LMFDB - Embedded newform 70.2.k.a.33.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,2,Mod(3,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	70.k (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.558952814149$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.3
Root			$1.01089 + 0.750919i$ of defining polynomial
Character	$\chi$	$=$	70.33
Dual form			70.2.k.a.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.279864 - 0.0749894i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.774197 + 2.09777i) q^{5} -0.289737i q^{6} +(2.64273 - 0.126334i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.52538 - 1.45803i) q^{9} +(-1.82591 + 1.29076i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(0.279864 - 0.0749894i) q^{12} +(1.42962 - 1.42962i) q^{13} +(0.806019 + 2.51999i) q^{14} +(-0.0593598 - 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.37400 + 5.12784i) q^{17} +(0.754730 - 2.81669i) q^{18} +(1.94590 - 3.37040i) q^{19} +(-1.71936 - 1.42962i) q^{20} +(-0.749081 - 0.162821i) q^{21} +(3.97801 - 3.97801i) q^{22} +(1.08562 - 0.290892i) q^{23} +(0.144868 + 0.250919i) q^{24} +(-3.80124 + 3.24817i) q^{25} +(1.75092 + 1.01089i) q^{26} +(1.21205 + 1.21205i) q^{27} +(-2.22551 + 1.43078i) q^{28} +3.15502i q^{29} +(0.607800 - 0.224313i) q^{30} +(-3.33287 + 1.92423i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.421872 + 1.57445i) q^{33} -5.30873 q^{34} +(2.31101 + 5.44603i) q^{35} +2.91605 q^{36} +(-1.30444 - 4.86824i) q^{37} +(3.75919 + 1.00727i) q^{38} +(-0.507306 + 0.292893i) q^{39} +(0.935904 - 2.03078i) q^{40} +7.21050i q^{41} +(-0.0366036 - 0.765697i) q^{42} +(1.85669 + 1.85669i) q^{43} +(4.87205 + 2.81288i) q^{44} +(1.10346 - 6.42644i) q^{45} +(0.561961 + 0.973344i) q^{46} +(-5.69475 + 1.52590i) q^{47} +(-0.204875 + 0.204875i) q^{48} +(6.96808 - 0.667734i) q^{49} +(-4.12132 - 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(-0.523277 + 1.95290i) q^{52} +(-0.357978 + 1.33599i) q^{53} +(-0.857049 + 1.48445i) q^{54} +(8.04270 - 9.67269i) q^{55} +(-1.95803 - 1.77936i) q^{56} +(-0.797333 + 0.797333i) q^{57} +(-3.04751 + 0.816578i) q^{58} +(-2.73923 - 4.74448i) q^{59} +(0.373980 + 0.529033i) q^{60} +(-3.99172 - 2.30462i) q^{61} +(-2.72127 - 2.72127i) q^{62} +(-6.85809 - 3.53413i) q^{63} +1.00000i q^{64} +(4.10581 + 1.89220i) q^{65} +(-1.41161 + 0.814995i) q^{66} +(-0.816193 - 0.218698i) q^{67} +(-1.37400 - 5.12784i) q^{68} -0.325641 q^{69} +(-4.66232 + 3.64180i) q^{70} +4.77710 q^{71} +(0.754730 + 2.81669i) q^{72} +(5.42104 + 1.45256i) q^{73} +(4.36475 - 2.51999i) q^{74} +(1.30741 - 0.623993i) q^{75} +3.89180i q^{76} +(-8.04920 - 12.5202i) q^{77} +(-0.414214 - 0.414214i) q^{78} +(-5.41079 - 3.12392i) q^{79} +(2.20382 + 0.378409i) q^{80} +(4.12576 + 7.14603i) q^{81} +(-6.96481 + 1.86622i) q^{82} +(-5.67281 + 5.67281i) q^{83} +(0.730133 - 0.233533i) q^{84} +(-11.8207 + 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(0.236593 - 0.882976i) q^{87} +(-1.45605 + 5.43407i) q^{88} +(5.96090 - 10.3246i) q^{89} +(6.49307 - 0.597426i) q^{90} +(3.59749 - 3.95871i) q^{91} +(-0.794732 + 0.794732i) q^{92} +(1.07705 - 0.288594i) q^{93} +(-2.94782 - 5.10577i) q^{94} +(8.57682 + 1.47269i) q^{95} +(-0.250919 - 0.144868i) q^{96} +(6.63103 + 6.63103i) q^{97} +(2.44845 + 6.55783i) q^{98} +16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35}+ \cdots + 40 q^{98}+O(q^{100}) $ 16 * q - 12 * q^5 + 8 * q^7 - 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 - 36 * q^17 - 8 * q^18 - 28 * q^21 - 8 * q^22 - 4 * q^23 + 12 * q^25 + 12 * q^26 + 4 * q^28 + 20 * q^30 + 24 * q^31 + 48 * q^33 + 8 * q^35 - 8 * q^36 + 4 * q^37 + 24 * q^38 + 36 * q^42 - 8 * q^43 - 12 * q^45 - 8 * q^46 + 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 - 4 * q^56 + 8 * q^57 - 32 * q^58 + 8 * q^60 - 12 * q^61 - 36 * q^63 - 8 * q^65 + 32 * q^67 - 36 * q^68 - 12 * q^70 + 16 * q^71 - 8 * q^72 - 12 * q^73 - 48 * q^75 + 16 * q^77 + 16 * q^78 - 12 * q^80 - 48 * q^82 + 24 * q^85 + 12 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^95 + 12 * q^96 + 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.279864	−	0.0749894i	−0.161580	−	0.0432952i	0.177122	−	0.984189i	$-0.443321\pi$
$3$	−0.279864	−	0.0749894i	−0.161580	−	0.0432952i	−0.338702	+	0.940894i	$0.609988\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.774197	+	2.09777i	0.346231	+	0.938149i
$5$	0.774197	+	2.09777i	0.346231	+	0.938149i
$6$		−	0.289737i		−	0.118285i
$7$	2.64273	−	0.126334i	0.998859	−	0.0477497i
$7$	2.64273	−	0.126334i	0.998859	−	0.0477497i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.52538	−	1.45803i	−0.841792	−	0.486009i
$10$	−1.82591	+	1.29076i	−0.577403	+	0.408174i
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	−0.882888	−	0.469583i	$-0.844404\pi$
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	0.0347729	−	0.999395i	$-0.488929\pi$
$12$	0.279864	−	0.0749894i	0.0807899	−	0.0216476i
$13$	1.42962	−	1.42962i	0.396505	−	0.396505i	−0.480493	−	0.876998i	$-0.659542\pi$
$13$	1.42962	−	1.42962i	0.396505	−	0.396505i	0.876998	+	0.480493i	$0.159542\pi$
$14$	0.806019	+	2.51999i	0.215418	+	0.673495i
$15$	−0.0593598	−	0.645146i	−0.0153266	−	0.166576i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.37400	+	5.12784i	−0.333244	+	1.24368i	0.572516	+	0.819893i	$0.305967\pi$
$17$	−1.37400	+	5.12784i	−0.333244	+	1.24368i	−0.905760	+	0.423790i	$0.860699\pi$
$18$	0.754730	−	2.81669i	0.177892	−	0.663900i
$19$	1.94590	−	3.37040i	0.446420	−	0.773223i	−0.551729	−	0.834023i	$-0.686032\pi$
$19$	1.94590	−	3.37040i	0.446420	−	0.773223i	0.998150	+	0.0608002i	$0.0193652\pi$
$20$	−1.71936	−	1.42962i	−0.384460	−	0.319673i
$21$	−0.749081	−	0.162821i	−0.163463	−	0.0355304i
$22$	3.97801	−	3.97801i	0.848115	−	0.848115i
$23$	1.08562	−	0.290892i	0.226368	−	0.0606552i	−0.143852	−	0.989599i	$-0.545949\pi$
$23$	1.08562	−	0.290892i	0.226368	−	0.0606552i	0.370220	+	0.928944i	$0.379282\pi$
$24$	0.144868	+	0.250919i	0.0295711	+	0.0512187i
$25$	−3.80124	+	3.24817i	−0.760248	+	0.649633i
$26$	1.75092	+	1.01089i	0.343384	+	0.198253i
$27$	1.21205	+	1.21205i	0.233259	+	0.233259i
$28$	−2.22551	+	1.43078i	−0.420581	+	0.270391i
$29$			3.15502i			0.585872i	0.956132	+	0.292936i	$0.0946322\pi$
$29$			3.15502i			0.585872i	−0.956132	+	0.292936i	$0.905368\pi$
$30$	0.607800	−	0.224313i	0.110969	−	0.0409538i
$31$	−3.33287	+	1.92423i	−0.598601	+	0.345602i	−0.768491	−	0.639861i	$-0.778992\pi$
$31$	−3.33287	+	1.92423i	−0.598601	+	0.345602i	0.169890	+	0.985463i	$0.445659\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	0.421872	+	1.57445i	0.0734386	+	0.274076i
$34$	−5.30873			−0.910440
$35$	2.31101	+	5.44603i	0.390633	+	0.920547i
$36$	2.91605			0.486009
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	−0.986360	−	0.164603i	$-0.947366\pi$
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	0.771911	−	0.635731i	$-0.219301\pi$
$38$	3.75919	+	1.00727i	0.609822	+	0.163401i
$39$	−0.507306	+	0.292893i	−0.0812340	+	0.0469005i
$40$	0.935904	−	2.03078i	0.147979	−	0.321095i
$41$			7.21050i			1.12609i	0.826426	+	0.563046i	$0.190371\pi$
$41$			7.21050i			1.12609i	−0.826426	+	0.563046i	$0.809629\pi$
$42$	−0.0366036	−	0.765697i	−0.00564806	−	0.118150i
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	0.834361	−	0.551218i	$-0.185837\pi$
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	−0.551218	+	0.834361i	$0.685837\pi$
$44$	4.87205	+	2.81288i	0.734489	+	0.424058i
$45$	1.10346	−	6.42644i	0.164494	−	0.957998i
$46$	0.561961	+	0.973344i	0.0828566	+	0.143512i
$47$	−5.69475	+	1.52590i	−0.830665	+	0.222576i	−0.649004	−	0.760785i	$-0.724814\pi$
$47$	−5.69475	+	1.52590i	−0.830665	+	0.222576i	−0.181661	+	0.983361i	$0.558147\pi$
$48$	−0.204875	+	0.204875i	−0.0295711	+	0.0295711i
$49$	6.96808	−	0.667734i	0.995440	−	0.0953905i
$50$	−4.12132	−	2.83103i	−0.582843	−	0.400368i
$51$	0.769067	−	1.33206i	0.107691	−	0.186526i
$52$	−0.523277	+	1.95290i	−0.0725655	+	0.270818i
$53$	−0.357978	+	1.33599i	−0.0491720	+	0.183512i	−0.986144	−	0.165892i	$-0.946950\pi$
$53$	−0.357978	+	1.33599i	−0.0491720	+	0.183512i	0.936972	+	0.349405i	$0.113616\pi$
$54$	−0.857049	+	1.48445i	−0.116630	+	0.202008i
$55$	8.04270	−	9.67269i	1.08448	−	1.30426i
$56$	−1.95803	−	1.77936i	−0.261652	−	0.237777i
$57$	−0.797333	+	0.797333i	−0.105609	+	0.105609i
$58$	−3.04751	+	0.816578i	−0.400158	+	0.107222i
$59$	−2.73923	−	4.74448i	−0.356617	−	0.617679i	0.630776	−	0.775965i	$-0.282737\pi$
$59$	−2.73923	−	4.74448i	−0.356617	−	0.617679i	−0.987393	+	0.158286i	$0.949403\pi$
$60$	0.373980	+	0.529033i	0.0482806	+	0.0682979i
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	0.222193	−	0.975003i	$-0.428678\pi$
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	−0.733281	+	0.679926i	$0.762012\pi$
$62$	−2.72127	−	2.72127i	−0.345602	−	0.345602i
$63$	−6.85809	−	3.53413i	−0.864038	−	0.445259i
$64$			1.00000i			0.125000i
$65$	4.10581	+	1.89220i	0.509264	+	0.234699i
$66$	−1.41161	+	0.814995i	−0.173758	+	0.100319i
$67$	−0.816193	−	0.218698i	−0.0997138	−	0.0267182i	0.208617	−	0.977997i	$-0.433104\pi$
$67$	−0.816193	−	0.218698i	−0.0997138	−	0.0267182i	−0.308331	+	0.951279i	$0.599770\pi$
$68$	−1.37400	−	5.12784i	−0.166622	−	0.621842i
$69$	−0.325641			−0.0392026
$70$	−4.66232	+	3.64180i	−0.557254	+	0.435279i
$71$	4.77710			0.566937			0.283469	−	0.958982i	$-0.408515\pi$
$71$	4.77710			0.566937			0.283469	+	0.958982i	$0.408515\pi$
