LMFDB - Embedded newform 950.2.u.e.199.4

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			199.4
Character	$\chi$	$=$	950.199
Dual form			950.2.u.e.549.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(1.07851 + 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.28531 + 1.07851i) q^{6} +(-0.411781 - 0.237742i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +O(q^{10})$	\(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} +(-0.411781 - 0.237742i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +(2.79789 + 4.84609i) q^{11} +(1.45307 + 0.838929i) q^{12} +(1.58261 - 1.88608i) q^{13} +(-0.446808 - 0.162625i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.82975 - 0.498962i) q^{17} -0.184793i q^{18} +(-3.17997 - 2.98124i) q^{19} +(-0.138535 - 0.785674i) q^{21} +(3.59690 + 4.28662i) q^{22} +(1.50010 + 4.12150i) q^{23} +(1.57667 + 0.573861i) q^{24} +(1.23105 - 2.13224i) q^{26} +(4.62772 - 2.67181i) q^{27} +(-0.468260 - 0.0825669i) q^{28} +(-1.51505 + 8.59227i) q^{29} +(-2.88192 + 4.99163i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-3.21120 + 8.82271i) q^{33} +(2.70012 - 0.982762i) q^{34} +(-0.0320889 - 0.181985i) q^{36} -6.02691i q^{37} +(-3.64935 - 2.38375i) q^{38} +4.13105 q^{39} +(5.18173 - 4.34799i) q^{41} +(-0.272862 - 0.749681i) q^{42} +(-0.157881 + 0.433776i) q^{43} +(4.28662 + 3.59690i) q^{44} +(2.19300 + 3.79839i) q^{46} +(-2.59093 - 0.456851i) q^{47} +(1.65237 + 0.291357i) q^{48} +(-3.38696 - 5.86638i) q^{49} +(3.69323 + 3.09899i) q^{51} +(0.842088 - 2.31362i) q^{52} +(-2.70479 - 7.43135i) q^{53} +(4.09346 - 3.43482i) q^{54} -0.475484 q^{56} +(0.402213 - 7.30255i) q^{57} +8.72482i q^{58} +(1.42203 + 8.06471i) q^{59} +(-2.98996 + 1.08826i) q^{61} +(-1.97135 + 5.41624i) q^{62} +(-0.0564791 + 0.0673091i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.63037 + 9.24629i) q^{66} +(0.148899 + 0.0262550i) q^{67} +(2.48844 - 1.43670i) q^{68} +(-3.67955 + 6.37316i) q^{69} +(-4.48601 - 1.63277i) q^{71} +(-0.0632028 - 0.173648i) q^{72} +(-5.91246 - 7.04620i) q^{73} +(-1.04656 - 5.93535i) q^{74} +(-4.00784 - 1.71384i) q^{76} -2.66070i q^{77} +(4.06829 - 0.717350i) q^{78} +(-9.48725 + 7.96075i) q^{79} +(7.90420 + 2.87689i) q^{81} +(4.34799 - 5.18173i) q^{82} +(-11.4239 - 6.59560i) q^{83} +(-0.398897 - 0.690910i) q^{84} +(-0.0801585 + 0.454602i) q^{86} +(-12.6777 + 7.31950i) q^{87} +(4.84609 + 2.79789i) q^{88} +(1.23909 + 1.03972i) q^{89} +(-1.10009 + 0.400399i) q^{91} +(2.81927 + 3.35987i) q^{92} +(-9.52398 + 1.67933i) q^{93} -2.63090 q^{94} +1.67786 q^{96} +(-4.95422 + 0.873563i) q^{97} +(-4.35419 - 5.18912i) q^{98} +(0.971697 - 0.353669i) 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
$7$	−0.411781	−	0.237742i	−0.155639	−	0.0898579i	0.420158	−	0.907451i	$-0.361975\pi$
$7$	−0.411781	−	0.237742i	−0.155639	−	0.0898579i	−0.575797	+	0.817593i	$0.695308\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	0.0320889	−	0.181985i	0.0106963	−	0.0606617i
$10$		0			0
$11$	2.79789	+	4.84609i	0.843596	+	1.46115i	0.886835	+	0.462086i	$0.152899\pi$
$11$	2.79789	+	4.84609i	0.843596	+	1.46115i	−0.0432392	+	0.999065i	$0.513768\pi$
$12$	1.45307	+	0.838929i	0.419465	+	0.242178i
$13$	1.58261	−	1.88608i	0.438936	−	0.523104i	−0.500542	−	0.865712i	$-0.666866\pi$
$13$	1.58261	−	1.88608i	0.438936	−	0.523104i	0.939478	+	0.342608i	$0.111310\pi$
$14$	−0.446808	−	0.162625i	−0.119415	−	0.0434633i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.82975	−	0.498962i	0.686316	−	0.121016i	0.180393	−	0.983595i	$-0.442263\pi$
$17$	2.82975	−	0.498962i	0.686316	−	0.121016i	0.505923	+	0.862579i	$0.331152\pi$
$18$		−	0.184793i		−	0.0435560i
$19$	−3.17997	−	2.98124i	−0.729535	−	0.683944i
$19$	−3.17997	−	2.98124i	−0.729535	−	0.683944i
$20$		0			0
$21$	−0.138535	−	0.785674i	−0.0302309	−	0.171448i
$22$	3.59690	+	4.28662i	0.766862	+	0.913910i
$23$	1.50010	+	4.12150i	0.312793	+	0.859391i	0.992090	+	0.125528i	$0.0400625\pi$
$23$	1.50010	+	4.12150i	0.312793	+	0.859391i	−0.679297	+	0.733863i	$0.737715\pi$
$24$	1.57667	+	0.573861i	0.321837	+	0.117139i
$25$		0			0
$26$	1.23105	−	2.13224i	0.241429	−	0.418167i
$27$	4.62772	−	2.67181i	0.890605	−	0.514191i
$28$	−0.468260	−	0.0825669i	−0.0884928	−	0.0156037i
$29$	−1.51505	+	8.59227i	−0.281337	+	1.59554i	0.436745	+	0.899586i	$0.356131\pi$
$29$	−1.51505	+	8.59227i	−0.281337	+	1.59554i	−0.718082	+	0.695958i	$0.754980\pi$
$30$		0			0
$31$	−2.88192	+	4.99163i	−0.517608	+	0.896524i	0.482183	+	0.876071i	$0.339844\pi$
$31$	−2.88192	+	4.99163i	−0.517608	+	0.896524i	−0.999791	+	0.0204528i	$0.993489\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−3.21120	+	8.82271i	−0.558999	+	1.53584i
$34$	2.70012	−	0.982762i	0.463066	−	0.168542i
$35$		0			0
$36$	−0.0320889	−	0.181985i	−0.00534815	−	0.0303309i
$37$		−	6.02691i		−	0.990819i	−0.868660	−	0.495409i	$-0.835018\pi$
$37$		−	6.02691i		−	0.990819i	0.868660	−	0.495409i	$-0.164982\pi$
$38$	−3.64935	−	2.38375i	−0.592002	−	0.386696i
$39$	4.13105			0.661498
$40$		0			0
$41$	5.18173	−	4.34799i	0.809250	−	0.679041i	−0.141179	−	0.989984i	$-0.545089\pi$
$41$	5.18173	−	4.34799i	0.809250	−	0.679041i	0.950429	+	0.310943i	$0.100645\pi$
$42$	−0.272862	−	0.749681i	−0.0421035	−	0.115678i
$43$	−0.157881	+	0.433776i	−0.0240767	+	0.0661502i	−0.951149	−	0.308733i	$-0.900095\pi$
$43$	−0.157881	+	0.433776i	−0.0240767	+	0.0661502i	0.927072	+	0.374883i	$0.122317\pi$
$44$	4.28662	+	3.59690i	0.646232	+	0.542253i
$45$		0			0
$46$	2.19300	+	3.79839i	0.323340	+	0.560042i
$47$	−2.59093	−	0.456851i	−0.377926	−	0.0666386i	−0.0185414	−	0.999828i	$-0.505902\pi$
$47$	−2.59093	−	0.456851i	−0.377926	−	0.0666386i	−0.359385	+	0.933190i	$0.617013\pi$
$48$	1.65237	+	0.291357i	0.238499	+	0.0420538i
$49$	−3.38696	−	5.86638i	−0.483851	−	0.838055i
$50$		0			0
$51$	3.69323	+	3.09899i	0.517155	+	0.433945i
$52$	0.842088	−	2.31362i	0.116777	−	0.320841i
$53$	−2.70479	−	7.43135i	−0.371531	−	1.02077i	−0.974770	−	0.223213i	$-0.928345\pi$
$53$	−2.70479	−	7.43135i	−0.371531	−	1.02077i	0.603238	−	0.797561i	$-0.293877\pi$
$54$	4.09346	−	3.43482i	0.557049	−	0.467420i
$55$		0			0
$56$	−0.475484			−0.0635392
$57$	0.402213	−	7.30255i	0.0532744	−	0.967246i
$58$			8.72482i			1.14562i
$59$	1.42203	+	8.06471i	0.185132	+	1.04994i	0.925786	+	0.378049i	$0.123405\pi$
$59$	1.42203	+	8.06471i	0.185132	+	1.04994i	−0.740653	+	0.671887i	$0.765484\pi$
$60$		0			0
$61$	−2.98996	+	1.08826i	−0.382825	+	0.139337i	−0.526262	−	0.850323i	$-0.676407\pi$
$61$	−2.98996	+	1.08826i	−0.382825	+	0.139337i	0.143437	+	0.989659i	$0.454185\pi$
$62$	−1.97135	+	5.41624i	−0.250362	+	0.687863i
$63$	−0.0564791	+	0.0673091i	−0.00711569	+	0.00848015i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−1.63037	+	9.24629i	−0.200685	+	1.13814i
$67$	0.148899	+	0.0262550i	0.0181910	+	0.00320756i	0.182736	−	0.983162i	$-0.441505\pi$
$67$	0.148899	+	0.0262550i	0.0181910	+	0.00320756i	−0.164545	+	0.986370i	$0.552616\pi$
$68$	2.48844	−	1.43670i	0.301768	−	0.174226i
$69$	−3.67955	+	6.37316i	−0.442965	+	0.767238i
$70$		0			0
$71$	−4.48601	−	1.63277i	−0.532392	−	0.193775i	0.0618143	−	0.998088i	$-0.480311\pi$
$71$	−4.48601	−	1.63277i	−0.532392	−	0.193775i	−0.594206	+	0.804313i	$0.702534\pi$
$72$	−0.0632028	−	0.173648i	−0.00744852	−	0.0204646i
$73$	−5.91246	−	7.04620i	−0.692001	−	0.824695i	0.299595	−	0.954066i	$-0.403148\pi$
$73$	−5.91246	−	7.04620i	−0.692001	−	0.824695i	−0.991596	+	0.129372i	$0.958704\pi$
$74$	−1.04656	−	5.93535i	−0.121660	−	0.689971i
$75$		0			0
$76$	−4.00784	−	1.71384i	−0.459731	−	0.196591i
$77$		−	2.66070i		−	0.303215i
$78$	4.06829	−	0.717350i	0.460643	−	0.0812239i
$79$	−9.48725	+	7.96075i	−1.06740	+	0.895654i	−0.994814	−	0.101708i	$-0.967569\pi$
$79$	−9.48725	+	7.96075i	−1.06740	+	0.895654i	−0.0725851	+	0.997362i	$0.523125\pi$
$80$		0			0
$81$	7.90420	+	2.87689i	0.878244	+	0.319655i
$82$	4.34799	−	5.18173i	0.480155	−	0.572226i
$83$	−11.4239	−	6.59560i	−1.25394	−	0.723961i	−0.282048	−	0.959400i	$-0.591014\pi$
$83$	−11.4239	−	6.59560i	−1.25394	−	0.723961i	−0.971889	+	0.235439i	$0.924347\pi$
$84$	−0.398897	−	0.690910i	−0.0435232	−	0.0753844i
$85$		0			0
$86$	−0.0801585	+	0.454602i	−0.00864372	+	0.0490209i
