LMFDB - Embedded newform 370.2.n.f.359.1

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			359.1
Root			$1.98293 - 0.531325i$ of defining polynomial
Character	$\chi$	$=$	370.359
Dual form			370.2.n.f.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-2.18708 - 1.26271i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.37659 + 1.76210i) q^{5} +2.52543 q^{6} +(-1.91766 - 1.10716i) q^{7} +1.00000i q^{8} +(1.68889 + 2.92525i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.18708 - 1.26271i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.37659 + 1.76210i) 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} +(5.23574 - 2.11563i) 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} +(0.837733 + 2.07321i) q^{20} +(2.79605 + 4.84290i) q^{21} +(2.32865 - 1.34445i) q^{22} +2.21432i q^{23} +(1.26271 - 2.18708i) q^{24} +(-1.21002 - 4.85138i) q^{25} -4.73975 q^{26} -0.954067i q^{27} +(-1.91766 + 1.10716i) q^{28} +10.6637 q^{29} +(-3.47647 + 4.45006i) q^{30} +6.73975 q^{31} +(0.866025 + 0.500000i) q^{32} +(5.88083 + 3.39530i) q^{33} +(-0.344446 + 0.596598i) q^{34} +(4.59075 - 1.85501i) q^{35} +3.37778 q^{36} +(6.08014 + 0.178520i) q^{37} +5.18421i q^{38} +(-5.98494 - 10.3662i) q^{39} +(-1.76210 - 1.37659i) 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} +(3.47359 + 3.59641i) q^{50} -1.73975 q^{51} +(4.10474 - 2.36987i) q^{52} +(-0.680419 + 0.392840i) q^{53} +(0.477034 + 0.826246i) q^{54} +(3.70149 - 4.73811i) 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} +(-9.82650 + 3.97064i) q^{65} -6.79060 q^{66} +(2.31068 + 1.33407i) q^{67} -0.688892i q^{68} +(2.79605 - 4.84290i) q^{69} +(-3.04820 + 3.90186i) 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} +(7.00286 - 2.82968i) 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} +(4.34298 + 10.7480i) 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

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	$-0.593361\pi$
$3$	−2.18708	−	1.26271i	−1.26271	−	0.729028i	−0.973599	+	0.228266i	$0.926694\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.37659	+	1.76210i	−0.615628	+	0.788037i
$5$	−1.37659	+	1.76210i	−0.615628	+	0.788037i
$6$	2.52543			1.03100
$7$	−1.91766	−	1.10716i	−0.724806	−	0.418467i	0.0917128	−	0.995785i	$-0.470766\pi$
$7$	−1.91766	−	1.10716i	−0.724806	−	0.418467i	−0.816519	+	0.577318i	$0.804099\pi$
$8$			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	$-0.105038\pi$
$13$	4.10474	+	2.36987i	1.13845	+	0.657285i	0.192404	+	0.981316i	$0.438372\pi$
$14$	2.21432			0.591802
$15$	5.23574	−	2.11563i	1.35186	−	0.546254i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.596598	−	0.344446i	0.144696	−	0.0835404i	−0.425904	−	0.904768i	$-0.640044\pi$
$17$	0.596598	−	0.344446i	0.144696	−	0.0835404i	0.570600	+	0.821228i	$0.306711\pi$
$18$	−2.92525	−	1.68889i	−0.689487	−	0.398076i
$19$	2.59210	−	4.48966i	0.594669	−	1.03000i	−0.398924	−	0.916984i	$-0.630616\pi$
$19$	2.59210	−	4.48966i	0.594669	−	1.03000i	0.993593	−	0.113014i	$-0.0360504\pi$
$20$	0.837733	+	2.07321i	0.187323	+	0.463584i
$21$	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
$25$	−1.21002	−	4.85138i	−0.242003	−	0.970275i
$26$	−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	$0.0448273\pi$
$30$	−3.47647	+	4.45006i	−0.634714	+	0.812467i
$31$	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
$35$	4.59075	−	1.85501i	0.775979	−	0.313554i
$36$	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
$40$	−1.76210	−	1.37659i	−0.278613	−	0.217658i
$41$	−3.71432	+	6.43339i	−0.580079	+	1.00473i	0.415390	+	0.909643i	$0.363645\pi$
$41$	−3.71432	+	6.43339i	−0.580079	+	1.00473i	−0.995469	+	0.0950834i	$0.969688\pi$
$42$	−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
$50$	3.47359	+	3.59641i	0.491240	+	0.508609i
$51$	−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	$-0.683851\pi$
$53$	−0.680419	+	0.392840i	−0.0934627	+	0.0539607i	0.452540	+	0.891744i	$0.350518\pi$
$54$	0.477034	+	0.826246i	0.0649160	+	0.112438i
$55$	3.70149	−	4.73811i	0.499109	−	0.638886i
$56$	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	0.874372	−	0.485257i	$-0.161274\pi$
$59$	0.130126	+	0.225385i	0.0169410	+	0.0293427i	−0.857431	+	0.514600i	$0.827941\pi$
$60$	0.785680	−	5.59210i	0.101431	−	0.721938i
$61$	−2.73975	+	4.74538i	−0.350789	+	0.607584i	−0.986388	−	0.164435i	$-0.947420\pi$
$61$	−2.73975	+	4.74538i	−0.350789	+	0.607584i	0.635599	+	0.772019i	$0.280753\pi$
$62$	−5.83679	+	3.36987i	−0.741273	+	0.427974i
$63$		−	7.47949i		−	0.942328i
$64$	−1.00000			−0.125000
$65$	−9.82650	+	3.97064i	−1.21883	+	0.492497i
$66$	−6.79060			−0.835865
$67$	2.31068	+	1.33407i	0.282295	+	0.162983i	0.634462	−	0.772954i	$-0.281222\pi$
$67$	2.31068	+	1.33407i	0.282295	+	0.162983i	−0.352167	+	0.935937i	$0.614555\pi$
$68$		−	0.688892i		−	0.0835404i
$69$	2.79605	−	4.84290i	0.336605	−	0.583017i
$70$	−3.04820	+	3.90186i	−0.364330	+	0.466361i
$71$	−4.90321	+	8.49261i	−0.581904	+	1.00789i	0.413349	+	0.910572i	$0.364359\pi$
