LMFDB - Embedded newform 950.2.u.e.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.2
Character	$\chi$	$=$	950.199
Dual form			950.2.u.e.549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.07851 + 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.28531 - 1.07851i) q^{6} +(-2.14383 - 1.23774i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(1.07851 + 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.28531 - 1.07851i) q^{6} +(-2.14383 - 1.23774i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +(-1.45059 - 2.51250i) q^{11} +(1.45307 + 0.838929i) q^{12} +(-0.833484 + 0.993308i) q^{13} +(2.32619 + 0.846665i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.22411 - 0.215843i) q^{17} +0.184793i q^{18} +(4.22186 - 1.08440i) q^{19} +(-0.721249 - 4.09041i) q^{21} +(1.86485 + 2.22244i) q^{22} +(-0.750979 - 2.06330i) q^{23} +(-1.57667 - 0.573861i) q^{24} +(0.648336 - 1.12295i) q^{26} +(4.62772 - 2.67181i) q^{27} +(-2.43788 - 0.429863i) q^{28} +(1.12586 - 6.38509i) q^{29} +(3.04442 - 5.27310i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(1.66488 - 4.57422i) q^{33} +(-1.16803 + 0.425128i) q^{34} +(-0.0320889 - 0.181985i) q^{36} -1.44520i q^{37} +(-3.96942 + 1.80104i) q^{38} -2.17563 q^{39} +(1.82601 - 1.53221i) q^{41} +(1.42058 + 3.90302i) q^{42} +(-3.14685 + 8.64591i) q^{43} +(-2.22244 - 1.86485i) q^{44} +(1.09786 + 1.90155i) q^{46} +(10.9588 + 1.93233i) q^{47} +(1.65237 + 0.291357i) q^{48} +(-0.435991 - 0.755158i) q^{49} +(1.59763 + 1.34057i) q^{51} +(-0.443488 + 1.21847i) q^{52} +(-4.11677 - 11.3107i) q^{53} +(-4.09346 + 3.43482i) q^{54} +2.47548 q^{56} +(5.94709 + 4.25688i) q^{57} +6.48359i q^{58} +(0.351292 + 1.99228i) q^{59} +(1.25853 - 0.458067i) q^{61} +(-2.08251 + 5.72164i) q^{62} +(-0.294044 + 0.350428i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.845282 + 4.79383i) q^{66} +(-3.31520 - 0.584560i) q^{67} +(1.07646 - 0.621495i) q^{68} +(1.84205 - 3.19052i) q^{69} +(-14.2805 - 5.19768i) q^{71} +(0.0632028 + 0.173648i) q^{72} +(0.360357 + 0.429457i) q^{73} +(0.250956 + 1.42324i) q^{74} +(3.59636 - 2.46296i) q^{76} +7.18185i q^{77} +(2.14258 - 0.377794i) q^{78} +(-4.96611 + 4.16706i) q^{79} +(7.90420 + 2.87689i) q^{81} +(-1.53221 + 1.82601i) q^{82} +(7.32198 + 4.22735i) q^{83} +(-2.07675 - 3.59705i) q^{84} +(1.59770 - 9.06100i) q^{86} +(9.42109 - 5.43927i) q^{87} +(2.51250 + 1.45059i) q^{88} +(9.11595 + 7.64919i) q^{89} +(3.01631 - 1.09785i) q^{91} +(-1.41138 - 1.68202i) q^{92} +(10.0610 - 1.77403i) q^{93} -11.1279 q^{94} -1.67786 q^{96} +(-2.66454 + 0.469830i) q^{97} +(0.560499 + 0.667976i) q^{98} +(-0.503786 + 0.183363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 36 q^{9}+O(q^{10}) $ 24 * q - 36 * q^9	$ 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) $ 24 * q - 36 * q^9 + 12 * q^11 + 24 * q^21 + 12 * q^29 + 12 * q^31 + 36 * q^36 + 72 * q^39 - 12 * q^41 - 12 * q^44 - 24 * q^46 + 36 * q^49 + 24 * q^56 + 48 * q^59 - 60 * q^61 + 12 * q^64 + 48 * q^66 - 12 * q^69 - 84 * q^71 - 12 * q^74 + 36 * q^76 - 120 * q^79 + 36 * q^81 + 48 * q^84 - 72 * q^86 + 24 * q^89 + 48 * q^91 - 120 * q^94 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	1.07851	+	1.28531i	0.622676	+	0.742076i	0.981528	−	0.191318i	$-0.0612762\pi$
$3$	1.07851	+	1.28531i	0.622676	+	0.742076i	−0.358852	+	0.933394i	$0.616832\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−1.28531	−	1.07851i	−0.524727	−	0.440298i
$7$	−2.14383	−	1.23774i	−0.810292	−	0.467822i	0.0367651	−	0.999324i	$-0.488295\pi$
$7$	−2.14383	−	1.23774i	−0.810292	−	0.467822i	−0.847057	+	0.531502i	$0.821628\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	0.0320889	−	0.181985i	0.0106963	−	0.0606617i
$10$		0			0
$11$	−1.45059	−	2.51250i	−0.437371	−	0.757548i	0.560115	−	0.828415i	$-0.310757\pi$
$11$	−1.45059	−	2.51250i	−0.437371	−	0.757548i	−0.997486	+	0.0708665i	$0.977424\pi$
$12$	1.45307	+	0.838929i	0.419465	+	0.242178i
$13$	−0.833484	+	0.993308i	−0.231167	+	0.275494i	−0.869142	−	0.494563i	$-0.835328\pi$
$13$	−0.833484	+	0.993308i	−0.231167	+	0.275494i	0.637975	+	0.770057i	$0.279772\pi$
$14$	2.32619	+	0.846665i	0.621701	+	0.226281i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.22411	−	0.215843i	0.296889	−	0.0523496i	−0.0232194	−	0.999730i	$-0.507392\pi$
$17$	1.22411	−	0.215843i	0.296889	−	0.0523496i	0.320109	+	0.947381i	$0.396281\pi$
$18$			0.184793i			0.0435560i
$19$	4.22186	−	1.08440i	0.968561	−	0.248777i
$19$	4.22186	−	1.08440i	0.968561	−	0.248777i
$20$		0			0
$21$	−0.721249	−	4.09041i	−0.157390	−	0.892600i
$22$	1.86485	+	2.22244i	0.397587	+	0.473826i
$23$	−0.750979	−	2.06330i	−0.156590	−	0.430227i	0.836445	−	0.548052i	$-0.184630\pi$
$23$	−0.750979	−	2.06330i	−0.156590	−	0.430227i	−0.993034	+	0.117824i	$0.962408\pi$
$24$	−1.57667	−	0.573861i	−0.321837	−	0.117139i
$25$		0			0
$26$	0.648336	−	1.12295i	0.127149	−	0.220229i
$27$	4.62772	−	2.67181i	0.890605	−	0.514191i
$28$	−2.43788	−	0.429863i	−0.460715	−	0.0812365i
$29$	1.12586	−	6.38509i	0.209068	−	1.18568i	−0.681842	−	0.731500i	$-0.738821\pi$
$29$	1.12586	−	6.38509i	0.209068	−	1.18568i	0.890909	−	0.454181i	$-0.150068\pi$
$30$		0			0
$31$	3.04442	−	5.27310i	0.546795	−	0.947076i	−0.451697	−	0.892171i	$-0.649181\pi$
$31$	3.04442	−	5.27310i	0.546795	−	0.947076i	0.998492	−	0.0549047i	$-0.0174855\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	1.66488	−	4.57422i	0.289818	−	0.796270i
$34$	−1.16803	+	0.425128i	−0.200315	+	0.0729088i
$35$		0			0
$36$	−0.0320889	−	0.181985i	−0.00534815	−	0.0303309i
$37$		−	1.44520i		−	0.237589i	−0.992919	−	0.118794i	$-0.962097\pi$
$37$		−	1.44520i		−	0.237589i	0.992919	−	0.118794i	$-0.0379029\pi$
$38$	−3.96942	+	1.80104i	−0.643924	+	0.292167i
$39$	−2.17563			−0.348380
$40$		0			0
$41$	1.82601	−	1.53221i	0.285175	−	0.239290i	−0.488967	−	0.872302i	$-0.662626\pi$
$41$	1.82601	−	1.53221i	0.285175	−	0.239290i	0.774142	+	0.633012i	$0.218182\pi$
$42$	1.42058	+	3.90302i	0.219201	+	0.602249i
$43$	−3.14685	+	8.64591i	−0.479891	+	1.31849i	0.429696	+	0.902974i	$0.358621\pi$
$43$	−3.14685	+	8.64591i	−0.479891	+	1.31849i	−0.909586	+	0.415515i	$0.863601\pi$
$44$	−2.22244	−	1.86485i	−0.335045	−	0.281136i
$45$		0			0
$46$	1.09786	+	1.90155i	0.161870	+	0.280368i
$47$	10.9588	+	1.93233i	1.59851	+	0.281860i	0.900705	−	0.434431i	$-0.143050\pi$
$47$	10.9588	+	1.93233i	1.59851	+	0.281860i	0.697802	+	0.716291i	$0.254162\pi$
$48$	1.65237	+	0.291357i	0.238499	+	0.0420538i
$49$	−0.435991	−	0.755158i	−0.0622844	−	0.107880i
$50$		0			0
$51$	1.59763	+	1.34057i	0.223713	+	0.187718i
$52$	−0.443488	+	1.21847i	−0.0615007	+	0.168972i
$53$	−4.11677	−	11.3107i	−0.565482	−	1.55365i	−0.811481	−	0.584379i	$-0.801338\pi$
$53$	−4.11677	−	11.3107i	−0.565482	−	1.55365i	0.245999	−	0.969270i	$-0.420884\pi$
$54$	−4.09346	+	3.43482i	−0.557049	+	0.467420i
$55$		0			0
$56$	2.47548			0.330800
$57$	5.94709	+	4.25688i	0.787711	+	0.563838i
$58$			6.48359i			0.851337i
$59$	0.351292	+	1.99228i	0.0457343	+	0.259372i	0.999099	−	0.0424499i	$-0.0135163\pi$
$59$	0.351292	+	1.99228i	0.0457343	+	0.259372i	−0.953364	+	0.301822i	$0.902405\pi$
$60$		0			0
$61$	1.25853	−	0.458067i	0.161138	−	0.0586494i	−0.260192	−	0.965557i	$-0.583786\pi$
$61$	1.25853	−	0.458067i	0.161138	−	0.0586494i	0.421330	+	0.906908i	$0.361564\pi$
$62$	−2.08251	+	5.72164i	−0.264479	+	0.726650i
$63$	−0.294044	+	0.350428i	−0.0370460	+	0.0441497i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−0.845282	+	4.79383i	−0.104047	+	0.590080i
$67$	−3.31520	−	0.584560i	−0.405016	−	0.0714153i	−0.0325710	−	0.999469i	$-0.510370\pi$
$67$	−3.31520	−	0.584560i	−0.405016	−	0.0714153i	−0.372445	+	0.928054i	$0.621481\pi$
$68$	1.07646	−	0.621495i	0.130540	−	0.0753673i
$69$	1.84205	−	3.19052i	0.221757	−	0.384094i
$70$		0			0
$71$	−14.2805	−	5.19768i	−1.69478	−	0.616851i	−0.699569	−	0.714565i	$-0.746625\pi$
$71$	−14.2805	−	5.19768i	−1.69478	−	0.616851i	−0.995215	+	0.0977142i	$0.968847\pi$
$72$	0.0632028	+	0.173648i	0.00744852	+	0.0204646i
$73$	0.360357	+	0.429457i	0.0421766	+	0.0502641i	0.786720	−	0.617310i	$-0.211777\pi$
$73$	0.360357	+	0.429457i	0.0421766	+	0.0502641i	−0.744544	+	0.667574i	$0.767333\pi$
$74$	0.250956	+	1.42324i	0.0291730	+	0.165448i
$75$		0			0
$76$	3.59636	−	2.46296i	0.412531	−	0.282521i
$77$			7.18185i			0.818447i
$78$	2.14258	−	0.377794i	0.242599	−	0.0427768i
