LMFDB - Embedded newform 847.2.f.z.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	847.323
Dual form			847.2.f.z.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12126 - 0.814642i) q^{2} +(-0.0378481 + 0.116485i) q^{3} +(-0.0244542 - 0.0752624i) q^{4} +(0.107603 - 0.0781781i) q^{5} +(0.137331 - 0.0997767i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.890458 + 2.74055i) q^{8} +(2.41491 + 1.75454i) q^{9} +O(q^{10})$	\(q+(-1.12126 - 0.814642i) q^{2} +(-0.0378481 + 0.116485i) q^{3} +(-0.0244542 - 0.0752624i) q^{4} +(0.107603 - 0.0781781i) q^{5} +(0.137331 - 0.0997767i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.890458 + 2.74055i) q^{8} +(2.41491 + 1.75454i) q^{9} -0.184338 q^{10} +0.00969245 q^{12} +(-0.518933 - 0.377027i) q^{13} +(-0.428283 + 1.31812i) q^{14} +(0.00503397 + 0.0154930i) q^{15} +(3.10296 - 2.25443i) q^{16} +(-1.15270 + 0.837488i) q^{17} +(-1.27842 - 3.93458i) q^{18} +(-2.21966 + 6.83141i) q^{19} +(-0.00851521 - 0.00618666i) q^{20} +0.122479 q^{21} +1.66655 q^{23} +(-0.285529 - 0.207449i) q^{24} +(-1.53962 + 4.73846i) q^{25} +(0.274716 + 0.845489i) q^{26} +(-0.593040 + 0.430869i) q^{27} +(-0.0640220 + 0.0465147i) q^{28} +(-1.38334 - 4.25747i) q^{29} +(0.00697684 - 0.0214725i) q^{30} +(5.52706 + 4.01565i) q^{31} +0.447392 q^{32} +1.97473 q^{34} +(-0.107603 - 0.0781781i) q^{35} +(0.0729958 - 0.224658i) q^{36} +(1.16457 + 3.58419i) q^{37} +(8.05397 - 5.85155i) q^{38} +(0.0635584 - 0.0461779i) q^{39} +(0.118435 + 0.364505i) q^{40} +(-1.90752 + 5.87074i) q^{41} +(-0.137331 - 0.0997767i) q^{42} +1.03970 q^{43} +0.397018 q^{45} +(-1.86863 - 1.35764i) q^{46} +(2.93238 - 9.02493i) q^{47} +(0.145165 + 0.446773i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(5.58646 - 4.05880i) q^{50} +(-0.0539268 - 0.165970i) q^{51} +(-0.0156858 + 0.0482760i) q^{52} +(0.539250 + 0.391788i) q^{53} +1.01595 q^{54} +2.88158 q^{56} +(-0.711744 - 0.517112i) q^{57} +(-1.91724 + 5.90065i) q^{58} +(2.52991 + 7.78625i) q^{59} +(0.00104294 - 0.000757737i) q^{60} +(7.68410 - 5.58282i) q^{61} +(-2.92595 - 9.00516i) q^{62} +(0.922415 - 2.83890i) q^{63} +(-6.70756 - 4.87333i) q^{64} -0.0853139 q^{65} +12.0398 q^{67} +(0.0912198 + 0.0662751i) q^{68} +(-0.0630758 + 0.194127i) q^{69} +(0.0569635 + 0.175316i) q^{70} +(-3.91093 + 2.84146i) q^{71} +(-6.95878 + 5.05585i) q^{72} +(2.73711 + 8.42396i) q^{73} +(1.61405 - 4.96752i) q^{74} +(-0.493685 - 0.358684i) q^{75} +0.568428 q^{76} -0.108884 q^{78} +(9.29614 + 6.75404i) q^{79} +(0.157640 - 0.485166i) q^{80} +(2.73950 + 8.43132i) q^{81} +(6.92137 - 5.02867i) q^{82} +(7.75037 - 5.63097i) q^{83} +(-0.00299513 - 0.00921807i) q^{84} +(-0.0585610 + 0.180232i) q^{85} +(-1.16577 - 0.846984i) q^{86} +0.548286 q^{87} -17.7001 q^{89} +(-0.445160 - 0.323428i) q^{90} +(-0.198215 + 0.610042i) q^{91} +(-0.0407542 - 0.125428i) q^{92} +(-0.676950 + 0.491833i) q^{93} +(-10.6400 + 7.73045i) q^{94} +(0.295225 + 0.908608i) q^{95} +(-0.0169329 + 0.0521142i) q^{96} +(-5.32446 - 3.86844i) q^{97} +1.38595 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9 + 32 * q^10 - 56 * q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 22 * q^17 + 24 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 20 * q^30 + 2 * q^31 - 32 * q^32 + 96 * q^34 - 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 + 20 * q^39 + 18 * q^40 + 26 * q^41 + 6 * q^42 + 16 * q^43 - 144 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 - 4 * q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 128 * q^54 + 48 * q^56 + 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 + 8 * q^63 - 26 * q^64 - 96 * q^65 + 24 * q^67 + 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 + 16 * q^72 + 14 * q^73 + 44 * q^74 + 20 * q^75 + 120 * q^76 + 128 * q^78 - 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 + 22 * q^83 - 14 * q^84 - 24 * q^85 + 30 * q^86 - 88 * q^87 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 - 38 * q^94 - 24 * q^95 - 62 * q^96 + 4 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.12126	−	0.814642i	−0.792850	−	0.576039i	0.115958	−	0.993254i	$-0.463006\pi$
$2$	−1.12126	−	0.814642i	−0.792850	−	0.576039i	−0.908808	+	0.417215i	$0.863006\pi$
$3$	−0.0378481	+	0.116485i	−0.0218516	+	0.0672524i	−0.961388	−	0.275198i	$-0.911257\pi$
$3$	−0.0378481	+	0.116485i	−0.0218516	+	0.0672524i	0.939536	+	0.342450i	$0.111257\pi$
$4$	−0.0244542	−	0.0752624i	−0.0122271	−	0.0376312i
$5$	0.107603	−	0.0781781i	0.0481215	−	0.0349623i	−0.563465	−	0.826140i	$-0.690532\pi$
$5$	0.107603	−	0.0781781i	0.0481215	−	0.0349623i	0.611586	+	0.791178i	$0.290532\pi$
$6$	0.137331	−	0.0997767i	0.0560651	−	0.0407337i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−0.890458	+	2.74055i	−0.314825	+	0.968930i
$9$	2.41491	+	1.75454i	0.804972	+	0.584846i
$10$	−0.184338			−0.0582928
$11$		0			0
$11$		0			0
$12$	0.00969245			0.00279797
$13$	−0.518933	−	0.377027i	−0.143926	−	0.104568i	0.513492	−	0.858094i	$-0.328352\pi$
$13$	−0.518933	−	0.377027i	−0.143926	−	0.104568i	−0.657418	+	0.753526i	$0.728352\pi$
$14$	−0.428283	+	1.31812i	−0.114463	+	0.352282i
$15$	0.00503397	+	0.0154930i	0.00129977	+	0.00400027i
$16$	3.10296	−	2.25443i	0.775739	−	0.563608i
$17$	−1.15270	+	0.837488i	−0.279572	+	0.203121i	−0.718731	−	0.695289i	$-0.755277\pi$
$17$	−1.15270	+	0.837488i	−0.279572	+	0.203121i	0.439159	+	0.898409i	$0.355277\pi$
$18$	−1.27842	−	3.93458i	−0.301327	−	0.927390i
$19$	−2.21966	+	6.83141i	−0.509225	+	1.56723i	0.284325	+	0.958728i	$0.408231\pi$
$19$	−2.21966	+	6.83141i	−0.509225	+	1.56723i	−0.793550	+	0.608505i	$0.791769\pi$
$20$	−0.00851521	−	0.00618666i	−0.00190406	−	0.00138338i
$21$	0.122479			0.0267271
$22$		0			0
$23$	1.66655			0.347500			0.173750	−	0.984790i	$-0.444412\pi$
$23$	1.66655			0.347500			0.173750	+	0.984790i	$0.444412\pi$
$24$	−0.285529	−	0.207449i	−0.0582834	−	0.0423454i
$25$	−1.53962	+	4.73846i	−0.307924	+	0.947692i
$26$	0.274716	+	0.845489i	0.0538763	+	0.165814i
$27$	−0.593040	+	0.430869i	−0.114131	+	0.0829207i
$28$	−0.0640220	+	0.0465147i	−0.0120990	+	0.00879045i
$29$	−1.38334	−	4.25747i	−0.256879	−	0.790592i	−0.993454	−	0.114236i	$-0.963558\pi$
$29$	−1.38334	−	4.25747i	−0.256879	−	0.790592i	0.736575	−	0.676356i	$-0.236442\pi$
$30$	0.00697684	−	0.0214725i	0.00127379	−	0.00392033i
$31$	5.52706	+	4.01565i	0.992690	+	0.721231i	0.960508	−	0.278251i	$-0.0897547\pi$
$31$	5.52706	+	4.01565i	0.992690	+	0.721231i	0.0321811	+	0.999482i	$0.489755\pi$
$32$	0.447392			0.0790885
$33$		0			0
$34$	1.97473			0.338664
$35$	−0.107603	−	0.0781781i	−0.0181882	−	0.0132145i
$36$	0.0729958	−	0.224658i	0.0121660	−	0.0374430i
$37$	1.16457	+	3.58419i	0.191455	+	0.589238i	1.00000		0.000802951i	$0.000255587\pi$
$37$	1.16457	+	3.58419i	0.191455	+	0.589238i	−0.808545	+	0.588435i	$0.799744\pi$
$38$	8.05397	−	5.85155i	1.30653	−	0.949247i
$39$	0.0635584	−	0.0461779i	0.0101775	−	0.00739438i
$40$	0.118435	+	0.364505i	0.0187262	+	0.0576333i
$41$	−1.90752	+	5.87074i	−0.297904	+	0.916855i	0.684326	+	0.729176i	$0.260096\pi$
$41$	−1.90752	+	5.87074i	−0.297904	+	0.916855i	−0.982230	+	0.187679i	$0.939904\pi$
$42$	−0.137331	−	0.0997767i	−0.0211906	−	0.0153959i
$43$	1.03970			0.158553			0.0792764	−	0.996853i	$-0.474739\pi$
$43$	1.03970			0.158553			0.0792764	+	0.996853i	$0.474739\pi$
$44$		0			0
$45$	0.397018			0.0591840
$46$	−1.86863	−	1.35764i	−0.275515	−	0.200173i
$47$	2.93238	−	9.02493i	0.427731	−	1.31642i	−0.472623	−	0.881265i	$-0.656693\pi$
$47$	2.93238	−	9.02493i	0.427731	−	1.31642i	0.900355	−	0.435157i	$-0.143307\pi$
$48$	0.145165	+	0.446773i	0.0209528	+	0.0644861i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	5.58646	−	4.05880i	0.790045	−	0.574001i
$51$	−0.0539268	−	0.165970i	−0.00755126	−	0.0232404i
$52$	−0.0156858	+	0.0482760i	−0.00217523	+	0.00669468i
$53$	0.539250	+	0.391788i	0.0740716	+	0.0538162i	0.624205	−	0.781261i	$-0.285423\pi$
$53$	0.539250	+	0.391788i	0.0740716	+	0.0538162i	−0.550133	+	0.835077i	$0.685423\pi$
$54$	1.01595			0.138254
$55$		0			0
$56$	2.88158			0.385068
$57$	−0.711744	−	0.517112i	−0.0942728	−	0.0684932i
$58$	−1.91724	+	5.90065i	−0.251746	+	0.774793i
$59$	2.52991	+	7.78625i	0.329366	+	1.01368i	0.969431	+	0.245363i	$0.0789072\pi$
$59$	2.52991	+	7.78625i	0.329366	+	1.01368i	−0.640065	+	0.768320i	$0.721093\pi$
$60$	0.00104294		0.000757737i	0.000134642		9.78234e-5i
$61$	7.68410	−	5.58282i	0.983848	−	0.714807i	0.0252825	−	0.999680i	$-0.491951\pi$
$61$	7.68410	−	5.58282i	0.983848	−	0.714807i	0.958565	+	0.284873i	$0.0919515\pi$
$62$	−2.92595	−	9.00516i	−0.371596	−	1.14366i
$63$	0.922415	−	2.83890i	0.116213	−	0.357668i
$64$	−6.70756	−	4.87333i	−0.838445	−	0.609166i
$65$	−0.0853139			−0.0105819
$66$		0			0
$67$	12.0398			1.47089			0.735446	−	0.677583i	$-0.236973\pi$
$67$	12.0398			1.47089			0.735446	+	0.677583i	$0.236973\pi$
$68$	0.0912198	+	0.0662751i	0.0110620	+	0.00803704i
$69$	−0.0630758	+	0.194127i	−0.00759343	+	0.0233702i
