LMFDB - Embedded newform 666.2.e.e.223.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(223,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.223"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$666 = 2 \cdot 3^{2} \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	666.e (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [20,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 28 x^{18} + 304 x^{16} + 1654 x^{14} + 4950 x^{12} + 8429 x^{10} + 8179 x^{8} + 4427 x^{6} + \cdots + 9$ x^20 + 28x^18 + 304x^16 + 1654x^14 + 4950x^12 + 8429x^10 + 8179x^8 + 4427x^6 + 1273x^4 + 177*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$3^{4}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			223.9
Root			$1.01469i$ of defining polynomial
Character	$\chi$	$=$	666.223
Dual form			666.2.e.e.445.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.58644 + 0.695127i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.474737 + 0.822268i) q^{5} +(-1.39522 + 1.02634i) q^{6} +(2.02158 - 3.50148i) q^{7} +1.00000 q^{8} +(2.03360 + 2.20556i) q^{9} -0.949474 q^{10} +(0.911568 - 1.57888i) q^{11} +(-0.191224 - 1.72146i) q^{12} +(-1.32641 - 2.29742i) q^{13} +(2.02158 + 3.50148i) q^{14} +(0.181562 + 1.63448i) q^{15} +(-0.500000 + 0.866025i) q^{16} +7.58372 q^{17} +(-2.92687 + 0.658370i) q^{18} -5.40297 q^{19} +(0.474737 - 0.822268i) q^{20} +(5.64110 - 4.14965i) q^{21} +(0.911568 + 1.57888i) q^{22} +(-1.77158 - 3.06847i) q^{23} +(1.58644 + 0.695127i) q^{24} +(2.04925 - 3.54941i) q^{25} +2.65283 q^{26} +(1.69305 + 4.91260i) q^{27} -4.04317 q^{28} +(-1.12647 + 1.95110i) q^{29} +(-1.50628 - 0.660004i) q^{30} +(2.61540 + 4.53000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.54367 - 1.87115i) q^{33} +(-3.79186 + 6.56769i) q^{34} +3.83888 q^{35} +(0.893269 - 2.86393i) q^{36} -1.00000 q^{37} +(2.70148 - 4.67911i) q^{38} +(-0.507284 - 4.56674i) q^{39} +(0.474737 + 0.822268i) q^{40} +(1.21367 + 2.10213i) q^{41} +(0.773150 + 6.96016i) q^{42} +(-4.89762 + 8.48292i) q^{43} -1.82314 q^{44} +(-0.848135 + 2.71922i) q^{45} +3.54317 q^{46} +(-0.755257 + 1.30814i) q^{47} +(-1.39522 + 1.02634i) q^{48} +(-4.67360 - 8.09490i) q^{49} +(2.04925 + 3.54941i) q^{50} +(12.0311 + 5.27164i) q^{51} +(-1.32641 + 2.29742i) q^{52} -4.98930 q^{53} +(-5.10096 - 0.990077i) q^{54} +1.73102 q^{55} +(2.02158 - 3.50148i) q^{56} +(-8.57149 - 3.75574i) q^{57} +(-1.12647 - 1.95110i) q^{58} +(6.10352 + 10.5716i) q^{59} +(1.32472 - 0.974479i) q^{60} +(-0.806303 + 1.39656i) q^{61} -5.23080 q^{62} +(11.8338 - 2.66190i) q^{63} +1.00000 q^{64} +(1.25939 - 2.18134i) q^{65} +(0.348627 + 3.13846i) q^{66} +(-4.51746 - 7.82447i) q^{67} +(-3.79186 - 6.56769i) q^{68} +(-0.677538 - 6.09943i) q^{69} +(-1.91944 + 3.32457i) q^{70} -10.3584 q^{71} +(2.03360 + 2.20556i) q^{72} +2.93156 q^{73} +(0.500000 - 0.866025i) q^{74} +(5.71830 - 4.20644i) q^{75} +(2.70148 + 4.67911i) q^{76} +(-3.68562 - 6.38369i) q^{77} +(4.20856 + 1.84405i) q^{78} +(-4.82010 + 8.34866i) q^{79} -0.949474 q^{80} +(-0.728956 + 8.97043i) q^{81} -2.42733 q^{82} +(-2.64545 + 4.58206i) q^{83} +(-6.41425 - 2.81051i) q^{84} +(3.60027 + 6.23585i) q^{85} +(-4.89762 - 8.48292i) q^{86} +(-3.14334 + 2.31227i) q^{87} +(0.911568 - 1.57888i) q^{88} +15.0956 q^{89} +(-1.93085 - 2.09412i) q^{90} -10.7258 q^{91} +(-1.77158 + 3.06847i) q^{92} +(1.00025 + 9.00462i) q^{93} +(-0.755257 - 1.30814i) q^{94} +(-2.56499 - 4.44269i) q^{95} +(-0.191224 - 1.72146i) q^{96} +(-4.66528 + 8.08051i) q^{97} +9.34719 q^{98} +(5.33608 - 1.20030i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 10 q^{2} + 2 q^{3} - 10 q^{4} - q^{5} + 2 q^{6} - q^{7} + 20 q^{8} + 2 q^{9} + 2 q^{10} - 3 q^{11} - 4 q^{12} - 12 q^{13} - q^{14} - 13 q^{15} - 10 q^{16} + 24 q^{17} + 2 q^{18} + 48 q^{19} - q^{20}+ \cdots + 49 q^{99}+O(q^{100})$ 20 * q - 10 * q^2 + 2 * q^3 - 10 * q^4 - q^5 + 2 * q^6 - q^7 + 20 * q^8 + 2 * q^9 + 2 * q^10 - 3 * q^11 - 4 * q^12 - 12 * q^13 - q^14 - 13 * q^15 - 10 * q^16 + 24 * q^17 + 2 * q^18 + 48 * q^19 - q^20 - 18 * q^21 - 3 * q^22 - 3 * q^23 + 2 * q^24 - 21 * q^25 + 24 * q^26 - q^27 + 2 * q^28 - 4 * q^29 + 2 * q^30 - 11 * q^31 - 10 * q^32 + 19 * q^33 - 12 * q^34 - 14 * q^35 - 4 * q^36 - 20 * q^37 - 24 * q^38 - 18 * q^39 - q^40 + 3 * q^41 + 30 * q^42 - 6 * q^43 + 6 * q^44 + 18 * q^45 + 6 * q^46 - 8 * q^47 + 2 * q^48 - 35 * q^49 - 21 * q^50 + 17 * q^51 - 12 * q^52 - 20 * q^53 - 31 * q^54 + 4 * q^55 - q^56 - 41 * q^57 - 4 * q^58 - 10 * q^59 + 11 * q^60 - 2 * q^61 + 22 * q^62 + 29 * q^63 + 20 * q^64 - 26 * q^65 - 17 * q^66 - 7 * q^67 - 12 * q^68 + 9 * q^69 + 7 * q^70 + 30 * q^71 + 2 * q^72 + 6 * q^73 + 10 * q^74 - 48 * q^75 - 24 * q^76 - 9 * q^77 + 48 * q^78 - 16 * q^79 + 2 * q^80 + 10 * q^81 - 6 * q^82 + 23 * q^83 - 12 * q^84 - 15 * q^85 - 6 * q^86 + 25 * q^87 - 3 * q^88 + 42 * q^89 - 15 * q^90 + 118 * q^91 - 3 * q^92 - 117 * q^93 - 8 * q^94 + 6 * q^95 - 4 * q^96 - 24 * q^97 + 70 * q^98 + 49 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$ .

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.58644	+	0.695127i	0.915933	+	0.401331i
$3$	1.58644	+	0.695127i	0.915933	+	0.401331i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.474737	+	0.822268i	0.212309	+	0.367730i	0.952437	−	0.304737i	$-0.0985684\pi$
$5$	0.474737	+	0.822268i	0.212309	+	0.367730i	−0.740128	+	0.672466i	$0.765235\pi$
$6$	−1.39522	+	1.02634i	−0.569596	+	0.419000i
$7$	2.02158	−	3.50148i	0.764087	−	1.32344i	−0.176642	−	0.984275i	$-0.556523\pi$
$7$	2.02158	−	3.50148i	0.764087	−	1.32344i	0.940728	−	0.339161i	$-0.110143\pi$
$8$	1.00000			0.353553
$9$	2.03360	+	2.20556i	0.677866	+	0.735185i
$10$	−0.949474			−0.300250
$11$	0.911568	−	1.57888i	0.274848	−	0.476051i	−0.695249	−	0.718769i	$-0.744706\pi$
$11$	0.911568	−	1.57888i	0.274848	−	0.476051i	0.970097	+	0.242718i	$0.0780391\pi$
$12$	−0.191224	−	1.72146i	−0.0552016	−	0.496943i
$13$	−1.32641	−	2.29742i	−0.367881	−	0.637189i	0.621353	−	0.783531i	$-0.286583\pi$
$13$	−1.32641	−	2.29742i	−0.367881	−	0.637189i	−0.989234	+	0.146342i	$0.953250\pi$
$14$	2.02158	+	3.50148i	0.540291	+	0.935811i
$15$	0.181562	+	1.63448i	0.0468791	+	0.422022i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	7.58372			1.83932			0.919661	−	0.392714i	$-0.128464\pi$
$17$	7.58372			1.83932			0.919661	+	0.392714i	$0.128464\pi$
$18$	−2.92687	+	0.658370i	−0.689869	+	0.155179i
$19$	−5.40297			−1.23953			−0.619763	−	0.784789i	$-0.712771\pi$
$19$	−5.40297			−1.23953			−0.619763	+	0.784789i	$0.712771\pi$
$20$	0.474737	−	0.822268i	0.106154	−	0.183865i
$21$	5.64110	−	4.14965i	1.23099	−	0.905527i
$22$	0.911568	+	1.57888i	0.194347	+	0.336619i
$23$	−1.77158	−	3.06847i	−0.369401	−	0.639821i	0.620071	−	0.784546i	$-0.287104\pi$
$23$	−1.77158	−	3.06847i	−0.369401	−	0.639821i	−0.989472	+	0.144725i	$0.953770\pi$
$24$	1.58644	+	0.695127i	0.323831	+	0.141892i
$25$	2.04925	−	3.54941i	0.409850	−	0.709881i
$26$	2.65283			0.520262
$27$	1.69305	+	4.91260i	0.325827	+	0.945429i
$28$	−4.04317			−0.764087
$29$	−1.12647	+	1.95110i	−0.209180	+	0.362311i	−0.951456	−	0.307783i	$-0.900413\pi$
$29$	−1.12647	+	1.95110i	−0.209180	+	0.362311i	0.742276	+	0.670094i	$0.233746\pi$
$30$	−1.50628	−	0.660004i	−0.275009	−	0.120500i
$31$	2.61540	+	4.53000i	0.469739	+	0.813612i	0.999401	−	0.0345964i	$-0.0110146\pi$
$31$	2.61540	+	4.53000i	0.469739	+	0.813612i	−0.529662	+	0.848209i	$0.677681\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.54367	−	1.87115i	0.442797	−	0.325726i
$34$	−3.79186	+	6.56769i	−0.650298	+	1.12635i
$35$	3.83888			0.648889
$36$	0.893269	−	2.86393i	0.148878	−	0.477321i
$37$	−1.00000			−0.164399
$37$	−1.00000			−0.164399
$38$	2.70148	−	4.67911i	0.438238	−	0.759051i
$39$	−0.507284	−	4.56674i	−0.0812305	−	0.731264i
$40$	0.474737	+	0.822268i	0.0750625	+	0.130012i
$41$	1.21367	+	2.10213i	0.189543	+	0.328298i	0.945098	−	0.326787i	$-0.105966\pi$
$41$	1.21367	+	2.10213i	0.189543	+	0.328298i	−0.755555	+	0.655085i	$0.772633\pi$
$42$	0.773150	+	6.96016i	0.119300	+	1.07398i
$43$	−4.89762	+	8.48292i	−0.746879	+	1.29363i	0.202432	+	0.979296i	$0.435115\pi$
$43$	−4.89762	+	8.48292i	−0.746879	+	1.29363i	−0.949312	+	0.314337i	$0.898218\pi$
$44$	−1.82314			−0.274848
$45$	−0.848135	+	2.71922i	−0.126432	+	0.405358i
$46$	3.54317			0.522412
$47$	−0.755257	+	1.30814i	−0.110166	+	0.190812i	−0.915837	−	0.401550i	$-0.868471\pi$
$47$	−0.755257	+	1.30814i	−0.110166	+	0.190812i	0.805671	+	0.592363i	$0.201805\pi$
$48$	−1.39522	+	1.02634i	−0.201382	+	0.148139i
