LMFDB - Embedded newform 930.2.s.d.439.10

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			439.10
Character	$\chi$	$=$	930.439
Dual form			930.2.s.d.769.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.0369558 + 2.23576i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.230788 + 0.133246i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.0369558 + 2.23576i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.230788 + 0.133246i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.23576 + 0.0369558i) 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} +(-0.0369558 - 2.23576i) q^{20} +(-0.133246 - 0.230788i) q^{21} +(3.74966 - 2.16487i) q^{22} +2.23029i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.99727 + 0.165249i) 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} +(2.23576 - 0.0369558i) 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} +(-1.91775 + 1.14989i) q^{45} -2.23029 q^{46} -9.03257i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.46449 - 6.00067i) q^{49} +(-0.165249 - 4.99727i) q^{50} +(1.81473 + 3.14320i) q^{51} +(3.19390 - 1.84400i) q^{52} +(6.70636 - 3.87192i) q^{53} +1.00000 q^{54} +(8.30335 - 4.97870i) 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} +(-4.24077 - 7.07265i) 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} +(4.41039 + 2.35552i) q^{75} +(-0.627100 + 1.08617i) q^{76} -1.15384i q^{77} +3.68799i q^{78} +(2.29709 - 3.97867i) q^{79} +(0.0369558 + 2.23576i) 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} +(-1.14989 - 1.91775i) 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
$5$	0.0369558	+	2.23576i	0.0165272	+	0.999863i
$5$	0.0369558	+	2.23576i	0.0165272	+	0.999863i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.230788	+	0.133246i	0.0872297	+	0.0503621i	0.542980	−	0.839745i	$-0.317296\pi$
$7$	0.230788	+	0.133246i	0.0872297	+	0.0503621i	−0.455751	+	0.890107i	$0.650629\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.23576	+	0.0369558i	−0.707010	+	0.0116865i
$11$	−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	−0.872575	−	0.488479i	$-0.837552\pi$
$13$	−3.19390	+	1.84400i	−0.885827	+	0.511433i	−0.0132520	+	0.999912i	$0.504218\pi$
$14$	−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	0.0677968	−	0.997699i	$-0.478403\pi$
$17$	−3.14320	−	1.81473i	−0.762338	−	0.440136i	−0.830134	+	0.557563i	$0.811736\pi$
$18$	−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	$0.120713\pi$
$20$	−0.0369558	−	2.23576i	−0.00826358	−	0.499932i
$21$	−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	$0.0746985\pi$
$23$			2.23029i			0.465048i	−0.972591	+	0.232524i	$0.925302\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.99727	+	0.165249i	−0.999454	+	0.0330498i
$26$	−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	−0.0706195	−	0.997503i	$-0.522498\pi$
$37$	−5.89902	−	3.40580i	−0.969793	−	0.559910i	−0.899173	+	0.437593i	$0.855831\pi$
$38$	1.08617	+	0.627100i	0.176200	+	0.101729i
$39$	3.68799			0.590552
$40$	2.23576	−	0.0369558i	0.353505	−	0.00584323i
$41$	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	−0.312503	−	0.949917i	$-0.601167\pi$
$43$	−8.46832	−	4.88919i	−1.29141	−	0.745594i	−0.978904	+	0.204323i	$0.934501\pi$
$44$	2.16487	+	3.74966i	0.326366	+	0.565283i
$45$	−1.91775	+	1.14989i	−0.285881	+	0.171415i
$46$	−2.23029			−0.328839
$47$		−	9.03257i		−	1.31754i	−0.752346	−	0.658768i	$-0.771078\pi$
$47$		−	9.03257i		−	1.31754i	0.752346	−	0.658768i	$-0.228922\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−3.46449	−	6.00067i	−0.494927	−	0.857239i
$50$	−0.165249	−	4.99727i	−0.0233697	−	0.706720i
$51$	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	0.0371753	−	0.999309i	$-0.488164\pi$
$53$	6.70636	−	3.87192i	0.921190	−	0.531849i	0.884014	+	0.467460i	$0.154831\pi$
$54$	1.00000			0.136083
$55$	8.30335	−	4.97870i	1.11962	−	0.671328i
$56$	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
$65$	−4.24077	−	7.07265i	−0.526003	−	0.877254i
$66$	−4.32974			−0.532954
$67$	1.14094	−	0.658723i	0.139388	−	0.0804759i	−0.428684	−	0.903454i	$-0.641023\pi$
$67$	1.14094	−	0.658723i	0.139388	−	0.0804759i	0.568072	+	0.822979i	$0.307689\pi$
$68$	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	−0.780817	−	0.624760i	$-0.785197\pi$
$73$	−5.38415	+	3.10854i	−0.630167	+	0.363827i	0.150650	+	0.988587i	$0.451863\pi$
