LMFDB - Embedded newform 798.2.bh.d.221.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(65,798)]

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, 1]))

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

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

chi := DirichletCharacter("798.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bh (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			221.24
Character	$\chi$	$=$	798.221
Dual form			798.2.bh.d.65.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.66299 - 0.484213i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.69457 + 0.978363i) q^{5} +(0.412154 - 1.68230i) q^{6} +(1.98940 - 1.74422i) q^{7} -1.00000 q^{8} +(2.53108 - 1.61048i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.66299 - 0.484213i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.69457 + 0.978363i) q^{5} +(0.412154 - 1.68230i) q^{6} +(1.98940 - 1.74422i) q^{7} -1.00000 q^{8} +(2.53108 - 1.61048i) q^{9} +(1.69457 - 0.978363i) q^{10} +(-1.30073 - 0.750974i) q^{11} +(-1.25084 - 1.19809i) q^{12} +(-0.271478 - 0.156738i) q^{13} +(-0.515836 - 2.59498i) q^{14} +(3.29180 + 0.806473i) q^{15} +(-0.500000 + 0.866025i) q^{16} +0.549617i q^{17} +(-0.129182 - 2.99722i) q^{18} +(-2.20865 + 3.75791i) q^{19} -1.95673i q^{20} +(2.46378 - 3.86391i) q^{21} +(-1.30073 + 0.750974i) q^{22} +3.36318i q^{23} +(-1.66299 + 0.484213i) q^{24} +(-0.585613 - 1.01431i) q^{25} +(-0.271478 + 0.156738i) q^{26} +(3.42934 - 3.90380i) q^{27} +(-2.50524 - 0.850762i) q^{28} +(-1.14433 + 1.98204i) q^{29} +(2.34432 - 2.44754i) q^{30} +(-0.673645 - 0.388929i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.52673 - 0.619035i) q^{33} +(0.475982 + 0.274809i) q^{34} +(5.07766 - 1.00935i) q^{35} +(-2.66026 - 1.38673i) q^{36} +(2.22529 - 1.28477i) q^{37} +(2.15012 + 3.79170i) q^{38} +(-0.527360 - 0.129200i) q^{39} +(-1.69457 - 0.978363i) q^{40} +(2.41328 + 4.17992i) q^{41} +(-2.11435 - 4.06565i) q^{42} +(-2.59988 - 4.50313i) q^{43} +1.50195i q^{44} +(5.86473 - 0.252774i) q^{45} +(2.91260 + 1.68159i) q^{46} +9.27527i q^{47} +(-0.412154 + 1.68230i) q^{48} +(0.915417 - 6.93989i) q^{49} -1.17123 q^{50} +(0.266132 + 0.914008i) q^{51} +0.313476i q^{52} +(-5.43443 - 9.41271i) q^{53} +(-1.66612 - 4.92179i) q^{54} +(-1.46945 - 2.54516i) q^{55} +(-1.98940 + 1.74422i) q^{56} +(-1.85334 + 7.31882i) q^{57} +(1.14433 + 1.98204i) q^{58} +10.6135 q^{59} +(-0.947472 - 3.25402i) q^{60} -10.5367 q^{61} +(-0.673645 + 0.388929i) q^{62} +(2.22629 - 7.61864i) q^{63} +1.00000 q^{64} +(-0.306693 - 0.531208i) q^{65} +(-1.79946 + 1.87869i) q^{66} +(-0.0170256 + 0.00982972i) q^{67} +(0.475982 - 0.274809i) q^{68} +(1.62850 + 5.59294i) q^{69} +(1.66471 - 4.90206i) q^{70} +(3.62859 + 6.28490i) q^{71} +(-2.53108 + 1.61048i) q^{72} -7.50160 q^{73} -2.56954i q^{74} +(-1.46501 - 1.40323i) q^{75} +(4.35877 + 0.0337967i) q^{76} +(-3.89752 + 0.774760i) q^{77} +(-0.375571 + 0.392107i) q^{78} +(-4.65887 - 2.68980i) q^{79} +(-1.69457 + 0.978363i) q^{80} +(3.81268 - 8.15251i) q^{81} +4.82655 q^{82} +11.1431i q^{83} +(-4.57813 - 0.201741i) q^{84} +(-0.537725 + 0.931367i) q^{85} -5.19977 q^{86} +(-0.943281 + 3.85021i) q^{87} +(1.30073 + 0.750974i) q^{88} -4.97067 q^{89} +(2.71346 - 5.20539i) q^{90} +(-0.813463 + 0.161702i) q^{91} +(2.91260 - 1.68159i) q^{92} +(-1.30859 - 0.320598i) q^{93} +(8.03262 + 4.63764i) q^{94} +(-7.41932 + 4.20719i) q^{95} +(1.25084 + 1.19809i) q^{96} +(-2.00828 + 1.15948i) q^{97} +(-5.55241 - 4.26272i) q^{98} +(-4.50167 + 0.194025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 25 q^{2} + 3 q^{3} - 25 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9}+O(q^{10}) $ 50 * q + 25 * q^2 + 3 * q^3 - 25 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9	$ 50 q + 25 q^{2} + 3 q^{3} - 25 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{13} + 3 q^{14} - 17 q^{15} - 25 q^{16} - 6 q^{18} + q^{19} - 2 q^{21} - 3 q^{22} - 3 q^{24} + 29 q^{25} - 3 q^{26} - 6 q^{27} + 3 q^{28} + 5 q^{29} - 13 q^{30} - 15 q^{31} + 25 q^{32} + 13 q^{33} + 3 q^{34} + 12 q^{35} - 3 q^{36} + 9 q^{37} + 11 q^{38} - 2 q^{39} + 17 q^{41} + 5 q^{42} + 15 q^{43} - 22 q^{45} - 9 q^{46} - 3 q^{48} + 8 q^{49} + 58 q^{50} + 19 q^{51} - 6 q^{53} + 24 q^{54} - 16 q^{55} - 4 q^{57} - 5 q^{58} - 2 q^{59} + 4 q^{60} - 46 q^{61} - 15 q^{62} - 46 q^{63} + 50 q^{64} + 14 q^{65} + 14 q^{66} + 18 q^{67} + 3 q^{68} + 31 q^{69} + 12 q^{70} - 3 q^{71} + 3 q^{72} - 30 q^{73} - 7 q^{75} + 10 q^{76} - 57 q^{77} + 17 q^{78} - 18 q^{79} - 7 q^{81} + 34 q^{82} + 7 q^{84} - 10 q^{85} + 30 q^{86} + 52 q^{87} + 3 q^{88} + 66 q^{89} - 26 q^{90} - 57 q^{91} - 9 q^{92} - 22 q^{93} - 21 q^{94} + 60 q^{95} - 21 q^{97} + 7 q^{98} + 19 q^{99}+O(q^{100}) $ 50 * q + 25 * q^2 + 3 * q^3 - 25 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^13 + 3 * q^14 - 17 * q^15 - 25 * q^16 - 6 * q^18 + q^19 - 2 * q^21 - 3 * q^22 - 3 * q^24 + 29 * q^25 - 3 * q^26 - 6 * q^27 + 3 * q^28 + 5 * q^29 - 13 * q^30 - 15 * q^31 + 25 * q^32 + 13 * q^33 + 3 * q^34 + 12 * q^35 - 3 * q^36 + 9 * q^37 + 11 * q^38 - 2 * q^39 + 17 * q^41 + 5 * q^42 + 15 * q^43 - 22 * q^45 - 9 * q^46 - 3 * q^48 + 8 * q^49 + 58 * q^50 + 19 * q^51 - 6 * q^53 + 24 * q^54 - 16 * q^55 - 4 * q^57 - 5 * q^58 - 2 * q^59 + 4 * q^60 - 46 * q^61 - 15 * q^62 - 46 * q^63 + 50 * q^64 + 14 * q^65 + 14 * q^66 + 18 * q^67 + 3 * q^68 + 31 * q^69 + 12 * q^70 - 3 * q^71 + 3 * q^72 - 30 * q^73 - 7 * q^75 + 10 * q^76 - 57 * q^77 + 17 * q^78 - 18 * q^79 - 7 * q^81 + 34 * q^82 + 7 * q^84 - 10 * q^85 + 30 * q^86 + 52 * q^87 + 3 * q^88 + 66 * q^89 - 26 * q^90 - 57 * q^91 - 9 * q^92 - 22 * q^93 - 21 * q^94 + 60 * q^95 - 21 * q^97 + 7 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.66299	−	0.484213i	0.960128	−	0.279561i
$3$	1.66299	−	0.484213i	0.960128	−	0.279561i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.69457	+	0.978363i	0.757837	+	0.437537i	0.828518	−	0.559962i	$-0.189184\pi$
$5$	1.69457	+	0.978363i	0.757837	+	0.437537i	−0.0706819	+	0.997499i	$0.522518\pi$
$6$	0.412154	−	1.68230i	0.168261	−	0.686796i
$7$	1.98940	−	1.74422i	0.751922	−	0.659252i
$7$	1.98940	−	1.74422i	0.751922	−	0.659252i
$8$	−1.00000			−0.353553
$9$	2.53108	−	1.61048i	0.843692	−	0.536828i
$10$	1.69457	−	0.978363i	0.535871	−	0.309385i
$11$	−1.30073	−	0.750974i	−0.392183	−	0.226427i	0.290922	−	0.956747i	$-0.406038\pi$
$11$	−1.30073	−	0.750974i	−0.392183	−	0.226427i	−0.683106	+	0.730319i	$0.739371\pi$
$12$	−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	$0.680508\pi$
$14$	−0.515836	−	2.59498i	−0.137863	−	0.693537i
$15$	3.29180	+	0.806473i	0.849938	+	0.208230i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			0.549617i			0.133302i	0.997776	+	0.0666509i	$0.0212314\pi$
$17$			0.549617i			0.133302i	−0.997776	+	0.0666509i	$0.978769\pi$
$18$	−0.129182	−	2.99722i	−0.0304485	−	0.706451i
$19$	−2.20865	+	3.75791i	−0.506700	+	0.862123i
$19$	−2.20865	+	3.75791i	−0.506700	+	0.862123i
$20$		−	1.95673i		−	0.437537i
$21$	2.46378	−	3.86391i	0.537641	−	0.843174i
$22$	−1.30073	+	0.750974i	−0.277316	+	0.160108i
$23$			3.36318i			0.701272i	0.936512	+	0.350636i	$0.114035\pi$
$23$			3.36318i			0.701272i	−0.936512	+	0.350636i	$0.885965\pi$
$24$	−1.66299	+	0.484213i	−0.339457	+	0.0988396i
$25$	−0.585613	−	1.01431i	−0.117123	−	0.202862i
$26$	−0.271478	+	0.156738i	−0.0532412	+	0.0307388i
$27$	3.42934	−	3.90380i	0.659976	−	0.751286i
$28$	−2.50524	−	0.850762i	−0.473445	−	0.160779i
$29$	−1.14433	+	1.98204i	−0.212497	+	0.368055i	−0.952495	−	0.304553i	$-0.901493\pi$
$29$	−1.14433	+	1.98204i	−0.212497	+	0.368055i	0.739999	+	0.672608i	$0.234826\pi$
$30$	2.34432	−	2.44754i	0.428013	−	0.446858i
$31$	−0.673645	−	0.388929i	−0.120990	−	0.0698537i	0.438284	−	0.898837i	$-0.355587\pi$
$31$	−0.673645	−	0.388929i	−0.120990	−	0.0698537i	−0.559274	+	0.828983i	$0.688920\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.52673	−	0.619035i	−0.439846	−	0.107760i
$34$	0.475982	+	0.274809i	0.0816303	+	0.0471293i
$35$	5.07766	−	1.00935i	0.858281	−	0.170611i
$36$	−2.66026	−	1.38673i	−0.443376	−	0.231122i
$37$	2.22529	−	1.28477i	0.365835	−	0.211215i	−0.305802	−	0.952095i	$-0.598925\pi$
$37$	2.22529	−	1.28477i	0.365835	−	0.211215i	0.671637	+	0.740880i	$0.265591\pi$
$38$	2.15012	+	3.79170i	0.348795	+	0.615095i
$39$	−0.527360	−	0.129200i	−0.0844451	−	0.0206886i
$40$	−1.69457	−	0.978363i	−0.267936	−	0.154693i
$41$	2.41328	+	4.17992i	0.376891	+	0.652794i	0.990608	−	0.136732i	$-0.0436600\pi$
$41$	2.41328	+	4.17992i	0.376891	+	0.652794i	−0.613718	+	0.789526i	$0.710327\pi$
$42$	−2.11435	−	4.06565i	−0.326252	−	0.627343i
$43$	−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	$0.963101\pi$
