LMFDB - Embedded newform 950.2.l.k.651.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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 $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			651.3
Character	$\chi$	$=$	950.651
Dual form			950.2.l.k.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.227288 - 1.28901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.227288 + 1.28901i) q^{6} +(-1.11539 - 1.93191i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.20918 + 0.440106i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.227288 - 1.28901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.227288 + 1.28901i) q^{6} +(-1.11539 - 1.93191i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.20918 + 0.440106i) q^{9} +(-2.90465 + 5.03101i) q^{11} +(-0.654450 - 1.13354i) q^{12} +(0.492485 + 2.79302i) q^{13} +(1.70888 + 1.43392i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-1.00651 + 0.366339i) q^{17} -1.28678 q^{18} +(-2.13101 + 3.80247i) q^{19} +(-2.74378 + 0.998653i) q^{21} +(1.00878 - 5.72105i) q^{22} +(-3.46454 + 2.90709i) q^{23} +(1.00267 + 0.841344i) q^{24} +(-1.41805 - 2.45614i) q^{26} +(2.80548 - 4.85924i) q^{27} +(-2.09625 - 0.762972i) q^{28} +(0.483478 + 0.175971i) q^{29} +(3.47213 + 6.01390i) q^{31} +(0.173648 + 0.984808i) q^{32} +(5.82484 + 4.88763i) q^{33} +(0.820514 - 0.688493i) q^{34} +(1.20918 - 0.440106i) q^{36} +2.58207 q^{37} +(0.701975 - 4.30200i) q^{38} +3.71218 q^{39} +(-0.665458 + 3.77400i) q^{41} +(2.23675 - 1.87685i) q^{42} +(6.41185 + 5.38018i) q^{43} +(1.00878 + 5.72105i) q^{44} +(2.26132 - 3.91672i) q^{46} +(-10.3659 - 3.77288i) q^{47} +(-1.22996 - 0.447670i) q^{48} +(1.01181 - 1.75251i) q^{49} +(0.243449 + 1.38067i) q^{51} +(2.17259 + 1.82302i) q^{52} +(2.26396 - 1.89969i) q^{53} +(-0.974334 + 5.52572i) q^{54} +2.23078 q^{56} +(4.41709 + 3.61116i) q^{57} -0.514506 q^{58} +(-6.57499 + 2.39310i) q^{59} +(11.2875 - 9.47136i) q^{61} +(-5.31961 - 4.46368i) q^{62} +(-0.498462 - 2.82692i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.14523 - 2.60065i) q^{66} +(-7.63250 - 2.77800i) q^{67} +(-0.535552 + 0.927604i) q^{68} +(2.95984 + 5.12659i) q^{69} +(5.09076 + 4.27166i) q^{71} +(-0.985733 + 0.827128i) q^{72} +(-0.589662 + 3.34414i) q^{73} +(-2.42635 + 0.883120i) q^{74} +(0.811731 + 4.28265i) q^{76} +12.9593 q^{77} +(-3.48831 + 1.26964i) q^{78} +(-0.901573 + 5.11307i) q^{79} +(-2.66878 - 2.23937i) q^{81} +(-0.665458 - 3.77400i) q^{82} +(8.27838 + 14.3386i) q^{83} +(-1.45993 + 2.52868i) q^{84} +(-7.86530 - 2.86273i) q^{86} +(0.336718 - 0.583213i) q^{87} +(-2.90465 - 5.03101i) q^{88} +(0.355224 + 2.01458i) q^{89} +(4.84656 - 4.06675i) q^{91} +(-0.785347 + 4.45392i) q^{92} +(8.54118 - 3.10873i) q^{93} +11.0312 q^{94} +1.30890 q^{96} +(-4.68331 + 1.70458i) q^{97} +(-0.351398 + 1.99288i) q^{98} +(-5.72642 + 4.80504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 3 * q^7 - 12 * q^8	$ 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.227288	−	1.28901i	0.131225	−	0.744213i	−0.846190	−	0.532882i	$-0.821109\pi$
$3$	0.227288	−	1.28901i	0.131225	−	0.744213i	0.977415	−	0.211331i	$-0.0677798\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	0.227288	+	1.28901i	0.0927899	+	0.526238i
$7$	−1.11539	−	1.93191i	−0.421578	−	0.730194i	0.574516	−	0.818493i	$-0.305190\pi$
$7$	−1.11539	−	1.93191i	−0.421578	−	0.730194i	−0.996094	+	0.0882992i	$0.971857\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.20918	+	0.440106i	0.403060	+	0.146702i
$10$		0			0
$11$	−2.90465	+	5.03101i	−0.875786	+	1.51691i	−0.0198623	+	0.999803i	$0.506323\pi$
$11$	−2.90465	+	5.03101i	−0.875786	+	1.51691i	−0.855923	+	0.517103i	$0.827011\pi$
$12$	−0.654450	−	1.13354i	−0.188923	−	0.327225i
$13$	0.492485	+	2.79302i	0.136591	+	0.774645i	0.973739	+	0.227668i	$0.0731102\pi$
$13$	0.492485	+	2.79302i	0.136591	+	0.774645i	−0.837148	+	0.546977i	$0.815779\pi$
$14$	1.70888	+	1.43392i	0.456716	+	0.383231i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.00651	+	0.366339i	−0.244114	+	0.0888504i	−0.461180	−	0.887307i	$-0.652574\pi$
$17$	−1.00651	+	0.366339i	−0.244114	+	0.0888504i	0.217065	+	0.976157i	$0.430351\pi$
$18$	−1.28678			−0.303298
$19$	−2.13101	+	3.80247i	−0.488888	+	0.872347i
$19$	−2.13101	+	3.80247i	−0.488888	+	0.872347i
$20$		0			0
$21$	−2.74378	+	0.998653i	−0.598741	+	0.217924i
$22$	1.00878	−	5.72105i	0.215072	−	1.21973i
$23$	−3.46454	+	2.90709i	−0.722406	+	0.606171i	−0.928050	−	0.372456i	$-0.878516\pi$
$23$	−3.46454	+	2.90709i	−0.722406	+	0.606171i	0.205644	+	0.978627i	$0.434071\pi$
$24$	1.00267	+	0.841344i	0.204670	+	0.171739i
$25$		0			0
$26$	−1.41805	−	2.45614i	−0.278103	−	0.481689i
$27$	2.80548	−	4.85924i	0.539916	−	0.935161i
$28$	−2.09625	−	0.762972i	−0.396153	−	0.144188i
$29$	0.483478	+	0.175971i	0.0897795	+	0.0326771i	0.386519	−	0.922281i	$-0.373677\pi$
$29$	0.483478	+	0.175971i	0.0897795	+	0.0326771i	−0.296740	+	0.954958i	$0.595899\pi$
$30$		0			0
$31$	3.47213	+	6.01390i	0.623613	+	1.08013i	0.988807	+	0.149198i	$0.0476690\pi$
$31$	3.47213	+	6.01390i	0.623613	+	1.08013i	−0.365195	+	0.930931i	$0.618998\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	5.82484	+	4.88763i	1.01398	+	0.850826i
$34$	0.820514	−	0.688493i	0.140717	−	0.118076i
$35$		0			0
$36$	1.20918	−	0.440106i	0.201530	−	0.0733509i
$37$	2.58207			0.424490			0.212245	−	0.977217i	$-0.431923\pi$
$37$	2.58207			0.424490			0.212245	+	0.977217i	$0.431923\pi$
$38$	0.701975	−	4.30200i	0.113875	−	0.697877i
$39$	3.71218			0.594425
$40$		0			0
$41$	−0.665458	+	3.77400i	−0.103927	+	0.589400i	0.887716	+	0.460391i	$0.152291\pi$
$41$	−0.665458	+	3.77400i	−0.103927	+	0.589400i	−0.991643	+	0.129009i	$0.958820\pi$
$42$	2.23675	−	1.87685i	0.345138	−	0.289605i
$43$	6.41185	+	5.38018i	0.977798	+	0.820470i	0.983756	−	0.179512i	$-0.0574520\pi$
$43$	6.41185	+	5.38018i	0.977798	+	0.820470i	−0.00595783	+	0.999982i	$0.501896\pi$
$44$	1.00878	+	5.72105i	0.152079	+	0.862481i
$45$		0			0
$46$	2.26132	−	3.91672i	0.333413	−	0.577488i
$47$	−10.3659	−	3.77288i	−1.51202	−	0.550331i	−0.552881	−	0.833260i	$-0.686472\pi$
$47$	−10.3659	−	3.77288i	−1.51202	−	0.550331i	−0.959141	+	0.282929i	$0.908694\pi$
$48$	−1.22996	−	0.447670i	−0.177530	−	0.0646156i
$49$	1.01181	−	1.75251i	0.144545	−	0.250358i
$50$		0			0
$51$	0.243449	+	1.38067i	0.0340897	+	0.193332i
$52$	2.17259	+	1.82302i	0.301283	+	0.252807i
$53$	2.26396	−	1.89969i	0.310979	−	0.260942i	−0.473917	−	0.880569i	$-0.657161\pi$
$53$	2.26396	−	1.89969i	0.310979	−	0.260942i	0.784897	+	0.619627i	$0.212716\pi$
$54$	−0.974334	+	5.52572i	−0.132590	+	0.751956i
$55$		0			0
$56$	2.23078			0.298100
$57$	4.41709	+	3.61116i	0.585057	+	0.478310i
$58$	−0.514506			−0.0675580
$59$	−6.57499	+	2.39310i	−0.855991	+	0.311555i	−0.732480	−	0.680788i	$-0.761637\pi$
$59$	−6.57499	+	2.39310i	−0.855991	+	0.311555i	−0.123510	+	0.992343i	$0.539415\pi$
$60$		0			0
$61$	11.2875	−	9.47136i	1.44522	−	1.21268i	0.509243	−	0.860623i	$-0.329925\pi$
$61$	11.2875	−	9.47136i	1.44522	−	1.21268i	0.935977	−	0.352061i	$-0.114519\pi$
$62$	−5.31961	−	4.46368i	−0.675591	−	0.566888i
$63$	−0.498462	−	2.82692i	−0.0628003	−	0.356158i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−7.14523	−	2.60065i	−0.879517	−	0.320118i
$67$	−7.63250	−	2.77800i	−0.932458	−	0.339387i	−0.169275	−	0.985569i	$-0.554143\pi$
$67$	−7.63250	−	2.77800i	−0.932458	−	0.339387i	−0.763183	+	0.646182i	$0.776365\pi$
$68$	−0.535552	+	0.927604i	−0.0649453	+	0.112488i
$69$	2.95984	+	5.12659i	0.356322	+	0.617168i
$70$		0			0
$71$	5.09076	+	4.27166i	0.604162	+	0.506952i	0.892780	−	0.450492i	$-0.148751\pi$
$71$	5.09076	+	4.27166i	0.604162	+	0.506952i	−0.288618	+	0.957444i	$0.593196\pi$
$72$	−0.985733	+	0.827128i	−0.116170	+	0.0974780i
$73$	−0.589662	+	3.34414i	−0.0690147	+	0.391402i	0.930660	+	0.365886i	$0.119234\pi$
$73$	−0.589662	+	3.34414i	−0.0690147	+	0.391402i	−0.999674	+	0.0255158i	$0.991877\pi$
$74$	−2.42635	+	0.883120i	−0.282058	+	0.102661i
$75$		0			0
$76$	0.811731	+	4.28265i	0.0931119	+	0.491254i
$77$	12.9593			1.47685
$78$	−3.48831	+	1.26964i	−0.394973	+	0.143758i
$79$	−0.901573	+	5.11307i	−0.101435	+	0.575266i	0.891150	+	0.453709i	$0.149900\pi$
