LMFDB - Embedded newform 950.2.q.g.293.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.8
Character	$\chi$	$=$	950.293
Dual form			950.2.q.g.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.869171 + 3.24379i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.67911 + 2.90830i) q^{6} +(-2.68888 + 2.68888i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-7.16865 + 4.13882i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.869171 + 3.24379i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.67911 + 2.90830i) q^{6} +(-2.68888 + 2.68888i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-7.16865 + 4.13882i) q^{9} +1.84171 q^{11} +(2.37462 + 2.37462i) q^{12} +(2.21346 + 0.593094i) q^{13} +(-1.90133 + 3.29320i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.0569314 + 0.212471i) q^{17} +(-5.85318 + 5.85318i) q^{18} +(-3.81269 - 2.11268i) q^{19} +(-11.0593 - 6.38508i) q^{21} +(1.77896 - 0.476670i) q^{22} +(0.872284 - 3.25541i) q^{23} +(2.90830 + 1.67911i) q^{24} +2.29154 q^{26} +(-12.5324 - 12.5324i) q^{27} +(-0.984199 + 3.67308i) q^{28} +(1.14196 + 1.97793i) q^{29} +3.03743i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.60076 + 5.97413i) q^{33} +(0.109983 + 0.190496i) q^{34} +(-4.13882 + 7.16865i) q^{36} +(5.08146 + 5.08146i) q^{37} +(-4.22957 - 1.05390i) q^{38} +7.69550i q^{39} +(8.86161 + 5.11625i) q^{41} +(-12.3350 - 3.30516i) q^{42} +(-2.40138 + 0.643448i) q^{43} +(1.59497 - 0.920856i) q^{44} -3.37025i q^{46} +(-0.816355 - 0.218742i) q^{47} +(3.24379 + 0.869171i) q^{48} -7.46018i q^{49} +(-0.639729 + 0.369347i) q^{51} +(2.21346 - 0.593094i) q^{52} +(-1.20622 - 0.323205i) q^{53} +(-15.3490 - 8.86175i) q^{54} +3.80265i q^{56} +(3.53923 - 14.2038i) q^{57} +(1.61497 + 1.61497i) q^{58} +(3.04615 - 5.27609i) q^{59} +(3.23884 + 5.60984i) q^{61} +(0.786144 + 2.93393i) q^{62} +(8.14685 - 30.4045i) q^{63} -1.00000i q^{64} +(3.09244 + 5.35626i) q^{66} +(-1.63025 + 6.08417i) q^{67} +(0.155540 + 0.155540i) q^{68} +11.3180 q^{69} +(-2.74701 - 1.58598i) q^{71} +(-2.14241 + 7.99559i) q^{72} +(-2.13784 + 0.572834i) q^{73} +(6.22350 + 3.59314i) q^{74} +(-4.35822 + 0.0767059i) q^{76} +(-4.95215 + 4.95215i) q^{77} +(1.99174 + 7.43328i) q^{78} +(2.94924 - 5.10824i) q^{79} +(17.3432 - 30.0394i) q^{81} +(9.88384 + 2.64837i) q^{82} +(-0.543549 - 0.543549i) q^{83} -12.7702 q^{84} +(-2.15302 + 1.24305i) q^{86} +(-5.42343 + 5.42343i) q^{87} +(1.30229 - 1.30229i) q^{88} +(8.67114 + 15.0189i) q^{89} +(-7.54649 + 4.35697i) q^{91} +(-0.872284 - 3.25541i) q^{92} +(-9.85278 + 2.64005i) q^{93} -0.845153 q^{94} +3.35822 q^{96} +(6.07404 - 1.62754i) q^{97} +(-1.93084 - 7.20598i) q^{98} +(-13.2026 + 7.62252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) $ 32 * q + 12 * q^3 - 24 * q^7	$ 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.869171	+	3.24379i	0.501816	+	1.87280i	0.487897	+	0.872901i	$0.337764\pi$
$3$	0.869171	+	3.24379i	0.501816	+	1.87280i	0.0139189	+	0.999903i	$0.495569\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.67911	+	2.90830i	0.685494	+	1.18731i
$7$	−2.68888	+	2.68888i	−1.01630	+	1.01630i	−0.0164373	+	0.999865i	$0.505232\pi$
$7$	−2.68888	+	2.68888i	−1.01630	+	1.01630i	−0.999865	+	0.0164373i	$0.994768\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−7.16865	+	4.13882i	−2.38955	+	1.37961i
$10$		0			0
$11$	1.84171			0.555297			0.277649	−	0.960683i	$-0.410445\pi$
$11$	1.84171			0.555297			0.277649	+	0.960683i	$0.410445\pi$
$12$	2.37462	+	2.37462i	0.685494	+	0.685494i
$13$	2.21346	+	0.593094i	0.613903	+	0.164495i	0.552355	−	0.833609i	$-0.313729\pi$
$13$	2.21346	+	0.593094i	0.613903	+	0.164495i	0.0615484	+	0.998104i	$0.480396\pi$
$14$	−1.90133	+	3.29320i	−0.508151	+	0.880144i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.0569314	+	0.212471i	0.0138079	+	0.0515318i	0.972486	−	0.232961i	$-0.0748415\pi$
$17$	0.0569314	+	0.212471i	0.0138079	+	0.0515318i	−0.958678	+	0.284493i	$0.908175\pi$
$18$	−5.85318	+	5.85318i	−1.37961	+	1.37961i
$19$	−3.81269	−	2.11268i	−0.874690	−	0.484683i
$19$	−3.81269	−	2.11268i	−0.874690	−	0.484683i
$20$		0			0
$21$	−11.0593	−	6.38508i	−2.41333	−	1.39334i
$22$	1.77896	−	0.476670i	0.379275	−	0.101626i
$23$	0.872284	−	3.25541i	0.181884	−	0.678799i	−0.813392	−	0.581715i	$-0.802382\pi$
$23$	0.872284	−	3.25541i	0.181884	−	0.678799i	0.995276	−	0.0970841i	$-0.0309516\pi$
$24$	2.90830	+	1.67911i	0.593655	+	0.342747i
$25$		0			0
$26$	2.29154			0.449408
$27$	−12.5324	−	12.5324i	−2.41186	−	2.41186i
$28$	−0.984199	+	3.67308i	−0.185996	+	0.694147i
$29$	1.14196	+	1.97793i	0.212056	+	0.367292i	0.952358	−	0.304983i	$-0.0986507\pi$
$29$	1.14196	+	1.97793i	0.212056	+	0.367292i	−0.740302	+	0.672275i	$0.765317\pi$
$30$		0			0
$31$			3.03743i			0.545538i	0.962080	+	0.272769i	$0.0879395\pi$
$31$			3.03743i			0.545538i	−0.962080	+	0.272769i	$0.912061\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.60076	+	5.97413i	0.278657	+	1.03996i
$34$	0.109983	+	0.190496i	0.0188619	+	0.0326698i
$35$		0			0
$36$	−4.13882	+	7.16865i	−0.689804	+	1.19478i
$37$	5.08146	+	5.08146i	0.835387	+	0.835387i	0.988248	−	0.152860i	$-0.0488485\pi$
$37$	5.08146	+	5.08146i	0.835387	+	0.835387i	−0.152860	+	0.988248i	$0.548848\pi$
$38$	−4.22957	−	1.05390i	−0.686128	−	0.170965i
$39$			7.69550i			1.23227i
$40$		0			0
$41$	8.86161	+	5.11625i	1.38395	+	0.799024i	0.992625	−	0.121228i	$-0.0386831\pi$
$41$	8.86161	+	5.11625i	1.38395	+	0.799024i	0.391326	+	0.920252i	$0.372016\pi$
$42$	−12.3350	−	3.30516i	−1.90333	−	0.509997i
$43$	−2.40138	+	0.643448i	−0.366207	+	0.0981249i	−0.437230	−	0.899350i	$-0.644040\pi$
$43$	−2.40138	+	0.643448i	−0.366207	+	0.0981249i	0.0710227	+	0.997475i	$0.477374\pi$
$44$	1.59497	−	0.920856i	0.240451	−	0.138824i
$45$		0			0
$46$		−	3.37025i		−	0.496916i
$47$	−0.816355	−	0.218742i	−0.119078	−	0.0319068i	0.198788	−	0.980043i	$-0.436299\pi$
$47$	−0.816355	−	0.218742i	−0.119078	−	0.0319068i	−0.317866	+	0.948136i	$0.602966\pi$
$48$	3.24379	+	0.869171i	0.468201	+	0.125454i
$49$		−	7.46018i		−	1.06574i
$50$		0			0
$51$	−0.639729	+	0.369347i	−0.0895799	+	0.0517190i
$52$	2.21346	−	0.593094i	0.306951	−	0.0822474i
$53$	−1.20622	−	0.323205i	−0.165687	−	0.0443956i	0.175022	−	0.984565i	$-0.444000\pi$
$53$	−1.20622	−	0.323205i	−0.165687	−	0.0443956i	−0.340709	+	0.940169i	$0.610667\pi$
$54$	−15.3490	−	8.86175i	−2.08873	−	1.20593i
$55$		0			0
$56$			3.80265i			0.508151i
$57$	3.53923	−	14.2038i	0.468782	−	1.88134i
$58$	1.61497	+	1.61497i	0.212056	+	0.212056i
$59$	3.04615	−	5.27609i	0.396575	−	0.686888i	−0.596726	−	0.802445i	$-0.703532\pi$
$59$	3.04615	−	5.27609i	0.396575	−	0.686888i	0.993301	+	0.115557i	$0.0368653\pi$
$60$		0			0
$61$	3.23884	+	5.60984i	0.414691	+	0.718266i	0.995396	−	0.0958480i	$-0.0305563\pi$
$61$	3.23884	+	5.60984i	0.414691	+	0.718266i	−0.580705	+	0.814114i	$0.697223\pi$
$62$	0.786144	+	2.93393i	0.0998404	+	0.372609i
$63$	8.14685	−	30.4045i	1.02641	−	3.83060i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	3.09244	+	5.35626i	0.380653	+	0.659310i
$67$	−1.63025	+	6.08417i	−0.199166	+	0.743299i	0.791982	+	0.610544i	$0.209049\pi$
$67$	−1.63025	+	6.08417i	−0.199166	+	0.743299i	−0.991149	+	0.132755i	$0.957618\pi$
$68$	0.155540	+	0.155540i	0.0188619	+	0.0188619i
$69$	11.3180			1.36253
$70$		0			0
$71$	−2.74701	−	1.58598i	−0.326010	−	0.188222i	0.328058	−	0.944657i	$-0.393606\pi$
$71$	−2.74701	−	1.58598i	−0.326010	−	0.188222i	−0.654068	+	0.756436i	$0.726939\pi$
$72$	−2.14241	+	7.99559i	−0.252486	+	0.942289i
$73$	−2.13784	+	0.572834i	−0.250216	+	0.0670451i	−0.381747	−	0.924267i	$-0.624677\pi$
$73$	−2.13784	+	0.572834i	−0.250216	+	0.0670451i	0.131531	+	0.991312i	$0.458011\pi$
$74$	6.22350	+	3.59314i	0.723467	+	0.417694i
$75$		0			0
$76$	−4.35822	+	0.0767059i	−0.499923	+	0.00879877i
$77$	−4.95215	+	4.95215i	−0.564350	+	0.564350i
$78$	1.99174	+	7.43328i	0.225520	+	0.841653i
$79$	2.94924	−	5.10824i	0.331816	−	0.574722i	−0.651052	−	0.759033i	$-0.725672\pi$
$79$	2.94924	−	5.10824i	0.331816	−	0.574722i	0.982868	+	0.184311i	$0.0590054\pi$