$44$			1.50195i			0.226427i
$45$	5.86473	−	0.252774i	0.874263	−	0.0376813i
$46$	2.91260	+	1.68159i	0.429440	+	0.247937i
$47$			9.27527i			1.35294i	0.736471	+	0.676469i	$0.236491\pi$
$47$			9.27527i			1.35294i	−0.736471	+	0.676469i	$0.763509\pi$
$48$	−0.412154	+	1.68230i	−0.0594894	+	0.242819i
$49$	0.915417	−	6.93989i	0.130774	−	0.991412i
$50$	−1.17123			−0.165636
$51$	0.266132	+	0.914008i	0.0372659	+	0.127987i
$52$			0.313476i			0.0434713i
$53$	−5.43443	−	9.41271i	−0.746477	−	1.29294i	−0.949502	−	0.313762i	$-0.898411\pi$
$53$	−5.43443	−	9.41271i	−0.746477	−	1.29294i	0.203025	−	0.979174i	$-0.434923\pi$
$54$	−1.66612	−	4.92179i	−0.226730	−	0.669771i
$55$	−1.46945	−	2.54516i	−0.198141	−	0.343190i
$56$	−1.98940	+	1.74422i	−0.265845	+	0.233081i
$57$	−1.85334	+	7.31882i	−0.245481	+	0.969401i
$58$	1.14433	+	1.98204i	0.150258	+	0.260254i
$59$	10.6135			1.38176			0.690879	−	0.722970i	$-0.257224\pi$
$59$	10.6135			1.38176			0.690879	+	0.722970i	$0.257224\pi$
$60$	−0.947472	−	3.25402i	−0.122318	−	0.420092i
$61$	−10.5367			−1.34909			−0.674545	−	0.738234i	$-0.735660\pi$
$61$	−10.5367			−1.34909			−0.674545	+	0.738234i	$0.735660\pi$
$62$	−0.673645	+	0.388929i	−0.0855530	+	0.0493941i
$63$	2.22629	−	7.61864i	0.280486	−	0.959858i
$64$	1.00000			0.125000
$65$	−0.306693	−	0.531208i	−0.0380406	−	0.0658882i
$66$	−1.79946	+	1.87869i	−0.221499	+	0.231251i
$67$	−0.0170256	+	0.00982972i	−0.00208001	+	0.00120089i	−0.501040	−	0.865424i	$-0.667049\pi$
$67$	−0.0170256	+	0.00982972i	−0.00208001	+	0.00120089i	0.498960	+	0.866625i	$0.333716\pi$
$68$	0.475982	−	0.274809i	0.0577213	−	0.0333254i
$69$	1.62850	+	5.59294i	0.196048	+	0.673311i
$70$	1.66471	−	4.90206i	0.198971	−	0.585908i
$71$	3.62859	+	6.28490i	0.430634	+	0.745880i	0.996928	−	0.0783233i	$-0.0249566\pi$
$71$	3.62859	+	6.28490i	0.430634	+	0.745880i	−0.566294	+	0.824203i	$0.691623\pi$
$72$	−2.53108	+	1.61048i	−0.298290	+	0.189797i
$73$	−7.50160			−0.877996			−0.438998	−	0.898488i	$-0.644666\pi$
$73$	−7.50160			−0.877996			−0.438998	+	0.898488i	$0.644666\pi$
$74$		−	2.56954i		−	0.298703i
$75$	−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
$78$	−0.375571	+	0.392107i	−0.0425250	+	0.0443973i
$79$	−4.65887	−	2.68980i	−0.524163	−	0.302626i	0.214473	−	0.976730i	$-0.431197\pi$
$79$	−4.65887	−	2.68980i	−0.524163	−	0.302626i	−0.738636	+	0.674104i	$0.764530\pi$
$80$	−1.69457	+	0.978363i	−0.189459	+	0.109384i
$81$	3.81268	−	8.15251i	0.423632	−	0.905835i
$82$	4.82655			0.533004
$83$			11.1431i			1.22312i	0.791198	+	0.611560i	$0.209458\pi$
$83$			11.1431i			1.22312i	−0.791198	+	0.611560i	$0.790542\pi$
$84$	−4.57813	−	0.201741i	−0.499515	−	0.0220117i
$85$	−0.537725	+	0.931367i	−0.0583244	+	0.101021i
$86$	−5.19977			−0.560705
$87$	−0.943281	+	3.85021i	−0.101130	+	0.412786i
$88$	1.30073	+	0.750974i	0.138658	+	0.0800541i
$89$	−4.97067			−0.526890			−0.263445	−	0.964674i	$-0.584859\pi$
$89$	−4.97067			−0.526890			−0.263445	+	0.964674i	$0.584859\pi$
$90$	2.71346	−	5.20539i	0.286024	−	0.548697i
$91$	−0.813463	+	0.161702i	−0.0852741	+	0.0169510i
$92$	2.91260	−	1.68159i	0.303660	−	0.175318i
$93$	−1.30859	−	0.320598i	−0.135694	−	0.0332444i
$94$	8.03262	+	4.63764i	0.828502	+	0.478336i
$95$	−7.41932	+	4.20719i	−0.761206	+	0.431648i
$96$	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	$0.370894\pi$
$98$	−5.55241	−	4.26272i	−0.560878	−	0.430599i
$99$	−4.50167	+	0.194025i	−0.452434	+	0.0195002i
$100$	−0.585613	+	1.01431i	−0.0585613	+	0.101431i
$101$	1.74157	−	1.00550i	0.173293	−	0.100051i	−0.410845	−	0.911705i	$-0.634766\pi$
$101$	1.74157	−	1.00550i	0.173293	−	0.100051i	0.584138	+	0.811655i	$0.301433\pi$
$102$	0.924620	+	0.226527i	0.0915510	+	0.0224295i
$103$	−2.37790	+	1.37288i	−0.234302	+	0.135274i	−0.612555	−	0.790428i	$-0.709858\pi$
$103$	−2.37790	+	1.37288i	−0.234302	+	0.135274i	0.378253	+	0.925702i	$0.376525\pi$
$104$	0.271478	+	0.156738i	0.0266206	+	0.0153694i
$105$	7.95536	−	4.13721i	0.776364	−	0.403750i
$106$	−10.8689			−1.05568
$107$	3.96645	+	6.87009i	0.383451	+	0.664157i	0.991553	−	0.129702i	$-0.0414021\pi$
$107$	3.96645	+	6.87009i	0.383451	+	0.664157i	−0.608102	+	0.793859i	$0.708069\pi$
$108$	−5.09546	−	1.01799i	−0.490311	−	0.0979565i
$109$			16.0166i			1.53411i	0.641580	+	0.767056i	$0.278279\pi$
$109$			16.0166i			1.53411i	−0.641580	+	0.767056i	$0.721721\pi$
$110$	−2.93890			−0.280213
$111$	3.07853	−	3.21408i	0.292201	−	0.305067i
$112$	0.515836	+	2.59498i	0.0487420	+	0.245202i
$113$	5.37956			0.506066			0.253033	−	0.967458i	$-0.418572\pi$
$113$	5.37956			0.506066			0.253033	+	0.967458i	$0.418572\pi$
$114$	5.41161	+	5.26445i	0.506844	+	0.493061i
$115$	−3.29041	+	5.69916i	−0.306833	+	0.531450i
$116$	2.28866			0.212497
$117$	−0.939555	+	0.0404955i	−0.0868619	+	0.00374381i
$118$	5.30675	−	9.19155i	0.488526	−	0.846151i
$119$	0.958651	+	1.09341i	0.0878794	+	0.100233i
$120$	−3.29180	−	0.806473i	−0.300499	−	0.0736206i
$121$	−4.37208	−	7.57266i	−0.397461	−	0.688423i
$122$	−5.26836	+	9.12507i	−0.476975	+	0.826145i
$123$	6.03723	+	5.78262i	0.544359	+	0.521402i
$124$			0.777858i			0.0698537i
$125$		−	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	$0.732839\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.50406	−	6.22977i	−0.572650	−	0.548500i
$130$	−0.613386			−0.0537975
$131$	6.46873	+	3.73472i	0.565175	+	0.326304i	0.755220	−	0.655471i	$-0.227530\pi$
$131$	6.46873	+	3.73472i	0.565175	+	0.326304i	−0.190045	+	0.981775i	$0.560863\pi$
$132$	0.727263	+	2.49773i	0.0633001	+	0.217399i
$133$	2.16071	+	11.3283i	0.187357	+	0.982292i
$134$			0.0196594i			0.00169832i
$135$	9.63060	−	3.26014i	0.828870	−	0.280588i
$136$		−	0.549617i		−	0.0471293i
$137$	−15.9908	+	9.23230i	−1.36619	+	0.788769i	−0.990439	−	0.137952i	$-0.955948\pi$
$137$	−15.9908	+	9.23230i	−1.36619	+	0.788769i	−0.375749	+	0.926721i	$0.622615\pi$
$138$	5.65788	+	1.38615i	0.481631	+	0.117997i
$139$	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
$142$	7.25717			0.609008
$143$	0.235412	+	0.407746i	0.0196862	+	0.0340974i
$144$	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
$147$	−1.83805	−	11.9842i	−0.151600	−	0.988442i
$148$	−2.22529	−	1.28477i	−0.182918	−	0.105608i
$149$	10.7487	+	6.20574i	0.880564	+	0.508394i	0.870844	−	0.491559i	$-0.163573\pi$
$149$	10.7487	+	6.20574i	0.880564	+	0.508394i	0.00971998	+	0.999953i	$0.496906\pi$
$150$	−1.94774	+	0.567123i	−0.159032	+	0.0463054i
$151$	1.29008	+	0.744830i	0.104985	+	0.0606134i	0.551573	−	0.834126i	$-0.314028\pi$
$151$	1.29008	+	0.744830i	0.104985	+	0.0606134i	−0.446588	+	0.894740i	$0.647361\pi$
$152$	2.20865	−	3.75791i	0.179145	−	0.304806i
$153$	0.885149	+	1.39112i	0.0715601	+	0.112466i
$154$	−1.27780	+	3.76273i	−0.102968	+	0.303210i
$155$	−0.761028	−	1.31814i	−0.0611272	−	0.105875i
$156$	0.151789	+	0.521307i	0.0121528	+	0.0417380i
$157$	12.6482			1.00944			0.504718	−	0.863285i	$-0.331597\pi$
$157$	12.6482			1.00944			0.504718	+	0.863285i	$0.331597\pi$
$158$	−4.65887	+	2.68980i	−0.370639	+	0.213989i
$159$	−13.5952	−	13.0218i	−1.07817	−	1.03270i
$160$			1.95673i			0.154693i
$161$	5.86612	+	6.69071i	0.462315	+	0.527302i
$162$	−5.15394	−	7.37814i	−0.404932	−	0.579681i
$163$	4.20038	+	7.27527i	0.328999	+	0.569843i	0.982314	−	0.187243i	$-0.0599553\pi$
$163$	4.20038	+	7.27527i	0.328999	+	0.569843i	−0.653314	+	0.757087i	$0.726622\pi$
$164$	2.41328	−	4.17992i	0.188445	−	0.326397i
$165$	−3.67608	−	3.52105i	−0.286183	−	0.274114i
$166$	9.65025	+	5.57157i	0.749005	+	0.432438i
$167$	−2.00846	+	3.47875i	−0.155419	+	0.269194i	−0.933212	−	0.359327i	$-0.883006\pi$
$167$	−2.00846	+	3.47875i	−0.155419	+	0.269194i	0.777792	+	0.628521i	$0.216339\pi$
$168$	−2.46378	+	3.86391i	−0.190085	+	0.298107i
$169$	−6.45087	−	11.1732i	−0.496220	−	0.859479i
$170$	0.537725	+	0.931367i	0.0412416	+	0.0714326i
$171$	0.461779	+	13.0685i	0.0353131	+	0.999376i
$172$	−2.59988	+	4.50313i	−0.198239	+	0.343361i
$173$	6.45572	−	11.1816i	0.490820	−	0.850125i	−0.509125	−	0.860693i	$-0.670031\pi$
$173$	6.45572	−	11.1816i	0.490820	−	0.850125i	0.999944	+	0.0105683i	$0.00336407\pi$
$174$	2.86274	+	2.74201i	0.217024	+	0.207871i
$175$	−2.93419	−	0.996434i	−0.221804	−	0.0753233i
$176$	1.30073	−	0.750974i	0.0980459	−	0.0566068i
$177$	17.6501	−	5.13919i	1.32667	−	0.386285i
$178$	−2.48533	+	4.30472i	−0.186284	+	0.322653i
$179$	−7.29410	+	12.6337i	−0.545186	+	0.944291i	0.453409	+	0.891303i	$0.350208\pi$
$179$	−7.29410	+	12.6337i	−0.545186	+	0.944291i	−0.998595	+	0.0529880i	$0.983126\pi$
$180$	−3.15127	−	4.95262i	−0.234882	−	0.369146i
$181$	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
$184$		−	3.36318i		−	0.247937i
$185$	5.02789			0.369658
$186$	−0.931941	+	0.972973i	−0.0683332	+	0.0713419i
$187$	0.412748	−	0.714901i	0.0301831	−	0.0522787i
