.997799i	$0.478875\pi$
$272$	−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	−0.576037	−	0.817424i	$-0.695401\pi$
$277$	−2.59877	+	1.50040i	−0.156145	+	0.0901505i	0.419891	+	0.907574i	$0.362068\pi$
$278$	−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	$0.656257\pi$
$282$	−13.5180	+	17.2312i	−0.804984	+	1.02610i
$283$	−9.56503	−	16.5671i	−0.568582	−	0.984813i	−0.996707	−	0.0810932i	$-0.974159\pi$
$283$	−9.56503	−	16.5671i	−0.568582	−	0.984813i	0.428124	−	0.903720i	$-0.359174\pi$
$284$	−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	$0.0751360\pi$
$293$			8.00610i			0.467721i	−0.972270	+	0.233861i	$0.924864\pi$
$294$	−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	−0.972867	−	0.231364i	$-0.925681\pi$
$311$	−12.1119	−	20.9784i	−0.686801	−	1.18957i	0.286066	−	0.958210i	$-0.407652\pi$
$312$	5.77981	+	3.48262i	0.327217	+	0.197164i
$313$	6.79503	+	3.92311i	0.384078	+	0.221747i	0.679591	−	0.733591i	$-0.262157\pi$
$313$	6.79503	+	3.92311i	0.384078	+	0.221747i	−0.295513	+	0.955339i	$0.595491\pi$
$314$	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	−0.970328	−	0.241794i	$-0.922264\pi$
$317$	−4.90985	+	8.50411i	−0.275765	+	0.477638i	0.694563	+	0.719432i	$0.255598\pi$
$318$	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	0.964245	−	0.265013i	$-0.0853762\pi$
$331$	22.1388	+	12.7819i	1.21686	+	0.702554i	0.252615	+	0.967567i	$0.418710\pi$
$332$	−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	0.895955	−	0.444145i	$-0.146493\pi$
$347$	1.17983	+	2.04352i	0.0633364	+	0.109702i	−0.832618	+	0.553847i	$0.813159\pi$
$348$	−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	0.942385	−	0.334529i	$-0.108577\pi$
$353$	3.40973	+	5.90583i	0.181482	+	0.314336i	−0.760904	+	0.648865i	$0.775244\pi$
$354$	−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	0.733280	−	0.679927i	$-0.237989\pi$
$359$	9.68369	+	5.59088i	0.511086	+	0.295076i	−0.222194	+	0.975002i	$0.571322\pi$
$360$	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	−0.252546	−	0.967585i	$-0.581268\pi$
$367$	8.79576	−	5.07823i	0.459135	−	0.265082i	0.711680	+	0.702503i	$0.247934\pi$
$368$	−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	0.909384	−	0.415958i	$-0.136554\pi$
$373$	19.3875	+	11.1934i	1.00384	+	0.579570i	0.0944613	+	0.995529i	$0.469887\pi$
$374$	−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	$0.120101\pi$
$379$			14.3447i			0.736837i	−0.929660	+	0.368418i	$0.879899\pi$
$380$	−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	−0.592649	−	0.805460i	$-0.701918\pi$
$383$	7.85212	−	13.6003i	0.401225	−	0.694941i	0.993874	+	0.110519i	$0.0352514\pi$
$384$	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	0.998351	+	0.0574120i	$0.0182849\pi$
$389$	10.8259	+	18.7510i	0.548896	+	0.950715i	−0.449455	+	0.893303i	$0.648382\pi$
$390$	−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	0.459371	+	0.888244i	$0.348075\pi$
$397$	−10.7506	+	18.6206i	−0.539557	+	0.934539i	−0.998928	+	0.0462950i	$0.985259\pi$
$398$	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	0.0197682	−	0.999805i	$-0.493707\pi$
$401$	−16.7450	−	9.66771i	−0.836204	−	0.482783i	−0.855972	+	0.517022i	$0.827041\pi$
$402$	−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	−0.234990	−	0.971998i	$-0.575506\pi$
$409$	9.89529	−	5.71305i	0.489290	−	0.282492i	0.724280	+	0.689506i	$0.242172\pi$
$410$	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	$0.0207425\pi$