$79$	−0.901573	+	5.11307i	−0.101435	+	0.575266i	−0.992585	+	0.121556i	$0.961212\pi$
$80$		0			0
$81$	−2.66878	−	2.23937i	−0.296531	−	0.248819i
$82$	−0.665458	−	3.77400i	−0.0734876	−	0.416769i
$83$	8.27838	+	14.3386i	0.908670	+	1.57386i	0.815913	+	0.578174i	$0.196235\pi$
$83$	8.27838	+	14.3386i	0.908670	+	1.57386i	0.0927571	+	0.995689i	$0.470432\pi$
$84$	−1.45993	+	2.52868i	−0.159292	+	0.275901i
$85$		0			0
$86$	−7.86530	−	2.86273i	−0.848137	−	0.308697i
$87$	0.336718	−	0.583213i	0.0361000	−	0.0625270i
$88$	−2.90465	−	5.03101i	−0.309637	−	0.536307i
$89$	0.355224	+	2.01458i	0.0376537	+	0.213545i	0.997829	−	0.0658523i	$-0.0209766\pi$
$89$	0.355224	+	2.01458i	0.0376537	+	0.213545i	−0.960176	+	0.279397i	$0.909866\pi$
$90$		0			0
$91$	4.84656	−	4.06675i	0.508057	−	0.426311i
$92$	−0.785347	+	4.45392i	−0.0818781	+	0.464354i
$93$	8.54118	−	3.10873i	0.885679	−	0.322361i
$94$	11.0312			1.13778
$95$		0			0
$96$	1.30890			0.133589
$97$	−4.68331	+	1.70458i	−0.475518	+	0.173074i	−0.568650	−	0.822579i	$-0.692534\pi$
$97$	−4.68331	+	1.70458i	−0.475518	+	0.173074i	0.0931326	+	0.995654i	$0.470312\pi$
$98$	−0.351398	+	1.99288i	−0.0354966	+	0.201311i
$99$	−5.72642	+	4.80504i	−0.575527	+	0.482925i
$100$		0			0
$101$	2.06712	+	11.7232i	0.205686	+	1.16650i	0.896356	+	0.443334i	$0.146204\pi$
$101$	2.06712	+	11.7232i	0.205686	+	1.16650i	−0.690670	+	0.723170i	$0.742684\pi$
$102$	−0.700984	−	1.21414i	−0.0694078	−	0.120218i
$103$	0.262848	−	0.455266i	0.0258992	−	0.0448587i	−0.852785	−	0.522262i	$-0.825088\pi$
$103$	0.262848	−	0.455266i	0.0258992	−	0.0448587i	0.878684	+	0.477403i	$0.158422\pi$
$104$	−2.66507	−	0.970006i	−0.261332	−	0.0951169i
$105$		0			0
$106$	−1.47770	+	2.55944i	−0.143527	+	0.248595i
$107$	5.79580	+	10.0386i	0.560301	+	0.970471i	0.997470	+	0.0710909i	$0.0226481\pi$
$107$	5.79580	+	10.0386i	0.560301	+	0.970471i	−0.437168	+	0.899380i	$0.644019\pi$
$108$	−0.974334	−	5.52572i	−0.0937553	−	0.531713i
$109$	−6.32655	−	5.30860i	−0.605973	−	0.508472i	0.287386	−	0.957815i	$-0.407214\pi$
$109$	−6.32655	−	5.30860i	−0.605973	−	0.508472i	−0.893359	+	0.449343i	$0.851658\pi$
$110$		0			0
$111$	0.586873	−	3.32832i	0.0557035	−	0.315910i
$112$	−2.09625	+	0.762972i	−0.198077	+	0.0720940i
$113$	−13.3771			−1.25841			−0.629205	−	0.777239i	$-0.716619\pi$
$113$	−13.3771			−1.25841			−0.629205	+	0.777239i	$0.716619\pi$
$114$	−5.38579	−	1.88265i	−0.504426	−	0.176326i
$115$		0			0
$116$	0.483478	−	0.175971i	0.0448898	−	0.0163385i
$117$	−0.633721	+	3.59401i	−0.0585876	+	0.332267i
$118$	5.35998	−	4.49756i	0.493426	−	0.414034i
$119$	1.83039	+	1.53588i	0.167791	+	0.140793i
$120$		0			0
$121$	−11.3740	−	19.7004i	−1.03400	−	1.79094i
$122$	−7.36741	+	12.7607i	−0.667014	+	1.15530i
$123$	4.71349	+	1.71557i	0.425001	+	0.154688i
$124$	6.52547	+	2.37508i	0.586004	+	0.213288i
$125$		0			0
$126$	1.43526	+	2.48595i	0.127864	+	0.221466i
$127$	3.04711	+	17.2810i	0.270388	+	1.53344i	0.753242	+	0.657744i	$0.228489\pi$
$127$	3.04711	+	17.2810i	0.270388	+	1.53344i	−0.482854	+	0.875701i	$0.660400\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	8.39246	−	7.04211i	0.738915	−	0.620024i
$130$		0			0
$131$	3.68597	−	1.34158i	0.322044	−	0.117215i	−0.175939	−	0.984401i	$-0.556296\pi$
$131$	3.68597	−	1.34158i	0.322044	−	0.117215i	0.497984	+	0.867186i	$0.334074\pi$
$132$	7.60379			0.661825
$133$	9.72295	−	0.124309i	0.843086	−	0.0107790i
$134$	8.12234			0.701663
$135$		0			0
$136$	0.185995	−	1.05483i	0.0159490	−	0.0904511i
$137$	2.03084	−	1.70408i	0.173507	−	0.145589i	−0.551899	−	0.833911i	$-0.686097\pi$
$137$	2.03084	−	1.70408i	0.173507	−	0.145589i	0.725406	+	0.688322i	$0.241652\pi$
$138$	−4.53473	−	3.80509i	−0.386022	−	0.323911i
$139$	−2.79736	−	15.8646i	−0.237269	−	1.34562i	−0.837782	−	0.546005i	$-0.816148\pi$
$139$	−2.79736	−	15.8646i	−0.237269	−	1.34562i	0.600513	−	0.799615i	$-0.294963\pi$
$140$		0			0
$141$	−7.21934	+	12.5043i	−0.607978	+	1.05305i
$142$	−6.24474	−	2.27290i	−0.524047	−	0.190738i
$143$	−15.4822	−	5.63506i	−1.29469	−	0.471228i
$144$	0.643391	−	1.11439i	0.0536160	−	0.0928656i
$145$		0			0
$146$	−0.589662	−	3.34414i	−0.0488007	−	0.276763i
$147$	−2.02904	−	1.70256i	−0.167352	−	0.140425i
$148$	1.97798	−	1.65972i	0.162589	−	0.136428i
$149$	2.40712	−	13.6515i	0.197199	−	1.11837i	−0.712053	−	0.702126i	$-0.752234\pi$
$149$	2.40712	−	13.6515i	0.197199	−	1.11837i	0.909252	−	0.416246i	$-0.136654\pi$
$150$		0			0
$151$	−8.66473			−0.705125			−0.352563	−	0.935788i	$-0.614690\pi$
$151$	−8.66473			−0.705125			−0.352563	+	0.935788i	$0.614690\pi$
$152$	−2.22753	−	3.74675i	−0.180677	−	0.303901i
$153$	−1.37828			−0.111427
$154$	−12.1777	+	4.43233i	−0.981310	+	0.357168i
$155$		0			0
$156$	2.84369	−	2.38614i	0.227678	−	0.191044i
$157$	3.05546	+	2.56383i	0.243852	+	0.204616i	0.756520	−	0.653971i	$-0.226898\pi$
$157$	3.05546	+	2.56383i	0.243852	+	0.204616i	−0.512667	+	0.858587i	$0.671343\pi$
$158$	−0.901573	−	5.11307i	−0.0717253	−	0.406774i
$159$	−1.93415	−	3.35005i	−0.153388	−	0.265677i
$160$		0			0
$161$	9.48056	+	3.45064i	0.747173	+	0.271949i
$162$	3.27374	+	1.19154i	0.257209	+	0.0936165i
$163$	−9.22440	+	15.9771i	−0.722511	+	1.25143i	0.237479	+	0.971393i	$0.423679\pi$
$163$	−9.22440	+	15.9771i	−0.722511	+	1.25143i	−0.959990	+	0.280033i	$0.909654\pi$
$164$	1.91611	+	3.31880i	0.149623	+	0.259155i
$165$		0			0
$166$	−12.6832	−	10.6425i	−0.984408	−	0.826017i
$167$	4.88766	−	4.10123i	0.378218	−	0.317363i	−0.433784	−	0.901017i	$-0.642822\pi$
$167$	4.88766	−	4.10123i	0.378218	−	0.317363i	0.812002	+	0.583654i	$0.198378\pi$
$168$	0.507029	−	2.87551i	0.0391182	−	0.221850i
$169$	4.65758	−	1.69522i	0.358275	−	0.130401i
$170$		0			0
$171$	−4.25027	+	3.66000i	−0.325026	+	0.279887i
$172$	8.37008			0.638212
$173$	−10.3198	+	3.75610i	−0.784600	+	0.285571i	−0.703090	−	0.711101i	$-0.748197\pi$
$173$	−10.3198	+	3.75610i	−0.784600	+	0.285571i	−0.0815108	+	0.996672i	$0.525975\pi$
$174$	−0.116941	+	0.663206i	−0.00886528	+	0.0502775i
$175$		0			0
$176$	4.45019	+	3.73415i	0.335445	+	0.281472i
$177$	1.59032	+	9.01918i	0.119536	+	0.677923i
$178$	−1.02283	−	1.77159i	−0.0766641	−	0.132786i
$179$	−1.72523	+	2.98818i	−0.128950	+	0.223347i	−0.923270	−	0.384152i	$-0.874494\pi$
$179$	−1.72523	+	2.98818i	−0.128950	+	0.223347i	0.794320	+	0.607499i	$0.207827\pi$
$180$		0			0
$181$	−10.4671	−	3.80969i	−0.778010	−	0.283172i	−0.0776672	−	0.996979i	$-0.524747\pi$
$181$	−10.4671	−	3.80969i	−0.778010	−	0.283172i	−0.700343	+	0.713807i	$0.746969\pi$
$182$	−3.16337	+	5.47911i	−0.234484	+	0.406139i
$183$	−9.64320	−	16.7025i	−0.712846	−	1.23469i
$184$	−0.785347	−	4.45392i	−0.0578966	−	0.328348i
$185$		0			0
$186$	−6.96283	+	5.84251i	−0.510540	+	0.428394i
$187$	1.08050	−	6.12784i	0.0790143	−	0.448112i
$188$	−10.3659	+	3.77288i	−0.756011	+	0.275166i
$189$	−12.5168			−0.910465
$190$		0			0
$191$	9.70152			0.701977			0.350989	−	0.936380i	$-0.385846\pi$
$191$	9.70152			0.701977			0.350989	+	0.936380i	$0.385846\pi$
$192$	−1.22996	+	0.447670i	−0.0887649	+	0.0323078i
$193$	0.618052	−	3.50514i	0.0444883	−	0.252306i	−0.954450	−	0.298370i	$-0.903557\pi$
$193$	0.618052	−	3.50514i	0.0444883	−	0.252306i	0.998938	+	0.0460647i	$0.0146680\pi$
$194$	3.81787	−	3.20357i	0.274107	−	0.230003i
$195$		0			0
$196$	−0.351398	−	1.99288i	−0.0250999	−	0.142349i
$197$	1.67669	+	2.90411i	0.119459	+	0.206909i	0.919553	−	0.392965i	$-0.128551\pi$
$197$	1.67669	+	2.90411i	0.119459	+	0.206909i	−0.800094	+	0.599874i	$0.795217\pi$
$198$	3.73766	−	6.47381i	0.265624	−	0.460074i
$199$	−17.4134	−	6.33797i	−1.23441	−	0.449287i	−0.359302	−	0.933222i	$-0.616985\pi$
$199$	−17.4134	−	6.33797i	−1.23441	−	0.449287i	−0.875104	+	0.483935i	$0.839207\pi$
$200$		0			0
$201$	−5.31566	+	9.20699i	−0.374938	+	0.649411i
$202$	−5.95203	−	10.3092i	−0.418784	−	0.725355i
$203$	−0.199305	−	1.13031i	−0.0139884	−	0.0793324i
$204$	1.07397	+	0.901168i	0.0751929	+	0.0630944i
$205$		0			0
$206$	−0.0912862	+	0.517710i	−0.00636021	+	0.0360705i
$207$	−5.46868	+	1.99044i	−0.380100	+	0.138345i
$208$	2.83611			0.196649
$209$	−12.9404	−	21.7660i	−0.895106	−	1.50559i
$210$		0			0
$211$	24.3786	−	8.87308i	1.67829	−	0.610848i	0.685218	−	0.728338i	$-0.259707\pi$