$79$	−4.96611	+	4.16706i	−0.558731	+	0.468831i	−0.877885	−	0.478872i	$-0.841046\pi$
$79$	−4.96611	+	4.16706i	−0.558731	+	0.468831i	0.319154	+	0.947703i	$0.396601\pi$
$80$		0			0
$81$	7.90420	+	2.87689i	0.878244	+	0.319655i
$82$	−1.53221	+	1.82601i	−0.169204	+	0.201649i
$83$	7.32198	+	4.22735i	0.803692	+	0.464012i	0.844760	−	0.535145i	$-0.179743\pi$
$83$	7.32198	+	4.22735i	0.803692	+	0.464012i	−0.0410686	+	0.999156i	$0.513076\pi$
$84$	−2.07675	−	3.59705i	−0.226593	−	0.392470i
$85$		0			0
$86$	1.59770	−	9.06100i	0.172284	−	0.977073i
$87$	9.42109	−	5.43927i	1.01005	−	0.583151i
$88$	2.51250	+	1.45059i	0.267834	+	0.154634i
$89$	9.11595	+	7.64919i	0.966289	+	0.810812i	0.981965	−	0.189065i	$-0.0605456\pi$
$89$	9.11595	+	7.64919i	0.966289	+	0.810812i	−0.0156760	+	0.999877i	$0.504990\pi$
$90$		0			0
$91$	3.01631	−	1.09785i	0.316195	−	0.115086i
$92$	−1.41138	−	1.68202i	−0.147146	−	0.175362i
$93$	10.0610	−	1.77403i	1.04328	−	0.183958i
$94$	−11.1279			−1.14775
$95$		0			0
$96$	−1.67786			−0.171246
$97$	−2.66454	+	0.469830i	−0.270543	+	0.0477040i	−0.307274	−	0.951621i	$-0.599417\pi$
$97$	−2.66454	+	0.469830i	−0.270543	+	0.0477040i	0.0367308	+	0.999325i	$0.488306\pi$
$98$	0.560499	+	0.667976i	0.0566189	+	0.0674758i
$99$	−0.503786	+	0.183363i	−0.0506324	+	0.0184287i
$100$		0			0
$101$	0.0902852	+	0.0757583i	0.00898372	+	0.00753823i	0.647268	−	0.762262i	$-0.275911\pi$
$101$	0.0902852	+	0.0757583i	0.00898372	+	0.00753823i	−0.638285	+	0.769800i	$0.720356\pi$
$102$	−1.80615	−	1.04278i	−0.178835	−	0.103251i
$103$	1.50808	−	0.870691i	0.148596	−	0.0857918i	−0.423859	−	0.905728i	$-0.639325\pi$
$103$	1.50808	−	0.870691i	0.148596	−	0.0857918i	0.572454	+	0.819937i	$0.305991\pi$
$104$	0.225165	−	1.27697i	0.0220792	−	0.125217i
$105$		0			0
$106$	6.01832	+	10.4240i	0.584551	+	1.01247i
$107$	−14.4681	−	8.35318i	−1.39869	−	0.807533i	−0.404432	−	0.914568i	$-0.632531\pi$
$107$	−14.4681	−	8.35318i	−1.39869	−	0.807533i	−0.994255	+	0.107035i	$0.965864\pi$
$108$	3.43482	−	4.09346i	0.330516	−	0.393893i
$109$	19.0267	+	6.92515i	1.82243	+	0.663309i	0.994778	+	0.102063i	$0.0325442\pi$
$109$	19.0267	+	6.92515i	1.82243	+	0.663309i	0.827649	+	0.561246i	$0.189678\pi$
$110$		0			0
$111$	1.85753	−	1.55865i	0.176309	−	0.147941i
$112$	−2.43788	+	0.429863i	−0.230358	+	0.0406183i
$113$		−	16.5448i		−	1.55641i	−0.628012	−	0.778204i	$-0.716131\pi$
$113$		−	16.5448i		−	1.55641i	0.628012	−	0.778204i	$-0.283869\pi$
$114$	−6.59594	−	3.15951i	−0.617766	−	0.295915i
$115$		0			0
$116$	−1.12586	−	6.38509i	−0.104534	−	0.592840i
$117$	0.154022	+	0.183556i	0.0142393	+	0.0169697i
$118$	−0.691910	−	1.90101i	−0.0636955	−	0.175002i
$119$	−2.89144	−	1.05240i	−0.265057	−	0.0964730i
$120$		0			0
$121$	1.29155	−	2.23703i	0.117414	−	0.203366i
$122$	−1.15987	+	0.669649i	−0.105009	+	0.0606272i
$123$	3.93873	+	0.694505i	0.355143	+	0.0626214i
$124$	1.05732	−	5.99634i	0.0949499	−	0.538488i
$125$		0			0
$126$	0.228725	−	0.396164i	0.0203765	−	0.0352931i
$127$	0.0842392	−	0.100392i	0.00747502	−	0.00890838i	−0.762294	−	0.647231i	$-0.775927\pi$
$127$	0.0842392	−	0.100392i	0.00747502	−	0.00890838i	0.769769	+	0.638323i	$0.220371\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−14.5066	+	5.27997i	−1.27724	+	0.464876i
$130$		0			0
$131$	2.22302	+	12.6074i	0.194226	+	1.10151i	0.913516	+	0.406802i	$0.133356\pi$
$131$	2.22302	+	12.6074i	0.194226	+	1.10151i	−0.719290	+	0.694710i	$0.755533\pi$
$132$		−	4.86778i		−	0.423686i
$133$	−10.3932	−	2.90081i	−0.901201	−	0.251532i
$134$	3.36634			0.290808
$135$		0			0
$136$	−0.952186	+	0.798979i	−0.0816492	+	0.0685119i
$137$	−5.34535	−	14.6862i	−0.456684	−	1.25473i	−0.927939	−	0.372732i	$-0.878421\pi$
$137$	−5.34535	−	14.6862i	−0.456684	−	1.25473i	0.471255	−	0.881997i	$-0.343801\pi$
$138$	−1.26004	+	3.46192i	−0.107261	+	0.294698i
$139$	8.79431	+	7.37930i	0.745924	+	0.625904i	0.934421	−	0.356169i	$-0.115917\pi$
$139$	8.79431	+	7.37930i	0.745924	+	0.625904i	−0.188498	+	0.982074i	$0.560362\pi$
$140$		0			0
$141$	9.33549	+	16.1695i	0.786190	+	1.36172i
$142$	14.9661	+	2.63893i	1.25593	+	0.221454i
$143$	3.70474	+	0.653245i	0.309806	+	0.0546271i
$144$	−0.0923963	−	0.160035i	−0.00769969	−	0.0133363i
$145$		0			0
$146$	−0.429457	−	0.360357i	−0.0355421	−	0.0298233i
$147$	0.500396	−	1.37483i	0.0412720	−	0.113394i
$148$	−0.494286	−	1.35804i	−0.0406301	−	0.111630i
$149$	11.6068	−	9.73926i	0.950866	−	0.797871i	−0.0285771	−	0.999592i	$-0.509098\pi$
$149$	11.6068	−	9.73926i	0.950866	−	0.797871i	0.979443	+	0.201720i	$0.0646532\pi$
$150$		0			0
$151$	−5.78759			−0.470988			−0.235494	−	0.971876i	$-0.575671\pi$
$151$	−5.78759			−0.470988			−0.235494	+	0.971876i	$0.575671\pi$
$152$	−3.11404	+	3.05004i	−0.252582	+	0.247391i
$153$		−	0.229695i		−	0.0185698i
$154$	−1.24711	−	7.07274i	−0.100495	−	0.569937i
$155$		0			0
$156$	−2.04442	+	0.744109i	−0.163685	+	0.0595764i
$157$	3.76870	−	10.3544i	0.300775	−	0.826372i	−0.693591	−	0.720369i	$-0.743972\pi$
$157$	3.76870	−	10.3544i	0.300775	−	0.826372i	0.994366	−	0.106003i	$-0.0338054\pi$
$158$	4.16706	−	4.96611i	0.331514	−	0.395082i
$159$	10.0979	−	17.4900i	0.800814	−	1.38705i
$160$		0			0
$161$	−0.943857	+	5.35288i	−0.0743864	+	0.421866i
$162$	−8.28368	−	1.46064i	−0.650828	−	0.114758i
$163$	−19.2078	+	11.0896i	−1.50447	+	0.868605i	−0.504481	+	0.863423i	$0.668316\pi$
$163$	−19.2078	+	11.0896i	−1.50447	+	0.868605i	−0.999987	+	0.00518168i	$0.998351\pi$
$164$	1.19184	−	2.06434i	0.0930675	−	0.161198i
$165$		0			0
$166$	−7.94481	−	2.89168i	−0.616637	−	0.224438i
$167$	−5.94713	−	16.3396i	−0.460203	−	1.26440i	−0.925333	−	0.379155i	$-0.876215\pi$
$167$	−5.94713	−	16.3396i	−0.460203	−	1.26440i	0.465130	−	0.885242i	$-0.346007\pi$
$168$	2.66982	+	3.18177i	0.205981	+	0.245479i
$169$	1.96546	+	11.1467i	0.151189	+	0.857438i
$170$		0			0
$171$	−0.0618692	−	0.803112i	−0.00473125	−	0.0614155i
$172$			9.20078i			0.701553i
$173$	−2.11553	+	0.373025i	−0.160841	+	0.0283606i	−0.253489	−	0.967338i	$-0.581578\pi$
$173$	−2.11553	+	0.373025i	−0.160841	+	0.0283606i	0.0926478	+	0.995699i	$0.470467\pi$
$174$	−8.33344	+	6.99259i	−0.631757	+	0.530107i
$175$		0			0
$176$	−2.72623	−	0.992265i	−0.205497	−	0.0747948i
$177$	−2.18183	+	2.60020i	−0.163996	+	0.195443i
$178$	−10.3057	−	5.95001i	−0.772447	−	0.445972i
$179$	−5.19089	−	8.99089i	−0.387985	−	0.672011i	0.604193	−	0.796838i	$-0.293496\pi$
$179$	−5.19089	−	8.99089i	−0.387985	−	0.672011i	−0.992178	+	0.124827i	$0.960162\pi$
$180$		0			0
$181$	−2.89049	+	16.3928i	−0.214848	+	1.21846i	0.666322	+	0.745664i	$0.267868\pi$
$181$	−2.89049	+	16.3928i	−0.214848	+	1.21846i	−0.881170	+	0.472800i	$0.843243\pi$
$182$	−2.77984	+	1.60494i	−0.206056	+	0.118966i
$183$	1.94609	+	1.12358i	0.143859	+	0.0830571i
$184$	1.68202	+	1.41138i	0.124000	+	0.104048i
$185$		0			0
$186$	−9.60011	+	3.49415i	−0.703914	+	0.256204i
$187$	−2.31799	−	2.76247i	−0.169508	−	0.202012i
$188$	10.9588	−	1.93233i	0.799254	−	0.140930i
$189$	−13.2281			−0.962200
$190$		0			0
$191$	−21.7916			−1.57679			−0.788393	−	0.615172i	$-0.789086\pi$
$191$	−21.7916			−1.57679			−0.788393	+	0.615172i	$0.789086\pi$
$192$	1.65237	−	0.291357i	0.119249	−	0.0210269i
$193$	14.7264	+	17.5503i	1.06003	+	1.26330i	0.963426	+	0.267974i	$0.0863542\pi$
$193$	14.7264	+	17.5503i	1.06003	+	1.26330i	0.0966060	+	0.995323i	$0.469201\pi$
$194$	2.54247	−	0.925384i	0.182539	−	0.0664387i
$195$		0			0
$196$	−0.667976	−	0.560499i	−0.0477126	−	0.0400356i
$197$	−4.29163	−	2.47777i	−0.305766	−	0.176534i	0.339264	−	0.940691i	$-0.389822\pi$
$197$	−4.29163	−	2.47777i	−0.305766	−	0.176534i	−0.645030	+	0.764157i	$0.723155\pi$
$198$	0.464292	−	0.268059i	0.0329958	−	0.0190501i
$199$	−4.27197	+	24.2276i	−0.302832	+	1.71745i	0.330704	+	0.943734i	$0.392714\pi$
$199$	−4.27197	+	24.2276i	−0.302832	+	1.71745i	−0.633537	+	0.773713i	$0.718397\pi$
$200$		0			0
$201$	−2.82412	−	4.89153i	−0.199198	−	0.345022i
$202$	−0.102069	−	0.0589295i	−0.00718154	−	0.00414626i
$203$	−10.3167	+	12.2950i	−0.724094	+	0.862941i
$204$	1.95979	+	0.713304i	0.137212	+	0.0499413i
$205$		0			0
$206$	−1.33398	+	1.11934i	−0.0929426	+	0.0779881i
$207$	−0.399588	+	0.0704581i	−0.0277733	+	0.00489717i
$208$			1.29667i			0.0899080i
$209$	−8.84875	−	9.03442i	−0.612081	−	0.624924i
$210$		0			0
$211$	−0.638032	−	3.61846i	−0.0439239	−	0.249105i	0.954938	−	0.296806i	$-0.0959215\pi$