$419$			2.66588i			0.130237i	−0.997878	+	0.0651184i	$0.979257\pi$
$420$	−8.04930	+	4.38278i	−0.392766	+	0.213858i
$421$			25.0185i			1.21933i	0.792661	+	0.609663i	$0.208695\pi$
$421$			25.0185i			1.21933i	−0.792661	+	0.609663i	$0.791305\pi$
$422$	−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	−0.794644	−	0.607076i	$-0.792343\pi$
$431$	−13.8312	+	7.98542i	−0.666223	+	0.384644i	0.128421	+	0.991720i	$0.459009\pi$
$432$	−16.8531	−	12.1644i	−0.810844	−	0.585262i
$433$			20.6616i			0.992932i	0.868056	+	0.496466i	$0.165369\pi$
$433$			20.6616i			0.992932i	−0.868056	+	0.496466i	$0.834631\pi$
$434$	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	1.00000		0.000439669i	$-0.000139951\pi$
$439$	31.4205	+	18.1406i	1.49962	+	0.865805i	0.499619	+	0.866245i	$0.333473\pi$
$440$	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	−0.968279	−	0.249871i	$-0.919612\pi$
$443$	−5.63538	+	9.76076i	−0.267745	+	0.463748i	0.700534	+	0.713619i	$0.252945\pi$
$444$	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	$-0.994470\pi$
$449$		−	0.736265i		−	0.0347465i	0.999849	−	0.0173732i	$-0.00553035\pi$
$450$	−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	−0.736895	−	0.676008i	$-0.763709\pi$
$457$	4.63877	−	8.03459i	0.216993	−	0.375842i	0.953887	+	0.300166i	$0.0970419\pi$
$458$	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	$-0.752587\pi$
$461$		−	30.1167i		−	1.40267i	0.712829	−	0.701337i	$-0.247413\pi$
$462$	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	0.602913	−	0.797807i	$-0.294007\pi$
$467$	4.61267	+	2.66313i	0.213449	+	0.123235i	−0.389464	+	0.921042i	$0.627340\pi$
$468$	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	−0.999967	−	0.00812429i	$-0.997414\pi$
$479$	−11.0967	−	19.2200i	−0.507019	−	0.878183i	0.492948	−	0.870059i	$-0.335919\pi$
$480$	−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	0.987719	+	0.156240i	$0.0499374\pi$
$487$	13.8845	+	24.0487i	0.629168	+	1.08975i	−0.358551	+	0.933510i	$0.616729\pi$
$488$	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	0.972992	+	0.230841i	$0.0741476\pi$
$499$	37.0682	+	21.4013i	1.65940	+	0.958056i	0.686410	+	0.727215i	$0.259186\pi$
$500$	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	−0.0855938	−	0.996330i	$-0.527279\pi$
$509$	−22.3633	−	12.9115i	−0.991238	−	0.572292i	−0.905644	+	0.424039i	$0.860612\pi$
$510$	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	0.990481	+	0.137649i	$0.0439546\pi$
$521$	14.0250	+	24.2921i	0.614448	+	1.06426i	−0.376033	+	0.926606i	$0.622712\pi$
$522$	−0.836046	−	0.0694770i	−0.0365927	−	0.00304092i
$523$	4.17316	−	7.22812i	0.182479	−	0.316064i	−0.760245	−	0.649637i	$-0.774921\pi$
$523$	4.17316	−	7.22812i	0.182479	−	0.316064i	0.942724	+	0.333573i	$0.108254\pi$
$524$	−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	0.523457	−	0.852052i	$-0.324642\pi$
$541$	1.09988	+	0.635014i	0.0472874	+	0.0273014i	−0.476170	+	0.879353i	$0.657975\pi$
$542$	−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	$-0.582380\pi$
$547$		−	45.2183i		−	1.93339i	0.255924	−	0.966697i	$-0.417620\pi$
$548$	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	0.595623	−	0.803264i	$-0.296905\pi$
$557$	−9.38926	−	16.2627i	−0.397836	−	0.689072i	−0.993459	+	0.114192i	$0.963572\pi$
$558$	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	−0.741707	−	0.670724i	$-0.765984\pi$
