LMFDB - Embedded newform 370.2.n.f.269.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.6
Root			$-0.531325 + 1.98293i$ of defining polynomial
Character	$\chi$	$=$	370.269
Dual form			370.2.n.f.359.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(2.18708 - 1.26271i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +2.52543 q^{6} +(1.91766 - 1.10716i) q^{7} +1.00000i q^{8} +(1.68889 - 2.92525i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(2.18708 - 1.26271i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +2.52543 q^{6} +(1.91766 - 1.10716i) q^{7} +1.00000i q^{8} +(1.68889 - 2.92525i) q^{9} +(0.311108 - 2.21432i) q^{10} -2.68889 q^{11} +(2.18708 + 1.26271i) q^{12} +(-4.10474 + 2.36987i) q^{13} +2.21432 q^{14} +(-4.45006 - 3.47647i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.596598 - 0.344446i) q^{17} +(2.92525 - 1.68889i) q^{18} +(2.59210 + 4.48966i) q^{19} +(1.37659 - 1.76210i) q^{20} +(2.79605 - 4.84290i) q^{21} +(-2.32865 - 1.34445i) q^{22} +2.21432i q^{23} +(1.26271 + 2.18708i) q^{24} +(-3.59641 + 3.47359i) q^{25} -4.73975 q^{26} -0.954067i q^{27} +(1.91766 + 1.10716i) q^{28} +10.6637 q^{29} +(-2.11563 - 5.23574i) q^{30} +6.73975 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.88083 + 3.39530i) q^{33} +(-0.344446 - 0.596598i) q^{34} +(-3.90186 - 3.04820i) q^{35} +3.37778 q^{36} +(-6.08014 + 0.178520i) q^{37} +5.18421i q^{38} +(-5.98494 + 10.3662i) q^{39} +(2.07321 - 0.837733i) q^{40} +(-3.71432 - 6.43339i) q^{41} +(4.84290 - 2.79605i) q^{42} +5.90321i q^{43} +(-1.34445 - 2.32865i) q^{44} +(-7.47949 - 1.05086i) q^{45} +(-1.10716 + 1.91766i) q^{46} -4.83654i q^{47} +2.52543i q^{48} +(-1.04839 + 1.81587i) q^{49} +(-4.85138 + 1.21002i) q^{50} -1.73975 q^{51} +(-4.10474 - 2.36987i) q^{52} +(0.680419 + 0.392840i) q^{53} +(0.477034 - 0.826246i) q^{54} +(2.25257 + 5.57464i) q^{55} +(1.10716 + 1.91766i) q^{56} +(11.3383 + 6.54617i) q^{57} +(9.23504 + 5.33185i) q^{58} +(0.130126 - 0.225385i) q^{59} +(0.785680 - 5.59210i) q^{60} +(-2.73975 - 4.74538i) q^{61} +(5.83679 + 3.36987i) q^{62} -7.47949i q^{63} -1.00000 q^{64} +(8.35192 + 6.52468i) q^{65} -6.79060 q^{66} +(-2.31068 + 1.33407i) q^{67} -0.688892i q^{68} +(2.79605 + 4.84290i) q^{69} +(-1.85501 - 4.59075i) q^{70} +(-4.90321 - 8.49261i) q^{71} +(2.92525 + 1.68889i) q^{72} -13.1175i q^{73} +(-5.35482 - 2.88547i) q^{74} +(-3.47949 + 12.1383i) q^{75} +(-2.59210 + 4.48966i) q^{76} +(-5.15637 + 2.97703i) q^{77} +(-10.3662 + 5.98494i) q^{78} +(-1.38493 - 2.39877i) q^{79} +(2.21432 + 0.311108i) q^{80} +(3.86196 + 6.68912i) q^{81} -7.42864i q^{82} +(-7.67063 - 4.42864i) q^{83} +5.59210 q^{84} +(-0.214320 + 1.52543i) q^{85} +(-2.95161 + 5.11233i) q^{86} +(23.3224 - 13.4652i) q^{87} -2.68889i q^{88} +(-0.334074 + 0.578634i) q^{89} +(-5.95200 - 4.64981i) q^{90} +(-5.24766 + 9.08921i) q^{91} +(-1.91766 + 1.10716i) q^{92} +(14.7404 - 8.51037i) q^{93} +(2.41827 - 4.18856i) q^{94} +(7.13651 - 9.13511i) q^{95} +(-1.26271 + 2.18708i) q^{96} +12.9906i q^{97} +(-1.81587 + 1.04839i) q^{98} +(-4.54125 + 7.86567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9	$ 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9} + 4 q^{10} - 32 q^{11} + 18 q^{15} - 6 q^{16} + 4 q^{19} + 20 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 32 q^{29} - 20 q^{30} + 28 q^{31} - 4 q^{34} + 4 q^{35} + 40 q^{36} - 58 q^{39} + 2 q^{40} - 18 q^{41} - 16 q^{44} + 16 q^{45} - 26 q^{49} - 8 q^{50} + 32 q^{51} - 34 q^{54} - 4 q^{55} + 28 q^{59} + 36 q^{60} + 20 q^{61} - 12 q^{64} - 22 q^{65} + 24 q^{66} + 20 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{74} + 64 q^{75} - 4 q^{76} - 4 q^{79} - 6 q^{81} + 40 q^{84} + 24 q^{85} - 22 q^{86} - 44 q^{89} - 20 q^{90} - 36 q^{91} + 16 q^{94} + 16 q^{95} - 2 q^{96} - 80 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9 + 4 * q^10 - 32 * q^11 + 18 * q^15 - 6 * q^16 + 4 * q^19 + 20 * q^21 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 32 * q^29 - 20 * q^30 + 28 * q^31 - 4 * q^34 + 4 * q^35 + 40 * q^36 - 58 * q^39 + 2 * q^40 - 18 * q^41 - 16 * q^44 + 16 * q^45 - 26 * q^49 - 8 * q^50 + 32 * q^51 - 34 * q^54 - 4 * q^55 + 28 * q^59 + 36 * q^60 + 20 * q^61 - 12 * q^64 - 22 * q^65 + 24 * q^66 + 20 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^74 + 64 * q^75 - 4 * q^76 - 4 * q^79 - 6 * q^81 + 40 * q^84 + 24 * q^85 - 22 * q^86 - 44 * q^89 - 20 * q^90 - 36 * q^91 + 16 * q^94 + 16 * q^95 - 2 * q^96 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	2.18708	−	1.26271i	1.26271	−	0.729028i	0.289115	−	0.957294i	$-0.406639\pi$
$3$	2.18708	−	1.26271i	1.26271	−	0.729028i	0.973599	+	0.228266i	$0.0733057\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.837733	−	2.07321i	−0.374645	−	0.927168i
$5$	−0.837733	−	2.07321i	−0.374645	−	0.927168i
$6$	2.52543			1.03100
$7$	1.91766	−	1.10716i	0.724806	−	0.418467i	−0.0917128	−	0.995785i	$-0.529234\pi$
$7$	1.91766	−	1.10716i	0.724806	−	0.418467i	0.816519	+	0.577318i	$0.195901\pi$
$8$			1.00000i			0.353553i
$9$	1.68889	−	2.92525i	0.562964	−	0.975082i
$10$	0.311108	−	2.21432i	0.0983809	−	0.700229i
$11$	−2.68889			−0.810731			−0.405366	−	0.914155i	$-0.632856\pi$
$11$	−2.68889			−0.810731			−0.405366	+	0.914155i	$0.632856\pi$
$12$	2.18708	+	1.26271i	0.631357	+	0.364514i
$13$	−4.10474	+	2.36987i	−1.13845	+	0.657285i	−0.946046	−	0.324031i	$-0.894962\pi$
$13$	−4.10474	+	2.36987i	−1.13845	+	0.657285i	−0.192404	+	0.981316i	$0.561628\pi$
$14$	2.21432			0.591802
$15$	−4.45006	−	3.47647i	−1.14900	−	0.897621i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.596598	−	0.344446i	−0.144696	−	0.0835404i	0.425904	−	0.904768i	$-0.359956\pi$
$17$	−0.596598	−	0.344446i	−0.144696	−	0.0835404i	−0.570600	+	0.821228i	$0.693289\pi$
$18$	2.92525	−	1.68889i	0.689487	−	0.398076i
$19$	2.59210	+	4.48966i	0.594669	+	1.03000i	0.993593	+	0.113014i	$0.0360504\pi$
$19$	2.59210	+	4.48966i	0.594669	+	1.03000i	−0.398924	+	0.916984i	$0.630616\pi$
$20$	1.37659	−	1.76210i	0.307814	−	0.394018i
$21$	2.79605	−	4.84290i	0.610149	−	1.05681i
$22$	−2.32865	−	1.34445i	−0.496470	−	0.286637i
$23$			2.21432i			0.461718i	0.972987	+	0.230859i	$0.0741535\pi$
$23$			2.21432i			0.461718i	−0.972987	+	0.230859i	$0.925846\pi$
$24$	1.26271	+	2.18708i	0.257750	+	0.446437i
$25$	−3.59641	+	3.47359i	−0.719282	+	0.694719i
$26$	−4.73975			−0.929541
$27$		−	0.954067i		−	0.183610i
$28$	1.91766	+	1.10716i	0.362403	+	0.209234i
$29$	10.6637			1.98020			0.990100	−	0.140364i	$-0.0448273\pi$
$29$	10.6637			1.98020			0.990100	+	0.140364i	$0.0448273\pi$
$30$	−2.11563	−	5.23574i	−0.386260	−	0.955912i
$31$	6.73975			1.21049			0.605247	−	0.796038i	$-0.293074\pi$
$31$	6.73975			1.21049			0.605247	+	0.796038i	$0.293074\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.88083	+	3.39530i	−1.02372	+	0.591046i
$34$	−0.344446	−	0.596598i	−0.0590720	−	0.102316i
$35$	−3.90186	−	3.04820i	−0.659535	−	0.515241i
$36$	3.37778			0.562964
$37$	−6.08014	+	0.178520i	−0.999569	+	0.0293486i
$37$	−6.08014	+	0.178520i	−0.999569	+	0.0293486i
$38$			5.18421i			0.840990i
$39$	−5.98494	+	10.3662i	−0.958358	+	1.65992i
$40$	2.07321	−	0.837733i	0.327803	−	0.132457i
$41$	−3.71432	−	6.43339i	−0.580079	−	1.00473i	−0.995469	−	0.0950834i	$-0.969688\pi$
$41$	−3.71432	−	6.43339i	−0.580079	−	1.00473i	0.415390	−	0.909643i	$-0.363645\pi$
$42$	4.84290	−	2.79605i	0.747276	−	0.431440i
$43$			5.90321i			0.900231i	0.892970	+	0.450116i	$0.148617\pi$
$43$			5.90321i			0.900231i	−0.892970	+	0.450116i	$0.851383\pi$
$44$	−1.34445	−	2.32865i	−0.202683	−	0.351057i
$45$	−7.47949	−	1.05086i	−1.11498	−	0.156652i
$46$	−1.10716	+	1.91766i	−0.163242	+	0.282743i
$47$		−	4.83654i		−	0.705481i	−0.935721	−	0.352741i	$-0.885250\pi$
$47$		−	4.83654i		−	0.705481i	0.935721	−	0.352741i	$-0.114750\pi$
$48$			2.52543i			0.364514i
$49$	−1.04839	+	1.81587i	−0.149771	+	0.259410i
$50$	−4.85138	+	1.21002i	−0.686088	+	0.171122i
$51$	−1.73975			−0.243613
$52$	−4.10474	−	2.36987i	−0.569225	−	0.328642i
$53$	0.680419	+	0.392840i	0.0934627	+	0.0539607i	0.546003	−	0.837783i	$-0.316149\pi$
$53$	0.680419	+	0.392840i	0.0934627	+	0.0539607i	−0.452540	+	0.891744i	$0.649482\pi$
$54$	0.477034	−	0.826246i	0.0649160	−	0.112438i
$55$	2.25257	+	5.57464i	0.303737	+	0.751684i
$56$	1.10716	+	1.91766i	0.147950	+	0.256258i
$57$	11.3383	+	6.54617i	1.50179	+	0.867062i
$58$	9.23504	+	5.33185i	1.21262	+	0.700106i
$59$	0.130126	−	0.225385i	0.0169410	−	0.0293427i	−0.857431	−	0.514600i	$-0.827941\pi$
$59$	0.130126	−	0.225385i	0.0169410	−	0.0293427i	0.874372	+	0.485257i	$0.161274\pi$
$60$	0.785680	−	5.59210i	0.101431	−	0.721938i
$61$	−2.73975	−	4.74538i	−0.350789	−	0.607584i	0.635599	−	0.772019i	$-0.280753\pi$
$61$	−2.73975	−	4.74538i	−0.350789	−	0.607584i	−0.986388	+	0.164435i	$0.947420\pi$
$62$	5.83679	+	3.36987i	0.741273	+	0.427974i
$63$		−	7.47949i		−	0.942328i
$64$	−1.00000			−0.125000
$65$	8.35192	+	6.52468i	1.03593	+	0.809286i
