LMFDB - Embedded newform 798.2.p.d.107.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(107,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

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

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

chi := DirichletCharacter("798.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.p (of order $6$, degree $2$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.18
Character	$\chi$	$=$	798.107
Dual form			798.2.p.d.179.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.25084 - 1.19809i) q^{3} +1.00000 q^{4} +1.95673i q^{5} +(1.25084 - 1.19809i) q^{6} +(1.98940 + 1.74422i) q^{7} +1.00000 q^{8} +(0.129182 - 2.99722i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.25084 - 1.19809i) q^{3} +1.00000 q^{4} +1.95673i q^{5} +(1.25084 - 1.19809i) q^{6} +(1.98940 + 1.74422i) q^{7} +1.00000 q^{8} +(0.129182 - 2.99722i) q^{9} +1.95673i q^{10} +(-1.30073 + 0.750974i) q^{11} +(1.25084 - 1.19809i) q^{12} +(-0.271478 - 0.156738i) q^{13} +(1.98940 + 1.74422i) q^{14} +(2.34432 + 2.44754i) q^{15} +1.00000 q^{16} +(0.475982 + 0.274809i) q^{17} +(0.129182 - 2.99722i) q^{18} +(4.35877 + 0.0337967i) q^{19} +1.95673i q^{20} +(4.57813 - 0.201741i) q^{21} +(-1.30073 + 0.750974i) q^{22} +(-2.91260 + 1.68159i) q^{23} +(1.25084 - 1.19809i) q^{24} +1.17123 q^{25} +(-0.271478 - 0.156738i) q^{26} +(-3.42934 - 3.90380i) q^{27} +(1.98940 + 1.74422i) q^{28} +(1.14433 - 1.98204i) q^{29} +(2.34432 + 2.44754i) q^{30} +(0.673645 - 0.388929i) q^{31} +1.00000 q^{32} +(-0.727263 + 2.49773i) q^{33} +(0.475982 + 0.274809i) q^{34} +(-3.41295 + 3.89271i) q^{35} +(0.129182 - 2.99722i) q^{36} +(-2.22529 - 1.28477i) q^{37} +(4.35877 + 0.0337967i) q^{38} +(-0.527360 + 0.129200i) q^{39} +1.95673i q^{40} +(-2.41328 - 4.17992i) q^{41} +(4.57813 - 0.201741i) q^{42} +(-2.59988 - 4.50313i) q^{43} +(-1.30073 + 0.750974i) q^{44} +(5.86473 + 0.252774i) q^{45} +(-2.91260 + 1.68159i) q^{46} +(-8.03262 + 4.63764i) q^{47} +(1.25084 - 1.19809i) q^{48} +(0.915417 + 6.93989i) q^{49} +1.17123 q^{50} +(0.924620 - 0.226527i) q^{51} +(-0.271478 - 0.156738i) q^{52} -10.8689 q^{53} +(-3.42934 - 3.90380i) q^{54} +(-1.46945 - 2.54516i) q^{55} +(1.98940 + 1.74422i) q^{56} +(5.49260 - 5.17990i) q^{57} +(1.14433 - 1.98204i) q^{58} +(5.30675 - 9.19155i) q^{59} +(2.34432 + 2.44754i) q^{60} +(5.26836 + 9.12507i) q^{61} +(0.673645 - 0.388929i) q^{62} +(5.48479 - 5.73734i) q^{63} +1.00000 q^{64} +(0.306693 - 0.531208i) q^{65} +(-0.727263 + 2.49773i) q^{66} -0.0196594i q^{67} +(0.475982 + 0.274809i) q^{68} +(-1.62850 + 5.59294i) q^{69} +(-3.41295 + 3.89271i) q^{70} +(-3.62859 - 6.28490i) q^{71} +(0.129182 - 2.99722i) q^{72} +(3.75080 - 6.49658i) q^{73} +(-2.22529 - 1.28477i) q^{74} +(1.46501 - 1.40323i) q^{75} +(4.35877 + 0.0337967i) q^{76} +(-3.89752 - 0.774760i) q^{77} +(-0.527360 + 0.129200i) q^{78} +5.37959i q^{79} +1.95673i q^{80} +(-8.96662 - 0.774374i) q^{81} +(-2.41328 - 4.17992i) q^{82} -11.1431i q^{83} +(4.57813 - 0.201741i) q^{84} +(-0.537725 + 0.931367i) q^{85} +(-2.59988 - 4.50313i) q^{86} +(-0.943281 - 3.85021i) q^{87} +(-1.30073 + 0.750974i) q^{88} +(-2.48533 - 4.30472i) q^{89} +(5.86473 + 0.252774i) q^{90} +(-0.266693 - 0.785330i) q^{91} +(-2.91260 + 1.68159i) q^{92} +(0.376649 - 1.29357i) q^{93} +(-8.03262 + 4.63764i) q^{94} +(-0.0661308 + 8.52891i) q^{95} +(1.25084 - 1.19809i) q^{96} +(-2.00828 + 1.15948i) q^{97} +(0.915417 + 6.93989i) q^{98} +(2.08280 + 3.99557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9	$ 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9} - 3 q^{11} - 3 q^{13} - 13 q^{15} + 50 q^{16} + 3 q^{17} + 6 q^{18} + 10 q^{19} - 7 q^{21} - 3 q^{22} + 9 q^{23} - 58 q^{25} - 3 q^{26} + 6 q^{27} - 5 q^{29} - 13 q^{30} + 15 q^{31} + 50 q^{32} - q^{33} + 3 q^{34} + 6 q^{36} - 9 q^{37} + 10 q^{38} - 2 q^{39} - 17 q^{41} - 7 q^{42} + 15 q^{43} - 3 q^{44} - 22 q^{45} + 9 q^{46} + 21 q^{47} + 8 q^{49} - 58 q^{50} - 4 q^{51} - 3 q^{52} - 12 q^{53} + 6 q^{54} - 16 q^{55} - 19 q^{57} - 5 q^{58} - q^{59} - 13 q^{60} + 23 q^{61} + 15 q^{62} + 41 q^{63} + 50 q^{64} - 14 q^{65} - q^{66} + 3 q^{68} - 31 q^{69} + 3 q^{71} + 6 q^{72} + 15 q^{73} - 9 q^{74} + 7 q^{75} + 10 q^{76} - 57 q^{77} - 2 q^{78} - 70 q^{81} - 17 q^{82} - 7 q^{84} - 10 q^{85} + 15 q^{86} + 52 q^{87} - 3 q^{88} + 33 q^{89} - 22 q^{90} - 15 q^{91} + 9 q^{92} + 53 q^{93} + 21 q^{94} + 30 q^{95} - 21 q^{97} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9 - 3 * q^11 - 3 * q^13 - 13 * q^15 + 50 * q^16 + 3 * q^17 + 6 * q^18 + 10 * q^19 - 7 * q^21 - 3 * q^22 + 9 * q^23 - 58 * q^25 - 3 * q^26 + 6 * q^27 - 5 * q^29 - 13 * q^30 + 15 * q^31 + 50 * q^32 - q^33 + 3 * q^34 + 6 * q^36 - 9 * q^37 + 10 * q^38 - 2 * q^39 - 17 * q^41 - 7 * q^42 + 15 * q^43 - 3 * q^44 - 22 * q^45 + 9 * q^46 + 21 * q^47 + 8 * q^49 - 58 * q^50 - 4 * q^51 - 3 * q^52 - 12 * q^53 + 6 * q^54 - 16 * q^55 - 19 * q^57 - 5 * q^58 - q^59 - 13 * q^60 + 23 * q^61 + 15 * q^62 + 41 * q^63 + 50 * q^64 - 14 * q^65 - q^66 + 3 * q^68 - 31 * q^69 + 3 * q^71 + 6 * q^72 + 15 * q^73 - 9 * q^74 + 7 * q^75 + 10 * q^76 - 57 * q^77 - 2 * q^78 - 70 * q^81 - 17 * q^82 - 7 * q^84 - 10 * q^85 + 15 * q^86 + 52 * q^87 - 3 * q^88 + 33 * q^89 - 22 * q^90 - 15 * q^91 + 9 * q^92 + 53 * q^93 + 21 * q^94 + 30 * q^95 - 21 * q^97 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.25084	−	1.19809i	0.722171	−	0.691715i
$3$	1.25084	−	1.19809i	0.722171	−	0.691715i
$4$	1.00000			0.500000
$5$			1.95673i			0.875074i	0.899200	+	0.437537i	$0.144149\pi$
$5$			1.95673i			0.875074i	−0.899200	+	0.437537i	$0.855851\pi$
$6$	1.25084	−	1.19809i	0.510652	−	0.489116i
$7$	1.98940	+	1.74422i	0.751922	+	0.659252i
$7$	1.98940	+	1.74422i	0.751922	+	0.659252i
$8$	1.00000			0.353553
$9$	0.129182	−	2.99722i	0.0430607	−	0.999072i
$10$			1.95673i			0.618771i
$11$	−1.30073	+	0.750974i	−0.392183	+	0.226427i	−0.683106	−	0.730319i	$-0.739371\pi$
$11$	−1.30073	+	0.750974i	−0.392183	+	0.226427i	0.290922	+	0.956747i	$0.406038\pi$
$12$	1.25084	−	1.19809i	0.361085	−	0.345858i
$13$	−0.271478	−	0.156738i	−0.0752944	−	0.0434713i	0.461880	−	0.886942i	$-0.347175\pi$
$13$	−0.271478	−	0.156738i	−0.0752944	−	0.0434713i	−0.537175	+	0.843471i	$0.680508\pi$
$14$	1.98940	+	1.74422i	0.531689	+	0.466161i
$15$	2.34432	+	2.44754i	0.605302	+	0.631953i
$16$	1.00000			0.250000
$17$	0.475982	+	0.274809i	0.115443	+	0.0666509i	0.556610	−	0.830774i	$-0.312102\pi$
$17$	0.475982	+	0.274809i	0.115443	+	0.0666509i	−0.441167	+	0.897425i	$0.645435\pi$
$18$	0.129182	−	2.99722i	0.0304485	−	0.706451i
$19$	4.35877	+	0.0337967i	0.999970	+	0.00775349i
$19$	4.35877	+	0.0337967i	0.999970	+	0.00775349i
$20$			1.95673i			0.437537i
$21$	4.57813	−	0.201741i	0.999030	−	0.0440235i
$22$	−1.30073	+	0.750974i	−0.277316	+	0.160108i
$23$	−2.91260	+	1.68159i	−0.607320	+	0.350636i	−0.771916	−	0.635725i	$-0.780701\pi$
$23$	−2.91260	+	1.68159i	−0.607320	+	0.350636i	0.164596	+	0.986361i	$0.447368\pi$
$24$	1.25084	−	1.19809i	0.255326	−	0.244558i
$25$	1.17123			0.234245
$26$	−0.271478	−	0.156738i	−0.0532412	−	0.0307388i
$27$	−3.42934	−	3.90380i	−0.659976	−	0.751286i
$28$	1.98940	+	1.74422i	0.375961	+	0.329626i
$29$	1.14433	−	1.98204i	0.212497	−	0.368055i	−0.739999	−	0.672608i	$-0.765174\pi$
$29$	1.14433	−	1.98204i	0.212497	−	0.368055i	0.952495	+	0.304553i	$0.0985072\pi$
$30$	2.34432	+	2.44754i	0.428013	+	0.446858i
$31$	0.673645	−	0.388929i	0.120990	−	0.0698537i	−0.438284	−	0.898837i	$-0.644413\pi$
$31$	0.673645	−	0.388929i	0.120990	−	0.0698537i	0.559274	+	0.828983i	$0.311080\pi$
$32$	1.00000			0.176777
$33$	−0.727263	+	2.49773i	−0.126600	+	0.434798i
$34$	0.475982	+	0.274809i	0.0816303	+	0.0471293i
$35$	−3.41295	+	3.89271i	−0.576894	+	0.657988i
$36$	0.129182	−	2.99722i	0.0215304	−	0.499536i
$37$	−2.22529	−	1.28477i	−0.365835	−	0.211215i	0.305802	−	0.952095i	$-0.401075\pi$
$37$	−2.22529	−	1.28477i	−0.365835	−	0.211215i	−0.671637	+	0.740880i	$0.734409\pi$
$38$	4.35877	+	0.0337967i	0.707086	+	0.00548255i
$39$	−0.527360	+	0.129200i	−0.0844451	+	0.0206886i
$40$			1.95673i			0.309385i
$41$	−2.41328	−	4.17992i	−0.376891	−	0.652794i	0.613718	−	0.789526i	$-0.289673\pi$
$41$	−2.41328	−	4.17992i	−0.376891	−	0.652794i	−0.990608	+	0.136732i	$0.956340\pi$
$42$	4.57813	−	0.201741i	0.706421	−	0.0311293i
$43$	−2.59988	−	4.50313i	−0.396479	−	0.686721i	0.596810	−	0.802383i	$-0.296435\pi$
$43$	−2.59988	−	4.50313i	−0.396479	−	0.686721i	−0.993289	+	0.115661i	$0.963101\pi$
$44$	−1.30073	+	0.750974i	−0.196092	+	0.113214i
$45$	5.86473	+	0.252774i	0.874263	+	0.0376813i
$46$	−2.91260	+	1.68159i	−0.429440	+	0.247937i
$47$	−8.03262	+	4.63764i	−1.17168	+	0.676469i	−0.954075	−	0.299569i	$-0.903157\pi$
$47$	−8.03262	+	4.63764i	−1.17168	+	0.676469i	−0.217603	+	0.976037i	$0.569824\pi$
$48$	1.25084	−	1.19809i	0.180543	−	0.172929i
$49$	0.915417	+	6.93989i	0.130774	+	0.991412i
$50$	1.17123			0.165636
$51$	0.924620	−	0.226527i	0.129473	−	0.0317201i
$52$	−0.271478	−	0.156738i	−0.0376472	−	0.0217356i
$53$	−10.8689			−1.49295			−0.746477	−	0.665411i	$-0.768256\pi$
$53$	−10.8689			−1.49295			−0.746477	+	0.665411i	$0.768256\pi$
$54$	−3.42934	−	3.90380i	−0.466674	−	0.531240i
$55$	−1.46945	−	2.54516i	−0.198141	−	0.343190i
$56$	1.98940	+	1.74422i	0.265845	+	0.233081i
$57$	5.49260	−	5.17990i	0.727512	−	0.686095i
$58$	1.14433	−	1.98204i	0.150258	−	0.260254i