$80$		0			0
$81$	17.3432	−	30.0394i	1.92703	−	3.33771i
$82$	9.88384	+	2.64837i	1.09149	+	0.292463i
$83$	−0.543549	−	0.543549i	−0.0596623	−	0.0596623i	0.676646	−	0.736308i	$-0.263433\pi$
$83$	−0.543549	−	0.543549i	−0.0596623	−	0.0596623i	−0.736308	+	0.676646i	$0.763433\pi$
$84$	−12.7702			−1.39334
$85$		0			0
$86$	−2.15302	+	1.24305i	−0.232166	+	0.134041i
$87$	−5.42343	+	5.42343i	−0.581453	+	0.581453i
$88$	1.30229	−	1.30229i	0.138824	−	0.138824i
$89$	8.67114	+	15.0189i	0.919139	+	1.59200i	0.800725	+	0.599032i	$0.204448\pi$
$89$	8.67114	+	15.0189i	0.919139	+	1.59200i	0.118414	+	0.992964i	$0.462219\pi$
$90$		0			0
$91$	−7.54649	+	4.35697i	−0.791087	+	0.456734i
$92$	−0.872284	−	3.25541i	−0.0909419	−	0.339400i
$93$	−9.85278	+	2.64005i	−1.02169	+	0.273760i
$94$	−0.845153			−0.0871709
$95$		0			0
$96$	3.35822			0.342747
$97$	6.07404	−	1.62754i	0.616726	−	0.165251i	0.0630869	−	0.998008i	$-0.479905\pi$
$97$	6.07404	−	1.62754i	0.616726	−	0.165251i	0.553639	+	0.832757i	$0.313239\pi$
$98$	−1.93084	−	7.20598i	−0.195044	−	0.727914i
$99$	−13.2026	+	7.62252i	−1.32691	+	0.766092i
$100$		0			0
$101$	2.36161	+	4.09042i	0.234989	+	0.407012i	0.959269	−	0.282493i	$-0.0911614\pi$
$101$	2.36161	+	4.09042i	0.234989	+	0.407012i	−0.724281	+	0.689505i	$0.757828\pi$
$102$	−0.522336	+	0.522336i	−0.0517190	+	0.0517190i
$103$	−3.73194	+	3.73194i	−0.367719	+	0.367719i	−0.866645	−	0.498925i	$-0.833728\pi$
$103$	−3.73194	+	3.73194i	−0.367719	+	0.367719i	0.498925	+	0.866645i	$0.333728\pi$
$104$	1.98453	−	1.14577i	0.194599	−	0.112352i
$105$		0			0
$106$	−1.24877			−0.121291
$107$	−0.314005	−	0.314005i	−0.0303560	−	0.0303560i	0.691766	−	0.722122i	$-0.256833\pi$
$107$	−0.314005	−	0.314005i	−0.0303560	−	0.0303560i	−0.722122	+	0.691766i	$0.756833\pi$
$108$	−17.1196	−	4.58718i	−1.64733	−	0.441401i
$109$	1.09411	−	1.89506i	0.104797	−	0.181514i	−0.808858	−	0.588004i	$-0.799914\pi$
$109$	1.09411	−	1.89506i	0.104797	−	0.181514i	0.913655	+	0.406490i	$0.133247\pi$
$110$		0			0
$111$	−12.0665	+	20.8999i	−1.14531	+	1.98373i
$112$	0.984199	+	3.67308i	0.0929981	+	0.347074i
$113$	12.5449	−	12.5449i	1.18013	−	1.18013i	0.200416	−	0.979711i	$-0.435771\pi$
$113$	12.5449	−	12.5449i	1.18013	−	1.18013i	0.979711	−	0.200416i	$-0.0642292\pi$
$114$	−0.257595	−	14.6359i	−0.0241260	−	1.37078i
$115$		0			0
$116$	1.97793	+	1.14196i	0.183646	+	0.106028i
$117$	−18.3222	+	4.90942i	−1.69389	+	0.453876i
$118$	1.57680	−	5.88471i	0.145157	−	0.541732i
$119$	−0.724392	−	0.418228i	−0.0664049	−	0.0383389i
$120$		0			0
$121$	−7.60809			−0.691645
$122$	4.58041	+	4.58041i	0.414691	+	0.414691i
$123$	−8.89380	+	33.1921i	−0.801927	+	2.99283i
$124$	1.51871	+	2.63049i	0.136385	+	0.236225i
$125$		0			0
$126$		−	31.4770i		−	2.80420i
$127$	1.00109	−	3.73612i	0.0888323	−	0.331527i	−0.907180	−	0.420743i	$-0.861769\pi$
$127$	1.00109	−	3.73612i	0.0888323	−	0.331527i	0.996012	+	0.0892161i	$0.0284362\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−4.17442	−	7.23031i	−0.367537	−	0.636594i
$130$		0			0
$131$	−1.96904	+	3.41048i	−0.172036	+	0.297975i	−0.939132	−	0.343558i	$-0.888368\pi$
$131$	−1.96904	+	3.41048i	−0.172036	+	0.297975i	0.767095	+	0.641533i	$0.221701\pi$
$132$	4.37337	+	4.37337i	0.380653	+	0.380653i
$133$	15.9326	−	4.57111i	1.38153	−	0.396365i
$134$			6.29879i			0.544133i
$135$		0			0
$136$	0.190496	+	0.109983i	0.0163349	+	0.00943097i
$137$	19.8028	+	5.30614i	1.69187	+	0.453334i	0.970871	−	0.239604i	$-0.0770177\pi$
$137$	19.8028	+	5.30614i	1.69187	+	0.453334i	0.720997	+	0.692939i	$0.243684\pi$
$138$	10.9324	−	2.92932i	0.930626	−	0.249360i
$139$	10.0826	−	5.82117i	0.855191	−	0.493745i	−0.00720779	−	0.999974i	$-0.502294\pi$
$139$	10.0826	−	5.82117i	0.855191	−	0.493745i	0.862399	+	0.506229i	$0.168961\pi$
$140$		0			0
$141$		−	2.83821i		−	0.239020i
$142$	−3.06389	−	0.820966i	−0.257116	−	0.0688939i
$143$	4.07656	+	1.09231i	0.340899	+	0.0913435i
$144$			8.27764i			0.689804i
$145$		0			0
$146$	−1.91674	+	1.10663i	−0.158630	+	0.0915853i
$147$	24.1993	−	6.48418i	1.99592	−	0.534806i
$148$	6.94141	+	1.85994i	0.570580	+	0.152887i
$149$	−7.73990	−	4.46863i	−0.634077	−	0.366085i	0.148252	−	0.988950i	$-0.452635\pi$
$149$	−7.73990	−	4.46863i	−0.634077	−	0.366085i	−0.782329	+	0.622865i	$0.785969\pi$
$150$		0			0
$151$			1.80751i			0.147093i	0.997292	+	0.0735465i	$0.0234317\pi$
$151$			1.80751i			0.147093i	−0.997292	+	0.0735465i	$0.976568\pi$
$152$	−4.18987	+	1.20208i	−0.339843	+	0.0975019i
$153$	−1.28750	−	1.28750i	−0.104088	−	0.104088i
$154$	−3.50170	+	6.06512i	−0.282175	+	0.488741i
$155$		0			0
$156$	3.84775	+	6.66450i	0.308067	+	0.533587i
$157$	−3.71774	−	13.8748i	−0.296708	−	1.10733i	−0.939852	−	0.341583i	$-0.889037\pi$
$157$	−3.71774	−	13.8748i	−0.296708	−	1.10733i	0.643144	−	0.765745i	$-0.277630\pi$
$158$	1.52664	−	5.69750i	0.121453	−	0.453269i
$159$		−	4.19364i		−	0.332577i
$160$		0			0
$161$	6.40794	+	11.0989i	0.505017	+	0.874714i
$162$	8.97752	−	33.5046i	0.705340	−	2.63237i
$163$	1.40807	+	1.40807i	0.110289	+	0.110289i	0.760098	−	0.649809i	$-0.225151\pi$
$163$	1.40807	+	1.40807i	0.110289	+	0.110289i	−0.649809	+	0.760098i	$0.725151\pi$
$164$	10.2325			0.799024
$165$		0			0
$166$	−0.665709	−	0.384347i	−0.0516690	−	0.0298311i
$167$	5.22819	−	19.5119i	0.404569	−	1.50987i	−0.400279	−	0.916393i	$-0.631087\pi$
$167$	5.22819	−	19.5119i	0.404569	−	1.50987i	0.804848	−	0.593480i	$-0.202247\pi$
$168$	−12.3350	+	3.30516i	−0.951667	+	0.254999i
$169$	−6.71069	−	3.87442i	−0.516207	−	0.298032i
$170$		0			0
$171$	36.0758	−	0.634944i	2.75879	−	0.0485554i
$172$	−1.75793	+	1.75793i	−0.134041	+	0.134041i
$173$	3.39934	+	12.6865i	0.258447	+	0.964539i	0.966140	+	0.258018i	$0.0830695\pi$
$173$	3.39934	+	12.6865i	0.258447	+	0.964539i	−0.707693	+	0.706520i	$0.750264\pi$
$174$	−3.83494	+	6.64232i	−0.290726	+	0.503553i
$175$		0			0
$176$	0.920856	−	1.59497i	0.0694122	−	0.120225i
$177$	19.7622	+	5.29525i	1.48541	+	0.398016i
$178$	12.2628	+	12.2628i	0.919139	+	0.919139i
$179$	7.55973			0.565041			0.282521	−	0.959261i	$-0.408829\pi$
$179$	7.55973			0.565041			0.282521	+	0.959261i	$0.408829\pi$
$180$		0			0
$181$	11.6291	−	6.71405i	0.864383	−	0.499052i	−0.00109481	−	0.999999i	$-0.500348\pi$
$181$	11.6291	−	6.71405i	0.864383	−	0.499052i	0.865477	+	0.500948i	$0.167015\pi$
$182$	−6.16168	+	6.16168i	−0.456734	+	0.456734i
$183$	−15.3820	+	15.3820i	−1.13707	+	1.13707i
$184$	−1.68512	−	2.91872i	−0.124229	−	0.215171i
$185$		0			0
$186$	−8.83376	+	5.10018i	−0.647723	+	0.373963i
$187$	0.104851	+	0.391311i	0.00766749	+	0.0286155i
$188$	−0.816355	+	0.218742i	−0.0595388	+	0.0159534i
$189$	67.3963			4.90236
$190$		0			0
$191$	−22.8015			−1.64986			−0.824928	−	0.565238i	$-0.808784\pi$
$191$	−22.8015			−1.64986			−0.824928	+	0.565238i	$0.808784\pi$
$192$	3.24379	−	0.869171i	0.234101	−	0.0627270i
$193$	−2.05099	−	7.65439i	−0.147633	−	0.550975i	−0.999624	−	0.0274181i	$-0.991271\pi$
$193$	−2.05099	−	7.65439i	−0.147633	−	0.550975i	0.851991	−	0.523557i	$-0.175395\pi$
$194$	5.44584	−	3.14416i	0.390989	−	0.225737i
$195$		0			0
$196$	−3.73009	−	6.46071i	−0.266435	−	0.461479i
$197$	−12.0169	+	12.0169i	−0.856169	+	0.856169i	−0.990884	−	0.134716i	$-0.956988\pi$
$197$	−12.0169	+	12.0169i	−0.856169	+	0.856169i	0.134716	+	0.990884i	$0.456988\pi$
$198$	−10.7799	+	10.7799i	−0.766092	+	0.766092i
$199$	−10.3210	+	5.95882i	−0.731635	+	0.422410i	−0.819020	−	0.573765i	$-0.805482\pi$
$199$	−10.3210	+	5.95882i	−0.731635	+	0.422410i	0.0873850	+	0.996175i	$0.472149\pi$
$200$		0			0
$201$	−21.1527			−1.49200
$202$	3.33981	+	3.33981i	0.234989	+	0.234989i
$203$	−8.38900	−	2.24783i	−0.588793	−	0.157767i
$204$	−0.369347	+	0.639729i	−0.0258595	+	0.0447900i
$205$		0			0
$206$	−2.63888	+	4.57068i	−0.183860	+	0.318454i
$207$	7.22046	+	26.9471i	0.501856	+	1.87295i
$208$	1.62036	−	1.62036i	0.112352	−	0.112352i
$209$	−7.02187	−	3.89096i	−0.485713	−	0.269143i
$210$		0			0
$211$	12.0000	+	6.92819i	0.826112	+	0.476956i	0.852520	−	0.522695i	$-0.175073\pi$
$211$	12.0000	+	6.92819i	0.826112	+	0.476956i	−0.0264075	+	0.999651i	$0.508407\pi$