$70$	0.0569635	+	0.175316i	0.00680845	+	0.0209542i
$71$	−3.91093	+	2.84146i	−0.464142	+	0.337219i	−0.795154	−	0.606408i	$-0.792610\pi$
$71$	−3.91093	+	2.84146i	−0.464142	+	0.337219i	0.331012	+	0.943627i	$0.392610\pi$
$72$	−6.95878	+	5.05585i	−0.820100	+	0.595837i
$73$	2.73711	+	8.42396i	0.320355	+	0.985950i	0.973494	+	0.228712i	$0.0734515\pi$
$73$	2.73711	+	8.42396i	0.320355	+	0.985950i	−0.653139	+	0.757238i	$0.726548\pi$
$74$	1.61405	−	4.96752i	0.187629	−	0.577463i
$75$	−0.493685	−	0.358684i	−0.0570059	−	0.0414172i
$76$	0.568428			0.0652032
$77$		0			0
$78$	−0.108884			−0.0123287
$79$	9.29614	+	6.75404i	1.04590	+	0.759889i	0.971428	−	0.237334i	$-0.0762736\pi$
$79$	9.29614	+	6.75404i	1.04590	+	0.759889i	0.0744696	+	0.997223i	$0.476274\pi$
$80$	0.157640	−	0.485166i	0.0176247	−	0.0542433i
$81$	2.73950	+	8.43132i	0.304389	+	0.936813i
$82$	6.92137	−	5.02867i	0.764338	−	0.555324i
$83$	7.75037	−	5.63097i	0.850714	−	0.618080i	−0.0746292	−	0.997211i	$-0.523777\pi$
$83$	7.75037	−	5.63097i	0.850714	−	0.618080i	0.925343	+	0.379132i	$0.123777\pi$
$84$	−0.00299513	−	0.00921807i	−0.000326796	−	0.00100577i
$85$	−0.0585610	+	0.180232i	−0.00635184	+	0.0195489i
$86$	−1.16577	−	0.846984i	−0.125709	−	0.0913327i
$87$	0.548286			0.0587824
$88$		0			0
$89$	−17.7001			−1.87621			−0.938104	−	0.346353i	$-0.887420\pi$
$89$	−17.7001			−1.87621			−0.938104	+	0.346353i	$0.887420\pi$
$90$	−0.445160	−	0.323428i	−0.0469240	−	0.0340923i
$91$	−0.198215	+	0.610042i	−0.0207785	+	0.0639498i
$92$	−0.0407542	−	0.125428i	−0.00424892	−	0.0130768i
$93$	−0.676950	+	0.491833i	−0.0701964	+	0.0510007i
$94$	−10.6400	+	7.73045i	−1.09744	+	0.797335i
$95$	0.295225	+	0.908608i	0.0302894	+	0.0932212i
$96$	−0.0169329	+	0.0521142i	−0.00172821	+	0.00531889i
$97$	−5.32446	−	3.86844i	−0.540617	−	0.392781i	0.283697	−	0.958914i	$-0.408439\pi$
$97$	−5.32446	−	3.86844i	−0.540617	−	0.392781i	−0.824314	+	0.566133i	$0.808439\pi$
$98$	1.38595			0.140002
$99$		0			0
$100$	0.394278			0.0394278
$101$	15.0642	+	10.9448i	1.49895	+	1.08905i	0.970799	+	0.239896i	$0.0771133\pi$
$101$	15.0642	+	10.9448i	1.49895	+	1.08905i	0.528148	+	0.849152i	$0.322887\pi$
$102$	−0.0747400	+	0.230026i	−0.00740036	+	0.0227760i
$103$	−2.13950	−	6.58470i	−0.210811	−	0.648809i	−0.999425	−	0.0339203i	$-0.989201\pi$
$103$	−2.13950	−	6.58470i	−0.210811	−	0.648809i	0.788614	−	0.614889i	$-0.210799\pi$
$104$	1.49535	−	1.08643i	0.146631	−	0.106534i
$105$	0.0131791	−	0.00957518i	0.00128615	−	0.000934442i
$106$	−0.285472	−	0.878591i	−0.0277275	−	0.0853363i
$107$	1.68243	−	5.17799i	0.162647	−	0.500575i	−0.836209	−	0.548412i	$-0.815233\pi$
$107$	1.68243	−	5.17799i	0.162647	−	0.500575i	0.998855	+	0.0478368i	$0.0152327\pi$
$108$	0.0469305	+	0.0340970i	0.00451589	+	0.00328099i
$109$	9.22316			0.883419			0.441709	−	0.897158i	$-0.354372\pi$
$109$	9.22316			0.883419			0.441709	+	0.897158i	$0.354372\pi$
$110$		0			0
$111$	−0.461580			−0.0438112
$112$	−3.10296	−	2.25443i	−0.293202	−	0.213024i
$113$	2.89927	−	8.92303i	0.272740	−	0.839408i	−0.717068	−	0.697003i	$-0.754516\pi$
$113$	2.89927	−	8.92303i	0.272740	−	0.839408i	0.989808	−	0.142405i	$-0.0454836\pi$
$114$	0.376788	+	1.15963i	0.0352894	+	0.108610i
$115$	0.179326	−	0.130288i	0.0167222	−	0.0121494i
$116$	−0.286599	+	0.208226i	−0.0266100	+	0.0193333i
$117$	−0.591671	−	1.82097i	−0.0547000	−	0.168349i
$118$	3.50633	−	10.7914i	0.322784	−	0.993427i
$119$	1.15270	+	0.837488i	0.105668	+	0.0767724i
$120$	−0.0469418			−0.00428518
$121$		0			0
$122$	−13.1639			−1.19180
$123$	−0.611654	−	0.444393i	−0.0551510	−	0.0400695i
$124$	0.167067	−	0.514179i	0.0150031	−	0.0461747i
$125$	0.410279	+	1.26271i	0.0366965	+	0.112940i
$126$	−3.34696	+	2.43171i	−0.298171	+	0.216634i
$127$	12.5042	−	9.08480i	1.10956	−	0.806146i	0.126970	−	0.991907i	$-0.459475\pi$
$127$	12.5042	−	9.08480i	1.10956	−	0.806146i	0.982595	+	0.185761i	$0.0594749\pi$
$128$	3.27439	+	10.0775i	0.289418	+	0.890736i
$129$	−0.0393507	+	0.121109i	−0.00346464	+	0.0106631i
$130$	0.0956590	+	0.0695003i	0.00838985	+	0.00609558i
$131$	−17.6675			−1.54362			−0.771810	−	0.635854i	$-0.780648\pi$
$131$	−17.6675			−1.54362			−0.771810	+	0.635854i	$0.780648\pi$
$132$		0			0
$133$	7.18297			0.622843
$134$	−13.4997	−	9.80811i	−1.16620	−	0.847292i
$135$	−0.0301283	+	0.0927254i	−0.00259303	+	0.00798053i
$136$	−1.26874	−	3.90479i	−0.108794	−	0.334833i
$137$	−15.3975	+	11.1869i	−1.31550	+	0.955763i	−0.315519	+	0.948919i	$0.602178\pi$
$137$	−15.3975	+	11.1869i	−1.31550	+	0.955763i	−0.999977	+	0.00684375i	$0.997822\pi$
$138$	0.228869	−	0.166283i	0.0194826	−	0.0141549i
$139$	4.34679	+	13.3780i	0.368690	+	1.13471i	0.947638	+	0.319346i	$0.103463\pi$
$139$	4.34679	+	13.3780i	0.368690	+	1.13471i	−0.578949	+	0.815364i	$0.696537\pi$
$140$	−0.00325252	+	0.0100102i	−0.000274888	+	0.000846019i
$141$	0.940280	+	0.683153i	0.0791859	+	0.0575319i
$142$	6.69994			0.562247
$143$		0			0
$144$	11.4489			0.954072
$145$	−0.481692	−	0.349969i	−0.0400023	−	0.0290634i
$146$	3.79351	−	11.6752i	0.313953	−	0.966247i
$147$	−0.0378481	−	0.116485i	−0.00312166	−	0.00960748i
$148$	0.241276	−	0.175297i	0.0198328	−	0.0144094i
$149$	−8.92886	+	6.48719i	−0.731480	+	0.531452i	−0.890031	−	0.455899i	$-0.849318\pi$
$149$	−8.92886	+	6.48719i	−0.731480	+	0.531452i	0.158551	+	0.987351i	$0.449318\pi$
$150$	0.261351	+	0.804354i	0.0213392	+	0.0656753i
$151$	4.98599	−	15.3453i	0.405754	−	1.24878i	−0.514511	−	0.857484i	$-0.672026\pi$
$151$	4.98599	−	15.3453i	0.405754	−	1.24878i	0.920264	−	0.391298i	$-0.127974\pi$
$152$	−16.7453	−	12.1662i	−1.35822	−	0.986807i
$153$	−4.25309			−0.343842
$154$		0			0
$155$	0.908663			0.0729856
$156$	−0.00502973	−	0.00365431i	−0.000402701	−	0.000292579i
$157$	−4.59504	+	14.1421i	−0.366724	+	1.12866i	0.582170	+	0.813067i	$0.302204\pi$
$157$	−4.59504	+	14.1421i	−0.366724	+	1.12866i	−0.948894	+	0.315594i	$0.897796\pi$
$158$	−4.92125	−	15.1461i	−0.391514	−	1.20496i
$159$	−0.0660468	+	0.0479858i	−0.00523785	+	0.00380552i
$160$	0.0481407	−	0.0349762i	0.00380585	−	0.00276511i
$161$	−0.514992	−	1.58498i	−0.0405871	−	0.124914i
$162$	3.79682	−	11.6854i	0.298306	−	0.918093i
$163$	13.3115	+	9.67137i	1.04264	+	0.757520i	0.970799	−	0.239896i	$-0.0771134\pi$
$163$	13.3115	+	9.67137i	1.04264	+	0.757520i	0.0718385	+	0.997416i	$0.477113\pi$
$164$	0.488493			0.0381449
$165$		0			0
$166$	−13.2774			−1.03053
$167$	−15.4942	−	11.2572i	−1.19898	−	0.871107i	−0.204792	−	0.978806i	$-0.565652\pi$
$167$	−15.4942	−	11.2572i	−1.19898	−	0.871107i	−0.994184	+	0.107699i	$0.965652\pi$
$168$	−0.109063	+	0.335660i	−0.00841436	+	0.0258967i
$169$	−3.89008	−	11.9724i	−0.299237	−	0.920956i
$170$	0.212487	−	0.154381i	0.0162970	−	0.0118405i
$171$	−17.3463	+	12.6028i	−1.32650	+	0.963760i
$172$	−0.0254251	−	0.0782503i	−0.00193864	−	0.00596653i
$173$	−4.70466	+	14.4794i	−0.357688	+	1.10085i	0.596746	+	0.802430i	$0.296460\pi$
$173$	−4.70466	+	14.4794i	−0.357688	+	1.10085i	−0.954434	+	0.298421i	$0.903540\pi$
$174$	−0.614771	−	0.446657i	−0.0466056	−	0.0338610i
$175$	4.98231			0.376627
$176$		0			0
$177$	−1.00273			−0.0753698
$178$	19.8464	+	14.4193i	1.48755	+	1.08077i
$179$	0.348764	−	1.07339i	0.0260679	−	0.0802286i	−0.937176	−	0.348856i	$-0.886570\pi$
$179$	0.348764	−	1.07339i	0.0260679	−	0.0802286i	0.963244	+	0.268628i	$0.0865701\pi$
$180$	−0.00970877	−	0.0298805i	−0.000723649	−	0.00222716i
$181$	−14.9486	+	10.8608i	−1.11112	+	0.807277i	−0.982840	−	0.184461i	$-0.940946\pi$
$181$	−14.9486	+	10.8608i	−1.11112	+	0.807277i	−0.128281	+	0.991738i	$0.540946\pi$
$182$	0.719216	−	0.522541i	0.0533118	−	0.0387333i
$183$	0.359484	+	1.10638i	0.0265738	+	0.0817858i
$184$	−1.48399	+	4.56726i	−0.109401	+	0.336703i
$185$	0.405517	+	0.294625i	0.0298142	+	0.0216613i
$186$	1.15970			0.0850336
$187$		0			0
$188$	−0.750947			−0.0547684
$189$	0.593040	+	0.430869i	0.0431373	+	0.0313411i
$190$	0.409167	−	1.25929i	0.0296841	−	0.0913584i
$191$	−0.750854	−	2.31089i	−0.0543299	−	0.167210i	0.920210	−	0.391426i	$-0.128018\pi$
$191$	−0.750854	−	2.31089i	−0.0543299	−	0.167210i	−0.974540	+	0.224216i	$0.928018\pi$
$192$	0.821536	−	0.596881i	0.0592892	−	0.0430761i
$193$	−0.213034	+	0.154778i	−0.0153345	+	0.0111412i	−0.595426	−	0.803410i	$-0.703017\pi$
$193$	−0.213034	+	0.154778i	−0.0153345	+	0.0111412i	0.580092	+	0.814551i	$0.303017\pi$
$194$	2.81870	+	8.67506i	0.202371	+	0.622833i
$195$	0.00322897	−	0.00993775i	0.000231231	−	0.000711657i
$196$	0.0640220	+	0.0465147i	0.00457300	+	0.00332248i
$197$	−17.4681			−1.24455			−0.622276	−	0.782798i	$-0.713792\pi$
$197$	−17.4681			−1.24455			−0.622276	+	0.782798i	$0.713792\pi$
$198$		0			0
$199$	−20.1415			−1.42780			−0.713898	−	0.700250i	$-0.753072\pi$
$199$	−20.1415			−1.42780			−0.713898	+	0.700250i	$0.753072\pi$
$200$	−11.6150	−	8.43880i	−0.821305	−	0.596713i
$201$	−0.455683	+	1.40245i	−0.0321414	+	0.0989210i
$202$	−7.97480	−	24.5439i	−0.561105	−	1.72690i