$72$	0.754730	+	2.81669i	0.0889458	+	0.331950i
$73$	5.42104	+	1.45256i	0.634485	+	0.170010i	0.561704	−	0.827338i	$-0.310146\pi$
$73$	5.42104	+	1.45256i	0.634485	+	0.170010i	0.0727807	+	0.997348i	$0.476813\pi$
$74$	4.36475	−	2.51999i	0.507391	−	0.292943i
$75$	1.30741	−	0.623993i	0.150967	−	0.0720525i
$76$			3.89180i			0.446420i
$77$	−8.04920	−	12.5202i	−0.917291	−	1.42681i
$78$	−0.414214	−	0.414214i	−0.0469005	−	0.0469005i
$79$	−5.41079	−	3.12392i	−0.608761	−	0.351469i	0.163719	−	0.986507i	$-0.447651\pi$
$79$	−5.41079	−	3.12392i	−0.608761	−	0.351469i	−0.772481	+	0.635038i	$0.780984\pi$
$80$	2.20382	+	0.378409i	0.246394	+	0.0423074i
$81$	4.12576	+	7.14603i	0.458418	+	0.794003i
$82$	−6.96481	+	1.86622i	−0.769135	+	0.206089i
$83$	−5.67281	+	5.67281i	−0.622672	+	0.622672i	−0.946214	−	0.323542i	$-0.895126\pi$
$83$	−5.67281	+	5.67281i	−0.622672	+	0.622672i	0.323542	+	0.946214i	$0.395126\pi$
$84$	0.730133	−	0.233533i	0.0796641	−	0.0254806i
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$	−1.31288	+	2.27397i	−0.141571	+	0.245209i
$87$	0.236593	−	0.882976i	0.0253654	−	0.0946650i
$88$	−1.45605	+	5.43407i	−0.155216	+	0.579273i
$89$	5.96090	−	10.3246i	0.631855	−	1.09440i	−0.355318	−	0.934746i	$-0.615627\pi$
$89$	5.96090	−	10.3246i	0.631855	−	1.09440i	0.987172	−	0.159659i	$-0.0510393\pi$
$90$	6.49307	−	0.597426i	0.684429	−	0.0629742i
$91$	3.59749	−	3.95871i	0.377120	−	0.414986i
$92$	−0.794732	+	0.794732i	−0.0828566	+	0.0828566i
$93$	1.07705	−	0.288594i	0.111685	−	0.0299258i
$94$	−2.94782	−	5.10577i	−0.304044	−	0.526620i
$95$	8.57682	+	1.47269i	0.879963	+	0.151095i
$96$	−0.250919	−	0.144868i	−0.0256094	−	0.0147856i
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	0.958471	−	0.285191i	$-0.0920572\pi$
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	−0.285191	+	0.958471i	$0.592057\pi$
$98$	2.44845	+	6.55783i	0.247331	+	0.662440i
$99$			16.4050i			1.64877i
$100$	1.66789	−	4.71361i	0.166789	−	0.471361i
$101$	13.9423	−	8.04960i	1.38731	−	0.800965i	0.394301	−	0.918981i	$-0.370987\pi$
$101$	13.9423	−	8.04960i	1.38731	−	0.800965i	0.993012	+	0.118016i	$0.0376535\pi$
$102$	1.48572	+	0.398099i	0.147109	+	0.0394176i
$103$	5.09084	+	18.9993i	0.501616	+	1.87206i	0.489271	+	0.872132i	$0.337263\pi$
$103$	5.09084	+	18.9993i	0.501616	+	1.87206i	0.0123445	+	0.999924i	$0.496071\pi$
$104$	−2.02179			−0.198253
$105$	−0.238376	−	1.69745i	−0.0232631	−	0.165654i
$106$	−1.38312			−0.134340
$107$	0.724955	+	2.70557i	0.0700840	+	0.261557i	0.992074	−	0.125657i	$-0.0401040\pi$
$107$	0.724955	+	2.70557i	0.0700840	+	0.261557i	−0.921990	+	0.387214i	$0.873437\pi$
$108$	−1.65569	−	0.443641i	−0.159319	−	0.0426894i
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	−0.234395	−	0.972141i	$-0.575311\pi$
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	0.724701	+	0.689063i	$0.241978\pi$
$110$	11.4247	+	5.26517i	1.08930	+	0.502015i
$111$			1.46027i			0.138602i
$112$	1.21196	−	2.35184i	0.114519	−	0.222228i
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.941970	−	0.335697i	$-0.891028\pi$
$113$	−13.5818	−	13.5818i	−1.27767	−	1.27767i	−0.335697	−	0.941970i	$-0.608972\pi$
$114$	−0.976529	−	0.563800i	−0.0914604	−	0.0528047i
$115$	1.45071	+	2.05218i	0.135279	+	0.191367i
$116$	−1.57751	−	2.73232i	−0.146468	−	0.253690i
$117$	−5.69475	+	1.52590i	−0.526480	+	0.141070i
$118$	3.87385	−	3.87385i	0.356617	−	0.356617i
$119$	−2.98330	+	13.7251i	−0.273478	+	1.25818i
$120$	−0.414214	+	0.498161i	−0.0378124	+	0.0454757i
$121$	−10.3246	+	17.8827i	−0.938599	+	1.62570i
$122$	1.19296	−	4.45219i	0.108006	−	0.403082i
$123$	0.540712	−	2.01796i	0.0487543	−	0.181954i
$124$	1.92423	−	3.33287i	0.172801	−	0.299300i
$125$	−9.75680	−	5.45939i	−0.872674	−	0.488303i
$126$	1.63871	−	7.53911i	0.145988	−	0.671637i
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	−0.470906	−	0.882184i	$-0.656073\pi$
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	0.882184	+	0.470906i	$0.156073\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−0.380390	−	0.658854i	−0.0334915	−	0.0580089i
$130$	−0.765062	+	4.45565i	−0.0671004	+	0.390786i
$131$	−6.66437	−	3.84768i	−0.582269	−	0.336173i	0.179766	−	0.983709i	$-0.442466\pi$
$131$	−6.66437	−	3.84768i	−0.582269	−	0.336173i	−0.762035	+	0.647536i	$0.775799\pi$
$132$	−1.15258	−	1.15258i	−0.100319	−	0.100319i
$133$	4.71670	−	9.15290i	0.408990	−	0.793657i
$134$		−	0.844985i		−	0.0729956i
$135$	−1.60423	+	3.48096i	−0.138070	+	0.299594i
$136$	4.59749	−	2.65436i	0.394232	−	0.227610i
$137$	8.53471	+	2.28687i	0.729170	+	0.195380i	0.604259	−	0.796788i	$-0.293469\pi$
$137$	8.53471	+	2.28687i	0.729170	+	0.195380i	0.124910	+	0.992168i	$0.460136\pi$
$138$	−0.0842822	−	0.314545i	−0.00717458	−	0.0267759i
$139$	−11.0631			−0.938361			−0.469180	−	0.883102i	$-0.655451\pi$
$139$	−11.0631			−0.938361			−0.469180	+	0.883102i	$0.655451\pi$
$140$	−4.72441	−	3.56089i	−0.399286	−	0.300950i
$141$	1.70818			0.143855
$142$	1.23640	+	4.61432i	0.103757	+	0.387225i
$143$	−10.9865	−	2.94383i	−0.918740	−	0.246176i
$144$	−2.52538	+	1.45803i	−0.210448	+	0.121502i
$145$	−6.61848	+	2.44260i	−0.549635	+	0.202847i
$146$			5.61227i			0.464475i
$147$	−2.00019	−	0.335657i	−0.164973	−	0.0276846i
$148$	3.56380	+	3.56380i	0.292943	+	0.292943i
$149$	4.37243	+	2.52443i	0.358204	+	0.206809i	0.668293	−	0.743899i	$-0.267025\pi$
$149$	4.37243	+	2.52443i	0.358204	+	0.206809i	−0.310089	+	0.950708i	$0.600359\pi$
$150$	0.941113	+	1.10136i	0.0768416	+	0.0899256i
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	−0.998479	−	0.0551270i	$-0.982444\pi$
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	0.451498	−	0.892272i	$-0.350890\pi$
$152$	−3.75919	+	1.00727i	−0.304911	+	0.0817006i
$153$	10.9464	−	10.9464i	0.884963	−	0.884963i
$154$	10.0103	−	11.0154i	0.806651	−	0.887645i
$155$	−6.61688	−	5.50184i	−0.531481	−	0.441918i
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	−0.285443	+	1.06529i	−0.0227808	+	0.0850191i	−0.976380	−	0.216059i	$-0.930680\pi$
$157$	−0.285443	+	1.06529i	−0.0227808	+	0.0850191i	0.953600	+	0.301078i	$0.0973464\pi$
$158$	1.61706	−	6.03495i	0.128646	−	0.480115i
$159$	0.200370	−	0.347052i	0.0158904	−	0.0275230i
$160$	0.204875	+	2.22666i	0.0161968	+	0.176033i
$161$	2.83227	−	0.905902i	0.223214	−	0.0713951i
$162$	−5.83471	+	5.83471i	−0.458418	+	0.458418i
$163$	12.7899	−	3.42705i	1.00179	−	0.268428i	0.279592	−	0.960119i	$-0.409801\pi$
$163$	12.7899	−	3.42705i	1.00179	−	0.268428i	0.722193	+	0.691691i	$0.243134\pi$
$164$	−3.60525	−	6.24448i	−0.281523	−	0.487612i
$165$	−2.97621	+	2.10392i	−0.231698	+	0.163790i
$166$	−6.94775	−	4.01128i	−0.539250	−	0.311336i
$167$	4.70680	+	4.70680i	0.364223	+	0.364223i	0.865365	−	0.501142i	$-0.167087\pi$
$167$	4.70680	+	4.70680i	0.364223	+	0.364223i	−0.501142	+	0.865365i	$0.667087\pi$
$168$	0.414548	+	0.644812i	0.0319831	+	0.0497483i
$169$			8.91237i			0.685567i
$170$	−4.11000	−	11.1365i	−0.315223	−	0.854128i
$171$	−9.82827	+	5.67435i	−0.751586	+	0.433929i
$172$	−2.53629	−	0.679597i	−0.193390	−	0.0518188i
$173$	−1.82586	−	6.81421i	−0.138818	−	0.518075i	−0.999953	−	0.00969875i	$-0.996913\pi$
$173$	−1.82586	−	6.81421i	−0.138818	−	0.518075i	0.861135	−	0.508376i	$-0.169754\pi$
$174$	0.914124			0.0692996
$175$	−9.63531	+	9.06426i	−0.728361	+	0.685194i
$176$	−5.62576			−0.424058
$177$	0.410826	+	1.53322i	0.0308796	+	0.115244i
$178$	11.5156	+	3.08559i	0.863129	+	0.231275i
$179$	−1.91075	+	1.10317i	−0.142816	+	0.0824550i	−0.569706	−	0.821849i	$-0.692943\pi$
$179$	−1.91075	+	1.10317i	−0.142816	+	0.0824550i	0.426889	+	0.904304i	$0.359609\pi$
$180$	2.25760	+	6.11719i	0.168271	+	0.455949i
$181$		−	4.11867i		−	0.306139i	−0.988215	−	0.153069i	$-0.951084\pi$
$181$		−	4.11867i		−	0.306139i	0.988215	−	0.153069i	$-0.0489158\pi$
$182$	4.75492	+	2.45032i	0.352458	+	0.181630i
$183$	0.944318	+	0.944318i	0.0698060	+	0.0698060i
$184$	−0.973344	−	0.561961i	−0.0717559	−	0.0414283i
$185$	9.20253	−	6.50539i	0.676584	−	0.478286i
$186$	0.557521	+	0.965654i	0.0408794	+	0.0708052i
$187$	28.8480	−	7.72980i	2.10957	−	0.565259i
$188$	4.16885	−	4.16885i	0.304044	−	0.304044i
$189$	3.35625	+	3.05000i	0.244131	+	0.221855i
$190$	0.797333	+	8.66573i	0.0578446	+	0.628678i
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	−0.366686	−	0.930345i	$-0.619508\pi$
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	0.989045	−	0.147613i	$-0.0471589\pi$
$192$	0.0749894	−	0.279864i	0.00541190	−	0.0201975i
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	0.757659	+	0.652650i	$0.226343\pi$
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	−0.982477	+	0.186382i	$0.940324\pi$
$194$	−4.68885	+	8.12132i	−0.336640	+	0.583077i
$195$	−1.00718	−	0.837452i	−0.0721254	−	0.0599712i
$196$	−5.70067	+	4.06231i	−0.407190	+	0.290165i
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.0199932	−	0.999800i	$-0.493636\pi$
$197$	14.3135	−	14.3135i	1.01979	−	1.01979i	0.999800	−	0.0199932i	$-0.00636444\pi$
$198$	−15.8460	+	4.24593i	−1.12613	+	0.301745i
$199$	3.76653	+	6.52383i	0.267002	+	0.462462i	0.968086	−	0.250617i	$-0.0806335\pi$
$199$	3.76653	+	6.52383i	0.267002	+	0.462462i	−0.701084	+	0.713079i	$0.747300\pi$
$200$	4.98468	+	0.391082i	0.352470	+	0.0276537i
$201$	0.212023	+	0.122412i	0.0149550	+	0.00863425i
$202$	11.3839	+	11.3839i	0.800965	+	0.800965i
$203$	0.398585	+	8.33786i	0.0279752	+	0.585203i
$204$			1.53813i			0.107691i
$205$	−15.1259	+	5.58235i	−1.05644	+	0.389888i
