LMFDB - Embedded newform 950.2.l.j.651.2

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			651.2
Character	$\chi$	$=$	950.651
Dual form			950.2.l.j.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.227288 + 1.28901i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.227288 + 1.28901i) q^{6} +(1.11539 + 1.93191i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.20918 + 0.440106i) q^{9} +O(q^{10})$	\(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	$0.178891\pi$
$3$	−0.227288	+	1.28901i	−0.131225	+	0.744213i	−0.977415	+	0.211331i	$0.932220\pi$
$4$	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	0.996094	−	0.0882992i	$-0.0281431\pi$
$7$	1.11539	+	1.93191i	0.421578	+	0.730194i	−0.574516	+	0.818493i	$0.694810\pi$
$8$	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	$-0.926890\pi$
$13$	−0.492485	−	2.79302i	−0.136591	−	0.774645i	0.837148	−	0.546977i	$-0.184221\pi$
$14$	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	−0.217065	−	0.976157i	$-0.569649\pi$
$17$	1.00651	−	0.366339i	0.244114	−	0.0888504i	0.461180	+	0.887307i	$0.347426\pi$
$18$	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	−0.205644	−	0.978627i	$-0.565929\pi$
$23$	3.46454	−	2.90709i	0.722406	−	0.606171i	0.928050	+	0.372456i	$0.121484\pi$
$24$	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	$-0.568077\pi$
$37$	−2.58207			−0.424490			−0.212245	+	0.977217i	$0.568077\pi$
$38$	−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	0.00595783	−	0.999982i	$-0.498104\pi$
$43$	−6.41185	−	5.38018i	−0.977798	−	0.820470i	−0.983756	+	0.179512i	$0.942548\pi$
$44$	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	0.959141	−	0.282929i	$-0.0913060\pi$
$47$	10.3659	+	3.77288i	1.51202	+	0.550331i	0.552881	+	0.833260i	$0.313528\pi$
$48$	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	−0.784897	−	0.619627i	$-0.787284\pi$
$53$	−2.26396	+	1.89969i	−0.310979	+	0.260942i	0.473917	+	0.880569i	$0.342839\pi$
$54$	−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	0.763183	−	0.646182i	$-0.223635\pi$
$67$	7.63250	+	2.77800i	0.932458	+	0.339387i	0.169275	+	0.985569i	$0.445857\pi$
$68$	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	$-0.880766\pi$
$73$	0.589662	−	3.34414i	0.0690147	−	0.391402i	0.999674	−	0.0255158i	$-0.00812281\pi$
$74$	−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	$-0.803765\pi$
$83$	−8.27838	−	14.3386i	−0.908670	−	1.57386i	−0.0927571	−	0.995689i	$-0.529568\pi$
$84$	−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	−0.0931326	−	0.995654i	$-0.529688\pi$
$97$	4.68331	−	1.70458i	0.475518	−	0.173074i	0.568650	+	0.822579i	$0.307466\pi$
$98$	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	−0.878684	−	0.477403i	$-0.841578\pi$
$103$	−0.262848	+	0.455266i	−0.0258992	+	0.0448587i	0.852785	+	0.522262i	$0.174912\pi$
$104$	−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	$-0.977352\pi$
$107$	−5.79580	−	10.0386i	−0.560301	−	0.970471i	0.437168	−	0.899380i	$-0.355981\pi$
$108$	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	$-0.283381\pi$
$113$	13.3771			1.25841			0.629205	+	0.777239i	$0.283381\pi$
$114$	−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	$-0.771511\pi$
$127$	−3.04711	−	17.2810i	−0.270388	−	1.53344i	0.482854	−	0.875701i	$-0.339600\pi$
$128$	−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	−0.725406	−	0.688322i	$-0.758348\pi$
$137$	−2.03084	+	1.70408i	−0.173507	+	0.145589i	0.551899	+	0.833911i	$0.313903\pi$
$138$	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	0.512667	−	0.858587i	$-0.328657\pi$
$157$	−3.05546	−	2.56383i	−0.243852	−	0.204616i	−0.756520	+	0.653971i	$0.773102\pi$
$158$	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	$-0.576321\pi$
$163$	9.22440	−	15.9771i	0.722511	−	1.25143i	0.959990	−	0.280033i	$-0.0903455\pi$
$164$	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	−0.812002	−	0.583654i	$-0.801622\pi$
$167$	−4.88766	+	4.10123i	−0.378218	+	0.317363i	0.433784	+	0.901017i	$0.357178\pi$