$203$	−3.62162	+	2.63126i	−0.254188	+	0.184678i
$204$	−0.0111725	+	0.00811731i	−0.000782233	+	0.000568326i
$205$	0.253708	+	0.780834i	0.0177198	+	0.0545358i
$206$	−2.96524	+	9.12608i	−0.206598	+	0.635844i
$207$	4.02457	+	2.92402i	0.279727	+	0.203234i
$208$	−2.46021			−0.170585
$209$		0			0
$210$	−0.0225775			−0.00155800
$211$	−11.3911	−	8.27613i	−0.784197	−	0.569752i	0.122039	−	0.992525i	$-0.461057\pi$
$211$	−11.3911	−	8.27613i	−0.784197	−	0.569752i	−0.906236	+	0.422773i	$0.861057\pi$
$212$	0.0162999	−	0.0501661i	0.00111948	−	0.00344542i
$213$	−0.182965	−	0.563107i	−0.0125365	−	0.0385835i
$214$	−6.10465	+	4.43529i	−0.417305	+	0.303190i
$215$	0.111875	−	0.0812818i	0.00762980	−	0.00554337i
$216$	−0.652739	−	2.00892i	−0.0444133	−	0.136690i
$217$	2.11115	−	6.49745i	0.143314	−	0.441076i
$218$	−10.3416	−	7.51358i	−0.700418	−	0.508884i
$219$	−1.08486			−0.0733078
$220$		0			0
$221$	0.913931			0.0614777
$222$	0.517551	+	0.376023i	0.0347357	+	0.0252370i
$223$	−2.97696	+	9.16213i	−0.199352	+	0.613542i	0.800546	+	0.599271i	$0.204543\pi$
$223$	−2.97696	+	9.16213i	−0.199352	+	0.613542i	−0.999898	+	0.0142710i	$0.995457\pi$
$224$	−0.138252	−	0.425495i	−0.00923733	−	0.0284296i
$225$	−12.0319	+	8.74165i	−0.802124	+	0.582777i
$226$	−10.5199	+	7.64316i	−0.699774	+	0.508416i
$227$	3.21661	+	9.89970i	0.213494	+	0.657066i	0.999257	+	0.0385390i	$0.0122704\pi$
$227$	3.21661	+	9.89970i	0.213494	+	0.657066i	−0.785763	+	0.618527i	$0.787730\pi$
$228$	−0.0215139	+	0.0662131i	−0.00142480	+	0.00438507i
$229$	7.54431	+	5.48127i	0.498542	+	0.362212i	0.808460	−	0.588551i	$-0.200301\pi$
$229$	7.54431	+	5.48127i	0.498542	+	0.362212i	−0.309918	+	0.950763i	$0.600301\pi$
$230$	−0.307208			−0.0202567
$231$		0			0
$232$	12.8996			0.846900
$233$	13.7177	+	9.96649i	0.898676	+	0.652926i	0.938126	−	0.346295i	$-0.112560\pi$
$233$	13.7177	+	9.96649i	0.898676	+	0.652926i	−0.0394495	+	0.999222i	$0.512560\pi$
$234$	−0.820027	+	2.52378i	−0.0536069	+	0.164985i
$235$	−0.390019	−	1.20036i	−0.0254421	−	0.0783026i
$236$	0.524145	−	0.380814i	0.0341189	−	0.0247888i
$237$	−1.13858	+	0.827229i	−0.0739589	+	0.0537343i
$238$	−0.610226	−	1.87808i	−0.0395551	−	0.121738i
$239$	−2.55855	+	7.87440i	−0.165499	+	0.509353i	−0.999073	−	0.0430552i	$-0.986291\pi$
$239$	−2.55855	+	7.87440i	−0.165499	+	0.509353i	0.833574	+	0.552408i	$0.186291\pi$
$240$	0.0505480	+	0.0367253i	0.00326286	+	0.00237061i
$241$	−9.31212			−0.599846			−0.299923	−	0.953963i	$-0.596961\pi$
$241$	−9.31212			−0.599846			−0.299923	+	0.953963i	$0.596961\pi$
$242$		0			0
$243$	−3.28492			−0.210727
$244$	−0.608085	−	0.441800i	−0.0389287	−	0.0282833i
$245$	−0.0411006	+	0.126495i	−0.00262582	+	0.00808146i
$246$	0.323802	+	0.996559i	0.0206448	+	0.0635383i
$247$	3.72748	−	2.70817i	0.237174	−	0.172317i
$248$	−15.9267	+	11.5714i	−1.01135	+	0.734786i
$249$	0.362584	+	1.11592i	0.0229779	+	0.0707186i
$250$	0.568628	−	1.75006i	0.0359632	−	0.110683i
$251$	3.99276	+	2.90091i	0.252021	+	0.183104i	0.706622	−	0.707591i	$-0.250218\pi$
$251$	3.99276	+	2.90091i	0.252021	+	0.183104i	−0.454601	+	0.890695i	$0.650218\pi$
$252$	−0.236220			−0.0148804
$253$		0			0
$254$	−21.4213			−1.34409
$255$	−0.0187779	−	0.0136429i	−0.00117592	−	0.000854352i
$256$	−0.585970	+	1.80343i	−0.0366232	+	0.112714i
$257$	−5.19641	−	15.9929i	−0.324143	−	0.997609i	−0.971826	−	0.235699i	$-0.924262\pi$
$257$	−5.19641	−	15.9929i	−0.324143	−	0.997609i	0.647683	−	0.761910i	$-0.275738\pi$
$258$	0.142783	−	0.103738i	0.00888928	−	0.00645844i
$259$	3.04890	−	2.21515i	0.189449	−	0.137643i
$260$	0.00208629	+	0.00642093i	0.000129386	+	0.000398209i
$261$	4.12925	−	12.7085i	0.255594	−	0.786639i
$262$	19.8099	+	14.3927i	1.22386	+	0.889185i
$263$	−4.11162			−0.253533			−0.126767	−	0.991933i	$-0.540460\pi$
$263$	−4.11162			−0.253533			−0.126767	+	0.991933i	$0.540460\pi$
$264$		0			0
$265$	0.0886540			0.00544597
$266$	−8.05397	−	5.85155i	−0.493821	−	0.358782i
$267$	0.669916	−	2.06179i	0.0409982	−	0.126179i
$268$	−0.294423	−	0.906142i	−0.0179848	−	0.0553514i
$269$	19.3908	−	14.0883i	1.18228	−	0.858977i	0.189854	−	0.981812i	$-0.439199\pi$
$269$	19.3908	−	14.0883i	1.18228	−	0.858977i	0.992427	+	0.122835i	$0.0391987\pi$
$270$	0.109320	−	0.0794254i	0.00665298	−	0.00483368i
$271$	1.85654	+	5.71386i	0.112777	+	0.347092i	0.991477	−	0.130283i	$-0.0415884\pi$
$271$	1.85654	+	5.71386i	0.112777	+	0.347092i	−0.878700	+	0.477375i	$0.841588\pi$
$272$	−1.68873	+	5.19738i	−0.102394	+	0.315138i
$273$	−0.0635584	−	0.0461779i	−0.00384673	−	0.00279481i
$274$	26.3779			1.59355
$275$		0			0
$276$	0.0161529			0.000972293
$277$	−7.41226	−	5.38532i	−0.445360	−	0.323573i	0.342401	−	0.939554i	$-0.388760\pi$
$277$	−7.41226	−	5.38532i	−0.445360	−	0.323573i	−0.787761	+	0.615981i	$0.788760\pi$
$278$	6.02444	−	18.5413i	0.361322	−	1.11203i
$279$	6.30178	+	19.3949i	0.377278	+	1.16114i
$280$	0.310067	−	0.225277i	0.0185300	−	0.0134629i
$281$	10.4832	−	7.61649i	0.625375	−	0.454362i	−0.229420	−	0.973328i	$-0.573683\pi$
$281$	10.4832	−	7.61649i	0.625375	−	0.454362i	0.854795	+	0.518966i	$0.173683\pi$
$282$	−0.497772	−	1.53198i	−0.0296419	−	0.0912283i
$283$	1.17050	−	3.60242i	0.0695789	−	0.214142i	−0.910221	−	0.414123i	$-0.864088\pi$
$283$	1.17050	−	3.60242i	0.0695789	−	0.214142i	0.979800	+	0.199982i	$0.0640882\pi$
$284$	0.309494	+	0.224860i	0.0183651	+	0.0133430i
$285$	−0.117013			−0.00693122
$286$		0			0
$287$	6.17286			0.364372
$288$	1.08041	+	0.784966i	0.0636640	+	0.0462546i
$289$	−4.62595	+	14.2372i	−0.272115	+	0.837483i
$290$	0.255001	+	0.784813i	0.0149742	+	0.0460858i
$291$	0.652135	−	0.473803i	0.0382288	−	0.0277749i
$292$	0.567073	−	0.412003i	0.0331855	−	0.0241106i
$293$	−6.60338	−	20.3231i	−0.385773	−	1.18729i	−0.935918	−	0.352219i	$-0.885427\pi$
$293$	−6.60338	−	20.3231i	−0.385773	−	1.18729i	0.550144	−	0.835070i	$-0.314573\pi$
$294$	−0.0524557	+	0.161442i	−0.00305928	+	0.00941549i
$295$	0.880939	+	0.640040i	0.0512903	+	0.0372646i
$296$	−10.8597			−0.631205
$297$		0			0
$298$	15.2963			0.886091
$299$	−0.864827	−	0.628334i	−0.0500142	−	0.0363375i
$300$	−0.0149227	+	0.0459273i	−0.000861561	+	0.00265161i
$301$	−0.321285	−	0.988814i	−0.0185186	−	0.0569943i
$302$	−18.0915	+	13.1442i	−1.04105	+	0.756366i
$303$	−1.84505	+	1.34051i	−0.105996	+	0.0770102i
$304$	8.51343	+	26.2016i	0.488279	+	1.50277i
$305$	0.390377	−	1.20146i	0.0223529	−	0.0687952i
$306$	4.76881	+	3.46475i	0.272615	+	0.198066i
$307$	8.44677			0.482082			0.241041	−	0.970515i	$-0.422511\pi$
$307$	8.44677			0.482082			0.241041	+	0.970515i	$0.422511\pi$
$308$		0			0
$309$	0.847991			0.0482405
$310$	−1.01885	−	0.740236i	−0.0578666	−	0.0420426i
$311$	5.56817	−	17.1371i	0.315742	−	0.971755i	−0.659706	−	0.751524i	$-0.729319\pi$
$311$	5.56817	−	17.1371i	0.315742	−	0.971755i	0.975448	−	0.220231i	$-0.0706810\pi$
$312$	0.0699566	+	0.215304i	0.00396051	+	0.0121892i
$313$	−0.191203	+	0.138917i	−0.0108075	+	0.00785207i	−0.593176	−	0.805073i	$-0.702126\pi$
$313$	−0.191203	+	0.138917i	−0.0108075	+	0.00785207i	0.582368	+	0.812925i	$0.302126\pi$
$314$	16.6730	−	12.1136i	0.940910	−	0.683611i
$315$	−0.122685	−	0.377587i	−0.00691254	−	0.0212746i
$316$	0.280995	−	0.864815i	0.0158072	−	0.0486496i
$317$	−13.8286	−	10.0471i	−0.776692	−	0.564300i	0.127292	−	0.991865i	$-0.459371\pi$
$317$	−13.8286	−	10.0471i	−0.776692	−	0.564300i	−0.903984	+	0.427565i	$0.859371\pi$
$318$	0.113147			0.00634496
$319$		0			0
$320$	−1.10274			−0.0616450
$321$	0.539479	+	0.391954i	0.0301108	+	0.0218767i
$322$	−0.713755	+	2.19671i	−0.0397760	+	0.122418i
$323$	−3.16262	−	9.73353i	−0.175973	−	0.541588i
$324$	0.567569	−	0.412363i	0.0315316	−	0.0229090i
$325$	2.58548	−	1.87846i	0.143417	−	0.104198i
$326$	−7.04693	−	21.6882i	−0.390293	−	1.20120i
$327$	−0.349079	+	1.07436i	−0.0193041	+	0.0594120i
$328$	−14.3905	−	10.4553i	−0.794581	−	0.577297i
$329$	−9.48937			−0.523166
$330$		0			0
$331$	4.41186			0.242498			0.121249	−	0.992622i	$-0.461310\pi$
$331$	4.41186			0.242498			0.121249	+	0.992622i	$0.461310\pi$
$332$	−0.613330	−	0.445610i	−0.0336608	−	0.0244560i
$333$	−3.47625	+	10.6988i	−0.190498	+	0.586291i
$334$	8.20241	+	25.2444i	0.448816	+	1.38131i
$335$	1.29551	−	0.941247i	0.0707815	−	0.0514258i
$336$	0.380047	−	0.276121i	0.0207333	−	0.0150636i
$337$	−8.58694	−	26.4279i	−0.467760	−	1.43962i	−0.855478	−	0.517840i	$-0.826736\pi$
$337$	−8.58694	−	26.4279i	−0.467760	−	1.43962i	0.387717	−	0.921778i	$-0.373264\pi$
$338$	−5.39146	+	16.5932i	−0.293257	+	0.902552i
$339$	0.929664	+	0.675440i	0.0504924	+	0.0366849i
$340$	0.0149968			0.000813315
$341$		0			0
$342$	29.7164			1.60688
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−0.925810	+	2.84935i	−0.0499163	+	0.153627i
$345$	0.00838936	+	0.0258198i	0.000451668	+	0.00139009i
$346$	17.0707	−	12.4026i	0.917727	−	0.666768i
$347$	25.2830	−	18.3692i	1.35726	−	0.986108i	0.358647	−	0.933473i	$-0.383238\pi$
$347$	25.2830	−	18.3692i	1.35726	−	0.986108i	0.998614	−	0.0526349i	$-0.0167620\pi$