$59$	5.30675	−	9.19155i	0.690879	−	1.19664i	−0.280671	−	0.959804i	$-0.590557\pi$
$59$	5.30675	−	9.19155i	0.690879	−	1.19664i	0.971550	−	0.236834i	$-0.0761098\pi$
$60$	2.34432	+	2.44754i	0.302651	+	0.315976i
$61$	5.26836	+	9.12507i	0.674545	+	1.16835i	0.976602	+	0.215056i	$0.0689933\pi$
$61$	5.26836	+	9.12507i	0.674545	+	1.16835i	−0.302057	+	0.953290i	$0.597673\pi$
$62$	0.673645	−	0.388929i	0.0855530	−	0.0493941i
$63$	5.48479	−	5.73734i	0.691019	−	0.722837i
$64$	1.00000			0.125000
$65$	0.306693	−	0.531208i	0.0380406	−	0.0658882i
$66$	−0.727263	+	2.49773i	−0.0895199	+	0.307449i
$67$		−	0.0196594i		−	0.00240178i	−0.999999	−	0.00120089i	$-0.999618\pi$
$67$		−	0.0196594i		−	0.00240178i	0.999999	−	0.00120089i	$-0.000382256\pi$
$68$	0.475982	+	0.274809i	0.0577213	+	0.0333254i
$69$	−1.62850	+	5.59294i	−0.196048	+	0.673311i
$70$	−3.41295	+	3.89271i	−0.407926	+	0.465268i
$71$	−3.62859	−	6.28490i	−0.430634	−	0.745880i	0.566294	−	0.824203i	$-0.308377\pi$
$71$	−3.62859	−	6.28490i	−0.430634	−	0.745880i	−0.996928	+	0.0783233i	$0.975043\pi$
$72$	0.129182	−	2.99722i	0.0152243	−	0.353225i
$73$	3.75080	−	6.49658i	0.438998	−	0.760367i	−0.558615	−	0.829427i	$-0.688667\pi$
$73$	3.75080	−	6.49658i	0.438998	−	0.760367i	0.997612	+	0.0690607i	$0.0220002\pi$
$74$	−2.22529	−	1.28477i	−0.258685	−	0.149352i
$75$	1.46501	−	1.40323i	0.169165	−	0.162031i
$76$	4.35877	+	0.0337967i	0.499985	+	0.00387675i
$77$	−3.89752	−	0.774760i	−0.444164	−	0.0882920i
$78$	−0.527360	+	0.129200i	−0.0597117	+	0.0146291i
$79$			5.37959i			0.605252i	0.953109	+	0.302626i	$0.0978632\pi$
$79$			5.37959i			0.605252i	−0.953109	+	0.302626i	$0.902137\pi$
$80$			1.95673i			0.218769i
$81$	−8.96662	−	0.774374i	−0.996292	−	0.0860416i
$82$	−2.41328	−	4.17992i	−0.266502	−	0.461595i
$83$		−	11.1431i		−	1.22312i	−0.791198	−	0.611560i	$-0.790542\pi$
$83$		−	11.1431i		−	1.22312i	0.791198	−	0.611560i	$-0.209458\pi$
$84$	4.57813	−	0.201741i	0.499515	−	0.0220117i
$85$	−0.537725	+	0.931367i	−0.0583244	+	0.101021i
$86$	−2.59988	−	4.50313i	−0.280353	−	0.485585i
$87$	−0.943281	−	3.85021i	−0.101130	−	0.412786i
$88$	−1.30073	+	0.750974i	−0.138658	+	0.0800541i
$89$	−2.48533	−	4.30472i	−0.263445	−	0.456300i	0.703710	−	0.710487i	$-0.251525\pi$
$89$	−2.48533	−	4.30472i	−0.263445	−	0.456300i	−0.967155	+	0.254187i	$0.918192\pi$
$90$	5.86473	+	0.252774i	0.618197	+	0.0266447i
$91$	−0.266693	−	0.785330i	−0.0279570	−	0.0823250i
$92$	−2.91260	+	1.68159i	−0.303660	+	0.175318i
$93$	0.376649	−	1.29357i	0.0390567	−	0.134137i
$94$	−8.03262	+	4.63764i	−0.828502	+	0.478336i
$95$	−0.0661308	+	8.52891i	−0.00678488	+	0.875048i
$96$	1.25084	−	1.19809i	0.127663	−	0.122279i
$97$	−2.00828	+	1.15948i	−0.203910	+	0.117727i	−0.598478	−	0.801139i	$-0.704228\pi$
$97$	−2.00828	+	1.15948i	−0.203910	+	0.117727i	0.394568	+	0.918867i	$0.370894\pi$
$98$	0.915417	+	6.93989i	0.0924711	+	0.701034i
$99$	2.08280	+	3.99557i	0.209329	+	0.401570i
$100$	1.17123			0.117123
$101$		−	2.01100i		−	0.200102i	−0.994982	−	0.100051i	$-0.968099\pi$
$101$		−	2.01100i		−	0.200102i	0.994982	−	0.100051i	$-0.0319005\pi$
$102$	0.924620	−	0.226527i	0.0915510	−	0.0224295i
$103$	2.37790	+	1.37288i	0.234302	+	0.135274i	0.612555	−	0.790428i	$-0.290142\pi$
$103$	2.37790	+	1.37288i	0.234302	+	0.135274i	−0.378253	+	0.925702i	$0.623475\pi$
$104$	−0.271478	−	0.156738i	−0.0266206	−	0.0153694i
$105$	0.394752	+	8.95815i	0.0385238	+	0.874226i
$106$	−10.8689			−1.05568
$107$	−3.96645	+	6.87009i	−0.383451	+	0.664157i	−0.991553	−	0.129702i	$-0.958598\pi$
$107$	−3.96645	+	6.87009i	−0.383451	+	0.664157i	0.608102	+	0.793859i	$0.291931\pi$
$108$	−3.42934	−	3.90380i	−0.329988	−	0.375643i
$109$	−13.8708	−	8.00830i	−1.32858	−	0.767056i	−0.343500	−	0.939153i	$-0.611612\pi$
$109$	−13.8708	−	8.00830i	−1.32858	−	0.767056i	−0.985080	+	0.172097i	$0.944946\pi$
$110$	−1.46945	−	2.54516i	−0.140107	−	0.242672i
$111$	−4.32274	+	1.05905i	−0.410296	+	0.100520i
$112$	1.98940	+	1.74422i	0.187981	+	0.164813i
$113$	−5.37956			−0.506066			−0.253033	−	0.967458i	$-0.581428\pi$
$113$	−5.37956			−0.506066			−0.253033	+	0.967458i	$0.581428\pi$
$114$	5.49260	−	5.17990i	0.514429	−	0.485142i
$115$	−3.29041	−	5.69916i	−0.306833	−	0.531450i
$116$	1.14433	−	1.98204i	0.106248	−	0.184028i
$117$	−0.504848	+	0.793431i	−0.0466732	+	0.0733527i
$118$	5.30675	−	9.19155i	0.488526	−	0.846151i
$119$	0.467593	+	1.37692i	0.0428642	+	0.126222i
$120$	2.34432	+	2.44754i	0.214007	+	0.223429i
$121$	−4.37208	+	7.57266i	−0.397461	+	0.688423i
$122$	5.26836	+	9.12507i	0.476975	+	0.826145i
$123$	−8.02651	−	2.33708i	−0.723726	−	0.210727i
$124$	0.673645	−	0.388929i	0.0604951	−	0.0349269i
$125$			12.0754i			1.08006i
$126$	5.48479	−	5.73734i	0.488624	−	0.511123i
$127$	−4.02863	−	2.32593i	−0.357483	−	0.206393i	0.310493	−	0.950576i	$-0.399506\pi$
$127$	−4.02863	−	2.32593i	−0.357483	−	0.206393i	−0.667976	+	0.744183i	$0.732839\pi$
$128$	1.00000			0.0883883
$129$	−8.64717	−	2.51780i	−0.761340	−	0.221680i
$130$	0.306693	−	0.531208i	0.0268988	−	0.0465900i
$131$			7.46944i			0.652608i	0.945265	+	0.326304i	$0.105803\pi$
$131$			7.46944i			0.652608i	−0.945265	+	0.326304i	$0.894197\pi$
$132$	−0.727263	+	2.49773i	−0.0633001	+	0.217399i
$133$	8.61238	+	7.66987i	0.746788	+	0.665062i
$134$		−	0.0196594i		−	0.00169832i
$135$	7.63866	−	6.71027i	0.657431	−	0.577528i
$136$	0.475982	+	0.274809i	0.0408151	+	0.0235646i
$137$			18.4646i			1.57754i	0.614690	+	0.788769i	$0.289281\pi$
$137$			18.4646i			1.57754i	−0.614690	+	0.788769i	$0.710719\pi$
$138$	−1.62850	+	5.59294i	−0.138627	+	0.476103i
$139$	9.32549	−	16.1522i	0.790978	−	1.37001i	−0.134384	−	0.990929i	$-0.542906\pi$
$139$	9.32549	−	16.1522i	0.790978	−	1.37001i	0.925362	−	0.379084i	$-0.123761\pi$
$140$	−3.41295	+	3.89271i	−0.288447	+	0.328994i
$141$	−4.49121	+	15.4247i	−0.378228	+	1.29899i
$142$	−3.62859	−	6.28490i	−0.304504	−	0.527417i
$143$	0.470824			0.0393723
$144$	0.129182	−	2.99722i	0.0107652	−	0.249768i
$145$	3.87830	+	2.23914i	0.322076	+	0.185950i
$146$	3.75080	−	6.49658i	0.310418	−	0.537660i
$147$	9.45961	+	7.58391i	0.780216	+	0.625511i
$148$	−2.22529	−	1.28477i	−0.182918	−	0.105608i
$149$			12.4115i			1.01679i	0.861125	+	0.508394i	$0.169761\pi$
$149$			12.4115i			1.01679i	−0.861125	+	0.508394i	$0.830239\pi$
$150$	1.46501	−	1.40323i	0.119618	−	0.114573i
$151$	−1.29008	+	0.744830i	−0.104985	+	0.0606134i	−0.551573	−	0.834126i	$-0.685972\pi$
$151$	−1.29008	+	0.744830i	−0.104985	+	0.0606134i	0.446588	+	0.894740i	$0.352639\pi$
$152$	4.35877	+	0.0337967i	0.353543	+	0.00274127i
$153$	0.885149	−	1.39112i	0.0715601	−	0.112466i
$154$	−3.89752	−	0.774760i	−0.314071	−	0.0624319i
$155$	0.761028	+	1.31814i	0.0611272	+	0.105875i
$156$	−0.527360	+	0.129200i	−0.0422226	+	0.0103443i
$157$	−6.32409	+	10.9536i	−0.504718	+	0.874196i	0.495268	+	0.868740i	$0.335070\pi$
$157$	−6.32409	+	10.9536i	−0.504718	+	0.874196i	−0.999985	+	0.00545593i	$0.998263\pi$
$158$			5.37959i			0.427978i
$159$	−13.5952	+	13.0218i	−1.07817	+	1.03270i
$160$			1.95673i			0.154693i
$161$	−8.72739	−	1.73485i	−0.687815	−	0.136726i
$162$	−8.96662	−	0.774374i	−0.704485	−	0.0608406i
$163$	4.20038	−	7.27527i	0.328999	−	0.569843i	−0.653314	−	0.757087i	$-0.726622\pi$
$163$	4.20038	−	7.27527i	0.328999	−	0.569843i	0.982314	+	0.187243i	$0.0599553\pi$
$164$	−2.41328	−	4.17992i	−0.188445	−	0.326397i
$165$	−4.88736	−	1.42305i	−0.380481	−	0.110785i
$166$		−	11.1431i		−	0.864876i
$167$	2.00846	−	3.47875i	0.155419	−	0.269194i	−0.777792	−	0.628521i	$-0.783661\pi$
$167$	2.00846	−	3.47875i	0.155419	−	0.269194i	0.933212	+	0.359327i	$0.116994\pi$
$168$	4.57813	−	0.201741i	0.353211	−	0.0155647i
$169$	−6.45087	−	11.1732i	−0.496220	−	0.859479i
$170$	−0.537725	+	0.931367i	−0.0412416	+	0.0714326i
$171$	0.664371	−	13.0598i	0.0508057	−	0.998709i
$172$	−2.59988	−	4.50313i	−0.198239	−	0.343361i
$173$	12.9114			0.981639			0.490820	−	0.871261i	$-0.336697\pi$
$173$	12.9114			0.981639			0.490820	+	0.871261i	$0.336697\pi$
$174$	−0.943281	−	3.85021i	−0.0715100	−	0.291884i
$175$	2.33003	+	2.04287i	0.176134	+	0.154426i
$176$	−1.30073	+	0.750974i	−0.0980459	+	0.0566068i
$177$	−4.37440	−	17.8551i	−0.328800	−	1.34207i
$178$	−2.48533	−	4.30472i	−0.186284	−	0.322653i
$179$	7.29410	+	12.6337i	0.545186	+	0.944291i	0.998595	+	0.0529880i	$0.0168745\pi$
$179$	7.29410	+	12.6337i	0.545186	+	0.944291i	−0.453409	+	0.891303i	$0.649792\pi$
$180$	5.86473	+	0.252774i	0.437131	+	0.0188407i
$181$	14.2653	+	8.23605i	1.06033	+	0.612181i	0.925523	−	0.378692i	$-0.123626\pi$
$181$	14.2653	+	8.23605i	1.06033	+	0.612181i	0.134805	+	0.990872i	$0.456959\pi$
$182$	−0.266693	−	0.785330i	−0.0197686	−	0.0582126i
$183$	17.5225	+	5.10202i	1.29530	+	0.377152i
$184$	−2.91260	+	1.68159i	−0.214720	+	0.123969i
$185$	2.51395	−	4.35428i	0.184829	−	0.320133i
$186$	0.376649	−	1.29357i	0.0276173	−	0.0948492i
$187$	−0.825496			−0.0603663
$188$	−8.03262	+	4.63764i	−0.585839	+	0.338234i
$189$	−0.0132486	−	13.7477i	−0.000963691	−	1.00000i
$190$	−0.0661308	+	8.52891i	−0.00479764	+	0.618752i
$191$	−3.39473	−	1.95995i	−0.245634	−	0.141817i	0.372129	−	0.928181i	$-0.378628\pi$
$191$	−3.39473	−	1.95995i	−0.245634	−	0.141817i	−0.617764	+	0.786364i	$0.711961\pi$
$192$	1.25084	−	1.19809i	0.0902713	−	0.0864644i
$193$	−14.0560	−	8.11521i	−1.01177	−	0.584146i	−0.100061	−	0.994981i	$-0.531904\pi$
$193$	−14.0560	−	8.11521i	−1.01177	−	0.584146i	−0.911710	+	0.410835i	$0.865237\pi$