$212$	−1.20622	+	0.323205i	−0.0828434	+	0.0221978i
$213$	2.75698	−	10.2892i	0.188905	−	0.705005i
$214$	−0.384576	−	0.222035i	−0.0262891	−	0.0151780i
$215$		0			0
$216$	−17.7235			−1.20593
$217$	−8.16729	−	8.16729i	−0.554432	−	0.554432i
$218$	0.566354	−	2.11366i	0.0383583	−	0.143155i
$219$	−3.71631	−	6.43683i	−0.251125	−	0.434961i
$220$		0			0
$221$			0.504061i			0.0339068i
$222$	−6.24610	+	23.3108i	−0.419211	+	1.56452i
$223$	−5.46672	−	20.4021i	−0.366079	−	1.36622i	−0.865953	−	0.500126i	$-0.833287\pi$
$223$	−5.46672	−	20.4021i	−0.366079	−	1.36622i	0.499874	−	0.866098i	$-0.333380\pi$
$224$	1.90133	+	3.29320i	0.127038	+	0.220036i
$225$		0			0
$226$	8.87060	−	15.3643i	0.590063	−	1.02202i
$227$	11.9610	+	11.9610i	0.793882	+	0.793882i	0.982123	−	0.188241i	$-0.0602787\pi$
$227$	11.9610	+	11.9610i	0.793882	+	0.793882i	−0.188241	+	0.982123i	$0.560279\pi$
$228$	−4.03686	−	14.0705i	−0.267348	−	0.931842i
$229$			27.2306i			1.79945i	0.436460	+	0.899724i	$0.356232\pi$
$229$			27.2306i			1.79945i	−0.436460	+	0.899724i	$0.643768\pi$
$230$		0			0
$231$	−20.3680	−	11.7595i	−1.34012	−	0.773717i
$232$	2.20609	+	0.591120i	0.144837	+	0.0388090i
$233$	0.348554	−	0.0933947i	0.0228345	−	0.00611849i	−0.247384	−	0.968918i	$-0.579571\pi$
$233$	0.348554	−	0.0933947i	0.0228345	−	0.00611849i	0.270218	+	0.962799i	$0.412904\pi$
$234$	−16.4273	+	9.48428i	−1.07388	+	0.620007i
$235$		0			0
$236$		−	6.09230i		−	0.396575i
$237$	19.1335	+	5.12679i	1.24285	+	0.333021i
$238$	−0.807954	−	0.216491i	−0.0523719	−	0.0140330i
$239$		−	13.8441i		−	0.895503i	−0.894158	−	0.447752i	$-0.852225\pi$
$239$		−	13.8441i		−	0.895503i	0.894158	−	0.447752i	$-0.147775\pi$
$240$		0			0
$241$	23.8040	−	13.7432i	1.53335	−	0.885279i	0.534144	−	0.845394i	$-0.320634\pi$
$241$	23.8040	−	13.7432i	1.53335	−	0.885279i	0.999204	−	0.0398850i	$-0.0126992\pi$
$242$	−7.34885	+	1.96912i	−0.472402	+	0.126580i
$243$	61.1569	+	16.3870i	3.92322	+	1.05122i
$244$	5.60984	+	3.23884i	0.359133	+	0.207346i
$245$		0			0
$246$			34.3630i			2.19091i
$247$	−7.18620	−	6.93762i	−0.457247	−	0.441430i
$248$	2.14779	+	2.14779i	0.136385	+	0.136385i
$249$	1.29072	−	2.23560i	0.0817962	−	0.141675i
$250$		0			0
$251$	−13.2016	−	22.8659i	−0.833279	−	1.44328i	−0.895424	−	0.445215i	$-0.853127\pi$
$251$	−13.2016	−	22.8659i	−0.833279	−	1.44328i	0.0621447	−	0.998067i	$-0.480206\pi$
$252$	−8.14685	−	30.4045i	−0.513204	−	1.91530i
$253$	1.60650	−	5.99553i	0.101000	−	0.376936i
$254$		−	3.86791i		−	0.242694i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.39190	−	8.92670i	0.149203	−	0.556832i	−0.850330	−	0.526250i	$-0.823597\pi$
$257$	2.39190	−	8.92670i	0.149203	−	0.556832i	0.999532	−	0.0305815i	$-0.00973591\pi$
$258$	−5.90353	−	5.90353i	−0.367537	−	0.367537i
$259$	−27.3269			−1.69801
$260$		0			0
$261$	−16.3726	−	9.45271i	−1.01344	−	0.585108i
$262$	−1.01925	+	3.80390i	−0.0629696	+	0.235006i
$263$	−8.20956	+	2.19974i	−0.506223	+	0.135642i	−0.502887	−	0.864352i	$-0.667729\pi$
$263$	−8.20956	+	2.19974i	−0.506223	+	0.135642i	−0.00333631	+	0.999994i	$0.501062\pi$
$264$	5.35626	+	3.09244i	0.329655	+	0.190326i
$265$		0			0
$266$	14.2066	−	8.53902i	0.871065	−	0.523561i
$267$	−41.1813	+	41.1813i	−2.52026	+	2.52026i
$268$	1.63025	+	6.08417i	0.0995832	+	0.371650i
$269$	−6.08475	+	10.5391i	−0.370994	+	0.642580i	−0.989719	−	0.143027i	$-0.954316\pi$
$269$	−6.08475	+	10.5391i	−0.370994	+	0.642580i	0.618725	+	0.785608i	$0.287650\pi$
$270$		0			0
$271$	6.69863	−	11.6024i	0.406913	−	0.704794i	−0.587629	−	0.809130i	$-0.699939\pi$
$271$	6.69863	−	11.6024i	0.406913	−	0.704794i	0.994542	+	0.104337i	$0.0332719\pi$
$272$	0.212471	+	0.0569314i	0.0128829	+	0.00345198i
$273$	−20.6923	−	20.6923i	−1.25235	−	1.25235i
$274$	20.5014			1.23853
$275$		0			0
$276$	9.80170	−	5.65901i	0.589993	−	0.340633i
$277$	4.26939	−	4.26939i	0.256523	−	0.256523i	−0.567115	−	0.823638i	$-0.691941\pi$
$277$	4.26939	−	4.26939i	0.256523	−	0.256523i	0.823638	+	0.567115i	$0.191941\pi$
$278$	8.23237	−	8.23237i	0.493745	−	0.493745i
$279$	−12.5714	−	21.7743i	−0.752628	−	1.30359i
$280$		0			0
$281$	−16.7012	+	9.64245i	−0.996311	+	0.575220i	−0.907155	−	0.420797i	$-0.861750\pi$
$281$	−16.7012	+	9.64245i	−0.996311	+	0.575220i	−0.0891562	+	0.996018i	$0.528417\pi$
$282$	−0.734583	−	2.74150i	−0.0437438	−	0.163254i
$283$	18.5602	−	4.97318i	1.10329	−	0.295625i	0.339185	−	0.940720i	$-0.389849\pi$
$283$	18.5602	−	4.97318i	1.10329	−	0.295625i	0.764103	+	0.645095i	$0.223182\pi$
$284$	−3.17197			−0.188222
$285$		0			0
$286$	4.22036			0.249555
$287$	−37.5848	+	10.0708i	−2.21856	+	0.594462i
$288$	2.14241	+	7.99559i	0.126243	+	0.471145i
$289$	14.6805	−	8.47581i	0.863561	−	0.498577i
$290$		0			0
$291$	10.5588	+	18.2883i	0.618966	+	1.07208i
$292$	−1.56501	+	1.56501i	−0.0915853	+	0.0915853i
$293$	−0.452586	+	0.452586i	−0.0264404	+	0.0264404i	−0.720203	−	0.693763i	$-0.755952\pi$
$293$	−0.452586	+	0.452586i	−0.0264404	+	0.0264404i	0.693763	+	0.720203i	$0.255952\pi$
$294$	21.6965	−	12.5265i	1.26536	−	0.730559i
$295$		0			0
$296$	7.18627			0.417694
$297$	−23.0811	−	23.0811i	−1.33930	−	1.33930i
$298$	−8.63273	−	2.31313i	−0.500081	−	0.133996i
$299$	3.86153	−	6.68836i	0.223318	−	0.386798i
$300$		0			0
$301$	4.72688	−	8.18719i	0.272453	−	0.471902i
$302$	0.467818	+	1.74592i	0.0269199	+	0.100466i
$303$	−11.2158	+	11.2158i	−0.644333	+	0.644333i
$304$	−3.73598	+	2.24554i	−0.214273	+	0.128791i
$305$		0			0
$306$	−1.57686	−	0.910401i	−0.0901431	−	0.0520442i
$307$	22.0022	−	5.89547i	1.25573	−	0.336472i	0.431183	−	0.902265i	$-0.358096\pi$
$307$	22.0022	−	5.89547i	1.25573	−	0.336472i	0.824548	+	0.565793i	$0.191430\pi$
$308$	−1.81261	+	6.76476i	−0.103283	+	0.385458i
$309$	−15.3494	−	8.86195i	−0.873194	−	0.504139i
$310$		0			0
$311$	−26.4815			−1.50163			−0.750813	−	0.660515i	$-0.770338\pi$
$311$	−26.4815			−1.50163			−0.750813	+	0.660515i	$0.770338\pi$
$312$	5.44154	+	5.44154i	0.308067	+	0.308067i
$313$	2.14638	−	8.01041i	0.121321	−	0.452775i	−0.878361	−	0.477998i	$-0.841363\pi$
$313$	2.14638	−	8.01041i	0.121321	−	0.452775i	0.999682	+	0.0252224i	$0.00802939\pi$
$314$	−7.18212	−	12.4398i	−0.405310	−	0.702018i
$315$		0			0
$316$		−	5.89849i		−	0.331816i
$317$	3.77106	−	14.0738i	0.211804	−	0.790463i	−0.775463	−	0.631393i	$-0.782484\pi$
$317$	3.77106	−	14.0738i	0.211804	−	0.790463i	0.987267	−	0.159071i	$-0.0508497\pi$
$318$	−1.08539	−	4.05075i	−0.0608659	−	0.227155i
$319$	2.10316	+	3.64277i	0.117754	+	0.203956i
$320$		0			0
$321$	0.745643	−	1.29149i	0.0416178	−	0.0720841i
$322$	9.06220	+	9.06220i	0.505017	+	0.505017i
$323$	0.231822	−	0.930363i	0.0128989	−	0.0517668i
$324$		−	34.6865i		−	1.92703i
$325$		0			0
$326$	1.72453	+	0.995656i	0.0955127	+	0.0551443i
$327$	7.09814	+	1.90194i	0.392528	+	0.105178i
$328$	9.88384	−	2.64837i	0.545744	−	0.146232i
$329$	2.78326	−	1.60691i	0.153446	−	0.0885920i
$330$		0			0
$331$		−	28.9972i		−	1.59383i	−0.604090	−	0.796916i	$-0.706463\pi$
$331$		−	28.9972i		−	1.59383i	0.604090	−	0.796916i	$-0.293537\pi$
$332$	−0.742502	−	0.198953i	−0.0407501	−	0.0109190i
$333$	−57.4585	−	15.3960i	−3.14871	−	0.843693i
$334$		−	20.2002i		−	1.10530i
$335$		0			0
$336$	−11.0593	+	6.38508i	−0.603333	+	0.348334i
$337$	−27.6235	+	7.40170i	−1.50475	+	0.403196i	−0.914687	−	0.404162i	$-0.867563\pi$
$337$	−27.6235	+	7.40170i	−1.50475	+	0.403196i	−0.590062	+	0.807358i	$0.700897\pi$
$338$	−7.48481	−	2.00555i	−0.407120	−	0.109087i
$339$	51.5968	+	29.7894i	2.80235	+	1.61794i
$340$		0			0
$341$			5.59407i			0.302936i
$342$	34.6822	−	9.95042i	1.87540	−	0.538057i
$343$	1.23738	+	1.23738i	0.0668122	+	0.0668122i
$344$	−1.24305	+	2.15302i	−0.0670206	+	0.116083i
$345$		0			0
$346$	6.56703	+	11.3744i	0.353046	+	0.611493i
$347$	0.816568	+	3.04747i	0.0438357	+	0.163597i	0.984374	−	0.176091i	$-0.0563453\pi$
$347$	0.816568	+	3.04747i	0.0438357	+	0.163597i	−0.940538	+	0.339688i	$0.889679\pi$
$348$	−1.98511	+	7.40854i	−0.106413	+	0.397140i
$349$		−	33.8221i		−	1.81046i	−0.424924	−	0.905229i	$-0.639699\pi$
$349$		−	33.8221i		−	1.81046i	0.424924	−	0.905229i	$-0.360301\pi$