$188$	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	−0.617764	−	0.786364i	$-0.711961\pi$
$191$	−3.39473	+	1.95995i	−0.245634	+	0.141817i	0.372129	+	0.928181i	$0.378628\pi$
$192$	1.66299	−	0.484213i	0.120016	−	0.0349451i
$193$			16.2304i			1.16829i	0.811649	+	0.584146i	$0.198570\pi$
$193$			16.2304i			1.16829i	−0.811649	+	0.584146i	$0.801430\pi$
$194$			2.31896i			0.166492i
$195$	−0.767245	−	0.734889i	−0.0549436	−	0.0526265i
$196$	−6.46783	+	2.67717i	−0.461988	+	0.191226i
$197$		−	11.6882i		−	0.832752i	−0.909192	−	0.416376i	$-0.863300\pi$
$197$		−	11.6882i		−	0.832752i	0.909192	−	0.416376i	$-0.136700\pi$
$198$	−2.08280	+	3.99557i	−0.148018	+	0.283953i
$199$	4.85635	+	8.41144i	0.344257	+	0.596271i	0.985219	−	0.171302i	$-0.0547974\pi$
$199$	4.85635	+	8.41144i	0.344257	+	0.596271i	−0.640961	+	0.767573i	$0.721464\pi$
$200$	0.585613	+	1.01431i	0.0414091	+	0.0717226i
$201$	−0.0235537	+	0.0245907i	−0.00166135	+	0.00173450i
$202$		−	2.01100i		−	0.141493i
$203$	1.18057	+	5.93902i	0.0828601	+	0.416838i
$204$	0.658488	−	0.687481i	0.0461034	−	0.0481333i
$205$			9.44424i			0.659614i
$206$			2.74576i			0.191306i
$207$	5.41635	+	8.51247i	0.376462	+	0.591658i
$208$	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	$0.525271\pi$
$212$	−5.43443	+	9.41271i	−0.373238	+	0.646468i
$213$	9.07753	+	8.69471i	0.621982	+	0.595752i
$214$	7.93290			0.542282
$215$		−	10.1745i		−	0.693896i
$216$	−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
$219$	−12.4751	+	3.63237i	−0.842988	+	0.245453i
$220$	−1.46945	+	2.54516i	−0.0990703	+	0.171595i
$221$	0.0861458	−	0.149209i	0.00579479	−	0.0100369i
$222$	−1.24421	−	4.27313i	−0.0835057	−	0.286793i
$223$	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	$0.126971\pi$
$224$	2.50524	+	0.850762i	0.167388	+	0.0568439i
$225$	−3.11576	−	1.62418i	−0.207717	−	0.108278i
$226$	2.68978	−	4.65884i	0.178921	−	0.309901i
$227$	−1.16303	+	2.01443i	−0.0771930	+	0.133702i	−0.902038	−	0.431657i	$-0.857929\pi$
$227$	−1.16303	+	2.01443i	−0.0771930	+	0.133702i	0.824845	+	0.565359i	$0.191262\pi$
$228$	7.26495	−	2.05437i	0.481133	−	0.136054i
$229$	−8.54257	−	14.7962i	−0.564509	−	0.977758i	−0.997095	−	0.0761657i	$-0.975732\pi$
$229$	−8.54257	−	14.7962i	−0.564509	−	0.977758i	0.432586	−	0.901593i	$-0.357601\pi$
$230$	3.29041	+	5.69916i	0.216963	+	0.375792i
$231$	−6.10640	+	3.17565i	−0.401771	+	0.208942i
$232$	1.14433	−	1.98204i	0.0751290	−	0.130127i
$233$	−19.3447	−	11.1687i	−1.26731	−	0.731683i	−0.292834	−	0.956163i	$-0.594598\pi$
$233$	−19.3447	−	11.1687i	−1.26731	−	0.731683i	−0.974479	+	0.224480i	$0.927932\pi$
$234$	−0.434707	+	0.833926i	−0.0284177	+	0.0545155i
$235$	−9.07458	+	15.7176i	−0.591960	+	1.02531i
$236$	−5.30675	−	9.19155i	−0.345440	−	0.598319i
$237$	−9.05008	−	2.21722i	−0.587866	−	0.144024i
$238$	1.42624	−	0.283512i	0.0924497	−	0.0183774i
$239$		−	1.32903i		−	0.0859679i	−0.999076	−	0.0429840i	$-0.986314\pi$
$239$		−	1.32903i		−	0.0859679i	0.999076	−	0.0429840i	$-0.0136864\pi$
$240$	−2.34432	+	2.44754i	−0.151326	+	0.157988i
$241$	2.69501	−	1.55597i	0.173601	−	0.100229i	−0.410682	−	0.911779i	$-0.634709\pi$
$241$	2.69501	−	1.55597i	0.173601	−	0.100229i	0.584283	+	0.811550i	$0.301376\pi$
$242$	−8.74415			−0.562095
$243$	2.39291	−	15.4037i	0.153505	−	0.988148i
$244$	5.26836	+	9.12507i	0.337272	+	0.584173i
$245$	8.34097	−	10.8645i	0.532885	−	0.694110i
$246$	8.02651	−	2.33708i	0.511752	−	0.149007i
$247$	1.18861	−	0.674009i	0.0756292	−	0.0428862i
$248$	0.673645	+	0.388929i	0.0427765	+	0.0246970i
$249$	5.39566	+	18.5309i	0.341936	+	1.17435i
$250$	−10.4576	−	6.03770i	−0.661397	−	0.381857i
$251$	−11.6792	−	6.74302i	−0.737187	−	0.425615i	0.0838584	−	0.996478i	$-0.473276\pi$
$251$	−11.6792	−	6.74302i	−0.737187	−	0.425615i	−0.821046	+	0.570862i	$0.806609\pi$
$252$	−7.71108	+	1.88130i	−0.485752	+	0.118511i
$253$	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
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.3783			−0.896894			−0.448447	−	0.893809i	$-0.648023\pi$
$257$	−14.3783			−0.896894			−0.448447	+	0.893809i	$0.648023\pi$
$258$	−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
$261$	0.295654	+	6.85961i	0.0183005	+	0.424599i
$262$	6.46873	−	3.73472i	0.399639	−	0.230732i
$263$			19.1047i			1.17805i	0.808116	+	0.589024i	$0.200488\pi$
$263$			19.1047i			1.17805i	−0.808116	+	0.589024i	$0.799512\pi$
$264$	2.52673	+	0.619035i	0.155509	+	0.0380989i
$265$		−	21.2674i		−	1.30645i
$266$	10.8910	+	3.79294i	0.667769	+	0.232560i
$267$	−8.26617	+	2.40686i	−0.505882	+	0.147298i
$268$	0.0170256	+	0.00982972i	0.00104000	+	0.000600446i
$269$	24.2023			1.47564			0.737820	−	0.674997i	$-0.235855\pi$
$269$	24.2023			1.47564			0.737820	+	0.674997i	$0.235855\pi$
$270$	1.99193	−	9.97041i	0.121225	−	0.606780i
$271$	−0.589025	+	1.02022i	−0.0357807	+	0.0619740i	−0.883361	−	0.468693i	$-0.844725\pi$
$271$	−0.589025	+	1.02022i	−0.0357807	+	0.0619740i	0.847581	+	0.530667i	$0.178058\pi$
$272$	−0.475982	−	0.274809i	−0.0288607	−	0.0166627i
$273$	−1.27448	+	0.662798i	−0.0771352	+	0.0401144i
$274$			18.4646i			1.11549i
$275$			1.75912i			0.106079i
$276$	4.02938	−	4.20679i	0.242540	−	0.253219i
$277$	−7.82530	+	13.5538i	−0.470177	+	0.814370i	−0.999418	−	0.0341010i	$-0.989143\pi$
$277$	−7.82530	+	13.5538i	−0.470177	+	0.814370i	0.529242	+	0.848471i	$0.322477\pi$
$278$	−9.32549	−	16.1522i	−0.559306	−	0.968746i
$279$	−2.33141	+	0.100485i	−0.139578	+	0.00601590i
$280$	−5.07766	+	1.00935i	−0.303448	+	0.0603202i
$281$	6.14057	−	10.6358i	0.366316	−	0.634477i	−0.622671	−	0.782484i	$-0.713952\pi$
$281$	6.14057	−	10.6358i	0.366316	−	0.634477i	0.988986	+	0.148007i	$0.0472857\pi$
$282$	15.6038	+	3.82284i	0.929191	+	0.227647i
$283$	−10.5478			−0.626999			−0.313499	−	0.949588i	$-0.601501\pi$
$283$	−10.5478			−0.626999			−0.313499	+	0.949588i	$0.601501\pi$
$284$	3.62859	−	6.28490i	0.215317	−	0.372940i
$285$	−10.3011	+	10.5890i	−0.610184	+	0.627241i
$286$	0.470824			0.0278404
$287$	12.0917	+	4.10625i	0.713748	+	0.242384i
$288$	2.66026	+	1.38673i	0.156757	+	0.0817141i
$289$	16.6979			0.982231
$290$			4.47828i			0.262974i
$291$	−2.77831	+	2.90064i	−0.162868	+	0.170039i
$292$	3.75080	+	6.49658i	0.219499	+	0.380183i
$293$	−17.7163			−1.03500			−0.517499	−	0.855684i	$-0.673137\pi$
$293$	−17.7163			−1.03500			−0.517499	+	0.855684i	$0.673137\pi$
$294$	−11.2977	−	4.40031i	−0.658893	−	0.256631i
$295$	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
$298$	10.7487	−	6.20574i	0.622653	−	0.359489i
$299$	0.527138	−	0.913030i	0.0304852	−	0.0528019i
$300$	−0.482726	+	1.97035i	−0.0278702	+	0.113758i
$301$	−13.0266	−	4.42376i	−0.750843	−	0.254982i
$302$	1.29008	−	0.744830i	0.0742360	−	0.0428601i
$303$	2.40935	−	2.51543i	0.138413	−	0.144508i
$304$	−2.15012	−	3.79170i	−0.123318	−	0.217469i
$305$	−17.8553	−	10.3087i	−1.02239	−	0.590277i
$306$	1.64732	−	0.0710007i	0.0941711	−	0.00405884i
$307$	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	$0.106543\pi$
$308$	2.61972	+	2.98797i	0.149273	+	0.170256i
$309$	−3.28966	+	3.43450i	−0.187142	+	0.195382i
$310$	−1.52206			−0.0864469
$311$	5.09596	+	2.94215i	0.288965	+	0.166834i	0.637475	−	0.770471i	$-0.279979\pi$
$311$	5.09596	+	2.94215i	0.288965	+	0.166834i	−0.348510	+	0.937305i	$0.613312\pi$
$312$	0.527360	+	0.129200i	0.0298559	+	0.00731453i
$313$	−25.7655			−1.45635			−0.728176	−	0.685391i	$-0.759631\pi$
$313$	−25.7655			−1.45635			−0.728176	+	0.685391i	$0.759631\pi$
$314$	6.32409	−	10.9536i	0.356889	−	0.618150i
$315$	11.2264	−	10.7322i	0.632536	−	0.604693i
$316$			5.37959i			0.302626i
$317$	−12.3340			−0.692747			−0.346373	−	0.938097i	$-0.612587\pi$
$317$	−12.3340			−0.692747			−0.346373	+	0.938097i	$0.612587\pi$
$318$	−18.0748	+	5.26285i	−1.01359	+	0.295126i
$319$	2.97692	−	1.71872i	0.166675	−	0.0962301i
$320$	1.69457	+	0.978363i	0.0947296	+	0.0546921i
$321$	9.92276	+	9.50429i	0.553834	+	0.530478i
$322$	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
$325$			0.367151i			0.0203659i
$326$	8.40076			0.465275
$327$	7.75544	+	26.6354i	0.428877	+	1.47294i
$328$	−2.41328	−	4.17992i	−0.133251	−	0.230797i
$329$	16.1781	+	18.4522i	0.891927	+	1.01730i
$330$	−4.88736	+	1.42305i	−0.269041	+	0.0783366i
$331$	−29.1242	+	16.8149i	−1.60081	+	0.924228i	−0.609485	+	0.792798i	$0.708624\pi$
$331$	−29.1242	+	16.8149i	−1.60081	+	0.924228i	−0.991325	+	0.131430i	$0.958043\pi$
$332$	9.65025	−	5.57157i	0.529626	−	0.305780i
$333$	3.56327	−	6.83565i	0.195266	−	0.374591i
$334$	2.00846	+	3.47875i	0.109898	+	0.190349i
$335$	−0.0384681			−0.00210174
$336$	2.11435	+	4.06565i	0.115347	+	0.221799i
$337$	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	$0.0480912\pi$
$338$	−12.9017			−0.701762