$74$	3.40580	−	5.89902i	0.395916	−	0.685747i
$75$	4.41039	+	2.35552i	0.509268	+	0.271993i
$76$	−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	$0.0834574\pi$
$80$	0.0369558	+	2.23576i	0.00413179	+	0.249966i
$81$	−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	0.123761	−	0.992312i	$-0.460504\pi$
$83$	9.52048	−	5.49665i	1.04501	−	0.603336i	0.921248	+	0.388976i	$0.127171\pi$
$84$	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	$0.763348\pi$
$90$	−1.14989	−	1.91775i	−0.121209	−	0.202149i
$91$	−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	$0.191835\pi$
$97$			11.1655i			1.13368i	−0.823827	+	0.566841i	$0.808165\pi$
$98$	6.00067	−	3.46449i	0.606160	−	0.349966i
$99$	2.16487	−	3.74966i	0.217578	−	0.376855i
$100$	4.99727	−	0.165249i	0.499727	−	0.0165249i
$101$	−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	−0.864286	−	0.503001i	$-0.832229\pi$
$103$	−8.73635	+	5.04393i	−0.860818	+	0.496993i	0.00346830	+	0.999994i	$0.498896\pi$
$104$	1.84400	+	3.19390i	0.180819	+	0.313187i
$105$	0.511063	−	0.306434i	0.0498746	−	0.0299049i
$106$	3.87192	+	6.70636i	0.376074	+	0.651380i
$107$	16.0181	+	9.24808i	1.54853	+	0.894045i	0.998254	+	0.0590638i	$0.0188115\pi$
$107$	16.0181	+	9.24808i	1.54853	+	0.894045i	0.550278	+	0.834982i	$0.314522\pi$
$108$			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	$0.586289\pi$
$110$	4.97870	+	8.30335i	0.474701	+	0.791693i
$111$	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	−0.842599	−	0.538541i	$-0.818976\pi$
$113$	−8.47763	+	4.89456i	−0.797509	+	0.460442i	0.0450906	+	0.998983i	$0.485642\pi$
$114$	−0.627100	−	1.08617i	−0.0587333	−	0.101729i
$115$	−4.98641	+	0.0824224i	−0.464985	+	0.00768593i
$116$	−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	0.785728	−	0.618572i	$-0.212288\pi$
$127$	7.24504	+	4.18292i	0.642893	+	0.371175i	−0.142835	+	0.989747i	$0.545622\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.88919	+	8.46832i	0.430469	+	0.745594i
$130$	7.07265	−	4.24077i	0.620312	−	0.371940i
$131$	−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
$135$	2.23576	−	0.0369558i	0.192424	−	0.00318065i
$136$	−1.81473	+	3.14320i	−0.155612	+	0.269527i
$137$	3.95509	−	2.28347i	0.337906	−	0.195090i	−0.321440	−	0.946930i	$-0.604167\pi$
$137$	3.95509	−	2.28347i	0.337906	−	0.195090i	0.659346	+	0.751840i	$0.270833\pi$
$138$	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
$145$	0.317270	+	19.1943i	0.0263478	+	1.59400i
$146$	−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	$0.145585\pi$
$150$	−2.35552	+	4.41039i	−0.192328	+	0.360107i
$151$	−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
$155$	8.20710	−	9.36181i	0.659210	−	0.751959i
$156$	−3.68799			−0.295276
$157$			6.43776i			0.513789i	0.966439	+	0.256894i	$0.0826993\pi$
$157$			6.43776i			0.513789i	−0.966439	+	0.256894i	$0.917301\pi$
$158$	3.97867	+	2.29709i	0.316526	+	0.182746i
$159$	−7.74384			−0.614126
$160$	−2.23576	+	0.0369558i	−0.176753	+	0.00292162i
$161$	−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	$0.0919091\pi$
$163$			7.27078i			0.569491i	−0.958603	+	0.284746i	$0.908091\pi$
$164$	−3.09949	−	5.36848i	−0.242030	−	0.419208i
$165$	−9.68027	+	0.160009i	−0.753608	+	0.0124567i
$166$	5.49665	+	9.52048i	0.426623	+	0.738933i
$167$	−4.28167	−	2.47202i	−0.331325	−	0.191291i	0.325104	−	0.945678i	$-0.394601\pi$
$167$	−4.28167	−	2.47202i	−0.331325	−	0.191291i	−0.656429	+	0.754387i	$0.727934\pi$
$168$	−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	−0.490326	−	0.871539i	$-0.663122\pi$
$173$	0.253665	−	0.146453i	0.0192858	−	0.0111347i	0.509612	+	0.860404i	$0.329789\pi$
$174$	4.29256	−	7.43493i	0.325418	−	0.563640i
$175$	−1.17533	−	0.627726i	−0.0888465	−	0.0474516i
$176$	−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	$0.880981\pi$
$180$	1.91775	−	1.14989i	0.142941	−	0.0857074i
$181$	−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	0.621548	−	0.783376i	$-0.286504\pi$
$193$	3.52728	+	2.03648i	0.253899	+	0.146589i	−0.367649	+	0.929965i	$0.619837\pi$
$194$	−11.1655			−0.801635
$195$	0.136293	+	8.24548i	0.00976014	+	0.590471i
$196$	3.46449	+	6.00067i	0.247464	+	0.428620i
$197$	21.7435	−	12.5536i	1.54916	−	0.894407i	0.550953	−	0.834536i	$-0.314264\pi$
$197$	21.7435	−	12.5536i	1.54916	−	0.894407i	0.998206	−	0.0598710i	$-0.0190689\pi$
