LMFDB - Embedded newform 840.2.dj.a.163.95

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.67"); 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.dj (of order $12$, degree $4$, 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:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			163.95
Character	$\chi$	$=$	840.163
Dual form			840.2.dj.a.67.95

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41370 + 0.0380074i) q^{2} +(0.258819 - 0.965926i) q^{3} +(1.99711 + 0.107462i) q^{4} +(-0.248009 - 2.22227i) q^{5} +(0.402606 - 1.35569i) q^{6} +(0.660700 + 2.56193i) q^{7} +(2.81924 + 0.227825i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.266148 - 3.15106i) q^{10} +(-1.25171 - 2.16802i) q^{11} +(0.620691 - 1.90125i) q^{12} +(2.91006 - 2.91006i) q^{13} +(0.836661 + 3.64692i) q^{14} +(-2.21074 - 0.335608i) q^{15} +(3.97690 + 0.429228i) q^{16} +(4.48505 + 1.20177i) q^{17} +(-1.20530 - 0.739767i) q^{18} +(-6.80025 - 3.92613i) q^{19} +(-0.256491 - 4.46477i) q^{20} +(2.64563 + 0.0248885i) q^{21} +(-1.68714 - 3.11251i) q^{22} +(1.18151 + 4.40947i) q^{23} +(0.949734 - 2.66421i) q^{24} +(-4.87698 + 1.10229i) q^{25} +(4.22457 - 4.00336i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.04418 + 5.18745i) q^{28} +4.44393 q^{29} +(-3.11257 - 0.558474i) q^{30} +(1.81658 - 1.04880i) q^{31} +(5.60585 + 0.757953i) q^{32} +(-2.41811 + 0.647932i) q^{33} +(6.29486 + 1.86941i) q^{34} +(5.52944 - 2.10364i) q^{35} +(-1.67582 - 1.09162i) q^{36} +(-7.94521 + 2.12891i) q^{37} +(-9.46432 - 5.80884i) q^{38} +(-2.05773 - 3.56409i) q^{39} +(-0.192907 - 6.32161i) q^{40} +0.898009 q^{41} +(3.73919 + 0.135739i) q^{42} +(0.112372 + 0.112372i) q^{43} +(-2.26682 - 4.46429i) q^{44} +(-0.896354 + 2.04855i) q^{45} +(1.50272 + 6.27858i) q^{46} +(6.46294 - 1.73174i) q^{47} +(1.44390 - 3.73030i) q^{48} +(-6.12695 + 3.38533i) q^{49} +(-6.93650 + 1.37294i) q^{50} +(2.32164 - 4.02119i) q^{51} +(6.12444 - 5.49900i) q^{52} +(0.970823 + 0.260131i) q^{53} +(-1.02651 + 0.972764i) q^{54} +(-4.50750 + 3.31932i) q^{55} +(1.27900 + 7.37321i) q^{56} +(-5.55238 + 5.55238i) q^{57} +(6.28239 + 0.168902i) q^{58} +(-8.96896 + 5.17823i) q^{59} +(-4.37903 - 0.907818i) q^{60} +(6.16163 + 3.55742i) q^{61} +(2.60797 - 1.41365i) q^{62} +(0.708781 - 2.54904i) q^{63} +(7.89619 + 1.28458i) q^{64} +(-7.18868 - 5.74523i) q^{65} +(-3.44312 + 0.824077i) q^{66} +(-11.7294 - 3.14289i) q^{67} +(8.82801 + 2.88204i) q^{68} +4.56502 q^{69} +(7.89694 - 2.76376i) q^{70} +12.0186i q^{71} +(-2.32762 - 1.60692i) q^{72} +(1.98659 - 7.41406i) q^{73} +(-11.3131 + 2.70767i) q^{74} +(-0.197529 + 4.99610i) q^{75} +(-13.1589 - 8.57168i) q^{76} +(4.72731 - 4.63920i) q^{77} +(-2.77355 - 5.11677i) q^{78} +(-3.56693 + 6.17810i) q^{79} +(-0.0324456 - 8.94421i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.26952 + 0.0341310i) q^{82} +(3.10456 + 3.10456i) q^{83} +(5.28095 + 0.334011i) q^{84} +(1.55832 - 10.2651i) q^{85} +(0.154589 + 0.163131i) q^{86} +(1.15017 - 4.29250i) q^{87} +(-3.03493 - 6.39734i) q^{88} +(-2.89589 - 1.67194i) q^{89} +(-1.34504 + 2.86197i) q^{90} +(9.37806 + 5.53270i) q^{91} +(1.88576 + 8.93316i) q^{92} +(-0.542901 - 2.02613i) q^{93} +(9.20249 - 2.20252i) q^{94} +(-7.03840 + 16.0857i) q^{95} +(2.18303 - 5.21866i) q^{96} +(1.21658 - 1.21658i) q^{97} +(-8.79035 + 4.55298i) q^{98} +2.50342i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	1.41370	+	0.0380074i	0.999639	+	0.0268753i
$2$	1.41370	+	0.0380074i	0.999639	+	0.0268753i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	1.99711	+	0.107462i	0.998555	+	0.0537311i
$5$	−0.248009	−	2.22227i	−0.110913	−	0.993830i
$5$	−0.248009	−	2.22227i	−0.110913	−	0.993830i
$6$	0.402606	−	1.35569i	0.164363	−	0.553460i
$7$	0.660700	+	2.56193i	0.249721	+	0.968318i
$7$	0.660700	+	2.56193i	0.249721	+	0.968318i
$8$	2.81924	+	0.227825i	0.996751	+	0.0805482i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.266148	−	3.15106i	−0.0841634	−	0.996452i
$11$	−1.25171	−	2.16802i	−0.377404	−	0.653683i	0.613280	−	0.789866i	$-0.289850\pi$
$11$	−1.25171	−	2.16802i	−0.377404	−	0.653683i	−0.990684	+	0.136183i	$0.956517\pi$
$12$	0.620691	−	1.90125i	0.179178	−	0.548843i
$13$	2.91006	−	2.91006i	0.807107	−	0.807107i	−0.177088	−	0.984195i	$-0.556668\pi$
$13$	2.91006	−	2.91006i	0.807107	−	0.807107i	0.984195	+	0.177088i	$0.0566678\pi$
$14$	0.836661	+	3.64692i	0.223607	+	0.974679i
$15$	−2.21074	−	0.335608i	−0.570810	−	0.0866536i
$16$	3.97690	+	0.429228i	0.994226	+	0.107307i
$17$	4.48505	+	1.20177i	1.08779	+	0.291471i	0.757782	−	0.652508i	$-0.226283\pi$
$17$	4.48505	+	1.20177i	1.08779	+	0.291471i	0.330004	+	0.943980i	$0.392950\pi$
$18$	−1.20530	−	0.739767i	−0.284092	−	0.174365i
$19$	−6.80025	−	3.92613i	−1.56009	−	0.900716i	−0.997247	−	0.0741484i	$-0.976376\pi$
$19$	−6.80025	−	3.92613i	−1.56009	−	0.900716i	−0.562838	−	0.826567i	$-0.690291\pi$
$20$	−0.256491	−	4.46477i	−0.0573531	−	0.998354i
$21$	2.64563	+	0.0248885i	0.577325	+	0.00543112i
$22$	−1.68714	−	3.11251i	−0.359700	−	0.663590i
$23$	1.18151	+	4.40947i	0.246363	+	0.919437i	0.972694	+	0.232093i	$0.0745572\pi$
$23$	1.18151	+	4.40947i	0.246363	+	0.919437i	−0.726331	+	0.687345i	$0.758776\pi$
$24$	0.949734	−	2.66421i	0.193864	−	0.543829i
$25$	−4.87698	+	1.10229i	−0.975397	+	0.220457i
$26$	4.22457	−	4.00336i	0.828506	−	0.785124i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.04418	+	5.18745i	0.197332	+	0.980337i
$29$	4.44393			0.825216			0.412608	−	0.910909i	$-0.364618\pi$
$29$	4.44393			0.825216			0.412608	+	0.910909i	$0.364618\pi$
$30$	−3.11257	−	0.558474i	−0.568275	−	0.101963i
$31$	1.81658	−	1.04880i	0.326268	−	0.188371i	−0.327915	−	0.944707i	$-0.606346\pi$
$31$	1.81658	−	1.04880i	0.326268	−	0.188371i	0.654183	+	0.756336i	$0.273013\pi$
$32$	5.60585	+	0.757953i	0.990983	+	0.133988i
$33$	−2.41811	+	0.647932i	−0.420940	+	0.112790i
$34$	6.29486	+	1.86941i	1.07956	+	0.320601i
$35$	5.52944	−	2.10364i	0.934646	−	0.355579i
$36$	−1.67582	−	1.09162i	−0.279303	−	0.181937i
$37$	−7.94521	+	2.12891i	−1.30618	+	0.349991i	−0.843785	−	0.536681i	$-0.819678\pi$
$37$	−7.94521	+	2.12891i	−1.30618	+	0.349991i	−0.462399	+	0.886672i	$0.653011\pi$
$38$	−9.46432	−	5.80884i	−1.53531	−	0.942318i
$39$	−2.05773	−	3.56409i	−0.329500	−	0.570711i
$40$	−0.192907	−	6.32161i	−0.0305013	−	0.999535i
$41$	0.898009			0.140245			0.0701227	−	0.997538i	$-0.477661\pi$
$41$	0.898009			0.140245			0.0701227	+	0.997538i	$0.477661\pi$
$42$	3.73919	+	0.135739i	0.576970	+	0.0209449i
$43$	0.112372	+	0.112372i	0.0171365	+	0.0171365i	0.715623	−	0.698487i	$-0.246143\pi$
$43$	0.112372	+	0.112372i	0.0171365	+	0.0171365i	−0.698487	+	0.715623i	$0.746143\pi$
$44$	−2.26682	−	4.46429i	−0.341736	−	0.673017i
$45$	−0.896354	+	2.04855i	−0.133621	+	0.305380i
$46$	1.50272	+	6.27858i	0.221563	+	0.925726i
$47$	6.46294	−	1.73174i	0.942716	−	0.252600i	0.245448	−	0.969410i	$-0.421065\pi$
$47$	6.46294	−	1.73174i	0.942716	−	0.252600i	0.697269	+	0.716810i	$0.254398\pi$
$48$	1.44390	−	3.73030i	0.208409	−	0.538423i
$49$	−6.12695	+	3.38533i	−0.875279	+	0.483619i
$50$	−6.93650	+	1.37294i	−0.980969	+	0.194164i
$51$	2.32164	−	4.02119i	0.325094	−	0.563079i
$52$	6.12444	−	5.49900i	0.849308	−	0.762574i
$53$	0.970823	+	0.260131i	0.133353	+	0.0357318i	0.324878	−	0.945756i	$-0.394677\pi$
$53$	0.970823	+	0.260131i	0.133353	+	0.0357318i	−0.191525	+	0.981488i	$0.561343\pi$
$54$	−1.02651	+	0.972764i	−0.139691	+	0.132376i
$55$	−4.50750	+	3.31932i	−0.607791	+	0.447578i
$56$	1.27900	+	7.37321i	0.170913	+	0.985286i
$57$	−5.55238	+	5.55238i	−0.735431	+	0.735431i
$58$	6.28239	+	0.168902i	0.824918	+	0.0221779i
$59$	−8.96896	+	5.17823i	−1.16766	+	0.674148i	−0.953127	−	0.302569i	$-0.902156\pi$
$59$	−8.96896	+	5.17823i	−1.16766	+	0.674148i	−0.214531	+	0.976717i	$0.568822\pi$
$60$	−4.37903	−	0.907818i	−0.565330	−	0.117199i
$61$	6.16163	+	3.55742i	0.788916	+	0.455481i	0.839581	−	0.543235i	$-0.182801\pi$
$61$	6.16163	+	3.55742i	0.788916	+	0.455481i	−0.0506651	+	0.998716i	$0.516134\pi$
$62$	2.60797	−	1.41365i	0.331212	−	0.179534i
$63$	0.708781	−	2.54904i	0.0892980	−	0.321149i
$64$	7.89619	+	1.28458i	0.987024	+	0.160573i
$65$	−7.18868	−	5.74523i	−0.891645	−	0.712608i
$66$	−3.44312	+	0.824077i	−0.423819	+	0.101437i
$67$	−11.7294	−	3.14289i	−1.43298	−	0.383965i	−0.542908	−	0.839792i	$-0.682677\pi$
$67$	−11.7294	−	3.14289i	−1.43298	−	0.383965i	−0.890068	+	0.455828i	$0.849343\pi$
$68$	8.82801	+	2.88204i	1.07055	+	0.349498i
$69$	4.56502			0.549563
$70$	7.89694	−	2.76376i	0.943865	−	0.330332i
$71$			12.0186i			1.42635i	0.700987	+	0.713174i	$0.252743\pi$
$71$			12.0186i			1.42635i	−0.700987	+	0.713174i	$0.747257\pi$
$72$	−2.32762	−	1.60692i	−0.274312	−	0.189377i
$73$	1.98659	−	7.41406i	0.232513	−	0.867750i	−0.746741	−	0.665115i	$-0.768383\pi$
$73$	1.98659	−	7.41406i	0.232513	−	0.867750i	0.979254	−	0.202636i	$-0.0649507\pi$
$74$	−11.3131	+	2.70767i	−1.31512	+	0.314761i
$75$	−0.197529	+	4.99610i	−0.0228087	+	0.576900i
$76$	−13.1589	−	8.57168i	−1.50944	−	0.983240i
$77$	4.72731	−	4.63920i	0.538727	−	0.528686i
$78$	−2.77355	−	5.11677i	−0.314043	−	0.579360i
$79$	−3.56693	+	6.17810i	−0.401311	+	0.695091i	−0.993884	−	0.110426i	$-0.964779\pi$
$79$	−3.56693	+	6.17810i	−0.401311	+	0.695091i	0.592574	+	0.805516i	$0.298112\pi$
