LMFDB - Embedded newform 930.2.s.d.439.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.7
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.91775 + 1.14989i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.230788 - 0.133246i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.91775 + 1.14989i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.230788 - 0.133246i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.14989 - 1.91775i) q^{10} +(-2.16487 - 3.74966i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(3.19390 - 1.84400i) q^{13} +(-0.133246 + 0.230788i) q^{14} +(1.08588 + 1.95471i) q^{15} +1.00000 q^{16} +(3.14320 + 1.81473i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.627100 - 1.08617i) q^{19} +(-1.91775 - 1.14989i) q^{20} +(-0.133246 - 0.230788i) q^{21} +(-3.74966 + 2.16487i) q^{22} -2.23029i q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.35552 + 4.41039i) q^{25} +(-1.84400 - 3.19390i) q^{26} +1.00000i q^{27} +(0.230788 + 0.133246i) q^{28} +8.58511 q^{29} +(1.95471 - 1.08588i) q^{30} +(-4.12550 - 3.73902i) q^{31} -1.00000i q^{32} -4.32974i q^{33} +(1.81473 - 3.14320i) q^{34} +(-0.289376 - 0.520911i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.89902 + 3.40580i) q^{37} +(-1.08617 - 0.627100i) q^{38} +3.68799 q^{39} +(-1.14989 + 1.91775i) q^{40} +(3.09949 + 5.36848i) q^{41} +(-0.230788 + 0.133246i) q^{42} +(8.46832 + 4.88919i) q^{43} +(2.16487 + 3.74966i) q^{44} +(-0.0369558 + 2.23576i) q^{45} -2.23029 q^{46} +9.03257i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.46449 - 6.00067i) q^{49} +(4.41039 - 2.35552i) q^{50} +(1.81473 + 3.14320i) q^{51} +(-3.19390 + 1.84400i) q^{52} +(-6.70636 + 3.87192i) q^{53} +1.00000 q^{54} +(0.160009 - 9.68027i) q^{55} +(0.133246 - 0.230788i) q^{56} +(1.08617 - 0.627100i) q^{57} -8.58511i q^{58} +(0.855490 - 1.48175i) q^{59} +(-1.08588 - 1.95471i) q^{60} -5.59976 q^{61} +(-3.73902 + 4.12550i) q^{62} -0.266491i q^{63} -1.00000 q^{64} +(8.24548 + 0.136293i) q^{65} -4.32974 q^{66} +(-1.14094 + 0.658723i) q^{67} +(-3.14320 - 1.81473i) q^{68} +(1.11515 - 1.93149i) q^{69} +(-0.520911 + 0.289376i) q^{70} +(-5.22463 - 9.04932i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.38415 - 3.10854i) q^{73} +(3.40580 - 5.89902i) q^{74} +(-0.165249 + 4.99727i) q^{75} +(-0.627100 + 1.08617i) q^{76} +1.15384i q^{77} -3.68799i q^{78} +(2.29709 - 3.97867i) q^{79} +(1.91775 + 1.14989i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.36848 - 3.09949i) q^{82} +(-9.52048 + 5.49665i) q^{83} +(0.133246 + 0.230788i) q^{84} +(3.94114 + 7.09451i) q^{85} +(4.88919 - 8.46832i) q^{86} +(7.43493 + 4.29256i) q^{87} +(3.74966 - 2.16487i) q^{88} -13.8892 q^{89} +(2.23576 + 0.0369558i) q^{90} -0.982817 q^{91} +2.23029i q^{92} +(-1.70328 - 5.30083i) q^{93} +9.03257 q^{94} +(2.45159 - 1.36191i) q^{95} +(0.500000 - 0.866025i) q^{96} -11.1655i q^{97} +(-6.00067 + 3.46449i) q^{98} +(2.16487 - 3.74966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.00000			−0.500000
$5$	1.91775	+	1.14989i	0.857644	+	0.514245i
$5$	1.91775	+	1.14989i	0.857644	+	0.514245i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.230788	−	0.133246i	−0.0872297	−	0.0503621i	0.455751	−	0.890107i	$-0.349371\pi$
$7$	−0.230788	−	0.133246i	−0.0872297	−	0.0503621i	−0.542980	+	0.839745i	$0.682704\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.14989	−	1.91775i	0.363626	−	0.606446i
$11$	−2.16487	−	3.74966i	−0.652733	−	1.13057i	−0.982457	−	0.186489i	$-0.940289\pi$
$11$	−2.16487	−	3.74966i	−0.652733	−	1.13057i	0.329725	−	0.944077i	$-0.393044\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	3.19390	−	1.84400i	0.885827	−	0.511433i	0.0132520	−	0.999912i	$-0.495782\pi$
$13$	3.19390	−	1.84400i	0.885827	−	0.511433i	0.872575	+	0.488479i	$0.162448\pi$
$14$	−0.133246	+	0.230788i	−0.0356114	+	0.0616807i
$15$	1.08588	+	1.95471i	0.280372	+	0.504703i
$16$	1.00000			0.250000
$17$	3.14320	+	1.81473i	0.762338	+	0.440136i	0.830134	−	0.557563i	$-0.188264\pi$
$17$	3.14320	+	1.81473i	0.762338	+	0.440136i	−0.0677968	+	0.997699i	$0.521597\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	0.627100	−	1.08617i	0.143867	−	0.249184i	−0.785083	−	0.619391i	$-0.787380\pi$
$19$	0.627100	−	1.08617i	0.143867	−	0.249184i	0.928950	+	0.370206i	$0.120713\pi$
$20$	−1.91775	−	1.14989i	−0.428822	−	0.257122i
$21$	−0.133246	−	0.230788i	−0.0290766	−	0.0503621i
$22$	−3.74966	+	2.16487i	−0.799431	+	0.461552i
$23$		−	2.23029i		−	0.465048i	−0.972591	−	0.232524i	$-0.925302\pi$
$23$		−	2.23029i		−	0.465048i	0.972591	−	0.232524i	$-0.0746985\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.35552	+	4.41039i	0.471105	+	0.882077i
$26$	−1.84400	−	3.19390i	−0.361638	−	0.626375i
$27$			1.00000i			0.192450i
$28$	0.230788	+	0.133246i	0.0436148	+	0.0251810i
$29$	8.58511			1.59422			0.797108	−	0.603837i	$-0.206362\pi$
$29$	8.58511			1.59422			0.797108	+	0.603837i	$0.206362\pi$
$30$	1.95471	−	1.08588i	0.356879	−	0.198253i
$31$	−4.12550	−	3.73902i	−0.740961	−	0.671548i
$31$	−4.12550	−	3.73902i	−0.740961	−	0.671548i
$32$		−	1.00000i		−	0.176777i
$33$		−	4.32974i		−	0.753711i
$34$	1.81473	−	3.14320i	0.311223	−	0.539054i
$35$	−0.289376	−	0.520911i	−0.0489135	−	0.0880501i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	5.89902	+	3.40580i	0.969793	+	0.559910i	0.899173	−	0.437593i	$-0.144169\pi$
$37$	5.89902	+	3.40580i	0.969793	+	0.559910i	0.0706195	+	0.997503i	$0.477502\pi$
$38$	−1.08617	−	0.627100i	−0.176200	−	0.101729i
$39$	3.68799			0.590552
$40$	−1.14989	+	1.91775i	−0.181813	+	0.303223i
$41$	3.09949	+	5.36848i	0.484060	+	0.838416i	0.999832	−	0.0183095i	$-0.00582843\pi$
$41$	3.09949	+	5.36848i	0.484060	+	0.838416i	−0.515773	+	0.856725i	$0.672495\pi$
$42$	−0.230788	+	0.133246i	−0.0356114	+	0.0205602i
$43$	8.46832	+	4.88919i	1.29141	+	0.745594i	0.978904	−	0.204323i	$-0.0654992\pi$
$43$	8.46832	+	4.88919i	1.29141	+	0.745594i	0.312503	+	0.949917i	$0.398833\pi$
$44$	2.16487	+	3.74966i	0.326366	+	0.565283i
$45$	−0.0369558	+	2.23576i	−0.00550905	+	0.333288i
$46$	−2.23029			−0.328839
$47$			9.03257i			1.31754i	0.752346	+	0.658768i	$0.228922\pi$
$47$			9.03257i			1.31754i	−0.752346	+	0.658768i	$0.771078\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−3.46449	−	6.00067i	−0.494927	−	0.857239i
$50$	4.41039	−	2.35552i	0.623723	−	0.333121i
$51$	1.81473	+	3.14320i	0.254113	+	0.440136i
$52$	−3.19390	+	1.84400i	−0.442914	+	0.255716i
$53$	−6.70636	+	3.87192i	−0.921190	+	0.531849i	−0.884014	−	0.467460i	$-0.845169\pi$
$53$	−6.70636	+	3.87192i	−0.921190	+	0.531849i	−0.0371753	+	0.999309i	$0.511836\pi$
$54$	1.00000			0.136083
$55$	0.160009	−	9.68027i	0.0215756	−	1.30529i
$56$	0.133246	−	0.230788i	0.0178057	−	0.0308403i
$57$	1.08617	−	0.627100i	0.143867	−	0.0830614i
$58$		−	8.58511i		−	1.12728i
$59$	0.855490	−	1.48175i	0.111375	−	0.192908i	−0.804950	−	0.593343i	$-0.797808\pi$
$59$	0.855490	−	1.48175i	0.111375	−	0.192908i	0.916325	+	0.400435i	$0.131141\pi$
$60$	−1.08588	−	1.95471i	−0.140186	−	0.252351i
$61$	−5.59976			−0.716976			−0.358488	−	0.933534i	$-0.616708\pi$
$61$	−5.59976			−0.716976			−0.358488	+	0.933534i	$0.616708\pi$
$62$	−3.73902	+	4.12550i	−0.474856	+	0.523939i
$63$		−	0.266491i		−	0.0335747i
$64$	−1.00000			−0.125000
$65$	8.24548	+	0.136293i	1.02273	+	0.0169051i
$66$	−4.32974			−0.532954
$67$	−1.14094	+	0.658723i	−0.139388	+	0.0804759i	−0.568072	−	0.822979i	$-0.692311\pi$
$67$	−1.14094	+	0.658723i	−0.139388	+	0.0804759i	0.428684	+	0.903454i	$0.358977\pi$
$68$	−3.14320	−	1.81473i	−0.381169	−	0.220068i
$69$	1.11515	−	1.93149i	0.134248	−	0.232524i
$70$	−0.520911	+	0.289376i	−0.0622608	+	0.0345871i
$71$	−5.22463	−	9.04932i	−0.620049	−	1.07396i	−0.989476	−	0.144697i	$-0.953779\pi$
$71$	−5.22463	−	9.04932i	−0.620049	−	1.07396i	0.369427	−	0.929260i	$-0.379554\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	5.38415	−	3.10854i	0.630167	−	0.363827i	−0.150650	−	0.988587i	$-0.548137\pi$
$73$	5.38415	−	3.10854i	0.630167	−	0.363827i	0.780817	+	0.624760i	$0.214803\pi$
$74$	3.40580	−	5.89902i	0.395916	−	0.685747i
$75$	−0.165249	+	4.99727i	−0.0190813	+	0.577035i
$76$	−0.627100	+	1.08617i	−0.0719333	+	0.124592i
$77$			1.15384i			0.131492i
$78$		−	3.68799i		−	0.417583i
$79$	2.29709	−	3.97867i	0.258443	−	0.447636i	−0.707382	−	0.706831i	$-0.750124\pi$
$79$	2.29709	−	3.97867i	0.258443	−	0.447636i	0.965825	+	0.259195i	$0.0834574\pi$
$80$	1.91775	+	1.14989i	0.214411	+	0.128561i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.36848	−	3.09949i	0.592850	−	0.342282i
$83$	−9.52048	+	5.49665i	−1.04501	+	0.603336i	−0.921248	−	0.388976i	$-0.872829\pi$
$83$	−9.52048	+	5.49665i	−1.04501	+	0.603336i	−0.123761	+	0.992312i	$0.539496\pi$
$84$	0.133246	+	0.230788i	0.0145383	+	0.0251810i