$194$	−2.00828	+	1.15948i	−0.144186	+	0.0832458i
$195$	−0.252810	−	1.03190i	−0.0181041	−	0.0738958i
$196$	0.915417	+	6.93989i	0.0653869	+	0.495706i
$197$			11.6882i			0.832752i	0.909192	+	0.416376i	$0.136700\pi$
$197$			11.6882i			0.832752i	−0.909192	+	0.416376i	$0.863300\pi$
$198$	2.08280	+	3.99557i	0.148018	+	0.283953i
$199$	−9.71269			−0.688515			−0.344257	−	0.938875i	$-0.611869\pi$
$199$	−9.71269			−0.688515			−0.344257	+	0.938875i	$0.611869\pi$
$200$	1.17123			0.0828181
$201$	−0.0235537	−	0.0245907i	−0.00166135	−	0.00173450i
$202$		−	2.01100i		−	0.141493i
$203$	5.73363	−	1.94710i	0.402422	−	0.136660i
$204$	0.924620	−	0.226527i	0.0647363	−	0.0158601i
$205$	8.17895	−	4.72212i	0.571243	−	0.329807i
$206$	2.37790	+	1.37288i	0.165676	+	0.0956532i
$207$	4.66384	+	8.94693i	0.324159	+	0.621855i
$208$	−0.271478	−	0.156738i	−0.0188236	−	0.0108678i
$209$	−5.69494	+	3.22936i	−0.393927	+	0.223380i
$210$	0.394752	+	8.95815i	0.0272405	+	0.618171i
$211$	−14.2681	+	8.23770i	−0.982257	+	0.567107i	−0.902951	−	0.429744i	$-0.858604\pi$
$211$	−14.2681	+	8.23770i	−0.982257	+	0.567107i	−0.0793065	+	0.996850i	$0.525271\pi$
$212$	−10.8689			−0.746477
$213$	−12.0686	−	3.51402i	−0.826928	−	0.240777i
$214$	−3.96645	+	6.87009i	−0.271141	+	0.469630i
$215$	8.81139	−	5.08726i	0.600932	−	0.346948i
$216$	−3.42934	−	3.90380i	−0.233337	−	0.265620i
$217$	2.01853	+	0.401248i	0.137026	+	0.0272385i
$218$	−13.8708	−	8.00830i	−0.939448	−	0.542390i
$219$	−3.09182	−	12.6199i	−0.208926	−	0.852776i
$220$	−1.46945	−	2.54516i	−0.0990703	−	0.171595i
$221$	−0.0861458	−	0.149209i	−0.00579479	−	0.0100369i
$222$	−4.32274	+	1.05905i	−0.290123	+	0.0710787i
$223$	15.6183	−	9.01722i	1.04588	−	0.603838i	0.124385	−	0.992234i	$-0.460304\pi$
$223$	15.6183	−	9.01722i	1.04588	−	0.603838i	0.921492	+	0.388396i	$0.126971\pi$
$224$	1.98940	+	1.74422i	0.132922	+	0.116540i
$225$	0.151301	−	3.51042i	0.0100868	−	0.234028i
$226$	−5.37956			−0.357843
$227$	1.16303	+	2.01443i	0.0771930	+	0.133702i	0.902038	−	0.431657i	$-0.142071\pi$
$227$	1.16303	+	2.01443i	0.0771930	+	0.133702i	−0.824845	+	0.565359i	$0.808738\pi$
$228$	5.49260	−	5.17990i	0.363756	−	0.343047i
$229$	−8.54257	+	14.7962i	−0.564509	+	0.977758i	0.432586	+	0.901593i	$0.357601\pi$
$229$	−8.54257	+	14.7962i	−0.564509	+	0.977758i	−0.997095	+	0.0761657i	$0.975732\pi$
$230$	−3.29041	−	5.69916i	−0.216963	−	0.375792i
$231$	−5.80339	+	3.70047i	−0.381835	+	0.243473i
$232$	1.14433	−	1.98204i	0.0751290	−	0.130127i
$233$		−	22.3373i		−	1.46337i	−0.681645	−	0.731683i	$-0.738735\pi$
$233$		−	22.3373i		−	1.46337i	0.681645	−	0.731683i	$-0.261265\pi$
$234$	−0.504848	+	0.793431i	−0.0330029	+	0.0518682i
$235$	−9.07458	−	15.7176i	−0.591960	−	1.02531i
$236$	5.30675	−	9.19155i	0.345440	−	0.598319i
$237$	6.44521	+	6.72899i	0.418662	+	0.437095i
$238$	0.467593	+	1.37692i	0.0303096	+	0.0892525i
$239$			1.32903i			0.0859679i	0.999076	+	0.0429840i	$0.0136864\pi$
$239$			1.32903i			0.0859679i	−0.999076	+	0.0429840i	$0.986314\pi$
$240$	2.34432	+	2.44754i	0.151326	+	0.157988i
$241$			3.11193i			0.200457i	0.994964	+	0.100229i	$0.0319574\pi$
$241$			3.11193i			0.200457i	−0.994964	+	0.100229i	$0.968043\pi$
$242$	−4.37208	+	7.57266i	−0.281048	+	0.486789i
$243$	−12.1435	+	9.77417i	−0.779009	+	0.627013i
$244$	5.26836	+	9.12507i	0.337272	+	0.584173i
$245$	−13.5795	+	1.79122i	−0.867559	+	0.114437i
$246$	−8.02651	−	2.33708i	−0.511752	−	0.149007i
$247$	−1.17801	−	0.692359i	−0.0749551	−	0.0440537i
$248$	0.673645	−	0.388929i	0.0427765	−	0.0246970i
$249$	−13.3504	−	13.9383i	−0.846050	−	0.883301i
$250$			12.0754i			0.763715i
$251$	11.6792	+	6.74302i	0.737187	+	0.425615i	0.821046	−	0.570862i	$-0.193391\pi$
$251$	11.6792	+	6.74302i	0.737187	+	0.425615i	−0.0838584	+	0.996478i	$0.526724\pi$
$252$	5.48479	−	5.73734i	0.345509	−	0.361418i
$253$	2.52566	−	4.37458i	0.158787	−	0.275027i
$254$	−4.02863	−	2.32593i	−0.252779	−	0.145942i
$255$	0.443251	+	1.80923i	0.0277575	+	0.113298i
$256$	1.00000			0.0625000
$257$	−7.18915	−	12.4520i	−0.448447	−	0.776733i	0.549838	−	0.835271i	$-0.314689\pi$
$257$	−7.18915	−	12.4520i	−0.448447	−	0.776733i	−0.998285	+	0.0585382i	$0.981356\pi$
$258$	−8.64717	−	2.51780i	−0.538349	−	0.156751i
$259$	−2.18607	−	6.43731i	−0.135836	−	0.399995i
$260$	0.306693	−	0.531208i	0.0190203	−	0.0329441i
$261$	−5.79277	−	3.68585i	−0.358564	−	0.228148i
$262$			7.46944i			0.461464i
$263$	16.5452	+	9.55236i	1.02022	+	0.589024i	0.914167	−	0.405337i	$-0.132846\pi$
$263$	16.5452	+	9.55236i	1.02022	+	0.589024i	0.106052	+	0.994361i	$0.466179\pi$
$264$	−0.727263	+	2.49773i	−0.0447599	+	0.153724i
$265$		−	21.2674i		−	1.30645i
$266$	8.61238	+	7.66987i	0.528059	+	0.470270i
$267$	−8.26617	−	2.40686i	−0.505882	−	0.147298i
$268$		−	0.0196594i		−	0.00120089i
$269$	12.1012	−	20.9598i	0.737820	−	1.27794i	−0.215655	−	0.976470i	$-0.569189\pi$
$269$	12.1012	−	20.9598i	0.737820	−	1.27794i	0.953475	−	0.301472i	$-0.0974781\pi$
$270$	7.63866	−	6.71027i	0.464874	−	0.408374i
$271$	1.17805			0.0715614			0.0357807	−	0.999360i	$-0.488608\pi$
$271$	1.17805			0.0715614			0.0357807	+	0.999360i	$0.488608\pi$
$272$	0.475982	+	0.274809i	0.0288607	+	0.0166627i
$273$	−1.27448	−	0.662798i	−0.0771352	−	0.0401144i
$274$			18.4646i			1.11549i
$275$	−1.52344	+	0.879560i	−0.0918670	+	0.0530394i
$276$	−1.62850	+	5.59294i	−0.0980240	+	0.336656i
$277$	−7.82530	−	13.5538i	−0.470177	−	0.814370i	0.529242	−	0.848471i	$-0.322477\pi$
$277$	−7.82530	−	13.5538i	−0.470177	−	0.814370i	−0.999418	+	0.0341010i	$0.989143\pi$
$278$	9.32549	−	16.1522i	0.559306	−	0.968746i
$279$	−1.07868	−	2.06930i	−0.0645790	−	0.123886i
$280$	−3.41295	+	3.89271i	−0.203963	+	0.232634i
$281$	−6.14057	+	10.6358i	−0.366316	+	0.634477i	−0.988986	−	0.148007i	$-0.952714\pi$
$281$	−6.14057	+	10.6358i	−0.366316	+	0.634477i	0.622671	+	0.782484i	$0.286048\pi$
$282$	−4.49121	+	15.4247i	−0.267448	+	0.918527i
$283$	5.27388	−	9.13462i	0.313499	−	0.542997i	−0.665618	−	0.746293i	$-0.731832\pi$
$283$	5.27388	−	9.13462i	0.313499	−	0.542997i	0.979117	+	0.203296i	$0.0651653\pi$
$284$	−3.62859	−	6.28490i	−0.215317	−	0.372940i
$285$	10.1356	+	10.7475i	0.600384	+	0.636627i
$286$	0.470824			0.0278404
$287$	2.48971	−	12.5248i	0.146963	−	0.739316i
$288$	0.129182	−	2.99722i	0.00761213	−	0.176613i
$289$	−8.34896	−	14.4608i	−0.491115	−	0.850637i
$290$	3.87830	+	2.23914i	0.227742	+	0.131487i
$291$	−1.12287	+	3.85641i	−0.0658239	+	0.226067i
$292$	3.75080	−	6.49658i	0.219499	−	0.380183i
$293$	17.7163			1.03500			0.517499	−	0.855684i	$-0.326863\pi$
$293$	17.7163			1.03500			0.517499	+	0.855684i	$0.326863\pi$
$294$	9.45961	+	7.58391i	0.551696	+	0.442303i
$295$	17.9853	+	10.3838i	1.04715	+	0.604571i
$296$	−2.22529	−	1.28477i	−0.129342	−	0.0746758i
$297$	7.39228	+	2.50243i	0.428943	+	0.145206i
$298$			12.4115i			0.718978i
$299$	1.05428			0.0609704
$300$	1.46501	−	1.40323i	0.0845824	−	0.0810154i
$301$	2.68223	−	13.4933i	0.154601	−	0.777740i
$302$	−1.29008	+	0.744830i	−0.0742360	+	0.0428601i
$303$	−2.40935	−	2.51543i	−0.138413	−	0.144508i
$304$	4.35877	+	0.0337967i	0.249992	+	0.00193837i
$305$	−17.8553	+	10.3087i	−1.02239	+	0.590277i
$306$	0.885149	−	1.39112i	0.0506006	−	0.0795252i
$307$	19.8389	−	11.4540i	1.13227	−	0.653714i	0.187762	−	0.982215i	$-0.439877\pi$
$307$	19.8389	−	11.4540i	1.13227	−	0.653714i	0.944504	+	0.328501i	$0.106543\pi$
$308$	−3.89752	−	0.774760i	−0.222082	−	0.0441460i
$309$	4.61919	−	1.13168i	0.262777	−	0.0643789i
$310$	0.761028	+	1.31814i	0.0432235	+	0.0748652i
$311$	5.09596	−	2.94215i	0.288965	−	0.166834i	−0.348510	−	0.937305i	$-0.613312\pi$
$311$	5.09596	−	2.94215i	0.288965	−	0.166834i	0.637475	+	0.770471i	$0.279979\pi$
$312$	−0.527360	+	0.129200i	−0.0298559	+	0.00731453i
$313$	12.8827	+	22.3136i	0.728176	+	1.26124i	0.957654	+	0.287923i	$0.0929648\pi$
$313$	12.8827	+	22.3136i	0.728176	+	1.26124i	−0.229478	+	0.973314i	$0.573702\pi$
$314$	−6.32409	+	10.9536i	−0.356889	+	0.618150i
$315$	11.2264	+	10.7322i	0.632536	+	0.604693i
$316$			5.37959i			0.302626i
$317$	−6.16700	−	10.6816i	−0.346373	−	0.599936i	0.639229	−	0.769016i	$-0.279254\pi$
$317$	−6.16700	−	10.6816i	−0.346373	−	0.599936i	−0.985602	+	0.169080i	$0.945920\pi$
$318$	−13.5952	+	13.0218i	−0.762379	+	0.730228i
$319$			3.43745i			0.192460i
$320$			1.95673i			0.109384i
$321$	3.26958	+	13.3455i	0.182490	+	0.744873i
$322$	−8.72739	−	1.73485i	−0.486358	−	0.0966795i
$323$	2.06541	+	1.21391i	0.114922	+	0.0675439i
$324$	−8.96662	−	0.774374i	−0.498146	−	0.0430208i
$325$	−0.317962	−	0.183575i	−0.0176373	−	0.0101829i
$326$	4.20038	−	7.27527i	0.232638	−	0.402940i
$327$	−26.9447	+	6.60131i	−1.49004	+	0.365053i
$328$	−2.41328	−	4.17992i	−0.133251	−	0.230797i
$329$	−24.0691	−	4.78452i	−1.32697	−	0.263779i
$330$	−4.88736	−	1.42305i	−0.269041	−	0.0783366i
$331$	29.1242	+	16.8149i	1.60081	+	0.924228i	0.991325	+	0.131430i	$0.0419570\pi$
$331$	29.1242	+	16.8149i	1.60081	+	0.924228i	0.609485	+	0.792798i	$0.291376\pi$
$332$		−	11.1431i		−	0.611560i
$333$	−4.13821	+	6.50371i	−0.226772	+	0.356401i
$334$	2.00846	−	3.47875i	0.109898	−	0.190349i
$335$	0.0384681			0.00210174
$336$	4.57813	−	0.201741i	0.249758	−	0.0110059i
$337$	24.8299	−	14.3355i	1.35257	−	0.780906i	0.363960	−	0.931415i	$-0.381425\pi$
$337$	24.8299	−	14.3355i	1.35257	−	0.780906i	0.988609	+	0.150509i	$0.0480912\pi$
$338$	−6.45087	−	11.1732i	−0.350881	−	0.607744i
$339$	−6.72895	+	6.44517i	−0.365466	+	0.350054i