$80$	−0.0324456	−	8.94421i	−0.00362753	−	0.999993i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.26952	+	0.0341310i	0.140195	+	0.00376913i
$83$	3.10456	+	3.10456i	0.340769	+	0.340769i	0.856657	−	0.515887i	$-0.172538\pi$
$83$	3.10456	+	3.10456i	0.340769	+	0.340769i	−0.515887	+	0.856657i	$0.672538\pi$
$84$	5.28095	+	0.334011i	0.576199	+	0.0364436i
$85$	1.55832	−	10.2651i	0.169023	−	1.11340i
$86$	0.154589	+	0.163131i	0.0166698	+	0.0175909i
$87$	1.15017	−	4.29250i	0.123311	−	0.460205i
$88$	−3.03493	−	6.39734i	−0.323525	−	0.681958i
$89$	−2.89589	−	1.67194i	−0.306964	−	0.177226i	0.338603	−	0.940929i	$-0.390046\pi$
$89$	−2.89589	−	1.67194i	−0.306964	−	0.177226i	−0.645567	+	0.763704i	$0.723379\pi$
$90$	−1.34504	+	2.86197i	−0.141779	+	0.301678i
$91$	9.37806	+	5.53270i	0.983087	+	0.579984i
$92$	1.88576	+	8.93316i	0.196604	+	0.931347i
$93$	−0.542901	−	2.02613i	−0.0562962	−	0.210100i
$94$	9.20249	−	2.20252i	0.949165	−	0.227173i
$95$	−7.03840	+	16.0857i	−0.722125	+	1.65036i
$96$	2.18303	−	5.21866i	0.222804	−	0.532627i
$97$	1.21658	−	1.21658i	0.123525	−	0.123525i	−0.642642	−	0.766167i	$-0.722162\pi$
$97$	1.21658	−	1.21658i	0.123525	−	0.123525i	0.766167	+	0.642642i	$0.222162\pi$
$98$	−8.79035	+	4.55298i	−0.887960	+	0.459921i
$99$			2.50342i			0.251603i
$100$	−9.85833	+	1.67730i	−0.985833	+	0.167730i
$101$	0.941621	−	0.543645i	0.0936948	−	0.0540947i	−0.452420	−	0.891805i	$-0.649439\pi$
$101$	0.941621	−	0.543645i	0.0936948	−	0.0540947i	0.546115	+	0.837710i	$0.316106\pi$
$102$	3.43494	−	5.59653i	0.340109	−	0.554139i
$103$	1.93754	+	7.23099i	0.190911	+	0.712491i	0.993287	+	0.115672i	$0.0369022\pi$
$103$	1.93754	+	7.23099i	0.190911	+	0.712491i	−0.802376	+	0.596819i	$0.796431\pi$
$104$	8.86715	−	7.54118i	0.869495	−	0.739473i
$105$	−0.600832	−	5.88549i	−0.0586352	−	0.574365i
$106$	1.36257	+	0.404647i	0.132344	+	0.0393028i
$107$	3.96775	+	14.8079i	0.383577	+	1.43153i	0.840398	+	0.541970i	$0.182321\pi$
$107$	3.96775	+	14.8079i	0.383577	+	1.43153i	−0.456821	+	0.889559i	$0.651012\pi$
$108$	−1.48816	+	1.33618i	−0.143198	+	0.128574i
$109$	8.39032	+	14.5325i	0.803646	+	1.39196i	0.917201	+	0.398425i	$0.130443\pi$
$109$	8.39032	+	14.5325i	0.803646	+	1.39196i	−0.113555	+	0.993532i	$0.536224\pi$
$110$	−6.49842	+	4.52122i	−0.619600	+	0.431081i
$111$			8.22549i			0.780729i
$112$	1.52789	+	10.4721i	0.144372	+	0.989523i
$113$	3.65855	+	3.65855i	0.344168	+	0.344168i	0.857932	−	0.513764i	$-0.171749\pi$
$113$	3.65855	+	3.65855i	0.344168	+	0.344168i	−0.513764	+	0.857932i	$0.671749\pi$
$114$	−8.06045	+	7.63839i	−0.754930	+	0.715401i
$115$	9.50601	−	3.71923i	0.886440	−	0.346820i
$116$	8.87501	+	0.477554i	0.824024	+	0.0443398i
$117$	−3.97522	+	1.06516i	−0.367509	+	0.0984738i
$118$	−12.8762	+	6.97959i	−1.18535	+	0.642523i
$119$	−0.115564	+	12.2844i	−0.0105937	+	1.12611i
$120$	−6.15614	−	1.44982i	−0.561976	−	0.132350i
$121$	2.36645	−	4.09882i	0.215132	−	0.372620i
$122$	8.57550	+	5.26332i	0.776389	+	0.476518i
$123$	0.232422	−	0.867410i	0.0209568	−	0.0782117i
$124$	3.74062	−	1.89936i	0.335918	−	0.170568i
$125$	3.65911	+	10.5646i	0.327281	+	0.944927i
$126$	1.09889	−	3.57665i	0.0978967	−	0.318634i
$127$	−6.55936	−	6.55936i	−0.582049	−	0.582049i	0.353417	−	0.935466i	$-0.385020\pi$
$127$	−6.55936	−	6.55936i	−0.582049	−	0.582049i	−0.935466	+	0.353417i	$0.885020\pi$
$128$	11.1140	+	2.11613i	0.982352	+	0.187041i
$129$	0.137627	−	0.0794589i	0.0121174	−	0.00699596i
$130$	−9.94429	−	8.39527i	−0.872172	−	0.736314i
$131$	3.85449	−	6.67616i	0.336768	−	0.583299i	−0.647055	−	0.762443i	$-0.724000\pi$
$131$	3.85449	−	6.67616i	0.336768	−	0.583299i	0.983823	+	0.179144i	$0.0573329\pi$
$132$	−4.89887	+	1.03414i	−0.426392	+	0.0900099i
$133$	5.56553	−	20.0158i	0.482593	−	1.73559i
$134$	−16.4625	−	4.88891i	−1.42214	−	0.422338i
$135$	1.74675	+	1.39601i	0.150336	+	0.120150i
$136$	12.3706	+	4.40987i	1.06077	+	0.378143i
$137$	−4.63067	−	1.24079i	−0.395625	−	0.106007i	0.0555210	−	0.998458i	$-0.482318\pi$
$137$	−4.63067	−	1.24079i	−0.395625	−	0.106007i	−0.451146	+	0.892450i	$0.648985\pi$
$138$	6.45358	+	0.173504i	0.549365	+	0.0147697i
$139$			20.9415i			1.77623i	0.459617	+	0.888117i	$0.347987\pi$
$139$			20.9415i			1.77623i	−0.459617	+	0.888117i	$0.652013\pi$
$140$	11.2690	−	3.60699i	0.952402	−	0.304846i
$141$		−	6.69093i		−	0.563478i
$142$	−0.456796	+	16.9908i	−0.0383335	+	1.42583i
$143$	−9.95163	−	2.66653i	−0.832197	−	0.222987i
$144$	−3.22949	−	2.36017i	−0.269124	−	0.196681i
$145$	−1.10213	−	9.87561i	−0.0915272	−	0.820125i
$146$	3.09024	−	10.4058i	0.255750	−	0.861188i
$147$	1.68421	+	6.79437i	0.138911	+	0.560390i
$148$	−16.0962	+	3.39786i	−1.32310	+	0.279303i
$149$	−1.65802	+	2.87177i	−0.135830	+	0.235265i	−0.925914	−	0.377734i	$-0.876703\pi$
$149$	−1.65802	+	2.87177i	−0.135830	+	0.235265i	0.790084	+	0.612998i	$0.210037\pi$
$150$	−0.469136	+	7.05549i	−0.0383048	+	0.576078i
$151$	4.94725	−	2.85630i	0.402602	−	0.232442i	−0.285004	−	0.958526i	$-0.591995\pi$
$151$	4.94725	−	2.85630i	0.402602	−	0.232442i	0.687606	+	0.726084i	$0.258662\pi$
$152$	−18.2771	−	12.6180i	−1.48247	−	1.02345i
$153$	−3.28329	−	3.28329i	−0.265438	−	0.265438i
$154$	6.85934	−	6.37877i	0.552741	−	0.514016i
$155$	−2.78126	−	3.77683i	−0.223396	−	0.303362i
$156$	−3.72650	−	7.33900i	−0.298359	−	0.587591i
$157$	−3.64705	+	13.6110i	−0.291067	+	1.08628i	0.653225	+	0.757164i	$0.273416\pi$
$157$	−3.64705	+	13.6110i	−0.291067	+	1.08628i	−0.944291	+	0.329111i	$0.893251\pi$
$158$	−5.27739	+	8.59843i	−0.419847	+	0.684054i
$159$	0.502535	−	0.870416i	0.0398536	−	0.0690285i
$160$	0.294078	−	12.6457i	0.0232489	−	0.999730i
$161$	−10.5161	+	5.94029i	−0.828786	+	0.468160i
$162$	0.673936	+	1.24331i	0.0529494	+	0.0976834i
$163$	−23.6129	+	6.32707i	−1.84951	+	0.495574i	−0.999513	−	0.0312150i	$-0.990062\pi$
$163$	−23.6129	+	6.32707i	−1.84951	+	0.495574i	−0.849996	+	0.526789i	$0.823396\pi$
$164$	1.79342	+	0.0965021i	0.140043	+	0.00753554i
$165$	2.03959	+	5.21301i	0.158782	+	0.405833i
$166$	4.27092	+	4.50692i	0.331488	+	0.349805i
$167$	−8.37606	−	8.37606i	−0.648159	−	0.648159i	0.304389	−	0.952548i	$-0.401548\pi$
$167$	−8.37606	−	8.37606i	−0.648159	−	0.648159i	−0.952548	+	0.304389i	$0.901548\pi$
$168$	7.45300	+	0.672907i	0.575011	+	0.0519159i
$169$		−	3.93695i		−	0.302842i
$170$	2.59315	−	14.4525i	0.198885	−	1.10846i
$171$	3.92613	+	6.80025i	0.300239	+	0.520028i
$172$	0.212343	+	0.236495i	0.0161910	+	0.0180325i
$173$	−5.32478	−	19.8724i	−0.404836	−	1.51087i	−0.804358	−	0.594144i	$-0.797491\pi$
$173$	−5.32478	−	19.8724i	−0.404836	−	1.51087i	0.399523	−	0.916723i	$-0.369176\pi$
$174$	1.78915	−	6.02461i	0.135635	−	0.456724i
$175$	−6.04620	−	11.7662i	−0.457050	−	0.889441i
$176$	−4.04735	−	9.15928i	−0.305080	−	0.690407i
$177$	2.68045	+	10.0036i	0.201475	+	0.751914i
$178$	−4.03038	−	2.47369i	−0.302090	−	0.185411i
$179$	4.73569	−	2.73415i	0.353962	−	0.204360i	−0.312467	−	0.949929i	$-0.601155\pi$
$179$	4.73569	−	2.73415i	0.353962	−	0.204360i	0.666429	+	0.745569i	$0.267822\pi$
$180$	−2.01026	+	3.99485i	−0.149836	+	0.297759i
$181$			1.91630i			0.142438i	0.997461	+	0.0712189i	$0.0226889\pi$
$181$			1.91630i			0.142438i	−0.997461	+	0.0712189i	$0.977311\pi$
$182$	13.0475	+	8.17802i	0.967145	+	0.606195i
$183$	5.03095	−	5.03095i	0.371898	−	0.371898i
$184$	2.32638	+	12.7005i	0.171503	+	0.936294i
$185$	6.70150	+	17.1284i	0.492704	+	1.25931i
$186$	−0.690492	−	2.88498i	−0.0506294	−	0.211537i
$187$	−3.00852	−	11.2280i	−0.220005	−	0.821070i
$188$	13.0933	−	2.76395i	0.954927	−	0.201582i
$189$	−2.27874	−	1.34437i	−0.165754	−	0.0977886i
$190$	−10.5616	+	22.4729i	−0.766218	+	1.63036i
$191$	1.95595	+	1.12927i	0.141528	+	0.0817110i	0.569092	−	0.822274i	$-0.307295\pi$
$191$	1.95595	+	1.12927i	0.141528	+	0.0817110i	−0.427564	+	0.903985i	$0.640628\pi$
$192$	3.28450	−	7.29466i	0.237038	−	0.526447i
$193$	4.31781	−	16.1143i	0.310802	−	1.15993i	−0.617032	−	0.786938i	$-0.711665\pi$
$193$	4.31781	−	16.1143i	0.310802	−	1.15993i	0.927834	−	0.372992i	$-0.121668\pi$
$194$	1.76612	−	1.67364i	0.126800	−	0.120161i
$195$	−7.41003	+	5.45675i	−0.530644	+	0.390766i
$196$	−12.6000	+	6.10247i	−0.900000	+	0.435891i
$197$	−16.7309	−	16.7309i	−1.19203	−	1.19203i	−0.976497	−	0.215530i	$-0.930852\pi$
$197$	−16.7309	−	16.7309i	−1.19203	−	1.19203i	−0.215530	−	0.976497i	$-0.569148\pi$
$198$	−0.0951483	+	3.53909i	−0.00676189	+	0.251512i
$199$	−8.68665	−	15.0457i	−0.615780	−	1.06656i	−0.990247	−	0.139322i	$-0.955508\pi$
$199$	−8.68665	−	15.0457i	−0.615780	−	1.06656i	0.374467	−	0.927240i	$-0.377826\pi$
$200$	−14.0005	+	1.99651i	−0.989985	+	0.141174i
$201$	−6.07159	+	10.5163i	−0.428257	+	0.741763i
$202$	1.35184	−	0.732764i	0.0951148	−	0.0515571i
$203$	2.93610	+	11.3850i	0.206074	+	0.799072i
$204$	5.06869	−	7.78127i	0.354879	−	0.544798i
$205$	−0.222714	−	1.99562i	−0.0155550	−	0.139380i
$206$	2.46427	+	10.2961i	0.171694	+	0.717364i
$207$	1.18151	−	4.40947i	0.0821208	−	0.306479i
$208$	12.8221	−	10.3240i	0.889055	−	0.715838i
$209$			19.6575i			1.35974i
$210$	−0.625705	−	8.34317i	−0.0431778	−	0.575733i
$211$	10.9810			0.755960			0.377980	−	0.925814i	$-0.376619\pi$
$211$	10.9810			0.755960			0.377980	+	0.925814i	$0.376619\pi$
$212$	1.91089	+	0.623838i	0.131240	+	0.0428454i