$85$	3.94114	+	7.09451i	0.427476	+	0.769508i
$86$	4.88919	−	8.46832i	0.527215	−	0.913163i
$87$	7.43493	+	4.29256i	0.797108	+	0.460210i
$88$	3.74966	−	2.16487i	0.399715	−	0.230776i
$89$	−13.8892			−1.47226			−0.736128	−	0.676843i	$-0.763348\pi$
$89$	−13.8892			−1.47226			−0.736128	+	0.676843i	$0.763348\pi$
$90$	2.23576	+	0.0369558i	0.235670	+	0.00389549i
$91$	−0.982817			−0.103027
$92$			2.23029i			0.232524i
$93$	−1.70328	−	5.30083i	−0.176622	−	0.549671i
$94$	9.03257			0.931639
$95$	2.45159	−	1.36191i	0.251528	−	0.139729i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	11.1655i		−	1.13368i	−0.823827	−	0.566841i	$-0.808165\pi$
$97$		−	11.1655i		−	1.13368i	0.823827	−	0.566841i	$-0.191835\pi$
$98$	−6.00067	+	3.46449i	−0.606160	+	0.349966i
$99$	2.16487	−	3.74966i	0.217578	−	0.376855i
$100$	−2.35552	−	4.41039i	−0.235552	−	0.441039i
$101$	−11.4933			−1.14363			−0.571815	−	0.820382i	$-0.693761\pi$
$101$	−11.4933			−1.14363			−0.571815	+	0.820382i	$0.693761\pi$
$102$	3.14320	−	1.81473i	0.311223	−	0.179685i
$103$	8.73635	−	5.04393i	0.860818	−	0.496993i	−0.00346830	−	0.999994i	$-0.501104\pi$
$103$	8.73635	−	5.04393i	0.860818	−	0.496993i	0.864286	+	0.503001i	$0.167771\pi$
$104$	1.84400	+	3.19390i	0.180819	+	0.313187i
$105$	0.00984840	−	0.595811i	0.000961105	−	0.0581452i
$106$	3.87192	+	6.70636i	0.376074	+	0.651380i
$107$	−16.0181	−	9.24808i	−1.54853	−	0.894045i	−0.998254	−	0.0590638i	$-0.981188\pi$
$107$	−16.0181	−	9.24808i	−1.54853	−	0.894045i	−0.550278	−	0.834982i	$-0.685478\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−5.59136			−0.535555			−0.267777	−	0.963481i	$-0.586289\pi$
$109$	−5.59136			−0.535555			−0.267777	+	0.963481i	$0.586289\pi$
$110$	−9.68027	−	0.160009i	−0.922977	−	0.0152563i
$111$	3.40580	+	5.89902i	0.323264	+	0.559910i
$112$	−0.230788	−	0.133246i	−0.0218074	−	0.0125905i
$113$	8.47763	−	4.89456i	0.797509	−	0.460442i	−0.0450906	−	0.998983i	$-0.514358\pi$
$113$	8.47763	−	4.89456i	0.797509	−	0.460442i	0.842599	+	0.538541i	$0.181024\pi$
$114$	−0.627100	−	1.08617i	−0.0587333	−	0.101729i
$115$	2.56458	−	4.27714i	0.239149	−	0.398846i
$116$	−8.58511			−0.797108
$117$	3.19390	+	1.84400i	0.295276	+	0.170478i
$118$	−1.48175	−	0.855490i	−0.136406	−	0.0787542i
$119$	−0.483608	−	0.837634i	−0.0443323	−	0.0767858i
$120$	−1.95471	+	1.08588i	−0.178439	+	0.0991265i
$121$	−3.87331	+	6.70878i	−0.352119	+	0.609889i
$122$			5.59976i			0.506978i
$123$			6.19899i			0.558944i
$124$	4.12550	+	3.73902i	0.370481	+	0.335774i
$125$	−0.554136	+	11.1666i	−0.0495634	+	0.998771i
$126$	−0.266491			−0.0237409
$127$	−7.24504	−	4.18292i	−0.642893	−	0.371175i	0.142835	−	0.989747i	$-0.454378\pi$
$127$	−7.24504	−	4.18292i	−0.642893	−	0.371175i	−0.785728	+	0.618572i	$0.787712\pi$
$128$			1.00000i			0.0883883i
$129$	4.88919	+	8.46832i	0.430469	+	0.745594i
$130$	0.136293	−	8.24548i	0.0119537	−	0.723176i
$131$	−10.6180	+	18.3909i	−0.927696	+	1.60682i	−0.140529	+	0.990077i	$0.544880\pi$
$131$	−10.6180	+	18.3909i	−0.927696	+	1.60682i	−0.787167	+	0.616740i	$0.788453\pi$
$132$			4.32974i			0.376855i
$133$	−0.289454	+	0.167117i	−0.0250989	+	0.0144908i
$134$	0.658723	+	1.14094i	0.0569050	+	0.0985624i
$135$	−1.14989	+	1.91775i	−0.0989664	+	0.165054i
$136$	−1.81473	+	3.14320i	−0.155612	+	0.269527i
$137$	−3.95509	+	2.28347i	−0.337906	+	0.195090i	−0.659346	−	0.751840i	$-0.729167\pi$
$137$	−3.95509	+	2.28347i	−0.337906	+	0.195090i	0.321440	+	0.946930i	$0.395833\pi$
$138$	−1.93149	−	1.11515i	−0.164419	−	0.0949276i
$139$	20.5780			1.74540			0.872701	−	0.488254i	$-0.162366\pi$
$139$	20.5780			1.74540			0.872701	+	0.488254i	$0.162366\pi$
$140$	0.289376	+	0.520911i	0.0244568	+	0.0440251i
$141$	−4.51629	+	7.82244i	−0.380340	+	0.658768i
$142$	−9.04932	+	5.22463i	−0.759402	+	0.438441i
$143$	−13.8287	−	7.98402i	−1.15642	−	0.667657i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	16.4641	+	9.87190i	1.36727	+	0.819817i
$146$	−3.10854	−	5.38415i	−0.257265	−	0.445596i
$147$		−	6.92898i		−	0.571493i
$148$	−5.89902	−	3.40580i	−0.484896	−	0.279955i
$149$	0.807842	−	1.39922i	0.0661810	−	0.114629i	−0.831036	−	0.556218i	$-0.812252\pi$
$149$	0.807842	−	1.39922i	0.0661810	−	0.114629i	0.897217	+	0.441589i	$0.145585\pi$
$150$	4.99727	+	0.165249i	0.408025	+	0.0134925i
$151$	−10.5314			−0.857029			−0.428515	−	0.903535i	$-0.640963\pi$
$151$	−10.5314			−0.857029			−0.428515	+	0.903535i	$0.640963\pi$
$152$	1.08617	+	0.627100i	0.0880999	+	0.0508645i
$153$			3.62945i			0.293424i
$154$	1.15384			0.0929788
$155$	−3.61223	−	11.9144i	−0.290141	−	0.956984i
$156$	−3.68799			−0.295276
$157$		−	6.43776i		−	0.513789i	−0.966439	−	0.256894i	$-0.917301\pi$
$157$		−	6.43776i		−	0.513789i	0.966439	−	0.256894i	$-0.0826993\pi$
$158$	−3.97867	−	2.29709i	−0.316526	−	0.182746i
$159$	−7.74384			−0.614126
$160$	1.14989	−	1.91775i	0.0909065	−	0.151611i
$161$	−0.297177	+	0.514725i	−0.0234208	+	0.0405660i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$		−	7.27078i		−	0.569491i	−0.958603	−	0.284746i	$-0.908091\pi$
$163$		−	7.27078i		−	0.569491i	0.958603	−	0.284746i	$-0.0919091\pi$
$164$	−3.09949	−	5.36848i	−0.242030	−	0.419208i
$165$	4.97870	−	8.30335i	0.387592	−	0.646415i
$166$	5.49665	+	9.52048i	0.426623	+	0.738933i
$167$	4.28167	+	2.47202i	0.331325	+	0.191291i	0.656429	−	0.754387i	$-0.272066\pi$
$167$	4.28167	+	2.47202i	0.331325	+	0.191291i	−0.325104	+	0.945678i	$0.605399\pi$
$168$	0.230788	−	0.133246i	0.0178057	−	0.0102801i
$169$	0.300648	−	0.520738i	0.0231268	−	0.0400568i
$170$	7.09451	−	3.94114i	0.544124	−	0.302271i
$171$	1.25420			0.0959111
$172$	−8.46832	−	4.88919i	−0.645703	−	0.372797i
$173$	−0.253665	+	0.146453i	−0.0192858	+	0.0111347i	−0.509612	−	0.860404i	$-0.670211\pi$
$173$	−0.253665	+	0.146453i	−0.0192858	+	0.0111347i	0.490326	+	0.871539i	$0.336878\pi$
$174$	4.29256	−	7.43493i	0.325418	−	0.563640i
$175$	0.0440374	−	1.33173i	0.00332891	−	0.100669i
$176$	−2.16487	−	3.74966i	−0.163183	−	0.282641i
$177$	1.48175	−	0.855490i	0.111375	−	0.0643026i
$178$			13.8892i			1.04104i
$179$	−10.4594	+	18.1163i	−0.781774	+	1.35407i	0.149133	+	0.988817i	$0.452352\pi$
$179$	−10.4594	+	18.1163i	−0.781774	+	1.35407i	−0.930907	+	0.365256i	$0.880981\pi$
$180$	0.0369558	−	2.23576i	0.00275453	−	0.166644i
$181$	−8.66164	−	15.0024i	−0.643815	−	1.11512i	−0.984574	−	0.174969i	$-0.944017\pi$
$181$	−8.66164	−	15.0024i	−0.643815	−	1.11512i	0.340759	−	0.940151i	$-0.389316\pi$
$182$			0.982817i			0.0728513i
$183$	−4.84953	−	2.79988i	−0.358488	−	0.206973i
$184$	2.23029			0.164419
$185$	7.39656	+	13.3147i	0.543806	+	0.978914i
$186$	−5.30083	+	1.70328i	−0.388676	+	0.124890i
$187$		−	15.7146i		−	1.14916i
$188$		−	9.03257i		−	0.658768i
$189$	0.133246	−	0.230788i	0.00969219	−	0.0167874i
$190$	−1.36191	−	2.45159i	−0.0988031	−	0.177857i
$191$	5.46670	+	9.46861i	0.395557	+	0.685125i	0.993172	−	0.116658i	$-0.0372183\pi$
$191$	5.46670	+	9.46861i	0.395557	+	0.685125i	−0.597615	+	0.801783i	$0.703885\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−3.52728	−	2.03648i	−0.253899	−	0.146589i	0.367649	−	0.929965i	$-0.380163\pi$
$193$	−3.52728	−	2.03648i	−0.253899	−	0.146589i	−0.621548	+	0.783376i	$0.713496\pi$
$194$	−11.1655			−0.801635
$195$	7.07265	+	4.24077i	0.506483	+	0.303688i
$196$	3.46449	+	6.00067i	0.247464	+	0.428620i
$197$	−21.7435	+	12.5536i	−1.54916	+	0.894407i	−0.550953	+	0.834536i	$0.685736\pi$
$197$	−21.7435	+	12.5536i	−1.54916	+	0.894407i	−0.998206	+	0.0598710i	$0.980931\pi$
$198$	−3.74966	−	2.16487i	−0.266477	−	0.153851i
$199$	2.36222	+	4.09149i	0.167454	+	0.290038i	0.937524	−	0.347921i	$-0.113112\pi$
$199$	2.36222	+	4.09149i	0.167454	+	0.290038i	−0.770070	+	0.637959i	$0.779779\pi$
$200$	−4.41039	+	2.35552i	−0.311861	+	0.166561i
$201$	−1.31745			−0.0929255
$202$			11.4933i			0.808669i
$203$	−1.98134	−	1.14393i	−0.139063	−	0.0802880i
$204$	−1.81473	−	3.14320i	−0.127056	−	0.220068i
$205$	−0.229089	+	13.8595i	−0.0160003	+	0.967987i
$206$	−5.04393	−	8.73635i	−0.351427	−	0.608690i
$207$	1.93149	−	1.11515i	0.134248	−	0.0775081i
$208$	3.19390	−	1.84400i	0.221457	−	0.127858i
$209$	−5.43036			−0.375626
$210$	−0.595811	−	0.00984840i	−0.0411148	−	0.000679604i
$211$	−2.09258	+	3.62445i	−0.144059	+	0.249518i	−0.929022	−	0.370026i	$-0.879349\pi$
$211$	−2.09258	+	3.62445i	−0.144059	+	0.249518i	0.784962	+	0.619543i	$0.212682\pi$
$212$	6.70636	−	3.87192i	0.460595	−	0.265925i
$213$		−	10.4493i		−	0.715971i
$214$	−9.24808	+	16.0181i	−0.632186	+	1.09498i
$215$	10.6181	+	19.1138i	0.724149	+	1.30355i
$216$	−1.00000			−0.0680414
$217$	0.453908	+	1.41262i	0.0308133	+	0.0958952i
$218$			5.59136i			0.378694i
$219$	6.21708			0.420112
$220$	−0.160009	+	9.68027i	−0.0107878	+	0.652643i
$221$	13.3854			0.900399
$222$	5.89902	−	3.40580i	0.395916	−	0.228582i