$211$	24.3786	−	8.87308i	1.67829	−	0.610848i	0.993074	+	0.117490i	$0.0374847\pi$
$212$	0.513198	−	2.91049i	0.0352466	−	0.199893i
$213$	6.66329	−	5.59117i	0.456561	−	0.383100i
$214$	−8.87969	−	7.45094i	−0.607003	−	0.509336i
$215$		0			0
$216$	2.80548	+	4.85924i	0.190889	+	0.330629i
$217$	7.74555	−	13.4157i	0.525802	−	0.910716i
$218$	7.76066	+	2.82465i	0.525618	+	0.191309i
$219$	4.17662	+	1.52016i	0.282230	+	0.102723i
$220$		0			0
$221$	−1.51888	−	2.63079i	−0.102171	−	0.176966i
$222$	0.586873	+	3.32832i	0.0393884	+	0.223382i
$223$	−4.08391	−	3.42681i	−0.273479	−	0.229476i	0.495725	−	0.868480i	$-0.334902\pi$
$223$	−4.08391	−	3.42681i	−0.273479	−	0.229476i	−0.769204	+	0.639004i	$0.779347\pi$
$224$	1.70888	−	1.43392i	0.114179	−	0.0958076i
$225$		0			0
$226$	12.5703	−	4.57523i	0.836167	−	0.304340i
$227$	−23.7640			−1.57727			−0.788636	−	0.614860i	$-0.789212\pi$
$227$	−23.7640			−1.57727			−0.788636	+	0.614860i	$0.789212\pi$
$228$	5.70489	−	0.0729378i	0.377816	−	0.00483042i
$229$	21.1887			1.40019			0.700094	−	0.714051i	$-0.253141\pi$
$229$	21.1887			1.40019			0.700094	+	0.714051i	$0.253141\pi$
$230$		0			0
$231$	2.94549	−	16.7047i	0.193799	−	1.09909i
$232$	−0.394135	+	0.330718i	−0.0258762	+	0.0217127i
$233$	11.6985	+	9.81621i	0.766395	+	0.643082i	0.939783	−	0.341772i	$-0.111027\pi$
$233$	11.6985	+	9.81621i	0.766395	+	0.643082i	−0.173388	+	0.984854i	$0.555472\pi$
$234$	−0.633721	−	3.59401i	−0.0414277	−	0.234948i
$235$		0			0
$236$	−3.49848	+	6.05954i	−0.227732	+	0.394443i
$237$	6.38591	+	2.32428i	0.414809	+	0.150978i
$238$	−2.24530	−	0.817222i	−0.145541	−	0.0529727i
$239$	9.80155	−	16.9768i	0.634010	−	1.09814i	−0.352714	−	0.935731i	$-0.614741\pi$
$239$	9.80155	−	16.9768i	0.634010	−	1.09814i	0.986724	−	0.162406i	$-0.0519255\pi$
$240$		0			0
$241$	−1.58431	−	8.98507i	−0.102054	−	0.578779i	−0.992356	−	0.123408i	$-0.960618\pi$
$241$	−1.58431	−	8.98507i	−0.102054	−	0.578779i	0.890302	−	0.455371i	$-0.150493\pi$
$242$	17.4260	+	14.6221i	1.12019	+	0.939947i
$243$	9.40159	−	7.88887i	0.603112	−	0.506071i
$244$	2.55868	−	14.5110i	0.163802	−	0.928970i
$245$		0			0
$246$	−5.01599			−0.319808
$247$	−11.6699	−	4.07930i	−0.742536	−	0.259560i
$248$	−6.94426			−0.440961
$249$	20.3642	−	7.41196i	1.29053	−	0.469714i
$250$		0			0
$251$	6.49099	−	5.44659i	0.409708	−	0.343786i	−0.414524	−	0.910038i	$-0.636052\pi$
$251$	6.49099	−	5.44659i	0.409708	−	0.343786i	0.824232	+	0.566253i	$0.191607\pi$
$252$	−2.19895	−	1.84514i	−0.138521	−	0.116233i
$253$	−4.56232	−	25.8742i	−0.286831	−	1.62670i
$254$	−8.77382	−	15.1967i	−0.550518	−	0.953525i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−4.60263	−	1.67522i	−0.287104	−	0.104497i	0.194454	−	0.980912i	$-0.437707\pi$
$257$	−4.60263	−	1.67522i	−0.287104	−	0.104497i	−0.481558	+	0.876414i	$0.659929\pi$
$258$	−5.47779	+	9.48781i	−0.341032	+	0.590686i
$259$	−2.88001	−	4.98833i	−0.178955	−	0.309960i
$260$		0			0
$261$	0.507166	+	0.425562i	0.0313928	+	0.0263417i
$262$	−3.00483	+	2.52135i	−0.185639	+	0.155770i
$263$	2.18699	−	12.4030i	0.134856	−	0.764805i	−0.840104	−	0.542425i	$-0.817506\pi$
$263$	2.18699	−	12.4030i	0.134856	−	0.764805i	0.974960	−	0.222380i	$-0.0713825\pi$
$264$	−7.14523	+	2.60065i	−0.439758	+	0.160059i
$265$		0			0
$266$	−9.09407	+	3.44226i	−0.557593	+	0.211058i
$267$	2.67755			0.163864
$268$	−7.63250	+	2.77800i	−0.466229	+	0.169694i
$269$	−0.460372	+	2.61090i	−0.0280694	+	0.159190i	−0.995621	−	0.0934853i	$-0.970199\pi$
$269$	−0.460372	+	2.61090i	−0.0280694	+	0.159190i	0.967551	+	0.252675i	$0.0813103\pi$
$270$		0			0
$271$	−16.0350	−	13.4549i	−0.974055	−	0.817329i	0.00912662	−	0.999958i	$-0.497095\pi$
$271$	−16.0350	−	13.4549i	−0.974055	−	0.817329i	−0.983182	+	0.182629i	$0.941539\pi$
$272$	0.185995	+	1.05483i	0.0112776	+	0.0639586i
$273$	−4.14053	−	7.17160i	−0.250596	−	0.434045i
$274$	−1.32554	+	2.29590i	−0.0800787	+	0.138700i
$275$		0			0
$276$	5.56267	+	2.02465i	0.334834	+	0.121869i
$277$	7.28081	−	12.6107i	0.437461	−	0.757705i	−0.560032	−	0.828471i	$-0.689211\pi$
$277$	7.28081	−	12.6107i	0.437461	−	0.757705i	0.997493	+	0.0707659i	$0.0225443\pi$
$278$	8.05468	+	13.9511i	0.483087	+	0.836732i
$279$	1.55168	+	8.80000i	0.0928964	+	0.526842i
$280$		0			0
$281$	−25.2645	+	21.1994i	−1.50715	+	1.26465i	−0.638082	+	0.769968i	$0.720272\pi$
$281$	−25.2645	+	21.1994i	−1.50715	+	1.26465i	−0.869072	+	0.494685i	$0.835283\pi$
$282$	2.50725	−	14.2193i	0.149305	−	0.846748i
$283$	−0.793827	+	0.288929i	−0.0471881	+	0.0171751i	−0.365506	−	0.930809i	$-0.619104\pi$
$283$	−0.793827	+	0.288929i	−0.0471881	+	0.0171751i	0.318318	+	0.947984i	$0.396882\pi$
$284$	6.64552			0.394339
$285$		0			0
$286$	16.4758			0.974236
$287$	8.03328	−	2.92388i	0.474190	−	0.172591i
$288$	−0.223448	+	1.26723i	−0.0131668	+	0.0746725i
$289$	−12.1439	+	10.1899i	−0.714347	+	0.599408i
$290$		0			0
$291$	1.13277	+	6.42428i	0.0664044	+	0.376598i
$292$	1.69786	+	2.94078i	0.0993599	+	0.172096i
$293$	12.3243	−	21.3463i	0.719992	−	1.24706i	−0.241010	−	0.970523i	$-0.577479\pi$
$293$	12.3243	−	21.3463i	0.719992	−	1.24706i	0.961002	−	0.276541i	$-0.0891880\pi$
$294$	2.48898	+	0.905915i	0.145160	+	0.0528340i
$295$		0			0
$296$	−1.29103	+	2.23614i	−0.0750399	+	0.129973i
$297$	16.2979	+	28.2288i	0.945701	+	1.63800i
$298$	2.40712	+	13.6515i	0.139441	+	0.790808i
$299$	−9.82581	−	8.24483i	−0.568241	−	0.476811i
$300$		0			0
$301$	3.24232	−	18.3881i	0.186884	−	1.05987i
$302$	8.14218	−	2.96351i	0.468530	−	0.170531i
$303$	15.5812			0.895118
$304$	3.37466	+	2.75893i	0.193550	+	0.158235i
$305$		0			0
$306$	1.29516	−	0.471399i	0.0740393	−	0.0269481i
$307$	5.90094	−	33.4659i	0.336785	−	1.91000i	−0.0720678	−	0.997400i	$-0.522960\pi$
$307$	5.90094	−	33.4659i	0.336785	−	1.91000i	0.408852	−	0.912601i	$-0.365929\pi$
$308$	9.92738	−	8.33006i	0.565665	−	0.474649i
$309$	−0.527102	−	0.442291i	−0.0299858	−	0.0251611i
$310$		0			0
$311$	14.7721	+	25.5861i	0.837650	+	1.45085i	0.891854	+	0.452323i	$0.149405\pi$
$311$	14.7721	+	25.5861i	0.837650	+	1.45085i	−0.0542040	+	0.998530i	$0.517262\pi$
$312$	−1.85609	+	3.21484i	−0.105080	+	0.182005i
$313$	−3.34887	−	1.21889i	−0.189289	−	0.0688956i	0.245636	−	0.969362i	$-0.421003\pi$
$313$	−3.34887	−	1.21889i	−0.189289	−	0.0688956i	−0.434926	+	0.900466i	$0.643225\pi$
$314$	−3.74808	−	1.36419i	−0.211516	−	0.0769856i
$315$		0			0
$316$	2.59598	+	4.49636i	0.146035	+	0.252940i
$317$	4.72141	+	26.7764i	0.265181	+	1.50391i	0.768520	+	0.639826i	$0.220993\pi$
$317$	4.72141	+	26.7764i	0.265181	+	1.50391i	−0.503340	+	0.864089i	$0.667895\pi$
$318$	2.96330	+	2.48650i	0.166173	+	0.139436i
$319$	−2.28965	+	1.92124i	−0.128196	+	0.107569i
$320$		0			0
$321$	14.2572	−	5.18921i	0.795762	−	0.289634i
$322$	−10.0890			−0.562238
$323$	0.751889	−	4.60790i	0.0418362	−	0.256390i
$324$	−3.48384			−0.193547
$325$		0			0
$326$	3.20360	−	18.1685i	0.177431	−	1.00626i
$327$	−8.28081	+	6.94843i	−0.457930	+	0.384249i
$328$	−2.93565	−	2.46330i	−0.162094	−	0.136013i
$329$	4.27315	+	24.2342i	0.235586	+	1.33608i
$330$		0			0
$331$	−14.6651	+	25.4007i	−0.806066	+	1.39615i	0.109503	+	0.993986i	$0.465074\pi$
$331$	−14.6651	+	25.4007i	−0.806066	+	1.39615i	−0.915569	+	0.402160i	$0.868259\pi$
$332$	15.5583	+	5.66275i	0.853871	+	0.310784i
$333$	3.12219	+	1.13638i	0.171095	+	0.0622734i
$334$	−3.19019	+	5.52557i	−0.174560	+	0.302346i
$335$		0			0
$336$	0.507029	+	2.87551i	0.0276607	+	0.156872i
$337$	7.60520	+	6.38152i	0.414282	+	0.347624i	0.825983	−	0.563695i	$-0.190621\pi$
$337$	7.60520	+	6.38152i	0.414282	+	0.347624i	−0.411701	+	0.911319i	$0.635065\pi$
$338$	−3.79689	+	3.18597i	−0.206524	+	0.173294i
$339$	−3.04045	+	17.2433i	−0.165135	+	0.936525i
$340$		0			0
$341$	−40.3413			−2.18460
$342$	2.74215	−	4.89295i	0.148279	−	0.264581i
$343$	−20.1297			−1.08690
$344$	−7.86530	+	2.86273i	−0.424068	+	0.154348i
$345$		0			0
$346$	8.41278	−	7.05916i	0.452274	−	0.379503i
$347$	−24.4740	−	20.5362i	−1.31384	−	1.10244i	−0.987573	−	0.157159i	$-0.949766\pi$
$347$	−24.4740	−	20.5362i	−1.31384	−	1.10244i	−0.326262	−	0.945279i	$-0.605789\pi$
$348$	−0.116941	−	0.663206i	−0.00626870	−	0.0355516i
$349$	9.46630	+	16.3961i	0.506719	+	0.877664i	0.999970	+	0.00777642i	$0.00247534\pi$