$213$	11.6091	+	3.11065i	0.795442	+	0.213138i
$214$	5.04641	+	21.0847i	0.344966	+	1.44132i
$215$	0.221851	−	0.277590i	0.0151301	−	0.0189315i
$216$	−2.15460	+	1.83241i	−0.146602	+	0.124679i
$217$	3.88718	+	3.96101i	0.263879	+	0.268891i
$218$	11.3091	+	20.8635i	0.765947	+	1.41305i
$219$	−6.64727	−	3.83780i	−0.449181	−	0.259335i
$220$	−9.35868	+	6.14467i	−0.630962	+	0.414274i
$221$	16.5490	−	9.55458i	1.11321	−	0.642711i
$222$	−0.312629	+	11.6284i	−0.0209823	+	0.780447i
$223$	−12.2628	+	12.2628i	−0.821178	+	0.821178i	−0.986277	−	0.165099i	$-0.947206\pi$
$223$	−12.2628	+	12.2628i	−0.821178	+	0.821178i	0.165099	+	0.986277i	$0.447206\pi$
$224$	1.76196	+	14.8626i	0.117726	+	0.993046i
$225$	4.77473	+	1.48388i	0.318316	+	0.0989256i
$226$	5.03306	+	5.31116i	0.334794	+	0.353293i
$227$	27.5850	+	7.39138i	1.83088	+	0.490583i	0.998020	−	0.0629007i	$-0.0200351\pi$
$227$	27.5850	+	7.39138i	1.83088	+	0.490583i	0.832860	+	0.553483i	$0.186702\pi$
$228$	−11.6854	+	10.4921i	−0.773884	+	0.694853i
$229$	−4.08294	+	7.07185i	−0.269808	+	0.467321i	−0.968812	−	0.247796i	$-0.920294\pi$
$229$	−4.08294	+	7.07185i	−0.269808	+	0.467321i	0.699004	+	0.715118i	$0.253627\pi$
$230$	13.5800	−	4.89659i	0.895441	−	0.322871i
$231$	−3.25760	−	5.76695i	−0.214335	−	0.379437i
$232$	12.5285	+	1.01244i	0.822535	+	0.0664697i
$233$	1.75405	−	0.469995i	0.114911	−	0.0307904i	−0.200905	−	0.979611i	$-0.564388\pi$
$233$	1.75405	−	0.469995i	0.114911	−	0.0307904i	0.315816	+	0.948820i	$0.397722\pi$
$234$	−5.66027	+	1.35473i	−0.370023	+	0.0885614i
$235$	−5.45126	−	13.9329i	−0.355601	−	0.908883i
$236$	−18.4685	+	9.37767i	−1.20219	+	0.610435i
$237$	5.04440	+	5.04440i	0.327669	+	0.327669i
$238$	−0.630271	+	17.3621i	−0.0408544	+	1.12542i
$239$	−7.43701			−0.481060			−0.240530	−	0.970642i	$-0.577321\pi$
$239$	−7.43701			−0.481060			−0.240530	+	0.970642i	$0.577321\pi$
$240$	−8.64784	−	2.28359i	−0.558216	−	0.147405i
$241$	−8.17415	−	14.1580i	−0.526543	−	0.912000i	−0.999522	−	0.0309256i	$-0.990155\pi$
$241$	−8.17415	−	14.1580i	−0.526543	−	0.912000i	0.472978	−	0.881074i	$-0.343179\pi$
$242$	3.50125	−	5.70457i	0.225069	−	0.366704i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	11.9232	+	7.76670i	0.763302	+	0.497212i
$245$	9.04267	+	12.7762i	0.577715	+	0.816239i
$246$	0.361543	−	1.21743i	0.0230512	−	0.0776202i
$247$	−31.2145	+	8.36389i	−1.98613	+	0.532182i
$248$	5.36032	−	2.54296i	0.340380	−	0.161478i
$249$	3.80229	−	2.19525i	0.240960	−	0.139119i
$250$	4.77137	+	15.0743i	0.301768	+	0.953381i
$251$	8.99623			0.567837			0.283918	−	0.958848i	$-0.408366\pi$
$251$	8.99623			0.567837			0.283918	+	0.958848i	$0.408366\pi$
$252$	1.68944	−	5.01456i	0.106425	−	0.315887i
$253$	8.08091	−	8.08091i	0.508042	−	0.508042i
$254$	−9.02368	−	9.52229i	−0.566196	−	0.597482i
$255$	−9.51196	−	4.16201i	−0.595662	−	0.260635i
$256$	15.6315	+	3.41400i	0.976970	+	0.213375i
$257$	0.483750	+	1.80538i	0.0301755	+	0.112617i	0.979371	−	0.202071i	$-0.0647671\pi$
$257$	0.483750	+	1.80538i	0.0301755	+	0.112617i	−0.949195	+	0.314687i	$0.898100\pi$
$258$	0.197583	−	0.107100i	0.0123010	−	0.00666778i
$259$	−10.7035	−	18.9485i	−0.665084	−	1.17740i
$260$	−13.7392	−	12.2464i	−0.852068	−	0.759488i
$261$	−3.84855	−	2.22196i	−0.238219	−	0.137536i
$262$	5.70284	−	9.29161i	0.352323	−	0.574038i
$263$	22.9662	+	6.15376i	1.41615	+	0.379457i	0.884118	−	0.467265i	$-0.154760\pi$
$263$	22.9662	+	6.15376i	1.41615	+	0.379457i	0.532036	+	0.846722i	$0.321427\pi$
$264$	−6.96485	+	1.27577i	−0.428657	+	0.0785180i
$265$	0.337310	−	2.22195i	0.0207208	−	0.136493i
$266$	8.62875	−	28.0848i	0.529063	−	1.72199i
$267$	−2.36448	+	2.36448i	−0.144704	+	0.144704i
$268$	−23.0872	−	7.53716i	−1.41028	−	0.460406i
$269$	−10.7987	−	18.7039i	−0.658410	−	1.14040i	−0.981027	−	0.193870i	$-0.937896\pi$
$269$	−10.7987	−	18.7039i	−0.658410	−	1.14040i	0.322618	−	0.946529i	$-0.395437\pi$
$270$	2.41633	+	2.03994i	0.147053	+	0.124147i
$271$	−19.0805	−	11.0161i	−1.15906	−	0.669182i	−0.207980	−	0.978133i	$-0.566689\pi$
$271$	−19.0805	−	11.0161i	−1.15906	−	0.669182i	−0.951078	+	0.308951i	$0.900022\pi$
$272$	17.3208	+	6.70442i	1.05023	+	0.406515i
$273$	7.77139	−	7.62654i	0.470346	−	0.461579i
$274$	−6.49924	−	1.93010i	−0.392633	−	0.116602i
$275$	8.49434	+	9.19366i	0.512228	+	0.554399i
$276$	9.11684	+	0.490567i	0.548769	+	0.0295287i
$277$	6.97992	−	26.0494i	0.419383	−	1.56516i	−0.356508	−	0.934292i	$-0.616033\pi$
$277$	6.97992	−	26.0494i	0.419383	−	1.56516i	0.775891	−	0.630867i	$-0.217300\pi$
$278$	−0.795932	+	29.6051i	−0.0477368	+	1.77559i
$279$	−2.09761			−0.125580
$280$	16.0681	−	4.67090i	0.960250	−	0.279140i
$281$	−9.91189			−0.591294			−0.295647	−	0.955297i	$-0.595535\pi$
$281$	−9.91189			−0.591294			−0.295647	+	0.955297i	$0.595535\pi$
$282$	0.254305	−	9.45898i	0.0151436	−	0.563274i
$283$	3.94140	−	14.7095i	0.234292	−	0.874390i	−0.744175	−	0.667985i	$-0.767157\pi$
$283$	3.94140	−	14.7095i	0.234292	−	0.874390i	0.978467	−	0.206405i	$-0.0661764\pi$
$284$	−1.29155	+	24.0025i	−0.0766393	+	1.42429i
$285$	13.7159	+	10.9619i	0.812463	+	0.649325i
$286$	−13.9673	−	4.14792i	−0.825904	−	0.245272i
$287$	0.593314	+	2.30063i	0.0350222	+	0.135802i
$288$	−4.47583	−	3.45933i	−0.263741	−	0.203843i
$289$	3.94904	+	2.27998i	0.232297	+	0.134116i
$290$	−1.18274	−	14.0031i	−0.0694530	−	0.822288i
$291$	−0.860252	−	1.49000i	−0.0504289	−	0.0873454i
$292$	4.76418	−	14.5932i	0.278802	−	0.854004i
$293$	−8.30117	+	8.30117i	−0.484959	+	0.484959i	−0.906711	−	0.421752i	$-0.861415\pi$
$293$	−8.30117	+	8.30117i	−0.484959	+	0.484959i	0.421752	+	0.906711i	$0.361415\pi$
$294$	2.12273	+	9.66923i	0.123800	+	0.563921i
$295$	13.7318	+	18.6472i	0.799497	+	1.08568i
$296$	−22.8844	+	4.19179i	−1.33013	+	0.243643i
$297$	2.41811	+	0.647932i	0.140313	+	0.0375968i
$298$	−2.45309	+	3.99681i	−0.142104	+	0.231529i
$299$	16.2701	+	9.39355i	0.940925	+	0.543243i
$300$	−0.931380	+	9.95653i	−0.0537733	+	0.574841i
$301$	−0.213644	+	0.362133i	−0.0123143	+	0.0208730i
$302$	7.10250	−	3.84992i	0.408703	−	0.221538i
$303$	−0.281412	−	1.05024i	−0.0161667	−	0.0603348i
$304$	−25.3587	−	18.5327i	−1.45442	−	1.06292i
$305$	6.37741	−	14.5751i	0.365169	−	0.834567i
$306$	−4.51680	−	4.76638i	−0.258209	−	0.272476i
$307$	−5.42854	+	5.42854i	−0.309823	+	0.309823i	−0.844841	−	0.535018i	$-0.820305\pi$
$307$	−5.42854	+	5.42854i	−0.309823	+	0.309823i	0.535018	+	0.844841i	$0.320305\pi$
$308$	9.93951	−	8.75698i	0.566356	−	0.498975i
$309$	7.48608			0.425868
$310$	−3.78832	−	5.44502i	−0.215162	−	0.309256i
$311$	10.4092	−	6.00978i	0.590254	−	0.340783i	−0.174944	−	0.984578i	$-0.555974\pi$
$311$	10.4092	−	6.00978i	0.590254	−	0.340783i	0.765198	+	0.643795i	$0.222641\pi$
$312$	−4.98923	−	10.5168i	−0.282460	−	0.595397i
$313$	−17.5475	+	4.70184i	−0.991845	+	0.265764i	−0.718025	−	0.696017i	$-0.754954\pi$
$313$	−17.5475	+	4.70184i	−0.991845	+	0.265764i	−0.273819	+	0.961781i	$0.588287\pi$
$314$	−5.67317	+	19.1033i	−0.320155	+	1.07806i
$315$	−5.84045	−	0.942918i	−0.329072	−	0.0531274i
$316$	−7.78746	+	11.9550i	−0.438079	+	0.672524i
$317$	28.5483	−	7.64949i	1.60343	−	0.429638i	0.657354	−	0.753582i	$-0.271676\pi$
$317$	28.5483	−	7.64949i	1.60343	−	0.429638i	0.946076	+	0.323944i	$0.105009\pi$
$318$	0.743517	−	1.21141i	0.0416944	−	0.0679325i
$319$	−5.56250	−	9.63453i	−0.311440	−	0.539430i
$320$	0.896368	−	17.8661i	0.0501085	−	0.998744i
$321$	15.3302			0.855649
$322$	−15.0924	+	7.99811i	−0.841068	+	0.445717i
$323$	−25.7812	−	25.7812i	−1.43451	−	1.43451i
$324$	0.905490	+	1.78328i	0.0503050	+	0.0990711i
$325$	−10.9846	+	17.4001i	−0.609317	+	0.965182i
$326$	−33.6222	+	8.04713i	−1.86216	+	0.445689i
$327$	16.2088	−	4.34315i	0.896351	−	0.240177i
$328$	2.53170	+	0.204589i	0.139790	+	0.0112965i
$329$	8.70666	+	15.4134i	0.480013	+	0.849770i
$330$	2.68525	+	7.44717i	0.147818	+	0.409953i
$331$	10.2623	−	17.7749i	0.564068	−	0.976995i	−0.433067	−	0.901362i	$-0.642569\pi$
$331$	10.2623	−	17.7749i	0.564068	−	0.976995i	0.997136	−	0.0756334i	$-0.0240979\pi$
$332$	5.86652	+	6.53377i	0.321967	+	0.358587i
$333$	7.94521	+	2.12891i	0.435395	+	0.116664i
$334$	−11.5229	−	12.1596i	−0.630505	−	0.665344i
$335$	−4.07535	+	26.8454i	−0.222660	+	1.46672i
$336$	10.5107	+	1.23456i	0.573408	+	0.0673508i
$337$	22.7509	−	22.7509i	1.23932	−	1.23932i	0.279041	−	0.960279i	$-0.409983\pi$
$337$	22.7509	−	22.7509i	1.23932	−	1.23932i	0.960279	−	0.279041i	$-0.0900165\pi$
$338$	0.149633	−	5.56568i	0.00813897	−	0.302733i
$339$	4.48079	−	2.58699i	0.243363	−	0.140506i
$340$	4.21524	−	20.3330i	0.228604	−	1.10271i
$341$	−4.54766	−	2.62559i	−0.246270	−	0.142184i
$342$	5.29192	+	9.76276i	0.286154	+	0.527910i
$343$	−12.7211	−	13.4601i	−0.686872	−	0.726778i
$344$	0.291202	+	0.342404i	0.0157005	+	0.0184612i
$345$	−1.13216	−	10.1447i	−0.0609537	−	0.546173i
$346$	−6.77236	−	28.2960i	−0.364085	−	1.52120i
$347$	−22.2741	−	5.96833i	−1.19574	−	0.320397i	−0.394586	−	0.918859i	$-0.629112\pi$
$347$	−22.2741	−	5.96833i	−1.19574	−	0.320397i	−0.801151	+	0.598462i	$0.795779\pi$
$348$	2.75830	−	8.44900i	0.147861	−	0.452914i
$349$	−14.4900			−0.775631			−0.387815	−	0.921737i	$-0.626770\pi$
$349$	−14.4900			−0.775631			−0.387815	+	0.921737i	$0.626770\pi$
$350$	−8.10033	−	16.8637i	−0.432981	−	0.901403i