$87$	−12.6777	+	7.31950i	−1.35920	+	0.784733i
$88$	4.84609	+	2.79789i	0.516595	+	0.298256i
$89$	1.23909	+	1.03972i	0.131343	+	0.110210i	0.706093	−	0.708119i	$-0.250456\pi$
$89$	1.23909	+	1.03972i	0.131343	+	0.110210i	−0.574750	+	0.818329i	$0.694901\pi$
$90$		0			0
$91$	−1.10009	+	0.400399i	−0.115320	+	0.0419732i
$92$	2.81927	+	3.35987i	0.293929	+	0.350291i
$93$	−9.52398	+	1.67933i	−0.987591	+	0.174139i
$94$	−2.63090			−0.271357
$95$		0			0
$96$	1.67786			0.171246
$97$	−4.95422	+	0.873563i	−0.503025	+	0.0886969i	−0.419402	−	0.907801i	$-0.637760\pi$
$97$	−4.95422	+	0.873563i	−0.503025	+	0.0886969i	−0.0836230	+	0.996497i	$0.526649\pi$
$98$	−4.35419	−	5.18912i	−0.439839	−	0.524180i
$99$	0.971697	−	0.353669i	0.0976593	−	0.0355451i
$100$		0			0
$101$	4.13640	+	3.47085i	0.411587	+	0.345362i	0.824952	−	0.565203i	$-0.191202\pi$
$101$	4.13640	+	3.47085i	0.411587	+	0.345362i	−0.413365	+	0.910565i	$0.635647\pi$
$102$	4.17525	+	2.41058i	0.413412	+	0.238683i
$103$	11.3123	−	6.53114i	1.11463	−	0.643532i	0.174605	−	0.984638i	$-0.444135\pi$
$103$	11.3123	−	6.53114i	1.11463	−	0.643532i	0.940025	+	0.341107i	$0.110802\pi$
$104$	0.427539	−	2.42469i	0.0419237	−	0.237761i
$105$		0			0
$106$	−3.95414	−	6.84877i	−0.384060	−	0.665211i
$107$	−1.02955	−	0.594412i	−0.0995305	−	0.0574640i	0.449409	−	0.893326i	$-0.351635\pi$
$107$	−1.02955	−	0.594412i	−0.0995305	−	0.0574640i	−0.548939	+	0.835862i	$0.684968\pi$
$108$	3.43482	−	4.09346i	0.330516	−	0.393893i
$109$	10.9101	+	3.97094i	1.04499	+	0.380347i	0.806771	−	0.590864i	$-0.201213\pi$
$109$	10.9101	+	3.97094i	1.04499	+	0.380347i	0.238223	+	0.971210i	$0.423435\pi$
$110$		0			0
$111$	7.74648	−	6.50007i	0.735263	−	0.616959i
$112$	−0.468260	+	0.0825669i	−0.0442464	+	0.00780183i
$113$		−	12.6577i		−	1.19074i	−0.803452	−	0.595369i	$-0.797006\pi$
$113$		−	12.6577i		−	1.19074i	0.803452	−	0.595369i	$-0.202994\pi$
$114$	−0.871971	−	7.26145i	−0.0816676	−	0.680097i
$115$		0			0
$116$	1.51505	+	8.59227i	0.140669	+	0.797772i
$117$	−0.292454	−	0.348533i	−0.0270374	−	0.0322219i
$118$	2.80085	+	7.69526i	0.257839	+	0.708406i
$119$	−1.28386	−	0.467287i	−0.117691	−	0.0428362i
$120$		0			0
$121$	−10.1564	+	17.5914i	−0.923308	+	1.59922i
$122$	−2.75556	+	1.59092i	−0.249477	+	0.144035i
$123$	11.1771	+	1.97082i	1.00780	+	0.177703i
$124$	−1.00088	+	5.67627i	−0.0898817	+	0.509744i
$125$		0			0
$126$	−0.0439329	+	0.0760940i	−0.00391385	+	0.00677899i
$127$	3.96962	−	4.73081i	0.352247	−	0.419791i	−0.560604	−	0.828084i	$-0.689431\pi$
$127$	3.96962	−	4.73081i	0.352247	−	0.419791i	0.912851	+	0.408292i	$0.133876\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−0.727814	+	0.264903i	−0.0640805	+	0.0233234i
$130$		0			0
$131$	−3.39327	−	19.2442i	−0.296471	−	1.68137i	−0.661163	−	0.750243i	$-0.729937\pi$
$131$	−3.39327	−	19.2442i	−0.296471	−	1.68137i	0.364692	−	0.931128i	$-0.381174\pi$
$132$			9.38893i			0.817201i
$133$	0.600685	+	1.98363i	0.0520860	+	0.172002i
$134$	0.151196			0.0130614
$135$		0			0
$136$	2.20116	−	1.84699i	0.188748	−	0.158378i
$137$	−4.56885	−	12.5528i	−0.390344	−	1.07246i	−0.966845	−	0.255364i	$-0.917805\pi$
$137$	−4.56885	−	12.5528i	−0.390344	−	1.07246i	0.576501	−	0.817096i	$-0.304418\pi$
$138$	−2.51696	+	6.91528i	−0.214258	+	0.588668i
$139$	−12.8285	−	10.7644i	−1.08810	−	0.913021i	−0.0915279	−	0.995803i	$-0.529175\pi$
$139$	−12.8285	−	10.7644i	−1.08810	−	0.913021i	−0.996568	+	0.0827819i	$0.973620\pi$
$140$		0			0
$141$	−2.20714	−	3.82288i	−0.185875	−	0.321944i
$142$	−4.70139	−	0.828981i	−0.394532	−	0.0695666i
$143$	13.5681	+	2.39242i	1.13462	+	0.200064i
$144$	−0.0923963	−	0.160035i	−0.00769969	−	0.0133363i
$145$		0			0
$146$	−7.04620	−	5.91246i	−0.583147	−	0.489319i
$147$	3.88729	−	10.6802i	0.320618	−	0.880891i
$148$	−2.06133	−	5.66345i	−0.169440	−	0.465533i
$149$	10.2016	−	8.56016i	0.835748	−	0.701276i	−0.120855	−	0.992670i	$-0.538564\pi$
$149$	10.2016	−	8.56016i	0.835748	−	0.701276i	0.956603	+	0.291395i	$0.0941193\pi$
$150$		0			0
$151$	−13.1191			−1.06762			−0.533810	−	0.845604i	$-0.679240\pi$
$151$	−13.1191			−1.06762			−0.533810	+	0.845604i	$0.679240\pi$
$152$	−4.24455	−	0.991846i	−0.344279	−	0.0804493i
$153$		−	0.530984i		−	0.0429275i
$154$	−0.462026	−	2.62028i	−0.0372311	−	0.211148i
$155$		0			0
$156$	3.88192	−	1.41290i	0.310802	−	0.113123i
$157$	−2.01029	+	5.52322i	−0.160438	+	0.440801i	−0.993699	−	0.112079i	$-0.964249\pi$
$157$	−2.01029	+	5.52322i	−0.160438	+	0.440801i	0.833261	+	0.552880i	$0.186471\pi$
$158$	−7.96075	+	9.48725i	−0.633323	+	0.754765i
$159$	6.63448	−	11.4913i	0.526149	−	0.911316i
$160$		0			0
$161$	0.362139	−	2.05379i	0.0285405	−	0.161861i
$162$	8.28368	+	1.46064i	0.650828	+	0.114758i
$163$	7.39670	−	4.27049i	0.579354	−	0.334490i	−0.181522	−	0.983387i	$-0.558102\pi$
$163$	7.39670	−	4.27049i	0.579354	−	0.334490i	0.760877	+	0.648896i	$0.224769\pi$
$164$	3.38213	−	5.85803i	0.264100	−	0.457435i
$165$		0			0
$166$	−12.3957	−	4.51166i	−0.962091	−	0.350172i
$167$	6.69625	+	18.3978i	0.518172	+	1.42367i	0.872532	+	0.488556i	$0.162476\pi$
$167$	6.69625	+	18.3978i	0.518172	+	1.42367i	−0.354361	+	0.935109i	$0.615302\pi$
$168$	−0.512812	−	0.611146i	−0.0395643	−	0.0471509i
$169$	1.20478	+	6.83266i	0.0926756	+	0.525589i
$170$		0			0
$171$	−0.644583	+	0.483042i	−0.0492925	+	0.0369392i
$172$			0.461615i			0.0351978i
$173$	−24.5344	+	4.32608i	−1.86532	+	0.328906i	−0.988417	−	0.151763i	$-0.951505\pi$
$173$	−24.5344	+	4.32608i	−1.86532	+	0.328906i	−0.876902	+	0.480669i	$0.840394\pi$
$174$	−11.2141	+	9.40977i	−0.850141	+	0.713353i
$175$		0			0
$176$	5.25832	+	1.91387i	0.396360	+	0.144263i
$177$	−8.83202	+	10.5256i	−0.663855	+	0.791152i
$178$	1.40081	+	0.808758i	0.104995	+	0.0606189i
$179$	0.0206472	+	0.0357621i	0.00154325	+	0.00267298i	0.866796	−	0.498663i	$-0.166175\pi$
$179$	0.0206472	+	0.0357621i	0.00154325	+	0.00267298i	−0.865253	+	0.501336i	$0.832842\pi$
$180$		0			0
$181$	2.23778	−	12.6911i	0.166333	−	0.943321i	−0.781346	−	0.624098i	$-0.785467\pi$
$181$	2.23778	−	12.6911i	0.166333	−	0.943321i	0.947679	−	0.319224i	$-0.103422\pi$
$182$	−1.01385	+	0.585344i	−0.0751512	+	0.0433886i
$183$	−4.62344	−	2.66934i	−0.341774	−	0.197324i
$184$	3.35987	+	2.81927i	0.247693	+	0.207839i
$185$		0			0
$186$	−9.08768	+	3.30764i	−0.666341	+	0.242528i
$187$	10.3353	+	12.3172i	0.755796	+	0.900722i
$188$	−2.59093	+	0.456851i	−0.188963	+	0.0333193i
$189$	−2.54081			−0.184817
$190$		0			0
$191$	−17.4110			−1.25982			−0.629909	−	0.776669i	$-0.716908\pi$
$191$	−17.4110			−1.25982			−0.629909	+	0.776669i	$0.716908\pi$
$192$	1.65237	−	0.291357i	0.119249	−	0.0210269i
$193$	14.2613	+	16.9959i	1.02655	+	1.22339i	0.974416	+	0.224752i	$0.0721572\pi$
$193$	14.2613	+	16.9959i	1.02655	+	1.22339i	0.0521318	+	0.998640i	$0.483398\pi$
$194$	−4.72726	+	1.72058i	−0.339398	+	0.123531i
$195$		0			0
$196$	−5.18912	−	4.35419i	−0.370651	−	0.311013i
$197$	−4.30504	−	2.48552i	−0.306721	−	0.177086i	0.338737	−	0.940881i	$-0.390000\pi$
$197$	−4.30504	−	2.48552i	−0.306721	−	0.177086i	−0.645458	+	0.763795i	$0.723334\pi$
$198$	0.895521	−	0.517029i	0.0636419	−	0.0367437i
$199$	−1.43717	+	8.15057i	−0.101878	+	0.577779i	0.890543	+	0.454898i	$0.150324\pi$
$199$	−1.43717	+	8.15057i	−0.101878	+	0.577779i	−0.992421	+	0.122881i	$0.960787\pi$
$200$		0			0
$201$	0.126843	+	0.219699i	0.00894682	+	0.0154963i
$202$	4.67626	+	2.69984i	0.329021	+	0.189960i
$203$	2.66661	−	3.17794i	0.187159	−	0.223048i
$204$	4.53041	+	1.64894i	0.317192	+	0.115449i
$205$		0			0
$206$	10.0063	−	8.39627i	0.697171	−	0.584996i
$207$	0.798187	−	0.140742i	0.0554779	−	0.00978224i
$208$		−	2.46210i		−	0.170716i
$209$	5.55015	−	23.7516i	0.383912	−	1.64293i
$210$		0			0
$211$	−2.81533	−	15.9665i	−0.193815	−	1.09918i	−0.914096	−	0.405499i	$-0.867098\pi$
$211$	−2.81533	−	15.9665i	−0.193815	−	1.09918i	0.720280	−	0.693683i	$-0.244013\pi$
$212$	−5.08334	−	6.05809i	−0.349125	−	0.416071i
$213$	−2.73956	−	7.52689i	−0.187712	−	0.515734i
$214$	−1.11713	−	0.406602i	−0.0763654	−	0.0277947i
$215$		0			0
$216$	2.67181	−	4.62772i	0.181794	−	0.314876i
$217$	2.37344	−	1.37031i	0.161120	−	0.0930224i
$218$	11.4339	+	2.01610i	0.774399	+	0.136547i
$219$	2.67995	−	15.1987i	0.181094	−	1.02704i