$339$	8.94616	−	2.60485i	0.485889	−	0.141476i
$340$	1.07545			0.0583244
$341$	0.584152	+	1.01178i	0.0316336	+	0.0547910i
$342$	11.5486	+	6.13436i	0.624476	+	0.331708i
$343$	−10.2835	−	15.4029i	−0.555259	−	0.831678i
$344$	2.59988	+	4.50313i	0.140176	+	0.242793i
$345$	−2.71232	+	11.0709i	−0.146026	+	0.596038i
$346$	−6.45572	−	11.1816i	−0.347062	−	0.601129i
$347$			32.8025i			1.76093i	0.474109	+	0.880466i	$0.342770\pi$
$347$			32.8025i			1.76093i	−0.474109	+	0.880466i	$0.657230\pi$
$348$	3.80602	−	1.10820i	0.204024	−	0.0594057i
$349$	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
$351$	−1.54286	+	0.522288i	−0.0823519	+	0.0278777i
$352$		−	1.50195i		−	0.0800541i
$353$	−30.2002	−	17.4361i	−1.60740	−	0.928031i	−0.989950	−	0.141418i	$-0.954834\pi$
$353$	−30.2002	−	17.4361i	−1.60740	−	0.928031i	−0.617446	−	0.786613i	$-0.711833\pi$
$354$	4.37440	−	17.8551i	0.232497	−	0.948986i
$355$			14.2003i			0.753674i
$356$	2.48533	+	4.30472i	0.131722	+	0.228150i
$357$	2.12367	+	1.35414i	0.112397	+	0.0716684i
$358$	7.29410	+	12.6337i	0.385505	+	0.667714i
$359$	−0.140731	−	0.0812512i	−0.00742751	−	0.00428827i	0.496282	−	0.868162i	$-0.334698\pi$
$359$	−0.140731	−	0.0812512i	−0.00742751	−	0.00428827i	−0.503709	+	0.863873i	$0.668032\pi$
$360$	−5.86473	+	0.252774i	−0.309099	+	0.0133224i
$361$	−9.24371	−	16.5998i	−0.486511	−	0.873675i
$362$	14.2653	−	8.23605i	0.749765	−	0.432877i
$363$	−10.9375	−	10.4762i	−0.574070	−	0.549860i
$364$	0.546770	+	0.623628i	0.0286585	+	0.0326870i
$365$	−12.7120	−	7.33929i	−0.665377	−	0.384156i
$366$	−4.34276	+	17.7259i	−0.227000	+	0.926548i
$367$	−13.0852	−	22.6642i	−0.683041	−	1.18306i	−0.974048	−	0.226341i	$-0.927323\pi$
$367$	−13.0852	−	22.6642i	−0.683041	−	1.18306i	0.291007	−	0.956721i	$-0.406010\pi$
$368$	−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
$371$	−27.2291	−	9.24682i	−1.41366	−	0.480071i
$372$	0.376649	+	1.29357i	0.0195284	+	0.0670685i
$373$	27.3424	−	15.7862i	1.41574	−	0.817376i	0.419816	−	0.907609i	$-0.362095\pi$
$373$	27.3424	−	15.7862i	1.41574	−	0.817376i	0.995921	+	0.0902333i	$0.0287613\pi$
$374$	−0.412748	−	0.714901i	−0.0213427	−	0.0369666i
$375$	−5.84706	−	20.0813i	−0.301941	−	1.03699i
$376$		−	9.27527i		−	0.478336i
$377$	0.621321	−	0.358720i	0.0319996	−	0.0184750i
$378$	−11.8993	−	6.88533i	−0.612031	−	0.354143i
$379$		−	31.9663i		−	1.64200i	−0.570930	−	0.820998i	$-0.693417\pi$
$379$		−	31.9663i		−	1.64200i	0.570930	−	0.820998i	$-0.306583\pi$
$380$	7.35319	+	4.32173i	0.377211	+	0.221700i
$381$	−7.82582	−	1.91728i	−0.400929	−	0.0982254i
$382$			3.91990i			0.200559i
$383$	13.6389	−	23.6233i	0.696916	−	1.20709i	−0.272614	−	0.962123i	$-0.587888\pi$
$383$	13.6389	−	23.6233i	0.696916	−	1.20709i	0.969530	−	0.244971i	$-0.0787783\pi$
$384$	0.412154	−	1.68230i	0.0210327	−	0.0858494i
$385$	−7.36264	−	2.50030i	−0.375235	−	0.127427i
$386$	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
$389$	13.8123	−	7.97456i	0.700313	−	0.404326i	−0.107151	−	0.994243i	$-0.534173\pi$
$389$	13.8123	−	7.97456i	0.700313	−	0.404326i	0.807464	+	0.589917i	$0.200839\pi$
$390$	−1.02006	+	0.297010i	−0.0516525	+	0.0150397i
$391$	−1.84846			−0.0934808
$392$	−0.915417	+	6.93989i	−0.0462355	+	0.350517i
$393$	12.5658	+	3.07856i	0.633862	+	0.155293i
$394$	−10.1223	−	5.84412i	−0.509955	−	0.294422i
$395$	−5.26319	−	9.11612i	−0.264820	−	0.458682i
$396$	2.41886	+	3.80154i	0.121552	+	0.191035i
$397$	16.6778	−	28.8867i	0.837033	−	1.44978i	−0.0553310	−	0.998468i	$-0.517621\pi$
$397$	16.6778	−	28.8867i	0.837033	−	1.44978i	0.892364	−	0.451316i	$-0.149045\pi$
$398$	9.71269			0.486853
$399$	9.07857	+	17.7927i	0.454497	+	0.890748i
$400$	1.17123			0.0585613
$401$	10.7987	−	18.7038i	0.539259	−	0.934024i	−0.459685	−	0.888082i	$-0.652038\pi$
$401$	10.7987	−	18.7038i	0.539259	−	0.934024i	0.998944	−	0.0459422i	$-0.0146290\pi$
$402$	0.00951936	+	0.0326935i	0.000474783	+	0.00163060i
$403$	0.121920	+	0.211171i	0.00607326	+	0.0105192i
$404$	−1.74157	−	1.00550i	−0.0866465	−	0.0500254i
$405$	14.4370	−	10.0848i	0.717380	−	0.501120i
$406$	5.73363	+	1.94710i	0.284555	+	0.0966332i
$407$	−3.85932			−0.191299
$408$	−0.266132	−	0.914008i	−0.0131755	−	0.0452501i
$409$	32.5459	−	18.7904i	1.60929	−	0.929125i	0.619764	−	0.784788i	$-0.287228\pi$
$409$	32.5459	−	18.7904i	1.60929	−	0.929125i	0.989529	−	0.144337i	$-0.0461049\pi$
$410$	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
$413$	21.1145	−	18.5122i	1.03898	−	0.910927i
$414$	10.0802	−	0.434463i	0.495414	−	0.0213527i
$415$	−10.9020	+	18.8829i	−0.535160	+	0.926924i
$416$		−	0.313476i		−	0.0153694i
$417$	7.68708	−	31.3765i	0.376438	−	1.53651i
$418$	0.0507609	−	6.54664i	0.00248280	−	0.320207i
$419$		−	11.3105i		−	0.552555i	−0.961078	−	0.276277i	$-0.910899\pi$
$419$		−	11.3105i		−	0.552555i	0.961078	−	0.276277i	$-0.0891009\pi$
$420$	−7.56061	−	4.82094i	−0.368920	−	0.235238i
$421$	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	$0.330445\pi$
$422$			16.4754i			0.802010i
$423$	14.9377	+	23.4764i	0.726295	+	1.14146i
$424$	5.43443	+	9.41271i	0.263919	+	0.457122i
$425$	0.557482	−	0.321863i	0.0270419	−	0.0156126i
$426$	12.0686	−	3.51402i	0.584726	−	0.170255i
$427$	−20.9617	+	18.3783i	−1.01441	+	0.889390i
$428$	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
$431$	−4.71281	−	8.16283i	−0.227008	−	0.393190i	0.729912	−	0.683541i	$-0.239561\pi$
$431$	−4.71281	−	8.16283i	−0.227008	−	0.393190i	−0.956920	+	0.290352i	$0.906228\pi$
$432$	1.66612	+	4.92179i	0.0801613	+	0.236800i
$433$	−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	$0.854765\pi$
$434$	−0.661772	+	1.94872i	−0.0317661	+	0.0935415i
$435$	−5.36536	+	5.60159i	−0.257249	+	0.268576i
$436$	13.8708	−	8.00830i	0.664290	−	0.383528i
$437$	−12.6385	−	7.42810i	−0.604583	−	0.355334i
$438$	−3.09182	+	12.6199i	−0.147733	+	0.603004i
$439$	0.366308	+	0.211488i	0.0174829	+	0.0100938i	0.508716	−	0.860934i	$-0.330120\pi$
$439$	0.366308	+	0.211488i	0.0174829	+	0.0100938i	−0.491233	+	0.871028i	$0.663454\pi$
$440$	1.46945	+	2.54516i	0.0700533	+	0.121336i
$441$	−8.85958	−	19.0396i	−0.421885	−	0.906649i
$442$	−0.0861458	−	0.149209i	−0.00409754	−	0.00709714i
$443$		−	26.8666i		−	1.27647i	−0.769842	−	0.638235i	$-0.779665\pi$
$443$		−	26.8666i		−	1.27647i	0.769842	−	0.638235i	$-0.220335\pi$
$444$	−4.32274	−	1.05905i	−0.205148	−	0.0502602i
$445$	−8.42316	−	4.86312i	−0.399296	−	0.230534i
$446$		−	18.0344i		−	0.853956i
$447$	20.8798	+	5.11545i	0.987582	+	0.241952i
$448$	1.98940	−	1.74422i	0.0939903	−	0.0824065i
$449$	−13.5101			−0.637581			−0.318790	−	0.947825i	$-0.603277\pi$
$449$	−13.5101			−0.637581			−0.318790	+	0.947825i	$0.603277\pi$
$450$	−2.96446	+	1.88624i	−0.139746	+	0.0889182i
$451$		−	7.24923i		−	0.341353i
$452$	−2.68978	−	4.65884i	−0.126517	−	0.219133i
$453$	2.50605	+	0.613970i	0.117745	+	0.0288468i
$454$	1.16303	+	2.01443i	0.0545837	+	0.0945417i
$455$	−1.53668	−	0.521845i	−0.0720405	−	0.0244645i
$456$	1.85334	−	7.31882i	0.0867907	−	0.342735i
$457$	−19.9506	−	34.5555i	−0.933251	−	1.61644i	−0.777723	−	0.628607i	$-0.783626\pi$
$457$	−19.9506	−	34.5555i	−0.933251	−	1.61644i	−0.155528	−	0.987832i	$-0.549708\pi$
$458$	−17.0851			−0.798336
$459$	2.14559	+	1.88482i	0.100148	+	0.0879760i
$460$	6.58083			0.306833
$461$	−15.6780	+	9.05172i	−0.730199	+	0.421580i	−0.818495	−	0.574514i	$-0.805191\pi$
$461$	−15.6780	+	9.05172i	−0.730199	+	0.421580i	0.0882961	+	0.996094i	$0.471858\pi$
$462$	−0.303005	+	6.87612i	−0.0140970	+	0.319906i
$463$	−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
$465$	−1.90384	−	1.82355i	−0.0882886	−	0.0845652i
$466$	−19.3447	+	11.1687i	−0.896126	+	0.517378i
$467$	−5.81673	+	3.35829i	−0.269166	+	0.155403i	−0.628509	−	0.777803i	$-0.716334\pi$
$467$	−5.81673	+	3.35829i	−0.269166	+	0.155403i	0.359342	+	0.933206i	$0.383001\pi$
$468$	0.504848	+	0.793431i	0.0233366	+	0.0366763i
$469$	−0.0167255	+	0.0492515i	−0.000772312	+	0.00227422i
$470$	9.07458	+	15.7176i	0.418579	+	0.725000i
$471$	21.0338	−	6.12442i	0.969187	−	0.282198i
$472$	−10.6135			−0.488526
$473$			7.80978i			0.359094i
$474$	−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
$477$	−28.9140	−	15.0722i	−1.32388	−	0.690110i
$478$	−1.15098	−	0.664516i	−0.0526444	−	0.0303943i
$479$	14.1732	−	8.18290i	0.647590	−	0.373886i	−0.139942	−	0.990160i	$-0.544692\pi$
$479$	14.1732	−	8.18290i	0.647590	−	0.373886i	0.787532	+	0.616274i	$0.211358\pi$
$480$	0.947472	+	3.25402i	0.0432460	+	0.148525i
$481$	−0.805489			−0.0367271
$482$		−	3.11193i		−	0.141745i
$483$	12.9950	+	8.28614i	0.591295	+	0.377032i
$484$	−4.37208	+	7.57266i	−0.198731	+	0.344212i
$485$	−4.53757			−0.206040
$486$	−12.1435	−	9.77417i	−0.550842	−	0.443365i
$487$	21.2291	+	12.2567i	0.961984	+	0.555402i	0.896783	−	0.442470i	$-0.145898\pi$