$66$	−6.79060			−0.835865
$67$	−2.31068	+	1.33407i	−0.282295	+	0.162983i	−0.634462	−	0.772954i	$-0.718778\pi$
$67$	−2.31068	+	1.33407i	−0.282295	+	0.162983i	0.352167	+	0.935937i	$0.385445\pi$
$68$		−	0.688892i		−	0.0835404i
$69$	2.79605	+	4.84290i	0.336605	+	0.583017i
$70$	−1.85501	−	4.59075i	−0.221716	−	0.548700i
$71$	−4.90321	−	8.49261i	−0.581904	−	1.00789i	−0.995254	−	0.0973151i	$-0.968975\pi$
$71$	−4.90321	−	8.49261i	−0.581904	−	1.00789i	0.413349	−	0.910572i	$-0.364359\pi$
$72$	2.92525	+	1.68889i	0.344744	+	0.199038i
$73$		−	13.1175i		−	1.53529i	−0.640875	−	0.767645i	$-0.721428\pi$
$73$		−	13.1175i		−	1.53529i	0.640875	−	0.767645i	$-0.278572\pi$
$74$	−5.35482	−	2.88547i	−0.622485	−	0.335429i
$75$	−3.47949	+	12.1383i	−0.401777	+	1.40161i
$76$	−2.59210	+	4.48966i	−0.297335	+	0.514999i
$77$	−5.15637	+	2.97703i	−0.587623	+	0.339264i
$78$	−10.3662	+	5.98494i	−1.17374	+	0.677661i
$79$	−1.38493	−	2.39877i	−0.155817	−	0.269882i	0.777539	−	0.628834i	$-0.216468\pi$
$79$	−1.38493	−	2.39877i	−0.155817	−	0.269882i	−0.933356	+	0.358952i	$0.883134\pi$
$80$	2.21432	+	0.311108i	0.247568	+	0.0347829i
$81$	3.86196	+	6.68912i	0.429107	+	0.743235i
$82$		−	7.42864i		−	0.820356i
$83$	−7.67063	−	4.42864i	−0.841961	−	0.486106i	0.0159694	−	0.999872i	$-0.494917\pi$
$83$	−7.67063	−	4.42864i	−0.841961	−	0.486106i	−0.857930	+	0.513766i	$0.828250\pi$
$84$	5.59210			0.610149
$85$	−0.214320	+	1.52543i	−0.0232462	+	0.165456i
$86$	−2.95161	+	5.11233i	−0.318280	+	0.551277i
$87$	23.3224	−	13.4652i	2.50043	−	1.44362i
$88$		−	2.68889i		−	0.286637i
$89$	−0.334074	+	0.578634i	−0.0354118	+	0.0613350i	−0.883188	−	0.469019i	$-0.844608\pi$
$89$	−0.334074	+	0.578634i	−0.0354118	+	0.0613350i	0.847776	+	0.530354i	$0.177941\pi$
$90$	−5.95200	−	4.64981i	−0.627396	−	0.490133i
$91$	−5.24766	+	9.08921i	−0.550104	+	0.952808i
$92$	−1.91766	+	1.10716i	−0.199930	+	0.115429i
$93$	14.7404	−	8.51037i	1.52851	−	0.882484i
$94$	2.41827	−	4.18856i	0.249425	−	0.432017i
$95$	7.13651	−	9.13511i	0.732191	−	0.937243i
$96$	−1.26271	+	2.18708i	−0.128875	+	0.223218i
$97$			12.9906i			1.31900i	0.751705	+	0.659499i	$0.229232\pi$
$97$			12.9906i			1.31900i	−0.751705	+	0.659499i	$0.770768\pi$
$98$	−1.81587	+	1.04839i	−0.183431	+	0.105904i
$99$	−4.54125	+	7.86567i	−0.456413	+	0.790530i
$100$	−4.80642	−	1.37778i	−0.480642	−	0.137778i
$101$	−5.72546			−0.569704			−0.284852	−	0.958571i	$-0.591945\pi$
$101$	−5.72546			−0.569704			−0.284852	+	0.958571i	$0.591945\pi$
$102$	−1.50667	−	0.869874i	−0.149182	−	0.0861303i
$103$		−	6.96989i		−	0.686764i	−0.939196	−	0.343382i	$-0.888428\pi$
$103$		−	6.96989i		−	0.686764i	0.939196	−	0.343382i	$-0.111572\pi$
$104$	−2.36987	−	4.10474i	−0.232385	−	0.402503i
$105$	−12.3827	−	1.73975i	−1.20843	−	0.169782i
$106$	0.392840	+	0.680419i	0.0381560	+	0.0660881i
$107$	−14.0916	+	8.13581i	−1.36229	+	0.786519i	−0.989928	−	0.141569i	$-0.954785\pi$
$107$	−14.0916	+	8.13581i	−1.36229	+	0.786519i	−0.372362	+	0.928088i	$0.621452\pi$
$108$	0.826246	−	0.477034i	0.0795056	−	0.0459026i
$109$	2.75557	−	4.77279i	0.263936	−	0.457150i	−0.703349	−	0.710845i	$-0.748313\pi$
$109$	2.75557	−	4.77279i	0.263936	−	0.457150i	0.967284	+	0.253695i	$0.0816460\pi$
$110$	−0.836535	+	5.95407i	−0.0797605	+	0.567698i
$111$	−13.0724	+	8.06792i	−1.24077	+	0.765773i
$112$			2.21432i			0.209234i
$113$	−7.78612	−	4.49532i	−0.732456	−	0.422884i	0.0868639	−	0.996220i	$-0.472315\pi$
$113$	−7.78612	−	4.49532i	−0.732456	−	0.422884i	−0.819320	+	0.573336i	$0.805649\pi$
$114$	6.54617	+	11.3383i	0.613105	+	1.06193i
$115$	4.59075	−	1.85501i	0.428090	−	0.172980i
$116$	5.33185	+	9.23504i	0.495050	+	0.857452i
$117$			16.0098i			1.48011i
$118$	0.225385	−	0.130126i	0.0207484	−	0.0119791i
$119$	−1.52543			−0.139836
$120$	3.47647	−	4.45006i	0.317357	−	0.406233i
$121$	−3.76986			−0.342714
$122$		−	5.47949i		−	0.496090i
$123$	−16.2471	−	9.38025i	−1.46495	−	0.845788i
$124$	3.36987	+	5.83679i	0.302624	+	0.524159i
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$	3.73975	−	6.47743i	0.333163	−	0.577056i
$127$	−18.7173	−	10.8064i	−1.66089	−	0.958915i	−0.972291	−	0.233772i	$-0.924893\pi$
$127$	−18.7173	−	10.8064i	−1.66089	−	0.958915i	−0.688598	−	0.725143i	$-0.741774\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	7.45407	+	12.9108i	0.656294	+	1.13673i
$130$	3.97064	+	9.82650i	0.348248	+	0.861841i
$131$	8.42864	−	14.5988i	0.736414	−	1.27551i	−0.217687	−	0.976019i	$-0.569851\pi$
$131$	8.42864	−	14.5988i	0.736414	−	1.27551i	0.954100	−	0.299487i	$-0.0968156\pi$
$132$	−5.88083	−	3.39530i	−0.511861	−	0.295523i
$133$	9.94153	+	5.73975i	0.862040	+	0.497699i
$134$	−2.66815			−0.230493
$135$	−1.97798	+	0.799253i	−0.170238	+	0.0687888i
$136$	0.344446	−	0.596598i	0.0295360	−	0.0511579i
$137$			3.87310i			0.330901i	0.986218	+	0.165451i	$0.0529079\pi$
$137$			3.87310i			0.330901i	−0.986218	+	0.165451i	$0.947092\pi$
$138$			5.59210i			0.476032i
$139$	−3.55877	+	6.16396i	−0.301851	+	0.522821i	−0.976555	−	0.215267i	$-0.930938\pi$
$139$	−3.55877	+	6.16396i	−0.301851	+	0.522821i	0.674705	+	0.738088i	$0.264271\pi$
$140$	0.688892	−	4.90321i	0.0582220	−	0.414397i
$141$	−6.10716	−	10.5779i	−0.514316	−	0.890821i
$142$		−	9.80642i		−	0.822937i
$143$	11.0372	−	6.37233i	0.922978	−	0.532881i
$144$	1.68889	+	2.92525i	0.140741	+	0.243771i
$145$	−8.93333	−	22.1081i	−0.741873	−	1.83598i
$146$	6.55877	−	11.3601i	0.542807	−	0.940170i
$147$			5.29529i			0.436748i
$148$	−3.19467	−	5.17630i	−0.262601	−	0.425489i
$149$	20.4701			1.67698			0.838489	−	0.544918i	$-0.183439\pi$
$149$	20.4701			1.67698			0.838489	+	0.544918i	$0.183439\pi$
$150$	−9.08247	+	8.77231i	−0.741580	+	0.716256i
$151$	−6.65801	−	11.5320i	−0.541822	−	0.938462i	−0.998800	−	0.0489845i	$-0.984402\pi$
$151$	−6.65801	−	11.5320i	−0.541822	−	0.938462i	0.456978	−	0.889478i	$-0.348932\pi$
$152$	−4.48966	+	2.59210i	−0.364159	+	0.210247i
$153$	−2.01518	+	1.16346i	−0.162918	+	0.0940605i
$154$	−5.95407			−0.479792
$155$	−5.64611	−	13.9729i	−0.453506	−	1.12233i
$156$	−11.9699			−0.958358
$157$	12.6371	+	7.29605i	1.00855	+	0.582288i	0.910768	−	0.412919i	$-0.135491\pi$
$157$	12.6371	+	7.29605i	1.00855	+	0.582288i	0.0977853	+	0.995208i	$0.468824\pi$
$158$		−	2.76986i		−	0.220358i
$159$	1.98418			0.157356
$160$	1.76210	+	1.37659i	0.139306	+	0.108829i
$161$	2.45161	+	4.24631i	0.193214	+	0.334656i
$162$			7.72393i			0.606849i
$163$	−3.58385	−	2.06914i	−0.280709	−	0.162067i	0.353035	−	0.935610i	$-0.385150\pi$
$163$	−3.58385	−	2.06914i	−0.280709	−	0.162067i	−0.633744	+	0.773543i	$0.718483\pi$
$164$	3.71432	−	6.43339i	0.290040	−	0.502363i
$165$	11.9657	+	9.34786i	0.931532	+	0.727730i
$166$	−4.42864	−	7.67063i	−0.343729	−	0.595356i
$167$	8.82790	−	5.09679i	0.683123	−	0.394401i	−0.117908	−	0.993025i	$-0.537619\pi$
$167$	8.82790	−	5.09679i	0.683123	−	0.394401i	0.801031	+	0.598623i	$0.204285\pi$
$168$	4.84290	+	2.79605i	0.373638	+	0.215720i
$169$	4.73260	−	8.19711i	0.364046	−	0.630547i
$170$	−0.948320	+	1.21390i	−0.0727328	+	0.0931018i
$171$	17.5111			1.33911
$172$	−5.11233	+	2.95161i	−0.389812	+	0.225058i
$173$	8.04569	+	4.64518i	0.611703	+	0.353167i	0.773632	−	0.633636i	$-0.218438\pi$
$173$	8.04569	+	4.64518i	0.611703	+	0.353167i	−0.161929	+	0.986802i	$0.551772\pi$
$174$	26.9304			2.04159
$175$	−3.05086	+	10.6430i	−0.230623	+	0.804532i
$176$	1.34445	−	2.32865i	0.101341	−	0.175529i
$177$		−	0.657249i		−	0.0494019i
$178$	−0.578634	+	0.334074i	−0.0433704	+	0.0250399i
$179$	14.3684			1.07395			0.536973	−	0.843599i	$-0.319568\pi$
$179$	14.3684			1.07395			0.536973	+	0.843599i	$0.319568\pi$
$180$	−2.82968	−	7.00286i	−0.210912	−	0.521962i
$181$	9.79605	+	16.9673i	0.728135	+	1.26117i	0.957671	+	0.287866i	$0.0929459\pi$
$181$	9.79605	+	16.9673i	0.728135	+	1.26117i	−0.229536	+	0.973300i	$0.573721\pi$
$182$	−9.08921	+	5.24766i	−0.673737	+	0.388982i
$183$	−11.9841	−	6.91903i	−0.885891	−	0.511470i
$184$	−2.21432			−0.163242
$185$	5.46364	+	12.4559i	0.401695	+	0.915773i
$186$	17.0207			1.24802
$187$	1.60419	+	0.926178i	0.117310	+	0.0677289i
$188$	4.18856	−	2.41827i	0.305482	−	0.176370i
$189$	−1.05630	−	1.82957i	−0.0768349	−	0.133082i
$190$	10.7480	−	4.34298i	0.779739	−	0.315073i
$191$	1.60147			0.115878			0.0579392	−	0.998320i	$-0.481547\pi$
$191$	1.60147			0.115878			0.0579392	+	0.998320i	$0.481547\pi$
$192$	−2.18708	+	1.26271i	−0.157839	+	0.0911285i
$193$			23.8415i			1.71615i	0.513528	+	0.858073i	$0.328338\pi$
$193$			23.8415i			1.71615i	−0.513528	+	0.858073i	$0.671662\pi$
$194$	−6.49532	+	11.2502i	−0.466337	+	0.807719i
$195$	26.5052	+	3.72393i	1.89807	+	0.266676i
$196$	−2.09679			−0.149771
$197$	−4.71930	−	2.72469i	−0.336237	−	0.194126i	0.322370	−	0.946614i	$-0.395520\pi$
$197$	−4.71930	−	2.72469i	−0.336237	−	0.194126i	−0.658607	+	0.752488i	$0.728854\pi$
$198$	−7.86567	+	4.54125i	−0.558989	+	0.322733i
$199$	8.03011			0.569240			0.284620	−	0.958640i	$-0.408133\pi$