$49$	−4.67360	−	8.09490i	−0.667656	−	1.15641i
$50$	2.04925	+	3.54941i	0.289808	+	0.501962i
$51$	12.0311	+	5.27164i	1.68469	+	0.738178i
$52$	−1.32641	+	2.29742i	−0.183941	+	0.318594i
$53$	−4.98930			−0.685333			−0.342666	−	0.939457i	$-0.611330\pi$
$53$	−4.98930			−0.685333			−0.342666	+	0.939457i	$0.611330\pi$
$54$	−5.10096	−	0.990077i	−0.694152	−	0.134732i
$55$	1.73102			0.233411
$56$	2.02158	−	3.50148i	0.270145	−	0.467906i
$57$	−8.57149	−	3.75574i	−1.13532	−	0.497461i
$58$	−1.12647	−	1.95110i	−0.147913	−	0.256192i
$59$	6.10352	+	10.5716i	0.794611	+	1.37631i	0.923086	+	0.384594i	$0.125658\pi$
$59$	6.10352	+	10.5716i	0.794611	+	1.37631i	−0.128475	+	0.991713i	$0.541008\pi$
$60$	1.32472	−	0.974479i	0.171021	−	0.125805i
$61$	−0.806303	+	1.39656i	−0.103236	+	0.178811i	−0.913016	−	0.407923i	$-0.866253\pi$
$61$	−0.806303	+	1.39656i	−0.103236	+	0.178811i	0.809780	+	0.586734i	$0.199587\pi$
$62$	−5.23080			−0.664312
$63$	11.8338	−	2.66190i	1.49092	−	0.335368i
$64$	1.00000			0.125000
$65$	1.25939	−	2.18134i	0.156209	−	0.270561i
$66$	0.348627	+	3.13846i	0.0429131	+	0.386318i
$67$	−4.51746	−	7.82447i	−0.551895	−	0.955911i	−0.998138	−	0.0609986i	$-0.980571\pi$
$67$	−4.51746	−	7.82447i	−0.551895	−	0.955911i	0.446243	−	0.894912i	$-0.352762\pi$
$68$	−3.79186	−	6.56769i	−0.459830	−	0.796449i
$69$	−0.677538	−	6.09943i	−0.0815660	−	0.734285i
$70$	−1.91944	+	3.32457i	−0.229417	+	0.397362i
$71$	−10.3584			−1.22932			−0.614658	−	0.788793i	$-0.710706\pi$
$71$	−10.3584			−1.22932			−0.614658	+	0.788793i	$0.710706\pi$
$72$	2.03360	+	2.20556i	0.239662	+	0.259927i
$73$	2.93156			0.343113			0.171557	−	0.985174i	$-0.445120\pi$
$73$	2.93156			0.343113			0.171557	+	0.985174i	$0.445120\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$	5.71830	−	4.20644i	0.660293	−	0.485718i
$76$	2.70148	+	4.67911i	0.309881	+	0.536730i
$77$	−3.68562	−	6.38369i	−0.420016	−	0.727488i
$78$	4.20856	+	1.84405i	0.476525	+	0.208798i
$79$	−4.82010	+	8.34866i	−0.542304	+	0.939298i	0.456468	+	0.889740i	$0.349114\pi$
$79$	−4.82010	+	8.34866i	−0.542304	+	0.939298i	−0.998771	+	0.0495576i	$0.984219\pi$
$80$	−0.949474			−0.106154
$81$	−0.728956	+	8.97043i	−0.0809952	+	0.996714i
$82$	−2.42733			−0.268054
$83$	−2.64545	+	4.58206i	−0.290376	+	0.502947i	−0.973899	−	0.226983i	$-0.927114\pi$
$83$	−2.64545	+	4.58206i	−0.290376	+	0.502947i	0.683522	+	0.729930i	$0.260447\pi$
$84$	−6.41425	−	2.81051i	−0.699852	−	0.306652i
$85$	3.60027	+	6.23585i	0.390504	+	0.676373i
$86$	−4.89762	−	8.48292i	−0.528124	−	0.914737i
$87$	−3.14334	+	2.31227i	−0.337002	+	0.247902i
$88$	0.911568	−	1.57888i	0.0971735	−	0.168309i
$89$	15.0956			1.60013			0.800066	−	0.599912i	$-0.204798\pi$
$89$	15.0956			1.60013			0.800066	+	0.599912i	$0.204798\pi$
$90$	−1.93085	−	2.09412i	−0.203529	−	0.220739i
$91$	−10.7258			−1.12437
$92$	−1.77158	+	3.06847i	−0.184700	+	0.319910i
$93$	1.00025	+	9.00462i	0.103721	+	0.933736i
$94$	−0.755257	−	1.30814i	−0.0778988	−	0.134925i
$95$	−2.56499	−	4.44269i	−0.263162	−	0.455810i
$96$	−0.191224	−	1.72146i	−0.0195167	−	0.175696i
$97$	−4.66528	+	8.08051i	−0.473688	+	0.820451i	−0.999546	−	0.0301209i	$-0.990411\pi$
$97$	−4.66528	+	8.08051i	−0.473688	+	0.820451i	0.525859	+	0.850572i	$0.323744\pi$
$98$	9.34719			0.944209
$99$	5.33608	−	1.20030i	0.536296	−	0.120634i
$100$	−4.09850			−0.409850
$101$	−3.84896	+	6.66660i	−0.382986	+	0.663351i	−0.991488	−	0.130202i	$-0.958438\pi$
$101$	−3.84896	+	6.66660i	−0.382986	+	0.663351i	0.608502	+	0.793553i	$0.291771\pi$
$102$	−10.5809	+	7.78344i	−1.04767	+	0.770676i
$103$	−8.69198	−	15.0550i	−0.856446	−	1.48341i	−0.875297	−	0.483586i	$-0.839334\pi$
$103$	−8.69198	−	15.0550i	−0.856446	−	1.48341i	0.0188502	−	0.999822i	$-0.493999\pi$
$104$	−1.32641	−	2.29742i	−0.130066	−	0.225280i
$105$	6.09016	+	2.66851i	0.594339	+	0.260420i
$106$	2.49465	−	4.32086i	0.242302	−	0.419679i
$107$	9.97908			0.964714			0.482357	−	0.875975i	$-0.339781\pi$
$107$	9.97908			0.964714			0.482357	+	0.875975i	$0.339781\pi$
$108$	3.40791	−	3.92252i	0.327926	−	0.377445i
$109$	7.02860			0.673218			0.336609	−	0.941644i	$-0.390720\pi$
$109$	7.02860			0.673218			0.336609	+	0.941644i	$0.390720\pi$
$110$	−0.865510	+	1.49911i	−0.0825231	+	0.142934i
$111$	−1.58644	−	0.695127i	−0.150578	−	0.0659785i
$112$	2.02158	+	3.50148i	0.191022	+	0.330859i
$113$	−6.36427	−	11.0232i	−0.598700	−	1.03698i	−0.993013	−	0.118003i	$-0.962351\pi$
$113$	−6.36427	−	11.0232i	−0.598700	−	1.03698i	0.394313	−	0.918976i	$-0.370982\pi$
$114$	7.53832	−	5.54526i	0.706028	−	0.519361i
$115$	1.68207	−	2.91343i	0.156854	−	0.271679i
$116$	2.25294			0.209180
$117$	2.36969	−	7.59750i	0.219078	−	0.702389i
$118$	−12.2070			−1.12375
$119$	15.3311	−	26.5543i	1.40540	−	2.43423i
$120$	0.181562	+	1.63448i	0.0165743	+	0.149207i
$121$	3.83809	+	6.64776i	0.348917	+	0.604342i
$122$	−0.806303	−	1.39656i	−0.0729992	−	0.126438i
$123$	0.464164	+	4.17856i	0.0418523	+	0.376768i
$124$	2.61540	−	4.53000i	0.234870	−	0.406806i
$125$	8.63878			0.772676
$126$	−3.61163	+	11.5793i	−0.321750	+	1.03157i
$127$	−2.00548			−0.177957			−0.0889786	−	0.996034i	$-0.528360\pi$
$127$	−2.00548			−0.177957			−0.0889786	+	0.996034i	$0.528360\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−13.6665	+	10.0532i	−1.20327	+	0.885135i
$130$	1.25939	+	2.18134i	0.110456	+	0.191316i
$131$	2.80347	+	4.85574i	0.244940	+	0.424248i	0.962115	−	0.272645i	$-0.0878984\pi$
$131$	2.80347	+	4.85574i	0.244940	+	0.424248i	−0.717175	+	0.696893i	$0.754565\pi$
$132$	−2.89230	−	1.26731i	−0.251743	−	0.110305i
$133$	−10.9225	+	18.9184i	−0.947105	+	1.64043i
$134$	9.03491			0.780498
$135$	−3.23572	+	3.72433i	−0.278486	+	0.320539i
$136$	7.58372			0.650298
$137$	3.05624	−	5.29356i	0.261112	−	0.452259i	−0.705426	−	0.708784i	$-0.749244\pi$
$137$	3.05624	−	5.29356i	0.261112	−	0.452259i	0.966538	+	0.256525i	$0.0825775\pi$
$138$	5.62103	+	2.46295i	0.478494	+	0.209660i
$139$	−4.69634	−	8.13430i	−0.398338	−	0.689942i	0.595183	−	0.803590i	$-0.297080\pi$
$139$	−4.69634	−	8.13430i	−0.398338	−	0.689942i	−0.993521	+	0.113648i	$0.963746\pi$
$140$	−1.91944	−	3.32457i	−0.162222	−	0.280977i
$141$	−2.10750	+	1.55030i	−0.177483	+	0.130558i
$142$	5.17920	−	8.97064i	0.434629	−	0.752800i
$143$	−4.83647			−0.404446
$144$	−2.92687	+	0.658370i	−0.243906	+	0.0548641i
$145$	−2.13911			−0.177643
$146$	−1.46578	+	2.53881i	−0.121309	+	0.210113i
$147$	−1.78741	−	16.0908i	−0.147423	−	1.32715i
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−2.65895	−	4.60544i	−0.217830	−	0.377292i	0.736315	−	0.676639i	$-0.236564\pi$
$149$	−2.65895	−	4.60544i	−0.217830	−	0.377292i	−0.954144	+	0.299347i	$0.903231\pi$
$150$	0.783731	+	7.05541i	0.0639914	+	0.576072i
$151$	−2.03911	+	3.53185i	−0.165941	+	0.287418i	−0.936989	−	0.349359i	$-0.886399\pi$
$151$	−2.03911	+	3.53185i	−0.165941	+	0.287418i	0.771048	+	0.636777i	$0.219733\pi$
$152$	−5.40297			−0.438238
$153$	15.4222	+	16.7263i	1.24681	+	1.35224i
$154$	7.37124			0.593992
$155$	−2.48325	+	4.30112i	−0.199460	+	0.345474i
$156$	−3.70127	+	2.72269i	−0.296339	+	0.217990i
$157$	−11.1831	−	19.3697i	−0.892509	−	1.54587i	−0.836857	−	0.547422i	$-0.815609\pi$
$157$	−11.1831	−	19.3697i	−0.892509	−	1.54587i	−0.0556525	−	0.998450i	$-0.517724\pi$
$158$	−4.82010	−	8.34866i	−0.383467	−	0.664184i
$159$	−7.91523	−	3.46819i	−0.627719	−	0.275046i
$160$	0.474737	−	0.822268i	0.0375312	−	0.0650060i
$161$	−14.3256			−1.12902
$162$	−7.40414	−	5.11651i	−0.581724	−	0.401991i
$163$	−3.87053			−0.303164			−0.151582	−	0.988445i	$-0.548437\pi$
$163$	−3.87053			−0.303164			−0.151582	+	0.988445i	$0.548437\pi$
$164$	1.21367	−	2.10213i	0.0947714	−	0.164149i
$165$	2.74616	+	1.20328i	0.213789	+	0.0936751i
$166$	−2.64545	−	4.58206i	−0.205327	−	0.355637i
$167$	−8.64990	−	14.9821i	−0.669349	−	1.15935i	−0.978086	−	0.208200i	$-0.933240\pi$
$167$	−8.64990	−	14.9821i	−0.669349	−	1.15935i	0.308737	−	0.951147i	$-0.400094\pi$
$168$	5.64110	−	4.14965i	0.435220	−	0.320152i
$169$	2.98125	−	5.16368i	0.229327	−	0.397206i
$170$	−7.20054			−0.552256
$171$	−10.9875	−	11.9165i	−0.840232	−	0.911281i
$172$	9.79523			0.746879
$173$	−5.11011	+	8.85097i	−0.388515	+	0.672927i	−0.992250	−	0.124258i	$-0.960345\pi$
$173$	−5.11011	+	8.85097i	−0.388515	+	0.672927i	0.603735	+	0.797185i	$0.293678\pi$
$174$	−0.430816	−	3.87835i	−0.0326601	−	0.294017i
$175$	−8.28546	−	14.3508i	−0.626322	−	1.08482i
$176$	0.911568	+	1.57888i	0.0687121	+	0.119013i
$177$	2.33428	+	21.0140i	0.175455	+	1.57951i
$178$	−7.54781	+	13.0732i	−0.565732	+	0.979877i
