LMFDB - Embedded newform 847.2.f.y.323.6

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			323.6
Character	$\chi$	$=$	847.323
Dual form			847.2.f.y.729.6

$q$-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	0.908808	−	0.417215i	$-0.136994\pi$
$2$	1.12126	+	0.814642i	0.792850	+	0.576039i	−0.115958	+	0.993254i	$0.536994\pi$
$3$	−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	0.657418	−	0.753526i	$-0.271648\pi$
$13$	0.518933	+	0.377027i	0.143926	+	0.104568i	−0.513492	+	0.858094i	$0.671648\pi$
$14$	−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	−0.439159	−	0.898409i	$-0.644723\pi$
$17$	1.15270	−	0.837488i	0.279572	−	0.203121i	0.718731	+	0.695289i	$0.244723\pi$
$18$	1.27842	+	3.93458i	0.301327	+	0.927390i
$19$	2.21966	−	6.83141i	0.509225	−	1.56723i	−0.284325	−	0.958728i	$-0.591769\pi$
$19$	2.21966	−	6.83141i	0.509225	−	1.56723i	0.793550	−	0.608505i	$-0.208231\pi$
$20$	−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	$0.0364420\pi$
$29$	1.38334	+	4.25747i	0.256879	+	0.790592i	−0.736575	+	0.676356i	$0.763558\pi$
$30$	−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	$-0.739904\pi$
$41$	1.90752	−	5.87074i	0.297904	−	0.916855i	0.982230	−	0.187679i	$-0.0600965\pi$
$42$	−0.137331	−	0.0997767i	−0.0211906	−	0.0153959i
$43$	−1.03970			−0.158553			−0.0792764	−	0.996853i	$-0.525261\pi$
$43$	−1.03970			−0.158553			−0.0792764	+	0.996853i	$0.525261\pi$
$44$		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	−0.958565	−	0.284873i	$-0.908049\pi$
$61$	−7.68410	+	5.58282i	−0.983848	+	0.714807i	−0.0252825	+	0.999680i	$0.508049\pi$
$62$	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	$-0.926548\pi$
$73$	−2.73711	−	8.42396i	−0.320355	−	0.985950i	0.653139	−	0.757238i	$-0.273452\pi$
$74$	−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	−0.0744696	−	0.997223i	$-0.523726\pi$
$79$	−9.29614	−	6.75404i	−1.04590	−	0.759889i	−0.971428	+	0.237334i	$0.923726\pi$
$80$	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	−0.925343	−	0.379132i	$-0.876223\pi$
$83$	−7.75037	+	5.63097i	−0.850714	+	0.618080i	0.0746292	+	0.997211i	$0.476223\pi$
$84$	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	$-0.922887\pi$
$101$	−15.0642	−	10.9448i	−1.49895	−	1.08905i	−0.528148	−	0.849152i	$-0.677113\pi$
$102$	−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	−0.998855	−	0.0478368i	$-0.984767\pi$
$107$	−1.68243	+	5.17799i	−0.162647	+	0.500575i	0.836209	+	0.548412i	$0.184767\pi$
$108$	0.0469305	+	0.0340970i	0.00451589	+	0.00328099i
$109$	−9.22316			−0.883419			−0.441709	−	0.897158i	$-0.645628\pi$
$109$	−9.22316			−0.883419			−0.441709	+	0.897158i	$0.645628\pi$
$110$		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	−0.982595	−	0.185761i	$-0.940525\pi$
$127$	−12.5042	+	9.08480i	−1.10956	+	0.806146i	−0.126970	+	0.991907i	$0.540525\pi$
$128$	−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	$-0.219352\pi$
$131$	17.6675			1.54362			0.771810	+	0.635854i	$0.219352\pi$
$132$		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	$-0.896537\pi$
$139$	−4.34679	−	13.3780i	−0.368690	−	1.13471i	0.578949	−	0.815364i	$-0.303463\pi$
$140$	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	−0.158551	−	0.987351i	$-0.550682\pi$
$149$	8.92886	−	6.48719i	0.731480	−	0.531452i	0.890031	+	0.455899i	$0.150682\pi$
$150$	−0.261351	−	0.804354i	−0.0213392	−	0.0656753i
$151$	−4.98599	+	15.3453i	−0.405754	+	1.24878i	0.514511	+	0.857484i	$0.327974\pi$
$151$	−4.98599	+	15.3453i	−0.405754	+	1.24878i	−0.920264	+	0.391298i	$0.872026\pi$
$152$	−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	0.994184	−	0.107699i	$-0.0343483\pi$
$167$	15.4942	+	11.2572i	1.19898	+	0.871107i	0.204792	+	0.978806i	$0.434348\pi$
$168$	−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	$-0.703540\pi$