$206$	−17.0343	+	9.83476i	−1.18684	+	0.685220i
$207$	−3.16574	−	0.848257i	−0.220034	−	0.0589579i
$208$	−0.523277	−	1.95290i	−0.0362827	−	0.135409i
$209$	−21.8944			−1.51446
$210$	1.57791	−	0.669586i	0.108886	−	0.0462058i
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	−0.357978	−	1.33599i	−0.0245860	−	0.0917562i
$213$	−1.33694	−	0.358232i	−0.0916056	−	0.0245456i
$214$	−2.42575	+	1.40051i	−0.165821	+	0.0957366i
$215$	−2.45746	+	5.33235i	−0.167597	+	0.363663i
$216$		−	1.71410i		−	0.116630i
$217$	−8.56478	+	5.50629i	−0.581415	+	0.373791i
$218$	4.17960	+	4.17960i	0.283078	+	0.283078i
$219$	−1.40823	−	0.813041i	−0.0951593	−	0.0549402i
$220$	−2.12884	+	12.3981i	−0.143526	+	0.835883i
$221$	5.36656	+	9.29516i	0.360994	+	0.625260i
$222$	−1.41051	+	0.377945i	−0.0946672	+	0.0253660i
$223$	−1.46027	+	1.46027i	−0.0977867	+	0.0977867i	−0.754308	−	0.656521i	$-0.772027\pi$
$223$	−1.46027	+	1.46027i	−0.0977867	+	0.0977867i	0.656521	+	0.754308i	$0.272027\pi$
$224$	2.58538	+	0.561961i	0.172743	+	0.0375476i
$225$	14.3355	−	2.66053i	0.955698	−	0.177369i
$226$	9.60377	−	16.6342i	0.638833	−	1.10649i
$227$	−4.82525	+	18.0081i	−0.320263	+	1.19524i	0.598726	+	0.800954i	$0.295674\pi$
$227$	−4.82525	+	18.0081i	−0.320263	+	1.19524i	−0.918989	+	0.394283i	$0.870993\pi$
$228$	0.291844	−	1.08918i	0.0193278	−	0.0721325i
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	−0.792191	−	0.610274i	$-0.791059\pi$
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	0.924608	+	0.380920i	$0.124393\pi$
$230$	−1.60678	+	1.93242i	−0.105948	+	0.127420i
$231$	1.31380	+	4.10755i	0.0864419	+	0.270257i
$232$	2.23093	−	2.23093i	0.146468	−	0.146468i
$233$	13.2637	−	3.55400i	0.868934	−	0.232830i	0.203307	−	0.979115i	$-0.434831\pi$
$233$	13.2637	−	3.55400i	0.868934	−	0.232830i	0.665627	+	0.746285i	$0.268164\pi$
$234$	−2.94782	−	5.10577i	−0.192705	−	0.333775i
$235$	−7.60984	−	10.7649i	−0.496412	−	0.702225i
$236$	4.74448	+	2.73923i	0.308839	+	0.178308i
$237$	1.28003	+	1.28003i	0.0831466	+	0.0831466i
$238$	−14.0296	+	0.670673i	−0.909401	+	0.0434732i
$239$		−	19.6621i		−	1.27183i	−0.771758	−	0.635916i	$-0.780622\pi$
$239$		−	19.6621i		−	1.27183i	0.771758	−	0.635916i	$-0.219378\pi$
$240$	−0.588393	−	0.271166i	−0.0379806	−	0.0175037i
$241$	−5.09667	+	2.94256i	−0.328305	+	0.189547i	−0.655088	−	0.755552i	$-0.727369\pi$
$241$	−5.09667	+	2.94256i	−0.328305	+	0.189547i	0.326783	+	0.945099i	$0.394035\pi$
$242$	−19.9456	−	5.34440i	−1.28215	−	0.343551i
$243$	−1.94970	−	7.27638i	−0.125073	−	0.466780i
$244$	4.60924			0.295077
$245$	6.79541	+	14.1004i	0.434143	+	0.900844i
$246$	2.08915			0.133199
$247$	−2.03649	−	7.60029i	−0.129579	−	0.483595i
$248$	3.71733	+	0.996056i	0.236051	+	0.0632496i
$249$	2.01302	−	1.16222i	0.127570	−	0.0736525i
$250$	2.74812	−	10.8373i	0.173806	−	0.685413i
$251$		−	7.09950i		−	0.448116i	−0.974576	−	0.224058i	$-0.928069\pi$
$251$		−	7.09950i		−	0.448116i	0.974576	−	0.224058i	$-0.0719306\pi$
$252$	7.70635	−	0.368396i	0.485454	−	0.0232068i
$253$	−4.47097	−	4.47097i	−0.281088	−	0.281088i
$254$	5.67653	+	3.27735i	0.356177	+	0.205639i
$255$	3.38977	+	0.582044i	0.212275	+	0.0364490i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.54998	+	2.55891i	−0.595711	+	0.159620i	−0.544062	−	0.839045i	$-0.683114\pi$
$257$	−9.54998	+	2.55891i	−0.595711	+	0.159620i	−0.0516491	+	0.998665i	$0.516448\pi$
$258$	0.537952	−	0.537952i	0.0334915	−	0.0334915i
$259$	−4.06231	−	12.7007i	−0.252420	−	0.789181i
$260$	−4.50184	+	0.414214i	−0.279192	+	0.0256884i
$261$	4.60010	−	7.96760i	0.284739	−	0.493182i
$262$	1.99170	−	7.43314i	0.123048	−	0.459221i
$263$	3.55829	−	13.2797i	0.219413	−	0.818861i	−0.765153	−	0.643849i	$-0.777337\pi$
$263$	3.55829	−	13.2797i	0.219413	−	0.818861i	0.984566	−	0.175013i	$-0.0559967\pi$
$264$	0.814995	−	1.41161i	0.0501595	−	0.0868788i
$265$	−3.07974	+	0.283366i	−0.189187	+	0.0174071i
$266$	10.0618	+	2.18704i	0.616929	+	0.134096i
$267$	−2.44248	+	2.44248i	−0.149477	+	0.149477i
$268$	0.816193	−	0.218698i	0.0498569	−	0.0133591i
$269$	13.2510	+	22.9514i	0.807928	+	1.39937i	0.914296	+	0.405046i	$0.132745\pi$
$269$	13.2510	+	22.9514i	0.807928	+	1.39937i	−0.106368	+	0.994327i	$0.533922\pi$
$270$	−3.77756	−	0.648630i	−0.229895	−	0.0394744i
$271$	−11.0824	−	6.39844i	−0.673209	−	0.388678i	0.124082	−	0.992272i	$-0.460401\pi$
$271$	−11.0824	−	6.39844i	−0.673209	−	0.388678i	−0.797292	+	0.603594i	$0.793735\pi$
$272$	3.75384	+	3.75384i	0.227610	+	0.227610i
$273$	−1.30367	+	0.838129i	−0.0789018	+	0.0507259i
$274$			8.83578i			0.533789i
$275$	26.5177	+	9.38313i	1.59908	+	0.565824i
$276$	0.282014	−	0.162821i	0.0169752	−	0.00980065i
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.377083	−	0.926180i	$-0.623073\pi$
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.789653	+	0.613554i	$0.789739\pi$
$278$	−2.86334	−	10.6861i	−0.171732	−	0.640912i
$279$	11.2223			0.671863
$280$	2.21679	−	5.48506i	0.132478	−	0.327795i
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$	0.442111	+	1.64998i	0.0263273	+	0.0982548i
$283$	−26.1454	−	7.00563i	−1.55418	−	0.416442i	−0.623366	−	0.781930i	$-0.714235\pi$
$283$	−26.1454	−	7.00563i	−1.55418	−	0.416442i	−0.930816	+	0.365489i	$0.880902\pi$
$284$	−4.13709	+	2.38855i	−0.245491	+	0.141734i
$285$	−2.28991	−	1.05532i	−0.135643	−	0.0625121i
$286$		−	11.3741i		−	0.672564i
$287$	0.910931	+	19.0554i	0.0537706	+	1.12481i
$288$	−2.06196	−	2.06196i	−0.121502	−	0.121502i
$289$	−9.68442	−	5.59130i	−0.569672	−	0.328900i
$290$	−4.07236	−	5.76077i	−0.239137	−	0.338284i
$291$	−1.35853	−	2.35305i	−0.0796385	−	0.137938i
$292$	−5.42104	+	1.45256i	−0.317242	+	0.0850048i
$293$	−17.1191	+	17.1191i	−1.00011	+	1.00011i	−0.000106876		1.00000i	$0.500034\pi$
$293$	−17.1191	+	17.1191i	−1.00011	+	1.00011i	−1.00000		0.000106876i	$0.999966\pi$
$294$	−0.193467	−	2.01891i	−0.0112832	−	0.117745i
$295$	7.83211	−	9.41941i	0.456003	−	0.548420i
$296$	−2.51999	+	4.36475i	−0.146471	+	0.253696i
$297$	2.49582	−	9.31453i	0.144822	−	0.540484i
$298$	−1.30674	+	4.87682i	−0.0756974	+	0.282506i
$299$	1.13616	−	1.96790i	0.0657061	−	0.113806i
$300$	−0.820253	+	1.19410i	−0.0473573	+	0.0689413i
$301$	5.14131	+	4.67218i	0.296340	+	0.269300i
$302$	9.50552	−	9.50552i	0.546981	−	0.546981i
$303$	−4.50559	+	1.20727i	−0.258840	+	0.0693558i
$304$	−1.94590	−	3.37040i	−0.111605	−	0.193306i
$305$	1.74418	−	10.1579i	0.0998713	−	0.581641i
$306$	13.4065	+	7.74027i	0.766401	+	0.442482i
$307$	−17.2974	−	17.2974i	−0.987217	−	0.987217i	0.0127019	−	0.999919i	$-0.495957\pi$
$307$	−17.2974	−	17.2974i	−0.987217	−	0.987217i	−0.999919	+	0.0127019i	$0.995957\pi$
$308$	13.2309	+	6.81819i	0.753900	+	0.388502i
$309$		−	5.69898i		−	0.324204i
$310$	3.60179	−	7.81540i	0.204568	−	0.443885i
$311$	−9.51095	+	5.49115i	−0.539316	+	0.311374i	−0.744802	−	0.667286i	$-0.767456\pi$
$311$	−9.51095	+	5.49115i	−0.539316	+	0.311374i	0.205486	+	0.978660i	$0.434123\pi$
$312$	0.565826	+	0.151613i	0.0320336	+	0.00858338i
$313$	7.61212	+	28.4088i	0.430262	+	1.60576i	0.752156	+	0.658985i	$0.229014\pi$
$313$	7.61212	+	28.4088i	0.430262	+	1.60576i	−0.321893	+	0.946776i	$0.604319\pi$
$314$	−1.10287			−0.0622383
$315$	2.10427	−	17.1228i	0.118562	−	0.964760i
$316$	6.24784			0.351469
$317$	1.11136	+	4.14766i	0.0624203	+	0.232956i	0.990087	−	0.140453i	$-0.0448558\pi$
$317$	1.11136	+	4.14766i	0.0624203	+	0.232956i	−0.927667	+	0.373408i	$0.878189\pi$
$318$	0.387086	+	0.103719i	0.0217067	+	0.00581629i
$319$	15.3714	−	8.87468i	0.860633	−	0.496887i
$320$	−2.09777	+	0.774197i	−0.117269	+	0.0432789i
$321$		−	0.811556i		−	0.0452966i
$322$	1.60808	+	2.50129i	0.0896147	+	0.139392i
$323$	14.6092	+	14.6092i	0.812878	+	0.812878i
$324$	−7.14603	−	4.12576i	−0.397001	−	0.229209i
$325$	−0.790684	+	10.0780i	−0.0438593	+	0.559025i
$326$	6.62056	+	11.4671i	0.366679	+	0.635106i
$327$	−1.65424	+	0.443251i	−0.0914795	+	0.0245119i
$328$	5.09860	−	5.09860i	0.281523	−	0.281523i
$329$	−14.8569	+	4.75200i	−0.819089	+	0.261986i
$330$	−2.80253	−	2.33027i	−0.154274	−	0.128277i
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.291863	+	0.956460i	$0.594275\pi$
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.682387	+	0.730991i	$0.739058\pi$
$332$	2.07639	−	7.74921i	0.113957	−	0.425293i
$333$	−3.80382	+	14.1960i	−0.208448	+	0.777939i
$334$	−3.32821	+	5.76463i	−0.182112	+	0.315426i
$335$	−0.173116	−	1.88150i	−0.00945835	−	0.102797i
$336$	−0.515547	+	0.567312i	−0.0281254	+	0.0309494i
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	−0.955782	−	0.294075i	$-0.904989\pi$
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	0.294075	+	0.955782i	$0.404989\pi$
$338$	−8.60869	+	2.30669i	−0.468251	+	0.125468i
$339$	2.78257	+	4.81955i	0.151128	+	0.261762i
$340$	9.69326	−	6.85229i	0.525691	−	0.371617i
$341$	18.7499	+	10.8253i	1.01536	+	0.586221i
$342$	−8.02475	−	8.02475i	−0.433929	−	0.433929i
$343$	18.3304	−	2.64495i	0.989750	−	0.142814i
$344$		−	2.62576i		−	0.141571i
$345$	−0.252110	−	0.683119i	−0.0135732	−	0.0367779i
$346$	6.10945	−	3.52729i	0.328446	−	0.189628i
$347$	−8.67040	−	2.32323i	−0.465452	−	0.124717i	0.0184687	−	0.999829i	$-0.494121\pi$
$347$	−8.67040	−	2.32323i	−0.465452	−	0.124717i	−0.483920	+	0.875112i	$0.660788\pi$
$348$	0.236593	+	0.882976i	0.0126827	+	0.0473325i
$349$	26.0251			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$349$	26.0251			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$350$	−11.2492	−	6.96099i	−0.601295	−	0.372081i