$487$	21.2291	+	12.2567i	0.961984	+	0.555402i	0.0652012	+	0.997872i	$0.479231\pi$
$488$	10.5367			0.476975
$489$	10.5080	+	10.0648i	0.475187	+	0.455147i
$490$	−5.23848	−	12.6558i	−0.236651	−	0.571729i
$491$	−28.4824	+	16.4443i	−1.28539	+	0.742121i	−0.977829	−	0.209406i	$-0.932847\pi$
$491$	−28.4824	+	16.4443i	−1.28539	+	0.742121i	−0.307563	+	0.951528i	$0.599514\pi$
$492$	1.98929	−	8.11971i	0.0896839	−	0.366065i
$493$	−1.08936	−	0.628943i	−0.0490624	−	0.0283262i
$494$	0.0105944	−	1.36637i	0.000476666	−	0.0614758i
$495$	−7.81823	−	4.07547i	−0.351403	−	0.183179i
$496$	0.673645	−	0.388929i	0.0302476	−	0.0174634i
$497$	18.1809	+	6.17413i	0.815526	+	0.276947i
$498$	18.7461	+	4.59270i	0.840033	+	0.205804i
$499$	0.193817	−	0.335701i	0.00867645	−	0.0150281i	−0.861655	−	0.507495i	$-0.830571\pi$
$499$	0.193817	−	0.335701i	0.00867645	−	0.0150281i	0.870331	+	0.492467i	$0.163905\pi$
$500$	−10.4576	+	6.03770i	−0.467678	+	0.270014i
$501$	−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	0.295134	−	0.955456i	$-0.404636\pi$
$503$	−8.62901	−	4.98196i	−0.384749	−	0.222135i	−0.679882	+	0.733321i	$0.737969\pi$
$504$	−2.22629	+	7.61864i	−0.0991667	+	0.339361i
$505$	3.93497			0.175104
$506$	−2.52566	−	4.37458i	−0.112279	−	0.194474i
$507$	−16.1380	−	15.4574i	−0.716712	−	0.686486i
$508$			4.65186i			0.206393i
$509$	35.7330			1.58384			0.791920	−	0.610625i	$-0.209082\pi$
$509$	35.7330			1.58384			0.791920	+	0.610625i	$0.209082\pi$
$510$	1.34521	+	1.28848i	0.0595670	+	0.0570549i
$511$	−14.9237	+	13.0844i	−0.660184	+	0.578820i
$512$	−1.00000			−0.0441942
$513$	7.09589	+	21.5093i	0.313291	+	0.949657i
$514$	−7.18915	+	12.4520i	−0.317100	+	0.549233i
$515$	−5.37271			−0.236750
$516$	−2.14311	+	8.74756i	−0.0943450	+	0.385090i
$517$	6.96549	−	12.0646i	0.306342	−	0.530600i
$518$	−4.48184	−	5.11185i	−0.196921	−	0.224602i
$519$	5.32151	−	21.7209i	0.233588	−	0.953442i
$520$	0.306693	+	0.531208i	0.0134494	+	0.0232950i
$521$	20.7756	−	35.9843i	0.910193	−	1.57650i	0.0964033	−	0.995342i	$-0.469266\pi$
$521$	20.7756	−	35.9843i	0.910193	−	1.57650i	0.813790	−	0.581159i	$-0.197401\pi$
$522$	6.08843	+	3.17376i	0.266483	+	0.138912i
$523$			7.33538i			0.320754i	0.987056	+	0.160377i	$0.0512710\pi$
$523$			7.33538i			0.320754i	−0.987056	+	0.160377i	$0.948729\pi$
$524$		−	7.46944i		−	0.326304i
$525$	−5.36202	−	0.236284i	−0.234018	−	0.0103123i
$526$	16.5452	+	9.55236i	0.721404	+	0.416503i
$527$	0.213762	−	0.370247i	0.00931162	−	0.0161282i
$528$	1.79946	−	1.87869i	0.0783116	−	0.0817595i
$529$	11.6890			0.508217
$530$	−18.4181	−	10.6337i	−0.800031	−	0.461898i
$531$	26.8635	−	17.0929i	1.16578	−	0.741767i
$532$	8.73028	−	7.53540i	0.378506	−	0.326701i
$533$		−	1.51301i		−	0.0655356i
$534$	−2.04868	+	8.36215i	−0.0886552	+	0.361865i
$535$			15.5225i			0.671096i
$536$	0.0170256	−	0.00982972i	0.000735393	−	0.000424579i
$537$	−6.01259	+	24.5417i	−0.259462	+	1.05905i
$538$	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
$541$	−31.0130			−1.33335			−0.666676	−	0.745348i	$-0.732283\pi$
$541$	−31.0130			−1.33335			−0.666676	+	0.745348i	$0.732283\pi$
$542$	0.589025	+	1.02022i	0.0253008	+	0.0438222i
$543$	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
$546$	−0.0632409	+	1.43513i	−0.00270646	+	0.0614180i
$547$	−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	$0.748614\pi$
$548$	15.9908	+	9.23230i	0.683094	+	0.394384i
$549$	−26.6692	+	16.9692i	−1.13822	+	0.724229i
$550$	1.52344	+	0.879560i	0.0649598	+	0.0375046i
$551$	−4.92088	−	8.67792i	−0.209637	−	0.369692i
$552$	−1.62850	−	5.59294i	−0.0693135	−	0.238051i
$553$	−13.9599	+	2.77499i	−0.593637	+	0.118005i
$554$	7.82530	+	13.5538i	0.332465	+	0.575847i
$555$	8.36133	−	2.43457i	0.354919	−	0.103342i
$556$	−18.6510			−0.790978
$557$	16.4038	−	9.47073i	0.695051	−	0.401288i	−0.110451	−	0.993882i	$-0.535229\pi$
$557$	16.4038	−	9.47073i	0.695051	−	0.401288i	0.805501	+	0.592594i	$0.201896\pi$
$558$	−1.07868	+	2.06930i	−0.0456643	+	0.0876006i
$559$			1.63000i			0.0689417i
$560$	−1.66471	+	4.90206i	−0.0703467	+	0.207150i
$561$	0.340232	−	1.38873i	0.0143646	−	0.0586323i
$562$	−6.14057	−	10.6358i	−0.259024	−	0.448643i
$563$	−6.55163	+	11.3478i	−0.276118	+	0.478251i	−0.970417	−	0.241436i	$-0.922381\pi$
$563$	−6.55163	+	11.3478i	−0.276118	+	0.478251i	0.694298	+	0.719687i	$0.255715\pi$
$564$	11.1126	−	11.6018i	0.467924	−	0.488526i
$565$	9.11606	+	5.26316i	0.383516	+	0.221423i
$566$	−5.27388	+	9.13462i	−0.221678	+	0.383957i
$567$	−6.63479	−	22.8687i	−0.278635	−	0.960397i
$568$	−3.62859	−	6.28490i	−0.152252	−	0.263708i
$569$	−0.848340	−	1.46937i	−0.0355643	−	0.0615991i	0.847695	−	0.530483i	$-0.177990\pi$
$569$	−0.848340	−	1.46937i	−0.0355643	−	0.0615991i	−0.883260	+	0.468884i	$0.844656\pi$
$570$	4.01984	+	14.2155i	0.168372	+	0.595423i
$571$	−6.96161	+	12.0579i	−0.291334	+	0.504606i	−0.974126	−	0.226008i	$-0.927433\pi$
$571$	−6.96161	+	12.0579i	−0.291334	+	0.504606i	0.682791	+	0.730614i	$0.260766\pi$
$572$	0.235412	−	0.407746i	0.00984308	−	0.0170487i
$573$	−4.69637	+	4.90315i	−0.196194	+	0.204832i
$574$	9.60194	−	8.41856i	0.400777	−	0.351384i
$575$	3.41131	−	1.96952i	0.142262	−	0.0821348i
$576$	2.53108	−	1.61048i	0.105461	−	0.0671035i
$577$	4.56240	−	7.90232i	0.189935	−	0.328978i	−0.755293	−	0.655387i	$-0.772505\pi$
$577$	4.56240	−	7.90232i	0.189935	−	0.328978i	0.945228	+	0.326409i	$0.105839\pi$
$578$	8.34896	−	14.4608i	0.347271	−	0.601491i
$579$	7.85899	+	26.9911i	0.326608	+	1.12171i
$580$	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
$583$			16.3245i			0.676091i
$584$	7.50160			0.310418
$585$	−1.63176	−	0.850603i	−0.0674652	−	0.0351681i
$586$	−8.85815	+	15.3428i	−0.365927	+	0.633804i
$587$	34.1873	−	19.7380i	1.41106	−	0.814675i	0.415571	−	0.909561i	$-0.363582\pi$
$587$	34.1873	−	19.7380i	1.41106	−	0.814675i	0.995488	+	0.0948856i	$0.0302485\pi$
$588$	−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
$591$	−5.65960	−	19.4374i	−0.232805	−	0.799549i
$592$			2.56954i			0.105608i
$593$			3.70698i			0.152227i	0.997099	+	0.0761137i	$0.0242512\pi$
$593$			3.70698i			0.152227i	−0.997099	+	0.0761137i	$0.975749\pi$
$594$	−1.52897	+	7.65311i	−0.0627345	+	0.314011i
$595$	0.554756	+	2.79077i	0.0227428	+	0.114410i
$596$		−	12.4115i		−	0.508394i
$597$	12.1490	+	11.6366i	0.497225	+	0.476256i
$598$	−0.527138	−	0.913030i	−0.0215563	−	0.0373366i
$599$	12.1719	+	21.0823i	0.497330	+	0.861400i	0.999995	−	0.00308075i	$-0.000980636\pi$
$599$	12.1719	+	21.0823i	0.497330	+	0.861400i	−0.502666	+	0.864481i	$0.667647\pi$
$600$	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	$0.812812\pi$
$602$	−10.3444	+	9.06952i	−0.421607	+	0.369646i
$603$	−0.0272624	+	0.0522992i	−0.00111021	+	0.00212979i
$604$		−	1.48966i		−	0.0606134i
$605$		−	17.1099i		−	0.695617i
$606$	−0.973751	−	3.34427i	−0.0395559	−	0.135852i
$607$	22.0425	−	12.7262i	0.894677	−	0.516542i	0.0192075	−	0.999816i	$-0.493886\pi$
$607$	22.0425	−	12.7262i	0.894677	−	0.516542i	0.875469	+	0.483274i	$0.160552\pi$
$608$	−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
$611$	1.45379	−	2.51803i	0.0588139	−	0.101869i
$612$	0.762172	−	1.46212i	0.0308090	−	0.0591028i
$613$	9.83488			0.397227			0.198613	−	0.980078i	$-0.436356\pi$
$613$	9.83488			0.397227			0.198613	+	0.980078i	$0.436356\pi$
$614$		−	22.9080i		−	0.924491i
$615$	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	0.547959	−	0.836505i	$-0.315405\pi$
$617$	2.42194	+	1.39831i	0.0975035	+	0.0562937i	−0.450455	+	0.892799i	$0.648738\pi$
$618$	1.32953	+	4.56618i	0.0534817	+	0.183679i
$619$	−12.8156	+	22.1972i	−0.515101	+	0.892181i	0.484745	+	0.874655i	$0.338912\pi$
$619$	−12.8156	+	22.1972i	−0.515101	+	0.892181i	−0.999846	+	0.0175258i	$0.994421\pi$
$620$	−0.761028	+	1.31814i	−0.0305636	+	0.0529377i
$621$	13.1292	+	11.5335i	0.526856	+	0.462823i
$622$	5.09596	−	2.94215i	0.204329	−	0.117970i
$623$	−9.88864	+	8.66992i	−0.396180	+	0.347353i
$624$	0.375571	−	0.392107i	0.0150349	−	0.0156968i
$625$	8.88605	−	15.3911i	0.355442	−	0.615644i
$626$	−12.8827	+	22.3136i	−0.514898	+	0.891829i
$627$	7.90693	−	8.12796i	0.315772	−	0.324600i
$628$	−6.32409	−	10.9536i	−0.252359	−	0.437098i
$629$	0.706132	+	1.22306i	0.0281553	+	0.0487665i
$630$	−3.68119	−	15.0885i	−0.146662	−	0.601139i
$631$	−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	$0.273488\pi$
$632$	4.65887	+	2.68980i	0.185320	+	0.106994i
$633$	−19.7389	+	20.6080i	−0.784552	+	0.819095i
$634$	−6.16700	+	10.6816i	−0.244923	+	0.424219i
$635$	−4.55121	−	7.88292i	−0.180609	−	0.312824i
$636$	−4.47965	+	18.2847i	−0.177630	+	0.725035i
$637$	−1.33626	+	1.74055i	−0.0529445	+	0.0689629i
$638$		−	3.43745i		−	0.136090i
$639$	19.3059	+	10.0638i	0.763732	+	0.398116i