$340$	−0.537725	+	0.931367i	−0.0291622	+	0.0505105i
$341$	−0.584152	+	1.01178i	−0.0316336	+	0.0547910i
$342$	0.664371	−	13.0598i	0.0359251	−	0.706194i
$343$	−10.2835	+	15.4029i	−0.555259	+	0.831678i
$344$	−2.59988	−	4.50313i	−0.140176	−	0.242793i
$345$	−10.9439	−	3.18652i	−0.589197	−	0.171557i
$346$	12.9114			0.694124
$347$	28.4078	+	16.4013i	1.52501	+	0.880466i	0.999561	+	0.0296431i	$0.00943709\pi$
$347$	28.4078	+	16.4013i	1.52501	+	0.880466i	0.525452	+	0.850823i	$0.323896\pi$
$348$	−0.943281	−	3.85021i	−0.0505652	−	0.206393i
$349$	21.2969			1.13999			0.569997	−	0.821646i	$-0.306944\pi$
$349$	21.2969			1.13999			0.569997	+	0.821646i	$0.306944\pi$
$350$	2.33003	+	2.04287i	0.124546	+	0.109196i
$351$	0.319116	+	1.59730i	0.0170332	+	0.0852577i
$352$	−1.30073	+	0.750974i	−0.0693289	+	0.0400271i
$353$	−30.2002	+	17.4361i	−1.60740	+	0.928031i	−0.617446	+	0.786613i	$0.711833\pi$
$353$	−30.2002	+	17.4361i	−1.60740	+	0.928031i	−0.989950	+	0.141418i	$0.954834\pi$
$354$	−4.37440	−	17.8551i	−0.232497	−	0.948986i
$355$	12.2978	−	7.10015i	0.652700	−	0.376837i
$356$	−2.48533	−	4.30472i	−0.131722	−	0.228150i
$357$	2.23455	+	1.16208i	0.118265	+	0.0615040i
$358$	7.29410	+	12.6337i	0.385505	+	0.667714i
$359$		−	0.162502i		−	0.00857655i	−0.999991	−	0.00428827i	$-0.998635\pi$
$359$		−	0.162502i		−	0.00857655i	0.999991	−	0.00428827i	$-0.00136500\pi$
$360$	5.86473	+	0.252774i	0.309099	+	0.0133224i
$361$	18.9977	+	0.294624i	0.999880	+	0.0155065i
$362$	14.2653	+	8.23605i	0.749765	+	0.432877i
$363$	3.60394	+	14.7103i	0.189158	+	0.772089i
$364$	−0.266693	−	0.785330i	−0.0139785	−	0.0411625i
$365$	12.7120	+	7.33929i	0.665377	+	0.384156i
$366$	17.5225	+	5.10202i	0.915914	+	0.266687i
$367$	26.1704			1.36608			0.683041	−	0.730380i	$-0.260657\pi$
$367$	26.1704			1.36608			0.683041	+	0.730380i	$0.260657\pi$
$368$	−2.91260	+	1.68159i	−0.151830	+	0.0876590i
$369$	−12.8399	+	6.69315i	−0.668417	+	0.348431i
$370$	2.51395	−	4.35428i	0.130694	−	0.226368i
$371$	−21.6225	−	18.9577i	−1.12258	−	0.984233i
$372$	0.376649	−	1.29357i	0.0195284	−	0.0670685i
$373$	−27.3424	−	15.7862i	−1.41574	−	0.817376i	−0.419816	−	0.907609i	$-0.637905\pi$
$373$	−27.3424	−	15.7862i	−1.41574	−	0.817376i	−0.995921	+	0.0902333i	$0.971239\pi$
$374$	−0.825496			−0.0426854
$375$	14.4674	+	15.1043i	0.747091	+	0.779985i
$376$	−8.03262	+	4.63764i	−0.414251	+	0.239168i
$377$	−0.621321	+	0.358720i	−0.0319996	+	0.0184750i
$378$	−0.0132486	−	13.7477i	−0.000681433	−	0.707106i
$379$		−	31.9663i		−	1.64200i	−0.570930	−	0.820998i	$-0.693417\pi$
$379$		−	31.9663i		−	1.64200i	0.570930	−	0.820998i	$-0.306583\pi$
$380$	−0.0661308	+	8.52891i	−0.00339244	+	0.437524i
$381$	−7.82582	+	1.91728i	−0.400929	+	0.0982254i
$382$	−3.39473	−	1.95995i	−0.173690	−	0.100280i
$383$	27.2778			1.39383			0.696916	−	0.717153i	$-0.254555\pi$
$383$	27.2778			1.39383			0.696916	+	0.717153i	$0.254555\pi$
$384$	1.25084	−	1.19809i	0.0638315	−	0.0611395i
$385$	1.51599	−	7.62638i	0.0772621	−	0.388676i
$386$	−14.0560	−	8.11521i	−0.715430	−	0.413054i
$387$	−13.8327	+	7.21069i	−0.703157	+	0.366540i
$388$	−2.00828	+	1.15948i	−0.101955	+	0.0588637i
$389$		−	15.9491i		−	0.808652i	−0.914615	−	0.404326i	$-0.867506\pi$
$389$		−	15.9491i		−	0.808652i	0.914615	−	0.404326i	$-0.132494\pi$
$390$	−0.252810	−	1.03190i	−0.0128015	−	0.0522522i
$391$	−1.84846			−0.0934808
$392$	0.915417	+	6.93989i	0.0462355	+	0.350517i
$393$	8.94903	+	9.34305i	0.451419	+	0.471294i
$394$			11.6882i			0.588845i
$395$	−10.5264			−0.529640
$396$	2.08280	+	3.99557i	0.104665	+	0.200785i
$397$	−33.3555			−1.67407			−0.837033	−	0.547152i	$-0.815712\pi$
$397$	−33.3555			−1.67407			−0.837033	+	0.547152i	$0.815712\pi$
$398$	−9.71269			−0.486853
$399$	19.9618	−	0.724616i	0.999342	−	0.0362762i
$400$	1.17123			0.0585613
$401$	21.5973			1.07852			0.539259	−	0.842140i	$-0.318704\pi$
$401$	21.5973			1.07852			0.539259	+	0.842140i	$0.318704\pi$
$402$	−0.0235537	−	0.0245907i	−0.00117475	−	0.00122647i
$403$	−0.243840			−0.0121465
$404$		−	2.01100i		−	0.100051i
$405$	1.51524	−	17.5452i	0.0752927	−	0.871829i
$406$	5.73363	−	1.94710i	0.284555	−	0.0966332i
$407$	3.85932			0.191299
$408$	0.924620	−	0.226527i	0.0457755	−	0.0112148i
$409$			37.5808i			1.85825i	0.369765	+	0.929125i	$0.379438\pi$
$409$			37.5808i			1.85825i	−0.369765	+	0.929125i	$0.620562\pi$
$410$	8.17895	−	4.72212i	0.403930	−	0.233209i
$411$	22.1222	+	23.0962i	1.09121	+	1.13925i
$412$	2.37790	+	1.37288i	0.117151	+	0.0676370i
$413$	26.5893	−	9.02955i	1.30837	−	0.444315i
$414$	4.66384	+	8.94693i	0.229215	+	0.439718i
$415$	21.8041			1.07032
$416$	−0.271478	−	0.156738i	−0.0133103	−	0.00768471i
$417$	−7.68708	−	31.3765i	−0.376438	−	1.53651i
$418$	−5.69494	+	3.22936i	−0.278549	+	0.157953i
$419$			11.3105i			0.552555i	0.961078	+	0.276277i	$0.0891009\pi$
$419$			11.3105i			0.552555i	−0.961078	+	0.276277i	$0.910899\pi$
$420$	0.394752	+	8.95815i	0.0192619	+	0.437113i
$421$	0.322455	−	0.186169i	0.0157155	−	0.00907334i	−0.492122	−	0.870526i	$-0.663778\pi$
$421$	0.322455	−	0.186169i	0.0157155	−	0.00907334i	0.507837	+	0.861453i	$0.330445\pi$
$422$	−14.2681	+	8.23770i	−0.694561	+	0.401005i
$423$	12.8623	+	24.6746i	0.625388	+	1.19972i
$424$	−10.8689			−0.527839
$425$	0.557482	+	0.321863i	0.0270419	+	0.0156126i
$426$	−12.0686	−	3.51402i	−0.584726	−	0.170255i
$427$	−5.43523	+	27.3426i	−0.263029	+	1.32320i
$428$	−3.96645	+	6.87009i	−0.191726	+	0.332078i
$429$	0.588924	−	0.564088i	0.0284335	−	0.0272344i
$430$	8.81139	−	5.08726i	0.424923	−	0.245329i
$431$	−9.42562			−0.454016			−0.227008	−	0.973893i	$-0.572894\pi$
$431$	−9.42562			−0.454016			−0.227008	+	0.973893i	$0.572894\pi$
$432$	−3.42934	−	3.90380i	−0.164994	−	0.187822i
$433$	−20.0799	−	11.5932i	−0.964980	−	0.557131i	−0.0672776	−	0.997734i	$-0.521431\pi$
$433$	−20.0799	−	11.5932i	−0.964980	−	0.557131i	−0.897702	+	0.440603i	$0.854765\pi$
$434$	2.01853	+	0.401248i	0.0968923	+	0.0192605i
$435$	7.53380	−	1.84574i	0.361218	−	0.0884966i
$436$	−13.8708	−	8.00830i	−0.664290	−	0.383528i
$437$	−12.7522	+	7.23123i	−0.610020	+	0.345917i
$438$	−3.09182	−	12.6199i	−0.147733	−	0.603004i
$439$		−	0.422976i		−	0.0201875i	−0.999949	−	0.0100938i	$-0.996787\pi$
$439$		−	0.422976i		−	0.0201875i	0.999949	−	0.0100938i	$-0.00321300\pi$
$440$	−1.46945	−	2.54516i	−0.0700533	−	0.121336i
$441$	20.9186	−	1.84719i	0.996124	−	0.0879616i
$442$	−0.0861458	−	0.149209i	−0.00409754	−	0.00709714i
$443$	23.2671	−	13.4333i	1.10546	−	0.638235i	0.167807	−	0.985820i	$-0.446331\pi$
$443$	23.2671	−	13.4333i	1.10546	−	0.638235i	0.937649	+	0.347585i	$0.112998\pi$
$444$	−4.32274	+	1.05905i	−0.205148	+	0.0502602i
$445$	8.42316	−	4.86312i	0.399296	−	0.230534i
$446$	15.6183	−	9.01722i	0.739547	−	0.426978i
$447$	14.8700	+	15.5247i	0.703328	+	0.734295i
$448$	1.98940	+	1.74422i	0.0939903	+	0.0824065i
$449$	13.5101			0.637581			0.318790	−	0.947825i	$-0.396723\pi$
$449$	13.5101			0.637581			0.318790	+	0.947825i	$0.396723\pi$
$450$	0.151301	−	3.51042i	0.00713241	−	0.165483i
$451$	6.27802	+	3.62462i	0.295620	+	0.170677i
$452$	−5.37956			−0.253033
$453$	−0.721313	+	2.47729i	−0.0338902	+	0.116393i
$454$	1.16303	+	2.01443i	0.0545837	+	0.0945417i
$455$	1.53668	−	0.521845i	0.0720405	−	0.0244645i
$456$	5.49260	−	5.17990i	0.257214	−	0.242571i
$457$	−19.9506	+	34.5555i	−0.933251	+	1.61644i	−0.155528	+	0.987832i	$0.549708\pi$
$457$	−19.9506	+	34.5555i	−0.933251	+	1.61644i	−0.777723	+	0.628607i	$0.783626\pi$
$458$	−8.54257	+	14.7962i	−0.399168	+	0.691380i
$459$	−0.559507	−	2.80055i	−0.0261155	−	0.130718i
$460$	−3.29041	−	5.69916i	−0.153416	−	0.265725i
$461$	15.6780	−	9.05172i	0.730199	−	0.421580i	−0.0882961	−	0.996094i	$-0.528142\pi$
$461$	15.6780	−	9.05172i	0.730199	−	0.421580i	0.818495	+	0.574514i	$0.194809\pi$
$462$	−5.80339	+	3.70047i	−0.269998	+	0.172161i
$463$	−12.9235			−0.600606			−0.300303	−	0.953844i	$-0.597088\pi$
$463$	−12.9235			−0.600606			−0.300303	+	0.953844i	$0.597088\pi$
$464$	1.14433	−	1.98204i	0.0531242	−	0.0920138i
$465$	2.53116	+	0.736999i	0.117380	+	0.0341775i
$466$		−	22.3373i		−	1.03476i
$467$	−5.81673	−	3.35829i	−0.269166	−	0.155403i	0.359342	−	0.933206i	$-0.383001\pi$
$467$	−5.81673	−	3.35829i	−0.269166	−	0.155403i	−0.628509	+	0.777803i	$0.716334\pi$
$468$	−0.504848	+	0.793431i	−0.0233366	+	0.0366763i
$469$	0.0342903	−	0.0391105i	0.00158338	−	0.00180595i
$470$	−9.07458	−	15.7176i	−0.418579	−	0.725000i
$471$	5.21301	+	21.2780i	0.240203	+	0.980440i
$472$	5.30675	−	9.19155i	0.244263	−	0.423076i
$473$	6.76347	+	3.90489i	0.310985	+	0.179547i
$474$	6.44521	+	6.72899i	0.296038	+	0.309073i
$475$	5.10510	+	0.0395835i	0.234238	+	0.00181622i
$476$	0.467593	+	1.37692i	0.0214321	+	0.0631110i
$477$	−1.40406	+	32.5764i	−0.0642877	+	1.49157i
$478$			1.32903i			0.0607885i
$479$		−	16.3658i		−	0.747772i	−0.927475	−	0.373886i	$-0.878025\pi$
$479$		−	16.3658i		−	0.747772i	0.927475	−	0.373886i	$-0.121975\pi$
$480$	2.34432	+	2.44754i	0.107003	+	0.111715i
$481$	0.402745	+	0.697574i	0.0183636	+	0.0318066i
$482$			3.11193i			0.141745i
$483$	−12.9950	+	8.28614i	−0.591295	+	0.377032i
$484$	−4.37208	+	7.57266i	−0.198731	+	0.344212i
$485$	−2.26879	−	3.92965i	−0.103020	−	0.178436i
$486$	−12.1435	+	9.77417i	−0.550842	+	0.443365i
$487$	−21.2291	+	12.2567i	−0.961984	+	0.555402i	−0.896783	−	0.442470i	$-0.854102\pi$
$487$	−21.2291	+	12.2567i	−0.961984	+	0.555402i	−0.0652012	+	0.997872i	$0.520769\pi$