$351$	3.46554			0.184977
$352$	−1.45605	−	5.43407i	−0.0776079	−	0.289637i
$353$	9.62659	+	2.57944i	0.512372	+	0.137290i	0.505736	−	0.862688i	$-0.331221\pi$
$353$	9.62659	+	2.57944i	0.512372	+	0.137290i	0.00663577	+	0.999978i	$0.497888\pi$
$354$	−1.37465	+	0.793655i	−0.0730619	+	0.0421823i
$355$	3.69841	+	10.0212i	0.196291	+	0.531872i
$356$			11.9218i			0.631855i
$357$	1.86416	−	3.61745i	0.0986615	−	0.191456i
$358$	−1.56012	−	1.56012i	−0.0824550	−	0.0824550i
$359$	−10.0235	−	5.78705i	−0.529019	−	0.305429i	0.211598	−	0.977357i	$-0.432133\pi$
$359$	−10.0235	−	5.78705i	−0.529019	−	0.305429i	−0.740617	+	0.671928i	$0.765467\pi$
$360$	−5.32445	+	3.76392i	−0.280623	+	0.198376i
$361$	1.92693	+	3.33754i	0.101417	+	0.175660i
$362$	3.97833	−	1.06599i	0.209097	−	0.0560273i
$363$	4.23050	−	4.23050i	0.222044	−	0.222044i
$364$	−1.13616	+	5.22709i	−0.0595512	+	0.273974i
$365$	1.14981	+	12.4966i	0.0601840	+	0.654104i
$366$	−0.667734	+	1.15655i	−0.0349030	+	0.0604538i
$367$	4.32083	−	16.1256i	0.225545	−	0.841747i	−0.756640	−	0.653832i	$-0.773160\pi$
$367$	4.32083	−	16.1256i	0.225545	−	0.841747i	0.982185	−	0.187915i	$-0.0601730\pi$
$368$	0.290892	−	1.08562i	0.0151638	−	0.0565921i
$369$	10.5131	−	18.2092i	0.547290	−	0.947935i
$370$	8.66551	+	7.20525i	0.450499	+	0.374583i
$371$	−0.777258	+	3.57589i	−0.0403532	+	0.185651i
$372$	−0.788454	+	0.788454i	−0.0408794	+	0.0408794i
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	−0.337436	−	0.941348i	$-0.609560\pi$
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	0.178446	+	0.983950i	$0.442893\pi$
$374$	14.9328	+	25.8644i	0.772158	+	1.33742i
$375$	2.32118	+	2.25954i	0.119865	+	0.116682i
$376$	5.10577	+	2.94782i	0.263310	+	0.152022i
$377$	4.51047	+	4.51047i	0.232301	+	0.232301i
$378$	−2.07742	+	4.03129i	−0.106851	+	0.207347i
$379$		−	7.15349i		−	0.367450i	−0.982978	−	0.183725i	$-0.941184\pi$
$379$		−	7.15349i		−	0.367450i	0.982978	−	0.183725i	$-0.0588156\pi$
$380$	−8.16409	+	3.01302i	−0.418809	+	0.154565i
$381$	−1.64470	+	0.949568i	−0.0842605	+	0.0486478i
$382$	16.6162	+	4.45229i	0.850158	+	0.227799i
$383$	−3.77704	−	14.0961i	−0.192998	−	0.720278i	−0.992776	−	0.119982i	$-0.961716\pi$
$383$	−3.77704	−	14.0961i	−0.192998	−	0.720278i	0.799778	−	0.600296i	$-0.204950\pi$
$384$	0.289737			0.0147856
$385$	20.0327	−	26.5784i	1.02096	−	1.35456i
$386$	−12.0674			−0.614214
$387$	−1.98174	−	7.39595i	−0.100737	−	0.375957i
$388$	−9.05816	−	2.42713i	−0.459858	−	0.123219i
$389$	−5.36634	+	3.09826i	−0.272084	+	0.157088i	−0.629834	−	0.776729i	$-0.716877\pi$
$389$	−5.36634	+	3.09826i	−0.272084	+	0.157088i	0.357750	+	0.933817i	$0.383544\pi$
$390$	0.548240	−	1.18961i	0.0277612	−	0.0602380i
$391$			5.96659i			0.301744i
$392$	−5.39934	−	4.45502i	−0.272708	−	0.225012i
$393$	1.57658	+	1.57658i	0.0795282	+	0.0795282i
$394$	17.5304	+	10.1212i	0.883167	+	0.509897i
$395$	2.36424	−	13.7691i	0.118958	−	0.692798i
$396$	−8.20251	−	14.2072i	−0.412191	−	0.713937i
$397$	2.81652	−	0.754685i	0.141357	−	0.0378766i	−0.187447	−	0.982275i	$-0.560021\pi$
$397$	2.81652	−	0.754685i	0.141357	−	0.0378766i	0.328804	+	0.944398i	$0.393354\pi$
$398$	−5.32668	+	5.32668i	−0.267002	+	0.267002i
$399$	−2.00641	+	2.20787i	−0.100446	+	0.110532i
$400$	0.912375	+	4.91605i	0.0456187	+	0.245803i
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$	−0.0633649	+	0.236481i	−0.00316035	+	0.0117946i
$403$	−2.01381	+	7.51565i	−0.100315	+	0.374381i
$404$	−8.04960	+	13.9423i	−0.400483	+	0.693656i
$405$	−11.7965	+	14.1873i	−0.586175	+	0.704973i
$406$	−7.95060	+	2.54300i	−0.394581	+	0.126207i
$407$	−20.0491	+	20.0491i	−0.993796	+	0.993796i
$408$	−1.48572	+	0.398099i	−0.0735543	+	0.0197088i
$409$	−17.1791	−	29.7550i	−0.849451	−	1.47129i	−0.881699	−	0.471812i	$-0.843600\pi$
$409$	−17.1791	−	29.7550i	−0.849451	−	1.47129i	0.0322484	−	0.999480i	$-0.489733\pi$
$410$	−9.30702	−	13.1657i	−0.459641	−	0.650209i
$411$	−2.21707	−	1.28003i	−0.109360	−	0.0631390i
$412$	−13.9084	−	13.9084i	−0.685220	−	0.685220i
$413$	−7.83843	−	12.1923i	−0.385704	−	0.599946i
$414$		−	3.27741i		−	0.161076i
$415$	−16.2921	−	7.50836i	−0.799748	−	0.368571i
$416$	1.75092	−	1.01089i	0.0858459	−	0.0495631i
$417$	3.09617	+	0.829616i	0.151620	+	0.0406265i
$418$	−5.66668	−	21.1483i	−0.277166	−	1.03440i
$419$	31.1360			1.52109			0.760547	−	0.649283i	$-0.224931\pi$
$419$	31.1360			1.52109			0.760547	+	0.649283i	$0.224931\pi$
$420$	1.05516	+	1.35085i	0.0514868	+	0.0659146i
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	5.06679	+	18.9095i	0.246648	+	0.920501i
$423$	16.6062	+	4.44962i	0.807421	+	0.216348i
$424$	1.19782	−	0.691560i	0.0581711	−	0.0335851i
$425$	−11.4332	−	23.9551i	−0.554590	−	1.16199i
$426$		−	1.38410i		−	0.0670599i
$427$	−10.8402	−	5.58621i	−0.524594	−	0.270336i
$428$	−1.98061	−	1.98061i	−0.0957366	−	0.0957366i
$429$	2.85398	+	1.64775i	0.137792	+	0.0795540i
$430$	−5.78669	−	0.993610i	−0.279059	−	0.0479162i
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	0.987141	−	0.159849i	$-0.0511008\pi$
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	−0.632004	+	0.774965i	$0.717767\pi$
$432$	1.65569	−	0.443641i	0.0796595	−	0.0213447i
$433$	9.98256	−	9.98256i	0.479731	−	0.479731i	−0.425315	−	0.905046i	$-0.639837\pi$
$433$	9.98256	−	9.98256i	0.479731	−	0.479731i	0.905046	+	0.425315i	$0.139837\pi$
$434$	−7.53539	−	6.84781i	−0.361710	−	0.328706i
$435$	2.03545	−	0.187281i	0.0975922	−	0.00897944i
$436$	−2.95543	+	5.11895i	−0.141539	+	0.245153i
$437$	1.13210	−	4.22504i	0.0541555	−	0.202111i
$438$	0.420861	−	1.57067i	0.0201095	−	0.0750498i
$439$	−19.2142	+	33.2800i	−0.917046	+	1.58837i	−0.113167	+	0.993576i	$0.536100\pi$
$439$	−19.2142	+	33.2800i	−0.917046	+	1.58837i	−0.803878	+	0.594794i	$0.797234\pi$
$440$	−12.5267	+	1.15258i	−0.597186	+	0.0549470i
$441$	−18.5706	−	8.47336i	−0.884314	−	0.403494i
$442$	−7.58946	+	7.58946i	−0.360994	+	0.360994i
$443$	−5.54016	+	1.48448i	−0.263221	+	0.0705299i	−0.388016	−	0.921653i	$-0.626839\pi$
$443$	−5.54016	+	1.48448i	−0.263221	+	0.0705299i	0.124795	+	0.992183i	$0.460173\pi$
$444$	−0.730133	−	1.26463i	−0.0346506	−	0.0600166i
$445$	26.2735	+	4.51132i	1.24548	+	0.213857i
$446$	−1.78845	−	1.03256i	−0.0846857	−	0.0488933i
$447$	−1.03438	−	1.03438i	−0.0489247	−	0.0489247i
$448$	0.126334	+	2.64273i	0.00596872	+	0.124857i
$449$		−	7.30267i		−	0.344635i	−0.985042	−	0.172317i	$-0.944875\pi$
$449$		−	7.30267i		−	0.344635i	0.985042	−	0.172317i	$-0.0551254\pi$
$450$	6.28017	+	13.1584i	0.296050	+	0.620293i
$451$	35.1299	−	20.2823i	1.65420	−	0.955055i
$452$	18.5531	+	4.97128i	0.872663	+	0.233829i
$453$	1.00807	+	3.76217i	0.0473633	+	0.176762i
$454$	−18.6433			−0.874974
$455$	11.0896	+	4.48188i	0.519889	+	0.210114i
$456$	1.12760			0.0528047
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	0.990055	−	0.140683i	$-0.0449299\pi$
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	−0.927754	+	0.373192i	$0.878263\pi$
$458$	3.87111	+	1.03726i	0.180885	+	0.0484680i
$459$	−7.88056	+	4.54984i	−0.367833	+	0.212368i
$460$	−2.28244	−	1.05188i	−0.106419	−	0.0490443i
$461$		−	29.4110i		−	1.36981i	−0.728634	−	0.684903i	$-0.759845\pi$
$461$		−	29.4110i		−	1.36981i	0.728634	−	0.684903i	$-0.240155\pi$
$462$	−3.62755	+	2.33215i	−0.168769	+	0.108501i
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	0.606805	−	0.794851i	$-0.292451\pi$
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	−0.794851	+	0.606805i	$0.792451\pi$
$464$	2.73232	+	1.57751i	0.126845	+	0.0732340i
$465$	1.43925	+	2.03596i	0.0667436	+	0.0944156i
$466$	6.86580	+	11.8919i	0.318052	+	0.550882i
$467$	16.0757	−	4.30747i	0.743894	−	0.199326i	0.133086	−	0.991105i	$-0.457511\pi$
$467$	16.0757	−	4.30747i	0.743894	−	0.199326i	0.610808	+	0.791779i	$0.290845\pi$
$468$	4.16885	−	4.16885i	0.192705	−	0.192705i
$469$	−2.18461	−	0.474848i	−0.100876	−	0.0219264i
$470$	8.42852	−	10.1367i	0.388779	−	0.467571i
$471$	0.159770	−	0.276731i	0.00736184	−	0.0127511i
$472$	−1.41793	+	5.29178i	−0.0652654	+	0.243574i
$473$	3.82325	−	14.2686i	0.175793	−	0.656069i
$474$	−0.905115	+	1.56771i	−0.0415733	+	0.0720071i
$475$	3.55078	+	19.1323i	0.162921	+	0.877851i
$476$	−4.27894	−	13.3779i	−0.196125	−	0.613176i
$477$	2.85194	−	2.85194i	0.130581	−	0.130581i
$478$	18.9921	−	5.08891i	0.868678	−	0.232762i
$479$	−7.69460	−	13.3274i	−0.351575	−	0.608946i	0.634950	−	0.772553i	$-0.281021\pi$
$479$	−7.69460	−	13.3274i	−0.351575	−	0.608946i	−0.986526	+	0.163607i	$0.947687\pi$
$480$	0.109639	−	0.638527i	0.00500431	−	0.0291446i
$481$	−8.82459	−	5.09488i	−0.402367	−	0.232306i
$482$	−4.16141	−	4.16141i	−0.189547	−	0.189547i
$483$	−0.860583	+	0.0411396i	−0.0391579	+	0.00187191i
$484$		−	20.6492i		−	0.938599i
$485$	−8.77662	+	19.0441i	−0.398526	+	0.864747i
$486$	6.52383	−	3.76653i	0.295927	−	0.170853i
$487$	34.7656	+	9.31541i	1.57538	+	0.422122i	0.937492	−	0.348007i	$-0.113142\pi$
$487$	34.7656	+	9.31541i	1.57538	+	0.422122i	0.637888	+	0.770129i	$0.279808\pi$
$488$	1.19296	+	4.45219i	0.0540028	+	0.201541i
$489$	−3.83644			−0.173490
$490$	−11.8612	+	10.2133i	−0.535834	+	0.461391i
$491$	−15.2823			−0.689680			−0.344840	−	0.938661i	$-0.612067\pi$
$491$	−15.2823			−0.689680			−0.344840	+	0.938661i	$0.612067\pi$
$492$	0.540712	+	2.01796i	0.0243772	+	0.0909768i
$493$	−16.1784	−	4.33499i	−0.728639	−	0.195238i
$494$	6.81423	−	3.93420i	0.306587	−	0.177008i
$495$	−34.4139	+	12.7007i	−1.54679	+	0.570854i