$348$	−0.0134079	−	0.0412653i	−0.000718739	−	0.00221205i
$349$	0.167932	−	0.516840i	0.00898917	−	0.0276658i	−0.946461	−	0.322817i	$-0.895370\pi$
$349$	0.167932	−	0.516840i	0.00898917	−	0.0276658i	0.955450	+	0.295151i	$0.0953701\pi$
$350$	−5.58646	−	4.05880i	−0.298609	−	0.216952i
$351$	0.470197			0.0250972
$352$		0			0
$353$	−17.8517			−0.950148			−0.475074	−	0.879946i	$-0.657579\pi$
$353$	−17.8517			−0.950148			−0.475074	+	0.879946i	$0.657579\pi$
$354$	1.12432	+	0.816867i	0.0597570	+	0.0434160i
$355$	−0.198688	+	0.611498i	−0.0105453	+	0.0324550i
$356$	0.432843	+	1.33215i	0.0229406	+	0.0706039i
$357$	−0.141182	+	0.102575i	−0.00747215	+	0.00542884i
$358$	−1.26548	+	0.919426i	−0.0668827	+	0.0485932i
$359$	3.70538	+	11.4040i	0.195562	+	0.601879i	0.999970	+	0.00780097i	$0.00248315\pi$
$359$	3.70538	+	11.4040i	0.195562	+	0.601879i	−0.804407	+	0.594078i	$0.797517\pi$
$360$	−0.353528	+	1.08805i	−0.0186326	+	0.0573451i
$361$	−26.3700	−	19.1589i	−1.38789	−	1.00836i
$362$	25.6089			1.34598
$363$		0			0
$364$	0.0507604			0.00266057
$365$	0.953090	+	0.692460i	0.0498870	+	0.0362450i
$366$	0.498228	−	1.53339i	0.0260428	−	0.0801514i
$367$	9.14560	+	28.1473i	0.477397	+	1.46928i	0.842698	+	0.538386i	$0.180966\pi$
$367$	9.14560	+	28.1473i	0.477397	+	1.46928i	−0.365302	+	0.930889i	$0.619034\pi$
$368$	5.17123	−	3.75712i	0.269569	−	0.195853i
$369$	−14.9069	+	10.8305i	−0.776024	+	0.563814i
$370$	−0.214675	−	0.660703i	−0.0111604	−	0.0343483i
$371$	0.205975	−	0.633926i	0.0106937	−	0.0329118i
$372$	0.0535708	+	0.0389214i	0.00277751	+	0.00201798i
$373$	−10.5209			−0.544753			−0.272377	−	0.962191i	$-0.587810\pi$
$373$	−10.5209			−0.544753			−0.272377	+	0.962191i	$0.587810\pi$
$374$		0			0
$375$	−0.162615			−0.00839738
$376$	22.1221	+	16.0726i	1.14086	+	0.828884i
$377$	−0.887321	+	2.73089i	−0.0456994	+	0.140648i
$378$	−0.313947	−	0.966231i	−0.0161477	−	0.0496975i
$379$	6.75459	−	4.90750i	0.346960	−	0.252081i	−0.400633	−	0.916239i	$-0.631210\pi$
$379$	6.75459	−	4.90750i	0.346960	−	0.252081i	0.747593	+	0.664158i	$0.231210\pi$
$380$	0.0611645	−	0.0444386i	0.00313767	−	0.00227965i
$381$	0.584980	+	1.80038i	0.0299694	+	0.0922365i
$382$	−1.04065	+	3.20278i	−0.0532442	+	0.163869i
$383$	14.9456	+	10.8586i	0.763683	+	0.554848i	0.900038	−	0.435812i	$-0.143539\pi$
$383$	14.9456	+	10.8586i	0.763683	+	0.554848i	−0.136355	+	0.990660i	$0.543539\pi$
$384$	−1.29781			−0.0662284
$385$		0			0
$386$	0.364955			0.0185757
$387$	2.51079	+	1.82419i	0.127631	+	0.0927290i
$388$	−0.160943	+	0.495331i	−0.00817063	+	0.0251466i
$389$	7.18651	+	22.1178i	0.364370	+	1.12142i	0.950374	+	0.311108i	$0.100700\pi$
$389$	7.18651	+	22.1178i	0.364370	+	1.12142i	−0.586004	+	0.810308i	$0.699300\pi$
$390$	−0.0117162	+	0.00851234i	−0.000593274	+	0.000431039i
$391$	−1.92104	+	1.39572i	−0.0971511	+	0.0705844i
$392$	−0.890458	−	2.74055i	−0.0449749	−	0.138419i
$393$	0.668683	−	2.05799i	0.0337306	−	0.103812i
$394$	19.5863	+	14.2303i	0.986743	+	0.716911i
$395$	1.52831			0.0768976
$396$		0			0
$397$	21.6794			1.08806			0.544029	−	0.839066i	$-0.316898\pi$
$397$	21.6794			1.08806			0.544029	+	0.839066i	$0.316898\pi$
$398$	22.5839	+	16.4081i	1.13203	+	0.822466i
$399$	−0.271862	+	0.836705i	−0.0136101	+	0.0418876i
$400$	5.90515	+	18.1742i	0.295258	+	0.908710i
$401$	28.1599	−	20.4594i	1.40624	−	1.02169i	0.412382	−	0.911011i	$-0.364697\pi$
$401$	28.1599	−	20.4594i	1.40624	−	1.02169i	0.993856	−	0.110681i	$-0.0353031\pi$
$402$	1.65343	−	1.20129i	0.0824657	−	0.0599148i
$403$	−1.35417	−	4.16770i	−0.0674559	−	0.207608i
$404$	0.455348	−	1.40142i	0.0226544	−	0.0697230i
$405$	0.953923	+	0.693065i	0.0474008	+	0.0344387i
$406$	6.20431			0.307915
$407$		0			0
$408$	0.502867			0.0248956
$409$	13.1810	+	9.57659i	0.651760	+	0.473532i	0.863870	−	0.503714i	$-0.168033\pi$
$409$	13.1810	+	9.57659i	0.651760	+	0.473532i	−0.212110	+	0.977246i	$0.568033\pi$
$410$	0.351628	−	1.08220i	0.0173657	−	0.0534460i
$411$	−0.720338	−	2.21697i	−0.0355316	−	0.109355i
$412$	−0.443260	+	0.322047i	−0.0218379	+	0.0158661i
$413$	6.62338	−	4.81217i	0.325915	−	0.236791i
$414$	−2.13056	−	6.55718i	−0.104711	−	0.322268i
$415$	0.393743	−	1.21182i	0.0193281	−	0.0594858i
$416$	−0.232166	−	0.168679i	−0.0113829	−	0.00827015i
$417$	−1.72285			−0.0843684
$418$		0			0
$419$	−22.6536			−1.10670			−0.553350	−	0.832949i	$-0.686651\pi$
$419$	−22.6536			−1.10670			−0.553350	+	0.832949i	$0.686651\pi$
$420$	−0.00104294		0.000757737i	−5.08900e−5		3.69738e-5i
$421$	−4.69896	+	14.4619i	−0.229013	+	0.704830i	0.768846	+	0.639434i	$0.220831\pi$
$421$	−4.69896	+	14.4619i	−0.229013	+	0.704830i	−0.997859	+	0.0653964i	$0.979169\pi$
$422$	6.03031	+	18.5594i	0.293551	+	0.903456i
$423$	22.9160	−	16.6495i	1.11422	−	0.809525i
$424$	−1.55389	+	1.12897i	−0.0754637	+	0.0548276i
$425$	−2.19368	−	6.75145i	−0.106409	−	0.327494i
$426$	−0.253580	+	0.780440i	−0.0122860	+	0.0378124i
$427$	−7.68410	−	5.58282i	−0.371860	−	0.270172i
$428$	−0.430850			−0.0208259
$429$		0			0
$430$	−0.191656			−0.00924249
$431$	−2.59444	−	1.88497i	−0.124970	−	0.0907959i	0.523545	−	0.851998i	$-0.324609\pi$
$431$	−2.59444	−	1.88497i	−0.124970	−	0.0907959i	−0.648514	+	0.761202i	$0.724609\pi$
$432$	−0.868814	+	2.67393i	−0.0418008	+	0.128650i
$433$	1.85177	+	5.69917i	0.0889905	+	0.273884i	0.985641	−	0.168855i	$-0.0540068\pi$
$433$	1.85177	+	5.69917i	0.0889905	+	0.273884i	−0.896651	+	0.442739i	$0.854007\pi$
$434$	−7.66024	+	5.56549i	−0.367704	+	0.267152i
$435$	0.0589971	−	0.0428639i	0.00282870	−	0.00205517i
$436$	−0.225545	−	0.694157i	−0.0108017	−	0.0332441i
$437$	−3.69917	+	11.3849i	−0.176955	+	0.544613i
$438$	1.21640	+	0.883770i	0.0581221	+	0.0422281i
$439$	7.68712			0.366886			0.183443	−	0.983030i	$-0.441276\pi$
$439$	7.68712			0.366886			0.183443	+	0.983030i	$0.441276\pi$
$440$		0			0
$441$	−2.98500			−0.142143
$442$	−1.02475	−	0.744527i	−0.0487426	−	0.0354135i
$443$	11.5109	−	35.4268i	0.546897	−	1.68318i	−0.169538	−	0.985524i	$-0.554228\pi$
$443$	11.5109	−	35.4268i	0.546897	−	1.68318i	0.716436	−	0.697653i	$-0.245772\pi$
$444$	0.0112876	+	0.0347396i	0.000535685	+	0.00164867i
$445$	−1.90458	+	1.38376i	−0.0902859	+	0.0655966i
$446$	10.8018	−	7.84797i	0.511480	−	0.371612i
$447$	−0.417717	−	1.28560i	−0.0197574	−	0.0608069i
$448$	−2.56206	+	7.88521i	−0.121046	+	0.372541i
$449$	−8.95776	−	6.50819i	−0.422743	−	0.307141i	0.355998	−	0.934487i	$-0.384141\pi$
$449$	−8.95776	−	6.50819i	−0.422743	−	0.307141i	−0.778740	+	0.627346i	$0.784141\pi$
$450$	20.6121			0.971666
$451$		0			0
$452$	−0.742468			−0.0349228
$453$	1.59878	+	1.16158i	0.0751172	+	0.0545758i
$454$	4.45807	−	13.7205i	0.209227	−	0.643936i
$455$	0.0263634	+	0.0811383i	0.00123594	+	0.00380382i
$456$	2.05095	−	1.49010i	0.0960445	−	0.0697804i
$457$	22.9729	−	16.6908i	1.07463	−	0.780763i	0.0978901	−	0.995197i	$-0.468791\pi$
$457$	22.9729	−	16.6908i	1.07463	−	0.780763i	0.976739	+	0.214434i	$0.0687906\pi$
$458$	−3.99386	−	12.2918i	−0.186621	−	0.574360i
$459$	0.322752	−	0.993328i	0.0150648	−	0.0463646i
$460$	−0.0141910	−	0.0103104i	−0.000661660	−	0.000480724i
$461$	25.7420			1.19892			0.599462	−	0.800403i	$-0.295381\pi$
$461$	25.7420			1.19892			0.599462	+	0.800403i	$0.295381\pi$
$462$		0			0
$463$	37.6543			1.74995			0.874973	−	0.484172i	$-0.160879\pi$
$463$	37.6543			1.74995			0.874973	+	0.484172i	$0.160879\pi$
$464$	−13.8906	−	10.0921i	−0.644855	−	0.468514i
$465$	−0.0343912	+	0.105845i	−0.00159485	+	0.00490845i
$466$	−7.26197	−	22.3500i	−0.336404	−	1.03535i
$467$	12.4487	−	9.04452i	0.576058	−	0.418530i	−0.261243	−	0.965273i	$-0.584132\pi$
$467$	12.4487	−	9.04452i	0.576058	−	0.418530i	0.837301	+	0.546743i	$0.184132\pi$
$468$	−0.122582	+	0.0890611i	−0.00566636	+	0.00411685i
$469$	−3.72050	−	11.4505i	−0.171797	−	0.528735i
$470$	−0.540548	+	1.66364i	−0.0249336	+	0.0767378i
$471$	−1.47342	−	1.07050i	−0.0678916	−	0.0493262i
$472$	−23.5914			−1.08588
$473$		0			0
$474$	1.95054			0.0895914
$475$	−28.9529	−	21.0355i	−1.32845	−	0.965176i
$476$	0.0348429	−	0.107235i	0.00159702	−	0.00491512i
$477$	0.614835	+	1.89227i	0.0281514	+	0.0866410i
$478$	9.28362	−	6.74494i	0.424623	−	0.308506i
$479$	−0.485554	+	0.352776i	−0.0221855	+	0.0161187i	−0.598823	−	0.800882i	$-0.704365\pi$
$479$	−0.485554	+	0.352776i	−0.0221855	+	0.0161187i	0.576637	+	0.817000i	$0.304365\pi$
$480$	0.00225216	+	0.00693143i	0.000102796	+	0.000316375i
$481$	0.747000	−	2.29903i	0.0340603	−	0.104827i
$482$	10.4413	+	7.58605i	0.475588	+	0.345535i
$483$	0.204117			0.00928767
$484$		0			0
$485$	−0.875354			−0.0397478
$486$	3.68324	+	2.67603i	0.167075	+	0.121387i
$487$	3.18260	−	9.79504i	0.144217	−	0.443856i	−0.852692	−	0.522414i	$-0.825032\pi$
$487$	3.18260	−	9.79504i	0.144217	−	0.443856i	0.996910	+	0.0785581i	$0.0250316\pi$
$488$	8.45763	+	26.0299i	0.382859	+	1.17832i
$489$	−1.63038	+	1.18454i	−0.0737284	+	0.0535668i
$490$	0.149132	−	0.108351i	0.00673712	−	0.00489480i