$223$	23.2266	+	13.4099i	1.55537	+	0.897992i	0.997690	+	0.0679350i	$0.0216410\pi$
$223$	23.2266	+	13.4099i	1.55537	+	0.897992i	0.557678	+	0.830057i	$0.311692\pi$
$224$	−0.133246	+	0.230788i	−0.00890284	+	0.0154202i
$225$	−2.64174	+	4.24514i	−0.176116	+	0.283009i
$226$	−4.89456	−	8.47763i	−0.325582	−	0.563924i
$227$	10.3257	−	5.96157i	0.685344	−	0.395684i	−0.116521	−	0.993188i	$-0.537174\pi$
$227$	10.3257	−	5.96157i	0.685344	−	0.395684i	0.801865	+	0.597505i	$0.203841\pi$
$228$	−1.08617	+	0.627100i	−0.0719333	+	0.0415307i
$229$	−10.7364	+	18.5959i	−0.709478	+	1.22885i	0.255573	+	0.966790i	$0.417736\pi$
$229$	−10.7364	+	18.5959i	−0.709478	+	1.22885i	−0.965051	+	0.262062i	$0.915597\pi$
$230$	−4.27714	−	2.56458i	−0.282027	−	0.169104i
$231$	−0.576918	+	0.999252i	−0.0379584	+	0.0657459i
$232$			8.58511i			0.563640i
$233$			4.79091i			0.313863i	0.987609	+	0.156931i	$0.0501602\pi$
$233$			4.79091i			0.313863i	−0.987609	+	0.156931i	$0.949840\pi$
$234$	1.84400	−	3.19390i	0.120546	−	0.208792i
$235$	−10.3864	+	17.3222i	−0.677536	+	1.12998i
$236$	−0.855490	+	1.48175i	−0.0556876	+	0.0964538i
$237$	3.97867	−	2.29709i	0.258443	−	0.149212i
$238$	−0.837634	+	0.483608i	−0.0542958	+	0.0313477i
$239$	−0.653110	−	1.13122i	−0.0422461	−	0.0731725i	0.844129	−	0.536140i	$-0.180118\pi$
$239$	−0.653110	−	1.13122i	−0.0422461	−	0.0731725i	−0.886375	+	0.462967i	$0.846785\pi$
$240$	1.08588	+	1.95471i	0.0700930	+	0.126176i
$241$	−1.90150	+	3.29349i	−0.122486	+	0.212153i	−0.920748	−	0.390159i	$-0.872420\pi$
$241$	−1.90150	+	3.29349i	−0.122486	+	0.212153i	0.798261	+	0.602311i	$0.205753\pi$
$242$	6.70878	+	3.87331i	0.431256	+	0.248986i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	5.59976			0.358488
$245$	0.256066	−	15.4916i	0.0163595	−	0.989719i
$246$	6.19899			0.395233
$247$		−	4.62548i		−	0.294312i
$248$	3.73902	−	4.12550i	0.237428	−	0.261969i
$249$	−10.9933			−0.696672
$250$	11.1666	+	0.554136i	0.706238	+	0.0350466i
$251$	7.46644	−	12.9323i	0.471278	−	0.816277i	−0.528182	−	0.849131i	$-0.677126\pi$
$251$	7.46644	−	12.9323i	0.471278	−	0.816277i	0.999460	+	0.0328539i	$0.0104596\pi$
$252$			0.266491i			0.0167874i
$253$	−8.36285	+	4.82829i	−0.525768	+	0.303552i
$254$	−4.18292	+	7.24504i	−0.262460	+	0.454594i
$255$	−0.134129	+	8.11459i	−0.00839951	+	0.508156i
$256$	1.00000			0.0625000
$257$	8.35871	−	4.82591i	0.521402	−	0.301032i	−0.216106	−	0.976370i	$-0.569336\pi$
$257$	8.35871	−	4.82591i	0.521402	−	0.301032i	0.737508	+	0.675338i	$0.236002\pi$
$258$	8.46832	−	4.88919i	0.527215	−	0.304388i
$259$	−0.907615	−	1.57204i	−0.0563965	−	0.0976815i
$260$	−8.24548	−	0.136293i	−0.511363	−	0.00845253i
$261$	4.29256	+	7.43493i	0.265703	+	0.460210i
$262$	18.3909	+	10.6180i	1.13619	+	0.655980i
$263$			2.93533i			0.181000i	0.995896	+	0.0905002i	$0.0288466\pi$
$263$			2.93533i			0.181000i	−0.995896	+	0.0905002i	$0.971153\pi$
$264$	4.32974			0.266477
$265$	−17.3134	−	0.286180i	−1.06355	−	0.0175799i
$266$	0.167117	+	0.289454i	0.0102466	+	0.0177476i
$267$	−12.0284	−	6.94462i	−0.736128	−	0.425004i
$268$	1.14094	−	0.658723i	0.0696941	−	0.0402379i
$269$	9.66773	+	16.7450i	0.589452	+	1.02096i	0.994304	+	0.106578i	$0.0339895\pi$
$269$	9.66773	+	16.7450i	0.589452	+	1.02096i	−0.404852	+	0.914382i	$0.632677\pi$
$270$	1.91775	+	1.14989i	0.116711	+	0.0699798i
$271$	−22.4980			−1.36665			−0.683327	−	0.730112i	$-0.739468\pi$
$271$	−22.4980			−1.36665			−0.683327	+	0.730112i	$0.739468\pi$
$272$	3.14320	+	1.81473i	0.190584	+	0.110034i
$273$	−0.851145	−	0.491409i	−0.0515136	−	0.0297414i
$274$	2.28347	+	3.95509i	0.137949	+	0.238936i
$275$	11.4381	−	18.3803i	0.689741	−	1.10838i
$276$	−1.11515	+	1.93149i	−0.0671240	+	0.116262i
$277$		−	0.541801i		−	0.0325537i	−0.999868	−	0.0162768i	$-0.994819\pi$
$277$		−	0.541801i		−	0.0325537i	0.999868	−	0.0162768i	$-0.00518131\pi$
$278$		−	20.5780i		−	1.23419i
$279$	1.17534	−	5.44230i	0.0703655	−	0.325822i
$280$	0.520911	−	0.289376i	0.0311304	−	0.0172935i
$281$	−24.9346			−1.48747			−0.743736	−	0.668473i	$-0.766948\pi$
$281$	−24.9346			−1.48747			−0.743736	+	0.668473i	$0.766948\pi$
$282$	7.82244	+	4.51629i	0.465819	+	0.268941i
$283$			15.0264i			0.893227i	0.894727	+	0.446613i	$0.147370\pi$
$283$			15.0264i			0.893227i	−0.894727	+	0.446613i	$0.852630\pi$
$284$	5.22463	+	9.04932i	0.310025	+	0.536978i
$285$	2.80409	+	0.0463500i	0.166100	+	0.00274554i
$286$	−7.98402	+	13.8287i	−0.472105	+	0.817710i
$287$		−	1.65197i		−	0.0975130i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−1.91354	−	3.31434i	−0.112561	−	0.194961i
$290$	9.87190	−	16.4641i	0.579698	−	0.966805i
$291$	5.58274	−	9.66959i	0.327266	−	0.566841i
$292$	−5.38415	+	3.10854i	−0.315084	+	0.181914i
$293$	15.0516	+	8.69003i	0.879322	+	0.507677i	0.870435	−	0.492284i	$-0.163838\pi$
$293$	15.0516	+	8.69003i	0.879322	+	0.507677i	0.00888739	+	0.999961i	$0.497171\pi$
$294$	−6.92898			−0.404106
$295$	3.34446	−	1.85791i	0.194722	−	0.108172i
$296$	−3.40580	+	5.89902i	−0.197958	+	0.342873i
$297$	3.74966	−	2.16487i	0.217578	−	0.125618i
$298$	−1.39922	−	0.807842i	−0.0810548	−	0.0467970i
$299$	−4.11265	−	7.12333i	−0.237841	−	0.411953i
$300$	0.165249	−	4.99727i	0.00954065	−	0.288517i
$301$	−1.30292	−	2.25673i	−0.0750993	−	0.130076i
$302$			10.5314i			0.606011i
$303$	−9.95353	−	5.74667i	−0.571815	−	0.330138i
$304$	0.627100	−	1.08617i	0.0359666	−	0.0622961i
$305$	−10.7389	−	6.43908i	−0.614910	−	0.368701i
$306$	3.62945			0.207482
$307$	−18.1839	−	10.4985i	−1.03781	−	0.599181i	−0.118599	−	0.992942i	$-0.537840\pi$
$307$	−18.1839	−	10.4985i	−1.03781	−	0.599181i	−0.919213	+	0.393761i	$0.871174\pi$
$308$		−	1.15384i		−	0.0657459i
$309$	10.0879			0.573879
$310$	−11.9144	+	3.61223i	−0.676690	+	0.205161i
$311$	−5.16307			−0.292771			−0.146385	−	0.989228i	$-0.546764\pi$
$311$	−5.16307			−0.292771			−0.146385	+	0.989228i	$0.546764\pi$
$312$			3.68799i			0.208792i
$313$	22.0577	+	12.7350i	1.24677	+	0.719825i	0.970465	−	0.241243i	$-0.0775552\pi$
$313$	22.0577	+	12.7350i	1.24677	+	0.719825i	0.276310	+	0.961069i	$0.410888\pi$
$314$	−6.43776			−0.363304
$315$	0.306434	−	0.511063i	0.0172656	−	0.0287951i
$316$	−2.29709	+	3.97867i	−0.129221	+	0.223818i
$317$	15.6311	+	9.02463i	0.877931	+	0.506874i	0.869976	−	0.493094i	$-0.164134\pi$
$317$	15.6311	+	9.02463i	0.877931	+	0.506874i	0.00795560	+	0.999968i	$0.497468\pi$
$318$			7.74384i			0.434253i
$319$	−18.5856	−	32.1913i	−1.04060	−	1.80237i
$320$	−1.91775	−	1.14989i	−0.107205	−	0.0642806i
$321$	−9.24808	−	16.0181i	−0.516177	−	0.894045i
$322$	0.514725	+	0.297177i	0.0286845	+	0.0165610i
$323$	3.94220	−	2.27603i	0.219350	−	0.126642i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	15.6560	+	9.74274i	0.868441	+	0.540430i
$326$	−7.27078			−0.402691
$327$	−4.84226	−	2.79568i	−0.267777	−	0.154601i
$328$	−5.36848	+	3.09949i	−0.296425	+	0.171141i
$329$	1.20355	−	2.08461i	0.0663539	−	0.114928i
$330$	−8.30335	−	4.97870i	−0.457084	−	0.274069i
$331$	−11.4196	−	19.7793i	−0.627678	−	1.08717i	−0.988017	−	0.154348i	$-0.950672\pi$
$331$	−11.4196	−	19.7793i	−0.627678	−	1.08717i	0.360339	−	0.932821i	$-0.382661\pi$
$332$	9.52048	−	5.49665i	0.522504	−	0.301668i
$333$			6.81160i			0.373273i
$334$	2.47202	−	4.28167i	0.135263	−	0.234282i
$335$	−2.94550	−	0.0486873i	−0.160930	−	0.00266007i
$336$	−0.133246	−	0.230788i	−0.00726914	−	0.0125905i
$337$		−	5.66462i		−	0.308572i	−0.988026	−	0.154286i	$-0.950692\pi$
$337$		−	5.66462i		−	0.308572i	0.988026	−	0.154286i	$-0.0493076\pi$
$338$	−0.520738	−	0.300648i	−0.0283244	−	0.0163531i
$339$	9.78913			0.531672
$340$	−3.94114	−	7.09451i	−0.213738	−	0.384754i
$341$	−5.08889	+	23.5637i	−0.275579	+	1.27605i
$342$		−	1.25420i		−	0.0678194i
$343$			3.71195i			0.200426i
$344$	−4.88919	+	8.46832i	−0.263607	+	0.456581i
$345$	4.35957	−	2.42182i	0.234711	−	0.130387i
$346$	0.146453	+	0.253665i	0.00787339	+	0.0136371i
$347$	−6.15256	−	3.55218i	−0.330287	−	0.190691i	0.325682	−	0.945480i	$-0.394406\pi$
$347$	−6.15256	−	3.55218i	−0.330287	−	0.190691i	−0.655969	+	0.754788i	$0.727740\pi$
$348$	−7.43493	−	4.29256i	−0.398554	−	0.230105i
$349$	8.84061			0.473227			0.236614	−	0.971604i	$-0.423962\pi$
$349$	8.84061			0.473227			0.236614	+	0.971604i	$0.423962\pi$
$350$	−1.33173	−	0.0440374i	−0.0711838	−	0.00235390i
$351$	1.84400	+	3.19390i	0.0984253	+	0.170478i
$352$	−3.74966	+	2.16487i	−0.199858	+	0.115388i
$353$	−19.0456	−	10.9960i	−1.01369	−	0.585256i	−0.101423	−	0.994843i	$-0.532339\pi$
$353$	−19.0456	−	10.9960i	−1.01369	−	0.585256i	−0.912271	+	0.409587i	$0.865673\pi$
$354$	−0.855490	−	1.48175i	−0.0454688	−	0.0787542i
$355$	0.386161	−	23.3620i	0.0204953	−	1.23993i
$356$	13.8892			0.736128
$357$		−	0.967217i		−	0.0511905i
$358$	18.1163	+	10.4594i	0.957474	+	0.552798i