$488$	5.26836	+	9.12507i	0.238488	+	0.413073i
$489$	−3.46241	−	14.1326i	−0.156576	−	0.639098i
$490$	−13.5795	+	1.79122i	−0.613457	+	0.0809191i
$491$	28.4824	−	16.4443i	1.28539	−	0.742121i	0.307563	−	0.951528i	$-0.400486\pi$
$491$	28.4824	−	16.4443i	1.28539	−	0.742121i	0.977829	+	0.209406i	$0.0671531\pi$
$492$	−8.02651	−	2.33708i	−0.361863	−	0.105364i
$493$	1.08936	−	0.628943i	0.0490624	−	0.0283262i
$494$	−1.17801	−	0.692359i	−0.0530013	−	0.0311507i
$495$	−7.81823	+	4.07547i	−0.351403	+	0.183179i
$496$	0.673645	−	0.388929i	0.0302476	−	0.0174634i
$497$	3.74351	−	18.8322i	0.167920	−	0.844740i
$498$	−13.3504	−	13.9383i	−0.598248	−	0.624588i
$499$	−0.387635			−0.0173529			−0.00867645	−	0.999962i	$-0.502762\pi$
$499$	−0.387635			−0.0173529			−0.00867645	+	0.999962i	$0.502762\pi$
$500$			12.0754i			0.540028i
$501$	−1.65559	−	6.75765i	−0.0739662	−	0.301909i
$502$	11.6792	+	6.74302i	0.521270	+	0.300956i
$503$	8.62901	+	4.98196i	0.384749	+	0.222135i	0.679882	−	0.733321i	$-0.262031\pi$
$503$	8.62901	+	4.98196i	0.384749	+	0.222135i	−0.295134	+	0.955456i	$0.595364\pi$
$504$	5.48479	−	5.73734i	0.244312	−	0.255561i
$505$	3.93497			0.175104
$506$	2.52566	−	4.37458i	0.112279	−	0.194474i
$507$	−21.4555	−	6.24719i	−0.952870	−	0.277447i
$508$	−4.02863	−	2.32593i	−0.178741	−	0.103196i
$509$	17.8665	+	30.9457i	0.791920	+	1.37165i	0.924777	+	0.380510i	$0.124252\pi$
$509$	17.8665	+	30.9457i	0.791920	+	1.37165i	−0.132857	+	0.991135i	$0.542415\pi$
$510$	0.443251	+	1.80923i	0.0196275	+	0.0801139i
$511$	18.7933	−	6.38207i	0.831365	−	0.282326i
$512$	1.00000			0.0441942
$513$	−14.8157	−	17.1317i	−0.654131	−	0.756381i
$514$	−7.18915	−	12.4520i	−0.317100	−	0.549233i
$515$	−2.68635	+	4.65290i	−0.118375	+	0.205031i
$516$	−8.64717	−	2.51780i	−0.380670	−	0.110840i
$517$	6.96549	−	12.0646i	0.306342	−	0.530600i
$518$	−2.18607	−	6.43731i	−0.0960503	−	0.282839i
$519$	16.1501	−	15.4690i	0.708911	−	0.679015i
$520$	0.306693	−	0.531208i	0.0134494	−	0.0232950i
$521$	−20.7756	−	35.9843i	−0.910193	−	1.57650i	−0.813790	−	0.581159i	$-0.802599\pi$
$521$	−20.7756	−	35.9843i	−0.910193	−	1.57650i	−0.0964033	−	0.995342i	$-0.530734\pi$
$522$	−5.79277	−	3.68585i	−0.253543	−	0.161325i
$523$	6.35263	−	3.66769i	0.277781	−	0.160377i	−0.354637	−	0.935004i	$-0.615396\pi$
$523$	6.35263	−	3.66769i	0.277781	−	0.160377i	0.632418	+	0.774627i	$0.282062\pi$
$524$			7.46944i			0.326304i
$525$	5.36202	−	0.236284i	0.234018	−	0.0103123i
$526$	16.5452	+	9.55236i	0.721404	+	0.416503i
$527$	0.427524			0.0186232
$528$	−0.727263	+	2.49773i	−0.0316501	+	0.108700i
$529$	−5.84450	+	10.1230i	−0.254109	+	0.440129i
$530$		−	21.2674i		−	0.923796i
$531$	−26.8635	−	17.0929i	−1.16578	−	0.741767i
$532$	8.61238	+	7.66987i	0.373394	+	0.332531i
$533$			1.51301i			0.0655356i
$534$	−8.26617	−	2.40686i	−0.357712	−	0.104155i
$535$	−13.4429	−	7.76125i	−0.581187	−	0.335548i
$536$		−	0.0196594i		−	0.000849159i
$537$	24.2600	+	7.06380i	1.04690	+	0.304825i
$538$	12.1012	−	20.9598i	0.521718	−	0.903642i
$539$	−6.40238	−	8.33943i	−0.275770	−	0.359205i
$540$	7.63866	−	6.71027i	0.328716	−	0.288764i
$541$	15.5065	+	26.8580i	0.666676	+	1.15472i	0.978828	+	0.204684i	$0.0656167\pi$
$541$	15.5065	+	26.8580i	0.666676	+	1.15472i	−0.312152	+	0.950032i	$0.601050\pi$
$542$	1.17805			0.0506016
$543$	27.7110	−	6.78905i	1.18919	−	0.291346i
$544$	0.475982	+	0.274809i	0.0204076	+	0.0117823i
$545$	15.6700	−	27.1413i	0.671231	−	1.16261i
$546$	−1.27448	−	0.662798i	−0.0545428	−	0.0283652i
$547$	−10.3141	−	5.95487i	−0.441001	−	0.254612i	0.263021	−	0.964790i	$-0.415281\pi$
$547$	−10.3141	−	5.95487i	−0.441001	−	0.254612i	−0.704022	+	0.710178i	$0.748614\pi$
$548$			18.4646i			0.788769i
$549$	28.0304	−	14.6116i	1.19631	−	0.623609i
$550$	−1.52344	+	0.879560i	−0.0649598	+	0.0375046i
$551$	5.05486	−	8.60057i	0.215344	−	0.366397i
$552$	−1.62850	+	5.59294i	−0.0693135	+	0.238051i
$553$	−9.38318	+	10.7022i	−0.399013	+	0.455102i
$554$	−7.82530	−	13.5538i	−0.332465	−	0.575847i
$555$	−2.07227	−	8.45841i	−0.0879628	−	0.359040i
$556$	9.32549	−	16.1522i	0.395489	−	0.685007i
$557$		−	18.9415i		−	0.802576i	−0.915952	−	0.401288i	$-0.868563\pi$
$557$		−	18.9415i		−	0.802576i	0.915952	−	0.401288i	$-0.131437\pi$
$558$	−1.07868	−	2.06930i	−0.0456643	−	0.0876006i
$559$			1.63000i			0.0689417i
$560$	−3.41295	+	3.89271i	−0.144224	+	0.164497i
$561$	−1.03256	+	0.989015i	−0.0435947	+	0.0417563i
$562$	−6.14057	+	10.6358i	−0.259024	+	0.448643i
$563$	6.55163	+	11.3478i	0.276118	+	0.478251i	0.970417	−	0.241436i	$-0.0776185\pi$
$563$	6.55163	+	11.3478i	0.276118	+	0.478251i	−0.694298	+	0.719687i	$0.744285\pi$
$564$	−4.49121	+	15.4247i	−0.189114	+	0.649497i
$565$		−	10.5263i		−	0.442846i
$566$	5.27388	−	9.13462i	0.221678	−	0.383957i
$567$	−16.4875	−	17.1803i	−0.692411	−	0.721504i
$568$	−3.62859	−	6.28490i	−0.152252	−	0.263708i
$569$	0.848340	−	1.46937i	0.0355643	−	0.0615991i	−0.847695	−	0.530483i	$-0.822010\pi$
$569$	0.848340	−	1.46937i	0.0355643	−	0.0615991i	0.883260	+	0.468884i	$0.155344\pi$
$570$	10.1356	+	10.7475i	0.424536	+	0.450163i
$571$	−6.96161	−	12.0579i	−0.291334	−	0.504606i	0.682791	−	0.730614i	$-0.260766\pi$
$571$	−6.96161	−	12.0579i	−0.291334	−	0.504606i	−0.974126	+	0.226008i	$0.927433\pi$
$572$	0.470824			0.0196862
$573$	−6.59444	+	1.61560i	−0.275487	+	0.0674928i
$574$	2.48971	−	12.5248i	0.103919	−	0.522775i
$575$	−3.41131	+	1.96952i	−0.142262	+	0.0821348i
$576$	0.129182	−	2.99722i	0.00538259	−	0.124884i
$577$	4.56240	+	7.90232i	0.189935	+	0.328978i	0.945228	−	0.326409i	$-0.105839\pi$
$577$	4.56240	+	7.90232i	0.189935	+	0.328978i	−0.755293	+	0.655387i	$0.772505\pi$
$578$	−8.34896	−	14.4608i	−0.347271	−	0.601491i
$579$	−27.3044	+	6.68944i	−1.13473	+	0.278004i
$580$	3.87830	+	2.23914i	0.161038	+	0.0929752i
$581$	19.4361	−	22.1682i	0.806344	−	0.919690i
$582$	−1.12287	+	3.85641i	−0.0465445	+	0.159853i
$583$	14.1374	−	8.16224i	0.585512	−	0.338045i
$584$	3.75080	−	6.49658i	0.155209	−	0.268830i
$585$	−1.55253	−	0.987848i	−0.0641890	−	0.0408425i
$586$	17.7163			0.731854
$587$	−34.1873	+	19.7380i	−1.41106	+	0.814675i	−0.995488	−	0.0948856i	$-0.969751\pi$
$587$	−34.1873	+	19.7380i	−1.41106	+	0.814675i	−0.415571	+	0.909561i	$0.636418\pi$
$588$	9.45961	+	7.58391i	0.390108	+	0.312755i
$589$	2.94941	−	1.67249i	0.121528	−	0.0689136i
$590$	17.9853	+	10.3838i	0.740445	+	0.427496i
$591$	14.0035	+	14.6201i	0.576027	+	0.601389i
$592$	−2.22529	−	1.28477i	−0.0914588	−	0.0528038i
$593$	−3.21034	+	1.85349i	−0.131833	+	0.0761137i	−0.564466	−	0.825456i	$-0.690918\pi$
$593$	−3.21034	+	1.85349i	−0.131833	+	0.0761137i	0.432633	+	0.901570i	$0.357585\pi$
$594$	7.39228	+	2.50243i	0.303309	+	0.102676i
$595$	−2.69425	+	0.914952i	−0.110454	+	0.0375094i
$596$			12.4115i			0.508394i
$597$	−12.1490	+	11.6366i	−0.497225	+	0.476256i
$598$	1.05428			0.0431126
$599$	24.3438			0.994659			0.497330	−	0.867562i	$-0.334314\pi$
$599$	24.3438			0.994659			0.497330	+	0.867562i	$0.334314\pi$
$600$	1.46501	−	1.40323i	0.0598088	−	0.0572865i
$601$			27.1999i			1.10951i	0.832015	+	0.554754i	$0.187188\pi$
$601$			27.1999i			1.10951i	−0.832015	+	0.554754i	$0.812812\pi$
$602$	2.68223	−	13.4933i	0.109320	−	0.549945i
$603$	−0.0589236	−	0.00253965i	−0.00239956	−	0.000103423i
$604$	−1.29008	+	0.744830i	−0.0524927	+	0.0303067i
$605$	−14.8176	−	8.55495i	−0.602422	−	0.347808i
$606$	−2.40935	−	2.51543i	−0.0978730	−	0.102182i
$607$	−22.0425	−	12.7262i	−0.894677	−	0.516542i	−0.0192075	−	0.999816i	$-0.506114\pi$
$607$	−22.0425	−	12.7262i	−0.894677	−	0.516542i	−0.875469	+	0.483274i	$0.839448\pi$
$608$	4.35877	+	0.0337967i	0.176771	+	0.00137064i
$609$	4.83904	−	9.30489i	0.196088	−	0.377053i
$610$	−17.8553	+	10.3087i	−0.722938	+	0.417389i
$611$	2.90757			0.117628
$612$	0.885149	−	1.39112i	0.0357800	−	0.0562328i
$613$	−4.91744	+	8.51725i	−0.198613	+	0.344009i	−0.948079	−	0.318035i	$-0.896977\pi$
$613$	−4.91744	+	8.51725i	−0.198613	+	0.344009i	0.749466	+	0.662043i	$0.230310\pi$
$614$	19.8389	−	11.4540i	0.800633	−	0.462245i
$615$	4.57303	−	15.7057i	0.184402	−	0.633314i
$616$	−3.89752	−	0.774760i	−0.157036	−	0.0312160i
$617$	−2.42194	−	1.39831i	−0.0975035	−	0.0562937i	0.450455	−	0.892799i	$-0.351262\pi$
$617$	−2.42194	−	1.39831i	−0.0975035	−	0.0562937i	−0.547959	+	0.836505i	$0.684595\pi$
$618$	4.61919	−	1.13168i	0.185811	−	0.0455228i
$619$	−12.8156	−	22.1972i	−0.515101	−	0.892181i	−0.999846	−	0.0175258i	$-0.994421\pi$
$619$	−12.8156	−	22.1972i	−0.515101	−	0.892181i	0.484745	−	0.874655i	$-0.338912\pi$
$620$	0.761028	+	1.31814i	0.0305636	+	0.0529377i
$621$	16.5529	+	5.60347i	0.664245	+	0.224859i
$622$	5.09596	−	2.94215i	0.204329	−	0.117970i
$623$	2.56405	−	12.8988i	0.102727	−	0.516778i
$624$	−0.527360	+	0.129200i	−0.0211113	+	0.00517216i
$625$	−17.7721			−0.710884
$626$	12.8827	+	22.3136i	0.514898	+	0.891829i
$627$	−3.25439	+	10.8624i	−0.129968	+	0.433804i
$628$	−6.32409	+	10.9536i	−0.252359	+	0.437098i
$629$	−0.706132	−	1.22306i	−0.0281553	−	0.0487665i
$630$	11.2264	+	10.7322i	0.447270	+	0.427582i
$631$	−8.27255	+	14.3285i	−0.329325	+	0.570408i	−0.982378	−	0.186904i	$-0.940155\pi$
$631$	−8.27255	+	14.3285i	−0.329325	+	0.570408i	0.653053	+	0.757312i	$0.273488\pi$
$632$			5.37959i			0.213989i
$633$	−7.97760	+	27.3984i	−0.317081	+	1.08899i
$634$	−6.16700	−	10.6816i	−0.244923	−	0.424219i
$635$	4.55121	−	7.88292i	0.180609	−	0.312824i
$636$	−13.5952	+	13.0218i	−0.539084	+	0.516349i