$491$	3.11874	+	9.59850i	0.140747	+	0.433174i	0.996440	−	0.0843101i	$-0.0268686\pi$
$491$	3.11874	+	9.59850i	0.140747	+	0.433174i	−0.855693	+	0.517484i	$0.826869\pi$
$492$	−0.0184885	+	0.0569018i	−0.000833527	+	0.00256533i
$493$	5.16016	+	3.74907i	0.232402	+	0.168850i
$494$	−6.38566			−0.287304
$495$		0			0
$496$	26.2032			1.17656
$497$	3.91093	+	2.84146i	0.175429	+	0.127457i
$498$	0.502525	−	1.54661i	0.0225187	−	0.0693053i
$499$	6.11716	+	18.8267i	0.273841	+	0.842797i	0.989524	+	0.144371i	$0.0461160\pi$
$499$	6.11716	+	18.8267i	0.273841	+	0.842797i	−0.715682	+	0.698426i	$0.753884\pi$
$500$	0.0850015	−	0.0617572i	0.00380138	−	0.00276187i
$501$	1.89771	−	1.37877i	0.0847835	−	0.0615989i
$502$	−2.11371	−	6.50534i	−0.0943396	−	0.290347i
$503$	4.41999	−	13.6033i	0.197078	−	0.606543i	−0.802868	−	0.596157i	$-0.796694\pi$
$503$	4.41999	−	13.6033i	0.197078	−	0.606543i	0.999946	−	0.0103866i	$-0.00330623\pi$
$504$	6.95878	+	5.05585i	0.309969	+	0.225205i
$505$	2.47660			0.110207
$506$		0			0
$507$	1.54184			0.0684753
$508$	−0.989523	−	0.718931i	−0.0439030	−	0.0318974i
$509$	−13.0089	+	40.0371i	−0.576607	+	1.77462i	0.0540320	+	0.998539i	$0.482793\pi$
$509$	−13.0089	+	40.0371i	−0.576607	+	1.77462i	−0.630639	+	0.776076i	$0.717207\pi$
$510$	0.00994075	+	0.0305945i	0.000440184	+	0.00135475i
$511$	7.16585	−	5.20629i	0.316999	−	0.230313i
$512$	19.2711	−	14.0013i	0.851670	−	0.618775i
$513$	−1.62709	−	5.00768i	−0.0718379	−	0.221094i
$514$	−7.20197	+	22.1654i	−0.317665	+	0.977673i
$515$	−0.744995	−	0.541271i	−0.0328284	−	0.0238512i
$516$	0.0100772			0.000443626
$517$		0			0
$518$	−5.22316			−0.229492
$519$	−1.50857	−	1.09604i	−0.0662188	−	0.0481108i
$520$	0.0759684	−	0.233807i	0.00333144	−	0.0102531i
$521$	−6.62755	−	20.3975i	−0.290358	−	0.893631i	−0.984741	−	0.174025i	$-0.944323\pi$
$521$	−6.62755	−	20.3975i	−0.290358	−	0.893631i	0.694383	−	0.719606i	$-0.255677\pi$
$522$	−14.9829	+	10.8857i	−0.655783	+	0.476454i
$523$	−28.7967	+	20.9220i	−1.25919	+	0.914855i	−0.998718	−	0.0506265i	$-0.983878\pi$
$523$	−28.7967	+	20.9220i	−1.25919	+	0.914855i	−0.260472	+	0.965481i	$0.583878\pi$
$524$	0.432046	+	1.32970i	0.0188740	+	0.0580882i
$525$	−0.188571	+	0.580362i	−0.00822992	+	0.0253291i
$526$	4.61019	+	3.34950i	0.201014	+	0.146045i
$527$	−9.73412			−0.424025
$528$		0			0
$529$	−20.2226			−0.879244
$530$	−0.0994041	−	0.0722213i	−0.00431784	−	0.00313709i
$531$	−7.55177	+	23.2420i	−0.327719	+	1.00861i
$532$	−0.175654	−	0.540607i	−0.00761557	−	0.0234383i
$533$	3.20330	−	2.32733i	0.138750	−	0.100808i
$534$	−2.43077	+	1.76606i	−0.105190	+	0.0764248i
$535$	−0.223771	−	0.688695i	−0.00967445	−	0.0297749i
$536$	−10.7209	+	32.9956i	−0.463073	+	1.42519i
$537$	0.111833	+	0.0812513i	0.00482594	+	0.00350625i
$538$	−33.2191			−1.43218
$539$		0			0
$540$	0.00771550			0.000332022
$541$	13.7007	+	9.95414i	0.589039	+	0.427962i	0.841971	−	0.539522i	$-0.181395\pi$
$541$	13.7007	+	9.95414i	0.589039	+	0.427962i	−0.252933	+	0.967484i	$0.581395\pi$
$542$	2.57308	−	7.91914i	0.110523	−	0.340156i
$543$	−0.699338	−	2.15234i	−0.0300115	−	0.0923658i
$544$	−0.515710	+	0.374685i	−0.0221109	+	0.0160645i
$545$	0.992439	−	0.721049i	0.0425114	−	0.0308863i
$546$	0.0336470	+	0.103555i	0.00143996	+	0.00443173i
$547$	2.71651	−	8.36056i	0.116150	−	0.357472i	−0.876035	−	0.482247i	$-0.839821\pi$
$547$	2.71651	−	8.36056i	0.116150	−	0.357472i	0.992185	+	0.124775i	$0.0398209\pi$
$548$	1.21849	+	0.885283i	0.0520512	+	0.0378174i
$549$	28.3517			1.21002
$550$		0			0
$551$	32.1551			1.36985
$552$	−0.475849	−	0.345724i	−0.0202535	−	0.0147150i
$553$	3.55081	−	10.9283i	0.150996	−	0.464717i
$554$	3.92395	+	12.0767i	0.166713	+	0.513089i
$555$	−0.0496673	+	0.0360854i	−0.00210826	+	0.00153174i
$556$	0.900565	−	0.654299i	0.0381925	−	0.0277485i
$557$	−6.71421	−	20.6642i	−0.284490	−	0.875571i	−0.986551	−	0.163454i	$-0.947737\pi$
$557$	−6.71421	−	20.6642i	−0.284490	−	0.875571i	0.702061	−	0.712117i	$-0.252263\pi$
$558$	8.73397	−	26.8804i	0.369738	−	1.13794i
$559$	−0.539535	−	0.391995i	−0.0228199	−	0.0165796i
$560$	−0.510134			−0.0215571
$561$		0			0
$562$	−17.9591			−0.757559
$563$	−1.47350	−	1.07056i	−0.0621006	−	0.0451187i	0.556302	−	0.830980i	$-0.312220\pi$
$563$	−1.47350	−	1.07056i	−0.0621006	−	0.0451187i	−0.618402	+	0.785862i	$0.712220\pi$
$564$	0.0284219	−	0.0874737i	0.00119678	−	0.00368331i
$565$	−0.385616	−	1.18680i	−0.0162230	−	0.0499292i
$566$	−4.24712	+	3.08571i	−0.178520	+	0.129702i
$567$	7.17211	−	5.21084i	0.301200	−	0.218835i
$568$	−4.30463	−	13.2483i	−0.180618	−	0.555886i
$569$	−10.1796	+	31.3295i	−0.426750	+	1.31340i	0.474559	+	0.880224i	$0.342608\pi$
$569$	−10.1796	+	31.3295i	−0.426750	+	1.31340i	−0.901309	+	0.433177i	$0.857392\pi$
$570$	0.131201	+	0.0953234i	0.00549542	+	0.00399266i
$571$	23.4394			0.980908			0.490454	−	0.871467i	$-0.336831\pi$
$571$	23.4394			0.980908			0.490454	+	0.871467i	$0.336831\pi$
$572$		0			0
$573$	0.297601			0.0124325
$574$	−6.92137	−	5.02867i	−0.288893	−	0.209893i
$575$	−2.56585	+	7.89687i	−0.107003	+	0.329322i
$576$	−7.64774	−	23.5373i	−0.318656	−	0.980722i
$577$	−27.8738	+	20.2515i	−1.16040	+	0.843080i	−0.989828	−	0.142266i	$-0.954561\pi$
$577$	−27.8738	+	20.2515i	−1.16040	+	0.843080i	−0.170571	+	0.985345i	$0.554561\pi$
$578$	16.7851	−	12.1951i	0.698169	−	0.507250i
$579$	−0.00996633	−	0.0306732i	−0.000414187	−	0.00127474i
$580$	−0.0145601	+	0.0448115i	−0.000604577	+	0.00186070i
$581$	−7.75037	−	5.63097i	−0.321539	−	0.233612i
$582$	−1.11719			−0.0463091
$583$		0			0
$584$	−25.5236			−1.05617
$585$	−0.206026	−	0.149686i	−0.00851812	−	0.00618877i
$586$	−9.15197	+	28.1669i	−0.378064	+	1.16356i
$587$	−6.44827	−	19.8457i	−0.266148	−	0.819121i	−0.991427	−	0.130665i	$-0.958289\pi$
$587$	−6.44827	−	19.8457i	−0.266148	−	0.819121i	0.725278	−	0.688456i	$-0.241711\pi$
$588$	−0.00784136	+	0.00569708i	−0.000323372	+	0.000234944i
$589$	−39.7007	+	28.8443i	−1.63584	+	1.18851i
$590$	−0.466358	−	1.43530i	−0.0191996	−	0.0590904i
$591$	0.661136	−	2.03477i	0.0271955	−	0.0836991i
$592$	11.6939	+	8.49614i	0.480618	+	0.349189i
$593$	−26.6381			−1.09389			−0.546947	−	0.837167i	$-0.684210\pi$
$593$	−26.6381			−1.09389			−0.546947	+	0.837167i	$0.684210\pi$
$594$		0			0
$595$	0.189507			0.00776905
$596$	0.706590	+	0.513368i	0.0289431	+	0.0210284i
$597$	0.762319	−	2.34618i	0.0311997	−	0.0960227i
$598$	0.457828	+	1.40905i	0.0187220	+	0.0576203i
$599$	16.7233	−	12.1502i	0.683297	−	0.496445i	−0.191153	−	0.981560i	$-0.561223\pi$
$599$	16.7233	−	12.1502i	0.683297	−	0.496445i	0.874450	+	0.485116i	$0.161223\pi$
$600$	1.42260	−	1.03358i	0.0580772	−	0.0421956i
$601$	1.52905	+	4.70594i	0.0623714	+	0.191959i	0.977387	−	0.211460i	$-0.0678217\pi$
$601$	1.52905	+	4.70594i	0.0623714	+	0.191959i	−0.915015	+	0.403419i	$0.867822\pi$
$602$	−0.445286	+	1.37045i	−0.0181485	+	0.0558554i
$603$	29.0750	+	21.1242i	1.18403	+	0.860246i
$604$	−1.27685			−0.0519543
$605$		0			0
$606$	3.16082			0.128399
$607$	−22.3359	−	16.2280i	−0.906585	−	0.658672i	0.0335641	−	0.999437i	$-0.489314\pi$
$607$	−22.3359	−	16.2280i	−0.906585	−	0.658672i	−0.940149	+	0.340764i	$0.889314\pi$
$608$	−0.993058	+	3.05632i	−0.0402738	+	0.123950i
$609$	−0.169430	−	0.521451i	−0.00686564	−	0.0211303i
$610$	−1.41647	+	1.02913i	−0.0573512	+	0.0416681i
$611$	−4.92435	+	3.57775i	−0.199218	+	0.144740i
$612$	0.104006	+	0.320097i	0.00420419	+	0.0129392i
$613$	−2.22158	+	6.83732i	−0.0897288	+	0.276157i	−0.985844	−	0.167664i	$-0.946377\pi$
$613$	−2.22158	+	6.83732i	−0.0897288	+	0.276157i	0.896115	+	0.443821i	$0.146377\pi$
$614$	−9.47101	−	6.88109i	−0.382219	−	0.277698i
$615$	−0.100558			−0.00405487
$616$		0			0
$617$	21.1215			0.850320			0.425160	−	0.905118i	$-0.360218\pi$
$617$	21.1215			0.850320			0.425160	+	0.905118i	$0.360218\pi$
$618$	−0.950818	−	0.690810i	−0.0382475	−	0.0277884i
$619$	0.857250	−	2.63834i	0.0344558	−	0.106044i	−0.932349	−	0.361558i	$-0.882245\pi$
$619$	0.857250	−	2.63834i	0.0344558	−	0.106044i	0.966805	+	0.255514i	$0.0822448\pi$
$620$	−0.0222207	−	0.0683881i	−0.000892403	−	0.00274653i
$621$	−0.988330	+	0.718064i	−0.0396603	+	0.0288149i
$622$	−20.2040	+	14.6790i	−0.810105	+	0.588576i
$623$	5.46964	+	16.8338i	0.219136	+	0.674432i
$624$	0.0931142	−	0.286576i	0.00372755	−	0.0114722i
$625$	−20.0110	−	14.5388i	−0.800440	−	0.581554i
$626$	0.327556			0.0130918
$627$		0			0
$628$	1.17673			0.0469568
$629$	−4.34413	−	3.15619i	−0.173212	−	0.125846i
$630$	−0.170036	+	0.523317i	−0.00677440	+	0.0208495i
$631$	−7.48098	−	23.0241i	−0.297813	−	0.916574i	−0.982262	−	0.187514i	$-0.939957\pi$
$631$	−7.48098	−	23.0241i	−0.297813	−	0.916574i	0.684449	−	0.729061i	$-0.260043\pi$
$632$	−26.7876	+	19.4623i	−1.06555	+	0.774170i
$633$	1.39517	−	1.01365i	0.0554532	−	0.0402891i
$634$	7.32068	+	22.5307i	0.290741	+	0.894810i
$635$	0.635251	−	1.95510i	0.0252092	−	0.0775859i
$636$	0.00522665	+	0.00379738i	0.000207250	+	0.000150576i