$496$			3.84846i			0.172801i
$497$	12.6246	−	0.603509i	0.566290	−	0.0270711i
$498$	1.64362	+	1.64362i	0.0736525	+	0.0736525i
$499$	27.3534	+	15.7925i	1.22451	+	0.706969i	0.965875	−	0.259008i	$-0.0833955\pi$
$499$	27.3534	+	15.7925i	1.22451	+	0.706969i	0.258630	+	0.965976i	$0.416729\pi$
$500$	11.1793	−	0.150429i	0.499955	−	0.00672739i
$501$	−0.964305	−	1.67023i	−0.0430820	−	0.0746202i
$502$	6.85759	−	1.83749i	0.306069	−	0.0820110i
$503$	−16.9777	+	16.9777i	−0.756997	+	0.756997i	−0.975775	−	0.218778i	$-0.929793\pi$
$503$	−16.9777	+	16.9777i	−0.756997	+	0.756997i	0.218778	+	0.975775i	$0.429793\pi$
$504$	2.35039	+	7.34841i	0.104695	+	0.327324i
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$	3.16146	−	5.47580i	0.140544	−	0.243429i
$507$	0.668334	−	2.49426i	0.0296817	−	0.110774i
$508$	−1.69648	+	6.33135i	−0.0752691	+	0.280908i
$509$	−10.7571	+	18.6318i	−0.476799	+	0.825840i	−0.999647	−	0.0265865i	$-0.991536\pi$
$509$	−10.7571	+	18.6318i	−0.476799	+	0.825840i	0.522848	+	0.852426i	$0.324870\pi$
$510$	0.315125	+	3.42491i	0.0139540	+	0.151657i
$511$	14.5099	+	3.15388i	0.641879	+	0.139519i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	6.44363	−	1.72657i	0.284493	−	0.0762297i
$514$	−4.94343	−	8.56228i	−0.218045	−	0.377666i
$515$	−35.9147	+	25.3886i	−1.58259	+	1.11875i
$516$	0.658854	+	0.380390i	0.0290044	+	0.0167457i
$517$	23.4529	+	23.4529i	1.03146	+	1.03146i
$518$	11.2165	−	7.21107i	0.492825	−	0.316836i
$519$			2.04397i			0.0897205i
$520$	−1.56526	−	4.24124i	−0.0686412	−	0.185991i
$521$	11.4657	−	6.61973i	0.502322	−	0.290016i	−0.227350	−	0.973813i	$-0.573006\pi$
$521$	11.4657	−	6.61973i	0.502322	−	0.290016i	0.729672	+	0.683798i	$0.239673\pi$
$522$	8.88670	+	2.38118i	0.388960	+	0.104222i
$523$	−6.97006	−	26.0126i	−0.304779	−	1.13745i	−0.933135	−	0.359526i	$-0.882938\pi$
$523$	−6.97006	−	26.0126i	−0.304779	−	1.13745i	0.628356	−	0.777926i	$-0.283728\pi$
$524$	7.69535			0.336173
$525$	3.37630	−	1.81422i	0.147354	−	0.0791789i
$526$	13.7482			0.599448
$527$	−5.28779	−	19.7343i	−0.230340	−	0.859640i
$528$	1.57445	+	0.421872i	0.0685191	+	0.0183596i
$529$	−18.8246	+	10.8684i	−0.818462	+	0.472539i
$530$	−1.07081	−	2.90146i	−0.0465129	−	0.126031i
$531$			15.9755i			0.693276i
$532$	0.491667	+	10.2850i	0.0213165	+	0.445911i
$533$	10.3083	+	10.3083i	0.446501	+	0.446501i
$534$	−2.99141	−	1.72709i	−0.129451	−	0.0747386i
$535$	−5.11439	+	3.61543i	−0.221114	+	0.156309i
$536$	0.422492	+	0.731778i	0.0182489	+	0.0316080i
$537$	0.617477	−	0.165453i	0.0266461	−	0.00713980i
$538$	−18.7398	+	18.7398i	−0.807928	+	0.807928i
$539$	−22.8536	−	32.0706i	−0.984374	−	1.38138i
$540$	−0.351176	−	3.81672i	−0.0151122	−	0.164245i
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	−0.718171	−	0.695867i	$-0.755020\pi$
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	0.961724	+	0.274020i	$0.0883536\pi$
$542$	3.31208	−	12.3608i	0.142266	−	0.530943i
$543$	−0.308857	+	1.15267i	−0.0132543	+	0.0494658i
$544$	−2.65436	+	4.59749i	−0.113805	+	0.197116i
$545$	10.1629	+	8.45027i	0.435329	+	0.361970i
$546$	−1.14699	−	1.04233i	−0.0490864	−	0.0446075i
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.409527	+	0.912298i	$0.634306\pi$
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.912298	+	0.409527i	$0.865694\pi$
$548$	−8.53471	+	2.28687i	−0.364585	+	0.0976902i
$549$	6.72040	+	11.6401i	0.286820	+	0.496786i
$550$	−2.20013	+	28.0426i	−0.0938140	+	1.19574i
$551$	10.6337	+	6.13935i	0.453009	+	0.261545i
$552$	0.230263	+	0.230263i	0.00980065	+	0.00980065i
$553$	−14.6939	−	7.57212i	−0.624850	−	0.321999i
$554$		−	20.1034i		−	0.854110i
$555$	−3.06330	+	1.13053i	−0.130030	+	0.0479885i
$556$	9.58094	−	5.53156i	0.406322	−	0.234590i
$557$	25.5003	+	6.83277i	1.08048	+	0.289514i	0.754793	−	0.655963i	$-0.227737\pi$
$557$	25.5003	+	6.83277i	1.08048	+	0.289514i	0.325688	+	0.945477i	$0.394404\pi$
$558$	2.90455	+	10.8399i	0.122959	+	0.458891i
$559$	5.30873			0.224535
$560$	5.87191	+	0.721617i	0.248133	+	0.0304939i
$561$	−8.65318			−0.365337
$562$	−3.66224	−	13.6677i	−0.154482	−	0.576536i
$563$	19.5055	+	5.22648i	0.822058	+	0.220270i	0.645246	−	0.763975i	$-0.276755\pi$
$563$	19.5055	+	5.22648i	0.822058	+	0.220270i	0.176812	+	0.984245i	$0.443422\pi$
$564$	−1.47933	+	0.854092i	−0.0622911	+	0.0359638i
$565$	17.9764	−	39.0064i	0.756274	−	1.64101i
$566$		−	27.0677i		−	1.13774i
$567$	11.8061	+	18.3638i	0.495808	+	0.771208i
$568$	−3.37792	−	3.37792i	−0.141734	−	0.141734i
$569$	−21.4890	−	12.4067i	−0.900867	−	0.520116i	−0.0233856	−	0.999727i	$-0.507445\pi$
$569$	−21.4890	−	12.4067i	−0.900867	−	0.520116i	−0.877481	+	0.479611i	$0.840778\pi$
$570$	0.426693	−	2.48502i	0.0178722	−	0.104086i
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	0.814116	−	0.580703i	$-0.197222\pi$
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	−0.909961	+	0.414693i	$0.863889\pi$
$572$	10.9865	−	2.94383i	0.459370	−	0.123088i
$573$	−3.52433	+	3.52433i	−0.147231	+	0.147231i
$574$	−18.1704	+	5.81180i	−0.758417	+	0.242580i
$575$	−3.18185	+	4.63204i	−0.132692	+	0.193169i
$576$	1.45803	−	2.52538i	0.0607511	−	0.105224i
$577$	−5.11957	+	19.1065i	−0.213131	+	0.795414i	0.773686	+	0.633570i	$0.218411\pi$
$577$	−5.11957	+	19.1065i	−0.213131	+	0.795414i	−0.986816	+	0.161845i	$0.948256\pi$
$578$	2.89427	−	10.8016i	0.120386	−	0.449286i
$579$	1.74818	−	3.02794i	0.0726520	−	0.125837i
$580$	4.51047	−	5.42460i	0.187287	−	0.225244i
$581$	−14.2751	+	15.7084i	−0.592229	+	0.651694i
$582$	1.92125	−	1.92125i	0.0796385	−	0.0796385i
$583$	7.51596	−	2.01390i	0.311279	−	0.0834071i
$584$	−2.80614	−	4.86037i	−0.116119	−	0.201124i
$585$	−7.60984	−	10.7649i	−0.314628	−	0.445074i
$586$	−20.9665	−	12.1050i	−0.866118	−	0.500053i
$587$	−19.3782	−	19.3782i	−0.799824	−	0.799824i	0.183244	−	0.983068i	$-0.441340\pi$
$587$	−19.3782	−	19.3782i	−0.799824	−	0.799824i	−0.983068	+	0.183244i	$0.941340\pi$
$588$	1.90004	−	0.709407i	0.0783565	−	0.0292555i
$589$			14.9775i			0.617136i
$590$	11.1256	+	5.12731i	0.458032	+	0.211088i
$591$	−5.07919	+	2.93247i	−0.208930	+	0.120626i
$592$	−4.86824	−	1.30444i	−0.200083	−	0.0536122i
$593$	0.837988	+	3.12741i	0.0344121	+	0.128428i	0.980995	−	0.194033i	$-0.0621568\pi$
$593$	0.837988	+	3.12741i	0.0344121	+	0.128428i	−0.946583	+	0.322460i	$0.895490\pi$
$594$	9.64311			0.395661
$595$	−31.1017	+	4.36767i	−1.27504	+	0.179057i
$596$	−5.04885			−0.206809
$597$	−0.564900	−	2.10824i	−0.0231198	−	0.0862844i
$598$	2.19490	+	0.588122i	0.0897562	+	0.0240501i
$599$	−6.75802	+	3.90174i	−0.276125	+	0.159421i	−0.631668	−	0.775239i	$-0.717629\pi$
$599$	−6.75802	+	3.90174i	−0.276125	+	0.159421i	0.355543	+	0.934660i	$0.384296\pi$
$600$	−1.36571	−	0.483248i	−0.0557548	−	0.0197285i
$601$		−	31.7170i		−	1.29377i	−0.762590	−	0.646883i	$-0.776072\pi$
$601$		−	31.7170i		−	1.29377i	0.762590	−	0.646883i	$-0.223928\pi$
$602$	−3.18231	+	6.17537i	−0.129701	+	0.251689i
$603$	1.74233	+	1.74233i	0.0709530	+	0.0709530i
$604$	11.6418	+	6.72142i	0.473699	+	0.273491i
$605$	−45.5070	−	7.81383i	−1.85012	−	0.317677i
$606$	−2.33227	−	4.03960i	−0.0947418	−	0.164098i
$607$	0.743495	−	0.199219i	0.0301775	−	0.00808604i	−0.243699	−	0.969851i	$-0.578361\pi$
$607$	0.743495	−	0.199219i	0.0301775	−	0.00808604i	0.273876	+	0.961765i	$0.411694\pi$
$608$	2.75192	−	2.75192i	0.111605	−	0.111605i
$609$	0.513702	−	2.36336i	0.0208162	−	0.0957682i
$610$	10.2632	−	0.944318i	0.415546	−	0.0382343i
$611$	−5.95987	+	10.3228i	−0.241110	+	0.417615i
$612$	−4.00666	+	14.9530i	−0.161960	+	0.604441i
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	−0.500323	−	0.865839i	$-0.666786\pi$
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	0.866212	−	0.499676i	$-0.166548\pi$
$614$	12.2311	−	21.1850i	0.493609	−	0.854955i
$615$	4.65183	−	0.428014i	0.187580	−	0.0172592i
$616$	−3.16146	+	14.5447i	−0.127379	+	0.586024i
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	−0.124980	−	0.992159i	$-0.539887\pi$
$617$	21.5403	−	21.5403i	0.867179	−	0.867179i	0.992159	+	0.124980i	$0.0398866\pi$
$618$	5.50479	−	1.47501i	0.221435	−	0.0593334i
$619$	21.6707	+	37.5348i	0.871021	+	1.50865i	0.860942	+	0.508703i	$0.169875\pi$
$619$	21.6707	+	37.5348i	0.871021	+	1.50865i	0.0100783	+	0.999949i	$0.496792\pi$
$620$	8.48131	+	1.45629i	0.340617	+	0.0584861i
$621$	1.66841	+	0.963256i	0.0669509	+	0.0386541i
$622$	−7.76566	−	7.76566i	−0.311374	−	0.311374i
$623$	14.4487	−	28.0382i	0.578876	−	1.12333i
$624$			0.585786i			0.0234502i
$625$	3.89884	−	24.6941i	0.155953	−	0.987764i
$626$	−25.4707	+	14.7055i	−1.01801	+	0.587749i
$627$	6.12745	+	1.64184i	0.244707	+	0.0655690i
$628$	−0.285443	−	1.06529i	−0.0113904	−	0.0425096i
$629$	26.7559			1.06683
$630$	17.0840	−	2.39913i	0.680641	−	0.0955837i
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	1.61706	+	6.03495i	0.0643232	+	0.240058i
$633$	−5.47879	−	1.46804i	−0.217762	−	0.0583492i
$634$	−3.71869	+	2.14699i	−0.147688	+	0.0852677i
$635$	13.3112	+	6.13457i	0.528237	+	0.243443i
$636$			0.400741i			0.0158904i
$637$	9.00710	−	10.9163i	0.356874	−	0.432520i
$638$	12.5507	+	12.5507i	0.496887	+	0.496887i
$639$	−12.0640	−	6.96513i	−0.477243	−	0.275536i
$640$	−1.29076	−	1.82591i	−0.0510217	−	0.0721754i
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	0.519233	−	0.854633i	$-0.326218\pi$
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	−0.999750	+	0.0223521i	$0.992885\pi$
$642$	0.783903	−	0.210046i	0.0309382	−	0.00828986i