$349$	9.46630	+	16.3961i	0.506719	+	0.877664i	−0.493250	+	0.869887i	$0.664191\pi$
$350$		0			0
$351$	14.9536	+	5.44267i	0.798165	+	0.290508i
$352$	−5.45896	−	1.98690i	−0.290964	−	0.105902i
$353$	1.60049	−	2.77214i	0.0851857	−	0.147546i	−0.820285	−	0.571956i	$-0.806185\pi$
$353$	1.60049	−	2.77214i	0.0851857	−	0.147546i	0.905470	+	0.424410i	$0.139518\pi$
$354$	−4.57916	−	7.93133i	−0.243379	−	0.421546i
$355$		0			0
$356$	1.56706	+	1.31492i	0.0830541	+	0.0696906i
$357$	2.39579	−	2.01031i	0.126799	−	0.106397i
$358$	0.599165	−	3.39804i	0.0316669	−	0.179592i
$359$	−21.1480	+	7.69725i	−1.11615	+	0.406245i	−0.833246	−	0.552903i	$-0.813520\pi$
$359$	−21.1480	+	7.69725i	−1.11615	+	0.406245i	−0.282904	+	0.959148i	$0.591298\pi$
$360$		0			0
$361$	−9.91757	−	16.2062i	−0.521977	−	0.852959i
$362$	11.1388			0.585442
$363$	−27.9792	+	10.1836i	−1.46853	+	0.534501i
$364$	1.09863	−	6.23062i	0.0575836	−	0.326573i
$365$		0			0
$366$	14.7742	+	12.3971i	0.772262	+	0.648005i
$367$	−0.891689	−	5.05702i	−0.0465458	−	0.263974i	0.952650	−	0.304069i	$-0.0983452\pi$
$367$	−0.891689	−	5.05702i	−0.0465458	−	0.263974i	−0.999196	+	0.0400944i	$0.987234\pi$
$368$	2.26132	+	3.91672i	0.117879	+	0.204173i
$369$	−2.46562	+	4.27058i	−0.128355	+	0.222317i
$370$		0			0
$371$	−6.19523	−	2.25488i	−0.321640	−	0.117068i
$372$	4.54467	−	7.87159i	0.235630	−	0.408123i
$373$	16.2258	+	28.1039i	0.840141	+	1.45517i	0.889775	+	0.456400i	$0.150861\pi$
$373$	16.2258	+	28.1039i	0.840141	+	1.45517i	−0.0496338	+	0.998767i	$0.515805\pi$
$374$	1.08050	+	6.12784i	0.0558715	+	0.316863i
$375$		0			0
$376$	8.45036	−	7.09070i	0.435794	−	0.365675i
$377$	−0.253387	+	1.43703i	−0.0130501	+	0.0740106i
$378$	11.7620	−	4.28101i	0.604971	−	0.220191i
$379$	−24.1904			−1.24258			−0.621288	−	0.783582i	$-0.713390\pi$
$379$	−24.1904			−1.24258			−0.621288	+	0.783582i	$0.713390\pi$
$380$		0			0
$381$	22.9681			1.17669
$382$	−9.11645	+	3.31812i	−0.466438	+	0.169770i
$383$	1.39132	−	7.89057i	0.0710932	−	0.403189i	−0.928407	−	0.371566i	$-0.878821\pi$
$383$	1.39132	−	7.89057i	0.0710932	−	0.403189i	0.999500	−	0.0316238i	$-0.0100678\pi$
$384$	1.00267	−	0.841344i	0.0511675	−	0.0429347i
$385$		0			0
$386$	0.618052	+	3.50514i	0.0314580	+	0.178407i
$387$	5.38523	+	9.32750i	0.273747	+	0.474143i
$388$	−2.49193	+	4.31616i	−0.126509	+	0.219120i
$389$	11.8250	+	4.30396i	0.599553	+	0.218220i	0.623926	−	0.781483i	$-0.285537\pi$
$389$	11.8250	+	4.30396i	0.599553	+	0.218220i	−0.0243728	+	0.999703i	$0.507759\pi$
$390$		0			0
$391$	2.42211	−	4.19521i	0.122491	−	0.212161i
$392$	1.01181	+	1.75251i	0.0511042	+	0.0885151i
$393$	−0.891543	−	5.05619i	−0.0449724	−	0.255051i
$394$	−2.56883	−	2.15551i	−0.129416	−	0.108593i
$395$		0			0
$396$	−1.29807	+	7.36175i	−0.0652307	+	0.369942i
$397$	−1.05047	+	0.382338i	−0.0527214	+	0.0191890i	−0.368246	−	0.929728i	$-0.620042\pi$
$397$	−1.05047	+	0.382338i	−0.0527214	+	0.0191890i	0.315525	+	0.948917i	$0.397819\pi$
$398$	18.5310			0.928875
$399$	2.04967	−	12.5613i	0.102612	−	0.628850i
$400$		0			0
$401$	−16.9221	+	6.15915i	−0.845050	+	0.307573i	−0.728021	−	0.685555i	$-0.759559\pi$
$401$	−16.9221	+	6.15915i	−0.845050	+	0.307573i	−0.117030	+	0.993128i	$0.537337\pi$
$402$	1.84611	−	10.4698i	0.0920756	−	0.522186i
$403$	−15.0870	+	12.6595i	−0.751536	+	0.630614i
$404$	9.11905	+	7.65179i	0.453689	+	0.380691i
$405$		0			0
$406$	0.573875	+	0.993980i	0.0284809	+	0.0493304i
$407$	−7.50001	+	12.9904i	−0.371762	+	0.643910i
$408$	−1.31742	−	0.479501i	−0.0652220	−	0.0237389i
$409$	22.8966	+	8.33368i	1.13216	+	0.412074i	0.839077	−	0.544012i	$-0.183096\pi$
$409$	22.8966	+	8.33368i	1.13216	+	0.412074i	0.293086	+	0.956086i	$0.405318\pi$
$410$		0			0
$411$	−1.73500	−	3.00510i	−0.0855810	−	0.148231i
$412$	−0.0912862	−	0.517710i	−0.00449735	−	0.0255057i
$413$	11.9569	+	10.0331i	0.588362	+	0.493695i
$414$	4.45811	−	3.74080i	0.219104	−	0.183850i
$415$		0			0
$416$	−2.66507	+	0.970006i	−0.130666	+	0.0475585i
$417$	−21.0855			−1.03256
$418$	19.6044	+	16.0275i	0.958883	+	0.783929i
$419$	17.2621			0.843311			0.421655	−	0.906756i	$-0.361449\pi$
$419$	17.2621			0.843311			0.421655	+	0.906756i	$0.361449\pi$
$420$		0			0
$421$	5.85430	−	33.2014i	0.285321	−	1.61814i	−0.418816	−	0.908071i	$-0.637555\pi$
$421$	5.85430	−	33.2014i	0.285321	−	1.61814i	0.704137	−	0.710064i	$-0.251334\pi$
$422$	−19.8736	+	16.6759i	−0.967433	+	0.811772i
$423$	−10.8738	−	9.12419i	−0.528701	−	0.443633i
$424$	0.513198	+	2.91049i	0.0249231	+	0.141346i
$425$		0			0
$426$	−4.34916	+	7.53296i	−0.210717	+	0.364973i
$427$	−30.8878	−	11.2423i	−1.49477	−	0.544051i
$428$	10.8925	+	3.96456i	0.526511	+	0.191634i
$429$	−10.7826	+	18.6760i	−0.520589	+	0.901686i
$430$		0			0
$431$	4.99240	+	28.3133i	0.240475	+	1.36380i	0.830770	+	0.556615i	$0.187900\pi$
$431$	4.99240	+	28.3133i	0.240475	+	1.36380i	−0.590295	+	0.807188i	$0.700989\pi$
$432$	−4.29825	−	3.60666i	−0.206800	−	0.173526i
$433$	−9.76078	+	8.19027i	−0.469073	+	0.393599i	−0.846456	−	0.532458i	$-0.821268\pi$
$433$	−9.76078	+	8.19027i	−0.469073	+	0.393599i	0.377383	+	0.926057i	$0.376824\pi$
$434$	−2.69000	+	15.2558i	−0.129124	+	0.732300i
$435$		0			0
$436$	−8.25872			−0.395521
$437$	−3.67116	−	19.3689i	−0.175615	−	0.926538i
$438$	−4.44466			−0.212374
$439$	28.3251	−	10.3095i	1.35188	−	0.492045i	0.438347	−	0.898806i	$-0.355564\pi$
$439$	28.3251	−	10.3095i	1.35188	−	0.492045i	0.913535	+	0.406761i	$0.133342\pi$
$440$		0			0
$441$	1.99475	−	1.67380i	0.0949882	−	0.0797046i
$442$	2.32707	+	1.95264i	0.110687	+	0.0928776i
$443$	−5.65947	−	32.0964i	−0.268889	−	1.52495i	−0.757726	−	0.652572i	$-0.773690\pi$
$443$	−5.65947	−	32.0964i	−0.268889	−	1.52495i	0.488837	−	0.872375i	$-0.337421\pi$
$444$	−1.68983	−	2.92688i	−0.0801960	−	0.138904i
$445$		0			0
$446$	5.00966	+	1.82337i	0.237214	+	0.0863389i
$447$	−17.0498	−	6.20563i	−0.806429	−	0.293516i
$448$	−1.11539	+	1.93191i	−0.0526972	+	0.0912742i
$449$	8.38799	+	14.5284i	0.395854	+	0.685638i	0.993210	−	0.116338i	$-0.0371155\pi$
$449$	8.38799	+	14.5284i	0.395854	+	0.685638i	−0.597356	+	0.801976i	$0.703782\pi$
$450$		0			0
$451$	−17.0541	−	14.3101i	−0.803046	−	0.673836i
$452$	−10.2474	+	8.59862i	−0.481999	+	0.404445i
$453$	−1.96939	+	11.1690i	−0.0925299	+	0.524763i
$454$	22.3309	−	8.12777i	1.04804	−	0.381455i
$455$		0			0
$456$	−5.33590	+	2.01973i	−0.249876	+	0.0945824i
$457$	16.4975			0.771722			0.385861	−	0.922557i	$-0.373904\pi$
$457$	16.4975			0.771722			0.385861	+	0.922557i	$0.373904\pi$
$458$	−19.9109	+	7.24696i	−0.930373	+	0.338628i
$459$	−1.04361	+	5.91863i	−0.0487117	+	0.276258i
$460$		0			0
$461$	11.1486	+	9.35479i	0.519242	+	0.435696i	0.864367	−	0.502861i	$-0.167719\pi$
$461$	11.1486	+	9.35479i	0.519242	+	0.435696i	−0.345125	+	0.938557i	$0.612164\pi$
$462$	2.94549	+	16.7047i	0.137037	+	0.777173i
$463$	9.47245	+	16.4068i	0.440222	+	0.762487i	0.997706	−	0.0677011i	$-0.0215664\pi$
$463$	9.47245	+	16.4068i	0.440222	+	0.762487i	−0.557484	+	0.830188i	$0.688233\pi$
$464$	0.257253	−	0.445575i	0.0119427	−	0.0206853i
$465$		0			0
$466$	−14.3503	−	5.22310i	−0.664767	−	0.241955i
$467$	−7.26529	+	12.5838i	−0.336197	+	0.582311i	−0.983714	−	0.179740i	$-0.942474\pi$
$467$	−7.26529	+	12.5838i	−0.336197	+	0.582311i	0.647517	+	0.762051i	$0.275808\pi$
$468$	1.82473	+	3.16052i	0.0843481	+	0.146095i
$469$	3.14636	+	17.8439i	0.145285	+	0.823953i
$470$		0			0
$471$	3.99929	−	3.35580i	0.184277	−	0.154627i
$472$	1.21501	−	6.89066i	0.0559253	−	0.317168i
$473$	−45.6919	+	16.6305i	−2.10092	+	0.764671i
$474$	−6.79574			−0.312139
$475$		0			0
$476$	2.38940			0.109518
$477$	3.57360	−	1.30068i	0.163624	−	0.0595543i
$478$	−3.40404	+	19.3053i	−0.155697	+	0.883004i
$479$	3.70285	−	3.10706i	0.169188	−	0.141965i	−0.554263	−	0.832342i	$-0.687000\pi$
$479$	3.70285	−	3.10706i	0.169188	−	0.141965i	0.723450	+	0.690377i	$0.242555\pi$
$480$		0			0
$481$	1.27163	+	7.21178i	0.0579814	+	0.328829i
$482$	4.56184	+	7.90134i	0.207786	+	0.359896i
$483$	6.60274	−	11.4363i	0.300435	−	0.520369i
$484$	−21.3762	−	7.78028i	−0.971643	−	0.353649i
$485$		0			0
$486$	−6.13645	+	10.6286i	−0.278355	+	0.482125i
$487$	13.8513	+	23.9912i	0.627664	+	1.08715i	0.988019	+	0.154330i	$0.0493220\pi$
