LMFDB - Embedded newform 231.2.p.a.208.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			208.1
Character	$\chi$	$=$	231.208
Dual form			231.2.p.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23994 - 1.29323i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.34487 + 4.06144i) q^{4} +(-1.30115 - 0.751219i) q^{5} +2.58645 q^{6} +(1.55637 - 2.13956i) q^{7} -6.95692i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.23994 - 1.29323i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.34487 + 4.06144i) q^{4} +(-1.30115 - 0.751219i) q^{5} +2.58645 q^{6} +(1.55637 - 2.13956i) q^{7} -6.95692i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.94300 + 3.36537i) q^{10} +(-2.72420 + 1.89176i) q^{11} +(-4.06144 - 2.34487i) q^{12} -3.99370 q^{13} +(-6.25310 + 2.77975i) q^{14} +1.50244 q^{15} +(-4.30712 + 7.46016i) q^{16} +(1.38189 + 2.39351i) q^{17} +(-2.23994 + 1.29323i) q^{18} +(-2.45877 + 4.25871i) q^{19} -7.04606i q^{20} +(-0.278071 + 2.63110i) q^{21} +(8.54850 - 0.714407i) q^{22} +(0.0359722 - 0.0623056i) q^{23} +(3.47846 + 6.02487i) q^{24} +(-1.37134 - 2.37523i) q^{25} +(8.94562 + 5.16476i) q^{26} +1.00000i q^{27} +(12.3392 + 1.30408i) q^{28} +5.06315i q^{29} +(-3.36537 - 1.94300i) q^{30} +(-8.84779 + 5.10827i) q^{31} +(7.24563 - 4.18327i) q^{32} +(1.41335 - 3.00041i) q^{33} -7.14840i q^{34} +(-3.63235 + 1.61472i) q^{35} +4.68975 q^{36} +(-3.90797 + 6.76881i) q^{37} +(11.0150 - 6.35949i) q^{38} +(3.45864 - 1.99685i) q^{39} +(-5.22617 + 9.05199i) q^{40} -2.98366 q^{41} +(4.02547 - 5.53388i) q^{42} -5.41033i q^{43} +(-14.0712 - 6.62824i) q^{44} +(-1.30115 + 0.751219i) q^{45} +(-0.161151 + 0.0930404i) q^{46} +(4.48684 + 2.59048i) q^{47} -8.61425i q^{48} +(-2.15545 - 6.65988i) q^{49} +7.09381i q^{50} +(-2.39351 - 1.38189i) q^{51} +(-9.36472 - 16.2202i) q^{52} +(-6.23215 - 10.7944i) q^{53} +(1.29323 - 2.23994i) q^{54} +(4.96572 - 0.414990i) q^{55} +(-14.8848 - 10.8275i) q^{56} -4.91754i q^{57} +(6.54781 - 11.3411i) q^{58} +(-5.52352 + 3.18901i) q^{59} +(3.52303 + 6.10207i) q^{60} +(0.688758 - 1.19296i) q^{61} +26.4246 q^{62} +(-1.07473 - 2.41763i) q^{63} -4.41117 q^{64} +(5.19640 + 3.00014i) q^{65} +(-7.04602 + 4.89295i) q^{66} +(2.27669 + 3.94334i) q^{67} +(-6.48072 + 11.2249i) q^{68} +0.0719444i q^{69} +(10.2244 + 1.08058i) q^{70} +9.59452 q^{71} +(-6.02487 - 3.47846i) q^{72} +(-4.48046 - 7.76039i) q^{73} +(17.5072 - 10.1078i) q^{74} +(2.37523 + 1.37134i) q^{75} -23.0620 q^{76} +(-0.192316 + 8.77286i) q^{77} -10.3295 q^{78} +(10.0932 + 5.82731i) q^{79} +(11.2084 - 6.47119i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.68320 + 3.85855i) q^{82} -9.34449 q^{83} +(-11.3381 + 5.04022i) q^{84} -4.15242i q^{85} +(-6.99679 + 12.1188i) q^{86} +(-2.53158 - 4.38482i) q^{87} +(13.1608 + 18.9520i) q^{88} +(-11.7889 - 6.80633i) q^{89} +3.88599 q^{90} +(-6.21565 + 8.54476i) q^{91} +0.337401 q^{92} +(5.10827 - 8.84779i) q^{93} +(-6.70015 - 11.6050i) q^{94} +(6.39846 - 3.69415i) q^{95} +(-4.18327 + 7.24563i) q^{96} -2.63550i q^{97} +(-3.78467 + 17.7052i) q^{98} +(0.276211 + 3.30510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.23994	−	1.29323i	−1.58387	−	0.914450i	−0.994286	−	0.106745i	$-0.965957\pi$
$2$	−2.23994	−	1.29323i	−1.58387	−	0.914450i	−0.589587	−	0.807705i	$-0.700710\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	2.34487	+	4.06144i	1.17244	+	2.03072i
$5$	−1.30115	−	0.751219i	−0.581892	−	0.335956i	0.179993	−	0.983668i	$-0.442393\pi$
$5$	−1.30115	−	0.751219i	−0.581892	−	0.335956i	−0.761885	+	0.647712i	$0.775726\pi$
$6$	2.58645			1.05592
$7$	1.55637	−	2.13956i	0.588251	−	0.808678i
$7$	1.55637	−	2.13956i	0.588251	−	0.808678i
$8$		−	6.95692i		−	2.45964i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.94300	+	3.36537i	0.614429	+	1.06422i
$11$	−2.72420	+	1.89176i	−0.821377	+	0.570386i
$11$	−2.72420	+	1.89176i	−0.821377	+	0.570386i
$12$	−4.06144	−	2.34487i	−1.17244	−	0.676907i
$13$	−3.99370			−1.10765			−0.553826	−	0.832632i	$-0.686833\pi$
$13$	−3.99370			−1.10765			−0.553826	+	0.832632i	$0.686833\pi$
$14$	−6.25310	+	2.77975i	−1.67121	+	0.742919i
$15$	1.50244			0.387928
$16$	−4.30712	+	7.46016i	−1.07678	+	1.86504i
$17$	1.38189	+	2.39351i	0.335158	+	0.580511i	0.983515	−	0.180826i	$-0.0578770\pi$
$17$	1.38189	+	2.39351i	0.335158	+	0.580511i	−0.648357	+	0.761336i	$0.724544\pi$
$18$	−2.23994	+	1.29323i	−0.527958	+	0.304817i
$19$	−2.45877	+	4.25871i	−0.564080	+	0.977016i	0.433054	+	0.901368i	$0.357436\pi$
$19$	−2.45877	+	4.25871i	−0.564080	+	0.977016i	−0.997135	+	0.0756478i	$0.975898\pi$
$20$		−	7.04606i		−	1.57555i
$21$	−0.278071	+	2.63110i	−0.0606801	+	0.574153i
$22$	8.54850	−	0.714407i	1.82255	−	0.152312i
$23$	0.0359722	−	0.0623056i	0.00750072	−	0.0129916i	−0.862251	−	0.506482i	$-0.830946\pi$
$23$	0.0359722	−	0.0623056i	0.00750072	−	0.0129916i	0.869751	+	0.493490i	$0.164279\pi$
$24$	3.47846	+	6.02487i	0.710037	+	1.22982i
$25$	−1.37134	−	2.37523i	−0.274268	−	0.475046i
$26$	8.94562	+	5.16476i	1.75438	+	1.01289i
$27$			1.00000i			0.192450i
$28$	12.3392	+	1.30408i	2.33189	+	0.246449i
$29$			5.06315i			0.940204i	0.882612	+	0.470102i	$0.155783\pi$
$29$			5.06315i			0.940204i	−0.882612	+	0.470102i	$0.844217\pi$
$30$	−3.36537	−	1.94300i	−0.614429	−	0.354741i
$31$	−8.84779	+	5.10827i	−1.58911	+	0.917473i	−0.595656	+	0.803239i	$0.703108\pi$
$31$	−8.84779	+	5.10827i	−1.58911	+	0.917473i	−0.993454	+	0.114234i	$0.963559\pi$
$32$	7.24563	−	4.18327i	1.28086	−	0.739504i
$33$	1.41335	−	3.00041i	0.246032	−	0.522304i
$34$		−	7.14840i		−	1.22594i
$35$	−3.63235	+	1.61472i	−0.613979	+	0.272937i
$36$	4.68975			0.781625
$37$	−3.90797	+	6.76881i	−0.642467	+	1.11278i	0.342414	+	0.939549i	$0.388756\pi$
$37$	−3.90797	+	6.76881i	−0.642467	+	1.11278i	−0.984880	+	0.173236i	$0.944578\pi$
$38$	11.0150	−	6.35949i	1.78686	−	1.03165i
$39$	3.45864	−	1.99685i	0.553826	−	0.319752i
$40$	−5.22617	+	9.05199i	−0.826330	+	1.43125i
$41$	−2.98366			−0.465969			−0.232984	−	0.972480i	$-0.574849\pi$
$41$	−2.98366			−0.465969			−0.232984	+	0.972480i	$0.574849\pi$
$42$	4.02547	−	5.53388i	0.621143	−	0.853896i
$43$		−	5.41033i		−	0.825068i	−0.910942	−	0.412534i	$-0.864644\pi$
$43$		−	5.41033i		−	0.825068i	0.910942	−	0.412534i	$-0.135356\pi$
$44$	−14.0712	−	6.62824i	−2.12131	−	0.999244i
$45$	−1.30115	+	0.751219i	−0.193964	+	0.111985i
$46$	−0.161151	+	0.0930404i	−0.0237604	+	0.0137181i
$47$	4.48684	+	2.59048i	0.654472	+	0.377860i	0.790168	−	0.612891i	$-0.209994\pi$
$47$	4.48684	+	2.59048i	0.654472	+	0.377860i	−0.135695	+	0.990751i	$0.543327\pi$
$48$		−	8.61425i		−	1.24336i
$49$	−2.15545	−	6.65988i	−0.307922	−	0.951412i
$50$			7.09381i			1.00322i
$51$	−2.39351	−	1.38189i	−0.335158	−	0.193504i
$52$	−9.36472	−	16.2202i	−1.29865	−	2.24933i
$53$	−6.23215	−	10.7944i	−0.856052	−	1.48273i	−0.875666	−	0.482918i	$-0.839577\pi$
$53$	−6.23215	−	10.7944i	−0.856052	−	1.48273i	0.0196135	−	0.999808i	$-0.493756\pi$
$54$	1.29323	−	2.23994i	0.175986	−	0.304817i
$55$	4.96572	−	0.414990i	0.669577	−	0.0559573i
$56$	−14.8848	−	10.8275i	−1.98906	−	1.44689i
$57$		−	4.91754i		−	0.651344i
$58$	6.54781	−	11.3411i	0.859770	−	1.48916i
$59$	−5.52352	+	3.18901i	−0.719101	+	0.415173i	−0.814422	−	0.580273i	$-0.802946\pi$
$59$	−5.52352	+	3.18901i	−0.719101	+	0.415173i	0.0953206	+	0.995447i	$0.469612\pi$
$60$	3.52303	+	6.10207i	0.454821	+	0.787774i
$61$	0.688758	−	1.19296i	0.0881865	−	0.152743i	−0.818558	−	0.574424i	$-0.805226\pi$
$61$	0.688758	−	1.19296i	0.0881865	−	0.152743i	0.906745	+	0.421680i	$0.138560\pi$
$62$	26.4246			3.35593
$63$	−1.07473	−	2.41763i	−0.135404	−	0.304593i
$64$	−4.41117			−0.551397
$65$	5.19640	+	3.00014i	0.644534	+	0.372122i
$66$	−7.04602	+	4.89295i	−0.867304	+	0.602280i
$67$	2.27669	+	3.94334i	0.278142	+	0.481755i	0.970923	−	0.239392i	$-0.0769482\pi$
$67$	2.27669	+	3.94334i	0.278142	+	0.481755i	−0.692781	+	0.721148i	$0.743615\pi$
$68$	−6.48072	+	11.2249i	−0.785903	+	1.36122i
$69$			0.0719444i			0.00866108i
$70$	10.2244	+	1.08058i	1.22205	+	0.129154i
$71$	9.59452			1.13866			0.569330	−	0.822109i	$-0.307203\pi$
$71$	9.59452			1.13866			0.569330	+	0.822109i	$0.307203\pi$
$72$	−6.02487	−	3.47846i	−0.710037	−	0.409940i
$73$	−4.48046	−	7.76039i	−0.524399	−	0.908285i	−0.999596	−	0.0284061i	$-0.990957\pi$
$73$	−4.48046	−	7.76039i	−0.524399	−	0.908285i	0.475198	−	0.879879i	$-0.342376\pi$
$74$	17.5072	−	10.1078i	2.03517	−	1.17501i
$75$	2.37523	+	1.37134i	0.274268	+	0.158349i
$76$	−23.0620			−2.64539
$77$	−0.192316	+	8.77286i	−0.0219164	+	0.999760i
$78$	−10.3295			−1.16959
$79$	10.0932	+	5.82731i	1.13557	+	0.655623i	0.945330	−	0.326114i	$-0.105739\pi$