$643$	6.21713	−	6.21713i	0.245180	−	0.245180i	−0.573809	−	0.818989i	$-0.694535\pi$
$643$	6.21713	−	6.21713i	0.245180	−	0.245180i	0.818989	+	0.573809i	$0.194535\pi$
$644$	−1.99986	+	2.20067i	−0.0788057	+	0.0867184i
$645$	1.08763	−	1.30805i	0.0428252	−	0.0515045i
$646$	−10.3303	+	17.8925i	−0.406439	+	0.703973i
$647$	5.33869	−	19.9243i	0.209886	−	0.783304i	−0.778019	−	0.628241i	$-0.783775\pi$
$647$	5.33869	−	19.9243i	0.209886	−	0.783304i	0.987905	−	0.155063i	$-0.0495581\pi$
$648$	2.13565	−	7.97036i	0.0838963	−	0.313105i
$649$	−15.4102	+	26.6913i	−0.604905	+	1.04773i
$650$	−9.93921	+	1.84463i	−0.389848	+	0.0723523i
$651$	2.80989	−	0.898745i	0.110128	−	0.0352246i
$652$	−9.36288	+	9.36288i	−0.366679	+	0.366679i
$653$	−25.2490	+	6.76544i	−0.988069	+	0.264752i	−0.716439	−	0.697650i	$-0.754229\pi$
$653$	−25.2490	+	6.76544i	−0.988069	+	0.264752i	−0.271630	+	0.962402i	$0.587563\pi$
$654$	−0.856296	−	1.48315i	−0.0334838	−	0.0579957i
$655$	2.91199	−	16.9591i	0.113781	−	0.662649i
$656$	6.24448	+	3.60525i	0.243806	+	0.140761i
$657$	−11.5723	−	11.5723i	−0.451478	−	0.451478i
$658$	−8.43533	−	13.1208i	−0.328844	−	0.511502i
$659$		−	24.2448i		−	0.944443i	−0.881480	−	0.472222i	$-0.843452\pi$
$659$		−	24.2448i		−	0.944443i	0.881480	−	0.472222i	$-0.156548\pi$
$660$	1.52551	−	3.31016i	0.0593806	−	0.128848i
$661$	15.5301	−	8.96630i	0.604050	−	0.348749i	−0.166583	−	0.986027i	$-0.553273\pi$
$661$	15.5301	−	8.96630i	0.604050	−	0.348749i	0.770633	+	0.637279i	$0.219940\pi$
$662$	−34.2419	−	9.17510i	−1.33085	−	0.356600i
$663$	−0.804871	−	3.00382i	−0.0312586	−	0.116659i
$664$	8.02257			0.311336
$665$	22.8523	+	2.80839i	0.886174	+	0.108905i
$666$	−14.6968			−0.569491
$667$	0.917769	+	3.42516i	0.0355362	+	0.132623i
$668$	−6.42961	−	1.72281i	−0.248769	−	0.0666574i
$669$	0.518181	−	0.299172i	0.0200340	−	0.0115667i
$670$	1.77258	−	0.654184i	0.0684807	−	0.0252733i
$671$			25.9305i			1.00104i
$672$	−0.681415	−	0.351149i	−0.0262862	−	0.0135459i
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	0.607340	−	0.794442i	$-0.292237\pi$
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	−0.794442	+	0.607340i	$0.792237\pi$
$674$	−14.8774	−	8.58946i	−0.573056	−	0.330854i
$675$	−8.54424	−	0.670353i	−0.328868	−	0.0258019i
$676$	−4.45619	−	7.71834i	−0.171392	−	0.296859i
$677$	−17.8506	+	4.78306i	−0.686055	+	0.183828i	−0.584976	−	0.811051i	$-0.698896\pi$
$677$	−17.8506	+	4.78306i	−0.686055	+	0.183828i	−0.101079	+	0.994878i	$0.532229\pi$
$678$	−3.93514	+	3.93514i	−0.151128	+	0.151128i
$679$	18.3618	+	16.6863i	0.704660	+	0.640362i
$680$	9.12760	+	7.58946i	0.350027	+	0.291043i
$681$	2.70083	−	4.67797i	0.103496	−	0.179260i
$682$	−5.60357	+	20.9128i	−0.214572	+	0.800793i
$683$	−6.93661	+	25.8878i	−0.265422	+	0.990569i	0.696569	+	0.717489i	$0.254709\pi$
$683$	−6.93661	+	25.8878i	−0.265422	+	0.990569i	−0.961992	+	0.273079i	$0.911958\pi$
$684$	5.67435	−	9.82827i	0.216964	−	0.375793i
$685$	1.81023	+	19.6743i	0.0691653	+	0.751717i
$686$	7.29908	+	17.0213i	0.278680	+	0.649875i
$687$	−0.821071	+	0.821071i	−0.0313258	+	0.0313258i
$688$	2.53629	−	0.679597i	0.0966951	−	0.0259094i
$689$	1.39819	+	2.42173i	0.0532667	+	0.0922606i
$690$	0.594591	−	0.420324i	0.0226357	−	0.0160015i
$691$	25.1773	+	14.5361i	0.957790	+	0.552980i	0.895492	−	0.445077i	$-0.146824\pi$
$691$	25.1773	+	14.5361i	0.957790	+	0.552980i	0.0622976	+	0.998058i	$0.480157\pi$
$692$	4.98835	+	4.98835i	0.189628	+	0.189628i
$693$	2.07251	+	43.3541i	0.0787281	+	1.64689i
$694$		−	8.97626i		−	0.340734i
$695$	−8.56502	−	23.2078i	−0.324890	−	0.880323i
$696$	−0.791655	+	0.457062i	−0.0300076	+	0.0173249i
$697$	−36.9743	−	9.90723i	−1.40050	−	0.375263i
$698$	6.73580	+	25.1383i	0.254954	+	0.951500i
$699$	−3.97855			−0.150483
$700$	3.81229	−	12.6675i	0.144091	−	0.478788i
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$	0.896949	+	3.34746i	0.0338531	+	0.126342i
$703$	−18.9462	−	5.07663i	−0.714571	−	0.191469i
$704$	4.87205	−	2.81288i	0.183622	−	0.106014i
$705$	1.32247	+	3.58337i	0.0498071	+	0.134957i
$706$			9.96618i			0.375082i
$707$	35.8289	−	23.0343i	1.34748	−	0.866295i
$708$	−1.12240	−	1.12240i	−0.0421823	−	0.0421823i
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.914537	−	0.404503i	$-0.132555\pi$
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.106958	+	0.994263i	$0.465889\pi$
$710$	−8.72254	+	6.16608i	−0.327351	+	0.231409i
$711$	9.10952	+	15.7781i	0.341634	+	0.591727i
$712$	−11.5156	+	3.08559i	−0.431565	+	0.115637i
$713$	−3.05850	+	3.05850i	−0.114542	+	0.114542i
$714$	3.97667	+	0.864371i	0.148823	+	0.0323483i
$715$	−2.33027	−	25.3263i	−0.0871470	−	0.947149i
$716$	1.10317	−	1.91075i	0.0412275	−	0.0714081i
$717$	−1.47445	+	5.50271i	−0.0550642	+	0.205502i
$718$	2.99560	−	11.1797i	0.111795	−	0.417224i
$719$	5.40214	−	9.35678i	0.201466	−	0.348949i	−0.747535	−	0.664222i	$-0.768763\pi$
$719$	5.40214	−	9.35678i	0.201466	−	0.348949i	0.949001	+	0.315273i	$0.102096\pi$
$720$	−5.01373	−	4.16885i	−0.186851	−	0.155364i
$721$	15.8540	+	49.5669i	0.590434	+	1.84597i
$722$	−2.72509	+	2.72509i	−0.101417	+	0.101417i
$723$	1.64704	−	0.441322i	0.0612539	−	0.0164129i
$724$	2.05934	+	3.56688i	0.0765347	+	0.132562i
$725$	−10.2480	−	11.9930i	−0.380602	−	0.445408i
$726$	5.18128	+	2.99141i	0.192295	+	0.111022i
$727$	−33.6108	−	33.6108i	−1.24656	−	1.24656i	−0.957231	−	0.289326i	$-0.906569\pi$
$727$	−33.6108	−	33.6108i	−1.24656	−	1.24656i	−0.289326	−	0.957231i	$-0.593431\pi$
$728$	−5.34305	+	0.255420i	−0.198026	+	0.00946651i
$729$		−	22.5720i		−	0.835998i
$730$	−11.7732	+	4.34500i	−0.435747	+	0.160816i
$731$	−12.0719	+	6.96972i	−0.446496	+	0.257785i
$732$	−1.28996	−	0.345644i	−0.0476784	−	0.0127754i
$733$	6.66658	+	24.8800i	0.246236	+	0.918964i	0.972758	+	0.231822i	$0.0744686\pi$
$733$	6.66658	+	24.8800i	0.246236	+	0.918964i	−0.726523	+	0.687143i	$0.758865\pi$
$734$	16.6944			0.616202
$735$	−0.844410	−	4.45579i	−0.0311465	−	0.164354i
$736$	1.12392			0.0414283
$737$	1.23034	+	4.59170i	0.0453203	+	0.169138i
$738$	20.3098	+	5.44198i	0.747613	+	0.200322i
$739$	−10.4948	+	6.05920i	−0.386059	+	0.222891i	−0.680451	−	0.732793i	$-0.738216\pi$
$739$	−10.4948	+	6.05920i	−0.386059	+	0.222891i	0.294392	+	0.955685i	$0.404883\pi$
$740$	−4.71693	+	10.2351i	−0.173398	+	0.376250i
$741$			2.27977i			0.0837493i
$742$	−3.65522	+	0.174735i	−0.134187	+	0.00641472i
$743$	23.2618	+	23.2618i	0.853393	+	0.853393i	0.990549	−	0.137157i	$-0.0437964\pi$
$743$	23.2618	+	23.2618i	0.853393	+	0.853393i	−0.137157	+	0.990549i	$0.543796\pi$
$744$	−0.965654	−	0.557521i	−0.0354026	−	0.0204397i
$745$	−1.91053	+	11.1267i	−0.0699964	+	0.407652i
$746$	−1.58946	−	2.75303i	−0.0581944	−	0.100796i
$747$	22.5971	−	6.05487i	0.826784	−	0.221536i
$748$	−21.1182	+	21.1182i	−0.772158	+	0.772158i
$749$	2.25767	+	7.05851i	0.0824934	+	0.257912i
$750$	−1.58179	+	2.82690i	−0.0577587	+	0.103224i
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	−0.964903	−	0.262607i	$-0.915418\pi$
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	0.709875	+	0.704327i	$0.248751\pi$
$752$	−1.52590	+	5.69475i	−0.0556440	+	0.207666i
$753$	−0.532387	+	1.98690i	−0.0194013	+	0.0724065i
$754$	−3.18939	+	5.52418i	−0.116151	+	0.201179i
$755$	19.2181	−	23.1130i	0.699420	−	0.841169i
$756$	−4.43160	−	0.963256i	−0.161176	−	0.0350333i
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	−0.312035	−	0.950071i	$-0.601010\pi$
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	0.950071	+	0.312035i	$0.101010\pi$
$758$	6.90974	−	1.85146i	0.250973	−	0.0672481i
$759$	0.915990	+	1.58654i	0.0332483	+	0.0575878i
$760$	−5.02338	−	7.10608i	−0.182217	−	0.257765i
$761$	18.9372	+	10.9334i	0.686471	+	0.396334i	0.802289	−	0.596936i	$-0.203615\pi$
$761$	18.9372	+	10.9334i	0.686471	+	0.396334i	−0.115817	+	0.993271i	$0.536949\pi$
$762$	−1.34289	−	1.34289i	−0.0486478	−	0.0486478i
$763$	13.1546	−	8.45710i	0.476230	−	0.306168i
$764$			17.2023i			0.622359i
$765$	31.4376	+	14.4883i	1.13663	+	0.523826i
$766$	12.6382	−	7.29669i	0.456638	−	0.263640i
$767$	−10.6989	−	2.86675i	−0.386313	−	0.103512i
$768$	0.0749894	+	0.279864i	0.00270595	+	0.0100987i
$769$	−31.0506			−1.11971			−0.559857	−	0.828589i	$-0.689144\pi$
$769$	−31.0506			−1.11971			−0.559857	+	0.828589i	$0.689144\pi$
$770$	30.8576	+	12.4711i	1.11203	+	0.449428i
$771$	2.86459			0.103166
$772$	−3.12327	−	11.6562i	−0.112409	−	0.419516i
$773$	−5.86173	−	1.57065i	−0.210832	−	0.0564922i	0.151857	−	0.988402i	$-0.451475\pi$
$773$	−5.86173	−	1.57065i	−0.210832	−	0.0564922i	−0.362689	+	0.931910i	$0.618141\pi$
$774$	6.63103	−	3.82843i	0.238347	−	0.137610i
$775$	6.41880	−	18.1402i	0.230570	−	0.651614i
$776$		−	9.37769i		−	0.336640i
$777$	0.184481	+	3.85909i	0.00661822	+	0.138444i
$778$	−4.38160	−	4.38160i	−0.157088	−	0.157088i
$779$	24.3023	+	14.0309i	0.870720	+	0.502710i
$780$	1.29097	+	0.221667i	0.0462240	+	0.00793694i
$781$	−13.4374	−	23.2743i	−0.480828	−	0.832819i
$782$	−5.76329	+	1.54427i	−0.206095	+	0.0552229i
$783$	−3.82404	+	3.82404i	−0.136660	+	0.136660i
$784$	2.90577	−	6.36840i	0.103777	−	0.227443i
$785$	−2.45571	+	0.225950i	−0.0876481	+	0.00806449i
$786$	−1.11481	+	1.93091i	−0.0397641	+	0.0688734i
$787$	−5.78752	+	21.5993i	−0.206303	+	0.769932i	0.782746	+	0.622342i	$0.213818\pi$
$787$	−5.78752	+	21.5993i	−0.206303	+	0.769932i	−0.989049	+	0.147591i	$0.952848\pi$
$788$	−5.23910	+	19.5526i	−0.186635	+	0.696532i
$789$	−1.99167	+	3.44968i	−0.0709055	+	0.122812i