$640$	1.69457	−	0.978363i	0.0669839	−	0.0386732i
$641$	−30.8990			−1.22044			−0.610218	−	0.792234i	$-0.708918\pi$
$641$	−30.8990			−1.22044			−0.610218	+	0.792234i	$0.708918\pi$
$642$	13.1923	−	3.84121i	0.520660	−	0.151601i
$643$	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	$0.622372\pi$
$644$	2.86127	−	8.42557i	0.112750	−	0.332014i
$645$	−4.92664	−	16.9201i	−0.193986	−	0.666229i
$646$	−2.08398	+	1.18174i	−0.0819933	+	0.0464949i
$647$	−4.74683	−	2.74059i	−0.186617	−	0.107744i	0.403781	−	0.914856i	$-0.367696\pi$
$647$	−4.74683	−	2.74059i	−0.186617	−	0.107744i	−0.590398	+	0.807112i	$0.701029\pi$
$648$	−3.81268	+	8.15251i	−0.149776	+	0.320261i
$649$	−13.8052	−	7.97046i	−0.541903	−	0.312868i
$650$	0.317962	+	0.183575i	0.0124715	+	0.00720042i
$651$	−3.16250	+	1.64467i	−0.123948	+	0.0644596i
$652$	4.20038	−	7.27527i	0.164500	−	0.284922i
$653$	21.1965	−	12.2378i	0.829485	−	0.478903i	−0.0241916	−	0.999707i	$-0.507701\pi$
$653$	21.1965	−	12.2378i	0.829485	−	0.478903i	0.853676	+	0.520804i	$0.174368\pi$
$654$	26.9447	+	6.60131i	1.05362	+	0.258132i
$655$	7.30783	+	12.6575i	0.285540	+	0.494570i
$656$	−4.82655			−0.188445
$657$	−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	−0.514878	−	0.857263i	$-0.672163\pi$
$659$	12.4497	−	21.5636i	0.484973	−	0.839997i	0.999851	+	0.0172661i	$0.00549624\pi$
$660$	−1.21128	+	4.94411i	−0.0471490	+	0.192449i
$661$	4.28117	−	2.47173i	0.166518	−	0.0961393i	−0.414425	−	0.910084i	$-0.636017\pi$
$661$	4.28117	−	2.47173i	0.166518	−	0.0961393i	0.580943	+	0.813944i	$0.302684\pi$
$662$			33.6297i			1.30706i
$663$	0.0710107	−	0.289846i	0.00275783	−	0.0112567i
$664$		−	11.1431i		−	0.432438i
$665$	−7.42175	+	21.3107i	−0.287803	+	0.826392i
$666$	−4.13821	−	6.50371i	−0.160352	−	0.252014i
$667$	−6.66596	−	3.84859i	−0.258107	−	0.149018i
$668$	4.01691			0.155419
$669$	21.6068	−	22.5581i	0.835367	−	0.872148i
$670$	−0.0192341	+	0.0333144i	−0.000743077	+	0.00128705i
$671$	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	$0.817819\pi$
$674$		−	28.6711i		−	1.10437i
$675$	−5.96793	−	1.19230i	−0.229706	−	0.0458916i
$676$	−6.45087	+	11.1732i	−0.248110	+	0.429740i
$677$	11.7861	+	20.4141i	0.452975	+	0.784576i	0.998569	−	0.0534736i	$-0.0170293\pi$
$677$	11.7861	+	20.4141i	0.452975	+	0.784576i	−0.545594	+	0.838050i	$0.683696\pi$
$678$	2.21721	−	9.05003i	0.0851514	−	0.347564i
$679$	−1.97288	+	5.80954i	−0.0757123	+	0.222950i
$680$	0.537725	−	0.931367i	0.0206208	−	0.0357163i
$681$	−0.958695	+	3.91312i	−0.0367373	+	0.149951i
$682$	1.16830			0.0447366
$683$	−4.70790	+	8.15433i	−0.180143	+	0.312017i	−0.941929	−	0.335812i	$-0.890989\pi$
$683$	−4.70790	+	8.15433i	−0.180143	+	0.312017i	0.761786	+	0.647829i	$0.224323\pi$
$684$	11.0868	−	6.93418i	0.423914	−	0.265135i
$685$	−36.1302			−1.38046
$686$	−18.4811	+	1.20436i	−0.705610	+	0.0459826i
$687$	−21.3707	−	20.4695i	−0.815344	−	0.780959i
$688$	5.19977			0.198239
$689$			3.40713i			0.129801i
$690$	8.23154	+	7.88439i	0.313369	+	0.300154i
$691$	17.0115	+	29.4647i	0.647147	+	1.12089i	0.983801	+	0.179263i	$0.0573712\pi$
$691$	17.0115	+	29.4647i	0.647147	+	1.12089i	−0.336655	+	0.941628i	$0.609295\pi$
$692$	−12.9114			−0.490820
$693$	−8.61719	+	8.23787i	−0.327340	+	0.312931i
$694$	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
$697$	−2.29735	+	1.32638i	−0.0870185	+	0.0502402i
$698$	10.6484	−	18.4436i	0.403049	−	0.698101i
$699$	−37.5781	−	9.20643i	−1.42133	−	0.348219i
$700$	0.604160	+	3.03930i	0.0228351	+	0.114875i
$701$	15.7654	−	9.10213i	0.595449	−	0.343783i	−0.171800	−	0.985132i	$-0.554958\pi$
$701$	15.7654	−	9.10213i	0.595449	−	0.343783i	0.767249	+	0.641349i	$0.221625\pi$
$702$	−0.319116	+	1.59730i	−0.0120443	+	0.0602863i
$703$	−0.0868420	+	11.2000i	−0.00327531	+	0.422418i
$704$	−1.30073	−	0.750974i	−0.0490229	−	0.0283034i
$705$	−7.48026	+	30.5323i	−0.281723	+	1.14991i
$706$	−30.2002	+	17.4361i	−1.13660	+	0.656217i
$707$	1.71088	−	5.03802i	0.0643442	−	0.189474i
$708$	−13.2757	−	12.7159i	−0.498933	−	0.477892i
$709$	−1.59238			−0.0598029			−0.0299015	−	0.999553i	$-0.509519\pi$
$709$	−1.59238			−0.0598029			−0.0299015	+	0.999553i	$0.509519\pi$
$710$	12.2978	+	7.10015i	0.461529	+	0.266464i
$711$	−16.1238	+	0.694948i	−0.604690	+	0.0260626i
$712$	4.97067			0.186284
$713$	1.30804	−	2.26559i	0.0489865	−	0.0848471i
$714$	2.23455	−	1.16208i	0.0836259	−	0.0434899i
$715$			0.921274i			0.0344537i
$716$	14.5882			0.545186
$717$	−0.643535	−	2.21017i	−0.0240332	−	0.0825402i
$718$	−0.140731	+	0.0812512i	−0.00525204	+	0.00303227i
$719$	−32.3757	−	18.6921i	−1.20741	−	0.697097i	−0.245216	−	0.969469i	$-0.578859\pi$
$719$	−32.3757	−	18.6921i	−1.20741	−	0.697097i	−0.962192	+	0.272371i	$0.912192\pi$
$720$	−2.71346	+	5.20539i	−0.101125	+	0.193994i
$721$	−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
$724$		−	16.4721i		−	0.612181i
$725$	2.68054			0.0995526
$726$	−14.5414	+	4.23403i	−0.539684	+	0.157140i
$727$	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	$0.665940\pi$
$728$	0.813463	−	0.161702i	0.0301489	−	0.00599308i
$729$	−3.47929	−	26.7749i	−0.128863	−	0.991662i
$730$	−12.7120	+	7.33929i	−0.470493	+	0.271639i
$731$	2.47500	−	1.42894i	0.0915411	−	0.0528513i
$732$	13.1797	+	12.6239i	0.487136	+	0.466593i
$733$	−7.71438	−	13.3617i	−0.284937	−	0.493526i	0.687657	−	0.726036i	$-0.258639\pi$
$733$	−7.71438	−	13.3617i	−0.284937	−	0.493526i	−0.972594	+	0.232510i	$0.925306\pi$
$734$	−26.1704			−0.965967
$735$	8.61020	−	22.1064i	0.317592	−	0.815408i
$736$	−2.91260	+	1.68159i	−0.107360	+	0.0619843i
$737$	0.0295275			0.00108766
$738$	12.2164	−	7.77309i	0.449691	−	0.286131i
$739$	1.69236			0.0622544			0.0311272	−	0.999515i	$-0.490090\pi$
$739$	1.69236			0.0622544			0.0311272	+	0.999515i	$0.490090\pi$
$740$	−2.51395	−	4.35428i	−0.0924145	−	0.160067i
$741$	1.65028	−	1.69641i	0.0606245	−	0.0623191i
$742$	−21.6225	+	18.9577i	−0.793787	+	0.695957i
$743$	3.56739	+	6.17890i	0.130875	+	0.226682i	0.924014	−	0.382359i	$-0.124888\pi$
$743$	3.56739	+	6.17890i	0.130875	+	0.226682i	−0.793139	+	0.609040i	$0.791555\pi$
$744$	1.30859	+	0.320598i	0.0479752	+	0.0117537i
$745$	12.1429	+	21.0322i	0.444883	+	0.770559i
$746$		−	31.5723i		−	1.15594i
$747$	17.9459	+	28.2041i	0.656605	+	1.03194i
$748$	−0.825496			−0.0301831
$749$	19.8738	+	6.74901i	0.726172	+	0.246603i
$750$	−20.3144	−	4.97693i	−0.741778	−	0.181732i
$751$			52.2485i			1.90658i	0.302064	+	0.953288i	$0.402325\pi$
$751$			52.2485i			1.90658i	−0.302064	+	0.953288i	$0.597675\pi$
$752$	−8.03262	−	4.63764i	−0.292920	−	0.169117i
$753$	−22.6875	−	5.55833i	−0.826780	−	0.202557i
$754$		−	0.717439i		−	0.0261276i
$755$	1.45743	+	2.52434i	0.0530412	+	0.0918701i
$756$	−11.9125	+	6.86239i	−0.433253	+	0.249583i
$757$	−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	$-0.401241\pi$
$758$	−27.6836	−	15.9831i	−1.00551	−	0.580534i
$759$	2.08193	−	8.49784i	0.0755692	−	0.308452i
$760$	7.41932	−	4.20719i	0.269127	−	0.152611i
$761$	−35.8953	+	20.7241i	−1.30120	+	0.751250i	−0.980610	−	0.195967i	$-0.937215\pi$
$761$	−35.8953	+	20.7241i	−1.30120	+	0.751250i	−0.320592	+	0.947217i	$0.603882\pi$
$762$	−5.57332	+	5.81871i	−0.201900	+	0.210790i
$763$	27.9364	+	31.8634i	1.01137	+	1.15353i
$764$	3.39473	+	1.95995i	0.122817	+	0.0709085i
$765$	0.138929	+	3.22336i	0.00502299	+	0.116541i
$766$	−13.6389	−	23.6233i	−0.492794	−	0.853544i
$767$	−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	$0.309640\pi$
$770$	−5.84665	+	5.12608i	−0.210698	+	0.184731i
$771$	−23.9110	+	6.96216i	−0.861133	+	0.250736i
$772$	14.0560	−	8.11521i	0.505885	−	0.292073i
$773$	−8.92124	−	15.4520i	−0.320875	−	0.555771i	0.659794	−	0.751446i	$-0.270643\pi$
$773$	−8.92124	−	15.4520i	−0.320875	−	0.555771i	−0.980669	+	0.195675i	$0.937310\pi$
$774$	−13.1610	+	8.37414i	−0.473063	+	0.301002i
$775$			0.911047i			0.0327258i
$776$	2.00828	−	1.15948i	0.0720930	−	0.0416229i
$777$	0.518382	−	11.7637i	0.0185969	−	0.422021i
$778$		−	15.9491i		−	0.571803i
$779$	−21.0378	−	0.163122i	−0.753758	−	0.00584444i
$780$	−0.252810	+	1.03190i	−0.00905204	+	0.0369479i
$781$		−	10.8999i		−	0.390029i
$782$	−0.924231	+	1.60082i	−0.0330504	+	0.0572451i
$783$	3.81318	+	11.2643i	0.136272	+	0.402554i
$784$	5.55241	+	4.26272i	0.198300	+	0.152240i
$785$	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	$-0.172221\pi$
$787$	23.5571	+	13.6007i	0.839719	+	0.484812i	−0.0174497	+	0.999848i	$0.505555\pi$
$788$	−10.1223	+	5.84412i	−0.360592	+	0.208188i
$789$	9.25076	+	31.7710i	0.329336	+	1.13108i
$790$	−10.5264			−0.374512
$791$	10.7021	−	9.38312i	0.380523	−	0.333625i
$792$	4.50167	−	0.194025i	0.159960	−	0.00689437i
$793$	2.86049	+	1.65150i	0.101579	+	0.0586466i
$794$	−16.6778	−	28.8867i	−0.591872	−	1.02515i
$795$	−10.2979	−	35.3675i	−0.365231	−	1.25435i