$359$	6.58726	+	11.4095i	0.347662	+	0.602169i	0.985834	−	0.167725i	$-0.0536422\pi$
$359$	6.58726	+	11.4095i	0.347662	+	0.602169i	−0.638171	+	0.769894i	$0.720309\pi$
$360$	−2.23576	−	0.0369558i	−0.117835	−	0.00194774i
$361$	8.71349	+	15.0922i	0.458605	+	0.794327i
$362$	−15.0024	+	8.66164i	−0.788509	+	0.455246i
$363$	−6.70878	+	3.87331i	−0.352119	+	0.203296i
$364$	0.982817			0.0515136
$365$	13.8999	+	0.229757i	0.727555	+	0.0120261i
$366$	−2.79988	+	4.84953i	−0.146352	+	0.253489i
$367$	7.57740	−	4.37481i	0.395537	−	0.228363i	−0.289020	−	0.957323i	$-0.593329\pi$
$367$	7.57740	−	4.37481i	0.395537	−	0.228363i	0.684556	+	0.728960i	$0.259996\pi$
$368$		−	2.23029i		−	0.116262i
$369$	−3.09949	+	5.36848i	−0.161353	+	0.279472i
$370$	13.3147	−	7.39656i	0.692197	−	0.384529i
$371$	2.06366			0.107140
$372$	1.70328	+	5.30083i	0.0883108	+	0.274835i
$373$		−	12.1156i		−	0.627320i	−0.949535	−	0.313660i	$-0.898445\pi$
$373$		−	12.1156i		−	0.627320i	0.949535	−	0.313660i	$-0.101555\pi$
$374$	−15.7146			−0.812582
$375$	−6.06320	+	9.39349i	−0.313102	+	0.485078i
$376$	−9.03257			−0.465819
$377$	27.4200	−	15.8309i	1.41220	−	0.815334i
$378$	−0.230788	−	0.133246i	−0.0118705	−	0.00685341i
$379$	0.249098	−	0.431450i	0.0127953	−	0.0221621i	−0.859557	−	0.511040i	$-0.829260\pi$
$379$	0.249098	−	0.431450i	0.0127953	−	0.0221621i	0.872352	+	0.488878i	$0.162594\pi$
$380$	−2.45159	+	1.36191i	−0.125764	+	0.0698643i
$381$	−4.18292	−	7.24504i	−0.214298	−	0.371175i
$382$	9.46861	−	5.46670i	0.484456	−	0.279701i
$383$	−31.6273	+	18.2600i	−1.61608	+	0.933043i	−0.628157	+	0.778086i	$0.716191\pi$
$383$	−31.6273	+	18.2600i	−1.61608	+	0.933043i	−0.987921	+	0.154957i	$0.950476\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−1.32678	+	2.21277i	−0.0676190	+	0.112773i
$386$	−2.03648	+	3.52728i	−0.103654	+	0.179534i
$387$			9.77837i			0.497063i
$388$			11.1655i			0.566841i
$389$	15.3806	−	26.6400i	0.779826	−	1.35070i	−0.152215	−	0.988347i	$-0.548641\pi$
$389$	15.3806	−	26.6400i	0.779826	−	1.35070i	0.932041	−	0.362352i	$-0.118026\pi$
$390$	4.24077	−	7.07265i	0.214740	−	0.358137i
$391$	4.04737	−	7.01026i	0.204684	−	0.354524i
$392$	6.00067	−	3.46449i	0.303080	−	0.174983i
$393$	−18.3909	+	10.6180i	−0.927696	+	0.535605i
$394$	12.5536	+	21.7435i	0.632442	+	1.09542i
$395$	8.98026	−	4.98871i	0.451846	−	0.251009i
$396$	−2.16487	+	3.74966i	−0.108789	+	0.188428i
$397$	−13.6400	−	7.87503i	−0.684570	−	0.395237i	0.117005	−	0.993131i	$-0.462671\pi$
$397$	−13.6400	−	7.87503i	−0.684570	−	0.395237i	−0.801575	+	0.597895i	$0.796004\pi$
$398$	4.09149	−	2.36222i	0.205088	−	0.118408i
$399$	−0.334233			−0.0167326
$400$	2.35552	+	4.41039i	0.117776	+	0.220519i
$401$	−17.8819			−0.892981			−0.446490	−	0.894788i	$-0.647326\pi$
$401$	−17.8819			−0.892981			−0.446490	+	0.894788i	$0.647326\pi$
$402$			1.31745i			0.0657083i
$403$	−20.0712	−	4.33463i	−0.999815	−	0.215923i
$404$	11.4933			0.571815
$405$	−1.95471	+	1.08588i	−0.0971301	+	0.0539576i
$406$	−1.14393	+	1.98134i	−0.0567722	+	0.0983323i
$407$		−	29.4924i		−	1.46189i
$408$	−3.14320	+	1.81473i	−0.155612	+	0.0898423i
$409$	14.1412	−	24.4933i	0.699237	−	1.21111i	−0.269494	−	0.963002i	$-0.586857\pi$
$409$	14.1412	−	24.4933i	0.699237	−	1.21111i	0.968731	−	0.248112i	$-0.0798102\pi$
$410$	13.8595	+	0.229089i	0.684470	+	0.0113139i
$411$	−4.56694			−0.225271
$412$	−8.73635	+	5.04393i	−0.430409	+	0.248497i
$413$	−0.394874	+	0.227980i	−0.0194305	+	0.0112182i
$414$	−1.11515	−	1.93149i	−0.0548065	−	0.0949276i
$415$	−24.5784	−	0.406267i	−1.20651	−	0.0199428i
$416$	−1.84400	−	3.19390i	−0.0904094	−	0.156594i
$417$	17.8211	+	10.2890i	0.872701	+	0.503854i
$418$			5.43036i			0.265607i
$419$	39.0309			1.90678			0.953391	−	0.301737i	$-0.0975664\pi$
$419$	39.0309			1.90678			0.953391	+	0.301737i	$0.0975664\pi$
$420$	−0.00984840	+	0.595811i	−0.000480553	+	0.0290726i
$421$	14.1724	+	24.5473i	0.690721	+	1.19636i	0.971602	+	0.236621i	$0.0760401\pi$
$421$	14.1724	+	24.5473i	0.690721	+	1.19636i	−0.280881	+	0.959743i	$0.590627\pi$
$422$	3.62445	+	2.09258i	0.176436	+	0.101865i
$423$	−7.82244	+	4.51629i	−0.380340	+	0.219589i
$424$	−3.87192	−	6.70636i	−0.188037	−	0.325690i
$425$	−0.599763	+	18.1374i	−0.0290928	+	0.879791i
$426$	−10.4493			−0.506268
$427$	1.29236	+	0.746143i	0.0625416	+	0.0361084i
$428$	16.0181	+	9.24808i	0.774266	+	0.447023i
$429$	−7.98402	−	13.8287i	−0.385472	−	0.667657i
$430$	19.1138	−	10.6181i	0.921751	−	0.512051i
$431$	1.70859	−	2.95937i	0.0823000	−	0.142548i	−0.821938	−	0.569578i	$-0.807107\pi$
$431$	1.70859	−	2.95937i	0.0823000	−	0.142548i	0.904237	+	0.427030i	$0.140440\pi$
$432$			1.00000i			0.0481125i
$433$			16.2632i			0.781558i	0.920485	+	0.390779i	$0.127794\pi$
$433$			16.2632i			0.781558i	−0.920485	+	0.390779i	$0.872206\pi$
$434$	1.41262	−	0.453908i	0.0678082	−	0.0217883i
$435$	9.32237	+	16.7814i	0.446974	+	0.804605i
$436$	5.59136			0.267777
$437$	−2.42248	−	1.39862i	−0.115883	−	0.0669049i
$438$		−	6.21708i		−	0.297064i
$439$	−4.56150	−	7.90075i	−0.217708	−	0.377082i	0.736399	−	0.676548i	$-0.236525\pi$
$439$	−4.56150	−	7.90075i	−0.217708	−	0.377082i	−0.954107	+	0.299466i	$0.903192\pi$
$440$	9.68027	+	0.160009i	0.461489	+	0.00762813i
$441$	3.46449	−	6.00067i	0.164976	−	0.285746i
$442$		−	13.3854i		−	0.636678i
$443$	−6.73466	+	3.88826i	−0.319973	+	0.184737i	−0.651381	−	0.758751i	$-0.725810\pi$
$443$	−6.73466	+	3.88826i	−0.319973	+	0.184737i	0.331407	+	0.943488i	$0.392477\pi$
$444$	−3.40580	−	5.89902i	−0.161632	−	0.279955i
$445$	−26.6361	−	15.9710i	−1.26267	−	0.757100i
$446$	13.4099	−	23.2266i	0.634976	−	1.09981i
$447$	1.39922	−	0.807842i	0.0661810	−	0.0382096i
$448$	0.230788	+	0.133246i	0.0109037	+	0.00629526i
$449$	−4.43184			−0.209152			−0.104576	−	0.994517i	$-0.533348\pi$
$449$	−4.43184			−0.209152			−0.104576	+	0.994517i	$0.533348\pi$
$450$	4.24514	+	2.64174i	0.200118	+	0.124533i
$451$	13.4200	−	23.2441i	0.631923	−	1.09452i
$452$	−8.47763	+	4.89456i	−0.398754	+	0.230221i
$453$	−9.12042	−	5.26568i	−0.428515	−	0.247403i
$454$	−5.96157	−	10.3257i	−0.279790	−	0.484611i
$455$	−1.88480	−	1.13013i	−0.0883607	−	0.0529812i
$456$	0.627100	+	1.08617i	0.0293666	+	0.0508645i
$457$			25.9754i			1.21508i	0.794289	+	0.607540i	$0.207844\pi$
$457$			25.9754i			1.21508i	−0.794289	+	0.607540i	$0.792156\pi$
$458$	18.5959	+	10.7364i	0.868930	+	0.501677i
$459$	−1.81473	+	3.14320i	−0.0847042	+	0.146712i
$460$	−2.56458	+	4.27714i	−0.119574	+	0.199423i
$461$	9.04776			0.421396			0.210698	−	0.977551i	$-0.432426\pi$
$461$	9.04776			0.421396			0.210698	+	0.977551i	$0.432426\pi$
$462$	0.999252	+	0.576918i	0.0464894	+	0.0268407i
$463$			3.88965i			0.180767i	0.995907	+	0.0903836i	$0.0288093\pi$
$463$			3.88965i			0.180767i	−0.995907	+	0.0903836i	$0.971191\pi$
$464$	8.58511			0.398554
$465$	2.82890	−	12.1242i	0.131187	−	0.562248i
$466$	4.79091			0.221935
$467$		−	25.9891i		−	1.20263i	−0.799011	−	0.601316i	$-0.794643\pi$
$467$		−	25.9891i		−	1.20263i	0.799011	−	0.601316i	$-0.205357\pi$
$468$	−3.19390	−	1.84400i	−0.147638	−	0.0852388i
$469$	0.351088			0.0162117
$470$	17.3222	+	10.3864i	0.799014	+	0.479090i
$471$	3.21888	−	5.57526i	0.148318	−	0.256894i
$472$	1.48175	+	0.855490i	0.0682032	+	0.0393771i
$473$		−	42.3378i		−	1.94669i
$474$	−2.29709	−	3.97867i	−0.105509	−	0.182746i
$475$	6.26757	+	0.207255i	0.287576	+	0.00950952i
$476$	0.483608	+	0.837634i	0.0221662	+	0.0383929i
$477$	−6.70636	−	3.87192i	−0.307063	−	0.177283i
$478$	−1.13122	+	0.653110i	−0.0517407	+	0.0298725i
$479$	4.38073	−	7.58764i	0.200161	−	0.346688i	−0.748419	−	0.663226i	$-0.769187\pi$
$479$	4.38073	−	7.58764i	0.200161	−	0.346688i	0.948580	+	0.316537i	$0.102520\pi$
$480$	1.95471	−	1.08588i	0.0892197	−	0.0495633i
$481$	25.1211			1.14543
$482$	3.29349	+	1.90150i	0.150015	+	0.0866110i
$483$	−0.514725	+	0.297177i	−0.0234208	+	0.0135220i
$484$	3.87331	−	6.70878i	0.176060	−	0.304944i
$485$	12.8390	−	21.4126i	0.582990	−	0.972295i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−24.1444	+	13.9398i	−1.09409	+	0.631672i	−0.934662	−	0.355538i	$-0.884298\pi$
$487$	−24.1444	+	13.9398i	−1.09409	+	0.631672i	−0.159426	+	0.987210i	$0.550964\pi$
$488$		−	5.59976i		−	0.253489i
$489$	3.63539	−	6.29668i	0.164398	−	0.284746i
$490$	−15.4916	−	0.256066i	−0.699837	−	0.0115679i
$491$	−18.3811	−	31.8370i	−0.829529	−	1.43679i	−0.898409	−	0.439161i	$-0.855276\pi$
$491$	−18.3811	−	31.8370i	−0.829529	−	1.43679i	0.0688801	−	0.997625i	$-0.478057\pi$
$492$		−	6.19899i		−	0.279472i
$493$	26.9847	+	15.5796i	1.21533	+	0.701671i
$494$	−4.62548			−0.208110
$495$	8.46336	−	4.70156i	0.380400	−	0.211319i
$496$	−4.12550	−	3.73902i	−0.185240	−	0.167887i
$497$			2.78463i			0.124908i
$498$			10.9933i			0.492622i
$499$	−5.53866	+	9.59325i	−0.247945	+	0.429453i	−0.962955	−	0.269661i	$-0.913088\pi$