$220$		0			0
$221$	3.53730	−	6.12679i	0.237945	−	0.412133i
$222$	6.50007	−	7.74648i	0.436256	−	0.519909i
$223$	−8.13268	+	22.3444i	−0.544605	+	1.49629i	0.296294	+	0.955097i	$0.404249\pi$
$223$	−8.13268	+	22.3444i	−0.544605	+	1.49629i	−0.840899	+	0.541192i	$0.817973\pi$
$224$	−0.446808	+	0.162625i	−0.0298536	+	0.0108658i
$225$		0			0
$226$	−2.19799	−	12.4654i	−0.146208	−	0.829187i
$227$		−	1.49007i		−	0.0988996i	−0.998777	−	0.0494498i	$-0.984253\pi$
$227$		−	1.49007i		−	0.0988996i	0.998777	−	0.0494498i	$-0.0157468\pi$
$228$	−2.11966	−	6.99971i	−0.140378	−	0.463567i
$229$	−17.9170			−1.18399			−0.591995	−	0.805942i	$-0.701659\pi$
$229$	−17.9170			−1.18399			−0.591995	+	0.805942i	$0.701659\pi$
$230$		0			0
$231$	3.41984	−	2.86958i	0.225009	−	0.188805i
$232$	2.98406	+	8.19865i	0.195913	+	0.538267i
$233$	6.77876	−	18.6245i	0.444091	−	1.22013i	−0.492687	−	0.870207i	$-0.663985\pi$
$233$	6.77876	−	18.6245i	0.444091	−	1.22013i	0.936778	−	0.349924i	$-0.113793\pi$
$234$	−0.348533	−	0.292454i	−0.0227843	−	0.0191183i
$235$		0			0
$236$	4.09456	+	7.09199i	0.266533	+	0.461649i
$237$	−20.4641	−	3.60838i	−1.32929	−	0.234389i
$238$	−1.34550	−	0.237248i	−0.0872158	−	0.0153785i
$239$	12.6431	+	21.8985i	0.817816	+	1.41650i	0.907288	+	0.420510i	$0.138149\pi$
$239$	12.6431	+	21.8985i	0.817816	+	1.41650i	−0.0894720	+	0.995989i	$0.528518\pi$
$240$		0			0
$241$	6.91515	+	5.80250i	0.445444	+	0.373772i	0.837742	−	0.546066i	$-0.183875\pi$
$241$	6.91515	+	5.80250i	0.445444	+	0.373772i	−0.392298	+	0.919838i	$0.628320\pi$
$242$	−6.94738	+	19.0878i	−0.446594	+	1.22701i
$243$	−0.655868	−	1.80198i	−0.0420740	−	0.115597i
$244$	−2.43744	+	2.04525i	−0.156041	+	0.130934i
$245$		0			0
$246$	11.3495			0.723616
$247$	−10.6555	+	1.27954i	−0.677993	+	0.0814149i
$248$			5.76384i			0.366004i
$249$	−3.84335	−	21.7967i	−0.243562	−	1.38131i
$250$		0			0
$251$	15.9786	−	5.81575i	1.00856	−	0.367087i	0.215682	−	0.976464i	$-0.430802\pi$
$251$	15.9786	−	5.81575i	1.00856	−	0.367087i	0.792881	+	0.609377i	$0.208580\pi$
$252$	−0.0300519	+	0.0825669i	−0.00189309	+	0.00520122i
$253$	−15.7760	+	18.8011i	−0.991829	+	1.18202i
$254$	3.08782	−	5.34825i	0.193747	−	0.335579i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−21.6071	−	3.80992i	−1.34782	−	0.237656i	−0.547284	−	0.836947i	$-0.684338\pi$
$257$	−21.6071	−	3.80992i	−1.34782	−	0.237656i	−0.800531	+	0.599291i	$0.795449\pi$
$258$	−0.670757	+	0.387262i	−0.0417595	+	0.0241099i
$259$	−1.43285	+	2.48177i	−0.0890329	+	0.154210i
$260$		0			0
$261$	1.51505	+	0.551433i	0.0937791	+	0.0341328i
$262$	−6.68343	−	18.3626i	−0.412904	−	1.13444i
$263$	17.6420	+	21.0249i	1.08785	+	1.29645i	0.952127	+	0.305703i	$0.0988914\pi$
$263$	17.6420	+	21.0249i	1.08785	+	1.29645i	0.135723	+	0.990747i	$0.456664\pi$
$264$	1.63037	+	9.24629i	0.100342	+	0.569070i
$265$		0			0
$266$	0.936013	+	1.84919i	0.0573906	+	0.113381i
$267$			2.71396i			0.166092i
$268$	0.148899	−	0.0262550i	0.00909548	−	0.00160378i
$269$	−12.1089	+	10.1606i	−0.738291	+	0.619500i	−0.932378	−	0.361484i	$-0.882270\pi$
$269$	−12.1089	+	10.1606i	−0.738291	+	0.619500i	0.194087	+	0.980984i	$0.437826\pi$
$270$		0			0
$271$	21.6087	+	7.86493i	1.31264	+	0.477760i	0.901091	−	0.433629i	$-0.142767\pi$
$271$	21.6087	+	7.86493i	1.31264	+	0.477760i	0.411544	+	0.911390i	$0.364989\pi$
$272$	1.84699	−	2.20116i	0.111990	−	0.133465i
$273$	−1.70109	−	0.982124i	−0.102955	−	0.0594408i
$274$	−6.67922	−	11.5687i	−0.403506	−	0.698893i
$275$		0			0
$276$	−1.27789	+	7.24729i	−0.0769201	+	0.436236i
$277$	−4.42336	+	2.55383i	−0.265774	+	0.153445i	−0.626966	−	0.779047i	$-0.715703\pi$
$277$	−4.42336	+	2.55383i	−0.265774	+	0.153445i	0.361192	+	0.932492i	$0.382370\pi$
$278$	−14.5028	−	8.37318i	−0.869819	−	0.502190i
$279$	0.815925	+	0.684642i	0.0488482	+	0.0409885i
$280$		0			0
$281$	−27.6841	+	10.0762i	−1.65150	+	0.601095i	−0.988993	−	0.147964i	$-0.952728\pi$
$281$	−27.6841	+	10.0762i	−1.65150	+	0.601095i	−0.662503	+	0.749059i	$0.730506\pi$
$282$	−2.83744	−	3.38153i	−0.168967	−	0.201367i
$283$	21.0618	−	3.71376i	1.25199	−	0.220760i	0.491944	−	0.870627i	$-0.336286\pi$
$283$	21.0618	−	3.71376i	1.25199	−	0.220760i	0.760048	+	0.649867i	$0.225175\pi$
$284$	−4.77391			−0.283280
$285$		0			0
$286$	13.7774			0.814673
$287$	−3.16743	+	0.558504i	−0.186968	+	0.0329675i
$288$	−0.118782	−	0.141559i	−0.00699932	−	0.00834146i
$289$	−8.21624	+	2.99047i	−0.483308	+	0.175910i
$290$		0			0
$291$	−6.46596	−	5.42559i	−0.379042	−	0.318054i
$292$	−7.96584	−	4.59908i	−0.466165	−	0.269141i
$293$	17.1612	−	9.90800i	1.00257	−	0.578831i	0.0935590	−	0.995614i	$-0.470176\pi$
$293$	17.1612	−	9.90800i	1.00257	−	0.578831i	0.909006	+	0.416782i	$0.136842\pi$
$294$	1.97363	−	11.1930i	0.115104	−	0.652789i
$295$		0			0
$296$	−3.01346	−	5.21946i	−0.175154	−	0.303375i
$297$	25.8957	+	14.9509i	1.50262	+	0.867539i
$298$	8.56016	−	10.2016i	0.495877	−	0.590963i
$299$	10.1475	+	3.69340i	0.586847	+	0.213595i
$300$		0			0
$301$	0.168139	−	0.141086i	0.00969138	−	0.00813203i
$302$	−12.9198	+	2.27811i	−0.743452	+	0.131091i
$303$			9.05990i			0.520478i
$304$	−4.35230	−	0.239718i	−0.249622	−	0.0137488i
$305$		0			0
$306$	−0.0922044	−	0.522917i	−0.00527097	−	0.0298932i
$307$	−2.95565	−	3.52240i	−0.168688	−	0.201034i	0.675077	−	0.737747i	$-0.264110\pi$
$307$	−2.95565	−	3.52240i	−0.168688	−	0.201034i	−0.843765	+	0.536713i	$0.819666\pi$
$308$	−0.910014	−	2.50024i	−0.0518528	−	0.142465i
$309$	20.5949	+	7.49593i	1.17160	+	0.426429i
$310$		0			0
$311$	7.18969	−	12.4529i	0.407690	−	0.706140i	−0.586940	−	0.809630i	$-0.699668\pi$
$311$	7.18969	−	12.4529i	0.407690	−	0.706140i	0.994630	+	0.103490i	$0.0330011\pi$
$312$	3.57760	−	2.06553i	0.202542	−	0.116937i
$313$	−14.9047	−	2.62811i	−0.842466	−	0.148550i	−0.264271	−	0.964448i	$-0.585131\pi$
$313$	−14.9047	−	2.62811i	−0.842466	−	0.148550i	−0.578195	+	0.815899i	$0.696243\pi$
$314$	−1.02065	+	5.78839i	−0.0575986	+	0.326658i
$315$		0			0
$316$	−6.19236	+	10.7255i	−0.348348	+	0.603356i
$317$	0.916667	−	1.09244i	0.0514851	−	0.0613576i	−0.739687	−	0.672951i	$-0.765027\pi$
$317$	0.916667	−	1.09244i	0.0514851	−	0.0613576i	0.791172	+	0.611593i	$0.209471\pi$
$318$	4.53825	−	12.4687i	0.254493	−	0.699213i
$319$	−45.8778	+	16.6982i	−2.56867	+	0.934918i
$320$		0			0
$321$	−0.346372	−	1.96437i	−0.0193326	−	0.109641i
$322$		−	2.08547i		−	0.116219i
$323$	−10.4860	−	6.84949i	−0.583459	−	0.381116i
$324$	8.41147			0.467304
$325$		0			0
$326$	6.54277	−	5.49003i	0.362370	−	0.304065i
$327$	6.66267	+	18.3055i	0.368446	+	1.01230i
$328$	2.31352	−	6.35633i	0.127743	−	0.350970i
$329$	0.958283	+	0.804095i	0.0528318	+	0.0443312i
$330$		0			0
$331$	−2.41089	−	4.17579i	−0.132515	−	0.229522i	0.792131	−	0.610352i	$-0.208972\pi$
$331$	−2.41089	−	4.17579i	−0.132515	−	0.229522i	−0.924645	+	0.380829i	$0.875638\pi$
$332$	−12.9908	−	2.29063i	−0.712963	−	0.125715i
$333$	−1.09681	−	0.193397i	−0.0601048	−	0.0105981i
$334$	9.78927	+	16.9555i	0.535645	+	0.927764i
$335$		0			0
$336$	−0.611146	−	0.512812i	−0.0333407	−	0.0279762i
$337$	−7.39701	+	20.3231i	−0.402941	+	1.10707i	0.557885	+	0.829918i	$0.311613\pi$
$337$	−7.39701	+	20.3231i	−0.402941	+	1.10707i	−0.960826	+	0.277152i	$0.910609\pi$
$338$	2.37296	+	6.51965i	0.129072	+	0.354622i
$339$	16.2691	−	13.6514i	0.883618	−	0.741444i
$340$		0			0
$341$	−32.2532			−1.74661
$342$	−0.550911	+	0.587635i	−0.0297899	+	0.0317756i
$343$			6.54927i			0.353627i
$344$	0.0801585	+	0.454602i	0.00432186	+	0.0245105i
$345$		0			0
$346$	−23.4105	+	8.52072i	−1.25856	+	0.458077i
$347$	−5.65111	+	15.5263i	−0.303368	+	0.833496i	0.690542	+	0.723293i	$0.257372\pi$
$347$	−5.65111	+	15.5263i	−0.303368	+	0.833496i	−0.993909	+	0.110203i	$0.964850\pi$
$348$	−9.40977	+	11.2141i	−0.504417	+	0.601140i
$349$	3.82195	−	6.61982i	0.204584	−	0.354351i	−0.745416	−	0.666600i	$-0.767749\pi$
$349$	3.82195	−	6.61982i	0.204584	−	0.354351i	0.950000	+	0.312249i	$0.101082\pi$
$350$		0			0
$351$	2.28461	−	12.9567i	0.121943	−	0.691576i
$352$	5.51077	+	0.971697i	0.293725	+	0.0517916i
$353$	8.41121	−	4.85621i	0.447684	−	0.258470i	−0.259168	−	0.965832i	$-0.583448\pi$
$353$	8.41121	−	4.85621i	0.447684	−	0.258470i	0.706851	+	0.707362i	$0.250115\pi$