$199$	8.03011			0.569240			0.284620	+	0.958640i	$0.408133\pi$
$200$	−3.47359	−	3.59641i	−0.245620	−	0.254304i
$201$	−3.36911	+	5.83547i	−0.237639	+	0.411602i
$202$	−4.95839	−	2.86273i	−0.348871	−	0.201421i
$203$	20.4493	−	11.8064i	1.43526	−	0.828649i
$204$	−0.869874	−	1.50667i	−0.0609033	−	0.105488i
$205$	−10.2262	+	13.0900i	−0.714227	+	0.914247i
$206$	3.48494	−	6.03610i	0.242808	−	0.420555i
$207$	6.47743	+	3.73975i	0.450213	+	0.259930i
$208$		−	4.73975i		−	0.328642i
$209$	−6.96989	−	12.0722i	−0.482117	−	0.835052i
$210$	−9.85386	−	7.69802i	−0.679981	−	0.531214i
$211$	24.8988			1.71410			0.857051	−	0.515232i	$-0.172294\pi$
$211$	24.8988			1.71410			0.857051	+	0.515232i	$0.172294\pi$
$212$			0.785680i			0.0539607i
$213$	−21.4475	−	12.3827i	−1.46956	−	0.848449i
$214$	−16.2716			−1.11231
$215$	12.2386	−	4.94531i	0.834666	−	0.337268i
$216$	0.954067			0.0649160
$217$	12.9245	−	7.46198i	0.877374	−	0.506552i
$218$	4.77279	−	2.75557i	0.323254	−	0.186631i
$219$	−16.5637	−	28.6891i	−1.11927	−	1.93863i
$220$	−3.70149	+	4.73811i	−0.249555	+	0.319443i
$221$	3.26517			0.219639
$222$	−15.3550	+	0.450840i	−1.03056	+	0.0302584i
$223$		−	9.65233i		−	0.646368i	−0.946336	−	0.323184i	$-0.895247\pi$
$223$		−	9.65233i		−	0.646368i	0.946336	−	0.323184i	$-0.104753\pi$
$224$	−1.10716	+	1.91766i	−0.0739752	+	0.128129i
$225$	4.08717	+	16.3869i	0.272478	+	1.09246i
$226$	−4.49532	−	7.78612i	−0.299024	−	0.517925i
$227$	17.8238	−	10.2906i	1.18301	−	0.683011i	0.226301	−	0.974057i	$-0.427337\pi$
$227$	17.8238	−	10.2906i	1.18301	−	0.683011i	0.956709	+	0.291046i	$0.0940033\pi$
$228$			13.0923i			0.867062i
$229$	13.6834	+	23.7004i	0.904227	+	1.56617i	0.821951	+	0.569558i	$0.192886\pi$
$229$	13.6834	+	23.7004i	0.904227	+	1.56617i	0.0822763	+	0.996610i	$0.473781\pi$
$230$	4.90321	+	0.688892i	0.323308	+	0.0454242i
$231$	−7.51828	+	13.0220i	−0.494667	+	0.856788i
$232$			10.6637i			0.700106i
$233$		−	15.0257i		−	0.984364i	−0.870492	−	0.492182i	$-0.836199\pi$
$233$		−	15.0257i		−	0.984364i	0.870492	−	0.492182i	$-0.163801\pi$
$234$	−8.00492	+	13.8649i	−0.523298	+	0.906379i
$235$	−10.0272	+	4.05172i	−0.654100	+	0.264305i
$236$	0.260253			0.0169410
$237$	−6.05792	−	3.49754i	−0.393504	−	0.227190i
$238$	−1.32106	−	0.762714i	−0.0856315	−	0.0494394i
$239$	−2.85013	+	4.93658i	−0.184360	+	0.319321i	−0.943361	−	0.331769i	$-0.892355\pi$
$239$	−2.85013	+	4.93658i	−0.184360	+	0.319321i	0.759001	+	0.651090i	$0.225688\pi$
$240$	5.23574	−	2.11563i	0.337966	−	0.136564i
$241$	7.02074	+	12.1603i	0.452246	+	0.783313i	0.998525	−	0.0542903i	$-0.0172896\pi$
$241$	7.02074	+	12.1603i	0.452246	+	0.783313i	−0.546279	+	0.837603i	$0.683956\pi$
$242$	−3.26479	−	1.88493i	−0.209869	−	0.121168i
$243$	19.3716	+	11.1842i	1.24269	+	0.717467i
$244$	2.73975	−	4.74538i	0.175394	−	0.303792i
$245$	4.64296	+	0.652327i	0.296628	+	0.0416757i
$246$	−9.38025	−	16.2471i	−0.598063	−	1.03587i
$247$	−21.2798	−	12.2859i	−1.35400	−	0.781734i
$248$			6.73975i			0.427974i
$249$	−22.3684			−1.41754
$250$	6.57277	+	9.04426i	0.415699	+	0.572009i
$251$	−30.2034			−1.90642			−0.953211	−	0.302304i	$-0.902244\pi$
$251$	−30.2034			−1.90642			−0.953211	+	0.302304i	$0.902244\pi$
$252$	6.47743	−	3.73975i	0.408040	−	0.235582i
$253$		−	5.95407i		−	0.374329i
$254$	−10.8064	−	18.7173i	−0.678055	−	1.17443i
$255$	1.45744	+	3.60686i	0.0912686	+	0.225871i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−23.4049	−	13.5128i	−1.45996	−	0.842907i	−0.460950	−	0.887426i	$-0.652491\pi$
$257$	−23.4049	−	13.5128i	−1.45996	−	0.842907i	−0.999009	+	0.0445188i	$0.985825\pi$
$258$			14.9081i			0.928140i
$259$	−11.4620	+	7.07403i	−0.712213	+	0.439559i
$260$	−1.47457	+	10.4953i	−0.0914491	+	0.650892i
$261$	18.0098	−	31.1940i	1.11478	−	1.93086i
$262$	14.5988	−	8.42864i	0.901919	−	0.520723i
$263$	−5.38176	+	3.10716i	−0.331853	+	0.191596i	−0.656664	−	0.754184i	$-0.728033\pi$
$263$	−5.38176	+	3.10716i	−0.331853	+	0.191596i	0.324810	+	0.945779i	$0.394700\pi$
$264$	−3.39530	−	5.88083i	−0.208966	−	0.361940i
$265$	0.244431	−	1.73975i	0.0150153	−	0.106872i
$266$	5.73975	+	9.94153i	0.351926	+	0.609555i
$267$			1.68736i			0.103265i
$268$	−2.31068	−	1.33407i	−0.141148	−	0.0814916i
$269$	7.22369			0.440436			0.220218	−	0.975451i	$-0.429323\pi$
$269$	7.22369			0.440436			0.220218	+	0.975451i	$0.429323\pi$
$270$	−2.11261	−	0.296818i	−0.128569	−	0.0180638i
$271$	8.02865	−	13.9060i	0.487706	−	0.844732i	−0.512194	−	0.858870i	$-0.671167\pi$
$271$	8.02865	−	13.9060i	0.487706	−	0.844732i	0.999900	+	0.0141382i	$0.00450047\pi$
$272$	0.596598	−	0.344446i	0.0361741	−	0.0208851i
$273$			26.5052i			1.60417i
$274$	−1.93655	+	3.35420i	−0.116991	+	0.202635i
$275$	9.67035	−	9.34012i	0.583144	−	0.563230i
$276$	−2.79605	+	4.84290i	−0.168303	+	0.291509i
$277$	−11.5196	+	6.65087i	−0.692148	+	0.399612i	−0.804416	−	0.594066i	$-0.797522\pi$
$277$	−11.5196	+	6.65087i	−0.692148	+	0.399612i	0.112268	+	0.993678i	$0.464188\pi$
$278$	−6.16396	+	3.55877i	−0.369690	+	0.213441i
$279$	11.3827	−	19.7154i	0.681465	−	1.18033i
$280$	3.04820	−	3.90186i	0.182165	−	0.233181i
$281$	−7.51360	+	13.0139i	−0.448224	+	0.776346i	−0.998271	−	0.0587876i	$-0.981277\pi$
$281$	−7.51360	+	13.0139i	−0.448224	+	0.776346i	0.550047	+	0.835134i	$0.314610\pi$
$282$		−	12.2143i		−	0.727352i
$283$	−12.9232	+	7.46121i	−0.768204	+	0.443523i	−0.832234	−	0.554425i	$-0.812938\pi$
$283$	−12.9232	+	7.46121i	−0.768204	+	0.443523i	0.0640293	+	0.997948i	$0.479605\pi$
$284$	4.90321	−	8.49261i	0.290952	−	0.503944i
$285$	4.07313	−	28.9906i	0.241271	−	1.71726i
$286$	12.7447			0.753608
$287$	−14.2456	−	8.22469i	−0.840890	−	0.485488i
$288$			3.37778i			0.199038i
$289$	−8.26271	−	14.3114i	−0.486042	−	0.841849i
$290$	3.31756	−	23.6128i	0.194814	−	1.38659i
$291$	16.4035	+	28.4116i	0.961587	+	1.66552i
$292$	11.3601	−	6.55877i	0.664800	−	0.383823i
$293$	23.2292	−	13.4114i	1.35706	−	0.783500i	0.367835	−	0.929891i	$-0.380099\pi$
$293$	23.2292	−	13.4114i	1.35706	−	0.783500i	0.989227	+	0.146391i	$0.0467658\pi$
$294$	−2.64764	+	4.58585i	−0.154414	+	0.267452i
$295$	−0.576283	−	0.0809666i	−0.0335525	−	0.00471406i
$296$	−0.178520	−	6.08014i	−0.0103763	−	0.353401i
$297$			2.56538i			0.148859i
$298$	17.7276	+	10.2351i	1.02694	+	0.592901i
$299$	−5.24766	−	9.08921i	−0.303480	−	0.525643i
$300$	−12.2518	+	3.05581i	−0.707358	+	0.176427i
$301$	6.53580	+	11.3203i	0.376717	+	0.652493i
$302$		−	13.3160i		−	0.766251i
$303$	−12.5221	+	7.22961i	−0.719373	+	0.415330i
$304$	−5.18421			−0.297335
$305$	−7.54300	+	9.65544i	−0.431911	+	0.552869i
$306$	−2.32693			−0.133022
$307$			29.6494i			1.69218i	0.533039	+	0.846091i	$0.321050\pi$
$307$			29.6494i			1.69218i	−0.533039	+	0.846091i	$0.678950\pi$
$308$	−5.15637	−	2.97703i	−0.293812	−	0.169632i
$309$	−8.80097	−	15.2437i	−0.500670	−	0.867186i
$310$	2.09679	−	14.9240i	0.119090	−	0.847624i
$311$	−2.83730	+	4.91435i	−0.160889	+	0.278667i	−0.935188	−	0.354153i	$-0.884769\pi$
$311$	−2.83730	+	4.91435i	−0.160889	+	0.278667i	0.774299	+	0.632820i	$0.218103\pi$
$312$	−10.3662	−	5.98494i	−0.586872	−	0.338831i
$313$	9.80130	+	5.65878i	0.554002	+	0.319853i	0.750735	−	0.660604i	$-0.229700\pi$
$313$	9.80130	+	5.65878i	0.554002	+	0.319853i	−0.196733	+	0.980457i	$0.563033\pi$
$314$	7.29605	+	12.6371i	0.411740	+	0.713155i
$315$	−15.5066	+	6.26582i	−0.873696	+	0.353039i
$316$	1.38493	−	2.39877i	0.0779084	−	0.134941i
$317$	−1.13119	−	0.653093i	−0.0635340	−	0.0366813i	0.467897	−	0.883783i	$-0.345012\pi$
$317$	−1.13119	−	0.653093i	−0.0635340	−	0.0366813i	−0.531430	+	0.847102i	$0.678345\pi$
$318$	1.71835	+	0.992089i	0.0963602	+	0.0556336i
$319$	−28.6735			−1.60541
$320$	0.837733	+	2.07321i	0.0468307	+	0.115896i
$321$	−20.5464	+	35.5874i	−1.14679	+	1.98630i
$322$			4.90321i			0.273245i
$323$		−	3.57136i		−	0.198716i
$324$	−3.86196	+	6.68912i	−0.214553	+	0.371618i
$325$	6.53035	−	22.7812i	0.362239	−	1.26368i
$326$	−2.06914	−	3.58385i	−0.114599	−	0.198491i
$327$		−	13.9180i		−	0.769666i
$328$	6.43339	−	3.71432i	0.355225	−	0.205089i
$329$	−5.35482	−	9.27482i	−0.295221	−	0.511337i
$330$	5.68871	+	14.0784i	0.313153	+	0.774988i
$331$	5.59533	−	9.69140i	0.307547	−	0.532687i	−0.670278	−	0.742110i	$-0.733825\pi$
$331$	5.59533	−	9.69140i	0.307547	−	0.532687i	0.977825	+	0.209423i	$0.0671585\pi$
$332$		−	8.85728i		−	0.486106i
$333$	−9.74649	+	18.0874i	−0.534104	+	0.991185i
$334$	10.1936			0.557768
$335$	4.70155	+	3.67294i	0.256873	+	0.200674i
$336$	2.79605	+	4.84290i	0.152537	+	0.264202i
$337$	14.6622	−	8.46520i	0.798699	−	0.461129i	−0.0443170	−	0.999018i	$-0.514111\pi$
$337$	14.6622	−	8.46520i	0.798699	−	0.461129i	0.843016	+	0.537888i	$0.180778\pi$
$338$	8.19711	−	4.73260i	0.445864	−	0.257420i
$339$	−22.7052			−1.23318
$340$	−1.42822	+	0.577107i	−0.0774560	+	0.0312980i
$341$	−18.1225			−0.981386
$342$	15.1651	+	8.75557i	0.820034	+	0.473447i
$343$			20.1432i			1.08763i
$344$	−5.90321			−0.318280