$351$			4.11545i			0.219667i
$352$	−5.37362	−	13.1023i	−0.286415	−	0.698357i
$353$	7.16622	−	26.7447i	0.381420	−	1.42348i	−0.462315	−	0.886716i	$-0.652981\pi$
$353$	7.16622	−	26.7447i	0.381420	−	1.42348i	0.843734	−	0.536761i	$-0.180352\pi$
$354$	3.40915	+	14.2440i	0.181194	+	0.757057i
$355$	26.7086	−	2.98072i	1.41755	−	0.158200i
$356$	−5.60374	−	3.65025i	−0.296998	−	0.193463i
$357$	11.8359	+	3.29106i	0.626422	+	0.174181i
$358$	6.79877	−	3.68528i	0.359326	−	0.194773i
$359$	−10.9619	+	18.9866i	−0.578548	+	1.00207i	0.417099	+	0.908861i	$0.363047\pi$
$359$	−10.9619	+	18.9866i	−0.578548	+	1.00207i	−0.995646	+	0.0932126i	$0.970286\pi$
$360$	−2.99374	+	5.57113i	−0.157784	+	0.293624i
$361$	21.3290	+	36.9429i	1.12258	+	1.94436i
$362$	−0.0728337	+	2.70908i	−0.00382805	+	0.142386i
$363$	−3.34667	−	3.34667i	−0.175655	−	0.175655i
$364$	18.1345	+	12.0572i	0.950504	+	0.631969i
$365$	−16.9688	−	2.57599i	−0.888185	−	0.134834i
$366$	7.30348	−	6.92105i	0.381759	−	0.361769i
$367$	4.32024	−	16.1234i	0.225515	−	0.841633i	−0.756683	−	0.653782i	$-0.773181\pi$
$367$	4.32024	−	16.1234i	0.225515	−	0.841633i	0.982198	−	0.187851i	$-0.0601521\pi$
$368$	2.80610	+	18.0432i	0.146278	+	0.940565i
$369$	−0.777698	−	0.449004i	−0.0404854	−	0.0233742i
$370$	8.82293	+	24.4692i	0.458682	+	1.27209i
$371$	−0.0250147	+	2.65905i	−0.00129870	+	0.138051i
$372$	−0.866500	−	4.10475i	−0.0449259	−	0.212822i
$373$	4.62726	+	17.2692i	0.239590	+	0.894164i	0.976026	+	0.217656i	$0.0698410\pi$
$373$	4.62726	+	17.2692i	0.239590	+	0.894164i	−0.736435	+	0.676508i	$0.763492\pi$
$374$	−3.82641	−	15.9873i	−0.197859	−	0.826686i
$375$	11.1517	−	0.800112i	0.575870	−	0.0413176i
$376$	18.6151	−	3.40977i	0.960000	−	0.175845i
$377$	12.9321	−	12.9321i	0.666037	−	0.666037i
$378$	−3.17037	−	1.98715i	−0.163066	−	0.102208i
$379$		−	6.18127i		−	0.317511i	−0.987318	−	0.158755i	$-0.949252\pi$
$379$		−	6.18127i		−	0.317511i	0.987318	−	0.158755i	$-0.0507481\pi$
$380$	−15.7851	+	31.3686i	−0.809757	+	1.60918i
$381$	−8.03355	+	4.63817i	−0.411571	+	0.237621i
$382$	2.72221	+	1.67079i	0.139280	+	0.0854851i
$383$	−2.03011	−	7.57648i	−0.103734	−	0.387140i	0.894465	−	0.447139i	$-0.147557\pi$
$383$	−2.03011	−	7.57648i	−0.103734	−	0.387140i	−0.998198	+	0.0599988i	$0.980890\pi$
$384$	4.92055	−	10.1876i	0.251101	−	0.519886i
$385$	−11.4820	−	9.35481i	−0.585176	−	0.476765i
$386$	6.71656	−	22.6167i	0.341864	−	1.15116i
$387$	−0.0411309	−	0.153503i	−0.00209080	−	0.00780298i
$388$	2.56038	−	2.29891i	0.129984	−	0.116709i
$389$	7.60813	+	13.1777i	0.385748	+	0.668135i	0.991873	−	0.127235i	$-0.0406102\pi$
$389$	7.60813	+	13.1777i	0.385748	+	0.668135i	−0.606125	+	0.795369i	$0.707277\pi$
$390$	−10.6830	+	7.43259i	−0.540954	+	0.376364i
$391$			21.1966i			1.07196i
$392$	−18.0446	+	8.14818i	−0.911389	+	0.411545i
$393$	−5.45107	−	5.45107i	−0.274970	−	0.274970i
$394$	−23.0166	−	24.2884i	−1.15956	−	1.22363i
$395$	14.6140	+	6.39446i	0.735312	+	0.321740i
$396$	−0.269023	+	4.99960i	−0.0135189	+	0.251239i
$397$	−24.7344	+	6.62755i	−1.24138	+	0.332627i	−0.819002	−	0.573791i	$-0.805472\pi$
$397$	−24.7344	+	6.62755i	−1.24138	+	0.332627i	−0.422381	+	0.906418i	$0.638805\pi$
$398$	−11.7085	−	21.6003i	−0.586893	−	1.08273i
$399$	−17.8933	−	10.5563i	−0.895784	−	0.528478i
$400$	−19.8684	+	2.29035i	−0.993421	+	0.114517i
$401$	−3.65413	+	6.32914i	−0.182479	+	0.316062i	−0.942724	−	0.333574i	$-0.891745\pi$
$401$	−3.65413	+	6.32914i	−0.182479	+	0.316062i	0.760245	+	0.649636i	$0.225079\pi$
$402$	−8.98312	+	14.6362i	−0.448037	+	0.729985i
$403$	2.23428	−	8.33846i	0.111298	−	0.415368i
$404$	1.93894	−	0.984531i	0.0964660	−	0.0489823i
$405$	1.80054	−	1.32592i	0.0894695	−	0.0658854i
$406$	3.71806	+	16.2066i	0.184524	+	0.804321i
$407$	14.5606	+	14.5606i	0.721743	+	0.721743i
$408$	7.46137	−	10.8078i	0.369393	−	0.535064i
$409$	10.5869	−	6.11237i	0.523490	−	0.302237i	−0.214871	−	0.976642i	$-0.568933\pi$
$409$	10.5869	−	6.11237i	0.523490	−	0.302237i	0.738362	+	0.674405i	$0.235600\pi$
$410$	−0.239003	−	2.82968i	−0.0118035	−	0.139748i
$411$	−2.39701	+	4.15175i	−0.118236	+	0.204791i
$412$	3.09242	+	14.6493i	0.152353	+	0.721720i
$413$	−19.1920	−	19.5566i	−0.944379	−	0.962316i
$414$	1.83790	−	6.18877i	0.0903279	−	0.304161i
$415$	6.12921	−	7.66913i	0.300871	−	0.376463i
$416$	18.5191	−	14.1077i	0.907972	−	0.691686i
$417$	20.2279	+	5.42006i	0.990566	+	0.265421i
$418$	−0.747129	+	27.7898i	−0.0365433	+	1.35924i
$419$		−	18.1365i		−	0.886025i	−0.896515	−	0.443013i	$-0.853910\pi$
$419$		−	18.1365i		−	0.886025i	0.896515	−	0.443013i	$-0.146090\pi$
$420$	−0.567459	−	11.8185i	−0.0276892	−	0.576686i
$421$			35.1440i			1.71282i	0.516300	+	0.856408i	$0.327309\pi$
$421$			35.1440i			1.71282i	−0.516300	+	0.856408i	$0.672691\pi$
$422$	15.5238	+	0.417357i	0.755687	+	0.0203166i
$423$	−6.46294	−	1.73174i	−0.314239	−	0.0842000i
$424$	2.67772	+	0.954549i	0.130041	+	0.0463570i
$425$	−23.1982	−	0.917182i	−1.12528	−	0.0444899i
$426$	16.2936	+	4.83876i	0.789426	+	0.234439i
$427$	−5.04286	+	18.1360i	−0.244041	+	0.877664i
$428$	6.33275	+	29.9993i	0.306105	+	1.45007i
$429$	−5.15134	+	8.92239i	−0.248709	+	0.430777i
$430$	0.324182	−	0.383998i	0.0156335	−	0.0185180i
$431$	8.59615	−	4.96299i	0.414062	−	0.239059i	−0.278472	−	0.960444i	$-0.589828\pi$
$431$	8.59615	−	4.96299i	0.414062	−	0.239059i	0.692533	+	0.721386i	$0.256494\pi$
$432$	−3.11561	+	2.50859i	−0.149900	+	0.120694i
$433$	17.6891	+	17.6891i	0.850083	+	0.850083i	0.990143	−	0.140060i	$-0.0447294\pi$
$433$	17.6891	+	17.6891i	0.850083	+	0.850083i	−0.140060	+	0.990143i	$0.544729\pi$
$434$	5.34476	+	5.74743i	0.256557	+	0.275885i
$435$	−9.82436	−	1.49142i	−0.471042	−	0.0715080i
$436$	15.1947	+	29.9246i	0.727694	+	1.43313i
$437$	9.27754	−	34.6243i	0.443805	−	1.65630i
$438$	−9.25139	−	5.67815i	−0.442049	−	0.271313i
$439$	8.92288	−	15.4549i	0.425866	−	0.737621i	−0.570635	−	0.821204i	$-0.693303\pi$
$439$	8.92288	−	15.4549i	0.425866	−	0.737621i	0.996501	+	0.0835826i	$0.0266362\pi$
$440$	−13.4639	+	8.33104i	−0.641868	+	0.397167i
$441$	6.99876	+	0.131692i	0.333274	+	0.00627103i
$442$	23.7585	−	12.8784i	1.13008	−	0.612561i
$443$	−4.45800	+	1.19452i	−0.211806	+	0.0567533i	−0.363162	−	0.931726i	$-0.618303\pi$
$443$	−4.45800	+	1.19452i	−0.211806	+	0.0567533i	0.151356	+	0.988479i	$0.451636\pi$
$444$	−0.883930	+	16.4272i	−0.0419494	+	0.779601i
$445$	−2.99730	+	6.85011i	−0.142086	+	0.324726i
$446$	−17.8020	+	16.8699i	−0.842951	+	0.798812i
$447$	2.34479	+	2.34479i	0.110905	+	0.110905i
$448$	1.92600	+	21.0782i	0.0909951	+	0.995851i
$449$			5.02676i			0.237228i	0.992940	+	0.118614i	$0.0378450\pi$
$449$			5.02676i			0.237228i	−0.992940	+	0.118614i	$0.962155\pi$
$450$	6.69366	+	2.27925i	0.315542	+	0.107445i
$451$	−1.12404	−	1.94690i	−0.0529292	−	0.0916760i
$452$	6.91338	+	7.69969i	0.325178	+	0.362163i
$453$	−1.47853	−	5.51794i	−0.0694673	−	0.259256i
$454$	38.7160	+	11.4976i	1.81703	+	0.539611i
$455$	9.96931	−	22.2127i	0.467369	−	1.04135i
$456$	−16.9185	+	14.3885i	−0.792279	+	0.673804i
$457$	−8.69348	−	32.4445i	−0.406664	−	1.51769i	−0.800967	−	0.598709i	$-0.795681\pi$
$457$	−8.69348	−	32.4445i	−0.406664	−	1.51769i	0.394303	−	0.918980i	$-0.370986\pi$
$458$	−6.04084	+	9.84232i	−0.282270	+	0.459901i
$459$	−4.02119	+	2.32164i	−0.187693	+	0.108365i
$460$	19.3842	−	6.40618i	0.903794	−	0.298690i
$461$			0.392085i			0.0182612i	0.999958	+	0.00913062i	$0.00290641\pi$
$461$			0.392085i			0.0182612i	−0.999958	+	0.00913062i	$0.997094\pi$
$462$	−4.38609	−	8.27656i	−0.204060	−	0.385060i
$463$	8.76491	−	8.76491i	0.407340	−	0.407340i	−0.473470	−	0.880810i	$-0.656999\pi$
$463$	8.76491	−	8.76491i	0.407340	−	0.407340i	0.880810	+	0.473470i	$0.156999\pi$
$464$	17.6731	+	1.90746i	0.820451	+	0.0885515i
$465$	−4.36797	+	1.70897i	−0.202560	+	0.0792517i
$466$	2.49756	−	0.597767i	0.115697	−	0.0276910i
$467$	−6.99059	−	26.0892i	−0.323486	−	1.20727i	−0.915825	−	0.401577i	$-0.868462\pi$
$467$	−6.99059	−	26.0892i	−0.323486	−	1.20727i	0.592339	−	0.805689i	$-0.298204\pi$
$468$	−8.05342	+	1.70005i	−0.372270	+	0.0785849i
$469$	0.302226	−	32.1264i	0.0139555	−	1.48346i
$470$	−7.17691	−	19.9042i	−0.331046	−	0.918112i
$471$	12.2033	+	7.04557i	0.562297	+	0.324643i
$472$	−26.4653	+	12.5553i	−1.21817	+	0.577905i
$473$	0.102968	−	0.384281i	0.00473447	−	0.0176693i
$474$	6.93955	+	7.32300i	0.318744	+	0.336357i
$475$	37.4924	+	11.6518i	1.72027	+	0.534623i
$476$	−1.55090	+	24.5209i	−0.0710855	+	1.12391i
$477$	−0.710692	−	0.710692i	−0.0325403	−	0.0325403i
$478$	−10.5137	−	0.282661i	−0.480887	−	0.0129286i
$479$	16.2572	+	28.1583i	0.742812	+	1.28659i	0.951210	+	0.308544i	$0.0998416\pi$
$479$	16.2572	+	28.1583i	0.742812	+	1.28659i	−0.208398	+	0.978044i	$0.566825\pi$
$480$	−12.1387	−	3.55700i	−0.554053	−	0.162354i
$481$	−16.9258	+	29.3163i	−0.771750	+	1.33671i
$482$	−11.0177	−	20.3259i	−0.501843	−	0.925821i
$483$	3.01611	+	11.6952i	0.137238	+	0.532152i
$484$	5.16654	−	7.93149i	0.234843	−	0.360522i
$485$	−3.00530	−	2.40185i	−0.136463	−	0.109062i
$486$	1.37537	−	0.329181i	0.0623880	−	0.0149319i
$487$	1.47724	−	5.51312i	0.0669399	−	0.249823i	−0.924345	−	0.381557i	$-0.875388\pi$
$487$	1.47724	−	5.51312i	0.0669399	−	0.249823i	0.991285	+	0.131734i	$0.0420545\pi$
$488$	16.5606	+	11.4330i	0.749664	+	0.517546i