$499$	−5.53866	+	9.59325i	−0.247945	+	0.429453i	0.715011	+	0.699113i	$0.246422\pi$
$500$	0.554136	−	11.1666i	0.0247817	−	0.499385i
$501$	2.47202	+	4.28167i	0.110442	+	0.191291i
$502$	−12.9323	−	7.46644i	−0.577195	−	0.333244i
$503$	26.6277	+	15.3735i	1.18727	+	0.685471i	0.957685	−	0.287818i	$-0.0929298\pi$
$503$	26.6277	+	15.3735i	1.18727	+	0.685471i	0.229585	+	0.973289i	$0.426263\pi$
$504$	0.266491			0.0118705
$505$	−22.0414	−	13.2160i	−0.980828	−	0.588106i
$506$	4.82829	+	8.36285i	0.214644	+	0.371774i
$507$	0.520738	−	0.300648i	0.0231268	−	0.0133523i
$508$	7.24504	+	4.18292i	0.321447	+	0.185587i
$509$	2.77148	+	4.80034i	0.122844	+	0.212771i	0.920888	−	0.389827i	$-0.127465\pi$
$509$	2.77148	+	4.80034i	0.122844	+	0.212771i	−0.798044	+	0.602599i	$0.794132\pi$
$510$	8.11459	+	0.134129i	0.359320	+	0.00593935i
$511$	−1.65680			−0.0732924
$512$		−	1.00000i		−	0.0441942i
$513$	1.08617	+	0.627100i	0.0479555	+	0.0276871i
$514$	−4.82591	−	8.35871i	−0.212862	−	0.368687i
$515$	22.5541	+	0.372805i	0.993851	+	0.0164278i
$516$	−4.88919	−	8.46832i	−0.215234	−	0.372797i
$517$	33.8691	−	19.5543i	1.48956	−	0.859999i
$518$	−1.57204	+	0.907615i	−0.0690713	+	0.0398783i
$519$	−0.292907			−0.0128572
$520$	−0.136293	+	8.24548i	−0.00597684	+	0.361588i
$521$	−5.61521	+	9.72582i	−0.246007	+	0.426096i	−0.962414	−	0.271586i	$-0.912452\pi$
$521$	−5.61521	+	9.72582i	−0.246007	+	0.426096i	0.716407	+	0.697682i	$0.245785\pi$
$522$	7.43493	−	4.29256i	0.325418	−	0.187880i
$523$		−	5.66729i		−	0.247813i	−0.992294	−	0.123907i	$-0.960458\pi$
$523$		−	5.66729i		−	0.247813i	0.992294	−	0.123907i	$-0.0395424\pi$
$524$	10.6180	−	18.3909i	0.463848	−	0.803408i
$525$	0.704001	−	1.13129i	0.0307251	−	0.0493736i
$526$	2.93533			0.127987
$527$	−6.18197	−	19.2391i	−0.269291	−	0.838070i
$528$		−	4.32974i		−	0.188428i
$529$	18.0258			0.783730
$530$	−0.286180	+	17.3134i	−0.0124309	+	0.752046i
$531$	1.71098			0.0742502
$532$	0.289454	−	0.167117i	0.0125494	−	0.00724542i
$533$	19.7989	+	11.4309i	0.857587	+	0.495128i
$534$	−6.94462	+	12.0284i	−0.300523	+	0.520521i
$535$	−20.0845	−	36.1545i	−0.868330	−	1.56310i
$536$	−0.658723	−	1.14094i	−0.0284525	−	0.0492812i
$537$	−18.1163	+	10.4594i	−0.781774	+	0.451358i
$538$	16.7450	−	9.66773i	0.721928	−	0.416805i
$539$	−15.0003	+	25.9813i	−0.646110	+	1.11910i
$540$	1.14989	−	1.91775i	0.0494832	−	0.0825268i
$541$	20.3599	−	35.2644i	0.875340	−	1.51613i	0.0189407	−	0.999821i	$-0.493971\pi$
$541$	20.3599	−	35.2644i	0.875340	−	1.51613i	0.856400	−	0.516313i	$-0.172696\pi$
$542$			22.4980i			0.966370i
$543$		−	17.3233i		−	0.743413i
$544$	1.81473	−	3.14320i	0.0778058	−	0.134764i
$545$	−10.7228	−	6.42942i	−0.459315	−	0.275406i
$546$	−0.491409	+	0.851145i	−0.0210303	+	0.0364256i
$547$	21.7522	−	12.5587i	0.930058	−	0.536969i	0.0432280	−	0.999065i	$-0.486236\pi$
$547$	21.7522	−	12.5587i	0.930058	−	0.536969i	0.886830	+	0.462096i	$0.152902\pi$
$548$	3.95509	−	2.28347i	0.168953	−	0.0975450i
$549$	−2.79988	−	4.84953i	−0.119496	−	0.206973i
$550$	−18.3803	−	11.4381i	−0.783740	−	0.487720i
$551$	5.38372	−	9.32488i	0.229354	−	0.397253i
$552$	1.93149	+	1.11515i	0.0822097	+	0.0474638i
$553$	−1.06028	+	0.612153i	−0.0450877	+	0.0260314i
$554$	−0.541801			−0.0230189
$555$	−0.251728	+	15.2291i	−0.0106853	+	0.646440i
$556$	−20.5780			−0.872701
$557$		−	27.0171i		−	1.14475i	−0.819991	−	0.572377i	$-0.806022\pi$
$557$		−	27.0171i		−	1.14475i	0.819991	−	0.572377i	$-0.193978\pi$
$558$	−5.44230	−	1.17534i	−0.230391	−	0.0497559i
$559$	36.0626			1.52528
$560$	−0.289376	−	0.520911i	−0.0122284	−	0.0220125i
$561$	7.85729	−	13.6092i	0.331735	−	0.574582i
$562$			24.9346i			1.05180i
$563$	−20.8550	+	12.0406i	−0.878933	+	0.507452i	−0.870306	−	0.492511i	$-0.836079\pi$
$563$	−20.8550	+	12.0406i	−0.878933	+	0.507452i	−0.00862638	+	0.999963i	$0.502746\pi$
$564$	4.51629	−	7.82244i	0.190170	−	0.329384i
$565$	21.8862	+	0.361765i	0.920758	+	0.0152196i
$566$	15.0264			0.631607
$567$	0.230788	−	0.133246i	0.00969219	−	0.00559579i
$568$	9.04932	−	5.22463i	0.379701	−	0.219220i
$569$	−8.56702	−	14.8385i	−0.359148	−	0.622063i	0.628671	−	0.777672i	$-0.283599\pi$
$569$	−8.56702	−	14.8385i	−0.359148	−	0.622063i	−0.987819	+	0.155609i	$0.950266\pi$
$570$	0.0463500	−	2.80409i	0.00194139	−	0.117451i
$571$	−16.0097	−	27.7295i	−0.669983	−	1.16045i	−0.977908	−	0.209035i	$-0.932968\pi$
$571$	−16.0097	−	27.7295i	−0.669983	−	1.16045i	0.307925	−	0.951411i	$-0.400365\pi$
$572$	13.8287	+	7.98402i	0.578208	+	0.333829i
$573$			10.9334i			0.456750i
$574$	−1.65197			−0.0689521
$575$	9.83646	−	5.25351i	0.410209	−	0.219087i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−40.0591	−	23.1282i	−1.66768	−	0.962838i	−0.968882	−	0.247523i	$-0.920384\pi$
$577$	−40.0591	−	23.1282i	−1.66768	−	0.962838i	−0.698802	−	0.715315i	$-0.746283\pi$
$578$	−3.31434	+	1.91354i	−0.137858	+	0.0795926i
$579$	−2.03648	−	3.52728i	−0.0846331	−	0.146589i
$580$	−16.4641	−	9.87190i	−0.683634	−	0.409908i
$581$	2.92962			0.121541
$582$	−9.66959	−	5.58274i	−0.400817	−	0.231412i
$583$	29.0368	+	16.7644i	1.20258	+	0.694310i
$584$	3.10854	+	5.38415i	0.128632	+	0.222798i
$585$	4.00471	+	7.20894i	0.165574	+	0.298053i
$586$	8.69003	−	15.0516i	0.358982	−	0.621775i
$587$		−	0.297043i		−	0.0122603i	−0.999981	−	0.00613014i	$-0.998049\pi$
$587$		−	0.297043i		−	0.0122603i	0.999981	−	0.00613014i	$-0.00195130\pi$
$588$			6.92898i			0.285746i
$589$	−6.64831	+	2.13625i	−0.273939	+	0.0880227i
$590$	−1.85791	−	3.34446i	−0.0764891	−	0.137689i
$591$	−25.1072			−1.03277
$592$	5.89902	+	3.40580i	0.242448	+	0.139977i
$593$		−	16.0986i		−	0.661089i	−0.943790	−	0.330544i	$-0.892768\pi$
$593$		−	16.0986i		−	0.661089i	0.943790	−	0.330544i	$-0.107232\pi$
$594$	−2.16487	−	3.74966i	−0.0888256	−	0.153851i
$595$	0.0357443	−	2.16247i	0.00146537	−	0.0886525i
$596$	−0.807842	+	1.39922i	−0.0330905	+	0.0573144i
$597$			4.72445i			0.193359i
$598$	−7.12333	+	4.11265i	−0.291294	+	0.168179i
$599$	−1.46139	−	2.53121i	−0.0597109	−	0.103422i	0.834625	−	0.550819i	$-0.185685\pi$
$599$	−1.46139	−	2.53121i	−0.0597109	−	0.103422i	−0.894336	+	0.447397i	$0.852351\pi$
$600$	−4.99727	−	0.165249i	−0.204013	−	0.00674626i
$601$	−15.6155	+	27.0468i	−0.636969	+	1.10326i	0.349125	+	0.937076i	$0.386479\pi$
$601$	−15.6155	+	27.0468i	−0.636969	+	1.10326i	−0.986094	+	0.166186i	$0.946855\pi$
$602$	−2.25673	+	1.30292i	−0.0919775	+	0.0531032i
$603$	−1.14094	−	0.658723i	−0.0464628	−	0.0268253i
$604$	10.5314			0.428515
$605$	−15.1424	+	8.41188i	−0.615625	+	0.341992i
$606$	−5.74667	+	9.95353i	−0.233443	+	0.404335i
$607$	−3.47437	+	2.00593i	−0.141020	+	0.0814181i	−0.568850	−	0.822441i	$-0.692612\pi$
$607$	−3.47437	+	2.00593i	−0.141020	+	0.0814181i	0.427830	+	0.903859i	$0.359278\pi$
$608$	−1.08617	−	0.627100i	−0.0440500	−	0.0254323i
$609$	−1.14393	−	1.98134i	−0.0463543	−	0.0802880i
$610$	−6.43908	+	10.7389i	−0.260711	+	0.434807i
$611$	16.6560	+	28.8491i	0.673831	+	1.16711i
$612$		−	3.62945i		−	0.146712i
$613$	26.1570	+	15.1017i	1.05647	+	0.609954i	0.924454	−	0.381294i	$-0.124521\pi$
$613$	26.1570	+	15.1017i	1.05647	+	0.609954i	0.132017	+	0.991247i	$0.457855\pi$
$614$	−10.4985	+	18.1839i	−0.423685	+	0.733844i
$615$	−7.12813	+	11.8881i	−0.287434	+	0.479375i
$616$	−1.15384			−0.0464894
$617$	29.6578	+	17.1229i	1.19398	+	0.689343i	0.959206	−	0.282708i	$-0.0912328\pi$
$617$	29.6578	+	17.1229i	1.19398	+	0.689343i	0.234771	+	0.972051i	$0.424566\pi$
$618$		−	10.0879i		−	0.405793i
$619$	−22.1807			−0.891516			−0.445758	−	0.895154i	$-0.647066\pi$
$619$	−22.1807			−0.891516			−0.445758	+	0.895154i	$0.647066\pi$
$620$	3.61223	+	11.9144i	0.145071	+	0.478492i
$621$	2.23029			0.0894986
$622$			5.16307i			0.207020i
$623$	3.20547	+	1.85068i	0.128424	+	0.0741458i
$624$	3.68799			0.147638
$625$	−13.9030	+	20.7775i	−0.556120	+	0.831102i
$626$	12.7350	−	22.0577i	0.508993	−	0.881603i
$627$	−4.70283	−	2.71518i	−0.187813	−	0.108434i
$628$			6.43776i			0.256894i
$629$	12.3612	+	21.4102i	0.492873	+	0.853681i
$630$	−0.511063	−	0.306434i	−0.0203612	−	0.0122086i
$631$	19.1952	+	33.2470i	0.764149	+	1.32354i	0.940696	+	0.339252i	$0.110174\pi$
$631$	19.1952	+	33.2470i	0.764149	+	1.32354i	−0.176547	+	0.984292i	$0.556493\pi$
$632$	3.97867	+	2.29709i	0.158263	+	0.0913732i
$633$	−3.62445	+	2.09258i	−0.144059	+	0.0831726i
$634$	9.02463	−	15.6311i	0.358414	−	0.620791i
$635$	−9.08428	−	16.3528i	−0.360499	−	0.648940i
$636$	7.74384			0.307063
$637$	−22.1305	−	12.7770i	−0.876840	−	0.506244i
$638$	−32.1913	+	18.5856i	−1.27446	+	0.735813i
$639$	5.22463	−	9.04932i	0.206683	−	0.357985i
$640$	−1.14989	+	1.91775i	−0.0454532	+	0.0758057i
$641$	−0.723934	−	1.25389i	−0.0285937	−	0.0495257i	0.851374	−	0.524558i	$-0.175770\pi$
$641$	−0.723934	−	1.25389i	−0.0285937	−	0.0495257i	−0.879968	+	0.475033i	$0.842436\pi$