$487$	13.8513	+	23.9912i	0.627664	+	1.08715i	−0.360356	+	0.932815i	$0.617345\pi$
$488$	2.55868	+	14.5110i	0.115826	+	0.656881i
$489$	18.4982	+	15.5218i	0.836516	+	0.701920i
$490$		0			0
$491$	5.69883	−	32.3197i	0.257185	−	1.45857i	−0.533218	−	0.845978i	$-0.679017\pi$
$491$	5.69883	−	32.3197i	0.257185	−	1.45857i	0.790402	−	0.612588i	$-0.209872\pi$
$492$	4.71349	−	1.71557i	0.212501	−	0.0773439i
$493$	−0.551090			−0.0248198
$494$	12.3613	−	0.158041i	0.556161	−	0.00711059i
$495$		0			0
$496$	6.52547	−	2.37508i	0.293002	−	0.106644i
$497$	2.57428	−	14.5995i	0.115472	−	0.654875i
$498$	−16.6010	+	13.9299i	−0.743911	+	0.624215i
$499$	14.9188	+	12.5184i	0.667857	+	0.560399i	0.912430	−	0.409232i	$-0.134203\pi$
$499$	14.9188	+	12.5184i	0.667857	+	0.560399i	−0.244573	+	0.969631i	$0.578648\pi$
$500$		0			0
$501$	−4.17564	−	7.23242i	−0.186554	−	0.323121i
$502$	−4.23670	+	7.33817i	−0.189093	+	0.327519i
$503$	27.1062	+	9.86583i	1.20860	+	0.439896i	0.866219	−	0.499664i	$-0.166543\pi$
$503$	27.1062	+	9.86583i	1.20860	+	0.439896i	0.342384	+	0.939560i	$0.388765\pi$
$504$	2.69741	+	0.981779i	0.120152	+	0.0437319i
$505$		0			0
$506$	13.1367	+	22.7534i	0.583997	+	1.01151i
$507$	−1.12655	−	6.38898i	−0.0500319	−	0.283745i
$508$	13.4423	+	11.2794i	0.596404	+	0.500442i
$509$	−23.1340	+	19.4117i	−1.02540	+	0.860410i	−0.990296	−	0.138974i	$-0.955620\pi$
$509$	−23.1340	+	19.4117i	−1.02540	+	0.860410i	−0.0351005	+	0.999384i	$0.511175\pi$
$510$		0			0
$511$	7.11828	−	2.59084i	0.314894	−	0.114612i
$512$	1.00000			0.0441942
$513$	12.4986	+	21.0229i	0.551827	+	0.928182i
$514$	4.89802			0.216042
$515$		0			0
$516$	1.90242	−	10.7891i	0.0837493	−	0.474966i
$517$	49.0907	−	41.1920i	2.15901	−	1.81162i
$518$	4.41244	+	3.70247i	0.193871	+	0.162677i
$519$	2.49610	+	14.1561i	0.109567	+	0.621384i
$520$		0			0
$521$	−18.6288	+	32.2661i	−0.816144	+	1.41360i	0.0923600	+	0.995726i	$0.470559\pi$
$521$	−18.6288	+	32.2661i	−0.816144	+	1.41360i	−0.908504	+	0.417877i	$0.862774\pi$
$522$	−0.622131	−	0.226437i	−0.0272299	−	0.00991088i
$523$	−7.22198	−	2.62859i	−0.315795	−	0.114940i	0.179260	−	0.983802i	$-0.442630\pi$
$523$	−7.22198	−	2.62859i	−0.315795	−	0.114940i	−0.495055	+	0.868862i	$0.664852\pi$
$524$	1.96126	−	3.39701i	0.0856781	−	0.148399i
$525$		0			0
$526$	2.18699	+	12.4030i	0.0953574	+	0.540798i
$527$	−5.69786	−	4.78107i	−0.248203	−	0.208267i
$528$	5.82484	−	4.88763i	0.253494	−	0.212707i
$529$	−0.442071	+	2.50711i	−0.0192205	+	0.109005i
$530$		0			0
$531$	−9.00357			−0.390721
$532$	7.36831	−	6.34502i	0.319457	−	0.275091i
$533$	−10.8686			−0.470771
$534$	−2.51608	+	0.915777i	−0.108881	+	0.0396296i
$535$		0			0
$536$	6.22207	−	5.22094i	0.268753	−	0.225510i
$537$	3.45969	+	2.90302i	0.149296	+	0.125275i
$538$	−0.460372	−	2.61090i	−0.0198481	−	0.112564i
$539$	5.87792	+	10.1809i	0.253180	+	0.438521i
$540$		0			0
$541$	10.8889	+	3.96325i	0.468152	+	0.170393i	0.565315	−	0.824875i	$-0.308755\pi$
$541$	10.8889	+	3.96325i	0.468152	+	0.170393i	−0.0971632	+	0.995268i	$0.530977\pi$
$542$	19.6698	+	7.15922i	0.844891	+	0.307515i
$543$	−7.28978	+	12.6263i	−0.312835	+	0.541845i
$544$	−0.535552	−	0.927604i	−0.0229616	−	0.0397707i
$545$		0			0
$546$	6.34366	+	5.32296i	0.271483	+	0.227802i
$547$	−11.0922	+	9.30744i	−0.474267	+	0.397958i	−0.848348	−	0.529438i	$-0.822403\pi$
$547$	−11.0922	+	9.30744i	−0.474267	+	0.397958i	0.374081	+	0.927396i	$0.377958\pi$
$548$	0.460355	−	2.61080i	0.0196654	−	0.111528i
$549$	17.8171	−	6.48488i	0.760414	−	0.276768i
$550$		0			0
$551$	−1.69942	+	1.46341i	−0.0723979	+	0.0623435i
$552$	−5.91967			−0.251958
$553$	10.8836	−	3.96131i	0.462818	−	0.168452i
$554$	−2.52860	+	14.3404i	−0.107430	+	0.609265i
$555$		0			0
$556$	−12.3405	−	10.3549i	−0.523353	−	0.439145i
$557$	−6.89180	−	39.0853i	−0.292015	−	1.65610i	−0.679094	−	0.734052i	$-0.737627\pi$
$557$	−6.89180	−	39.0853i	−0.292015	−	1.65610i	0.387079	−	0.922047i	$-0.373484\pi$
$558$	−4.46787	−	7.73859i	−0.189140	−	0.327600i
$559$	−11.8692	+	20.5581i	−0.502015	+	0.869515i
$560$		0			0
$561$	−7.65329	−	2.78557i	−0.323122	−	0.117607i
$562$	16.4902	−	28.5619i	0.695599	−	1.20481i
$563$	−6.20077	−	10.7400i	−0.261331	−	0.452639i	0.705265	−	0.708944i	$-0.250828\pi$
$563$	−6.20077	−	10.7400i	−0.261331	−	0.452639i	−0.966596	+	0.256305i	$0.917495\pi$
$564$	2.50725	+	14.2193i	0.105574	+	0.598742i
$565$		0			0
$566$	0.647134	−	0.543009i	0.0272011	−	0.0228244i
$567$	−1.34954	+	7.65361i	−0.0566753	+	0.321421i
$568$	−6.24474	+	2.27290i	−0.262024	+	0.0953688i
$569$	33.6313			1.40990			0.704949	−	0.709258i	$-0.250970\pi$
$569$	33.6313			1.40990			0.704949	+	0.709258i	$0.250970\pi$
$570$		0			0
$571$	−4.64608			−0.194432			−0.0972162	−	0.995263i	$-0.530994\pi$
$571$	−4.64608			−0.194432			−0.0972162	+	0.995263i	$0.530994\pi$
$572$	−15.4822	+	5.63506i	−0.647344	+	0.235614i
$573$	2.20504	−	12.5054i	0.0921168	−	0.522421i
$574$	−6.54879	+	5.49509i	−0.273341	+	0.229361i
$575$		0			0
$576$	−0.223448	−	1.26723i	−0.00931031	−	0.0528014i
$577$	−10.4098	−	18.0303i	−0.433366	−	0.750612i	0.563794	−	0.825915i	$-0.309341\pi$
$577$	−10.4098	−	18.0303i	−0.433366	−	0.750612i	−0.997161	+	0.0753028i	$0.976008\pi$
$578$	7.92637	−	13.7289i	0.329693	−	0.571046i
$579$	−4.37770	−	1.59335i	−0.181931	−	0.0662175i
$580$		0			0
$581$	18.4672	−	31.9862i	0.766150	−	1.32701i
$582$	−3.26169	−	5.64942i	−0.135201	−	0.234176i
$583$	2.98133	+	16.9079i	0.123474	+	0.700255i
$584$	−2.60128	−	2.18273i	−0.107642	−	0.0903220i
$585$		0			0
$586$	−4.28018	+	24.2741i	−0.176813	+	1.00275i
$587$	3.69616	−	1.34529i	0.152557	−	0.0555262i	−0.264613	−	0.964355i	$-0.585244\pi$
$587$	3.69616	−	1.34529i	0.152557	−	0.0555262i	0.417170	+	0.908828i	$0.363022\pi$
$588$	−2.64872			−0.109231
$589$	−30.2668	+	0.386965i	−1.24712	+	0.0159446i
$590$		0			0
$591$	4.12453	−	1.50120i	0.169660	−	0.0617513i
$592$	0.448372	−	2.54284i	0.0184280	−	0.104510i
$593$	0.229047	−	0.192194i	0.00940585	−	0.00789244i	−0.638073	−	0.769976i	$-0.720268\pi$
$593$	0.229047	−	0.192194i	0.00940585	−	0.00789244i	0.647478	+	0.762084i	$0.275824\pi$
$594$	−24.9698	−	20.9522i	−1.02453	−	0.859679i
$595$		0			0
$596$	−6.93103	−	12.0049i	−0.283906	−	0.491740i
$597$	−12.1276	+	21.0056i	−0.496350	+	0.859703i
$598$	12.0531	+	4.38698i	0.492889	+	0.179397i
$599$	−20.7035	−	7.53546i	−0.845922	−	0.307891i	−0.117546	−	0.993067i	$-0.537503\pi$
$599$	−20.7035	−	7.53546i	−0.845922	−	0.307891i	−0.728377	+	0.685177i	$0.759725\pi$
$600$		0			0
$601$	18.1695	+	31.4705i	0.741150	+	1.28371i	0.951972	+	0.306185i	$0.0990525\pi$
$601$	18.1695	+	31.4705i	0.741150	+	1.28371i	−0.210822	+	0.977524i	$0.567614\pi$
$602$	3.24232	+	18.3881i	0.132147	+	0.749444i
$603$	−8.00645	−	6.71821i	−0.326048	−	0.273587i
$604$	−6.63757	+	5.56958i	−0.270079	+	0.226623i
$605$		0			0
$606$	−14.6416	+	5.32909i	−0.594773	+	0.216480i
$607$	21.1463			0.858301			0.429150	−	0.903233i	$-0.358813\pi$
$607$	21.1463			0.858301			0.429150	+	0.903233i	$0.358813\pi$
$608$	−4.11475	−	1.43835i	−0.166875	−	0.0583326i
$609$	−1.50229			−0.0608758
$610$		0			0
$611$	5.43268	−	30.8103i	0.219783	−	1.24645i
$612$	−1.05582	+	0.885941i	−0.0426791	+	0.0358120i
$613$	30.5326	+	25.6199i	1.23320	+	1.03478i	0.998025	+	0.0628228i	$0.0200103\pi$
$613$	30.5326	+	25.6199i	1.23320	+	1.03478i	0.235174	+	0.971953i	$0.424434\pi$
$614$	5.90094	+	33.4659i	0.238143	+	1.35057i
$615$		0			0
$616$	−6.47964	+	11.2231i	−0.261072	+	0.452190i
$617$	−4.38350	−	1.59546i	−0.176473	−	0.0642309i	0.252272	−	0.967656i	$-0.418822\pi$
$617$	−4.38350	−	1.59546i	−0.176473	−	0.0642309i	−0.428746	+	0.903425i	$0.641044\pi$
$618$	0.646587	+	0.235338i	0.0260095	+	0.00946669i
$619$	11.5280	−	19.9671i	0.463351	−	0.802547i	−0.535775	−	0.844361i	$-0.679980\pi$
$619$	11.5280	−	19.9671i	0.463351	−	0.802547i	0.999125	+	0.0418139i	$0.0133137\pi$
$620$		0			0
$621$	4.40656	+	24.9908i	0.176829	+	1.00285i
$622$	−22.6322	−	18.9907i	−0.907469	−	0.761457i
$623$	3.49577	−	2.93330i	0.140055	−	0.117520i
$624$	0.644613	−	3.65578i	0.0258052	−	0.146348i
$625$		0			0
$626$	3.56379			0.142438
$627$	−30.9979	+	11.7332i	−1.23794	+	0.468579i
$628$	3.98862			0.159163
$629$	−2.59888	+	0.945914i	−0.103624	+	0.0377160i
$630$		0			0