$79$	10.0932	+	5.82731i	1.13557	+	0.655623i	0.190242	+	0.981737i	$0.439073\pi$
$80$	11.2084	−	6.47119i	1.25314	−	0.723501i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.68320	+	3.85855i	0.738036	+	0.426105i
$83$	−9.34449			−1.02569			−0.512845	−	0.858481i	$-0.671409\pi$
$83$	−9.34449			−1.02569			−0.512845	+	0.858481i	$0.671409\pi$
$84$	−11.3381	+	5.04022i	−1.23709	+	0.549934i
$85$		−	4.15242i		−	0.450393i
$86$	−6.99679	+	12.1188i	−0.754483	+	1.30680i
$87$	−2.53158	−	4.38482i	−0.271414	−	0.470102i
$88$	13.1608	+	18.9520i	1.40295	+	2.02029i
$89$	−11.7889	−	6.80633i	−1.24962	−	0.721470i	−0.278588	−	0.960411i	$-0.589866\pi$
$89$	−11.7889	−	6.80633i	−1.24962	−	0.721470i	−0.971034	+	0.238941i	$0.923200\pi$
$90$	3.88599			0.409619
$91$	−6.21565	+	8.54476i	−0.651577	+	0.895734i
$92$	0.337401			0.0351765
$93$	5.10827	−	8.84779i	0.529703	−	0.917473i
$94$	−6.70015	−	11.6050i	−0.691068	−	1.19696i
$95$	6.39846	−	3.69415i	0.656468	−	0.379012i
$96$	−4.18327	+	7.24563i	−0.426953	+	0.739504i
$97$		−	2.63550i		−	0.267594i	−0.991009	−	0.133797i	$-0.957283\pi$
$97$		−	2.63550i		−	0.267594i	0.991009	−	0.133797i	$-0.0427171\pi$
$98$	−3.78467	+	17.7052i	−0.382309	+	1.78849i
$99$	0.276211	+	3.30510i	0.0277603	+	0.332175i
$100$	6.43123	−	11.1392i	0.643123	−	1.11392i
$101$	3.18007	+	5.50804i	0.316429	+	0.548070i	0.979740	−	0.200273i	$-0.0641829\pi$
$101$	3.18007	+	5.50804i	0.316429	+	0.548070i	−0.663312	+	0.748343i	$0.730850\pi$
$102$	3.57420	+	6.19070i	0.353899	+	0.612970i
$103$	4.63770	+	2.67758i	0.456966	+	0.263829i	0.710768	−	0.703427i	$-0.248348\pi$
$103$	4.63770	+	2.67758i	0.456966	+	0.263829i	−0.253802	+	0.967256i	$0.581681\pi$
$104$			27.7838i			2.72443i
$105$	2.33834	−	3.21456i	0.228199	−	0.313709i
$106$			32.2384i			3.13127i
$107$	10.5000	+	6.06216i	1.01507	+	0.586051i	0.912672	−	0.408693i	$-0.134015\pi$
$107$	10.5000	+	6.06216i	1.01507	+	0.586051i	0.102398	+	0.994744i	$0.467349\pi$
$108$	−4.06144	+	2.34487i	−0.390812	+	0.225636i
$109$	16.3041	−	9.41320i	1.56165	−	0.901621i	0.564564	−	0.825390i	$-0.309045\pi$
$109$	16.3041	−	9.41320i	1.56165	−	0.901621i	0.997090	−	0.0762315i	$-0.0242888\pi$
$110$	−11.6596	−	5.49225i	−1.11170	−	0.523665i
$111$		−	7.81594i		−	0.741857i
$112$	9.25801	+	20.8261i	0.874800	+	1.96788i
$113$	2.11831			0.199273			0.0996367	−	0.995024i	$-0.468232\pi$
$113$	2.11831			0.199273			0.0996367	+	0.995024i	$0.468232\pi$
$114$	−6.35949	+	11.0150i	−0.595621	+	1.03165i
$115$	−0.0936104	+	0.0540460i	−0.00872922	+	0.00503982i
$116$	−20.5637	+	11.8725i	−1.90929	+	1.10233i
$117$	−1.99685	+	3.45864i	−0.184609	+	0.319752i
$118$	16.4964			1.51862
$119$	7.27178	+	0.768529i	0.666603	+	0.0704509i
$120$		−	10.4523i		−	0.954164i
$121$	3.84251	−	10.3070i	0.349319	−	0.937004i
$122$	−3.08555	+	1.78144i	−0.279352	+	0.161284i
$123$	2.58392	−	1.49183i	0.232984	−	0.134514i
$124$	−41.4939	−	23.9565i	−3.72626	−	2.15136i
$125$			11.6329i			1.04048i
$126$	−0.719219	+	6.80522i	−0.0640731	+	0.606257i
$127$		−	0.665478i		−	0.0590516i	−0.999564	−	0.0295258i	$-0.990600\pi$
$127$		−	0.665478i		−	0.0590516i	0.999564	−	0.0295258i	$-0.00939973\pi$
$128$	−4.61052	−	2.66189i	−0.407516	−	0.235280i
$129$	2.70517	+	4.68549i	0.238177	+	0.412534i
$130$	−7.75973	−	13.4403i	−0.680574	−	1.17879i
$131$	0.737438	−	1.27728i	0.0644303	−	0.111597i	−0.832011	−	0.554759i	$-0.812810\pi$
$131$	0.737438	−	1.27728i	0.0644303	−	0.111597i	0.896441	+	0.443163i	$0.146144\pi$
$132$	15.5001	−	1.29536i	1.34911	−	0.112747i
$133$	5.28504	+	11.8888i	0.458271	+	1.03089i
$134$		−	11.7771i		−	1.01739i
$135$	0.751219	−	1.30115i	0.0646547	−	0.111985i
$136$	16.6514	−	9.61370i	1.42785	−	0.824368i
$137$	−9.40810	−	16.2953i	−0.803788	−	1.39220i	−0.917106	−	0.398643i	$-0.869481\pi$
$137$	−9.40810	−	16.2953i	−0.803788	−	1.39220i	0.113318	−	0.993559i	$-0.463852\pi$
$138$	0.0930404	−	0.161151i	0.00792013	−	0.0137181i
$139$	−6.54622			−0.555243			−0.277622	−	0.960691i	$-0.589546\pi$
$139$	−6.54622			−0.555243			−0.277622	+	0.960691i	$0.589546\pi$
$140$	−15.0755	−	10.9662i	−1.27411	−	0.926817i
$141$	−5.18095			−0.436315
$142$	−21.4911	−	12.4079i	−1.80349	−	1.04125i
$143$	10.8796	−	7.55510i	0.909799	−	0.631790i
$144$	4.30712	+	7.46016i	0.358927	+	0.621680i
$145$	3.80354	−	6.58792i	0.315867	−	0.547097i
$146$			23.1770i			1.91815i
$147$	5.19662	+	4.68990i	0.428610	+	0.386817i
$148$	−36.6548			−3.01301
$149$	−11.0720	−	6.39240i	−0.907050	−	0.523686i	−0.0275695	−	0.999620i	$-0.508777\pi$
$149$	−11.0720	−	6.39240i	−0.907050	−	0.523686i	−0.879481	+	0.475934i	$0.842110\pi$
$150$	−3.54691	−	6.14342i	−0.289604	−	0.501608i
$151$	−12.7783	+	7.37753i	−1.03988	+	0.600375i	−0.919799	−	0.392389i	$-0.871649\pi$
$151$	−12.7783	+	7.37753i	−1.03988	+	0.600375i	−0.120081	+	0.992764i	$0.538315\pi$
$152$	29.6275	+	17.1054i	2.40311	+	1.38743i
$153$	2.76378			0.223439
$154$	11.7761	−	19.4019i	0.948943	−	1.56345i
$155$	15.3497			1.23292
$156$	16.2202	+	9.36472i	1.29865	+	0.749777i
$157$	−15.0333	+	8.67945i	−1.19978	+	0.692696i	−0.960507	−	0.278256i	$-0.910244\pi$
$157$	−15.0333	+	8.67945i	−1.19978	+	0.692696i	−0.239277	+	0.970951i	$0.576910\pi$
$158$	−15.0721	−	26.1056i	−1.19907	−	2.07685i
$159$	10.7944	+	6.23215i	0.856052	+	0.494242i
$160$	−12.5702			−0.993762
$161$	−0.0773209	−	0.173935i	−0.00609374	−	0.0137080i
$162$			2.58645i			0.203211i
$163$	−1.28442	+	2.22468i	−0.100603	+	0.174250i	−0.911933	−	0.410338i	$-0.865411\pi$
$163$	−1.28442	+	2.22468i	−0.100603	+	0.174250i	0.811330	+	0.584588i	$0.198744\pi$
$164$	−6.99630	−	12.1179i	−0.546319	−	0.946253i
$165$	−4.09294	+	2.84225i	−0.318635	+	0.221269i
$166$	20.9310	+	12.0845i	1.62456	+	0.937943i
$167$	0.481460			0.0372565			0.0186282	−	0.999826i	$-0.494070\pi$
$167$	0.481460			0.0372565			0.0186282	+	0.999826i	$0.494070\pi$
$168$	18.3043	+	1.93452i	1.41221	+	0.149251i
$169$	2.94961			0.226893
$170$	−5.37002	+	9.30114i	−0.411862	+	0.713365i
$171$	2.45877	+	4.25871i	0.188027	+	0.325672i
$172$	21.9738	−	12.6866i	1.67548	−	0.967341i
$173$	0.955231	−	1.65451i	0.0726248	−	0.125790i	−0.827426	−	0.561575i	$-0.810196\pi$
$173$	0.955231	−	1.65451i	0.0726248	−	0.125790i	0.900051	+	0.435785i	$0.143529\pi$
$174$			13.0956i			0.992776i
$175$	−7.21625	−	0.762660i	−0.545497	−	0.0576516i
$176$	−2.37935	−	28.4710i	−0.179350	−	2.14608i
$177$	3.18901	−	5.52352i	0.239700	−	0.415173i
$178$	17.6043	+	30.4915i	1.31950	+	2.28543i
$179$	6.83060	+	11.8309i	0.510543	+	0.884287i	0.999925	+	0.0122172i	$0.00388897\pi$
$179$	6.83060	+	11.8309i	0.510543	+	0.884287i	−0.489382	+	0.872069i	$0.662778\pi$
$180$	−6.10207	−	3.52303i	−0.454821	−	0.262591i
$181$		−	15.6168i		−	1.16079i	−0.814337	−	0.580393i	$-0.802899\pi$
$181$		−	15.6168i		−	1.16079i	0.814337	−	0.580393i	$-0.197101\pi$
$182$	24.9730	−	11.1015i	1.85112	−	0.822895i
$183$			1.37752i			0.101829i
$184$	−0.433455	−	0.250255i	−0.0319547	−	0.0184491i
$185$	10.1697	−	5.87149i	0.747693	−	0.431680i
$186$	−22.8844	+	13.2123i	−1.67797	+	0.968775i
$187$	−8.29248	−	3.90618i	−0.606406	−	0.285648i
$188$			24.2974i			1.77207i
$189$	2.13956	+	1.55637i	0.155630	+	0.113209i
$190$	−19.1095			−1.38635
$191$	−5.84299	+	10.1203i	−0.422784	+	0.732283i	−0.996211	−	0.0869740i	$-0.972280\pi$
$191$	−5.84299	+	10.1203i	−0.422784	+	0.732283i	0.573427	+	0.819257i	$0.305614\pi$
$192$	3.82019	−	2.20559i	0.275698	−	0.159175i
$193$	−15.4067	+	8.89508i	−1.10900	+	0.640282i	−0.938570	−	0.345088i	$-0.887849\pi$
$193$	−15.4067	+	8.89508i	−1.10900	+	0.640282i	−0.170430	+	0.985370i	$0.554516\pi$
$194$	−3.40830	+	5.90335i	−0.244702	+	0.423836i
$195$	−6.00028			−0.429689
$196$	21.9945	−	24.3708i	1.57103	−	1.74077i
$197$		−	17.6962i		−	1.26080i	−0.776270	−	0.630400i	$-0.782891\pi$
$197$		−	17.6962i		−	1.26080i	0.776270	−	0.630400i	$-0.217109\pi$
$198$	3.65556	−	7.76042i	0.259789	−	0.551509i
$199$	−2.02214	+	1.16748i	−0.143345	+	0.0827605i	−0.569957	−	0.821674i	$-0.693040\pi$
$199$	−2.02214	+	1.16748i	−0.143345	+	0.0827605i	0.426612	+	0.904435i	$0.359707\pi$
$200$	−16.5243	+	9.54029i	−1.16844	+	0.674600i
$201$	−3.94334	−	2.27669i	−0.278142	−	0.160585i
$202$		−	16.4502i		−	1.15743i
$203$	10.8329	+	7.88012i	0.760323	+	0.553076i
$204$		−	12.9614i		−	0.907483i
$205$	3.88219	+	2.24138i	0.271144	+	0.156545i
$206$	−6.92543	−	11.9952i	−0.482518	−	0.835745i
$207$	−0.0359722	−	0.0623056i	−0.00250024	−	0.00433054i
$208$	17.2013	−	29.7936i	1.19270	−	2.06581i
$209$	−1.35828	−	16.2530i	−0.0939541	−	1.12424i
$210$	−9.39490	+	4.17640i	−0.648310	+	0.288199i
$211$		−	11.1551i		−	0.767950i	−0.923344	−	0.383975i	$-0.874555\pi$
$211$		−	11.1551i		−	0.767950i	0.923344	−	0.383975i	$-0.125445\pi$
$212$	29.2272	−	50.6231i	2.00733	−	3.47681i