$796$	4.85635	−	8.41144i	0.172129	−	0.298136i
$797$	−37.0412			−1.31207			−0.656033	−	0.754732i	$-0.727767\pi$
$797$	−37.0412			−1.31207			−0.656033	+	0.754732i	$0.727767\pi$
$798$	19.9482	+	1.03407i	0.706159	+	0.0366056i
$799$	−5.09785			−0.180349
$800$	0.585613	−	1.01431i	0.0207045	−	0.0358613i
$801$	−12.5811	+	8.00518i	−0.444532	+	0.282849i
$802$	−10.7987	−	18.7038i	−0.381314	−	0.660455i
$803$	9.75752	+	5.63351i	0.344335	+	0.198802i
$804$	0.0330731	+	0.00810273i	0.00116640	+	0.000285761i
$805$	3.39463	+	17.0771i	0.119645	+	0.601889i
$806$	0.243840			0.00858889
$807$	40.2482	−	11.7191i	1.41680	−	0.412531i
$808$	−1.74157	+	1.00550i	−0.0612684	+	0.0353733i
$809$	−23.5211	−	13.5799i	−0.826957	−	0.477444i	0.0258527	−	0.999666i	$-0.491770\pi$
$809$	−23.5211	−	13.5799i	−0.826957	−	0.477444i	−0.852810	+	0.522222i	$0.825103\pi$
$810$	−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	$0.837841\pi$
$812$	4.55306	−	3.99192i	0.159781	−	0.140089i
$813$	−0.485538	+	1.98183i	−0.0170286	+	0.0695059i
$814$	−1.92966	+	3.34227i	−0.0676346	+	0.117146i
$815$			16.4380i			0.575797i
$816$	−0.924620	−	0.226527i	−0.0323682	−	0.00793003i
$817$	22.6646	+	0.175735i	0.792933	+	0.00614819i
$818$		−	37.5808i		−	1.31398i
$819$	−1.79852	+	1.71935i	−0.0628453	+	0.0600789i
$820$	8.17895	−	4.72212i	0.285621	−	0.164904i
$821$		−	13.8291i		−	0.482640i	−0.970446	−	0.241320i	$-0.922420\pi$
$821$		−	13.8291i		−	0.482640i	0.970446	−	0.241320i	$-0.0775803\pi$
$822$	8.94081	+	30.7065i	0.311846	+	1.07101i
$823$	−5.59109	−	9.68406i	−0.194893	−	0.337565i	0.751972	−	0.659195i	$-0.229103\pi$
$823$	−5.59109	−	9.68406i	−0.194893	−	0.337565i	−0.946866	+	0.321630i	$0.895769\pi$
$824$	2.37790	−	1.37288i	0.0828381	−	0.0478266i
$825$	0.851789	+	2.92540i	0.0296555	+	0.101849i
$826$	−5.47482	−	27.5418i	−0.190494	−	0.958301i
$827$	6.11154	−	10.5855i	0.212519	−	0.368094i	−0.739983	−	0.672625i	$-0.765167\pi$
$827$	6.11154	−	10.5855i	0.212519	−	0.368094i	0.952502	+	0.304531i	$0.0984999\pi$
$828$	4.66384	−	8.94693i	0.162080	−	0.310927i
$829$	36.2004	+	20.9003i	1.25729	+	0.725898i	0.972547	−	0.232706i	$-0.0747579\pi$
$829$	36.2004	+	20.9003i	1.25729	+	0.725898i	0.284745	+	0.958603i	$0.408091\pi$
$830$	10.9020	+	18.8829i	0.378415	+	0.655435i
$831$	−6.45047	+	26.3290i	−0.223764	+	0.913343i
$832$	−0.271478	−	0.156738i	−0.00941180	−	0.00543391i
$833$	3.81428	+	0.503129i	0.132157	+	0.0174324i
$834$	−23.3293	−	22.3455i	−0.807828	−	0.773760i
$835$	−6.80696	+	3.93000i	−0.235564	+	0.136003i
$836$	−5.64418	−	3.31728i	−0.195208	−	0.114731i
$837$	−3.82846	+	1.29601i	−0.132331	+	0.0447965i
$838$	−9.79520	−	5.65526i	−0.338369	−	0.195358i
$839$	−6.29185	−	10.8978i	−0.217219	−	0.376234i	0.736738	−	0.676178i	$-0.236365\pi$
$839$	−6.29185	−	10.8978i	−0.217219	−	0.376234i	−0.953957	+	0.299945i	$0.903032\pi$
$840$	−7.95536	+	4.13721i	−0.274486	+	0.142747i
$841$	11.8810	+	20.5785i	0.409690	+	0.709604i
$842$		−	0.372339i		−	0.0128316i
$843$	5.06173	−	20.6605i	0.174335	−	0.711587i
$844$	14.2681	+	8.23770i	0.491129	+	0.283553i
$845$		−	25.2452i		−	0.868460i
$846$	27.8000	−	1.19820i	0.955784	−	0.0411950i
$847$	−21.9062	−	7.43919i	−0.752704	−	0.255614i
$848$	10.8689			0.373238
$849$	−17.5408	+	5.10736i	−0.601999	+	0.175284i
$850$		−	0.643725i		−	0.0220796i
$851$	4.32092	+	7.48406i	0.148119	+	0.256550i
$852$	2.99108	−	12.2087i	0.102473	−	0.418264i
$853$	−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
$855$	−12.0033	+	22.5974i	−0.410503	+	0.772815i
$856$	−3.96645	−	6.87009i	−0.135570	−	0.234815i
$857$	5.07199			0.173256			0.0866280	−	0.996241i	$-0.472391\pi$
$857$	5.07199			0.173256			0.0866280	+	0.996241i	$0.472391\pi$
$858$	0.782976	−	0.227979i	0.0267304	−	0.00778308i
$859$	55.3188			1.88745			0.943727	−	0.330725i	$-0.107293\pi$
$859$	55.3188			1.88745			0.943727	+	0.330725i	$0.107293\pi$
$860$	−8.81139	+	5.08726i	−0.300466	+	0.173474i
$861$	22.0966	+	0.973714i	0.753050	+	0.0331841i
$862$	−9.42562			−0.321038
$863$	9.01119	+	15.6078i	0.306744	+	0.531297i	0.977648	−	0.210248i	$-0.0674270\pi$
$863$	9.01119	+	15.6078i	0.306744	+	0.531297i	−0.670904	+	0.741544i	$0.734094\pi$
$864$	5.09546	+	1.01799i	0.173351	+	0.0346328i
$865$	21.8794	−	12.6321i	0.743922	−	0.429504i
$866$	−20.0799	+	11.5932i	−0.682344	+	0.393951i
$867$	27.7685	−	8.08535i	0.943067	−	0.274593i
$868$	1.35675	+	1.54747i	0.0460512	+	0.0525246i
$869$	4.03994	+	6.99737i	0.137045	+	0.237370i
$870$	2.16844	+	7.44734i	0.0735171	+	0.252488i
$871$	0.00616276			0.000208817
$872$		−	16.0166i		−	0.542390i
$873$	−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
$876$	9.38327	+	8.98756i	0.317031	+	0.303661i
$877$	23.1244	+	13.3509i	0.780856	+	0.450828i	0.836734	−	0.547610i	$-0.184462\pi$
$877$	23.1244	+	13.3509i	0.780856	+	0.450828i	−0.0558773	+	0.998438i	$0.517796\pi$
$878$	0.366308	−	0.211488i	0.0123623	−	0.00713738i
$879$	−29.4620	+	8.57847i	−0.993730	+	0.289344i
$880$	2.93890			0.0990703
$881$			16.8396i			0.567340i	0.958922	+	0.283670i	$0.0915520\pi$
$881$			16.8396i			0.567340i	−0.958922	+	0.283670i	$0.908448\pi$
$882$	−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	$0.0792208\pi$
$884$	−0.172292			−0.00579479
$885$	34.9375	+	8.55949i	1.17441	+	0.287724i
$886$	−23.2671	−	13.4333i	−0.781675	−	0.451300i
$887$	2.57712			0.0865311			0.0432655	−	0.999064i	$-0.486224\pi$
$887$	2.57712			0.0865311			0.0432655	+	0.999064i	$0.486224\pi$
$888$	−3.07853	+	3.21408i	−0.103309	+	0.107857i
$889$	−12.0715	+	2.39960i	−0.404864	+	0.0804799i
$890$	−8.42316	+	4.86312i	−0.282345	+	0.163012i
$891$	−11.0816	+	7.74095i	−0.371247	+	0.259332i
$892$	−15.6183	−	9.01722i	−0.522939	−	0.301919i
$893$	−34.8556	−	20.4859i	−1.16640	−	0.685533i
$894$	14.8700	−	15.5247i	0.497328	−	0.519225i
$895$	−24.7208	+	14.2725i	−0.826325	+	0.477079i
$896$	−0.515836	−	2.59498i	−0.0172329	−	0.0866921i
$897$	0.434525	−	1.77361i	0.0145084	−	0.0592190i
$898$	−6.75505	+	11.7001i	−0.225419	+	0.390437i
$899$	1.54174	−	0.890127i	0.0514201	−	0.0296874i
$900$	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
$903$	−23.8052	−	1.04901i	−0.792188	−	0.0349087i
$904$	−5.37956			−0.178921
$905$	16.1157	+	27.9132i	0.535704	+	0.927866i
$906$	1.78474	−	1.86332i	0.0592940	−	0.0619047i
$907$		−	56.8144i		−	1.88649i	−0.332095	−	0.943246i	$-0.607755\pi$
$907$		−	56.8144i		−	1.88649i	0.332095	−	0.943246i	$-0.392245\pi$
$908$	2.32606			0.0771930
$909$	2.78872	−	5.34977i	0.0924959	−	0.177441i
$910$	−1.22027	+	1.06988i	−0.0404515	+	0.0354661i
$911$	29.4855			0.976897			0.488449	−	0.872593i	$-0.337563\pi$
$911$	29.4855			0.976897			0.488449	+	0.872593i	$0.337563\pi$
$912$	−5.41161	−	5.26445i	−0.179196	−	0.174323i
$913$	8.36821	−	14.4942i	0.276947	−	0.479687i
$914$	−39.9013			−1.31982
$915$	−34.6848	−	8.49758i	−1.14664	−	0.280921i
$916$	−8.54257	+	14.7962i	−0.282255	+	0.488879i
$917$	19.3830	−	3.85301i	0.640084	−	0.127238i
$918$	2.70510	−	0.915728i	0.0892816	−	0.0302235i
$919$	−13.5597	−	23.4861i	−0.447293	−	0.774734i	0.550916	−	0.834561i	$-0.314278\pi$
$919$	−13.5597	−	23.4861i	−0.447293	−	0.774734i	−0.998209	+	0.0598270i	$0.980945\pi$
$920$	3.29041	−	5.69916i	0.108482	−	0.187896i
$921$	27.4457	−	28.6541i	0.904367	−	0.944186i
$922$			18.1034i			0.596205i
$923$		−	2.27495i		−	0.0748808i
$924$	5.80339	+	3.70047i	0.190918	+	0.121736i
$925$	−2.60631	−	1.50476i	−0.0856951	−	0.0494761i
$926$	−6.46175	+	11.1921i	−0.212346	+	0.367795i
$927$	−3.80764	+	7.30444i	−0.125059	+	0.239909i
$928$	−2.28866			−0.0751290
$929$	15.6143	+	9.01490i	0.512287	+	0.295769i	0.733773	−	0.679394i	$-0.237757\pi$
$929$	15.6143	+	9.01490i	0.512287	+	0.295769i	−0.221486	+	0.975164i	$0.571091\pi$
$930$	−2.53116	+	0.736999i	−0.0830001	+	0.0241672i
$931$	24.0576	+	18.7678i	0.788456	+	0.615091i
$932$			22.3373i			0.731683i
$933$	9.89916	+	2.42524i	0.324084	+	0.0793989i
$934$			6.71659i			0.219773i
$935$	1.39886	−	0.807635i	0.0457478	−	0.0264125i
$936$	0.939555	−	0.0404955i	0.0307103	−	0.00132364i
$937$	−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
$940$	18.1492			0.591960
$941$	26.7805	+	46.3852i	0.873019	+	1.51211i	0.858858	+	0.512214i	$0.171174\pi$
$941$	26.7805	+	46.3852i	0.873019	+	1.51211i	0.0141612	+	0.999900i	$0.495492\pi$
$942$	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
$945$	13.4727	−	23.2836i	0.438267	−	0.757415i
$946$	6.76347	+	3.90489i	0.219899	+	0.126959i
$947$	−27.2747	−	15.7471i	−0.886310	−	0.511711i	−0.0135761	−	0.999908i	$-0.504322\pi$
$947$	−27.2747	−	15.7471i	−0.886310	−	0.511711i	−0.872734	+	0.488197i	$0.837655\pi$
$948$	2.60487	+	8.94621i	0.0846022	+	0.290560i
$949$	2.03652	+	1.17578i	0.0661082	+	0.0381676i
$950$	2.58683	−	4.40135i	0.0839278	−	0.142799i