$179$	−21.1620			−1.58172			−0.790861	−	0.611995i	$-0.790367\pi$
$179$	−21.1620			−1.58172			−0.790861	+	0.611995i	$0.790367\pi$
$180$	2.77898	−	0.625105i	0.207133	−	0.0465925i
$181$	−9.76447			−0.725787			−0.362894	−	0.931831i	$-0.618211\pi$
$181$	−9.76447			−0.725787			−0.362894	+	0.931831i	$0.618211\pi$
$182$	5.36291	−	9.28883i	0.397525	−	0.688534i
$183$	−2.24994	+	1.65508i	−0.166320	+	0.122347i
$184$	−1.77158	−	3.06847i	−0.130603	−	0.226211i
$185$	−0.474737	−	0.822268i	−0.0349033	−	0.0604544i
$186$	−8.29836	−	3.63606i	−0.608465	−	0.266609i
$187$	6.91308	−	11.9738i	0.505534	−	0.875611i
$188$	1.51051			0.110166
$189$	20.6240	+	4.00305i	1.50018	+	0.291179i
$190$	5.12997			0.372167
$191$	−4.01073	+	6.94679i	−0.290206	+	0.502652i	−0.973858	−	0.227156i	$-0.927057\pi$
$191$	−4.01073	+	6.94679i	−0.290206	+	0.502652i	0.683652	+	0.729808i	$0.260391\pi$
$192$	1.58644	+	0.695127i	0.114492	+	0.0501664i
$193$	−6.14776	−	10.6482i	−0.442525	−	0.766476i	0.555351	−	0.831616i	$-0.312584\pi$
$193$	−6.14776	−	10.6482i	−0.442525	−	0.766476i	−0.997876	+	0.0651399i	$0.979251\pi$
$194$	−4.66528	−	8.08051i	−0.334948	−	0.580147i
$195$	3.51426	−	2.58512i	0.251661	−	0.185125i
$196$	−4.67360	+	8.09490i	−0.333828	+	0.578207i
$197$	23.3938			1.66674			0.833370	−	0.552715i	$-0.186408\pi$
$197$	23.3938			1.66674			0.833370	+	0.552715i	$0.186408\pi$
$198$	−1.62855	+	5.22133i	−0.115736	+	0.371064i
$199$	9.00271			0.638185			0.319092	−	0.947724i	$-0.396622\pi$
$199$	9.00271			0.638185			0.319092	+	0.947724i	$0.396622\pi$
$200$	2.04925	−	3.54941i	0.144904	−	0.250981i
$201$	−1.72769	−	15.5533i	−0.121862	−	1.09704i
$202$	−3.84896	−	6.66660i	−0.270812	−	0.469060i
$203$	4.55450	+	7.88863i	0.319663	+	0.553673i
$204$	−1.45019	−	13.0551i	−0.101533	−	0.914039i
$205$	−1.15234	+	1.99592i	−0.0804832	+	0.139401i
$206$	17.3840			1.21120
$207$	3.16500	−	10.1474i	0.219983	−	0.705291i
$208$	2.65283			0.183941
$209$	−4.92517	+	8.53065i	−0.340681	+	0.590077i
$210$	−5.35607	+	3.93998i	−0.369604	+	0.271884i
$211$	−11.9261	−	20.6566i	−0.821025	−	1.42206i	−0.904919	−	0.425583i	$-0.860069\pi$
$211$	−11.9261	−	20.6566i	−0.821025	−	1.42206i	0.0838940	−	0.996475i	$-0.473264\pi$
$212$	2.49465	+	4.32086i	0.171333	+	0.296758i
$213$	−16.4330	−	7.20040i	−1.12597	−	0.493364i
$214$	−4.98954	+	8.64214i	−0.341078	+	0.590764i
$215$	−9.30031			−0.634276
$216$	1.69305	+	4.91260i	0.115197	+	0.334260i
$217$	21.1490			1.43569
$218$	−3.51430	+	6.08695i	−0.238019	+	0.412260i
$219$	4.65075	+	2.03781i	0.314269	+	0.137702i
$220$	−0.865510	−	1.49911i	−0.0583527	−	0.101070i
$221$	−10.0591	−	17.4230i	−0.676651	−	1.17199i
$222$	1.39522	−	1.02634i	0.0936409	−	0.0688832i
$223$	5.37634	−	9.31209i	0.360026	−	0.623583i	−0.627939	−	0.778263i	$-0.716101\pi$
$223$	5.37634	−	9.31209i	0.360026	−	0.623583i	0.987965	+	0.154679i	$0.0494345\pi$
$224$	−4.04317			−0.270145
$225$	11.9958	−	2.69833i	0.799718	−	0.179889i
$226$	12.7285			0.846689
$227$	−0.584445	+	1.01229i	−0.0387910	+	0.0671879i	−0.884769	−	0.466030i	$-0.845684\pi$
$227$	−0.584445	+	1.01229i	−0.0387910	+	0.0671879i	0.845978	+	0.533218i	$0.179017\pi$
$228$	1.03318	+	9.30100i	0.0684238	+	0.615974i
$229$	−8.75623	−	15.1662i	−0.578628	−	1.00221i	−0.995637	−	0.0933109i	$-0.970255\pi$
$229$	−8.75623	−	15.1662i	−0.578628	−	1.00221i	0.417009	−	0.908902i	$-0.363078\pi$
$230$	1.68207	+	2.91343i	0.110913	+	0.192106i
$231$	−1.40956	−	12.6893i	−0.0927421	−	0.834896i
$232$	−1.12647	+	1.95110i	−0.0739563	+	0.128096i
$233$	13.6563			0.894657			0.447328	−	0.894370i	$-0.352376\pi$
$233$	13.6563			0.894657			0.447328	+	0.894370i	$0.352376\pi$
$234$	5.39479	+	5.85096i	0.352668	+	0.382489i
$235$	−1.43419			−0.0935565
$236$	6.10352	−	10.5716i	0.397305	−	0.688153i
$237$	−13.4502	+	9.89409i	−0.873684	+	0.642690i
$238$	15.3311	+	26.5543i	0.993768	+	1.72126i
$239$	10.0358	+	17.3825i	0.649160	+	1.12438i	0.983324	+	0.181862i	$0.0582126\pi$
$239$	10.0358	+	17.3825i	0.649160	+	1.12438i	−0.334164	+	0.942515i	$0.608454\pi$
$240$	−1.50628	−	0.660004i	−0.0972303	−	0.0426031i
$241$	−1.52109	+	2.63461i	−0.0979822	+	0.169710i	−0.910849	−	0.412739i	$-0.864572\pi$
$241$	−1.52109	+	2.63461i	−0.0979822	+	0.169710i	0.812867	+	0.582449i	$0.197906\pi$
$242$	−7.67617			−0.493443
$243$	−7.39203	+	13.7244i	−0.474199	+	0.880418i
$244$	1.61261			0.103236
$245$	4.43746	−	7.68590i	0.283499	−	0.491034i
$246$	−3.85082	−	1.68730i	−0.245519	−	0.107579i
$247$	7.16657	+	12.4129i	0.455998	+	0.789811i
$248$	2.61540	+	4.53000i	0.166078	+	0.287655i
$249$	−7.38197	+	5.43025i	−0.467814	+	0.344128i
$250$	−4.31939	+	7.48141i	−0.273182	+	0.473166i
$251$	−30.0821			−1.89877			−0.949383	−	0.314121i	$-0.898290\pi$
$251$	−30.0821			−1.89877			−0.949383	+	0.314121i	$0.898290\pi$
$252$	−8.22218	−	8.91743i	−0.517948	−	0.561745i
$253$	−6.45968			−0.406117
$254$	1.00274	−	1.73679i	0.0629174	−	0.108976i
$255$	1.37691	+	12.3955i	0.0862258	+	0.776234i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0114	+	26.0005i	0.936384	+	1.62187i	0.772147	+	0.635444i	$0.219183\pi$
$257$	15.0114	+	26.0005i	0.936384	+	1.62187i	0.164238	+	0.986421i	$0.447484\pi$
$258$	−1.87308	−	16.8621i	−0.116613	−	1.04979i
$259$	−2.02158	+	3.50148i	−0.125615	+	0.217572i
$260$	−2.51879			−0.156209
$261$	−6.59405	+	1.48327i	−0.408162	+	0.0918119i
$262$	−5.60693			−0.346397
$263$	−2.92534	+	5.06684i	−0.180384	+	0.312435i	−0.942011	−	0.335581i	$-0.891067\pi$
$263$	−2.92534	+	5.06684i	−0.180384	+	0.312435i	0.761627	+	0.648015i	$0.224401\pi$
$264$	2.54367	−	1.87115i	0.156552	−	0.115161i
$265$	−2.36860	−	4.10254i	−0.145502	−	0.252017i
$266$	−10.9225	−	18.9184i	−0.669704	−	1.15996i
$267$	23.9483	+	10.4934i	1.46561	+	0.642184i
$268$	−4.51746	+	7.82447i	−0.275948	+	0.477955i
$269$	−13.2488			−0.807794			−0.403897	−	0.914804i	$-0.632345\pi$
$269$	−13.2488			−0.807794			−0.403897	+	0.914804i	$0.632345\pi$
$270$	−1.60750	−	4.66438i	−0.0978295	−	0.283865i
$271$	28.1980			1.71290			0.856452	−	0.516227i	$-0.172664\pi$
$271$	28.1980			1.71290			0.856452	+	0.516227i	$0.172664\pi$
$272$	−3.79186	+	6.56769i	−0.229915	+	0.398225i
$273$	−17.0159	−	7.45580i	−1.02985	−	0.451246i
$274$	3.05624	+	5.29356i	0.184634	+	0.319796i
$275$	−3.73606	−	6.47105i	−0.225293	−	0.390219i
$276$	−4.94349	+	3.63648i	−0.297563	+	0.218890i
$277$	−8.26768	+	14.3200i	−0.496756	+	0.860407i	−0.999993	−	0.00374124i	$-0.998809\pi$
$277$	−8.26768	+	14.3200i	−0.496756	+	0.860407i	0.503237	+	0.864149i	$0.332142\pi$
$278$	9.39268			0.563336
$279$	−4.67251	+	14.9806i	−0.279736	+	0.896866i
$280$	3.83888			0.229417
$281$	−10.2811	+	17.8074i	−0.613319	+	1.06230i	0.377358	+	0.926068i	$0.376833\pi$
$281$	−10.2811	+	17.8074i	−0.613319	+	1.06230i	−0.990677	+	0.136232i	$0.956501\pi$
$282$	−0.288846	−	2.60029i	−0.0172006	−	0.154845i
$283$	14.3491	+	24.8534i	0.852966	+	1.47738i	0.878519	+	0.477707i	$0.158532\pi$
$283$	14.3491	+	24.8534i	0.852966	+	1.47738i	−0.0255535	+	0.999673i	$0.508135\pi$
$284$	5.17920	+	8.97064i	0.307329	+	0.532310i
$285$	−0.980973	−	8.83106i	−0.0581079	−	0.523107i
$286$	2.41823	−	4.18850i	0.142993	−	0.247671i
$287$	9.81411			0.579308
$288$	0.893269	−	2.86393i	0.0526364	−	0.168758i
$289$	40.5127			2.38310
$290$	1.06955	−	1.85252i	0.0628063	−	0.108784i
$291$	−13.0182	+	9.57629i	−0.763139	+	0.561372i
$292$	−1.46578	−	2.53881i	−0.0857784	−	0.148572i
$293$	6.22185	+	10.7766i	0.363484	+	0.629574i	0.988532	−	0.151013i	$-0.0482536\pi$
$293$	6.22185	+	10.7766i	0.363484	+	0.629574i	−0.625047	+	0.780587i	$0.714920\pi$
$294$	14.8288	+	6.49748i	0.864832	+	0.378941i
$295$	−5.79513	+	10.0375i	−0.337406	+	0.584404i
$296$	−1.00000			−0.0581238
$297$	9.29974	+	1.80505i	0.539626	+	0.104739i
$298$	5.31790			0.308058
$299$	−4.69971	+	8.14013i	−0.271791	+	0.470756i
$300$	−6.50203	−	2.84898i	−0.375395	−	0.164486i
$301$	19.8019	+	34.2979i	1.14136	+	1.97690i
$302$	−2.03911	−	3.53185i	−0.117338	−	0.203235i
$303$	−10.7403	+	7.90065i	−0.617013	+	0.453881i
$304$	2.70148	−	4.67911i	0.154941	−	0.268365i
$305$	−1.53113			−0.0876720
$306$	−22.1965	+	4.99289i	−1.26889	+	0.285424i
$307$	0.945546			0.0539652			0.0269826	−	0.999636i	$-0.491410\pi$
$307$	0.945546			0.0539652			0.0269826	+	0.999636i	$0.491410\pi$
$308$	−3.68562	+	6.38369i	−0.210008	+	0.363744i
$309$	−3.32423	−	29.9258i	−0.189109	−	1.70242i
$310$	−2.48325	−	4.30112i	−0.141039	−	0.244287i
$311$	0.176724	+	0.306094i	0.0100211	+	0.0173570i	0.870992	−	0.491296i	$-0.163477\pi$
$311$	0.176724	+	0.306094i	0.0100211	+	0.0173570i	−0.860971	+	0.508653i	$0.830143\pi$