$211$	−0.638032	−	3.61846i	−0.0439239	−	0.249105i	−0.998862	+	0.0477014i	$0.984810\pi$
$212$	−7.73700	−	9.22060i	−0.531379	−	0.633273i
$213$	−8.72096	−	23.9607i	−0.597551	−	1.64176i
$214$	15.6988	+	5.71391i	1.07315	+	0.390595i
$215$		0			0
$216$	−2.67181	+	4.62772i	−0.181794	+	0.314876i
$217$	−13.0535	+	7.53642i	−0.886127	+	0.511606i
$218$	−19.9402	−	3.51599i	−1.35052	−	0.238133i
$219$	−0.163339	+	0.926343i	−0.0110374	+	0.0625965i
$220$		0			0
$221$	−0.805875	+	1.39582i	−0.0542090	+	0.0938927i
$222$	−1.55865	+	1.85753i	−0.104610	+	0.124669i
$223$	2.54920	−	7.00387i	0.170707	−	0.469014i	−0.824607	−	0.565706i	$-0.808604\pi$
$223$	2.54920	−	7.00387i	0.170707	−	0.469014i	0.995314	+	0.0966918i	$0.0308261\pi$
$224$	2.32619	−	0.846665i	0.155425	−	0.0565702i
$225$		0			0
$226$	2.87298	+	16.2935i	0.191108	+	1.08383i
$227$			11.4167i			0.757750i	0.925448	+	0.378875i	$0.123689\pi$
$227$			11.4167i			0.757750i	−0.925448	+	0.378875i	$0.876311\pi$
$228$	7.04438	+	1.96614i	0.466525	+	0.130211i
$229$	3.19332			0.211021			0.105510	−	0.994418i	$-0.466352\pi$
$229$	3.19332			0.211021			0.105510	+	0.994418i	$0.466352\pi$
$230$		0			0
$231$	−9.23093	+	7.74567i	−0.607350	+	0.509627i
$232$	2.21752	+	6.09258i	0.145587	+	0.399997i
$233$	−7.96876	+	21.8940i	−0.522051	+	1.43432i	0.346183	+	0.938167i	$0.387478\pi$
$233$	−7.96876	+	21.8940i	−0.522051	+	1.43432i	−0.868234	+	0.496156i	$0.834745\pi$
$234$	−0.183556	−	0.154022i	−0.0119994	−	0.0100687i
$235$		0			0
$236$	1.01150	+	1.75198i	0.0658433	+	0.114044i
$237$	−10.7120	−	1.88881i	−0.695817	−	0.122691i
$238$	3.03025	+	0.534316i	0.196422	+	0.0346345i
$239$	−4.11104	−	7.12053i	−0.265921	−	0.460589i	0.701883	−	0.712292i	$-0.252343\pi$
$239$	−4.11104	−	7.12053i	−0.265921	−	0.460589i	−0.967805	+	0.251703i	$0.919009\pi$
$240$		0			0
$241$	15.9574	+	13.3899i	1.02791	+	0.862518i	0.990601	−	0.136786i	$-0.0436773\pi$
$241$	15.9574	+	13.3899i	1.02791	+	0.862518i	0.0373080	+	0.999304i	$0.488122\pi$
$242$	−0.883473	+	2.42732i	−0.0567918	+	0.156034i
$243$	−0.655868	−	1.80198i	−0.0420740	−	0.115597i
$244$	1.02596	−	0.860884i	0.0656805	−	0.0551124i
$245$		0			0
$246$	−3.99949			−0.254998
$247$	−2.44171	+	5.09743i	−0.155363	+	0.324342i
$248$			6.08885i			0.386642i
$249$	2.46333	+	13.9703i	0.156107	+	0.885330i
$250$		0			0
$251$	−10.7939	+	3.92864i	−0.681302	+	0.247974i	−0.659406	−	0.751787i	$-0.729192\pi$
$251$	−10.7939	+	3.92864i	−0.681302	+	0.247974i	−0.0218955	+	0.999760i	$0.506970\pi$
$252$	−0.156457	+	0.429863i	−0.00985589	+	0.0270788i
$253$	−4.09468	+	4.87985i	−0.257430	+	0.306793i
$254$	−0.0655264	+	0.113495i	−0.00411149	+	0.00712132i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.82847	−	0.322408i	−0.114057	−	0.0201112i	0.116329	−	0.993211i	$-0.462887\pi$
$257$	−1.82847	−	0.322408i	−0.114057	−	0.0201112i	−0.230385	+	0.973100i	$0.573999\pi$
$258$	13.3694	−	7.71881i	0.832340	−	0.480552i
$259$	−1.78878	+	3.09826i	−0.111149	+	0.192516i
$260$		0			0
$261$	−1.12586	−	0.409781i	−0.0696892	−	0.0253648i
$262$	−4.37850	−	12.0298i	−0.270505	−	0.743205i
$263$	6.59082	+	7.85464i	0.406407	+	0.484338i	0.929963	−	0.367654i	$-0.119839\pi$
$263$	6.59082	+	7.85464i	0.406407	+	0.484338i	−0.523555	+	0.851992i	$0.675395\pi$
$264$	0.845282	+	4.79383i	0.0520235	+	0.295040i
$265$		0			0
$266$	10.7390	+	1.05199i	0.658449	+	0.0645014i
$267$			19.9666i			1.22193i
$268$	−3.31520	+	0.584560i	−0.202508	+	0.0357077i
$269$	−20.2958	+	17.0302i	−1.23746	+	1.03835i	−0.239738	+	0.970838i	$0.577061\pi$
$269$	−20.2958	+	17.0302i	−1.23746	+	1.03835i	−0.997719	+	0.0675114i	$0.978494\pi$
$270$		0			0
$271$	−23.4094	−	8.52031i	−1.42202	−	0.517572i	−0.487385	−	0.873187i	$-0.662049\pi$
$271$	−23.4094	−	8.52031i	−1.42202	−	0.517572i	−0.934633	+	0.355615i	$0.884272\pi$
$272$	0.798979	−	0.952186i	0.0484452	−	0.0577347i
$273$	4.66419	+	2.69287i	0.282289	+	0.162980i
$274$	7.81438	+	13.5349i	0.472084	+	0.817673i
$275$		0			0
$276$	0.639737	−	3.62813i	0.0385076	−	0.218388i
$277$	12.4407	−	7.18265i	0.747490	−	0.431564i	−0.0772960	−	0.997008i	$-0.524629\pi$
$277$	12.4407	−	7.18265i	0.747490	−	0.431564i	0.824786	+	0.565444i	$0.191295\pi$
$278$	−9.94211	−	5.74008i	−0.596288	−	0.344267i
$279$	−0.861933	−	0.723248i	−0.0516026	−	0.0432997i
$280$		0			0
$281$	25.2726	−	9.19849i	1.50764	−	0.548736i	0.549614	−	0.835419i	$-0.314775\pi$
$281$	25.2726	−	9.19849i	1.50764	−	0.548736i	0.958025	+	0.286683i	$0.0925527\pi$
$282$	−12.0015	−	14.3028i	−0.714678	−	0.851720i
$283$	19.8587	−	3.50163i	1.18048	−	0.208150i	0.451235	−	0.892405i	$-0.350984\pi$
$283$	19.8587	−	3.50163i	1.18048	−	0.208150i	0.729243	+	0.684255i	$0.239873\pi$
$284$	−15.1970			−0.901776
$285$		0			0
$286$	−3.76189			−0.222445
$287$	−5.81114	+	1.02466i	−0.343021	+	0.0604838i
$288$	0.118782	+	0.141559i	0.00699932	+	0.00834146i
$289$	−14.5229	+	5.28591i	−0.854290	+	0.310936i
$290$		0			0
$291$	−3.47760	−	2.91805i	−0.203860	−	0.171059i
$292$	0.485507	+	0.280308i	0.0284122	+	0.0164038i
$293$	17.3197	−	9.99952i	1.01183	−	0.584178i	0.100100	−	0.994977i	$-0.468084\pi$
$293$	17.3197	−	9.99952i	1.01183	−	0.584178i	0.911726	+	0.410799i	$0.134750\pi$
$294$	−0.254058	+	1.44083i	−0.0148170	+	0.0840311i
$295$		0			0
$296$	0.722598	+	1.25158i	0.0420002	+	0.0727464i
$297$	−13.4259	−	7.75144i	−0.779049	−	0.449784i
$298$	−9.73926	+	11.6068i	−0.564180	+	0.672364i
$299$	2.67542	+	0.973773i	0.154723	+	0.0563147i
$300$		0			0
$301$	17.4477	−	14.6404i	1.00567	−	0.843858i
$302$	5.69967	−	1.00500i	0.327979	−	0.0578315i
$303$			0.197751i			0.0113605i
$304$	2.53709	−	3.54445i	0.145512	−	0.203288i
$305$		0			0
$306$	0.0398862	+	0.226206i	0.00228014	+	0.0129313i
$307$	12.4713	+	14.8627i	0.711772	+	0.848257i	0.993804	−	0.111148i	$-0.0354528\pi$
$307$	12.4713	+	14.8627i	0.711772	+	0.848257i	−0.282032	+	0.959405i	$0.591008\pi$
$308$	2.45634	+	6.74873i	0.139963	+	0.384544i
$309$	2.74559	+	0.999312i	0.156191	+	0.0568489i
$310$		0			0
$311$	−2.69949	+	4.67566i	−0.153074	+	0.265132i	−0.932356	−	0.361541i	$-0.882251\pi$
$311$	−2.69949	+	4.67566i	−0.153074	+	0.265132i	0.779282	+	0.626673i	$0.215584\pi$
$312$	1.88415	−	1.08782i	0.106669	−	0.0615854i
$313$	−15.9375	−	2.81021i	−0.900841	−	0.158843i	−0.295999	−	0.955188i	$-0.595653\pi$
$313$	−15.9375	−	2.81021i	−0.900841	−	0.158843i	−0.604842	+	0.796345i	$0.706764\pi$
$314$	−1.91342	+	10.8515i	−0.107980	+	0.612388i
$315$		0			0
$316$	−3.24140	+	5.61427i	−0.182343	+	0.315827i
$317$	−1.57543	+	1.87753i	−0.0884852	+	0.105453i	−0.808470	−	0.588537i	$-0.799704\pi$
$317$	−1.57543	+	1.87753i	−0.0884852	+	0.105453i	0.719985	+	0.693989i	$0.244149\pi$
$318$	−6.90736	+	18.9778i	−0.387345	+	1.06422i
$319$	−17.6757	+	6.43344i	−0.989651	+	0.360203i
$320$		0			0
$321$	−4.86752	−	27.6051i	−0.271678	−	1.54076i
$322$		−	5.43546i		−	0.302906i
$323$	4.93394	−	2.23867i	0.274532	−	0.124563i
$324$	8.41147			0.467304
$325$		0			0
$326$	16.9903	−	14.2565i	0.941003	−	0.789595i
$327$	11.6194	+	31.9241i	0.642555	+	1.76541i
$328$	−0.815270	+	2.23994i	−0.0450158	+	0.123680i
$329$	−21.1021	−	17.7068i	−1.16340	−	0.976206i
$330$		0			0
$331$	−1.51812	−	2.62947i	−0.0834436	−	0.144529i	0.821283	−	0.570521i	$-0.193259\pi$
$331$	−1.51812	−	2.62947i	−0.0834436	−	0.144529i	−0.904727	+	0.425992i	$0.859925\pi$
$332$	8.32625	+	1.46814i	0.456962	+	0.0805748i
$333$	−0.263004	−	0.0463747i	−0.0144125	−	0.00254132i
$334$	8.69412	+	15.0587i	0.475721	+	0.823973i
$335$		0			0
$336$	−3.18177	−	2.66982i	−0.173580	−	0.145651i
$337$	2.07369	−	5.69742i	0.112961	−	0.310358i	−0.870310	−	0.492504i	$-0.836082\pi$
$337$	2.07369	−	5.69742i	0.112961	−	0.310358i	0.983272	+	0.182145i	$0.0583041\pi$
$338$	−3.87120	−	10.6360i	−0.210566	−	0.578525i
$339$	21.2653	−	17.8437i	1.15497	−	0.969138i
$340$		0			0
$341$	−17.6649			−0.956608
$342$	0.200388	+	0.780168i	0.0108358	+	0.0421866i
$343$			19.4870i			1.05220i
$344$	−1.59770	−	9.06100i	−0.0861422	−	0.488537i
$345$		0			0
$346$	2.01862	−	0.734716i	0.108522	−	0.0394986i
$347$	−0.983940	+	2.70335i	−0.0528207	+	0.145124i	−0.963297	−	0.268437i	$-0.913493\pi$
$347$	−0.983940	+	2.70335i	−0.0528207	+	0.145124i	0.910477	+	0.413561i	$0.135715\pi$
$348$	6.99259	−	8.33344i	0.374842	−	0.446719i
$349$	16.3979	−	28.4020i	0.877761	−	1.52033i	0.0239680	−	0.999713i	$-0.492370\pi$