$489$			24.4459i			1.10548i
$490$	12.2981	+	18.4054i	0.555569	+	0.831470i
$491$	−24.8485			−1.12140			−0.560699	−	0.828020i	$-0.689467\pi$
$491$	−24.8485			−1.12140			−0.560699	+	0.828020i	$0.689467\pi$
$492$	0.557386	−	1.70734i	0.0251289	−	0.0769727i
$493$	19.9312	+	5.34056i	0.897658	+	0.240527i
$494$	−44.4459	+	10.6377i	−1.99971	+	0.478612i
$495$	5.56327	−	0.620869i	0.250050	−	0.0279060i
$496$	7.67455	−	3.39126i	0.344597	−	0.152272i
$497$	−30.7908	+	7.94070i	−1.38116	+	0.356189i
$498$	5.45874	−	2.95892i	0.244612	−	0.132592i
$499$	5.26914	+	3.04214i	0.235879	+	0.136185i	0.613281	−	0.789865i	$-0.289849\pi$
$499$	5.26914	+	3.04214i	0.235879	+	0.136185i	−0.377402	+	0.926049i	$0.623183\pi$
$500$	6.17236	+	21.4919i	0.276036	+	0.961147i
$501$	−10.2585	+	5.92277i	−0.458318	+	0.264610i
$502$	12.7180	+	0.341923i	0.567632	+	0.0152608i
$503$	27.8070	−	27.8070i	1.23985	−	1.23985i	0.279790	−	0.960061i	$-0.409735\pi$
$503$	27.8070	−	27.8070i	1.23985	−	1.23985i	0.960061	−	0.279790i	$-0.0902650\pi$
$504$	2.57896	−	7.02488i	0.114876	−	0.312913i
$505$	−1.44166	−	1.95771i	−0.0641529	−	0.0871169i
$506$	11.7311	−	11.1169i	0.521513	−	0.494205i
$507$	−3.80280	−	1.01896i	−0.168888	−	0.0452535i
$508$	−12.3949	−	13.8047i	−0.549934	−	0.612483i
$509$	16.5276	−	28.6266i	0.732571	−	1.26885i	−0.223210	−	0.974770i	$-0.571654\pi$
$509$	16.5276	−	28.6266i	0.732571	−	1.26885i	0.955781	−	0.294080i	$-0.0950131\pi$
$510$	−13.2889	−	6.24537i	−0.588442	−	0.276550i
$511$	20.3068	+	0.191034i	0.898321	+	0.00845085i
$512$	21.9686	+	5.42049i	0.970883	+	0.239554i
$513$	7.58470	−	2.03231i	0.334873	−	0.0897288i
$514$	0.615261	+	2.57066i	0.0271380	+	0.113387i
$515$	15.5887	−	6.09909i	0.686920	−	0.268758i
$516$	0.283395	−	0.143898i	0.0124758	−	0.00633478i
$517$	−11.8442	−	11.8442i	−0.520906	−	0.520906i
$518$	−14.4114	−	27.1943i	−0.633201	−	1.19485i
$519$	−20.5734			−0.903071
$520$	−18.9577	−	17.8349i	−0.831349	−	0.782113i
$521$	−18.5173	−	32.0729i	−0.811258	−	1.40514i	−0.911984	−	0.410227i	$-0.865450\pi$
$521$	−18.5173	−	32.0729i	−0.811258	−	1.40514i	0.100725	−	0.994914i	$-0.467884\pi$
$522$	−5.35626	−	3.28747i	−0.234437	−	0.143889i
$523$	−5.22057	+	1.39885i	−0.228280	+	0.0611673i	−0.371145	−	0.928575i	$-0.621035\pi$
$523$	−5.22057	+	1.39885i	−0.228280	+	0.0611673i	0.142866	+	0.989742i	$0.454368\pi$
$524$	8.41527	−	12.9188i	0.367623	−	0.564362i
$525$	−12.9301	+	2.79487i	−0.564318	+	0.121978i
$526$	32.2334	+	9.57247i	1.40544	+	0.417380i
$527$	9.40789	−	2.52084i	0.409814	−	0.109809i
$528$	−9.89472	+	1.53884i	−0.430612	+	0.0669694i
$529$	1.87116	−	1.08031i	0.0813547	−	0.0469702i
$530$	0.561306	−	3.12835i	0.0243816	−	0.135887i
$531$	10.3565			0.449432
$532$	13.2659	−	39.3756i	0.575151	−	1.70715i
$533$	2.61326	−	2.61326i	0.113193	−	0.113193i
$534$	−3.43254	+	3.25281i	−0.148541	+	0.140763i
$535$	31.9230	−	12.4899i	1.38015	−	0.539985i
$536$	−32.3520	−	11.5328i	−1.39739	−	0.498141i
$537$	−1.41530	−	5.28197i	−0.0610747	−	0.227934i
$538$	−14.5553	−	26.8522i	−0.627523	−	1.15768i
$539$	15.0086	+	9.04591i	0.646467	+	0.389635i
$540$	3.33844	+	2.97571i	0.143664	+	0.128054i
$541$	5.14830	+	2.97237i	0.221343	+	0.127792i	0.606572	−	0.795029i	$-0.292544\pi$
$541$	5.14830	+	2.97237i	0.221343	+	0.127792i	−0.385229	+	0.922821i	$0.625878\pi$
$542$	−26.5555	−	16.2987i	−1.14065	−	0.700091i
$543$	1.85101	+	0.495976i	0.0794343	+	0.0212844i
$544$	24.2316	+	10.1364i	1.03892	+	0.434594i
$545$	30.2142	−	22.2497i	1.29423	−	0.953074i
$546$	11.2763	−	10.4863i	0.482581	−	0.448772i
$547$	9.36495	−	9.36495i	0.400416	−	0.400416i	−0.477963	−	0.878380i	$-0.658625\pi$
$547$	9.36495	−	9.36495i	0.400416	−	0.400416i	0.878380	+	0.477963i	$0.158625\pi$
$548$	−9.11463	−	2.97561i	−0.389358	−	0.127112i
$549$	−3.55742	−	6.16163i	−0.151827	−	0.262972i
$550$	11.6590	+	13.3200i	0.497143	+	0.567965i
$551$	−30.2198	−	17.4474i	−1.28741	−	0.743285i
$552$	12.8699	+	1.04002i	0.547778	+	0.0442663i
$553$	−18.1845	−	5.05634i	−0.773284	−	0.215017i
$554$	10.8576	−	36.5609i	0.461296	−	1.55332i
$555$	18.2793	−	2.03999i	0.775912	−	0.0865929i
$556$	−2.25042	+	41.8225i	−0.0954391	+	1.77367i
$557$	−0.258379	+	0.964283i	−0.0109479	+	0.0408580i	−0.971184	−	0.238332i	$-0.923399\pi$
$557$	−0.258379	+	0.964283i	−0.0109479	+	0.0408580i	0.960236	+	0.279190i	$0.0900660\pi$
$558$	−2.96539	−	0.0797246i	−0.125535	−	0.00337501i
$559$	0.654018			0.0276620
$560$	22.8930	−	5.99257i	0.967406	−	0.253232i
$561$	−11.6240			−0.490767
$562$	−14.0125	−	0.376725i	−0.591080	−	0.0158912i
$563$	−9.73850	+	36.3446i	−0.410429	+	1.53174i	0.383390	+	0.923587i	$0.374756\pi$
$563$	−9.73850	+	36.3446i	−0.410429	+	1.53174i	−0.793819	+	0.608154i	$0.791910\pi$
$564$	0.719022	−	13.3625i	0.0302763	−	0.562664i
$565$	7.22295	−	9.03765i	0.303872	−	0.380217i
$566$	6.13104	−	20.6451i	0.257707	−	0.867777i
$567$	−1.88834	+	1.85315i	−0.0793030	+	0.0778249i
$568$	−2.73814	+	33.8833i	−0.114890	+	1.42171i
$569$	−2.34364	−	1.35310i	−0.0982505	−	0.0567249i	0.450070	−	0.892993i	$-0.351399\pi$
$569$	−2.34364	−	1.35310i	−0.0982505	−	0.0567249i	−0.548320	+	0.836268i	$0.684732\pi$
$570$	18.9736	+	16.0181i	0.794718	+	0.670925i
$571$	3.58498	+	6.20936i	0.150027	+	0.259854i	0.931237	−	0.364414i	$-0.118731\pi$
$571$	3.58498	+	6.20936i	0.150027	+	0.259854i	−0.781210	+	0.624268i	$0.785397\pi$
$572$	−19.5880	−	6.39479i	−0.819014	−	0.267379i
$573$	1.59703	−	1.59703i	0.0667168	−	0.0667168i
$574$	0.751329	+	3.27496i	0.0313599	+	0.136694i
$575$	−10.6227	−	20.2025i	−0.442998	−	0.842504i
$576$	−6.19601	−	5.06058i	−0.258167	−	0.210857i
$577$	−26.2319	−	7.02881i	−1.09205	−	0.292613i	−0.332525	−	0.943094i	$-0.607901\pi$
$577$	−26.2319	−	7.02881i	−1.09205	−	0.292613i	−0.759522	+	0.650481i	$0.774567\pi$
$578$	5.49611	+	3.37331i	0.228608	+	0.140311i
$579$	−14.4477	−	8.34136i	−0.600424	−	0.346655i
$580$	−1.13983	−	19.8411i	−0.0473287	−	0.823858i
$581$	−5.90247	+	10.0048i	−0.244876	+	0.415070i
$582$	−1.15951	−	2.13911i	−0.0480632	−	0.0886691i
$583$	−0.651217	−	2.43037i	−0.0269706	−	0.100656i
$584$	7.28978	−	20.4494i	0.301653	−	0.846202i
$585$	3.35296	+	8.56985i	0.138628	+	0.354320i
$586$	−12.0509	+	11.4199i	−0.497818	+	0.471751i
$587$	−24.6708	+	24.6708i	−1.01827	+	1.01827i	−0.0184450	+	0.999830i	$0.505872\pi$
$587$	−24.6708	+	24.6708i	−1.01827	+	1.01827i	−0.999830	+	0.0184450i	$0.994128\pi$
$588$	2.63341	+	13.7501i	0.108600	+	0.567044i
$589$	−16.4710			−0.678674
$590$	18.7040	+	26.8835i	0.770030	+	1.10678i
$591$	−20.4911	+	11.8305i	−0.842891	+	0.486643i
$592$	−32.5111	+	5.05617i	−1.33620	+	0.207807i
$593$	18.2308	−	4.88492i	0.748648	−	0.200600i	0.135730	−	0.990746i	$-0.456662\pi$
$593$	18.2308	−	4.88492i	0.748648	−	0.200600i	0.612918	+	0.790146i	$0.289995\pi$
$594$	3.39387	+	1.00789i	0.139252	+	0.0413542i
$595$	27.3279	−	2.78982i	1.12034	−	0.114372i
$596$	−3.61985	+	5.55707i	−0.148275	+	0.227626i
$597$	−16.7813	+	4.49654i	−0.686813	+	0.184031i
$598$	22.6441	+	13.8981i	0.925985	+	0.568335i
$599$	20.8175	+	36.0569i	0.850579	+	1.47325i	0.880686	+	0.473700i	$0.157082\pi$
$599$	20.8175	+	36.0569i	0.850579	+	1.47325i	−0.0301067	+	0.999547i	$0.509585\pi$
$600$	−1.69512	+	14.0402i	−0.0692028	+	0.573188i
$601$	−21.5895			−0.880654			−0.440327	−	0.897837i	$-0.645137\pi$
$601$	−21.5895			−0.880654			−0.440327	+	0.897837i	$0.645137\pi$
$602$	−0.315793	+	0.503828i	−0.0128708	+	0.0205345i
$603$	8.58653	+	8.58653i	0.349670	+	0.349670i
$604$	10.1872	−	5.17270i	0.414509	−	0.210474i
$605$	−9.69559	−	4.24236i	−0.394182	−	0.172477i
$606$	−0.357915	−	1.49543i	−0.0145393	−	0.0607475i
$607$	−5.67556	+	1.52076i	−0.230364	+	0.0617258i	−0.372154	−	0.928171i	$-0.621381\pi$
$607$	−5.67556	+	1.52076i	−0.230364	+	0.0617258i	0.141790	+	0.989897i	$0.454714\pi$
$608$	−35.1454	−	27.1635i	−1.42533	−	1.10163i
$609$	11.7570	+	0.110603i	0.476418	+	0.00448184i
$610$	9.56972	−	20.3624i	0.387467	−	0.824451i
$611$	13.7681	−	23.8470i	0.556997	−	0.964748i
$612$	−6.20426	−	6.90992i	−0.250792	−	0.279317i
$613$	11.4187	+	3.05963i	0.461197	+	0.123577i	0.481934	−	0.876208i	$-0.339935\pi$
$613$	11.4187	+	3.05963i	0.461197	+	0.123577i	−0.0207368	+	0.999785i	$0.506601\pi$
$614$	−7.88067	+	7.46802i	−0.318038	+	0.301385i
$615$	−1.98526	−	0.301379i	−0.0800535	−	0.0121528i
$616$	14.3843	−	12.0020i	0.579561	−	0.483574i
$617$	−4.22652	+	4.22652i	−0.170153	+	0.170153i	−0.787047	−	0.616893i	$-0.788391\pi$
$617$	−4.22652	+	4.22652i	−0.170153	+	0.170153i	0.616893	+	0.787047i	$0.288391\pi$
$618$	10.5831	+	0.284526i	0.425714	+	0.0114453i
$619$	−33.6158	+	19.4081i	−1.35113	+	0.780078i	−0.988408	−	0.151818i	$-0.951487\pi$
$619$	−33.6158	+	19.4081i	−1.35113	+	0.780078i	−0.362726	+	0.931896i	$0.618154\pi$
$620$	−5.14861	−	7.84162i	−0.206773	−	0.314927i
$621$	−3.95342	−	2.28251i	−0.158645	−	0.0915939i
$622$	14.9440	−	8.10041i	0.599199	−	0.324797i
$623$	2.37008	−	8.52371i	0.0949553	−	0.341495i
$624$	−6.65357	−	15.0573i	−0.266356	−	0.602773i
$625$	22.5699	−	10.7517i	0.902797	−	0.430067i
$626$	−24.9857	+	5.98008i	−0.998629	+	0.239012i
$627$	18.9877	+	5.08773i	0.758294	+	0.203184i
$628$	−8.74624	+	26.7907i	−0.349013	+	1.06907i
$629$	−38.1932			−1.52286
$630$	−8.22083	−	1.55499i	−0.327526	−	0.0619521i
$631$		−	12.3972i		−	0.493524i	−0.969076	−	0.246762i	$-0.920633\pi$