$312$	−0.507284	−	4.56674i	−0.0287193	−	0.258541i
$313$	−6.62891	+	11.4816i	−0.374688	+	0.648979i	−0.990280	−	0.139086i	$-0.955584\pi$
$313$	−6.62891	+	11.4816i	−0.374688	+	0.648979i	0.615592	+	0.788065i	$0.288917\pi$
$314$	22.3662			1.26220
$315$	7.80674	+	8.46686i	0.439860	+	0.477054i
$316$	9.64020			0.542304
$317$	−5.66282	+	9.80829i	−0.318055	+	0.550888i	−0.980082	−	0.198592i	$-0.936363\pi$
$317$	−5.66282	+	9.80829i	−0.318055	+	0.550888i	0.662027	+	0.749480i	$0.269696\pi$
$318$	6.96116	−	5.12070i	0.390362	−	0.287154i
$319$	2.05371	+	3.55713i	0.114986	+	0.199161i
$320$	0.474737	+	0.822268i	0.0265386	+	0.0459662i
$321$	15.8312	+	6.93672i	0.883613	+	0.387170i
$322$	7.16281	−	12.4063i	0.399168	−	0.691379i
$323$	−40.9746			−2.27989
$324$	8.13310	−	3.85392i	0.451839	−	0.214107i
$325$	−10.8726			−0.603104
$326$	1.93527	−	3.35198i	0.107185	−	0.185649i
$327$	11.1505	+	4.88577i	0.616623	+	0.270184i
$328$	1.21367	+	2.10213i	0.0670135	+	0.116071i
$329$	3.05363	+	5.28904i	0.168352	+	0.291594i
$330$	−2.41515	+	1.77661i	−0.132950	+	0.0977991i
$331$	13.3935	−	23.1983i	0.736174	−	1.27509i	−0.218032	−	0.975942i	$-0.569964\pi$
$331$	13.3935	−	23.1983i	0.736174	−	1.27509i	0.954206	−	0.299150i	$-0.0967030\pi$
$332$	5.29091			0.290376
$333$	−2.03360	−	2.20556i	−0.111440	−	0.120864i
$334$	17.2998			0.946603
$335$	4.28921	−	7.42912i	0.234344	−	0.405896i
$336$	0.773150	+	6.96016i	0.0421788	+	0.379708i
$337$	10.0289	+	17.3706i	0.546310	+	0.946237i	0.998523	+	0.0543274i	$0.0173015\pi$
$337$	10.0289	+	17.3706i	0.546310	+	0.946237i	−0.452213	+	0.891910i	$0.649365\pi$
$338$	2.98125	+	5.16368i	0.162159	+	0.280867i
$339$	−2.43400	−	21.9117i	−0.132197	−	1.19008i
$340$	3.60027	−	6.23585i	0.195252	−	0.338186i
$341$	9.53646			0.516428
$342$	15.8138	−	3.55715i	0.855110	−	0.192349i
$343$	−9.49008			−0.512416
$344$	−4.89762	+	8.48292i	−0.264062	+	0.457368i
$345$	4.69372	−	3.45274i	0.252701	−	0.185889i
$346$	−5.11011	−	8.85097i	−0.274721	−	0.475831i
$347$	8.10628	+	14.0405i	0.435168	+	0.753732i	0.997309	−	0.0733085i	$-0.0233558\pi$
$347$	8.10628	+	14.0405i	0.435168	+	0.753732i	−0.562142	+	0.827041i	$0.690022\pi$
$348$	3.57416	+	1.56608i	0.191595	+	0.0839506i
$349$	8.69662	−	15.0630i	0.465519	−	0.806303i	−0.533706	−	0.845670i	$-0.679201\pi$
$349$	8.69662	−	15.0630i	0.465519	−	0.806303i	0.999225	+	0.0393674i	$0.0125343\pi$
$350$	16.5709			0.885753
$351$	9.04060	−	10.4058i	0.482551	−	0.555419i
$352$	−1.82314			−0.0971735
$353$	6.33891	−	10.9793i	0.337386	−	0.584370i	−0.646554	−	0.762868i	$-0.723791\pi$
$353$	6.33891	−	10.9793i	0.337386	−	0.584370i	0.983940	+	0.178498i	$0.0571239\pi$
$354$	−19.3658	−	8.48544i	−1.02928	−	0.450996i
$355$	−4.91752	−	8.51739i	−0.260995	−	0.452056i
$356$	−7.54781	−	13.0732i	−0.400033	−	0.692878i
$357$	42.7805	−	31.4697i	2.26418	−	1.66556i
$358$	10.5810	−	18.3268i	0.559223	−	0.968603i
$359$	−15.4716			−0.816560			−0.408280	−	0.912857i	$-0.633871\pi$
$359$	−15.4716			−0.816560			−0.408280	+	0.912857i	$0.633871\pi$
$360$	−0.848135	+	2.71922i	−0.0447006	+	0.143316i
$361$	10.1920			0.536423
$362$	4.88223	−	8.45628i	0.256604	−	0.444452i
$363$	1.46787	+	13.2142i	0.0770431	+	0.693568i
$364$	5.36291	+	9.28883i	0.281093	+	0.486867i
$365$	1.39172	+	2.41053i	0.0728460	+	0.126173i
$366$	−0.308369	−	2.77604i	−0.0161187	−	0.145106i
$367$	8.96186	−	15.5224i	0.467805	−	0.810263i	−0.531518	−	0.847047i	$-0.678378\pi$
$367$	8.96186	−	15.5224i	0.467805	−	0.810263i	0.999323	+	0.0367845i	$0.0117115\pi$
$368$	3.54317			0.184700
$369$	−2.16826	+	6.95170i	−0.112875	+	0.361891i
$370$	0.949474			0.0493608
$371$	−10.0863	+	17.4699i	−0.523654	+	0.906995i
$372$	7.29810	−	5.36855i	0.378389	−	0.278347i
$373$	10.4072	+	18.0257i	0.538862	+	0.933336i	0.998966	+	0.0454709i	$0.0144788\pi$
$373$	10.4072	+	18.0257i	0.538862	+	0.933336i	−0.460104	+	0.887865i	$0.652188\pi$
$374$	6.91308	+	11.9738i	0.357467	+	0.619150i
$375$	13.7049	+	6.00505i	0.707720	+	0.310099i
$376$	−0.755257	+	1.30814i	−0.0389494	+	0.0674624i
$377$	5.97666			0.307814
$378$	−13.7787	+	15.8594i	−0.708702	+	0.815719i
$379$	−24.4311			−1.25494			−0.627472	−	0.778639i	$-0.715910\pi$
$379$	−24.4311			−1.25494			−0.627472	+	0.778639i	$0.715910\pi$
$380$	−2.56499	+	4.44269i	−0.131581	+	0.227905i
$381$	−3.18157	−	1.39406i	−0.162997	−	0.0714198i
$382$	−4.01073	−	6.94679i	−0.205207	−	0.355429i
$383$	−8.65222	−	14.9861i	−0.442108	−	0.765754i	0.555738	−	0.831358i	$-0.312436\pi$
$383$	−8.65222	−	14.9861i	−0.442108	−	0.765754i	−0.997846	+	0.0656042i	$0.979103\pi$
$384$	−1.39522	+	1.02634i	−0.0711994	+	0.0523750i
$385$	3.49940	−	6.06114i	0.178346	−	0.308904i
$386$	12.2955			0.625825
$387$	−28.6693	+	6.44888i	−1.45734	+	0.327815i
$388$	9.33056			0.473688
$389$	2.74544	−	4.75524i	0.139199	−	0.241100i	−0.787994	−	0.615682i	$-0.788880\pi$
$389$	2.74544	−	4.75524i	0.139199	−	0.241100i	0.927194	+	0.374582i	$0.122214\pi$
$390$	0.481653	+	4.33600i	0.0243894	+	0.219562i
$391$	−13.4352	−	23.2704i	−0.679447	−	1.17684i
$392$	−4.67360	−	8.09490i	−0.236052	−	0.408854i
$393$	1.07218	+	9.65212i	0.0540843	+	0.486885i
$394$	−11.6969	+	20.2596i	−0.589282	+	1.02067i
$395$	−9.15312			−0.460543
$396$	−3.70753	−	4.02103i	−0.186310	−	0.202064i
$397$	26.3543			1.32269			0.661343	−	0.750084i	$-0.269987\pi$
$397$	26.3543			1.32269			0.661343	+	0.750084i	$0.269987\pi$
$398$	−4.50135	+	7.79657i	−0.225632	+	0.390807i
$399$	−30.4787	+	22.4204i	−1.52584	+	1.12242i
$400$	2.04925	+	3.54941i	0.102463	+	0.177470i
$401$	15.1979	+	26.3235i	0.758945	+	1.31453i	0.943389	+	0.331689i	$0.107618\pi$
$401$	15.1979	+	26.3235i	0.758945	+	1.31453i	−0.184443	+	0.982843i	$0.559048\pi$
$402$	14.3334	+	6.28041i	0.714884	+	0.313238i
$403$	6.93820	−	12.0173i	0.345616	−	0.598625i
$404$	7.69792			0.382986
$405$	−7.72216	+	3.65920i	−0.383717	+	0.181827i
$406$	−9.10901			−0.452072
$407$	−0.911568	+	1.57888i	−0.0451848	+	0.0782623i
$408$	12.0311	+	5.27164i	0.595630	+	0.260985i
$409$	−1.37794	−	2.38665i	−0.0681345	−	0.118012i	0.829946	−	0.557844i	$-0.188371\pi$
$409$	−1.37794	−	2.38665i	−0.0681345	−	0.118012i	−0.898080	+	0.439832i	$0.855038\pi$
$410$	−1.15234	−	1.99592i	−0.0569102	−	0.0985714i
$411$	8.52824	−	6.27345i	0.420667	−	0.309447i
$412$	−8.69198	+	15.0550i	−0.428223	+	0.741704i
$413$	49.3551			2.42861
$414$	7.20538	+	7.81466i	0.354125	+	0.384069i
$415$	−5.02358			−0.246598
$416$	−1.32641	+	2.29742i	−0.0650328	+	0.112640i
$417$	−1.79611	−	16.1691i	−0.0879556	−	0.791807i
$418$	−4.92517	−	8.53065i	−0.240898	−	0.417248i
$419$	13.8711	+	24.0254i	0.677647	+	1.17372i	0.975688	+	0.219166i	$0.0703336\pi$
$419$	13.8711	+	24.0254i	0.677647	+	1.17372i	−0.298040	+	0.954553i	$0.596333\pi$
$420$	−0.734085	−	6.60849i	−0.0358197	−	0.322461i
$421$	9.45571	−	16.3778i	0.460843	−	0.798204i	−0.538160	−	0.842843i	$-0.680880\pi$
$421$	9.45571	−	16.3778i	0.460843	−	0.798204i	0.999003	+	0.0446391i	$0.0142138\pi$
$422$	23.8522			1.16111
$423$	−4.42107	+	0.994477i	−0.214960	+	0.0483531i
$424$	−4.98930			−0.242302
$425$	15.5409	−	26.9177i	0.753846	−	1.30570i
$426$	14.4522	−	10.6312i	0.700213	−	0.515084i
$427$	3.26002	+	5.64651i	0.157763	+	0.273254i
$428$	−4.98954	−	8.64214i	−0.241178	−	0.417733i
$429$	−7.67278	−	3.36196i	−0.370445	−	0.162317i
$430$	4.65016	−	8.05431i	0.224250	−	0.388413i
$431$	−38.0148			−1.83111			−0.915555	−	0.402192i	$-0.868248\pi$
$431$	−38.0148			−1.83111			−0.915555	+	0.402192i	$0.868248\pi$
$432$	−5.10096	−	0.990077i	−0.245420	−	0.0476351i
$433$	−36.4405			−1.75122			−0.875609	−	0.483021i	$-0.839539\pi$
$433$	−36.4405			−1.75122			−0.875609	+	0.483021i	$0.839539\pi$
$434$	−10.5745	+	18.3156i	−0.507592	+	0.879175i
$435$	−3.39357	−	1.48695i	−0.162709	−	0.0712938i
$436$	−3.51430	−	6.08695i	−0.168305	−	0.291512i
$437$	9.57181	+	16.5789i	0.457882	+	0.793074i
$438$	−4.09017	+	3.00877i	−0.195436	+	0.143764i
$439$	−10.6640	+	18.4705i	−0.508963	+	0.881549i	0.490983	+	0.871169i	$0.336638\pi$
$439$	−10.6640	+	18.4705i	−0.508963	+	0.881549i	−0.999946	+	0.0103804i	$0.996696\pi$
$440$	1.73102			0.0825231
$441$	8.34955	−	26.7697i	0.397598	−	1.27475i
$442$	20.1183			0.956930
$443$	−4.05738	+	7.02759i	−0.192772	+	0.333891i	−0.946168	−	0.323676i	$-0.895081\pi$
$443$	−4.05738	+	7.02759i	−0.192772	+	0.333891i	0.753396	+	0.657567i	$0.228414\pi$
$444$	0.191224	+	1.72146i	0.00907509	+	0.0816970i
$445$	7.16645	+	12.4126i	0.339722	+	0.588416i
$446$	5.37634	+	9.31209i	0.254577	+	0.440940i
$447$	−1.01691	−	9.15456i	−0.0480982	−	0.432996i
$448$	2.02158	−	3.50148i	0.0955108	−	0.165430i