$349$	16.3979	−	28.4020i	0.877761	−	1.52033i	0.853793	−	0.520613i	$-0.174297\pi$
$350$		0			0
$351$	−1.20320	+	6.82367i	−0.0642219	+	0.364220i
$352$	2.85711	+	0.503786i	0.152285	+	0.0268519i
$353$	18.3605	−	10.6004i	0.977231	−	0.564204i	0.0757977	−	0.997123i	$-0.475850\pi$
$353$	18.3605	−	10.6004i	0.977231	−	0.564204i	0.901433	+	0.432919i	$0.142516\pi$
$354$	1.69716	−	2.93957i	0.0902031	−	0.156236i
$355$		0			0
$356$	11.1824	+	4.07005i	0.592664	+	0.215712i
$357$	−1.76577	−	4.85142i	−0.0934546	−	0.256764i
$358$	6.67328	+	7.95291i	0.352694	+	0.420324i
$359$	−3.22806	−	18.3072i	−0.170370	−	0.966218i	−0.943353	−	0.331791i	$-0.892347\pi$
$359$	−3.22806	−	18.3072i	−0.170370	−	0.966218i	0.772983	−	0.634427i	$-0.218764\pi$
$360$		0			0
$361$	16.6482	−	9.15633i	0.876220	−	0.481912i
$362$		−	16.6456i		−	0.874876i
$363$	4.26823	−	0.752605i	0.224024	−	0.0395015i
$364$	2.45892	−	2.06328i	0.128882	−	0.108145i
$365$		0			0
$366$	−2.11163	−	0.768571i	−0.110377	−	0.0401739i
$367$	−13.9628	+	16.6403i	−0.728855	+	0.868615i	−0.995459	−	0.0951910i	$-0.969654\pi$
$367$	−13.9628	+	16.6403i	−0.728855	+	0.868615i	0.266605	+	0.963806i	$0.414098\pi$
$368$	−1.90155	−	1.09786i	−0.0991249	−	0.0572298i
$369$	−0.220244	−	0.381474i	−0.0114654	−	0.0198587i
$370$		0			0
$371$	−5.17411	+	29.3438i	−0.268626	+	1.52345i
$372$	8.84751	−	5.10811i	0.458722	−	0.264843i
$373$	−19.4123	−	11.2077i	−1.00513	−	0.580312i	−0.0953679	−	0.995442i	$-0.530403\pi$
$373$	−19.4123	−	11.2077i	−1.00513	−	0.580312i	−0.909762	+	0.415130i	$0.863736\pi$
$374$	2.76247	+	2.31799i	0.142844	+	0.119860i
$375$		0			0
$376$	−10.4568	+	3.80596i	−0.539267	+	0.196277i
$377$	5.40397	+	6.44020i	0.278318	+	0.331687i
$378$	13.0271	−	2.29703i	0.670042	−	0.118146i
$379$	8.45251			0.434176			0.217088	−	0.976152i	$-0.430344\pi$
$379$	8.45251			0.434176			0.217088	+	0.976152i	$0.430344\pi$
$380$		0			0
$381$	0.219888			0.0112652
$382$	21.4605	−	3.78407i	1.09802	−	0.193610i
$383$	−6.32838	−	7.54187i	−0.323365	−	0.385372i	0.579732	−	0.814807i	$-0.303157\pi$
$383$	−6.32838	−	7.54187i	−0.323365	−	0.385372i	−0.903098	+	0.429435i	$0.858713\pi$
$384$	−1.57667	+	0.573861i	−0.0804591	+	0.0292847i
$385$		0			0
$386$	−17.5503	−	14.7264i	−0.893286	−	0.749556i
$387$	1.47245	+	0.850118i	0.0748487	+	0.0432139i
$388$	−2.34315	+	1.35282i	−0.118956	+	0.0686791i
$389$	1.47850	−	8.38497i	0.0749627	−	0.425135i	−0.924112	−	0.382122i	$-0.875193\pi$
$389$	1.47850	−	8.38497i	0.0749627	−	0.425135i	0.999075	−	0.0430125i	$-0.0136955\pi$
$390$		0			0
$391$	−1.36463	−	2.36360i	−0.0690121	−	0.119532i
$392$	0.755158	+	0.435991i	0.0381412	+	0.0220208i
$393$	−13.8069	+	16.4544i	−0.696466	+	0.830016i
$394$	4.65669	+	1.69490i	0.234601	+	0.0853877i
$395$		0			0
$396$	−0.410690	+	0.344610i	−0.0206380	+	0.0173173i
$397$	24.1425	−	4.25698i	1.21168	−	0.213651i	0.468938	−	0.883231i	$-0.344637\pi$
$397$	24.1425	−	4.25698i	1.21168	−	0.213651i	0.742740	+	0.669580i	$0.233526\pi$
$398$		−	24.6013i		−	1.23315i
$399$	−7.48063	−	16.4870i	−0.374500	−	0.825383i
$400$		0			0
$401$	−0.863801	−	4.89886i	−0.0431362	−	0.244637i	0.955614	−	0.294622i	$-0.0951938\pi$
$401$	−0.863801	−	4.89886i	−0.0431362	−	0.244637i	−0.998750	+	0.0499849i	$0.984083\pi$
$402$	3.63062	+	4.32681i	0.181079	+	0.215802i
$403$	2.70033	+	7.41909i	0.134513	+	0.369571i
$404$	0.110751	+	0.0403101i	0.00551008	+	0.00200550i
$405$		0			0
$406$	8.02501	−	13.8997i	0.398274	−	0.689831i
$407$	−3.63106	+	2.09639i	−0.179985	+	0.103914i
$408$	−2.05388	−	0.362154i	−0.101682	−	0.0179293i
$409$	−3.14232	+	17.8210i	−0.155377	+	0.881189i	0.803062	+	0.595895i	$0.203203\pi$
$409$	−3.14232	+	17.8210i	−0.155377	+	0.881189i	−0.958440	+	0.285295i	$0.907909\pi$
$410$		0			0
$411$	13.1114	−	22.7096i	0.646739	−	1.12018i
$412$	1.11934	−	1.33398i	0.0551459	−	0.0657203i
$413$	1.71281	−	4.70591i	0.0842819	−	0.231563i
$414$	0.381282	−	0.138775i	0.0187390	−	0.00682043i
$415$		0			0
$416$	−0.225165	−	1.27697i	−0.0110396	−	0.0626087i
$417$			19.2621i			0.943268i
$418$	10.2831	+	7.36059i	0.502964	+	0.360018i
$419$	10.5816			0.516945			0.258472	−	0.966019i	$-0.416781\pi$
$419$	10.5816			0.516945			0.258472	+	0.966019i	$0.416781\pi$
$420$		0			0
$421$	−18.5815	+	15.5917i	−0.905605	+	0.759893i	−0.971278	−	0.237949i	$-0.923525\pi$
$421$	−18.5815	+	15.5917i	−0.905605	+	0.759893i	0.0656729	+	0.997841i	$0.479081\pi$
$422$	1.25668	+	3.45269i	0.0611741	+	0.168074i
$423$	0.703312	−	1.93233i	0.0341962	−	0.0939533i
$424$	9.22060	+	7.73700i	0.447792	+	0.375742i
$425$		0			0
$426$	12.7492	+	22.0823i	0.617701	+	1.06989i
$427$	−3.26504	−	0.575715i	−0.158006	−	0.0278608i
$428$	−16.4526	−	2.90103i	−0.795264	−	0.140227i
$429$	3.15596	+	5.46628i	0.152371	+	0.263914i
$430$		0			0
$431$	27.3497	+	22.9491i	1.31739	+	1.10542i	0.986852	+	0.161626i	$0.0516738\pi$
$431$	27.3497	+	22.9491i	1.31739	+	1.10542i	0.330536	+	0.943794i	$0.392771\pi$
$432$	1.82763	−	5.02137i	0.0879318	−	0.241591i
$433$	−11.3099	−	31.0738i	−0.543521	−	1.49331i	−0.842311	−	0.538992i	$-0.818805\pi$
$433$	−11.3099	−	31.0738i	−0.543521	−	1.49331i	0.298790	−	0.954319i	$-0.403417\pi$
$434$	11.5465	−	9.68864i	0.554248	−	0.465069i
$435$		0			0
$436$	20.2478			0.969693
$437$	−5.40796	−	7.89659i	−0.258698	−	0.377745i
$438$		−	0.940634i		−	0.0449452i
$439$	−1.02662	−	5.82227i	−0.0489981	−	0.277882i	0.950458	−	0.310852i	$-0.100614\pi$
$439$	−1.02662	−	5.82227i	−0.0489981	−	0.277882i	−0.999456	+	0.0329703i	$0.989503\pi$
$440$		0			0
$441$	−0.151418	+	0.0551116i	−0.00721038	+	0.00262436i
$442$	0.551251	−	1.51455i	0.0262203	−	0.0720398i
$443$	−7.60590	+	9.06436i	−0.361367	+	0.430661i	−0.915841	−	0.401540i	$-0.868475\pi$
$443$	−7.60590	+	9.06436i	−0.361367	+	0.430661i	0.554474	+	0.832201i	$0.312919\pi$
$444$	1.21242	−	2.09997i	0.0575388	−	0.0996601i
$445$		0			0
$446$	−1.29426	+	7.34013i	−0.0612851	+	0.347565i
$447$	25.0360	+	4.41452i	1.18416	+	0.208800i
$448$	−2.14383	+	1.23774i	−0.101287	+	0.0584778i
$449$	−3.79197	+	6.56789i	−0.178954	+	0.309958i	−0.941523	−	0.336950i	$-0.890605\pi$
$449$	−3.79197	+	6.56789i	−0.178954	+	0.309958i	0.762568	+	0.646908i	$0.223938\pi$
$450$		0			0
$451$	−6.49848	−	2.36525i	−0.306001	−	0.111375i
$452$	−5.65867	−	15.5471i	−0.266161	−	0.731273i
$453$	−6.24195	−	7.43887i	−0.293273	−	0.349509i
$454$	−1.98248	−	11.2432i	−0.0930424	−	0.527670i
$455$		0			0
$456$	−7.27877	−	0.713026i	−0.340860	−	0.0333905i
$457$		−	13.0616i		−	0.610995i	−0.952193	−	0.305497i	$-0.901177\pi$
$457$		−	13.0616i		−	0.610995i	0.952193	−	0.305497i	$-0.0988227\pi$
$458$	−3.14481	+	0.554515i	−0.146947	+	0.0259108i
$459$	5.08813	−	4.26945i	0.237493	−	0.199281i
$460$		0			0
$461$	29.3589	+	10.6858i	1.36738	+	0.497685i	0.918328	−	0.395821i	$-0.129540\pi$
$461$	29.3589	+	10.6858i	1.36738	+	0.497685i	0.449051	+	0.893506i	$0.351762\pi$
$462$	7.74567	−	9.23093i	0.360361	−	0.429462i
$463$	12.0928	+	6.98180i	0.562002	+	0.324472i	0.753949	−	0.656933i	$-0.228147\pi$
$463$	12.0928	+	6.98180i	0.562002	+	0.324472i	−0.191947	+	0.981405i	$0.561480\pi$
$464$	−3.24179	−	5.61495i	−0.150496	−	0.260668i
$465$		0			0
$466$	4.04585	−	22.9451i	0.187420	−	1.06291i
$467$	10.2252	−	5.90352i	0.473165	−	0.273182i	−0.244399	−	0.969675i	$-0.578591\pi$
$467$	10.2252	−	5.90352i	0.473165	−	0.273182i	0.717564	+	0.696493i	$0.245257\pi$
$468$	0.207513	+	0.119808i	0.00959228	+	0.00553811i
$469$	6.38370	+	5.35656i	0.294772	+	0.247343i
$470$		0			0
$471$	17.3732	−	6.32334i	0.800517	−	0.291364i
$472$	−1.30037	−	1.54971i	−0.0598542	−	0.0713314i
$473$	26.2877	−	4.63523i	1.20871	−	0.213128i
$474$	10.8772			0.499607
$475$		0			0
$476$	−3.07700			−0.141034
$477$	−2.19049	+	0.386242i	−0.100296	+	0.0176848i
$478$	5.28505	+	6.29848i	0.241733	+	0.288086i
$479$	−30.1189	+	10.9624i	−1.37617	+	0.500884i	−0.921014	−	0.389529i	$-0.872638\pi$
$479$	−30.1189	+	10.9624i	−1.37617	+	0.500884i	−0.455153	+	0.890413i	$0.650415\pi$
$480$		0			0
$481$	1.43552	+	1.20455i	0.0654543	+	0.0549227i
$482$	−18.0401	−	10.4155i	−0.821705	−	0.474412i
$483$	−7.89809	+	4.55996i	−0.359375	+	0.207485i
$484$	0.448551	−	2.54386i	0.0203887	−	0.115630i
$485$		0			0
$486$	0.958815	+	1.66072i	0.0434927	+	0.0753316i
$487$	−15.1334	−	8.73726i	−0.685759	−	0.395923i	0.116263	−	0.993219i	$-0.462909\pi$
$487$	−15.1334	−	8.73726i	−0.685759	−	0.395923i	−0.802021	+	0.597296i	$0.796242\pi$
$488$	−0.860884	+	1.02596i	−0.0389704	+	0.0464431i