$198$	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	$0.779779\pi$
$200$	0.165249	+	4.99727i	0.0116849	+	0.353360i
$201$	−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
$205$	−11.8881	+	7.12813i	−0.830301	+	0.497850i
$206$	−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
$210$	0.306434	+	0.511063i	0.0211460	+	0.0352667i
$211$	−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
$220$	−8.30335	+	4.97870i	−0.559812	+	0.335664i
$221$	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	$-0.978359\pi$
$223$	−23.2266	−	13.4099i	−1.55537	−	0.897992i	−0.557678	−	0.830057i	$-0.688308\pi$
$224$	−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	−0.801865	−	0.597505i	$-0.796159\pi$
$227$	−10.3257	+	5.96157i	−0.685344	+	0.395684i	0.116521	+	0.993188i	$0.462826\pi$
$228$	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	$0.915597\pi$
$230$	−0.0824224	−	4.98641i	−0.00543477	−	0.328794i
$231$	−0.576918	+	0.999252i	−0.0379584	+	0.0657459i
$232$		−	8.58511i		−	0.563640i
$233$		−	4.79091i		−	0.313863i	−0.987609	−	0.156931i	$-0.949840\pi$
$233$		−	4.79091i		−	0.313863i	0.987609	−	0.156931i	$-0.0501602\pi$
$234$	1.84400	−	3.19390i	0.120546	−	0.208792i
$235$	20.1947	−	0.333806i	1.31736	−	0.0217751i
$236$	−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
$245$	13.2881	−	7.96754i	0.848942	−	0.509027i
$246$	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
$255$	−6.96038	+	4.17346i	−0.435876	+	0.261352i
$256$	1.00000			0.0625000
$257$	−8.35871	+	4.82591i	−0.521402	+	0.301032i	−0.737508	−	0.675338i	$-0.763998\pi$
$257$	−8.35871	+	4.82591i	−0.521402	+	0.301032i	0.216106	+	0.976370i	$0.430664\pi$
$258$	−8.46832	+	4.88919i	−0.527215	+	0.304388i
$259$	−0.907615	−	1.57204i	−0.0563965	−	0.0976815i
$260$	4.24077	+	7.07265i	0.263002	+	0.438627i
$261$	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	$-0.971153\pi$
$263$		−	2.93533i		−	0.181000i	0.995896	−	0.0905002i	$-0.0288466\pi$
$264$	4.32974			0.266477
$265$	8.90453	+	14.8507i	0.547001	+	0.912274i
$266$	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	$0.632677\pi$
$270$	0.0369558	+	2.23576i	0.00224906	+	0.136064i
$271$	−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	$0.00518131\pi$
$277$			0.541801i			0.0325537i	−0.999868	+	0.0162768i	$0.994819\pi$
$278$			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	$-0.852630\pi$
$283$		−	15.0264i		−	0.893227i	0.894727	−	0.446613i	$-0.147370\pi$
$284$	5.22463	+	9.04932i	0.310025	+	0.536978i
$285$	−1.44219	−	2.40524i	−0.0854278	−	0.142474i
$286$	−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
$290$	−19.1943	+	0.317270i	−1.12713	+	0.0186307i
$291$	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	−0.00888739	−	0.999961i	$-0.502829\pi$
$293$	−15.0516	−	8.69003i	−0.879322	−	0.507677i	−0.870435	+	0.492284i	$0.836162\pi$
$294$	−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
$300$	−4.41039	−	2.35552i	−0.254634	−	0.135996i
$301$	−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
$305$	−0.206944	−	12.5197i	−0.0118496	−	0.716878i
$306$	3.62945			0.207482
$307$	18.1839	+	10.4985i	1.03781	+	0.599181i	0.919213	−	0.393761i	$-0.128826\pi$
$307$	18.1839	+	10.4985i	1.03781	+	0.599181i	0.118599	+	0.992942i	$0.462160\pi$
$308$			1.15384i			0.0657459i
$309$	10.0879			0.573879
$310$	9.36181	+	8.20710i	0.531715	+	0.466132i
$311$	−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	−0.276310	−	0.961069i	$-0.589112\pi$
$313$	−22.0577	−	12.7350i	−1.24677	−	0.719825i	−0.970465	+	0.241243i	$0.922445\pi$
$314$	−6.43776			−0.363304
$315$	−0.595811	+	0.00984840i	−0.0335701	+	0.000554894i
$316$	−2.29709	+	3.97867i	−0.129221	+	0.223818i
$317$	−15.6311	−	9.02463i	−0.877931	−	0.506874i	−0.00795560	−	0.999968i	$-0.502532\pi$
$317$	−15.6311	−	9.02463i	−0.877931	−	0.506874i	−0.869976	+	0.493094i	$0.835866\pi$
$318$		−	7.74384i		−	0.434253i
$319$	−18.5856	−	32.1913i	−1.04060	−	1.80237i
$320$	−0.0369558	−	2.23576i	−0.00206589	−	0.124983i
$321$	−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
$330$	−0.160009	−	9.68027i	−0.00880821	−	0.532881i
$331$	−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
$335$	1.51491	+	2.52653i	0.0827685	+	0.138039i
$336$	−0.133246	−	0.230788i	−0.00726914	−	0.0125905i
$337$			5.66462i			0.308572i	0.988026	+	0.154286i	$0.0493076\pi$