$449$	−11.0770			−0.522757			−0.261378	−	0.965236i	$-0.584177\pi$
$449$	−11.0770			−0.522757			−0.261378	+	0.965236i	$0.584177\pi$
$450$	−3.66106	+	11.7378i	−0.172584	+	0.553325i
$451$	4.42536			0.208382
$452$	−6.36427	+	11.0232i	−0.299350	+	0.518489i
$453$	−5.69002	+	4.18563i	−0.267341	+	0.196658i
$454$	−0.584445	−	1.01229i	−0.0274294	−	0.0475090i
$455$	−5.09194	−	8.81950i	−0.238714	−	0.413465i
$456$	−8.57149	−	3.75574i	−0.401397	−	0.175879i
$457$	−9.24353	+	16.0103i	−0.432394	+	0.748929i	−0.997079	−	0.0763780i	$-0.975664\pi$
$457$	−9.24353	+	16.0103i	−0.432394	+	0.748929i	0.564685	+	0.825307i	$0.308998\pi$
$458$	17.5125			0.818304
$459$	12.8396	+	37.2557i	0.599300	+	1.73895i
$460$	−3.36414			−0.156854
$461$	−6.80618	+	11.7887i	−0.316996	+	0.549052i	−0.979860	−	0.199687i	$-0.936007\pi$
$461$	−6.80618	+	11.7887i	−0.316996	+	0.549052i	0.662864	+	0.748740i	$0.269341\pi$
$462$	11.6941	+	5.12395i	0.544057	+	0.238388i
$463$	3.93671	+	6.81859i	0.182955	+	0.316887i	0.942885	−	0.333117i	$-0.108101\pi$
$463$	3.93671	+	6.81859i	0.182955	+	0.316887i	−0.759931	+	0.650004i	$0.774767\pi$
$464$	−1.12647	−	1.95110i	−0.0522950	−	0.0905776i
$465$	−6.92936	+	5.09730i	−0.321341	+	0.236382i
$466$	−6.82817	+	11.8267i	−0.316309	+	0.547863i
$467$	7.42635			0.343650			0.171825	−	0.985127i	$-0.445034\pi$
$467$	7.42635			0.343650			0.171825	+	0.985127i	$0.445034\pi$
$468$	−7.76447	+	1.74654i	−0.358913	+	0.0807339i
$469$	−36.5297			−1.68678
$470$	0.717097	−	1.24205i	0.0330772	−	0.0572914i
$471$	−4.27696	−	38.5026i	−0.197072	−	1.77411i
$472$	6.10352	+	10.5716i	0.280937	+	0.486598i
$473$	8.92902	+	15.4655i	0.410557	+	0.711105i
$474$	−1.84344	−	16.5952i	−0.0846719	−	0.762245i
$475$	−11.0720	+	19.1773i	−0.508019	+	0.879915i
$476$	−30.6622			−1.40540
$477$	−10.1462	−	11.0042i	−0.464564	−	0.503847i
$478$	−20.0715			−0.918050
$479$	12.2682	−	21.2491i	0.560546	−	0.970895i	−0.436902	−	0.899509i	$-0.643925\pi$
$479$	12.2682	−	21.2491i	0.560546	−	0.970895i	0.997449	−	0.0713858i	$-0.0227421\pi$
$480$	1.32472	−	0.974479i	0.0604651	−	0.0444787i
$481$	1.32641	+	2.29742i	0.0604793	+	0.104753i
$482$	−1.52109	−	2.63461i	−0.0692839	−	0.120003i
$483$	−22.7268	−	9.95811i	−1.03410	−	0.453110i
$484$	3.83809	−	6.64776i	0.174458	−	0.302171i
$485$	−8.85912			−0.402272
$486$	−8.18962	−	13.2639i	−0.371489	−	0.601661i
$487$	22.7588			1.03130			0.515650	−	0.856800i	$-0.327551\pi$
$487$	22.7588			1.03130			0.515650	+	0.856800i	$0.327551\pi$
$488$	−0.806303	+	1.39656i	−0.0364996	+	0.0632192i
$489$	−6.14038	−	2.69051i	−0.277678	−	0.121669i
$490$	4.43746	+	7.68590i	0.200464	+	0.347213i
$491$	−17.0663	−	29.5598i	−0.770193	−	1.33401i	−0.937457	−	0.348101i	$-0.886826\pi$
$491$	−17.0663	−	29.5598i	−0.770193	−	1.33401i	0.167264	−	0.985912i	$-0.446507\pi$
$492$	3.38666	−	2.49126i	0.152682	−	0.112315i
$493$	−8.54282	+	14.7966i	−0.384749	+	0.666406i
$494$	−14.3331			−0.644878
$495$	3.52020	+	3.81786i	0.158221	+	0.171600i
$496$	−5.23080			−0.234870
$497$	−20.9404	+	36.2698i	−0.939304	+	1.62692i
$498$	−1.01175	−	9.10810i	−0.0453375	−	0.408144i
$499$	−20.2515	−	35.0766i	−0.906580	−	1.57024i	−0.818782	−	0.574105i	$-0.805350\pi$
$499$	−20.2515	−	35.0766i	−0.906580	−	1.57024i	−0.0877986	−	0.996138i	$-0.527983\pi$
$500$	−4.31939	−	7.48141i	−0.193169	−	0.334579i
$501$	−3.30813	−	29.7810i	−0.147797	−	1.33051i
$502$	15.0411	−	26.0519i	0.671315	−	1.16275i
$503$	2.32706			0.103758			0.0518792	−	0.998653i	$-0.483479\pi$
$503$	2.32706			0.103758			0.0518792	+	0.998653i	$0.483479\pi$
$504$	11.8338	−	2.66190i	0.527120	−	0.118570i
$505$	−7.30897			−0.325245
$506$	3.22984	−	5.59425i	0.143584	−	0.248695i
$507$	8.31900	−	6.11953i	0.369460	−	0.271778i
$508$	1.00274	+	1.73679i	0.0444893	+	0.0770577i
$509$	0.839776	+	1.45453i	0.0372224	+	0.0644711i	0.884036	−	0.467418i	$-0.154816\pi$
$509$	0.839776	+	1.45453i	0.0372224	+	0.0644711i	−0.846814	+	0.531889i	$0.821482\pi$
$510$	−11.4232	−	5.00528i	−0.505829	−	0.221638i
$511$	5.92640	−	10.2648i	0.262168	−	0.454089i
$512$	1.00000			0.0441942
$513$	−9.14747	−	26.5426i	−0.403871	−	1.17188i
$514$	−30.0228			−1.32425
$515$	8.25281	−	14.2943i	0.363662	−	0.629881i
$516$	15.5396	+	6.80893i	0.684091	+	0.299746i
$517$	1.37694	+	2.38492i	0.0605576	+	0.104889i
$518$	−2.02158	−	3.50148i	−0.0888233	−	0.153846i
$519$	−14.2594	+	10.4894i	−0.625920	+	0.460433i
$520$	1.25939	−	2.18134i	0.0552281	−	0.0956579i
$521$	−14.0917			−0.617370			−0.308685	−	0.951164i	$-0.599889\pi$
$521$	−14.0917			−0.617370			−0.308685	+	0.951164i	$0.599889\pi$
$522$	2.01248	−	6.45225i	0.0880838	−	0.282407i
$523$	14.8457			0.649159			0.324580	−	0.945858i	$-0.394777\pi$
$523$	14.8457			0.649159			0.324580	+	0.945858i	$0.394777\pi$
$524$	2.80347	−	4.85574i	0.122470	−	0.212124i
$525$	−3.16876	−	28.5262i	−0.138296	−	1.24499i
$526$	−2.92534	−	5.06684i	−0.127551	−	0.220925i
$527$	19.8344	+	34.3543i	0.864002	+	1.49649i
$528$	0.348627	+	3.13846i	0.0151721	+	0.136584i
$529$	5.22298	−	9.04647i	0.227086	−	0.393325i
$530$	4.73721			0.205771
$531$	−10.9042	+	34.9601i	−0.473201	+	1.51714i
$532$	21.8451			0.947105
$533$	3.21965	−	5.57659i	0.139458	−	0.241549i
$534$	−21.0617	+	15.4932i	−0.911428	+	0.670456i
$535$	4.73744	+	8.20548i	0.204817	+	0.354754i
$536$	−4.51746	−	7.82447i	−0.195124	−	0.337965i
$537$	−33.5723	−	14.7103i	−1.44875	−	0.634795i
$538$	6.62441	−	11.4738i	0.285598	−	0.494671i
$539$	−17.0412			−0.734017
$540$	4.84322	+	0.940052i	0.208419	+	0.0404534i
$541$	−25.4514			−1.09424			−0.547120	−	0.837054i	$-0.684276\pi$
$541$	−25.4514			−1.09424			−0.547120	+	0.837054i	$0.684276\pi$
$542$	−14.0990	+	24.4201i	−0.605603	+	1.04894i
$543$	−15.4908	−	6.78754i	−0.664772	−	0.291281i
$544$	−3.79186	−	6.56769i	−0.162575	−	0.281587i
$545$	3.33674	+	5.77940i	0.142930	+	0.247562i
$546$	14.9649	−	11.0083i	0.640437	−	0.471112i
$547$	20.1911	−	34.9720i	0.863308	−	1.49529i	−0.00540984	−	0.999985i	$-0.501722\pi$
$547$	20.1911	−	34.9720i	0.863308	−	1.49529i	0.868718	−	0.495308i	$-0.164945\pi$
$548$	−6.11247			−0.261112
$549$	−4.71988	+	1.06169i	−0.201440	+	0.0453118i
$550$	7.47213			0.318613
$551$	6.08628	−	10.5417i	0.259284	−	0.449093i
$552$	−0.677538	−	6.09943i	−0.0288379	−	0.259609i
$553$	19.4885	+	33.7550i	0.828734	+	1.43541i
$554$	−8.26768	−	14.3200i	−0.351260	−	0.608400i
$555$	−0.181562	−	1.63448i	−0.00770688	−	0.0693799i
$556$	−4.69634	+	8.13430i	−0.199169	+	0.344971i
$557$	14.3391			0.607568			0.303784	−	0.952741i	$-0.401750\pi$
$557$	14.3391			0.607568			0.303784	+	0.952741i	$0.401750\pi$
$558$	−10.6373	−	11.5368i	−0.450314	−	0.488392i
$559$	25.9851			1.09905
$560$	−1.91944	+	3.32457i	−0.0811111	+	0.140489i
$561$	19.2905	−	14.1903i	0.814446	−	0.599114i
$562$	−10.2811	−	17.8074i	−0.433682	−	0.751160i
$563$	−2.08040	−	3.60336i	−0.0876785	−	0.151864i	0.818851	−	0.574006i	$-0.194611\pi$
$563$	−2.08040	−	3.60336i	−0.0876785	−	0.151864i	−0.906529	+	0.422143i	$0.861278\pi$
$564$	2.39634	+	1.05000i	0.100904	+	0.0442129i
$565$	6.04270	−	10.4663i	0.254218	−	0.440319i
$566$	−28.6982			−1.20628
$567$	29.9362	+	20.6869i	1.25720	+	0.868768i
$568$	−10.3584			−0.434629
$569$	7.08032	−	12.2635i	0.296822	−	0.514112i	−0.678585	−	0.734522i	$-0.737406\pi$
$569$	7.08032	−	12.2635i	0.296822	−	0.514112i	0.975407	+	0.220411i	$0.0707397\pi$
$570$	8.13841	+	3.56598i	0.340880	+	0.149362i
$571$	3.39868	+	5.88669i	0.142230	+	0.246350i	0.928336	−	0.371742i	$-0.121239\pi$
$571$	3.39868	+	5.88669i	0.142230	+	0.246350i	−0.786106	+	0.618092i	$0.787906\pi$
$572$	2.41823	+	4.18850i	0.101111	+	0.175130i
$573$	−11.1917	+	8.23272i	−0.467540	+	0.343927i
$574$	−4.90705	+	8.49927i	−0.204816	+	0.354753i
$575$	−14.5217			−0.605596
$576$	2.03360	+	2.20556i	0.0847333	+	0.0918982i
$577$	42.6431			1.77526			0.887628	−	0.460561i	$-0.152352\pi$
$577$	42.6431			1.77526			0.887628	+	0.460561i	$0.152352\pi$
$578$	−20.2564	+	35.0851i	−0.842554	+	1.45935i
$579$	−2.35120	−	21.1663i	−0.0977124	−	0.879640i
$580$	1.06955	+	1.85252i	0.0444108	+	0.0769217i
$581$	10.6960	+	18.5260i	0.443745	+	0.768589i
$582$	−1.78423	−	16.0622i	−0.0739586	−	0.665800i
$583$	−4.54809	+	7.87752i	−0.188362	+	0.326253i
$584$	2.93156			0.121309
$585$	7.37216	−	1.65829i	0.304801	−	0.0685620i
$586$	−12.4437			−0.514045
$587$	1.46892	−	2.54424i	0.0606286	−	0.105012i	−0.834118	−	0.551586i	$-0.814023\pi$
$587$	1.46892	−	2.54424i	0.0606286	−	0.105012i	0.894747	+	0.446574i	$0.147356\pi$
$588$	−13.0414	+	9.59336i	−0.537817	+	0.395623i
$589$	−14.1309	−	24.4754i	−0.582254	−	1.00849i