$71$	−4.90321	+	8.49261i	−0.581904	+	1.00789i	−0.995254	+	0.0973151i	$0.968975\pi$
$72$	−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	−0.933356	−	0.358952i	$-0.883134\pi$
$79$	−1.38493	+	2.39877i	−0.155817	+	0.269882i	0.777539	+	0.628834i	$0.216468\pi$
$80$	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	$-0.505083\pi$
$83$	7.67063	−	4.42864i	0.841961	−	0.486106i	0.857930	+	0.513766i	$0.171750\pi$
$84$	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	0.847776	−	0.530354i	$-0.177941\pi$
$89$	−0.334074	−	0.578634i	−0.0354118	−	0.0613350i	−0.883188	+	0.469019i	$0.844608\pi$
$90$	7.00286	−	2.82968i	0.738166	−	0.298274i
$91$	−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
$95$	4.34298	+	10.7480i	0.445580	+	1.10272i
$96$	−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	$-0.0452146\pi$
$107$	14.0916	+	8.13581i	1.36229	+	0.786519i	0.372362	+	0.928088i	$0.378548\pi$
$108$	−0.826246	−	0.477034i	−0.0795056	−	0.0459026i
$109$	2.75557	+	4.77279i	0.263936	+	0.457150i	0.967284	−	0.253695i	$-0.0816460\pi$
$109$	2.75557	+	4.77279i	0.263936	+	0.457150i	−0.703349	+	0.710845i	$0.748313\pi$
$110$	−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	$-0.527685\pi$
$113$	7.78612	−	4.49532i	0.732456	−	0.422884i	0.819320	+	0.573336i	$0.194351\pi$
$114$	6.54617	−	11.3383i	0.613105	−	1.06193i
$115$	−3.90186	−	3.04820i	−0.363850	−	0.284246i
$116$	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
$120$	2.11563	+	5.23574i	0.193130	+	0.477956i
$121$	−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	0.688598	−	0.725143i	$-0.258226\pi$
$127$	18.7173	−	10.8064i	1.66089	−	0.958915i	0.972291	−	0.233772i	$-0.0751069\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	7.45407	−	12.9108i	0.656294	−	1.13673i
$130$	6.52468	−	8.35192i	0.572252	−	0.732512i
$131$	8.42864	+	14.5988i	0.736414	+	1.27551i	0.954100	+	0.299487i	$0.0968156\pi$
$131$	8.42864	+	14.5988i	0.736414	+	1.27551i	−0.217687	+	0.976019i	$0.569851\pi$
$132$	5.88083	−	3.39530i	0.511861	−	0.295523i
$133$	−9.94153	+	5.73975i	−0.862040	+	0.497699i
$134$	−2.66815			−0.230493
$135$	1.68116	+	1.31336i	0.144692	+	0.113036i
$136$	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	0.674705	−	0.738088i	$-0.264271\pi$
$139$	−3.55877	−	6.16396i	−0.301851	−	0.522821i	−0.976555	+	0.215267i	$0.930938\pi$
$140$	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
$145$	−14.6795	+	18.7905i	−1.21907	+	1.56047i
$146$	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	$0.183439\pi$
$150$	−3.05581	−	12.2518i	−0.249506	−	1.00036i
$151$	−6.65801	+	11.5320i	−0.541822	+	0.938462i	0.456978	+	0.889478i	$0.348932\pi$
$151$	−6.65801	+	11.5320i	−0.541822	+	0.938462i	−0.998800	+	0.0489845i	$0.984402\pi$
$152$	4.48966	+	2.59210i	0.364159	+	0.210247i
$153$	2.01518	+	1.16346i	0.162918	+	0.0940605i
$154$	−5.95407			−0.479792
$155$	−9.27785	+	11.8761i	−0.745215	+	0.953914i
$156$	−11.9699			−0.958358
$157$	−12.6371	+	7.29605i	−1.00855	+	0.582288i	−0.910768	−	0.412919i	$-0.864509\pi$
$157$	−12.6371	+	7.29605i	−1.00855	+	0.582288i	−0.0977853	+	0.995208i	$0.531176\pi$
$158$		−	2.76986i		−	0.220358i
$159$	1.98418			0.157356
$160$	−2.07321	+	0.837733i	−0.163902	+	0.0662286i
$161$	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	$-0.614850\pi$
$163$	3.58385	−	2.06914i	0.280709	−	0.162067i	0.633744	+	0.773543i	$0.281517\pi$
$164$	3.71432	+	6.43339i	0.290040	+	0.502363i
$165$	−14.0784	+	5.68871i	−1.09600	+	0.442865i
$166$	−4.42864	+	7.67063i	−0.343729	+	0.595356i
$167$	−8.82790	−	5.09679i	−0.683123	−	0.394401i	0.117908	−	0.993025i	$-0.462381\pi$
$167$	−8.82790	−	5.09679i	−0.683123	−	0.394401i	−0.801031	+	0.598623i	$0.795715\pi$
$168$	−4.84290	+	2.79605i	−0.373638	+	0.215720i
$169$	4.73260	+	8.19711i	0.364046	+	0.630547i
$170$	−0.577107	−	1.42822i	−0.0442621	−	0.109539i
$171$	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	$-0.781562\pi$
$173$	−8.04569	+	4.64518i	−0.611703	+	0.353167i	0.161929	+	0.986802i	$0.448228\pi$
$174$	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	$0.319568\pi$
$180$	−4.64981	+	5.95200i	−0.346577	+	0.443636i
$181$	9.79605	−	16.9673i	0.728135	−	1.26117i	−0.229536	−	0.973300i	$-0.573721\pi$
$181$	9.79605	−	16.9673i	0.728135	−	1.26117i	0.957671	−	0.287866i	$-0.0929459\pi$
$182$	9.08921	+	5.24766i	0.673737	+	0.388982i
$183$	11.9841	−	6.91903i	0.885891	−	0.511470i
$184$	−2.21432			−0.163242
$185$	−8.68442	+	10.4681i	−0.638491	+	0.769629i
$186$	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
$190$	−9.13511	−	7.13651i	−0.662731	−	0.517737i
$191$	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	$-0.604480\pi$
$197$	4.71930	−	2.72469i	0.336237	−	0.194126i	0.658607	+	0.752488i	$0.271146\pi$
$198$	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	$0.408133\pi$
$200$	4.85138	−	1.21002i	0.343044	−	0.0855610i
$201$	−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
$205$	−6.22321	−	15.4011i	−0.434648	−	1.07566i
$206$	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