$173$	4.70466	−	14.4794i	0.357688	−	1.10085i	0.954434	−	0.298421i	$-0.0964600\pi$
$174$	−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	−0.580092	−	0.814551i	$-0.696983\pi$
$193$	0.213034	−	0.154778i	0.0153345	−	0.0111412i	0.595426	+	0.803410i	$0.296983\pi$
$194$	−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	$-0.286208\pi$
$197$	17.4681			1.24455			0.622276	+	0.782798i	$0.286208\pi$
$198$		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	0.906236	−	0.422773i	$-0.138943\pi$
$211$	11.3911	+	8.27613i	0.784197	+	0.569752i	−0.122039	+	0.992525i	$0.538943\pi$
$212$	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	$-0.987730\pi$
$227$	−3.21661	−	9.89970i	−0.213494	−	0.657066i	0.785763	−	0.618527i	$-0.212270\pi$
$228$	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	0.0394495	−	0.999222i	$-0.487440\pi$
$233$	−13.7177	−	9.96649i	−0.898676	−	0.652926i	−0.938126	+	0.346295i	$0.887440\pi$
$234$	−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	−0.833574	−	0.552408i	$-0.813709\pi$
$239$	2.55855	−	7.87440i	0.165499	−	0.509353i	0.999073	+	0.0430552i	$0.0137091\pi$
$240$	0.0505480	+	0.0367253i	0.00326286	+	0.00237061i
$241$	9.31212			0.599846			0.299923	−	0.953963i	$-0.403039\pi$
$241$	9.31212			0.599846			0.299923	+	0.953963i	$0.403039\pi$
$242$		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	$-0.459540\pi$
$263$	4.11162			0.253533			0.126767	+	0.991933i	$0.459540\pi$
$264$		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	0.878700	−	0.477375i	$-0.158412\pi$
$271$	−1.85654	−	5.71386i	−0.112777	−	0.347092i	−0.991477	+	0.130283i	$0.958412\pi$
$272$	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	0.787761	−	0.615981i	$-0.211240\pi$
$277$	7.41226	+	5.38532i	0.445360	+	0.323573i	−0.342401	+	0.939554i	$0.611240\pi$
$278$	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	−0.854795	−	0.518966i	$-0.826317\pi$
$281$	−10.4832	+	7.61649i	−0.625375	+	0.454362i	0.229420	+	0.973328i	$0.426317\pi$
$282$	0.497772	+	1.53198i	0.0296419	+	0.0912283i
$283$	−1.17050	+	3.60242i	−0.0695789	+	0.214142i	−0.979800	−	0.199982i	$-0.935912\pi$
$283$	−1.17050	+	3.60242i	−0.0695789	+	0.214142i	0.910221	+	0.414123i	$0.135912\pi$
$284$	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	$0.114573\pi$
$293$	6.60338	+	20.3231i	0.385773	+	1.18729i	−0.550144	+	0.835070i	$0.685427\pi$
$294$	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	$-0.577489\pi$
$307$	−8.44677			−0.482082			−0.241041	+	0.970515i	$0.577489\pi$
$308$		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	$0.173264\pi$
$337$	8.58694	+	26.4279i	0.467760	+	1.43962i	−0.387717	+	0.921778i	$0.626736\pi$
$338$	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	$0.616762\pi$
$347$	−25.2830	+	18.3692i	−1.35726	+	0.986108i	−0.998614	+	0.0526349i	$0.983238\pi$
$348$	0.0134079	+	0.0412653i	0.000718739	+	0.00221205i
$349$	−0.167932	+	0.516840i	−0.00898917	+	0.0276658i	−0.955450	−	0.295151i	$-0.904630\pi$
$349$	−0.167932	+	0.516840i	−0.00898917	+	0.0276658i	0.946461	+	0.322817i	$0.104630\pi$
$350$	−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	$-0.997517\pi$
$359$	−3.70538	−	11.4040i	−0.195562	−	0.601879i	0.804407	−	0.594078i	$-0.202483\pi$
$360$	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	$-0.412190\pi$
$373$	10.5209			0.544753			0.272377	+	0.962191i	$0.412190\pi$
$374$		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	0.212110	−	0.977246i	$-0.431967\pi$
$409$	−13.1810	−	9.57659i	−0.651760	−	0.473532i	−0.863870	+	0.503714i	$0.831967\pi$
$410$	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	0.648514	−	0.761202i	$-0.275391\pi$
$431$	2.59444	+	1.88497i	0.124970	+	0.0907959i	−0.523545	+	0.851998i	$0.675391\pi$
$432$	−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	$-0.558724\pi$