$631$		−	12.3972i		−	0.493524i	0.969076	−	0.246762i	$-0.0793666\pi$
$632$	−11.4635	+	16.6049i	−0.455995	+	0.660507i
$633$	2.84208	−	10.6068i	0.112963	−	0.421582i
$634$	40.6495	−	9.72905i	1.61440	−	0.386390i
$635$	−12.9499	+	16.2035i	−0.513901	+	0.643015i
$636$	1.09716	−	1.68431i	0.0435050	−	0.0667874i
$637$	−7.97829	+	27.6814i	−0.316111	+	1.09678i
$638$	−7.49753	−	13.8318i	−0.296830	−	0.547605i
$639$	6.00931	−	10.4084i	0.237725	−	0.411751i
$640$	1.94624	−	25.2232i	0.0769319	−	0.997036i
$641$	19.7202	+	34.1565i	0.778903	+	1.34910i	0.932574	+	0.360978i	$0.117557\pi$
$641$	19.7202	+	34.1565i	0.778903	+	1.34910i	−0.153671	+	0.988122i	$0.549110\pi$
$642$	21.6724	+	0.582661i	0.855340	+	0.0229958i
$643$	−27.8250	−	27.8250i	−1.09731	−	1.09731i	−0.994724	−	0.102589i	$-0.967287\pi$
$643$	−27.8250	−	27.8250i	−1.09731	−	1.09731i	−0.102589	−	0.994724i	$-0.532713\pi$
$644$	−21.6402	+	10.7333i	−0.852743	+	0.422952i
$645$	−0.210712	−	0.286138i	−0.00829677	−	0.0112667i
$646$	−35.4671	−	37.4269i	−1.39543	−	1.47254i
$647$	6.83790	−	25.5194i	0.268826	−	1.00327i	−0.691041	−	0.722815i	$-0.742848\pi$
$647$	6.83790	−	25.5194i	0.268826	−	1.00327i	0.959867	−	0.280456i	$-0.0904855\pi$
$648$	1.21232	+	2.55544i	0.0476243	+	0.100387i
$649$	22.4530	+	12.9633i	0.881358	+	0.508852i
$650$	−16.1903	+	24.1810i	−0.635036	+	0.948457i
$651$	4.83211	−	2.72954i	0.189385	−	0.106979i
$652$	−47.8376	+	10.0984i	−1.87346	+	0.395482i
$653$	0.836253	+	3.12094i	0.0327251	+	0.122132i	0.980356	−	0.197235i	$-0.0631963\pi$
$653$	0.836253	+	3.12094i	0.0327251	+	0.122132i	−0.947631	+	0.319367i	$0.896530\pi$
$654$	23.0796	−	5.52386i	0.902482	−	0.216000i
$655$	−15.7922	−	6.90997i	−0.617052	−	0.269995i
$656$	3.57129	+	0.385451i	0.139436	+	0.0150493i
$657$	−5.42747	+	5.42747i	−0.211746	+	0.211746i
$658$	11.7228	+	22.1209i	0.457002	+	0.862363i
$659$		−	39.2336i		−	1.52832i	−0.645025	−	0.764161i	$-0.723153\pi$
$659$		−	39.2336i		−	1.52832i	0.645025	−	0.764161i	$-0.276847\pi$
$660$	3.51309	+	10.6301i	0.136747	+	0.413778i
$661$	−20.4849	+	11.8269i	−0.796769	+	0.460015i	−0.842340	−	0.538946i	$-0.818823\pi$
$661$	−20.4849	+	11.8269i	−0.796769	+	0.460015i	0.0455709	+	0.998961i	$0.485489\pi$
$662$	15.1835	−	24.7383i	0.590122	−	0.961483i
$663$	−4.94581	−	18.4580i	−0.192080	−	0.716851i
$664$	8.04519	+	9.45978i	0.312214	+	0.367110i
$665$	−45.8607	−	7.40404i	−1.77840	−	0.287116i
$666$	11.1512	+	3.31163i	0.432102	+	0.128323i
$667$	5.25056	+	19.5953i	0.203302	+	0.758735i
$668$	−15.8278	−	17.6280i	−0.612396	−	0.682049i
$669$	8.67111	+	15.0188i	0.335245	+	0.580661i
$670$	−6.78166	+	37.7965i	−0.261998	+	1.46021i
$671$		−	17.8114i		−	0.687601i
$672$	14.8122	+	2.14479i	0.571391	+	0.0827370i
$673$	34.4348	+	34.4348i	1.32737	+	1.32737i	0.907661	+	0.419704i	$0.137866\pi$
$673$	34.4348	+	34.4348i	1.32737	+	1.32737i	0.419704	+	0.907661i	$0.362134\pi$
$674$	33.0277	−	31.2983i	1.27218	−	1.20557i
$675$	2.66911	−	4.22798i	0.102734	−	0.162735i
$676$	0.423074	−	7.86253i	0.0162721	−	0.302405i
$677$	−16.0692	+	4.30573i	−0.617590	+	0.165483i	−0.554032	−	0.832496i	$-0.686911\pi$
$677$	−16.0692	+	4.30573i	−0.617590	+	0.165483i	−0.0635578	+	0.997978i	$0.520245\pi$
$678$	6.43284	−	3.48693i	0.247052	−	0.133915i
$679$	3.92059	+	2.31300i	0.150458	+	0.0887647i
$680$	6.73190	−	28.5846i	0.258157	−	1.09617i
$681$	14.2790	−	24.7320i	0.547174	−	0.947733i
$682$	−6.32925	−	3.88465i	−0.242359	−	0.148751i
$683$	7.14976	−	26.6833i	0.273578	−	1.02101i	−0.683210	−	0.730222i	$-0.739417\pi$
$683$	7.14976	−	26.6833i	0.273578	−	1.02101i	0.956788	−	0.290785i	$-0.0939165\pi$
$684$	7.11014	+	14.0028i	0.271863	+	0.535409i
$685$	−1.60891	+	10.5983i	−0.0614734	+	0.404942i
$686$	−17.4722	−	19.5121i	−0.667092	−	0.744975i
$687$	5.77415	+	5.77415i	0.220297	+	0.220297i
$688$	0.398659	+	0.495125i	0.0151987	+	0.0188765i
$689$	3.58216	−	2.06816i	0.136469	−	0.0787906i
$690$	−1.21497	−	14.3846i	−0.0462531	−	0.547613i
$691$	11.5239	−	19.9599i	0.438389	−	0.759311i	−0.559177	−	0.829048i	$-0.688883\pi$
$691$	11.5239	−	19.9599i	0.438389	−	0.759311i	0.997565	+	0.0697372i	$0.0222161\pi$
$692$	−8.49865	−	40.2595i	−0.323070	−	1.53044i
$693$	−6.41357	+	1.65401i	−0.243631	+	0.0628305i
$694$	−31.2621	−	9.28403i	−1.18669	−	0.352417i
$695$	46.5377	−	5.19368i	1.76528	−	0.197007i
$696$	4.22055	−	11.8395i	0.159979	−	0.448777i
$697$	4.02762	+	1.07920i	0.152557	+	0.0408775i
$698$	−20.4845	−	0.550726i	−0.775351	−	0.0208453i
$699$		−	1.81592i		−	0.0686845i
$700$	−10.8105	−	24.1481i	−0.408599	−	0.912714i
$701$		−	19.9955i		−	0.755219i	−0.925965	−	0.377610i	$-0.876746\pi$
$701$		−	19.9955i		−	0.755219i	0.925965	−	0.377610i	$-0.123254\pi$
$702$	−0.156418	+	5.81803i	−0.00590360	+	0.219587i
$703$	62.3878	+	16.7168i	2.35300	+	0.630485i
$704$	−7.09872	−	18.7270i	−0.267543	−	0.705802i
$705$	−14.8691	+	1.65941i	−0.560001	+	0.0624970i
$706$	11.1474	−	37.5367i	0.419538	−	1.41271i
$707$	2.01491	+	2.05318i	0.0757785	+	0.0772178i
$708$	4.27815	+	20.2663i	0.160783	+	0.761654i
$709$	−9.81393	+	16.9982i	−0.368570	+	0.638381i	−0.989342	−	0.145609i	$-0.953486\pi$
$709$	−9.81393	+	16.9982i	−0.368570	+	0.638381i	0.620772	+	0.783991i	$0.286819\pi$
$710$	37.8714	−	3.19873i	1.42129	−	0.120046i
$711$	6.17810	−	3.56693i	0.231697	−	0.133770i
$712$	−7.78329	−	5.37336i	−0.291691	−	0.201375i
$713$	6.77098	+	6.77098i	0.253575	+	0.253575i
$714$	16.6074	+	5.10243i	0.621515	+	0.190954i
$715$	−3.45767	+	22.7766i	−0.129309	+	0.851795i
$716$	9.75151	−	4.95149i	0.364431	−	0.185046i
$717$	−1.92484	+	7.18360i	−0.0718845	+	0.268277i
$718$	−16.2185	+	26.4248i	−0.605270	+	0.986163i
$719$	−7.81531	+	13.5365i	−0.291462	+	0.504827i	−0.974156	−	0.225878i	$-0.927475\pi$
$719$	−7.81531	+	13.5365i	−0.291462	+	0.504827i	0.682694	+	0.730705i	$0.260808\pi$
$720$	−4.44401	+	7.76214i	−0.165618	+	0.289278i
$721$	−17.2452	+	9.74135i	−0.642243	+	0.362787i
$722$	28.7487	+	53.0369i	1.06992	+	1.97383i
$723$	−15.7912	+	4.23125i	−0.587283	+	0.157362i
$724$	−0.205930	+	3.82707i	−0.00765334	+	0.142232i
$725$	−21.6729	+	4.89848i	−0.804913	+	0.181925i
$726$	−4.60400	−	4.85840i	−0.170871	−	0.180312i
$727$	0.213513	+	0.213513i	0.00791876	+	0.00791876i	0.711055	−	0.703136i	$-0.248218\pi$
$727$	0.213513	+	0.213513i	0.00791876	+	0.00791876i	−0.703136	+	0.711055i	$0.748218\pi$
$728$	25.1785	+	17.7345i	0.933176	+	0.657286i
$729$		−	1.00000i		−	0.0370370i
$730$	−23.8909	−	4.28663i	−0.884241	−	0.158655i
$731$	0.368949	+	0.639038i	0.0136461	+	0.0236357i
$732$	10.5880	−	9.50672i	0.391344	−	0.351379i
$733$	10.4380	+	38.9553i	0.385537	+	1.43885i	0.837318	+	0.546716i	$0.184122\pi$
$733$	10.4380	+	38.9553i	0.385537	+	1.43885i	−0.451781	+	0.892129i	$0.649211\pi$
$734$	6.72035	−	22.6295i	0.248053	−	0.835268i
$735$	14.6812	−	5.42783i	0.541525	−	0.200209i
$736$	3.28121	+	25.6143i	0.120947	+	0.944156i
$737$	7.86795	+	29.3636i	0.289820	+	1.08162i
$738$	−1.08237	−	0.664317i	−0.0398425	−	0.0244538i
$739$	−14.0619	+	8.11863i	−0.517275	+	0.298649i	−0.735819	−	0.677178i	$-0.763203\pi$
$739$	−14.0619	+	8.11863i	−0.517275	+	0.298649i	0.218544	+	0.975827i	$0.429869\pi$
$740$	11.5430	+	34.9275i	0.424329	+	1.28396i
$741$			32.3156i			1.18714i
$742$	−0.136427	+	3.75815i	−0.00500839	+	0.137966i
$743$	−4.93484	+	4.93484i	−0.181042	+	0.181042i	−0.791810	−	0.610768i	$-0.790861\pi$
$743$	−4.93484	+	4.93484i	−0.181042	+	0.181042i	0.610768	+	0.791810i	$0.290861\pi$
$744$	−1.06896	−	5.83584i	−0.0391901	−	0.213952i
$745$	6.79306	+	2.97234i	0.248878	+	0.108898i
$746$	5.88522	+	24.5893i	0.215473	+	0.900280i
$747$	−1.13635	−	4.24090i	−0.0415768	−	0.155167i
$748$	−4.80177	−	22.7468i	−0.175570	−	0.831705i
$749$	−35.3152	+	19.9486i	−1.29039	+	0.728908i
$750$	15.7956	−	0.707275i	0.576772	−	0.0258260i
$751$	−7.57077	−	4.37098i	−0.276261	−	0.159499i	0.355468	−	0.934688i	$-0.384321\pi$
$751$	−7.57077	−	4.37098i	−0.276261	−	0.159499i	−0.631730	+	0.775189i	$0.717655\pi$
$752$	26.4458	−	4.11288i	0.964379	−	0.149981i
$753$	2.32840	−	8.68969i	0.0848514	−	0.316670i
$754$	18.7737	−	17.7906i	0.683697	−	0.647897i
$755$	−7.57443	−	10.2858i	−0.275662	−	0.374337i
$756$	−4.40643	−	2.92974i	−0.160260	−	0.106554i
$757$	32.9245	+	32.9245i	1.19666	+	1.19666i	0.975160	+	0.221502i	$0.0710958\pi$
$757$	32.9245	+	32.9245i	1.19666	+	1.19666i	0.221502	+	0.975160i	$0.428904\pi$
$758$	0.234934	−	8.73848i	0.00853319	−	0.317396i
$759$	−5.71407	−	9.89705i	−0.207407	−	0.359240i
$760$	−23.5076	+	43.7459i	−0.852712	+	1.58683i
$761$	−25.3417	+	43.8932i	−0.918637	+	1.59113i	−0.117151	+	0.993114i	$0.537376\pi$
$761$	−25.3417	+	43.8932i	−0.918637	+	1.59113i	−0.801487	+	0.598013i	$0.795957\pi$
$762$	−11.5333	+	6.25166i	−0.417808	+	0.226474i
$763$	−31.6876	+	31.0970i	−1.14717	+	1.12579i
$764$	3.78490	+	2.46547i	0.136933	+	0.0891974i
$765$	−6.48207	+	8.11064i	−0.234360	+	0.293241i
$766$	−2.58201	−	10.7880i	−0.0932919	−	0.389788i
$767$	−11.0313	+	41.1692i	−0.398316	+	1.48653i
$768$	7.34341	−	14.2153i	0.264982	−	0.512950i
$769$			31.8160i			1.14731i	0.819095	+	0.573657i	$0.194476\pi$
$769$			31.8160i			1.14731i	−0.819095	+	0.573657i	$0.805524\pi$
$770$	−15.8765	−	13.6613i	−0.572151	−	0.492320i
$771$	1.86907			0.0673128
$772$	10.3548	−	31.7180i	0.372678	−	1.14156i