$210$	11.5936	−	4.68469i	0.800035	−	0.323274i
$211$	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
$215$	−10.4021	−	8.12629i	−0.709415	−	0.554208i
$216$	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
$220$	−2.25257	−	5.57464i	−0.151868	−	0.375842i
$221$	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
$225$	12.1479	−	11.7330i	0.809859	−	0.782203i
$226$	−4.49532	+	7.78612i	−0.299024	+	0.517925i
$227$	−17.8238	−	10.2906i	−1.18301	−	0.683011i	−0.226301	−	0.974057i	$-0.572663\pi$
$227$	−17.8238	−	10.2906i	−1.18301	−	0.683011i	−0.956709	+	0.291046i	$0.905997\pi$
$228$			13.0923i			0.867062i
$229$	13.6834	−	23.7004i	0.904227	−	1.56617i	0.0822763	−	0.996610i	$-0.473781\pi$
$229$	13.6834	−	23.7004i	0.904227	−	1.56617i	0.821951	−	0.569558i	$-0.192886\pi$
$230$	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
$235$	8.52247	+	6.65791i	0.555945	+	0.434314i
$236$	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	0.759001	−	0.651090i	$-0.225688\pi$
$239$	−2.85013	−	4.93658i	−0.184360	−	0.319321i	−0.943361	+	0.331769i	$0.892355\pi$
$240$	−4.45006	−	3.47647i	−0.287250	−	0.224405i
$241$	7.02074	−	12.1603i	0.452246	−	0.783313i	−0.546279	−	0.837603i	$-0.683956\pi$
$241$	7.02074	−	12.1603i	0.452246	−	0.783313i	0.998525	+	0.0542903i	$0.0172896\pi$
$242$	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
$250$	−11.1189	+	1.17006i	−0.703224	+	0.0740011i
$251$	−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
$255$	2.39491	−	3.06561i	0.149975	−	0.191976i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.4049	−	13.5128i	1.45996	−	0.842907i	0.460950	−	0.887426i	$-0.347509\pi$
$257$	23.4049	−	13.5128i	1.45996	−	0.842907i	0.999009	+	0.0445188i	$0.0141755\pi$
$258$			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	$-0.271967\pi$
$263$	5.38176	+	3.10716i	0.331853	+	0.191596i	−0.324810	+	0.945779i	$0.605300\pi$
$264$	−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	0.999900	−	0.0141382i	$-0.00450047\pi$
$271$	8.02865	+	13.9060i	0.487706	+	0.844732i	−0.512194	+	0.858870i	$0.671167\pi$
$272$	−0.596598	−	0.344446i	−0.0361741	−	0.0208851i
$273$			26.5052i			1.60417i
$274$	−1.93655	−	3.35420i	−0.116991	−	0.202635i
$275$	3.25360	+	13.0448i	0.196200	+	0.786633i
$276$	−2.79605	−	4.84290i	−0.168303	−	0.291509i
$277$	11.5196	+	6.65087i	0.692148	+	0.399612i	0.804416	−	0.594066i	$-0.202478\pi$
$277$	11.5196	+	6.65087i	0.692148	+	0.399612i	−0.112268	+	0.993678i	$0.535812\pi$
$278$	6.16396	+	3.55877i	0.369690	+	0.213441i
$279$	11.3827	+	19.7154i	0.681465	+	1.18033i
$280$	1.85501	+	4.59075i	0.110858	+	0.274350i
$281$	−7.51360	−	13.0139i	−0.448224	−	0.776346i	0.550047	−	0.835134i	$-0.314610\pi$
$281$	−7.51360	−	13.0139i	−0.448224	−	0.776346i	−0.998271	+	0.0587876i	$0.981277\pi$
$282$		−	12.2143i		−	0.727352i
$283$	12.9232	+	7.46121i	0.768204	+	0.443523i	0.832234	−	0.554425i	$-0.187062\pi$
$283$	12.9232	+	7.46121i	0.768204	+	0.443523i	−0.0640293	+	0.997948i	$0.520395\pi$
$284$	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	$-0.619901\pi$
$293$	−23.2292	−	13.4114i	−1.35706	−	0.783500i	−0.989227	+	0.146391i	$0.953234\pi$
$294$	−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
$300$	8.77231	+	9.08247i	0.506469	+	0.524377i
$301$	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
$305$	−4.59035	−	11.3601i	−0.262843	−	0.650480i
$306$	−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	0.774299	−	0.632820i	$-0.218103\pi$
$311$	−2.83730	−	4.91435i	−0.160889	−	0.278667i	−0.935188	+	0.354153i	$0.884769\pi$
$312$	10.3662	−	5.98494i	0.586872	−	0.338831i
$313$	−9.80130	+	5.65878i	−0.554002	+	0.319853i	−0.750735	−	0.660604i	$-0.770300\pi$
$313$	−9.80130	+	5.65878i	−0.554002	+	0.319853i	0.196733	+	0.980457i	$0.436967\pi$
$314$	7.29605	−	12.6371i	0.411740	−	0.713155i
$315$	13.1796	+	10.2962i	0.742589	+	0.580124i
$316$	1.38493	+	2.39877i	0.0779084	+	0.134941i
$317$	1.13119	−	0.653093i	0.0635340	−	0.0366813i	−0.467897	−	0.883783i	$-0.654988\pi$
$317$	1.13119	−	0.653093i	0.0635340	−	0.0366813i	0.531430	+	0.847102i	$0.321655\pi$
$318$	−1.71835	+	0.992089i	−0.0963602	+	0.0556336i
$319$	−28.6735			−1.60541
$320$	1.37659	−	1.76210i	0.0769536	−	0.0985046i
$321$	−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
$330$	9.34786	−	11.9657i	0.514583	−	0.658692i
$331$	5.59533	+	9.69140i	0.307547	+	0.532687i	0.977825	−	0.209423i	$-0.0671585\pi$
$331$	5.59533	+	9.69140i	0.307547	+	0.532687i	−0.670278	+	0.742110i	$0.733825\pi$
$332$		−	8.85728i		−	0.486106i
$333$	9.74649	+	18.0874i	0.534104	+	0.991185i
$334$	10.1936			0.557768
$335$	−5.53164	+	2.23520i	−0.302226	+	0.122122i
$336$	2.79605	−	4.84290i	0.152537	−	0.264202i
$337$	−14.6622	−	8.46520i	−0.798699	−	0.461129i	0.0443170	−	0.999018i	$-0.485889\pi$
$337$	−14.6622	−	8.46520i	−0.798699	−	0.461129i	−0.843016	+	0.537888i	$0.819222\pi$
$338$	−8.19711	−	4.73260i	−0.445864	−	0.257420i
$339$	−22.7052			−1.23318
$340$	1.21390	+	0.948320i	0.0658329	+	0.0514299i
$341$	−18.1225			−0.981386
$342$	−15.1651	+	8.75557i	−0.820034	+	0.473447i