$345$	7.69802	−	9.85386i	0.414447	−	0.530514i
$346$	4.64518	+	8.04569i	0.249727	+	0.432539i
$347$			4.51606i			0.242435i	0.992626	+	0.121217i	$0.0386798\pi$
$347$			4.51606i			0.242435i	−0.992626	+	0.121217i	$0.961320\pi$
$348$	23.3224	+	13.4652i	1.25021	+	0.721811i
$349$	12.2859	−	21.2798i	0.657650	−	1.13908i	−0.323572	−	0.946203i	$-0.604884\pi$
$349$	12.2859	−	21.2798i	0.657650	−	1.13908i	0.981222	−	0.192880i	$-0.0617828\pi$
$350$	−7.96360	+	7.69165i	−0.425672	+	0.411136i
$351$	2.26102	+	3.91620i	0.120684	+	0.209031i
$352$	2.32865	−	1.34445i	0.124117	−	0.0716592i
$353$	11.9623	+	6.90644i	0.636689	+	0.367593i	0.783338	−	0.621596i	$-0.213515\pi$
$353$	11.9623	+	6.90644i	0.636689	+	0.367593i	−0.146649	+	0.989189i	$0.546849\pi$
$354$	0.328625	−	0.569195i	0.0174662	−	0.0302524i
$355$	−13.4994	+	17.2799i	−0.716474	+	0.917124i
$356$	−0.668149			−0.0354118
$357$	−3.33624	+	1.92618i	−0.176572	+	0.101944i
$358$	12.4434	+	7.18421i	0.657655	+	0.379697i
$359$	−30.2464			−1.59635			−0.798173	−	0.602428i	$-0.794200\pi$
$359$	−30.2464			−1.59635			−0.798173	+	0.602428i	$0.794200\pi$
$360$	1.05086	−	7.47949i	0.0553849	−	0.394204i
$361$	−3.93801	+	6.82083i	−0.207264	+	0.358991i
$362$			19.5921i			1.02974i
$363$	−8.24500	+	4.76025i	−0.432750	+	0.249848i
$364$	−10.4953			−0.550104
$365$	−27.1954	+	10.9890i	−1.42347	+	0.575190i
$366$	−6.91903	−	11.9841i	−0.361664	−	0.626420i
$367$	24.6918	−	14.2558i	1.28890	−	0.744147i	0.310442	−	0.950592i	$-0.399523\pi$
$367$	24.6918	−	14.2558i	1.28890	−	0.744147i	0.978458	+	0.206445i	$0.0661895\pi$
$368$	−1.91766	−	1.10716i	−0.0999648	−	0.0577147i
$369$	−25.0923			−1.30626
$370$	−1.49628	+	13.5189i	−0.0777878	+	0.702815i
$371$	1.73975			0.0903232
$372$	14.7404	+	8.51037i	0.764254	+	0.441242i
$373$	7.41358	−	4.28023i	0.383860	−	0.221622i	−0.295636	−	0.955301i	$-0.595532\pi$
$373$	7.41358	−	4.28023i	0.383860	−	0.221622i	0.679497	+	0.733679i	$0.262198\pi$
$374$	0.926178	+	1.60419i	0.0478915	+	0.0829506i
$375$	28.0801	−	2.95490i	1.45005	−	0.152590i
$376$	4.83654			0.249425
$377$	−43.7717	+	25.2716i	−2.25436	+	1.30156i
$378$		−	2.11261i		−	0.108661i
$379$	0.411123	−	0.712085i	0.0211180	−	0.0365774i	−0.855273	−	0.518177i	$-0.826611\pi$
$379$	0.411123	−	0.712085i	0.0211180	−	0.0365774i	0.876391	+	0.481600i	$0.159944\pi$
$380$	11.4795	+	1.61285i	0.588886	+	0.0827373i
$381$	−54.5817			−2.79630
$382$	1.38692	+	0.800736i	0.0709608	+	0.0409692i
$383$	4.30405	−	2.48494i	0.219927	−	0.126975i	−0.385990	−	0.922503i	$-0.626140\pi$
$383$	4.30405	−	2.48494i	0.219927	−	0.126975i	0.605916	+	0.795528i	$0.292807\pi$
$384$	−2.52543			−0.128875
$385$	10.4917	+	8.19629i	0.534706	+	0.417722i
$386$	−11.9207	+	20.6473i	−0.606749	+	1.05092i
$387$	17.2684	+	9.96989i	0.877800	+	0.506798i
$388$	−11.2502	+	6.49532i	−0.571143	+	0.329750i
$389$	14.8272	+	25.6814i	0.751767	+	1.30210i	0.946966	+	0.321335i	$0.104132\pi$
$389$	14.8272	+	25.6814i	0.751767	+	1.30210i	−0.195198	+	0.980764i	$0.562535\pi$
$390$	21.0922	+	16.4776i	1.06804	+	0.834375i
$391$	0.762714	−	1.32106i	0.0385721	−	0.0668088i
$392$	−1.81587	−	1.04839i	−0.0917154	−	0.0529519i
$393$		−	42.5718i		−	2.14747i
$394$	−2.72469	−	4.71930i	−0.137268	−	0.237755i
$395$	−3.81295	+	4.88078i	−0.191850	+	0.245579i
$396$	−9.08250			−0.456413
$397$			4.38424i			0.220039i	0.993929	+	0.110019i	$0.0350913\pi$
$397$			4.38424i			0.220039i	−0.993929	+	0.110019i	$0.964909\pi$
$398$	6.95428	+	4.01506i	0.348587	+	0.201257i
$399$	28.9906			1.45135
$400$	−1.21002	−	4.85138i	−0.0605008	−	0.242569i
$401$	31.5067			1.57337			0.786685	−	0.617355i	$-0.211796\pi$
$401$	31.5067			1.57337			0.786685	+	0.617355i	$0.211796\pi$
$402$	−5.83547	+	3.36911i	−0.291047	+	0.168036i
$403$	−27.6649	+	15.9723i	−1.37809	+	0.795639i
$404$	−2.86273	−	4.95839i	−0.142426	−	0.246689i
$405$	10.6327	−	13.6104i	0.528341	−	0.676304i
$406$	23.6128			1.17189
$407$	16.3488	−	0.480022i	0.810382	−	0.0237938i
$408$		−	1.73975i		−	0.0861303i
$409$	−5.88271	+	10.1891i	−0.290881	+	0.503821i	−0.974018	−	0.226469i	$-0.927282\pi$
$409$	−5.88271	+	10.1891i	−0.290881	+	0.503821i	0.683137	+	0.730290i	$0.260615\pi$
$410$	−15.4011	+	6.22321i	−0.760608	+	0.307343i
$411$	4.89062	+	8.47080i	0.241236	+	0.417834i
$412$	6.03610	−	3.48494i	0.297377	−	0.171691i
$413$		−	0.576283i		−	0.0283570i
$414$	3.73975	+	6.47743i	0.183799	+	0.318348i
$415$	−2.75557	+	19.6128i	−0.135266	+	0.962757i
$416$	2.36987	−	4.10474i	0.116193	−	0.201252i
$417$			17.9748i			0.880230i
$418$		−	13.9398i		−	0.681817i
$419$	−5.96666	+	10.3346i	−0.291490	+	0.504876i	−0.974162	−	0.225849i	$-0.927485\pi$
$419$	−5.96666	+	10.3346i	−0.291490	+	0.504876i	0.682672	+	0.730725i	$0.260818\pi$
$420$	−4.68469	−	11.5936i	−0.228589	−	0.565710i
$421$	−17.3985			−0.847952			−0.423976	−	0.905673i	$-0.639366\pi$
$421$	−17.3985			−0.847952			−0.423976	+	0.905673i	$0.639366\pi$
$422$	21.5630	+	12.4494i	1.04967	+	0.606026i
$423$	−14.1481	−	8.16839i	−0.687902	−	0.397161i
$424$	−0.392840	+	0.680419i	−0.0190780	+	0.0330441i
$425$	3.34208	−	0.833570i	0.162114	−	0.0404341i
$426$	−12.3827	−	21.4475i	−0.599944	−	1.03913i
$427$	−10.5078	−	6.06668i	−0.508508	−	0.293587i
$428$	−14.0916	−	8.13581i	−0.681145	−	0.393259i
$429$	16.0929	−	27.8737i	0.776971	−	1.34575i
$430$	13.0716	+	1.83654i	0.630368	+	0.0885656i
$431$	−15.9849	−	27.6867i	−0.769968	−	1.33362i	−0.937580	−	0.347770i	$-0.886939\pi$
$431$	−15.9849	−	27.6867i	−0.769968	−	1.33362i	0.167612	−	0.985853i	$-0.446394\pi$
$432$	0.826246	+	0.477034i	0.0397528	+	0.0229513i
$433$			3.24443i			0.155917i	0.996957	+	0.0779587i	$0.0248402\pi$
$433$			3.24443i			0.155917i	−0.996957	+	0.0779587i	$0.975160\pi$
$434$	14.9240			0.716373
$435$	−47.4542	−	37.0721i	−2.27525	−	1.77747i
$436$	5.51114			0.263936
$437$	−9.94153	+	5.73975i	−0.475568	+	0.274569i
$438$		−	33.1274i		−	1.58289i
$439$	6.67161	+	11.5556i	0.318419	+	0.551517i	0.980158	−	0.198216i	$-0.0635149\pi$
$439$	6.67161	+	11.5556i	0.318419	+	0.551517i	−0.661740	+	0.749734i	$0.730182\pi$
$440$	−5.57464	+	2.25257i	−0.265761	+	0.107387i
$441$	3.54125	+	6.13362i	0.168631	+	0.292077i
$442$	2.82772	+	1.63259i	0.134501	+	0.0776543i
$443$			10.1526i			0.482363i	0.970480	+	0.241181i	$0.0775349\pi$
$443$			10.1526i			0.482363i	−0.970480	+	0.241181i	$0.922465\pi$
$444$	−13.5232	−	7.28704i	−0.641783	−	0.345828i
$445$	1.47949	+	0.207866i	0.0701348	+	0.00985381i
$446$	4.82616	−	8.35916i	0.228525	−	0.395818i
$447$	44.7699	−	25.8479i	2.11754	−	1.22256i
$448$	−1.91766	+	1.10716i	−0.0906008	+	0.0523084i
$449$	−8.46121	−	14.6552i	−0.399309	−	0.691624i	0.594332	−	0.804220i	$-0.297417\pi$
$449$	−8.46121	−	14.6552i	−0.399309	−	0.691624i	−0.993641	+	0.112596i	$0.964083\pi$
$450$	−4.65386	+	16.2351i	−0.219385	+	0.765328i
$451$	9.98741	+	17.2987i	0.470289	+	0.814564i
$452$		−	8.99063i		−	0.422884i
$453$	−29.1233	−	16.8143i	−1.36833	−	0.790006i
$454$	20.5812			0.965924
$455$	23.2400	+	3.26517i	1.08951	+	0.153074i
$456$	−6.54617	+	11.3383i	−0.306553	+	0.530965i
$457$	−12.5674	+	7.25581i	−0.587879	+	0.339412i	−0.764259	−	0.644910i	$-0.776895\pi$
$457$	−12.5674	+	7.25581i	−0.587879	+	0.339412i	0.176379	+	0.984322i	$0.443562\pi$
$458$			27.3669i			1.27877i
$459$	−0.328625	+	0.569195i	−0.0153389	+	0.0265677i
$460$	3.90186	+	3.04820i	0.181925	+	0.142123i
$461$	11.3620	−	19.6795i	0.529179	−	0.916566i	−0.470242	−	0.882538i	$-0.655833\pi$
$461$	11.3620	−	19.6795i	0.529179	−	0.916566i	0.999421	−	0.0340278i	$-0.0108335\pi$
$462$	−13.0220	+	7.51828i	−0.605840	+	0.349782i
$463$	−3.52743	+	2.03657i	−0.163934	+	0.0946472i	−0.579722	−	0.814814i	$-0.696839\pi$
$463$	−3.52743	+	2.03657i	−0.163934	+	0.0946472i	0.415789	+	0.909461i	$0.363506\pi$
$464$	−5.33185	+	9.23504i	−0.247525	+	0.428726i
$465$	−29.9923	−	23.4305i	−1.39086	−	1.08657i
$466$	7.51283	−	13.0126i	0.348025	−	0.602797i
$467$			17.3412i			0.802456i	0.915978	+	0.401228i	$0.131416\pi$
$467$			17.3412i			0.802456i	−0.915978	+	0.401228i	$0.868584\pi$
$468$	−13.8649	+	8.00492i	−0.640907	+	0.370028i
$469$	−2.95407	+	5.11659i	−0.136406	+	0.236262i
$470$	−10.7096	−	1.50468i	−0.493999	−	0.0694059i
$471$	36.8513			1.69802
$472$	0.225385	+	0.130126i	0.0103742	+	0.00598955i
$473$		−	15.8731i		−	0.729846i
$474$	−3.49754	−	6.05792i	−0.160647	−	0.278249i
$475$	−24.9175	−	7.14272i	−1.14329	−	0.327731i
$476$	−0.762714	−	1.32106i	−0.0349589	−	0.0605506i
$477$	2.29831	−	1.32693i	0.105232	−	0.0607559i
$478$	−4.93658	+	2.85013i	−0.225794	+	0.130362i
$479$	−13.2294	+	22.9140i	−0.604466	+	1.04697i	0.387670	+	0.921798i	$0.373280\pi$
$479$	−13.2294	+	22.9140i	−0.604466	+	1.04697i	−0.992136	+	0.125167i	$0.960053\pi$
$480$	5.59210	+	0.785680i	0.255243	+	0.0358612i
$481$	24.5343	−	15.1419i	1.11867	−	0.690413i
$482$			14.0415i			0.639572i
$483$	10.7237	+	6.19135i	0.487947	+	0.281716i
$484$	−1.88493	−	3.26479i	−0.0856786	−	0.148400i
$485$	26.9323	−	10.8827i	1.22293	−	0.494157i
$486$	11.1842	+	19.3716i	0.507326	+	0.878714i