$590$	−5.79513	−	10.0375i	−0.238582	−	0.413236i
$591$	37.1129	+	16.2617i	1.52662	+	0.668915i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	7.58214			0.311361			0.155681	−	0.987807i	$-0.450243\pi$
$593$	7.58214			0.311361			0.155681	+	0.987807i	$0.450243\pi$
$594$	−6.21309	+	7.15129i	−0.254926	+	0.293421i
$595$	29.1130			1.19352
$596$	−2.65895	+	4.60544i	−0.108915	+	0.188646i
$597$	14.2823	+	6.25802i	0.584535	+	0.256124i
$598$	−4.69971	−	8.14013i	−0.192185	−	0.332875i
$599$	−6.24125	−	10.8102i	−0.255011	−	0.441691i	0.709888	−	0.704315i	$-0.248746\pi$
$599$	−6.24125	−	10.8102i	−0.255011	−	0.441691i	−0.964898	+	0.262624i	$0.915412\pi$
$600$	5.71830	−	4.20644i	0.233449	−	0.171727i
$601$	−12.8957	+	22.3360i	−0.526027	+	0.911105i	0.473514	+	0.880787i	$0.342985\pi$
$601$	−12.8957	+	22.3360i	−0.526027	+	0.911105i	−0.999540	+	0.0303185i	$0.990348\pi$
$602$	−39.6037			−1.61413
$603$	8.07061	−	25.8753i	0.328660	−	1.05372i
$604$	4.07823			0.165941
$605$	−3.64416	+	6.31187i	−0.148156	+	0.256614i
$606$	−1.47203	−	13.2517i	−0.0597970	−	0.538313i
$607$	−20.8559	−	36.1234i	−0.846513	−	1.46620i	−0.884301	−	0.466918i	$-0.845364\pi$
$607$	−20.8559	−	36.1234i	−0.846513	−	1.46620i	0.0377880	−	0.999286i	$-0.487969\pi$
$608$	2.70148	+	4.67911i	0.109560	+	0.189763i
$609$	1.74186	+	15.6808i	0.0705837	+	0.635419i
$610$	0.765563	−	1.32599i	0.0309967	−	0.0536879i
$611$	4.00713			0.162111
$612$	6.77430	−	21.7192i	0.273835	−	0.877947i
$613$	−17.2841			−0.698099			−0.349049	−	0.937104i	$-0.613495\pi$
$613$	−17.2841			−0.698099			−0.349049	+	0.937104i	$0.613495\pi$
$614$	−0.472773	+	0.818867i	−0.0190796	+	0.0330468i
$615$	−3.21554	+	2.36538i	−0.129663	+	0.0953815i
$616$	−3.68562	−	6.38369i	−0.148498	−	0.257206i
$617$	−16.6835	−	28.8966i	−0.671651	−	1.16333i	−0.977436	−	0.211234i	$-0.932252\pi$
$617$	−16.6835	−	28.8966i	−0.671651	−	1.16333i	0.305784	−	0.952101i	$-0.401081\pi$
$618$	27.5787	+	12.0841i	1.10938	+	0.486092i
$619$	−14.8227	+	25.6737i	−0.595776	+	1.03192i	0.397660	+	0.917533i	$0.369822\pi$
$619$	−14.8227	+	25.6737i	−0.595776	+	1.03192i	−0.993437	+	0.114382i	$0.963511\pi$
$620$	4.96650			0.199460
$621$	12.0748	−	13.8981i	0.484545	−	0.557713i
$622$	−0.353447			−0.0141719
$623$	30.5171	−	52.8571i	1.22264	−	2.11767i
$624$	4.20856	+	1.84405i	0.168477	+	0.0738211i
$625$	−6.14510	−	10.6436i	−0.245804	−	0.425745i
$626$	−6.62891	−	11.4816i	−0.264944	−	0.458897i
$627$	−13.7434	+	10.1098i	−0.548858	+	0.403745i
$628$	−11.1831	+	19.3697i	−0.446255	+	0.772936i
$629$	−7.58372			−0.302383
$630$	−11.2359	+	2.52740i	−0.447648	+	0.100694i
$631$	1.45670			0.0579903			0.0289952	−	0.999580i	$-0.490769\pi$
$631$	1.45670			0.0579903			0.0289952	+	0.999580i	$0.490769\pi$
$632$	−4.82010	+	8.34866i	−0.191733	+	0.332092i
$633$	−4.56110	−	41.0606i	−0.181288	−	1.63201i
$634$	−5.66282	−	9.80829i	−0.224899	−	0.389537i
$635$	−0.952073	−	1.64904i	−0.0377819	−	0.0654401i
$636$	0.954073	+	8.58889i	0.0378315	+	0.340572i
$637$	−12.3982	+	21.4744i	−0.491236	+	0.850846i
$638$	−4.10742			−0.162614
$639$	−21.0648	−	22.8460i	−0.833312	−	0.903776i
$640$	−0.949474			−0.0375312
$641$	1.96253	−	3.39921i	0.0775154	−	0.134261i	−0.824662	−	0.565626i	$-0.808635\pi$
$641$	1.96253	−	3.39921i	0.0775154	−	0.134261i	0.902177	+	0.431365i	$0.141968\pi$
$642$	−13.9230	+	10.2419i	−0.549497	+	0.404215i
$643$	12.4498	+	21.5636i	0.490971	+	0.850387i	0.999946	−	0.0103943i	$-0.00330866\pi$
$643$	12.4498	+	21.5636i	0.490971	+	0.850387i	−0.508975	+	0.860781i	$0.669975\pi$
$644$	7.16281	+	12.4063i	0.282254	+	0.488879i
$645$	−14.7544	−	6.46489i	−0.580954	−	0.254555i
$646$	20.4873	−	35.4850i	0.806061	−	1.39614i
$647$	2.56819			0.100966			0.0504829	−	0.998725i	$-0.483924\pi$
$647$	2.56819			0.100966			0.0504829	+	0.998725i	$0.483924\pi$
$648$	−0.728956	+	8.97043i	−0.0286361	+	0.352392i
$649$	22.2551			0.873590
$650$	5.43631	−	9.41596i	0.213230	−	0.369324i
$651$	33.5516	+	14.7012i	1.31499	+	0.576186i
$652$	1.93527	+	3.35198i	0.0757909	+	0.131274i
$653$	−0.384437	−	0.665864i	−0.0150442	−	0.0260573i	0.858405	−	0.512972i	$-0.171456\pi$
$653$	−0.384437	−	0.665864i	−0.0150442	−	0.0260573i	−0.873449	+	0.486915i	$0.838122\pi$
$654$	−9.80644	+	7.21371i	−0.383462	+	0.282078i
$655$	−2.66182	+	4.61040i	−0.104006	+	0.180143i
$656$	−2.42733			−0.0947714
$657$	5.96162	+	6.46573i	0.232585	+	0.252252i
$658$	−6.10726			−0.238086
$659$	−4.82224	+	8.35237i	−0.187848	+	0.325362i	−0.944532	−	0.328418i	$-0.893485\pi$
$659$	−4.82224	+	8.35237i	−0.187848	+	0.325362i	0.756685	+	0.653780i	$0.226818\pi$
$660$	−0.331012	−	2.97989i	−0.0128846	−	0.115992i
$661$	1.93403	+	3.34984i	0.0752250	+	0.130294i	0.901184	−	0.433437i	$-0.142699\pi$
$661$	1.93403	+	3.34984i	0.0752250	+	0.130294i	−0.825959	+	0.563730i	$0.809366\pi$
$662$	13.3935	+	23.1983i	0.520554	+	0.901626i
$663$	−3.84710	−	34.6329i	−0.149409	−	1.34503i
$664$	−2.64545	+	4.58206i	−0.102664	+	0.177818i
$665$	−20.7413			−0.804314
$666$	2.92687	−	0.658370i	0.113414	−	0.0255113i
$667$	7.98254			0.309085
$668$	−8.64990	+	14.9821i	−0.334675	+	0.579673i
$669$	15.0023	−	11.0359i	0.580023	−	0.426671i
$670$	4.28921	+	7.42912i	0.165706	+	0.287012i
$671$	1.47000	+	2.54612i	0.0567487	+	0.0982917i
$672$	−6.41425	−	2.81051i	−0.247435	−	0.108418i
$673$	−20.1037	+	34.8206i	−0.774940	+	1.34224i	0.159888	+	0.987135i	$0.448887\pi$
$673$	−20.1037	+	34.8206i	−0.774940	+	1.34224i	−0.934828	+	0.355100i	$0.884447\pi$
$674$	−20.0579			−0.772600
$675$	20.9063	+	4.05783i	0.804683	+	0.156186i
$676$	−5.96251			−0.229327
$677$	8.73810	−	15.1348i	0.335832	−	0.581679i	−0.647812	−	0.761800i	$-0.724316\pi$
$677$	8.73810	−	15.1348i	0.335832	−	0.581679i	0.983644	+	0.180121i	$0.0576491\pi$
$678$	20.1931	+	8.84794i	0.775511	+	0.339803i
$679$	18.8625	+	32.6708i	0.723877	+	1.25379i
$680$	3.60027	+	6.23585i	0.138064	+	0.239134i
$681$	−1.63086	+	1.19967i	−0.0624945	+	0.0459716i
$682$	−4.76823	+	8.25881i	−0.182585	+	0.316246i
$683$	7.05834			0.270080			0.135040	−	0.990840i	$-0.456884\pi$
$683$	7.05834			0.270080			0.135040	+	0.990840i	$0.456884\pi$
$684$	−4.82630	+	15.4737i	−0.184538	+	0.591651i
$685$	5.80363			0.221745
$686$	4.74504	−	8.21865i	0.181167	−	0.313790i
$687$	−3.34880	−	30.1471i	−0.127765	−	1.15018i
$688$	−4.89762	−	8.48292i	−0.186720	−	0.323408i
$689$	6.61787	+	11.4625i	0.252121	+	0.436686i
$690$	0.643305	+	5.79125i	0.0244902	+	0.220469i
$691$	−9.41394	+	16.3054i	−0.358123	+	0.620287i	−0.987647	−	0.156694i	$-0.949916\pi$
$691$	−9.41394	+	16.3054i	−0.358123	+	0.620287i	0.629524	+	0.776981i	$0.283250\pi$
$692$	10.2202			0.388515
$693$	6.58450	−	21.1107i	0.250125	−	0.801929i
$694$	−16.2126			−0.615420
$695$	4.45905	−	7.72330i	0.169141	−	0.292962i
$696$	−3.14334	+	2.31227i	−0.119148	+	0.0876465i
$697$	9.20410	+	15.9420i	0.348630	+	0.603845i
$698$	8.69662	+	15.0630i	0.329172	+	0.570142i
$699$	21.6650	+	9.49289i	0.819446	+	0.359054i
$700$	−8.28546	+	14.3508i	−0.313161	+	0.542411i
$701$	35.9910			1.35936			0.679681	−	0.733507i	$-0.262118\pi$
$701$	35.9910			1.35936			0.679681	+	0.733507i	$0.262118\pi$
$702$	4.49136	+	13.0323i	0.169515	+	0.491871i
$703$	5.40297			0.203777
$704$	0.911568	−	1.57888i	0.0343560	−	0.0595064i
$705$	−2.27526	−	0.996946i	−0.0856914	−	0.0375471i
$706$	6.33891	+	10.9793i	0.238568	+	0.413212i
$707$	15.5620	+	26.9542i	0.585269	+	1.01372i
$708$	17.0315	−	12.5285i	0.640083	−	0.470851i
$709$	9.67862	−	16.7639i	0.363488	−	0.629580i	−0.625044	−	0.780589i	$-0.714919\pi$
$709$	9.67862	−	16.7639i	0.363488	−	0.629580i	0.988532	+	0.151009i	$0.0482524\pi$
$710$	9.83503			0.369102
$711$	−28.2156	+	6.34682i	−1.05817	+	0.238024i
$712$	15.0956			0.565732
$713$	9.26679	−	16.0506i	0.347044	−	0.601098i
$714$	5.86335	+	52.7839i	0.219430	+	1.97539i
$715$	−2.29605	−	3.97687i	−0.0858674	−	0.148727i
$716$	10.5810	+	18.3268i	0.395431	+	0.684906i
$717$	3.83816	+	34.5524i	0.143339	+	1.29038i
$718$	7.73580	−	13.3988i	0.288697	−	0.500039i
$719$	−0.921503			−0.0343663			−0.0171831	−	0.999852i	$-0.505470\pi$
$719$	−0.921503			−0.0343663			−0.0171831	+	0.999852i	$0.505470\pi$
$720$	−1.93085	−	2.09412i	−0.0719584	−	0.0780431i
$721$	−70.2862			−2.61760
$722$	−5.09602	+	8.82656i	−0.189654	+	0.328491i
$723$	−4.24451	+	3.12231i	−0.157855	+	0.116120i
$724$	4.88223	+	8.45628i	0.181447	+	0.314275i
$725$	4.61683	+	7.99659i	0.171465	+	0.296986i
$726$	−12.1778	−	5.33591i	−0.451961	−	0.198034i
$727$	18.8943	−	32.7260i	0.700753	−	1.21374i	−0.267450	−	0.963572i	$-0.586181\pi$