$637$	0.641436			0.0254146
$638$		0			0
$639$	−14.4300			−0.570843
$640$	1.14018	+	0.828386i	0.0450694	+	0.0327448i
$641$	13.4391	−	41.3612i	0.530811	−	1.63367i	−0.221718	−	0.975111i	$-0.571166\pi$
$641$	13.4391	−	41.3612i	0.530811	−	1.63367i	0.752529	−	0.658559i	$-0.228834\pi$
$642$	−0.285593	−	0.878964i	−0.0112714	−	0.0346900i
$643$	13.8760	−	10.0815i	0.547217	−	0.397576i	−0.279541	−	0.960134i	$-0.590182\pi$
$643$	13.8760	−	10.0815i	0.547217	−	0.397576i	0.826758	+	0.562557i	$0.190182\pi$
$644$	−0.106696	+	0.0775190i	−0.00420440	+	0.00305468i
$645$	0.00523382	+	0.0161080i	0.000206082	+	0.000634254i
$646$	−4.38324	+	13.4902i	−0.172456	+	0.530765i
$647$	−11.5616	−	8.39997i	−0.454532	−	0.330237i	0.336850	−	0.941558i	$-0.390638\pi$
$647$	−11.5616	−	8.39997i	−0.454532	−	0.330237i	−0.791383	+	0.611321i	$0.790638\pi$
$648$	−25.5459			−1.00354
$649$		0			0
$650$	−4.42927			−0.173730
$651$	0.676950	+	0.491833i	0.0265317	+	0.0192764i
$652$	0.402368	−	1.23836i	0.0157579	−	0.0484980i
$653$	−11.6969	−	35.9992i	−0.457733	−	1.40876i	−0.867896	−	0.496746i	$-0.834528\pi$
$653$	−11.6969	−	35.9992i	−0.457733	−	1.40876i	0.410163	−	0.912012i	$-0.365472\pi$
$654$	1.26662	−	0.920256i	0.0495289	−	0.0359849i
$655$	−1.90108	+	1.38121i	−0.0742812	+	0.0539685i
$656$	7.31622	+	22.5170i	0.285650	+	0.879142i
$657$	−8.17027	+	25.1455i	−0.318753	+	0.981020i
$658$	10.6400	+	7.73045i	0.414792	+	0.301364i
$659$	−8.13829			−0.317023			−0.158511	−	0.987357i	$-0.550669\pi$
$659$	−8.13829			−0.317023			−0.158511	+	0.987357i	$0.550669\pi$
$660$		0			0
$661$	−5.33161			−0.207375			−0.103688	−	0.994610i	$-0.533064\pi$
$661$	−5.33161			−0.207375			−0.103688	+	0.994610i	$0.533064\pi$
$662$	−4.94684	−	3.59409i	−0.192264	−	0.139688i
$663$	−0.0345906	+	0.106459i	−0.00134339	+	0.00413452i
$664$	8.53057	+	26.2544i	0.331050	+	1.01887i
$665$	0.772908	−	0.561551i	0.0299721	−	0.0217760i
$666$	12.6135	−	9.16423i	0.488763	−	0.355107i
$667$	−2.30540	−	7.09528i	−0.0892653	−	0.274730i
$668$	−0.468344	+	1.44141i	−0.0181208	+	0.0557700i
$669$	−0.954575	−	0.693539i	−0.0369060	−	0.0268138i
$670$	−2.21939			−0.0857424
$671$		0			0
$672$	0.0547962			0.00211381
$673$	−15.7350	−	11.4321i	−0.606539	−	0.440677i	0.241655	−	0.970362i	$-0.422310\pi$
$673$	−15.7350	−	11.4321i	−0.606539	−	0.440677i	−0.848194	+	0.529686i	$0.822310\pi$
$674$	−11.9011	+	36.6278i	−0.458413	+	1.41085i
$675$	−1.12860	−	3.47347i	−0.0434397	−	0.133694i
$676$	−0.805945	+	0.585553i	−0.0309979	+	0.0225213i
$677$	−29.3707	+	21.3391i	−1.12881	+	0.820128i	−0.985521	−	0.169553i	$-0.945768\pi$
$677$	−29.3707	+	21.3391i	−1.12881	+	0.820128i	−0.143288	+	0.989681i	$0.545768\pi$
$678$	−0.492152	−	1.51469i	−0.0189010	−	0.0581712i
$679$	−2.03376	+	6.25927i	−0.0780486	+	0.240209i
$680$	−0.441789	−	0.320979i	−0.0169418	−	0.0123090i
$681$	−1.27490			−0.0488545
$682$		0			0
$683$	−20.7805			−0.795142			−0.397571	−	0.917571i	$-0.630147\pi$
$683$	−20.7805			−0.795142			−0.397571	+	0.917571i	$0.630147\pi$
$684$	1.37271	+	0.997329i	0.0524867	+	0.0381338i
$685$	−0.782241	+	2.40749i	−0.0298879	+	0.0919855i
$686$	−0.428283	−	1.31812i	−0.0163519	−	0.0503260i
$687$	−0.924021	+	0.671340i	−0.0352536	+	0.0256132i
$688$	3.22615	−	2.34393i	0.122996	−	0.0893616i
$689$	−0.132120	−	0.406623i	−0.00503336	−	0.0154911i
$690$	0.0116273	−	0.0357850i	0.000442642	−	0.00136231i
$691$	40.5358	+	29.4510i	1.54205	+	1.12037i	0.949031	+	0.315183i	$0.102066\pi$
$691$	40.5358	+	29.4510i	1.54205	+	1.12037i	0.593023	+	0.805185i	$0.297934\pi$
$692$	1.20481			0.0457998
$693$		0			0
$694$	−43.3131			−1.64414
$695$	1.51360	+	1.09969i	0.0574139	+	0.0417137i
$696$	−0.488226	+	1.50260i	−0.0185061	+	0.0569561i
$697$	−2.71787	−	8.36475i	−0.102947	−	0.316837i
$698$	−0.609335	+	0.442708i	−0.0230637	+	0.0167567i
$699$	−1.68013	+	1.22069i	−0.0635484	+	0.0461706i
$700$	−0.121839	−	0.374980i	−0.00460506	−	0.0141729i
$701$	5.04406	−	15.5240i	0.190511	−	0.586334i	−0.809488	−	0.587136i	$-0.800255\pi$
$701$	5.04406	−	15.5240i	0.190511	−	0.586334i	1.00000		0.000802204i	$0.000255349\pi$
$702$	−0.527212	−	0.383042i	−0.0198983	−	0.0144570i
$703$	−27.0701			−1.02097
$704$		0			0
$705$	0.154584			0.00582199
$706$	20.0163	+	14.5427i	0.753325	+	0.547323i
$707$	5.75402	−	17.7091i	0.216402	−	0.666018i
$708$	0.0245210	+	0.0754679i	0.000921555	+	0.00283626i
$709$	−26.8836	+	19.5321i	−1.00963	+	0.733542i	−0.964132	−	0.265423i	$-0.914489\pi$
$709$	−26.8836	+	19.5321i	−1.00963	+	0.733542i	−0.0455013	+	0.998964i	$0.514489\pi$
$710$	0.720933	−	0.523788i	0.0270561	−	0.0196574i
$711$	10.5992	+	32.6209i	0.397500	+	1.22338i
$712$	15.7612	−	48.5080i	0.590676	−	1.81791i
$713$	9.21112	+	6.69227i	0.344959	+	0.250627i
$714$	0.241864			0.00905152
$715$		0			0
$716$	−0.0893143			−0.00333783
$717$	−0.820410	−	0.596063i	−0.0306388	−	0.0222604i
$718$	5.13548	−	15.8054i	0.191654	−	0.589852i
$719$	−7.80128	−	24.0099i	−0.290939	−	0.895418i	−0.984555	−	0.175073i	$-0.943984\pi$
$719$	−7.80128	−	24.0099i	−0.290939	−	0.895418i	0.693617	−	0.720344i	$-0.256016\pi$
$720$	1.23193	−	0.895050i	0.0459113	−	0.0333565i
$721$	−5.60128	+	4.06957i	−0.208602	+	0.151559i
$722$	13.9599	+	42.9642i	0.519534	+	1.59896i
$723$	0.352446	−	1.08472i	0.0131076	−	0.0403411i
$724$	1.18297	+	0.859475i	0.0439646	+	0.0319421i
$725$	22.3036			0.828337
$726$		0			0
$727$	1.86242			0.0690733			0.0345366	−	0.999403i	$-0.489004\pi$
$727$	1.86242			0.0690733			0.0345366	+	0.999403i	$0.489004\pi$
$728$	−1.49535	−	1.08643i	−0.0554213	−	0.0402659i
$729$	−8.09418	+	24.9113i	−0.299784	+	0.922641i
$730$	−0.504553	−	1.55286i	−0.0186744	−	0.0574738i
$731$	−1.19847	+	0.870737i	−0.0443269	+	0.0322054i
$732$	0.0744777	−	0.0541112i	0.00275278	−	0.00200001i
$733$	−6.20047	−	19.0831i	−0.229019	−	0.704849i	−0.997859	−	0.0654072i	$-0.979165\pi$
$733$	−6.20047	−	19.0831i	−0.229019	−	0.704849i	0.768839	−	0.639442i	$-0.220835\pi$
$734$	12.6754	−	39.0108i	0.467856	−	1.43991i
$735$	−0.0131791	−	0.00957518i	−0.000486119	−	0.000353186i
$736$	0.745601			0.0274832
$737$		0			0
$738$	25.5375			0.940049
$739$	−18.1195	−	13.1646i	−0.666538	−	0.484268i	0.202327	−	0.979318i	$-0.435150\pi$
$739$	−18.1195	−	13.1646i	−0.666538	−	0.484268i	−0.868864	+	0.495050i	$0.835150\pi$
$740$	0.0122576	−	0.0377250i	0.000450598	−	0.00138680i
$741$	0.174382	+	0.536693i	0.00640609	+	0.0197159i
$742$	−0.747374	+	0.542999i	−0.0274370	+	0.0199341i
$743$	−29.3434	+	21.3192i	−1.07651	+	0.782127i	−0.977070	−	0.212917i	$-0.931704\pi$
$743$	−29.3434	+	21.3192i	−1.07651	+	0.782127i	−0.0994354	+	0.995044i	$0.531704\pi$
$744$	−0.745096	−	2.29317i	−0.0273165	−	0.0840717i
$745$	−0.453614	+	1.39608i	−0.0166191	+	0.0511485i
$746$	11.7967	+	8.57079i	0.431907	+	0.313799i
$747$	28.5962			1.04628
$748$		0			0
$749$	−5.44446			−0.198936
$750$	0.182333	+	0.132473i	0.00665786	+	0.00483722i
$751$	13.7895	−	42.4396i	0.503185	−	1.54864i	−0.300616	−	0.953745i	$-0.597192\pi$
$751$	13.7895	−	42.4396i	0.503185	−	1.54864i	0.803801	−	0.594899i	$-0.202808\pi$
$752$	−11.2470	−	34.6148i	−0.410137	−	1.26227i
$753$	−0.489029	+	0.355300i	−0.0178212	+	0.0129479i
$754$	3.21962	−	2.33919i	0.117252	−	0.0851883i
$755$	−0.663158	−	2.04099i	−0.0241348	−	0.0742793i
$756$	0.0179259	−	0.0551701i	0.000651957	−	0.00200652i
$757$	−7.28086	−	5.28985i	−0.264627	−	0.192263i	0.447557	−	0.894255i	$-0.352294\pi$
$757$	−7.28086	−	5.28985i	−0.264627	−	0.192263i	−0.712185	+	0.701992i	$0.752294\pi$
$758$	−11.5715			−0.420296
$759$		0			0
$760$	−2.75297			−0.0998607
$761$	4.16769	+	3.02800i	0.151079	+	0.109765i	0.660757	−	0.750600i	$-0.270235\pi$
$761$	4.16769	+	3.02800i	0.151079	+	0.109765i	−0.509678	+	0.860365i	$0.670235\pi$
$762$	0.810755	−	2.49525i	0.0293705	−	0.0903932i
$763$	−2.85011	−	8.77175i	−0.103181	−	0.317559i
$764$	−0.155562	+	0.113022i	−0.00562802	+	0.00408899i
$765$	−0.457644	+	0.332498i	−0.0165462	+	0.0120215i
$766$	−7.91199	−	24.3506i	−0.285872	−	0.879823i
$767$	1.62277	−	4.99438i	0.0585949	−	0.180337i
$768$	−0.187894	−	0.136513i	−0.00678004	−	0.00492599i
$769$	38.5242			1.38922			0.694608	−	0.719388i	$-0.255578\pi$
$769$	38.5242			1.38922			0.694608	+	0.719388i	$0.255578\pi$
$770$		0			0
$771$	2.05960			0.0741746
$772$	0.0168585	+	0.0122485i	0.000606752	+	0.000440831i
$773$	−2.16010	+	6.64811i	−0.0776934	+	0.239116i	−0.982358	−	0.187008i	$-0.940121\pi$
$773$	−2.16010	+	6.64811i	−0.0776934	+	0.239116i	0.904665	+	0.426123i	$0.140121\pi$
$774$	−1.32918	−	4.09079i	−0.0477763	−	0.147040i
$775$	−27.5375	+	20.0072i	−0.989177	+	0.718679i
$776$	15.3429	−	11.1472i	0.550777	−	0.400163i
$777$	0.142636	+	0.438989i	0.00511704	+	0.0157486i
$778$	9.96016	−	30.6542i	0.357089	−	1.09901i
$779$	−35.8714	−	26.0621i	−1.28523	−	0.933771i
$780$	−0.000826901	0		−2.96078e−5	0
$781$		0			0
$782$	3.29099			0.117686
$783$	2.65478	+	1.92881i	0.0948742	+	0.0689301i
$784$	−1.18522	+	3.64775i	−0.0423294	+	0.130277i