$631$	26.1036	−	21.9035i	1.03917	−	0.871964i	0.0472529	−	0.998883i	$-0.484953\pi$
$631$	26.1036	−	21.9035i	1.03917	−	0.871964i	0.991913	+	0.126919i	$0.0405089\pi$
$632$	−3.97726	−	3.33732i	−0.158207	−	0.132752i
$633$	−5.89657	−	33.4411i	−0.234368	−	1.32916i
$634$	−13.5948	−	23.5468i	−0.539917	−	0.935163i
$635$		0			0
$636$	−3.63502	−	1.32304i	−0.144138	−	0.0524619i
$637$	5.39310	+	1.96293i	0.213682	+	0.0777740i
$638$	1.49446	−	2.58848i	0.0591663	−	0.102479i
$639$	4.27567	+	7.40568i	0.169143	+	0.292964i
$640$		0			0
$641$	−30.9804	−	25.9956i	−1.22365	−	1.02676i	−0.998626	−	0.0524120i	$-0.983309\pi$
$641$	−30.9804	−	25.9956i	−1.22365	−	1.02676i	−0.225025	−	0.974353i	$-0.572246\pi$
$642$	−11.6226	+	9.75253i	−0.458708	+	0.384902i
$643$	5.50401	−	31.2148i	0.217057	−	1.23099i	−0.660244	−	0.751051i	$-0.729547\pi$
$643$	5.50401	−	31.2148i	0.217057	−	1.23099i	0.877301	−	0.479940i	$-0.159342\pi$
$644$	9.48056	−	3.45064i	0.373586	−	0.135974i
$645$		0			0
$646$	0.869449	+	4.58717i	0.0342080	+	0.180480i
$647$	−0.479708			−0.0188593			−0.00942963	−	0.999956i	$-0.503002\pi$
$647$	−0.479708			−0.0188593			−0.00942963	+	0.999956i	$0.503002\pi$
$648$	3.27374	−	1.19154i	0.128605	−	0.0468083i
$649$	7.05836	−	40.0299i	0.277065	−	1.57131i
$650$		0			0
$651$	−15.5325	−	13.0333i	−0.608768	−	0.510817i
$652$	3.20360	+	18.1685i	0.125463	+	0.711535i
$653$	6.02190	+	10.4302i	0.235655	+	0.408167i	0.959463	−	0.281835i	$-0.0909431\pi$
$653$	6.02190	+	10.4302i	0.235655	+	0.408167i	−0.723808	+	0.690002i	$0.757610\pi$
$654$	5.40492	−	9.36159i	0.211349	−	0.366067i
$655$		0			0
$656$	3.60111	+	1.31070i	0.140600	+	0.0511741i
$657$	−2.18478	+	3.78415i	−0.0852364	+	0.147634i
$658$	−12.3040	−	21.3112i	−0.479662	−	0.830798i
$659$	−6.50457	−	36.8893i	−0.253382	−	1.43700i	−0.800192	−	0.599744i	$-0.795269\pi$
$659$	−6.50457	−	36.8893i	−0.253382	−	1.43700i	0.546809	−	0.837257i	$-0.315842\pi$
$660$		0			0
$661$	6.71174	−	5.63182i	0.261056	−	0.219052i	−0.502859	−	0.864368i	$-0.667719\pi$
$661$	6.71174	−	5.63182i	0.261056	−	0.219052i	0.763916	+	0.645316i	$0.223274\pi$
$662$	5.09313	−	28.8846i	0.197950	−	1.12263i
$663$	−3.73634	+	1.35992i	−0.145108	+	0.0528148i
$664$	−16.5568			−0.642527
$665$		0			0
$666$	−3.32256			−0.128747
$667$	−2.18659	+	0.795855i	−0.0846652	+	0.0308156i
$668$	1.10794	−	6.28345i	0.0428676	−	0.243114i
$669$	−5.34543	+	4.48534i	−0.206666	+	0.173413i
$670$		0			0
$671$	14.8641	+	84.2986i	0.573823	+	3.25431i
$672$	−1.45993	−	2.52868i	−0.0563181	−	0.0975459i
$673$	−22.3313	+	38.6790i	−0.860810	+	1.49097i	0.0103382	+	0.999947i	$0.496709\pi$
$673$	−22.3313	+	38.6790i	−0.860810	+	1.49097i	−0.871148	+	0.491020i	$0.836624\pi$
$674$	−9.32916	−	3.39554i	−0.359346	−	0.130791i
$675$		0			0
$676$	2.47824	−	4.29245i	0.0953171	−	0.165094i
$677$	2.49459	+	4.32076i	0.0958750	+	0.166060i	0.909973	−	0.414667i	$-0.136102\pi$
$677$	2.49459	+	4.32076i	0.0958750	+	0.166060i	−0.814098	+	0.580727i	$0.802768\pi$
$678$	−3.04045	−	17.2433i	−0.116768	−	0.662223i
$679$	8.51682	+	7.14646i	0.326845	+	0.274256i
$680$		0			0
$681$	−5.40127	+	30.6321i	−0.206977	+	1.17383i
$682$	37.9084	−	13.7975i	1.45159	−	0.528335i
$683$	28.7691			1.10082			0.550409	−	0.834895i	$-0.314472\pi$
$683$	28.7691			1.10082			0.550409	+	0.834895i	$0.314472\pi$
$684$	−0.903289	+	5.53574i	−0.0345381	+	0.211664i
$685$		0			0
$686$	18.9157	−	6.88477i	0.722206	−	0.262862i
$687$	4.81594	−	27.3125i	0.183739	−	1.04204i
$688$	6.41185	−	5.38018i	0.244449	−	0.205117i
$689$	6.42084	+	5.38772i	0.244615	+	0.205256i
$690$		0			0
$691$	−12.7430	−	22.0716i	−0.484767	−	0.839642i	0.515080	−	0.857142i	$-0.327762\pi$
$691$	−12.7430	−	22.0716i	−0.484767	−	0.839642i	−0.999847	+	0.0175008i	$0.994429\pi$
$692$	−5.49105	+	9.51079i	−0.208739	+	0.361546i
$693$	15.6701	+	5.70345i	0.595258	+	0.216656i
$694$	30.0218	+	10.9271i	1.13961	+	0.414785i
$695$		0			0
$696$	0.336718	+	0.583213i	0.0127633	+	0.0221066i
$697$	−0.712775	−	4.04235i	−0.0269983	−	0.153115i
$698$	−14.5032	−	12.1696i	−0.548955	−	0.460628i
$699$	15.3122	−	12.8484i	0.579159	−	0.485972i
$700$		0			0
$701$	27.6845	−	10.0763i	1.04563	−	0.380578i	0.238617	−	0.971114i	$-0.423306\pi$
$701$	27.6845	−	10.0763i	1.04563	−	0.380578i	0.807011	+	0.590536i	$0.201084\pi$
$702$	−15.9133			−0.600609
$703$	−5.50242	+	9.81824i	−0.207528	+	0.370302i
$704$	5.80931			0.218946
$705$		0			0
$706$	−0.555846	+	3.15236i	−0.0209195	+	0.118641i
$707$	20.3426	−	17.0695i	0.765061	−	0.641963i
$708$	7.01567	+	5.88685i	0.263665	+	0.221241i
$709$	−0.217936	−	1.23598i	−0.00818476	−	0.0464181i	0.980442	−	0.196809i	$-0.0630579\pi$
$709$	−0.217936	−	1.23598i	−0.00818476	−	0.0464181i	−0.988627	+	0.150391i	$0.951947\pi$
$710$		0			0
$711$	−3.34046	+	5.78584i	−0.125277	+	0.216986i
$712$	−1.92229	−	0.699655i	−0.0720407	−	0.0262207i
$713$	−29.5123	−	10.7416i	−1.10524	−	0.402276i
$714$	−1.56374	+	2.70848i	−0.0585215	+	0.101362i
$715$		0			0
$716$	0.599165	+	3.39804i	0.0223919	+	0.126991i
$717$	−19.6555	−	16.4930i	−0.734050	−	0.615941i
$718$	17.2400	−	14.4661i	0.643392	−	0.539870i
$719$	−4.48596	+	25.4412i	−0.167298	+	0.948795i	0.779365	+	0.626570i	$0.215542\pi$
$719$	−4.48596	+	25.4412i	−0.167298	+	0.948795i	−0.946663	+	0.322225i	$0.895569\pi$
$720$		0			0
$721$	−1.17271			−0.0436741
$722$	14.8623	+	11.8369i	0.553118	+	0.440522i
$723$	−11.9420			−0.444127
$724$	−10.4671	+	3.80969i	−0.389005	+	0.141586i
$725$		0			0
$726$	22.8089	−	19.1389i	0.846517	−	0.710312i
$727$	25.0093	+	20.9853i	0.927543	+	0.778301i	0.975375	−	0.220554i	$-0.0707866\pi$
$727$	25.0093	+	20.9853i	0.927543	+	0.778301i	−0.0478314	+	0.998855i	$0.515231\pi$
$728$	1.09863	+	6.23062i	0.0407178	+	0.230922i
$729$	−13.2578	−	22.9631i	−0.491028	−	0.850486i
$730$		0			0
$731$	−8.42456	−	3.06629i	−0.311594	−	0.113411i
$732$	−18.1233	−	6.59634i	−0.669856	−	0.243808i
$733$	17.3827	−	30.1077i	0.642044	−	1.11205i	−0.342932	−	0.939360i	$-0.611420\pi$
$733$	17.3827	−	30.1077i	0.642044	−	1.11205i	0.984976	−	0.172693i	$-0.0552468\pi$
$734$	2.56752	+	4.44707i	0.0947687	+	0.164144i
$735$		0			0
$736$	−3.46454	−	2.90709i	−0.127705	−	0.107157i
$737$	36.1459	−	30.3300i	1.33145	−	1.11722i
$738$	0.856300	−	4.85632i	0.0315208	−	0.178764i
$739$	−28.3181	+	10.3069i	−1.04170	+	0.379147i	−0.805523	−	0.592564i	$-0.798116\pi$
$739$	−28.3181	+	10.3069i	−1.04170	+	0.379147i	−0.236174	+	0.971711i	$0.575893\pi$
$740$		0			0
$741$	−7.91070	+	14.1155i	−0.290607	+	0.518544i
$742$	6.59283			0.242030
$743$	17.5877	−	6.40141i	0.645231	−	0.234845i	0.00138410	−	0.999999i	$-0.499559\pi$
$743$	17.5877	−	6.40141i	0.645231	−	0.234845i	0.643847	+	0.765154i	$0.277337\pi$
$744$	−1.57835	+	8.95124i	−0.0578650	+	0.328168i
$745$		0			0
$746$	−24.8594	−	20.8595i	−0.910167	−	0.763721i
$747$	3.69957	+	20.9813i	0.135360	+	0.767665i
$748$	−3.11119	−	5.38873i	−0.113756	−	0.197032i
$749$	12.9292	−	22.3940i	0.472421	−	0.818258i
$750$		0			0
$751$	5.65553	+	2.05844i	0.206373	+	0.0751137i	0.443138	−	0.896453i	$-0.353865\pi$
$751$	5.65553	+	2.05844i	0.206373	+	0.0751137i	−0.236765	+	0.971567i	$0.576087\pi$
$752$	−5.51558	+	9.55327i	−0.201133	+	0.348372i
$753$	−5.54541	−	9.60493i	−0.202086	−	0.350023i
$754$	−0.253387	−	1.43703i	−0.00922780	−	0.0523334i
$755$		0			0
$756$	−9.58845	+	8.04566i	−0.348728	+	0.292618i
$757$	−7.06485	+	40.0667i	−0.256776	+	1.45625i	0.534695	+	0.845045i	$0.320426\pi$
$757$	−7.06485	+	40.0667i	−0.256776	+	1.45625i	−0.791472	+	0.611206i	$0.790685\pi$
$758$	22.7315	−	8.27360i	0.825646	−	0.300511i
$759$	−34.3892			−1.24825
$760$		0			0
$761$	39.9978			1.44992			0.724960	−	0.688791i	$-0.241858\pi$
$761$	39.9978			1.44992			0.724960	+	0.688791i	$0.241858\pi$
$762$	−21.5829	+	7.85555i	−0.781867	+	0.284576i
$763$	−3.19919	+	18.1435i	−0.115818	+	0.656838i
$764$	7.43180	−	6.23602i	0.268873	−	0.225611i
$765$		0			0
$766$	1.39132	+	7.89057i	0.0502705	+	0.285098i
$767$	−9.92207	−	17.1855i	−0.358265	−	0.620533i
$768$	−0.654450	+	1.13354i	−0.0236154	+	0.0409031i
$769$	−21.0594	−	7.66500i	−0.759422	−	0.276407i	−0.0668569	−	0.997763i	$-0.521297\pi$
$769$	−21.0594	−	7.66500i	−0.759422	−	0.276407i	−0.692565	+	0.721356i	$0.743519\pi$
$770$		0			0
$771$	−3.20551	+	5.55210i	−0.115444	+	0.199954i