$343$			20.1432i			1.08763i
$344$	−5.90321			−0.318280
$345$	4.68469	+	11.5936i	0.252215	+	0.624179i
$346$	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	0.981222	+	0.192880i	$0.0617828\pi$
$349$	12.2859	+	21.2798i	0.657650	+	1.13908i	−0.323572	+	0.946203i	$0.604884\pi$
$350$	−2.67936	−	10.7425i	−0.143218	−	0.574211i
$351$	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	$-0.786485\pi$
$353$	−11.9623	+	6.90644i	−0.636689	+	0.367593i	0.146649	+	0.989189i	$0.453151\pi$
$354$	0.328625	+	0.569195i	0.0174662	+	0.0302524i
$355$	−8.21516	−	20.3308i	−0.436015	−	1.07905i
$356$	−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
$365$	23.1144	+	18.0574i	1.20987	+	0.945169i
$366$	−6.91903	+	11.9841i	−0.361664	+	0.626420i
$367$	−24.6918	−	14.2558i	−1.28890	−	0.744147i	−0.310442	−	0.950592i	$-0.600477\pi$
$367$	−24.6918	−	14.2558i	−1.28890	−	0.744147i	−0.978458	+	0.206445i	$0.933811\pi$
$368$	1.91766	−	1.10716i	0.0999648	−	0.0577147i
$369$	−25.0923			−1.30626
$370$	2.28688	−	13.4078i	0.118889	−	0.697040i
$371$	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	$-0.404468\pi$
$373$	−7.41358	−	4.28023i	−0.383860	−	0.221622i	−0.679497	+	0.733679i	$0.737802\pi$
$374$	0.926178	−	1.60419i	0.0478915	−	0.0829506i
$375$	−16.5991	−	22.8406i	−0.857172	−	1.17948i
$376$	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	0.876391	−	0.481600i	$-0.159944\pi$
$379$	0.411123	+	0.712085i	0.0211180	+	0.0365774i	−0.855273	+	0.518177i	$0.826611\pi$
$380$	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	$-0.373860\pi$
$383$	−4.30405	−	2.48494i	−0.219927	−	0.126975i	−0.605916	+	0.795528i	$0.707193\pi$
$384$	−2.52543			−0.128875
$385$	−12.3440	+	4.98792i	−0.629110	+	0.254208i
$386$	−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	−0.195198	−	0.980764i	$-0.562535\pi$
$389$	14.8272	−	25.6814i	0.751767	−	1.30210i	0.946966	−	0.321335i	$-0.104132\pi$
$390$	−24.8161	+	10.0276i	−1.25661	+	0.507766i
$391$	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
$395$	−2.32040	−	5.74250i	−0.116752	−	0.288937i
$396$	−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
$400$	−3.59641	+	3.47359i	−0.179820	+	0.173680i
$401$	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
$405$	6.47058	+	16.0133i	0.321526	+	0.795709i
$406$	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	0.683137	−	0.730290i	$-0.260615\pi$
$409$	−5.88271	−	10.1891i	−0.290881	−	0.503821i	−0.974018	+	0.226469i	$0.927282\pi$
$410$	13.0900	+	10.2262i	0.646470	+	0.505035i
$411$	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	0.682672	−	0.730725i	$-0.260818\pi$
$419$	−5.96666	−	10.3346i	−0.291490	−	0.504876i	−0.974162	+	0.225849i	$0.927485\pi$
$420$	−7.69802	+	9.85386i	−0.375625	+	0.480819i
$421$	−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
$425$	−2.39293	−	2.47754i	−0.116074	−	0.120178i
$426$	−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	0.167612	+	0.985853i	$0.446394\pi$
$431$	−15.9849	+	27.6867i	−0.769968	+	1.33362i	−0.937580	+	0.347770i	$0.886939\pi$
$432$	−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
$435$	55.8324	−	22.5605i	2.67696	−	1.08169i
$436$	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	−0.661740	−	0.749734i	$-0.730182\pi$
$439$	6.67161	−	11.5556i	0.318419	−	0.551517i	0.980158	+	0.198216i	$0.0635149\pi$
$440$	4.73811	+	3.70149i	0.225880	+	0.176462i
$441$	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	−0.993641	−	0.112596i	$-0.964083\pi$
$449$	−8.46121	+	14.6552i	−0.399309	+	0.691624i	0.594332	+	0.804220i	$0.297417\pi$
$450$	−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	$-0.223105\pi$
$457$	12.5674	+	7.25581i	0.587879	+	0.339412i	−0.176379	+	0.984322i	$0.556438\pi$
$458$			27.3669i			1.27877i
$459$	−0.328625	−	0.569195i	−0.0153389	−	0.0265677i
$460$	−4.59075	+	1.85501i	−0.214045	+	0.0864902i
$461$	11.3620	+	19.6795i	0.529179	+	0.916566i	0.999421	+	0.0340278i	$0.0108335\pi$
$461$	11.3620	+	19.6795i	0.529179	+	0.916566i	−0.470242	+	0.882538i	$0.655833\pi$
$462$	13.0220	+	7.51828i	0.605840	+	0.349782i
$463$	3.52743	+	2.03657i	0.163934	+	0.0946472i	0.579722	−	0.814814i	$-0.303161\pi$
$463$	3.52743	+	2.03657i	0.163934	+	0.0946472i	−0.415789	+	0.909461i	$0.636494\pi$
$464$	−5.33185	−	9.23504i	−0.247525	−	0.428726i
$465$	35.2876	−	14.2588i	1.63642	−	0.661237i
$466$	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	−0.992136	−	0.125167i	$-0.960053\pi$
$479$	−13.2294	−	22.9140i	−0.604466	−	1.04697i	0.387670	−	0.921798i	$-0.373280\pi$
$480$	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
$485$	−22.8908	−	17.8827i	−1.03942	−	0.812013i
$486$	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
$490$	−4.34708	+	1.75655i	−0.196381	+	0.0793527i
$491$	−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	−0.996340	−	0.0854822i	$-0.972757\pi$
$499$	−9.47457	+	16.4104i	−0.424140	+	0.734632i	0.572200	+	0.820114i	$0.306090\pi$
$500$	9.04426	−	6.57277i	0.404472	−	0.293943i