$785$	0.611161	+	1.88096i	0.0218133	+	0.0671344i
$786$	−2.42630	+	1.76281i	−0.0865431	+	0.0628773i
$787$	25.3917	−	18.4482i	0.905117	−	0.657606i	−0.0346585	−	0.999399i	$-0.511034\pi$
$787$	25.3917	−	18.4482i	0.905117	−	0.657606i	0.939775	+	0.341794i	$0.111034\pi$
$788$	0.427169	+	1.31469i	0.0152173	+	0.0468340i
$789$	0.155617	−	0.478940i	0.00554011	−	0.0170507i
$790$	−1.71363	−	1.24503i	−0.0609683	−	0.0442960i
$791$	−9.38223			−0.333594
$792$		0			0
$793$	−6.09240			−0.216348
$794$	−24.3082	−	17.6610i	−0.862667	−	0.626764i
$795$	−0.00335539	+	0.0103268i	−0.000119003	+	0.000366255i
$796$	0.492546	+	1.51590i	0.0174578	+	0.0537296i
$797$	−21.2749	+	15.4571i	−0.753596	+	0.547520i	−0.896939	−	0.442153i	$-0.854215\pi$
$797$	−21.2749	+	15.4571i	−0.753596	+	0.547520i	0.143343	+	0.989673i	$0.454215\pi$
$798$	0.986443	−	0.716693i	0.0349197	−	0.0253707i
$799$	4.17811	+	12.8589i	0.147811	+	0.454915i
$800$	−0.688813	+	2.11995i	−0.0243532	+	0.0749515i
$801$	−42.7443	−	31.0555i	−1.51029	−	1.09729i
$802$	−48.2416			−1.70347
$803$		0			0
$804$	0.116695			0.00411551
$805$	−0.179326	−	0.130288i	−0.00632039	−	0.00459203i
$806$	−1.87681	+	5.77623i	−0.0661079	+	0.203459i
$807$	0.907159	+	2.79195i	0.0319335	+	0.0982812i
$808$	−43.4088	+	31.5384i	−1.52712	+	1.10952i
$809$	9.51675	−	6.91433i	0.334591	−	0.243095i	−0.407785	−	0.913078i	$-0.633699\pi$
$809$	9.51675	−	6.91433i	0.334591	−	0.243095i	0.742376	+	0.669983i	$0.233699\pi$
$810$	−0.504994	−	1.55421i	−0.0177437	−	0.0546094i
$811$	2.55651	−	7.86813i	0.0897712	−	0.276287i	−0.896085	−	0.443883i	$-0.853600\pi$
$811$	2.55651	−	7.86813i	0.0897712	−	0.276287i	0.985856	+	0.167596i	$0.0536004\pi$
$812$	0.286599	+	0.208226i	0.0100576	+	0.00730731i
$813$	−0.735843			−0.0258071
$814$		0			0
$815$	2.18844			0.0766579
$816$	−0.541499	−	0.393422i	−0.0189563	−	0.0137725i
$817$	−2.30778	+	7.10262i	−0.0807391	+	0.248489i
$818$	−6.97787	−	21.4757i	−0.243975	−	0.750879i
$819$	−1.54901	+	1.12542i	−0.0541269	+	0.0393255i
$820$	0.0525632	−	0.0381894i	0.00183559	−	0.00133363i
$821$	2.28213	+	7.02368i	0.0796469	+	0.245128i	0.982949	−	0.183876i	$-0.0588645\pi$
$821$	2.28213	+	7.02368i	0.0796469	+	0.245128i	−0.903302	+	0.429004i	$0.858865\pi$
$822$	−0.998354	+	3.07262i	−0.0348216	+	0.107170i
$823$	−40.0005	−	29.0621i	−1.39433	−	1.01304i	−0.995375	−	0.0960694i	$-0.969373\pi$
$823$	−40.0005	−	29.0621i	−1.39433	−	1.01304i	−0.398955	−	0.916970i	$-0.630627\pi$
$824$	19.9508			0.695019
$825$		0			0
$826$	−11.3467			−0.394803
$827$	18.7966	+	13.6566i	0.653623	+	0.474885i	0.864503	−	0.502627i	$-0.167633\pi$
$827$	18.7966	+	13.6566i	0.653623	+	0.474885i	−0.210880	+	0.977512i	$0.567633\pi$
$828$	0.121651	−	0.374404i	0.00422767	−	0.0130114i
$829$	9.33038	+	28.7160i	0.324058	+	0.997347i	0.971864	+	0.235542i	$0.0756865\pi$
$829$	9.33038	+	28.7160i	0.324058	+	0.997347i	−0.647807	+	0.761805i	$0.724314\pi$
$830$	−1.42869	+	1.03800i	−0.0495904	+	0.0360296i
$831$	0.907847	−	0.659589i	0.0314929	−	0.0228809i
$832$	1.64340	+	5.05786i	0.0569745	+	0.175350i
$833$	0.440294	−	1.35508i	0.0152553	−	0.0469509i
$834$	1.93176	+	1.40351i	0.0668915	+	0.0485995i
$835$	−2.54728			−0.0881523
$836$		0			0
$837$	−5.00798			−0.173101
$838$	25.4005	+	18.4546i	0.877447	+	0.637502i
$839$	5.13356	−	15.7995i	0.177230	−	0.545458i	−0.822498	−	0.568768i	$-0.807420\pi$
$839$	5.13356	−	15.7995i	0.177230	−	0.545458i	0.999728	+	0.0233095i	$0.00742032\pi$
$840$	0.0145058	+	0.0446443i	0.000500498	+	0.00154037i
$841$	7.24907	−	5.26676i	0.249968	−	0.181612i
$842$	17.0500	−	12.3876i	0.587583	−	0.426904i
$843$	0.490434	+	1.50940i	0.0168914	+	0.0519865i
$844$	−0.344320	+	1.05971i	−0.0118520	+	0.0364767i
$845$	−1.35457	−	0.984149i	−0.0465985	−	0.0338558i
$846$	−39.2582			−1.34972
$847$		0			0
$848$	2.55653			0.0877915
$849$	0.375325	+	0.272690i	0.0128811	+	0.00935869i
$850$	−3.04034	+	9.35719i	−0.104283	+	0.320949i
$851$	1.94082	+	5.97323i	0.0665305	+	0.204760i
$852$	−0.0379065	+	0.0275407i	−0.00129866	+	0.000943529i
$853$	−32.4017	+	23.5412i	−1.10941	+	0.806035i	−0.982571	−	0.185888i	$-0.940484\pi$
$853$	−32.4017	+	23.5412i	−1.10941	+	0.806035i	−0.126841	+	0.991923i	$0.540484\pi$
$854$	4.06786	+	12.5196i	0.139199	+	0.428411i
$855$	−0.881245	+	2.71219i	−0.0301380	+	0.0927551i
$856$	12.6924	+	9.22156i	0.433817	+	0.315186i
$857$	31.7070			1.08309			0.541546	−	0.840671i	$-0.317839\pi$
$857$	31.7070			1.08309			0.541546	+	0.840671i	$0.317839\pi$
$858$		0			0
$859$	1.63654			0.0558381			0.0279190	−	0.999610i	$-0.491112\pi$
$859$	1.63654			0.0558381			0.0279190	+	0.999610i	$0.491112\pi$
$860$	−0.00885327	−	0.00643228i	−0.000301894	−	0.000219339i
$861$	−0.233631	+	0.719043i	−0.00796213	+	0.0245049i
$862$	1.37346	+	4.22708i	0.0467803	+	0.143975i
$863$	14.0813	−	10.2307i	0.479334	−	0.348256i	−0.321734	−	0.946830i	$-0.604266\pi$
$863$	14.0813	−	10.2307i	0.479334	−	0.348256i	0.801068	+	0.598574i	$0.204266\pi$
$864$	−0.265321	+	0.192767i	−0.00902641	+	0.00655807i
$865$	0.625740	+	1.92583i	0.0212758	+	0.0654802i
$866$	2.56647	−	7.89877i	0.0872121	−	0.268411i
$867$	−1.48333	−	1.07770i	−0.0503766	−	0.0366007i
$868$	−0.540640			−0.0183505
$869$		0			0
$870$	−0.101070			−0.00342659
$871$	−6.24783	−	4.53932i	−0.211700	−	0.153809i
$872$	−8.21284	+	25.2765i	−0.278122	+	0.855971i
$873$	−6.07077	−	18.6839i	−0.205465	−	0.632355i
$874$	13.4223	−	9.75190i	0.454017	−	0.329863i
$875$	1.07413	−	0.780398i	0.0363121	−	0.0263823i
$876$	0.0265293	+	0.0816488i	0.000896342	+	0.00275866i
$877$	14.8843	−	45.8092i	0.502608	−	1.54687i	−0.302147	−	0.953261i	$-0.597703\pi$
$877$	14.8843	−	45.8092i	0.502608	−	1.54687i	0.804755	−	0.593607i	$-0.202297\pi$
$878$	−8.61925	−	6.26225i	−0.290886	−	0.211341i
$879$	2.61725			0.0882778
$880$		0			0
$881$	−30.0141			−1.01120			−0.505601	−	0.862767i	$-0.668729\pi$
$881$	−30.0141			−1.01120			−0.505601	+	0.862767i	$0.668729\pi$
$882$	3.34696	+	2.43171i	0.112698	+	0.0818798i
$883$	17.4086	−	53.5783i	0.585847	−	1.80305i	−0.00999363	−	0.999950i	$-0.503181\pi$
$883$	17.4086	−	53.5783i	0.585847	−	1.80305i	0.595841	−	0.803102i	$-0.296819\pi$
$884$	−0.0223495	−	0.0687846i	−0.000751694	−	0.00231348i
$885$	−0.107897	+	0.0783915i	−0.00362691	+	0.00263510i
$886$	−41.7668	+	30.3454i	−1.40318	+	1.01947i
$887$	1.40014	+	4.30919i	0.0470122	+	0.144689i	0.971807	−	0.235777i	$-0.0757636\pi$
$887$	1.40014	+	4.30919i	0.0470122	+	0.144689i	−0.924795	+	0.380466i	$0.875764\pi$
$888$	0.411018	−	1.26498i	0.0137929	−	0.0424500i
$889$	−12.5042	−	9.08480i	−0.419376	−	0.304694i
$890$	3.26280			0.109369
$891$		0			0
$892$	0.762363			0.0255258
$893$	55.1441	+	40.0646i	1.84533	+	1.34071i
$894$	−0.578936	+	1.78178i	−0.0193625	+	0.0595917i
$895$	−0.0463872	−	0.142765i	−0.00155055	−	0.00477211i
$896$	8.57246	−	6.22826i	0.286386	−	0.208071i
$897$	0.105923	−	0.0769577i	0.00353667	−	0.00256954i
$898$	4.74212	+	14.5947i	0.158247	+	0.487033i
$899$	9.45070	−	29.0863i	0.315199	−	0.970082i
$900$	0.952147	+	0.691775i	0.0317382	+	0.0230592i
$901$	−0.949713			−0.0316395
$902$		0			0
$903$	0.127342			0.00423766
$904$	21.8723	+	15.8912i	0.727463	+	0.528533i
$905$	−0.759437	+	2.33731i	−0.0252445	+	0.0776947i
$906$	−0.846372	−	2.60487i	−0.0281188	−	0.0865409i
$907$	16.7959	−	12.2030i	0.557700	−	0.405193i	−0.272916	−	0.962038i	$-0.587988\pi$
$907$	16.7959	−	12.2030i	0.557700	−	0.405193i	0.830617	+	0.556845i	$0.187988\pi$
$908$	0.666415	−	0.484179i	0.0221158	−	0.0160680i
$909$	17.1757	+	52.8615i	0.569684	+	1.75331i
$910$	0.0365385	−	0.112454i	0.00121124	−	0.00372781i
$911$	12.4550	+	9.04908i	0.412652	+	0.299809i	0.774675	−	0.632360i	$-0.217914\pi$
$911$	12.4550	+	9.04908i	0.412652	+	0.299809i	−0.362022	+	0.932169i	$0.617914\pi$
$912$	−3.37430			−0.111734
$913$		0			0
$914$	−39.3557			−1.30177
$915$	0.125176	+	0.0909457i	0.00413819	+	0.00300657i
$916$	0.228043	−	0.701843i	0.00753474	−	0.0231895i
$917$	5.45957	+	16.8028i	0.180291	+	0.554878i
$918$	−1.17110	+	0.850850i	−0.0386519	+	0.0280822i
$919$	17.2791	−	12.5540i	0.569985	−	0.414118i	−0.265115	−	0.964217i	$-0.585410\pi$
$919$	17.2791	−	12.5540i	0.569985	−	0.414118i	0.835100	+	0.550099i	$0.185410\pi$
$920$	0.197378	+	0.607466i	0.00650735	+	0.0200276i
$921$	−0.319694	+	0.983918i	−0.0105343	+	0.0324212i
$922$	−28.8634	−	20.9705i	−0.950566	−	0.690627i
$923$	3.10082			0.102065
$924$		0			0
$925$	−18.7765			−0.617369
$926$	−42.2203	−	30.6748i	−1.38744	−	1.00804i
$927$	6.38640	−	19.6553i	0.209757	−	0.645565i
$928$	−0.618893	−	1.90476i	−0.0203162	−	0.0625267i
$929$	−13.0523	+	9.48307i	−0.428233	+	0.311129i	−0.780942	−	0.624604i	$-0.785261\pi$
$929$	−13.0523	+	9.48307i	−0.428233	+	0.311129i	0.352709	+	0.935733i	$0.385261\pi$
$930$	0.124787	−	0.0906634i	0.00409194	−	0.00297297i
$931$	−2.21966	−	6.83141i	−0.0727464	−	0.223890i
$932$	0.414646	−	1.27615i	0.0135822	−	0.0418017i
$933$	1.78546	+	1.29721i	0.0584533	+	0.0424688i
$934$	−21.3263			−0.697817
$935$		0			0
$936$	5.51733			0.180339