$213$	−8.30910	+	4.79726i	−0.569330	+	0.328703i
$214$	−15.6795	−	27.1577i	−1.07183	−	1.85646i
$215$	−4.06435	+	7.03966i	−0.277186	+	0.480101i
$216$	6.95692			0.473358
$217$	−2.84093	+	26.8807i	−0.192855	+	1.82478i
$218$	−48.6936			−3.29795
$219$	7.76039	+	4.48046i	0.524399	+	0.302762i
$220$	13.3294	+	19.1949i	0.898671	+	1.29412i
$221$	−5.51886	−	9.55894i	−0.371238	−	0.643004i
$222$	−10.1078	+	17.5072i	−0.678391	+	1.17501i
$223$			18.8511i			1.26236i	0.775635	+	0.631182i	$0.217430\pi$
$223$			18.8511i			1.26236i	−0.775635	+	0.631182i	$0.782570\pi$
$224$	2.32649	−	22.0132i	0.155445	−	1.47082i
$225$	−2.74268			−0.182845
$226$	−4.74487	−	2.73945i	−0.315624	−	0.182226i
$227$	−0.634068	−	1.09824i	−0.0420846	−	0.0728926i	0.844216	−	0.536003i	$-0.180067\pi$
$227$	−0.634068	−	1.09824i	−0.0420846	−	0.0728926i	−0.886300	+	0.463111i	$0.846733\pi$
$228$	19.9723	−	11.5310i	1.32270	−	0.763660i
$229$	23.5072	+	13.5719i	1.55340	+	0.896857i	0.997861	+	0.0653679i	$0.0208221\pi$
$229$	23.5072	+	13.5719i	1.55340	+	0.896857i	0.555541	+	0.831489i	$0.312511\pi$
$230$	0.279575			0.0184346
$231$	−4.21988	−	7.69367i	−0.277648	−	0.506207i
$232$	35.2239			2.31256
$233$	−0.273856	−	0.158111i	−0.0179409	−	0.0103582i	0.491003	−	0.871158i	$-0.336631\pi$
$233$	−0.273856	−	0.158111i	−0.0179409	−	0.0103582i	−0.508944	+	0.860800i	$0.669964\pi$
$234$	8.94562	−	5.16476i	0.584794	−	0.337631i
$235$	−3.89203	−	6.74120i	−0.253888	−	0.439747i
$236$	−25.9039	−	14.9556i	−1.68620	−	0.973529i
$237$	−11.6546			−0.757048
$238$	−15.2944	−	11.1255i	−0.991392	−	0.721161i
$239$		−	0.351465i		−	0.0227344i	−0.999935	−	0.0113672i	$-0.996382\pi$
$239$		−	0.351465i		−	0.0227344i	0.999935	−	0.0113672i	$-0.00361837\pi$
$240$	−6.47119	+	11.2084i	−0.417714	+	0.723501i
$241$	10.1998	+	17.6665i	0.657026	+	1.13800i	0.981382	+	0.192067i	$0.0615191\pi$
$241$	10.1998	+	17.6665i	0.657026	+	1.13800i	−0.324356	+	0.945935i	$0.605148\pi$
$242$	−21.9363	+	18.1179i	−1.41012	+	1.16466i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	6.46021			0.413572
$245$	−2.19847	+	10.2847i	−0.140455	+	0.657067i
$246$	−7.71709			−0.492024
$247$	9.81958	−	17.0080i	0.624805	−	1.08219i
$248$	35.5378	+	61.5533i	2.25665	+	3.90864i
$249$	8.09256	−	4.67224i	0.512845	−	0.296091i
$250$	15.0440	−	26.0569i	0.951465	−	1.64799i
$251$		−	21.9352i		−	1.38454i	−0.721639	−	0.692269i	$-0.756611\pi$
$251$		−	21.9352i		−	1.38454i	0.721639	−	0.692269i	$-0.243389\pi$
$252$	7.29896	−	10.0340i	0.459792	−	0.632083i
$253$	0.0198718	+	0.237784i	0.00124933	+	0.0149493i
$254$	−0.860615	+	1.49063i	−0.0539998	+	0.0935304i
$255$	2.07621	+	3.59610i	0.130017	+	0.225196i
$256$	11.2960	+	19.5653i	0.706001	+	1.22283i
$257$	0.967481	+	0.558576i	0.0603498	+	0.0348430i	0.529871	−	0.848078i	$-0.322240\pi$
$257$	0.967481	+	0.558576i	0.0603498	+	0.0348430i	−0.469521	+	0.882921i	$0.655574\pi$
$258$		−	13.9936i		−	0.871202i
$259$	8.40005	+	18.8961i	0.521954	+	1.17415i
$260$			28.1398i			1.74516i
$261$	4.38482	+	2.53158i	0.271414	+	0.156701i
$262$	−3.30363	+	1.90735i	−0.204099	+	0.117837i
$263$	1.06423	−	0.614435i	0.0656234	−	0.0378877i	−0.466829	−	0.884347i	$-0.654604\pi$
$263$	1.06423	−	0.614435i	0.0656234	−	0.0378877i	0.532453	+	0.846460i	$0.321270\pi$
$264$	−20.8736	−	9.83253i	−1.28468	−	0.605150i
$265$			18.7269i			1.15038i
$266$	3.53678	−	33.4649i	0.216854	−	2.05186i
$267$	13.6127			0.833082
$268$	−10.6771	+	18.4933i	−0.652207	+	1.12966i
$269$	−5.38708	+	3.11023i	−0.328456	+	0.189634i	−0.655156	−	0.755494i	$-0.727397\pi$
$269$	−5.38708	+	3.11023i	−0.328456	+	0.189634i	0.326699	+	0.945128i	$0.394064\pi$
$270$	−3.36537	+	1.94300i	−0.204810	+	0.118247i
$271$	−0.0554755	+	0.0960864i	−0.00336990	+	0.00583683i	−0.867705	−	0.497079i	$-0.834406\pi$
$271$	−0.0554755	+	0.0960864i	−0.00336990	+	0.00583683i	0.864336	+	0.502916i	$0.167739\pi$
$272$	−23.8079			−1.44357
$273$	1.11053	−	10.5078i	0.0672124	−	0.635961i
$274$			48.6672i			2.94010i
$275$	8.22915	+	3.87635i	0.496237	+	0.233753i
$276$	−0.292198	+	0.168700i	−0.0175882	+	0.0101546i
$277$	−12.8506	+	7.41932i	−0.772120	+	0.445784i	−0.833630	−	0.552323i	$-0.813742\pi$
$277$	−12.8506	+	7.41932i	−0.772120	+	0.445784i	0.0615103	+	0.998106i	$0.480408\pi$
$278$	14.6631	+	8.46575i	0.879435	+	0.507742i
$279$			10.2165i			0.611649i
$280$	11.2335	+	25.2699i	0.671328	+	1.51017i
$281$		−	4.77342i		−	0.284759i	−0.989812	−	0.142379i	$-0.954525\pi$
$281$		−	4.77342i		−	0.284759i	0.989812	−	0.142379i	$-0.0454753\pi$
$282$	11.6050	+	6.70015i	0.691068	+	0.398988i
$283$	−15.9287	−	27.5893i	−0.946862	−	1.64001i	−0.751979	−	0.659187i	$-0.770900\pi$
$283$	−15.9287	−	27.5893i	−0.946862	−	1.64001i	−0.194884	−	0.980826i	$-0.562433\pi$
$284$	22.4979	+	38.9676i	1.33501	+	2.31230i
$285$	−3.69415	+	6.39846i	−0.218823	+	0.379012i
$286$	−34.1401	+	2.85313i	−2.01875	+	0.168709i
$287$	−4.64366	+	6.38372i	−0.274107	+	0.376819i
$288$		−	8.36654i		−	0.493003i
$289$	4.68075	−	8.10730i	0.275338	−	0.476900i
$290$	−17.0394	+	9.83768i	−1.00059	+	0.577689i
$291$	1.31775	+	2.28241i	0.0772478	+	0.133797i
$292$	21.0123	−	36.3943i	1.22965	−	2.12981i
$293$	−21.1094			−1.23322			−0.616611	−	0.787268i	$-0.711495\pi$
$293$	−21.1094			−1.23322			−0.616611	+	0.787268i	$0.711495\pi$
$294$	−5.57498	−	17.2255i	−0.325139	−	1.00461i
$295$	9.58257			0.557919
$296$	47.0900	+	27.1874i	2.73705	+	1.58024i
$297$	−1.89176	−	2.72420i	−0.109771	−	0.158074i
$298$	16.5337	+	28.6371i	0.957769	+	1.65890i
$299$	−0.143662	+	0.248830i	−0.00830819	+	0.0143902i
$300$			12.8625i			0.742615i
$301$	−11.5757	−	8.42046i	−0.667215	−	0.485347i
$302$	38.1633			2.19605
$303$	−5.50804	−	3.18007i	−0.316429	−	0.182690i
$304$	−21.1804	−	36.6856i	−1.21478	−	2.10406i
$305$	−1.79236	+	1.03482i	−0.102630	+	0.0592535i
$306$	−6.19070	−	3.57420i	−0.353899	−	0.204323i
$307$	7.64034			0.436057			0.218029	−	0.975942i	$-0.430037\pi$
$307$	7.64034			0.436057			0.218029	+	0.975942i	$0.430037\pi$
$308$	−36.0814	+	19.7902i	−2.05593	+	1.12765i
$309$	−5.35515			−0.304644
$310$	−34.3824	−	19.8507i	−1.95279	−	1.12744i
$311$	7.61926	−	4.39898i	0.432049	−	0.249444i	−0.268170	−	0.963372i	$-0.586419\pi$
$311$	7.61926	−	4.39898i	0.432049	−	0.249444i	0.700219	+	0.713928i	$0.253086\pi$
$312$	−13.8919	−	24.0615i	−0.786474	−	1.36221i
$313$	−0.915184	−	0.528382i	−0.0517293	−	0.0298659i	0.473912	−	0.880572i	$-0.342841\pi$
$313$	−0.915184	−	0.528382i	−0.0517293	−	0.0298659i	−0.525642	+	0.850706i	$0.676175\pi$
$314$	44.8980			2.53374
$315$	−0.417785	+	3.95306i	−0.0235395	+	0.222730i
$316$			54.6572i			3.07471i
$317$	−1.75229	+	3.03505i	−0.0984182	+	0.170465i	−0.911030	−	0.412340i	$-0.864712\pi$
$317$	−1.75229	+	3.03505i	−0.0984182	+	0.170465i	0.812612	+	0.582805i	$0.198045\pi$
$318$	−16.1192	−	27.9192i	−0.903919	−	1.56563i
$319$	−9.57826	−	13.7930i	−0.536280	−	0.772262i
$320$	5.73960	+	3.31376i	0.320853	+	0.185245i
$321$	−12.1243			−0.676713
$322$	−0.0517437	+	0.489597i	−0.00288356	+	0.0272842i
$323$	−13.5910			−0.756224
$324$	2.34487	−	4.06144i	0.130271	−	0.225636i
$325$	5.47671	+	9.48594i	0.303793	+	0.526185i
$326$	5.75402	−	3.32209i	0.318686	−	0.183993i
$327$	−9.41320	+	16.3041i	−0.520551	+	0.901621i
$328$			20.7570i			1.14612i
$329$	12.5256	−	5.56814i	0.690561	−	0.306981i
$330$	12.8436	−	1.07335i	0.707017	−	0.0590862i
$331$	−2.79600	+	4.84282i	−0.153682	+	0.266185i	−0.932578	−	0.360967i	$-0.882447\pi$
$331$	−2.79600	+	4.84282i	−0.153682	+	0.266185i	0.778896	+	0.627153i	$0.215780\pi$
$332$	−21.9116	−	37.9521i	−1.20256	−	2.08289i
$333$	3.90797	+	6.76881i	0.214156	+	0.370928i
$334$	−1.07844	−	0.622637i	−0.0590095	−	0.0340692i
$335$		−	6.84117i		−	0.373773i
$336$	−18.4307	−	13.4069i	−1.00548	−	0.731408i
$337$			0.965186i			0.0525770i	0.999654	+	0.0262885i	$0.00836886\pi$
$337$			0.965186i			0.0525770i	−0.999654	+	0.0262885i	$0.991631\pi$
$338$	−6.60693	−	3.81452i	−0.359370	−	0.207482i
$339$	−1.83451	+	1.05915i	−0.0996367	+	0.0575253i
$340$	16.8648	−	9.73689i	0.914622	−	0.528057i
$341$	14.4395	−	30.6538i	0.781944	−	1.66000i
$342$		−	12.7190i		−	0.687764i
$343$	−17.6039	−	5.75349i	−0.950521	−	0.310659i
$344$	−37.6392			−2.02937
$345$	0.0540460	−	0.0936104i	0.00290974	−	0.00503982i
$346$	−4.27931	+	2.47066i	−0.230057	+	0.132824i
$347$	31.5153	−	18.1954i	1.69183	−	0.976778i	0.738789	−	0.673937i	$-0.235398\pi$
$347$	31.5153	−	18.1954i	1.69183	−	0.976778i	0.953041	−	0.302841i	$-0.0979351\pi$
$348$	11.8725	−	20.5637i	0.636431	−	1.10233i
$349$	12.6498			0.677128			0.338564	−	0.940943i	$-0.390059\pi$
$349$	12.6498			0.677128			0.338564	+	0.940943i	$0.390059\pi$
$350$	15.1776	+	11.0406i	0.811279	+	0.590143i