$487$			11.3047i			0.512263i	0.966642	+	0.256131i	$0.0824480\pi$
$487$			11.3047i			0.512263i	−0.966642	+	0.256131i	$0.917552\pi$
$488$	4.74538	−	2.73975i	0.214813	−	0.124023i
$489$	−10.4509			−0.472607
$490$	3.69476	+	2.88641i	0.166912	+	0.130395i
$491$	−16.0765			−0.725523			−0.362762	−	0.931882i	$-0.618166\pi$
$491$	−16.0765			−0.725523			−0.362762	+	0.931882i	$0.618166\pi$
$492$		−	18.7605i		−	0.845788i
$493$	−6.36195	−	3.67307i	−0.286528	−	0.165427i
$494$	−12.2859	−	21.2798i	−0.552770	−	0.957425i
$495$	20.1116	+	2.82564i	0.903947	+	0.127003i
$496$	−3.36987	+	5.83679i	−0.151312	+	0.262080i
$497$	−18.8054	−	10.8573i	−0.843536	−	0.487016i
$498$	−19.3716	−	11.1842i	−0.868063	−	0.501176i
$499$	−9.47457	−	16.4104i	−0.424140	−	0.734632i	0.572200	−	0.820114i	$-0.306090\pi$
$499$	−9.47457	−	16.4104i	−0.424140	−	0.734632i	−0.996340	+	0.0854822i	$0.972757\pi$
$500$	1.17006	+	11.1189i	0.0523267	+	0.497254i
$501$	12.8716	−	22.2942i	0.575059	−	0.996032i
$502$	−26.1569	−	15.1017i	−1.16744	−	0.674022i
$503$	−8.88179	−	5.12790i	−0.396019	−	0.228642i	0.288746	−	0.957406i	$-0.406762\pi$
$503$	−8.88179	−	5.12790i	−0.396019	−	0.228642i	−0.684765	+	0.728764i	$0.740095\pi$
$504$	7.47949			0.333163
$505$	4.79640	+	11.8701i	0.213437	+	0.528212i
$506$	2.97703	−	5.15637i	0.132345	−	0.229229i
$507$		−	23.9037i		−	1.06160i
$508$		−	21.6128i		−	0.958915i
$509$	1.32148	−	2.28887i	0.0585736	−	0.101452i	−0.835252	−	0.549868i	$-0.814678\pi$
$509$	1.32148	−	2.28887i	0.0585736	−	0.101452i	0.893825	+	0.448415i	$0.148011\pi$
$510$	−0.541249	+	3.85236i	−0.0239669	+	0.170585i
$511$	−14.5232	−	25.1549i	−0.642469	−	1.11279i
$512$		−	1.00000i		−	0.0441942i
$513$	4.28343	−	2.47304i	0.189118	−	0.109187i
$514$	−13.5128	−	23.4049i	−0.596026	−	1.03235i
$515$	−14.4500	+	5.83890i	−0.636745	+	0.257293i
$516$	−7.45407	+	12.9108i	−0.328147	+	0.568367i
$517$			13.0049i			0.571956i
$518$	−13.4634	+	0.395301i	−0.591547	+	0.0173685i
$519$	23.4621			1.02987
$520$	−6.52468	+	8.35192i	−0.286126	+	0.366256i
$521$	2.44692	+	4.23819i	0.107202	+	0.185679i	0.914636	−	0.404279i	$-0.132478\pi$
$521$	2.44692	+	4.23819i	0.107202	+	0.185679i	−0.807434	+	0.589958i	$0.799144\pi$
$522$	31.1940	−	18.0098i	1.36532	−	0.788269i
$523$	−24.8316	+	14.3365i	−1.08581	+	0.626893i	−0.932458	−	0.361279i	$-0.882340\pi$
$523$	−24.8316	+	14.3365i	−1.08581	+	0.626893i	−0.153352	+	0.988172i	$0.549007\pi$
$524$	16.8573			0.736414
$525$	6.76653	+	27.1294i	0.295316	+	1.18402i
$526$	−6.21432			−0.270957
$527$	−4.02092	−	2.32148i	−0.175154	−	0.101125i
$528$		−	6.79060i		−	0.295523i
$529$	18.0968			0.786817
$530$	1.08156	−	1.38445i	0.0469798	−	0.0601367i
$531$	−0.439539	−	0.761303i	−0.0190744	−	0.0330378i
$532$			11.4795i			0.497699i
$533$	30.4926	+	17.6049i	1.32078	+	0.762554i
$534$	−0.843680	+	1.46130i	−0.0365096	+	0.0632365i
$535$	28.6723	+	22.3993i	1.23961	+	0.968407i
$536$	−1.33407	−	2.31068i	−0.0576232	−	0.0998064i
$537$	31.4249	−	18.1432i	1.35609	−	0.782937i
$538$	6.25590	+	3.61184i	0.269711	+	0.155718i
$539$	2.81902	−	4.88268i	0.121424	−	0.210312i
$540$	−1.68116	−	1.31336i	−0.0723458	−	0.0565179i
$541$	4.82564			0.207470			0.103735	−	0.994605i	$-0.466921\pi$
$541$	4.82564			0.207470			0.103735	+	0.994605i	$0.466921\pi$
$542$	13.9060	−	8.02865i	0.597315	−	0.344860i
$543$	42.8496	+	24.7392i	1.83885	+	1.06166i
$544$	0.688892			0.0295360
$545$	−12.2034	−	1.71456i	−0.522737	−	0.0734436i
$546$	−13.2526	+	22.9541i	−0.567158	+	0.982347i
$547$		−	2.47949i		−	0.106016i	−0.998594	−	0.0530078i	$-0.983119\pi$
$547$		−	2.47949i		−	0.106016i	0.998594	−	0.0530078i	$-0.0168808\pi$
$548$	−3.35420	+	1.93655i	−0.143284	+	0.0827253i
$549$	−18.5086			−0.789926
$550$	13.0448	−	3.25360i	0.556233	−	0.138734i
$551$	27.6414	+	47.8764i	1.17756	+	2.03960i
$552$	−4.84290	+	2.79605i	−0.206128	+	0.119008i
$553$	−5.31164	−	3.06668i	−0.225874	−	0.130408i
$554$	−13.3017			−0.565137
$555$	27.6776	+	20.3430i	1.17485	+	0.863513i
$556$	−7.11753			−0.301851
$557$	−10.6741	−	6.16270i	−0.452276	−	0.261122i	0.256515	−	0.966540i	$-0.417426\pi$
$557$	−10.6741	−	6.16270i	−0.452276	−	0.261122i	−0.708791	+	0.705418i	$0.750759\pi$
$558$	19.7154	−	11.3827i	0.834621	−	0.481868i
$559$	−13.9899	−	24.2312i	−0.591708	−	1.02487i
$560$	4.59075	−	1.85501i	0.193995	−	0.0783884i
$561$	4.67799			0.197505
$562$	−13.0139	+	7.51360i	−0.548960	+	0.316942i
$563$		−	14.6178i		−	0.616066i	−0.951376	−	0.308033i	$-0.900329\pi$
$563$		−	14.6178i		−	0.616066i	0.951376	−	0.308033i	$-0.0996706\pi$
$564$	6.10716	−	10.5779i	0.257158	−	0.445410i
$565$	−2.79706	+	19.9081i	−0.117673	+	0.837541i
$566$	−14.9224			−0.627236
$567$	14.8118	+	8.55162i	0.622039	+	0.359134i
$568$	8.49261	−	4.90321i	0.356342	−	0.205734i
$569$	12.1111			0.507723			0.253861	−	0.967241i	$-0.418299\pi$
$569$	12.1111			0.507723			0.253861	+	0.967241i	$0.418299\pi$
$570$	18.0228	−	23.0701i	0.754890	−	0.966298i
$571$	−7.32540	+	12.6880i	−0.306558	+	0.530975i	−0.977607	−	0.210439i	$-0.932511\pi$
$571$	−7.32540	+	12.6880i	−0.306558	+	0.530975i	0.671049	+	0.741413i	$0.265844\pi$
$572$	11.0372	+	6.37233i	0.461489	+	0.266441i
$573$	3.50255	−	2.02220i	0.146321	−	0.0844787i
$574$	−8.22469	−	14.2456i	−0.343292	−	0.594599i
$575$	−7.69165	−	7.96360i	−0.320764	−	0.332105i
$576$	−1.68889	+	2.92525i	−0.0703705	+	0.121885i
$577$	8.94632	+	5.16516i	0.372440	+	0.215028i	0.674524	−	0.738253i	$-0.264349\pi$
$577$	8.94632	+	5.16516i	0.372440	+	0.215028i	−0.302084	+	0.953281i	$0.597682\pi$
$578$		−	16.5254i		−	0.687367i
$579$	30.1049	+	52.1433i	1.25112	+	2.16700i
$580$	14.6795	−	18.7905i	0.609534	−	0.780235i
$581$	−19.6128			−0.813678
$582$			32.8069i			1.35989i
$583$	−1.82957	−	1.05630i	−0.0757732	−	0.0437477i
$584$	13.1175			0.542807
$585$	33.1918	−	13.4120i	1.37231	−	0.554517i
$586$	26.8227			1.10804
$587$	33.1566	−	19.1430i	1.36852	−	0.790114i	0.377780	−	0.925896i	$-0.376688\pi$
$587$	33.1566	−	19.1430i	1.36852	−	0.790114i	0.990739	+	0.135781i	$0.0433544\pi$
$588$	−4.58585	+	2.64764i	−0.189117	+	0.109187i
$589$	17.4701	+	30.2591i	0.719844	+	1.24681i
$590$	−0.458592	−	0.358261i	−0.0188799	−	0.0147494i
$591$	−13.7620			−0.566094
$592$	2.88547	−	5.35482i	0.118592	−	0.220082i
$593$		−	42.0894i		−	1.72841i	−0.503144	−	0.864203i	$-0.667823\pi$
$593$		−	42.0894i		−	1.72841i	0.503144	−	0.864203i	$-0.332177\pi$
$594$	−1.28269	+	2.22169i	−0.0526295	+	0.0911569i
$595$	1.27790	+	3.16253i	0.0523888	+	0.129651i
$596$	10.2351	+	17.7276i	0.419245	+	0.726153i
$597$	17.5625	−	10.1397i	0.718787	−	0.414992i
$598$		−	10.4953i		−	0.429185i
$599$	−7.50815	−	13.0045i	−0.306775	−	0.531349i	0.670880	−	0.741566i	$-0.265916\pi$
$599$	−7.50815	−	13.0045i	−0.306775	−	0.531349i	−0.977655	+	0.210216i	$0.932583\pi$
$600$	−12.1383	−	3.47949i	−0.495543	−	0.142050i
$601$	21.9472	−	38.0136i	0.895243	−	1.55061i	0.0617402	−	0.998092i	$-0.480335\pi$
$601$	21.9472	−	38.0136i	0.895243	−	1.55061i	0.833503	−	0.552515i	$-0.186332\pi$
$602$			13.0716i			0.532759i
$603$			9.01243i			0.367015i
$604$	6.65801	−	11.5320i	0.270911	−	0.469231i
$605$	3.15813	+	7.81571i	0.128396	+	0.317754i
$606$	−14.4592			−0.587366
$607$	−22.4551	−	12.9644i	−0.911423	−	0.526210i	−0.0305343	−	0.999534i	$-0.509721\pi$
$607$	−22.4551	−	12.9644i	−0.911423	−	0.526210i	−0.880889	+	0.473323i	$0.843054\pi$
$608$	−4.48966	−	2.59210i	−0.182080	−	0.105124i
$609$	29.8163	−	51.6433i	1.20822	−	2.09269i
$610$	−11.3601	+	4.59035i	−0.459959	+	0.185858i
$611$	11.4620	+	19.8527i	0.463702	+	0.803155i
$612$	−2.01518	−	1.16346i	−0.0814588	−	0.0470303i
$613$	−23.6055	−	13.6287i	−0.953419	−	0.550457i	−0.0592777	−	0.998242i	$-0.518880\pi$
$613$	−23.6055	−	13.6287i	−0.953419	−	0.550457i	−0.894141	+	0.447785i	$0.852213\pi$
$614$	−14.8247	+	25.6771i	−0.598276	+	1.03625i
$615$	−5.83654	+	41.5417i	−0.235352	+	1.67512i
$616$	−2.97703	−	5.15637i	−0.119948	−	0.207756i
$617$	26.0252	+	15.0257i	1.04774	+	0.604911i	0.922015	−	0.387155i	$-0.126542\pi$
$617$	26.0252	+	15.0257i	1.04774	+	0.604911i	0.125721	+	0.992066i	$0.459876\pi$
$618$		−	17.6019i		−	0.708054i
$619$	−14.3872			−0.578268			−0.289134	−	0.957289i	$-0.593367\pi$
$619$	−14.3872			−0.578268			−0.289134	+	0.957289i	$0.593367\pi$
$620$	9.27785	−	11.8761i	0.372607	−	0.476957i
$621$	2.11261			0.0847761
$622$	−4.91435	+	2.83730i	−0.197047	+	0.113765i
$623$			1.47949i			0.0592747i
$624$	−5.98494	−	10.3662i	−0.239590	−	0.414981i
$625$	0.868304	−	24.9849i	0.0347321	−	0.999397i
$626$	5.65878	+	9.80130i	0.226170	+	0.391739i
$627$	−30.4875	−	17.6019i	−1.21755	−	0.702954i
$628$			14.5921i			0.582288i
$629$	3.68889	+	1.98778i	0.147086	+	0.0792578i
$630$	−16.5620	−	2.32693i	−0.659846	−	0.0927071i
$631$	15.6192	−	27.0533i	0.621792	−	1.07697i	−0.367360	−	0.930079i	$-0.619738\pi$
$631$	15.6192	−	27.0533i	0.621792	−	1.07697i	0.989152	−	0.146896i	$-0.0469283\pi$
$632$	2.39877	−	1.38493i	0.0954179	−	0.0550895i