$337$			5.66462i			0.308572i	−0.988026	+	0.154286i	$0.950692\pi$
$338$	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	0.655969	−	0.754788i	$-0.272260\pi$
$347$	6.15256	+	3.55218i	0.330287	+	0.190691i	−0.325682	+	0.945480i	$0.605594\pi$
$348$	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	$0.423962\pi$
$350$	0.627726	−	1.17533i	0.0335534	−	0.0628239i
$351$	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	0.912271	−	0.409587i	$-0.134327\pi$
$353$	19.0456	+	10.9960i	1.01369	+	0.585256i	0.101423	+	0.994843i	$0.467661\pi$
$354$	−0.855490	−	1.48175i	−0.0454688	−	0.0787542i
$355$	20.0390	−	12.0154i	1.06356	−	0.637714i
$356$	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	$0.720309\pi$
$360$	1.14989	+	1.91775i	0.0606043	+	0.101074i
$361$	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
$365$	−7.14894	−	11.9228i	−0.374192	−	0.624068i
$366$	−2.79988	+	4.84953i	−0.146352	+	0.253489i
$367$	−7.57740	+	4.37481i	−0.395537	+	0.228363i	−0.684556	−	0.728960i	$-0.740004\pi$
$367$	−7.57740	+	4.37481i	−0.395537	+	0.228363i	0.289020	+	0.957323i	$0.406671\pi$
$368$			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	$0.101555\pi$
$373$			12.1156i			0.627320i	−0.949535	+	0.313660i	$0.898445\pi$
$374$	−15.7146			−0.812582
$375$	−5.10340	+	9.94763i	−0.263539	+	0.513693i
$376$	−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	$-0.283809\pi$
$383$	31.6273	−	18.2600i	1.61608	−	0.933043i	0.987921	−	0.154957i	$-0.0495239\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	2.57970	−	0.0426410i	0.131474	−	0.00217319i
$386$	−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	$-0.118026\pi$
$390$	−8.24548	+	0.136293i	−0.417526	+	0.00690146i
$391$	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	0.801575	−	0.597895i	$-0.203996\pi$
$397$	13.6400	+	7.87503i	0.684570	+	0.395237i	−0.117005	+	0.993131i	$0.537329\pi$
$398$	−4.09149	+	2.36222i	−0.205088	+	0.118408i
$399$	−0.334233			−0.0167326
$400$	−4.99727	+	0.165249i	−0.249863	+	0.00826245i
$401$	−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	$-0.0798102\pi$
$410$	−7.12813	−	11.8881i	−0.352033	−	0.587112i
$411$	−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
$415$	12.6410	+	21.0824i	0.620525	+	1.03489i
$416$	−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	$0.0975664\pi$
$420$	−0.511063	+	0.306434i	−0.0249373	+	0.0149525i
$421$	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
$425$	16.0073	+	8.54927i	0.776468	+	0.414700i
$426$	−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	$-0.872206\pi$
$433$		−	16.2632i		−	0.781558i	0.920485	−	0.390779i	$-0.127794\pi$
$434$	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	$0.903192\pi$
$440$	−4.97870	−	8.30335i	−0.237350	−	0.395847i
$441$	3.46449	−	6.00067i	0.164976	−	0.285746i
$442$			13.3854i			0.636678i
$443$	6.73466	−	3.88826i	0.319973	−	0.184737i	−0.331407	−	0.943488i	$-0.607523\pi$
$443$	6.73466	−	3.88826i	0.319973	−	0.184737i	0.651381	+	0.758751i	$0.274190\pi$
$444$	−3.40580	−	5.89902i	−0.161632	−	0.279955i
$445$	−0.513288	−	31.0530i	−0.0243322	−	1.47205i
$446$	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
$455$	−0.0363208	−	2.19735i	−0.00170275	−	0.103013i
$456$	0.627100	+	1.08617i	0.0293666	+	0.0508645i
$457$		−	25.9754i		−	1.21508i	−0.794289	−	0.607540i	$-0.792156\pi$
$457$		−	25.9754i		−	1.21508i	0.794289	−	0.607540i	$-0.207844\pi$
$458$	−18.5959	−	10.7364i	−0.868930	−	0.501677i
$459$	−1.81473	+	3.14320i	−0.0847042	+	0.146712i
$460$	4.98641	−	0.0824224i	0.232492	−	0.00384296i
$461$	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	$-0.971191\pi$
$463$		−	3.88965i		−	0.180767i	0.995907	−	0.0903836i	$-0.0288093\pi$
$464$	8.58511			0.398554
$465$	−11.7885	+	4.00402i	−0.546677	+	0.185682i
$466$	4.79091			0.221935
$467$			25.9891i			1.20263i	0.799011	+	0.601316i	$0.205357\pi$
$467$			25.9891i			1.20263i	−0.799011	+	0.601316i	$0.794643\pi$
$468$	3.19390	+	1.84400i	0.147638	+	0.0852388i
$469$	0.351088			0.0162117
$470$	0.333806	+	20.1947i	0.0153973	+	0.931512i
$471$	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
$475$	−2.95430	+	5.53151i	−0.135553	+	0.253803i
$476$	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
$485$	−24.9634	+	0.412630i	−1.13353	+	0.0187365i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	24.1444	−	13.9398i	1.09409	−	0.631672i	0.159426	−	0.987210i	$-0.449036\pi$