$563$	−12.6159	+	7.28380i	−0.531697	+	0.306975i	0.210010	+	0.977699i	$0.432650\pi$
$564$	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	−0.322439	−	0.946590i	$-0.604503\pi$
$569$	−31.0916	−	17.9508i	−1.30343	−	0.752535i	−0.980991	+	0.194055i	$0.937836\pi$
$570$	−5.91180	+	2.37480i	−0.247618	+	0.0994695i
$571$	−1.12979	+	0.652286i	−0.0472804	+	0.0272973i	−0.523454	−	0.852054i	$-0.675357\pi$
$571$	−1.12979	+	0.652286i	−0.0472804	+	0.0272973i	0.476174	+	0.879351i	$0.342023\pi$
$572$	−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	−0.462148	−	0.886803i	$-0.652921\pi$
$577$	1.79607	−	1.03696i	0.0747714	−	0.0431693i	0.536920	+	0.843633i	$0.319588\pi$
$578$	−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	$0.220417\pi$
$587$			30.9360i			1.27687i	−0.769677	+	0.638434i	$0.779583\pi$
$588$	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	−0.980379	−	0.197119i	$-0.936841\pi$
$593$	−7.77983	+	13.4751i	−0.319479	+	0.553355i	0.660900	+	0.750474i	$0.270175\pi$
$594$	−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	0.181020	−	0.983479i	$-0.442060\pi$
$599$	27.4909	−	15.8719i	1.12325	−	0.648508i	0.942228	+	0.334972i	$0.108727\pi$
$600$	−0.0915695	+	4.89812i	−0.00373831	+	0.199965i
$601$		−	25.8424i		−	1.05413i	−0.849824	−	0.527067i	$-0.823292\pi$
$601$		−	25.8424i		−	1.05413i	0.849824	−	0.527067i	$-0.176708\pi$
$602$	−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	−0.106537	−	0.994309i	$-0.533976\pi$
$607$	−25.1523	−	14.5217i	−1.02090	−	0.589418i	−0.914365	+	0.404891i	$0.867310\pi$
$608$	−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	0.453152	−	0.891433i	$-0.350300\pi$
$613$	35.9432	−	20.7518i	1.45173	−	0.838158i	0.998580	+	0.0532757i	$0.0169662\pi$
$614$	−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	$-0.0186870\pi$
$618$	7.13254	+	5.59552i	0.286913	+	0.225085i
$619$	5.02146	+	8.69742i	0.201829	+	0.349579i	0.949118	−	0.314921i	$-0.101978\pi$
$619$	5.02146	+	8.69742i	0.201829	+	0.349579i	−0.747289	+	0.664500i	$0.768645\pi$
$620$	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	−0.705952	−	0.708260i	$-0.749481\pi$
$641$	−11.2806	+	6.51286i	−0.445557	+	0.257242i	0.260395	+	0.965502i	$0.416147\pi$
$642$	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	0.973268	−	0.229674i	$-0.0737658\pi$
$647$	7.31878	+	12.6765i	0.287731	+	0.498364i	−0.685537	+	0.728038i	$0.740433\pi$
$648$	−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	−0.729800	−	0.683660i	$-0.760387\pi$
$653$	5.80499	−	10.0545i	0.227167	−	0.393465i	0.956967	+	0.290196i	$0.0937204\pi$
$654$	−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	0.840727	−	0.541459i	$-0.182128\pi$
$661$	−1.24831	−	2.16213i	−0.0485535	−	0.0840971i	−0.889281	+	0.457362i	$0.848794\pi$
$662$	−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	0.924262	−	0.381759i	$-0.124682\pi$
$677$	27.4706	+	15.8601i	1.05578	+	0.609554i	0.131517	+	0.991314i	$0.458015\pi$
$678$	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	0.980386	−	0.197085i	$-0.0631473\pi$
$683$	8.35024	+	14.4630i	0.319513	+	0.553413i	−0.660873	+	0.750497i	$0.729814\pi$
$684$	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	−0.896700	−	0.442639i	$-0.854042\pi$
$691$	−1.70899	+	2.96006i	−0.0650131	+	0.112606i	0.831687	+	0.555245i	$0.187376\pi$
$692$	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	−0.156553	−	0.987670i	$-0.550038\pi$
$709$	−29.0282	−	16.7594i	−1.09018	−	0.629414i	−0.933624	+	0.358256i	$0.883372\pi$