$633$	54.4557	−	31.4400i	2.16442	−	1.24963i
$634$	−0.653093	−	1.13119i	−0.0259376	−	0.0449253i
$635$	−6.72393	+	47.8578i	−0.266831	+	1.89918i
$636$	0.992089	+	1.71835i	0.0393389	+	0.0681370i
$637$		−	9.93825i		−	0.393768i
$638$	−24.8320	−	14.3368i	−0.983109	−	0.567598i
$639$	−33.1240			−1.31036
$640$	−0.311108	+	2.21432i	−0.0122976	+	0.0875287i
$641$	−4.52789	+	7.84253i	−0.178841	+	0.309761i	−0.941484	−	0.337058i	$-0.890568\pi$
$641$	−4.52789	+	7.84253i	−0.178841	+	0.309761i	0.762643	+	0.646820i	$0.223901\pi$
$642$	−35.5874	+	20.5464i	−1.40452	+	0.810902i
$643$			22.1842i			0.874860i	0.899253	+	0.437430i	$0.144111\pi$
$643$			22.1842i			0.874860i	−0.899253	+	0.437430i	$0.855889\pi$
$644$	−2.45161	+	4.24631i	−0.0966068	+	0.167328i
$645$	20.5223	−	26.2697i	0.808067	−	1.03437i
$646$	1.78568	−	3.09289i	0.0702567	−	0.121688i
$647$	−12.9711	+	7.48886i	−0.509946	+	0.294418i	−0.732812	−	0.680432i	$-0.761792\pi$
$647$	−12.9711	+	7.48886i	−0.509946	+	0.294418i	0.222865	+	0.974849i	$0.428459\pi$
$648$	−6.68912	+	3.86196i	−0.262773	+	0.151712i
$649$	−0.349896	+	0.606037i	−0.0137346	+	0.0237890i
$650$	17.0461	−	16.4640i	0.668602	−	0.645769i
$651$	18.8447	−	32.6400i	0.738581	−	1.27926i
$652$		−	4.13828i		−	0.162067i
$653$	−21.3333	+	12.3168i	−0.834837	+	0.481993i	−0.855506	−	0.517793i	$-0.826754\pi$
$653$	−21.3333	+	12.3168i	−0.834837	+	0.481993i	0.0206688	+	0.999786i	$0.493420\pi$
$654$	6.95899	−	12.0533i	0.272118	−	0.471322i
$655$	−37.3274	−	5.24443i	−1.45850	−	0.204917i
$656$	7.42864			0.290040
$657$	−38.3720	−	22.1541i	−1.49704	−	0.864314i
$658$		−	10.7096i		−	0.417505i
$659$	12.9240	+	22.3849i	0.503446	+	0.871994i	0.999992	+	0.00398348i	$0.00126798\pi$
$659$	12.9240	+	22.3849i	0.503446	+	0.871994i	−0.496546	+	0.868010i	$0.665399\pi$
$660$	−2.11261	+	15.0366i	−0.0822332	+	0.585297i
$661$	−6.47558	−	11.2160i	−0.251871	−	0.436253i	0.712170	−	0.702007i	$-0.247712\pi$
$661$	−6.47558	−	11.2160i	−0.251871	−	0.436253i	−0.964041	+	0.265754i	$0.914379\pi$
$662$	9.69140	−	5.59533i	0.376667	−	0.217469i
$663$	7.14121	−	4.12298i	0.277342	−	0.160123i
$664$	4.42864	−	7.67063i	0.171865	−	0.297678i
$665$	3.57136	−	25.4193i	0.138491	−	0.985717i
$666$	−17.4844	+	10.7909i	−0.677507	+	0.418140i
$667$			23.6128i			0.914293i
$668$	8.82790	+	5.09679i	0.341562	+	0.197201i
$669$	−12.1881	−	21.1105i	−0.471220	−	0.816177i
$670$	2.23520	+	5.53164i	0.0863531	+	0.213706i
$671$	7.36689	+	12.7598i	0.284395	+	0.492587i
$672$			5.59210i			0.215720i
$673$	−28.5848	+	16.5035i	−1.10186	+	0.636162i	−0.936710	−	0.350106i	$-0.886146\pi$
$673$	−28.5848	+	16.5035i	−1.10186	+	0.636162i	−0.165154	+	0.986268i	$0.552812\pi$
$674$	16.9304			0.652135
$675$	3.31404	+	3.43121i	0.127557	+	0.132068i
$676$	9.46520			0.364046
$677$		−	4.71408i		−	0.181177i	−0.995888	−	0.0905884i	$-0.971125\pi$
$677$		−	4.71408i		−	0.181177i	0.995888	−	0.0905884i	$-0.0288748\pi$
$678$	−19.6633	−	11.3526i	−0.755163	−	0.435994i
$679$	14.3827	+	24.9116i	0.551958	+	0.956019i
$680$	−1.52543	−	0.214320i	−0.0584975	−	0.00821879i
$681$	25.9882	−	45.0128i	0.995869	−	1.72490i
$682$	−15.6945	−	9.06123i	−0.600974	−	0.346972i
$683$	27.4536	+	15.8504i	1.05048	+	0.606498i	0.922785	−	0.385315i	$-0.125907\pi$
$683$	27.4536	+	15.8504i	1.05048	+	0.606498i	0.127700	+	0.991813i	$0.459241\pi$
$684$	8.75557	+	15.1651i	0.334778	+	0.579852i
$685$	8.02975	−	3.24462i	0.306801	−	0.123971i
$686$	−10.0716	+	17.4445i	−0.384535	+	0.666035i
$687$	59.8537	+	34.5565i	2.28356	+	1.31841i
$688$	−5.11233	−	2.95161i	−0.194906	−	0.112529i
$689$	−3.72393			−0.141870
$690$	11.5936	−	4.68469i	0.441361	−	0.178343i
$691$	15.3400	−	26.5697i	0.583561	−	1.01076i	−0.411492	−	0.911413i	$-0.634992\pi$
$691$	15.3400	−	26.5697i	0.583561	−	1.01076i	0.995053	−	0.0993441i	$-0.0316745\pi$
$692$			9.29036i			0.353167i
$693$			20.1116i			0.763975i
$694$	−2.25803	+	3.91102i	−0.0857136	+	0.148460i
$695$	15.7605	+	2.21432i	0.597829	+	0.0839939i
$696$	13.4652	+	23.3224i	0.510397	+	0.884034i
$697$			5.11753i			0.193840i
$698$	21.2798	−	12.2859i	0.805454	−	0.465029i
$699$	−18.9731	−	32.8624i	−0.717629	−	1.24297i
$700$	−10.7425	+	2.67936i	−0.406028	+	0.101270i
$701$	−9.77631	+	16.9331i	−0.369246	+	0.639553i	−0.989448	−	0.144889i	$-0.953717\pi$
$701$	−9.77631	+	16.9331i	−0.369246	+	0.639553i	0.620202	+	0.784442i	$0.287051\pi$
$702$			4.52204i			0.170673i
$703$	−16.5619	−	26.8350i	−0.624642	−	1.01210i
$704$	2.68889			0.101341
$705$	−16.8141	+	21.5229i	−0.633255	+	0.810599i
$706$	6.90644	+	11.9623i	0.259927	+	0.450207i
$707$	−10.9795	+	6.33900i	−0.412925	+	0.238402i
$708$	0.569195	−	0.328625i	0.0213916	−	0.0123505i
$709$	−40.6766			−1.52764			−0.763821	−	0.645428i	$-0.776679\pi$
$709$	−40.6766			−1.52764			−0.763821	+	0.645428i	$0.776679\pi$
$710$	−20.3308	+	8.21516i	−0.763001	+	0.308309i
$711$	−9.35599			−0.350877
$712$	−0.578634	−	0.334074i	−0.0216852	−	0.0125200i
$713$			14.9240i			0.558907i
$714$	−3.85236			−0.144171
$715$	−22.4574	−	17.5441i	−0.839860	−	0.656114i
$716$	7.18421	+	12.4434i	0.268486	+	0.465032i
$717$			14.3956i			0.537614i
$718$	−26.1942	−	15.1232i	−0.977558	−	0.564394i
$719$	−10.6072	+	18.3721i	−0.395580	+	0.685165i	−0.993175	−	0.116633i	$-0.962790\pi$
$719$	−10.6072	+	18.3721i	−0.395580	+	0.685165i	0.597595	+	0.801798i	$0.296123\pi$
$720$	4.64981	−	5.95200i	0.173288	−	0.221818i
$721$	−7.71678	−	13.3659i	−0.287388	−	0.497771i
$722$	−6.82083	+	3.93801i	−0.253845	+	0.146557i
$723$	30.7099	+	17.7304i	1.14211	+	0.659400i
$724$	−9.79605	+	16.9673i	−0.364067	+	0.630583i
$725$	−38.3510	+	37.0414i	−1.42432	+	1.37568i
$726$	−9.52051			−0.353339
$727$	16.1795	−	9.34122i	0.600063	−	0.346447i	−0.169003	−	0.985615i	$-0.554055\pi$
$727$	16.1795	−	9.34122i	0.600063	−	0.346447i	0.769066	+	0.639169i	$0.220722\pi$
$728$	−9.08921	−	5.24766i	−0.336869	−	0.194491i
$729$	33.3180			1.23400
$730$	−29.0464	−	4.08097i	−1.07506	−	0.151043i
$731$	2.03334	−	3.52185i	0.0752057	−	0.130260i
$732$		−	13.8381i		−	0.511470i
$733$	43.5245	−	25.1289i	1.60762	−	0.928157i	0.617714	−	0.786403i	$-0.288059\pi$
$733$	43.5245	−	25.1289i	1.60762	−	0.928157i	0.989902	−	0.141754i	$-0.0452743\pi$
$734$	28.5116			1.05238
$735$	10.9782	−	4.43603i	0.404939	−	0.163626i
$736$	−1.10716	−	1.91766i	−0.0408105	−	0.0706858i
$737$	6.21318	−	3.58718i	0.228865	−	0.132136i
$738$	−21.7306	−	12.5462i	−0.799915	−	0.461831i
$739$	−14.1970			−0.522244			−0.261122	−	0.965306i	$-0.584092\pi$
$739$	−14.1970			−0.522244			−0.261122	+	0.965306i	$0.584092\pi$
$740$	−8.05527	+	10.9596i	−0.296118	+	0.402882i
$741$	−62.0544			−2.27963
$742$	1.50667	+	0.869874i	0.0553114	+	0.0319341i
$743$	12.9481	−	7.47558i	0.475019	−	0.274252i	−0.243319	−	0.969946i	$-0.578236\pi$
$743$	12.9481	−	7.47558i	0.475019	−	0.274252i	0.718338	+	0.695694i	$0.244903\pi$
$744$	8.51037	+	14.7404i	0.312005	+	0.540409i
$745$	−17.1485	−	42.4389i	−0.628272	−	1.55484i
$746$	8.56046			0.313421
$747$	−25.9097	+	14.9590i	−0.947987	+	0.547321i
$748$			1.85236i			0.0677289i
$749$	−18.0153	+	31.2034i	−0.658265	+	1.14015i
$750$	25.7955	+	11.4810i	0.941919	+	0.419228i
$751$	38.7482			1.41394			0.706971	−	0.707242i	$-0.250061\pi$
$751$	38.7482			1.41394			0.706971	+	0.707242i	$0.250061\pi$
$752$	4.18856	+	2.41827i	0.152741	+	0.0881851i
$753$	−66.0574	+	38.1383i	−2.40727	+	1.38984i
$754$	−50.5433			−1.84068
$755$	−18.3307	+	23.4642i	−0.667122	+	0.853950i
$756$	1.05630	−	1.82957i	0.0384174	−	0.0665409i
$757$	13.8624	+	8.00346i	0.503838	+	0.290891i	0.730297	−	0.683130i	$-0.239382\pi$
$757$	13.8624	+	8.00346i	0.503838	+	0.290891i	−0.226459	+	0.974021i	$0.572715\pi$
$758$	0.712085	−	0.411123i	0.0258641	−	0.0149326i
$759$	−7.51828	−	13.0220i	−0.272896	−	0.472670i
$760$	9.13511	+	7.13651i	0.331365	+	0.258869i
$761$	−23.2931	+	40.3448i	−0.844373	+	1.46250i	0.0417918	+	0.999126i	$0.486693\pi$
$761$	−23.2931	+	40.3448i	−0.844373	+	1.46250i	−0.886165	+	0.463370i	$0.846640\pi$
$762$	−47.2691	−	27.2908i	−1.71238	−	0.988643i
$763$		−	12.2034i		−	0.441793i
$764$	0.800736	+	1.38692i	0.0289696	+	0.0501768i
$765$	4.10029	+	3.20322i	0.148246	+	0.115813i
$766$	4.96989			0.179569
$767$			1.23353i			0.0445403i
$768$	−2.18708	−	1.26271i	−0.0789196	−	0.0455643i
$769$	−2.69979			−0.0973570			−0.0486785	−	0.998814i	$-0.515501\pi$
$769$	−2.69979			−0.0973570			−0.0486785	+	0.998814i	$0.515501\pi$
$770$	4.98792	+	12.3440i	0.179752	+	0.444848i
$771$	−68.2514			−2.45801
$772$	−20.6473	+	11.9207i	−0.743113	+	0.429036i
$773$	−38.1273	+	22.0128i	−1.37135	+	0.791747i	−0.991097	−	0.133138i	$-0.957495\pi$
$773$	−38.1273	+	22.0128i	−1.37135	+	0.791747i	−0.380248	+	0.924885i	$0.624161\pi$
$774$	9.96989	+	17.2684i	0.358360	+	0.620698i
$775$	−24.2389	+	23.4111i	−0.870686	+	0.840953i
$776$	−12.9906			−0.466337
$777$	−16.1358	+	29.9447i	−0.578870	+	1.07426i
$778$			29.6543i			1.06316i
$779$	19.2558	−	33.3520i	0.689911	−	1.19496i
$780$	10.0276	+	24.8161i	0.359044	+	0.888559i