$354$	−6.87009	+	11.8994i	−0.365141	+	0.632443i
$355$		0			0
$356$	1.51997	+	0.553223i	0.0805581	+	0.0293208i
$357$	−0.784042	−	2.15414i	−0.0414959	−	0.114009i
$358$	0.0265436	+	0.0316334i	0.00140287	+	0.00167188i
$359$	0.602693	+	3.41804i	0.0318089	+	0.180397i	0.996573	−	0.0827196i	$-0.0263606\pi$
$359$	0.602693	+	3.41804i	0.0318089	+	0.180397i	−0.964764	+	0.263117i	$0.915249\pi$
$360$		0			0
$361$	1.22441	+	18.9605i	0.0644424	+	0.997921i
$362$		−	12.8869i		−	0.677319i
$363$	−33.5642	+	5.91827i	−1.76166	+	0.310629i
$364$	−0.896799	+	0.752504i	−0.0470050	+	0.0394419i
$365$		0			0
$366$	−5.01672	−	1.82594i	−0.262228	−	0.0954433i
$367$	18.4153	−	21.9465i	0.961271	−	1.14560i	−0.0280151	−	0.999608i	$-0.508919\pi$
$367$	18.4153	−	21.9465i	0.961271	−	1.14560i	0.989286	−	0.145991i	$-0.0466369\pi$
$368$	3.79839	+	2.19300i	0.198005	+	0.114318i
$369$	−0.624993	−	1.08252i	−0.0325358	−	0.0563537i
$370$		0			0
$371$	−0.652962	+	3.70313i	−0.0339001	+	0.192257i
$372$	−8.37525	+	4.83545i	−0.434236	+	0.250707i
$373$	−8.59750	−	4.96377i	−0.445162	−	0.257014i	0.260623	−	0.965441i	$-0.416072\pi$
$373$	−8.59750	−	4.96377i	−0.445162	−	0.257014i	−0.705785	+	0.708426i	$0.749405\pi$
$374$	12.3172	+	10.3353i	0.636907	+	0.534428i
$375$		0			0
$376$	−2.47224	+	0.899821i	−0.127496	+	0.0464047i
$377$	13.8080	+	16.4557i	0.711146	+	0.847511i
$378$	−2.50221	+	0.441207i	−0.128700	+	0.0226932i
$379$	−6.49171			−0.333457			−0.166728	−	0.986003i	$-0.553320\pi$
$379$	−6.49171			−0.333457			−0.166728	+	0.986003i	$0.553320\pi$
$380$		0			0
$381$	10.3618			0.530853
$382$	−17.1465	+	3.02339i	−0.877292	+	0.154690i
$383$	6.09960	+	7.26922i	0.311675	+	0.371440i	0.899028	−	0.437891i	$-0.144274\pi$
$383$	6.09960	+	7.26922i	0.311675	+	0.371440i	−0.587353	+	0.809331i	$0.699830\pi$
$384$	1.57667	−	0.573861i	0.0804591	−	0.0292847i
$385$		0			0
$386$	16.9959	+	14.2613i	0.865069	+	0.725879i
$387$	0.0738745	+	0.0426515i	0.00375525	+	0.00216810i
$388$	−4.35667	+	2.51532i	−0.221176	+	0.127696i
$389$	−2.98830	+	16.9475i	−0.151513	+	0.859271i	0.810393	+	0.585887i	$0.199254\pi$
$389$	−2.98830	+	16.9475i	−0.151513	+	0.859271i	−0.961905	+	0.273383i	$0.911857\pi$
$390$		0			0
$391$	6.30138	+	10.9143i	0.318675	+	0.551961i
$392$	−5.86638	−	3.38696i	−0.296297	−	0.171067i
$393$	21.0751	−	25.1164i	1.06310	−	1.26695i
$394$	−4.67124	−	1.70019i	−0.235334	−	0.0856545i
$395$		0			0
$396$	0.792135	−	0.664680i	0.0398063	−	0.0334014i
$397$	30.4692	−	5.37254i	1.52920	−	0.269640i	0.655161	−	0.755489i	$-0.272601\pi$
$397$	30.4692	−	5.37254i	1.52920	−	0.269640i	0.874043	+	0.485849i	$0.161490\pi$
$398$			8.27631i			0.414854i
$399$	−1.90174	+	2.91143i	−0.0952063	+	0.145754i
$400$		0			0
$401$	3.78096	+	21.4429i	0.188812	+	1.07081i	0.920959	+	0.389659i	$0.127407\pi$
$401$	3.78096	+	21.4429i	0.188812	+	1.07081i	−0.732147	+	0.681147i	$0.761482\pi$
$402$	0.163066	+	0.194335i	0.00813301	+	0.00969254i
$403$	4.85366	+	13.3353i	0.241778	+	0.664279i
$404$	5.07404	+	1.84680i	0.252443	+	0.0918817i
$405$		0			0
$406$	2.07425	−	3.59271i	0.102943	−	0.178303i
$407$	29.2070	−	16.8627i	1.44774	−	0.835851i
$408$	4.74792	+	0.837187i	0.235057	+	0.0414469i
$409$	4.32980	−	24.5555i	0.214095	−	1.21419i	−0.668376	−	0.743824i	$-0.733010\pi$
$409$	4.32980	−	24.5555i	0.214095	−	1.21419i	0.882471	−	0.470367i	$-0.155879\pi$
$410$		0			0
$411$	11.2068	−	19.4107i	0.552790	−	0.957460i
$412$	8.39627	−	10.0063i	0.413654	−	0.492974i
$413$	1.33176	−	3.65897i	0.0655314	−	0.180046i
$414$	0.761621	−	0.277208i	0.0374317	−	0.0136240i
$415$		0			0
$416$	−0.427539	−	2.42469i	−0.0209618	−	0.118880i
$417$		−	28.0980i		−	1.37597i
$418$	1.34141	−	24.3545i	0.0656106	−	1.19122i
$419$	20.5082			1.00189			0.500945	−	0.865479i	$-0.332986\pi$
$419$	20.5082			1.00189			0.500945	+	0.865479i	$0.332986\pi$
$420$		0			0
$421$	−21.5897	+	18.1159i	−1.05222	+	0.882916i	−0.993325	−	0.115348i	$-0.963202\pi$
$421$	−21.5897	+	18.1159i	−1.05222	+	0.882916i	−0.0588935	+	0.998264i	$0.518757\pi$
$422$	−5.54512	−	15.2351i	−0.269932	−	0.741633i
$423$	−0.166280	+	0.456851i	−0.00808482	+	0.0222129i
$424$	−6.05809	−	5.08334i	−0.294207	−	0.246869i
$425$		0			0
$426$	−4.00497	−	6.93682i	−0.194042	−	0.336090i
$427$	1.48993	+	0.262715i	0.0721028	+	0.0127137i
$428$	−1.17076	−	0.206437i	−0.0565910	−	0.00997852i
$429$	11.5582	+	20.0195i	0.558037	+	0.966548i
$430$		0			0
$431$	4.08645	+	3.42894i	0.196837	+	0.165166i	0.735879	−	0.677113i	$-0.236769\pi$
$431$	4.08645	+	3.42894i	0.196837	+	0.165166i	−0.539042	+	0.842279i	$0.681214\pi$
$432$	1.82763	−	5.02137i	0.0879318	−	0.241591i
$433$	10.5127	+	28.8835i	0.505210	+	1.38805i	0.886127	+	0.463443i	$0.153386\pi$
$433$	10.5127	+	28.8835i	0.505210	+	1.38805i	−0.380917	+	0.924609i	$0.624392\pi$
$434$	2.09943	−	1.76163i	0.100776	−	0.0845610i
$435$		0			0
$436$	11.6102			0.556030
$437$	7.51689	−	17.5784i	0.359582	−	0.840888i
$438$		−	15.4332i		−	0.737427i
$439$	1.25836	+	7.13650i	0.0600581	+	0.340607i	1.00000		0.000728694i	$-0.000231951\pi$
$439$	1.25836	+	7.13650i	0.0600581	+	0.340607i	−0.939942	+	0.341335i	$0.889121\pi$
$440$		0			0
$441$	−1.17628	+	0.428130i	−0.0560132	+	0.0203872i
$442$	2.41966	−	6.64796i	0.115091	−	0.316211i
$443$	−0.182669	+	0.217696i	−0.00867885	+	0.0103431i	−0.770366	−	0.637601i	$-0.779927\pi$
$443$	−0.182669	+	0.217696i	−0.00867885	+	0.0103431i	0.761688	+	0.647944i	$0.224371\pi$
$444$	5.05615	−	8.75752i	0.239954	−	0.415613i
$445$		0			0
$446$	−4.12907	+	23.4171i	−0.195517	+	1.10883i
$447$	22.0050	+	3.88007i	1.04080	+	0.183521i
$448$	−0.411781	+	0.237742i	−0.0194548	+	0.0112322i
$449$	18.8885	−	32.7159i	0.891405	−	1.54396i	0.0532142	−	0.998583i	$-0.483053\pi$
$449$	18.8885	−	32.7159i	0.891405	−	1.54396i	0.838191	−	0.545376i	$-0.183613\pi$
$450$		0			0
$451$	35.5686	+	12.9459i	1.67486	+	0.609600i
$452$	−4.32919	−	11.8944i	−0.203628	−	0.559464i
$453$	−14.1491	−	16.8622i	−0.664781	−	0.792256i
$454$	−0.258748	−	1.46744i	−0.0121437	−	0.0688702i
$455$		0			0
$456$	−3.30295	−	6.52530i	−0.154675	−	0.305575i
$457$			4.61342i			0.215807i	0.994161	+	0.107903i	$0.0344137\pi$
$457$			4.61342i			0.215807i	−0.994161	+	0.107903i	$0.965586\pi$
$458$	−17.6448	+	3.11126i	−0.824488	+	0.145379i
$459$	11.7622	−	9.86963i	0.549011	−	0.460675i
$460$		0			0
$461$	22.5856	+	8.22050i	1.05192	+	0.382867i	0.809386	−	0.587277i	$-0.199800\pi$
$461$	22.5856	+	8.22050i	1.05192	+	0.382867i	0.242531	+	0.970144i	$0.422022\pi$
$462$	2.86958	−	3.41984i	0.133505	−	0.159105i
$463$	−29.9596	−	17.2972i	−1.39234	−	0.803869i	−0.398768	−	0.917052i	$-0.630562\pi$
$463$	−29.9596	−	17.2972i	−1.39234	−	0.803869i	−0.993574	+	0.113183i	$0.963895\pi$
$464$	4.36241	+	7.55591i	0.202520	+	0.350774i
$465$		0			0
$466$	3.44167	−	19.5187i	0.159432	−	0.904184i
$467$	31.5995	−	18.2440i	1.46225	−	0.844232i	0.463137	−	0.886287i	$-0.346724\pi$
$467$	31.5995	−	18.2440i	1.46225	−	0.844232i	0.999115	+	0.0420547i	$0.0133904\pi$
$468$	−0.394022	−	0.227489i	−0.0182137	−	0.0105157i
$469$	−0.0550720	−	0.0462109i	−0.00254299	−	0.00213382i
$470$		0			0
$471$	−9.26717	+	3.37297i	−0.427009	+	0.155418i
$472$	5.26387	+	6.27323i	0.242289	+	0.288749i
$473$	−2.54385	+	0.448550i	−0.116966	+	0.0206243i
$474$	−20.7798			−0.954449
$475$		0			0
$476$	−1.36626			−0.0626223
$477$	−1.43919	+	0.253768i	−0.0658959	+	0.0116192i
$478$	16.2537	+	19.3704i	0.743427	+	0.885981i
$479$	8.32833	−	3.03127i	0.380531	−	0.138502i	−0.144670	−	0.989480i	$-0.546212\pi$
$479$	8.32833	−	3.03127i	0.380531	−	0.138502i	0.525202	+	0.850978i	$0.323990\pi$
$480$		0			0
$481$	−11.3672	−	9.53824i	−0.518301	−	0.434906i
$482$	7.81768	+	4.51354i	0.356086	+	0.205586i
$483$	3.03033	−	1.74956i	0.137885	−	0.0796079i
$484$	−3.52728	+	20.0042i	−0.160331	+	0.909281i
$485$		0			0
$486$	−0.958815	−	1.66072i	−0.0434927	−	0.0753316i
$487$	−7.76519	−	4.48323i	−0.351874	−	0.203155i	0.313636	−	0.949543i	$-0.398453\pi$
$487$	−7.76519	−	4.48323i	−0.351874	−	0.203155i	−0.665510	+	0.746389i	$0.731786\pi$
$488$	−2.04525	+	2.43744i	−0.0925842	+	0.110338i
$489$	13.4663	+	4.90134i	0.608967	+	0.221646i
$490$		0			0
$491$	−24.0360	+	20.1686i	−1.08473	+	0.910195i	−0.996305	−	0.0858884i	$-0.972627\pi$