$350$		0			0
$351$	−20.3071	−	35.1728i	−1.08391	−	1.87739i
$352$	0.476670	−	1.77896i	0.0254066	−	0.0948188i
$353$	10.2395	+	10.2395i	0.544993	+	0.544993i	0.924989	−	0.379995i	$-0.124074\pi$
$353$	10.2395	+	10.2395i	0.544993	+	0.544993i	−0.379995	+	0.924989i	$0.624074\pi$
$354$	20.4593			1.08740
$355$		0			0
$356$	15.0189	+	8.67114i	0.795998	+	0.459570i
$357$	0.727023	−	2.71329i	0.0384781	−	0.143602i
$358$	7.30214	−	1.95660i	0.385930	−	0.103410i
$359$	21.1774	+	12.2268i	1.11770	+	0.645306i	0.940813	−	0.338925i	$-0.110063\pi$
$359$	21.1774	+	12.2268i	1.11770	+	0.645306i	0.176889	+	0.984231i	$0.443397\pi$
$360$		0			0
$361$	10.0731	+	16.1100i	0.530165	+	0.847894i
$362$	9.49510	−	9.49510i	0.499052	−	0.499052i
$363$	−6.61274	−	24.6791i	−0.347079	−	1.29532i
$364$	−4.35697	+	7.54649i	−0.228367	+	0.395544i
$365$		0			0
$366$	−10.8767	+	18.8391i	−0.568537	+	0.984734i
$367$	28.2646	+	7.57347i	1.47540	+	0.395332i	0.904778	−	0.425883i	$-0.140036\pi$
$367$	28.2646	+	7.57347i	1.47540	+	0.395332i	0.570620	+	0.821214i	$0.306703\pi$
$368$	−2.38312	−	2.38312i	−0.124229	−	0.124229i
$369$	−84.7010			−4.40936
$370$		0			0
$371$	4.11244	−	2.37432i	0.213507	−	0.123268i
$372$	−7.21274	+	7.21274i	−0.373963	+	0.373963i
$373$	−15.3386	+	15.3386i	−0.794201	+	0.794201i	−0.982174	−	0.187974i	$-0.939808\pi$
$373$	−15.3386	+	15.3386i	−0.794201	+	0.794201i	0.187974	+	0.982174i	$0.439808\pi$
$374$	0.202557	+	0.350840i	0.0104740	+	0.0181415i
$375$		0			0
$376$	−0.731924	+	0.422577i	−0.0377461	+	0.0217927i
$377$	1.35458	+	5.05535i	0.0697642	+	0.260364i
$378$	65.0999	−	17.4435i	3.34838	−	0.897194i
$379$	−35.1388			−1.80496			−0.902478	−	0.430735i	$-0.858254\pi$
$379$	−35.1388			−1.80496			−0.902478	+	0.430735i	$0.858254\pi$
$380$		0			0
$381$	12.9893			0.665462
$382$	−22.0245	+	5.90145i	−1.12687	+	0.301945i
$383$	−1.76168	−	6.57469i	−0.0900177	−	0.335951i	0.906199	−	0.422851i	$-0.138971\pi$
$383$	−1.76168	−	6.57469i	−0.0900177	−	0.335951i	−0.996217	+	0.0869001i	$0.972304\pi$
$384$	2.90830	−	1.67911i	0.148414	−	0.0856867i
$385$		0			0
$386$	−3.96220	−	6.86274i	−0.201671	−	0.349304i
$387$	14.5515	−	14.5515i	0.739697	−	0.739697i
$388$	4.44651	−	4.44651i	0.225737	−	0.225737i
$389$	−13.4174	+	7.74655i	−0.680290	+	0.392766i	−0.799964	−	0.600047i	$-0.795148\pi$
$389$	−13.4174	+	7.74655i	−0.680290	+	0.392766i	0.119674	+	0.992813i	$0.461815\pi$
$390$		0			0
$391$	0.741340			0.0374912
$392$	−5.27515	−	5.27515i	−0.266435	−	0.266435i
$393$	−12.7743	−	3.42287i	−0.644380	−	0.172661i
$394$	−8.49723	+	14.7176i	−0.428084	+	0.741464i
$395$		0			0
$396$	−7.62252	+	13.2026i	−0.383046	+	0.663455i
$397$	−8.91890	−	33.2858i	−0.447627	−	1.67057i	−0.708906	−	0.705303i	$-0.750811\pi$
$397$	−8.91890	−	33.2858i	−0.447627	−	1.67057i	0.261280	−	0.965263i	$-0.415856\pi$
$398$	−8.42705	+	8.42705i	−0.422410	+	0.422410i
$399$	28.6759	+	47.7090i	1.43559	+	2.38844i
$400$		0			0
$401$	7.09392	+	4.09567i	0.354253	+	0.204528i	0.666557	−	0.745454i	$-0.267767\pi$
$401$	7.09392	+	4.09567i	0.354253	+	0.204528i	−0.312304	+	0.949982i	$0.601101\pi$
$402$	−20.4320	+	5.47473i	−1.01905	+	0.273055i
$403$	−1.80148	+	6.72322i	−0.0897382	+	0.334907i
$404$	4.09042	+	2.36161i	0.203506	+	0.117494i
$405$		0			0
$406$	−8.68494			−0.431026
$407$	9.35860	+	9.35860i	0.463888	+	0.463888i
$408$	−0.191188	+	0.713525i	−0.00946523	+	0.0353247i
$409$	−5.94591	−	10.2986i	−0.294006	−	0.509234i	0.680747	−	0.732519i	$-0.261655\pi$
$409$	−5.94591	−	10.2986i	−0.294006	−	0.509234i	−0.974753	+	0.223285i	$0.928322\pi$
$410$		0			0
$411$			68.8481i			3.39603i
$412$	−1.36599	+	5.09793i	−0.0672973	+	0.251157i
$413$	5.99604	+	22.3775i	0.295046	+	1.10113i
$414$	13.9488	+	24.1601i	0.685549	+	1.18740i
$415$		0			0
$416$	1.14577	−	1.98453i	0.0561760	−	0.0972997i
$417$	27.6461	+	27.6461i	1.35384	+	1.35384i
$418$	−7.78966	−	1.94098i	−0.381005	−	0.0949364i
$419$			17.1215i			0.836439i	0.908346	+	0.418219i	$0.137346\pi$
$419$			17.1215i			0.836439i	−0.908346	+	0.418219i	$0.862654\pi$
$420$		0			0
$421$	−22.5528	−	13.0209i	−1.09916	−	0.634599i	−0.163158	−	0.986600i	$-0.552168\pi$
$421$	−22.5528	−	13.0209i	−1.09916	−	0.634599i	−0.936000	+	0.352001i	$0.885501\pi$
$422$	13.3842	+	3.58629i	0.651534	+	0.174578i
$423$	6.75750	−	1.81067i	0.328561	−	0.0880376i
$424$	−1.08147	+	0.624384i	−0.0525206	+	0.0303228i
$425$		0			0
$426$		−	10.6522i		−	0.516099i
$427$	−23.7931	−	6.37533i	−1.15143	−	0.308524i
$428$	−0.428939	−	0.114934i	−0.0207336	−	0.00555554i
$429$			14.1729i			0.684274i
$430$		0			0
$431$	−33.2058	+	19.1714i	−1.59947	+	0.923453i	−0.607879	+	0.794030i	$0.707979\pi$
$431$	−33.2058	+	19.1714i	−1.59947	+	0.923453i	−0.991589	+	0.129423i	$0.958687\pi$
$432$	−17.1196	+	4.58718i	−0.823666	+	0.220701i
$433$	−15.6010	−	4.18029i	−0.749738	−	0.200892i	−0.136336	−	0.990663i	$-0.543533\pi$
$433$	−15.6010	−	4.18029i	−0.749738	−	0.200892i	−0.613402	+	0.789771i	$0.710199\pi$
$434$	−10.0028	−	5.77514i	−0.480152	−	0.277216i
$435$		0			0
$436$		−	2.18822i		−	0.104797i
$437$	−10.2034	+	10.5690i	−0.488094	+	0.505583i
$438$	−5.25565	−	5.25565i	−0.251125	−	0.251125i
$439$	−14.5951	+	25.2794i	−0.696585	+	1.20652i	0.273059	+	0.961997i	$0.411965\pi$
$439$	−14.5951	+	25.2794i	−0.696585	+	1.20652i	−0.969644	+	0.244523i	$0.921369\pi$
$440$		0			0
$441$	30.8764	+	53.4794i	1.47030	+	2.54664i
$442$	0.130461	+	0.486886i	0.00620538	+	0.0231588i
$443$	2.54135	−	9.48446i	0.120743	−	0.450620i	−0.878909	−	0.476990i	$-0.841728\pi$
$443$	2.54135	−	9.48446i	0.120743	−	0.450620i	0.999652	+	0.0263692i	$0.00839456\pi$
$444$			24.1331i			1.14531i
$445$		0			0
$446$	−10.5609	−	18.2920i	−0.500073	−	0.866151i
$447$	7.76801	−	28.9906i	0.367414	−	1.37121i
$448$	2.68888	+	2.68888i	0.127038	+	0.127038i
$449$	−13.1857			−0.622270			−0.311135	−	0.950366i	$-0.600709\pi$
$449$	−13.1857			−0.622270			−0.311135	+	0.950366i	$0.600709\pi$
$450$		0			0
$451$	16.3205	+	9.42267i	0.768504	+	0.443696i
$452$	4.59176	−	17.1367i	0.215978	−	0.806041i
$453$	−5.86318	+	1.57104i	−0.275476	+	0.0738137i
$454$	14.6492	+	8.45773i	0.687522	+	0.396941i
$455$		0			0
$456$	−7.54102	−	12.5462i	−0.353141	−	0.587532i
$457$	21.9261	−	21.9261i	1.02566	−	1.02566i	0.0259956	−	0.999662i	$-0.491724\pi$
$457$	21.9261	−	21.9261i	1.02566	−	1.02566i	0.999662	−	0.0259956i	$-0.00827559\pi$
$458$	7.04779	+	26.3027i	0.329322	+	1.22905i
$459$	1.94928	−	3.37626i	0.0909848	−	0.157590i
$460$		0			0
$461$	−10.7331	+	18.5903i	−0.499890	+	0.865835i	−1.00000		0.000126855i	$-0.999960\pi$
$461$	−10.7331	+	18.5903i	−0.499890	+	0.865835i	0.500110	+	0.865962i	$0.333293\pi$
$462$	−22.7176	−	6.08715i	−1.05692	−	0.283200i
$463$	17.7722	+	17.7722i	0.825944	+	0.825944i	0.986953	−	0.161009i	$-0.0514748\pi$
$463$	17.7722	+	17.7722i	0.825944	+	0.825944i	−0.161009	+	0.986953i	$0.551475\pi$
$464$	2.28391			0.106028
$465$		0			0
$466$	0.312505	−	0.180425i	0.0144765	−	0.00835801i
$467$	−2.49870	+	2.49870i	−0.115626	+	0.115626i	−0.762553	−	0.646926i	$-0.776054\pi$
$467$	−2.49870	+	2.49870i	−0.115626	+	0.115626i	0.646926	+	0.762553i	$0.276054\pi$
$468$	−13.4128	+	13.4128i	−0.620007	+	0.620007i
$469$	−11.9761	−	20.7432i	−0.553003	−	0.957830i
$470$		0			0
$471$	41.7756	−	24.1191i	1.92492	−	1.11135i
$472$	−1.57680	−	5.88471i	−0.0725783	−	0.270866i
$473$	−4.42265	+	1.18505i	−0.203354	+	0.0544885i
$474$	19.8084			0.909831
$475$		0			0
$476$	−0.836455			−0.0383389
$477$	9.98464	−	2.67538i	0.457165	−	0.122497i
$478$	−3.58313	−	13.3724i	−0.163889	−	0.611640i
$479$	30.5712	−	17.6503i	1.39683	−	0.806461i	0.402772	−	0.915300i	$-0.368047\pi$
$479$	30.5712	−	17.6503i	1.39683	−	0.806461i	0.994059	+	0.108839i	$0.0347133\pi$
$480$		0			0
$481$	8.23382	+	14.2614i	0.375430	+	0.650264i
$482$	19.4359	−	19.4359i	0.885279	−	0.885279i
$483$	−30.4329	+	30.4329i	−1.38474	+	1.38474i
$484$	−6.58880	+	3.80405i	−0.299491	+	0.172911i
$485$		0			0
$486$	63.3143			2.87200
$487$	−5.10431	−	5.10431i	−0.231299	−	0.231299i	0.581936	−	0.813235i	$-0.302295\pi$
$487$	−5.10431	−	5.10431i	−0.231299	−	0.231299i	−0.813235	+	0.581936i	$0.802295\pi$