$439$	−7.68712			−0.366886			−0.183443	+	0.983030i	$0.558724\pi$
$440$		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	−0.976739	−	0.214434i	$-0.931209\pi$
$457$	−22.9729	+	16.6908i	−1.07463	+	0.780763i	−0.0978901	+	0.995197i	$0.531209\pi$
$458$	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	$-0.704619\pi$
$461$	−25.7420			−1.19892			−0.599462	+	0.800403i	$0.704619\pi$
$462$		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	−0.576637	−	0.817000i	$-0.695635\pi$
$479$	0.485554	−	0.352776i	0.0221855	−	0.0161187i	0.598823	+	0.800882i	$0.295635\pi$
$480$	−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	0.855693	−	0.517484i	$-0.173131\pi$
$491$	−3.11874	−	9.59850i	−0.140747	−	0.433174i	−0.996440	+	0.0843101i	$0.973131\pi$
$492$	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	$0.203306\pi$
$503$	−4.41999	+	13.6033i	−0.197078	+	0.606543i	−0.999946	+	0.0103866i	$0.996694\pi$
$504$	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	0.260472	−	0.965481i	$-0.416122\pi$
$523$	28.7967	−	20.9220i	1.25919	−	0.914855i	0.998718	+	0.0506265i	$0.0161218\pi$
$524$	−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	0.252933	−	0.967484i	$-0.418605\pi$
$541$	−13.7007	−	9.95414i	−0.589039	−	0.427962i	−0.841971	+	0.539522i	$0.818605\pi$
$542$	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	−0.992185	−	0.124775i	$-0.960179\pi$
$547$	−2.71651	+	8.36056i	−0.116150	+	0.357472i	0.876035	+	0.482247i	$0.160179\pi$
$548$	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	$0.0522634\pi$
$557$	6.71421	+	20.6642i	0.284490	+	0.875571i	−0.702061	+	0.712117i	$0.747737\pi$
$558$	−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	0.618402	−	0.785862i	$-0.287780\pi$
$563$	1.47350	+	1.07056i	0.0621006	+	0.0451187i	−0.556302	+	0.830980i	$0.687780\pi$
$564$	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	$-0.657392\pi$
$569$	10.1796	−	31.3295i	0.426750	−	1.31340i	0.901309	−	0.433177i	$-0.142608\pi$
$570$	0.131201	+	0.0953234i	0.00549542	+	0.00399266i
$571$	−23.4394			−0.980908			−0.490454	−	0.871467i	$-0.663169\pi$
$571$	−23.4394			−0.980908			−0.490454	+	0.871467i	$0.663169\pi$
$572$		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	$-0.315790\pi$
$593$	26.6381			1.09389			0.546947	+	0.837167i	$0.315790\pi$
$594$		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	0.915015	−	0.403419i	$-0.132178\pi$
$601$	−1.52905	−	4.70594i	−0.0623714	−	0.191959i	−0.977387	+	0.211460i	$0.932178\pi$
$602$	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	0.940149	−	0.340764i	$-0.110686\pi$
$607$	22.3359	+	16.2280i	0.906585	+	0.658672i	−0.0335641	+	0.999437i	$0.510686\pi$
$608$	−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	−0.896115	−	0.443821i	$-0.853623\pi$
$613$	2.22158	−	6.83732i	0.0897288	−	0.276157i	0.985844	+	0.167664i	$0.0536225\pi$
$614$	−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	$-0.449331\pi$
$659$	8.13829			0.317023			0.158511	+	0.987357i	$0.449331\pi$
$660$		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	0.848194	−	0.529686i	$-0.177690\pi$
$673$	15.7350	+	11.4321i	0.606539	+	0.440677i	−0.241655	+	0.970362i	$0.577690\pi$
$674$	−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	0.143288	−	0.989681i	$-0.454232\pi$
$677$	29.3707	−	21.3391i	1.12881	−	0.820128i	0.985521	+	0.169553i	$0.0542324\pi$
$678$	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	−1.00000		0.000802204i	$-0.999745\pi$
$701$	−5.04406	+	15.5240i	−0.190511	+	0.586334i	0.809488	+	0.587136i	$0.199745\pi$
$702$	−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	$0.0208346\pi$
$733$	6.20047	+	19.0831i	0.229019	+	0.704849i	−0.768839	+	0.639442i	$0.779165\pi$
$734$	−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	0.868864	−	0.495050i	$-0.164850\pi$