$642$	−16.0181	+	9.24808i	−0.632186	+	0.364993i
$643$			8.44585i			0.333072i	0.986035	+	0.166536i	$0.0532582\pi$
$643$			8.44585i			0.333072i	−0.986035	+	0.166536i	$0.946742\pi$
$644$	0.297177	−	0.514725i	0.0117104	−	0.0202830i
$645$	−0.361368	+	21.8621i	−0.0142289	+	0.860820i
$646$	−2.27603	−	3.94220i	−0.0895492	−	0.155104i
$647$			6.43945i			0.253161i	0.991956	+	0.126580i	$0.0404002\pi$
$647$			6.43945i			0.253161i	−0.991956	+	0.126580i	$0.959600\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−7.40809			−0.290793
$650$	9.74274	−	15.6560i	0.382142	−	0.614080i
$651$	−0.313216	+	1.45032i	−0.0122759	+	0.0568426i
$652$			7.27078i			0.284746i
$653$			6.36693i			0.249157i	0.992210	+	0.124579i	$0.0397579\pi$
$653$			6.36693i			0.249157i	−0.992210	+	0.124579i	$0.960242\pi$
$654$	−2.79568	+	4.84226i	−0.109320	+	0.189347i
$655$	−41.5100	+	23.0596i	−1.62193	+	0.901013i
$656$	3.09949	+	5.36848i	0.121015	+	0.209604i
$657$	5.38415	+	3.10854i	0.210056	+	0.121276i
$658$	−2.08461	−	1.20355i	−0.0812666	−	0.0469193i
$659$	−21.1180			−0.822641			−0.411321	−	0.911491i	$-0.634932\pi$
$659$	−21.1180			−0.822641			−0.411321	+	0.911491i	$0.634932\pi$
$660$	−4.97870	+	8.30335i	−0.193796	+	0.323208i
$661$	12.2331	+	21.1883i	0.475812	+	0.824131i	0.999616	−	0.0277079i	$-0.00882082\pi$
$661$	12.2331	+	21.1883i	0.475812	+	0.824131i	−0.523804	+	0.851839i	$0.675487\pi$
$662$	−19.7793	+	11.4196i	−0.768745	+	0.443835i
$663$	11.5921	+	6.69270i	0.450200	+	0.259923i
$664$	−5.49665	−	9.52048i	−0.213311	−	0.369466i
$665$	−0.747266	−	0.0123519i	−0.0289777	−	0.000478985i
$666$	6.81160			0.263944
$667$		−	19.1473i		−	0.741387i
$668$	−4.28167	−	2.47202i	−0.165663	−	0.0956454i
$669$	13.4099	+	23.2266i	0.518456	+	0.897992i
$670$	−0.0486873	+	2.94550i	−0.00188096	+	0.113794i
$671$	12.1227	+	20.9972i	0.467993	+	0.810588i
$672$	−0.230788	+	0.133246i	−0.00890284	+	0.00514006i
$673$	−7.84426	+	4.52889i	−0.302374	+	0.174576i	−0.643509	−	0.765439i	$-0.722522\pi$
$673$	−7.84426	+	4.52889i	−0.302374	+	0.174576i	0.341135	+	0.940014i	$0.389189\pi$
$674$	−5.66462			−0.218193
$675$	−4.41039	+	2.35552i	−0.169756	+	0.0906642i
$676$	−0.300648	+	0.520738i	−0.0115634	+	0.0200284i
$677$	22.8564	−	13.1961i	0.878443	−	0.507169i	0.00829817	−	0.999966i	$-0.497359\pi$
$677$	22.8564	−	13.1961i	0.878443	−	0.507169i	0.870145	+	0.492796i	$0.164025\pi$
$678$		−	9.78913i		−	0.375949i
$679$	−1.48775	+	2.57686i	−0.0570946	+	0.0988908i
$680$	−7.09451	+	3.94114i	−0.272062	+	0.151136i
$681$	11.9231			0.456896
$682$	23.5637	+	5.08889i	0.902301	+	0.194864i
$683$		−	9.69801i		−	0.371084i	−0.982636	−	0.185542i	$-0.940596\pi$
$683$		−	9.69801i		−	0.371084i	0.982636	−	0.185542i	$-0.0594041\pi$
$684$	−1.25420			−0.0479555
$685$	−10.2106	−	0.168775i	−0.390127	−	0.00644857i
$686$	3.71195			0.141723
$687$	−18.5959	+	10.7364i	−0.709478	+	0.409617i
$688$	8.46832	+	4.88919i	0.322852	+	0.186399i
$689$	−14.2796	+	24.7330i	−0.544010	+	0.942253i
$690$	−2.42182	−	4.35957i	−0.0921973	−	0.165966i
$691$	−19.4040	−	33.6087i	−0.738162	−	1.27853i	−0.953322	−	0.301955i	$-0.902361\pi$
$691$	−19.4040	−	33.6087i	−0.738162	−	1.27853i	0.215160	−	0.976579i	$-0.430973\pi$
$692$	0.253665	−	0.146453i	0.00964289	−	0.00556733i
$693$	−0.999252	+	0.576918i	−0.0379584	+	0.0219153i
$694$	−3.55218	+	6.15256i	−0.134839	+	0.233548i
$695$	39.4634	+	23.6623i	1.49693	+	0.897564i
$696$	−4.29256	+	7.43493i	−0.162709	+	0.281820i
$697$			22.4989i			0.852208i
$698$		−	8.84061i		−	0.334622i
$699$	−2.39545	+	4.14905i	−0.0906044	+	0.156931i
$700$	−0.0440374	+	1.33173i	−0.00166446	+	0.0503346i
$701$	16.0523	−	27.8033i	0.606286	−	1.05012i	−0.385561	−	0.922682i	$-0.625992\pi$
$701$	16.0523	−	27.8033i	0.606286	−	1.05012i	0.991847	−	0.127435i	$-0.0406745\pi$
$702$	3.19390	−	1.84400i	0.120546	−	0.0695972i
$703$	7.39855	−	4.27155i	0.279041	−	0.161105i
$704$	2.16487	+	3.74966i	0.0815916	+	0.141321i
$705$	−17.6560	+	9.80826i	−0.664964	+	0.369400i
$706$	−10.9960	+	19.0456i	−0.413839	+	0.716790i
$707$	2.65253	+	1.53144i	0.0997585	+	0.0575956i
$708$	−1.48175	+	0.855490i	−0.0556876	+	0.0321513i
$709$	17.9306			0.673399			0.336700	−	0.941612i	$-0.390689\pi$
$709$	17.9306			0.673399			0.336700	+	0.941612i	$0.390689\pi$
$710$	−23.3620	−	0.386161i	−0.876762	−	0.0144924i
$711$	4.59418			0.172295
$712$		−	13.8892i		−	0.520521i
$713$	−8.33911	+	9.20108i	−0.312302	+	0.344583i
$714$	−0.967217			−0.0361972
$715$	−17.3393	−	31.2128i	−0.648454	−	1.16729i
$716$	10.4594	−	18.1163i	0.390887	−	0.677037i
$717$		−	1.30622i		−	0.0487816i
$718$	11.4095	−	6.58726i	0.425798	−	0.245835i
$719$	−6.39283	+	11.0727i	−0.238412	+	0.412942i	−0.960259	−	0.279111i	$-0.909960\pi$
$719$	−6.39283	+	11.0727i	−0.238412	+	0.412942i	0.721847	+	0.692053i	$0.243294\pi$
$720$	−0.0369558	+	2.23576i	−0.00137726	+	0.0833220i
$721$	−2.68833			−0.100118
$722$	15.0922	−	8.71349i	0.561674	−	0.324283i
$723$	−3.29349	+	1.90150i	−0.122486	+	0.0707175i
$724$	8.66164	+	15.0024i	0.321907	+	0.557560i
$725$	20.2224	+	37.8637i	0.751043	+	1.40622i
$726$	3.87331	+	6.70878i	0.143752	+	0.248986i
$727$	26.9302	+	15.5482i	0.998787	+	0.576650i	0.907889	−	0.419210i	$-0.137693\pi$
$727$	26.9302	+	15.5482i	0.998787	+	0.576650i	0.0908978	+	0.995860i	$0.471026\pi$
$728$		−	0.982817i		−	0.0364256i
$729$	−1.00000			−0.0370370
$730$	0.229757	−	13.8999i	0.00850371	−	0.514459i
$731$	17.7451	+	30.7354i	0.656325	+	1.13679i
$732$	4.84953	+	2.79988i	0.179244	+	0.103487i
$733$	8.09007	−	4.67080i	0.298813	−	0.172520i	−0.343096	−	0.939300i	$-0.611476\pi$
$733$	8.09007	−	4.67080i	0.298813	−	0.172520i	0.641910	+	0.766780i	$0.278142\pi$
$734$	−4.37481	−	7.57740i	−0.161477	−	0.279687i
$735$	7.96754	−	13.2881i	0.293887	−	0.490137i
$736$	−2.23029			−0.0822097
$737$	4.93998	+	2.85210i	0.181966	+	0.105058i
$738$	5.36848	+	3.09949i	0.197617	+	0.114094i
$739$	−10.2182	−	17.6984i	−0.375882	−	0.651046i	0.614577	−	0.788857i	$-0.289327\pi$
$739$	−10.2182	−	17.6984i	−0.375882	−	0.651046i	−0.990459	+	0.137811i	$0.955993\pi$
$740$	−7.39656	−	13.3147i	−0.271903	−	0.489457i
$741$	2.31274	−	4.00578i	0.0849606	−	0.147156i
$742$		−	2.06366i		−	0.0757595i
$743$			52.6303i			1.93082i	0.260738	+	0.965410i	$0.416034\pi$
$743$			52.6303i			1.93082i	−0.260738	+	0.965410i	$0.583966\pi$
$744$	5.30083	−	1.70328i	0.194338	−	0.0624452i
$745$	3.15819	−	1.75443i	0.115707	−	0.0642775i
$746$	−12.1156			−0.443582
$747$	−9.52048	−	5.49665i	−0.348336	−	0.201112i
$748$			15.7146i			0.574582i
$749$	2.46453	+	4.26869i	0.0900520	+	0.155975i
$750$	9.39349	+	6.06320i	0.343002	+	0.221397i
$751$	22.7555	−	39.4136i	0.830359	−	1.43822i	−0.0673952	−	0.997726i	$-0.521469\pi$
$751$	22.7555	−	39.4136i	0.830359	−	1.43822i	0.897754	−	0.440497i	$-0.145198\pi$
$752$			9.03257i			0.329384i
$753$	12.9323	−	7.46644i	0.471278	−	0.272092i
$754$	−15.8309	−	27.4200i	−0.576528	−	0.998576i
$755$	−20.1965	−	12.1099i	−0.735026	−	0.440723i
$756$	−0.133246	+	0.230788i	−0.00484609	+	0.00839368i
$757$	−33.4714	+	19.3247i	−1.21654	+	0.702369i	−0.964176	−	0.265264i	$-0.914541\pi$
$757$	−33.4714	+	19.3247i	−1.21654	+	0.702369i	−0.252362	+	0.967633i	$0.581208\pi$
$758$	−0.431450	−	0.249098i	−0.0156710	−	0.00904764i
$759$	−9.65659			−0.350512
$760$	1.36191	+	2.45159i	0.0494015	+	0.0889285i
$761$	−11.5933	+	20.0801i	−0.420256	+	0.727904i	−0.995964	−	0.0897508i	$-0.971393\pi$
$761$	−11.5933	+	20.0801i	−0.420256	+	0.727904i	0.575709	+	0.817655i	$0.304726\pi$
$762$	−7.24504	+	4.18292i	−0.262460	+	0.151531i
$763$	1.29042	+	0.745023i	0.0467163	+	0.0269717i
$764$	−5.46670	−	9.46861i	−0.197778	−	0.342562i
$765$	−4.17346	+	6.96038i	−0.150892	+	0.251653i
$766$	18.2600	+	31.6273i	0.659761	+	1.14274i
$767$		−	6.31008i		−	0.227844i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−26.1235	+	45.2472i	−0.942037	+	1.63166i	−0.180459	+	0.983583i	$0.557758\pi$
$769$	−26.1235	+	45.2472i	−0.942037	+	1.63166i	−0.761578	+	0.648073i	$0.775575\pi$
$770$	2.21277	+	1.32678i	0.0797427	+	0.0478138i
$771$	9.65181			0.347602
$772$	3.52728	+	2.03648i	0.126950	+	0.0732944i
$773$		−	19.5483i		−	0.703103i	−0.936169	−	0.351551i	$-0.885654\pi$
$773$		−	19.5483i		−	0.703103i	0.936169	−	0.351551i	$-0.114346\pi$
$774$	9.77837			0.351476
$775$	6.77280	−	27.0024i	0.243286	−	0.969955i
$776$	11.1655			0.400817
$777$		−	1.81523i		−	0.0651210i
$778$	−26.6400	−	15.3806i	−0.955089	−	0.551421i
$779$	7.77477			0.278560
$780$	−7.07265	−	4.24077i	−0.253241	−	0.151844i
$781$	−22.6213	+	39.1812i	−0.809452	+	1.40201i
$782$	−7.01026	−	4.04737i	−0.250686	−	0.144734i
$783$			8.58511i			0.306807i
$784$	−3.46449	−	6.00067i	−0.123732	−	0.214310i
$785$	7.40269	−	12.3460i	0.264213	−	0.440648i
$786$	10.6180	+	18.3909i	0.378730	+	0.655980i