$488$	6.25696	+	1.67655i	0.283239	+	0.0758938i
$489$	−3.34363	+	5.79134i	−0.151204	+	0.261894i
$490$		0			0
$491$	9.55823	−	16.5553i	0.431357	−	0.747132i	−0.565634	−	0.824657i	$-0.691368\pi$
$491$	9.55823	−	16.5553i	0.431357	−	0.747132i	0.996990	+	0.0775248i	$0.0247017\pi$
$492$	8.89380	+	33.1921i	0.400964	+	1.49642i
$493$	−0.355239	+	0.355239i	−0.0159992	+	0.0159992i
$494$	−8.73692	−	4.84130i	−0.393093	−	0.217820i
$495$		0			0
$496$	2.63049	+	1.51871i	0.118112	+	0.0681923i
$497$	11.6509	−	3.12185i	0.522614	−	0.140034i
$498$	0.668127	−	2.49348i	0.0299395	−	0.111736i
$499$	−12.2512	−	7.07321i	−0.548437	−	0.316640i	0.200054	−	0.979785i	$-0.435888\pi$
$499$	−12.2512	−	7.07321i	−0.548437	−	0.316640i	−0.748491	+	0.663145i	$0.769221\pi$
$500$		0			0
$501$	67.8366			3.03072
$502$	−18.6699	−	18.6699i	−0.833279	−	0.833279i
$503$	−0.838536	+	3.12946i	−0.0373885	+	0.139536i	−0.982097	−	0.188375i	$-0.939678\pi$
$503$	−0.838536	+	3.12946i	−0.0373885	+	0.139536i	0.944709	+	0.327911i	$0.106345\pi$
$504$	−15.7385	−	27.2599i	−0.701049	−	1.21425i
$505$		0			0
$506$		−	6.20703i		−	0.275936i
$507$	6.73507	−	25.1356i	0.299115	−	1.11631i
$508$	−1.00109	−	3.73612i	−0.0444162	−	0.165763i
$509$	−6.99061	−	12.1081i	−0.309853	−	0.536682i	0.668477	−	0.743733i	$-0.266947\pi$
$509$	−6.99061	−	12.1081i	−0.309853	−	0.536682i	−0.978330	+	0.207051i	$0.933613\pi$
$510$		0			0
$511$	4.20813	−	7.28870i	0.186157	−	0.322433i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	21.3051	+	74.2591i	0.940644	+	3.27862i
$514$		−	9.24160i		−	0.407629i
$515$		0			0
$516$	−7.23031	−	4.17442i	−0.318297	−	0.183769i
$517$	−1.50349	−	0.402860i	−0.0661235	−	0.0177177i
$518$	−26.3958	+	7.07273i	−1.15976	+	0.310758i
$519$	−38.1978	+	22.0535i	−1.67670	+	0.968042i
$520$		0			0
$521$			2.07548i			0.0909285i	0.998966	+	0.0454643i	$0.0144767\pi$
$521$			2.07548i			0.0909285i	−0.998966	+	0.0454643i	$0.985523\pi$
$522$	−18.2612	−	4.89308i	−0.799273	−	0.214165i
$523$	35.4231	+	9.49158i	1.54894	+	0.415038i	0.929143	−	0.369722i	$-0.120547\pi$
$523$	35.4231	+	9.49158i	1.54894	+	0.415038i	0.619800	+	0.784760i	$0.287214\pi$
$524$			3.93809i			0.172036i
$525$		0			0
$526$	−7.36049	+	4.24958i	−0.320932	+	0.185290i
$527$	−0.645365	+	0.172925i	−0.0281126	+	0.00753274i
$528$	5.97413	+	1.60076i	0.259991	+	0.0696643i
$529$	10.0818	+	5.82072i	0.438338	+	0.253075i
$530$		0			0
$531$			50.4299i			2.18847i
$532$	11.5125	−	11.9250i	0.499130	−	0.517015i
$533$	16.5804	+	16.5804i	0.718176	+	0.718176i
$534$	−29.1196	+	50.4366i	−1.26013	+	2.18261i
$535$		0			0
$536$	3.14940	+	5.45491i	0.136033	+	0.235616i
$537$	6.57070	+	24.5222i	0.283547	+	1.05821i
$538$	−3.14970	+	11.7548i	−0.135793	+	0.506787i
$539$		−	13.7395i		−	0.591803i
$540$		0			0
$541$	1.84174	+	3.18999i	0.0791828	+	0.137149i	0.902898	−	0.429856i	$-0.141436\pi$
$541$	1.84174	+	3.18999i	0.0791828	+	0.137149i	−0.823715	+	0.567004i	$0.808102\pi$
$542$	3.46747	−	12.9408i	0.148940	−	0.555853i
$543$	31.8867	+	31.8867i	1.36839	+	1.36839i
$544$	0.219966			0.00943097
$545$		0			0
$546$	−25.3428	−	14.6317i	−1.08457	−	0.626177i
$547$	−5.27195	+	19.6752i	−0.225412	+	0.841249i	0.756827	+	0.653615i	$0.226749\pi$
$547$	−5.27195	+	19.6752i	−0.225412	+	0.841249i	−0.982239	+	0.187634i	$0.939918\pi$
$548$	19.8028	−	5.30614i	0.845934	−	0.226667i
$549$	−46.4362	−	26.8100i	−1.98185	−	1.14422i
$550$		0			0
$551$	−0.175190	−	9.95381i	−0.00746333	−	0.424047i
$552$	8.00306	−	8.00306i	0.340633	−	0.340633i
$553$	5.80529	+	21.6656i	0.246866	+	0.921316i
$554$	3.01892	−	5.22891i	0.128261	−	0.222155i
$555$		0			0
$556$	5.82117	−	10.0826i	0.246872	−	0.427596i
$557$	−32.9590	−	8.83134i	−1.39652	−	0.374196i	−0.519425	−	0.854516i	$-0.673854\pi$
$557$	−32.9590	−	8.83134i	−1.39652	−	0.374196i	−0.877093	+	0.480320i	$0.840520\pi$
$558$	−17.7786	−	17.7786i	−0.752628	−	0.752628i
$559$	−5.69698			−0.240957
$560$		0			0
$561$	−1.17820	+	0.680232i	−0.0497435	+	0.0287194i
$562$	−13.6365	+	13.6365i	−0.575220	+	0.575220i
$563$	13.9796	−	13.9796i	0.589170	−	0.589170i	−0.348236	−	0.937407i	$-0.613219\pi$
$563$	13.9796	−	13.9796i	0.589170	−	0.589170i	0.937407	+	0.348236i	$0.113219\pi$
$564$	−1.41911	−	2.45796i	−0.0597551	−	0.103499i
$565$		0			0
$566$	16.6406	−	9.60745i	0.699456	−	0.403831i
$567$	34.1384	+	127.406i	1.43368	+	5.35056i
$568$	−3.06389	+	0.820966i	−0.128558	+	0.0344470i
$569$	−12.0295			−0.504302			−0.252151	−	0.967688i	$-0.581138\pi$
$569$	−12.0295			−0.504302			−0.252151	+	0.967688i	$0.581138\pi$
$570$		0			0
$571$	−3.63902			−0.152288			−0.0761440	−	0.997097i	$-0.524261\pi$
$571$	−3.63902			−0.152288			−0.0761440	+	0.997097i	$0.524261\pi$
$572$	4.07656	−	1.09231i	0.170449	−	0.0456718i
$573$	−19.8184	−	73.9632i	−0.827925	−	3.08986i
$574$	−33.6976	+	19.4553i	−1.40651	+	0.812050i
$575$		0			0
$576$	4.13882	+	7.16865i	0.172451	+	0.298694i
$577$	−13.4159	+	13.4159i	−0.558511	+	0.558511i	−0.928883	−	0.370373i	$-0.879230\pi$
$577$	−13.4159	+	13.4159i	−0.558511	+	0.558511i	0.370373	+	0.928883i	$0.379230\pi$
$578$	11.9866	−	11.9866i	0.498577	−	0.498577i
$579$	23.0466	−	13.3059i	0.957783	−	0.552976i
$580$		0			0
$581$	2.92308			0.121270
$582$	14.9324	+	14.9324i	0.618966	+	0.618966i
$583$	−2.22151	−	0.595251i	−0.0920054	−	0.0246528i
$584$	−1.10663	+	1.91674i	−0.0457927	+	0.0793152i
$585$		0			0
$586$	−0.320027	+	0.554303i	−0.0132202	+	0.0228980i
$587$	1.12928	+	4.21455i	0.0466106	+	0.173953i	0.985307	−	0.170791i	$-0.0546324\pi$
$587$	1.12928	+	4.21455i	0.0466106	+	0.173953i	−0.938697	+	0.344744i	$0.887966\pi$
$588$	17.7151	−	17.7151i	0.730559	−	0.730559i
$589$	6.41712	−	11.5808i	0.264413	−	0.477177i
$590$		0			0
$591$	−49.4251	−	28.5356i	−2.03308	−	1.17380i
$592$	6.94141	−	1.85994i	0.285290	−	0.0764433i
$593$	−2.93680	+	10.9603i	−0.120600	+	0.450085i	−0.999645	−	0.0266539i	$-0.991515\pi$
$593$	−2.93680	+	10.9603i	−0.120600	+	0.450085i	0.879045	+	0.476739i	$0.158181\pi$
$594$	−28.2684	−	16.3208i	−1.15987	−	0.669650i
$595$		0			0
$596$	−8.93726			−0.366085
$597$	−28.2999	−	28.2999i	−1.15824	−	1.15824i
$598$	1.99887	−	7.45990i	0.0817400	−	0.305058i
$599$	18.9979	+	32.9053i	0.776232	+	1.34447i	0.934099	+	0.357013i	$0.116205\pi$
$599$	18.9979	+	32.9053i	0.776232	+	1.34447i	−0.157867	+	0.987460i	$0.550462\pi$
$600$		0			0
$601$		−	37.3803i		−	1.52477i	−0.647122	−	0.762386i	$-0.724028\pi$
$601$		−	37.3803i		−	1.52477i	0.647122	−	0.762386i	$-0.275972\pi$
$602$	2.44681	−	9.13162i	0.0997246	−	0.372177i
$603$	−13.4946	−	50.3626i	−0.549543	−	2.05092i
$604$	0.903755	+	1.56535i	0.0367733	+	0.0636931i
$605$		0			0
$606$	−7.93079	+	13.7365i	−0.322166	+	0.558009i
$607$	−22.2906	−	22.2906i	−0.904749	−	0.904749i	0.0910931	−	0.995842i	$-0.470964\pi$
$607$	−22.2906	−	22.2906i	−0.904749	−	0.904749i	−0.995842	+	0.0910931i	$0.970964\pi$
$608$	−3.02749	+	3.13597i	−0.122781	+	0.127180i
$609$		−	29.1659i		−	1.18186i
$610$		0			0
$611$	−1.67723	−	0.968352i	−0.0678536	−	0.0391753i
$612$	−1.75876	−	0.471258i	−0.0710936	−	0.0190495i
$613$	−22.7345	+	6.09169i	−0.918238	+	0.246041i	−0.686832	−	0.726816i	$-0.740999\pi$
$613$	−22.7345	+	6.09169i	−0.918238	+	0.246041i	−0.231406	+	0.972857i	$0.574332\pi$
$614$	19.7266	−	11.3892i	0.796101	−	0.459629i
$615$		0			0
$616$			7.00340i			0.282175i
$617$	21.6904	+	5.81194i	0.873224	+	0.233980i	0.667481	−	0.744626i	$-0.267372\pi$
$617$	21.6904	+	5.81194i	0.873224	+	0.233980i	0.205743	+	0.978606i	$0.434039\pi$
$618$	−17.1200	−	4.58728i	−0.688666	−	0.184528i
$619$		−	19.5412i		−	0.785426i	−0.919661	−	0.392713i	$-0.871537\pi$
$619$		−	19.5412i		−	0.785426i	0.919661	−	0.392713i	$-0.128463\pi$
$620$		0			0
$621$	−51.7299	+	29.8663i	−2.07585	+	1.19849i
$622$	−25.5791	+	6.85391i	−1.02563	+	0.274817i
$623$	−63.6996	−	17.0683i	−2.55207	−	0.683826i
$624$	6.66450	+	3.84775i	0.266793	+	0.154033i
$625$		0			0
$626$		−	8.29299i		−	0.331455i
$627$	6.51824	−	26.1594i	0.260313	−	1.04471i
$628$	−10.1570	−	10.1570i	−0.405310	−	0.405310i
$629$	−0.790369	+	1.36896i	−0.0315141	+	0.0545840i