$491$	−24.0360	+	20.1686i	−1.08473	+	0.910195i	−0.0884230	+	0.996083i	$0.528183\pi$
$492$	11.1771	−	1.97082i	0.503900	−	0.0888513i
$493$			25.0699i			1.12909i
$494$	−10.2714	+	3.11040i	−0.462133	+	0.139944i
$495$		0			0
$496$	1.00088	+	5.67627i	0.0449409	+	0.254872i
$497$	1.45907	+	1.73886i	0.0654484	+	0.0779984i
$498$	−7.56992	−	20.7982i	−0.339216	−	0.931989i
$499$	22.0882	+	8.03943i	0.988802	+	0.359894i	0.785256	−	0.619171i	$-0.212531\pi$
$499$	22.0882	+	8.03943i	0.988802	+	0.359894i	0.203546	+	0.979065i	$0.434754\pi$
$500$		0			0
$501$	−16.4250	+	28.4489i	−0.733815	+	1.27100i
$502$	14.7260	−	8.50206i	0.657254	−	0.379466i
$503$	18.1583	+	3.20180i	0.809639	+	0.142761i	0.563118	−	0.826376i	$-0.309602\pi$
$503$	18.1583	+	3.20180i	0.809639	+	0.142761i	0.246521	+	0.969138i	$0.420713\pi$
$504$	−0.0152577	+	0.0865309i	−0.000679634	+	0.00385439i
$505$		0			0
$506$	−12.2716	+	21.2550i	−0.545537	+	0.944898i
$507$	−7.48275	+	8.91759i	−0.332321	+	0.396044i
$508$	2.11219	−	5.80319i	0.0937133	−	0.257475i
$509$	−17.0220	+	6.19551i	−0.754488	+	0.274611i	−0.690493	−	0.723339i	$-0.742606\pi$
$509$	−17.0220	+	6.19551i	−0.754488	+	0.274611i	−0.0639951	+	0.997950i	$0.520384\pi$
$510$		0			0
$511$	0.759463	+	4.30713i	0.0335967	+	0.190536i
$512$		−	1.00000i		−	0.0441942i
$513$	−22.6813	−	5.30006i	−1.00141	−	0.234003i
$514$	−21.9405			−0.967752
$515$		0			0
$516$	−0.593319	+	0.497854i	−0.0261194	+	0.0219168i
$517$	−5.03520	−	13.8341i	−0.221448	−	0.608423i
$518$	−0.980127	+	2.69288i	−0.0430643	+	0.118318i
$519$	−32.0209	−	26.8687i	−1.40556	−	1.17941i
$520$		0			0
$521$	−2.01668	−	3.49299i	−0.0883524	−	0.153031i	0.818462	−	0.574560i	$-0.194827\pi$
$521$	−2.01668	−	3.49299i	−0.0883524	−	0.153031i	−0.906815	+	0.421529i	$0.861494\pi$
$522$	1.58779	+	0.279970i	0.0694955	+	0.0122539i
$523$	12.2353	+	2.15741i	0.535012	+	0.0943371i	0.434625	−	0.900611i	$-0.356881\pi$
$523$	12.2353	+	2.15741i	0.535012	+	0.0943371i	0.100387	+	0.994948i	$0.467992\pi$
$524$	−9.77052	−	16.9230i	−0.426827	−	0.739286i
$525$		0			0
$526$	21.0249	+	17.6420i	0.916728	+	0.769226i
$527$	−5.66448	+	15.5630i	−0.246749	+	0.677937i
$528$	3.21120	+	8.82271i	0.139750	+	0.383959i
$529$	2.88261	−	2.41879i	0.125331	−	0.105165i
$530$		0			0
$531$	1.51329			0.0656712
$532$	1.24290	+	1.65856i	0.0538866	+	0.0719075i
$533$		−	16.6543i		−	0.721378i
$534$	0.471274	+	2.67273i	0.0203940	+	0.115660i
$535$		0			0
$536$	0.142078	−	0.0517122i	0.00613684	−	0.00223363i
$537$	−0.0236973	+	0.0651078i	−0.00102261	+	0.00280961i
$538$	−10.1606	+	12.1089i	−0.438053	+	0.522051i
$539$	18.9527	−	32.8270i	0.816350	−	1.41396i
$540$		0			0
$541$	−0.859303	+	4.87335i	−0.0369443	+	0.209522i	−0.997692	−	0.0679020i	$-0.978369\pi$
$541$	−0.859303	+	4.87335i	−0.0369443	+	0.209522i	0.960748	+	0.277424i	$0.0894806\pi$
$542$	22.6462	+	3.99313i	0.972736	+	0.171520i
$543$	18.7255	−	10.8112i	0.803588	−	0.463952i
$544$	1.43670	−	2.48844i	0.0615981	−	0.106691i
$545$		0			0
$546$	−1.84579	−	0.671812i	−0.0789925	−	0.0287509i
$547$	7.98811	+	21.9471i	0.341547	+	0.938392i	0.984946	+	0.172861i	$0.0553013\pi$
$547$	7.98811	+	21.9471i	0.341547	+	0.938392i	−0.643399	+	0.765531i	$0.722476\pi$
$548$	−8.58664	−	10.2332i	−0.366803	−	0.437139i
$549$	0.102102	+	0.579049i	0.00435760	+	0.0247132i
$550$		0			0
$551$	30.4334	−	22.8064i	1.29651	−	0.971586i
$552$			7.35909i			0.313224i
$553$	5.79927	−	1.02257i	0.246610	−	0.0434840i
$554$	−3.91269	+	3.28314i	−0.166234	+	0.139487i
$555$		0			0
$556$	−15.7364	−	5.72759i	−0.667373	−	0.242904i
$557$	−20.9651	+	24.9853i	−0.888321	+	1.05866i	0.109585	+	0.993977i	$0.465048\pi$
$557$	−20.9651	+	24.9853i	−0.888321	+	1.05866i	−0.997906	+	0.0646825i	$0.979397\pi$
$558$	0.922416	+	0.532557i	0.0390490	+	0.0225449i
$559$	0.568270	+	0.984273i	0.0240353	+	0.0416303i
$560$		0			0
$561$	−4.68471	+	26.5683i	−0.197789	+	1.12172i
$562$	−25.5138	+	14.7304i	−1.07624	+	0.621365i
$563$	16.7067	+	9.64564i	0.704105	+	0.406515i	0.808875	−	0.587981i	$-0.200077\pi$
$563$	16.7067	+	9.64564i	0.704105	+	0.406515i	−0.104769	+	0.994497i	$0.533410\pi$
$564$	−3.38153	−	2.83744i	−0.142388	−	0.119478i
$565$		0			0
$566$	20.0969	−	7.31468i	0.844736	−	0.307459i
$567$	−2.57084	−	3.06381i	−0.107965	−	0.128668i
$568$	−4.70139	+	0.828981i	−0.197266	+	0.0347833i
$569$	−7.98732			−0.334846			−0.167423	−	0.985885i	$-0.553545\pi$
$569$	−7.98732			−0.334846			−0.167423	+	0.985885i	$0.553545\pi$
$570$		0			0
$571$	20.2098			0.845756			0.422878	−	0.906187i	$-0.361020\pi$
$571$	20.2098			0.845756			0.422878	+	0.906187i	$0.361020\pi$
$572$	13.5681	−	2.39242i	0.567309	−	0.100032i
$573$	−18.7779	−	22.3786i	−0.784458	−	0.934881i
$574$	−3.02233	+	1.10004i	−0.126150	+	0.0459147i
$575$		0			0
$576$	−0.141559	−	0.118782i	−0.00589830	−	0.00494926i
$577$	21.4587	+	12.3892i	0.893338	+	0.515769i	0.875033	−	0.484063i	$-0.160840\pi$
$577$	21.4587	+	12.3892i	0.893338	+	0.515769i	0.0183054	+	0.999832i	$0.494173\pi$
$578$	−7.57213	+	4.37177i	−0.314959	+	0.181842i
$579$	−6.46421	+	36.6604i	−0.268644	+	1.52355i
$580$		0			0
$581$	3.13610	+	5.43188i	0.130107	+	0.225353i
$582$	−7.30987	−	4.22036i	−0.303004	−	0.174939i
$583$	28.4453	−	33.8998i	1.17808	−	1.40398i
$584$	−8.64344	−	3.14595i	−0.357668	−	0.130181i
$585$		0			0
$586$	15.1799	−	12.7375i	0.627077	−	0.526180i
$587$	−37.1185	+	6.54499i	−1.53204	+	0.270141i	−0.875153	−	0.483846i	$-0.839240\pi$
$587$	−37.1185	+	6.54499i	−1.53204	+	0.270141i	−0.656890	+	0.753986i	$0.728129\pi$
$588$		−	11.3657i		−	0.468712i
$589$	24.0457	−	7.28154i	0.990785	−	0.300031i
$590$		0			0
$591$	−1.44834	−	8.21397i	−0.0595769	−	0.337878i
$592$	−3.87403	−	4.61688i	−0.159221	−	0.189753i
$593$	9.07572	+	24.9353i	0.372695	+	1.02397i	0.974315	+	0.225189i	$0.0723000\pi$
$593$	9.07572	+	24.9353i	0.372695	+	1.02397i	−0.601620	+	0.798783i	$0.705478\pi$
$594$	28.0985	+	10.2270i	1.15289	+	0.419619i
$595$		0			0
$596$	6.65862	−	11.5331i	0.272748	−	0.472413i
$597$	−12.0260	+	6.94324i	−0.492193	+	0.284168i
$598$	10.6347	+	1.87519i	0.434886	+	0.0766821i
$599$	−0.468352	+	2.65616i	−0.0191363	+	0.108528i	−0.992880	−	0.119121i	$-0.961992\pi$
$599$	−0.468352	+	2.65616i	−0.0191363	+	0.108528i	0.973743	+	0.227648i	$0.0731036\pi$
$600$		0			0
$601$	0.233471	−	0.404383i	0.00952347	−	0.0164951i	−0.861224	−	0.508225i	$-0.830302\pi$
$601$	0.233471	−	0.404383i	0.00952347	−	0.0164951i	0.870748	+	0.491730i	$0.163635\pi$
$602$	0.141086	−	0.168139i	0.00575022	−	0.00685284i
$603$	0.00955603	−	0.0262550i	0.000389152	−	0.00106919i
$604$	−12.3280	+	4.48701i	−0.501617	+	0.182574i
$605$		0			0
$606$	1.57324	+	8.92226i	0.0639083	+	0.362442i
$607$		−	5.91389i		−	0.240038i	−0.992772	−	0.120019i	$-0.961705\pi$
$607$		−	5.91389i		−	0.240038i	0.992772	−	0.120019i	$-0.0382955\pi$
$608$	−4.32781	+	0.519693i	−0.175516	+	0.0210763i
$609$	6.96061			0.282058
$610$		0			0
$611$	−4.96208	+	4.16368i	−0.200744	+	0.168444i
$612$	−0.181607	−	0.498962i	−0.00734103	−	0.0201693i
$613$	−12.7303	+	34.9761i	−0.514170	+	1.41267i	0.362683	+	0.931912i	$0.381861\pi$
$613$	−12.7303	+	34.9761i	−0.514170	+	1.41267i	−0.876853	+	0.480758i	$0.840362\pi$
$614$	−3.52240	−	2.95565i	−0.142153	−	0.119280i
$615$		0			0
$616$	−1.33035	−	2.30424i	−0.0536014	−	0.0928403i
$617$	40.9593	+	7.22223i	1.64896	+	0.290756i	0.919448	−	0.393212i	$-0.128636\pi$
$617$	40.9593	+	7.22223i	1.64896	+	0.290756i	0.729512	+	0.683968i	$0.239747\pi$
$618$	21.5837	+	3.80578i	0.868223	+	0.153091i
$619$	−0.842548	−	1.45934i	−0.0338649	−	0.0586557i	0.848596	−	0.529041i	$-0.177448\pi$
$619$	−0.842548	−	1.45934i	−0.0338649	−	0.0586557i	−0.882461	+	0.470385i	$0.844115\pi$
$620$		0			0
$621$	17.9539	+	15.0651i	0.720466	+	0.604543i
$622$	4.91804	−	13.5122i	0.197195	−	0.541790i
$623$	−0.263048	−	0.722719i	−0.0105388	−	0.0289551i
$624$	3.16457	−	2.65539i	0.126684	−	0.106301i
$625$		0			0
$626$	−15.1347			−0.604903
$627$	36.5141	−	18.4826i	1.45823	−	0.738123i
$628$			5.87768i			0.234545i
$629$	−3.00720	−	17.0547i	−0.119905	−	0.680014i
$630$		0			0
$631$	6.04729	−	2.20104i	0.240739	−	0.0876218i	−0.218833	−	0.975762i	$-0.570225\pi$
$631$	6.04729	−	2.20104i	0.240739	−	0.0876218i	0.459572	+	0.888140i	$0.348003\pi$
$632$	−4.23583	+	11.6378i	−0.168492	+	0.462928i