$772$	−1.77961	−	3.08237i	−0.0640495	−	0.110937i
$773$	−9.05225	−	51.3378i	−0.325587	−	1.84649i	−0.505520	−	0.862815i	$-0.668699\pi$
$773$	−9.05225	−	51.3378i	−0.325587	−	1.84649i	0.179933	−	0.983679i	$-0.442412\pi$
$774$	−8.25066	−	6.92312i	−0.296564	−	0.248847i
$775$		0			0
$776$	0.865440	−	4.90815i	0.0310675	−	0.176192i
$777$	−7.08462	+	2.57859i	−0.254159	+	0.0925064i
$778$	−12.5839			−0.451156
$779$	−12.9324	−	10.5728i	−0.463352	−	0.378811i
$780$		0			0
$781$	−36.2776	+	13.2040i	−1.29812	+	0.472475i
$782$	−0.841189	+	4.77062i	−0.0300809	+	0.170597i
$783$	2.21148	−	1.85565i	0.0790317	−	0.0663155i
$784$	−1.55019	−	1.30076i	−0.0553638	−	0.0464557i
$785$		0			0
$786$	2.56709	+	4.44634i	0.0915652	+	0.158596i
$787$	3.25466	−	5.63724i	0.116016	−	0.200946i	−0.802169	−	0.597097i	$-0.796321\pi$
$787$	3.25466	−	5.63724i	0.116016	−	0.200946i	0.918186	+	0.396151i	$0.129654\pi$
$788$	3.15114	+	1.14692i	0.112255	+	0.0408574i
$789$	−15.4906	−	5.63813i	−0.551481	−	0.200723i
$790$		0			0
$791$	14.9207	+	25.8433i	0.530518	+	0.918884i
$792$	−1.29807	−	7.36175i	−0.0461251	−	0.261588i
$793$	32.0127	+	26.8618i	1.13680	+	0.953891i
$794$	0.856348	−	0.718561i	0.0303906	−	0.0255008i
$795$		0			0
$796$	−17.4134	+	6.33797i	−0.617203	+	0.224643i
$797$	3.20848			0.113650			0.0568251	−	0.998384i	$-0.481902\pi$
$797$	3.20848			0.113650			0.0568251	+	0.998384i	$0.481902\pi$
$798$	2.37015	+	12.5048i	0.0839022	+	0.442664i
$799$	11.8155			0.418003
$800$		0			0
$801$	−0.457096	+	2.59232i	−0.0161507	+	0.0915952i
$802$	13.7950	−	11.5754i	0.487120	−	0.408742i
$803$	−15.1116	−	12.6801i	−0.533277	−	0.447473i
$804$	1.84611	+	10.4698i	0.0651073	+	0.369242i
$805$		0			0
$806$	9.84733	−	17.0561i	0.346857	−	0.600775i
$807$	3.26085	+	1.18685i	0.114787	+	0.0417792i
$808$	−11.1862	−	4.07143i	−0.393528	−	0.143232i
$809$	−3.42148	+	5.92617i	−0.120293	+	0.208353i	−0.919883	−	0.392193i	$-0.871717\pi$
$809$	−3.42148	+	5.92617i	−0.120293	+	0.208353i	0.799590	+	0.600546i	$0.205050\pi$
$810$		0			0
$811$	0.958834	+	5.43782i	0.0336692	+	0.190948i	0.997004	−	0.0773564i	$-0.0246479\pi$
$811$	0.958834	+	5.43782i	0.0336692	+	0.190948i	−0.963334	+	0.268304i	$0.913537\pi$
$812$	−0.879227	−	0.737759i	−0.0308548	−	0.0258903i
$813$	−20.9882	+	17.6112i	−0.736087	+	0.617650i
$814$	2.60473	−	14.7721i	0.0912957	−	0.517763i
$815$		0			0
$816$	1.40197			0.0490787
$817$	−34.1217	+	12.9156i	−1.19377	+	0.451861i
$818$	−24.3660			−0.851939
$819$	7.65016	−	2.78443i	0.267318	−	0.0972959i
$820$		0			0
$821$	19.7227	−	16.5493i	0.688326	−	0.577574i	−0.230100	−	0.973167i	$-0.573905\pi$
$821$	19.7227	−	16.5493i	0.688326	−	0.577574i	0.918426	+	0.395593i	$0.129461\pi$
$822$	2.65817	+	2.23047i	0.0927143	+	0.0777965i
$823$	−2.95546	−	16.7613i	−0.103021	−	0.584260i	−0.991992	−	0.126298i	$-0.959690\pi$
$823$	−2.95546	−	16.7613i	−0.103021	−	0.584260i	0.888971	−	0.457963i	$-0.151421\pi$
$824$	0.262848	+	0.455266i	0.00915674	+	0.0158599i
$825$		0			0
$826$	−14.6674	−	5.33848i	−0.510342	−	0.185749i
$827$	36.8739	+	13.4210i	1.28223	+	0.466695i	0.891170	−	0.453669i	$-0.149885\pi$
$827$	36.8739	+	13.4210i	1.28223	+	0.466695i	0.391063	+	0.920364i	$0.372108\pi$
$828$	−2.90982	+	5.03996i	−0.101123	+	0.175151i
$829$	−3.37098	−	5.83871i	−0.117079	−	0.202787i	0.801530	−	0.597955i	$-0.204020\pi$
$829$	−3.37098	−	5.83871i	−0.117079	−	0.202787i	−0.918609	+	0.395168i	$0.870686\pi$
$830$		0			0
$831$	−14.6006	−	12.2513i	−0.506488	−	0.424994i
$832$	2.17259	−	1.82302i	0.0753208	−	0.0632017i
$833$	−0.376385	+	2.13458i	−0.0130410	+	0.0739589i
$834$	19.8139	−	7.21167i	0.686100	−	0.249720i
$835$		0			0
$836$	−23.9038	−	8.35579i	−0.826731	−	0.288991i
$837$	38.9640			1.34679
$838$	−16.2211	+	5.90400i	−0.560349	+	0.203950i
$839$	8.81270	−	49.9793i	0.304248	−	1.72548i	−0.322773	−	0.946476i	$-0.604615\pi$
$839$	8.81270	−	49.9793i	0.304248	−	1.72548i	0.627022	−	0.779002i	$-0.284274\pi$
$840$		0			0
$841$	−22.0125	−	18.4707i	−0.759052	−	0.636920i
$842$	5.85430	+	33.2014i	0.201752	+	1.14419i
$843$	21.5841	+	37.3847i	0.743395	+	1.28760i
$844$	12.9716	−	22.4674i	0.446500	−	0.773361i
$845$		0			0
$846$	13.3387	+	4.85488i	0.458593	+	0.166914i
$847$	−25.3729	+	43.9472i	−0.871824	+	1.51004i
$848$	−1.47770	−	2.55944i	−0.0507443	−	0.0878917i
$849$	0.192007	+	1.08892i	0.00658965	+	0.0373718i
$850$		0			0
$851$	−8.94568	+	7.50632i	−0.306654	+	0.257313i
$852$	1.51045	−	8.56616i	0.0517470	−	0.293472i
$853$	27.2486	−	9.91768i	0.932974	−	0.339575i	0.169587	−	0.985515i	$-0.445757\pi$
$853$	27.2486	−	9.91768i	0.932974	−	0.339575i	0.763388	+	0.645940i	$0.223535\pi$
$854$	32.8701			1.12479
$855$		0			0
$856$	−11.5916			−0.396193
$857$	18.8584	−	6.86388i	0.644189	−	0.234466i	0.000793759	−	1.00000i	$-0.499747\pi$
$857$	18.8584	−	6.86388i	0.644189	−	0.234466i	0.643395	+	0.765534i	$0.277525\pi$
$858$	3.74476	−	21.2376i	0.127844	−	0.725038i
$859$	25.1028	−	21.0638i	0.856498	−	0.718687i	−0.104713	−	0.994502i	$-0.533392\pi$
$859$	25.1028	−	21.0638i	0.856498	−	0.718687i	0.961211	+	0.275816i	$0.0889479\pi$
$860$		0			0
$861$	−1.94305	−	11.0196i	−0.0662189	−	0.375546i
$862$	−14.3750	−	24.8983i	−0.489616	−	0.848039i
$863$	16.0015	−	27.7154i	0.544698	−	0.943444i	−0.453928	−	0.891038i	$-0.649978\pi$
$863$	16.0015	−	27.7154i	0.544698	−	0.943444i	0.998626	−	0.0524056i	$-0.0166889\pi$
$864$	5.27258	+	1.91906i	0.179377	+	0.0652879i
$865$		0			0
$866$	6.37090	−	11.0347i	0.216492	−	0.374975i
$867$	10.3748	+	17.9697i	0.352347	+	0.610283i
$868$	−2.69000	−	15.2558i	−0.0913046	−	0.517814i
$869$	−23.1051	−	19.3875i	−0.783788	−	0.657676i
$870$		0			0
$871$	4.00013	−	22.6859i	0.135539	−	0.768681i
$872$	7.76066	−	2.82465i	0.262809	−	0.0956547i
$873$	−6.41316			−0.217053
$874$	10.0743	+	16.9452i	0.340768	+	0.573179i
$875$		0			0
$876$	4.17662	−	1.52016i	0.141115	−	0.0513616i
$877$	−5.98494	+	33.9423i	−0.202097	+	1.14615i	0.699846	+	0.714294i	$0.253252\pi$
$877$	−5.98494	+	33.9423i	−0.202097	+	1.14615i	−0.901943	+	0.431856i	$0.857859\pi$
$878$	−23.0908	+	19.3755i	−0.779277	+	0.653891i
$879$	−24.7145	−	20.7379i	−0.833599	−	0.699473i
$880$		0			0
$881$	−18.6285	−	32.2656i	−0.627612	−	1.08706i	−0.988030	−	0.154264i	$-0.950699\pi$
$881$	−18.6285	−	32.2656i	−0.627612	−	1.08706i	0.360418	−	0.932791i	$-0.382634\pi$
$882$	−1.30198	+	2.25510i	−0.0438400	+	0.0759331i
$883$	23.3474	+	8.49776i	0.785702	+	0.285972i	0.703548	−	0.710647i	$-0.251598\pi$
$883$	23.3474	+	8.49776i	0.785702	+	0.285972i	0.0821540	+	0.996620i	$0.473820\pi$
$884$	−2.85457	−	1.03898i	−0.0960096	−	0.0349446i
$885$		0			0
$886$	16.2958	+	28.2251i	0.547468	+	0.948242i
$887$	−5.80563	−	32.9254i	−0.194934	−	1.10553i	−0.912513	−	0.409049i	$-0.865861\pi$
$887$	−5.80563	−	32.9254i	−0.194934	−	1.10553i	0.717578	−	0.696478i	$-0.245251\pi$
$888$	2.58898	+	2.17241i	0.0868804	+	0.0729013i
$889$	29.9867	−	25.1619i	1.00572	−	0.843902i
$890$		0			0
$891$	19.0182	−	6.92204i	0.637132	−	0.231897i
$892$	−5.33117			−0.178501
$893$	36.4361	−	31.3760i	1.21929	−	1.04996i
$894$	18.1440			0.606828
$895$		0			0
$896$	0.387371	−	2.19689i	0.0129411	−	0.0733929i
$897$	−12.8610	+	10.7917i	−0.429416	+	0.360323i
$898$	−12.8511	−	10.7834i	−0.428848	−	0.359846i
$899$	0.620421	+	3.51858i	0.0206922	+	0.117351i
$900$		0			0
$901$	−1.58277	+	2.74143i	−0.0527296	+	0.0913304i
$902$	20.9199	+	7.61424i	0.696558	+	0.253526i
$903$	−22.9656	−	8.35880i	−0.764248	−	0.278163i
$904$	6.68854	−	11.5849i	0.222458	−	0.385308i
$905$		0			0
$906$	−1.96939	−	11.1690i	−0.0654285	−	0.371064i
$907$	−19.4940	−	16.3574i	−0.647288	−	0.543139i	0.258958	−	0.965888i	$-0.416621\pi$
$907$	−19.4940	−	16.3574i	−0.647288	−	0.543139i	−0.906247	+	0.422749i	$0.861065\pi$
$908$	−18.2043	+	15.2752i	−0.604130	+	0.506926i
$909$	−2.65993	+	15.0852i	−0.0882245	+	0.500346i
$910$		0			0
$911$	−0.722711			−0.0239445			−0.0119722	−	0.999928i	$-0.503811\pi$
$911$	−0.722711			−0.0239445			−0.0119722	+	0.999928i	$0.503811\pi$
$912$	4.32332	−	3.72291i	0.143159	−	0.123278i
$913$	−96.1833			−3.18320
$914$	−15.5026	+	5.64249i	−0.512781	+	0.186637i
$915$		0			0
$916$	16.2315	−	13.6198i	0.536303	−	0.450012i
$917$	−6.70311	−	5.62458i	−0.221356	−	0.185740i