$951$	−20.5113	+	5.97229i	−0.665125	+	0.193665i
$952$	−0.958651	−	1.09341i	−0.0310701	−	0.0354375i
$953$	8.39492	+	14.5404i	0.271938	+	0.471011i	0.969358	−	0.245652i	$-0.0790021\pi$
$953$	8.39492	+	14.5404i	0.271938	+	0.471011i	−0.697420	+	0.716663i	$0.745669\pi$
$954$	−27.5099	+	17.5041i	−0.890667	+	0.566717i
$955$	−7.67016			−0.248201
$956$	−1.15098	+	0.664516i	−0.0372252	+	0.0214920i
$957$	4.11836	−	4.29969i	0.133128	−	0.138989i
$958$		−	16.3658i		−	0.528755i
$959$	−15.7090	+	46.2582i	−0.507270	+	1.49375i
$960$	3.29180	+	0.806473i	0.106242	+	0.0260288i
$961$	−15.1975	−	26.3228i	−0.490241	−	0.849122i
$962$	−0.402745	+	0.697574i	−0.0129850	+	0.0224907i
$963$	21.1036	+	11.0008i	0.680053	+	0.354496i
$964$	−2.69501	−	1.55597i	−0.0868005	−	0.0501143i
$965$	−15.8792	+	27.5037i	−0.511171	+	0.885374i
$966$	13.6735	−	7.11096i	0.439938	−	0.228791i
$967$	−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
$969$	−4.02255	−	1.01863i	−0.129223	−	0.0327230i
$970$	−2.26879	+	3.92965i	−0.0728463	+	0.126173i
$971$	−9.45248	+	16.3722i	−0.303345	+	0.525408i	−0.976891	−	0.213736i	$-0.931437\pi$
$971$	−9.45248	+	16.3722i	−0.303345	+	0.525408i	0.673547	+	0.739145i	$0.264770\pi$
$972$	−14.5364	+	5.62953i	−0.466257	+	0.180567i
$973$	−9.62085	−	48.3989i	−0.308430	−	1.55160i
$974$	21.2291	−	12.2567i	0.680226	−	0.392728i
$975$	0.177779	+	0.610568i	0.00569349	+	0.0195538i
$976$	5.26836	−	9.12507i	0.168636	−	0.292086i
$977$	1.45757	−	2.52459i	0.0466318	−	0.0807687i	−0.841767	−	0.539840i	$-0.818485\pi$
$977$	1.45757	−	2.52459i	0.0466318	−	0.0807687i	0.888399	+	0.459072i	$0.151818\pi$
$978$	13.9704	−	4.06776i	0.446724	−	0.130073i
$979$	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
$982$			32.8886i			1.04952i
$983$	19.6503			0.626749			0.313374	−	0.949630i	$-0.398541\pi$
$983$	19.6503			0.626749			0.313374	+	0.949630i	$0.398541\pi$
$984$	−6.03723	−	5.78262i	−0.192460	−	0.184343i
$985$	11.4353	−	19.8066i	0.364360	−	0.631090i
$986$	−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
$990$	−7.43858	+	4.73305i	−0.236414	+	0.150426i
$991$		−	15.9112i		−	0.505437i	−0.967540	−	0.252718i	$-0.918675\pi$
$991$		−	15.9112i		−	0.505437i	0.967540	−	0.252718i	$-0.0813246\pi$
$992$		−	0.777858i		−	0.0246970i
$993$	−40.2913	+	42.0653i	−1.27860	+	1.33490i
$994$	14.4374	−	12.6581i	0.457927	−	0.401490i
$995$			19.0051i			0.602501i
$996$	13.3504	−	13.9383i	0.423025	−	0.441650i
$997$	14.2478	+	24.6779i	0.451232	+	0.781556i	0.998463	−	0.0554253i	$-0.0176515\pi$
$997$	14.2478	+	24.6779i	0.451232	+	0.781556i	−0.547231	+	0.836982i	$0.684318\pi$
$998$	−0.193817	−	0.335701i	−0.00613518	−	0.0106264i
$999$	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.bh.d.221.24	yes	50
3.2	odd	2		798.2.bh.c.221.2	yes	50
7.2	even	3		798.2.p.c.107.10	✓	50
19.8	odd	6		798.2.p.d.179.18	yes	50
21.2	odd	6		798.2.p.d.107.18	yes	50
57.8	even	6		798.2.p.c.179.10	yes	50
133.65	odd	6		798.2.bh.c.65.2	yes	50
399.65	even	6	inner	798.2.bh.d.65.24	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.p.c.107.10	✓	50	7.2	even	3
798.2.p.c.179.10	yes	50	57.8	even	6
798.2.p.d.107.18	yes	50	21.2	odd	6
798.2.p.d.179.18	yes	50	19.8	odd	6
798.2.bh.c.65.2	yes	50	133.65	odd	6
798.2.bh.c.221.2	yes	50	3.2	odd	2
798.2.bh.d.65.24	yes	50	399.65	even	6	inner
798.2.bh.d.221.24	yes	50	1.1	even	1	trivial

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.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.66299 - 0.484213i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.69457 + 0.978363i) q^{5} +(0.412154 - 1.68230i) q^{6} +(1.98940 - 1.74422i) q^{7} -1.00000 q^{8} +(2.53108 - 1.61048i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.66299 - 0.484213i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.69457 + 0.978363i) q^{5} +(0.412154 - 1.68230i) q^{6} +(1.98940 - 1.74422i) q^{7} -1.00000 q^{8} +(2.53108 - 1.61048i) q^{9} +(1.69457 - 0.978363i) q^{10} +(-1.30073 - 0.750974i) q^{11} +(-1.25084 - 1.19809i) q^{12} +(-0.271478 - 0.156738i) q^{13} +(-0.515836 - 2.59498i) q^{14} +(3.29180 + 0.806473i) q^{15} +(-0.500000 + 0.866025i) q^{16} +0.549617i q^{17} +(-0.129182 - 2.99722i) q^{18} +(-2.20865 + 3.75791i) q^{19} -1.95673i q^{20} +(2.46378 - 3.86391i) q^{21} +(-1.30073 + 0.750974i) q^{22} +3.36318i q^{23} +(-1.66299 + 0.484213i) q^{24} +(-0.585613 - 1.01431i) q^{25} +(-0.271478 + 0.156738i) q^{26} +(3.42934 - 3.90380i) q^{27} +(-2.50524 - 0.850762i) q^{28} +(-1.14433 + 1.98204i) q^{29} +(2.34432 - 2.44754i) q^{30} +(-0.673645 - 0.388929i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.52673 - 0.619035i) q^{33} +(0.475982 + 0.274809i) q^{34} +(5.07766 - 1.00935i) q^{35} +(-2.66026 - 1.38673i) q^{36} +(2.22529 - 1.28477i) q^{37} +(2.15012 + 3.79170i) q^{38} +(-0.527360 - 0.129200i) q^{39} +(-1.69457 - 0.978363i) q^{40} +(2.41328 + 4.17992i) q^{41} +(-2.11435 - 4.06565i) q^{42} +(-2.59988 - 4.50313i) q^{43} +1.50195i q^{44} +(5.86473 - 0.252774i) q^{45} +(2.91260 + 1.68159i) q^{46} +9.27527i q^{47} +(-0.412154 + 1.68230i) q^{48} +(0.915417 - 6.93989i) q^{49} -1.17123 q^{50} +(0.266132 + 0.914008i) q^{51} +0.313476i q^{52} +(-5.43443 - 9.41271i) q^{53} +(-1.66612 - 4.92179i) q^{54} +(-1.46945 - 2.54516i) q^{55} +(-1.98940 + 1.74422i) q^{56} +(-1.85334 + 7.31882i) q^{57} +(1.14433 + 1.98204i) q^{58} +10.6135 q^{59} +(-0.947472 - 3.25402i) q^{60} -10.5367 q^{61} +(-0.673645 + 0.388929i) q^{62} +(2.22629 - 7.61864i) q^{63} +1.00000 q^{64} +(-0.306693 - 0.531208i) q^{65} +(-1.79946 + 1.87869i) q^{66} +(-0.0170256 + 0.00982972i) q^{67} +(0.475982 - 0.274809i) q^{68} +(1.62850 + 5.59294i) q^{69} +(1.66471 - 4.90206i) q^{70} +(3.62859 + 6.28490i) q^{71} +(-2.53108 + 1.61048i) q^{72} -7.50160 q^{73} -2.56954i q^{74} +(-1.46501 - 1.40323i) q^{75} +(4.35877 + 0.0337967i) q^{76} +(-3.89752 + 0.774760i) q^{77} +(-0.375571 + 0.392107i) q^{78} +(-4.65887 - 2.68980i) q^{79} +(-1.69457 + 0.978363i) q^{80} +(3.81268 - 8.15251i) q^{81} +4.82655 q^{82} +11.1431i q^{83} +(-4.57813 - 0.201741i) q^{84} +(-0.537725 + 0.931367i) q^{85} -5.19977 q^{86} +(-0.943281 + 3.85021i) q^{87} +(1.30073 + 0.750974i) q^{88} -4.97067 q^{89} +(2.71346 - 5.20539i) q^{90} +(-0.813463 + 0.161702i) q^{91} +(2.91260 - 1.68159i) q^{92} +(-1.30859 - 0.320598i) q^{93} +(8.03262 + 4.63764i) q^{94} +(-7.41932 + 4.20719i) q^{95} +(1.25084 + 1.19809i) q^{96} +(-2.00828 + 1.15948i) q^{97} +(-5.55241 - 4.26272i) q^{98} +(-4.50167 + 0.194025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 25 q^{2} + 3 q^{3} - 25 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9}+O(q^{10}) \) 50 * q + 25 * q^2 + 3 * q^3 - 25 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9	\( 50 q + 25 q^{2} + 3 q^{3} - 25 q^{4} + 3 q^{6} - 50 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{13} + 3 q^{14} - 17 q^{15} - 25 q^{16} - 6 q^{18} + q^{19} - 2 q^{21} - 3 q^{22} - 3 q^{24} + 29 q^{25} - 3 q^{26} - 6 q^{27} + 3 q^{28} + 5 q^{29} - 13 q^{30} - 15 q^{31} + 25 q^{32} + 13 q^{33} + 3 q^{34} + 12 q^{35} - 3 q^{36} + 9 q^{37} + 11 q^{38} - 2 q^{39} + 17 q^{41} + 5 q^{42} + 15 q^{43} - 22 q^{45} - 9 q^{46} - 3 q^{48} + 8 q^{49} + 58 q^{50} + 19 q^{51} - 6 q^{53} + 24 q^{54} - 16 q^{55} - 4 q^{57} - 5 q^{58} - 2 q^{59} + 4 q^{60} - 46 q^{61} - 15 q^{62} - 46 q^{63} + 50 q^{64} + 14 q^{65} + 14 q^{66} + 18 q^{67} + 3 q^{68} + 31 q^{69} + 12 q^{70} - 3 q^{71} + 3 q^{72} - 30 q^{73} - 7 q^{75} + 10 q^{76} - 57 q^{77} + 17 q^{78} - 18 q^{79} - 7 q^{81} + 34 q^{82} + 7 q^{84} - 10 q^{85} + 30 q^{86} + 52 q^{87} + 3 q^{88} + 66 q^{89} - 26 q^{90} - 57 q^{91} - 9 q^{92} - 22 q^{93} - 21 q^{94} + 60 q^{95} - 21 q^{97} + 7 q^{98} + 19 q^{99}+O(q^{100}) \) 50 * q + 25 * q^2 + 3 * q^3 - 25 * q^4 + 3 * q^6 - 50 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^13 + 3 * q^14 - 17 * q^15 - 25 * q^16 - 6 * q^18 + q^19 - 2 * q^21 - 3 * q^22 - 3 * q^24 + 29 * q^25 - 3 * q^26 - 6 * q^27 + 3 * q^28 + 5 * q^29 - 13 * q^30 - 15 * q^31 + 25 * q^32 + 13 * q^33 + 3 * q^34 + 12 * q^35 - 3 * q^36 + 9 * q^37 + 11 * q^38 - 2 * q^39 + 17 * q^41 + 5 * q^42 + 15 * q^43 - 22 * q^45 - 9 * q^46 - 3 * q^48 + 8 * q^49 + 58 * q^50 + 19 * q^51 - 6 * q^53 + 24 * q^54 - 16 * q^55 - 4 * q^57 - 5 * q^58 - 2 * q^59 + 4 * q^60 - 46 * q^61 - 15 * q^62 - 46 * q^63 + 50 * q^64 + 14 * q^65 + 14 * q^66 + 18 * q^67 + 3 * q^68 + 31 * q^69 + 12 * q^70 - 3 * q^71 + 3 * q^72 - 30 * q^73 - 7 * q^75 + 10 * q^76 - 57 * q^77 + 17 * q^78 - 18 * q^79 - 7 * q^81 + 34 * q^82 + 7 * q^84 - 10 * q^85 + 30 * q^86 + 52 * q^87 + 3 * q^88 + 66 * q^89 - 26 * q^90 - 57 * q^91 - 9 * q^92 - 22 * q^93 - 21 * q^94 + 60 * q^95 - 21 * q^97 + 7 * q^98 + 19 * q^99

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