$630$		0			0
$631$	−4.68469	−	8.11412i	−0.186495	−	0.323018i	0.757585	−	0.652737i	$-0.226379\pi$
$631$	−4.68469	−	8.11412i	−0.186495	−	0.323018i	−0.944079	+	0.329719i	$0.893046\pi$
$632$	−1.52664	−	5.69750i	−0.0607265	−	0.226634i
$633$	−12.0436	+	44.9472i	−0.478689	+	1.78649i
$634$		−	14.5703i		−	0.578659i
$635$		0			0
$636$	−2.09682	−	3.63180i	−0.0831443	−	0.144010i
$637$	4.42459	−	16.5128i	0.175309	−	0.654261i
$638$	2.97431	+	2.97431i	0.117754	+	0.117754i
$639$	26.2564			1.03869
$640$		0			0
$641$	−20.7327	−	11.9701i	−0.818894	−	0.472789i	0.0311407	−	0.999515i	$-0.490086\pi$
$641$	−20.7327	−	11.9701i	−0.818894	−	0.472789i	−0.850035	+	0.526726i	$0.823419\pi$
$642$	0.385973	−	1.44047i	0.0152332	−	0.0568509i
$643$	−21.2850	+	5.70330i	−0.839399	+	0.224916i	−0.652810	−	0.757522i	$-0.726410\pi$
$643$	−21.2850	+	5.70330i	−0.839399	+	0.224916i	−0.186589	+	0.982438i	$0.559743\pi$
$644$	11.0989	+	6.40794i	0.437357	+	0.252508i
$645$		0			0
$646$	−0.0168727	−	0.958662i	−0.000663848	−	0.0377180i
$647$	−20.0704	+	20.0704i	−0.789048	+	0.789048i	−0.981338	−	0.192290i	$-0.938409\pi$
$647$	−20.0704	+	20.0704i	−0.789048	+	0.789048i	0.192290	+	0.981338i	$0.438409\pi$
$648$	−8.97752	−	33.5046i	−0.352670	−	1.31618i
$649$	5.61014	−	9.71704i	0.220217	−	0.381427i
$650$		0			0
$651$	19.3942	−	33.5918i	0.760119	−	1.31656i
$652$	1.92346	+	0.515390i	0.0753285	+	0.0201842i
$653$	−3.44054	−	3.44054i	−0.134639	−	0.134639i	0.636576	−	0.771214i	$-0.280350\pi$
$653$	−3.44054	−	3.44054i	−0.134639	−	0.134639i	−0.771214	+	0.636576i	$0.780350\pi$
$654$	7.34854			0.287350
$655$		0			0
$656$	8.86161	−	5.11625i	0.345988	−	0.199756i
$657$	12.9546	−	12.9546i	0.505407	−	0.505407i
$658$	2.27252	−	2.27252i	0.0885920	−	0.0885920i
$659$	8.60016	+	14.8959i	0.335015	+	0.580263i	0.983488	−	0.180975i	$-0.0579254\pi$
$659$	8.60016	+	14.8959i	0.335015	+	0.580263i	−0.648473	+	0.761238i	$0.724592\pi$
$660$		0			0
$661$	10.2060	−	5.89242i	0.396966	−	0.229189i	−0.288208	−	0.957568i	$-0.593059\pi$
$661$	10.2060	−	5.89242i	0.396966	−	0.229189i	0.685174	+	0.728379i	$0.259726\pi$
$662$	−7.50504	−	28.0092i	−0.291692	−	1.08861i
$663$	−1.63507	+	0.438116i	−0.0635009	+	0.0170150i
$664$	−0.768695			−0.0298311
$665$		0			0
$666$	−59.4854			−2.30501
$667$	7.43507	−	1.99222i	0.287887	−	0.0771391i
$668$	−5.22819	−	19.5119i	−0.202285	−	0.754937i
$669$	61.4286	−	35.4658i	2.37497	−	1.37119i
$670$		0			0
$671$	5.96502	+	10.3317i	0.230277	+	0.398851i
$672$	−9.02986	+	9.02986i	−0.348334	+	0.348334i
$673$	0.406182	−	0.406182i	0.0156572	−	0.0156572i	−0.699235	−	0.714892i	$-0.746476\pi$
$673$	0.406182	−	0.406182i	0.0156572	−	0.0156572i	0.714892	+	0.699235i	$0.246476\pi$
$674$	−24.7666	+	14.2990i	−0.953973	+	0.550776i
$675$		0			0
$676$	−7.74884			−0.298032
$677$	−12.1451	−	12.1451i	−0.466774	−	0.466774i	0.434094	−	0.900868i	$-0.357069\pi$
$677$	−12.1451	−	12.1451i	−0.466774	−	0.466774i	−0.900868	+	0.434094i	$0.857069\pi$
$678$	57.5487	+	15.4201i	2.21015	+	0.592207i
$679$	−11.9561	+	20.7086i	−0.458835	+	0.794725i
$680$		0			0
$681$	−28.4029	+	49.1953i	−1.08840	+	1.88517i
$682$	1.44785	+	5.40346i	0.0554411	+	0.206909i
$683$	2.75985	−	2.75985i	0.105603	−	0.105603i	−0.652331	−	0.757934i	$-0.726209\pi$
$683$	2.75985	−	2.75985i	0.105603	−	0.105603i	0.757934	+	0.652331i	$0.226209\pi$
$684$	30.9251	−	18.5878i	1.18245	−	0.710722i
$685$		0			0
$686$	1.51547	+	0.874959i	0.0578610	+	0.0334061i
$687$	−88.3303	+	23.6680i	−3.37001	+	0.902992i
$688$	−0.643448	+	2.40138i	−0.0245312	+	0.0915518i
$689$	−2.47822	−	1.43080i	−0.0944127	−	0.0545092i
$690$		0			0
$691$	−20.4915			−0.779533			−0.389766	−	0.920914i	$-0.627444\pi$
$691$	−20.4915			−0.779533			−0.389766	+	0.920914i	$0.627444\pi$
$692$	9.28718	+	9.28718i	0.353046	+	0.353046i
$693$	15.0042	−	55.9963i	0.569961	−	2.12712i
$694$	1.57749	+	2.73229i	0.0598806	+	0.103716i
$695$		0			0
$696$			7.66989i			0.290726i
$697$	−0.582551	+	2.17411i	−0.0220657	+	0.0823503i
$698$	−8.75381	−	32.6697i	−0.331337	−	1.23657i
$699$	0.605906	+	1.04946i	0.0229175	+	0.0396942i
$700$		0			0
$701$	−0.419107	+	0.725914i	−0.0158294	+	0.0274174i	−0.873832	−	0.486229i	$-0.838372\pi$
$701$	−0.419107	+	0.725914i	−0.0158294	+	0.0274174i	0.858002	+	0.513646i	$0.171706\pi$
$702$	−28.7185	−	28.7185i	−1.08391	−	1.08391i
$703$	−8.63850	−	30.1095i	−0.325807	−	1.13560i
$704$		−	1.84171i		−	0.0694122i
$705$		0			0
$706$	12.5408	+	7.24042i	0.471978	+	0.272497i
$707$	−17.3487	−	4.64858i	−0.652467	−	0.174828i
$708$	19.7622	−	5.29525i	0.742707	−	0.199008i
$709$	3.83347	−	2.21326i	0.143969	−	0.0831206i	−0.426285	−	0.904589i	$-0.640178\pi$
$709$	3.83347	−	2.21326i	0.143969	−	0.0831206i	0.570254	+	0.821468i	$0.306845\pi$
$710$		0			0
$711$			48.8256i			1.83110i
$712$	16.7514	+	4.48851i	0.627784	+	0.168214i
$713$	9.88807	+	2.64950i	0.370311	+	0.0992245i
$714$		−	2.80900i		−	0.105124i
$715$		0			0
$716$	6.54692	−	3.77987i	0.244670	−	0.141260i
$717$	44.9075	−	12.0329i	1.67710	−	0.449378i
$718$	23.6204	+	6.32905i	0.881504	+	0.236198i
$719$	16.3271	+	9.42648i	0.608900	+	0.351548i	0.772535	−	0.634973i	$-0.218989\pi$
$719$	16.3271	+	9.42648i	0.608900	+	0.351548i	−0.163635	+	0.986521i	$0.552322\pi$
$720$		0			0
$721$		−	20.0695i		−	0.747428i
$722$	13.8995	+	12.9539i	0.517285	+	0.482096i
$723$	65.2699	+	65.2699i	2.42741	+	2.42741i
$724$	6.71405	−	11.6291i	0.249526	−	0.432191i
$725$		0			0
$726$	−12.7748	−	22.1266i	−0.474118	−	0.821197i
$727$	4.27375	+	15.9499i	0.158505	+	0.591548i	0.998780	+	0.0493872i	$0.0157268\pi$
$727$	4.27375	+	15.9499i	0.158505	+	0.591548i	−0.840275	+	0.542160i	$0.817607\pi$
$728$	−2.25533	+	8.41702i	−0.0835882	+	0.311955i
$729$			108.564i			4.02089i
$730$		0			0
$731$	−0.273428	−	0.473591i	−0.0101131	−	0.0175164i
$732$	−5.63022	+	21.0123i	−0.208099	+	0.776635i
$733$	−11.7943	−	11.7943i	−0.435632	−	0.435632i	0.454907	−	0.890539i	$-0.349672\pi$
$733$	−11.7943	−	11.7943i	−0.435632	−	0.435632i	−0.890539	+	0.454907i	$0.849672\pi$
$734$	29.2616			1.08007
$735$		0			0
$736$	−2.91872	−	1.68512i	−0.107585	−	0.0621145i
$737$	−3.00245	+	11.2053i	−0.110597	+	0.412752i
$738$	−81.8149	+	21.9222i	−3.01165	+	0.806969i
$739$	−23.8803	−	13.7873i	−0.878450	−	0.507174i	−0.00830316	−	0.999966i	$-0.502643\pi$
$739$	−23.8803	−	13.7873i	−0.878450	−	0.507174i	−0.870147	+	0.492792i	$0.835976\pi$
$740$		0			0
$741$	16.2581	−	29.3405i	0.597258	−	1.07785i
$742$	3.35779	−	3.35779i	0.123268	−	0.123268i
$743$	5.26901	+	19.6642i	0.193301	+	0.721410i	0.992700	+	0.120609i	$0.0384848\pi$
$743$	5.26901	+	19.6642i	0.193301	+	0.721410i	−0.799399	+	0.600801i	$0.794849\pi$
$744$	−5.10018	+	8.83376i	−0.186982	+	0.323862i
$745$		0			0
$746$	−10.8460	+	18.7858i	−0.397100	+	0.687798i
$747$	6.14617	+	1.64686i	0.224876	+	0.0602555i
$748$	0.286459	+	0.286459i	0.0104740	+	0.0104740i
$749$	1.68865			0.0617018
$750$		0			0
$751$	6.03448	−	3.48401i	0.220201	−	0.127133i	−0.385842	−	0.922565i	$-0.626089\pi$
$751$	6.03448	−	3.48401i	0.220201	−	0.127133i	0.606044	+	0.795431i	$0.292756\pi$
$752$	−0.597614	+	0.597614i	−0.0217927	+	0.0217927i
$753$	62.6977	−	62.6977i	2.28483	−	2.28483i
$754$	2.61684	+	4.53250i	0.0952997	+	0.165064i
$755$		0			0
$756$	58.3669	−	33.6982i	2.12278	−	1.22559i
$757$	−7.45208	−	27.8115i	−0.270850	−	1.01083i	−0.958571	−	0.284852i	$-0.908055\pi$
$757$	−7.45208	−	27.8115i	−0.270850	−	1.01083i	0.687721	−	0.725975i	$-0.258611\pi$
$758$	−33.9414	+	9.09458i	−1.23281	+	0.330330i
$759$	20.8446			0.756610
$760$		0			0
$761$	51.1823			1.85536			0.927679	−	0.373378i	$-0.121801\pi$
$761$	51.1823			1.85536			0.927679	+	0.373378i	$0.121801\pi$
$762$	12.5467	−	3.36188i	0.454519	−	0.121788i
$763$	2.15365	+	8.03752i	0.0779673	+	0.290978i
$764$	−19.7466	+	11.4007i	−0.714409	+	0.412464i
$765$		0			0
$766$	−3.40331	−	5.89470i	−0.122967	−	0.212984i
$767$	9.87175	−	9.87175i	0.356448	−	0.356448i
$768$	2.37462	−	2.37462i	0.0856867	−	0.0856867i
$769$	16.4146	−	9.47696i	0.591924	−	0.341748i	−0.173934	−	0.984757i	$-0.555648\pi$
$769$	16.4146	−	9.47696i	0.591924	−	0.341748i	0.765858	+	0.643010i	$0.222314\pi$