$727$	18.8943	−	32.7260i	0.700753	−	1.21374i	0.968203	−	0.250167i	$-0.0804856\pi$
$728$	−10.7258			−0.397525
$729$	−21.2672	+	16.6345i	−0.787674	+	0.616092i
$730$	−2.78344			−0.103020
$731$	−37.1421	+	64.3321i	−1.37375	+	2.37941i
$732$	2.55831	+	1.12096i	0.0945577	+	0.0414321i
$733$	−20.1869	−	34.9647i	−0.745619	−	1.29145i	−0.949905	−	0.312538i	$-0.898821\pi$
$733$	−20.1869	−	34.9647i	−0.745619	−	1.29145i	0.204286	−	0.978911i	$-0.434513\pi$
$734$	8.96186	+	15.5224i	0.330788	+	0.572942i
$735$	12.3824	−	9.10864i	0.456733	−	0.335977i
$736$	−1.77158	+	3.06847i	−0.0653014	+	0.113105i
$737$	−16.4719			−0.606750
$738$	−4.93622	−	5.35362i	−0.181705	−	0.197069i
$739$	40.9013			1.50458			0.752290	−	0.658832i	$-0.228949\pi$
$739$	40.9013			1.50458			0.752290	+	0.658832i	$0.228949\pi$
$740$	−0.474737	+	0.822268i	−0.0174517	+	0.0302272i
$741$	2.74084	+	24.6740i	0.100687	+	0.906420i
$742$	−10.0863	−	17.4699i	−0.370279	−	0.641342i
$743$	17.5906	+	30.4679i	0.645338	+	1.11776i	0.984223	+	0.176931i	$0.0566168\pi$
$743$	17.5906	+	30.4679i	0.645338	+	1.11776i	−0.338885	+	0.940828i	$0.610050\pi$
$744$	1.00025	+	9.00462i	0.0366711	+	0.330125i
$745$	2.52460	−	4.37274i	0.0924943	−	0.160205i
$746$	−20.8143			−0.762066
$747$	−15.4858	+	3.48337i	−0.566595	+	0.127450i
$748$	−13.8262			−0.505534
$749$	20.1735	−	34.9416i	0.737125	−	1.27674i
$750$	−12.0530	+	8.86630i	−0.440113	+	0.323751i
$751$	−15.7662	−	27.3078i	−0.575315	−	0.996475i	−0.996007	−	0.0892719i	$-0.971546\pi$
$751$	−15.7662	−	27.3078i	−0.575315	−	0.996475i	0.420692	−	0.907204i	$-0.361787\pi$
$752$	−0.755257	−	1.30814i	−0.0275414	−	0.0477031i
$753$	−47.7235	−	20.9109i	−1.73914	−	0.762035i
$754$	−2.98833	+	5.17594i	−0.108829	+	0.188497i
$755$	−3.87217			−0.140923
$756$	−6.84526	−	19.8624i	−0.248960	−	0.722390i
$757$	−21.9828			−0.798980			−0.399490	−	0.916738i	$-0.630813\pi$
$757$	−21.9828			−0.798980			−0.399490	+	0.916738i	$0.630813\pi$
$758$	12.2156	−	21.1580i	0.443690	−	0.768493i
$759$	−10.2479	−	4.49029i	−0.371976	−	0.162987i
$760$	−2.56499	−	4.44269i	−0.0930418	−	0.161153i
$761$	−0.361419	−	0.625996i	−0.0131014	−	0.0226924i	0.859400	−	0.511303i	$-0.170837\pi$
$761$	−0.361419	−	0.625996i	−0.0131014	−	0.0226924i	−0.872502	+	0.488611i	$0.837504\pi$
$762$	2.79808	−	2.05829i	0.101364	−	0.0745640i
$763$	14.2089	−	24.6105i	0.514397	−	0.890962i
$764$	8.02147			0.290206
$765$	−6.43201	+	20.6218i	−0.232550	+	0.745583i
$766$	17.3044			0.625235
$767$	16.1916	−	28.0447i	0.584644	−	1.01263i
$768$	−0.191224	−	1.72146i	−0.00690020	−	0.0621179i
$769$	−2.60604	−	4.51379i	−0.0939761	−	0.162771i	0.815205	−	0.579173i	$-0.196624\pi$
$769$	−2.60604	−	4.51379i	−0.0939761	−	0.162771i	−0.909181	+	0.416402i	$0.863291\pi$
$770$	3.49940	+	6.06114i	0.126110	+	0.218428i
$771$	5.74107	+	51.6831i	0.206760	+	1.86132i
$772$	−6.14776	+	10.6482i	−0.221263	+	0.383238i
$773$	−14.8217			−0.533100			−0.266550	−	0.963821i	$-0.585884\pi$
$773$	−14.8217			−0.533100			−0.266550	+	0.963821i	$0.585884\pi$
$774$	8.74977	−	28.0528i	0.314504	−	1.00834i
$775$	21.4384			0.770091
$776$	−4.66528	+	8.08051i	−0.167474	+	0.290073i
$777$	−5.64110	+	4.14965i	−0.202373	+	0.148868i
$778$	2.74544	+	4.75524i	0.0984288	+	0.170484i
$779$	−6.55740	−	11.3577i	−0.234943	−	0.406933i
$780$	−3.99591	−	1.75088i	−0.143077	−	0.0626915i
$781$	−9.44240	+	16.3547i	−0.337876	+	0.585218i
$782$	26.8704			0.960883
$783$	−11.4921	−	2.23058i	−0.410696	−	0.0797146i
$784$	9.34719			0.333828
$785$	10.6181	−	18.3910i	0.378975	−	0.656404i
$786$	−8.89507	−	3.89753i	−0.317277	−	0.139020i
$787$	−12.2172	−	21.1608i	−0.435496	−	0.754301i	0.561840	−	0.827246i	$-0.310094\pi$
$787$	−12.2172	−	21.1608i	−0.435496	−	0.754301i	−0.997336	+	0.0729448i	$0.976760\pi$
$788$	−11.6969	−	20.2596i	−0.416685	−	0.721720i
$789$	−8.16298	+	6.00476i	−0.290610	+	0.213775i
$790$	4.57656	−	7.92683i	0.162827	−	0.282024i
$791$	−51.4636			−1.82983
$792$	5.33608	−	1.20030i	0.189609	−	0.0426507i
$793$	4.27796			0.151915
$794$	−13.1772	+	22.8235i	−0.467640	+	0.809976i
$795$	−0.905867	−	8.15492i	−0.0321278	−	0.289225i
$796$	−4.50135	−	7.79657i	−0.159546	−	0.276342i
$797$	1.26071	+	2.18362i	0.0446567	+	0.0773476i	0.887490	−	0.460827i	$-0.152447\pi$
$797$	1.26071	+	2.18362i	0.0446567	+	0.0773476i	−0.842833	+	0.538175i	$0.819114\pi$
$798$	−4.17730	−	37.6055i	−0.147875	−	1.33122i
$799$	−5.72766	+	9.92059i	−0.202630	+	0.350965i
$800$	−4.09850			−0.144904
$801$	30.6984	+	33.2942i	1.08468	+	1.17639i
$802$	−30.3957			−1.07331
$803$	2.67232	−	4.62859i	0.0943041	−	0.163340i
$804$	−12.6057	+	9.27286i	−0.444568	+	0.327029i
$805$	−6.80090	−	11.7795i	−0.239700	−	0.415173i
$806$	6.93820	+	12.0173i	0.244388	+	0.423292i
$807$	−21.0185	−	9.20960i	−0.739886	−	0.324193i
$808$	−3.84896	+	6.66660i	−0.135406	+	0.234530i
$809$	−15.8013			−0.555543			−0.277771	−	0.960647i	$-0.589596\pi$
$809$	−15.8013			−0.555543			−0.277771	+	0.960647i	$0.589596\pi$
$810$	0.692125	−	8.51719i	0.0243188	−	0.299263i
$811$	−8.96155			−0.314683			−0.157341	−	0.987544i	$-0.550292\pi$
$811$	−8.96155			−0.314683			−0.157341	+	0.987544i	$0.550292\pi$
$812$	4.55450	−	7.88863i	0.159832	−	0.276837i
$813$	44.7344	+	19.6011i	1.56890	+	0.687442i
$814$	−0.911568	−	1.57888i	−0.0319505	−	0.0553398i
$815$	−1.83749	−	3.18262i	−0.0643643	−	0.111482i
$816$	−10.5809	+	7.78344i	−0.370407	+	0.272475i
$817$	26.4616	−	45.8329i	0.925776	−	1.60349i
$818$	2.75587			0.0963567
$819$	−21.8120	−	23.6564i	−0.762173	−	0.826622i
$820$	2.30469			0.0804832
$821$	23.9719	−	41.5205i	0.836625	−	1.44908i	−0.0560762	−	0.998426i	$-0.517859\pi$
$821$	23.9719	−	41.5205i	0.836625	−	1.44908i	0.892701	−	0.450650i	$-0.148808\pi$
$822$	1.16885	+	10.5224i	0.0407684	+	0.367011i
$823$	−14.5191	−	25.1477i	−0.506102	−	0.876595i	−0.999975	−	0.00706073i	$-0.997752\pi$
$823$	−14.5191	−	25.1477i	−0.506102	−	0.876595i	0.493873	−	0.869534i	$-0.335581\pi$
$824$	−8.69198	−	15.0550i	−0.302800	−	0.524464i
$825$	−1.42885	−	12.8630i	−0.0497461	−	0.447832i
$826$	−24.6776	+	42.7428i	−0.858642	+	1.48721i
$827$	21.6384			0.752442			0.376221	−	0.926530i	$-0.377223\pi$
$827$	21.6384			0.752442			0.376221	+	0.926530i	$0.377223\pi$
$828$	−10.3704	+	2.33271i	−0.360396	+	0.0810674i
$829$	47.7197			1.65737			0.828687	−	0.559712i	$-0.189088\pi$
$829$	47.7197			1.65737			0.828687	+	0.559712i	$0.189088\pi$
$830$	2.51179	−	4.35055i	0.0871855	−	0.151010i
$831$	−23.0704	+	16.9708i	−0.800304	+	0.588711i
$832$	−1.32641	−	2.29742i	−0.0459851	−	0.0796486i
$833$	−35.4432	−	61.3895i	−1.22803	−	2.12702i
$834$	14.9009	+	6.52910i	0.515978	+	0.226084i
$835$	8.21285	−	14.2251i	0.284217	−	0.492279i
$836$	9.85034			0.340681
$837$	−17.8261	+	20.5179i	−0.616160	+	0.709202i
$838$	−27.7422			−0.958338
$839$	12.2369	−	21.1950i	0.422466	−	0.731733i	−0.573714	−	0.819056i	$-0.694498\pi$
$839$	12.2369	−	21.1950i	0.422466	−	0.731733i	0.996180	+	0.0873229i	$0.0278312\pi$
$840$	6.09016	+	2.66851i	0.210130	+	0.0920722i
$841$	11.9621	+	20.7190i	0.412487	+	0.714449i
$842$	9.45571	+	16.3778i	0.325865	+	0.564415i
$843$	−28.6888	+	21.1037i	−0.988094	+	0.726851i
$844$	−11.9261	+	20.6566i	−0.410513	+	0.711029i
$845$	5.66124			0.194753
$846$	1.34929	−	4.32600i	0.0463897	−	0.148731i
$847$	31.0360			1.06641
$848$	2.49465	−	4.32086i	0.0856666	−	0.148379i
$849$	5.48778	+	49.4029i	0.188340	+	1.69550i
$850$	15.5409	+	26.9177i	0.533050	+	0.923269i
$851$	1.77158	+	3.06847i	0.0607291	+	0.105186i
$852$	1.98078	+	17.8316i	0.0678602	+	0.610901i
$853$	16.6106	−	28.7703i	0.568735	−	0.985078i	−0.427957	−	0.903799i	$-0.640766\pi$
$853$	16.6106	−	28.7703i	0.568735	−	0.985078i	0.996691	−	0.0812783i	$-0.0259002\pi$
$854$	−6.52003			−0.223111
$855$	4.58244	−	14.6919i	0.156716	−	0.502451i
$856$	9.97908			0.341078
$857$	−13.0500	+	22.6033i	−0.445780	+	0.772113i	−0.998106	−	0.0615145i	$-0.980407\pi$
$857$	−13.0500	+	22.6033i	−0.445780	+	0.772113i	0.552326	+	0.833628i	$0.313740\pi$
$858$	6.74793	−	4.96384i	0.230370	−	0.169463i
$859$	5.40200	+	9.35653i	0.184314	+	0.319241i	0.943345	−	0.331813i	$-0.107660\pi$
$859$	5.40200	+	9.35653i	0.184314	+	0.319241i	−0.759031	+	0.651054i	$0.774327\pi$
$860$	4.65016	+	8.05431i	0.158569	+	0.274650i
$861$	15.5695	+	6.82205i	0.530608	+	0.232495i
$862$	19.0074	−	32.9218i	0.647395	−	1.12132i
$863$	53.9732			1.83727			0.918634	−	0.395110i	$-0.129294\pi$
$863$	53.9732			1.83727			0.918634	+	0.395110i	$0.129294\pi$
$864$	3.40791	−	3.92252i	0.115939	−	0.133447i
$865$	−9.70383			−0.329940
$866$	18.2202	−	31.5584i	0.619149	−	1.07240i
$867$	64.2711	+	28.1615i	2.18276	+	0.956414i