$489$	−34.9693	−	12.7278i	−1.58137	−	0.575570i
$490$		0			0
$491$	−1.62811	+	1.36614i	−0.0734754	+	0.0616531i	−0.678786	−	0.734336i	$-0.737493\pi$
$491$	−1.62811	+	1.36614i	−0.0734754	+	0.0616531i	0.605310	+	0.795990i	$0.293049\pi$
$492$	3.93873	−	0.694505i	0.177572	−	0.0313107i
$493$		−	8.05903i		−	0.362961i
$494$	1.51946	−	5.44399i	0.0683637	−	0.244937i
$495$		0			0
$496$	−1.05732	−	5.99634i	−0.0474749	−	0.269244i
$497$	24.1816	+	28.8185i	1.08469	+	1.29269i
$498$	−4.85182	−	13.3303i	−0.217415	−	0.597344i
$499$	34.1891	+	12.4438i	1.53051	+	0.557062i	0.963747	−	0.266817i	$-0.0859719\pi$
$499$	34.1891	+	12.4438i	1.53051	+	0.557062i	0.566767	+	0.823878i	$0.308194\pi$
$500$		0			0
$501$	14.5875	−	25.2663i	0.651722	−	1.12882i
$502$	9.94767	−	5.74329i	0.443986	−	0.256336i
$503$	9.07677	+	1.60048i	0.404713	+	0.0713619i	0.372299	−	0.928113i	$-0.378569\pi$
$503$	9.07677	+	1.60048i	0.404713	+	0.0713619i	0.0324139	+	0.999475i	$0.489681\pi$
$504$	0.0794355	−	0.450501i	0.00353834	−	0.0200669i
$505$		0			0
$506$	3.18509	−	5.51674i	0.141595	−	0.245249i
$507$	−12.2072	+	14.5480i	−0.542142	+	0.646100i
$508$	0.0448227	−	0.123149i	0.00198869	−	0.00546387i
$509$	16.3916	−	5.96606i	0.726546	−	0.264441i	0.0478437	−	0.998855i	$-0.484765\pi$
$509$	16.3916	−	5.96606i	0.726546	−	0.264441i	0.678702	+	0.734414i	$0.262543\pi$
$510$		0			0
$511$	−0.240988	−	1.36671i	−0.0106607	−	0.0604597i
$512$			1.00000i			0.0441942i
$513$	16.6403	−	16.2983i	0.734686	−	0.719588i
$514$	1.85667			0.0818943
$515$		0			0
$516$	−11.8259	+	9.92310i	−0.520606	+	0.436840i
$517$	−11.0418	−	30.3371i	−0.485618	−	1.33422i
$518$	1.22360	−	3.36181i	0.0537618	−	0.147709i
$519$	−2.76107	−	2.31681i	−0.121197	−	0.101697i
$520$		0			0
$521$	−10.5137	−	18.2102i	−0.460611	−	0.797802i	0.538380	−	0.842702i	$-0.319037\pi$
$521$	−10.5137	−	18.2102i	−0.460611	−	0.797802i	−0.998992	+	0.0448997i	$0.985703\pi$
$522$	1.17992	+	0.208051i	0.0516435	+	0.00910615i
$523$	−8.44161	−	1.48848i	−0.369126	−	0.0650868i	−0.0139914	−	0.999902i	$-0.504454\pi$
$523$	−8.44161	−	1.48848i	−0.369126	−	0.0650868i	−0.355134	+	0.934815i	$0.615565\pi$
$524$	6.40094	+	11.0867i	0.279626	+	0.484327i
$525$		0			0
$526$	−7.85464	−	6.59082i	−0.342478	−	0.287373i
$527$	2.58854	−	7.11195i	0.112758	−	0.309801i
$528$	−1.66488	−	4.57422i	−0.0724546	−	0.199067i
$529$	13.9258	−	11.6851i	0.605469	−	0.508049i
$530$		0			0
$531$	0.373837			0.0162231
$532$	−10.7585	+	0.828800i	−0.466440	+	0.0359330i
$533$			3.09086i			0.133880i
$534$	−3.46716	−	19.6632i	−0.150038	−	0.850911i
$535$		0			0
$536$	3.16333	−	1.15136i	0.136635	−	0.0497311i
$537$	5.95770	−	16.3687i	0.257094	−	0.706360i
$538$	17.0302	−	20.2958i	0.734224	−	0.875014i
$539$	−1.26489	+	2.19086i	−0.0544827	+	0.0943668i
$540$		0			0
$541$	3.75653	−	21.3044i	0.161506	−	0.915946i	−0.791088	−	0.611702i	$-0.790485\pi$
$541$	3.75653	−	21.3044i	0.161506	−	0.915946i	0.952594	−	0.304244i	$-0.0984038\pi$
$542$	24.5333	+	4.32588i	1.05379	+	0.185812i
$543$	−24.1872	+	13.9645i	−1.03797	+	0.599275i
$544$	−0.621495	+	1.07646i	−0.0266464	+	0.0461529i
$545$		0			0
$546$	−5.06094	−	1.84203i	−0.216588	−	0.0788316i
$547$	10.7349	+	29.4938i	0.458989	+	1.26106i	0.926239	+	0.376937i	$0.123023\pi$
$547$	10.7349	+	29.4938i	0.458989	+	1.26106i	−0.467249	+	0.884126i	$0.654755\pi$
$548$	−10.0460	−	11.9723i	−0.429143	−	0.511432i
$549$	−0.0429766	−	0.243732i	−0.00183420	−	0.0104022i
$550$		0			0
$551$	−2.17073	−	28.1778i	−0.0924761	−	1.20042i
$552$			3.68410i			0.156806i
$553$	15.8042	−	2.78672i	0.672065	−	0.118503i
$554$	−11.0045	+	9.23384i	−0.467535	+	0.392308i
$555$		0			0
$556$	10.7878	+	3.92644i	0.457505	+	0.166518i
$557$	3.66096	−	4.36296i	0.155120	−	0.184864i	−0.682888	−	0.730523i	$-0.739276\pi$
$557$	3.66096	−	4.36296i	0.155120	−	0.184864i	0.838007	+	0.545659i	$0.183721\pi$
$558$	0.974429	+	0.562587i	0.0412509	+	0.0238162i
$559$	−5.96520	−	10.3320i	−0.252301	−	0.436998i
$560$		0			0
$561$	1.05068	−	5.95868i	0.0443596	−	0.251576i
$562$	−23.2914	+	13.4473i	−0.982488	+	0.567240i
$563$	−6.97904	−	4.02935i	−0.294132	−	0.169817i	0.345672	−	0.938355i	$-0.387651\pi$
$563$	−6.97904	−	4.02935i	−0.294132	−	0.169817i	−0.639804	+	0.768538i	$0.720984\pi$
$564$	14.3028	+	12.0015i	0.602257	+	0.505353i
$565$		0			0
$566$	−18.9490	+	6.89686i	−0.796484	+	0.289896i
$567$	−13.3844	−	15.9509i	−0.562093	−	0.669876i
$568$	14.9661	−	2.63893i	0.627964	−	0.110727i
$569$	−22.1220			−0.927404			−0.463702	−	0.885991i	$-0.653479\pi$
$569$	−22.1220			−0.927404			−0.463702	+	0.885991i	$0.653479\pi$
$570$		0			0
$571$	45.8413			1.91840			0.959200	−	0.282729i	$-0.0912396\pi$
$571$	45.8413			1.91840			0.959200	+	0.282729i	$0.0912396\pi$
$572$	3.70474	−	0.653245i	0.154903	−	0.0273136i
$573$	−23.5024	−	28.0091i	−0.981826	−	1.17009i
$574$	5.54492	−	2.01819i	0.231441	−	0.0842375i
$575$		0			0
$576$	−0.141559	−	0.118782i	−0.00589830	−	0.00494926i
$577$	27.4535	+	15.8503i	1.14291	+	0.659857i	0.947148	−	0.320796i	$-0.103950\pi$
$577$	27.4535	+	15.8503i	1.14291	+	0.659857i	0.195757	+	0.980652i	$0.437284\pi$
$578$	13.3844	−	7.72749i	0.556718	−	0.321421i
$579$	−6.67507	+	37.8562i	−0.277406	+	1.57325i
$580$		0			0
$581$	−10.4647	−	18.1254i	−0.434150	−	0.751970i
$582$	3.93148	+	2.26984i	0.162965	+	0.0940880i
$583$	−22.4465	+	26.7507i	−0.929639	+	1.10790i
$584$	−0.526806	−	0.191742i	−0.0217994	−	0.00793434i
$585$		0			0
$586$	−15.3201	+	12.8551i	−0.632869	+	0.531041i
$587$	12.6088	−	2.22328i	0.520422	−	0.0917644i	0.0927341	−	0.995691i	$-0.470439\pi$
$587$	12.6088	−	2.22328i	0.520422	−	0.0917644i	0.427688	+	0.903926i	$0.359328\pi$
$588$		−	1.46306i		−	0.0603356i
$589$	7.13500	−	25.5636i	0.293993	−	1.05333i
$590$		0			0
$591$	−1.44383	−	8.18839i	−0.0593914	−	0.336825i
$592$	−0.928954	−	1.10708i	−0.0381798	−	0.0455009i
$593$	12.6662	+	34.8002i	0.520140	+	1.42907i	0.870365	+	0.492407i	$0.163883\pi$
$593$	12.6662	+	34.8002i	0.520140	+	1.42907i	−0.350225	+	0.936665i	$0.613895\pi$
$594$	14.5679	+	5.30230i	0.597730	+	0.217556i
$595$		0			0
$596$	7.57580	−	13.1217i	0.310317	−	0.537485i
$597$	−35.7474	+	20.6388i	−1.46304	+	0.844688i
$598$	−2.80387	−	0.494397i	−0.114659	−	0.0202174i
$599$	−1.00225	+	5.68403i	−0.0409507	+	0.232243i	−0.998413	−	0.0563153i	$-0.982065\pi$
$599$	−1.00225	+	5.68403i	−0.0409507	+	0.232243i	0.957462	+	0.288558i	$0.0931759\pi$
$600$		0			0
$601$	−8.26350	+	14.3128i	−0.337075	+	0.583831i	−0.983881	−	0.178823i	$-0.942771\pi$
$601$	−8.26350	+	14.3128i	−0.337075	+	0.583831i	0.646806	+	0.762655i	$0.276104\pi$
$602$	−14.6404	+	17.4477i	−0.596697	+	0.711116i
$603$	−0.212762	+	0.584560i	−0.00866435	+	0.0238051i
$604$	−5.43856	+	1.97947i	−0.221292	+	0.0805436i
$605$		0			0
$606$	−0.0343390	−	0.194746i	−0.00139493	−	0.00791103i
$607$			2.34282i			0.0950920i	0.998869	+	0.0475460i	$0.0151401\pi$
$607$			2.34282i			0.0950920i	−0.998869	+	0.0475460i	$0.984860\pi$
$608$	−1.88306	+	3.93117i	−0.0763683	+	0.159430i
$609$	−26.9296			−1.09124
$610$		0			0
$611$	−11.0534	+	9.27490i	−0.447173	+	0.375222i
$612$	−0.0785604	−	0.215843i	−0.00317562	−	0.00872493i
$613$	−10.2703	+	28.2173i	−0.414812	+	1.13969i	0.539789	+	0.841800i	$0.318504\pi$
$613$	−10.2703	+	28.2173i	−0.414812	+	1.13969i	−0.954601	+	0.297886i	$0.903718\pi$
$614$	−14.8627	−	12.4713i	−0.599808	−	0.503299i
$615$		0			0
$616$	−3.59092	−	6.21966i	−0.144682	−	0.250597i
$617$	15.9792	+	2.81756i	0.643298	+	0.113431i	0.485774	−	0.874084i	$-0.338538\pi$
$617$	15.9792	+	2.81756i	0.643298	+	0.113431i	0.157524	+	0.987515i	$0.449649\pi$
$618$	−2.87740	−	0.507364i	−0.115746	−	0.0204092i
$619$	23.8503	+	41.3099i	0.958624	+	1.66039i	0.725848	+	0.687855i	$0.241448\pi$
$619$	23.8503	+	41.3099i	0.958624	+	1.66039i	0.232776	+	0.972530i	$0.425219\pi$
$620$		0			0
$621$	−8.98807	−	7.54188i	−0.360679	−	0.302645i
$622$	1.84656	−	5.07338i	0.0740403	−	0.203424i
$623$	−10.0753	−	27.6818i	−0.403660	−	1.10905i
$624$	−1.66663	+	1.39847i	−0.0667186	+	0.0559835i
$625$		0			0
$626$	16.1834			0.646818
$627$	2.06862	−	21.1171i	0.0826128	−	0.843336i
$628$		−	11.0189i		−	0.439704i
$629$	−0.311935	−	1.76907i	−0.0124377	−	0.0705376i
$630$		0			0
$631$	11.5071	−	4.18824i	0.458090	−	0.166731i	−0.102660	−	0.994717i	$-0.532735\pi$
$631$	11.5071	−	4.18824i	0.458090	−	0.166731i	0.560750	+	0.827985i	$0.310513\pi$