$633$	17.4857	−	20.8386i	0.694993	−	0.828260i
$634$	0.713040	−	1.23502i	0.0283184	−	0.0490490i
$635$		0			0
$636$	2.30413	−	13.0674i	0.0913648	−	0.518155i
$637$	−16.4247	−	2.89611i	−0.650769	−	0.114748i
$638$	−42.2812	+	24.4111i	−1.67393	+	0.966444i
$639$	−0.441092	+	0.763993i	−0.0174493	+	0.0302231i
$640$		0			0
$641$	19.4415	+	7.07614i	0.767894	+	0.279491i	0.696115	−	0.717930i	$-0.254910\pi$
$641$	19.4415	+	7.07614i	0.767894	+	0.279491i	0.0717787	+	0.997421i	$0.477132\pi$
$642$	−0.682220	−	1.87438i	−0.0269251	−	0.0739760i
$643$	17.1026	+	20.3821i	0.674460	+	0.803791i	0.989384	−	0.145327i	$-0.0464233\pi$
$643$	17.1026	+	20.3821i	0.674460	+	0.803791i	−0.314923	+	0.949117i	$0.601979\pi$
$644$	−0.362139	−	2.05379i	−0.0142703	−	0.0809306i
$645$		0			0
$646$	−11.5161	−	4.92455i	−0.453097	−	0.193754i
$647$		−	28.0058i		−	1.10102i	−0.834828	−	0.550511i	$-0.814433\pi$
$647$		−	28.0058i		−	1.10102i	0.834828	−	0.550511i	$-0.185567\pi$
$648$	8.28368	−	1.46064i	0.325414	−	0.0573792i
$649$	−35.1036	+	29.4555i	−1.37794	+	1.15623i
$650$		0			0
$651$	4.32104	+	1.57273i	0.169355	+	0.0616402i
$652$	5.49003	−	6.54277i	0.215006	−	0.256235i
$653$	−42.7772	−	24.6974i	−1.67400	−	0.966484i	−0.965363	−	0.260910i	$-0.915977\pi$
$653$	−42.7772	−	24.6974i	−1.67400	−	0.966484i	−0.708636	−	0.705574i	$-0.750689\pi$
$654$	9.74017	+	16.8705i	0.380871	+	0.659688i
$655$		0			0
$656$	1.17460	−	6.66150i	0.0458605	−	0.260088i
$657$	−1.47203	+	0.849875i	−0.0574292	+	0.0331568i
$658$	1.08335	+	0.625475i	0.0422335	+	0.0243835i
$659$	34.8775	+	29.2657i	1.35863	+	1.14003i	0.976401	+	0.215964i	$0.0692892\pi$
$659$	34.8775	+	29.2657i	1.35863	+	1.14003i	0.382233	+	0.924066i	$0.375155\pi$
$660$		0			0
$661$	−13.0816	+	4.76133i	−0.508817	+	0.185194i	−0.583655	−	0.812002i	$-0.698378\pi$
$661$	−13.0816	+	4.76133i	−0.508817	+	0.185194i	0.0748387	+	0.997196i	$0.476156\pi$
$662$	−3.09938	−	3.69370i	−0.120461	−	0.143560i
$663$	11.6899	−	2.06124i	0.453996	−	0.0800518i
$664$	−13.1912			−0.511918
$665$		0			0
$666$	−1.11373			−0.0431561
$667$	−37.6857	+	6.64501i	−1.45920	+	0.257296i
$668$	12.5848	+	14.9980i	0.486922	+	0.580291i
$669$	−37.4907	+	13.6455i	−1.44947	+	0.527565i
$670$		0			0
$671$	−13.6394	−	11.4448i	−0.526542	−	0.441821i
$672$	−0.690910	−	0.398897i	−0.0266524	−	0.0153878i
$673$	−33.8746	+	19.5575i	−1.30577	+	0.753888i	−0.981388	−	0.192038i	$-0.938490\pi$
$673$	−33.8746	+	19.5575i	−1.30577	+	0.753888i	−0.324384	+	0.945925i	$0.605157\pi$
$674$	−3.75556	+	21.2988i	−0.144659	+	0.820400i
$675$		0			0
$676$	3.46903	+	6.00854i	0.133424	+	0.231098i
$677$	−7.44452	−	4.29810i	−0.286116	−	0.165189i	0.350073	−	0.936723i	$-0.386157\pi$
$677$	−7.44452	−	4.29810i	−0.286116	−	0.165189i	−0.636189	+	0.771533i	$0.719490\pi$
$678$	13.6514	−	16.2691i	0.524280	−	0.624812i
$679$	2.24774	+	0.818109i	0.0862602	+	0.0313962i
$680$		0			0
$681$	1.91521	−	1.60705i	0.0733911	−	0.0615824i
$682$	−31.7632	+	5.60071i	−1.21628	+	0.214462i
$683$		−	5.34403i		−	0.204484i	−0.994760	−	0.102242i	$-0.967398\pi$
$683$		−	5.34403i		−	0.204484i	0.994760	−	0.102242i	$-0.0326015\pi$
$684$	−0.440500	+	0.674372i	−0.0168429	+	0.0257852i
$685$		0			0
$686$	1.13727	+	6.44977i	0.0434211	+	0.246253i
$687$	−19.3236	−	23.0290i	−0.737242	−	0.878611i
$688$	0.157881	+	0.433776i	0.00601917	+	0.0165375i
$689$	−18.2967	−	6.65946i	−0.697050	−	0.253705i
$690$		0			0
$691$	11.1783	−	19.3614i	0.425243	−	0.736542i	−0.571200	−	0.820811i	$-0.693522\pi$
$691$	11.1783	−	19.3614i	0.425243	−	0.736542i	0.996443	+	0.0842688i	$0.0268554\pi$
$692$	−21.5752	+	12.4565i	−0.820167	+	0.473524i
$693$	−0.484208	−	0.0853790i	−0.0183935	−	0.00324328i
$694$	−2.86914	+	16.2717i	−0.108911	+	0.617666i
$695$		0			0
$696$	−7.31950	+	12.6777i	−0.277445	+	0.480549i
$697$	12.4935	−	14.8892i	0.473226	−	0.563969i
$698$	2.61437	−	7.18292i	0.0989554	−	0.271878i
$699$	31.2492	−	11.3738i	1.18195	−	0.430196i
$700$		0			0
$701$	−6.61580	−	37.5201i	−0.249875	−	1.41711i	−0.808892	−	0.587957i	$-0.799933\pi$
$701$	−6.61580	−	37.5201i	−0.249875	−	1.41711i	0.559017	−	0.829156i	$-0.311179\pi$
$702$		−	13.1565i		−	0.496562i
$703$	−17.9677	+	19.1654i	−0.677664	+	0.722837i
$704$	5.59578			0.210899
$705$		0			0
$706$	7.44015	−	6.24303i	0.280014	−	0.234960i
$707$	−0.878123	−	2.41262i	−0.0330252	−	0.0907360i
$708$	−4.69942	+	12.9116i	−0.176615	+	0.485246i
$709$	27.1169	+	22.7538i	1.01840	+	0.854535i	0.989425	−	0.145045i	$-0.0463327\pi$
$709$	27.1169	+	22.7538i	1.01840	+	0.854535i	0.0289703	+	0.999580i	$0.490777\pi$
$710$		0			0
$711$	1.14430	+	1.98199i	0.0429147	+	0.0743305i
$712$	1.59294	+	0.280879i	0.0596980	+	0.0105264i
$713$	−24.8962	−	4.38986i	−0.932368	−	0.164402i
$714$	−1.14619	−	1.98526i	−0.0428952	−	0.0742966i
$715$		0			0
$716$	0.0316334	+	0.0265436i	0.00118220	+	0.000991980i
$717$	−14.5108	+	39.8681i	−0.541916	+	1.48890i
$718$	1.18707	+	3.26146i	0.0443012	+	0.121717i
$719$	21.7324	−	18.2357i	0.810482	−	0.680075i	−0.140241	−	0.990117i	$-0.544788\pi$
$719$	21.7324	−	18.2357i	0.810482	−	0.680075i	0.950723	+	0.310042i	$0.100343\pi$
$720$		0			0
$721$	−6.21090			−0.231306
$722$	4.49826	+	18.4598i	0.167408	+	0.687004i
$723$			15.1462i			0.563292i
$724$	−2.23778	−	12.6911i	−0.0831665	−	0.471661i
$725$		0			0
$726$	−32.0266	+	11.6567i	−1.18862	+	0.432621i
$727$	7.82658	−	21.5033i	0.290272	−	0.797515i	−0.705755	−	0.708456i	$-0.749392\pi$
$727$	7.82658	−	21.5033i	0.290272	−	0.797515i	0.996026	−	0.0890587i	$-0.0283859\pi$
$728$	−0.752504	+	0.896799i	−0.0278896	+	0.0332376i
$729$	14.2260	−	24.6401i	0.526888	−	0.912596i
$730$		0			0
$731$	−0.230328	+	1.30625i	−0.00851898	+	0.0483136i
$732$	−5.25758	−	0.927053i	−0.194326	−	0.0342649i
$733$	16.8423	−	9.72391i	0.622085	−	0.359161i	−0.155595	−	0.987821i	$-0.549730\pi$
$733$	16.8423	−	9.72391i	0.622085	−	0.359161i	0.777680	+	0.628660i	$0.216396\pi$
$734$	14.3246	−	24.8109i	0.528729	−	0.915786i
$735$		0			0
$736$	4.12150	+	1.50010i	0.151920	+	0.0552945i
$737$	0.289370	+	0.795038i	0.0106591	+	0.0292856i
$738$	−0.803475	−	0.957545i	−0.0295763	−	0.0352477i
$739$	−2.82258	−	16.0077i	−0.103830	−	0.588852i	−0.991681	−	0.128720i	$-0.958913\pi$
$739$	−2.82258	−	16.0077i	−0.103830	−	0.588852i	0.887851	−	0.460132i	$-0.152198\pi$
$740$		0			0
$741$	−13.1366	−	12.3157i	−0.482586	−	0.452427i
$742$			3.76026i			0.138043i
$743$	23.9162	−	4.21706i	0.877398	−	0.154709i	0.283232	−	0.959051i	$-0.408593\pi$
$743$	23.9162	−	4.21706i	0.877398	−	0.154709i	0.594166	+	0.804342i	$0.297482\pi$
$744$	−7.40834	+	6.21634i	−0.271603	+	0.227902i
$745$		0			0
$746$	−9.32883	−	3.39542i	−0.341553	−	0.124315i
$747$	−1.56688	+	1.86734i	−0.0573292	+	0.0683223i
$748$	13.9248	+	8.03947i	0.509140	+	0.293952i
$749$	0.282633	+	0.489535i	0.0103272	+	0.0178872i
$750$		0			0
$751$	−2.31768	+	13.1442i	−0.0845733	+	0.479639i	0.912875	+	0.408240i	$0.133857\pi$
$751$	−2.31768	+	13.1442i	−0.0845733	+	0.479639i	−0.997448	+	0.0713987i	$0.977254\pi$
$752$	−2.27843	+	1.31545i	−0.0830856	+	0.0479695i
$753$	24.7081	+	14.2652i	0.900415	+	0.519855i
$754$	16.4557	+	13.8080i	0.599280	+	0.502856i
$755$		0			0
$756$	−2.38758	+	0.869008i	−0.0868354	+	0.0316055i
$757$	−6.22247	−	7.41565i	−0.226159	−	0.269526i	0.641018	−	0.767526i	$-0.278513\pi$
$757$	−6.22247	−	7.41565i	−0.226159	−	0.269526i	−0.867177	+	0.498000i	$0.834068\pi$
$758$	−6.39309	+	1.12727i	−0.232207	+	0.0409444i
$759$	−41.1799			−1.49473
$760$		0			0
$761$	14.3031			0.518486			0.259243	−	0.965812i	$-0.416527\pi$
$761$	14.3031			0.518486			0.259243	+	0.965812i	$0.416527\pi$
$762$	10.2044	−	1.79931i	0.369667	−	0.0651822i
$763$	−3.54850	−	4.22893i	−0.128464	−	0.153098i
$764$	−16.3610	+	5.95492i	−0.591921	+	0.215442i
$765$		0			0
$766$	7.26922	+	6.09960i	0.262647	+	0.220387i
$767$	17.4612	+	10.0812i	0.630487	+	0.364012i
$768$	1.45307	−	0.838929i	0.0524331	−	0.0302722i
$769$	−6.79200	+	38.5194i	−0.244926	+	1.38904i	0.575739	+	0.817634i	$0.304715\pi$
$769$	−6.79200	+	38.5194i	−0.244926	+	1.38904i	−0.820665	+	0.571410i	$0.806397\pi$
$770$		0			0
$771$	−18.4065	−	31.8810i	−0.662893	−	1.14816i
$772$	19.2141	+	11.0933i	0.691532	+	0.399256i
$773$	5.10649	−	6.08567i	0.183668	−	0.218886i	−0.666352	−	0.745637i	$-0.732145\pi$