$739$	18.1195	+	13.1646i	0.666538	+	0.484268i	−0.202327	+	0.979318i	$0.564850\pi$
$740$	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	0.0994354	−	0.995044i	$-0.468296\pi$
$743$	29.3434	−	21.3192i	1.07651	−	0.782127i	0.977070	+	0.212917i	$0.0682964\pi$
$744$	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	0.509678	−	0.860365i	$-0.329765\pi$
$761$	−4.16769	−	3.02800i	−0.151079	−	0.109765i	−0.660757	+	0.750600i	$0.729765\pi$
$762$	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	$-0.744422\pi$
$769$	−38.5242			−1.38922			−0.694608	+	0.719388i	$0.744422\pi$
$770$		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	−0.939775	−	0.341794i	$-0.888966\pi$
$787$	−25.3917	+	18.4482i	−0.905117	+	0.657606i	0.0346585	+	0.999399i	$0.488966\pi$
$788$	−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	−0.742376	−	0.669983i	$-0.766301\pi$
$809$	−9.51675	+	6.91433i	−0.334591	+	0.243095i	0.407785	+	0.913078i	$0.366301\pi$
$810$	0.504994	+	1.55421i	0.0177437	+	0.0546094i
$811$	−2.55651	+	7.86813i	−0.0897712	+	0.276287i	−0.985856	−	0.167596i	$-0.946400\pi$
$811$	−2.55651	+	7.86813i	−0.0897712	+	0.276287i	0.896085	+	0.443883i	$0.146400\pi$
$812$	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	0.903302	−	0.429004i	$-0.141135\pi$
$821$	−2.28213	−	7.02368i	−0.0796469	−	0.245128i	−0.982949	+	0.183876i	$0.941135\pi$
$822$	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	0.210880	−	0.977512i	$-0.432367\pi$
$827$	−18.7966	−	13.6566i	−0.653623	−	0.474885i	−0.864503	+	0.502627i	$0.832367\pi$
$828$	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	0.126841	−	0.991923i	$-0.459516\pi$
$853$	32.4017	−	23.5412i	1.10941	−	0.806035i	0.982571	+	0.185888i	$0.0595162\pi$
$854$	−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	$-0.682161\pi$
$857$	−31.7070			−1.08309			−0.541546	+	0.840671i	$0.682161\pi$
$858$		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	$0.402297\pi$
$877$	−14.8843	+	45.8092i	−0.502608	+	1.54687i	−0.804755	+	0.593607i	$0.797703\pi$
$878$	−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	0.924795	−	0.380466i	$-0.124236\pi$
$887$	−1.40014	−	4.30919i	−0.0470122	−	0.144689i	−0.971807	+	0.235777i	$0.924236\pi$
$888$	−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	−0.835100	−	0.550099i	$-0.814590\pi$
$919$	−17.2791	+	12.5540i	−0.569985	+	0.414118i	0.265115	+	0.964217i	$0.414590\pi$
$920$	−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	0.646450	−	0.762956i	$-0.276253\pi$
$937$	3.69159	+	2.68210i	0.120599	+	0.0876204i	−0.525851	+	0.850577i	$0.676253\pi$
$938$	−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	−0.740852	−	0.671668i	$-0.765578\pi$
$941$	−10.1535	+	7.37692i	−0.330993	+	0.240481i	0.409859	+	0.912149i	$0.365578\pi$
$942$	−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	0.957457	−	0.288574i	$-0.0931812\pi$
$953$	0.408678	+	1.25778i	0.0132384	+	0.0407436i	−0.944219	+	0.329318i	$0.893181\pi$
$954$	−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	$-0.751045\pi$
$967$	−44.1214			−1.41885			−0.709425	+	0.704781i	$0.751045\pi$
$968$		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	0.996386	−	0.0849366i	$-0.0270688\pi$
$997$	4.43217	+	13.6408i	0.140368	+	0.432009i	−0.856018	+	0.516946i	$0.827069\pi$
$998$	−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.y.323.6		24
11.2	odd	10		847.2.f.z.148.6		24
11.3	even	5	inner	847.2.f.y.729.6		24
11.4	even	5	inner	847.2.f.y.372.1		24
11.5	even	5		847.2.a.n.1.1	yes	6
11.6	odd	10		847.2.a.m.1.6	✓	6
11.7	odd	10		847.2.f.z.372.6		24
11.8	odd	10		847.2.f.z.729.1		24
11.9	even	5	inner	847.2.f.y.148.1		24
11.10	odd	2		847.2.f.z.323.1		24
33.5	odd	10		7623.2.a.cp.1.6		6
33.17	even	10		7623.2.a.cs.1.1		6
77.6	even	10		5929.2.a.bj.1.6		6
77.27	odd	10		5929.2.a.bm.1.1		6

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