$637$	0.839227	−	2.02751i	0.0332514	−	0.0803327i
$638$			3.43745i			0.136090i
$639$	−19.3059	+	10.0638i	−0.763732	+	0.398116i
$640$			1.95673i			0.0773464i
$641$	−15.4495	+	26.7593i	−0.610218	+	1.05693i	0.380985	+	0.924581i	$0.375585\pi$
$641$	−15.4495	+	26.7593i	−0.610218	+	1.05693i	−0.991203	+	0.132348i	$0.957749\pi$
$642$	3.26958	+	13.3455i	0.129040	+	0.526705i
$643$	15.6022	+	27.0237i	0.615289	+	1.06571i	0.990334	+	0.138706i	$0.0442942\pi$
$643$	15.6022	+	27.0237i	0.615289	+	1.06571i	−0.375044	+	0.927007i	$0.622372\pi$
$644$	−8.72739	−	1.73485i	−0.343907	−	0.0683628i
$645$	4.92664	−	16.9201i	0.193986	−	0.666229i
$646$	2.06541	+	1.21391i	0.0812624	+	0.0477608i
$647$	−4.74683	+	2.74059i	−0.186617	+	0.107744i	−0.590398	−	0.807112i	$-0.701029\pi$
$647$	−4.74683	+	2.74059i	−0.186617	+	0.107744i	0.403781	+	0.914856i	$0.367696\pi$
$648$	−8.96662	−	0.774374i	−0.352242	−	0.0304203i
$649$			15.9409i			0.625736i
$650$	−0.317962	−	0.183575i	−0.0124715	−	0.00720042i
$651$	3.00557	−	1.91647i	0.117798	−	0.0751124i
$652$	4.20038	−	7.27527i	0.164500	−	0.284922i
$653$	21.1965	+	12.2378i	0.829485	+	0.478903i	0.853676	−	0.520804i	$-0.174368\pi$
$653$	21.1965	+	12.2378i	0.829485	+	0.478903i	−0.0241916	+	0.999707i	$0.507701\pi$
$654$	−26.9447	+	6.60131i	−1.05362	+	0.258132i
$655$	−14.6157			−0.571081
$656$	−2.41328	−	4.17992i	−0.0942226	−	0.163198i
$657$	−18.9871	−	12.0812i	−0.740758	−	0.471333i
$658$	−24.0691	−	4.78452i	−0.938312	−	0.186520i
$659$	−12.4497	+	21.5636i	−0.484973	+	0.839997i	−0.999851	−	0.0172661i	$-0.994504\pi$
$659$	−12.4497	+	21.5636i	−0.484973	+	0.839997i	0.514878	+	0.857263i	$0.327837\pi$
$660$	−4.88736	−	1.42305i	−0.190240	−	0.0553923i
$661$			4.94347i			0.192279i	0.995368	+	0.0961393i	$0.0306494\pi$
$661$			4.94347i			0.192279i	−0.995368	+	0.0961393i	$0.969351\pi$
$662$	29.1242	+	16.8149i	1.13194	+	0.653528i
$663$	−0.286519	−	0.0834258i	−0.0111275	−	0.00323999i
$664$		−	11.1431i		−	0.432438i
$665$	−15.0078	+	16.8521i	−0.581979	+	0.653495i
$666$	−4.13821	+	6.50371i	−0.160352	+	0.252014i
$667$			7.69718i			0.298036i
$668$	2.00846	−	3.47875i	0.0777095	−	0.134597i
$669$	8.73251	−	29.9911i	0.337618	−	1.15952i
$670$	0.0384681			0.00148615
$671$	−13.7054	−	7.91281i	−0.529090	−	0.305471i
$672$	4.57813	−	0.201741i	0.176605	−	0.00778233i
$673$			28.1006i			1.08320i	0.840637	+	0.541599i	$0.182181\pi$
$673$			28.1006i			1.08320i	−0.840637	+	0.541599i	$0.817819\pi$
$674$	24.8299	−	14.3355i	0.956410	−	0.552184i
$675$	−4.01653	−	4.57223i	−0.154596	−	0.175985i
$676$	−6.45087	−	11.1732i	−0.248110	−	0.429740i
$677$	−11.7861	+	20.4141i	−0.452975	+	0.784576i	−0.998569	−	0.0534736i	$-0.982971\pi$
$677$	−11.7861	+	20.4141i	−0.452975	+	0.784576i	0.545594	+	0.838050i	$0.316304\pi$
$678$	−6.72895	+	6.44517i	−0.258424	+	0.247525i
$679$	−6.01765	−	1.19620i	−0.230936	−	0.0459061i
$680$	−0.537725	+	0.931367i	−0.0206208	+	0.0357163i
$681$	3.86821	+	1.12631i	0.148230	+	0.0431602i
$682$	−0.584152	+	1.01178i	−0.0223683	+	0.0387431i
$683$	4.70790	+	8.15433i	0.180143	+	0.312017i	0.941929	−	0.335812i	$-0.109011\pi$
$683$	4.70790	+	8.15433i	0.180143	+	0.312017i	−0.761786	+	0.647829i	$0.775677\pi$
$684$	0.664371	−	13.0598i	0.0254029	−	0.499354i
$685$	−36.1302			−1.38046
$686$	−10.2835	+	15.4029i	−0.392627	+	0.588085i
$687$	7.04172	+	28.7423i	0.268658	+	1.09659i
$688$	−2.59988	−	4.50313i	−0.0991196	−	0.171680i
$689$	2.95066	+	1.70356i	0.112411	+	0.0649006i
$690$	−10.9439	−	3.18652i	−0.416625	−	0.121309i
$691$	17.0115	−	29.4647i	0.647147	−	1.12089i	−0.336655	−	0.941628i	$-0.609295\pi$
$691$	17.0115	−	29.4647i	0.647147	−	1.12089i	0.983801	−	0.179263i	$-0.0573712\pi$
$692$	12.9114			0.490820
$693$	−2.82561	+	11.5816i	−0.107336	+	0.439950i
$694$	28.4078	+	16.4013i	1.07835	+	0.622584i
$695$	31.6055	+	18.2474i	1.19886	+	0.692164i
$696$	−0.943281	−	3.85021i	−0.0357550	−	0.145942i
$697$		−	2.65276i		−	0.100480i
$698$	21.2969			0.806098
$699$	−26.7620	−	27.9403i	−1.01223	−	1.05680i
$700$	2.33003	+	2.04287i	0.0880670	+	0.0772132i
$701$	−15.7654	+	9.10213i	−0.595449	+	0.343783i	−0.767249	−	0.641349i	$-0.778375\pi$
$701$	−15.7654	+	9.10213i	−0.595449	+	0.343783i	0.171800	+	0.985132i	$0.445042\pi$
$702$	0.319116	+	1.59730i	0.0120443	+	0.0602863i
$703$	−9.65610	−	5.67523i	−0.364187	−	0.214045i
$704$	−1.30073	+	0.750974i	−0.0490229	+	0.0283034i
$705$	−30.1819	−	8.78806i	−1.13672	−	0.330978i
$706$	−30.2002	+	17.4361i	−1.13660	+	0.656217i
$707$	3.50761	−	4.00067i	0.131917	−	0.150461i
$708$	−4.37440	−	17.8551i	−0.164400	−	0.671034i
$709$	0.796188	+	1.37904i	0.0299015	+	0.0517908i	0.880589	−	0.473881i	$-0.157147\pi$
$709$	0.796188	+	1.37904i	0.0299015	+	0.0517908i	−0.850687	+	0.525672i	$0.823814\pi$
$710$	12.2978	−	7.10015i	0.461529	−	0.266464i
$711$	16.1238	+	0.694948i	0.604690	+	0.0260626i
$712$	−2.48533	−	4.30472i	−0.0931418	−	0.161326i
$713$	−1.30804	+	2.26559i	−0.0489865	+	0.0848471i
$714$	2.23455	+	1.16208i	0.0836259	+	0.0434899i
$715$			0.921274i			0.0344537i
$716$	7.29410	+	12.6337i	0.272593	+	0.472145i
$717$	1.59229	+	1.66240i	0.0594653	+	0.0620835i
$718$		−	0.162502i		−	0.00606453i
$719$		−	37.3842i		−	1.39419i	−0.716976	−	0.697097i	$-0.754475\pi$
$719$		−	37.3842i		−	1.39419i	0.716976	−	0.697097i	$-0.245525\pi$
$720$	5.86473	+	0.252774i	0.218566	+	0.00942033i
$721$	2.33599	+	6.87878i	0.0869968	+	0.256179i
$722$	18.9977	+	0.294624i	0.707022	+	0.0109648i
$723$	3.72836	+	3.89252i	0.138659	+	0.144764i
$724$	14.2653	+	8.23605i	0.530164	+	0.306090i
$725$	1.34027	−	2.32141i	0.0497763	−	0.0862151i
$726$	3.60394	+	14.7103i	0.133755	+	0.545949i
$727$	13.5347	+	23.4428i	0.501975	+	0.869447i	0.999997	+	0.00228239i	$0.000726509\pi$
$727$	13.5347	+	23.4428i	0.501975	+	0.869447i	−0.498022	+	0.867164i	$0.665940\pi$
$728$	−0.266693	−	0.785330i	−0.00988431	−	0.0291063i
$729$	−3.47929	+	26.7749i	−0.128863	+	0.991662i
$730$	12.7120	+	7.33929i	0.470493	+	0.271639i
$731$		−	2.85788i		−	0.105703i
$732$	17.5225	+	5.10202i	0.647649	+	0.188576i
$733$	−7.71438	+	13.3617i	−0.284937	+	0.493526i	−0.972594	−	0.232510i	$-0.925306\pi$
$733$	−7.71438	+	13.3617i	−0.284937	+	0.493526i	0.687657	+	0.726036i	$0.258639\pi$
$734$	26.1704			0.965967
$735$	−14.8396	+	18.5099i	−0.547368	+	0.682747i
$736$	−2.91260	+	1.68159i	−0.107360	+	0.0619843i
$737$	0.0147637	+	0.0255715i	0.000543829	+	0.000941940i
$738$	−12.8399	+	6.69315i	−0.472642	+	0.246378i
$739$	−0.846179	+	1.46562i	−0.0311272	+	0.0539139i	−0.881169	−	0.472801i	$-0.843243\pi$
$739$	−0.846179	+	1.46562i	−0.0311272	+	0.0539139i	0.850042	+	0.526715i	$0.176576\pi$
$740$	2.51395	−	4.35428i	0.0924145	−	0.160067i
$741$	−2.30301	+	0.545332i	−0.0846030	+	0.0200333i
$742$	−21.6225	−	18.9577i	−0.793787	−	0.695957i
$743$	−3.56739	−	6.17890i	−0.130875	−	0.226682i	0.793139	−	0.609040i	$-0.208445\pi$
$743$	−3.56739	−	6.17890i	−0.130875	−	0.226682i	−0.924014	+	0.382359i	$0.875112\pi$
$744$	0.376649	−	1.29357i	0.0138086	−	0.0474246i
$745$	−24.2859			−0.889765
$746$	−27.3424	−	15.7862i	−1.00108	−	0.577972i
$747$	−33.3984	−	1.43950i	−1.22198	−	0.0526684i
$748$	−0.825496			−0.0301831
$749$	−19.8738	+	6.74901i	−0.726172	+	0.246603i
$750$	14.4674	+	15.1043i	0.528273	+	0.551532i
$751$	45.2485	−	26.1243i	1.65114	−	0.953288i	0.674540	−	0.738239i	$-0.264342\pi$
$751$	45.2485	−	26.1243i	1.65114	−	0.953288i	0.976603	−	0.215049i	$-0.0689912\pi$
$752$	−8.03262	+	4.63764i	−0.292920	+	0.169117i
$753$	22.6875	−	5.55833i	0.826780	−	0.202557i
$754$	−0.621321	+	0.358720i	−0.0226272	+	0.0130638i
$755$	−1.45743	−	2.52434i	−0.0530412	−	0.0918701i
$756$	−0.0132486	−	13.7477i	−0.000481846	−	0.500000i
$757$	−18.4898	−	32.0253i	−0.672023	−	1.16398i	−0.977330	−	0.211724i	$-0.932092\pi$
$757$	−18.4898	−	32.0253i	−0.672023	−	1.16398i	0.305307	−	0.952254i	$-0.401241\pi$
$758$		−	31.9663i		−	1.16107i
$759$	−2.08193	−	8.49784i	−0.0755692	−	0.308452i
$760$	−0.0661308	+	8.52891i	−0.00239882	+	0.309376i
$761$	−35.8953	−	20.7241i	−1.30120	−	0.751250i	−0.320592	−	0.947217i	$-0.603882\pi$
$761$	−35.8953	−	20.7241i	−1.30120	−	0.751250i	−0.980610	+	0.195967i	$0.937215\pi$
$762$	−7.82582	+	1.91728i	−0.283499	+	0.0694559i
$763$	−13.6263	−	40.1253i	−0.493305	−	1.45263i
$764$	−3.39473	−	1.95995i	−0.122817	−	0.0709085i
$765$	2.72204	+	1.73199i	0.0984157	+	0.0626204i
$766$	27.2778			0.985588
$767$	−2.88133	+	1.66354i	−0.104039	+	0.0600668i
$768$	1.25084	−	1.19809i	0.0451357	−	0.0432322i
$769$	−12.0411	+	20.8558i	−0.434213	+	0.752079i	−0.997231	−	0.0743659i	$-0.976307\pi$
$769$	−12.0411	+	20.8558i	−0.434213	+	0.752079i	0.563018	+	0.826444i	$0.309640\pi$
$770$	1.51599	−	7.62638i	0.0546326	−	0.274836i
$771$	−23.9110	−	6.96216i	−0.861133	−	0.250736i
$772$	−14.0560	−	8.11521i	−0.505885	−	0.292073i
$773$	−17.8425			−0.641749			−0.320875	−	0.947122i	$-0.603977\pi$
$773$	−17.8425			−0.641749			−0.320875	+	0.947122i	$0.603977\pi$
$774$	−13.8327	+	7.21069i	−0.497207	+	0.259183i
$775$	0.788990	−	0.455524i	0.0283414	−	0.0163629i
$776$	−2.00828	+	1.15948i	−0.0720930	+	0.0416229i
$777$	−10.4469	−	5.43292i	−0.374779	−	0.194905i
$778$		−	15.9491i		−	0.571803i
$779$	−10.3776	−	18.3009i	−0.371818	−	0.655696i
$780$	−0.252810	−	1.03190i	−0.00905204	−	0.0369479i
$781$	9.43959	+	5.44995i	0.337775	+	0.195015i
$782$	−1.84846			−0.0661009
$783$	−11.6618	+	2.32984i	−0.416758	+	0.0832617i
$784$	0.915417	+	6.93989i	0.0326935	+	0.247853i