$632$	2.21725	−	6.09184i	0.0881973	−	0.242320i
$633$	3.96273	−	4.72260i	0.157504	−	0.187706i
$634$	1.22547	−	2.12258i	0.0486696	−	0.0842983i
$635$		0			0
$636$	3.50696	−	19.8889i	0.139060	−	0.788648i
$637$	1.11350	+	0.196339i	0.0441183	+	0.00777925i
$638$	16.2900	−	9.40506i	0.644929	−	0.372350i
$639$	−1.40415	+	2.43205i	−0.0555471	+	0.0962104i
$640$		0			0
$641$	27.9385	+	10.1688i	1.10350	+	0.401643i	0.828607	−	0.559831i	$-0.189134\pi$
$641$	27.9385	+	10.1688i	1.10350	+	0.401643i	0.274897	+	0.961474i	$0.411356\pi$
$642$	9.58714	+	26.3404i	0.378374	+	1.03957i
$643$	13.5109	+	16.1016i	0.532817	+	0.634987i	0.963561	−	0.267487i	$-0.0861933\pi$
$643$	13.5109	+	16.1016i	0.532817	+	0.634987i	−0.430744	+	0.902474i	$0.641749\pi$
$644$	0.943857	+	5.35288i	0.0371932	+	0.210933i
$645$		0			0
$646$	−4.47024	+	3.06143i	−0.175879	+	0.120451i
$647$			10.8225i			0.425476i	0.977109	+	0.212738i	$0.0682381\pi$
$647$			10.8225i			0.425476i	−0.977109	+	0.212738i	$0.931762\pi$
$648$	−8.28368	+	1.46064i	−0.325414	+	0.0573792i
$649$	4.49602	−	3.77261i	0.176484	−	0.148088i
$650$		0			0
$651$	−23.7649	−	8.64972i	−0.931420	−	0.339009i
$652$	−14.2565	+	16.9903i	−0.558328	+	0.665390i
$653$	37.1937	+	21.4738i	1.45550	+	0.840334i	0.998785	−	0.0492789i	$-0.0156923\pi$
$653$	37.1937	+	21.4738i	1.45550	+	0.840334i	0.456716	+	0.889613i	$0.349026\pi$
$654$	−16.9865	−	29.4214i	−0.664223	−	1.15047i
$655$		0			0
$656$	0.413923	−	2.34748i	0.0161610	−	0.0916536i
$657$	0.0897182	−	0.0517988i	0.00350024	−	0.00202086i
$658$	23.8563	+	13.7734i	0.930015	+	0.536944i
$659$	4.59278	+	3.85380i	0.178909	+	0.150123i	0.727845	−	0.685742i	$-0.240522\pi$
$659$	4.59278	+	3.85380i	0.178909	+	0.150123i	−0.548935	+	0.835865i	$0.684967\pi$
$660$		0			0
$661$	−16.9338	+	6.16342i	−0.658650	+	0.239729i	−0.649654	−	0.760230i	$-0.725086\pi$
$661$	−16.9338	+	6.16342i	−0.658650	+	0.239729i	−0.00899680	+	0.999960i	$0.502864\pi$
$662$	1.95166	+	2.32590i	0.0758535	+	0.0903986i
$663$	−2.66320	+	0.469594i	−0.103430	+	0.0182375i
$664$	−8.45470			−0.328106
$665$		0			0
$666$	0.267061			0.0103484
$667$	−14.0198	+	2.47207i	−0.542850	+	0.0957191i
$668$	−11.1770	−	13.3202i	−0.432449	−	0.515373i
$669$	11.7515	−	4.27719i	0.454339	−	0.165366i
$670$		0			0
$671$	−2.97651	−	2.49759i	−0.114907	−	0.0964183i
$672$	3.59705	+	2.07675i	0.138759	+	0.0801126i
$673$	−23.6912	+	13.6781i	−0.913231	+	0.527254i	−0.881469	−	0.472242i	$-0.843445\pi$
$673$	−23.6912	+	13.6781i	−0.913231	+	0.527254i	−0.0317614	+	0.999495i	$0.510112\pi$
$674$	−1.05284	+	5.97096i	−0.0405539	+	0.229993i
$675$		0			0
$676$	5.65932	+	9.80223i	0.217666	+	0.377009i
$677$	26.1566	+	15.1015i	1.00528	+	0.580398i	0.909806	−	0.415034i	$-0.136230\pi$
$677$	26.1566	+	15.1015i	1.00528	+	0.580398i	0.0954734	+	0.995432i	$0.469564\pi$
$678$	−17.8437	+	21.2653i	−0.685284	+	0.816689i
$679$	6.29385	+	2.29077i	0.241536	+	0.0879118i
$680$		0			0
$681$	−14.6740	+	12.3129i	−0.562308	+	0.471833i
$682$	17.3965	−	3.06748i	0.666148	−	0.117460i
$683$			42.2829i			1.61791i	0.587871	+	0.808955i	$0.299966\pi$
$683$			42.2829i			1.61791i	−0.587871	+	0.808955i	$0.700034\pi$
$684$	−0.332819	−	0.733518i	−0.0127256	−	0.0280468i
$685$		0			0
$686$	−3.38388	−	19.1909i	−0.129197	−	0.732712i
$687$	3.44402	+	4.10442i	0.131398	+	0.156594i
$688$	3.14685	+	8.64591i	0.119973	+	0.329622i
$689$	14.6663	+	5.33810i	0.558742	+	0.203365i
$690$		0			0
$691$	−7.96853	+	13.8019i	−0.303137	+	0.525049i	−0.976845	−	0.213949i	$-0.931367\pi$
$691$	−7.96853	+	13.8019i	−0.303137	+	0.525049i	0.673708	+	0.738998i	$0.264701\pi$
$692$	−1.86037	+	1.07408i	−0.0707205	+	0.0408305i
$693$	1.30699	+	0.230457i	0.0496484	+	0.00875435i
$694$	0.499559	−	2.83314i	0.0189630	−	0.107545i
$695$		0			0
$696$	−5.43927	+	9.42109i	−0.206175	+	0.357106i
$697$	1.90452	−	2.26972i	0.0721387	−	0.0859716i
$698$	−11.2168	+	30.8180i	−0.424564	+	1.16648i
$699$	−36.7350	+	13.3704i	−1.38945	+	0.505717i
$700$		0			0
$701$	−1.03691	−	5.88059i	−0.0391634	−	0.222107i	0.958944	−	0.283594i	$-0.0915268\pi$
$701$	−1.03691	−	5.88059i	−0.0391634	−	0.222107i	−0.998108	+	0.0614872i	$0.980416\pi$
$702$		−	6.92893i		−	0.261516i
$703$	−1.56716	−	6.10141i	−0.0591067	−	0.230119i
$704$	−2.90119			−0.109343
$705$		0			0
$706$	−16.2408	+	13.6277i	−0.611231	+	0.512884i
$707$	−0.0997871	−	0.274163i	−0.00375288	−	0.0103110i
$708$	−1.16093	+	3.18962i	−0.0436303	+	0.119873i
$709$	−35.7131	−	29.9669i	−1.34123	−	1.12543i	−0.981307	−	0.192450i	$-0.938357\pi$
$709$	−35.7131	−	29.9669i	−1.34123	−	1.12543i	−0.359928	−	0.932980i	$-0.617199\pi$
$710$		0			0
$711$	0.598986	+	1.03747i	0.0224637	+	0.0389083i
$712$	−11.7192	−	2.06642i	−0.439197	−	0.0774423i
$713$	−13.1663	−	2.32157i	−0.493080	−	0.0869434i
$714$	2.58139	+	4.47109i	0.0966059	+	0.167326i
$715$		0			0
$716$	−7.95291	−	6.67328i	−0.297214	−	0.249392i
$717$	4.71833	−	12.9635i	0.176209	−	0.484131i
$718$	6.35803	+	17.4685i	0.237280	+	0.651920i
$719$	31.8698	−	26.7420i	1.18854	−	0.997307i	0.188661	−	0.982042i	$-0.439585\pi$
$719$	31.8698	−	26.7420i	1.18854	−	0.997307i	0.999883	−	0.0152650i	$-0.00485920\pi$
$720$		0			0
$721$	−4.31076			−0.160541
$722$	−14.8053	+	11.9081i	−0.550995	+	0.443175i
$723$			34.9514i			1.29986i
$724$	2.89049	+	16.3928i	0.107424	+	0.609232i
$725$		0			0
$726$	−4.07270	+	1.48234i	−0.151152	+	0.0550149i
$727$	−7.10304	+	19.5154i	−0.263437	+	0.723787i	0.735493	+	0.677533i	$0.236951\pi$
$727$	−7.10304	+	19.5154i	−0.263437	+	0.723787i	−0.998930	+	0.0462546i	$0.985271\pi$
$728$	−2.06328	+	2.45892i	−0.0764701	+	0.0911335i
$729$	14.2260	−	24.6401i	0.526888	−	0.912596i
$730$		0			0
$731$	−1.98592	+	11.2627i	−0.0734521	+	0.416567i
$732$	2.21301	+	0.390214i	0.0817953	+	0.0144227i
$733$	−25.5184	+	14.7331i	−0.942545	+	0.544179i	−0.890757	−	0.454480i	$-0.849825\pi$
$733$	−25.5184	+	14.7331i	−0.942545	+	0.544179i	−0.0517877	+	0.998658i	$0.516492\pi$
$734$	10.8612	−	18.8121i	0.400893	−	0.694367i
$735$		0			0
$736$	2.06330	+	0.750979i	0.0760542	+	0.0276814i
$737$	3.34031	+	9.17742i	0.123042	+	0.338054i
$738$	0.283140	+	0.337433i	0.0104225	+	0.0124211i
$739$	−4.63253	−	26.2724i	−0.170410	−	0.966446i	−0.943309	−	0.331916i	$-0.892305\pi$
$739$	−4.63253	−	26.2724i	−0.170410	−	0.966446i	0.772898	−	0.634530i	$-0.218806\pi$
$740$		0			0
$741$	−9.18520	+	2.35924i	−0.337427	+	0.0866690i
$742$		−	29.7965i		−	1.09386i
$743$	44.5252	−	7.85099i	1.63347	−	0.288025i	0.719708	−	0.694276i	$-0.244275\pi$
$743$	44.5252	−	7.85099i	1.63347	−	0.288025i	0.913761	+	0.406252i	$0.133164\pi$
$744$	−7.82608	+	6.56686i	−0.286918	+	0.240753i
$745$		0			0
$746$	21.0636	+	7.66651i	0.771192	+	0.280691i
$747$	1.00427	−	1.19684i	0.0367443	−	0.0437901i
$748$	−3.12302	−	1.80307i	−0.114189	−	0.0659269i
$749$	20.6782	+	35.8156i	0.755564	+	1.30867i
$750$		0			0
$751$	−0.599478	+	3.39981i	−0.0218753	+	0.124061i	−0.993790	−	0.111273i	$-0.964507\pi$
$751$	−0.599478	+	3.39981i	−0.0218753	+	0.124061i	0.971915	+	0.235334i	$0.0756183\pi$
$752$	9.63702	−	5.56394i	0.351426	−	0.202896i
$753$	−16.6908	−	9.63642i	−0.608246	−	0.351171i
$754$	−6.44020	−	5.40397i	−0.234538	−	0.196801i
$755$		0			0
$756$	−12.4303	+	4.52427i	−0.452086	+	0.164546i
$757$	−25.9373	−	30.9109i	−0.942708	−	1.12348i	−0.992194	−	0.124701i	$-0.960203\pi$
$757$	−25.9373	−	30.9109i	−0.942708	−	1.12348i	0.0494862	−	0.998775i	$-0.484242\pi$
$758$	−8.32410	+	1.46776i	−0.302345	+	0.0533116i
$759$	−10.6883			−0.387960
$760$		0			0
$761$	−12.4450			−0.451132			−0.225566	−	0.974228i	$-0.572423\pi$
$761$	−12.4450			−0.451132			−0.225566	+	0.974228i	$0.572423\pi$
$762$	−0.216547	+	0.0381832i	−0.00784469	+	0.00138323i
$763$	−32.2185	−	38.3965i	−1.16639	−	1.39005i
$764$	−20.4774	+	7.45317i	−0.740847	+	0.269646i
$765$		0			0
$766$	7.54187	+	6.32838i	0.272499	+	0.228654i
$767$	−2.27174	−	1.31159i	−0.0820277	−	0.0473587i
$768$	1.45307	−	0.838929i	0.0524331	−	0.0302722i
$769$	−5.55178	+	31.4857i	−0.200202	+	1.13540i	0.704610	+	0.709594i	$0.251122\pi$
$769$	−5.55178	+	31.4857i	−0.200202	+	1.13540i	−0.904813	+	0.425810i	$0.859989\pi$
$770$		0			0
$771$	−1.55762	−	2.69787i	−0.0560962	−	0.0971615i
$772$	19.8409	+	11.4551i	0.714089	+	0.412279i
$773$	22.6745	−	27.0224i	0.815545	−	0.971929i	−0.184395	−	0.982852i	$-0.559033\pi$
$773$	22.6745	−	27.0224i	0.815545	−	0.971929i	0.999940	+	0.0109230i	$0.00347697\pi$