$501$	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	$-0.593238\pi$
$503$	8.88179	−	5.12790i	0.396019	−	0.228642i	0.684765	+	0.728764i	$0.259905\pi$
$504$	7.47949			0.333163
$505$	7.88159	−	10.0888i	0.350726	−	0.448948i
$506$	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	0.893825	−	0.448415i	$-0.148011\pi$
$509$	1.32148	+	2.28887i	0.0585736	+	0.101452i	−0.835252	+	0.549868i	$0.814678\pi$
$510$	−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
$515$	12.2817	+	9.59466i	0.541195	+	0.422791i
$516$	−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
$520$	−3.97064	−	9.82650i	−0.174124	−	0.430920i
$521$	2.44692	−	4.23819i	0.107202	−	0.185679i	−0.807434	−	0.589958i	$-0.799144\pi$
$521$	2.44692	−	4.23819i	0.107202	−	0.185679i	0.914636	+	0.404279i	$0.132478\pi$
$522$	−31.1940	−	18.0098i	−1.36532	−	0.788269i
$523$	24.8316	+	14.3365i	1.08581	+	0.626893i	0.932458	−	0.361279i	$-0.117660\pi$
$523$	24.8316	+	14.3365i	1.08581	+	0.626893i	0.153352	+	0.988172i	$0.450993\pi$
$524$	16.8573			0.736414
$525$	20.1115	−	19.4247i	0.877737	−	0.847763i
$526$	−6.21432			−0.270957
$527$	4.02092	−	2.32148i	0.175154	−	0.101125i
$528$		−	6.79060i		−	0.295523i
$529$	18.0968			0.786817
$530$	0.658190	+	1.62888i	0.0285899	+	0.0707541i
$531$	−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
$535$	−33.7345	+	13.6313i	−1.45847	+	0.589331i
$536$	−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
$540$	1.97798	−	0.799253i	0.0851188	−	0.0343944i
$541$	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
$550$	−9.34012	−	9.67035i	−0.398264	−	0.412345i
$551$	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
$555$	32.2118	−	11.9287i	1.36731	−	0.506344i
$556$	−7.11753			−0.301851
$557$	10.6741	−	6.16270i	0.452276	−	0.261122i	−0.256515	−	0.966540i	$-0.582574\pi$
$557$	10.6741	−	6.16270i	0.452276	−	0.261122i	0.708791	+	0.705418i	$0.249241\pi$
$558$	−19.7154	−	11.3827i	−0.834621	−	0.481868i
$559$	−13.9899	+	24.2312i	−0.591708	+	1.02487i
$560$	−3.90186	−	3.04820i	−0.164884	−	0.128810i
$561$	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	$0.418299\pi$
$570$	10.9679	+	27.1432i	0.459394	+	1.13690i
$571$	−7.32540	−	12.6880i	−0.306558	−	0.530975i	0.671049	−	0.741413i	$-0.265844\pi$
$571$	−7.32540	−	12.6880i	−0.306558	−	0.530975i	−0.977607	+	0.210439i	$0.932511\pi$
$572$	−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
$575$	10.7425	−	2.67936i	0.447993	−	0.111737i
$576$	−1.68889	−	2.92525i	−0.0703705	−	0.121885i
$577$	−8.94632	+	5.16516i	−0.372440	+	0.215028i	−0.674524	−	0.738253i	$-0.735651\pi$
$577$	−8.94632	+	5.16516i	−0.372440	+	0.215028i	0.302084	+	0.953281i	$0.402318\pi$
$578$		−	16.5254i		−	0.687367i
$579$	30.1049	−	52.1433i	1.25112	−	2.16700i
$580$	8.93333	+	22.1081i	0.370936	+	0.917989i
$581$	−19.6128			−0.813678
$582$			32.8069i			1.35989i
$583$	1.82957	−	1.05630i	0.0757732	−	0.0437477i
$584$	13.1175			0.542807
$585$	−28.2110	−	22.0389i	−1.16638	−	0.911198i
$586$	26.8227			1.10804
$587$	−33.1566	−	19.1430i	−1.36852	−	0.790114i	−0.377780	−	0.925896i	$-0.623312\pi$
$587$	−33.1566	−	19.1430i	−1.36852	−	0.790114i	−0.990739	+	0.135781i	$0.956646\pi$
$588$	4.58585	+	2.64764i	0.189117	+	0.109187i
$589$	17.4701	−	30.2591i	0.719844	−	1.24681i
$590$	0.539559	−	0.218022i	0.0222133	−	0.00897583i
$591$	−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
$595$	2.09988	−	2.68796i	0.0860868	−	0.110196i
$596$	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	−0.977655	−	0.210216i	$-0.932583\pi$
$599$	−7.50815	+	13.0045i	−0.306775	+	0.531349i	0.670880	+	0.741566i	$0.265916\pi$
$600$	−12.1383	−	3.47949i	−0.495543	−	0.142050i
$601$	21.9472	+	38.0136i	0.895243	+	1.55061i	0.833503	+	0.552515i	$0.186332\pi$
$601$	21.9472	+	38.0136i	0.895243	+	1.55061i	0.0617402	+	0.998092i	$0.480335\pi$
$602$			13.0716i			0.532759i
$603$			9.01243i			0.367015i
$604$	6.65801	+	11.5320i	0.270911	+	0.469231i
$605$	5.18954	−	6.64288i	0.210985	−	0.270071i
$606$	−14.4592			−0.587366
$607$	22.4551	−	12.9644i	0.911423	−	0.526210i	0.0305343	−	0.999534i	$-0.490279\pi$
$607$	22.4551	−	12.9644i	0.911423	−	0.526210i	0.880889	+	0.473323i	$0.156946\pi$
$608$	4.48966	−	2.59210i	0.182080	−	0.105124i
$609$	29.8163	+	51.6433i	1.20822	+	2.09269i
$610$	9.65544	+	7.54300i	0.390937	+	0.305407i
$611$	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	$-0.481120\pi$
$613$	23.6055	−	13.6287i	0.953419	−	0.550457i	0.894141	+	0.447785i	$0.147787\pi$
$614$	−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	$-0.873458\pi$
$617$	−26.0252	+	15.0257i	−1.04774	+	0.604911i	−0.125721	+	0.992066i	$0.540124\pi$
$618$		−	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	$0.593367\pi$
$620$	5.64611	+	13.9729i	0.226753	+	0.561166i
$621$	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
$625$	−22.0717	+	11.7405i	−0.882869	+	0.469619i
$626$	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	0.989152	+	0.146896i	$0.0469283\pi$
$631$	15.6192	+	27.0533i	0.621792	+	1.07697i	−0.367360	+	0.930079i	$0.619738\pi$