$770$		0			0
$771$	31.0353			1.11771
$772$	−5.60340	−	5.60340i	−0.201671	−	0.201671i
$773$	−39.2924	−	10.5284i	−1.41325	−	0.378679i	−0.530166	−	0.847894i	$-0.677871\pi$
$773$	−39.2924	−	10.5284i	−1.41325	−	0.378679i	−0.883084	+	0.469214i	$0.844537\pi$
$774$	10.2895	−	17.8219i	0.369848	−	0.640596i
$775$		0			0
$776$	3.14416	−	5.44584i	0.112869	−	0.195494i
$777$	−23.7518	−	88.6428i	−0.852090	−	3.18004i
$778$	−10.9553	+	10.9553i	−0.392766	+	0.392766i
$779$	−22.9775	−	38.2284i	−0.823255	−	1.36968i
$780$		0			0
$781$	−5.05920	−	2.92093i	−0.181032	−	0.104519i
$782$	0.716080	−	0.191873i	0.0256070	−	0.00686136i
$783$	10.4767	−	39.0996i	0.374407	−	1.39731i
$784$	−6.46071	−	3.73009i	−0.230740	−	0.133218i
$785$		0			0
$786$	−13.2250			−0.471719
$787$	20.3327	+	20.3327i	0.724783	+	0.724783i	0.969575	−	0.244793i	$-0.0787199\pi$
$787$	20.3327	+	20.3327i	0.724783	+	0.724783i	−0.244793	+	0.969575i	$0.578720\pi$
$788$	−4.39849	+	16.4154i	−0.156690	+	0.584774i
$789$	−14.2710	−	24.7181i	−0.508062	−	0.879989i
$790$		0			0
$791$			67.4636i			2.39873i
$792$	−3.94571	+	14.7256i	−0.140205	+	0.523251i
$793$	3.84188	+	14.3381i	0.136429	+	0.509160i
$794$	−17.2300	−	29.8432i	−0.611469	−	1.05910i
$795$		0			0
$796$	−5.95882	+	10.3210i	−0.211205	+	0.365818i
$797$	19.4404	+	19.4404i	0.688613	+	0.688613i	0.961925	−	0.273312i	$-0.0881192\pi$
$797$	19.4404	+	19.4404i	0.688613	+	0.688613i	−0.273312	+	0.961925i	$0.588119\pi$
$798$	40.0468	+	38.6615i	1.41764	+	1.36860i
$799$		−	0.185905i		−	0.00657685i
$800$		0			0
$801$	−124.321	−	71.7766i	−4.39266	−	2.53610i
$802$	7.91224	+	2.12008i	0.279391	+	0.0748625i
$803$	−3.93730	+	1.05500i	−0.138944	+	0.0372300i
$804$	−18.3188	+	10.5764i	−0.646054	+	0.373000i
$805$		0			0
$806$			6.96039i			0.245169i
$807$	−39.4753	−	10.5774i	−1.38960	−	0.372342i
$808$	4.56227	+	1.22246i	0.160500	+	0.0430059i
$809$			17.4696i			0.614199i	0.951677	+	0.307100i	$0.0993585\pi$
$809$			17.4696i			0.614199i	−0.951677	+	0.307100i	$0.900641\pi$
$810$		0			0
$811$	23.2520	−	13.4246i	0.816489	−	0.471400i	−0.0327151	−	0.999465i	$-0.510415\pi$
$811$	23.2520	−	13.4246i	0.816489	−	0.471400i	0.849204	+	0.528064i	$0.177082\pi$
$812$	−8.38900	+	2.24783i	−0.294396	+	0.0788833i
$813$	43.4579	+	11.6445i	1.52414	+	0.408391i
$814$	11.4619	+	6.61753i	0.401739	+	0.231944i
$815$		0			0
$816$			0.738695i			0.0258595i
$817$	10.5151	+	2.62009i	0.367877	+	0.0916654i
$818$	−8.40879	−	8.40879i	−0.294006	−	0.294006i
$819$	36.0654	−	62.4672i	1.26023	−	2.18278i
$820$		0			0
$821$	8.42685	+	14.5957i	0.294099	+	0.509395i	0.974775	−	0.223190i	$-0.0716471\pi$
$821$	8.42685	+	14.5957i	0.294099	+	0.509395i	−0.680676	+	0.732585i	$0.738314\pi$
$822$	17.8192	+	66.5022i	0.621516	+	2.31953i
$823$	2.68028	−	10.0029i	0.0934286	−	0.348680i	−0.903348	−	0.428908i	$-0.858898\pi$
$823$	2.68028	−	10.0029i	0.0934286	−	0.348680i	0.996777	+	0.0802283i	$0.0255649\pi$
$824$			5.27777i			0.183860i
$825$		0			0
$826$	11.5835	+	20.0631i	0.403040	+	0.698086i
$827$	−8.87006	+	33.1035i	−0.308442	+	1.15112i	0.621500	+	0.783414i	$0.286524\pi$
$827$	−8.87006	+	33.1035i	−0.308442	+	1.15112i	−0.929942	+	0.367707i	$0.880143\pi$
$828$	19.7267	+	19.7267i	0.685549	+	0.685549i
$829$	8.77573			0.304794			0.152397	−	0.988319i	$-0.451301\pi$
$829$	8.77573			0.304794			0.152397	+	0.988319i	$0.451301\pi$
$830$		0			0
$831$	17.5598	+	10.1382i	0.609144	+	0.351690i
$832$	0.593094	−	2.21346i	0.0205618	−	0.0767379i
$833$	1.58507	−	0.424719i	0.0549195	−	0.0147156i
$834$	33.8594	+	19.5488i	1.17246	+	0.676918i
$835$		0			0
$836$	−8.02660	+	0.141270i	−0.277606	+	0.00488593i
$837$	38.0663	−	38.0663i	1.31576	−	1.31576i
$838$	4.43136	+	16.5381i	0.153079	+	0.571298i
$839$	−12.3466	+	21.3849i	−0.426251	+	0.738289i	−0.996536	−	0.0831578i	$-0.973499\pi$
$839$	−12.3466	+	21.3849i	−0.426251	+	0.738289i	0.570285	+	0.821447i	$0.306833\pi$
$840$		0			0
$841$	11.8919	−	20.5973i	0.410064	−	0.710252i
$842$	−25.1544	−	6.74010i	−0.866878	−	0.232279i
$843$	−45.7943	−	45.7943i	−1.57724	−	1.57724i
$844$	13.8564			0.476956
$845$		0			0
$846$	6.05861	−	3.49794i	0.208299	−	0.120262i
$847$	20.4573	−	20.4573i	0.702920	−	0.702920i
$848$	−0.883013	+	0.883013i	−0.0303228	+	0.0303228i
$849$	32.2639	+	55.8828i	1.10730	+	1.91789i
$850$		0			0
$851$	20.9747	−	12.1098i	0.719004	−	0.415117i
$852$	−2.75698	−	10.2892i	−0.0944527	−	0.352502i
$853$	0.895350	−	0.239908i	0.0306562	−	0.00821430i	−0.243458	−	0.969911i	$-0.578282\pi$
$853$	0.895350	−	0.239908i	0.0306562	−	0.00821430i	0.274115	+	0.961697i	$0.411615\pi$
$854$	−24.6324			−0.842903
$855$		0			0
$856$	−0.444071			−0.0151780
$857$	−28.0076	+	7.50461i	−0.956721	+	0.256353i	−0.703212	−	0.710980i	$-0.748251\pi$
$857$	−28.0076	+	7.50461i	−0.956721	+	0.256353i	−0.253509	+	0.967333i	$0.581585\pi$
$858$	3.66822	+	13.6900i	0.125231	+	0.467368i
$859$	18.2948	−	10.5625i	0.624210	−	0.360388i	−0.154296	−	0.988025i	$-0.549311\pi$
$859$	18.2948	−	10.5625i	0.624210	−	0.360388i	0.778506	+	0.627637i	$0.215978\pi$
$860$		0			0
$861$	−65.3353	−	113.164i	−2.22662	−	3.85662i
$862$	−27.1124	+	27.1124i	−0.923453	+	0.923453i
$863$	−17.2242	+	17.2242i	−0.586320	+	0.586320i	−0.936633	−	0.350313i	$-0.886075\pi$
$863$	−17.2242	+	17.2242i	−0.586320	+	0.586320i	0.350313	+	0.936633i	$0.386075\pi$
$864$	−15.3490	+	8.86175i	−0.522183	+	0.301483i
$865$		0			0
$866$	−16.1514			−0.548847
$867$	40.2537	+	40.2537i	1.36709	+	1.36709i
$868$	−11.1567	−	2.98943i	−0.378684	−	0.101468i
$869$	5.43166	−	9.40791i	0.184256	−	0.319141i
$870$		0			0
$871$	−7.21697	+	12.5002i	−0.244538	+	0.423552i
$872$	−0.566354	−	2.11366i	−0.0191792	−	0.0715776i
$873$	−36.8066	+	36.8066i	−1.24572	+	1.24572i
$874$	−7.12026	+	12.8497i	−0.240846	+	0.434647i
$875$		0			0
$876$	−6.43683	−	3.71631i	−0.217480	−	0.125562i
$877$	−16.7207	+	4.48030i	−0.564619	+	0.151289i	−0.529827	−	0.848106i	$-0.677743\pi$
$877$	−16.7207	+	4.48030i	−0.564619	+	0.151289i	−0.0347912	+	0.999395i	$0.511077\pi$
$878$	−7.55496	+	28.1955i	−0.254968	+	0.951552i
$879$	−1.86147	−	1.07472i	−0.0627858	−	0.0362494i
$880$		0			0
$881$	3.57093			0.120308			0.0601538	−	0.998189i	$-0.480841\pi$
$881$	3.57093			0.120308			0.0601538	+	0.998189i	$0.480841\pi$
$882$	43.6658	+	43.6658i	1.47030	+	1.47030i
$883$	−6.82865	+	25.4849i	−0.229802	+	0.857634i	0.750621	+	0.660733i	$0.229754\pi$
$883$	−6.82865	+	25.4849i	−0.229802	+	0.857634i	−0.980423	+	0.196901i	$0.936912\pi$
$884$	0.252031	+	0.436530i	0.00847671	+	0.0146821i
$885$		0			0
$886$		−	9.81904i		−	0.329877i
$887$	−2.54658	+	9.50396i	−0.0855057	+	0.319112i	−0.995409	−	0.0957077i	$-0.969489\pi$
$887$	−2.54658	+	9.50396i	−0.0855057	+	0.319112i	0.909904	+	0.414819i	$0.136155\pi$
$888$	6.24610	+	23.3108i	0.209606	+	0.782259i
$889$	7.35417	+	12.7378i	0.246651	+	0.427212i
$890$		0			0
$891$	31.9413	−	55.3239i	1.07007	−	1.85342i
$892$	−14.9354	−	14.9354i	−0.500073	−	0.500073i
$893$	2.65037	+	2.55869i	0.0886914	+	0.0856234i
$894$		−	30.0133i		−	1.00379i
$895$		0			0
$896$	3.29320	+	1.90133i	0.110018	+	0.0635189i
$897$	25.0520	+	6.71266i	0.836462	+	0.224129i
$898$	−12.7364	+	3.41270i	−0.425018	+	0.113883i
$899$	−6.00781	+	3.46861i	−0.200372	+	0.115685i
$900$		0			0
$901$		−	0.274687i		−	0.00915115i
$902$	18.2032	+	4.87753i	0.606100	+	0.162404i
$903$	30.6660	+	8.21693i	1.02050	+	0.273442i
$904$		−	17.7412i		−	0.590063i
$905$		0			0
$906$	−5.25679	+	3.03501i	−0.174645	+	0.100831i
$907$	7.86353	−	2.10703i	0.261104	−	0.0699627i	−0.125892	−	0.992044i	$-0.540179\pi$
$907$	7.86353	−	2.10703i	0.261104	−	0.0699627i	0.386996	+	0.922081i	$0.373513\pi$
$908$	16.3391	+	4.37804i	0.542231	+	0.145290i
$909$	−33.8590	−	19.5485i	−1.12303	−	0.648384i
$910$		0			0
$911$		−	2.03383i		−	0.0673837i	−0.999432	−	0.0336918i	$-0.989274\pi$
$911$		−	2.03383i		−	0.0673837i	0.999432	−	0.0336918i	$-0.0107265\pi$
$912$	−10.5313	−	10.1670i	−0.348725	−	0.336662i
$913$	−1.00106	−	1.00106i	−0.0331303	−	0.0331303i
$914$	15.5041	−	26.8538i	0.512829	−	0.888246i
$915$		0			0
$916$	13.6153	+	23.5824i	0.449862	+	0.779183i