$487$	24.1444	−	13.9398i	1.09409	−	0.631672i	0.934662	+	0.355538i	$0.115702\pi$
$488$			5.59976i			0.253489i
$489$	3.63539	−	6.29668i	0.164398	−	0.284746i
$490$	7.96754	+	13.2881i	0.359937	+	0.600293i
$491$	−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	−0.229585	−	0.973289i	$-0.573737\pi$
$503$	−26.6277	−	15.3735i	−1.18727	−	0.685471i	−0.957685	+	0.287818i	$0.907070\pi$
$504$	0.266491			0.0118705
$505$	−0.424746	−	25.6964i	−0.0189010	−	1.14347i
$506$	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	$0.794132\pi$
$510$	−4.17346	−	6.96038i	−0.184804	−	0.308211i
$511$	−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
$515$	−11.5999	−	19.3460i	−0.511152	−	0.852486i
$516$	−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
$520$	−7.07265	+	4.24077i	−0.310156	+	0.185970i
$521$	−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	$0.0395424\pi$
$523$			5.66729i			0.247813i	−0.992294	+	0.123907i	$0.960458\pi$
$524$	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
$530$	−14.8507	+	8.90453i	−0.645075	+	0.386788i
$531$	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
$540$	−2.23576	+	0.0369558i	−0.0962119	+	0.00159033i
$541$	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
$545$	−0.206633	−	12.5009i	−0.00885120	−	0.535482i
$546$	−0.491409	+	0.851145i	−0.0210303	+	0.0364256i
$547$	−21.7522	+	12.5587i	−0.930058	+	0.536969i	−0.886830	−	0.462096i	$-0.847098\pi$
$547$	−21.7522	+	12.5587i	−0.930058	+	0.536969i	−0.0432280	+	0.999065i	$0.513764\pi$
$548$	−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
$555$	−13.0629	+	7.83256i	−0.554491	+	0.332474i
$556$	−20.5780			−0.872701
$557$			27.0171i			1.14475i	0.819991	+	0.572377i	$0.193978\pi$
$557$			27.0171i			1.14475i	−0.819991	+	0.572377i	$0.806022\pi$
$558$	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	0.00862638	−	0.999963i	$-0.497254\pi$
$563$	20.8550	−	12.0406i	0.878933	−	0.507452i	0.870306	+	0.492511i	$0.163921\pi$
$564$	4.51629	−	7.82244i	0.190170	−	0.329384i
$565$	−11.2564	−	18.7731i	−0.473559	−	0.789790i
$566$	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	$0.950266\pi$
$570$	2.40524	−	1.44219i	0.100744	−	0.0604066i
$571$	−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
$575$	−0.368554	−	11.1454i	−0.0153698	−	0.464794i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	40.0591	+	23.1282i	1.66768	+	0.962838i	0.968882	+	0.247523i	$0.0796165\pi$
$577$	40.0591	+	23.1282i	1.66768	+	0.962838i	0.698802	+	0.715315i	$0.253717\pi$
$578$	3.31434	−	1.91354i	0.137858	−	0.0795926i
$579$	−2.03648	−	3.52728i	−0.0846331	−	0.146589i
$580$	−0.317270	−	19.1943i	−0.0131739	−	0.796999i
$581$	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	$0.00195130\pi$
$587$			0.297043i			0.0122603i	−0.999981	+	0.00613014i	$0.998049\pi$
$588$		−	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	$0.107232\pi$
$593$			16.0986i			0.661089i	−0.943790	+	0.330544i	$0.892768\pi$
$594$	−2.16487	−	3.74966i	−0.0888256	−	0.153851i
$595$	1.85488	−	1.11219i	0.0760426	−	0.0455953i
$596$	−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	$0.852351\pi$
$600$	2.35552	−	4.41039i	0.0961639	−	0.180053i
$601$	−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	−0.427830	−	0.903859i	$-0.640722\pi$
$607$	3.47437	−	2.00593i	0.141020	−	0.0814181i	0.568850	+	0.822441i	$0.307388\pi$
$608$	1.08617	+	0.627100i	0.0440500	+	0.0254323i
$609$	−1.14393	−	1.98134i	−0.0463543	−	0.0802880i
$610$	12.5197	−	0.206944i	0.506909	−	0.00837891i
$611$	16.6560	+	28.8491i	0.673831	+	1.16711i
$612$			3.62945i			0.146712i
$613$	−26.1570	−	15.1017i	−1.05647	−	0.609954i	−0.132017	−	0.991247i	$-0.542145\pi$
$613$	−26.1570	−	15.1017i	−1.05647	−	0.609954i	−0.924454	+	0.381294i	$0.875479\pi$
$614$	−10.4985	+	18.1839i	−0.423685	+	0.733844i
$615$	13.8595	−	0.229089i	0.558868	−	0.00923775i
$616$	−1.15384			−0.0464894
$617$	−29.6578	−	17.1229i	−1.19398	−	0.689343i	−0.234771	−	0.972051i	$-0.575434\pi$
$617$	−29.6578	−	17.1229i	−1.19398	−	0.689343i	−0.959206	+	0.282708i	$0.908767\pi$
$618$			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	$0.647066\pi$
$620$	−8.20710	+	9.36181i	−0.329605	+	0.375980i
$621$	2.23029			0.0894986
$622$		−	5.16307i		−	0.207020i
$623$	−3.20547	−	1.85068i	−0.128424	−	0.0741458i