$632$	−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	0.762643	−	0.646820i	$-0.223901\pi$
$641$	−4.52789	−	7.84253i	−0.178841	−	0.309761i	−0.941484	+	0.337058i	$0.890568\pi$
$642$	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
$645$	12.4890	+	30.9077i	0.491755	+	1.21699i
$646$	1.78568	+	3.09289i	0.0702567	+	0.121688i
$647$	12.9711	+	7.48886i	0.509946	+	0.294418i	0.732812	−	0.680432i	$-0.238208\pi$
$647$	12.9711	+	7.48886i	0.509946	+	0.294418i	−0.222865	+	0.974849i	$0.571541\pi$
$648$	6.68912	+	3.86196i	0.262773	+	0.151712i
$649$	−0.349896	−	0.606037i	−0.0137346	−	0.0237890i
$650$	5.73517	+	22.9943i	0.224952	+	0.901911i
$651$	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	$-0.173246\pi$
$653$	21.3333	+	12.3168i	0.834837	+	0.481993i	−0.0206688	+	0.999786i	$0.506580\pi$
$654$	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	−0.496546	−	0.868010i	$-0.665399\pi$
$659$	12.9240	−	22.3849i	0.503446	−	0.871994i	0.999992	−	0.00398348i	$-0.00126798\pi$
$660$	−2.11261	+	15.0366i	−0.0822332	+	0.585297i
$661$	−6.47558	+	11.2160i	−0.251871	+	0.436253i	−0.964041	−	0.265754i	$-0.914379\pi$
$661$	−6.47558	+	11.2160i	−0.251871	+	0.436253i	0.712170	+	0.702007i	$0.247712\pi$
$662$	−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
$670$	3.67294	−	4.70155i	0.141898	−	0.181637i
$671$	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	$-0.113854\pi$
$673$	28.5848	+	16.5035i	1.10186	+	0.636162i	0.165154	+	0.986268i	$0.447188\pi$
$674$	16.9304			0.652135
$675$	−4.62854	+	1.15444i	−0.178153	+	0.0444343i
$676$	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	$-0.874093\pi$
$683$	−27.4536	+	15.8504i	−1.05048	+	0.606498i	−0.127700	+	0.991813i	$0.540759\pi$
$684$	8.75557	−	15.1651i	0.334778	−	0.579852i
$685$	−6.82480	−	5.33166i	−0.260762	−	0.203712i
$686$	−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
$690$	−9.85386	−	7.69802i	−0.375130	−	0.293059i
$691$	15.3400	+	26.5697i	0.583561	+	1.01076i	0.995053	+	0.0993441i	$0.0316745\pi$
$691$	15.3400	+	26.5697i	0.583561	+	1.01076i	−0.411492	+	0.911413i	$0.634992\pi$
$692$			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
$700$	7.69165	+	7.96360i	0.290717	+	0.300996i
$701$	−9.77631	−	16.9331i	−0.369246	−	0.639553i	0.620202	−	0.784442i	$-0.287051\pi$
$701$	−9.77631	−	16.9331i	−0.369246	−	0.639553i	−0.989448	+	0.144889i	$0.953717\pi$
$702$			4.52204i			0.170673i
$703$	16.5619	−	26.8350i	0.624642	−	1.01210i
$704$	2.68889			0.101341
$705$	−10.2323	−	25.3229i	−0.385372	−	0.953714i
$706$	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	$0.776679\pi$
$710$	17.2799	+	13.4994i	0.648504	+	0.506623i
$711$	−9.35599			−0.350877
$712$	0.578634	−	0.334074i	0.0216852	−	0.0125200i
$713$			14.9240i			0.558907i
$714$	−3.85236			−0.144171
$715$	26.4224	−	10.6766i	0.988141	−	0.399283i
$716$	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	0.597595	−	0.801798i	$-0.296123\pi$
$719$	−10.6072	−	18.3721i	−0.395580	−	0.685165i	−0.993175	+	0.116633i	$0.962790\pi$
$720$	2.82968	+	7.00286i	0.105456	+	0.260981i
$721$	−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
$725$	−12.9032	−	51.7336i	−0.479215	−	1.92134i
$726$	−9.52051			−0.353339
$727$	−16.1795	−	9.34122i	−0.600063	−	0.346447i	0.169003	−	0.985615i	$-0.445945\pi$
$727$	−16.1795	−	9.34122i	−0.600063	−	0.346447i	−0.769066	+	0.639169i	$0.779278\pi$
$728$	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	−0.989902	−	0.141754i	$-0.954726\pi$
$733$	−43.5245	−	25.1289i	−1.60762	−	0.928157i	−0.617714	−	0.786403i	$-0.711941\pi$
$734$	28.5116			1.05238
$735$	−9.33084	−	7.28942i	−0.344173	−	0.268874i
$736$	−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	$0.584092\pi$
$740$	4.72342	+	12.7550i	0.173636	+	0.468882i
$741$	−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	$-0.421764\pi$
$743$	−12.9481	−	7.47558i	−0.475019	−	0.274252i	−0.718338	+	0.695694i	$0.755097\pi$
$744$	8.51037	−	14.7404i	0.312005	−	0.540409i
$745$	−28.1789	+	36.0705i	−1.03240	+	1.32152i
$746$	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
$755$	−11.1553	−	27.6069i	−0.405982	−	1.00472i
$756$	1.05630	+	1.82957i	0.0384174	+	0.0665409i
$757$	−13.8624	+	8.00346i	−0.503838	+	0.290891i	−0.730297	−	0.683130i	$-0.760618\pi$
$757$	−13.8624	+	8.00346i	−0.503838	+	0.290891i	0.226459	+	0.974021i	$0.427285\pi$
$758$	−0.712085	−	0.411123i	−0.0258641	−	0.0149326i
$759$	−7.51828	+	13.0220i	−0.272896	+	0.472670i
$760$	−10.7480	+	4.34298i	−0.389869	+	0.157536i
$761$	−23.2931	−	40.3448i	−0.844373	−	1.46250i	−0.886165	−	0.463370i	$-0.846640\pi$
$761$	−23.2931	−	40.3448i	−0.844373	−	1.46250i	0.0417918	−	0.999126i	$-0.486693\pi$
$762$	47.2691	−	27.2908i	1.71238	−	0.988643i
$763$		−	12.2034i		−	0.441793i
$764$	0.800736	−	1.38692i	0.0289696	−	0.0501768i
$765$	−4.82422	+	1.94934i	−0.174420	+	0.0704787i
$766$	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	$0.515501\pi$
$770$	8.19629	−	10.4917i	0.295374	−	0.378094i
$771$	−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	$-0.0425054\pi$