$781$	13.1842	+	22.8357i	0.471768	+	0.817126i
$782$	1.32106	−	0.762714i	0.0472410	−	0.0272746i
$783$		−	10.1739i		−	0.363585i
$784$	−1.04839	−	1.81587i	−0.0374426	−	0.0648526i
$785$	4.53972	−	32.3116i	0.162029	−	1.15325i
$786$	21.2859	−	36.8683i	0.759244	−	1.31505i
$787$		−	18.1097i		−	0.645541i	−0.946477	−	0.322770i	$-0.895386\pi$
$787$		−	18.1097i		−	0.645541i	0.946477	−	0.322770i	$-0.104614\pi$
$788$		−	5.44938i		−	0.194126i
$789$	−7.84691	+	13.5912i	−0.279357	+	0.483861i
$790$	−5.74250	+	2.32040i	−0.204309	+	0.0825562i
$791$	−19.9081			−0.707852
$792$	−7.86567	−	4.54125i	−0.279495	−	0.161366i
$793$	22.4919	+	12.9857i	0.798711	+	0.461136i
$794$	−2.19212	+	3.79686i	−0.0777954	+	0.134746i
$795$	−1.66221	−	4.11362i	−0.0589526	−	0.145895i
$796$	4.01506	+	6.95428i	0.142310	+	0.246488i
$797$	−18.9743	−	10.9548i	−0.672105	−	0.388040i	0.124769	−	0.992186i	$-0.460181\pi$
$797$	−18.9743	−	10.9548i	−0.672105	−	0.388040i	−0.796874	+	0.604146i	$0.793514\pi$
$798$	25.1066	+	14.4953i	0.888765	+	0.513129i
$799$	−1.66593	+	2.88547i	−0.0589362	+	0.102081i
$800$	1.37778	−	4.80642i	0.0487120	−	0.169933i
$801$	1.12843	+	1.95450i	0.0398711	+	0.0690589i
$802$	27.2856	+	15.7533i	0.963488	+	0.556270i
$803$			35.2716i			1.24471i
$804$	−6.73822			−0.237639
$805$	6.74970	−	8.63997i	0.237896	−	0.304519i
$806$	−31.9447			−1.12520
$807$	15.7988	−	9.12145i	0.556145	−	0.321090i
$808$		−	5.72546i		−	0.201421i
$809$	9.72077	+	16.8369i	0.341764	+	0.591953i	0.984760	−	0.173916i	$-0.0556423\pi$
$809$	9.72077	+	16.8369i	0.341764	+	0.591953i	−0.642996	+	0.765869i	$0.722309\pi$
$810$	16.0133	−	6.47058i	0.562651	−	0.227353i
$811$	−20.8113	−	36.0463i	−0.730785	−	1.26576i	−0.956548	−	0.291575i	$-0.905821\pi$
$811$	−20.8113	−	36.0463i	−0.730785	−	1.26576i	0.225763	−	0.974182i	$-0.427513\pi$
$812$	20.4493	+	11.8064i	0.717631	+	0.414324i
$813$		−	40.5516i		−	1.42221i
$814$	14.3985	+	7.75871i	0.504668	+	0.271943i
$815$	−1.28745	+	9.16346i	−0.0450974	+	0.320982i
$816$	0.869874	−	1.50667i	0.0304517	−	0.0527438i
$817$	−26.5034	+	15.3017i	−0.927236	+	0.535340i
$818$	−10.1891	+	5.88271i	−0.356255	+	0.205684i
$819$	17.7255	+	30.7014i	0.619378	+	1.07279i
$820$	−16.4494	−	2.31111i	−0.574437	−	0.0807074i
$821$	−19.9813	−	34.6086i	−0.697351	−	1.20785i	−0.969382	−	0.245559i	$-0.921029\pi$
$821$	−19.9813	−	34.6086i	−0.697351	−	1.20785i	0.272031	−	0.962289i	$-0.412305\pi$
$822$			9.78123i			0.341160i
$823$	−7.16596	−	4.13727i	−0.249790	−	0.144216i	0.369878	−	0.929080i	$-0.379399\pi$
$823$	−7.16596	−	4.13727i	−0.249790	−	0.144216i	−0.619668	+	0.784864i	$0.712733\pi$
$824$	6.96989			0.242808
$825$	9.35599	−	32.6385i	0.325734	−	1.13633i
$826$	0.288141	−	0.499075i	0.0100257	−	0.0173651i
$827$	24.1294	−	13.9311i	0.839061	−	0.484432i	−0.0178842	−	0.999840i	$-0.505693\pi$
$827$	24.1294	−	13.9311i	0.839061	−	0.484432i	0.856945	+	0.515408i	$0.172360\pi$
$828$			7.47949i			0.259930i
$829$	−20.3422	+	35.2338i	−0.706515	+	1.22372i	0.259628	+	0.965709i	$0.416400\pi$
$829$	−20.3422	+	35.2338i	−0.706515	+	1.22372i	−0.966142	+	0.258010i	$0.916933\pi$
$830$	−12.1928	+	15.6074i	−0.423219	+	0.541742i
$831$	−16.7963	+	29.0920i	−0.582657	+	1.00919i
$832$	4.10474	−	2.36987i	0.142306	−	0.0821606i
$833$	1.25094	−	0.722230i	0.0433425	−	0.0250238i
$834$	−8.98741	+	15.5666i	−0.311208	+	0.539029i
$835$	−17.9621	−	14.0323i	−0.621605	−	0.485609i
$836$	6.96989	−	12.0722i	0.241059	−	0.417526i
$837$		−	6.43017i		−	0.222259i
$838$	−10.3346	+	5.96666i	−0.357001	+	0.206115i
$839$	12.6208	−	21.8598i	0.435717	−	0.754684i	−0.561637	−	0.827384i	$-0.689828\pi$
$839$	12.6208	−	21.8598i	0.435717	−	0.754684i	0.997354	+	0.0726999i	$0.0231615\pi$
$840$	1.73975	−	12.3827i	0.0600270	−	0.427244i
$841$	84.7146			2.92119
$842$	−15.0676	−	8.69926i	−0.519263	−	0.299796i
$843$			37.9501i			1.30707i
$844$	12.4494	+	21.5630i	0.428525	+	0.742228i
$845$	−20.9590	−	2.94470i	−0.721011	−	0.101301i
$846$	−8.16839	−	14.1481i	−0.280835	−	0.486420i
$847$	−7.22930	+	4.17384i	−0.248402	+	0.143415i
$848$	−0.680419	+	0.392840i	−0.0233657	+	0.0134902i
$849$	−18.8428	+	32.6366i	−0.646682	+	1.12009i
$850$	3.31111	+	0.949145i	0.113570	+	0.0325554i
$851$	−0.395301	−	13.4634i	−0.0135508	−	0.461519i
$852$		−	24.7654i		−	0.848449i
$853$	46.7949	+	27.0171i	1.60223	+	0.925047i	0.991041	+	0.133560i	$0.0426410\pi$
$853$	46.7949	+	27.0171i	1.60223	+	0.925047i	0.611187	+	0.791486i	$0.290692\pi$
$854$	−6.06668	−	10.5078i	−0.207597	−	0.359569i
$855$	−14.6697	−	36.3043i	−0.501691	−	1.24158i
$856$	−8.13581	−	14.0916i	−0.278076	−	0.481642i
$857$			34.8004i			1.18876i	0.804184	+	0.594380i	$0.202603\pi$
$857$			34.8004i			1.18876i	−0.804184	+	0.594380i	$0.797397\pi$
$858$	27.8737	−	16.0929i	0.951591	−	0.549402i
$859$	44.4701			1.51730			0.758651	−	0.651498i	$-0.225859\pi$
$859$	44.4701			1.51730			0.758651	+	0.651498i	$0.225859\pi$
$860$	10.4021	+	8.12629i	0.354708	+	0.277104i
$861$	−41.5417			−1.41574
$862$		−	31.9699i		−	1.08890i
$863$	9.05887	+	5.23014i	0.308368	+	0.178036i	0.646196	−	0.763172i	$-0.276359\pi$
$863$	9.05887	+	5.23014i	0.308368	+	0.178036i	−0.337828	+	0.941208i	$0.609692\pi$
$864$	0.477034	+	0.826246i	0.0162290	+	0.0281095i
$865$	2.89030	−	20.5718i	0.0982733	−	0.699463i
$866$	−1.62222	+	2.80976i	−0.0551251	+	0.0954795i
$867$	−36.1425	−	20.8669i	−1.22746	−	0.708677i
$868$	12.9245	+	7.46198i	0.438687	+	0.253276i
$869$	3.72393	+	6.45003i	0.126326	+	0.218802i
$870$	−22.5605	−	55.8324i	−0.764872	−	1.89290i
$871$	6.32318	−	10.9521i	0.214253	−	0.371096i
$872$	4.77279	+	2.75557i	0.161627	+	0.0933153i
$873$	38.0008	+	21.9398i	1.28613	+	0.742549i
$874$	−11.4795			−0.388300
$875$	24.6209	−	2.59089i	0.832338	−	0.0875880i
$876$	16.5637	−	28.6891i	0.559635	−	0.969317i
$877$		−	52.7768i		−	1.78215i	−0.453860	−	0.891073i	$-0.649954\pi$
$877$		−	52.7768i		−	1.78215i	0.453860	−	0.891073i	$-0.350046\pi$
$878$			13.3432i			0.450312i
$879$	33.8694	−	58.6636i	1.14239	−	1.97867i
$880$	−5.95407	−	0.836535i	−0.200712	−	0.0281996i
$881$	14.1820	+	24.5639i	0.477803	+	0.827579i	0.999676	−	0.0254437i	$-0.00809986\pi$
$881$	14.1820	+	24.5639i	0.477803	+	0.827579i	−0.521873	+	0.853023i	$0.674767\pi$
$882$			7.08250i			0.238480i
$883$	−15.2698	+	8.81603i	−0.513870	+	0.296683i	−0.734423	−	0.678692i	$-0.762547\pi$
$883$	−15.2698	+	8.81603i	−0.513870	+	0.296683i	0.220553	+	0.975375i	$0.429214\pi$
$884$	1.63259	+	2.82772i	0.0549099	+	0.0951067i
$885$	−1.36262	+	0.550599i	−0.0458039	+	0.0185082i
$886$	−5.07628	+	8.79238i	−0.170541	+	0.295386i
$887$			3.76494i			0.126414i	0.998000	+	0.0632071i	$0.0201329\pi$
$887$			3.76494i			0.126414i	−0.998000	+	0.0632071i	$0.979867\pi$
$888$	−8.06792	−	13.0724i	−0.270742	−	0.438680i
$889$	−47.8578			−1.60510
$890$	1.17735	+	0.919765i	0.0394648	+	0.0308306i
$891$	−10.3844	−	17.9863i	−0.347891	−	0.602564i
$892$	8.35916	−	4.82616i	0.279885	−	0.161592i
$893$	21.7144	−	12.5368i	0.726644	−	0.419528i
$894$	51.6958			1.72897
$895$	−12.0369	−	29.7888i	−0.402349	−	0.995728i
$896$	−2.21432			−0.0739752
$897$	−22.9541	−	13.2526i	−0.766417	−	0.442491i
$898$		−	16.9224i		−	0.564709i
$899$	71.8707			2.39702
$900$	−12.1479	+	11.7330i	−0.404930	+	0.391102i
$901$	−0.270624	−	0.468735i	−0.00901581	−	0.0156158i
$902$			19.9748i			0.665088i
$903$	28.5887	+	16.5057i	0.951372	+	0.549275i
$904$	4.49532	−	7.78612i	0.149512	−	0.258962i
$905$	26.9702	−	34.5233i	0.896521	−	1.14759i
$906$	−16.8143	−	29.1233i	−0.558619	−	0.967556i
$907$	3.01718	−	1.74197i	0.100184	−	0.0578412i	−0.449071	−	0.893496i	$-0.648245\pi$
$907$	3.01718	−	1.74197i	0.100184	−	0.0578412i	0.549255	+	0.835655i	$0.314912\pi$
$908$	17.8238	+	10.2906i	0.591505	+	0.341506i
$909$	−9.66968	+	16.7484i	−0.320723	+	0.555509i
$910$	18.4938	+	14.4477i	0.613065	+	0.478937i
$911$	−51.3946			−1.70278			−0.851389	−	0.524535i	$-0.824239\pi$
$911$	−51.3946			−1.70278			−0.851389	+	0.524535i	$0.824239\pi$
$912$	−11.3383	+	6.54617i	−0.375449	+	0.216765i
$913$	20.6255	+	11.9081i	0.682604	+	0.394102i
$914$	−14.5116			−0.480002
$915$	−4.30513	+	30.6419i	−0.142323	+	1.01299i
$916$	−13.6834	+	23.7004i	−0.452114	+	0.783084i
$917$		−	37.3274i		−	1.23266i
$918$	−0.569195	+	0.328625i	−0.0187862	+	0.0108462i
$919$	23.0923			0.761746			0.380873	−	0.924627i	$-0.375623\pi$
$919$	23.0923			0.761746			0.380873	+	0.924627i	$0.375623\pi$
$920$	1.85501	+	4.59075i	0.0611578	+	0.151353i
$921$	37.4387	+	64.8458i	1.23365	+	2.13674i
$922$	19.6795	−	11.3620i	0.648110	−	0.374186i
$923$	40.2528	+	23.2400i	1.32494	+	0.764953i
$924$	−15.0366			−0.494667
$925$	21.2466	−	21.7620i	0.698583	−	0.715529i
$926$	−4.07313			−0.133851
$927$	−20.3886	−	11.7714i	−0.669651	−	0.386623i
$928$	−9.23504	+	5.33185i	−0.303155	+	0.175027i
$929$	−3.70787	−	6.42221i	−0.121651	−	0.210706i	0.798768	−	0.601639i	$-0.205486\pi$
$929$	−3.70787	−	6.42221i	−0.121651	−	0.210706i	−0.920419	+	0.390933i	$0.872152\pi$
$930$	−14.2588	−	35.2876i	−0.467566	−	1.15713i