$773$	−1.01572	−	0.272161i	−0.0365329	−	0.00978897i	0.240506	−	0.970648i	$-0.422687\pi$
$773$	−1.01572	−	0.272161i	−0.0365329	−	0.00978897i	−0.277039	+	0.960859i	$0.589353\pi$
$774$	−0.0523127	−	0.218571i	−0.00188034	−	0.00785635i
$775$	−7.70336	+	7.11739i	−0.276713	+	0.255664i
$776$	3.70700	−	3.15266i	0.133073	−	0.113174i
$777$	−21.0731	+	5.43458i	−0.755993	+	0.194964i
$778$	10.2548	+	18.9185i	0.367652	+	0.678260i
$779$	−6.10669	−	3.52570i	−0.218795	−	0.126321i
$780$	−15.3851	+	10.1014i	−0.550873	+	0.361690i
$781$	26.0566	−	15.0438i	0.932379	−	0.538309i
$782$	−0.805628	+	29.9657i	−0.0288092	+	1.07157i
$783$	−3.14233	+	3.14233i	−0.112298	+	0.112298i
$784$	−25.8194	+	10.8333i	−0.922120	+	0.386903i
$785$	31.1518	+	4.72910i	1.11186	+	0.168789i
$786$	−7.49901	−	7.91337i	−0.267481	−	0.282260i
$787$	8.55647	+	2.29270i	0.305005	+	0.0817259i	0.408076	−	0.912948i	$-0.366200\pi$
$787$	8.55647	+	2.29270i	0.305005	+	0.0817259i	−0.103070	+	0.994674i	$0.532867\pi$
$788$	−31.6155	−	35.2114i	−1.12626	−	1.25435i
$789$	11.8882	−	20.5909i	0.423229	−	0.733055i
$790$	20.4169	+	9.59531i	0.726400	+	0.341386i
$791$	−6.95574	+	11.7902i	−0.247318	+	0.419210i
$792$	−0.570340	+	7.05772i	−0.0202661	+	0.250785i
$793$	28.2830	−	7.57842i	1.00436	−	0.269118i
$794$	−35.2189	+	8.42930i	−1.24987	+	0.299145i
$795$	−2.05893	−	0.900899i	−0.0730229	−	0.0319516i
$796$	−15.7314	−	30.9814i	−0.557583	−	1.09811i
$797$	−15.8496	−	15.8496i	−0.561423	−	0.561423i	0.368289	−	0.929711i	$-0.379944\pi$
$797$	−15.8496	−	15.8496i	−0.561423	−	0.561423i	−0.929711	+	0.368289i	$0.879944\pi$
$798$	−24.8945	−	15.6036i	−0.881257	−	0.552362i
$799$	31.0678			1.09910
$800$	−28.1751	+	2.48272i	−0.996140	+	0.0877775i
$801$	1.67194	+	2.89589i	0.0590752	+	0.102321i
$802$	−5.40641	+	8.80864i	−0.190907	+	0.311044i
$803$	−18.5605	+	4.97326i	−0.654985	+	0.175503i
$804$	−13.2557	+	20.3498i	−0.467494	+	0.717681i
$805$	15.8090	+	21.8964i	0.557195	+	0.771747i
$806$	3.47553	−	11.7032i	0.122420	−	0.412227i
$807$	−20.8615	+	5.58983i	−0.734360	+	0.196771i
$808$	2.77851	−	1.31814i	0.0977476	−	0.0463720i
$809$	25.4348	−	14.6848i	0.894241	−	0.516290i	0.0189137	−	0.999821i	$-0.493979\pi$
$809$	25.4348	−	14.6848i	0.894241	−	0.516290i	0.875327	+	0.483531i	$0.160646\pi$
$810$	2.59582	−	1.80602i	0.0912079	−	0.0634571i
$811$	−32.8020			−1.15184			−0.575918	−	0.817508i	$-0.695355\pi$
$811$	−32.8020			−1.15184			−0.575918	+	0.817508i	$0.695355\pi$
$812$	4.64026	+	23.0527i	0.162841	+	0.808990i
$813$	−15.5792	+	15.5792i	−0.546385	+	0.546385i
$814$	20.0310	+	21.1378i	0.702085	+	0.740879i
$815$	19.9167	+	50.9052i	0.697651	+	1.78313i
$816$	10.9589	−	14.9954i	0.383639	−	0.524943i
$817$	−0.322971	−	1.20534i	−0.0112993	−	0.0421696i
$818$	15.1991	−	8.23869i	0.531424	−	0.288059i
$819$	−5.35529	−	9.48048i	−0.187129	−	0.331275i
$820$	−0.230331	−	4.00941i	−0.00804351	−	0.140015i
$821$	18.7866	+	10.8465i	0.655657	+	0.378544i	0.790620	−	0.612307i	$-0.209758\pi$
$821$	18.7866	+	10.8465i	0.655657	+	0.378544i	−0.134963	+	0.990851i	$0.543092\pi$
$822$	−3.54646	+	5.77823i	−0.123697	+	0.201539i
$823$	1.13033	+	0.302870i	0.0394007	+	0.0105574i	0.278466	−	0.960446i	$-0.410174\pi$
$823$	1.13033	+	0.302870i	0.0394007	+	0.0105574i	−0.239065	+	0.971004i	$0.576841\pi$
$824$	3.81498	+	20.8273i	0.132901	+	0.725553i
$825$	11.0789	−	5.82541i	0.385718	−	0.202815i
$826$	−26.3885	−	28.3766i	−0.918175	−	0.987348i
$827$	−9.30990	+	9.30990i	−0.323737	+	0.323737i	−0.850199	−	0.526462i	$-0.823518\pi$
$827$	−9.30990	+	9.30990i	−0.323737	+	0.323737i	0.526462	+	0.850199i	$0.323518\pi$
$828$	2.83346	−	8.67923i	0.0984697	−	0.301624i
$829$	−12.3629	−	21.4132i	−0.429382	−	0.743711i	0.567437	−	0.823417i	$-0.307935\pi$
$829$	−12.3629	−	21.4132i	−0.429382	−	0.743711i	−0.996818	+	0.0797060i	$0.974602\pi$
$830$	8.95637	−	10.6089i	0.310880	−	0.368241i
$831$	−23.3553	−	13.4842i	−0.810186	−	0.467761i
$832$	26.7166	−	19.2402i	0.926233	−	0.667034i
$833$	−31.5481	+	7.82023i	−1.09308	+	0.270955i
$834$	28.3903	+	8.43116i	0.983075	+	0.291947i
$835$	−16.5365	+	20.6912i	−0.572271	+	0.716049i
$836$	−2.11244	+	39.2581i	−0.0730601	+	1.35777i
$837$	−0.542901	+	2.02613i	−0.0187654	+	0.0700334i
$838$	0.689320	−	25.6396i	0.0238122	−	0.885705i
$839$	−10.4974			−0.362411			−0.181206	−	0.983445i	$-0.558000\pi$
$839$	−10.4974			−0.362411			−0.181206	+	0.983445i	$0.558000\pi$
$840$	−0.353027	−	16.7295i	−0.0121806	−	0.577222i
$841$	−9.25153			−0.319018
$842$	−1.33573	+	49.6832i	−0.0460324	+	1.71220i
$843$	−2.56539	+	9.57415i	−0.0883566	+	0.329751i
$844$	21.9302	+	1.18004i	0.754868	+	0.0406186i
$845$	−8.74897	+	0.976399i	−0.300974	+	0.0335891i
$846$	−9.07085	−	2.69380i	−0.311862	−	0.0926149i
$847$	12.0644	+	3.35460i	0.414538	+	0.115265i
$848$	3.74921	+	1.45122i	0.128749	+	0.0498352i
$849$	−13.1882	−	7.61421i	−0.452618	−	0.261319i
$850$	−32.7605	−	2.17833i	−1.12368	−	0.0747160i
$851$	−18.7747	−	32.5188i	−0.643590	−	1.11473i
$852$	22.8504	+	7.45985i	0.782841	+	0.255570i
$853$	15.0268	−	15.0268i	0.514506	−	0.514506i	−0.401398	−	0.915904i	$-0.631475\pi$
$853$	15.0268	−	15.0268i	0.514506	−	0.514506i	0.915904	+	0.401398i	$0.131475\pi$
$854$	−7.81841	+	25.4473i	−0.267540	+	0.870788i
$855$	14.1383	−	10.4114i	0.483520	−	0.356064i
$856$	7.81244	+	42.6508i	0.267024	+	1.45777i
$857$	−49.2244	−	13.1896i	−1.68147	−	0.450549i	−0.713306	−	0.700853i	$-0.752803\pi$
$857$	−49.2244	−	13.1896i	−1.68147	−	0.450549i	−0.968167	+	0.250304i	$0.919470\pi$
$858$	−7.62159	+	12.4178i	−0.260197	+	0.423937i
$859$	43.0456	+	24.8524i	1.46870	+	0.847953i	0.999385	−	0.0350780i	$-0.0111680\pi$
$859$	43.0456	+	24.8524i	1.46870	+	0.847953i	0.469314	+	0.883031i	$0.344501\pi$
$860$	0.472892	−	0.530537i	0.0161255	−	0.0180912i
$861$	2.37580	+	0.0223501i	0.0809671	+	0.000761689i
$862$	12.3410	−	6.68947i	0.420337	−	0.227844i
$863$	4.08534	+	15.2467i	0.139067	+	0.519004i	0.999948	+	0.0101982i	$0.00324625\pi$
$863$	4.08534	+	15.2467i	0.139067	+	0.519004i	−0.860881	+	0.508806i	$0.830087\pi$
$864$	−4.49989	+	3.42798i	−0.153089	+	0.116622i
$865$	−42.8412	+	16.7616i	−1.45664	+	0.569913i
$866$	24.3348	+	25.6794i	0.826930	+	0.872623i
$867$	3.22438	−	3.22438i	0.109506	−	0.109506i
$868$	7.33746	+	8.32829i	0.249050	+	0.282681i
$869$	17.8590			0.605825
$870$	−13.8320	−	2.48182i	−0.468950	−	0.0841415i
$871$	−43.2794	+	24.9873i	−1.46646	+	0.846664i
$872$	20.3434	+	42.8819i	0.688916	+	1.45217i
$873$	−1.66188	+	0.445299i	−0.0562461	+	0.0150711i
$874$	14.4317	−	48.5958i	0.488158	−	1.64378i
$875$	−24.6482	+	16.3544i	−0.833261	+	0.552880i
$876$	−12.8629	−	8.37884i	−0.434597	−	0.283095i
$877$	−36.4571	+	9.76865i	−1.23107	+	0.329864i	−0.814996	−	0.579467i	$-0.803261\pi$
$877$	−36.4571	+	9.76865i	−1.23107	+	0.329864i	−0.416073	+	0.909331i	$0.636594\pi$
$878$	13.2017	−	21.5095i	0.445536	−	0.725910i
$879$	5.86981	+	10.1668i	0.197984	+	0.342918i
$880$	−19.3506	+	11.2659i	−0.652310	+	0.379773i
$881$	4.63113			0.156027			0.0780134	−	0.996952i	$-0.475142\pi$
$881$	4.63113			0.156027			0.0780134	+	0.996952i	$0.475142\pi$
$882$	9.88916	+	0.452178i	0.332985	+	0.0152256i
$883$	−29.9909	−	29.9909i	−1.00927	−	1.00927i	−0.999957	−	0.00931616i	$-0.997035\pi$
$883$	−29.9909	−	29.9909i	−1.00927	−	1.00927i	−0.00931616	−	0.999957i	$-0.502965\pi$
$884$	34.0770	−	17.3032i	1.14613	−	0.581968i
$885$	21.5659	−	8.43766i	0.724929	−	0.283629i
$886$	−6.34769	+	1.51926i	−0.213255	+	0.0510404i
$887$	−19.3624	+	5.18814i	−0.650126	+	0.174201i	−0.568786	−	0.822486i	$-0.692587\pi$
$887$	−19.3624	+	5.18814i	−0.650126	+	0.174201i	−0.0813404	+	0.996686i	$0.525920\pi$
$888$	−1.87397	+	23.1896i	−0.0628863	+	0.778192i
$889$	12.4708	−	21.1384i	0.418259	−	0.708959i
$890$	−4.49765	+	9.57010i	−0.150762	+	0.320790i
$891$	1.25171	−	2.16802i	0.0419338	−	0.0726315i
$892$	−25.8080	+	23.1724i	−0.864115	+	0.775869i
$893$	−50.7487	−	13.5981i	−1.69824	−	0.455042i
$894$	3.22572	+	3.40396i	0.107884	+	0.113845i
$895$	−7.25052	−	9.84589i	−0.242358	−	0.329112i
$896$	1.92167	+	29.8715i	0.0641985	+	0.997937i
$897$	13.2845	−	13.2845i	0.443556	−	0.443556i
$898$	−0.191054	+	7.10635i	−0.00637556	+	0.237142i
$899$	8.07275	−	4.66081i	0.269241	−	0.155447i
$900$	9.37621	+	3.47658i	0.312540	+	0.115886i
$901$	4.04158	+	2.33341i	0.134644	+	0.0777370i
$902$	−1.51507	−	2.79506i	−0.0504462	−	0.0930654i
$903$	0.294498	+	0.300091i	0.00980028	+	0.00998642i
$904$	9.48082	+	11.1478i	0.315327	+	0.370772i
$905$	4.25855	−	0.475260i	0.141559	−	0.0157982i
$906$	−1.88048	−	7.85693i	−0.0624747	−	0.261029i
$907$	−6.15054	−	1.64803i	−0.204225	−	0.0547220i	0.155256	−	0.987874i	$-0.450380\pi$
$907$	−6.15054	−	1.64803i	−0.204225	−	0.0547220i	−0.359481	+	0.933152i	$0.617046\pi$
$908$	54.2960	+	17.7257i	1.80188	+	0.588249i
$909$	−1.08729			−0.0360632
$910$	14.9379	−	31.0233i	0.495186	−	1.02841i
$911$		−	30.7362i		−	1.01833i	−0.860668	−	0.509167i	$-0.829953\pi$
$911$		−	30.7362i		−	1.01833i	0.860668	−	0.509167i	$-0.170047\pi$
$912$	−24.4645	+	19.6981i	−0.810102	+	0.652268i
$913$	2.84475	−	10.6167i	0.0941474	−	0.351363i
$914$	−11.0569	−	46.1973i	−0.365728	−	1.52807i
$915$	−12.4279	−	9.93241i	−0.410852	−	0.328355i
$916$	−8.91404	+	13.6845i	−0.294528	+	0.452149i
$917$	19.6505	+	5.46397i	0.648917	+	0.180436i
$918$	−5.77301	+	3.12927i	−0.190538	+	0.103281i