$774$	−1.59770	−	0.581515i	−0.0574281	−	0.0209021i
$775$		0			0
$776$	2.07264	−	1.73915i	0.0744035	−	0.0624320i
$777$	−5.91144	+	1.04235i	−0.212072	+	0.0373940i
$778$			8.51432i			0.305253i
$779$	6.04765	−	8.44888i	0.216679	−	0.302712i
$780$		0			0
$781$	7.65603	+	43.4195i	0.273954	+	1.55367i
$782$	1.75433	+	2.09073i	0.0627347	+	0.0747643i
$783$	−11.8496	−	32.5565i	−0.423470	−	1.16347i
$784$	−0.819394	−	0.298235i	−0.0292641	−	0.0106513i
$785$		0			0
$786$	10.7399	−	18.6020i	0.383078	−	0.663511i
$787$	34.2030	−	19.7471i	1.21921	−	0.703909i	0.254458	−	0.967084i	$-0.418103\pi$
$787$	34.2030	−	19.7471i	1.21921	−	0.703909i	0.964748	+	0.263175i	$0.0847696\pi$
$788$	−4.88026	−	0.860522i	−0.173852	−	0.0306548i
$789$	−2.98743	+	16.9425i	−0.106355	+	0.603171i
$790$		0			0
$791$	−20.4782	+	35.4694i	−0.728123	+	1.26115i
$792$	0.344610	−	0.410690i	0.0122452	−	0.0145932i
$793$	−0.593962	+	1.63190i	−0.0210922	+	0.0579504i
$794$	−23.0365	+	8.38460i	−0.817535	+	0.297558i
$795$		0			0
$796$	4.27197	+	24.2276i	0.151416	+	0.858724i
$797$			18.0151i			0.638128i	0.947733	+	0.319064i	$0.103369\pi$
$797$			18.0151i			0.638128i	−0.947733	+	0.319064i	$0.896631\pi$
$798$	10.2299	+	14.9375i	0.362135	+	0.528783i
$799$	13.8318			0.489335
$800$		0			0
$801$	1.68456	−	1.41351i	0.0595210	−	0.0499440i
$802$	1.70136	+	4.67444i	0.0600770	+	0.165060i
$803$	0.556279	−	1.52837i	0.0196307	−	0.0539348i
$804$	−4.32681	−	3.63062i	−0.152595	−	0.128042i
$805$		0			0
$806$	−3.94762	−	6.83747i	−0.139049	−	0.240840i
$807$	−43.7783	−	7.71929i	−1.54107	−	0.271732i
$808$	−0.116068	−	0.0204660i	−0.00408327	−	0.000719991i
$809$	14.5518	+	25.2045i	0.511615	+	0.886144i	0.999909	+	0.0134647i	$0.00428607\pi$
$809$	14.5518	+	25.2045i	0.511615	+	0.886144i	−0.488294	+	0.872679i	$0.662381\pi$
$810$		0			0
$811$	12.3496	+	10.3626i	0.433654	+	0.363879i	0.833328	−	0.552779i	$-0.186432\pi$
$811$	12.3496	+	10.3626i	0.433654	+	0.363879i	−0.399675	+	0.916657i	$0.630877\pi$
$812$	−5.48943	+	15.0821i	−0.192641	+	0.529277i
$813$	−14.2959	−	39.2776i	−0.501378	−	1.37753i
$814$	3.21186	−	2.69507i	0.112576	−	0.0944622i
$815$		0			0
$816$	2.08556			0.0730092
$817$	−3.90998	+	39.9142i	−0.136793	+	1.39642i
$818$		−	18.0959i		−	0.632707i
$819$	−0.103002	−	0.584152i	−0.00359917	−	0.0204119i
$820$		0			0
$821$	−27.8660	+	10.1424i	−0.972530	+	0.353972i	−0.778932	−	0.627109i	$-0.784238\pi$
$821$	−27.8660	+	10.1424i	−0.972530	+	0.353972i	−0.193598	+	0.981081i	$0.562016\pi$
$822$	−8.96874	+	24.6414i	−0.312821	+	0.859468i
$823$	15.2315	−	18.1522i	0.530937	−	0.632746i	−0.432194	−	0.901781i	$-0.642260\pi$
$823$	15.2315	−	18.1522i	0.530937	−	0.632746i	0.963130	+	0.269035i	$0.0867047\pi$
$824$	−0.870691	+	1.50808i	−0.0303320	+	0.0525365i
$825$		0			0
$826$	−0.869617	+	4.93184i	−0.0302579	+	0.171601i
$827$	−37.4692	−	6.60682i	−1.30293	−	0.229742i	−0.521241	−	0.853410i	$-0.674531\pi$
$827$	−37.4692	−	6.60682i	−1.30293	−	0.229742i	−0.781689	+	0.623668i	$0.785642\pi$
$828$	−0.351391	+	0.202876i	−0.0122117	+	0.00705042i
$829$	11.9638	−	20.7219i	0.415520	−	0.719701i	−0.579963	−	0.814643i	$-0.696933\pi$
$829$	11.9638	−	20.7219i	0.415520	−	0.719701i	0.995483	+	0.0949413i	$0.0302664\pi$
$830$		0			0
$831$	22.6494	+	8.24369i	0.785698	+	0.285971i
$832$	0.443488	+	1.21847i	0.0153752	+	0.0422429i
$833$	−0.696694	−	0.830288i	−0.0241390	−	0.0287678i
$834$	−3.34482	−	18.9694i	−0.115822	−	0.656858i
$835$		0			0
$836$	−11.4051	−	5.46312i	−0.394452	−	0.188946i
$837$		−	32.5365i		−	1.12463i
$838$	−10.4208	+	1.83747i	−0.359982	+	0.0634745i
$839$	−13.6980	+	11.4940i	−0.472908	+	0.396817i	−0.847854	−	0.530230i	$-0.822106\pi$
$839$	−13.6980	+	11.4940i	−0.472908	+	0.396817i	0.374946	+	0.927047i	$0.377661\pi$
$840$		0			0
$841$	−12.2507	−	4.45888i	−0.422437	−	0.153755i
$842$	15.5917	−	18.5815i	0.537325	−	0.640359i
$843$	39.0796	+	22.5626i	1.34597	+	0.777099i
$844$	−1.83714	−	3.18202i	−0.0632369	−	0.109530i
$845$		0			0
$846$	−0.357081	+	2.02511i	−0.0122767	+	0.0696246i
$847$	−5.53773	+	3.19721i	−0.190279	+	0.109858i
$848$	−10.4240	−	6.01832i	−0.357963	−	0.206670i
$849$	25.9184	+	21.7481i	0.889518	+	0.746394i
$850$		0			0
$851$	−2.98187	+	1.08531i	−0.102217	+	0.0372040i
$852$	−16.3901	−	19.5329i	−0.561514	−	0.669186i
$853$	−35.3934	+	6.24081i	−1.21185	+	0.213681i	−0.742813	−	0.669499i	$-0.766509\pi$
$853$	−35.3934	+	6.24081i	−1.21185	+	0.213681i	−0.469033	+	0.883181i	$0.655398\pi$
$854$	3.31541			0.113451
$855$		0			0
$856$	16.7064			0.571012
$857$	5.25121	−	0.925930i	0.179378	−	0.0316292i	−0.0832376	−	0.996530i	$-0.526526\pi$
$857$	5.25121	−	0.925930i	0.179378	−	0.0316292i	0.262615	+	0.964901i	$0.415415\pi$
$858$	−4.05722	−	4.83521i	−0.138511	−	0.165071i
$859$	−8.81020	+	3.20665i	−0.300600	+	0.109410i	−0.487917	−	0.872890i	$-0.662243\pi$
$859$	−8.81020	+	3.20665i	−0.300600	+	0.109410i	0.187317	+	0.982300i	$0.440021\pi$
$860$		0			0
$861$	−7.58436	−	6.36403i	−0.258474	−	0.216886i
$862$	−30.9192	−	17.8512i	−1.05311	−	0.608015i
$863$	−4.57608	+	2.64200i	−0.155772	+	0.0899348i	−0.575860	−	0.817549i	$-0.695333\pi$
$863$	−4.57608	+	2.64200i	−0.155772	+	0.0899348i	0.420088	+	0.907483i	$0.361999\pi$
$864$	−0.927912	+	5.26245i	−0.0315682	+	0.179032i
$865$		0			0
$866$	16.5340	+	28.6378i	0.561849	+	0.973151i
$867$	−22.4571	−	12.9656i	−0.762684	−	0.440336i
$868$	−9.68864	+	11.5465i	−0.328854	+	0.391913i
$869$	17.6736	+	6.43265i	0.599535	+	0.218213i
$870$		0			0
$871$	3.34382	−	2.80580i	0.113301	−	0.0950707i
$872$	−19.9402	+	3.51599i	−0.675260	+	0.119066i
$873$			0.499982i			0.0169218i
$874$	6.69703	+	6.83754i	0.226530	+	0.231283i
$875$		0			0
$876$	0.163339	+	0.926343i	0.00551872	+	0.0312982i
$877$	−32.4457	−	38.6673i	−1.09561	−	1.30570i	−0.948569	−	0.316572i	$-0.897468\pi$
$877$	−32.4457	−	38.6673i	−1.09561	−	1.30570i	−0.147045	−	0.989130i	$-0.546976\pi$
$878$	2.02205	+	5.55555i	0.0682410	+	0.187491i
$879$	31.5319	+	11.4767i	1.06354	+	0.387098i
$880$		0			0
$881$	−10.2170	+	17.6964i	−0.344221	+	0.596208i	−0.985212	−	0.171340i	$-0.945190\pi$
$881$	−10.2170	+	17.6964i	−0.344221	+	0.596208i	0.640991	+	0.767549i	$0.278524\pi$
$882$	0.139548	−	0.0805678i	0.00469881	−	0.00271286i
$883$	0.124596	+	0.0219697i	0.00419300	+	0.000739339i	0.175744	−	0.984436i	$-0.443767\pi$
$883$	0.124596	+	0.0219697i	0.00419300	+	0.000739339i	−0.171551	+	0.985175i	$0.554878\pi$
$884$	−0.279877	+	1.58726i	−0.00941329	+	0.0533854i
$885$		0			0
$886$	5.91634	−	10.2474i	0.198763	−	0.344268i
$887$	−16.6336	+	19.8231i	−0.558500	+	0.665594i	−0.969228	−	0.246163i	$-0.920830\pi$
$887$	−16.6336	+	19.8231i	−0.558500	+	0.665594i	0.410728	+	0.911758i	$0.365274\pi$
$888$	−0.829342	+	2.27860i	−0.0278309	+	0.0764648i
$889$	−0.304854	+	0.110958i	−0.0102245	+	0.00372141i
$890$		0			0
$891$	−4.23758	−	24.0325i	−0.141964	−	0.805120i
$892$		−	7.45336i		−	0.249557i
$893$	48.3620	−	3.72565i	1.61837	−	0.124674i
$894$	−25.4222			−0.850247
$895$		0			0
$896$	1.89633	−	1.59121i	0.0633520	−	0.0531586i
$897$	1.63385	+	4.48897i	0.0545527	+	0.149882i
$898$	2.59386	−	7.12658i	0.0865583	−	0.237817i
$899$	−30.2416	−	25.3757i	−1.00861	−	0.846327i
$900$		0			0
$901$	−7.48071	−	12.9570i	−0.249218	−	0.431659i
$902$	6.81047	+	1.20087i	0.226764	+	0.0399846i
$903$	37.6350	+	6.63606i	1.25241	+	0.220834i
$904$	8.27242	+	14.3283i	0.275137	+	0.476551i
$905$		0			0
$906$	7.43887	+	6.24195i	0.247140	+	0.207375i
$907$	18.4176	−	50.6020i	0.611547	−	1.68021i	−0.115229	−	0.993339i	$-0.536760\pi$
$907$	18.4176	−	50.6020i	0.611547	−	1.68021i	0.726777	−	0.686874i	$-0.241018\pi$
$908$	3.90473	+	10.7281i	0.129583	+	0.356026i
$909$	0.0166840	−	0.0139996i	0.000553374	−	0.000464336i
$910$		0			0
$911$	2.63989			0.0874634			0.0437317	−	0.999043i	$-0.486075\pi$
$911$	2.63989			0.0874634			0.0437317	+	0.999043i	$0.486075\pi$
$912$	7.29201	−	0.561752i	0.241463	−	0.0186015i
$913$		−	24.5287i		−	0.811781i
$914$	2.26812	+	12.8631i	0.0750227	+	0.425475i
$915$		0			0
$916$	3.00074	−	1.09218i	0.0991474	−	0.0360867i
$917$	10.8389	−	29.7796i	0.357932	−	0.983410i
$918$	−4.26945	+	5.08813i	−0.140913	+	0.167933i
$919$	−15.6083	+	27.0343i	−0.514869	+	0.891779i	0.484982	+	0.874524i	$0.338826\pi$
$919$	−15.6083	+	27.0343i	−0.514869	+	0.891779i	−0.999851	+	0.0172553i	$0.994507\pi$
$920$		0			0
$921$	−5.65286	+	32.0589i	−0.186268	+	1.05638i