$624$	3.68799			0.147638
$625$	24.9454	−	1.65159i	0.997815	−	0.0660635i
$626$	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
$630$	−0.00984840	−	0.595811i	−0.000392370	−	0.0237377i
$631$	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
$640$	2.23576	−	0.0369558i	0.0883763	−	0.00146081i
$641$	−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	$-0.946742\pi$
$643$		−	8.44585i		−	0.333072i	0.986035	−	0.166536i	$-0.0532582\pi$
$644$	0.297177	−	0.514725i	0.0117104	−	0.0202830i
$645$	−18.7525	+	11.2440i	−0.738378	+	0.442733i
$646$	−2.27603	−	3.94220i	−0.0895492	−	0.155104i
$647$		−	6.43945i		−	0.253161i	−0.991956	−	0.126580i	$-0.959600\pi$
$647$		−	6.43945i		−	0.253161i	0.991956	−	0.126580i	$-0.0404002\pi$
$648$	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	$-0.960242\pi$
$653$		−	6.36693i		−	0.249157i	0.992210	−	0.124579i	$-0.0397579\pi$
$654$	−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	$0.634932\pi$
$660$	9.68027	−	0.160009i	0.376804	−	0.00622834i
$661$	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
$665$	0.384330	+	0.640975i	0.0149037	+	0.0248560i
$666$	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
$670$	−2.52653	+	1.51491i	−0.0976084	+	0.0585262i
$671$	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	−0.341135	−	0.940014i	$-0.610811\pi$
$673$	7.84426	−	4.52889i	0.302374	−	0.174576i	0.643509	+	0.765439i	$0.277478\pi$
$674$	−5.66462			−0.218193
$675$	0.165249	+	4.99727i	0.00636043	+	0.192345i
$676$	−0.300648	+	0.520738i	−0.0115634	+	0.0200284i
$677$	−22.8564	+	13.1961i	−0.878443	+	0.507169i	−0.870145	−	0.492796i	$-0.835975\pi$
$677$	−22.8564	+	13.1961i	−0.878443	+	0.507169i	−0.00829817	+	0.999966i	$0.502641\pi$
$678$			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	$0.0594041\pi$
$683$			9.69801i			0.371084i	−0.982636	+	0.185542i	$0.940596\pi$
$684$	−1.25420			−0.0479555
$685$	5.25146	+	8.75825i	0.200648	+	0.334635i
$686$	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
$695$	0.760477	+	46.0075i	0.0288465	+	1.74516i
$696$	−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
$700$	1.17533	+	0.627726i	0.0444232	+	0.0237258i
$701$	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	$0.390689\pi$
$710$	12.0154	+	20.0390i	0.450932	+	0.752052i
$711$	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	$0.243294\pi$
$720$	−1.91775	+	1.14989i	−0.0714703	+	0.0428537i
$721$	−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
$725$	−42.9021	+	1.41868i	−1.59334	+	0.0526885i
$726$	3.87331	+	6.70878i	0.143752	+	0.248986i
$727$	−26.9302	−	15.5482i	−0.998787	−	0.576650i	−0.0908978	−	0.995860i	$-0.528974\pi$
$727$	−26.9302	−	15.5482i	−0.998787	−	0.576650i	−0.907889	+	0.419210i	$0.862307\pi$
$728$			0.982817i			0.0364256i
$729$	−1.00000			−0.0370370
$730$	11.9228	−	7.14894i	0.441283	−	0.264594i
$731$	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	−0.641910	−	0.766780i	$-0.721858\pi$
$733$	−8.09007	+	4.67080i	−0.298813	+	0.172520i	0.343096	+	0.939300i	$0.388524\pi$
$734$	−4.37481	−	7.57740i	−0.161477	−	0.279687i
$735$	−15.4916	+	0.256066i	−0.571415	+	0.00944515i
$736$	−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	$-0.583966\pi$
$743$		−	52.6303i		−	1.93082i	0.260738	−	0.965410i	$-0.416034\pi$
$744$	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
$750$	−9.94763	−	5.10340i	−0.363236	−	0.186350i
$751$	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
$755$	−0.389195	−	23.5456i	−0.0141643	−	0.856912i
$756$	−0.133246	+	0.230788i	−0.00484609	+	0.00839368i
$757$	33.4714	−	19.3247i	1.21654	−	0.702369i	0.252362	−	0.967633i	$-0.418792\pi$
$757$	33.4714	−	19.3247i	1.21654	−	0.702369i	0.964176	+	0.265264i	$0.0854592\pi$
$758$	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
$765$	8.11459	−	0.134129i	0.293384	−	0.00484946i
$766$	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	$0.775575\pi$
$770$	0.0426410	+	2.57970i	0.00153667	+	0.0929661i
$771$	9.65181			0.347602
$772$	−3.52728	−	2.03648i	−0.126950	−	0.0732944i
$773$			19.5483i			0.703103i	0.936169	+	0.351551i	$0.114346\pi$
$773$			19.5483i			0.703103i	−0.936169	+	0.351551i	$0.885654\pi$
$774$	9.77837			0.351476
$775$	21.2341	+	18.0031i	0.762751	+	0.646692i
$776$	11.1655			0.400817
$777$			1.81523i			0.0651210i
$778$	26.6400	+	15.3806i	0.955089	+	0.551421i