$919$	−3.29202	+	5.70195i	−0.108594	+	0.188090i	−0.915201	−	0.402998i	$-0.867968\pi$
$919$	−3.29202	+	5.70195i	−0.108594	+	0.188090i	0.806607	+	0.591088i	$0.201301\pi$
$920$	27.6470	−	8.31969i	0.911495	−	0.274292i
$921$	3.83856	+	6.64858i	0.126485	+	0.219078i
$922$	−0.0149021	+	0.554292i	−0.000490776	+	0.0182546i
$923$	34.9749	+	34.9749i	1.15121	+	1.15121i
$924$	−5.88606	−	11.8673i	−0.193637	−	0.390405i
$925$	36.4020	−	19.1406i	1.19689	−	0.629338i
$926$	12.7241	−	12.0578i	0.418140	−	0.396245i
$927$	1.93754	−	7.23099i	0.0636371	−	0.237497i
$928$	24.9120	+	3.36829i	0.817775	+	0.110569i
$929$	7.49183	+	4.32541i	0.245799	+	0.141912i	0.617839	−	0.786305i	$-0.288008\pi$
$929$	7.49183	+	4.32541i	0.245799	+	0.141912i	−0.372040	+	0.928217i	$0.621342\pi$
$930$	−6.23997	+	2.24996i	−0.204617	+	0.0737792i
$931$	54.9561	+	1.03408i	1.80111	+	0.0338905i
$932$	3.55353	−	0.750139i	0.116400	−	0.0245716i
$933$	−3.11089	−	11.6100i	−0.101846	−	0.380094i
$934$	−8.89103	−	37.1481i	−0.290923	−	1.21552i
$935$	−24.2054	+	9.47039i	−0.791602	+	0.309715i
$936$	−11.4498	+	2.09728i	−0.374247	+	0.0685517i
$937$	−3.38898	+	3.38898i	−0.110713	+	0.110713i	−0.760293	−	0.649580i	$-0.774945\pi$
$937$	−3.38898	+	3.38898i	−0.110713	+	0.110713i	0.649580	+	0.760293i	$0.274945\pi$
$938$	1.64830	−	45.4057i	0.0538189	−	1.48255i
$939$			18.1665i			0.592842i
$940$	−9.38951	−	28.4114i	−0.306252	−	0.926677i
$941$	−10.1441	+	5.85669i	−0.330688	+	0.190923i	−0.656146	−	0.754634i	$-0.727815\pi$
$941$	−10.1441	+	5.85669i	−0.330688	+	0.190923i	0.325459	+	0.945556i	$0.394481\pi$
$942$	16.9840	+	10.4242i	0.553369	+	0.339637i
$943$	1.06101	+	3.95974i	0.0345512	+	0.128947i
$944$	−37.8913	+	16.7436i	−1.23326	+	0.544957i
$945$	−2.42241	+	5.39740i	−0.0788010	+	0.175577i
$946$	0.160171	−	0.539346i	0.00520762	−	0.0175356i
$947$	−0.594235	−	2.21772i	−0.0193101	−	0.0720661i	0.955598	−	0.294672i	$-0.0952104\pi$
$947$	−0.594235	−	2.21772i	−0.0193101	−	0.0720661i	−0.974909	+	0.222606i	$0.928544\pi$
$948$	9.53214	+	10.6163i	0.309589	+	0.344802i
$949$	−15.7943	−	27.3565i	−0.512704	−	0.888030i
$950$	52.5603	+	17.8972i	1.70528	+	0.580663i
$951$		−	29.5553i		−	0.958398i
$952$	−3.12449	+	34.6063i	−0.101265	+	1.12160i
$953$	29.5710	+	29.5710i	0.957898	+	0.957898i	0.999149	−	0.0412511i	$-0.0131344\pi$
$953$	29.5710	+	29.5710i	0.957898	+	0.957898i	−0.0412511	+	0.999149i	$0.513134\pi$
$954$	−0.977696	−	1.03172i	−0.0316541	−	0.0334031i
$955$	2.02445	−	4.62672i	0.0655096	−	0.149717i
$956$	−14.8525	−	0.799198i	−0.480365	−	0.0258479i
$957$	−10.7459	+	2.87936i	−0.347366	+	0.0930765i
$958$	21.9127	+	40.4254i	0.707966	+	1.30609i
$959$	0.119316	−	12.6832i	0.00385292	−	0.409563i
$960$	−17.0253	−	5.48990i	−0.549489	−	0.177186i
$961$	−13.3000	+	23.0363i	−0.429033	+	0.743107i
$962$	−25.0423	+	40.8013i	−0.807396	+	1.31549i
$963$	3.96775	−	14.8079i	0.127859	−	0.477176i
$964$	−14.8032	−	29.1536i	−0.476780	−	0.938974i
$965$	−36.8811	−	5.59886i	−1.18725	−	0.180234i
$966$	3.81937	+	16.6482i	0.122886	+	0.535648i
$967$	2.12188	+	2.12188i	0.0682349	+	0.0682349i	0.740401	−	0.672166i	$-0.234636\pi$
$967$	2.12188	+	2.12188i	0.0682349	+	0.0682349i	−0.672166	+	0.740401i	$0.734636\pi$
$968$	7.60541	−	11.0164i	0.244447	−	0.354081i
$969$	−31.5754	+	18.2301i	−1.01435	+	0.585634i
$970$	−4.15731	−	3.50972i	−0.133483	−	0.112690i
$971$	25.3451	−	43.8989i	0.813362	−	1.40878i	−0.0971368	−	0.995271i	$-0.530968\pi$
$971$	25.3451	−	43.8989i	0.813362	−	1.40878i	0.910498	−	0.413513i	$-0.135698\pi$
$972$	1.95687	−	0.413090i	0.0627668	−	0.0132499i
$973$	−53.6506	+	13.8361i	−1.71996	+	0.443563i
$974$	2.29791	−	7.73776i	0.0736298	−	0.247934i
$975$	13.9641	+	15.1138i	0.447210	+	0.484029i
$976$	22.9773	+	16.7922i	0.735484	+	0.537507i
$977$	−42.8061	−	11.4699i	−1.36949	−	0.366954i	−0.502197	−	0.864753i	$-0.667475\pi$
$977$	−42.8061	−	11.4699i	−1.36949	−	0.366954i	−0.867292	+	0.497799i	$0.834142\pi$
$978$	−0.929125	+	34.5593i	−0.0297102	+	1.10508i
$979$			8.37113i			0.267543i
$980$	16.6863	+	26.4871i	0.533023	+	0.846101i
$981$		−	16.7806i		−	0.535764i
$982$	−35.1284	−	0.944427i	−1.12099	−	0.0301379i
$983$	−11.6732	−	3.12783i	−0.372318	−	0.0997622i	0.0678081	−	0.997698i	$-0.478399\pi$
$983$	−11.6732	−	3.12783i	−0.372318	−	0.0997622i	−0.440126	+	0.897936i	$0.645066\pi$
$984$	0.852869	−	2.39248i	0.0271885	−	0.0762695i
$985$	−33.0312	+	41.3300i	−1.05246	+	1.31688i
$986$	27.9739	+	8.30750i	0.890870	+	0.264565i
$987$	17.1417	−	4.42070i	0.545625	−	0.140712i
$988$	−63.2375	+	13.3492i	−2.01185	+	0.424696i
$989$	−0.362731	+	0.628268i	−0.0115342	+	0.0199778i
$990$	7.88841	−	0.666279i	0.250710	−	0.0211757i
$991$	3.47494	−	2.00626i	0.110385	−	0.0637309i	−0.443791	−	0.896130i	$-0.646367\pi$
$991$	3.47494	−	2.00626i	0.110385	−	0.0637309i	0.554176	+	0.832399i	$0.313033\pi$
$992$	10.9784	−	4.50255i	0.348565	−	0.142956i
$993$	−14.5131	−	14.5131i	−0.460560	−	0.460560i
$994$	−43.8309	+	10.0555i	−1.39023	+	0.318941i
$995$	−31.2813	+	23.0356i	−0.991684	+	0.730276i
$996$	7.82950	−	3.97556i	0.248087	−	0.125970i
$997$	−6.49294	+	24.2320i	−0.205633	+	0.767435i	0.783622	+	0.621238i	$0.213370\pi$
$997$	−6.49294	+	24.2320i	−0.205633	+	0.767435i	−0.989256	+	0.146197i	$0.953297\pi$
$998$	7.33337	+	4.50094i	0.232134	+	0.142475i
$999$	4.11274	−	7.12348i	0.130121	−	0.225377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.163.95	yes	384
5.2	odd	4	inner	840.2.dj.a.667.49	yes	384
7.4	even	3	inner	840.2.dj.a.403.32	yes	384
8.3	odd	2	inner	840.2.dj.a.163.16	yes	384
35.32	odd	12	inner	840.2.dj.a.67.16	✓	384
40.27	even	4	inner	840.2.dj.a.667.32	yes	384
56.11	odd	6	inner	840.2.dj.a.403.49	yes	384
280.67	even	12	inner	840.2.dj.a.67.95	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.16	✓	384	35.32	odd	12	inner
840.2.dj.a.67.95	yes	384	280.67	even	12	inner
840.2.dj.a.163.16	yes	384	8.3	odd	2	inner
840.2.dj.a.163.95	yes	384	1.1	even	1	trivial
840.2.dj.a.403.32	yes	384	7.4	even	3	inner
840.2.dj.a.403.49	yes	384	56.11	odd	6	inner
840.2.dj.a.667.32	yes	384	40.27	even	4	inner
840.2.dj.a.667.49	yes	384	5.2	odd	4	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.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41370 + 0.0380074i) q^{2} +(0.258819 - 0.965926i) q^{3} +(1.99711 + 0.107462i) q^{4} +(-0.248009 - 2.22227i) q^{5} +(0.402606 - 1.35569i) q^{6} +(0.660700 + 2.56193i) q^{7} +(2.81924 + 0.227825i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.266148 - 3.15106i) q^{10} +(-1.25171 - 2.16802i) q^{11} +(0.620691 - 1.90125i) q^{12} +(2.91006 - 2.91006i) q^{13} +(0.836661 + 3.64692i) q^{14} +(-2.21074 - 0.335608i) q^{15} +(3.97690 + 0.429228i) q^{16} +(4.48505 + 1.20177i) q^{17} +(-1.20530 - 0.739767i) q^{18} +(-6.80025 - 3.92613i) q^{19} +(-0.256491 - 4.46477i) q^{20} +(2.64563 + 0.0248885i) q^{21} +(-1.68714 - 3.11251i) q^{22} +(1.18151 + 4.40947i) q^{23} +(0.949734 - 2.66421i) q^{24} +(-4.87698 + 1.10229i) q^{25} +(4.22457 - 4.00336i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.04418 + 5.18745i) q^{28} +4.44393 q^{29} +(-3.11257 - 0.558474i) q^{30} +(1.81658 - 1.04880i) q^{31} +(5.60585 + 0.757953i) q^{32} +(-2.41811 + 0.647932i) q^{33} +(6.29486 + 1.86941i) q^{34} +(5.52944 - 2.10364i) q^{35} +(-1.67582 - 1.09162i) q^{36} +(-7.94521 + 2.12891i) q^{37} +(-9.46432 - 5.80884i) q^{38} +(-2.05773 - 3.56409i) q^{39} +(-0.192907 - 6.32161i) q^{40} +0.898009 q^{41} +(3.73919 + 0.135739i) q^{42} +(0.112372 + 0.112372i) q^{43} +(-2.26682 - 4.46429i) q^{44} +(-0.896354 + 2.04855i) q^{45} +(1.50272 + 6.27858i) q^{46} +(6.46294 - 1.73174i) q^{47} +(1.44390 - 3.73030i) q^{48} +(-6.12695 + 3.38533i) q^{49} +(-6.93650 + 1.37294i) q^{50} +(2.32164 - 4.02119i) q^{51} +(6.12444 - 5.49900i) q^{52} +(0.970823 + 0.260131i) q^{53} +(-1.02651 + 0.972764i) q^{54} +(-4.50750 + 3.31932i) q^{55} +(1.27900 + 7.37321i) q^{56} +(-5.55238 + 5.55238i) q^{57} +(6.28239 + 0.168902i) q^{58} +(-8.96896 + 5.17823i) q^{59} +(-4.37903 - 0.907818i) q^{60} +(6.16163 + 3.55742i) q^{61} +(2.60797 - 1.41365i) q^{62} +(0.708781 - 2.54904i) q^{63} +(7.89619 + 1.28458i) q^{64} +(-7.18868 - 5.74523i) q^{65} +(-3.44312 + 0.824077i) q^{66} +(-11.7294 - 3.14289i) q^{67} +(8.82801 + 2.88204i) q^{68} +4.56502 q^{69} +(7.89694 - 2.76376i) q^{70} +12.0186i q^{71} +(-2.32762 - 1.60692i) q^{72} +(1.98659 - 7.41406i) q^{73} +(-11.3131 + 2.70767i) q^{74} +(-0.197529 + 4.99610i) q^{75} +(-13.1589 - 8.57168i) q^{76} +(4.72731 - 4.63920i) q^{77} +(-2.77355 - 5.11677i) q^{78} +(-3.56693 + 6.17810i) q^{79} +(-0.0324456 - 8.94421i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.26952 + 0.0341310i) q^{82} +(3.10456 + 3.10456i) q^{83} +(5.28095 + 0.334011i) q^{84} +(1.55832 - 10.2651i) q^{85} +(0.154589 + 0.163131i) q^{86} +(1.15017 - 4.29250i) q^{87} +(-3.03493 - 6.39734i) q^{88} +(-2.89589 - 1.67194i) q^{89} +(-1.34504 + 2.86197i) q^{90} +(9.37806 + 5.53270i) q^{91} +(1.88576 + 8.93316i) q^{92} +(-0.542901 - 2.02613i) q^{93} +(9.20249 - 2.20252i) q^{94} +(-7.03840 + 16.0857i) q^{95} +(2.18303 - 5.21866i) q^{96} +(1.21658 - 1.21658i) q^{97} +(-8.79035 + 4.55298i) q^{98} +2.50342i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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