$787$	−14.2677	−	8.23744i	−0.508588	−	0.293633i	0.223665	−	0.974666i	$-0.428198\pi$
$787$	−14.2677	−	8.23744i	−0.508588	−	0.293633i	−0.732253	+	0.681033i	$0.761531\pi$
$788$	21.7435	−	12.5536i	0.774579	−	0.447204i
$789$	−1.46767	+	2.54207i	−0.0522503	+	0.0905002i
$790$	−4.98871	−	8.98026i	−0.177490	−	0.319503i
$791$	−2.60871			−0.0927552
$792$	3.74966	+	2.16487i	0.133238	+	0.0769253i
$793$	−17.8851	+	10.3259i	−0.635117	+	0.366685i
$794$	−7.87503	+	13.6400i	−0.279474	+	0.484064i
$795$	−14.8507	−	8.90453i	−0.526702	−	0.315811i
$796$	−2.36222	−	4.09149i	−0.0837268	−	0.145019i
$797$	−42.3198	+	24.4334i	−1.49904	+	0.865474i	−0.999999	−	0.00110208i	$-0.999649\pi$
$797$	−42.3198	+	24.4334i	−1.49904	+	0.865474i	−0.499045	+	0.866576i	$0.666316\pi$
$798$			0.334233i			0.0118317i
$799$	−16.3917	+	28.3912i	−0.579895	+	1.00441i
$800$	4.41039	−	2.35552i	0.155931	−	0.0832804i
$801$	−6.94462	−	12.0284i	−0.245376	−	0.425004i
$802$			17.8819i			0.631433i
$803$	−23.3120	−	13.4592i	−0.822661	−	0.474964i
$804$	1.31745			0.0464628
$805$	−1.16179	+	0.645394i	−0.0409476	+	0.0227472i
$806$	−4.33463	+	20.0712i	−0.152681	+	0.706976i
$807$			19.3355i			0.680640i
$808$		−	11.4933i		−	0.404335i
$809$	−6.01536	+	10.4189i	−0.211489	+	0.366309i	−0.952181	−	0.305536i	$-0.901164\pi$
$809$	−6.01536	+	10.4189i	−0.211489	+	0.366309i	0.740692	+	0.671845i	$0.234498\pi$
$810$	1.08588	+	1.95471i	0.0381538	+	0.0686813i
$811$	−6.89192	−	11.9371i	−0.242008	−	0.419170i	0.719278	−	0.694722i	$-0.244473\pi$
$811$	−6.89192	−	11.9371i	−0.242008	−	0.419170i	−0.961286	+	0.275552i	$0.911139\pi$
$812$	1.98134	+	1.14393i	0.0695314	+	0.0401440i
$813$	−19.4838	−	11.2490i	−0.683327	−	0.394519i
$814$	−29.4924			−1.03371
$815$	8.36056	−	13.9435i	0.292858	−	0.488420i
$816$	1.81473	+	3.14320i	0.0635281	+	0.110034i
$817$	10.6210	−	6.13202i	0.371581	−	0.214532i
$818$	−24.4933	−	14.1412i	−0.856387	−	0.494435i
$819$	−0.491409	−	0.851145i	−0.0171712	−	0.0297414i
$820$	0.229089	−	13.8595i	0.00800013	−	0.483994i
$821$	19.6441			0.685584			0.342792	−	0.939411i	$-0.388627\pi$
$821$	19.6441			0.685584			0.342792	+	0.939411i	$0.388627\pi$
$822$			4.56694i			0.159290i
$823$	16.8064	+	9.70317i	0.585834	+	0.338231i	0.763448	−	0.645869i	$-0.223505\pi$
$823$	16.8064	+	9.70317i	0.585834	+	0.338231i	−0.177614	+	0.984100i	$0.556838\pi$
$824$	5.04393	+	8.73635i	0.175714	+	0.304345i
$825$	19.0958	−	10.1988i	0.664831	−	0.355077i
$826$	0.227980	+	0.394874i	0.00793245	+	0.0137394i
$827$	−13.4072	+	7.74065i	−0.466214	+	0.269169i	−0.714653	−	0.699479i	$-0.753416\pi$
$827$	−13.4072	+	7.74065i	−0.466214	+	0.269169i	0.248440	+	0.968647i	$0.420082\pi$
$828$	−1.93149	+	1.11515i	−0.0671240	+	0.0387540i
$829$	−33.5677			−1.16585			−0.582927	−	0.812524i	$-0.698093\pi$
$829$	−33.5677			−1.16585			−0.582927	+	0.812524i	$0.698093\pi$
$830$	−0.406267	+	24.5784i	−0.0141017	+	0.853129i
$831$	0.270901	−	0.469214i	0.00939744	−	0.0162768i
$832$	−3.19390	+	1.84400i	−0.110728	+	0.0639291i
$833$		−	25.1484i		−	0.871341i
$834$	10.2890	−	17.8211i	0.356279	−	0.617093i
$835$	5.36862	+	9.66415i	0.185789	+	0.334442i
$836$	5.43036			0.187813
$837$	3.73902	−	4.12550i	0.129239	−	0.142598i
$838$		−	39.0309i		−	1.34830i
$839$	28.2027			0.973667			0.486833	−	0.873495i	$-0.338152\pi$
$839$	28.2027			0.973667			0.486833	+	0.873495i	$0.338152\pi$
$840$	0.595811	+	0.00984840i	0.0205574	+	0.000339802i
$841$	44.7042			1.54152
$842$	24.5473	−	14.1724i	0.845957	−	0.488414i
$843$	−21.5940	−	12.4673i	−0.743736	−	0.429396i
$844$	2.09258	−	3.62445i	0.0720295	−	0.124759i
$845$	1.17536	−	0.652934i	0.0404335	−	0.0224616i
$846$	4.51629	+	7.82244i	0.155273	+	0.268941i
$847$	1.78783	−	1.03220i	0.0614305	−	0.0354669i
$848$	−6.70636	+	3.87192i	−0.230297	+	0.132962i
$849$	−7.51320	+	13.0132i	−0.257852	+	0.446613i
$850$	18.1374	+	0.599763i	0.622106	+	0.0205717i
$851$	7.59593	−	13.1565i	0.260385	−	0.451000i
$852$			10.4493i			0.357985i
$853$		−	16.2835i		−	0.557535i	−0.960359	−	0.278767i	$-0.910074\pi$
$853$		−	16.2835i		−	0.557535i	0.960359	−	0.278767i	$-0.0899258\pi$
$854$	0.746143	−	1.29236i	0.0255325	−	0.0442236i
$855$	2.40524	+	1.44219i	0.0822575	+	0.0493218i
$856$	9.24808	−	16.0181i	0.316093	−	0.547489i
$857$	0.433193	−	0.250104i	0.0147976	−	0.00854339i	−0.492583	−	0.870265i	$-0.663947\pi$
$857$	0.433193	−	0.250104i	0.0147976	−	0.00854339i	0.507381	+	0.861722i	$0.330614\pi$
$858$	−13.8287	+	7.98402i	−0.472105	+	0.272570i
$859$	−4.60020	−	7.96778i	−0.156957	−	0.271857i	0.776813	−	0.629731i	$-0.216835\pi$
$859$	−4.60020	−	7.96778i	−0.156957	−	0.271857i	−0.933770	+	0.357874i	$0.883502\pi$
$860$	−10.6181	−	19.1138i	−0.362074	−	0.651776i
$861$	0.825987	−	1.43065i	0.0281496	−	0.0487565i
$862$	−2.95937	−	1.70859i	−0.100796	−	0.0581949i
$863$	−20.7405	+	11.9745i	−0.706014	+	0.407617i	−0.809583	−	0.587005i	$-0.800307\pi$
$863$	−20.7405	+	11.9745i	−0.706014	+	0.407617i	0.103569	+	0.994622i	$0.466974\pi$
$864$	1.00000			0.0340207
$865$	−0.654870	−	0.0108246i	−0.0222663	−	0.000368048i
$866$	16.2632			0.552645
$867$		−	3.82707i		−	0.129974i
$868$	−0.453908	−	1.41262i	−0.0154067	−	0.0479476i
$869$	−19.8916			−0.674775
$870$	16.7814	−	9.32237i	0.568942	−	0.316058i
$871$	−2.42937	+	4.20779i	−0.0823160	+	0.142575i
$872$		−	5.59136i		−	0.189347i
$873$	9.66959	−	5.58274i	0.327266	−	0.188947i
$874$	−1.39862	+	2.42248i	−0.0473089	+	0.0819415i
$875$	1.61579	−	2.50328i	0.0546236	−	0.0846264i
$876$	−6.21708			−0.210056
$877$	−14.4895	+	8.36549i	−0.489274	+	0.282483i	−0.724273	−	0.689513i	$-0.757825\pi$
$877$	−14.4895	+	8.36549i	−0.489274	+	0.282483i	0.234999	+	0.971996i	$0.424491\pi$
$878$	−7.90075	+	4.56150i	−0.266637	+	0.153943i
$879$	8.69003	+	15.0516i	0.293107	+	0.507677i
$880$	0.160009	−	9.68027i	0.00539390	−	0.326322i
$881$	3.86819	+	6.69990i	0.130323	+	0.225725i	0.923801	−	0.382873i	$-0.125065\pi$
$881$	3.86819	+	6.69990i	0.130323	+	0.225725i	−0.793478	+	0.608598i	$0.791732\pi$
$882$	−6.00067	−	3.46449i	−0.202053	−	0.116655i
$883$			16.2969i			0.548434i	0.961668	+	0.274217i	$0.0884186\pi$
$883$			16.2969i			0.548434i	−0.961668	+	0.274217i	$0.911581\pi$
$884$	−13.3854			−0.450200
$885$	3.82534	+	0.0632307i	0.128588	+	0.00212548i
$886$	3.88826	+	6.73466i	0.130629	+	0.226255i
$887$	37.3280	+	21.5513i	1.25335	+	0.723623i	0.971774	−	0.235915i	$-0.0758088\pi$
$887$	37.3280	+	21.5513i	1.25335	+	0.723623i	0.281578	+	0.959538i	$0.409142\pi$
$888$	−5.89902	+	3.40580i	−0.197958	+	0.114291i
$889$	1.11471	+	1.93074i	0.0373862	+	0.0647549i
$890$	−15.9710	+	26.6361i	−0.535350	+	0.892843i
$891$	4.32974			0.145052
$892$	−23.2266	−	13.4099i	−0.777684	−	0.448996i
$893$	9.81090	+	5.66433i	0.328309	+	0.189549i
$894$	−0.807842	−	1.39922i	−0.0270183	−	0.0467970i
$895$	−40.8902	+	22.7153i	−1.36681	+	0.759289i
$896$	0.133246	−	0.230788i	0.00445142	−	0.00771009i
$897$		−	8.22531i		−	0.274635i
$898$			4.43184i			0.147892i
$899$	−35.4179	−	32.0999i	−1.18125	−	1.07059i
$900$	2.64174	−	4.24514i	0.0880581	−	0.141505i
$901$	−28.1059			−0.936343
$902$	−23.2441	−	13.4200i	−0.773944	−	0.446837i
$903$		−	2.60585i		−	0.0867172i
$904$	4.89456	+	8.47763i	0.162791	+	0.281962i
$905$	0.640196	−	38.7308i	0.0212808	−	1.28745i
$906$	−5.26568	+	9.12042i	−0.174940	+	0.303006i
$907$			5.75164i			0.190980i	0.995430	+	0.0954900i	$0.0304418\pi$
$907$			5.75164i			0.190980i	−0.995430	+	0.0954900i	$0.969558\pi$
$908$	−10.3257	+	5.96157i	−0.342672	+	0.197842i
$909$	−5.74667	−	9.95353i	−0.190605	−	0.330138i
$910$	−1.13013	+	1.88480i	−0.0374634	+	0.0624804i
$911$	−22.0925	+	38.2653i	−0.731957	+	1.26779i	0.224088	+	0.974569i	$0.428060\pi$
$911$	−22.0925	+	38.2653i	−0.731957	+	1.26779i	−0.956045	+	0.293218i	$0.905274\pi$
$912$	1.08617	−	0.627100i	0.0359666	−	0.0207654i
$913$	41.2212	+	23.7991i	1.36422	+	0.787634i
$914$	25.9754			0.859191
$915$	−6.08065	−	10.9459i	−0.201020	−	0.361860i
$916$	10.7364	−	18.5959i	0.354739	−	0.614426i
$917$	4.90100	−	2.82959i	0.161845	−	0.0934414i
$918$	3.14320	+	1.81473i	0.103741	+	0.0598949i
$919$	−12.2334	−	21.1889i	−0.403544	−	0.698958i	0.590607	−	0.806959i	$-0.298888\pi$
$919$	−12.2334	−	21.1889i	−0.403544	−	0.698958i	−0.994151	+	0.108001i	$0.965555\pi$
$920$	4.27714	+	2.56458i	0.141013	+	0.0845518i
$921$	−10.4985	−	18.1839i	−0.345937	−	0.599181i
$922$		−	9.04776i		−	0.297972i
$923$	−33.3738	−	19.2684i	−1.09851	−	0.634227i
$924$	0.576918	−	0.999252i	0.0189792	−	0.0328730i
$925$	−1.12561	+	34.0394i	−0.0370098	+	1.11921i
$926$	3.88965			0.127822
$927$	8.73635	+	5.04393i	0.286939	+	0.165664i
$928$		−	8.58511i		−	0.281820i
$929$	57.2383			1.87793			0.938964	−	0.344016i	$-0.111788\pi$
$929$	57.2383			1.87793			0.938964	+	0.344016i	$0.111788\pi$
$930$	−12.1242	−	2.82890i	−0.397570	−	0.0927631i
$931$	−8.69033			−0.284814
$932$		−	4.79091i		−	0.156931i