$168$	−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	0.0815108	−	0.996672i	$-0.474025\pi$
$173$	10.3198	−	3.75610i	0.784600	−	0.285571i	0.703090	+	0.711101i	$0.251803\pi$
$174$	−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	−0.998938	−	0.0460647i	$-0.985332\pi$
$193$	−0.618052	+	3.50514i	−0.0444883	+	0.252306i	0.954450	+	0.298370i	$0.0964431\pi$
$194$	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	0.800094	−	0.599874i	$-0.204783\pi$
$197$	−1.67669	−	2.90411i	−0.119459	−	0.206909i	−0.919553	+	0.392965i	$0.871449\pi$
$198$	−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	0.769204	−	0.639004i	$-0.220653\pi$
$223$	4.08391	+	3.42681i	0.273479	+	0.229476i	−0.495725	+	0.868480i	$0.665098\pi$
$224$	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	$-0.210788\pi$
$227$	23.7640			1.57727			0.788636	+	0.614860i	$0.210788\pi$
$228$	−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	0.173388	−	0.984854i	$-0.444528\pi$
$233$	−11.6985	−	9.81621i	−0.766395	−	0.643082i	−0.939783	+	0.341772i	$0.888973\pi$
$234$	−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	0.481558	−	0.876414i	$-0.340071\pi$
$257$	4.60263	+	1.67522i	0.287104	+	0.104497i	−0.194454	+	0.980912i	$0.562293\pi$
$258$	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	$0.182494\pi$
$263$	−2.18699	+	12.4030i	−0.134856	+	0.764805i	−0.974960	+	0.222380i	$0.928617\pi$
$264$	−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	−0.997493	−	0.0707659i	$-0.977456\pi$
$277$	−7.28081	+	12.6107i	−0.437461	+	0.757705i	0.560032	+	0.828471i	$0.310789\pi$
$278$	−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	−0.318318	−	0.947984i	$-0.603118\pi$
$283$	0.793827	−	0.288929i	0.0471881	−	0.0171751i	0.365506	+	0.930809i	$0.380896\pi$
$284$	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	$0.422521\pi$
$293$	−12.3243	+	21.3463i	−0.719992	+	1.24706i	−0.961002	+	0.276541i	$0.910812\pi$
$294$	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	$0.477040\pi$
$307$	−5.90094	+	33.4659i	−0.336785	+	1.91000i	−0.408852	+	0.912601i	$0.634071\pi$
$308$	−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	0.434926	−	0.900466i	$-0.356775\pi$
$313$	3.34887	+	1.21889i	0.189289	+	0.0688956i	−0.245636	+	0.969362i	$0.578997\pi$
$314$	−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	$-0.779007\pi$
$317$	−4.72141	−	26.7764i	−0.265181	−	1.50391i	0.503340	−	0.864089i	$-0.332105\pi$
$318$	−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	0.411701	−	0.911319i	$-0.364935\pi$
$337$	−7.60520	−	6.38152i	−0.414282	−	0.347624i	−0.825983	+	0.563695i	$0.809379\pi$
$338$	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	$0.0502335\pi$
$347$	24.4740	+	20.5362i	1.31384	+	1.10244i	0.326262	+	0.945279i	$0.394211\pi$
$348$	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	−0.905470	−	0.424410i	$-0.860482\pi$
$353$	−1.60049	+	2.77214i	−0.0851857	+	0.147546i	0.820285	+	0.571956i	$0.193815\pi$
$354$	−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	0.999196	−	0.0400944i	$-0.0127659\pi$
$367$	0.891689	+	5.05702i	0.0465458	+	0.263974i	−0.952650	+	0.304069i	$0.901655\pi$
$368$	−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	$-0.849139\pi$
$373$	−16.2258	−	28.1039i	−0.840141	−	1.45517i	0.0496338	−	0.998767i	$-0.484195\pi$
$374$	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	$0.121179\pi$
$383$	−1.39132	+	7.89057i	−0.0710932	+	0.403189i	−0.999500	+	0.0316238i	$0.989932\pi$
$384$	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	−0.315525	−	0.948917i	$-0.602181\pi$
$397$	1.05047	−	0.382338i	0.0527214	−	0.0191890i	0.368246	+	0.929728i	$0.379958\pi$
$398$	−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	−0.377383	−	0.926057i	$-0.623176\pi$
$433$	9.76078	−	8.19027i	0.469073	−	0.393599i	0.846456	+	0.532458i	$0.178732\pi$
$434$	−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	$0.226310\pi$
$443$	5.65947	+	32.0964i	0.268889	+	1.52495i	−0.488837	+	0.872375i	$0.662579\pi$