$937$	−3.69159	−	2.68210i	−0.120599	−	0.0876204i	0.525851	−	0.850577i	$-0.323747\pi$
$937$	−3.69159	−	2.68210i	−0.120599	−	0.0876204i	−0.646450	+	0.762956i	$0.723747\pi$
$938$	−5.15643	+	15.8699i	−0.168363	+	0.518169i
$939$	−0.00894504	−	0.0275300i	−0.000291910	−	0.000898407i
$940$	−0.0808040	+	0.0587076i	−0.00263554	+	0.00191483i
$941$	10.1535	−	7.37692i	0.330993	−	0.240481i	−0.409859	−	0.912149i	$-0.634422\pi$
$941$	10.1535	−	7.37692i	0.330993	−	0.240481i	0.740852	+	0.671668i	$0.234422\pi$
$942$	0.780009	+	2.40062i	0.0254141	+	0.0782165i
$943$	−3.17897	+	9.78387i	−0.103522	+	0.318607i
$944$	25.4038	+	18.4569i	0.826822	+	0.600721i
$945$	0.0974972			0.00317159
$946$		0			0
$947$	51.6790			1.67934			0.839672	−	0.543094i	$-0.182747\pi$
$947$	51.6790			1.67934			0.839672	+	0.543094i	$0.182747\pi$
$948$	0.0901024	+	0.0654632i	0.00292639	+	0.00212615i
$949$	1.75568	−	5.40343i	0.0569918	−	0.175403i
$950$	15.3273	+	47.1726i	0.497283	+	1.53048i
$951$	1.69372	−	1.23056i	0.0549225	−	0.0399035i
$952$	−3.32161	+	2.41329i	−0.107654	+	0.0782153i
$953$	−0.408678	−	1.25778i	−0.0132384	−	0.0407436i	0.944219	−	0.329318i	$-0.106819\pi$
$953$	−0.408678	−	1.25778i	−0.0132384	−	0.0407436i	−0.957457	+	0.288574i	$0.906819\pi$
$954$	0.852132	−	2.62259i	0.0275888	−	0.0849096i
$955$	−0.261455	−	0.189958i	−0.00846048	−	0.00614690i
$956$	0.655213			0.0211911
$957$		0			0
$958$	0.831818			0.0268748
$959$	15.3975	+	11.1869i	0.497210	+	0.361245i
$960$	0.0417366	−	0.128452i	0.00134704	−	0.00414577i
$961$	4.84348	+	14.9067i	0.156241	+	0.480861i
$962$	−2.71047	+	1.96927i	−0.0873890	+	0.0634918i
$963$	13.1479	−	9.55251i	0.423685	−	0.307825i
$964$	0.227721	+	0.700852i	0.00733439	+	0.0225729i
$965$	−0.0108228	+	0.0333092i	−0.000348398	+	0.00107226i
$966$	−0.228869	−	0.166283i	−0.00736373	−	0.00535006i
$967$	44.1214			1.41885			0.709425	−	0.704781i	$-0.248955\pi$
$967$	44.1214			1.41885			0.709425	+	0.704781i	$0.248955\pi$
$968$		0			0
$969$	1.25351			0.0402684
$970$	0.981499	+	0.713101i	0.0315140	+	0.0228963i
$971$	−0.405337	+	1.24750i	−0.0130079	+	0.0400342i	−0.957350	−	0.288931i	$-0.906700\pi$
$971$	−0.405337	+	1.24750i	−0.0130079	+	0.0400342i	0.944342	+	0.328966i	$0.106700\pi$
$972$	0.0803301	+	0.247231i	0.00257659	+	0.00792992i
$973$	11.3800	−	8.26808i	0.364827	−	0.265062i
$974$	−11.5480	+	8.39010i	−0.370021	+	0.268836i
$975$	0.120956	+	0.372265i	0.00387370	+	0.0119220i
$976$	11.2573	−	34.6465i	0.360339	−	1.10901i
$977$	10.0400	+	7.29451i	0.321209	+	0.233372i	0.736691	−	0.676229i	$-0.236387\pi$
$977$	10.0400	+	7.29451i	0.321209	+	0.233372i	−0.415482	+	0.909601i	$0.636387\pi$
$978$	2.79306			0.0893121
$979$		0			0
$980$	0.0105254			0.000336221
$981$	22.2731	+	16.1824i	0.711127	+	0.516664i
$982$	4.32243	−	13.3031i	0.137934	−	0.424518i
$983$	−9.87510	−	30.3924i	−0.314967	−	0.969368i	−0.975768	−	0.218807i	$-0.929783\pi$
$983$	−9.87510	−	30.3924i	−0.314967	−	0.969368i	0.660801	−	0.750561i	$-0.270217\pi$
$984$	1.76253	−	1.28055i	0.0561875	−	0.0408226i
$985$	−1.87962	+	1.36562i	−0.0598897	+	0.0435124i
$986$	−2.73172	−	8.40737i	−0.0869956	−	0.267745i
$987$	0.359155	−	1.10537i	0.0114320	−	0.0351842i
$988$	−0.294976	−	0.214313i	−0.00938444	−	0.00681819i
$989$	1.73271			0.0550970
$990$		0			0
$991$	−9.17926			−0.291589			−0.145794	−	0.989315i	$-0.546574\pi$
$991$	−9.17926			−0.291589			−0.145794	+	0.989315i	$0.546574\pi$
$992$	2.47276	+	1.79657i	0.0785103	+	0.0570411i
$993$	−0.166981	+	0.513913i	−0.00529897	+	0.0163085i
$994$	−2.07040	−	6.37202i	−0.0656690	−	0.202108i
$995$	−2.16729	+	1.57463i	−0.0687076	+	0.0499190i
$996$	0.0751201	−	0.0545779i	0.00238027	−	0.00172937i
$997$	−4.43217	−	13.6408i	−0.140368	−	0.432009i	0.856018	−	0.516946i	$-0.172931\pi$
$997$	−4.43217	−	13.6408i	−0.140368	−	0.432009i	−0.996386	+	0.0849366i	$0.972931\pi$
$998$	8.47809	−	26.0929i	0.268369	−	0.825955i
$999$	−2.23495	−	1.62379i	−0.0707108	−	0.0513744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.z.323.1		24
11.2	odd	10		847.2.f.y.148.1		24
11.3	even	5	inner	847.2.f.z.729.1		24
11.4	even	5	inner	847.2.f.z.372.6		24
11.5	even	5		847.2.a.m.1.6	✓	6
11.6	odd	10		847.2.a.n.1.1	yes	6
11.7	odd	10		847.2.f.y.372.1		24
11.8	odd	10		847.2.f.y.729.6		24
11.9	even	5	inner	847.2.f.z.148.6		24
11.10	odd	2		847.2.f.y.323.6		24
33.5	odd	10		7623.2.a.cs.1.1		6
33.17	even	10		7623.2.a.cp.1.6		6
77.6	even	10		5929.2.a.bm.1.1		6
77.27	odd	10		5929.2.a.bj.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.6	✓	6	11.5	even	5
847.2.a.n.1.1	yes	6	11.6	odd	10
847.2.f.y.148.1		24	11.2	odd	10
847.2.f.y.323.6		24	11.10	odd	2
847.2.f.y.372.1		24	11.7	odd	10
847.2.f.y.729.6		24	11.8	odd	10
847.2.f.z.148.6		24	11.9	even	5	inner
847.2.f.z.323.1		24	1.1	even	1	trivial
847.2.f.z.372.6		24	11.4	even	5	inner
847.2.f.z.729.1		24	11.3	even	5	inner
5929.2.a.bj.1.6		6	77.27	odd	10
5929.2.a.bm.1.1		6	77.6	even	10
7623.2.a.cp.1.6		6	33.17	even	10
7623.2.a.cs.1.1		6	33.5	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.12126 - 0.814642i) q^{2} +(-0.0378481 + 0.116485i) q^{3} +(-0.0244542 - 0.0752624i) q^{4} +(0.107603 - 0.0781781i) q^{5} +(0.137331 - 0.0997767i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.890458 + 2.74055i) q^{8} +(2.41491 + 1.75454i) q^{9} +O(q^{10})\)	\(q+(-1.12126 - 0.814642i) q^{2} +(-0.0378481 + 0.116485i) q^{3} +(-0.0244542 - 0.0752624i) q^{4} +(0.107603 - 0.0781781i) q^{5} +(0.137331 - 0.0997767i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.890458 + 2.74055i) q^{8} +(2.41491 + 1.75454i) q^{9} -0.184338 q^{10} +0.00969245 q^{12} +(-0.518933 - 0.377027i) q^{13} +(-0.428283 + 1.31812i) q^{14} +(0.00503397 + 0.0154930i) q^{15} +(3.10296 - 2.25443i) q^{16} +(-1.15270 + 0.837488i) q^{17} +(-1.27842 - 3.93458i) q^{18} +(-2.21966 + 6.83141i) q^{19} +(-0.00851521 - 0.00618666i) q^{20} +0.122479 q^{21} +1.66655 q^{23} +(-0.285529 - 0.207449i) q^{24} +(-1.53962 + 4.73846i) q^{25} +(0.274716 + 0.845489i) q^{26} +(-0.593040 + 0.430869i) q^{27} +(-0.0640220 + 0.0465147i) q^{28} +(-1.38334 - 4.25747i) q^{29} +(0.00697684 - 0.0214725i) q^{30} +(5.52706 + 4.01565i) q^{31} +0.447392 q^{32} +1.97473 q^{34} +(-0.107603 - 0.0781781i) q^{35} +(0.0729958 - 0.224658i) q^{36} +(1.16457 + 3.58419i) q^{37} +(8.05397 - 5.85155i) q^{38} +(0.0635584 - 0.0461779i) q^{39} +(0.118435 + 0.364505i) q^{40} +(-1.90752 + 5.87074i) q^{41} +(-0.137331 - 0.0997767i) q^{42} +1.03970 q^{43} +0.397018 q^{45} +(-1.86863 - 1.35764i) q^{46} +(2.93238 - 9.02493i) q^{47} +(0.145165 + 0.446773i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(5.58646 - 4.05880i) q^{50} +(-0.0539268 - 0.165970i) q^{51} +(-0.0156858 + 0.0482760i) q^{52} +(0.539250 + 0.391788i) q^{53} +1.01595 q^{54} +2.88158 q^{56} +(-0.711744 - 0.517112i) q^{57} +(-1.91724 + 5.90065i) q^{58} +(2.52991 + 7.78625i) q^{59} +(0.00104294 - 0.000757737i) q^{60} +(7.68410 - 5.58282i) q^{61} +(-2.92595 - 9.00516i) q^{62} +(0.922415 - 2.83890i) q^{63} +(-6.70756 - 4.87333i) q^{64} -0.0853139 q^{65} +12.0398 q^{67} +(0.0912198 + 0.0662751i) q^{68} +(-0.0630758 + 0.194127i) q^{69} +(0.0569635 + 0.175316i) q^{70} +(-3.91093 + 2.84146i) q^{71} +(-6.95878 + 5.05585i) q^{72} +(2.73711 + 8.42396i) q^{73} +(1.61405 - 4.96752i) q^{74} +(-0.493685 - 0.358684i) q^{75} +0.568428 q^{76} -0.108884 q^{78} +(9.29614 + 6.75404i) q^{79} +(0.157640 - 0.485166i) q^{80} +(2.73950 + 8.43132i) q^{81} +(6.92137 - 5.02867i) q^{82} +(7.75037 - 5.63097i) q^{83} +(-0.00299513 - 0.00921807i) q^{84} +(-0.0585610 + 0.180232i) q^{85} +(-1.16577 - 0.846984i) q^{86} +0.548286 q^{87} -17.7001 q^{89} +(-0.445160 - 0.323428i) q^{90} +(-0.198215 + 0.610042i) q^{91} +(-0.0407542 - 0.125428i) q^{92} +(-0.676950 + 0.491833i) q^{93} +(-10.6400 + 7.73045i) q^{94} +(0.295225 + 0.908608i) q^{95} +(-0.0169329 + 0.0521142i) q^{96} +(-5.32446 - 3.86844i) q^{97} +1.38595 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9 + 32 * q^10 - 56 * q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 22 * q^17 + 24 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 20 * q^30 + 2 * q^31 - 32 * q^32 + 96 * q^34 - 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 + 20 * q^39 + 18 * q^40 + 26 * q^41 + 6 * q^42 + 16 * q^43 - 144 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 - 4 * q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 128 * q^54 + 48 * q^56 + 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 + 8 * q^63 - 26 * q^64 - 96 * q^65 + 24 * q^67 + 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 + 16 * q^72 + 14 * q^73 + 44 * q^74 + 20 * q^75 + 120 * q^76 + 128 * q^78 - 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 + 22 * q^83 - 14 * q^84 - 24 * q^85 + 30 * q^86 - 88 * q^87 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 - 38 * q^94 - 24 * q^95 - 62 * q^96 + 4 * q^97 - 16 * q^98

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