$933$	−4.47135	−	2.58153i	−0.146385	−	0.0845156i
$934$	−25.9891			−0.850389
$935$	18.0700	−	30.1366i	0.590951	−	0.985573i
$936$	−1.84400	+	3.19390i	−0.0602729	+	0.104396i
$937$	20.4787	+	11.8234i	0.669011	+	0.386254i	0.795702	−	0.605688i	$-0.207102\pi$
$937$	20.4787	+	11.8234i	0.669011	+	0.386254i	−0.126691	+	0.991942i	$0.540436\pi$
$938$		−	0.351088i		−	0.0114634i
$939$	12.7350	+	22.0577i	0.415591	+	0.719825i
$940$	10.3864	−	17.3222i	0.338768	−	0.564988i
$941$	11.2069	+	19.4108i	0.365333	+	0.632776i	0.988830	−	0.149051i	$-0.0476217\pi$
$941$	11.2069	+	19.4108i	0.365333	+	0.632776i	−0.623496	+	0.781826i	$0.714288\pi$
$942$	−5.57526	−	3.21888i	−0.181652	−	0.104877i
$943$	11.9733	−	6.91278i	0.389904	−	0.225111i
$944$	0.855490	−	1.48175i	0.0278438	−	0.0482269i
$945$	0.520911	−	0.289376i	0.0169453	−	0.00941342i
$946$	−42.3378			−1.37652
$947$	−0.619713	−	0.357792i	−0.0201380	−	0.0116267i	0.489897	−	0.871780i	$-0.337034\pi$
$947$	−0.619713	−	0.357792i	−0.0201380	−	0.0116267i	−0.510035	+	0.860154i	$0.670368\pi$
$948$	−3.97867	+	2.29709i	−0.129221	+	0.0746059i
$949$	11.4643	−	19.8567i	0.372146	−	0.644576i
$950$	0.207255	−	6.26757i	0.00672425	−	0.203347i
$951$	9.02463	+	15.6311i	0.292644	+	0.506874i
$952$	0.837634	−	0.483608i	0.0271479	−	0.0156738i
$953$		−	48.4392i		−	1.56910i	−0.620067	−	0.784549i	$-0.712894\pi$
$953$		−	48.4392i		−	1.56910i	0.620067	−	0.784549i	$-0.287106\pi$
$954$	−3.87192	+	6.70636i	−0.125358	+	0.217127i
$955$	−0.404053	+	24.4445i	−0.0130749	+	0.791006i
$956$	0.653110	+	1.13122i	0.0211231	+	0.0365862i
$957$		−	37.1713i		−	1.20158i
$958$	−7.58764	−	4.38073i	−0.245146	−	0.141535i
$959$	1.21705			0.0393006
$960$	−1.08588	−	1.95471i	−0.0350465	−	0.0630878i
$961$	3.03948	+	30.8506i	0.0980479	+	0.995182i
$962$		−	25.1211i		−	0.809938i
$963$		−	18.4962i		−	0.596030i
$964$	1.90150	−	3.29349i	0.0612432	−	0.106076i
$965$	−4.42272	−	7.96142i	−0.142373	−	0.256287i
$966$	0.297177	+	0.514725i	0.00956150	+	0.0165610i
$967$	−9.87190	−	5.69955i	−0.317459	−	0.183285i	0.332800	−	0.942997i	$-0.392006\pi$
$967$	−9.87190	−	5.69955i	−0.317459	−	0.183285i	−0.650259	+	0.759712i	$0.725340\pi$
$968$	−6.70878	−	3.87331i	−0.215628	−	0.124493i
$969$	4.55206			0.146233
$970$	−21.4126	−	12.8390i	−0.687517	−	0.412236i
$971$	14.1622	+	24.5297i	0.454487	+	0.787194i	0.998659	−	0.0517795i	$-0.0164893\pi$
$971$	14.1622	+	24.5297i	0.454487	+	0.787194i	−0.544172	+	0.838974i	$0.683156\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−4.74915	−	2.74193i	−0.152251	−	0.0879021i
$974$	13.9398	+	24.1444i	0.446660	+	0.773637i
$975$	8.68716	+	16.2655i	0.278212	+	0.520912i
$976$	−5.59976			−0.179244
$977$		−	25.8409i		−	0.826722i	−0.910567	−	0.413361i	$-0.864355\pi$
$977$		−	25.8409i		−	0.826722i	0.910567	−	0.413361i	$-0.135645\pi$
$978$	−6.29668	−	3.63539i	−0.201346	−	0.116247i
$979$	30.0684	+	52.0799i	0.960989	+	1.66448i
$980$	−0.256066	+	15.4916i	−0.00817974	+	0.494860i
$981$	−2.79568	−	4.84226i	−0.0892591	−	0.154601i
$982$	−31.8370	+	18.3811i	−1.01596	+	0.586565i
$983$	39.1500	−	22.6032i	1.24869	−	0.720931i	0.277842	−	0.960627i	$-0.410381\pi$
$983$	39.1500	−	22.6032i	1.24869	−	0.720931i	0.970848	+	0.239696i	$0.0770476\pi$
$984$	−6.19899			−0.197617
$985$	−56.1338	−	0.927858i	−1.78857	−	0.0295640i
$986$	15.5796	−	26.9847i	0.496157	−	0.859368i
$987$	2.08461	−	1.20355i	0.0663539	−	0.0383094i
$988$			4.62548i			0.147156i
$989$	10.9043	−	18.8868i	0.346737	−	0.600567i
$990$	−4.70156	−	8.46336i	−0.149425	−	0.268983i
$991$	9.21575			0.292748			0.146374	−	0.989229i	$-0.453240\pi$
$991$	9.21575			0.292748			0.146374	+	0.989229i	$0.453240\pi$
$992$	−3.73902	+	4.12550i	−0.118714	+	0.130985i
$993$		−	22.8392i		−	0.724780i
$994$	2.78463			0.0883232
$995$	−0.174596	+	10.5627i	−0.00553506	+	0.334861i
$996$	10.9933			0.348336
$997$	−3.53132	+	2.03881i	−0.111838	+	0.0645698i	−0.554876	−	0.831933i	$-0.687234\pi$
$997$	−3.53132	+	2.03881i	−0.111838	+	0.0645698i	0.443038	+	0.896503i	$0.353901\pi$
$998$	9.59325	+	5.53866i	0.303669	+	0.175323i
$999$	−3.40580	+	5.89902i	−0.107755	+	0.186637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.d.439.7	✓	28
5.4	even	2	inner	930.2.s.d.439.10	yes	28
31.25	even	3	inner	930.2.s.d.769.3	yes	28
155.149	even	6	inner	930.2.s.d.769.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.d.439.7	✓	28	1.1	even	1	trivial
930.2.s.d.439.10	yes	28	5.4	even	2	inner
930.2.s.d.769.3	yes	28	31.25	even	3	inner
930.2.s.d.769.14	yes	28	155.149	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.91775 + 1.14989i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.230788 - 0.133246i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(1.91775 + 1.14989i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.230788 - 0.133246i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.14989 - 1.91775i) q^{10} +(-2.16487 - 3.74966i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(3.19390 - 1.84400i) q^{13} +(-0.133246 + 0.230788i) q^{14} +(1.08588 + 1.95471i) q^{15} +1.00000 q^{16} +(3.14320 + 1.81473i) q^{17} +(0.866025 - 0.500000i) q^{18} +(0.627100 - 1.08617i) q^{19} +(-1.91775 - 1.14989i) q^{20} +(-0.133246 - 0.230788i) q^{21} +(-3.74966 + 2.16487i) q^{22} -2.23029i q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.35552 + 4.41039i) q^{25} +(-1.84400 - 3.19390i) q^{26} +1.00000i q^{27} +(0.230788 + 0.133246i) q^{28} +8.58511 q^{29} +(1.95471 - 1.08588i) q^{30} +(-4.12550 - 3.73902i) q^{31} -1.00000i q^{32} -4.32974i q^{33} +(1.81473 - 3.14320i) q^{34} +(-0.289376 - 0.520911i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.89902 + 3.40580i) q^{37} +(-1.08617 - 0.627100i) q^{38} +3.68799 q^{39} +(-1.14989 + 1.91775i) q^{40} +(3.09949 + 5.36848i) q^{41} +(-0.230788 + 0.133246i) q^{42} +(8.46832 + 4.88919i) q^{43} +(2.16487 + 3.74966i) q^{44} +(-0.0369558 + 2.23576i) q^{45} -2.23029 q^{46} +9.03257i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.46449 - 6.00067i) q^{49} +(4.41039 - 2.35552i) q^{50} +(1.81473 + 3.14320i) q^{51} +(-3.19390 + 1.84400i) q^{52} +(-6.70636 + 3.87192i) q^{53} +1.00000 q^{54} +(0.160009 - 9.68027i) q^{55} +(0.133246 - 0.230788i) q^{56} +(1.08617 - 0.627100i) q^{57} -8.58511i q^{58} +(0.855490 - 1.48175i) q^{59} +(-1.08588 - 1.95471i) q^{60} -5.59976 q^{61} +(-3.73902 + 4.12550i) q^{62} -0.266491i q^{63} -1.00000 q^{64} +(8.24548 + 0.136293i) q^{65} -4.32974 q^{66} +(-1.14094 + 0.658723i) q^{67} +(-3.14320 - 1.81473i) q^{68} +(1.11515 - 1.93149i) q^{69} +(-0.520911 + 0.289376i) q^{70} +(-5.22463 - 9.04932i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(5.38415 - 3.10854i) q^{73} +(3.40580 - 5.89902i) q^{74} +(-0.165249 + 4.99727i) q^{75} +(-0.627100 + 1.08617i) q^{76} +1.15384i q^{77} -3.68799i q^{78} +(2.29709 - 3.97867i) q^{79} +(1.91775 + 1.14989i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.36848 - 3.09949i) q^{82} +(-9.52048 + 5.49665i) q^{83} +(0.133246 + 0.230788i) q^{84} +(3.94114 + 7.09451i) q^{85} +(4.88919 - 8.46832i) q^{86} +(7.43493 + 4.29256i) q^{87} +(3.74966 - 2.16487i) q^{88} -13.8892 q^{89} +(2.23576 + 0.0369558i) q^{90} -0.982817 q^{91} +2.23029i q^{92} +(-1.70328 - 5.30083i) q^{93} +9.03257 q^{94} +(2.45159 - 1.36191i) q^{95} +(0.500000 - 0.866025i) q^{96} -11.1655i q^{97} +(-6.00067 + 3.46449i) q^{98} +(2.16487 - 3.74966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 14 q^{6} + 14 q^{9} + 4 q^{10} + 2 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} - 14 q^{24} - 14 q^{25} - 12 q^{26} + 24 q^{29} + 4 q^{30} + 10 q^{34} + 8 q^{35} - 14 q^{36} + 24 q^{39} - 4 q^{40} + 20 q^{41} - 2 q^{44} - 2 q^{45} + 12 q^{46} + 2 q^{49} - 8 q^{50} + 10 q^{51} + 28 q^{54} + 6 q^{55} + 8 q^{56} - 20 q^{59} + 8 q^{60} + 32 q^{61} - 28 q^{64} - 12 q^{65} + 4 q^{66} - 6 q^{69} - 16 q^{70} - 16 q^{71} - 6 q^{74} - 8 q^{75} - 4 q^{76} + 10 q^{79} + 2 q^{80} - 14 q^{81} + 8 q^{84} + 72 q^{85} + 18 q^{86} - 80 q^{89} - 4 q^{90} + 32 q^{91} - 12 q^{94} - 32 q^{95} + 14 q^{96} - 2 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 14 * q^6 + 14 * q^9 + 4 * q^10 + 2 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 - 14 * q^24 - 14 * q^25 - 12 * q^26 + 24 * q^29 + 4 * q^30 + 10 * q^34 + 8 * q^35 - 14 * q^36 + 24 * q^39 - 4 * q^40 + 20 * q^41 - 2 * q^44 - 2 * q^45 + 12 * q^46 + 2 * q^49 - 8 * q^50 + 10 * q^51 + 28 * q^54 + 6 * q^55 + 8 * q^56 - 20 * q^59 + 8 * q^60 + 32 * q^61 - 28 * q^64 - 12 * q^65 + 4 * q^66 - 6 * q^69 - 16 * q^70 - 16 * q^71 - 6 * q^74 - 8 * q^75 - 4 * q^76 + 10 * q^79 + 2 * q^80 - 14 * q^81 + 8 * q^84 + 72 * q^85 + 18 * q^86 - 80 * q^89 - 4 * q^90 + 32 * q^91 - 12 * q^94 - 32 * q^95 + 14 * q^96 - 2 * q^99

Introduction

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