$790$	13.9118	−	1.28003i	0.494961	−	0.0455413i
$791$	−37.6089	−	34.1772i	−1.33722	−	1.21520i
$792$	11.6001	−	11.6001i	0.412191	−	0.412191i
$793$	−9.00138	+	2.41191i	−0.319648	+	0.0856495i
$794$	1.45794	+	2.52523i	0.0517403	+	0.0896169i
$795$	0.883159	+	0.151644i	0.0313224	+	0.00537825i
$796$	−6.52383	−	3.76653i	−0.231231	−	0.133501i
$797$	−16.5528	−	16.5528i	−0.586330	−	0.586330i	0.350305	−	0.936636i	$-0.386078\pi$
$797$	−16.5528	−	16.5528i	−0.586330	−	0.586330i	−0.936636	+	0.350305i	$0.886078\pi$
$798$	−2.65193	−	1.36660i	−0.0938774	−	0.0483772i
$799$		−	31.2984i		−	1.10726i
$800$	−4.51240	+	2.15365i	−0.159538	+	0.0761432i
$801$	−30.1070	+	17.3823i	−1.06378	+	0.614174i
$802$	19.2901	+	5.16876i	0.681156	+	0.182515i
$803$	−8.17177	−	30.4975i	−0.288376	−	1.07623i
$804$	−0.244823			−0.00863425
$805$	4.09310	+	5.24008i	0.144263	+	0.184689i
$806$	−7.78078			−0.274066
$807$	−1.98737	−	7.41697i	−0.0699588	−	0.261090i
$808$	−15.5506	−	4.16678i	−0.547069	−	0.146587i
$809$	−2.84139	+	1.64048i	−0.0998980	+	0.0576762i	−0.549117	−	0.835746i	$-0.685036\pi$
$809$	−2.84139	+	1.64048i	−0.0998980	+	0.0576762i	0.449219	+	0.893422i	$0.351702\pi$
$810$	−16.7571	−	7.72263i	−0.588783	−	0.271346i
$811$			17.8693i			0.627476i	0.949510	+	0.313738i	$0.101581\pi$
$811$			17.8693i			0.627476i	−0.949510	+	0.313738i	$0.898419\pi$
$812$	−4.51412	−	7.02151i	−0.158414	−	0.246407i
$813$	2.62176	+	2.62176i	0.0919491	+	0.0919491i
$814$	−24.5550	−	14.1768i	−0.860653	−	0.496898i
$815$	17.0911	+	24.1771i	0.598674	+	0.846886i
$816$	−0.769067	−	1.33206i	−0.0269227	−	0.0466316i
$817$	9.87074	−	2.64486i	0.345333	−	0.0925318i
$818$	24.2949	−	24.2949i	0.849451	−	0.849451i
$819$	−14.8569	+	4.75200i	−0.519143	+	0.166048i
$820$	10.3083	−	12.3974i	0.359981	−	0.432937i
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	−0.744312	−	0.667832i	$-0.767222\pi$
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	0.950516	+	0.310677i	$0.100556\pi$
$822$	0.662590	−	2.47282i	0.0231105	−	0.0862495i
$823$	9.13692	−	34.0995i	0.318493	−	1.18863i	−0.602200	−	0.798345i	$-0.705709\pi$
$823$	9.13692	−	34.0995i	0.318493	−	1.18863i	0.920693	−	0.390287i	$-0.127624\pi$
$824$	9.83476	−	17.0343i	0.342610	−	0.593418i
$825$	−6.71771	−	4.61455i	−0.233881	−	0.160658i
$826$	9.74816	−	10.7270i	0.339182	−	0.373239i
$827$	−17.2835	+	17.2835i	−0.601005	+	0.601005i	−0.940579	−	0.339574i	$-0.889717\pi$
$827$	−17.2835	+	17.2835i	−0.601005	+	0.601005i	0.339574	+	0.940579i	$0.389717\pi$
$828$	3.16574	−	0.848257i	0.110017	−	0.0294790i
$829$	−17.2877	−	29.9431i	−0.600426	−	1.03997i	−0.992756	−	0.120144i	$-0.961664\pi$
$829$	−17.2877	−	29.9431i	−0.600426	−	1.03997i	0.392330	−	0.919824i	$-0.371669\pi$
$830$	3.03581	−	17.6803i	0.105374	−	0.613691i
$831$	5.04433	+	2.91234i	0.174986	+	0.101028i
$832$	1.42962	+	1.42962i	0.0495631	+	0.0495631i
$833$	−6.15011	+	36.6487i	−0.213089	+	1.26980i
$834$			3.20539i			0.110994i
$835$	−6.22977	+	13.5177i	−0.215590	+	0.467801i
$836$	18.9611	−	10.9472i	0.655782	−	0.378616i
$837$	−6.37187	−	1.70734i	−0.220244	−	0.0590142i
$838$	8.05859	+	30.0751i	0.278379	+	1.03893i
$839$	50.1328			1.73078			0.865388	−	0.501102i	$-0.167072\pi$
$839$	50.1328			1.73078			0.865388	+	0.501102i	$0.167072\pi$
$840$	−1.03172	+	1.36884i	−0.0355978	+	0.0472293i
$841$	19.0459			0.656754
$842$	−8.71515	−	32.5254i	−0.300344	−	1.12090i
$843$	3.96003	+	1.06109i	0.136391	+	0.0365458i
$844$	−16.9538	+	9.78829i	−0.583575	+	0.336927i
$845$	−18.6961	+	6.89993i	−0.643164	+	0.237365i
$846$			17.1920i			0.591073i
$847$	−25.0259	+	48.5636i	−0.859901	+	1.66866i
$848$	0.978013	+	0.978013i	0.0335851	+	0.0335851i
$849$	6.79181	+	3.92125i	0.233094	+	0.134577i
$850$	20.1797	−	17.2436i	0.692160	−	0.591452i
$851$	−2.83227	−	4.90563i	−0.0970888	−	0.168163i
$852$	1.33694	−	0.358232i	0.0458028	−	0.0122728i
$853$	2.37500	−	2.37500i	0.0813183	−	0.0813183i	−0.665278	−	0.746596i	$-0.731687\pi$
$853$	2.37500	−	2.37500i	0.0813183	−	0.0813183i	0.746596	+	0.665278i	$0.231687\pi$
$854$	2.59021	−	11.9167i	0.0886352	−	0.407779i
$855$	−19.5125	−	16.2243i	−0.667312	−	0.554860i
$856$	1.40051	−	2.42575i	0.0478683	−	0.0829103i
$857$	−10.8545	+	40.5097i	−0.370784	+	1.38378i	0.488624	+	0.872494i	$0.337499\pi$
$857$	−10.8545	+	40.5097i	−0.370784	+	1.38378i	−0.859408	+	0.511290i	$0.829168\pi$
$858$	−0.852937	+	3.18320i	−0.0291188	+	0.108673i
$859$	1.17847	−	2.04117i	0.0402090	−	0.0696440i	−0.845221	−	0.534418i	$-0.820531\pi$
$859$	1.17847	−	2.04117i	0.0402090	−	0.0696440i	0.885430	+	0.464774i	$0.153864\pi$
$860$	−0.537952	−	5.84668i	−0.0183440	−	0.199370i
$861$	1.17402	−	5.40125i	0.0400105	−	0.184074i
$862$	−10.4268	+	10.4268i	−0.355137	+	0.355137i
$863$	−46.7022	+	12.5138i	−1.58976	+	0.425975i	−0.941930	−	0.335808i	$-0.890991\pi$
$863$	−46.7022	+	12.5138i	−1.58976	+	0.425975i	−0.647831	+	0.761784i	$0.724324\pi$
$864$	0.857049	+	1.48445i	0.0291574	+	0.0505021i
$865$	12.8810	−	9.10577i	0.437968	−	0.309605i
$866$	12.2261	+	7.05873i	0.415459	+	0.239865i
$867$	2.29104	+	2.29104i	0.0778076	+	0.0778076i
$868$	4.66418	−	9.05097i	0.158312	−	0.307210i
$869$			35.1489i			1.19234i
$870$	0.707712	+	1.91762i	0.0239937	+	0.0650133i
$871$	−1.47950	+	0.854190i	−0.0501310	+	0.0289431i
$872$	−5.70944	−	1.52984i	−0.193346	−	0.0518069i
$873$	−7.07763	−	26.4141i	−0.239541	−	0.893980i
$874$	4.37408			0.147955
$875$	−26.4743	−	13.1951i	−0.894995	−	0.446076i
$876$	1.62608			0.0549402
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	0.879194	−	0.476465i	$-0.158082\pi$
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	−0.999636	+	0.0269665i	$0.991415\pi$
$878$	−37.1191	−	9.94602i	−1.25271	−	0.335662i
$879$	6.07477	−	3.50727i	0.204897	−	0.118297i
$880$	−4.35544	−	11.8015i	−0.146822	−	0.397829i
$881$			3.32542i			0.112036i	0.998430	+	0.0560181i	$0.0178405\pi$
$881$			3.32542i			0.112036i	−0.998430	+	0.0560181i	$0.982160\pi$
$882$	3.37822	−	20.1309i	0.113751	−	0.677842i
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.959358	−	0.282191i	$-0.908939\pi$
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.282191	−	0.959358i	$-0.591061\pi$
$884$	−9.29516	−	5.36656i	−0.312630	−	0.180497i
$885$	−2.89828	+	2.04883i	−0.0974247	+	0.0688708i
$886$	−2.86780	−	4.96718i	−0.0963456	−	0.166876i
$887$	−34.6001	+	9.27107i	−1.16176	+	0.311292i	−0.787668	−	0.616101i	$-0.788711\pi$
$887$	−34.6001	+	9.27107i	−1.16176	+	0.311292i	−0.374090	+	0.927392i	$0.622045\pi$
$888$	1.03256	−	1.03256i	0.0346506	−	0.0346506i
$889$	11.6632	−	12.8343i	0.391170	−	0.430447i
$890$	2.44248	+	26.5458i	0.0818721	+	0.889819i
$891$	23.2105	−	40.2018i	0.777582	−	1.34681i
$892$	0.534495	−	1.99476i	0.0178962	−	0.0667895i
$893$	−5.93852	+	22.1628i	−0.198725	+	0.741651i
$894$	0.731419	−	1.26686i	0.0244623	−	0.0423700i
$895$	−3.79349	−	3.15423i	−0.126803	−	0.105434i
$896$	−2.51999	+	0.806019i	−0.0841869	+	0.0269272i
$897$	−0.465543	+	0.465543i	−0.0155440	+	0.0155440i
$898$	7.05384	−	1.89007i	0.235390	−	0.0630725i
$899$	−6.07098	−	10.5152i	−0.202479	−	0.350703i
$900$	−11.0846	+	9.47182i	−0.369487	+	0.315727i
$901$	−6.35888	−	3.67130i	−0.211845	−	0.122309i
$902$	28.6835	+	28.6835i	0.955055	+	0.955055i
$903$	−1.08850	−	1.69312i	−0.0362232	−	0.0563435i
$904$			19.2075i			0.638833i
$905$	8.64001	−	3.18866i	0.287204	−	0.105995i
$906$	−3.37307	+	1.94744i	−0.112063	+	0.0646994i
$907$	16.6696	+	4.46661i	0.553506	+	0.148312i	0.524721	−	0.851274i	$-0.324170\pi$
$907$	16.6696	+	4.46661i	0.553506	+	0.148312i	0.0287849	+	0.999586i	$0.490836\pi$
$908$	−4.82525	−	18.0081i	−0.160131	−	0.597618i
$909$	−46.9461			−1.55710
$910$	−1.45896	+	11.8717i	−0.0483639	+	0.393545i
$911$	5.56820			0.184483			0.0922414	−	0.995737i	$-0.470597\pi$
$911$	5.56820			0.184483			0.0922414	+	0.995737i	$0.470597\pi$
$912$	0.291844	+	1.08918i	0.00966392	+	0.0360663i
$913$	43.5952	+	11.6813i	1.44279	+	0.386594i
$914$	−4.45641	+	2.57291i	−0.147405	+	0.0851042i
$915$	−1.24987	+	2.71205i	−0.0413194	+	0.0896575i
$916$			4.00767i			0.132417i
$917$	−18.0982	−	9.32645i	−0.597657	−	0.307986i
$918$	−6.43445	−	6.43445i	−0.212368	−	0.212368i
$919$	−5.37964	−	3.10593i	−0.177458	−	0.102455i	0.408640	−	0.912696i	$-0.366003\pi$
$919$	−5.37964	−	3.10593i	−0.177458	−	0.102455i	−0.586098	+	0.810240i	$0.699337\pi$
$920$	0.425302	−	2.47692i	0.0140218	−	0.0816615i
$921$	3.54381	+	6.13806i	0.116773	+	0.202256i
$922$	28.4088	−	7.61212i	0.935595	−	0.250692i
$923$	6.82943	−	6.82943i	0.224794	−	0.224794i
$924$	−3.19156	−	2.90034i	−0.104995	−	0.0954143i
$925$	20.7713	+	14.2683i	0.682958	+	0.469139i
$926$	2.86113	−	4.95563i	0.0940226	−	0.162852i
$927$	14.8452	−	55.4029i	0.487579	−	1.81967i
$928$	−0.816578	+	3.04751i	−0.0268055	+	0.100039i
$929$	−0.0947297	+	0.164077i	−0.00310798	+	0.00538318i	−0.867575	−	0.497306i	$-0.834323\pi$
$929$	−0.0947297	+	0.164077i	−0.00310798	+	0.00538318i	0.864467	+	0.502689i	$0.167656\pi$
$930$	−1.59409	+	1.91715i	−0.0522721	+	0.0628660i
$931$	11.3087	−	24.7846i	0.370627	−	0.812281i
$932$	−9.70971	+	9.70971i	−0.318052	+	0.318052i
$933$	3.07355	−	0.823556i	0.100624	−	0.0269620i
$934$	8.32139	+	14.4131i	0.272284	+	0.471610i
$935$	38.5493	+	54.5319i	1.26070	+	1.78338i
$936$	5.10577	+	2.94782i	0.166887	+	0.0963525i
$937$	34.2022	+	34.2022i	1.11734	+	1.11734i	0.992131	+	0.125208i	$0.0399598\pi$
$937$	34.2022	+	34.2022i	1.11734	+	1.11734i	0.125208	+	0.992131i	$0.460040\pi$
$938$	−0.106750	−	2.23307i	−0.00348552	−	0.0729123i