$351$		−	3.99370i		−	0.213168i
$352$	−11.8248	+	25.1030i	−0.630265	+	1.33800i
$353$	−1.58250	+	0.913659i	−0.0842282	+	0.0486292i	−0.541523	−	0.840686i	$-0.682152\pi$
$353$	−1.58250	+	0.913659i	−0.0842282	+	0.0486292i	0.457294	+	0.889315i	$0.348819\pi$
$354$	−14.2863	+	8.24822i	−0.759310	+	0.438388i
$355$	−12.4839	−	7.20759i	−0.662577	−	0.382539i
$356$		−	63.8400i		−	3.38351i
$357$	−6.68181	+	2.97033i	−0.353639	+	0.157206i
$358$		−	35.3341i		−	1.86746i
$359$	14.7139	+	8.49508i	0.776571	+	0.448353i	0.835214	−	0.549926i	$-0.185344\pi$
$359$	14.7139	+	8.49508i	0.776571	+	0.448353i	−0.0586430	+	0.998279i	$0.518677\pi$
$360$	5.22617	+	9.05199i	0.275443	+	0.477082i
$361$	−2.59109	−	4.48789i	−0.136373	−	0.236205i
$362$	−20.1960	+	34.9806i	−1.06148	+	1.83854i
$363$	1.82581	+	10.8474i	0.0958303	+	0.569342i
$364$	−49.2790	−	5.20812i	−2.58292	−	0.272979i
$365$			13.4632i			0.704699i
$366$	1.78144	−	3.08555i	0.0931175	−	0.161284i
$367$	−10.2798	+	5.93504i	−0.536601	+	0.309807i	−0.743700	−	0.668513i	$-0.766931\pi$
$367$	−10.2798	+	5.93504i	−0.536601	+	0.309807i	0.207099	+	0.978320i	$0.433598\pi$
$368$	0.309873	+	0.536716i	0.0161533	+	0.0279783i
$369$	−1.49183	+	2.58392i	−0.0776615	+	0.134514i
$370$	−30.3727			−1.57900
$371$	−32.7948	−	3.46596i	−1.70262	−	0.179944i
$372$	47.9131			2.48418
$373$	−12.7965	−	7.38809i	−0.662580	−	0.382541i	0.130679	−	0.991425i	$-0.458284\pi$
$373$	−12.7965	−	7.38809i	−0.662580	−	0.382541i	−0.793259	+	0.608884i	$0.791617\pi$
$374$	13.5230	+	19.4737i	0.699260	+	1.00696i
$375$	−5.81645	−	10.0744i	−0.300360	−	0.520239i
$376$	18.0217	−	31.2145i	0.929399	−	1.60977i
$377$		−	20.2207i		−	1.04142i
$378$	−2.77975	−	6.25310i	−0.142975	−	0.321625i
$379$	−19.7260			−1.01326			−0.506628	−	0.862165i	$-0.669108\pi$
$379$	−19.7260			−1.01326			−0.506628	+	0.862165i	$0.669108\pi$
$380$	30.0071	+	17.3246i	1.53933	+	0.888735i
$381$	0.332739	+	0.576321i	0.0170467	+	0.0295258i
$382$	26.1758	−	15.1126i	1.33927	−	0.773229i
$383$	10.9399	+	6.31615i	0.559002	+	0.322740i	0.752745	−	0.658312i	$-0.228729\pi$
$383$	10.9399	+	6.31615i	0.559002	+	0.322740i	−0.193743	+	0.981052i	$0.562063\pi$
$384$	5.32377			0.271678
$385$	6.84057	−	11.2703i	0.348628	−	0.574389i
$386$	46.0134			2.34202
$387$	−4.68549	−	2.70517i	−0.238177	−	0.137511i
$388$	10.7039	−	6.17991i	0.543409	−	0.313738i
$389$	14.3810	+	24.9086i	0.729144	+	1.26291i	0.957245	+	0.289277i	$0.0934149\pi$
$389$	14.3810	+	24.9086i	0.729144	+	1.26291i	−0.228102	+	0.973637i	$0.573252\pi$
$390$	13.4403	+	7.75973i	0.680574	+	0.392929i
$391$	0.198839			0.0100557
$392$	−46.3322	+	14.9953i	−2.34013	+	0.757377i
$393$			1.47488i			0.0743977i
$394$	−22.8852	+	39.6383i	−1.15294	+	1.99695i
$395$	−8.75517	−	15.1644i	−0.440520	−	0.763004i
$396$	−12.7758	+	8.87187i	−0.642008	+	0.445828i
$397$	19.3944	+	11.1974i	0.973378	+	0.561980i	0.900264	−	0.435344i	$-0.143373\pi$
$397$	19.3944	+	11.1974i	0.973378	+	0.561980i	0.0731135	+	0.997324i	$0.476706\pi$
$398$	6.03927			0.302721
$399$	−10.5214	−	7.65349i	−0.526728	−	0.383154i
$400$	23.6261			1.18131
$401$	−7.85831	+	13.6110i	−0.392425	+	0.679701i	−0.992769	−	0.120042i	$-0.961697\pi$
$401$	−7.85831	+	13.6110i	−0.392425	+	0.679701i	0.600343	+	0.799742i	$0.295031\pi$
$402$	5.88855	+	10.1993i	0.293694	+	0.508693i
$403$	35.3354	−	20.4009i	1.76018	−	1.01624i
$404$	−14.9137	+	25.8313i	−0.741985	+	1.28516i
$405$			1.50244i			0.0746568i
$406$	−14.0743	−	31.6604i	−0.698495	−	1.57128i
$407$	−2.15885	−	25.8325i	−0.107010	−	1.28047i
$408$	−9.61370	+	16.6514i	−0.475949	+	0.824368i
$409$	2.85696	+	4.94841i	0.141268	+	0.244683i	0.927974	−	0.372644i	$-0.121549\pi$
$409$	2.85696	+	4.94841i	0.141268	+	0.244683i	−0.786707	+	0.617327i	$0.788215\pi$
$410$	−5.79723	−	10.0411i	−0.286305	−	0.495895i
$411$	16.2953	+	9.40810i	0.803788	+	0.464067i
$412$			25.1143i			1.23729i
$413$	−1.77354	+	16.7812i	−0.0872703	+	0.825748i
$414$			0.186081i			0.00914537i
$415$	12.1586	+	7.01976i	0.596841	+	0.344586i
$416$	−28.9369	+	16.7067i	−1.41875	+	0.819114i
$417$	5.66919	−	3.27311i	0.277622	−	0.160285i
$418$	−17.9763	+	38.1622i	−0.879251	+	1.86657i
$419$			7.07742i			0.345755i	0.984943	+	0.172877i	$0.0553064\pi$
$419$			7.07742i			0.345755i	−0.984943	+	0.172877i	$0.944694\pi$
$420$	18.5389	+	1.95931i	0.904605	+	0.0956044i
$421$	12.8275			0.625173			0.312586	−	0.949889i	$-0.398805\pi$
$421$	12.8275			0.625173			0.312586	+	0.949889i	$0.398805\pi$
$422$	−14.4261	+	24.9867i	−0.702252	+	1.21634i
$423$	4.48684	−	2.59048i	0.218157	−	0.125953i
$424$	−75.0958	+	43.3566i	−3.64697	+	2.10558i
$425$	3.79008	−	6.56462i	0.183846	−	0.318431i
$426$	24.8158			1.20233
$427$	−1.48046	−	3.33033i	−0.0716446	−	0.161166i
$428$			56.8600i			2.74843i
$429$	−5.64447	+	11.9827i	−0.272518	+	0.578531i
$430$	18.2078	−	10.5123i	0.878056	−	0.506946i
$431$	−9.62549	+	5.55728i	−0.463644	+	0.267685i	−0.713575	−	0.700579i	$-0.752925\pi$
$431$	−9.62549	+	5.55728i	−0.463644	+	0.267685i	0.249932	+	0.968264i	$0.419592\pi$
$432$	−7.46016	−	4.30712i	−0.358927	−	0.207227i
$433$		−	10.6990i		−	0.514162i	−0.966390	−	0.257081i	$-0.917239\pi$
$433$		−	10.6990i		−	0.514162i	0.966390	−	0.257081i	$-0.0827607\pi$
$434$	41.1264	−	56.5372i	1.97413	−	2.71387i
$435$			7.60708i			0.364732i
$436$	76.4623	+	44.1456i	3.66188	+	2.11419i
$437$	0.176895	+	0.306390i	0.00846201	+	0.0146566i
$438$	−11.5885	−	20.0719i	−0.553721	−	0.959073i
$439$	−1.92165	+	3.32839i	−0.0917152	+	0.158855i	−0.908233	−	0.418465i	$-0.862568\pi$
$439$	−1.92165	+	3.32839i	−0.0917152	+	0.158855i	0.816518	+	0.577320i	$0.195902\pi$
$440$	−2.88705	−	34.5461i	−0.137635	−	1.64692i
$441$	−6.84535	−	1.46327i	−0.325969	−	0.0696793i
$442$			28.5485i			1.35792i
$443$	−20.5906	+	35.6640i	−0.978289	+	1.69445i	−0.309664	+	0.950846i	$0.600217\pi$
$443$	−20.5906	+	35.6640i	−0.978289	+	1.69445i	−0.668625	+	0.743600i	$0.733117\pi$
$444$	31.7440	−	18.3274i	1.50650	−	0.869780i
$445$	10.2261	+	17.7121i	0.484764	+	0.839635i
$446$	24.3788	−	42.2253i	1.15437	−	1.99942i
$447$	12.7848			0.604700
$448$	−6.86540	+	9.43798i	−0.324360	+	0.445903i
$449$	−4.60643			−0.217391			−0.108695	−	0.994075i	$-0.534667\pi$
$449$	−4.60643			−0.217391			−0.108695	+	0.994075i	$0.534667\pi$
$450$	6.14342	+	3.54691i	0.289604	+	0.167203i
$451$	8.12807	−	5.64436i	0.382736	−	0.265782i
$452$	4.96716	+	8.60337i	0.233636	+	0.404669i
$453$	7.37753	−	12.7783i	0.346627	−	0.600375i
$454$			3.27998i			0.153937i
$455$	14.5065	−	6.44870i	0.680075	−	0.302320i
$456$	−34.2109			−1.60207
$457$	−9.61430	−	5.55082i	−0.449738	−	0.259656i	0.257982	−	0.966150i	$-0.416943\pi$
$457$	−9.61430	−	5.55082i	−0.449738	−	0.259656i	−0.707720	+	0.706493i	$0.750276\pi$
$458$	−35.1031	−	60.8004i	−1.64026	−	2.84102i
$459$	−2.39351	+	1.38189i	−0.111719	+	0.0645012i
$460$	−0.439009	−	0.253462i	−0.0204689	−	0.0118177i
$461$	36.8801			1.71768			0.858838	−	0.512247i	$-0.171187\pi$
$461$	36.8801			1.71768			0.858838	+	0.512247i	$0.171187\pi$
$462$	−0.497416	+	22.6906i	−0.0231419	+	1.05566i
$463$	−8.86148			−0.411828			−0.205914	−	0.978570i	$-0.566017\pi$
$463$	−8.86148			−0.411828			−0.205914	+	0.978570i	$0.566017\pi$
$464$	−37.7719	−	21.8076i	−1.75352	−	1.01239i
$465$	−13.2933	+	7.67487i	−0.616460	+	0.355914i
$466$	0.408947	+	0.708317i	0.0189441	+	0.0328122i
$467$	−26.2487	−	15.1547i	−1.21464	−	0.701276i	−0.250877	−	0.968019i	$-0.580719\pi$
$467$	−26.2487	−	15.1547i	−1.21464	−	0.701276i	−0.963768	+	0.266743i	$0.914052\pi$
$468$	−18.7294			−0.865768
$469$	11.9804	+	1.26616i	0.553202	+	0.0584659i
$470$			20.1331i			0.928672i
$471$	8.67945	−	15.0333i	0.399928	−	0.692696i
$472$	22.1856	+	38.4267i	1.02118	+	1.76873i
$473$	10.2350	+	14.7388i	0.470608	+	0.677692i
$474$	26.1056	+	15.0721i	1.19907	+	0.692283i
$475$	13.4872			0.618836
$476$	13.9301	+	31.3360i	0.638485	+	1.43628i
$477$	−12.4643			−0.570701
$478$	−0.454525	+	0.787260i	−0.0207895	+	0.0360084i
$479$	8.13051	+	14.0825i	0.371493	+	0.643444i	0.989795	−	0.142496i	$-0.0455128\pi$
$479$	8.13051	+	14.0825i	0.371493	+	0.643444i	−0.618303	+	0.785940i	$0.712179\pi$
$480$	10.8861	−	6.28511i	0.496881	−	0.286875i
$481$	15.6073	−	27.0326i	0.711629	−	1.23258i
$482$		−	52.7626i		−	2.40327i
$483$	0.153929	+	0.111972i	0.00700403	+	0.00509489i
$484$	50.8717	−	8.56260i	2.31235	−	0.389209i
$485$	−1.97984	+	3.42918i	−0.0898998	+	0.155711i
$486$	−1.29323	−	2.23994i	−0.0586620	−	0.101606i
$487$	−6.11165	−	10.5857i	−0.276945	−	0.479684i	0.693679	−	0.720285i	$-0.255989\pi$
$487$	−6.11165	−	10.5857i	−0.276945	−	0.479684i	−0.970624	+	0.240601i	$0.922655\pi$
$488$	−8.29935	−	4.79163i	−0.375694	−	0.216907i
$489$		−	2.56883i		−	0.116167i