$773$	38.1273	+	22.0128i	1.37135	+	0.791747i	0.380248	+	0.924885i	$0.375839\pi$
$774$	9.96989	−	17.2684i	0.358360	−	0.620698i
$775$	−8.15520	−	32.6971i	−0.292943	−	1.17451i
$776$	−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
$780$	16.4776	−	21.0922i	0.589993	−	0.755221i
$781$	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
$790$	4.88078	+	3.81295i	0.173650	+	0.135659i
$791$	−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
$795$	−2.73139	+	3.49633i	−0.0968726	+	0.124002i
$796$	4.01506	−	6.95428i	0.142310	−	0.246488i
$797$	18.9743	−	10.9548i	0.672105	−	0.388040i	−0.124769	−	0.992186i	$-0.539819\pi$
$797$	18.9743	−	10.9548i	0.672105	−	0.388040i	0.796874	+	0.604146i	$0.206486\pi$
$798$	−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
$805$	4.10758	+	10.1654i	0.144773	+	0.358283i
$806$	−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	−0.642996	−	0.765869i	$-0.722309\pi$
$809$	9.72077	−	16.8369i	0.341764	−	0.591953i	0.984760	+	0.173916i	$0.0556423\pi$
$810$	−13.6104	−	10.6327i	−0.478219	−	0.373593i
$811$	−20.8113	+	36.0463i	−0.730785	+	1.26576i	0.225763	+	0.974182i	$0.427513\pi$
$811$	−20.8113	+	36.0463i	−0.730785	+	1.26576i	−0.956548	+	0.291575i	$0.905821\pi$
$812$	−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	0.272031	+	0.962289i	$0.412305\pi$
$821$	−19.9813	+	34.6086i	−0.697351	+	1.20785i	−0.969382	+	0.245559i	$0.921029\pi$
$822$			9.78123i			0.341160i
$823$	7.16596	−	4.13727i	0.249790	−	0.144216i	−0.369878	−	0.929080i	$-0.620601\pi$
$823$	7.16596	−	4.13727i	0.249790	−	0.144216i	0.619668	+	0.784864i	$0.287267\pi$
$824$	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	$-0.494307\pi$
$827$	−24.1294	−	13.9311i	−0.839061	−	0.484432i	−0.856945	+	0.515408i	$0.827640\pi$
$828$			7.47949i			0.259930i
$829$	−20.3422	−	35.2338i	−0.706515	−	1.22372i	−0.966142	−	0.258010i	$-0.916933\pi$
$829$	−20.3422	−	35.2338i	−0.706515	−	1.22372i	0.259628	−	0.965709i	$-0.416400\pi$
$830$	−7.42003	−	18.3630i	−0.257553	−	0.637389i
$831$	−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
$835$	21.1334	−	8.53949i	0.731353	−	0.295521i
$836$	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	0.997354	−	0.0726999i	$-0.0231615\pi$
$839$	12.6208	+	21.8598i	0.435717	+	0.754684i	−0.561637	+	0.827384i	$0.689828\pi$
$840$	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	−0.611187	+	0.791486i	$0.709308\pi$
$853$	−46.7949	+	27.0171i	−1.60223	+	0.925047i	−0.991041	+	0.133560i	$0.957359\pi$
$854$	−6.06668	+	10.5078i	−0.207597	+	0.359569i
$855$	−24.1056	+	30.8564i	−0.824394	+	1.05527i
$856$	−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	$0.225859\pi$
$860$	−12.2386	+	4.94531i	−0.417333	+	0.168634i
$861$	−41.5417			−1.41574
$862$		−	31.9699i		−	1.08890i
$863$	−9.05887	+	5.23014i	−0.308368	+	0.178036i	−0.646196	−	0.763172i	$-0.723641\pi$
$863$	−9.05887	+	5.23014i	−0.308368	+	0.178036i	0.337828	+	0.941208i	$0.390308\pi$
$864$	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
$870$	−37.0721	+	47.4542i	−1.25686	+	1.60885i
$871$	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
$875$	−14.5542	−	20.0269i	−0.492023	−	0.677032i
$876$	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	−0.521873	−	0.853023i	$-0.674767\pi$
$881$	14.1820	−	24.5639i	0.477803	−	0.827579i	0.999676	+	0.0254437i	$0.00809986\pi$
$882$			7.08250i			0.238480i
$883$	15.2698	+	8.81603i	0.513870	+	0.296683i	0.734423	−	0.678692i	$-0.237453\pi$
$883$	15.2698	+	8.81603i	0.513870	+	0.296683i	−0.220553	+	0.975375i	$0.570786\pi$
$884$	1.63259	−	2.82772i	0.0549099	−	0.0951067i
$885$	1.15814	+	0.904761i	0.0389305	+	0.0304132i
$886$	−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
$890$	−1.38521	+	0.559730i	−0.0464324	+	0.0187622i
$891$	−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
$895$	−19.7794	+	25.3186i	−0.661152	+	0.846309i
$896$	−2.21432			−0.0739752
$897$	22.9541	−	13.2526i	0.766417	−	0.442491i
$898$		−	16.9224i		−	0.564709i
$899$	71.8707			2.39702
$900$	−4.08717	−	16.3869i	−0.136239	−	0.546230i
$901$	−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
$905$	16.4129	+	40.6186i	0.545585	+	1.35021i
$906$	−16.8143	+	29.1233i	−0.558619	+	0.967556i
$907$	−3.01718	−	1.74197i	−0.100184	−	0.0578412i	0.449071	−	0.893496i	$-0.351755\pi$
$907$	−3.01718	−	1.74197i	−0.100184	−	0.0578412i	−0.549255	+	0.835655i	$0.685088\pi$
$908$	−17.8238	+	10.2906i	−0.591505	+	0.341506i
$909$	−9.66968	−	16.7484i	−0.320723	−	0.555509i
$910$	−21.7590	+	8.79227i	−0.721304	+	0.291461i
$911$	−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	$0.375623\pi$
$920$	3.04820	−	3.90186i	0.100496	−	0.128641i
$921$	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
$925$	−6.49100	−	29.7131i	−0.213423	−	0.976960i
$926$	−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	−0.920419	−	0.390933i	$-0.872152\pi$
$929$	−3.70787	+	6.42221i	−0.121651	+	0.210706i	0.798768	+	0.601639i	$0.205486\pi$
$930$	−23.4305	+	29.9923i	−0.768318	+	0.983487i
$931$	−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	$-0.622921\pi$