$710$	−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	−0.151758	−	0.988418i	$-0.548493\pi$
$719$	20.9182	−	36.2313i	0.780116	−	1.35120i	0.931874	−	0.362783i	$-0.118173\pi$
$720$	−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	$0.171104\pi$
$727$			27.6114i			1.02405i	−0.858971	+	0.512025i	$0.828896\pi$
$728$	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	−0.939635	−	0.342179i	$-0.888835\pi$
$733$	−4.69685	+	8.13519i	−0.173482	+	0.300480i	0.766153	+	0.642658i	$0.222169\pi$
$734$	−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	0.141914	−	0.989879i	$-0.454674\pi$
$739$	29.0910	−	16.7957i	1.07013	−	0.617841i	0.928217	+	0.372038i	$0.121341\pi$
$740$	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	$-0.152658\pi$
$744$	−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	0.135852	−	0.990729i	$-0.456623\pi$
$751$	25.3743	−	43.9496i	0.925922	−	1.60374i	0.790071	−	0.613016i	$-0.210044\pi$
$752$	−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	$-0.945441\pi$
$757$		−	9.38564i		−	0.341127i	0.985347	−	0.170563i	$-0.0545588\pi$
$758$	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	−0.647653	−	0.761936i	$-0.724249\pi$
$761$	9.26978	−	16.0557i	0.336029	−	0.582019i	0.983682	+	0.179916i	$0.0575826\pi$
$762$	−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	$0.286065\pi$
$769$			43.3998i			1.56504i	−0.622628	+	0.782518i	$0.713935\pi$
$770$	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	$-0.531334\pi$
$773$	19.8628	−	11.4678i	0.714415	−	0.412468i	0.812694	+	0.582691i	$0.198000\pi$
$774$	−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	−0.990792	−	0.135393i	$-0.956770\pi$
$787$	−17.1870	−	29.7687i	−0.612650	−	1.06114i	0.378142	−	0.925748i	$-0.376563\pi$
$788$	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	$-0.842228\pi$
$797$		−	26.8539i		−	0.951216i	0.879657	−	0.475608i	$-0.157772\pi$
$798$	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	−0.264026	−	0.964516i	$-0.585050\pi$
$809$	12.4937	−	7.21326i	0.439256	−	0.253605i	0.703282	+	0.710911i	$0.251717\pi$
$810$	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	−0.846020	−	0.533151i	$-0.821008\pi$
$821$	1.10924	−	1.92127i	0.0387128	−	0.0670526i	0.884733	+	0.466099i	$0.154341\pi$
$822$	34.1937	−	13.7358i	1.19264	−	0.479091i
$823$	9.77481	+	16.9305i	0.340728	+	0.590159i	0.984568	−	0.175001i	$-0.0559930\pi$
$823$	9.77481	+	16.9305i	0.340728	+	0.590159i	−0.643840	+	0.765160i	$0.722660\pi$
$824$	−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	0.604555	−	0.796564i	$-0.293351\pi$
$829$	−11.1590	−	19.3279i	−0.387567	−	0.671286i	−0.992122	+	0.125278i	$0.960018\pi$
$830$	−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	0.994986	−	0.100016i	$-0.0318893\pi$
$857$	12.0282	+	20.8335i	0.410877	+	0.711659i	−0.584109	+	0.811675i	$0.698556\pi$
$858$	−2.07199	−	5.15798i	−0.0707366	−	0.176091i
$859$	16.8953	−	29.2636i	0.576461	−	0.998460i	−0.419420	−	0.907792i	$-0.637767\pi$
$859$	16.8953	−	29.2636i	0.576461	−	0.998460i	0.995881	−	0.0906678i	$-0.0289001\pi$
$860$	−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	0.479927	−	0.877308i	$-0.340663\pi$
$863$	−1.17157	−	0.676409i	−0.0398808	−	0.0230252i	−0.519808	+	0.854283i	$0.673996\pi$
$864$	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	−0.0419959	−	0.999118i	$-0.513372\pi$