$868$	−10.5745	−	18.3156i	−0.358922	−	0.621670i
$869$	8.78770	+	15.2207i	0.298102	+	0.516329i
$870$	2.98452	−	2.19544i	0.101185	−	0.0744324i
$871$	−11.9840	+	20.7570i	−0.406064	+	0.703323i
$872$	7.02860			0.238019
$873$	−27.3093	+	6.14296i	−0.924280	+	0.207908i
$874$	−19.1436			−0.647542
$875$	17.4640	−	30.2486i	0.590392	−	1.02259i
$876$	−0.560585	−	5.04657i	−0.0189404	−	0.170508i
$877$	18.4206	+	31.9054i	0.622018	+	1.07737i	0.989109	+	0.147182i	$0.0470204\pi$
$877$	18.4206	+	31.9054i	0.622018	+	1.07737i	−0.367091	+	0.930185i	$0.619646\pi$
$878$	−10.6640	−	18.4705i	−0.359891	−	0.623349i
$879$	2.37953	+	21.4214i	0.0802597	+	0.722525i
$880$	−0.865510	+	1.49911i	−0.0291763	+	0.0505349i
$881$	−9.98724			−0.336479			−0.168239	−	0.985746i	$-0.553808\pi$
$881$	−9.98724			−0.336479			−0.168239	+	0.985746i	$0.553808\pi$
$882$	19.0084	+	20.6158i	0.640047	+	0.694169i
$883$	14.4722			0.487029			0.243514	−	0.969897i	$-0.421700\pi$
$883$	14.4722			0.487029			0.243514	+	0.969897i	$0.421700\pi$
$884$	−10.0591	+	17.4230i	−0.338326	+	0.585997i
$885$	−16.1710	+	11.8955i	−0.543581	+	0.399863i
$886$	−4.05738	−	7.02759i	−0.136310	−	0.236097i
$887$	−25.9870	−	45.0109i	−0.872559	−	1.51132i	−0.859340	−	0.511405i	$-0.829125\pi$
$887$	−25.9870	−	45.0109i	−0.872559	−	1.51132i	−0.0132195	−	0.999913i	$-0.504208\pi$
$888$	−1.58644	−	0.695127i	−0.0532375	−	0.0233269i
$889$	−4.05423	+	7.02214i	−0.135975	+	0.235515i
$890$	−14.3329			−0.480440
$891$	13.4988	+	9.32810i	0.452226	+	0.312503i
$892$	−10.7527			−0.360026
$893$	4.08063	−	7.06786i	0.136553	−	0.236517i
$894$	8.43654	+	3.69661i	0.282160	+	0.123633i
$895$	−10.0464	−	17.4008i	−0.335814	−	0.581646i
$896$	2.02158	+	3.50148i	0.0675363	+	0.116976i
$897$	−13.1142	+	9.64696i	−0.437872	+	0.322103i
$898$	5.53851	−	9.59298i	0.184822	−	0.320122i
$899$	−11.7847			−0.393041
$900$	−8.33470	−	9.03947i	−0.277823	−	0.301316i
$901$	−37.8374			−1.26055
$902$	−2.21268	+	3.83247i	−0.0736742	+	0.127607i
$903$	7.57318	+	68.1764i	0.252020	+	2.26877i
$904$	−6.36427	−	11.0232i	−0.211672	−	0.366627i
$905$	−4.63555	−	8.02901i	−0.154091	−	0.266893i
$906$	−0.779855	−	7.02052i	−0.0259089	−	0.233241i
$907$	−18.4855	+	32.0178i	−0.613801	+	1.06313i	0.376793	+	0.926298i	$0.377027\pi$
$907$	−18.4855	+	32.0178i	−0.613801	+	1.06313i	−0.990594	+	0.136837i	$0.956306\pi$
$908$	1.16889			0.0387910
$909$	−22.5308	+	5.06808i	−0.747299	+	0.168098i
$910$	10.1839			0.337592
$911$	−2.90459	+	5.03090i	−0.0962335	+	0.166681i	−0.910123	−	0.414339i	$-0.864013\pi$
$911$	−2.90459	+	5.03090i	−0.0962335	+	0.166681i	0.813889	+	0.581020i	$0.197346\pi$
$912$	7.53832	−	5.54526i	0.249619	−	0.183622i
$913$	4.82302	+	8.35372i	0.159619	+	0.276468i
$914$	−9.24353	−	16.0103i	−0.305749	−	0.529573i
$915$	−2.42904	−	1.06433i	−0.0803017	−	0.0351855i
$916$	−8.75623	+	15.1662i	−0.289314	+	0.501107i
$917$	22.6698			0.748621
$918$	−38.6842	−	7.50847i	−1.27677	−	0.247816i
$919$	−44.1079			−1.45499			−0.727493	−	0.686115i	$-0.759315\pi$
$919$	−44.1079			−1.45499			−0.727493	+	0.686115i	$0.759315\pi$
$920$	1.68207	−	2.91343i	0.0554563	−	0.0960531i
$921$	1.50005	+	0.657274i	0.0494285	+	0.0216579i
$922$	−6.80618	−	11.7887i	−0.224150	−	0.388239i
$923$	13.7395	+	23.7976i	0.452242	+	0.783307i
$924$	−10.2845	+	7.56537i	−0.338335	+	0.248883i
$925$	−2.04925	+	3.54941i	−0.0673789	+	0.116704i
$926$	−7.87343			−0.258737
$927$	15.5285	−	49.7864i	0.510024	−	1.63520i
$928$	2.25294			0.0739563
$929$	7.01272	−	12.1464i	0.230080	−	0.398510i	−0.727752	−	0.685841i	$-0.759435\pi$
$929$	7.01272	−	12.1464i	0.230080	−	0.398510i	0.957831	+	0.287331i	$0.0927680\pi$
$930$	−0.949714	−	8.54965i	−0.0311423	−	0.280354i
$931$	25.2513	+	43.7365i	0.827577	+	1.43341i
$932$	−6.82817	−	11.8267i	−0.223664	−	0.387398i
$933$	0.0675876	+	0.608446i	0.00221272	+	0.0199196i
$934$	−3.71317	+	6.43140i	−0.121499	+	0.210442i
$935$	13.1276			0.429317
$936$	2.36969	−	7.59750i	0.0774557	−	0.248332i
$937$	−26.5435			−0.867138			−0.433569	−	0.901120i	$-0.642746\pi$
$937$	−26.5435			−0.867138			−0.433569	+	0.901120i	$0.642746\pi$
$938$	18.2648	−	31.6356i	0.596368	−	1.03294i
$939$	−18.4975	+	13.6070i	−0.603645	+	0.444047i
$940$	0.717097	+	1.24205i	0.0233891	+	0.0405111i
$941$	−7.70823	−	13.3510i	−0.251281	−	0.435231i	0.712598	−	0.701573i	$-0.247518\pi$
$941$	−7.70823	−	13.3510i	−0.251281	−	0.435231i	−0.963879	+	0.266341i	$0.914185\pi$
$942$	35.4827	+	15.5474i	1.15609	+	0.506560i
$943$	4.30022	−	7.44820i	0.140035	−	0.242547i
$944$	−12.2070			−0.397305
$945$	6.49940	+	18.8589i	0.211425	+	0.613479i
$946$	−17.8580			−0.580615
$947$	6.27960	−	10.8766i	0.204060	−	0.353442i	−0.745773	−	0.666200i	$-0.767920\pi$
$947$	6.27960	−	10.8766i	0.204060	−	0.353442i	0.949833	+	0.312758i	$0.101253\pi$
$948$	15.2936	+	6.70116i	0.496714	+	0.217644i
$949$	−3.88846	−	6.73502i	−0.126225	−	0.218628i
$950$	−11.0720	−	19.1773i	−0.359224	−	0.622194i
$951$	−15.8017	+	11.6239i	−0.512406	+	0.376931i
$952$	15.3311	−	26.5543i	0.496884	−	0.860629i
$953$	41.9349			1.35841			0.679203	−	0.733951i	$-0.262326\pi$
$953$	41.9349			1.35841			0.679203	+	0.733951i	$0.262326\pi$
$954$	14.6030	−	3.28480i	0.472790	−	0.106349i
$955$	−7.61617			−0.246453
$956$	10.0358	−	17.3825i	0.324580	−	0.562189i
$957$	0.785436	+	7.07076i	0.0253895	+	0.228565i
$958$	12.2682	+	21.2491i	0.396366	+	0.686526i
$959$	−12.3569	−	21.4027i	−0.399024	−	0.691130i
$960$	0.181562	+	1.63448i	0.00585989	+	0.0527527i
$961$	1.81939	−	3.15127i	0.0586899	−	0.101654i
$962$	−2.65283			−0.0855306
$963$	20.2934	+	22.0094i	0.653947	+	0.709244i
$964$	3.04219			0.0979822
$965$	5.83713	−	10.1102i	0.187904	−	0.325459i
$966$	19.9874	−	14.7029i	0.643083	−	0.473058i
$967$	−3.66991	−	6.35647i	−0.118016	−	0.204410i	0.800965	−	0.598711i	$-0.204320\pi$
$967$	−3.66991	−	6.35647i	−0.118016	−	0.204410i	−0.918981	+	0.394301i	$0.870987\pi$
$968$	3.83809	+	6.64776i	0.123361	+	0.213667i
$969$	−65.0038	−	28.4825i	−2.08822	−	0.914990i
$970$	4.42956	−	7.67223i	0.142225	−	0.246340i
$971$	9.43859			0.302899			0.151449	−	0.988465i	$-0.451606\pi$
$971$	9.43859			0.302899			0.151449	+	0.988465i	$0.451606\pi$
$972$	15.5817	−	0.460490i	0.499782	−	0.0147702i
$973$	−37.9762			−1.21746
$974$	−11.3794	+	19.7097i	−0.364619	+	0.631539i
$975$	−17.2488	−	7.55784i	−0.552403	−	0.242045i
$976$	−0.806303	−	1.39656i	−0.0258091	−	0.0447027i
$977$	−21.6465	−	37.4929i	−0.692533	−	1.19950i	−0.971005	−	0.239059i	$-0.923161\pi$
$977$	−21.6465	−	37.4929i	−0.692533	−	1.19950i	0.278472	−	0.960444i	$-0.410172\pi$
$978$	5.40024	−	3.97247i	0.172681	−	0.127026i
$979$	13.7607	−	23.8342i	0.439794	−	0.761745i
$980$	−8.87491			−0.283499
$981$	14.2934	+	15.5020i	0.456352	+	0.494940i
$982$	34.1327			1.08922
$983$	−23.1891	+	40.1647i	−0.739617	+	1.28105i	0.213051	+	0.977041i	$0.431660\pi$
$983$	−23.1891	+	40.1647i	−0.739617	+	1.28105i	−0.952668	+	0.304013i	$0.901673\pi$
$984$	0.464164	+	4.17856i	0.0147970	+	0.133208i
$985$	11.1059	+	19.2360i	0.353864	+	0.612910i
$986$	−8.54282	−	14.7966i	−0.272059	−	0.471220i
$987$	1.16785	+	10.5134i	0.0371732	+	0.334646i
$988$	7.16657	−	12.4129i	0.227999	−	0.394906i
$989$	34.7061			1.10359
$990$	−5.06647	+	1.13965i	−0.161023	+	0.0362205i
$991$	56.1550			1.78382			0.891911	−	0.452211i	$-0.149365\pi$
$991$	56.1550			1.78382			0.891911	+	0.452211i	$0.149365\pi$
$992$	2.61540	−	4.53000i	0.0830390	−	0.143828i
$993$	37.3738	−	27.4925i	1.18602	−	0.872448i
$994$	−20.9404	−	36.2698i	−0.664189	−	1.15041i
$995$	4.27392	+	7.40264i	0.135492	+	0.234679i
$996$	8.39372	+	3.67785i	0.265965	+	0.116537i
$997$	−19.5934	+	33.9367i	−0.620529	+	1.07479i	0.368859	+	0.929486i	$0.379749\pi$
$997$	−19.5934	+	33.9367i	−0.620529	+	1.07479i	−0.989387	+	0.145302i	$0.953585\pi$
$998$	40.5029			1.28210
$999$	−1.69305	−	4.91260i	−0.0535656	−	0.155428i

Display

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.e.e.223.9	✓	20
3.2	odd	2		1998.2.e.e.667.4		20
9.2	odd	6		5994.2.a.ba.1.7		10
9.4	even	3	inner	666.2.e.e.445.9	yes	20
9.5	odd	6		1998.2.e.e.1333.4		20
9.7	even	3		5994.2.a.bb.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.e.e.223.9	✓	20	1.1	even	1	trivial
666.2.e.e.445.9	yes	20	9.4	even	3	inner
1998.2.e.e.667.4		20	3.2	odd	2
1998.2.e.e.1333.4		20	9.5	odd	6
5994.2.a.ba.1.7		10	9.2	odd	6
5994.2.a.bb.1.4		10	9.7	even	3

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	666.2.e.e.223.9

Level	$666$
Weight	$2$
Character	666.223
Analytic conductor	$5.318$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$