$937$	7.26349	−	4.19358i	0.237288	−	0.136998i	0.613930	+	0.789361i	$0.289588\pi$
$938$	5.11659	+	2.95407i	0.167063	+	0.0964537i
$939$	28.5817			0.932728
$940$	10.0272	−	4.05172i	0.327050	−	0.132153i
$941$	−22.7042	−	39.3248i	−0.740135	−	1.28195i	−0.952433	−	0.304747i	$-0.901428\pi$
$941$	−22.7042	−	39.3248i	−0.740135	−	1.28195i	0.212298	−	0.977205i	$-0.431905\pi$
$942$	−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
$945$	−1.76980	−	4.37989i	−0.0575717	−	0.142478i
$946$	7.93655	+	13.7465i	0.258040	+	0.446938i
$947$	6.03358	−	3.48349i	0.196065	−	0.113198i	−0.398754	−	0.917058i	$-0.630557\pi$
$947$	6.03358	−	3.48349i	0.196065	−	0.113198i	0.594819	+	0.803860i	$0.297224\pi$
$948$		−	6.99508i		−	0.227190i
$949$	31.0869	−	53.8441i	1.00912	−	1.74785i
$950$	25.1506	−	6.27297i	0.815992	−	0.203522i
$951$	−3.29868			−0.106967
$952$		−	1.52543i		−	0.0494394i
$953$	23.5973	−	13.6239i	0.764392	−	0.441322i	−0.0664786	−	0.997788i	$-0.521176\pi$
$953$	23.5973	−	13.6239i	0.764392	−	0.441322i	0.830870	+	0.556466i	$0.187843\pi$
$954$	2.65386			0.0859218
$955$	−2.20457	+	2.82196i	−0.0713381	+	0.0913165i
$956$	−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
$960$	−5.23574	+	2.11563i	−0.168983	+	0.0682818i
$961$	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
$965$	−42.0111	−	32.8198i	−1.35239	−	1.05651i
$966$	6.19135	−	10.7237i	0.199204	−	0.345031i
$967$	−48.1544	−	27.8020i	−1.54854	−	0.894051i	−0.998253	−	0.0590770i	$-0.981184\pi$
$967$	−48.1544	−	27.8020i	−1.54854	−	0.894051i	−0.550289	−	0.834974i	$-0.685482\pi$
$968$		−	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	0.792581	−	0.609767i	$-0.208737\pi$
$971$	−4.10647	−	7.11261i	−0.131783	−	0.228255i	−0.924364	+	0.381512i	$0.875403\pi$
$972$			22.3684i			0.717467i
$973$			15.7605i			0.505258i
$974$	−5.65233	−	9.79012i	−0.181112	−	0.313696i
$975$	−43.0486	+	41.5785i	−1.37866	+	1.33158i
$976$	5.47949			0.175394
$977$	−0.159116	+	0.0918659i	−0.00509059	+	0.00293905i	−0.502543	−	0.864552i	$-0.667602\pi$
$977$	−0.159116	+	0.0918659i	−0.00509059	+	0.00293905i	0.497453	+	0.867491i	$0.334269\pi$
$978$	9.05076	−	5.22546i	0.289411	−	0.167092i
$979$	0.898290	+	1.55588i	0.0287095	+	0.0497263i
$980$	2.88641	−	3.69476i	0.0922030	−	0.118025i
$981$	−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	$-0.634752\pi$
$983$	5.43565	−	3.13828i	0.173370	−	0.100095i	0.584174	+	0.811628i	$0.301419\pi$
$984$	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
$990$	−18.8299	+	7.60870i	−0.598455	+	0.241821i
$991$	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
$995$	−11.0541	+	14.1499i	−0.350440	+	0.448582i
$996$	−11.1842	+	19.3716i	−0.354385	+	0.613813i
$997$	−26.2737	+	15.1692i	−0.832098	+	0.480412i	−0.854570	−	0.519336i	$-0.826179\pi$
$997$	−26.2737	+	15.1692i	−0.832098	+	0.480412i	0.0224726	+	0.999747i	$0.492846\pi$
$998$		−	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.359.1	yes	12
5.4	even	2	inner	370.2.n.f.359.6	yes	12
37.10	even	3	inner	370.2.n.f.269.6	yes	12
185.84	even	6	inner	370.2.n.f.269.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.f.269.1	✓	12	185.84	even	6	inner
370.2.n.f.269.6	yes	12	37.10	even	3	inner
370.2.n.f.359.1	yes	12	1.1	even	1	trivial
370.2.n.f.359.6	yes	12	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.18708 - 1.26271i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.37659 + 1.76210i) q^{5} +2.52543 q^{6} +(-1.91766 - 1.10716i) q^{7} +1.00000i q^{8} +(1.68889 + 2.92525i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.18708 - 1.26271i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.37659 + 1.76210i) 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} +(5.23574 - 2.11563i) 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} +(0.837733 + 2.07321i) q^{20} +(2.79605 + 4.84290i) q^{21} +(2.32865 - 1.34445i) q^{22} +2.21432i q^{23} +(1.26271 - 2.18708i) q^{24} +(-1.21002 - 4.85138i) q^{25} -4.73975 q^{26} -0.954067i q^{27} +(-1.91766 + 1.10716i) q^{28} +10.6637 q^{29} +(-3.47647 + 4.45006i) q^{30} +6.73975 q^{31} +(0.866025 + 0.500000i) q^{32} +(5.88083 + 3.39530i) q^{33} +(-0.344446 + 0.596598i) q^{34} +(4.59075 - 1.85501i) q^{35} +3.37778 q^{36} +(6.08014 + 0.178520i) q^{37} +5.18421i q^{38} +(-5.98494 - 10.3662i) q^{39} +(-1.76210 - 1.37659i) 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} +(3.47359 + 3.59641i) q^{50} -1.73975 q^{51} +(4.10474 - 2.36987i) q^{52} +(-0.680419 + 0.392840i) q^{53} +(0.477034 + 0.826246i) q^{54} +(3.70149 - 4.73811i) 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} +(-9.82650 + 3.97064i) q^{65} -6.79060 q^{66} +(2.31068 + 1.33407i) q^{67} -0.688892i q^{68} +(2.79605 - 4.84290i) q^{69} +(-3.04820 + 3.90186i) 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} +(7.00286 - 2.82968i) 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} +(4.34298 + 10.7480i) 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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