$877$	−27.4895	−	15.8711i	−0.928255	−	0.535928i	−0.886259	+	0.463189i	$0.846705\pi$
$878$	−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	$0.342440\pi$
$883$			52.2974i			1.75995i	−0.475023	+	0.879974i	$0.657560\pi$
$884$	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	−0.625498	−	0.780226i	$-0.715104\pi$
$887$	10.8095	−	18.7226i	0.362947	−	0.628642i	0.988444	+	0.151584i	$0.0484374\pi$
$888$	−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	−0.0422424	−	0.999107i	$-0.513450\pi$
$907$	24.1500	−	13.9430i	0.801889	−	0.462971i	0.844131	+	0.536137i	$0.180117\pi$
$908$	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	$0.748380\pi$
$912$	−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	0.287020	+	0.957925i	$0.407335\pi$
$919$	−20.7984	+	36.0240i	−0.686077	+	1.18832i	−0.973097	+	0.230396i	$0.925998\pi$
$920$	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	0.153702	+	0.988117i	$0.450880\pi$
$929$	−23.7400	+	41.1188i	−0.778883	+	1.34907i	−0.932586	+	0.360948i	$0.882453\pi$
$930$	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	$0.380790\pi$
$937$			56.9775i			1.86137i	−0.365815	+	0.930687i	$0.619210\pi$
$938$	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	$-0.566735\pi$
$941$	16.4078	−	9.47305i	0.534879	−	0.308812i	0.743001	+	0.669290i	$0.233402\pi$
$942$	−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	−0.816609	−	0.577191i	$-0.804149\pi$
$947$	2.81753	−	4.88010i	0.0915573	−	0.158582i	0.908167	+	0.418609i	$0.137482\pi$
$948$	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	$0.00168330\pi$
$953$			0.326501i			0.0105764i	−0.999986	+	0.00528821i	$0.998317\pi$
$954$	−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	0.926672	−	0.375872i	$-0.122657\pi$
$971$	33.1705	+	19.1510i	1.06449	+	0.614585i	0.137821	+	0.990457i	$0.455990\pi$
$972$	−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	0.490214	−	0.871602i	$-0.336919\pi$
$977$	46.5776	−	26.8916i	1.49015	−	0.860339i	0.999937	+	0.0112636i	$0.00358538\pi$
$978$	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	0.802181	−	0.597081i	$-0.203673\pi$
$983$	−3.63683	−	6.29918i	−0.115997	−	0.200913i	−0.918178	+	0.396168i	$0.870340\pi$
$984$	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	0.798655	−	0.601789i	$-0.205545\pi$
$991$	−3.83543	−	6.64316i	−0.121837	−	0.211027i	−0.920492	+	0.390762i	$0.872212\pi$
$992$	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	−0.984897	−	0.173139i	$-0.944609\pi$
$997$	−20.2837	−	35.1324i	−0.642391	−	1.11265i	0.342506	−	0.939516i	$-0.388724\pi$
$998$	−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.341.8	yes	256
3.2	odd	2	inner	840.2.cf.a.341.121	yes	256
7.3	odd	6	inner	840.2.cf.a.101.92	yes	256
8.5	even	2	inner	840.2.cf.a.341.37	yes	256
21.17	even	6	inner	840.2.cf.a.101.37	yes	256
24.5	odd	2	inner	840.2.cf.a.341.92	yes	256
56.45	odd	6	inner	840.2.cf.a.101.121	yes	256
168.101	even	6	inner	840.2.cf.a.101.8	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.8	✓	256	168.101	even	6	inner
840.2.cf.a.101.37	yes	256	21.17	even	6	inner
840.2.cf.a.101.92	yes	256	7.3	odd	6	inner
840.2.cf.a.101.121	yes	256	56.45	odd	6	inner
840.2.cf.a.341.8	yes	256	1.1	even	1	trivial
840.2.cf.a.341.37	yes	256	8.5	even	2	inner
840.2.cf.a.341.92	yes	256	24.5	odd	2	inner
840.2.cf.a.341.121	yes	256	3.2	odd	2	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

Introduction

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