$779$	7.77477			0.278560
$780$	−0.136293	−	8.24548i	−0.00488007	−	0.295235i
$781$	−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
$785$	−14.3933	+	0.237913i	−0.513719	+	0.00849147i
$786$	10.6180	+	18.3909i	0.378730	+	0.655980i
$787$	14.2677	+	8.23744i	0.508588	+	0.293633i	0.732253	−	0.681033i	$-0.238469\pi$
$787$	14.2677	+	8.23744i	0.508588	+	0.293633i	−0.223665	+	0.974666i	$0.571802\pi$
$788$	−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
$795$	−0.286180	−	17.3134i	−0.0101498	−	0.614043i
$796$	−2.36222	−	4.09149i	−0.0837268	−	0.145019i
$797$	42.3198	−	24.4334i	1.49904	−	0.865474i	0.499045	−	0.866576i	$-0.333684\pi$
$797$	42.3198	−	24.4334i	1.49904	−	0.865474i	0.999999	+	0.00110208i	$0.000350802\pi$
$798$		−	0.334233i		−	0.0118317i
$799$	−16.3917	+	28.3912i	−0.579895	+	1.00441i
$800$	−0.165249	−	4.99727i	−0.00584243	−	0.176680i
$801$	−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
$815$	−16.2557	+	0.268698i	−0.569413	+	0.00941207i
$816$	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
$820$	11.8881	−	7.12813i	0.415151	−	0.248925i
$821$	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	0.177614	−	0.984100i	$-0.443162\pi$
$823$	−16.8064	−	9.70317i	−0.585834	−	0.338231i	−0.763448	+	0.645869i	$0.776495\pi$
$824$	5.04393	+	8.73635i	0.175714	+	0.304345i
$825$	−0.715485	−	21.6369i	−0.0249100	−	0.753299i
$826$	0.227980	+	0.394874i	0.00793245	+	0.0137394i
$827$	13.4072	−	7.74065i	0.466214	−	0.269169i	−0.248440	−	0.968647i	$-0.579918\pi$
$827$	13.4072	−	7.74065i	0.466214	−	0.269169i	0.714653	+	0.699479i	$0.246584\pi$
$828$	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	$0.698093\pi$
$830$	−21.0824	+	12.6410i	−0.731781	+	0.438777i
$831$	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	$0.338152\pi$
$840$	−0.306434	−	0.511063i	−0.0105730	−	0.0176333i
$841$	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
$850$	−8.54927	+	16.0073i	−0.293237	+	0.549045i
$851$	7.59593	−	13.1565i	0.260385	−	0.451000i
$852$		−	10.4493i		−	0.357985i
$853$			16.2835i			0.557535i	0.960359	+	0.278767i	$0.0899258\pi$
$853$			16.2835i			0.557535i	−0.960359	+	0.278767i	$0.910074\pi$
$854$	0.746143	−	1.29236i	0.0255325	−	0.0442236i
$855$	0.0463500	+	2.80409i	0.00158514	+	0.0958980i
$856$	9.24808	−	16.0181i	0.316093	−	0.547489i
$857$	−0.433193	+	0.250104i	−0.0147976	+	0.00854339i	−0.507381	−	0.861722i	$-0.669386\pi$
$857$	−0.433193	+	0.250104i	−0.0147976	+	0.00854339i	0.492583	+	0.870265i	$0.336053\pi$
$858$	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	−0.103569	−	0.994622i	$-0.533026\pi$
$863$	20.7405	−	11.9745i	0.706014	−	0.407617i	0.809583	+	0.587005i	$0.199693\pi$
$864$	1.00000			0.0340207
$865$	0.336810	+	0.561722i	0.0114519	+	0.0190991i
$866$	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
$875$	1.36001	−	2.65095i	0.0459768	−	0.0896186i
$876$	−6.21708			−0.210056
$877$	14.4895	−	8.36549i	0.489274	−	0.282483i	−0.234999	−	0.971996i	$-0.575509\pi$
$877$	14.4895	−	8.36549i	0.489274	−	0.282483i	0.724273	+	0.689513i	$0.242175\pi$
$878$	7.90075	−	4.56150i	0.266637	−	0.153943i
$879$	8.69003	+	15.0516i	0.293107	+	0.507677i
$880$	8.30335	−	4.97870i	0.279906	−	0.167832i
$881$	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	$-0.911581\pi$
$883$		−	16.2969i		−	0.548434i	0.961668	−	0.274217i	$-0.0884186\pi$
$884$	−13.3854			−0.450200
$885$	−1.96743	−	3.28123i	−0.0661345	−	0.110297i
$886$	3.88826	+	6.73466i	0.130629	+	0.226255i
$887$	−37.3280	−	21.5513i	−1.25335	−	0.723623i	−0.281578	−	0.959538i	$-0.590858\pi$
$887$	−37.3280	−	21.5513i	−1.25335	−	0.723623i	−0.971774	+	0.235915i	$0.924191\pi$
$888$	5.89902	−	3.40580i	0.197958	−	0.114291i
$889$	1.11471	+	1.93074i	0.0373862	+	0.0647549i
$890$	31.0530	−	0.513288i	1.04090	−	0.0172055i
$891$	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
$905$	33.2217	−	19.9198i	1.10433	−	0.662157i
$906$	−5.26568	+	9.12042i	−0.174940	+	0.303006i
$907$		−	5.75164i		−	0.190980i	−0.995430	−	0.0954900i	$-0.969558\pi$
$907$		−	5.75164i		−	0.190980i	0.995430	−	0.0954900i	$-0.0304418\pi$
$908$	10.3257	−	5.96157i	0.342672	−	0.197842i
$909$	−5.74667	−	9.95353i	−0.190605	−	0.330138i
$910$	2.19735	−	0.0363208i	0.0728413	−	0.00120402i
$911$	−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	$0.965555\pi$
$920$	0.0824224	+	4.98641i	0.00271739	+	0.164397i