$918$	−1.04361	−	5.91863i	−0.0344444	−	0.195344i
$919$	−1.12765	−	1.95314i	−0.0371976	−	0.0644281i	0.846827	−	0.531868i	$-0.178510\pi$
$919$	−1.12765	−	1.95314i	−0.0371976	−	0.0644281i	−0.884025	+	0.467440i	$0.845176\pi$
$920$		0			0
$921$	−41.7968	−	15.2128i	−1.37725	−	0.501279i
$922$	−13.6758	−	4.97758i	−0.450388	−	0.163928i
$923$	−9.42370	+	16.3223i	−0.310185	+	0.537256i
$924$	−8.48119	−	14.6899i	−0.279011	−	0.483261i
$925$		0			0
$926$	−14.5126	−	12.1775i	−0.476915	−	0.400179i
$927$	0.518196	−	0.434818i	0.0170198	−	0.0142813i
$928$	−0.0893431	+	0.506690i	−0.00293283	+	0.0166329i
$929$	−1.24934	+	0.454722i	−0.0409895	+	0.0149189i	−0.362434	−	0.932010i	$-0.618054\pi$
$929$	−1.24934	+	0.454722i	−0.0409895	+	0.0149189i	0.321444	+	0.946929i	$0.395832\pi$
$930$		0			0
$931$	4.50768	+	7.58200i	0.147733	+	0.248490i
$932$	15.2713			0.500229
$933$	36.3383	−	13.2261i	1.18966	−	0.433002i
$934$	2.52321	−	14.3098i	0.0825619	−	0.468232i
$935$		0			0
$936$	−2.79565	−	2.34583i	−0.0913785	−	0.0766757i
$937$	6.77813	+	38.4407i	0.221432	+	1.25580i	0.869390	+	0.494126i	$0.164512\pi$
$937$	6.77813	+	38.4407i	0.221432	+	1.25580i	−0.647959	+	0.761676i	$0.724377\pi$
$938$	−9.05957	−	15.6916i	−0.295805	−	0.512350i
$939$	−2.33232	+	4.03970i	−0.0761124	+	0.131831i
$940$		0			0
$941$	12.0825	+	4.39766i	0.393878	+	0.143360i	0.531363	−	0.847144i	$-0.321680\pi$
$941$	12.0825	+	4.39766i	0.393878	+	0.143360i	−0.137486	+	0.990504i	$0.543902\pi$
$942$	−2.61035	+	4.52126i	−0.0850498	+	0.147311i
$943$	−8.66587	−	15.0097i	−0.282199	−	0.488784i
$944$	1.21501	+	6.89066i	0.0395452	+	0.224272i
$945$		0			0
$946$	37.2484	−	31.2551i	1.21105	−	1.01619i
$947$	−8.15361	+	46.2414i	−0.264957	+	1.50264i	0.504202	+	0.863586i	$0.331787\pi$
$947$	−8.15361	+	46.2414i	−0.264957	+	1.50264i	−0.769158	+	0.639058i	$0.779324\pi$
$948$	6.38591	−	2.32428i	0.207405	−	0.0754891i
$949$	−9.63065			−0.312624
$950$		0			0
$951$	35.5883			1.15403
$952$	−2.24530	+	0.817222i	−0.0727706	+	0.0264863i
$953$	−3.07965	+	17.4656i	−0.0997596	+	0.565765i	0.893425	+	0.449213i	$0.148295\pi$
$953$	−3.07965	+	17.4656i	−0.0997596	+	0.565765i	−0.993185	+	0.116552i	$0.962816\pi$
$954$	−2.91323	+	2.44449i	−0.0943192	+	0.0791432i
$955$		0			0
$956$	−3.40404	−	19.3053i	−0.110095	−	0.624378i
$957$	1.95610	+	3.38806i	0.0632317	+	0.109521i
$958$	−2.41686	+	4.18613i	−0.0780853	+	0.135248i
$959$	−5.55731	−	2.02270i	−0.179455	−	0.0653163i
$960$		0			0
$961$	−8.61134	+	14.9153i	−0.277785	+	0.481138i
$962$	−3.66151	−	6.34193i	−0.118052	−	0.204472i
$963$	2.59012	+	14.6893i	0.0834653	+	0.473355i
$964$	−6.98914	−	5.86459i	−0.225105	−	0.188886i
$965$		0			0
$966$	−2.29311	+	13.0049i	−0.0737795	+	0.418425i
$967$	−9.13568	+	3.32511i	−0.293784	+	0.106928i	−0.484707	−	0.874676i	$-0.661074\pi$
$967$	−9.13568	+	3.32511i	−0.293784	+	0.106928i	0.190924	+	0.981605i	$0.438852\pi$
$968$	22.7480			0.731149
$969$	−5.76875	−	2.01651i	−0.185319	−	0.0647798i
$970$		0			0
$971$	−34.4686	+	12.5455i	−1.10615	+	0.402606i	−0.829580	−	0.558388i	$-0.811420\pi$
$971$	−34.4686	+	12.5455i	−1.10615	+	0.402606i	−0.276570	+	0.960994i	$0.589198\pi$
$972$	2.13117	−	12.0865i	0.0683572	−	0.387673i
$973$	−27.5289	+	23.0995i	−0.882536	+	0.740536i
$974$	−21.2215	−	17.8069i	−0.679980	−	0.570571i
$975$		0			0
$976$	−7.36741	−	12.7607i	−0.235825	−	0.408461i
$977$	−18.6954	+	32.3814i	−0.598119	+	1.03597i	0.394980	+	0.918690i	$0.370752\pi$
$977$	−18.6954	+	32.3814i	−0.598119	+	1.03597i	−0.993099	+	0.117283i	$0.962582\pi$
$978$	−22.6914	−	8.25898i	−0.725589	−	0.264093i
$979$	−11.1671	−	4.06451i	−0.356903	−	0.129902i
$980$		0			0
$981$	−5.31359	−	9.20341i	−0.169650	−	0.293842i
$982$	5.69883	+	32.3197i	0.181857	+	1.03136i
$983$	8.83452	+	7.41304i	0.281777	+	0.236439i	0.772711	−	0.634757i	$-0.218900\pi$
$983$	8.83452	+	7.41304i	0.281777	+	0.236439i	−0.490934	+	0.871197i	$0.663344\pi$
$984$	−3.84247	+	3.22422i	−0.122494	+	0.102784i
$985$		0			0
$986$	0.517855	−	0.188484i	0.0164919	−	0.00600255i
$987$	32.2095			1.02524
$988$	−11.5618	+	4.37632i	−0.367829	+	0.139229i
$989$	−37.8548			−1.20371
$990$		0			0
$991$	4.49126	−	25.4712i	0.142670	−	0.809119i	−0.826539	−	0.562879i	$-0.809694\pi$
$991$	4.49126	−	25.4712i	0.142670	−	0.809119i	0.969209	−	0.246240i	$-0.0791952\pi$
$992$	−5.31961	+	4.46368i	−0.168898	+	0.141722i
$993$	29.4086	+	24.6768i	0.933254	+	0.783093i
$994$	2.57428	+	14.5995i	0.0816512	+	0.463067i
$995$		0			0
$996$	10.8356	−	18.7678i	0.343338	−	0.594679i
$997$	0.685188	+	0.249388i	0.0217001	+	0.00789819i	0.352847	−	0.935681i	$-0.385213\pi$
$997$	0.685188	+	0.249388i	0.0217001	+	0.00789819i	−0.331147	+	0.943579i	$0.607436\pi$
$998$	−18.3006	−	6.66088i	−0.579296	−	0.210846i
$999$	7.24395	−	12.5469i	0.229189	−	0.396966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.k.651.3	yes	24
5.2	odd	4		950.2.u.h.499.2		48
5.3	odd	4		950.2.u.h.499.7		48
5.4	even	2		950.2.l.j.651.2	yes	24
19.4	even	9	inner	950.2.l.k.251.3	yes	24
95.4	even	18		950.2.l.j.251.2	✓	24
95.23	odd	36		950.2.u.h.99.2		48
95.42	odd	36		950.2.u.h.99.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.251.2	✓	24	95.4	even	18
950.2.l.j.651.2	yes	24	5.4	even	2
950.2.l.k.251.3	yes	24	19.4	even	9	inner
950.2.l.k.651.3	yes	24	1.1	even	1	trivial
950.2.u.h.99.2		48	95.23	odd	36
950.2.u.h.99.7		48	95.42	odd	36
950.2.u.h.499.2		48	5.2	odd	4
950.2.u.h.499.7		48	5.3	odd	4

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.227288 - 1.28901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.227288 + 1.28901i) q^{6} +(-1.11539 - 1.93191i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.20918 + 0.440106i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.227288 - 1.28901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.227288 + 1.28901i) q^{6} +(-1.11539 - 1.93191i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.20918 + 0.440106i) q^{9} +(-2.90465 + 5.03101i) q^{11} +(-0.654450 - 1.13354i) q^{12} +(0.492485 + 2.79302i) q^{13} +(1.70888 + 1.43392i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-1.00651 + 0.366339i) q^{17} -1.28678 q^{18} +(-2.13101 + 3.80247i) q^{19} +(-2.74378 + 0.998653i) q^{21} +(1.00878 - 5.72105i) q^{22} +(-3.46454 + 2.90709i) q^{23} +(1.00267 + 0.841344i) q^{24} +(-1.41805 - 2.45614i) q^{26} +(2.80548 - 4.85924i) q^{27} +(-2.09625 - 0.762972i) q^{28} +(0.483478 + 0.175971i) q^{29} +(3.47213 + 6.01390i) q^{31} +(0.173648 + 0.984808i) q^{32} +(5.82484 + 4.88763i) q^{33} +(0.820514 - 0.688493i) q^{34} +(1.20918 - 0.440106i) q^{36} +2.58207 q^{37} +(0.701975 - 4.30200i) q^{38} +3.71218 q^{39} +(-0.665458 + 3.77400i) q^{41} +(2.23675 - 1.87685i) q^{42} +(6.41185 + 5.38018i) q^{43} +(1.00878 + 5.72105i) q^{44} +(2.26132 - 3.91672i) q^{46} +(-10.3659 - 3.77288i) q^{47} +(-1.22996 - 0.447670i) q^{48} +(1.01181 - 1.75251i) q^{49} +(0.243449 + 1.38067i) q^{51} +(2.17259 + 1.82302i) q^{52} +(2.26396 - 1.89969i) q^{53} +(-0.974334 + 5.52572i) q^{54} +2.23078 q^{56} +(4.41709 + 3.61116i) q^{57} -0.514506 q^{58} +(-6.57499 + 2.39310i) q^{59} +(11.2875 - 9.47136i) q^{61} +(-5.31961 - 4.46368i) q^{62} +(-0.498462 - 2.82692i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.14523 - 2.60065i) q^{66} +(-7.63250 - 2.77800i) q^{67} +(-0.535552 + 0.927604i) q^{68} +(2.95984 + 5.12659i) q^{69} +(5.09076 + 4.27166i) q^{71} +(-0.985733 + 0.827128i) q^{72} +(-0.589662 + 3.34414i) q^{73} +(-2.42635 + 0.883120i) q^{74} +(0.811731 + 4.28265i) q^{76} +12.9593 q^{77} +(-3.48831 + 1.26964i) q^{78} +(-0.901573 + 5.11307i) q^{79} +(-2.66878 - 2.23937i) q^{81} +(-0.665458 - 3.77400i) q^{82} +(8.27838 + 14.3386i) q^{83} +(-1.45993 + 2.52868i) q^{84} +(-7.86530 - 2.86273i) q^{86} +(0.336718 - 0.583213i) q^{87} +(-2.90465 - 5.03101i) q^{88} +(0.355224 + 2.01458i) q^{89} +(4.84656 - 4.06675i) q^{91} +(-0.785347 + 4.45392i) q^{92} +(8.54118 - 3.10873i) q^{93} +11.0312 q^{94} +1.30890 q^{96} +(-4.68331 + 1.70458i) q^{97} +(-0.351398 + 1.99288i) q^{98} +(-5.72642 + 4.80504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 3 * q^7 - 12 * q^8	\( 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Introduction

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