$490$	18.2249	−	20.1940i	0.823318	−	0.912272i
$491$		−	0.0272318i		−	0.00122895i	−1.00000		0.000614476i	$-0.999804\pi$
$491$		−	0.0272318i		−	0.00122895i	1.00000		0.000614476i	$-0.000195594\pi$
$492$	12.1179	+	6.99630i	0.546319	+	0.315418i
$493$	−12.1187	+	6.99673i	−0.545798	+	0.315117i
$494$	−43.9904	+	25.3979i	−1.97922	+	1.14271i
$495$	2.12347	−	4.50793i	0.0954427	−	0.202616i
$496$		−	88.0079i		−	3.95167i
$497$	14.9326	−	20.5281i	0.669818	−	0.920810i
$498$	−24.1691			−1.08304
$499$	7.25817	−	12.5715i	0.324921	−	0.562779i	−0.656576	−	0.754260i	$-0.727996\pi$
$499$	7.25817	−	12.5715i	0.324921	−	0.562779i	0.981496	+	0.191481i	$0.0613291\pi$
$500$	−47.2463	+	27.2777i	−2.11292	+	1.21990i
$501$	−0.416956	+	0.240730i	−0.0186282	+	0.0107550i
$502$	−28.3672	+	49.1335i	−1.26609	+	2.19293i
$503$	−11.2845			−0.503153			−0.251577	−	0.967837i	$-0.580949\pi$
$503$	−11.2845			−0.503153			−0.251577	+	0.967837i	$0.580949\pi$
$504$	−16.8193	+	7.47682i	−0.749190	+	0.333044i
$505$		−	9.55571i		−	0.425224i
$506$	0.262997	−	0.558319i	0.0116916	−	0.0248203i
$507$	−2.55444	+	1.47480i	−0.113447	+	0.0654984i
$508$	2.70280	−	1.56046i	0.119917	−	0.0692344i
$509$	−35.2796	−	20.3687i	−1.56374	−	0.902827i	−0.996873	−	0.0790187i	$-0.974821\pi$
$509$	−35.2796	−	20.3687i	−1.56374	−	0.902827i	−0.566869	−	0.823808i	$-0.691845\pi$
$510$		−	10.7400i		−	0.475577i
$511$	−23.5771	−	2.49178i	−1.04299	−	0.110230i
$512$		−	47.7858i		−	2.11185i
$513$	−4.25871	−	2.45877i	−0.188027	−	0.108557i
$514$	−1.44473	−	2.50235i	−0.0637243	−	0.110374i
$515$	−4.02289	−	6.96786i	−0.177270	−	0.307040i
$516$	−12.6866	+	21.9738i	−0.558494	+	0.967341i
$517$	−17.1236	+	1.43104i	−0.753094	+	0.0629369i
$518$	5.62137	−	53.1892i	0.246989	−	2.33700i
$519$			1.91046i			0.0838599i
$520$	20.8717	−	36.1509i	0.915286	−	1.58532i
$521$	19.4307	−	11.2183i	0.851276	−	0.491484i	−0.00980511	−	0.999952i	$-0.503121\pi$
$521$	19.4307	−	11.2183i	0.851276	−	0.491484i	0.861081	+	0.508467i	$0.169788\pi$
$522$	−6.54781	−	11.3411i	−0.286590	−	0.496388i
$523$	−17.8274	+	30.8780i	−0.779539	+	1.35020i	0.152669	+	0.988277i	$0.451213\pi$
$523$	−17.8274	+	30.8780i	−0.779539	+	1.35020i	−0.932208	+	0.361924i	$0.882120\pi$
$524$	6.91680			0.302162
$525$	6.63079	−	2.94764i	0.289391	−	0.128646i
$526$	−3.17841			−0.138585
$527$	−24.4534	−	14.1182i	−1.06521	−	0.614997i
$528$	16.2961	+	23.4669i	0.709195	+	1.02127i
$529$	11.4974	+	19.9141i	0.499887	+	0.865831i
$530$	24.2181	−	41.9470i	1.05197	−	1.82206i
$531$			6.37801i			0.276782i
$532$	−35.8929	+	49.3426i	−1.55616	+	2.13927i
$533$	11.9158			0.516131
$534$	−30.4915	−	17.6043i	−1.31950	−	0.761811i
$535$	−9.10802	−	15.7756i	−0.393774	−	0.682037i
$536$	27.4335	−	15.8387i	1.18495	−	0.684128i
$537$	−11.8309	−	6.83060i	−0.510543	−	0.294762i
$538$	16.0890			0.693644
$539$	18.4708	+	14.0652i	0.795592	+	0.605833i
$540$	7.04606			0.303214
$541$	8.94502	+	5.16441i	0.384576	+	0.222035i	0.679808	−	0.733391i	$-0.262063\pi$
$541$	8.94502	+	5.16441i	0.384576	+	0.222035i	−0.295231	+	0.955426i	$0.595397\pi$
$542$	0.248523	−	0.143485i	0.0106750	−	0.00616321i
$543$	7.80839	+	13.5245i	0.335090	+	0.580393i
$544$	20.0254	+	11.5616i	0.858580	+	0.495702i
$545$	−28.2855			−1.21162
$546$	−16.0765	+	22.1006i	−0.688011	+	0.945820i
$547$			21.7253i			0.928908i	0.885597	+	0.464454i	$0.153749\pi$
$547$			21.7253i			0.928908i	−0.885597	+	0.464454i	$0.846251\pi$
$548$	44.1216	−	76.4209i	1.88478	−	3.26454i
$549$	−0.688758	−	1.19296i	−0.0293955	−	0.0509145i
$550$	−13.4198	−	19.3249i	−0.572221	−	0.824018i
$551$	−21.5625	−	12.4491i	−0.918594	−	0.530351i
$552$	0.500511			0.0213032
$553$	28.1766	−	12.5256i	1.19819	−	0.532642i
$554$	38.3795			1.63059
$555$	−5.87149	+	10.1697i	−0.249231	+	0.431680i
$556$	−15.3501	−	26.5871i	−0.650988	−	1.12754i
$557$	−9.45189	+	5.45705i	−0.400490	+	0.231223i	−0.686695	−	0.726945i	$-0.740939\pi$
$557$	−9.45189	+	5.45705i	−0.400490	+	0.231223i	0.286206	+	0.958168i	$0.407606\pi$
$558$	13.2123	−	22.8844i	0.559322	−	0.968775i
$559$			21.6072i			0.913888i
$560$	3.59890	−	34.0527i	0.152081	−	1.43899i
$561$	9.13459	−	0.763387i	0.385663	−	0.0322302i
$562$	−6.17312	+	10.6922i	−0.260397	+	0.451022i
$563$	16.2284	+	28.1084i	0.683945	+	1.18463i	0.973767	+	0.227547i	$0.0730706\pi$
$563$	16.2284	+	28.1084i	0.683945	+	1.18463i	−0.289822	+	0.957081i	$0.593596\pi$
$564$	−12.1487	−	21.0421i	−0.511552	−	0.886034i
$565$	−2.75623	−	1.59131i	−0.115956	−	0.0669470i
$566$			82.3977i			3.46343i
$567$	−2.63110	−	0.278071i	−0.110496	−	0.0116779i
$568$		−	66.7483i		−	2.80069i
$569$	−5.24498	−	3.02819i	−0.219881	−	0.126948i	0.386014	−	0.922493i	$-0.373852\pi$
$569$	−5.24498	−	3.02819i	−0.219881	−	0.126948i	−0.605895	+	0.795545i	$0.707185\pi$
$570$	16.5493	−	9.55475i	0.693175	−	0.400205i
$571$	−12.2207	+	7.05564i	−0.511421	+	0.295269i	−0.733418	−	0.679778i	$-0.762076\pi$
$571$	−12.2207	+	7.05564i	−0.511421	+	0.295269i	0.221996	+	0.975047i	$0.428743\pi$
$572$	56.1960	+	26.4712i	2.34967	+	1.10682i
$573$		−	11.6860i		−	0.488188i
$574$	18.6571	−	8.29381i	0.778732	−	0.346177i
$575$	−0.197320			−0.00822882
$576$	−2.20559	+	3.82019i	−0.0918994	+	0.159175i
$577$	38.7222	−	22.3563i	1.61203	−	0.930704i	0.623127	−	0.782121i	$-0.285862\pi$
$577$	38.7222	−	22.3563i	1.61203	−	0.930704i	0.988900	−	0.148583i	$-0.0474712\pi$
$578$	−20.9692	+	12.1066i	−0.872202	+	0.503566i
$579$	8.89508	−	15.4067i	0.369667	−	0.640282i
$580$	35.6753			1.48134
$581$	−14.5434	+	19.9931i	−0.603363	+	0.829454i
$582$		−	6.81660i		−	0.282557i
$583$	37.3980	+	17.6164i	1.54887	+	0.729596i
$584$	−53.9884	+	31.1702i	−2.23406	+	1.28983i
$585$	5.19640	−	3.00014i	0.214845	−	0.124041i
$586$	47.2836	+	27.2992i	1.95327	+	1.12772i
$587$			24.7377i			1.02103i	0.859868	+	0.510517i	$0.170546\pi$
$587$			24.7377i			1.02103i	−0.859868	+	0.510517i	$0.829454\pi$
$588$	−6.86235	+	32.1030i	−0.282998	+	1.32390i
$589$		−	50.2403i		−	2.07011i
$590$	−21.4644	−	12.3924i	−0.883673	−	0.510189i
$591$	8.84809	+	15.3253i	0.363962	+	0.630400i
$592$	−33.6642	−	58.3082i	−1.38359	−	2.39645i
$593$	−5.58906	+	9.68053i	−0.229515	+	0.397532i	−0.957664	−	0.287887i	$-0.907047\pi$
$593$	−5.58906	+	9.68053i	−0.229515	+	0.397532i	0.728149	+	0.685418i	$0.240381\pi$
$594$	0.714407	+	8.54850i	0.0293125	+	0.350749i
$595$	−8.88435	−	6.46268i	−0.364223	−	0.264944i
$596$		−	59.9575i		−	2.45596i
$597$	1.16748	−	2.02214i	0.0477818	−	0.0827605i
$598$	0.643587	−	0.371575i	0.0263182	−	0.0151948i
$599$	13.8999	+	24.0753i	0.567935	+	0.983692i	0.996770	+	0.0803093i	$0.0255908\pi$
$599$	13.8999	+	24.0753i	0.567935	+	0.983692i	−0.428835	+	0.903383i	$0.641076\pi$
$600$	9.54029	−	16.5243i	0.389481	−	0.674600i
$601$	−27.1607			−1.10791			−0.553955	−	0.832547i	$-0.686882\pi$
$601$	−27.1607			−1.10791			−0.553955	+	0.832547i	$0.686882\pi$
$602$	15.0394	+	33.8314i	0.612958	+	1.37886i
$603$	4.55337			0.185428
$604$	−59.9269	−	34.5988i	−2.43839	−	1.40780i
$605$	−12.7425	+	10.5244i	−0.518058	+	0.427880i
$606$	8.22510	+	14.2463i	0.334122	+	0.578716i
$607$	6.40473	−	11.0933i	0.259960	−	0.450264i	−0.706271	−	0.707942i	$-0.749624\pi$
$607$	6.40473	−	11.0933i	0.259960	−	0.450264i	0.966231	+	0.257678i	$0.0829572\pi$
$608$			41.1428i			1.66856i
$609$	−13.3217	−	1.40792i	−0.539821	−	0.0570517i
$610$	5.35302			0.216737
$611$	−17.9191	−	10.3456i	−0.724927	−	0.418537i
$612$	6.48072	+	11.2249i	0.261968	+	0.453742i
$613$	−37.1358	+	21.4403i	−1.49990	+	0.865968i	−1.00000		0.000115644i	$-0.999963\pi$
$613$	−37.1358	+	21.4403i	−1.49990	+	0.865968i	−0.499900	+	0.866083i	$0.666630\pi$
$614$	−17.1139	−	9.88070i	−0.690660	−	0.398753i
$615$	−4.48276			−0.180762
$616$	61.0320	+	1.33792i	2.45905	+	0.0539065i
$617$	−13.3792			−0.538627			−0.269313	−	0.963053i	$-0.586797\pi$
$617$	−13.3792			−0.538627			−0.269313	+	0.963053i	$0.586797\pi$
$618$	11.9952	+	6.92543i	0.482518	+	0.278582i
$619$	25.5309	−	14.7403i	1.02618	−	0.592463i	0.110289	−	0.993900i	$-0.464822\pi$
$619$	25.5309	−	14.7403i	1.02618	−	0.592463i	0.915887	+	0.401437i	$0.131489\pi$
$620$	35.9932	+	62.3421i	1.44552	+	2.50372i
$621$	0.0623056	+	0.0359722i	0.00250024	+	0.00144351i
$622$	−22.7555			−0.912414
$623$	−32.9104	+	14.6300i	−1.31853	+	0.586137i
$624$			34.4027i			1.37721i
$625$	1.88217	−	3.26001i	0.0752867	−	0.130400i
$626$	1.36664	+	2.36708i	0.0546217	+	0.0946076i
$627$	9.30279	+	13.3963i	0.371518	+	0.534998i
$628$	−70.5022	−	40.7044i	−2.81334	−	1.62428i
$629$	−21.6016			−0.861311
$630$	6.04802	−	8.31432i	0.240959	−	0.331250i
$631$	−14.9445			−0.594932			−0.297466	−	0.954732i	$-0.596142\pi$
$631$	−14.9445			−0.594932			−0.297466	+	0.954732i	$0.596142\pi$
$632$	40.5401	−	70.2175i	1.61260	−	2.79310i