$773$	5.10649	−	6.08567i	0.183668	−	0.218886i	0.850020	+	0.526751i	$0.176590\pi$
$774$	0.0801585	+	0.0291753i	0.00288124	+	0.00104869i
$775$		0			0
$776$	−3.85370	+	3.23364i	−0.138340	+	0.116081i
$777$	−4.73519	+	0.834941i	−0.169874	+	0.0299534i
$778$			17.2089i			0.616969i
$779$	−29.4401	−	1.62152i	−1.05480	−	0.0580969i
$780$		0			0
$781$	−4.63880	−	26.3079i	−0.165989	−	0.941372i
$782$	8.10090	+	9.65428i	0.289688	+	0.345236i
$783$	15.9457	+	43.8105i	0.569854	+	1.56566i
$784$	−6.36540	−	2.31682i	−0.227336	−	0.0827434i
$785$		0			0
$786$	16.3935	−	28.3945i	0.584738	−	1.01280i
$787$	−31.4462	+	18.1555i	−1.12094	+	0.647173i	−0.941640	−	0.336622i	$-0.890716\pi$
$787$	−31.4462	+	18.1555i	−1.12094	+	0.647173i	−0.179297	+	0.983795i	$0.557382\pi$
$788$	−4.89551	−	0.863210i	−0.174395	−	0.0307506i
$789$	−7.99659	+	45.3509i	−0.284686	+	1.61454i
$790$		0			0
$791$	−3.00927	+	5.21221i	−0.106997	+	0.185325i
$792$	0.664680	−	0.792135i	0.0236184	−	0.0281473i
$793$	−2.67939	+	7.36157i	−0.0951480	+	0.261417i
$794$	29.0733	−	10.5818i	1.03177	−	0.375535i
$795$		0			0
$796$	1.43717	+	8.15057i	0.0509390	+	0.288889i
$797$			0.408428i			0.0144673i	0.999974	+	0.00723363i	$0.00230256\pi$
$797$			0.408428i			0.0144673i	−0.999974	+	0.00723363i	$0.997697\pi$
$798$	−1.36729	+	3.19743i	−0.0484015	+	0.113188i
$799$	−7.55964			−0.267441
$800$		0			0
$801$	0.228974	−	0.192132i	0.00809041	−	0.00678866i
$802$	7.44703	+	20.4605i	0.262964	+	0.722487i
$803$	17.6041	−	48.3668i	0.621234	−	1.70683i
$804$	0.194335	+	0.163066i	0.00685366	+	0.00575090i
$805$		0			0
$806$	7.09557	+	12.2899i	0.249931	+	0.432893i
$807$	−26.1190	−	4.60548i	−0.919432	−	0.162121i
$808$	5.31765	+	0.937645i	0.187074	+	0.0329862i
$809$	9.00584	+	15.5986i	0.316628	+	0.548416i	0.979782	−	0.200067i	$-0.0641159\pi$
$809$	9.00584	+	15.5986i	0.316628	+	0.548416i	−0.663154	+	0.748483i	$0.730783\pi$
$810$		0			0
$811$	−10.5463	−	8.84937i	−0.370329	−	0.310743i	0.438562	−	0.898701i	$-0.355488\pi$
$811$	−10.5463	−	8.84937i	−0.370329	−	0.310743i	−0.808892	+	0.587957i	$0.799932\pi$
$812$	1.41887	−	3.89832i	0.0497927	−	0.136804i
$813$	13.1962	+	36.2564i	0.462812	+	1.27157i
$814$	25.8351	−	21.6782i	0.905519	−	0.759821i
$815$		0			0
$816$	4.82117			0.168775
$817$	1.79525	−	0.908711i	0.0628078	−	0.0317918i
$818$		−	24.9343i		−	0.871807i
$819$	0.0375661	+	0.213048i	0.00131266	+	0.00744449i
$820$		0			0
$821$	24.0012	−	8.73571i	0.837646	−	0.304878i	0.112653	−	0.993634i	$-0.464065\pi$
$821$	24.0012	−	8.73571i	0.837646	−	0.304878i	0.724993	+	0.688756i	$0.241843\pi$
$822$	7.66589	−	21.0619i	0.267379	−	0.734617i
$823$	−4.61625	+	5.50144i	−0.160912	+	0.191768i	−0.840476	−	0.541848i	$-0.817725\pi$
$823$	−4.61625	+	5.50144i	−0.160912	+	0.191768i	0.679564	+	0.733616i	$0.262169\pi$
$824$	6.53114	−	11.3123i	0.227523	−	0.394081i
$825$		0			0
$826$	0.676150	−	3.83464i	0.0235263	−	0.133424i
$827$	−20.9843	−	3.70010i	−0.729695	−	0.128665i	−0.203556	−	0.979063i	$-0.565250\pi$
$827$	−20.9843	−	3.70010i	−0.729695	−	0.128665i	−0.526139	+	0.850398i	$0.676361\pi$
$828$	0.701914	−	0.405250i	0.0243932	−	0.0140834i
$829$	11.6453	−	20.1702i	0.404457	−	0.700540i	−0.589801	−	0.807548i	$-0.700794\pi$
$829$	11.6453	−	20.1702i	0.404457	−	0.700540i	0.994258	+	0.107009i	$0.0341273\pi$
$830$		0			0
$831$	−8.05309	−	2.93109i	−0.279359	−	0.101678i
$832$	−0.842088	−	2.31362i	−0.0291941	−	0.0802102i
$833$	−12.5113	−	14.9104i	−0.433493	−	0.516616i
$834$	−4.87917	−	27.6711i	−0.168952	−	0.958173i
$835$		0			0
$836$	−2.90809	−	24.2175i	−0.100578	−	0.837579i
$837$			30.7998i			1.06460i
$838$	20.1966	−	3.56121i	0.697680	−	0.123020i
$839$	2.17636	−	1.82619i	0.0751365	−	0.0630470i	−0.604446	−	0.796646i	$-0.706605\pi$
$839$	2.17636	−	1.82619i	0.0751365	−	0.0630470i	0.679582	+	0.733599i	$0.262161\pi$
$840$		0			0
$841$	−44.2806	−	16.1168i	−1.52692	−	0.555752i
$842$	−18.1159	+	21.5897i	−0.624316	+	0.744031i
$843$	−42.8086	−	24.7155i	−1.47441	−	0.851248i
$844$	−8.10642	−	14.0407i	−0.279035	−	0.483302i
$845$		0			0
$846$	−0.0844226	+	0.478785i	−0.00290251	+	0.0164610i
$847$	8.36441	−	4.82920i	0.287405	−	0.165933i
$848$	−6.84877	−	3.95414i	−0.235188	−	0.135786i
$849$	27.4886	+	23.0657i	0.943406	+	0.791612i
$850$		0			0
$851$	24.8399	−	9.04098i	0.851501	−	0.309921i
$852$	−5.14870	−	6.13598i	−0.176391	−	0.210215i
$853$	−31.4927	+	5.55302i	−1.07829	+	0.190132i	−0.684459	−	0.729051i	$-0.739962\pi$
$853$	−31.4927	+	5.55302i	−1.07829	+	0.190132i	−0.393831	+	0.919183i	$0.628851\pi$
$854$	1.51292			0.0517709
$855$		0			0
$856$	−1.18882			−0.0406332
$857$	34.2191	−	6.03375i	1.16890	−	0.206109i	0.444689	−	0.895685i	$-0.353314\pi$
$857$	34.2191	−	6.03375i	1.16890	−	0.206109i	0.724213	+	0.689576i	$0.242203\pi$
$858$	14.8590	+	17.7082i	0.507277	+	0.604549i
$859$	−45.7819	+	16.6633i	−1.56206	+	0.568543i	−0.971207	−	0.238236i	$-0.923431\pi$
$859$	−45.7819	+	16.6633i	−1.56206	+	0.568543i	−0.590853	+	0.806780i	$0.701208\pi$
$860$		0			0
$861$	−4.13395	−	3.46880i	−0.140885	−	0.118216i
$862$	4.61980	+	2.66724i	0.157351	+	0.0908466i
$863$	−17.8649	+	10.3143i	−0.608128	+	0.351103i	−0.772233	−	0.635340i	$-0.780860\pi$
$863$	−17.8649	+	10.3143i	−0.608128	+	0.351103i	0.164104	+	0.986443i	$0.447527\pi$
$864$	0.927912	−	5.26245i	0.0315682	−	0.179032i
$865$		0			0
$866$	15.3686	+	26.6192i	0.522246	+	0.904557i
$867$	−12.7050	−	7.33521i	−0.431483	−	0.249117i
$868$	1.76163	−	2.09943i	0.0597936	−	0.0712593i
$869$	−65.1228	−	23.7028i	−2.20914	−	0.804061i
$870$		0			0
$871$	0.285168	−	0.239284i	0.00966255	−	0.00810784i
$872$	11.4339	−	2.01610i	0.387199	−	0.0682737i
$873$			0.929627i			0.0314631i
$874$	4.35024	−	18.6166i	0.147149	−	0.629717i
$875$		0			0
$876$	−2.67995	−	15.1987i	−0.0905470	−	0.513518i
$877$	−20.5941	−	24.5431i	−0.695412	−	0.828760i	0.296587	−	0.955006i	$-0.404152\pi$
$877$	−20.5941	−	24.5431i	−0.695412	−	0.828760i	−0.991999	+	0.126246i	$0.959707\pi$
$878$	2.47848	+	6.80957i	0.0836447	+	0.229812i
$879$	31.2433	+	11.3716i	1.05381	+	0.383556i
$880$		0			0
$881$	25.0768	−	43.4343i	0.844860	−	1.46334i	−0.0408828	−	0.999164i	$-0.513017\pi$
$881$	25.0768	−	43.4343i	0.844860	−	1.46334i	0.885743	−	0.464176i	$-0.153650\pi$
$882$	−1.08406	+	0.625884i	−0.0365023	+	0.0210746i
$883$	−23.3962	−	4.12538i	−0.787344	−	0.138830i	−0.234501	−	0.972116i	$-0.575346\pi$
$883$	−23.3962	−	4.12538i	−0.787344	−	0.138830i	−0.552842	+	0.833286i	$0.686457\pi$
$884$	1.22849	−	6.96713i	0.0413187	−	0.234330i
$885$		0			0
$886$	−0.142091	+	0.246109i	−0.00477364	+	0.00826819i
$887$	−14.2087	+	16.9333i	−0.477082	+	0.568564i	−0.949883	−	0.312605i	$-0.898798\pi$
$887$	−14.2087	+	16.9333i	−0.477082	+	0.568564i	0.472801	+	0.881169i	$0.343243\pi$
$888$	3.45861	−	9.50246i	0.116063	−	0.318882i
$889$	−2.75932	+	1.00431i	−0.0925447	+	0.0336835i
$890$		0			0
$891$	8.17341	+	46.3537i	0.273819	+	1.55291i
$892$			23.7784i			0.796159i
$893$	6.87710	+	9.17696i	0.230133	+	0.307095i
$894$	22.3444			0.747310
$895$		0			0
$896$	−0.364242	+	0.305635i	−0.0121685	+	0.0102105i
$897$	6.19700	+	17.0261i	0.206912	+	0.568485i
$898$	12.9205	−	35.4988i	0.431163	−	1.18461i
$899$	−38.5232	−	32.3248i	−1.28482	−	1.07809i
$900$		0			0
$901$	−11.3618	−	19.6793i	−0.378518	−	0.655612i
$902$	37.2763	+	6.57282i	1.24117	+	0.218851i
$903$	0.362678	+	0.0639500i	0.0120692	+	0.00212812i
$904$	−6.32886	−	10.9619i	−0.210495	−	0.364588i
$905$		0			0
$906$	−16.8622	−	14.1491i	−0.560209	−	0.470071i
$907$	7.69531	−	21.1427i	0.255518	−	0.702031i	−0.743912	−	0.668278i	$-0.767032\pi$
$907$	7.69531	−	21.1427i	0.255518	−	0.702031i	0.999430	−	0.0337533i	$-0.0107461\pi$
$908$	−0.509635	−	1.40021i	−0.0169128	−	0.0464676i
$909$	0.764375	−	0.641387i	0.0253527	−	0.0212735i
$910$		0			0
$911$	−9.88173			−0.327396			−0.163698	−	0.986510i	$-0.552342\pi$
$911$	−9.88173			−0.327396			−0.163698	+	0.986510i	$0.552342\pi$
$912$	−4.38587	−	5.85261i	−0.145231	−	0.193799i
$913$		−	73.8151i		−	2.44292i
$914$	0.801112	+	4.54333i	0.0264984	+	0.150280i
$915$		0			0
$916$	−16.8365	+	6.12798i	−0.556293	+	0.202474i
$917$	−3.17786	+	8.73110i	−0.104942	+	0.288326i
$918$	9.86963	−	11.7622i	0.325746	−	0.388209i