$444$	−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	$-0.626096\pi$
$457$	−16.4975			−0.771722			−0.385861	+	0.922557i	$0.626096\pi$
$458$	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	0.557484	−	0.830188i	$-0.311767\pi$
$463$	−9.47245	−	16.4068i	−0.440222	−	0.762487i	−0.997706	+	0.0677011i	$0.978434\pi$
$464$	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	−0.647517	−	0.762051i	$-0.724192\pi$
$467$	7.26529	−	12.5838i	0.336197	−	0.582311i	0.983714	+	0.179740i	$0.0575257\pi$
$468$	−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	$-0.950678\pi$
$487$	−13.8513	−	23.9912i	−0.627664	−	1.08715i	0.360356	−	0.932815i	$-0.382655\pi$
$488$	−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	−0.342384	−	0.939560i	$-0.611235\pi$
$503$	−27.1062	−	9.86583i	−1.20860	−	0.439896i	−0.866219	+	0.499664i	$0.833457\pi$
$504$	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	0.495055	−	0.868862i	$-0.335148\pi$
$523$	7.22198	+	2.62859i	0.315795	+	0.114940i	−0.179260	+	0.983802i	$0.557370\pi$
$524$	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	−0.374081	−	0.927396i	$-0.622042\pi$
$547$	11.0922	−	9.30744i	0.474267	−	0.397958i	0.848348	+	0.529438i	$0.177597\pi$
$548$	−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	$0.262373\pi$
$557$	6.89180	+	39.0853i	0.292015	+	1.65610i	−0.387079	+	0.922047i	$0.626516\pi$
$558$	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	0.966596	−	0.256305i	$-0.0825052\pi$
$563$	6.20077	+	10.7400i	0.261331	+	0.452639i	−0.705265	+	0.708944i	$0.749172\pi$
$564$	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	0.997161	−	0.0753028i	$-0.0239923\pi$
$577$	10.4098	+	18.0303i	0.433366	+	0.750612i	−0.563794	+	0.825915i	$0.690659\pi$
$578$	−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	−0.417170	−	0.908828i	$-0.636978\pi$
$587$	−3.69616	+	1.34529i	−0.152557	+	0.0555262i	0.264613	+	0.964355i	$0.414756\pi$
$588$	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	−0.647478	−	0.762084i	$-0.724176\pi$
$593$	−0.229047	+	0.192194i	−0.00940585	+	0.00789244i	0.638073	+	0.769976i	$0.279732\pi$
$594$	−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	$-0.641187\pi$
$607$	−21.1463			−0.858301			−0.429150	+	0.903233i	$0.641187\pi$
$608$	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	$-0.979990\pi$
$613$	−30.5326	−	25.6199i	−1.23320	−	1.03478i	−0.235174	−	0.971953i	$-0.575566\pi$
$614$	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	0.428746	−	0.903425i	$-0.358956\pi$
$617$	4.38350	+	1.59546i	0.176473	+	0.0642309i	−0.252272	+	0.967656i	$0.581178\pi$
$618$	−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	$0.270453\pi$
$643$	−5.50401	+	31.2148i	−0.217057	+	1.23099i	−0.877301	+	0.479940i	$0.840658\pi$
$644$	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	$-0.496998\pi$
$647$	0.479708			0.0188593			0.00942963	+	0.999956i	$0.496998\pi$
$648$	−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	0.723808	−	0.690002i	$-0.242390\pi$
$653$	−6.02190	−	10.4302i	−0.235655	−	0.408167i	−0.959463	+	0.281835i	$0.909057\pi$
$654$	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	$-0.503291\pi$
$673$	22.3313	−	38.6790i	0.860810	−	1.49097i	0.871148	−	0.491020i	$-0.163376\pi$
$674$	−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	0.814098	−	0.580727i	$-0.197232\pi$
$677$	−2.49459	−	4.32076i	−0.0958750	−	0.166060i	−0.909973	+	0.414667i	$0.863898\pi$
$678$	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	$-0.685528\pi$
$683$	−28.7691			−1.10082			−0.550409	+	0.834895i	$0.685528\pi$
$684$	−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	0.0478314	−	0.998855i	$-0.484769\pi$
$727$	−25.0093	−	20.9853i	−0.927543	−	0.778301i	−0.975375	+	0.220554i	$0.929213\pi$
$728$	−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	$0.388580\pi$
$733$	−17.3827	+	30.1077i	−0.642044	+	1.11205i	−0.984976	+	0.172693i	$0.944753\pi$