$633$	5.57756	+	9.66061i	0.221688	+	0.383975i
$634$	7.85002	−	4.53221i	0.311764	−	0.179997i
$635$	−0.499920	+	0.865887i	−0.0198387	+	0.0343617i
$636$			58.4545i			2.31787i
$637$	8.60822	+	26.5975i	0.341070	+	1.05383i
$638$	3.61716	+	43.2824i	0.143205	+	1.71357i
$639$	4.79726	−	8.30910i	0.189777	−	0.328703i
$640$	3.99932	+	6.92703i	0.158087	+	0.273815i
$641$	−6.83538	−	11.8392i	−0.269981	−	0.467621i	0.698876	−	0.715243i	$-0.253684\pi$
$641$	−6.83538	−	11.8392i	−0.269981	−	0.467621i	−0.968857	+	0.247622i	$0.920351\pi$
$642$	27.1577	+	15.6795i	1.07183	+	0.618820i
$643$		−	31.9795i		−	1.26115i	−0.776129	−	0.630574i	$-0.782819\pi$
$643$		−	31.9795i		−	1.26115i	0.776129	−	0.630574i	$-0.217181\pi$
$644$	0.525119	−	0.721890i	0.0206926	−	0.0284465i
$645$		−	8.12870i		−	0.320067i
$646$	30.4430	+	17.5763i	1.19776	+	0.691529i
$647$	−0.719312	+	0.415295i	−0.0282791	+	0.0163269i	−0.514073	−	0.857747i	$-0.671864\pi$
$647$	−0.719312	+	0.415295i	−0.0282791	+	0.0163269i	0.485794	+	0.874073i	$0.338531\pi$
$648$	−6.02487	+	3.47846i	−0.236679	+	0.136647i
$649$	9.01434	−	19.1366i	0.353844	−	0.751179i
$650$		−	28.3305i		−	1.11121i
$651$	−10.9801	−	24.6999i	−0.430342	−	0.968064i
$652$	−12.0472			−0.471804
$653$	−9.73594	+	16.8632i	−0.380997	+	0.659906i	−0.991205	−	0.132335i	$-0.957752\pi$
$653$	−9.73594	+	16.8632i	−0.380997	+	0.659906i	0.610208	+	0.792241i	$0.291086\pi$
$654$	42.1699	−	24.3468i	1.64897	−	0.952036i
$655$	−1.91904	+	1.10796i	−0.0749830	+	0.0432914i
$656$	12.8510	−	22.2586i	0.501747	−	0.869051i
$657$	−8.96093			−0.349599
$658$	−35.2575	−	3.72624i	−1.37448	−	0.145264i
$659$		−	8.85133i		−	0.344799i	−0.985027	−	0.172399i	$-0.944848\pi$
$659$		−	8.85133i		−	0.344799i	0.985027	−	0.172399i	$-0.0551520\pi$
$660$	−21.1411	−	9.95852i	−0.822915	−	0.387635i
$661$	2.79645	−	1.61453i	0.108769	−	0.0627980i	−0.444628	−	0.895715i	$-0.646664\pi$
$661$	2.79645	−	1.61453i	0.108769	−	0.0627980i	0.553398	+	0.832917i	$0.313331\pi$
$662$	12.5257	−	7.23174i	0.486827	−	0.281069i
$663$	9.55894	+	5.51886i	0.371238	+	0.214335i
$664$			65.0088i			2.52283i
$665$	2.05447	−	19.4393i	0.0796691	−	0.753825i
$666$		−	20.2156i		−	0.783338i
$667$	0.315463	+	0.182133i	0.0122148	+	0.00705221i
$668$	1.12896	+	1.95542i	0.0436809	+	0.0756575i
$669$	−9.42556	−	16.3255i	−0.364413	−	0.631182i
$670$	−8.84718	+	15.3238i	−0.341797	+	0.592009i
$671$	0.380485	+	4.55284i	0.0146885	+	0.175760i
$672$	8.99179	+	20.2272i	0.346866	+	0.780282i
$673$			3.90455i			0.150509i	0.997164	+	0.0752547i	$0.0239770\pi$
$673$			3.90455i			0.150509i	−0.997164	+	0.0752547i	$0.976023\pi$
$674$	1.24821	−	2.16195i	0.0480791	−	0.0832754i
$675$	2.37523	−	1.37134i	0.0914226	−	0.0527828i
$676$	6.91646	+	11.9797i	0.266018	+	0.460756i
$677$	−21.1440	+	36.6224i	−0.812628	+	1.40751i	0.0983902	+	0.995148i	$0.468631\pi$
$677$	−21.1440	+	36.6224i	−0.812628	+	1.40751i	−0.911018	+	0.412366i	$0.864703\pi$
$678$	5.47890			0.210416
$679$	−5.63881	−	4.10180i	−0.216398	−	0.157413i
$680$	−28.8880			−1.10780
$681$	1.09824	+	0.634068i	0.0420846	+	0.0242975i
$682$	−71.9860	+	49.9890i	−2.75649	+	1.91418i
$683$	−6.92623	−	11.9966i	−0.265025	−	0.459036i	0.702545	−	0.711639i	$-0.252047\pi$
$683$	−6.92623	−	11.9966i	−0.265025	−	0.459036i	−0.967570	+	0.252603i	$0.918713\pi$
$684$	−11.5310	+	19.9723i	−0.440899	+	0.763660i
$685$			28.2702i			1.08015i
$686$	31.9910	+	35.6533i	1.22142	+	1.36125i
$687$	−27.1438			−1.03560
$688$	40.3619	+	23.3030i	1.53878	+	0.888418i
$689$	24.8893	+	43.1096i	0.948208	+	1.64234i
$690$	−0.242119	+	0.139788i	−0.00921732	+	0.00532162i
$691$	−23.8073	−	13.7452i	−0.905674	−	0.522891i	−0.0266373	−	0.999645i	$-0.508480\pi$
$691$	−23.8073	−	13.7452i	−0.905674	−	0.522891i	−0.879037	+	0.476754i	$0.841813\pi$
$692$	8.95958			0.340592
$693$	7.50136	+	4.55298i	0.284953	+	0.172953i
$694$	−94.1230			−3.57286
$695$	8.51761	+	4.91765i	0.323092	+	0.186537i
$696$	−30.5048	+	17.6120i	−1.15628	+	0.667580i
$697$	−4.12309	−	7.14140i	−0.156173	−	0.270500i
$698$	−28.3347	−	16.3591i	−1.07249	−	0.619200i
$699$	0.316222			0.0119606
$700$	−13.8237	−	31.0967i	−0.522487	−	1.17535i
$701$			26.9901i			1.01940i	0.860352	+	0.509700i	$0.170244\pi$
$701$			26.9901i			1.01940i	−0.860352	+	0.509700i	$0.829756\pi$
$702$	−5.16476	+	8.94562i	−0.194931	+	0.337631i
$703$	−19.2176	−	33.2859i	−0.724805	−	1.25540i
$704$	12.0169	−	8.34487i	0.452904	−	0.314509i
$705$	6.74120	+	3.89203i	0.253888	+	0.146582i
$706$	4.72628			0.177876
$707$	16.7341	+	1.76857i	0.629352	+	0.0665139i
$708$	29.9113			1.12413
$709$	−7.89225	+	13.6698i	−0.296400	+	0.513379i	−0.975310	−	0.220842i	$-0.929119\pi$
$709$	−7.89225	+	13.6698i	−0.296400	+	0.513379i	0.678910	+	0.734222i	$0.262453\pi$
$710$	18.6421	+	32.2891i	0.699626	+	1.21179i
$711$	10.0932	−	5.82731i	0.378524	−	0.218541i
$712$	−47.3511	+	82.0145i	−1.77456	+	3.07362i
$713$			0.735023i			0.0275268i
$714$	18.8081	+	1.98776i	0.703877	+	0.0743902i
$715$	−19.8316	+	1.65734i	−0.741658	+	0.0619812i
$716$	−32.0338	+	55.4842i	−1.19716	+	2.07354i
$717$	0.175733	+	0.304378i	0.00656286	+	0.0113672i
$718$	−21.9721	−	38.0569i	−0.819993	−	1.42027i
$719$	−32.4564	−	18.7387i	−1.21042	−	0.698836i	−0.247569	−	0.968870i	$-0.579632\pi$
$719$	−32.4564	−	18.7387i	−1.21042	−	0.698836i	−0.962851	+	0.270034i	$0.912965\pi$
$720$		−	12.9424i		−	0.482334i
$721$	12.9468	−	5.75535i	0.482164	−	0.214341i
$722$			13.4035i			0.498825i
$723$	−17.6665	−	10.1998i	−0.657026	−	0.379334i
$724$	63.4266	−	36.6194i	2.35723	−	1.36095i
$725$	12.0261	−	6.94330i	0.446640	−	0.257868i
$726$	9.93847	−	26.6587i	0.368851	−	0.989397i
$727$			4.00301i			0.148464i	0.997241	+	0.0742318i	$0.0236505\pi$
$727$			4.00301i			0.148464i	−0.997241	+	0.0742318i	$0.976350\pi$
$728$	59.4452	+	43.2418i	2.20318	+	1.60265i
$729$	−1.00000			−0.0370370
$730$	17.4110	−	30.1568i	0.644412	−	1.11615i
$731$	12.9497	−	7.47649i	0.478961	−	0.276528i
$732$	−5.59470	+	3.23010i	−0.206786	+	0.119388i
$733$	−0.144448	+	0.250191i	−0.00533530	+	0.00924101i	−0.868681	−	0.495372i	$-0.835032\pi$
$733$	−0.144448	+	0.250191i	−0.00533530	+	0.00924101i	0.863345	+	0.504613i	$0.168365\pi$
$734$	30.7014			1.13321
$735$	−3.23843	−	10.0061i	−0.119451	−	0.369079i
$736$		−	0.601925i		−	0.0221873i
$737$	−13.6620	−	6.43549i	−0.503246	−	0.237054i
$738$	6.68320	−	3.85855i	0.246012	−	0.142035i
$739$	3.55233	−	2.05094i	0.130674	−	0.0754449i	−0.433238	−	0.901280i	$-0.642629\pi$
$739$	3.55233	−	2.05094i	0.130674	−	0.0754449i	0.563912	+	0.825835i	$0.309296\pi$
$740$	47.6934	+	27.5358i	1.75325	+	1.01224i
$741$			19.6392i			0.721462i
$742$	68.9760	+	50.1747i	2.53219	+	1.84197i
$743$			23.5527i			0.864063i	0.901858	+	0.432032i	$0.142203\pi$
$743$			23.5527i			0.864063i	−0.901858	+	0.432032i	$0.857797\pi$
$744$	−61.5533	−	35.5378i	−2.25665	−	1.30288i
$745$	9.60419	+	16.6349i	0.351870	+	0.609457i
$746$	19.1090	+	33.0977i	0.699629	+	1.21179i
$747$	−4.67224	+	8.09256i	−0.170948	+	0.296091i
$748$	−3.58010	−	42.8389i	−0.130901	−	1.56635i
$749$	29.3121	−	13.0304i	1.07104	−	0.476120i
$750$			30.0880i			1.09866i
$751$	−7.21540	+	12.4974i	−0.263294	+	0.456038i	−0.967115	−	0.254339i	$-0.918142\pi$
$751$	−7.21540	+	12.4974i	−0.263294	+	0.456038i	0.703821	+	0.710377i	$0.251476\pi$
$752$	−38.6507	+	22.3150i	−1.40945	+	0.813744i
$753$	10.9676	+	18.9965i	0.399682	+	0.692269i
$754$	−26.1500	+	45.2931i	−0.952326	+	1.64948i
$755$	22.1686			0.806798
$756$	−1.30408	+	12.3392i	−0.0474291	+	0.448772i
$757$	13.1686			0.478620			0.239310	−	0.970943i	$-0.423079\pi$
$757$	13.1686			0.478620			0.239310	+	0.970943i	$0.423079\pi$
$758$	44.1849	+	25.5102i	1.60487	+	0.926572i
$759$	−0.136101	−	0.195991i	−0.00494016	−	0.00711401i
$760$	−25.6999	−	44.5135i	−0.932233	−	1.61467i
$761$	−15.0583	+	26.0817i	−0.545863	+	0.945462i	0.452689	+	0.891668i	$0.350465\pi$
$761$	−15.0583	+	26.0817i	−0.545863	+	0.945462i	−0.998552	+	0.0537940i	$0.982869\pi$
$762$		−	1.72123i		−	0.0623536i
$763$	5.23508	−	49.5341i	0.189523	−	1.79326i
$764$	−54.8043			−1.98275
$765$	−3.59610	−	2.07621i	−0.130017	−	0.0750654i
$766$	−16.3364	−	28.2955i	−0.590259	−	1.02236i
$767$	22.0593	−	12.7359i	0.796514	−	0.459867i
$768$	−19.5653	−	11.2960i	−0.706001	−	0.407610i
$769$	26.3978			0.951930			0.475965	−	0.879464i	$-0.342099\pi$
$769$	26.3978			0.951930			0.475965	+	0.879464i	$0.342099\pi$
$770$	−29.8975	+	16.3984i	−1.07743	+	0.590958i
$771$	−1.11715			−0.0402332
$772$	−72.2537	−	41.7157i	−2.60047	−	1.50138i
$773$	28.3502	−	16.3680i	1.01969	−	0.588716i	0.105673	−	0.994401i	$-0.466300\pi$
$773$	28.3502	−	16.3680i	1.01969	−	0.588716i	0.914013	+	0.405685i	$0.132967\pi$
$774$	6.99679	+	12.1188i	0.251494	+	0.435601i