$922$	−30.7684	−	5.42530i	−1.01330	−	0.178673i
$923$	17.0655	−	9.85275i	0.561717	−	0.324307i
$924$	−6.02506	+	10.4357i	−0.198210	+	0.343310i
$925$		0			0
$926$	−13.1215	−	4.77583i	−0.431199	−	0.156944i
$927$	−0.110060	−	0.302388i	−0.00361485	−	0.00993172i
$928$	4.16757	+	4.96672i	0.136807	+	0.163040i
$929$	−0.849031	−	4.81509i	−0.0278558	−	0.157978i	0.967707	−	0.252078i	$-0.0811139\pi$
$929$	−0.849031	−	4.81509i	−0.0278558	−	0.157978i	−0.995563	+	0.0940997i	$0.970003\pi$
$930$		0			0
$931$	−2.65958	−	2.71538i	−0.0871642	−	0.0889931i
$932$			23.2991i			0.763187i
$933$	−8.92110	+	1.57303i	−0.292064	+	0.0514987i
$934$	−9.04471	+	7.58941i	−0.295952	+	0.248333i
$935$		0			0
$936$	−0.225165	−	0.0819532i	−0.00735974	−	0.00267872i
$937$	5.11059	−	6.09056i	0.166956	−	0.198970i	−0.676079	−	0.736829i	$-0.736322\pi$
$937$	5.11059	−	6.09056i	0.166956	−	0.198970i	0.843035	+	0.537859i	$0.180767\pi$
$938$	−7.21688	−	4.16667i	−0.235639	−	0.136046i
$939$	−13.5767	−	23.5155i	−0.443059	−	0.767401i
$940$		0			0
$941$	−4.40739	+	24.9956i	−0.143677	+	0.814832i	0.824743	+	0.565508i	$0.191320\pi$
$941$	−4.40739	+	24.9956i	−0.143677	+	0.814832i	−0.968420	+	0.249325i	$0.919791\pi$
$942$	−16.0113	+	9.24411i	−0.521675	+	0.301189i
$943$	−4.53269	−	2.61695i	−0.147605	−	0.0852197i
$944$	1.54971	+	1.30037i	0.0504389	+	0.0423233i
$945$		0			0
$946$	−25.0834	+	9.12962i	−0.815532	+	0.296829i
$947$	19.0425	+	22.6940i	0.618799	+	0.737456i	0.980863	−	0.194697i	$-0.0623724\pi$
$947$	19.0425	+	22.6940i	0.618799	+	0.737456i	−0.362064	+	0.932153i	$0.617928\pi$
$948$	−10.7120	+	1.88881i	−0.347908	+	0.0613456i
$949$	−0.726934			−0.0235973
$950$		0			0
$951$	−4.11233			−0.133351
$952$	3.03025	−	0.534316i	0.0982111	−	0.0173173i
$953$	9.63837	+	11.4866i	0.312217	+	0.372086i	0.899218	−	0.437500i	$-0.144136\pi$
$953$	9.63837	+	11.4866i	0.312217	+	0.372086i	−0.587001	+	0.809586i	$0.699692\pi$
$954$	2.09014	−	0.760748i	0.0676708	−	0.0246301i
$955$		0			0
$956$	−6.29848	−	5.28505i	−0.203707	−	0.170931i
$957$	−27.3324	−	15.7803i	−0.883530	−	0.510106i
$958$	27.7577	−	16.0259i	0.896811	−	0.517774i
$959$	−6.71823	+	38.1010i	−0.216943	+	1.23034i
$960$		0			0
$961$	−3.03703	−	5.26029i	−0.0979688	−	0.169687i
$962$	−1.62288	−	0.936972i	−0.0523239	−	0.0302092i
$963$	−1.98442	+	2.36494i	−0.0639471	+	0.0762092i
$964$	19.5747	+	7.12460i	0.630458	+	0.229468i
$965$		0			0
$966$	6.98627	−	5.86218i	0.224779	−	0.188612i
$967$	13.6825	−	2.41259i	0.439998	−	0.0775835i	0.0507392	−	0.998712i	$-0.483842\pi$
$967$	13.6825	−	2.41259i	0.439998	−	0.0775835i	0.389259	+	0.921128i	$0.372731\pi$
$968$			2.58310i			0.0830240i
$969$	8.19869	+	3.92724i	0.263380	+	0.126161i
$970$		0			0
$971$	−2.47187	−	14.0186i	−0.0793260	−	0.449880i	−0.998437	−	0.0558821i	$-0.982203\pi$
$971$	−2.47187	−	14.0186i	−0.0793260	−	0.449880i	0.919111	−	0.393998i	$-0.128908\pi$
$972$	−1.23263	−	1.46899i	−0.0395366	−	0.0471179i
$973$	−9.71985	−	26.7051i	−0.311604	−	0.856125i
$974$	16.4207	+	5.97664i	0.526152	+	0.191504i
$975$		0			0
$976$	0.669649	−	1.15987i	0.0214349	−	0.0371264i
$977$	−7.14552	+	4.12547i	−0.228606	+	0.131985i	−0.609929	−	0.792456i	$-0.708802\pi$
$977$	−7.14552	+	4.12547i	−0.228606	+	0.131985i	0.381323	+	0.924442i	$0.375469\pi$
$978$	36.6482	+	6.46207i	1.17188	+	0.206634i
$979$	5.99507	−	33.9997i	0.191603	−	1.08664i
$980$		0			0
$981$	1.87082	−	3.24035i	0.0597307	−	0.103457i
$982$	1.36614	−	1.62811i	0.0435954	−	0.0519549i
$983$	4.49274	−	12.3437i	0.143296	−	0.393703i	−0.847194	−	0.531283i	$-0.821710\pi$
$983$	4.49274	−	12.3437i	0.143296	−	0.393703i	0.990491	+	0.137580i	$0.0439323\pi$
$984$	−3.75829	+	1.36791i	−0.119810	+	0.0436073i
$985$		0			0
$986$	1.39944	+	7.93660i	0.0445671	+	0.252753i
$987$		−	46.2197i		−	1.47119i
$988$	−0.551036	+	5.62513i	−0.0175308	+	0.178959i
$989$	20.2023			0.642396
$990$		0			0
$991$	−19.4973	+	16.3602i	−0.619352	+	0.519698i	−0.897600	−	0.440811i	$-0.854691\pi$
$991$	−19.4973	+	16.3602i	−0.619352	+	0.519698i	0.278248	+	0.960509i	$0.410246\pi$
$992$	2.08251	+	5.72164i	0.0661197	+	0.181662i
$993$	1.74238	−	4.78716i	0.0552929	−	0.151916i
$994$	−28.8185	−	24.1816i	−0.914068	−	0.766994i
$995$		0			0
$996$	7.09289	+	12.2852i	0.224747	+	0.389273i
$997$	−22.1625	−	3.90784i	−0.701892	−	0.123763i	−0.188698	−	0.982035i	$-0.560427\pi$
$997$	−22.1625	−	3.90784i	−0.701892	−	0.123763i	−0.513194	+	0.858273i	$0.671538\pi$
$998$	−35.8305	−	6.31789i	−1.13420	−	0.199989i
$999$	−3.86130	−	6.68796i	−0.122166	−	0.211598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.e.199.2		24
5.2	odd	4		190.2.k.b.161.2	yes	12
5.3	odd	4		950.2.l.h.351.1		12
5.4	even	2	inner	950.2.u.e.199.3		24
19.17	even	9	inner	950.2.u.e.549.3		24
95.17	odd	36		190.2.k.b.131.2	✓	12
95.32	even	36		3610.2.a.be.1.2		6
95.74	even	18	inner	950.2.u.e.549.2		24
95.82	odd	36		3610.2.a.bc.1.5		6
95.93	odd	36		950.2.l.h.701.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.131.2	✓	12	95.17	odd	36
190.2.k.b.161.2	yes	12	5.2	odd	4
950.2.l.h.351.1		12	5.3	odd	4
950.2.l.h.701.1		12	95.93	odd	36
950.2.u.e.199.2		24	1.1	even	1	trivial
950.2.u.e.199.3		24	5.4	even	2	inner
950.2.u.e.549.2		24	95.74	even	18	inner
950.2.u.e.549.3		24	19.17	even	9	inner
3610.2.a.bc.1.5		6	95.82	odd	36
3610.2.a.be.1.2		6	95.32	even	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.07851 + 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.28531 - 1.07851i) q^{6} +(-2.14383 - 1.23774i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.07851 + 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.28531 - 1.07851i) q^{6} +(-2.14383 - 1.23774i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +(-1.45059 - 2.51250i) q^{11} +(1.45307 + 0.838929i) q^{12} +(-0.833484 + 0.993308i) q^{13} +(2.32619 + 0.846665i) q^{14} +(0.766044 - 0.642788i) q^{16} +(1.22411 - 0.215843i) q^{17} +0.184793i q^{18} +(4.22186 - 1.08440i) q^{19} +(-0.721249 - 4.09041i) q^{21} +(1.86485 + 2.22244i) q^{22} +(-0.750979 - 2.06330i) q^{23} +(-1.57667 - 0.573861i) q^{24} +(0.648336 - 1.12295i) q^{26} +(4.62772 - 2.67181i) q^{27} +(-2.43788 - 0.429863i) q^{28} +(1.12586 - 6.38509i) q^{29} +(3.04442 - 5.27310i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(1.66488 - 4.57422i) q^{33} +(-1.16803 + 0.425128i) q^{34} +(-0.0320889 - 0.181985i) q^{36} -1.44520i q^{37} +(-3.96942 + 1.80104i) q^{38} -2.17563 q^{39} +(1.82601 - 1.53221i) q^{41} +(1.42058 + 3.90302i) q^{42} +(-3.14685 + 8.64591i) q^{43} +(-2.22244 - 1.86485i) q^{44} +(1.09786 + 1.90155i) q^{46} +(10.9588 + 1.93233i) q^{47} +(1.65237 + 0.291357i) q^{48} +(-0.435991 - 0.755158i) q^{49} +(1.59763 + 1.34057i) q^{51} +(-0.443488 + 1.21847i) q^{52} +(-4.11677 - 11.3107i) q^{53} +(-4.09346 + 3.43482i) q^{54} +2.47548 q^{56} +(5.94709 + 4.25688i) q^{57} +6.48359i q^{58} +(0.351292 + 1.99228i) q^{59} +(1.25853 - 0.458067i) q^{61} +(-2.08251 + 5.72164i) q^{62} +(-0.294044 + 0.350428i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.845282 + 4.79383i) q^{66} +(-3.31520 - 0.584560i) q^{67} +(1.07646 - 0.621495i) q^{68} +(1.84205 - 3.19052i) q^{69} +(-14.2805 - 5.19768i) q^{71} +(0.0632028 + 0.173648i) q^{72} +(0.360357 + 0.429457i) q^{73} +(0.250956 + 1.42324i) q^{74} +(3.59636 - 2.46296i) q^{76} +7.18185i q^{77} +(2.14258 - 0.377794i) q^{78} +(-4.96611 + 4.16706i) q^{79} +(7.90420 + 2.87689i) q^{81} +(-1.53221 + 1.82601i) q^{82} +(7.32198 + 4.22735i) q^{83} +(-2.07675 - 3.59705i) q^{84} +(1.59770 - 9.06100i) q^{86} +(9.42109 - 5.43927i) q^{87} +(2.51250 + 1.45059i) q^{88} +(9.11595 + 7.64919i) q^{89} +(3.01631 - 1.09785i) q^{91} +(-1.41138 - 1.68202i) q^{92} +(10.0610 - 1.77403i) q^{93} -11.1279 q^{94} -1.67786 q^{96} +(-2.66454 + 0.469830i) q^{97} +(0.560499 + 0.667976i) q^{98} +(-0.503786 + 0.183363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 36 q^{9}+O(q^{10}) \) 24 * q - 36 * q^9	\( 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) \) 24 * q - 36 * q^9 + 12 * q^11 + 24 * q^21 + 12 * q^29 + 12 * q^31 + 36 * q^36 + 72 * q^39 - 12 * q^41 - 12 * q^44 - 24 * q^46 + 36 * q^49 + 24 * q^56 + 48 * q^59 - 60 * q^61 + 12 * q^64 + 48 * q^66 - 12 * q^69 - 84 * q^71 - 12 * q^74 + 36 * q^76 - 120 * q^79 + 36 * q^81 + 48 * q^84 - 72 * q^86 + 24 * q^89 + 48 * q^91 - 120 * q^94 + 24 * q^99

Introduction

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