$931$	−10.8702			−0.356256
$932$	13.0126	−	7.51283i	0.426242	−	0.246091i
$933$			14.3308i			0.469169i
$934$	−8.67061	+	15.0179i	−0.283711	+	0.491402i
$935$	0.576283	−	4.10171i	0.0188465	−	0.134140i
$936$	−16.0098			−0.523298
$937$	−7.26349	−	4.19358i	−0.237288	−	0.136998i	0.376642	−	0.926359i	$-0.377079\pi$
$937$	−7.26349	−	4.19358i	−0.237288	−	0.136998i	−0.613930	+	0.789361i	$0.710412\pi$
$938$	−5.11659	+	2.95407i	−0.167063	+	0.0964537i
$939$	28.5817			0.932728
$940$	−8.52247	−	6.65791i	−0.277972	−	0.217157i
$941$	−22.7042	+	39.3248i	−0.740135	+	1.28195i	0.212298	+	0.977205i	$0.431905\pi$
$941$	−22.7042	+	39.3248i	−0.740135	+	1.28195i	−0.952433	+	0.304747i	$0.901428\pi$
$942$	31.9142	+	18.4257i	1.03982	+	0.600340i
$943$	14.2456	−	8.22469i	0.463900	−	0.267833i
$944$	0.130126	+	0.225385i	0.00423525	+	0.00733567i
$945$	−2.90819	+	3.72264i	−0.0946035	+	0.121097i
$946$	7.93655	−	13.7465i	0.258040	−	0.446938i
$947$	−6.03358	−	3.48349i	−0.196065	−	0.113198i	0.398754	−	0.917058i	$-0.369443\pi$
$947$	−6.03358	−	3.48349i	−0.196065	−	0.113198i	−0.594819	+	0.803860i	$0.702776\pi$
$948$		−	6.99508i		−	0.227190i
$949$	31.0869	+	53.8441i	1.00912	+	1.74785i
$950$	−18.0078	−	18.6445i	−0.584251	−	0.604908i
$951$	−3.29868			−0.106967
$952$		−	1.52543i		−	0.0494394i
$953$	−23.5973	−	13.6239i	−0.764392	−	0.441322i	0.0664786	−	0.997788i	$-0.478824\pi$
$953$	−23.5973	−	13.6239i	−0.764392	−	0.441322i	−0.830870	+	0.556466i	$0.812157\pi$
$954$	2.65386			0.0859218
$955$	−1.34161	−	3.32019i	−0.0434133	−	0.107439i
$956$	−5.70027			−0.184360
$957$	−62.7115	+	36.2065i	−2.02717	+	1.17039i
$958$	−22.9140	+	13.2294i	−0.740316	+	0.427422i
$959$	4.28814	+	7.42728i	0.138471	+	0.239839i
$960$	4.45006	+	3.47647i	0.143625	+	0.112203i
$961$	14.4242			0.465297
$962$	28.8183	−	0.846142i	0.929141	−	0.0272807i
$963$			54.9621i			1.77113i
$964$	−7.02074	+	12.1603i	−0.226123	+	0.391656i
$965$	49.4284	−	19.9728i	1.59116	−	0.642946i
$966$	6.19135	+	10.7237i	0.199204	+	0.345031i
$967$	48.1544	−	27.8020i	1.54854	−	0.894051i	0.550289	−	0.834974i	$-0.314518\pi$
$967$	48.1544	−	27.8020i	1.54854	−	0.894051i	0.998253	−	0.0590770i	$-0.0188158\pi$
$968$		−	3.76986i		−	0.121168i
$969$	−4.50961	−	7.81087i	−0.144869	−	0.250921i
$970$	28.7654	+	4.04149i	0.923602	+	0.129764i
$971$	−4.10647	+	7.11261i	−0.131783	+	0.228255i	−0.924364	−	0.381512i	$-0.875403\pi$
$971$	−4.10647	+	7.11261i	−0.131783	+	0.228255i	0.792581	+	0.609767i	$0.208737\pi$
$972$			22.3684i			0.717467i
$973$			15.7605i			0.505258i
$974$	−5.65233	+	9.79012i	−0.181112	+	0.313696i
$975$	−14.4838	−	58.0704i	−0.463851	−	1.85974i
$976$	5.47949			0.175394
$977$	0.159116	+	0.0918659i	0.00509059	+	0.00293905i	0.502543	−	0.864552i	$-0.332398\pi$
$977$	0.159116	+	0.0918659i	0.00509059	+	0.00293905i	−0.497453	+	0.867491i	$0.665731\pi$
$978$	−9.05076	−	5.22546i	−0.289411	−	0.167092i
$979$	0.898290	−	1.55588i	0.0287095	−	0.0497263i
$980$	1.75655	+	4.34708i	0.0561109	+	0.138863i
$981$	−9.30772	−	16.1214i	−0.297173	−	0.514718i
$982$	−13.9227	−	8.03826i	−0.444290	−	0.256511i
$983$	−5.43565	−	3.13828i	−0.173370	−	0.100095i	0.410804	−	0.911724i	$-0.365248\pi$
$983$	−5.43565	−	3.13828i	−0.173370	−	0.100095i	−0.584174	+	0.811628i	$0.698581\pi$
$984$	9.38025	−	16.2471i	0.299031	−	0.517937i
$985$	−1.69535	+	12.0667i	−0.0540182	+	0.384476i
$986$	−3.67307	−	6.36195i	−0.116974	−	0.202606i
$987$	−23.4229	−	13.5232i	−0.745558	−	0.430448i
$988$		−	24.5718i		−	0.781734i
$989$	−13.0716			−0.415653
$990$	16.0043	+	12.5028i	0.508650	+	0.397367i
$991$	9.27010			0.294474			0.147237	−	0.989101i	$-0.452962\pi$
$991$	9.27010			0.294474			0.147237	+	0.989101i	$0.452962\pi$
$992$	−5.83679	+	3.36987i	−0.185318	+	0.106994i
$993$		−	28.2612i		−	0.896842i
$994$	−10.8573	−	18.8054i	−0.344372	−	0.596470i
$995$	−6.72709	−	16.6481i	−0.213263	−	0.527781i
$996$	−11.1842	−	19.3716i	−0.354385	−	0.613813i
$997$	26.2737	+	15.1692i	0.832098	+	0.480412i	0.854570	−	0.519336i	$-0.173821\pi$
$997$	26.2737	+	15.1692i	0.832098	+	0.480412i	−0.0224726	+	0.999747i	$0.507154\pi$
$998$		−	18.9491i		−	0.599825i
$999$	0.170320	+	5.80086i	0.00538870	+	0.183531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.f.269.6	yes	12
5.4	even	2	inner	370.2.n.f.269.1	✓	12
37.26	even	3	inner	370.2.n.f.359.1	yes	12
185.174	even	6	inner	370.2.n.f.359.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.f.269.1	✓	12	5.4	even	2	inner
370.2.n.f.269.6	yes	12	1.1	even	1	trivial
370.2.n.f.359.1	yes	12	37.26	even	3	inner
370.2.n.f.359.6	yes	12	185.174	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(2.18708 - 1.26271i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +2.52543 q^{6} +(1.91766 - 1.10716i) q^{7} +1.00000i q^{8} +(1.68889 - 2.92525i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(2.18708 - 1.26271i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.837733 - 2.07321i) q^{5} +2.52543 q^{6} +(1.91766 - 1.10716i) q^{7} +1.00000i q^{8} +(1.68889 - 2.92525i) q^{9} +(0.311108 - 2.21432i) q^{10} -2.68889 q^{11} +(2.18708 + 1.26271i) q^{12} +(-4.10474 + 2.36987i) q^{13} +2.21432 q^{14} +(-4.45006 - 3.47647i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.596598 - 0.344446i) q^{17} +(2.92525 - 1.68889i) q^{18} +(2.59210 + 4.48966i) q^{19} +(1.37659 - 1.76210i) q^{20} +(2.79605 - 4.84290i) q^{21} +(-2.32865 - 1.34445i) q^{22} +2.21432i q^{23} +(1.26271 + 2.18708i) q^{24} +(-3.59641 + 3.47359i) q^{25} -4.73975 q^{26} -0.954067i q^{27} +(1.91766 + 1.10716i) q^{28} +10.6637 q^{29} +(-2.11563 - 5.23574i) q^{30} +6.73975 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.88083 + 3.39530i) q^{33} +(-0.344446 - 0.596598i) q^{34} +(-3.90186 - 3.04820i) q^{35} +3.37778 q^{36} +(-6.08014 + 0.178520i) q^{37} +5.18421i q^{38} +(-5.98494 + 10.3662i) q^{39} +(2.07321 - 0.837733i) q^{40} +(-3.71432 - 6.43339i) q^{41} +(4.84290 - 2.79605i) q^{42} +5.90321i q^{43} +(-1.34445 - 2.32865i) q^{44} +(-7.47949 - 1.05086i) q^{45} +(-1.10716 + 1.91766i) q^{46} -4.83654i q^{47} +2.52543i q^{48} +(-1.04839 + 1.81587i) q^{49} +(-4.85138 + 1.21002i) q^{50} -1.73975 q^{51} +(-4.10474 - 2.36987i) q^{52} +(0.680419 + 0.392840i) q^{53} +(0.477034 - 0.826246i) q^{54} +(2.25257 + 5.57464i) q^{55} +(1.10716 + 1.91766i) q^{56} +(11.3383 + 6.54617i) q^{57} +(9.23504 + 5.33185i) q^{58} +(0.130126 - 0.225385i) q^{59} +(0.785680 - 5.59210i) q^{60} +(-2.73975 - 4.74538i) q^{61} +(5.83679 + 3.36987i) q^{62} -7.47949i q^{63} -1.00000 q^{64} +(8.35192 + 6.52468i) q^{65} -6.79060 q^{66} +(-2.31068 + 1.33407i) q^{67} -0.688892i q^{68} +(2.79605 + 4.84290i) q^{69} +(-1.85501 - 4.59075i) q^{70} +(-4.90321 - 8.49261i) q^{71} +(2.92525 + 1.68889i) q^{72} -13.1175i q^{73} +(-5.35482 - 2.88547i) q^{74} +(-3.47949 + 12.1383i) q^{75} +(-2.59210 + 4.48966i) q^{76} +(-5.15637 + 2.97703i) q^{77} +(-10.3662 + 5.98494i) q^{78} +(-1.38493 - 2.39877i) q^{79} +(2.21432 + 0.311108i) q^{80} +(3.86196 + 6.68912i) q^{81} -7.42864i q^{82} +(-7.67063 - 4.42864i) q^{83} +5.59210 q^{84} +(-0.214320 + 1.52543i) q^{85} +(-2.95161 + 5.11233i) q^{86} +(23.3224 - 13.4652i) q^{87} -2.68889i q^{88} +(-0.334074 + 0.578634i) q^{89} +(-5.95200 - 4.64981i) q^{90} +(-5.24766 + 9.08921i) q^{91} +(-1.91766 + 1.10716i) q^{92} +(14.7404 - 8.51037i) q^{93} +(2.41827 - 4.18856i) q^{94} +(7.13651 - 9.13511i) q^{95} +(-1.26271 + 2.18708i) q^{96} +12.9906i q^{97} +(-1.81587 + 1.04839i) q^{98} +(-4.54125 + 7.86567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9	\( 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9} + 4 q^{10} - 32 q^{11} + 18 q^{15} - 6 q^{16} + 4 q^{19} + 20 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 32 q^{29} - 20 q^{30} + 28 q^{31} - 4 q^{34} + 4 q^{35} + 40 q^{36} - 58 q^{39} + 2 q^{40} - 18 q^{41} - 16 q^{44} + 16 q^{45} - 26 q^{49} - 8 q^{50} + 32 q^{51} - 34 q^{54} - 4 q^{55} + 28 q^{59} + 36 q^{60} + 20 q^{61} - 12 q^{64} - 22 q^{65} + 24 q^{66} + 20 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{74} + 64 q^{75} - 4 q^{76} - 4 q^{79} - 6 q^{81} + 40 q^{84} + 24 q^{85} - 22 q^{86} - 44 q^{89} - 20 q^{90} - 36 q^{91} + 16 q^{94} + 16 q^{95} - 2 q^{96} - 80 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9 + 4 * q^10 - 32 * q^11 + 18 * q^15 - 6 * q^16 + 4 * q^19 + 20 * q^21 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 32 * q^29 - 20 * q^30 + 28 * q^31 - 4 * q^34 + 4 * q^35 + 40 * q^36 - 58 * q^39 + 2 * q^40 - 18 * q^41 - 16 * q^44 + 16 * q^45 - 26 * q^49 - 8 * q^50 + 32 * q^51 - 34 * q^54 - 4 * q^55 + 28 * q^59 + 36 * q^60 + 20 * q^61 - 12 * q^64 - 22 * q^65 + 24 * q^66 + 20 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^74 + 64 * q^75 - 4 * q^76 - 4 * q^79 - 6 * q^81 + 40 * q^84 + 24 * q^85 - 22 * q^86 - 44 * q^89 - 20 * q^90 - 36 * q^91 + 16 * q^94 + 16 * q^95 - 2 * q^96 - 80 * q^99

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