$775$	24.2666	+	14.0103i	0.871683	+	0.503267i
$776$	−18.3349			−0.658186
$777$	−16.7227	−	12.1645i	−0.599923	−	0.436398i
$778$		−	74.3914i		−	2.66706i
$779$	7.33612	−	12.7065i	0.262844	−	0.455259i
$780$	−14.0699	−	24.3698i	−0.503784	−	0.872579i
$781$	−26.1374	+	18.1505i	−0.935269	+	0.649476i
$782$	−0.445386	−	0.257144i	−0.0159270	−	0.00919543i
$783$	−5.06315			−0.180942
$784$	58.9676	+	12.6049i	2.10598	+	0.450176i
$785$	26.0807			0.930860
$786$	1.90735	−	3.30363i	0.0680330	−	0.117837i
$787$	−8.55882	−	14.8243i	−0.305089	−	0.528430i	0.672192	−	0.740377i	$-0.265353\pi$
$787$	−8.55882	−	14.8243i	−0.305089	−	0.528430i	−0.977281	+	0.211947i	$0.932020\pi$
$788$	71.8720	−	41.4953i	2.56033	−	1.47821i
$789$	−0.614435	+	1.06423i	−0.0218745	+	0.0378877i
$790$			45.2897i			1.61134i
$791$	3.29686	−	4.53225i	0.117223	−	0.161148i
$792$	22.9933	−	1.92158i	0.817032	−	0.0682803i
$793$	−2.75069	+	4.76434i	−0.0976799	+	0.169187i
$794$	−28.9615	−	50.1628i	−1.02781	−	1.78021i
$795$	−9.36343	−	16.2179i	−0.332087	−	0.575191i
$796$	−9.48331	−	5.47519i	−0.336127	−	0.194063i
$797$			45.0372i			1.59530i	0.603121	+	0.797650i	$0.293924\pi$
$797$			45.0372i			1.59530i	−0.603121	+	0.797650i	$0.706076\pi$
$798$	13.6695	+	30.7499i	0.483895	+	1.08853i
$799$			14.3190i			0.506571i
$800$	−19.8724	−	11.4734i	−0.702597	−	0.405644i
$801$	−11.7889	+	6.80633i	−0.416541	+	0.240490i
$802$	35.2042	−	20.3252i	1.24310	−	0.717707i
$803$	26.8864	+	12.6649i	0.948802	+	0.446934i
$804$		−	21.3542i		−	0.753104i
$805$	−0.0300573	+	0.284401i	−0.00105938	+	0.0100238i
$806$	−105.532			−3.71721
$807$	3.11023	−	5.38708i	0.109485	−	0.189634i
$808$	38.3190	−	22.1235i	1.34806	−	0.778301i
$809$	−3.56209	+	2.05657i	−0.125236	+	0.0723053i	−0.561310	−	0.827606i	$-0.689702\pi$
$809$	−3.56209	+	2.05657i	−0.125236	+	0.0723053i	0.436073	+	0.899911i	$0.356369\pi$
$810$	1.94300	−	3.36537i	0.0682699	−	0.118247i
$811$	−24.9774			−0.877076			−0.438538	−	0.898713i	$-0.644504\pi$
$811$	−24.9774			−0.877076			−0.438538	+	0.898713i	$0.644504\pi$
$812$	−6.60278	+	62.4752i	−0.231712	+	2.19245i
$813$		−	0.110951i		−	0.00389122i
$814$	−28.5716	+	60.6550i	−1.00143	+	2.12596i
$815$	3.34244	−	1.92976i	0.117081	−	0.0675965i
$816$	20.6183	−	11.9040i	0.721784	−	0.416722i
$817$	23.0411	+	13.3028i	0.806104	+	0.465405i
$818$		−	14.7788i		−	0.516729i
$819$	4.29215	+	9.65529i	0.149980	+	0.337383i
$820$			21.0230i			0.734156i
$821$	−4.32057	−	2.49448i	−0.150789	−	0.0870580i	0.422707	−	0.906266i	$-0.361080\pi$
$821$	−4.32057	−	2.49448i	−0.150789	−	0.0870580i	−0.573496	+	0.819208i	$0.694413\pi$
$822$	−24.3336	−	42.1471i	−0.848732	−	1.47005i
$823$	23.0872	+	39.9882i	0.804769	+	1.39390i	0.916447	+	0.400157i	$0.131044\pi$
$823$	23.0872	+	39.9882i	0.804769	+	1.39390i	−0.111677	+	0.993745i	$0.535622\pi$
$824$	18.6277	−	32.2641i	0.648926	−	1.12397i
$825$	−9.06483	+	0.757558i	−0.315597	+	0.0263748i
$826$	25.6745	−	35.2952i	0.893330	−	1.22808i
$827$			35.2177i			1.22464i	0.790611	+	0.612319i	$0.209763\pi$
$827$			35.2177i			1.22464i	−0.790611	+	0.612319i	$0.790237\pi$
$828$	0.168700	−	0.292198i	0.00586275	−	0.0101546i
$829$	17.2715	−	9.97168i	0.599862	−	0.346331i	−0.169125	−	0.985595i	$-0.554094\pi$
$829$	17.2715	−	9.97168i	0.599862	−	0.346331i	0.768987	+	0.639264i	$0.220761\pi$
$830$	−18.1563	−	31.4476i	−0.630214	−	1.09156i
$831$	7.41932	−	12.8506i	0.257373	−	0.445784i
$832$	17.6169			0.610756
$833$	12.9619	−	14.3623i	0.449102	−	0.497625i
$834$	−16.9315			−0.586290
$835$	−0.626451	−	0.361682i	−0.0216792	−	0.0125165i
$836$	62.8255	−	43.6277i	2.17287	−	1.50890i
$837$	−5.10827	−	8.84779i	−0.176568	−	0.305824i
$838$	9.15271	−	15.8530i	0.316175	−	0.547632i
$839$		−	41.5888i		−	1.43580i	−0.696144	−	0.717902i	$-0.745103\pi$
$839$		−	41.5888i		−	1.43580i	0.696144	−	0.717902i	$-0.254897\pi$
$840$	−22.3634	−	16.2677i	−0.771612	−	0.561288i
$841$	3.36447			0.116016
$842$	−28.7327	−	16.5888i	−0.990195	−	0.571689i
$843$	2.38671	+	4.13391i	0.0822027	+	0.142379i
$844$	45.3058	−	26.1573i	1.55949	−	0.900373i
$845$	−3.83788	−	2.21580i	−0.132027	−	0.0762260i
$846$	−13.4003			−0.460712
$847$	−16.0722	−	24.2628i	−0.552248	−	0.833680i
$848$	107.371			3.68712
$849$	27.5893	+	15.9287i	0.946862	+	0.546671i
$850$	−16.9791	+	9.80288i	−0.582378	+	0.336236i
$851$	0.281157	+	0.486977i	0.00963792	+	0.0166934i
$852$	−38.9676	−	22.4979i	−1.33501	−	0.770767i
$853$	45.8254			1.56903			0.784516	−	0.620108i	$-0.212911\pi$
$853$	45.8254			1.56903			0.784516	+	0.620108i	$0.212911\pi$
$854$	−0.990736	+	9.37430i	−0.0339023	+	0.320782i
$855$		−	7.38830i		−	0.252675i
$856$	42.1739	−	73.0473i	1.44147	−	2.49671i
$857$	16.3773	+	28.3663i	0.559437	+	0.968973i	0.997543	+	0.0700500i	$0.0223159\pi$
$857$	16.3773	+	28.3663i	0.559437	+	0.968973i	−0.438107	+	0.898923i	$0.644351\pi$
$858$	28.1396	−	19.5409i	0.960672	−	0.667117i
$859$	17.0590	+	9.84903i	0.582046	+	0.336045i	0.761946	−	0.647640i	$-0.224244\pi$
$859$	17.0590	+	9.84903i	0.582046	+	0.336045i	−0.179900	+	0.983685i	$0.557577\pi$
$860$	−38.1215			−1.29993
$861$	0.829669	−	7.85029i	0.0282750	−	0.267537i
$862$	28.7473			0.979137
$863$	−2.67915	+	4.64042i	−0.0911993	+	0.157962i	−0.908016	−	0.418935i	$-0.862403\pi$
$863$	−2.67915	+	4.64042i	−0.0911993	+	0.157962i	0.816817	+	0.576897i	$0.195737\pi$
$864$	4.18327	+	7.24563i	0.142318	+	0.246501i
$865$	−2.48580	+	1.43518i	−0.0845196	+	0.0487974i
$866$	−13.8363	+	23.9651i	−0.470175	+	0.814367i
$867$			9.36150i			0.317933i
$868$	−115.836	+	51.4937i	−3.93174	+	1.74781i
$869$	−38.5197	+	3.21913i	−1.30669	+	0.109202i
$870$	9.83768	−	17.0394i	0.333529	−	0.577689i
$871$	−9.09240	−	15.7485i	−0.308084	−	0.533617i
$872$	−65.4868	−	113.427i	−2.21766	−	3.84111i
$873$	−2.28241	−	1.31775i	−0.0772478	−	0.0445991i
$874$		−	0.915059i		−	0.0309523i
$875$	24.8893	+	18.1050i	0.841412	+	0.612062i
$876$			42.0245i			1.41988i
$877$	−0.913271	−	0.527277i	−0.0308390	−	0.0178049i	0.484501	−	0.874791i	$-0.339001\pi$
$877$	−0.913271	−	0.527277i	−0.0308390	−	0.0178049i	−0.515340	+	0.856986i	$0.672334\pi$
$878$	8.60873	−	4.97025i	0.290530	−	0.167738i
$879$	18.2812	−	10.5547i	0.616611	−	0.356001i
$880$	−18.2921	+	38.8324i	−0.616625	+	1.30904i
$881$		−	24.1996i		−	0.815304i	−0.913137	−	0.407652i	$-0.866348\pi$
$881$		−	24.1996i		−	0.815304i	0.913137	−	0.407652i	$-0.133652\pi$
$882$	13.4408	+	12.1302i	0.452576	+	0.408446i
$883$	−14.1892			−0.477506			−0.238753	−	0.971080i	$-0.576739\pi$
$883$	−14.1892			−0.477506			−0.238753	+	0.971080i	$0.576739\pi$
$884$	25.8820	−	44.8290i	0.870507	−	1.50776i
$885$	−8.29875	+	4.79129i	−0.278960	+	0.161057i
$886$	92.2432	−	53.2567i	3.09897	−	1.78919i
$887$	1.74971	−	3.03058i	0.0587494	−	0.101757i	−0.835155	−	0.550015i	$-0.814622\pi$
$887$	1.74971	−	3.03058i	0.0587494	−	0.101757i	0.893904	+	0.448258i	$0.147955\pi$
$888$	−54.3749			−1.82470
$889$	−1.42383	−	1.03573i	−0.0477538	−	0.0347372i
$890$		−	52.8987i		−	1.77317i
$891$	3.00041	+	1.41335i	0.100517	+	0.0473489i
$892$	−76.5627	+	44.2035i	−2.56351	+	1.48004i
$893$	−22.0642	+	12.7388i	−0.738350	+	0.426286i
$894$	−28.6371	−	16.5337i	−0.957769	−	0.552968i
$895$		−	20.5251i		−	0.686079i
$896$	−12.8709	+	5.72163i	−0.429988	+	0.191146i
$897$		−	0.287324i		−	0.00959347i
$898$	10.3181	+	5.95716i	0.344319	+	0.198793i
$899$	−25.8640	−	44.7977i	−0.862612	−	1.49409i
$900$	−6.43123	−	11.1392i	−0.214374	−	0.371307i
$901$	17.2243	−	29.8334i	0.573825	−	0.993895i
$902$	−25.5058	+	2.13155i	−0.849250	+	0.0709727i
$903$	14.2351	+	1.50446i	0.473715	+	0.0500652i
$904$		−	14.7369i		−	0.490141i
$905$	−11.7316	+	20.3198i	−0.389972	+	0.675452i
$906$	−33.0504	+	19.0817i	−1.09803	+	0.633946i
$907$	−6.44449	−	11.1622i	−0.213986	−	0.370635i	0.738972	−	0.673736i	$-0.235311\pi$
$907$	−6.44449	−	11.1622i	−0.213986	−	0.370635i	−0.952958	+	0.303101i	$0.901978\pi$
$908$	2.97362	−	5.15046i	0.0986831	−	0.170924i
$909$	6.36013			0.210952
$910$	−40.8332	−	4.31552i	−1.35361	−	0.143058i
$911$	−48.9915			−1.62316			−0.811581	−	0.584240i	$-0.801393\pi$
$911$	−48.9915			−1.62316			−0.811581	+	0.584240i	$0.801393\pi$
$912$	36.6856	+	21.1804i	1.21478	+	0.701355i
$913$	25.4562	−	17.6775i	0.842478	−	0.585040i
$914$	14.3569	+	24.8670i	0.474885	+	0.822526i
$915$	1.03482	−	1.79236i	0.0342100	−	0.0592535i
$916$			127.298i			4.20604i
$917$	−1.58510	−	3.56571i	−0.0523445	−	0.117750i
$918$	7.14840			0.235932
$919$	7.78774	+	4.49625i	0.256894	+	0.148318i	0.622917	−	0.782288i	$-0.285948\pi$
$919$	7.78774	+	4.49625i	0.256894	+	0.148318i	−0.366023	+	0.930606i	$0.619281\pi$
$920$	0.375993	+	0.651240i	0.0123961	+	0.0214707i
$921$	−6.61673	+	3.82017i	−0.218029	+	0.125879i