$785$	−21.4333	−	12.3745i	−0.764987	−	0.441665i
$786$	8.94903	+	9.34305i	0.319201	+	0.333256i
$787$	−23.5571	+	13.6007i	−0.839719	+	0.484812i	−0.857169	−	0.515036i	$-0.827779\pi$
$787$	−23.5571	+	13.6007i	−0.839719	+	0.484812i	0.0174497	+	0.999848i	$0.494445\pi$
$788$			11.6882i			0.416376i
$789$	32.1398	−	7.87409i	1.14421	−	0.280325i
$790$	−10.5264			−0.374512
$791$	−10.7021	−	9.38312i	−0.380523	−	0.333625i
$792$	2.08280	+	3.99557i	0.0740092	+	0.141976i
$793$		−	3.30301i		−	0.117293i
$794$	−33.3555			−1.18374
$795$	−25.4802	−	26.6020i	−0.903688	−	0.943476i
$796$	−9.71269			−0.344257
$797$	37.0412			1.31207			0.656033	−	0.754732i	$-0.272233\pi$
$797$	37.0412			1.31207			0.656033	+	0.754732i	$0.272233\pi$
$798$	19.9618	−	0.724616i	0.706641	−	0.0256511i
$799$	−5.09785			−0.180349
$800$	1.17123			0.0414091
$801$	−13.2233	+	6.89299i	−0.467221	+	0.243552i
$802$	21.5973			0.762628
$803$			11.2670i			0.397604i
$804$	−0.0235537	−	0.0245907i	−0.000830675	−	0.000867249i
$805$	3.39463	−	17.0771i	0.119645	−	0.601889i
$806$	−0.243840			−0.00858889
$807$	−9.97509	−	40.7155i	−0.351140	−	1.43325i
$808$		−	2.01100i		−	0.0707466i
$809$	−23.5211	+	13.5799i	−0.826957	+	0.477444i	−0.852810	−	0.522222i	$-0.825103\pi$
$809$	−23.5211	+	13.5799i	−0.826957	+	0.477444i	0.0258527	+	0.999666i	$0.491770\pi$
$810$	1.51524	−	17.5452i	0.0532400	−	0.616476i
$811$	−25.2652	−	14.5869i	−0.887181	−	0.512214i	−0.0141613	−	0.999900i	$-0.504508\pi$
$811$	−25.2652	−	14.5869i	−0.887181	−	0.512214i	−0.873019	+	0.487686i	$0.837841\pi$
$812$	5.73363	−	1.94710i	0.201211	−	0.0683300i
$813$	1.47355	−	1.41140i	0.0516796	−	0.0495001i
$814$	3.85932			0.135269
$815$	14.2357	+	8.21899i	0.498655	+	0.287899i
$816$	0.924620	−	0.226527i	0.0323682	−	0.00793003i
$817$	−11.1801	−	19.7160i	−0.391142	−	0.689775i
$818$			37.5808i			1.31398i
$819$	−2.38826	+	0.697887i	−0.0834525	+	0.0243861i
$820$	8.17895	−	4.72212i	0.285621	−	0.164904i
$821$	11.9764	−	6.91456i	0.417978	−	0.241320i	−0.276234	−	0.961090i	$-0.589086\pi$
$821$	11.9764	−	6.91456i	0.417978	−	0.241320i	0.694212	+	0.719771i	$0.255753\pi$
$822$	22.1222	+	23.0962i	0.771600	+	0.805572i
$823$	11.1822			0.389786			0.194893	−	0.980824i	$-0.437564\pi$
$823$	11.1822			0.389786			0.194893	+	0.980824i	$0.437564\pi$
$824$	2.37790	+	1.37288i	0.0828381	+	0.0478266i
$825$	−0.851789	+	2.92540i	−0.0296555	+	0.101849i
$826$	26.5893	−	9.02955i	0.925160	−	0.314178i
$827$	−6.11154	+	10.5855i	−0.212519	+	0.368094i	−0.952502	−	0.304531i	$-0.901500\pi$
$827$	−6.11154	+	10.5855i	−0.212519	+	0.368094i	0.739983	+	0.672625i	$0.234833\pi$
$828$	4.66384	+	8.94693i	0.162080	+	0.310927i
$829$	−36.2004	+	20.9003i	−1.25729	+	0.725898i	−0.972547	−	0.232706i	$-0.925242\pi$
$829$	−36.2004	+	20.9003i	−1.25729	+	0.725898i	−0.284745	+	0.958603i	$0.591909\pi$
$830$	21.8041			0.756831
$831$	−26.0268	−	7.57823i	−0.902860	−	0.262886i
$832$	−0.271478	−	0.156738i	−0.00941180	−	0.00543391i
$833$	−1.47142	+	3.55483i	−0.0509816	+	0.123167i
$834$	−7.68708	−	31.3765i	−0.266182	−	1.08648i
$835$	6.80696	+	3.93000i	0.235564	+	0.136003i
$836$	−5.69494	+	3.22936i	−0.196964	+	0.111690i
$837$	−3.82846	−	1.29601i	−0.132331	−	0.0447965i
$838$			11.3105i			0.390715i
$839$	6.29185	+	10.8978i	0.217219	+	0.376234i	0.953957	−	0.299945i	$-0.0969682\pi$
$839$	6.29185	+	10.8978i	0.217219	+	0.376234i	−0.736738	+	0.676178i	$0.763635\pi$
$840$	0.394752	+	8.95815i	0.0136202	+	0.309086i
$841$	11.8810	+	20.5785i	0.409690	+	0.709604i
$842$	0.322455	−	0.186169i	0.0111125	−	0.00641582i
$843$	5.06173	+	20.6605i	0.174335	+	0.711587i
$844$	−14.2681	+	8.23770i	−0.491129	+	0.283553i
$845$	21.8629	−	12.6226i	0.752108	−	0.434230i
$846$	12.8623	+	24.6746i	0.442216	+	0.848331i
$847$	−21.9062	+	7.43919i	−0.752704	+	0.255614i
$848$	−10.8689			−0.373238
$849$	−4.34730	−	17.7445i	−0.149199	−	0.608989i
$850$	0.557482	+	0.321863i	0.0191215	+	0.0110398i
$851$	8.64184			0.296239
$852$	−12.0686	−	3.51402i	−0.413464	−	0.120388i
$853$	−2.25392	−	3.90390i	−0.0771726	−	0.133667i	0.824856	−	0.565342i	$-0.191256\pi$
$853$	−2.25392	−	3.90390i	−0.0771726	−	0.133667i	−0.902029	+	0.431675i	$0.857923\pi$
$854$	−5.43523	+	27.3426i	−0.185990	+	0.935643i
$855$	25.5545	+	1.29999i	0.873944	+	0.0444588i
$856$	−3.96645	+	6.87009i	−0.135570	+	0.234815i
$857$	2.53600	−	4.39247i	0.0866280	−	0.150044i	−0.819456	−	0.573142i	$-0.805724\pi$
$857$	2.53600	−	4.39247i	0.0866280	−	0.150044i	0.906084	+	0.423098i	$0.139058\pi$
$858$	0.588924	−	0.564088i	0.0201055	−	0.0192576i
$859$	−27.6594	−	47.9075i	−0.943727	−	1.63458i	−0.758280	−	0.651929i	$-0.773960\pi$
$859$	−27.6594	−	47.9075i	−0.943727	−	1.63458i	−0.185447	−	0.982654i	$-0.559373\pi$
$860$	8.81139	−	5.08726i	0.300466	−	0.173474i
$861$	−11.8916	−	18.6494i	−0.405263	−	0.635569i
$862$	−9.42562			−0.321038
$863$	−9.01119	+	15.6078i	−0.306744	+	0.531297i	−0.977648	−	0.210248i	$-0.932573\pi$
$863$	−9.01119	+	15.6078i	−0.306744	+	0.531297i	0.670904	+	0.741544i	$0.265906\pi$
$864$	−3.42934	−	3.90380i	−0.116668	−	0.132810i
$865$			25.2642i			0.859007i
$866$	−20.0799	−	11.5932i	−0.682344	−	0.393951i
$867$	−27.7685	−	8.08535i	−0.943067	−	0.274593i
$868$	2.01853	+	0.401248i	0.0685132	+	0.0136192i
$869$	−4.03994	−	6.99737i	−0.137045	−	0.237370i
$870$	7.53380	−	1.84574i	0.255420	−	0.0625765i
$871$	−0.00308138	+	0.00533710i	−0.000104409	+	0.000180841i
$872$	−13.8708	−	8.00830i	−0.469724	−	0.271195i
$873$	3.21578	+	6.16903i	0.108838	+	0.208790i
$874$	−12.7522	+	7.23123i	−0.431349	+	0.244600i
$875$	−21.0621	+	24.0228i	−0.712029	+	0.812118i
$876$	−3.09182	−	12.6199i	−0.104463	−	0.426388i
$877$		−	26.7018i		−	0.901655i	−0.892611	−	0.450828i	$-0.851129\pi$
$877$		−	26.7018i		−	0.901655i	0.892611	−	0.450828i	$-0.148871\pi$
$878$		−	0.422976i		−	0.0142748i
$879$	22.1602	−	21.2256i	0.747445	−	0.715923i
$880$	−1.46945	−	2.54516i	−0.0495352	−	0.0857974i
$881$		−	16.8396i		−	0.567340i	−0.958922	−	0.283670i	$-0.908448\pi$
$881$		−	16.8396i		−	0.567340i	0.958922	−	0.283670i	$-0.0915520\pi$
$882$	20.9186	−	1.84719i	0.704366	−	0.0621983i
$883$	8.06108	−	13.9622i	0.271277	−	0.469865i	−0.697912	−	0.716183i	$-0.745887\pi$
$883$	8.06108	−	13.9622i	0.271277	−	0.469865i	0.969189	+	0.246318i	$0.0792208\pi$
$884$	−0.0861458	−	0.149209i	−0.00289740	−	0.00501844i
$885$	34.9375	−	8.55949i	1.17441	−	0.287724i
$886$	23.2671	−	13.4333i	0.781675	−	0.451300i
$887$	1.28856	+	2.23185i	0.0432655	+	0.0749381i	0.886847	−	0.462063i	$-0.152891\pi$
$887$	1.28856	+	2.23185i	0.0432655	+	0.0749381i	−0.843582	+	0.537001i	$0.819557\pi$
$888$	−4.32274	+	1.05905i	−0.145062	+	0.0355393i
$889$	−3.95762	−	11.6540i	−0.132734	−	0.390863i
$890$	8.42316	−	4.86312i	0.282345	−	0.163012i
$891$	12.2446	−	5.72645i	0.410211	−	0.191843i
$892$	15.6183	−	9.01722i	0.522939	−	0.301919i
$893$	−35.1691	+	19.9429i	−1.17689	+	0.667364i
$894$	14.8700	+	15.5247i	0.497328	+	0.519225i
$895$	−24.7208	+	14.2725i	−0.826325	+	0.477079i
$896$	1.98940	+	1.74422i	0.0664612	+	0.0582702i
$897$	1.31873	−	1.26311i	0.0440310	−	0.0421741i
$898$	13.5101			0.450838
$899$		−	1.78025i		−	0.0593748i
$900$	0.151301	−	3.51042i	0.00504338	−	0.117014i
$901$	−5.17339	−	2.98686i	−0.172351	−	0.0995066i
$902$	6.27802	+	3.62462i	0.209035	+	0.120687i
$903$	−12.8111	−	20.0914i	−0.426326	−	0.668601i
$904$	−5.37956			−0.178921
$905$	−16.1157	+	27.9132i	−0.535704	+	0.927866i
$906$	−0.721313	+	2.47729i	−0.0239640	+	0.0823025i
$907$	49.2027	+	28.4072i	1.63375	+	0.943246i	0.982922	+	0.184020i	$0.0589112\pi$
$907$	49.2027	+	28.4072i	1.63375	+	0.943246i	0.650828	+	0.759226i	$0.274422\pi$
$908$	1.16303	+	2.01443i	0.0385965	+	0.0668511i
$909$	−6.02739	−	0.259785i	−0.199916	−	0.00861652i
$910$	1.53668	−	0.521845i	0.0509403	−	0.0172990i
$911$	−29.4855			−0.976897			−0.488449	−	0.872593i	$-0.662437\pi$
$911$	−29.4855			−0.976897			−0.488449	+	0.872593i	$0.662437\pi$
$912$	5.49260	−	5.17990i	0.181878	−	0.171524i
$913$	8.36821	+	14.4942i	0.276947	+	0.479687i
$914$	−19.9506	+	34.5555i	−0.659908	+	1.14299i
$915$	−9.98325	+	34.2867i	−0.330036	+	1.13348i
$916$	−8.54257	+	14.7962i	−0.282255	+	0.488879i
$917$	−13.0283	+	14.8597i	−0.430233	+	0.490711i
$918$	−0.559507	−	2.80055i	−0.0184665	−	0.0924319i
$919$	−13.5597	+	23.4861i	−0.447293	+	0.774734i	−0.998209	−	0.0598270i	$-0.980945\pi$
$919$	−13.5597	+	23.4861i	−0.447293	+	0.774734i	0.550916	+	0.834561i	$0.314278\pi$
$920$	−3.29041	−	5.69916i	−0.108482	−	0.187896i
$921$	11.0923	−	38.0958i	0.365505	−	1.25530i
$922$	15.6780	−	9.05172i	0.516329	−	0.298102i
$923$			2.27495i			0.0748808i
$924$	−5.80339	+	3.70047i	−0.190918	+	0.121736i
$925$	−2.60631	−	1.50476i	−0.0856951	−	0.0494761i
$926$	−12.9235			−0.424693
$927$	4.42201	−	6.94973i	0.145238	−	0.228259i
$928$	1.14433	−	1.98204i	0.0375645	−	0.0650636i
$929$			18.0298i			0.591538i	0.955259	+	0.295769i	$0.0955759\pi$
$929$			18.0298i			0.591538i	−0.955259	+	0.295769i	$0.904424\pi$
$930$	2.53116	+	0.736999i	0.0830001	+	0.0241672i
$931$	3.75554	+	30.2803i	0.123083	+	0.992396i
$932$		−	22.3373i		−	0.731683i
$933$	2.84926	−	9.78555i	0.0932805	−	0.320364i
$934$	−5.81673	−	3.35829i	−0.190329	−	0.109887i
$935$		−	1.61527i		−	0.0528250i
$936$	−0.504848	+	0.793431i	−0.0165015	+	0.0259341i
$937$	−19.5792	+	33.9122i	−0.639625	+	1.10786i	0.345890	+	0.938275i	$0.387577\pi$
$937$	−19.5792	+	33.9122i	−0.639625	+	1.10786i	−0.985515	+	0.169588i	$0.945756\pi$
$938$	0.0342903	−	0.0391105i	0.00111962	−	0.00127700i