$734$	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	−0.643847	−	0.765154i	$-0.722663\pi$
$743$	−17.5877	+	6.40141i	−0.645231	+	0.234845i	−0.00138410	+	0.999999i	$0.500441\pi$
$744$	−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	$-0.679574\pi$
$757$	7.06485	−	40.0667i	0.256776	−	1.45625i	0.791472	−	0.611206i	$-0.209315\pi$
$758$	−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	$0.331301\pi$
$773$	9.05225	+	51.3378i	0.325587	+	1.84649i	−0.179933	+	0.983679i	$0.557588\pi$
$774$	−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	−0.918186	−	0.396151i	$-0.870346\pi$
$787$	−3.25466	+	5.63724i	−0.116016	+	0.200946i	0.802169	+	0.597097i	$0.203679\pi$
$788$	−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	$-0.518098\pi$
$797$	−3.20848			−0.113650			−0.0568251	+	0.998384i	$0.518098\pi$
$798$	−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	$0.0403095\pi$
$823$	2.95546	+	16.7613i	0.103021	+	0.584260i	−0.888971	+	0.457963i	$0.848579\pi$
$824$	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	−0.391063	−	0.920364i	$-0.627892\pi$
$827$	−36.8739	−	13.4210i	−1.28223	−	0.466695i	−0.891170	+	0.453669i	$0.850115\pi$
$828$	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	−0.763388	−	0.645940i	$-0.776465\pi$
$853$	−27.2486	+	9.91768i	−0.932974	+	0.339575i	−0.169587	+	0.985515i	$0.554243\pi$
$854$	32.8701			1.12479
$855$		0			0
$856$	−11.5916			−0.396193
$857$	−18.8584	+	6.86388i	−0.644189	+	0.234466i	−0.643395	−	0.765534i	$-0.722475\pi$
$857$	−18.8584	+	6.86388i	−0.644189	+	0.234466i	−0.000793759		1.00000i	$0.500253\pi$
$858$	−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	$0.350022\pi$
$863$	−16.0015	+	27.7154i	−0.544698	+	0.943444i	−0.998626	+	0.0524056i	$0.983311\pi$
$864$	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	$-0.746748\pi$
$877$	5.98494	−	33.9423i	0.202097	−	1.14615i	0.901943	−	0.431856i	$-0.142141\pi$
$878$	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	−0.0821540	−	0.996620i	$-0.526180\pi$
$883$	−23.3474	−	8.49776i	−0.785702	−	0.285972i	−0.703548	+	0.710647i	$0.748402\pi$
$884$	−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	$0.134139\pi$
$887$	5.80563	+	32.9254i	0.194934	+	1.10553i	−0.717578	+	0.696478i	$0.754749\pi$
$888$	−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	0.906247	−	0.422749i	$-0.138935\pi$
$907$	19.4940	+	16.3574i	0.647288	+	0.543139i	−0.258958	+	0.965888i	$0.583379\pi$
$908$	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	$-0.835488\pi$
$937$	−6.77813	−	38.4407i	−0.221432	−	1.25580i	0.647959	−	0.761676i	$-0.275623\pi$
$938$	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	$-0.668213\pi$
$947$	8.15361	−	46.2414i	0.264957	−	1.50264i	0.769158	−	0.639058i	$-0.220676\pi$
$948$	−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	$-0.851705\pi$
$953$	3.07965	−	17.4656i	0.0997596	−	0.565765i	0.993185	−	0.116552i	$-0.0371843\pi$
$954$	−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	−0.190924	−	0.981605i	$-0.561148\pi$
$967$	9.13568	−	3.32511i	0.293784	−	0.106928i	0.484707	+	0.874676i	$0.338926\pi$
$968$	−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	$-0.629248\pi$
$977$	18.6954	−	32.3814i	0.598119	−	1.03597i	0.993099	−	0.117283i	$-0.0374183\pi$
$978$	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	0.490934	−	0.871197i	$-0.336656\pi$
$983$	−8.83452	−	7.41304i	−0.281777	−	0.236439i	−0.772711	+	0.634757i	$0.781100\pi$
$984$	−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	0.331147	−	0.943579i	$-0.392564\pi$
$997$	−0.685188	−	0.249388i	−0.0217001	−	0.00789819i	−0.352847	+	0.935681i	$0.614787\pi$
$998$	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.j.651.2	yes	24
5.2	odd	4		950.2.u.h.499.7		48
5.3	odd	4		950.2.u.h.499.2		48
5.4	even	2		950.2.l.k.651.3	yes	24
19.4	even	9	inner	950.2.l.j.251.2	✓	24
95.4	even	18		950.2.l.k.251.3	yes	24
95.23	odd	36		950.2.u.h.99.7		48
95.42	odd	36		950.2.u.h.99.2		48

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