$919$	10.8786	−	18.8423i	0.358852	−	0.621549i	−0.628918	−	0.777472i	$-0.716502\pi$
$919$	10.8786	−	18.8423i	0.358852	−	0.621549i	0.987769	+	0.155923i	$0.0498351\pi$
$920$		0			0
$921$	1.33971	−	7.59787i	0.0441449	−	0.250358i
$922$	23.6700	+	4.17366i	0.779529	+	0.137452i
$923$	−10.1791	+	5.87692i	−0.335050	+	0.193441i
$924$	2.23214	−	3.86618i	0.0734320	−	0.127188i
$925$		0			0
$926$	−32.5081	−	11.8320i	−1.06828	−	0.388823i
$927$	−0.825572	−	2.26824i	−0.0271153	−	0.0744988i
$928$	5.60820	+	6.68360i	0.184098	+	0.219400i
$929$	−6.70803	−	38.0432i	−0.220083	−	1.24816i	−0.871864	−	0.489748i	$-0.837089\pi$
$929$	−6.70803	−	38.0432i	−0.220083	−	1.24816i	0.651781	−	0.758408i	$-0.274022\pi$
$930$		0			0
$931$	−6.71868	+	28.7523i	−0.220196	+	0.942317i
$932$		−	19.8198i		−	0.649218i
$933$	23.7600	−	4.18953i	0.777868	−	0.137159i
$934$	27.9514	−	23.4540i	0.914599	−	0.767440i
$935$		0			0
$936$	−0.427539	−	0.155611i	−0.0139746	−	0.00508632i
$937$	−12.1187	+	14.4425i	−0.395899	+	0.471815i	−0.926765	−	0.375641i	$-0.877422\pi$
$937$	−12.1187	+	14.4425i	−0.395899	+	0.471815i	0.530866	+	0.847456i	$0.321867\pi$
$938$	−0.0622598	−	0.0359457i	−0.00203285	−	0.00117367i
$939$	−12.6969	−	21.9917i	−0.414348	−	0.717672i
$940$		0			0
$941$	6.07196	−	34.4358i	0.197940	−	1.12257i	−0.710229	−	0.703971i	$-0.751409\pi$
$941$	6.07196	−	34.4358i	0.197940	−	1.12257i	0.908169	−	0.418604i	$-0.137480\pi$
$942$	−8.54067	+	4.93096i	−0.278270	+	0.160659i
$943$	25.6933	+	14.8340i	0.836690	+	0.483063i
$944$	6.27323	+	5.26387i	0.204176	+	0.171324i
$945$		0			0
$946$	−2.42731	+	0.883470i	−0.0789188	+	0.0287241i
$947$	27.3083	+	32.5448i	0.887401	+	1.05756i	0.997969	+	0.0636950i	$0.0202885\pi$
$947$	27.3083	+	32.5448i	0.887401	+	1.05756i	−0.110568	+	0.993869i	$0.535267\pi$
$948$	−20.4641	+	3.60838i	−0.664644	+	0.117195i
$949$	−22.6468			−0.735145
$950$		0			0
$951$	2.39276			0.0775906
$952$	−1.34550	+	0.237248i	−0.0436079	+	0.00768925i
$953$	12.6495	+	15.0751i	0.409757	+	0.488330i	0.930969	−	0.365097i	$-0.118964\pi$
$953$	12.6495	+	15.0751i	0.409757	+	0.488330i	−0.521212	+	0.853427i	$0.674520\pi$
$954$	−1.37326	+	0.499825i	−0.0444609	+	0.0161824i
$955$		0			0
$956$	19.3704	+	16.2537i	0.626483	+	0.525682i
$957$	−70.9419	−	40.9583i	−2.29323	−	1.32399i
$958$	7.67543	−	4.43141i	0.247982	−	0.143172i
$959$	−1.10296	+	6.25522i	−0.0356166	+	0.201992i
$960$		0			0
$961$	−1.11092	−	1.92418i	−0.0358363	−	0.0620702i
$962$	−12.8508	−	7.41943i	−0.414327	−	0.239212i
$963$	−0.141211	+	0.168289i	−0.00455047	+	0.00542304i
$964$	8.48268	+	3.08744i	0.273209	+	0.0994399i
$965$		0			0
$966$	2.68049	−	2.24920i	0.0862432	−	0.0723667i
$967$	−41.1719	+	7.25972i	−1.32400	+	0.233457i	−0.790562	−	0.612383i	$-0.790211\pi$
$967$	−41.1719	+	7.25972i	−1.32400	+	0.233457i	−0.533438	+	0.845839i	$0.679100\pi$
$968$			20.3128i			0.652877i
$969$	−2.50553	−	20.8651i	−0.0804891	−	0.670283i
$970$		0			0
$971$	−1.11254	−	6.30953i	−0.0357031	−	0.202483i	0.961738	−	0.273969i	$-0.0883367\pi$
$971$	−1.11254	−	6.30953i	−0.0357031	−	0.202483i	−0.997442	+	0.0714869i	$0.977226\pi$
$972$	−1.23263	−	1.46899i	−0.0395366	−	0.0471179i
$973$	2.72338	+	7.48242i	0.0873074	+	0.239875i
$974$	−8.42572	−	3.06671i	−0.269978	−	0.0982638i
$975$		0			0
$976$	−1.59092	+	2.75556i	−0.0509242	+	0.0882033i
$977$	44.5748	−	25.7352i	1.42607	−	0.823344i	0.429265	−	0.903179i	$-0.358773\pi$
$977$	44.5748	−	25.7352i	1.42607	−	0.823344i	0.996808	+	0.0798351i	$0.0254394\pi$
$978$	14.1128	+	2.48847i	0.451279	+	0.0795726i
$979$	−1.57174	+	8.91375i	−0.0502329	+	0.284885i
$980$		0			0
$981$	1.07274	−	1.85805i	0.0342501	−	0.0593228i
$982$	−20.1686	+	24.0360i	−0.643605	+	0.767018i
$983$	5.25745	−	14.4447i	0.167687	−	0.460715i	−0.827177	−	0.561942i	$-0.810055\pi$
$983$	5.25745	−	14.4447i	0.167687	−	0.460715i	0.994863	+	0.101227i	$0.0322767\pi$
$984$	10.6650	−	3.88175i	0.339988	−	0.123746i
$985$		0			0
$986$	4.35335	+	24.6891i	0.138639	+	0.786260i
$987$			2.09892i			0.0668092i
$988$	−9.57526	+	4.84676i	−0.304630	+	0.154196i
$989$	−2.02464			−0.0643799
$990$		0			0
$991$	−36.3462	+	30.4981i	−1.15457	+	0.968803i	−0.999817	−	0.0191497i	$-0.993904\pi$
$991$	−36.3462	+	30.4981i	−1.15457	+	0.968803i	−0.154758	+	0.987952i	$0.549460\pi$
$992$	1.97135	+	5.41624i	0.0625904	+	0.171966i
$993$	2.76704	−	7.60237i	0.0878092	−	0.241254i
$994$	1.73886	+	1.45907i	0.0551532	+	0.0462790i
$995$		0			0
$996$	−11.0665	−	19.1677i	−0.350655	−	0.607352i
$997$	−0.693816	−	0.122338i	−0.0219734	−	0.00387450i	0.162651	−	0.986684i	$-0.447996\pi$
$997$	−0.693816	−	0.122338i	−0.0219734	−	0.00387450i	−0.184624	+	0.982809i	$0.559107\pi$
$998$	23.1486	+	4.08173i	0.732757	+	0.129205i
$999$	−16.1028	−	27.8909i	−0.509470	−	0.882428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.e.199.4		24
5.2	odd	4		950.2.l.h.351.2		12
5.3	odd	4		190.2.k.b.161.1	yes	12
5.4	even	2	inner	950.2.u.e.199.1		24
19.17	even	9	inner	950.2.u.e.549.1		24
95.13	even	36		3610.2.a.be.1.5		6
95.17	odd	36		950.2.l.h.701.2		12
95.63	odd	36		3610.2.a.bc.1.2		6
95.74	even	18	inner	950.2.u.e.549.4		24
95.93	odd	36		190.2.k.b.131.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.131.1	✓	12	95.93	odd	36
190.2.k.b.161.1	yes	12	5.3	odd	4
950.2.l.h.351.2		12	5.2	odd	4
950.2.l.h.701.2		12	95.17	odd	36
950.2.u.e.199.1		24	5.4	even	2	inner
950.2.u.e.199.4		24	1.1	even	1	trivial
950.2.u.e.549.1		24	19.17	even	9	inner
950.2.u.e.549.4		24	95.74	even	18	inner
3610.2.a.bc.1.2		6	95.63	odd	36
3610.2.a.be.1.5		6	95.13	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)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(1.07851 + 1.28531i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.28531 + 1.07851i) q^{6} +(-0.411781 - 0.237742i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +O(q^{10})\)	\(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} +(-0.411781 - 0.237742i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.0320889 - 0.181985i) q^{9} +(2.79789 + 4.84609i) q^{11} +(1.45307 + 0.838929i) q^{12} +(1.58261 - 1.88608i) q^{13} +(-0.446808 - 0.162625i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.82975 - 0.498962i) q^{17} -0.184793i q^{18} +(-3.17997 - 2.98124i) q^{19} +(-0.138535 - 0.785674i) q^{21} +(3.59690 + 4.28662i) q^{22} +(1.50010 + 4.12150i) q^{23} +(1.57667 + 0.573861i) q^{24} +(1.23105 - 2.13224i) q^{26} +(4.62772 - 2.67181i) q^{27} +(-0.468260 - 0.0825669i) q^{28} +(-1.51505 + 8.59227i) q^{29} +(-2.88192 + 4.99163i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-3.21120 + 8.82271i) q^{33} +(2.70012 - 0.982762i) q^{34} +(-0.0320889 - 0.181985i) q^{36} -6.02691i q^{37} +(-3.64935 - 2.38375i) q^{38} +4.13105 q^{39} +(5.18173 - 4.34799i) q^{41} +(-0.272862 - 0.749681i) q^{42} +(-0.157881 + 0.433776i) q^{43} +(4.28662 + 3.59690i) q^{44} +(2.19300 + 3.79839i) q^{46} +(-2.59093 - 0.456851i) q^{47} +(1.65237 + 0.291357i) q^{48} +(-3.38696 - 5.86638i) q^{49} +(3.69323 + 3.09899i) q^{51} +(0.842088 - 2.31362i) q^{52} +(-2.70479 - 7.43135i) q^{53} +(4.09346 - 3.43482i) q^{54} -0.475484 q^{56} +(0.402213 - 7.30255i) q^{57} +8.72482i q^{58} +(1.42203 + 8.06471i) q^{59} +(-2.98996 + 1.08826i) q^{61} +(-1.97135 + 5.41624i) q^{62} +(-0.0564791 + 0.0673091i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.63037 + 9.24629i) q^{66} +(0.148899 + 0.0262550i) q^{67} +(2.48844 - 1.43670i) q^{68} +(-3.67955 + 6.37316i) q^{69} +(-4.48601 - 1.63277i) q^{71} +(-0.0632028 - 0.173648i) q^{72} +(-5.91246 - 7.04620i) q^{73} +(-1.04656 - 5.93535i) q^{74} +(-4.00784 - 1.71384i) q^{76} -2.66070i q^{77} +(4.06829 - 0.717350i) q^{78} +(-9.48725 + 7.96075i) q^{79} +(7.90420 + 2.87689i) q^{81} +(4.34799 - 5.18173i) q^{82} +(-11.4239 - 6.59560i) q^{83} +(-0.398897 - 0.690910i) q^{84} +(-0.0801585 + 0.454602i) q^{86} +(-12.6777 + 7.31950i) q^{87} +(4.84609 + 2.79789i) q^{88} +(1.23909 + 1.03972i) q^{89} +(-1.10009 + 0.400399i) q^{91} +(2.81927 + 3.35987i) q^{92} +(-9.52398 + 1.67933i) q^{93} -2.63090 q^{94} +1.67786 q^{96} +(-4.95422 + 0.873563i) q^{97} +(-4.35419 - 5.18912i) q^{98} +(0.971697 - 0.353669i) 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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