$939$	42.8478	+	12.4760i	1.39828	+	0.407138i
$940$	−9.07458	−	15.7176i	−0.295980	−	0.512653i
$941$	53.5610			1.74604			0.873019	−	0.487686i	$-0.162159\pi$
$941$	53.5610			1.74604			0.873019	+	0.487686i	$0.162159\pi$
$942$	5.21301	+	21.2780i	0.169849	+	0.693276i
$943$	14.0578	+	8.11629i	0.457786	+	0.264303i
$944$	5.30675	−	9.19155i	0.172720	−	0.299160i
$945$	26.9005	−	0.0259238i	0.875074	−	0.000843301i
$946$	6.76347	+	3.90489i	0.219899	+	0.126959i
$947$		−	31.4941i		−	1.02342i	−0.859158	−	0.511711i	$-0.829012\pi$
$947$		−	31.4941i		−	1.02342i	0.859158	−	0.511711i	$-0.170988\pi$
$948$	6.44521	+	6.72899i	0.209331	+	0.218547i
$949$	−2.03652	+	1.17578i	−0.0661082	+	0.0381676i
$950$	5.10510	+	0.0395835i	0.165631	+	0.00128426i
$951$	−20.5113	−	5.97229i	−0.665125	−	0.193665i
$952$	0.467593	+	1.37692i	0.0151548	+	0.0446262i
$953$	−8.39492	−	14.5404i	−0.271938	−	0.471011i	0.697420	−	0.716663i	$-0.254331\pi$
$953$	−8.39492	−	14.5404i	−0.271938	−	0.471011i	−0.969358	+	0.245652i	$0.920998\pi$
$954$	−1.40406	+	32.5764i	−0.0454582	+	1.05470i
$955$	3.83508	−	6.64256i	0.124100	−	0.214948i
$956$			1.32903i			0.0429840i
$957$	4.11836	+	4.29969i	0.133128	+	0.138989i
$958$		−	16.3658i		−	0.528755i
$959$	−32.2063	+	36.7335i	−1.03999	+	1.18619i
$960$	2.34432	+	2.44754i	0.0756628	+	0.0789941i
$961$	−15.1975	+	26.3228i	−0.490241	+	0.849122i
$962$	0.402745	+	0.697574i	0.0129850	+	0.0224907i
$963$	20.0788	+	12.7758i	0.647029	+	0.411695i
$964$			3.11193i			0.100229i
$965$	15.8792	−	27.5037i	0.511171	−	0.885374i
$966$	−12.9950	+	8.28614i	−0.418108	+	0.266602i
$967$	−6.07362	−	10.5198i	−0.195314	−	0.338295i	0.751689	−	0.659518i	$-0.229239\pi$
$967$	−6.07362	−	10.5198i	−0.195314	−	0.338295i	−0.947004	+	0.321223i	$0.895906\pi$
$968$	−4.37208	+	7.57266i	−0.140524	+	0.243394i
$969$	4.03786	−	0.956130i	0.129715	−	0.0307153i
$970$	−2.26879	−	3.92965i	−0.0728463	−	0.126173i
$971$	−18.9050			−0.606689			−0.303345	−	0.952881i	$-0.598103\pi$
$971$	−18.9050			−0.606689			−0.303345	+	0.952881i	$0.598103\pi$
$972$	−12.1435	+	9.77417i	−0.389504	+	0.313507i
$973$	46.7251	−	15.8675i	1.49794	−	0.508690i
$974$	−21.2291	+	12.2567i	−0.680226	+	0.392728i
$975$	−0.617657	+	0.151323i	−0.0197809	+	0.00484621i
$976$	5.26836	+	9.12507i	0.168636	+	0.292086i
$977$	−1.45757	−	2.52459i	−0.0466318	−	0.0807687i	0.841767	−	0.539840i	$-0.181515\pi$
$977$	−1.45757	−	2.52459i	−0.0466318	−	0.0807687i	−0.888399	+	0.459072i	$0.848182\pi$
$978$	−3.46241	−	14.1326i	−0.110716	−	0.451910i
$979$	6.46547	+	3.73284i	0.206637	+	0.119302i
$980$	−13.5795	+	1.79122i	−0.433780	+	0.0572184i
$981$	−25.7945	+	40.5392i	−0.823554	+	1.29432i
$982$	28.4824	−	16.4443i	0.908909	−	0.524759i
$983$	9.82517	−	17.0177i	0.313374	−	0.542780i	−0.665716	−	0.746205i	$-0.731874\pi$
$983$	9.82517	−	17.0177i	0.313374	−	0.542780i	0.979091	+	0.203425i	$0.0652072\pi$
$984$	−8.02651	−	2.33708i	−0.255876	−	0.0745034i
$985$	−22.8707			−0.728720
$986$	1.08936	−	0.628943i	0.0346923	−	0.0200296i
$987$	−35.8388	+	22.8522i	−1.14076	+	0.727394i
$988$	−1.17801	−	0.692359i	−0.0374776	−	0.0220269i
$989$	15.1449	+	8.74389i	0.481578	+	0.278039i
$990$	−7.81823	+	4.07547i	−0.248480	+	0.129527i
$991$	13.7795	+	7.95561i	0.437721	+	0.252718i	0.702631	−	0.711555i	$-0.252009\pi$
$991$	13.7795	+	7.95561i	0.437721	+	0.252718i	−0.264909	+	0.964273i	$0.585342\pi$
$992$	0.673645	−	0.388929i	0.0213883	−	0.0123485i
$993$	56.5752	−	13.8606i	1.79536	−	0.439854i
$994$	3.74351	−	18.8322i	0.118737	−	0.597321i
$995$		−	19.0051i		−	0.602501i
$996$	−13.3504	−	13.9383i	−0.423025	−	0.441650i
$997$	−28.4956			−0.902463			−0.451232	−	0.892407i	$-0.649015\pi$
$997$	−28.4956			−0.902463			−0.451232	+	0.892407i	$0.649015\pi$
$998$	−0.387635			−0.0122704
$999$	2.61578	+	13.0930i	0.0827595	+	0.414244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.p.d.107.18	yes	50
3.2	odd	2		798.2.p.c.107.10	✓	50
7.4	even	3		798.2.bh.c.221.2	yes	50
19.8	odd	6		798.2.bh.d.65.24	yes	50
21.11	odd	6		798.2.bh.d.221.24	yes	50
57.8	even	6		798.2.bh.c.65.2	yes	50
133.46	odd	6		798.2.p.c.179.10	yes	50
399.179	even	6	inner	798.2.p.d.179.18	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.p.c.107.10	✓	50	3.2	odd	2
798.2.p.c.179.10	yes	50	133.46	odd	6
798.2.p.d.107.18	yes	50	1.1	even	1	trivial
798.2.p.d.179.18	yes	50	399.179	even	6	inner
798.2.bh.c.65.2	yes	50	57.8	even	6
798.2.bh.c.221.2	yes	50	7.4	even	3
798.2.bh.d.65.24	yes	50	19.8	odd	6
798.2.bh.d.221.24	yes	50	21.11	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.25084 - 1.19809i) q^{3} +1.00000 q^{4} +1.95673i q^{5} +(1.25084 - 1.19809i) q^{6} +(1.98940 + 1.74422i) q^{7} +1.00000 q^{8} +(0.129182 - 2.99722i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.25084 - 1.19809i) q^{3} +1.00000 q^{4} +1.95673i q^{5} +(1.25084 - 1.19809i) q^{6} +(1.98940 + 1.74422i) q^{7} +1.00000 q^{8} +(0.129182 - 2.99722i) q^{9} +1.95673i q^{10} +(-1.30073 + 0.750974i) q^{11} +(1.25084 - 1.19809i) q^{12} +(-0.271478 - 0.156738i) q^{13} +(1.98940 + 1.74422i) q^{14} +(2.34432 + 2.44754i) q^{15} +1.00000 q^{16} +(0.475982 + 0.274809i) q^{17} +(0.129182 - 2.99722i) q^{18} +(4.35877 + 0.0337967i) q^{19} +1.95673i q^{20} +(4.57813 - 0.201741i) q^{21} +(-1.30073 + 0.750974i) q^{22} +(-2.91260 + 1.68159i) q^{23} +(1.25084 - 1.19809i) q^{24} +1.17123 q^{25} +(-0.271478 - 0.156738i) q^{26} +(-3.42934 - 3.90380i) q^{27} +(1.98940 + 1.74422i) q^{28} +(1.14433 - 1.98204i) q^{29} +(2.34432 + 2.44754i) q^{30} +(0.673645 - 0.388929i) q^{31} +1.00000 q^{32} +(-0.727263 + 2.49773i) q^{33} +(0.475982 + 0.274809i) q^{34} +(-3.41295 + 3.89271i) q^{35} +(0.129182 - 2.99722i) q^{36} +(-2.22529 - 1.28477i) q^{37} +(4.35877 + 0.0337967i) q^{38} +(-0.527360 + 0.129200i) q^{39} +1.95673i q^{40} +(-2.41328 - 4.17992i) q^{41} +(4.57813 - 0.201741i) q^{42} +(-2.59988 - 4.50313i) q^{43} +(-1.30073 + 0.750974i) q^{44} +(5.86473 + 0.252774i) q^{45} +(-2.91260 + 1.68159i) q^{46} +(-8.03262 + 4.63764i) q^{47} +(1.25084 - 1.19809i) q^{48} +(0.915417 + 6.93989i) q^{49} +1.17123 q^{50} +(0.924620 - 0.226527i) q^{51} +(-0.271478 - 0.156738i) q^{52} -10.8689 q^{53} +(-3.42934 - 3.90380i) q^{54} +(-1.46945 - 2.54516i) q^{55} +(1.98940 + 1.74422i) q^{56} +(5.49260 - 5.17990i) q^{57} +(1.14433 - 1.98204i) q^{58} +(5.30675 - 9.19155i) q^{59} +(2.34432 + 2.44754i) q^{60} +(5.26836 + 9.12507i) q^{61} +(0.673645 - 0.388929i) q^{62} +(5.48479 - 5.73734i) q^{63} +1.00000 q^{64} +(0.306693 - 0.531208i) q^{65} +(-0.727263 + 2.49773i) q^{66} -0.0196594i q^{67} +(0.475982 + 0.274809i) q^{68} +(-1.62850 + 5.59294i) q^{69} +(-3.41295 + 3.89271i) q^{70} +(-3.62859 - 6.28490i) q^{71} +(0.129182 - 2.99722i) q^{72} +(3.75080 - 6.49658i) q^{73} +(-2.22529 - 1.28477i) q^{74} +(1.46501 - 1.40323i) q^{75} +(4.35877 + 0.0337967i) q^{76} +(-3.89752 - 0.774760i) q^{77} +(-0.527360 + 0.129200i) q^{78} +5.37959i q^{79} +1.95673i q^{80} +(-8.96662 - 0.774374i) q^{81} +(-2.41328 - 4.17992i) q^{82} -11.1431i q^{83} +(4.57813 - 0.201741i) q^{84} +(-0.537725 + 0.931367i) q^{85} +(-2.59988 - 4.50313i) q^{86} +(-0.943281 - 3.85021i) q^{87} +(-1.30073 + 0.750974i) q^{88} +(-2.48533 - 4.30472i) q^{89} +(5.86473 + 0.252774i) q^{90} +(-0.266693 - 0.785330i) q^{91} +(-2.91260 + 1.68159i) q^{92} +(0.376649 - 1.29357i) q^{93} +(-8.03262 + 4.63764i) q^{94} +(-0.0661308 + 8.52891i) q^{95} +(1.25084 - 1.19809i) q^{96} +(-2.00828 + 1.15948i) q^{97} +(0.915417 + 6.93989i) q^{98} +(2.08280 + 3.99557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9	\( 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9} - 3 q^{11} - 3 q^{13} - 13 q^{15} + 50 q^{16} + 3 q^{17} + 6 q^{18} + 10 q^{19} - 7 q^{21} - 3 q^{22} + 9 q^{23} - 58 q^{25} - 3 q^{26} + 6 q^{27} - 5 q^{29} - 13 q^{30} + 15 q^{31} + 50 q^{32} - q^{33} + 3 q^{34} + 6 q^{36} - 9 q^{37} + 10 q^{38} - 2 q^{39} - 17 q^{41} - 7 q^{42} + 15 q^{43} - 3 q^{44} - 22 q^{45} + 9 q^{46} + 21 q^{47} + 8 q^{49} - 58 q^{50} - 4 q^{51} - 3 q^{52} - 12 q^{53} + 6 q^{54} - 16 q^{55} - 19 q^{57} - 5 q^{58} - q^{59} - 13 q^{60} + 23 q^{61} + 15 q^{62} + 41 q^{63} + 50 q^{64} - 14 q^{65} - q^{66} + 3 q^{68} - 31 q^{69} + 3 q^{71} + 6 q^{72} + 15 q^{73} - 9 q^{74} + 7 q^{75} + 10 q^{76} - 57 q^{77} - 2 q^{78} - 70 q^{81} - 17 q^{82} - 7 q^{84} - 10 q^{85} + 15 q^{86} + 52 q^{87} - 3 q^{88} + 33 q^{89} - 22 q^{90} - 15 q^{91} + 9 q^{92} + 53 q^{93} + 21 q^{94} + 30 q^{95} - 21 q^{97} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9 - 3 * q^11 - 3 * q^13 - 13 * q^15 + 50 * q^16 + 3 * q^17 + 6 * q^18 + 10 * q^19 - 7 * q^21 - 3 * q^22 + 9 * q^23 - 58 * q^25 - 3 * q^26 + 6 * q^27 - 5 * q^29 - 13 * q^30 + 15 * q^31 + 50 * q^32 - q^33 + 3 * q^34 + 6 * q^36 - 9 * q^37 + 10 * q^38 - 2 * q^39 - 17 * q^41 - 7 * q^42 + 15 * q^43 - 3 * q^44 - 22 * q^45 + 9 * q^46 + 21 * q^47 + 8 * q^49 - 58 * q^50 - 4 * q^51 - 3 * q^52 - 12 * q^53 + 6 * q^54 - 16 * q^55 - 19 * q^57 - 5 * q^58 - q^59 - 13 * q^60 + 23 * q^61 + 15 * q^62 + 41 * q^63 + 50 * q^64 - 14 * q^65 - q^66 + 3 * q^68 - 31 * q^69 + 3 * q^71 + 6 * q^72 + 15 * q^73 - 9 * q^74 + 7 * q^75 + 10 * q^76 - 57 * q^77 - 2 * q^78 - 70 * q^81 - 17 * q^82 - 7 * q^84 - 10 * q^85 + 15 * q^86 + 52 * q^87 - 3 * q^88 + 33 * q^89 - 22 * q^90 - 15 * q^91 + 9 * q^92 + 53 * q^93 + 21 * q^94 + 30 * q^95 - 21 * q^97 + 8 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more