$939$		−	8.52144i		−	0.278087i
$940$	11.9728	+	5.51775i	0.390509	+	0.179969i
$941$	−16.3826	+	9.45851i	−0.534058	+	0.308339i	−0.742667	−	0.669660i	$-0.766440\pi$
$941$	−16.3826	+	9.45851i	−0.534058	+	0.308339i	0.208609	+	0.977999i	$0.433106\pi$
$942$	0.308653	+	0.0827033i	0.0100565	+	0.00269462i
$943$	2.09748	+	7.82790i	0.0683033	+	0.254911i
$944$	−5.47845			−0.178308
$945$	−3.79979	+	9.40193i	−0.123607	+	0.305845i
$946$	14.7719			0.480276
$947$	12.2033	+	45.5435i	0.396555	+	1.47996i	0.819115	+	0.573629i	$0.194465\pi$
$947$	12.2033	+	45.5435i	0.396555	+	1.47996i	−0.422560	+	0.906335i	$0.638869\pi$
$948$	−1.74855	−	0.468522i	−0.0567902	−	0.0152169i
$949$	9.82664	−	5.67341i	0.318986	−	0.184167i
$950$	−17.5614	+	8.38160i	−0.569767	+	0.271935i
$951$		−	1.24412i		−	0.0403434i
$952$	11.8146	−	7.59560i	0.382914	−	0.246175i
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	0.943047	−	0.332658i	$-0.107946\pi$
$953$	18.8431	+	18.8431i	0.610389	+	0.610389i	−0.332658	+	0.943047i	$0.607946\pi$
$954$	3.49290	+	2.01662i	0.113087	+	0.0652906i
$955$	37.9108	+	6.50952i	1.22677	+	0.210643i
$956$	9.83103	+	17.0278i	0.317958	+	0.550720i
$957$	−4.96741	+	1.33101i	−0.160574	+	0.0430256i
$958$	10.8818	−	10.8818i	0.351575	−	0.351575i
$959$	22.8439	+	4.96536i	0.737667	+	0.160340i
$960$	0.645146	−	0.0593598i	0.0208220	−	0.00191583i
$961$	−8.09467	+	14.0204i	−0.261118	+	0.452270i
$962$	2.63730	−	9.84255i	0.0850301	−	0.317337i
$963$	2.11401	−	7.88958i	0.0681229	−	0.254238i
$964$	2.94256	−	5.09667i	0.0947735	−	0.164153i
$965$	−26.8700	+	2.47231i	−0.864976	+	0.0795863i
$966$	−0.262473	−	0.820612i	−0.00844493	−	0.0264028i
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	−0.113383	−	0.993551i	$-0.536169\pi$
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	0.993551	+	0.113383i	$0.0361687\pi$
$968$	19.9456	−	5.34440i	0.641075	−	0.171776i
$969$	−2.99306	−	5.18413i	−0.0961509	−	0.166538i
$970$	−20.6667	−	3.54860i	−0.663568	−	0.113939i
$971$	−27.8750	−	16.0936i	−0.894550	−	0.516469i	−0.0191221	−	0.999817i	$-0.506087\pi$
$971$	−27.8750	−	16.0936i	−0.894550	−	0.516469i	−0.875428	+	0.483348i	$0.839420\pi$
$972$	5.32668	+	5.32668i	0.170853	+	0.170853i
$973$	−29.2369	+	1.39765i	−0.937291	+	0.0448065i
$974$			35.9920i			1.15326i
$975$	0.977025	−	2.76117i	0.0312899	−	0.0884282i
$976$	−3.99172	+	2.30462i	−0.127772	+	0.0737691i
$977$	22.4848	+	6.02479i	0.719353	+	0.192750i	0.599883	−	0.800088i	$-0.295214\pi$
$977$	22.4848	+	6.02479i	0.719353	+	0.192750i	0.119470	+	0.992838i	$0.461881\pi$
$978$	−0.992944	−	3.70572i	−0.0317508	−	0.118496i
$979$	−67.0692			−2.14354
$980$	−12.9352	−	8.81363i	−0.413200	−	0.281541i
$981$	−17.2364			−0.550314
$982$	−3.95535	−	14.7616i	−0.126220	−	0.471060i
$983$	55.0964	+	14.7630i	1.75730	+	0.470868i	0.986160	−	0.165793i	$-0.0530185\pi$
$983$	55.0964	+	14.7630i	1.75730	+	0.470868i	0.771143	+	0.636662i	$0.219685\pi$
$984$	−1.80926	+	1.04457i	−0.0576770	+	0.0332998i
$985$	41.1078	+	18.9449i	1.30980	+	0.603634i
$986$		−	16.7491i		−	0.533401i
$987$	4.51427	−	0.215802i	0.143691	−	0.00686904i
$988$	5.56380	+	5.56380i	0.177008	+	0.177008i
$989$	2.55577	+	1.47557i	0.0812687	+	0.0469205i
$990$	−21.1749	−	29.9541i	−0.672983	−	0.952002i
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.808478	+	0.588526i	$0.200292\pi$
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.105440	+	0.994426i	$0.466375\pi$
$992$	−3.71733	+	0.996056i	−0.118025	+	0.0316248i
$993$	7.26279	−	7.26279i	0.230478	−	0.230478i
$994$	3.85043	+	12.0382i	0.122128	+	0.381829i
$995$	−10.7694	+	12.9520i	−0.341414	+	0.410607i
$996$	−1.16222	+	2.01302i	−0.0368262	+	0.0637849i
$997$	6.27762	−	23.4284i	0.198814	−	0.741985i	−0.792432	−	0.609960i	$-0.791185\pi$
$997$	6.27762	−	23.4284i	0.198814	−	0.741985i	0.991246	−	0.132025i	$-0.0421479\pi$
$998$	−8.17479	+	30.5087i	−0.258768	+	0.965737i
$999$	4.31951	−	7.48160i	0.136663	−	0.236707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.k.a.33.3	yes	16
3.2	odd	2		630.2.bv.c.523.1		16
4.3	odd	2		560.2.ci.c.33.3		16
5.2	odd	4	inner	70.2.k.a.47.1	yes	16
5.3	odd	4		350.2.o.c.257.4		16
5.4	even	2		350.2.o.c.243.2		16
7.2	even	3		490.2.g.c.293.7		16
7.3	odd	6	inner	70.2.k.a.3.1	✓	16
7.4	even	3		490.2.l.c.423.2		16
7.5	odd	6		490.2.g.c.293.6		16
7.6	odd	2		490.2.l.c.313.4		16
15.2	even	4		630.2.bv.c.397.3		16
20.7	even	4		560.2.ci.c.257.3		16
21.17	even	6		630.2.bv.c.73.3		16
28.3	even	6		560.2.ci.c.353.3		16
35.2	odd	12		490.2.g.c.97.6		16
35.3	even	12		350.2.o.c.157.2		16
35.12	even	12		490.2.g.c.97.7		16
35.17	even	12	inner	70.2.k.a.17.3	yes	16
35.24	odd	6		350.2.o.c.143.4		16
35.27	even	4		490.2.l.c.117.2		16
35.32	odd	12		490.2.l.c.227.4		16
105.17	odd	12		630.2.bv.c.577.1		16
140.87	odd	12		560.2.ci.c.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	7.3	odd	6	inner
70.2.k.a.17.3	yes	16	35.17	even	12	inner
70.2.k.a.33.3	yes	16	1.1	even	1	trivial
70.2.k.a.47.1	yes	16	5.2	odd	4	inner
350.2.o.c.143.4		16	35.24	odd	6
350.2.o.c.157.2		16	35.3	even	12
350.2.o.c.243.2		16	5.4	even	2
350.2.o.c.257.4		16	5.3	odd	4
490.2.g.c.97.6		16	35.2	odd	12
490.2.g.c.97.7		16	35.12	even	12
490.2.g.c.293.6		16	7.5	odd	6
490.2.g.c.293.7		16	7.2	even	3
490.2.l.c.117.2		16	35.27	even	4
490.2.l.c.227.4		16	35.32	odd	12
490.2.l.c.313.4		16	7.6	odd	2
490.2.l.c.423.2		16	7.4	even	3
560.2.ci.c.17.3		16	140.87	odd	12
560.2.ci.c.33.3		16	4.3	odd	2
560.2.ci.c.257.3		16	20.7	even	4
560.2.ci.c.353.3		16	28.3	even	6
630.2.bv.c.73.3		16	21.17	even	6
630.2.bv.c.397.3		16	15.2	even	4
630.2.bv.c.523.1		16	3.2	odd	2
630.2.bv.c.577.1		16	105.17	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.279864 - 0.0749894i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.774197 + 2.09777i) q^{5} -0.289737i q^{6} +(2.64273 - 0.126334i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.52538 - 1.45803i) q^{9} +(-1.82591 + 1.29076i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(0.279864 - 0.0749894i) q^{12} +(1.42962 - 1.42962i) q^{13} +(0.806019 + 2.51999i) q^{14} +(-0.0593598 - 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.37400 + 5.12784i) q^{17} +(0.754730 - 2.81669i) q^{18} +(1.94590 - 3.37040i) q^{19} +(-1.71936 - 1.42962i) q^{20} +(-0.749081 - 0.162821i) q^{21} +(3.97801 - 3.97801i) q^{22} +(1.08562 - 0.290892i) q^{23} +(0.144868 + 0.250919i) q^{24} +(-3.80124 + 3.24817i) q^{25} +(1.75092 + 1.01089i) q^{26} +(1.21205 + 1.21205i) q^{27} +(-2.22551 + 1.43078i) q^{28} +3.15502i q^{29} +(0.607800 - 0.224313i) q^{30} +(-3.33287 + 1.92423i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.421872 + 1.57445i) q^{33} -5.30873 q^{34} +(2.31101 + 5.44603i) q^{35} +2.91605 q^{36} +(-1.30444 - 4.86824i) q^{37} +(3.75919 + 1.00727i) q^{38} +(-0.507306 + 0.292893i) q^{39} +(0.935904 - 2.03078i) q^{40} +7.21050i q^{41} +(-0.0366036 - 0.765697i) q^{42} +(1.85669 + 1.85669i) q^{43} +(4.87205 + 2.81288i) q^{44} +(1.10346 - 6.42644i) q^{45} +(0.561961 + 0.973344i) q^{46} +(-5.69475 + 1.52590i) q^{47} +(-0.204875 + 0.204875i) q^{48} +(6.96808 - 0.667734i) q^{49} +(-4.12132 - 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(-0.523277 + 1.95290i) q^{52} +(-0.357978 + 1.33599i) q^{53} +(-0.857049 + 1.48445i) q^{54} +(8.04270 - 9.67269i) q^{55} +(-1.95803 - 1.77936i) q^{56} +(-0.797333 + 0.797333i) q^{57} +(-3.04751 + 0.816578i) q^{58} +(-2.73923 - 4.74448i) q^{59} +(0.373980 + 0.529033i) q^{60} +(-3.99172 - 2.30462i) q^{61} +(-2.72127 - 2.72127i) q^{62} +(-6.85809 - 3.53413i) q^{63} +1.00000i q^{64} +(4.10581 + 1.89220i) q^{65} +(-1.41161 + 0.814995i) q^{66} +(-0.816193 - 0.218698i) q^{67} +(-1.37400 - 5.12784i) q^{68} -0.325641 q^{69} +(-4.66232 + 3.64180i) q^{70} +4.77710 q^{71} +(0.754730 + 2.81669i) q^{72} +(5.42104 + 1.45256i) q^{73} +(4.36475 - 2.51999i) q^{74} +(1.30741 - 0.623993i) q^{75} +3.89180i q^{76} +(-8.04920 - 12.5202i) q^{77} +(-0.414214 - 0.414214i) q^{78} +(-5.41079 - 3.12392i) q^{79} +(2.20382 + 0.378409i) q^{80} +(4.12576 + 7.14603i) q^{81} +(-6.96481 + 1.86622i) q^{82} +(-5.67281 + 5.67281i) q^{83} +(0.730133 - 0.233533i) q^{84} +(-11.8207 + 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(0.236593 - 0.882976i) q^{87} +(-1.45605 + 5.43407i) q^{88} +(5.96090 - 10.3246i) q^{89} +(6.49307 - 0.597426i) q^{90} +(3.59749 - 3.95871i) q^{91} +(-0.794732 + 0.794732i) q^{92} +(1.07705 - 0.288594i) q^{93} +(-2.94782 - 5.10577i) q^{94} +(8.57682 + 1.47269i) q^{95} +(-0.250919 - 0.144868i) q^{96} +(6.63103 + 6.63103i) q^{97} +(2.44845 + 6.55783i) q^{98} +16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35}+ \cdots + 40 q^{98}+O(q^{100}) \) 16 * q - 12 * q^5 + 8 * q^7 - 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 - 36 * q^17 - 8 * q^18 - 28 * q^21 - 8 * q^22 - 4 * q^23 + 12 * q^25 + 12 * q^26 + 4 * q^28 + 20 * q^30 + 24 * q^31 + 48 * q^33 + 8 * q^35 - 8 * q^36 + 4 * q^37 + 24 * q^38 + 36 * q^42 - 8 * q^43 - 12 * q^45 - 8 * q^46 + 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 - 4 * q^56 + 8 * q^57 - 32 * q^58 + 8 * q^60 - 12 * q^61 - 36 * q^63 - 8 * q^65 + 32 * q^67 - 36 * q^68 - 12 * q^70 + 16 * q^71 - 8 * q^72 - 12 * q^73 - 48 * q^75 + 16 * q^77 + 16 * q^78 - 12 * q^80 - 48 * q^82 + 24 * q^85 + 12 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^95 + 12 * q^96 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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