$917$	−3.87586	−	14.4649i	−0.127992	−	0.477674i
$918$	1.00902	−	3.76573i	0.0333028	−	0.124288i
$919$			44.8974i			1.48103i	0.672041	+	0.740514i	$0.265418\pi$
$919$			44.8974i			1.48103i	−0.672041	+	0.740514i	$0.734582\pi$
$920$		0			0
$921$	38.2473	+	66.2463i	1.26029	+	2.18289i
$922$	−5.55586	+	20.7348i	−0.182972	+	0.682863i
$923$	−5.13974	−	5.13974i	−0.169177	−	0.169177i
$924$	−23.5190			−0.773717
$925$		0			0
$926$	21.7664	+	12.5668i	0.715289	+	0.412972i
$927$	11.3072	−	42.1989i	0.371376	−	1.38599i
$928$	2.20609	−	0.591120i	0.0724185	−	0.0194045i
$929$	3.38174	+	1.95245i	0.110951	+	0.0640577i	0.554449	−	0.832218i	$-0.312929\pi$
$929$	3.38174	+	1.95245i	0.110951	+	0.0640577i	−0.443498	+	0.896276i	$0.646262\pi$
$930$		0			0
$931$	−15.7610	+	28.4433i	−0.516546	+	0.932193i
$932$	0.255159	−	0.255159i	0.00835801	−	0.00835801i
$933$	−23.0169	−	85.9004i	−0.753540	−	2.81225i
$934$	−1.76685	+	3.06028i	−0.0578131	+	0.100135i
$935$		0			0
$936$	−9.48428	+	16.4273i	−0.310003	+	0.536942i
$937$	45.6756	+	12.2387i	1.49216	+	0.399822i	0.910464	−	0.413588i	$-0.135725\pi$
$937$	45.6756	+	12.2387i	1.49216	+	0.399822i	0.581691	+	0.813410i	$0.302391\pi$
$938$	−16.9367	−	16.9367i	−0.553003	−	0.553003i
$939$	27.8497			0.908840
$940$		0			0
$941$	20.8096	−	12.0144i	0.678372	−	0.391659i	−0.120869	−	0.992668i	$-0.538568\pi$
$941$	20.8096	−	12.0144i	0.678372	−	0.391659i	0.799242	+	0.601010i	$0.205235\pi$
$942$	34.1096	−	34.1096i	1.11135	−	1.11135i
$943$	24.3853	−	24.3853i	0.794096	−	0.794096i
$944$	−3.04615	−	5.27609i	−0.0991438	−	0.171722i
$945$		0			0
$946$	−3.96524	+	2.28933i	−0.128921	+	0.0744327i
$947$	−2.46962	−	9.21674i	−0.0802518	−	0.299504i	0.914121	−	0.405442i	$-0.132882\pi$
$947$	−2.46962	−	9.21674i	−0.0802518	−	0.299504i	−0.994373	+	0.105938i	$0.966216\pi$
$948$	19.1335	−	5.12679i	0.621426	−	0.166511i
$949$	−5.07178			−0.164637
$950$		0			0
$951$	48.9302			1.58667
$952$	−0.807954	+	0.216491i	−0.0261859	+	0.00701650i
$953$	9.97705	+	37.2349i	0.323188	+	1.20616i	0.916121	+	0.400903i	$0.131304\pi$
$953$	9.97705	+	37.2349i	0.323188	+	1.20616i	−0.592932	+	0.805252i	$0.702030\pi$
$954$	8.95198	−	5.16843i	0.289831	−	0.167334i
$955$		0			0
$956$	−6.92207	−	11.9894i	−0.223876	−	0.387764i
$957$	−9.98840	+	9.98840i	−0.322879	+	0.322879i
$958$	24.9612	−	24.9612i	0.806461	−	0.806461i
$959$	−67.5150	+	38.9798i	−2.18017	+	1.25872i
$960$		0			0
$961$	21.7740			0.702388
$962$	11.6444	+	11.6444i	0.375430	+	0.375430i
$963$	3.55061	+	0.951382i	0.114417	+	0.0306579i
$964$	13.7432	−	23.8040i	0.442639	−	0.766674i
$965$		0			0
$966$	−21.5193	+	37.2725i	−0.692371	+	1.19922i
$967$	−14.7886	−	55.1920i	−0.475571	−	1.77485i	−0.619212	−	0.785224i	$-0.712548\pi$
$967$	−14.7886	−	55.1920i	−0.475571	−	1.77485i	0.143641	−	0.989630i	$-0.454119\pi$
$968$	−5.37973	+	5.37973i	−0.172911	+	0.172911i
$969$	3.21940	−	0.0566623i	0.103422	−	0.00182025i
$970$		0			0
$971$	−3.40601	−	1.96646i	−0.109304	−	0.0631068i	0.444351	−	0.895853i	$-0.353434\pi$
$971$	−3.40601	−	1.96646i	−0.109304	−	0.0631068i	−0.553655	+	0.832746i	$0.686768\pi$
$972$	61.1569	−	16.3870i	1.96161	−	0.525612i
$973$	−11.4584	+	42.7632i	−0.367339	+	1.37093i
$974$	−6.25148	−	3.60930i	−0.200310	−	0.115649i
$975$		0			0
$976$	6.47768			0.207346
$977$	29.5112	+	29.5112i	0.944146	+	0.944146i	0.998521	−	0.0543743i	$-0.0173164\pi$
$977$	29.5112	+	29.5112i	0.944146	+	0.944146i	−0.0543743	+	0.998521i	$0.517316\pi$
$978$	−1.73079	+	6.45940i	−0.0553446	+	0.206549i
$979$	15.9698	+	27.6604i	0.510396	+	0.884031i
$980$		0			0
$981$			18.1133i			0.578314i
$982$	4.94770	−	18.4651i	0.157888	−	0.589244i
$983$	−10.0937	−	37.6702i	−0.321939	−	1.20149i	−0.917353	−	0.398074i	$-0.869679\pi$
$983$	−10.0937	−	37.6702i	−0.321939	−	1.20149i	0.595415	−	0.803419i	$-0.296988\pi$
$984$	17.1815	+	29.7592i	0.547726	+	0.948690i
$985$		0			0
$986$	−0.251192	+	0.435077i	−0.00799958	+	0.0138557i
$987$	7.63162	+	7.63162i	0.242917	+	0.242917i
$988$	−9.69224	−	2.41505i	−0.308351	−	0.0768331i
$989$			8.37874i			0.266429i
$990$		0			0
$991$	−18.1623	−	10.4860i	−0.576944	−	0.333099i	0.182974	−	0.983118i	$-0.441428\pi$
$991$	−18.1623	−	10.4860i	−0.576944	−	0.333099i	−0.759918	+	0.650019i	$0.774761\pi$
$992$	2.93393	+	0.786144i	0.0931524	+	0.0249601i
$993$	94.0610	−	25.2036i	2.98494	−	0.799811i
$994$	10.4459	−	6.03095i	0.331324	−	0.191290i
$995$		0			0
$996$		−	2.58145i		−	0.0817962i
$997$	32.2028	+	8.62870i	1.01987	+	0.273274i	0.729749	−	0.683716i	$-0.239637\pi$
$997$	32.2028	+	8.62870i	1.01987	+	0.273274i	0.290123	+	0.956989i	$0.406304\pi$
$998$	−13.6644	−	3.66136i	−0.432539	−	0.115898i
$999$		−	127.366i		−	4.02968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.g.293.8		32
5.2	odd	4	inner	950.2.q.g.407.8		32
5.3	odd	4		190.2.m.b.27.1	✓	32
5.4	even	2		190.2.m.b.103.1	yes	32
19.12	odd	6	inner	950.2.q.g.943.8		32
95.12	even	12	inner	950.2.q.g.107.8		32
95.69	odd	6		190.2.m.b.183.1	yes	32
95.88	even	12		190.2.m.b.107.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.b.27.1	✓	32	5.3	odd	4
190.2.m.b.103.1	yes	32	5.4	even	2
190.2.m.b.107.1	yes	32	95.88	even	12
190.2.m.b.183.1	yes	32	95.69	odd	6
950.2.q.g.107.8		32	95.12	even	12	inner
950.2.q.g.293.8		32	1.1	even	1	trivial
950.2.q.g.407.8		32	5.2	odd	4	inner
950.2.q.g.943.8		32	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.869171 + 3.24379i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.67911 + 2.90830i) q^{6} +(-2.68888 + 2.68888i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-7.16865 + 4.13882i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.869171 + 3.24379i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.67911 + 2.90830i) q^{6} +(-2.68888 + 2.68888i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-7.16865 + 4.13882i) q^{9} +1.84171 q^{11} +(2.37462 + 2.37462i) q^{12} +(2.21346 + 0.593094i) q^{13} +(-1.90133 + 3.29320i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.0569314 + 0.212471i) q^{17} +(-5.85318 + 5.85318i) q^{18} +(-3.81269 - 2.11268i) q^{19} +(-11.0593 - 6.38508i) q^{21} +(1.77896 - 0.476670i) q^{22} +(0.872284 - 3.25541i) q^{23} +(2.90830 + 1.67911i) q^{24} +2.29154 q^{26} +(-12.5324 - 12.5324i) q^{27} +(-0.984199 + 3.67308i) q^{28} +(1.14196 + 1.97793i) q^{29} +3.03743i q^{31} +(0.258819 - 0.965926i) q^{32} +(1.60076 + 5.97413i) q^{33} +(0.109983 + 0.190496i) q^{34} +(-4.13882 + 7.16865i) q^{36} +(5.08146 + 5.08146i) q^{37} +(-4.22957 - 1.05390i) q^{38} +7.69550i q^{39} +(8.86161 + 5.11625i) q^{41} +(-12.3350 - 3.30516i) q^{42} +(-2.40138 + 0.643448i) q^{43} +(1.59497 - 0.920856i) q^{44} -3.37025i q^{46} +(-0.816355 - 0.218742i) q^{47} +(3.24379 + 0.869171i) q^{48} -7.46018i q^{49} +(-0.639729 + 0.369347i) q^{51} +(2.21346 - 0.593094i) q^{52} +(-1.20622 - 0.323205i) q^{53} +(-15.3490 - 8.86175i) q^{54} +3.80265i q^{56} +(3.53923 - 14.2038i) q^{57} +(1.61497 + 1.61497i) q^{58} +(3.04615 - 5.27609i) q^{59} +(3.23884 + 5.60984i) q^{61} +(0.786144 + 2.93393i) q^{62} +(8.14685 - 30.4045i) q^{63} -1.00000i q^{64} +(3.09244 + 5.35626i) q^{66} +(-1.63025 + 6.08417i) q^{67} +(0.155540 + 0.155540i) q^{68} +11.3180 q^{69} +(-2.74701 - 1.58598i) q^{71} +(-2.14241 + 7.99559i) q^{72} +(-2.13784 + 0.572834i) q^{73} +(6.22350 + 3.59314i) q^{74} +(-4.35822 + 0.0767059i) q^{76} +(-4.95215 + 4.95215i) q^{77} +(1.99174 + 7.43328i) q^{78} +(2.94924 - 5.10824i) q^{79} +(17.3432 - 30.0394i) q^{81} +(9.88384 + 2.64837i) q^{82} +(-0.543549 - 0.543549i) q^{83} -12.7702 q^{84} +(-2.15302 + 1.24305i) q^{86} +(-5.42343 + 5.42343i) q^{87} +(1.30229 - 1.30229i) q^{88} +(8.67114 + 15.0189i) q^{89} +(-7.54649 + 4.35697i) q^{91} +(-0.872284 - 3.25541i) q^{92} +(-9.85278 + 2.64005i) q^{93} -0.845153 q^{94} +3.35822 q^{96} +(6.07404 - 1.62754i) q^{97} +(-1.93084 - 7.20598i) q^{98} +(-13.2026 + 7.62252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) 32 * q + 12 * q^3 - 24 * q^7	\( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Introduction

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