$921$	−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
$925$	30.0418	+	16.0449i	0.987768	+	0.527553i
$926$	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	$0.111788\pi$
$930$	−4.00402	−	11.7885i	−0.131297	−	0.386559i
$931$	−8.69033			−0.284814
$932$			4.79091i			0.156931i
$933$	4.47135	+	2.58153i	0.146385	+	0.0845156i
$934$	−25.9891			−0.850389
$935$	−35.1341	+	0.580745i	−1.14901	+	0.0189924i
$936$	−1.84400	+	3.19390i	−0.0602729	+	0.104396i
$937$	−20.4787	−	11.8234i	−0.669011	−	0.386254i	0.126691	−	0.991942i	$-0.459564\pi$
$937$	−20.4787	−	11.8234i	−0.669011	−	0.386254i	−0.795702	+	0.605688i	$0.792898\pi$
$938$			0.351088i			0.0114634i
$939$	12.7350	+	22.0577i	0.415591	+	0.719825i
$940$	−20.1947	+	0.333806i	−0.658678	+	0.0108876i
$941$	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	0.510035	−	0.860154i	$-0.329632\pi$
$947$	0.619713	+	0.357792i	0.0201380	+	0.0116267i	−0.489897	+	0.871780i	$0.662966\pi$
$948$	3.97867	−	2.29709i	0.129221	−	0.0746059i
$949$	11.4643	−	19.8567i	0.372146	−	0.644576i
$950$	−5.53151	−	2.95430i	−0.179466	−	0.0958501i
$951$	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	$0.287106\pi$
$953$			48.4392i			1.56910i	−0.620067	+	0.784549i	$0.712894\pi$
$954$	−3.87192	+	6.70636i	−0.125358	+	0.217127i
$955$	−20.9675	+	12.5722i	−0.678494	+	0.406826i
$956$	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	0.650259	−	0.759712i	$-0.274660\pi$
$967$	9.87190	+	5.69955i	0.317459	+	0.183285i	−0.332800	+	0.942997i	$0.607994\pi$
$968$	6.70878	+	3.87331i	0.215628	+	0.124493i
$969$	4.55206			0.146233
$970$	−0.412630	−	24.9634i	−0.0132487	−	0.801525i
$971$	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
$975$	−18.4299	+	0.609437i	−0.590229	+	0.0195176i
$976$	−5.59976			−0.179244
$977$			25.8409i			0.826722i	0.910567	+	0.413361i	$0.135645\pi$
$977$			25.8409i			0.826722i	−0.910567	+	0.413361i	$0.864355\pi$
$978$	6.29668	+	3.63539i	0.201346	+	0.116247i
$979$	30.0684	+	52.0799i	0.960989	+	1.66448i
$980$	−13.2881	+	7.96754i	−0.424471	+	0.254514i
$981$	−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	−0.970848	−	0.239696i	$-0.922952\pi$
$983$	−39.1500	+	22.6032i	−1.24869	+	0.720931i	−0.277842	+	0.960627i	$0.589619\pi$
$984$	−6.19899			−0.197617
$985$	28.8704	+	48.1493i	0.919888	+	1.53417i
$986$	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
$995$	−9.06030	+	5.43257i	−0.287231	+	0.172224i
$996$	10.9933			0.348336
$997$	3.53132	−	2.03881i	0.111838	−	0.0645698i	−0.443038	−	0.896503i	$-0.646099\pi$
$997$	3.53132	−	2.03881i	0.111838	−	0.0645698i	0.554876	+	0.831933i	$0.312766\pi$
$998$	−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.439.10	yes	28
5.4	even	2	inner	930.2.s.d.439.7	✓	28
31.25	even	3	inner	930.2.s.d.769.14	yes	28
155.149	even	6	inner	930.2.s.d.769.3	yes	28

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.0369558 + 2.23576i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.230788 + 0.133246i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.0369558 + 2.23576i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.230788 + 0.133246i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.23576 + 0.0369558i) 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} +(-0.0369558 - 2.23576i) q^{20} +(-0.133246 - 0.230788i) q^{21} +(3.74966 - 2.16487i) q^{22} +2.23029i q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.99727 + 0.165249i) 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} +(2.23576 - 0.0369558i) 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} +(-1.91775 + 1.14989i) q^{45} -2.23029 q^{46} -9.03257i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.46449 - 6.00067i) q^{49} +(-0.165249 - 4.99727i) q^{50} +(1.81473 + 3.14320i) q^{51} +(3.19390 - 1.84400i) q^{52} +(6.70636 - 3.87192i) q^{53} +1.00000 q^{54} +(8.30335 - 4.97870i) 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} +(-4.24077 - 7.07265i) 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} +(4.41039 + 2.35552i) q^{75} +(-0.627100 + 1.08617i) q^{76} -1.15384i q^{77} +3.68799i q^{78} +(2.29709 - 3.97867i) q^{79} +(0.0369558 + 2.23576i) 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} +(-1.14989 - 1.91775i) 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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