$922$	−82.6090	−	47.6943i	−2.72058	−	1.57073i
$923$	−38.3176			−1.26124
$924$	21.3523	−	35.1795i	0.702440	−	1.15732i
$925$	21.4366			0.704831
$926$	19.8492	+	11.4599i	0.652284	+	0.376596i
$927$	4.63770	−	2.67758i	0.152322	−	0.0879431i
$928$	21.1805	+	36.6858i	0.695285	+	1.20427i
$929$	22.7642	+	13.1429i	0.746868	+	0.431204i	0.824561	−	0.565773i	$-0.191422\pi$
$929$	22.7642	+	13.1429i	0.746868	+	0.431204i	−0.0776934	+	0.996977i	$0.524756\pi$
$930$	39.7014			1.30186
$931$	33.6623	+	7.19566i	1.10324	+	0.235828i
$932$		−	1.48300i		−	0.0485773i
$933$	−4.39898	+	7.61926i	−0.144016	+	0.249444i
$934$	39.1969	+	67.8911i	1.28256	+	2.22146i
$935$	7.85536	+	11.3120i	0.256898	+	0.369942i
$936$	24.0615	+	13.8919i	0.786474	+	0.454071i
$937$	−8.07052			−0.263653			−0.131826	−	0.991273i	$-0.542084\pi$
$937$	−8.07052			−0.263653			−0.131826	+	0.991273i	$0.542084\pi$
$938$	−25.1978	−	18.3295i	−0.822738	−	0.598478i
$939$	1.05676			0.0344862
$940$	18.2527	−	31.6145i	0.595336	−	1.03115i
$941$	−28.9544	−	50.1505i	−0.943887	−	1.63486i	−0.757965	−	0.652296i	$-0.773806\pi$
$941$	−28.9544	−	50.1505i	−0.943887	−	1.63486i	−0.185922	−	0.982564i	$-0.559527\pi$
$942$	−38.8828	+	22.4490i	−1.26687	+	0.731428i
$943$	−0.107329	+	0.185899i	−0.00349510	+	0.00605369i
$944$		−	54.9418i		−	1.78820i
$945$	−1.61472	−	3.63235i	−0.0525268	−	0.118160i
$946$	−3.86518	−	46.2502i	−0.125668	−	1.50373i
$947$	17.8816	−	30.9719i	0.581075	−	1.00645i	−0.414277	−	0.910151i	$-0.635966\pi$
$947$	17.8816	−	30.9719i	0.581075	−	1.00645i	0.995352	−	0.0963005i	$-0.0307010\pi$
$948$	−27.3286	−	47.3345i	−0.887592	−	1.53735i
$949$	17.8936	+	30.9926i	0.580851	+	1.00606i
$950$	−30.2105	−	17.4420i	−0.980158	−	0.565895i
$951$		−	3.50457i		−	0.113644i
$952$	5.34659	−	50.5892i	0.173284	−	1.63960i
$953$		−	26.3682i		−	0.854148i	−0.904217	−	0.427074i	$-0.859544\pi$
$953$		−	26.3682i		−	0.854148i	0.904217	−	0.427074i	$-0.140456\pi$
$954$	27.9192	+	16.1192i	0.903919	+	0.521878i
$955$	15.2052	−	8.77873i	0.492029	−	0.284073i
$956$	1.42746	−	0.824142i	0.0461672	−	0.0266547i
$957$	15.1915	+	7.15599i	0.491073	+	0.231320i
$958$		−	42.0584i		−	1.35885i
$959$	−49.5072	−	5.23224i	−1.59867	−	0.168958i
$960$	−6.62752			−0.213902
$961$	36.6889	−	63.5471i	1.18351	−	2.04991i
$962$	−69.9185	+	40.3675i	−2.25426	+	1.30150i
$963$	10.5000	−	6.06216i	0.338357	−	0.195350i
$964$	−47.8344	+	82.8517i	−1.54064	+	2.66847i
$965$	26.7286			0.860425
$966$	−0.199987	−	0.449875i	−0.00643448	−	0.0144745i
$967$		0	0.000437698i		0	1.40754e-5i	−1.00000		7.03771e-6i	$-0.999998\pi$
$967$		0	0.000437698i		0	1.40754e-5i	1.00000		7.03771e-6i	$-2.24017e-6\pi$
$968$	−71.7052	−	26.7320i	−2.30469	−	0.859199i
$969$	11.7702	−	6.79550i	0.378112	−	0.218303i
$970$	8.86942	−	5.12076i	0.284780	−	0.164418i
$971$	11.4443	+	6.60737i	0.367265	+	0.212041i	0.672263	−	0.740312i	$-0.265322\pi$
$971$	11.4443	+	6.60737i	0.367265	+	0.212041i	−0.304998	+	0.952353i	$0.598656\pi$
$972$			4.68975i			0.150424i
$973$	−10.1883	+	14.0060i	−0.326622	+	0.449013i
$974$			31.6150i			1.01301i
$975$	−9.48594	−	5.47671i	−0.303793	−	0.175395i
$976$	5.93314	+	10.2765i	0.189915	+	0.328943i
$977$	21.9449	+	38.0096i	0.702079	+	1.21604i	0.967735	+	0.251969i	$0.0810780\pi$
$977$	21.9449	+	38.0096i	0.702079	+	1.21604i	−0.265657	+	0.964068i	$0.585589\pi$
$978$	−3.32209	+	5.75402i	−0.106229	+	0.183993i
$979$	44.9913	−	3.75997i	1.43793	−	0.120169i
$980$	−46.9259	+	15.1874i	−1.49899	+	0.485145i
$981$		−	18.8264i		−	0.601081i
$982$	−0.0352169	+	0.0609974i	−0.00112382	+	0.00194650i
$983$	21.4957	−	12.4105i	0.685605	−	0.395834i	−0.116358	−	0.993207i	$-0.537122\pi$
$983$	21.4957	−	12.4105i	0.685605	−	0.395834i	0.801964	+	0.597373i	$0.203789\pi$
$984$	−10.3785	−	17.9761i	−0.330855	−	0.573058i
$985$	−13.2937	+	23.0254i	−0.423573	+	0.733650i
$986$	36.1935			1.15263
$987$	−8.06345	+	11.0850i	−0.256663	+	0.352838i
$988$	92.1027			2.93018
$989$	−0.337094	−	0.194621i	−0.0107190	−	0.00618860i
$990$	−10.5862	+	7.35135i	−0.336452	+	0.233641i
$991$	−4.94241	−	8.56050i	−0.157001	−	0.271933i	0.776785	−	0.629766i	$-0.216849\pi$
$991$	−4.94241	−	8.56050i	−0.157001	−	0.271933i	−0.933786	+	0.357833i	$0.883516\pi$
$992$	−42.7386	+	74.0254i	−1.35695	+	2.35031i
$993$		−	5.59201i		−	0.177457i
$994$	−59.9955	+	26.6703i	−1.90294	+	0.845932i
$995$	3.50814			0.111215
$996$	37.9521	+	21.9116i	1.20256	+	0.694297i
$997$	−16.5675	−	28.6958i	−0.524699	−	0.908806i	−0.999586	−	0.0287590i	$-0.990844\pi$
$997$	−16.5675	−	28.6958i	−0.524699	−	0.908806i	0.474887	−	0.880047i	$-0.342489\pi$
$998$	−32.5157	+	18.7729i	−1.02927	+	0.594247i
$999$	−6.76881	−	3.90797i	−0.214156	−	0.123643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.208.1	yes	32
3.2	odd	2		693.2.bg.b.208.16		32
7.2	even	3		1617.2.c.a.538.31		32
7.3	odd	6	inner	231.2.p.a.10.16	yes	32
7.5	odd	6		1617.2.c.a.538.32		32
11.10	odd	2	inner	231.2.p.a.208.16	yes	32
21.17	even	6		693.2.bg.b.10.1		32
33.32	even	2		693.2.bg.b.208.1		32
77.10	even	6	inner	231.2.p.a.10.1	✓	32
77.54	even	6		1617.2.c.a.538.2		32
77.65	odd	6		1617.2.c.a.538.1		32
231.164	odd	6		693.2.bg.b.10.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.1	✓	32	77.10	even	6	inner
231.2.p.a.10.16	yes	32	7.3	odd	6	inner
231.2.p.a.208.1	yes	32	1.1	even	1	trivial
231.2.p.a.208.16	yes	32	11.10	odd	2	inner
693.2.bg.b.10.1		32	21.17	even	6
693.2.bg.b.10.16		32	231.164	odd	6
693.2.bg.b.208.1		32	33.32	even	2
693.2.bg.b.208.16		32	3.2	odd	2
1617.2.c.a.538.1		32	77.65	odd	6
1617.2.c.a.538.2		32	77.54	even	6
1617.2.c.a.538.31		32	7.2	even	3
1617.2.c.a.538.32		32	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23994 - 1.29323i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.34487 + 4.06144i) q^{4} +(-1.30115 - 0.751219i) q^{5} +2.58645 q^{6} +(1.55637 - 2.13956i) q^{7} -6.95692i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.23994 - 1.29323i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.34487 + 4.06144i) q^{4} +(-1.30115 - 0.751219i) q^{5} +2.58645 q^{6} +(1.55637 - 2.13956i) q^{7} -6.95692i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.94300 + 3.36537i) q^{10} +(-2.72420 + 1.89176i) q^{11} +(-4.06144 - 2.34487i) q^{12} -3.99370 q^{13} +(-6.25310 + 2.77975i) q^{14} +1.50244 q^{15} +(-4.30712 + 7.46016i) q^{16} +(1.38189 + 2.39351i) q^{17} +(-2.23994 + 1.29323i) q^{18} +(-2.45877 + 4.25871i) q^{19} -7.04606i q^{20} +(-0.278071 + 2.63110i) q^{21} +(8.54850 - 0.714407i) q^{22} +(0.0359722 - 0.0623056i) q^{23} +(3.47846 + 6.02487i) q^{24} +(-1.37134 - 2.37523i) q^{25} +(8.94562 + 5.16476i) q^{26} +1.00000i q^{27} +(12.3392 + 1.30408i) q^{28} +5.06315i q^{29} +(-3.36537 - 1.94300i) q^{30} +(-8.84779 + 5.10827i) q^{31} +(7.24563 - 4.18327i) q^{32} +(1.41335 - 3.00041i) q^{33} -7.14840i q^{34} +(-3.63235 + 1.61472i) q^{35} +4.68975 q^{36} +(-3.90797 + 6.76881i) q^{37} +(11.0150 - 6.35949i) q^{38} +(3.45864 - 1.99685i) q^{39} +(-5.22617 + 9.05199i) q^{40} -2.98366 q^{41} +(4.02547 - 5.53388i) q^{42} -5.41033i q^{43} +(-14.0712 - 6.62824i) q^{44} +(-1.30115 + 0.751219i) q^{45} +(-0.161151 + 0.0930404i) q^{46} +(4.48684 + 2.59048i) q^{47} -8.61425i q^{48} +(-2.15545 - 6.65988i) q^{49} +7.09381i q^{50} +(-2.39351 - 1.38189i) q^{51} +(-9.36472 - 16.2202i) q^{52} +(-6.23215 - 10.7944i) q^{53} +(1.29323 - 2.23994i) q^{54} +(4.96572 - 0.414990i) q^{55} +(-14.8848 - 10.8275i) q^{56} -4.91754i q^{57} +(6.54781 - 11.3411i) q^{58} +(-5.52352 + 3.18901i) q^{59} +(3.52303 + 6.10207i) q^{60} +(0.688758 - 1.19296i) q^{61} +26.4246 q^{62} +(-1.07473 - 2.41763i) q^{63} -4.41117 q^{64} +(5.19640 + 3.00014i) q^{65} +(-7.04602 + 4.89295i) q^{66} +(2.27669 + 3.94334i) q^{67} +(-6.48072 + 11.2249i) q^{68} +0.0719444i q^{69} +(10.2244 + 1.08058i) q^{70} +9.59452 q^{71} +(-6.02487 - 3.47846i) q^{72} +(-4.48046 - 7.76039i) q^{73} +(17.5072 - 10.1078i) q^{74} +(2.37523 + 1.37134i) q^{75} -23.0620 q^{76} +(-0.192316 + 8.77286i) q^{77} -10.3295 q^{78} +(10.0932 + 5.82731i) q^{79} +(11.2084 - 6.47119i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.68320 + 3.85855i) q^{82} -9.34449 q^{83} +(-11.3381 + 5.04022i) q^{84} -4.15242i q^{85} +(-6.99679 + 12.1188i) q^{86} +(-2.53158 - 4.38482i) q^{87} +(13.1608 + 18.9520i) q^{88} +(-11.7889 - 6.80633i) q^{89} +3.88599 q^{90} +(-6.21565 + 8.54476i) q^{91} +0.337401 q^{92} +(5.10827 - 8.84779i) q^{93} +(-6.70015 - 11.6050i) q^{94} +(6.39846 - 3.69415i) q^{95} +(-4.18327 + 7.24563i) q^{96} -2.63550i q^{97} +(-3.78467 + 17.7052i) q^{98} +(0.276211 + 3.30510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

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